diff --git a/lib/python3.11/site-packages/cusparselt/LICENSE.txt b/lib/python3.11/site-packages/cusparselt/LICENSE.txt new file mode 100644 index 0000000000000000000000000000000000000000..890839b670533e4bbd2d96c3ab36525be2aff773 --- /dev/null +++ b/lib/python3.11/site-packages/cusparselt/LICENSE.txt @@ -0,0 +1,165 @@ +LICENSE AGREEMENT FOR NVIDIA SOFTWARE DEVELOPMENT KITS + +This license agreement, including exhibits attached ("Agreement”) is a legal agreement between you and NVIDIA Corporation ("NVIDIA") and governs your use of a NVIDIA software development kit (“SDK”). + +Each SDK has its own set of software and materials, but here is a description of the types of items that may be included in a SDK: source code, header files, APIs, data sets and assets (examples include images, textures, models, scenes, videos, native API input/output files), binary software, sample code, libraries, utility programs, programming code and documentation. + +This Agreement can be accepted only by an adult of legal age of majority in the country in which the SDK is used. + +If you are entering into this Agreement on behalf of a company or other legal entity, you represent that you have the legal authority to bind the entity to this Agreement, in which case “you” will mean the entity you represent. + +If you don’t have the required age or authority to accept this Agreement, or if you don’t accept all the terms and conditions of this Agreement, do not download, install or use the SDK. + +You agree to use the SDK only for purposes that are permitted by (a) this Agreement, and (b) any applicable law, regulation or generally accepted practices or guidelines in the relevant jurisdictions. + +1. 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The following portions of the SDK are distributable under the Agreement: the runtimes files ending with .so and .h as part of your application. + +3. Licensing. If the distribution terms in this Agreement are not suitable for your organization, or for any questions regarding this Agreement, please contact NVIDIA at nvidia-compute-license-questions@nvidia.com + +(v. October 12, 2020) diff --git a/lib/python3.11/site-packages/cusparselt/include/cusparseLt.h b/lib/python3.11/site-packages/cusparselt/include/cusparseLt.h new file mode 100644 index 0000000000000000000000000000000000000000..b5e988363460bb3553ae9d116108e7b7b45d37f2 --- /dev/null +++ b/lib/python3.11/site-packages/cusparselt/include/cusparseLt.h @@ -0,0 +1,371 @@ +/* + * Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved. + * + * NVIDIA CORPORATION and its licensors retain all intellectual property + * and proprietary rights in and to this software, related documentation + * and any modifications thereto. Any use, reproduction, disclosure or + * distribution of this software and related documentation without an express + * license agreement from NVIDIA CORPORATION is strictly prohibited. + */ +#if !defined(CUSPARSELT_HEADER_) +#define CUSPARSELT_HEADER_ + +#include "cusparse.h" // cusparseStatus_t + +#include // size_t +#include // cudaStream_t +#include // cudaDataType +#include // uint8_t + +//############################################################################## +//# CUSPARSELT VERSION INFORMATION +//############################################################################## + +#define CUSPARSELT_VER_MAJOR 0 +#define CUSPARSELT_VER_MINOR 6 +#define CUSPARSELT_VER_PATCH 2 +#define CUSPARSELT_VER_BUILD 3 +#define CUSPARSELT_VERSION (CUSPARSELT_VER_MAJOR * 1000 + \ + CUSPARSELT_VER_MINOR * 100 + \ + CUSPARSELT_VER_PATCH) + +// ############################################################################# +// # MACRO +// ############################################################################# + +#if !defined(CUSPARSELT_API) +# if defined(_WIN32) +# define CUSPARSELT_API __stdcall +# else +# define CUSPARSELT_API +# endif +#endif + +//------------------------------------------------------------------------------ + +#if defined(__cplusplus) +extern "C" { +#endif // defined(__cplusplus) + +//############################################################################## +//# OPAQUE DATA STRUCTURES +//############################################################################## + +typedef struct { uint8_t data[13072]; } cusparseLtHandle_t; + +typedef struct { uint8_t data[13072]; } cusparseLtMatDescriptor_t; + +typedef struct { uint8_t data[13072]; } cusparseLtMatmulDescriptor_t; + +typedef struct { uint8_t data[13072]; } cusparseLtMatmulAlgSelection_t; + +typedef struct { uint8_t data[13072]; } cusparseLtMatmulPlan_t; + +//############################################################################## +//# INITIALIZATION, DESTROY +//############################################################################## + +cusparseStatus_t CUSPARSELT_API +cusparseLtInit(cusparseLtHandle_t* handle); + +cusparseStatus_t CUSPARSELT_API +cusparseLtDestroy(const cusparseLtHandle_t* handle); + +cusparseStatus_t CUSPARSELT_API +cusparseLtGetVersion(const cusparseLtHandle_t* handle, + int* version); + +cusparseStatus_t CUSPARSELT_API +cusparseLtGetProperty(libraryPropertyType propertyType, + int* value); + +//############################################################################## +//# MATRIX DESCRIPTOR +//############################################################################## +// Dense Matrix + +cusparseStatus_t CUSPARSELT_API +cusparseLtDenseDescriptorInit(const cusparseLtHandle_t* handle, + cusparseLtMatDescriptor_t* matDescr, + int64_t rows, + int64_t cols, + int64_t ld, + uint32_t alignment, + cudaDataType valueType, + cusparseOrder_t order); + +//------------------------------------------------------------------------------ +// Structured Matrix + +typedef enum { + CUSPARSELT_SPARSITY_50_PERCENT +} cusparseLtSparsity_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtStructuredDescriptorInit(const cusparseLtHandle_t* handle, + cusparseLtMatDescriptor_t* matDescr, + int64_t rows, + int64_t cols, + int64_t ld, + uint32_t alignment, + cudaDataType valueType, + cusparseOrder_t order, + cusparseLtSparsity_t sparsity); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatDescriptorDestroy(const cusparseLtMatDescriptor_t* matDescr); + +//------------------------------------------------------------------------------ + +typedef enum { + CUSPARSELT_MAT_NUM_BATCHES, // READ/WRITE + CUSPARSELT_MAT_BATCH_STRIDE // READ/WRITE +} cusparseLtMatDescAttribute_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatDescSetAttribute(const cusparseLtHandle_t* handle, + cusparseLtMatDescriptor_t* matmulDescr, + cusparseLtMatDescAttribute_t matAttribute, + const void* data, + size_t dataSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatDescGetAttribute(const cusparseLtHandle_t* handle, + const cusparseLtMatDescriptor_t* matmulDescr, + cusparseLtMatDescAttribute_t matAttribute, + void* data, + size_t dataSize); + +//############################################################################## +//# MATMUL DESCRIPTOR +//############################################################################## + +typedef enum { + CUSPARSE_COMPUTE_32I, + CUSPARSE_COMPUTE_16F, + CUSPARSE_COMPUTE_32F +} cusparseComputeType; + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulDescriptorInit(const cusparseLtHandle_t* handle, + cusparseLtMatmulDescriptor_t* matmulDescr, + cusparseOperation_t opA, + cusparseOperation_t opB, + const cusparseLtMatDescriptor_t* matA, + const cusparseLtMatDescriptor_t* matB, + const cusparseLtMatDescriptor_t* matC, + const cusparseLtMatDescriptor_t* matD, + cusparseComputeType computeType); + +//------------------------------------------------------------------------------ + +typedef enum { + CUSPARSELT_MATMUL_ACTIVATION_RELU, // READ/WRITE + CUSPARSELT_MATMUL_ACTIVATION_RELU_UPPERBOUND, // READ/WRITE + CUSPARSELT_MATMUL_ACTIVATION_RELU_THRESHOLD, // READ/WRITE + CUSPARSELT_MATMUL_ACTIVATION_GELU, // READ/WRITE + CUSPARSELT_MATMUL_ACTIVATION_GELU_SCALING, // READ/WRITE + CUSPARSELT_MATMUL_ALPHA_VECTOR_SCALING, // READ/WRITE + CUSPARSELT_MATMUL_BETA_VECTOR_SCALING, // READ/WRITE + CUSPARSELT_MATMUL_BIAS_STRIDE, // READ/WRITE + CUSPARSELT_MATMUL_BIAS_POINTER, // READ/WRITE + CUSPARSELT_MATMUL_SPARSE_MAT_POINTER, // READ/WRITE +} cusparseLtMatmulDescAttribute_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulDescSetAttribute(const cusparseLtHandle_t* handle, + cusparseLtMatmulDescriptor_t* matmulDescr, + cusparseLtMatmulDescAttribute_t matmulAttribute, + const void* data, + size_t dataSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulDescGetAttribute( + const cusparseLtHandle_t* handle, + const cusparseLtMatmulDescriptor_t* matmulDescr, + cusparseLtMatmulDescAttribute_t matmulAttribute, + void* data, + size_t dataSize); + +//############################################################################## +//# ALGORITHM SELECTION +//############################################################################## + +typedef enum { + CUSPARSELT_MATMUL_ALG_DEFAULT +} cusparseLtMatmulAlg_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulAlgSelectionInit( + const cusparseLtHandle_t* handle, + cusparseLtMatmulAlgSelection_t* algSelection, + const cusparseLtMatmulDescriptor_t* matmulDescr, + cusparseLtMatmulAlg_t alg); + +typedef enum { + CUSPARSELT_MATMUL_ALG_CONFIG_ID, // READ/WRITE + CUSPARSELT_MATMUL_ALG_CONFIG_MAX_ID, // READ-ONLY + CUSPARSELT_MATMUL_SEARCH_ITERATIONS, // READ/WRITE + CUSPARSELT_MATMUL_SPLIT_K, // READ/WRITE + CUSPARSELT_MATMUL_SPLIT_K_MODE, // READ/WRITE + CUSPARSELT_MATMUL_SPLIT_K_BUFFERS // READ/WRITE +} cusparseLtMatmulAlgAttribute_t; + +typedef enum { + CUSPARSELT_INVALID_MODE = 0, + CUSPARSELT_SPLIT_K_MODE_ONE_KERNEL = 1, + CUSPARSELT_SPLIT_K_MODE_TWO_KERNELS = 2 +} cusparseLtSplitKMode_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulAlgSetAttribute(const cusparseLtHandle_t* handle, + cusparseLtMatmulAlgSelection_t* algSelection, + cusparseLtMatmulAlgAttribute_t attribute, + const void* data, + size_t dataSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulAlgGetAttribute( + const cusparseLtHandle_t* handle, + const cusparseLtMatmulAlgSelection_t* algSelection, + cusparseLtMatmulAlgAttribute_t attribute, + void* data, + size_t dataSize); + +//############################################################################## +//# MATMUL PLAN +//############################################################################## + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulGetWorkspace( + const cusparseLtHandle_t* handle, + const cusparseLtMatmulPlan_t* plan, + size_t* workspaceSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulPlanInit(const cusparseLtHandle_t* handle, + cusparseLtMatmulPlan_t* plan, + const cusparseLtMatmulDescriptor_t* matmulDescr, + const cusparseLtMatmulAlgSelection_t* algSelection); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulPlanDestroy(const cusparseLtMatmulPlan_t* plan); + +//############################################################################## +//# MATMUL EXECUTION +//############################################################################## + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmul(const cusparseLtHandle_t* handle, + const cusparseLtMatmulPlan_t* plan, + const void* alpha, + const void* d_A, + const void* d_B, + const void* beta, + const void* d_C, + void* d_D, + void* workspace, + cudaStream_t* streams, + int32_t numStreams); + +cusparseStatus_t CUSPARSELT_API +cusparseLtMatmulSearch(const cusparseLtHandle_t* handle, + cusparseLtMatmulPlan_t* plan, + const void* alpha, + const void* d_A, + const void* d_B, + const void* beta, + const void* d_C, + void* d_D, + void* workspace, + // void* device_buf, + cudaStream_t* streams, + int32_t numStreams); + +//############################################################################## +//# HELPER ROUTINES +//############################################################################## +// PRUNING + +typedef enum { + CUSPARSELT_PRUNE_SPMMA_TILE = 0, + CUSPARSELT_PRUNE_SPMMA_STRIP = 1 +} cusparseLtPruneAlg_t; + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMAPrune(const cusparseLtHandle_t* handle, + const cusparseLtMatmulDescriptor_t* matmulDescr, + const void* d_in, + void* d_out, + cusparseLtPruneAlg_t pruneAlg, + cudaStream_t stream); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMAPruneCheck(const cusparseLtHandle_t* handle, + const cusparseLtMatmulDescriptor_t* matmulDescr, + const void* d_in, + int* valid, + cudaStream_t stream); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMAPrune2(const cusparseLtHandle_t* handle, + const cusparseLtMatDescriptor_t* sparseMatDescr, + int isSparseA, + cusparseOperation_t op, + const void* d_in, + void* d_out, + cusparseLtPruneAlg_t pruneAlg, + cudaStream_t stream); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMAPruneCheck2(const cusparseLtHandle_t* handle, + const cusparseLtMatDescriptor_t* sparseMatDescr, + int isSparseA, + cusparseOperation_t op, + const void* d_in, + int* d_valid, + cudaStream_t stream); + +//------------------------------------------------------------------------------ +// COMPRESSION + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMACompressedSize( + const cusparseLtHandle_t* handle, + const cusparseLtMatmulPlan_t* plan, + size_t* compressedSize, + size_t* compressedBufferSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMACompress(const cusparseLtHandle_t* handle, + const cusparseLtMatmulPlan_t* plan, + const void* d_dense, + void* d_compressed, + void* d_compressed_buffer, + cudaStream_t stream); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMACompressedSize2( + const cusparseLtHandle_t* handle, + const cusparseLtMatDescriptor_t* sparseMatDescr, + size_t* compressedSize, + size_t* compressedBufferSize); + +cusparseStatus_t CUSPARSELT_API +cusparseLtSpMMACompress2(const cusparseLtHandle_t* handle, + const cusparseLtMatDescriptor_t* sparseMatDescr, + int isSparseA, + cusparseOperation_t op, + const void* d_dense, + void* d_compressed, + void* d_compressed_buffer, + cudaStream_t stream); + +//============================================================================== +//============================================================================== + +#if defined(__cplusplus) +} +#endif // defined(__cplusplus) + +#endif // !defined(CUSPARSELT_HEADER_) diff --git a/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/INSTALLER b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/INSTALLER new file mode 100644 index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68 --- /dev/null +++ b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/INSTALLER @@ -0,0 +1 @@ +pip diff --git a/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/METADATA b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/METADATA new file mode 100644 index 0000000000000000000000000000000000000000..386f4589a7a765637bcd6dfdaf8174f18216d80d --- /dev/null +++ b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/METADATA @@ -0,0 +1,129 @@ +Metadata-Version: 2.1 +Name: nvidia-cusparselt-cu12 +Version: 0.6.2 +Summary: NVIDIA cuSPARSELt +Home-page: https://developer.nvidia.com/cusparselt +Author: NVIDIA Corporation +Author-email: cuda_installer@nvidia.com +License: NVIDIA Proprietary Software +Keywords: cuda,nvidia,machine learning,high-performance computing +Classifier: Topic :: Scientific/Engineering +Classifier: Environment :: GPU :: NVIDIA CUDA +Classifier: Environment :: GPU :: NVIDIA CUDA :: 12 +Description-Content-Type: text/x-rst + +################################################################################### +cuSPARSELt: A High-Performance CUDA Library for Sparse Matrix-Matrix Multiplication +################################################################################### + +**NVIDIA cuSPARSELt** is a high-performance CUDA library dedicated to general matrix-matrix operations in which at least one operand is a sparse matrix: + +.. math:: + + D = Activation(\alpha op(A) \cdot op(B) + \beta op(C) + bias) \cdot scale + +where :math:`op(A)/op(B)` refers to in-place operations such as transpose/non-transpose, and :math:`alpha, beta, scale` are scalars. + +The *cuSPARSELt APIs* allow flexibility in the algorithm/operation selection, epilogue, and matrix characteristics, including memory layout, alignment, and data types. + +**Download:** `developer.nvidia.com/cusparselt/downloads `_ + +**Provide Feedback:** `Math-Libs-Feedback@nvidia.com `_ + +**Examples**: +`cuSPARSELt Example 1 `_, +`cuSPARSELt Example 2 `_ + +**Blog post**: + +- `Exploiting NVIDIA Ampere Structured Sparsity with cuSPARSELt `_ +- `Structured Sparsity in the NVIDIA Ampere Architecture and Applications in Search Engines `__ +- `Making the Most of Structured Sparsity in the NVIDIA Ampere Architecture `__ + +================================================================================ +Key Features +================================================================================ + +* *NVIDIA Sparse MMA tensor core* support +* Mixed-precision computation support: + + +--------------+----------------+-----------------+-------------+ + | Input A/B | Input C | Output D | Compute | + +==============+================+=================+=============+ + | `FP32` | `FP32` | `FP32` | `FP32` | + +--------------+----------------+-----------------+-------------+ + | `FP16` | `FP16` | `FP16` | `FP32` | + + + + +-------------+ + | | | | `FP16` | + +--------------+----------------+-----------------+-------------+ + | `BF16` | `BF16` | `BF16` | `FP32` | + +--------------+----------------+-----------------+-------------+ + | `INT8` | `INT8` | `INT8` | `INT32` | + + +----------------+-----------------+ + + | | `INT32` | `INT32` | | + + +----------------+-----------------+ + + | | `FP16` | `FP16` | | + + +----------------+-----------------+ + + | | `BF16` | `BF16` | | + +--------------+----------------+-----------------+-------------+ + | `E4M3` | `FP16` | `E4M3` | `FP32` | + + +----------------+-----------------+ + + | | `BF16` | `E4M3` | | + + +----------------+-----------------+ + + | | `FP16` | `FP16` | | + + +----------------+-----------------+ + + | | `BF16` | `BF16` | | + + +----------------+-----------------+ + + | | `FP32` | `FP32` | | + +--------------+----------------+-----------------+-------------+ + | `E5M2` | `FP16` | `E5M2` | `FP32` | + + +----------------+-----------------+ + + | | `BF16` | `E5M2` | | + + +----------------+-----------------+ + + | | `FP16` | `FP16` | | + + +----------------+-----------------+ + + | | `BF16` | `BF16` | | + + +----------------+-----------------+ + + | | `FP32` | `FP32` | | + +--------------+----------------+-----------------+-------------+ + +* Matrix pruning and compression functionalities +* Activation functions, bias vector, and output scaling +* Batched computation (multiple matrices in a single run) +* GEMM Split-K mode +* Auto-tuning functionality (see `cusparseLtMatmulSearch()`) +* NVTX ranging and Logging functionalities + +================================================================================ +Support +================================================================================ + +* *Supported SM Architectures*: `SM 8.0`, `SM 8.6`, `SM 8.9`, `SM 9.0` +* *Supported CPU architectures and operating systems*: + ++------------+--------------------+ +| OS | CPU archs | ++============+====================+ +| `Windows` | `x86_64` | ++------------+--------------------+ +| `Linux` | `x86_64`, `Arm64` | ++------------+--------------------+ + + +================================================================================ +Documentation +================================================================================ + +Please refer to https://docs.nvidia.com/cuda/cusparselt/index.html for the cuSPARSELt documentation. + +================================================================================ +Installation +================================================================================ + +The cuSPARSELt wheel can be installed as follows: + +.. code-block:: bash + + pip install cusparselt-cuXX + +where XX is the CUDA major version (currently CUDA 12 only is supported). diff --git a/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/RECORD b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/RECORD new file mode 100644 index 0000000000000000000000000000000000000000..dba0fa36fa89bde32de2cac4cbe1e396dcb70c18 --- /dev/null +++ b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/RECORD @@ -0,0 +1,8 @@ +cusparselt/LICENSE.txt,sha256=6NFYiFpoG5Xsem_AbdjUpSmJ83TLE4DIpMj7J_09XV4,17948 +cusparselt/include/cusparseLt.h,sha256=JIn_hLTOwxBiufqpo7vOcVGX3zo0n-BkU0AkavkaPjI,16823 +cusparselt/lib/libcusparseLt.so.0,sha256=QjhfQT_ofOHIRLE4kPkgtmhz29NgMKOw_SwUPXIvaHk,212602113 +nvidia_cusparselt_cu12-0.6.2.dist-info/INSTALLER,sha256=zuuue4knoyJ-UwPPXg8fezS7VCrXJQrAP7zeNuwvFQg,4 +nvidia_cusparselt_cu12-0.6.2.dist-info/METADATA,sha256=2t-ZJ3GY27zycJbOlcBokphKdUCYpmK7BWuPuwUyQoo,6761 +nvidia_cusparselt_cu12-0.6.2.dist-info/RECORD,, +nvidia_cusparselt_cu12-0.6.2.dist-info/WHEEL,sha256=zI13KrVJiX3p6ASi2Ky9G4dSxIeOhCoZtSUXtMKDRAw,108 +nvidia_cusparselt_cu12-0.6.2.dist-info/top_level.txt,sha256=xqh0KNKTy3sVRvMfvpVzqXt3n2uEz0ruWp1XKEDANvk,11 diff --git a/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/WHEEL b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/WHEEL new file mode 100644 index 0000000000000000000000000000000000000000..6cd8f79576f5790d97cd198c8374d3fe0c319145 --- /dev/null +++ b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/WHEEL @@ -0,0 +1,5 @@ +Wheel-Version: 1.0 +Generator: setuptools (71.0.4) +Root-Is-Purelib: true +Tag: py3-none-manylinux2014_x86_64 + diff --git a/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/top_level.txt b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/top_level.txt new file mode 100644 index 0000000000000000000000000000000000000000..c46ed7c937f80185a9d1cafc27f6a64aa846fe07 --- /dev/null +++ b/lib/python3.11/site-packages/nvidia_cusparselt_cu12-0.6.2.dist-info/top_level.txt @@ -0,0 +1 @@ +cusparselt diff --git a/lib/python3.11/site-packages/sympy/__init__.py b/lib/python3.11/site-packages/sympy/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..196a8069e8e0fc794abcb1b9e799e73d76e8fd95 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/__init__.py @@ -0,0 +1,542 @@ +""" +SymPy is a Python library for symbolic mathematics. It aims to become a +full-featured computer algebra system (CAS) while keeping the code as simple +as possible in order to be comprehensible and easily extensible. SymPy is +written entirely in Python. It depends on mpmath, and other external libraries +may be optionally for things like plotting support. + +See the webpage for more information and documentation: + + https://sympy.org + +""" + + +import sys +if sys.version_info < (3, 8): + raise ImportError("Python version 3.8 or above is required for SymPy.") +del sys + + +try: + import mpmath +except ImportError: + raise ImportError("SymPy now depends on mpmath as an external library. " + "See https://docs.sympy.org/latest/install.html#mpmath for more information.") + +del mpmath + +from sympy.release import __version__ +from sympy.core.cache import lazy_function + +if 'dev' in __version__: + def enable_warnings(): + import warnings + warnings.filterwarnings('default', '.*', DeprecationWarning, module='sympy.*') + del warnings + enable_warnings() + del enable_warnings + + +def __sympy_debug(): + # helper function so we don't import os globally + import os + debug_str = os.getenv('SYMPY_DEBUG', 'False') + if debug_str in ('True', 'False'): + return eval(debug_str) + else: + raise RuntimeError("unrecognized value for SYMPY_DEBUG: %s" % + debug_str) +SYMPY_DEBUG = __sympy_debug() # type: bool + +from .core import (sympify, SympifyError, cacheit, Basic, Atom, + preorder_traversal, S, Expr, AtomicExpr, UnevaluatedExpr, Symbol, + Wild, Dummy, symbols, var, Number, Float, Rational, Integer, + NumberSymbol, RealNumber, igcd, ilcm, seterr, E, I, nan, oo, pi, zoo, + AlgebraicNumber, comp, mod_inverse, Pow, integer_nthroot, integer_log, + trailing, Mul, prod, Add, Mod, Rel, Eq, Ne, Lt, Le, Gt, Ge, Equality, + GreaterThan, LessThan, Unequality, StrictGreaterThan, StrictLessThan, + vectorize, Lambda, WildFunction, Derivative, diff, FunctionClass, + Function, Subs, expand, PoleError, count_ops, expand_mul, expand_log, + expand_func, expand_trig, expand_complex, expand_multinomial, nfloat, + expand_power_base, expand_power_exp, arity, PrecisionExhausted, N, + evalf, Tuple, Dict, gcd_terms, factor_terms, factor_nc, evaluate, + Catalan, EulerGamma, GoldenRatio, TribonacciConstant, bottom_up, use, + postorder_traversal, default_sort_key, ordered, num_digits) + +from .logic import (to_cnf, to_dnf, to_nnf, And, Or, Not, Xor, Nand, Nor, + Implies, Equivalent, ITE, POSform, SOPform, simplify_logic, bool_map, + true, false, satisfiable) + +from .assumptions import (AppliedPredicate, Predicate, AssumptionsContext, + assuming, Q, ask, register_handler, remove_handler, refine) + +from .polys import (Poly, PurePoly, poly_from_expr, parallel_poly_from_expr, + degree, total_degree, degree_list, LC, LM, LT, pdiv, prem, pquo, + pexquo, div, rem, quo, exquo, half_gcdex, gcdex, invert, + subresultants, resultant, discriminant, cofactors, gcd_list, gcd, + lcm_list, lcm, terms_gcd, trunc, monic, content, primitive, compose, + decompose, sturm, gff_list, gff, sqf_norm, sqf_part, sqf_list, sqf, + factor_list, factor, intervals, refine_root, count_roots, all_roots, + real_roots, nroots, ground_roots, nth_power_roots_poly, cancel, + reduced, groebner, is_zero_dimensional, GroebnerBasis, poly, + symmetrize, horner, interpolate, rational_interpolate, viete, together, + BasePolynomialError, ExactQuotientFailed, PolynomialDivisionFailed, + OperationNotSupported, HeuristicGCDFailed, HomomorphismFailed, + IsomorphismFailed, ExtraneousFactors, EvaluationFailed, + RefinementFailed, CoercionFailed, NotInvertible, NotReversible, + NotAlgebraic, DomainError, PolynomialError, UnificationFailed, + GeneratorsError, GeneratorsNeeded, ComputationFailed, + UnivariatePolynomialError, MultivariatePolynomialError, + PolificationFailed, OptionError, FlagError, minpoly, + minimal_polynomial, primitive_element, field_isomorphism, + to_number_field, isolate, round_two, prime_decomp, prime_valuation, + galois_group, itermonomials, Monomial, lex, grlex, + grevlex, ilex, igrlex, igrevlex, CRootOf, rootof, RootOf, + ComplexRootOf, RootSum, roots, Domain, FiniteField, IntegerRing, + RationalField, RealField, ComplexField, PythonFiniteField, + GMPYFiniteField, PythonIntegerRing, GMPYIntegerRing, PythonRational, + GMPYRationalField, AlgebraicField, PolynomialRing, FractionField, + ExpressionDomain, FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python, + QQ_gmpy, GF, FF, ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW, + construct_domain, swinnerton_dyer_poly, cyclotomic_poly, + symmetric_poly, random_poly, interpolating_poly, jacobi_poly, + chebyshevt_poly, chebyshevu_poly, hermite_poly, hermite_prob_poly, + legendre_poly, laguerre_poly, apart, apart_list, assemble_partfrac_list, + Options, ring, xring, vring, sring, field, xfield, vfield, sfield) + +from .series import (Order, O, limit, Limit, gruntz, series, approximants, + residue, EmptySequence, SeqPer, SeqFormula, sequence, SeqAdd, SeqMul, + fourier_series, fps, difference_delta, limit_seq) + +from .functions import (factorial, factorial2, rf, ff, binomial, + RisingFactorial, FallingFactorial, subfactorial, carmichael, + fibonacci, lucas, motzkin, tribonacci, harmonic, bernoulli, bell, euler, + catalan, genocchi, andre, partition, divisor_sigma, legendre_symbol, + jacobi_symbol, kronecker_symbol, mobius, primenu, primeomega, + totient, reduced_totient, primepi, sqrt, root, Min, Max, Id, + real_root, Rem, cbrt, re, im, sign, Abs, conjugate, arg, polar_lift, + periodic_argument, unbranched_argument, principal_branch, transpose, + adjoint, polarify, unpolarify, sin, cos, tan, sec, csc, cot, sinc, + asin, acos, atan, asec, acsc, acot, atan2, exp_polar, exp, ln, log, + LambertW, sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh, + acoth, asech, acsch, floor, ceiling, frac, Piecewise, piecewise_fold, + piecewise_exclusive, erf, erfc, erfi, erf2, erfinv, erfcinv, erf2inv, + Ei, expint, E1, li, Li, Si, Ci, Shi, Chi, fresnels, fresnelc, gamma, + lowergamma, uppergamma, polygamma, loggamma, digamma, trigamma, + multigamma, dirichlet_eta, zeta, lerchphi, polylog, stieltjes, Eijk, + LeviCivita, KroneckerDelta, SingularityFunction, DiracDelta, Heaviside, + bspline_basis, bspline_basis_set, interpolating_spline, besselj, + bessely, besseli, besselk, hankel1, hankel2, jn, yn, jn_zeros, hn1, + hn2, airyai, airybi, airyaiprime, airybiprime, marcumq, hyper, + meijerg, appellf1, legendre, assoc_legendre, hermite, hermite_prob, + chebyshevt, chebyshevu, chebyshevu_root, chebyshevt_root, laguerre, + assoc_laguerre, gegenbauer, jacobi, jacobi_normalized, Ynm, Ynm_c, + Znm, elliptic_k, elliptic_f, elliptic_e, elliptic_pi, beta, mathieus, + mathieuc, mathieusprime, mathieucprime, riemann_xi, betainc, betainc_regularized) + +from .ntheory import (nextprime, prevprime, prime, primerange, + randprime, Sieve, sieve, primorial, cycle_length, composite, + compositepi, isprime, divisors, proper_divisors, factorint, + multiplicity, perfect_power, pollard_pm1, pollard_rho, primefactors, + divisor_count, proper_divisor_count, + factorrat, + mersenne_prime_exponent, is_perfect, is_mersenne_prime, is_abundant, + is_deficient, is_amicable, is_carmichael, abundance, npartitions, is_primitive_root, + is_quad_residue, n_order, sqrt_mod, + quadratic_residues, primitive_root, nthroot_mod, is_nthpow_residue, + sqrt_mod_iter, discrete_log, quadratic_congruence, + binomial_coefficients, binomial_coefficients_list, + multinomial_coefficients, continued_fraction_periodic, + continued_fraction_iterator, continued_fraction_reduce, + continued_fraction_convergents, continued_fraction, egyptian_fraction) + +from .concrete import product, Product, summation, Sum + +from .discrete import (fft, ifft, ntt, intt, fwht, ifwht, mobius_transform, + inverse_mobius_transform, convolution, covering_product, + intersecting_product) + +from .simplify import (simplify, hypersimp, hypersimilar, logcombine, + separatevars, posify, besselsimp, kroneckersimp, signsimp, + nsimplify, FU, fu, sqrtdenest, cse, epath, EPath, hyperexpand, + collect, rcollect, radsimp, collect_const, fraction, numer, denom, + trigsimp, exptrigsimp, powsimp, powdenest, combsimp, gammasimp, + ratsimp, ratsimpmodprime) + +from .sets import (Set, Interval, Union, EmptySet, FiniteSet, ProductSet, + Intersection, DisjointUnion, imageset, Complement, SymmetricDifference, ImageSet, + Range, ComplexRegion, Complexes, Reals, Contains, ConditionSet, Ordinal, + OmegaPower, ord0, PowerSet, Naturals, Naturals0, UniversalSet, + Integers, Rationals) + +from .solvers import (solve, solve_linear_system, solve_linear_system_LU, + solve_undetermined_coeffs, nsolve, solve_linear, checksol, det_quick, + inv_quick, check_assumptions, failing_assumptions, diophantine, + rsolve, rsolve_poly, rsolve_ratio, rsolve_hyper, checkodesol, + classify_ode, dsolve, homogeneous_order, solve_poly_system, + solve_triangulated, pde_separate, pde_separate_add, pde_separate_mul, + pdsolve, classify_pde, checkpdesol, ode_order, reduce_inequalities, + reduce_abs_inequality, reduce_abs_inequalities, solve_poly_inequality, + solve_rational_inequalities, solve_univariate_inequality, decompogen, + solveset, linsolve, linear_eq_to_matrix, nonlinsolve, substitution) + +from .matrices import (ShapeError, NonSquareMatrixError, GramSchmidt, + casoratian, diag, eye, hessian, jordan_cell, list2numpy, matrix2numpy, + matrix_multiply_elementwise, ones, randMatrix, rot_axis1, rot_axis2, + rot_axis3, symarray, wronskian, zeros, MutableDenseMatrix, + DeferredVector, MatrixBase, Matrix, MutableMatrix, + MutableSparseMatrix, banded, ImmutableDenseMatrix, + ImmutableSparseMatrix, ImmutableMatrix, SparseMatrix, MatrixSlice, + BlockDiagMatrix, BlockMatrix, FunctionMatrix, Identity, Inverse, + MatAdd, MatMul, MatPow, MatrixExpr, MatrixSymbol, Trace, Transpose, + ZeroMatrix, OneMatrix, blockcut, block_collapse, matrix_symbols, + Adjoint, hadamard_product, HadamardProduct, HadamardPower, + Determinant, det, diagonalize_vector, DiagMatrix, DiagonalMatrix, + DiagonalOf, trace, DotProduct, kronecker_product, KroneckerProduct, + PermutationMatrix, MatrixPermute, Permanent, per, rot_ccw_axis1, + rot_ccw_axis2, rot_ccw_axis3, rot_givens) + +from .geometry import (Point, Point2D, Point3D, Line, Ray, Segment, Line2D, + Segment2D, Ray2D, Line3D, Segment3D, Ray3D, Plane, Ellipse, Circle, + Polygon, RegularPolygon, Triangle, rad, deg, are_similar, centroid, + convex_hull, idiff, intersection, closest_points, farthest_points, + GeometryError, Curve, Parabola) + +from .utilities import (flatten, group, take, subsets, variations, + numbered_symbols, cartes, capture, dict_merge, prefixes, postfixes, + sift, topological_sort, unflatten, has_dups, has_variety, reshape, + rotations, filldedent, lambdify, + threaded, xthreaded, public, memoize_property, timed) + +from .integrals import (integrate, Integral, line_integrate, mellin_transform, + inverse_mellin_transform, MellinTransform, InverseMellinTransform, + laplace_transform, laplace_correspondence, laplace_initial_conds, + inverse_laplace_transform, LaplaceTransform, + InverseLaplaceTransform, fourier_transform, inverse_fourier_transform, + FourierTransform, InverseFourierTransform, sine_transform, + inverse_sine_transform, SineTransform, InverseSineTransform, + cosine_transform, inverse_cosine_transform, CosineTransform, + InverseCosineTransform, hankel_transform, inverse_hankel_transform, + HankelTransform, InverseHankelTransform, singularityintegrate) + +from .tensor import (IndexedBase, Idx, Indexed, get_contraction_structure, + get_indices, shape, MutableDenseNDimArray, ImmutableDenseNDimArray, + MutableSparseNDimArray, ImmutableSparseNDimArray, NDimArray, + tensorproduct, tensorcontraction, tensordiagonal, derive_by_array, + permutedims, Array, DenseNDimArray, SparseNDimArray) + +from .parsing import parse_expr + +from .calculus import (euler_equations, singularities, is_increasing, + is_strictly_increasing, is_decreasing, is_strictly_decreasing, + is_monotonic, finite_diff_weights, apply_finite_diff, + differentiate_finite, periodicity, not_empty_in, AccumBounds, + is_convex, stationary_points, minimum, maximum) + +from .algebras import Quaternion + +from .printing import (pager_print, pretty, pretty_print, pprint, + pprint_use_unicode, pprint_try_use_unicode, latex, print_latex, + multiline_latex, mathml, print_mathml, python, print_python, pycode, + ccode, print_ccode, smtlib_code, glsl_code, print_glsl, cxxcode, fcode, + print_fcode, rcode, print_rcode, jscode, print_jscode, julia_code, + mathematica_code, octave_code, rust_code, print_gtk, preview, srepr, + print_tree, StrPrinter, sstr, sstrrepr, TableForm, dotprint, + maple_code, print_maple_code) + +test = lazy_function('sympy.testing.runtests_pytest', 'test') +doctest = lazy_function('sympy.testing.runtests', 'doctest') + +# This module causes conflicts with other modules: +# from .stats import * +# Adds about .04-.05 seconds of import time +# from combinatorics import * +# This module is slow to import: +#from physics import units +from .plotting import plot, textplot, plot_backends, plot_implicit, plot_parametric +from .interactive import init_session, init_printing, interactive_traversal + +evalf._create_evalf_table() + +__all__ = [ + '__version__', + + # sympy.core + 'sympify', 'SympifyError', 'cacheit', 'Basic', 'Atom', + 'preorder_traversal', 'S', 'Expr', 'AtomicExpr', 'UnevaluatedExpr', + 'Symbol', 'Wild', 'Dummy', 'symbols', 'var', 'Number', 'Float', + 'Rational', 'Integer', 'NumberSymbol', 'RealNumber', 'igcd', 'ilcm', + 'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo', 'AlgebraicNumber', 'comp', + 'mod_inverse', 'Pow', 'integer_nthroot', 'integer_log', 'trailing', 'Mul', 'prod', + 'Add', 'Mod', 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality', + 'GreaterThan', 'LessThan', 'Unequality', 'StrictGreaterThan', + 'StrictLessThan', 'vectorize', 'Lambda', 'WildFunction', 'Derivative', + 'diff', 'FunctionClass', 'Function', 'Subs', 'expand', 'PoleError', + 'count_ops', 'expand_mul', 'expand_log', 'expand_func', 'expand_trig', + 'expand_complex', 'expand_multinomial', 'nfloat', 'expand_power_base', + 'expand_power_exp', 'arity', 'PrecisionExhausted', 'N', 'evalf', 'Tuple', + 'Dict', 'gcd_terms', 'factor_terms', 'factor_nc', 'evaluate', 'Catalan', + 'EulerGamma', 'GoldenRatio', 'TribonacciConstant', 'bottom_up', 'use', + 'postorder_traversal', 'default_sort_key', 'ordered', 'num_digits', + + # sympy.logic + 'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor', + 'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic', + 'bool_map', 'true', 'false', 'satisfiable', + + # sympy.assumptions + 'AppliedPredicate', 'Predicate', 'AssumptionsContext', 'assuming', 'Q', + 'ask', 'register_handler', 'remove_handler', 'refine', + + # sympy.polys + 'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree', + 'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo', + 'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert', + 'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list', + 'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content', + 'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff', + 'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor', + 'intervals', 'refine_root', 'count_roots', 'all_roots', 'real_roots', + 'nroots', 'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', + 'groebner', 'is_zero_dimensional', 'GroebnerBasis', 'poly', 'symmetrize', + 'horner', 'interpolate', 'rational_interpolate', 'viete', 'together', + 'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed', + 'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed', + 'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed', + 'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible', + 'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed', + 'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed', + 'UnivariatePolynomialError', 'MultivariatePolynomialError', + 'PolificationFailed', 'OptionError', 'FlagError', 'minpoly', + 'minimal_polynomial', 'primitive_element', 'field_isomorphism', + 'to_number_field', 'isolate', 'round_two', 'prime_decomp', + 'prime_valuation', 'galois_group', 'itermonomials', 'Monomial', 'lex', 'grlex', + 'grevlex', 'ilex', 'igrlex', 'igrevlex', 'CRootOf', 'rootof', 'RootOf', + 'ComplexRootOf', 'RootSum', 'roots', 'Domain', 'FiniteField', + 'IntegerRing', 'RationalField', 'RealField', 'ComplexField', + 'PythonFiniteField', 'GMPYFiniteField', 'PythonIntegerRing', + 'GMPYIntegerRing', 'PythonRational', 'GMPYRationalField', + 'AlgebraicField', 'PolynomialRing', 'FractionField', 'ExpressionDomain', + 'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', 'QQ_python', 'QQ_gmpy', + 'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', 'CC', 'EX', 'EXRAW', + 'construct_domain', 'swinnerton_dyer_poly', 'cyclotomic_poly', + 'symmetric_poly', 'random_poly', 'interpolating_poly', 'jacobi_poly', + 'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', 'hermite_prob_poly', + 'legendre_poly', 'laguerre_poly', 'apart', 'apart_list', 'assemble_partfrac_list', + 'Options', 'ring', 'xring', 'vring', 'sring', 'field', 'xfield', 'vfield', + 'sfield', + + # sympy.series + 'Order', 'O', 'limit', 'Limit', 'gruntz', 'series', 'approximants', + 'residue', 'EmptySequence', 'SeqPer', 'SeqFormula', 'sequence', 'SeqAdd', + 'SeqMul', 'fourier_series', 'fps', 'difference_delta', 'limit_seq', + + # sympy.functions + 'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial', + 'FallingFactorial', 'subfactorial', 'carmichael', 'fibonacci', 'lucas', + 'motzkin', 'tribonacci', 'harmonic', 'bernoulli', 'bell', 'euler', 'catalan', + 'genocchi', 'andre', 'partition', 'divisor_sigma', 'legendre_symbol', 'jacobi_symbol', + 'kronecker_symbol', 'mobius', 'primenu', 'primeomega', 'totient', 'primepi', + 'reduced_totient', 'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root', + 'Rem', 'cbrt', 're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift', + 'periodic_argument', 'unbranched_argument', 'principal_branch', + 'transpose', 'adjoint', 'polarify', 'unpolarify', 'sin', 'cos', 'tan', + 'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan', 'asec', 'acsc', + 'acot', 'atan2', 'exp_polar', 'exp', 'ln', 'log', 'LambertW', 'sinh', + 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh', + 'acoth', 'asech', 'acsch', 'floor', 'ceiling', 'frac', 'Piecewise', + 'piecewise_fold', 'piecewise_exclusive', 'erf', 'erfc', 'erfi', 'erf2', + 'erfinv', 'erfcinv', 'erf2inv', 'Ei', 'expint', 'E1', 'li', 'Li', 'Si', + 'Ci', 'Shi', 'Chi', 'fresnels', 'fresnelc', 'gamma', 'lowergamma', + 'uppergamma', 'polygamma', 'loggamma', 'digamma', 'trigamma', 'multigamma', + 'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'Eijk', 'LeviCivita', + 'KroneckerDelta', 'SingularityFunction', 'DiracDelta', 'Heaviside', + 'bspline_basis', 'bspline_basis_set', 'interpolating_spline', 'besselj', + 'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn', 'yn', + 'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime', + 'airybiprime', 'marcumq', 'hyper', 'meijerg', 'appellf1', 'legendre', + 'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt', 'chebyshevu', + 'chebyshevu_root', 'chebyshevt_root', 'laguerre', 'assoc_laguerre', + 'gegenbauer', 'jacobi', 'jacobi_normalized', 'Ynm', 'Ynm_c', 'Znm', + 'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi', 'beta', + 'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime', 'riemann_xi','betainc', + 'betainc_regularized', + + # sympy.ntheory + 'nextprime', 'prevprime', 'prime', 'primerange', 'randprime', + 'Sieve', 'sieve', 'primorial', 'cycle_length', 'composite', 'compositepi', + 'isprime', 'divisors', 'proper_divisors', 'factorint', 'multiplicity', + 'perfect_power', 'pollard_pm1', 'pollard_rho', 'primefactors', + 'divisor_count', 'proper_divisor_count', + 'factorrat', + 'mersenne_prime_exponent', 'is_perfect', 'is_mersenne_prime', + 'is_abundant', 'is_deficient', 'is_amicable', 'is_carmichael', 'abundance', + 'npartitions', + 'is_primitive_root', 'is_quad_residue', + 'n_order', 'sqrt_mod', 'quadratic_residues', + 'primitive_root', 'nthroot_mod', 'is_nthpow_residue', 'sqrt_mod_iter', + 'discrete_log', 'quadratic_congruence', 'binomial_coefficients', + 'binomial_coefficients_list', 'multinomial_coefficients', + 'continued_fraction_periodic', 'continued_fraction_iterator', + 'continued_fraction_reduce', 'continued_fraction_convergents', + 'continued_fraction', 'egyptian_fraction', + + # sympy.concrete + 'product', 'Product', 'summation', 'Sum', + + # sympy.discrete + 'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform', + 'inverse_mobius_transform', 'convolution', 'covering_product', + 'intersecting_product', + + # sympy.simplify + 'simplify', 'hypersimp', 'hypersimilar', 'logcombine', 'separatevars', + 'posify', 'besselsimp', 'kroneckersimp', 'signsimp', + 'nsimplify', 'FU', 'fu', 'sqrtdenest', 'cse', 'epath', 'EPath', + 'hyperexpand', 'collect', 'rcollect', 'radsimp', 'collect_const', + 'fraction', 'numer', 'denom', 'trigsimp', 'exptrigsimp', 'powsimp', + 'powdenest', 'combsimp', 'gammasimp', 'ratsimp', 'ratsimpmodprime', + + # sympy.sets + 'Set', 'Interval', 'Union', 'EmptySet', 'FiniteSet', 'ProductSet', + 'Intersection', 'imageset', 'DisjointUnion', 'Complement', 'SymmetricDifference', + 'ImageSet', 'Range', 'ComplexRegion', 'Reals', 'Contains', 'ConditionSet', + 'Ordinal', 'OmegaPower', 'ord0', 'PowerSet', 'Naturals', + 'Naturals0', 'UniversalSet', 'Integers', 'Rationals', 'Complexes', + + # sympy.solvers + 'solve', 'solve_linear_system', 'solve_linear_system_LU', + 'solve_undetermined_coeffs', 'nsolve', 'solve_linear', 'checksol', + 'det_quick', 'inv_quick', 'check_assumptions', 'failing_assumptions', + 'diophantine', 'rsolve', 'rsolve_poly', 'rsolve_ratio', 'rsolve_hyper', + 'checkodesol', 'classify_ode', 'dsolve', 'homogeneous_order', + 'solve_poly_system', 'solve_triangulated', 'pde_separate', + 'pde_separate_add', 'pde_separate_mul', 'pdsolve', 'classify_pde', + 'checkpdesol', 'ode_order', 'reduce_inequalities', + 'reduce_abs_inequality', 'reduce_abs_inequalities', + 'solve_poly_inequality', 'solve_rational_inequalities', + 'solve_univariate_inequality', 'decompogen', 'solveset', 'linsolve', + 'linear_eq_to_matrix', 'nonlinsolve', 'substitution', + + # sympy.matrices + 'ShapeError', 'NonSquareMatrixError', 'GramSchmidt', 'casoratian', 'diag', + 'eye', 'hessian', 'jordan_cell', 'list2numpy', 'matrix2numpy', + 'matrix_multiply_elementwise', 'ones', 'randMatrix', 'rot_axis1', + 'rot_axis2', 'rot_axis3', 'symarray', 'wronskian', 'zeros', + 'MutableDenseMatrix', 'DeferredVector', 'MatrixBase', 'Matrix', + 'MutableMatrix', 'MutableSparseMatrix', 'banded', 'ImmutableDenseMatrix', + 'ImmutableSparseMatrix', 'ImmutableMatrix', 'SparseMatrix', 'MatrixSlice', + 'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix', 'Identity', 'Inverse', + 'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr', 'MatrixSymbol', 'Trace', + 'Transpose', 'ZeroMatrix', 'OneMatrix', 'blockcut', 'block_collapse', + 'matrix_symbols', 'Adjoint', 'hadamard_product', 'HadamardProduct', + 'HadamardPower', 'Determinant', 'det', 'diagonalize_vector', 'DiagMatrix', + 'DiagonalMatrix', 'DiagonalOf', 'trace', 'DotProduct', + 'kronecker_product', 'KroneckerProduct', 'PermutationMatrix', + 'MatrixPermute', 'Permanent', 'per', 'rot_ccw_axis1', 'rot_ccw_axis2', + 'rot_ccw_axis3', 'rot_givens', + + # sympy.geometry + 'Point', 'Point2D', 'Point3D', 'Line', 'Ray', 'Segment', 'Line2D', + 'Segment2D', 'Ray2D', 'Line3D', 'Segment3D', 'Ray3D', 'Plane', 'Ellipse', + 'Circle', 'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg', + 'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection', + 'closest_points', 'farthest_points', 'GeometryError', 'Curve', 'Parabola', + + # sympy.utilities + 'flatten', 'group', 'take', 'subsets', 'variations', 'numbered_symbols', + 'cartes', 'capture', 'dict_merge', 'prefixes', 'postfixes', 'sift', + 'topological_sort', 'unflatten', 'has_dups', 'has_variety', 'reshape', + 'rotations', 'filldedent', 'lambdify', 'threaded', 'xthreaded', + 'public', 'memoize_property', 'timed', + + # sympy.integrals + 'integrate', 'Integral', 'line_integrate', 'mellin_transform', + 'inverse_mellin_transform', 'MellinTransform', 'InverseMellinTransform', + 'laplace_transform', 'inverse_laplace_transform', 'LaplaceTransform', + 'laplace_correspondence', 'laplace_initial_conds', + 'InverseLaplaceTransform', 'fourier_transform', + 'inverse_fourier_transform', 'FourierTransform', + 'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform', + 'SineTransform', 'InverseSineTransform', 'cosine_transform', + 'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform', + 'hankel_transform', 'inverse_hankel_transform', 'HankelTransform', + 'InverseHankelTransform', 'singularityintegrate', + + # sympy.tensor + 'IndexedBase', 'Idx', 'Indexed', 'get_contraction_structure', + 'get_indices', 'shape', 'MutableDenseNDimArray', 'ImmutableDenseNDimArray', + 'MutableSparseNDimArray', 'ImmutableSparseNDimArray', 'NDimArray', + 'tensorproduct', 'tensorcontraction', 'tensordiagonal', 'derive_by_array', + 'permutedims', 'Array', 'DenseNDimArray', 'SparseNDimArray', + + # sympy.parsing + 'parse_expr', + + # sympy.calculus + 'euler_equations', 'singularities', 'is_increasing', + 'is_strictly_increasing', 'is_decreasing', 'is_strictly_decreasing', + 'is_monotonic', 'finite_diff_weights', 'apply_finite_diff', + 'differentiate_finite', 'periodicity', 'not_empty_in', + 'AccumBounds', 'is_convex', 'stationary_points', 'minimum', 'maximum', + + # sympy.algebras + 'Quaternion', + + # sympy.printing + 'pager_print', 'pretty', 'pretty_print', 'pprint', 'pprint_use_unicode', + 'pprint_try_use_unicode', 'latex', 'print_latex', 'multiline_latex', + 'mathml', 'print_mathml', 'python', 'print_python', 'pycode', 'ccode', + 'print_ccode', 'smtlib_code', 'glsl_code', 'print_glsl', 'cxxcode', 'fcode', + 'print_fcode', 'rcode', 'print_rcode', 'jscode', 'print_jscode', + 'julia_code', 'mathematica_code', 'octave_code', 'rust_code', 'print_gtk', + 'preview', 'srepr', 'print_tree', 'StrPrinter', 'sstr', 'sstrrepr', + 'TableForm', 'dotprint', 'maple_code', 'print_maple_code', + + # sympy.plotting + 'plot', 'textplot', 'plot_backends', 'plot_implicit', 'plot_parametric', + + # sympy.interactive + 'init_session', 'init_printing', 'interactive_traversal', + + # sympy.testing + 'test', 'doctest', +] + + +#===========================================================================# +# # +# XXX: The names below were importable before SymPy 1.6 using # +# # +# from sympy import * # +# # +# This happened implicitly because there was no __all__ defined in this # +# __init__.py file. Not every package is imported. The list matches what # +# would have been imported before. It is possible that these packages will # +# not be imported by a star-import from sympy in future. # +# # +#===========================================================================# + + +__all__.extend(( + 'algebras', + 'assumptions', + 'calculus', + 'concrete', + 'discrete', + 'external', + 'functions', + 'geometry', + 'interactive', + 'multipledispatch', + 'ntheory', + 'parsing', + 'plotting', + 'polys', + 'printing', + 'release', + 'strategies', + 'tensor', + 'utilities', +)) diff --git a/lib/python3.11/site-packages/sympy/abc.py b/lib/python3.11/site-packages/sympy/abc.py new file mode 100644 index 0000000000000000000000000000000000000000..177e8902e78dd6c23f2a5a4970098a27503f683a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/abc.py @@ -0,0 +1,111 @@ +""" +This module exports all latin and greek letters as Symbols, so you can +conveniently do + + >>> from sympy.abc import x, y + +instead of the slightly more clunky-looking + + >>> from sympy import symbols + >>> x, y = symbols('x y') + +Caveats +======= + +1. As of the time of writing this, the names ``O``, ``S``, ``I``, ``N``, +``E``, and ``Q`` are colliding with names defined in SymPy. If you import them +from both ``sympy.abc`` and ``sympy``, the second import will "win". +This is an issue only for * imports, which should only be used for short-lived +code such as interactive sessions and throwaway scripts that do not survive +until the next SymPy upgrade, where ``sympy`` may contain a different set of +names. + +2. This module does not define symbol names on demand, i.e. +``from sympy.abc import foo`` will be reported as an error because +``sympy.abc`` does not contain the name ``foo``. To get a symbol named ``foo``, +you still need to use ``Symbol('foo')`` or ``symbols('foo')``. +You can freely mix usage of ``sympy.abc`` and ``Symbol``/``symbols``, though +sticking with one and only one way to get the symbols does tend to make the code +more readable. + +The module also defines some special names to help detect which names clash +with the default SymPy namespace. + +``_clash1`` defines all the single letter variables that clash with +SymPy objects; ``_clash2`` defines the multi-letter clashing symbols; +and ``_clash`` is the union of both. These can be passed for ``locals`` +during sympification if one desires Symbols rather than the non-Symbol +objects for those names. + +Examples +======== + +>>> from sympy import S +>>> from sympy.abc import _clash1, _clash2, _clash +>>> S("Q & C", locals=_clash1) +C & Q +>>> S('pi(x)', locals=_clash2) +pi(x) +>>> S('pi(C, Q)', locals=_clash) +pi(C, Q) + +""" + +from typing import Any, Dict as tDict + +import string + +from .core import Symbol, symbols +from .core.alphabets import greeks +from sympy.parsing.sympy_parser import null + +##### Symbol definitions ##### + +# Implementation note: The easiest way to avoid typos in the symbols() +# parameter is to copy it from the left-hand side of the assignment. + +a, b, c, d, e, f, g, h, i, j = symbols('a, b, c, d, e, f, g, h, i, j') +k, l, m, n, o, p, q, r, s, t = symbols('k, l, m, n, o, p, q, r, s, t') +u, v, w, x, y, z = symbols('u, v, w, x, y, z') + +A, B, C, D, E, F, G, H, I, J = symbols('A, B, C, D, E, F, G, H, I, J') +K, L, M, N, O, P, Q, R, S, T = symbols('K, L, M, N, O, P, Q, R, S, T') +U, V, W, X, Y, Z = symbols('U, V, W, X, Y, Z') + +alpha, beta, gamma, delta = symbols('alpha, beta, gamma, delta') +epsilon, zeta, eta, theta = symbols('epsilon, zeta, eta, theta') +iota, kappa, lamda, mu = symbols('iota, kappa, lamda, mu') +nu, xi, omicron, pi = symbols('nu, xi, omicron, pi') +rho, sigma, tau, upsilon = symbols('rho, sigma, tau, upsilon') +phi, chi, psi, omega = symbols('phi, chi, psi, omega') + + +##### Clashing-symbols diagnostics ##### + +# We want to know which names in SymPy collide with those in here. +# This is mostly for diagnosing SymPy's namespace during SymPy development. + +_latin = list(string.ascii_letters) +# QOSINE should not be imported as they clash; gamma, pi and zeta clash, too +_greek = list(greeks) # make a copy, so we can mutate it +# Note: We import lamda since lambda is a reserved keyword in Python +_greek.remove("lambda") +_greek.append("lamda") + +ns: tDict[str, Any] = {} +exec('from sympy import *', ns) +_clash1: tDict[str, Any] = {} +_clash2: tDict[str, Any] = {} +while ns: + _k, _ = ns.popitem() + if _k in _greek: + _clash2[_k] = null + _greek.remove(_k) + elif _k in _latin: + _clash1[_k] = null + _latin.remove(_k) +_clash = {} +_clash.update(_clash1) +_clash.update(_clash2) + +del _latin, _greek, Symbol, _k, null diff --git a/lib/python3.11/site-packages/sympy/algebras/__init__.py b/lib/python3.11/site-packages/sympy/algebras/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..58013d2e0377a016d1a21fbf21c344ee76765189 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/algebras/__init__.py @@ -0,0 +1,3 @@ +from .quaternion import Quaternion + +__all__ = ["Quaternion",] diff --git a/lib/python3.11/site-packages/sympy/algebras/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/algebras/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..2455afd9056cc94904c7cc8ed0f970e1b1d2cbf4 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/algebras/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/algebras/__pycache__/quaternion.cpython-311.pyc b/lib/python3.11/site-packages/sympy/algebras/__pycache__/quaternion.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..a1725ba04d14eb08b47e37522e648dec60659242 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/algebras/__pycache__/quaternion.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/algebras/quaternion.py b/lib/python3.11/site-packages/sympy/algebras/quaternion.py new file mode 100644 index 0000000000000000000000000000000000000000..3251d92af3850abd8b07421d71c0cfc360efcf30 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/algebras/quaternion.py @@ -0,0 +1,1667 @@ +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.core.relational import is_eq +from sympy.functions.elementary.complexes import (conjugate, im, re, sign) +from sympy.functions.elementary.exponential import (exp, log as ln) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, asin, atan2) +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.simplify.trigsimp import trigsimp +from sympy.integrals.integrals import integrate +from sympy.matrices.dense import MutableDenseMatrix as Matrix +from sympy.core.sympify import sympify, _sympify +from sympy.core.expr import Expr +from sympy.core.logic import fuzzy_not, fuzzy_or +from sympy.utilities.misc import as_int + +from mpmath.libmp.libmpf import prec_to_dps + + +def _check_norm(elements, norm): + """validate if input norm is consistent""" + if norm is not None and norm.is_number: + if norm.is_positive is False: + raise ValueError("Input norm must be positive.") + + numerical = all(i.is_number and i.is_real is True for i in elements) + if numerical and is_eq(norm**2, sum(i**2 for i in elements)) is False: + raise ValueError("Incompatible value for norm.") + + +def _is_extrinsic(seq): + """validate seq and return True if seq is lowercase and False if uppercase""" + if type(seq) != str: + raise ValueError('Expected seq to be a string.') + if len(seq) != 3: + raise ValueError("Expected 3 axes, got `{}`.".format(seq)) + + intrinsic = seq.isupper() + extrinsic = seq.islower() + if not (intrinsic or extrinsic): + raise ValueError("seq must either be fully uppercase (for extrinsic " + "rotations), or fully lowercase, for intrinsic " + "rotations).") + + i, j, k = seq.lower() + if (i == j) or (j == k): + raise ValueError("Consecutive axes must be different") + + bad = set(seq) - set('xyzXYZ') + if bad: + raise ValueError("Expected axes from `seq` to be from " + "['x', 'y', 'z'] or ['X', 'Y', 'Z'], " + "got {}".format(''.join(bad))) + + return extrinsic + + +class Quaternion(Expr): + """Provides basic quaternion operations. + Quaternion objects can be instantiated as ``Quaternion(a, b, c, d)`` + as in $q = a + bi + cj + dk$. + + Parameters + ========== + + norm : None or number + Pre-defined quaternion norm. If a value is given, Quaternion.norm + returns this pre-defined value instead of calculating the norm + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 2, 3, 4) + >>> q + 1 + 2*i + 3*j + 4*k + + Quaternions over complex fields can be defined as: + + >>> from sympy import Quaternion + >>> from sympy import symbols, I + >>> x = symbols('x') + >>> q1 = Quaternion(x, x**3, x, x**2, real_field = False) + >>> q2 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + >>> q1 + x + x**3*i + x*j + x**2*k + >>> q2 + (3 + 4*I) + (2 + 5*I)*i + 0*j + (7 + 8*I)*k + + Defining symbolic unit quaternions: + + >>> from sympy import Quaternion + >>> from sympy.abc import w, x, y, z + >>> q = Quaternion(w, x, y, z, norm=1) + >>> q + w + x*i + y*j + z*k + >>> q.norm() + 1 + + References + ========== + + .. [1] https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/ + .. [2] https://en.wikipedia.org/wiki/Quaternion + + """ + _op_priority = 11.0 + + is_commutative = False + + def __new__(cls, a=0, b=0, c=0, d=0, real_field=True, norm=None): + a, b, c, d = map(sympify, (a, b, c, d)) + + if any(i.is_commutative is False for i in [a, b, c, d]): + raise ValueError("arguments have to be commutative") + obj = super().__new__(cls, a, b, c, d) + obj._real_field = real_field + obj.set_norm(norm) + return obj + + def set_norm(self, norm): + """Sets norm of an already instantiated quaternion. + + Parameters + ========== + + norm : None or number + Pre-defined quaternion norm. If a value is given, Quaternion.norm + returns this pre-defined value instead of calculating the norm + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> q = Quaternion(a, b, c, d) + >>> q.norm() + sqrt(a**2 + b**2 + c**2 + d**2) + + Setting the norm: + + >>> q.set_norm(1) + >>> q.norm() + 1 + + Removing set norm: + + >>> q.set_norm(None) + >>> q.norm() + sqrt(a**2 + b**2 + c**2 + d**2) + + """ + norm = sympify(norm) + _check_norm(self.args, norm) + self._norm = norm + + @property + def a(self): + return self.args[0] + + @property + def b(self): + return self.args[1] + + @property + def c(self): + return self.args[2] + + @property + def d(self): + return self.args[3] + + @property + def real_field(self): + return self._real_field + + @property + def product_matrix_left(self): + r"""Returns 4 x 4 Matrix equivalent to a Hamilton product from the + left. This can be useful when treating quaternion elements as column + vectors. Given a quaternion $q = a + bi + cj + dk$ where a, b, c and d + are real numbers, the product matrix from the left is: + + .. math:: + + M = \begin{bmatrix} a &-b &-c &-d \\ + b & a &-d & c \\ + c & d & a &-b \\ + d &-c & b & a \end{bmatrix} + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> q1 = Quaternion(1, 0, 0, 1) + >>> q2 = Quaternion(a, b, c, d) + >>> q1.product_matrix_left + Matrix([ + [1, 0, 0, -1], + [0, 1, -1, 0], + [0, 1, 1, 0], + [1, 0, 0, 1]]) + + >>> q1.product_matrix_left * q2.to_Matrix() + Matrix([ + [a - d], + [b - c], + [b + c], + [a + d]]) + + This is equivalent to: + + >>> (q1 * q2).to_Matrix() + Matrix([ + [a - d], + [b - c], + [b + c], + [a + d]]) + """ + return Matrix([ + [self.a, -self.b, -self.c, -self.d], + [self.b, self.a, -self.d, self.c], + [self.c, self.d, self.a, -self.b], + [self.d, -self.c, self.b, self.a]]) + + @property + def product_matrix_right(self): + r"""Returns 4 x 4 Matrix equivalent to a Hamilton product from the + right. This can be useful when treating quaternion elements as column + vectors. Given a quaternion $q = a + bi + cj + dk$ where a, b, c and d + are real numbers, the product matrix from the left is: + + .. math:: + + M = \begin{bmatrix} a &-b &-c &-d \\ + b & a & d &-c \\ + c &-d & a & b \\ + d & c &-b & a \end{bmatrix} + + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> q1 = Quaternion(a, b, c, d) + >>> q2 = Quaternion(1, 0, 0, 1) + >>> q2.product_matrix_right + Matrix([ + [1, 0, 0, -1], + [0, 1, 1, 0], + [0, -1, 1, 0], + [1, 0, 0, 1]]) + + Note the switched arguments: the matrix represents the quaternion on + the right, but is still considered as a matrix multiplication from the + left. + + >>> q2.product_matrix_right * q1.to_Matrix() + Matrix([ + [ a - d], + [ b + c], + [-b + c], + [ a + d]]) + + This is equivalent to: + + >>> (q1 * q2).to_Matrix() + Matrix([ + [ a - d], + [ b + c], + [-b + c], + [ a + d]]) + """ + return Matrix([ + [self.a, -self.b, -self.c, -self.d], + [self.b, self.a, self.d, -self.c], + [self.c, -self.d, self.a, self.b], + [self.d, self.c, -self.b, self.a]]) + + def to_Matrix(self, vector_only=False): + """Returns elements of quaternion as a column vector. + By default, a ``Matrix`` of length 4 is returned, with the real part as the + first element. + If ``vector_only`` is ``True``, returns only imaginary part as a Matrix of + length 3. + + Parameters + ========== + + vector_only : bool + If True, only imaginary part is returned. + Default value: False + + Returns + ======= + + Matrix + A column vector constructed by the elements of the quaternion. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> q = Quaternion(a, b, c, d) + >>> q + a + b*i + c*j + d*k + + >>> q.to_Matrix() + Matrix([ + [a], + [b], + [c], + [d]]) + + + >>> q.to_Matrix(vector_only=True) + Matrix([ + [b], + [c], + [d]]) + + """ + if vector_only: + return Matrix(self.args[1:]) + else: + return Matrix(self.args) + + @classmethod + def from_Matrix(cls, elements): + """Returns quaternion from elements of a column vector`. + If vector_only is True, returns only imaginary part as a Matrix of + length 3. + + Parameters + ========== + + elements : Matrix, list or tuple of length 3 or 4. If length is 3, + assume real part is zero. + Default value: False + + Returns + ======= + + Quaternion + A quaternion created from the input elements. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> q = Quaternion.from_Matrix([a, b, c, d]) + >>> q + a + b*i + c*j + d*k + + >>> q = Quaternion.from_Matrix([b, c, d]) + >>> q + 0 + b*i + c*j + d*k + + """ + length = len(elements) + if length != 3 and length != 4: + raise ValueError("Input elements must have length 3 or 4, got {} " + "elements".format(length)) + + if length == 3: + return Quaternion(0, *elements) + else: + return Quaternion(*elements) + + @classmethod + def from_euler(cls, angles, seq): + """Returns quaternion equivalent to rotation represented by the Euler + angles, in the sequence defined by ``seq``. + + Parameters + ========== + + angles : list, tuple or Matrix of 3 numbers + The Euler angles (in radians). + seq : string of length 3 + Represents the sequence of rotations. + For extrinsic rotations, seq must be all lowercase and its elements + must be from the set ``{'x', 'y', 'z'}`` + For intrinsic rotations, seq must be all uppercase and its elements + must be from the set ``{'X', 'Y', 'Z'}`` + + Returns + ======= + + Quaternion + The normalized rotation quaternion calculated from the Euler angles + in the given sequence. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import pi + >>> q = Quaternion.from_euler([pi/2, 0, 0], 'xyz') + >>> q + sqrt(2)/2 + sqrt(2)/2*i + 0*j + 0*k + + >>> q = Quaternion.from_euler([0, pi/2, pi] , 'zyz') + >>> q + 0 + (-sqrt(2)/2)*i + 0*j + sqrt(2)/2*k + + >>> q = Quaternion.from_euler([0, pi/2, pi] , 'ZYZ') + >>> q + 0 + sqrt(2)/2*i + 0*j + sqrt(2)/2*k + + """ + + if len(angles) != 3: + raise ValueError("3 angles must be given.") + + extrinsic = _is_extrinsic(seq) + i, j, k = seq.lower() + + # get elementary basis vectors + ei = [1 if n == i else 0 for n in 'xyz'] + ej = [1 if n == j else 0 for n in 'xyz'] + ek = [1 if n == k else 0 for n in 'xyz'] + + # calculate distinct quaternions + qi = cls.from_axis_angle(ei, angles[0]) + qj = cls.from_axis_angle(ej, angles[1]) + qk = cls.from_axis_angle(ek, angles[2]) + + if extrinsic: + return trigsimp(qk * qj * qi) + else: + return trigsimp(qi * qj * qk) + + def to_euler(self, seq, angle_addition=True, avoid_square_root=False): + r"""Returns Euler angles representing same rotation as the quaternion, + in the sequence given by ``seq``. This implements the method described + in [1]_. + + For degenerate cases (gymbal lock cases), the third angle is + set to zero. + + Parameters + ========== + + seq : string of length 3 + Represents the sequence of rotations. + For extrinsic rotations, seq must be all lowercase and its elements + must be from the set ``{'x', 'y', 'z'}`` + For intrinsic rotations, seq must be all uppercase and its elements + must be from the set ``{'X', 'Y', 'Z'}`` + + angle_addition : bool + When True, first and third angles are given as an addition and + subtraction of two simpler ``atan2`` expressions. When False, the + first and third angles are each given by a single more complicated + ``atan2`` expression. This equivalent expression is given by: + + .. math:: + + \operatorname{atan_2} (b,a) \pm \operatorname{atan_2} (d,c) = + \operatorname{atan_2} (bc\pm ad, ac\mp bd) + + Default value: True + + avoid_square_root : bool + When True, the second angle is calculated with an expression based + on ``acos``, which is slightly more complicated but avoids a square + root. When False, second angle is calculated with ``atan2``, which + is simpler and can be better for numerical reasons (some + numerical implementations of ``acos`` have problems near zero). + Default value: False + + + Returns + ======= + + Tuple + The Euler angles calculated from the quaternion + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy.abc import a, b, c, d + >>> euler = Quaternion(a, b, c, d).to_euler('zyz') + >>> euler + (-atan2(-b, c) + atan2(d, a), + 2*atan2(sqrt(b**2 + c**2), sqrt(a**2 + d**2)), + atan2(-b, c) + atan2(d, a)) + + + References + ========== + + .. [1] https://doi.org/10.1371/journal.pone.0276302 + + """ + if self.is_zero_quaternion(): + raise ValueError('Cannot convert a quaternion with norm 0.') + + angles = [0, 0, 0] + + extrinsic = _is_extrinsic(seq) + i, j, k = seq.lower() + + # get index corresponding to elementary basis vectors + i = 'xyz'.index(i) + 1 + j = 'xyz'.index(j) + 1 + k = 'xyz'.index(k) + 1 + + if not extrinsic: + i, k = k, i + + # check if sequence is symmetric + symmetric = i == k + if symmetric: + k = 6 - i - j + + # parity of the permutation + sign = (i - j) * (j - k) * (k - i) // 2 + + # permutate elements + elements = [self.a, self.b, self.c, self.d] + a = elements[0] + b = elements[i] + c = elements[j] + d = elements[k] * sign + + if not symmetric: + a, b, c, d = a - c, b + d, c + a, d - b + + if avoid_square_root: + if symmetric: + n2 = self.norm()**2 + angles[1] = acos((a * a + b * b - c * c - d * d) / n2) + else: + n2 = 2 * self.norm()**2 + angles[1] = asin((c * c + d * d - a * a - b * b) / n2) + else: + angles[1] = 2 * atan2(sqrt(c * c + d * d), sqrt(a * a + b * b)) + if not symmetric: + angles[1] -= S.Pi / 2 + + # Check for singularities in numerical cases + case = 0 + if is_eq(c, S.Zero) and is_eq(d, S.Zero): + case = 1 + if is_eq(a, S.Zero) and is_eq(b, S.Zero): + case = 2 + + if case == 0: + if angle_addition: + angles[0] = atan2(b, a) + atan2(d, c) + angles[2] = atan2(b, a) - atan2(d, c) + else: + angles[0] = atan2(b*c + a*d, a*c - b*d) + angles[2] = atan2(b*c - a*d, a*c + b*d) + + else: # any degenerate case + angles[2 * (not extrinsic)] = S.Zero + if case == 1: + angles[2 * extrinsic] = 2 * atan2(b, a) + else: + angles[2 * extrinsic] = 2 * atan2(d, c) + angles[2 * extrinsic] *= (-1 if extrinsic else 1) + + # for Tait-Bryan angles + if not symmetric: + angles[0] *= sign + + if extrinsic: + return tuple(angles[::-1]) + else: + return tuple(angles) + + @classmethod + def from_axis_angle(cls, vector, angle): + """Returns a rotation quaternion given the axis and the angle of rotation. + + Parameters + ========== + + vector : tuple of three numbers + The vector representation of the given axis. + angle : number + The angle by which axis is rotated (in radians). + + Returns + ======= + + Quaternion + The normalized rotation quaternion calculated from the given axis and the angle of rotation. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import pi, sqrt + >>> q = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), 2*pi/3) + >>> q + 1/2 + 1/2*i + 1/2*j + 1/2*k + + """ + (x, y, z) = vector + norm = sqrt(x**2 + y**2 + z**2) + (x, y, z) = (x / norm, y / norm, z / norm) + s = sin(angle * S.Half) + a = cos(angle * S.Half) + b = x * s + c = y * s + d = z * s + + # note that this quaternion is already normalized by construction: + # c^2 + (s*x)^2 + (s*y)^2 + (s*z)^2 = c^2 + s^2*(x^2 + y^2 + z^2) = c^2 + s^2 * 1 = c^2 + s^2 = 1 + # so, what we return is a normalized quaternion + + return cls(a, b, c, d) + + @classmethod + def from_rotation_matrix(cls, M): + """Returns the equivalent quaternion of a matrix. The quaternion will be normalized + only if the matrix is special orthogonal (orthogonal and det(M) = 1). + + Parameters + ========== + + M : Matrix + Input matrix to be converted to equivalent quaternion. M must be special + orthogonal (orthogonal and det(M) = 1) for the quaternion to be normalized. + + Returns + ======= + + Quaternion + The quaternion equivalent to given matrix. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import Matrix, symbols, cos, sin, trigsimp + >>> x = symbols('x') + >>> M = Matrix([[cos(x), -sin(x), 0], [sin(x), cos(x), 0], [0, 0, 1]]) + >>> q = trigsimp(Quaternion.from_rotation_matrix(M)) + >>> q + sqrt(2)*sqrt(cos(x) + 1)/2 + 0*i + 0*j + sqrt(2 - 2*cos(x))*sign(sin(x))/2*k + + """ + + absQ = M.det()**Rational(1, 3) + + a = sqrt(absQ + M[0, 0] + M[1, 1] + M[2, 2]) / 2 + b = sqrt(absQ + M[0, 0] - M[1, 1] - M[2, 2]) / 2 + c = sqrt(absQ - M[0, 0] + M[1, 1] - M[2, 2]) / 2 + d = sqrt(absQ - M[0, 0] - M[1, 1] + M[2, 2]) / 2 + + b = b * sign(M[2, 1] - M[1, 2]) + c = c * sign(M[0, 2] - M[2, 0]) + d = d * sign(M[1, 0] - M[0, 1]) + + return Quaternion(a, b, c, d) + + def __add__(self, other): + return self.add(other) + + def __radd__(self, other): + return self.add(other) + + def __sub__(self, other): + return self.add(other*-1) + + def __mul__(self, other): + return self._generic_mul(self, _sympify(other)) + + def __rmul__(self, other): + return self._generic_mul(_sympify(other), self) + + def __pow__(self, p): + return self.pow(p) + + def __neg__(self): + return Quaternion(-self.a, -self.b, -self.c, -self.d) + + def __truediv__(self, other): + return self * sympify(other)**-1 + + def __rtruediv__(self, other): + return sympify(other) * self**-1 + + def _eval_Integral(self, *args): + return self.integrate(*args) + + def diff(self, *symbols, **kwargs): + kwargs.setdefault('evaluate', True) + return self.func(*[a.diff(*symbols, **kwargs) for a in self.args]) + + def add(self, other): + """Adds quaternions. + + Parameters + ========== + + other : Quaternion + The quaternion to add to current (self) quaternion. + + Returns + ======= + + Quaternion + The resultant quaternion after adding self to other + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import symbols + >>> q1 = Quaternion(1, 2, 3, 4) + >>> q2 = Quaternion(5, 6, 7, 8) + >>> q1.add(q2) + 6 + 8*i + 10*j + 12*k + >>> q1 + 5 + 6 + 2*i + 3*j + 4*k + >>> x = symbols('x', real = True) + >>> q1.add(x) + (x + 1) + 2*i + 3*j + 4*k + + Quaternions over complex fields : + + >>> from sympy import Quaternion + >>> from sympy import I + >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + >>> q3.add(2 + 3*I) + (5 + 7*I) + (2 + 5*I)*i + 0*j + (7 + 8*I)*k + + """ + q1 = self + q2 = sympify(other) + + # If q2 is a number or a SymPy expression instead of a quaternion + if not isinstance(q2, Quaternion): + if q1.real_field and q2.is_complex: + return Quaternion(re(q2) + q1.a, im(q2) + q1.b, q1.c, q1.d) + elif q2.is_commutative: + return Quaternion(q1.a + q2, q1.b, q1.c, q1.d) + else: + raise ValueError("Only commutative expressions can be added with a Quaternion.") + + return Quaternion(q1.a + q2.a, q1.b + q2.b, q1.c + q2.c, q1.d + + q2.d) + + def mul(self, other): + """Multiplies quaternions. + + Parameters + ========== + + other : Quaternion or symbol + The quaternion to multiply to current (self) quaternion. + + Returns + ======= + + Quaternion + The resultant quaternion after multiplying self with other + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import symbols + >>> q1 = Quaternion(1, 2, 3, 4) + >>> q2 = Quaternion(5, 6, 7, 8) + >>> q1.mul(q2) + (-60) + 12*i + 30*j + 24*k + >>> q1.mul(2) + 2 + 4*i + 6*j + 8*k + >>> x = symbols('x', real = True) + >>> q1.mul(x) + x + 2*x*i + 3*x*j + 4*x*k + + Quaternions over complex fields : + + >>> from sympy import Quaternion + >>> from sympy import I + >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + >>> q3.mul(2 + 3*I) + (2 + 3*I)*(3 + 4*I) + (2 + 3*I)*(2 + 5*I)*i + 0*j + (2 + 3*I)*(7 + 8*I)*k + + """ + return self._generic_mul(self, _sympify(other)) + + @staticmethod + def _generic_mul(q1, q2): + """Generic multiplication. + + Parameters + ========== + + q1 : Quaternion or symbol + q2 : Quaternion or symbol + + It is important to note that if neither q1 nor q2 is a Quaternion, + this function simply returns q1 * q2. + + Returns + ======= + + Quaternion + The resultant quaternion after multiplying q1 and q2 + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import Symbol, S + >>> q1 = Quaternion(1, 2, 3, 4) + >>> q2 = Quaternion(5, 6, 7, 8) + >>> Quaternion._generic_mul(q1, q2) + (-60) + 12*i + 30*j + 24*k + >>> Quaternion._generic_mul(q1, S(2)) + 2 + 4*i + 6*j + 8*k + >>> x = Symbol('x', real = True) + >>> Quaternion._generic_mul(q1, x) + x + 2*x*i + 3*x*j + 4*x*k + + Quaternions over complex fields : + + >>> from sympy import I + >>> q3 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + >>> Quaternion._generic_mul(q3, 2 + 3*I) + (2 + 3*I)*(3 + 4*I) + (2 + 3*I)*(2 + 5*I)*i + 0*j + (2 + 3*I)*(7 + 8*I)*k + + """ + # None is a Quaternion: + if not isinstance(q1, Quaternion) and not isinstance(q2, Quaternion): + return q1 * q2 + + # If q1 is a number or a SymPy expression instead of a quaternion + if not isinstance(q1, Quaternion): + if q2.real_field and q1.is_complex: + return Quaternion(re(q1), im(q1), 0, 0) * q2 + elif q1.is_commutative: + return Quaternion(q1 * q2.a, q1 * q2.b, q1 * q2.c, q1 * q2.d) + else: + raise ValueError("Only commutative expressions can be multiplied with a Quaternion.") + + # If q2 is a number or a SymPy expression instead of a quaternion + if not isinstance(q2, Quaternion): + if q1.real_field and q2.is_complex: + return q1 * Quaternion(re(q2), im(q2), 0, 0) + elif q2.is_commutative: + return Quaternion(q2 * q1.a, q2 * q1.b, q2 * q1.c, q2 * q1.d) + else: + raise ValueError("Only commutative expressions can be multiplied with a Quaternion.") + + # If any of the quaternions has a fixed norm, pre-compute norm + if q1._norm is None and q2._norm is None: + norm = None + else: + norm = q1.norm() * q2.norm() + + return Quaternion(-q1.b*q2.b - q1.c*q2.c - q1.d*q2.d + q1.a*q2.a, + q1.b*q2.a + q1.c*q2.d - q1.d*q2.c + q1.a*q2.b, + -q1.b*q2.d + q1.c*q2.a + q1.d*q2.b + q1.a*q2.c, + q1.b*q2.c - q1.c*q2.b + q1.d*q2.a + q1.a * q2.d, + norm=norm) + + def _eval_conjugate(self): + """Returns the conjugate of the quaternion.""" + q = self + return Quaternion(q.a, -q.b, -q.c, -q.d, norm=q._norm) + + def norm(self): + """Returns the norm of the quaternion.""" + if self._norm is None: # check if norm is pre-defined + q = self + # trigsimp is used to simplify sin(x)^2 + cos(x)^2 (these terms + # arise when from_axis_angle is used). + return sqrt(trigsimp(q.a**2 + q.b**2 + q.c**2 + q.d**2)) + + return self._norm + + def normalize(self): + """Returns the normalized form of the quaternion.""" + q = self + return q * (1/q.norm()) + + def inverse(self): + """Returns the inverse of the quaternion.""" + q = self + if not q.norm(): + raise ValueError("Cannot compute inverse for a quaternion with zero norm") + return conjugate(q) * (1/q.norm()**2) + + def pow(self, p): + """Finds the pth power of the quaternion. + + Parameters + ========== + + p : int + Power to be applied on quaternion. + + Returns + ======= + + Quaternion + Returns the p-th power of the current quaternion. + Returns the inverse if p = -1. + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 2, 3, 4) + >>> q.pow(4) + 668 + (-224)*i + (-336)*j + (-448)*k + + """ + try: + q, p = self, as_int(p) + except ValueError: + return NotImplemented + + if p < 0: + q, p = q.inverse(), -p + + if p == 1: + return q + + res = Quaternion(1, 0, 0, 0) + while p > 0: + if p & 1: + res *= q + q *= q + p >>= 1 + + return res + + def exp(self): + """Returns the exponential of $q$, given by $e^q$. + + Returns + ======= + + Quaternion + The exponential of the quaternion. + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 2, 3, 4) + >>> q.exp() + E*cos(sqrt(29)) + + 2*sqrt(29)*E*sin(sqrt(29))/29*i + + 3*sqrt(29)*E*sin(sqrt(29))/29*j + + 4*sqrt(29)*E*sin(sqrt(29))/29*k + + """ + # exp(q) = e^a(cos||v|| + v/||v||*sin||v||) + q = self + vector_norm = sqrt(q.b**2 + q.c**2 + q.d**2) + a = exp(q.a) * cos(vector_norm) + b = exp(q.a) * sin(vector_norm) * q.b / vector_norm + c = exp(q.a) * sin(vector_norm) * q.c / vector_norm + d = exp(q.a) * sin(vector_norm) * q.d / vector_norm + + return Quaternion(a, b, c, d) + + def log(self): + r"""Returns the logarithm of the quaternion, given by $\log q$. + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 2, 3, 4) + >>> q.log() + log(sqrt(30)) + + 2*sqrt(29)*acos(sqrt(30)/30)/29*i + + 3*sqrt(29)*acos(sqrt(30)/30)/29*j + + 4*sqrt(29)*acos(sqrt(30)/30)/29*k + + """ + # log(q) = log||q|| + v/||v||*arccos(a/||q||) + q = self + vector_norm = sqrt(q.b**2 + q.c**2 + q.d**2) + q_norm = q.norm() + a = ln(q_norm) + b = q.b * acos(q.a / q_norm) / vector_norm + c = q.c * acos(q.a / q_norm) / vector_norm + d = q.d * acos(q.a / q_norm) / vector_norm + + return Quaternion(a, b, c, d) + + def _eval_subs(self, *args): + elements = [i.subs(*args) for i in self.args] + norm = self._norm + if norm is not None: + norm = norm.subs(*args) + _check_norm(elements, norm) + return Quaternion(*elements, norm=norm) + + def _eval_evalf(self, prec): + """Returns the floating point approximations (decimal numbers) of the quaternion. + + Returns + ======= + + Quaternion + Floating point approximations of quaternion(self) + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import sqrt + >>> q = Quaternion(1/sqrt(1), 1/sqrt(2), 1/sqrt(3), 1/sqrt(4)) + >>> q.evalf() + 1.00000000000000 + + 0.707106781186547*i + + 0.577350269189626*j + + 0.500000000000000*k + + """ + nprec = prec_to_dps(prec) + return Quaternion(*[arg.evalf(n=nprec) for arg in self.args]) + + def pow_cos_sin(self, p): + """Computes the pth power in the cos-sin form. + + Parameters + ========== + + p : int + Power to be applied on quaternion. + + Returns + ======= + + Quaternion + The p-th power in the cos-sin form. + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 2, 3, 4) + >>> q.pow_cos_sin(4) + 900*cos(4*acos(sqrt(30)/30)) + + 1800*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*i + + 2700*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*j + + 3600*sqrt(29)*sin(4*acos(sqrt(30)/30))/29*k + + """ + # q = ||q||*(cos(a) + u*sin(a)) + # q^p = ||q||^p * (cos(p*a) + u*sin(p*a)) + + q = self + (v, angle) = q.to_axis_angle() + q2 = Quaternion.from_axis_angle(v, p * angle) + return q2 * (q.norm()**p) + + def integrate(self, *args): + """Computes integration of quaternion. + + Returns + ======= + + Quaternion + Integration of the quaternion(self) with the given variable. + + Examples + ======== + + Indefinite Integral of quaternion : + + >>> from sympy import Quaternion + >>> from sympy.abc import x + >>> q = Quaternion(1, 2, 3, 4) + >>> q.integrate(x) + x + 2*x*i + 3*x*j + 4*x*k + + Definite integral of quaternion : + + >>> from sympy import Quaternion + >>> from sympy.abc import x + >>> q = Quaternion(1, 2, 3, 4) + >>> q.integrate((x, 1, 5)) + 4 + 8*i + 12*j + 16*k + + """ + # TODO: is this expression correct? + return Quaternion(integrate(self.a, *args), integrate(self.b, *args), + integrate(self.c, *args), integrate(self.d, *args)) + + @staticmethod + def rotate_point(pin, r): + """Returns the coordinates of the point pin (a 3 tuple) after rotation. + + Parameters + ========== + + pin : tuple + A 3-element tuple of coordinates of a point which needs to be + rotated. + r : Quaternion or tuple + Axis and angle of rotation. + + It's important to note that when r is a tuple, it must be of the form + (axis, angle) + + Returns + ======= + + tuple + The coordinates of the point after rotation. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import symbols, trigsimp, cos, sin + >>> x = symbols('x') + >>> q = Quaternion(cos(x/2), 0, 0, sin(x/2)) + >>> trigsimp(Quaternion.rotate_point((1, 1, 1), q)) + (sqrt(2)*cos(x + pi/4), sqrt(2)*sin(x + pi/4), 1) + >>> (axis, angle) = q.to_axis_angle() + >>> trigsimp(Quaternion.rotate_point((1, 1, 1), (axis, angle))) + (sqrt(2)*cos(x + pi/4), sqrt(2)*sin(x + pi/4), 1) + + """ + if isinstance(r, tuple): + # if r is of the form (vector, angle) + q = Quaternion.from_axis_angle(r[0], r[1]) + else: + # if r is a quaternion + q = r.normalize() + pout = q * Quaternion(0, pin[0], pin[1], pin[2]) * conjugate(q) + return (pout.b, pout.c, pout.d) + + def to_axis_angle(self): + """Returns the axis and angle of rotation of a quaternion. + + Returns + ======= + + tuple + Tuple of (axis, angle) + + Examples + ======== + + >>> from sympy import Quaternion + >>> q = Quaternion(1, 1, 1, 1) + >>> (axis, angle) = q.to_axis_angle() + >>> axis + (sqrt(3)/3, sqrt(3)/3, sqrt(3)/3) + >>> angle + 2*pi/3 + + """ + q = self + if q.a.is_negative: + q = q * -1 + + q = q.normalize() + angle = trigsimp(2 * acos(q.a)) + + # Since quaternion is normalised, q.a is less than 1. + s = sqrt(1 - q.a*q.a) + + x = trigsimp(q.b / s) + y = trigsimp(q.c / s) + z = trigsimp(q.d / s) + + v = (x, y, z) + t = (v, angle) + + return t + + def to_rotation_matrix(self, v=None, homogeneous=True): + """Returns the equivalent rotation transformation matrix of the quaternion + which represents rotation about the origin if ``v`` is not passed. + + Parameters + ========== + + v : tuple or None + Default value: None + homogeneous : bool + When True, gives an expression that may be more efficient for + symbolic calculations but less so for direct evaluation. Both + formulas are mathematically equivalent. + Default value: True + + Returns + ======= + + tuple + Returns the equivalent rotation transformation matrix of the quaternion + which represents rotation about the origin if v is not passed. + + Examples + ======== + + >>> from sympy import Quaternion + >>> from sympy import symbols, trigsimp, cos, sin + >>> x = symbols('x') + >>> q = Quaternion(cos(x/2), 0, 0, sin(x/2)) + >>> trigsimp(q.to_rotation_matrix()) + Matrix([ + [cos(x), -sin(x), 0], + [sin(x), cos(x), 0], + [ 0, 0, 1]]) + + Generates a 4x4 transformation matrix (used for rotation about a point + other than the origin) if the point(v) is passed as an argument. + """ + + q = self + s = q.norm()**-2 + + # diagonal elements are different according to parameter normal + if homogeneous: + m00 = s*(q.a**2 + q.b**2 - q.c**2 - q.d**2) + m11 = s*(q.a**2 - q.b**2 + q.c**2 - q.d**2) + m22 = s*(q.a**2 - q.b**2 - q.c**2 + q.d**2) + else: + m00 = 1 - 2*s*(q.c**2 + q.d**2) + m11 = 1 - 2*s*(q.b**2 + q.d**2) + m22 = 1 - 2*s*(q.b**2 + q.c**2) + + m01 = 2*s*(q.b*q.c - q.d*q.a) + m02 = 2*s*(q.b*q.d + q.c*q.a) + + m10 = 2*s*(q.b*q.c + q.d*q.a) + m12 = 2*s*(q.c*q.d - q.b*q.a) + + m20 = 2*s*(q.b*q.d - q.c*q.a) + m21 = 2*s*(q.c*q.d + q.b*q.a) + + if not v: + return Matrix([[m00, m01, m02], [m10, m11, m12], [m20, m21, m22]]) + + else: + (x, y, z) = v + + m03 = x - x*m00 - y*m01 - z*m02 + m13 = y - x*m10 - y*m11 - z*m12 + m23 = z - x*m20 - y*m21 - z*m22 + m30 = m31 = m32 = 0 + m33 = 1 + + return Matrix([[m00, m01, m02, m03], [m10, m11, m12, m13], + [m20, m21, m22, m23], [m30, m31, m32, m33]]) + + def scalar_part(self): + r"""Returns scalar part($\mathbf{S}(q)$) of the quaternion q. + + Explanation + =========== + + Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{S}(q) = a$. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(4, 8, 13, 12) + >>> q.scalar_part() + 4 + + """ + + return self.a + + def vector_part(self): + r""" + Returns $\mathbf{V}(q)$, the vector part of the quaternion $q$. + + Explanation + =========== + + Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{V}(q) = bi + cj + dk$. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(1, 1, 1, 1) + >>> q.vector_part() + 0 + 1*i + 1*j + 1*k + + >>> q = Quaternion(4, 8, 13, 12) + >>> q.vector_part() + 0 + 8*i + 13*j + 12*k + + """ + + return Quaternion(0, self.b, self.c, self.d) + + def axis(self): + r""" + Returns $\mathbf{Ax}(q)$, the axis of the quaternion $q$. + + Explanation + =========== + + Given a quaternion $q = a + bi + cj + dk$, returns $\mathbf{Ax}(q)$ i.e., the versor of the vector part of that quaternion + equal to $\mathbf{U}[\mathbf{V}(q)]$. + The axis is always an imaginary unit with square equal to $-1 + 0i + 0j + 0k$. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(1, 1, 1, 1) + >>> q.axis() + 0 + sqrt(3)/3*i + sqrt(3)/3*j + sqrt(3)/3*k + + See Also + ======== + + vector_part + + """ + axis = self.vector_part().normalize() + + return Quaternion(0, axis.b, axis.c, axis.d) + + def is_pure(self): + """ + Returns true if the quaternion is pure, false if the quaternion is not pure + or returns none if it is unknown. + + Explanation + =========== + + A pure quaternion (also a vector quaternion) is a quaternion with scalar + part equal to 0. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(0, 8, 13, 12) + >>> q.is_pure() + True + + See Also + ======== + scalar_part + + """ + + return self.a.is_zero + + def is_zero_quaternion(self): + """ + Returns true if the quaternion is a zero quaternion or false if it is not a zero quaternion + and None if the value is unknown. + + Explanation + =========== + + A zero quaternion is a quaternion with both scalar part and + vector part equal to 0. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(1, 0, 0, 0) + >>> q.is_zero_quaternion() + False + + >>> q = Quaternion(0, 0, 0, 0) + >>> q.is_zero_quaternion() + True + + See Also + ======== + scalar_part + vector_part + + """ + + return self.norm().is_zero + + def angle(self): + r""" + Returns the angle of the quaternion measured in the real-axis plane. + + Explanation + =========== + + Given a quaternion $q = a + bi + cj + dk$ where $a$, $b$, $c$ and $d$ + are real numbers, returns the angle of the quaternion given by + + .. math:: + \theta := 2 \operatorname{atan_2}\left(\sqrt{b^2 + c^2 + d^2}, {a}\right) + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(1, 4, 4, 4) + >>> q.angle() + 2*atan(4*sqrt(3)) + + """ + + return 2 * atan2(self.vector_part().norm(), self.scalar_part()) + + + def arc_coplanar(self, other): + """ + Returns True if the transformation arcs represented by the input quaternions happen in the same plane. + + Explanation + =========== + + Two quaternions are said to be coplanar (in this arc sense) when their axes are parallel. + The plane of a quaternion is the one normal to its axis. + + Parameters + ========== + + other : a Quaternion + + Returns + ======= + + True : if the planes of the two quaternions are the same, apart from its orientation/sign. + False : if the planes of the two quaternions are not the same, apart from its orientation/sign. + None : if plane of either of the quaternion is unknown. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q1 = Quaternion(1, 4, 4, 4) + >>> q2 = Quaternion(3, 8, 8, 8) + >>> Quaternion.arc_coplanar(q1, q2) + True + + >>> q1 = Quaternion(2, 8, 13, 12) + >>> Quaternion.arc_coplanar(q1, q2) + False + + See Also + ======== + + vector_coplanar + is_pure + + """ + if (self.is_zero_quaternion()) or (other.is_zero_quaternion()): + raise ValueError('Neither of the given quaternions can be 0') + + return fuzzy_or([(self.axis() - other.axis()).is_zero_quaternion(), (self.axis() + other.axis()).is_zero_quaternion()]) + + @classmethod + def vector_coplanar(cls, q1, q2, q3): + r""" + Returns True if the axis of the pure quaternions seen as 3D vectors + ``q1``, ``q2``, and ``q3`` are coplanar. + + Explanation + =========== + + Three pure quaternions are vector coplanar if the quaternions seen as 3D vectors are coplanar. + + Parameters + ========== + + q1 + A pure Quaternion. + q2 + A pure Quaternion. + q3 + A pure Quaternion. + + Returns + ======= + + True : if the axis of the pure quaternions seen as 3D vectors + q1, q2, and q3 are coplanar. + False : if the axis of the pure quaternions seen as 3D vectors + q1, q2, and q3 are not coplanar. + None : if the axis of the pure quaternions seen as 3D vectors + q1, q2, and q3 are coplanar is unknown. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q1 = Quaternion(0, 4, 4, 4) + >>> q2 = Quaternion(0, 8, 8, 8) + >>> q3 = Quaternion(0, 24, 24, 24) + >>> Quaternion.vector_coplanar(q1, q2, q3) + True + + >>> q1 = Quaternion(0, 8, 16, 8) + >>> q2 = Quaternion(0, 8, 3, 12) + >>> Quaternion.vector_coplanar(q1, q2, q3) + False + + See Also + ======== + + axis + is_pure + + """ + + if fuzzy_not(q1.is_pure()) or fuzzy_not(q2.is_pure()) or fuzzy_not(q3.is_pure()): + raise ValueError('The given quaternions must be pure') + + M = Matrix([[q1.b, q1.c, q1.d], [q2.b, q2.c, q2.d], [q3.b, q3.c, q3.d]]).det() + return M.is_zero + + def parallel(self, other): + """ + Returns True if the two pure quaternions seen as 3D vectors are parallel. + + Explanation + =========== + + Two pure quaternions are called parallel when their vector product is commutative which + implies that the quaternions seen as 3D vectors have same direction. + + Parameters + ========== + + other : a Quaternion + + Returns + ======= + + True : if the two pure quaternions seen as 3D vectors are parallel. + False : if the two pure quaternions seen as 3D vectors are not parallel. + None : if the two pure quaternions seen as 3D vectors are parallel is unknown. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(0, 4, 4, 4) + >>> q1 = Quaternion(0, 8, 8, 8) + >>> q.parallel(q1) + True + + >>> q1 = Quaternion(0, 8, 13, 12) + >>> q.parallel(q1) + False + + """ + + if fuzzy_not(self.is_pure()) or fuzzy_not(other.is_pure()): + raise ValueError('The provided quaternions must be pure') + + return (self*other - other*self).is_zero_quaternion() + + def orthogonal(self, other): + """ + Returns the orthogonality of two quaternions. + + Explanation + =========== + + Two pure quaternions are called orthogonal when their product is anti-commutative. + + Parameters + ========== + + other : a Quaternion + + Returns + ======= + + True : if the two pure quaternions seen as 3D vectors are orthogonal. + False : if the two pure quaternions seen as 3D vectors are not orthogonal. + None : if the two pure quaternions seen as 3D vectors are orthogonal is unknown. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(0, 4, 4, 4) + >>> q1 = Quaternion(0, 8, 8, 8) + >>> q.orthogonal(q1) + False + + >>> q1 = Quaternion(0, 2, 2, 0) + >>> q = Quaternion(0, 2, -2, 0) + >>> q.orthogonal(q1) + True + + """ + + if fuzzy_not(self.is_pure()) or fuzzy_not(other.is_pure()): + raise ValueError('The given quaternions must be pure') + + return (self*other + other*self).is_zero_quaternion() + + def index_vector(self): + r""" + Returns the index vector of the quaternion. + + Explanation + =========== + + The index vector is given by $\mathbf{T}(q)$, the norm (or magnitude) of + the quaternion $q$, multiplied by $\mathbf{Ax}(q)$, the axis of $q$. + + Returns + ======= + + Quaternion: representing index vector of the provided quaternion. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(2, 4, 2, 4) + >>> q.index_vector() + 0 + 4*sqrt(10)/3*i + 2*sqrt(10)/3*j + 4*sqrt(10)/3*k + + See Also + ======== + + axis + norm + + """ + + return self.norm() * self.axis() + + def mensor(self): + """ + Returns the natural logarithm of the norm(magnitude) of the quaternion. + + Examples + ======== + + >>> from sympy.algebras.quaternion import Quaternion + >>> q = Quaternion(2, 4, 2, 4) + >>> q.mensor() + log(2*sqrt(10)) + >>> q.norm() + 2*sqrt(10) + + See Also + ======== + + norm + + """ + + return ln(self.norm()) diff --git a/lib/python3.11/site-packages/sympy/algebras/tests/__init__.py b/lib/python3.11/site-packages/sympy/algebras/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/algebras/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/algebras/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 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@@ -0,0 +1,428 @@ +from sympy.testing.pytest import slow +from sympy.core.function import diff +from sympy.core.function import expand +from sympy.core.numbers import (E, I, Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (Abs, conjugate, im, re, sign) +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, asin, cos, sin, atan2, atan) +from sympy.integrals.integrals import integrate +from sympy.matrices.dense import Matrix +from sympy.simplify import simplify +from sympy.simplify.trigsimp import trigsimp +from sympy.algebras.quaternion import Quaternion +from sympy.testing.pytest import raises +import math +from itertools import permutations, product + +w, x, y, z = symbols('w:z') +phi = symbols('phi') + +def test_quaternion_construction(): + q = Quaternion(w, x, y, z) + assert q + q == Quaternion(2*w, 2*x, 2*y, 2*z) + + q2 = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), + pi*Rational(2, 3)) + assert q2 == Quaternion(S.Half, S.Half, + S.Half, S.Half) + + M = Matrix([[cos(phi), -sin(phi), 0], [sin(phi), cos(phi), 0], [0, 0, 1]]) + q3 = trigsimp(Quaternion.from_rotation_matrix(M)) + assert q3 == Quaternion( + sqrt(2)*sqrt(cos(phi) + 1)/2, 0, 0, sqrt(2 - 2*cos(phi))*sign(sin(phi))/2) + + nc = Symbol('nc', commutative=False) + raises(ValueError, lambda: Quaternion(w, x, nc, z)) + + +def test_quaternion_construction_norm(): + q1 = Quaternion(*symbols('a:d')) + + q2 = Quaternion(w, x, y, z) + assert expand((q1*q2).norm()**2 - (q1.norm()**2 * q2.norm()**2)) == 0 + + q3 = Quaternion(w, x, y, z, norm=1) + assert (q1 * q3).norm() == q1.norm() + + +def test_issue_25254(): + # calculating the inverse cached the norm which caused problems + # when multiplying + p = Quaternion(1, 0, 0, 0) + q = Quaternion.from_axis_angle((1, 1, 1), 3 * math.pi/4) + qi = q.inverse() # this operation cached the norm + test = q * p * qi + assert ((test - p).norm() < 1E-10) + + +def test_to_and_from_Matrix(): + q = Quaternion(w, x, y, z) + q_full = Quaternion.from_Matrix(q.to_Matrix()) + q_vect = Quaternion.from_Matrix(q.to_Matrix(True)) + assert (q - q_full).is_zero_quaternion() + assert (q.vector_part() - q_vect).is_zero_quaternion() + + +def test_product_matrices(): + q1 = Quaternion(w, x, y, z) + q2 = Quaternion(*(symbols("a:d"))) + assert (q1 * q2).to_Matrix() == q1.product_matrix_left * q2.to_Matrix() + assert (q1 * q2).to_Matrix() == q2.product_matrix_right * q1.to_Matrix() + + R1 = (q1.product_matrix_left * q1.product_matrix_right.T)[1:, 1:] + R2 = simplify(q1.to_rotation_matrix()*q1.norm()**2) + assert R1 == R2 + + +def test_quaternion_axis_angle(): + + test_data = [ # axis, angle, expected_quaternion + ((1, 0, 0), 0, (1, 0, 0, 0)), + ((1, 0, 0), pi/2, (sqrt(2)/2, sqrt(2)/2, 0, 0)), + ((0, 1, 0), pi/2, (sqrt(2)/2, 0, sqrt(2)/2, 0)), + ((0, 0, 1), pi/2, (sqrt(2)/2, 0, 0, sqrt(2)/2)), + ((1, 0, 0), pi, (0, 1, 0, 0)), + ((0, 1, 0), pi, (0, 0, 1, 0)), + ((0, 0, 1), pi, (0, 0, 0, 1)), + ((1, 1, 1), pi, (0, 1/sqrt(3),1/sqrt(3),1/sqrt(3))), + ((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), pi*2/3, (S.Half, S.Half, S.Half, S.Half)) + ] + + for axis, angle, expected in test_data: + assert Quaternion.from_axis_angle(axis, angle) == Quaternion(*expected) + + +def test_quaternion_axis_angle_simplification(): + result = Quaternion.from_axis_angle((1, 2, 3), asin(4)) + assert result.a == cos(asin(4)/2) + assert result.b == sqrt(14)*sin(asin(4)/2)/14 + assert result.c == sqrt(14)*sin(asin(4)/2)/7 + assert result.d == 3*sqrt(14)*sin(asin(4)/2)/14 + +def test_quaternion_complex_real_addition(): + a = symbols("a", complex=True) + b = symbols("b", real=True) + # This symbol is not complex: + c = symbols("c", commutative=False) + + q = Quaternion(w, x, y, z) + assert a + q == Quaternion(w + re(a), x + im(a), y, z) + assert 1 + q == Quaternion(1 + w, x, y, z) + assert I + q == Quaternion(w, 1 + x, y, z) + assert b + q == Quaternion(w + b, x, y, z) + raises(ValueError, lambda: c + q) + raises(ValueError, lambda: q * c) + raises(ValueError, lambda: c * q) + + assert -q == Quaternion(-w, -x, -y, -z) + + q1 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + q2 = Quaternion(1, 4, 7, 8) + + assert q1 + (2 + 3*I) == Quaternion(5 + 7*I, 2 + 5*I, 0, 7 + 8*I) + assert q2 + (2 + 3*I) == Quaternion(3, 7, 7, 8) + assert q1 * (2 + 3*I) == \ + Quaternion((2 + 3*I)*(3 + 4*I), (2 + 3*I)*(2 + 5*I), 0, (2 + 3*I)*(7 + 8*I)) + assert q2 * (2 + 3*I) == Quaternion(-10, 11, 38, -5) + + q1 = Quaternion(1, 2, 3, 4) + q0 = Quaternion(0, 0, 0, 0) + assert q1 + q0 == q1 + assert q1 - q0 == q1 + assert q1 - q1 == q0 + + +def test_quaternion_subs(): + q = Quaternion.from_axis_angle((0, 0, 1), phi) + assert q.subs(phi, 0) == Quaternion(1, 0, 0, 0) + + +def test_quaternion_evalf(): + assert (Quaternion(sqrt(2), 0, 0, sqrt(3)).evalf() == + Quaternion(sqrt(2).evalf(), 0, 0, sqrt(3).evalf())) + assert (Quaternion(1/sqrt(2), 0, 0, 1/sqrt(2)).evalf() == + Quaternion((1/sqrt(2)).evalf(), 0, 0, (1/sqrt(2)).evalf())) + + +def test_quaternion_functions(): + q = Quaternion(w, x, y, z) + q1 = Quaternion(1, 2, 3, 4) + q0 = Quaternion(0, 0, 0, 0) + + assert conjugate(q) == Quaternion(w, -x, -y, -z) + assert q.norm() == sqrt(w**2 + x**2 + y**2 + z**2) + assert q.normalize() == Quaternion(w, x, y, z) / sqrt(w**2 + x**2 + y**2 + z**2) + assert q.inverse() == Quaternion(w, -x, -y, -z) / (w**2 + x**2 + y**2 + z**2) + assert q.inverse() == q.pow(-1) + raises(ValueError, lambda: q0.inverse()) + assert q.pow(2) == Quaternion(w**2 - x**2 - y**2 - z**2, 2*w*x, 2*w*y, 2*w*z) + assert q**(2) == Quaternion(w**2 - x**2 - y**2 - z**2, 2*w*x, 2*w*y, 2*w*z) + assert q1.pow(-2) == Quaternion( + Rational(-7, 225), Rational(-1, 225), Rational(-1, 150), Rational(-2, 225)) + assert q1**(-2) == Quaternion( + Rational(-7, 225), Rational(-1, 225), Rational(-1, 150), Rational(-2, 225)) + assert q1.pow(-0.5) == NotImplemented + raises(TypeError, lambda: q1**(-0.5)) + + assert q1.exp() == \ + Quaternion(E * cos(sqrt(29)), + 2 * sqrt(29) * E * sin(sqrt(29)) / 29, + 3 * sqrt(29) * E * sin(sqrt(29)) / 29, + 4 * sqrt(29) * E * sin(sqrt(29)) / 29) + assert q1.log() == \ + Quaternion(log(sqrt(30)), + 2 * sqrt(29) * acos(sqrt(30)/30) / 29, + 3 * sqrt(29) * acos(sqrt(30)/30) / 29, + 4 * sqrt(29) * acos(sqrt(30)/30) / 29) + + assert q1.pow_cos_sin(2) == \ + Quaternion(30 * cos(2 * acos(sqrt(30)/30)), + 60 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29, + 90 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29, + 120 * sqrt(29) * sin(2 * acos(sqrt(30)/30)) / 29) + + assert diff(Quaternion(x, x, x, x), x) == Quaternion(1, 1, 1, 1) + + assert integrate(Quaternion(x, x, x, x), x) == \ + Quaternion(x**2 / 2, x**2 / 2, x**2 / 2, x**2 / 2) + + assert Quaternion.rotate_point((1, 1, 1), q1) == (S.One / 5, 1, S(7) / 5) + n = Symbol('n') + raises(TypeError, lambda: q1**n) + n = Symbol('n', integer=True) + raises(TypeError, lambda: q1**n) + + assert Quaternion(22, 23, 55, 8).scalar_part() == 22 + assert Quaternion(w, x, y, z).scalar_part() == w + + assert Quaternion(22, 23, 55, 8).vector_part() == Quaternion(0, 23, 55, 8) + assert Quaternion(w, x, y, z).vector_part() == Quaternion(0, x, y, z) + + assert q1.axis() == Quaternion(0, 2*sqrt(29)/29, 3*sqrt(29)/29, 4*sqrt(29)/29) + assert q1.axis().pow(2) == Quaternion(-1, 0, 0, 0) + assert q0.axis().scalar_part() == 0 + assert (q.axis() == Quaternion(0, + x/sqrt(x**2 + y**2 + z**2), + y/sqrt(x**2 + y**2 + z**2), + z/sqrt(x**2 + y**2 + z**2))) + + assert q0.is_pure() is True + assert q1.is_pure() is False + assert Quaternion(0, 0, 0, 3).is_pure() is True + assert Quaternion(0, 2, 10, 3).is_pure() is True + assert Quaternion(w, 2, 10, 3).is_pure() is None + + assert q1.angle() == 2*atan(sqrt(29)) + assert q.angle() == 2*atan2(sqrt(x**2 + y**2 + z**2), w) + + assert Quaternion.arc_coplanar(q1, Quaternion(2, 4, 6, 8)) is True + assert Quaternion.arc_coplanar(q1, Quaternion(1, -2, -3, -4)) is True + assert Quaternion.arc_coplanar(q1, Quaternion(1, 8, 12, 16)) is True + assert Quaternion.arc_coplanar(q1, Quaternion(1, 2, 3, 4)) is True + assert Quaternion.arc_coplanar(q1, Quaternion(w, 4, 6, 8)) is True + assert Quaternion.arc_coplanar(q1, Quaternion(2, 7, 4, 1)) is False + assert Quaternion.arc_coplanar(q1, Quaternion(w, x, y, z)) is None + raises(ValueError, lambda: Quaternion.arc_coplanar(q1, q0)) + + assert Quaternion.vector_coplanar( + Quaternion(0, 8, 12, 16), + Quaternion(0, 4, 6, 8), + Quaternion(0, 2, 3, 4)) is True + assert Quaternion.vector_coplanar( + Quaternion(0, 0, 0, 0), Quaternion(0, 4, 6, 8), Quaternion(0, 2, 3, 4)) is True + assert Quaternion.vector_coplanar( + Quaternion(0, 8, 2, 6), Quaternion(0, 1, 6, 6), Quaternion(0, 0, 3, 4)) is False + assert Quaternion.vector_coplanar( + Quaternion(0, 1, 3, 4), + Quaternion(0, 4, w, 6), + Quaternion(0, 6, 8, 1)) is None + raises(ValueError, lambda: + Quaternion.vector_coplanar(q0, Quaternion(0, 4, 6, 8), q1)) + + assert Quaternion(0, 1, 2, 3).parallel(Quaternion(0, 2, 4, 6)) is True + assert Quaternion(0, 1, 2, 3).parallel(Quaternion(0, 2, 2, 6)) is False + assert Quaternion(0, 1, 2, 3).parallel(Quaternion(w, x, y, 6)) is None + raises(ValueError, lambda: q0.parallel(q1)) + + assert Quaternion(0, 1, 2, 3).orthogonal(Quaternion(0, -2, 1, 0)) is True + assert Quaternion(0, 2, 4, 7).orthogonal(Quaternion(0, 2, 2, 6)) is False + assert Quaternion(0, 2, 4, 7).orthogonal(Quaternion(w, x, y, 6)) is None + raises(ValueError, lambda: q0.orthogonal(q1)) + + assert q1.index_vector() == Quaternion( + 0, 2*sqrt(870)/29, + 3*sqrt(870)/29, + 4*sqrt(870)/29) + assert Quaternion(0, 3, 9, 4).index_vector() == Quaternion(0, 3, 9, 4) + + assert Quaternion(4, 3, 9, 4).mensor() == log(sqrt(122)) + assert Quaternion(3, 3, 0, 2).mensor() == log(sqrt(22)) + + assert q0.is_zero_quaternion() is True + assert q1.is_zero_quaternion() is False + assert Quaternion(w, 0, 0, 0).is_zero_quaternion() is None + +def test_quaternion_conversions(): + q1 = Quaternion(1, 2, 3, 4) + + assert q1.to_axis_angle() == ((2 * sqrt(29)/29, + 3 * sqrt(29)/29, + 4 * sqrt(29)/29), + 2 * acos(sqrt(30)/30)) + + assert (q1.to_rotation_matrix() == + Matrix([[Rational(-2, 3), Rational(2, 15), Rational(11, 15)], + [Rational(2, 3), Rational(-1, 3), Rational(2, 3)], + [Rational(1, 3), Rational(14, 15), Rational(2, 15)]])) + + assert (q1.to_rotation_matrix((1, 1, 1)) == + Matrix([ + [Rational(-2, 3), Rational(2, 15), Rational(11, 15), Rational(4, 5)], + [Rational(2, 3), Rational(-1, 3), Rational(2, 3), S.Zero], + [Rational(1, 3), Rational(14, 15), Rational(2, 15), Rational(-2, 5)], + [S.Zero, S.Zero, S.Zero, S.One]])) + + theta = symbols("theta", real=True) + q2 = Quaternion(cos(theta/2), 0, 0, sin(theta/2)) + + assert trigsimp(q2.to_rotation_matrix()) == Matrix([ + [cos(theta), -sin(theta), 0], + [sin(theta), cos(theta), 0], + [0, 0, 1]]) + + assert q2.to_axis_angle() == ((0, 0, sin(theta/2)/Abs(sin(theta/2))), + 2*acos(cos(theta/2))) + + assert trigsimp(q2.to_rotation_matrix((1, 1, 1))) == Matrix([ + [cos(theta), -sin(theta), 0, sin(theta) - cos(theta) + 1], + [sin(theta), cos(theta), 0, -sin(theta) - cos(theta) + 1], + [0, 0, 1, 0], + [0, 0, 0, 1]]) + + +def test_rotation_matrix_homogeneous(): + q = Quaternion(w, x, y, z) + R1 = q.to_rotation_matrix(homogeneous=True) * q.norm()**2 + R2 = simplify(q.to_rotation_matrix(homogeneous=False) * q.norm()**2) + assert R1 == R2 + + +def test_quaternion_rotation_iss1593(): + """ + There was a sign mistake in the definition, + of the rotation matrix. This tests that particular sign mistake. + See issue 1593 for reference. + See wikipedia + https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix + for the correct definition + """ + q = Quaternion(cos(phi/2), sin(phi/2), 0, 0) + assert(trigsimp(q.to_rotation_matrix()) == Matrix([ + [1, 0, 0], + [0, cos(phi), -sin(phi)], + [0, sin(phi), cos(phi)]])) + + +def test_quaternion_multiplication(): + q1 = Quaternion(3 + 4*I, 2 + 5*I, 0, 7 + 8*I, real_field = False) + q2 = Quaternion(1, 2, 3, 5) + q3 = Quaternion(1, 1, 1, y) + + assert Quaternion._generic_mul(S(4), S.One) == 4 + assert (Quaternion._generic_mul(S(4), q1) == + Quaternion(12 + 16*I, 8 + 20*I, 0, 28 + 32*I)) + assert q2.mul(2) == Quaternion(2, 4, 6, 10) + assert q2.mul(q3) == Quaternion(-5*y - 4, 3*y - 2, 9 - 2*y, y + 4) + assert q2.mul(q3) == q2*q3 + + z = symbols('z', complex=True) + z_quat = Quaternion(re(z), im(z), 0, 0) + q = Quaternion(*symbols('q:4', real=True)) + + assert z * q == z_quat * q + assert q * z == q * z_quat + + +def test_issue_16318(): + #for rtruediv + q0 = Quaternion(0, 0, 0, 0) + raises(ValueError, lambda: 1/q0) + #for rotate_point + q = Quaternion(1, 2, 3, 4) + (axis, angle) = q.to_axis_angle() + assert Quaternion.rotate_point((1, 1, 1), (axis, angle)) == (S.One / 5, 1, S(7) / 5) + #test for to_axis_angle + q = Quaternion(-1, 1, 1, 1) + axis = (-sqrt(3)/3, -sqrt(3)/3, -sqrt(3)/3) + angle = 2*pi/3 + assert (axis, angle) == q.to_axis_angle() + + +@slow +def test_to_euler(): + q = Quaternion(w, x, y, z) + q_normalized = q.normalize() + + seqs = ['zxy', 'zyx', 'zyz', 'zxz'] + seqs += [seq.upper() for seq in seqs] + + for seq in seqs: + euler_from_q = q.to_euler(seq) + q_back = simplify(Quaternion.from_euler(euler_from_q, seq)) + assert q_back == q_normalized + + +def test_to_euler_iss24504(): + """ + There was a mistake in the degenerate case testing + See issue 24504 for reference. + """ + q = Quaternion.from_euler((phi, 0, 0), 'zyz') + assert trigsimp(q.to_euler('zyz'), inverse=True) == (phi, 0, 0) + + +def test_to_euler_numerical_singilarities(): + + def test_one_case(angles, seq): + q = Quaternion.from_euler(angles, seq) + assert q.to_euler(seq) == angles + + # symmetric + test_one_case((pi/2, 0, 0), 'zyz') + test_one_case((pi/2, 0, 0), 'ZYZ') + test_one_case((pi/2, pi, 0), 'zyz') + test_one_case((pi/2, pi, 0), 'ZYZ') + + # asymmetric + test_one_case((pi/2, pi/2, 0), 'zyx') + test_one_case((pi/2, -pi/2, 0), 'zyx') + test_one_case((pi/2, pi/2, 0), 'ZYX') + test_one_case((pi/2, -pi/2, 0), 'ZYX') + + +@slow +def test_to_euler_options(): + def test_one_case(q): + angles1 = Matrix(q.to_euler(seq, True, True)) + angles2 = Matrix(q.to_euler(seq, False, False)) + angle_errors = simplify(angles1-angles2).evalf() + for angle_error in angle_errors: + # forcing angles to set {-pi, pi} + angle_error = (angle_error + pi) % (2 * pi) - pi + assert angle_error < 10e-7 + + for xyz in ('xyz', 'XYZ'): + for seq_tuple in permutations(xyz): + for symmetric in (True, False): + if symmetric: + seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + else: + seq = ''.join(seq_tuple) + + for elements in product([-1, 0, 1], repeat=4): + q = Quaternion(*elements) + if not q.is_zero_quaternion(): + test_one_case(q) diff --git a/lib/python3.11/site-packages/sympy/assumptions/__init__.py b/lib/python3.11/site-packages/sympy/assumptions/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..af862653f3ce0eeb67f7764e16c32f3466e87024 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/__init__.py @@ -0,0 +1,18 @@ +""" +A module to implement logical predicates and assumption system. +""" + +from .assume import ( + AppliedPredicate, Predicate, AssumptionsContext, assuming, + global_assumptions +) +from .ask import Q, ask, register_handler, remove_handler +from .refine import refine +from .relation import BinaryRelation, AppliedBinaryRelation + +__all__ = [ + 'AppliedPredicate', 'Predicate', 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0000000000000000000000000000000000000000..205850932de0a4db01bfd68679c7af25e9db8690 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/ask.py @@ -0,0 +1,651 @@ +"""Module for querying SymPy objects about assumptions.""" + +from sympy.assumptions.assume import (global_assumptions, Predicate, + AppliedPredicate) +from sympy.assumptions.cnf import CNF, EncodedCNF, Literal +from sympy.core import sympify +from sympy.core.kind import BooleanKind +from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le +from sympy.logic.inference import satisfiable +from sympy.utilities.decorator import memoize_property +from sympy.utilities.exceptions import (sympy_deprecation_warning, + SymPyDeprecationWarning, + ignore_warnings) + + +# Memoization is necessary for the properties of AssumptionKeys to +# ensure that only one object of Predicate objects are created. +# This is because assumption handlers are registered on those objects. + + +class AssumptionKeys: + """ + This class contains all the supported keys by ``ask``. + It should be accessed via the instance ``sympy.Q``. + + """ + + # DO NOT add methods or properties other than predicate keys. + # SAT solver checks the properties of Q and use them to compute the + # fact system. Non-predicate attributes will break this. + + @memoize_property + def hermitian(self): + from .handlers.sets import HermitianPredicate + return HermitianPredicate() + + @memoize_property + def antihermitian(self): + from .handlers.sets import AntihermitianPredicate + return AntihermitianPredicate() + + @memoize_property + def real(self): + from .handlers.sets import RealPredicate + return RealPredicate() + + @memoize_property + def extended_real(self): + from .handlers.sets import ExtendedRealPredicate + return ExtendedRealPredicate() + + @memoize_property + def imaginary(self): + from .handlers.sets import ImaginaryPredicate + return ImaginaryPredicate() + + @memoize_property + def complex(self): + from .handlers.sets import ComplexPredicate + return ComplexPredicate() + + @memoize_property + def algebraic(self): + from .handlers.sets import AlgebraicPredicate + return AlgebraicPredicate() + + @memoize_property + def transcendental(self): + from .predicates.sets import TranscendentalPredicate + return TranscendentalPredicate() + + @memoize_property + def integer(self): + from .handlers.sets import IntegerPredicate + return IntegerPredicate() + + @memoize_property + def noninteger(self): + from .predicates.sets import NonIntegerPredicate + return NonIntegerPredicate() + + @memoize_property + def rational(self): + from .handlers.sets import RationalPredicate + return RationalPredicate() + + @memoize_property + def irrational(self): + from .handlers.sets import IrrationalPredicate + return IrrationalPredicate() + + @memoize_property + def finite(self): + from .handlers.calculus import FinitePredicate + return FinitePredicate() + + @memoize_property + def infinite(self): + from .handlers.calculus import InfinitePredicate + return InfinitePredicate() + + @memoize_property + def positive_infinite(self): + from .handlers.calculus import PositiveInfinitePredicate + return PositiveInfinitePredicate() + + @memoize_property + def negative_infinite(self): + from .handlers.calculus import NegativeInfinitePredicate + return NegativeInfinitePredicate() + + @memoize_property + def positive(self): + from .handlers.order import PositivePredicate + return PositivePredicate() + + @memoize_property + def negative(self): + from .handlers.order import NegativePredicate + return NegativePredicate() + + @memoize_property + def zero(self): + from .handlers.order import ZeroPredicate + return ZeroPredicate() + + @memoize_property + def extended_positive(self): + from .handlers.order import ExtendedPositivePredicate + return ExtendedPositivePredicate() + + @memoize_property + def extended_negative(self): + from .handlers.order import ExtendedNegativePredicate + return ExtendedNegativePredicate() + + @memoize_property + def nonzero(self): + from .handlers.order import NonZeroPredicate + return NonZeroPredicate() + + @memoize_property + def nonpositive(self): + from .handlers.order import NonPositivePredicate + return NonPositivePredicate() + + @memoize_property + def nonnegative(self): + from .handlers.order import NonNegativePredicate + return NonNegativePredicate() + + @memoize_property + def extended_nonzero(self): + from .handlers.order import ExtendedNonZeroPredicate + return ExtendedNonZeroPredicate() + + @memoize_property + def extended_nonpositive(self): + from .handlers.order import ExtendedNonPositivePredicate + return ExtendedNonPositivePredicate() + + @memoize_property + def extended_nonnegative(self): + from .handlers.order import ExtendedNonNegativePredicate + return ExtendedNonNegativePredicate() + + @memoize_property + def even(self): + from .handlers.ntheory import EvenPredicate + return EvenPredicate() + + @memoize_property + def odd(self): + from .handlers.ntheory import OddPredicate + return OddPredicate() + + @memoize_property + def prime(self): + from .handlers.ntheory import PrimePredicate + return PrimePredicate() + + @memoize_property + def composite(self): + from .handlers.ntheory import CompositePredicate + return CompositePredicate() + + @memoize_property + def commutative(self): + from .handlers.common import CommutativePredicate + return CommutativePredicate() + + @memoize_property + def is_true(self): + from .handlers.common import IsTruePredicate + return IsTruePredicate() + + @memoize_property + def symmetric(self): + from .handlers.matrices import SymmetricPredicate + return SymmetricPredicate() + + @memoize_property + def invertible(self): + from .handlers.matrices import InvertiblePredicate + return InvertiblePredicate() + + @memoize_property + def orthogonal(self): + from .handlers.matrices import OrthogonalPredicate + return OrthogonalPredicate() + + @memoize_property + def unitary(self): + from .handlers.matrices import UnitaryPredicate + return UnitaryPredicate() + + @memoize_property + def positive_definite(self): + from .handlers.matrices import PositiveDefinitePredicate + return PositiveDefinitePredicate() + + @memoize_property + def upper_triangular(self): + from .handlers.matrices import UpperTriangularPredicate + return UpperTriangularPredicate() + + @memoize_property + def lower_triangular(self): + from .handlers.matrices import LowerTriangularPredicate + return LowerTriangularPredicate() + + @memoize_property + def diagonal(self): + from .handlers.matrices import DiagonalPredicate + return DiagonalPredicate() + + @memoize_property + def fullrank(self): + from .handlers.matrices import FullRankPredicate + return FullRankPredicate() + + @memoize_property + def square(self): + from .handlers.matrices import SquarePredicate + return SquarePredicate() + + @memoize_property + def integer_elements(self): + from .handlers.matrices import IntegerElementsPredicate + return IntegerElementsPredicate() + + @memoize_property + def real_elements(self): + from .handlers.matrices import RealElementsPredicate + return RealElementsPredicate() + + @memoize_property + def complex_elements(self): + from .handlers.matrices import ComplexElementsPredicate + return ComplexElementsPredicate() + + @memoize_property + def singular(self): + from .predicates.matrices import SingularPredicate + return SingularPredicate() + + @memoize_property + def normal(self): + from .predicates.matrices import NormalPredicate + return NormalPredicate() + + @memoize_property + def triangular(self): + from .predicates.matrices import TriangularPredicate + return TriangularPredicate() + + @memoize_property + def unit_triangular(self): + from .predicates.matrices import UnitTriangularPredicate + return UnitTriangularPredicate() + + @memoize_property + def eq(self): + from .relation.equality import EqualityPredicate + return EqualityPredicate() + + @memoize_property + def ne(self): + from .relation.equality import UnequalityPredicate + return UnequalityPredicate() + + @memoize_property + def gt(self): + from .relation.equality import StrictGreaterThanPredicate + return StrictGreaterThanPredicate() + + @memoize_property + def ge(self): + from .relation.equality import GreaterThanPredicate + return GreaterThanPredicate() + + @memoize_property + def lt(self): + from .relation.equality import StrictLessThanPredicate + return StrictLessThanPredicate() + + @memoize_property + def le(self): + from .relation.equality import LessThanPredicate + return LessThanPredicate() + + +Q = AssumptionKeys() + +def _extract_all_facts(assump, exprs): + """ + Extract all relevant assumptions from *assump* with respect to given *exprs*. + + Parameters + ========== + + assump : sympy.assumptions.cnf.CNF + + exprs : tuple of expressions + + Returns + ======= + + sympy.assumptions.cnf.CNF + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.cnf import CNF + >>> from sympy.assumptions.ask import _extract_all_facts + >>> from sympy.abc import x, y + >>> assump = CNF.from_prop(Q.positive(x) & Q.integer(y)) + >>> exprs = (x,) + >>> cnf = _extract_all_facts(assump, exprs) + >>> cnf.clauses + {frozenset({Literal(Q.positive, False)})} + + """ + facts = set() + + for clause in assump.clauses: + args = [] + for literal in clause: + if isinstance(literal.lit, AppliedPredicate) and len(literal.lit.arguments) == 1: + if literal.lit.arg in exprs: + # Add literal if it has matching in it + args.append(Literal(literal.lit.function, literal.is_Not)) + else: + # If any of the literals doesn't have matching expr don't add the whole clause. + break + else: + # If any of the literals aren't unary predicate don't add the whole clause. + break + + else: + if args: + facts.add(frozenset(args)) + return CNF(facts) + + +def ask(proposition, assumptions=True, context=global_assumptions): + """ + Function to evaluate the proposition with assumptions. + + Explanation + =========== + + This function evaluates the proposition to ``True`` or ``False`` if + the truth value can be determined. If not, it returns ``None``. + + It should be discerned from :func:`~.refine()` which, when applied to a + proposition, simplifies the argument to symbolic ``Boolean`` instead of + Python built-in ``True``, ``False`` or ``None``. + + **Syntax** + + * ask(proposition) + Evaluate the *proposition* in global assumption context. + + * ask(proposition, assumptions) + Evaluate the *proposition* with respect to *assumptions* in + global assumption context. + + Parameters + ========== + + proposition : Boolean + Proposition which will be evaluated to boolean value. If this is + not ``AppliedPredicate``, it will be wrapped by ``Q.is_true``. + + assumptions : Boolean, optional + Local assumptions to evaluate the *proposition*. + + context : AssumptionsContext, optional + Default assumptions to evaluate the *proposition*. By default, + this is ``sympy.assumptions.global_assumptions`` variable. + + Returns + ======= + + ``True``, ``False``, or ``None`` + + Raises + ====== + + TypeError : *proposition* or *assumptions* is not valid logical expression. + + ValueError : assumptions are inconsistent. + + Examples + ======== + + >>> from sympy import ask, Q, pi + >>> from sympy.abc import x, y + >>> ask(Q.rational(pi)) + False + >>> ask(Q.even(x*y), Q.even(x) & Q.integer(y)) + True + >>> ask(Q.prime(4*x), Q.integer(x)) + False + + If the truth value cannot be determined, ``None`` will be returned. + + >>> print(ask(Q.odd(3*x))) # cannot determine unless we know x + None + + ``ValueError`` is raised if assumptions are inconsistent. + + >>> ask(Q.integer(x), Q.even(x) & Q.odd(x)) + Traceback (most recent call last): + ... + ValueError: inconsistent assumptions Q.even(x) & Q.odd(x) + + Notes + ===== + + Relations in assumptions are not implemented (yet), so the following + will not give a meaningful result. + + >>> ask(Q.positive(x), x > 0) + + It is however a work in progress. + + See Also + ======== + + sympy.assumptions.refine.refine : Simplification using assumptions. + Proposition is not reduced to ``None`` if the truth value cannot + be determined. + """ + from sympy.assumptions.satask import satask + from sympy.assumptions.lra_satask import lra_satask + from sympy.logic.algorithms.lra_theory import UnhandledInput + + proposition = sympify(proposition) + assumptions = sympify(assumptions) + + if isinstance(proposition, Predicate) or proposition.kind is not BooleanKind: + raise TypeError("proposition must be a valid logical expression") + + if isinstance(assumptions, Predicate) or assumptions.kind is not BooleanKind: + raise TypeError("assumptions must be a valid logical expression") + + binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le} + if isinstance(proposition, AppliedPredicate): + key, args = proposition.function, proposition.arguments + elif proposition.func in binrelpreds: + key, args = binrelpreds[type(proposition)], proposition.args + else: + key, args = Q.is_true, (proposition,) + + # convert local and global assumptions to CNF + assump_cnf = CNF.from_prop(assumptions) + assump_cnf.extend(context) + + # extract the relevant facts from assumptions with respect to args + local_facts = _extract_all_facts(assump_cnf, args) + + # convert default facts and assumed facts to encoded CNF + known_facts_cnf = get_all_known_facts() + enc_cnf = EncodedCNF() + enc_cnf.from_cnf(CNF(known_facts_cnf)) + enc_cnf.add_from_cnf(local_facts) + + # check the satisfiability of given assumptions + if local_facts.clauses and satisfiable(enc_cnf) is False: + raise ValueError("inconsistent assumptions %s" % assumptions) + + # quick computation for single fact + res = _ask_single_fact(key, local_facts) + if res is not None: + return res + + # direct resolution method, no logic + res = key(*args)._eval_ask(assumptions) + if res is not None: + return bool(res) + + # using satask (still costly) + res = satask(proposition, assumptions=assumptions, context=context) + if res is not None: + return res + + try: + res = lra_satask(proposition, assumptions=assumptions, context=context) + except UnhandledInput: + return None + + return res + + +def _ask_single_fact(key, local_facts): + """ + Compute the truth value of single predicate using assumptions. + + Parameters + ========== + + key : sympy.assumptions.assume.Predicate + Proposition predicate. + + local_facts : sympy.assumptions.cnf.CNF + Local assumption in CNF form. + + Returns + ======= + + ``True``, ``False`` or ``None`` + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.cnf import CNF + >>> from sympy.assumptions.ask import _ask_single_fact + + If prerequisite of proposition is rejected by the assumption, + return ``False``. + + >>> key, assump = Q.zero, ~Q.zero + >>> local_facts = CNF.from_prop(assump) + >>> _ask_single_fact(key, local_facts) + False + >>> key, assump = Q.zero, ~Q.even + >>> local_facts = CNF.from_prop(assump) + >>> _ask_single_fact(key, local_facts) + False + + If assumption implies the proposition, return ``True``. + + >>> key, assump = Q.even, Q.zero + >>> local_facts = CNF.from_prop(assump) + >>> _ask_single_fact(key, local_facts) + True + + If proposition rejects the assumption, return ``False``. + + >>> key, assump = Q.even, Q.odd + >>> local_facts = CNF.from_prop(assump) + >>> _ask_single_fact(key, local_facts) + False + """ + if local_facts.clauses: + + known_facts_dict = get_known_facts_dict() + + if len(local_facts.clauses) == 1: + cl, = local_facts.clauses + if len(cl) == 1: + f, = cl + prop_facts = known_facts_dict.get(key, None) + prop_req = prop_facts[0] if prop_facts is not None else set() + if f.is_Not and f.arg in prop_req: + # the prerequisite of proposition is rejected + return False + + for clause in local_facts.clauses: + if len(clause) == 1: + f, = clause + prop_facts = known_facts_dict.get(f.arg, None) if not f.is_Not else None + if prop_facts is None: + continue + + prop_req, prop_rej = prop_facts + if key in prop_req: + # assumption implies the proposition + return True + elif key in prop_rej: + # proposition rejects the assumption + return False + + return None + + +def register_handler(key, handler): + """ + Register a handler in the ask system. key must be a string and handler a + class inheriting from AskHandler. + + .. deprecated:: 1.8. + Use multipledispatch handler instead. See :obj:`~.Predicate`. + + """ + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. The register_handler() function + should be replaced with the multipledispatch handler of Predicate. + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + ) + if isinstance(key, Predicate): + key = key.name.name + Qkey = getattr(Q, key, None) + if Qkey is not None: + Qkey.add_handler(handler) + else: + setattr(Q, key, Predicate(key, handlers=[handler])) + + +def remove_handler(key, handler): + """ + Removes a handler from the ask system. + + .. deprecated:: 1.8. + Use multipledispatch handler instead. See :obj:`~.Predicate`. + + """ + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. The remove_handler() function + should be replaced with the multipledispatch handler of Predicate. + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + ) + if isinstance(key, Predicate): + key = key.name.name + # Don't show the same warning again recursively + with ignore_warnings(SymPyDeprecationWarning): + getattr(Q, key).remove_handler(handler) + + +from sympy.assumptions.ask_generated import (get_all_known_facts, + get_known_facts_dict) diff --git a/lib/python3.11/site-packages/sympy/assumptions/ask_generated.py b/lib/python3.11/site-packages/sympy/assumptions/ask_generated.py new file mode 100644 index 0000000000000000000000000000000000000000..d90cdffc1e127d78e18f70cda13d8d5e0530d41b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/ask_generated.py @@ -0,0 +1,352 @@ +""" +Do NOT manually edit this file. +Instead, run ./bin/ask_update.py. +""" + +from sympy.assumptions.ask import Q +from sympy.assumptions.cnf import Literal +from sympy.core.cache import cacheit + +@cacheit +def get_all_known_facts(): + """ + Known facts between unary predicates as CNF clauses. + """ + return { + frozenset((Literal(Q.algebraic, False), Literal(Q.imaginary, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.negative, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.positive, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.rational, True))), + frozenset((Literal(Q.algebraic, False), Literal(Q.transcendental, False), Literal(Q.zero, True))), + frozenset((Literal(Q.algebraic, True), Literal(Q.finite, False))), + frozenset((Literal(Q.algebraic, True), Literal(Q.transcendental, True))), + frozenset((Literal(Q.antihermitian, False), Literal(Q.hermitian, False), Literal(Q.zero, True))), + frozenset((Literal(Q.antihermitian, False), Literal(Q.imaginary, True))), + frozenset((Literal(Q.commutative, False), Literal(Q.finite, True))), + frozenset((Literal(Q.commutative, False), Literal(Q.infinite, True))), + frozenset((Literal(Q.complex_elements, False), Literal(Q.real_elements, True))), + frozenset((Literal(Q.composite, False), Literal(Q.even, True), Literal(Q.positive, True), Literal(Q.prime, False))), + frozenset((Literal(Q.composite, True), Literal(Q.even, False), Literal(Q.odd, False))), + frozenset((Literal(Q.composite, True), Literal(Q.positive, False))), + frozenset((Literal(Q.composite, True), Literal(Q.prime, True))), + frozenset((Literal(Q.diagonal, False), Literal(Q.lower_triangular, True), Literal(Q.upper_triangular, True))), + frozenset((Literal(Q.diagonal, True), Literal(Q.lower_triangular, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.normal, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.symmetric, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.upper_triangular, False))), + frozenset((Literal(Q.even, False), Literal(Q.odd, False), Literal(Q.prime, True))), + frozenset((Literal(Q.even, False), Literal(Q.zero, True))), + frozenset((Literal(Q.even, True), Literal(Q.odd, True))), + frozenset((Literal(Q.even, True), Literal(Q.rational, False))), + frozenset((Literal(Q.finite, False), Literal(Q.transcendental, True))), + frozenset((Literal(Q.finite, True), Literal(Q.infinite, True))), + frozenset((Literal(Q.fullrank, False), Literal(Q.invertible, True))), + frozenset((Literal(Q.fullrank, True), Literal(Q.invertible, False), Literal(Q.square, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.negative, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.positive, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.zero, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.negative, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.positive, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.zero, True))), + frozenset((Literal(Q.infinite, False), Literal(Q.negative_infinite, True))), + frozenset((Literal(Q.infinite, False), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.integer_elements, True), Literal(Q.real_elements, False))), + frozenset((Literal(Q.invertible, False), Literal(Q.positive_definite, True))), + frozenset((Literal(Q.invertible, False), Literal(Q.singular, False))), + frozenset((Literal(Q.invertible, False), Literal(Q.unitary, True))), + frozenset((Literal(Q.invertible, True), Literal(Q.singular, True))), + frozenset((Literal(Q.invertible, True), Literal(Q.square, False))), + frozenset((Literal(Q.irrational, False), Literal(Q.negative, True), Literal(Q.rational, False))), + frozenset((Literal(Q.irrational, False), Literal(Q.positive, True), Literal(Q.rational, False))), + frozenset((Literal(Q.irrational, False), Literal(Q.rational, False), Literal(Q.zero, True))), + frozenset((Literal(Q.irrational, True), Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.zero, False))), + frozenset((Literal(Q.irrational, True), Literal(Q.rational, True))), + frozenset((Literal(Q.lower_triangular, False), Literal(Q.triangular, True), Literal(Q.upper_triangular, False))), + frozenset((Literal(Q.lower_triangular, True), Literal(Q.triangular, False))), + frozenset((Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.rational, True), Literal(Q.zero, False))), + frozenset((Literal(Q.negative, True), Literal(Q.negative_infinite, True))), + frozenset((Literal(Q.negative, True), Literal(Q.positive, True))), + frozenset((Literal(Q.negative, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.negative, True), Literal(Q.zero, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.zero, True))), + frozenset((Literal(Q.normal, False), Literal(Q.unitary, True))), + frozenset((Literal(Q.normal, True), Literal(Q.square, False))), + frozenset((Literal(Q.odd, True), Literal(Q.rational, False))), + frozenset((Literal(Q.orthogonal, False), Literal(Q.real_elements, True), Literal(Q.unitary, True))), + frozenset((Literal(Q.orthogonal, True), Literal(Q.positive_definite, False))), + frozenset((Literal(Q.orthogonal, True), Literal(Q.unitary, False))), + frozenset((Literal(Q.positive, False), Literal(Q.prime, True))), + frozenset((Literal(Q.positive, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.positive, True), Literal(Q.zero, True))), + frozenset((Literal(Q.positive_infinite, True), Literal(Q.zero, True))), + frozenset((Literal(Q.square, False), Literal(Q.symmetric, True))), + frozenset((Literal(Q.triangular, False), Literal(Q.unit_triangular, True))), + frozenset((Literal(Q.triangular, False), Literal(Q.upper_triangular, True))) + } + +@cacheit +def get_all_known_matrix_facts(): + """ + Known facts between unary predicates for matrices as CNF clauses. + """ + return { + frozenset((Literal(Q.complex_elements, False), Literal(Q.real_elements, True))), + frozenset((Literal(Q.diagonal, False), Literal(Q.lower_triangular, True), Literal(Q.upper_triangular, True))), + frozenset((Literal(Q.diagonal, True), Literal(Q.lower_triangular, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.normal, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.symmetric, False))), + frozenset((Literal(Q.diagonal, True), Literal(Q.upper_triangular, False))), + frozenset((Literal(Q.fullrank, False), Literal(Q.invertible, True))), + frozenset((Literal(Q.fullrank, True), Literal(Q.invertible, False), Literal(Q.square, True))), + frozenset((Literal(Q.integer_elements, True), Literal(Q.real_elements, False))), + frozenset((Literal(Q.invertible, False), Literal(Q.positive_definite, True))), + frozenset((Literal(Q.invertible, False), Literal(Q.singular, False))), + frozenset((Literal(Q.invertible, False), Literal(Q.unitary, True))), + frozenset((Literal(Q.invertible, True), Literal(Q.singular, True))), + frozenset((Literal(Q.invertible, True), Literal(Q.square, False))), + frozenset((Literal(Q.lower_triangular, False), Literal(Q.triangular, True), Literal(Q.upper_triangular, False))), + frozenset((Literal(Q.lower_triangular, True), Literal(Q.triangular, False))), + frozenset((Literal(Q.normal, False), Literal(Q.unitary, True))), + frozenset((Literal(Q.normal, True), Literal(Q.square, False))), + frozenset((Literal(Q.orthogonal, False), Literal(Q.real_elements, True), Literal(Q.unitary, True))), + frozenset((Literal(Q.orthogonal, True), Literal(Q.positive_definite, False))), + frozenset((Literal(Q.orthogonal, True), Literal(Q.unitary, False))), + frozenset((Literal(Q.square, False), Literal(Q.symmetric, True))), + frozenset((Literal(Q.triangular, False), Literal(Q.unit_triangular, True))), + frozenset((Literal(Q.triangular, False), Literal(Q.upper_triangular, True))) + } + +@cacheit +def get_all_known_number_facts(): + """ + Known facts between unary predicates for numbers as CNF clauses. + """ + return { + frozenset((Literal(Q.algebraic, False), Literal(Q.imaginary, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.negative, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.positive, True), Literal(Q.transcendental, False))), + frozenset((Literal(Q.algebraic, False), Literal(Q.rational, True))), + frozenset((Literal(Q.algebraic, False), Literal(Q.transcendental, False), Literal(Q.zero, True))), + frozenset((Literal(Q.algebraic, True), Literal(Q.finite, False))), + frozenset((Literal(Q.algebraic, True), Literal(Q.transcendental, True))), + frozenset((Literal(Q.antihermitian, False), Literal(Q.hermitian, False), Literal(Q.zero, True))), + frozenset((Literal(Q.antihermitian, False), Literal(Q.imaginary, True))), + frozenset((Literal(Q.commutative, False), Literal(Q.finite, True))), + frozenset((Literal(Q.commutative, False), Literal(Q.infinite, True))), + frozenset((Literal(Q.composite, False), Literal(Q.even, True), Literal(Q.positive, True), Literal(Q.prime, False))), + frozenset((Literal(Q.composite, True), Literal(Q.even, False), Literal(Q.odd, False))), + frozenset((Literal(Q.composite, True), Literal(Q.positive, False))), + frozenset((Literal(Q.composite, True), Literal(Q.prime, True))), + frozenset((Literal(Q.even, False), Literal(Q.odd, False), Literal(Q.prime, True))), + frozenset((Literal(Q.even, False), Literal(Q.zero, True))), + frozenset((Literal(Q.even, True), Literal(Q.odd, True))), + frozenset((Literal(Q.even, True), Literal(Q.rational, False))), + frozenset((Literal(Q.finite, False), Literal(Q.transcendental, True))), + frozenset((Literal(Q.finite, True), Literal(Q.infinite, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.negative, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.positive, True))), + frozenset((Literal(Q.hermitian, False), Literal(Q.zero, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.negative, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.positive, True))), + frozenset((Literal(Q.imaginary, True), Literal(Q.zero, True))), + frozenset((Literal(Q.infinite, False), Literal(Q.negative_infinite, True))), + frozenset((Literal(Q.infinite, False), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.irrational, False), Literal(Q.negative, True), Literal(Q.rational, False))), + frozenset((Literal(Q.irrational, False), Literal(Q.positive, True), Literal(Q.rational, False))), + frozenset((Literal(Q.irrational, False), Literal(Q.rational, False), Literal(Q.zero, True))), + frozenset((Literal(Q.irrational, True), Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.zero, False))), + frozenset((Literal(Q.irrational, True), Literal(Q.rational, True))), + frozenset((Literal(Q.negative, False), Literal(Q.positive, False), Literal(Q.rational, True), Literal(Q.zero, False))), + frozenset((Literal(Q.negative, True), Literal(Q.negative_infinite, True))), + frozenset((Literal(Q.negative, True), Literal(Q.positive, True))), + frozenset((Literal(Q.negative, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.negative, True), Literal(Q.zero, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.negative_infinite, True), Literal(Q.zero, True))), + frozenset((Literal(Q.odd, True), Literal(Q.rational, False))), + frozenset((Literal(Q.positive, False), Literal(Q.prime, True))), + frozenset((Literal(Q.positive, True), Literal(Q.positive_infinite, True))), + frozenset((Literal(Q.positive, True), Literal(Q.zero, True))), + frozenset((Literal(Q.positive_infinite, True), Literal(Q.zero, True))) + } + +@cacheit +def get_known_facts_dict(): + """ + Logical relations between unary predicates as dictionary. + + Each key is a predicate, and item is two groups of predicates. + First group contains the predicates which are implied by the key, and + second group contains the predicates which are rejected by the key. + + """ + return { + Q.algebraic: (set([Q.algebraic, Q.commutative, Q.complex, Q.finite]), + set([Q.infinite, Q.negative_infinite, Q.positive_infinite, + Q.transcendental])), + Q.antihermitian: (set([Q.antihermitian]), set([])), + Q.commutative: (set([Q.commutative]), set([])), + Q.complex: (set([Q.commutative, Q.complex, Q.finite]), + set([Q.infinite, Q.negative_infinite, Q.positive_infinite])), + Q.complex_elements: (set([Q.complex_elements]), set([])), + Q.composite: (set([Q.algebraic, Q.commutative, Q.complex, Q.composite, + Q.extended_nonnegative, Q.extended_nonzero, + Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian, + Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.rational, + Q.real]), set([Q.extended_negative, Q.extended_nonpositive, + Q.imaginary, Q.infinite, Q.irrational, Q.negative, + Q.negative_infinite, Q.nonpositive, Q.positive_infinite, + Q.prime, Q.transcendental, Q.zero])), + Q.diagonal: (set([Q.diagonal, Q.lower_triangular, Q.normal, Q.square, + Q.symmetric, Q.triangular, Q.upper_triangular]), set([])), + Q.even: (set([Q.algebraic, Q.commutative, Q.complex, Q.even, + Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational, + Q.real]), set([Q.imaginary, Q.infinite, Q.irrational, + Q.negative_infinite, Q.odd, Q.positive_infinite, + Q.transcendental])), + Q.extended_negative: (set([Q.commutative, Q.extended_negative, + Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real]), + set([Q.composite, Q.extended_nonnegative, Q.extended_positive, + Q.imaginary, Q.nonnegative, Q.positive, Q.positive_infinite, + Q.prime, Q.zero])), + Q.extended_nonnegative: (set([Q.commutative, Q.extended_nonnegative, + Q.extended_real]), set([Q.extended_negative, Q.imaginary, + Q.negative, Q.negative_infinite])), + Q.extended_nonpositive: (set([Q.commutative, Q.extended_nonpositive, + Q.extended_real]), set([Q.composite, Q.extended_positive, + Q.imaginary, Q.positive, Q.positive_infinite, Q.prime])), + Q.extended_nonzero: (set([Q.commutative, Q.extended_nonzero, + Q.extended_real]), set([Q.imaginary, Q.zero])), + Q.extended_positive: (set([Q.commutative, Q.extended_nonnegative, + Q.extended_nonzero, Q.extended_positive, Q.extended_real]), + set([Q.extended_negative, Q.extended_nonpositive, Q.imaginary, + Q.negative, Q.negative_infinite, Q.nonpositive, Q.zero])), + Q.extended_real: (set([Q.commutative, Q.extended_real]), + set([Q.imaginary])), + Q.finite: (set([Q.commutative, Q.finite]), set([Q.infinite, + Q.negative_infinite, Q.positive_infinite])), + Q.fullrank: (set([Q.fullrank]), set([])), + Q.hermitian: (set([Q.hermitian]), set([])), + Q.imaginary: (set([Q.antihermitian, Q.commutative, Q.complex, + Q.finite, Q.imaginary]), set([Q.composite, Q.even, + Q.extended_negative, Q.extended_nonnegative, + Q.extended_nonpositive, Q.extended_nonzero, + Q.extended_positive, Q.extended_real, Q.infinite, Q.integer, + Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative, + Q.nonpositive, Q.nonzero, Q.odd, Q.positive, + Q.positive_infinite, Q.prime, Q.rational, Q.real, Q.zero])), + Q.infinite: (set([Q.commutative, Q.infinite]), set([Q.algebraic, + Q.complex, Q.composite, Q.even, Q.finite, Q.imaginary, + Q.integer, Q.irrational, Q.negative, Q.nonnegative, + Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime, + Q.rational, Q.real, Q.transcendental, Q.zero])), + Q.integer: (set([Q.algebraic, Q.commutative, Q.complex, + Q.extended_real, Q.finite, Q.hermitian, Q.integer, Q.rational, + Q.real]), set([Q.imaginary, Q.infinite, Q.irrational, + Q.negative_infinite, Q.positive_infinite, Q.transcendental])), + Q.integer_elements: (set([Q.complex_elements, Q.integer_elements, + Q.real_elements]), set([])), + Q.invertible: (set([Q.fullrank, Q.invertible, Q.square]), + set([Q.singular])), + Q.irrational: (set([Q.commutative, Q.complex, Q.extended_nonzero, + Q.extended_real, Q.finite, Q.hermitian, Q.irrational, + Q.nonzero, Q.real]), set([Q.composite, Q.even, Q.imaginary, + Q.infinite, Q.integer, Q.negative_infinite, Q.odd, + Q.positive_infinite, Q.prime, Q.rational, Q.zero])), + Q.is_true: (set([Q.is_true]), set([])), + Q.lower_triangular: (set([Q.lower_triangular, Q.triangular]), set([])), + Q.negative: (set([Q.commutative, Q.complex, Q.extended_negative, + Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real, + Q.finite, Q.hermitian, Q.negative, Q.nonpositive, Q.nonzero, + Q.real]), set([Q.composite, Q.extended_nonnegative, + Q.extended_positive, Q.imaginary, Q.infinite, + Q.negative_infinite, Q.nonnegative, Q.positive, + Q.positive_infinite, Q.prime, Q.zero])), + Q.negative_infinite: (set([Q.commutative, Q.extended_negative, + Q.extended_nonpositive, Q.extended_nonzero, Q.extended_real, + Q.infinite, Q.negative_infinite]), set([Q.algebraic, + Q.complex, Q.composite, Q.even, Q.extended_nonnegative, + Q.extended_positive, Q.finite, Q.imaginary, Q.integer, + Q.irrational, Q.negative, Q.nonnegative, Q.nonpositive, + Q.nonzero, Q.odd, Q.positive, Q.positive_infinite, Q.prime, + Q.rational, Q.real, Q.transcendental, Q.zero])), + Q.noninteger: (set([Q.noninteger]), set([])), + Q.nonnegative: (set([Q.commutative, Q.complex, Q.extended_nonnegative, + Q.extended_real, Q.finite, Q.hermitian, Q.nonnegative, + Q.real]), set([Q.extended_negative, Q.imaginary, Q.infinite, + Q.negative, Q.negative_infinite, Q.positive_infinite])), + Q.nonpositive: (set([Q.commutative, Q.complex, Q.extended_nonpositive, + Q.extended_real, Q.finite, Q.hermitian, Q.nonpositive, + Q.real]), set([Q.composite, Q.extended_positive, Q.imaginary, + Q.infinite, Q.negative_infinite, Q.positive, + Q.positive_infinite, Q.prime])), + Q.nonzero: (set([Q.commutative, Q.complex, Q.extended_nonzero, + Q.extended_real, Q.finite, Q.hermitian, Q.nonzero, Q.real]), + set([Q.imaginary, Q.infinite, Q.negative_infinite, + Q.positive_infinite, Q.zero])), + Q.normal: (set([Q.normal, Q.square]), set([])), + Q.odd: (set([Q.algebraic, Q.commutative, Q.complex, + Q.extended_nonzero, Q.extended_real, Q.finite, Q.hermitian, + Q.integer, Q.nonzero, Q.odd, Q.rational, Q.real]), + set([Q.even, Q.imaginary, Q.infinite, Q.irrational, + Q.negative_infinite, Q.positive_infinite, Q.transcendental, + Q.zero])), + Q.orthogonal: (set([Q.fullrank, Q.invertible, Q.normal, Q.orthogonal, + Q.positive_definite, Q.square, Q.unitary]), set([Q.singular])), + Q.positive: (set([Q.commutative, Q.complex, Q.extended_nonnegative, + Q.extended_nonzero, Q.extended_positive, Q.extended_real, + Q.finite, Q.hermitian, Q.nonnegative, Q.nonzero, Q.positive, + Q.real]), set([Q.extended_negative, Q.extended_nonpositive, + Q.imaginary, Q.infinite, Q.negative, Q.negative_infinite, + Q.nonpositive, Q.positive_infinite, Q.zero])), + Q.positive_definite: (set([Q.fullrank, Q.invertible, + Q.positive_definite, Q.square]), set([Q.singular])), + Q.positive_infinite: (set([Q.commutative, Q.extended_nonnegative, + Q.extended_nonzero, Q.extended_positive, Q.extended_real, + Q.infinite, Q.positive_infinite]), set([Q.algebraic, + Q.complex, Q.composite, Q.even, Q.extended_negative, + Q.extended_nonpositive, Q.finite, Q.imaginary, Q.integer, + Q.irrational, Q.negative, Q.negative_infinite, Q.nonnegative, + Q.nonpositive, Q.nonzero, Q.odd, Q.positive, Q.prime, + Q.rational, Q.real, Q.transcendental, Q.zero])), + Q.prime: (set([Q.algebraic, Q.commutative, Q.complex, + Q.extended_nonnegative, Q.extended_nonzero, + Q.extended_positive, Q.extended_real, Q.finite, Q.hermitian, + Q.integer, Q.nonnegative, Q.nonzero, Q.positive, Q.prime, + Q.rational, Q.real]), set([Q.composite, Q.extended_negative, + Q.extended_nonpositive, Q.imaginary, Q.infinite, Q.irrational, + Q.negative, Q.negative_infinite, Q.nonpositive, + Q.positive_infinite, Q.transcendental, Q.zero])), + Q.rational: (set([Q.algebraic, Q.commutative, Q.complex, + Q.extended_real, Q.finite, Q.hermitian, Q.rational, Q.real]), + set([Q.imaginary, Q.infinite, Q.irrational, + Q.negative_infinite, Q.positive_infinite, Q.transcendental])), + Q.real: (set([Q.commutative, Q.complex, Q.extended_real, Q.finite, + Q.hermitian, Q.real]), set([Q.imaginary, Q.infinite, + Q.negative_infinite, Q.positive_infinite])), + Q.real_elements: (set([Q.complex_elements, Q.real_elements]), set([])), + Q.singular: (set([Q.singular]), set([Q.invertible, Q.orthogonal, + Q.positive_definite, Q.unitary])), + Q.square: (set([Q.square]), set([])), + Q.symmetric: (set([Q.square, Q.symmetric]), set([])), + Q.transcendental: (set([Q.commutative, Q.complex, Q.finite, + Q.transcendental]), set([Q.algebraic, Q.composite, Q.even, + Q.infinite, Q.integer, Q.negative_infinite, Q.odd, + Q.positive_infinite, Q.prime, Q.rational, Q.zero])), + Q.triangular: (set([Q.triangular]), set([])), + Q.unit_triangular: (set([Q.triangular, Q.unit_triangular]), set([])), + Q.unitary: (set([Q.fullrank, Q.invertible, Q.normal, Q.square, + Q.unitary]), set([Q.singular])), + Q.upper_triangular: (set([Q.triangular, Q.upper_triangular]), set([])), + Q.zero: (set([Q.algebraic, Q.commutative, Q.complex, Q.even, + Q.extended_nonnegative, Q.extended_nonpositive, + Q.extended_real, Q.finite, Q.hermitian, Q.integer, + Q.nonnegative, Q.nonpositive, Q.rational, Q.real, Q.zero]), + set([Q.composite, Q.extended_negative, Q.extended_nonzero, + Q.extended_positive, Q.imaginary, Q.infinite, Q.irrational, + Q.negative, Q.negative_infinite, Q.nonzero, Q.odd, Q.positive, + Q.positive_infinite, Q.prime, Q.transcendental])), + } diff --git a/lib/python3.11/site-packages/sympy/assumptions/assume.py b/lib/python3.11/site-packages/sympy/assumptions/assume.py new file mode 100644 index 0000000000000000000000000000000000000000..743195a865a1d39389d471b95728ca79834ed019 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/assume.py @@ -0,0 +1,485 @@ +"""A module which implements predicates and assumption context.""" + +from contextlib import contextmanager +import inspect +from sympy.core.symbol import Str +from sympy.core.sympify import _sympify +from sympy.logic.boolalg import Boolean, false, true +from sympy.multipledispatch.dispatcher import Dispatcher, str_signature +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import is_sequence +from sympy.utilities.source import get_class + + +class AssumptionsContext(set): + """ + Set containing default assumptions which are applied to the ``ask()`` + function. + + Explanation + =========== + + This is used to represent global assumptions, but you can also use this + class to create your own local assumptions contexts. It is basically a thin + wrapper to Python's set, so see its documentation for advanced usage. + + Examples + ======== + + The default assumption context is ``global_assumptions``, which is initially empty: + + >>> from sympy import ask, Q + >>> from sympy.assumptions import global_assumptions + >>> global_assumptions + AssumptionsContext() + + You can add default assumptions: + + >>> from sympy.abc import x + >>> global_assumptions.add(Q.real(x)) + >>> global_assumptions + AssumptionsContext({Q.real(x)}) + >>> ask(Q.real(x)) + True + + And remove them: + + >>> global_assumptions.remove(Q.real(x)) + >>> print(ask(Q.real(x))) + None + + The ``clear()`` method removes every assumption: + + >>> global_assumptions.add(Q.positive(x)) + >>> global_assumptions + AssumptionsContext({Q.positive(x)}) + >>> global_assumptions.clear() + >>> global_assumptions + AssumptionsContext() + + See Also + ======== + + assuming + + """ + + def add(self, *assumptions): + """Add assumptions.""" + for a in assumptions: + super().add(a) + + def _sympystr(self, printer): + if not self: + return "%s()" % self.__class__.__name__ + return "{}({})".format(self.__class__.__name__, printer._print_set(self)) + +global_assumptions = AssumptionsContext() + + +class AppliedPredicate(Boolean): + """ + The class of expressions resulting from applying ``Predicate`` to + the arguments. ``AppliedPredicate`` merely wraps its argument and + remain unevaluated. To evaluate it, use the ``ask()`` function. + + Examples + ======== + + >>> from sympy import Q, ask + >>> Q.integer(1) + Q.integer(1) + + The ``function`` attribute returns the predicate, and the ``arguments`` + attribute returns the tuple of arguments. + + >>> type(Q.integer(1)) + + >>> Q.integer(1).function + Q.integer + >>> Q.integer(1).arguments + (1,) + + Applied predicates can be evaluated to a boolean value with ``ask``: + + >>> ask(Q.integer(1)) + True + + """ + __slots__ = () + + def __new__(cls, predicate, *args): + if not isinstance(predicate, Predicate): + raise TypeError("%s is not a Predicate." % predicate) + args = map(_sympify, args) + return super().__new__(cls, predicate, *args) + + @property + def arg(self): + """ + Return the expression used by this assumption. + + Examples + ======== + + >>> from sympy import Q, Symbol + >>> x = Symbol('x') + >>> a = Q.integer(x + 1) + >>> a.arg + x + 1 + + """ + # Will be deprecated + args = self._args + if len(args) == 2: + # backwards compatibility + return args[1] + raise TypeError("'arg' property is allowed only for unary predicates.") + + @property + def function(self): + """ + Return the predicate. + """ + # Will be changed to self.args[0] after args overriding is removed + return self._args[0] + + @property + def arguments(self): + """ + Return the arguments which are applied to the predicate. + """ + # Will be changed to self.args[1:] after args overriding is removed + return self._args[1:] + + def _eval_ask(self, assumptions): + return self.function.eval(self.arguments, assumptions) + + @property + def binary_symbols(self): + from .ask import Q + if self.function == Q.is_true: + i = self.arguments[0] + if i.is_Boolean or i.is_Symbol: + return i.binary_symbols + if self.function in (Q.eq, Q.ne): + if true in self.arguments or false in self.arguments: + if self.arguments[0].is_Symbol: + return {self.arguments[0]} + elif self.arguments[1].is_Symbol: + return {self.arguments[1]} + return set() + + +class PredicateMeta(type): + def __new__(cls, clsname, bases, dct): + # If handler is not defined, assign empty dispatcher. + if "handler" not in dct: + name = f"Ask{clsname.capitalize()}Handler" + handler = Dispatcher(name, doc="Handler for key %s" % name) + dct["handler"] = handler + + dct["_orig_doc"] = dct.get("__doc__", "") + + return super().__new__(cls, clsname, bases, dct) + + @property + def __doc__(cls): + handler = cls.handler + doc = cls._orig_doc + if cls is not Predicate and handler is not None: + doc += "Handler\n" + doc += " =======\n\n" + + # Append the handler's doc without breaking sphinx documentation. + docs = [" Multiply dispatched method: %s" % handler.name] + if handler.doc: + for line in handler.doc.splitlines(): + if not line: + continue + docs.append(" %s" % line) + other = [] + for sig in handler.ordering[::-1]: + func = handler.funcs[sig] + if func.__doc__: + s = ' Inputs: <%s>' % str_signature(sig) + lines = [] + for line in func.__doc__.splitlines(): + lines.append(" %s" % line) + s += "\n".join(lines) + docs.append(s) + else: + other.append(str_signature(sig)) + if other: + othersig = " Other signatures:" + for line in other: + othersig += "\n * %s" % line + docs.append(othersig) + + doc += '\n\n'.join(docs) + + return doc + + +class Predicate(Boolean, metaclass=PredicateMeta): + """ + Base class for mathematical predicates. It also serves as a + constructor for undefined predicate objects. + + Explanation + =========== + + Predicate is a function that returns a boolean value [1]. + + Predicate function is object, and it is instance of predicate class. + When a predicate is applied to arguments, ``AppliedPredicate`` + instance is returned. This merely wraps the argument and remain + unevaluated. To obtain the truth value of applied predicate, use the + function ``ask``. + + Evaluation of predicate is done by multiple dispatching. You can + register new handler to the predicate to support new types. + + Every predicate in SymPy can be accessed via the property of ``Q``. + For example, ``Q.even`` returns the predicate which checks if the + argument is even number. + + To define a predicate which can be evaluated, you must subclass this + class, make an instance of it, and register it to ``Q``. After then, + dispatch the handler by argument types. + + If you directly construct predicate using this class, you will get + ``UndefinedPredicate`` which cannot be dispatched. This is useful + when you are building boolean expressions which do not need to be + evaluated. + + Examples + ======== + + Applying and evaluating to boolean value: + + >>> from sympy import Q, ask + >>> ask(Q.prime(7)) + True + + You can define a new predicate by subclassing and dispatching. Here, + we define a predicate for sexy primes [2] as an example. + + >>> from sympy import Predicate, Integer + >>> class SexyPrimePredicate(Predicate): + ... name = "sexyprime" + >>> Q.sexyprime = SexyPrimePredicate() + >>> @Q.sexyprime.register(Integer, Integer) + ... def _(int1, int2, assumptions): + ... args = sorted([int1, int2]) + ... if not all(ask(Q.prime(a), assumptions) for a in args): + ... return False + ... return args[1] - args[0] == 6 + >>> ask(Q.sexyprime(5, 11)) + True + + Direct constructing returns ``UndefinedPredicate``, which can be + applied but cannot be dispatched. + + >>> from sympy import Predicate, Integer + >>> Q.P = Predicate("P") + >>> type(Q.P) + + >>> Q.P(1) + Q.P(1) + >>> Q.P.register(Integer)(lambda expr, assump: True) + Traceback (most recent call last): + ... + TypeError: cannot be dispatched. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Predicate_%28mathematical_logic%29 + .. [2] https://en.wikipedia.org/wiki/Sexy_prime + + """ + + is_Atom = True + + def __new__(cls, *args, **kwargs): + if cls is Predicate: + return UndefinedPredicate(*args, **kwargs) + obj = super().__new__(cls, *args) + return obj + + @property + def name(self): + # May be overridden + return type(self).__name__ + + @classmethod + def register(cls, *types, **kwargs): + """ + Register the signature to the handler. + """ + if cls.handler is None: + raise TypeError("%s cannot be dispatched." % type(cls)) + return cls.handler.register(*types, **kwargs) + + @classmethod + def register_many(cls, *types, **kwargs): + """ + Register multiple signatures to same handler. + """ + def _(func): + for t in types: + if not is_sequence(t): + t = (t,) # for convenience, allow passing `type` to mean `(type,)` + cls.register(*t, **kwargs)(func) + return _ + + def __call__(self, *args): + return AppliedPredicate(self, *args) + + def eval(self, args, assumptions=True): + """ + Evaluate ``self(*args)`` under the given assumptions. + + This uses only direct resolution methods, not logical inference. + """ + result = None + try: + result = self.handler(*args, assumptions=assumptions) + except NotImplementedError: + pass + return result + + def _eval_refine(self, assumptions): + # When Predicate is no longer Boolean, delete this method + return self + + +class UndefinedPredicate(Predicate): + """ + Predicate without handler. + + Explanation + =========== + + This predicate is generated by using ``Predicate`` directly for + construction. It does not have a handler, and evaluating this with + arguments is done by SAT solver. + + Examples + ======== + + >>> from sympy import Predicate, Q + >>> Q.P = Predicate('P') + >>> Q.P.func + + >>> Q.P.name + Str('P') + + """ + + handler = None + + def __new__(cls, name, handlers=None): + # "handlers" parameter supports old design + if not isinstance(name, Str): + name = Str(name) + obj = super(Boolean, cls).__new__(cls, name) + obj.handlers = handlers or [] + return obj + + @property + def name(self): + return self.args[0] + + def _hashable_content(self): + return (self.name,) + + def __getnewargs__(self): + return (self.name,) + + def __call__(self, expr): + return AppliedPredicate(self, expr) + + def add_handler(self, handler): + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. Predicate.add_handler() + should be replaced with the multipledispatch handler of Predicate. + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + ) + self.handlers.append(handler) + + def remove_handler(self, handler): + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. Predicate.remove_handler() + should be replaced with the multipledispatch handler of Predicate. + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + ) + self.handlers.remove(handler) + + def eval(self, args, assumptions=True): + # Support for deprecated design + # When old design is removed, this will always return None + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. Evaluating UndefinedPredicate + objects should be replaced with the multipledispatch handler of + Predicate. + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + stacklevel=5, + ) + expr, = args + res, _res = None, None + mro = inspect.getmro(type(expr)) + for handler in self.handlers: + cls = get_class(handler) + for subclass in mro: + eval_ = getattr(cls, subclass.__name__, None) + if eval_ is None: + continue + res = eval_(expr, assumptions) + # Do not stop if value returned is None + # Try to check for higher classes + if res is None: + continue + if _res is None: + _res = res + else: + # only check consistency if both resolutors have concluded + if _res != res: + raise ValueError('incompatible resolutors') + break + return res + + +@contextmanager +def assuming(*assumptions): + """ + Context manager for assumptions. + + Examples + ======== + + >>> from sympy import assuming, Q, ask + >>> from sympy.abc import x, y + >>> print(ask(Q.integer(x + y))) + None + >>> with assuming(Q.integer(x), Q.integer(y)): + ... print(ask(Q.integer(x + y))) + True + """ + old_global_assumptions = global_assumptions.copy() + global_assumptions.update(assumptions) + try: + yield + finally: + global_assumptions.clear() + global_assumptions.update(old_global_assumptions) diff --git a/lib/python3.11/site-packages/sympy/assumptions/cnf.py b/lib/python3.11/site-packages/sympy/assumptions/cnf.py new file mode 100644 index 0000000000000000000000000000000000000000..a95d27bed6eeb64c42f4edd9d49bd8e5753069e5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/cnf.py @@ -0,0 +1,445 @@ +""" +The classes used here are for the internal use of assumptions system +only and should not be used anywhere else as these do not possess the +signatures common to SymPy objects. For general use of logic constructs +please refer to sympy.logic classes And, Or, Not, etc. +""" +from itertools import combinations, product, zip_longest +from sympy.assumptions.assume import AppliedPredicate, Predicate +from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le +from sympy.core.singleton import S +from sympy.logic.boolalg import Or, And, Not, Xnor +from sympy.logic.boolalg import (Equivalent, ITE, Implies, Nand, Nor, Xor) + + +class Literal: + """ + The smallest element of a CNF object. + + Parameters + ========== + + lit : Boolean expression + + is_Not : bool + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.cnf import Literal + >>> from sympy.abc import x + >>> Literal(Q.even(x)) + Literal(Q.even(x), False) + >>> Literal(~Q.even(x)) + Literal(Q.even(x), True) + """ + + def __new__(cls, lit, is_Not=False): + if isinstance(lit, Not): + lit = lit.args[0] + is_Not = True + elif isinstance(lit, (AND, OR, Literal)): + return ~lit if is_Not else lit + obj = super().__new__(cls) + obj.lit = lit + obj.is_Not = is_Not + return obj + + @property + def arg(self): + return self.lit + + def rcall(self, expr): + if callable(self.lit): + lit = self.lit(expr) + else: + lit = self.lit.apply(expr) + return type(self)(lit, self.is_Not) + + def __invert__(self): + is_Not = not self.is_Not + return Literal(self.lit, is_Not) + + def __str__(self): + return '{}({}, {})'.format(type(self).__name__, self.lit, self.is_Not) + + __repr__ = __str__ + + def __eq__(self, other): + return self.arg == other.arg and self.is_Not == other.is_Not + + def __hash__(self): + h = hash((type(self).__name__, self.arg, self.is_Not)) + return h + + +class OR: + """ + A low-level implementation for Or + """ + def __init__(self, *args): + self._args = args + + @property + def args(self): + return sorted(self._args, key=str) + + def rcall(self, expr): + return type(self)(*[arg.rcall(expr) + for arg in self._args + ]) + + def __invert__(self): + return AND(*[~arg for arg in self._args]) + + def __hash__(self): + return hash((type(self).__name__,) + tuple(self.args)) + + def __eq__(self, other): + return self.args == other.args + + def __str__(self): + s = '(' + ' | '.join([str(arg) for arg in self.args]) + ')' + return s + + __repr__ = __str__ + + +class AND: + """ + A low-level implementation for And + """ + def __init__(self, *args): + self._args = args + + def __invert__(self): + return OR(*[~arg for arg in self._args]) + + @property + def args(self): + return sorted(self._args, key=str) + + def rcall(self, expr): + return type(self)(*[arg.rcall(expr) + for arg in self._args + ]) + + def __hash__(self): + return hash((type(self).__name__,) + tuple(self.args)) + + def __eq__(self, other): + return self.args == other.args + + def __str__(self): + s = '('+' & '.join([str(arg) for arg in self.args])+')' + return s + + __repr__ = __str__ + + +def to_NNF(expr, composite_map=None): + """ + Generates the Negation Normal Form of any boolean expression in terms + of AND, OR, and Literal objects. + + Examples + ======== + + >>> from sympy import Q, Eq + >>> from sympy.assumptions.cnf import to_NNF + >>> from sympy.abc import x, y + >>> expr = Q.even(x) & ~Q.positive(x) + >>> to_NNF(expr) + (Literal(Q.even(x), False) & Literal(Q.positive(x), True)) + + Supported boolean objects are converted to corresponding predicates. + + >>> to_NNF(Eq(x, y)) + Literal(Q.eq(x, y), False) + + If ``composite_map`` argument is given, ``to_NNF`` decomposes the + specified predicate into a combination of primitive predicates. + + >>> cmap = {Q.nonpositive: Q.negative | Q.zero} + >>> to_NNF(Q.nonpositive, cmap) + (Literal(Q.negative, False) | Literal(Q.zero, False)) + >>> to_NNF(Q.nonpositive(x), cmap) + (Literal(Q.negative(x), False) | Literal(Q.zero(x), False)) + """ + from sympy.assumptions.ask import Q + + if composite_map is None: + composite_map = {} + + + binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le} + if type(expr) in binrelpreds: + pred = binrelpreds[type(expr)] + expr = pred(*expr.args) + + if isinstance(expr, Not): + arg = expr.args[0] + tmp = to_NNF(arg, composite_map) # Strategy: negate the NNF of expr + return ~tmp + + if isinstance(expr, Or): + return OR(*[to_NNF(x, composite_map) for x in Or.make_args(expr)]) + + if isinstance(expr, And): + return AND(*[to_NNF(x, composite_map) for x in And.make_args(expr)]) + + if isinstance(expr, Nand): + tmp = AND(*[to_NNF(x, composite_map) for x in expr.args]) + return ~tmp + + if isinstance(expr, Nor): + tmp = OR(*[to_NNF(x, composite_map) for x in expr.args]) + return ~tmp + + if isinstance(expr, Xor): + cnfs = [] + for i in range(0, len(expr.args) + 1, 2): + for neg in combinations(expr.args, i): + clause = [~to_NNF(s, composite_map) if s in neg else to_NNF(s, composite_map) + for s in expr.args] + cnfs.append(OR(*clause)) + return AND(*cnfs) + + if isinstance(expr, Xnor): + cnfs = [] + for i in range(0, len(expr.args) + 1, 2): + for neg in combinations(expr.args, i): + clause = [~to_NNF(s, composite_map) if s in neg else to_NNF(s, composite_map) + for s in expr.args] + cnfs.append(OR(*clause)) + return ~AND(*cnfs) + + if isinstance(expr, Implies): + L, R = to_NNF(expr.args[0], composite_map), to_NNF(expr.args[1], composite_map) + return OR(~L, R) + + if isinstance(expr, Equivalent): + cnfs = [] + for a, b in zip_longest(expr.args, expr.args[1:], fillvalue=expr.args[0]): + a = to_NNF(a, composite_map) + b = to_NNF(b, composite_map) + cnfs.append(OR(~a, b)) + return AND(*cnfs) + + if isinstance(expr, ITE): + L = to_NNF(expr.args[0], composite_map) + M = to_NNF(expr.args[1], composite_map) + R = to_NNF(expr.args[2], composite_map) + return AND(OR(~L, M), OR(L, R)) + + if isinstance(expr, AppliedPredicate): + pred, args = expr.function, expr.arguments + newpred = composite_map.get(pred, None) + if newpred is not None: + return to_NNF(newpred.rcall(*args), composite_map) + + if isinstance(expr, Predicate): + newpred = composite_map.get(expr, None) + if newpred is not None: + return to_NNF(newpred, composite_map) + + return Literal(expr) + + +def distribute_AND_over_OR(expr): + """ + Distributes AND over OR in the NNF expression. + Returns the result( Conjunctive Normal Form of expression) + as a CNF object. + """ + if not isinstance(expr, (AND, OR)): + tmp = set() + tmp.add(frozenset((expr,))) + return CNF(tmp) + + if isinstance(expr, OR): + return CNF.all_or(*[distribute_AND_over_OR(arg) + for arg in expr._args]) + + if isinstance(expr, AND): + return CNF.all_and(*[distribute_AND_over_OR(arg) + for arg in expr._args]) + + +class CNF: + """ + Class to represent CNF of a Boolean expression. + Consists of set of clauses, which themselves are stored as + frozenset of Literal objects. + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.cnf import CNF + >>> from sympy.abc import x + >>> cnf = CNF.from_prop(Q.real(x) & ~Q.zero(x)) + >>> cnf.clauses + {frozenset({Literal(Q.zero(x), True)}), + frozenset({Literal(Q.negative(x), False), + Literal(Q.positive(x), False), Literal(Q.zero(x), False)})} + """ + def __init__(self, clauses=None): + if not clauses: + clauses = set() + self.clauses = clauses + + def add(self, prop): + clauses = CNF.to_CNF(prop).clauses + self.add_clauses(clauses) + + def __str__(self): + s = ' & '.join( + ['(' + ' | '.join([str(lit) for lit in clause]) +')' + for clause in self.clauses] + ) + return s + + def extend(self, props): + for p in props: + self.add(p) + return self + + def copy(self): + return CNF(set(self.clauses)) + + def add_clauses(self, clauses): + self.clauses |= clauses + + @classmethod + def from_prop(cls, prop): + res = cls() + res.add(prop) + return res + + def __iand__(self, other): + self.add_clauses(other.clauses) + return self + + def all_predicates(self): + predicates = set() + for c in self.clauses: + predicates |= {arg.lit for arg in c} + return predicates + + def _or(self, cnf): + clauses = set() + for a, b in product(self.clauses, cnf.clauses): + tmp = set(a) + tmp.update(b) + clauses.add(frozenset(tmp)) + return CNF(clauses) + + def _and(self, cnf): + clauses = self.clauses.union(cnf.clauses) + return CNF(clauses) + + def _not(self): + clss = list(self.clauses) + ll = {frozenset((~x,)) for x in clss[-1]} + ll = CNF(ll) + + for rest in clss[:-1]: + p = {frozenset((~x,)) for x in rest} + ll = ll._or(CNF(p)) + return ll + + def rcall(self, expr): + clause_list = [] + for clause in self.clauses: + lits = [arg.rcall(expr) for arg in clause] + clause_list.append(OR(*lits)) + expr = AND(*clause_list) + return distribute_AND_over_OR(expr) + + @classmethod + def all_or(cls, *cnfs): + b = cnfs[0].copy() + for rest in cnfs[1:]: + b = b._or(rest) + return b + + @classmethod + def all_and(cls, *cnfs): + b = cnfs[0].copy() + for rest in cnfs[1:]: + b = b._and(rest) + return b + + @classmethod + def to_CNF(cls, expr): + from sympy.assumptions.facts import get_composite_predicates + expr = to_NNF(expr, get_composite_predicates()) + expr = distribute_AND_over_OR(expr) + return expr + + @classmethod + def CNF_to_cnf(cls, cnf): + """ + Converts CNF object to SymPy's boolean expression + retaining the form of expression. + """ + def remove_literal(arg): + return Not(arg.lit) if arg.is_Not else arg.lit + + return And(*(Or(*(remove_literal(arg) for arg in clause)) for clause in cnf.clauses)) + + +class EncodedCNF: + """ + Class for encoding the CNF expression. + """ + def __init__(self, data=None, encoding=None): + if not data and not encoding: + data = [] + encoding = {} + self.data = data + self.encoding = encoding + self._symbols = list(encoding.keys()) + + def from_cnf(self, cnf): + self._symbols = list(cnf.all_predicates()) + n = len(self._symbols) + self.encoding = dict(zip(self._symbols, range(1, n + 1))) + self.data = [self.encode(clause) for clause in cnf.clauses] + + @property + def symbols(self): + return self._symbols + + @property + def variables(self): + return range(1, len(self._symbols) + 1) + + def copy(self): + new_data = [set(clause) for clause in self.data] + return EncodedCNF(new_data, dict(self.encoding)) + + def add_prop(self, prop): + cnf = CNF.from_prop(prop) + self.add_from_cnf(cnf) + + def add_from_cnf(self, cnf): + clauses = [self.encode(clause) for clause in cnf.clauses] + self.data += clauses + + def encode_arg(self, arg): + literal = arg.lit + value = self.encoding.get(literal, None) + if value is None: + n = len(self._symbols) + self._symbols.append(literal) + value = self.encoding[literal] = n + 1 + if arg.is_Not: + return -value + else: + return value + + def encode(self, clause): + return {self.encode_arg(arg) if not arg.lit == S.false else 0 for arg in clause} diff --git a/lib/python3.11/site-packages/sympy/assumptions/facts.py b/lib/python3.11/site-packages/sympy/assumptions/facts.py new file mode 100644 index 0000000000000000000000000000000000000000..2ff268677cf74e252ac6c3bc3eecbea08b9414d0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/facts.py @@ -0,0 +1,270 @@ +""" +Known facts in assumptions module. + +This module defines the facts between unary predicates in ``get_known_facts()``, +and supports functions to generate the contents in +``sympy.assumptions.ask_generated`` file. +""" + +from sympy.assumptions.ask import Q +from sympy.assumptions.assume import AppliedPredicate +from sympy.core.cache import cacheit +from sympy.core.symbol import Symbol +from sympy.logic.boolalg import (to_cnf, And, Not, Implies, Equivalent, + Exclusive,) +from sympy.logic.inference import satisfiable + + +@cacheit +def get_composite_predicates(): + # To reduce the complexity of sat solver, these predicates are + # transformed into the combination of primitive predicates. + return { + Q.real : Q.negative | Q.zero | Q.positive, + Q.integer : Q.even | Q.odd, + Q.nonpositive : Q.negative | Q.zero, + Q.nonzero : Q.negative | Q.positive, + Q.nonnegative : Q.zero | Q.positive, + Q.extended_real : Q.negative_infinite | Q.negative | Q.zero | Q.positive | Q.positive_infinite, + Q.extended_positive: Q.positive | Q.positive_infinite, + Q.extended_negative: Q.negative | Q.negative_infinite, + Q.extended_nonzero: Q.negative_infinite | Q.negative | Q.positive | Q.positive_infinite, + Q.extended_nonpositive: Q.negative_infinite | Q.negative | Q.zero, + Q.extended_nonnegative: Q.zero | Q.positive | Q.positive_infinite, + Q.complex : Q.algebraic | Q.transcendental + } + + +@cacheit +def get_known_facts(x=None): + """ + Facts between unary predicates. + + Parameters + ========== + + x : Symbol, optional + Placeholder symbol for unary facts. Default is ``Symbol('x')``. + + Returns + ======= + + fact : Known facts in conjugated normal form. + + """ + if x is None: + x = Symbol('x') + + fact = And( + get_number_facts(x), + get_matrix_facts(x) + ) + return fact + + +@cacheit +def get_number_facts(x = None): + """ + Facts between unary number predicates. + + Parameters + ========== + + x : Symbol, optional + Placeholder symbol for unary facts. Default is ``Symbol('x')``. + + Returns + ======= + + fact : Known facts in conjugated normal form. + + """ + if x is None: + x = Symbol('x') + + fact = And( + # primitive predicates for extended real exclude each other. + Exclusive(Q.negative_infinite(x), Q.negative(x), Q.zero(x), + Q.positive(x), Q.positive_infinite(x)), + + # build complex plane + Exclusive(Q.real(x), Q.imaginary(x)), + Implies(Q.real(x) | Q.imaginary(x), Q.complex(x)), + + # other subsets of complex + Exclusive(Q.transcendental(x), Q.algebraic(x)), + Equivalent(Q.real(x), Q.rational(x) | Q.irrational(x)), + Exclusive(Q.irrational(x), Q.rational(x)), + Implies(Q.rational(x), Q.algebraic(x)), + + # integers + Exclusive(Q.even(x), Q.odd(x)), + Implies(Q.integer(x), Q.rational(x)), + Implies(Q.zero(x), Q.even(x)), + Exclusive(Q.composite(x), Q.prime(x)), + Implies(Q.composite(x) | Q.prime(x), Q.integer(x) & Q.positive(x)), + Implies(Q.even(x) & Q.positive(x) & ~Q.prime(x), Q.composite(x)), + + # hermitian and antihermitian + Implies(Q.real(x), Q.hermitian(x)), + Implies(Q.imaginary(x), Q.antihermitian(x)), + Implies(Q.zero(x), Q.hermitian(x) | Q.antihermitian(x)), + + # define finity and infinity, and build extended real line + Exclusive(Q.infinite(x), Q.finite(x)), + Implies(Q.complex(x), Q.finite(x)), + Implies(Q.negative_infinite(x) | Q.positive_infinite(x), Q.infinite(x)), + + # commutativity + Implies(Q.finite(x) | Q.infinite(x), Q.commutative(x)), + ) + return fact + + +@cacheit +def get_matrix_facts(x = None): + """ + Facts between unary matrix predicates. + + Parameters + ========== + + x : Symbol, optional + Placeholder symbol for unary facts. Default is ``Symbol('x')``. + + Returns + ======= + + fact : Known facts in conjugated normal form. + + """ + if x is None: + x = Symbol('x') + + fact = And( + # matrices + Implies(Q.orthogonal(x), Q.positive_definite(x)), + Implies(Q.orthogonal(x), Q.unitary(x)), + Implies(Q.unitary(x) & Q.real_elements(x), Q.orthogonal(x)), + Implies(Q.unitary(x), Q.normal(x)), + Implies(Q.unitary(x), Q.invertible(x)), + Implies(Q.normal(x), Q.square(x)), + Implies(Q.diagonal(x), Q.normal(x)), + Implies(Q.positive_definite(x), Q.invertible(x)), + Implies(Q.diagonal(x), Q.upper_triangular(x)), + Implies(Q.diagonal(x), Q.lower_triangular(x)), + Implies(Q.lower_triangular(x), Q.triangular(x)), + Implies(Q.upper_triangular(x), Q.triangular(x)), + Implies(Q.triangular(x), Q.upper_triangular(x) | Q.lower_triangular(x)), + Implies(Q.upper_triangular(x) & Q.lower_triangular(x), Q.diagonal(x)), + Implies(Q.diagonal(x), Q.symmetric(x)), + Implies(Q.unit_triangular(x), Q.triangular(x)), + Implies(Q.invertible(x), Q.fullrank(x)), + Implies(Q.invertible(x), Q.square(x)), + Implies(Q.symmetric(x), Q.square(x)), + Implies(Q.fullrank(x) & Q.square(x), Q.invertible(x)), + Equivalent(Q.invertible(x), ~Q.singular(x)), + Implies(Q.integer_elements(x), Q.real_elements(x)), + Implies(Q.real_elements(x), Q.complex_elements(x)), + ) + return fact + + + +def generate_known_facts_dict(keys, fact): + """ + Computes and returns a dictionary which contains the relations between + unary predicates. + + Each key is a predicate, and item is two groups of predicates. + First group contains the predicates which are implied by the key, and + second group contains the predicates which are rejected by the key. + + All predicates in *keys* and *fact* must be unary and have same placeholder + symbol. + + Parameters + ========== + + keys : list of AppliedPredicate instances. + + fact : Fact between predicates in conjugated normal form. + + Examples + ======== + + >>> from sympy import Q, And, Implies + >>> from sympy.assumptions.facts import generate_known_facts_dict + >>> from sympy.abc import x + >>> keys = [Q.even(x), Q.odd(x), Q.zero(x)] + >>> fact = And(Implies(Q.even(x), ~Q.odd(x)), + ... Implies(Q.zero(x), Q.even(x))) + >>> generate_known_facts_dict(keys, fact) + {Q.even: ({Q.even}, {Q.odd}), + Q.odd: ({Q.odd}, {Q.even, Q.zero}), + Q.zero: ({Q.even, Q.zero}, {Q.odd})} + """ + fact_cnf = to_cnf(fact) + mapping = single_fact_lookup(keys, fact_cnf) + + ret = {} + for key, value in mapping.items(): + implied = set() + rejected = set() + for expr in value: + if isinstance(expr, AppliedPredicate): + implied.add(expr.function) + elif isinstance(expr, Not): + pred = expr.args[0] + rejected.add(pred.function) + ret[key.function] = (implied, rejected) + return ret + + +@cacheit +def get_known_facts_keys(): + """ + Return every unary predicates registered to ``Q``. + + This function is used to generate the keys for + ``generate_known_facts_dict``. + + """ + # exclude polyadic predicates + exclude = {Q.eq, Q.ne, Q.gt, Q.lt, Q.ge, Q.le} + + result = [] + for attr in Q.__class__.__dict__: + if attr.startswith('__'): + continue + pred = getattr(Q, attr) + if pred in exclude: + continue + result.append(pred) + return result + + +def single_fact_lookup(known_facts_keys, known_facts_cnf): + # Return the dictionary for quick lookup of single fact + mapping = {} + for key in known_facts_keys: + mapping[key] = {key} + for other_key in known_facts_keys: + if other_key != key: + if ask_full_inference(other_key, key, known_facts_cnf): + mapping[key].add(other_key) + if ask_full_inference(~other_key, key, known_facts_cnf): + mapping[key].add(~other_key) + return mapping + + +def ask_full_inference(proposition, assumptions, known_facts_cnf): + """ + Method for inferring properties about objects. + + """ + if not satisfiable(And(known_facts_cnf, assumptions, proposition)): + return False + if not satisfiable(And(known_facts_cnf, assumptions, Not(proposition))): + return True + return None diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/__init__.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/__init__.py new file mode 100644 index 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@@ +""" +This module contains query handlers responsible for calculus queries: +infinitesimal, finite, etc. +""" + +from sympy.assumptions import Q, ask +from sympy.core import Add, Mul, Pow, Symbol +from sympy.core.numbers import (NegativeInfinity, GoldenRatio, + Infinity, Exp1, ComplexInfinity, ImaginaryUnit, NaN, Number, Pi, E, + TribonacciConstant) +from sympy.functions import cos, exp, log, sign, sin +from sympy.logic.boolalg import conjuncts + +from ..predicates.calculus import (FinitePredicate, InfinitePredicate, + PositiveInfinitePredicate, NegativeInfinitePredicate) + + +# FinitePredicate + + +@FinitePredicate.register(Symbol) +def _(expr, assumptions): + """ + Handles Symbol. + """ + if expr.is_finite is not None: + return expr.is_finite + if Q.finite(expr) in conjuncts(assumptions): + return True + return None + +@FinitePredicate.register(Add) +def _(expr, assumptions): + """ + Return True if expr is bounded, False if not and None if unknown. + + Truth Table: + + +-------+-----+-----------+-----------+ + | | | | | + | | B | U | ? | + | | | | | + +-------+-----+---+---+---+---+---+---+ + | | | | | | | | | + | | |'+'|'-'|'x'|'+'|'-'|'x'| + | | | | | | | | | + +-------+-----+---+---+---+---+---+---+ + | | | | | + | B | B | U | ? | + | | | | | + +---+---+-----+---+---+---+---+---+---+ + | | | | | | | | | | + | |'+'| | U | ? | ? | U | ? | ? | + | | | | | | | | | | + | +---+-----+---+---+---+---+---+---+ + | | | | | | | | | | + | U |'-'| | ? | U | ? | ? | U | ? | + | | | | | | | | | | + | +---+-----+---+---+---+---+---+---+ + | | | | | | + | |'x'| | ? | ? | + | | | | | | + +---+---+-----+---+---+---+---+---+---+ + | | | | | + | ? | | | ? | + | | | | | + +-------+-----+-----------+---+---+---+ + + * 'B' = Bounded + + * 'U' = Unbounded + + * '?' = unknown boundedness + + * '+' = positive sign + + * '-' = negative sign + + * 'x' = sign unknown + + * All Bounded -> True + + * 1 Unbounded and the rest Bounded -> False + + * >1 Unbounded, all with same known sign -> False + + * Any Unknown and unknown sign -> None + + * Else -> None + + When the signs are not the same you can have an undefined + result as in oo - oo, hence 'bounded' is also undefined. + """ + sign = -1 # sign of unknown or infinite + result = True + for arg in expr.args: + _bounded = ask(Q.finite(arg), assumptions) + if _bounded: + continue + s = ask(Q.extended_positive(arg), assumptions) + # if there has been more than one sign or if the sign of this arg + # is None and Bounded is None or there was already + # an unknown sign, return None + if sign != -1 and s != sign or \ + s is None and None in (_bounded, sign): + return None + else: + sign = s + # once False, do not change + if result is not False: + result = _bounded + return result + +@FinitePredicate.register(Mul) +def _(expr, assumptions): + """ + Return True if expr is bounded, False if not and None if unknown. + + Truth Table: + + +---+---+---+--------+ + | | | | | + | | B | U | ? | + | | | | | + +---+---+---+---+----+ + | | | | | | + | | | | s | /s | + | | | | | | + +---+---+---+---+----+ + | | | | | + | B | B | U | ? | + | | | | | + +---+---+---+---+----+ + | | | | | | + | U | | U | U | ? | + | | | | | | + +---+---+---+---+----+ + | | | | | + | ? | | | ? | + | | | | | + +---+---+---+---+----+ + + * B = Bounded + + * U = Unbounded + + * ? = unknown boundedness + + * s = signed (hence nonzero) + + * /s = not signed + """ + result = True + for arg in expr.args: + _bounded = ask(Q.finite(arg), assumptions) + if _bounded: + continue + elif _bounded is None: + if result is None: + return None + if ask(Q.extended_nonzero(arg), assumptions) is None: + return None + if result is not False: + result = None + else: + result = False + return result + +@FinitePredicate.register(Pow) +def _(expr, assumptions): + """ + * Unbounded ** NonZero -> Unbounded + + * Bounded ** Bounded -> Bounded + + * Abs()<=1 ** Positive -> Bounded + + * Abs()>=1 ** Negative -> Bounded + + * Otherwise unknown + """ + if expr.base == E: + return ask(Q.finite(expr.exp), assumptions) + + base_bounded = ask(Q.finite(expr.base), assumptions) + exp_bounded = ask(Q.finite(expr.exp), assumptions) + if base_bounded is None and exp_bounded is None: # Common Case + return None + if base_bounded is False and ask(Q.extended_nonzero(expr.exp), assumptions): + return False + if base_bounded and exp_bounded: + return True + if (abs(expr.base) <= 1) == True and ask(Q.extended_positive(expr.exp), assumptions): + return True + if (abs(expr.base) >= 1) == True and ask(Q.extended_negative(expr.exp), assumptions): + return True + if (abs(expr.base) >= 1) == True and exp_bounded is False: + return False + return None + +@FinitePredicate.register(exp) +def _(expr, assumptions): + return ask(Q.finite(expr.exp), assumptions) + +@FinitePredicate.register(log) +def _(expr, assumptions): + # After complex -> finite fact is registered to new assumption system, + # querying Q.infinite may be removed. + if ask(Q.infinite(expr.args[0]), assumptions): + return False + return ask(~Q.zero(expr.args[0]), assumptions) + +@FinitePredicate.register_many(cos, sin, Number, Pi, Exp1, GoldenRatio, + TribonacciConstant, ImaginaryUnit, sign) +def _(expr, assumptions): + return True + +@FinitePredicate.register_many(ComplexInfinity, Infinity, NegativeInfinity) +def _(expr, assumptions): + return False + +@FinitePredicate.register(NaN) +def _(expr, assumptions): + return None + + +# InfinitePredicate + + +@InfinitePredicate.register_many(ComplexInfinity, Infinity, NegativeInfinity) +def _(expr, assumptions): + return True + + +# PositiveInfinitePredicate + + +@PositiveInfinitePredicate.register(Infinity) +def _(expr, assumptions): + return True + + +@PositiveInfinitePredicate.register_many(NegativeInfinity, ComplexInfinity) +def _(expr, assumptions): + return False + + +# NegativeInfinitePredicate + + +@NegativeInfinitePredicate.register(NegativeInfinity) +def _(expr, assumptions): + return True + + +@NegativeInfinitePredicate.register_many(Infinity, ComplexInfinity) +def _(expr, assumptions): + return False diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/common.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/common.py new file mode 100644 index 0000000000000000000000000000000000000000..b89ffe8402e789e6d1e2b42d955bf1096c615237 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/handlers/common.py @@ -0,0 +1,156 @@ +""" +This module defines base class for handlers and some core handlers: +``Q.commutative`` and ``Q.is_true``. +""" + +from sympy.assumptions import Q, ask, AppliedPredicate +from sympy.core import Basic, Symbol +from sympy.core.logic import _fuzzy_group +from sympy.core.numbers import NaN, Number +from sympy.logic.boolalg import (And, BooleanTrue, BooleanFalse, conjuncts, + Equivalent, Implies, Not, Or) +from sympy.utilities.exceptions import sympy_deprecation_warning + +from ..predicates.common import CommutativePredicate, IsTruePredicate + + +class AskHandler: + """Base class that all Ask Handlers must inherit.""" + def __new__(cls, *args, **kwargs): + sympy_deprecation_warning( + """ + The AskHandler system is deprecated. The AskHandler class should + be replaced with the multipledispatch handler of Predicate + """, + deprecated_since_version="1.8", + active_deprecations_target='deprecated-askhandler', + ) + return super().__new__(cls, *args, **kwargs) + + +class CommonHandler(AskHandler): + # Deprecated + """Defines some useful methods common to most Handlers. """ + + @staticmethod + def AlwaysTrue(expr, assumptions): + return True + + @staticmethod + def AlwaysFalse(expr, assumptions): + return False + + @staticmethod + def AlwaysNone(expr, assumptions): + return None + + NaN = AlwaysFalse + + +# CommutativePredicate + +@CommutativePredicate.register(Symbol) +def _(expr, assumptions): + """Objects are expected to be commutative unless otherwise stated""" + assumps = conjuncts(assumptions) + if expr.is_commutative is not None: + return expr.is_commutative and not ~Q.commutative(expr) in assumps + if Q.commutative(expr) in assumps: + return True + elif ~Q.commutative(expr) in assumps: + return False + return True + +@CommutativePredicate.register(Basic) +def _(expr, assumptions): + for arg in expr.args: + if not ask(Q.commutative(arg), assumptions): + return False + return True + +@CommutativePredicate.register(Number) +def _(expr, assumptions): + return True + +@CommutativePredicate.register(NaN) +def _(expr, assumptions): + return True + + +# IsTruePredicate + +@IsTruePredicate.register(bool) +def _(expr, assumptions): + return expr + +@IsTruePredicate.register(BooleanTrue) +def _(expr, assumptions): + return True + +@IsTruePredicate.register(BooleanFalse) +def _(expr, assumptions): + return False + +@IsTruePredicate.register(AppliedPredicate) +def _(expr, assumptions): + return ask(expr, assumptions) + +@IsTruePredicate.register(Not) +def _(expr, assumptions): + arg = expr.args[0] + if arg.is_Symbol: + # symbol used as abstract boolean object + return None + value = ask(arg, assumptions=assumptions) + if value in (True, False): + return not value + else: + return None + +@IsTruePredicate.register(Or) +def _(expr, assumptions): + result = False + for arg in expr.args: + p = ask(arg, assumptions=assumptions) + if p is True: + return True + if p is None: + result = None + return result + +@IsTruePredicate.register(And) +def _(expr, assumptions): + result = True + for arg in expr.args: + p = ask(arg, assumptions=assumptions) + if p is False: + return False + if p is None: + result = None + return result + +@IsTruePredicate.register(Implies) +def _(expr, assumptions): + p, q = expr.args + return ask(~p | q, assumptions=assumptions) + +@IsTruePredicate.register(Equivalent) +def _(expr, assumptions): + p, q = expr.args + pt = ask(p, assumptions=assumptions) + if pt is None: + return None + qt = ask(q, assumptions=assumptions) + if qt is None: + return None + return pt == qt + + +#### Helper methods +def test_closed_group(expr, assumptions, key): + """ + Test for membership in a group with respect + to the current operation. + """ + return _fuzzy_group( + (ask(key(a), assumptions) for a in expr.args), quick_exit=True) diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/matrices.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/matrices.py new file mode 100644 index 0000000000000000000000000000000000000000..3b20385360136629ea037eb7238c45b70ba57fd2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/handlers/matrices.py @@ -0,0 +1,716 @@ +""" +This module contains query handlers responsible for Matrices queries: +Square, Symmetric, Invertible etc. +""" + +from sympy.logic.boolalg import conjuncts +from sympy.assumptions import Q, ask +from sympy.assumptions.handlers import test_closed_group +from sympy.matrices import MatrixBase +from sympy.matrices.expressions import (BlockMatrix, BlockDiagMatrix, Determinant, + DiagMatrix, DiagonalMatrix, HadamardProduct, Identity, Inverse, MatAdd, MatMul, + MatPow, MatrixExpr, MatrixSlice, MatrixSymbol, OneMatrix, Trace, Transpose, + ZeroMatrix) +from sympy.matrices.expressions.blockmatrix import reblock_2x2 +from sympy.matrices.expressions.factorizations import Factorization +from sympy.matrices.expressions.fourier import DFT +from sympy.core.logic import fuzzy_and +from sympy.utilities.iterables import sift +from sympy.core import Basic + +from ..predicates.matrices import (SquarePredicate, SymmetricPredicate, + InvertiblePredicate, OrthogonalPredicate, UnitaryPredicate, + FullRankPredicate, PositiveDefinitePredicate, UpperTriangularPredicate, + LowerTriangularPredicate, DiagonalPredicate, IntegerElementsPredicate, + RealElementsPredicate, ComplexElementsPredicate) + + +def _Factorization(predicate, expr, assumptions): + if predicate in expr.predicates: + return True + + +# SquarePredicate + +@SquarePredicate.register(MatrixExpr) +def _(expr, assumptions): + return expr.shape[0] == expr.shape[1] + + +# SymmetricPredicate + +@SymmetricPredicate.register(MatMul) +def _(expr, assumptions): + factor, mmul = expr.as_coeff_mmul() + if all(ask(Q.symmetric(arg), assumptions) for arg in mmul.args): + return True + # TODO: implement sathandlers system for the matrices. + # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric). + if ask(Q.diagonal(expr), assumptions): + return True + if len(mmul.args) >= 2 and mmul.args[0] == mmul.args[-1].T: + if len(mmul.args) == 2: + return True + return ask(Q.symmetric(MatMul(*mmul.args[1:-1])), assumptions) + +@SymmetricPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.symmetric(base), assumptions) + return None + +@SymmetricPredicate.register(MatAdd) +def _(expr, assumptions): + return all(ask(Q.symmetric(arg), assumptions) for arg in expr.args) + +@SymmetricPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if not expr.is_square: + return False + # TODO: implement sathandlers system for the matrices. + # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric). + if ask(Q.diagonal(expr), assumptions): + return True + if Q.symmetric(expr) in conjuncts(assumptions): + return True + +@SymmetricPredicate.register_many(OneMatrix, ZeroMatrix) +def _(expr, assumptions): + return ask(Q.square(expr), assumptions) + +@SymmetricPredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.symmetric(expr.arg), assumptions) + +@SymmetricPredicate.register(MatrixSlice) +def _(expr, assumptions): + # TODO: implement sathandlers system for the matrices. + # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric). + if ask(Q.diagonal(expr), assumptions): + return True + if not expr.on_diag: + return None + else: + return ask(Q.symmetric(expr.parent), assumptions) + +@SymmetricPredicate.register(Identity) +def _(expr, assumptions): + return True + + +# InvertiblePredicate + +@InvertiblePredicate.register(MatMul) +def _(expr, assumptions): + factor, mmul = expr.as_coeff_mmul() + if all(ask(Q.invertible(arg), assumptions) for arg in mmul.args): + return True + if any(ask(Q.invertible(arg), assumptions) is False + for arg in mmul.args): + return False + +@InvertiblePredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + if exp.is_negative == False: + return ask(Q.invertible(base), assumptions) + return None + +@InvertiblePredicate.register(MatAdd) +def _(expr, assumptions): + return None + +@InvertiblePredicate.register(MatrixSymbol) +def _(expr, assumptions): + if not expr.is_square: + return False + if Q.invertible(expr) in conjuncts(assumptions): + return True + +@InvertiblePredicate.register_many(Identity, Inverse) +def _(expr, assumptions): + return True + +@InvertiblePredicate.register(ZeroMatrix) +def _(expr, assumptions): + return False + +@InvertiblePredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@InvertiblePredicate.register(Transpose) +def _(expr, assumptions): + return ask(Q.invertible(expr.arg), assumptions) + +@InvertiblePredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.invertible(expr.parent), assumptions) + +@InvertiblePredicate.register(MatrixBase) +def _(expr, assumptions): + if not expr.is_square: + return False + return expr.rank() == expr.rows + +@InvertiblePredicate.register(MatrixExpr) +def _(expr, assumptions): + if not expr.is_square: + return False + return None + +@InvertiblePredicate.register(BlockMatrix) +def _(expr, assumptions): + if not expr.is_square: + return False + if expr.blockshape == (1, 1): + return ask(Q.invertible(expr.blocks[0, 0]), assumptions) + expr = reblock_2x2(expr) + if expr.blockshape == (2, 2): + [[A, B], [C, D]] = expr.blocks.tolist() + if ask(Q.invertible(A), assumptions) == True: + invertible = ask(Q.invertible(D - C * A.I * B), assumptions) + if invertible is not None: + return invertible + if ask(Q.invertible(B), assumptions) == True: + invertible = ask(Q.invertible(C - D * B.I * A), assumptions) + if invertible is not None: + return invertible + if ask(Q.invertible(C), assumptions) == True: + invertible = ask(Q.invertible(B - A * C.I * D), assumptions) + if invertible is not None: + return invertible + if ask(Q.invertible(D), assumptions) == True: + invertible = ask(Q.invertible(A - B * D.I * C), assumptions) + if invertible is not None: + return invertible + return None + +@InvertiblePredicate.register(BlockDiagMatrix) +def _(expr, assumptions): + if expr.rowblocksizes != expr.colblocksizes: + return None + return fuzzy_and([ask(Q.invertible(a), assumptions) for a in expr.diag]) + + +# OrthogonalPredicate + +@OrthogonalPredicate.register(MatMul) +def _(expr, assumptions): + factor, mmul = expr.as_coeff_mmul() + if (all(ask(Q.orthogonal(arg), assumptions) for arg in mmul.args) and + factor == 1): + return True + if any(ask(Q.invertible(arg), assumptions) is False + for arg in mmul.args): + return False + +@OrthogonalPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if int_exp: + return ask(Q.orthogonal(base), assumptions) + return None + +@OrthogonalPredicate.register(MatAdd) +def _(expr, assumptions): + if (len(expr.args) == 1 and + ask(Q.orthogonal(expr.args[0]), assumptions)): + return True + +@OrthogonalPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if (not expr.is_square or + ask(Q.invertible(expr), assumptions) is False): + return False + if Q.orthogonal(expr) in conjuncts(assumptions): + return True + +@OrthogonalPredicate.register(Identity) +def _(expr, assumptions): + return True + +@OrthogonalPredicate.register(ZeroMatrix) +def _(expr, assumptions): + return False + +@OrthogonalPredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.orthogonal(expr.arg), assumptions) + +@OrthogonalPredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.orthogonal(expr.parent), assumptions) + +@OrthogonalPredicate.register(Factorization) +def _(expr, assumptions): + return _Factorization(Q.orthogonal, expr, assumptions) + + +# UnitaryPredicate + +@UnitaryPredicate.register(MatMul) +def _(expr, assumptions): + factor, mmul = expr.as_coeff_mmul() + if (all(ask(Q.unitary(arg), assumptions) for arg in mmul.args) and + abs(factor) == 1): + return True + if any(ask(Q.invertible(arg), assumptions) is False + for arg in mmul.args): + return False + +@UnitaryPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if int_exp: + return ask(Q.unitary(base), assumptions) + return None + +@UnitaryPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if (not expr.is_square or + ask(Q.invertible(expr), assumptions) is False): + return False + if Q.unitary(expr) in conjuncts(assumptions): + return True + +@UnitaryPredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.unitary(expr.arg), assumptions) + +@UnitaryPredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.unitary(expr.parent), assumptions) + +@UnitaryPredicate.register_many(DFT, Identity) +def _(expr, assumptions): + return True + +@UnitaryPredicate.register(ZeroMatrix) +def _(expr, assumptions): + return False + +@UnitaryPredicate.register(Factorization) +def _(expr, assumptions): + return _Factorization(Q.unitary, expr, assumptions) + + +# FullRankPredicate + +@FullRankPredicate.register(MatMul) +def _(expr, assumptions): + if all(ask(Q.fullrank(arg), assumptions) for arg in expr.args): + return True + +@FullRankPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if int_exp and ask(~Q.negative(exp), assumptions): + return ask(Q.fullrank(base), assumptions) + return None + +@FullRankPredicate.register(Identity) +def _(expr, assumptions): + return True + +@FullRankPredicate.register(ZeroMatrix) +def _(expr, assumptions): + return False + +@FullRankPredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@FullRankPredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.fullrank(expr.arg), assumptions) + +@FullRankPredicate.register(MatrixSlice) +def _(expr, assumptions): + if ask(Q.orthogonal(expr.parent), assumptions): + return True + + +# PositiveDefinitePredicate + +@PositiveDefinitePredicate.register(MatMul) +def _(expr, assumptions): + factor, mmul = expr.as_coeff_mmul() + if (all(ask(Q.positive_definite(arg), assumptions) + for arg in mmul.args) and factor > 0): + return True + if (len(mmul.args) >= 2 + and mmul.args[0] == mmul.args[-1].T + and ask(Q.fullrank(mmul.args[0]), assumptions)): + return ask(Q.positive_definite( + MatMul(*mmul.args[1:-1])), assumptions) + +@PositiveDefinitePredicate.register(MatPow) +def _(expr, assumptions): + # a power of a positive definite matrix is positive definite + if ask(Q.positive_definite(expr.args[0]), assumptions): + return True + +@PositiveDefinitePredicate.register(MatAdd) +def _(expr, assumptions): + if all(ask(Q.positive_definite(arg), assumptions) + for arg in expr.args): + return True + +@PositiveDefinitePredicate.register(MatrixSymbol) +def _(expr, assumptions): + if not expr.is_square: + return False + if Q.positive_definite(expr) in conjuncts(assumptions): + return True + +@PositiveDefinitePredicate.register(Identity) +def _(expr, assumptions): + return True + +@PositiveDefinitePredicate.register(ZeroMatrix) +def _(expr, assumptions): + return False + +@PositiveDefinitePredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@PositiveDefinitePredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.positive_definite(expr.arg), assumptions) + +@PositiveDefinitePredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.positive_definite(expr.parent), assumptions) + + +# UpperTriangularPredicate + +@UpperTriangularPredicate.register(MatMul) +def _(expr, assumptions): + factor, matrices = expr.as_coeff_matrices() + if all(ask(Q.upper_triangular(m), assumptions) for m in matrices): + return True + +@UpperTriangularPredicate.register(MatAdd) +def _(expr, assumptions): + if all(ask(Q.upper_triangular(arg), assumptions) for arg in expr.args): + return True + +@UpperTriangularPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.upper_triangular(base), assumptions) + return None + +@UpperTriangularPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if Q.upper_triangular(expr) in conjuncts(assumptions): + return True + +@UpperTriangularPredicate.register_many(Identity, ZeroMatrix) +def _(expr, assumptions): + return True + +@UpperTriangularPredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@UpperTriangularPredicate.register(Transpose) +def _(expr, assumptions): + return ask(Q.lower_triangular(expr.arg), assumptions) + +@UpperTriangularPredicate.register(Inverse) +def _(expr, assumptions): + return ask(Q.upper_triangular(expr.arg), assumptions) + +@UpperTriangularPredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.upper_triangular(expr.parent), assumptions) + +@UpperTriangularPredicate.register(Factorization) +def _(expr, assumptions): + return _Factorization(Q.upper_triangular, expr, assumptions) + +# LowerTriangularPredicate + +@LowerTriangularPredicate.register(MatMul) +def _(expr, assumptions): + factor, matrices = expr.as_coeff_matrices() + if all(ask(Q.lower_triangular(m), assumptions) for m in matrices): + return True + +@LowerTriangularPredicate.register(MatAdd) +def _(expr, assumptions): + if all(ask(Q.lower_triangular(arg), assumptions) for arg in expr.args): + return True + +@LowerTriangularPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.lower_triangular(base), assumptions) + return None + +@LowerTriangularPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if Q.lower_triangular(expr) in conjuncts(assumptions): + return True + +@LowerTriangularPredicate.register_many(Identity, ZeroMatrix) +def _(expr, assumptions): + return True + +@LowerTriangularPredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@LowerTriangularPredicate.register(Transpose) +def _(expr, assumptions): + return ask(Q.upper_triangular(expr.arg), assumptions) + +@LowerTriangularPredicate.register(Inverse) +def _(expr, assumptions): + return ask(Q.lower_triangular(expr.arg), assumptions) + +@LowerTriangularPredicate.register(MatrixSlice) +def _(expr, assumptions): + if not expr.on_diag: + return None + else: + return ask(Q.lower_triangular(expr.parent), assumptions) + +@LowerTriangularPredicate.register(Factorization) +def _(expr, assumptions): + return _Factorization(Q.lower_triangular, expr, assumptions) + + +# DiagonalPredicate + +def _is_empty_or_1x1(expr): + return expr.shape in ((0, 0), (1, 1)) + +@DiagonalPredicate.register(MatMul) +def _(expr, assumptions): + if _is_empty_or_1x1(expr): + return True + factor, matrices = expr.as_coeff_matrices() + if all(ask(Q.diagonal(m), assumptions) for m in matrices): + return True + +@DiagonalPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.diagonal(base), assumptions) + return None + +@DiagonalPredicate.register(MatAdd) +def _(expr, assumptions): + if all(ask(Q.diagonal(arg), assumptions) for arg in expr.args): + return True + +@DiagonalPredicate.register(MatrixSymbol) +def _(expr, assumptions): + if _is_empty_or_1x1(expr): + return True + if Q.diagonal(expr) in conjuncts(assumptions): + return True + +@DiagonalPredicate.register(OneMatrix) +def _(expr, assumptions): + return expr.shape[0] == 1 and expr.shape[1] == 1 + +@DiagonalPredicate.register_many(Inverse, Transpose) +def _(expr, assumptions): + return ask(Q.diagonal(expr.arg), assumptions) + +@DiagonalPredicate.register(MatrixSlice) +def _(expr, assumptions): + if _is_empty_or_1x1(expr): + return True + if not expr.on_diag: + return None + else: + return ask(Q.diagonal(expr.parent), assumptions) + +@DiagonalPredicate.register_many(DiagonalMatrix, DiagMatrix, Identity, ZeroMatrix) +def _(expr, assumptions): + return True + +@DiagonalPredicate.register(Factorization) +def _(expr, assumptions): + return _Factorization(Q.diagonal, expr, assumptions) + + +# IntegerElementsPredicate + +def BM_elements(predicate, expr, assumptions): + """ Block Matrix elements. """ + return all(ask(predicate(b), assumptions) for b in expr.blocks) + +def MS_elements(predicate, expr, assumptions): + """ Matrix Slice elements. """ + return ask(predicate(expr.parent), assumptions) + +def MatMul_elements(matrix_predicate, scalar_predicate, expr, assumptions): + d = sift(expr.args, lambda x: isinstance(x, MatrixExpr)) + factors, matrices = d[False], d[True] + return fuzzy_and([ + test_closed_group(Basic(*factors), assumptions, scalar_predicate), + test_closed_group(Basic(*matrices), assumptions, matrix_predicate)]) + + +@IntegerElementsPredicate.register_many(Determinant, HadamardProduct, MatAdd, + Trace, Transpose) +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.integer_elements) + +@IntegerElementsPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + if exp.is_negative == False: + return ask(Q.integer_elements(base), assumptions) + return None + +@IntegerElementsPredicate.register_many(Identity, OneMatrix, ZeroMatrix) +def _(expr, assumptions): + return True + +@IntegerElementsPredicate.register(MatMul) +def _(expr, assumptions): + return MatMul_elements(Q.integer_elements, Q.integer, expr, assumptions) + +@IntegerElementsPredicate.register(MatrixSlice) +def _(expr, assumptions): + return MS_elements(Q.integer_elements, expr, assumptions) + +@IntegerElementsPredicate.register(BlockMatrix) +def _(expr, assumptions): + return BM_elements(Q.integer_elements, expr, assumptions) + + +# RealElementsPredicate + +@RealElementsPredicate.register_many(Determinant, Factorization, HadamardProduct, + MatAdd, Trace, Transpose) +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.real_elements) + +@RealElementsPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.real_elements(base), assumptions) + return None + +@RealElementsPredicate.register(MatMul) +def _(expr, assumptions): + return MatMul_elements(Q.real_elements, Q.real, expr, assumptions) + +@RealElementsPredicate.register(MatrixSlice) +def _(expr, assumptions): + return MS_elements(Q.real_elements, expr, assumptions) + +@RealElementsPredicate.register(BlockMatrix) +def _(expr, assumptions): + return BM_elements(Q.real_elements, expr, assumptions) + + +# ComplexElementsPredicate + +@ComplexElementsPredicate.register_many(Determinant, Factorization, HadamardProduct, + Inverse, MatAdd, Trace, Transpose) +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.complex_elements) + +@ComplexElementsPredicate.register(MatPow) +def _(expr, assumptions): + # only for integer powers + base, exp = expr.args + int_exp = ask(Q.integer(exp), assumptions) + if not int_exp: + return None + non_negative = ask(~Q.negative(exp), assumptions) + if (non_negative or non_negative == False + and ask(Q.invertible(base), assumptions)): + return ask(Q.complex_elements(base), assumptions) + return None + +@ComplexElementsPredicate.register(MatMul) +def _(expr, assumptions): + return MatMul_elements(Q.complex_elements, Q.complex, expr, assumptions) + +@ComplexElementsPredicate.register(MatrixSlice) +def _(expr, assumptions): + return MS_elements(Q.complex_elements, expr, assumptions) + +@ComplexElementsPredicate.register(BlockMatrix) +def _(expr, assumptions): + return BM_elements(Q.complex_elements, expr, assumptions) + +@ComplexElementsPredicate.register(DFT) +def _(expr, assumptions): + return True diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/ntheory.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/ntheory.py new file mode 100644 index 0000000000000000000000000000000000000000..ccb91f726e2ee5c10d915725f60f5093934d4e7b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/handlers/ntheory.py @@ -0,0 +1,269 @@ +""" +Handlers for keys related to number theory: prime, even, odd, etc. +""" + +from sympy.assumptions import Q, ask +from sympy.core import Add, Basic, Expr, Float, Mul, Pow, S +from sympy.core.numbers import (ImaginaryUnit, Infinity, Integer, NaN, + NegativeInfinity, NumberSymbol, Rational, int_valued) +from sympy.functions import Abs, im, re +from sympy.ntheory import isprime + +from sympy.multipledispatch import MDNotImplementedError + +from ..predicates.ntheory import (PrimePredicate, CompositePredicate, + EvenPredicate, OddPredicate) + + +# PrimePredicate + +def _PrimePredicate_number(expr, assumptions): + # helper method + exact = not expr.atoms(Float) + try: + i = int(expr.round()) + if (expr - i).equals(0) is False: + raise TypeError + except TypeError: + return False + if exact: + return isprime(i) + # when not exact, we won't give a True or False + # since the number represents an approximate value + +@PrimePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_prime + if ret is None: + raise MDNotImplementedError + return ret + +@PrimePredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + return _PrimePredicate_number(expr, assumptions) + +@PrimePredicate.register(Mul) +def _(expr, assumptions): + if expr.is_number: + return _PrimePredicate_number(expr, assumptions) + for arg in expr.args: + if not ask(Q.integer(arg), assumptions): + return None + for arg in expr.args: + if arg.is_number and arg.is_composite: + return False + +@PrimePredicate.register(Pow) +def _(expr, assumptions): + """ + Integer**Integer -> !Prime + """ + if expr.is_number: + return _PrimePredicate_number(expr, assumptions) + if ask(Q.integer(expr.exp), assumptions) and \ + ask(Q.integer(expr.base), assumptions): + return False + +@PrimePredicate.register(Integer) +def _(expr, assumptions): + return isprime(expr) + +@PrimePredicate.register_many(Rational, Infinity, NegativeInfinity, ImaginaryUnit) +def _(expr, assumptions): + return False + +@PrimePredicate.register(Float) +def _(expr, assumptions): + return _PrimePredicate_number(expr, assumptions) + +@PrimePredicate.register(NumberSymbol) +def _(expr, assumptions): + return _PrimePredicate_number(expr, assumptions) + +@PrimePredicate.register(NaN) +def _(expr, assumptions): + return None + + +# CompositePredicate + +@CompositePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_composite + if ret is None: + raise MDNotImplementedError + return ret + +@CompositePredicate.register(Basic) +def _(expr, assumptions): + _positive = ask(Q.positive(expr), assumptions) + if _positive: + _integer = ask(Q.integer(expr), assumptions) + if _integer: + _prime = ask(Q.prime(expr), assumptions) + if _prime is None: + return + # Positive integer which is not prime is not + # necessarily composite + if expr.equals(1): + return False + return not _prime + else: + return _integer + else: + return _positive + + +# EvenPredicate + +def _EvenPredicate_number(expr, assumptions): + # helper method + if isinstance(expr, (float, Float)): + if int_valued(expr): + return None + return False + try: + i = int(expr.round()) + except TypeError: + return False + if not (expr - i).equals(0): + return False + return i % 2 == 0 + +@EvenPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_even + if ret is None: + raise MDNotImplementedError + return ret + +@EvenPredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + return _EvenPredicate_number(expr, assumptions) + +@EvenPredicate.register(Mul) +def _(expr, assumptions): + """ + Even * Integer -> Even + Even * Odd -> Even + Integer * Odd -> ? + Odd * Odd -> Odd + Even * Even -> Even + Integer * Integer -> Even if Integer + Integer = Odd + otherwise -> ? + """ + if expr.is_number: + return _EvenPredicate_number(expr, assumptions) + even, odd, irrational, acc = False, 0, False, 1 + for arg in expr.args: + # check for all integers and at least one even + if ask(Q.integer(arg), assumptions): + if ask(Q.even(arg), assumptions): + even = True + elif ask(Q.odd(arg), assumptions): + odd += 1 + elif not even and acc != 1: + if ask(Q.odd(acc + arg), assumptions): + even = True + elif ask(Q.irrational(arg), assumptions): + # one irrational makes the result False + # two makes it undefined + if irrational: + break + irrational = True + else: + break + acc = arg + else: + if irrational: + return False + if even: + return True + if odd == len(expr.args): + return False + +@EvenPredicate.register(Add) +def _(expr, assumptions): + """ + Even + Odd -> Odd + Even + Even -> Even + Odd + Odd -> Even + + """ + if expr.is_number: + return _EvenPredicate_number(expr, assumptions) + _result = True + for arg in expr.args: + if ask(Q.even(arg), assumptions): + pass + elif ask(Q.odd(arg), assumptions): + _result = not _result + else: + break + else: + return _result + +@EvenPredicate.register(Pow) +def _(expr, assumptions): + if expr.is_number: + return _EvenPredicate_number(expr, assumptions) + if ask(Q.integer(expr.exp), assumptions): + if ask(Q.positive(expr.exp), assumptions): + return ask(Q.even(expr.base), assumptions) + elif ask(~Q.negative(expr.exp) & Q.odd(expr.base), assumptions): + return False + elif expr.base is S.NegativeOne: + return False + +@EvenPredicate.register(Integer) +def _(expr, assumptions): + return not bool(expr.p & 1) + +@EvenPredicate.register_many(Rational, Infinity, NegativeInfinity, ImaginaryUnit) +def _(expr, assumptions): + return False + +@EvenPredicate.register(NumberSymbol) +def _(expr, assumptions): + return _EvenPredicate_number(expr, assumptions) + +@EvenPredicate.register(Abs) +def _(expr, assumptions): + if ask(Q.real(expr.args[0]), assumptions): + return ask(Q.even(expr.args[0]), assumptions) + +@EvenPredicate.register(re) +def _(expr, assumptions): + if ask(Q.real(expr.args[0]), assumptions): + return ask(Q.even(expr.args[0]), assumptions) + +@EvenPredicate.register(im) +def _(expr, assumptions): + if ask(Q.real(expr.args[0]), assumptions): + return True + +@EvenPredicate.register(NaN) +def _(expr, assumptions): + return None + + +# OddPredicate + +@OddPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_odd + if ret is None: + raise MDNotImplementedError + return ret + +@OddPredicate.register(Basic) +def _(expr, assumptions): + _integer = ask(Q.integer(expr), assumptions) + if _integer: + _even = ask(Q.even(expr), assumptions) + if _even is None: + return None + return not _even + return _integer diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/order.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/order.py new file mode 100644 index 0000000000000000000000000000000000000000..f4a5378c20a9fcf152914fc5cc9488583f2e39a3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/handlers/order.py @@ -0,0 +1,436 @@ +""" +Handlers related to order relations: positive, negative, etc. +""" + +from sympy.assumptions import Q, ask +from sympy.core import Add, Basic, Expr, Mul, Pow +from sympy.core.logic import fuzzy_not, fuzzy_and, fuzzy_or +from sympy.core.numbers import E, ImaginaryUnit, NaN, I, pi +from sympy.functions import Abs, acos, acot, asin, atan, exp, factorial, log +from sympy.matrices import Determinant, Trace +from sympy.matrices.expressions.matexpr import MatrixElement + +from sympy.multipledispatch import MDNotImplementedError + +from ..predicates.order import (NegativePredicate, NonNegativePredicate, + NonZeroPredicate, ZeroPredicate, NonPositivePredicate, PositivePredicate, + ExtendedNegativePredicate, ExtendedNonNegativePredicate, + ExtendedNonPositivePredicate, ExtendedNonZeroPredicate, + ExtendedPositivePredicate,) + + +# NegativePredicate + +def _NegativePredicate_number(expr, assumptions): + r, i = expr.as_real_imag() + # If the imaginary part can symbolically be shown to be zero then + # we just evaluate the real part; otherwise we evaluate the imaginary + # part to see if it actually evaluates to zero and if it does then + # we make the comparison between the real part and zero. + if not i: + r = r.evalf(2) + if r._prec != 1: + return r < 0 + else: + i = i.evalf(2) + if i._prec != 1: + if i != 0: + return False + r = r.evalf(2) + if r._prec != 1: + return r < 0 + +@NegativePredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + return _NegativePredicate_number(expr, assumptions) + +@NegativePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_negative + if ret is None: + raise MDNotImplementedError + return ret + +@NegativePredicate.register(Add) +def _(expr, assumptions): + """ + Positive + Positive -> Positive, + Negative + Negative -> Negative + """ + if expr.is_number: + return _NegativePredicate_number(expr, assumptions) + + r = ask(Q.real(expr), assumptions) + if r is not True: + return r + + nonpos = 0 + for arg in expr.args: + if ask(Q.negative(arg), assumptions) is not True: + if ask(Q.positive(arg), assumptions) is False: + nonpos += 1 + else: + break + else: + if nonpos < len(expr.args): + return True + +@NegativePredicate.register(Mul) +def _(expr, assumptions): + if expr.is_number: + return _NegativePredicate_number(expr, assumptions) + result = None + for arg in expr.args: + if result is None: + result = False + if ask(Q.negative(arg), assumptions): + result = not result + elif ask(Q.positive(arg), assumptions): + pass + else: + return + return result + +@NegativePredicate.register(Pow) +def _(expr, assumptions): + """ + Real ** Even -> NonNegative + Real ** Odd -> same_as_base + NonNegative ** Positive -> NonNegative + """ + if expr.base == E: + # Exponential is always positive: + if ask(Q.real(expr.exp), assumptions): + return False + return + + if expr.is_number: + return _NegativePredicate_number(expr, assumptions) + if ask(Q.real(expr.base), assumptions): + if ask(Q.positive(expr.base), assumptions): + if ask(Q.real(expr.exp), assumptions): + return False + if ask(Q.even(expr.exp), assumptions): + return False + if ask(Q.odd(expr.exp), assumptions): + return ask(Q.negative(expr.base), assumptions) + +@NegativePredicate.register_many(Abs, ImaginaryUnit) +def _(expr, assumptions): + return False + +@NegativePredicate.register(exp) +def _(expr, assumptions): + if ask(Q.real(expr.exp), assumptions): + return False + raise MDNotImplementedError + + +# NonNegativePredicate + +@NonNegativePredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + notnegative = fuzzy_not(_NegativePredicate_number(expr, assumptions)) + if notnegative: + return ask(Q.real(expr), assumptions) + else: + return notnegative + +@NonNegativePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_nonnegative + if ret is None: + raise MDNotImplementedError + return ret + + +# NonZeroPredicate + +@NonZeroPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_nonzero + if ret is None: + raise MDNotImplementedError + return ret + +@NonZeroPredicate.register(Basic) +def _(expr, assumptions): + if ask(Q.real(expr)) is False: + return False + if expr.is_number: + # if there are no symbols just evalf + i = expr.evalf(2) + def nonz(i): + if i._prec != 1: + return i != 0 + return fuzzy_or(nonz(i) for i in i.as_real_imag()) + +@NonZeroPredicate.register(Add) +def _(expr, assumptions): + if all(ask(Q.positive(x), assumptions) for x in expr.args) \ + or all(ask(Q.negative(x), assumptions) for x in expr.args): + return True + +@NonZeroPredicate.register(Mul) +def _(expr, assumptions): + for arg in expr.args: + result = ask(Q.nonzero(arg), assumptions) + if result: + continue + return result + return True + +@NonZeroPredicate.register(Pow) +def _(expr, assumptions): + return ask(Q.nonzero(expr.base), assumptions) + +@NonZeroPredicate.register(Abs) +def _(expr, assumptions): + return ask(Q.nonzero(expr.args[0]), assumptions) + +@NonZeroPredicate.register(NaN) +def _(expr, assumptions): + return None + + +# ZeroPredicate + +@ZeroPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_zero + if ret is None: + raise MDNotImplementedError + return ret + +@ZeroPredicate.register(Basic) +def _(expr, assumptions): + return fuzzy_and([fuzzy_not(ask(Q.nonzero(expr), assumptions)), + ask(Q.real(expr), assumptions)]) + +@ZeroPredicate.register(Mul) +def _(expr, assumptions): + # TODO: This should be deducible from the nonzero handler + return fuzzy_or(ask(Q.zero(arg), assumptions) for arg in expr.args) + + +# NonPositivePredicate + +@NonPositivePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_nonpositive + if ret is None: + raise MDNotImplementedError + return ret + +@NonPositivePredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + notpositive = fuzzy_not(_PositivePredicate_number(expr, assumptions)) + if notpositive: + return ask(Q.real(expr), assumptions) + else: + return notpositive + + +# PositivePredicate + +def _PositivePredicate_number(expr, assumptions): + r, i = expr.as_real_imag() + # If the imaginary part can symbolically be shown to be zero then + # we just evaluate the real part; otherwise we evaluate the imaginary + # part to see if it actually evaluates to zero and if it does then + # we make the comparison between the real part and zero. + if not i: + r = r.evalf(2) + if r._prec != 1: + return r > 0 + else: + i = i.evalf(2) + if i._prec != 1: + if i != 0: + return False + r = r.evalf(2) + if r._prec != 1: + return r > 0 + +@PositivePredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_positive + if ret is None: + raise MDNotImplementedError + return ret + +@PositivePredicate.register(Basic) +def _(expr, assumptions): + if expr.is_number: + return _PositivePredicate_number(expr, assumptions) + +@PositivePredicate.register(Mul) +def _(expr, assumptions): + if expr.is_number: + return _PositivePredicate_number(expr, assumptions) + result = True + for arg in expr.args: + if ask(Q.positive(arg), assumptions): + continue + elif ask(Q.negative(arg), assumptions): + result = result ^ True + else: + return + return result + +@PositivePredicate.register(Add) +def _(expr, assumptions): + if expr.is_number: + return _PositivePredicate_number(expr, assumptions) + + r = ask(Q.real(expr), assumptions) + if r is not True: + return r + + nonneg = 0 + for arg in expr.args: + if ask(Q.positive(arg), assumptions) is not True: + if ask(Q.negative(arg), assumptions) is False: + nonneg += 1 + else: + break + else: + if nonneg < len(expr.args): + return True + +@PositivePredicate.register(Pow) +def _(expr, assumptions): + if expr.base == E: + if ask(Q.real(expr.exp), assumptions): + return True + if ask(Q.imaginary(expr.exp), assumptions): + return ask(Q.even(expr.exp/(I*pi)), assumptions) + return + + if expr.is_number: + return _PositivePredicate_number(expr, assumptions) + if ask(Q.positive(expr.base), assumptions): + if ask(Q.real(expr.exp), assumptions): + return True + if ask(Q.negative(expr.base), assumptions): + if ask(Q.even(expr.exp), assumptions): + return True + if ask(Q.odd(expr.exp), assumptions): + return False + +@PositivePredicate.register(exp) +def _(expr, assumptions): + if ask(Q.real(expr.exp), assumptions): + return True + if ask(Q.imaginary(expr.exp), assumptions): + return ask(Q.even(expr.exp/(I*pi)), assumptions) + +@PositivePredicate.register(log) +def _(expr, assumptions): + r = ask(Q.real(expr.args[0]), assumptions) + if r is not True: + return r + if ask(Q.positive(expr.args[0] - 1), assumptions): + return True + if ask(Q.negative(expr.args[0] - 1), assumptions): + return False + +@PositivePredicate.register(factorial) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.integer(x) & Q.positive(x), assumptions): + return True + +@PositivePredicate.register(ImaginaryUnit) +def _(expr, assumptions): + return False + +@PositivePredicate.register(Abs) +def _(expr, assumptions): + return ask(Q.nonzero(expr), assumptions) + +@PositivePredicate.register(Trace) +def _(expr, assumptions): + if ask(Q.positive_definite(expr.arg), assumptions): + return True + +@PositivePredicate.register(Determinant) +def _(expr, assumptions): + if ask(Q.positive_definite(expr.arg), assumptions): + return True + +@PositivePredicate.register(MatrixElement) +def _(expr, assumptions): + if (expr.i == expr.j + and ask(Q.positive_definite(expr.parent), assumptions)): + return True + +@PositivePredicate.register(atan) +def _(expr, assumptions): + return ask(Q.positive(expr.args[0]), assumptions) + +@PositivePredicate.register(asin) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.positive(x) & Q.nonpositive(x - 1), assumptions): + return True + if ask(Q.negative(x) & Q.nonnegative(x + 1), assumptions): + return False + +@PositivePredicate.register(acos) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.nonpositive(x - 1) & Q.nonnegative(x + 1), assumptions): + return True + +@PositivePredicate.register(acot) +def _(expr, assumptions): + return ask(Q.real(expr.args[0]), assumptions) + +@PositivePredicate.register(NaN) +def _(expr, assumptions): + return None + + +# ExtendedNegativePredicate + +@ExtendedNegativePredicate.register(object) +def _(expr, assumptions): + return ask(Q.negative(expr) | Q.negative_infinite(expr), assumptions) + + +# ExtendedPositivePredicate + +@ExtendedPositivePredicate.register(object) +def _(expr, assumptions): + return ask(Q.positive(expr) | Q.positive_infinite(expr), assumptions) + + +# ExtendedNonZeroPredicate + +@ExtendedNonZeroPredicate.register(object) +def _(expr, assumptions): + return ask( + Q.negative_infinite(expr) | Q.negative(expr) | Q.positive(expr) | Q.positive_infinite(expr), + assumptions) + + +# ExtendedNonPositivePredicate + +@ExtendedNonPositivePredicate.register(object) +def _(expr, assumptions): + return ask( + Q.negative_infinite(expr) | Q.negative(expr) | Q.zero(expr), + assumptions) + + +# ExtendedNonNegativePredicate + +@ExtendedNonNegativePredicate.register(object) +def _(expr, assumptions): + return ask( + Q.zero(expr) | Q.positive(expr) | Q.positive_infinite(expr), + assumptions) diff --git a/lib/python3.11/site-packages/sympy/assumptions/handlers/sets.py b/lib/python3.11/site-packages/sympy/assumptions/handlers/sets.py new file mode 100644 index 0000000000000000000000000000000000000000..b53bcfedef30681ea4450c6dad9120bc2ea9016e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/handlers/sets.py @@ -0,0 +1,772 @@ +""" +Handlers for predicates related to set membership: integer, rational, etc. +""" + +from sympy.assumptions import Q, ask +from sympy.core import Add, Basic, Expr, Mul, Pow, S +from sympy.core.numbers import (AlgebraicNumber, ComplexInfinity, Exp1, Float, + GoldenRatio, ImaginaryUnit, Infinity, Integer, NaN, NegativeInfinity, + Number, NumberSymbol, Pi, pi, Rational, TribonacciConstant, E) +from sympy.core.logic import fuzzy_bool +from sympy.functions import (Abs, acos, acot, asin, atan, cos, cot, exp, im, + log, re, sin, tan) +from sympy.core.numbers import I +from sympy.core.relational import Eq +from sympy.functions.elementary.complexes import conjugate +from sympy.matrices import Determinant, MatrixBase, Trace +from sympy.matrices.expressions.matexpr import MatrixElement + +from sympy.multipledispatch import MDNotImplementedError + +from .common import test_closed_group +from ..predicates.sets import (IntegerPredicate, RationalPredicate, + IrrationalPredicate, RealPredicate, ExtendedRealPredicate, + HermitianPredicate, ComplexPredicate, ImaginaryPredicate, + AntihermitianPredicate, AlgebraicPredicate) + + +# IntegerPredicate + +def _IntegerPredicate_number(expr, assumptions): + # helper function + try: + i = int(expr.round()) + if not (expr - i).equals(0): + raise TypeError + return True + except TypeError: + return False + +@IntegerPredicate.register_many(int, Integer) # type:ignore +def _(expr, assumptions): + return True + +@IntegerPredicate.register_many(Exp1, GoldenRatio, ImaginaryUnit, Infinity, + NegativeInfinity, Pi, Rational, TribonacciConstant) +def _(expr, assumptions): + return False + +@IntegerPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_integer + if ret is None: + raise MDNotImplementedError + return ret + +@IntegerPredicate.register_many(Add, Pow) +def _(expr, assumptions): + """ + * Integer + Integer -> Integer + * Integer + !Integer -> !Integer + * !Integer + !Integer -> ? + """ + if expr.is_number: + return _IntegerPredicate_number(expr, assumptions) + return test_closed_group(expr, assumptions, Q.integer) + +@IntegerPredicate.register(Mul) +def _(expr, assumptions): + """ + * Integer*Integer -> Integer + * Integer*Irrational -> !Integer + * Odd/Even -> !Integer + * Integer*Rational -> ? + """ + if expr.is_number: + return _IntegerPredicate_number(expr, assumptions) + _output = True + for arg in expr.args: + if not ask(Q.integer(arg), assumptions): + if arg.is_Rational: + if arg.q == 2: + return ask(Q.even(2*expr), assumptions) + if ~(arg.q & 1): + return None + elif ask(Q.irrational(arg), assumptions): + if _output: + _output = False + else: + return + else: + return + + return _output + +@IntegerPredicate.register(Abs) +def _(expr, assumptions): + return ask(Q.integer(expr.args[0]), assumptions) + +@IntegerPredicate.register_many(Determinant, MatrixElement, Trace) +def _(expr, assumptions): + return ask(Q.integer_elements(expr.args[0]), assumptions) + + +# RationalPredicate + +@RationalPredicate.register(Rational) +def _(expr, assumptions): + return True + +@RationalPredicate.register(Float) +def _(expr, assumptions): + return None + +@RationalPredicate.register_many(Exp1, GoldenRatio, ImaginaryUnit, Infinity, + NegativeInfinity, Pi, TribonacciConstant) +def _(expr, assumptions): + return False + +@RationalPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_rational + if ret is None: + raise MDNotImplementedError + return ret + +@RationalPredicate.register_many(Add, Mul) +def _(expr, assumptions): + """ + * Rational + Rational -> Rational + * Rational + !Rational -> !Rational + * !Rational + !Rational -> ? + """ + if expr.is_number: + if expr.as_real_imag()[1]: + return False + return test_closed_group(expr, assumptions, Q.rational) + +@RationalPredicate.register(Pow) +def _(expr, assumptions): + """ + * Rational ** Integer -> Rational + * Irrational ** Rational -> Irrational + * Rational ** Irrational -> ? + """ + if expr.base == E: + x = expr.exp + if ask(Q.rational(x), assumptions): + return ask(~Q.nonzero(x), assumptions) + return + + if ask(Q.integer(expr.exp), assumptions): + return ask(Q.rational(expr.base), assumptions) + elif ask(Q.rational(expr.exp), assumptions): + if ask(Q.prime(expr.base), assumptions): + return False + +@RationalPredicate.register_many(asin, atan, cos, sin, tan) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.rational(x), assumptions): + return ask(~Q.nonzero(x), assumptions) + +@RationalPredicate.register(exp) +def _(expr, assumptions): + x = expr.exp + if ask(Q.rational(x), assumptions): + return ask(~Q.nonzero(x), assumptions) + +@RationalPredicate.register_many(acot, cot) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.rational(x), assumptions): + return False + +@RationalPredicate.register_many(acos, log) +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.rational(x), assumptions): + return ask(~Q.nonzero(x - 1), assumptions) + + +# IrrationalPredicate + +@IrrationalPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_irrational + if ret is None: + raise MDNotImplementedError + return ret + +@IrrationalPredicate.register(Basic) +def _(expr, assumptions): + _real = ask(Q.real(expr), assumptions) + if _real: + _rational = ask(Q.rational(expr), assumptions) + if _rational is None: + return None + return not _rational + else: + return _real + + +# RealPredicate + +def _RealPredicate_number(expr, assumptions): + # let as_real_imag() work first since the expression may + # be simpler to evaluate + i = expr.as_real_imag()[1].evalf(2) + if i._prec != 1: + return not i + # allow None to be returned if we couldn't show for sure + # that i was 0 + +@RealPredicate.register_many(Abs, Exp1, Float, GoldenRatio, im, Pi, Rational, + re, TribonacciConstant) +def _(expr, assumptions): + return True + +@RealPredicate.register_many(ImaginaryUnit, Infinity, NegativeInfinity) +def _(expr, assumptions): + return False + +@RealPredicate.register(Expr) +def _(expr, assumptions): + ret = expr.is_real + if ret is None: + raise MDNotImplementedError + return ret + +@RealPredicate.register(Add) +def _(expr, assumptions): + """ + * Real + Real -> Real + * Real + (Complex & !Real) -> !Real + """ + if expr.is_number: + return _RealPredicate_number(expr, assumptions) + return test_closed_group(expr, assumptions, Q.real) + +@RealPredicate.register(Mul) +def _(expr, assumptions): + """ + * Real*Real -> Real + * Real*Imaginary -> !Real + * Imaginary*Imaginary -> Real + """ + if expr.is_number: + return _RealPredicate_number(expr, assumptions) + result = True + for arg in expr.args: + if ask(Q.real(arg), assumptions): + pass + elif ask(Q.imaginary(arg), assumptions): + result = result ^ True + else: + break + else: + return result + +@RealPredicate.register(Pow) +def _(expr, assumptions): + """ + * Real**Integer -> Real + * Positive**Real -> Real + * Real**(Integer/Even) -> Real if base is nonnegative + * Real**(Integer/Odd) -> Real + * Imaginary**(Integer/Even) -> Real + * Imaginary**(Integer/Odd) -> not Real + * Imaginary**Real -> ? since Real could be 0 (giving real) + or 1 (giving imaginary) + * b**Imaginary -> Real if log(b) is imaginary and b != 0 + and exponent != integer multiple of + I*pi/log(b) + * Real**Real -> ? e.g. sqrt(-1) is imaginary and + sqrt(2) is not + """ + if expr.is_number: + return _RealPredicate_number(expr, assumptions) + + if expr.base == E: + return ask( + Q.integer(expr.exp/I/pi) | Q.real(expr.exp), assumptions + ) + + if expr.base.func == exp or (expr.base.is_Pow and expr.base.base == E): + if ask(Q.imaginary(expr.base.exp), assumptions): + if ask(Q.imaginary(expr.exp), assumptions): + return True + # If the i = (exp's arg)/(I*pi) is an integer or half-integer + # multiple of I*pi then 2*i will be an integer. In addition, + # exp(i*I*pi) = (-1)**i so the overall realness of the expr + # can be determined by replacing exp(i*I*pi) with (-1)**i. + i = expr.base.exp/I/pi + if ask(Q.integer(2*i), assumptions): + return ask(Q.real((S.NegativeOne**i)**expr.exp), assumptions) + return + + if ask(Q.imaginary(expr.base), assumptions): + if ask(Q.integer(expr.exp), assumptions): + odd = ask(Q.odd(expr.exp), assumptions) + if odd is not None: + return not odd + return + + if ask(Q.imaginary(expr.exp), assumptions): + imlog = ask(Q.imaginary(log(expr.base)), assumptions) + if imlog is not None: + # I**i -> real, log(I) is imag; + # (2*I)**i -> complex, log(2*I) is not imag + return imlog + + if ask(Q.real(expr.base), assumptions): + if ask(Q.real(expr.exp), assumptions): + if expr.exp.is_Rational and \ + ask(Q.even(expr.exp.q), assumptions): + return ask(Q.positive(expr.base), assumptions) + elif ask(Q.integer(expr.exp), assumptions): + return True + elif ask(Q.positive(expr.base), assumptions): + return True + elif ask(Q.negative(expr.base), assumptions): + return False + +@RealPredicate.register_many(cos, sin) +def _(expr, assumptions): + if ask(Q.real(expr.args[0]), assumptions): + return True + +@RealPredicate.register(exp) +def _(expr, assumptions): + return ask( + Q.integer(expr.exp/I/pi) | Q.real(expr.exp), assumptions + ) + +@RealPredicate.register(log) +def _(expr, assumptions): + return ask(Q.positive(expr.args[0]), assumptions) + +@RealPredicate.register_many(Determinant, MatrixElement, Trace) +def _(expr, assumptions): + return ask(Q.real_elements(expr.args[0]), assumptions) + + +# ExtendedRealPredicate + +@ExtendedRealPredicate.register(object) +def _(expr, assumptions): + return ask(Q.negative_infinite(expr) + | Q.negative(expr) + | Q.zero(expr) + | Q.positive(expr) + | Q.positive_infinite(expr), + assumptions) + +@ExtendedRealPredicate.register_many(Infinity, NegativeInfinity) +def _(expr, assumptions): + return True + +@ExtendedRealPredicate.register_many(Add, Mul, Pow) # type:ignore +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.extended_real) + + +# HermitianPredicate + +@HermitianPredicate.register(object) # type:ignore +def _(expr, assumptions): + if isinstance(expr, MatrixBase): + return None + return ask(Q.real(expr), assumptions) + +@HermitianPredicate.register(Add) # type:ignore +def _(expr, assumptions): + """ + * Hermitian + Hermitian -> Hermitian + * Hermitian + !Hermitian -> !Hermitian + """ + if expr.is_number: + raise MDNotImplementedError + return test_closed_group(expr, assumptions, Q.hermitian) + +@HermitianPredicate.register(Mul) # type:ignore +def _(expr, assumptions): + """ + As long as there is at most only one noncommutative term: + + * Hermitian*Hermitian -> Hermitian + * Hermitian*Antihermitian -> !Hermitian + * Antihermitian*Antihermitian -> Hermitian + """ + if expr.is_number: + raise MDNotImplementedError + nccount = 0 + result = True + for arg in expr.args: + if ask(Q.antihermitian(arg), assumptions): + result = result ^ True + elif not ask(Q.hermitian(arg), assumptions): + break + if ask(~Q.commutative(arg), assumptions): + nccount += 1 + if nccount > 1: + break + else: + return result + +@HermitianPredicate.register(Pow) # type:ignore +def _(expr, assumptions): + """ + * Hermitian**Integer -> Hermitian + """ + if expr.is_number: + raise MDNotImplementedError + if expr.base == E: + if ask(Q.hermitian(expr.exp), assumptions): + return True + raise MDNotImplementedError + if ask(Q.hermitian(expr.base), assumptions): + if ask(Q.integer(expr.exp), assumptions): + return True + raise MDNotImplementedError + +@HermitianPredicate.register_many(cos, sin) # type:ignore +def _(expr, assumptions): + if ask(Q.hermitian(expr.args[0]), assumptions): + return True + raise MDNotImplementedError + +@HermitianPredicate.register(exp) # type:ignore +def _(expr, assumptions): + if ask(Q.hermitian(expr.exp), assumptions): + return True + raise MDNotImplementedError + +@HermitianPredicate.register(MatrixBase) # type:ignore +def _(mat, assumptions): + rows, cols = mat.shape + ret_val = True + for i in range(rows): + for j in range(i, cols): + cond = fuzzy_bool(Eq(mat[i, j], conjugate(mat[j, i]))) + if cond is None: + ret_val = None + if cond == False: + return False + if ret_val is None: + raise MDNotImplementedError + return ret_val + + +# ComplexPredicate + +@ComplexPredicate.register_many(Abs, cos, exp, im, ImaginaryUnit, log, Number, # type:ignore + NumberSymbol, re, sin) +def _(expr, assumptions): + return True + +@ComplexPredicate.register_many(Infinity, NegativeInfinity) # type:ignore +def _(expr, assumptions): + return False + +@ComplexPredicate.register(Expr) # type:ignore +def _(expr, assumptions): + ret = expr.is_complex + if ret is None: + raise MDNotImplementedError + return ret + +@ComplexPredicate.register_many(Add, Mul) # type:ignore +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.complex) + +@ComplexPredicate.register(Pow) # type:ignore +def _(expr, assumptions): + if expr.base == E: + return True + return test_closed_group(expr, assumptions, Q.complex) + +@ComplexPredicate.register_many(Determinant, MatrixElement, Trace) # type:ignore +def _(expr, assumptions): + return ask(Q.complex_elements(expr.args[0]), assumptions) + +@ComplexPredicate.register(NaN) # type:ignore +def _(expr, assumptions): + return None + + +# ImaginaryPredicate + +def _Imaginary_number(expr, assumptions): + # let as_real_imag() work first since the expression may + # be simpler to evaluate + r = expr.as_real_imag()[0].evalf(2) + if r._prec != 1: + return not r + # allow None to be returned if we couldn't show for sure + # that r was 0 + +@ImaginaryPredicate.register(ImaginaryUnit) # type:ignore +def _(expr, assumptions): + return True + +@ImaginaryPredicate.register(Expr) # type:ignore +def _(expr, assumptions): + ret = expr.is_imaginary + if ret is None: + raise MDNotImplementedError + return ret + +@ImaginaryPredicate.register(Add) # type:ignore +def _(expr, assumptions): + """ + * Imaginary + Imaginary -> Imaginary + * Imaginary + Complex -> ? + * Imaginary + Real -> !Imaginary + """ + if expr.is_number: + return _Imaginary_number(expr, assumptions) + + reals = 0 + for arg in expr.args: + if ask(Q.imaginary(arg), assumptions): + pass + elif ask(Q.real(arg), assumptions): + reals += 1 + else: + break + else: + if reals == 0: + return True + if reals in (1, len(expr.args)): + # two reals could sum 0 thus giving an imaginary + return False + +@ImaginaryPredicate.register(Mul) # type:ignore +def _(expr, assumptions): + """ + * Real*Imaginary -> Imaginary + * Imaginary*Imaginary -> Real + """ + if expr.is_number: + return _Imaginary_number(expr, assumptions) + result = False + reals = 0 + for arg in expr.args: + if ask(Q.imaginary(arg), assumptions): + result = result ^ True + elif not ask(Q.real(arg), assumptions): + break + else: + if reals == len(expr.args): + return False + return result + +@ImaginaryPredicate.register(Pow) # type:ignore +def _(expr, assumptions): + """ + * Imaginary**Odd -> Imaginary + * Imaginary**Even -> Real + * b**Imaginary -> !Imaginary if exponent is an integer + multiple of I*pi/log(b) + * Imaginary**Real -> ? + * Positive**Real -> Real + * Negative**Integer -> Real + * Negative**(Integer/2) -> Imaginary + * Negative**Real -> not Imaginary if exponent is not Rational + """ + if expr.is_number: + return _Imaginary_number(expr, assumptions) + + if expr.base == E: + a = expr.exp/I/pi + return ask(Q.integer(2*a) & ~Q.integer(a), assumptions) + + if expr.base.func == exp or (expr.base.is_Pow and expr.base.base == E): + if ask(Q.imaginary(expr.base.exp), assumptions): + if ask(Q.imaginary(expr.exp), assumptions): + return False + i = expr.base.exp/I/pi + if ask(Q.integer(2*i), assumptions): + return ask(Q.imaginary((S.NegativeOne**i)**expr.exp), assumptions) + + if ask(Q.imaginary(expr.base), assumptions): + if ask(Q.integer(expr.exp), assumptions): + odd = ask(Q.odd(expr.exp), assumptions) + if odd is not None: + return odd + return + + if ask(Q.imaginary(expr.exp), assumptions): + imlog = ask(Q.imaginary(log(expr.base)), assumptions) + if imlog is not None: + # I**i -> real; (2*I)**i -> complex ==> not imaginary + return False + + if ask(Q.real(expr.base) & Q.real(expr.exp), assumptions): + if ask(Q.positive(expr.base), assumptions): + return False + else: + rat = ask(Q.rational(expr.exp), assumptions) + if not rat: + return rat + if ask(Q.integer(expr.exp), assumptions): + return False + else: + half = ask(Q.integer(2*expr.exp), assumptions) + if half: + return ask(Q.negative(expr.base), assumptions) + return half + +@ImaginaryPredicate.register(log) # type:ignore +def _(expr, assumptions): + if ask(Q.real(expr.args[0]), assumptions): + if ask(Q.positive(expr.args[0]), assumptions): + return False + return + # XXX it should be enough to do + # return ask(Q.nonpositive(expr.args[0]), assumptions) + # but ask(Q.nonpositive(exp(x)), Q.imaginary(x)) -> None; + # it should return True since exp(x) will be either 0 or complex + if expr.args[0].func == exp or (expr.args[0].is_Pow and expr.args[0].base == E): + if expr.args[0].exp in [I, -I]: + return True + im = ask(Q.imaginary(expr.args[0]), assumptions) + if im is False: + return False + +@ImaginaryPredicate.register(exp) # type:ignore +def _(expr, assumptions): + a = expr.exp/I/pi + return ask(Q.integer(2*a) & ~Q.integer(a), assumptions) + +@ImaginaryPredicate.register_many(Number, NumberSymbol) # type:ignore +def _(expr, assumptions): + return not (expr.as_real_imag()[1] == 0) + +@ImaginaryPredicate.register(NaN) # type:ignore +def _(expr, assumptions): + return None + + +# AntihermitianPredicate + +@AntihermitianPredicate.register(object) # type:ignore +def _(expr, assumptions): + if isinstance(expr, MatrixBase): + return None + if ask(Q.zero(expr), assumptions): + return True + return ask(Q.imaginary(expr), assumptions) + +@AntihermitianPredicate.register(Add) # type:ignore +def _(expr, assumptions): + """ + * Antihermitian + Antihermitian -> Antihermitian + * Antihermitian + !Antihermitian -> !Antihermitian + """ + if expr.is_number: + raise MDNotImplementedError + return test_closed_group(expr, assumptions, Q.antihermitian) + +@AntihermitianPredicate.register(Mul) # type:ignore +def _(expr, assumptions): + """ + As long as there is at most only one noncommutative term: + + * Hermitian*Hermitian -> !Antihermitian + * Hermitian*Antihermitian -> Antihermitian + * Antihermitian*Antihermitian -> !Antihermitian + """ + if expr.is_number: + raise MDNotImplementedError + nccount = 0 + result = False + for arg in expr.args: + if ask(Q.antihermitian(arg), assumptions): + result = result ^ True + elif not ask(Q.hermitian(arg), assumptions): + break + if ask(~Q.commutative(arg), assumptions): + nccount += 1 + if nccount > 1: + break + else: + return result + +@AntihermitianPredicate.register(Pow) # type:ignore +def _(expr, assumptions): + """ + * Hermitian**Integer -> !Antihermitian + * Antihermitian**Even -> !Antihermitian + * Antihermitian**Odd -> Antihermitian + """ + if expr.is_number: + raise MDNotImplementedError + if ask(Q.hermitian(expr.base), assumptions): + if ask(Q.integer(expr.exp), assumptions): + return False + elif ask(Q.antihermitian(expr.base), assumptions): + if ask(Q.even(expr.exp), assumptions): + return False + elif ask(Q.odd(expr.exp), assumptions): + return True + raise MDNotImplementedError + +@AntihermitianPredicate.register(MatrixBase) # type:ignore +def _(mat, assumptions): + rows, cols = mat.shape + ret_val = True + for i in range(rows): + for j in range(i, cols): + cond = fuzzy_bool(Eq(mat[i, j], -conjugate(mat[j, i]))) + if cond is None: + ret_val = None + if cond == False: + return False + if ret_val is None: + raise MDNotImplementedError + return ret_val + + +# AlgebraicPredicate + +@AlgebraicPredicate.register_many(AlgebraicNumber, Float, GoldenRatio, # type:ignore + ImaginaryUnit, TribonacciConstant) +def _(expr, assumptions): + return True + +@AlgebraicPredicate.register_many(ComplexInfinity, Exp1, Infinity, # type:ignore + NegativeInfinity, Pi) +def _(expr, assumptions): + return False + +@AlgebraicPredicate.register_many(Add, Mul) # type:ignore +def _(expr, assumptions): + return test_closed_group(expr, assumptions, Q.algebraic) + +@AlgebraicPredicate.register(Pow) # type:ignore +def _(expr, assumptions): + if expr.base == E: + if ask(Q.algebraic(expr.exp), assumptions): + return ask(~Q.nonzero(expr.exp), assumptions) + return + return expr.exp.is_Rational and ask(Q.algebraic(expr.base), assumptions) + +@AlgebraicPredicate.register(Rational) # type:ignore +def _(expr, assumptions): + return expr.q != 0 + +@AlgebraicPredicate.register_many(asin, atan, cos, sin, tan) # type:ignore +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.algebraic(x), assumptions): + return ask(~Q.nonzero(x), assumptions) + +@AlgebraicPredicate.register(exp) # type:ignore +def _(expr, assumptions): + x = expr.exp + if ask(Q.algebraic(x), assumptions): + return ask(~Q.nonzero(x), assumptions) + +@AlgebraicPredicate.register_many(acot, cot) # type:ignore +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.algebraic(x), assumptions): + return False + +@AlgebraicPredicate.register_many(acos, log) # type:ignore +def _(expr, assumptions): + x = expr.args[0] + if ask(Q.algebraic(x), assumptions): + return ask(~Q.nonzero(x - 1), assumptions) diff --git a/lib/python3.11/site-packages/sympy/assumptions/lra_satask.py b/lib/python3.11/site-packages/sympy/assumptions/lra_satask.py new file mode 100644 index 0000000000000000000000000000000000000000..53afe3e5abe99109ec01a47f19f1a8a4c99c5628 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/lra_satask.py @@ -0,0 +1,286 @@ +from sympy.assumptions.assume import global_assumptions +from sympy.assumptions.cnf import CNF, EncodedCNF +from sympy.assumptions.ask import Q +from sympy.logic.inference import satisfiable +from sympy.logic.algorithms.lra_theory import UnhandledInput, ALLOWED_PRED +from sympy.matrices.kind import MatrixKind +from sympy.core.kind import NumberKind +from sympy.assumptions.assume import AppliedPredicate +from sympy.core.mul import Mul +from sympy.core.singleton import S + + +def lra_satask(proposition, assumptions=True, context=global_assumptions): + """ + Function to evaluate the proposition with assumptions using SAT algorithm + in conjunction with an Linear Real Arithmetic theory solver. + + Used to handle inequalities. Should eventually be depreciated and combined + into satask, but infinity handling and other things need to be implemented + before that can happen. + """ + props = CNF.from_prop(proposition) + _props = CNF.from_prop(~proposition) + + cnf = CNF.from_prop(assumptions) + assumptions = EncodedCNF() + assumptions.from_cnf(cnf) + + context_cnf = CNF() + if context: + context_cnf = context_cnf.extend(context) + + assumptions.add_from_cnf(context_cnf) + + return check_satisfiability(props, _props, assumptions) + +# Some predicates such as Q.prime can't be handled by lra_satask. +# For example, (x > 0) & (x < 1) & Q.prime(x) is unsat but lra_satask would think it was sat. +# WHITE_LIST is a list of predicates that can always be handled. +WHITE_LIST = ALLOWED_PRED | {Q.positive, Q.negative, Q.zero, Q.nonzero, Q.nonpositive, Q.nonnegative, + Q.extended_positive, Q.extended_negative, Q.extended_nonpositive, + Q.extended_negative, Q.extended_nonzero, Q.negative_infinite, + Q.positive_infinite} + + +def check_satisfiability(prop, _prop, factbase): + sat_true = factbase.copy() + sat_false = factbase.copy() + sat_true.add_from_cnf(prop) + sat_false.add_from_cnf(_prop) + + all_pred, all_exprs = get_all_pred_and_expr_from_enc_cnf(sat_true) + + for pred in all_pred: + if pred.function not in WHITE_LIST and pred.function != Q.ne: + raise UnhandledInput(f"LRASolver: {pred} is an unhandled predicate") + for expr in all_exprs: + if expr.kind == MatrixKind(NumberKind): + raise UnhandledInput(f"LRASolver: {expr} is of MatrixKind") + if expr == S.NaN: + raise UnhandledInput("LRASolver: nan") + + # convert old assumptions into predicates and add them to sat_true and sat_false + # also check for unhandled predicates + for assm in extract_pred_from_old_assum(all_exprs): + n = len(sat_true.encoding) + if assm not in sat_true.encoding: + sat_true.encoding[assm] = n+1 + sat_true.data.append([sat_true.encoding[assm]]) + + n = len(sat_false.encoding) + if assm not in sat_false.encoding: + sat_false.encoding[assm] = n+1 + sat_false.data.append([sat_false.encoding[assm]]) + + + sat_true = _preprocess(sat_true) + sat_false = _preprocess(sat_false) + + can_be_true = satisfiable(sat_true, use_lra_theory=True) is not False + can_be_false = satisfiable(sat_false, use_lra_theory=True) is not False + + if can_be_true and can_be_false: + return None + + if can_be_true and not can_be_false: + return True + + if not can_be_true and can_be_false: + return False + + if not can_be_true and not can_be_false: + raise ValueError("Inconsistent assumptions") + + +def _preprocess(enc_cnf): + """ + Returns an encoded cnf with only Q.eq, Q.gt, Q.lt, + Q.ge, and Q.le predicate. + + Converts every unequality into a disjunction of strict + inequalities. For example, x != 3 would become + x < 3 OR x > 3. + + Also converts all negated Q.ne predicates into + equalities. + """ + + # loops through each literal in each clause + # to construct a new, preprocessed encodedCNF + + enc_cnf = enc_cnf.copy() + cur_enc = 1 + rev_encoding = {value: key for key, value in enc_cnf.encoding.items()} + + new_encoding = {} + new_data = [] + for clause in enc_cnf.data: + new_clause = [] + for lit in clause: + if lit == 0: + new_clause.append(lit) + new_encoding[lit] = False + continue + prop = rev_encoding[abs(lit)] + negated = lit < 0 + sign = (lit > 0) - (lit < 0) + + prop = _pred_to_binrel(prop) + + if not isinstance(prop, AppliedPredicate): + if prop not in new_encoding: + new_encoding[prop] = cur_enc + cur_enc += 1 + lit = new_encoding[prop] + new_clause.append(sign*lit) + continue + + + if negated and prop.function == Q.eq: + negated = False + prop = Q.ne(*prop.arguments) + + if prop.function == Q.ne: + arg1, arg2 = prop.arguments + if negated: + new_prop = Q.eq(arg1, arg2) + if new_prop not in new_encoding: + new_encoding[new_prop] = cur_enc + cur_enc += 1 + + new_enc = new_encoding[new_prop] + new_clause.append(new_enc) + continue + else: + new_props = (Q.gt(arg1, arg2), Q.lt(arg1, arg2)) + for new_prop in new_props: + if new_prop not in new_encoding: + new_encoding[new_prop] = cur_enc + cur_enc += 1 + + new_enc = new_encoding[new_prop] + new_clause.append(new_enc) + continue + + if prop.function == Q.eq and negated: + assert False + + if prop not in new_encoding: + new_encoding[prop] = cur_enc + cur_enc += 1 + new_clause.append(new_encoding[prop]*sign) + new_data.append(new_clause) + + assert len(new_encoding) >= cur_enc - 1 + + enc_cnf = EncodedCNF(new_data, new_encoding) + return enc_cnf + + +def _pred_to_binrel(pred): + if not isinstance(pred, AppliedPredicate): + return pred + + if pred.function in pred_to_pos_neg_zero: + f = pred_to_pos_neg_zero[pred.function] + if f is False: + return False + pred = f(pred.arguments[0]) + + if pred.function == Q.positive: + pred = Q.gt(pred.arguments[0], 0) + elif pred.function == Q.negative: + pred = Q.lt(pred.arguments[0], 0) + elif pred.function == Q.zero: + pred = Q.eq(pred.arguments[0], 0) + elif pred.function == Q.nonpositive: + pred = Q.le(pred.arguments[0], 0) + elif pred.function == Q.nonnegative: + pred = Q.ge(pred.arguments[0], 0) + elif pred.function == Q.nonzero: + pred = Q.ne(pred.arguments[0], 0) + + return pred + +pred_to_pos_neg_zero = { + Q.extended_positive: Q.positive, + Q.extended_negative: Q.negative, + Q.extended_nonpositive: Q.nonpositive, + Q.extended_negative: Q.negative, + Q.extended_nonzero: Q.nonzero, + Q.negative_infinite: False, + Q.positive_infinite: False +} + +def get_all_pred_and_expr_from_enc_cnf(enc_cnf): + all_exprs = set() + all_pred = set() + for pred in enc_cnf.encoding.keys(): + if isinstance(pred, AppliedPredicate): + all_pred.add(pred) + all_exprs.update(pred.arguments) + + return all_pred, all_exprs + +def extract_pred_from_old_assum(all_exprs): + """ + Returns a list of relevant new assumption predicate + based on any old assumptions. + + Raises an UnhandledInput exception if any of the assumptions are + unhandled. + + Ignored predicate: + - commutative + - complex + - algebraic + - transcendental + - extended_real + - real + - all matrix predicate + - rational + - irrational + + Example + ======= + >>> from sympy.assumptions.lra_satask import extract_pred_from_old_assum + >>> from sympy import symbols + >>> x, y = symbols("x y", positive=True) + >>> extract_pred_from_old_assum([x, y, 2]) + [Q.positive(x), Q.positive(y)] + """ + ret = [] + for expr in all_exprs: + if not hasattr(expr, "free_symbols"): + continue + if len(expr.free_symbols) == 0: + continue + + if expr.is_real is not True: + raise UnhandledInput(f"LRASolver: {expr} must be real") + # test for I times imaginary variable; such expressions are considered real + if isinstance(expr, Mul) and any(arg.is_real is not True for arg in expr.args): + raise UnhandledInput(f"LRASolver: {expr} must be real") + + if expr.is_integer == True and expr.is_zero != True: + raise UnhandledInput(f"LRASolver: {expr} is an integer") + if expr.is_integer == False: + raise UnhandledInput(f"LRASolver: {expr} can't be an integer") + if expr.is_rational == False: + raise UnhandledInput(f"LRASolver: {expr} is irational") + + if expr.is_zero: + ret.append(Q.zero(expr)) + elif expr.is_positive: + ret.append(Q.positive(expr)) + elif expr.is_negative: + ret.append(Q.negative(expr)) + elif expr.is_nonzero: + ret.append(Q.nonzero(expr)) + elif expr.is_nonpositive: + ret.append(Q.nonpositive(expr)) + elif expr.is_nonnegative: + ret.append(Q.nonnegative(expr)) + + return ret diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/__init__.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..8e294544bfdce13633ecff762ff42861aa12719f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/__init__.py @@ -0,0 +1,5 @@ +""" +Module to implement predicate classes. + +Class of every predicate registered to ``Q`` is defined here. +""" diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..4a70e793198aa85d0a947f42d788613b21214345 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/calculus.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/calculus.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..54da5f249cad856e3e8cee0c4159c38d6f7ce5e5 Binary files 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b/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/sets.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..486d11d67f1dd2e9a317f533b491abf0b81fca05 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/predicates/__pycache__/sets.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/calculus.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/calculus.py new file mode 100644 index 0000000000000000000000000000000000000000..f300703788683c07649ee3a0afd6e9d4eabd4567 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/calculus.py @@ -0,0 +1,82 @@ +from sympy.assumptions import Predicate +from sympy.multipledispatch import Dispatcher + +class FinitePredicate(Predicate): + """ + Finite number predicate. + + Explanation + =========== + + ``Q.finite(x)`` is true if ``x`` is a number but neither an infinity + nor a ``NaN``. In other words, ``ask(Q.finite(x))`` is true for all + numerical ``x`` having a bounded absolute value. + + Examples + ======== + + >>> from sympy import Q, ask, S, oo, I, zoo + >>> from sympy.abc import x + >>> ask(Q.finite(oo)) + False + >>> ask(Q.finite(-oo)) + False + >>> ask(Q.finite(zoo)) + False + >>> ask(Q.finite(1)) + True + >>> ask(Q.finite(2 + 3*I)) + True + >>> ask(Q.finite(x), Q.positive(x)) + True + >>> print(ask(Q.finite(S.NaN))) + None + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Finite + + """ + name = 'finite' + handler = Dispatcher( + "FiniteHandler", + doc=("Handler for Q.finite. Test that an expression is bounded respect" + " to all its variables.") + ) + + +class InfinitePredicate(Predicate): + """ + Infinite number predicate. + + ``Q.infinite(x)`` is true iff the absolute value of ``x`` is + infinity. + + """ + # TODO: Add examples + name = 'infinite' + handler = Dispatcher( + "InfiniteHandler", + doc="""Handler for Q.infinite key.""" + ) + + +class PositiveInfinitePredicate(Predicate): + """ + Positive infinity predicate. + + ``Q.positive_infinite(x)`` is true iff ``x`` is positive infinity ``oo``. + """ + name = 'positive_infinite' + handler = Dispatcher("PositiveInfiniteHandler") + + +class NegativeInfinitePredicate(Predicate): + """ + Negative infinity predicate. + + ``Q.negative_infinite(x)`` is true iff ``x`` is negative infinity ``-oo``. + """ + name = 'negative_infinite' + handler = Dispatcher("NegativeInfiniteHandler") diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/common.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/common.py new file mode 100644 index 0000000000000000000000000000000000000000..a53892747131b03636abeb8f563c4f76cf3e281e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/common.py @@ -0,0 +1,81 @@ +from sympy.assumptions import Predicate, AppliedPredicate, Q +from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le +from sympy.multipledispatch import Dispatcher + + +class CommutativePredicate(Predicate): + """ + Commutative predicate. + + Explanation + =========== + + ``ask(Q.commutative(x))`` is true iff ``x`` commutes with any other + object with respect to multiplication operation. + + """ + # TODO: Add examples + name = 'commutative' + handler = Dispatcher("CommutativeHandler", doc="Handler for key 'commutative'.") + + +binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le} + +class IsTruePredicate(Predicate): + """ + Generic predicate. + + Explanation + =========== + + ``ask(Q.is_true(x))`` is true iff ``x`` is true. This only makes + sense if ``x`` is a boolean object. + + Examples + ======== + + >>> from sympy import ask, Q + >>> from sympy.abc import x, y + >>> ask(Q.is_true(True)) + True + + Wrapping another applied predicate just returns the applied predicate. + + >>> Q.is_true(Q.even(x)) + Q.even(x) + + Wrapping binary relation classes in SymPy core returns applied binary + relational predicates. + + >>> from sympy import Eq, Gt + >>> Q.is_true(Eq(x, y)) + Q.eq(x, y) + >>> Q.is_true(Gt(x, y)) + Q.gt(x, y) + + Notes + ===== + + This class is designed to wrap the boolean objects so that they can + behave as if they are applied predicates. Consequently, wrapping another + applied predicate is unnecessary and thus it just returns the argument. + Also, binary relation classes in SymPy core have binary predicates to + represent themselves and thus wrapping them with ``Q.is_true`` converts them + to these applied predicates. + + """ + name = 'is_true' + handler = Dispatcher( + "IsTrueHandler", + doc="Wrapper allowing to query the truth value of a boolean expression." + ) + + def __call__(self, arg): + # No need to wrap another predicate + if isinstance(arg, AppliedPredicate): + return arg + # Convert relational predicates instead of wrapping them + if getattr(arg, "is_Relational", False): + pred = binrelpreds[type(arg)] + return pred(*arg.args) + return super().__call__(arg) diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/matrices.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/matrices.py new file mode 100644 index 0000000000000000000000000000000000000000..151e78c4ff345800e1d2f17973fb0591b8d379d2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/matrices.py @@ -0,0 +1,511 @@ +from sympy.assumptions import Predicate +from sympy.multipledispatch import Dispatcher + +class SquarePredicate(Predicate): + """ + Square matrix predicate. + + Explanation + =========== + + ``Q.square(x)`` is true iff ``x`` is a square matrix. A square matrix + is a matrix with the same number of rows and columns. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('X', 2, 3) + >>> ask(Q.square(X)) + True + >>> ask(Q.square(Y)) + False + >>> ask(Q.square(ZeroMatrix(3, 3))) + True + >>> ask(Q.square(Identity(3))) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Square_matrix + + """ + name = 'square' + handler = Dispatcher("SquareHandler", doc="Handler for Q.square.") + + +class SymmetricPredicate(Predicate): + """ + Symmetric matrix predicate. + + Explanation + =========== + + ``Q.symmetric(x)`` is true iff ``x`` is a square matrix and is equal to + its transpose. Every square diagonal matrix is a symmetric matrix. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('Y', 2, 3) + >>> Z = MatrixSymbol('Z', 2, 2) + >>> ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z)) + True + >>> ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z)) + True + >>> ask(Q.symmetric(Y)) + False + + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Symmetric_matrix + + """ + # TODO: Add handlers to make these keys work with + # actual matrices and add more examples in the docstring. + name = 'symmetric' + handler = Dispatcher("SymmetricHandler", doc="Handler for Q.symmetric.") + + +class InvertiblePredicate(Predicate): + """ + Invertible matrix predicate. + + Explanation + =========== + + ``Q.invertible(x)`` is true iff ``x`` is an invertible matrix. + A square matrix is called invertible only if its determinant is 0. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('Y', 2, 3) + >>> Z = MatrixSymbol('Z', 2, 2) + >>> ask(Q.invertible(X*Y), Q.invertible(X)) + False + >>> ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z)) + True + >>> ask(Q.invertible(X), Q.fullrank(X) & Q.square(X)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Invertible_matrix + + """ + name = 'invertible' + handler = Dispatcher("InvertibleHandler", doc="Handler for Q.invertible.") + + +class OrthogonalPredicate(Predicate): + """ + Orthogonal matrix predicate. + + Explanation + =========== + + ``Q.orthogonal(x)`` is true iff ``x`` is an orthogonal matrix. + A square matrix ``M`` is an orthogonal matrix if it satisfies + ``M^TM = MM^T = I`` where ``M^T`` is the transpose matrix of + ``M`` and ``I`` is an identity matrix. Note that an orthogonal + matrix is necessarily invertible. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, Identity + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('Y', 2, 3) + >>> Z = MatrixSymbol('Z', 2, 2) + >>> ask(Q.orthogonal(Y)) + False + >>> ask(Q.orthogonal(X*Z*X), Q.orthogonal(X) & Q.orthogonal(Z)) + True + >>> ask(Q.orthogonal(Identity(3))) + True + >>> ask(Q.invertible(X), Q.orthogonal(X)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Orthogonal_matrix + + """ + name = 'orthogonal' + handler = Dispatcher("OrthogonalHandler", doc="Handler for key 'orthogonal'.") + + +class UnitaryPredicate(Predicate): + """ + Unitary matrix predicate. + + Explanation + =========== + + ``Q.unitary(x)`` is true iff ``x`` is a unitary matrix. + Unitary matrix is an analogue to orthogonal matrix. A square + matrix ``M`` with complex elements is unitary if :math:``M^TM = MM^T= I`` + where :math:``M^T`` is the conjugate transpose matrix of ``M``. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, Identity + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('Y', 2, 3) + >>> Z = MatrixSymbol('Z', 2, 2) + >>> ask(Q.unitary(Y)) + False + >>> ask(Q.unitary(X*Z*X), Q.unitary(X) & Q.unitary(Z)) + True + >>> ask(Q.unitary(Identity(3))) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Unitary_matrix + + """ + name = 'unitary' + handler = Dispatcher("UnitaryHandler", doc="Handler for key 'unitary'.") + + +class FullRankPredicate(Predicate): + """ + Fullrank matrix predicate. + + Explanation + =========== + + ``Q.fullrank(x)`` is true iff ``x`` is a full rank matrix. + A matrix is full rank if all rows and columns of the matrix + are linearly independent. A square matrix is full rank iff + its determinant is nonzero. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity + >>> X = MatrixSymbol('X', 2, 2) + >>> ask(Q.fullrank(X.T), Q.fullrank(X)) + True + >>> ask(Q.fullrank(ZeroMatrix(3, 3))) + False + >>> ask(Q.fullrank(Identity(3))) + True + + """ + name = 'fullrank' + handler = Dispatcher("FullRankHandler", doc="Handler for key 'fullrank'.") + + +class PositiveDefinitePredicate(Predicate): + r""" + Positive definite matrix predicate. + + Explanation + =========== + + If $M$ is a :math:`n \times n` symmetric real matrix, it is said + to be positive definite if :math:`Z^TMZ` is positive for + every non-zero column vector $Z$ of $n$ real numbers. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, Identity + >>> X = MatrixSymbol('X', 2, 2) + >>> Y = MatrixSymbol('Y', 2, 3) + >>> Z = MatrixSymbol('Z', 2, 2) + >>> ask(Q.positive_definite(Y)) + False + >>> ask(Q.positive_definite(Identity(3))) + True + >>> ask(Q.positive_definite(X + Z), Q.positive_definite(X) & + ... Q.positive_definite(Z)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Positive-definite_matrix + + """ + name = "positive_definite" + handler = Dispatcher("PositiveDefiniteHandler", doc="Handler for key 'positive_definite'.") + + +class UpperTriangularPredicate(Predicate): + """ + Upper triangular matrix predicate. + + Explanation + =========== + + A matrix $M$ is called upper triangular matrix if :math:`M_{ij}=0` + for :math:`i>> from sympy import Q, ask, ZeroMatrix, Identity + >>> ask(Q.upper_triangular(Identity(3))) + True + >>> ask(Q.upper_triangular(ZeroMatrix(3, 3))) + True + + References + ========== + + .. [1] https://mathworld.wolfram.com/UpperTriangularMatrix.html + + """ + name = "upper_triangular" + handler = Dispatcher("UpperTriangularHandler", doc="Handler for key 'upper_triangular'.") + + +class LowerTriangularPredicate(Predicate): + """ + Lower triangular matrix predicate. + + Explanation + =========== + + A matrix $M$ is called lower triangular matrix if :math:`M_{ij}=0` + for :math:`i>j`. + + Examples + ======== + + >>> from sympy import Q, ask, ZeroMatrix, Identity + >>> ask(Q.lower_triangular(Identity(3))) + True + >>> ask(Q.lower_triangular(ZeroMatrix(3, 3))) + True + + References + ========== + + .. [1] https://mathworld.wolfram.com/LowerTriangularMatrix.html + + """ + name = "lower_triangular" + handler = Dispatcher("LowerTriangularHandler", doc="Handler for key 'lower_triangular'.") + + +class DiagonalPredicate(Predicate): + """ + Diagonal matrix predicate. + + Explanation + =========== + + ``Q.diagonal(x)`` is true iff ``x`` is a diagonal matrix. A diagonal + matrix is a matrix in which the entries outside the main diagonal + are all zero. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix + >>> X = MatrixSymbol('X', 2, 2) + >>> ask(Q.diagonal(ZeroMatrix(3, 3))) + True + >>> ask(Q.diagonal(X), Q.lower_triangular(X) & + ... Q.upper_triangular(X)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Diagonal_matrix + + """ + name = "diagonal" + handler = Dispatcher("DiagonalHandler", doc="Handler for key 'diagonal'.") + + +class IntegerElementsPredicate(Predicate): + """ + Integer elements matrix predicate. + + Explanation + =========== + + ``Q.integer_elements(x)`` is true iff all the elements of ``x`` + are integers. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.integer(X[1, 2]), Q.integer_elements(X)) + True + + """ + name = "integer_elements" + handler = Dispatcher("IntegerElementsHandler", doc="Handler for key 'integer_elements'.") + + +class RealElementsPredicate(Predicate): + """ + Real elements matrix predicate. + + Explanation + =========== + + ``Q.real_elements(x)`` is true iff all the elements of ``x`` + are real numbers. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.real(X[1, 2]), Q.real_elements(X)) + True + + """ + name = "real_elements" + handler = Dispatcher("RealElementsHandler", doc="Handler for key 'real_elements'.") + + +class ComplexElementsPredicate(Predicate): + """ + Complex elements matrix predicate. + + Explanation + =========== + + ``Q.complex_elements(x)`` is true iff all the elements of ``x`` + are complex numbers. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.complex(X[1, 2]), Q.complex_elements(X)) + True + >>> ask(Q.complex_elements(X), Q.integer_elements(X)) + True + + """ + name = "complex_elements" + handler = Dispatcher("ComplexElementsHandler", doc="Handler for key 'complex_elements'.") + + +class SingularPredicate(Predicate): + """ + Singular matrix predicate. + + A matrix is singular iff the value of its determinant is 0. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.singular(X), Q.invertible(X)) + False + >>> ask(Q.singular(X), ~Q.invertible(X)) + True + + References + ========== + + .. [1] https://mathworld.wolfram.com/SingularMatrix.html + + """ + name = "singular" + handler = Dispatcher("SingularHandler", doc="Predicate fore key 'singular'.") + + +class NormalPredicate(Predicate): + """ + Normal matrix predicate. + + A matrix is normal if it commutes with its conjugate transpose. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.normal(X), Q.unitary(X)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Normal_matrix + + """ + name = "normal" + handler = Dispatcher("NormalHandler", doc="Predicate fore key 'normal'.") + + +class TriangularPredicate(Predicate): + """ + Triangular matrix predicate. + + Explanation + =========== + + ``Q.triangular(X)`` is true if ``X`` is one that is either lower + triangular or upper triangular. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.triangular(X), Q.upper_triangular(X)) + True + >>> ask(Q.triangular(X), Q.lower_triangular(X)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Triangular_matrix + + """ + name = "triangular" + handler = Dispatcher("TriangularHandler", doc="Predicate fore key 'triangular'.") + + +class UnitTriangularPredicate(Predicate): + """ + Unit triangular matrix predicate. + + Explanation + =========== + + A unit triangular matrix is a triangular matrix with 1s + on the diagonal. + + Examples + ======== + + >>> from sympy import Q, ask, MatrixSymbol + >>> X = MatrixSymbol('X', 4, 4) + >>> ask(Q.triangular(X), Q.unit_triangular(X)) + True + + """ + name = "unit_triangular" + handler = Dispatcher("UnitTriangularHandler", doc="Predicate fore key 'unit_triangular'.") diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/ntheory.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/ntheory.py new file mode 100644 index 0000000000000000000000000000000000000000..6c598e0ed1bd4a1170aa28044f9ae6de2fa1a1e0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/ntheory.py @@ -0,0 +1,126 @@ +from sympy.assumptions import Predicate +from sympy.multipledispatch import Dispatcher + + +class PrimePredicate(Predicate): + """ + Prime number predicate. + + Explanation + =========== + + ``ask(Q.prime(x))`` is true iff ``x`` is a natural number greater + than 1 that has no positive divisors other than ``1`` and the + number itself. + + Examples + ======== + + >>> from sympy import Q, ask + >>> ask(Q.prime(0)) + False + >>> ask(Q.prime(1)) + False + >>> ask(Q.prime(2)) + True + >>> ask(Q.prime(20)) + False + >>> ask(Q.prime(-3)) + False + + """ + name = 'prime' + handler = Dispatcher( + "PrimeHandler", + doc=("Handler for key 'prime'. Test that an expression represents a prime" + " number. When the expression is an exact number, the result (when True)" + " is subject to the limitations of isprime() which is used to return the " + "result.") + ) + + +class CompositePredicate(Predicate): + """ + Composite number predicate. + + Explanation + =========== + + ``ask(Q.composite(x))`` is true iff ``x`` is a positive integer and has + at least one positive divisor other than ``1`` and the number itself. + + Examples + ======== + + >>> from sympy import Q, ask + >>> ask(Q.composite(0)) + False + >>> ask(Q.composite(1)) + False + >>> ask(Q.composite(2)) + False + >>> ask(Q.composite(20)) + True + + """ + name = 'composite' + handler = Dispatcher("CompositeHandler", doc="Handler for key 'composite'.") + + +class EvenPredicate(Predicate): + """ + Even number predicate. + + Explanation + =========== + + ``ask(Q.even(x))`` is true iff ``x`` belongs to the set of even + integers. + + Examples + ======== + + >>> from sympy import Q, ask, pi + >>> ask(Q.even(0)) + True + >>> ask(Q.even(2)) + True + >>> ask(Q.even(3)) + False + >>> ask(Q.even(pi)) + False + + """ + name = 'even' + handler = Dispatcher("EvenHandler", doc="Handler for key 'even'.") + + +class OddPredicate(Predicate): + """ + Odd number predicate. + + Explanation + =========== + + ``ask(Q.odd(x))`` is true iff ``x`` belongs to the set of odd numbers. + + Examples + ======== + + >>> from sympy import Q, ask, pi + >>> ask(Q.odd(0)) + False + >>> ask(Q.odd(2)) + False + >>> ask(Q.odd(3)) + True + >>> ask(Q.odd(pi)) + False + + """ + name = 'odd' + handler = Dispatcher( + "OddHandler", + doc=("Handler for key 'odd'. Test that an expression represents an odd" + " number.") + ) diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/order.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/order.py new file mode 100644 index 0000000000000000000000000000000000000000..86bfb2ae49789efd5b0df99e2cfc63984e956dd0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/order.py @@ -0,0 +1,390 @@ +from sympy.assumptions import Predicate +from sympy.multipledispatch import Dispatcher + + +class NegativePredicate(Predicate): + r""" + Negative number predicate. + + Explanation + =========== + + ``Q.negative(x)`` is true iff ``x`` is a real number and :math:`x < 0`, that is, + it is in the interval :math:`(-\infty, 0)`. Note in particular that negative + infinity is not negative. + + A few important facts about negative numbers: + + - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same + thing. ``~Q.negative(x)`` simply means that ``x`` is not negative, + whereas ``Q.nonnegative(x)`` means that ``x`` is real and not + negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to + ``Q.zero(x) | Q.positive(x)``. So for example, ``~Q.negative(I)`` is + true, whereas ``Q.nonnegative(I)`` is false. + + - See the documentation of ``Q.real`` for more information about + related facts. + + Examples + ======== + + >>> from sympy import Q, ask, symbols, I + >>> x = symbols('x') + >>> ask(Q.negative(x), Q.real(x) & ~Q.positive(x) & ~Q.zero(x)) + True + >>> ask(Q.negative(-1)) + True + >>> ask(Q.nonnegative(I)) + False + >>> ask(~Q.negative(I)) + True + + """ + name = 'negative' + handler = Dispatcher( + "NegativeHandler", + doc=("Handler for Q.negative. Test that an expression is strictly less" + " than zero.") + ) + + +class NonNegativePredicate(Predicate): + """ + Nonnegative real number predicate. + + Explanation + =========== + + ``ask(Q.nonnegative(x))`` is true iff ``x`` belongs to the set of + positive numbers including zero. + + - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same + thing. ``~Q.negative(x)`` simply means that ``x`` is not negative, + whereas ``Q.nonnegative(x)`` means that ``x`` is real and not + negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to + ``Q.zero(x) | Q.positive(x)``. So for example, ``~Q.negative(I)`` is + true, whereas ``Q.nonnegative(I)`` is false. + + Examples + ======== + + >>> from sympy import Q, ask, I + >>> ask(Q.nonnegative(1)) + True + >>> ask(Q.nonnegative(0)) + True + >>> ask(Q.nonnegative(-1)) + False + >>> ask(Q.nonnegative(I)) + False + >>> ask(Q.nonnegative(-I)) + False + + """ + name = 'nonnegative' + handler = Dispatcher( + "NonNegativeHandler", + doc=("Handler for Q.nonnegative.") + ) + + +class NonZeroPredicate(Predicate): + """ + Nonzero real number predicate. + + Explanation + =========== + + ``ask(Q.nonzero(x))`` is true iff ``x`` is real and ``x`` is not zero. Note in + particular that ``Q.nonzero(x)`` is false if ``x`` is not real. Use + ``~Q.zero(x)`` if you want the negation of being zero without any real + assumptions. + + A few important facts about nonzero numbers: + + - ``Q.nonzero`` is logically equivalent to ``Q.positive | Q.negative``. + + - See the documentation of ``Q.real`` for more information about + related facts. + + Examples + ======== + + >>> from sympy import Q, ask, symbols, I, oo + >>> x = symbols('x') + >>> print(ask(Q.nonzero(x), ~Q.zero(x))) + None + >>> ask(Q.nonzero(x), Q.positive(x)) + True + >>> ask(Q.nonzero(x), Q.zero(x)) + False + >>> ask(Q.nonzero(0)) + False + >>> ask(Q.nonzero(I)) + False + >>> ask(~Q.zero(I)) + True + >>> ask(Q.nonzero(oo)) + False + + """ + name = 'nonzero' + handler = Dispatcher( + "NonZeroHandler", + doc=("Handler for key 'nonzero'. Test that an expression is not identically" + " zero.") + ) + + +class ZeroPredicate(Predicate): + """ + Zero number predicate. + + Explanation + =========== + + ``ask(Q.zero(x))`` is true iff the value of ``x`` is zero. + + Examples + ======== + + >>> from sympy import ask, Q, oo, symbols + >>> x, y = symbols('x, y') + >>> ask(Q.zero(0)) + True + >>> ask(Q.zero(1/oo)) + True + >>> print(ask(Q.zero(0*oo))) + None + >>> ask(Q.zero(1)) + False + >>> ask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) + True + + """ + name = 'zero' + handler = Dispatcher( + "ZeroHandler", + doc="Handler for key 'zero'." + ) + + +class NonPositivePredicate(Predicate): + """ + Nonpositive real number predicate. + + Explanation + =========== + + ``ask(Q.nonpositive(x))`` is true iff ``x`` belongs to the set of + negative numbers including zero. + + - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same + thing. ``~Q.positive(x)`` simply means that ``x`` is not positive, + whereas ``Q.nonpositive(x)`` means that ``x`` is real and not + positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to + `Q.negative(x) | Q.zero(x)``. So for example, ``~Q.positive(I)`` is + true, whereas ``Q.nonpositive(I)`` is false. + + Examples + ======== + + >>> from sympy import Q, ask, I + + >>> ask(Q.nonpositive(-1)) + True + >>> ask(Q.nonpositive(0)) + True + >>> ask(Q.nonpositive(1)) + False + >>> ask(Q.nonpositive(I)) + False + >>> ask(Q.nonpositive(-I)) + False + + """ + name = 'nonpositive' + handler = Dispatcher( + "NonPositiveHandler", + doc="Handler for key 'nonpositive'." + ) + + +class PositivePredicate(Predicate): + r""" + Positive real number predicate. + + Explanation + =========== + + ``Q.positive(x)`` is true iff ``x`` is real and `x > 0`, that is if ``x`` + is in the interval `(0, \infty)`. In particular, infinity is not + positive. + + A few important facts about positive numbers: + + - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same + thing. ``~Q.positive(x)`` simply means that ``x`` is not positive, + whereas ``Q.nonpositive(x)`` means that ``x`` is real and not + positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to + `Q.negative(x) | Q.zero(x)``. So for example, ``~Q.positive(I)`` is + true, whereas ``Q.nonpositive(I)`` is false. + + - See the documentation of ``Q.real`` for more information about + related facts. + + Examples + ======== + + >>> from sympy import Q, ask, symbols, I + >>> x = symbols('x') + >>> ask(Q.positive(x), Q.real(x) & ~Q.negative(x) & ~Q.zero(x)) + True + >>> ask(Q.positive(1)) + True + >>> ask(Q.nonpositive(I)) + False + >>> ask(~Q.positive(I)) + True + + """ + name = 'positive' + handler = Dispatcher( + "PositiveHandler", + doc=("Handler for key 'positive'. Test that an expression is strictly" + " greater than zero.") + ) + + +class ExtendedPositivePredicate(Predicate): + r""" + Positive extended real number predicate. + + Explanation + =========== + + ``Q.extended_positive(x)`` is true iff ``x`` is extended real and + `x > 0`, that is if ``x`` is in the interval `(0, \infty]`. + + Examples + ======== + + >>> from sympy import ask, I, oo, Q + >>> ask(Q.extended_positive(1)) + True + >>> ask(Q.extended_positive(oo)) + True + >>> ask(Q.extended_positive(I)) + False + + """ + name = 'extended_positive' + handler = Dispatcher("ExtendedPositiveHandler") + + +class ExtendedNegativePredicate(Predicate): + r""" + Negative extended real number predicate. + + Explanation + =========== + + ``Q.extended_negative(x)`` is true iff ``x`` is extended real and + `x < 0`, that is if ``x`` is in the interval `[-\infty, 0)`. + + Examples + ======== + + >>> from sympy import ask, I, oo, Q + >>> ask(Q.extended_negative(-1)) + True + >>> ask(Q.extended_negative(-oo)) + True + >>> ask(Q.extended_negative(-I)) + False + + """ + name = 'extended_negative' + handler = Dispatcher("ExtendedNegativeHandler") + + +class ExtendedNonZeroPredicate(Predicate): + """ + Nonzero extended real number predicate. + + Explanation + =========== + + ``ask(Q.extended_nonzero(x))`` is true iff ``x`` is extended real and + ``x`` is not zero. + + Examples + ======== + + >>> from sympy import ask, I, oo, Q + >>> ask(Q.extended_nonzero(-1)) + True + >>> ask(Q.extended_nonzero(oo)) + True + >>> ask(Q.extended_nonzero(I)) + False + + """ + name = 'extended_nonzero' + handler = Dispatcher("ExtendedNonZeroHandler") + + +class ExtendedNonPositivePredicate(Predicate): + """ + Nonpositive extended real number predicate. + + Explanation + =========== + + ``ask(Q.extended_nonpositive(x))`` is true iff ``x`` is extended real and + ``x`` is not positive. + + Examples + ======== + + >>> from sympy import ask, I, oo, Q + >>> ask(Q.extended_nonpositive(-1)) + True + >>> ask(Q.extended_nonpositive(oo)) + False + >>> ask(Q.extended_nonpositive(0)) + True + >>> ask(Q.extended_nonpositive(I)) + False + + """ + name = 'extended_nonpositive' + handler = Dispatcher("ExtendedNonPositiveHandler") + + +class ExtendedNonNegativePredicate(Predicate): + """ + Nonnegative extended real number predicate. + + Explanation + =========== + + ``ask(Q.extended_nonnegative(x))`` is true iff ``x`` is extended real and + ``x`` is not negative. + + Examples + ======== + + >>> from sympy import ask, I, oo, Q + >>> ask(Q.extended_nonnegative(-1)) + False + >>> ask(Q.extended_nonnegative(oo)) + True + >>> ask(Q.extended_nonnegative(0)) + True + >>> ask(Q.extended_nonnegative(I)) + False + + """ + name = 'extended_nonnegative' + handler = Dispatcher("ExtendedNonNegativeHandler") diff --git a/lib/python3.11/site-packages/sympy/assumptions/predicates/sets.py b/lib/python3.11/site-packages/sympy/assumptions/predicates/sets.py new file mode 100644 index 0000000000000000000000000000000000000000..18261cee2d9de65df14a31a56b2cd22328328ed0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/predicates/sets.py @@ -0,0 +1,399 @@ +from sympy.assumptions import Predicate +from sympy.multipledispatch import Dispatcher + + +class IntegerPredicate(Predicate): + """ + Integer predicate. + + Explanation + =========== + + ``Q.integer(x)`` is true iff ``x`` belongs to the set of integer + numbers. + + Examples + ======== + + >>> from sympy import Q, ask, S + >>> ask(Q.integer(5)) + True + >>> ask(Q.integer(S(1)/2)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Integer + + """ + name = 'integer' + handler = Dispatcher( + "IntegerHandler", + doc=("Handler for Q.integer.\n\n" + "Test that an expression belongs to the field of integer numbers.") + ) + + +class NonIntegerPredicate(Predicate): + """ + Non-integer extended real predicate. + """ + name = 'noninteger' + handler = Dispatcher( + "NonIntegerHandler", + doc=("Handler for Q.noninteger.\n\n" + "Test that an expression is a non-integer extended real number.") + ) + + +class RationalPredicate(Predicate): + """ + Rational number predicate. + + Explanation + =========== + + ``Q.rational(x)`` is true iff ``x`` belongs to the set of + rational numbers. + + Examples + ======== + + >>> from sympy import ask, Q, pi, S + >>> ask(Q.rational(0)) + True + >>> ask(Q.rational(S(1)/2)) + True + >>> ask(Q.rational(pi)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Rational_number + + """ + name = 'rational' + handler = Dispatcher( + "RationalHandler", + doc=("Handler for Q.rational.\n\n" + "Test that an expression belongs to the field of rational numbers.") + ) + + +class IrrationalPredicate(Predicate): + """ + Irrational number predicate. + + Explanation + =========== + + ``Q.irrational(x)`` is true iff ``x`` is any real number that + cannot be expressed as a ratio of integers. + + Examples + ======== + + >>> from sympy import ask, Q, pi, S, I + >>> ask(Q.irrational(0)) + False + >>> ask(Q.irrational(S(1)/2)) + False + >>> ask(Q.irrational(pi)) + True + >>> ask(Q.irrational(I)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Irrational_number + + """ + name = 'irrational' + handler = Dispatcher( + "IrrationalHandler", + doc=("Handler for Q.irrational.\n\n" + "Test that an expression is irrational numbers.") + ) + + +class RealPredicate(Predicate): + r""" + Real number predicate. + + Explanation + =========== + + ``Q.real(x)`` is true iff ``x`` is a real number, i.e., it is in the + interval `(-\infty, \infty)`. Note that, in particular the + infinities are not real. Use ``Q.extended_real`` if you want to + consider those as well. + + A few important facts about reals: + + - Every real number is positive, negative, or zero. Furthermore, + because these sets are pairwise disjoint, each real number is + exactly one of those three. + + - Every real number is also complex. + + - Every real number is finite. + + - Every real number is either rational or irrational. + + - Every real number is either algebraic or transcendental. + + - The facts ``Q.negative``, ``Q.zero``, ``Q.positive``, + ``Q.nonnegative``, ``Q.nonpositive``, ``Q.nonzero``, + ``Q.integer``, ``Q.rational``, and ``Q.irrational`` all imply + ``Q.real``, as do all facts that imply those facts. + + - The facts ``Q.algebraic``, and ``Q.transcendental`` do not imply + ``Q.real``; they imply ``Q.complex``. An algebraic or + transcendental number may or may not be real. + + - The "non" facts (i.e., ``Q.nonnegative``, ``Q.nonzero``, + ``Q.nonpositive`` and ``Q.noninteger``) are not equivalent to + not the fact, but rather, not the fact *and* ``Q.real``. + For example, ``Q.nonnegative`` means ``~Q.negative & Q.real``. + So for example, ``I`` is not nonnegative, nonzero, or + nonpositive. + + Examples + ======== + + >>> from sympy import Q, ask, symbols + >>> x = symbols('x') + >>> ask(Q.real(x), Q.positive(x)) + True + >>> ask(Q.real(0)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Real_number + + """ + name = 'real' + handler = Dispatcher( + "RealHandler", + doc=("Handler for Q.real.\n\n" + "Test that an expression belongs to the field of real numbers.") + ) + + +class ExtendedRealPredicate(Predicate): + r""" + Extended real predicate. + + Explanation + =========== + + ``Q.extended_real(x)`` is true iff ``x`` is a real number or + `\{-\infty, \infty\}`. + + See documentation of ``Q.real`` for more information about related + facts. + + Examples + ======== + + >>> from sympy import ask, Q, oo, I + >>> ask(Q.extended_real(1)) + True + >>> ask(Q.extended_real(I)) + False + >>> ask(Q.extended_real(oo)) + True + + """ + name = 'extended_real' + handler = Dispatcher( + "ExtendedRealHandler", + doc=("Handler for Q.extended_real.\n\n" + "Test that an expression belongs to the field of extended real\n" + "numbers, that is real numbers union {Infinity, -Infinity}.") + ) + + +class HermitianPredicate(Predicate): + """ + Hermitian predicate. + + Explanation + =========== + + ``ask(Q.hermitian(x))`` is true iff ``x`` belongs to the set of + Hermitian operators. + + References + ========== + + .. [1] https://mathworld.wolfram.com/HermitianOperator.html + + """ + # TODO: Add examples + name = 'hermitian' + handler = Dispatcher( + "HermitianHandler", + doc=("Handler for Q.hermitian.\n\n" + "Test that an expression belongs to the field of Hermitian operators.") + ) + + +class ComplexPredicate(Predicate): + """ + Complex number predicate. + + Explanation + =========== + + ``Q.complex(x)`` is true iff ``x`` belongs to the set of complex + numbers. Note that every complex number is finite. + + Examples + ======== + + >>> from sympy import Q, Symbol, ask, I, oo + >>> x = Symbol('x') + >>> ask(Q.complex(0)) + True + >>> ask(Q.complex(2 + 3*I)) + True + >>> ask(Q.complex(oo)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Complex_number + + """ + name = 'complex' + handler = Dispatcher( + "ComplexHandler", + doc=("Handler for Q.complex.\n\n" + "Test that an expression belongs to the field of complex numbers.") + ) + + +class ImaginaryPredicate(Predicate): + """ + Imaginary number predicate. + + Explanation + =========== + + ``Q.imaginary(x)`` is true iff ``x`` can be written as a real + number multiplied by the imaginary unit ``I``. Please note that ``0`` + is not considered to be an imaginary number. + + Examples + ======== + + >>> from sympy import Q, ask, I + >>> ask(Q.imaginary(3*I)) + True + >>> ask(Q.imaginary(2 + 3*I)) + False + >>> ask(Q.imaginary(0)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Imaginary_number + + """ + name = 'imaginary' + handler = Dispatcher( + "ImaginaryHandler", + doc=("Handler for Q.imaginary.\n\n" + "Test that an expression belongs to the field of imaginary numbers,\n" + "that is, numbers in the form x*I, where x is real.") + ) + + +class AntihermitianPredicate(Predicate): + """ + Antihermitian predicate. + + Explanation + =========== + + ``Q.antihermitian(x)`` is true iff ``x`` belongs to the field of + antihermitian operators, i.e., operators in the form ``x*I``, where + ``x`` is Hermitian. + + References + ========== + + .. [1] https://mathworld.wolfram.com/HermitianOperator.html + + """ + # TODO: Add examples + name = 'antihermitian' + handler = Dispatcher( + "AntiHermitianHandler", + doc=("Handler for Q.antihermitian.\n\n" + "Test that an expression belongs to the field of anti-Hermitian\n" + "operators, that is, operators in the form x*I, where x is Hermitian.") + ) + + +class AlgebraicPredicate(Predicate): + r""" + Algebraic number predicate. + + Explanation + =========== + + ``Q.algebraic(x)`` is true iff ``x`` belongs to the set of + algebraic numbers. ``x`` is algebraic if there is some polynomial + in ``p(x)\in \mathbb\{Q\}[x]`` such that ``p(x) = 0``. + + Examples + ======== + + >>> from sympy import ask, Q, sqrt, I, pi + >>> ask(Q.algebraic(sqrt(2))) + True + >>> ask(Q.algebraic(I)) + True + >>> ask(Q.algebraic(pi)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Algebraic_number + + """ + name = 'algebraic' + AlgebraicHandler = Dispatcher( + "AlgebraicHandler", + doc="""Handler for Q.algebraic key.""" + ) + + +class TranscendentalPredicate(Predicate): + """ + Transcedental number predicate. + + Explanation + =========== + + ``Q.transcendental(x)`` is true iff ``x`` belongs to the set of + transcendental numbers. A transcendental number is a real + or complex number that is not algebraic. + + """ + # TODO: Add examples + name = 'transcendental' + handler = Dispatcher( + "Transcendental", + doc="""Handler for Q.transcendental key.""" + ) diff --git a/lib/python3.11/site-packages/sympy/assumptions/refine.py b/lib/python3.11/site-packages/sympy/assumptions/refine.py new file mode 100644 index 0000000000000000000000000000000000000000..8d5d0f6028fda7a15c0ac66bd7001779fa2fc068 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/refine.py @@ -0,0 +1,405 @@ +from __future__ import annotations +from typing import Callable + +from sympy.core import S, Add, Expr, Basic, Mul, Pow, Rational +from sympy.core.logic import fuzzy_not +from sympy.logic.boolalg import Boolean + +from sympy.assumptions import ask, Q # type: ignore + + +def refine(expr, assumptions=True): + """ + Simplify an expression using assumptions. + + Explanation + =========== + + Unlike :func:`~.simplify()` which performs structural simplification + without any assumption, this function transforms the expression into + the form which is only valid under certain assumptions. Note that + ``simplify()`` is generally not done in refining process. + + Refining boolean expression involves reducing it to ``S.true`` or + ``S.false``. Unlike :func:`~.ask()`, the expression will not be reduced + if the truth value cannot be determined. + + Examples + ======== + + >>> from sympy import refine, sqrt, Q + >>> from sympy.abc import x + >>> refine(sqrt(x**2), Q.real(x)) + Abs(x) + >>> refine(sqrt(x**2), Q.positive(x)) + x + + >>> refine(Q.real(x), Q.positive(x)) + True + >>> refine(Q.positive(x), Q.real(x)) + Q.positive(x) + + See Also + ======== + + sympy.simplify.simplify.simplify : Structural simplification without assumptions. + sympy.assumptions.ask.ask : Query for boolean expressions using assumptions. + """ + if not isinstance(expr, Basic): + return expr + + if not expr.is_Atom: + args = [refine(arg, assumptions) for arg in expr.args] + # TODO: this will probably not work with Integral or Polynomial + expr = expr.func(*args) + if hasattr(expr, '_eval_refine'): + ref_expr = expr._eval_refine(assumptions) + if ref_expr is not None: + return ref_expr + name = expr.__class__.__name__ + handler = handlers_dict.get(name, None) + if handler is None: + return expr + new_expr = handler(expr, assumptions) + if (new_expr is None) or (expr == new_expr): + return expr + if not isinstance(new_expr, Expr): + return new_expr + return refine(new_expr, assumptions) + + +def refine_abs(expr, assumptions): + """ + Handler for the absolute value. + + Examples + ======== + + >>> from sympy import Q, Abs + >>> from sympy.assumptions.refine import refine_abs + >>> from sympy.abc import x + >>> refine_abs(Abs(x), Q.real(x)) + >>> refine_abs(Abs(x), Q.positive(x)) + x + >>> refine_abs(Abs(x), Q.negative(x)) + -x + + """ + from sympy.functions.elementary.complexes import Abs + arg = expr.args[0] + if ask(Q.real(arg), assumptions) and \ + fuzzy_not(ask(Q.negative(arg), assumptions)): + # if it's nonnegative + return arg + if ask(Q.negative(arg), assumptions): + return -arg + # arg is Mul + if isinstance(arg, Mul): + r = [refine(abs(a), assumptions) for a in arg.args] + non_abs = [] + in_abs = [] + for i in r: + if isinstance(i, Abs): + in_abs.append(i.args[0]) + else: + non_abs.append(i) + return Mul(*non_abs) * Abs(Mul(*in_abs)) + + +def refine_Pow(expr, assumptions): + """ + Handler for instances of Pow. + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.refine import refine_Pow + >>> from sympy.abc import x,y,z + >>> refine_Pow((-1)**x, Q.real(x)) + >>> refine_Pow((-1)**x, Q.even(x)) + 1 + >>> refine_Pow((-1)**x, Q.odd(x)) + -1 + + For powers of -1, even parts of the exponent can be simplified: + + >>> refine_Pow((-1)**(x+y), Q.even(x)) + (-1)**y + >>> refine_Pow((-1)**(x+y+z), Q.odd(x) & Q.odd(z)) + (-1)**y + >>> refine_Pow((-1)**(x+y+2), Q.odd(x)) + (-1)**(y + 1) + >>> refine_Pow((-1)**(x+3), True) + (-1)**(x + 1) + + """ + from sympy.functions.elementary.complexes import Abs + from sympy.functions import sign + if isinstance(expr.base, Abs): + if ask(Q.real(expr.base.args[0]), assumptions) and \ + ask(Q.even(expr.exp), assumptions): + return expr.base.args[0] ** expr.exp + if ask(Q.real(expr.base), assumptions): + if expr.base.is_number: + if ask(Q.even(expr.exp), assumptions): + return abs(expr.base) ** expr.exp + if ask(Q.odd(expr.exp), assumptions): + return sign(expr.base) * abs(expr.base) ** expr.exp + if isinstance(expr.exp, Rational): + if isinstance(expr.base, Pow): + return abs(expr.base.base) ** (expr.base.exp * expr.exp) + + if expr.base is S.NegativeOne: + if expr.exp.is_Add: + + old = expr + + # For powers of (-1) we can remove + # - even terms + # - pairs of odd terms + # - a single odd term + 1 + # - A numerical constant N can be replaced with mod(N,2) + + coeff, terms = expr.exp.as_coeff_add() + terms = set(terms) + even_terms = set() + odd_terms = set() + initial_number_of_terms = len(terms) + + for t in terms: + if ask(Q.even(t), assumptions): + even_terms.add(t) + elif ask(Q.odd(t), assumptions): + odd_terms.add(t) + + terms -= even_terms + if len(odd_terms) % 2: + terms -= odd_terms + new_coeff = (coeff + S.One) % 2 + else: + terms -= odd_terms + new_coeff = coeff % 2 + + if new_coeff != coeff or len(terms) < initial_number_of_terms: + terms.add(new_coeff) + expr = expr.base**(Add(*terms)) + + # Handle (-1)**((-1)**n/2 + m/2) + e2 = 2*expr.exp + if ask(Q.even(e2), assumptions): + if e2.could_extract_minus_sign(): + e2 *= expr.base + if e2.is_Add: + i, p = e2.as_two_terms() + if p.is_Pow and p.base is S.NegativeOne: + if ask(Q.integer(p.exp), assumptions): + i = (i + 1)/2 + if ask(Q.even(i), assumptions): + return expr.base**p.exp + elif ask(Q.odd(i), assumptions): + return expr.base**(p.exp + 1) + else: + return expr.base**(p.exp + i) + + if old != expr: + return expr + + +def refine_atan2(expr, assumptions): + """ + Handler for the atan2 function. + + Examples + ======== + + >>> from sympy import Q, atan2 + >>> from sympy.assumptions.refine import refine_atan2 + >>> from sympy.abc import x, y + >>> refine_atan2(atan2(y,x), Q.real(y) & Q.positive(x)) + atan(y/x) + >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.negative(x)) + atan(y/x) - pi + >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.negative(x)) + atan(y/x) + pi + >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.negative(x)) + pi + >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.zero(x)) + pi/2 + >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.zero(x)) + -pi/2 + >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.zero(x)) + nan + """ + from sympy.functions.elementary.trigonometric import atan + y, x = expr.args + if ask(Q.real(y) & Q.positive(x), assumptions): + return atan(y / x) + elif ask(Q.negative(y) & Q.negative(x), assumptions): + return atan(y / x) - S.Pi + elif ask(Q.positive(y) & Q.negative(x), assumptions): + return atan(y / x) + S.Pi + elif ask(Q.zero(y) & Q.negative(x), assumptions): + return S.Pi + elif ask(Q.positive(y) & Q.zero(x), assumptions): + return S.Pi/2 + elif ask(Q.negative(y) & Q.zero(x), assumptions): + return -S.Pi/2 + elif ask(Q.zero(y) & Q.zero(x), assumptions): + return S.NaN + else: + return expr + + +def refine_re(expr, assumptions): + """ + Handler for real part. + + Examples + ======== + + >>> from sympy.assumptions.refine import refine_re + >>> from sympy import Q, re + >>> from sympy.abc import x + >>> refine_re(re(x), Q.real(x)) + x + >>> refine_re(re(x), Q.imaginary(x)) + 0 + """ + arg = expr.args[0] + if ask(Q.real(arg), assumptions): + return arg + if ask(Q.imaginary(arg), assumptions): + return S.Zero + return _refine_reim(expr, assumptions) + + +def refine_im(expr, assumptions): + """ + Handler for imaginary part. + + Explanation + =========== + + >>> from sympy.assumptions.refine import refine_im + >>> from sympy import Q, im + >>> from sympy.abc import x + >>> refine_im(im(x), Q.real(x)) + 0 + >>> refine_im(im(x), Q.imaginary(x)) + -I*x + """ + arg = expr.args[0] + if ask(Q.real(arg), assumptions): + return S.Zero + if ask(Q.imaginary(arg), assumptions): + return - S.ImaginaryUnit * arg + return _refine_reim(expr, assumptions) + +def refine_arg(expr, assumptions): + """ + Handler for complex argument + + Explanation + =========== + + >>> from sympy.assumptions.refine import refine_arg + >>> from sympy import Q, arg + >>> from sympy.abc import x + >>> refine_arg(arg(x), Q.positive(x)) + 0 + >>> refine_arg(arg(x), Q.negative(x)) + pi + """ + rg = expr.args[0] + if ask(Q.positive(rg), assumptions): + return S.Zero + if ask(Q.negative(rg), assumptions): + return S.Pi + return None + + +def _refine_reim(expr, assumptions): + # Helper function for refine_re & refine_im + expanded = expr.expand(complex = True) + if expanded != expr: + refined = refine(expanded, assumptions) + if refined != expanded: + return refined + # Best to leave the expression as is + return None + + +def refine_sign(expr, assumptions): + """ + Handler for sign. + + Examples + ======== + + >>> from sympy.assumptions.refine import refine_sign + >>> from sympy import Symbol, Q, sign, im + >>> x = Symbol('x', real = True) + >>> expr = sign(x) + >>> refine_sign(expr, Q.positive(x) & Q.nonzero(x)) + 1 + >>> refine_sign(expr, Q.negative(x) & Q.nonzero(x)) + -1 + >>> refine_sign(expr, Q.zero(x)) + 0 + >>> y = Symbol('y', imaginary = True) + >>> expr = sign(y) + >>> refine_sign(expr, Q.positive(im(y))) + I + >>> refine_sign(expr, Q.negative(im(y))) + -I + """ + arg = expr.args[0] + if ask(Q.zero(arg), assumptions): + return S.Zero + if ask(Q.real(arg)): + if ask(Q.positive(arg), assumptions): + return S.One + if ask(Q.negative(arg), assumptions): + return S.NegativeOne + if ask(Q.imaginary(arg)): + arg_re, arg_im = arg.as_real_imag() + if ask(Q.positive(arg_im), assumptions): + return S.ImaginaryUnit + if ask(Q.negative(arg_im), assumptions): + return -S.ImaginaryUnit + return expr + + +def refine_matrixelement(expr, assumptions): + """ + Handler for symmetric part. + + Examples + ======== + + >>> from sympy.assumptions.refine import refine_matrixelement + >>> from sympy import MatrixSymbol, Q + >>> X = MatrixSymbol('X', 3, 3) + >>> refine_matrixelement(X[0, 1], Q.symmetric(X)) + X[0, 1] + >>> refine_matrixelement(X[1, 0], Q.symmetric(X)) + X[0, 1] + """ + from sympy.matrices.expressions.matexpr import MatrixElement + matrix, i, j = expr.args + if ask(Q.symmetric(matrix), assumptions): + if (i - j).could_extract_minus_sign(): + return expr + return MatrixElement(matrix, j, i) + +handlers_dict: dict[str, Callable[[Expr, Boolean], Expr]] = { + 'Abs': refine_abs, + 'Pow': refine_Pow, + 'atan2': refine_atan2, + 're': refine_re, + 'im': refine_im, + 'arg': refine_arg, + 'sign': refine_sign, + 'MatrixElement': refine_matrixelement +} diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/__init__.py b/lib/python3.11/site-packages/sympy/assumptions/relation/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..04f5ed37893766feec941614691a9177f14e4027 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/relation/__init__.py @@ -0,0 +1,13 @@ +""" +A module to implement finitary relations [1] as predicate. + +References +========== + +.. [1] https://en.wikipedia.org/wiki/Finitary_relation + +""" + +__all__ = ['BinaryRelation', 'AppliedBinaryRelation'] + +from .binrel import BinaryRelation, AppliedBinaryRelation diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..0bdb42bf0c76b9576fcee740e072c1b26bc35503 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/binrel.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/binrel.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..3c451b1b35fc61bf4d1add3bc7edf9f288ae3ae3 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/binrel.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/equality.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/equality.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..8a1b82b5c9dd6ad769220212d7b812c5e4d22ee5 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/relation/__pycache__/equality.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/binrel.py b/lib/python3.11/site-packages/sympy/assumptions/relation/binrel.py new file mode 100644 index 0000000000000000000000000000000000000000..4b4eba05bcce40f1a05483a30136b6ccd891c42f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/relation/binrel.py @@ -0,0 +1,212 @@ +""" +General binary relations. +""" +from typing import Optional + +from sympy.core.singleton import S +from sympy.assumptions import AppliedPredicate, ask, Predicate, Q # type: ignore +from sympy.core.kind import BooleanKind +from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le +from sympy.logic.boolalg import conjuncts, Not + +__all__ = ["BinaryRelation", "AppliedBinaryRelation"] + + +class BinaryRelation(Predicate): + """ + Base class for all binary relational predicates. + + Explanation + =========== + + Binary relation takes two arguments and returns ``AppliedBinaryRelation`` + instance. To evaluate it to boolean value, use :obj:`~.ask()` or + :obj:`~.refine()` function. + + You can add support for new types by registering the handler to dispatcher. + See :obj:`~.Predicate()` for more information about predicate dispatching. + + Examples + ======== + + Applying and evaluating to boolean value: + + >>> from sympy import Q, ask, sin, cos + >>> from sympy.abc import x + >>> Q.eq(sin(x)**2+cos(x)**2, 1) + Q.eq(sin(x)**2 + cos(x)**2, 1) + >>> ask(_) + True + + You can define a new binary relation by subclassing and dispatching. + Here, we define a relation $R$ such that $x R y$ returns true if + $x = y + 1$. + + >>> from sympy import ask, Number, Q + >>> from sympy.assumptions import BinaryRelation + >>> class MyRel(BinaryRelation): + ... name = "R" + ... is_reflexive = False + >>> Q.R = MyRel() + >>> @Q.R.register(Number, Number) + ... def _(n1, n2, assumptions): + ... return ask(Q.zero(n1 - n2 - 1), assumptions) + >>> Q.R(2, 1) + Q.R(2, 1) + + Now, we can use ``ask()`` to evaluate it to boolean value. + + >>> ask(Q.R(2, 1)) + True + >>> ask(Q.R(1, 2)) + False + + ``Q.R`` returns ``False`` with minimum cost if two arguments have same + structure because it is antireflexive relation [1] by + ``is_reflexive = False``. + + >>> ask(Q.R(x, x)) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Reflexive_relation + """ + + is_reflexive: Optional[bool] = None + is_symmetric: Optional[bool] = None + + def __call__(self, *args): + if not len(args) == 2: + raise ValueError("Binary relation takes two arguments, but got %s." % len(args)) + return AppliedBinaryRelation(self, *args) + + @property + def reversed(self): + if self.is_symmetric: + return self + return None + + @property + def negated(self): + return None + + def _compare_reflexive(self, lhs, rhs): + # quick exit for structurally same arguments + # do not check != here because it cannot catch the + # equivalent arguments with different structures. + + # reflexivity does not hold to NaN + if lhs is S.NaN or rhs is S.NaN: + return None + + reflexive = self.is_reflexive + if reflexive is None: + pass + elif reflexive and (lhs == rhs): + return True + elif not reflexive and (lhs == rhs): + return False + return None + + def eval(self, args, assumptions=True): + # quick exit for structurally same arguments + ret = self._compare_reflexive(*args) + if ret is not None: + return ret + + # don't perform simplify on args here. (done by AppliedBinaryRelation._eval_ask) + # evaluate by multipledispatch + lhs, rhs = args + ret = self.handler(lhs, rhs, assumptions=assumptions) + if ret is not None: + return ret + + # check reversed order if the relation is reflexive + if self.is_reflexive: + types = (type(lhs), type(rhs)) + if self.handler.dispatch(*types) is not self.handler.dispatch(*reversed(types)): + ret = self.handler(rhs, lhs, assumptions=assumptions) + + return ret + + +class AppliedBinaryRelation(AppliedPredicate): + """ + The class of expressions resulting from applying ``BinaryRelation`` + to the arguments. + + """ + + @property + def lhs(self): + """The left-hand side of the relation.""" + return self.arguments[0] + + @property + def rhs(self): + """The right-hand side of the relation.""" + return self.arguments[1] + + @property + def reversed(self): + """ + Try to return the relationship with sides reversed. + """ + revfunc = self.function.reversed + if revfunc is None: + return self + return revfunc(self.rhs, self.lhs) + + @property + def reversedsign(self): + """ + Try to return the relationship with signs reversed. + """ + revfunc = self.function.reversed + if revfunc is None: + return self + if not any(side.kind is BooleanKind for side in self.arguments): + return revfunc(-self.lhs, -self.rhs) + return self + + @property + def negated(self): + neg_rel = self.function.negated + if neg_rel is None: + return Not(self, evaluate=False) + return neg_rel(*self.arguments) + + def _eval_ask(self, assumptions): + conj_assumps = set() + binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le} + for a in conjuncts(assumptions): + if a.func in binrelpreds: + conj_assumps.add(binrelpreds[type(a)](*a.args)) + else: + conj_assumps.add(a) + + # After CNF in assumptions module is modified to take polyadic + # predicate, this will be removed + if any(rel in conj_assumps for rel in (self, self.reversed)): + return True + neg_rels = (self.negated, self.reversed.negated, Not(self, evaluate=False), + Not(self.reversed, evaluate=False)) + if any(rel in conj_assumps for rel in neg_rels): + return False + + # evaluation using multipledispatching + ret = self.function.eval(self.arguments, assumptions) + if ret is not None: + return ret + + # simplify the args and try again + args = tuple(a.simplify() for a in self.arguments) + return self.function.eval(args, assumptions) + + def __bool__(self): + ret = ask(self) + if ret is None: + raise TypeError("Cannot determine truth value of %s" % self) + return ret diff --git a/lib/python3.11/site-packages/sympy/assumptions/relation/equality.py b/lib/python3.11/site-packages/sympy/assumptions/relation/equality.py new file mode 100644 index 0000000000000000000000000000000000000000..e7857632997b84aa3ec6e127ee75caf2c85bf22d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/relation/equality.py @@ -0,0 +1,302 @@ +""" +Module for mathematical equality [1] and inequalities [2]. + +The purpose of this module is to provide the instances which represent the +binary predicates in order to combine the relationals into logical inference +system. Objects such as ``Q.eq``, ``Q.lt`` should remain internal to +assumptions module, and user must use the classes such as :obj:`~.Eq()`, +:obj:`~.Lt()` instead to construct the relational expressions. + +References +========== + +.. [1] https://en.wikipedia.org/wiki/Equality_(mathematics) +.. [2] https://en.wikipedia.org/wiki/Inequality_(mathematics) +""" +from sympy.assumptions import Q +from sympy.core.relational import is_eq, is_neq, is_gt, is_ge, is_lt, is_le + +from .binrel import BinaryRelation + +__all__ = ['EqualityPredicate', 'UnequalityPredicate', 'StrictGreaterThanPredicate', + 'GreaterThanPredicate', 'StrictLessThanPredicate', 'LessThanPredicate'] + + +class EqualityPredicate(BinaryRelation): + """ + Binary predicate for $=$. + + The purpose of this class is to provide the instance which represent + the equality predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Eq()` instead to construct the equality expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_eq()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.eq(0, 0) + Q.eq(0, 0) + >>> ask(_) + True + + See Also + ======== + + sympy.core.relational.Eq + + """ + is_reflexive = True + is_symmetric = True + + name = 'eq' + handler = None # Do not allow dispatching by this predicate + + @property + def negated(self): + return Q.ne + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_eq is None + assumptions = None + return is_eq(*args, assumptions) + + +class UnequalityPredicate(BinaryRelation): + r""" + Binary predicate for $\neq$. + + The purpose of this class is to provide the instance which represent + the inequation predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Ne()` instead to construct the inequation expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_neq()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.ne(0, 0) + Q.ne(0, 0) + >>> ask(_) + False + + See Also + ======== + + sympy.core.relational.Ne + + """ + is_reflexive = False + is_symmetric = True + + name = 'ne' + handler = None + + @property + def negated(self): + return Q.eq + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_neq is None + assumptions = None + return is_neq(*args, assumptions) + + +class StrictGreaterThanPredicate(BinaryRelation): + """ + Binary predicate for $>$. + + The purpose of this class is to provide the instance which represent + the ">" predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Gt()` instead to construct the equality expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_gt()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.gt(0, 0) + Q.gt(0, 0) + >>> ask(_) + False + + See Also + ======== + + sympy.core.relational.Gt + + """ + is_reflexive = False + is_symmetric = False + + name = 'gt' + handler = None + + @property + def reversed(self): + return Q.lt + + @property + def negated(self): + return Q.le + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_gt is None + assumptions = None + return is_gt(*args, assumptions) + + +class GreaterThanPredicate(BinaryRelation): + """ + Binary predicate for $>=$. + + The purpose of this class is to provide the instance which represent + the ">=" predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Ge()` instead to construct the equality expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_ge()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.ge(0, 0) + Q.ge(0, 0) + >>> ask(_) + True + + See Also + ======== + + sympy.core.relational.Ge + + """ + is_reflexive = True + is_symmetric = False + + name = 'ge' + handler = None + + @property + def reversed(self): + return Q.le + + @property + def negated(self): + return Q.lt + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_ge is None + assumptions = None + return is_ge(*args, assumptions) + + +class StrictLessThanPredicate(BinaryRelation): + """ + Binary predicate for $<$. + + The purpose of this class is to provide the instance which represent + the "<" predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Lt()` instead to construct the equality expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_lt()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.lt(0, 0) + Q.lt(0, 0) + >>> ask(_) + False + + See Also + ======== + + sympy.core.relational.Lt + + """ + is_reflexive = False + is_symmetric = False + + name = 'lt' + handler = None + + @property + def reversed(self): + return Q.gt + + @property + def negated(self): + return Q.ge + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_lt is None + assumptions = None + return is_lt(*args, assumptions) + + +class LessThanPredicate(BinaryRelation): + """ + Binary predicate for $<=$. + + The purpose of this class is to provide the instance which represent + the "<=" predicate in order to allow the logical inference. + This class must remain internal to assumptions module and user must + use :obj:`~.Le()` instead to construct the equality expression. + + Evaluating this predicate to ``True`` or ``False`` is done by + :func:`~.core.relational.is_le()` + + Examples + ======== + + >>> from sympy import ask, Q + >>> Q.le(0, 0) + Q.le(0, 0) + >>> ask(_) + True + + See Also + ======== + + sympy.core.relational.Le + + """ + is_reflexive = True + is_symmetric = False + + name = 'le' + handler = None + + @property + def reversed(self): + return Q.ge + + @property + def negated(self): + return Q.gt + + def eval(self, args, assumptions=True): + if assumptions == True: + # default assumptions for is_le is None + assumptions = None + return is_le(*args, assumptions) diff --git a/lib/python3.11/site-packages/sympy/assumptions/satask.py b/lib/python3.11/site-packages/sympy/assumptions/satask.py new file mode 100644 index 0000000000000000000000000000000000000000..ffc13f6d3bc3fb7f573c8d5d0564b780440c1a8c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/satask.py @@ -0,0 +1,369 @@ +""" +Module to evaluate the proposition with assumptions using SAT algorithm. +""" + +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.kind import NumberKind, UndefinedKind +from sympy.assumptions.ask_generated import get_all_known_matrix_facts, get_all_known_number_facts +from sympy.assumptions.assume import global_assumptions, AppliedPredicate +from sympy.assumptions.sathandlers import class_fact_registry +from sympy.core import oo +from sympy.logic.inference import satisfiable +from sympy.assumptions.cnf import CNF, EncodedCNF +from sympy.matrices.kind import MatrixKind + + +def satask(proposition, assumptions=True, context=global_assumptions, + use_known_facts=True, iterations=oo): + """ + Function to evaluate the proposition with assumptions using SAT algorithm. + + This function extracts every fact relevant to the expressions composing + proposition and assumptions. For example, if a predicate containing + ``Abs(x)`` is proposed, then ``Q.zero(Abs(x)) | Q.positive(Abs(x))`` + will be found and passed to SAT solver because ``Q.nonnegative`` is + registered as a fact for ``Abs``. + + Proposition is evaluated to ``True`` or ``False`` if the truth value can be + determined. If not, ``None`` is returned. + + Parameters + ========== + + proposition : Any boolean expression. + Proposition which will be evaluated to boolean value. + + assumptions : Any boolean expression, optional. + Local assumptions to evaluate the *proposition*. + + context : AssumptionsContext, optional. + Default assumptions to evaluate the *proposition*. By default, + this is ``sympy.assumptions.global_assumptions`` variable. + + use_known_facts : bool, optional. + If ``True``, facts from ``sympy.assumptions.ask_generated`` + module are passed to SAT solver as well. + + iterations : int, optional. + Number of times that relevant facts are recursively extracted. + Default is infinite times until no new fact is found. + + Returns + ======= + + ``True``, ``False``, or ``None`` + + Examples + ======== + + >>> from sympy import Abs, Q + >>> from sympy.assumptions.satask import satask + >>> from sympy.abc import x + >>> satask(Q.zero(Abs(x)), Q.zero(x)) + True + + """ + props = CNF.from_prop(proposition) + _props = CNF.from_prop(~proposition) + + assumptions = CNF.from_prop(assumptions) + + context_cnf = CNF() + if context: + context_cnf = context_cnf.extend(context) + + sat = get_all_relevant_facts(props, assumptions, context_cnf, + use_known_facts=use_known_facts, iterations=iterations) + sat.add_from_cnf(assumptions) + if context: + sat.add_from_cnf(context_cnf) + + return check_satisfiability(props, _props, sat) + + +def check_satisfiability(prop, _prop, factbase): + sat_true = factbase.copy() + sat_false = factbase.copy() + sat_true.add_from_cnf(prop) + sat_false.add_from_cnf(_prop) + can_be_true = satisfiable(sat_true) + can_be_false = satisfiable(sat_false) + + if can_be_true and can_be_false: + return None + + if can_be_true and not can_be_false: + return True + + if not can_be_true and can_be_false: + return False + + if not can_be_true and not can_be_false: + # TODO: Run additional checks to see which combination of the + # assumptions, global_assumptions, and relevant_facts are + # inconsistent. + raise ValueError("Inconsistent assumptions") + + +def extract_predargs(proposition, assumptions=None, context=None): + """ + Extract every expression in the argument of predicates from *proposition*, + *assumptions* and *context*. + + Parameters + ========== + + proposition : sympy.assumptions.cnf.CNF + + assumptions : sympy.assumptions.cnf.CNF, optional. + + context : sympy.assumptions.cnf.CNF, optional. + CNF generated from assumptions context. + + Examples + ======== + + >>> from sympy import Q, Abs + >>> from sympy.assumptions.cnf import CNF + >>> from sympy.assumptions.satask import extract_predargs + >>> from sympy.abc import x, y + >>> props = CNF.from_prop(Q.zero(Abs(x*y))) + >>> assump = CNF.from_prop(Q.zero(x) & Q.zero(y)) + >>> extract_predargs(props, assump) + {x, y, Abs(x*y)} + + """ + req_keys = find_symbols(proposition) + keys = proposition.all_predicates() + # XXX: We need this since True/False are not Basic + lkeys = set() + if assumptions: + lkeys |= assumptions.all_predicates() + if context: + lkeys |= context.all_predicates() + + lkeys = lkeys - {S.true, S.false} + tmp_keys = None + while tmp_keys != set(): + tmp = set() + for l in lkeys: + syms = find_symbols(l) + if (syms & req_keys) != set(): + tmp |= syms + tmp_keys = tmp - req_keys + req_keys |= tmp_keys + keys |= {l for l in lkeys if find_symbols(l) & req_keys != set()} + + exprs = set() + for key in keys: + if isinstance(key, AppliedPredicate): + exprs |= set(key.arguments) + else: + exprs.add(key) + return exprs + +def find_symbols(pred): + """ + Find every :obj:`~.Symbol` in *pred*. + + Parameters + ========== + + pred : sympy.assumptions.cnf.CNF, or any Expr. + + """ + if isinstance(pred, CNF): + symbols = set() + for a in pred.all_predicates(): + symbols |= find_symbols(a) + return symbols + return pred.atoms(Symbol) + + +def get_relevant_clsfacts(exprs, relevant_facts=None): + """ + Extract relevant facts from the items in *exprs*. Facts are defined in + ``assumptions.sathandlers`` module. + + This function is recursively called by ``get_all_relevant_facts()``. + + Parameters + ========== + + exprs : set + Expressions whose relevant facts are searched. + + relevant_facts : sympy.assumptions.cnf.CNF, optional. + Pre-discovered relevant facts. + + Returns + ======= + + exprs : set + Candidates for next relevant fact searching. + + relevant_facts : sympy.assumptions.cnf.CNF + Updated relevant facts. + + Examples + ======== + + Here, we will see how facts relevant to ``Abs(x*y)`` are recursively + extracted. On the first run, set containing the expression is passed + without pre-discovered relevant facts. The result is a set containing + candidates for next run, and ``CNF()`` instance containing facts + which are relevant to ``Abs`` and its argument. + + >>> from sympy import Abs + >>> from sympy.assumptions.satask import get_relevant_clsfacts + >>> from sympy.abc import x, y + >>> exprs = {Abs(x*y)} + >>> exprs, facts = get_relevant_clsfacts(exprs) + >>> exprs + {x*y} + >>> facts.clauses #doctest: +SKIP + {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), + frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}), + frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}), + frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}), + frozenset({Literal(Q.even(Abs(x*y)), False), + Literal(Q.odd(Abs(x*y)), False), + Literal(Q.odd(x*y), True)}), + frozenset({Literal(Q.even(Abs(x*y)), False), + Literal(Q.even(x*y), True), + Literal(Q.odd(Abs(x*y)), False)}), + frozenset({Literal(Q.positive(Abs(x*y)), False), + Literal(Q.zero(Abs(x*y)), False)})} + + We pass the first run's results to the second run, and get the expressions + for next run and updated facts. + + >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) + >>> exprs + {x, y} + + On final run, no more candidate is returned thus we know that all + relevant facts are successfully retrieved. + + >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) + >>> exprs + set() + + """ + if not relevant_facts: + relevant_facts = CNF() + + newexprs = set() + for expr in exprs: + for fact in class_fact_registry(expr): + newfact = CNF.to_CNF(fact) + relevant_facts = relevant_facts._and(newfact) + for key in newfact.all_predicates(): + if isinstance(key, AppliedPredicate): + newexprs |= set(key.arguments) + + return newexprs - exprs, relevant_facts + + +def get_all_relevant_facts(proposition, assumptions, context, + use_known_facts=True, iterations=oo): + """ + Extract all relevant facts from *proposition* and *assumptions*. + + This function extracts the facts by recursively calling + ``get_relevant_clsfacts()``. Extracted facts are converted to + ``EncodedCNF`` and returned. + + Parameters + ========== + + proposition : sympy.assumptions.cnf.CNF + CNF generated from proposition expression. + + assumptions : sympy.assumptions.cnf.CNF + CNF generated from assumption expression. + + context : sympy.assumptions.cnf.CNF + CNF generated from assumptions context. + + use_known_facts : bool, optional. + If ``True``, facts from ``sympy.assumptions.ask_generated`` + module are encoded as well. + + iterations : int, optional. + Number of times that relevant facts are recursively extracted. + Default is infinite times until no new fact is found. + + Returns + ======= + + sympy.assumptions.cnf.EncodedCNF + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.cnf import CNF + >>> from sympy.assumptions.satask import get_all_relevant_facts + >>> from sympy.abc import x, y + >>> props = CNF.from_prop(Q.nonzero(x*y)) + >>> assump = CNF.from_prop(Q.nonzero(x)) + >>> context = CNF.from_prop(Q.nonzero(y)) + >>> get_all_relevant_facts(props, assump, context) #doctest: +SKIP + + + """ + # The relevant facts might introduce new keys, e.g., Q.zero(x*y) will + # introduce the keys Q.zero(x) and Q.zero(y), so we need to run it until + # we stop getting new things. Hopefully this strategy won't lead to an + # infinite loop in the future. + i = 0 + relevant_facts = CNF() + all_exprs = set() + while True: + if i == 0: + exprs = extract_predargs(proposition, assumptions, context) + all_exprs |= exprs + exprs, relevant_facts = get_relevant_clsfacts(exprs, relevant_facts) + i += 1 + if i >= iterations: + break + if not exprs: + break + + if use_known_facts: + known_facts_CNF = CNF() + + if any(expr.kind == MatrixKind(NumberKind) for expr in all_exprs): + known_facts_CNF.add_clauses(get_all_known_matrix_facts()) + # check for undefinedKind since kind system isn't fully implemented + if any(((expr.kind == NumberKind) or (expr.kind == UndefinedKind)) for expr in all_exprs): + known_facts_CNF.add_clauses(get_all_known_number_facts()) + + kf_encoded = EncodedCNF() + kf_encoded.from_cnf(known_facts_CNF) + + def translate_literal(lit, delta): + if lit > 0: + return lit + delta + else: + return lit - delta + + def translate_data(data, delta): + return [{translate_literal(i, delta) for i in clause} for clause in data] + data = [] + symbols = [] + n_lit = len(kf_encoded.symbols) + for i, expr in enumerate(all_exprs): + symbols += [pred(expr) for pred in kf_encoded.symbols] + data += translate_data(kf_encoded.data, i * n_lit) + + encoding = dict(list(zip(symbols, range(1, len(symbols)+1)))) + ctx = EncodedCNF(data, encoding) + else: + ctx = EncodedCNF() + + ctx.add_from_cnf(relevant_facts) + + return ctx diff --git a/lib/python3.11/site-packages/sympy/assumptions/sathandlers.py b/lib/python3.11/site-packages/sympy/assumptions/sathandlers.py new file mode 100644 index 0000000000000000000000000000000000000000..a11199eb0e547187ab280c18196c0259c178e004 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/sathandlers.py @@ -0,0 +1,322 @@ +from collections import defaultdict + +from sympy.assumptions.ask import Q +from sympy.core import (Add, Mul, Pow, Number, NumberSymbol, Symbol) +from sympy.core.numbers import ImaginaryUnit +from sympy.functions.elementary.complexes import Abs +from sympy.logic.boolalg import (Equivalent, And, Or, Implies) +from sympy.matrices.expressions import MatMul + +# APIs here may be subject to change + + +### Helper functions ### + +def allargs(symbol, fact, expr): + """ + Apply all arguments of the expression to the fact structure. + + Parameters + ========== + + symbol : Symbol + A placeholder symbol. + + fact : Boolean + Resulting ``Boolean`` expression. + + expr : Expr + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.sathandlers import allargs + >>> from sympy.abc import x, y + >>> allargs(x, Q.negative(x) | Q.positive(x), x*y) + (Q.negative(x) | Q.positive(x)) & (Q.negative(y) | Q.positive(y)) + + """ + return And(*[fact.subs(symbol, arg) for arg in expr.args]) + + +def anyarg(symbol, fact, expr): + """ + Apply any argument of the expression to the fact structure. + + Parameters + ========== + + symbol : Symbol + A placeholder symbol. + + fact : Boolean + Resulting ``Boolean`` expression. + + expr : Expr + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.sathandlers import anyarg + >>> from sympy.abc import x, y + >>> anyarg(x, Q.negative(x) & Q.positive(x), x*y) + (Q.negative(x) & Q.positive(x)) | (Q.negative(y) & Q.positive(y)) + + """ + return Or(*[fact.subs(symbol, arg) for arg in expr.args]) + + +def exactlyonearg(symbol, fact, expr): + """ + Apply exactly one argument of the expression to the fact structure. + + Parameters + ========== + + symbol : Symbol + A placeholder symbol. + + fact : Boolean + Resulting ``Boolean`` expression. + + expr : Expr + + Examples + ======== + + >>> from sympy import Q + >>> from sympy.assumptions.sathandlers import exactlyonearg + >>> from sympy.abc import x, y + >>> exactlyonearg(x, Q.positive(x), x*y) + (Q.positive(x) & ~Q.positive(y)) | (Q.positive(y) & ~Q.positive(x)) + + """ + pred_args = [fact.subs(symbol, arg) for arg in expr.args] + res = Or(*[And(pred_args[i], *[~lit for lit in pred_args[:i] + + pred_args[i+1:]]) for i in range(len(pred_args))]) + return res + + +### Fact registry ### + +class ClassFactRegistry: + """ + Register handlers against classes. + + Explanation + =========== + + ``register`` method registers the handler function for a class. Here, + handler function should return a single fact. ``multiregister`` method + registers the handler function for multiple classes. Here, handler function + should return a container of multiple facts. + + ``registry(expr)`` returns a set of facts for *expr*. + + Examples + ======== + + Here, we register the facts for ``Abs``. + + >>> from sympy import Abs, Equivalent, Q + >>> from sympy.assumptions.sathandlers import ClassFactRegistry + >>> reg = ClassFactRegistry() + >>> @reg.register(Abs) + ... def f1(expr): + ... return Q.nonnegative(expr) + >>> @reg.register(Abs) + ... def f2(expr): + ... arg = expr.args[0] + ... return Equivalent(~Q.zero(arg), ~Q.zero(expr)) + + Calling the registry with expression returns the defined facts for the + expression. + + >>> from sympy.abc import x + >>> reg(Abs(x)) + {Q.nonnegative(Abs(x)), Equivalent(~Q.zero(x), ~Q.zero(Abs(x)))} + + Multiple facts can be registered at once by ``multiregister`` method. + + >>> reg2 = ClassFactRegistry() + >>> @reg2.multiregister(Abs) + ... def _(expr): + ... arg = expr.args[0] + ... return [Q.even(arg) >> Q.even(expr), Q.odd(arg) >> Q.odd(expr)] + >>> reg2(Abs(x)) + {Implies(Q.even(x), Q.even(Abs(x))), Implies(Q.odd(x), Q.odd(Abs(x)))} + + """ + def __init__(self): + self.singlefacts = defaultdict(frozenset) + self.multifacts = defaultdict(frozenset) + + def register(self, cls): + def _(func): + self.singlefacts[cls] |= {func} + return func + return _ + + def multiregister(self, *classes): + def _(func): + for cls in classes: + self.multifacts[cls] |= {func} + return func + return _ + + def __getitem__(self, key): + ret1 = self.singlefacts[key] + for k in self.singlefacts: + if issubclass(key, k): + ret1 |= self.singlefacts[k] + + ret2 = self.multifacts[key] + for k in self.multifacts: + if issubclass(key, k): + ret2 |= self.multifacts[k] + + return ret1, ret2 + + def __call__(self, expr): + ret = set() + + handlers1, handlers2 = self[type(expr)] + + ret.update(h(expr) for h in handlers1) + for h in handlers2: + ret.update(h(expr)) + return ret + +class_fact_registry = ClassFactRegistry() + + + +### Class fact registration ### + +x = Symbol('x') + +## Abs ## + +@class_fact_registry.multiregister(Abs) +def _(expr): + arg = expr.args[0] + return [Q.nonnegative(expr), + Equivalent(~Q.zero(arg), ~Q.zero(expr)), + Q.even(arg) >> Q.even(expr), + Q.odd(arg) >> Q.odd(expr), + Q.integer(arg) >> Q.integer(expr), + ] + + +### Add ## + +@class_fact_registry.multiregister(Add) +def _(expr): + return [allargs(x, Q.positive(x), expr) >> Q.positive(expr), + allargs(x, Q.negative(x), expr) >> Q.negative(expr), + allargs(x, Q.real(x), expr) >> Q.real(expr), + allargs(x, Q.rational(x), expr) >> Q.rational(expr), + allargs(x, Q.integer(x), expr) >> Q.integer(expr), + exactlyonearg(x, ~Q.integer(x), expr) >> ~Q.integer(expr), + ] + +@class_fact_registry.register(Add) +def _(expr): + allargs_real = allargs(x, Q.real(x), expr) + onearg_irrational = exactlyonearg(x, Q.irrational(x), expr) + return Implies(allargs_real, Implies(onearg_irrational, Q.irrational(expr))) + + +### Mul ### + +@class_fact_registry.multiregister(Mul) +def _(expr): + return [Equivalent(Q.zero(expr), anyarg(x, Q.zero(x), expr)), + allargs(x, Q.positive(x), expr) >> Q.positive(expr), + allargs(x, Q.real(x), expr) >> Q.real(expr), + allargs(x, Q.rational(x), expr) >> Q.rational(expr), + allargs(x, Q.integer(x), expr) >> Q.integer(expr), + exactlyonearg(x, ~Q.rational(x), expr) >> ~Q.integer(expr), + allargs(x, Q.commutative(x), expr) >> Q.commutative(expr), + ] + +@class_fact_registry.register(Mul) +def _(expr): + # Implicitly assumes Mul has more than one arg + # Would be allargs(x, Q.prime(x) | Q.composite(x)) except 1 is composite + # More advanced prime assumptions will require inequalities, as 1 provides + # a corner case. + allargs_prime = allargs(x, Q.prime(x), expr) + return Implies(allargs_prime, ~Q.prime(expr)) + +@class_fact_registry.register(Mul) +def _(expr): + # General Case: Odd number of imaginary args implies mul is imaginary(To be implemented) + allargs_imag_or_real = allargs(x, Q.imaginary(x) | Q.real(x), expr) + onearg_imaginary = exactlyonearg(x, Q.imaginary(x), expr) + return Implies(allargs_imag_or_real, Implies(onearg_imaginary, Q.imaginary(expr))) + +@class_fact_registry.register(Mul) +def _(expr): + allargs_real = allargs(x, Q.real(x), expr) + onearg_irrational = exactlyonearg(x, Q.irrational(x), expr) + return Implies(allargs_real, Implies(onearg_irrational, Q.irrational(expr))) + +@class_fact_registry.register(Mul) +def _(expr): + # Including the integer qualification means we don't need to add any facts + # for odd, since the assumptions already know that every integer is + # exactly one of even or odd. + allargs_integer = allargs(x, Q.integer(x), expr) + anyarg_even = anyarg(x, Q.even(x), expr) + return Implies(allargs_integer, Equivalent(anyarg_even, Q.even(expr))) + + +### MatMul ### + +@class_fact_registry.register(MatMul) +def _(expr): + allargs_square = allargs(x, Q.square(x), expr) + allargs_invertible = allargs(x, Q.invertible(x), expr) + return Implies(allargs_square, Equivalent(Q.invertible(expr), allargs_invertible)) + + +### Pow ### + +@class_fact_registry.multiregister(Pow) +def _(expr): + base, exp = expr.base, expr.exp + return [ + (Q.real(base) & Q.even(exp) & Q.nonnegative(exp)) >> Q.nonnegative(expr), + (Q.nonnegative(base) & Q.odd(exp) & Q.nonnegative(exp)) >> Q.nonnegative(expr), + (Q.nonpositive(base) & Q.odd(exp) & Q.nonnegative(exp)) >> Q.nonpositive(expr), + Equivalent(Q.zero(expr), Q.zero(base) & Q.positive(exp)) + ] + + +### Numbers ### + +_old_assump_getters = { + Q.positive: lambda o: o.is_positive, + Q.zero: lambda o: o.is_zero, + Q.negative: lambda o: o.is_negative, + Q.rational: lambda o: o.is_rational, + Q.irrational: lambda o: o.is_irrational, + Q.even: lambda o: o.is_even, + Q.odd: lambda o: o.is_odd, + Q.imaginary: lambda o: o.is_imaginary, + Q.prime: lambda o: o.is_prime, + Q.composite: lambda o: o.is_composite, +} + +@class_fact_registry.multiregister(Number, NumberSymbol, ImaginaryUnit) +def _(expr): + ret = [] + for p, getter in _old_assump_getters.items(): + pred = p(expr) + prop = getter(expr) + if prop is not None: + ret.append(Equivalent(pred, prop)) + return ret diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/__init__.py b/lib/python3.11/site-packages/sympy/assumptions/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/assumptions/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..08fc1adac6d0f144aca869e20e508d285e9c5183 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/assumptions/tests/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/__pycache__/test_assumptions_2.cpython-311.pyc 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assumptions system is deleted +""" +from sympy.abc import x, y +from sympy.assumptions.assume import global_assumptions +from sympy.assumptions.ask import Q +from sympy.printing import pretty + + +def test_equal(): + """Test for equality""" + assert Q.positive(x) == Q.positive(x) + assert Q.positive(x) != ~Q.positive(x) + assert ~Q.positive(x) == ~Q.positive(x) + + +def test_pretty(): + assert pretty(Q.positive(x)) == "Q.positive(x)" + assert pretty( + {Q.positive, Q.integer}) == "{Q.integer, Q.positive}" + + +def test_global(): + """Test for global assumptions""" + global_assumptions.add(x > 0) + assert (x > 0) in global_assumptions + global_assumptions.remove(x > 0) + assert not (x > 0) in global_assumptions + # same with multiple of assumptions + global_assumptions.add(x > 0, y > 0) + assert (x > 0) in global_assumptions + assert (y > 0) in global_assumptions + global_assumptions.clear() + assert not (x > 0) in global_assumptions + assert not (y > 0) in global_assumptions diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_context.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_context.py new file mode 100644 index 0000000000000000000000000000000000000000..be162f1c69492218ff90ea69492925d7779567a4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_context.py @@ -0,0 +1,39 @@ +from sympy.assumptions import ask, Q +from sympy.assumptions.assume import assuming, global_assumptions +from sympy.abc import x, y + +def test_assuming(): + with assuming(Q.integer(x)): + assert ask(Q.integer(x)) + assert not ask(Q.integer(x)) + +def test_assuming_nested(): + assert not ask(Q.integer(x)) + assert not ask(Q.integer(y)) + with assuming(Q.integer(x)): + assert ask(Q.integer(x)) + assert not ask(Q.integer(y)) + with assuming(Q.integer(y)): + assert ask(Q.integer(x)) + assert ask(Q.integer(y)) + assert ask(Q.integer(x)) + assert not ask(Q.integer(y)) + assert not ask(Q.integer(x)) + assert not ask(Q.integer(y)) + +def test_finally(): + try: + with assuming(Q.integer(x)): + 1/0 + except ZeroDivisionError: + pass + assert not ask(Q.integer(x)) + +def test_remove_safe(): + global_assumptions.add(Q.integer(x)) + with assuming(): + assert ask(Q.integer(x)) + global_assumptions.remove(Q.integer(x)) + assert not ask(Q.integer(x)) + assert ask(Q.integer(x)) + global_assumptions.clear() # for the benefit of other tests diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_matrices.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_matrices.py new file mode 100644 index 0000000000000000000000000000000000000000..8bfa990f080eebe4d6dd5bfdd733ce1a19adf329 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_matrices.py @@ -0,0 +1,283 @@ +from sympy.assumptions.ask import (Q, ask) +from sympy.core.symbol import Symbol +from sympy.matrices.expressions.diagonal import (DiagMatrix, DiagonalMatrix) +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions import (MatrixSymbol, Identity, ZeroMatrix, + OneMatrix, Trace, MatrixSlice, Determinant, BlockMatrix, BlockDiagMatrix) +from sympy.matrices.expressions.factorizations import LofLU +from sympy.testing.pytest import XFAIL + +X = MatrixSymbol('X', 2, 2) +Y = MatrixSymbol('Y', 2, 3) +Z = MatrixSymbol('Z', 2, 2) +A1x1 = MatrixSymbol('A1x1', 1, 1) +B1x1 = MatrixSymbol('B1x1', 1, 1) +C0x0 = MatrixSymbol('C0x0', 0, 0) +V1 = MatrixSymbol('V1', 2, 1) +V2 = MatrixSymbol('V2', 2, 1) + +def test_square(): + assert ask(Q.square(X)) + assert not ask(Q.square(Y)) + assert ask(Q.square(Y*Y.T)) + +def test_invertible(): + assert ask(Q.invertible(X), Q.invertible(X)) + assert ask(Q.invertible(Y)) is False + assert ask(Q.invertible(X*Y), Q.invertible(X)) is False + assert ask(Q.invertible(X*Z), Q.invertible(X)) is None + assert ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z)) is True + assert ask(Q.invertible(X.T)) is None + assert ask(Q.invertible(X.T), Q.invertible(X)) is True + assert ask(Q.invertible(X.I)) is True + assert ask(Q.invertible(Identity(3))) is True + assert ask(Q.invertible(ZeroMatrix(3, 3))) is False + assert ask(Q.invertible(OneMatrix(1, 1))) is True + assert ask(Q.invertible(OneMatrix(3, 3))) is False + assert ask(Q.invertible(X), Q.fullrank(X) & Q.square(X)) + +def test_singular(): + assert ask(Q.singular(X)) is None + assert ask(Q.singular(X), Q.invertible(X)) is False + assert ask(Q.singular(X), ~Q.invertible(X)) is True + +@XFAIL +def test_invertible_fullrank(): + assert ask(Q.invertible(X), Q.fullrank(X)) is True + + +def test_invertible_BlockMatrix(): + assert ask(Q.invertible(BlockMatrix([Identity(3)]))) == True + assert ask(Q.invertible(BlockMatrix([ZeroMatrix(3, 3)]))) == False + + X = Matrix([[1, 2, 3], [3, 5, 4]]) + Y = Matrix([[4, 2, 7], [2, 3, 5]]) + # non-invertible A block + assert ask(Q.invertible(BlockMatrix([ + [Matrix.ones(3, 3), Y.T], + [X, Matrix.eye(2)], + ]))) == True + # non-invertible B block + assert ask(Q.invertible(BlockMatrix([ + [Y.T, Matrix.ones(3, 3)], + [Matrix.eye(2), X], + ]))) == True + # non-invertible C block + assert ask(Q.invertible(BlockMatrix([ + [X, Matrix.eye(2)], + [Matrix.ones(3, 3), Y.T], + ]))) == True + # non-invertible D block + assert ask(Q.invertible(BlockMatrix([ + [Matrix.eye(2), X], + [Y.T, Matrix.ones(3, 3)], + ]))) == True + + +def test_invertible_BlockDiagMatrix(): + assert ask(Q.invertible(BlockDiagMatrix(Identity(3), Identity(5)))) == True + assert ask(Q.invertible(BlockDiagMatrix(ZeroMatrix(3, 3), Identity(5)))) == False + assert ask(Q.invertible(BlockDiagMatrix(Identity(3), OneMatrix(5, 5)))) == False + + +def test_symmetric(): + assert ask(Q.symmetric(X), Q.symmetric(X)) + assert ask(Q.symmetric(X*Z), Q.symmetric(X)) is None + assert ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z)) is True + assert ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z)) is True + assert ask(Q.symmetric(Y)) is False + assert ask(Q.symmetric(Y*Y.T)) is True + assert ask(Q.symmetric(Y.T*X*Y)) is None + assert ask(Q.symmetric(Y.T*X*Y), Q.symmetric(X)) is True + assert ask(Q.symmetric(X**10), Q.symmetric(X)) is True + assert ask(Q.symmetric(A1x1)) is True + assert ask(Q.symmetric(A1x1 + B1x1)) is True + assert ask(Q.symmetric(A1x1 * B1x1)) is True + assert ask(Q.symmetric(V1.T*V1)) is True + assert ask(Q.symmetric(V1.T*(V1 + V2))) is True + assert ask(Q.symmetric(V1.T*(V1 + V2) + A1x1)) is True + assert ask(Q.symmetric(MatrixSlice(Y, (0, 1), (1, 2)))) is True + assert ask(Q.symmetric(Identity(3))) is True + assert ask(Q.symmetric(ZeroMatrix(3, 3))) is True + assert ask(Q.symmetric(OneMatrix(3, 3))) is True + +def _test_orthogonal_unitary(predicate): + assert ask(predicate(X), predicate(X)) + assert ask(predicate(X.T), predicate(X)) is True + assert ask(predicate(X.I), predicate(X)) is True + assert ask(predicate(X**2), predicate(X)) + assert ask(predicate(Y)) is False + assert ask(predicate(X)) is None + assert ask(predicate(X), ~Q.invertible(X)) is False + assert ask(predicate(X*Z*X), predicate(X) & predicate(Z)) is True + assert ask(predicate(Identity(3))) is True + assert ask(predicate(ZeroMatrix(3, 3))) is False + assert ask(Q.invertible(X), predicate(X)) + assert not ask(predicate(X + Z), predicate(X) & predicate(Z)) + +def test_orthogonal(): + _test_orthogonal_unitary(Q.orthogonal) + +def test_unitary(): + _test_orthogonal_unitary(Q.unitary) + assert ask(Q.unitary(X), Q.orthogonal(X)) + +def test_fullrank(): + assert ask(Q.fullrank(X), Q.fullrank(X)) + assert ask(Q.fullrank(X**2), Q.fullrank(X)) + assert ask(Q.fullrank(X.T), Q.fullrank(X)) is True + assert ask(Q.fullrank(X)) is None + assert ask(Q.fullrank(Y)) is None + assert ask(Q.fullrank(X*Z), Q.fullrank(X) & Q.fullrank(Z)) is True + assert ask(Q.fullrank(Identity(3))) is True + assert ask(Q.fullrank(ZeroMatrix(3, 3))) is False + assert ask(Q.fullrank(OneMatrix(1, 1))) is True + assert ask(Q.fullrank(OneMatrix(3, 3))) is False + assert ask(Q.invertible(X), ~Q.fullrank(X)) == False + + +def test_positive_definite(): + assert ask(Q.positive_definite(X), Q.positive_definite(X)) + assert ask(Q.positive_definite(X.T), Q.positive_definite(X)) is True + assert ask(Q.positive_definite(X.I), Q.positive_definite(X)) is True + assert ask(Q.positive_definite(Y)) is False + assert ask(Q.positive_definite(X)) is None + assert ask(Q.positive_definite(X**3), Q.positive_definite(X)) + assert ask(Q.positive_definite(X*Z*X), + Q.positive_definite(X) & Q.positive_definite(Z)) is True + assert ask(Q.positive_definite(X), Q.orthogonal(X)) + assert ask(Q.positive_definite(Y.T*X*Y), + Q.positive_definite(X) & Q.fullrank(Y)) is True + assert not ask(Q.positive_definite(Y.T*X*Y), Q.positive_definite(X)) + assert ask(Q.positive_definite(Identity(3))) is True + assert ask(Q.positive_definite(ZeroMatrix(3, 3))) is False + assert ask(Q.positive_definite(OneMatrix(1, 1))) is True + assert ask(Q.positive_definite(OneMatrix(3, 3))) is False + assert ask(Q.positive_definite(X + Z), Q.positive_definite(X) & + Q.positive_definite(Z)) is True + assert not ask(Q.positive_definite(-X), Q.positive_definite(X)) + assert ask(Q.positive(X[1, 1]), Q.positive_definite(X)) + +def test_triangular(): + assert ask(Q.upper_triangular(X + Z.T + Identity(2)), Q.upper_triangular(X) & + Q.lower_triangular(Z)) is True + assert ask(Q.upper_triangular(X*Z.T), Q.upper_triangular(X) & + Q.lower_triangular(Z)) is True + assert ask(Q.lower_triangular(Identity(3))) is True + assert ask(Q.lower_triangular(ZeroMatrix(3, 3))) is True + assert ask(Q.upper_triangular(ZeroMatrix(3, 3))) is True + assert ask(Q.lower_triangular(OneMatrix(1, 1))) is True + assert ask(Q.upper_triangular(OneMatrix(1, 1))) is True + assert ask(Q.lower_triangular(OneMatrix(3, 3))) is False + assert ask(Q.upper_triangular(OneMatrix(3, 3))) is False + assert ask(Q.triangular(X), Q.unit_triangular(X)) + assert ask(Q.upper_triangular(X**3), Q.upper_triangular(X)) + assert ask(Q.lower_triangular(X**3), Q.lower_triangular(X)) + + +def test_diagonal(): + assert ask(Q.diagonal(X + Z.T + Identity(2)), Q.diagonal(X) & + Q.diagonal(Z)) is True + assert ask(Q.diagonal(ZeroMatrix(3, 3))) + assert ask(Q.diagonal(OneMatrix(1, 1))) is True + assert ask(Q.diagonal(OneMatrix(3, 3))) is False + assert ask(Q.lower_triangular(X) & Q.upper_triangular(X), Q.diagonal(X)) + assert ask(Q.diagonal(X), Q.lower_triangular(X) & Q.upper_triangular(X)) + assert ask(Q.symmetric(X), Q.diagonal(X)) + assert ask(Q.triangular(X), Q.diagonal(X)) + assert ask(Q.diagonal(C0x0)) + assert ask(Q.diagonal(A1x1)) + assert ask(Q.diagonal(A1x1 + B1x1)) + assert ask(Q.diagonal(A1x1*B1x1)) + assert ask(Q.diagonal(V1.T*V2)) + assert ask(Q.diagonal(V1.T*(X + Z)*V1)) + assert ask(Q.diagonal(MatrixSlice(Y, (0, 1), (1, 2)))) is True + assert ask(Q.diagonal(V1.T*(V1 + V2))) is True + assert ask(Q.diagonal(X**3), Q.diagonal(X)) + assert ask(Q.diagonal(Identity(3))) + assert ask(Q.diagonal(DiagMatrix(V1))) + assert ask(Q.diagonal(DiagonalMatrix(X))) + + +def test_non_atoms(): + assert ask(Q.real(Trace(X)), Q.positive(Trace(X))) + +@XFAIL +def test_non_trivial_implies(): + X = MatrixSymbol('X', 3, 3) + Y = MatrixSymbol('Y', 3, 3) + assert ask(Q.lower_triangular(X+Y), Q.lower_triangular(X) & + Q.lower_triangular(Y)) is True + assert ask(Q.triangular(X), Q.lower_triangular(X)) is True + assert ask(Q.triangular(X+Y), Q.lower_triangular(X) & + Q.lower_triangular(Y)) is True + +def test_MatrixSlice(): + X = MatrixSymbol('X', 4, 4) + B = MatrixSlice(X, (1, 3), (1, 3)) + C = MatrixSlice(X, (0, 3), (1, 3)) + assert ask(Q.symmetric(B), Q.symmetric(X)) + assert ask(Q.invertible(B), Q.invertible(X)) + assert ask(Q.diagonal(B), Q.diagonal(X)) + assert ask(Q.orthogonal(B), Q.orthogonal(X)) + assert ask(Q.upper_triangular(B), Q.upper_triangular(X)) + + assert not ask(Q.symmetric(C), Q.symmetric(X)) + assert not ask(Q.invertible(C), Q.invertible(X)) + assert not ask(Q.diagonal(C), Q.diagonal(X)) + assert not ask(Q.orthogonal(C), Q.orthogonal(X)) + assert not ask(Q.upper_triangular(C), Q.upper_triangular(X)) + +def test_det_trace_positive(): + X = MatrixSymbol('X', 4, 4) + assert ask(Q.positive(Trace(X)), Q.positive_definite(X)) + assert ask(Q.positive(Determinant(X)), Q.positive_definite(X)) + +def test_field_assumptions(): + X = MatrixSymbol('X', 4, 4) + Y = MatrixSymbol('Y', 4, 4) + assert ask(Q.real_elements(X), Q.real_elements(X)) + assert not ask(Q.integer_elements(X), Q.real_elements(X)) + assert ask(Q.complex_elements(X), Q.real_elements(X)) + assert ask(Q.complex_elements(X**2), Q.real_elements(X)) + assert ask(Q.real_elements(X**2), Q.integer_elements(X)) + assert ask(Q.real_elements(X+Y), Q.real_elements(X)) is None + assert ask(Q.real_elements(X+Y), Q.real_elements(X) & Q.real_elements(Y)) + from sympy.matrices.expressions.hadamard import HadamardProduct + assert ask(Q.real_elements(HadamardProduct(X, Y)), + Q.real_elements(X) & Q.real_elements(Y)) + assert ask(Q.complex_elements(X+Y), Q.real_elements(X) & Q.complex_elements(Y)) + + assert ask(Q.real_elements(X.T), Q.real_elements(X)) + assert ask(Q.real_elements(X.I), Q.real_elements(X) & Q.invertible(X)) + assert ask(Q.real_elements(Trace(X)), Q.real_elements(X)) + assert ask(Q.integer_elements(Determinant(X)), Q.integer_elements(X)) + assert not ask(Q.integer_elements(X.I), Q.integer_elements(X)) + alpha = Symbol('alpha') + assert ask(Q.real_elements(alpha*X), Q.real_elements(X) & Q.real(alpha)) + assert ask(Q.real_elements(LofLU(X)), Q.real_elements(X)) + e = Symbol('e', integer=True, negative=True) + assert ask(Q.real_elements(X**e), Q.real_elements(X) & Q.invertible(X)) + assert ask(Q.real_elements(X**e), Q.real_elements(X)) is None + +def test_matrix_element_sets(): + X = MatrixSymbol('X', 4, 4) + assert ask(Q.real(X[1, 2]), Q.real_elements(X)) + assert ask(Q.integer(X[1, 2]), Q.integer_elements(X)) + assert ask(Q.complex(X[1, 2]), Q.complex_elements(X)) + assert ask(Q.integer_elements(Identity(3))) + assert ask(Q.integer_elements(ZeroMatrix(3, 3))) + assert ask(Q.integer_elements(OneMatrix(3, 3))) + from sympy.matrices.expressions.fourier import DFT + assert ask(Q.complex_elements(DFT(3))) + + +def test_matrix_element_sets_slices_blocks(): + X = MatrixSymbol('X', 4, 4) + assert ask(Q.integer_elements(X[:, 3]), Q.integer_elements(X)) + assert ask(Q.integer_elements(BlockMatrix([[X], [X]])), + Q.integer_elements(X)) + +def test_matrix_element_sets_determinant_trace(): + assert ask(Q.integer(Determinant(X)), Q.integer_elements(X)) + assert ask(Q.integer(Trace(X)), Q.integer_elements(X)) diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_query.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_query.py new file mode 100644 index 0000000000000000000000000000000000000000..797a6dcc4dba46c0292508adcbb47316dc197e9d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_query.py @@ -0,0 +1,2417 @@ +from sympy.abc import t, w, x, y, z, n, k, m, p, i +from sympy.assumptions import (ask, AssumptionsContext, Q, register_handler, + remove_handler) +from sympy.assumptions.assume import assuming, global_assumptions, Predicate +from sympy.assumptions.cnf import CNF, Literal +from sympy.assumptions.facts import (single_fact_lookup, + get_known_facts, generate_known_facts_dict, get_known_facts_keys) +from sympy.assumptions.handlers import AskHandler +from sympy.assumptions.ask_generated import (get_all_known_facts, + get_known_facts_dict) +from sympy.core.add import Add +from sympy.core.numbers import (I, Integer, Rational, oo, zoo, pi) +from sympy.core.singleton import S +from sympy.core.power import Pow +from sympy.core.symbol import Str, symbols, Symbol +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import (Abs, im, re, sign) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import ( + acos, acot, asin, atan, cos, cot, sin, tan) +from sympy.logic.boolalg import Equivalent, Implies, Xor, And, to_cnf +from sympy.matrices import Matrix, SparseMatrix +from sympy.testing.pytest import (XFAIL, slow, raises, warns_deprecated_sympy, + _both_exp_pow) +import math + + +def test_int_1(): + z = 1 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is True + assert ask(Q.rational(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is True + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_int_11(): + z = 11 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is True + assert ask(Q.rational(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is True + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is True + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_int_12(): + z = 12 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is True + assert ask(Q.rational(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is True + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is True + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_float_1(): + z = 1.0 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is None + assert ask(Q.rational(z)) is None + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is None + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is None + assert ask(Q.odd(z)) is None + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is None + assert ask(Q.composite(z)) is None + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + z = 7.2123 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is None + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is None + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + # test for issue #12168 + assert ask(Q.rational(math.pi)) is None + + +def test_zero_0(): + z = Integer(0) + assert ask(Q.nonzero(z)) is False + assert ask(Q.zero(z)) is True + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is True + assert ask(Q.rational(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is False + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is True + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is True + + +def test_negativeone(): + z = Integer(-1) + assert ask(Q.nonzero(z)) is True + assert ask(Q.zero(z)) is False + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is True + assert ask(Q.rational(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is False + assert ask(Q.negative(z)) is True + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is True + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_infinity(): + assert ask(Q.commutative(oo)) is True + assert ask(Q.integer(oo)) is False + assert ask(Q.rational(oo)) is False + assert ask(Q.algebraic(oo)) is False + assert ask(Q.real(oo)) is False + assert ask(Q.extended_real(oo)) is True + assert ask(Q.complex(oo)) is False + assert ask(Q.irrational(oo)) is False + assert ask(Q.imaginary(oo)) is False + assert ask(Q.positive(oo)) is False + assert ask(Q.extended_positive(oo)) is True + assert ask(Q.negative(oo)) is False + assert ask(Q.even(oo)) is False + assert ask(Q.odd(oo)) is False + assert ask(Q.finite(oo)) is False + assert ask(Q.infinite(oo)) is True + assert ask(Q.prime(oo)) is False + assert ask(Q.composite(oo)) is False + assert ask(Q.hermitian(oo)) is False + assert ask(Q.antihermitian(oo)) is False + assert ask(Q.positive_infinite(oo)) is True + assert ask(Q.negative_infinite(oo)) is False + + +def test_neg_infinity(): + mm = S.NegativeInfinity + assert ask(Q.commutative(mm)) is True + assert ask(Q.integer(mm)) is False + assert ask(Q.rational(mm)) is False + assert ask(Q.algebraic(mm)) is False + assert ask(Q.real(mm)) is False + assert ask(Q.extended_real(mm)) is True + assert ask(Q.complex(mm)) is False + assert ask(Q.irrational(mm)) is False + assert ask(Q.imaginary(mm)) is False + assert ask(Q.positive(mm)) is False + assert ask(Q.negative(mm)) is False + assert ask(Q.extended_negative(mm)) is True + assert ask(Q.even(mm)) is False + assert ask(Q.odd(mm)) is False + assert ask(Q.finite(mm)) is False + assert ask(Q.infinite(oo)) is True + assert ask(Q.prime(mm)) is False + assert ask(Q.composite(mm)) is False + assert ask(Q.hermitian(mm)) is False + assert ask(Q.antihermitian(mm)) is False + assert ask(Q.positive_infinite(-oo)) is False + assert ask(Q.negative_infinite(-oo)) is True + + +def test_complex_infinity(): + assert ask(Q.commutative(zoo)) is True + assert ask(Q.integer(zoo)) is False + assert ask(Q.rational(zoo)) is False + assert ask(Q.algebraic(zoo)) is False + assert ask(Q.real(zoo)) is False + assert ask(Q.extended_real(zoo)) is False + assert ask(Q.complex(zoo)) is False + assert ask(Q.irrational(zoo)) is False + assert ask(Q.imaginary(zoo)) is False + assert ask(Q.positive(zoo)) is False + assert ask(Q.negative(zoo)) is False + assert ask(Q.zero(zoo)) is False + assert ask(Q.nonzero(zoo)) is False + assert ask(Q.even(zoo)) is False + assert ask(Q.odd(zoo)) is False + assert ask(Q.finite(zoo)) is False + assert ask(Q.infinite(zoo)) is True + assert ask(Q.prime(zoo)) is False + assert ask(Q.composite(zoo)) is False + assert ask(Q.hermitian(zoo)) is False + assert ask(Q.antihermitian(zoo)) is False + assert ask(Q.positive_infinite(zoo)) is False + assert ask(Q.negative_infinite(zoo)) is False + + +def test_nan(): + nan = S.NaN + assert ask(Q.commutative(nan)) is True + assert ask(Q.integer(nan)) is None + assert ask(Q.rational(nan)) is None + assert ask(Q.algebraic(nan)) is None + assert ask(Q.real(nan)) is None + assert ask(Q.extended_real(nan)) is None + assert ask(Q.complex(nan)) is None + assert ask(Q.irrational(nan)) is None + assert ask(Q.imaginary(nan)) is None + assert ask(Q.positive(nan)) is None + assert ask(Q.nonzero(nan)) is None + assert ask(Q.zero(nan)) is None + assert ask(Q.even(nan)) is None + assert ask(Q.odd(nan)) is None + assert ask(Q.finite(nan)) is None + assert ask(Q.infinite(nan)) is None + assert ask(Q.prime(nan)) is None + assert ask(Q.composite(nan)) is None + assert ask(Q.hermitian(nan)) is None + assert ask(Q.antihermitian(nan)) is None + + +def test_Rational_number(): + r = Rational(3, 4) + assert ask(Q.commutative(r)) is True + assert ask(Q.integer(r)) is False + assert ask(Q.rational(r)) is True + assert ask(Q.real(r)) is True + assert ask(Q.complex(r)) is True + assert ask(Q.irrational(r)) is False + assert ask(Q.imaginary(r)) is False + assert ask(Q.positive(r)) is True + assert ask(Q.negative(r)) is False + assert ask(Q.even(r)) is False + assert ask(Q.odd(r)) is False + assert ask(Q.finite(r)) is True + assert ask(Q.prime(r)) is False + assert ask(Q.composite(r)) is False + assert ask(Q.hermitian(r)) is True + assert ask(Q.antihermitian(r)) is False + + r = Rational(1, 4) + assert ask(Q.positive(r)) is True + assert ask(Q.negative(r)) is False + + r = Rational(5, 4) + assert ask(Q.negative(r)) is False + assert ask(Q.positive(r)) is True + + r = Rational(5, 3) + assert ask(Q.positive(r)) is True + assert ask(Q.negative(r)) is False + + r = Rational(-3, 4) + assert ask(Q.positive(r)) is False + assert ask(Q.negative(r)) is True + + r = Rational(-1, 4) + assert ask(Q.positive(r)) is False + assert ask(Q.negative(r)) is True + + r = Rational(-5, 4) + assert ask(Q.negative(r)) is True + assert ask(Q.positive(r)) is False + + r = Rational(-5, 3) + assert ask(Q.positive(r)) is False + assert ask(Q.negative(r)) is True + + +def test_sqrt_2(): + z = sqrt(2) + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_pi(): + z = S.Pi + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + z = S.Pi + 1 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + z = 2*S.Pi + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + z = S.Pi ** 2 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + z = (1 + S.Pi) ** 2 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_E(): + z = S.Exp1 + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is False + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_GoldenRatio(): + z = S.GoldenRatio + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_TribonacciConstant(): + z = S.TribonacciConstant + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is True + assert ask(Q.real(z)) is True + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is True + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is True + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is True + assert ask(Q.antihermitian(z)) is False + + +def test_I(): + z = I + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is True + assert ask(Q.real(z)) is False + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is True + assert ask(Q.positive(z)) is False + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is False + assert ask(Q.antihermitian(z)) is True + + z = 1 + I + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is True + assert ask(Q.real(z)) is False + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is False + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is False + assert ask(Q.antihermitian(z)) is False + + z = I*(1 + I) + assert ask(Q.commutative(z)) is True + assert ask(Q.integer(z)) is False + assert ask(Q.rational(z)) is False + assert ask(Q.algebraic(z)) is True + assert ask(Q.real(z)) is False + assert ask(Q.complex(z)) is True + assert ask(Q.irrational(z)) is False + assert ask(Q.imaginary(z)) is False + assert ask(Q.positive(z)) is False + assert ask(Q.negative(z)) is False + assert ask(Q.even(z)) is False + assert ask(Q.odd(z)) is False + assert ask(Q.finite(z)) is True + assert ask(Q.prime(z)) is False + assert ask(Q.composite(z)) is False + assert ask(Q.hermitian(z)) is False + assert ask(Q.antihermitian(z)) is False + + z = I**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (-I)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (3*I)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is False + + z = (1)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (-1)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (1+I)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is False + + z = (I)**(I+3) + assert ask(Q.imaginary(z)) is True + assert ask(Q.real(z)) is False + + z = (I)**(I+2) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (I)**(2) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + + z = (I)**(3) + assert ask(Q.imaginary(z)) is True + assert ask(Q.real(z)) is False + + z = (3)**(I) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is False + + z = (I)**(0) + assert ask(Q.imaginary(z)) is False + assert ask(Q.real(z)) is True + +def test_bounded(): + x, y, z = symbols('x,y,z') + a = x + y + x, y = a.args + assert ask(Q.finite(a), Q.positive_infinite(y)) is None + assert ask(Q.finite(x)) is None + assert ask(Q.finite(x), Q.finite(x)) is True + assert ask(Q.finite(x), Q.finite(y)) is None + assert ask(Q.finite(x), Q.complex(x)) is True + assert ask(Q.finite(x), Q.extended_real(x)) is None + + assert ask(Q.finite(x + 1)) is None + assert ask(Q.finite(x + 1), Q.finite(x)) is True + a = x + y + x, y = a.args + # B + B + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True + assert ask(Q.finite(a), Q.positive(x) & Q.finite(y)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is True + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is True + assert ask(Q.finite(a), Q.positive(x) & Q.finite(y) + & ~Q.positive(y)) is True + assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) + & Q.positive(y)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) & ~Q.positive(x) + & ~Q.positive(y)) is True + # B + U + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is False + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is False + assert ask(Q.finite(a), Q.finite(x) + & Q.positive_infinite(y)) is False + assert ask(Q.finite(a), Q.positive(x) + & Q.positive_infinite(y)) is False + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y) + & ~Q.positive(y)) is False + assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) + & Q.positive_infinite(y)) is False + assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) & ~Q.finite(y) + & ~Q.positive(y)) is False + # B + ? + assert ask(Q.finite(a), Q.finite(x)) is None + assert ask(Q.finite(a), Q.positive(x)) is None + assert ask(Q.finite(a), Q.finite(x) + & Q.extended_positive(y)) is None + assert ask(Q.finite(a), Q.positive(x) + & Q.extended_positive(y)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.positive(y)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) + & Q.extended_positive(y)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) + & ~Q.positive(y)) is None + # U + U + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & ~Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.positive_infinite(y)) is False + assert ask(Q.finite(a), Q.positive_infinite(x) & ~Q.finite(y) + & ~Q.extended_positive(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.extended_positive(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & ~Q.extended_positive(x) & ~Q.extended_positive(y)) is False + # U + ? + assert ask(Q.finite(a), ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.extended_positive(x) + & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.extended_positive(x) + & Q.positive_infinite(y)) is False + assert ask(Q.finite(a), Q.extended_positive(x) + & ~Q.finite(y) & ~Q.extended_positive(y)) is None + assert ask(Q.finite(a), ~Q.extended_positive(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), ~Q.extended_positive(x) & ~Q.finite(y) + & ~Q.extended_positive(y)) is False + # ? + ? + assert ask(Q.finite(a)) is None + assert ask(Q.finite(a), Q.extended_positive(x)) is None + assert ask(Q.finite(a), Q.extended_positive(y)) is None + assert ask(Q.finite(a), Q.extended_positive(x) + & Q.extended_positive(y)) is None + assert ask(Q.finite(a), Q.extended_positive(x) + & ~Q.extended_positive(y)) is None + assert ask(Q.finite(a), ~Q.extended_positive(x) + & Q.extended_positive(y)) is None + assert ask(Q.finite(a), ~Q.extended_positive(x) + & ~Q.extended_positive(y)) is None + + x, y, z = symbols('x,y,z') + a = x + y + z + x, y, z = a.args + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.negative(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.finite(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.finite(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y) + & Q.finite(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y) + & Q.extended_negative(z)) is False + assert ask(Q.finite(a), Q.negative(x) + & Q.negative_infinite(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y) + & Q.negative_infinite(z)) is None + assert ask(Q.finite(a), Q.negative(x) & + Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y) + & Q.extended_positive(z)) is False + assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x)) is None + assert ask(Q.finite(a), Q.negative(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.finite(z)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y) + & Q.extended_negative(z)) is False + assert ask(Q.finite(a), Q.finite(x) + & Q.negative_infinite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.finite(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y) + & Q.extended_positive(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.finite(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x)) is None + assert ask(Q.finite(a), Q.finite(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.extended_positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & Q.positive(z)) is True + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y) + & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y) + & Q.extended_negative(z)) is False + assert ask(Q.finite(a), Q.positive(x) + & Q.negative_infinite(y)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y) + & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y) + & Q.extended_positive(z)) is False + assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x)) is None + assert ask(Q.finite(a), Q.positive(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive(x) & Q.extended_positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y) & Q.negative_infinite(z)) is False + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y) & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y)& Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y) & Q.extended_negative(z)) is False + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.negative_infinite(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & ~Q.finite(y) & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & ~Q.finite(y) & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & ~Q.finite(y) & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & ~Q.finite(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.positive_infinite(y) & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.positive_infinite(y) & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.positive_infinite(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.extended_negative(y) & Q.extended_negative(z)) is False + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.extended_negative(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.negative_infinite(x) + & Q.extended_positive(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(z) + & ~Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y) + & Q.positive_infinite(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y) + & Q.extended_negative(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), ~Q.finite(x)) is None + assert ask(Q.finite(a), ~Q.finite(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.positive_infinite(y) & Q.positive_infinite(z)) is False + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.positive_infinite(y) & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.positive_infinite(y)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.positive_infinite(y) & Q.extended_positive(z)) is False + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.extended_negative(y) & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.extended_negative(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive_infinite(x)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.positive_infinite(x) + & Q.extended_positive(y) & Q.extended_positive(z)) is False + assert ask(Q.finite(a), Q.extended_negative(x) + & Q.extended_negative(y) & Q.extended_negative(z)) is None + assert ask(Q.finite(a), Q.extended_negative(x) + & Q.extended_negative(y)) is None + assert ask(Q.finite(a), Q.extended_negative(x) + & Q.extended_negative(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.extended_negative(x)) is None + assert ask(Q.finite(a), Q.extended_negative(x) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.extended_negative(x) + & Q.extended_positive(y) & Q.extended_positive(z)) is None + assert ask(Q.finite(a)) is None + assert ask(Q.finite(a), Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.extended_positive(y) + & Q.extended_positive(z)) is None + assert ask(Q.finite(a), Q.extended_positive(x) + & Q.extended_positive(y) & Q.extended_positive(z)) is None + + assert ask(Q.finite(2*x)) is None + assert ask(Q.finite(2*x), Q.finite(x)) is True + + x, y, z = symbols('x,y,z') + a = x*y + x, y = a.args + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is False + assert ask(Q.finite(a), Q.finite(x)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)) is False + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is False + assert ask(Q.finite(a), ~Q.finite(x)) is None + assert ask(Q.finite(a), Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(y)) is None + assert ask(Q.finite(a)) is None + a = x*y*z + x, y, z = a.args + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & Q.finite(z)) is True + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & Q.finite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.finite(x) & Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(x)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y) + & Q.finite(z)) is False + assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & Q.finite(z)) is False + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y) + & ~Q.finite(z)) is False + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(x)) is None + assert ask(Q.finite(a), Q.finite(y) & Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(y) & ~Q.finite(z)) is None + assert ask(Q.finite(a), Q.finite(y)) is None + assert ask(Q.finite(a), ~Q.finite(y) & Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(y) & ~Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(y)) is None + assert ask(Q.finite(a), Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(z)) is None + assert ask(Q.finite(a), ~Q.finite(z) & Q.extended_nonzero(x) + & Q.extended_nonzero(y) & Q.extended_nonzero(z)) is None + assert ask(Q.finite(a), Q.extended_nonzero(x) & ~Q.finite(y) + & Q.extended_nonzero(y) & ~Q.finite(z) + & Q.extended_nonzero(z)) is False + + x, y, z = symbols('x,y,z') + assert ask(Q.finite(x**2)) is None + assert ask(Q.finite(2**x)) is None + assert ask(Q.finite(2**x), Q.finite(x)) is True + assert ask(Q.finite(x**x)) is None + assert ask(Q.finite(S.Half ** x)) is None + assert ask(Q.finite(S.Half ** x), Q.extended_positive(x)) is True + assert ask(Q.finite(S.Half ** x), Q.extended_negative(x)) is None + assert ask(Q.finite(2**x), Q.extended_negative(x)) is True + assert ask(Q.finite(sqrt(x))) is None + assert ask(Q.finite(2**x), ~Q.finite(x)) is False + assert ask(Q.finite(x**2), ~Q.finite(x)) is False + + # sign function + assert ask(Q.finite(sign(x))) is True + assert ask(Q.finite(sign(x)), ~Q.finite(x)) is True + + # exponential functions + assert ask(Q.finite(log(x))) is None + assert ask(Q.finite(log(x)), Q.finite(x)) is None + assert ask(Q.finite(log(x)), ~Q.zero(x)) is True + assert ask(Q.finite(log(x)), Q.infinite(x)) is False + assert ask(Q.finite(log(x)), Q.zero(x)) is False + assert ask(Q.finite(exp(x))) is None + assert ask(Q.finite(exp(x)), Q.finite(x)) is True + assert ask(Q.finite(exp(2))) is True + + # trigonometric functions + assert ask(Q.finite(sin(x))) is True + assert ask(Q.finite(sin(x)), ~Q.finite(x)) is True + assert ask(Q.finite(cos(x))) is True + assert ask(Q.finite(cos(x)), ~Q.finite(x)) is True + assert ask(Q.finite(2*sin(x))) is True + assert ask(Q.finite(sin(x)**2)) is True + assert ask(Q.finite(cos(x)**2)) is True + assert ask(Q.finite(cos(x) + sin(x))) is True + + +@XFAIL +def test_bounded_xfail(): + """We need to support relations in ask for this to work""" + assert ask(Q.finite(sin(x)**x)) is True + assert ask(Q.finite(cos(x)**x)) is True + + +def test_commutative(): + """By default objects are Q.commutative that is why it returns True + for both key=True and key=False""" + assert ask(Q.commutative(x)) is True + assert ask(Q.commutative(x), ~Q.commutative(x)) is False + assert ask(Q.commutative(x), Q.complex(x)) is True + assert ask(Q.commutative(x), Q.imaginary(x)) is True + assert ask(Q.commutative(x), Q.real(x)) is True + assert ask(Q.commutative(x), Q.positive(x)) is True + assert ask(Q.commutative(x), ~Q.commutative(y)) is True + + assert ask(Q.commutative(2*x)) is True + assert ask(Q.commutative(2*x), ~Q.commutative(x)) is False + + assert ask(Q.commutative(x + 1)) is True + assert ask(Q.commutative(x + 1), ~Q.commutative(x)) is False + + assert ask(Q.commutative(x**2)) is True + assert ask(Q.commutative(x**2), ~Q.commutative(x)) is False + + assert ask(Q.commutative(log(x))) is True + + +@_both_exp_pow +def test_complex(): + assert ask(Q.complex(x)) is None + assert ask(Q.complex(x), Q.complex(x)) is True + assert ask(Q.complex(x), Q.complex(y)) is None + assert ask(Q.complex(x), ~Q.complex(x)) is False + assert ask(Q.complex(x), Q.real(x)) is True + assert ask(Q.complex(x), ~Q.real(x)) is None + assert ask(Q.complex(x), Q.rational(x)) is True + assert ask(Q.complex(x), Q.irrational(x)) is True + assert ask(Q.complex(x), Q.positive(x)) is True + assert ask(Q.complex(x), Q.imaginary(x)) is True + assert ask(Q.complex(x), Q.algebraic(x)) is True + + # a+b + assert ask(Q.complex(x + 1), Q.complex(x)) is True + assert ask(Q.complex(x + 1), Q.real(x)) is True + assert ask(Q.complex(x + 1), Q.rational(x)) is True + assert ask(Q.complex(x + 1), Q.irrational(x)) is True + assert ask(Q.complex(x + 1), Q.imaginary(x)) is True + assert ask(Q.complex(x + 1), Q.integer(x)) is True + assert ask(Q.complex(x + 1), Q.even(x)) is True + assert ask(Q.complex(x + 1), Q.odd(x)) is True + assert ask(Q.complex(x + y), Q.complex(x) & Q.complex(y)) is True + assert ask(Q.complex(x + y), Q.real(x) & Q.imaginary(y)) is True + + # a*x +b + assert ask(Q.complex(2*x + 1), Q.complex(x)) is True + assert ask(Q.complex(2*x + 1), Q.real(x)) is True + assert ask(Q.complex(2*x + 1), Q.positive(x)) is True + assert ask(Q.complex(2*x + 1), Q.rational(x)) is True + assert ask(Q.complex(2*x + 1), Q.irrational(x)) is True + assert ask(Q.complex(2*x + 1), Q.imaginary(x)) is True + assert ask(Q.complex(2*x + 1), Q.integer(x)) is True + assert ask(Q.complex(2*x + 1), Q.even(x)) is True + assert ask(Q.complex(2*x + 1), Q.odd(x)) is True + + # x**2 + assert ask(Q.complex(x**2), Q.complex(x)) is True + assert ask(Q.complex(x**2), Q.real(x)) is True + assert ask(Q.complex(x**2), Q.positive(x)) is True + assert ask(Q.complex(x**2), Q.rational(x)) is True + assert ask(Q.complex(x**2), Q.irrational(x)) is True + assert ask(Q.complex(x**2), Q.imaginary(x)) is True + assert ask(Q.complex(x**2), Q.integer(x)) is True + assert ask(Q.complex(x**2), Q.even(x)) is True + assert ask(Q.complex(x**2), Q.odd(x)) is True + + # 2**x + assert ask(Q.complex(2**x), Q.complex(x)) is True + assert ask(Q.complex(2**x), Q.real(x)) is True + assert ask(Q.complex(2**x), Q.positive(x)) is True + assert ask(Q.complex(2**x), Q.rational(x)) is True + assert ask(Q.complex(2**x), Q.irrational(x)) is True + assert ask(Q.complex(2**x), Q.imaginary(x)) is True + assert ask(Q.complex(2**x), Q.integer(x)) is True + assert ask(Q.complex(2**x), Q.even(x)) is True + assert ask(Q.complex(2**x), Q.odd(x)) is True + assert ask(Q.complex(x**y), Q.complex(x) & Q.complex(y)) is True + + # trigonometric expressions + assert ask(Q.complex(sin(x))) is True + assert ask(Q.complex(sin(2*x + 1))) is True + assert ask(Q.complex(cos(x))) is True + assert ask(Q.complex(cos(2*x + 1))) is True + + # exponential + assert ask(Q.complex(exp(x))) is True + assert ask(Q.complex(exp(x))) is True + + # Q.complexes + assert ask(Q.complex(Abs(x))) is True + assert ask(Q.complex(re(x))) is True + assert ask(Q.complex(im(x))) is True + + +def test_even_query(): + assert ask(Q.even(x)) is None + assert ask(Q.even(x), Q.integer(x)) is None + assert ask(Q.even(x), ~Q.integer(x)) is False + assert ask(Q.even(x), Q.rational(x)) is None + assert ask(Q.even(x), Q.positive(x)) is None + + assert ask(Q.even(2*x)) is None + assert ask(Q.even(2*x), Q.integer(x)) is True + assert ask(Q.even(2*x), Q.even(x)) is True + assert ask(Q.even(2*x), Q.irrational(x)) is False + assert ask(Q.even(2*x), Q.odd(x)) is True + assert ask(Q.even(2*x), ~Q.integer(x)) is None + assert ask(Q.even(3*x), Q.integer(x)) is None + assert ask(Q.even(3*x), Q.even(x)) is True + assert ask(Q.even(3*x), Q.odd(x)) is False + + assert ask(Q.even(x + 1), Q.odd(x)) is True + assert ask(Q.even(x + 1), Q.even(x)) is False + assert ask(Q.even(x + 2), Q.odd(x)) is False + assert ask(Q.even(x + 2), Q.even(x)) is True + assert ask(Q.even(7 - x), Q.odd(x)) is True + assert ask(Q.even(7 + x), Q.odd(x)) is True + assert ask(Q.even(x + y), Q.odd(x) & Q.odd(y)) is True + assert ask(Q.even(x + y), Q.odd(x) & Q.even(y)) is False + assert ask(Q.even(x + y), Q.even(x) & Q.even(y)) is True + + assert ask(Q.even(2*x + 1), Q.integer(x)) is False + assert ask(Q.even(2*x*y), Q.rational(x) & Q.rational(x)) is None + assert ask(Q.even(2*x*y), Q.irrational(x) & Q.irrational(x)) is None + + assert ask(Q.even(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is True + assert ask(Q.even(x + y + z + t), + Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None + + assert ask(Q.even(Abs(x)), Q.even(x)) is True + assert ask(Q.even(Abs(x)), ~Q.even(x)) is None + assert ask(Q.even(re(x)), Q.even(x)) is True + assert ask(Q.even(re(x)), ~Q.even(x)) is None + assert ask(Q.even(im(x)), Q.even(x)) is True + assert ask(Q.even(im(x)), Q.real(x)) is True + + assert ask(Q.even((-1)**n), Q.integer(n)) is False + + assert ask(Q.even(k**2), Q.even(k)) is True + assert ask(Q.even(n**2), Q.odd(n)) is False + assert ask(Q.even(2**k), Q.even(k)) is None + assert ask(Q.even(x**2)) is None + + assert ask(Q.even(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.even(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is False + + assert ask(Q.even(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is True + assert ask(Q.even(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is False + + assert ask(Q.even(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.even(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None + + assert ask(Q.even(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.even(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None + + assert ask(Q.even(k**x), Q.even(k)) is None + assert ask(Q.even(n**x), Q.odd(n)) is None + + assert ask(Q.even(x*y), Q.integer(x) & Q.integer(y)) is None + assert ask(Q.even(x*x), Q.integer(x)) is None + assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.odd(y)) is True + assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.even(y)) is None + + +@XFAIL +def test_evenness_in_ternary_integer_product_with_odd(): + # Tests that oddness inference is independent of term ordering. + # Term ordering at the point of testing depends on SymPy's symbol order, so + # we try to force a different order by modifying symbol names. + assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True + assert ask(Q.even(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True + + +def test_evenness_in_ternary_integer_product_with_even(): + assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None + + +def test_extended_real(): + assert ask(Q.extended_real(x), Q.positive_infinite(x)) is True + assert ask(Q.extended_real(x), Q.positive(x)) is True + assert ask(Q.extended_real(x), Q.zero(x)) is True + assert ask(Q.extended_real(x), Q.negative(x)) is True + assert ask(Q.extended_real(x), Q.negative_infinite(x)) is True + + assert ask(Q.extended_real(-x), Q.positive(x)) is True + assert ask(Q.extended_real(-x), Q.negative(x)) is True + + assert ask(Q.extended_real(x + S.Infinity), Q.real(x)) is True + + assert ask(Q.extended_real(x), Q.infinite(x)) is None + + +@_both_exp_pow +def test_rational(): + assert ask(Q.rational(x), Q.integer(x)) is True + assert ask(Q.rational(x), Q.irrational(x)) is False + assert ask(Q.rational(x), Q.real(x)) is None + assert ask(Q.rational(x), Q.positive(x)) is None + assert ask(Q.rational(x), Q.negative(x)) is None + assert ask(Q.rational(x), Q.nonzero(x)) is None + assert ask(Q.rational(x), ~Q.algebraic(x)) is False + + assert ask(Q.rational(2*x), Q.rational(x)) is True + assert ask(Q.rational(2*x), Q.integer(x)) is True + assert ask(Q.rational(2*x), Q.even(x)) is True + assert ask(Q.rational(2*x), Q.odd(x)) is True + assert ask(Q.rational(2*x), Q.irrational(x)) is False + + assert ask(Q.rational(x/2), Q.rational(x)) is True + assert ask(Q.rational(x/2), Q.integer(x)) is True + assert ask(Q.rational(x/2), Q.even(x)) is True + assert ask(Q.rational(x/2), Q.odd(x)) is True + assert ask(Q.rational(x/2), Q.irrational(x)) is False + + assert ask(Q.rational(1/x), Q.rational(x)) is True + assert ask(Q.rational(1/x), Q.integer(x)) is True + assert ask(Q.rational(1/x), Q.even(x)) is True + assert ask(Q.rational(1/x), Q.odd(x)) is True + assert ask(Q.rational(1/x), Q.irrational(x)) is False + + assert ask(Q.rational(2/x), Q.rational(x)) is True + assert ask(Q.rational(2/x), Q.integer(x)) is True + assert ask(Q.rational(2/x), Q.even(x)) is True + assert ask(Q.rational(2/x), Q.odd(x)) is True + assert ask(Q.rational(2/x), Q.irrational(x)) is False + + assert ask(Q.rational(x), ~Q.algebraic(x)) is False + + # with multiple symbols + assert ask(Q.rational(x*y), Q.irrational(x) & Q.irrational(y)) is None + assert ask(Q.rational(y/x), Q.rational(x) & Q.rational(y)) is True + assert ask(Q.rational(y/x), Q.integer(x) & Q.rational(y)) is True + assert ask(Q.rational(y/x), Q.even(x) & Q.rational(y)) is True + assert ask(Q.rational(y/x), Q.odd(x) & Q.rational(y)) is True + assert ask(Q.rational(y/x), Q.irrational(x) & Q.rational(y)) is False + + for f in [exp, sin, tan, asin, atan, cos]: + assert ask(Q.rational(f(7))) is False + assert ask(Q.rational(f(7, evaluate=False))) is False + assert ask(Q.rational(f(0, evaluate=False))) is True + assert ask(Q.rational(f(x)), Q.rational(x)) is None + assert ask(Q.rational(f(x)), Q.rational(x) & Q.nonzero(x)) is False + + for g in [log, acos]: + assert ask(Q.rational(g(7))) is False + assert ask(Q.rational(g(7, evaluate=False))) is False + assert ask(Q.rational(g(1, evaluate=False))) is True + assert ask(Q.rational(g(x)), Q.rational(x)) is None + assert ask(Q.rational(g(x)), Q.rational(x) & Q.nonzero(x - 1)) is False + + for h in [cot, acot]: + assert ask(Q.rational(h(7))) is False + assert ask(Q.rational(h(7, evaluate=False))) is False + assert ask(Q.rational(h(x)), Q.rational(x)) is False + + +def test_hermitian(): + assert ask(Q.hermitian(x)) is None + assert ask(Q.hermitian(x), Q.antihermitian(x)) is None + assert ask(Q.hermitian(x), Q.imaginary(x)) is False + assert ask(Q.hermitian(x), Q.prime(x)) is True + assert ask(Q.hermitian(x), Q.real(x)) is True + assert ask(Q.hermitian(x), Q.zero(x)) is True + + assert ask(Q.hermitian(x + 1), Q.antihermitian(x)) is None + assert ask(Q.hermitian(x + 1), Q.complex(x)) is None + assert ask(Q.hermitian(x + 1), Q.hermitian(x)) is True + assert ask(Q.hermitian(x + 1), Q.imaginary(x)) is False + assert ask(Q.hermitian(x + 1), Q.real(x)) is True + assert ask(Q.hermitian(x + I), Q.antihermitian(x)) is None + assert ask(Q.hermitian(x + I), Q.complex(x)) is None + assert ask(Q.hermitian(x + I), Q.hermitian(x)) is False + assert ask(Q.hermitian(x + I), Q.imaginary(x)) is None + assert ask(Q.hermitian(x + I), Q.real(x)) is False + assert ask( + Q.hermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y)) is None + assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None + assert ask( + Q.hermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None + assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is None + assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.real(y)) is None + assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None + assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.hermitian(y)) is True + assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is False + assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.real(y)) is True + assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None + assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is None + assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.real(y)) is False + assert ask(Q.hermitian(x + y), Q.real(x) & Q.complex(y)) is None + assert ask(Q.hermitian(x + y), Q.real(x) & Q.real(y)) is True + + assert ask(Q.hermitian(I*x), Q.antihermitian(x)) is True + assert ask(Q.hermitian(I*x), Q.complex(x)) is None + assert ask(Q.hermitian(I*x), Q.hermitian(x)) is False + assert ask(Q.hermitian(I*x), Q.imaginary(x)) is True + assert ask(Q.hermitian(I*x), Q.real(x)) is False + assert ask(Q.hermitian(x*y), Q.hermitian(x) & Q.real(y)) is True + + assert ask( + Q.hermitian(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True + assert ask(Q.hermitian(x + y + z), + Q.real(x) & Q.real(y) & Q.imaginary(z)) is False + assert ask(Q.hermitian(x + y + z), + Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is None + assert ask(Q.hermitian(x + y + z), + Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is None + + assert ask(Q.antihermitian(x)) is None + assert ask(Q.antihermitian(x), Q.real(x)) is False + assert ask(Q.antihermitian(x), Q.prime(x)) is False + + assert ask(Q.antihermitian(x + 1), Q.antihermitian(x)) is False + assert ask(Q.antihermitian(x + 1), Q.complex(x)) is None + assert ask(Q.antihermitian(x + 1), Q.hermitian(x)) is None + assert ask(Q.antihermitian(x + 1), Q.imaginary(x)) is False + assert ask(Q.antihermitian(x + 1), Q.real(x)) is None + assert ask(Q.antihermitian(x + I), Q.antihermitian(x)) is True + assert ask(Q.antihermitian(x + I), Q.complex(x)) is None + assert ask(Q.antihermitian(x + I), Q.hermitian(x)) is None + assert ask(Q.antihermitian(x + I), Q.imaginary(x)) is True + assert ask(Q.antihermitian(x + I), Q.real(x)) is False + assert ask(Q.antihermitian(x), Q.zero(x)) is True + + assert ask( + Q.antihermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y) + ) is True + assert ask( + Q.antihermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None + assert ask( + Q.antihermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None + assert ask( + Q.antihermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is True + assert ask(Q.antihermitian(x + y), Q.antihermitian(x) & Q.real(y) + ) is False + assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None + assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.hermitian(y) + ) is None + assert ask( + Q.antihermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is None + assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.real(y)) is None + assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None + assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is True + assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.real(y)) is False + assert ask(Q.antihermitian(x + y), Q.real(x) & Q.complex(y)) is None + assert ask(Q.antihermitian(x + y), Q.real(x) & Q.real(y)) is None + + assert ask(Q.antihermitian(I*x), Q.real(x)) is True + assert ask(Q.antihermitian(I*x), Q.antihermitian(x)) is False + assert ask(Q.antihermitian(I*x), Q.complex(x)) is None + assert ask(Q.antihermitian(x*y), Q.antihermitian(x) & Q.real(y)) is True + + assert ask(Q.antihermitian(x + y + z), + Q.real(x) & Q.real(y) & Q.real(z)) is None + assert ask(Q.antihermitian(x + y + z), + Q.real(x) & Q.real(y) & Q.imaginary(z)) is None + assert ask(Q.antihermitian(x + y + z), + Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False + assert ask(Q.antihermitian(x + y + z), + Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is True + + +@_both_exp_pow +def test_imaginary(): + assert ask(Q.imaginary(x)) is None + assert ask(Q.imaginary(x), Q.real(x)) is False + assert ask(Q.imaginary(x), Q.prime(x)) is False + + assert ask(Q.imaginary(x + 1), Q.real(x)) is False + assert ask(Q.imaginary(x + 1), Q.imaginary(x)) is False + assert ask(Q.imaginary(x + I), Q.real(x)) is False + assert ask(Q.imaginary(x + I), Q.imaginary(x)) is True + assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.imaginary(y)) is True + assert ask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False + assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.real(y)) is False + assert ask(Q.imaginary(x + y), Q.complex(x) & Q.real(y)) is None + assert ask( + Q.imaginary(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is False + assert ask(Q.imaginary(x + y + z), + Q.real(x) & Q.real(y) & Q.imaginary(z)) is None + assert ask(Q.imaginary(x + y + z), + Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False + + assert ask(Q.imaginary(I*x), Q.real(x)) is True + assert ask(Q.imaginary(I*x), Q.imaginary(x)) is False + assert ask(Q.imaginary(I*x), Q.complex(x)) is None + assert ask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True + assert ask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False + + assert ask(Q.imaginary(I**x), Q.negative(x)) is None + assert ask(Q.imaginary(I**x), Q.positive(x)) is None + assert ask(Q.imaginary(I**x), Q.even(x)) is False + assert ask(Q.imaginary(I**x), Q.odd(x)) is True + assert ask(Q.imaginary(I**x), Q.imaginary(x)) is False + assert ask(Q.imaginary((2*I)**x), Q.imaginary(x)) is False + assert ask(Q.imaginary(x**0), Q.imaginary(x)) is False + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.imaginary(y)) is None + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.real(y)) is None + assert ask(Q.imaginary(x**y), Q.real(x) & Q.imaginary(y)) is None + assert ask(Q.imaginary(x**y), Q.real(x) & Q.real(y)) is None + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.integer(y)) is None + assert ask(Q.imaginary(x**y), Q.imaginary(y) & Q.integer(x)) is None + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.odd(y)) is True + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.rational(y)) is None + assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.even(y)) is False + + assert ask(Q.imaginary(x**y), Q.real(x) & Q.integer(y)) is False + assert ask(Q.imaginary(x**y), Q.positive(x) & Q.real(y)) is False + assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y)) is None + assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y) & ~Q.rational(y)) is False + assert ask(Q.imaginary(x**y), Q.integer(x) & Q.imaginary(y)) is None + assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & Q.integer(2*y)) is True + assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & ~Q.integer(2*y)) is False + assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y)) is None + assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & ~Q.integer(2*y)) is False + assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & Q.integer(2*y)) is None + + # logarithm + assert ask(Q.imaginary(log(I))) is True + assert ask(Q.imaginary(log(2*I))) is False + assert ask(Q.imaginary(log(I + 1))) is False + assert ask(Q.imaginary(log(x)), Q.complex(x)) is None + assert ask(Q.imaginary(log(x)), Q.imaginary(x)) is None + assert ask(Q.imaginary(log(x)), Q.positive(x)) is False + assert ask(Q.imaginary(log(exp(x))), Q.complex(x)) is None + assert ask(Q.imaginary(log(exp(x))), Q.imaginary(x)) is None # zoo/I/a+I*b + assert ask(Q.imaginary(log(exp(I)))) is True + + # exponential + assert ask(Q.imaginary(exp(x)**x), Q.imaginary(x)) is False + eq = Pow(exp(pi*I*x, evaluate=False), x, evaluate=False) + assert ask(Q.imaginary(eq), Q.even(x)) is False + eq = Pow(exp(pi*I*x/2, evaluate=False), x, evaluate=False) + assert ask(Q.imaginary(eq), Q.odd(x)) is True + assert ask(Q.imaginary(exp(3*I*pi*x)**x), Q.integer(x)) is False + assert ask(Q.imaginary(exp(2*pi*I, evaluate=False))) is False + assert ask(Q.imaginary(exp(pi*I/2, evaluate=False))) is True + + # issue 7886 + assert ask(Q.imaginary(Pow(x, Rational(1, 4))), Q.real(x) & Q.negative(x)) is False + + +def test_integer(): + assert ask(Q.integer(x)) is None + assert ask(Q.integer(x), Q.integer(x)) is True + assert ask(Q.integer(x), ~Q.integer(x)) is False + assert ask(Q.integer(x), ~Q.real(x)) is False + assert ask(Q.integer(x), ~Q.positive(x)) is None + assert ask(Q.integer(x), Q.even(x) | Q.odd(x)) is True + + assert ask(Q.integer(2*x), Q.integer(x)) is True + assert ask(Q.integer(2*x), Q.even(x)) is True + assert ask(Q.integer(2*x), Q.prime(x)) is True + assert ask(Q.integer(2*x), Q.rational(x)) is None + assert ask(Q.integer(2*x), Q.real(x)) is None + assert ask(Q.integer(sqrt(2)*x), Q.integer(x)) is False + assert ask(Q.integer(sqrt(2)*x), Q.irrational(x)) is None + + assert ask(Q.integer(x/2), Q.odd(x)) is False + assert ask(Q.integer(x/2), Q.even(x)) is True + assert ask(Q.integer(x/3), Q.odd(x)) is None + assert ask(Q.integer(x/3), Q.even(x)) is None + + +def test_negative(): + assert ask(Q.negative(x), Q.negative(x)) is True + assert ask(Q.negative(x), Q.positive(x)) is False + assert ask(Q.negative(x), ~Q.real(x)) is False + assert ask(Q.negative(x), Q.prime(x)) is False + assert ask(Q.negative(x), ~Q.prime(x)) is None + + assert ask(Q.negative(-x), Q.positive(x)) is True + assert ask(Q.negative(-x), ~Q.positive(x)) is None + assert ask(Q.negative(-x), Q.negative(x)) is False + assert ask(Q.negative(-x), Q.positive(x)) is True + + assert ask(Q.negative(x - 1), Q.negative(x)) is True + assert ask(Q.negative(x + y)) is None + assert ask(Q.negative(x + y), Q.negative(x)) is None + assert ask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True + assert ask(Q.negative(x + y), Q.negative(x) & Q.nonpositive(y)) is True + assert ask(Q.negative(2 + I)) is False + # although this could be False, it is representative of expressions + # that don't evaluate to a zero with precision + assert ask(Q.negative(cos(I)**2 + sin(I)**2 - 1)) is None + assert ask(Q.negative(-I + I*(cos(2)**2 + sin(2)**2))) is None + + assert ask(Q.negative(x**2)) is None + assert ask(Q.negative(x**2), Q.real(x)) is False + assert ask(Q.negative(x**1.4), Q.real(x)) is None + + assert ask(Q.negative(x**I), Q.positive(x)) is None + + assert ask(Q.negative(x*y)) is None + assert ask(Q.negative(x*y), Q.positive(x) & Q.positive(y)) is False + assert ask(Q.negative(x*y), Q.positive(x) & Q.negative(y)) is True + assert ask(Q.negative(x*y), Q.complex(x) & Q.complex(y)) is None + + assert ask(Q.negative(x**y)) is None + assert ask(Q.negative(x**y), Q.negative(x) & Q.even(y)) is False + assert ask(Q.negative(x**y), Q.negative(x) & Q.odd(y)) is True + assert ask(Q.negative(x**y), Q.positive(x) & Q.integer(y)) is False + + assert ask(Q.negative(Abs(x))) is False + + +def test_nonzero(): + assert ask(Q.nonzero(x)) is None + assert ask(Q.nonzero(x), Q.real(x)) is None + assert ask(Q.nonzero(x), Q.positive(x)) is True + assert ask(Q.nonzero(x), Q.negative(x)) is True + assert ask(Q.nonzero(x), Q.negative(x) | Q.positive(x)) is True + + assert ask(Q.nonzero(x + y)) is None + assert ask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True + assert ask(Q.nonzero(x + y), Q.positive(x) & Q.negative(y)) is None + assert ask(Q.nonzero(x + y), Q.negative(x) & Q.negative(y)) is True + + assert ask(Q.nonzero(2*x)) is None + assert ask(Q.nonzero(2*x), Q.positive(x)) is True + assert ask(Q.nonzero(2*x), Q.negative(x)) is True + assert ask(Q.nonzero(x*y), Q.nonzero(x)) is None + assert ask(Q.nonzero(x*y), Q.nonzero(x) & Q.nonzero(y)) is True + + assert ask(Q.nonzero(x**y), Q.nonzero(x)) is True + + assert ask(Q.nonzero(Abs(x))) is None + assert ask(Q.nonzero(Abs(x)), Q.nonzero(x)) is True + + assert ask(Q.nonzero(log(exp(2*I)))) is False + # although this could be False, it is representative of expressions + # that don't evaluate to a zero with precision + assert ask(Q.nonzero(cos(1)**2 + sin(1)**2 - 1)) is None + + +def test_zero(): + assert ask(Q.zero(x)) is None + assert ask(Q.zero(x), Q.real(x)) is None + assert ask(Q.zero(x), Q.positive(x)) is False + assert ask(Q.zero(x), Q.negative(x)) is False + assert ask(Q.zero(x), Q.negative(x) | Q.positive(x)) is False + + assert ask(Q.zero(x), Q.nonnegative(x) & Q.nonpositive(x)) is True + + assert ask(Q.zero(x + y)) is None + assert ask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False + assert ask(Q.zero(x + y), Q.positive(x) & Q.negative(y)) is None + assert ask(Q.zero(x + y), Q.negative(x) & Q.negative(y)) is False + + assert ask(Q.zero(2*x)) is None + assert ask(Q.zero(2*x), Q.positive(x)) is False + assert ask(Q.zero(2*x), Q.negative(x)) is False + assert ask(Q.zero(x*y), Q.nonzero(x)) is None + + assert ask(Q.zero(Abs(x))) is None + assert ask(Q.zero(Abs(x)), Q.zero(x)) is True + + assert ask(Q.integer(x), Q.zero(x)) is True + assert ask(Q.even(x), Q.zero(x)) is True + assert ask(Q.odd(x), Q.zero(x)) is False + assert ask(Q.zero(x), Q.even(x)) is None + assert ask(Q.zero(x), Q.odd(x)) is False + assert ask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True + + +def test_odd_query(): + assert ask(Q.odd(x)) is None + assert ask(Q.odd(x), Q.odd(x)) is True + assert ask(Q.odd(x), Q.integer(x)) is None + assert ask(Q.odd(x), ~Q.integer(x)) is False + assert ask(Q.odd(x), Q.rational(x)) is None + assert ask(Q.odd(x), Q.positive(x)) is None + + assert ask(Q.odd(-x), Q.odd(x)) is True + + assert ask(Q.odd(2*x)) is None + assert ask(Q.odd(2*x), Q.integer(x)) is False + assert ask(Q.odd(2*x), Q.odd(x)) is False + assert ask(Q.odd(2*x), Q.irrational(x)) is False + assert ask(Q.odd(2*x), ~Q.integer(x)) is None + assert ask(Q.odd(3*x), Q.integer(x)) is None + + assert ask(Q.odd(x/3), Q.odd(x)) is None + assert ask(Q.odd(x/3), Q.even(x)) is None + + assert ask(Q.odd(x + 1), Q.even(x)) is True + assert ask(Q.odd(x + 2), Q.even(x)) is False + assert ask(Q.odd(x + 2), Q.odd(x)) is True + assert ask(Q.odd(3 - x), Q.odd(x)) is False + assert ask(Q.odd(3 - x), Q.even(x)) is True + assert ask(Q.odd(3 + x), Q.odd(x)) is False + assert ask(Q.odd(3 + x), Q.even(x)) is True + assert ask(Q.odd(x + y), Q.odd(x) & Q.odd(y)) is False + assert ask(Q.odd(x + y), Q.odd(x) & Q.even(y)) is True + assert ask(Q.odd(x - y), Q.even(x) & Q.odd(y)) is True + assert ask(Q.odd(x - y), Q.odd(x) & Q.odd(y)) is False + + assert ask(Q.odd(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is False + assert ask(Q.odd(x + y + z + t), + Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None + + assert ask(Q.odd(2*x + 1), Q.integer(x)) is True + assert ask(Q.odd(2*x + y), Q.integer(x) & Q.odd(y)) is True + assert ask(Q.odd(2*x + y), Q.integer(x) & Q.even(y)) is False + assert ask(Q.odd(2*x + y), Q.integer(x) & Q.integer(y)) is None + assert ask(Q.odd(x*y), Q.odd(x) & Q.even(y)) is False + assert ask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True + assert ask(Q.odd(2*x*y), Q.rational(x) & Q.rational(x)) is None + assert ask(Q.odd(2*x*y), Q.irrational(x) & Q.irrational(x)) is None + + assert ask(Q.odd(Abs(x)), Q.odd(x)) is True + + assert ask(Q.odd((-1)**n), Q.integer(n)) is True + + assert ask(Q.odd(k**2), Q.even(k)) is False + assert ask(Q.odd(n**2), Q.odd(n)) is True + assert ask(Q.odd(3**k), Q.even(k)) is None + + assert ask(Q.odd(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.odd(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is True + + assert ask(Q.odd(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is False + assert ask(Q.odd(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is True + + assert ask(Q.odd(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.odd(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None + + assert ask(Q.odd(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None + assert ask(Q.odd(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None + + assert ask(Q.odd(k**x), Q.even(k)) is None + assert ask(Q.odd(n**x), Q.odd(n)) is None + + assert ask(Q.odd(x*y), Q.integer(x) & Q.integer(y)) is None + assert ask(Q.odd(x*x), Q.integer(x)) is None + assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.odd(y)) is False + assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.even(y)) is None + + +@XFAIL +def test_oddness_in_ternary_integer_product_with_odd(): + # Tests that oddness inference is independent of term ordering. + # Term ordering at the point of testing depends on SymPy's symbol order, so + # we try to force a different order by modifying symbol names. + assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False + assert ask(Q.odd(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False + + +def test_oddness_in_ternary_integer_product_with_even(): + assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None + + +def test_prime(): + assert ask(Q.prime(x), Q.prime(x)) is True + assert ask(Q.prime(x), ~Q.prime(x)) is False + assert ask(Q.prime(x), Q.integer(x)) is None + assert ask(Q.prime(x), ~Q.integer(x)) is False + + assert ask(Q.prime(2*x), Q.integer(x)) is None + assert ask(Q.prime(x*y)) is None + assert ask(Q.prime(x*y), Q.prime(x)) is None + assert ask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None + assert ask(Q.prime(4*x), Q.integer(x)) is False + assert ask(Q.prime(4*x)) is None + + assert ask(Q.prime(x**2), Q.integer(x)) is False + assert ask(Q.prime(x**2), Q.prime(x)) is False + assert ask(Q.prime(x**y), Q.integer(x) & Q.integer(y)) is False + + +@_both_exp_pow +def test_positive(): + assert ask(Q.positive(cos(I) ** 2 + sin(I) ** 2 - 1)) is None + assert ask(Q.positive(x), Q.positive(x)) is True + assert ask(Q.positive(x), Q.negative(x)) is False + assert ask(Q.positive(x), Q.nonzero(x)) is None + + assert ask(Q.positive(-x), Q.positive(x)) is False + assert ask(Q.positive(-x), Q.negative(x)) is True + + assert ask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True + assert ask(Q.positive(x + y), Q.positive(x) & Q.nonnegative(y)) is True + assert ask(Q.positive(x + y), Q.positive(x) & Q.negative(y)) is None + assert ask(Q.positive(x + y), Q.positive(x) & Q.imaginary(y)) is False + + assert ask(Q.positive(2*x), Q.positive(x)) is True + assumptions = Q.positive(x) & Q.negative(y) & Q.negative(z) & Q.positive(w) + assert ask(Q.positive(x*y*z)) is None + assert ask(Q.positive(x*y*z), assumptions) is True + assert ask(Q.positive(-x*y*z), assumptions) is False + + assert ask(Q.positive(x**I), Q.positive(x)) is None + + assert ask(Q.positive(x**2), Q.positive(x)) is True + assert ask(Q.positive(x**2), Q.negative(x)) is True + assert ask(Q.positive(x**3), Q.negative(x)) is False + assert ask(Q.positive(1/(1 + x**2)), Q.real(x)) is True + assert ask(Q.positive(2**I)) is False + assert ask(Q.positive(2 + I)) is False + # although this could be False, it is representative of expressions + # that don't evaluate to a zero with precision + assert ask(Q.positive(cos(I)**2 + sin(I)**2 - 1)) is None + assert ask(Q.positive(-I + I*(cos(2)**2 + sin(2)**2))) is None + + #exponential + assert ask(Q.positive(exp(x)), Q.real(x)) is True + assert ask(~Q.negative(exp(x)), Q.real(x)) is True + assert ask(Q.positive(x + exp(x)), Q.real(x)) is None + assert ask(Q.positive(exp(x)), Q.imaginary(x)) is None + assert ask(Q.positive(exp(2*pi*I, evaluate=False)), Q.imaginary(x)) is True + assert ask(Q.negative(exp(pi*I, evaluate=False)), Q.imaginary(x)) is True + assert ask(Q.positive(exp(x*pi*I)), Q.even(x)) is True + assert ask(Q.positive(exp(x*pi*I)), Q.odd(x)) is False + assert ask(Q.positive(exp(x*pi*I)), Q.real(x)) is None + + # logarithm + assert ask(Q.positive(log(x)), Q.imaginary(x)) is False + assert ask(Q.positive(log(x)), Q.negative(x)) is False + assert ask(Q.positive(log(x)), Q.positive(x)) is None + assert ask(Q.positive(log(x + 2)), Q.positive(x)) is True + + # factorial + assert ask(Q.positive(factorial(x)), Q.integer(x) & Q.positive(x)) + assert ask(Q.positive(factorial(x)), Q.integer(x)) is None + + #absolute value + assert ask(Q.positive(Abs(x))) is None # Abs(0) = 0 + assert ask(Q.positive(Abs(x)), Q.positive(x)) is True + + +def test_nonpositive(): + assert ask(Q.nonpositive(-1)) + assert ask(Q.nonpositive(0)) + assert ask(Q.nonpositive(1)) is False + assert ask(~Q.positive(x), Q.nonpositive(x)) + assert ask(Q.nonpositive(x), Q.positive(x)) is False + assert ask(Q.nonpositive(sqrt(-1))) is False + assert ask(Q.nonpositive(x), Q.imaginary(x)) is False + + +def test_nonnegative(): + assert ask(Q.nonnegative(-1)) is False + assert ask(Q.nonnegative(0)) + assert ask(Q.nonnegative(1)) + assert ask(~Q.negative(x), Q.nonnegative(x)) + assert ask(Q.nonnegative(x), Q.negative(x)) is False + assert ask(Q.nonnegative(sqrt(-1))) is False + assert ask(Q.nonnegative(x), Q.imaginary(x)) is False + +def test_real_basic(): + assert ask(Q.real(x)) is None + assert ask(Q.real(x), Q.real(x)) is True + assert ask(Q.real(x), Q.nonzero(x)) is True + assert ask(Q.real(x), Q.positive(x)) is True + assert ask(Q.real(x), Q.negative(x)) is True + assert ask(Q.real(x), Q.integer(x)) is True + assert ask(Q.real(x), Q.even(x)) is True + assert ask(Q.real(x), Q.prime(x)) is True + + assert ask(Q.real(x/sqrt(2)), Q.real(x)) is True + assert ask(Q.real(x/sqrt(-2)), Q.real(x)) is False + + assert ask(Q.real(x + 1), Q.real(x)) is True + assert ask(Q.real(x + I), Q.real(x)) is False + assert ask(Q.real(x + I), Q.complex(x)) is None + + assert ask(Q.real(2*x), Q.real(x)) is True + assert ask(Q.real(I*x), Q.real(x)) is False + assert ask(Q.real(I*x), Q.imaginary(x)) is True + assert ask(Q.real(I*x), Q.complex(x)) is None + + +def test_real_pow(): + assert ask(Q.real(x**2), Q.real(x)) is True + assert ask(Q.real(sqrt(x)), Q.negative(x)) is False + assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) is True + assert ask(Q.real(x**y), Q.real(x) & Q.real(y)) is None + assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True + assert ask(Q.real(x**y), Q.imaginary(x) & Q.imaginary(y)) is None # I**I or (2*I)**I + assert ask(Q.real(x**y), Q.imaginary(x) & Q.real(y)) is None # I**1 or I**0 + assert ask(Q.real(x**y), Q.real(x) & Q.imaginary(y)) is None # could be exp(2*pi*I) or 2**I + assert ask(Q.real(x**0), Q.imaginary(x)) is True + assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) is True + assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True + assert ask(Q.real(x**y), Q.real(x) & Q.rational(y)) is None + assert ask(Q.real(x**y), Q.imaginary(x) & Q.integer(y)) is None + assert ask(Q.real(x**y), Q.imaginary(x) & Q.odd(y)) is False + assert ask(Q.real(x**y), Q.imaginary(x) & Q.even(y)) is True + assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.rational(y/z) & Q.even(z) & Q.positive(x)) is True + assert ask(Q.real(x**(y/z)), Q.real(x) & Q.rational(y/z) & Q.even(z) & Q.negative(x)) is False + assert ask(Q.real(x**(y/z)), Q.real(x) & Q.integer(y/z)) is True + assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.positive(x)) is True + assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.negative(x)) is False + assert ask(Q.real((-I)**i), Q.imaginary(i)) is True + assert ask(Q.real(I**i), Q.imaginary(i)) is True + assert ask(Q.real(i**i), Q.imaginary(i)) is None # i might be 2*I + assert ask(Q.real(x**i), Q.imaginary(i)) is None # x could be 0 + assert ask(Q.real(x**(I*pi/log(x))), Q.real(x)) is True + + +@_both_exp_pow +def test_real_functions(): + # trigonometric functions + assert ask(Q.real(sin(x))) is None + assert ask(Q.real(cos(x))) is None + assert ask(Q.real(sin(x)), Q.real(x)) is True + assert ask(Q.real(cos(x)), Q.real(x)) is True + + # exponential function + assert ask(Q.real(exp(x))) is None + assert ask(Q.real(exp(x)), Q.real(x)) is True + assert ask(Q.real(x + exp(x)), Q.real(x)) is True + assert ask(Q.real(exp(2*pi*I, evaluate=False))) is True + assert ask(Q.real(exp(pi*I, evaluate=False))) is True + assert ask(Q.real(exp(pi*I/2, evaluate=False))) is False + + # logarithm + assert ask(Q.real(log(I))) is False + assert ask(Q.real(log(2*I))) is False + assert ask(Q.real(log(I + 1))) is False + assert ask(Q.real(log(x)), Q.complex(x)) is None + assert ask(Q.real(log(x)), Q.imaginary(x)) is False + assert ask(Q.real(log(exp(x))), Q.imaginary(x)) is None # exp(2*pi*I) is 1, log(exp(pi*I)) is pi*I (disregarding periodicity) + assert ask(Q.real(log(exp(x))), Q.complex(x)) is None + eq = Pow(exp(2*pi*I*x, evaluate=False), x, evaluate=False) + assert ask(Q.real(eq), Q.integer(x)) is True + assert ask(Q.real(exp(x)**x), Q.imaginary(x)) is True + assert ask(Q.real(exp(x)**x), Q.complex(x)) is None + + # Q.complexes + assert ask(Q.real(re(x))) is True + assert ask(Q.real(im(x))) is True + + +def test_matrix(): + + # hermitian + assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 - I, 3, I], [4, -I, 1]]))) == True + assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 + I, 3, I], [4, -I, 1]]))) == False + z = symbols('z', complex=True) + assert ask(Q.hermitian(Matrix([[2, 2 + I, z], [2 - I, 3, I], [4, -I, 1]]))) == None + assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))))) == True + assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, I, 0), (-5, 0, 11))))) == False + assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, z, 0), (-5, 0, 11))))) == None + + # antihermitian + A = Matrix([[0, -2 - I, 0], [2 - I, 0, -I], [0, -I, 0]]) + B = Matrix([[-I, 2 + I, 0], [-2 + I, 0, 2 + I], [0, -2 + I, -I]]) + assert ask(Q.antihermitian(A)) is True + assert ask(Q.antihermitian(B)) is True + assert ask(Q.antihermitian(A**2)) is False + C = (B**3) + C.simplify() + assert ask(Q.antihermitian(C)) is True + _A = Matrix([[0, -2 - I, 0], [z, 0, -I], [0, -I, 0]]) + assert ask(Q.antihermitian(_A)) is None + + +@_both_exp_pow +def test_algebraic(): + assert ask(Q.algebraic(x)) is None + + assert ask(Q.algebraic(I)) is True + assert ask(Q.algebraic(2*I)) is True + assert ask(Q.algebraic(I/3)) is True + + assert ask(Q.algebraic(sqrt(7))) is True + assert ask(Q.algebraic(2*sqrt(7))) is True + assert ask(Q.algebraic(sqrt(7)/3)) is True + + assert ask(Q.algebraic(I*sqrt(3))) is True + assert ask(Q.algebraic(sqrt(1 + I*sqrt(3)))) is True + + assert ask(Q.algebraic(1 + I*sqrt(3)**Rational(17, 31))) is True + assert ask(Q.algebraic(1 + I*sqrt(3)**(17/pi))) is False + + for f in [exp, sin, tan, asin, atan, cos]: + assert ask(Q.algebraic(f(7))) is False + assert ask(Q.algebraic(f(7, evaluate=False))) is False + assert ask(Q.algebraic(f(0, evaluate=False))) is True + assert ask(Q.algebraic(f(x)), Q.algebraic(x)) is None + assert ask(Q.algebraic(f(x)), Q.algebraic(x) & Q.nonzero(x)) is False + + for g in [log, acos]: + assert ask(Q.algebraic(g(7))) is False + assert ask(Q.algebraic(g(7, evaluate=False))) is False + assert ask(Q.algebraic(g(1, evaluate=False))) is True + assert ask(Q.algebraic(g(x)), Q.algebraic(x)) is None + assert ask(Q.algebraic(g(x)), Q.algebraic(x) & Q.nonzero(x - 1)) is False + + for h in [cot, acot]: + assert ask(Q.algebraic(h(7))) is False + assert ask(Q.algebraic(h(7, evaluate=False))) is False + assert ask(Q.algebraic(h(x)), Q.algebraic(x)) is False + + assert ask(Q.algebraic(sqrt(sin(7)))) is False + assert ask(Q.algebraic(sqrt(y + I*sqrt(7)))) is None + + assert ask(Q.algebraic(2.47)) is True + + assert ask(Q.algebraic(x), Q.transcendental(x)) is False + assert ask(Q.transcendental(x), Q.algebraic(x)) is False + + +def test_global(): + """Test ask with global assumptions""" + assert ask(Q.integer(x)) is None + global_assumptions.add(Q.integer(x)) + assert ask(Q.integer(x)) is True + global_assumptions.clear() + assert ask(Q.integer(x)) is None + + +def test_custom_context(): + """Test ask with custom assumptions context""" + assert ask(Q.integer(x)) is None + local_context = AssumptionsContext() + local_context.add(Q.integer(x)) + assert ask(Q.integer(x), context=local_context) is True + assert ask(Q.integer(x)) is None + + +def test_functions_in_assumptions(): + assert ask(Q.negative(x), Q.real(x) >> Q.positive(x)) is False + assert ask(Q.negative(x), Equivalent(Q.real(x), Q.positive(x))) is False + assert ask(Q.negative(x), Xor(Q.real(x), Q.negative(x))) is False + + +def test_composite_ask(): + assert ask(Q.negative(x) & Q.integer(x), + assumptions=Q.real(x) >> Q.positive(x)) is False + + +def test_composite_proposition(): + assert ask(True) is True + assert ask(False) is False + assert ask(~Q.negative(x), Q.positive(x)) is True + assert ask(~Q.real(x), Q.commutative(x)) is None + assert ask(Q.negative(x) & Q.integer(x), Q.positive(x)) is False + assert ask(Q.negative(x) & Q.integer(x)) is None + assert ask(Q.real(x) | Q.integer(x), Q.positive(x)) is True + assert ask(Q.real(x) | Q.integer(x)) is None + assert ask(Q.real(x) >> Q.positive(x), Q.negative(x)) is False + assert ask(Implies( + Q.real(x), Q.positive(x), evaluate=False), Q.negative(x)) is False + assert ask(Implies(Q.real(x), Q.positive(x), evaluate=False)) is None + assert ask(Equivalent(Q.integer(x), Q.even(x)), Q.even(x)) is True + assert ask(Equivalent(Q.integer(x), Q.even(x))) is None + assert ask(Equivalent(Q.positive(x), Q.integer(x)), Q.integer(x)) is None + assert ask(Q.real(x) | Q.integer(x), Q.real(x) | Q.integer(x)) is True + +def test_tautology(): + assert ask(Q.real(x) | ~Q.real(x)) is True + assert ask(Q.real(x) & ~Q.real(x)) is False + +def test_composite_assumptions(): + assert ask(Q.real(x), Q.real(x) & Q.real(y)) is True + assert ask(Q.positive(x), Q.positive(x) | Q.positive(y)) is None + assert ask(Q.positive(x), Q.real(x) >> Q.positive(y)) is None + assert ask(Q.real(x), ~(Q.real(x) >> Q.real(y))) is True + +def test_key_extensibility(): + """test that you can add keys to the ask system at runtime""" + # make sure the key is not defined + raises(AttributeError, lambda: ask(Q.my_key(x))) + + # Old handler system + class MyAskHandler(AskHandler): + @staticmethod + def Symbol(expr, assumptions): + return True + try: + with warns_deprecated_sympy(): + register_handler('my_key', MyAskHandler) + with warns_deprecated_sympy(): + assert ask(Q.my_key(x)) is True + with warns_deprecated_sympy(): + assert ask(Q.my_key(x + 1)) is None + finally: + # We have to disable the stacklevel testing here because this raises + # the warning twice from two different places + with warns_deprecated_sympy(): + remove_handler('my_key', MyAskHandler) + del Q.my_key + raises(AttributeError, lambda: ask(Q.my_key(x))) + + # New handler system + class MyPredicate(Predicate): + pass + try: + Q.my_key = MyPredicate() + @Q.my_key.register(Symbol) + def _(expr, assumptions): + return True + assert ask(Q.my_key(x)) is True + assert ask(Q.my_key(x+1)) is None + finally: + del Q.my_key + raises(AttributeError, lambda: ask(Q.my_key(x))) + + +def test_type_extensibility(): + """test that new types can be added to the ask system at runtime + """ + from sympy.core import Basic + + class MyType(Basic): + pass + + @Q.prime.register(MyType) + def _(expr, assumptions): + return True + + assert ask(Q.prime(MyType())) is True + + +def test_single_fact_lookup(): + known_facts = And(Implies(Q.integer, Q.rational), + Implies(Q.rational, Q.real), + Implies(Q.real, Q.complex)) + known_facts_keys = {Q.integer, Q.rational, Q.real, Q.complex} + + known_facts_cnf = to_cnf(known_facts) + mapping = single_fact_lookup(known_facts_keys, known_facts_cnf) + + assert mapping[Q.rational] == {Q.real, Q.rational, Q.complex} + + +def test_generate_known_facts_dict(): + known_facts = And(Implies(Q.integer(x), Q.rational(x)), + Implies(Q.rational(x), Q.real(x)), + Implies(Q.real(x), Q.complex(x))) + known_facts_keys = {Q.integer(x), Q.rational(x), Q.real(x), Q.complex(x)} + + assert generate_known_facts_dict(known_facts_keys, known_facts) == \ + {Q.complex: ({Q.complex}, set()), + Q.integer: ({Q.complex, Q.integer, Q.rational, Q.real}, set()), + Q.rational: ({Q.complex, Q.rational, Q.real}, set()), + Q.real: ({Q.complex, Q.real}, set())} + + +@slow +def test_known_facts_consistent(): + """"Test that ask_generated.py is up-to-date""" + x = Symbol('x') + fact = get_known_facts(x) + # test cnf clauses of fact between unary predicates + cnf = CNF.to_CNF(fact) + clauses = set() + clauses.update(frozenset(Literal(lit.arg.function, lit.is_Not) for lit in sorted(cl, key=str)) for cl in cnf.clauses) + assert get_all_known_facts() == clauses + # test dictionary of fact between unary predicates + keys = [pred(x) for pred in get_known_facts_keys()] + mapping = generate_known_facts_dict(keys, fact) + assert get_known_facts_dict() == mapping + + +def test_Add_queries(): + assert ask(Q.prime(12345678901234567890 + (cos(1)**2 + sin(1)**2))) is True + assert ask(Q.even(Add(S(2), S(2), evaluate=0))) is True + assert ask(Q.prime(Add(S(2), S(2), evaluate=0))) is False + assert ask(Q.integer(Add(S(2), S(2), evaluate=0))) is True + + +def test_positive_assuming(): + with assuming(Q.positive(x + 1)): + assert not ask(Q.positive(x)) + + +def test_issue_5421(): + raises(TypeError, lambda: ask(pi/log(x), Q.real)) + + +def test_issue_3906(): + raises(TypeError, lambda: ask(Q.positive)) + + +def test_issue_5833(): + assert ask(Q.positive(log(x)**2), Q.positive(x)) is None + assert ask(~Q.negative(log(x)**2), Q.positive(x)) is True + + +def test_issue_6732(): + raises(ValueError, lambda: ask(Q.positive(x), Q.positive(x) & Q.negative(x))) + raises(ValueError, lambda: ask(Q.negative(x), Q.positive(x) & Q.negative(x))) + + +def test_issue_7246(): + assert ask(Q.positive(atan(p)), Q.positive(p)) is True + assert ask(Q.positive(atan(p)), Q.negative(p)) is False + assert ask(Q.positive(atan(p)), Q.zero(p)) is False + assert ask(Q.positive(atan(x))) is None + + assert ask(Q.positive(asin(p)), Q.positive(p)) is None + assert ask(Q.positive(asin(p)), Q.zero(p)) is None + assert ask(Q.positive(asin(Rational(1, 7)))) is True + assert ask(Q.positive(asin(x)), Q.positive(x) & Q.nonpositive(x - 1)) is True + assert ask(Q.positive(asin(x)), Q.negative(x) & Q.nonnegative(x + 1)) is False + + assert ask(Q.positive(acos(p)), Q.positive(p)) is None + assert ask(Q.positive(acos(Rational(1, 7)))) is True + assert ask(Q.positive(acos(x)), Q.nonnegative(x + 1) & Q.nonpositive(x - 1)) is True + assert ask(Q.positive(acos(x)), Q.nonnegative(x - 1)) is None + + assert ask(Q.positive(acot(x)), Q.positive(x)) is True + assert ask(Q.positive(acot(x)), Q.real(x)) is True + assert ask(Q.positive(acot(x)), Q.imaginary(x)) is False + assert ask(Q.positive(acot(x))) is None + + +@XFAIL +def test_issue_7246_failing(): + #Move this test to test_issue_7246 once + #the new assumptions module is improved. + assert ask(Q.positive(acos(x)), Q.zero(x)) is True + + +def test_check_old_assumption(): + x = symbols('x', real=True) + assert ask(Q.real(x)) is True + assert ask(Q.imaginary(x)) is False + assert ask(Q.complex(x)) is True + + x = symbols('x', imaginary=True) + assert ask(Q.real(x)) is False + assert ask(Q.imaginary(x)) is True + assert ask(Q.complex(x)) is True + + x = symbols('x', complex=True) + assert ask(Q.real(x)) is None + assert ask(Q.complex(x)) is True + + x = symbols('x', positive=True) + assert ask(Q.positive(x)) is True + assert ask(Q.negative(x)) is False + assert ask(Q.real(x)) is True + + x = symbols('x', commutative=False) + assert ask(Q.commutative(x)) is False + + x = symbols('x', negative=True) + assert ask(Q.positive(x)) is False + assert ask(Q.negative(x)) is True + + x = symbols('x', nonnegative=True) + assert ask(Q.negative(x)) is False + assert ask(Q.positive(x)) is None + assert ask(Q.zero(x)) is None + + x = symbols('x', finite=True) + assert ask(Q.finite(x)) is True + + x = symbols('x', prime=True) + assert ask(Q.prime(x)) is True + assert ask(Q.composite(x)) is False + + x = symbols('x', composite=True) + assert ask(Q.prime(x)) is False + assert ask(Q.composite(x)) is True + + x = symbols('x', even=True) + assert ask(Q.even(x)) is True + assert ask(Q.odd(x)) is False + + x = symbols('x', odd=True) + assert ask(Q.even(x)) is False + assert ask(Q.odd(x)) is True + + x = symbols('x', nonzero=True) + assert ask(Q.nonzero(x)) is True + assert ask(Q.zero(x)) is False + + x = symbols('x', zero=True) + assert ask(Q.zero(x)) is True + + x = symbols('x', integer=True) + assert ask(Q.integer(x)) is True + + x = symbols('x', rational=True) + assert ask(Q.rational(x)) is True + assert ask(Q.irrational(x)) is False + + x = symbols('x', irrational=True) + assert ask(Q.irrational(x)) is True + assert ask(Q.rational(x)) is False + + +def test_issue_9636(): + assert ask(Q.integer(1.0)) is None + assert ask(Q.prime(3.0)) is None + assert ask(Q.composite(4.0)) is None + assert ask(Q.even(2.0)) is None + assert ask(Q.odd(3.0)) is None + + +def test_autosimp_used_to_fail(): + # See issue #9807 + assert ask(Q.imaginary(0**I)) is None + assert ask(Q.imaginary(0**(-I))) is None + assert ask(Q.real(0**I)) is None + assert ask(Q.real(0**(-I))) is None + + +def test_custom_AskHandler(): + from sympy.logic.boolalg import conjuncts + + # Old handler system + class MersenneHandler(AskHandler): + @staticmethod + def Integer(expr, assumptions): + if ask(Q.integer(log(expr + 1, 2))): + return True + @staticmethod + def Symbol(expr, assumptions): + if expr in conjuncts(assumptions): + return True + try: + with warns_deprecated_sympy(): + register_handler('mersenne', MersenneHandler) + n = Symbol('n', integer=True) + with warns_deprecated_sympy(): + assert ask(Q.mersenne(7)) + with warns_deprecated_sympy(): + assert ask(Q.mersenne(n), Q.mersenne(n)) + finally: + del Q.mersenne + + # New handler system + class MersennePredicate(Predicate): + pass + try: + Q.mersenne = MersennePredicate() + @Q.mersenne.register(Integer) + def _(expr, assumptions): + if ask(Q.integer(log(expr + 1, 2))): + return True + @Q.mersenne.register(Symbol) + def _(expr, assumptions): + if expr in conjuncts(assumptions): + return True + assert ask(Q.mersenne(7)) + assert ask(Q.mersenne(n), Q.mersenne(n)) + finally: + del Q.mersenne + + +def test_polyadic_predicate(): + + class SexyPredicate(Predicate): + pass + try: + Q.sexyprime = SexyPredicate() + + @Q.sexyprime.register(Integer, Integer) + def _(int1, int2, assumptions): + args = sorted([int1, int2]) + if not all(ask(Q.prime(a), assumptions) for a in args): + return False + return args[1] - args[0] == 6 + + @Q.sexyprime.register(Integer, Integer, Integer) + def _(int1, int2, int3, assumptions): + args = sorted([int1, int2, int3]) + if not all(ask(Q.prime(a), assumptions) for a in args): + return False + return args[2] - args[1] == 6 and args[1] - args[0] == 6 + + assert ask(Q.sexyprime(5, 11)) + assert ask(Q.sexyprime(7, 13, 19)) + finally: + del Q.sexyprime + + +def test_Predicate_handler_is_unique(): + + # Undefined predicate does not have a handler + assert Predicate('mypredicate').handler is None + + # Handler of defined predicate is unique to the class + class MyPredicate(Predicate): + pass + mp1 = MyPredicate(Str('mp1')) + mp2 = MyPredicate(Str('mp2')) + assert mp1.handler is mp2.handler + + +def test_relational(): + assert ask(Q.eq(x, 0), Q.zero(x)) + assert not ask(Q.eq(x, 0), Q.nonzero(x)) + assert not ask(Q.ne(x, 0), Q.zero(x)) + assert ask(Q.ne(x, 0), Q.nonzero(x)) + + +def test_issue_25221(): + assert ask(Q.transcendental(x), Q.algebraic(x) | Q.positive(y,y)) is None + assert ask(Q.transcendental(x), Q.algebraic(x) | (0 > y)) is None + assert ask(Q.transcendental(x), Q.algebraic(x) | Q.gt(0,y)) is None diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_refine.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_refine.py new file mode 100644 index 0000000000000000000000000000000000000000..81533a88b232cd5c3cfb9be17d09dad404d679dc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_refine.py @@ -0,0 +1,227 @@ +from sympy.assumptions.ask import Q +from sympy.assumptions.refine import refine +from sympy.core.expr import Expr +from sympy.core.numbers import (I, Rational, nan, pi) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import (Abs, arg, im, re, sign) +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (atan, atan2) +from sympy.abc import w, x, y, z +from sympy.core.relational import Eq, Ne +from sympy.functions.elementary.piecewise import Piecewise +from sympy.matrices.expressions.matexpr import MatrixSymbol + + +def test_Abs(): + assert refine(Abs(x), Q.positive(x)) == x + assert refine(1 + Abs(x), Q.positive(x)) == 1 + x + assert refine(Abs(x), Q.negative(x)) == -x + assert refine(1 + Abs(x), Q.negative(x)) == 1 - x + + assert refine(Abs(x**2)) != x**2 + assert refine(Abs(x**2), Q.real(x)) == x**2 + + +def test_pow1(): + assert refine((-1)**x, Q.even(x)) == 1 + assert refine((-1)**x, Q.odd(x)) == -1 + assert refine((-2)**x, Q.even(x)) == 2**x + + # nested powers + assert refine(sqrt(x**2)) != Abs(x) + assert refine(sqrt(x**2), Q.complex(x)) != Abs(x) + assert refine(sqrt(x**2), Q.real(x)) == Abs(x) + assert refine(sqrt(x**2), Q.positive(x)) == x + assert refine((x**3)**Rational(1, 3)) != x + + assert refine((x**3)**Rational(1, 3), Q.real(x)) != x + assert refine((x**3)**Rational(1, 3), Q.positive(x)) == x + + assert refine(sqrt(1/x), Q.real(x)) != 1/sqrt(x) + assert refine(sqrt(1/x), Q.positive(x)) == 1/sqrt(x) + + # powers of (-1) + assert refine((-1)**(x + y), Q.even(x)) == (-1)**y + assert refine((-1)**(x + y + z), Q.odd(x) & Q.odd(z)) == (-1)**y + assert refine((-1)**(x + y + 1), Q.odd(x)) == (-1)**y + assert refine((-1)**(x + y + 2), Q.odd(x)) == (-1)**(y + 1) + assert refine((-1)**(x + 3)) == (-1)**(x + 1) + + # continuation + assert refine((-1)**((-1)**x/2 - S.Half), Q.integer(x)) == (-1)**x + assert refine((-1)**((-1)**x/2 + S.Half), Q.integer(x)) == (-1)**(x + 1) + assert refine((-1)**((-1)**x/2 + 5*S.Half), Q.integer(x)) == (-1)**(x + 1) + + +def test_pow2(): + assert refine((-1)**((-1)**x/2 - 7*S.Half), Q.integer(x)) == (-1)**(x + 1) + assert refine((-1)**((-1)**x/2 - 9*S.Half), Q.integer(x)) == (-1)**x + + # powers of Abs + assert refine(Abs(x)**2, Q.real(x)) == x**2 + assert refine(Abs(x)**3, Q.real(x)) == Abs(x)**3 + assert refine(Abs(x)**2) == Abs(x)**2 + + +def test_exp(): + x = Symbol('x', integer=True) + assert refine(exp(pi*I*2*x)) == 1 + assert refine(exp(pi*I*2*(x + S.Half))) == -1 + assert refine(exp(pi*I*2*(x + Rational(1, 4)))) == I + assert refine(exp(pi*I*2*(x + Rational(3, 4)))) == -I + + +def test_Piecewise(): + assert refine(Piecewise((1, x < 0), (3, True)), (x < 0)) == 1 + assert refine(Piecewise((1, x < 0), (3, True)), ~(x < 0)) == 3 + assert refine(Piecewise((1, x < 0), (3, True)), (y < 0)) == \ + Piecewise((1, x < 0), (3, True)) + assert refine(Piecewise((1, x > 0), (3, True)), (x > 0)) == 1 + assert refine(Piecewise((1, x > 0), (3, True)), ~(x > 0)) == 3 + assert refine(Piecewise((1, x > 0), (3, True)), (y > 0)) == \ + Piecewise((1, x > 0), (3, True)) + assert refine(Piecewise((1, x <= 0), (3, True)), (x <= 0)) == 1 + assert refine(Piecewise((1, x <= 0), (3, True)), ~(x <= 0)) == 3 + assert refine(Piecewise((1, x <= 0), (3, True)), (y <= 0)) == \ + Piecewise((1, x <= 0), (3, True)) + assert refine(Piecewise((1, x >= 0), (3, True)), (x >= 0)) == 1 + assert refine(Piecewise((1, x >= 0), (3, True)), ~(x >= 0)) == 3 + assert refine(Piecewise((1, x >= 0), (3, True)), (y >= 0)) == \ + Piecewise((1, x >= 0), (3, True)) + assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(x, 0)))\ + == 1 + assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(0, x)))\ + == 1 + assert refine(Piecewise((1, Eq(x, 0)), (3, True)), ~(Eq(x, 0)))\ + == 3 + assert refine(Piecewise((1, Eq(x, 0)), (3, True)), ~(Eq(0, x)))\ + == 3 + assert refine(Piecewise((1, Eq(x, 0)), (3, True)), (Eq(y, 0)))\ + == Piecewise((1, Eq(x, 0)), (3, True)) + assert refine(Piecewise((1, Ne(x, 0)), (3, True)), (Ne(x, 0)))\ + == 1 + assert refine(Piecewise((1, Ne(x, 0)), (3, True)), ~(Ne(x, 0)))\ + == 3 + assert refine(Piecewise((1, Ne(x, 0)), (3, True)), (Ne(y, 0)))\ + == Piecewise((1, Ne(x, 0)), (3, True)) + + +def test_atan2(): + assert refine(atan2(y, x), Q.real(y) & Q.positive(x)) == atan(y/x) + assert refine(atan2(y, x), Q.negative(y) & Q.positive(x)) == atan(y/x) + assert refine(atan2(y, x), Q.negative(y) & Q.negative(x)) == atan(y/x) - pi + assert refine(atan2(y, x), Q.positive(y) & Q.negative(x)) == atan(y/x) + pi + assert refine(atan2(y, x), Q.zero(y) & Q.negative(x)) == pi + assert refine(atan2(y, x), Q.positive(y) & Q.zero(x)) == pi/2 + assert refine(atan2(y, x), Q.negative(y) & Q.zero(x)) == -pi/2 + assert refine(atan2(y, x), Q.zero(y) & Q.zero(x)) is nan + + +def test_re(): + assert refine(re(x), Q.real(x)) == x + assert refine(re(x), Q.imaginary(x)) is S.Zero + assert refine(re(x+y), Q.real(x) & Q.real(y)) == x + y + assert refine(re(x+y), Q.real(x) & Q.imaginary(y)) == x + assert refine(re(x*y), Q.real(x) & Q.real(y)) == x * y + assert refine(re(x*y), Q.real(x) & Q.imaginary(y)) == 0 + assert refine(re(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) == x * y * z + + +def test_im(): + assert refine(im(x), Q.imaginary(x)) == -I*x + assert refine(im(x), Q.real(x)) is S.Zero + assert refine(im(x+y), Q.imaginary(x) & Q.imaginary(y)) == -I*x - I*y + assert refine(im(x+y), Q.real(x) & Q.imaginary(y)) == -I*y + assert refine(im(x*y), Q.imaginary(x) & Q.real(y)) == -I*x*y + assert refine(im(x*y), Q.imaginary(x) & Q.imaginary(y)) == 0 + assert refine(im(1/x), Q.imaginary(x)) == -I/x + assert refine(im(x*y*z), Q.imaginary(x) & Q.imaginary(y) + & Q.imaginary(z)) == -I*x*y*z + + +def test_complex(): + assert refine(re(1/(x + I*y)), Q.real(x) & Q.real(y)) == \ + x/(x**2 + y**2) + assert refine(im(1/(x + I*y)), Q.real(x) & Q.real(y)) == \ + -y/(x**2 + y**2) + assert refine(re((w + I*x) * (y + I*z)), Q.real(w) & Q.real(x) & Q.real(y) + & Q.real(z)) == w*y - x*z + assert refine(im((w + I*x) * (y + I*z)), Q.real(w) & Q.real(x) & Q.real(y) + & Q.real(z)) == w*z + x*y + + +def test_sign(): + x = Symbol('x', real = True) + assert refine(sign(x), Q.positive(x)) == 1 + assert refine(sign(x), Q.negative(x)) == -1 + assert refine(sign(x), Q.zero(x)) == 0 + assert refine(sign(x), True) == sign(x) + assert refine(sign(Abs(x)), Q.nonzero(x)) == 1 + + x = Symbol('x', imaginary=True) + assert refine(sign(x), Q.positive(im(x))) == S.ImaginaryUnit + assert refine(sign(x), Q.negative(im(x))) == -S.ImaginaryUnit + assert refine(sign(x), True) == sign(x) + + x = Symbol('x', complex=True) + assert refine(sign(x), Q.zero(x)) == 0 + +def test_arg(): + x = Symbol('x', complex = True) + assert refine(arg(x), Q.positive(x)) == 0 + assert refine(arg(x), Q.negative(x)) == pi + +def test_func_args(): + class MyClass(Expr): + # A class with nontrivial .func + + def __init__(self, *args): + self.my_member = "" + + @property + def func(self): + def my_func(*args): + obj = MyClass(*args) + obj.my_member = self.my_member + return obj + return my_func + + x = MyClass() + x.my_member = "A very important value" + assert x.my_member == refine(x).my_member + +def test_issue_refine_9384(): + assert refine(Piecewise((1, x < 0), (0, True)), Q.positive(x)) == 0 + assert refine(Piecewise((1, x < 0), (0, True)), Q.negative(x)) == 1 + assert refine(Piecewise((1, x > 0), (0, True)), Q.positive(x)) == 1 + assert refine(Piecewise((1, x > 0), (0, True)), Q.negative(x)) == 0 + + +def test_eval_refine(): + class MockExpr(Expr): + def _eval_refine(self, assumptions): + return True + + mock_obj = MockExpr() + assert refine(mock_obj) + +def test_refine_issue_12724(): + expr1 = refine(Abs(x * y), Q.positive(x)) + expr2 = refine(Abs(x * y * z), Q.positive(x)) + assert expr1 == x * Abs(y) + assert expr2 == x * Abs(y * z) + y1 = Symbol('y1', real = True) + expr3 = refine(Abs(x * y1**2 * z), Q.positive(x)) + assert expr3 == x * y1**2 * Abs(z) + + +def test_matrixelement(): + x = MatrixSymbol('x', 3, 3) + i = Symbol('i', positive = True) + j = Symbol('j', positive = True) + assert refine(x[0, 1], Q.symmetric(x)) == x[0, 1] + assert refine(x[1, 0], Q.symmetric(x)) == x[0, 1] + assert refine(x[i, j], Q.symmetric(x)) == x[j, i] + assert refine(x[j, i], Q.symmetric(x)) == x[j, i] diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_rel_queries.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_rel_queries.py new file mode 100644 index 0000000000000000000000000000000000000000..6f7d50b7f9bb5674d699cef0358f2366a0bd0f48 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_rel_queries.py @@ -0,0 +1,172 @@ +from sympy.assumptions.lra_satask import lra_satask +from sympy.logic.algorithms.lra_theory import UnhandledInput +from sympy.assumptions.ask import Q, ask + +from sympy.core import symbols, Symbol +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.core.numbers import I + +from sympy.testing.pytest import raises, XFAIL +x, y, z = symbols("x y z", real=True) + +def test_lra_satask(): + im = Symbol('im', imaginary=True) + + # test preprocessing of unequalities is working correctly + assert lra_satask(Q.eq(x, 1), ~Q.ne(x, 0)) is False + assert lra_satask(Q.eq(x, 0), ~Q.ne(x, 0)) is True + assert lra_satask(~Q.ne(x, 0), Q.eq(x, 0)) is True + assert lra_satask(~Q.eq(x, 0), Q.eq(x, 0)) is False + assert lra_satask(Q.ne(x, 0), Q.eq(x, 0)) is False + + # basic tests + assert lra_satask(Q.ne(x, x)) is False + assert lra_satask(Q.eq(x, x)) is True + assert lra_satask(Q.gt(x, 0), Q.gt(x, 1)) is True + + # check that True/False are handled + assert lra_satask(Q.gt(x, 0), True) is None + assert raises(ValueError, lambda: lra_satask(Q.gt(x, 0), False)) + + # check imaginary numbers are correctly handled + # (im * I).is_real returns True so this is an edge case + raises(UnhandledInput, lambda: lra_satask(Q.gt(im * I, 0), Q.gt(im * I, 0))) + + # check matrix inputs + X = MatrixSymbol("X", 2, 2) + raises(UnhandledInput, lambda: lra_satask(Q.lt(X, 2) & Q.gt(X, 3))) + + +def test_old_assumptions(): + # test unhandled old assumptions + w = symbols("w") + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", rational=False, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", odd=True, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", even=True, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", prime=True, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", composite=True, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", integer=True, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + w = symbols("w", integer=False, real=True) + raises(UnhandledInput, lambda: lra_satask(Q.lt(w, 2) & Q.gt(w, 3))) + + # test handled + w = symbols("w", positive=True, real=True) + assert lra_satask(Q.le(w, 0)) is False + assert lra_satask(Q.gt(w, 0)) is True + w = symbols("w", negative=True, real=True) + assert lra_satask(Q.lt(w, 0)) is True + assert lra_satask(Q.ge(w, 0)) is False + w = symbols("w", zero=True, real=True) + assert lra_satask(Q.eq(w, 0)) is True + assert lra_satask(Q.ne(w, 0)) is False + w = symbols("w", nonzero=True, real=True) + assert lra_satask(Q.ne(w, 0)) is True + assert lra_satask(Q.eq(w, 1)) is None + w = symbols("w", nonpositive=True, real=True) + assert lra_satask(Q.le(w, 0)) is True + assert lra_satask(Q.gt(w, 0)) is False + w = symbols("w", nonnegative=True, real=True) + assert lra_satask(Q.ge(w, 0)) is True + assert lra_satask(Q.lt(w, 0)) is False + + +def test_rel_queries(): + assert ask(Q.lt(x, 2) & Q.gt(x, 3)) is False + assert ask(Q.positive(x - z), (x > y) & (y > z)) is True + assert ask(x + y > 2, (x < 0) & (y <0)) is False + assert ask(x > z, (x > y) & (y > z)) is True + + +def test_unhandled_queries(): + X = MatrixSymbol("X", 2, 2) + assert ask(Q.lt(X, 2) & Q.gt(X, 3)) is None + + +def test_all_pred(): + # test usable pred + assert lra_satask(Q.extended_positive(x), (x > 2)) is True + assert lra_satask(Q.positive_infinite(x)) is False + assert lra_satask(Q.negative_infinite(x)) is False + + # test disallowed pred + raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.prime(x))) + raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.composite(x))) + raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.odd(x))) + raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.even(x))) + raises(UnhandledInput, lambda: lra_satask((x > 0), (x > 2) & Q.integer(x))) + + +def test_number_line_properties(): + # From: + # https://en.wikipedia.org/wiki/Inequality_(mathematics)#Properties_on_the_number_line + + a, b, c = symbols("a b c", real=True) + + # Transitivity + # If a <= b and b <= c, then a <= c. + assert ask(a <= c, (a <= b) & (b <= c)) is True + # If a <= b and b < c, then a < c. + assert ask(a < c, (a <= b) & (b < c)) is True + # If a < b and b <= c, then a < c. + assert ask(a < c, (a < b) & (b <= c)) is True + + # Addition and subtraction + # If a <= b, then a + c <= b + c and a - c <= b - c. + assert ask(a + c <= b + c, a <= b) is True + assert ask(a - c <= b - c, a <= b) is True + + +@XFAIL +def test_failing_number_line_properties(): + # From: + # https://en.wikipedia.org/wiki/Inequality_(mathematics)#Properties_on_the_number_line + + a, b, c = symbols("a b c", real=True) + + # Multiplication and division + # If a <= b and c > 0, then ac <= bc and a/c <= b/c. (True for non-zero c) + assert ask(a*c <= b*c, (a <= b) & (c > 0) & ~ Q.zero(c)) is True + assert ask(a/c <= b/c, (a <= b) & (c > 0) & ~ Q.zero(c)) is True + # If a <= b and c < 0, then ac >= bc and a/c >= b/c. (True for non-zero c) + assert ask(a*c >= b*c, (a <= b) & (c < 0) & ~ Q.zero(c)) is True + assert ask(a/c >= b/c, (a <= b) & (c < 0) & ~ Q.zero(c)) is True + + # Additive inverse + # If a <= b, then -a >= -b. + assert ask(-a >= -b, a <= b) is True + + # Multiplicative inverse + # For a, b that are both negative or both positive: + # If a <= b, then 1/a >= 1/b . + assert ask(1/a >= 1/b, (a <= b) & Q.positive(x) & Q.positive(b)) is True + assert ask(1/a >= 1/b, (a <= b) & Q.negative(x) & Q.negative(b)) is True + + +def test_equality(): + # test symetry and reflexivity + assert ask(Q.eq(x, x)) is True + assert ask(Q.eq(y, x), Q.eq(x, y)) is True + assert ask(Q.eq(y, x), ~Q.eq(z, z) | Q.eq(x, y)) is True + + # test transitivity + assert ask(Q.eq(x,z), Q.eq(x,y) & Q.eq(y,z)) is True + + +@XFAIL +def test_equality_failing(): + # Note that implementing the substitution property of equality + # most likely requires a redesign of the new assumptions. + # See issue #25485 for why this is the case and general ideas + # about how things could be redesigned. + + # test substitution property + assert ask(Q.prime(x), Q.eq(x, y) & Q.prime(y)) is True + assert ask(Q.real(x), Q.eq(x, y) & Q.real(y)) is True + assert ask(Q.imaginary(x), Q.eq(x, y) & Q.imaginary(y)) is True diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_satask.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_satask.py new file mode 100644 index 0000000000000000000000000000000000000000..5831b69e3e6bf2b1a906d1140967510c2ea8b630 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_satask.py @@ -0,0 +1,378 @@ +from sympy.assumptions.ask import Q +from sympy.assumptions.assume import assuming +from sympy.core.numbers import (I, pi) +from sympy.core.relational import (Eq, Gt) +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.complexes import Abs +from sympy.logic.boolalg import Implies +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.assumptions.cnf import CNF, Literal +from sympy.assumptions.satask import (satask, extract_predargs, + get_relevant_clsfacts) + +from sympy.testing.pytest import raises, XFAIL + + +x, y, z = symbols('x y z') + + +def test_satask(): + # No relevant facts + assert satask(Q.real(x), Q.real(x)) is True + assert satask(Q.real(x), ~Q.real(x)) is False + assert satask(Q.real(x)) is None + + assert satask(Q.real(x), Q.positive(x)) is True + assert satask(Q.positive(x), Q.real(x)) is None + assert satask(Q.real(x), ~Q.positive(x)) is None + assert satask(Q.positive(x), ~Q.real(x)) is False + + raises(ValueError, lambda: satask(Q.real(x), Q.real(x) & ~Q.real(x))) + + with assuming(Q.positive(x)): + assert satask(Q.real(x)) is True + assert satask(~Q.positive(x)) is False + raises(ValueError, lambda: satask(Q.real(x), ~Q.positive(x))) + + assert satask(Q.zero(x), Q.nonzero(x)) is False + assert satask(Q.positive(x), Q.zero(x)) is False + assert satask(Q.real(x), Q.zero(x)) is True + assert satask(Q.zero(x), Q.zero(x*y)) is None + assert satask(Q.zero(x*y), Q.zero(x)) + + +def test_zero(): + """ + Everything in this test doesn't work with the ask handlers, and most + things would be very difficult or impossible to make work under that + model. + + """ + assert satask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True + assert satask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) is True + + assert satask(Implies(Q.zero(x), Q.zero(x*y))) is True + + # This one in particular requires computing the fixed-point of the + # relevant facts, because going from Q.nonzero(x*y) -> ~Q.zero(x*y) and + # Q.zero(x*y) -> Equivalent(Q.zero(x*y), Q.zero(x) | Q.zero(y)) takes two + # steps. + assert satask(Q.zero(x) | Q.zero(y), Q.nonzero(x*y)) is False + + assert satask(Q.zero(x), Q.zero(x**2)) is True + + +def test_zero_positive(): + assert satask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False + assert satask(Q.positive(x) & Q.positive(y), Q.zero(x + y)) is False + assert satask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True + assert satask(Q.positive(x) & Q.positive(y), Q.nonzero(x + y)) is None + + # This one requires several levels of forward chaining + assert satask(Q.zero(x*(x + y)), Q.positive(x) & Q.positive(y)) is False + + assert satask(Q.positive(pi*x*y + 1), Q.positive(x) & Q.positive(y)) is True + assert satask(Q.positive(pi*x*y - 5), Q.positive(x) & Q.positive(y)) is None + + +def test_zero_pow(): + assert satask(Q.zero(x**y), Q.zero(x) & Q.positive(y)) is True + assert satask(Q.zero(x**y), Q.nonzero(x) & Q.zero(y)) is False + + assert satask(Q.zero(x), Q.zero(x**y)) is True + + assert satask(Q.zero(x**y), Q.zero(x)) is None + + +@XFAIL +# Requires correct Q.square calculation first +def test_invertible(): + A = MatrixSymbol('A', 5, 5) + B = MatrixSymbol('B', 5, 5) + assert satask(Q.invertible(A*B), Q.invertible(A) & Q.invertible(B)) is True + assert satask(Q.invertible(A), Q.invertible(A*B)) is True + assert satask(Q.invertible(A) & Q.invertible(B), Q.invertible(A*B)) is True + + +def test_prime(): + assert satask(Q.prime(5)) is True + assert satask(Q.prime(6)) is False + assert satask(Q.prime(-5)) is False + + assert satask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None + assert satask(Q.prime(x*y), Q.prime(x) & Q.prime(y)) is False + + +def test_old_assump(): + assert satask(Q.positive(1)) is True + assert satask(Q.positive(-1)) is False + assert satask(Q.positive(0)) is False + assert satask(Q.positive(I)) is False + assert satask(Q.positive(pi)) is True + + assert satask(Q.negative(1)) is False + assert satask(Q.negative(-1)) is True + assert satask(Q.negative(0)) is False + assert satask(Q.negative(I)) is False + assert satask(Q.negative(pi)) is False + + assert satask(Q.zero(1)) is False + assert satask(Q.zero(-1)) is False + assert satask(Q.zero(0)) is True + assert satask(Q.zero(I)) is False + assert satask(Q.zero(pi)) is False + + assert satask(Q.nonzero(1)) is True + assert satask(Q.nonzero(-1)) is True + assert satask(Q.nonzero(0)) is False + assert satask(Q.nonzero(I)) is False + assert satask(Q.nonzero(pi)) is True + + assert satask(Q.nonpositive(1)) is False + assert satask(Q.nonpositive(-1)) is True + assert satask(Q.nonpositive(0)) is True + assert satask(Q.nonpositive(I)) is False + assert satask(Q.nonpositive(pi)) is False + + assert satask(Q.nonnegative(1)) is True + assert satask(Q.nonnegative(-1)) is False + assert satask(Q.nonnegative(0)) is True + assert satask(Q.nonnegative(I)) is False + assert satask(Q.nonnegative(pi)) is True + + +def test_rational_irrational(): + assert satask(Q.irrational(2)) is False + assert satask(Q.rational(2)) is True + assert satask(Q.irrational(pi)) is True + assert satask(Q.rational(pi)) is False + assert satask(Q.irrational(I)) is False + assert satask(Q.rational(I)) is False + + assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.irrational(y) & + Q.rational(z)) is None + assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.rational(y) & + Q.rational(z)) is True + assert satask(Q.irrational(pi*x*y), Q.rational(x) & Q.rational(y)) is True + + assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.irrational(y) & + Q.rational(z)) is None + assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.rational(y) & + Q.rational(z)) is True + assert satask(Q.irrational(pi + x + y), Q.rational(x) & Q.rational(y)) is True + + assert satask(Q.irrational(x*y*z), Q.rational(x) & Q.rational(y) & + Q.rational(z)) is False + assert satask(Q.rational(x*y*z), Q.rational(x) & Q.rational(y) & + Q.rational(z)) is True + + assert satask(Q.irrational(x + y + z), Q.rational(x) & Q.rational(y) & + Q.rational(z)) is False + assert satask(Q.rational(x + y + z), Q.rational(x) & Q.rational(y) & + Q.rational(z)) is True + + +def test_even_satask(): + assert satask(Q.even(2)) is True + assert satask(Q.even(3)) is False + + assert satask(Q.even(x*y), Q.even(x) & Q.odd(y)) is True + assert satask(Q.even(x*y), Q.even(x) & Q.integer(y)) is True + assert satask(Q.even(x*y), Q.even(x) & Q.even(y)) is True + assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False + assert satask(Q.even(x*y), Q.even(x)) is None + assert satask(Q.even(x*y), Q.odd(x) & Q.integer(y)) is None + assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False + + assert satask(Q.even(abs(x)), Q.even(x)) is True + assert satask(Q.even(abs(x)), Q.odd(x)) is False + assert satask(Q.even(x), Q.even(abs(x))) is None # x could be complex + + +def test_odd_satask(): + assert satask(Q.odd(2)) is False + assert satask(Q.odd(3)) is True + + assert satask(Q.odd(x*y), Q.even(x) & Q.odd(y)) is False + assert satask(Q.odd(x*y), Q.even(x) & Q.integer(y)) is False + assert satask(Q.odd(x*y), Q.even(x) & Q.even(y)) is False + assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True + assert satask(Q.odd(x*y), Q.even(x)) is None + assert satask(Q.odd(x*y), Q.odd(x) & Q.integer(y)) is None + assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True + + assert satask(Q.odd(abs(x)), Q.even(x)) is False + assert satask(Q.odd(abs(x)), Q.odd(x)) is True + assert satask(Q.odd(x), Q.odd(abs(x))) is None # x could be complex + + +def test_integer(): + assert satask(Q.integer(1)) is True + assert satask(Q.integer(S.Half)) is False + + assert satask(Q.integer(x + y), Q.integer(x) & Q.integer(y)) is True + assert satask(Q.integer(x + y), Q.integer(x)) is None + + assert satask(Q.integer(x + y), Q.integer(x) & ~Q.integer(y)) is False + assert satask(Q.integer(x + y + z), Q.integer(x) & Q.integer(y) & + ~Q.integer(z)) is False + assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y) & + ~Q.integer(z)) is None + assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y)) is None + assert satask(Q.integer(x + y), Q.integer(x) & Q.irrational(y)) is False + + assert satask(Q.integer(x*y), Q.integer(x) & Q.integer(y)) is True + assert satask(Q.integer(x*y), Q.integer(x)) is None + + assert satask(Q.integer(x*y), Q.integer(x) & ~Q.integer(y)) is None + assert satask(Q.integer(x*y), Q.integer(x) & ~Q.rational(y)) is False + assert satask(Q.integer(x*y*z), Q.integer(x) & Q.integer(y) & + ~Q.rational(z)) is False + assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y) & + ~Q.rational(z)) is None + assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y)) is None + assert satask(Q.integer(x*y), Q.integer(x) & Q.irrational(y)) is False + + +def test_abs(): + assert satask(Q.nonnegative(abs(x))) is True + assert satask(Q.positive(abs(x)), ~Q.zero(x)) is True + assert satask(Q.zero(x), ~Q.zero(abs(x))) is False + assert satask(Q.zero(x), Q.zero(abs(x))) is True + assert satask(Q.nonzero(x), ~Q.zero(abs(x))) is None # x could be complex + assert satask(Q.zero(abs(x)), Q.zero(x)) is True + + +def test_imaginary(): + assert satask(Q.imaginary(2*I)) is True + assert satask(Q.imaginary(x*y), Q.imaginary(x)) is None + assert satask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True + assert satask(Q.imaginary(x), Q.real(x)) is False + assert satask(Q.imaginary(1)) is False + assert satask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False + assert satask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False + + +def test_real(): + assert satask(Q.real(x*y), Q.real(x) & Q.real(y)) is True + assert satask(Q.real(x + y), Q.real(x) & Q.real(y)) is True + assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) is True + assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y)) is None + assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.imaginary(z)) is False + assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True + assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y)) is None + + +def test_pos_neg(): + assert satask(~Q.positive(x), Q.negative(x)) is True + assert satask(~Q.negative(x), Q.positive(x)) is True + assert satask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True + assert satask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True + assert satask(Q.positive(x + y), Q.negative(x) & Q.negative(y)) is False + assert satask(Q.negative(x + y), Q.positive(x) & Q.positive(y)) is False + + +def test_pow_pos_neg(): + assert satask(Q.nonnegative(x**2), Q.positive(x)) is True + assert satask(Q.nonpositive(x**2), Q.positive(x)) is False + assert satask(Q.positive(x**2), Q.positive(x)) is True + assert satask(Q.negative(x**2), Q.positive(x)) is False + assert satask(Q.real(x**2), Q.positive(x)) is True + + assert satask(Q.nonnegative(x**2), Q.negative(x)) is True + assert satask(Q.nonpositive(x**2), Q.negative(x)) is False + assert satask(Q.positive(x**2), Q.negative(x)) is True + assert satask(Q.negative(x**2), Q.negative(x)) is False + assert satask(Q.real(x**2), Q.negative(x)) is True + + assert satask(Q.nonnegative(x**2), Q.nonnegative(x)) is True + assert satask(Q.nonpositive(x**2), Q.nonnegative(x)) is None + assert satask(Q.positive(x**2), Q.nonnegative(x)) is None + assert satask(Q.negative(x**2), Q.nonnegative(x)) is False + assert satask(Q.real(x**2), Q.nonnegative(x)) is True + + assert satask(Q.nonnegative(x**2), Q.nonpositive(x)) is True + assert satask(Q.nonpositive(x**2), Q.nonpositive(x)) is None + assert satask(Q.positive(x**2), Q.nonpositive(x)) is None + assert satask(Q.negative(x**2), Q.nonpositive(x)) is False + assert satask(Q.real(x**2), Q.nonpositive(x)) is True + + assert satask(Q.nonnegative(x**3), Q.positive(x)) is True + assert satask(Q.nonpositive(x**3), Q.positive(x)) is False + assert satask(Q.positive(x**3), Q.positive(x)) is True + assert satask(Q.negative(x**3), Q.positive(x)) is False + assert satask(Q.real(x**3), Q.positive(x)) is True + + assert satask(Q.nonnegative(x**3), Q.negative(x)) is False + assert satask(Q.nonpositive(x**3), Q.negative(x)) is True + assert satask(Q.positive(x**3), Q.negative(x)) is False + assert satask(Q.negative(x**3), Q.negative(x)) is True + assert satask(Q.real(x**3), Q.negative(x)) is True + + assert satask(Q.nonnegative(x**3), Q.nonnegative(x)) is True + assert satask(Q.nonpositive(x**3), Q.nonnegative(x)) is None + assert satask(Q.positive(x**3), Q.nonnegative(x)) is None + assert satask(Q.negative(x**3), Q.nonnegative(x)) is False + assert satask(Q.real(x**3), Q.nonnegative(x)) is True + + assert satask(Q.nonnegative(x**3), Q.nonpositive(x)) is None + assert satask(Q.nonpositive(x**3), Q.nonpositive(x)) is True + assert satask(Q.positive(x**3), Q.nonpositive(x)) is False + assert satask(Q.negative(x**3), Q.nonpositive(x)) is None + assert satask(Q.real(x**3), Q.nonpositive(x)) is True + + # If x is zero, x**negative is not real. + assert satask(Q.nonnegative(x**-2), Q.nonpositive(x)) is None + assert satask(Q.nonpositive(x**-2), Q.nonpositive(x)) is None + assert satask(Q.positive(x**-2), Q.nonpositive(x)) is None + assert satask(Q.negative(x**-2), Q.nonpositive(x)) is None + assert satask(Q.real(x**-2), Q.nonpositive(x)) is None + + # We could deduce things for negative powers if x is nonzero, but it + # isn't implemented yet. + + +def test_prime_composite(): + assert satask(Q.prime(x), Q.composite(x)) is False + assert satask(Q.composite(x), Q.prime(x)) is False + assert satask(Q.composite(x), ~Q.prime(x)) is None + assert satask(Q.prime(x), ~Q.composite(x)) is None + # since 1 is neither prime nor composite the following should hold + assert satask(Q.prime(x), Q.integer(x) & Q.positive(x) & ~Q.composite(x)) is None + assert satask(Q.prime(2)) is True + assert satask(Q.prime(4)) is False + assert satask(Q.prime(1)) is False + assert satask(Q.composite(1)) is False + + +def test_extract_predargs(): + props = CNF.from_prop(Q.zero(Abs(x*y)) & Q.zero(x*y)) + assump = CNF.from_prop(Q.zero(x)) + context = CNF.from_prop(Q.zero(y)) + assert extract_predargs(props) == {Abs(x*y), x*y} + assert extract_predargs(props, assump) == {Abs(x*y), x*y, x} + assert extract_predargs(props, assump, context) == {Abs(x*y), x*y, x, y} + + props = CNF.from_prop(Eq(x, y)) + assump = CNF.from_prop(Gt(y, z)) + assert extract_predargs(props, assump) == {x, y, z} + + +def test_get_relevant_clsfacts(): + exprs = {Abs(x*y)} + exprs, facts = get_relevant_clsfacts(exprs) + assert exprs == {x*y} + assert facts.clauses == \ + {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), + frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}), + frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}), + frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}), + frozenset({Literal(Q.even(Abs(x*y)), False), + Literal(Q.odd(Abs(x*y)), False), + Literal(Q.odd(x*y), True)}), + frozenset({Literal(Q.even(Abs(x*y)), False), + Literal(Q.even(x*y), True), + Literal(Q.odd(Abs(x*y)), False)}), + frozenset({Literal(Q.positive(Abs(x*y)), False), + Literal(Q.zero(Abs(x*y)), False)})} diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_sathandlers.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_sathandlers.py new file mode 100644 index 0000000000000000000000000000000000000000..9d568ad8efe6ba7cf7f5eb03879ad6764c16e729 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_sathandlers.py @@ -0,0 +1,50 @@ +from sympy.assumptions.ask import Q +from sympy.core.basic import Basic +from sympy.core.expr import Expr +from sympy.core.mul import Mul +from sympy.core.symbol import symbols +from sympy.logic.boolalg import (And, Or) + +from sympy.assumptions.sathandlers import (ClassFactRegistry, allargs, + anyarg, exactlyonearg,) + +x, y, z = symbols('x y z') + + +def test_class_handler_registry(): + my_handler_registry = ClassFactRegistry() + + # The predicate doesn't matter here, so just pass + @my_handler_registry.register(Mul) + def fact1(expr): + pass + @my_handler_registry.multiregister(Expr) + def fact2(expr): + pass + + assert my_handler_registry[Basic] == (frozenset(), frozenset()) + assert my_handler_registry[Expr] == (frozenset(), frozenset({fact2})) + assert my_handler_registry[Mul] == (frozenset({fact1}), frozenset({fact2})) + + +def test_allargs(): + assert allargs(x, Q.zero(x), x*y) == And(Q.zero(x), Q.zero(y)) + assert allargs(x, Q.positive(x) | Q.negative(x), x*y) == And(Q.positive(x) | Q.negative(x), Q.positive(y) | Q.negative(y)) + + +def test_anyarg(): + assert anyarg(x, Q.zero(x), x*y) == Or(Q.zero(x), Q.zero(y)) + assert anyarg(x, Q.positive(x) & Q.negative(x), x*y) == \ + Or(Q.positive(x) & Q.negative(x), Q.positive(y) & Q.negative(y)) + + +def test_exactlyonearg(): + assert exactlyonearg(x, Q.zero(x), x*y) == \ + Or(Q.zero(x) & ~Q.zero(y), Q.zero(y) & ~Q.zero(x)) + assert exactlyonearg(x, Q.zero(x), x*y*z) == \ + Or(Q.zero(x) & ~Q.zero(y) & ~Q.zero(z), Q.zero(y) + & ~Q.zero(x) & ~Q.zero(z), Q.zero(z) & ~Q.zero(x) & ~Q.zero(y)) + assert exactlyonearg(x, Q.positive(x) | Q.negative(x), x*y) == \ + Or((Q.positive(x) | Q.negative(x)) & + ~(Q.positive(y) | Q.negative(y)), (Q.positive(y) | Q.negative(y)) & + ~(Q.positive(x) | Q.negative(x))) diff --git a/lib/python3.11/site-packages/sympy/assumptions/tests/test_wrapper.py b/lib/python3.11/site-packages/sympy/assumptions/tests/test_wrapper.py new file mode 100644 index 0000000000000000000000000000000000000000..af9afd5d51fb1341e0b08149dc842b78a39c329b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/tests/test_wrapper.py @@ -0,0 +1,39 @@ +from sympy.assumptions.ask import Q +from sympy.assumptions.wrapper import (AssumptionsWrapper, is_infinite, + is_extended_real) +from sympy.core.symbol import Symbol +from sympy.core.assumptions import _assume_defined + + +def test_all_predicates(): + for fact in _assume_defined: + method_name = f'_eval_is_{fact}' + assert hasattr(AssumptionsWrapper, method_name) + + +def test_AssumptionsWrapper(): + x = Symbol('x', positive=True) + y = Symbol('y') + assert AssumptionsWrapper(x).is_positive + assert AssumptionsWrapper(y).is_positive is None + assert AssumptionsWrapper(y, Q.positive(y)).is_positive + + +def test_is_infinite(): + x = Symbol('x', infinite=True) + y = Symbol('y', infinite=False) + z = Symbol('z') + assert is_infinite(x) + assert not is_infinite(y) + assert is_infinite(z) is None + assert is_infinite(z, Q.infinite(z)) + + +def test_is_extended_real(): + x = Symbol('x', extended_real=True) + y = Symbol('y', extended_real=False) + z = Symbol('z') + assert is_extended_real(x) + assert not is_extended_real(y) + assert is_extended_real(z) is None + assert is_extended_real(z, Q.extended_real(z)) diff --git a/lib/python3.11/site-packages/sympy/assumptions/wrapper.py b/lib/python3.11/site-packages/sympy/assumptions/wrapper.py new file mode 100644 index 0000000000000000000000000000000000000000..cb06e9de770ed41a2b3d6fe63381ad1cb59acacc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/assumptions/wrapper.py @@ -0,0 +1,164 @@ +""" +Functions and wrapper object to call assumption property and predicate +query with same syntax. + +In SymPy, there are two assumption systems. Old assumption system is +defined in sympy/core/assumptions, and it can be accessed by attribute +such as ``x.is_even``. New assumption system is defined in +sympy/assumptions, and it can be accessed by predicates such as +``Q.even(x)``. + +Old assumption is fast, while new assumptions can freely take local facts. +In general, old assumption is used in evaluation method and new assumption +is used in refinement method. + +In most cases, both evaluation and refinement follow the same process, and +the only difference is which assumption system is used. This module provides +``is_[...]()`` functions and ``AssumptionsWrapper()`` class which allows +using two systems with same syntax so that parallel code implementation can be +avoided. + +Examples +======== + +For multiple use, use ``AssumptionsWrapper()``. + +>>> from sympy import Q, Symbol +>>> from sympy.assumptions.wrapper import AssumptionsWrapper +>>> x = Symbol('x') +>>> _x = AssumptionsWrapper(x, Q.even(x)) +>>> _x.is_integer +True +>>> _x.is_odd +False + +For single use, use ``is_[...]()`` functions. + +>>> from sympy.assumptions.wrapper import is_infinite +>>> a = Symbol('a') +>>> print(is_infinite(a)) +None +>>> is_infinite(a, Q.finite(a)) +False + +""" + +from sympy.assumptions import ask, Q +from sympy.core.basic import Basic +from sympy.core.sympify import _sympify + + +def make_eval_method(fact): + def getit(self): + pred = getattr(Q, fact) + ret = ask(pred(self.expr), self.assumptions) + return ret + return getit + + +# we subclass Basic to use the fact deduction and caching +class AssumptionsWrapper(Basic): + """ + Wrapper over ``Basic`` instances to call predicate query by + ``.is_[...]`` property + + Parameters + ========== + + expr : Basic + + assumptions : Boolean, optional + + Examples + ======== + + >>> from sympy import Q, Symbol + >>> from sympy.assumptions.wrapper import AssumptionsWrapper + >>> x = Symbol('x', even=True) + >>> AssumptionsWrapper(x).is_integer + True + >>> y = Symbol('y') + >>> AssumptionsWrapper(y, Q.even(y)).is_integer + True + + With ``AssumptionsWrapper``, both evaluation and refinement can be supported + by single implementation. + + >>> from sympy import Function + >>> class MyAbs(Function): + ... @classmethod + ... def eval(cls, x, assumptions=True): + ... _x = AssumptionsWrapper(x, assumptions) + ... if _x.is_nonnegative: + ... return x + ... if _x.is_negative: + ... return -x + ... def _eval_refine(self, assumptions): + ... return MyAbs.eval(self.args[0], assumptions) + >>> MyAbs(x) + MyAbs(x) + >>> MyAbs(x).refine(Q.positive(x)) + x + >>> MyAbs(Symbol('y', negative=True)) + -y + + """ + def __new__(cls, expr, assumptions=None): + if assumptions is None: + return expr + obj = super().__new__(cls, expr, _sympify(assumptions)) + obj.expr = expr + obj.assumptions = assumptions + return obj + + _eval_is_algebraic = make_eval_method("algebraic") + _eval_is_antihermitian = make_eval_method("antihermitian") + _eval_is_commutative = make_eval_method("commutative") + _eval_is_complex = make_eval_method("complex") + _eval_is_composite = make_eval_method("composite") + _eval_is_even = make_eval_method("even") + _eval_is_extended_negative = make_eval_method("extended_negative") + _eval_is_extended_nonnegative = make_eval_method("extended_nonnegative") + _eval_is_extended_nonpositive = make_eval_method("extended_nonpositive") + _eval_is_extended_nonzero = make_eval_method("extended_nonzero") + _eval_is_extended_positive = make_eval_method("extended_positive") + _eval_is_extended_real = make_eval_method("extended_real") + _eval_is_finite = make_eval_method("finite") + _eval_is_hermitian = make_eval_method("hermitian") + _eval_is_imaginary = make_eval_method("imaginary") + _eval_is_infinite = make_eval_method("infinite") + _eval_is_integer = make_eval_method("integer") + _eval_is_irrational = make_eval_method("irrational") + _eval_is_negative = make_eval_method("negative") + _eval_is_noninteger = make_eval_method("noninteger") + _eval_is_nonnegative = make_eval_method("nonnegative") + _eval_is_nonpositive = make_eval_method("nonpositive") + _eval_is_nonzero = make_eval_method("nonzero") + _eval_is_odd = make_eval_method("odd") + _eval_is_polar = make_eval_method("polar") + _eval_is_positive = make_eval_method("positive") + _eval_is_prime = make_eval_method("prime") + _eval_is_rational = make_eval_method("rational") + _eval_is_real = make_eval_method("real") + _eval_is_transcendental = make_eval_method("transcendental") + _eval_is_zero = make_eval_method("zero") + + +# one shot functions which are faster than AssumptionsWrapper + +def is_infinite(obj, assumptions=None): + if assumptions is None: + return obj.is_infinite + return ask(Q.infinite(obj), assumptions) + + +def is_extended_real(obj, assumptions=None): + if assumptions is None: + return obj.is_extended_real + return ask(Q.extended_real(obj), assumptions) + + +def is_extended_nonnegative(obj, assumptions=None): + if assumptions is None: + return obj.is_extended_nonnegative + return ask(Q.extended_nonnegative(obj), assumptions) diff --git a/lib/python3.11/site-packages/sympy/benchmarks/__init__.py b/lib/python3.11/site-packages/sympy/benchmarks/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/benchmarks/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/benchmarks/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 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_discrete_log_trial_mul, _discrete_log_shanks_steps, + _discrete_log_pollard_rho, _discrete_log_pohlig_hellman) + + +# Cyclic group (Z/pZ)* with p prime, order p - 1 and generator g +data_set_1 = [ + # p, p - 1, g + [191, 190, 19], + [46639, 46638, 6], + [14789363, 14789362, 2], + [4254225211, 4254225210, 2], + [432751500361, 432751500360, 7], + [158505390797053, 158505390797052, 2], + [6575202655312007, 6575202655312006, 5], + [8430573471995353769, 8430573471995353768, 3], + [3938471339744997827267, 3938471339744997827266, 2], + [875260951364705563393093, 875260951364705563393092, 5], + ] + + +# Cyclic sub-groups of (Z/nZ)* with prime order p and generator g +# (n, p are primes and n = 2 * p + 1) +data_set_2 = [ + # n, p, g + [227, 113, 3], + [2447, 1223, 2], + [24527, 12263, 2], + [245639, 122819, 2], + [2456747, 1228373, 3], + [24567899, 12283949, 3], + [245679023, 122839511, 2], + [2456791307, 1228395653, 3], + [24567913439, 12283956719, 2], + [245679135407, 122839567703, 2], + [2456791354763, 1228395677381, 3], + [24567913550903, 12283956775451, 2], + [245679135509519, 122839567754759, 2], + ] + + +# Cyclic sub-groups of (Z/nZ)* with smooth order o and generator g +data_set_3 = [ + # n, o, g + [2**118, 2**116, 3], + ] + + +def bench_discrete_log(data_set, algo=None): + if algo is None: + f = discrete_log + elif algo == 'trial': + f = _discrete_log_trial_mul + elif algo == 'shanks': + f = _discrete_log_shanks_steps + elif algo == 'rho': + f = _discrete_log_pollard_rho + elif algo == 'ph': + f = _discrete_log_pohlig_hellman + else: + raise ValueError("Argument 'algo' should be one" + " of ('trial', 'shanks', 'rho' or 'ph')") + + for i, data in enumerate(data_set): + for j, (n, p, g) in enumerate(data): + t = time() + l = f(n, pow(g, p - 1, n), g, p) + t = time() - t + print('[%02d-%03d] %15.10f' % (i, j, t)) + assert l == p - 1 + + +if __name__ == '__main__': + algo = sys.argv[1] \ + if len(sys.argv) > 1 else None + data_set = [ + data_set_1, + data_set_2, + data_set_3, + ] + bench_discrete_log(data_set, algo) diff --git a/lib/python3.11/site-packages/sympy/benchmarks/bench_meijerint.py b/lib/python3.11/site-packages/sympy/benchmarks/bench_meijerint.py new file mode 100644 index 0000000000000000000000000000000000000000..d648c3e02463d5a7ee1dcbe3b22af5cc22fef43d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/benchmarks/bench_meijerint.py @@ -0,0 +1,261 @@ +# conceal the implicit import from the code quality tester +from sympy.core.numbers import (oo, pi) +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.bessel import besseli +from sympy.functions.special.gamma_functions import gamma +from sympy.integrals.integrals import integrate +from sympy.integrals.transforms import (mellin_transform, + inverse_fourier_transform, inverse_mellin_transform, + laplace_transform, inverse_laplace_transform, fourier_transform) + +LT = laplace_transform +FT = fourier_transform +MT = mellin_transform +IFT = inverse_fourier_transform +ILT = inverse_laplace_transform +IMT = inverse_mellin_transform + +from sympy.abc import x, y +nu, beta, rho = symbols('nu beta rho') + +apos, bpos, cpos, dpos, posk, p = symbols('a b c d k p', positive=True) +k = Symbol('k', real=True) +negk = Symbol('k', negative=True) + +mu1, mu2 = symbols('mu1 mu2', real=True, nonzero=True, finite=True) +sigma1, sigma2 = symbols('sigma1 sigma2', real=True, nonzero=True, + finite=True, positive=True) +rate = Symbol('lambda', positive=True) + + +def normal(x, mu, sigma): + return 1/sqrt(2*pi*sigma**2)*exp(-(x - mu)**2/2/sigma**2) + + +def exponential(x, rate): + return rate*exp(-rate*x) +alpha, beta = symbols('alpha beta', positive=True) +betadist = x**(alpha - 1)*(1 + x)**(-alpha - beta)*gamma(alpha + beta) \ + /gamma(alpha)/gamma(beta) +kint = Symbol('k', integer=True, positive=True) +chi = 2**(1 - kint/2)*x**(kint - 1)*exp(-x**2/2)/gamma(kint/2) +chisquared = 2**(-k/2)/gamma(k/2)*x**(k/2 - 1)*exp(-x/2) +dagum = apos*p/x*(x/bpos)**(apos*p)/(1 + x**apos/bpos**apos)**(p + 1) +d1, d2 = symbols('d1 d2', positive=True) +f = sqrt(((d1*x)**d1 * d2**d2)/(d1*x + d2)**(d1 + d2))/x \ + /gamma(d1/2)/gamma(d2/2)*gamma((d1 + d2)/2) +nupos, sigmapos = symbols('nu sigma', positive=True) +rice = x/sigmapos**2*exp(-(x**2 + nupos**2)/2/sigmapos**2)*besseli(0, x* + nupos/sigmapos**2) +mu = Symbol('mu', real=True) +laplace = exp(-abs(x - mu)/bpos)/2/bpos + +u = Symbol('u', polar=True) +tpos = Symbol('t', positive=True) + + +def E(expr): + integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1), + (x, 0, oo), (y, -oo, oo), meijerg=True) + integrate(expr*exponential(x, rate)*normal(y, mu1, sigma1), + (y, -oo, oo), (x, 0, oo), meijerg=True) + +bench = [ + 'MT(x**nu*Heaviside(x - 1), x, s)', + 'MT(x**nu*Heaviside(1 - x), x, s)', + 'MT((1-x)**(beta - 1)*Heaviside(1-x), x, s)', + 'MT((x-1)**(beta - 1)*Heaviside(x-1), x, s)', + 'MT((1+x)**(-rho), x, s)', + 'MT(abs(1-x)**(-rho), x, s)', + 'MT((1-x)**(beta-1)*Heaviside(1-x) + a*(x-1)**(beta-1)*Heaviside(x-1), x, s)', + 'MT((x**a-b**a)/(x-b), x, s)', + 'MT((x**a-bpos**a)/(x-bpos), x, s)', + 'MT(exp(-x), x, s)', + 'MT(exp(-1/x), x, s)', + 'MT(log(x)**4*Heaviside(1-x), x, s)', + 'MT(log(x)**3*Heaviside(x-1), x, s)', + 'MT(log(x + 1), x, s)', + 'MT(log(1/x + 1), x, s)', + 'MT(log(abs(1 - x)), x, s)', + 'MT(log(abs(1 - 1/x)), x, s)', + 'MT(log(x)/(x+1), x, s)', + 'MT(log(x)**2/(x+1), x, s)', + 'MT(log(x)/(x+1)**2, x, s)', + 'MT(erf(sqrt(x)), x, s)', + + 'MT(besselj(a, 2*sqrt(x)), x, s)', + 'MT(sin(sqrt(x))*besselj(a, sqrt(x)), x, s)', + 'MT(cos(sqrt(x))*besselj(a, sqrt(x)), x, s)', + 'MT(besselj(a, sqrt(x))**2, x, s)', + 'MT(besselj(a, sqrt(x))*besselj(-a, sqrt(x)), x, s)', + 'MT(besselj(a - 1, sqrt(x))*besselj(a, sqrt(x)), x, s)', + 'MT(besselj(a, sqrt(x))*besselj(b, sqrt(x)), x, s)', + 'MT(besselj(a, sqrt(x))**2 + besselj(-a, sqrt(x))**2, x, s)', + 'MT(bessely(a, 2*sqrt(x)), x, s)', + 'MT(sin(sqrt(x))*bessely(a, sqrt(x)), x, s)', + 'MT(cos(sqrt(x))*bessely(a, sqrt(x)), x, s)', + 'MT(besselj(a, sqrt(x))*bessely(a, sqrt(x)), x, s)', + 'MT(besselj(a, sqrt(x))*bessely(b, sqrt(x)), x, s)', + 'MT(bessely(a, sqrt(x))**2, x, s)', + + 'MT(besselk(a, 2*sqrt(x)), x, s)', + 'MT(besselj(a, 2*sqrt(2*sqrt(x)))*besselk(a, 2*sqrt(2*sqrt(x))), x, s)', + 'MT(besseli(a, sqrt(x))*besselk(a, sqrt(x)), x, s)', + 'MT(besseli(b, sqrt(x))*besselk(a, sqrt(x)), x, s)', + 'MT(exp(-x/2)*besselk(a, x/2), x, s)', + + # later: ILT, IMT + + 'LT((t-apos)**bpos*exp(-cpos*(t-apos))*Heaviside(t-apos), t, s)', + 'LT(t**apos, t, s)', + 'LT(Heaviside(t), t, s)', + 'LT(Heaviside(t - apos), t, s)', + 'LT(1 - exp(-apos*t), t, s)', + 'LT((exp(2*t)-1)*exp(-bpos - t)*Heaviside(t)/2, t, s, noconds=True)', + 'LT(exp(t), t, s)', + 'LT(exp(2*t), t, s)', + 'LT(exp(apos*t), t, s)', + 'LT(log(t/apos), t, s)', + 'LT(erf(t), t, s)', + 'LT(sin(apos*t), t, s)', + 'LT(cos(apos*t), t, s)', + 'LT(exp(-apos*t)*sin(bpos*t), t, s)', + 'LT(exp(-apos*t)*cos(bpos*t), t, s)', + 'LT(besselj(0, t), t, s, noconds=True)', + 'LT(besselj(1, t), t, s, noconds=True)', + + 'FT(Heaviside(1 - abs(2*apos*x)), x, k)', + 'FT(Heaviside(1-abs(apos*x))*(1-abs(apos*x)), x, k)', + 'FT(exp(-apos*x)*Heaviside(x), x, k)', + 'IFT(1/(apos + 2*pi*I*x), x, posk, noconds=False)', + 'IFT(1/(apos + 2*pi*I*x), x, -posk, noconds=False)', + 'IFT(1/(apos + 2*pi*I*x), x, negk)', + 'FT(x*exp(-apos*x)*Heaviside(x), x, k)', + 'FT(exp(-apos*x)*sin(bpos*x)*Heaviside(x), x, k)', + 'FT(exp(-apos*x**2), x, k)', + 'IFT(sqrt(pi/apos)*exp(-(pi*k)**2/apos), k, x)', + 'FT(exp(-apos*abs(x)), x, k)', + + 'integrate(normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)', + 'integrate(x*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)', + 'integrate(x**2*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)', + 'integrate(x**3*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)', + 'integrate(normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(x*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(x*y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate((x+y+1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate((x+y-1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(x**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(y**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),' + ' (x, -oo, oo), (y, -oo, oo), meijerg=True)', + 'integrate(exponential(x, rate), (x, 0, oo), meijerg=True)', + 'integrate(x*exponential(x, rate), (x, 0, oo), meijerg=True)', + 'integrate(x**2*exponential(x, rate), (x, 0, oo), meijerg=True)', + 'E(1)', + 'E(x*y)', + 'E(x*y**2)', + 'E((x+y+1)**2)', + 'E(x+y+1)', + 'E((x+y-1)**2)', + 'integrate(betadist, (x, 0, oo), meijerg=True)', + 'integrate(x*betadist, (x, 0, oo), meijerg=True)', + 'integrate(x**2*betadist, (x, 0, oo), meijerg=True)', + 'integrate(chi, (x, 0, oo), meijerg=True)', + 'integrate(x*chi, (x, 0, oo), meijerg=True)', + 'integrate(x**2*chi, (x, 0, oo), meijerg=True)', + 'integrate(chisquared, (x, 0, oo), meijerg=True)', + 'integrate(x*chisquared, (x, 0, oo), meijerg=True)', + 'integrate(x**2*chisquared, (x, 0, oo), meijerg=True)', + 'integrate(((x-k)/sqrt(2*k))**3*chisquared, (x, 0, oo), meijerg=True)', + 'integrate(dagum, (x, 0, oo), meijerg=True)', + 'integrate(x*dagum, (x, 0, oo), meijerg=True)', + 'integrate(x**2*dagum, (x, 0, oo), meijerg=True)', + 'integrate(f, (x, 0, oo), meijerg=True)', + 'integrate(x*f, (x, 0, oo), meijerg=True)', + 'integrate(x**2*f, (x, 0, oo), meijerg=True)', + 'integrate(rice, (x, 0, oo), meijerg=True)', + 'integrate(laplace, (x, -oo, oo), meijerg=True)', + 'integrate(x*laplace, (x, -oo, oo), meijerg=True)', + 'integrate(x**2*laplace, (x, -oo, oo), meijerg=True)', + 'integrate(log(x) * x**(k-1) * exp(-x) / gamma(k), (x, 0, oo))', + + 'integrate(sin(z*x)*(x**2-1)**(-(y+S(1)/2)), (x, 1, oo), meijerg=True)', + 'integrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)', + 'integrate(besselj(0,x)*besselj(1,x)*besselk(0,x), (x, 0, oo), meijerg=True)', + 'integrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)', + 'integrate(besselj(a,x)*besselj(b,x)/x, (x,0,oo), meijerg=True)', + + 'hyperexpand(meijerg((-s - a/2 + 1, -s + a/2 + 1), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), (a/2, -a/2), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), 1))', + "gammasimp(S('2**(2*s)*(-pi*gamma(-a + 1)*gamma(a + 1)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 3/2)*gamma(a + s + 1)/(a*(a + s)) - gamma(-a - 1/2)*gamma(-a + 1)*gamma(a + 1)*gamma(a + 3/2)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a + s + 1)*gamma(a - s + 1)/(a*(-a + s)))*gamma(-2*s + 1)*gamma(s + 1)/(pi*s*gamma(-a - 1/2)*gamma(a + 3/2)*gamma(-s + 1)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 1)*gamma(a - s + 3/2))'))", + + 'mellin_transform(E1(x), x, s)', + 'inverse_mellin_transform(gamma(s)/s, s, x, (0, oo))', + 'mellin_transform(expint(a, x), x, s)', + 'mellin_transform(Si(x), x, s)', + 'inverse_mellin_transform(-2**s*sqrt(pi)*gamma((s + 1)/2)/(2*s*gamma(-s/2 + 1)), s, x, (-1, 0))', + 'mellin_transform(Ci(sqrt(x)), x, s)', + 'inverse_mellin_transform(-4**s*sqrt(pi)*gamma(s)/(2*s*gamma(-s + S(1)/2)),s, u, (0, 1))', + 'laplace_transform(Ci(x), x, s)', + 'laplace_transform(expint(a, x), x, s)', + 'laplace_transform(expint(1, x), x, s)', + 'laplace_transform(expint(2, x), x, s)', + 'inverse_laplace_transform(-log(1 + s**2)/2/s, s, u)', + 'inverse_laplace_transform(log(s + 1)/s, s, x)', + 'inverse_laplace_transform((s - log(s + 1))/s**2, s, x)', + 'laplace_transform(Chi(x), x, s)', + 'laplace_transform(Shi(x), x, s)', + + 'integrate(exp(-z*x)/x, (x, 1, oo), meijerg=True, conds="none")', + 'integrate(exp(-z*x)/x**2, (x, 1, oo), meijerg=True, conds="none")', + 'integrate(exp(-z*x)/x**3, (x, 1, oo), meijerg=True,conds="none")', + 'integrate(-cos(x)/x, (x, tpos, oo), meijerg=True)', + 'integrate(-sin(x)/x, (x, tpos, oo), meijerg=True)', + 'integrate(sin(x)/x, (x, 0, z), meijerg=True)', + 'integrate(sinh(x)/x, (x, 0, z), meijerg=True)', + 'integrate(exp(-x)/x, x, meijerg=True)', + 'integrate(exp(-x)/x**2, x, meijerg=True)', + 'integrate(cos(u)/u, u, meijerg=True)', + 'integrate(cosh(u)/u, u, meijerg=True)', + 'integrate(expint(1, x), x, meijerg=True)', + 'integrate(expint(2, x), x, meijerg=True)', + 'integrate(Si(x), x, meijerg=True)', + 'integrate(Ci(u), u, meijerg=True)', + 'integrate(Shi(x), x, meijerg=True)', + 'integrate(Chi(u), u, meijerg=True)', + 'integrate(Si(x)*exp(-x), (x, 0, oo), meijerg=True)', + 'integrate(expint(1, x)*sin(x), (x, 0, oo), meijerg=True)' +] + +from time import time +from sympy.core.cache import clear_cache +import sys + +timings = [] + +if __name__ == '__main__': + for n, string in enumerate(bench): + clear_cache() + _t = time() + exec(string) + _t = time() - _t + timings += [(_t, string)] + sys.stdout.write('.') + sys.stdout.flush() + if n % (len(bench) // 10) == 0: + sys.stdout.write('%s' % (10*n // len(bench))) + print() + + timings.sort(key=lambda x: -x[0]) + + for ti, string in timings: + print('%.2fs %s' % (ti, string)) diff --git a/lib/python3.11/site-packages/sympy/benchmarks/bench_symbench.py b/lib/python3.11/site-packages/sympy/benchmarks/bench_symbench.py new file mode 100644 index 0000000000000000000000000000000000000000..8ea700b44b677107f5345196a8895e8ed5a9d56d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/benchmarks/bench_symbench.py @@ -0,0 +1,134 @@ +#!/usr/bin/env python +from sympy.core.random import random +from sympy.core.numbers import (I, Integer, pi) +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin +from sympy.polys.polytools import factor +from sympy.simplify.simplify import simplify +from sympy.abc import x, y, z +from timeit import default_timer as clock + + +def bench_R1(): + "real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))" + def f(z): + return sqrt(Integer(1)/3)*z**2 + I/3 + f(f(f(f(f(f(f(f(f(f(I/2)))))))))).as_real_imag()[0] + + +def bench_R2(): + "Hermite polynomial hermite(15, y)" + def hermite(n, y): + if n == 1: + return 2*y + if n == 0: + return 1 + return (2*y*hermite(n - 1, y) - 2*(n - 1)*hermite(n - 2, y)).expand() + + hermite(15, y) + + +def bench_R3(): + "a = [bool(f==f) for _ in range(10)]" + f = x + y + z + [bool(f == f) for _ in range(10)] + + +def bench_R4(): + # we don't have Tuples + pass + + +def bench_R5(): + "blowup(L, 8); L=uniq(L)" + def blowup(L, n): + for i in range(n): + L.append( (L[i] + L[i + 1]) * L[i + 2] ) + + def uniq(x): + v = set(x) + return v + L = [x, y, z] + blowup(L, 8) + L = uniq(L) + + +def bench_R6(): + "sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))" + sum(simplify((x + sin(i))/x + (x - sin(i))/x) for i in range(100)) + + +def bench_R7(): + "[f.subs(x, random()) for _ in range(10**4)]" + f = x**24 + 34*x**12 + 45*x**3 + 9*x**18 + 34*x**10 + 32*x**21 + [f.subs(x, random()) for _ in range(10**4)] + + +def bench_R8(): + "right(x^2,0,5,10^4)" + def right(f, a, b, n): + a = sympify(a) + b = sympify(b) + n = sympify(n) + x = f.atoms(Symbol).pop() + Deltax = (b - a)/n + c = a + est = 0 + for i in range(n): + c += Deltax + est += f.subs(x, c) + return est*Deltax + + right(x**2, 0, 5, 10**4) + + +def _bench_R9(): + "factor(x^20 - pi^5*y^20)" + factor(x**20 - pi**5*y**20) + + +def bench_R10(): + "v = [-pi,-pi+1/10..,pi]" + def srange(min, max, step): + v = [min] + while (max - v[-1]).evalf() > 0: + v.append(v[-1] + step) + return v[:-1] + srange(-pi, pi, sympify(1)/10) + + +def bench_R11(): + "a = [random() + random()*I for w in [0..1000]]" + [random() + random()*I for w in range(1000)] + + +def bench_S1(): + "e=(x+y+z+1)**7;f=e*(e+1);f.expand()" + e = (x + y + z + 1)**7 + f = e*(e + 1) + f.expand() + + +if __name__ == '__main__': + benchmarks = [ + bench_R1, + bench_R2, + bench_R3, + bench_R5, + bench_R6, + bench_R7, + bench_R8, + #_bench_R9, + bench_R10, + bench_R11, + #bench_S1, + ] + + report = [] + for b in benchmarks: + t = clock() + b() + t = clock() - t + print("%s%65s: %f" % (b.__name__, b.__doc__, t)) diff --git a/lib/python3.11/site-packages/sympy/calculus/__init__.py b/lib/python3.11/site-packages/sympy/calculus/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..865c0556769e35ca7e8a09a4c208a1cfbd17369c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/__init__.py @@ -0,0 +1,25 @@ +"""Calculus-related methods.""" + +from .euler import euler_equations +from .singularities import (singularities, is_increasing, + is_strictly_increasing, is_decreasing, + is_strictly_decreasing, is_monotonic) +from .finite_diff import finite_diff_weights, apply_finite_diff, differentiate_finite +from .util import (periodicity, not_empty_in, is_convex, + stationary_points, minimum, maximum) +from .accumulationbounds import AccumBounds + +__all__ = [ +'euler_equations', + +'singularities', 'is_increasing', +'is_strictly_increasing', 'is_decreasing', +'is_strictly_decreasing', 'is_monotonic', + +'finite_diff_weights', 'apply_finite_diff', 'differentiate_finite', + +'periodicity', 'not_empty_in', 'is_convex', 'stationary_points', +'minimum', 'maximum', + +'AccumBounds' +] diff --git a/lib/python3.11/site-packages/sympy/calculus/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/calculus/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 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a/lib/python3.11/site-packages/sympy/calculus/__pycache__/util.cpython-311.pyc b/lib/python3.11/site-packages/sympy/calculus/__pycache__/util.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..4e6480cc6e93d70b7c7d784a2c0606f6a0f01644 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/calculus/__pycache__/util.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/calculus/accumulationbounds.py b/lib/python3.11/site-packages/sympy/calculus/accumulationbounds.py new file mode 100644 index 0000000000000000000000000000000000000000..8be303014cea8b5005098f9a52d908cf2160ccba --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/accumulationbounds.py @@ -0,0 +1,804 @@ +from sympy.core import Add, Mul, Pow, S +from sympy.core.basic import Basic +from sympy.core.expr import Expr +from sympy.core.numbers import _sympifyit, oo, zoo +from sympy.core.relational import is_le, is_lt, is_ge, is_gt +from sympy.core.sympify import _sympify +from sympy.functions.elementary.miscellaneous import Min, Max +from sympy.logic.boolalg import And +from sympy.multipledispatch import dispatch +from sympy.series.order import Order +from sympy.sets.sets import FiniteSet + + +class AccumulationBounds(Expr): + r"""An accumulation bounds. + + # Note AccumulationBounds has an alias: AccumBounds + + AccumulationBounds represent an interval `[a, b]`, which is always closed + at the ends. Here `a` and `b` can be any value from extended real numbers. + + The intended meaning of AccummulationBounds is to give an approximate + location of the accumulation points of a real function at a limit point. + + Let `a` and `b` be reals such that `a \le b`. + + `\left\langle a, b\right\rangle = \{x \in \mathbb{R} \mid a \le x \le b\}` + + `\left\langle -\infty, b\right\rangle = \{x \in \mathbb{R} \mid x \le b\} \cup \{-\infty, \infty\}` + + `\left\langle a, \infty \right\rangle = \{x \in \mathbb{R} \mid a \le x\} \cup \{-\infty, \infty\}` + + `\left\langle -\infty, \infty \right\rangle = \mathbb{R} \cup \{-\infty, \infty\}` + + ``oo`` and ``-oo`` are added to the second and third definition respectively, + since if either ``-oo`` or ``oo`` is an argument, then the other one should + be included (though not as an end point). This is forced, since we have, + for example, ``1/AccumBounds(0, 1) = AccumBounds(1, oo)``, and the limit at + `0` is not one-sided. As `x` tends to `0-`, then `1/x \rightarrow -\infty`, so `-\infty` + should be interpreted as belonging to ``AccumBounds(1, oo)`` though it need + not appear explicitly. + + In many cases it suffices to know that the limit set is bounded. + However, in some other cases more exact information could be useful. + For example, all accumulation values of `\cos(x) + 1` are non-negative. + (``AccumBounds(-1, 1) + 1 = AccumBounds(0, 2)``) + + A AccumulationBounds object is defined to be real AccumulationBounds, + if its end points are finite reals. + + Let `X`, `Y` be real AccumulationBounds, then their sum, difference, + product are defined to be the following sets: + + `X + Y = \{ x+y \mid x \in X \cap y \in Y\}` + + `X - Y = \{ x-y \mid x \in X \cap y \in Y\}` + + `X \times Y = \{ x \times y \mid x \in X \cap y \in Y\}` + + When an AccumBounds is raised to a negative power, if 0 is contained + between the bounds then an infinite range is returned, otherwise if an + endpoint is 0 then a semi-infinite range with consistent sign will be returned. + + AccumBounds in expressions behave a lot like Intervals but the + semantics are not necessarily the same. Division (or exponentiation + to a negative integer power) could be handled with *intervals* by + returning a union of the results obtained after splitting the + bounds between negatives and positives, but that is not done with + AccumBounds. In addition, bounds are assumed to be independent of + each other; if the same bound is used in more than one place in an + expression, the result may not be the supremum or infimum of the + expression (see below). Finally, when a boundary is ``1``, + exponentiation to the power of ``oo`` yields ``oo``, neither + ``1`` nor ``nan``. + + Examples + ======== + + >>> from sympy import AccumBounds, sin, exp, log, pi, E, S, oo + >>> from sympy.abc import x + + >>> AccumBounds(0, 1) + AccumBounds(1, 2) + AccumBounds(1, 3) + + >>> AccumBounds(0, 1) - AccumBounds(0, 2) + AccumBounds(-2, 1) + + >>> AccumBounds(-2, 3)*AccumBounds(-1, 1) + AccumBounds(-3, 3) + + >>> AccumBounds(1, 2)*AccumBounds(3, 5) + AccumBounds(3, 10) + + The exponentiation of AccumulationBounds is defined + as follows: + + If 0 does not belong to `X` or `n > 0` then + + `X^n = \{ x^n \mid x \in X\}` + + >>> AccumBounds(1, 4)**(S(1)/2) + AccumBounds(1, 2) + + otherwise, an infinite or semi-infinite result is obtained: + + >>> 1/AccumBounds(-1, 1) + AccumBounds(-oo, oo) + >>> 1/AccumBounds(0, 2) + AccumBounds(1/2, oo) + >>> 1/AccumBounds(-oo, 0) + AccumBounds(-oo, 0) + + A boundary of 1 will always generate all nonnegatives: + + >>> AccumBounds(1, 2)**oo + AccumBounds(0, oo) + >>> AccumBounds(0, 1)**oo + AccumBounds(0, oo) + + If the exponent is itself an AccumulationBounds or is not an + integer then unevaluated results will be returned unless the base + values are positive: + + >>> AccumBounds(2, 3)**AccumBounds(-1, 2) + AccumBounds(1/3, 9) + >>> AccumBounds(-2, 3)**AccumBounds(-1, 2) + AccumBounds(-2, 3)**AccumBounds(-1, 2) + + >>> AccumBounds(-2, -1)**(S(1)/2) + sqrt(AccumBounds(-2, -1)) + + Note: `\left\langle a, b\right\rangle^2` is not same as `\left\langle a, b\right\rangle \times \left\langle a, b\right\rangle` + + >>> AccumBounds(-1, 1)**2 + AccumBounds(0, 1) + + >>> AccumBounds(1, 3) < 4 + True + + >>> AccumBounds(1, 3) < -1 + False + + Some elementary functions can also take AccumulationBounds as input. + A function `f` evaluated for some real AccumulationBounds `\left\langle a, b \right\rangle` + is defined as `f(\left\langle a, b\right\rangle) = \{ f(x) \mid a \le x \le b \}` + + >>> sin(AccumBounds(pi/6, pi/3)) + AccumBounds(1/2, sqrt(3)/2) + + >>> exp(AccumBounds(0, 1)) + AccumBounds(1, E) + + >>> log(AccumBounds(1, E)) + AccumBounds(0, 1) + + Some symbol in an expression can be substituted for a AccumulationBounds + object. But it does not necessarily evaluate the AccumulationBounds for + that expression. + + The same expression can be evaluated to different values depending upon + the form it is used for substitution since each instance of an + AccumulationBounds is considered independent. For example: + + >>> (x**2 + 2*x + 1).subs(x, AccumBounds(-1, 1)) + AccumBounds(-1, 4) + + >>> ((x + 1)**2).subs(x, AccumBounds(-1, 1)) + AccumBounds(0, 4) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Interval_arithmetic + + .. [2] https://fab.cba.mit.edu/classes/S62.12/docs/Hickey_interval.pdf + + Notes + ===== + + Do not use ``AccumulationBounds`` for floating point interval arithmetic + calculations, use ``mpmath.iv`` instead. + """ + + is_extended_real = True + is_number = False + + def __new__(cls, min, max): + + min = _sympify(min) + max = _sympify(max) + + # Only allow real intervals (use symbols with 'is_extended_real=True'). + if not min.is_extended_real or not max.is_extended_real: + raise ValueError("Only real AccumulationBounds are supported") + + if max == min: + return max + + # Make sure that the created AccumBounds object will be valid. + if max.is_number and min.is_number: + bad = max.is_comparable and min.is_comparable and max < min + else: + bad = (max - min).is_extended_negative + if bad: + raise ValueError( + "Lower limit should be smaller than upper limit") + + return Basic.__new__(cls, min, max) + + # setting the operation priority + _op_priority = 11.0 + + def _eval_is_real(self): + if self.min.is_real and self.max.is_real: + return True + + @property + def min(self): + """ + Returns the minimum possible value attained by AccumulationBounds + object. + + Examples + ======== + + >>> from sympy import AccumBounds + >>> AccumBounds(1, 3).min + 1 + + """ + return self.args[0] + + @property + def max(self): + """ + Returns the maximum possible value attained by AccumulationBounds + object. + + Examples + ======== + + >>> from sympy import AccumBounds + >>> AccumBounds(1, 3).max + 3 + + """ + return self.args[1] + + @property + def delta(self): + """ + Returns the difference of maximum possible value attained by + AccumulationBounds object and minimum possible value attained + by AccumulationBounds object. + + Examples + ======== + + >>> from sympy import AccumBounds + >>> AccumBounds(1, 3).delta + 2 + + """ + return self.max - self.min + + @property + def mid(self): + """ + Returns the mean of maximum possible value attained by + AccumulationBounds object and minimum possible value + attained by AccumulationBounds object. + + Examples + ======== + + >>> from sympy import AccumBounds + >>> AccumBounds(1, 3).mid + 2 + + """ + return (self.min + self.max) / 2 + + @_sympifyit('other', NotImplemented) + def _eval_power(self, other): + return self.__pow__(other) + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if isinstance(other, Expr): + if isinstance(other, AccumBounds): + return AccumBounds( + Add(self.min, other.min), + Add(self.max, other.max)) + if other is S.Infinity and self.min is S.NegativeInfinity or \ + other is S.NegativeInfinity and self.max is S.Infinity: + return AccumBounds(-oo, oo) + elif other.is_extended_real: + if self.min is S.NegativeInfinity and self.max is S.Infinity: + return AccumBounds(-oo, oo) + elif self.min is S.NegativeInfinity: + return AccumBounds(-oo, self.max + other) + elif self.max is S.Infinity: + return AccumBounds(self.min + other, oo) + else: + return AccumBounds(Add(self.min, other), Add(self.max, other)) + return Add(self, other, evaluate=False) + return NotImplemented + + __radd__ = __add__ + + def __neg__(self): + return AccumBounds(-self.max, -self.min) + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if isinstance(other, Expr): + if isinstance(other, AccumBounds): + return AccumBounds( + Add(self.min, -other.max), + Add(self.max, -other.min)) + if other is S.NegativeInfinity and self.min is S.NegativeInfinity or \ + other is S.Infinity and self.max is S.Infinity: + return AccumBounds(-oo, oo) + elif other.is_extended_real: + if self.min is S.NegativeInfinity and self.max is S.Infinity: + return AccumBounds(-oo, oo) + elif self.min is S.NegativeInfinity: + return AccumBounds(-oo, self.max - other) + elif self.max is S.Infinity: + return AccumBounds(self.min - other, oo) + else: + return AccumBounds( + Add(self.min, -other), + Add(self.max, -other)) + return Add(self, -other, evaluate=False) + return NotImplemented + + @_sympifyit('other', NotImplemented) + def __rsub__(self, other): + return self.__neg__() + other + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if self.args == (-oo, oo): + return self + if isinstance(other, Expr): + if isinstance(other, AccumBounds): + if other.args == (-oo, oo): + return other + v = set() + for a in self.args: + vi = other*a + v.update(vi.args or (vi,)) + return AccumBounds(Min(*v), Max(*v)) + if other is S.Infinity: + if self.min.is_zero: + return AccumBounds(0, oo) + if self.max.is_zero: + return AccumBounds(-oo, 0) + if other is S.NegativeInfinity: + if self.min.is_zero: + return AccumBounds(-oo, 0) + if self.max.is_zero: + return AccumBounds(0, oo) + if other.is_extended_real: + if other.is_zero: + if self.max is S.Infinity: + return AccumBounds(0, oo) + if self.min is S.NegativeInfinity: + return AccumBounds(-oo, 0) + return S.Zero + if other.is_extended_positive: + return AccumBounds( + Mul(self.min, other), + Mul(self.max, other)) + elif other.is_extended_negative: + return AccumBounds( + Mul(self.max, other), + Mul(self.min, other)) + if isinstance(other, Order): + return other + return Mul(self, other, evaluate=False) + return NotImplemented + + __rmul__ = __mul__ + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if isinstance(other, Expr): + if isinstance(other, AccumBounds): + if other.min.is_positive or other.max.is_negative: + return self * AccumBounds(1/other.max, 1/other.min) + + if (self.min.is_extended_nonpositive and self.max.is_extended_nonnegative and + other.min.is_extended_nonpositive and other.max.is_extended_nonnegative): + if self.min.is_zero and other.min.is_zero: + return AccumBounds(0, oo) + if self.max.is_zero and other.min.is_zero: + return AccumBounds(-oo, 0) + return AccumBounds(-oo, oo) + + if self.max.is_extended_negative: + if other.min.is_extended_negative: + if other.max.is_zero: + return AccumBounds(self.max / other.min, oo) + if other.max.is_extended_positive: + # if we were dealing with intervals we would return + # Union(Interval(-oo, self.max/other.max), + # Interval(self.max/other.min, oo)) + return AccumBounds(-oo, oo) + + if other.min.is_zero and other.max.is_extended_positive: + return AccumBounds(-oo, self.max / other.max) + + if self.min.is_extended_positive: + if other.min.is_extended_negative: + if other.max.is_zero: + return AccumBounds(-oo, self.min / other.min) + if other.max.is_extended_positive: + # if we were dealing with intervals we would return + # Union(Interval(-oo, self.min/other.min), + # Interval(self.min/other.max, oo)) + return AccumBounds(-oo, oo) + + if other.min.is_zero and other.max.is_extended_positive: + return AccumBounds(self.min / other.max, oo) + + elif other.is_extended_real: + if other in (S.Infinity, S.NegativeInfinity): + if self == AccumBounds(-oo, oo): + return AccumBounds(-oo, oo) + if self.max is S.Infinity: + return AccumBounds(Min(0, other), Max(0, other)) + if self.min is S.NegativeInfinity: + return AccumBounds(Min(0, -other), Max(0, -other)) + if other.is_extended_positive: + return AccumBounds(self.min / other, self.max / other) + elif other.is_extended_negative: + return AccumBounds(self.max / other, self.min / other) + if (1 / other) is S.ComplexInfinity: + return Mul(self, 1 / other, evaluate=False) + else: + return Mul(self, 1 / other) + + return NotImplemented + + @_sympifyit('other', NotImplemented) + def __rtruediv__(self, other): + if isinstance(other, Expr): + if other.is_extended_real: + if other.is_zero: + return S.Zero + if (self.min.is_extended_nonpositive and self.max.is_extended_nonnegative): + if self.min.is_zero: + if other.is_extended_positive: + return AccumBounds(Mul(other, 1 / self.max), oo) + if other.is_extended_negative: + return AccumBounds(-oo, Mul(other, 1 / self.max)) + if self.max.is_zero: + if other.is_extended_positive: + return AccumBounds(-oo, Mul(other, 1 / self.min)) + if other.is_extended_negative: + return AccumBounds(Mul(other, 1 / self.min), oo) + return AccumBounds(-oo, oo) + else: + return AccumBounds(Min(other / self.min, other / self.max), + Max(other / self.min, other / self.max)) + return Mul(other, 1 / self, evaluate=False) + else: + return NotImplemented + + @_sympifyit('other', NotImplemented) + def __pow__(self, other): + if isinstance(other, Expr): + if other is S.Infinity: + if self.min.is_extended_nonnegative: + if self.max < 1: + return S.Zero + if self.min > 1: + return S.Infinity + return AccumBounds(0, oo) + elif self.max.is_extended_negative: + if self.min > -1: + return S.Zero + if self.max < -1: + return zoo + return S.NaN + else: + if self.min > -1: + if self.max < 1: + return S.Zero + return AccumBounds(0, oo) + return AccumBounds(-oo, oo) + + if other is S.NegativeInfinity: + return (1/self)**oo + + # generically true + if (self.max - self.min).is_nonnegative: + # well defined + if self.min.is_nonnegative: + # no 0 to worry about + if other.is_nonnegative: + # no infinity to worry about + return self.func(self.min**other, self.max**other) + + if other.is_zero: + return S.One # x**0 = 1 + + if other.is_Integer or other.is_integer: + if self.min.is_extended_positive: + return AccumBounds( + Min(self.min**other, self.max**other), + Max(self.min**other, self.max**other)) + elif self.max.is_extended_negative: + return AccumBounds( + Min(self.max**other, self.min**other), + Max(self.max**other, self.min**other)) + + if other % 2 == 0: + if other.is_extended_negative: + if self.min.is_zero: + return AccumBounds(self.max**other, oo) + if self.max.is_zero: + return AccumBounds(self.min**other, oo) + return (1/self)**(-other) + return AccumBounds( + S.Zero, Max(self.min**other, self.max**other)) + elif other % 2 == 1: + if other.is_extended_negative: + if self.min.is_zero: + return AccumBounds(self.max**other, oo) + if self.max.is_zero: + return AccumBounds(-oo, self.min**other) + return (1/self)**(-other) + return AccumBounds(self.min**other, self.max**other) + + # non-integer exponent + # 0**neg or neg**frac yields complex + if (other.is_number or other.is_rational) and ( + self.min.is_extended_nonnegative or ( + other.is_extended_nonnegative and + self.min.is_extended_nonnegative)): + num, den = other.as_numer_denom() + if num is S.One: + return AccumBounds(*[i**(1/den) for i in self.args]) + + elif den is not S.One: # e.g. if other is not Float + return (self**num)**(1/den) # ok for non-negative base + + if isinstance(other, AccumBounds): + if (self.min.is_extended_positive or + self.min.is_extended_nonnegative and + other.min.is_extended_nonnegative): + p = [self**i for i in other.args] + if not any(i.is_Pow for i in p): + a = [j for i in p for j in i.args or (i,)] + try: + return self.func(min(a), max(a)) + except TypeError: # can't sort + pass + + return Pow(self, other, evaluate=False) + + return NotImplemented + + @_sympifyit('other', NotImplemented) + def __rpow__(self, other): + if other.is_real and other.is_extended_nonnegative and ( + self.max - self.min).is_extended_positive: + if other is S.One: + return S.One + if other.is_extended_positive: + a, b = [other**i for i in self.args] + if min(a, b) != a: + a, b = b, a + return self.func(a, b) + if other.is_zero: + if self.min.is_zero: + return self.func(0, 1) + if self.min.is_extended_positive: + return S.Zero + + return Pow(other, self, evaluate=False) + + def __abs__(self): + if self.max.is_extended_negative: + return self.__neg__() + elif self.min.is_extended_negative: + return AccumBounds(S.Zero, Max(abs(self.min), self.max)) + else: + return self + + + def __contains__(self, other): + """ + Returns ``True`` if other is contained in self, where other + belongs to extended real numbers, ``False`` if not contained, + otherwise TypeError is raised. + + Examples + ======== + + >>> from sympy import AccumBounds, oo + >>> 1 in AccumBounds(-1, 3) + True + + -oo and oo go together as limits (in AccumulationBounds). + + >>> -oo in AccumBounds(1, oo) + True + + >>> oo in AccumBounds(-oo, 0) + True + + """ + other = _sympify(other) + + if other in (S.Infinity, S.NegativeInfinity): + if self.min is S.NegativeInfinity or self.max is S.Infinity: + return True + return False + + rv = And(self.min <= other, self.max >= other) + if rv not in (True, False): + raise TypeError("input failed to evaluate") + return rv + + def intersection(self, other): + """ + Returns the intersection of 'self' and 'other'. + Here other can be an instance of :py:class:`~.FiniteSet` or AccumulationBounds. + + Parameters + ========== + + other : AccumulationBounds + Another AccumulationBounds object with which the intersection + has to be computed. + + Returns + ======= + + AccumulationBounds + Intersection of ``self`` and ``other``. + + Examples + ======== + + >>> from sympy import AccumBounds, FiniteSet + >>> AccumBounds(1, 3).intersection(AccumBounds(2, 4)) + AccumBounds(2, 3) + + >>> AccumBounds(1, 3).intersection(AccumBounds(4, 6)) + EmptySet + + >>> AccumBounds(1, 4).intersection(FiniteSet(1, 2, 5)) + {1, 2} + + """ + if not isinstance(other, (AccumBounds, FiniteSet)): + raise TypeError( + "Input must be AccumulationBounds or FiniteSet object") + + if isinstance(other, FiniteSet): + fin_set = S.EmptySet + for i in other: + if i in self: + fin_set = fin_set + FiniteSet(i) + return fin_set + + if self.max < other.min or self.min > other.max: + return S.EmptySet + + if self.min <= other.min: + if self.max <= other.max: + return AccumBounds(other.min, self.max) + if self.max > other.max: + return other + + if other.min <= self.min: + if other.max < self.max: + return AccumBounds(self.min, other.max) + if other.max > self.max: + return self + + def union(self, other): + # TODO : Devise a better method for Union of AccumBounds + # this method is not actually correct and + # can be made better + if not isinstance(other, AccumBounds): + raise TypeError( + "Input must be AccumulationBounds or FiniteSet object") + + if self.min <= other.min and self.max >= other.min: + return AccumBounds(self.min, Max(self.max, other.max)) + + if other.min <= self.min and other.max >= self.min: + return AccumBounds(other.min, Max(self.max, other.max)) + + +@dispatch(AccumulationBounds, AccumulationBounds) # type: ignore # noqa:F811 +def _eval_is_le(lhs, rhs): # noqa:F811 + if is_le(lhs.max, rhs.min): + return True + if is_gt(lhs.min, rhs.max): + return False + + +@dispatch(AccumulationBounds, Basic) # type: ignore # noqa:F811 +def _eval_is_le(lhs, rhs): # noqa: F811 + + """ + Returns ``True `` if range of values attained by ``lhs`` AccumulationBounds + object is greater than the range of values attained by ``rhs``, + where ``rhs`` may be any value of type AccumulationBounds object or + extended real number value, ``False`` if ``rhs`` satisfies + the same property, else an unevaluated :py:class:`~.Relational`. + + Examples + ======== + + >>> from sympy import AccumBounds, oo + >>> AccumBounds(1, 3) > AccumBounds(4, oo) + False + >>> AccumBounds(1, 4) > AccumBounds(3, 4) + AccumBounds(1, 4) > AccumBounds(3, 4) + >>> AccumBounds(1, oo) > -1 + True + + """ + if not rhs.is_extended_real: + raise TypeError( + "Invalid comparison of %s %s" % + (type(rhs), rhs)) + elif rhs.is_comparable: + if is_le(lhs.max, rhs): + return True + if is_gt(lhs.min, rhs): + return False + + +@dispatch(AccumulationBounds, AccumulationBounds) +def _eval_is_ge(lhs, rhs): # noqa:F811 + if is_ge(lhs.min, rhs.max): + return True + if is_lt(lhs.max, rhs.min): + return False + + +@dispatch(AccumulationBounds, Expr) # type:ignore +def _eval_is_ge(lhs, rhs): # noqa: F811 + """ + Returns ``True`` if range of values attained by ``lhs`` AccumulationBounds + object is less that the range of values attained by ``rhs``, where + other may be any value of type AccumulationBounds object or extended + real number value, ``False`` if ``rhs`` satisfies the same + property, else an unevaluated :py:class:`~.Relational`. + + Examples + ======== + + >>> from sympy import AccumBounds, oo + >>> AccumBounds(1, 3) >= AccumBounds(4, oo) + False + >>> AccumBounds(1, 4) >= AccumBounds(3, 4) + AccumBounds(1, 4) >= AccumBounds(3, 4) + >>> AccumBounds(1, oo) >= 1 + True + """ + + if not rhs.is_extended_real: + raise TypeError( + "Invalid comparison of %s %s" % + (type(rhs), rhs)) + elif rhs.is_comparable: + if is_ge(lhs.min, rhs): + return True + if is_lt(lhs.max, rhs): + return False + + +@dispatch(Expr, AccumulationBounds) # type:ignore +def _eval_is_ge(lhs, rhs): # noqa:F811 + if not lhs.is_extended_real: + raise TypeError( + "Invalid comparison of %s %s" % + (type(lhs), lhs)) + elif lhs.is_comparable: + if is_le(rhs.max, lhs): + return True + if is_gt(rhs.min, lhs): + return False + + +@dispatch(AccumulationBounds, AccumulationBounds) # type:ignore +def _eval_is_ge(lhs, rhs): # noqa:F811 + if is_ge(lhs.min, rhs.max): + return True + if is_lt(lhs.max, rhs.min): + return False + +# setting an alias for AccumulationBounds +AccumBounds = AccumulationBounds diff --git a/lib/python3.11/site-packages/sympy/calculus/euler.py b/lib/python3.11/site-packages/sympy/calculus/euler.py new file mode 100644 index 0000000000000000000000000000000000000000..817acf76091dfba2dba40487ca7735e307c0fc15 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/euler.py @@ -0,0 +1,108 @@ +""" +This module implements a method to find +Euler-Lagrange Equations for given Lagrangian. +""" +from itertools import combinations_with_replacement +from sympy.core.function import (Derivative, Function, diff) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.utilities.iterables import iterable + + +def euler_equations(L, funcs=(), vars=()): + r""" + Find the Euler-Lagrange equations [1]_ for a given Lagrangian. + + Parameters + ========== + + L : Expr + The Lagrangian that should be a function of the functions listed + in the second argument and their derivatives. + + For example, in the case of two functions $f(x,y)$, $g(x,y)$ and + two independent variables $x$, $y$ the Lagrangian has the form: + + .. math:: L\left(f(x,y),g(x,y),\frac{\partial f(x,y)}{\partial x}, + \frac{\partial f(x,y)}{\partial y}, + \frac{\partial g(x,y)}{\partial x}, + \frac{\partial g(x,y)}{\partial y},x,y\right) + + In many cases it is not necessary to provide anything, except the + Lagrangian, it will be auto-detected (and an error raised if this + cannot be done). + + funcs : Function or an iterable of Functions + The functions that the Lagrangian depends on. The Euler equations + are differential equations for each of these functions. + + vars : Symbol or an iterable of Symbols + The Symbols that are the independent variables of the functions. + + Returns + ======= + + eqns : list of Eq + The list of differential equations, one for each function. + + Examples + ======== + + >>> from sympy import euler_equations, Symbol, Function + >>> x = Function('x') + >>> t = Symbol('t') + >>> L = (x(t).diff(t))**2/2 - x(t)**2/2 + >>> euler_equations(L, x(t), t) + [Eq(-x(t) - Derivative(x(t), (t, 2)), 0)] + >>> u = Function('u') + >>> x = Symbol('x') + >>> L = (u(t, x).diff(t))**2/2 - (u(t, x).diff(x))**2/2 + >>> euler_equations(L, u(t, x), [t, x]) + [Eq(-Derivative(u(t, x), (t, 2)) + Derivative(u(t, x), (x, 2)), 0)] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation + + """ + + funcs = tuple(funcs) if iterable(funcs) else (funcs,) + + if not funcs: + funcs = tuple(L.atoms(Function)) + else: + for f in funcs: + if not isinstance(f, Function): + raise TypeError('Function expected, got: %s' % f) + + vars = tuple(vars) if iterable(vars) else (vars,) + + if not vars: + vars = funcs[0].args + else: + vars = tuple(sympify(var) for var in vars) + + if not all(isinstance(v, Symbol) for v in vars): + raise TypeError('Variables are not symbols, got %s' % vars) + + for f in funcs: + if not vars == f.args: + raise ValueError("Variables %s do not match args: %s" % (vars, f)) + + order = max([len(d.variables) for d in L.atoms(Derivative) + if d.expr in funcs] + [0]) + + eqns = [] + for f in funcs: + eq = diff(L, f) + for i in range(1, order + 1): + for p in combinations_with_replacement(vars, i): + eq = eq + S.NegativeOne**i*diff(L, diff(f, *p), *p) + new_eq = Eq(eq, 0) + if isinstance(new_eq, Eq): + eqns.append(new_eq) + + return eqns diff --git a/lib/python3.11/site-packages/sympy/calculus/finite_diff.py b/lib/python3.11/site-packages/sympy/calculus/finite_diff.py new file mode 100644 index 0000000000000000000000000000000000000000..17eece149aadad236cefeb350e1ef4a383c84f01 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/finite_diff.py @@ -0,0 +1,476 @@ +""" +Finite difference weights +========================= + +This module implements an algorithm for efficient generation of finite +difference weights for ordinary differentials of functions for +derivatives from 0 (interpolation) up to arbitrary order. + +The core algorithm is provided in the finite difference weight generating +function (``finite_diff_weights``), and two convenience functions are provided +for: + +- estimating a derivative (or interpolate) directly from a series of points + is also provided (``apply_finite_diff``). +- differentiating by using finite difference approximations + (``differentiate_finite``). + +""" + +from sympy.core.function import Derivative +from sympy.core.singleton import S +from sympy.core.function import Subs +from sympy.core.traversal import preorder_traversal +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import iterable + + + +def finite_diff_weights(order, x_list, x0=S.One): + """ + Calculates the finite difference weights for an arbitrarily spaced + one-dimensional grid (``x_list``) for derivatives at ``x0`` of order + 0, 1, ..., up to ``order`` using a recursive formula. Order of accuracy + is at least ``len(x_list) - order``, if ``x_list`` is defined correctly. + + Parameters + ========== + + order: int + Up to what derivative order weights should be calculated. + 0 corresponds to interpolation. + x_list: sequence + Sequence of (unique) values for the independent variable. + It is useful (but not necessary) to order ``x_list`` from + nearest to furthest from ``x0``; see examples below. + x0: Number or Symbol + Root or value of the independent variable for which the finite + difference weights should be generated. Default is ``S.One``. + + Returns + ======= + + list + A list of sublists, each corresponding to coefficients for + increasing derivative order, and each containing lists of + coefficients for increasing subsets of x_list. + + Examples + ======== + + >>> from sympy import finite_diff_weights, S + >>> res = finite_diff_weights(1, [-S(1)/2, S(1)/2, S(3)/2, S(5)/2], 0) + >>> res + [[[1, 0, 0, 0], + [1/2, 1/2, 0, 0], + [3/8, 3/4, -1/8, 0], + [5/16, 15/16, -5/16, 1/16]], + [[0, 0, 0, 0], + [-1, 1, 0, 0], + [-1, 1, 0, 0], + [-23/24, 7/8, 1/8, -1/24]]] + >>> res[0][-1] # FD weights for 0th derivative, using full x_list + [5/16, 15/16, -5/16, 1/16] + >>> res[1][-1] # FD weights for 1st derivative + [-23/24, 7/8, 1/8, -1/24] + >>> res[1][-2] # FD weights for 1st derivative, using x_list[:-1] + [-1, 1, 0, 0] + >>> res[1][-1][0] # FD weight for 1st deriv. for x_list[0] + -23/24 + >>> res[1][-1][1] # FD weight for 1st deriv. for x_list[1], etc. + 7/8 + + Each sublist contains the most accurate formula at the end. + Note, that in the above example ``res[1][1]`` is the same as ``res[1][2]``. + Since res[1][2] has an order of accuracy of + ``len(x_list[:3]) - order = 3 - 1 = 2``, the same is true for ``res[1][1]``! + + >>> res = finite_diff_weights(1, [S(0), S(1), -S(1), S(2), -S(2)], 0)[1] + >>> res + [[0, 0, 0, 0, 0], + [-1, 1, 0, 0, 0], + [0, 1/2, -1/2, 0, 0], + [-1/2, 1, -1/3, -1/6, 0], + [0, 2/3, -2/3, -1/12, 1/12]] + >>> res[0] # no approximation possible, using x_list[0] only + [0, 0, 0, 0, 0] + >>> res[1] # classic forward step approximation + [-1, 1, 0, 0, 0] + >>> res[2] # classic centered approximation + [0, 1/2, -1/2, 0, 0] + >>> res[3:] # higher order approximations + [[-1/2, 1, -1/3, -1/6, 0], [0, 2/3, -2/3, -1/12, 1/12]] + + Let us compare this to a differently defined ``x_list``. Pay attention to + ``foo[i][k]`` corresponding to the gridpoint defined by ``x_list[k]``. + + >>> foo = finite_diff_weights(1, [-S(2), -S(1), S(0), S(1), S(2)], 0)[1] + >>> foo + [[0, 0, 0, 0, 0], + [-1, 1, 0, 0, 0], + [1/2, -2, 3/2, 0, 0], + [1/6, -1, 1/2, 1/3, 0], + [1/12, -2/3, 0, 2/3, -1/12]] + >>> foo[1] # not the same and of lower accuracy as res[1]! + [-1, 1, 0, 0, 0] + >>> foo[2] # classic double backward step approximation + [1/2, -2, 3/2, 0, 0] + >>> foo[4] # the same as res[4] + [1/12, -2/3, 0, 2/3, -1/12] + + Note that, unless you plan on using approximations based on subsets of + ``x_list``, the order of gridpoints does not matter. + + The capability to generate weights at arbitrary points can be + used e.g. to minimize Runge's phenomenon by using Chebyshev nodes: + + >>> from sympy import cos, symbols, pi, simplify + >>> N, (h, x) = 4, symbols('h x') + >>> x_list = [x+h*cos(i*pi/(N)) for i in range(N,-1,-1)] # chebyshev nodes + >>> print(x_list) + [-h + x, -sqrt(2)*h/2 + x, x, sqrt(2)*h/2 + x, h + x] + >>> mycoeffs = finite_diff_weights(1, x_list, 0)[1][4] + >>> [simplify(c) for c in mycoeffs] #doctest: +NORMALIZE_WHITESPACE + [(h**3/2 + h**2*x - 3*h*x**2 - 4*x**3)/h**4, + (-sqrt(2)*h**3 - 4*h**2*x + 3*sqrt(2)*h*x**2 + 8*x**3)/h**4, + (6*h**2*x - 8*x**3)/h**4, + (sqrt(2)*h**3 - 4*h**2*x - 3*sqrt(2)*h*x**2 + 8*x**3)/h**4, + (-h**3/2 + h**2*x + 3*h*x**2 - 4*x**3)/h**4] + + Notes + ===== + + If weights for a finite difference approximation of 3rd order + derivative is wanted, weights for 0th, 1st and 2nd order are + calculated "for free", so are formulae using subsets of ``x_list``. + This is something one can take advantage of to save computational cost. + Be aware that one should define ``x_list`` from nearest to furthest from + ``x0``. If not, subsets of ``x_list`` will yield poorer approximations, + which might not grand an order of accuracy of ``len(x_list) - order``. + + See also + ======== + + sympy.calculus.finite_diff.apply_finite_diff + + References + ========== + + .. [1] Generation of Finite Difference Formulas on Arbitrarily Spaced + Grids, Bengt Fornberg; Mathematics of computation; 51; 184; + (1988); 699-706; doi:10.1090/S0025-5718-1988-0935077-0 + + """ + # The notation below closely corresponds to the one used in the paper. + order = S(order) + if not order.is_number: + raise ValueError("Cannot handle symbolic order.") + if order < 0: + raise ValueError("Negative derivative order illegal.") + if int(order) != order: + raise ValueError("Non-integer order illegal") + M = order + N = len(x_list) - 1 + delta = [[[0 for nu in range(N+1)] for n in range(N+1)] for + m in range(M+1)] + delta[0][0][0] = S.One + c1 = S.One + for n in range(1, N+1): + c2 = S.One + for nu in range(n): + c3 = x_list[n] - x_list[nu] + c2 = c2 * c3 + if n <= M: + delta[n][n-1][nu] = 0 + for m in range(min(n, M)+1): + delta[m][n][nu] = (x_list[n]-x0)*delta[m][n-1][nu] -\ + m*delta[m-1][n-1][nu] + delta[m][n][nu] /= c3 + for m in range(min(n, M)+1): + delta[m][n][n] = c1/c2*(m*delta[m-1][n-1][n-1] - + (x_list[n-1]-x0)*delta[m][n-1][n-1]) + c1 = c2 + return delta + + +def apply_finite_diff(order, x_list, y_list, x0=S.Zero): + """ + Calculates the finite difference approximation of + the derivative of requested order at ``x0`` from points + provided in ``x_list`` and ``y_list``. + + Parameters + ========== + + order: int + order of derivative to approximate. 0 corresponds to interpolation. + x_list: sequence + Sequence of (unique) values for the independent variable. + y_list: sequence + The function value at corresponding values for the independent + variable in x_list. + x0: Number or Symbol + At what value of the independent variable the derivative should be + evaluated. Defaults to 0. + + Returns + ======= + + sympy.core.add.Add or sympy.core.numbers.Number + The finite difference expression approximating the requested + derivative order at ``x0``. + + Examples + ======== + + >>> from sympy import apply_finite_diff + >>> cube = lambda arg: (1.0*arg)**3 + >>> xlist = range(-3,3+1) + >>> apply_finite_diff(2, xlist, map(cube, xlist), 2) - 12 # doctest: +SKIP + -3.55271367880050e-15 + + we see that the example above only contain rounding errors. + apply_finite_diff can also be used on more abstract objects: + + >>> from sympy import IndexedBase, Idx + >>> x, y = map(IndexedBase, 'xy') + >>> i = Idx('i') + >>> x_list, y_list = zip(*[(x[i+j], y[i+j]) for j in range(-1,2)]) + >>> apply_finite_diff(1, x_list, y_list, x[i]) + ((x[i + 1] - x[i])/(-x[i - 1] + x[i]) - 1)*y[i]/(x[i + 1] - x[i]) - + (x[i + 1] - x[i])*y[i - 1]/((x[i + 1] - x[i - 1])*(-x[i - 1] + x[i])) + + (-x[i - 1] + x[i])*y[i + 1]/((x[i + 1] - x[i - 1])*(x[i + 1] - x[i])) + + Notes + ===== + + Order = 0 corresponds to interpolation. + Only supply so many points you think makes sense + to around x0 when extracting the derivative (the function + need to be well behaved within that region). Also beware + of Runge's phenomenon. + + See also + ======== + + sympy.calculus.finite_diff.finite_diff_weights + + References + ========== + + Fortran 90 implementation with Python interface for numerics: finitediff_ + + .. _finitediff: https://github.com/bjodah/finitediff + + """ + + # In the original paper the following holds for the notation: + # M = order + # N = len(x_list) - 1 + + N = len(x_list) - 1 + if len(x_list) != len(y_list): + raise ValueError("x_list and y_list not equal in length.") + + delta = finite_diff_weights(order, x_list, x0) + + derivative = 0 + for nu in range(len(x_list)): + derivative += delta[order][N][nu]*y_list[nu] + return derivative + + +def _as_finite_diff(derivative, points=1, x0=None, wrt=None): + """ + Returns an approximation of a derivative of a function in + the form of a finite difference formula. The expression is a + weighted sum of the function at a number of discrete values of + (one of) the independent variable(s). + + Parameters + ========== + + derivative: a Derivative instance + + points: sequence or coefficient, optional + If sequence: discrete values (length >= order+1) of the + independent variable used for generating the finite + difference weights. + If it is a coefficient, it will be used as the step-size + for generating an equidistant sequence of length order+1 + centered around ``x0``. default: 1 (step-size 1) + + x0: number or Symbol, optional + the value of the independent variable (``wrt``) at which the + derivative is to be approximated. Default: same as ``wrt``. + + wrt: Symbol, optional + "with respect to" the variable for which the (partial) + derivative is to be approximated for. If not provided it + is required that the Derivative is ordinary. Default: ``None``. + + Examples + ======== + + >>> from sympy import symbols, Function, exp, sqrt, Symbol + >>> from sympy.calculus.finite_diff import _as_finite_diff + >>> x, h = symbols('x h') + >>> f = Function('f') + >>> _as_finite_diff(f(x).diff(x)) + -f(x - 1/2) + f(x + 1/2) + + The default step size and number of points are 1 and ``order + 1`` + respectively. We can change the step size by passing a symbol + as a parameter: + + >>> _as_finite_diff(f(x).diff(x), h) + -f(-h/2 + x)/h + f(h/2 + x)/h + + We can also specify the discretized values to be used in a sequence: + + >>> _as_finite_diff(f(x).diff(x), [x, x+h, x+2*h]) + -3*f(x)/(2*h) + 2*f(h + x)/h - f(2*h + x)/(2*h) + + The algorithm is not restricted to use equidistant spacing, nor + do we need to make the approximation around ``x0``, but we can get + an expression estimating the derivative at an offset: + + >>> e, sq2 = exp(1), sqrt(2) + >>> xl = [x-h, x+h, x+e*h] + >>> _as_finite_diff(f(x).diff(x, 1), xl, x+h*sq2) + 2*h*((h + sqrt(2)*h)/(2*h) - (-sqrt(2)*h + h)/(2*h))*f(E*h + x)/((-h + E*h)*(h + E*h)) + + (-(-sqrt(2)*h + h)/(2*h) - (-sqrt(2)*h + E*h)/(2*h))*f(-h + x)/(h + E*h) + + (-(h + sqrt(2)*h)/(2*h) + (-sqrt(2)*h + E*h)/(2*h))*f(h + x)/(-h + E*h) + + Partial derivatives are also supported: + + >>> y = Symbol('y') + >>> d2fdxdy=f(x,y).diff(x,y) + >>> _as_finite_diff(d2fdxdy, wrt=x) + -Derivative(f(x - 1/2, y), y) + Derivative(f(x + 1/2, y), y) + + See also + ======== + + sympy.calculus.finite_diff.apply_finite_diff + sympy.calculus.finite_diff.finite_diff_weights + + """ + if derivative.is_Derivative: + pass + elif derivative.is_Atom: + return derivative + else: + return derivative.fromiter( + [_as_finite_diff(ar, points, x0, wrt) for ar + in derivative.args], **derivative.assumptions0) + + if wrt is None: + old = None + for v in derivative.variables: + if old is v: + continue + derivative = _as_finite_diff(derivative, points, x0, v) + old = v + return derivative + + order = derivative.variables.count(wrt) + + if x0 is None: + x0 = wrt + + if not iterable(points): + if getattr(points, 'is_Function', False) and wrt in points.args: + points = points.subs(wrt, x0) + # points is simply the step-size, let's make it a + # equidistant sequence centered around x0 + if order % 2 == 0: + # even order => odd number of points, grid point included + points = [x0 + points*i for i + in range(-order//2, order//2 + 1)] + else: + # odd order => even number of points, half-way wrt grid point + points = [x0 + points*S(i)/2 for i + in range(-order, order + 1, 2)] + others = [wrt, 0] + for v in set(derivative.variables): + if v == wrt: + continue + others += [v, derivative.variables.count(v)] + if len(points) < order+1: + raise ValueError("Too few points for order %d" % order) + return apply_finite_diff(order, points, [ + Derivative(derivative.expr.subs({wrt: x}), *others) for + x in points], x0) + + +def differentiate_finite(expr, *symbols, + points=1, x0=None, wrt=None, evaluate=False): + r""" Differentiate expr and replace Derivatives with finite differences. + + Parameters + ========== + + expr : expression + \*symbols : differentiate with respect to symbols + points: sequence, coefficient or undefined function, optional + see ``Derivative.as_finite_difference`` + x0: number or Symbol, optional + see ``Derivative.as_finite_difference`` + wrt: Symbol, optional + see ``Derivative.as_finite_difference`` + + Examples + ======== + + >>> from sympy import sin, Function, differentiate_finite + >>> from sympy.abc import x, y, h + >>> f, g = Function('f'), Function('g') + >>> differentiate_finite(f(x)*g(x), x, points=[x-h, x+h]) + -f(-h + x)*g(-h + x)/(2*h) + f(h + x)*g(h + x)/(2*h) + + ``differentiate_finite`` works on any expression, including the expressions + with embedded derivatives: + + >>> differentiate_finite(f(x) + sin(x), x, 2) + -2*f(x) + f(x - 1) + f(x + 1) - 2*sin(x) + sin(x - 1) + sin(x + 1) + >>> differentiate_finite(f(x, y), x, y) + f(x - 1/2, y - 1/2) - f(x - 1/2, y + 1/2) - f(x + 1/2, y - 1/2) + f(x + 1/2, y + 1/2) + >>> differentiate_finite(f(x)*g(x).diff(x), x) + (-g(x) + g(x + 1))*f(x + 1/2) - (g(x) - g(x - 1))*f(x - 1/2) + + To make finite difference with non-constant discretization step use + undefined functions: + + >>> dx = Function('dx') + >>> differentiate_finite(f(x)*g(x).diff(x), points=dx(x)) + -(-g(x - dx(x)/2 - dx(x - dx(x)/2)/2)/dx(x - dx(x)/2) + + g(x - dx(x)/2 + dx(x - dx(x)/2)/2)/dx(x - dx(x)/2))*f(x - dx(x)/2)/dx(x) + + (-g(x + dx(x)/2 - dx(x + dx(x)/2)/2)/dx(x + dx(x)/2) + + g(x + dx(x)/2 + dx(x + dx(x)/2)/2)/dx(x + dx(x)/2))*f(x + dx(x)/2)/dx(x) + + """ + if any(term.is_Derivative for term in list(preorder_traversal(expr))): + evaluate = False + + Dexpr = expr.diff(*symbols, evaluate=evaluate) + if evaluate: + sympy_deprecation_warning(""" + The evaluate flag to differentiate_finite() is deprecated. + + evaluate=True expands the intermediate derivatives before computing + differences, but this usually not what you want, as it does not + satisfy the product rule. + """, + deprecated_since_version="1.5", + active_deprecations_target="deprecated-differentiate_finite-evaluate", + ) + return Dexpr.replace( + lambda arg: arg.is_Derivative, + lambda arg: arg.as_finite_difference(points=points, x0=x0, wrt=wrt)) + else: + DFexpr = Dexpr.as_finite_difference(points=points, x0=x0, wrt=wrt) + return DFexpr.replace( + lambda arg: isinstance(arg, Subs), + lambda arg: arg.expr.as_finite_difference( + points=points, x0=arg.point[0], wrt=arg.variables[0])) diff --git a/lib/python3.11/site-packages/sympy/calculus/singularities.py b/lib/python3.11/site-packages/sympy/calculus/singularities.py new file mode 100644 index 0000000000000000000000000000000000000000..5adafc59efaf0bff44707f6b5e3f074be6bc1f32 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/singularities.py @@ -0,0 +1,406 @@ +""" +Singularities +============= + +This module implements algorithms for finding singularities for a function +and identifying types of functions. + +The differential calculus methods in this module include methods to identify +the following function types in the given ``Interval``: +- Increasing +- Strictly Increasing +- Decreasing +- Strictly Decreasing +- Monotonic + +""" + +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.trigonometric import sec, csc, cot, tan, cos +from sympy.functions.elementary.hyperbolic import ( + sech, csch, coth, tanh, cosh, asech, acsch, atanh, acoth) +from sympy.utilities.misc import filldedent + + +def singularities(expression, symbol, domain=None): + """ + Find singularities of a given function. + + Parameters + ========== + + expression : Expr + The target function in which singularities need to be found. + symbol : Symbol + The symbol over the values of which the singularity in + expression in being searched for. + + Returns + ======= + + Set + A set of values for ``symbol`` for which ``expression`` has a + singularity. An ``EmptySet`` is returned if ``expression`` has no + singularities for any given value of ``Symbol``. + + Raises + ====== + + NotImplementedError + Methods for determining the singularities of this function have + not been developed. + + Notes + ===== + + This function does not find non-isolated singularities + nor does it find branch points of the expression. + + Currently supported functions are: + - univariate continuous (real or complex) functions + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Mathematical_singularity + + Examples + ======== + + >>> from sympy import singularities, Symbol, log + >>> x = Symbol('x', real=True) + >>> y = Symbol('y', real=False) + >>> singularities(x**2 + x + 1, x) + EmptySet + >>> singularities(1/(x + 1), x) + {-1} + >>> singularities(1/(y**2 + 1), y) + {-I, I} + >>> singularities(1/(y**3 + 1), y) + {-1, 1/2 - sqrt(3)*I/2, 1/2 + sqrt(3)*I/2} + >>> singularities(log(x), x) + {0} + + """ + from sympy.solvers.solveset import solveset + + if domain is None: + domain = S.Reals if symbol.is_real else S.Complexes + try: + sings = S.EmptySet + e = expression.rewrite([sec, csc, cot, tan], cos) + e = e.rewrite([sech, csch, coth, tanh], cosh) + for i in e.atoms(Pow): + if i.exp.is_infinite: + raise NotImplementedError + if i.exp.is_negative: + # XXX: exponent of varying sign not handled + sings += solveset(i.base, symbol, domain) + for i in expression.atoms(log, asech, acsch): + sings += solveset(i.args[0], symbol, domain) + for i in expression.atoms(atanh, acoth): + sings += solveset(i.args[0] - 1, symbol, domain) + sings += solveset(i.args[0] + 1, symbol, domain) + return sings + except NotImplementedError: + raise NotImplementedError(filldedent(''' + Methods for determining the singularities + of this function have not been developed.''')) + + +########################################################################### +# DIFFERENTIAL CALCULUS METHODS # +########################################################################### + + +def monotonicity_helper(expression, predicate, interval=S.Reals, symbol=None): + """ + Helper function for functions checking function monotonicity. + + Parameters + ========== + + expression : Expr + The target function which is being checked + predicate : function + The property being tested for. The function takes in an integer + and returns a boolean. The integer input is the derivative and + the boolean result should be true if the property is being held, + and false otherwise. + interval : Set, optional + The range of values in which we are testing, defaults to all reals. + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + It returns a boolean indicating whether the interval in which + the function's derivative satisfies given predicate is a superset + of the given interval. + + Returns + ======= + + Boolean + True if ``predicate`` is true for all the derivatives when ``symbol`` + is varied in ``range``, False otherwise. + + """ + from sympy.solvers.solveset import solveset + + expression = sympify(expression) + free = expression.free_symbols + + if symbol is None: + if len(free) > 1: + raise NotImplementedError( + 'The function has not yet been implemented' + ' for all multivariate expressions.' + ) + + variable = symbol or (free.pop() if free else Symbol('x')) + derivative = expression.diff(variable) + predicate_interval = solveset(predicate(derivative), variable, S.Reals) + return interval.is_subset(predicate_interval) + + +def is_increasing(expression, interval=S.Reals, symbol=None): + """ + Return whether the function is increasing in the given interval. + + Parameters + ========== + + expression : Expr + The target function which is being checked. + interval : Set, optional + The range of values in which we are testing (defaults to set of + all real numbers). + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + Returns + ======= + + Boolean + True if ``expression`` is increasing (either strictly increasing or + constant) in the given ``interval``, False otherwise. + + Examples + ======== + + >>> from sympy import is_increasing + >>> from sympy.abc import x, y + >>> from sympy import S, Interval, oo + >>> is_increasing(x**3 - 3*x**2 + 4*x, S.Reals) + True + >>> is_increasing(-x**2, Interval(-oo, 0)) + True + >>> is_increasing(-x**2, Interval(0, oo)) + False + >>> is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) + False + >>> is_increasing(x**2 + y, Interval(1, 2), x) + True + + """ + return monotonicity_helper(expression, lambda x: x >= 0, interval, symbol) + + +def is_strictly_increasing(expression, interval=S.Reals, symbol=None): + """ + Return whether the function is strictly increasing in the given interval. + + Parameters + ========== + + expression : Expr + The target function which is being checked. + interval : Set, optional + The range of values in which we are testing (defaults to set of + all real numbers). + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + Returns + ======= + + Boolean + True if ``expression`` is strictly increasing in the given ``interval``, + False otherwise. + + Examples + ======== + + >>> from sympy import is_strictly_increasing + >>> from sympy.abc import x, y + >>> from sympy import Interval, oo + >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2)) + True + >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo)) + True + >>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) + False + >>> is_strictly_increasing(-x**2, Interval(0, oo)) + False + >>> is_strictly_increasing(-x**2 + y, Interval(-oo, 0), x) + False + + """ + return monotonicity_helper(expression, lambda x: x > 0, interval, symbol) + + +def is_decreasing(expression, interval=S.Reals, symbol=None): + """ + Return whether the function is decreasing in the given interval. + + Parameters + ========== + + expression : Expr + The target function which is being checked. + interval : Set, optional + The range of values in which we are testing (defaults to set of + all real numbers). + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + Returns + ======= + + Boolean + True if ``expression`` is decreasing (either strictly decreasing or + constant) in the given ``interval``, False otherwise. + + Examples + ======== + + >>> from sympy import is_decreasing + >>> from sympy.abc import x, y + >>> from sympy import S, Interval, oo + >>> is_decreasing(1/(x**2 - 3*x), Interval.open(S(3)/2, 3)) + True + >>> is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3)) + True + >>> is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + True + >>> is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2)) + False + >>> is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, 1.5)) + False + >>> is_decreasing(-x**2, Interval(-oo, 0)) + False + >>> is_decreasing(-x**2 + y, Interval(-oo, 0), x) + False + + """ + return monotonicity_helper(expression, lambda x: x <= 0, interval, symbol) + + +def is_strictly_decreasing(expression, interval=S.Reals, symbol=None): + """ + Return whether the function is strictly decreasing in the given interval. + + Parameters + ========== + + expression : Expr + The target function which is being checked. + interval : Set, optional + The range of values in which we are testing (defaults to set of + all real numbers). + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + Returns + ======= + + Boolean + True if ``expression`` is strictly decreasing in the given ``interval``, + False otherwise. + + Examples + ======== + + >>> from sympy import is_strictly_decreasing + >>> from sympy.abc import x, y + >>> from sympy import S, Interval, oo + >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + True + >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2)) + False + >>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, 1.5)) + False + >>> is_strictly_decreasing(-x**2, Interval(-oo, 0)) + False + >>> is_strictly_decreasing(-x**2 + y, Interval(-oo, 0), x) + False + + """ + return monotonicity_helper(expression, lambda x: x < 0, interval, symbol) + + +def is_monotonic(expression, interval=S.Reals, symbol=None): + """ + Return whether the function is monotonic in the given interval. + + Parameters + ========== + + expression : Expr + The target function which is being checked. + interval : Set, optional + The range of values in which we are testing (defaults to set of + all real numbers). + symbol : Symbol, optional + The symbol present in expression which gets varied over the given range. + + Returns + ======= + + Boolean + True if ``expression`` is monotonic in the given ``interval``, + False otherwise. + + Raises + ====== + + NotImplementedError + Monotonicity check has not been implemented for the queried function. + + Examples + ======== + + >>> from sympy import is_monotonic + >>> from sympy.abc import x, y + >>> from sympy import S, Interval, oo + >>> is_monotonic(1/(x**2 - 3*x), Interval.open(S(3)/2, 3)) + True + >>> is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3)) + True + >>> is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + True + >>> is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals) + True + >>> is_monotonic(-x**2, S.Reals) + False + >>> is_monotonic(x**2 + y + 1, Interval(1, 2), x) + True + + """ + from sympy.solvers.solveset import solveset + + expression = sympify(expression) + + free = expression.free_symbols + if symbol is None and len(free) > 1: + raise NotImplementedError( + 'is_monotonic has not yet been implemented' + ' for all multivariate expressions.' + ) + + variable = symbol or (free.pop() if free else Symbol('x')) + turning_points = solveset(expression.diff(variable), variable, interval) + return interval.intersection(turning_points) is S.EmptySet diff --git a/lib/python3.11/site-packages/sympy/calculus/tests/__init__.py b/lib/python3.11/site-packages/sympy/calculus/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git 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b/lib/python3.11/site-packages/sympy/calculus/tests/test_accumulationbounds.py @@ -0,0 +1,336 @@ +from sympy.core.numbers import (E, Rational, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt) +from sympy.functions.elementary.trigonometric import (cos, sin, tan) +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.core import Add, Mul, Pow +from sympy.core.expr import unchanged +from sympy.testing.pytest import raises, XFAIL +from sympy.abc import x + +a = Symbol('a', real=True) +B = AccumBounds + + +def test_AccumBounds(): + assert B(1, 2).args == (1, 2) + assert B(1, 2).delta is S.One + assert B(1, 2).mid == Rational(3, 2) + assert B(1, 3).is_real == True + + assert B(1, 1) is S.One + + assert B(1, 2) + 1 == B(2, 3) + assert 1 + B(1, 2) == B(2, 3) + assert B(1, 2) + B(2, 3) == B(3, 5) + + assert -B(1, 2) == B(-2, -1) + + assert B(1, 2) - 1 == B(0, 1) + assert 1 - B(1, 2) == B(-1, 0) + assert B(2, 3) - B(1, 2) == B(0, 2) + + assert x + B(1, 2) == Add(B(1, 2), x) + assert a + B(1, 2) == B(1 + a, 2 + a) + assert B(1, 2) - x == Add(B(1, 2), -x) + + assert B(-oo, 1) + oo == B(-oo, oo) + assert B(1, oo) + oo is oo + assert B(1, oo) - oo == B(-oo, oo) + assert (-oo - B(-1, oo)) is -oo + assert B(-oo, 1) - oo is -oo + + assert B(1, oo) - oo == B(-oo, oo) + assert B(-oo, 1) - (-oo) == B(-oo, oo) + assert (oo - B(1, oo)) == B(-oo, oo) + assert (-oo - B(1, oo)) is -oo + + assert B(1, 2)/2 == B(S.Half, 1) + assert 2/B(2, 3) == B(Rational(2, 3), 1) + assert 1/B(-1, 1) == B(-oo, oo) + + assert abs(B(1, 2)) == B(1, 2) + assert abs(B(-2, -1)) == B(1, 2) + assert abs(B(-2, 1)) == B(0, 2) + assert abs(B(-1, 2)) == B(0, 2) + c = Symbol('c') + raises(ValueError, lambda: B(0, c)) + raises(ValueError, lambda: B(1, -1)) + r = Symbol('r', real=True) + raises(ValueError, lambda: B(r, r - 1)) + + +def test_AccumBounds_mul(): + assert B(1, 2)*2 == B(2, 4) + assert 2*B(1, 2) == B(2, 4) + assert B(1, 2)*B(2, 3) == B(2, 6) + assert B(0, 2)*B(2, oo) == B(0, oo) + l, r = B(-oo, oo), B(-a, a) + assert l*r == B(-oo, oo) + assert r*l == B(-oo, oo) + l, r = B(1, oo), B(-3, -2) + assert l*r == B(-oo, -2) + assert r*l == B(-oo, -2) + assert B(1, 2)*0 == 0 + assert B(1, oo)*0 == B(0, oo) + assert B(-oo, 1)*0 == B(-oo, 0) + assert B(-oo, oo)*0 == B(-oo, oo) + + assert B(1, 2)*x == Mul(B(1, 2), x, evaluate=False) + + assert B(0, 2)*oo == B(0, oo) + assert B(-2, 0)*oo == B(-oo, 0) + assert B(0, 2)*(-oo) == B(-oo, 0) + assert B(-2, 0)*(-oo) == B(0, oo) + assert B(-1, 1)*oo == B(-oo, oo) + assert B(-1, 1)*(-oo) == B(-oo, oo) + assert B(-oo, oo)*oo == B(-oo, oo) + + +def test_AccumBounds_div(): + assert B(-1, 3)/B(3, 4) == B(Rational(-1, 3), 1) + assert B(-2, 4)/B(-3, 4) == B(-oo, oo) + assert B(-3, -2)/B(-4, 0) == B(S.Half, oo) + + # these two tests can have a better answer + # after Union of B is improved + assert B(-3, -2)/B(-2, 1) == B(-oo, oo) + assert B(2, 3)/B(-2, 2) == B(-oo, oo) + + assert B(-3, -2)/B(0, 4) == B(-oo, Rational(-1, 2)) + assert B(2, 4)/B(-3, 0) == B(-oo, Rational(-2, 3)) + assert B(2, 4)/B(0, 3) == B(Rational(2, 3), oo) + + assert B(0, 1)/B(0, 1) == B(0, oo) + assert B(-1, 0)/B(0, 1) == B(-oo, 0) + assert B(-1, 2)/B(-2, 2) == B(-oo, oo) + + assert 1/B(-1, 2) == B(-oo, oo) + assert 1/B(0, 2) == B(S.Half, oo) + assert (-1)/B(0, 2) == B(-oo, Rational(-1, 2)) + assert 1/B(-oo, 0) == B(-oo, 0) + assert 1/B(-1, 0) == B(-oo, -1) + assert (-2)/B(-oo, 0) == B(0, oo) + assert 1/B(-oo, -1) == B(-1, 0) + + assert B(1, 2)/a == Mul(B(1, 2), 1/a, evaluate=False) + + assert B(1, 2)/0 == B(1, 2)*zoo + assert B(1, oo)/oo == B(0, oo) + assert B(1, oo)/(-oo) == B(-oo, 0) + assert B(-oo, -1)/oo == B(-oo, 0) + assert B(-oo, -1)/(-oo) == B(0, oo) + assert B(-oo, oo)/oo == B(-oo, oo) + assert B(-oo, oo)/(-oo) == B(-oo, oo) + assert B(-1, oo)/oo == B(0, oo) + assert B(-1, oo)/(-oo) == B(-oo, 0) + assert B(-oo, 1)/oo == B(-oo, 0) + assert B(-oo, 1)/(-oo) == B(0, oo) + + +def test_issue_18795(): + r = Symbol('r', real=True) + a = B(-1,1) + c = B(7, oo) + b = B(-oo, oo) + assert c - tan(r) == B(7-tan(r), oo) + assert b + tan(r) == B(-oo, oo) + assert (a + r)/a == B(-oo, oo)*B(r - 1, r + 1) + assert (b + a)/a == B(-oo, oo) + + +def test_AccumBounds_func(): + assert (x**2 + 2*x + 1).subs(x, B(-1, 1)) == B(-1, 4) + assert exp(B(0, 1)) == B(1, E) + assert exp(B(-oo, oo)) == B(0, oo) + assert log(B(3, 6)) == B(log(3), log(6)) + + +@XFAIL +def test_AccumBounds_powf(): + nn = Symbol('nn', nonnegative=True) + assert B(1 + nn, 2 + nn)**B(1, 2) == B(1 + nn, (2 + nn)**2) + i = Symbol('i', integer=True, negative=True) + assert B(1, 2)**i == B(2**i, 1) + + +def test_AccumBounds_pow(): + assert B(0, 2)**2 == B(0, 4) + assert B(-1, 1)**2 == B(0, 1) + assert B(1, 2)**2 == B(1, 4) + assert B(-1, 2)**3 == B(-1, 8) + assert B(-1, 1)**0 == 1 + + assert B(1, 2)**Rational(5, 2) == B(1, 4*sqrt(2)) + assert B(0, 2)**S.Half == B(0, sqrt(2)) + + neg = Symbol('neg', negative=True) + assert unchanged(Pow, B(neg, 1), S.Half) + nn = Symbol('nn', nonnegative=True) + assert B(nn, nn + 1)**S.Half == B(sqrt(nn), sqrt(nn + 1)) + assert B(nn, nn + 1)**nn == B(nn**nn, (nn + 1)**nn) + assert unchanged(Pow, B(nn, nn + 1), x) + i = Symbol('i', integer=True) + assert B(1, 2)**i == B(Min(1, 2**i), Max(1, 2**i)) + i = Symbol('i', integer=True, nonnegative=True) + assert B(1, 2)**i == B(1, 2**i) + assert B(0, 1)**i == B(0**i, 1) + + assert B(1, 5)**(-2) == B(Rational(1, 25), 1) + assert B(-1, 3)**(-2) == B(0, oo) + assert B(0, 2)**(-3) == B(Rational(1, 8), oo) + assert B(-2, 0)**(-3) == B(-oo, -Rational(1, 8)) + assert B(0, 2)**(-2) == B(Rational(1, 4), oo) + assert B(-1, 2)**(-3) == B(-oo, oo) + assert B(-3, -2)**(-3) == B(Rational(-1, 8), Rational(-1, 27)) + assert B(-3, -2)**(-2) == B(Rational(1, 9), Rational(1, 4)) + assert B(0, oo)**S.Half == B(0, oo) + assert B(-oo, 0)**(-2) == B(0, oo) + assert B(-2, 0)**(-2) == B(Rational(1, 4), oo) + + assert B(Rational(1, 3), S.Half)**oo is S.Zero + assert B(0, S.Half)**oo is S.Zero + assert B(S.Half, 1)**oo == B(0, oo) + assert B(0, 1)**oo == B(0, oo) + assert B(2, 3)**oo is oo + assert B(1, 2)**oo == B(0, oo) + assert B(S.Half, 3)**oo == B(0, oo) + assert B(Rational(-1, 3), Rational(-1, 4))**oo is S.Zero + assert B(-1, Rational(-1, 2))**oo is S.NaN + assert B(-3, -2)**oo is zoo + assert B(-2, -1)**oo is S.NaN + assert B(-2, Rational(-1, 2))**oo is S.NaN + assert B(Rational(-1, 2), S.Half)**oo is S.Zero + assert B(Rational(-1, 2), 1)**oo == B(0, oo) + assert B(Rational(-2, 3), 2)**oo == B(0, oo) + assert B(-1, 1)**oo == B(-oo, oo) + assert B(-1, S.Half)**oo == B(-oo, oo) + assert B(-1, 2)**oo == B(-oo, oo) + assert B(-2, S.Half)**oo == B(-oo, oo) + + assert B(1, 2)**x == Pow(B(1, 2), x, evaluate=False) + + assert B(2, 3)**(-oo) is S.Zero + assert B(0, 2)**(-oo) == B(0, oo) + assert B(-1, 2)**(-oo) == B(-oo, oo) + + assert (tan(x)**sin(2*x)).subs(x, B(0, pi/2)) == \ + Pow(B(-oo, oo), B(0, 1)) + + +def test_AccumBounds_exponent(): + # base is 0 + z = 0**B(a, a + S.Half) + assert z.subs(a, 0) == B(0, 1) + assert z.subs(a, 1) == 0 + p = z.subs(a, -1) + assert p.is_Pow and p.args == (0, B(-1, -S.Half)) + # base > 0 + # when base is 1 the type of bounds does not matter + assert 1**B(a, a + 1) == 1 + # otherwise we need to know if 0 is in the bounds + assert S.Half**B(-2, 2) == B(S(1)/4, 4) + assert 2**B(-2, 2) == B(S(1)/4, 4) + + # +eps may introduce +oo + # if there is a negative integer exponent + assert B(0, 1)**B(S(1)/2, 1) == B(0, 1) + assert B(0, 1)**B(0, 1) == B(0, 1) + + # positive bases have positive bounds + assert B(2, 3)**B(-3, -2) == B(S(1)/27, S(1)/4) + assert B(2, 3)**B(-3, 2) == B(S(1)/27, 9) + + # bounds generating imaginary parts unevaluated + assert unchanged(Pow, B(-1, 1), B(1, 2)) + assert B(0, S(1)/2)**B(1, oo) == B(0, S(1)/2) + assert B(0, 1)**B(1, oo) == B(0, oo) + assert B(0, 2)**B(1, oo) == B(0, oo) + assert B(0, oo)**B(1, oo) == B(0, oo) + assert B(S(1)/2, 1)**B(1, oo) == B(0, oo) + assert B(S(1)/2, 1)**B(-oo, -1) == B(0, oo) + assert B(S(1)/2, 1)**B(-oo, oo) == B(0, oo) + assert B(S(1)/2, 2)**B(1, oo) == B(0, oo) + assert B(S(1)/2, 2)**B(-oo, -1) == B(0, oo) + assert B(S(1)/2, 2)**B(-oo, oo) == B(0, oo) + assert B(S(1)/2, oo)**B(1, oo) == B(0, oo) + assert B(S(1)/2, oo)**B(-oo, -1) == B(0, oo) + assert B(S(1)/2, oo)**B(-oo, oo) == B(0, oo) + assert B(1, 2)**B(1, oo) == B(0, oo) + assert B(1, 2)**B(-oo, -1) == B(0, oo) + assert B(1, 2)**B(-oo, oo) == B(0, oo) + assert B(1, oo)**B(1, oo) == B(0, oo) + assert B(1, oo)**B(-oo, -1) == B(0, oo) + assert B(1, oo)**B(-oo, oo) == B(0, oo) + assert B(2, oo)**B(1, oo) == B(2, oo) + assert B(2, oo)**B(-oo, -1) == B(0, S(1)/2) + assert B(2, oo)**B(-oo, oo) == B(0, oo) + + +def test_comparison_AccumBounds(): + assert (B(1, 3) < 4) == S.true + assert (B(1, 3) < -1) == S.false + assert (B(1, 3) < 2).rel_op == '<' + assert (B(1, 3) <= 2).rel_op == '<=' + + assert (B(1, 3) > 4) == S.false + assert (B(1, 3) > -1) == S.true + assert (B(1, 3) > 2).rel_op == '>' + assert (B(1, 3) >= 2).rel_op == '>=' + + assert (B(1, 3) < B(4, 6)) == S.true + assert (B(1, 3) < B(2, 4)).rel_op == '<' + assert (B(1, 3) < B(-2, 0)) == S.false + + assert (B(1, 3) <= B(4, 6)) == S.true + assert (B(1, 3) <= B(-2, 0)) == S.false + + assert (B(1, 3) > B(4, 6)) == S.false + assert (B(1, 3) > B(-2, 0)) == S.true + + assert (B(1, 3) >= B(4, 6)) == S.false + assert (B(1, 3) >= B(-2, 0)) == S.true + + # issue 13499 + assert (cos(x) > 0).subs(x, oo) == (B(-1, 1) > 0) + + c = Symbol('c') + raises(TypeError, lambda: (B(0, 1) < c)) + raises(TypeError, lambda: (B(0, 1) <= c)) + raises(TypeError, lambda: (B(0, 1) > c)) + raises(TypeError, lambda: (B(0, 1) >= c)) + + +def test_contains_AccumBounds(): + assert (1 in B(1, 2)) == S.true + raises(TypeError, lambda: a in B(1, 2)) + assert 0 in B(-1, 0) + raises(TypeError, lambda: + (cos(1)**2 + sin(1)**2 - 1) in B(-1, 0)) + assert (-oo in B(1, oo)) == S.true + assert (oo in B(-oo, 0)) == S.true + + # issue 13159 + assert Mul(0, B(-1, 1)) == Mul(B(-1, 1), 0) == 0 + import itertools + for perm in itertools.permutations([0, B(-1, 1), x]): + assert Mul(*perm) == 0 + + +def test_intersection_AccumBounds(): + assert B(0, 3).intersection(B(1, 2)) == B(1, 2) + assert B(0, 3).intersection(B(1, 4)) == B(1, 3) + assert B(0, 3).intersection(B(-1, 2)) == B(0, 2) + assert B(0, 3).intersection(B(-1, 4)) == B(0, 3) + assert B(0, 1).intersection(B(2, 3)) == S.EmptySet + raises(TypeError, lambda: B(0, 3).intersection(1)) + + +def test_union_AccumBounds(): + assert B(0, 3).union(B(1, 2)) == B(0, 3) + assert B(0, 3).union(B(1, 4)) == B(0, 4) + assert B(0, 3).union(B(-1, 2)) == B(-1, 3) + assert B(0, 3).union(B(-1, 4)) == B(-1, 4) + raises(TypeError, lambda: B(0, 3).union(1)) diff --git a/lib/python3.11/site-packages/sympy/calculus/tests/test_euler.py b/lib/python3.11/site-packages/sympy/calculus/tests/test_euler.py new file mode 100644 index 0000000000000000000000000000000000000000..56371c8c787d9459d1390e18c306fddde94d2745 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/tests/test_euler.py @@ -0,0 +1,74 @@ +from sympy.core.function import (Derivative as D, Function) +from sympy.core.relational import Eq +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.testing.pytest import raises +from sympy.calculus.euler import euler_equations as euler + + +def test_euler_interface(): + x = Function('x') + y = Symbol('y') + t = Symbol('t') + raises(TypeError, lambda: euler()) + raises(TypeError, lambda: euler(D(x(t), t)*y(t), [x(t), y])) + raises(ValueError, lambda: euler(D(x(t), t)*x(y), [x(t), x(y)])) + raises(TypeError, lambda: euler(D(x(t), t)**2, x(0))) + raises(TypeError, lambda: euler(D(x(t), t)*y(t), [t])) + assert euler(D(x(t), t)**2/2, {x(t)}) == [Eq(-D(x(t), t, t), 0)] + assert euler(D(x(t), t)**2/2, x(t), {t}) == [Eq(-D(x(t), t, t), 0)] + + +def test_euler_pendulum(): + x = Function('x') + t = Symbol('t') + L = D(x(t), t)**2/2 + cos(x(t)) + assert euler(L, x(t), t) == [Eq(-sin(x(t)) - D(x(t), t, t), 0)] + + +def test_euler_henonheiles(): + x = Function('x') + y = Function('y') + t = Symbol('t') + L = sum(D(z(t), t)**2/2 - z(t)**2/2 for z in [x, y]) + L += -x(t)**2*y(t) + y(t)**3/3 + assert euler(L, [x(t), y(t)], t) == [Eq(-2*x(t)*y(t) - x(t) - + D(x(t), t, t), 0), + Eq(-x(t)**2 + y(t)**2 - + y(t) - D(y(t), t, t), 0)] + + +def test_euler_sineg(): + psi = Function('psi') + t = Symbol('t') + x = Symbol('x') + L = D(psi(t, x), t)**2/2 - D(psi(t, x), x)**2/2 + cos(psi(t, x)) + assert euler(L, psi(t, x), [t, x]) == [Eq(-sin(psi(t, x)) - + D(psi(t, x), t, t) + + D(psi(t, x), x, x), 0)] + + +def test_euler_high_order(): + # an example from hep-th/0309038 + m = Symbol('m') + k = Symbol('k') + x = Function('x') + y = Function('y') + t = Symbol('t') + L = (m*D(x(t), t)**2/2 + m*D(y(t), t)**2/2 - + k*D(x(t), t)*D(y(t), t, t) + k*D(y(t), t)*D(x(t), t, t)) + assert euler(L, [x(t), y(t)]) == [Eq(2*k*D(y(t), t, t, t) - + m*D(x(t), t, t), 0), + Eq(-2*k*D(x(t), t, t, t) - + m*D(y(t), t, t), 0)] + + w = Symbol('w') + L = D(x(t, w), t, w)**2/2 + assert euler(L) == [Eq(D(x(t, w), t, t, w, w), 0)] + +def test_issue_18653(): + x, y, z = symbols("x y z") + f, g, h = symbols("f g h", cls=Function, args=(x, y)) + f, g, h = f(), g(), h() + expr2 = f.diff(x)*h.diff(z) + assert euler(expr2, (f,), (x, y)) == [] diff --git a/lib/python3.11/site-packages/sympy/calculus/tests/test_finite_diff.py b/lib/python3.11/site-packages/sympy/calculus/tests/test_finite_diff.py new file mode 100644 index 0000000000000000000000000000000000000000..ce695c6c6ac7aa86a8a8545e81458236a0ebda9c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/tests/test_finite_diff.py @@ -0,0 +1,168 @@ +from itertools import product + +from sympy.core.function import (Function, diff) +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import exp +from sympy.calculus.finite_diff import ( + apply_finite_diff, differentiate_finite, finite_diff_weights, + _as_finite_diff +) +from sympy.testing.pytest import raises, warns_deprecated_sympy + + +def test_apply_finite_diff(): + x, h = symbols('x h') + f = Function('f') + assert (apply_finite_diff(1, [x-h, x+h], [f(x-h), f(x+h)], x) - + (f(x+h)-f(x-h))/(2*h)).simplify() == 0 + + assert (apply_finite_diff(1, [5, 6, 7], [f(5), f(6), f(7)], 5) - + (Rational(-3, 2)*f(5) + 2*f(6) - S.Half*f(7))).simplify() == 0 + raises(ValueError, lambda: apply_finite_diff(1, [x, h], [f(x)])) + + +def test_finite_diff_weights(): + + d = finite_diff_weights(1, [5, 6, 7], 5) + assert d[1][2] == [Rational(-3, 2), 2, Rational(-1, 2)] + + # Table 1, p. 702 in doi:10.1090/S0025-5718-1988-0935077-0 + # -------------------------------------------------------- + xl = [0, 1, -1, 2, -2, 3, -3, 4, -4] + + # d holds all coefficients + d = finite_diff_weights(4, xl, S.Zero) + + # Zeroeth derivative + for i in range(5): + assert d[0][i] == [S.One] + [S.Zero]*8 + + # First derivative + assert d[1][0] == [S.Zero]*9 + assert d[1][2] == [S.Zero, S.Half, Rational(-1, 2)] + [S.Zero]*6 + assert d[1][4] == [S.Zero, Rational(2, 3), Rational(-2, 3), Rational(-1, 12), Rational(1, 12)] + [S.Zero]*4 + assert d[1][6] == [S.Zero, Rational(3, 4), Rational(-3, 4), Rational(-3, 20), Rational(3, 20), + Rational(1, 60), Rational(-1, 60)] + [S.Zero]*2 + assert d[1][8] == [S.Zero, Rational(4, 5), Rational(-4, 5), Rational(-1, 5), Rational(1, 5), + Rational(4, 105), Rational(-4, 105), Rational(-1, 280), Rational(1, 280)] + + # Second derivative + for i in range(2): + assert d[2][i] == [S.Zero]*9 + assert d[2][2] == [-S(2), S.One, S.One] + [S.Zero]*6 + assert d[2][4] == [Rational(-5, 2), Rational(4, 3), Rational(4, 3), Rational(-1, 12), Rational(-1, 12)] + [S.Zero]*4 + assert d[2][6] == [Rational(-49, 18), Rational(3, 2), Rational(3, 2), Rational(-3, 20), Rational(-3, 20), + Rational(1, 90), Rational(1, 90)] + [S.Zero]*2 + assert d[2][8] == [Rational(-205, 72), Rational(8, 5), Rational(8, 5), Rational(-1, 5), Rational(-1, 5), + Rational(8, 315), Rational(8, 315), Rational(-1, 560), Rational(-1, 560)] + + # Third derivative + for i in range(3): + assert d[3][i] == [S.Zero]*9 + assert d[3][4] == [S.Zero, -S.One, S.One, S.Half, Rational(-1, 2)] + [S.Zero]*4 + assert d[3][6] == [S.Zero, Rational(-13, 8), Rational(13, 8), S.One, -S.One, + Rational(-1, 8), Rational(1, 8)] + [S.Zero]*2 + assert d[3][8] == [S.Zero, Rational(-61, 30), Rational(61, 30), Rational(169, 120), Rational(-169, 120), + Rational(-3, 10), Rational(3, 10), Rational(7, 240), Rational(-7, 240)] + + # Fourth derivative + for i in range(4): + assert d[4][i] == [S.Zero]*9 + assert d[4][4] == [S(6), -S(4), -S(4), S.One, S.One] + [S.Zero]*4 + assert d[4][6] == [Rational(28, 3), Rational(-13, 2), Rational(-13, 2), S(2), S(2), + Rational(-1, 6), Rational(-1, 6)] + [S.Zero]*2 + assert d[4][8] == [Rational(91, 8), Rational(-122, 15), Rational(-122, 15), Rational(169, 60), Rational(169, 60), + Rational(-2, 5), Rational(-2, 5), Rational(7, 240), Rational(7, 240)] + + # Table 2, p. 703 in doi:10.1090/S0025-5718-1988-0935077-0 + # -------------------------------------------------------- + xl = [[j/S(2) for j in list(range(-i*2+1, 0, 2))+list(range(1, i*2+1, 2))] + for i in range(1, 5)] + + # d holds all coefficients + d = [finite_diff_weights({0: 1, 1: 2, 2: 4, 3: 4}[i], xl[i], 0) for + i in range(4)] + + # Zeroth derivative + assert d[0][0][1] == [S.Half, S.Half] + assert d[1][0][3] == [Rational(-1, 16), Rational(9, 16), Rational(9, 16), Rational(-1, 16)] + assert d[2][0][5] == [Rational(3, 256), Rational(-25, 256), Rational(75, 128), Rational(75, 128), + Rational(-25, 256), Rational(3, 256)] + assert d[3][0][7] == [Rational(-5, 2048), Rational(49, 2048), Rational(-245, 2048), Rational(1225, 2048), + Rational(1225, 2048), Rational(-245, 2048), Rational(49, 2048), Rational(-5, 2048)] + + # First derivative + assert d[0][1][1] == [-S.One, S.One] + assert d[1][1][3] == [Rational(1, 24), Rational(-9, 8), Rational(9, 8), Rational(-1, 24)] + assert d[2][1][5] == [Rational(-3, 640), Rational(25, 384), Rational(-75, 64), + Rational(75, 64), Rational(-25, 384), Rational(3, 640)] + assert d[3][1][7] == [Rational(5, 7168), Rational(-49, 5120), + Rational(245, 3072), Rational(-1225, 1024), + Rational(1225, 1024), Rational(-245, 3072), + Rational(49, 5120), Rational(-5, 7168)] + + # Reasonably the rest of the table is also correct... (testing of that + # deemed excessive at the moment) + raises(ValueError, lambda: finite_diff_weights(-1, [1, 2])) + raises(ValueError, lambda: finite_diff_weights(1.2, [1, 2])) + x = symbols('x') + raises(ValueError, lambda: finite_diff_weights(x, [1, 2])) + + +def test_as_finite_diff(): + x = symbols('x') + f = Function('f') + dx = Function('dx') + + _as_finite_diff(f(x).diff(x), [x-2, x-1, x, x+1, x+2]) + + # Use of undefined functions in ``points`` + df_true = -f(x+dx(x)/2-dx(x+dx(x)/2)/2) / dx(x+dx(x)/2) \ + + f(x+dx(x)/2+dx(x+dx(x)/2)/2) / dx(x+dx(x)/2) + df_test = diff(f(x), x).as_finite_difference(points=dx(x), x0=x+dx(x)/2) + assert (df_test - df_true).simplify() == 0 + + +def test_differentiate_finite(): + x, y, h = symbols('x y h') + f = Function('f') + with warns_deprecated_sympy(): + res0 = differentiate_finite(f(x, y) + exp(42), x, y, evaluate=True) + xm, xp, ym, yp = [v + sign*S.Half for v, sign in product([x, y], [-1, 1])] + ref0 = f(xm, ym) + f(xp, yp) - f(xm, yp) - f(xp, ym) + assert (res0 - ref0).simplify() == 0 + + g = Function('g') + with warns_deprecated_sympy(): + res1 = differentiate_finite(f(x)*g(x) + 42, x, evaluate=True) + ref1 = (-f(x - S.Half) + f(x + S.Half))*g(x) + \ + (-g(x - S.Half) + g(x + S.Half))*f(x) + assert (res1 - ref1).simplify() == 0 + + res2 = differentiate_finite(f(x) + x**3 + 42, x, points=[x-1, x+1]) + ref2 = (f(x + 1) + (x + 1)**3 - f(x - 1) - (x - 1)**3)/2 + assert (res2 - ref2).simplify() == 0 + raises(TypeError, lambda: differentiate_finite(f(x)*g(x), x, + pints=[x-1, x+1])) + + res3 = differentiate_finite(f(x)*g(x).diff(x), x) + ref3 = (-g(x) + g(x + 1))*f(x + S.Half) - (g(x) - g(x - 1))*f(x - S.Half) + assert res3 == ref3 + + res4 = differentiate_finite(f(x)*g(x).diff(x).diff(x), x) + ref4 = -((g(x - Rational(3, 2)) - 2*g(x - S.Half) + g(x + S.Half))*f(x - S.Half)) \ + + (g(x - S.Half) - 2*g(x + S.Half) + g(x + Rational(3, 2)))*f(x + S.Half) + assert res4 == ref4 + + res5_expr = f(x).diff(x)*g(x).diff(x) + res5 = differentiate_finite(res5_expr, points=[x-h, x, x+h]) + ref5 = (-2*f(x)/h + f(-h + x)/(2*h) + 3*f(h + x)/(2*h))*(-2*g(x)/h + g(-h + x)/(2*h) \ + + 3*g(h + x)/(2*h))/(2*h) - (2*f(x)/h - 3*f(-h + x)/(2*h) - \ + f(h + x)/(2*h))*(2*g(x)/h - 3*g(-h + x)/(2*h) - g(h + x)/(2*h))/(2*h) + assert res5 == ref5 + + res6 = res5.limit(h, 0).doit() + ref6 = diff(res5_expr, x) + assert res6 == ref6 diff --git a/lib/python3.11/site-packages/sympy/calculus/tests/test_singularities.py b/lib/python3.11/site-packages/sympy/calculus/tests/test_singularities.py new file mode 100644 index 0000000000000000000000000000000000000000..19a042332326658021ce12a38f4e058f55903869 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/tests/test_singularities.py @@ -0,0 +1,122 @@ +from sympy.core.numbers import (I, Rational, pi, oo) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol, Dummy +from sympy.core.function import Lambda +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.trigonometric import sec, csc +from sympy.functions.elementary.hyperbolic import (coth, sech, + atanh, asech, acoth, acsch) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.calculus.singularities import ( + singularities, + is_increasing, + is_strictly_increasing, + is_decreasing, + is_strictly_decreasing, + is_monotonic +) +from sympy.sets import Interval, FiniteSet, Union, ImageSet +from sympy.testing.pytest import raises +from sympy.abc import x, y + + +def test_singularities(): + x = Symbol('x') + assert singularities(x**2, x) == S.EmptySet + assert singularities(x/(x**2 + 3*x + 2), x) == FiniteSet(-2, -1) + assert singularities(1/(x**2 + 1), x) == FiniteSet(I, -I) + assert singularities(x/(x**3 + 1), x) == \ + FiniteSet(-1, (1 - sqrt(3) * I) / 2, (1 + sqrt(3) * I) / 2) + assert singularities(1/(y**2 + 2*I*y + 1), y) == \ + FiniteSet(-I + sqrt(2)*I, -I - sqrt(2)*I) + _n = Dummy('n') + assert singularities(sech(x), x).dummy_eq(Union( + ImageSet(Lambda(_n, 2*_n*I*pi + I*pi/2), S.Integers), + ImageSet(Lambda(_n, 2*_n*I*pi + 3*I*pi/2), S.Integers))) + assert singularities(coth(x), x).dummy_eq(Union( + ImageSet(Lambda(_n, 2*_n*I*pi + I*pi), S.Integers), + ImageSet(Lambda(_n, 2*_n*I*pi), S.Integers))) + assert singularities(atanh(x), x) == FiniteSet(-1, 1) + assert singularities(acoth(x), x) == FiniteSet(-1, 1) + assert singularities(asech(x), x) == FiniteSet(0) + assert singularities(acsch(x), x) == FiniteSet(0) + + x = Symbol('x', real=True) + assert singularities(1/(x**2 + 1), x) == S.EmptySet + assert singularities(exp(1/x), x, S.Reals) == FiniteSet(0) + assert singularities(exp(1/x), x, Interval(1, 2)) == S.EmptySet + assert singularities(log((x - 2)**2), x, Interval(1, 3)) == FiniteSet(2) + raises(NotImplementedError, lambda: singularities(x**-oo, x)) + assert singularities(sec(x), x, Interval(0, 3*pi)) == FiniteSet( + pi/2, 3*pi/2, 5*pi/2) + assert singularities(csc(x), x, Interval(0, 3*pi)) == FiniteSet( + 0, pi, 2*pi, 3*pi) + + +def test_is_increasing(): + """Test whether is_increasing returns correct value.""" + a = Symbol('a', negative=True) + + assert is_increasing(x**3 - 3*x**2 + 4*x, S.Reals) + assert is_increasing(-x**2, Interval(-oo, 0)) + assert not is_increasing(-x**2, Interval(0, oo)) + assert not is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) + assert is_increasing(x**2 + y, Interval(1, oo), x) + assert is_increasing(-x**2*a, Interval(1, oo), x) + assert is_increasing(1) + + assert is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) is False + + +def test_is_strictly_increasing(): + """Test whether is_strictly_increasing returns correct value.""" + assert is_strictly_increasing( + 4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2)) + assert is_strictly_increasing( + 4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo)) + assert not is_strictly_increasing( + 4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) + assert not is_strictly_increasing(-x**2, Interval(0, oo)) + assert not is_strictly_decreasing(1) + + assert is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) is False + + +def test_is_decreasing(): + """Test whether is_decreasing returns correct value.""" + b = Symbol('b', positive=True) + + assert is_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3)) + assert is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3)) + assert is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + assert not is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2))) + assert not is_decreasing(-x**2, Interval(-oo, 0)) + assert not is_decreasing(-x**2*b, Interval(-oo, 0), x) + + +def test_is_strictly_decreasing(): + """Test whether is_strictly_decreasing returns correct value.""" + assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + assert not is_strictly_decreasing( + 1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2))) + assert not is_strictly_decreasing(-x**2, Interval(-oo, 0)) + assert not is_strictly_decreasing(1) + assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3)) + assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3)) + + +def test_is_monotonic(): + """Test whether is_monotonic returns correct value.""" + assert is_monotonic(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3)) + assert is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3)) + assert is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo)) + assert is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals) + assert not is_monotonic(-x**2, S.Reals) + assert is_monotonic(x**2 + y + 1, Interval(1, 2), x) + raises(NotImplementedError, lambda: is_monotonic(x**2 + y + 1)) + + +def test_issue_23401(): + x = Symbol('x') + expr = (x + 1)/(-1.0e-3*x**2 + 0.1*x + 0.1) + assert is_increasing(expr, Interval(1,2), x) diff --git a/lib/python3.11/site-packages/sympy/calculus/tests/test_util.py b/lib/python3.11/site-packages/sympy/calculus/tests/test_util.py new file mode 100644 index 0000000000000000000000000000000000000000..c18b7a79fd54fdb2638cc746d43ab26753fc72a9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/tests/test_util.py @@ -0,0 +1,392 @@ +from sympy.core.function import Lambda +from sympy.core.numbers import (E, I, Rational, oo, pi) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.elementary.complexes import (Abs, re) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.integers import frac +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import ( + cos, cot, csc, sec, sin, tan, asin, acos, atan, acot, asec, acsc) +from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth, + sech, csch, asinh, acosh, atanh, acoth, asech, acsch) +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.error_functions import expint +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.simplify.simplify import simplify +from sympy.calculus.util import (function_range, continuous_domain, not_empty_in, + periodicity, lcim, is_convex, + stationary_points, minimum, maximum) +from sympy.sets.sets import (Interval, FiniteSet, Complement, Union) +from sympy.sets.fancysets import ImageSet +from sympy.sets.conditionset import ConditionSet +from sympy.testing.pytest import XFAIL, raises, _both_exp_pow, slow +from sympy.abc import x, y + +a = Symbol('a', real=True) + +def test_function_range(): + assert function_range(sin(x), x, Interval(-pi/2, pi/2) + ) == Interval(-1, 1) + assert function_range(sin(x), x, Interval(0, pi) + ) == Interval(0, 1) + assert function_range(tan(x), x, Interval(0, pi) + ) == Interval(-oo, oo) + assert function_range(tan(x), x, Interval(pi/2, pi) + ) == Interval(-oo, 0) + assert function_range((x + 3)/(x - 2), x, Interval(-5, 5) + ) == Union(Interval(-oo, Rational(2, 7)), Interval(Rational(8, 3), oo)) + assert function_range(1/(x**2), x, Interval(-1, 1) + ) == Interval(1, oo) + assert function_range(exp(x), x, Interval(-1, 1) + ) == Interval(exp(-1), exp(1)) + assert function_range(log(x) - x, x, S.Reals + ) == Interval(-oo, -1) + assert function_range(sqrt(3*x - 1), x, Interval(0, 2) + ) == Interval(0, sqrt(5)) + assert function_range(x*(x - 1) - (x**2 - x), x, S.Reals + ) == FiniteSet(0) + assert function_range(x*(x - 1) - (x**2 - x) + y, x, S.Reals + ) == FiniteSet(y) + assert function_range(sin(x), x, Union(Interval(-5, -3), FiniteSet(4)) + ) == Union(Interval(-sin(3), 1), FiniteSet(sin(4))) + assert function_range(cos(x), x, Interval(-oo, -4) + ) == Interval(-1, 1) + assert function_range(cos(x), x, S.EmptySet) == S.EmptySet + assert function_range(x/sqrt(x**2+1), x, S.Reals) == Interval.open(-1,1) + raises(NotImplementedError, lambda : function_range( + exp(x)*(sin(x) - cos(x))/2 - x, x, S.Reals)) + raises(NotImplementedError, lambda : function_range( + sin(x) + x, x, S.Reals)) # issue 13273 + raises(NotImplementedError, lambda : function_range( + log(x), x, S.Integers)) + raises(NotImplementedError, lambda : function_range( + sin(x)/2, x, S.Naturals)) + + +@slow +def test_function_range1(): + assert function_range(tan(x)**2 + tan(3*x)**2 + 1, x, S.Reals) == Interval(1,oo) + + +def test_continuous_domain(): + assert continuous_domain(sin(x), x, Interval(0, 2*pi)) == Interval(0, 2*pi) + assert continuous_domain(tan(x), x, Interval(0, 2*pi)) == \ + Union(Interval(0, pi/2, False, True), Interval(pi/2, pi*Rational(3, 2), True, True), + Interval(pi*Rational(3, 2), 2*pi, True, False)) + assert continuous_domain(cot(x), x, Interval(0, 2*pi)) == Union( + Interval.open(0, pi), Interval.open(pi, 2*pi)) + assert continuous_domain((x - 1)/((x - 1)**2), x, S.Reals) == \ + Union(Interval(-oo, 1, True, True), Interval(1, oo, True, True)) + assert continuous_domain(log(x) + log(4*x - 1), x, S.Reals) == \ + Interval(Rational(1, 4), oo, True, True) + assert continuous_domain(1/sqrt(x - 3), x, S.Reals) == Interval(3, oo, True, True) + assert continuous_domain(1/x - 2, x, S.Reals) == \ + Union(Interval.open(-oo, 0), Interval.open(0, oo)) + assert continuous_domain(1/(x**2 - 4) + 2, x, S.Reals) == \ + Union(Interval.open(-oo, -2), Interval.open(-2, 2), Interval.open(2, oo)) + assert continuous_domain((x+1)**pi, x, S.Reals) == Interval(-1, oo) + assert continuous_domain((x+1)**(pi/2), x, S.Reals) == Interval(-1, oo) + assert continuous_domain(x**x, x, S.Reals) == Interval(0, oo) + assert continuous_domain((x+1)**log(x**2), x, S.Reals) == Union( + Interval.Ropen(-1, 0), Interval.open(0, oo)) + domain = continuous_domain(log(tan(x)**2 + 1), x, S.Reals) + assert not domain.contains(3*pi/2) + assert domain.contains(5) + d = Symbol('d', even=True, zero=False) + assert continuous_domain(x**(1/d), x, S.Reals) == Interval(0, oo) + n = Dummy('n') + assert continuous_domain(1/sin(x), x, S.Reals).dummy_eq(Complement( + S.Reals, Union(ImageSet(Lambda(n, 2*n*pi + pi), S.Integers), + ImageSet(Lambda(n, 2*n*pi), S.Integers)))) + assert continuous_domain(sin(x) + cos(x), x, S.Reals) == S.Reals + assert continuous_domain(asin(x), x, S.Reals) == Interval(-1, 1) # issue #21786 + assert continuous_domain(1/acos(log(x)), x, S.Reals) == Interval.Ropen(exp(-1), E) + assert continuous_domain(sinh(x)+cosh(x), x, S.Reals) == S.Reals + assert continuous_domain(tanh(x)+sech(x), x, S.Reals) == S.Reals + assert continuous_domain(atan(x)+asinh(x), x, S.Reals) == S.Reals + assert continuous_domain(acosh(x), x, S.Reals) == Interval(1, oo) + assert continuous_domain(atanh(x), x, S.Reals) == Interval.open(-1, 1) + assert continuous_domain(atanh(x)+acosh(x), x, S.Reals) == S.EmptySet + assert continuous_domain(asech(x), x, S.Reals) == Interval.Lopen(0, 1) + assert continuous_domain(acoth(x), x, S.Reals) == Union( + Interval.open(-oo, -1), Interval.open(1, oo)) + assert continuous_domain(asec(x), x, S.Reals) == Union( + Interval(-oo, -1), Interval(1, oo)) + assert continuous_domain(acsc(x), x, S.Reals) == Union( + Interval(-oo, -1), Interval(1, oo)) + for f in (coth, acsch, csch): + assert continuous_domain(f(x), x, S.Reals) == Union( + Interval.open(-oo, 0), Interval.open(0, oo)) + assert continuous_domain(acot(x), x, S.Reals).contains(0) == False + assert continuous_domain(1/(exp(x) - x), x, S.Reals) == Complement( + S.Reals, ConditionSet(x, Eq(-x + exp(x), 0), S.Reals)) + assert continuous_domain(frac(x**2), x, Interval(-2,-1)) == Union( + Interval.open(-2, -sqrt(3)), Interval.open(-sqrt(2), -1), + Interval.open(-sqrt(3), -sqrt(2))) + assert continuous_domain(frac(x), x, S.Reals) == Complement( + S.Reals, S.Integers) + raises(NotImplementedError, lambda : continuous_domain( + 1/(x**2+1), x, S.Complexes)) + raises(NotImplementedError, lambda : continuous_domain( + gamma(x), x, Interval(-5,0))) + assert continuous_domain(x + gamma(pi), x, S.Reals) == S.Reals + + +@XFAIL +def test_continuous_domain_acot(): + acot_cont = Piecewise((pi+acot(x), x<0), (acot(x), True)) + assert continuous_domain(acot_cont, x, S.Reals) == S.Reals + +@XFAIL +def test_continuous_domain_gamma(): + assert continuous_domain(gamma(x), x, S.Reals).contains(-1) == False + +@XFAIL +def test_continuous_domain_neg_power(): + assert continuous_domain((x-2)**(1-x), x, S.Reals) == Interval.open(2, oo) + + +def test_not_empty_in(): + assert not_empty_in(FiniteSet(x, 2*x).intersect(Interval(1, 2, True, False)), x) == \ + Interval(S.Half, 2, True, False) + assert not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x) == \ + Union(Interval(-sqrt(2), -1), Interval(1, 2)) + assert not_empty_in(FiniteSet(x**2 + x, x).intersect(Interval(2, 4)), x) == \ + Union(Interval(-sqrt(17)/2 - S.Half, -2), + Interval(1, Rational(-1, 2) + sqrt(17)/2), Interval(2, 4)) + assert not_empty_in(FiniteSet(x/(x - 1)).intersect(S.Reals), x) == \ + Complement(S.Reals, FiniteSet(1)) + assert not_empty_in(FiniteSet(a/(a - 1)).intersect(S.Reals), a) == \ + Complement(S.Reals, FiniteSet(1)) + assert not_empty_in(FiniteSet((x**2 - 3*x + 2)/(x - 1)).intersect(S.Reals), x) == \ + Complement(S.Reals, FiniteSet(1)) + assert not_empty_in(FiniteSet(3, 4, x/(x - 1)).intersect(Interval(2, 3)), x) == \ + Interval(-oo, oo) + assert not_empty_in(FiniteSet(4, x/(x - 1)).intersect(Interval(2, 3)), x) == \ + Interval(S(3)/2, 2) + assert not_empty_in(FiniteSet(x/(x**2 - 1)).intersect(S.Reals), x) == \ + Complement(S.Reals, FiniteSet(-1, 1)) + assert not_empty_in(FiniteSet(x, x**2).intersect(Union(Interval(1, 3, True, True), + Interval(4, 5))), x) == \ + Union(Interval(-sqrt(5), -2), Interval(-sqrt(3), -1, True, True), + Interval(1, 3, True, True), Interval(4, 5)) + assert not_empty_in(FiniteSet(1).intersect(Interval(3, 4)), x) == S.EmptySet + assert not_empty_in(FiniteSet(x**2/(x + 2)).intersect(Interval(1, oo)), x) == \ + Union(Interval(-2, -1, True, False), Interval(2, oo)) + raises(ValueError, lambda: not_empty_in(x)) + raises(ValueError, lambda: not_empty_in(Interval(0, 1), x)) + raises(NotImplementedError, + lambda: not_empty_in(FiniteSet(x).intersect(S.Reals), x, a)) + + +@_both_exp_pow +def test_periodicity(): + assert periodicity(sin(2*x), x) == pi + assert periodicity((-2)*tan(4*x), x) == pi/4 + assert periodicity(sin(x)**2, x) == 2*pi + assert periodicity(3**tan(3*x), x) == pi/3 + assert periodicity(tan(x)*cos(x), x) == 2*pi + assert periodicity(sin(x)**(tan(x)), x) == 2*pi + assert periodicity(tan(x)*sec(x), x) == 2*pi + assert periodicity(sin(2*x)*cos(2*x) - y, x) == pi/2 + assert periodicity(tan(x) + cot(x), x) == pi + assert periodicity(sin(x) - cos(2*x), x) == 2*pi + assert periodicity(sin(x) - 1, x) == 2*pi + assert periodicity(sin(4*x) + sin(x)*cos(x), x) == pi + assert periodicity(exp(sin(x)), x) == 2*pi + assert periodicity(log(cot(2*x)) - sin(cos(2*x)), x) == pi + assert periodicity(sin(2*x)*exp(tan(x) - csc(2*x)), x) == pi + assert periodicity(cos(sec(x) - csc(2*x)), x) == 2*pi + assert periodicity(tan(sin(2*x)), x) == pi + assert periodicity(2*tan(x)**2, x) == pi + assert periodicity(sin(x%4), x) == 4 + assert periodicity(sin(x)%4, x) == 2*pi + assert periodicity(tan((3*x-2)%4), x) == Rational(4, 3) + assert periodicity((sqrt(2)*(x+1)+x) % 3, x) == 3 / (sqrt(2)+1) + assert periodicity((x**2+1) % x, x) is None + assert periodicity(sin(re(x)), x) == 2*pi + assert periodicity(sin(x)**2 + cos(x)**2, x) is S.Zero + assert periodicity(tan(x), y) is S.Zero + assert periodicity(sin(x) + I*cos(x), x) == 2*pi + assert periodicity(x - sin(2*y), y) == pi + + assert periodicity(exp(x), x) is None + assert periodicity(exp(I*x), x) == 2*pi + assert periodicity(exp(I*a), a) == 2*pi + assert periodicity(exp(a), a) is None + assert periodicity(exp(log(sin(a) + I*cos(2*a)), evaluate=False), a) == 2*pi + assert periodicity(exp(log(sin(2*a) + I*cos(a)), evaluate=False), a) == 2*pi + assert periodicity(exp(sin(a)), a) == 2*pi + assert periodicity(exp(2*I*a), a) == pi + assert periodicity(exp(a + I*sin(a)), a) is None + assert periodicity(exp(cos(a/2) + sin(a)), a) == 4*pi + assert periodicity(log(x), x) is None + assert periodicity(exp(x)**sin(x), x) is None + assert periodicity(sin(x)**y, y) is None + + assert periodicity(Abs(sin(Abs(sin(x)))), x) == pi + assert all(periodicity(Abs(f(x)), x) == pi for f in ( + cos, sin, sec, csc, tan, cot)) + assert periodicity(Abs(sin(tan(x))), x) == pi + assert periodicity(Abs(sin(sin(x) + tan(x))), x) == 2*pi + assert periodicity(sin(x) > S.Half, x) == 2*pi + + assert periodicity(x > 2, x) is None + assert periodicity(x**3 - x**2 + 1, x) is None + assert periodicity(Abs(x), x) is None + assert periodicity(Abs(x**2 - 1), x) is None + + assert periodicity((x**2 + 4)%2, x) is None + assert periodicity((E**x)%3, x) is None + + assert periodicity(sin(expint(1, x))/expint(1, x), x) is None + # returning `None` for any Piecewise + p = Piecewise((0, x < -1), (x**2, x <= 1), (log(x), True)) + assert periodicity(p, x) is None + + m = MatrixSymbol('m', 3, 3) + raises(NotImplementedError, lambda: periodicity(sin(m), m)) + raises(NotImplementedError, lambda: periodicity(sin(m[0, 0]), m)) + raises(NotImplementedError, lambda: periodicity(sin(m), m[0, 0])) + raises(NotImplementedError, lambda: periodicity(sin(m[0, 0]), m[0, 0])) + + +def test_periodicity_check(): + assert periodicity(tan(x), x, check=True) == pi + assert periodicity(sin(x) + cos(x), x, check=True) == 2*pi + assert periodicity(sec(x), x) == 2*pi + assert periodicity(sin(x*y), x) == 2*pi/abs(y) + assert periodicity(Abs(sec(sec(x))), x) == pi + + +def test_lcim(): + assert lcim([S.Half, S(2), S(3)]) == 6 + assert lcim([pi/2, pi/4, pi]) == pi + assert lcim([2*pi, pi/2]) == 2*pi + assert lcim([S.One, 2*pi]) is None + assert lcim([S(2) + 2*E, E/3 + Rational(1, 3), S.One + E]) == S(2) + 2*E + + +def test_is_convex(): + assert is_convex(1/x, x, domain=Interval.open(0, oo)) == True + assert is_convex(1/x, x, domain=Interval(-oo, 0)) == False + assert is_convex(x**2, x, domain=Interval(0, oo)) == True + assert is_convex(1/x**3, x, domain=Interval.Lopen(0, oo)) == True + assert is_convex(-1/x**3, x, domain=Interval.Ropen(-oo, 0)) == True + assert is_convex(log(x) ,x) == False + assert is_convex(x**2+y**2, x, y) == True + assert is_convex(cos(x) + cos(y), x) == False + assert is_convex(8*x**2 - 2*y**2, x, y) == False + + +def test_stationary_points(): + assert stationary_points(sin(x), x, Interval(-pi/2, pi/2) + ) == {-pi/2, pi/2} + assert stationary_points(sin(x), x, Interval.Ropen(0, pi/4) + ) is S.EmptySet + assert stationary_points(tan(x), x, + ) is S.EmptySet + assert stationary_points(sin(x)*cos(x), x, Interval(0, pi) + ) == {pi/4, pi*Rational(3, 4)} + assert stationary_points(sec(x), x, Interval(0, pi) + ) == {0, pi} + assert stationary_points((x+3)*(x-2), x + ) == FiniteSet(Rational(-1, 2)) + assert stationary_points((x + 3)/(x - 2), x, Interval(-5, 5) + ) is S.EmptySet + assert stationary_points((x**2+3)/(x-2), x + ) == {2 - sqrt(7), 2 + sqrt(7)} + assert stationary_points((x**2+3)/(x-2), x, Interval(0, 5) + ) == {2 + sqrt(7)} + assert stationary_points(x**4 + x**3 - 5*x**2, x, S.Reals + ) == FiniteSet(-2, 0, Rational(5, 4)) + assert stationary_points(exp(x), x + ) is S.EmptySet + assert stationary_points(log(x) - x, x, S.Reals + ) == {1} + assert stationary_points(cos(x), x, Union(Interval(0, 5), Interval(-6, -3)) + ) == {0, -pi, pi} + assert stationary_points(y, x, S.Reals + ) == S.Reals + assert stationary_points(y, x, S.EmptySet) == S.EmptySet + + +def test_maximum(): + assert maximum(sin(x), x) is S.One + assert maximum(sin(x), x, Interval(0, 1)) == sin(1) + assert maximum(tan(x), x) is oo + assert maximum(tan(x), x, Interval(-pi/4, pi/4)) is S.One + assert maximum(sin(x)*cos(x), x, S.Reals) == S.Half + assert simplify(maximum(sin(x)*cos(x), x, Interval(pi*Rational(3, 8), pi*Rational(5, 8))) + ) == sqrt(2)/4 + assert maximum((x+3)*(x-2), x) is oo + assert maximum((x+3)*(x-2), x, Interval(-5, 0)) == S(14) + assert maximum((x+3)/(x-2), x, Interval(-5, 0)) == Rational(2, 7) + assert simplify(maximum(-x**4-x**3+x**2+10, x) + ) == 41*sqrt(41)/512 + Rational(5419, 512) + assert maximum(exp(x), x, Interval(-oo, 2)) == exp(2) + assert maximum(log(x) - x, x, S.Reals) is S.NegativeOne + assert maximum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3)) + ) is S.One + assert maximum(cos(x)-sin(x), x, S.Reals) == sqrt(2) + assert maximum(y, x, S.Reals) == y + assert maximum(abs(a**3 + a), a, Interval(0, 2)) == 10 + assert maximum(abs(60*a**3 + 24*a), a, Interval(0, 2)) == 528 + assert maximum(abs(12*a*(5*a**2 + 2)), a, Interval(0, 2)) == 528 + assert maximum(x/sqrt(x**2+1), x, S.Reals) == 1 + + raises(ValueError, lambda : maximum(sin(x), x, S.EmptySet)) + raises(ValueError, lambda : maximum(log(cos(x)), x, S.EmptySet)) + raises(ValueError, lambda : maximum(1/(x**2 + y**2 + 1), x, S.EmptySet)) + raises(ValueError, lambda : maximum(sin(x), sin(x))) + raises(ValueError, lambda : maximum(sin(x), x*y, S.EmptySet)) + raises(ValueError, lambda : maximum(sin(x), S.One)) + + +def test_minimum(): + assert minimum(sin(x), x) is S.NegativeOne + assert minimum(sin(x), x, Interval(1, 4)) == sin(4) + assert minimum(tan(x), x) is -oo + assert minimum(tan(x), x, Interval(-pi/4, pi/4)) is S.NegativeOne + assert minimum(sin(x)*cos(x), x, S.Reals) == Rational(-1, 2) + assert simplify(minimum(sin(x)*cos(x), x, Interval(pi*Rational(3, 8), pi*Rational(5, 8))) + ) == -sqrt(2)/4 + assert minimum((x+3)*(x-2), x) == Rational(-25, 4) + assert minimum((x+3)/(x-2), x, Interval(-5, 0)) == Rational(-3, 2) + assert minimum(x**4-x**3+x**2+10, x) == S(10) + assert minimum(exp(x), x, Interval(-2, oo)) == exp(-2) + assert minimum(log(x) - x, x, S.Reals) is -oo + assert minimum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3)) + ) is S.NegativeOne + assert minimum(cos(x)-sin(x), x, S.Reals) == -sqrt(2) + assert minimum(y, x, S.Reals) == y + assert minimum(x/sqrt(x**2+1), x, S.Reals) == -1 + + raises(ValueError, lambda : minimum(sin(x), x, S.EmptySet)) + raises(ValueError, lambda : minimum(log(cos(x)), x, S.EmptySet)) + raises(ValueError, lambda : minimum(1/(x**2 + y**2 + 1), x, S.EmptySet)) + raises(ValueError, lambda : minimum(sin(x), sin(x))) + raises(ValueError, lambda : minimum(sin(x), x*y, S.EmptySet)) + raises(ValueError, lambda : minimum(sin(x), S.One)) + + +def test_issue_19869(): + assert (maximum(sqrt(3)*(x - 1)/(3*sqrt(x**2 + 1)), x) + ) == sqrt(3)/3 + + +def test_issue_16469(): + f = abs(a) + assert function_range(f, a, S.Reals) == Interval(0, oo, False, True) + + +@_both_exp_pow +def test_issue_18747(): + assert periodicity(exp(pi*I*(x/4 + S.Half/2)), x) == 8 + + +def test_issue_25942(): + assert (acos(x) > pi/3).as_set() == Interval.Ropen(-1, S(1)/2) diff --git a/lib/python3.11/site-packages/sympy/calculus/util.py b/lib/python3.11/site-packages/sympy/calculus/util.py new file mode 100644 index 0000000000000000000000000000000000000000..f0863259b26686ecb29caf639f0fcd5df195cd93 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/calculus/util.py @@ -0,0 +1,905 @@ +from .accumulationbounds import AccumBounds, AccumulationBounds # noqa: F401 +from .singularities import singularities +from sympy.core import Pow, S +from sympy.core.function import diff, expand_mul, Function +from sympy.core.kind import NumberKind +from sympy.core.mod import Mod +from sympy.core.numbers import equal_valued +from sympy.core.relational import Relational +from sympy.core.symbol import Symbol, Dummy +from sympy.core.sympify import _sympify +from sympy.functions.elementary.complexes import Abs, im, re +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.integers import frac +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import ( + TrigonometricFunction, sin, cos, tan, cot, csc, sec, + asin, acos, acot, atan, asec, acsc) +from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth, + sech, csch, asinh, acosh, atanh, acoth, asech, acsch) +from sympy.polys.polytools import degree, lcm_list +from sympy.sets.sets import (Interval, Intersection, FiniteSet, Union, + Complement) +from sympy.sets.fancysets import ImageSet +from sympy.sets.conditionset import ConditionSet +from sympy.utilities import filldedent +from sympy.utilities.iterables import iterable +from sympy.matrices.dense import hessian + + +def continuous_domain(f, symbol, domain): + """ + Returns the domain on which the function expression f is continuous. + + This function is limited by the ability to determine the various + singularities and discontinuities of the given function. + The result is either given as a union of intervals or constructed using + other set operations. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for which the intervals are to be determined. + domain : :py:class:`~.Interval` + The domain over which the continuity of the symbol has to be checked. + + Examples + ======== + + >>> from sympy import Interval, Symbol, S, tan, log, pi, sqrt + >>> from sympy.calculus.util import continuous_domain + >>> x = Symbol('x') + >>> continuous_domain(1/x, x, S.Reals) + Union(Interval.open(-oo, 0), Interval.open(0, oo)) + >>> continuous_domain(tan(x), x, Interval(0, pi)) + Union(Interval.Ropen(0, pi/2), Interval.Lopen(pi/2, pi)) + >>> continuous_domain(sqrt(x - 2), x, Interval(-5, 5)) + Interval(2, 5) + >>> continuous_domain(log(2*x - 1), x, S.Reals) + Interval.open(1/2, oo) + + Returns + ======= + + :py:class:`~.Interval` + Union of all intervals where the function is continuous. + + Raises + ====== + + NotImplementedError + If the method to determine continuity of such a function + has not yet been developed. + + """ + from sympy.solvers.inequalities import solve_univariate_inequality + + if not domain.is_subset(S.Reals): + raise NotImplementedError(filldedent(''' + Domain must be a subset of S.Reals. + ''')) + implemented = [Pow, exp, log, Abs, frac, + sin, cos, tan, cot, sec, csc, + asin, acos, atan, acot, asec, acsc, + sinh, cosh, tanh, coth, sech, csch, + asinh, acosh, atanh, acoth, asech, acsch] + used = [fct.func for fct in f.atoms(Function) if fct.has(symbol)] + if any(func not in implemented for func in used): + raise NotImplementedError(filldedent(''' + Unable to determine the domain of the given function. + ''')) + + x = Symbol('x') + constraints = { + log: (x > 0,), + asin: (x >= -1, x <= 1), + acos: (x >= -1, x <= 1), + acosh: (x >= 1,), + atanh: (x > -1, x < 1), + asech: (x > 0, x <= 1) + } + constraints_union = { + asec: (x <= -1, x >= 1), + acsc: (x <= -1, x >= 1), + acoth: (x < -1, x > 1) + } + + cont_domain = domain + for atom in f.atoms(Pow): + den = atom.exp.as_numer_denom()[1] + if atom.exp.is_rational and den.is_odd: + pass # 0**negative handled by singularities() + else: + constraint = solve_univariate_inequality(atom.base >= 0, + symbol).as_set() + cont_domain = Intersection(constraint, cont_domain) + + for atom in f.atoms(Function): + if atom.func in constraints: + for c in constraints[atom.func]: + constraint_relational = c.subs(x, atom.args[0]) + constraint_set = solve_univariate_inequality( + constraint_relational, symbol).as_set() + cont_domain = Intersection(constraint_set, cont_domain) + elif atom.func in constraints_union: + constraint_set = S.EmptySet + for c in constraints_union[atom.func]: + constraint_relational = c.subs(x, atom.args[0]) + constraint_set += solve_univariate_inequality( + constraint_relational, symbol).as_set() + cont_domain = Intersection(constraint_set, cont_domain) + # XXX: the discontinuities below could be factored out in + # a new "discontinuities()". + elif atom.func == acot: + from sympy.solvers.solveset import solveset_real + # Sympy's acot() has a step discontinuity at 0. Since it's + # neither an essential singularity nor a pole, singularities() + # will not report it. But it's still relevant for determining + # the continuity of the function f. + cont_domain -= solveset_real(atom.args[0], symbol) + # Note that the above may introduce spurious discontinuities, e.g. + # for abs(acot(x)) at 0. + elif atom.func == frac: + from sympy.solvers.solveset import solveset_real + r = function_range(atom.args[0], symbol, domain) + r = Intersection(r, S.Integers) + if r.is_finite_set: + discont = S.EmptySet + for n in r: + discont += solveset_real(atom.args[0]-n, symbol) + else: + discont = ConditionSet( + symbol, S.Integers.contains(atom.args[0]), cont_domain) + cont_domain -= discont + + return cont_domain - singularities(f, symbol, domain) + + +def function_range(f, symbol, domain): + """ + Finds the range of a function in a given domain. + This method is limited by the ability to determine the singularities and + determine limits. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for which the range of function is to be determined. + domain : :py:class:`~.Interval` + The domain under which the range of the function has to be found. + + Examples + ======== + + >>> from sympy import Interval, Symbol, S, exp, log, pi, sqrt, sin, tan + >>> from sympy.calculus.util import function_range + >>> x = Symbol('x') + >>> function_range(sin(x), x, Interval(0, 2*pi)) + Interval(-1, 1) + >>> function_range(tan(x), x, Interval(-pi/2, pi/2)) + Interval(-oo, oo) + >>> function_range(1/x, x, S.Reals) + Union(Interval.open(-oo, 0), Interval.open(0, oo)) + >>> function_range(exp(x), x, S.Reals) + Interval.open(0, oo) + >>> function_range(log(x), x, S.Reals) + Interval(-oo, oo) + >>> function_range(sqrt(x), x, Interval(-5, 9)) + Interval(0, 3) + + Returns + ======= + + :py:class:`~.Interval` + Union of all ranges for all intervals under domain where function is + continuous. + + Raises + ====== + + NotImplementedError + If any of the intervals, in the given domain, for which function + is continuous are not finite or real, + OR if the critical points of the function on the domain cannot be found. + """ + + if domain is S.EmptySet: + return S.EmptySet + + period = periodicity(f, symbol) + if period == S.Zero: + # the expression is constant wrt symbol + return FiniteSet(f.expand()) + + from sympy.series.limits import limit + from sympy.solvers.solveset import solveset + + if period is not None: + if isinstance(domain, Interval): + if (domain.inf - domain.sup).is_infinite: + domain = Interval(0, period) + elif isinstance(domain, Union): + for sub_dom in domain.args: + if isinstance(sub_dom, Interval) and \ + ((sub_dom.inf - sub_dom.sup).is_infinite): + domain = Interval(0, period) + + intervals = continuous_domain(f, symbol, domain) + range_int = S.EmptySet + if isinstance(intervals,(Interval, FiniteSet)): + interval_iter = (intervals,) + + elif isinstance(intervals, Union): + interval_iter = intervals.args + + else: + raise NotImplementedError(filldedent(''' + Unable to find range for the given domain. + ''')) + + for interval in interval_iter: + if isinstance(interval, FiniteSet): + for singleton in interval: + if singleton in domain: + range_int += FiniteSet(f.subs(symbol, singleton)) + elif isinstance(interval, Interval): + vals = S.EmptySet + critical_points = S.EmptySet + critical_values = S.EmptySet + bounds = ((interval.left_open, interval.inf, '+'), + (interval.right_open, interval.sup, '-')) + + for is_open, limit_point, direction in bounds: + if is_open: + critical_values += FiniteSet(limit(f, symbol, limit_point, direction)) + vals += critical_values + + else: + vals += FiniteSet(f.subs(symbol, limit_point)) + + solution = solveset(f.diff(symbol), symbol, interval) + + if not iterable(solution): + raise NotImplementedError( + 'Unable to find critical points for {}'.format(f)) + if isinstance(solution, ImageSet): + raise NotImplementedError( + 'Infinite number of critical points for {}'.format(f)) + + critical_points += solution + + for critical_point in critical_points: + vals += FiniteSet(f.subs(symbol, critical_point)) + + left_open, right_open = False, False + + if critical_values is not S.EmptySet: + if critical_values.inf == vals.inf: + left_open = True + + if critical_values.sup == vals.sup: + right_open = True + + range_int += Interval(vals.inf, vals.sup, left_open, right_open) + else: + raise NotImplementedError(filldedent(''' + Unable to find range for the given domain. + ''')) + + return range_int + + +def not_empty_in(finset_intersection, *syms): + """ + Finds the domain of the functions in ``finset_intersection`` in which the + ``finite_set`` is not-empty. + + Parameters + ========== + + finset_intersection : Intersection of FiniteSet + The unevaluated intersection of FiniteSet containing + real-valued functions with Union of Sets + syms : Tuple of symbols + Symbol for which domain is to be found + + Raises + ====== + + NotImplementedError + The algorithms to find the non-emptiness of the given FiniteSet are + not yet implemented. + ValueError + The input is not valid. + RuntimeError + It is a bug, please report it to the github issue tracker + (https://github.com/sympy/sympy/issues). + + Examples + ======== + + >>> from sympy import FiniteSet, Interval, not_empty_in, oo + >>> from sympy.abc import x + >>> not_empty_in(FiniteSet(x/2).intersect(Interval(0, 1)), x) + Interval(0, 2) + >>> not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x) + Union(Interval(1, 2), Interval(-sqrt(2), -1)) + >>> not_empty_in(FiniteSet(x**2/(x + 2)).intersect(Interval(1, oo)), x) + Union(Interval.Lopen(-2, -1), Interval(2, oo)) + """ + + # TODO: handle piecewise defined functions + # TODO: handle transcendental functions + # TODO: handle multivariate functions + if len(syms) == 0: + raise ValueError("One or more symbols must be given in syms.") + + if finset_intersection is S.EmptySet: + return S.EmptySet + + if isinstance(finset_intersection, Union): + elm_in_sets = finset_intersection.args[0] + return Union(not_empty_in(finset_intersection.args[1], *syms), + elm_in_sets) + + if isinstance(finset_intersection, FiniteSet): + finite_set = finset_intersection + _sets = S.Reals + else: + finite_set = finset_intersection.args[1] + _sets = finset_intersection.args[0] + + if not isinstance(finite_set, FiniteSet): + raise ValueError('A FiniteSet must be given, not %s: %s' % + (type(finite_set), finite_set)) + + if len(syms) == 1: + symb = syms[0] + else: + raise NotImplementedError('more than one variables %s not handled' % + (syms,)) + + def elm_domain(expr, intrvl): + """ Finds the domain of an expression in any given interval """ + from sympy.solvers.solveset import solveset + + _start = intrvl.start + _end = intrvl.end + _singularities = solveset(expr.as_numer_denom()[1], symb, + domain=S.Reals) + + if intrvl.right_open: + if _end is S.Infinity: + _domain1 = S.Reals + else: + _domain1 = solveset(expr < _end, symb, domain=S.Reals) + else: + _domain1 = solveset(expr <= _end, symb, domain=S.Reals) + + if intrvl.left_open: + if _start is S.NegativeInfinity: + _domain2 = S.Reals + else: + _domain2 = solveset(expr > _start, symb, domain=S.Reals) + else: + _domain2 = solveset(expr >= _start, symb, domain=S.Reals) + + # domain in the interval + expr_with_sing = Intersection(_domain1, _domain2) + expr_domain = Complement(expr_with_sing, _singularities) + return expr_domain + + if isinstance(_sets, Interval): + return Union(*[elm_domain(element, _sets) for element in finite_set]) + + if isinstance(_sets, Union): + _domain = S.EmptySet + for intrvl in _sets.args: + _domain_element = Union(*[elm_domain(element, intrvl) + for element in finite_set]) + _domain = Union(_domain, _domain_element) + return _domain + + +def periodicity(f, symbol, check=False): + """ + Tests the given function for periodicity in the given symbol. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for which the period is to be determined. + check : bool, optional + The flag to verify whether the value being returned is a period or not. + + Returns + ======= + + period + The period of the function is returned. + ``None`` is returned when the function is aperiodic or has a complex period. + The value of $0$ is returned as the period of a constant function. + + Raises + ====== + + NotImplementedError + The value of the period computed cannot be verified. + + + Notes + ===== + + Currently, we do not support functions with a complex period. + The period of functions having complex periodic values such + as ``exp``, ``sinh`` is evaluated to ``None``. + + The value returned might not be the "fundamental" period of the given + function i.e. it may not be the smallest periodic value of the function. + + The verification of the period through the ``check`` flag is not reliable + due to internal simplification of the given expression. Hence, it is set + to ``False`` by default. + + Examples + ======== + >>> from sympy import periodicity, Symbol, sin, cos, tan, exp + >>> x = Symbol('x') + >>> f = sin(x) + sin(2*x) + sin(3*x) + >>> periodicity(f, x) + 2*pi + >>> periodicity(sin(x)*cos(x), x) + pi + >>> periodicity(exp(tan(2*x) - 1), x) + pi/2 + >>> periodicity(sin(4*x)**cos(2*x), x) + pi + >>> periodicity(exp(x), x) + """ + if symbol.kind is not NumberKind: + raise NotImplementedError("Cannot use symbol of kind %s" % symbol.kind) + temp = Dummy('x', real=True) + f = f.subs(symbol, temp) + symbol = temp + + def _check(orig_f, period): + '''Return the checked period or raise an error.''' + new_f = orig_f.subs(symbol, symbol + period) + if new_f.equals(orig_f): + return period + else: + raise NotImplementedError(filldedent(''' + The period of the given function cannot be verified. + When `%s` was replaced with `%s + %s` in `%s`, the result + was `%s` which was not recognized as being the same as + the original function. + So either the period was wrong or the two forms were + not recognized as being equal. + Set check=False to obtain the value.''' % + (symbol, symbol, period, orig_f, new_f))) + + orig_f = f + period = None + + if isinstance(f, Relational): + f = f.lhs - f.rhs + + f = f.simplify() + + if symbol not in f.free_symbols: + return S.Zero + + if isinstance(f, TrigonometricFunction): + try: + period = f.period(symbol) + except NotImplementedError: + pass + + if isinstance(f, Abs): + arg = f.args[0] + if isinstance(arg, (sec, csc, cos)): + # all but tan and cot might have a + # a period that is half as large + # so recast as sin + arg = sin(arg.args[0]) + period = periodicity(arg, symbol) + if period is not None and isinstance(arg, sin): + # the argument of Abs was a trigonometric other than + # cot or tan; test to see if the half-period + # is valid. Abs(arg) has behaviour equivalent to + # orig_f, so use that for test: + orig_f = Abs(arg) + try: + return _check(orig_f, period/2) + except NotImplementedError as err: + if check: + raise NotImplementedError(err) + # else let new orig_f and period be + # checked below + + if isinstance(f, exp) or (f.is_Pow and f.base == S.Exp1): + f = Pow(S.Exp1, expand_mul(f.exp)) + if im(f) != 0: + period_real = periodicity(re(f), symbol) + period_imag = periodicity(im(f), symbol) + if period_real is not None and period_imag is not None: + period = lcim([period_real, period_imag]) + + if f.is_Pow and f.base != S.Exp1: + base, expo = f.args + base_has_sym = base.has(symbol) + expo_has_sym = expo.has(symbol) + + if base_has_sym and not expo_has_sym: + period = periodicity(base, symbol) + + elif expo_has_sym and not base_has_sym: + period = periodicity(expo, symbol) + + else: + period = _periodicity(f.args, symbol) + + elif f.is_Mul: + coeff, g = f.as_independent(symbol, as_Add=False) + if isinstance(g, TrigonometricFunction) or not equal_valued(coeff, 1): + period = periodicity(g, symbol) + else: + period = _periodicity(g.args, symbol) + + elif f.is_Add: + k, g = f.as_independent(symbol) + if k is not S.Zero: + return periodicity(g, symbol) + + period = _periodicity(g.args, symbol) + + elif isinstance(f, Mod): + a, n = f.args + + if a == symbol: + period = n + elif isinstance(a, TrigonometricFunction): + period = periodicity(a, symbol) + #check if 'f' is linear in 'symbol' + elif (a.is_polynomial(symbol) and degree(a, symbol) == 1 and + symbol not in n.free_symbols): + period = Abs(n / a.diff(symbol)) + + elif isinstance(f, Piecewise): + pass # not handling Piecewise yet as the return type is not favorable + + elif period is None: + from sympy.solvers.decompogen import compogen, decompogen + g_s = decompogen(f, symbol) + num_of_gs = len(g_s) + if num_of_gs > 1: + for index, g in enumerate(reversed(g_s)): + start_index = num_of_gs - 1 - index + g = compogen(g_s[start_index:], symbol) + if g not in (orig_f, f): # Fix for issue 12620 + period = periodicity(g, symbol) + if period is not None: + break + + if period is not None: + if check: + return _check(orig_f, period) + return period + + return None + + +def _periodicity(args, symbol): + """ + Helper for `periodicity` to find the period of a list of simpler + functions. + It uses the `lcim` method to find the least common period of + all the functions. + + Parameters + ========== + + args : Tuple of :py:class:`~.Symbol` + All the symbols present in a function. + + symbol : :py:class:`~.Symbol` + The symbol over which the function is to be evaluated. + + Returns + ======= + + period + The least common period of the function for all the symbols + of the function. + ``None`` if for at least one of the symbols the function is aperiodic. + + """ + periods = [] + for f in args: + period = periodicity(f, symbol) + if period is None: + return None + + if period is not S.Zero: + periods.append(period) + + if len(periods) > 1: + return lcim(periods) + + if periods: + return periods[0] + + +def lcim(numbers): + """Returns the least common integral multiple of a list of numbers. + + The numbers can be rational or irrational or a mixture of both. + `None` is returned for incommensurable numbers. + + Parameters + ========== + + numbers : list + Numbers (rational and/or irrational) for which lcim is to be found. + + Returns + ======= + + number + lcim if it exists, otherwise ``None`` for incommensurable numbers. + + Examples + ======== + + >>> from sympy.calculus.util import lcim + >>> from sympy import S, pi + >>> lcim([S(1)/2, S(3)/4, S(5)/6]) + 15/2 + >>> lcim([2*pi, 3*pi, pi, pi/2]) + 6*pi + >>> lcim([S(1), 2*pi]) + """ + result = None + if all(num.is_irrational for num in numbers): + factorized_nums = [num.factor() for num in numbers] + factors_num = [num.as_coeff_Mul() for num in factorized_nums] + term = factors_num[0][1] + if all(factor == term for coeff, factor in factors_num): + common_term = term + coeffs = [coeff for coeff, factor in factors_num] + result = lcm_list(coeffs) * common_term + + elif all(num.is_rational for num in numbers): + result = lcm_list(numbers) + + else: + pass + + return result + +def is_convex(f, *syms, domain=S.Reals): + r"""Determines the convexity of the function passed in the argument. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + syms : Tuple of :py:class:`~.Symbol` + The variables with respect to which the convexity is to be determined. + domain : :py:class:`~.Interval`, optional + The domain over which the convexity of the function has to be checked. + If unspecified, S.Reals will be the default domain. + + Returns + ======= + + bool + The method returns ``True`` if the function is convex otherwise it + returns ``False``. + + Raises + ====== + + NotImplementedError + The check for the convexity of multivariate functions is not implemented yet. + + Notes + ===== + + To determine concavity of a function pass `-f` as the concerned function. + To determine logarithmic convexity of a function pass `\log(f)` as + concerned function. + To determine logarithmic concavity of a function pass `-\log(f)` as + concerned function. + + Currently, convexity check of multivariate functions is not handled. + + Examples + ======== + + >>> from sympy import is_convex, symbols, exp, oo, Interval + >>> x = symbols('x') + >>> is_convex(exp(x), x) + True + >>> is_convex(x**3, x, domain = Interval(-1, oo)) + False + >>> is_convex(1/x**2, x, domain=Interval.open(0, oo)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Convex_function + .. [2] http://www.ifp.illinois.edu/~angelia/L3_convfunc.pdf + .. [3] https://en.wikipedia.org/wiki/Logarithmically_convex_function + .. [4] https://en.wikipedia.org/wiki/Logarithmically_concave_function + .. [5] https://en.wikipedia.org/wiki/Concave_function + + """ + if len(syms) > 1 : + return hessian(f, syms).is_positive_semidefinite + from sympy.solvers.inequalities import solve_univariate_inequality + f = _sympify(f) + var = syms[0] + if any(s in domain for s in singularities(f, var)): + return False + condition = f.diff(var, 2) < 0 + if solve_univariate_inequality(condition, var, False, domain): + return False + return True + + +def stationary_points(f, symbol, domain=S.Reals): + """ + Returns the stationary points of a function (where derivative of the + function is 0) in the given domain. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for which the stationary points are to be determined. + domain : :py:class:`~.Interval` + The domain over which the stationary points have to be checked. + If unspecified, ``S.Reals`` will be the default domain. + + Returns + ======= + + Set + A set of stationary points for the function. If there are no + stationary point, an :py:class:`~.EmptySet` is returned. + + Examples + ======== + + >>> from sympy import Interval, Symbol, S, sin, pi, pprint, stationary_points + >>> x = Symbol('x') + + >>> stationary_points(1/x, x, S.Reals) + EmptySet + + >>> pprint(stationary_points(sin(x), x), use_unicode=False) + pi 3*pi + {2*n*pi + -- | n in Integers} U {2*n*pi + ---- | n in Integers} + 2 2 + + >>> stationary_points(sin(x),x, Interval(0, 4*pi)) + {pi/2, 3*pi/2, 5*pi/2, 7*pi/2} + + """ + from sympy.solvers.solveset import solveset + + if domain is S.EmptySet: + return S.EmptySet + + domain = continuous_domain(f, symbol, domain) + set = solveset(diff(f, symbol), symbol, domain) + + return set + + +def maximum(f, symbol, domain=S.Reals): + """ + Returns the maximum value of a function in the given domain. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for maximum value needs to be determined. + domain : :py:class:`~.Interval` + The domain over which the maximum have to be checked. + If unspecified, then the global maximum is returned. + + Returns + ======= + + number + Maximum value of the function in given domain. + + Examples + ======== + + >>> from sympy import Interval, Symbol, S, sin, cos, pi, maximum + >>> x = Symbol('x') + + >>> f = -x**2 + 2*x + 5 + >>> maximum(f, x, S.Reals) + 6 + + >>> maximum(sin(x), x, Interval(-pi, pi/4)) + sqrt(2)/2 + + >>> maximum(sin(x)*cos(x), x) + 1/2 + + """ + if isinstance(symbol, Symbol): + if domain is S.EmptySet: + raise ValueError("Maximum value not defined for empty domain.") + + return function_range(f, symbol, domain).sup + else: + raise ValueError("%s is not a valid symbol." % symbol) + + +def minimum(f, symbol, domain=S.Reals): + """ + Returns the minimum value of a function in the given domain. + + Parameters + ========== + + f : :py:class:`~.Expr` + The concerned function. + symbol : :py:class:`~.Symbol` + The variable for minimum value needs to be determined. + domain : :py:class:`~.Interval` + The domain over which the minimum have to be checked. + If unspecified, then the global minimum is returned. + + Returns + ======= + + number + Minimum value of the function in the given domain. + + Examples + ======== + + >>> from sympy import Interval, Symbol, S, sin, cos, minimum + >>> x = Symbol('x') + + >>> f = x**2 + 2*x + 5 + >>> minimum(f, x, S.Reals) + 4 + + >>> minimum(sin(x), x, Interval(2, 3)) + sin(3) + + >>> minimum(sin(x)*cos(x), x) + -1/2 + + """ + if isinstance(symbol, Symbol): + if domain is S.EmptySet: + raise ValueError("Minimum value not defined for empty domain.") + + return function_range(f, symbol, domain).inf + else: + raise ValueError("%s is not a valid symbol." % symbol) diff --git a/lib/python3.11/site-packages/sympy/categories/__init__.py b/lib/python3.11/site-packages/sympy/categories/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..4c5007308a1b232e57f9ed164276862df0c5f265 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/categories/__init__.py @@ -0,0 +1,33 @@ +""" +Category Theory module. + +Provides some of the fundamental category-theory-related classes, +including categories, morphisms, diagrams. Functors are not +implemented yet. + +The general reference work this module tries to follow is + + [JoyOfCats] J. Adamek, H. Herrlich. G. E. Strecker: Abstract and + Concrete Categories. The Joy of Cats. + +The latest version of this book should be available for free download +from + + katmat.math.uni-bremen.de/acc/acc.pdf + +""" + +from .baseclasses import (Object, Morphism, IdentityMorphism, + NamedMorphism, CompositeMorphism, Category, + Diagram) + +from .diagram_drawing import (DiagramGrid, XypicDiagramDrawer, + xypic_draw_diagram, preview_diagram) + +__all__ = [ + 'Object', 'Morphism', 'IdentityMorphism', 'NamedMorphism', + 'CompositeMorphism', 'Category', 'Diagram', + + 'DiagramGrid', 'XypicDiagramDrawer', 'xypic_draw_diagram', + 'preview_diagram', +] diff --git a/lib/python3.11/site-packages/sympy/categories/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..b462a15026d6245a72f71dfd2fd74632406606f7 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/__pycache__/baseclasses.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/__pycache__/baseclasses.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..e68dbc1686e275b7e664695e30fe306e01d00de8 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/__pycache__/baseclasses.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/__pycache__/diagram_drawing.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/__pycache__/diagram_drawing.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..8b26f0234478d3ce38471fb7877e9e72748f9dad Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/__pycache__/diagram_drawing.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/baseclasses.py b/lib/python3.11/site-packages/sympy/categories/baseclasses.py new file mode 100644 index 0000000000000000000000000000000000000000..e6ab5153ae4e95f193030864c8f32a52254f2458 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/categories/baseclasses.py @@ -0,0 +1,978 @@ +from sympy.core import S, Basic, Dict, Symbol, Tuple, sympify +from sympy.core.symbol import Str +from sympy.sets import Set, FiniteSet, EmptySet +from sympy.utilities.iterables import iterable + + +class Class(Set): + r""" + The base class for any kind of class in the set-theoretic sense. + + Explanation + =========== + + In axiomatic set theories, everything is a class. A class which + can be a member of another class is a set. A class which is not a + member of another class is a proper class. The class `\{1, 2\}` + is a set; the class of all sets is a proper class. + + This class is essentially a synonym for :class:`sympy.core.Set`. + The goal of this class is to assure easier migration to the + eventual proper implementation of set theory. + """ + is_proper = False + + +class Object(Symbol): + """ + The base class for any kind of object in an abstract category. + + Explanation + =========== + + While technically any instance of :class:`~.Basic` will do, this + class is the recommended way to create abstract objects in + abstract categories. + """ + + +class Morphism(Basic): + """ + The base class for any morphism in an abstract category. + + Explanation + =========== + + In abstract categories, a morphism is an arrow between two + category objects. The object where the arrow starts is called the + domain, while the object where the arrow ends is called the + codomain. + + Two morphisms between the same pair of objects are considered to + be the same morphisms. To distinguish between morphisms between + the same objects use :class:`NamedMorphism`. + + It is prohibited to instantiate this class. Use one of the + derived classes instead. + + See Also + ======== + + IdentityMorphism, NamedMorphism, CompositeMorphism + """ + def __new__(cls, domain, codomain): + raise(NotImplementedError( + "Cannot instantiate Morphism. Use derived classes instead.")) + + @property + def domain(self): + """ + Returns the domain of the morphism. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> f.domain + Object("A") + + """ + return self.args[0] + + @property + def codomain(self): + """ + Returns the codomain of the morphism. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> f.codomain + Object("B") + + """ + return self.args[1] + + def compose(self, other): + r""" + Composes self with the supplied morphism. + + The order of elements in the composition is the usual order, + i.e., to construct `g\circ f` use ``g.compose(f)``. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> g * f + CompositeMorphism((NamedMorphism(Object("A"), Object("B"), "f"), + NamedMorphism(Object("B"), Object("C"), "g"))) + >>> (g * f).domain + Object("A") + >>> (g * f).codomain + Object("C") + + """ + return CompositeMorphism(other, self) + + def __mul__(self, other): + r""" + Composes self with the supplied morphism. + + The semantics of this operation is given by the following + equation: ``g * f == g.compose(f)`` for composable morphisms + ``g`` and ``f``. + + See Also + ======== + + compose + """ + return self.compose(other) + + +class IdentityMorphism(Morphism): + """ + Represents an identity morphism. + + Explanation + =========== + + An identity morphism is a morphism with equal domain and codomain, + which acts as an identity with respect to composition. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, IdentityMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> id_A = IdentityMorphism(A) + >>> id_B = IdentityMorphism(B) + >>> f * id_A == f + True + >>> id_B * f == f + True + + See Also + ======== + + Morphism + """ + def __new__(cls, domain): + return Basic.__new__(cls, domain) + + @property + def codomain(self): + return self.domain + + +class NamedMorphism(Morphism): + """ + Represents a morphism which has a name. + + Explanation + =========== + + Names are used to distinguish between morphisms which have the + same domain and codomain: two named morphisms are equal if they + have the same domains, codomains, and names. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> f + NamedMorphism(Object("A"), Object("B"), "f") + >>> f.name + 'f' + + See Also + ======== + + Morphism + """ + def __new__(cls, domain, codomain, name): + if not name: + raise ValueError("Empty morphism names not allowed.") + + if not isinstance(name, Str): + name = Str(name) + + return Basic.__new__(cls, domain, codomain, name) + + @property + def name(self): + """ + Returns the name of the morphism. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> f.name + 'f' + + """ + return self.args[2].name + + +class CompositeMorphism(Morphism): + r""" + Represents a morphism which is a composition of other morphisms. + + Explanation + =========== + + Two composite morphisms are equal if the morphisms they were + obtained from (components) are the same and were listed in the + same order. + + The arguments to the constructor for this class should be listed + in diagram order: to obtain the composition `g\circ f` from the + instances of :class:`Morphism` ``g`` and ``f`` use + ``CompositeMorphism(f, g)``. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, CompositeMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> g * f + CompositeMorphism((NamedMorphism(Object("A"), Object("B"), "f"), + NamedMorphism(Object("B"), Object("C"), "g"))) + >>> CompositeMorphism(f, g) == g * f + True + + """ + @staticmethod + def _add_morphism(t, morphism): + """ + Intelligently adds ``morphism`` to tuple ``t``. + + Explanation + =========== + + If ``morphism`` is a composite morphism, its components are + added to the tuple. If ``morphism`` is an identity, nothing + is added to the tuple. + + No composability checks are performed. + """ + if isinstance(morphism, CompositeMorphism): + # ``morphism`` is a composite morphism; we have to + # denest its components. + return t + morphism.components + elif isinstance(morphism, IdentityMorphism): + # ``morphism`` is an identity. Nothing happens. + return t + else: + return t + Tuple(morphism) + + def __new__(cls, *components): + if components and not isinstance(components[0], Morphism): + # Maybe the user has explicitly supplied a list of + # morphisms. + return CompositeMorphism.__new__(cls, *components[0]) + + normalised_components = Tuple() + + for current, following in zip(components, components[1:]): + if not isinstance(current, Morphism) or \ + not isinstance(following, Morphism): + raise TypeError("All components must be morphisms.") + + if current.codomain != following.domain: + raise ValueError("Uncomposable morphisms.") + + normalised_components = CompositeMorphism._add_morphism( + normalised_components, current) + + # We haven't added the last morphism to the list of normalised + # components. Add it now. + normalised_components = CompositeMorphism._add_morphism( + normalised_components, components[-1]) + + if not normalised_components: + # If ``normalised_components`` is empty, only identities + # were supplied. Since they all were composable, they are + # all the same identities. + return components[0] + elif len(normalised_components) == 1: + # No sense to construct a whole CompositeMorphism. + return normalised_components[0] + + return Basic.__new__(cls, normalised_components) + + @property + def components(self): + """ + Returns the components of this composite morphism. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> (g * f).components + (NamedMorphism(Object("A"), Object("B"), "f"), + NamedMorphism(Object("B"), Object("C"), "g")) + + """ + return self.args[0] + + @property + def domain(self): + """ + Returns the domain of this composite morphism. + + The domain of the composite morphism is the domain of its + first component. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> (g * f).domain + Object("A") + + """ + return self.components[0].domain + + @property + def codomain(self): + """ + Returns the codomain of this composite morphism. + + The codomain of the composite morphism is the codomain of its + last component. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> (g * f).codomain + Object("C") + + """ + return self.components[-1].codomain + + def flatten(self, new_name): + """ + Forgets the composite structure of this morphism. + + Explanation + =========== + + If ``new_name`` is not empty, returns a :class:`NamedMorphism` + with the supplied name, otherwise returns a :class:`Morphism`. + In both cases the domain of the new morphism is the domain of + this composite morphism and the codomain of the new morphism + is the codomain of this composite morphism. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> (g * f).flatten("h") + NamedMorphism(Object("A"), Object("C"), "h") + + """ + return NamedMorphism(self.domain, self.codomain, new_name) + + +class Category(Basic): + r""" + An (abstract) category. + + Explanation + =========== + + A category [JoyOfCats] is a quadruple `\mbox{K} = (O, \hom, id, + \circ)` consisting of + + * a (set-theoretical) class `O`, whose members are called + `K`-objects, + + * for each pair `(A, B)` of `K`-objects, a set `\hom(A, B)` whose + members are called `K`-morphisms from `A` to `B`, + + * for a each `K`-object `A`, a morphism `id:A\rightarrow A`, + called the `K`-identity of `A`, + + * a composition law `\circ` associating with every `K`-morphisms + `f:A\rightarrow B` and `g:B\rightarrow C` a `K`-morphism `g\circ + f:A\rightarrow C`, called the composite of `f` and `g`. + + Composition is associative, `K`-identities are identities with + respect to composition, and the sets `\hom(A, B)` are pairwise + disjoint. + + This class knows nothing about its objects and morphisms. + Concrete cases of (abstract) categories should be implemented as + classes derived from this one. + + Certain instances of :class:`Diagram` can be asserted to be + commutative in a :class:`Category` by supplying the argument + ``commutative_diagrams`` in the constructor. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram, Category + >>> from sympy import FiniteSet + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> K = Category("K", commutative_diagrams=[d]) + >>> K.commutative_diagrams == FiniteSet(d) + True + + See Also + ======== + + Diagram + """ + def __new__(cls, name, objects=EmptySet, commutative_diagrams=EmptySet): + if not name: + raise ValueError("A Category cannot have an empty name.") + + if not isinstance(name, Str): + name = Str(name) + + if not isinstance(objects, Class): + objects = Class(objects) + + new_category = Basic.__new__(cls, name, objects, + FiniteSet(*commutative_diagrams)) + return new_category + + @property + def name(self): + """ + Returns the name of this category. + + Examples + ======== + + >>> from sympy.categories import Category + >>> K = Category("K") + >>> K.name + 'K' + + """ + return self.args[0].name + + @property + def objects(self): + """ + Returns the class of objects of this category. + + Examples + ======== + + >>> from sympy.categories import Object, Category + >>> from sympy import FiniteSet + >>> A = Object("A") + >>> B = Object("B") + >>> K = Category("K", FiniteSet(A, B)) + >>> K.objects + Class({Object("A"), Object("B")}) + + """ + return self.args[1] + + @property + def commutative_diagrams(self): + """ + Returns the :class:`~.FiniteSet` of diagrams which are known to + be commutative in this category. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram, Category + >>> from sympy import FiniteSet + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> K = Category("K", commutative_diagrams=[d]) + >>> K.commutative_diagrams == FiniteSet(d) + True + + """ + return self.args[2] + + def hom(self, A, B): + raise NotImplementedError( + "hom-sets are not implemented in Category.") + + def all_morphisms(self): + raise NotImplementedError( + "Obtaining the class of morphisms is not implemented in Category.") + + +class Diagram(Basic): + r""" + Represents a diagram in a certain category. + + Explanation + =========== + + Informally, a diagram is a collection of objects of a category and + certain morphisms between them. A diagram is still a monoid with + respect to morphism composition; i.e., identity morphisms, as well + as all composites of morphisms included in the diagram belong to + the diagram. For a more formal approach to this notion see + [Pare1970]. + + The components of composite morphisms are also added to the + diagram. No properties are assigned to such morphisms by default. + + A commutative diagram is often accompanied by a statement of the + following kind: "if such morphisms with such properties exist, + then such morphisms which such properties exist and the diagram is + commutative". To represent this, an instance of :class:`Diagram` + includes a collection of morphisms which are the premises and + another collection of conclusions. ``premises`` and + ``conclusions`` associate morphisms belonging to the corresponding + categories with the :class:`~.FiniteSet`'s of their properties. + + The set of properties of a composite morphism is the intersection + of the sets of properties of its components. The domain and + codomain of a conclusion morphism should be among the domains and + codomains of the morphisms listed as the premises of a diagram. + + No checks are carried out of whether the supplied object and + morphisms do belong to one and the same category. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy import pprint, default_sort_key + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> premises_keys = sorted(d.premises.keys(), key=default_sort_key) + >>> pprint(premises_keys, use_unicode=False) + [g*f:A-->C, id:A-->A, id:B-->B, id:C-->C, f:A-->B, g:B-->C] + >>> pprint(d.premises, use_unicode=False) + {g*f:A-->C: EmptySet, id:A-->A: EmptySet, id:B-->B: EmptySet, + id:C-->C: EmptySet, f:A-->B: EmptySet, g:B-->C: EmptySet} + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> pprint(d.conclusions,use_unicode=False) + {g*f:A-->C: {unique}} + + References + ========== + + [Pare1970] B. Pareigis: Categories and functors. Academic Press, 1970. + + """ + @staticmethod + def _set_dict_union(dictionary, key, value): + """ + If ``key`` is in ``dictionary``, set the new value of ``key`` + to be the union between the old value and ``value``. + Otherwise, set the value of ``key`` to ``value. + + Returns ``True`` if the key already was in the dictionary and + ``False`` otherwise. + """ + if key in dictionary: + dictionary[key] = dictionary[key] | value + return True + else: + dictionary[key] = value + return False + + @staticmethod + def _add_morphism_closure(morphisms, morphism, props, add_identities=True, + recurse_composites=True): + """ + Adds a morphism and its attributes to the supplied dictionary + ``morphisms``. If ``add_identities`` is True, also adds the + identity morphisms for the domain and the codomain of + ``morphism``. + """ + if not Diagram._set_dict_union(morphisms, morphism, props): + # We have just added a new morphism. + + if isinstance(morphism, IdentityMorphism): + if props: + # Properties for identity morphisms don't really + # make sense, because very much is known about + # identity morphisms already, so much that they + # are trivial. Having properties for identity + # morphisms would only be confusing. + raise ValueError( + "Instances of IdentityMorphism cannot have properties.") + return + + if add_identities: + empty = EmptySet + + id_dom = IdentityMorphism(morphism.domain) + id_cod = IdentityMorphism(morphism.codomain) + + Diagram._set_dict_union(morphisms, id_dom, empty) + Diagram._set_dict_union(morphisms, id_cod, empty) + + for existing_morphism, existing_props in list(morphisms.items()): + new_props = existing_props & props + if morphism.domain == existing_morphism.codomain: + left = morphism * existing_morphism + Diagram._set_dict_union(morphisms, left, new_props) + if morphism.codomain == existing_morphism.domain: + right = existing_morphism * morphism + Diagram._set_dict_union(morphisms, right, new_props) + + if isinstance(morphism, CompositeMorphism) and recurse_composites: + # This is a composite morphism, add its components as + # well. + empty = EmptySet + for component in morphism.components: + Diagram._add_morphism_closure(morphisms, component, empty, + add_identities) + + def __new__(cls, *args): + """ + Construct a new instance of Diagram. + + Explanation + =========== + + If no arguments are supplied, an empty diagram is created. + + If at least an argument is supplied, ``args[0]`` is + interpreted as the premises of the diagram. If ``args[0]`` is + a list, it is interpreted as a list of :class:`Morphism`'s, in + which each :class:`Morphism` has an empty set of properties. + If ``args[0]`` is a Python dictionary or a :class:`Dict`, it + is interpreted as a dictionary associating to some + :class:`Morphism`'s some properties. + + If at least two arguments are supplied ``args[1]`` is + interpreted as the conclusions of the diagram. The type of + ``args[1]`` is interpreted in exactly the same way as the type + of ``args[0]``. If only one argument is supplied, the diagram + has no conclusions. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import IdentityMorphism, Diagram + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> IdentityMorphism(A) in d.premises.keys() + True + >>> g * f in d.premises.keys() + True + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> d.conclusions[g * f] + {unique} + + """ + premises = {} + conclusions = {} + + # Here we will keep track of the objects which appear in the + # premises. + objects = EmptySet + + if len(args) >= 1: + # We've got some premises in the arguments. + premises_arg = args[0] + + if isinstance(premises_arg, list): + # The user has supplied a list of morphisms, none of + # which have any attributes. + empty = EmptySet + + for morphism in premises_arg: + objects |= FiniteSet(morphism.domain, morphism.codomain) + Diagram._add_morphism_closure(premises, morphism, empty) + elif isinstance(premises_arg, (dict, Dict)): + # The user has supplied a dictionary of morphisms and + # their properties. + for morphism, props in premises_arg.items(): + objects |= FiniteSet(morphism.domain, morphism.codomain) + Diagram._add_morphism_closure( + premises, morphism, FiniteSet(*props) if iterable(props) else FiniteSet(props)) + + if len(args) >= 2: + # We also have some conclusions. + conclusions_arg = args[1] + + if isinstance(conclusions_arg, list): + # The user has supplied a list of morphisms, none of + # which have any attributes. + empty = EmptySet + + for morphism in conclusions_arg: + # Check that no new objects appear in conclusions. + if ((sympify(objects.contains(morphism.domain)) is S.true) and + (sympify(objects.contains(morphism.codomain)) is S.true)): + # No need to add identities and recurse + # composites this time. + Diagram._add_morphism_closure( + conclusions, morphism, empty, add_identities=False, + recurse_composites=False) + elif isinstance(conclusions_arg, (dict, Dict)): + # The user has supplied a dictionary of morphisms and + # their properties. + for morphism, props in conclusions_arg.items(): + # Check that no new objects appear in conclusions. + if (morphism.domain in objects) and \ + (morphism.codomain in objects): + # No need to add identities and recurse + # composites this time. + Diagram._add_morphism_closure( + conclusions, morphism, FiniteSet(*props) if iterable(props) else FiniteSet(props), + add_identities=False, recurse_composites=False) + + return Basic.__new__(cls, Dict(premises), Dict(conclusions), objects) + + @property + def premises(self): + """ + Returns the premises of this diagram. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import IdentityMorphism, Diagram + >>> from sympy import pretty + >>> A = Object("A") + >>> B = Object("B") + >>> f = NamedMorphism(A, B, "f") + >>> id_A = IdentityMorphism(A) + >>> id_B = IdentityMorphism(B) + >>> d = Diagram([f]) + >>> print(pretty(d.premises, use_unicode=False)) + {id:A-->A: EmptySet, id:B-->B: EmptySet, f:A-->B: EmptySet} + + """ + return self.args[0] + + @property + def conclusions(self): + """ + Returns the conclusions of this diagram. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import IdentityMorphism, Diagram + >>> from sympy import FiniteSet + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> IdentityMorphism(A) in d.premises.keys() + True + >>> g * f in d.premises.keys() + True + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> d.conclusions[g * f] == FiniteSet("unique") + True + + """ + return self.args[1] + + @property + def objects(self): + """ + Returns the :class:`~.FiniteSet` of objects that appear in this + diagram. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g]) + >>> d.objects + {Object("A"), Object("B"), Object("C")} + + """ + return self.args[2] + + def hom(self, A, B): + """ + Returns a 2-tuple of sets of morphisms between objects ``A`` and + ``B``: one set of morphisms listed as premises, and the other set + of morphisms listed as conclusions. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy import pretty + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> print(pretty(d.hom(A, C), use_unicode=False)) + ({g*f:A-->C}, {g*f:A-->C}) + + See Also + ======== + Object, Morphism + """ + premises = EmptySet + conclusions = EmptySet + + for morphism in self.premises.keys(): + if (morphism.domain == A) and (morphism.codomain == B): + premises |= FiniteSet(morphism) + for morphism in self.conclusions.keys(): + if (morphism.domain == A) and (morphism.codomain == B): + conclusions |= FiniteSet(morphism) + + return (premises, conclusions) + + def is_subdiagram(self, diagram): + """ + Checks whether ``diagram`` is a subdiagram of ``self``. + Diagram `D'` is a subdiagram of `D` if all premises + (conclusions) of `D'` are contained in the premises + (conclusions) of `D`. The morphisms contained + both in `D'` and `D` should have the same properties for `D'` + to be a subdiagram of `D`. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> d1 = Diagram([f]) + >>> d.is_subdiagram(d1) + True + >>> d1.is_subdiagram(d) + False + """ + premises = all((m in self.premises) and + (diagram.premises[m] == self.premises[m]) + for m in diagram.premises) + if not premises: + return False + + conclusions = all((m in self.conclusions) and + (diagram.conclusions[m] == self.conclusions[m]) + for m in diagram.conclusions) + + # Premises is surely ``True`` here. + return conclusions + + def subdiagram_from_objects(self, objects): + """ + If ``objects`` is a subset of the objects of ``self``, returns + a diagram which has as premises all those premises of ``self`` + which have a domains and codomains in ``objects``, likewise + for conclusions. Properties are preserved. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy import FiniteSet + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g], {f: "unique", g*f: "veryunique"}) + >>> d1 = d.subdiagram_from_objects(FiniteSet(A, B)) + >>> d1 == Diagram([f], {f: "unique"}) + True + """ + if not objects.is_subset(self.objects): + raise ValueError( + "Supplied objects should all belong to the diagram.") + + new_premises = {} + for morphism, props in self.premises.items(): + if ((sympify(objects.contains(morphism.domain)) is S.true) and + (sympify(objects.contains(morphism.codomain)) is S.true)): + new_premises[morphism] = props + + new_conclusions = {} + for morphism, props in self.conclusions.items(): + if ((sympify(objects.contains(morphism.domain)) is S.true) and + (sympify(objects.contains(morphism.codomain)) is S.true)): + new_conclusions[morphism] = props + + return Diagram(new_premises, new_conclusions) diff --git a/lib/python3.11/site-packages/sympy/categories/diagram_drawing.py b/lib/python3.11/site-packages/sympy/categories/diagram_drawing.py new file mode 100644 index 0000000000000000000000000000000000000000..97997d1b934e7393fc8fb29211eff6a55f29a90c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/categories/diagram_drawing.py @@ -0,0 +1,2582 @@ +r""" +This module contains the functionality to arrange the nodes of a +diagram on an abstract grid, and then to produce a graphical +representation of the grid. + +The currently supported back-ends are Xy-pic [Xypic]. + +Layout Algorithm +================ + +This section provides an overview of the algorithms implemented in +:class:`DiagramGrid` to lay out diagrams. + +The first step of the algorithm is the removal composite and identity +morphisms which do not have properties in the supplied diagram. The +premises and conclusions of the diagram are then merged. + +The generic layout algorithm begins with the construction of the +"skeleton" of the diagram. The skeleton is an undirected graph which +has the objects of the diagram as vertices and has an (undirected) +edge between each pair of objects between which there exist morphisms. +The direction of the morphisms does not matter at this stage. The +skeleton also includes an edge between each pair of vertices `A` and +`C` such that there exists an object `B` which is connected via +a morphism to `A`, and via a morphism to `C`. + +The skeleton constructed in this way has the property that every +object is a vertex of a triangle formed by three edges of the +skeleton. This property lies at the base of the generic layout +algorithm. + +After the skeleton has been constructed, the algorithm lists all +triangles which can be formed. Note that some triangles will not have +all edges corresponding to morphisms which will actually be drawn. +Triangles which have only one edge or less which will actually be +drawn are immediately discarded. + +The list of triangles is sorted according to the number of edges which +correspond to morphisms, then the triangle with the least number of such +edges is selected. One of such edges is picked and the corresponding +objects are placed horizontally, on a grid. This edge is recorded to +be in the fringe. The algorithm then finds a "welding" of a triangle +to the fringe. A welding is an edge in the fringe where a triangle +could be attached. If the algorithm succeeds in finding such a +welding, it adds to the grid that vertex of the triangle which was not +yet included in any edge in the fringe and records the two new edges in +the fringe. This process continues iteratively until all objects of +the diagram has been placed or until no more weldings can be found. + +An edge is only removed from the fringe when a welding to this edge +has been found, and there is no room around this edge to place +another vertex. + +When no more weldings can be found, but there are still triangles +left, the algorithm searches for a possibility of attaching one of the +remaining triangles to the existing structure by a vertex. If such a +possibility is found, the corresponding edge of the found triangle is +placed in the found space and the iterative process of welding +triangles restarts. + +When logical groups are supplied, each of these groups is laid out +independently. Then a diagram is constructed in which groups are +objects and any two logical groups between which there exist morphisms +are connected via a morphism. This diagram is laid out. Finally, +the grid which includes all objects of the initial diagram is +constructed by replacing the cells which contain logical groups with +the corresponding laid out grids, and by correspondingly expanding the +rows and columns. + +The sequential layout algorithm begins by constructing the +underlying undirected graph defined by the morphisms obtained after +simplifying premises and conclusions and merging them (see above). +The vertex with the minimal degree is then picked up and depth-first +search is started from it. All objects which are located at distance +`n` from the root in the depth-first search tree, are positioned in +the `n`-th column of the resulting grid. The sequential layout will +therefore attempt to lay the objects out along a line. + +References +========== + +.. [Xypic] https://xy-pic.sourceforge.net/ + +""" +from sympy.categories import (CompositeMorphism, IdentityMorphism, + NamedMorphism, Diagram) +from sympy.core import Dict, Symbol, default_sort_key +from sympy.printing.latex import latex +from sympy.sets import FiniteSet +from sympy.utilities.iterables import iterable +from sympy.utilities.decorator import doctest_depends_on + +from itertools import chain + + +__doctest_requires__ = {('preview_diagram',): 'pyglet'} + + +class _GrowableGrid: + """ + Holds a growable grid of objects. + + Explanation + =========== + + It is possible to append or prepend a row or a column to the grid + using the corresponding methods. Prepending rows or columns has + the effect of changing the coordinates of the already existing + elements. + + This class currently represents a naive implementation of the + functionality with little attempt at optimisation. + """ + def __init__(self, width, height): + self._width = width + self._height = height + + self._array = [[None for j in range(width)] for i in range(height)] + + @property + def width(self): + return self._width + + @property + def height(self): + return self._height + + def __getitem__(self, i_j): + """ + Returns the element located at in the i-th line and j-th + column. + """ + i, j = i_j + return self._array[i][j] + + def __setitem__(self, i_j, newvalue): + """ + Sets the element located at in the i-th line and j-th + column. + """ + i, j = i_j + self._array[i][j] = newvalue + + def append_row(self): + """ + Appends an empty row to the grid. + """ + self._height += 1 + self._array.append([None for j in range(self._width)]) + + def append_column(self): + """ + Appends an empty column to the grid. + """ + self._width += 1 + for i in range(self._height): + self._array[i].append(None) + + def prepend_row(self): + """ + Prepends the grid with an empty row. + """ + self._height += 1 + self._array.insert(0, [None for j in range(self._width)]) + + def prepend_column(self): + """ + Prepends the grid with an empty column. + """ + self._width += 1 + for i in range(self._height): + self._array[i].insert(0, None) + + +class DiagramGrid: + r""" + Constructs and holds the fitting of the diagram into a grid. + + Explanation + =========== + + The mission of this class is to analyse the structure of the + supplied diagram and to place its objects on a grid such that, + when the objects and the morphisms are actually drawn, the diagram + would be "readable", in the sense that there will not be many + intersections of moprhisms. This class does not perform any + actual drawing. It does strive nevertheless to offer sufficient + metadata to draw a diagram. + + Consider the following simple diagram. + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> from sympy import pprint + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + + The simplest way to have a diagram laid out is the following: + + >>> grid = DiagramGrid(diagram) + >>> (grid.width, grid.height) + (2, 2) + >>> pprint(grid) + A B + + C + + Sometimes one sees the diagram as consisting of logical groups. + One can advise ``DiagramGrid`` as to such groups by employing the + ``groups`` keyword argument. + + Consider the following diagram: + + >>> D = Object("D") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> h = NamedMorphism(D, A, "h") + >>> k = NamedMorphism(D, B, "k") + >>> diagram = Diagram([f, g, h, k]) + + Lay it out with generic layout: + + >>> grid = DiagramGrid(diagram) + >>> pprint(grid) + A B D + + C + + Now, we can group the objects `A` and `D` to have them near one + another: + + >>> grid = DiagramGrid(diagram, groups=[[A, D], B, C]) + >>> pprint(grid) + B C + + A D + + Note how the positioning of the other objects changes. + + Further indications can be supplied to the constructor of + :class:`DiagramGrid` using keyword arguments. The currently + supported hints are explained in the following paragraphs. + + :class:`DiagramGrid` does not automatically guess which layout + would suit the supplied diagram better. Consider, for example, + the following linear diagram: + + >>> E = Object("E") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> h = NamedMorphism(C, D, "h") + >>> i = NamedMorphism(D, E, "i") + >>> diagram = Diagram([f, g, h, i]) + + When laid out with the generic layout, it does not get to look + linear: + + >>> grid = DiagramGrid(diagram) + >>> pprint(grid) + A B + + C D + + E + + To get it laid out in a line, use ``layout="sequential"``: + + >>> grid = DiagramGrid(diagram, layout="sequential") + >>> pprint(grid) + A B C D E + + One may sometimes need to transpose the resulting layout. While + this can always be done by hand, :class:`DiagramGrid` provides a + hint for that purpose: + + >>> grid = DiagramGrid(diagram, layout="sequential", transpose=True) + >>> pprint(grid) + A + + B + + C + + D + + E + + Separate hints can also be provided for each group. For an + example, refer to ``tests/test_drawing.py``, and see the different + ways in which the five lemma [FiveLemma] can be laid out. + + See Also + ======== + + Diagram + + References + ========== + + .. [FiveLemma] https://en.wikipedia.org/wiki/Five_lemma + """ + @staticmethod + def _simplify_morphisms(morphisms): + """ + Given a dictionary mapping morphisms to their properties, + returns a new dictionary in which there are no morphisms which + do not have properties, and which are compositions of other + morphisms included in the dictionary. Identities are dropped + as well. + """ + newmorphisms = {} + for morphism, props in morphisms.items(): + if isinstance(morphism, CompositeMorphism) and not props: + continue + elif isinstance(morphism, IdentityMorphism): + continue + else: + newmorphisms[morphism] = props + return newmorphisms + + @staticmethod + def _merge_premises_conclusions(premises, conclusions): + """ + Given two dictionaries of morphisms and their properties, + produces a single dictionary which includes elements from both + dictionaries. If a morphism has some properties in premises + and also in conclusions, the properties in conclusions take + priority. + """ + return dict(chain(premises.items(), conclusions.items())) + + @staticmethod + def _juxtapose_edges(edge1, edge2): + """ + If ``edge1`` and ``edge2`` have precisely one common endpoint, + returns an edge which would form a triangle with ``edge1`` and + ``edge2``. + + If ``edge1`` and ``edge2`` do not have a common endpoint, + returns ``None``. + + If ``edge1`` and ``edge`` are the same edge, returns ``None``. + """ + intersection = edge1 & edge2 + if len(intersection) != 1: + # The edges either have no common points or are equal. + return None + + # The edges have a common endpoint. Extract the different + # endpoints and set up the new edge. + return (edge1 - intersection) | (edge2 - intersection) + + @staticmethod + def _add_edge_append(dictionary, edge, elem): + """ + If ``edge`` is not in ``dictionary``, adds ``edge`` to the + dictionary and sets its value to ``[elem]``. Otherwise + appends ``elem`` to the value of existing entry. + + Note that edges are undirected, thus `(A, B) = (B, A)`. + """ + if edge in dictionary: + dictionary[edge].append(elem) + else: + dictionary[edge] = [elem] + + @staticmethod + def _build_skeleton(morphisms): + """ + Creates a dictionary which maps edges to corresponding + morphisms. Thus for a morphism `f:A\rightarrow B`, the edge + `(A, B)` will be associated with `f`. This function also adds + to the list those edges which are formed by juxtaposition of + two edges already in the list. These new edges are not + associated with any morphism and are only added to assure that + the diagram can be decomposed into triangles. + """ + edges = {} + # Create edges for morphisms. + for morphism in morphisms: + DiagramGrid._add_edge_append( + edges, frozenset([morphism.domain, morphism.codomain]), morphism) + + # Create new edges by juxtaposing existing edges. + edges1 = dict(edges) + for w in edges1: + for v in edges1: + wv = DiagramGrid._juxtapose_edges(w, v) + if wv and wv not in edges: + edges[wv] = [] + + return edges + + @staticmethod + def _list_triangles(edges): + """ + Builds the set of triangles formed by the supplied edges. The + triangles are arbitrary and need not be commutative. A + triangle is a set that contains all three of its sides. + """ + triangles = set() + + for w in edges: + for v in edges: + wv = DiagramGrid._juxtapose_edges(w, v) + if wv and wv in edges: + triangles.add(frozenset([w, v, wv])) + + return triangles + + @staticmethod + def _drop_redundant_triangles(triangles, skeleton): + """ + Returns a list which contains only those triangles who have + morphisms associated with at least two edges. + """ + return [tri for tri in triangles + if len([e for e in tri if skeleton[e]]) >= 2] + + @staticmethod + def _morphism_length(morphism): + """ + Returns the length of a morphism. The length of a morphism is + the number of components it consists of. A non-composite + morphism is of length 1. + """ + if isinstance(morphism, CompositeMorphism): + return len(morphism.components) + else: + return 1 + + @staticmethod + def _compute_triangle_min_sizes(triangles, edges): + r""" + Returns a dictionary mapping triangles to their minimal sizes. + The minimal size of a triangle is the sum of maximal lengths + of morphisms associated to the sides of the triangle. The + length of a morphism is the number of components it consists + of. A non-composite morphism is of length 1. + + Sorting triangles by this metric attempts to address two + aspects of layout. For triangles with only simple morphisms + in the edge, this assures that triangles with all three edges + visible will get typeset after triangles with less visible + edges, which sometimes minimizes the necessity in diagonal + arrows. For triangles with composite morphisms in the edges, + this assures that objects connected with shorter morphisms + will be laid out first, resulting the visual proximity of + those objects which are connected by shorter morphisms. + """ + triangle_sizes = {} + for triangle in triangles: + size = 0 + for e in triangle: + morphisms = edges[e] + if morphisms: + size += max(DiagramGrid._morphism_length(m) + for m in morphisms) + triangle_sizes[triangle] = size + return triangle_sizes + + @staticmethod + def _triangle_objects(triangle): + """ + Given a triangle, returns the objects included in it. + """ + # A triangle is a frozenset of three two-element frozensets + # (the edges). This chains the three edges together and + # creates a frozenset from the iterator, thus producing a + # frozenset of objects of the triangle. + return frozenset(chain(*tuple(triangle))) + + @staticmethod + def _other_vertex(triangle, edge): + """ + Given a triangle and an edge of it, returns the vertex which + opposes the edge. + """ + # This gets the set of objects of the triangle and then + # subtracts the set of objects employed in ``edge`` to get the + # vertex opposite to ``edge``. + return list(DiagramGrid._triangle_objects(triangle) - set(edge))[0] + + @staticmethod + def _empty_point(pt, grid): + """ + Checks if the cell at coordinates ``pt`` is either empty or + out of the bounds of the grid. + """ + if (pt[0] < 0) or (pt[1] < 0) or \ + (pt[0] >= grid.height) or (pt[1] >= grid.width): + return True + return grid[pt] is None + + @staticmethod + def _put_object(coords, obj, grid, fringe): + """ + Places an object at the coordinate ``cords`` in ``grid``, + growing the grid and updating ``fringe``, if necessary. + Returns (0, 0) if no row or column has been prepended, (1, 0) + if a row was prepended, (0, 1) if a column was prepended and + (1, 1) if both a column and a row were prepended. + """ + (i, j) = coords + offset = (0, 0) + if i == -1: + grid.prepend_row() + i = 0 + offset = (1, 0) + for k in range(len(fringe)): + ((i1, j1), (i2, j2)) = fringe[k] + fringe[k] = ((i1 + 1, j1), (i2 + 1, j2)) + elif i == grid.height: + grid.append_row() + + if j == -1: + j = 0 + offset = (offset[0], 1) + grid.prepend_column() + for k in range(len(fringe)): + ((i1, j1), (i2, j2)) = fringe[k] + fringe[k] = ((i1, j1 + 1), (i2, j2 + 1)) + elif j == grid.width: + grid.append_column() + + grid[i, j] = obj + return offset + + @staticmethod + def _choose_target_cell(pt1, pt2, edge, obj, skeleton, grid): + """ + Given two points, ``pt1`` and ``pt2``, and the welding edge + ``edge``, chooses one of the two points to place the opposing + vertex ``obj`` of the triangle. If neither of this points + fits, returns ``None``. + """ + pt1_empty = DiagramGrid._empty_point(pt1, grid) + pt2_empty = DiagramGrid._empty_point(pt2, grid) + + if pt1_empty and pt2_empty: + # Both cells are empty. Of these two, choose that cell + # which will assure that a visible edge of the triangle + # will be drawn perpendicularly to the current welding + # edge. + + A = grid[edge[0]] + + if skeleton.get(frozenset([A, obj])): + return pt1 + else: + return pt2 + if pt1_empty: + return pt1 + elif pt2_empty: + return pt2 + else: + return None + + @staticmethod + def _find_triangle_to_weld(triangles, fringe, grid): + """ + Finds, if possible, a triangle and an edge in the ``fringe`` to + which the triangle could be attached. Returns the tuple + containing the triangle and the index of the corresponding + edge in the ``fringe``. + + This function relies on the fact that objects are unique in + the diagram. + """ + for triangle in triangles: + for (a, b) in fringe: + if frozenset([grid[a], grid[b]]) in triangle: + return (triangle, (a, b)) + return None + + @staticmethod + def _weld_triangle(tri, welding_edge, fringe, grid, skeleton): + """ + If possible, welds the triangle ``tri`` to ``fringe`` and + returns ``False``. If this method encounters a degenerate + situation in the fringe and corrects it such that a restart of + the search is required, it returns ``True`` (which means that + a restart in finding triangle weldings is required). + + A degenerate situation is a situation when an edge listed in + the fringe does not belong to the visual boundary of the + diagram. + """ + a, b = welding_edge + target_cell = None + + obj = DiagramGrid._other_vertex(tri, (grid[a], grid[b])) + + # We now have a triangle and an edge where it can be welded to + # the fringe. Decide where to place the other vertex of the + # triangle and check for degenerate situations en route. + + if (abs(a[0] - b[0]) == 1) and (abs(a[1] - b[1]) == 1): + # A diagonal edge. + target_cell = (a[0], b[1]) + if grid[target_cell]: + # That cell is already occupied. + target_cell = (b[0], a[1]) + + if grid[target_cell]: + # Degenerate situation, this edge is not + # on the actual fringe. Correct the + # fringe and go on. + fringe.remove((a, b)) + return True + elif a[0] == b[0]: + # A horizontal edge. We first attempt to build the + # triangle in the downward direction. + + down_left = a[0] + 1, a[1] + down_right = a[0] + 1, b[1] + + target_cell = DiagramGrid._choose_target_cell( + down_left, down_right, (a, b), obj, skeleton, grid) + + if not target_cell: + # No room below this edge. Check above. + up_left = a[0] - 1, a[1] + up_right = a[0] - 1, b[1] + + target_cell = DiagramGrid._choose_target_cell( + up_left, up_right, (a, b), obj, skeleton, grid) + + if not target_cell: + # This edge is not in the fringe, remove it + # and restart. + fringe.remove((a, b)) + return True + elif a[1] == b[1]: + # A vertical edge. We will attempt to place the other + # vertex of the triangle to the right of this edge. + right_up = a[0], a[1] + 1 + right_down = b[0], a[1] + 1 + + target_cell = DiagramGrid._choose_target_cell( + right_up, right_down, (a, b), obj, skeleton, grid) + + if not target_cell: + # No room to the left. See what's to the right. + left_up = a[0], a[1] - 1 + left_down = b[0], a[1] - 1 + + target_cell = DiagramGrid._choose_target_cell( + left_up, left_down, (a, b), obj, skeleton, grid) + + if not target_cell: + # This edge is not in the fringe, remove it + # and restart. + fringe.remove((a, b)) + return True + + # We now know where to place the other vertex of the + # triangle. + offset = DiagramGrid._put_object(target_cell, obj, grid, fringe) + + # Take care of the displacement of coordinates if a row or + # a column was prepended. + target_cell = (target_cell[0] + offset[0], + target_cell[1] + offset[1]) + a = (a[0] + offset[0], a[1] + offset[1]) + b = (b[0] + offset[0], b[1] + offset[1]) + + fringe.extend([(a, target_cell), (b, target_cell)]) + + # No restart is required. + return False + + @staticmethod + def _triangle_key(tri, triangle_sizes): + """ + Returns a key for the supplied triangle. It should be the + same independently of the hash randomisation. + """ + objects = sorted( + DiagramGrid._triangle_objects(tri), key=default_sort_key) + return (triangle_sizes[tri], default_sort_key(objects)) + + @staticmethod + def _pick_root_edge(tri, skeleton): + """ + For a given triangle always picks the same root edge. The + root edge is the edge that will be placed first on the grid. + """ + candidates = [sorted(e, key=default_sort_key) + for e in tri if skeleton[e]] + sorted_candidates = sorted(candidates, key=default_sort_key) + # Don't forget to assure the proper ordering of the vertices + # in this edge. + return tuple(sorted(sorted_candidates[0], key=default_sort_key)) + + @staticmethod + def _drop_irrelevant_triangles(triangles, placed_objects): + """ + Returns only those triangles whose set of objects is not + completely included in ``placed_objects``. + """ + return [tri for tri in triangles if not placed_objects.issuperset( + DiagramGrid._triangle_objects(tri))] + + @staticmethod + def _grow_pseudopod(triangles, fringe, grid, skeleton, placed_objects): + """ + Starting from an object in the existing structure on the ``grid``, + adds an edge to which a triangle from ``triangles`` could be + welded. If this method has found a way to do so, it returns + the object it has just added. + + This method should be applied when ``_weld_triangle`` cannot + find weldings any more. + """ + for i in range(grid.height): + for j in range(grid.width): + obj = grid[i, j] + if not obj: + continue + + # Here we need to choose a triangle which has only + # ``obj`` in common with the existing structure. The + # situations when this is not possible should be + # handled elsewhere. + + def good_triangle(tri): + objs = DiagramGrid._triangle_objects(tri) + return obj in objs and \ + placed_objects & (objs - {obj}) == set() + + tris = [tri for tri in triangles if good_triangle(tri)] + if not tris: + # This object is not interesting. + continue + + # Pick the "simplest" of the triangles which could be + # attached. Remember that the list of triangles is + # sorted according to their "simplicity" (see + # _compute_triangle_min_sizes for the metric). + # + # Note that ``tris`` are sequentially built from + # ``triangles``, so we don't have to worry about hash + # randomisation. + tri = tris[0] + + # We have found a triangle which could be attached to + # the existing structure by a vertex. + + candidates = sorted([e for e in tri if skeleton[e]], + key=lambda e: FiniteSet(*e).sort_key()) + edges = [e for e in candidates if obj in e] + + # Note that a meaningful edge (i.e., and edge that is + # associated with a morphism) containing ``obj`` + # always exists. That's because all triangles are + # guaranteed to have at least two meaningful edges. + # See _drop_redundant_triangles. + + # Get the object at the other end of the edge. + edge = edges[0] + other_obj = tuple(edge - frozenset([obj]))[0] + + # Now check for free directions. When checking for + # free directions, prefer the horizontal and vertical + # directions. + neighbours = [(i - 1, j), (i, j + 1), (i + 1, j), (i, j - 1), + (i - 1, j - 1), (i - 1, j + 1), (i + 1, j - 1), (i + 1, j + 1)] + + for pt in neighbours: + if DiagramGrid._empty_point(pt, grid): + # We have a found a place to grow the + # pseudopod into. + offset = DiagramGrid._put_object( + pt, other_obj, grid, fringe) + + i += offset[0] + j += offset[1] + pt = (pt[0] + offset[0], pt[1] + offset[1]) + fringe.append(((i, j), pt)) + + return other_obj + + # This diagram is actually cooler that I can handle. Fail cowardly. + return None + + @staticmethod + def _handle_groups(diagram, groups, merged_morphisms, hints): + """ + Given the slightly preprocessed morphisms of the diagram, + produces a grid laid out according to ``groups``. + + If a group has hints, it is laid out with those hints only, + without any influence from ``hints``. Otherwise, it is laid + out with ``hints``. + """ + def lay_out_group(group, local_hints): + """ + If ``group`` is a set of objects, uses a ``DiagramGrid`` + to lay it out and returns the grid. Otherwise returns the + object (i.e., ``group``). If ``local_hints`` is not + empty, it is supplied to ``DiagramGrid`` as the dictionary + of hints. Otherwise, the ``hints`` argument of + ``_handle_groups`` is used. + """ + if isinstance(group, FiniteSet): + # Set up the corresponding object-to-group + # mappings. + for obj in group: + obj_groups[obj] = group + + # Lay out the current group. + if local_hints: + groups_grids[group] = DiagramGrid( + diagram.subdiagram_from_objects(group), **local_hints) + else: + groups_grids[group] = DiagramGrid( + diagram.subdiagram_from_objects(group), **hints) + else: + obj_groups[group] = group + + def group_to_finiteset(group): + """ + Converts ``group`` to a :class:``FiniteSet`` if it is an + iterable. + """ + if iterable(group): + return FiniteSet(*group) + else: + return group + + obj_groups = {} + groups_grids = {} + + # We would like to support various containers to represent + # groups. To achieve that, before laying each group out, it + # should be converted to a FiniteSet, because that is what the + # following code expects. + + if isinstance(groups, (dict, Dict)): + finiteset_groups = {} + for group, local_hints in groups.items(): + finiteset_group = group_to_finiteset(group) + finiteset_groups[finiteset_group] = local_hints + lay_out_group(group, local_hints) + groups = finiteset_groups + else: + finiteset_groups = [] + for group in groups: + finiteset_group = group_to_finiteset(group) + finiteset_groups.append(finiteset_group) + lay_out_group(finiteset_group, None) + groups = finiteset_groups + + new_morphisms = [] + for morphism in merged_morphisms: + dom = obj_groups[morphism.domain] + cod = obj_groups[morphism.codomain] + # Note that we are not really interested in morphisms + # which do not employ two different groups, because + # these do not influence the layout. + if dom != cod: + # These are essentially unnamed morphisms; they are + # not going to mess in the final layout. By giving + # them the same names, we avoid unnecessary + # duplicates. + new_morphisms.append(NamedMorphism(dom, cod, "dummy")) + + # Lay out the new diagram. Since these are dummy morphisms, + # properties and conclusions are irrelevant. + top_grid = DiagramGrid(Diagram(new_morphisms)) + + # We now have to substitute the groups with the corresponding + # grids, laid out at the beginning of this function. Compute + # the size of each row and column in the grid, so that all + # nested grids fit. + + def group_size(group): + """ + For the supplied group (or object, eventually), returns + the size of the cell that will hold this group (object). + """ + if group in groups_grids: + grid = groups_grids[group] + return (grid.height, grid.width) + else: + return (1, 1) + + row_heights = [max(group_size(top_grid[i, j])[0] + for j in range(top_grid.width)) + for i in range(top_grid.height)] + + column_widths = [max(group_size(top_grid[i, j])[1] + for i in range(top_grid.height)) + for j in range(top_grid.width)] + + grid = _GrowableGrid(sum(column_widths), sum(row_heights)) + + real_row = 0 + real_column = 0 + for logical_row in range(top_grid.height): + for logical_column in range(top_grid.width): + obj = top_grid[logical_row, logical_column] + + if obj in groups_grids: + # This is a group. Copy the corresponding grid in + # place. + local_grid = groups_grids[obj] + for i in range(local_grid.height): + for j in range(local_grid.width): + grid[real_row + i, + real_column + j] = local_grid[i, j] + else: + # This is an object. Just put it there. + grid[real_row, real_column] = obj + + real_column += column_widths[logical_column] + real_column = 0 + real_row += row_heights[logical_row] + + return grid + + @staticmethod + def _generic_layout(diagram, merged_morphisms): + """ + Produces the generic layout for the supplied diagram. + """ + all_objects = set(diagram.objects) + if len(all_objects) == 1: + # There only one object in the diagram, just put in on 1x1 + # grid. + grid = _GrowableGrid(1, 1) + grid[0, 0] = tuple(all_objects)[0] + return grid + + skeleton = DiagramGrid._build_skeleton(merged_morphisms) + + grid = _GrowableGrid(2, 1) + + if len(skeleton) == 1: + # This diagram contains only one morphism. Draw it + # horizontally. + objects = sorted(all_objects, key=default_sort_key) + grid[0, 0] = objects[0] + grid[0, 1] = objects[1] + + return grid + + triangles = DiagramGrid._list_triangles(skeleton) + triangles = DiagramGrid._drop_redundant_triangles(triangles, skeleton) + triangle_sizes = DiagramGrid._compute_triangle_min_sizes( + triangles, skeleton) + + triangles = sorted(triangles, key=lambda tri: + DiagramGrid._triangle_key(tri, triangle_sizes)) + + # Place the first edge on the grid. + root_edge = DiagramGrid._pick_root_edge(triangles[0], skeleton) + grid[0, 0], grid[0, 1] = root_edge + fringe = [((0, 0), (0, 1))] + + # Record which objects we now have on the grid. + placed_objects = set(root_edge) + + while placed_objects != all_objects: + welding = DiagramGrid._find_triangle_to_weld( + triangles, fringe, grid) + + if welding: + (triangle, welding_edge) = welding + + restart_required = DiagramGrid._weld_triangle( + triangle, welding_edge, fringe, grid, skeleton) + if restart_required: + continue + + placed_objects.update( + DiagramGrid._triangle_objects(triangle)) + else: + # No more weldings found. Try to attach triangles by + # vertices. + new_obj = DiagramGrid._grow_pseudopod( + triangles, fringe, grid, skeleton, placed_objects) + + if not new_obj: + # No more triangles can be attached, not even by + # the edge. We will set up a new diagram out of + # what has been left, laid it out independently, + # and then attach it to this one. + + remaining_objects = all_objects - placed_objects + + remaining_diagram = diagram.subdiagram_from_objects( + FiniteSet(*remaining_objects)) + remaining_grid = DiagramGrid(remaining_diagram) + + # Now, let's glue ``remaining_grid`` to ``grid``. + final_width = grid.width + remaining_grid.width + final_height = max(grid.height, remaining_grid.height) + final_grid = _GrowableGrid(final_width, final_height) + + for i in range(grid.width): + for j in range(grid.height): + final_grid[i, j] = grid[i, j] + + start_j = grid.width + for i in range(remaining_grid.height): + for j in range(remaining_grid.width): + final_grid[i, start_j + j] = remaining_grid[i, j] + + return final_grid + + placed_objects.add(new_obj) + + triangles = DiagramGrid._drop_irrelevant_triangles( + triangles, placed_objects) + + return grid + + @staticmethod + def _get_undirected_graph(objects, merged_morphisms): + """ + Given the objects and the relevant morphisms of a diagram, + returns the adjacency lists of the underlying undirected + graph. + """ + adjlists = {} + for obj in objects: + adjlists[obj] = [] + + for morphism in merged_morphisms: + adjlists[morphism.domain].append(morphism.codomain) + adjlists[morphism.codomain].append(morphism.domain) + + # Assure that the objects in the adjacency list are always in + # the same order. + for obj in adjlists.keys(): + adjlists[obj].sort(key=default_sort_key) + + return adjlists + + @staticmethod + def _sequential_layout(diagram, merged_morphisms): + r""" + Lays out the diagram in "sequential" layout. This method + will attempt to produce a result as close to a line as + possible. For linear diagrams, the result will actually be a + line. + """ + objects = diagram.objects + sorted_objects = sorted(objects, key=default_sort_key) + + # Set up the adjacency lists of the underlying undirected + # graph of ``merged_morphisms``. + adjlists = DiagramGrid._get_undirected_graph(objects, merged_morphisms) + + root = min(sorted_objects, key=lambda x: len(adjlists[x])) + grid = _GrowableGrid(1, 1) + grid[0, 0] = root + + placed_objects = {root} + + def place_objects(pt, placed_objects): + """ + Does depth-first search in the underlying graph of the + diagram and places the objects en route. + """ + # We will start placing new objects from here. + new_pt = (pt[0], pt[1] + 1) + + for adjacent_obj in adjlists[grid[pt]]: + if adjacent_obj in placed_objects: + # This object has already been placed. + continue + + DiagramGrid._put_object(new_pt, adjacent_obj, grid, []) + placed_objects.add(adjacent_obj) + placed_objects.update(place_objects(new_pt, placed_objects)) + + new_pt = (new_pt[0] + 1, new_pt[1]) + + return placed_objects + + place_objects((0, 0), placed_objects) + + return grid + + @staticmethod + def _drop_inessential_morphisms(merged_morphisms): + r""" + Removes those morphisms which should appear in the diagram, + but which have no relevance to object layout. + + Currently this removes "loop" morphisms: the non-identity + morphisms with the same domains and codomains. + """ + morphisms = [m for m in merged_morphisms if m.domain != m.codomain] + return morphisms + + @staticmethod + def _get_connected_components(objects, merged_morphisms): + """ + Given a container of morphisms, returns a list of connected + components formed by these morphisms. A connected component + is represented by a diagram consisting of the corresponding + morphisms. + """ + component_index = {} + for o in objects: + component_index[o] = None + + # Get the underlying undirected graph of the diagram. + adjlist = DiagramGrid._get_undirected_graph(objects, merged_morphisms) + + def traverse_component(object, current_index): + """ + Does a depth-first search traversal of the component + containing ``object``. + """ + component_index[object] = current_index + for o in adjlist[object]: + if component_index[o] is None: + traverse_component(o, current_index) + + # Traverse all components. + current_index = 0 + for o in adjlist: + if component_index[o] is None: + traverse_component(o, current_index) + current_index += 1 + + # List the objects of the components. + component_objects = [[] for i in range(current_index)] + for o, idx in component_index.items(): + component_objects[idx].append(o) + + # Finally, list the morphisms belonging to each component. + # + # Note: If some objects are isolated, they will not get any + # morphisms at this stage, and since the layout algorithm + # relies, we are essentially going to lose this object. + # Therefore, check if there are isolated objects and, for each + # of them, provide the trivial identity morphism. It will get + # discarded later, but the object will be there. + + component_morphisms = [] + for component in component_objects: + current_morphisms = {} + for m in merged_morphisms: + if (m.domain in component) and (m.codomain in component): + current_morphisms[m] = merged_morphisms[m] + + if len(component) == 1: + # Let's add an identity morphism, for the sake of + # surely having morphisms in this component. + current_morphisms[IdentityMorphism(component[0])] = FiniteSet() + + component_morphisms.append(Diagram(current_morphisms)) + + return component_morphisms + + def __init__(self, diagram, groups=None, **hints): + premises = DiagramGrid._simplify_morphisms(diagram.premises) + conclusions = DiagramGrid._simplify_morphisms(diagram.conclusions) + all_merged_morphisms = DiagramGrid._merge_premises_conclusions( + premises, conclusions) + merged_morphisms = DiagramGrid._drop_inessential_morphisms( + all_merged_morphisms) + + # Store the merged morphisms for later use. + self._morphisms = all_merged_morphisms + + components = DiagramGrid._get_connected_components( + diagram.objects, all_merged_morphisms) + + if groups and (groups != diagram.objects): + # Lay out the diagram according to the groups. + self._grid = DiagramGrid._handle_groups( + diagram, groups, merged_morphisms, hints) + elif len(components) > 1: + # Note that we check for connectedness _before_ checking + # the layout hints because the layout strategies don't + # know how to deal with disconnected diagrams. + + # The diagram is disconnected. Lay out the components + # independently. + grids = [] + + # Sort the components to eventually get the grids arranged + # in a fixed, hash-independent order. + components = sorted(components, key=default_sort_key) + + for component in components: + grid = DiagramGrid(component, **hints) + grids.append(grid) + + # Throw the grids together, in a line. + total_width = sum(g.width for g in grids) + total_height = max(g.height for g in grids) + + grid = _GrowableGrid(total_width, total_height) + start_j = 0 + for g in grids: + for i in range(g.height): + for j in range(g.width): + grid[i, start_j + j] = g[i, j] + + start_j += g.width + + self._grid = grid + elif "layout" in hints: + if hints["layout"] == "sequential": + self._grid = DiagramGrid._sequential_layout( + diagram, merged_morphisms) + else: + self._grid = DiagramGrid._generic_layout(diagram, merged_morphisms) + + if hints.get("transpose"): + # Transpose the resulting grid. + grid = _GrowableGrid(self._grid.height, self._grid.width) + for i in range(self._grid.height): + for j in range(self._grid.width): + grid[j, i] = self._grid[i, j] + self._grid = grid + + @property + def width(self): + """ + Returns the number of columns in this diagram layout. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + >>> grid = DiagramGrid(diagram) + >>> grid.width + 2 + + """ + return self._grid.width + + @property + def height(self): + """ + Returns the number of rows in this diagram layout. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + >>> grid = DiagramGrid(diagram) + >>> grid.height + 2 + + """ + return self._grid.height + + def __getitem__(self, i_j): + """ + Returns the object placed in the row ``i`` and column ``j``. + The indices are 0-based. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + >>> grid = DiagramGrid(diagram) + >>> (grid[0, 0], grid[0, 1]) + (Object("A"), Object("B")) + >>> (grid[1, 0], grid[1, 1]) + (None, Object("C")) + + """ + i, j = i_j + return self._grid[i, j] + + @property + def morphisms(self): + """ + Returns those morphisms (and their properties) which are + sufficiently meaningful to be drawn. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + >>> grid = DiagramGrid(diagram) + >>> grid.morphisms + {NamedMorphism(Object("A"), Object("B"), "f"): EmptySet, + NamedMorphism(Object("B"), Object("C"), "g"): EmptySet} + + """ + return self._morphisms + + def __str__(self): + """ + Produces a string representation of this class. + + This method returns a string representation of the underlying + list of lists of objects. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism + >>> from sympy.categories import Diagram, DiagramGrid + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g]) + >>> grid = DiagramGrid(diagram) + >>> print(grid) + [[Object("A"), Object("B")], + [None, Object("C")]] + + """ + return repr(self._grid._array) + + +class ArrowStringDescription: + r""" + Stores the information necessary for producing an Xy-pic + description of an arrow. + + The principal goal of this class is to abstract away the string + representation of an arrow and to also provide the functionality + to produce the actual Xy-pic string. + + ``unit`` sets the unit which will be used to specify the amount of + curving and other distances. ``horizontal_direction`` should be a + string of ``"r"`` or ``"l"`` specifying the horizontal offset of the + target cell of the arrow relatively to the current one. + ``vertical_direction`` should specify the vertical offset using a + series of either ``"d"`` or ``"u"``. ``label_position`` should be + either ``"^"``, ``"_"``, or ``"|"`` to specify that the label should + be positioned above the arrow, below the arrow or just over the arrow, + in a break. Note that the notions "above" and "below" are relative + to arrow direction. ``label`` stores the morphism label. + + This works as follows (disregard the yet unexplained arguments): + + >>> from sympy.categories.diagram_drawing import ArrowStringDescription + >>> astr = ArrowStringDescription( + ... unit="mm", curving=None, curving_amount=None, + ... looping_start=None, looping_end=None, horizontal_direction="d", + ... vertical_direction="r", label_position="_", label="f") + >>> print(str(astr)) + \ar[dr]_{f} + + ``curving`` should be one of ``"^"``, ``"_"`` to specify in which + direction the arrow is going to curve. ``curving_amount`` is a number + describing how many ``unit``'s the morphism is going to curve: + + >>> astr = ArrowStringDescription( + ... unit="mm", curving="^", curving_amount=12, + ... looping_start=None, looping_end=None, horizontal_direction="d", + ... vertical_direction="r", label_position="_", label="f") + >>> print(str(astr)) + \ar@/^12mm/[dr]_{f} + + ``looping_start`` and ``looping_end`` are currently only used for + loop morphisms, those which have the same domain and codomain. + These two attributes should store a valid Xy-pic direction and + specify, correspondingly, the direction the arrow gets out into + and the direction the arrow gets back from: + + >>> astr = ArrowStringDescription( + ... unit="mm", curving=None, curving_amount=None, + ... looping_start="u", looping_end="l", horizontal_direction="", + ... vertical_direction="", label_position="_", label="f") + >>> print(str(astr)) + \ar@(u,l)[]_{f} + + ``label_displacement`` controls how far the arrow label is from + the ends of the arrow. For example, to position the arrow label + near the arrow head, use ">": + + >>> astr = ArrowStringDescription( + ... unit="mm", curving="^", curving_amount=12, + ... looping_start=None, looping_end=None, horizontal_direction="d", + ... vertical_direction="r", label_position="_", label="f") + >>> astr.label_displacement = ">" + >>> print(str(astr)) + \ar@/^12mm/[dr]_>{f} + + Finally, ``arrow_style`` is used to specify the arrow style. To + get a dashed arrow, for example, use "{-->}" as arrow style: + + >>> astr = ArrowStringDescription( + ... unit="mm", curving="^", curving_amount=12, + ... looping_start=None, looping_end=None, horizontal_direction="d", + ... vertical_direction="r", label_position="_", label="f") + >>> astr.arrow_style = "{-->}" + >>> print(str(astr)) + \ar@/^12mm/@{-->}[dr]_{f} + + Notes + ===== + + Instances of :class:`ArrowStringDescription` will be constructed + by :class:`XypicDiagramDrawer` and provided for further use in + formatters. The user is not expected to construct instances of + :class:`ArrowStringDescription` themselves. + + To be able to properly utilise this class, the reader is encouraged + to checkout the Xy-pic user guide, available at [Xypic]. + + See Also + ======== + + XypicDiagramDrawer + + References + ========== + + .. [Xypic] https://xy-pic.sourceforge.net/ + """ + def __init__(self, unit, curving, curving_amount, looping_start, + looping_end, horizontal_direction, vertical_direction, + label_position, label): + self.unit = unit + self.curving = curving + self.curving_amount = curving_amount + self.looping_start = looping_start + self.looping_end = looping_end + self.horizontal_direction = horizontal_direction + self.vertical_direction = vertical_direction + self.label_position = label_position + self.label = label + + self.label_displacement = "" + self.arrow_style = "" + + # This flag shows that the position of the label of this + # morphism was set while typesetting a curved morphism and + # should not be modified later. + self.forced_label_position = False + + def __str__(self): + if self.curving: + curving_str = "@/%s%d%s/" % (self.curving, self.curving_amount, + self.unit) + else: + curving_str = "" + + if self.looping_start and self.looping_end: + looping_str = "@(%s,%s)" % (self.looping_start, self.looping_end) + else: + looping_str = "" + + if self.arrow_style: + + style_str = "@" + self.arrow_style + else: + style_str = "" + + return "\\ar%s%s%s[%s%s]%s%s{%s}" % \ + (curving_str, looping_str, style_str, self.horizontal_direction, + self.vertical_direction, self.label_position, + self.label_displacement, self.label) + + +class XypicDiagramDrawer: + r""" + Given a :class:`~.Diagram` and the corresponding + :class:`DiagramGrid`, produces the Xy-pic representation of the + diagram. + + The most important method in this class is ``draw``. Consider the + following triangle diagram: + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy.categories import DiagramGrid, XypicDiagramDrawer + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g], {g * f: "unique"}) + + To draw this diagram, its objects need to be laid out with a + :class:`DiagramGrid`:: + + >>> grid = DiagramGrid(diagram) + + Finally, the drawing: + + >>> drawer = XypicDiagramDrawer() + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + For further details see the docstring of this method. + + To control the appearance of the arrows, formatters are used. The + dictionary ``arrow_formatters`` maps morphisms to formatter + functions. A formatter is accepts an + :class:`ArrowStringDescription` and is allowed to modify any of + the arrow properties exposed thereby. For example, to have all + morphisms with the property ``unique`` appear as dashed arrows, + and to have their names prepended with `\exists !`, the following + should be done: + + >>> def formatter(astr): + ... astr.label = r"\exists !" + astr.label + ... astr.arrow_style = "{-->}" + >>> drawer.arrow_formatters["unique"] = formatter + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar@{-->}[d]_{\exists !g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + To modify the appearance of all arrows in the diagram, set + ``default_arrow_formatter``. For example, to place all morphism + labels a little bit farther from the arrow head so that they look + more centred, do as follows: + + >>> def default_formatter(astr): + ... astr.label_displacement = "(0.45)" + >>> drawer.default_arrow_formatter = default_formatter + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar@{-->}[d]_(0.45){\exists !g\circ f} \ar[r]^(0.45){f} & B \ar[ld]^(0.45){g} \\ + C & + } + + In some diagrams some morphisms are drawn as curved arrows. + Consider the following diagram: + + >>> D = Object("D") + >>> E = Object("E") + >>> h = NamedMorphism(D, A, "h") + >>> k = NamedMorphism(D, B, "k") + >>> diagram = Diagram([f, g, h, k]) + >>> grid = DiagramGrid(diagram) + >>> drawer = XypicDiagramDrawer() + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar[r]_{f} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_3mm/[ll]_{h} \\ + & C & + } + + To control how far the morphisms are curved by default, one can + use the ``unit`` and ``default_curving_amount`` attributes: + + >>> drawer.unit = "cm" + >>> drawer.default_curving_amount = 1 + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar[r]_{f} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_1cm/[ll]_{h} \\ + & C & + } + + In some diagrams, there are multiple curved morphisms between the + same two objects. To control by how much the curving changes + between two such successive morphisms, use + ``default_curving_step``: + + >>> drawer.default_curving_step = 1 + >>> h1 = NamedMorphism(A, D, "h1") + >>> diagram = Diagram([f, g, h, k, h1]) + >>> grid = DiagramGrid(diagram) + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar[r]_{f} \ar@/^1cm/[rr]^{h_{1}} & B \ar[d]^{g} & D \ar[l]^{k} \ar@/_2cm/[ll]_{h} \\ + & C & + } + + The default value of ``default_curving_step`` is 4 units. + + See Also + ======== + + draw, ArrowStringDescription + """ + def __init__(self): + self.unit = "mm" + self.default_curving_amount = 3 + self.default_curving_step = 4 + + # This dictionary maps properties to the corresponding arrow + # formatters. + self.arrow_formatters = {} + + # This is the default arrow formatter which will be applied to + # each arrow independently of its properties. + self.default_arrow_formatter = None + + @staticmethod + def _process_loop_morphism(i, j, grid, morphisms_str_info, object_coords): + """ + Produces the information required for constructing the string + representation of a loop morphism. This function is invoked + from ``_process_morphism``. + + See Also + ======== + + _process_morphism + """ + curving = "" + label_pos = "^" + looping_start = "" + looping_end = "" + + # This is a loop morphism. Count how many morphisms stick + # in each of the four quadrants. Note that straight + # vertical and horizontal morphisms count in two quadrants + # at the same time (i.e., a morphism going up counts both + # in the first and the second quadrants). + + # The usual numbering (counterclockwise) of quadrants + # applies. + quadrant = [0, 0, 0, 0] + + obj = grid[i, j] + + for m, m_str_info in morphisms_str_info.items(): + if (m.domain == obj) and (m.codomain == obj): + # That's another loop morphism. Check how it + # loops and mark the corresponding quadrants as + # busy. + (l_s, l_e) = (m_str_info.looping_start, m_str_info.looping_end) + + if (l_s, l_e) == ("r", "u"): + quadrant[0] += 1 + elif (l_s, l_e) == ("u", "l"): + quadrant[1] += 1 + elif (l_s, l_e) == ("l", "d"): + quadrant[2] += 1 + elif (l_s, l_e) == ("d", "r"): + quadrant[3] += 1 + + continue + if m.domain == obj: + (end_i, end_j) = object_coords[m.codomain] + goes_out = True + elif m.codomain == obj: + (end_i, end_j) = object_coords[m.domain] + goes_out = False + else: + continue + + d_i = end_i - i + d_j = end_j - j + m_curving = m_str_info.curving + + if (d_i != 0) and (d_j != 0): + # This is really a diagonal morphism. Detect the + # quadrant. + if (d_i > 0) and (d_j > 0): + quadrant[0] += 1 + elif (d_i > 0) and (d_j < 0): + quadrant[1] += 1 + elif (d_i < 0) and (d_j < 0): + quadrant[2] += 1 + elif (d_i < 0) and (d_j > 0): + quadrant[3] += 1 + elif d_i == 0: + # Knowing where the other end of the morphism is + # and which way it goes, we now have to decide + # which quadrant is now the upper one and which is + # the lower one. + if d_j > 0: + if goes_out: + upper_quadrant = 0 + lower_quadrant = 3 + else: + upper_quadrant = 3 + lower_quadrant = 0 + else: + if goes_out: + upper_quadrant = 2 + lower_quadrant = 1 + else: + upper_quadrant = 1 + lower_quadrant = 2 + + if m_curving: + if m_curving == "^": + quadrant[upper_quadrant] += 1 + elif m_curving == "_": + quadrant[lower_quadrant] += 1 + else: + # This morphism counts in both upper and lower + # quadrants. + quadrant[upper_quadrant] += 1 + quadrant[lower_quadrant] += 1 + elif d_j == 0: + # Knowing where the other end of the morphism is + # and which way it goes, we now have to decide + # which quadrant is now the left one and which is + # the right one. + if d_i < 0: + if goes_out: + left_quadrant = 1 + right_quadrant = 0 + else: + left_quadrant = 0 + right_quadrant = 1 + else: + if goes_out: + left_quadrant = 3 + right_quadrant = 2 + else: + left_quadrant = 2 + right_quadrant = 3 + + if m_curving: + if m_curving == "^": + quadrant[left_quadrant] += 1 + elif m_curving == "_": + quadrant[right_quadrant] += 1 + else: + # This morphism counts in both upper and lower + # quadrants. + quadrant[left_quadrant] += 1 + quadrant[right_quadrant] += 1 + + # Pick the freest quadrant to curve our morphism into. + freest_quadrant = 0 + for i in range(4): + if quadrant[i] < quadrant[freest_quadrant]: + freest_quadrant = i + + # Now set up proper looping. + (looping_start, looping_end) = [("r", "u"), ("u", "l"), ("l", "d"), + ("d", "r")][freest_quadrant] + + return (curving, label_pos, looping_start, looping_end) + + @staticmethod + def _process_horizontal_morphism(i, j, target_j, grid, morphisms_str_info, + object_coords): + """ + Produces the information required for constructing the string + representation of a horizontal morphism. This function is + invoked from ``_process_morphism``. + + See Also + ======== + + _process_morphism + """ + # The arrow is horizontal. Check if it goes from left to + # right (``backwards == False``) or from right to left + # (``backwards == True``). + backwards = False + start = j + end = target_j + if end < start: + (start, end) = (end, start) + backwards = True + + # Let's see which objects are there between ``start`` and + # ``end``, and then count how many morphisms stick out + # upwards, and how many stick out downwards. + # + # For example, consider the situation: + # + # B1 C1 + # | | + # A--B--C--D + # | + # B2 + # + # Between the objects `A` and `D` there are two objects: + # `B` and `C`. Further, there are two morphisms which + # stick out upward (the ones between `B1` and `B` and + # between `C` and `C1`) and one morphism which sticks out + # downward (the one between `B and `B2`). + # + # We need this information to decide how to curve the + # arrow between `A` and `D`. First of all, since there + # are two objects between `A` and `D``, we must curve the + # arrow. Then, we will have it curve downward, because + # there is more space (less morphisms stick out downward + # than upward). + up = [] + down = [] + straight_horizontal = [] + for k in range(start + 1, end): + obj = grid[i, k] + if not obj: + continue + + for m in morphisms_str_info: + if m.domain == obj: + (end_i, end_j) = object_coords[m.codomain] + elif m.codomain == obj: + (end_i, end_j) = object_coords[m.domain] + else: + continue + + if end_i > i: + down.append(m) + elif end_i < i: + up.append(m) + elif not morphisms_str_info[m].curving: + # This is a straight horizontal morphism, + # because it has no curving. + straight_horizontal.append(m) + + if len(up) < len(down): + # More morphisms stick out downward than upward, let's + # curve the morphism up. + if backwards: + curving = "_" + label_pos = "_" + else: + curving = "^" + label_pos = "^" + + # Assure that the straight horizontal morphisms have + # their labels on the lower side of the arrow. + for m in straight_horizontal: + (i1, j1) = object_coords[m.domain] + (i2, j2) = object_coords[m.codomain] + + m_str_info = morphisms_str_info[m] + if j1 < j2: + m_str_info.label_position = "_" + else: + m_str_info.label_position = "^" + + # Don't allow any further modifications of the + # position of this label. + m_str_info.forced_label_position = True + else: + # More morphisms stick out downward than upward, let's + # curve the morphism up. + if backwards: + curving = "^" + label_pos = "^" + else: + curving = "_" + label_pos = "_" + + # Assure that the straight horizontal morphisms have + # their labels on the upper side of the arrow. + for m in straight_horizontal: + (i1, j1) = object_coords[m.domain] + (i2, j2) = object_coords[m.codomain] + + m_str_info = morphisms_str_info[m] + if j1 < j2: + m_str_info.label_position = "^" + else: + m_str_info.label_position = "_" + + # Don't allow any further modifications of the + # position of this label. + m_str_info.forced_label_position = True + + return (curving, label_pos) + + @staticmethod + def _process_vertical_morphism(i, j, target_i, grid, morphisms_str_info, + object_coords): + """ + Produces the information required for constructing the string + representation of a vertical morphism. This function is + invoked from ``_process_morphism``. + + See Also + ======== + + _process_morphism + """ + # This arrow is vertical. Check if it goes from top to + # bottom (``backwards == False``) or from bottom to top + # (``backwards == True``). + backwards = False + start = i + end = target_i + if end < start: + (start, end) = (end, start) + backwards = True + + # Let's see which objects are there between ``start`` and + # ``end``, and then count how many morphisms stick out to + # the left, and how many stick out to the right. + # + # See the corresponding comment in the previous branch of + # this if-statement for more details. + left = [] + right = [] + straight_vertical = [] + for k in range(start + 1, end): + obj = grid[k, j] + if not obj: + continue + + for m in morphisms_str_info: + if m.domain == obj: + (end_i, end_j) = object_coords[m.codomain] + elif m.codomain == obj: + (end_i, end_j) = object_coords[m.domain] + else: + continue + + if end_j > j: + right.append(m) + elif end_j < j: + left.append(m) + elif not morphisms_str_info[m].curving: + # This is a straight vertical morphism, + # because it has no curving. + straight_vertical.append(m) + + if len(left) < len(right): + # More morphisms stick out to the left than to the + # right, let's curve the morphism to the right. + if backwards: + curving = "^" + label_pos = "^" + else: + curving = "_" + label_pos = "_" + + # Assure that the straight vertical morphisms have + # their labels on the left side of the arrow. + for m in straight_vertical: + (i1, j1) = object_coords[m.domain] + (i2, j2) = object_coords[m.codomain] + + m_str_info = morphisms_str_info[m] + if i1 < i2: + m_str_info.label_position = "^" + else: + m_str_info.label_position = "_" + + # Don't allow any further modifications of the + # position of this label. + m_str_info.forced_label_position = True + else: + # More morphisms stick out to the right than to the + # left, let's curve the morphism to the left. + if backwards: + curving = "_" + label_pos = "_" + else: + curving = "^" + label_pos = "^" + + # Assure that the straight vertical morphisms have + # their labels on the right side of the arrow. + for m in straight_vertical: + (i1, j1) = object_coords[m.domain] + (i2, j2) = object_coords[m.codomain] + + m_str_info = morphisms_str_info[m] + if i1 < i2: + m_str_info.label_position = "_" + else: + m_str_info.label_position = "^" + + # Don't allow any further modifications of the + # position of this label. + m_str_info.forced_label_position = True + + return (curving, label_pos) + + def _process_morphism(self, diagram, grid, morphism, object_coords, + morphisms, morphisms_str_info): + """ + Given the required information, produces the string + representation of ``morphism``. + """ + def repeat_string_cond(times, str_gt, str_lt): + """ + If ``times > 0``, repeats ``str_gt`` ``times`` times. + Otherwise, repeats ``str_lt`` ``-times`` times. + """ + if times > 0: + return str_gt * times + else: + return str_lt * (-times) + + def count_morphisms_undirected(A, B): + """ + Counts how many processed morphisms there are between the + two supplied objects. + """ + return len([m for m in morphisms_str_info + if {m.domain, m.codomain} == {A, B}]) + + def count_morphisms_filtered(dom, cod, curving): + """ + Counts the processed morphisms which go out of ``dom`` + into ``cod`` with curving ``curving``. + """ + return len([m for m, m_str_info in morphisms_str_info.items() + if (m.domain, m.codomain) == (dom, cod) and + (m_str_info.curving == curving)]) + + (i, j) = object_coords[morphism.domain] + (target_i, target_j) = object_coords[morphism.codomain] + + # We now need to determine the direction of + # the arrow. + delta_i = target_i - i + delta_j = target_j - j + vertical_direction = repeat_string_cond(delta_i, + "d", "u") + horizontal_direction = repeat_string_cond(delta_j, + "r", "l") + + curving = "" + label_pos = "^" + looping_start = "" + looping_end = "" + + if (delta_i == 0) and (delta_j == 0): + # This is a loop morphism. + (curving, label_pos, looping_start, + looping_end) = XypicDiagramDrawer._process_loop_morphism( + i, j, grid, morphisms_str_info, object_coords) + elif (delta_i == 0) and (abs(j - target_j) > 1): + # This is a horizontal morphism. + (curving, label_pos) = XypicDiagramDrawer._process_horizontal_morphism( + i, j, target_j, grid, morphisms_str_info, object_coords) + elif (delta_j == 0) and (abs(i - target_i) > 1): + # This is a vertical morphism. + (curving, label_pos) = XypicDiagramDrawer._process_vertical_morphism( + i, j, target_i, grid, morphisms_str_info, object_coords) + + count = count_morphisms_undirected(morphism.domain, morphism.codomain) + curving_amount = "" + if curving: + # This morphisms should be curved anyway. + curving_amount = self.default_curving_amount + count * \ + self.default_curving_step + elif count: + # There are no objects between the domain and codomain of + # the current morphism, but this is not there already are + # some morphisms with the same domain and codomain, so we + # have to curve this one. + curving = "^" + filtered_morphisms = count_morphisms_filtered( + morphism.domain, morphism.codomain, curving) + curving_amount = self.default_curving_amount + \ + filtered_morphisms * \ + self.default_curving_step + + # Let's now get the name of the morphism. + morphism_name = "" + if isinstance(morphism, IdentityMorphism): + morphism_name = "id_{%s}" + latex(grid[i, j]) + elif isinstance(morphism, CompositeMorphism): + component_names = [latex(Symbol(component.name)) for + component in morphism.components] + component_names.reverse() + morphism_name = "\\circ ".join(component_names) + elif isinstance(morphism, NamedMorphism): + morphism_name = latex(Symbol(morphism.name)) + + return ArrowStringDescription( + self.unit, curving, curving_amount, looping_start, + looping_end, horizontal_direction, vertical_direction, + label_pos, morphism_name) + + @staticmethod + def _check_free_space_horizontal(dom_i, dom_j, cod_j, grid): + """ + For a horizontal morphism, checks whether there is free space + (i.e., space not occupied by any objects) above the morphism + or below it. + """ + if dom_j < cod_j: + (start, end) = (dom_j, cod_j) + backwards = False + else: + (start, end) = (cod_j, dom_j) + backwards = True + + # Check for free space above. + if dom_i == 0: + free_up = True + else: + free_up = all(grid[dom_i - 1, j] for j in + range(start, end + 1)) + + # Check for free space below. + if dom_i == grid.height - 1: + free_down = True + else: + free_down = not any(grid[dom_i + 1, j] for j in + range(start, end + 1)) + + return (free_up, free_down, backwards) + + @staticmethod + def _check_free_space_vertical(dom_i, cod_i, dom_j, grid): + """ + For a vertical morphism, checks whether there is free space + (i.e., space not occupied by any objects) to the left of the + morphism or to the right of it. + """ + if dom_i < cod_i: + (start, end) = (dom_i, cod_i) + backwards = False + else: + (start, end) = (cod_i, dom_i) + backwards = True + + # Check if there's space to the left. + if dom_j == 0: + free_left = True + else: + free_left = not any(grid[i, dom_j - 1] for i in + range(start, end + 1)) + + if dom_j == grid.width - 1: + free_right = True + else: + free_right = not any(grid[i, dom_j + 1] for i in + range(start, end + 1)) + + return (free_left, free_right, backwards) + + @staticmethod + def _check_free_space_diagonal(dom_i, cod_i, dom_j, cod_j, grid): + """ + For a diagonal morphism, checks whether there is free space + (i.e., space not occupied by any objects) above the morphism + or below it. + """ + def abs_xrange(start, end): + if start < end: + return range(start, end + 1) + else: + return range(end, start + 1) + + if dom_i < cod_i and dom_j < cod_j: + # This morphism goes from top-left to + # bottom-right. + (start_i, start_j) = (dom_i, dom_j) + (end_i, end_j) = (cod_i, cod_j) + backwards = False + elif dom_i > cod_i and dom_j > cod_j: + # This morphism goes from bottom-right to + # top-left. + (start_i, start_j) = (cod_i, cod_j) + (end_i, end_j) = (dom_i, dom_j) + backwards = True + if dom_i < cod_i and dom_j > cod_j: + # This morphism goes from top-right to + # bottom-left. + (start_i, start_j) = (dom_i, dom_j) + (end_i, end_j) = (cod_i, cod_j) + backwards = True + elif dom_i > cod_i and dom_j < cod_j: + # This morphism goes from bottom-left to + # top-right. + (start_i, start_j) = (cod_i, cod_j) + (end_i, end_j) = (dom_i, dom_j) + backwards = False + + # This is an attempt at a fast and furious strategy to + # decide where there is free space on the two sides of + # a diagonal morphism. For a diagonal morphism + # starting at ``(start_i, start_j)`` and ending at + # ``(end_i, end_j)`` the rectangle defined by these + # two points is considered. The slope of the diagonal + # ``alpha`` is then computed. Then, for every cell + # ``(i, j)`` within the rectangle, the slope + # ``alpha1`` of the line through ``(start_i, + # start_j)`` and ``(i, j)`` is considered. If + # ``alpha1`` is between 0 and ``alpha``, the point + # ``(i, j)`` is above the diagonal, if ``alpha1`` is + # between ``alpha`` and infinity, the point is below + # the diagonal. Also note that, with some beforehand + # precautions, this trick works for both the main and + # the secondary diagonals of the rectangle. + + # I have considered the possibility to only follow the + # shorter diagonals immediately above and below the + # main (or secondary) diagonal. This, however, + # wouldn't have resulted in much performance gain or + # better detection of outer edges, because of + # relatively small sizes of diagram grids, while the + # code would have become harder to understand. + + alpha = float(end_i - start_i)/(end_j - start_j) + free_up = True + free_down = True + for i in abs_xrange(start_i, end_i): + if not free_up and not free_down: + break + + for j in abs_xrange(start_j, end_j): + if not free_up and not free_down: + break + + if (i, j) == (start_i, start_j): + continue + + if j == start_j: + alpha1 = "inf" + else: + alpha1 = float(i - start_i)/(j - start_j) + + if grid[i, j]: + if (alpha1 == "inf") or (abs(alpha1) > abs(alpha)): + free_down = False + elif abs(alpha1) < abs(alpha): + free_up = False + + return (free_up, free_down, backwards) + + def _push_labels_out(self, morphisms_str_info, grid, object_coords): + """ + For all straight morphisms which form the visual boundary of + the laid out diagram, puts their labels on their outer sides. + """ + def set_label_position(free1, free2, pos1, pos2, backwards, m_str_info): + """ + Given the information about room available to one side and + to the other side of a morphism (``free1`` and ``free2``), + sets the position of the morphism label in such a way that + it is on the freer side. This latter operations involves + choice between ``pos1`` and ``pos2``, taking ``backwards`` + in consideration. + + Thus this function will do nothing if either both ``free1 + == True`` and ``free2 == True`` or both ``free1 == False`` + and ``free2 == False``. In either case, choosing one side + over the other presents no advantage. + """ + if backwards: + (pos1, pos2) = (pos2, pos1) + + if free1 and not free2: + m_str_info.label_position = pos1 + elif free2 and not free1: + m_str_info.label_position = pos2 + + for m, m_str_info in morphisms_str_info.items(): + if m_str_info.curving or m_str_info.forced_label_position: + # This is either a curved morphism, and curved + # morphisms have other magic, or the position of this + # label has already been fixed. + continue + + if m.domain == m.codomain: + # This is a loop morphism, their labels, again have a + # different magic. + continue + + (dom_i, dom_j) = object_coords[m.domain] + (cod_i, cod_j) = object_coords[m.codomain] + + if dom_i == cod_i: + # Horizontal morphism. + (free_up, free_down, + backwards) = XypicDiagramDrawer._check_free_space_horizontal( + dom_i, dom_j, cod_j, grid) + + set_label_position(free_up, free_down, "^", "_", + backwards, m_str_info) + elif dom_j == cod_j: + # Vertical morphism. + (free_left, free_right, + backwards) = XypicDiagramDrawer._check_free_space_vertical( + dom_i, cod_i, dom_j, grid) + + set_label_position(free_left, free_right, "_", "^", + backwards, m_str_info) + else: + # A diagonal morphism. + (free_up, free_down, + backwards) = XypicDiagramDrawer._check_free_space_diagonal( + dom_i, cod_i, dom_j, cod_j, grid) + + set_label_position(free_up, free_down, "^", "_", + backwards, m_str_info) + + @staticmethod + def _morphism_sort_key(morphism, object_coords): + """ + Provides a morphism sorting key such that horizontal or + vertical morphisms between neighbouring objects come + first, then horizontal or vertical morphisms between more + far away objects, and finally, all other morphisms. + """ + (i, j) = object_coords[morphism.domain] + (target_i, target_j) = object_coords[morphism.codomain] + + if morphism.domain == morphism.codomain: + # Loop morphisms should get after diagonal morphisms + # so that the proper direction in which to curve the + # loop can be determined. + return (3, 0, default_sort_key(morphism)) + + if target_i == i: + return (1, abs(target_j - j), default_sort_key(morphism)) + + if target_j == j: + return (1, abs(target_i - i), default_sort_key(morphism)) + + # Diagonal morphism. + return (2, 0, default_sort_key(morphism)) + + @staticmethod + def _build_xypic_string(diagram, grid, morphisms, + morphisms_str_info, diagram_format): + """ + Given a collection of :class:`ArrowStringDescription` + describing the morphisms of a diagram and the object layout + information of a diagram, produces the final Xy-pic picture. + """ + # Build the mapping between objects and morphisms which have + # them as domains. + object_morphisms = {} + for obj in diagram.objects: + object_morphisms[obj] = [] + for morphism in morphisms: + object_morphisms[morphism.domain].append(morphism) + + result = "\\xymatrix%s{\n" % diagram_format + + for i in range(grid.height): + for j in range(grid.width): + obj = grid[i, j] + if obj: + result += latex(obj) + " " + + morphisms_to_draw = object_morphisms[obj] + for morphism in morphisms_to_draw: + result += str(morphisms_str_info[morphism]) + " " + + # Don't put the & after the last column. + if j < grid.width - 1: + result += "& " + + # Don't put the line break after the last row. + if i < grid.height - 1: + result += "\\\\" + result += "\n" + + result += "}\n" + + return result + + def draw(self, diagram, grid, masked=None, diagram_format=""): + r""" + Returns the Xy-pic representation of ``diagram`` laid out in + ``grid``. + + Consider the following simple triangle diagram. + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy.categories import DiagramGrid, XypicDiagramDrawer + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g], {g * f: "unique"}) + + To draw this diagram, its objects need to be laid out with a + :class:`DiagramGrid`:: + + >>> grid = DiagramGrid(diagram) + + Finally, the drawing: + + >>> drawer = XypicDiagramDrawer() + >>> print(drawer.draw(diagram, grid)) + \xymatrix{ + A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + The argument ``masked`` can be used to skip morphisms in the + presentation of the diagram: + + >>> print(drawer.draw(diagram, grid, masked=[g * f])) + \xymatrix{ + A \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + Finally, the ``diagram_format`` argument can be used to + specify the format string of the diagram. For example, to + increase the spacing by 1 cm, proceeding as follows: + + >>> print(drawer.draw(diagram, grid, diagram_format="@+1cm")) + \xymatrix@+1cm{ + A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + """ + # This method works in several steps. It starts by removing + # the masked morphisms, if necessary, and then maps objects to + # their positions in the grid (coordinate tuples). Remember + # that objects are unique in ``Diagram`` and in the layout + # produced by ``DiagramGrid``, so every object is mapped to a + # single coordinate pair. + # + # The next step is the central step and is concerned with + # analysing the morphisms of the diagram and deciding how to + # draw them. For example, how to curve the arrows is decided + # at this step. The bulk of the analysis is implemented in + # ``_process_morphism``, to the result of which the + # appropriate formatters are applied. + # + # The result of the previous step is a list of + # ``ArrowStringDescription``. After the analysis and + # application of formatters, some extra logic tries to assure + # better positioning of morphism labels (for example, an + # attempt is made to avoid the situations when arrows cross + # labels). This functionality constitutes the next step and + # is implemented in ``_push_labels_out``. Note that label + # positions which have been set via a formatter are not + # affected in this step. + # + # Finally, at the closing step, the array of + # ``ArrowStringDescription`` and the layout information + # incorporated in ``DiagramGrid`` are combined to produce the + # resulting Xy-pic picture. This part of code lies in + # ``_build_xypic_string``. + + if not masked: + morphisms_props = grid.morphisms + else: + morphisms_props = {} + for m, props in grid.morphisms.items(): + if m in masked: + continue + morphisms_props[m] = props + + # Build the mapping between objects and their position in the + # grid. + object_coords = {} + for i in range(grid.height): + for j in range(grid.width): + if grid[i, j]: + object_coords[grid[i, j]] = (i, j) + + morphisms = sorted(morphisms_props, + key=lambda m: XypicDiagramDrawer._morphism_sort_key( + m, object_coords)) + + # Build the tuples defining the string representations of + # morphisms. + morphisms_str_info = {} + for morphism in morphisms: + string_description = self._process_morphism( + diagram, grid, morphism, object_coords, morphisms, + morphisms_str_info) + + if self.default_arrow_formatter: + self.default_arrow_formatter(string_description) + + for prop in morphisms_props[morphism]: + # prop is a Symbol. TODO: Find out why. + if prop.name in self.arrow_formatters: + formatter = self.arrow_formatters[prop.name] + formatter(string_description) + + morphisms_str_info[morphism] = string_description + + # Reposition the labels a bit. + self._push_labels_out(morphisms_str_info, grid, object_coords) + + return XypicDiagramDrawer._build_xypic_string( + diagram, grid, morphisms, morphisms_str_info, diagram_format) + + +def xypic_draw_diagram(diagram, masked=None, diagram_format="", + groups=None, **hints): + r""" + Provides a shortcut combining :class:`DiagramGrid` and + :class:`XypicDiagramDrawer`. Returns an Xy-pic presentation of + ``diagram``. The argument ``masked`` is a list of morphisms which + will be not be drawn. The argument ``diagram_format`` is the + format string inserted after "\xymatrix". ``groups`` should be a + set of logical groups. The ``hints`` will be passed directly to + the constructor of :class:`DiagramGrid`. + + For more information about the arguments, see the docstrings of + :class:`DiagramGrid` and ``XypicDiagramDrawer.draw``. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy.categories import xypic_draw_diagram + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> diagram = Diagram([f, g], {g * f: "unique"}) + >>> print(xypic_draw_diagram(diagram)) + \xymatrix{ + A \ar[d]_{g\circ f} \ar[r]^{f} & B \ar[ld]^{g} \\ + C & + } + + See Also + ======== + + XypicDiagramDrawer, DiagramGrid + """ + grid = DiagramGrid(diagram, groups, **hints) + drawer = XypicDiagramDrawer() + return drawer.draw(diagram, grid, masked, diagram_format) + + +@doctest_depends_on(exe=('latex', 'dvipng'), modules=('pyglet',)) +def preview_diagram(diagram, masked=None, diagram_format="", groups=None, + output='png', viewer=None, euler=True, **hints): + """ + Combines the functionality of ``xypic_draw_diagram`` and + ``sympy.printing.preview``. The arguments ``masked``, + ``diagram_format``, ``groups``, and ``hints`` are passed to + ``xypic_draw_diagram``, while ``output``, ``viewer, and ``euler`` + are passed to ``preview``. + + Examples + ======== + + >>> from sympy.categories import Object, NamedMorphism, Diagram + >>> from sympy.categories import preview_diagram + >>> A = Object("A") + >>> B = Object("B") + >>> C = Object("C") + >>> f = NamedMorphism(A, B, "f") + >>> g = NamedMorphism(B, C, "g") + >>> d = Diagram([f, g], {g * f: "unique"}) + >>> preview_diagram(d) + + See Also + ======== + + XypicDiagramDrawer + """ + from sympy.printing import preview + latex_output = xypic_draw_diagram(diagram, masked, diagram_format, + groups, **hints) + preview(latex_output, output, viewer, euler, ("xypic",)) diff --git a/lib/python3.11/site-packages/sympy/categories/tests/__init__.py b/lib/python3.11/site-packages/sympy/categories/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..c2954106bc32815f10c08165ef18a22f2e983446 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_baseclasses.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_baseclasses.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..d9ca3a254707a7a60233efcb61a7d149e3f8af9a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_baseclasses.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_drawing.cpython-311.pyc b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_drawing.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..39da620970b464a11ed19c47b85484f029060bf4 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/categories/tests/__pycache__/test_drawing.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/categories/tests/test_baseclasses.py b/lib/python3.11/site-packages/sympy/categories/tests/test_baseclasses.py new file mode 100644 index 0000000000000000000000000000000000000000..cfac32229768fb5903b23b11ffb236912c0b931e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/categories/tests/test_baseclasses.py @@ -0,0 +1,209 @@ +from sympy.categories import (Object, Morphism, IdentityMorphism, + NamedMorphism, CompositeMorphism, + Diagram, Category) +from sympy.categories.baseclasses import Class +from sympy.testing.pytest import raises +from sympy.core.containers import (Dict, Tuple) +from sympy.sets import EmptySet +from sympy.sets.sets import FiniteSet + + +def test_morphisms(): + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + + # Test the base morphism. + f = NamedMorphism(A, B, "f") + assert f.domain == A + assert f.codomain == B + assert f == NamedMorphism(A, B, "f") + + # Test identities. + id_A = IdentityMorphism(A) + id_B = IdentityMorphism(B) + assert id_A.domain == A + assert id_A.codomain == A + assert id_A == IdentityMorphism(A) + assert id_A != id_B + + # Test named morphisms. + g = NamedMorphism(B, C, "g") + assert g.name == "g" + assert g != f + assert g == NamedMorphism(B, C, "g") + assert g != NamedMorphism(B, C, "f") + + # Test composite morphisms. + assert f == CompositeMorphism(f) + + k = g.compose(f) + assert k.domain == A + assert k.codomain == C + assert k.components == Tuple(f, g) + assert g * f == k + assert CompositeMorphism(f, g) == k + + assert CompositeMorphism(g * f) == g * f + + # Test the associativity of composition. + h = NamedMorphism(C, D, "h") + + p = h * g + u = h * g * f + + assert h * k == u + assert p * f == u + assert CompositeMorphism(f, g, h) == u + + # Test flattening. + u2 = u.flatten("u") + assert isinstance(u2, NamedMorphism) + assert u2.name == "u" + assert u2.domain == A + assert u2.codomain == D + + # Test identities. + assert f * id_A == f + assert id_B * f == f + assert id_A * id_A == id_A + assert CompositeMorphism(id_A) == id_A + + # Test bad compositions. + raises(ValueError, lambda: f * g) + + raises(TypeError, lambda: f.compose(None)) + raises(TypeError, lambda: id_A.compose(None)) + raises(TypeError, lambda: f * None) + raises(TypeError, lambda: id_A * None) + + raises(TypeError, lambda: CompositeMorphism(f, None, 1)) + + raises(ValueError, lambda: NamedMorphism(A, B, "")) + raises(NotImplementedError, lambda: Morphism(A, B)) + + +def test_diagram(): + A = Object("A") + B = Object("B") + C = Object("C") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + id_A = IdentityMorphism(A) + id_B = IdentityMorphism(B) + + empty = EmptySet + + # Test the addition of identities. + d1 = Diagram([f]) + + assert d1.objects == FiniteSet(A, B) + assert d1.hom(A, B) == (FiniteSet(f), empty) + assert d1.hom(A, A) == (FiniteSet(id_A), empty) + assert d1.hom(B, B) == (FiniteSet(id_B), empty) + + assert d1 == Diagram([id_A, f]) + assert d1 == Diagram([f, f]) + + # Test the addition of composites. + d2 = Diagram([f, g]) + homAC = d2.hom(A, C)[0] + + assert d2.objects == FiniteSet(A, B, C) + assert g * f in d2.premises.keys() + assert homAC == FiniteSet(g * f) + + # Test equality, inequality and hash. + d11 = Diagram([f]) + + assert d1 == d11 + assert d1 != d2 + assert hash(d1) == hash(d11) + + d11 = Diagram({f: "unique"}) + assert d1 != d11 + + # Make sure that (re-)adding composites (with new properties) + # works as expected. + d = Diagram([f, g], {g * f: "unique"}) + assert d.conclusions == Dict({g * f: FiniteSet("unique")}) + + # Check the hom-sets when there are premises and conclusions. + assert d.hom(A, C) == (FiniteSet(g * f), FiniteSet(g * f)) + d = Diagram([f, g], [g * f]) + assert d.hom(A, C) == (FiniteSet(g * f), FiniteSet(g * f)) + + # Check how the properties of composite morphisms are computed. + d = Diagram({f: ["unique", "isomorphism"], g: "unique"}) + assert d.premises[g * f] == FiniteSet("unique") + + # Check that conclusion morphisms with new objects are not allowed. + d = Diagram([f], [g]) + assert d.conclusions == Dict({}) + + # Test an empty diagram. + d = Diagram() + assert d.premises == Dict({}) + assert d.conclusions == Dict({}) + assert d.objects == empty + + # Check a SymPy Dict object. + d = Diagram(Dict({f: FiniteSet("unique", "isomorphism"), g: "unique"})) + assert d.premises[g * f] == FiniteSet("unique") + + # Check the addition of components of composite morphisms. + d = Diagram([g * f]) + assert f in d.premises + assert g in d.premises + + # Check subdiagrams. + d = Diagram([f, g], {g * f: "unique"}) + + d1 = Diagram([f]) + assert d.is_subdiagram(d1) + assert not d1.is_subdiagram(d) + + d = Diagram([NamedMorphism(B, A, "f'")]) + assert not d.is_subdiagram(d1) + assert not d1.is_subdiagram(d) + + d1 = Diagram([f, g], {g * f: ["unique", "something"]}) + assert not d.is_subdiagram(d1) + assert not d1.is_subdiagram(d) + + d = Diagram({f: "blooh"}) + d1 = Diagram({f: "bleeh"}) + assert not d.is_subdiagram(d1) + assert not d1.is_subdiagram(d) + + d = Diagram([f, g], {f: "unique", g * f: "veryunique"}) + d1 = d.subdiagram_from_objects(FiniteSet(A, B)) + assert d1 == Diagram([f], {f: "unique"}) + raises(ValueError, lambda: d.subdiagram_from_objects(FiniteSet(A, + Object("D")))) + + raises(ValueError, lambda: Diagram({IdentityMorphism(A): "unique"})) + + +def test_category(): + A = Object("A") + B = Object("B") + C = Object("C") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + + d1 = Diagram([f, g]) + d2 = Diagram([f]) + + objects = d1.objects | d2.objects + + K = Category("K", objects, commutative_diagrams=[d1, d2]) + + assert K.name == "K" + assert K.objects == Class(objects) + assert K.commutative_diagrams == FiniteSet(d1, d2) + + raises(ValueError, lambda: Category("")) diff --git a/lib/python3.11/site-packages/sympy/categories/tests/test_drawing.py b/lib/python3.11/site-packages/sympy/categories/tests/test_drawing.py new file mode 100644 index 0000000000000000000000000000000000000000..63a13266cd6b58f6a85aad4af0813b395acbb5e1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/categories/tests/test_drawing.py @@ -0,0 +1,919 @@ +from sympy.categories.diagram_drawing import _GrowableGrid, ArrowStringDescription +from sympy.categories import (DiagramGrid, Object, NamedMorphism, + Diagram, XypicDiagramDrawer, xypic_draw_diagram) +from sympy.sets.sets import FiniteSet + + +def test_GrowableGrid(): + grid = _GrowableGrid(1, 2) + + # Check dimensions. + assert grid.width == 1 + assert grid.height == 2 + + # Check initialization of elements. + assert grid[0, 0] is None + assert grid[1, 0] is None + + # Check assignment to elements. + grid[0, 0] = 1 + grid[1, 0] = "two" + + assert grid[0, 0] == 1 + assert grid[1, 0] == "two" + + # Check appending a row. + grid.append_row() + + assert grid.width == 1 + assert grid.height == 3 + + assert grid[0, 0] == 1 + assert grid[1, 0] == "two" + assert grid[2, 0] is None + + # Check appending a column. + grid.append_column() + assert grid.width == 2 + assert grid.height == 3 + + assert grid[0, 0] == 1 + assert grid[1, 0] == "two" + assert grid[2, 0] is None + + assert grid[0, 1] is None + assert grid[1, 1] is None + assert grid[2, 1] is None + + grid = _GrowableGrid(1, 2) + grid[0, 0] = 1 + grid[1, 0] = "two" + + # Check prepending a row. + grid.prepend_row() + assert grid.width == 1 + assert grid.height == 3 + + assert grid[0, 0] is None + assert grid[1, 0] == 1 + assert grid[2, 0] == "two" + + # Check prepending a column. + grid.prepend_column() + assert grid.width == 2 + assert grid.height == 3 + + assert grid[0, 0] is None + assert grid[1, 0] is None + assert grid[2, 0] is None + + assert grid[0, 1] is None + assert grid[1, 1] == 1 + assert grid[2, 1] == "two" + + +def test_DiagramGrid(): + # Set up some objects and morphisms. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(D, A, "h") + k = NamedMorphism(D, B, "k") + + # A one-morphism diagram. + d = Diagram([f]) + grid = DiagramGrid(d) + + assert grid.width == 2 + assert grid.height == 1 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid.morphisms == {f: FiniteSet()} + + # A triangle. + d = Diagram([f, g], {g * f: "unique"}) + grid = DiagramGrid(d) + + assert grid.width == 2 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[1, 0] == C + assert grid[1, 1] is None + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), + g * f: FiniteSet("unique")} + + # A triangle with a "loop" morphism. + l_A = NamedMorphism(A, A, "l_A") + d = Diagram([f, g, l_A]) + grid = DiagramGrid(d) + + assert grid.width == 2 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), l_A: FiniteSet()} + + # A simple diagram. + d = Diagram([f, g, h, k]) + grid = DiagramGrid(d) + + assert grid.width == 3 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == D + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid[1, 2] is None + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(), + k: FiniteSet()} + + assert str(grid) == '[[Object("A"), Object("B"), Object("D")], ' \ + '[None, Object("C"), None]]' + + # A chain of morphisms. + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + k = NamedMorphism(D, E, "k") + d = Diagram([f, g, h, k]) + grid = DiagramGrid(d) + + assert grid.width == 3 + assert grid.height == 3 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] is None + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid[1, 2] == D + assert grid[2, 0] is None + assert grid[2, 1] is None + assert grid[2, 2] == E + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(), + k: FiniteSet()} + + # A square. + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, D, "g") + h = NamedMorphism(A, C, "h") + k = NamedMorphism(C, D, "k") + d = Diagram([f, g, h, k]) + grid = DiagramGrid(d) + + assert grid.width == 2 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[1, 0] == C + assert grid[1, 1] == D + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(), + k: FiniteSet()} + + # A strange diagram which resulted from a typo when creating a + # test for five lemma, but which allowed to stop one extra problem + # in the algorithm. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + A_ = Object("A'") + B_ = Object("B'") + C_ = Object("C'") + D_ = Object("D'") + E_ = Object("E'") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + i = NamedMorphism(D, E, "i") + + # These 4 morphisms should be between primed objects. + j = NamedMorphism(A, B, "j") + k = NamedMorphism(B, C, "k") + l = NamedMorphism(C, D, "l") + m = NamedMorphism(D, E, "m") + + o = NamedMorphism(A, A_, "o") + p = NamedMorphism(B, B_, "p") + q = NamedMorphism(C, C_, "q") + r = NamedMorphism(D, D_, "r") + s = NamedMorphism(E, E_, "s") + + d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s]) + grid = DiagramGrid(d) + + assert grid.width == 3 + assert grid.height == 4 + assert grid[0, 0] is None + assert grid[0, 1] == A + assert grid[0, 2] == A_ + assert grid[1, 0] == C + assert grid[1, 1] == B + assert grid[1, 2] == B_ + assert grid[2, 0] == C_ + assert grid[2, 1] == D + assert grid[2, 2] == D_ + assert grid[3, 0] is None + assert grid[3, 1] == E + assert grid[3, 2] == E_ + + morphisms = {} + for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]: + morphisms[m] = FiniteSet() + assert grid.morphisms == morphisms + + # A cube. + A1 = Object("A1") + A2 = Object("A2") + A3 = Object("A3") + A4 = Object("A4") + A5 = Object("A5") + A6 = Object("A6") + A7 = Object("A7") + A8 = Object("A8") + + # The top face of the cube. + f1 = NamedMorphism(A1, A2, "f1") + f2 = NamedMorphism(A1, A3, "f2") + f3 = NamedMorphism(A2, A4, "f3") + f4 = NamedMorphism(A3, A4, "f3") + + # The bottom face of the cube. + f5 = NamedMorphism(A5, A6, "f5") + f6 = NamedMorphism(A5, A7, "f6") + f7 = NamedMorphism(A6, A8, "f7") + f8 = NamedMorphism(A7, A8, "f8") + + # The remaining morphisms. + f9 = NamedMorphism(A1, A5, "f9") + f10 = NamedMorphism(A2, A6, "f10") + f11 = NamedMorphism(A3, A7, "f11") + f12 = NamedMorphism(A4, A8, "f11") + + d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12]) + grid = DiagramGrid(d) + + assert grid.width == 4 + assert grid.height == 3 + assert grid[0, 0] is None + assert grid[0, 1] == A5 + assert grid[0, 2] == A6 + assert grid[0, 3] is None + assert grid[1, 0] is None + assert grid[1, 1] == A1 + assert grid[1, 2] == A2 + assert grid[1, 3] is None + assert grid[2, 0] == A7 + assert grid[2, 1] == A3 + assert grid[2, 2] == A4 + assert grid[2, 3] == A8 + + morphisms = {} + for m in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12]: + morphisms[m] = FiniteSet() + assert grid.morphisms == morphisms + + # A line diagram. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + i = NamedMorphism(D, E, "i") + d = Diagram([f, g, h, i]) + grid = DiagramGrid(d, layout="sequential") + + assert grid.width == 5 + assert grid.height == 1 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == C + assert grid[0, 3] == D + assert grid[0, 4] == E + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(), + i: FiniteSet()} + + # Test the transposed version. + grid = DiagramGrid(d, layout="sequential", transpose=True) + + assert grid.width == 1 + assert grid.height == 5 + assert grid[0, 0] == A + assert grid[1, 0] == B + assert grid[2, 0] == C + assert grid[3, 0] == D + assert grid[4, 0] == E + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(), + i: FiniteSet()} + + # A pullback. + m1 = NamedMorphism(A, B, "m1") + m2 = NamedMorphism(A, C, "m2") + s1 = NamedMorphism(B, D, "s1") + s2 = NamedMorphism(C, D, "s2") + f1 = NamedMorphism(E, B, "f1") + f2 = NamedMorphism(E, C, "f2") + g = NamedMorphism(E, A, "g") + + d = Diagram([m1, m2, s1, s2, f1, f2], {g: "unique"}) + grid = DiagramGrid(d) + + assert grid.width == 3 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == E + assert grid[1, 0] == C + assert grid[1, 1] == D + assert grid[1, 2] is None + + morphisms = {g: FiniteSet("unique")} + for m in [m1, m2, s1, s2, f1, f2]: + morphisms[m] = FiniteSet() + assert grid.morphisms == morphisms + + # Test the pullback with sequential layout, just for stress + # testing. + grid = DiagramGrid(d, layout="sequential") + + assert grid.width == 5 + assert grid.height == 1 + assert grid[0, 0] == D + assert grid[0, 1] == B + assert grid[0, 2] == A + assert grid[0, 3] == C + assert grid[0, 4] == E + assert grid.morphisms == morphisms + + # Test a pullback with object grouping. + grid = DiagramGrid(d, groups=FiniteSet(E, FiniteSet(A, B, C, D))) + + assert grid.width == 3 + assert grid.height == 2 + assert grid[0, 0] == E + assert grid[0, 1] == A + assert grid[0, 2] == B + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid[1, 2] == D + assert grid.morphisms == morphisms + + # Five lemma, actually. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + A_ = Object("A'") + B_ = Object("B'") + C_ = Object("C'") + D_ = Object("D'") + E_ = Object("E'") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + i = NamedMorphism(D, E, "i") + + j = NamedMorphism(A_, B_, "j") + k = NamedMorphism(B_, C_, "k") + l = NamedMorphism(C_, D_, "l") + m = NamedMorphism(D_, E_, "m") + + o = NamedMorphism(A, A_, "o") + p = NamedMorphism(B, B_, "p") + q = NamedMorphism(C, C_, "q") + r = NamedMorphism(D, D_, "r") + s = NamedMorphism(E, E_, "s") + + d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s]) + grid = DiagramGrid(d) + + assert grid.width == 5 + assert grid.height == 3 + assert grid[0, 0] is None + assert grid[0, 1] == A + assert grid[0, 2] == A_ + assert grid[0, 3] is None + assert grid[0, 4] is None + assert grid[1, 0] == C + assert grid[1, 1] == B + assert grid[1, 2] == B_ + assert grid[1, 3] == C_ + assert grid[1, 4] is None + assert grid[2, 0] == D + assert grid[2, 1] == E + assert grid[2, 2] is None + assert grid[2, 3] == D_ + assert grid[2, 4] == E_ + + morphisms = {} + for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]: + morphisms[m] = FiniteSet() + assert grid.morphisms == morphisms + + # Test the five lemma with object grouping. + grid = DiagramGrid(d, FiniteSet( + FiniteSet(A, B, C, D, E), FiniteSet(A_, B_, C_, D_, E_))) + + assert grid.width == 6 + assert grid.height == 3 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] is None + assert grid[0, 3] == A_ + assert grid[0, 4] == B_ + assert grid[0, 5] is None + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid[1, 2] == D + assert grid[1, 3] is None + assert grid[1, 4] == C_ + assert grid[1, 5] == D_ + assert grid[2, 0] is None + assert grid[2, 1] is None + assert grid[2, 2] == E + assert grid[2, 3] is None + assert grid[2, 4] is None + assert grid[2, 5] == E_ + assert grid.morphisms == morphisms + + # Test the five lemma with object grouping, but mixing containers + # to represent groups. + grid = DiagramGrid(d, [(A, B, C, D, E), {A_, B_, C_, D_, E_}]) + + assert grid.width == 6 + assert grid.height == 3 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] is None + assert grid[0, 3] == A_ + assert grid[0, 4] == B_ + assert grid[0, 5] is None + assert grid[1, 0] is None + assert grid[1, 1] == C + assert grid[1, 2] == D + assert grid[1, 3] is None + assert grid[1, 4] == C_ + assert grid[1, 5] == D_ + assert grid[2, 0] is None + assert grid[2, 1] is None + assert grid[2, 2] == E + assert grid[2, 3] is None + assert grid[2, 4] is None + assert grid[2, 5] == E_ + assert grid.morphisms == morphisms + + # Test the five lemma with object grouping and hints. + grid = DiagramGrid(d, { + FiniteSet(A, B, C, D, E): {"layout": "sequential", + "transpose": True}, + FiniteSet(A_, B_, C_, D_, E_): {"layout": "sequential", + "transpose": True}}, + transpose=True) + + assert grid.width == 5 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == C + assert grid[0, 3] == D + assert grid[0, 4] == E + assert grid[1, 0] == A_ + assert grid[1, 1] == B_ + assert grid[1, 2] == C_ + assert grid[1, 3] == D_ + assert grid[1, 4] == E_ + assert grid.morphisms == morphisms + + # A two-triangle disconnected diagram. + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + f_ = NamedMorphism(A_, B_, "f") + g_ = NamedMorphism(B_, C_, "g") + d = Diagram([f, g, f_, g_], {g * f: "unique", g_ * f_: "unique"}) + grid = DiagramGrid(d) + + assert grid.width == 4 + assert grid.height == 2 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == A_ + assert grid[0, 3] == B_ + assert grid[1, 0] == C + assert grid[1, 1] is None + assert grid[1, 2] == C_ + assert grid[1, 3] is None + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), f_: FiniteSet(), + g_: FiniteSet(), g * f: FiniteSet("unique"), + g_ * f_: FiniteSet("unique")} + + # A two-morphism disconnected diagram. + f = NamedMorphism(A, B, "f") + g = NamedMorphism(C, D, "g") + d = Diagram([f, g]) + grid = DiagramGrid(d) + + assert grid.width == 4 + assert grid.height == 1 + assert grid[0, 0] == A + assert grid[0, 1] == B + assert grid[0, 2] == C + assert grid[0, 3] == D + assert grid.morphisms == {f: FiniteSet(), g: FiniteSet()} + + # Test a one-object diagram. + f = NamedMorphism(A, A, "f") + d = Diagram([f]) + grid = DiagramGrid(d) + + assert grid.width == 1 + assert grid.height == 1 + assert grid[0, 0] == A + + # Test a two-object disconnected diagram. + g = NamedMorphism(B, B, "g") + d = Diagram([f, g]) + grid = DiagramGrid(d) + + assert grid.width == 2 + assert grid.height == 1 + assert grid[0, 0] == A + assert grid[0, 1] == B + + +def test_DiagramGrid_pseudopod(): + # Test a diagram in which even growing a pseudopod does not + # eventually help. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + F = Object("F") + A_ = Object("A'") + B_ = Object("B'") + C_ = Object("C'") + D_ = Object("D'") + E_ = Object("E'") + + f1 = NamedMorphism(A, B, "f1") + f2 = NamedMorphism(A, C, "f2") + f3 = NamedMorphism(A, D, "f3") + f4 = NamedMorphism(A, E, "f4") + f5 = NamedMorphism(A, A_, "f5") + f6 = NamedMorphism(A, B_, "f6") + f7 = NamedMorphism(A, C_, "f7") + f8 = NamedMorphism(A, D_, "f8") + f9 = NamedMorphism(A, E_, "f9") + f10 = NamedMorphism(A, F, "f10") + d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10]) + grid = DiagramGrid(d) + + assert grid.width == 5 + assert grid.height == 3 + assert grid[0, 0] == E + assert grid[0, 1] == C + assert grid[0, 2] == C_ + assert grid[0, 3] == E_ + assert grid[0, 4] == F + assert grid[1, 0] == D + assert grid[1, 1] == A + assert grid[1, 2] == A_ + assert grid[1, 3] is None + assert grid[1, 4] is None + assert grid[2, 0] == D_ + assert grid[2, 1] == B + assert grid[2, 2] == B_ + assert grid[2, 3] is None + assert grid[2, 4] is None + + morphisms = {} + for f in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10]: + morphisms[f] = FiniteSet() + assert grid.morphisms == morphisms + + +def test_ArrowStringDescription(): + astr = ArrowStringDescription("cm", "", None, "", "", "d", "r", "_", "f") + assert str(astr) == "\\ar[dr]_{f}" + + astr = ArrowStringDescription("cm", "", 12, "", "", "d", "r", "_", "f") + assert str(astr) == "\\ar[dr]_{f}" + + astr = ArrowStringDescription("cm", "^", 12, "", "", "d", "r", "_", "f") + assert str(astr) == "\\ar@/^12cm/[dr]_{f}" + + astr = ArrowStringDescription("cm", "", 12, "r", "", "d", "r", "_", "f") + assert str(astr) == "\\ar[dr]_{f}" + + astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f") + assert str(astr) == "\\ar@(r,u)[dr]_{f}" + + astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f") + assert str(astr) == "\\ar@(r,u)[dr]_{f}" + + astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f") + astr.arrow_style = "{-->}" + assert str(astr) == "\\ar@(r,u)@{-->}[dr]_{f}" + + astr = ArrowStringDescription("cm", "_", 12, "", "", "d", "r", "_", "f") + astr.arrow_style = "{-->}" + assert str(astr) == "\\ar@/_12cm/@{-->}[dr]_{f}" + + +def test_XypicDiagramDrawer_line(): + # A linear diagram. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + i = NamedMorphism(D, E, "i") + d = Diagram([f, g, h, i]) + grid = DiagramGrid(d, layout="sequential") + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]^{f} & B \\ar[r]^{g} & C \\ar[r]^{h} & D \\ar[r]^{i} & E \n" \ + "}\n" + + # The same diagram, transposed. + grid = DiagramGrid(d, layout="sequential", transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]^{f} \\\\\n" \ + "B \\ar[d]^{g} \\\\\n" \ + "C \\ar[d]^{h} \\\\\n" \ + "D \\ar[d]^{i} \\\\\n" \ + "E \n" \ + "}\n" + + +def test_XypicDiagramDrawer_triangle(): + # A triangle diagram. + A = Object("A") + B = Object("B") + C = Object("C") + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + + d = Diagram([f, g], {g * f: "unique"}) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]_{g\\circ f} \\ar[r]^{f} & B \\ar[ld]^{g} \\\\\n" \ + "C & \n" \ + "}\n" + + # The same diagram, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \ + "B \\ar[ru]_{g} & \n" \ + "}\n" + + # The same diagram, with a masked morphism. + assert drawer.draw(d, grid, masked=[g]) == "\\xymatrix{\n" \ + "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \ + "B & \n" \ + "}\n" + + # The same diagram with a formatter for "unique". + def formatter(astr): + astr.label = "\\exists !" + astr.label + astr.arrow_style = "{-->}" + + drawer.arrow_formatters["unique"] = formatter + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar@{-->}[r]^{\\exists !g\\circ f} \\ar[d]_{f} & C \\\\\n" \ + "B \\ar[ru]_{g} & \n" \ + "}\n" + + # The same diagram with a default formatter. + def default_formatter(astr): + astr.label_displacement = "(0.45)" + + drawer.default_arrow_formatter = default_formatter + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar@{-->}[r]^(0.45){\\exists !g\\circ f} \\ar[d]_(0.45){f} & C \\\\\n" \ + "B \\ar[ru]_(0.45){g} & \n" \ + "}\n" + + # A triangle diagram with a lot of morphisms between the same + # objects. + f1 = NamedMorphism(B, A, "f1") + f2 = NamedMorphism(A, B, "f2") + g1 = NamedMorphism(C, B, "g1") + g2 = NamedMorphism(B, C, "g2") + d = Diagram([f, f1, f2, g, g1, g2], {f1 * g1: "unique", g2 * f2: "unique"}) + + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid, masked=[f1*g1*g2*f2, g2*f2*f1*g1]) == \ + "\\xymatrix{\n" \ + "A \\ar[r]^{g_{2}\\circ f_{2}} \\ar[d]_{f} \\ar@/^3mm/[d]^{f_{2}} " \ + "& C \\ar@/^3mm/[l]^{f_{1}\\circ g_{1}} \\ar@/^3mm/[ld]^{g_{1}} \\\\\n" \ + "B \\ar@/^3mm/[u]^{f_{1}} \\ar[ru]_{g} \\ar@/^3mm/[ru]^{g_{2}} & \n" \ + "}\n" + + +def test_XypicDiagramDrawer_cube(): + # A cube diagram. + A1 = Object("A1") + A2 = Object("A2") + A3 = Object("A3") + A4 = Object("A4") + A5 = Object("A5") + A6 = Object("A6") + A7 = Object("A7") + A8 = Object("A8") + + # The top face of the cube. + f1 = NamedMorphism(A1, A2, "f1") + f2 = NamedMorphism(A1, A3, "f2") + f3 = NamedMorphism(A2, A4, "f3") + f4 = NamedMorphism(A3, A4, "f3") + + # The bottom face of the cube. + f5 = NamedMorphism(A5, A6, "f5") + f6 = NamedMorphism(A5, A7, "f6") + f7 = NamedMorphism(A6, A8, "f7") + f8 = NamedMorphism(A7, A8, "f8") + + # The remaining morphisms. + f9 = NamedMorphism(A1, A5, "f9") + f10 = NamedMorphism(A2, A6, "f10") + f11 = NamedMorphism(A3, A7, "f11") + f12 = NamedMorphism(A4, A8, "f11") + + d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12]) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "& A_{5} \\ar[r]^{f_{5}} \\ar[ldd]_{f_{6}} & A_{6} \\ar[rdd]^{f_{7}} " \ + "& \\\\\n" \ + "& A_{1} \\ar[r]^{f_{1}} \\ar[d]^{f_{2}} \\ar[u]^{f_{9}} & A_{2} " \ + "\\ar[d]^{f_{3}} \\ar[u]_{f_{10}} & \\\\\n" \ + "A_{7} \\ar@/_3mm/[rrr]_{f_{8}} & A_{3} \\ar[r]^{f_{3}} \\ar[l]_{f_{11}} " \ + "& A_{4} \\ar[r]^{f_{11}} & A_{8} \n" \ + "}\n" + + # The same diagram, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "& & A_{7} \\ar@/^3mm/[ddd]^{f_{8}} \\\\\n" \ + "A_{5} \\ar[d]_{f_{5}} \\ar[rru]^{f_{6}} & A_{1} \\ar[d]^{f_{1}} " \ + "\\ar[r]^{f_{2}} \\ar[l]^{f_{9}} & A_{3} \\ar[d]_{f_{3}} " \ + "\\ar[u]^{f_{11}} \\\\\n" \ + "A_{6} \\ar[rrd]_{f_{7}} & A_{2} \\ar[r]^{f_{3}} \\ar[l]^{f_{10}} " \ + "& A_{4} \\ar[d]_{f_{11}} \\\\\n" \ + "& & A_{8} \n" \ + "}\n" + + +def test_XypicDiagramDrawer_curved_and_loops(): + # A simple diagram, with a curved arrow. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(D, A, "h") + k = NamedMorphism(D, B, "k") + d = Diagram([f, g, h, k]) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]_{f} & B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_3mm/[ll]_{h} \\\\\n" \ + "& C & \n" \ + "}\n" + + # The same diagram, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]^{f} & \\\\\n" \ + "B \\ar[r]^{g} & C \\\\\n" \ + "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \ + "}\n" + + # The same diagram, larger and rotated. + assert drawer.draw(d, grid, diagram_format="@+1cm@dr") == \ + "\\xymatrix@+1cm@dr{\n" \ + "A \\ar[d]^{f} & \\\\\n" \ + "B \\ar[r]^{g} & C \\\\\n" \ + "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \ + "}\n" + + # A simple diagram with three curved arrows. + h1 = NamedMorphism(D, A, "h1") + h2 = NamedMorphism(A, D, "h2") + k = NamedMorphism(D, B, "k") + d = Diagram([f, g, h, k, h1, h2]) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \ + "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\\\\n" \ + "& C & \n" \ + "}\n" + + # The same diagram, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} & \\\\\n" \ + "B \\ar[r]^{g} & C \\\\\n" \ + "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} & \n" \ + "}\n" + + # The same diagram, with "loop" morphisms. + l_A = NamedMorphism(A, A, "l_A") + l_D = NamedMorphism(D, D, "l_D") + l_C = NamedMorphism(C, C, "l_C") + d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C]) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \ + "& B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_7mm/[ll]_{h} " \ + "\\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} \\\\\n" \ + "& C \\ar@(l,d)[]^{l_{C}} & \n" \ + "}\n" + + # The same diagram with "loop" morphisms, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} & \\\\\n" \ + "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\\\\n" \ + "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \ + "\\ar@(l,d)[]^{l_{D}} & \n" \ + "}\n" + + # The same diagram with two "loop" morphisms per object. + l_A_ = NamedMorphism(A, A, "n_A") + l_D_ = NamedMorphism(D, D, "n_D") + l_C_ = NamedMorphism(C, C, "n_C") + d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C, l_A_, l_D_, l_C_]) + grid = DiagramGrid(d) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \ + "\\ar@/^3mm/@(l,d)[]^{n_{A}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \ + "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} " \ + "\\ar@/^3mm/@(d,r)[]^{n_{D}} \\\\\n" \ + "& C \\ar@(l,d)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} & \n" \ + "}\n" + + # The same diagram with two "loop" morphisms per object, transposed. + grid = DiagramGrid(d, transpose=True) + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == "\\xymatrix{\n" \ + "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} " \ + "\\ar@/^3mm/@(u,l)[]^{n_{A}} & \\\\\n" \ + "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} \\\\\n" \ + "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \ + "\\ar@(l,d)[]^{l_{D}} \\ar@/^3mm/@(d,r)[]^{n_{D}} & \n" \ + "}\n" + + +def test_xypic_draw_diagram(): + # A linear diagram. + A = Object("A") + B = Object("B") + C = Object("C") + D = Object("D") + E = Object("E") + + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + h = NamedMorphism(C, D, "h") + i = NamedMorphism(D, E, "i") + d = Diagram([f, g, h, i]) + + grid = DiagramGrid(d, layout="sequential") + drawer = XypicDiagramDrawer() + assert drawer.draw(d, grid) == xypic_draw_diagram(d, layout="sequential") diff --git a/lib/python3.11/site-packages/sympy/codegen/__init__.py b/lib/python3.11/site-packages/sympy/codegen/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..62b195633bae28371bdf9e79317050d7fa7125ae --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/__init__.py @@ -0,0 +1,24 @@ +""" The ``sympy.codegen`` module contains classes and functions for building +abstract syntax trees of algorithms. These trees may then be printed by the +code-printers in ``sympy.printing``. + +There are several submodules available: +- ``sympy.codegen.ast``: AST nodes useful across multiple languages. +- ``sympy.codegen.cnodes``: AST nodes useful for the C family of languages. +- ``sympy.codegen.fnodes``: AST nodes useful for Fortran. +- ``sympy.codegen.cfunctions``: functions specific to C (C99 math functions) +- ``sympy.codegen.ffunctions``: functions specific to Fortran (e.g. ``kind``). + + + +""" +from .ast import ( + Assignment, aug_assign, CodeBlock, For, Attribute, Variable, Declaration, + While, Scope, Print, FunctionPrototype, FunctionDefinition, FunctionCall +) + +__all__ = [ + 'Assignment', 'aug_assign', 'CodeBlock', 'For', 'Attribute', 'Variable', + 'Declaration', 'While', 'Scope', 'Print', 'FunctionPrototype', + 'FunctionDefinition', 'FunctionCall', +] diff --git a/lib/python3.11/site-packages/sympy/codegen/__pycache__/__init__.cpython-311.pyc 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b/lib/python3.11/site-packages/sympy/codegen/abstract_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..ae0a8b3e996a7112edf2568c00138e11c3f3327d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/abstract_nodes.py @@ -0,0 +1,18 @@ +"""This module provides containers for python objects that are valid +printing targets but are not a subclass of SymPy's Printable. +""" + + +from sympy.core.containers import Tuple + + +class List(Tuple): + """Represents a (frozen) (Python) list (for code printing purposes).""" + def __eq__(self, other): + if isinstance(other, list): + return self == List(*other) + else: + return self.args == other + + def __hash__(self): + return super().__hash__() diff --git a/lib/python3.11/site-packages/sympy/codegen/algorithms.py b/lib/python3.11/site-packages/sympy/codegen/algorithms.py new file mode 100644 index 0000000000000000000000000000000000000000..f4890eb8c25e565095600e2713c0de270aa0cf97 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/algorithms.py @@ -0,0 +1,180 @@ +from sympy.core.containers import Tuple +from sympy.core.numbers import oo +from sympy.core.relational import (Gt, Lt) +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.miscellaneous import Min, Max +from sympy.logic.boolalg import And +from sympy.codegen.ast import ( + Assignment, AddAugmentedAssignment, break_, CodeBlock, Declaration, FunctionDefinition, + Print, Return, Scope, While, Variable, Pointer, real +) +from sympy.codegen.cfunctions import isnan + +""" This module collects functions for constructing ASTs representing algorithms. """ + +def newtons_method(expr, wrt, atol=1e-12, delta=None, *, rtol=4e-16, debug=False, + itermax=None, counter=None, delta_fn=lambda e, x: -e/e.diff(x), + cse=False, handle_nan=None, + bounds=None): + """ Generates an AST for Newton-Raphson method (a root-finding algorithm). + + Explanation + =========== + + Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's + method of root-finding. + + Parameters + ========== + + expr : expression + wrt : Symbol + With respect to, i.e. what is the variable. + atol : number or expression + Absolute tolerance (stopping criterion) + rtol : number or expression + Relative tolerance (stopping criterion) + delta : Symbol + Will be a ``Dummy`` if ``None``. + debug : bool + Whether to print convergence information during iterations + itermax : number or expr + Maximum number of iterations. + counter : Symbol + Will be a ``Dummy`` if ``None``. + delta_fn: Callable[[Expr, Symbol], Expr] + computes the step, default is newtons method. For e.g. Halley's method + use delta_fn=lambda e, x: -2*e*e.diff(x)/(2*e.diff(x)**2 - e*e.diff(x, 2)) + cse: bool + Perform common sub-expression elimination on delta expression + handle_nan: Token + How to handle occurrence of not-a-number (NaN). + bounds: Optional[tuple[Expr, Expr]] + Perform optimization within bounds + + Examples + ======== + + >>> from sympy import symbols, cos + >>> from sympy.codegen.ast import Assignment + >>> from sympy.codegen.algorithms import newtons_method + >>> x, dx, atol = symbols('x dx atol') + >>> expr = cos(x) - x**3 + >>> algo = newtons_method(expr, x, atol=atol, delta=dx) + >>> algo.has(Assignment(dx, -expr/expr.diff(x))) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Newton%27s_method + + """ + + if delta is None: + delta = Dummy() + Wrapper = Scope + name_d = 'delta' + else: + Wrapper = lambda x: x + name_d = delta.name + + delta_expr = delta_fn(expr, wrt) + if cse: + from sympy.simplify.cse_main import cse + cses, (red,) = cse([delta_expr.factor()]) + whl_bdy = [Assignment(dum, sub_e) for dum, sub_e in cses] + whl_bdy += [Assignment(delta, red)] + else: + whl_bdy = [Assignment(delta, delta_expr)] + if handle_nan is not None: + whl_bdy += [While(isnan(delta), CodeBlock(handle_nan, break_))] + whl_bdy += [AddAugmentedAssignment(wrt, delta)] + if bounds is not None: + whl_bdy += [Assignment(wrt, Min(Max(wrt, bounds[0]), bounds[1]))] + if debug: + prnt = Print([wrt, delta], r"{}=%12.5g {}=%12.5g\n".format(wrt.name, name_d)) + whl_bdy += [prnt] + req = Gt(Abs(delta), atol + rtol*Abs(wrt)) + declars = [Declaration(Variable(delta, type=real, value=oo))] + if itermax is not None: + counter = counter or Dummy(integer=True) + v_counter = Variable.deduced(counter, 0) + declars.append(Declaration(v_counter)) + whl_bdy.append(AddAugmentedAssignment(counter, 1)) + req = And(req, Lt(counter, itermax)) + whl = While(req, CodeBlock(*whl_bdy)) + blck = declars + if debug: + blck.append(Print([wrt], r"{}=%12.5g\n".format(wrt.name))) + blck += [whl] + return Wrapper(CodeBlock(*blck)) + + +def _symbol_of(arg): + if isinstance(arg, Declaration): + arg = arg.variable.symbol + elif isinstance(arg, Variable): + arg = arg.symbol + return arg + + +def newtons_method_function(expr, wrt, params=None, func_name="newton", attrs=Tuple(), *, delta=None, **kwargs): + """ Generates an AST for a function implementing the Newton-Raphson method. + + Parameters + ========== + + expr : expression + wrt : Symbol + With respect to, i.e. what is the variable + params : iterable of symbols + Symbols appearing in expr that are taken as constants during the iterations + (these will be accepted as parameters to the generated function). + func_name : str + Name of the generated function. + attrs : Tuple + Attribute instances passed as ``attrs`` to ``FunctionDefinition``. + \\*\\*kwargs : + Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. + + Examples + ======== + + >>> from sympy import symbols, cos + >>> from sympy.codegen.algorithms import newtons_method_function + >>> from sympy.codegen.pyutils import render_as_module + >>> x = symbols('x') + >>> expr = cos(x) - x**3 + >>> func = newtons_method_function(expr, x) + >>> py_mod = render_as_module(func) # source code as string + >>> namespace = {} + >>> exec(py_mod, namespace, namespace) + >>> res = eval('newton(0.5)', namespace) + >>> abs(res - 0.865474033102) < 1e-12 + True + + See Also + ======== + + sympy.codegen.algorithms.newtons_method + + """ + if params is None: + params = (wrt,) + pointer_subs = {p.symbol: Symbol('(*%s)' % p.symbol.name) + for p in params if isinstance(p, Pointer)} + if delta is None: + delta = Symbol('d_' + wrt.name) + if expr.has(delta): + delta = None # will use Dummy + algo = newtons_method(expr, wrt, delta=delta, **kwargs).xreplace(pointer_subs) + if isinstance(algo, Scope): + algo = algo.body + not_in_params = expr.free_symbols.difference({_symbol_of(p) for p in params}) + if not_in_params: + raise ValueError("Missing symbols in params: %s" % ', '.join(map(str, not_in_params))) + declars = tuple(Variable(p, real) for p in params) + body = CodeBlock(algo, Return(wrt)) + return FunctionDefinition(real, func_name, declars, body, attrs=attrs) diff --git a/lib/python3.11/site-packages/sympy/codegen/approximations.py b/lib/python3.11/site-packages/sympy/codegen/approximations.py new file mode 100644 index 0000000000000000000000000000000000000000..4f15266ab18f93b18b50269356c94484dd2f8ac4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/approximations.py @@ -0,0 +1,187 @@ +import math +from sympy.sets.sets import Interval +from sympy.calculus.singularities import is_increasing, is_decreasing +from sympy.codegen.rewriting import Optimization +from sympy.core.function import UndefinedFunction + +""" +This module collects classes useful for approimate rewriting of expressions. +This can be beneficial when generating numeric code for which performance is +of greater importance than precision (e.g. for preconditioners used in iterative +methods). +""" + +class SumApprox(Optimization): + """ + Approximates sum by neglecting small terms. + + Explanation + =========== + + If terms are expressions which can be determined to be monotonic, then + bounds for those expressions are added. + + Parameters + ========== + + bounds : dict + Mapping expressions to length 2 tuple of bounds (low, high). + reltol : number + Threshold for when to ignore a term. Taken relative to the largest + lower bound among bounds. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.abc import x, y, z + >>> from sympy.codegen.rewriting import optimize + >>> from sympy.codegen.approximations import SumApprox + >>> bounds = {x: (-1, 1), y: (1000, 2000), z: (-10, 3)} + >>> sum_approx3 = SumApprox(bounds, reltol=1e-3) + >>> sum_approx2 = SumApprox(bounds, reltol=1e-2) + >>> sum_approx1 = SumApprox(bounds, reltol=1e-1) + >>> expr = 3*(x + y + exp(z)) + >>> optimize(expr, [sum_approx3]) + 3*(x + y + exp(z)) + >>> optimize(expr, [sum_approx2]) + 3*y + 3*exp(z) + >>> optimize(expr, [sum_approx1]) + 3*y + + """ + + def __init__(self, bounds, reltol, **kwargs): + super().__init__(**kwargs) + self.bounds = bounds + self.reltol = reltol + + def __call__(self, expr): + return expr.factor().replace(self.query, lambda arg: self.value(arg)) + + def query(self, expr): + return expr.is_Add + + def value(self, add): + for term in add.args: + if term.is_number or term in self.bounds or len(term.free_symbols) != 1: + continue + fs, = term.free_symbols + if fs not in self.bounds: + continue + intrvl = Interval(*self.bounds[fs]) + if is_increasing(term, intrvl, fs): + self.bounds[term] = ( + term.subs({fs: self.bounds[fs][0]}), + term.subs({fs: self.bounds[fs][1]}) + ) + elif is_decreasing(term, intrvl, fs): + self.bounds[term] = ( + term.subs({fs: self.bounds[fs][1]}), + term.subs({fs: self.bounds[fs][0]}) + ) + else: + return add + + if all(term.is_number or term in self.bounds for term in add.args): + bounds = [(term, term) if term.is_number else self.bounds[term] for term in add.args] + largest_abs_guarantee = 0 + for lo, hi in bounds: + if lo <= 0 <= hi: + continue + largest_abs_guarantee = max(largest_abs_guarantee, + min(abs(lo), abs(hi))) + new_terms = [] + for term, (lo, hi) in zip(add.args, bounds): + if max(abs(lo), abs(hi)) >= largest_abs_guarantee*self.reltol: + new_terms.append(term) + return add.func(*new_terms) + else: + return add + + +class SeriesApprox(Optimization): + """ Approximates functions by expanding them as a series. + + Parameters + ========== + + bounds : dict + Mapping expressions to length 2 tuple of bounds (low, high). + reltol : number + Threshold for when to ignore a term. Taken relative to the largest + lower bound among bounds. + max_order : int + Largest order to include in series expansion + n_point_checks : int (even) + The validity of an expansion (with respect to reltol) is checked at + discrete points (linearly spaced over the bounds of the variable). The + number of points used in this numerical check is given by this number. + + Examples + ======== + + >>> from sympy import sin, pi + >>> from sympy.abc import x, y + >>> from sympy.codegen.rewriting import optimize + >>> from sympy.codegen.approximations import SeriesApprox + >>> bounds = {x: (-.1, .1), y: (pi-1, pi+1)} + >>> series_approx2 = SeriesApprox(bounds, reltol=1e-2) + >>> series_approx3 = SeriesApprox(bounds, reltol=1e-3) + >>> series_approx8 = SeriesApprox(bounds, reltol=1e-8) + >>> expr = sin(x)*sin(y) + >>> optimize(expr, [series_approx2]) + x*(-y + (y - pi)**3/6 + pi) + >>> optimize(expr, [series_approx3]) + (-x**3/6 + x)*sin(y) + >>> optimize(expr, [series_approx8]) + sin(x)*sin(y) + + """ + def __init__(self, bounds, reltol, max_order=4, n_point_checks=4, **kwargs): + super().__init__(**kwargs) + self.bounds = bounds + self.reltol = reltol + self.max_order = max_order + if n_point_checks % 2 == 1: + raise ValueError("Checking the solution at expansion point is not helpful") + self.n_point_checks = n_point_checks + self._prec = math.ceil(-math.log10(self.reltol)) + + def __call__(self, expr): + return expr.factor().replace(self.query, lambda arg: self.value(arg)) + + def query(self, expr): + return (expr.is_Function and not isinstance(expr, UndefinedFunction) + and len(expr.args) == 1) + + def value(self, fexpr): + free_symbols = fexpr.free_symbols + if len(free_symbols) != 1: + return fexpr + symb, = free_symbols + if symb not in self.bounds: + return fexpr + lo, hi = self.bounds[symb] + x0 = (lo + hi)/2 + cheapest = None + for n in range(self.max_order+1, 0, -1): + fseri = fexpr.series(symb, x0=x0, n=n).removeO() + n_ok = True + for idx in range(self.n_point_checks): + x = lo + idx*(hi - lo)/(self.n_point_checks - 1) + val = fseri.xreplace({symb: x}) + ref = fexpr.xreplace({symb: x}) + if abs((1 - val/ref).evalf(self._prec)) > self.reltol: + n_ok = False + break + + if n_ok: + cheapest = fseri + else: + break + + if cheapest is None: + return fexpr + else: + return cheapest diff --git a/lib/python3.11/site-packages/sympy/codegen/ast.py b/lib/python3.11/site-packages/sympy/codegen/ast.py new file mode 100644 index 0000000000000000000000000000000000000000..0522a25eb301108c4eb2a50b6ec99c74d41869c6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/ast.py @@ -0,0 +1,1906 @@ +""" +Types used to represent a full function/module as an Abstract Syntax Tree. + +Most types are small, and are merely used as tokens in the AST. A tree diagram +has been included below to illustrate the relationships between the AST types. + + +AST Type Tree +------------- +:: + + *Basic* + | + | + CodegenAST + | + |--->AssignmentBase + | |--->Assignment + | |--->AugmentedAssignment + | |--->AddAugmentedAssignment + | |--->SubAugmentedAssignment + | |--->MulAugmentedAssignment + | |--->DivAugmentedAssignment + | |--->ModAugmentedAssignment + | + |--->CodeBlock + | + | + |--->Token + |--->Attribute + |--->For + |--->String + | |--->QuotedString + | |--->Comment + |--->Type + | |--->IntBaseType + | | |--->_SizedIntType + | | |--->SignedIntType + | | |--->UnsignedIntType + | |--->FloatBaseType + | |--->FloatType + | |--->ComplexBaseType + | |--->ComplexType + |--->Node + | |--->Variable + | | |---> Pointer + | |--->FunctionPrototype + | |--->FunctionDefinition + |--->Element + |--->Declaration + |--->While + |--->Scope + |--->Stream + |--->Print + |--->FunctionCall + |--->BreakToken + |--->ContinueToken + |--->NoneToken + |--->Return + + +Predefined types +---------------- + +A number of ``Type`` instances are provided in the ``sympy.codegen.ast`` module +for convenience. Perhaps the two most common ones for code-generation (of numeric +codes) are ``float32`` and ``float64`` (known as single and double precision respectively). +There are also precision generic versions of Types (for which the codeprinters selects the +underlying data type at time of printing): ``real``, ``integer``, ``complex_``, ``bool_``. + +The other ``Type`` instances defined are: + +- ``intc``: Integer type used by C's "int". +- ``intp``: Integer type used by C's "unsigned". +- ``int8``, ``int16``, ``int32``, ``int64``: n-bit integers. +- ``uint8``, ``uint16``, ``uint32``, ``uint64``: n-bit unsigned integers. +- ``float80``: known as "extended precision" on modern x86/amd64 hardware. +- ``complex64``: Complex number represented by two ``float32`` numbers +- ``complex128``: Complex number represented by two ``float64`` numbers + +Using the nodes +--------------- + +It is possible to construct simple algorithms using the AST nodes. Let's construct a loop applying +Newton's method:: + + >>> from sympy import symbols, cos + >>> from sympy.codegen.ast import While, Assignment, aug_assign, Print, QuotedString + >>> t, dx, x = symbols('tol delta val') + >>> expr = cos(x) - x**3 + >>> whl = While(abs(dx) > t, [ + ... Assignment(dx, -expr/expr.diff(x)), + ... aug_assign(x, '+', dx), + ... Print([x]) + ... ]) + >>> from sympy import pycode + >>> py_str = pycode(whl) + >>> print(py_str) + while (abs(delta) > tol): + delta = (val**3 - math.cos(val))/(-3*val**2 - math.sin(val)) + val += delta + print(val) + >>> import math + >>> tol, val, delta = 1e-5, 0.5, float('inf') + >>> exec(py_str) + 1.1121416371 + 0.909672693737 + 0.867263818209 + 0.865477135298 + 0.865474033111 + >>> print('%3.1g' % (math.cos(val) - val**3)) + -3e-11 + +If we want to generate Fortran code for the same while loop we simple call ``fcode``:: + + >>> from sympy import fcode + >>> print(fcode(whl, standard=2003, source_format='free')) + do while (abs(delta) > tol) + delta = (val**3 - cos(val))/(-3*val**2 - sin(val)) + val = val + delta + print *, val + end do + +There is a function constructing a loop (or a complete function) like this in +:mod:`sympy.codegen.algorithms`. + +""" + +from __future__ import annotations +from typing import Any + +from collections import defaultdict + +from sympy.core.relational import (Ge, Gt, Le, Lt) +from sympy.core import Symbol, Tuple, Dummy +from sympy.core.basic import Basic +from sympy.core.expr import Expr, Atom +from sympy.core.numbers import Float, Integer, oo +from sympy.core.sympify import _sympify, sympify, SympifyError +from sympy.utilities.iterables import (iterable, topological_sort, + numbered_symbols, filter_symbols) + + +def _mk_Tuple(args): + """ + Create a SymPy Tuple object from an iterable, converting Python strings to + AST strings. + + Parameters + ========== + + args: iterable + Arguments to :class:`sympy.Tuple`. + + Returns + ======= + + sympy.Tuple + """ + args = [String(arg) if isinstance(arg, str) else arg for arg in args] + return Tuple(*args) + + +class CodegenAST(Basic): + __slots__ = () + + +class Token(CodegenAST): + """ Base class for the AST types. + + Explanation + =========== + + Defining fields are set in ``_fields``. Attributes (defined in _fields) + are only allowed to contain instances of Basic (unless atomic, see + ``String``). The arguments to ``__new__()`` correspond to the attributes in + the order defined in ``_fields`. The ``defaults`` class attribute is a + dictionary mapping attribute names to their default values. + + Subclasses should not need to override the ``__new__()`` method. They may + define a class or static method named ``_construct_`` for each + attribute to process the value passed to ``__new__()``. Attributes listed + in the class attribute ``not_in_args`` are not passed to :class:`~.Basic`. + """ + + __slots__: tuple[str, ...] = () + _fields = __slots__ + defaults: dict[str, Any] = {} + not_in_args: list[str] = [] + indented_args = ['body'] + + @property + def is_Atom(self): + return len(self._fields) == 0 + + @classmethod + def _get_constructor(cls, attr): + """ Get the constructor function for an attribute by name. """ + return getattr(cls, '_construct_%s' % attr, lambda x: x) + + @classmethod + def _construct(cls, attr, arg): + """ Construct an attribute value from argument passed to ``__new__()``. """ + # arg may be ``NoneToken()``, so comparison is done using == instead of ``is`` operator + if arg == None: + return cls.defaults.get(attr, none) + else: + if isinstance(arg, Dummy): # SymPy's replace uses Dummy instances + return arg + else: + return cls._get_constructor(attr)(arg) + + def __new__(cls, *args, **kwargs): + # Pass through existing instances when given as sole argument + if len(args) == 1 and not kwargs and isinstance(args[0], cls): + return args[0] + + if len(args) > len(cls._fields): + raise ValueError("Too many arguments (%d), expected at most %d" % (len(args), len(cls._fields))) + + attrvals = [] + + # Process positional arguments + for attrname, argval in zip(cls._fields, args): + if attrname in kwargs: + raise TypeError('Got multiple values for attribute %r' % attrname) + + attrvals.append(cls._construct(attrname, argval)) + + # Process keyword arguments + for attrname in cls._fields[len(args):]: + if attrname in kwargs: + argval = kwargs.pop(attrname) + + elif attrname in cls.defaults: + argval = cls.defaults[attrname] + + else: + raise TypeError('No value for %r given and attribute has no default' % attrname) + + attrvals.append(cls._construct(attrname, argval)) + + if kwargs: + raise ValueError("Unknown keyword arguments: %s" % ' '.join(kwargs)) + + # Parent constructor + basic_args = [ + val for attr, val in zip(cls._fields, attrvals) + if attr not in cls.not_in_args + ] + obj = CodegenAST.__new__(cls, *basic_args) + + # Set attributes + for attr, arg in zip(cls._fields, attrvals): + setattr(obj, attr, arg) + + return obj + + def __eq__(self, other): + if not isinstance(other, self.__class__): + return False + for attr in self._fields: + if getattr(self, attr) != getattr(other, attr): + return False + return True + + def _hashable_content(self): + return tuple([getattr(self, attr) for attr in self._fields]) + + def __hash__(self): + return super().__hash__() + + def _joiner(self, k, indent_level): + return (',\n' + ' '*indent_level) if k in self.indented_args else ', ' + + def _indented(self, printer, k, v, *args, **kwargs): + il = printer._context['indent_level'] + def _print(arg): + if isinstance(arg, Token): + return printer._print(arg, *args, joiner=self._joiner(k, il), **kwargs) + else: + return printer._print(arg, *args, **kwargs) + + if isinstance(v, Tuple): + joined = self._joiner(k, il).join([_print(arg) for arg in v.args]) + if k in self.indented_args: + return '(\n' + ' '*il + joined + ',\n' + ' '*(il - 4) + ')' + else: + return ('({0},)' if len(v.args) == 1 else '({0})').format(joined) + else: + return _print(v) + + def _sympyrepr(self, printer, *args, joiner=', ', **kwargs): + from sympy.printing.printer import printer_context + exclude = kwargs.get('exclude', ()) + values = [getattr(self, k) for k in self._fields] + indent_level = printer._context.get('indent_level', 0) + + arg_reprs = [] + + for i, (attr, value) in enumerate(zip(self._fields, values)): + if attr in exclude: + continue + + # Skip attributes which have the default value + if attr in self.defaults and value == self.defaults[attr]: + continue + + ilvl = indent_level + 4 if attr in self.indented_args else 0 + with printer_context(printer, indent_level=ilvl): + indented = self._indented(printer, attr, value, *args, **kwargs) + arg_reprs.append(('{1}' if i == 0 else '{0}={1}').format(attr, indented.lstrip())) + + return "{}({})".format(self.__class__.__name__, joiner.join(arg_reprs)) + + _sympystr = _sympyrepr + + def __repr__(self): # sympy.core.Basic.__repr__ uses sstr + from sympy.printing import srepr + return srepr(self) + + def kwargs(self, exclude=(), apply=None): + """ Get instance's attributes as dict of keyword arguments. + + Parameters + ========== + + exclude : collection of str + Collection of keywords to exclude. + + apply : callable, optional + Function to apply to all values. + """ + kwargs = {k: getattr(self, k) for k in self._fields if k not in exclude} + if apply is not None: + return {k: apply(v) for k, v in kwargs.items()} + else: + return kwargs + +class BreakToken(Token): + """ Represents 'break' in C/Python ('exit' in Fortran). + + Use the premade instance ``break_`` or instantiate manually. + + Examples + ======== + + >>> from sympy import ccode, fcode + >>> from sympy.codegen.ast import break_ + >>> ccode(break_) + 'break' + >>> fcode(break_, source_format='free') + 'exit' + """ + +break_ = BreakToken() + + +class ContinueToken(Token): + """ Represents 'continue' in C/Python ('cycle' in Fortran) + + Use the premade instance ``continue_`` or instantiate manually. + + Examples + ======== + + >>> from sympy import ccode, fcode + >>> from sympy.codegen.ast import continue_ + >>> ccode(continue_) + 'continue' + >>> fcode(continue_, source_format='free') + 'cycle' + """ + +continue_ = ContinueToken() + +class NoneToken(Token): + """ The AST equivalence of Python's NoneType + + The corresponding instance of Python's ``None`` is ``none``. + + Examples + ======== + + >>> from sympy.codegen.ast import none, Variable + >>> from sympy import pycode + >>> print(pycode(Variable('x').as_Declaration(value=none))) + x = None + + """ + def __eq__(self, other): + return other is None or isinstance(other, NoneToken) + + def _hashable_content(self): + return () + + def __hash__(self): + return super().__hash__() + + +none = NoneToken() + + +class AssignmentBase(CodegenAST): + """ Abstract base class for Assignment and AugmentedAssignment. + + Attributes: + =========== + + op : str + Symbol for assignment operator, e.g. "=", "+=", etc. + """ + + def __new__(cls, lhs, rhs): + lhs = _sympify(lhs) + rhs = _sympify(rhs) + + cls._check_args(lhs, rhs) + + return super().__new__(cls, lhs, rhs) + + @property + def lhs(self): + return self.args[0] + + @property + def rhs(self): + return self.args[1] + + @classmethod + def _check_args(cls, lhs, rhs): + """ Check arguments to __new__ and raise exception if any problems found. + + Derived classes may wish to override this. + """ + from sympy.matrices.expressions.matexpr import ( + MatrixElement, MatrixSymbol) + from sympy.tensor.indexed import Indexed + from sympy.tensor.array.expressions import ArrayElement + + # Tuple of things that can be on the lhs of an assignment + assignable = (Symbol, MatrixSymbol, MatrixElement, Indexed, Element, Variable, + ArrayElement) + if not isinstance(lhs, assignable): + raise TypeError("Cannot assign to lhs of type %s." % type(lhs)) + + # Indexed types implement shape, but don't define it until later. This + # causes issues in assignment validation. For now, matrices are defined + # as anything with a shape that is not an Indexed + lhs_is_mat = hasattr(lhs, 'shape') and not isinstance(lhs, Indexed) + rhs_is_mat = hasattr(rhs, 'shape') and not isinstance(rhs, Indexed) + + # If lhs and rhs have same structure, then this assignment is ok + if lhs_is_mat: + if not rhs_is_mat: + raise ValueError("Cannot assign a scalar to a matrix.") + elif lhs.shape != rhs.shape: + raise ValueError("Dimensions of lhs and rhs do not align.") + elif rhs_is_mat and not lhs_is_mat: + raise ValueError("Cannot assign a matrix to a scalar.") + + +class Assignment(AssignmentBase): + """ + Represents variable assignment for code generation. + + Parameters + ========== + + lhs : Expr + SymPy object representing the lhs of the expression. These should be + singular objects, such as one would use in writing code. Notable types + include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that + subclass these types are also supported. + + rhs : Expr + SymPy object representing the rhs of the expression. This can be any + type, provided its shape corresponds to that of the lhs. For example, + a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as + the dimensions will not align. + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol, Matrix + >>> from sympy.codegen.ast import Assignment + >>> x, y, z = symbols('x, y, z') + >>> Assignment(x, y) + Assignment(x, y) + >>> Assignment(x, 0) + Assignment(x, 0) + >>> A = MatrixSymbol('A', 1, 3) + >>> mat = Matrix([x, y, z]).T + >>> Assignment(A, mat) + Assignment(A, Matrix([[x, y, z]])) + >>> Assignment(A[0, 1], x) + Assignment(A[0, 1], x) + """ + + op = ':=' + + +class AugmentedAssignment(AssignmentBase): + """ + Base class for augmented assignments. + + Attributes: + =========== + + binop : str + Symbol for binary operation being applied in the assignment, such as "+", + "*", etc. + """ + binop = None # type: str + + @property + def op(self): + return self.binop + '=' + + +class AddAugmentedAssignment(AugmentedAssignment): + binop = '+' + + +class SubAugmentedAssignment(AugmentedAssignment): + binop = '-' + + +class MulAugmentedAssignment(AugmentedAssignment): + binop = '*' + + +class DivAugmentedAssignment(AugmentedAssignment): + binop = '/' + + +class ModAugmentedAssignment(AugmentedAssignment): + binop = '%' + + +# Mapping from binary op strings to AugmentedAssignment subclasses +augassign_classes = { + cls.binop: cls for cls in [ + AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment, + DivAugmentedAssignment, ModAugmentedAssignment + ] +} + + +def aug_assign(lhs, op, rhs): + """ + Create 'lhs op= rhs'. + + Explanation + =========== + + Represents augmented variable assignment for code generation. This is a + convenience function. You can also use the AugmentedAssignment classes + directly, like AddAugmentedAssignment(x, y). + + Parameters + ========== + + lhs : Expr + SymPy object representing the lhs of the expression. These should be + singular objects, such as one would use in writing code. Notable types + include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that + subclass these types are also supported. + + op : str + Operator (+, -, /, \\*, %). + + rhs : Expr + SymPy object representing the rhs of the expression. This can be any + type, provided its shape corresponds to that of the lhs. For example, + a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as + the dimensions will not align. + + Examples + ======== + + >>> from sympy import symbols + >>> from sympy.codegen.ast import aug_assign + >>> x, y = symbols('x, y') + >>> aug_assign(x, '+', y) + AddAugmentedAssignment(x, y) + """ + if op not in augassign_classes: + raise ValueError("Unrecognized operator %s" % op) + return augassign_classes[op](lhs, rhs) + + +class CodeBlock(CodegenAST): + """ + Represents a block of code. + + Explanation + =========== + + For now only assignments are supported. This restriction will be lifted in + the future. + + Useful attributes on this object are: + + ``left_hand_sides``: + Tuple of left-hand sides of assignments, in order. + ``left_hand_sides``: + Tuple of right-hand sides of assignments, in order. + ``free_symbols``: Free symbols of the expressions in the right-hand sides + which do not appear in the left-hand side of an assignment. + + Useful methods on this object are: + + ``topological_sort``: + Class method. Return a CodeBlock with assignments + sorted so that variables are assigned before they + are used. + ``cse``: + Return a new CodeBlock with common subexpressions eliminated and + pulled out as assignments. + + Examples + ======== + + >>> from sympy import symbols, ccode + >>> from sympy.codegen.ast import CodeBlock, Assignment + >>> x, y = symbols('x y') + >>> c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1)) + >>> print(ccode(c)) + x = 1; + y = x + 1; + + """ + def __new__(cls, *args): + left_hand_sides = [] + right_hand_sides = [] + for i in args: + if isinstance(i, Assignment): + lhs, rhs = i.args + left_hand_sides.append(lhs) + right_hand_sides.append(rhs) + + obj = CodegenAST.__new__(cls, *args) + + obj.left_hand_sides = Tuple(*left_hand_sides) + obj.right_hand_sides = Tuple(*right_hand_sides) + return obj + + def __iter__(self): + return iter(self.args) + + def _sympyrepr(self, printer, *args, **kwargs): + il = printer._context.get('indent_level', 0) + joiner = ',\n' + ' '*il + joined = joiner.join(map(printer._print, self.args)) + return ('{}(\n'.format(' '*(il-4) + self.__class__.__name__,) + + ' '*il + joined + '\n' + ' '*(il - 4) + ')') + + _sympystr = _sympyrepr + + @property + def free_symbols(self): + return super().free_symbols - set(self.left_hand_sides) + + @classmethod + def topological_sort(cls, assignments): + """ + Return a CodeBlock with topologically sorted assignments so that + variables are assigned before they are used. + + Examples + ======== + + The existing order of assignments is preserved as much as possible. + + This function assumes that variables are assigned to only once. + + This is a class constructor so that the default constructor for + CodeBlock can error when variables are used before they are assigned. + + >>> from sympy import symbols + >>> from sympy.codegen.ast import CodeBlock, Assignment + >>> x, y, z = symbols('x y z') + + >>> assignments = [ + ... Assignment(x, y + z), + ... Assignment(y, z + 1), + ... Assignment(z, 2), + ... ] + >>> CodeBlock.topological_sort(assignments) + CodeBlock( + Assignment(z, 2), + Assignment(y, z + 1), + Assignment(x, y + z) + ) + + """ + + if not all(isinstance(i, Assignment) for i in assignments): + # Will support more things later + raise NotImplementedError("CodeBlock.topological_sort only supports Assignments") + + if any(isinstance(i, AugmentedAssignment) for i in assignments): + raise NotImplementedError("CodeBlock.topological_sort does not yet work with AugmentedAssignments") + + # Create a graph where the nodes are assignments and there is a directed edge + # between nodes that use a variable and nodes that assign that + # variable, like + + # [(x := 1, y := x + 1), (x := 1, z := y + z), (y := x + 1, z := y + z)] + + # If we then topologically sort these nodes, they will be in + # assignment order, like + + # x := 1 + # y := x + 1 + # z := y + z + + # A = The nodes + # + # enumerate keeps nodes in the same order they are already in if + # possible. It will also allow us to handle duplicate assignments to + # the same variable when those are implemented. + A = list(enumerate(assignments)) + + # var_map = {variable: [nodes for which this variable is assigned to]} + # like {x: [(1, x := y + z), (4, x := 2 * w)], ...} + var_map = defaultdict(list) + for node in A: + i, a = node + var_map[a.lhs].append(node) + + # E = Edges in the graph + E = [] + for dst_node in A: + i, a = dst_node + for s in a.rhs.free_symbols: + for src_node in var_map[s]: + E.append((src_node, dst_node)) + + ordered_assignments = topological_sort([A, E]) + + # De-enumerate the result + return cls(*[a for i, a in ordered_assignments]) + + def cse(self, symbols=None, optimizations=None, postprocess=None, + order='canonical'): + """ + Return a new code block with common subexpressions eliminated. + + Explanation + =========== + + See the docstring of :func:`sympy.simplify.cse_main.cse` for more + information. + + Examples + ======== + + >>> from sympy import symbols, sin + >>> from sympy.codegen.ast import CodeBlock, Assignment + >>> x, y, z = symbols('x y z') + + >>> c = CodeBlock( + ... Assignment(x, 1), + ... Assignment(y, sin(x) + 1), + ... Assignment(z, sin(x) - 1), + ... ) + ... + >>> c.cse() + CodeBlock( + Assignment(x, 1), + Assignment(x0, sin(x)), + Assignment(y, x0 + 1), + Assignment(z, x0 - 1) + ) + + """ + from sympy.simplify.cse_main import cse + + # Check that the CodeBlock only contains assignments to unique variables + if not all(isinstance(i, Assignment) for i in self.args): + # Will support more things later + raise NotImplementedError("CodeBlock.cse only supports Assignments") + + if any(isinstance(i, AugmentedAssignment) for i in self.args): + raise NotImplementedError("CodeBlock.cse does not yet work with AugmentedAssignments") + + for i, lhs in enumerate(self.left_hand_sides): + if lhs in self.left_hand_sides[:i]: + raise NotImplementedError("Duplicate assignments to the same " + "variable are not yet supported (%s)" % lhs) + + # Ensure new symbols for subexpressions do not conflict with existing + existing_symbols = self.atoms(Symbol) + if symbols is None: + symbols = numbered_symbols() + symbols = filter_symbols(symbols, existing_symbols) + + replacements, reduced_exprs = cse(list(self.right_hand_sides), + symbols=symbols, optimizations=optimizations, postprocess=postprocess, + order=order) + + new_block = [Assignment(var, expr) for var, expr in + zip(self.left_hand_sides, reduced_exprs)] + new_assignments = [Assignment(var, expr) for var, expr in replacements] + return self.topological_sort(new_assignments + new_block) + + +class For(Token): + """Represents a 'for-loop' in the code. + + Expressions are of the form: + "for target in iter: + body..." + + Parameters + ========== + + target : symbol + iter : iterable + body : CodeBlock or iterable +! When passed an iterable it is used to instantiate a CodeBlock. + + Examples + ======== + + >>> from sympy import symbols, Range + >>> from sympy.codegen.ast import aug_assign, For + >>> x, i, j, k = symbols('x i j k') + >>> for_i = For(i, Range(10), [aug_assign(x, '+', i*j*k)]) + >>> for_i # doctest: -NORMALIZE_WHITESPACE + For(i, iterable=Range(0, 10, 1), body=CodeBlock( + AddAugmentedAssignment(x, i*j*k) + )) + >>> for_ji = For(j, Range(7), [for_i]) + >>> for_ji # doctest: -NORMALIZE_WHITESPACE + For(j, iterable=Range(0, 7, 1), body=CodeBlock( + For(i, iterable=Range(0, 10, 1), body=CodeBlock( + AddAugmentedAssignment(x, i*j*k) + )) + )) + >>> for_kji =For(k, Range(5), [for_ji]) + >>> for_kji # doctest: -NORMALIZE_WHITESPACE + For(k, iterable=Range(0, 5, 1), body=CodeBlock( + For(j, iterable=Range(0, 7, 1), body=CodeBlock( + For(i, iterable=Range(0, 10, 1), body=CodeBlock( + AddAugmentedAssignment(x, i*j*k) + )) + )) + )) + """ + __slots__ = _fields = ('target', 'iterable', 'body') + _construct_target = staticmethod(_sympify) + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + @classmethod + def _construct_iterable(cls, itr): + if not iterable(itr): + raise TypeError("iterable must be an iterable") + if isinstance(itr, list): # _sympify errors on lists because they are mutable + itr = tuple(itr) + return _sympify(itr) + + +class String(Atom, Token): + """ SymPy object representing a string. + + Atomic object which is not an expression (as opposed to Symbol). + + Parameters + ========== + + text : str + + Examples + ======== + + >>> from sympy.codegen.ast import String + >>> f = String('foo') + >>> f + foo + >>> str(f) + 'foo' + >>> f.text + 'foo' + >>> print(repr(f)) + String('foo') + + """ + __slots__ = _fields = ('text',) + not_in_args = ['text'] + is_Atom = True + + @classmethod + def _construct_text(cls, text): + if not isinstance(text, str): + raise TypeError("Argument text is not a string type.") + return text + + def _sympystr(self, printer, *args, **kwargs): + return self.text + + def kwargs(self, exclude = (), apply = None): + return {} + + #to be removed when Atom is given a suitable func + @property + def func(self): + return lambda: self + + def _latex(self, printer): + from sympy.printing.latex import latex_escape + return r'\texttt{{"{}"}}'.format(latex_escape(self.text)) + +class QuotedString(String): + """ Represents a string which should be printed with quotes. """ + +class Comment(String): + """ Represents a comment. """ + +class Node(Token): + """ Subclass of Token, carrying the attribute 'attrs' (Tuple) + + Examples + ======== + + >>> from sympy.codegen.ast import Node, value_const, pointer_const + >>> n1 = Node([value_const]) + >>> n1.attr_params('value_const') # get the parameters of attribute (by name) + () + >>> from sympy.codegen.fnodes import dimension + >>> n2 = Node([value_const, dimension(5, 3)]) + >>> n2.attr_params(value_const) # get the parameters of attribute (by Attribute instance) + () + >>> n2.attr_params('dimension') # get the parameters of attribute (by name) + (5, 3) + >>> n2.attr_params(pointer_const) is None + True + + """ + + __slots__: tuple[str, ...] = ('attrs',) + _fields = __slots__ + + defaults: dict[str, Any] = {'attrs': Tuple()} + + _construct_attrs = staticmethod(_mk_Tuple) + + def attr_params(self, looking_for): + """ Returns the parameters of the Attribute with name ``looking_for`` in self.attrs """ + for attr in self.attrs: + if str(attr.name) == str(looking_for): + return attr.parameters + + +class Type(Token): + """ Represents a type. + + Explanation + =========== + + The naming is a super-set of NumPy naming. Type has a classmethod + ``from_expr`` which offer type deduction. It also has a method + ``cast_check`` which casts the argument to its type, possibly raising an + exception if rounding error is not within tolerances, or if the value is not + representable by the underlying data type (e.g. unsigned integers). + + Parameters + ========== + + name : str + Name of the type, e.g. ``object``, ``int16``, ``float16`` (where the latter two + would use the ``Type`` sub-classes ``IntType`` and ``FloatType`` respectively). + If a ``Type`` instance is given, the said instance is returned. + + Examples + ======== + + >>> from sympy.codegen.ast import Type + >>> t = Type.from_expr(42) + >>> t + integer + >>> print(repr(t)) + IntBaseType(String('integer')) + >>> from sympy.codegen.ast import uint8 + >>> uint8.cast_check(-1) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Minimum value for data type bigger than new value. + >>> from sympy.codegen.ast import float32 + >>> v6 = 0.123456 + >>> float32.cast_check(v6) + 0.123456 + >>> v10 = 12345.67894 + >>> float32.cast_check(v10) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Casting gives a significantly different value. + >>> boost_mp50 = Type('boost::multiprecision::cpp_dec_float_50') + >>> from sympy import cxxcode + >>> from sympy.codegen.ast import Declaration, Variable + >>> cxxcode(Declaration(Variable('x', type=boost_mp50))) + 'boost::multiprecision::cpp_dec_float_50 x' + + References + ========== + + .. [1] https://numpy.org/doc/stable/user/basics.types.html + + """ + __slots__: tuple[str, ...] = ('name',) + _fields = __slots__ + + _construct_name = String + + def _sympystr(self, printer, *args, **kwargs): + return str(self.name) + + @classmethod + def from_expr(cls, expr): + """ Deduces type from an expression or a ``Symbol``. + + Parameters + ========== + + expr : number or SymPy object + The type will be deduced from type or properties. + + Examples + ======== + + >>> from sympy.codegen.ast import Type, integer, complex_ + >>> Type.from_expr(2) == integer + True + >>> from sympy import Symbol + >>> Type.from_expr(Symbol('z', complex=True)) == complex_ + True + >>> Type.from_expr(sum) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Could not deduce type from expr. + + Raises + ====== + + ValueError when type deduction fails. + + """ + if isinstance(expr, (float, Float)): + return real + if isinstance(expr, (int, Integer)) or getattr(expr, 'is_integer', False): + return integer + if getattr(expr, 'is_real', False): + return real + if isinstance(expr, complex) or getattr(expr, 'is_complex', False): + return complex_ + if isinstance(expr, bool) or getattr(expr, 'is_Relational', False): + return bool_ + else: + raise ValueError("Could not deduce type from expr.") + + def _check(self, value): + pass + + def cast_check(self, value, rtol=None, atol=0, precision_targets=None): + """ Casts a value to the data type of the instance. + + Parameters + ========== + + value : number + rtol : floating point number + Relative tolerance. (will be deduced if not given). + atol : floating point number + Absolute tolerance (in addition to ``rtol``). + type_aliases : dict + Maps substitutions for Type, e.g. {integer: int64, real: float32} + + Examples + ======== + + >>> from sympy.codegen.ast import integer, float32, int8 + >>> integer.cast_check(3.0) == 3 + True + >>> float32.cast_check(1e-40) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Minimum value for data type bigger than new value. + >>> int8.cast_check(256) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Maximum value for data type smaller than new value. + >>> v10 = 12345.67894 + >>> float32.cast_check(v10) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Casting gives a significantly different value. + >>> from sympy.codegen.ast import float64 + >>> float64.cast_check(v10) + 12345.67894 + >>> from sympy import Float + >>> v18 = Float('0.123456789012345646') + >>> float64.cast_check(v18) + Traceback (most recent call last): + ... + ValueError: Casting gives a significantly different value. + >>> from sympy.codegen.ast import float80 + >>> float80.cast_check(v18) + 0.123456789012345649 + + """ + val = sympify(value) + + ten = Integer(10) + exp10 = getattr(self, 'decimal_dig', None) + + if rtol is None: + rtol = 1e-15 if exp10 is None else 2.0*ten**(-exp10) + + def tol(num): + return atol + rtol*abs(num) + + new_val = self.cast_nocheck(value) + self._check(new_val) + + delta = new_val - val + if abs(delta) > tol(val): # rounding, e.g. int(3.5) != 3.5 + raise ValueError("Casting gives a significantly different value.") + + return new_val + + def _latex(self, printer): + from sympy.printing.latex import latex_escape + type_name = latex_escape(self.__class__.__name__) + name = latex_escape(self.name.text) + return r"\text{{{}}}\left(\texttt{{{}}}\right)".format(type_name, name) + + +class IntBaseType(Type): + """ Integer base type, contains no size information. """ + __slots__ = () + cast_nocheck = lambda self, i: Integer(int(i)) + + +class _SizedIntType(IntBaseType): + __slots__ = ('nbits',) + _fields = Type._fields + __slots__ + + _construct_nbits = Integer + + def _check(self, value): + if value < self.min: + raise ValueError("Value is too small: %d < %d" % (value, self.min)) + if value > self.max: + raise ValueError("Value is too big: %d > %d" % (value, self.max)) + + +class SignedIntType(_SizedIntType): + """ Represents a signed integer type. """ + __slots__ = () + @property + def min(self): + return -2**(self.nbits-1) + + @property + def max(self): + return 2**(self.nbits-1) - 1 + + +class UnsignedIntType(_SizedIntType): + """ Represents an unsigned integer type. """ + __slots__ = () + @property + def min(self): + return 0 + + @property + def max(self): + return 2**self.nbits - 1 + +two = Integer(2) + +class FloatBaseType(Type): + """ Represents a floating point number type. """ + __slots__ = () + cast_nocheck = Float + +class FloatType(FloatBaseType): + """ Represents a floating point type with fixed bit width. + + Base 2 & one sign bit is assumed. + + Parameters + ========== + + name : str + Name of the type. + nbits : integer + Number of bits used (storage). + nmant : integer + Number of bits used to represent the mantissa. + nexp : integer + Number of bits used to represent the mantissa. + + Examples + ======== + + >>> from sympy import S + >>> from sympy.codegen.ast import FloatType + >>> half_precision = FloatType('f16', nbits=16, nmant=10, nexp=5) + >>> half_precision.max + 65504 + >>> half_precision.tiny == S(2)**-14 + True + >>> half_precision.eps == S(2)**-10 + True + >>> half_precision.dig == 3 + True + >>> half_precision.decimal_dig == 5 + True + >>> half_precision.cast_check(1.0) + 1.0 + >>> half_precision.cast_check(1e5) # doctest: +ELLIPSIS + Traceback (most recent call last): + ... + ValueError: Maximum value for data type smaller than new value. + """ + + __slots__ = ('nbits', 'nmant', 'nexp',) + _fields = Type._fields + __slots__ + + _construct_nbits = _construct_nmant = _construct_nexp = Integer + + + @property + def max_exponent(self): + """ The largest positive number n, such that 2**(n - 1) is a representable finite value. """ + # cf. C++'s ``std::numeric_limits::max_exponent`` + return two**(self.nexp - 1) + + @property + def min_exponent(self): + """ The lowest negative number n, such that 2**(n - 1) is a valid normalized number. """ + # cf. C++'s ``std::numeric_limits::min_exponent`` + return 3 - self.max_exponent + + @property + def max(self): + """ Maximum value representable. """ + return (1 - two**-(self.nmant+1))*two**self.max_exponent + + @property + def tiny(self): + """ The minimum positive normalized value. """ + # See C macros: FLT_MIN, DBL_MIN, LDBL_MIN + # or C++'s ``std::numeric_limits::min`` + # or numpy.finfo(dtype).tiny + return two**(self.min_exponent - 1) + + + @property + def eps(self): + """ Difference between 1.0 and the next representable value. """ + return two**(-self.nmant) + + @property + def dig(self): + """ Number of decimal digits that are guaranteed to be preserved in text. + + When converting text -> float -> text, you are guaranteed that at least ``dig`` + number of digits are preserved with respect to rounding or overflow. + """ + from sympy.functions import floor, log + return floor(self.nmant * log(2)/log(10)) + + @property + def decimal_dig(self): + """ Number of digits needed to store & load without loss. + + Explanation + =========== + + Number of decimal digits needed to guarantee that two consecutive conversions + (float -> text -> float) to be idempotent. This is useful when one do not want + to loose precision due to rounding errors when storing a floating point value + as text. + """ + from sympy.functions import ceiling, log + return ceiling((self.nmant + 1) * log(2)/log(10) + 1) + + def cast_nocheck(self, value): + """ Casts without checking if out of bounds or subnormal. """ + if value == oo: # float(oo) or oo + return float(oo) + elif value == -oo: # float(-oo) or -oo + return float(-oo) + return Float(str(sympify(value).evalf(self.decimal_dig)), self.decimal_dig) + + def _check(self, value): + if value < -self.max: + raise ValueError("Value is too small: %d < %d" % (value, -self.max)) + if value > self.max: + raise ValueError("Value is too big: %d > %d" % (value, self.max)) + if abs(value) < self.tiny: + raise ValueError("Smallest (absolute) value for data type bigger than new value.") + +class ComplexBaseType(FloatBaseType): + + __slots__ = () + + def cast_nocheck(self, value): + """ Casts without checking if out of bounds or subnormal. """ + from sympy.functions import re, im + return ( + super().cast_nocheck(re(value)) + + super().cast_nocheck(im(value))*1j + ) + + def _check(self, value): + from sympy.functions import re, im + super()._check(re(value)) + super()._check(im(value)) + + +class ComplexType(ComplexBaseType, FloatType): + """ Represents a complex floating point number. """ + __slots__ = () + + +# NumPy types: +intc = IntBaseType('intc') +intp = IntBaseType('intp') +int8 = SignedIntType('int8', 8) +int16 = SignedIntType('int16', 16) +int32 = SignedIntType('int32', 32) +int64 = SignedIntType('int64', 64) +uint8 = UnsignedIntType('uint8', 8) +uint16 = UnsignedIntType('uint16', 16) +uint32 = UnsignedIntType('uint32', 32) +uint64 = UnsignedIntType('uint64', 64) +float16 = FloatType('float16', 16, nexp=5, nmant=10) # IEEE 754 binary16, Half precision +float32 = FloatType('float32', 32, nexp=8, nmant=23) # IEEE 754 binary32, Single precision +float64 = FloatType('float64', 64, nexp=11, nmant=52) # IEEE 754 binary64, Double precision +float80 = FloatType('float80', 80, nexp=15, nmant=63) # x86 extended precision (1 integer part bit), "long double" +float128 = FloatType('float128', 128, nexp=15, nmant=112) # IEEE 754 binary128, Quadruple precision +float256 = FloatType('float256', 256, nexp=19, nmant=236) # IEEE 754 binary256, Octuple precision + +complex64 = ComplexType('complex64', nbits=64, **float32.kwargs(exclude=('name', 'nbits'))) +complex128 = ComplexType('complex128', nbits=128, **float64.kwargs(exclude=('name', 'nbits'))) + +# Generic types (precision may be chosen by code printers): +untyped = Type('untyped') +real = FloatBaseType('real') +integer = IntBaseType('integer') +complex_ = ComplexBaseType('complex') +bool_ = Type('bool') + + +class Attribute(Token): + """ Attribute (possibly parametrized) + + For use with :class:`sympy.codegen.ast.Node` (which takes instances of + ``Attribute`` as ``attrs``). + + Parameters + ========== + + name : str + parameters : Tuple + + Examples + ======== + + >>> from sympy.codegen.ast import Attribute + >>> volatile = Attribute('volatile') + >>> volatile + volatile + >>> print(repr(volatile)) + Attribute(String('volatile')) + >>> a = Attribute('foo', [1, 2, 3]) + >>> a + foo(1, 2, 3) + >>> a.parameters == (1, 2, 3) + True + """ + __slots__ = _fields = ('name', 'parameters') + defaults = {'parameters': Tuple()} + + _construct_name = String + _construct_parameters = staticmethod(_mk_Tuple) + + def _sympystr(self, printer, *args, **kwargs): + result = str(self.name) + if self.parameters: + result += '(%s)' % ', '.join((printer._print( + arg, *args, **kwargs) for arg in self.parameters)) + return result + +value_const = Attribute('value_const') +pointer_const = Attribute('pointer_const') + + +class Variable(Node): + """ Represents a variable. + + Parameters + ========== + + symbol : Symbol + type : Type (optional) + Type of the variable. + attrs : iterable of Attribute instances + Will be stored as a Tuple. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.codegen.ast import Variable, float32, integer + >>> x = Symbol('x') + >>> v = Variable(x, type=float32) + >>> v.attrs + () + >>> v == Variable('x') + False + >>> v == Variable('x', type=float32) + True + >>> v + Variable(x, type=float32) + + One may also construct a ``Variable`` instance with the type deduced from + assumptions about the symbol using the ``deduced`` classmethod: + + >>> i = Symbol('i', integer=True) + >>> v = Variable.deduced(i) + >>> v.type == integer + True + >>> v == Variable('i') + False + >>> from sympy.codegen.ast import value_const + >>> value_const in v.attrs + False + >>> w = Variable('w', attrs=[value_const]) + >>> w + Variable(w, attrs=(value_const,)) + >>> value_const in w.attrs + True + >>> w.as_Declaration(value=42) + Declaration(Variable(w, value=42, attrs=(value_const,))) + + """ + + __slots__ = ('symbol', 'type', 'value') + _fields = __slots__ + Node._fields + + defaults = Node.defaults.copy() + defaults.update({'type': untyped, 'value': none}) + + _construct_symbol = staticmethod(sympify) + _construct_value = staticmethod(sympify) + + @classmethod + def deduced(cls, symbol, value=None, attrs=Tuple(), cast_check=True): + """ Alt. constructor with type deduction from ``Type.from_expr``. + + Deduces type primarily from ``symbol``, secondarily from ``value``. + + Parameters + ========== + + symbol : Symbol + value : expr + (optional) value of the variable. + attrs : iterable of Attribute instances + cast_check : bool + Whether to apply ``Type.cast_check`` on ``value``. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.codegen.ast import Variable, complex_ + >>> n = Symbol('n', integer=True) + >>> str(Variable.deduced(n).type) + 'integer' + >>> x = Symbol('x', real=True) + >>> v = Variable.deduced(x) + >>> v.type + real + >>> z = Symbol('z', complex=True) + >>> Variable.deduced(z).type == complex_ + True + + """ + if isinstance(symbol, Variable): + return symbol + + try: + type_ = Type.from_expr(symbol) + except ValueError: + type_ = Type.from_expr(value) + + if value is not None and cast_check: + value = type_.cast_check(value) + return cls(symbol, type=type_, value=value, attrs=attrs) + + def as_Declaration(self, **kwargs): + """ Convenience method for creating a Declaration instance. + + Explanation + =========== + + If the variable of the Declaration need to wrap a modified + variable keyword arguments may be passed (overriding e.g. + the ``value`` of the Variable instance). + + Examples + ======== + + >>> from sympy.codegen.ast import Variable, NoneToken + >>> x = Variable('x') + >>> decl1 = x.as_Declaration() + >>> # value is special NoneToken() which must be tested with == operator + >>> decl1.variable.value is None # won't work + False + >>> decl1.variable.value == None # not PEP-8 compliant + True + >>> decl1.variable.value == NoneToken() # OK + True + >>> decl2 = x.as_Declaration(value=42.0) + >>> decl2.variable.value == 42.0 + True + + """ + kw = self.kwargs() + kw.update(kwargs) + return Declaration(self.func(**kw)) + + def _relation(self, rhs, op): + try: + rhs = _sympify(rhs) + except SympifyError: + raise TypeError("Invalid comparison %s < %s" % (self, rhs)) + return op(self, rhs, evaluate=False) + + __lt__ = lambda self, other: self._relation(other, Lt) + __le__ = lambda self, other: self._relation(other, Le) + __ge__ = lambda self, other: self._relation(other, Ge) + __gt__ = lambda self, other: self._relation(other, Gt) + +class Pointer(Variable): + """ Represents a pointer. See ``Variable``. + + Examples + ======== + + Can create instances of ``Element``: + + >>> from sympy import Symbol + >>> from sympy.codegen.ast import Pointer + >>> i = Symbol('i', integer=True) + >>> p = Pointer('x') + >>> p[i+1] + Element(x, indices=(i + 1,)) + + """ + __slots__ = () + + def __getitem__(self, key): + try: + return Element(self.symbol, key) + except TypeError: + return Element(self.symbol, (key,)) + + +class Element(Token): + """ Element in (a possibly N-dimensional) array. + + Examples + ======== + + >>> from sympy.codegen.ast import Element + >>> elem = Element('x', 'ijk') + >>> elem.symbol.name == 'x' + True + >>> elem.indices + (i, j, k) + >>> from sympy import ccode + >>> ccode(elem) + 'x[i][j][k]' + >>> ccode(Element('x', 'ijk', strides='lmn', offset='o')) + 'x[i*l + j*m + k*n + o]' + + """ + __slots__ = _fields = ('symbol', 'indices', 'strides', 'offset') + defaults = {'strides': none, 'offset': none} + _construct_symbol = staticmethod(sympify) + _construct_indices = staticmethod(lambda arg: Tuple(*arg)) + _construct_strides = staticmethod(lambda arg: Tuple(*arg)) + _construct_offset = staticmethod(sympify) + + +class Declaration(Token): + """ Represents a variable declaration + + Parameters + ========== + + variable : Variable + + Examples + ======== + + >>> from sympy.codegen.ast import Declaration, NoneToken, untyped + >>> z = Declaration('z') + >>> z.variable.type == untyped + True + >>> # value is special NoneToken() which must be tested with == operator + >>> z.variable.value is None # won't work + False + >>> z.variable.value == None # not PEP-8 compliant + True + >>> z.variable.value == NoneToken() # OK + True + """ + __slots__ = _fields = ('variable',) + _construct_variable = Variable + + +class While(Token): + """ Represents a 'for-loop' in the code. + + Expressions are of the form: + "while condition: + body..." + + Parameters + ========== + + condition : expression convertible to Boolean + body : CodeBlock or iterable + When passed an iterable it is used to instantiate a CodeBlock. + + Examples + ======== + + >>> from sympy import symbols, Gt, Abs + >>> from sympy.codegen import aug_assign, Assignment, While + >>> x, dx = symbols('x dx') + >>> expr = 1 - x**2 + >>> whl = While(Gt(Abs(dx), 1e-9), [ + ... Assignment(dx, -expr/expr.diff(x)), + ... aug_assign(x, '+', dx) + ... ]) + + """ + __slots__ = _fields = ('condition', 'body') + _construct_condition = staticmethod(lambda cond: _sympify(cond)) + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + +class Scope(Token): + """ Represents a scope in the code. + + Parameters + ========== + + body : CodeBlock or iterable + When passed an iterable it is used to instantiate a CodeBlock. + + """ + __slots__ = _fields = ('body',) + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + +class Stream(Token): + """ Represents a stream. + + There are two predefined Stream instances ``stdout`` & ``stderr``. + + Parameters + ========== + + name : str + + Examples + ======== + + >>> from sympy import pycode, Symbol + >>> from sympy.codegen.ast import Print, stderr, QuotedString + >>> print(pycode(Print(['x'], file=stderr))) + print(x, file=sys.stderr) + >>> x = Symbol('x') + >>> print(pycode(Print([QuotedString('x')], file=stderr))) # print literally "x" + print("x", file=sys.stderr) + + """ + __slots__ = _fields = ('name',) + _construct_name = String + +stdout = Stream('stdout') +stderr = Stream('stderr') + + +class Print(Token): + r""" Represents print command in the code. + + Parameters + ========== + + formatstring : str + *args : Basic instances (or convertible to such through sympify) + + Examples + ======== + + >>> from sympy.codegen.ast import Print + >>> from sympy import pycode + >>> print(pycode(Print('x y'.split(), "coordinate: %12.5g %12.5g\\n"))) + print("coordinate: %12.5g %12.5g\n" % (x, y), end="") + + """ + + __slots__ = _fields = ('print_args', 'format_string', 'file') + defaults = {'format_string': none, 'file': none} + + _construct_print_args = staticmethod(_mk_Tuple) + _construct_format_string = QuotedString + _construct_file = Stream + + +class FunctionPrototype(Node): + """ Represents a function prototype + + Allows the user to generate forward declaration in e.g. C/C++. + + Parameters + ========== + + return_type : Type + name : str + parameters: iterable of Variable instances + attrs : iterable of Attribute instances + + Examples + ======== + + >>> from sympy import ccode, symbols + >>> from sympy.codegen.ast import real, FunctionPrototype + >>> x, y = symbols('x y', real=True) + >>> fp = FunctionPrototype(real, 'foo', [x, y]) + >>> ccode(fp) + 'double foo(double x, double y)' + + """ + + __slots__ = ('return_type', 'name', 'parameters') + _fields: tuple[str, ...] = __slots__ + Node._fields + + _construct_return_type = Type + _construct_name = String + + @staticmethod + def _construct_parameters(args): + def _var(arg): + if isinstance(arg, Declaration): + return arg.variable + elif isinstance(arg, Variable): + return arg + else: + return Variable.deduced(arg) + return Tuple(*map(_var, args)) + + @classmethod + def from_FunctionDefinition(cls, func_def): + if not isinstance(func_def, FunctionDefinition): + raise TypeError("func_def is not an instance of FunctionDefinition") + return cls(**func_def.kwargs(exclude=('body',))) + + +class FunctionDefinition(FunctionPrototype): + """ Represents a function definition in the code. + + Parameters + ========== + + return_type : Type + name : str + parameters: iterable of Variable instances + body : CodeBlock or iterable + attrs : iterable of Attribute instances + + Examples + ======== + + >>> from sympy import ccode, symbols + >>> from sympy.codegen.ast import real, FunctionPrototype + >>> x, y = symbols('x y', real=True) + >>> fp = FunctionPrototype(real, 'foo', [x, y]) + >>> ccode(fp) + 'double foo(double x, double y)' + >>> from sympy.codegen.ast import FunctionDefinition, Return + >>> body = [Return(x*y)] + >>> fd = FunctionDefinition.from_FunctionPrototype(fp, body) + >>> print(ccode(fd)) + double foo(double x, double y){ + return x*y; + } + """ + + __slots__ = ('body', ) + _fields = FunctionPrototype._fields[:-1] + __slots__ + Node._fields + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + @classmethod + def from_FunctionPrototype(cls, func_proto, body): + if not isinstance(func_proto, FunctionPrototype): + raise TypeError("func_proto is not an instance of FunctionPrototype") + return cls(body=body, **func_proto.kwargs()) + + +class Return(Token): + """ Represents a return command in the code. + + Parameters + ========== + + return : Basic + + Examples + ======== + + >>> from sympy.codegen.ast import Return + >>> from sympy.printing.pycode import pycode + >>> from sympy import Symbol + >>> x = Symbol('x') + >>> print(pycode(Return(x))) + return x + + """ + __slots__ = _fields = ('return',) + _construct_return=staticmethod(_sympify) + + +class FunctionCall(Token, Expr): + """ Represents a call to a function in the code. + + Parameters + ========== + + name : str + function_args : Tuple + + Examples + ======== + + >>> from sympy.codegen.ast import FunctionCall + >>> from sympy import pycode + >>> fcall = FunctionCall('foo', 'bar baz'.split()) + >>> print(pycode(fcall)) + foo(bar, baz) + + """ + __slots__ = _fields = ('name', 'function_args') + + _construct_name = String + _construct_function_args = staticmethod(lambda args: Tuple(*args)) + + +class Raise(Token): + """ Prints as 'raise ...' in Python, 'throw ...' in C++""" + __slots__ = _fields = ('exception',) + + +class RuntimeError_(Token): + """ Represents 'std::runtime_error' in C++ and 'RuntimeError' in Python. + + Note that the latter is uncommon, and you might want to use e.g. ValueError. + """ + __slots__ = _fields = ('message',) + _construct_message = String diff --git a/lib/python3.11/site-packages/sympy/codegen/cfunctions.py b/lib/python3.11/site-packages/sympy/codegen/cfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..2eb3176ea8cd0967de9aa6d93b54f0c1c1354755 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/cfunctions.py @@ -0,0 +1,536 @@ +""" +This module contains SymPy functions mathcin corresponding to special math functions in the +C standard library (since C99, also available in C++11). + +The functions defined in this module allows the user to express functions such as ``expm1`` +as a SymPy function for symbolic manipulation. + +""" +from sympy.core.function import ArgumentIndexError, Function +from sympy.core.numbers import Rational +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.miscellaneous import sqrt + + +def _expm1(x): + return exp(x) - S.One + + +class expm1(Function): + """ + Represents the exponential function minus one. + + Explanation + =========== + + The benefit of using ``expm1(x)`` over ``exp(x) - 1`` + is that the latter is prone to cancellation under finite precision + arithmetic when x is close to zero. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import expm1 + >>> '%.0e' % expm1(1e-99).evalf() + '1e-99' + >>> from math import exp + >>> exp(1e-99) - 1 + 0.0 + >>> expm1(x).diff(x) + exp(x) + + See Also + ======== + + log1p + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return exp(*self.args) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_expand_func(self, **hints): + return _expm1(*self.args) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return exp(arg) - S.One + + _eval_rewrite_as_tractable = _eval_rewrite_as_exp + + @classmethod + def eval(cls, arg): + exp_arg = exp.eval(arg) + if exp_arg is not None: + return exp_arg - S.One + + def _eval_is_real(self): + return self.args[0].is_real + + def _eval_is_finite(self): + return self.args[0].is_finite + + +def _log1p(x): + return log(x + S.One) + + +class log1p(Function): + """ + Represents the natural logarithm of a number plus one. + + Explanation + =========== + + The benefit of using ``log1p(x)`` over ``log(x + 1)`` + is that the latter is prone to cancellation under finite precision + arithmetic when x is close to zero. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log1p + >>> from sympy import expand_log + >>> '%.0e' % expand_log(log1p(1e-99)).evalf() + '1e-99' + >>> from math import log + >>> log(1 + 1e-99) + 0.0 + >>> log1p(x).diff(x) + 1/(x + 1) + + See Also + ======== + + expm1 + """ + nargs = 1 + + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(self.args[0] + S.One) + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _log1p(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log1p(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + @classmethod + def eval(cls, arg): + if arg.is_Rational: + return log(arg + S.One) + elif not arg.is_Float: # not safe to add 1 to Float + return log.eval(arg + S.One) + elif arg.is_number: + return log(Rational(arg) + S.One) + + def _eval_is_real(self): + return (self.args[0] + S.One).is_nonnegative + + def _eval_is_finite(self): + if (self.args[0] + S.One).is_zero: + return False + return self.args[0].is_finite + + def _eval_is_positive(self): + return self.args[0].is_positive + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_is_nonnegative(self): + return self.args[0].is_nonnegative + +_Two = S(2) + +def _exp2(x): + return Pow(_Two, x) + +class exp2(Function): + """ + Represents the exponential function with base two. + + Explanation + =========== + + The benefit of using ``exp2(x)`` over ``2**x`` + is that the latter is not as efficient under finite precision + arithmetic. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import exp2 + >>> exp2(2).evalf() == 4.0 + True + >>> exp2(x).diff(x) + log(2)*exp2(x) + + See Also + ======== + + log2 + """ + nargs = 1 + + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return self*log(_Two) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _exp2(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + def _eval_expand_func(self, **hints): + return _exp2(*self.args) + + @classmethod + def eval(cls, arg): + if arg.is_number: + return _exp2(arg) + + +def _log2(x): + return log(x)/log(_Two) + + +class log2(Function): + """ + Represents the logarithm function with base two. + + Explanation + =========== + + The benefit of using ``log2(x)`` over ``log(x)/log(2)`` + is that the latter is not as efficient under finite precision + arithmetic. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log2 + >>> log2(4).evalf() == 2.0 + True + >>> log2(x).diff(x) + 1/(x*log(2)) + + See Also + ======== + + exp2 + log10 + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(log(_Two)*self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + + @classmethod + def eval(cls, arg): + if arg.is_number: + result = log.eval(arg, base=_Two) + if result.is_Atom: + return result + elif arg.is_Pow and arg.base == _Two: + return arg.exp + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(log).evalf(*args, **kwargs) + + def _eval_expand_func(self, **hints): + return _log2(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log2(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + +def _fma(x, y, z): + return x*y + z + + +class fma(Function): + """ + Represents "fused multiply add". + + Explanation + =========== + + The benefit of using ``fma(x, y, z)`` over ``x*y + z`` + is that, under finite precision arithmetic, the former is + supported by special instructions on some CPUs. + + Examples + ======== + + >>> from sympy.abc import x, y, z + >>> from sympy.codegen.cfunctions import fma + >>> fma(x, y, z).diff(x) + y + + """ + nargs = 3 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex in (1, 2): + return self.args[2 - argindex] + elif argindex == 3: + return S.One + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _fma(*self.args) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + return _fma(arg) + + +_Ten = S(10) + + +def _log10(x): + return log(x)/log(_Ten) + + +class log10(Function): + """ + Represents the logarithm function with base ten. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log10 + >>> log10(100).evalf() == 2.0 + True + >>> log10(x).diff(x) + 1/(x*log(10)) + + See Also + ======== + + log2 + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(log(_Ten)*self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + + @classmethod + def eval(cls, arg): + if arg.is_number: + result = log.eval(arg, base=_Ten) + if result.is_Atom: + return result + elif arg.is_Pow and arg.base == _Ten: + return arg.exp + + def _eval_expand_func(self, **hints): + return _log10(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log10(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + +def _Sqrt(x): + return Pow(x, S.Half) + + +class Sqrt(Function): # 'sqrt' already defined in sympy.functions.elementary.miscellaneous + """ + Represents the square root function. + + Explanation + =========== + + The reason why one would use ``Sqrt(x)`` over ``sqrt(x)`` + is that the latter is internally represented as ``Pow(x, S.Half)`` which + may not be what one wants when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import Sqrt + >>> Sqrt(x) + Sqrt(x) + >>> Sqrt(x).diff(x) + 1/(2*sqrt(x)) + + See Also + ======== + + Cbrt + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return Pow(self.args[0], Rational(-1, 2))/_Two + else: + raise ArgumentIndexError(self, argindex) + + def _eval_expand_func(self, **hints): + return _Sqrt(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _Sqrt(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +def _Cbrt(x): + return Pow(x, Rational(1, 3)) + + +class Cbrt(Function): # 'cbrt' already defined in sympy.functions.elementary.miscellaneous + """ + Represents the cube root function. + + Explanation + =========== + + The reason why one would use ``Cbrt(x)`` over ``cbrt(x)`` + is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which + may not be what one wants when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import Cbrt + >>> Cbrt(x) + Cbrt(x) + >>> Cbrt(x).diff(x) + 1/(3*x**(2/3)) + + See Also + ======== + + Sqrt + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return Pow(self.args[0], Rational(-_Two/3))/3 + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _Cbrt(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _Cbrt(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +def _hypot(x, y): + return sqrt(Pow(x, 2) + Pow(y, 2)) + + +class hypot(Function): + """ + Represents the hypotenuse function. + + Explanation + =========== + + The hypotenuse function is provided by e.g. the math library + in the C99 standard, hence one may want to represent the function + symbolically when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.codegen.cfunctions import hypot + >>> hypot(3, 4).evalf() == 5.0 + True + >>> hypot(x, y) + hypot(x, y) + >>> hypot(x, y).diff(x) + x/hypot(x, y) + + """ + nargs = 2 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex in (1, 2): + return 2*self.args[argindex-1]/(_Two*self.func(*self.args)) + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _hypot(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _hypot(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +class isnan(Function): + nargs = 1 diff --git a/lib/python3.11/site-packages/sympy/codegen/cnodes.py b/lib/python3.11/site-packages/sympy/codegen/cnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..dd2a324ee49cabcd42e99ca5d8e5379cc9262c4e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/cnodes.py @@ -0,0 +1,156 @@ +""" +AST nodes specific to the C family of languages +""" + +from sympy.codegen.ast import ( + Attribute, Declaration, Node, String, Token, Type, none, + FunctionCall, CodeBlock + ) +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.sympify import sympify + +void = Type('void') + +restrict = Attribute('restrict') # guarantees no pointer aliasing +volatile = Attribute('volatile') +static = Attribute('static') + + +def alignof(arg): + """ Generate of FunctionCall instance for calling 'alignof' """ + return FunctionCall('alignof', [String(arg) if isinstance(arg, str) else arg]) + + +def sizeof(arg): + """ Generate of FunctionCall instance for calling 'sizeof' + + Examples + ======== + + >>> from sympy.codegen.ast import real + >>> from sympy.codegen.cnodes import sizeof + >>> from sympy import ccode + >>> ccode(sizeof(real)) + 'sizeof(double)' + """ + return FunctionCall('sizeof', [String(arg) if isinstance(arg, str) else arg]) + + +class CommaOperator(Basic): + """ Represents the comma operator in C """ + def __new__(cls, *args): + return Basic.__new__(cls, *[sympify(arg) for arg in args]) + + +class Label(Node): + """ Label for use with e.g. goto statement. + + Examples + ======== + + >>> from sympy import ccode, Symbol + >>> from sympy.codegen.cnodes import Label, PreIncrement + >>> print(ccode(Label('foo'))) + foo: + >>> print(ccode(Label('bar', [PreIncrement(Symbol('a'))]))) + bar: + ++(a); + + """ + __slots__ = _fields = ('name', 'body') + defaults = {'body': none} + _construct_name = String + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + +class goto(Token): + """ Represents goto in C """ + __slots__ = _fields = ('label',) + _construct_label = Label + + +class PreDecrement(Basic): + """ Represents the pre-decrement operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PreDecrement + >>> from sympy import ccode + >>> ccode(PreDecrement(x)) + '--(x)' + + """ + nargs = 1 + + +class PostDecrement(Basic): + """ Represents the post-decrement operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PostDecrement + >>> from sympy import ccode + >>> ccode(PostDecrement(x)) + '(x)--' + + """ + nargs = 1 + + +class PreIncrement(Basic): + """ Represents the pre-increment operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PreIncrement + >>> from sympy import ccode + >>> ccode(PreIncrement(x)) + '++(x)' + + """ + nargs = 1 + + +class PostIncrement(Basic): + """ Represents the post-increment operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PostIncrement + >>> from sympy import ccode + >>> ccode(PostIncrement(x)) + '(x)++' + + """ + nargs = 1 + + +class struct(Node): + """ Represents a struct in C """ + __slots__ = _fields = ('name', 'declarations') + defaults = {'name': none} + _construct_name = String + + @classmethod + def _construct_declarations(cls, args): + return Tuple(*[Declaration(arg) for arg in args]) + + +class union(struct): + """ Represents a union in C """ + __slots__ = () diff --git a/lib/python3.11/site-packages/sympy/codegen/cutils.py b/lib/python3.11/site-packages/sympy/codegen/cutils.py new file mode 100644 index 0000000000000000000000000000000000000000..2182ac1f3455da490a0bb57f8d6731fe8a29a232 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/cutils.py @@ -0,0 +1,8 @@ +from sympy.printing.c import C99CodePrinter + +def render_as_source_file(content, Printer=C99CodePrinter, settings=None): + """ Renders a C source file (with required #include statements) """ + printer = Printer(settings or {}) + code_str = printer.doprint(content) + includes = '\n'.join(['#include <%s>' % h for h in printer.headers]) + return includes + '\n\n' + code_str diff --git a/lib/python3.11/site-packages/sympy/codegen/cxxnodes.py b/lib/python3.11/site-packages/sympy/codegen/cxxnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..7f7aafd01ab2de99ad0f668275889863fc73f5aa --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/cxxnodes.py @@ -0,0 +1,14 @@ +""" +AST nodes specific to C++. +""" + +from sympy.codegen.ast import Attribute, String, Token, Type, none + +class using(Token): + """ Represents a 'using' statement in C++ """ + __slots__ = _fields = ('type', 'alias') + defaults = {'alias': none} + _construct_type = Type + _construct_alias = String + +constexpr = Attribute('constexpr') diff --git a/lib/python3.11/site-packages/sympy/codegen/fnodes.py b/lib/python3.11/site-packages/sympy/codegen/fnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..6d38a60e5f5c1e53d70641ec395053bfe9dd95ea --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/fnodes.py @@ -0,0 +1,657 @@ +""" +AST nodes specific to Fortran. + +The functions defined in this module allows the user to express functions such as ``dsign`` +as a SymPy function for symbolic manipulation. +""" + +from sympy.codegen.ast import ( + Attribute, CodeBlock, FunctionCall, Node, none, String, + Token, _mk_Tuple, Variable +) +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.expr import Expr +from sympy.core.function import Function +from sympy.core.numbers import Float, Integer +from sympy.core.symbol import Str +from sympy.core.sympify import sympify +from sympy.logic import true, false +from sympy.utilities.iterables import iterable + + + +pure = Attribute('pure') +elemental = Attribute('elemental') # (all elemental procedures are also pure) + +intent_in = Attribute('intent_in') +intent_out = Attribute('intent_out') +intent_inout = Attribute('intent_inout') + +allocatable = Attribute('allocatable') + +class Program(Token): + """ Represents a 'program' block in Fortran. + + Examples + ======== + + >>> from sympy.codegen.ast import Print + >>> from sympy.codegen.fnodes import Program + >>> prog = Program('myprogram', [Print([42])]) + >>> from sympy import fcode + >>> print(fcode(prog, source_format='free')) + program myprogram + print *, 42 + end program + + """ + __slots__ = _fields = ('name', 'body') + _construct_name = String + _construct_body = staticmethod(lambda body: CodeBlock(*body)) + + +class use_rename(Token): + """ Represents a renaming in a use statement in Fortran. + + Examples + ======== + + >>> from sympy.codegen.fnodes import use_rename, use + >>> from sympy import fcode + >>> ren = use_rename("thingy", "convolution2d") + >>> print(fcode(ren, source_format='free')) + thingy => convolution2d + >>> full = use('signallib', only=['snr', ren]) + >>> print(fcode(full, source_format='free')) + use signallib, only: snr, thingy => convolution2d + + """ + __slots__ = _fields = ('local', 'original') + _construct_local = String + _construct_original = String + +def _name(arg): + if hasattr(arg, 'name'): + return arg.name + else: + return String(arg) + +class use(Token): + """ Represents a use statement in Fortran. + + Examples + ======== + + >>> from sympy.codegen.fnodes import use + >>> from sympy import fcode + >>> fcode(use('signallib'), source_format='free') + 'use signallib' + >>> fcode(use('signallib', [('metric', 'snr')]), source_format='free') + 'use signallib, metric => snr' + >>> fcode(use('signallib', only=['snr', 'convolution2d']), source_format='free') + 'use signallib, only: snr, convolution2d' + + """ + __slots__ = _fields = ('namespace', 'rename', 'only') + defaults = {'rename': none, 'only': none} + _construct_namespace = staticmethod(_name) + _construct_rename = staticmethod(lambda args: Tuple(*[arg if isinstance(arg, use_rename) else use_rename(*arg) for arg in args])) + _construct_only = staticmethod(lambda args: Tuple(*[arg if isinstance(arg, use_rename) else _name(arg) for arg in args])) + + +class Module(Token): + """ Represents a module in Fortran. + + Examples + ======== + + >>> from sympy.codegen.fnodes import Module + >>> from sympy import fcode + >>> print(fcode(Module('signallib', ['implicit none'], []), source_format='free')) + module signallib + implicit none + + contains + + + end module + + """ + __slots__ = _fields = ('name', 'declarations', 'definitions') + defaults = {'declarations': Tuple()} + _construct_name = String + + @classmethod + def _construct_declarations(cls, args): + args = [Str(arg) if isinstance(arg, str) else arg for arg in args] + return CodeBlock(*args) + + _construct_definitions = staticmethod(lambda arg: CodeBlock(*arg)) + + +class Subroutine(Node): + """ Represents a subroutine in Fortran. + + Examples + ======== + + >>> from sympy import fcode, symbols + >>> from sympy.codegen.ast import Print + >>> from sympy.codegen.fnodes import Subroutine + >>> x, y = symbols('x y', real=True) + >>> sub = Subroutine('mysub', [x, y], [Print([x**2 + y**2, x*y])]) + >>> print(fcode(sub, source_format='free', standard=2003)) + subroutine mysub(x, y) + real*8 :: x + real*8 :: y + print *, x**2 + y**2, x*y + end subroutine + + """ + __slots__ = ('name', 'parameters', 'body') + _fields = __slots__ + Node._fields + _construct_name = String + _construct_parameters = staticmethod(lambda params: Tuple(*map(Variable.deduced, params))) + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + +class SubroutineCall(Token): + """ Represents a call to a subroutine in Fortran. + + Examples + ======== + + >>> from sympy.codegen.fnodes import SubroutineCall + >>> from sympy import fcode + >>> fcode(SubroutineCall('mysub', 'x y'.split())) + ' call mysub(x, y)' + + """ + __slots__ = _fields = ('name', 'subroutine_args') + _construct_name = staticmethod(_name) + _construct_subroutine_args = staticmethod(_mk_Tuple) + + +class Do(Token): + """ Represents a Do loop in in Fortran. + + Examples + ======== + + >>> from sympy import fcode, symbols + >>> from sympy.codegen.ast import aug_assign, Print + >>> from sympy.codegen.fnodes import Do + >>> i, n = symbols('i n', integer=True) + >>> r = symbols('r', real=True) + >>> body = [aug_assign(r, '+', 1/i), Print([i, r])] + >>> do1 = Do(body, i, 1, n) + >>> print(fcode(do1, source_format='free')) + do i = 1, n + r = r + 1d0/i + print *, i, r + end do + >>> do2 = Do(body, i, 1, n, 2) + >>> print(fcode(do2, source_format='free')) + do i = 1, n, 2 + r = r + 1d0/i + print *, i, r + end do + + """ + + __slots__ = _fields = ('body', 'counter', 'first', 'last', 'step', 'concurrent') + defaults = {'step': Integer(1), 'concurrent': false} + _construct_body = staticmethod(lambda body: CodeBlock(*body)) + _construct_counter = staticmethod(sympify) + _construct_first = staticmethod(sympify) + _construct_last = staticmethod(sympify) + _construct_step = staticmethod(sympify) + _construct_concurrent = staticmethod(lambda arg: true if arg else false) + + +class ArrayConstructor(Token): + """ Represents an array constructor. + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.fnodes import ArrayConstructor + >>> ac = ArrayConstructor([1, 2, 3]) + >>> fcode(ac, standard=95, source_format='free') + '(/1, 2, 3/)' + >>> fcode(ac, standard=2003, source_format='free') + '[1, 2, 3]' + + """ + __slots__ = _fields = ('elements',) + _construct_elements = staticmethod(_mk_Tuple) + + +class ImpliedDoLoop(Token): + """ Represents an implied do loop in Fortran. + + Examples + ======== + + >>> from sympy import Symbol, fcode + >>> from sympy.codegen.fnodes import ImpliedDoLoop, ArrayConstructor + >>> i = Symbol('i', integer=True) + >>> idl = ImpliedDoLoop(i**3, i, -3, 3, 2) # -27, -1, 1, 27 + >>> ac = ArrayConstructor([-28, idl, 28]) # -28, -27, -1, 1, 27, 28 + >>> fcode(ac, standard=2003, source_format='free') + '[-28, (i**3, i = -3, 3, 2), 28]' + + """ + __slots__ = _fields = ('expr', 'counter', 'first', 'last', 'step') + defaults = {'step': Integer(1)} + _construct_expr = staticmethod(sympify) + _construct_counter = staticmethod(sympify) + _construct_first = staticmethod(sympify) + _construct_last = staticmethod(sympify) + _construct_step = staticmethod(sympify) + + +class Extent(Basic): + """ Represents a dimension extent. + + Examples + ======== + + >>> from sympy.codegen.fnodes import Extent + >>> e = Extent(-3, 3) # -3, -2, -1, 0, 1, 2, 3 + >>> from sympy import fcode + >>> fcode(e, source_format='free') + '-3:3' + >>> from sympy.codegen.ast import Variable, real + >>> from sympy.codegen.fnodes import dimension, intent_out + >>> dim = dimension(e, e) + >>> arr = Variable('x', real, attrs=[dim, intent_out]) + >>> fcode(arr.as_Declaration(), source_format='free', standard=2003) + 'real*8, dimension(-3:3, -3:3), intent(out) :: x' + + """ + def __new__(cls, *args): + if len(args) == 2: + low, high = args + return Basic.__new__(cls, sympify(low), sympify(high)) + elif len(args) == 0 or (len(args) == 1 and args[0] in (':', None)): + return Basic.__new__(cls) # assumed shape + else: + raise ValueError("Expected 0 or 2 args (or one argument == None or ':')") + + def _sympystr(self, printer): + if len(self.args) == 0: + return ':' + return ":".join(str(arg) for arg in self.args) + +assumed_extent = Extent() # or Extent(':'), Extent(None) + + +def dimension(*args): + """ Creates a 'dimension' Attribute with (up to 7) extents. + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.fnodes import dimension, intent_in + >>> dim = dimension('2', ':') # 2 rows, runtime determined number of columns + >>> from sympy.codegen.ast import Variable, integer + >>> arr = Variable('a', integer, attrs=[dim, intent_in]) + >>> fcode(arr.as_Declaration(), source_format='free', standard=2003) + 'integer*4, dimension(2, :), intent(in) :: a' + + """ + if len(args) > 7: + raise ValueError("Fortran only supports up to 7 dimensional arrays") + parameters = [] + for arg in args: + if isinstance(arg, Extent): + parameters.append(arg) + elif isinstance(arg, str): + if arg == ':': + parameters.append(Extent()) + else: + parameters.append(String(arg)) + elif iterable(arg): + parameters.append(Extent(*arg)) + else: + parameters.append(sympify(arg)) + if len(args) == 0: + raise ValueError("Need at least one dimension") + return Attribute('dimension', parameters) + + +assumed_size = dimension('*') + +def array(symbol, dim, intent=None, *, attrs=(), value=None, type=None): + """ Convenience function for creating a Variable instance for a Fortran array. + + Parameters + ========== + + symbol : symbol + dim : Attribute or iterable + If dim is an ``Attribute`` it need to have the name 'dimension'. If it is + not an ``Attribute``, then it is passed to :func:`dimension` as ``*dim`` + intent : str + One of: 'in', 'out', 'inout' or None + \\*\\*kwargs: + Keyword arguments for ``Variable`` ('type' & 'value') + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.ast import integer, real + >>> from sympy.codegen.fnodes import array + >>> arr = array('a', '*', 'in', type=integer) + >>> print(fcode(arr.as_Declaration(), source_format='free', standard=2003)) + integer*4, dimension(*), intent(in) :: a + >>> x = array('x', [3, ':', ':'], intent='out', type=real) + >>> print(fcode(x.as_Declaration(value=1), source_format='free', standard=2003)) + real*8, dimension(3, :, :), intent(out) :: x = 1 + + """ + if isinstance(dim, Attribute): + if str(dim.name) != 'dimension': + raise ValueError("Got an unexpected Attribute argument as dim: %s" % str(dim)) + else: + dim = dimension(*dim) + + attrs = list(attrs) + [dim] + if intent is not None: + if intent not in (intent_in, intent_out, intent_inout): + intent = {'in': intent_in, 'out': intent_out, 'inout': intent_inout}[intent] + attrs.append(intent) + if type is None: + return Variable.deduced(symbol, value=value, attrs=attrs) + else: + return Variable(symbol, type, value=value, attrs=attrs) + +def _printable(arg): + return String(arg) if isinstance(arg, str) else sympify(arg) + + +def allocated(array): + """ Creates an AST node for a function call to Fortran's "allocated(...)" + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.fnodes import allocated + >>> alloc = allocated('x') + >>> fcode(alloc, source_format='free') + 'allocated(x)' + + """ + return FunctionCall('allocated', [_printable(array)]) + + +def lbound(array, dim=None, kind=None): + """ Creates an AST node for a function call to Fortran's "lbound(...)" + + Parameters + ========== + + array : Symbol or String + dim : expr + kind : expr + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.fnodes import lbound + >>> lb = lbound('arr', dim=2) + >>> fcode(lb, source_format='free') + 'lbound(arr, 2)' + + """ + return FunctionCall( + 'lbound', + [_printable(array)] + + ([_printable(dim)] if dim else []) + + ([_printable(kind)] if kind else []) + ) + + +def ubound(array, dim=None, kind=None): + return FunctionCall( + 'ubound', + [_printable(array)] + + ([_printable(dim)] if dim else []) + + ([_printable(kind)] if kind else []) + ) + + +def shape(source, kind=None): + """ Creates an AST node for a function call to Fortran's "shape(...)" + + Parameters + ========== + + source : Symbol or String + kind : expr + + Examples + ======== + + >>> from sympy import fcode + >>> from sympy.codegen.fnodes import shape + >>> shp = shape('x') + >>> fcode(shp, source_format='free') + 'shape(x)' + + """ + return FunctionCall( + 'shape', + [_printable(source)] + + ([_printable(kind)] if kind else []) + ) + + +def size(array, dim=None, kind=None): + """ Creates an AST node for a function call to Fortran's "size(...)" + + Examples + ======== + + >>> from sympy import fcode, Symbol + >>> from sympy.codegen.ast import FunctionDefinition, real, Return + >>> from sympy.codegen.fnodes import array, sum_, size + >>> a = Symbol('a', real=True) + >>> body = [Return((sum_(a**2)/size(a))**.5)] + >>> arr = array(a, dim=[':'], intent='in') + >>> fd = FunctionDefinition(real, 'rms', [arr], body) + >>> print(fcode(fd, source_format='free', standard=2003)) + real*8 function rms(a) + real*8, dimension(:), intent(in) :: a + rms = sqrt(sum(a**2)*1d0/size(a)) + end function + + """ + return FunctionCall( + 'size', + [_printable(array)] + + ([_printable(dim)] if dim else []) + + ([_printable(kind)] if kind else []) + ) + + +def reshape(source, shape, pad=None, order=None): + """ Creates an AST node for a function call to Fortran's "reshape(...)" + + Parameters + ========== + + source : Symbol or String + shape : ArrayExpr + + """ + return FunctionCall( + 'reshape', + [_printable(source), _printable(shape)] + + ([_printable(pad)] if pad else []) + + ([_printable(order)] if pad else []) + ) + + +def bind_C(name=None): + """ Creates an Attribute ``bind_C`` with a name. + + Parameters + ========== + + name : str + + Examples + ======== + + >>> from sympy import fcode, Symbol + >>> from sympy.codegen.ast import FunctionDefinition, real, Return + >>> from sympy.codegen.fnodes import array, sum_, bind_C + >>> a = Symbol('a', real=True) + >>> s = Symbol('s', integer=True) + >>> arr = array(a, dim=[s], intent='in') + >>> body = [Return((sum_(a**2)/s)**.5)] + >>> fd = FunctionDefinition(real, 'rms', [arr, s], body, attrs=[bind_C('rms')]) + >>> print(fcode(fd, source_format='free', standard=2003)) + real*8 function rms(a, s) bind(C, name="rms") + real*8, dimension(s), intent(in) :: a + integer*4 :: s + rms = sqrt(sum(a**2)/s) + end function + + """ + return Attribute('bind_C', [String(name)] if name else []) + +class GoTo(Token): + """ Represents a goto statement in Fortran + + Examples + ======== + + >>> from sympy.codegen.fnodes import GoTo + >>> go = GoTo([10, 20, 30], 'i') + >>> from sympy import fcode + >>> fcode(go, source_format='free') + 'go to (10, 20, 30), i' + + """ + __slots__ = _fields = ('labels', 'expr') + defaults = {'expr': none} + _construct_labels = staticmethod(_mk_Tuple) + _construct_expr = staticmethod(sympify) + + +class FortranReturn(Token): + """ AST node explicitly mapped to a fortran "return". + + Explanation + =========== + + Because a return statement in fortran is different from C, and + in order to aid reuse of our codegen ASTs the ordinary + ``.codegen.ast.Return`` is interpreted as assignment to + the result variable of the function. If one for some reason needs + to generate a fortran RETURN statement, this node should be used. + + Examples + ======== + + >>> from sympy.codegen.fnodes import FortranReturn + >>> from sympy import fcode + >>> fcode(FortranReturn('x')) + ' return x' + + """ + __slots__ = _fields = ('return_value',) + defaults = {'return_value': none} + _construct_return_value = staticmethod(sympify) + + +class FFunction(Function): + _required_standard = 77 + + def _fcode(self, printer): + name = self.__class__.__name__ + if printer._settings['standard'] < self._required_standard: + raise NotImplementedError("%s requires Fortran %d or newer" % + (name, self._required_standard)) + return '{}({})'.format(name, ', '.join(map(printer._print, self.args))) + + +class F95Function(FFunction): + _required_standard = 95 + + +class isign(FFunction): + """ Fortran sign intrinsic for integer arguments. """ + nargs = 2 + + +class dsign(FFunction): + """ Fortran sign intrinsic for double precision arguments. """ + nargs = 2 + + +class cmplx(FFunction): + """ Fortran complex conversion function. """ + nargs = 2 # may be extended to (2, 3) at a later point + + +class kind(FFunction): + """ Fortran kind function. """ + nargs = 1 + + +class merge(F95Function): + """ Fortran merge function """ + nargs = 3 + + +class _literal(Float): + _token = None # type: str + _decimals = None # type: int + + def _fcode(self, printer, *args, **kwargs): + mantissa, sgnd_ex = ('%.{}e'.format(self._decimals) % self).split('e') + mantissa = mantissa.strip('0').rstrip('.') + ex_sgn, ex_num = sgnd_ex[0], sgnd_ex[1:].lstrip('0') + ex_sgn = '' if ex_sgn == '+' else ex_sgn + return (mantissa or '0') + self._token + ex_sgn + (ex_num or '0') + + +class literal_sp(_literal): + """ Fortran single precision real literal """ + _token = 'e' + _decimals = 9 + + +class literal_dp(_literal): + """ Fortran double precision real literal """ + _token = 'd' + _decimals = 17 + + +class sum_(Token, Expr): + __slots__ = _fields = ('array', 'dim', 'mask') + defaults = {'dim': none, 'mask': none} + _construct_array = staticmethod(sympify) + _construct_dim = staticmethod(sympify) + + +class product_(Token, Expr): + __slots__ = _fields = ('array', 'dim', 'mask') + defaults = {'dim': none, 'mask': none} + _construct_array = staticmethod(sympify) + _construct_dim = staticmethod(sympify) diff --git a/lib/python3.11/site-packages/sympy/codegen/futils.py b/lib/python3.11/site-packages/sympy/codegen/futils.py new file mode 100644 index 0000000000000000000000000000000000000000..4a1f5751fbd4d6b44d99c69a74ad89a8496f8648 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/futils.py @@ -0,0 +1,40 @@ +from itertools import chain +from sympy.codegen.fnodes import Module +from sympy.core.symbol import Dummy +from sympy.printing.fortran import FCodePrinter + +""" This module collects utilities for rendering Fortran code. """ + + +def render_as_module(definitions, name, declarations=(), printer_settings=None): + """ Creates a ``Module`` instance and renders it as a string. + + This generates Fortran source code for a module with the correct ``use`` statements. + + Parameters + ========== + + definitions : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. + name : str + Passed to :class:`sympy.codegen.fnodes.Module`. + declarations : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. It will be extended with + use statements, 'implicit none' and public list generated from ``definitions``. + printer_settings : dict + Passed to ``FCodePrinter`` (default: ``{'standard': 2003, 'source_format': 'free'}``). + + """ + printer_settings = printer_settings or {'standard': 2003, 'source_format': 'free'} + printer = FCodePrinter(printer_settings) + dummy = Dummy() + if isinstance(definitions, Module): + raise ValueError("This function expects to construct a module on its own.") + mod = Module(name, chain(declarations, [dummy]), definitions) + fstr = printer.doprint(mod) + module_use_str = ' %s\n' % ' \n'.join(['use %s, only: %s' % (k, ', '.join(v)) for + k, v in printer.module_uses.items()]) + module_use_str += ' implicit none\n' + module_use_str += ' private\n' + module_use_str += ' public %s\n' % ', '.join([str(node.name) for node in definitions if getattr(node, 'name', None)]) + return fstr.replace(printer.doprint(dummy), module_use_str) diff --git a/lib/python3.11/site-packages/sympy/codegen/matrix_nodes.py b/lib/python3.11/site-packages/sympy/codegen/matrix_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..cf0a13a81c963e2c9e2b885dabd0ff3e2d2b3eb9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/matrix_nodes.py @@ -0,0 +1,71 @@ +""" +Additional AST nodes for operations on matrices. The nodes in this module +are meant to represent optimization of matrix expressions within codegen's +target languages that cannot be represented by SymPy expressions. + +As an example, we can use :meth:`sympy.codegen.rewriting.optimize` and the +``matin_opt`` optimization provided in :mod:`sympy.codegen.rewriting` to +transform matrix multiplication under certain assumptions: + + >>> from sympy import symbols, MatrixSymbol + >>> n = symbols('n', integer=True) + >>> A = MatrixSymbol('A', n, n) + >>> x = MatrixSymbol('x', n, 1) + >>> expr = A**(-1) * x + >>> from sympy import assuming, Q + >>> from sympy.codegen.rewriting import matinv_opt, optimize + >>> with assuming(Q.fullrank(A)): + ... optimize(expr, [matinv_opt]) + MatrixSolve(A, vector=x) +""" + +from .ast import Token +from sympy.matrices import MatrixExpr +from sympy.core.sympify import sympify + + +class MatrixSolve(Token, MatrixExpr): + """Represents an operation to solve a linear matrix equation. + + Parameters + ========== + + matrix : MatrixSymbol + + Matrix representing the coefficients of variables in the linear + equation. This matrix must be square and full-rank (i.e. all columns must + be linearly independent) for the solving operation to be valid. + + vector : MatrixSymbol + + One-column matrix representing the solutions to the equations + represented in ``matrix``. + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol + >>> from sympy.codegen.matrix_nodes import MatrixSolve + >>> n = symbols('n', integer=True) + >>> A = MatrixSymbol('A', n, n) + >>> x = MatrixSymbol('x', n, 1) + >>> from sympy.printing.numpy import NumPyPrinter + >>> NumPyPrinter().doprint(MatrixSolve(A, x)) + 'numpy.linalg.solve(A, x)' + >>> from sympy import octave_code + >>> octave_code(MatrixSolve(A, x)) + 'A \\\\ x' + + """ + __slots__ = _fields = ('matrix', 'vector') + + _construct_matrix = staticmethod(sympify) + _construct_vector = staticmethod(sympify) + + @property + def shape(self): + return self.vector.shape + + def _eval_derivative(self, x): + A, b = self.matrix, self.vector + return MatrixSolve(A, b.diff(x) - A.diff(x) * MatrixSolve(A, b)) diff --git a/lib/python3.11/site-packages/sympy/codegen/numpy_nodes.py b/lib/python3.11/site-packages/sympy/codegen/numpy_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..2132718e63855b5756ee183b4fd19d42a7b764f5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/numpy_nodes.py @@ -0,0 +1,110 @@ +from sympy.core.function import Add, ArgumentIndexError, Function +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.sorting import default_sort_key +from sympy.functions.elementary.exponential import exp, log + + +def _logaddexp(x1, x2, *, evaluate=True): + return log(Add(exp(x1, evaluate=evaluate), exp(x2, evaluate=evaluate), evaluate=evaluate)) + + +_two = S.One*2 +_ln2 = log(_two) + + +def _lb(x, *, evaluate=True): + return log(x, evaluate=evaluate)/_ln2 + + +def _exp2(x, *, evaluate=True): + return Pow(_two, x, evaluate=evaluate) + + +def _logaddexp2(x1, x2, *, evaluate=True): + return _lb(Add(_exp2(x1, evaluate=evaluate), + _exp2(x2, evaluate=evaluate), evaluate=evaluate)) + + +class logaddexp(Function): + """ Logarithm of the sum of exponentiations of the inputs. + + Helper class for use with e.g. numpy.logaddexp + + See Also + ======== + + https://numpy.org/doc/stable/reference/generated/numpy.logaddexp.html + """ + nargs = 2 + + def __new__(cls, *args): + return Function.__new__(cls, *sorted(args, key=default_sort_key)) + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + wrt, other = self.args + elif argindex == 2: + other, wrt = self.args + else: + raise ArgumentIndexError(self, argindex) + return S.One/(S.One + exp(other-wrt)) + + def _eval_rewrite_as_log(self, x1, x2, **kwargs): + return _logaddexp(x1, x2) + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(log).evalf(*args, **kwargs) + + def _eval_simplify(self, *args, **kwargs): + a, b = (x.simplify(**kwargs) for x in self.args) + candidate = _logaddexp(a, b) + if candidate != _logaddexp(a, b, evaluate=False): + return candidate + else: + return logaddexp(a, b) + + +class logaddexp2(Function): + """ Logarithm of the sum of exponentiations of the inputs in base-2. + + Helper class for use with e.g. numpy.logaddexp2 + + See Also + ======== + + https://numpy.org/doc/stable/reference/generated/numpy.logaddexp2.html + """ + nargs = 2 + + def __new__(cls, *args): + return Function.__new__(cls, *sorted(args, key=default_sort_key)) + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + wrt, other = self.args + elif argindex == 2: + other, wrt = self.args + else: + raise ArgumentIndexError(self, argindex) + return S.One/(S.One + _exp2(other-wrt)) + + def _eval_rewrite_as_log(self, x1, x2, **kwargs): + return _logaddexp2(x1, x2) + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(log).evalf(*args, **kwargs) + + def _eval_simplify(self, *args, **kwargs): + a, b = (x.simplify(**kwargs).factor() for x in self.args) + candidate = _logaddexp2(a, b) + if candidate != _logaddexp2(a, b, evaluate=False): + return candidate + else: + return logaddexp2(a, b) diff --git a/lib/python3.11/site-packages/sympy/codegen/pynodes.py b/lib/python3.11/site-packages/sympy/codegen/pynodes.py new file mode 100644 index 0000000000000000000000000000000000000000..f0a08b4a79d32f63d345947d6be310b44504dbf5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/pynodes.py @@ -0,0 +1,11 @@ +from .abstract_nodes import List as AbstractList +from .ast import Token + + +class List(AbstractList): + pass + + +class NumExprEvaluate(Token): + """represents a call to :class:`numexpr`s :func:`evaluate`""" + __slots__ = _fields = ('expr',) diff --git a/lib/python3.11/site-packages/sympy/codegen/pyutils.py b/lib/python3.11/site-packages/sympy/codegen/pyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..e14eabe92ce50105a4055b71a49767aae04610b9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/pyutils.py @@ -0,0 +1,24 @@ +from sympy.printing.pycode import PythonCodePrinter + +""" This module collects utilities for rendering Python code. """ + + +def render_as_module(content, standard='python3'): + """Renders Python code as a module (with the required imports). + + Parameters + ========== + + standard : + See the parameter ``standard`` in + :meth:`sympy.printing.pycode.pycode` + """ + + printer = PythonCodePrinter({'standard':standard}) + pystr = printer.doprint(content) + if printer._settings['fully_qualified_modules']: + module_imports_str = '\n'.join('import %s' % k for k in printer.module_imports) + else: + module_imports_str = '\n'.join(['from %s import %s' % (k, ', '.join(v)) for + k, v in printer.module_imports.items()]) + return module_imports_str + '\n\n' + pystr diff --git a/lib/python3.11/site-packages/sympy/codegen/rewriting.py b/lib/python3.11/site-packages/sympy/codegen/rewriting.py new file mode 100644 index 0000000000000000000000000000000000000000..274b7770b46ded6711468ab2a01db3a53d6fde87 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/rewriting.py @@ -0,0 +1,357 @@ +""" +Classes and functions useful for rewriting expressions for optimized code +generation. Some languages (or standards thereof), e.g. C99, offer specialized +math functions for better performance and/or precision. + +Using the ``optimize`` function in this module, together with a collection of +rules (represented as instances of ``Optimization``), one can rewrite the +expressions for this purpose:: + + >>> from sympy import Symbol, exp, log + >>> from sympy.codegen.rewriting import optimize, optims_c99 + >>> x = Symbol('x') + >>> optimize(3*exp(2*x) - 3, optims_c99) + 3*expm1(2*x) + >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99) + expm1(2*x) - exp(-33) + >>> optimize(log(3*x + 3), optims_c99) + log1p(x) + log(3) + >>> optimize(log(2*x + 3), optims_c99) + log(2*x + 3) + +The ``optims_c99`` imported above is tuple containing the following instances +(which may be imported from ``sympy.codegen.rewriting``): + +- ``expm1_opt`` +- ``log1p_opt`` +- ``exp2_opt`` +- ``log2_opt`` +- ``log2const_opt`` + + +""" +from sympy.core.function import expand_log +from sympy.core.singleton import S +from sympy.core.symbol import Wild +from sympy.functions.elementary.complexes import sign +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import (Max, Min) +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.assumptions import Q, ask +from sympy.codegen.cfunctions import log1p, log2, exp2, expm1 +from sympy.codegen.matrix_nodes import MatrixSolve +from sympy.core.expr import UnevaluatedExpr +from sympy.core.power import Pow +from sympy.codegen.numpy_nodes import logaddexp, logaddexp2 +from sympy.codegen.scipy_nodes import cosm1, powm1 +from sympy.core.mul import Mul +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.utilities.iterables import sift + + +class Optimization: + """ Abstract base class for rewriting optimization. + + Subclasses should implement ``__call__`` taking an expression + as argument. + + Parameters + ========== + cost_function : callable returning number + priority : number + + """ + def __init__(self, cost_function=None, priority=1): + self.cost_function = cost_function + self.priority=priority + + def cheapest(self, *args): + return min(args, key=self.cost_function) + + +class ReplaceOptim(Optimization): + """ Rewriting optimization calling replace on expressions. + + Explanation + =========== + + The instance can be used as a function on expressions for which + it will apply the ``replace`` method (see + :meth:`sympy.core.basic.Basic.replace`). + + Parameters + ========== + + query : + First argument passed to replace. + value : + Second argument passed to replace. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.codegen.rewriting import ReplaceOptim + >>> from sympy.codegen.cfunctions import exp2 + >>> x = Symbol('x') + >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2, + ... lambda p: exp2(p.exp)) + >>> exp2_opt(2**x) + exp2(x) + + """ + + def __init__(self, query, value, **kwargs): + super().__init__(**kwargs) + self.query = query + self.value = value + + def __call__(self, expr): + return expr.replace(self.query, self.value) + + +def optimize(expr, optimizations): + """ Apply optimizations to an expression. + + Parameters + ========== + + expr : expression + optimizations : iterable of ``Optimization`` instances + The optimizations will be sorted with respect to ``priority`` (highest first). + + Examples + ======== + + >>> from sympy import log, Symbol + >>> from sympy.codegen.rewriting import optims_c99, optimize + >>> x = Symbol('x') + >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99) + log1p(x**2) + log2(x + 3) + + """ + + for optim in sorted(optimizations, key=lambda opt: opt.priority, reverse=True): + new_expr = optim(expr) + if optim.cost_function is None: + expr = new_expr + else: + expr = optim.cheapest(expr, new_expr) + return expr + + +exp2_opt = ReplaceOptim( + lambda p: p.is_Pow and p.base == 2, + lambda p: exp2(p.exp) +) + + +_d = Wild('d', properties=[lambda x: x.is_Dummy]) +_u = Wild('u', properties=[lambda x: not x.is_number and not x.is_Add]) +_v = Wild('v') +_w = Wild('w') +_n = Wild('n', properties=[lambda x: x.is_number]) + +sinc_opt1 = ReplaceOptim( + sin(_w)/_w, sinc(_w) +) +sinc_opt2 = ReplaceOptim( + sin(_n*_w)/_w, _n*sinc(_n*_w) +) +sinc_opts = (sinc_opt1, sinc_opt2) + +log2_opt = ReplaceOptim(_v*log(_w)/log(2), _v*log2(_w), cost_function=lambda expr: expr.count( + lambda e: ( # division & eval of transcendentals are expensive floating point operations... + e.is_Pow and e.exp.is_negative # division + or (isinstance(e, (log, log2)) and not e.args[0].is_number)) # transcendental + ) +) + +log2const_opt = ReplaceOptim(log(2)*log2(_w), log(_w)) + +logsumexp_2terms_opt = ReplaceOptim( + lambda l: (isinstance(l, log) + and l.args[0].is_Add + and len(l.args[0].args) == 2 + and all(isinstance(t, exp) for t in l.args[0].args)), + lambda l: ( + Max(*[e.args[0] for e in l.args[0].args]) + + log1p(exp(Min(*[e.args[0] for e in l.args[0].args]))) + ) +) + + +class FuncMinusOneOptim(ReplaceOptim): + """Specialization of ReplaceOptim for functions evaluating "f(x) - 1". + + Explanation + =========== + + Numerical functions which go toward one as x go toward zero is often best + implemented by a dedicated function in order to avoid catastrophic + cancellation. One such example is ``expm1(x)`` in the C standard library + which evaluates ``exp(x) - 1``. Such functions preserves many more + significant digits when its argument is much smaller than one, compared + to subtracting one afterwards. + + Parameters + ========== + + func : + The function which is subtracted by one. + func_m_1 : + The specialized function evaluating ``func(x) - 1``. + opportunistic : bool + When ``True``, apply the transformation as long as the magnitude of the + remaining number terms decreases. When ``False``, only apply the + transformation if it completely eliminates the number term. + + Examples + ======== + + >>> from sympy import symbols, exp + >>> from sympy.codegen.rewriting import FuncMinusOneOptim + >>> from sympy.codegen.cfunctions import expm1 + >>> x, y = symbols('x y') + >>> expm1_opt = FuncMinusOneOptim(exp, expm1) + >>> expm1_opt(exp(x) + 2*exp(5*y) - 3) + expm1(x) + 2*expm1(5*y) + + + """ + + def __init__(self, func, func_m_1, opportunistic=True): + weight = 10 # <-- this is an arbitrary number (heuristic) + super().__init__(lambda e: e.is_Add, self.replace_in_Add, + cost_function=lambda expr: expr.count_ops() - weight*expr.count(func_m_1)) + self.func = func + self.func_m_1 = func_m_1 + self.opportunistic = opportunistic + + def _group_Add_terms(self, add): + numbers, non_num = sift(add.args, lambda arg: arg.is_number, binary=True) + numsum = sum(numbers) + terms_with_func, other = sift(non_num, lambda arg: arg.has(self.func), binary=True) + return numsum, terms_with_func, other + + def replace_in_Add(self, e): + """ passed as second argument to Basic.replace(...) """ + numsum, terms_with_func, other_non_num_terms = self._group_Add_terms(e) + if numsum == 0: + return e + substituted, untouched = [], [] + for with_func in terms_with_func: + if with_func.is_Mul: + func, coeff = sift(with_func.args, lambda arg: arg.func == self.func, binary=True) + if len(func) == 1 and len(coeff) == 1: + func, coeff = func[0], coeff[0] + else: + coeff = None + elif with_func.func == self.func: + func, coeff = with_func, S.One + else: + coeff = None + + if coeff is not None and coeff.is_number and sign(coeff) == -sign(numsum): + if self.opportunistic: + do_substitute = abs(coeff+numsum) < abs(numsum) + else: + do_substitute = coeff+numsum == 0 + + if do_substitute: # advantageous substitution + numsum += coeff + substituted.append(coeff*self.func_m_1(*func.args)) + continue + untouched.append(with_func) + + return e.func(numsum, *substituted, *untouched, *other_non_num_terms) + + def __call__(self, expr): + alt1 = super().__call__(expr) + alt2 = super().__call__(expr.factor()) + return self.cheapest(alt1, alt2) + + +expm1_opt = FuncMinusOneOptim(exp, expm1) +cosm1_opt = FuncMinusOneOptim(cos, cosm1) +powm1_opt = FuncMinusOneOptim(Pow, powm1) + +log1p_opt = ReplaceOptim( + lambda e: isinstance(e, log), + lambda l: expand_log(l.replace( + log, lambda arg: log(arg.factor()) + )).replace(log(_u+1), log1p(_u)) +) + +def create_expand_pow_optimization(limit, *, base_req=lambda b: b.is_symbol): + """ Creates an instance of :class:`ReplaceOptim` for expanding ``Pow``. + + Explanation + =========== + + The requirements for expansions are that the base needs to be a symbol + and the exponent needs to be an Integer (and be less than or equal to + ``limit``). + + Parameters + ========== + + limit : int + The highest power which is expanded into multiplication. + base_req : function returning bool + Requirement on base for expansion to happen, default is to return + the ``is_symbol`` attribute of the base. + + Examples + ======== + + >>> from sympy import Symbol, sin + >>> from sympy.codegen.rewriting import create_expand_pow_optimization + >>> x = Symbol('x') + >>> expand_opt = create_expand_pow_optimization(3) + >>> expand_opt(x**5 + x**3) + x**5 + x*x*x + >>> expand_opt(x**5 + x**3 + sin(x)**3) + x**5 + sin(x)**3 + x*x*x + >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function) + >>> opt2((x+1)**2 + sin(x)**2) + sin(x)**2 + (x + 1)*(x + 1) + + """ + return ReplaceOptim( + lambda e: e.is_Pow and base_req(e.base) and e.exp.is_Integer and abs(e.exp) <= limit, + lambda p: ( + UnevaluatedExpr(Mul(*([p.base]*+p.exp), evaluate=False)) if p.exp > 0 else + 1/UnevaluatedExpr(Mul(*([p.base]*-p.exp), evaluate=False)) + )) + +# Optimization procedures for turning A**(-1) * x into MatrixSolve(A, x) +def _matinv_predicate(expr): + # TODO: We should be able to support more than 2 elements + if expr.is_MatMul and len(expr.args) == 2: + left, right = expr.args + if left.is_Inverse and right.shape[1] == 1: + inv_arg = left.arg + if isinstance(inv_arg, MatrixSymbol): + return bool(ask(Q.fullrank(left.arg))) + + return False + +def _matinv_transform(expr): + left, right = expr.args + inv_arg = left.arg + return MatrixSolve(inv_arg, right) + + +matinv_opt = ReplaceOptim(_matinv_predicate, _matinv_transform) + + +logaddexp_opt = ReplaceOptim(log(exp(_v)+exp(_w)), logaddexp(_v, _w)) +logaddexp2_opt = ReplaceOptim(log(Pow(2, _v)+Pow(2, _w)), logaddexp2(_v, _w)*log(2)) + +# Collections of optimizations: +optims_c99 = (expm1_opt, log1p_opt, exp2_opt, log2_opt, log2const_opt) + +optims_numpy = optims_c99 + (logaddexp_opt, logaddexp2_opt,) + sinc_opts + +optims_scipy = (cosm1_opt, powm1_opt) diff --git a/lib/python3.11/site-packages/sympy/codegen/scipy_nodes.py b/lib/python3.11/site-packages/sympy/codegen/scipy_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..059a853fc8cac6e0b9a1a3c7395dd3a15384dcba --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/scipy_nodes.py @@ -0,0 +1,79 @@ +from sympy.core.function import Add, ArgumentIndexError, Function +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.trigonometric import cos, sin + + +def _cosm1(x, *, evaluate=True): + return Add(cos(x, evaluate=evaluate), -S.One, evaluate=evaluate) + + +class cosm1(Function): + """ Minus one plus cosine of x, i.e. cos(x) - 1. For use when x is close to zero. + + Helper class for use with e.g. scipy.special.cosm1 + See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.cosm1.html + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return -sin(*self.args) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_cos(self, x, **kwargs): + return _cosm1(x) + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(cos).evalf(*args, **kwargs) + + def _eval_simplify(self, **kwargs): + x, = self.args + candidate = _cosm1(x.simplify(**kwargs)) + if candidate != _cosm1(x, evaluate=False): + return candidate + else: + return cosm1(x) + + +def _powm1(x, y, *, evaluate=True): + return Add(Pow(x, y, evaluate=evaluate), -S.One, evaluate=evaluate) + + +class powm1(Function): + """ Minus one plus x to the power of y, i.e. x**y - 1. For use when x is close to one or y is close to zero. + + Helper class for use with e.g. scipy.special.powm1 + See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.powm1.html + """ + nargs = 2 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return Pow(self.args[0], self.args[1])*self.args[1]/self.args[0] + elif argindex == 2: + return log(self.args[0])*Pow(*self.args) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Pow(self, x, y, **kwargs): + return _powm1(x, y) + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(Pow).evalf(*args, **kwargs) + + def _eval_simplify(self, **kwargs): + x, y = self.args + candidate = _powm1(x.simplify(**kwargs), y.simplify(**kwargs)) + if candidate != _powm1(x, y, evaluate=False): + return candidate + else: + return powm1(x, y) diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/__init__.py 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can call e.g. "replace" on List. + m = l.replace(lambda arg: arg.is_Pow and arg.exp>2, lambda p: p.base-p.exp) + assert m == [x**2, y-3, z-4] + hash(m) diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/test_algorithms.py b/lib/python3.11/site-packages/sympy/codegen/tests/test_algorithms.py new file mode 100644 index 0000000000000000000000000000000000000000..09446258d461d71e299408555399c7f09fbd8419 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/tests/test_algorithms.py @@ -0,0 +1,179 @@ +import tempfile +from sympy import log, Min, Max, sqrt +from sympy.core.numbers import Float +from sympy.core.symbol import Symbol, symbols +from sympy.functions.elementary.trigonometric import cos +from sympy.codegen.ast import Assignment, Raise, RuntimeError_, QuotedString +from sympy.codegen.algorithms import newtons_method, newtons_method_function +from sympy.codegen.cfunctions import expm1 +from sympy.codegen.fnodes import bind_C +from sympy.codegen.futils import render_as_module as f_module +from sympy.codegen.pyutils import render_as_module as py_module +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.utilities._compilation import compile_link_import_strings, has_c, has_fortran +from sympy.utilities._compilation.util import may_xfail +from sympy.testing.pytest import skip, raises + +cython = import_module('cython') +wurlitzer = import_module('wurlitzer') + +def test_newtons_method(): + x, dx, atol = symbols('x dx atol') + expr = cos(x) - x**3 + algo = newtons_method(expr, x, atol, dx) + assert algo.has(Assignment(dx, -expr/expr.diff(x))) + + +@may_xfail +def test_newtons_method_function__ccode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x) + + if not cython: + skip("cython not installed.") + if not has_c(): + skip("No C compiler found.") + + compile_kw = {"std": 'c99'} + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton.c', ('#include \n' + '#include \n') + ccode(func)), + ('_newton.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double)\n" + "def py_newton(x):\n" + " return newton(x)\n")) + ], build_dir=folder, compile_kwargs=compile_kw) + assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12 + + +@may_xfail +def test_newtons_method_function__fcode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x, attrs=[bind_C(name='newton')]) + + if not cython: + skip("cython not installed.") + if not has_fortran(): + skip("No Fortran compiler found.") + + f_mod = f_module([func], 'mod_newton') + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton.f90', f_mod), + ('_newton.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double*)\n" + "def py_newton(double x):\n" + " return newton(&x)\n")) + ], build_dir=folder) + assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12 + + +def test_newtons_method_function__pycode(): + x = Symbol('x', real=True) + expr = cos(x) - x**3 + func = newtons_method_function(expr, x) + py_mod = py_module(func) + namespace = {} + exec(py_mod, namespace, namespace) + res = eval('newton(0.5)', namespace) + assert abs(res - 0.865474033102) < 1e-12 + + +@may_xfail +def test_newtons_method_function__ccode_parameters(): + args = x, A, k, p = symbols('x A k p') + expr = A*cos(k*x) - p*x**3 + raises(ValueError, lambda: newtons_method_function(expr, x)) + use_wurlitzer = wurlitzer + + func = newtons_method_function(expr, x, args, debug=use_wurlitzer) + + if not has_c(): + skip("No C compiler found.") + if not cython: + skip("cython not installed.") + + compile_kw = {"std": 'c99'} + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings([ + ('newton_par.c', ('#include \n' + '#include \n') + ccode(func)), + ('_newton_par.pyx', ("#cython: language_level={}\n".format("3") + + "cdef extern double newton(double, double, double, double)\n" + "def py_newton(x, A=1, k=1, p=1):\n" + " return newton(x, A, k, p)\n")) + ], compile_kwargs=compile_kw, build_dir=folder) + + if use_wurlitzer: + with wurlitzer.pipes() as (out, err): + result = mod.py_newton(0.5) + else: + result = mod.py_newton(0.5) + + assert abs(result - 0.865474033102) < 1e-12 + + if not use_wurlitzer: + skip("C-level output only tested when package 'wurlitzer' is available.") + + out, err = out.read(), err.read() + assert err == '' + assert out == """\ +x= 0.5 +x= 1.1121 d_x= 0.61214 +x= 0.90967 d_x= -0.20247 +x= 0.86726 d_x= -0.042409 +x= 0.86548 d_x= -0.0017867 +x= 0.86547 d_x= -3.1022e-06 +x= 0.86547 d_x= -9.3421e-12 +x= 0.86547 d_x= 3.6902e-17 +""" # try to run tests with LC_ALL=C if this assertion fails + + +def test_newtons_method_function__rtol_cse_nan(): + a, b, c, N_geo, N_tot = symbols('a b c N_geo N_tot', real=True, nonnegative=True) + i = Symbol('i', integer=True, nonnegative=True) + N_ari = N_tot - N_geo - 1 + delta_ari = (c-b)/N_ari + ln_delta_geo = log(b) + log(-expm1((log(a)-log(b))/N_geo)) + eqb_log = ln_delta_geo - log(delta_ari) + + def _clamp(low, expr, high): + return Min(Max(low, expr), high) + + meth_kw = { + 'clamped_newton': {'delta_fn': lambda e, x: _clamp( + (sqrt(a*x)-x)*0.99, + -e/e.diff(x), + (sqrt(c*x)-x)*0.99 + )}, + 'halley': {'delta_fn': lambda e, x: (-2*(e*e.diff(x))/(2*e.diff(x)**2 - e*e.diff(x, 2)))}, + 'halley_alt': {'delta_fn': lambda e, x: (-e/e.diff(x)/(1-e/e.diff(x)*e.diff(x,2)/2/e.diff(x)))}, + } + args = eqb_log, b + for use_cse in [False, True]: + kwargs = { + 'params': (b, a, c, N_geo, N_tot), 'itermax': 60, 'debug': True, 'cse': use_cse, + 'counter': i, 'atol': 1e-100, 'rtol': 2e-16, 'bounds': (a,c), + 'handle_nan': Raise(RuntimeError_(QuotedString("encountered NaN."))) + } + func = {k: newtons_method_function(*args, func_name=f"{k}_b", **dict(kwargs, **kw)) for k, kw in meth_kw.items()} + py_mod = {k: py_module(v) for k, v in func.items()} + namespace = {} + root_find_b = {} + for k, v in py_mod.items(): + ns = namespace[k] = {} + exec(v, ns, ns) + root_find_b[k] = ns[f'{k}_b'] + ref = Float('13.2261515064168768938151923226496') + reftol = {'clamped_newton': 2e-16, 'halley': 2e-16, 'halley_alt': 3e-16} + guess = 4.0 + for meth, func in root_find_b.items(): + result = func(guess, 1e-2, 1e2, 50, 100) + req = ref*reftol[meth] + if use_cse: + req *= 2 + assert abs(result - ref) < req diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/test_applications.py b/lib/python3.11/site-packages/sympy/codegen/tests/test_applications.py new file mode 100644 index 0000000000000000000000000000000000000000..26d5d0f699b947db13b658d793f808d632f67a1a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/tests/test_applications.py @@ -0,0 +1,57 @@ +# This file contains tests that exercise multiple AST nodes + +import tempfile + +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.utilities._compilation import compile_link_import_strings, has_c +from sympy.utilities._compilation.util import may_xfail +from sympy.testing.pytest import skip +from sympy.codegen.ast import ( + FunctionDefinition, FunctionPrototype, Variable, Pointer, real, Assignment, + integer, CodeBlock, While +) +from sympy.codegen.cnodes import void, PreIncrement +from sympy.codegen.cutils import render_as_source_file + +cython = import_module('cython') +np = import_module('numpy') + +def _mk_func1(): + declars = n, inp, out = Variable('n', integer), Pointer('inp', real), Pointer('out', real) + i = Variable('i', integer) + whl = While(i2, lambda p: p.base-p.exp) + assert m == [x**2, y-3, z-4] diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/test_pyutils.py b/lib/python3.11/site-packages/sympy/codegen/tests/test_pyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..0a2f0ff358f333635c8d44195a5c39d63ac8f16f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/tests/test_pyutils.py @@ -0,0 +1,7 @@ +from sympy.codegen.ast import Print +from sympy.codegen.pyutils import render_as_module + +def test_standard(): + ast = Print('x y'.split(), r"coordinate: %12.5g %12.5g\n") + assert render_as_module(ast, standard='python3') == \ + '\n\nprint("coordinate: %12.5g %12.5g\\n" % (x, y), end="")' diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/test_rewriting.py b/lib/python3.11/site-packages/sympy/codegen/tests/test_rewriting.py new file mode 100644 index 0000000000000000000000000000000000000000..51e0c9ecc940f60186cc04d4bf15650281d31cd8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/tests/test_rewriting.py @@ -0,0 +1,479 @@ +import tempfile +from sympy.core.numbers import pi, Rational +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.assumptions import assuming, Q +from sympy.external import import_module +from sympy.printing.codeprinter import ccode +from sympy.codegen.matrix_nodes import MatrixSolve +from sympy.codegen.cfunctions import log2, exp2, expm1, log1p +from sympy.codegen.numpy_nodes import logaddexp, logaddexp2 +from sympy.codegen.scipy_nodes import cosm1, powm1 +from sympy.codegen.rewriting import ( + optimize, cosm1_opt, log2_opt, exp2_opt, expm1_opt, log1p_opt, powm1_opt, optims_c99, + create_expand_pow_optimization, matinv_opt, logaddexp_opt, logaddexp2_opt, + optims_numpy, optims_scipy, sinc_opts, FuncMinusOneOptim +) +from sympy.testing.pytest import XFAIL, skip +from sympy.utilities import lambdify +from sympy.utilities._compilation import compile_link_import_strings, has_c +from sympy.utilities._compilation.util import may_xfail + +cython = import_module('cython') +numpy = import_module('numpy') +scipy = import_module('scipy') + + +def test_log2_opt(): + x = Symbol('x') + expr1 = 7*log(3*x + 5)/(log(2)) + opt1 = optimize(expr1, [log2_opt]) + assert opt1 == 7*log2(3*x + 5) + assert opt1.rewrite(log) == expr1 + + expr2 = 3*log(5*x + 7)/(13*log(2)) + opt2 = optimize(expr2, [log2_opt]) + assert opt2 == 3*log2(5*x + 7)/13 + assert opt2.rewrite(log) == expr2 + + expr3 = log(x)/log(2) + opt3 = optimize(expr3, [log2_opt]) + assert opt3 == log2(x) + assert opt3.rewrite(log) == expr3 + + expr4 = log(x)/log(2) + log(x+1) + opt4 = optimize(expr4, [log2_opt]) + assert opt4 == log2(x) + log(2)*log2(x+1) + assert opt4.rewrite(log) == expr4 + + expr5 = log(17) + opt5 = optimize(expr5, [log2_opt]) + assert opt5 == expr5 + + expr6 = log(x + 3)/log(2) + opt6 = optimize(expr6, [log2_opt]) + assert str(opt6) == 'log2(x + 3)' + assert opt6.rewrite(log) == expr6 + + +def test_exp2_opt(): + x = Symbol('x') + expr1 = 1 + 2**x + opt1 = optimize(expr1, [exp2_opt]) + assert opt1 == 1 + exp2(x) + assert opt1.rewrite(Pow) == expr1 + + expr2 = 1 + 3**x + assert expr2 == optimize(expr2, [exp2_opt]) + + +def test_expm1_opt(): + x = Symbol('x') + + expr1 = exp(x) - 1 + opt1 = optimize(expr1, [expm1_opt]) + assert expm1(x) - opt1 == 0 + assert opt1.rewrite(exp) == expr1 + + expr2 = 3*exp(x) - 3 + opt2 = optimize(expr2, [expm1_opt]) + assert 3*expm1(x) == opt2 + assert opt2.rewrite(exp) == expr2 + + expr3 = 3*exp(x) - 5 + opt3 = optimize(expr3, [expm1_opt]) + assert 3*expm1(x) - 2 == opt3 + assert opt3.rewrite(exp) == expr3 + expm1_opt_non_opportunistic = FuncMinusOneOptim(exp, expm1, opportunistic=False) + assert expr3 == optimize(expr3, [expm1_opt_non_opportunistic]) + assert opt1 == optimize(expr1, [expm1_opt_non_opportunistic]) + assert opt2 == optimize(expr2, [expm1_opt_non_opportunistic]) + + expr4 = 3*exp(x) + log(x) - 3 + opt4 = optimize(expr4, [expm1_opt]) + assert 3*expm1(x) + log(x) == opt4 + assert opt4.rewrite(exp) == expr4 + + expr5 = 3*exp(2*x) - 3 + opt5 = optimize(expr5, [expm1_opt]) + assert 3*expm1(2*x) == opt5 + assert opt5.rewrite(exp) == expr5 + + expr6 = (2*exp(x) + 1)/(exp(x) + 1) + 1 + opt6 = optimize(expr6, [expm1_opt]) + assert opt6.count_ops() <= expr6.count_ops() + + def ev(e): + return e.subs(x, 3).evalf() + assert abs(ev(expr6) - ev(opt6)) < 1e-15 + + y = Symbol('y') + expr7 = (2*exp(x) - 1)/(1 - exp(y)) - 1/(1-exp(y)) + opt7 = optimize(expr7, [expm1_opt]) + assert -2*expm1(x)/expm1(y) == opt7 + assert (opt7.rewrite(exp) - expr7).factor() == 0 + + expr8 = (1+exp(x))**2 - 4 + opt8 = optimize(expr8, [expm1_opt]) + tgt8a = (exp(x) + 3)*expm1(x) + tgt8b = 2*expm1(x) + expm1(2*x) + # Both tgt8a & tgt8b seem to give full precision (~16 digits for double) + # for x=1e-7 (compare with expr8 which only achieves ~8 significant digits). + # If we can show that either tgt8a or tgt8b is preferable, we can + # change this test to ensure the preferable version is returned. + assert (tgt8a - tgt8b).rewrite(exp).factor() == 0 + assert opt8 in (tgt8a, tgt8b) + assert (opt8.rewrite(exp) - expr8).factor() == 0 + + expr9 = sin(expr8) + opt9 = optimize(expr9, [expm1_opt]) + tgt9a = sin(tgt8a) + tgt9b = sin(tgt8b) + assert opt9 in (tgt9a, tgt9b) + assert (opt9.rewrite(exp) - expr9.rewrite(exp)).factor().is_zero + + +def test_expm1_two_exp_terms(): + x, y = map(Symbol, 'x y'.split()) + expr1 = exp(x) + exp(y) - 2 + opt1 = optimize(expr1, [expm1_opt]) + assert opt1 == expm1(x) + expm1(y) + + +def test_cosm1_opt(): + x = Symbol('x') + + expr1 = cos(x) - 1 + opt1 = optimize(expr1, [cosm1_opt]) + assert cosm1(x) - opt1 == 0 + assert opt1.rewrite(cos) == expr1 + + expr2 = 3*cos(x) - 3 + opt2 = optimize(expr2, [cosm1_opt]) + assert 3*cosm1(x) == opt2 + assert opt2.rewrite(cos) == expr2 + + expr3 = 3*cos(x) - 5 + opt3 = optimize(expr3, [cosm1_opt]) + assert 3*cosm1(x) - 2 == opt3 + assert opt3.rewrite(cos) == expr3 + cosm1_opt_non_opportunistic = FuncMinusOneOptim(cos, cosm1, opportunistic=False) + assert expr3 == optimize(expr3, [cosm1_opt_non_opportunistic]) + assert opt1 == optimize(expr1, [cosm1_opt_non_opportunistic]) + assert opt2 == optimize(expr2, [cosm1_opt_non_opportunistic]) + + expr4 = 3*cos(x) + log(x) - 3 + opt4 = optimize(expr4, [cosm1_opt]) + assert 3*cosm1(x) + log(x) == opt4 + assert opt4.rewrite(cos) == expr4 + + expr5 = 3*cos(2*x) - 3 + opt5 = optimize(expr5, [cosm1_opt]) + assert 3*cosm1(2*x) == opt5 + assert opt5.rewrite(cos) == expr5 + + expr6 = 2 - 2*cos(x) + opt6 = optimize(expr6, [cosm1_opt]) + assert -2*cosm1(x) == opt6 + assert opt6.rewrite(cos) == expr6 + + +def test_cosm1_two_cos_terms(): + x, y = map(Symbol, 'x y'.split()) + expr1 = cos(x) + cos(y) - 2 + opt1 = optimize(expr1, [cosm1_opt]) + assert opt1 == cosm1(x) + cosm1(y) + + +def test_expm1_cosm1_mixed(): + x = Symbol('x') + expr1 = exp(x) + cos(x) - 2 + opt1 = optimize(expr1, [expm1_opt, cosm1_opt]) + assert opt1 == cosm1(x) + expm1(x) + + +def _check_num_lambdify(expr, opt, val_subs, approx_ref, lambdify_kw=None, poorness=1e10): + """ poorness=1e10 signifies that `expr` loses precision of at least ten decimal digits. """ + num_ref = expr.subs(val_subs).evalf() + eps = numpy.finfo(numpy.float64).eps + assert abs(num_ref - approx_ref) < approx_ref*eps + f1 = lambdify(list(val_subs.keys()), opt, **(lambdify_kw or {})) + args_float = tuple(map(float, val_subs.values())) + num_err1 = abs(f1(*args_float) - approx_ref) + assert num_err1 < abs(num_ref*eps) + f2 = lambdify(list(val_subs.keys()), expr, **(lambdify_kw or {})) + num_err2 = abs(f2(*args_float) - approx_ref) + assert num_err2 > abs(num_ref*eps*poorness) # this only ensures that the *test* works as intended + + +def test_cosm1_apart(): + x = Symbol('x') + + expr1 = 1/cos(x) - 1 + opt1 = optimize(expr1, [cosm1_opt]) + assert opt1 == -cosm1(x)/cos(x) + if scipy: + _check_num_lambdify(expr1, opt1, {x: S(10)**-30}, 5e-61, lambdify_kw={"modules": 'scipy'}) + + expr2 = 2/cos(x) - 2 + opt2 = optimize(expr2, optims_scipy) + assert opt2 == -2*cosm1(x)/cos(x) + if scipy: + _check_num_lambdify(expr2, opt2, {x: S(10)**-30}, 1e-60, lambdify_kw={"modules": 'scipy'}) + + expr3 = pi/cos(3*x) - pi + opt3 = optimize(expr3, [cosm1_opt]) + assert opt3 == -pi*cosm1(3*x)/cos(3*x) + if scipy: + _check_num_lambdify(expr3, opt3, {x: S(10)**-30/3}, float(5e-61*pi), lambdify_kw={"modules": 'scipy'}) + + +def test_powm1(): + args = x, y = map(Symbol, "xy") + + expr1 = x**y - 1 + opt1 = optimize(expr1, [powm1_opt]) + assert opt1 == powm1(x, y) + for arg in args: + assert expr1.diff(arg) == opt1.diff(arg) + if scipy and tuple(map(int, scipy.version.version.split('.')[:3])) >= (1, 10, 0): + subs1_a = {x: Rational(*(1.0+1e-13).as_integer_ratio()), y: pi} + ref1_f64_a = 3.139081648208105e-13 + _check_num_lambdify(expr1, opt1, subs1_a, ref1_f64_a, lambdify_kw={"modules": 'scipy'}, poorness=10**11) + + subs1_b = {x: pi, y: Rational(*(1e-10).as_integer_ratio())} + ref1_f64_b = 1.1447298859149205e-10 + _check_num_lambdify(expr1, opt1, subs1_b, ref1_f64_b, lambdify_kw={"modules": 'scipy'}, poorness=10**9) + + +def test_log1p_opt(): + x = Symbol('x') + expr1 = log(x + 1) + opt1 = optimize(expr1, [log1p_opt]) + assert log1p(x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + expr2 = log(3*x + 3) + opt2 = optimize(expr2, [log1p_opt]) + assert log1p(x) + log(3) == opt2 + assert (opt2.rewrite(log) - expr2).simplify() == 0 + + expr3 = log(2*x + 1) + opt3 = optimize(expr3, [log1p_opt]) + assert log1p(2*x) - opt3 == 0 + assert opt3.rewrite(log) == expr3 + + expr4 = log(x+3) + opt4 = optimize(expr4, [log1p_opt]) + assert str(opt4) == 'log(x + 3)' + + +def test_optims_c99(): + x = Symbol('x') + + expr1 = 2**x + log(x)/log(2) + log(x + 1) + exp(x) - 1 + opt1 = optimize(expr1, optims_c99).simplify() + assert opt1 == exp2(x) + log2(x) + log1p(x) + expm1(x) + assert opt1.rewrite(exp).rewrite(log).rewrite(Pow) == expr1 + + expr2 = log(x)/log(2) + log(x + 1) + opt2 = optimize(expr2, optims_c99) + assert opt2 == log2(x) + log1p(x) + assert opt2.rewrite(log) == expr2 + + expr3 = log(x)/log(2) + log(17*x + 17) + opt3 = optimize(expr3, optims_c99) + delta3 = opt3 - (log2(x) + log(17) + log1p(x)) + assert delta3 == 0 + assert (opt3.rewrite(log) - expr3).simplify() == 0 + + expr4 = 2**x + 3*log(5*x + 7)/(13*log(2)) + 11*exp(x) - 11 + log(17*x + 17) + opt4 = optimize(expr4, optims_c99).simplify() + delta4 = opt4 - (exp2(x) + 3*log2(5*x + 7)/13 + 11*expm1(x) + log(17) + log1p(x)) + assert delta4 == 0 + assert (opt4.rewrite(exp).rewrite(log).rewrite(Pow) - expr4).simplify() == 0 + + expr5 = 3*exp(2*x) - 3 + opt5 = optimize(expr5, optims_c99) + delta5 = opt5 - 3*expm1(2*x) + assert delta5 == 0 + assert opt5.rewrite(exp) == expr5 + + expr6 = exp(2*x) - 3 + opt6 = optimize(expr6, optims_c99) + assert opt6 in (expm1(2*x) - 2, expr6) # expm1(2*x) - 2 is not better or worse + + expr7 = log(3*x + 3) + opt7 = optimize(expr7, optims_c99) + delta7 = opt7 - (log(3) + log1p(x)) + assert delta7 == 0 + assert (opt7.rewrite(log) - expr7).simplify() == 0 + + expr8 = log(2*x + 3) + opt8 = optimize(expr8, optims_c99) + assert opt8 == expr8 + + +def test_create_expand_pow_optimization(): + cc = lambda x: ccode( + optimize(x, [create_expand_pow_optimization(4)])) + x = Symbol('x') + assert cc(x**4) == 'x*x*x*x' + assert cc(x**4 + x**2) == 'x*x + x*x*x*x' + assert cc(x**5 + x**4) == 'pow(x, 5) + x*x*x*x' + assert cc(sin(x)**4) == 'pow(sin(x), 4)' + # gh issue 15335 + assert cc(x**(-4)) == '1.0/(x*x*x*x)' + assert cc(x**(-5)) == 'pow(x, -5)' + assert cc(-x**4) == '-(x*x*x*x)' + assert cc(x**4 - x**2) == '-(x*x) + x*x*x*x' + i = Symbol('i', integer=True) + assert cc(x**i - x**2) == 'pow(x, i) - (x*x)' + y = Symbol('y', real=True) + assert cc(Abs(exp(y**4))) == "exp(y*y*y*y)" + + # gh issue 20753 + cc2 = lambda x: ccode(optimize(x, [create_expand_pow_optimization( + 4, base_req=lambda b: b.is_Function)])) + assert cc2(x**3 + sin(x)**3) == "pow(x, 3) + sin(x)*sin(x)*sin(x)" + + +def test_matsolve(): + n = Symbol('n', integer=True) + A = MatrixSymbol('A', n, n) + x = MatrixSymbol('x', n, 1) + + with assuming(Q.fullrank(A)): + assert optimize(A**(-1) * x, [matinv_opt]) == MatrixSolve(A, x) + assert optimize(A**(-1) * x + x, [matinv_opt]) == MatrixSolve(A, x) + x + + +def test_logaddexp_opt(): + x, y = map(Symbol, 'x y'.split()) + expr1 = log(exp(x) + exp(y)) + opt1 = optimize(expr1, [logaddexp_opt]) + assert logaddexp(x, y) - opt1 == 0 + assert logaddexp(y, x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + +def test_logaddexp2_opt(): + x, y = map(Symbol, 'x y'.split()) + expr1 = log(2**x + 2**y)/log(2) + opt1 = optimize(expr1, [logaddexp2_opt]) + assert logaddexp2(x, y) - opt1 == 0 + assert logaddexp2(y, x) - opt1 == 0 + assert opt1.rewrite(log) == expr1 + + +def test_sinc_opts(): + def check(d): + for k, v in d.items(): + assert optimize(k, sinc_opts) == v + + x = Symbol('x') + check({ + sin(x)/x : sinc(x), + sin(2*x)/(2*x) : sinc(2*x), + sin(3*x)/x : 3*sinc(3*x), + x*sin(x) : x*sin(x) + }) + + y = Symbol('y') + check({ + sin(x*y)/(x*y) : sinc(x*y), + y*sin(x/y)/x : sinc(x/y), + sin(sin(x))/sin(x) : sinc(sin(x)), + sin(3*sin(x))/sin(x) : 3*sinc(3*sin(x)), + sin(x)/y : sin(x)/y + }) + + +def test_optims_numpy(): + def check(d): + for k, v in d.items(): + assert optimize(k, optims_numpy) == v + + x = Symbol('x') + check({ + sin(2*x)/(2*x) + exp(2*x) - 1: sinc(2*x) + expm1(2*x), + log(x+3)/log(2) + log(x**2 + 1): log1p(x**2) + log2(x+3) + }) + + +@XFAIL # room for improvement, ideally this test case should pass. +def test_optims_numpy_TODO(): + def check(d): + for k, v in d.items(): + assert optimize(k, optims_numpy) == v + + x, y = map(Symbol, 'x y'.split()) + check({ + log(x*y)*sin(x*y)*log(x*y+1)/(log(2)*x*y): log2(x*y)*sinc(x*y)*log1p(x*y), + exp(x*sin(y)/y) - 1: expm1(x*sinc(y)) + }) + + +@may_xfail +def test_compiled_ccode_with_rewriting(): + if not cython: + skip("cython not installed.") + if not has_c(): + skip("No C compiler found.") + + x = Symbol('x') + about_two = 2**(58/S(117))*3**(97/S(117))*5**(4/S(39))*7**(92/S(117))/S(30)*pi + # about_two: 1.999999999999581826 + unchanged = 2*exp(x) - about_two + xval = S(10)**-11 + ref = unchanged.subs(x, xval).n(19) # 2.0418173913673213e-11 + + rewritten = optimize(2*exp(x) - about_two, [expm1_opt]) + + # Unfortunately, we need to call ``.n()`` on our expressions before we hand them + # to ``ccode``, and we need to request a large number of significant digits. + # In this test, results converged for double precision when the following number + # of significant digits were chosen: + NUMBER_OF_DIGITS = 25 # TODO: this should ideally be automatically handled. + + func_c = ''' +#include + +double func_unchanged(double x) { + return %(unchanged)s; +} +double func_rewritten(double x) { + return %(rewritten)s; +} +''' % {"unchanged": ccode(unchanged.n(NUMBER_OF_DIGITS)), + "rewritten": ccode(rewritten.n(NUMBER_OF_DIGITS))} + + func_pyx = ''' +#cython: language_level=3 +cdef extern double func_unchanged(double) +cdef extern double func_rewritten(double) +def py_unchanged(x): + return func_unchanged(x) +def py_rewritten(x): + return func_rewritten(x) +''' + with tempfile.TemporaryDirectory() as folder: + mod, info = compile_link_import_strings( + [('func.c', func_c), ('_func.pyx', func_pyx)], + build_dir=folder, compile_kwargs={"std": 'c99'} + ) + err_rewritten = abs(mod.py_rewritten(1e-11) - ref) + err_unchanged = abs(mod.py_unchanged(1e-11) - ref) + assert 1e-27 < err_rewritten < 1e-25 # highly accurate. + assert 1e-19 < err_unchanged < 1e-16 # quite poor. + + # Tolerances used above were determined as follows: + # >>> no_opt = unchanged.subs(x, xval.evalf()).evalf() + # >>> with_opt = rewritten.n(25).subs(x, 1e-11).evalf() + # >>> with_opt - ref, no_opt - ref + # (1.1536301877952077e-26, 1.6547074214222335e-18) diff --git a/lib/python3.11/site-packages/sympy/codegen/tests/test_scipy_nodes.py b/lib/python3.11/site-packages/sympy/codegen/tests/test_scipy_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..c0d1461037eec81ade0c99b18fbbf5a4517ce0b7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/codegen/tests/test_scipy_nodes.py @@ -0,0 +1,44 @@ +from itertools import product +from sympy.core.power import Pow +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.trigonometric import cos +from sympy.core.numbers import pi +from sympy.codegen.scipy_nodes import cosm1, powm1 + +x, y, z = symbols('x y z') + + +def test_cosm1(): + cm1_xy = cosm1(x*y) + ref_xy = cos(x*y) - 1 + for wrt, deriv_order in product([x, y, z], range(3)): + assert ( + cm1_xy.diff(wrt, deriv_order) - + ref_xy.diff(wrt, deriv_order) + ).rewrite(cos).simplify() == 0 + + expr_minus2 = cosm1(pi) + assert expr_minus2.rewrite(cos) == -2 + assert cosm1(3.14).simplify() == cosm1(3.14) # cannot simplify with 3.14 + assert cosm1(pi/2).simplify() == -1 + assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0 + + +def test_powm1(): + cases = { + powm1(x, y): x**y - 1, + powm1(x*y, z): (x*y)**z - 1, + powm1(x, y*z): x**(y*z)-1, + powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1 + } + for pm1_e, ref_e in cases.items(): + for wrt, deriv_order in product([x, y, z], range(3)): + der = pm1_e.diff(wrt, deriv_order) + ref = ref_e.diff(wrt, deriv_order) + delta = (der - ref).rewrite(Pow) + assert delta.simplify() == 0 + + eulers_constant_m1 = powm1(x, 1/log(x)) + assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1 + assert eulers_constant_m1.simplify() == exp(1) - 1 diff --git a/lib/python3.11/site-packages/sympy/combinatorics/__init__.py b/lib/python3.11/site-packages/sympy/combinatorics/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..220c27a42975555f8fe7770fcef0dd18475c89e1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/__init__.py @@ -0,0 +1,43 @@ +from sympy.combinatorics.permutations import Permutation, Cycle +from sympy.combinatorics.prufer import Prufer +from sympy.combinatorics.generators import cyclic, alternating, symmetric, dihedral +from sympy.combinatorics.subsets import Subset +from sympy.combinatorics.partitions import (Partition, IntegerPartition, + RGS_rank, RGS_unrank, RGS_enum) +from sympy.combinatorics.polyhedron import (Polyhedron, tetrahedron, cube, + octahedron, dodecahedron, icosahedron) +from sympy.combinatorics.perm_groups import PermutationGroup, Coset, SymmetricPermutationGroup +from sympy.combinatorics.group_constructs import DirectProduct +from sympy.combinatorics.graycode import GrayCode +from sympy.combinatorics.named_groups import (SymmetricGroup, DihedralGroup, + CyclicGroup, AlternatingGroup, AbelianGroup, RubikGroup) +from sympy.combinatorics.pc_groups import PolycyclicGroup, Collector +from sympy.combinatorics.free_groups import free_group + +__all__ = [ + 'Permutation', 'Cycle', + + 'Prufer', + + 'cyclic', 'alternating', 'symmetric', 'dihedral', + + 'Subset', + + 'Partition', 'IntegerPartition', 'RGS_rank', 'RGS_unrank', 'RGS_enum', + + 'Polyhedron', 'tetrahedron', 'cube', 'octahedron', 'dodecahedron', + 'icosahedron', + + 'PermutationGroup', 'Coset', 'SymmetricPermutationGroup', + + 'DirectProduct', + + 'GrayCode', + + 'SymmetricGroup', 'DihedralGroup', 'CyclicGroup', 'AlternatingGroup', + 'AbelianGroup', 'RubikGroup', + + 'PolycyclicGroup', 'Collector', + + 'free_group', +] diff --git a/lib/python3.11/site-packages/sympy/combinatorics/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/combinatorics/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..6a1b9240eddadae29e51d9b80bce2c2d0c0eab7a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/combinatorics/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/combinatorics/__pycache__/coset_table.cpython-311.pyc b/lib/python3.11/site-packages/sympy/combinatorics/__pycache__/coset_table.cpython-311.pyc new file mode 100644 index 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represented by an integer between i with 1 <= i <= n + # alpha in c + # x: Mathematically an element of "A" (set of generators and + # their inverses), represented using "FpGroupElement" + # fp_grp: Finitely Presented Group with < X|R > as presentation. + # H: subgroup of fp_grp. + # NOTE: We start with H as being only a list of words in generators + # of "fp_grp". Since `.subgroup` method has not been implemented. + + r""" + + Properties + ========== + + [1] `0 \in \Omega` and `\tau(1) = \epsilon` + [2] `\alpha^x = \beta \Leftrightarrow \beta^{x^{-1}} = \alpha` + [3] If `\alpha^x = \beta`, then `H \tau(\alpha)x = H \tau(\beta)` + [4] `\forall \alpha \in \Omega, 1^{\tau(\alpha)} = \alpha` + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + + .. [2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson + Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490. + "Implementation and Analysis of the Todd-Coxeter Algorithm" + + """ + # default limit for the number of cosets allowed in a + # coset enumeration. + coset_table_max_limit = 4096000 + # limit for the current instance + coset_table_limit = None + # maximum size of deduction stack above or equal to + # which it is emptied + max_stack_size = 100 + + def __init__(self, fp_grp, subgroup, max_cosets=None): + if not max_cosets: + max_cosets = CosetTable.coset_table_max_limit + self.fp_group = fp_grp + self.subgroup = subgroup + self.coset_table_limit = max_cosets + # "p" is setup independent of Omega and n + self.p = [0] + # a list of the form `[gen_1, gen_1^{-1}, ... , gen_k, gen_k^{-1}]` + self.A = list(chain.from_iterable((gen, gen**-1) \ + for gen in self.fp_group.generators)) + #P[alpha, x] Only defined when alpha^x is defined. + self.P = [[None]*len(self.A)] + # the mathematical coset table which is a list of lists + self.table = [[None]*len(self.A)] + self.A_dict = {x: self.A.index(x) for x in self.A} + self.A_dict_inv = {} + for x, index in self.A_dict.items(): + if index % 2 == 0: + self.A_dict_inv[x] = self.A_dict[x] + 1 + else: + self.A_dict_inv[x] = self.A_dict[x] - 1 + # used in the coset-table based method of coset enumeration. Each of + # the element is called a "deduction" which is the form (alpha, x) whenever + # a value is assigned to alpha^x during a definition or "deduction process" + self.deduction_stack = [] + # Attributes for modified methods. + H = self.subgroup + self._grp = free_group(', ' .join(["a_%d" % i for i in range(len(H))]))[0] + self.P = [[None]*len(self.A)] + self.p_p = {} + + @property + def omega(self): + """Set of live cosets. """ + return [coset for coset in range(len(self.p)) if self.p[coset] == coset] + + def copy(self): + """ + Return a shallow copy of Coset Table instance ``self``. + + """ + self_copy = self.__class__(self.fp_group, self.subgroup) + self_copy.table = [list(perm_rep) for perm_rep in self.table] + self_copy.p = list(self.p) + self_copy.deduction_stack = list(self.deduction_stack) + return self_copy + + def __str__(self): + return "Coset Table on %s with %s as subgroup generators" \ + % (self.fp_group, self.subgroup) + + __repr__ = __str__ + + @property + def n(self): + """The number `n` represents the length of the sublist containing the + live cosets. + + """ + if not self.table: + return 0 + return max(self.omega) + 1 + + # Pg. 152 [1] + def is_complete(self): + r""" + The coset table is called complete if it has no undefined entries + on the live cosets; that is, `\alpha^x` is defined for all + `\alpha \in \Omega` and `x \in A`. + + """ + return not any(None in self.table[coset] for coset in self.omega) + + # Pg. 153 [1] + def define(self, alpha, x, modified=False): + r""" + This routine is used in the relator-based strategy of Todd-Coxeter + algorithm if some `\alpha^x` is undefined. We check whether there is + space available for defining a new coset. If there is enough space + then we remedy this by adjoining a new coset `\beta` to `\Omega` + (i.e to set of live cosets) and put that equal to `\alpha^x`, then + make an assignment satisfying Property[1]. If there is not enough space + then we halt the Coset Table creation. The maximum amount of space that + can be used by Coset Table can be manipulated using the class variable + ``CosetTable.coset_table_max_limit``. + + See Also + ======== + + define_c + + """ + A = self.A + table = self.table + len_table = len(table) + if len_table >= self.coset_table_limit: + # abort the further generation of cosets + raise ValueError("the coset enumeration has defined more than " + "%s cosets. Try with a greater value max number of cosets " + % self.coset_table_limit) + table.append([None]*len(A)) + self.P.append([None]*len(self.A)) + # beta is the new coset generated + beta = len_table + self.p.append(beta) + table[alpha][self.A_dict[x]] = beta + table[beta][self.A_dict_inv[x]] = alpha + # P[alpha][x] = epsilon, P[beta][x**-1] = epsilon + if modified: + self.P[alpha][self.A_dict[x]] = self._grp.identity + self.P[beta][self.A_dict_inv[x]] = self._grp.identity + self.p_p[beta] = self._grp.identity + + def define_c(self, alpha, x): + r""" + A variation of ``define`` routine, described on Pg. 165 [1], used in + the coset table-based strategy of Todd-Coxeter algorithm. It differs + from ``define`` routine in that for each definition it also adds the + tuple `(\alpha, x)` to the deduction stack. + + See Also + ======== + + define + + """ + A = self.A + table = self.table + len_table = len(table) + if len_table >= self.coset_table_limit: + # abort the further generation of cosets + raise ValueError("the coset enumeration has defined more than " + "%s cosets. Try with a greater value max number of cosets " + % self.coset_table_limit) + table.append([None]*len(A)) + # beta is the new coset generated + beta = len_table + self.p.append(beta) + table[alpha][self.A_dict[x]] = beta + table[beta][self.A_dict_inv[x]] = alpha + # append to deduction stack + self.deduction_stack.append((alpha, x)) + + def scan_c(self, alpha, word): + """ + A variation of ``scan`` routine, described on pg. 165 of [1], which + puts at tuple, whenever a deduction occurs, to deduction stack. + + See Also + ======== + + scan, scan_check, scan_and_fill, scan_and_fill_c + + """ + # alpha is an integer representing a "coset" + # since scanning can be in two cases + # 1. for alpha=0 and w in Y (i.e generating set of H) + # 2. alpha in Omega (set of live cosets), w in R (relators) + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + f = alpha + i = 0 + r = len(word) + b = alpha + j = r - 1 + # list of union of generators and their inverses + while i <= j and table[f][A_dict[word[i]]] is not None: + f = table[f][A_dict[word[i]]] + i += 1 + if i > j: + if f != b: + self.coincidence_c(f, b) + return + while j >= i and table[b][A_dict_inv[word[j]]] is not None: + b = table[b][A_dict_inv[word[j]]] + j -= 1 + if j < i: + # we have an incorrect completed scan with coincidence f ~ b + # run the "coincidence" routine + self.coincidence_c(f, b) + elif j == i: + # deduction process + table[f][A_dict[word[i]]] = b + table[b][A_dict_inv[word[i]]] = f + self.deduction_stack.append((f, word[i])) + # otherwise scan is incomplete and yields no information + + # alpha, beta coincide, i.e. alpha, beta represent the pair of cosets where + # coincidence occurs + def coincidence_c(self, alpha, beta): + """ + A variation of ``coincidence`` routine used in the coset-table based + method of coset enumeration. The only difference being on addition of + a new coset in coset table(i.e new coset introduction), then it is + appended to ``deduction_stack``. + + See Also + ======== + + coincidence + + """ + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + # behaves as a queue + q = [] + self.merge(alpha, beta, q) + while len(q) > 0: + gamma = q.pop(0) + for x in A_dict: + delta = table[gamma][A_dict[x]] + if delta is not None: + table[delta][A_dict_inv[x]] = None + # only line of difference from ``coincidence`` routine + self.deduction_stack.append((delta, x**-1)) + mu = self.rep(gamma) + nu = self.rep(delta) + if table[mu][A_dict[x]] is not None: + self.merge(nu, table[mu][A_dict[x]], q) + elif table[nu][A_dict_inv[x]] is not None: + self.merge(mu, table[nu][A_dict_inv[x]], q) + else: + table[mu][A_dict[x]] = nu + table[nu][A_dict_inv[x]] = mu + + def scan(self, alpha, word, y=None, fill=False, modified=False): + r""" + ``scan`` performs a scanning process on the input ``word``. + It first locates the largest prefix ``s`` of ``word`` for which + `\alpha^s` is defined (i.e is not ``None``), ``s`` may be empty. Let + ``word=sv``, let ``t`` be the longest suffix of ``v`` for which + `\alpha^{t^{-1}}` is defined, and let ``v=ut``. Then three + possibilities are there: + + 1. If ``t=v``, then we say that the scan completes, and if, in addition + `\alpha^s = \alpha^{t^{-1}}`, then we say that the scan completes + correctly. + + 2. It can also happen that scan does not complete, but `|u|=1`; that + is, the word ``u`` consists of a single generator `x \in A`. In that + case, if `\alpha^s = \beta` and `\alpha^{t^{-1}} = \gamma`, then we can + set `\beta^x = \gamma` and `\gamma^{x^{-1}} = \beta`. These assignments + are known as deductions and enable the scan to complete correctly. + + 3. See ``coicidence`` routine for explanation of third condition. + + Notes + ===== + + The code for the procedure of scanning `\alpha \in \Omega` + under `w \in A*` is defined on pg. 155 [1] + + See Also + ======== + + scan_c, scan_check, scan_and_fill, scan_and_fill_c + + Scan and Fill + ============= + + Performed when the default argument fill=True. + + Modified Scan + ============= + + Performed when the default argument modified=True + + """ + # alpha is an integer representing a "coset" + # since scanning can be in two cases + # 1. for alpha=0 and w in Y (i.e generating set of H) + # 2. alpha in Omega (set of live cosets), w in R (relators) + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + f = alpha + i = 0 + r = len(word) + b = alpha + j = r - 1 + b_p = y + if modified: + f_p = self._grp.identity + flag = 0 + while fill or flag == 0: + flag = 1 + while i <= j and table[f][A_dict[word[i]]] is not None: + if modified: + f_p = f_p*self.P[f][A_dict[word[i]]] + f = table[f][A_dict[word[i]]] + i += 1 + if i > j: + if f != b: + if modified: + self.modified_coincidence(f, b, f_p**-1*y) + else: + self.coincidence(f, b) + return + while j >= i and table[b][A_dict_inv[word[j]]] is not None: + if modified: + b_p = b_p*self.P[b][self.A_dict_inv[word[j]]] + b = table[b][A_dict_inv[word[j]]] + j -= 1 + if j < i: + # we have an incorrect completed scan with coincidence f ~ b + # run the "coincidence" routine + if modified: + self.modified_coincidence(f, b, f_p**-1*b_p) + else: + self.coincidence(f, b) + elif j == i: + # deduction process + table[f][A_dict[word[i]]] = b + table[b][A_dict_inv[word[i]]] = f + if modified: + self.P[f][self.A_dict[word[i]]] = f_p**-1*b_p + self.P[b][self.A_dict_inv[word[i]]] = b_p**-1*f_p + return + elif fill: + self.define(f, word[i], modified=modified) + # otherwise scan is incomplete and yields no information + + # used in the low-index subgroups algorithm + def scan_check(self, alpha, word): + r""" + Another version of ``scan`` routine, described on, it checks whether + `\alpha` scans correctly under `word`, it is a straightforward + modification of ``scan``. ``scan_check`` returns ``False`` (rather than + calling ``coincidence``) if the scan completes incorrectly; otherwise + it returns ``True``. + + See Also + ======== + + scan, scan_c, scan_and_fill, scan_and_fill_c + + """ + # alpha is an integer representing a "coset" + # since scanning can be in two cases + # 1. for alpha=0 and w in Y (i.e generating set of H) + # 2. alpha in Omega (set of live cosets), w in R (relators) + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + f = alpha + i = 0 + r = len(word) + b = alpha + j = r - 1 + while i <= j and table[f][A_dict[word[i]]] is not None: + f = table[f][A_dict[word[i]]] + i += 1 + if i > j: + return f == b + while j >= i and table[b][A_dict_inv[word[j]]] is not None: + b = table[b][A_dict_inv[word[j]]] + j -= 1 + if j < i: + # we have an incorrect completed scan with coincidence f ~ b + # return False, instead of calling coincidence routine + return False + elif j == i: + # deduction process + table[f][A_dict[word[i]]] = b + table[b][A_dict_inv[word[i]]] = f + return True + + def merge(self, k, lamda, q, w=None, modified=False): + """ + Merge two classes with representatives ``k`` and ``lamda``, described + on Pg. 157 [1] (for pseudocode), start by putting ``p[k] = lamda``. + It is more efficient to choose the new representative from the larger + of the two classes being merged, i.e larger among ``k`` and ``lamda``. + procedure ``merge`` performs the merging operation, adds the deleted + class representative to the queue ``q``. + + Parameters + ========== + + 'k', 'lamda' being the two class representatives to be merged. + + Notes + ===== + + Pg. 86-87 [1] contains a description of this method. + + See Also + ======== + + coincidence, rep + + """ + p = self.p + rep = self.rep + phi = rep(k, modified=modified) + psi = rep(lamda, modified=modified) + if phi != psi: + mu = min(phi, psi) + v = max(phi, psi) + p[v] = mu + if modified: + if v == phi: + self.p_p[phi] = self.p_p[k]**-1*w*self.p_p[lamda] + else: + self.p_p[psi] = self.p_p[lamda]**-1*w**-1*self.p_p[k] + q.append(v) + + def rep(self, k, modified=False): + r""" + Parameters + ========== + + `k \in [0 \ldots n-1]`, as for ``self`` only array ``p`` is used + + Returns + ======= + + Representative of the class containing ``k``. + + Returns the representative of `\sim` class containing ``k``, it also + makes some modification to array ``p`` of ``self`` to ease further + computations, described on Pg. 157 [1]. + + The information on classes under `\sim` is stored in array `p` of + ``self`` argument, which will always satisfy the property: + + `p[\alpha] \sim \alpha` and `p[\alpha]=\alpha \iff \alpha=rep(\alpha)` + `\forall \in [0 \ldots n-1]`. + + So, for `\alpha \in [0 \ldots n-1]`, we find `rep(self, \alpha)` by + continually replacing `\alpha` by `p[\alpha]` until it becomes + constant (i.e satisfies `p[\alpha] = \alpha`):w + + To increase the efficiency of later ``rep`` calculations, whenever we + find `rep(self, \alpha)=\beta`, we set + `p[\gamma] = \beta \forall \gamma \in p-chain` from `\alpha` to `\beta` + + Notes + ===== + + ``rep`` routine is also described on Pg. 85-87 [1] in Atkinson's + algorithm, this results from the fact that ``coincidence`` routine + introduces functionality similar to that introduced by the + ``minimal_block`` routine on Pg. 85-87 [1]. + + See Also + ======== + + coincidence, merge + + """ + p = self.p + lamda = k + rho = p[lamda] + if modified: + s = p[:] + while rho != lamda: + if modified: + s[rho] = lamda + lamda = rho + rho = p[lamda] + if modified: + rho = s[lamda] + while rho != k: + mu = rho + rho = s[mu] + p[rho] = lamda + self.p_p[rho] = self.p_p[rho]*self.p_p[mu] + else: + mu = k + rho = p[mu] + while rho != lamda: + p[mu] = lamda + mu = rho + rho = p[mu] + return lamda + + # alpha, beta coincide, i.e. alpha, beta represent the pair of cosets + # where coincidence occurs + def coincidence(self, alpha, beta, w=None, modified=False): + r""" + The third situation described in ``scan`` routine is handled by this + routine, described on Pg. 156-161 [1]. + + The unfortunate situation when the scan completes but not correctly, + then ``coincidence`` routine is run. i.e when for some `i` with + `1 \le i \le r+1`, we have `w=st` with `s = x_1 x_2 \dots x_{i-1}`, + `t = x_i x_{i+1} \dots x_r`, and `\beta = \alpha^s` and + `\gamma = \alpha^{t-1}` are defined but unequal. This means that + `\beta` and `\gamma` represent the same coset of `H` in `G`. Described + on Pg. 156 [1]. ``rep`` + + See Also + ======== + + scan + + """ + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + # behaves as a queue + q = [] + if modified: + self.modified_merge(alpha, beta, w, q) + else: + self.merge(alpha, beta, q) + while len(q) > 0: + gamma = q.pop(0) + for x in A_dict: + delta = table[gamma][A_dict[x]] + if delta is not None: + table[delta][A_dict_inv[x]] = None + mu = self.rep(gamma, modified=modified) + nu = self.rep(delta, modified=modified) + if table[mu][A_dict[x]] is not None: + if modified: + v = self.p_p[delta]**-1*self.P[gamma][self.A_dict[x]]**-1 + v = v*self.p_p[gamma]*self.P[mu][self.A_dict[x]] + self.modified_merge(nu, table[mu][self.A_dict[x]], v, q) + else: + self.merge(nu, table[mu][A_dict[x]], q) + elif table[nu][A_dict_inv[x]] is not None: + if modified: + v = self.p_p[gamma]**-1*self.P[gamma][self.A_dict[x]] + v = v*self.p_p[delta]*self.P[mu][self.A_dict_inv[x]] + self.modified_merge(mu, table[nu][self.A_dict_inv[x]], v, q) + else: + self.merge(mu, table[nu][A_dict_inv[x]], q) + else: + table[mu][A_dict[x]] = nu + table[nu][A_dict_inv[x]] = mu + if modified: + v = self.p_p[gamma]**-1*self.P[gamma][self.A_dict[x]]*self.p_p[delta] + self.P[mu][self.A_dict[x]] = v + self.P[nu][self.A_dict_inv[x]] = v**-1 + + # method used in the HLT strategy + def scan_and_fill(self, alpha, word): + """ + A modified version of ``scan`` routine used in the relator-based + method of coset enumeration, described on pg. 162-163 [1], which + follows the idea that whenever the procedure is called and the scan + is incomplete then it makes new definitions to enable the scan to + complete; i.e it fills in the gaps in the scan of the relator or + subgroup generator. + + """ + self.scan(alpha, word, fill=True) + + def scan_and_fill_c(self, alpha, word): + """ + A modified version of ``scan`` routine, described on Pg. 165 second + para. [1], with modification similar to that of ``scan_anf_fill`` the + only difference being it calls the coincidence procedure used in the + coset-table based method i.e. the routine ``coincidence_c`` is used. + + See Also + ======== + + scan, scan_and_fill + + """ + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + r = len(word) + f = alpha + i = 0 + b = alpha + j = r - 1 + # loop until it has filled the alpha row in the table. + while True: + # do the forward scanning + while i <= j and table[f][A_dict[word[i]]] is not None: + f = table[f][A_dict[word[i]]] + i += 1 + if i > j: + if f != b: + self.coincidence_c(f, b) + return + # forward scan was incomplete, scan backwards + while j >= i and table[b][A_dict_inv[word[j]]] is not None: + b = table[b][A_dict_inv[word[j]]] + j -= 1 + if j < i: + self.coincidence_c(f, b) + elif j == i: + table[f][A_dict[word[i]]] = b + table[b][A_dict_inv[word[i]]] = f + self.deduction_stack.append((f, word[i])) + else: + self.define_c(f, word[i]) + + # method used in the HLT strategy + def look_ahead(self): + """ + When combined with the HLT method this is known as HLT+Lookahead + method of coset enumeration, described on pg. 164 [1]. Whenever + ``define`` aborts due to lack of space available this procedure is + executed. This routine helps in recovering space resulting from + "coincidence" of cosets. + + """ + R = self.fp_group.relators + p = self.p + # complete scan all relators under all cosets(obviously live) + # without making new definitions + for beta in self.omega: + for w in R: + self.scan(beta, w) + if p[beta] < beta: + break + + # Pg. 166 + def process_deductions(self, R_c_x, R_c_x_inv): + """ + Processes the deductions that have been pushed onto ``deduction_stack``, + described on Pg. 166 [1] and is used in coset-table based enumeration. + + See Also + ======== + + deduction_stack + + """ + p = self.p + table = self.table + while len(self.deduction_stack) > 0: + if len(self.deduction_stack) >= CosetTable.max_stack_size: + self.look_ahead() + del self.deduction_stack[:] + continue + else: + alpha, x = self.deduction_stack.pop() + if p[alpha] == alpha: + for w in R_c_x: + self.scan_c(alpha, w) + if p[alpha] < alpha: + break + beta = table[alpha][self.A_dict[x]] + if beta is not None and p[beta] == beta: + for w in R_c_x_inv: + self.scan_c(beta, w) + if p[beta] < beta: + break + + def process_deductions_check(self, R_c_x, R_c_x_inv): + """ + A variation of ``process_deductions``, this calls ``scan_check`` + wherever ``process_deductions`` calls ``scan``, described on Pg. [1]. + + See Also + ======== + + process_deductions + + """ + table = self.table + while len(self.deduction_stack) > 0: + alpha, x = self.deduction_stack.pop() + for w in R_c_x: + if not self.scan_check(alpha, w): + return False + beta = table[alpha][self.A_dict[x]] + if beta is not None: + for w in R_c_x_inv: + if not self.scan_check(beta, w): + return False + return True + + def switch(self, beta, gamma): + r"""Switch the elements `\beta, \gamma \in \Omega` of ``self``, used + by the ``standardize`` procedure, described on Pg. 167 [1]. + + See Also + ======== + + standardize + + """ + A = self.A + A_dict = self.A_dict + table = self.table + for x in A: + z = table[gamma][A_dict[x]] + table[gamma][A_dict[x]] = table[beta][A_dict[x]] + table[beta][A_dict[x]] = z + for alpha in range(len(self.p)): + if self.p[alpha] == alpha: + if table[alpha][A_dict[x]] == beta: + table[alpha][A_dict[x]] = gamma + elif table[alpha][A_dict[x]] == gamma: + table[alpha][A_dict[x]] = beta + + def standardize(self): + r""" + A coset table is standardized if when running through the cosets and + within each coset through the generator images (ignoring generator + inverses), the cosets appear in order of the integers + `0, 1, \dots, n`. "Standardize" reorders the elements of `\Omega` + such that, if we scan the coset table first by elements of `\Omega` + and then by elements of A, then the cosets occur in ascending order. + ``standardize()`` is used at the end of an enumeration to permute the + cosets so that they occur in some sort of standard order. + + Notes + ===== + + procedure is described on pg. 167-168 [1], it also makes use of the + ``switch`` routine to replace by smaller integer value. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r + >>> F, x, y = free_group("x, y") + + # Example 5.3 from [1] + >>> f = FpGroup(F, [x**2*y**2, x**3*y**5]) + >>> C = coset_enumeration_r(f, []) + >>> C.compress() + >>> C.table + [[1, 3, 1, 3], [2, 0, 2, 0], [3, 1, 3, 1], [0, 2, 0, 2]] + >>> C.standardize() + >>> C.table + [[1, 2, 1, 2], [3, 0, 3, 0], [0, 3, 0, 3], [2, 1, 2, 1]] + + """ + A = self.A + A_dict = self.A_dict + gamma = 1 + for alpha, x in product(range(self.n), A): + beta = self.table[alpha][A_dict[x]] + if beta >= gamma: + if beta > gamma: + self.switch(gamma, beta) + gamma += 1 + if gamma == self.n: + return + + # Compression of a Coset Table + def compress(self): + """Removes the non-live cosets from the coset table, described on + pg. 167 [1]. + + """ + gamma = -1 + A = self.A + A_dict = self.A_dict + A_dict_inv = self.A_dict_inv + table = self.table + chi = tuple([i for i in range(len(self.p)) if self.p[i] != i]) + for alpha in self.omega: + gamma += 1 + if gamma != alpha: + # replace alpha by gamma in coset table + for x in A: + beta = table[alpha][A_dict[x]] + table[gamma][A_dict[x]] = beta + table[beta][A_dict_inv[x]] == gamma + # all the cosets in the table are live cosets + self.p = list(range(gamma + 1)) + # delete the useless columns + del table[len(self.p):] + # re-define values + for row in table: + for j in range(len(self.A)): + row[j] -= bisect_left(chi, row[j]) + + def conjugates(self, R): + R_c = list(chain.from_iterable((rel.cyclic_conjugates(), \ + (rel**-1).cyclic_conjugates()) for rel in R)) + R_set = set() + for conjugate in R_c: + R_set = R_set.union(conjugate) + R_c_list = [] + for x in self.A: + r = {word for word in R_set if word[0] == x} + R_c_list.append(r) + R_set.difference_update(r) + return R_c_list + + def coset_representative(self, coset): + ''' + Compute the coset representative of a given coset. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + >>> C = coset_enumeration_r(f, [x]) + >>> C.compress() + >>> C.table + [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]] + >>> C.coset_representative(0) + + >>> C.coset_representative(1) + y + >>> C.coset_representative(2) + y**-1 + + ''' + for x in self.A: + gamma = self.table[coset][self.A_dict[x]] + if coset == 0: + return self.fp_group.identity + if gamma < coset: + return self.coset_representative(gamma)*x**-1 + + ############################## + # Modified Methods # + ############################## + + def modified_define(self, alpha, x): + r""" + Define a function p_p from from [1..n] to A* as + an additional component of the modified coset table. + + Parameters + ========== + + \alpha \in \Omega + x \in A* + + See Also + ======== + + define + + """ + self.define(alpha, x, modified=True) + + def modified_scan(self, alpha, w, y, fill=False): + r""" + Parameters + ========== + \alpha \in \Omega + w \in A* + y \in (YUY^-1) + fill -- `modified_scan_and_fill` when set to True. + + See Also + ======== + + scan + """ + self.scan(alpha, w, y=y, fill=fill, modified=True) + + def modified_scan_and_fill(self, alpha, w, y): + self.modified_scan(alpha, w, y, fill=True) + + def modified_merge(self, k, lamda, w, q): + r""" + Parameters + ========== + + 'k', 'lamda' -- the two class representatives to be merged. + q -- queue of length l of elements to be deleted from `\Omega` *. + w -- Word in (YUY^-1) + + See Also + ======== + + merge + """ + self.merge(k, lamda, q, w=w, modified=True) + + def modified_rep(self, k): + r""" + Parameters + ========== + + `k \in [0 \ldots n-1]` + + See Also + ======== + + rep + """ + self.rep(k, modified=True) + + def modified_coincidence(self, alpha, beta, w): + r""" + Parameters + ========== + + A coincident pair `\alpha, \beta \in \Omega, w \in Y \cup Y^{-1}` + + See Also + ======== + + coincidence + + """ + self.coincidence(alpha, beta, w=w, modified=True) + +############################################################################### +# COSET ENUMERATION # +############################################################################### + +# relator-based method +def coset_enumeration_r(fp_grp, Y, max_cosets=None, draft=None, + incomplete=False, modified=False): + """ + This is easier of the two implemented methods of coset enumeration. + and is often called the HLT method, after Hazelgrove, Leech, Trotter + The idea is that we make use of ``scan_and_fill`` makes new definitions + whenever the scan is incomplete to enable the scan to complete; this way + we fill in the gaps in the scan of the relator or subgroup generator, + that's why the name relator-based method. + + An instance of `CosetTable` for `fp_grp` can be passed as the keyword + argument `draft` in which case the coset enumeration will start with + that instance and attempt to complete it. + + When `incomplete` is `True` and the function is unable to complete for + some reason, the partially complete table will be returned. + + # TODO: complete the docstring + + See Also + ======== + + scan_and_fill, + + Examples + ======== + + >>> from sympy.combinatorics.free_groups import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r + >>> F, x, y = free_group("x, y") + + # Example 5.1 from [1] + >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + >>> C = coset_enumeration_r(f, [x]) + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... print(C.table[i]) + [0, 0, 1, 2] + [1, 1, 2, 0] + [2, 2, 0, 1] + >>> C.p + [0, 1, 2, 1, 1] + + # Example from exercises Q2 [1] + >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3]) + >>> C = coset_enumeration_r(f, []) + >>> C.compress(); C.standardize() + >>> C.table + [[1, 2, 3, 4], + [5, 0, 6, 7], + [0, 5, 7, 6], + [7, 6, 5, 0], + [6, 7, 0, 5], + [2, 1, 4, 3], + [3, 4, 2, 1], + [4, 3, 1, 2]] + + # Example 5.2 + >>> f = FpGroup(F, [x**2, y**3, (x*y)**3]) + >>> Y = [x*y] + >>> C = coset_enumeration_r(f, Y) + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... print(C.table[i]) + [1, 1, 2, 1] + [0, 0, 0, 2] + [3, 3, 1, 0] + [2, 2, 3, 3] + + # Example 5.3 + >>> f = FpGroup(F, [x**2*y**2, x**3*y**5]) + >>> Y = [] + >>> C = coset_enumeration_r(f, Y) + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... print(C.table[i]) + [1, 3, 1, 3] + [2, 0, 2, 0] + [3, 1, 3, 1] + [0, 2, 0, 2] + + # Example 5.4 + >>> F, a, b, c, d, e = free_group("a, b, c, d, e") + >>> f = FpGroup(F, [a*b*c**-1, b*c*d**-1, c*d*e**-1, d*e*a**-1, e*a*b**-1]) + >>> Y = [a] + >>> C = coset_enumeration_r(f, Y) + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... print(C.table[i]) + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + + # example of "compress" method + >>> C.compress() + >>> C.table + [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] + + # Exercises Pg. 161, Q2. + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3]) + >>> Y = [] + >>> C = coset_enumeration_r(f, Y) + >>> C.compress() + >>> C.standardize() + >>> C.table + [[1, 2, 3, 4], + [5, 0, 6, 7], + [0, 5, 7, 6], + [7, 6, 5, 0], + [6, 7, 0, 5], + [2, 1, 4, 3], + [3, 4, 2, 1], + [4, 3, 1, 2]] + + # John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson + # Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490 + # from 1973chwd.pdf + # Table 1. Ex. 1 + >>> F, r, s, t = free_group("r, s, t") + >>> E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2]) + >>> C = coset_enumeration_r(E1, [r]) + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... print(C.table[i]) + [0, 0, 0, 0, 0, 0] + + Ex. 2 + >>> F, a, b = free_group("a, b") + >>> Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5]) + >>> C = coset_enumeration_r(Cox, [a]) + >>> index = 0 + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... index += 1 + >>> index + 500 + + # Ex. 3 + >>> F, a, b = free_group("a, b") + >>> B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \ + (a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4]) + >>> C = coset_enumeration_r(B_2_4, [a]) + >>> index = 0 + >>> for i in range(len(C.p)): + ... if C.p[i] == i: + ... index += 1 + >>> index + 1024 + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of computational group theory" + + """ + # 1. Initialize a coset table C for < X|R > + C = CosetTable(fp_grp, Y, max_cosets=max_cosets) + # Define coset table methods. + if modified: + _scan_and_fill = C.modified_scan_and_fill + _define = C.modified_define + else: + _scan_and_fill = C.scan_and_fill + _define = C.define + if draft: + C.table = draft.table[:] + C.p = draft.p[:] + R = fp_grp.relators + A_dict = C.A_dict + p = C.p + for i in range(len(Y)): + if modified: + _scan_and_fill(0, Y[i], C._grp.generators[i]) + else: + _scan_and_fill(0, Y[i]) + alpha = 0 + while alpha < C.n: + if p[alpha] == alpha: + try: + for w in R: + if modified: + _scan_and_fill(alpha, w, C._grp.identity) + else: + _scan_and_fill(alpha, w) + # if alpha was eliminated during the scan then break + if p[alpha] < alpha: + break + if p[alpha] == alpha: + for x in A_dict: + if C.table[alpha][A_dict[x]] is None: + _define(alpha, x) + except ValueError as e: + if incomplete: + return C + raise e + alpha += 1 + return C + +def modified_coset_enumeration_r(fp_grp, Y, max_cosets=None, draft=None, + incomplete=False): + r""" + Introduce a new set of symbols y \in Y that correspond to the + generators of the subgroup. Store the elements of Y as a + word P[\alpha, x] and compute the coset table similar to that of + the regular coset enumeration methods. + + Examples + ======== + + >>> from sympy.combinatorics.free_groups import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup + >>> from sympy.combinatorics.coset_table import modified_coset_enumeration_r + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + >>> C = modified_coset_enumeration_r(f, [x]) + >>> C.table + [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1], [None, 1, None, None], [1, 3, None, None]] + + See Also + ======== + + coset_enumertation_r + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E., + "Handbook of Computational Group Theory", + Section 5.3.2 + """ + return coset_enumeration_r(fp_grp, Y, max_cosets=max_cosets, draft=draft, + incomplete=incomplete, modified=True) + +# Pg. 166 +# coset-table based method +def coset_enumeration_c(fp_grp, Y, max_cosets=None, draft=None, + incomplete=False): + """ + >>> from sympy.combinatorics.free_groups import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_c + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + >>> C = coset_enumeration_c(f, [x]) + >>> C.table + [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]] + + """ + # Initialize a coset table C for < X|R > + X = fp_grp.generators + R = fp_grp.relators + C = CosetTable(fp_grp, Y, max_cosets=max_cosets) + if draft: + C.table = draft.table[:] + C.p = draft.p[:] + C.deduction_stack = draft.deduction_stack + for alpha, x in product(range(len(C.table)), X): + if C.table[alpha][C.A_dict[x]] is not None: + C.deduction_stack.append((alpha, x)) + A = C.A + # replace all the elements by cyclic reductions + R_cyc_red = [rel.identity_cyclic_reduction() for rel in R] + R_c = list(chain.from_iterable((rel.cyclic_conjugates(), (rel**-1).cyclic_conjugates()) \ + for rel in R_cyc_red)) + R_set = set() + for conjugate in R_c: + R_set = R_set.union(conjugate) + # a list of subsets of R_c whose words start with "x". + R_c_list = [] + for x in C.A: + r = {word for word in R_set if word[0] == x} + R_c_list.append(r) + R_set.difference_update(r) + for w in Y: + C.scan_and_fill_c(0, w) + for x in A: + C.process_deductions(R_c_list[C.A_dict[x]], R_c_list[C.A_dict_inv[x]]) + alpha = 0 + while alpha < len(C.table): + if C.p[alpha] == alpha: + try: + for x in C.A: + if C.p[alpha] != alpha: + break + if C.table[alpha][C.A_dict[x]] is None: + C.define_c(alpha, x) + C.process_deductions(R_c_list[C.A_dict[x]], R_c_list[C.A_dict_inv[x]]) + except ValueError as e: + if incomplete: + return C + raise e + alpha += 1 + return C diff --git a/lib/python3.11/site-packages/sympy/combinatorics/fp_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/fp_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..0e9858683750ef0f7a0f11b1cc7daec2b6a8051d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/fp_groups.py @@ -0,0 +1,1354 @@ +"""Finitely Presented Groups and its algorithms. """ + +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.combinatorics.free_groups import (FreeGroup, FreeGroupElement, + free_group) +from sympy.combinatorics.rewritingsystem import RewritingSystem +from sympy.combinatorics.coset_table import (CosetTable, + coset_enumeration_r, + coset_enumeration_c) +from sympy.combinatorics import PermutationGroup +from sympy.matrices.normalforms import invariant_factors +from sympy.matrices import Matrix +from sympy.polys.polytools import gcd +from sympy.printing.defaults import DefaultPrinting +from sympy.utilities import public +from sympy.utilities.magic import pollute + +from itertools import product + + +@public +def fp_group(fr_grp, relators=()): + _fp_group = FpGroup(fr_grp, relators) + return (_fp_group,) + tuple(_fp_group._generators) + +@public +def xfp_group(fr_grp, relators=()): + _fp_group = FpGroup(fr_grp, relators) + return (_fp_group, _fp_group._generators) + +# Does not work. Both symbols and pollute are undefined. Never tested. +@public +def vfp_group(fr_grpm, relators): + _fp_group = FpGroup(symbols, relators) + pollute([sym.name for sym in _fp_group.symbols], _fp_group.generators) + return _fp_group + + +def _parse_relators(rels): + """Parse the passed relators.""" + return rels + + +############################################################################### +# FINITELY PRESENTED GROUPS # +############################################################################### + + +class FpGroup(DefaultPrinting): + """ + The FpGroup would take a FreeGroup and a list/tuple of relators, the + relators would be specified in such a way that each of them be equal to the + identity of the provided free group. + + """ + is_group = True + is_FpGroup = True + is_PermutationGroup = False + + def __init__(self, fr_grp, relators): + relators = _parse_relators(relators) + self.free_group = fr_grp + self.relators = relators + self.generators = self._generators() + self.dtype = type("FpGroupElement", (FpGroupElement,), {"group": self}) + + # CosetTable instance on identity subgroup + self._coset_table = None + # returns whether coset table on identity subgroup + # has been standardized + self._is_standardized = False + + self._order = None + self._center = None + + self._rewriting_system = RewritingSystem(self) + self._perm_isomorphism = None + return + + def _generators(self): + return self.free_group.generators + + def make_confluent(self): + ''' + Try to make the group's rewriting system confluent + + ''' + self._rewriting_system.make_confluent() + return + + def reduce(self, word): + ''' + Return the reduced form of `word` in `self` according to the group's + rewriting system. If it's confluent, the reduced form is the unique normal + form of the word in the group. + + ''' + return self._rewriting_system.reduce(word) + + def equals(self, word1, word2): + ''' + Compare `word1` and `word2` for equality in the group + using the group's rewriting system. If the system is + confluent, the returned answer is necessarily correct. + (If it is not, `False` could be returned in some cases + where in fact `word1 == word2`) + + ''' + if self.reduce(word1*word2**-1) == self.identity: + return True + elif self._rewriting_system.is_confluent: + return False + return None + + @property + def identity(self): + return self.free_group.identity + + def __contains__(self, g): + return g in self.free_group + + def subgroup(self, gens, C=None, homomorphism=False): + ''' + Return the subgroup generated by `gens` using the + Reidemeister-Schreier algorithm + homomorphism -- When set to True, return a dictionary containing the images + of the presentation generators in the original group. + + Examples + ======== + + >>> from sympy.combinatorics.fp_groups import FpGroup + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**3, y**5, (x*y)**2]) + >>> H = [x*y, x**-1*y**-1*x*y*x] + >>> K, T = f.subgroup(H, homomorphism=True) + >>> T(K.generators) + [x*y, x**-1*y**2*x**-1] + + ''' + + if not all(isinstance(g, FreeGroupElement) for g in gens): + raise ValueError("Generators must be `FreeGroupElement`s") + if not all(g.group == self.free_group for g in gens): + raise ValueError("Given generators are not members of the group") + if homomorphism: + g, rels, _gens = reidemeister_presentation(self, gens, C=C, homomorphism=True) + else: + g, rels = reidemeister_presentation(self, gens, C=C) + if g: + g = FpGroup(g[0].group, rels) + else: + g = FpGroup(free_group('')[0], []) + if homomorphism: + from sympy.combinatorics.homomorphisms import homomorphism + return g, homomorphism(g, self, g.generators, _gens, check=False) + return g + + def coset_enumeration(self, H, strategy="relator_based", max_cosets=None, + draft=None, incomplete=False): + """ + Return an instance of ``coset table``, when Todd-Coxeter algorithm is + run over the ``self`` with ``H`` as subgroup, using ``strategy`` + argument as strategy. The returned coset table is compressed but not + standardized. + + An instance of `CosetTable` for `fp_grp` can be passed as the keyword + argument `draft` in which case the coset enumeration will start with + that instance and attempt to complete it. + + When `incomplete` is `True` and the function is unable to complete for + some reason, the partially complete table will be returned. + + """ + if not max_cosets: + max_cosets = CosetTable.coset_table_max_limit + if strategy == 'relator_based': + C = coset_enumeration_r(self, H, max_cosets=max_cosets, + draft=draft, incomplete=incomplete) + else: + C = coset_enumeration_c(self, H, max_cosets=max_cosets, + draft=draft, incomplete=incomplete) + if C.is_complete(): + C.compress() + return C + + def standardize_coset_table(self): + """ + Standardized the coset table ``self`` and makes the internal variable + ``_is_standardized`` equal to ``True``. + + """ + self._coset_table.standardize() + self._is_standardized = True + + def coset_table(self, H, strategy="relator_based", max_cosets=None, + draft=None, incomplete=False): + """ + Return the mathematical coset table of ``self`` in ``H``. + + """ + if not H: + if self._coset_table is not None: + if not self._is_standardized: + self.standardize_coset_table() + else: + C = self.coset_enumeration([], strategy, max_cosets=max_cosets, + draft=draft, incomplete=incomplete) + self._coset_table = C + self.standardize_coset_table() + return self._coset_table.table + else: + C = self.coset_enumeration(H, strategy, max_cosets=max_cosets, + draft=draft, incomplete=incomplete) + C.standardize() + return C.table + + def order(self, strategy="relator_based"): + """ + Returns the order of the finitely presented group ``self``. It uses + the coset enumeration with identity group as subgroup, i.e ``H=[]``. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x, y**2]) + >>> f.order(strategy="coset_table_based") + 2 + + """ + if self._order is not None: + return self._order + if self._coset_table is not None: + self._order = len(self._coset_table.table) + elif len(self.relators) == 0: + self._order = self.free_group.order() + elif len(self.generators) == 1: + self._order = abs(gcd([r.array_form[0][1] for r in self.relators])) + elif self._is_infinite(): + self._order = S.Infinity + else: + gens, C = self._finite_index_subgroup() + if C: + ind = len(C.table) + self._order = ind*self.subgroup(gens, C=C).order() + else: + self._order = self.index([]) + return self._order + + def _is_infinite(self): + ''' + Test if the group is infinite. Return `True` if the test succeeds + and `None` otherwise + + ''' + used_gens = set() + for r in self.relators: + used_gens.update(r.contains_generators()) + if not set(self.generators) <= used_gens: + return True + # Abelianisation test: check is the abelianisation is infinite + abelian_rels = [] + for rel in self.relators: + abelian_rels.append([rel.exponent_sum(g) for g in self.generators]) + m = Matrix(Matrix(abelian_rels)) + if 0 in invariant_factors(m): + return True + else: + return None + + + def _finite_index_subgroup(self, s=None): + ''' + Find the elements of `self` that generate a finite index subgroup + and, if found, return the list of elements and the coset table of `self` by + the subgroup, otherwise return `(None, None)` + + ''' + gen = self.most_frequent_generator() + rels = list(self.generators) + rels.extend(self.relators) + if not s: + if len(self.generators) == 2: + s = [gen] + [g for g in self.generators if g != gen] + else: + rand = self.free_group.identity + i = 0 + while ((rand in rels or rand**-1 in rels or rand.is_identity) + and i<10): + rand = self.random() + i += 1 + s = [gen, rand] + [g for g in self.generators if g != gen] + mid = (len(s)+1)//2 + half1 = s[:mid] + half2 = s[mid:] + draft1 = None + draft2 = None + m = 200 + C = None + while not C and (m/2 < CosetTable.coset_table_max_limit): + m = min(m, CosetTable.coset_table_max_limit) + draft1 = self.coset_enumeration(half1, max_cosets=m, + draft=draft1, incomplete=True) + if draft1.is_complete(): + C = draft1 + half = half1 + else: + draft2 = self.coset_enumeration(half2, max_cosets=m, + draft=draft2, incomplete=True) + if draft2.is_complete(): + C = draft2 + half = half2 + if not C: + m *= 2 + if not C: + return None, None + C.compress() + return half, C + + def most_frequent_generator(self): + gens = self.generators + rels = self.relators + freqs = [sum(r.generator_count(g) for r in rels) for g in gens] + return gens[freqs.index(max(freqs))] + + def random(self): + import random + r = self.free_group.identity + for i in range(random.randint(2,3)): + r = r*random.choice(self.generators)**random.choice([1,-1]) + return r + + def index(self, H, strategy="relator_based"): + """ + Return the index of subgroup ``H`` in group ``self``. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**5, y**4, y*x*y**3*x**3]) + >>> f.index([x]) + 4 + + """ + # TODO: use |G:H| = |G|/|H| (currently H can't be made into a group) + # when we know |G| and |H| + + if H == []: + return self.order() + else: + C = self.coset_enumeration(H, strategy) + return len(C.table) + + def __str__(self): + if self.free_group.rank > 30: + str_form = "" % self.free_group.rank + else: + str_form = "" % str(self.generators) + return str_form + + __repr__ = __str__ + +#============================================================================== +# PERMUTATION GROUP METHODS +#============================================================================== + + def _to_perm_group(self): + ''' + Return an isomorphic permutation group and the isomorphism. + The implementation is dependent on coset enumeration so + will only terminate for finite groups. + + ''' + from sympy.combinatorics import Permutation + from sympy.combinatorics.homomorphisms import homomorphism + if self.order() is S.Infinity: + raise NotImplementedError("Permutation presentation of infinite " + "groups is not implemented") + if self._perm_isomorphism: + T = self._perm_isomorphism + P = T.image() + else: + C = self.coset_table([]) + gens = self.generators + images = [[C[i][2*gens.index(g)] for i in range(len(C))] for g in gens] + images = [Permutation(i) for i in images] + P = PermutationGroup(images) + T = homomorphism(self, P, gens, images, check=False) + self._perm_isomorphism = T + return P, T + + def _perm_group_list(self, method_name, *args): + ''' + Given the name of a `PermutationGroup` method (returning a subgroup + or a list of subgroups) and (optionally) additional arguments it takes, + return a list or a list of lists containing the generators of this (or + these) subgroups in terms of the generators of `self`. + + ''' + P, T = self._to_perm_group() + perm_result = getattr(P, method_name)(*args) + single = False + if isinstance(perm_result, PermutationGroup): + perm_result, single = [perm_result], True + result = [] + for group in perm_result: + gens = group.generators + result.append(T.invert(gens)) + return result[0] if single else result + + def derived_series(self): + ''' + Return the list of lists containing the generators + of the subgroups in the derived series of `self`. + + ''' + return self._perm_group_list('derived_series') + + def lower_central_series(self): + ''' + Return the list of lists containing the generators + of the subgroups in the lower central series of `self`. + + ''' + return self._perm_group_list('lower_central_series') + + def center(self): + ''' + Return the list of generators of the center of `self`. + + ''' + return self._perm_group_list('center') + + + def derived_subgroup(self): + ''' + Return the list of generators of the derived subgroup of `self`. + + ''' + return self._perm_group_list('derived_subgroup') + + + def centralizer(self, other): + ''' + Return the list of generators of the centralizer of `other` + (a list of elements of `self`) in `self`. + + ''' + T = self._to_perm_group()[1] + other = T(other) + return self._perm_group_list('centralizer', other) + + def normal_closure(self, other): + ''' + Return the list of generators of the normal closure of `other` + (a list of elements of `self`) in `self`. + + ''' + T = self._to_perm_group()[1] + other = T(other) + return self._perm_group_list('normal_closure', other) + + def _perm_property(self, attr): + ''' + Given an attribute of a `PermutationGroup`, return + its value for a permutation group isomorphic to `self`. + + ''' + P = self._to_perm_group()[0] + return getattr(P, attr) + + @property + def is_abelian(self): + ''' + Check if `self` is abelian. + + ''' + return self._perm_property("is_abelian") + + @property + def is_nilpotent(self): + ''' + Check if `self` is nilpotent. + + ''' + return self._perm_property("is_nilpotent") + + @property + def is_solvable(self): + ''' + Check if `self` is solvable. + + ''' + return self._perm_property("is_solvable") + + @property + def elements(self): + ''' + List the elements of `self`. + + ''' + P, T = self._to_perm_group() + return T.invert(P.elements) + + @property + def is_cyclic(self): + """ + Return ``True`` if group is Cyclic. + + """ + if len(self.generators) <= 1: + return True + try: + P, T = self._to_perm_group() + except NotImplementedError: + raise NotImplementedError("Check for infinite Cyclic group " + "is not implemented") + return P.is_cyclic + + def abelian_invariants(self): + """ + Return Abelian Invariants of a group. + """ + try: + P, T = self._to_perm_group() + except NotImplementedError: + raise NotImplementedError("abelian invariants is not implemented" + "for infinite group") + return P.abelian_invariants() + + def composition_series(self): + """ + Return subnormal series of maximum length for a group. + """ + try: + P, T = self._to_perm_group() + except NotImplementedError: + raise NotImplementedError("composition series is not implemented" + "for infinite group") + return P.composition_series() + + +class FpSubgroup(DefaultPrinting): + ''' + The class implementing a subgroup of an FpGroup or a FreeGroup + (only finite index subgroups are supported at this point). This + is to be used if one wishes to check if an element of the original + group belongs to the subgroup + + ''' + def __init__(self, G, gens, normal=False): + super().__init__() + self.parent = G + self.generators = list({g for g in gens if g != G.identity}) + self._min_words = None #for use in __contains__ + self.C = None + self.normal = normal + + def __contains__(self, g): + + if isinstance(self.parent, FreeGroup): + if self._min_words is None: + # make _min_words - a list of subwords such that + # g is in the subgroup if and only if it can be + # partitioned into these subwords. Infinite families of + # subwords are presented by tuples, e.g. (r, w) + # stands for the family of subwords r*w**n*r**-1 + + def _process(w): + # this is to be used before adding new words + # into _min_words; if the word w is not cyclically + # reduced, it will generate an infinite family of + # subwords so should be written as a tuple; + # if it is, w**-1 should be added to the list + # as well + p, r = w.cyclic_reduction(removed=True) + if not r.is_identity: + return [(r, p)] + else: + return [w, w**-1] + + # make the initial list + gens = [] + for w in self.generators: + if self.normal: + w = w.cyclic_reduction() + gens.extend(_process(w)) + + for w1 in gens: + for w2 in gens: + # if w1 and w2 are equal or are inverses, continue + if w1 == w2 or (not isinstance(w1, tuple) + and w1**-1 == w2): + continue + + # if the start of one word is the inverse of the + # end of the other, their multiple should be added + # to _min_words because of cancellation + if isinstance(w1, tuple): + # start, end + s1, s2 = w1[0][0], w1[0][0]**-1 + else: + s1, s2 = w1[0], w1[len(w1)-1] + + if isinstance(w2, tuple): + # start, end + r1, r2 = w2[0][0], w2[0][0]**-1 + else: + r1, r2 = w2[0], w2[len(w1)-1] + + # p1 and p2 are w1 and w2 or, in case when + # w1 or w2 is an infinite family, a representative + p1, p2 = w1, w2 + if isinstance(w1, tuple): + p1 = w1[0]*w1[1]*w1[0]**-1 + if isinstance(w2, tuple): + p2 = w2[0]*w2[1]*w2[0]**-1 + + # add the product of the words to the list is necessary + if r1**-1 == s2 and not (p1*p2).is_identity: + new = _process(p1*p2) + if new not in gens: + gens.extend(new) + + if r2**-1 == s1 and not (p2*p1).is_identity: + new = _process(p2*p1) + if new not in gens: + gens.extend(new) + + self._min_words = gens + + min_words = self._min_words + + def _is_subword(w): + # check if w is a word in _min_words or one of + # the infinite families in it + w, r = w.cyclic_reduction(removed=True) + if r.is_identity or self.normal: + return w in min_words + else: + t = [s[1] for s in min_words if isinstance(s, tuple) + and s[0] == r] + return [s for s in t if w.power_of(s)] != [] + + # store the solution of words for which the result of + # _word_break (below) is known + known = {} + + def _word_break(w): + # check if w can be written as a product of words + # in min_words + if len(w) == 0: + return True + i = 0 + while i < len(w): + i += 1 + prefix = w.subword(0, i) + if not _is_subword(prefix): + continue + rest = w.subword(i, len(w)) + if rest not in known: + known[rest] = _word_break(rest) + if known[rest]: + return True + return False + + if self.normal: + g = g.cyclic_reduction() + return _word_break(g) + else: + if self.C is None: + C = self.parent.coset_enumeration(self.generators) + self.C = C + i = 0 + C = self.C + for j in range(len(g)): + i = C.table[i][C.A_dict[g[j]]] + return i == 0 + + def order(self): + if not self.generators: + return S.One + if isinstance(self.parent, FreeGroup): + return S.Infinity + if self.C is None: + C = self.parent.coset_enumeration(self.generators) + self.C = C + # This is valid because `len(self.C.table)` (the index of the subgroup) + # will always be finite - otherwise coset enumeration doesn't terminate + return self.parent.order()/len(self.C.table) + + def to_FpGroup(self): + if isinstance(self.parent, FreeGroup): + gen_syms = [('x_%d'%i) for i in range(len(self.generators))] + return free_group(', '.join(gen_syms))[0] + return self.parent.subgroup(C=self.C) + + def __str__(self): + if len(self.generators) > 30: + str_form = "" % len(self.generators) + else: + str_form = "" % str(self.generators) + return str_form + + __repr__ = __str__ + + +############################################################################### +# LOW INDEX SUBGROUPS # +############################################################################### + +def low_index_subgroups(G, N, Y=()): + """ + Implements the Low Index Subgroups algorithm, i.e find all subgroups of + ``G`` upto a given index ``N``. This implements the method described in + [Sim94]. This procedure involves a backtrack search over incomplete Coset + Tables, rather than over forced coincidences. + + Parameters + ========== + + G: An FpGroup < X|R > + N: positive integer, representing the maximum index value for subgroups + Y: (an optional argument) specifying a list of subgroup generators, such + that each of the resulting subgroup contains the subgroup generated by Y. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, low_index_subgroups + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**2, y**3, (x*y)**4]) + >>> L = low_index_subgroups(f, 4) + >>> for coset_table in L: + ... print(coset_table.table) + [[0, 0, 0, 0]] + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 3, 3]] + [[0, 0, 1, 2], [2, 2, 2, 0], [1, 1, 0, 1]] + [[1, 1, 0, 0], [0, 0, 1, 1]] + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + Section 5.4 + + .. [2] Marston Conder and Peter Dobcsanyi + "Applications and Adaptions of the Low Index Subgroups Procedure" + + """ + C = CosetTable(G, []) + R = G.relators + # length chosen for the length of the short relators + len_short_rel = 5 + # elements of R2 only checked at the last step for complete + # coset tables + R2 = {rel for rel in R if len(rel) > len_short_rel} + # elements of R1 are used in inner parts of the process to prune + # branches of the search tree, + R1 = {rel.identity_cyclic_reduction() for rel in set(R) - R2} + R1_c_list = C.conjugates(R1) + S = [] + descendant_subgroups(S, C, R1_c_list, C.A[0], R2, N, Y) + return S + + +def descendant_subgroups(S, C, R1_c_list, x, R2, N, Y): + A_dict = C.A_dict + A_dict_inv = C.A_dict_inv + if C.is_complete(): + # if C is complete then it only needs to test + # whether the relators in R2 are satisfied + for w, alpha in product(R2, C.omega): + if not C.scan_check(alpha, w): + return + # relators in R2 are satisfied, append the table to list + S.append(C) + else: + # find the first undefined entry in Coset Table + for alpha, x in product(range(len(C.table)), C.A): + if C.table[alpha][A_dict[x]] is None: + # this is "x" in pseudo-code (using "y" makes it clear) + undefined_coset, undefined_gen = alpha, x + break + # for filling up the undefine entry we try all possible values + # of beta in Omega or beta = n where beta^(undefined_gen^-1) is undefined + reach = C.omega + [C.n] + for beta in reach: + if beta < N: + if beta == C.n or C.table[beta][A_dict_inv[undefined_gen]] is None: + try_descendant(S, C, R1_c_list, R2, N, undefined_coset, \ + undefined_gen, beta, Y) + + +def try_descendant(S, C, R1_c_list, R2, N, alpha, x, beta, Y): + r""" + Solves the problem of trying out each individual possibility + for `\alpha^x. + + """ + D = C.copy() + if beta == D.n and beta < N: + D.table.append([None]*len(D.A)) + D.p.append(beta) + D.table[alpha][D.A_dict[x]] = beta + D.table[beta][D.A_dict_inv[x]] = alpha + D.deduction_stack.append((alpha, x)) + if not D.process_deductions_check(R1_c_list[D.A_dict[x]], \ + R1_c_list[D.A_dict_inv[x]]): + return + for w in Y: + if not D.scan_check(0, w): + return + if first_in_class(D, Y): + descendant_subgroups(S, D, R1_c_list, x, R2, N, Y) + + +def first_in_class(C, Y=()): + """ + Checks whether the subgroup ``H=G1`` corresponding to the Coset Table + could possibly be the canonical representative of its conjugacy class. + + Parameters + ========== + + C: CosetTable + + Returns + ======= + + bool: True/False + + If this returns False, then no descendant of C can have that property, and + so we can abandon C. If it returns True, then we need to process further + the node of the search tree corresponding to C, and so we call + ``descendant_subgroups`` recursively on C. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, CosetTable, first_in_class + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**2, y**3, (x*y)**4]) + >>> C = CosetTable(f, []) + >>> C.table = [[0, 0, None, None]] + >>> first_in_class(C) + True + >>> C.table = [[1, 1, 1, None], [0, 0, None, 1]]; C.p = [0, 1] + >>> first_in_class(C) + True + >>> C.table = [[1, 1, 2, 1], [0, 0, 0, None], [None, None, None, 0]] + >>> C.p = [0, 1, 2] + >>> first_in_class(C) + False + >>> C.table = [[1, 1, 1, 2], [0, 0, 2, 0], [2, None, 0, 1]] + >>> first_in_class(C) + False + + # TODO:: Sims points out in [Sim94] that performance can be improved by + # remembering some of the information computed by ``first_in_class``. If + # the ``continue alpha`` statement is executed at line 14, then the same thing + # will happen for that value of alpha in any descendant of the table C, and so + # the values the values of alpha for which this occurs could profitably be + # stored and passed through to the descendants of C. Of course this would + # make the code more complicated. + + # The code below is taken directly from the function on page 208 of [Sim94] + # nu[alpha] + + """ + n = C.n + # lamda is the largest numbered point in Omega_c_alpha which is currently defined + lamda = -1 + # for alpha in Omega_c, nu[alpha] is the point in Omega_c_alpha corresponding to alpha + nu = [None]*n + # for alpha in Omega_c_alpha, mu[alpha] is the point in Omega_c corresponding to alpha + mu = [None]*n + # mutually nu and mu are the mutually-inverse equivalence maps between + # Omega_c_alpha and Omega_c + next_alpha = False + # For each 0!=alpha in [0 .. nc-1], we start by constructing the equivalent + # standardized coset table C_alpha corresponding to H_alpha + for alpha in range(1, n): + # reset nu to "None" after previous value of alpha + for beta in range(lamda+1): + nu[mu[beta]] = None + # we only want to reject our current table in favour of a preceding + # table in the ordering in which 1 is replaced by alpha, if the subgroup + # G_alpha corresponding to this preceding table definitely contains the + # given subgroup + for w in Y: + # TODO: this should support input of a list of general words + # not just the words which are in "A" (i.e gen and gen^-1) + if C.table[alpha][C.A_dict[w]] != alpha: + # continue with alpha + next_alpha = True + break + if next_alpha: + next_alpha = False + continue + # try alpha as the new point 0 in Omega_C_alpha + mu[0] = alpha + nu[alpha] = 0 + # compare corresponding entries in C and C_alpha + lamda = 0 + for beta in range(n): + for x in C.A: + gamma = C.table[beta][C.A_dict[x]] + delta = C.table[mu[beta]][C.A_dict[x]] + # if either of the entries is undefined, + # we move with next alpha + if gamma is None or delta is None: + # continue with alpha + next_alpha = True + break + if nu[delta] is None: + # delta becomes the next point in Omega_C_alpha + lamda += 1 + nu[delta] = lamda + mu[lamda] = delta + if nu[delta] < gamma: + return False + if nu[delta] > gamma: + # continue with alpha + next_alpha = True + break + if next_alpha: + next_alpha = False + break + return True + +#======================================================================== +# Simplifying Presentation +#======================================================================== + +def simplify_presentation(*args, change_gens=False): + ''' + For an instance of `FpGroup`, return a simplified isomorphic copy of + the group (e.g. remove redundant generators or relators). Alternatively, + a list of generators and relators can be passed in which case the + simplified lists will be returned. + + By default, the generators of the group are unchanged. If you would + like to remove redundant generators, set the keyword argument + `change_gens = True`. + + ''' + if len(args) == 1: + if not isinstance(args[0], FpGroup): + raise TypeError("The argument must be an instance of FpGroup") + G = args[0] + gens, rels = simplify_presentation(G.generators, G.relators, + change_gens=change_gens) + if gens: + return FpGroup(gens[0].group, rels) + return FpGroup(FreeGroup([]), []) + elif len(args) == 2: + gens, rels = args[0][:], args[1][:] + if not gens: + return gens, rels + identity = gens[0].group.identity + else: + if len(args) == 0: + m = "Not enough arguments" + else: + m = "Too many arguments" + raise RuntimeError(m) + + prev_gens = [] + prev_rels = [] + while not set(prev_rels) == set(rels): + prev_rels = rels + while change_gens and not set(prev_gens) == set(gens): + prev_gens = gens + gens, rels = elimination_technique_1(gens, rels, identity) + rels = _simplify_relators(rels) + + if change_gens: + syms = [g.array_form[0][0] for g in gens] + F = free_group(syms)[0] + identity = F.identity + gens = F.generators + subs = dict(zip(syms, gens)) + for j, r in enumerate(rels): + a = r.array_form + rel = identity + for sym, p in a: + rel = rel*subs[sym]**p + rels[j] = rel + return gens, rels + +def _simplify_relators(rels): + """ + Simplifies a set of relators. All relators are checked to see if they are + of the form `gen^n`. If any such relators are found then all other relators + are processed for strings in the `gen` known order. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import _simplify_relators + >>> F, x, y = free_group("x, y") + >>> w1 = [x**2*y**4, x**3] + >>> _simplify_relators(w1) + [x**3, x**-1*y**4] + + >>> w2 = [x**2*y**-4*x**5, x**3, x**2*y**8, y**5] + >>> _simplify_relators(w2) + [x**-1*y**-2, x**-1*y*x**-1, x**3, y**5] + + >>> w3 = [x**6*y**4, x**4] + >>> _simplify_relators(w3) + [x**4, x**2*y**4] + + >>> w4 = [x**2, x**5, y**3] + >>> _simplify_relators(w4) + [x, y**3] + + """ + rels = rels[:] + + if not rels: + return [] + + identity = rels[0].group.identity + + # build dictionary with "gen: n" where gen^n is one of the relators + exps = {} + for i in range(len(rels)): + rel = rels[i] + if rel.number_syllables() == 1: + g = rel[0] + exp = abs(rel.array_form[0][1]) + if rel.array_form[0][1] < 0: + rels[i] = rels[i]**-1 + g = g**-1 + if g in exps: + exp = gcd(exp, exps[g].array_form[0][1]) + exps[g] = g**exp + + one_syllables_words = list(exps.values()) + # decrease some of the exponents in relators, making use of the single + # syllable relators + for i, rel in enumerate(rels): + if rel in one_syllables_words: + continue + rel = rel.eliminate_words(one_syllables_words, _all = True) + # if rels[i] contains g**n where abs(n) is greater than half of the power p + # of g in exps, g**n can be replaced by g**(n-p) (or g**(p-n) if n<0) + for g in rel.contains_generators(): + if g in exps: + exp = exps[g].array_form[0][1] + max_exp = (exp + 1)//2 + rel = rel.eliminate_word(g**(max_exp), g**(max_exp-exp), _all = True) + rel = rel.eliminate_word(g**(-max_exp), g**(-(max_exp-exp)), _all = True) + rels[i] = rel + + rels = [r.identity_cyclic_reduction() for r in rels] + + rels += one_syllables_words # include one_syllable_words in the list of relators + rels = list(set(rels)) # get unique values in rels + rels.sort() + + # remove entries in rels + try: + rels.remove(identity) + except ValueError: + pass + return rels + +# Pg 350, section 2.5.1 from [2] +def elimination_technique_1(gens, rels, identity): + rels = rels[:] + # the shorter relators are examined first so that generators selected for + # elimination will have shorter strings as equivalent + rels.sort() + gens = gens[:] + redundant_gens = {} + redundant_rels = [] + used_gens = set() + # examine each relator in relator list for any generator occurring exactly + # once + for rel in rels: + # don't look for a redundant generator in a relator which + # depends on previously found ones + contained_gens = rel.contains_generators() + if any(g in contained_gens for g in redundant_gens): + continue + contained_gens = list(contained_gens) + contained_gens.sort(reverse = True) + for gen in contained_gens: + if rel.generator_count(gen) == 1 and gen not in used_gens: + k = rel.exponent_sum(gen) + gen_index = rel.index(gen**k) + bk = rel.subword(gen_index + 1, len(rel)) + fw = rel.subword(0, gen_index) + chi = bk*fw + redundant_gens[gen] = chi**(-1*k) + used_gens.update(chi.contains_generators()) + redundant_rels.append(rel) + break + rels = [r for r in rels if r not in redundant_rels] + # eliminate the redundant generators from remaining relators + rels = [r.eliminate_words(redundant_gens, _all = True).identity_cyclic_reduction() for r in rels] + rels = list(set(rels)) + try: + rels.remove(identity) + except ValueError: + pass + gens = [g for g in gens if g not in redundant_gens] + return gens, rels + +############################################################################### +# SUBGROUP PRESENTATIONS # +############################################################################### + +# Pg 175 [1] +def define_schreier_generators(C, homomorphism=False): + ''' + Parameters + ========== + + C -- Coset table. + homomorphism -- When set to True, return a dictionary containing the images + of the presentation generators in the original group. + ''' + y = [] + gamma = 1 + f = C.fp_group + X = f.generators + if homomorphism: + # `_gens` stores the elements of the parent group to + # to which the schreier generators correspond to. + _gens = {} + # compute the schreier Traversal + tau = {} + tau[0] = f.identity + C.P = [[None]*len(C.A) for i in range(C.n)] + for alpha, x in product(C.omega, C.A): + beta = C.table[alpha][C.A_dict[x]] + if beta == gamma: + C.P[alpha][C.A_dict[x]] = "" + C.P[beta][C.A_dict_inv[x]] = "" + gamma += 1 + if homomorphism: + tau[beta] = tau[alpha]*x + elif x in X and C.P[alpha][C.A_dict[x]] is None: + y_alpha_x = '%s_%s' % (x, alpha) + y.append(y_alpha_x) + C.P[alpha][C.A_dict[x]] = y_alpha_x + if homomorphism: + _gens[y_alpha_x] = tau[alpha]*x*tau[beta]**-1 + grp_gens = list(free_group(', '.join(y))) + C._schreier_free_group = grp_gens.pop(0) + C._schreier_generators = grp_gens + if homomorphism: + C._schreier_gen_elem = _gens + # replace all elements of P by, free group elements + for i, j in product(range(len(C.P)), range(len(C.A))): + # if equals "", replace by identity element + if C.P[i][j] == "": + C.P[i][j] = C._schreier_free_group.identity + elif isinstance(C.P[i][j], str): + r = C._schreier_generators[y.index(C.P[i][j])] + C.P[i][j] = r + beta = C.table[i][j] + C.P[beta][j + 1] = r**-1 + +def reidemeister_relators(C): + R = C.fp_group.relators + rels = [rewrite(C, coset, word) for word in R for coset in range(C.n)] + order_1_gens = {i for i in rels if len(i) == 1} + + # remove all the order 1 generators from relators + rels = list(filter(lambda rel: rel not in order_1_gens, rels)) + + # replace order 1 generators by identity element in reidemeister relators + for i in range(len(rels)): + w = rels[i] + w = w.eliminate_words(order_1_gens, _all=True) + rels[i] = w + + C._schreier_generators = [i for i in C._schreier_generators + if not (i in order_1_gens or i**-1 in order_1_gens)] + + # Tietze transformation 1 i.e TT_1 + # remove cyclic conjugate elements from relators + i = 0 + while i < len(rels): + w = rels[i] + j = i + 1 + while j < len(rels): + if w.is_cyclic_conjugate(rels[j]): + del rels[j] + else: + j += 1 + i += 1 + + C._reidemeister_relators = rels + + +def rewrite(C, alpha, w): + """ + Parameters + ========== + + C: CosetTable + alpha: A live coset + w: A word in `A*` + + Returns + ======= + + rho(tau(alpha), w) + + Examples + ======== + + >>> from sympy.combinatorics.fp_groups import FpGroup, CosetTable, define_schreier_generators, rewrite + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**2, y**3, (x*y)**6]) + >>> C = CosetTable(f, []) + >>> C.table = [[1, 1, 2, 3], [0, 0, 4, 5], [4, 4, 3, 0], [5, 5, 0, 2], [2, 2, 5, 1], [3, 3, 1, 4]] + >>> C.p = [0, 1, 2, 3, 4, 5] + >>> define_schreier_generators(C) + >>> rewrite(C, 0, (x*y)**6) + x_4*y_2*x_3*x_1*x_2*y_4*x_5 + + """ + v = C._schreier_free_group.identity + for i in range(len(w)): + x_i = w[i] + v = v*C.P[alpha][C.A_dict[x_i]] + alpha = C.table[alpha][C.A_dict[x_i]] + return v + +# Pg 350, section 2.5.2 from [2] +def elimination_technique_2(C): + """ + This technique eliminates one generator at a time. Heuristically this + seems superior in that we may select for elimination the generator with + shortest equivalent string at each stage. + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r, \ + reidemeister_relators, define_schreier_generators, elimination_technique_2 + >>> F, x, y = free_group("x, y") + >>> f = FpGroup(F, [x**3, y**5, (x*y)**2]); H = [x*y, x**-1*y**-1*x*y*x] + >>> C = coset_enumeration_r(f, H) + >>> C.compress(); C.standardize() + >>> define_schreier_generators(C) + >>> reidemeister_relators(C) + >>> elimination_technique_2(C) + ([y_1, y_2], [y_2**-3, y_2*y_1*y_2*y_1*y_2*y_1, y_1**2]) + + """ + rels = C._reidemeister_relators + rels.sort(reverse=True) + gens = C._schreier_generators + for i in range(len(gens) - 1, -1, -1): + rel = rels[i] + for j in range(len(gens) - 1, -1, -1): + gen = gens[j] + if rel.generator_count(gen) == 1: + k = rel.exponent_sum(gen) + gen_index = rel.index(gen**k) + bk = rel.subword(gen_index + 1, len(rel)) + fw = rel.subword(0, gen_index) + rep_by = (bk*fw)**(-1*k) + del rels[i]; del gens[j] + for l in range(len(rels)): + rels[l] = rels[l].eliminate_word(gen, rep_by) + break + C._reidemeister_relators = rels + C._schreier_generators = gens + return C._schreier_generators, C._reidemeister_relators + +def reidemeister_presentation(fp_grp, H, C=None, homomorphism=False): + """ + Parameters + ========== + + fp_group: A finitely presented group, an instance of FpGroup + H: A subgroup whose presentation is to be found, given as a list + of words in generators of `fp_grp` + homomorphism: When set to True, return a homomorphism from the subgroup + to the parent group + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> from sympy.combinatorics.fp_groups import FpGroup, reidemeister_presentation + >>> F, x, y = free_group("x, y") + + Example 5.6 Pg. 177 from [1] + >>> f = FpGroup(F, [x**3, y**5, (x*y)**2]) + >>> H = [x*y, x**-1*y**-1*x*y*x] + >>> reidemeister_presentation(f, H) + ((y_1, y_2), (y_1**2, y_2**3, y_2*y_1*y_2*y_1*y_2*y_1)) + + Example 5.8 Pg. 183 from [1] + >>> f = FpGroup(F, [x**3, y**3, (x*y)**3]) + >>> H = [x*y, x*y**-1] + >>> reidemeister_presentation(f, H) + ((x_0, y_0), (x_0**3, y_0**3, x_0*y_0*x_0*y_0*x_0*y_0)) + + Exercises Q2. Pg 187 from [1] + >>> f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3]) + >>> H = [x] + >>> reidemeister_presentation(f, H) + ((x_0,), (x_0**4,)) + + Example 5.9 Pg. 183 from [1] + >>> f = FpGroup(F, [x**3*y**-3, (x*y)**3, (x*y**-1)**2]) + >>> H = [x] + >>> reidemeister_presentation(f, H) + ((x_0,), (x_0**6,)) + + """ + if not C: + C = coset_enumeration_r(fp_grp, H) + C.compress(); C.standardize() + define_schreier_generators(C, homomorphism=homomorphism) + reidemeister_relators(C) + gens, rels = C._schreier_generators, C._reidemeister_relators + gens, rels = simplify_presentation(gens, rels, change_gens=True) + + C.schreier_generators = tuple(gens) + C.reidemeister_relators = tuple(rels) + + if homomorphism: + _gens = [] + for gen in gens: + _gens.append(C._schreier_gen_elem[str(gen)]) + return C.schreier_generators, C.reidemeister_relators, _gens + + return C.schreier_generators, C.reidemeister_relators + + +FpGroupElement = FreeGroupElement diff --git a/lib/python3.11/site-packages/sympy/combinatorics/free_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/free_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..53bd0f4d75a0dc5987cf91706390cdfa0bc048ed --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/free_groups.py @@ -0,0 +1,1354 @@ +from __future__ import annotations + +from sympy.core import S +from sympy.core.expr import Expr +from sympy.core.symbol import Symbol, symbols as _symbols +from sympy.core.sympify import CantSympify +from sympy.printing.defaults import DefaultPrinting +from sympy.utilities import public +from sympy.utilities.iterables import flatten, is_sequence +from sympy.utilities.magic import pollute +from sympy.utilities.misc import as_int + + +@public +def free_group(symbols): + """Construct a free group returning ``(FreeGroup, (f_0, f_1, ..., f_(n-1))``. + + Parameters + ========== + + symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty) + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y, z = free_group("x, y, z") + >>> F + + >>> x**2*y**-1 + x**2*y**-1 + >>> type(_) + + + """ + _free_group = FreeGroup(symbols) + return (_free_group,) + tuple(_free_group.generators) + +@public +def xfree_group(symbols): + """Construct a free group returning ``(FreeGroup, (f_0, f_1, ..., f_(n-1)))``. + + Parameters + ========== + + symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty) + + Examples + ======== + + >>> from sympy.combinatorics.free_groups import xfree_group + >>> F, (x, y, z) = xfree_group("x, y, z") + >>> F + + >>> y**2*x**-2*z**-1 + y**2*x**-2*z**-1 + >>> type(_) + + + """ + _free_group = FreeGroup(symbols) + return (_free_group, _free_group.generators) + +@public +def vfree_group(symbols): + """Construct a free group and inject ``f_0, f_1, ..., f_(n-1)`` as symbols + into the global namespace. + + Parameters + ========== + + symbols : str, Symbol/Expr or sequence of str, Symbol/Expr (may be empty) + + Examples + ======== + + >>> from sympy.combinatorics.free_groups import vfree_group + >>> vfree_group("x, y, z") + + >>> x**2*y**-2*z # noqa: F821 + x**2*y**-2*z + >>> type(_) + + + """ + _free_group = FreeGroup(symbols) + pollute([sym.name for sym in _free_group.symbols], _free_group.generators) + return _free_group + + +def _parse_symbols(symbols): + if not symbols: + return () + if isinstance(symbols, str): + return _symbols(symbols, seq=True) + elif isinstance(symbols, (Expr, FreeGroupElement)): + return (symbols,) + elif is_sequence(symbols): + if all(isinstance(s, str) for s in symbols): + return _symbols(symbols) + elif all(isinstance(s, Expr) for s in symbols): + return symbols + raise ValueError("The type of `symbols` must be one of the following: " + "a str, Symbol/Expr or a sequence of " + "one of these types") + + +############################################################################## +# FREE GROUP # +############################################################################## + +_free_group_cache: dict[int, FreeGroup] = {} + +class FreeGroup(DefaultPrinting): + """ + Free group with finite or infinite number of generators. Its input API + is that of a str, Symbol/Expr or a sequence of one of + these types (which may be empty) + + See Also + ======== + + sympy.polys.rings.PolyRing + + References + ========== + + .. [1] https://www.gap-system.org/Manuals/doc/ref/chap37.html + + .. [2] https://en.wikipedia.org/wiki/Free_group + + """ + is_associative = True + is_group = True + is_FreeGroup = True + is_PermutationGroup = False + relators: list[Expr] = [] + + def __new__(cls, symbols): + symbols = tuple(_parse_symbols(symbols)) + rank = len(symbols) + _hash = hash((cls.__name__, symbols, rank)) + obj = _free_group_cache.get(_hash) + + if obj is None: + obj = object.__new__(cls) + obj._hash = _hash + obj._rank = rank + # dtype method is used to create new instances of FreeGroupElement + obj.dtype = type("FreeGroupElement", (FreeGroupElement,), {"group": obj}) + obj.symbols = symbols + obj.generators = obj._generators() + obj._gens_set = set(obj.generators) + for symbol, generator in zip(obj.symbols, obj.generators): + if isinstance(symbol, Symbol): + name = symbol.name + if hasattr(obj, name): + setattr(obj, name, generator) + + _free_group_cache[_hash] = obj + + return obj + + def _generators(group): + """Returns the generators of the FreeGroup. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y, z = free_group("x, y, z") + >>> F.generators + (x, y, z) + + """ + gens = [] + for sym in group.symbols: + elm = ((sym, 1),) + gens.append(group.dtype(elm)) + return tuple(gens) + + def clone(self, symbols=None): + return self.__class__(symbols or self.symbols) + + def __contains__(self, i): + """Return True if ``i`` is contained in FreeGroup.""" + if not isinstance(i, FreeGroupElement): + return False + group = i.group + return self == group + + def __hash__(self): + return self._hash + + def __len__(self): + return self.rank + + def __str__(self): + if self.rank > 30: + str_form = "" % self.rank + else: + str_form = "" + return str_form + + __repr__ = __str__ + + def __getitem__(self, index): + symbols = self.symbols[index] + return self.clone(symbols=symbols) + + def __eq__(self, other): + """No ``FreeGroup`` is equal to any "other" ``FreeGroup``. + """ + return self is other + + def index(self, gen): + """Return the index of the generator `gen` from ``(f_0, ..., f_(n-1))``. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> F.index(y) + 1 + >>> F.index(x) + 0 + + """ + if isinstance(gen, self.dtype): + return self.generators.index(gen) + else: + raise ValueError("expected a generator of Free Group %s, got %s" % (self, gen)) + + def order(self): + """Return the order of the free group. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> F.order() + oo + + >>> free_group("")[0].order() + 1 + + """ + if self.rank == 0: + return S.One + else: + return S.Infinity + + @property + def elements(self): + """ + Return the elements of the free group. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> (z,) = free_group("") + >>> z.elements + {} + + """ + if self.rank == 0: + # A set containing Identity element of `FreeGroup` self is returned + return {self.identity} + else: + raise ValueError("Group contains infinitely many elements" + ", hence cannot be represented") + + @property + def rank(self): + r""" + In group theory, the `rank` of a group `G`, denoted `G.rank`, + can refer to the smallest cardinality of a generating set + for G, that is + + \operatorname{rank}(G)=\min\{ |X|: X\subseteq G, \left\langle X\right\rangle =G\}. + + """ + return self._rank + + @property + def is_abelian(self): + """Returns if the group is Abelian. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> f.is_abelian + False + + """ + return self.rank in (0, 1) + + @property + def identity(self): + """Returns the identity element of free group.""" + return self.dtype() + + def contains(self, g): + """Tests if Free Group element ``g`` belong to self, ``G``. + + In mathematical terms any linear combination of generators + of a Free Group is contained in it. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> f.contains(x**3*y**2) + True + + """ + if not isinstance(g, FreeGroupElement): + return False + elif self != g.group: + return False + else: + return True + + def center(self): + """Returns the center of the free group `self`.""" + return {self.identity} + + +############################################################################ +# FreeGroupElement # +############################################################################ + + +class FreeGroupElement(CantSympify, DefaultPrinting, tuple): + """Used to create elements of FreeGroup. It cannot be used directly to + create a free group element. It is called by the `dtype` method of the + `FreeGroup` class. + + """ + is_assoc_word = True + + def new(self, init): + return self.__class__(init) + + _hash = None + + def __hash__(self): + _hash = self._hash + if _hash is None: + self._hash = _hash = hash((self.group, frozenset(tuple(self)))) + return _hash + + def copy(self): + return self.new(self) + + @property + def is_identity(self): + if self.array_form == (): + return True + else: + return False + + @property + def array_form(self): + """ + SymPy provides two different internal kinds of representation + of associative words. The first one is called the `array_form` + which is a tuple containing `tuples` as its elements, where the + size of each tuple is two. At the first position the tuple + contains the `symbol-generator`, while at the second position + of tuple contains the exponent of that generator at the position. + Since elements (i.e. words) do not commute, the indexing of tuple + makes that property to stay. + + The structure in ``array_form`` of ``FreeGroupElement`` is of form: + + ``( ( symbol_of_gen, exponent ), ( , ), ... ( , ) )`` + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> (x*z).array_form + ((x, 1), (z, 1)) + >>> (x**2*z*y*x**2).array_form + ((x, 2), (z, 1), (y, 1), (x, 2)) + + See Also + ======== + + letter_repr + + """ + return tuple(self) + + @property + def letter_form(self): + """ + The letter representation of a ``FreeGroupElement`` is a tuple + of generator symbols, with each entry corresponding to a group + generator. Inverses of the generators are represented by + negative generator symbols. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b, c, d = free_group("a b c d") + >>> (a**3).letter_form + (a, a, a) + >>> (a**2*d**-2*a*b**-4).letter_form + (a, a, -d, -d, a, -b, -b, -b, -b) + >>> (a**-2*b**3*d).letter_form + (-a, -a, b, b, b, d) + + See Also + ======== + + array_form + + """ + return tuple(flatten([(i,)*j if j > 0 else (-i,)*(-j) + for i, j in self.array_form])) + + def __getitem__(self, i): + group = self.group + r = self.letter_form[i] + if r.is_Symbol: + return group.dtype(((r, 1),)) + else: + return group.dtype(((-r, -1),)) + + def index(self, gen): + if len(gen) != 1: + raise ValueError() + return (self.letter_form).index(gen.letter_form[0]) + + @property + def letter_form_elm(self): + """ + """ + group = self.group + r = self.letter_form + return [group.dtype(((elm,1),)) if elm.is_Symbol \ + else group.dtype(((-elm,-1),)) for elm in r] + + @property + def ext_rep(self): + """This is called the External Representation of ``FreeGroupElement`` + """ + return tuple(flatten(self.array_form)) + + def __contains__(self, gen): + return gen.array_form[0][0] in tuple([r[0] for r in self.array_form]) + + def __str__(self): + if self.is_identity: + return "" + + str_form = "" + array_form = self.array_form + for i in range(len(array_form)): + if i == len(array_form) - 1: + if array_form[i][1] == 1: + str_form += str(array_form[i][0]) + else: + str_form += str(array_form[i][0]) + \ + "**" + str(array_form[i][1]) + else: + if array_form[i][1] == 1: + str_form += str(array_form[i][0]) + "*" + else: + str_form += str(array_form[i][0]) + \ + "**" + str(array_form[i][1]) + "*" + return str_form + + __repr__ = __str__ + + def __pow__(self, n): + n = as_int(n) + result = self.group.identity + if n == 0: + return result + if n < 0: + n = -n + x = self.inverse() + else: + x = self + while True: + if n % 2: + result *= x + n >>= 1 + if not n: + break + x *= x + return result + + def __mul__(self, other): + """Returns the product of elements belonging to the same ``FreeGroup``. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> x*y**2*y**-4 + x*y**-2 + >>> z*y**-2 + z*y**-2 + >>> x**2*y*y**-1*x**-2 + + + """ + group = self.group + if not isinstance(other, group.dtype): + raise TypeError("only FreeGroup elements of same FreeGroup can " + "be multiplied") + if self.is_identity: + return other + if other.is_identity: + return self + r = list(self.array_form + other.array_form) + zero_mul_simp(r, len(self.array_form) - 1) + return group.dtype(tuple(r)) + + def __truediv__(self, other): + group = self.group + if not isinstance(other, group.dtype): + raise TypeError("only FreeGroup elements of same FreeGroup can " + "be multiplied") + return self*(other.inverse()) + + def __rtruediv__(self, other): + group = self.group + if not isinstance(other, group.dtype): + raise TypeError("only FreeGroup elements of same FreeGroup can " + "be multiplied") + return other*(self.inverse()) + + def __add__(self, other): + return NotImplemented + + def inverse(self): + """ + Returns the inverse of a ``FreeGroupElement`` element + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> x.inverse() + x**-1 + >>> (x*y).inverse() + y**-1*x**-1 + + """ + group = self.group + r = tuple([(i, -j) for i, j in self.array_form[::-1]]) + return group.dtype(r) + + def order(self): + """Find the order of a ``FreeGroupElement``. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y = free_group("x y") + >>> (x**2*y*y**-1*x**-2).order() + 1 + + """ + if self.is_identity: + return S.One + else: + return S.Infinity + + def commutator(self, other): + """ + Return the commutator of `self` and `x`: ``~x*~self*x*self`` + + """ + group = self.group + if not isinstance(other, group.dtype): + raise ValueError("commutator of only FreeGroupElement of the same " + "FreeGroup exists") + else: + return self.inverse()*other.inverse()*self*other + + def eliminate_words(self, words, _all=False, inverse=True): + ''' + Replace each subword from the dictionary `words` by words[subword]. + If words is a list, replace the words by the identity. + + ''' + again = True + new = self + if isinstance(words, dict): + while again: + again = False + for sub in words: + prev = new + new = new.eliminate_word(sub, words[sub], _all=_all, inverse=inverse) + if new != prev: + again = True + else: + while again: + again = False + for sub in words: + prev = new + new = new.eliminate_word(sub, _all=_all, inverse=inverse) + if new != prev: + again = True + return new + + def eliminate_word(self, gen, by=None, _all=False, inverse=True): + """ + For an associative word `self`, a subword `gen`, and an associative + word `by` (identity by default), return the associative word obtained by + replacing each occurrence of `gen` in `self` by `by`. If `_all = True`, + the occurrences of `gen` that may appear after the first substitution will + also be replaced and so on until no occurrences are found. This might not + always terminate (e.g. `(x).eliminate_word(x, x**2, _all=True)`). + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y = free_group("x y") + >>> w = x**5*y*x**2*y**-4*x + >>> w.eliminate_word( x, x**2 ) + x**10*y*x**4*y**-4*x**2 + >>> w.eliminate_word( x, y**-1 ) + y**-11 + >>> w.eliminate_word(x**5) + y*x**2*y**-4*x + >>> w.eliminate_word(x*y, y) + x**4*y*x**2*y**-4*x + + See Also + ======== + substituted_word + + """ + if by is None: + by = self.group.identity + if self.is_independent(gen) or gen == by: + return self + if gen == self: + return by + if gen**-1 == by: + _all = False + word = self + l = len(gen) + + try: + i = word.subword_index(gen) + k = 1 + except ValueError: + if not inverse: + return word + try: + i = word.subword_index(gen**-1) + k = -1 + except ValueError: + return word + + word = word.subword(0, i)*by**k*word.subword(i+l, len(word)).eliminate_word(gen, by) + + if _all: + return word.eliminate_word(gen, by, _all=True, inverse=inverse) + else: + return word + + def __len__(self): + """ + For an associative word `self`, returns the number of letters in it. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> w = a**5*b*a**2*b**-4*a + >>> len(w) + 13 + >>> len(a**17) + 17 + >>> len(w**0) + 0 + + """ + return sum(abs(j) for (i, j) in self) + + def __eq__(self, other): + """ + Two associative words are equal if they are words over the + same alphabet and if they are sequences of the same letters. + This is equivalent to saying that the external representations + of the words are equal. + There is no "universal" empty word, every alphabet has its own + empty word. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, swapnil0, swapnil1 = free_group("swapnil0 swapnil1") + >>> f + + >>> g, swap0, swap1 = free_group("swap0 swap1") + >>> g + + + >>> swapnil0 == swapnil1 + False + >>> swapnil0*swapnil1 == swapnil1/swapnil1*swapnil0*swapnil1 + True + >>> swapnil0*swapnil1 == swapnil1*swapnil0 + False + >>> swapnil1**0 == swap0**0 + False + + """ + group = self.group + if not isinstance(other, group.dtype): + return False + return tuple.__eq__(self, other) + + def __lt__(self, other): + """ + The ordering of associative words is defined by length and + lexicography (this ordering is called short-lex ordering), that + is, shorter words are smaller than longer words, and words of the + same length are compared w.r.t. the lexicographical ordering induced + by the ordering of generators. Generators are sorted according + to the order in which they were created. If the generators are + invertible then each generator `g` is larger than its inverse `g^{-1}`, + and `g^{-1}` is larger than every generator that is smaller than `g`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> b < a + False + >>> a < a.inverse() + False + + """ + group = self.group + if not isinstance(other, group.dtype): + raise TypeError("only FreeGroup elements of same FreeGroup can " + "be compared") + l = len(self) + m = len(other) + # implement lenlex order + if l < m: + return True + elif l > m: + return False + for i in range(l): + a = self[i].array_form[0] + b = other[i].array_form[0] + p = group.symbols.index(a[0]) + q = group.symbols.index(b[0]) + if p < q: + return True + elif p > q: + return False + elif a[1] < b[1]: + return True + elif a[1] > b[1]: + return False + return False + + def __le__(self, other): + return (self == other or self < other) + + def __gt__(self, other): + """ + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, x, y, z = free_group("x y z") + >>> y**2 > x**2 + True + >>> y*z > z*y + False + >>> x > x.inverse() + True + + """ + group = self.group + if not isinstance(other, group.dtype): + raise TypeError("only FreeGroup elements of same FreeGroup can " + "be compared") + return not self <= other + + def __ge__(self, other): + return not self < other + + def exponent_sum(self, gen): + """ + For an associative word `self` and a generator or inverse of generator + `gen`, ``exponent_sum`` returns the number of times `gen` appears in + `self` minus the number of times its inverse appears in `self`. If + neither `gen` nor its inverse occur in `self` then 0 is returned. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> w = x**2*y**3 + >>> w.exponent_sum(x) + 2 + >>> w.exponent_sum(x**-1) + -2 + >>> w = x**2*y**4*x**-3 + >>> w.exponent_sum(x) + -1 + + See Also + ======== + + generator_count + + """ + if len(gen) != 1: + raise ValueError("gen must be a generator or inverse of a generator") + s = gen.array_form[0] + return s[1]*sum(i[1] for i in self.array_form if i[0] == s[0]) + + def generator_count(self, gen): + """ + For an associative word `self` and a generator `gen`, + ``generator_count`` returns the multiplicity of generator + `gen` in `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> w = x**2*y**3 + >>> w.generator_count(x) + 2 + >>> w = x**2*y**4*x**-3 + >>> w.generator_count(x) + 5 + + See Also + ======== + + exponent_sum + + """ + if len(gen) != 1 or gen.array_form[0][1] < 0: + raise ValueError("gen must be a generator") + s = gen.array_form[0] + return s[1]*sum(abs(i[1]) for i in self.array_form if i[0] == s[0]) + + def subword(self, from_i, to_j, strict=True): + """ + For an associative word `self` and two positive integers `from_i` and + `to_j`, `subword` returns the subword of `self` that begins at position + `from_i` and ends at `to_j - 1`, indexing is done with origin 0. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> w = a**5*b*a**2*b**-4*a + >>> w.subword(2, 6) + a**3*b + + """ + group = self.group + if not strict: + from_i = max(from_i, 0) + to_j = min(len(self), to_j) + if from_i < 0 or to_j > len(self): + raise ValueError("`from_i`, `to_j` must be positive and no greater than " + "the length of associative word") + if to_j <= from_i: + return group.identity + else: + letter_form = self.letter_form[from_i: to_j] + array_form = letter_form_to_array_form(letter_form, group) + return group.dtype(array_form) + + def subword_index(self, word, start = 0): + ''' + Find the index of `word` in `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> w = a**2*b*a*b**3 + >>> w.subword_index(a*b*a*b) + 1 + + ''' + l = len(word) + self_lf = self.letter_form + word_lf = word.letter_form + index = None + for i in range(start,len(self_lf)-l+1): + if self_lf[i:i+l] == word_lf: + index = i + break + if index is not None: + return index + else: + raise ValueError("The given word is not a subword of self") + + def is_dependent(self, word): + """ + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> (x**4*y**-3).is_dependent(x**4*y**-2) + True + >>> (x**2*y**-1).is_dependent(x*y) + False + >>> (x*y**2*x*y**2).is_dependent(x*y**2) + True + >>> (x**12).is_dependent(x**-4) + True + + See Also + ======== + + is_independent + + """ + try: + return self.subword_index(word) is not None + except ValueError: + pass + try: + return self.subword_index(word**-1) is not None + except ValueError: + return False + + def is_independent(self, word): + """ + + See Also + ======== + + is_dependent + + """ + return not self.is_dependent(word) + + def contains_generators(self): + """ + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y, z = free_group("x, y, z") + >>> (x**2*y**-1).contains_generators() + {x, y} + >>> (x**3*z).contains_generators() + {x, z} + + """ + group = self.group + gens = {group.dtype(((syllable[0], 1),)) for syllable in self.array_form} + return gens + + def cyclic_subword(self, from_i, to_j): + group = self.group + l = len(self) + letter_form = self.letter_form + period1 = int(from_i/l) + if from_i >= l: + from_i -= l*period1 + to_j -= l*period1 + diff = to_j - from_i + word = letter_form[from_i: to_j] + period2 = int(to_j/l) - 1 + word += letter_form*period2 + letter_form[:diff-l+from_i-l*period2] + word = letter_form_to_array_form(word, group) + return group.dtype(word) + + def cyclic_conjugates(self): + """Returns a words which are cyclic to the word `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> w = x*y*x*y*x + >>> w.cyclic_conjugates() + {x*y*x**2*y, x**2*y*x*y, y*x*y*x**2, y*x**2*y*x, x*y*x*y*x} + >>> s = x*y*x**2*y*x + >>> s.cyclic_conjugates() + {x**2*y*x**2*y, y*x**2*y*x**2, x*y*x**2*y*x} + + References + ========== + + .. [1] https://planetmath.org/cyclicpermutation + + """ + return {self.cyclic_subword(i, i+len(self)) for i in range(len(self))} + + def is_cyclic_conjugate(self, w): + """ + Checks whether words ``self``, ``w`` are cyclic conjugates. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> w1 = x**2*y**5 + >>> w2 = x*y**5*x + >>> w1.is_cyclic_conjugate(w2) + True + >>> w3 = x**-1*y**5*x**-1 + >>> w3.is_cyclic_conjugate(w2) + False + + """ + l1 = len(self) + l2 = len(w) + if l1 != l2: + return False + w1 = self.identity_cyclic_reduction() + w2 = w.identity_cyclic_reduction() + letter1 = w1.letter_form + letter2 = w2.letter_form + str1 = ' '.join(map(str, letter1)) + str2 = ' '.join(map(str, letter2)) + if len(str1) != len(str2): + return False + + return str1 in str2 + ' ' + str2 + + def number_syllables(self): + """Returns the number of syllables of the associative word `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, swapnil0, swapnil1 = free_group("swapnil0 swapnil1") + >>> (swapnil1**3*swapnil0*swapnil1**-1).number_syllables() + 3 + + """ + return len(self.array_form) + + def exponent_syllable(self, i): + """ + Returns the exponent of the `i`-th syllable of the associative word + `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> w = a**5*b*a**2*b**-4*a + >>> w.exponent_syllable( 2 ) + 2 + + """ + return self.array_form[i][1] + + def generator_syllable(self, i): + """ + Returns the symbol of the generator that is involved in the + i-th syllable of the associative word `self`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a b") + >>> w = a**5*b*a**2*b**-4*a + >>> w.generator_syllable( 3 ) + b + + """ + return self.array_form[i][0] + + def sub_syllables(self, from_i, to_j): + """ + `sub_syllables` returns the subword of the associative word `self` that + consists of syllables from positions `from_to` to `to_j`, where + `from_to` and `to_j` must be positive integers and indexing is done + with origin 0. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> f, a, b = free_group("a, b") + >>> w = a**5*b*a**2*b**-4*a + >>> w.sub_syllables(1, 2) + b + >>> w.sub_syllables(3, 3) + + + """ + if not isinstance(from_i, int) or not isinstance(to_j, int): + raise ValueError("both arguments should be integers") + group = self.group + if to_j <= from_i: + return group.identity + else: + r = tuple(self.array_form[from_i: to_j]) + return group.dtype(r) + + def substituted_word(self, from_i, to_j, by): + """ + Returns the associative word obtained by replacing the subword of + `self` that begins at position `from_i` and ends at position `to_j - 1` + by the associative word `by`. `from_i` and `to_j` must be positive + integers, indexing is done with origin 0. In other words, + `w.substituted_word(w, from_i, to_j, by)` is the product of the three + words: `w.subword(0, from_i)`, `by`, and + `w.subword(to_j len(w))`. + + See Also + ======== + + eliminate_word + + """ + lw = len(self) + if from_i >= to_j or from_i > lw or to_j > lw: + raise ValueError("values should be within bounds") + + # otherwise there are four possibilities + + # first if from=1 and to=lw then + if from_i == 0 and to_j == lw: + return by + elif from_i == 0: # second if from_i=1 (and to_j < lw) then + return by*self.subword(to_j, lw) + elif to_j == lw: # third if to_j=1 (and from_i > 1) then + return self.subword(0, from_i)*by + else: # finally + return self.subword(0, from_i)*by*self.subword(to_j, lw) + + def is_cyclically_reduced(self): + r"""Returns whether the word is cyclically reduced or not. + A word is cyclically reduced if by forming the cycle of the + word, the word is not reduced, i.e a word w = `a_1 ... a_n` + is called cyclically reduced if `a_1 \ne a_n^{-1}`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> (x**2*y**-1*x**-1).is_cyclically_reduced() + False + >>> (y*x**2*y**2).is_cyclically_reduced() + True + + """ + if not self: + return True + return self[0] != self[-1]**-1 + + def identity_cyclic_reduction(self): + """Return a unique cyclically reduced version of the word. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> (x**2*y**2*x**-1).identity_cyclic_reduction() + x*y**2 + >>> (x**-3*y**-1*x**5).identity_cyclic_reduction() + x**2*y**-1 + + References + ========== + + .. [1] https://planetmath.org/cyclicallyreduced + + """ + word = self.copy() + group = self.group + while not word.is_cyclically_reduced(): + exp1 = word.exponent_syllable(0) + exp2 = word.exponent_syllable(-1) + r = exp1 + exp2 + if r == 0: + rep = word.array_form[1: word.number_syllables() - 1] + else: + rep = ((word.generator_syllable(0), exp1 + exp2),) + \ + word.array_form[1: word.number_syllables() - 1] + word = group.dtype(rep) + return word + + def cyclic_reduction(self, removed=False): + """Return a cyclically reduced version of the word. Unlike + `identity_cyclic_reduction`, this will not cyclically permute + the reduced word - just remove the "unreduced" bits on either + side of it. Compare the examples with those of + `identity_cyclic_reduction`. + + When `removed` is `True`, return a tuple `(word, r)` where + self `r` is such that before the reduction the word was either + `r*word*r**-1`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> (x**2*y**2*x**-1).cyclic_reduction() + x*y**2 + >>> (x**-3*y**-1*x**5).cyclic_reduction() + y**-1*x**2 + >>> (x**-3*y**-1*x**5).cyclic_reduction(removed=True) + (y**-1*x**2, x**-3) + + """ + word = self.copy() + g = self.group.identity + while not word.is_cyclically_reduced(): + exp1 = abs(word.exponent_syllable(0)) + exp2 = abs(word.exponent_syllable(-1)) + exp = min(exp1, exp2) + start = word[0]**abs(exp) + end = word[-1]**abs(exp) + word = start**-1*word*end**-1 + g = g*start + if removed: + return word, g + return word + + def power_of(self, other): + ''' + Check if `self == other**n` for some integer n. + + Examples + ======== + + >>> from sympy.combinatorics import free_group + >>> F, x, y = free_group("x, y") + >>> ((x*y)**2).power_of(x*y) + True + >>> (x**-3*y**-2*x**3).power_of(x**-3*y*x**3) + True + + ''' + if self.is_identity: + return True + + l = len(other) + if l == 1: + # self has to be a power of one generator + gens = self.contains_generators() + s = other in gens or other**-1 in gens + return len(gens) == 1 and s + + # if self is not cyclically reduced and it is a power of other, + # other isn't cyclically reduced and the parts removed during + # their reduction must be equal + reduced, r1 = self.cyclic_reduction(removed=True) + if not r1.is_identity: + other, r2 = other.cyclic_reduction(removed=True) + if r1 == r2: + return reduced.power_of(other) + return False + + if len(self) < l or len(self) % l: + return False + + prefix = self.subword(0, l) + if prefix == other or prefix**-1 == other: + rest = self.subword(l, len(self)) + return rest.power_of(other) + return False + + +def letter_form_to_array_form(array_form, group): + """ + This method converts a list given with possible repetitions of elements in + it. It returns a new list such that repetitions of consecutive elements is + removed and replace with a tuple element of size two such that the first + index contains `value` and the second index contains the number of + consecutive repetitions of `value`. + + """ + a = list(array_form[:]) + new_array = [] + n = 1 + symbols = group.symbols + for i in range(len(a)): + if i == len(a) - 1: + if a[i] == a[i - 1]: + if (-a[i]) in symbols: + new_array.append((-a[i], -n)) + else: + new_array.append((a[i], n)) + else: + if (-a[i]) in symbols: + new_array.append((-a[i], -1)) + else: + new_array.append((a[i], 1)) + return new_array + elif a[i] == a[i + 1]: + n += 1 + else: + if (-a[i]) in symbols: + new_array.append((-a[i], -n)) + else: + new_array.append((a[i], n)) + n = 1 + + +def zero_mul_simp(l, index): + """Used to combine two reduced words.""" + while index >=0 and index < len(l) - 1 and l[index][0] == l[index + 1][0]: + exp = l[index][1] + l[index + 1][1] + base = l[index][0] + l[index] = (base, exp) + del l[index + 1] + if l[index][1] == 0: + del l[index] + index -= 1 diff --git a/lib/python3.11/site-packages/sympy/combinatorics/galois.py b/lib/python3.11/site-packages/sympy/combinatorics/galois.py new file mode 100644 index 0000000000000000000000000000000000000000..f8ff89886283903e116bf40e1be6f6131386e802 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/galois.py @@ -0,0 +1,611 @@ +r""" +Construct transitive subgroups of symmetric groups, useful in Galois theory. + +Besides constructing instances of the :py:class:`~.PermutationGroup` class to +represent the transitive subgroups of $S_n$ for small $n$, this module provides +*names* for these groups. + +In some applications, it may be preferable to know the name of a group, +rather than receive an instance of the :py:class:`~.PermutationGroup` +class, and then have to do extra work to determine which group it is, by +checking various properties. + +Names are instances of ``Enum`` classes defined in this module. With a name in +hand, the name's ``get_perm_group`` method can then be used to retrieve a +:py:class:`~.PermutationGroup`. + +The names used for groups in this module are taken from [1]. + +References +========== + +.. [1] Cohen, H. *A Course in Computational Algebraic Number Theory*. + +""" + +from collections import defaultdict +from enum import Enum +import itertools + +from sympy.combinatorics.named_groups import ( + SymmetricGroup, AlternatingGroup, CyclicGroup, DihedralGroup, + set_symmetric_group_properties, set_alternating_group_properties, +) +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.combinatorics.permutations import Permutation + + +class S1TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S1. + """ + S1 = "S1" + + def get_perm_group(self): + return SymmetricGroup(1) + + +class S2TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S2. + """ + S2 = "S2" + + def get_perm_group(self): + return SymmetricGroup(2) + + +class S3TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S3. + """ + A3 = "A3" + S3 = "S3" + + def get_perm_group(self): + if self == S3TransitiveSubgroups.A3: + return AlternatingGroup(3) + elif self == S3TransitiveSubgroups.S3: + return SymmetricGroup(3) + + +class S4TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S4. + """ + C4 = "C4" + V = "V" + D4 = "D4" + A4 = "A4" + S4 = "S4" + + def get_perm_group(self): + if self == S4TransitiveSubgroups.C4: + return CyclicGroup(4) + elif self == S4TransitiveSubgroups.V: + return four_group() + elif self == S4TransitiveSubgroups.D4: + return DihedralGroup(4) + elif self == S4TransitiveSubgroups.A4: + return AlternatingGroup(4) + elif self == S4TransitiveSubgroups.S4: + return SymmetricGroup(4) + + +class S5TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S5. + """ + C5 = "C5" + D5 = "D5" + M20 = "M20" + A5 = "A5" + S5 = "S5" + + def get_perm_group(self): + if self == S5TransitiveSubgroups.C5: + return CyclicGroup(5) + elif self == S5TransitiveSubgroups.D5: + return DihedralGroup(5) + elif self == S5TransitiveSubgroups.M20: + return M20() + elif self == S5TransitiveSubgroups.A5: + return AlternatingGroup(5) + elif self == S5TransitiveSubgroups.S5: + return SymmetricGroup(5) + + +class S6TransitiveSubgroups(Enum): + """ + Names for the transitive subgroups of S6. + """ + C6 = "C6" + S3 = "S3" + D6 = "D6" + A4 = "A4" + G18 = "G18" + A4xC2 = "A4 x C2" + S4m = "S4-" + S4p = "S4+" + G36m = "G36-" + G36p = "G36+" + S4xC2 = "S4 x C2" + PSL2F5 = "PSL2(F5)" + G72 = "G72" + PGL2F5 = "PGL2(F5)" + A6 = "A6" + S6 = "S6" + + def get_perm_group(self): + if self == S6TransitiveSubgroups.C6: + return CyclicGroup(6) + elif self == S6TransitiveSubgroups.S3: + return S3_in_S6() + elif self == S6TransitiveSubgroups.D6: + return DihedralGroup(6) + elif self == S6TransitiveSubgroups.A4: + return A4_in_S6() + elif self == S6TransitiveSubgroups.G18: + return G18() + elif self == S6TransitiveSubgroups.A4xC2: + return A4xC2() + elif self == S6TransitiveSubgroups.S4m: + return S4m() + elif self == S6TransitiveSubgroups.S4p: + return S4p() + elif self == S6TransitiveSubgroups.G36m: + return G36m() + elif self == S6TransitiveSubgroups.G36p: + return G36p() + elif self == S6TransitiveSubgroups.S4xC2: + return S4xC2() + elif self == S6TransitiveSubgroups.PSL2F5: + return PSL2F5() + elif self == S6TransitiveSubgroups.G72: + return G72() + elif self == S6TransitiveSubgroups.PGL2F5: + return PGL2F5() + elif self == S6TransitiveSubgroups.A6: + return AlternatingGroup(6) + elif self == S6TransitiveSubgroups.S6: + return SymmetricGroup(6) + + +def four_group(): + """ + Return a representation of the Klein four-group as a transitive subgroup + of S4. + """ + return PermutationGroup( + Permutation(0, 1)(2, 3), + Permutation(0, 2)(1, 3) + ) + + +def M20(): + """ + Return a representation of the metacyclic group M20, a transitive subgroup + of S5 that is one of the possible Galois groups for polys of degree 5. + + Notes + ===== + + See [1], Page 323. + + """ + G = PermutationGroup(Permutation(0, 1, 2, 3, 4), Permutation(1, 2, 4, 3)) + G._degree = 5 + G._order = 20 + G._is_transitive = True + G._is_sym = False + G._is_alt = False + G._is_cyclic = False + G._is_dihedral = False + return G + + +def S3_in_S6(): + """ + Return a representation of S3 as a transitive subgroup of S6. + + Notes + ===== + + The representation is found by viewing the group as the symmetries of a + triangular prism. + + """ + G = PermutationGroup(Permutation(0, 1, 2)(3, 4, 5), Permutation(0, 3)(2, 4)(1, 5)) + set_symmetric_group_properties(G, 3, 6) + return G + + +def A4_in_S6(): + """ + Return a representation of A4 as a transitive subgroup of S6. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + G = PermutationGroup(Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 1, 2)(3, 5, 4)) + set_alternating_group_properties(G, 4, 6) + return G + + +def S4m(): + """ + Return a representation of the S4- transitive subgroup of S6. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + G = PermutationGroup(Permutation(1, 4, 5, 3), Permutation(0, 4)(1, 5)(2, 3)) + set_symmetric_group_properties(G, 4, 6) + return G + + +def S4p(): + """ + Return a representation of the S4+ transitive subgroup of S6. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + G = PermutationGroup(Permutation(0, 2, 4, 1)(3, 5), Permutation(0, 3)(4, 5)) + set_symmetric_group_properties(G, 4, 6) + return G + + +def A4xC2(): + """ + Return a representation of the (A4 x C2) transitive subgroup of S6. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + return PermutationGroup( + Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 1, 2)(3, 5, 4), + Permutation(5)(2, 4)) + + +def S4xC2(): + """ + Return a representation of the (S4 x C2) transitive subgroup of S6. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + return PermutationGroup( + Permutation(1, 4, 5, 3), Permutation(0, 4)(1, 5)(2, 3), + Permutation(1, 4)(3, 5)) + + +def G18(): + """ + Return a representation of the group G18, a transitive subgroup of S6 + isomorphic to the semidirect product of C3^2 with C2. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + return PermutationGroup( + Permutation(5)(0, 1, 2), Permutation(3, 4, 5), + Permutation(0, 4)(1, 5)(2, 3)) + + +def G36m(): + """ + Return a representation of the group G36-, a transitive subgroup of S6 + isomorphic to the semidirect product of C3^2 with C2^2. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + return PermutationGroup( + Permutation(5)(0, 1, 2), Permutation(3, 4, 5), + Permutation(1, 2)(3, 5), Permutation(0, 4)(1, 5)(2, 3)) + + +def G36p(): + """ + Return a representation of the group G36+, a transitive subgroup of S6 + isomorphic to the semidirect product of C3^2 with C4. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + return PermutationGroup( + Permutation(5)(0, 1, 2), Permutation(3, 4, 5), + Permutation(0, 5, 2, 3)(1, 4)) + + +def G72(): + """ + Return a representation of the group G72, a transitive subgroup of S6 + isomorphic to the semidirect product of C3^2 with D4. + + Notes + ===== + + See [1], Page 325. + + """ + return PermutationGroup( + Permutation(5)(0, 1, 2), + Permutation(0, 4, 1, 3)(2, 5), Permutation(0, 3)(1, 4)(2, 5)) + + +def PSL2F5(): + r""" + Return a representation of the group $PSL_2(\mathbb{F}_5)$, as a transitive + subgroup of S6, isomorphic to $A_5$. + + Notes + ===== + + This was computed using :py:func:`~.find_transitive_subgroups_of_S6`. + + """ + G = PermutationGroup( + Permutation(0, 4, 5)(1, 3, 2), Permutation(0, 4, 3, 1, 5)) + set_alternating_group_properties(G, 5, 6) + return G + + +def PGL2F5(): + r""" + Return a representation of the group $PGL_2(\mathbb{F}_5)$, as a transitive + subgroup of S6, isomorphic to $S_5$. + + Notes + ===== + + See [1], Page 325. + + """ + G = PermutationGroup( + Permutation(0, 1, 2, 3, 4), Permutation(0, 5)(1, 2)(3, 4)) + set_symmetric_group_properties(G, 5, 6) + return G + + +def find_transitive_subgroups_of_S6(*targets, print_report=False): + r""" + Search for certain transitive subgroups of $S_6$. + + The symmetric group $S_6$ has 16 different transitive subgroups, up to + conjugacy. Some are more easily constructed than others. For example, the + dihedral group $D_6$ is immediately found, but it is not at all obvious how + to realize $S_4$ or $S_5$ *transitively* within $S_6$. + + In some cases there are well-known constructions that can be used. For + example, $S_5$ is isomorphic to $PGL_2(\mathbb{F}_5)$, which acts in a + natural way on the projective line $P^1(\mathbb{F}_5)$, a set of order 6. + + In absence of such special constructions however, we can simply search for + generators. For example, transitive instances of $A_4$ and $S_4$ can be + found within $S_6$ in this way. + + Once we are engaged in such searches, it may then be easier (if less + elegant) to find even those groups like $S_5$ that do have special + constructions, by mere search. + + This function locates generators for transitive instances in $S_6$ of the + following subgroups: + + * $A_4$ + * $S_4^-$ ($S_4$ not contained within $A_6$) + * $S_4^+$ ($S_4$ contained within $A_6$) + * $A_4 \times C_2$ + * $S_4 \times C_2$ + * $G_{18} = C_3^2 \rtimes C_2$ + * $G_{36}^- = C_3^2 \rtimes C_2^2$ + * $G_{36}^+ = C_3^2 \rtimes C_4$ + * $G_{72} = C_3^2 \rtimes D_4$ + * $A_5$ + * $S_5$ + + Note: Each of these groups also has a dedicated function in this module + that returns the group immediately, using generators that were found by + this search procedure. + + The search procedure serves as a record of how these generators were + found. Also, due to randomness in the generation of the elements of + permutation groups, it can be called again, in order to (probably) get + different generators for the same groups. + + Parameters + ========== + + targets : list of :py:class:`~.S6TransitiveSubgroups` values + The groups you want to find. + + print_report : bool (default False) + If True, print to stdout the generators found for each group. + + Returns + ======= + + dict + mapping each name in *targets* to the :py:class:`~.PermutationGroup` + that was found + + References + ========== + + .. [2] https://en.wikipedia.org/wiki/Projective_linear_group#Exceptional_isomorphisms + .. [3] https://en.wikipedia.org/wiki/Automorphisms_of_the_symmetric_and_alternating_groups#PGL%282,5%29 + + """ + def elts_by_order(G): + """Sort the elements of a group by their order. """ + elts = defaultdict(list) + for g in G.elements: + elts[g.order()].append(g) + return elts + + def order_profile(G, name=None): + """Determine how many elements a group has, of each order. """ + elts = elts_by_order(G) + profile = {o:len(e) for o, e in elts.items()} + if name: + print(f'{name}: ' + ' '.join(f'{len(profile[r])}@{r}' for r in sorted(profile.keys()))) + return profile + + S6 = SymmetricGroup(6) + A6 = AlternatingGroup(6) + S6_by_order = elts_by_order(S6) + + def search(existing_gens, needed_gen_orders, order, alt=None, profile=None, anti_profile=None): + """ + Find a transitive subgroup of S6. + + Parameters + ========== + + existing_gens : list of Permutation + Optionally empty list of generators that must be in the group. + + needed_gen_orders : list of positive int + Nonempty list of the orders of the additional generators that are + to be found. + + order: int + The order of the group being sought. + + alt: bool, None + If True, require the group to be contained in A6. + If False, require the group not to be contained in A6. + + profile : dict + If given, the group's order profile must equal this. + + anti_profile : dict + If given, the group's order profile must *not* equal this. + + """ + for gens in itertools.product(*[S6_by_order[n] for n in needed_gen_orders]): + if len(set(gens)) < len(gens): + continue + G = PermutationGroup(existing_gens + list(gens)) + if G.order() == order and G.is_transitive(): + if alt is not None and G.is_subgroup(A6) != alt: + continue + if profile and order_profile(G) != profile: + continue + if anti_profile and order_profile(G) == anti_profile: + continue + return G + + def match_known_group(G, alt=None): + needed = [g.order() for g in G.generators] + return search([], needed, G.order(), alt=alt, profile=order_profile(G)) + + found = {} + + def finish_up(name, G): + found[name] = G + if print_report: + print("=" * 40) + print(f"{name}:") + print(G.generators) + + if S6TransitiveSubgroups.A4 in targets or S6TransitiveSubgroups.A4xC2 in targets: + A4_in_S6 = match_known_group(AlternatingGroup(4)) + finish_up(S6TransitiveSubgroups.A4, A4_in_S6) + + if S6TransitiveSubgroups.S4m in targets or S6TransitiveSubgroups.S4xC2 in targets: + S4m_in_S6 = match_known_group(SymmetricGroup(4), alt=False) + finish_up(S6TransitiveSubgroups.S4m, S4m_in_S6) + + if S6TransitiveSubgroups.S4p in targets: + S4p_in_S6 = match_known_group(SymmetricGroup(4), alt=True) + finish_up(S6TransitiveSubgroups.S4p, S4p_in_S6) + + if S6TransitiveSubgroups.A4xC2 in targets: + A4xC2_in_S6 = search(A4_in_S6.generators, [2], 24, anti_profile=order_profile(SymmetricGroup(4))) + finish_up(S6TransitiveSubgroups.A4xC2, A4xC2_in_S6) + + if S6TransitiveSubgroups.S4xC2 in targets: + S4xC2_in_S6 = search(S4m_in_S6.generators, [2], 48) + finish_up(S6TransitiveSubgroups.S4xC2, S4xC2_in_S6) + + # For the normal factor N = C3^2 in any of the G_n subgroups, we take one + # obvious instance of C3^2 in S6: + N_gens = [Permutation(5)(0, 1, 2), Permutation(5)(3, 4, 5)] + + if S6TransitiveSubgroups.G18 in targets: + G18_in_S6 = search(N_gens, [2], 18) + finish_up(S6TransitiveSubgroups.G18, G18_in_S6) + + if S6TransitiveSubgroups.G36m in targets: + G36m_in_S6 = search(N_gens, [2, 2], 36, alt=False) + finish_up(S6TransitiveSubgroups.G36m, G36m_in_S6) + + if S6TransitiveSubgroups.G36p in targets: + G36p_in_S6 = search(N_gens, [4], 36, alt=True) + finish_up(S6TransitiveSubgroups.G36p, G36p_in_S6) + + if S6TransitiveSubgroups.G72 in targets: + G72_in_S6 = search(N_gens, [4, 2], 72) + finish_up(S6TransitiveSubgroups.G72, G72_in_S6) + + # The PSL2(F5) and PGL2(F5) subgroups are isomorphic to A5 and S5, resp. + + if S6TransitiveSubgroups.PSL2F5 in targets: + PSL2F5_in_S6 = match_known_group(AlternatingGroup(5)) + finish_up(S6TransitiveSubgroups.PSL2F5, PSL2F5_in_S6) + + if S6TransitiveSubgroups.PGL2F5 in targets: + PGL2F5_in_S6 = match_known_group(SymmetricGroup(5)) + finish_up(S6TransitiveSubgroups.PGL2F5, PGL2F5_in_S6) + + # There is little need to "search" for any of the groups C6, S3, D6, A6, + # or S6, since they all have obvious realizations within S6. However, we + # support them here just in case a random representation is desired. + + if S6TransitiveSubgroups.C6 in targets: + C6 = match_known_group(CyclicGroup(6)) + finish_up(S6TransitiveSubgroups.C6, C6) + + if S6TransitiveSubgroups.S3 in targets: + S3 = match_known_group(SymmetricGroup(3)) + finish_up(S6TransitiveSubgroups.S3, S3) + + if S6TransitiveSubgroups.D6 in targets: + D6 = match_known_group(DihedralGroup(6)) + finish_up(S6TransitiveSubgroups.D6, D6) + + if S6TransitiveSubgroups.A6 in targets: + A6 = match_known_group(A6) + finish_up(S6TransitiveSubgroups.A6, A6) + + if S6TransitiveSubgroups.S6 in targets: + S6 = match_known_group(S6) + finish_up(S6TransitiveSubgroups.S6, S6) + + return found diff --git a/lib/python3.11/site-packages/sympy/combinatorics/generators.py b/lib/python3.11/site-packages/sympy/combinatorics/generators.py new file mode 100644 index 0000000000000000000000000000000000000000..9f136502d4e082e6c2554e7fb294d0036c5b0034 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/generators.py @@ -0,0 +1,302 @@ +from sympy.combinatorics.permutations import Permutation +from sympy.core.symbol import symbols +from sympy.matrices import Matrix +from sympy.utilities.iterables import variations, rotate_left + + +def symmetric(n): + """ + Generates the symmetric group of order n, Sn. + + Examples + ======== + + >>> from sympy.combinatorics.generators import symmetric + >>> list(symmetric(3)) + [(2), (1 2), (2)(0 1), (0 1 2), (0 2 1), (0 2)] + """ + for perm in variations(range(n), n): + yield Permutation(perm) + + +def cyclic(n): + """ + Generates the cyclic group of order n, Cn. + + Examples + ======== + + >>> from sympy.combinatorics.generators import cyclic + >>> list(cyclic(5)) + [(4), (0 1 2 3 4), (0 2 4 1 3), + (0 3 1 4 2), (0 4 3 2 1)] + + See Also + ======== + + dihedral + """ + gen = list(range(n)) + for i in range(n): + yield Permutation(gen) + gen = rotate_left(gen, 1) + + +def alternating(n): + """ + Generates the alternating group of order n, An. + + Examples + ======== + + >>> from sympy.combinatorics.generators import alternating + >>> list(alternating(3)) + [(2), (0 1 2), (0 2 1)] + """ + for perm in variations(range(n), n): + p = Permutation(perm) + if p.is_even: + yield p + + +def dihedral(n): + """ + Generates the dihedral group of order 2n, Dn. + + The result is given as a subgroup of Sn, except for the special cases n=1 + (the group S2) and n=2 (the Klein 4-group) where that's not possible + and embeddings in S2 and S4 respectively are given. + + Examples + ======== + + >>> from sympy.combinatorics.generators import dihedral + >>> list(dihedral(3)) + [(2), (0 2), (0 1 2), (1 2), (0 2 1), (2)(0 1)] + + See Also + ======== + + cyclic + """ + if n == 1: + yield Permutation([0, 1]) + yield Permutation([1, 0]) + elif n == 2: + yield Permutation([0, 1, 2, 3]) + yield Permutation([1, 0, 3, 2]) + yield Permutation([2, 3, 0, 1]) + yield Permutation([3, 2, 1, 0]) + else: + gen = list(range(n)) + for i in range(n): + yield Permutation(gen) + yield Permutation(gen[::-1]) + gen = rotate_left(gen, 1) + + +def rubik_cube_generators(): + """Return the permutations of the 3x3 Rubik's cube, see + https://www.gap-system.org/Doc/Examples/rubik.html + """ + a = [ + [(1, 3, 8, 6), (2, 5, 7, 4), (9, 33, 25, 17), (10, 34, 26, 18), + (11, 35, 27, 19)], + [(9, 11, 16, 14), (10, 13, 15, 12), (1, 17, 41, 40), (4, 20, 44, 37), + (6, 22, 46, 35)], + [(17, 19, 24, 22), (18, 21, 23, 20), (6, 25, 43, 16), (7, 28, 42, 13), + (8, 30, 41, 11)], + [(25, 27, 32, 30), (26, 29, 31, 28), (3, 38, 43, 19), (5, 36, 45, 21), + (8, 33, 48, 24)], + [(33, 35, 40, 38), (34, 37, 39, 36), (3, 9, 46, 32), (2, 12, 47, 29), + (1, 14, 48, 27)], + [(41, 43, 48, 46), (42, 45, 47, 44), (14, 22, 30, 38), + (15, 23, 31, 39), (16, 24, 32, 40)] + ] + return [Permutation([[i - 1 for i in xi] for xi in x], size=48) for x in a] + + +def rubik(n): + """Return permutations for an nxn Rubik's cube. + + Permutations returned are for rotation of each of the slice + from the face up to the last face for each of the 3 sides (in this order): + front, right and bottom. Hence, the first n - 1 permutations are for the + slices from the front. + """ + + if n < 2: + raise ValueError('dimension of cube must be > 1') + + # 1-based reference to rows and columns in Matrix + def getr(f, i): + return faces[f].col(n - i) + + def getl(f, i): + return faces[f].col(i - 1) + + def getu(f, i): + return faces[f].row(i - 1) + + def getd(f, i): + return faces[f].row(n - i) + + def setr(f, i, s): + faces[f][:, n - i] = Matrix(n, 1, s) + + def setl(f, i, s): + faces[f][:, i - 1] = Matrix(n, 1, s) + + def setu(f, i, s): + faces[f][i - 1, :] = Matrix(1, n, s) + + def setd(f, i, s): + faces[f][n - i, :] = Matrix(1, n, s) + + # motion of a single face + def cw(F, r=1): + for _ in range(r): + face = faces[F] + rv = [] + for c in range(n): + for r in range(n - 1, -1, -1): + rv.append(face[r, c]) + faces[F] = Matrix(n, n, rv) + + def ccw(F): + cw(F, 3) + + # motion of plane i from the F side; + # fcw(0) moves the F face, fcw(1) moves the plane + # just behind the front face, etc... + def fcw(i, r=1): + for _ in range(r): + if i == 0: + cw(F) + i += 1 + temp = getr(L, i) + setr(L, i, list(getu(D, i))) + setu(D, i, list(reversed(getl(R, i)))) + setl(R, i, list(getd(U, i))) + setd(U, i, list(reversed(temp))) + i -= 1 + + def fccw(i): + fcw(i, 3) + + # motion of the entire cube from the F side + def FCW(r=1): + for _ in range(r): + cw(F) + ccw(B) + cw(U) + t = faces[U] + cw(L) + faces[U] = faces[L] + cw(D) + faces[L] = faces[D] + cw(R) + faces[D] = faces[R] + faces[R] = t + + def FCCW(): + FCW(3) + + # motion of the entire cube from the U side + def UCW(r=1): + for _ in range(r): + cw(U) + ccw(D) + t = faces[F] + faces[F] = faces[R] + faces[R] = faces[B] + faces[B] = faces[L] + faces[L] = t + + def UCCW(): + UCW(3) + + # defining the permutations for the cube + + U, F, R, B, L, D = names = symbols('U, F, R, B, L, D') + + # the faces are represented by nxn matrices + faces = {} + count = 0 + for fi in range(6): + f = [] + for a in range(n**2): + f.append(count) + count += 1 + faces[names[fi]] = Matrix(n, n, f) + + # this will either return the value of the current permutation + # (show != 1) or else append the permutation to the group, g + def perm(show=0): + # add perm to the list of perms + p = [] + for f in names: + p.extend(faces[f]) + if show: + return p + g.append(Permutation(p)) + + g = [] # container for the group's permutations + I = list(range(6*n**2)) # the identity permutation used for checking + + # define permutations corresponding to cw rotations of the planes + # up TO the last plane from that direction; by not including the + # last plane, the orientation of the cube is maintained. + + # F slices + for i in range(n - 1): + fcw(i) + perm() + fccw(i) # restore + assert perm(1) == I + + # R slices + # bring R to front + UCW() + for i in range(n - 1): + fcw(i) + # put it back in place + UCCW() + # record + perm() + # restore + # bring face to front + UCW() + fccw(i) + # restore + UCCW() + assert perm(1) == I + + # D slices + # bring up bottom + FCW() + UCCW() + FCCW() + for i in range(n - 1): + # turn strip + fcw(i) + # put bottom back on the bottom + FCW() + UCW() + FCCW() + # record + perm() + # restore + # bring up bottom + FCW() + UCCW() + FCCW() + # turn strip + fccw(i) + # put bottom back on the bottom + FCW() + UCW() + FCCW() + assert perm(1) == I + + return g diff --git a/lib/python3.11/site-packages/sympy/combinatorics/graycode.py b/lib/python3.11/site-packages/sympy/combinatorics/graycode.py new file mode 100644 index 0000000000000000000000000000000000000000..930fd337862a70e920a985947d74375b27741293 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/graycode.py @@ -0,0 +1,430 @@ +from sympy.core import Basic, Integer + +import random + + +class GrayCode(Basic): + """ + A Gray code is essentially a Hamiltonian walk on + a n-dimensional cube with edge length of one. + The vertices of the cube are represented by vectors + whose values are binary. The Hamilton walk visits + each vertex exactly once. The Gray code for a 3d + cube is ['000','100','110','010','011','111','101', + '001']. + + A Gray code solves the problem of sequentially + generating all possible subsets of n objects in such + a way that each subset is obtained from the previous + one by either deleting or adding a single object. + In the above example, 1 indicates that the object is + present, and 0 indicates that its absent. + + Gray codes have applications in statistics as well when + we want to compute various statistics related to subsets + in an efficient manner. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> list(a.generate_gray()) + ['000', '001', '011', '010', '110', '111', '101', '100'] + >>> a = GrayCode(4) + >>> list(a.generate_gray()) + ['0000', '0001', '0011', '0010', '0110', '0111', '0101', '0100', \ + '1100', '1101', '1111', '1110', '1010', '1011', '1001', '1000'] + + References + ========== + + .. [1] Nijenhuis,A. and Wilf,H.S.(1978). + Combinatorial Algorithms. Academic Press. + .. [2] Knuth, D. (2011). The Art of Computer Programming, Vol 4 + Addison Wesley + + + """ + + _skip = False + _current = 0 + _rank = None + + def __new__(cls, n, *args, **kw_args): + """ + Default constructor. + + It takes a single argument ``n`` which gives the dimension of the Gray + code. The starting Gray code string (``start``) or the starting ``rank`` + may also be given; the default is to start at rank = 0 ('0...0'). + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> a + GrayCode(3) + >>> a.n + 3 + + >>> a = GrayCode(3, start='100') + >>> a.current + '100' + + >>> a = GrayCode(4, rank=4) + >>> a.current + '0110' + >>> a.rank + 4 + + """ + if n < 1 or int(n) != n: + raise ValueError( + 'Gray code dimension must be a positive integer, not %i' % n) + n = Integer(n) + args = (n,) + args + obj = Basic.__new__(cls, *args) + if 'start' in kw_args: + obj._current = kw_args["start"] + if len(obj._current) > n: + raise ValueError('Gray code start has length %i but ' + 'should not be greater than %i' % (len(obj._current), n)) + elif 'rank' in kw_args: + if int(kw_args["rank"]) != kw_args["rank"]: + raise ValueError('Gray code rank must be a positive integer, ' + 'not %i' % kw_args["rank"]) + obj._rank = int(kw_args["rank"]) % obj.selections + obj._current = obj.unrank(n, obj._rank) + return obj + + def next(self, delta=1): + """ + Returns the Gray code a distance ``delta`` (default = 1) from the + current value in canonical order. + + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3, start='110') + >>> a.next().current + '111' + >>> a.next(-1).current + '010' + """ + return GrayCode(self.n, rank=(self.rank + delta) % self.selections) + + @property + def selections(self): + """ + Returns the number of bit vectors in the Gray code. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> a.selections + 8 + """ + return 2**self.n + + @property + def n(self): + """ + Returns the dimension of the Gray code. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(5) + >>> a.n + 5 + """ + return self.args[0] + + def generate_gray(self, **hints): + """ + Generates the sequence of bit vectors of a Gray Code. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> list(a.generate_gray()) + ['000', '001', '011', '010', '110', '111', '101', '100'] + >>> list(a.generate_gray(start='011')) + ['011', '010', '110', '111', '101', '100'] + >>> list(a.generate_gray(rank=4)) + ['110', '111', '101', '100'] + + See Also + ======== + + skip + + References + ========== + + .. [1] Knuth, D. (2011). The Art of Computer Programming, + Vol 4, Addison Wesley + + """ + bits = self.n + start = None + if "start" in hints: + start = hints["start"] + elif "rank" in hints: + start = GrayCode.unrank(self.n, hints["rank"]) + if start is not None: + self._current = start + current = self.current + graycode_bin = gray_to_bin(current) + if len(graycode_bin) > self.n: + raise ValueError('Gray code start has length %i but should ' + 'not be greater than %i' % (len(graycode_bin), bits)) + self._current = int(current, 2) + graycode_int = int(''.join(graycode_bin), 2) + for i in range(graycode_int, 1 << bits): + if self._skip: + self._skip = False + else: + yield self.current + bbtc = (i ^ (i + 1)) + gbtc = (bbtc ^ (bbtc >> 1)) + self._current = (self._current ^ gbtc) + self._current = 0 + + def skip(self): + """ + Skips the bit generation. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> for i in a.generate_gray(): + ... if i == '010': + ... a.skip() + ... print(i) + ... + 000 + 001 + 011 + 010 + 111 + 101 + 100 + + See Also + ======== + + generate_gray + """ + self._skip = True + + @property + def rank(self): + """ + Ranks the Gray code. + + A ranking algorithm determines the position (or rank) + of a combinatorial object among all the objects w.r.t. + a given order. For example, the 4 bit binary reflected + Gray code (BRGC) '0101' has a rank of 6 as it appears in + the 6th position in the canonical ordering of the family + of 4 bit Gray codes. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> a = GrayCode(3) + >>> list(a.generate_gray()) + ['000', '001', '011', '010', '110', '111', '101', '100'] + >>> GrayCode(3, start='100').rank + 7 + >>> GrayCode(3, rank=7).current + '100' + + See Also + ======== + + unrank + + References + ========== + + .. [1] https://web.archive.org/web/20200224064753/http://statweb.stanford.edu/~susan/courses/s208/node12.html + + """ + if self._rank is None: + self._rank = int(gray_to_bin(self.current), 2) + return self._rank + + @property + def current(self): + """ + Returns the currently referenced Gray code as a bit string. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> GrayCode(3, start='100').current + '100' + """ + rv = self._current or '0' + if not isinstance(rv, str): + rv = bin(rv)[2:] + return rv.rjust(self.n, '0') + + @classmethod + def unrank(self, n, rank): + """ + Unranks an n-bit sized Gray code of rank k. This method exists + so that a derivative GrayCode class can define its own code of + a given rank. + + The string here is generated in reverse order to allow for tail-call + optimization. + + Examples + ======== + + >>> from sympy.combinatorics import GrayCode + >>> GrayCode(5, rank=3).current + '00010' + >>> GrayCode.unrank(5, 3) + '00010' + + See Also + ======== + + rank + """ + def _unrank(k, n): + if n == 1: + return str(k % 2) + m = 2**(n - 1) + if k < m: + return '0' + _unrank(k, n - 1) + return '1' + _unrank(m - (k % m) - 1, n - 1) + return _unrank(rank, n) + + +def random_bitstring(n): + """ + Generates a random bitlist of length n. + + Examples + ======== + + >>> from sympy.combinatorics.graycode import random_bitstring + >>> random_bitstring(3) # doctest: +SKIP + 100 + """ + return ''.join([random.choice('01') for i in range(n)]) + + +def gray_to_bin(bin_list): + """ + Convert from Gray coding to binary coding. + + We assume big endian encoding. + + Examples + ======== + + >>> from sympy.combinatorics.graycode import gray_to_bin + >>> gray_to_bin('100') + '111' + + See Also + ======== + + bin_to_gray + """ + b = [bin_list[0]] + for i in range(1, len(bin_list)): + b += str(int(b[i - 1] != bin_list[i])) + return ''.join(b) + + +def bin_to_gray(bin_list): + """ + Convert from binary coding to gray coding. + + We assume big endian encoding. + + Examples + ======== + + >>> from sympy.combinatorics.graycode import bin_to_gray + >>> bin_to_gray('111') + '100' + + See Also + ======== + + gray_to_bin + """ + b = [bin_list[0]] + for i in range(1, len(bin_list)): + b += str(int(bin_list[i]) ^ int(bin_list[i - 1])) + return ''.join(b) + + +def get_subset_from_bitstring(super_set, bitstring): + """ + Gets the subset defined by the bitstring. + + Examples + ======== + + >>> from sympy.combinatorics.graycode import get_subset_from_bitstring + >>> get_subset_from_bitstring(['a', 'b', 'c', 'd'], '0011') + ['c', 'd'] + >>> get_subset_from_bitstring(['c', 'a', 'c', 'c'], '1100') + ['c', 'a'] + + See Also + ======== + + graycode_subsets + """ + if len(super_set) != len(bitstring): + raise ValueError("The sizes of the lists are not equal") + return [super_set[i] for i, j in enumerate(bitstring) + if bitstring[i] == '1'] + + +def graycode_subsets(gray_code_set): + """ + Generates the subsets as enumerated by a Gray code. + + Examples + ======== + + >>> from sympy.combinatorics.graycode import graycode_subsets + >>> list(graycode_subsets(['a', 'b', 'c'])) + [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], \ + ['a', 'c'], ['a']] + >>> list(graycode_subsets(['a', 'b', 'c', 'c'])) + [[], ['c'], ['c', 'c'], ['c'], ['b', 'c'], ['b', 'c', 'c'], \ + ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], ['a', 'b', 'c', 'c'], \ + ['a', 'b', 'c'], ['a', 'c'], ['a', 'c', 'c'], ['a', 'c'], ['a']] + + See Also + ======== + + get_subset_from_bitstring + """ + for bitstring in list(GrayCode(len(gray_code_set)).generate_gray()): + yield get_subset_from_bitstring(gray_code_set, bitstring) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/group_constructs.py b/lib/python3.11/site-packages/sympy/combinatorics/group_constructs.py new file mode 100644 index 0000000000000000000000000000000000000000..a5c16ec254191646b26eee869763e2926e187da5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/group_constructs.py @@ -0,0 +1,61 @@ +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.combinatorics.permutations import Permutation +from sympy.utilities.iterables import uniq + +_af_new = Permutation._af_new + + +def DirectProduct(*groups): + """ + Returns the direct product of several groups as a permutation group. + + Explanation + =========== + + This is implemented much like the __mul__ procedure for taking the direct + product of two permutation groups, but the idea of shifting the + generators is realized in the case of an arbitrary number of groups. + A call to DirectProduct(G1, G2, ..., Gn) is generally expected to be faster + than a call to G1*G2*...*Gn (and thus the need for this algorithm). + + Examples + ======== + + >>> from sympy.combinatorics.group_constructs import DirectProduct + >>> from sympy.combinatorics.named_groups import CyclicGroup + >>> C = CyclicGroup(4) + >>> G = DirectProduct(C, C, C) + >>> G.order() + 64 + + See Also + ======== + + sympy.combinatorics.perm_groups.PermutationGroup.__mul__ + + """ + degrees = [] + gens_count = [] + total_degree = 0 + total_gens = 0 + for group in groups: + current_deg = group.degree + current_num_gens = len(group.generators) + degrees.append(current_deg) + total_degree += current_deg + gens_count.append(current_num_gens) + total_gens += current_num_gens + array_gens = [] + for i in range(total_gens): + array_gens.append(list(range(total_degree))) + current_gen = 0 + current_deg = 0 + for i in range(len(gens_count)): + for j in range(current_gen, current_gen + gens_count[i]): + gen = ((groups[i].generators)[j - current_gen]).array_form + array_gens[j][current_deg:current_deg + degrees[i]] = \ + [x + current_deg for x in gen] + current_gen += gens_count[i] + current_deg += degrees[i] + perm_gens = list(uniq([_af_new(list(a)) for a in array_gens])) + return PermutationGroup(perm_gens, dups=False) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/group_numbers.py b/lib/python3.11/site-packages/sympy/combinatorics/group_numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..6c81b0ee4fa1f98e4fad04207dd683cccbdb4eb3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/group_numbers.py @@ -0,0 +1,296 @@ +from itertools import chain, combinations + +from sympy.external.gmpy import gcd +from sympy.ntheory.factor_ import factorint +from sympy.utilities.misc import as_int + + +def _is_nilpotent_number(factors: dict) -> bool: + """ Check whether `n` is a nilpotent number. + Note that ``factors`` is a prime factorization of `n`. + + This is a low-level helper for ``is_nilpotent_number``, for internal use. + """ + for p in factors.keys(): + for q, e in factors.items(): + # We want to calculate + # any(pow(q, k, p) == 1 for k in range(1, e + 1)) + m = 1 + for _ in range(e): + m = m*q % p + if m == 1: + return False + return True + + +def is_nilpotent_number(n) -> bool: + """ + Check whether `n` is a nilpotent number. A number `n` is said to be + nilpotent if and only if every finite group of order `n` is nilpotent. + For more information see [1]_. + + Examples + ======== + + >>> from sympy.combinatorics.group_numbers import is_nilpotent_number + >>> from sympy import randprime + >>> is_nilpotent_number(21) + False + >>> is_nilpotent_number(randprime(1, 30)**12) + True + + References + ========== + + .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers, + The American Mathematical Monthly, 107(7), 631-634. + .. [2] https://oeis.org/A056867 + + """ + n = as_int(n) + if n <= 0: + raise ValueError("n must be a positive integer, not %i" % n) + return _is_nilpotent_number(factorint(n)) + + +def is_abelian_number(n) -> bool: + """ + Check whether `n` is an abelian number. A number `n` is said to be abelian + if and only if every finite group of order `n` is abelian. For more + information see [1]_. + + Examples + ======== + + >>> from sympy.combinatorics.group_numbers import is_abelian_number + >>> from sympy import randprime + >>> is_abelian_number(4) + True + >>> is_abelian_number(randprime(1, 2000)**2) + True + >>> is_abelian_number(60) + False + + References + ========== + + .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers, + The American Mathematical Monthly, 107(7), 631-634. + .. [2] https://oeis.org/A051532 + + """ + n = as_int(n) + if n <= 0: + raise ValueError("n must be a positive integer, not %i" % n) + factors = factorint(n) + return all(e < 3 for e in factors.values()) and _is_nilpotent_number(factors) + + +def is_cyclic_number(n) -> bool: + """ + Check whether `n` is a cyclic number. A number `n` is said to be cyclic + if and only if every finite group of order `n` is cyclic. For more + information see [1]_. + + Examples + ======== + + >>> from sympy.combinatorics.group_numbers import is_cyclic_number + >>> from sympy import randprime + >>> is_cyclic_number(15) + True + >>> is_cyclic_number(randprime(1, 2000)**2) + False + >>> is_cyclic_number(4) + False + + References + ========== + + .. [1] Pakianathan, J., Shankar, K., Nilpotent Numbers, + The American Mathematical Monthly, 107(7), 631-634. + .. [2] https://oeis.org/A003277 + + """ + n = as_int(n) + if n <= 0: + raise ValueError("n must be a positive integer, not %i" % n) + factors = factorint(n) + return all(e == 1 for e in factors.values()) and _is_nilpotent_number(factors) + + +def _holder_formula(prime_factors): + r""" Number of groups of order `n`. + where `n` is squarefree and its prime factors are ``prime_factors``. + i.e., ``n == math.prod(prime_factors)`` + + Explanation + =========== + + When `n` is squarefree, the number of groups of order `n` is expressed by + + .. math :: + \sum_{d \mid n} \prod_p \frac{p^{c(p, d)} - 1}{p - 1} + + where `n=de`, `p` is the prime factor of `e`, + and `c(p, d)` is the number of prime factors `q` of `d` such that `q \equiv 1 \pmod{p}` [2]_. + + The formula is elegant, but can be improved when implemented as an algorithm. + Since `n` is assumed to be squarefree, the divisor `d` of `n` can be identified with the power set of prime factors. + We let `N` be the set of prime factors of `n`. + `F = \{p \in N : \forall q \in N, q \not\equiv 1 \pmod{p} \}, M = N \setminus F`, we have the following. + + .. math :: + \sum_{d \in 2^{M}} \prod_{p \in M \setminus d} \frac{p^{c(p, F \cup d)} - 1}{p - 1} + + Practically, many prime factors are expected to be members of `F`, thus reducing computation time. + + Parameters + ========== + + prime_factors : set + The set of prime factors of ``n``. where `n` is squarefree. + + Returns + ======= + + int : Number of groups of order ``n`` + + Examples + ======== + + >>> from sympy.combinatorics.group_numbers import _holder_formula + >>> _holder_formula({2}) # n = 2 + 1 + >>> _holder_formula({2, 3}) # n = 2*3 = 6 + 2 + + See Also + ======== + + groups_count + + References + ========== + + .. [1] Otto Holder, Die Gruppen der Ordnungen p^3, pq^2, pqr, p^4, + Math. Ann. 43 pp. 301-412 (1893). + http://dx.doi.org/10.1007/BF01443651 + .. [2] John H. Conway, Heiko Dietrich and E.A. O'Brien, + Counting groups: gnus, moas and other exotica + The Mathematical Intelligencer 30, 6-15 (2008) + https://doi.org/10.1007/BF02985731 + + """ + F = {p for p in prime_factors if all(q % p != 1 for q in prime_factors)} + M = prime_factors - F + + s = 0 + powerset = chain.from_iterable(combinations(M, r) for r in range(len(M)+1)) + for ps in powerset: + ps = set(ps) + prod = 1 + for p in M - ps: + c = len([q for q in F | ps if q % p == 1]) + prod *= (p**c - 1) // (p - 1) + if not prod: + break + s += prod + return s + + +def groups_count(n): + r""" Number of groups of order `n`. + In [1]_, ``gnu(n)`` is given, so we follow this notation here as well. + + Parameters + ========== + + n : Integer + ``n`` is a positive integer + + Returns + ======= + + int : ``gnu(n)`` + + Raises + ====== + + ValueError + Number of groups of order ``n`` is unknown or not implemented. + For example, gnu(`2^{11}`) is not yet known. + On the other hand, gnu(12) is known to be 5, + but this has not yet been implemented in this function. + + Examples + ======== + + >>> from sympy.combinatorics.group_numbers import groups_count + >>> groups_count(3) # There is only one cyclic group of order 3 + 1 + >>> # There are two groups of order 10: the cyclic group and the dihedral group + >>> groups_count(10) + 2 + + See Also + ======== + + is_cyclic_number + `n` is cyclic iff gnu(n) = 1 + + References + ========== + + .. [1] John H. Conway, Heiko Dietrich and E.A. O'Brien, + Counting groups: gnus, moas and other exotica + The Mathematical Intelligencer 30, 6-15 (2008) + https://doi.org/10.1007/BF02985731 + .. [2] https://oeis.org/A000001 + + """ + n = as_int(n) + if n <= 0: + raise ValueError("n must be a positive integer, not %i" % n) + factors = factorint(n) + if len(factors) == 1: + (p, e) = list(factors.items())[0] + if p == 2: + A000679 = [1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289] + if e < len(A000679): + return A000679[e] + if p == 3: + A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645] + if e < len(A090091): + return A090091[e] + if e <= 2: # gnu(p) = 1, gnu(p**2) = 2 + return e + if e == 3: # gnu(p**3) = 5 + return 5 + if e == 4: # if p is an odd prime, gnu(p**4) = 15 + return 15 + if e == 5: # if p >= 5, gnu(p**5) is expressed by the following equation + return 61 + 2*p + 2*gcd(p-1, 3) + gcd(p-1, 4) + if e == 6: # if p >= 6, gnu(p**6) is expressed by the following equation + return 3*p**2 + 39*p + 344 +\ + 24*gcd(p-1, 3) + 11*gcd(p-1, 4) + 2*gcd(p-1, 5) + if e == 7: # if p >= 7, gnu(p**7) is expressed by the following equation + if p == 5: + return 34297 + return 3*p**5 + 12*p**4 + 44*p**3 + 170*p**2 + 707*p + 2455 +\ + (4*p**2 + 44*p + 291)*gcd(p-1, 3) + (p**2 + 19*p + 135)*gcd(p-1, 4) + \ + (3*p + 31)*gcd(p-1, 5) + 4*gcd(p-1, 7) + 5*gcd(p-1, 8) + gcd(p-1, 9) + if any(e > 1 for e in factors.values()): # n is not squarefree + # some known values for small n that have more than 1 factor and are not square free (https://oeis.org/A000001) + small = {12: 5, 18: 5, 20: 5, 24: 15, 28: 4, 36: 14, 40: 14, 44: 4, 45: 2, 48: 52, + 50: 5, 52: 5, 54: 15, 56: 13, 60: 13, 63: 4, 68: 5, 72: 50, 75: 3, 76: 4, + 80: 52, 84: 15, 88: 12, 90: 10, 92: 4} + if n in small: + return small[n] + raise ValueError("Number of groups of order n is unknown or not implemented") + if len(factors) == 2: # n is squarefree semiprime + p, q = list(factors.keys()) + if p > q: + p, q = q, p + return 2 if q % p == 1 else 1 + return _holder_formula(set(factors.keys())) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/homomorphisms.py b/lib/python3.11/site-packages/sympy/combinatorics/homomorphisms.py new file mode 100644 index 0000000000000000000000000000000000000000..256f56b3aa7c5404d332f42e37d4f1117ea81db7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/homomorphisms.py @@ -0,0 +1,549 @@ +import itertools +from sympy.combinatorics.fp_groups import FpGroup, FpSubgroup, simplify_presentation +from sympy.combinatorics.free_groups import FreeGroup +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.core.intfunc import igcd +from sympy.functions.combinatorial.numbers import totient +from sympy.core.singleton import S + +class GroupHomomorphism: + ''' + A class representing group homomorphisms. Instantiate using `homomorphism()`. + + References + ========== + + .. [1] Holt, D., Eick, B. and O'Brien, E. (2005). Handbook of computational group theory. + + ''' + + def __init__(self, domain, codomain, images): + self.domain = domain + self.codomain = codomain + self.images = images + self._inverses = None + self._kernel = None + self._image = None + + def _invs(self): + ''' + Return a dictionary with `{gen: inverse}` where `gen` is a rewriting + generator of `codomain` (e.g. strong generator for permutation groups) + and `inverse` is an element of its preimage + + ''' + image = self.image() + inverses = {} + for k in list(self.images.keys()): + v = self.images[k] + if not (v in inverses + or v.is_identity): + inverses[v] = k + if isinstance(self.codomain, PermutationGroup): + gens = image.strong_gens + else: + gens = image.generators + for g in gens: + if g in inverses or g.is_identity: + continue + w = self.domain.identity + if isinstance(self.codomain, PermutationGroup): + parts = image._strong_gens_slp[g][::-1] + else: + parts = g + for s in parts: + if s in inverses: + w = w*inverses[s] + else: + w = w*inverses[s**-1]**-1 + inverses[g] = w + + return inverses + + def invert(self, g): + ''' + Return an element of the preimage of ``g`` or of each element + of ``g`` if ``g`` is a list. + + Explanation + =========== + + If the codomain is an FpGroup, the inverse for equal + elements might not always be the same unless the FpGroup's + rewriting system is confluent. However, making a system + confluent can be time-consuming. If it's important, try + `self.codomain.make_confluent()` first. + + ''' + from sympy.combinatorics import Permutation + from sympy.combinatorics.free_groups import FreeGroupElement + if isinstance(g, (Permutation, FreeGroupElement)): + if isinstance(self.codomain, FpGroup): + g = self.codomain.reduce(g) + if self._inverses is None: + self._inverses = self._invs() + image = self.image() + w = self.domain.identity + if isinstance(self.codomain, PermutationGroup): + gens = image.generator_product(g)[::-1] + else: + gens = g + # the following can't be "for s in gens:" + # because that would be equivalent to + # "for s in gens.array_form:" when g is + # a FreeGroupElement. On the other hand, + # when you call gens by index, the generator + # (or inverse) at position i is returned. + for i in range(len(gens)): + s = gens[i] + if s.is_identity: + continue + if s in self._inverses: + w = w*self._inverses[s] + else: + w = w*self._inverses[s**-1]**-1 + return w + elif isinstance(g, list): + return [self.invert(e) for e in g] + + def kernel(self): + ''' + Compute the kernel of `self`. + + ''' + if self._kernel is None: + self._kernel = self._compute_kernel() + return self._kernel + + def _compute_kernel(self): + G = self.domain + G_order = G.order() + if G_order is S.Infinity: + raise NotImplementedError( + "Kernel computation is not implemented for infinite groups") + gens = [] + if isinstance(G, PermutationGroup): + K = PermutationGroup(G.identity) + else: + K = FpSubgroup(G, gens, normal=True) + i = self.image().order() + while K.order()*i != G_order: + r = G.random() + k = r*self.invert(self(r))**-1 + if k not in K: + gens.append(k) + if isinstance(G, PermutationGroup): + K = PermutationGroup(gens) + else: + K = FpSubgroup(G, gens, normal=True) + return K + + def image(self): + ''' + Compute the image of `self`. + + ''' + if self._image is None: + values = list(set(self.images.values())) + if isinstance(self.codomain, PermutationGroup): + self._image = self.codomain.subgroup(values) + else: + self._image = FpSubgroup(self.codomain, values) + return self._image + + def _apply(self, elem): + ''' + Apply `self` to `elem`. + + ''' + if elem not in self.domain: + if isinstance(elem, (list, tuple)): + return [self._apply(e) for e in elem] + raise ValueError("The supplied element does not belong to the domain") + if elem.is_identity: + return self.codomain.identity + else: + images = self.images + value = self.codomain.identity + if isinstance(self.domain, PermutationGroup): + gens = self.domain.generator_product(elem, original=True) + for g in gens: + if g in self.images: + value = images[g]*value + else: + value = images[g**-1]**-1*value + else: + i = 0 + for _, p in elem.array_form: + if p < 0: + g = elem[i]**-1 + else: + g = elem[i] + value = value*images[g]**p + i += abs(p) + return value + + def __call__(self, elem): + return self._apply(elem) + + def is_injective(self): + ''' + Check if the homomorphism is injective + + ''' + return self.kernel().order() == 1 + + def is_surjective(self): + ''' + Check if the homomorphism is surjective + + ''' + im = self.image().order() + oth = self.codomain.order() + if im is S.Infinity and oth is S.Infinity: + return None + else: + return im == oth + + def is_isomorphism(self): + ''' + Check if `self` is an isomorphism. + + ''' + return self.is_injective() and self.is_surjective() + + def is_trivial(self): + ''' + Check is `self` is a trivial homomorphism, i.e. all elements + are mapped to the identity. + + ''' + return self.image().order() == 1 + + def compose(self, other): + ''' + Return the composition of `self` and `other`, i.e. + the homomorphism phi such that for all g in the domain + of `other`, phi(g) = self(other(g)) + + ''' + if not other.image().is_subgroup(self.domain): + raise ValueError("The image of `other` must be a subgroup of " + "the domain of `self`") + images = {g: self(other(g)) for g in other.images} + return GroupHomomorphism(other.domain, self.codomain, images) + + def restrict_to(self, H): + ''' + Return the restriction of the homomorphism to the subgroup `H` + of the domain. + + ''' + if not isinstance(H, PermutationGroup) or not H.is_subgroup(self.domain): + raise ValueError("Given H is not a subgroup of the domain") + domain = H + images = {g: self(g) for g in H.generators} + return GroupHomomorphism(domain, self.codomain, images) + + def invert_subgroup(self, H): + ''' + Return the subgroup of the domain that is the inverse image + of the subgroup ``H`` of the homomorphism image + + ''' + if not H.is_subgroup(self.image()): + raise ValueError("Given H is not a subgroup of the image") + gens = [] + P = PermutationGroup(self.image().identity) + for h in H.generators: + h_i = self.invert(h) + if h_i not in P: + gens.append(h_i) + P = PermutationGroup(gens) + for k in self.kernel().generators: + if k*h_i not in P: + gens.append(k*h_i) + P = PermutationGroup(gens) + return P + +def homomorphism(domain, codomain, gens, images=(), check=True): + ''' + Create (if possible) a group homomorphism from the group ``domain`` + to the group ``codomain`` defined by the images of the domain's + generators ``gens``. ``gens`` and ``images`` can be either lists or tuples + of equal sizes. If ``gens`` is a proper subset of the group's generators, + the unspecified generators will be mapped to the identity. If the + images are not specified, a trivial homomorphism will be created. + + If the given images of the generators do not define a homomorphism, + an exception is raised. + + If ``check`` is ``False``, do not check whether the given images actually + define a homomorphism. + + ''' + if not isinstance(domain, (PermutationGroup, FpGroup, FreeGroup)): + raise TypeError("The domain must be a group") + if not isinstance(codomain, (PermutationGroup, FpGroup, FreeGroup)): + raise TypeError("The codomain must be a group") + + generators = domain.generators + if not all(g in generators for g in gens): + raise ValueError("The supplied generators must be a subset of the domain's generators") + if not all(g in codomain for g in images): + raise ValueError("The images must be elements of the codomain") + + if images and len(images) != len(gens): + raise ValueError("The number of images must be equal to the number of generators") + + gens = list(gens) + images = list(images) + + images.extend([codomain.identity]*(len(generators)-len(images))) + gens.extend([g for g in generators if g not in gens]) + images = dict(zip(gens,images)) + + if check and not _check_homomorphism(domain, codomain, images): + raise ValueError("The given images do not define a homomorphism") + return GroupHomomorphism(domain, codomain, images) + +def _check_homomorphism(domain, codomain, images): + """ + Check that a given mapping of generators to images defines a homomorphism. + + Parameters + ========== + domain : PermutationGroup, FpGroup, FreeGroup + codomain : PermutationGroup, FpGroup, FreeGroup + images : dict + The set of keys must be equal to domain.generators. + The values must be elements of the codomain. + + """ + pres = domain if hasattr(domain, 'relators') else domain.presentation() + rels = pres.relators + gens = pres.generators + symbols = [g.ext_rep[0] for g in gens] + symbols_to_domain_generators = dict(zip(symbols, domain.generators)) + identity = codomain.identity + + def _image(r): + w = identity + for symbol, power in r.array_form: + g = symbols_to_domain_generators[symbol] + w *= images[g]**power + return w + + for r in rels: + if isinstance(codomain, FpGroup): + s = codomain.equals(_image(r), identity) + if s is None: + # only try to make the rewriting system + # confluent when it can't determine the + # truth of equality otherwise + success = codomain.make_confluent() + s = codomain.equals(_image(r), identity) + if s is None and not success: + raise RuntimeError("Can't determine if the images " + "define a homomorphism. Try increasing " + "the maximum number of rewriting rules " + "(group._rewriting_system.set_max(new_value); " + "the current value is stored in group._rewriting" + "_system.maxeqns)") + else: + s = _image(r).is_identity + if not s: + return False + return True + +def orbit_homomorphism(group, omega): + ''' + Return the homomorphism induced by the action of the permutation + group ``group`` on the set ``omega`` that is closed under the action. + + ''' + from sympy.combinatorics import Permutation + from sympy.combinatorics.named_groups import SymmetricGroup + codomain = SymmetricGroup(len(omega)) + identity = codomain.identity + omega = list(omega) + images = {g: identity*Permutation([omega.index(o^g) for o in omega]) for g in group.generators} + group._schreier_sims(base=omega) + H = GroupHomomorphism(group, codomain, images) + if len(group.basic_stabilizers) > len(omega): + H._kernel = group.basic_stabilizers[len(omega)] + else: + H._kernel = PermutationGroup([group.identity]) + return H + +def block_homomorphism(group, blocks): + ''' + Return the homomorphism induced by the action of the permutation + group ``group`` on the block system ``blocks``. The latter should be + of the same form as returned by the ``minimal_block`` method for + permutation groups, namely a list of length ``group.degree`` where + the i-th entry is a representative of the block i belongs to. + + ''' + from sympy.combinatorics import Permutation + from sympy.combinatorics.named_groups import SymmetricGroup + + n = len(blocks) + + # number the blocks; m is the total number, + # b is such that b[i] is the number of the block i belongs to, + # p is the list of length m such that p[i] is the representative + # of the i-th block + m = 0 + p = [] + b = [None]*n + for i in range(n): + if blocks[i] == i: + p.append(i) + b[i] = m + m += 1 + for i in range(n): + b[i] = b[blocks[i]] + + codomain = SymmetricGroup(m) + # the list corresponding to the identity permutation in codomain + identity = range(m) + images = {g: Permutation([b[p[i]^g] for i in identity]) for g in group.generators} + H = GroupHomomorphism(group, codomain, images) + return H + +def group_isomorphism(G, H, isomorphism=True): + ''' + Compute an isomorphism between 2 given groups. + + Parameters + ========== + + G : A finite ``FpGroup`` or a ``PermutationGroup``. + First group. + + H : A finite ``FpGroup`` or a ``PermutationGroup`` + Second group. + + isomorphism : bool + This is used to avoid the computation of homomorphism + when the user only wants to check if there exists + an isomorphism between the groups. + + Returns + ======= + + If isomorphism = False -- Returns a boolean. + If isomorphism = True -- Returns a boolean and an isomorphism between `G` and `H`. + + Examples + ======== + + >>> from sympy.combinatorics import free_group, Permutation + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> from sympy.combinatorics.fp_groups import FpGroup + >>> from sympy.combinatorics.homomorphisms import group_isomorphism + >>> from sympy.combinatorics.named_groups import DihedralGroup, AlternatingGroup + + >>> D = DihedralGroup(8) + >>> p = Permutation(0, 1, 2, 3, 4, 5, 6, 7) + >>> P = PermutationGroup(p) + >>> group_isomorphism(D, P) + (False, None) + + >>> F, a, b = free_group("a, b") + >>> G = FpGroup(F, [a**3, b**3, (a*b)**2]) + >>> H = AlternatingGroup(4) + >>> (check, T) = group_isomorphism(G, H) + >>> check + True + >>> T(b*a*b**-1*a**-1*b**-1) + (0 2 3) + + Notes + ===== + + Uses the approach suggested by Robert Tarjan to compute the isomorphism between two groups. + First, the generators of ``G`` are mapped to the elements of ``H`` and + we check if the mapping induces an isomorphism. + + ''' + if not isinstance(G, (PermutationGroup, FpGroup)): + raise TypeError("The group must be a PermutationGroup or an FpGroup") + if not isinstance(H, (PermutationGroup, FpGroup)): + raise TypeError("The group must be a PermutationGroup or an FpGroup") + + if isinstance(G, FpGroup) and isinstance(H, FpGroup): + G = simplify_presentation(G) + H = simplify_presentation(H) + # Two infinite FpGroups with the same generators are isomorphic + # when the relators are same but are ordered differently. + if G.generators == H.generators and (G.relators).sort() == (H.relators).sort(): + if not isomorphism: + return True + return (True, homomorphism(G, H, G.generators, H.generators)) + + # `_H` is the permutation group isomorphic to `H`. + _H = H + g_order = G.order() + h_order = H.order() + + if g_order is S.Infinity: + raise NotImplementedError("Isomorphism methods are not implemented for infinite groups.") + + if isinstance(H, FpGroup): + if h_order is S.Infinity: + raise NotImplementedError("Isomorphism methods are not implemented for infinite groups.") + _H, h_isomorphism = H._to_perm_group() + + if (g_order != h_order) or (G.is_abelian != H.is_abelian): + if not isomorphism: + return False + return (False, None) + + if not isomorphism: + # Two groups of the same cyclic numbered order + # are isomorphic to each other. + n = g_order + if (igcd(n, totient(n))) == 1: + return True + + # Match the generators of `G` with subsets of `_H` + gens = list(G.generators) + for subset in itertools.permutations(_H, len(gens)): + images = list(subset) + images.extend([_H.identity]*(len(G.generators)-len(images))) + _images = dict(zip(gens,images)) + if _check_homomorphism(G, _H, _images): + if isinstance(H, FpGroup): + images = h_isomorphism.invert(images) + T = homomorphism(G, H, G.generators, images, check=False) + if T.is_isomorphism(): + # It is a valid isomorphism + if not isomorphism: + return True + return (True, T) + + if not isomorphism: + return False + return (False, None) + +def is_isomorphic(G, H): + ''' + Check if the groups are isomorphic to each other + + Parameters + ========== + + G : A finite ``FpGroup`` or a ``PermutationGroup`` + First group. + + H : A finite ``FpGroup`` or a ``PermutationGroup`` + Second group. + + Returns + ======= + + boolean + ''' + return group_isomorphism(G, H, isomorphism=False) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/named_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/named_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..59f10c40ef716e3b644e00f936323e9f6936eb88 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/named_groups.py @@ -0,0 +1,332 @@ +from sympy.combinatorics.group_constructs import DirectProduct +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.combinatorics.permutations import Permutation + +_af_new = Permutation._af_new + + +def AbelianGroup(*cyclic_orders): + """ + Returns the direct product of cyclic groups with the given orders. + + Explanation + =========== + + According to the structure theorem for finite abelian groups ([1]), + every finite abelian group can be written as the direct product of + finitely many cyclic groups. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AbelianGroup + >>> AbelianGroup(3, 4) + PermutationGroup([ + (6)(0 1 2), + (3 4 5 6)]) + >>> _.is_group + True + + See Also + ======== + + DirectProduct + + References + ========== + + .. [1] https://groupprops.subwiki.org/wiki/Structure_theorem_for_finitely_generated_abelian_groups + + """ + groups = [] + degree = 0 + order = 1 + for size in cyclic_orders: + degree += size + order *= size + groups.append(CyclicGroup(size)) + G = DirectProduct(*groups) + G._is_abelian = True + G._degree = degree + G._order = order + + return G + + +def AlternatingGroup(n): + """ + Generates the alternating group on ``n`` elements as a permutation group. + + Explanation + =========== + + For ``n > 2``, the generators taken are ``(0 1 2), (0 1 2 ... n-1)`` for + ``n`` odd + and ``(0 1 2), (1 2 ... n-1)`` for ``n`` even (See [1], p.31, ex.6.9.). + After the group is generated, some of its basic properties are set. + The cases ``n = 1, 2`` are handled separately. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> G = AlternatingGroup(4) + >>> G.is_group + True + >>> a = list(G.generate_dimino()) + >>> len(a) + 12 + >>> all(perm.is_even for perm in a) + True + + See Also + ======== + + SymmetricGroup, CyclicGroup, DihedralGroup + + References + ========== + + .. [1] Armstrong, M. "Groups and Symmetry" + + """ + # small cases are special + if n in (1, 2): + return PermutationGroup([Permutation([0])]) + + a = list(range(n)) + a[0], a[1], a[2] = a[1], a[2], a[0] + gen1 = a + if n % 2: + a = list(range(1, n)) + a.append(0) + gen2 = a + else: + a = list(range(2, n)) + a.append(1) + a.insert(0, 0) + gen2 = a + gens = [gen1, gen2] + if gen1 == gen2: + gens = gens[:1] + G = PermutationGroup([_af_new(a) for a in gens], dups=False) + + set_alternating_group_properties(G, n, n) + G._is_alt = True + return G + + +def set_alternating_group_properties(G, n, degree): + """Set known properties of an alternating group. """ + if n < 4: + G._is_abelian = True + G._is_nilpotent = True + else: + G._is_abelian = False + G._is_nilpotent = False + if n < 5: + G._is_solvable = True + else: + G._is_solvable = False + G._degree = degree + G._is_transitive = True + G._is_dihedral = False + + +def CyclicGroup(n): + """ + Generates the cyclic group of order ``n`` as a permutation group. + + Explanation + =========== + + The generator taken is the ``n``-cycle ``(0 1 2 ... n-1)`` + (in cycle notation). After the group is generated, some of its basic + properties are set. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import CyclicGroup + >>> G = CyclicGroup(6) + >>> G.is_group + True + >>> G.order() + 6 + >>> list(G.generate_schreier_sims(af=True)) + [[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], + [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]] + + See Also + ======== + + SymmetricGroup, DihedralGroup, AlternatingGroup + + """ + a = list(range(1, n)) + a.append(0) + gen = _af_new(a) + G = PermutationGroup([gen]) + + G._is_abelian = True + G._is_nilpotent = True + G._is_solvable = True + G._degree = n + G._is_transitive = True + G._order = n + G._is_dihedral = (n == 2) + return G + + +def DihedralGroup(n): + r""" + Generates the dihedral group `D_n` as a permutation group. + + Explanation + =========== + + The dihedral group `D_n` is the group of symmetries of the regular + ``n``-gon. The generators taken are the ``n``-cycle ``a = (0 1 2 ... n-1)`` + (a rotation of the ``n``-gon) and ``b = (0 n-1)(1 n-2)...`` + (a reflection of the ``n``-gon) in cycle rotation. It is easy to see that + these satisfy ``a**n = b**2 = 1`` and ``bab = ~a`` so they indeed generate + `D_n` (See [1]). After the group is generated, some of its basic properties + are set. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> G = DihedralGroup(5) + >>> G.is_group + True + >>> a = list(G.generate_dimino()) + >>> [perm.cyclic_form for perm in a] + [[], [[0, 1, 2, 3, 4]], [[0, 2, 4, 1, 3]], + [[0, 3, 1, 4, 2]], [[0, 4, 3, 2, 1]], [[0, 4], [1, 3]], + [[1, 4], [2, 3]], [[0, 1], [2, 4]], [[0, 2], [3, 4]], + [[0, 3], [1, 2]]] + + See Also + ======== + + SymmetricGroup, CyclicGroup, AlternatingGroup + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Dihedral_group + + """ + # small cases are special + if n == 1: + return PermutationGroup([Permutation([1, 0])]) + if n == 2: + return PermutationGroup([Permutation([1, 0, 3, 2]), + Permutation([2, 3, 0, 1]), Permutation([3, 2, 1, 0])]) + + a = list(range(1, n)) + a.append(0) + gen1 = _af_new(a) + a = list(range(n)) + a.reverse() + gen2 = _af_new(a) + G = PermutationGroup([gen1, gen2]) + # if n is a power of 2, group is nilpotent + if n & (n-1) == 0: + G._is_nilpotent = True + else: + G._is_nilpotent = False + G._is_dihedral = True + G._is_abelian = False + G._is_solvable = True + G._degree = n + G._is_transitive = True + G._order = 2*n + return G + + +def SymmetricGroup(n): + """ + Generates the symmetric group on ``n`` elements as a permutation group. + + Explanation + =========== + + The generators taken are the ``n``-cycle + ``(0 1 2 ... n-1)`` and the transposition ``(0 1)`` (in cycle notation). + (See [1]). After the group is generated, some of its basic properties + are set. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> G = SymmetricGroup(4) + >>> G.is_group + True + >>> G.order() + 24 + >>> list(G.generate_schreier_sims(af=True)) + [[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 1, 2, 0], [0, 2, 3, 1], + [1, 3, 0, 2], [2, 0, 1, 3], [3, 2, 0, 1], [0, 3, 1, 2], [1, 0, 2, 3], + [2, 1, 3, 0], [3, 0, 1, 2], [0, 1, 3, 2], [1, 2, 0, 3], [2, 3, 1, 0], + [3, 1, 0, 2], [0, 2, 1, 3], [1, 3, 2, 0], [2, 0, 3, 1], [3, 2, 1, 0], + [0, 3, 2, 1], [1, 0, 3, 2], [2, 1, 0, 3], [3, 0, 2, 1]] + + See Also + ======== + + CyclicGroup, DihedralGroup, AlternatingGroup + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Symmetric_group#Generators_and_relations + + """ + if n == 1: + G = PermutationGroup([Permutation([0])]) + elif n == 2: + G = PermutationGroup([Permutation([1, 0])]) + else: + a = list(range(1, n)) + a.append(0) + gen1 = _af_new(a) + a = list(range(n)) + a[0], a[1] = a[1], a[0] + gen2 = _af_new(a) + G = PermutationGroup([gen1, gen2]) + set_symmetric_group_properties(G, n, n) + G._is_sym = True + return G + + +def set_symmetric_group_properties(G, n, degree): + """Set known properties of a symmetric group. """ + if n < 3: + G._is_abelian = True + G._is_nilpotent = True + else: + G._is_abelian = False + G._is_nilpotent = False + if n < 5: + G._is_solvable = True + else: + G._is_solvable = False + G._degree = degree + G._is_transitive = True + G._is_dihedral = (n in [2, 3]) # cf Landau's func and Stirling's approx + + +def RubikGroup(n): + """Return a group of Rubik's cube generators + + >>> from sympy.combinatorics.named_groups import RubikGroup + >>> RubikGroup(2).is_group + True + """ + from sympy.combinatorics.generators import rubik + if n <= 1: + raise ValueError("Invalid cube. n has to be greater than 1") + return PermutationGroup(rubik(n)) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/partitions.py b/lib/python3.11/site-packages/sympy/combinatorics/partitions.py new file mode 100644 index 0000000000000000000000000000000000000000..dfe646baabbb5bf2350cba859a265ac32bbfaf53 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/partitions.py @@ -0,0 +1,745 @@ +from sympy.core import Basic, Dict, sympify, Tuple +from sympy.core.numbers import Integer +from sympy.core.sorting import default_sort_key +from sympy.core.sympify import _sympify +from sympy.functions.combinatorial.numbers import bell +from sympy.matrices import zeros +from sympy.sets.sets import FiniteSet, Union +from sympy.utilities.iterables import flatten, group +from sympy.utilities.misc import as_int + + +from collections import defaultdict + + +class Partition(FiniteSet): + """ + This class represents an abstract partition. + + A partition is a set of disjoint sets whose union equals a given set. + + See Also + ======== + + sympy.utilities.iterables.partitions, + sympy.utilities.iterables.multiset_partitions + """ + + _rank = None + _partition = None + + def __new__(cls, *partition): + """ + Generates a new partition object. + + This method also verifies if the arguments passed are + valid and raises a ValueError if they are not. + + Examples + ======== + + Creating Partition from Python lists: + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3]) + >>> a + Partition({3}, {1, 2}) + >>> a.partition + [[1, 2], [3]] + >>> len(a) + 2 + >>> a.members + (1, 2, 3) + + Creating Partition from Python sets: + + >>> Partition({1, 2, 3}, {4, 5}) + Partition({4, 5}, {1, 2, 3}) + + Creating Partition from SymPy finite sets: + + >>> from sympy import FiniteSet + >>> a = FiniteSet(1, 2, 3) + >>> b = FiniteSet(4, 5) + >>> Partition(a, b) + Partition({4, 5}, {1, 2, 3}) + """ + args = [] + dups = False + for arg in partition: + if isinstance(arg, list): + as_set = set(arg) + if len(as_set) < len(arg): + dups = True + break # error below + arg = as_set + args.append(_sympify(arg)) + + if not all(isinstance(part, FiniteSet) for part in args): + raise ValueError( + "Each argument to Partition should be " \ + "a list, set, or a FiniteSet") + + # sort so we have a canonical reference for RGS + U = Union(*args) + if dups or len(U) < sum(len(arg) for arg in args): + raise ValueError("Partition contained duplicate elements.") + + obj = FiniteSet.__new__(cls, *args) + obj.members = tuple(U) + obj.size = len(U) + return obj + + def sort_key(self, order=None): + """Return a canonical key that can be used for sorting. + + Ordering is based on the size and sorted elements of the partition + and ties are broken with the rank. + + Examples + ======== + + >>> from sympy import default_sort_key + >>> from sympy.combinatorics import Partition + >>> from sympy.abc import x + >>> a = Partition([1, 2]) + >>> b = Partition([3, 4]) + >>> c = Partition([1, x]) + >>> d = Partition(list(range(4))) + >>> l = [d, b, a + 1, a, c] + >>> l.sort(key=default_sort_key); l + [Partition({1, 2}), Partition({1}, {2}), Partition({1, x}), Partition({3, 4}), Partition({0, 1, 2, 3})] + """ + if order is None: + members = self.members + else: + members = tuple(sorted(self.members, + key=lambda w: default_sort_key(w, order))) + return tuple(map(default_sort_key, (self.size, members, self.rank))) + + @property + def partition(self): + """Return partition as a sorted list of lists. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> Partition([1], [2, 3]).partition + [[1], [2, 3]] + """ + if self._partition is None: + self._partition = sorted([sorted(p, key=default_sort_key) + for p in self.args]) + return self._partition + + def __add__(self, other): + """ + Return permutation whose rank is ``other`` greater than current rank, + (mod the maximum rank for the set). + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3]) + >>> a.rank + 1 + >>> (a + 1).rank + 2 + >>> (a + 100).rank + 1 + """ + other = as_int(other) + offset = self.rank + other + result = RGS_unrank((offset) % + RGS_enum(self.size), + self.size) + return Partition.from_rgs(result, self.members) + + def __sub__(self, other): + """ + Return permutation whose rank is ``other`` less than current rank, + (mod the maximum rank for the set). + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3]) + >>> a.rank + 1 + >>> (a - 1).rank + 0 + >>> (a - 100).rank + 1 + """ + return self.__add__(-other) + + def __le__(self, other): + """ + Checks if a partition is less than or equal to + the other based on rank. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3, 4, 5]) + >>> b = Partition([1], [2, 3], [4], [5]) + >>> a.rank, b.rank + (9, 34) + >>> a <= a + True + >>> a <= b + True + """ + return self.sort_key() <= sympify(other).sort_key() + + def __lt__(self, other): + """ + Checks if a partition is less than the other. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3, 4, 5]) + >>> b = Partition([1], [2, 3], [4], [5]) + >>> a.rank, b.rank + (9, 34) + >>> a < b + True + """ + return self.sort_key() < sympify(other).sort_key() + + @property + def rank(self): + """ + Gets the rank of a partition. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3], [4, 5]) + >>> a.rank + 13 + """ + if self._rank is not None: + return self._rank + self._rank = RGS_rank(self.RGS) + return self._rank + + @property + def RGS(self): + """ + Returns the "restricted growth string" of the partition. + + Explanation + =========== + + The RGS is returned as a list of indices, L, where L[i] indicates + the block in which element i appears. For example, in a partition + of 3 elements (a, b, c) into 2 blocks ([c], [a, b]) the RGS is + [1, 1, 0]: "a" is in block 1, "b" is in block 1 and "c" is in block 0. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> a = Partition([1, 2], [3], [4, 5]) + >>> a.members + (1, 2, 3, 4, 5) + >>> a.RGS + (0, 0, 1, 2, 2) + >>> a + 1 + Partition({3}, {4}, {5}, {1, 2}) + >>> _.RGS + (0, 0, 1, 2, 3) + """ + rgs = {} + partition = self.partition + for i, part in enumerate(partition): + for j in part: + rgs[j] = i + return tuple([rgs[i] for i in sorted( + [i for p in partition for i in p], key=default_sort_key)]) + + @classmethod + def from_rgs(self, rgs, elements): + """ + Creates a set partition from a restricted growth string. + + Explanation + =========== + + The indices given in rgs are assumed to be the index + of the element as given in elements *as provided* (the + elements are not sorted by this routine). Block numbering + starts from 0. If any block was not referenced in ``rgs`` + an error will be raised. + + Examples + ======== + + >>> from sympy.combinatorics import Partition + >>> Partition.from_rgs([0, 1, 2, 0, 1], list('abcde')) + Partition({c}, {a, d}, {b, e}) + >>> Partition.from_rgs([0, 1, 2, 0, 1], list('cbead')) + Partition({e}, {a, c}, {b, d}) + >>> a = Partition([1, 4], [2], [3, 5]) + >>> Partition.from_rgs(a.RGS, a.members) + Partition({2}, {1, 4}, {3, 5}) + """ + if len(rgs) != len(elements): + raise ValueError('mismatch in rgs and element lengths') + max_elem = max(rgs) + 1 + partition = [[] for i in range(max_elem)] + j = 0 + for i in rgs: + partition[i].append(elements[j]) + j += 1 + if not all(p for p in partition): + raise ValueError('some blocks of the partition were empty.') + return Partition(*partition) + + +class IntegerPartition(Basic): + """ + This class represents an integer partition. + + Explanation + =========== + + In number theory and combinatorics, a partition of a positive integer, + ``n``, also called an integer partition, is a way of writing ``n`` as a + list of positive integers that sum to n. Two partitions that differ only + in the order of summands are considered to be the same partition; if order + matters then the partitions are referred to as compositions. For example, + 4 has five partitions: [4], [3, 1], [2, 2], [2, 1, 1], and [1, 1, 1, 1]; + the compositions [1, 2, 1] and [1, 1, 2] are the same as partition + [2, 1, 1]. + + See Also + ======== + + sympy.utilities.iterables.partitions, + sympy.utilities.iterables.multiset_partitions + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Partition_%28number_theory%29 + """ + + _dict = None + _keys = None + + def __new__(cls, partition, integer=None): + """ + Generates a new IntegerPartition object from a list or dictionary. + + Explanation + =========== + + The partition can be given as a list of positive integers or a + dictionary of (integer, multiplicity) items. If the partition is + preceded by an integer an error will be raised if the partition + does not sum to that given integer. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> a = IntegerPartition([5, 4, 3, 1, 1]) + >>> a + IntegerPartition(14, (5, 4, 3, 1, 1)) + >>> print(a) + [5, 4, 3, 1, 1] + >>> IntegerPartition({1:3, 2:1}) + IntegerPartition(5, (2, 1, 1, 1)) + + If the value that the partition should sum to is given first, a check + will be made to see n error will be raised if there is a discrepancy: + + >>> IntegerPartition(10, [5, 4, 3, 1]) + Traceback (most recent call last): + ... + ValueError: The partition is not valid + + """ + if integer is not None: + integer, partition = partition, integer + if isinstance(partition, (dict, Dict)): + _ = [] + for k, v in sorted(partition.items(), reverse=True): + if not v: + continue + k, v = as_int(k), as_int(v) + _.extend([k]*v) + partition = tuple(_) + else: + partition = tuple(sorted(map(as_int, partition), reverse=True)) + sum_ok = False + if integer is None: + integer = sum(partition) + sum_ok = True + else: + integer = as_int(integer) + + if not sum_ok and sum(partition) != integer: + raise ValueError("Partition did not add to %s" % integer) + if any(i < 1 for i in partition): + raise ValueError("All integer summands must be greater than one") + + obj = Basic.__new__(cls, Integer(integer), Tuple(*partition)) + obj.partition = list(partition) + obj.integer = integer + return obj + + def prev_lex(self): + """Return the previous partition of the integer, n, in lexical order, + wrapping around to [1, ..., 1] if the partition is [n]. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> p = IntegerPartition([4]) + >>> print(p.prev_lex()) + [3, 1] + >>> p.partition > p.prev_lex().partition + True + """ + d = defaultdict(int) + d.update(self.as_dict()) + keys = self._keys + if keys == [1]: + return IntegerPartition({self.integer: 1}) + if keys[-1] != 1: + d[keys[-1]] -= 1 + if keys[-1] == 2: + d[1] = 2 + else: + d[keys[-1] - 1] = d[1] = 1 + else: + d[keys[-2]] -= 1 + left = d[1] + keys[-2] + new = keys[-2] + d[1] = 0 + while left: + new -= 1 + if left - new >= 0: + d[new] += left//new + left -= d[new]*new + return IntegerPartition(self.integer, d) + + def next_lex(self): + """Return the next partition of the integer, n, in lexical order, + wrapping around to [n] if the partition is [1, ..., 1]. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> p = IntegerPartition([3, 1]) + >>> print(p.next_lex()) + [4] + >>> p.partition < p.next_lex().partition + True + """ + d = defaultdict(int) + d.update(self.as_dict()) + key = self._keys + a = key[-1] + if a == self.integer: + d.clear() + d[1] = self.integer + elif a == 1: + if d[a] > 1: + d[a + 1] += 1 + d[a] -= 2 + else: + b = key[-2] + d[b + 1] += 1 + d[1] = (d[b] - 1)*b + d[b] = 0 + else: + if d[a] > 1: + if len(key) == 1: + d.clear() + d[a + 1] = 1 + d[1] = self.integer - a - 1 + else: + a1 = a + 1 + d[a1] += 1 + d[1] = d[a]*a - a1 + d[a] = 0 + else: + b = key[-2] + b1 = b + 1 + d[b1] += 1 + need = d[b]*b + d[a]*a - b1 + d[a] = d[b] = 0 + d[1] = need + return IntegerPartition(self.integer, d) + + def as_dict(self): + """Return the partition as a dictionary whose keys are the + partition integers and the values are the multiplicity of that + integer. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> IntegerPartition([1]*3 + [2] + [3]*4).as_dict() + {1: 3, 2: 1, 3: 4} + """ + if self._dict is None: + groups = group(self.partition, multiple=False) + self._keys = [g[0] for g in groups] + self._dict = dict(groups) + return self._dict + + @property + def conjugate(self): + """ + Computes the conjugate partition of itself. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> a = IntegerPartition([6, 3, 3, 2, 1]) + >>> a.conjugate + [5, 4, 3, 1, 1, 1] + """ + j = 1 + temp_arr = list(self.partition) + [0] + k = temp_arr[0] + b = [0]*k + while k > 0: + while k > temp_arr[j]: + b[k - 1] = j + k -= 1 + j += 1 + return b + + def __lt__(self, other): + """Return True if self is less than other when the partition + is listed from smallest to biggest. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> a = IntegerPartition([3, 1]) + >>> a < a + False + >>> b = a.next_lex() + >>> a < b + True + >>> a == b + False + """ + return list(reversed(self.partition)) < list(reversed(other.partition)) + + def __le__(self, other): + """Return True if self is less than other when the partition + is listed from smallest to biggest. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> a = IntegerPartition([4]) + >>> a <= a + True + """ + return list(reversed(self.partition)) <= list(reversed(other.partition)) + + def as_ferrers(self, char='#'): + """ + Prints the ferrer diagram of a partition. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import IntegerPartition + >>> print(IntegerPartition([1, 1, 5]).as_ferrers()) + ##### + # + # + """ + return "\n".join([char*i for i in self.partition]) + + def __str__(self): + return str(list(self.partition)) + + +def random_integer_partition(n, seed=None): + """ + Generates a random integer partition summing to ``n`` as a list + of reverse-sorted integers. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import random_integer_partition + + For the following, a seed is given so a known value can be shown; in + practice, the seed would not be given. + + >>> random_integer_partition(100, seed=[1, 1, 12, 1, 2, 1, 85, 1]) + [85, 12, 2, 1] + >>> random_integer_partition(10, seed=[1, 2, 3, 1, 5, 1]) + [5, 3, 1, 1] + >>> random_integer_partition(1) + [1] + """ + from sympy.core.random import _randint + + n = as_int(n) + if n < 1: + raise ValueError('n must be a positive integer') + + randint = _randint(seed) + + partition = [] + while (n > 0): + k = randint(1, n) + mult = randint(1, n//k) + partition.append((k, mult)) + n -= k*mult + partition.sort(reverse=True) + partition = flatten([[k]*m for k, m in partition]) + return partition + + +def RGS_generalized(m): + """ + Computes the m + 1 generalized unrestricted growth strings + and returns them as rows in matrix. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import RGS_generalized + >>> RGS_generalized(6) + Matrix([ + [ 1, 1, 1, 1, 1, 1, 1], + [ 1, 2, 3, 4, 5, 6, 0], + [ 2, 5, 10, 17, 26, 0, 0], + [ 5, 15, 37, 77, 0, 0, 0], + [ 15, 52, 151, 0, 0, 0, 0], + [ 52, 203, 0, 0, 0, 0, 0], + [203, 0, 0, 0, 0, 0, 0]]) + """ + d = zeros(m + 1) + for i in range(m + 1): + d[0, i] = 1 + + for i in range(1, m + 1): + for j in range(m): + if j <= m - i: + d[i, j] = j * d[i - 1, j] + d[i - 1, j + 1] + else: + d[i, j] = 0 + return d + + +def RGS_enum(m): + """ + RGS_enum computes the total number of restricted growth strings + possible for a superset of size m. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import RGS_enum + >>> from sympy.combinatorics import Partition + >>> RGS_enum(4) + 15 + >>> RGS_enum(5) + 52 + >>> RGS_enum(6) + 203 + + We can check that the enumeration is correct by actually generating + the partitions. Here, the 15 partitions of 4 items are generated: + + >>> a = Partition(list(range(4))) + >>> s = set() + >>> for i in range(20): + ... s.add(a) + ... a += 1 + ... + >>> assert len(s) == 15 + + """ + if (m < 1): + return 0 + elif (m == 1): + return 1 + else: + return bell(m) + + +def RGS_unrank(rank, m): + """ + Gives the unranked restricted growth string for a given + superset size. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import RGS_unrank + >>> RGS_unrank(14, 4) + [0, 1, 2, 3] + >>> RGS_unrank(0, 4) + [0, 0, 0, 0] + """ + if m < 1: + raise ValueError("The superset size must be >= 1") + if rank < 0 or RGS_enum(m) <= rank: + raise ValueError("Invalid arguments") + + L = [1] * (m + 1) + j = 1 + D = RGS_generalized(m) + for i in range(2, m + 1): + v = D[m - i, j] + cr = j*v + if cr <= rank: + L[i] = j + 1 + rank -= cr + j += 1 + else: + L[i] = int(rank / v + 1) + rank %= v + return [x - 1 for x in L[1:]] + + +def RGS_rank(rgs): + """ + Computes the rank of a restricted growth string. + + Examples + ======== + + >>> from sympy.combinatorics.partitions import RGS_rank, RGS_unrank + >>> RGS_rank([0, 1, 2, 1, 3]) + 42 + >>> RGS_rank(RGS_unrank(4, 7)) + 4 + """ + rgs_size = len(rgs) + rank = 0 + D = RGS_generalized(rgs_size) + for i in range(1, rgs_size): + n = len(rgs[(i + 1):]) + m = max(rgs[0:i]) + rank += D[n, m + 1] * rgs[i] + return rank diff --git a/lib/python3.11/site-packages/sympy/combinatorics/pc_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/pc_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..dbb4b0e442ec70d4c088fb51924fadc30cdf2fbf --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/pc_groups.py @@ -0,0 +1,709 @@ +from sympy.ntheory.primetest import isprime +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.printing.defaults import DefaultPrinting +from sympy.combinatorics.free_groups import free_group + + +class PolycyclicGroup(DefaultPrinting): + + is_group = True + is_solvable = True + + def __init__(self, pc_sequence, pc_series, relative_order, collector=None): + """ + + Parameters + ========== + + pc_sequence : list + A sequence of elements whose classes generate the cyclic factor + groups of pc_series. + pc_series : list + A subnormal sequence of subgroups where each factor group is cyclic. + relative_order : list + The orders of factor groups of pc_series. + collector : Collector + By default, it is None. Collector class provides the + polycyclic presentation with various other functionalities. + + """ + self.pcgs = pc_sequence + self.pc_series = pc_series + self.relative_order = relative_order + self.collector = Collector(self.pcgs, pc_series, relative_order) if not collector else collector + + def is_prime_order(self): + return all(isprime(order) for order in self.relative_order) + + def length(self): + return len(self.pcgs) + + +class Collector(DefaultPrinting): + + """ + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + Section 8.1.3 + """ + + def __init__(self, pcgs, pc_series, relative_order, free_group_=None, pc_presentation=None): + """ + + Most of the parameters for the Collector class are the same as for PolycyclicGroup. + Others are described below. + + Parameters + ========== + + free_group_ : tuple + free_group_ provides the mapping of polycyclic generating + sequence with the free group elements. + pc_presentation : dict + Provides the presentation of polycyclic groups with the + help of power and conjugate relators. + + See Also + ======== + + PolycyclicGroup + + """ + self.pcgs = pcgs + self.pc_series = pc_series + self.relative_order = relative_order + self.free_group = free_group('x:{}'.format(len(pcgs)))[0] if not free_group_ else free_group_ + self.index = {s: i for i, s in enumerate(self.free_group.symbols)} + self.pc_presentation = self.pc_relators() + + def minimal_uncollected_subword(self, word): + r""" + Returns the minimal uncollected subwords. + + Explanation + =========== + + A word ``v`` defined on generators in ``X`` is a minimal + uncollected subword of the word ``w`` if ``v`` is a subword + of ``w`` and it has one of the following form + + * `v = {x_{i+1}}^{a_j}x_i` + + * `v = {x_{i+1}}^{a_j}{x_i}^{-1}` + + * `v = {x_i}^{a_j}` + + for `a_j` not in `\{1, \ldots, s-1\}`. Where, ``s`` is the power + exponent of the corresponding generator. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics import free_group + >>> G = SymmetricGroup(4) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> F, x1, x2 = free_group("x1, x2") + >>> word = x2**2*x1**7 + >>> collector.minimal_uncollected_subword(word) + ((x2, 2),) + + """ + # To handle the case word = + if not word: + return None + + array = word.array_form + re = self.relative_order + index = self.index + + for i in range(len(array)): + s1, e1 = array[i] + + if re[index[s1]] and (e1 < 0 or e1 > re[index[s1]]-1): + return ((s1, e1), ) + + for i in range(len(array)-1): + s1, e1 = array[i] + s2, e2 = array[i+1] + + if index[s1] > index[s2]: + e = 1 if e2 > 0 else -1 + return ((s1, e1), (s2, e)) + + return None + + def relations(self): + """ + Separates the given relators of pc presentation in power and + conjugate relations. + + Returns + ======= + + (power_rel, conj_rel) + Separates pc presentation into power and conjugate relations. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> G = SymmetricGroup(3) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> power_rel, conj_rel = collector.relations() + >>> power_rel + {x0**2: (), x1**3: ()} + >>> conj_rel + {x0**-1*x1*x0: x1**2} + + See Also + ======== + + pc_relators + + """ + power_relators = {} + conjugate_relators = {} + for key, value in self.pc_presentation.items(): + if len(key.array_form) == 1: + power_relators[key] = value + else: + conjugate_relators[key] = value + return power_relators, conjugate_relators + + def subword_index(self, word, w): + """ + Returns the start and ending index of a given + subword in a word. + + Parameters + ========== + + word : FreeGroupElement + word defined on free group elements for a + polycyclic group. + w : FreeGroupElement + subword of a given word, whose starting and + ending index to be computed. + + Returns + ======= + + (i, j) + A tuple containing starting and ending index of ``w`` + in the given word. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics import free_group + >>> G = SymmetricGroup(4) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> F, x1, x2 = free_group("x1, x2") + >>> word = x2**2*x1**7 + >>> w = x2**2*x1 + >>> collector.subword_index(word, w) + (0, 3) + >>> w = x1**7 + >>> collector.subword_index(word, w) + (2, 9) + + """ + low = -1 + high = -1 + for i in range(len(word)-len(w)+1): + if word.subword(i, i+len(w)) == w: + low = i + high = i+len(w) + break + if low == high == -1: + return -1, -1 + return low, high + + def map_relation(self, w): + """ + Return a conjugate relation. + + Explanation + =========== + + Given a word formed by two free group elements, the + corresponding conjugate relation with those free + group elements is formed and mapped with the collected + word in the polycyclic presentation. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics import free_group + >>> G = SymmetricGroup(3) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> F, x0, x1 = free_group("x0, x1") + >>> w = x1*x0 + >>> collector.map_relation(w) + x1**2 + + See Also + ======== + + pc_presentation + + """ + array = w.array_form + s1 = array[0][0] + s2 = array[1][0] + key = ((s2, -1), (s1, 1), (s2, 1)) + key = self.free_group.dtype(key) + return self.pc_presentation[key] + + + def collected_word(self, word): + r""" + Return the collected form of a word. + + Explanation + =========== + + A word ``w`` is called collected, if `w = {x_{i_1}}^{a_1} * \ldots * + {x_{i_r}}^{a_r}` with `i_1 < i_2< \ldots < i_r` and `a_j` is in + `\{1, \ldots, {s_j}-1\}`. + + Otherwise w is uncollected. + + Parameters + ========== + + word : FreeGroupElement + An uncollected word. + + Returns + ======= + + word + A collected word of form `w = {x_{i_1}}^{a_1}, \ldots, + {x_{i_r}}^{a_r}` with `i_1, i_2, \ldots, i_r` and `a_j \in + \{1, \ldots, {s_j}-1\}`. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> from sympy.combinatorics import free_group + >>> G = SymmetricGroup(4) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> F, x0, x1, x2, x3 = free_group("x0, x1, x2, x3") + >>> word = x3*x2*x1*x0 + >>> collected_word = collector.collected_word(word) + >>> free_to_perm = {} + >>> free_group = collector.free_group + >>> for sym, gen in zip(free_group.symbols, collector.pcgs): + ... free_to_perm[sym] = gen + >>> G1 = PermutationGroup() + >>> for w in word: + ... sym = w[0] + ... perm = free_to_perm[sym] + ... G1 = PermutationGroup([perm] + G1.generators) + >>> G2 = PermutationGroup() + >>> for w in collected_word: + ... sym = w[0] + ... perm = free_to_perm[sym] + ... G2 = PermutationGroup([perm] + G2.generators) + + The two are not identical, but they are equivalent: + + >>> G1.equals(G2), G1 == G2 + (True, False) + + See Also + ======== + + minimal_uncollected_subword + + """ + free_group = self.free_group + while True: + w = self.minimal_uncollected_subword(word) + if not w: + break + + low, high = self.subword_index(word, free_group.dtype(w)) + if low == -1: + continue + + s1, e1 = w[0] + if len(w) == 1: + re = self.relative_order[self.index[s1]] + q = e1 // re + r = e1-q*re + + key = ((w[0][0], re), ) + key = free_group.dtype(key) + if self.pc_presentation[key]: + presentation = self.pc_presentation[key].array_form + sym, exp = presentation[0] + word_ = ((w[0][0], r), (sym, q*exp)) + word_ = free_group.dtype(word_) + else: + if r != 0: + word_ = ((w[0][0], r), ) + word_ = free_group.dtype(word_) + else: + word_ = None + word = word.eliminate_word(free_group.dtype(w), word_) + + if len(w) == 2 and w[1][1] > 0: + s2, e2 = w[1] + s2 = ((s2, 1), ) + s2 = free_group.dtype(s2) + word_ = self.map_relation(free_group.dtype(w)) + word_ = s2*word_**e1 + word_ = free_group.dtype(word_) + word = word.substituted_word(low, high, word_) + + elif len(w) == 2 and w[1][1] < 0: + s2, e2 = w[1] + s2 = ((s2, 1), ) + s2 = free_group.dtype(s2) + word_ = self.map_relation(free_group.dtype(w)) + word_ = s2**-1*word_**e1 + word_ = free_group.dtype(word_) + word = word.substituted_word(low, high, word_) + + return word + + + def pc_relators(self): + r""" + Return the polycyclic presentation. + + Explanation + =========== + + There are two types of relations used in polycyclic + presentation. + + * Power relations : Power relators are of the form `x_i^{re_i}`, + where `i \in \{0, \ldots, \mathrm{len(pcgs)}\}`, ``x`` represents polycyclic + generator and ``re`` is the corresponding relative order. + + * Conjugate relations : Conjugate relators are of the form `x_j^-1x_ix_j`, + where `j < i \in \{0, \ldots, \mathrm{len(pcgs)}\}`. + + Returns + ======= + + A dictionary with power and conjugate relations as key and + their collected form as corresponding values. + + Notes + ===== + + Identity Permutation is mapped with empty ``()``. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.permutations import Permutation + >>> S = SymmetricGroup(49).sylow_subgroup(7) + >>> der = S.derived_series() + >>> G = der[len(der)-2] + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> pcgs = PcGroup.pcgs + >>> len(pcgs) + 6 + >>> free_group = collector.free_group + >>> pc_resentation = collector.pc_presentation + >>> free_to_perm = {} + >>> for s, g in zip(free_group.symbols, pcgs): + ... free_to_perm[s] = g + + >>> for k, v in pc_resentation.items(): + ... k_array = k.array_form + ... if v != (): + ... v_array = v.array_form + ... lhs = Permutation() + ... for gen in k_array: + ... s = gen[0] + ... e = gen[1] + ... lhs = lhs*free_to_perm[s]**e + ... if v == (): + ... assert lhs.is_identity + ... continue + ... rhs = Permutation() + ... for gen in v_array: + ... s = gen[0] + ... e = gen[1] + ... rhs = rhs*free_to_perm[s]**e + ... assert lhs == rhs + + """ + free_group = self.free_group + rel_order = self.relative_order + pc_relators = {} + perm_to_free = {} + pcgs = self.pcgs + + for gen, s in zip(pcgs, free_group.generators): + perm_to_free[gen**-1] = s**-1 + perm_to_free[gen] = s + + pcgs = pcgs[::-1] + series = self.pc_series[::-1] + rel_order = rel_order[::-1] + collected_gens = [] + + for i, gen in enumerate(pcgs): + re = rel_order[i] + relation = perm_to_free[gen]**re + G = series[i] + + l = G.generator_product(gen**re, original = True) + l.reverse() + + word = free_group.identity + for g in l: + word = word*perm_to_free[g] + + word = self.collected_word(word) + pc_relators[relation] = word if word else () + self.pc_presentation = pc_relators + + collected_gens.append(gen) + if len(collected_gens) > 1: + conj = collected_gens[len(collected_gens)-1] + conjugator = perm_to_free[conj] + + for j in range(len(collected_gens)-1): + conjugated = perm_to_free[collected_gens[j]] + + relation = conjugator**-1*conjugated*conjugator + gens = conj**-1*collected_gens[j]*conj + + l = G.generator_product(gens, original = True) + l.reverse() + word = free_group.identity + for g in l: + word = word*perm_to_free[g] + + word = self.collected_word(word) + pc_relators[relation] = word if word else () + self.pc_presentation = pc_relators + + return pc_relators + + def exponent_vector(self, element): + r""" + Return the exponent vector of length equal to the + length of polycyclic generating sequence. + + Explanation + =========== + + For a given generator/element ``g`` of the polycyclic group, + it can be represented as `g = {x_1}^{e_1}, \ldots, {x_n}^{e_n}`, + where `x_i` represents polycyclic generators and ``n`` is + the number of generators in the free_group equal to the length + of pcgs. + + Parameters + ========== + + element : Permutation + Generator of a polycyclic group. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.permutations import Permutation + >>> G = SymmetricGroup(4) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> pcgs = PcGroup.pcgs + >>> collector.exponent_vector(G[0]) + [1, 0, 0, 0] + >>> exp = collector.exponent_vector(G[1]) + >>> g = Permutation() + >>> for i in range(len(exp)): + ... g = g*pcgs[i]**exp[i] if exp[i] else g + >>> assert g == G[1] + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + Section 8.1.1, Definition 8.4 + + """ + free_group = self.free_group + G = PermutationGroup() + for g in self.pcgs: + G = PermutationGroup([g] + G.generators) + gens = G.generator_product(element, original = True) + gens.reverse() + + perm_to_free = {} + for sym, g in zip(free_group.generators, self.pcgs): + perm_to_free[g**-1] = sym**-1 + perm_to_free[g] = sym + w = free_group.identity + for g in gens: + w = w*perm_to_free[g] + + word = self.collected_word(w) + + index = self.index + exp_vector = [0]*len(free_group) + word = word.array_form + for t in word: + exp_vector[index[t[0]]] = t[1] + return exp_vector + + def depth(self, element): + r""" + Return the depth of a given element. + + Explanation + =========== + + The depth of a given element ``g`` is defined by + `\mathrm{dep}[g] = i` if `e_1 = e_2 = \ldots = e_{i-1} = 0` + and `e_i != 0`, where ``e`` represents the exponent-vector. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> G = SymmetricGroup(3) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> collector.depth(G[0]) + 2 + >>> collector.depth(G[1]) + 1 + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + Section 8.1.1, Definition 8.5 + + """ + exp_vector = self.exponent_vector(element) + return next((i+1 for i, x in enumerate(exp_vector) if x), len(self.pcgs)+1) + + def leading_exponent(self, element): + r""" + Return the leading non-zero exponent. + + Explanation + =========== + + The leading exponent for a given element `g` is defined + by `\mathrm{leading\_exponent}[g]` `= e_i`, if `\mathrm{depth}[g] = i`. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> G = SymmetricGroup(3) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> collector.leading_exponent(G[1]) + 1 + + """ + exp_vector = self.exponent_vector(element) + depth = self.depth(element) + if depth != len(self.pcgs)+1: + return exp_vector[depth-1] + return None + + def _sift(self, z, g): + h = g + d = self.depth(h) + while d < len(self.pcgs) and z[d-1] != 1: + k = z[d-1] + e = self.leading_exponent(h)*(self.leading_exponent(k))**-1 + e = e % self.relative_order[d-1] + h = k**-e*h + d = self.depth(h) + return h + + def induced_pcgs(self, gens): + """ + + Parameters + ========== + + gens : list + A list of generators on which polycyclic subgroup + is to be defined. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> S = SymmetricGroup(8) + >>> G = S.sylow_subgroup(2) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> gens = [G[0], G[1]] + >>> ipcgs = collector.induced_pcgs(gens) + >>> [gen.order() for gen in ipcgs] + [2, 2, 2] + >>> G = S.sylow_subgroup(3) + >>> PcGroup = G.polycyclic_group() + >>> collector = PcGroup.collector + >>> gens = [G[0], G[1]] + >>> ipcgs = collector.induced_pcgs(gens) + >>> [gen.order() for gen in ipcgs] + [3] + + """ + z = [1]*len(self.pcgs) + G = gens + while G: + g = G.pop(0) + h = self._sift(z, g) + d = self.depth(h) + if d < len(self.pcgs): + for gen in z: + if gen != 1: + G.append(h**-1*gen**-1*h*gen) + z[d-1] = h; + z = [gen for gen in z if gen != 1] + return z + + def constructive_membership_test(self, ipcgs, g): + """ + Return the exponent vector for induced pcgs. + """ + e = [0]*len(ipcgs) + h = g + d = self.depth(h) + for i, gen in enumerate(ipcgs): + while self.depth(gen) == d: + f = self.leading_exponent(h)*self.leading_exponent(gen) + f = f % self.relative_order[d-1] + h = gen**(-f)*h + e[i] = f + d = self.depth(h) + if h == 1: + return e + return False diff --git a/lib/python3.11/site-packages/sympy/combinatorics/perm_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/perm_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..1a72aea90b2c65eac42e5f62316b86c94f9eebad --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/perm_groups.py @@ -0,0 +1,5463 @@ +from math import factorial as _factorial, log, prod +from itertools import chain, product + + +from sympy.combinatorics import Permutation +from sympy.combinatorics.permutations import (_af_commutes_with, _af_invert, + _af_rmul, _af_rmuln, _af_pow, Cycle) +from sympy.combinatorics.util import (_check_cycles_alt_sym, + _distribute_gens_by_base, _orbits_transversals_from_bsgs, + _handle_precomputed_bsgs, _base_ordering, _strong_gens_from_distr, + _strip, _strip_af) +from sympy.core import Basic +from sympy.core.random import _randrange, randrange, choice +from sympy.core.symbol import Symbol +from sympy.core.sympify import _sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.ntheory import primefactors, sieve +from sympy.ntheory.factor_ import (factorint, multiplicity) +from sympy.ntheory.primetest import isprime +from sympy.utilities.iterables import has_variety, is_sequence, uniq + +rmul = Permutation.rmul_with_af +_af_new = Permutation._af_new + + +class PermutationGroup(Basic): + r"""The class defining a Permutation group. + + Explanation + =========== + + ``PermutationGroup([p1, p2, ..., pn])`` returns the permutation group + generated by the list of permutations. This group can be supplied + to Polyhedron if one desires to decorate the elements to which the + indices of the permutation refer. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> from sympy.combinatorics import Polyhedron + + The permutations corresponding to motion of the front, right and + bottom face of a $2 \times 2$ Rubik's cube are defined: + + >>> F = Permutation(2, 19, 21, 8)(3, 17, 20, 10)(4, 6, 7, 5) + >>> R = Permutation(1, 5, 21, 14)(3, 7, 23, 12)(8, 10, 11, 9) + >>> D = Permutation(6, 18, 14, 10)(7, 19, 15, 11)(20, 22, 23, 21) + + These are passed as permutations to PermutationGroup: + + >>> G = PermutationGroup(F, R, D) + >>> G.order() + 3674160 + + The group can be supplied to a Polyhedron in order to track the + objects being moved. An example involving the $2 \times 2$ Rubik's cube is + given there, but here is a simple demonstration: + + >>> a = Permutation(2, 1) + >>> b = Permutation(1, 0) + >>> G = PermutationGroup(a, b) + >>> P = Polyhedron(list('ABC'), pgroup=G) + >>> P.corners + (A, B, C) + >>> P.rotate(0) # apply permutation 0 + >>> P.corners + (A, C, B) + >>> P.reset() + >>> P.corners + (A, B, C) + + Or one can make a permutation as a product of selected permutations + and apply them to an iterable directly: + + >>> P10 = G.make_perm([0, 1]) + >>> P10('ABC') + ['C', 'A', 'B'] + + See Also + ======== + + sympy.combinatorics.polyhedron.Polyhedron, + sympy.combinatorics.permutations.Permutation + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of Computational Group Theory" + + .. [2] Seress, A. + "Permutation Group Algorithms" + + .. [3] https://en.wikipedia.org/wiki/Schreier_vector + + .. [4] https://en.wikipedia.org/wiki/Nielsen_transformation#Product_replacement_algorithm + + .. [5] Frank Celler, Charles R.Leedham-Green, Scott H.Murray, + Alice C.Niemeyer, and E.A.O'Brien. "Generating Random + Elements of a Finite Group" + + .. [6] https://en.wikipedia.org/wiki/Block_%28permutation_group_theory%29 + + .. [7] https://algorithmist.com/wiki/Union_find + + .. [8] https://en.wikipedia.org/wiki/Multiply_transitive_group#Multiply_transitive_groups + + .. [9] https://en.wikipedia.org/wiki/Center_%28group_theory%29 + + .. [10] https://en.wikipedia.org/wiki/Centralizer_and_normalizer + + .. [11] https://groupprops.subwiki.org/wiki/Derived_subgroup + + .. [12] https://en.wikipedia.org/wiki/Nilpotent_group + + .. [13] https://www.math.colostate.edu/~hulpke/CGT/cgtnotes.pdf + + .. [14] https://docs.gap-system.org/doc/ref/manual.pdf + + """ + is_group = True + + def __new__(cls, *args, dups=True, **kwargs): + """The default constructor. Accepts Cycle and Permutation forms. + Removes duplicates unless ``dups`` keyword is ``False``. + """ + if not args: + args = [Permutation()] + else: + args = list(args[0] if is_sequence(args[0]) else args) + if not args: + args = [Permutation()] + if any(isinstance(a, Cycle) for a in args): + args = [Permutation(a) for a in args] + if has_variety(a.size for a in args): + degree = kwargs.pop('degree', None) + if degree is None: + degree = max(a.size for a in args) + for i in range(len(args)): + if args[i].size != degree: + args[i] = Permutation(args[i], size=degree) + if dups: + args = list(uniq([_af_new(list(a)) for a in args])) + if len(args) > 1: + args = [g for g in args if not g.is_identity] + return Basic.__new__(cls, *args, **kwargs) + + def __init__(self, *args, **kwargs): + self._generators = list(self.args) + self._order = None + self._elements = [] + self._center = None + self._is_abelian = None + self._is_transitive = None + self._is_sym = None + self._is_alt = None + self._is_primitive = None + self._is_nilpotent = None + self._is_solvable = None + self._is_trivial = None + self._transitivity_degree = None + self._max_div = None + self._is_perfect = None + self._is_cyclic = None + self._is_dihedral = None + self._r = len(self._generators) + self._degree = self._generators[0].size + + # these attributes are assigned after running schreier_sims + self._base = [] + self._strong_gens = [] + self._strong_gens_slp = [] + self._basic_orbits = [] + self._transversals = [] + self._transversal_slp = [] + + # these attributes are assigned after running _random_pr_init + self._random_gens = [] + + # finite presentation of the group as an instance of `FpGroup` + self._fp_presentation = None + + def __getitem__(self, i): + return self._generators[i] + + def __contains__(self, i): + """Return ``True`` if *i* is contained in PermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> p = Permutation(1, 2, 3) + >>> Permutation(3) in PermutationGroup(p) + True + + """ + if not isinstance(i, Permutation): + raise TypeError("A PermutationGroup contains only Permutations as " + "elements, not elements of type %s" % type(i)) + return self.contains(i) + + def __len__(self): + return len(self._generators) + + def equals(self, other): + """Return ``True`` if PermutationGroup generated by elements in the + group are same i.e they represent the same PermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> p = Permutation(0, 1, 2, 3, 4, 5) + >>> G = PermutationGroup([p, p**2]) + >>> H = PermutationGroup([p**2, p]) + >>> G.generators == H.generators + False + >>> G.equals(H) + True + + """ + if not isinstance(other, PermutationGroup): + return False + + set_self_gens = set(self.generators) + set_other_gens = set(other.generators) + + # before reaching the general case there are also certain + # optimisation and obvious cases requiring less or no actual + # computation. + if set_self_gens == set_other_gens: + return True + + # in the most general case it will check that each generator of + # one group belongs to the other PermutationGroup and vice-versa + for gen1 in set_self_gens: + if not other.contains(gen1): + return False + for gen2 in set_other_gens: + if not self.contains(gen2): + return False + return True + + def __mul__(self, other): + """ + Return the direct product of two permutation groups as a permutation + group. + + Explanation + =========== + + This implementation realizes the direct product by shifting the index + set for the generators of the second group: so if we have ``G`` acting + on ``n1`` points and ``H`` acting on ``n2`` points, ``G*H`` acts on + ``n1 + n2`` points. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import CyclicGroup + >>> G = CyclicGroup(5) + >>> H = G*G + >>> H + PermutationGroup([ + (9)(0 1 2 3 4), + (5 6 7 8 9)]) + >>> H.order() + 25 + + """ + if isinstance(other, Permutation): + return Coset(other, self, dir='+') + gens1 = [perm._array_form for perm in self.generators] + gens2 = [perm._array_form for perm in other.generators] + n1 = self._degree + n2 = other._degree + start = list(range(n1)) + end = list(range(n1, n1 + n2)) + for i in range(len(gens2)): + gens2[i] = [x + n1 for x in gens2[i]] + gens2 = [start + gen for gen in gens2] + gens1 = [gen + end for gen in gens1] + together = gens1 + gens2 + gens = [_af_new(x) for x in together] + return PermutationGroup(gens) + + def _random_pr_init(self, r, n, _random_prec_n=None): + r"""Initialize random generators for the product replacement algorithm. + + Explanation + =========== + + The implementation uses a modification of the original product + replacement algorithm due to Leedham-Green, as described in [1], + pp. 69-71; also, see [2], pp. 27-29 for a detailed theoretical + analysis of the original product replacement algorithm, and [4]. + + The product replacement algorithm is used for producing random, + uniformly distributed elements of a group `G` with a set of generators + `S`. For the initialization ``_random_pr_init``, a list ``R`` of + `\max\{r, |S|\}` group generators is created as the attribute + ``G._random_gens``, repeating elements of `S` if necessary, and the + identity element of `G` is appended to ``R`` - we shall refer to this + last element as the accumulator. Then the function ``random_pr()`` + is called ``n`` times, randomizing the list ``R`` while preserving + the generation of `G` by ``R``. The function ``random_pr()`` itself + takes two random elements ``g, h`` among all elements of ``R`` but + the accumulator and replaces ``g`` with a randomly chosen element + from `\{gh, g(~h), hg, (~h)g\}`. Then the accumulator is multiplied + by whatever ``g`` was replaced by. The new value of the accumulator is + then returned by ``random_pr()``. + + The elements returned will eventually (for ``n`` large enough) become + uniformly distributed across `G` ([5]). For practical purposes however, + the values ``n = 50, r = 11`` are suggested in [1]. + + Notes + ===== + + THIS FUNCTION HAS SIDE EFFECTS: it changes the attribute + self._random_gens + + See Also + ======== + + random_pr + + """ + deg = self.degree + random_gens = [x._array_form for x in self.generators] + k = len(random_gens) + if k < r: + for i in range(k, r): + random_gens.append(random_gens[i - k]) + acc = list(range(deg)) + random_gens.append(acc) + self._random_gens = random_gens + + # handle randomized input for testing purposes + if _random_prec_n is None: + for i in range(n): + self.random_pr() + else: + for i in range(n): + self.random_pr(_random_prec=_random_prec_n[i]) + + def _union_find_merge(self, first, second, ranks, parents, not_rep): + """Merges two classes in a union-find data structure. + + Explanation + =========== + + Used in the implementation of Atkinson's algorithm as suggested in [1], + pp. 83-87. The class merging process uses union by rank as an + optimization. ([7]) + + Notes + ===== + + THIS FUNCTION HAS SIDE EFFECTS: the list of class representatives, + ``parents``, the list of class sizes, ``ranks``, and the list of + elements that are not representatives, ``not_rep``, are changed due to + class merging. + + See Also + ======== + + minimal_block, _union_find_rep + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of computational group theory" + + .. [7] https://algorithmist.com/wiki/Union_find + + """ + rep_first = self._union_find_rep(first, parents) + rep_second = self._union_find_rep(second, parents) + if rep_first != rep_second: + # union by rank + if ranks[rep_first] >= ranks[rep_second]: + new_1, new_2 = rep_first, rep_second + else: + new_1, new_2 = rep_second, rep_first + total_rank = ranks[new_1] + ranks[new_2] + if total_rank > self.max_div: + return -1 + parents[new_2] = new_1 + ranks[new_1] = total_rank + not_rep.append(new_2) + return 1 + return 0 + + def _union_find_rep(self, num, parents): + """Find representative of a class in a union-find data structure. + + Explanation + =========== + + Used in the implementation of Atkinson's algorithm as suggested in [1], + pp. 83-87. After the representative of the class to which ``num`` + belongs is found, path compression is performed as an optimization + ([7]). + + Notes + ===== + + THIS FUNCTION HAS SIDE EFFECTS: the list of class representatives, + ``parents``, is altered due to path compression. + + See Also + ======== + + minimal_block, _union_find_merge + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of computational group theory" + + .. [7] https://algorithmist.com/wiki/Union_find + + """ + rep, parent = num, parents[num] + while parent != rep: + rep = parent + parent = parents[rep] + # path compression + temp, parent = num, parents[num] + while parent != rep: + parents[temp] = rep + temp = parent + parent = parents[temp] + return rep + + @property + def base(self): + r"""Return a base from the Schreier-Sims algorithm. + + Explanation + =========== + + For a permutation group `G`, a base is a sequence of points + `B = (b_1, b_2, \dots, b_k)` such that no element of `G` apart + from the identity fixes all the points in `B`. The concepts of + a base and strong generating set and their applications are + discussed in depth in [1], pp. 87-89 and [2], pp. 55-57. + + An alternative way to think of `B` is that it gives the + indices of the stabilizer cosets that contain more than the + identity permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> G = PermutationGroup([Permutation(0, 1, 3)(2, 4)]) + >>> G.base + [0, 2] + + See Also + ======== + + strong_gens, basic_transversals, basic_orbits, basic_stabilizers + + """ + if self._base == []: + self.schreier_sims() + return self._base + + def baseswap(self, base, strong_gens, pos, randomized=False, + transversals=None, basic_orbits=None, strong_gens_distr=None): + r"""Swap two consecutive base points in base and strong generating set. + + Explanation + =========== + + If a base for a group `G` is given by `(b_1, b_2, \dots, b_k)`, this + function returns a base `(b_1, b_2, \dots, b_{i+1}, b_i, \dots, b_k)`, + where `i` is given by ``pos``, and a strong generating set relative + to that base. The original base and strong generating set are not + modified. + + The randomized version (default) is of Las Vegas type. + + Parameters + ========== + + base, strong_gens + The base and strong generating set. + pos + The position at which swapping is performed. + randomized + A switch between randomized and deterministic version. + transversals + The transversals for the basic orbits, if known. + basic_orbits + The basic orbits, if known. + strong_gens_distr + The strong generators distributed by basic stabilizers, if known. + + Returns + ======= + + (base, strong_gens) + ``base`` is the new base, and ``strong_gens`` is a generating set + relative to it. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> S = SymmetricGroup(4) + >>> S.schreier_sims() + >>> S.base + [0, 1, 2] + >>> base, gens = S.baseswap(S.base, S.strong_gens, 1, randomized=False) + >>> base, gens + ([0, 2, 1], + [(0 1 2 3), (3)(0 1), (1 3 2), + (2 3), (1 3)]) + + check that base, gens is a BSGS + + >>> S1 = PermutationGroup(gens) + >>> _verify_bsgs(S1, base, gens) + True + + See Also + ======== + + schreier_sims + + Notes + ===== + + The deterministic version of the algorithm is discussed in + [1], pp. 102-103; the randomized version is discussed in [1], p.103, and + [2], p.98. It is of Las Vegas type. + Notice that [1] contains a mistake in the pseudocode and + discussion of BASESWAP: on line 3 of the pseudocode, + `|\beta_{i+1}^{\left\langle T\right\rangle}|` should be replaced by + `|\beta_{i}^{\left\langle T\right\rangle}|`, and the same for the + discussion of the algorithm. + + """ + # construct the basic orbits, generators for the stabilizer chain + # and transversal elements from whatever was provided + transversals, basic_orbits, strong_gens_distr = \ + _handle_precomputed_bsgs(base, strong_gens, transversals, + basic_orbits, strong_gens_distr) + base_len = len(base) + degree = self.degree + # size of orbit of base[pos] under the stabilizer we seek to insert + # in the stabilizer chain at position pos + 1 + size = len(basic_orbits[pos])*len(basic_orbits[pos + 1]) \ + //len(_orbit(degree, strong_gens_distr[pos], base[pos + 1])) + # initialize the wanted stabilizer by a subgroup + if pos + 2 > base_len - 1: + T = [] + else: + T = strong_gens_distr[pos + 2][:] + # randomized version + if randomized is True: + stab_pos = PermutationGroup(strong_gens_distr[pos]) + schreier_vector = stab_pos.schreier_vector(base[pos + 1]) + # add random elements of the stabilizer until they generate it + while len(_orbit(degree, T, base[pos])) != size: + new = stab_pos.random_stab(base[pos + 1], + schreier_vector=schreier_vector) + T.append(new) + # deterministic version + else: + Gamma = set(basic_orbits[pos]) + Gamma.remove(base[pos]) + if base[pos + 1] in Gamma: + Gamma.remove(base[pos + 1]) + # add elements of the stabilizer until they generate it by + # ruling out member of the basic orbit of base[pos] along the way + while len(_orbit(degree, T, base[pos])) != size: + gamma = next(iter(Gamma)) + x = transversals[pos][gamma] + temp = x._array_form.index(base[pos + 1]) # (~x)(base[pos + 1]) + if temp not in basic_orbits[pos + 1]: + Gamma = Gamma - _orbit(degree, T, gamma) + else: + y = transversals[pos + 1][temp] + el = rmul(x, y) + if el(base[pos]) not in _orbit(degree, T, base[pos]): + T.append(el) + Gamma = Gamma - _orbit(degree, T, base[pos]) + # build the new base and strong generating set + strong_gens_new_distr = strong_gens_distr[:] + strong_gens_new_distr[pos + 1] = T + base_new = base[:] + base_new[pos], base_new[pos + 1] = base_new[pos + 1], base_new[pos] + strong_gens_new = _strong_gens_from_distr(strong_gens_new_distr) + for gen in T: + if gen not in strong_gens_new: + strong_gens_new.append(gen) + return base_new, strong_gens_new + + @property + def basic_orbits(self): + r""" + Return the basic orbits relative to a base and strong generating set. + + Explanation + =========== + + If `(b_1, b_2, \dots, b_k)` is a base for a group `G`, and + `G^{(i)} = G_{b_1, b_2, \dots, b_{i-1}}` is the ``i``-th basic stabilizer + (so that `G^{(1)} = G`), the ``i``-th basic orbit relative to this base + is the orbit of `b_i` under `G^{(i)}`. See [1], pp. 87-89 for more + information. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> S = SymmetricGroup(4) + >>> S.basic_orbits + [[0, 1, 2, 3], [1, 2, 3], [2, 3]] + + See Also + ======== + + base, strong_gens, basic_transversals, basic_stabilizers + + """ + if self._basic_orbits == []: + self.schreier_sims() + return self._basic_orbits + + @property + def basic_stabilizers(self): + r""" + Return a chain of stabilizers relative to a base and strong generating + set. + + Explanation + =========== + + The ``i``-th basic stabilizer `G^{(i)}` relative to a base + `(b_1, b_2, \dots, b_k)` is `G_{b_1, b_2, \dots, b_{i-1}}`. For more + information, see [1], pp. 87-89. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> A = AlternatingGroup(4) + >>> A.schreier_sims() + >>> A.base + [0, 1] + >>> for g in A.basic_stabilizers: + ... print(g) + ... + PermutationGroup([ + (3)(0 1 2), + (1 2 3)]) + PermutationGroup([ + (1 2 3)]) + + See Also + ======== + + base, strong_gens, basic_orbits, basic_transversals + + """ + + if self._transversals == []: + self.schreier_sims() + strong_gens = self._strong_gens + base = self._base + if not base: # e.g. if self is trivial + return [] + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + basic_stabilizers = [] + for gens in strong_gens_distr: + basic_stabilizers.append(PermutationGroup(gens)) + return basic_stabilizers + + @property + def basic_transversals(self): + """ + Return basic transversals relative to a base and strong generating set. + + Explanation + =========== + + The basic transversals are transversals of the basic orbits. They + are provided as a list of dictionaries, each dictionary having + keys - the elements of one of the basic orbits, and values - the + corresponding transversal elements. See [1], pp. 87-89 for more + information. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> A = AlternatingGroup(4) + >>> A.basic_transversals + [{0: (3), 1: (3)(0 1 2), 2: (3)(0 2 1), 3: (0 3 1)}, {1: (3), 2: (1 2 3), 3: (1 3 2)}] + + See Also + ======== + + strong_gens, base, basic_orbits, basic_stabilizers + + """ + + if self._transversals == []: + self.schreier_sims() + return self._transversals + + def composition_series(self): + r""" + Return the composition series for a group as a list + of permutation groups. + + Explanation + =========== + + The composition series for a group `G` is defined as a + subnormal series `G = H_0 > H_1 > H_2 \ldots` A composition + series is a subnormal series such that each factor group + `H(i+1) / H(i)` is simple. + A subnormal series is a composition series only if it is of + maximum length. + + The algorithm works as follows: + Starting with the derived series the idea is to fill + the gap between `G = der[i]` and `H = der[i+1]` for each + `i` independently. Since, all subgroups of the abelian group + `G/H` are normal so, first step is to take the generators + `g` of `G` and add them to generators of `H` one by one. + + The factor groups formed are not simple in general. Each + group is obtained from the previous one by adding one + generator `g`, if the previous group is denoted by `H` + then the next group `K` is generated by `g` and `H`. + The factor group `K/H` is cyclic and it's order is + `K.order()//G.order()`. The series is then extended between + `K` and `H` by groups generated by powers of `g` and `H`. + The series formed is then prepended to the already existing + series. + + Examples + ======== + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.named_groups import CyclicGroup + >>> S = SymmetricGroup(12) + >>> G = S.sylow_subgroup(2) + >>> C = G.composition_series() + >>> [H.order() for H in C] + [1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1] + >>> G = S.sylow_subgroup(3) + >>> C = G.composition_series() + >>> [H.order() for H in C] + [243, 81, 27, 9, 3, 1] + >>> G = CyclicGroup(12) + >>> C = G.composition_series() + >>> [H.order() for H in C] + [12, 6, 3, 1] + + """ + der = self.derived_series() + if not all(g.is_identity for g in der[-1].generators): + raise NotImplementedError('Group should be solvable') + series = [] + + for i in range(len(der)-1): + H = der[i+1] + up_seg = [] + for g in der[i].generators: + K = PermutationGroup([g] + H.generators) + order = K.order() // H.order() + down_seg = [] + for p, e in factorint(order).items(): + for _ in range(e): + down_seg.append(PermutationGroup([g] + H.generators)) + g = g**p + up_seg = down_seg + up_seg + H = K + up_seg[0] = der[i] + series.extend(up_seg) + series.append(der[-1]) + return series + + def coset_transversal(self, H): + """Return a transversal of the right cosets of self by its subgroup H + using the second method described in [1], Subsection 4.6.7 + + """ + + if not H.is_subgroup(self): + raise ValueError("The argument must be a subgroup") + + if H.order() == 1: + return self.elements + + self._schreier_sims(base=H.base) # make G.base an extension of H.base + + base = self.base + base_ordering = _base_ordering(base, self.degree) + identity = Permutation(self.degree - 1) + + transversals = self.basic_transversals[:] + # transversals is a list of dictionaries. Get rid of the keys + # so that it is a list of lists and sort each list in + # the increasing order of base[l]^x + for l, t in enumerate(transversals): + transversals[l] = sorted(t.values(), + key = lambda x: base_ordering[base[l]^x]) + + orbits = H.basic_orbits + h_stabs = H.basic_stabilizers + g_stabs = self.basic_stabilizers + + indices = [x.order()//y.order() for x, y in zip(g_stabs, h_stabs)] + + # T^(l) should be a right transversal of H^(l) in G^(l) for + # 1<=l<=len(base). While H^(l) is the trivial group, T^(l) + # contains all the elements of G^(l) so we might just as well + # start with l = len(h_stabs)-1 + if len(g_stabs) > len(h_stabs): + T = g_stabs[len(h_stabs)].elements + else: + T = [identity] + l = len(h_stabs)-1 + t_len = len(T) + while l > -1: + T_next = [] + for u in transversals[l]: + if u == identity: + continue + b = base_ordering[base[l]^u] + for t in T: + p = t*u + if all(base_ordering[h^p] >= b for h in orbits[l]): + T_next.append(p) + if t_len + len(T_next) == indices[l]: + break + if t_len + len(T_next) == indices[l]: + break + T += T_next + t_len += len(T_next) + l -= 1 + T.remove(identity) + T = [identity] + T + return T + + def _coset_representative(self, g, H): + """Return the representative of Hg from the transversal that + would be computed by ``self.coset_transversal(H)``. + + """ + if H.order() == 1: + return g + # The base of self must be an extension of H.base. + if not(self.base[:len(H.base)] == H.base): + self._schreier_sims(base=H.base) + orbits = H.basic_orbits[:] + h_transversals = [list(_.values()) for _ in H.basic_transversals] + transversals = [list(_.values()) for _ in self.basic_transversals] + base = self.base + base_ordering = _base_ordering(base, self.degree) + def step(l, x): + gamma = min(orbits[l], key = lambda y: base_ordering[y^x]) + i = [base[l]^h for h in h_transversals[l]].index(gamma) + x = h_transversals[l][i]*x + if l < len(orbits)-1: + for u in transversals[l]: + if base[l]^u == base[l]^x: + break + x = step(l+1, x*u**-1)*u + return x + return step(0, g) + + def coset_table(self, H): + """Return the standardised (right) coset table of self in H as + a list of lists. + """ + # Maybe this should be made to return an instance of CosetTable + # from fp_groups.py but the class would need to be changed first + # to be compatible with PermutationGroups + + if not H.is_subgroup(self): + raise ValueError("The argument must be a subgroup") + T = self.coset_transversal(H) + n = len(T) + + A = list(chain.from_iterable((gen, gen**-1) + for gen in self.generators)) + + table = [] + for i in range(n): + row = [self._coset_representative(T[i]*x, H) for x in A] + row = [T.index(r) for r in row] + table.append(row) + + # standardize (this is the same as the algorithm used in coset_table) + # If CosetTable is made compatible with PermutationGroups, this + # should be replaced by table.standardize() + A = range(len(A)) + gamma = 1 + for alpha, a in product(range(n), A): + beta = table[alpha][a] + if beta >= gamma: + if beta > gamma: + for x in A: + z = table[gamma][x] + table[gamma][x] = table[beta][x] + table[beta][x] = z + for i in range(n): + if table[i][x] == beta: + table[i][x] = gamma + elif table[i][x] == gamma: + table[i][x] = beta + gamma += 1 + if gamma >= n-1: + return table + + def center(self): + r""" + Return the center of a permutation group. + + Explanation + =========== + + The center for a group `G` is defined as + `Z(G) = \{z\in G | \forall g\in G, zg = gz \}`, + the set of elements of `G` that commute with all elements of `G`. + It is equal to the centralizer of `G` inside `G`, and is naturally a + subgroup of `G` ([9]). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(4) + >>> G = D.center() + >>> G.order() + 2 + + See Also + ======== + + centralizer + + Notes + ===== + + This is a naive implementation that is a straightforward application + of ``.centralizer()`` + + """ + if not self._center: + self._center = self.centralizer(self) + return self._center + + def centralizer(self, other): + r""" + Return the centralizer of a group/set/element. + + Explanation + =========== + + The centralizer of a set of permutations ``S`` inside + a group ``G`` is the set of elements of ``G`` that commute with all + elements of ``S``:: + + `C_G(S) = \{ g \in G | gs = sg \forall s \in S\}` ([10]) + + Usually, ``S`` is a subset of ``G``, but if ``G`` is a proper subgroup of + the full symmetric group, we allow for ``S`` to have elements outside + ``G``. + + It is naturally a subgroup of ``G``; the centralizer of a permutation + group is equal to the centralizer of any set of generators for that + group, since any element commuting with the generators commutes with + any product of the generators. + + Parameters + ========== + + other + a permutation group/list of permutations/single permutation + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... CyclicGroup) + >>> S = SymmetricGroup(6) + >>> C = CyclicGroup(6) + >>> H = S.centralizer(C) + >>> H.is_subgroup(C) + True + + See Also + ======== + + subgroup_search + + Notes + ===== + + The implementation is an application of ``.subgroup_search()`` with + tests using a specific base for the group ``G``. + + """ + if hasattr(other, 'generators'): + if other.is_trivial or self.is_trivial: + return self + degree = self.degree + identity = _af_new(list(range(degree))) + orbits = other.orbits() + num_orbits = len(orbits) + orbits.sort(key=lambda x: -len(x)) + long_base = [] + orbit_reps = [None]*num_orbits + orbit_reps_indices = [None]*num_orbits + orbit_descr = [None]*degree + for i in range(num_orbits): + orbit = list(orbits[i]) + orbit_reps[i] = orbit[0] + orbit_reps_indices[i] = len(long_base) + for point in orbit: + orbit_descr[point] = i + long_base = long_base + orbit + base, strong_gens = self.schreier_sims_incremental(base=long_base) + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + i = 0 + for i in range(len(base)): + if strong_gens_distr[i] == [identity]: + break + base = base[:i] + base_len = i + for j in range(num_orbits): + if base[base_len - 1] in orbits[j]: + break + rel_orbits = orbits[: j + 1] + num_rel_orbits = len(rel_orbits) + transversals = [None]*num_rel_orbits + for j in range(num_rel_orbits): + rep = orbit_reps[j] + transversals[j] = dict( + other.orbit_transversal(rep, pairs=True)) + trivial_test = lambda x: True + tests = [None]*base_len + for l in range(base_len): + if base[l] in orbit_reps: + tests[l] = trivial_test + else: + def test(computed_words, l=l): + g = computed_words[l] + rep_orb_index = orbit_descr[base[l]] + rep = orbit_reps[rep_orb_index] + im = g._array_form[base[l]] + im_rep = g._array_form[rep] + tr_el = transversals[rep_orb_index][base[l]] + # using the definition of transversal, + # base[l]^g = rep^(tr_el*g); + # if g belongs to the centralizer, then + # base[l]^g = (rep^g)^tr_el + return im == tr_el._array_form[im_rep] + tests[l] = test + + def prop(g): + return [rmul(g, gen) for gen in other.generators] == \ + [rmul(gen, g) for gen in other.generators] + return self.subgroup_search(prop, base=base, + strong_gens=strong_gens, tests=tests) + elif hasattr(other, '__getitem__'): + gens = list(other) + return self.centralizer(PermutationGroup(gens)) + elif hasattr(other, 'array_form'): + return self.centralizer(PermutationGroup([other])) + + def commutator(self, G, H): + """ + Return the commutator of two subgroups. + + Explanation + =========== + + For a permutation group ``K`` and subgroups ``G``, ``H``, the + commutator of ``G`` and ``H`` is defined as the group generated + by all the commutators `[g, h] = hgh^{-1}g^{-1}` for ``g`` in ``G`` and + ``h`` in ``H``. It is naturally a subgroup of ``K`` ([1], p.27). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... AlternatingGroup) + >>> S = SymmetricGroup(5) + >>> A = AlternatingGroup(5) + >>> G = S.commutator(S, A) + >>> G.is_subgroup(A) + True + + See Also + ======== + + derived_subgroup + + Notes + ===== + + The commutator of two subgroups `H, G` is equal to the normal closure + of the commutators of all the generators, i.e. `hgh^{-1}g^{-1}` for `h` + a generator of `H` and `g` a generator of `G` ([1], p.28) + + """ + ggens = G.generators + hgens = H.generators + commutators = [] + for ggen in ggens: + for hgen in hgens: + commutator = rmul(hgen, ggen, ~hgen, ~ggen) + if commutator not in commutators: + commutators.append(commutator) + res = self.normal_closure(commutators) + return res + + def coset_factor(self, g, factor_index=False): + """Return ``G``'s (self's) coset factorization of ``g`` + + Explanation + =========== + + If ``g`` is an element of ``G`` then it can be written as the product + of permutations drawn from the Schreier-Sims coset decomposition, + + The permutations returned in ``f`` are those for which + the product gives ``g``: ``g = f[n]*...f[1]*f[0]`` where ``n = len(B)`` + and ``B = G.base``. f[i] is one of the permutations in + ``self._basic_orbits[i]``. + + If factor_index==True, + returns a tuple ``[b[0],..,b[n]]``, where ``b[i]`` + belongs to ``self._basic_orbits[i]`` + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation(0, 1, 3, 7, 6, 4)(2, 5) + >>> b = Permutation(0, 1, 3, 2)(4, 5, 7, 6) + >>> G = PermutationGroup([a, b]) + + Define g: + + >>> g = Permutation(7)(1, 2, 4)(3, 6, 5) + + Confirm that it is an element of G: + + >>> G.contains(g) + True + + Thus, it can be written as a product of factors (up to + 3) drawn from u. See below that a factor from u1 and u2 + and the Identity permutation have been used: + + >>> f = G.coset_factor(g) + >>> f[2]*f[1]*f[0] == g + True + >>> f1 = G.coset_factor(g, True); f1 + [0, 4, 4] + >>> tr = G.basic_transversals + >>> f[0] == tr[0][f1[0]] + True + + If g is not an element of G then [] is returned: + + >>> c = Permutation(5, 6, 7) + >>> G.coset_factor(c) + [] + + See Also + ======== + + sympy.combinatorics.util._strip + + """ + if isinstance(g, (Cycle, Permutation)): + g = g.list() + if len(g) != self._degree: + # this could either adjust the size or return [] immediately + # but we don't choose between the two and just signal a possible + # error + raise ValueError('g should be the same size as permutations of G') + I = list(range(self._degree)) + basic_orbits = self.basic_orbits + transversals = self._transversals + factors = [] + base = self.base + h = g + for i in range(len(base)): + beta = h[base[i]] + if beta == base[i]: + factors.append(beta) + continue + if beta not in basic_orbits[i]: + return [] + u = transversals[i][beta]._array_form + h = _af_rmul(_af_invert(u), h) + factors.append(beta) + if h != I: + return [] + if factor_index: + return factors + tr = self.basic_transversals + factors = [tr[i][factors[i]] for i in range(len(base))] + return factors + + def generator_product(self, g, original=False): + r''' + Return a list of strong generators `[s1, \dots, sn]` + s.t `g = sn \times \dots \times s1`. If ``original=True``, make the + list contain only the original group generators + + ''' + product = [] + if g.is_identity: + return [] + if g in self.strong_gens: + if not original or g in self.generators: + return [g] + else: + slp = self._strong_gens_slp[g] + for s in slp: + product.extend(self.generator_product(s, original=True)) + return product + elif g**-1 in self.strong_gens: + g = g**-1 + if not original or g in self.generators: + return [g**-1] + else: + slp = self._strong_gens_slp[g] + for s in slp: + product.extend(self.generator_product(s, original=True)) + l = len(product) + product = [product[l-i-1]**-1 for i in range(l)] + return product + + f = self.coset_factor(g, True) + for i, j in enumerate(f): + slp = self._transversal_slp[i][j] + for s in slp: + if not original: + product.append(self.strong_gens[s]) + else: + s = self.strong_gens[s] + product.extend(self.generator_product(s, original=True)) + return product + + def coset_rank(self, g): + """rank using Schreier-Sims representation. + + Explanation + =========== + + The coset rank of ``g`` is the ordering number in which + it appears in the lexicographic listing according to the + coset decomposition + + The ordering is the same as in G.generate(method='coset'). + If ``g`` does not belong to the group it returns None. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation(0, 1, 3, 7, 6, 4)(2, 5) + >>> b = Permutation(0, 1, 3, 2)(4, 5, 7, 6) + >>> G = PermutationGroup([a, b]) + >>> c = Permutation(7)(2, 4)(3, 5) + >>> G.coset_rank(c) + 16 + >>> G.coset_unrank(16) + (7)(2 4)(3 5) + + See Also + ======== + + coset_factor + + """ + factors = self.coset_factor(g, True) + if not factors: + return None + rank = 0 + b = 1 + transversals = self._transversals + base = self._base + basic_orbits = self._basic_orbits + for i in range(len(base)): + k = factors[i] + j = basic_orbits[i].index(k) + rank += b*j + b = b*len(transversals[i]) + return rank + + def coset_unrank(self, rank, af=False): + """unrank using Schreier-Sims representation + + coset_unrank is the inverse operation of coset_rank + if 0 <= rank < order; otherwise it returns None. + + """ + if rank < 0 or rank >= self.order(): + return None + base = self.base + transversals = self.basic_transversals + basic_orbits = self.basic_orbits + m = len(base) + v = [0]*m + for i in range(m): + rank, c = divmod(rank, len(transversals[i])) + v[i] = basic_orbits[i][c] + a = [transversals[i][v[i]]._array_form for i in range(m)] + h = _af_rmuln(*a) + if af: + return h + else: + return _af_new(h) + + @property + def degree(self): + """Returns the size of the permutations in the group. + + Explanation + =========== + + The number of permutations comprising the group is given by + ``len(group)``; the number of permutations that can be generated + by the group is given by ``group.order()``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a]) + >>> G.degree + 3 + >>> len(G) + 1 + >>> G.order() + 2 + >>> list(G.generate()) + [(2), (2)(0 1)] + + See Also + ======== + + order + """ + return self._degree + + @property + def identity(self): + ''' + Return the identity element of the permutation group. + + ''' + return _af_new(list(range(self.degree))) + + @property + def elements(self): + """Returns all the elements of the permutation group as a list + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> p = PermutationGroup(Permutation(1, 3), Permutation(1, 2)) + >>> p.elements + [(3), (3)(1 2), (1 3), (2 3), (1 2 3), (1 3 2)] + + """ + if not self._elements: + self._elements = list(self.generate()) + + return self._elements + + def derived_series(self): + r"""Return the derived series for the group. + + Explanation + =========== + + The derived series for a group `G` is defined as + `G = G_0 > G_1 > G_2 > \ldots` where `G_i = [G_{i-1}, G_{i-1}]`, + i.e. `G_i` is the derived subgroup of `G_{i-1}`, for + `i\in\mathbb{N}`. When we have `G_k = G_{k-1}` for some + `k\in\mathbb{N}`, the series terminates. + + Returns + ======= + + A list of permutation groups containing the members of the derived + series in the order `G = G_0, G_1, G_2, \ldots`. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... AlternatingGroup, DihedralGroup) + >>> A = AlternatingGroup(5) + >>> len(A.derived_series()) + 1 + >>> S = SymmetricGroup(4) + >>> len(S.derived_series()) + 4 + >>> S.derived_series()[1].is_subgroup(AlternatingGroup(4)) + True + >>> S.derived_series()[2].is_subgroup(DihedralGroup(2)) + True + + See Also + ======== + + derived_subgroup + + """ + res = [self] + current = self + nxt = self.derived_subgroup() + while not current.is_subgroup(nxt): + res.append(nxt) + current = nxt + nxt = nxt.derived_subgroup() + return res + + def derived_subgroup(self): + r"""Compute the derived subgroup. + + Explanation + =========== + + The derived subgroup, or commutator subgroup is the subgroup generated + by all commutators `[g, h] = hgh^{-1}g^{-1}` for `g, h\in G` ; it is + equal to the normal closure of the set of commutators of the generators + ([1], p.28, [11]). + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([1, 0, 2, 4, 3]) + >>> b = Permutation([0, 1, 3, 2, 4]) + >>> G = PermutationGroup([a, b]) + >>> C = G.derived_subgroup() + >>> list(C.generate(af=True)) + [[0, 1, 2, 3, 4], [0, 1, 3, 4, 2], [0, 1, 4, 2, 3]] + + See Also + ======== + + derived_series + + """ + r = self._r + gens = [p._array_form for p in self.generators] + set_commutators = set() + degree = self._degree + rng = list(range(degree)) + for i in range(r): + for j in range(r): + p1 = gens[i] + p2 = gens[j] + c = list(range(degree)) + for k in rng: + c[p2[p1[k]]] = p1[p2[k]] + ct = tuple(c) + if ct not in set_commutators: + set_commutators.add(ct) + cms = [_af_new(p) for p in set_commutators] + G2 = self.normal_closure(cms) + return G2 + + def generate(self, method="coset", af=False): + """Return iterator to generate the elements of the group. + + Explanation + =========== + + Iteration is done with one of these methods:: + + method='coset' using the Schreier-Sims coset representation + method='dimino' using the Dimino method + + If ``af = True`` it yields the array form of the permutations + + Examples + ======== + + >>> from sympy.combinatorics import PermutationGroup + >>> from sympy.combinatorics.polyhedron import tetrahedron + + The permutation group given in the tetrahedron object is also + true groups: + + >>> G = tetrahedron.pgroup + >>> G.is_group + True + + Also the group generated by the permutations in the tetrahedron + pgroup -- even the first two -- is a proper group: + + >>> H = PermutationGroup(G[0], G[1]) + >>> J = PermutationGroup(list(H.generate())); J + PermutationGroup([ + (0 1)(2 3), + (1 2 3), + (1 3 2), + (0 3 1), + (0 2 3), + (0 3)(1 2), + (0 1 3), + (3)(0 2 1), + (0 3 2), + (3)(0 1 2), + (0 2)(1 3)]) + >>> _.is_group + True + """ + if method == "coset": + return self.generate_schreier_sims(af) + elif method == "dimino": + return self.generate_dimino(af) + else: + raise NotImplementedError('No generation defined for %s' % method) + + def generate_dimino(self, af=False): + """Yield group elements using Dimino's algorithm. + + If ``af == True`` it yields the array form of the permutations. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1, 3]) + >>> b = Permutation([0, 2, 3, 1]) + >>> g = PermutationGroup([a, b]) + >>> list(g.generate_dimino(af=True)) + [[0, 1, 2, 3], [0, 2, 1, 3], [0, 2, 3, 1], + [0, 1, 3, 2], [0, 3, 2, 1], [0, 3, 1, 2]] + + References + ========== + + .. [1] The Implementation of Various Algorithms for Permutation Groups in + the Computer Algebra System: AXIOM, N.J. Doye, M.Sc. Thesis + + """ + idn = list(range(self.degree)) + order = 0 + element_list = [idn] + set_element_list = {tuple(idn)} + if af: + yield idn + else: + yield _af_new(idn) + gens = [p._array_form for p in self.generators] + + for i in range(len(gens)): + # D elements of the subgroup G_i generated by gens[:i] + D = element_list[:] + N = [idn] + while N: + A = N + N = [] + for a in A: + for g in gens[:i + 1]: + ag = _af_rmul(a, g) + if tuple(ag) not in set_element_list: + # produce G_i*g + for d in D: + order += 1 + ap = _af_rmul(d, ag) + if af: + yield ap + else: + p = _af_new(ap) + yield p + element_list.append(ap) + set_element_list.add(tuple(ap)) + N.append(ap) + self._order = len(element_list) + + def generate_schreier_sims(self, af=False): + """Yield group elements using the Schreier-Sims representation + in coset_rank order + + If ``af = True`` it yields the array form of the permutations + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1, 3]) + >>> b = Permutation([0, 2, 3, 1]) + >>> g = PermutationGroup([a, b]) + >>> list(g.generate_schreier_sims(af=True)) + [[0, 1, 2, 3], [0, 2, 1, 3], [0, 3, 2, 1], + [0, 1, 3, 2], [0, 2, 3, 1], [0, 3, 1, 2]] + """ + + n = self._degree + u = self.basic_transversals + basic_orbits = self._basic_orbits + if len(u) == 0: + for x in self.generators: + if af: + yield x._array_form + else: + yield x + return + if len(u) == 1: + for i in basic_orbits[0]: + if af: + yield u[0][i]._array_form + else: + yield u[0][i] + return + + u = list(reversed(u)) + basic_orbits = basic_orbits[::-1] + # stg stack of group elements + stg = [list(range(n))] + posmax = [len(x) for x in u] + n1 = len(posmax) - 1 + pos = [0]*n1 + h = 0 + while 1: + # backtrack when finished iterating over coset + if pos[h] >= posmax[h]: + if h == 0: + return + pos[h] = 0 + h -= 1 + stg.pop() + continue + p = _af_rmul(u[h][basic_orbits[h][pos[h]]]._array_form, stg[-1]) + pos[h] += 1 + stg.append(p) + h += 1 + if h == n1: + if af: + for i in basic_orbits[-1]: + p = _af_rmul(u[-1][i]._array_form, stg[-1]) + yield p + else: + for i in basic_orbits[-1]: + p = _af_rmul(u[-1][i]._array_form, stg[-1]) + p1 = _af_new(p) + yield p1 + stg.pop() + h -= 1 + + @property + def generators(self): + """Returns the generators of the group. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.generators + [(1 2), (2)(0 1)] + + """ + return self._generators + + def contains(self, g, strict=True): + """Test if permutation ``g`` belong to self, ``G``. + + Explanation + =========== + + If ``g`` is an element of ``G`` it can be written as a product + of factors drawn from the cosets of ``G``'s stabilizers. To see + if ``g`` is one of the actual generators defining the group use + ``G.has(g)``. + + If ``strict`` is not ``True``, ``g`` will be resized, if necessary, + to match the size of permutations in ``self``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + + >>> a = Permutation(1, 2) + >>> b = Permutation(2, 3, 1) + >>> G = PermutationGroup(a, b, degree=5) + >>> G.contains(G[0]) # trivial check + True + >>> elem = Permutation([[2, 3]], size=5) + >>> G.contains(elem) + True + >>> G.contains(Permutation(4)(0, 1, 2, 3)) + False + + If strict is False, a permutation will be resized, if + necessary: + + >>> H = PermutationGroup(Permutation(5)) + >>> H.contains(Permutation(3)) + False + >>> H.contains(Permutation(3), strict=False) + True + + To test if a given permutation is present in the group: + + >>> elem in G.generators + False + >>> G.has(elem) + False + + See Also + ======== + + coset_factor, sympy.core.basic.Basic.has, __contains__ + + """ + if not isinstance(g, Permutation): + return False + if g.size != self.degree: + if strict: + return False + g = Permutation(g, size=self.degree) + if g in self.generators: + return True + return bool(self.coset_factor(g.array_form, True)) + + @property + def is_perfect(self): + """Return ``True`` if the group is perfect. + A group is perfect if it equals to its derived subgroup. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation(1,2,3)(4,5) + >>> b = Permutation(1,2,3,4,5) + >>> G = PermutationGroup([a, b]) + >>> G.is_perfect + False + + """ + if self._is_perfect is None: + self._is_perfect = self.equals(self.derived_subgroup()) + return self._is_perfect + + @property + def is_abelian(self): + """Test if the group is Abelian. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.is_abelian + False + >>> a = Permutation([0, 2, 1]) + >>> G = PermutationGroup([a]) + >>> G.is_abelian + True + + """ + if self._is_abelian is not None: + return self._is_abelian + + self._is_abelian = True + gens = [p._array_form for p in self.generators] + for x in gens: + for y in gens: + if y <= x: + continue + if not _af_commutes_with(x, y): + self._is_abelian = False + return False + return True + + def abelian_invariants(self): + """ + Returns the abelian invariants for the given group. + Let ``G`` be a nontrivial finite abelian group. Then G is isomorphic to + the direct product of finitely many nontrivial cyclic groups of + prime-power order. + + Explanation + =========== + + The prime-powers that occur as the orders of the factors are uniquely + determined by G. More precisely, the primes that occur in the orders of the + factors in any such decomposition of ``G`` are exactly the primes that divide + ``|G|`` and for any such prime ``p``, if the orders of the factors that are + p-groups in one such decomposition of ``G`` are ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``, + then the orders of the factors that are p-groups in any such decomposition of ``G`` + are ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``. + + The uniquely determined integers ``p^{t_1} >= p^{t_2} >= ... p^{t_r}``, taken + for all primes that divide ``|G|`` are called the invariants of the nontrivial + group ``G`` as suggested in ([14], p. 542). + + Notes + ===== + + We adopt the convention that the invariants of a trivial group are []. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.abelian_invariants() + [2] + >>> from sympy.combinatorics import CyclicGroup + >>> G = CyclicGroup(7) + >>> G.abelian_invariants() + [7] + + """ + if self.is_trivial: + return [] + gns = self.generators + inv = [] + G = self + H = G.derived_subgroup() + Hgens = H.generators + for p in primefactors(G.order()): + ranks = [] + while True: + pows = [] + for g in gns: + elm = g**p + if not H.contains(elm): + pows.append(elm) + K = PermutationGroup(Hgens + pows) if pows else H + r = G.order()//K.order() + G = K + gns = pows + if r == 1: + break + ranks.append(multiplicity(p, r)) + + if ranks: + pows = [1]*ranks[0] + for i in ranks: + for j in range(i): + pows[j] = pows[j]*p + inv.extend(pows) + inv.sort() + return inv + + def is_elementary(self, p): + """Return ``True`` if the group is elementary abelian. An elementary + abelian group is a finite abelian group, where every nontrivial + element has order `p`, where `p` is a prime. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1]) + >>> G = PermutationGroup([a]) + >>> G.is_elementary(2) + True + >>> a = Permutation([0, 2, 1, 3]) + >>> b = Permutation([3, 1, 2, 0]) + >>> G = PermutationGroup([a, b]) + >>> G.is_elementary(2) + True + >>> G.is_elementary(3) + False + + """ + return self.is_abelian and all(g.order() == p for g in self.generators) + + def _eval_is_alt_sym_naive(self, only_sym=False, only_alt=False): + """A naive test using the group order.""" + if only_sym and only_alt: + raise ValueError( + "Both {} and {} cannot be set to True" + .format(only_sym, only_alt)) + + n = self.degree + sym_order = _factorial(n) + order = self.order() + + if order == sym_order: + self._is_sym = True + self._is_alt = False + if only_alt: + return False + return True + + elif 2*order == sym_order: + self._is_sym = False + self._is_alt = True + if only_sym: + return False + return True + + return False + + def _eval_is_alt_sym_monte_carlo(self, eps=0.05, perms=None): + """A test using monte-carlo algorithm. + + Parameters + ========== + + eps : float, optional + The criterion for the incorrect ``False`` return. + + perms : list[Permutation], optional + If explicitly given, it tests over the given candidates + for testing. + + If ``None``, it randomly computes ``N_eps`` and chooses + ``N_eps`` sample of the permutation from the group. + + See Also + ======== + + _check_cycles_alt_sym + """ + if perms is None: + n = self.degree + if n < 17: + c_n = 0.34 + else: + c_n = 0.57 + d_n = (c_n*log(2))/log(n) + N_eps = int(-log(eps)/d_n) + + perms = (self.random_pr() for i in range(N_eps)) + return self._eval_is_alt_sym_monte_carlo(perms=perms) + + for perm in perms: + if _check_cycles_alt_sym(perm): + return True + return False + + def is_alt_sym(self, eps=0.05, _random_prec=None): + r"""Monte Carlo test for the symmetric/alternating group for degrees + >= 8. + + Explanation + =========== + + More specifically, it is one-sided Monte Carlo with the + answer True (i.e., G is symmetric/alternating) guaranteed to be + correct, and the answer False being incorrect with probability eps. + + For degree < 8, the order of the group is checked so the test + is deterministic. + + Notes + ===== + + The algorithm itself uses some nontrivial results from group theory and + number theory: + 1) If a transitive group ``G`` of degree ``n`` contains an element + with a cycle of length ``n/2 < p < n-2`` for ``p`` a prime, ``G`` is the + symmetric or alternating group ([1], pp. 81-82) + 2) The proportion of elements in the symmetric/alternating group having + the property described in 1) is approximately `\log(2)/\log(n)` + ([1], p.82; [2], pp. 226-227). + The helper function ``_check_cycles_alt_sym`` is used to + go over the cycles in a permutation and look for ones satisfying 1). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(10) + >>> D.is_alt_sym() + False + + See Also + ======== + + _check_cycles_alt_sym + + """ + if _random_prec is not None: + N_eps = _random_prec['N_eps'] + perms= (_random_prec[i] for i in range(N_eps)) + return self._eval_is_alt_sym_monte_carlo(perms=perms) + + if self._is_sym or self._is_alt: + return True + if self._is_sym is False and self._is_alt is False: + return False + + n = self.degree + if n < 8: + return self._eval_is_alt_sym_naive() + elif self.is_transitive(): + return self._eval_is_alt_sym_monte_carlo(eps=eps) + + self._is_sym, self._is_alt = False, False + return False + + @property + def is_nilpotent(self): + """Test if the group is nilpotent. + + Explanation + =========== + + A group `G` is nilpotent if it has a central series of finite length. + Alternatively, `G` is nilpotent if its lower central series terminates + with the trivial group. Every nilpotent group is also solvable + ([1], p.29, [12]). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... CyclicGroup) + >>> C = CyclicGroup(6) + >>> C.is_nilpotent + True + >>> S = SymmetricGroup(5) + >>> S.is_nilpotent + False + + See Also + ======== + + lower_central_series, is_solvable + + """ + if self._is_nilpotent is None: + lcs = self.lower_central_series() + terminator = lcs[len(lcs) - 1] + gens = terminator.generators + degree = self.degree + identity = _af_new(list(range(degree))) + if all(g == identity for g in gens): + self._is_solvable = True + self._is_nilpotent = True + return True + else: + self._is_nilpotent = False + return False + else: + return self._is_nilpotent + + def is_normal(self, gr, strict=True): + """Test if ``G=self`` is a normal subgroup of ``gr``. + + Explanation + =========== + + G is normal in gr if + for each g2 in G, g1 in gr, ``g = g1*g2*g1**-1`` belongs to G + It is sufficient to check this for each g1 in gr.generators and + g2 in G.generators. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([1, 2, 0]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G1 = PermutationGroup([a, Permutation([2, 0, 1])]) + >>> G1.is_normal(G) + True + + """ + if not self.is_subgroup(gr, strict=strict): + return False + d_self = self.degree + d_gr = gr.degree + if self.is_trivial and (d_self == d_gr or not strict): + return True + if self._is_abelian: + return True + new_self = self.copy() + if not strict and d_self != d_gr: + if d_self < d_gr: + new_self = PermGroup(new_self.generators + [Permutation(d_gr - 1)]) + else: + gr = PermGroup(gr.generators + [Permutation(d_self - 1)]) + gens2 = [p._array_form for p in new_self.generators] + gens1 = [p._array_form for p in gr.generators] + for g1 in gens1: + for g2 in gens2: + p = _af_rmuln(g1, g2, _af_invert(g1)) + if not new_self.coset_factor(p, True): + return False + return True + + def is_primitive(self, randomized=True): + r"""Test if a group is primitive. + + Explanation + =========== + + A permutation group ``G`` acting on a set ``S`` is called primitive if + ``S`` contains no nontrivial block under the action of ``G`` + (a block is nontrivial if its cardinality is more than ``1``). + + Notes + ===== + + The algorithm is described in [1], p.83, and uses the function + minimal_block to search for blocks of the form `\{0, k\}` for ``k`` + ranging over representatives for the orbits of `G_0`, the stabilizer of + ``0``. This algorithm has complexity `O(n^2)` where ``n`` is the degree + of the group, and will perform badly if `G_0` is small. + + There are two implementations offered: one finds `G_0` + deterministically using the function ``stabilizer``, and the other + (default) produces random elements of `G_0` using ``random_stab``, + hoping that they generate a subgroup of `G_0` with not too many more + orbits than `G_0` (this is suggested in [1], p.83). Behavior is changed + by the ``randomized`` flag. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(10) + >>> D.is_primitive() + False + + See Also + ======== + + minimal_block, random_stab + + """ + if self._is_primitive is not None: + return self._is_primitive + + if self.is_transitive() is False: + return False + + if randomized: + random_stab_gens = [] + v = self.schreier_vector(0) + for _ in range(len(self)): + random_stab_gens.append(self.random_stab(0, v)) + stab = PermutationGroup(random_stab_gens) + else: + stab = self.stabilizer(0) + orbits = stab.orbits() + for orb in orbits: + x = orb.pop() + if x != 0 and any(e != 0 for e in self.minimal_block([0, x])): + self._is_primitive = False + return False + self._is_primitive = True + return True + + def minimal_blocks(self, randomized=True): + ''' + For a transitive group, return the list of all minimal + block systems. If a group is intransitive, return `False`. + + Examples + ======== + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> DihedralGroup(6).minimal_blocks() + [[0, 1, 0, 1, 0, 1], [0, 1, 2, 0, 1, 2]] + >>> G = PermutationGroup(Permutation(1,2,5)) + >>> G.minimal_blocks() + False + + See Also + ======== + + minimal_block, is_transitive, is_primitive + + ''' + def _number_blocks(blocks): + # number the blocks of a block system + # in order and return the number of + # blocks and the tuple with the + # reordering + n = len(blocks) + appeared = {} + m = 0 + b = [None]*n + for i in range(n): + if blocks[i] not in appeared: + appeared[blocks[i]] = m + b[i] = m + m += 1 + else: + b[i] = appeared[blocks[i]] + return tuple(b), m + + if not self.is_transitive(): + return False + blocks = [] + num_blocks = [] + rep_blocks = [] + if randomized: + random_stab_gens = [] + v = self.schreier_vector(0) + for i in range(len(self)): + random_stab_gens.append(self.random_stab(0, v)) + stab = PermutationGroup(random_stab_gens) + else: + stab = self.stabilizer(0) + orbits = stab.orbits() + for orb in orbits: + x = orb.pop() + if x != 0: + block = self.minimal_block([0, x]) + num_block, _ = _number_blocks(block) + # a representative block (containing 0) + rep = {j for j in range(self.degree) if num_block[j] == 0} + # check if the system is minimal with + # respect to the already discovere ones + minimal = True + blocks_remove_mask = [False] * len(blocks) + for i, r in enumerate(rep_blocks): + if len(r) > len(rep) and rep.issubset(r): + # i-th block system is not minimal + blocks_remove_mask[i] = True + elif len(r) < len(rep) and r.issubset(rep): + # the system being checked is not minimal + minimal = False + break + # remove non-minimal representative blocks + blocks = [b for i, b in enumerate(blocks) if not blocks_remove_mask[i]] + num_blocks = [n for i, n in enumerate(num_blocks) if not blocks_remove_mask[i]] + rep_blocks = [r for i, r in enumerate(rep_blocks) if not blocks_remove_mask[i]] + + if minimal and num_block not in num_blocks: + blocks.append(block) + num_blocks.append(num_block) + rep_blocks.append(rep) + return blocks + + @property + def is_solvable(self): + """Test if the group is solvable. + + ``G`` is solvable if its derived series terminates with the trivial + group ([1], p.29). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> S = SymmetricGroup(3) + >>> S.is_solvable + True + + See Also + ======== + + is_nilpotent, derived_series + + """ + if self._is_solvable is None: + if self.order() % 2 != 0: + return True + ds = self.derived_series() + terminator = ds[len(ds) - 1] + gens = terminator.generators + degree = self.degree + identity = _af_new(list(range(degree))) + if all(g == identity for g in gens): + self._is_solvable = True + return True + else: + self._is_solvable = False + return False + else: + return self._is_solvable + + def is_subgroup(self, G, strict=True): + """Return ``True`` if all elements of ``self`` belong to ``G``. + + If ``strict`` is ``False`` then if ``self``'s degree is smaller + than ``G``'s, the elements will be resized to have the same degree. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> from sympy.combinatorics import SymmetricGroup, CyclicGroup + + Testing is strict by default: the degree of each group must be the + same: + + >>> p = Permutation(0, 1, 2, 3, 4, 5) + >>> G1 = PermutationGroup([Permutation(0, 1, 2), Permutation(0, 1)]) + >>> G2 = PermutationGroup([Permutation(0, 2), Permutation(0, 1, 2)]) + >>> G3 = PermutationGroup([p, p**2]) + >>> assert G1.order() == G2.order() == G3.order() == 6 + >>> G1.is_subgroup(G2) + True + >>> G1.is_subgroup(G3) + False + >>> G3.is_subgroup(PermutationGroup(G3[1])) + False + >>> G3.is_subgroup(PermutationGroup(G3[0])) + True + + To ignore the size, set ``strict`` to ``False``: + + >>> S3 = SymmetricGroup(3) + >>> S5 = SymmetricGroup(5) + >>> S3.is_subgroup(S5, strict=False) + True + >>> C7 = CyclicGroup(7) + >>> G = S5*C7 + >>> S5.is_subgroup(G, False) + True + >>> C7.is_subgroup(G, 0) + False + + """ + if isinstance(G, SymmetricPermutationGroup): + if self.degree != G.degree: + return False + return True + if not isinstance(G, PermutationGroup): + return False + if self == G or self.generators[0]==Permutation(): + return True + if G.order() % self.order() != 0: + return False + if self.degree == G.degree or \ + (self.degree < G.degree and not strict): + gens = self.generators + else: + return False + return all(G.contains(g, strict=strict) for g in gens) + + @property + def is_polycyclic(self): + """Return ``True`` if a group is polycyclic. A group is polycyclic if + it has a subnormal series with cyclic factors. For finite groups, + this is the same as if the group is solvable. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1, 3]) + >>> b = Permutation([2, 0, 1, 3]) + >>> G = PermutationGroup([a, b]) + >>> G.is_polycyclic + True + + """ + return self.is_solvable + + def is_transitive(self, strict=True): + """Test if the group is transitive. + + Explanation + =========== + + A group is transitive if it has a single orbit. + + If ``strict`` is ``False`` the group is transitive if it has + a single orbit of length different from 1. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1, 3]) + >>> b = Permutation([2, 0, 1, 3]) + >>> G1 = PermutationGroup([a, b]) + >>> G1.is_transitive() + False + >>> G1.is_transitive(strict=False) + True + >>> c = Permutation([2, 3, 0, 1]) + >>> G2 = PermutationGroup([a, c]) + >>> G2.is_transitive() + True + >>> d = Permutation([1, 0, 2, 3]) + >>> e = Permutation([0, 1, 3, 2]) + >>> G3 = PermutationGroup([d, e]) + >>> G3.is_transitive() or G3.is_transitive(strict=False) + False + + """ + if self._is_transitive: # strict or not, if True then True + return self._is_transitive + if strict: + if self._is_transitive is not None: # we only store strict=True + return self._is_transitive + + ans = len(self.orbit(0)) == self.degree + self._is_transitive = ans + return ans + + got_orb = False + for x in self.orbits(): + if len(x) > 1: + if got_orb: + return False + got_orb = True + return got_orb + + @property + def is_trivial(self): + """Test if the group is the trivial group. + + This is true if the group contains only the identity permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> G = PermutationGroup([Permutation([0, 1, 2])]) + >>> G.is_trivial + True + + """ + if self._is_trivial is None: + self._is_trivial = len(self) == 1 and self[0].is_Identity + return self._is_trivial + + def lower_central_series(self): + r"""Return the lower central series for the group. + + The lower central series for a group `G` is the series + `G = G_0 > G_1 > G_2 > \ldots` where + `G_k = [G, G_{k-1}]`, i.e. every term after the first is equal to the + commutator of `G` and the previous term in `G1` ([1], p.29). + + Returns + ======= + + A list of permutation groups in the order `G = G_0, G_1, G_2, \ldots` + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (AlternatingGroup, + ... DihedralGroup) + >>> A = AlternatingGroup(4) + >>> len(A.lower_central_series()) + 2 + >>> A.lower_central_series()[1].is_subgroup(DihedralGroup(2)) + True + + See Also + ======== + + commutator, derived_series + + """ + res = [self] + current = self + nxt = self.commutator(self, current) + while not current.is_subgroup(nxt): + res.append(nxt) + current = nxt + nxt = self.commutator(self, current) + return res + + @property + def max_div(self): + """Maximum proper divisor of the degree of a permutation group. + + Explanation + =========== + + Obviously, this is the degree divided by its minimal proper divisor + (larger than ``1``, if one exists). As it is guaranteed to be prime, + the ``sieve`` from ``sympy.ntheory`` is used. + This function is also used as an optimization tool for the functions + ``minimal_block`` and ``_union_find_merge``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> G = PermutationGroup([Permutation([0, 2, 1, 3])]) + >>> G.max_div + 2 + + See Also + ======== + + minimal_block, _union_find_merge + + """ + if self._max_div is not None: + return self._max_div + n = self.degree + if n == 1: + return 1 + for x in sieve: + if n % x == 0: + d = n//x + self._max_div = d + return d + + def minimal_block(self, points): + r"""For a transitive group, finds the block system generated by + ``points``. + + Explanation + =========== + + If a group ``G`` acts on a set ``S``, a nonempty subset ``B`` of ``S`` + is called a block under the action of ``G`` if for all ``g`` in ``G`` + we have ``gB = B`` (``g`` fixes ``B``) or ``gB`` and ``B`` have no + common points (``g`` moves ``B`` entirely). ([1], p.23; [6]). + + The distinct translates ``gB`` of a block ``B`` for ``g`` in ``G`` + partition the set ``S`` and this set of translates is known as a block + system. Moreover, we obviously have that all blocks in the partition + have the same size, hence the block size divides ``|S|`` ([1], p.23). + A ``G``-congruence is an equivalence relation ``~`` on the set ``S`` + such that ``a ~ b`` implies ``g(a) ~ g(b)`` for all ``g`` in ``G``. + For a transitive group, the equivalence classes of a ``G``-congruence + and the blocks of a block system are the same thing ([1], p.23). + + The algorithm below checks the group for transitivity, and then finds + the ``G``-congruence generated by the pairs ``(p_0, p_1), (p_0, p_2), + ..., (p_0,p_{k-1})`` which is the same as finding the maximal block + system (i.e., the one with minimum block size) such that + ``p_0, ..., p_{k-1}`` are in the same block ([1], p.83). + + It is an implementation of Atkinson's algorithm, as suggested in [1], + and manipulates an equivalence relation on the set ``S`` using a + union-find data structure. The running time is just above + `O(|points||S|)`. ([1], pp. 83-87; [7]). + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(10) + >>> D.minimal_block([0, 5]) + [0, 1, 2, 3, 4, 0, 1, 2, 3, 4] + >>> D.minimal_block([0, 1]) + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + + See Also + ======== + + _union_find_rep, _union_find_merge, is_transitive, is_primitive + + """ + if not self.is_transitive(): + return False + n = self.degree + gens = self.generators + # initialize the list of equivalence class representatives + parents = list(range(n)) + ranks = [1]*n + not_rep = [] + k = len(points) + # the block size must divide the degree of the group + if k > self.max_div: + return [0]*n + for i in range(k - 1): + parents[points[i + 1]] = points[0] + not_rep.append(points[i + 1]) + ranks[points[0]] = k + i = 0 + len_not_rep = k - 1 + while i < len_not_rep: + gamma = not_rep[i] + i += 1 + for gen in gens: + # find has side effects: performs path compression on the list + # of representatives + delta = self._union_find_rep(gamma, parents) + # union has side effects: performs union by rank on the list + # of representatives + temp = self._union_find_merge(gen(gamma), gen(delta), ranks, + parents, not_rep) + if temp == -1: + return [0]*n + len_not_rep += temp + for i in range(n): + # force path compression to get the final state of the equivalence + # relation + self._union_find_rep(i, parents) + + # rewrite result so that block representatives are minimal + new_reps = {} + return [new_reps.setdefault(r, i) for i, r in enumerate(parents)] + + def conjugacy_class(self, x): + r"""Return the conjugacy class of an element in the group. + + Explanation + =========== + + The conjugacy class of an element ``g`` in a group ``G`` is the set of + elements ``x`` in ``G`` that are conjugate with ``g``, i.e. for which + + ``g = xax^{-1}`` + + for some ``a`` in ``G``. + + Note that conjugacy is an equivalence relation, and therefore that + conjugacy classes are partitions of ``G``. For a list of all the + conjugacy classes of the group, use the conjugacy_classes() method. + + In a permutation group, each conjugacy class corresponds to a particular + `cycle structure': for example, in ``S_3``, the conjugacy classes are: + + * the identity class, ``{()}`` + * all transpositions, ``{(1 2), (1 3), (2 3)}`` + * all 3-cycles, ``{(1 2 3), (1 3 2)}`` + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, SymmetricGroup + >>> S3 = SymmetricGroup(3) + >>> S3.conjugacy_class(Permutation(0, 1, 2)) + {(0 1 2), (0 2 1)} + + Notes + ===== + + This procedure computes the conjugacy class directly by finding the + orbit of the element under conjugation in G. This algorithm is only + feasible for permutation groups of relatively small order, but is like + the orbit() function itself in that respect. + """ + # Ref: "Computing the conjugacy classes of finite groups"; Butler, G. + # Groups '93 Galway/St Andrews; edited by Campbell, C. M. + new_class = {x} + last_iteration = new_class + + while len(last_iteration) > 0: + this_iteration = set() + + for y in last_iteration: + for s in self.generators: + conjugated = s * y * (~s) + if conjugated not in new_class: + this_iteration.add(conjugated) + + new_class.update(last_iteration) + last_iteration = this_iteration + + return new_class + + + def conjugacy_classes(self): + r"""Return the conjugacy classes of the group. + + Explanation + =========== + + As described in the documentation for the .conjugacy_class() function, + conjugacy is an equivalence relation on a group G which partitions the + set of elements. This method returns a list of all these conjugacy + classes of G. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> SymmetricGroup(3).conjugacy_classes() + [{(2)}, {(0 1 2), (0 2 1)}, {(0 2), (1 2), (2)(0 1)}] + + """ + identity = _af_new(list(range(self.degree))) + known_elements = {identity} + classes = [known_elements.copy()] + + for x in self.generate(): + if x not in known_elements: + new_class = self.conjugacy_class(x) + classes.append(new_class) + known_elements.update(new_class) + + return classes + + def normal_closure(self, other, k=10): + r"""Return the normal closure of a subgroup/set of permutations. + + Explanation + =========== + + If ``S`` is a subset of a group ``G``, the normal closure of ``A`` in ``G`` + is defined as the intersection of all normal subgroups of ``G`` that + contain ``A`` ([1], p.14). Alternatively, it is the group generated by + the conjugates ``x^{-1}yx`` for ``x`` a generator of ``G`` and ``y`` a + generator of the subgroup ``\left\langle S\right\rangle`` generated by + ``S`` (for some chosen generating set for ``\left\langle S\right\rangle``) + ([1], p.73). + + Parameters + ========== + + other + a subgroup/list of permutations/single permutation + k + an implementation-specific parameter that determines the number + of conjugates that are adjoined to ``other`` at once + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... CyclicGroup, AlternatingGroup) + >>> S = SymmetricGroup(5) + >>> C = CyclicGroup(5) + >>> G = S.normal_closure(C) + >>> G.order() + 60 + >>> G.is_subgroup(AlternatingGroup(5)) + True + + See Also + ======== + + commutator, derived_subgroup, random_pr + + Notes + ===== + + The algorithm is described in [1], pp. 73-74; it makes use of the + generation of random elements for permutation groups by the product + replacement algorithm. + + """ + if hasattr(other, 'generators'): + degree = self.degree + identity = _af_new(list(range(degree))) + + if all(g == identity for g in other.generators): + return other + Z = PermutationGroup(other.generators[:]) + base, strong_gens = Z.schreier_sims_incremental() + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + basic_orbits, basic_transversals = \ + _orbits_transversals_from_bsgs(base, strong_gens_distr) + + self._random_pr_init(r=10, n=20) + + _loop = True + while _loop: + Z._random_pr_init(r=10, n=10) + for _ in range(k): + g = self.random_pr() + h = Z.random_pr() + conj = h^g + res = _strip(conj, base, basic_orbits, basic_transversals) + if res[0] != identity or res[1] != len(base) + 1: + gens = Z.generators + gens.append(conj) + Z = PermutationGroup(gens) + strong_gens.append(conj) + temp_base, temp_strong_gens = \ + Z.schreier_sims_incremental(base, strong_gens) + base, strong_gens = temp_base, temp_strong_gens + strong_gens_distr = \ + _distribute_gens_by_base(base, strong_gens) + basic_orbits, basic_transversals = \ + _orbits_transversals_from_bsgs(base, + strong_gens_distr) + _loop = False + for g in self.generators: + for h in Z.generators: + conj = h^g + res = _strip(conj, base, basic_orbits, + basic_transversals) + if res[0] != identity or res[1] != len(base) + 1: + _loop = True + break + if _loop: + break + return Z + elif hasattr(other, '__getitem__'): + return self.normal_closure(PermutationGroup(other)) + elif hasattr(other, 'array_form'): + return self.normal_closure(PermutationGroup([other])) + + def orbit(self, alpha, action='tuples'): + r"""Compute the orbit of alpha `\{g(\alpha) | g \in G\}` as a set. + + Explanation + =========== + + The time complexity of the algorithm used here is `O(|Orb|*r)` where + `|Orb|` is the size of the orbit and ``r`` is the number of generators of + the group. For a more detailed analysis, see [1], p.78, [2], pp. 19-21. + Here alpha can be a single point, or a list of points. + + If alpha is a single point, the ordinary orbit is computed. + if alpha is a list of points, there are three available options: + + 'union' - computes the union of the orbits of the points in the list + 'tuples' - computes the orbit of the list interpreted as an ordered + tuple under the group action ( i.e., g((1,2,3)) = (g(1), g(2), g(3)) ) + 'sets' - computes the orbit of the list interpreted as a sets + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([1, 2, 0, 4, 5, 6, 3]) + >>> G = PermutationGroup([a]) + >>> G.orbit(0) + {0, 1, 2} + >>> G.orbit([0, 4], 'union') + {0, 1, 2, 3, 4, 5, 6} + + See Also + ======== + + orbit_transversal + + """ + return _orbit(self.degree, self.generators, alpha, action) + + def orbit_rep(self, alpha, beta, schreier_vector=None): + """Return a group element which sends ``alpha`` to ``beta``. + + Explanation + =========== + + If ``beta`` is not in the orbit of ``alpha``, the function returns + ``False``. This implementation makes use of the schreier vector. + For a proof of correctness, see [1], p.80 + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> G = AlternatingGroup(5) + >>> G.orbit_rep(0, 4) + (0 4 1 2 3) + + See Also + ======== + + schreier_vector + + """ + if schreier_vector is None: + schreier_vector = self.schreier_vector(alpha) + if schreier_vector[beta] is None: + return False + k = schreier_vector[beta] + gens = [x._array_form for x in self.generators] + a = [] + while k != -1: + a.append(gens[k]) + beta = gens[k].index(beta) # beta = (~gens[k])(beta) + k = schreier_vector[beta] + if a: + return _af_new(_af_rmuln(*a)) + else: + return _af_new(list(range(self._degree))) + + def orbit_transversal(self, alpha, pairs=False): + r"""Computes a transversal for the orbit of ``alpha`` as a set. + + Explanation + =========== + + For a permutation group `G`, a transversal for the orbit + `Orb = \{g(\alpha) | g \in G\}` is a set + `\{g_\beta | g_\beta(\alpha) = \beta\}` for `\beta \in Orb`. + Note that there may be more than one possible transversal. + If ``pairs`` is set to ``True``, it returns the list of pairs + `(\beta, g_\beta)`. For a proof of correctness, see [1], p.79 + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> G = DihedralGroup(6) + >>> G.orbit_transversal(0) + [(5), (0 1 2 3 4 5), (0 5)(1 4)(2 3), (0 2 4)(1 3 5), (5)(0 4)(1 3), (0 3)(1 4)(2 5)] + + See Also + ======== + + orbit + + """ + return _orbit_transversal(self._degree, self.generators, alpha, pairs) + + def orbits(self, rep=False): + """Return the orbits of ``self``, ordered according to lowest element + in each orbit. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation(1, 5)(2, 3)(4, 0, 6) + >>> b = Permutation(1, 5)(3, 4)(2, 6, 0) + >>> G = PermutationGroup([a, b]) + >>> G.orbits() + [{0, 2, 3, 4, 6}, {1, 5}] + """ + return _orbits(self._degree, self._generators) + + def order(self): + """Return the order of the group: the number of permutations that + can be generated from elements of the group. + + The number of permutations comprising the group is given by + ``len(group)``; the length of each permutation in the group is + given by ``group.size``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + + >>> a = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a]) + >>> G.degree + 3 + >>> len(G) + 1 + >>> G.order() + 2 + >>> list(G.generate()) + [(2), (2)(0 1)] + + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.order() + 6 + + See Also + ======== + + degree + + """ + if self._order is not None: + return self._order + if self._is_sym: + n = self._degree + self._order = factorial(n) + return self._order + if self._is_alt: + n = self._degree + self._order = factorial(n)/2 + return self._order + + m = prod([len(x) for x in self.basic_transversals]) + self._order = m + return m + + def index(self, H): + """ + Returns the index of a permutation group. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation(1,2,3) + >>> b =Permutation(3) + >>> G = PermutationGroup([a]) + >>> H = PermutationGroup([b]) + >>> G.index(H) + 3 + + """ + if H.is_subgroup(self): + return self.order()//H.order() + + @property + def is_symmetric(self): + """Return ``True`` if the group is symmetric. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> g = SymmetricGroup(5) + >>> g.is_symmetric + True + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> g = PermutationGroup( + ... Permutation(0, 1, 2, 3, 4), + ... Permutation(2, 3)) + >>> g.is_symmetric + True + + Notes + ===== + + This uses a naive test involving the computation of the full + group order. + If you need more quicker taxonomy for large groups, you can use + :meth:`PermutationGroup.is_alt_sym`. + However, :meth:`PermutationGroup.is_alt_sym` may not be accurate + and is not able to distinguish between an alternating group and + a symmetric group. + + See Also + ======== + + is_alt_sym + """ + _is_sym = self._is_sym + if _is_sym is not None: + return _is_sym + + n = self.degree + if n >= 8: + if self.is_transitive(): + _is_alt_sym = self._eval_is_alt_sym_monte_carlo() + if _is_alt_sym: + if any(g.is_odd for g in self.generators): + self._is_sym, self._is_alt = True, False + return True + + self._is_sym, self._is_alt = False, True + return False + + return self._eval_is_alt_sym_naive(only_sym=True) + + self._is_sym, self._is_alt = False, False + return False + + return self._eval_is_alt_sym_naive(only_sym=True) + + + @property + def is_alternating(self): + """Return ``True`` if the group is alternating. + + Examples + ======== + + >>> from sympy.combinatorics import AlternatingGroup + >>> g = AlternatingGroup(5) + >>> g.is_alternating + True + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> g = PermutationGroup( + ... Permutation(0, 1, 2, 3, 4), + ... Permutation(2, 3, 4)) + >>> g.is_alternating + True + + Notes + ===== + + This uses a naive test involving the computation of the full + group order. + If you need more quicker taxonomy for large groups, you can use + :meth:`PermutationGroup.is_alt_sym`. + However, :meth:`PermutationGroup.is_alt_sym` may not be accurate + and is not able to distinguish between an alternating group and + a symmetric group. + + See Also + ======== + + is_alt_sym + """ + _is_alt = self._is_alt + if _is_alt is not None: + return _is_alt + + n = self.degree + if n >= 8: + if self.is_transitive(): + _is_alt_sym = self._eval_is_alt_sym_monte_carlo() + if _is_alt_sym: + if all(g.is_even for g in self.generators): + self._is_sym, self._is_alt = False, True + return True + + self._is_sym, self._is_alt = True, False + return False + + return self._eval_is_alt_sym_naive(only_alt=True) + + self._is_sym, self._is_alt = False, False + return False + + return self._eval_is_alt_sym_naive(only_alt=True) + + @classmethod + def _distinct_primes_lemma(cls, primes): + """Subroutine to test if there is only one cyclic group for the + order.""" + primes = sorted(primes) + l = len(primes) + for i in range(l): + for j in range(i+1, l): + if primes[j] % primes[i] == 1: + return None + return True + + @property + def is_cyclic(self): + r""" + Return ``True`` if the group is Cyclic. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AbelianGroup + >>> G = AbelianGroup(3, 4) + >>> G.is_cyclic + True + >>> G = AbelianGroup(4, 4) + >>> G.is_cyclic + False + + Notes + ===== + + If the order of a group $n$ can be factored into the distinct + primes $p_1, p_2, \dots , p_s$ and if + + .. math:: + \forall i, j \in \{1, 2, \dots, s \}: + p_i \not \equiv 1 \pmod {p_j} + + holds true, there is only one group of the order $n$ which + is a cyclic group [1]_. This is a generalization of the lemma + that the group of order $15, 35, \dots$ are cyclic. + + And also, these additional lemmas can be used to test if a + group is cyclic if the order of the group is already found. + + - If the group is abelian and the order of the group is + square-free, the group is cyclic. + - If the order of the group is less than $6$ and is not $4$, the + group is cyclic. + - If the order of the group is prime, the group is cyclic. + + References + ========== + + .. [1] 1978: John S. Rose: A Course on Group Theory, + Introduction to Finite Group Theory: 1.4 + """ + if self._is_cyclic is not None: + return self._is_cyclic + + if len(self.generators) == 1: + self._is_cyclic = True + self._is_abelian = True + return True + + if self._is_abelian is False: + self._is_cyclic = False + return False + + order = self.order() + + if order < 6: + self._is_abelian = True + if order != 4: + self._is_cyclic = True + return True + + factors = factorint(order) + if all(v == 1 for v in factors.values()): + if self._is_abelian: + self._is_cyclic = True + return True + + primes = list(factors.keys()) + if PermutationGroup._distinct_primes_lemma(primes) is True: + self._is_cyclic = True + self._is_abelian = True + return True + + if not self.is_abelian: + self._is_cyclic = False + return False + + self._is_cyclic = all( + any(g**(order//p) != self.identity for g in self.generators) + for p, e in factors.items() if e > 1 + ) + return self._is_cyclic + + @property + def is_dihedral(self): + r""" + Return ``True`` if the group is dihedral. + + Examples + ======== + + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> from sympy.combinatorics.permutations import Permutation + >>> from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup + >>> G = PermutationGroup(Permutation(1, 6)(2, 5)(3, 4), Permutation(0, 1, 2, 3, 4, 5, 6)) + >>> G.is_dihedral + True + >>> G = SymmetricGroup(3) + >>> G.is_dihedral + True + >>> G = CyclicGroup(6) + >>> G.is_dihedral + False + + References + ========== + + .. [Di1] https://math.stackexchange.com/questions/827230/given-a-cayley-table-is-there-an-algorithm-to-determine-if-it-is-a-dihedral-gro/827273#827273 + .. [Di2] https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral.pdf + .. [Di3] https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral2.pdf + .. [Di4] https://en.wikipedia.org/wiki/Dihedral_group + """ + if self._is_dihedral is not None: + return self._is_dihedral + + order = self.order() + + if order % 2 == 1: + self._is_dihedral = False + return False + if order == 2: + self._is_dihedral = True + return True + if order == 4: + # The dihedral group of order 4 is the Klein 4-group. + self._is_dihedral = not self.is_cyclic + return self._is_dihedral + if self.is_abelian: + # The only abelian dihedral groups are the ones of orders 2 and 4. + self._is_dihedral = False + return False + + # Now we know the group is of even order >= 6, and nonabelian. + n = order // 2 + + # Handle special cases where there are exactly two generators. + gens = self.generators + if len(gens) == 2: + x, y = gens + a, b = x.order(), y.order() + # Make a >= b + if a < b: + x, y, a, b = y, x, b, a + # Using Theorem 2.1 of [Di3]: + if a == 2 == b: + self._is_dihedral = True + return True + # Using Theorem 1.1 of [Di3]: + if a == n and b == 2 and y*x*y == ~x: + self._is_dihedral = True + return True + + # Proceed with algorithm of [Di1] + # Find elements of orders 2 and n + order_2, order_n = [], [] + for p in self.elements: + k = p.order() + if k == 2: + order_2.append(p) + elif k == n: + order_n.append(p) + + if len(order_2) != n + 1 - (n % 2): + self._is_dihedral = False + return False + + if not order_n: + self._is_dihedral = False + return False + + x = order_n[0] + # Want an element y of order 2 that is not a power of x + # (i.e. that is not the 180-deg rotation, when n is even). + y = order_2[0] + if n % 2 == 0 and y == x**(n//2): + y = order_2[1] + + self._is_dihedral = (y*x*y == ~x) + return self._is_dihedral + + def pointwise_stabilizer(self, points, incremental=True): + r"""Return the pointwise stabilizer for a set of points. + + Explanation + =========== + + For a permutation group `G` and a set of points + `\{p_1, p_2,\ldots, p_k\}`, the pointwise stabilizer of + `p_1, p_2, \ldots, p_k` is defined as + `G_{p_1,\ldots, p_k} = + \{g\in G | g(p_i) = p_i \forall i\in\{1, 2,\ldots,k\}\}` ([1],p20). + It is a subgroup of `G`. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> S = SymmetricGroup(7) + >>> Stab = S.pointwise_stabilizer([2, 3, 5]) + >>> Stab.is_subgroup(S.stabilizer(2).stabilizer(3).stabilizer(5)) + True + + See Also + ======== + + stabilizer, schreier_sims_incremental + + Notes + ===== + + When incremental == True, + rather than the obvious implementation using successive calls to + ``.stabilizer()``, this uses the incremental Schreier-Sims algorithm + to obtain a base with starting segment - the given points. + + """ + if incremental: + base, strong_gens = self.schreier_sims_incremental(base=points) + stab_gens = [] + degree = self.degree + for gen in strong_gens: + if [gen(point) for point in points] == points: + stab_gens.append(gen) + if not stab_gens: + stab_gens = _af_new(list(range(degree))) + return PermutationGroup(stab_gens) + else: + gens = self._generators + degree = self.degree + for x in points: + gens = _stabilizer(degree, gens, x) + return PermutationGroup(gens) + + def make_perm(self, n, seed=None): + """ + Multiply ``n`` randomly selected permutations from + pgroup together, starting with the identity + permutation. If ``n`` is a list of integers, those + integers will be used to select the permutations and they + will be applied in L to R order: make_perm((A, B, C)) will + give CBA(I) where I is the identity permutation. + + ``seed`` is used to set the seed for the random selection + of permutations from pgroup. If this is a list of integers, + the corresponding permutations from pgroup will be selected + in the order give. This is mainly used for testing purposes. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a, b = [Permutation([1, 0, 3, 2]), Permutation([1, 3, 0, 2])] + >>> G = PermutationGroup([a, b]) + >>> G.make_perm(1, [0]) + (0 1)(2 3) + >>> G.make_perm(3, [0, 1, 0]) + (0 2 3 1) + >>> G.make_perm([0, 1, 0]) + (0 2 3 1) + + See Also + ======== + + random + """ + if is_sequence(n): + if seed is not None: + raise ValueError('If n is a sequence, seed should be None') + n, seed = len(n), n + else: + try: + n = int(n) + except TypeError: + raise ValueError('n must be an integer or a sequence.') + randomrange = _randrange(seed) + + # start with the identity permutation + result = Permutation(list(range(self.degree))) + m = len(self) + for _ in range(n): + p = self[randomrange(m)] + result = rmul(result, p) + return result + + def random(self, af=False): + """Return a random group element + """ + rank = randrange(self.order()) + return self.coset_unrank(rank, af) + + def random_pr(self, gen_count=11, iterations=50, _random_prec=None): + """Return a random group element using product replacement. + + Explanation + =========== + + For the details of the product replacement algorithm, see + ``_random_pr_init`` In ``random_pr`` the actual 'product replacement' + is performed. Notice that if the attribute ``_random_gens`` + is empty, it needs to be initialized by ``_random_pr_init``. + + See Also + ======== + + _random_pr_init + + """ + if self._random_gens == []: + self._random_pr_init(gen_count, iterations) + random_gens = self._random_gens + r = len(random_gens) - 1 + + # handle randomized input for testing purposes + if _random_prec is None: + s = randrange(r) + t = randrange(r - 1) + if t == s: + t = r - 1 + x = choice([1, 2]) + e = choice([-1, 1]) + else: + s = _random_prec['s'] + t = _random_prec['t'] + if t == s: + t = r - 1 + x = _random_prec['x'] + e = _random_prec['e'] + + if x == 1: + random_gens[s] = _af_rmul(random_gens[s], _af_pow(random_gens[t], e)) + random_gens[r] = _af_rmul(random_gens[r], random_gens[s]) + else: + random_gens[s] = _af_rmul(_af_pow(random_gens[t], e), random_gens[s]) + random_gens[r] = _af_rmul(random_gens[s], random_gens[r]) + return _af_new(random_gens[r]) + + def random_stab(self, alpha, schreier_vector=None, _random_prec=None): + """Random element from the stabilizer of ``alpha``. + + The schreier vector for ``alpha`` is an optional argument used + for speeding up repeated calls. The algorithm is described in [1], p.81 + + See Also + ======== + + random_pr, orbit_rep + + """ + if schreier_vector is None: + schreier_vector = self.schreier_vector(alpha) + if _random_prec is None: + rand = self.random_pr() + else: + rand = _random_prec['rand'] + beta = rand(alpha) + h = self.orbit_rep(alpha, beta, schreier_vector) + return rmul(~h, rand) + + def schreier_sims(self): + """Schreier-Sims algorithm. + + Explanation + =========== + + It computes the generators of the chain of stabilizers + `G > G_{b_1} > .. > G_{b1,..,b_r} > 1` + in which `G_{b_1,..,b_i}` stabilizes `b_1,..,b_i`, + and the corresponding ``s`` cosets. + An element of the group can be written as the product + `h_1*..*h_s`. + + We use the incremental Schreier-Sims algorithm. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.schreier_sims() + >>> G.basic_transversals + [{0: (2)(0 1), 1: (2), 2: (1 2)}, + {0: (2), 2: (0 2)}] + """ + if self._transversals: + return + self._schreier_sims() + return + + def _schreier_sims(self, base=None): + schreier = self.schreier_sims_incremental(base=base, slp_dict=True) + base, strong_gens = schreier[:2] + self._base = base + self._strong_gens = strong_gens + self._strong_gens_slp = schreier[2] + if not base: + self._transversals = [] + self._basic_orbits = [] + return + + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + basic_orbits, transversals, slps = _orbits_transversals_from_bsgs(base,\ + strong_gens_distr, slp=True) + + # rewrite the indices stored in slps in terms of strong_gens + for i, slp in enumerate(slps): + gens = strong_gens_distr[i] + for k in slp: + slp[k] = [strong_gens.index(gens[s]) for s in slp[k]] + + self._transversals = transversals + self._basic_orbits = [sorted(x) for x in basic_orbits] + self._transversal_slp = slps + + def schreier_sims_incremental(self, base=None, gens=None, slp_dict=False): + """Extend a sequence of points and generating set to a base and strong + generating set. + + Parameters + ========== + + base + The sequence of points to be extended to a base. Optional + parameter with default value ``[]``. + gens + The generating set to be extended to a strong generating set + relative to the base obtained. Optional parameter with default + value ``self.generators``. + + slp_dict + If `True`, return a dictionary `{g: gens}` for each strong + generator `g` where `gens` is a list of strong generators + coming before `g` in `strong_gens`, such that the product + of the elements of `gens` is equal to `g`. + + Returns + ======= + + (base, strong_gens) + ``base`` is the base obtained, and ``strong_gens`` is the strong + generating set relative to it. The original parameters ``base``, + ``gens`` remain unchanged. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> A = AlternatingGroup(7) + >>> base = [2, 3] + >>> seq = [2, 3] + >>> base, strong_gens = A.schreier_sims_incremental(base=seq) + >>> _verify_bsgs(A, base, strong_gens) + True + >>> base[:2] + [2, 3] + + Notes + ===== + + This version of the Schreier-Sims algorithm runs in polynomial time. + There are certain assumptions in the implementation - if the trivial + group is provided, ``base`` and ``gens`` are returned immediately, + as any sequence of points is a base for the trivial group. If the + identity is present in the generators ``gens``, it is removed as + it is a redundant generator. + The implementation is described in [1], pp. 90-93. + + See Also + ======== + + schreier_sims, schreier_sims_random + + """ + if base is None: + base = [] + if gens is None: + gens = self.generators[:] + degree = self.degree + id_af = list(range(degree)) + # handle the trivial group + if len(gens) == 1 and gens[0].is_Identity: + if slp_dict: + return base, gens, {gens[0]: [gens[0]]} + return base, gens + # prevent side effects + _base, _gens = base[:], gens[:] + # remove the identity as a generator + _gens = [x for x in _gens if not x.is_Identity] + # make sure no generator fixes all base points + for gen in _gens: + if all(x == gen._array_form[x] for x in _base): + for new in id_af: + if gen._array_form[new] != new: + break + else: + assert None # can this ever happen? + _base.append(new) + # distribute generators according to basic stabilizers + strong_gens_distr = _distribute_gens_by_base(_base, _gens) + strong_gens_slp = [] + # initialize the basic stabilizers, basic orbits and basic transversals + orbs = {} + transversals = {} + slps = {} + base_len = len(_base) + for i in range(base_len): + transversals[i], slps[i] = _orbit_transversal(degree, strong_gens_distr[i], + _base[i], pairs=True, af=True, slp=True) + transversals[i] = dict(transversals[i]) + orbs[i] = list(transversals[i].keys()) + # main loop: amend the stabilizer chain until we have generators + # for all stabilizers + i = base_len - 1 + while i >= 0: + # this flag is used to continue with the main loop from inside + # a nested loop + continue_i = False + # test the generators for being a strong generating set + db = {} + for beta, u_beta in list(transversals[i].items()): + for j, gen in enumerate(strong_gens_distr[i]): + gb = gen._array_form[beta] + u1 = transversals[i][gb] + g1 = _af_rmul(gen._array_form, u_beta) + slp = [(i, g) for g in slps[i][beta]] + slp = [(i, j)] + slp + if g1 != u1: + # test if the schreier generator is in the i+1-th + # would-be basic stabilizer + y = True + try: + u1_inv = db[gb] + except KeyError: + u1_inv = db[gb] = _af_invert(u1) + schreier_gen = _af_rmul(u1_inv, g1) + u1_inv_slp = slps[i][gb][:] + u1_inv_slp.reverse() + u1_inv_slp = [(i, (g,)) for g in u1_inv_slp] + slp = u1_inv_slp + slp + h, j, slp = _strip_af(schreier_gen, _base, orbs, transversals, i, slp=slp, slps=slps) + if j <= base_len: + # new strong generator h at level j + y = False + elif h: + # h fixes all base points + y = False + moved = 0 + while h[moved] == moved: + moved += 1 + _base.append(moved) + base_len += 1 + strong_gens_distr.append([]) + if y is False: + # if a new strong generator is found, update the + # data structures and start over + h = _af_new(h) + strong_gens_slp.append((h, slp)) + for l in range(i + 1, j): + strong_gens_distr[l].append(h) + transversals[l], slps[l] =\ + _orbit_transversal(degree, strong_gens_distr[l], + _base[l], pairs=True, af=True, slp=True) + transversals[l] = dict(transversals[l]) + orbs[l] = list(transversals[l].keys()) + i = j - 1 + # continue main loop using the flag + continue_i = True + if continue_i is True: + break + if continue_i is True: + break + if continue_i is True: + continue + i -= 1 + + strong_gens = _gens[:] + + if slp_dict: + # create the list of the strong generators strong_gens and + # rewrite the indices of strong_gens_slp in terms of the + # elements of strong_gens + for k, slp in strong_gens_slp: + strong_gens.append(k) + for i in range(len(slp)): + s = slp[i] + if isinstance(s[1], tuple): + slp[i] = strong_gens_distr[s[0]][s[1][0]]**-1 + else: + slp[i] = strong_gens_distr[s[0]][s[1]] + strong_gens_slp = dict(strong_gens_slp) + # add the original generators + for g in _gens: + strong_gens_slp[g] = [g] + return (_base, strong_gens, strong_gens_slp) + + strong_gens.extend([k for k, _ in strong_gens_slp]) + return _base, strong_gens + + def schreier_sims_random(self, base=None, gens=None, consec_succ=10, + _random_prec=None): + r"""Randomized Schreier-Sims algorithm. + + Explanation + =========== + + The randomized Schreier-Sims algorithm takes the sequence ``base`` + and the generating set ``gens``, and extends ``base`` to a base, and + ``gens`` to a strong generating set relative to that base with + probability of a wrong answer at most `2^{-consec\_succ}`, + provided the random generators are sufficiently random. + + Parameters + ========== + + base + The sequence to be extended to a base. + gens + The generating set to be extended to a strong generating set. + consec_succ + The parameter defining the probability of a wrong answer. + _random_prec + An internal parameter used for testing purposes. + + Returns + ======= + + (base, strong_gens) + ``base`` is the base and ``strong_gens`` is the strong generating + set relative to it. + + Examples + ======== + + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> S = SymmetricGroup(5) + >>> base, strong_gens = S.schreier_sims_random(consec_succ=5) + >>> _verify_bsgs(S, base, strong_gens) #doctest: +SKIP + True + + Notes + ===== + + The algorithm is described in detail in [1], pp. 97-98. It extends + the orbits ``orbs`` and the permutation groups ``stabs`` to + basic orbits and basic stabilizers for the base and strong generating + set produced in the end. + The idea of the extension process + is to "sift" random group elements through the stabilizer chain + and amend the stabilizers/orbits along the way when a sift + is not successful. + The helper function ``_strip`` is used to attempt + to decompose a random group element according to the current + state of the stabilizer chain and report whether the element was + fully decomposed (successful sift) or not (unsuccessful sift). In + the latter case, the level at which the sift failed is reported and + used to amend ``stabs``, ``base``, ``gens`` and ``orbs`` accordingly. + The halting condition is for ``consec_succ`` consecutive successful + sifts to pass. This makes sure that the current ``base`` and ``gens`` + form a BSGS with probability at least `1 - 1/\text{consec\_succ}`. + + See Also + ======== + + schreier_sims + + """ + if base is None: + base = [] + if gens is None: + gens = self.generators + base_len = len(base) + n = self.degree + # make sure no generator fixes all base points + for gen in gens: + if all(gen(x) == x for x in base): + new = 0 + while gen._array_form[new] == new: + new += 1 + base.append(new) + base_len += 1 + # distribute generators according to basic stabilizers + strong_gens_distr = _distribute_gens_by_base(base, gens) + # initialize the basic stabilizers, basic transversals and basic orbits + transversals = {} + orbs = {} + for i in range(base_len): + transversals[i] = dict(_orbit_transversal(n, strong_gens_distr[i], + base[i], pairs=True)) + orbs[i] = list(transversals[i].keys()) + # initialize the number of consecutive elements sifted + c = 0 + # start sifting random elements while the number of consecutive sifts + # is less than consec_succ + while c < consec_succ: + if _random_prec is None: + g = self.random_pr() + else: + g = _random_prec['g'].pop() + h, j = _strip(g, base, orbs, transversals) + y = True + # determine whether a new base point is needed + if j <= base_len: + y = False + elif not h.is_Identity: + y = False + moved = 0 + while h(moved) == moved: + moved += 1 + base.append(moved) + base_len += 1 + strong_gens_distr.append([]) + # if the element doesn't sift, amend the strong generators and + # associated stabilizers and orbits + if y is False: + for l in range(1, j): + strong_gens_distr[l].append(h) + transversals[l] = dict(_orbit_transversal(n, + strong_gens_distr[l], base[l], pairs=True)) + orbs[l] = list(transversals[l].keys()) + c = 0 + else: + c += 1 + # build the strong generating set + strong_gens = strong_gens_distr[0][:] + for gen in strong_gens_distr[1]: + if gen not in strong_gens: + strong_gens.append(gen) + return base, strong_gens + + def schreier_vector(self, alpha): + """Computes the schreier vector for ``alpha``. + + Explanation + =========== + + The Schreier vector efficiently stores information + about the orbit of ``alpha``. It can later be used to quickly obtain + elements of the group that send ``alpha`` to a particular element + in the orbit. Notice that the Schreier vector depends on the order + in which the group generators are listed. For a definition, see [3]. + Since list indices start from zero, we adopt the convention to use + "None" instead of 0 to signify that an element does not belong + to the orbit. + For the algorithm and its correctness, see [2], pp.78-80. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([2, 4, 6, 3, 1, 5, 0]) + >>> b = Permutation([0, 1, 3, 5, 4, 6, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.schreier_vector(0) + [-1, None, 0, 1, None, 1, 0] + + See Also + ======== + + orbit + + """ + n = self.degree + v = [None]*n + v[alpha] = -1 + orb = [alpha] + used = [False]*n + used[alpha] = True + gens = self.generators + r = len(gens) + for b in orb: + for i in range(r): + temp = gens[i]._array_form[b] + if used[temp] is False: + orb.append(temp) + used[temp] = True + v[temp] = i + return v + + def stabilizer(self, alpha): + r"""Return the stabilizer subgroup of ``alpha``. + + Explanation + =========== + + The stabilizer of `\alpha` is the group `G_\alpha = + \{g \in G | g(\alpha) = \alpha\}`. + For a proof of correctness, see [1], p.79. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> G = DihedralGroup(6) + >>> G.stabilizer(5) + PermutationGroup([ + (5)(0 4)(1 3)]) + + See Also + ======== + + orbit + + """ + return PermGroup(_stabilizer(self._degree, self._generators, alpha)) + + @property + def strong_gens(self): + r"""Return a strong generating set from the Schreier-Sims algorithm. + + Explanation + =========== + + A generating set `S = \{g_1, g_2, \dots, g_t\}` for a permutation group + `G` is a strong generating set relative to the sequence of points + (referred to as a "base") `(b_1, b_2, \dots, b_k)` if, for + `1 \leq i \leq k` we have that the intersection of the pointwise + stabilizer `G^{(i+1)} := G_{b_1, b_2, \dots, b_i}` with `S` generates + the pointwise stabilizer `G^{(i+1)}`. The concepts of a base and + strong generating set and their applications are discussed in depth + in [1], pp. 87-89 and [2], pp. 55-57. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(4) + >>> D.strong_gens + [(0 1 2 3), (0 3)(1 2), (1 3)] + >>> D.base + [0, 1] + + See Also + ======== + + base, basic_transversals, basic_orbits, basic_stabilizers + + """ + if self._strong_gens == []: + self.schreier_sims() + return self._strong_gens + + def subgroup(self, gens): + """ + Return the subgroup generated by `gens` which is a list of + elements of the group + """ + + if not all(g in self for g in gens): + raise ValueError("The group does not contain the supplied generators") + + G = PermutationGroup(gens) + return G + + def subgroup_search(self, prop, base=None, strong_gens=None, tests=None, + init_subgroup=None): + """Find the subgroup of all elements satisfying the property ``prop``. + + Explanation + =========== + + This is done by a depth-first search with respect to base images that + uses several tests to prune the search tree. + + Parameters + ========== + + prop + The property to be used. Has to be callable on group elements + and always return ``True`` or ``False``. It is assumed that + all group elements satisfying ``prop`` indeed form a subgroup. + base + A base for the supergroup. + strong_gens + A strong generating set for the supergroup. + tests + A list of callables of length equal to the length of ``base``. + These are used to rule out group elements by partial base images, + so that ``tests[l](g)`` returns False if the element ``g`` is known + not to satisfy prop base on where g sends the first ``l + 1`` base + points. + init_subgroup + if a subgroup of the sought group is + known in advance, it can be passed to the function as this + parameter. + + Returns + ======= + + res + The subgroup of all elements satisfying ``prop``. The generating + set for this group is guaranteed to be a strong generating set + relative to the base ``base``. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... AlternatingGroup) + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> S = SymmetricGroup(7) + >>> prop_even = lambda x: x.is_even + >>> base, strong_gens = S.schreier_sims_incremental() + >>> G = S.subgroup_search(prop_even, base=base, strong_gens=strong_gens) + >>> G.is_subgroup(AlternatingGroup(7)) + True + >>> _verify_bsgs(G, base, G.generators) + True + + Notes + ===== + + This function is extremely lengthy and complicated and will require + some careful attention. The implementation is described in + [1], pp. 114-117, and the comments for the code here follow the lines + of the pseudocode in the book for clarity. + + The complexity is exponential in general, since the search process by + itself visits all members of the supergroup. However, there are a lot + of tests which are used to prune the search tree, and users can define + their own tests via the ``tests`` parameter, so in practice, and for + some computations, it's not terrible. + + A crucial part in the procedure is the frequent base change performed + (this is line 11 in the pseudocode) in order to obtain a new basic + stabilizer. The book mentiones that this can be done by using + ``.baseswap(...)``, however the current implementation uses a more + straightforward way to find the next basic stabilizer - calling the + function ``.stabilizer(...)`` on the previous basic stabilizer. + + """ + # initialize BSGS and basic group properties + def get_reps(orbits): + # get the minimal element in the base ordering + return [min(orbit, key = lambda x: base_ordering[x]) \ + for orbit in orbits] + + def update_nu(l): + temp_index = len(basic_orbits[l]) + 1 -\ + len(res_basic_orbits_init_base[l]) + # this corresponds to the element larger than all points + if temp_index >= len(sorted_orbits[l]): + nu[l] = base_ordering[degree] + else: + nu[l] = sorted_orbits[l][temp_index] + + if base is None: + base, strong_gens = self.schreier_sims_incremental() + base_len = len(base) + degree = self.degree + identity = _af_new(list(range(degree))) + base_ordering = _base_ordering(base, degree) + # add an element larger than all points + base_ordering.append(degree) + # add an element smaller than all points + base_ordering.append(-1) + # compute BSGS-related structures + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + basic_orbits, transversals = _orbits_transversals_from_bsgs(base, + strong_gens_distr) + # handle subgroup initialization and tests + if init_subgroup is None: + init_subgroup = PermutationGroup([identity]) + if tests is None: + trivial_test = lambda x: True + tests = [] + for i in range(base_len): + tests.append(trivial_test) + # line 1: more initializations. + res = init_subgroup + f = base_len - 1 + l = base_len - 1 + # line 2: set the base for K to the base for G + res_base = base[:] + # line 3: compute BSGS and related structures for K + res_base, res_strong_gens = res.schreier_sims_incremental( + base=res_base) + res_strong_gens_distr = _distribute_gens_by_base(res_base, + res_strong_gens) + res_generators = res.generators + res_basic_orbits_init_base = \ + [_orbit(degree, res_strong_gens_distr[i], res_base[i])\ + for i in range(base_len)] + # initialize orbit representatives + orbit_reps = [None]*base_len + # line 4: orbit representatives for f-th basic stabilizer of K + orbits = _orbits(degree, res_strong_gens_distr[f]) + orbit_reps[f] = get_reps(orbits) + # line 5: remove the base point from the representatives to avoid + # getting the identity element as a generator for K + orbit_reps[f].remove(base[f]) + # line 6: more initializations + c = [0]*base_len + u = [identity]*base_len + sorted_orbits = [None]*base_len + for i in range(base_len): + sorted_orbits[i] = basic_orbits[i][:] + sorted_orbits[i].sort(key=lambda point: base_ordering[point]) + # line 7: initializations + mu = [None]*base_len + nu = [None]*base_len + # this corresponds to the element smaller than all points + mu[l] = degree + 1 + update_nu(l) + # initialize computed words + computed_words = [identity]*base_len + # line 8: main loop + while True: + # apply all the tests + while l < base_len - 1 and \ + computed_words[l](base[l]) in orbit_reps[l] and \ + base_ordering[mu[l]] < \ + base_ordering[computed_words[l](base[l])] < \ + base_ordering[nu[l]] and \ + tests[l](computed_words): + # line 11: change the (partial) base of K + new_point = computed_words[l](base[l]) + res_base[l] = new_point + new_stab_gens = _stabilizer(degree, res_strong_gens_distr[l], + new_point) + res_strong_gens_distr[l + 1] = new_stab_gens + # line 12: calculate minimal orbit representatives for the + # l+1-th basic stabilizer + orbits = _orbits(degree, new_stab_gens) + orbit_reps[l + 1] = get_reps(orbits) + # line 13: amend sorted orbits + l += 1 + temp_orbit = [computed_words[l - 1](point) for point + in basic_orbits[l]] + temp_orbit.sort(key=lambda point: base_ordering[point]) + sorted_orbits[l] = temp_orbit + # lines 14 and 15: update variables used minimality tests + new_mu = degree + 1 + for i in range(l): + if base[l] in res_basic_orbits_init_base[i]: + candidate = computed_words[i](base[i]) + if base_ordering[candidate] > base_ordering[new_mu]: + new_mu = candidate + mu[l] = new_mu + update_nu(l) + # line 16: determine the new transversal element + c[l] = 0 + temp_point = sorted_orbits[l][c[l]] + gamma = computed_words[l - 1]._array_form.index(temp_point) + u[l] = transversals[l][gamma] + # update computed words + computed_words[l] = rmul(computed_words[l - 1], u[l]) + # lines 17 & 18: apply the tests to the group element found + g = computed_words[l] + temp_point = g(base[l]) + if l == base_len - 1 and \ + base_ordering[mu[l]] < \ + base_ordering[temp_point] < base_ordering[nu[l]] and \ + temp_point in orbit_reps[l] and \ + tests[l](computed_words) and \ + prop(g): + # line 19: reset the base of K + res_generators.append(g) + res_base = base[:] + # line 20: recalculate basic orbits (and transversals) + res_strong_gens.append(g) + res_strong_gens_distr = _distribute_gens_by_base(res_base, + res_strong_gens) + res_basic_orbits_init_base = \ + [_orbit(degree, res_strong_gens_distr[i], res_base[i]) \ + for i in range(base_len)] + # line 21: recalculate orbit representatives + # line 22: reset the search depth + orbit_reps[f] = get_reps(orbits) + l = f + # line 23: go up the tree until in the first branch not fully + # searched + while l >= 0 and c[l] == len(basic_orbits[l]) - 1: + l = l - 1 + # line 24: if the entire tree is traversed, return K + if l == -1: + return PermutationGroup(res_generators) + # lines 25-27: update orbit representatives + if l < f: + # line 26 + f = l + c[l] = 0 + # line 27 + temp_orbits = _orbits(degree, res_strong_gens_distr[f]) + orbit_reps[f] = get_reps(temp_orbits) + # line 28: update variables used for minimality testing + mu[l] = degree + 1 + temp_index = len(basic_orbits[l]) + 1 - \ + len(res_basic_orbits_init_base[l]) + if temp_index >= len(sorted_orbits[l]): + nu[l] = base_ordering[degree] + else: + nu[l] = sorted_orbits[l][temp_index] + # line 29: set the next element from the current branch and update + # accordingly + c[l] += 1 + if l == 0: + gamma = sorted_orbits[l][c[l]] + else: + gamma = computed_words[l - 1]._array_form.index(sorted_orbits[l][c[l]]) + + u[l] = transversals[l][gamma] + if l == 0: + computed_words[l] = u[l] + else: + computed_words[l] = rmul(computed_words[l - 1], u[l]) + + @property + def transitivity_degree(self): + r"""Compute the degree of transitivity of the group. + + Explanation + =========== + + A permutation group `G` acting on `\Omega = \{0, 1, \dots, n-1\}` is + ``k``-fold transitive, if, for any `k` points + `(a_1, a_2, \dots, a_k) \in \Omega` and any `k` points + `(b_1, b_2, \dots, b_k) \in \Omega` there exists `g \in G` such that + `g(a_1) = b_1, g(a_2) = b_2, \dots, g(a_k) = b_k` + The degree of transitivity of `G` is the maximum ``k`` such that + `G` is ``k``-fold transitive. ([8]) + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> a = Permutation([1, 2, 0]) + >>> b = Permutation([1, 0, 2]) + >>> G = PermutationGroup([a, b]) + >>> G.transitivity_degree + 3 + + See Also + ======== + + is_transitive, orbit + + """ + if self._transitivity_degree is None: + n = self.degree + G = self + # if G is k-transitive, a tuple (a_0,..,a_k) + # can be brought to (b_0,...,b_(k-1), b_k) + # where b_0,...,b_(k-1) are fixed points; + # consider the group G_k which stabilizes b_0,...,b_(k-1) + # if G_k is transitive on the subset excluding b_0,...,b_(k-1) + # then G is (k+1)-transitive + for i in range(n): + orb = G.orbit(i) + if len(orb) != n - i: + self._transitivity_degree = i + return i + G = G.stabilizer(i) + self._transitivity_degree = n + return n + else: + return self._transitivity_degree + + def _p_elements_group(self, p): + ''' + For an abelian p-group, return the subgroup consisting of + all elements of order p (and the identity) + + ''' + gens = self.generators[:] + gens = sorted(gens, key=lambda x: x.order(), reverse=True) + gens_p = [g**(g.order()/p) for g in gens] + gens_r = [] + for i in range(len(gens)): + x = gens[i] + x_order = x.order() + # x_p has order p + x_p = x**(x_order/p) + if i > 0: + P = PermutationGroup(gens_p[:i]) + else: + P = PermutationGroup(self.identity) + if x**(x_order/p) not in P: + gens_r.append(x**(x_order/p)) + else: + # replace x by an element of order (x.order()/p) + # so that gens still generates G + g = P.generator_product(x_p, original=True) + for s in g: + x = x*s**-1 + x_order = x_order/p + # insert x to gens so that the sorting is preserved + del gens[i] + del gens_p[i] + j = i - 1 + while j < len(gens) and gens[j].order() >= x_order: + j += 1 + gens = gens[:j] + [x] + gens[j:] + gens_p = gens_p[:j] + [x] + gens_p[j:] + return PermutationGroup(gens_r) + + def _sylow_alt_sym(self, p): + ''' + Return a p-Sylow subgroup of a symmetric or an + alternating group. + + Explanation + =========== + + The algorithm for this is hinted at in [1], Chapter 4, + Exercise 4. + + For Sym(n) with n = p^i, the idea is as follows. Partition + the interval [0..n-1] into p equal parts, each of length p^(i-1): + [0..p^(i-1)-1], [p^(i-1)..2*p^(i-1)-1]...[(p-1)*p^(i-1)..p^i-1]. + Find a p-Sylow subgroup of Sym(p^(i-1)) (treated as a subgroup + of ``self``) acting on each of the parts. Call the subgroups + P_1, P_2...P_p. The generators for the subgroups P_2...P_p + can be obtained from those of P_1 by applying a "shifting" + permutation to them, that is, a permutation mapping [0..p^(i-1)-1] + to the second part (the other parts are obtained by using the shift + multiple times). The union of this permutation and the generators + of P_1 is a p-Sylow subgroup of ``self``. + + For n not equal to a power of p, partition + [0..n-1] in accordance with how n would be written in base p. + E.g. for p=2 and n=11, 11 = 2^3 + 2^2 + 1 so the partition + is [[0..7], [8..9], {10}]. To generate a p-Sylow subgroup, + take the union of the generators for each of the parts. + For the above example, {(0 1), (0 2)(1 3), (0 4), (1 5)(2 7)} + from the first part, {(8 9)} from the second part and + nothing from the third. This gives 4 generators in total, and + the subgroup they generate is p-Sylow. + + Alternating groups are treated the same except when p=2. In this + case, (0 1)(s s+1) should be added for an appropriate s (the start + of a part) for each part in the partitions. + + See Also + ======== + + sylow_subgroup, is_alt_sym + + ''' + n = self.degree + gens = [] + identity = Permutation(n-1) + # the case of 2-sylow subgroups of alternating groups + # needs special treatment + alt = p == 2 and all(g.is_even for g in self.generators) + + # find the presentation of n in base p + coeffs = [] + m = n + while m > 0: + coeffs.append(m % p) + m = m // p + + power = len(coeffs)-1 + # for a symmetric group, gens[:i] is the generating + # set for a p-Sylow subgroup on [0..p**(i-1)-1]. For + # alternating groups, the same is given by gens[:2*(i-1)] + for i in range(1, power+1): + if i == 1 and alt: + # (0 1) shouldn't be added for alternating groups + continue + gen = Permutation([(j + p**(i-1)) % p**i for j in range(p**i)]) + gens.append(identity*gen) + if alt: + gen = Permutation(0, 1)*gen*Permutation(0, 1)*gen + gens.append(gen) + + # the first point in the current part (see the algorithm + # description in the docstring) + start = 0 + + while power > 0: + a = coeffs[power] + + # make the permutation shifting the start of the first + # part ([0..p^i-1] for some i) to the current one + for _ in range(a): + shift = Permutation() + if start > 0: + for i in range(p**power): + shift = shift(i, start + i) + + if alt: + gen = Permutation(0, 1)*shift*Permutation(0, 1)*shift + gens.append(gen) + j = 2*(power - 1) + else: + j = power + + for i, gen in enumerate(gens[:j]): + if alt and i % 2 == 1: + continue + # shift the generator to the start of the + # partition part + gen = shift*gen*shift + gens.append(gen) + + start += p**power + power = power-1 + + return gens + + def sylow_subgroup(self, p): + ''' + Return a p-Sylow subgroup of the group. + + The algorithm is described in [1], Chapter 4, Section 7 + + Examples + ======== + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> from sympy.combinatorics.named_groups import SymmetricGroup + >>> from sympy.combinatorics.named_groups import AlternatingGroup + + >>> D = DihedralGroup(6) + >>> S = D.sylow_subgroup(2) + >>> S.order() + 4 + >>> G = SymmetricGroup(6) + >>> S = G.sylow_subgroup(5) + >>> S.order() + 5 + + >>> G1 = AlternatingGroup(3) + >>> G2 = AlternatingGroup(5) + >>> G3 = AlternatingGroup(9) + + >>> S1 = G1.sylow_subgroup(3) + >>> S2 = G2.sylow_subgroup(3) + >>> S3 = G3.sylow_subgroup(3) + + >>> len1 = len(S1.lower_central_series()) + >>> len2 = len(S2.lower_central_series()) + >>> len3 = len(S3.lower_central_series()) + + >>> len1 == len2 + True + >>> len1 < len3 + True + + ''' + from sympy.combinatorics.homomorphisms import ( + orbit_homomorphism, block_homomorphism) + + if not isprime(p): + raise ValueError("p must be a prime") + + def is_p_group(G): + # check if the order of G is a power of p + # and return the power + m = G.order() + n = 0 + while m % p == 0: + m = m/p + n += 1 + if m == 1: + return True, n + return False, n + + def _sylow_reduce(mu, nu): + # reduction based on two homomorphisms + # mu and nu with trivially intersecting + # kernels + Q = mu.image().sylow_subgroup(p) + Q = mu.invert_subgroup(Q) + nu = nu.restrict_to(Q) + R = nu.image().sylow_subgroup(p) + return nu.invert_subgroup(R) + + order = self.order() + if order % p != 0: + return PermutationGroup([self.identity]) + p_group, n = is_p_group(self) + if p_group: + return self + + if self.is_alt_sym(): + return PermutationGroup(self._sylow_alt_sym(p)) + + # if there is a non-trivial orbit with size not divisible + # by p, the sylow subgroup is contained in its stabilizer + # (by orbit-stabilizer theorem) + orbits = self.orbits() + non_p_orbits = [o for o in orbits if len(o) % p != 0 and len(o) != 1] + if non_p_orbits: + G = self.stabilizer(list(non_p_orbits[0]).pop()) + return G.sylow_subgroup(p) + + if not self.is_transitive(): + # apply _sylow_reduce to orbit actions + orbits = sorted(orbits, key=len) + omega1 = orbits.pop() + omega2 = orbits[0].union(*orbits) + mu = orbit_homomorphism(self, omega1) + nu = orbit_homomorphism(self, omega2) + return _sylow_reduce(mu, nu) + + blocks = self.minimal_blocks() + if len(blocks) > 1: + # apply _sylow_reduce to block system actions + mu = block_homomorphism(self, blocks[0]) + nu = block_homomorphism(self, blocks[1]) + return _sylow_reduce(mu, nu) + elif len(blocks) == 1: + block = list(blocks)[0] + if any(e != 0 for e in block): + # self is imprimitive + mu = block_homomorphism(self, block) + if not is_p_group(mu.image())[0]: + S = mu.image().sylow_subgroup(p) + return mu.invert_subgroup(S).sylow_subgroup(p) + + # find an element of order p + g = self.random() + g_order = g.order() + while g_order % p != 0 or g_order == 0: + g = self.random() + g_order = g.order() + g = g**(g_order // p) + if order % p**2 != 0: + return PermutationGroup(g) + + C = self.centralizer(g) + while C.order() % p**n != 0: + S = C.sylow_subgroup(p) + s_order = S.order() + Z = S.center() + P = Z._p_elements_group(p) + h = P.random() + C_h = self.centralizer(h) + while C_h.order() % p*s_order != 0: + h = P.random() + C_h = self.centralizer(h) + C = C_h + + return C.sylow_subgroup(p) + + def _block_verify(self, L, alpha): + delta = sorted(self.orbit(alpha)) + # p[i] will be the number of the block + # delta[i] belongs to + p = [-1]*len(delta) + blocks = [-1]*len(delta) + + B = [[]] # future list of blocks + u = [0]*len(delta) # u[i] in L s.t. alpha^u[i] = B[0][i] + + t = L.orbit_transversal(alpha, pairs=True) + for a, beta in t: + B[0].append(a) + i_a = delta.index(a) + p[i_a] = 0 + blocks[i_a] = alpha + u[i_a] = beta + + rho = 0 + m = 0 # number of blocks - 1 + + while rho <= m: + beta = B[rho][0] + for g in self.generators: + d = beta^g + i_d = delta.index(d) + sigma = p[i_d] + if sigma < 0: + # define a new block + m += 1 + sigma = m + u[i_d] = u[delta.index(beta)]*g + p[i_d] = sigma + rep = d + blocks[i_d] = rep + newb = [rep] + for gamma in B[rho][1:]: + i_gamma = delta.index(gamma) + d = gamma^g + i_d = delta.index(d) + if p[i_d] < 0: + u[i_d] = u[i_gamma]*g + p[i_d] = sigma + blocks[i_d] = rep + newb.append(d) + else: + # B[rho] is not a block + s = u[i_gamma]*g*u[i_d]**(-1) + return False, s + + B.append(newb) + else: + for h in B[rho][1:]: + if h^g not in B[sigma]: + # B[rho] is not a block + s = u[delta.index(beta)]*g*u[i_d]**(-1) + return False, s + rho += 1 + + return True, blocks + + def _verify(H, K, phi, z, alpha): + ''' + Return a list of relators ``rels`` in generators ``gens`_h` that + are mapped to ``H.generators`` by ``phi`` so that given a finite + presentation of ``K`` on a subset of ``gens_h`` + is a finite presentation of ``H``. + + Explanation + =========== + + ``H`` should be generated by the union of ``K.generators`` and ``z`` + (a single generator), and ``H.stabilizer(alpha) == K``; ``phi`` is a + canonical injection from a free group into a permutation group + containing ``H``. + + The algorithm is described in [1], Chapter 6. + + Examples + ======== + + >>> from sympy.combinatorics import free_group, Permutation, PermutationGroup + >>> from sympy.combinatorics.homomorphisms import homomorphism + >>> from sympy.combinatorics.fp_groups import FpGroup + + >>> H = PermutationGroup(Permutation(0, 2), Permutation (1, 5)) + >>> K = PermutationGroup(Permutation(5)(0, 2)) + >>> F = free_group("x_0 x_1")[0] + >>> gens = F.generators + >>> phi = homomorphism(F, H, F.generators, H.generators) + >>> rels_k = [gens[0]**2] # relators for presentation of K + >>> z= Permutation(1, 5) + >>> check, rels_h = H._verify(K, phi, z, 1) + >>> check + True + >>> rels = rels_k + rels_h + >>> G = FpGroup(F, rels) # presentation of H + >>> G.order() == H.order() + True + + See also + ======== + + strong_presentation, presentation, stabilizer + + ''' + + orbit = H.orbit(alpha) + beta = alpha^(z**-1) + + K_beta = K.stabilizer(beta) + + # orbit representatives of K_beta + gammas = [alpha, beta] + orbits = list({tuple(K_beta.orbit(o)) for o in orbit}) + orbit_reps = [orb[0] for orb in orbits] + for rep in orbit_reps: + if rep not in gammas: + gammas.append(rep) + + # orbit transversal of K + betas = [alpha, beta] + transversal = {alpha: phi.invert(H.identity), beta: phi.invert(z**-1)} + + for s, g in K.orbit_transversal(beta, pairs=True): + if s not in transversal: + transversal[s] = transversal[beta]*phi.invert(g) + + + union = K.orbit(alpha).union(K.orbit(beta)) + while (len(union) < len(orbit)): + for gamma in gammas: + if gamma in union: + r = gamma^z + if r not in union: + betas.append(r) + transversal[r] = transversal[gamma]*phi.invert(z) + for s, g in K.orbit_transversal(r, pairs=True): + if s not in transversal: + transversal[s] = transversal[r]*phi.invert(g) + union = union.union(K.orbit(r)) + break + + # compute relators + rels = [] + + for b in betas: + k_gens = K.stabilizer(b).generators + for y in k_gens: + new_rel = transversal[b] + gens = K.generator_product(y, original=True) + for g in gens[::-1]: + new_rel = new_rel*phi.invert(g) + new_rel = new_rel*transversal[b]**-1 + + perm = phi(new_rel) + try: + gens = K.generator_product(perm, original=True) + except ValueError: + return False, perm + for g in gens: + new_rel = new_rel*phi.invert(g)**-1 + if new_rel not in rels: + rels.append(new_rel) + + for gamma in gammas: + new_rel = transversal[gamma]*phi.invert(z)*transversal[gamma^z]**-1 + perm = phi(new_rel) + try: + gens = K.generator_product(perm, original=True) + except ValueError: + return False, perm + for g in gens: + new_rel = new_rel*phi.invert(g)**-1 + if new_rel not in rels: + rels.append(new_rel) + + return True, rels + + def strong_presentation(self): + ''' + Return a strong finite presentation of group. The generators + of the returned group are in the same order as the strong + generators of group. + + The algorithm is based on Sims' Verify algorithm described + in [1], Chapter 6. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> P = DihedralGroup(4) + >>> G = P.strong_presentation() + >>> P.order() == G.order() + True + + See Also + ======== + + presentation, _verify + + ''' + from sympy.combinatorics.fp_groups import (FpGroup, + simplify_presentation) + from sympy.combinatorics.free_groups import free_group + from sympy.combinatorics.homomorphisms import (block_homomorphism, + homomorphism, GroupHomomorphism) + + strong_gens = self.strong_gens[:] + stabs = self.basic_stabilizers[:] + base = self.base[:] + + # injection from a free group on len(strong_gens) + # generators into G + gen_syms = [('x_%d'%i) for i in range(len(strong_gens))] + F = free_group(', '.join(gen_syms))[0] + phi = homomorphism(F, self, F.generators, strong_gens) + + H = PermutationGroup(self.identity) + while stabs: + alpha = base.pop() + K = H + H = stabs.pop() + new_gens = [g for g in H.generators if g not in K] + + if K.order() == 1: + z = new_gens.pop() + rels = [F.generators[-1]**z.order()] + intermediate_gens = [z] + K = PermutationGroup(intermediate_gens) + + # add generators one at a time building up from K to H + while new_gens: + z = new_gens.pop() + intermediate_gens = [z] + intermediate_gens + K_s = PermutationGroup(intermediate_gens) + orbit = K_s.orbit(alpha) + orbit_k = K.orbit(alpha) + + # split into cases based on the orbit of K_s + if orbit_k == orbit: + if z in K: + rel = phi.invert(z) + perm = z + else: + t = K.orbit_rep(alpha, alpha^z) + rel = phi.invert(z)*phi.invert(t)**-1 + perm = z*t**-1 + for g in K.generator_product(perm, original=True): + rel = rel*phi.invert(g)**-1 + new_rels = [rel] + elif len(orbit_k) == 1: + # `success` is always true because `strong_gens` + # and `base` are already a verified BSGS. Later + # this could be changed to start with a randomly + # generated (potential) BSGS, and then new elements + # would have to be appended to it when `success` + # is false. + success, new_rels = K_s._verify(K, phi, z, alpha) + else: + # K.orbit(alpha) should be a block + # under the action of K_s on K_s.orbit(alpha) + check, block = K_s._block_verify(K, alpha) + if check: + # apply _verify to the action of K_s + # on the block system; for convenience, + # add the blocks as additional points + # that K_s should act on + t = block_homomorphism(K_s, block) + m = t.codomain.degree # number of blocks + d = K_s.degree + + # conjugating with p will shift + # permutations in t.image() to + # higher numbers, e.g. + # p*(0 1)*p = (m m+1) + p = Permutation() + for i in range(m): + p *= Permutation(i, i+d) + + t_img = t.images + # combine generators of K_s with their + # action on the block system + images = {g: g*p*t_img[g]*p for g in t_img} + for g in self.strong_gens[:-len(K_s.generators)]: + images[g] = g + K_s_act = PermutationGroup(list(images.values())) + f = GroupHomomorphism(self, K_s_act, images) + + K_act = PermutationGroup([f(g) for g in K.generators]) + success, new_rels = K_s_act._verify(K_act, f.compose(phi), f(z), d) + + for n in new_rels: + if n not in rels: + rels.append(n) + K = K_s + + group = FpGroup(F, rels) + return simplify_presentation(group) + + def presentation(self, eliminate_gens=True): + ''' + Return an `FpGroup` presentation of the group. + + The algorithm is described in [1], Chapter 6.1. + + ''' + from sympy.combinatorics.fp_groups import (FpGroup, + simplify_presentation) + from sympy.combinatorics.coset_table import CosetTable + from sympy.combinatorics.free_groups import free_group + from sympy.combinatorics.homomorphisms import homomorphism + + if self._fp_presentation: + return self._fp_presentation + + def _factor_group_by_rels(G, rels): + if isinstance(G, FpGroup): + rels.extend(G.relators) + return FpGroup(G.free_group, list(set(rels))) + return FpGroup(G, rels) + + gens = self.generators + len_g = len(gens) + + if len_g == 1: + order = gens[0].order() + # handle the trivial group + if order == 1: + return free_group([])[0] + F, x = free_group('x') + return FpGroup(F, [x**order]) + + if self.order() > 20: + half_gens = self.generators[0:(len_g+1)//2] + else: + half_gens = [] + H = PermutationGroup(half_gens) + H_p = H.presentation() + + len_h = len(H_p.generators) + + C = self.coset_table(H) + n = len(C) # subgroup index + + gen_syms = [('x_%d'%i) for i in range(len(gens))] + F = free_group(', '.join(gen_syms))[0] + + # mapping generators of H_p to those of F + images = [F.generators[i] for i in range(len_h)] + R = homomorphism(H_p, F, H_p.generators, images, check=False) + + # rewrite relators + rels = R(H_p.relators) + G_p = FpGroup(F, rels) + + # injective homomorphism from G_p into self + T = homomorphism(G_p, self, G_p.generators, gens) + + C_p = CosetTable(G_p, []) + + C_p.table = [[None]*(2*len_g) for i in range(n)] + + # initiate the coset transversal + transversal = [None]*n + transversal[0] = G_p.identity + + # fill in the coset table as much as possible + for i in range(2*len_h): + C_p.table[0][i] = 0 + + gamma = 1 + for alpha, x in product(range(n), range(2*len_g)): + beta = C[alpha][x] + if beta == gamma: + gen = G_p.generators[x//2]**((-1)**(x % 2)) + transversal[beta] = transversal[alpha]*gen + C_p.table[alpha][x] = beta + C_p.table[beta][x + (-1)**(x % 2)] = alpha + gamma += 1 + if gamma == n: + break + + C_p.p = list(range(n)) + beta = x = 0 + + while not C_p.is_complete(): + # find the first undefined entry + while C_p.table[beta][x] == C[beta][x]: + x = (x + 1) % (2*len_g) + if x == 0: + beta = (beta + 1) % n + + # define a new relator + gen = G_p.generators[x//2]**((-1)**(x % 2)) + new_rel = transversal[beta]*gen*transversal[C[beta][x]]**-1 + perm = T(new_rel) + nxt = G_p.identity + for s in H.generator_product(perm, original=True): + nxt = nxt*T.invert(s)**-1 + new_rel = new_rel*nxt + + # continue coset enumeration + G_p = _factor_group_by_rels(G_p, [new_rel]) + C_p.scan_and_fill(0, new_rel) + C_p = G_p.coset_enumeration([], strategy="coset_table", + draft=C_p, max_cosets=n, incomplete=True) + + self._fp_presentation = simplify_presentation(G_p) + return self._fp_presentation + + def polycyclic_group(self): + """ + Return the PolycyclicGroup instance with below parameters: + + Explanation + =========== + + * pc_sequence : Polycyclic sequence is formed by collecting all + the missing generators between the adjacent groups in the + derived series of given permutation group. + + * pc_series : Polycyclic series is formed by adding all the missing + generators of ``der[i+1]`` in ``der[i]``, where ``der`` represents + the derived series. + + * relative_order : A list, computed by the ratio of adjacent groups in + pc_series. + + """ + from sympy.combinatorics.pc_groups import PolycyclicGroup + if not self.is_polycyclic: + raise ValueError("The group must be solvable") + + der = self.derived_series() + pc_series = [] + pc_sequence = [] + relative_order = [] + pc_series.append(der[-1]) + der.reverse() + + for i in range(len(der)-1): + H = der[i] + for g in der[i+1].generators: + if g not in H: + H = PermutationGroup([g] + H.generators) + pc_series.insert(0, H) + pc_sequence.insert(0, g) + + G1 = pc_series[0].order() + G2 = pc_series[1].order() + relative_order.insert(0, G1 // G2) + + return PolycyclicGroup(pc_sequence, pc_series, relative_order, collector=None) + + +def _orbit(degree, generators, alpha, action='tuples'): + r"""Compute the orbit of alpha `\{g(\alpha) | g \in G\}` as a set. + + Explanation + =========== + + The time complexity of the algorithm used here is `O(|Orb|*r)` where + `|Orb|` is the size of the orbit and ``r`` is the number of generators of + the group. For a more detailed analysis, see [1], p.78, [2], pp. 19-21. + Here alpha can be a single point, or a list of points. + + If alpha is a single point, the ordinary orbit is computed. + if alpha is a list of points, there are three available options: + + 'union' - computes the union of the orbits of the points in the list + 'tuples' - computes the orbit of the list interpreted as an ordered + tuple under the group action ( i.e., g((1, 2, 3)) = (g(1), g(2), g(3)) ) + 'sets' - computes the orbit of the list interpreted as a sets + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> from sympy.combinatorics.perm_groups import _orbit + >>> a = Permutation([1, 2, 0, 4, 5, 6, 3]) + >>> G = PermutationGroup([a]) + >>> _orbit(G.degree, G.generators, 0) + {0, 1, 2} + >>> _orbit(G.degree, G.generators, [0, 4], 'union') + {0, 1, 2, 3, 4, 5, 6} + + See Also + ======== + + orbit, orbit_transversal + + """ + if not hasattr(alpha, '__getitem__'): + alpha = [alpha] + + gens = [x._array_form for x in generators] + if len(alpha) == 1 or action == 'union': + orb = alpha + used = [False]*degree + for el in alpha: + used[el] = True + for b in orb: + for gen in gens: + temp = gen[b] + if used[temp] == False: + orb.append(temp) + used[temp] = True + return set(orb) + elif action == 'tuples': + alpha = tuple(alpha) + orb = [alpha] + used = {alpha} + for b in orb: + for gen in gens: + temp = tuple([gen[x] for x in b]) + if temp not in used: + orb.append(temp) + used.add(temp) + return set(orb) + elif action == 'sets': + alpha = frozenset(alpha) + orb = [alpha] + used = {alpha} + for b in orb: + for gen in gens: + temp = frozenset([gen[x] for x in b]) + if temp not in used: + orb.append(temp) + used.add(temp) + return {tuple(x) for x in orb} + + +def _orbits(degree, generators): + """Compute the orbits of G. + + If ``rep=False`` it returns a list of sets else it returns a list of + representatives of the orbits + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy.combinatorics.perm_groups import _orbits + >>> a = Permutation([0, 2, 1]) + >>> b = Permutation([1, 0, 2]) + >>> _orbits(a.size, [a, b]) + [{0, 1, 2}] + """ + + orbs = [] + sorted_I = list(range(degree)) + I = set(sorted_I) + while I: + i = sorted_I[0] + orb = _orbit(degree, generators, i) + orbs.append(orb) + # remove all indices that are in this orbit + I -= orb + sorted_I = [i for i in sorted_I if i not in orb] + return orbs + + +def _orbit_transversal(degree, generators, alpha, pairs, af=False, slp=False): + r"""Computes a transversal for the orbit of ``alpha`` as a set. + + Explanation + =========== + + generators generators of the group ``G`` + + For a permutation group ``G``, a transversal for the orbit + `Orb = \{g(\alpha) | g \in G\}` is a set + `\{g_\beta | g_\beta(\alpha) = \beta\}` for `\beta \in Orb`. + Note that there may be more than one possible transversal. + If ``pairs`` is set to ``True``, it returns the list of pairs + `(\beta, g_\beta)`. For a proof of correctness, see [1], p.79 + + if ``af`` is ``True``, the transversal elements are given in + array form. + + If `slp` is `True`, a dictionary `{beta: slp_beta}` is returned + for `\beta \in Orb` where `slp_beta` is a list of indices of the + generators in `generators` s.t. if `slp_beta = [i_1 \dots i_n]` + `g_\beta = generators[i_n] \times \dots \times generators[i_1]`. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> from sympy.combinatorics.perm_groups import _orbit_transversal + >>> G = DihedralGroup(6) + >>> _orbit_transversal(G.degree, G.generators, 0, False) + [(5), (0 1 2 3 4 5), (0 5)(1 4)(2 3), (0 2 4)(1 3 5), (5)(0 4)(1 3), (0 3)(1 4)(2 5)] + """ + + tr = [(alpha, list(range(degree)))] + slp_dict = {alpha: []} + used = [False]*degree + used[alpha] = True + gens = [x._array_form for x in generators] + for x, px in tr: + px_slp = slp_dict[x] + for gen in gens: + temp = gen[x] + if used[temp] == False: + slp_dict[temp] = [gens.index(gen)] + px_slp + tr.append((temp, _af_rmul(gen, px))) + used[temp] = True + if pairs: + if not af: + tr = [(x, _af_new(y)) for x, y in tr] + if not slp: + return tr + return tr, slp_dict + + if af: + tr = [y for _, y in tr] + if not slp: + return tr + return tr, slp_dict + + tr = [_af_new(y) for _, y in tr] + if not slp: + return tr + return tr, slp_dict + + +def _stabilizer(degree, generators, alpha): + r"""Return the stabilizer subgroup of ``alpha``. + + Explanation + =========== + + The stabilizer of `\alpha` is the group `G_\alpha = + \{g \in G | g(\alpha) = \alpha\}`. + For a proof of correctness, see [1], p.79. + + degree : degree of G + generators : generators of G + + Examples + ======== + + >>> from sympy.combinatorics.perm_groups import _stabilizer + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> G = DihedralGroup(6) + >>> _stabilizer(G.degree, G.generators, 5) + [(5)(0 4)(1 3), (5)] + + See Also + ======== + + orbit + + """ + orb = [alpha] + table = {alpha: list(range(degree))} + table_inv = {alpha: list(range(degree))} + used = [False]*degree + used[alpha] = True + gens = [x._array_form for x in generators] + stab_gens = [] + for b in orb: + for gen in gens: + temp = gen[b] + if used[temp] is False: + gen_temp = _af_rmul(gen, table[b]) + orb.append(temp) + table[temp] = gen_temp + table_inv[temp] = _af_invert(gen_temp) + used[temp] = True + else: + schreier_gen = _af_rmuln(table_inv[temp], gen, table[b]) + if schreier_gen not in stab_gens: + stab_gens.append(schreier_gen) + return [_af_new(x) for x in stab_gens] + + +PermGroup = PermutationGroup + + +class SymmetricPermutationGroup(Basic): + """ + The class defining the lazy form of SymmetricGroup. + + deg : int + + """ + def __new__(cls, deg): + deg = _sympify(deg) + obj = Basic.__new__(cls, deg) + return obj + + def __init__(self, *args, **kwargs): + self._deg = self.args[0] + self._order = None + + def __contains__(self, i): + """Return ``True`` if *i* is contained in SymmetricPermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, SymmetricPermutationGroup + >>> G = SymmetricPermutationGroup(4) + >>> Permutation(1, 2, 3) in G + True + + """ + if not isinstance(i, Permutation): + raise TypeError("A SymmetricPermutationGroup contains only Permutations as " + "elements, not elements of type %s" % type(i)) + return i.size == self.degree + + def order(self): + """ + Return the order of the SymmetricPermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricPermutationGroup + >>> G = SymmetricPermutationGroup(4) + >>> G.order() + 24 + """ + if self._order is not None: + return self._order + n = self._deg + self._order = factorial(n) + return self._order + + @property + def degree(self): + """ + Return the degree of the SymmetricPermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricPermutationGroup + >>> G = SymmetricPermutationGroup(4) + >>> G.degree + 4 + + """ + return self._deg + + @property + def identity(self): + ''' + Return the identity element of the SymmetricPermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricPermutationGroup + >>> G = SymmetricPermutationGroup(4) + >>> G.identity() + (3) + + ''' + return _af_new(list(range(self._deg))) + + +class Coset(Basic): + """A left coset of a permutation group with respect to an element. + + Parameters + ========== + + g : Permutation + + H : PermutationGroup + + dir : "+" or "-", If not specified by default it will be "+" + here ``dir`` specified the type of coset "+" represent the + right coset and "-" represent the left coset. + + G : PermutationGroup, optional + The group which contains *H* as its subgroup and *g* as its + element. + + If not specified, it would automatically become a symmetric + group ``SymmetricPermutationGroup(g.size)`` and + ``SymmetricPermutationGroup(H.degree)`` if ``g.size`` and ``H.degree`` + are matching.``SymmetricPermutationGroup`` is a lazy form of SymmetricGroup + used for representation purpose. + + """ + + def __new__(cls, g, H, G=None, dir="+"): + g = _sympify(g) + if not isinstance(g, Permutation): + raise NotImplementedError + + H = _sympify(H) + if not isinstance(H, PermutationGroup): + raise NotImplementedError + + if G is not None: + G = _sympify(G) + if not isinstance(G, (PermutationGroup, SymmetricPermutationGroup)): + raise NotImplementedError + if not H.is_subgroup(G): + raise ValueError("{} must be a subgroup of {}.".format(H, G)) + if g not in G: + raise ValueError("{} must be an element of {}.".format(g, G)) + else: + g_size = g.size + h_degree = H.degree + if g_size != h_degree: + raise ValueError( + "The size of the permutation {} and the degree of " + "the permutation group {} should be matching " + .format(g, H)) + G = SymmetricPermutationGroup(g.size) + + if isinstance(dir, str): + dir = Symbol(dir) + elif not isinstance(dir, Symbol): + raise TypeError("dir must be of type basestring or " + "Symbol, not %s" % type(dir)) + if str(dir) not in ('+', '-'): + raise ValueError("dir must be one of '+' or '-' not %s" % dir) + obj = Basic.__new__(cls, g, H, G, dir) + return obj + + def __init__(self, *args, **kwargs): + self._dir = self.args[3] + + @property + def is_left_coset(self): + """ + Check if the coset is left coset that is ``gH``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup, Coset + >>> a = Permutation(1, 2) + >>> b = Permutation(0, 1) + >>> G = PermutationGroup([a, b]) + >>> cst = Coset(a, G, dir="-") + >>> cst.is_left_coset + True + + """ + return str(self._dir) == '-' + + @property + def is_right_coset(self): + """ + Check if the coset is right coset that is ``Hg``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, PermutationGroup, Coset + >>> a = Permutation(1, 2) + >>> b = Permutation(0, 1) + >>> G = PermutationGroup([a, b]) + >>> cst = Coset(a, G, dir="+") + >>> cst.is_right_coset + True + + """ + return str(self._dir) == '+' + + def as_list(self): + """ + Return all the elements of coset in the form of list. + """ + g = self.args[0] + H = self.args[1] + cst = [] + if str(self._dir) == '+': + for h in H.elements: + cst.append(h*g) + else: + for h in H.elements: + cst.append(g*h) + return cst diff --git a/lib/python3.11/site-packages/sympy/combinatorics/permutations.py b/lib/python3.11/site-packages/sympy/combinatorics/permutations.py new file mode 100644 index 0000000000000000000000000000000000000000..21914003b2b95cb3f9f1232a9f0dc012aac0b789 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/permutations.py @@ -0,0 +1,3115 @@ +import random +from collections import defaultdict +from collections.abc import Iterable +from functools import reduce + +from sympy.core.parameters import global_parameters +from sympy.core.basic import Atom +from sympy.core.expr import Expr +from sympy.core.numbers import int_valued +from sympy.core.numbers import Integer +from sympy.core.sympify import _sympify +from sympy.matrices import zeros +from sympy.polys.polytools import lcm +from sympy.printing.repr import srepr +from sympy.utilities.iterables import (flatten, has_variety, minlex, + has_dups, runs, is_sequence) +from sympy.utilities.misc import as_int +from mpmath.libmp.libintmath import ifac +from sympy.multipledispatch import dispatch + +def _af_rmul(a, b): + """ + Return the product b*a; input and output are array forms. The ith value + is a[b[i]]. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_rmul, Permutation + + >>> a, b = [1, 0, 2], [0, 2, 1] + >>> _af_rmul(a, b) + [1, 2, 0] + >>> [a[b[i]] for i in range(3)] + [1, 2, 0] + + This handles the operands in reverse order compared to the ``*`` operator: + + >>> a = Permutation(a) + >>> b = Permutation(b) + >>> list(a*b) + [2, 0, 1] + >>> [b(a(i)) for i in range(3)] + [2, 0, 1] + + See Also + ======== + + rmul, _af_rmuln + """ + return [a[i] for i in b] + + +def _af_rmuln(*abc): + """ + Given [a, b, c, ...] return the product of ...*c*b*a using array forms. + The ith value is a[b[c[i]]]. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_rmul, Permutation + + >>> a, b = [1, 0, 2], [0, 2, 1] + >>> _af_rmul(a, b) + [1, 2, 0] + >>> [a[b[i]] for i in range(3)] + [1, 2, 0] + + This handles the operands in reverse order compared to the ``*`` operator: + + >>> a = Permutation(a); b = Permutation(b) + >>> list(a*b) + [2, 0, 1] + >>> [b(a(i)) for i in range(3)] + [2, 0, 1] + + See Also + ======== + + rmul, _af_rmul + """ + a = abc + m = len(a) + if m == 3: + p0, p1, p2 = a + return [p0[p1[i]] for i in p2] + if m == 4: + p0, p1, p2, p3 = a + return [p0[p1[p2[i]]] for i in p3] + if m == 5: + p0, p1, p2, p3, p4 = a + return [p0[p1[p2[p3[i]]]] for i in p4] + if m == 6: + p0, p1, p2, p3, p4, p5 = a + return [p0[p1[p2[p3[p4[i]]]]] for i in p5] + if m == 7: + p0, p1, p2, p3, p4, p5, p6 = a + return [p0[p1[p2[p3[p4[p5[i]]]]]] for i in p6] + if m == 8: + p0, p1, p2, p3, p4, p5, p6, p7 = a + return [p0[p1[p2[p3[p4[p5[p6[i]]]]]]] for i in p7] + if m == 1: + return a[0][:] + if m == 2: + a, b = a + return [a[i] for i in b] + if m == 0: + raise ValueError("String must not be empty") + p0 = _af_rmuln(*a[:m//2]) + p1 = _af_rmuln(*a[m//2:]) + return [p0[i] for i in p1] + + +def _af_parity(pi): + """ + Computes the parity of a permutation in array form. + + Explanation + =========== + + The parity of a permutation reflects the parity of the + number of inversions in the permutation, i.e., the + number of pairs of x and y such that x > y but p[x] < p[y]. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_parity + >>> _af_parity([0, 1, 2, 3]) + 0 + >>> _af_parity([3, 2, 0, 1]) + 1 + + See Also + ======== + + Permutation + """ + n = len(pi) + a = [0] * n + c = 0 + for j in range(n): + if a[j] == 0: + c += 1 + a[j] = 1 + i = j + while pi[i] != j: + i = pi[i] + a[i] = 1 + return (n - c) % 2 + + +def _af_invert(a): + """ + Finds the inverse, ~A, of a permutation, A, given in array form. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_invert, _af_rmul + >>> A = [1, 2, 0, 3] + >>> _af_invert(A) + [2, 0, 1, 3] + >>> _af_rmul(_, A) + [0, 1, 2, 3] + + See Also + ======== + + Permutation, __invert__ + """ + inv_form = [0] * len(a) + for i, ai in enumerate(a): + inv_form[ai] = i + return inv_form + + +def _af_pow(a, n): + """ + Routine for finding powers of a permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy.combinatorics.permutations import _af_pow + >>> p = Permutation([2, 0, 3, 1]) + >>> p.order() + 4 + >>> _af_pow(p._array_form, 4) + [0, 1, 2, 3] + """ + if n == 0: + return list(range(len(a))) + if n < 0: + return _af_pow(_af_invert(a), -n) + if n == 1: + return a[:] + elif n == 2: + b = [a[i] for i in a] + elif n == 3: + b = [a[a[i]] for i in a] + elif n == 4: + b = [a[a[a[i]]] for i in a] + else: + # use binary multiplication + b = list(range(len(a))) + while 1: + if n & 1: + b = [b[i] for i in a] + n -= 1 + if not n: + break + if n % 4 == 0: + a = [a[a[a[i]]] for i in a] + n = n // 4 + elif n % 2 == 0: + a = [a[i] for i in a] + n = n // 2 + return b + + +def _af_commutes_with(a, b): + """ + Checks if the two permutations with array forms + given by ``a`` and ``b`` commute. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_commutes_with + >>> _af_commutes_with([1, 2, 0], [0, 2, 1]) + False + + See Also + ======== + + Permutation, commutes_with + """ + return not any(a[b[i]] != b[a[i]] for i in range(len(a) - 1)) + + +class Cycle(dict): + """ + Wrapper around dict which provides the functionality of a disjoint cycle. + + Explanation + =========== + + A cycle shows the rule to use to move subsets of elements to obtain + a permutation. The Cycle class is more flexible than Permutation in + that 1) all elements need not be present in order to investigate how + multiple cycles act in sequence and 2) it can contain singletons: + + >>> from sympy.combinatorics.permutations import Perm, Cycle + + A Cycle will automatically parse a cycle given as a tuple on the rhs: + + >>> Cycle(1, 2)(2, 3) + (1 3 2) + + The identity cycle, Cycle(), can be used to start a product: + + >>> Cycle()(1, 2)(2, 3) + (1 3 2) + + The array form of a Cycle can be obtained by calling the list + method (or passing it to the list function) and all elements from + 0 will be shown: + + >>> a = Cycle(1, 2) + >>> a.list() + [0, 2, 1] + >>> list(a) + [0, 2, 1] + + If a larger (or smaller) range is desired use the list method and + provide the desired size -- but the Cycle cannot be truncated to + a size smaller than the largest element that is out of place: + + >>> b = Cycle(2, 4)(1, 2)(3, 1, 4)(1, 3) + >>> b.list() + [0, 2, 1, 3, 4] + >>> b.list(b.size + 1) + [0, 2, 1, 3, 4, 5] + >>> b.list(-1) + [0, 2, 1] + + Singletons are not shown when printing with one exception: the largest + element is always shown -- as a singleton if necessary: + + >>> Cycle(1, 4, 10)(4, 5) + (1 5 4 10) + >>> Cycle(1, 2)(4)(5)(10) + (1 2)(10) + + The array form can be used to instantiate a Permutation so other + properties of the permutation can be investigated: + + >>> Perm(Cycle(1, 2)(3, 4).list()).transpositions() + [(1, 2), (3, 4)] + + Notes + ===== + + The underlying structure of the Cycle is a dictionary and although + the __iter__ method has been redefined to give the array form of the + cycle, the underlying dictionary items are still available with the + such methods as items(): + + >>> list(Cycle(1, 2).items()) + [(1, 2), (2, 1)] + + See Also + ======== + + Permutation + """ + def __missing__(self, arg): + """Enter arg into dictionary and return arg.""" + return as_int(arg) + + def __iter__(self): + yield from self.list() + + def __call__(self, *other): + """Return product of cycles processed from R to L. + + Examples + ======== + + >>> from sympy.combinatorics import Cycle + >>> Cycle(1, 2)(2, 3) + (1 3 2) + + An instance of a Cycle will automatically parse list-like + objects and Permutations that are on the right. It is more + flexible than the Permutation in that all elements need not + be present: + + >>> a = Cycle(1, 2) + >>> a(2, 3) + (1 3 2) + >>> a(2, 3)(4, 5) + (1 3 2)(4 5) + + """ + rv = Cycle(*other) + for k, v in zip(list(self.keys()), [rv[self[k]] for k in self.keys()]): + rv[k] = v + return rv + + def list(self, size=None): + """Return the cycles as an explicit list starting from 0 up + to the greater of the largest value in the cycles and size. + + Truncation of trailing unmoved items will occur when size + is less than the maximum element in the cycle; if this is + desired, setting ``size=-1`` will guarantee such trimming. + + Examples + ======== + + >>> from sympy.combinatorics import Cycle + >>> p = Cycle(2, 3)(4, 5) + >>> p.list() + [0, 1, 3, 2, 5, 4] + >>> p.list(10) + [0, 1, 3, 2, 5, 4, 6, 7, 8, 9] + + Passing a length too small will trim trailing, unchanged elements + in the permutation: + + >>> Cycle(2, 4)(1, 2, 4).list(-1) + [0, 2, 1] + """ + if not self and size is None: + raise ValueError('must give size for empty Cycle') + if size is not None: + big = max([i for i in self.keys() if self[i] != i] + [0]) + size = max(size, big + 1) + else: + size = self.size + return [self[i] for i in range(size)] + + def __repr__(self): + """We want it to print as a Cycle, not as a dict. + + Examples + ======== + + >>> from sympy.combinatorics import Cycle + >>> Cycle(1, 2) + (1 2) + >>> print(_) + (1 2) + >>> list(Cycle(1, 2).items()) + [(1, 2), (2, 1)] + """ + if not self: + return 'Cycle()' + cycles = Permutation(self).cyclic_form + s = ''.join(str(tuple(c)) for c in cycles) + big = self.size - 1 + if not any(i == big for c in cycles for i in c): + s += '(%s)' % big + return 'Cycle%s' % s + + def __str__(self): + """We want it to be printed in a Cycle notation with no + comma in-between. + + Examples + ======== + + >>> from sympy.combinatorics import Cycle + >>> Cycle(1, 2) + (1 2) + >>> Cycle(1, 2, 4)(5, 6) + (1 2 4)(5 6) + """ + if not self: + return '()' + cycles = Permutation(self).cyclic_form + s = ''.join(str(tuple(c)) for c in cycles) + big = self.size - 1 + if not any(i == big for c in cycles for i in c): + s += '(%s)' % big + s = s.replace(',', '') + return s + + def __init__(self, *args): + """Load up a Cycle instance with the values for the cycle. + + Examples + ======== + + >>> from sympy.combinatorics import Cycle + >>> Cycle(1, 2, 6) + (1 2 6) + """ + + if not args: + return + if len(args) == 1: + if isinstance(args[0], Permutation): + for c in args[0].cyclic_form: + self.update(self(*c)) + return + elif isinstance(args[0], Cycle): + for k, v in args[0].items(): + self[k] = v + return + args = [as_int(a) for a in args] + if any(i < 0 for i in args): + raise ValueError('negative integers are not allowed in a cycle.') + if has_dups(args): + raise ValueError('All elements must be unique in a cycle.') + for i in range(-len(args), 0): + self[args[i]] = args[i + 1] + + @property + def size(self): + if not self: + return 0 + return max(self.keys()) + 1 + + def copy(self): + return Cycle(self) + + +class Permutation(Atom): + r""" + A permutation, alternatively known as an 'arrangement number' or 'ordering' + is an arrangement of the elements of an ordered list into a one-to-one + mapping with itself. The permutation of a given arrangement is given by + indicating the positions of the elements after re-arrangement [2]_. For + example, if one started with elements ``[x, y, a, b]`` (in that order) and + they were reordered as ``[x, y, b, a]`` then the permutation would be + ``[0, 1, 3, 2]``. Notice that (in SymPy) the first element is always referred + to as 0 and the permutation uses the indices of the elements in the + original ordering, not the elements ``(a, b, ...)`` themselves. + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + + Permutations Notation + ===================== + + Permutations are commonly represented in disjoint cycle or array forms. + + Array Notation and 2-line Form + ------------------------------------ + + In the 2-line form, the elements and their final positions are shown + as a matrix with 2 rows: + + [0 1 2 ... n-1] + [p(0) p(1) p(2) ... p(n-1)] + + Since the first line is always ``range(n)``, where n is the size of p, + it is sufficient to represent the permutation by the second line, + referred to as the "array form" of the permutation. This is entered + in brackets as the argument to the Permutation class: + + >>> p = Permutation([0, 2, 1]); p + Permutation([0, 2, 1]) + + Given i in range(p.size), the permutation maps i to i^p + + >>> [i^p for i in range(p.size)] + [0, 2, 1] + + The composite of two permutations p*q means first apply p, then q, so + i^(p*q) = (i^p)^q which is i^p^q according to Python precedence rules: + + >>> q = Permutation([2, 1, 0]) + >>> [i^p^q for i in range(3)] + [2, 0, 1] + >>> [i^(p*q) for i in range(3)] + [2, 0, 1] + + One can use also the notation p(i) = i^p, but then the composition + rule is (p*q)(i) = q(p(i)), not p(q(i)): + + >>> [(p*q)(i) for i in range(p.size)] + [2, 0, 1] + >>> [q(p(i)) for i in range(p.size)] + [2, 0, 1] + >>> [p(q(i)) for i in range(p.size)] + [1, 2, 0] + + Disjoint Cycle Notation + ----------------------- + + In disjoint cycle notation, only the elements that have shifted are + indicated. + + For example, [1, 3, 2, 0] can be represented as (0, 1, 3)(2). + This can be understood from the 2 line format of the given permutation. + In the 2-line form, + [0 1 2 3] + [1 3 2 0] + + The element in the 0th position is 1, so 0 -> 1. The element in the 1st + position is three, so 1 -> 3. And the element in the third position is again + 0, so 3 -> 0. Thus, 0 -> 1 -> 3 -> 0, and 2 -> 2. Thus, this can be represented + as 2 cycles: (0, 1, 3)(2). + In common notation, singular cycles are not explicitly written as they can be + inferred implicitly. + + Only the relative ordering of elements in a cycle matter: + + >>> Permutation(1,2,3) == Permutation(2,3,1) == Permutation(3,1,2) + True + + The disjoint cycle notation is convenient when representing + permutations that have several cycles in them: + + >>> Permutation(1, 2)(3, 5) == Permutation([[1, 2], [3, 5]]) + True + + It also provides some economy in entry when computing products of + permutations that are written in disjoint cycle notation: + + >>> Permutation(1, 2)(1, 3)(2, 3) + Permutation([0, 3, 2, 1]) + >>> _ == Permutation([[1, 2]])*Permutation([[1, 3]])*Permutation([[2, 3]]) + True + + Caution: when the cycles have common elements between them then the order + in which the permutations are applied matters. This module applies + the permutations from *left to right*. + + >>> Permutation(1, 2)(2, 3) == Permutation([(1, 2), (2, 3)]) + True + >>> Permutation(1, 2)(2, 3).list() + [0, 3, 1, 2] + + In the above case, (1,2) is computed before (2,3). + As 0 -> 0, 0 -> 0, element in position 0 is 0. + As 1 -> 2, 2 -> 3, element in position 1 is 3. + As 2 -> 1, 1 -> 1, element in position 2 is 1. + As 3 -> 3, 3 -> 2, element in position 3 is 2. + + If the first and second elements had been + swapped first, followed by the swapping of the second + and third, the result would have been [0, 2, 3, 1]. + If, you want to apply the cycles in the conventional + right to left order, call the function with arguments in reverse order + as demonstrated below: + + >>> Permutation([(1, 2), (2, 3)][::-1]).list() + [0, 2, 3, 1] + + Entering a singleton in a permutation is a way to indicate the size of the + permutation. The ``size`` keyword can also be used. + + Array-form entry: + + >>> Permutation([[1, 2], [9]]) + Permutation([0, 2, 1], size=10) + >>> Permutation([[1, 2]], size=10) + Permutation([0, 2, 1], size=10) + + Cyclic-form entry: + + >>> Permutation(1, 2, size=10) + Permutation([0, 2, 1], size=10) + >>> Permutation(9)(1, 2) + Permutation([0, 2, 1], size=10) + + Caution: no singleton containing an element larger than the largest + in any previous cycle can be entered. This is an important difference + in how Permutation and Cycle handle the ``__call__`` syntax. A singleton + argument at the start of a Permutation performs instantiation of the + Permutation and is permitted: + + >>> Permutation(5) + Permutation([], size=6) + + A singleton entered after instantiation is a call to the permutation + -- a function call -- and if the argument is out of range it will + trigger an error. For this reason, it is better to start the cycle + with the singleton: + + The following fails because there is no element 3: + + >>> Permutation(1, 2)(3) + Traceback (most recent call last): + ... + IndexError: list index out of range + + This is ok: only the call to an out of range singleton is prohibited; + otherwise the permutation autosizes: + + >>> Permutation(3)(1, 2) + Permutation([0, 2, 1, 3]) + >>> Permutation(1, 2)(3, 4) == Permutation(3, 4)(1, 2) + True + + + Equality testing + ---------------- + + The array forms must be the same in order for permutations to be equal: + + >>> Permutation([1, 0, 2, 3]) == Permutation([1, 0]) + False + + + Identity Permutation + -------------------- + + The identity permutation is a permutation in which no element is out of + place. It can be entered in a variety of ways. All the following create + an identity permutation of size 4: + + >>> I = Permutation([0, 1, 2, 3]) + >>> all(p == I for p in [ + ... Permutation(3), + ... Permutation(range(4)), + ... Permutation([], size=4), + ... Permutation(size=4)]) + True + + Watch out for entering the range *inside* a set of brackets (which is + cycle notation): + + >>> I == Permutation([range(4)]) + False + + + Permutation Printing + ==================== + + There are a few things to note about how Permutations are printed. + + .. deprecated:: 1.6 + + Configuring Permutation printing by setting + ``Permutation.print_cyclic`` is deprecated. Users should use the + ``perm_cyclic`` flag to the printers, as described below. + + 1) If you prefer one form (array or cycle) over another, you can set + ``init_printing`` with the ``perm_cyclic`` flag. + + >>> from sympy import init_printing + >>> p = Permutation(1, 2)(4, 5)(3, 4) + >>> p + Permutation([0, 2, 1, 4, 5, 3]) + + >>> init_printing(perm_cyclic=True, pretty_print=False) + >>> p + (1 2)(3 4 5) + + 2) Regardless of the setting, a list of elements in the array for cyclic + form can be obtained and either of those can be copied and supplied as + the argument to Permutation: + + >>> p.array_form + [0, 2, 1, 4, 5, 3] + >>> p.cyclic_form + [[1, 2], [3, 4, 5]] + >>> Permutation(_) == p + True + + 3) Printing is economical in that as little as possible is printed while + retaining all information about the size of the permutation: + + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> Permutation([1, 0, 2, 3]) + Permutation([1, 0, 2, 3]) + >>> Permutation([1, 0, 2, 3], size=20) + Permutation([1, 0], size=20) + >>> Permutation([1, 0, 2, 4, 3, 5, 6], size=20) + Permutation([1, 0, 2, 4, 3], size=20) + + >>> p = Permutation([1, 0, 2, 3]) + >>> init_printing(perm_cyclic=True, pretty_print=False) + >>> p + (3)(0 1) + >>> init_printing(perm_cyclic=False, pretty_print=False) + + The 2 was not printed but it is still there as can be seen with the + array_form and size methods: + + >>> p.array_form + [1, 0, 2, 3] + >>> p.size + 4 + + Short introduction to other methods + =================================== + + The permutation can act as a bijective function, telling what element is + located at a given position + + >>> q = Permutation([5, 2, 3, 4, 1, 0]) + >>> q.array_form[1] # the hard way + 2 + >>> q(1) # the easy way + 2 + >>> {i: q(i) for i in range(q.size)} # showing the bijection + {0: 5, 1: 2, 2: 3, 3: 4, 4: 1, 5: 0} + + The full cyclic form (including singletons) can be obtained: + + >>> p.full_cyclic_form + [[0, 1], [2], [3]] + + Any permutation can be factored into transpositions of pairs of elements: + + >>> Permutation([[1, 2], [3, 4, 5]]).transpositions() + [(1, 2), (3, 5), (3, 4)] + >>> Permutation.rmul(*[Permutation([ti], size=6) for ti in _]).cyclic_form + [[1, 2], [3, 4, 5]] + + The number of permutations on a set of n elements is given by n! and is + called the cardinality. + + >>> p.size + 4 + >>> p.cardinality + 24 + + A given permutation has a rank among all the possible permutations of the + same elements, but what that rank is depends on how the permutations are + enumerated. (There are a number of different methods of doing so.) The + lexicographic rank is given by the rank method and this rank is used to + increment a permutation with addition/subtraction: + + >>> p.rank() + 6 + >>> p + 1 + Permutation([1, 0, 3, 2]) + >>> p.next_lex() + Permutation([1, 0, 3, 2]) + >>> _.rank() + 7 + >>> p.unrank_lex(p.size, rank=7) + Permutation([1, 0, 3, 2]) + + The product of two permutations p and q is defined as their composition as + functions, (p*q)(i) = q(p(i)) [6]_. + + >>> p = Permutation([1, 0, 2, 3]) + >>> q = Permutation([2, 3, 1, 0]) + >>> list(q*p) + [2, 3, 0, 1] + >>> list(p*q) + [3, 2, 1, 0] + >>> [q(p(i)) for i in range(p.size)] + [3, 2, 1, 0] + + The permutation can be 'applied' to any list-like object, not only + Permutations: + + >>> p(['zero', 'one', 'four', 'two']) + ['one', 'zero', 'four', 'two'] + >>> p('zo42') + ['o', 'z', '4', '2'] + + If you have a list of arbitrary elements, the corresponding permutation + can be found with the from_sequence method: + + >>> Permutation.from_sequence('SymPy') + Permutation([1, 3, 2, 0, 4]) + + Checking if a Permutation is contained in a Group + ================================================= + + Generally if you have a group of permutations G on n symbols, and + you're checking if a permutation on less than n symbols is part + of that group, the check will fail. + + Here is an example for n=5 and we check if the cycle + (1,2,3) is in G: + + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=True, pretty_print=False) + >>> from sympy.combinatorics import Cycle, Permutation + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> G = PermutationGroup(Cycle(2, 3)(4, 5), Cycle(1, 2, 3, 4, 5)) + >>> p1 = Permutation(Cycle(2, 5, 3)) + >>> p2 = Permutation(Cycle(1, 2, 3)) + >>> a1 = Permutation(Cycle(1, 2, 3).list(6)) + >>> a2 = Permutation(Cycle(1, 2, 3)(5)) + >>> a3 = Permutation(Cycle(1, 2, 3),size=6) + >>> for p in [p1,p2,a1,a2,a3]: p, G.contains(p) + ((2 5 3), True) + ((1 2 3), False) + ((5)(1 2 3), True) + ((5)(1 2 3), True) + ((5)(1 2 3), True) + + The check for p2 above will fail. + + Checking if p1 is in G works because SymPy knows + G is a group on 5 symbols, and p1 is also on 5 symbols + (its largest element is 5). + + For ``a1``, the ``.list(6)`` call will extend the permutation to 5 + symbols, so the test will work as well. In the case of ``a2`` the + permutation is being extended to 5 symbols by using a singleton, + and in the case of ``a3`` it's extended through the constructor + argument ``size=6``. + + There is another way to do this, which is to tell the ``contains`` + method that the number of symbols the group is on does not need to + match perfectly the number of symbols for the permutation: + + >>> G.contains(p2,strict=False) + True + + This can be via the ``strict`` argument to the ``contains`` method, + and SymPy will try to extend the permutation on its own and then + perform the containment check. + + See Also + ======== + + Cycle + + References + ========== + + .. [1] Skiena, S. 'Permutations.' 1.1 in Implementing Discrete Mathematics + Combinatorics and Graph Theory with Mathematica. Reading, MA: + Addison-Wesley, pp. 3-16, 1990. + + .. [2] Knuth, D. E. The Art of Computer Programming, Vol. 4: Combinatorial + Algorithms, 1st ed. Reading, MA: Addison-Wesley, 2011. + + .. [3] Wendy Myrvold and Frank Ruskey. 2001. Ranking and unranking + permutations in linear time. Inf. Process. Lett. 79, 6 (September 2001), + 281-284. DOI=10.1016/S0020-0190(01)00141-7 + + .. [4] D. L. Kreher, D. R. Stinson 'Combinatorial Algorithms' + CRC Press, 1999 + + .. [5] Graham, R. L.; Knuth, D. E.; and Patashnik, O. + Concrete Mathematics: A Foundation for Computer Science, 2nd ed. + Reading, MA: Addison-Wesley, 1994. + + .. [6] https://en.wikipedia.org/w/index.php?oldid=499948155#Product_and_inverse + + .. [7] https://en.wikipedia.org/wiki/Lehmer_code + + """ + + is_Permutation = True + + _array_form = None + _cyclic_form = None + _cycle_structure = None + _size = None + _rank = None + + def __new__(cls, *args, size=None, **kwargs): + """ + Constructor for the Permutation object from a list or a + list of lists in which all elements of the permutation may + appear only once. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + + Permutations entered in array-form are left unaltered: + + >>> Permutation([0, 2, 1]) + Permutation([0, 2, 1]) + + Permutations entered in cyclic form are converted to array form; + singletons need not be entered, but can be entered to indicate the + largest element: + + >>> Permutation([[4, 5, 6], [0, 1]]) + Permutation([1, 0, 2, 3, 5, 6, 4]) + >>> Permutation([[4, 5, 6], [0, 1], [19]]) + Permutation([1, 0, 2, 3, 5, 6, 4], size=20) + + All manipulation of permutations assumes that the smallest element + is 0 (in keeping with 0-based indexing in Python) so if the 0 is + missing when entering a permutation in array form, an error will be + raised: + + >>> Permutation([2, 1]) + Traceback (most recent call last): + ... + ValueError: Integers 0 through 2 must be present. + + If a permutation is entered in cyclic form, it can be entered without + singletons and the ``size`` specified so those values can be filled + in, otherwise the array form will only extend to the maximum value + in the cycles: + + >>> Permutation([[1, 4], [3, 5, 2]], size=10) + Permutation([0, 4, 3, 5, 1, 2], size=10) + >>> _.array_form + [0, 4, 3, 5, 1, 2, 6, 7, 8, 9] + """ + if size is not None: + size = int(size) + + #a) () + #b) (1) = identity + #c) (1, 2) = cycle + #d) ([1, 2, 3]) = array form + #e) ([[1, 2]]) = cyclic form + #f) (Cycle) = conversion to permutation + #g) (Permutation) = adjust size or return copy + ok = True + if not args: # a + return cls._af_new(list(range(size or 0))) + elif len(args) > 1: # c + return cls._af_new(Cycle(*args).list(size)) + if len(args) == 1: + a = args[0] + if isinstance(a, cls): # g + if size is None or size == a.size: + return a + return cls(a.array_form, size=size) + if isinstance(a, Cycle): # f + return cls._af_new(a.list(size)) + if not is_sequence(a): # b + if size is not None and a + 1 > size: + raise ValueError('size is too small when max is %s' % a) + return cls._af_new(list(range(a + 1))) + if has_variety(is_sequence(ai) for ai in a): + ok = False + else: + ok = False + if not ok: + raise ValueError("Permutation argument must be a list of ints, " + "a list of lists, Permutation or Cycle.") + + # safe to assume args are valid; this also makes a copy + # of the args + args = list(args[0]) + + is_cycle = args and is_sequence(args[0]) + if is_cycle: # e + args = [[int(i) for i in c] for c in args] + else: # d + args = [int(i) for i in args] + + # if there are n elements present, 0, 1, ..., n-1 should be present + # unless a cycle notation has been provided. A 0 will be added + # for convenience in case one wants to enter permutations where + # counting starts from 1. + + temp = flatten(args) + if has_dups(temp) and not is_cycle: + raise ValueError('there were repeated elements.') + temp = set(temp) + + if not is_cycle: + if temp != set(range(len(temp))): + raise ValueError('Integers 0 through %s must be present.' % + max(temp)) + if size is not None and temp and max(temp) + 1 > size: + raise ValueError('max element should not exceed %s' % (size - 1)) + + if is_cycle: + # it's not necessarily canonical so we won't store + # it -- use the array form instead + c = Cycle() + for ci in args: + c = c(*ci) + aform = c.list() + else: + aform = list(args) + if size and size > len(aform): + # don't allow for truncation of permutation which + # might split a cycle and lead to an invalid aform + # but do allow the permutation size to be increased + aform.extend(list(range(len(aform), size))) + + return cls._af_new(aform) + + @classmethod + def _af_new(cls, perm): + """A method to produce a Permutation object from a list; + the list is bound to the _array_form attribute, so it must + not be modified; this method is meant for internal use only; + the list ``a`` is supposed to be generated as a temporary value + in a method, so p = Perm._af_new(a) is the only object + to hold a reference to ``a``:: + + Examples + ======== + + >>> from sympy.combinatorics.permutations import Perm + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> a = [2, 1, 3, 0] + >>> p = Perm._af_new(a) + >>> p + Permutation([2, 1, 3, 0]) + + """ + p = super().__new__(cls) + p._array_form = perm + p._size = len(perm) + return p + + def copy(self): + return self.__class__(self.array_form) + + def __getnewargs__(self): + return (self.array_form,) + + def _hashable_content(self): + # the array_form (a list) is the Permutation arg, so we need to + # return a tuple, instead + return tuple(self.array_form) + + @property + def array_form(self): + """ + Return a copy of the attribute _array_form + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([[2, 0], [3, 1]]) + >>> p.array_form + [2, 3, 0, 1] + >>> Permutation([[2, 0, 3, 1]]).array_form + [3, 2, 0, 1] + >>> Permutation([2, 0, 3, 1]).array_form + [2, 0, 3, 1] + >>> Permutation([[1, 2], [4, 5]]).array_form + [0, 2, 1, 3, 5, 4] + """ + return self._array_form[:] + + def list(self, size=None): + """Return the permutation as an explicit list, possibly + trimming unmoved elements if size is less than the maximum + element in the permutation; if this is desired, setting + ``size=-1`` will guarantee such trimming. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation(2, 3)(4, 5) + >>> p.list() + [0, 1, 3, 2, 5, 4] + >>> p.list(10) + [0, 1, 3, 2, 5, 4, 6, 7, 8, 9] + + Passing a length too small will trim trailing, unchanged elements + in the permutation: + + >>> Permutation(2, 4)(1, 2, 4).list(-1) + [0, 2, 1] + >>> Permutation(3).list(-1) + [] + """ + if not self and size is None: + raise ValueError('must give size for empty Cycle') + rv = self.array_form + if size is not None: + if size > self.size: + rv.extend(list(range(self.size, size))) + else: + # find first value from rhs where rv[i] != i + i = self.size - 1 + while rv: + if rv[-1] != i: + break + rv.pop() + i -= 1 + return rv + + @property + def cyclic_form(self): + """ + This is used to convert to the cyclic notation + from the canonical notation. Singletons are omitted. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 3, 1, 2]) + >>> p.cyclic_form + [[1, 3, 2]] + >>> Permutation([1, 0, 2, 4, 3, 5]).cyclic_form + [[0, 1], [3, 4]] + + See Also + ======== + + array_form, full_cyclic_form + """ + if self._cyclic_form is not None: + return list(self._cyclic_form) + array_form = self.array_form + unchecked = [True] * len(array_form) + cyclic_form = [] + for i in range(len(array_form)): + if unchecked[i]: + cycle = [] + cycle.append(i) + unchecked[i] = False + j = i + while unchecked[array_form[j]]: + j = array_form[j] + cycle.append(j) + unchecked[j] = False + if len(cycle) > 1: + cyclic_form.append(cycle) + assert cycle == list(minlex(cycle)) + cyclic_form.sort() + self._cyclic_form = cyclic_form[:] + return cyclic_form + + @property + def full_cyclic_form(self): + """Return permutation in cyclic form including singletons. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([0, 2, 1]).full_cyclic_form + [[0], [1, 2]] + """ + need = set(range(self.size)) - set(flatten(self.cyclic_form)) + rv = self.cyclic_form + [[i] for i in need] + rv.sort() + return rv + + @property + def size(self): + """ + Returns the number of elements in the permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([[3, 2], [0, 1]]).size + 4 + + See Also + ======== + + cardinality, length, order, rank + """ + return self._size + + def support(self): + """Return the elements in permutation, P, for which P[i] != i. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([[3, 2], [0, 1], [4]]) + >>> p.array_form + [1, 0, 3, 2, 4] + >>> p.support() + [0, 1, 2, 3] + """ + a = self.array_form + return [i for i, e in enumerate(a) if a[i] != i] + + def __add__(self, other): + """Return permutation that is other higher in rank than self. + + The rank is the lexicographical rank, with the identity permutation + having rank of 0. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> I = Permutation([0, 1, 2, 3]) + >>> a = Permutation([2, 1, 3, 0]) + >>> I + a.rank() == a + True + + See Also + ======== + + __sub__, inversion_vector + + """ + rank = (self.rank() + other) % self.cardinality + rv = self.unrank_lex(self.size, rank) + rv._rank = rank + return rv + + def __sub__(self, other): + """Return the permutation that is other lower in rank than self. + + See Also + ======== + + __add__ + """ + return self.__add__(-other) + + @staticmethod + def rmul(*args): + """ + Return product of Permutations [a, b, c, ...] as the Permutation whose + ith value is a(b(c(i))). + + a, b, c, ... can be Permutation objects or tuples. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + + >>> a, b = [1, 0, 2], [0, 2, 1] + >>> a = Permutation(a); b = Permutation(b) + >>> list(Permutation.rmul(a, b)) + [1, 2, 0] + >>> [a(b(i)) for i in range(3)] + [1, 2, 0] + + This handles the operands in reverse order compared to the ``*`` operator: + + >>> a = Permutation(a); b = Permutation(b) + >>> list(a*b) + [2, 0, 1] + >>> [b(a(i)) for i in range(3)] + [2, 0, 1] + + Notes + ===== + + All items in the sequence will be parsed by Permutation as + necessary as long as the first item is a Permutation: + + >>> Permutation.rmul(a, [0, 2, 1]) == Permutation.rmul(a, b) + True + + The reverse order of arguments will raise a TypeError. + + """ + rv = args[0] + for i in range(1, len(args)): + rv = args[i]*rv + return rv + + @classmethod + def rmul_with_af(cls, *args): + """ + same as rmul, but the elements of args are Permutation objects + which have _array_form + """ + a = [x._array_form for x in args] + rv = cls._af_new(_af_rmuln(*a)) + return rv + + def mul_inv(self, other): + """ + other*~self, self and other have _array_form + """ + a = _af_invert(self._array_form) + b = other._array_form + return self._af_new(_af_rmul(a, b)) + + def __rmul__(self, other): + """This is needed to coerce other to Permutation in rmul.""" + cls = type(self) + return cls(other)*self + + def __mul__(self, other): + """ + Return the product a*b as a Permutation; the ith value is b(a(i)). + + Examples + ======== + + >>> from sympy.combinatorics.permutations import _af_rmul, Permutation + + >>> a, b = [1, 0, 2], [0, 2, 1] + >>> a = Permutation(a); b = Permutation(b) + >>> list(a*b) + [2, 0, 1] + >>> [b(a(i)) for i in range(3)] + [2, 0, 1] + + This handles operands in reverse order compared to _af_rmul and rmul: + + >>> al = list(a); bl = list(b) + >>> _af_rmul(al, bl) + [1, 2, 0] + >>> [al[bl[i]] for i in range(3)] + [1, 2, 0] + + It is acceptable for the arrays to have different lengths; the shorter + one will be padded to match the longer one: + + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> b*Permutation([1, 0]) + Permutation([1, 2, 0]) + >>> Permutation([1, 0])*b + Permutation([2, 0, 1]) + + It is also acceptable to allow coercion to handle conversion of a + single list to the left of a Permutation: + + >>> [0, 1]*a # no change: 2-element identity + Permutation([1, 0, 2]) + >>> [[0, 1]]*a # exchange first two elements + Permutation([0, 1, 2]) + + You cannot use more than 1 cycle notation in a product of cycles + since coercion can only handle one argument to the left. To handle + multiple cycles it is convenient to use Cycle instead of Permutation: + + >>> [[1, 2]]*[[2, 3]]*Permutation([]) # doctest: +SKIP + >>> from sympy.combinatorics.permutations import Cycle + >>> Cycle(1, 2)(2, 3) + (1 3 2) + + """ + from sympy.combinatorics.perm_groups import PermutationGroup, Coset + if isinstance(other, PermutationGroup): + return Coset(self, other, dir='-') + a = self.array_form + # __rmul__ makes sure the other is a Permutation + b = other.array_form + if not b: + perm = a + else: + b.extend(list(range(len(b), len(a)))) + perm = [b[i] for i in a] + b[len(a):] + return self._af_new(perm) + + def commutes_with(self, other): + """ + Checks if the elements are commuting. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> a = Permutation([1, 4, 3, 0, 2, 5]) + >>> b = Permutation([0, 1, 2, 3, 4, 5]) + >>> a.commutes_with(b) + True + >>> b = Permutation([2, 3, 5, 4, 1, 0]) + >>> a.commutes_with(b) + False + """ + a = self.array_form + b = other.array_form + return _af_commutes_with(a, b) + + def __pow__(self, n): + """ + Routine for finding powers of a permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([2, 0, 3, 1]) + >>> p.order() + 4 + >>> p**4 + Permutation([0, 1, 2, 3]) + """ + if isinstance(n, Permutation): + raise NotImplementedError( + 'p**p is not defined; do you mean p^p (conjugate)?') + n = int(n) + return self._af_new(_af_pow(self.array_form, n)) + + def __rxor__(self, i): + """Return self(i) when ``i`` is an int. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation(1, 2, 9) + >>> 2^p == p(2) == 9 + True + """ + if int_valued(i): + return self(i) + else: + raise NotImplementedError( + "i^p = p(i) when i is an integer, not %s." % i) + + def __xor__(self, h): + """Return the conjugate permutation ``~h*self*h` `. + + Explanation + =========== + + If ``a`` and ``b`` are conjugates, ``a = h*b*~h`` and + ``b = ~h*a*h`` and both have the same cycle structure. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation(1, 2, 9) + >>> q = Permutation(6, 9, 8) + >>> p*q != q*p + True + + Calculate and check properties of the conjugate: + + >>> c = p^q + >>> c == ~q*p*q and p == q*c*~q + True + + The expression q^p^r is equivalent to q^(p*r): + + >>> r = Permutation(9)(4, 6, 8) + >>> q^p^r == q^(p*r) + True + + If the term to the left of the conjugate operator, i, is an integer + then this is interpreted as selecting the ith element from the + permutation to the right: + + >>> all(i^p == p(i) for i in range(p.size)) + True + + Note that the * operator as higher precedence than the ^ operator: + + >>> q^r*p^r == q^(r*p)^r == Permutation(9)(1, 6, 4) + True + + Notes + ===== + + In Python the precedence rule is p^q^r = (p^q)^r which differs + in general from p^(q^r) + + >>> q^p^r + (9)(1 4 8) + >>> q^(p^r) + (9)(1 8 6) + + For a given r and p, both of the following are conjugates of p: + ~r*p*r and r*p*~r. But these are not necessarily the same: + + >>> ~r*p*r == r*p*~r + True + + >>> p = Permutation(1, 2, 9)(5, 6) + >>> ~r*p*r == r*p*~r + False + + The conjugate ~r*p*r was chosen so that ``p^q^r`` would be equivalent + to ``p^(q*r)`` rather than ``p^(r*q)``. To obtain r*p*~r, pass ~r to + this method: + + >>> p^~r == r*p*~r + True + """ + + if self.size != h.size: + raise ValueError("The permutations must be of equal size.") + a = [None]*self.size + h = h._array_form + p = self._array_form + for i in range(self.size): + a[h[i]] = h[p[i]] + return self._af_new(a) + + def transpositions(self): + """ + Return the permutation decomposed into a list of transpositions. + + Explanation + =========== + + It is always possible to express a permutation as the product of + transpositions, see [1] + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([[1, 2, 3], [0, 4, 5, 6, 7]]) + >>> t = p.transpositions() + >>> t + [(0, 7), (0, 6), (0, 5), (0, 4), (1, 3), (1, 2)] + >>> print(''.join(str(c) for c in t)) + (0, 7)(0, 6)(0, 5)(0, 4)(1, 3)(1, 2) + >>> Permutation.rmul(*[Permutation([ti], size=p.size) for ti in t]) == p + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Transposition_%28mathematics%29#Properties + + """ + a = self.cyclic_form + res = [] + for x in a: + nx = len(x) + if nx == 2: + res.append(tuple(x)) + elif nx > 2: + first = x[0] + for y in x[nx - 1:0:-1]: + res.append((first, y)) + return res + + @classmethod + def from_sequence(self, i, key=None): + """Return the permutation needed to obtain ``i`` from the sorted + elements of ``i``. If custom sorting is desired, a key can be given. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + + >>> Permutation.from_sequence('SymPy') + (4)(0 1 3) + >>> _(sorted("SymPy")) + ['S', 'y', 'm', 'P', 'y'] + >>> Permutation.from_sequence('SymPy', key=lambda x: x.lower()) + (4)(0 2)(1 3) + """ + ic = list(zip(i, list(range(len(i))))) + if key: + ic.sort(key=lambda x: key(x[0])) + else: + ic.sort() + return ~Permutation([i[1] for i in ic]) + + def __invert__(self): + """ + Return the inverse of the permutation. + + A permutation multiplied by its inverse is the identity permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([[2, 0], [3, 1]]) + >>> ~p + Permutation([2, 3, 0, 1]) + >>> _ == p**-1 + True + >>> p*~p == ~p*p == Permutation([0, 1, 2, 3]) + True + """ + return self._af_new(_af_invert(self._array_form)) + + def __iter__(self): + """Yield elements from array form. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> list(Permutation(range(3))) + [0, 1, 2] + """ + yield from self.array_form + + def __repr__(self): + return srepr(self) + + def __call__(self, *i): + """ + Allows applying a permutation instance as a bijective function. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([[2, 0], [3, 1]]) + >>> p.array_form + [2, 3, 0, 1] + >>> [p(i) for i in range(4)] + [2, 3, 0, 1] + + If an array is given then the permutation selects the items + from the array (i.e. the permutation is applied to the array): + + >>> from sympy.abc import x + >>> p([x, 1, 0, x**2]) + [0, x**2, x, 1] + """ + # list indices can be Integer or int; leave this + # as it is (don't test or convert it) because this + # gets called a lot and should be fast + if len(i) == 1: + i = i[0] + if not isinstance(i, Iterable): + i = as_int(i) + if i < 0 or i > self.size: + raise TypeError( + "{} should be an integer between 0 and {}" + .format(i, self.size-1)) + return self._array_form[i] + # P([a, b, c]) + if len(i) != self.size: + raise TypeError( + "{} should have the length {}.".format(i, self.size)) + return [i[j] for j in self._array_form] + # P(1, 2, 3) + return self*Permutation(Cycle(*i), size=self.size) + + def atoms(self): + """ + Returns all the elements of a permutation + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([0, 1, 2, 3, 4, 5]).atoms() + {0, 1, 2, 3, 4, 5} + >>> Permutation([[0, 1], [2, 3], [4, 5]]).atoms() + {0, 1, 2, 3, 4, 5} + """ + return set(self.array_form) + + def apply(self, i): + r"""Apply the permutation to an expression. + + Parameters + ========== + + i : Expr + It should be an integer between $0$ and $n-1$ where $n$ + is the size of the permutation. + + If it is a symbol or a symbolic expression that can + have integer values, an ``AppliedPermutation`` object + will be returned which can represent an unevaluated + function. + + Notes + ===== + + Any permutation can be defined as a bijective function + $\sigma : \{ 0, 1, \dots, n-1 \} \rightarrow \{ 0, 1, \dots, n-1 \}$ + where $n$ denotes the size of the permutation. + + The definition may even be extended for any set with distinctive + elements, such that the permutation can even be applied for + real numbers or such, however, it is not implemented for now for + computational reasons and the integrity with the group theory + module. + + This function is similar to the ``__call__`` magic, however, + ``__call__`` magic already has some other applications like + permuting an array or attaching new cycles, which would + not always be mathematically consistent. + + This also guarantees that the return type is a SymPy integer, + which guarantees the safety to use assumptions. + """ + i = _sympify(i) + if i.is_integer is False: + raise NotImplementedError("{} should be an integer.".format(i)) + + n = self.size + if (i < 0) == True or (i >= n) == True: + raise NotImplementedError( + "{} should be an integer between 0 and {}".format(i, n-1)) + + if i.is_Integer: + return Integer(self._array_form[i]) + return AppliedPermutation(self, i) + + def next_lex(self): + """ + Returns the next permutation in lexicographical order. + If self is the last permutation in lexicographical order + it returns None. + See [4] section 2.4. + + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([2, 3, 1, 0]) + >>> p = Permutation([2, 3, 1, 0]); p.rank() + 17 + >>> p = p.next_lex(); p.rank() + 18 + + See Also + ======== + + rank, unrank_lex + """ + perm = self.array_form[:] + n = len(perm) + i = n - 2 + while perm[i + 1] < perm[i]: + i -= 1 + if i == -1: + return None + else: + j = n - 1 + while perm[j] < perm[i]: + j -= 1 + perm[j], perm[i] = perm[i], perm[j] + i += 1 + j = n - 1 + while i < j: + perm[j], perm[i] = perm[i], perm[j] + i += 1 + j -= 1 + return self._af_new(perm) + + @classmethod + def unrank_nonlex(self, n, r): + """ + This is a linear time unranking algorithm that does not + respect lexicographic order [3]. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> Permutation.unrank_nonlex(4, 5) + Permutation([2, 0, 3, 1]) + >>> Permutation.unrank_nonlex(4, -1) + Permutation([0, 1, 2, 3]) + + See Also + ======== + + next_nonlex, rank_nonlex + """ + def _unrank1(n, r, a): + if n > 0: + a[n - 1], a[r % n] = a[r % n], a[n - 1] + _unrank1(n - 1, r//n, a) + + id_perm = list(range(n)) + n = int(n) + r = r % ifac(n) + _unrank1(n, r, id_perm) + return self._af_new(id_perm) + + def rank_nonlex(self, inv_perm=None): + """ + This is a linear time ranking algorithm that does not + enforce lexicographic order [3]. + + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.rank_nonlex() + 23 + + See Also + ======== + + next_nonlex, unrank_nonlex + """ + def _rank1(n, perm, inv_perm): + if n == 1: + return 0 + s = perm[n - 1] + t = inv_perm[n - 1] + perm[n - 1], perm[t] = perm[t], s + inv_perm[n - 1], inv_perm[s] = inv_perm[s], t + return s + n*_rank1(n - 1, perm, inv_perm) + + if inv_perm is None: + inv_perm = (~self).array_form + if not inv_perm: + return 0 + perm = self.array_form[:] + r = _rank1(len(perm), perm, inv_perm) + return r + + def next_nonlex(self): + """ + Returns the next permutation in nonlex order [3]. + If self is the last permutation in this order it returns None. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([2, 0, 3, 1]); p.rank_nonlex() + 5 + >>> p = p.next_nonlex(); p + Permutation([3, 0, 1, 2]) + >>> p.rank_nonlex() + 6 + + See Also + ======== + + rank_nonlex, unrank_nonlex + """ + r = self.rank_nonlex() + if r == ifac(self.size) - 1: + return None + return self.unrank_nonlex(self.size, r + 1) + + def rank(self): + """ + Returns the lexicographic rank of the permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.rank() + 0 + >>> p = Permutation([3, 2, 1, 0]) + >>> p.rank() + 23 + + See Also + ======== + + next_lex, unrank_lex, cardinality, length, order, size + """ + if self._rank is not None: + return self._rank + rank = 0 + rho = self.array_form[:] + n = self.size - 1 + size = n + 1 + psize = int(ifac(n)) + for j in range(size - 1): + rank += rho[j]*psize + for i in range(j + 1, size): + if rho[i] > rho[j]: + rho[i] -= 1 + psize //= n + n -= 1 + self._rank = rank + return rank + + @property + def cardinality(self): + """ + Returns the number of all possible permutations. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.cardinality + 24 + + See Also + ======== + + length, order, rank, size + """ + return int(ifac(self.size)) + + def parity(self): + """ + Computes the parity of a permutation. + + Explanation + =========== + + The parity of a permutation reflects the parity of the + number of inversions in the permutation, i.e., the + number of pairs of x and y such that ``x > y`` but ``p[x] < p[y]``. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.parity() + 0 + >>> p = Permutation([3, 2, 0, 1]) + >>> p.parity() + 1 + + See Also + ======== + + _af_parity + """ + if self._cyclic_form is not None: + return (self.size - self.cycles) % 2 + + return _af_parity(self.array_form) + + @property + def is_even(self): + """ + Checks if a permutation is even. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.is_even + True + >>> p = Permutation([3, 2, 1, 0]) + >>> p.is_even + True + + See Also + ======== + + is_odd + """ + return not self.is_odd + + @property + def is_odd(self): + """ + Checks if a permutation is odd. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.is_odd + False + >>> p = Permutation([3, 2, 0, 1]) + >>> p.is_odd + True + + See Also + ======== + + is_even + """ + return bool(self.parity() % 2) + + @property + def is_Singleton(self): + """ + Checks to see if the permutation contains only one number and is + thus the only possible permutation of this set of numbers + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([0]).is_Singleton + True + >>> Permutation([0, 1]).is_Singleton + False + + See Also + ======== + + is_Empty + """ + return self.size == 1 + + @property + def is_Empty(self): + """ + Checks to see if the permutation is a set with zero elements + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([]).is_Empty + True + >>> Permutation([0]).is_Empty + False + + See Also + ======== + + is_Singleton + """ + return self.size == 0 + + @property + def is_identity(self): + return self.is_Identity + + @property + def is_Identity(self): + """ + Returns True if the Permutation is an identity permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([]) + >>> p.is_Identity + True + >>> p = Permutation([[0], [1], [2]]) + >>> p.is_Identity + True + >>> p = Permutation([0, 1, 2]) + >>> p.is_Identity + True + >>> p = Permutation([0, 2, 1]) + >>> p.is_Identity + False + + See Also + ======== + + order + """ + af = self.array_form + return not af or all(i == af[i] for i in range(self.size)) + + def ascents(self): + """ + Returns the positions of ascents in a permutation, ie, the location + where p[i] < p[i+1] + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([4, 0, 1, 3, 2]) + >>> p.ascents() + [1, 2] + + See Also + ======== + + descents, inversions, min, max + """ + a = self.array_form + pos = [i for i in range(len(a) - 1) if a[i] < a[i + 1]] + return pos + + def descents(self): + """ + Returns the positions of descents in a permutation, ie, the location + where p[i] > p[i+1] + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([4, 0, 1, 3, 2]) + >>> p.descents() + [0, 3] + + See Also + ======== + + ascents, inversions, min, max + """ + a = self.array_form + pos = [i for i in range(len(a) - 1) if a[i] > a[i + 1]] + return pos + + def max(self) -> int: + """ + The maximum element moved by the permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([1, 0, 2, 3, 4]) + >>> p.max() + 1 + + See Also + ======== + + min, descents, ascents, inversions + """ + a = self.array_form + if not a: + return 0 + return max(_a for i, _a in enumerate(a) if _a != i) + + def min(self) -> int: + """ + The minimum element moved by the permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 4, 3, 2]) + >>> p.min() + 2 + + See Also + ======== + + max, descents, ascents, inversions + """ + a = self.array_form + if not a: + return 0 + return min(_a for i, _a in enumerate(a) if _a != i) + + def inversions(self): + """ + Computes the number of inversions of a permutation. + + Explanation + =========== + + An inversion is where i > j but p[i] < p[j]. + + For small length of p, it iterates over all i and j + values and calculates the number of inversions. + For large length of p, it uses a variation of merge + sort to calculate the number of inversions. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3, 4, 5]) + >>> p.inversions() + 0 + >>> Permutation([3, 2, 1, 0]).inversions() + 6 + + See Also + ======== + + descents, ascents, min, max + + References + ========== + + .. [1] https://www.cp.eng.chula.ac.th/~prabhas//teaching/algo/algo2008/count-inv.htm + + """ + inversions = 0 + a = self.array_form + n = len(a) + if n < 130: + for i in range(n - 1): + b = a[i] + for c in a[i + 1:]: + if b > c: + inversions += 1 + else: + k = 1 + right = 0 + arr = a[:] + temp = a[:] + while k < n: + i = 0 + while i + k < n: + right = i + k * 2 - 1 + if right >= n: + right = n - 1 + inversions += _merge(arr, temp, i, i + k, right) + i = i + k * 2 + k = k * 2 + return inversions + + def commutator(self, x): + """Return the commutator of ``self`` and ``x``: ``~x*~self*x*self`` + + If f and g are part of a group, G, then the commutator of f and g + is the group identity iff f and g commute, i.e. fg == gf. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([0, 2, 3, 1]) + >>> x = Permutation([2, 0, 3, 1]) + >>> c = p.commutator(x); c + Permutation([2, 1, 3, 0]) + >>> c == ~x*~p*x*p + True + + >>> I = Permutation(3) + >>> p = [I + i for i in range(6)] + >>> for i in range(len(p)): + ... for j in range(len(p)): + ... c = p[i].commutator(p[j]) + ... if p[i]*p[j] == p[j]*p[i]: + ... assert c == I + ... else: + ... assert c != I + ... + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Commutator + """ + + a = self.array_form + b = x.array_form + n = len(a) + if len(b) != n: + raise ValueError("The permutations must be of equal size.") + inva = [None]*n + for i in range(n): + inva[a[i]] = i + invb = [None]*n + for i in range(n): + invb[b[i]] = i + return self._af_new([a[b[inva[i]]] for i in invb]) + + def signature(self): + """ + Gives the signature of the permutation needed to place the + elements of the permutation in canonical order. + + The signature is calculated as (-1)^ + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2]) + >>> p.inversions() + 0 + >>> p.signature() + 1 + >>> q = Permutation([0,2,1]) + >>> q.inversions() + 1 + >>> q.signature() + -1 + + See Also + ======== + + inversions + """ + if self.is_even: + return 1 + return -1 + + def order(self): + """ + Computes the order of a permutation. + + When the permutation is raised to the power of its + order it equals the identity permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([3, 1, 5, 2, 4, 0]) + >>> p.order() + 4 + >>> (p**(p.order())) + Permutation([], size=6) + + See Also + ======== + + identity, cardinality, length, rank, size + """ + + return reduce(lcm, [len(cycle) for cycle in self.cyclic_form], 1) + + def length(self): + """ + Returns the number of integers moved by a permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([0, 3, 2, 1]).length() + 2 + >>> Permutation([[0, 1], [2, 3]]).length() + 4 + + See Also + ======== + + min, max, support, cardinality, order, rank, size + """ + + return len(self.support()) + + @property + def cycle_structure(self): + """Return the cycle structure of the permutation as a dictionary + indicating the multiplicity of each cycle length. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation(3).cycle_structure + {1: 4} + >>> Permutation(0, 4, 3)(1, 2)(5, 6).cycle_structure + {2: 2, 3: 1} + """ + if self._cycle_structure: + rv = self._cycle_structure + else: + rv = defaultdict(int) + singletons = self.size + for c in self.cyclic_form: + rv[len(c)] += 1 + singletons -= len(c) + if singletons: + rv[1] = singletons + self._cycle_structure = rv + return dict(rv) # make a copy + + @property + def cycles(self): + """ + Returns the number of cycles contained in the permutation + (including singletons). + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation([0, 1, 2]).cycles + 3 + >>> Permutation([0, 1, 2]).full_cyclic_form + [[0], [1], [2]] + >>> Permutation(0, 1)(2, 3).cycles + 2 + + See Also + ======== + sympy.functions.combinatorial.numbers.stirling + """ + return len(self.full_cyclic_form) + + def index(self): + """ + Returns the index of a permutation. + + The index of a permutation is the sum of all subscripts j such + that p[j] is greater than p[j+1]. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([3, 0, 2, 1, 4]) + >>> p.index() + 2 + """ + a = self.array_form + + return sum(j for j in range(len(a) - 1) if a[j] > a[j + 1]) + + def runs(self): + """ + Returns the runs of a permutation. + + An ascending sequence in a permutation is called a run [5]. + + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([2, 5, 7, 3, 6, 0, 1, 4, 8]) + >>> p.runs() + [[2, 5, 7], [3, 6], [0, 1, 4, 8]] + >>> q = Permutation([1,3,2,0]) + >>> q.runs() + [[1, 3], [2], [0]] + """ + return runs(self.array_form) + + def inversion_vector(self): + """Return the inversion vector of the permutation. + + The inversion vector consists of elements whose value + indicates the number of elements in the permutation + that are lesser than it and lie on its right hand side. + + The inversion vector is the same as the Lehmer encoding of a + permutation. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([4, 8, 0, 7, 1, 5, 3, 6, 2]) + >>> p.inversion_vector() + [4, 7, 0, 5, 0, 2, 1, 1] + >>> p = Permutation([3, 2, 1, 0]) + >>> p.inversion_vector() + [3, 2, 1] + + The inversion vector increases lexicographically with the rank + of the permutation, the -ith element cycling through 0..i. + + >>> p = Permutation(2) + >>> while p: + ... print('%s %s %s' % (p, p.inversion_vector(), p.rank())) + ... p = p.next_lex() + (2) [0, 0] 0 + (1 2) [0, 1] 1 + (2)(0 1) [1, 0] 2 + (0 1 2) [1, 1] 3 + (0 2 1) [2, 0] 4 + (0 2) [2, 1] 5 + + See Also + ======== + + from_inversion_vector + """ + self_array_form = self.array_form + n = len(self_array_form) + inversion_vector = [0] * (n - 1) + + for i in range(n - 1): + val = 0 + for j in range(i + 1, n): + if self_array_form[j] < self_array_form[i]: + val += 1 + inversion_vector[i] = val + return inversion_vector + + def rank_trotterjohnson(self): + """ + Returns the Trotter Johnson rank, which we get from the minimal + change algorithm. See [4] section 2.4. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 1, 2, 3]) + >>> p.rank_trotterjohnson() + 0 + >>> p = Permutation([0, 2, 1, 3]) + >>> p.rank_trotterjohnson() + 7 + + See Also + ======== + + unrank_trotterjohnson, next_trotterjohnson + """ + if self.array_form == [] or self.is_Identity: + return 0 + if self.array_form == [1, 0]: + return 1 + perm = self.array_form + n = self.size + rank = 0 + for j in range(1, n): + k = 1 + i = 0 + while perm[i] != j: + if perm[i] < j: + k += 1 + i += 1 + j1 = j + 1 + if rank % 2 == 0: + rank = j1*rank + j1 - k + else: + rank = j1*rank + k - 1 + return rank + + @classmethod + def unrank_trotterjohnson(cls, size, rank): + """ + Trotter Johnson permutation unranking. See [4] section 2.4. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> Permutation.unrank_trotterjohnson(5, 10) + Permutation([0, 3, 1, 2, 4]) + + See Also + ======== + + rank_trotterjohnson, next_trotterjohnson + """ + perm = [0]*size + r2 = 0 + n = ifac(size) + pj = 1 + for j in range(2, size + 1): + pj *= j + r1 = (rank * pj) // n + k = r1 - j*r2 + if r2 % 2 == 0: + for i in range(j - 1, j - k - 1, -1): + perm[i] = perm[i - 1] + perm[j - k - 1] = j - 1 + else: + for i in range(j - 1, k, -1): + perm[i] = perm[i - 1] + perm[k] = j - 1 + r2 = r1 + return cls._af_new(perm) + + def next_trotterjohnson(self): + """ + Returns the next permutation in Trotter-Johnson order. + If self is the last permutation it returns None. + See [4] section 2.4. If it is desired to generate all such + permutations, they can be generated in order more quickly + with the ``generate_bell`` function. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation([3, 0, 2, 1]) + >>> p.rank_trotterjohnson() + 4 + >>> p = p.next_trotterjohnson(); p + Permutation([0, 3, 2, 1]) + >>> p.rank_trotterjohnson() + 5 + + See Also + ======== + + rank_trotterjohnson, unrank_trotterjohnson, sympy.utilities.iterables.generate_bell + """ + pi = self.array_form[:] + n = len(pi) + st = 0 + rho = pi[:] + done = False + m = n-1 + while m > 0 and not done: + d = rho.index(m) + for i in range(d, m): + rho[i] = rho[i + 1] + par = _af_parity(rho[:m]) + if par == 1: + if d == m: + m -= 1 + else: + pi[st + d], pi[st + d + 1] = pi[st + d + 1], pi[st + d] + done = True + else: + if d == 0: + m -= 1 + st += 1 + else: + pi[st + d], pi[st + d - 1] = pi[st + d - 1], pi[st + d] + done = True + if m == 0: + return None + return self._af_new(pi) + + def get_precedence_matrix(self): + """ + Gets the precedence matrix. This is used for computing the + distance between two permutations. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> p = Permutation.josephus(3, 6, 1) + >>> p + Permutation([2, 5, 3, 1, 4, 0]) + >>> p.get_precedence_matrix() + Matrix([ + [0, 0, 0, 0, 0, 0], + [1, 0, 0, 0, 1, 0], + [1, 1, 0, 1, 1, 1], + [1, 1, 0, 0, 1, 0], + [1, 0, 0, 0, 0, 0], + [1, 1, 0, 1, 1, 0]]) + + See Also + ======== + + get_precedence_distance, get_adjacency_matrix, get_adjacency_distance + """ + m = zeros(self.size) + perm = self.array_form + for i in range(m.rows): + for j in range(i + 1, m.cols): + m[perm[i], perm[j]] = 1 + return m + + def get_precedence_distance(self, other): + """ + Computes the precedence distance between two permutations. + + Explanation + =========== + + Suppose p and p' represent n jobs. The precedence metric + counts the number of times a job j is preceded by job i + in both p and p'. This metric is commutative. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([2, 0, 4, 3, 1]) + >>> q = Permutation([3, 1, 2, 4, 0]) + >>> p.get_precedence_distance(q) + 7 + >>> q.get_precedence_distance(p) + 7 + + See Also + ======== + + get_precedence_matrix, get_adjacency_matrix, get_adjacency_distance + """ + if self.size != other.size: + raise ValueError("The permutations must be of equal size.") + self_prec_mat = self.get_precedence_matrix() + other_prec_mat = other.get_precedence_matrix() + n_prec = 0 + for i in range(self.size): + for j in range(self.size): + if i == j: + continue + if self_prec_mat[i, j] * other_prec_mat[i, j] == 1: + n_prec += 1 + d = self.size * (self.size - 1)//2 - n_prec + return d + + def get_adjacency_matrix(self): + """ + Computes the adjacency matrix of a permutation. + + Explanation + =========== + + If job i is adjacent to job j in a permutation p + then we set m[i, j] = 1 where m is the adjacency + matrix of p. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation.josephus(3, 6, 1) + >>> p.get_adjacency_matrix() + Matrix([ + [0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 1, 0], + [0, 0, 0, 0, 0, 1], + [0, 1, 0, 0, 0, 0], + [1, 0, 0, 0, 0, 0], + [0, 0, 0, 1, 0, 0]]) + >>> q = Permutation([0, 1, 2, 3]) + >>> q.get_adjacency_matrix() + Matrix([ + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1], + [0, 0, 0, 0]]) + + See Also + ======== + + get_precedence_matrix, get_precedence_distance, get_adjacency_distance + """ + m = zeros(self.size) + perm = self.array_form + for i in range(self.size - 1): + m[perm[i], perm[i + 1]] = 1 + return m + + def get_adjacency_distance(self, other): + """ + Computes the adjacency distance between two permutations. + + Explanation + =========== + + This metric counts the number of times a pair i,j of jobs is + adjacent in both p and p'. If n_adj is this quantity then + the adjacency distance is n - n_adj - 1 [1] + + [1] Reeves, Colin R. Landscapes, Operators and Heuristic search, Annals + of Operational Research, 86, pp 473-490. (1999) + + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 3, 1, 2, 4]) + >>> q = Permutation.josephus(4, 5, 2) + >>> p.get_adjacency_distance(q) + 3 + >>> r = Permutation([0, 2, 1, 4, 3]) + >>> p.get_adjacency_distance(r) + 4 + + See Also + ======== + + get_precedence_matrix, get_precedence_distance, get_adjacency_matrix + """ + if self.size != other.size: + raise ValueError("The permutations must be of the same size.") + self_adj_mat = self.get_adjacency_matrix() + other_adj_mat = other.get_adjacency_matrix() + n_adj = 0 + for i in range(self.size): + for j in range(self.size): + if i == j: + continue + if self_adj_mat[i, j] * other_adj_mat[i, j] == 1: + n_adj += 1 + d = self.size - n_adj - 1 + return d + + def get_positional_distance(self, other): + """ + Computes the positional distance between two permutations. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> p = Permutation([0, 3, 1, 2, 4]) + >>> q = Permutation.josephus(4, 5, 2) + >>> r = Permutation([3, 1, 4, 0, 2]) + >>> p.get_positional_distance(q) + 12 + >>> p.get_positional_distance(r) + 12 + + See Also + ======== + + get_precedence_distance, get_adjacency_distance + """ + a = self.array_form + b = other.array_form + if len(a) != len(b): + raise ValueError("The permutations must be of the same size.") + return sum(abs(a[i] - b[i]) for i in range(len(a))) + + @classmethod + def josephus(cls, m, n, s=1): + """Return as a permutation the shuffling of range(n) using the Josephus + scheme in which every m-th item is selected until all have been chosen. + The returned permutation has elements listed by the order in which they + were selected. + + The parameter ``s`` stops the selection process when there are ``s`` + items remaining and these are selected by continuing the selection, + counting by 1 rather than by ``m``. + + Consider selecting every 3rd item from 6 until only 2 remain:: + + choices chosen + ======== ====== + 012345 + 01 345 2 + 01 34 25 + 01 4 253 + 0 4 2531 + 0 25314 + 253140 + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation.josephus(3, 6, 2).array_form + [2, 5, 3, 1, 4, 0] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Flavius_Josephus + .. [2] https://en.wikipedia.org/wiki/Josephus_problem + .. [3] https://web.archive.org/web/20171008094331/http://www.wou.edu/~burtonl/josephus.html + + """ + from collections import deque + m -= 1 + Q = deque(list(range(n))) + perm = [] + while len(Q) > max(s, 1): + for dp in range(m): + Q.append(Q.popleft()) + perm.append(Q.popleft()) + perm.extend(list(Q)) + return cls(perm) + + @classmethod + def from_inversion_vector(cls, inversion): + """ + Calculates the permutation from the inversion vector. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> Permutation.from_inversion_vector([3, 2, 1, 0, 0]) + Permutation([3, 2, 1, 0, 4, 5]) + + """ + size = len(inversion) + N = list(range(size + 1)) + perm = [] + try: + for k in range(size): + val = N[inversion[k]] + perm.append(val) + N.remove(val) + except IndexError: + raise ValueError("The inversion vector is not valid.") + perm.extend(N) + return cls._af_new(perm) + + @classmethod + def random(cls, n): + """ + Generates a random permutation of length ``n``. + + Uses the underlying Python pseudo-random number generator. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1])) + True + + """ + perm_array = list(range(n)) + random.shuffle(perm_array) + return cls._af_new(perm_array) + + @classmethod + def unrank_lex(cls, size, rank): + """ + Lexicographic permutation unranking. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy import init_printing + >>> init_printing(perm_cyclic=False, pretty_print=False) + >>> a = Permutation.unrank_lex(5, 10) + >>> a.rank() + 10 + >>> a + Permutation([0, 2, 4, 1, 3]) + + See Also + ======== + + rank, next_lex + """ + perm_array = [0] * size + psize = 1 + for i in range(size): + new_psize = psize*(i + 1) + d = (rank % new_psize) // psize + rank -= d*psize + perm_array[size - i - 1] = d + for j in range(size - i, size): + if perm_array[j] > d - 1: + perm_array[j] += 1 + psize = new_psize + return cls._af_new(perm_array) + + def resize(self, n): + """Resize the permutation to the new size ``n``. + + Parameters + ========== + + n : int + The new size of the permutation. + + Raises + ====== + + ValueError + If the permutation cannot be resized to the given size. + This may only happen when resized to a smaller size than + the original. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + + Increasing the size of a permutation: + + >>> p = Permutation(0, 1, 2) + >>> p = p.resize(5) + >>> p + (4)(0 1 2) + + Decreasing the size of the permutation: + + >>> p = p.resize(4) + >>> p + (3)(0 1 2) + + If resizing to the specific size breaks the cycles: + + >>> p.resize(2) + Traceback (most recent call last): + ... + ValueError: The permutation cannot be resized to 2 because the + cycle (0, 1, 2) may break. + """ + aform = self.array_form + l = len(aform) + if n > l: + aform += list(range(l, n)) + return Permutation._af_new(aform) + + elif n < l: + cyclic_form = self.full_cyclic_form + new_cyclic_form = [] + for cycle in cyclic_form: + cycle_min = min(cycle) + cycle_max = max(cycle) + if cycle_min <= n-1: + if cycle_max > n-1: + raise ValueError( + "The permutation cannot be resized to {} " + "because the cycle {} may break." + .format(n, tuple(cycle))) + + new_cyclic_form.append(cycle) + return Permutation(new_cyclic_form) + + return self + + # XXX Deprecated flag + print_cyclic = None + + +def _merge(arr, temp, left, mid, right): + """ + Merges two sorted arrays and calculates the inversion count. + + Helper function for calculating inversions. This method is + for internal use only. + """ + i = k = left + j = mid + inv_count = 0 + while i < mid and j <= right: + if arr[i] < arr[j]: + temp[k] = arr[i] + k += 1 + i += 1 + else: + temp[k] = arr[j] + k += 1 + j += 1 + inv_count += (mid -i) + while i < mid: + temp[k] = arr[i] + k += 1 + i += 1 + if j <= right: + k += right - j + 1 + j += right - j + 1 + arr[left:k + 1] = temp[left:k + 1] + else: + arr[left:right + 1] = temp[left:right + 1] + return inv_count + +Perm = Permutation +_af_new = Perm._af_new + + +class AppliedPermutation(Expr): + """A permutation applied to a symbolic variable. + + Parameters + ========== + + perm : Permutation + x : Expr + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.combinatorics import Permutation + + Creating a symbolic permutation function application: + + >>> x = Symbol('x') + >>> p = Permutation(0, 1, 2) + >>> p.apply(x) + AppliedPermutation((0 1 2), x) + >>> _.subs(x, 1) + 2 + """ + def __new__(cls, perm, x, evaluate=None): + if evaluate is None: + evaluate = global_parameters.evaluate + + perm = _sympify(perm) + x = _sympify(x) + + if not isinstance(perm, Permutation): + raise ValueError("{} must be a Permutation instance." + .format(perm)) + + if evaluate: + if x.is_Integer: + return perm.apply(x) + + obj = super().__new__(cls, perm, x) + return obj + + +@dispatch(Permutation, Permutation) +def _eval_is_eq(lhs, rhs): + if lhs._size != rhs._size: + return None + return lhs._array_form == rhs._array_form diff --git a/lib/python3.11/site-packages/sympy/combinatorics/polyhedron.py b/lib/python3.11/site-packages/sympy/combinatorics/polyhedron.py new file mode 100644 index 0000000000000000000000000000000000000000..2bc05d7d97c840649661f3290442499c841ca7c1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/polyhedron.py @@ -0,0 +1,1019 @@ +from sympy.combinatorics import Permutation as Perm +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.core import Basic, Tuple, default_sort_key +from sympy.sets import FiniteSet +from sympy.utilities.iterables import (minlex, unflatten, flatten) +from sympy.utilities.misc import as_int + +rmul = Perm.rmul + + +class Polyhedron(Basic): + """ + Represents the polyhedral symmetry group (PSG). + + Explanation + =========== + + The PSG is one of the symmetry groups of the Platonic solids. + There are three polyhedral groups: the tetrahedral group + of order 12, the octahedral group of order 24, and the + icosahedral group of order 60. + + All doctests have been given in the docstring of the + constructor of the object. + + References + ========== + + .. [1] https://mathworld.wolfram.com/PolyhedralGroup.html + + """ + _edges = None + + def __new__(cls, corners, faces=(), pgroup=()): + """ + The constructor of the Polyhedron group object. + + Explanation + =========== + + It takes up to three parameters: the corners, faces, and + allowed transformations. + + The corners/vertices are entered as a list of arbitrary + expressions that are used to identify each vertex. + + The faces are entered as a list of tuples of indices; a tuple + of indices identifies the vertices which define the face. They + should be entered in a cw or ccw order; they will be standardized + by reversal and rotation to be give the lowest lexical ordering. + If no faces are given then no edges will be computed. + + >>> from sympy.combinatorics.polyhedron import Polyhedron + >>> Polyhedron(list('abc'), [(1, 2, 0)]).faces + {(0, 1, 2)} + >>> Polyhedron(list('abc'), [(1, 0, 2)]).faces + {(0, 1, 2)} + + The allowed transformations are entered as allowable permutations + of the vertices for the polyhedron. Instance of Permutations + (as with faces) should refer to the supplied vertices by index. + These permutation are stored as a PermutationGroup. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import Permutation + >>> from sympy import init_printing + >>> from sympy.abc import w, x, y, z + >>> init_printing(pretty_print=False, perm_cyclic=False) + + Here we construct the Polyhedron object for a tetrahedron. + + >>> corners = [w, x, y, z] + >>> faces = [(0, 1, 2), (0, 2, 3), (0, 3, 1), (1, 2, 3)] + + Next, allowed transformations of the polyhedron must be given. This + is given as permutations of vertices. + + Although the vertices of a tetrahedron can be numbered in 24 (4!) + different ways, there are only 12 different orientations for a + physical tetrahedron. The following permutations, applied once or + twice, will generate all 12 of the orientations. (The identity + permutation, Permutation(range(4)), is not included since it does + not change the orientation of the vertices.) + + >>> pgroup = [Permutation([[0, 1, 2], [3]]), \ + Permutation([[0, 1, 3], [2]]), \ + Permutation([[0, 2, 3], [1]]), \ + Permutation([[1, 2, 3], [0]]), \ + Permutation([[0, 1], [2, 3]]), \ + Permutation([[0, 2], [1, 3]]), \ + Permutation([[0, 3], [1, 2]])] + + The Polyhedron is now constructed and demonstrated: + + >>> tetra = Polyhedron(corners, faces, pgroup) + >>> tetra.size + 4 + >>> tetra.edges + {(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)} + >>> tetra.corners + (w, x, y, z) + + It can be rotated with an arbitrary permutation of vertices, e.g. + the following permutation is not in the pgroup: + + >>> tetra.rotate(Permutation([0, 1, 3, 2])) + >>> tetra.corners + (w, x, z, y) + + An allowed permutation of the vertices can be constructed by + repeatedly applying permutations from the pgroup to the vertices. + Here is a demonstration that applying p and p**2 for every p in + pgroup generates all the orientations of a tetrahedron and no others: + + >>> all = ( (w, x, y, z), \ + (x, y, w, z), \ + (y, w, x, z), \ + (w, z, x, y), \ + (z, w, y, x), \ + (w, y, z, x), \ + (y, z, w, x), \ + (x, z, y, w), \ + (z, y, x, w), \ + (y, x, z, w), \ + (x, w, z, y), \ + (z, x, w, y) ) + + >>> got = [] + >>> for p in (pgroup + [p**2 for p in pgroup]): + ... h = Polyhedron(corners) + ... h.rotate(p) + ... got.append(h.corners) + ... + >>> set(got) == set(all) + True + + The make_perm method of a PermutationGroup will randomly pick + permutations, multiply them together, and return the permutation that + can be applied to the polyhedron to give the orientation produced + by those individual permutations. + + Here, 3 permutations are used: + + >>> tetra.pgroup.make_perm(3) # doctest: +SKIP + Permutation([0, 3, 1, 2]) + + To select the permutations that should be used, supply a list + of indices to the permutations in pgroup in the order they should + be applied: + + >>> use = [0, 0, 2] + >>> p002 = tetra.pgroup.make_perm(3, use) + >>> p002 + Permutation([1, 0, 3, 2]) + + + Apply them one at a time: + + >>> tetra.reset() + >>> for i in use: + ... tetra.rotate(pgroup[i]) + ... + >>> tetra.vertices + (x, w, z, y) + >>> sequentially = tetra.vertices + + Apply the composite permutation: + + >>> tetra.reset() + >>> tetra.rotate(p002) + >>> tetra.corners + (x, w, z, y) + >>> tetra.corners in all and tetra.corners == sequentially + True + + Notes + ===== + + Defining permutation groups + --------------------------- + + It is not necessary to enter any permutations, nor is necessary to + enter a complete set of transformations. In fact, for a polyhedron, + all configurations can be constructed from just two permutations. + For example, the orientations of a tetrahedron can be generated from + an axis passing through a vertex and face and another axis passing + through a different vertex or from an axis passing through the + midpoints of two edges opposite of each other. + + For simplicity of presentation, consider a square -- + not a cube -- with vertices 1, 2, 3, and 4: + + 1-----2 We could think of axes of rotation being: + | | 1) through the face + | | 2) from midpoint 1-2 to 3-4 or 1-3 to 2-4 + 3-----4 3) lines 1-4 or 2-3 + + + To determine how to write the permutations, imagine 4 cameras, + one at each corner, labeled A-D: + + A B A B + 1-----2 1-----3 vertex index: + | | | | 1 0 + | | | | 2 1 + 3-----4 2-----4 3 2 + C D C D 4 3 + + original after rotation + along 1-4 + + A diagonal and a face axis will be chosen for the "permutation group" + from which any orientation can be constructed. + + >>> pgroup = [] + + Imagine a clockwise rotation when viewing 1-4 from camera A. The new + orientation is (in camera-order): 1, 3, 2, 4 so the permutation is + given using the *indices* of the vertices as: + + >>> pgroup.append(Permutation((0, 2, 1, 3))) + + Now imagine rotating clockwise when looking down an axis entering the + center of the square as viewed. The new camera-order would be + 3, 1, 4, 2 so the permutation is (using indices): + + >>> pgroup.append(Permutation((2, 0, 3, 1))) + + The square can now be constructed: + ** use real-world labels for the vertices, entering them in + camera order + ** for the faces we use zero-based indices of the vertices + in *edge-order* as the face is traversed; neither the + direction nor the starting point matter -- the faces are + only used to define edges (if so desired). + + >>> square = Polyhedron((1, 2, 3, 4), [(0, 1, 3, 2)], pgroup) + + To rotate the square with a single permutation we can do: + + >>> square.rotate(square.pgroup[0]) + >>> square.corners + (1, 3, 2, 4) + + To use more than one permutation (or to use one permutation more + than once) it is more convenient to use the make_perm method: + + >>> p011 = square.pgroup.make_perm([0, 1, 1]) # diag flip + 2 rotations + >>> square.reset() # return to initial orientation + >>> square.rotate(p011) + >>> square.corners + (4, 2, 3, 1) + + Thinking outside the box + ------------------------ + + Although the Polyhedron object has a direct physical meaning, it + actually has broader application. In the most general sense it is + just a decorated PermutationGroup, allowing one to connect the + permutations to something physical. For example, a Rubik's cube is + not a proper polyhedron, but the Polyhedron class can be used to + represent it in a way that helps to visualize the Rubik's cube. + + >>> from sympy import flatten, unflatten, symbols + >>> from sympy.combinatorics import RubikGroup + >>> facelets = flatten([symbols(s+'1:5') for s in 'UFRBLD']) + >>> def show(): + ... pairs = unflatten(r2.corners, 2) + ... print(pairs[::2]) + ... print(pairs[1::2]) + ... + >>> r2 = Polyhedron(facelets, pgroup=RubikGroup(2)) + >>> show() + [(U1, U2), (F1, F2), (R1, R2), (B1, B2), (L1, L2), (D1, D2)] + [(U3, U4), (F3, F4), (R3, R4), (B3, B4), (L3, L4), (D3, D4)] + >>> r2.rotate(0) # cw rotation of F + >>> show() + [(U1, U2), (F3, F1), (U3, R2), (B1, B2), (L1, D1), (R3, R1)] + [(L4, L2), (F4, F2), (U4, R4), (B3, B4), (L3, D2), (D3, D4)] + + Predefined Polyhedra + ==================== + + For convenience, the vertices and faces are defined for the following + standard solids along with a permutation group for transformations. + When the polyhedron is oriented as indicated below, the vertices in + a given horizontal plane are numbered in ccw direction, starting from + the vertex that will give the lowest indices in a given face. (In the + net of the vertices, indices preceded by "-" indicate replication of + the lhs index in the net.) + + tetrahedron, tetrahedron_faces + ------------------------------ + + 4 vertices (vertex up) net: + + 0 0-0 + 1 2 3-1 + + 4 faces: + + (0, 1, 2) (0, 2, 3) (0, 3, 1) (1, 2, 3) + + cube, cube_faces + ---------------- + + 8 vertices (face up) net: + + 0 1 2 3-0 + 4 5 6 7-4 + + 6 faces: + + (0, 1, 2, 3) + (0, 1, 5, 4) (1, 2, 6, 5) (2, 3, 7, 6) (0, 3, 7, 4) + (4, 5, 6, 7) + + octahedron, octahedron_faces + ---------------------------- + + 6 vertices (vertex up) net: + + 0 0 0-0 + 1 2 3 4-1 + 5 5 5-5 + + 8 faces: + + (0, 1, 2) (0, 2, 3) (0, 3, 4) (0, 1, 4) + (1, 2, 5) (2, 3, 5) (3, 4, 5) (1, 4, 5) + + dodecahedron, dodecahedron_faces + -------------------------------- + + 20 vertices (vertex up) net: + + 0 1 2 3 4 -0 + 5 6 7 8 9 -5 + 14 10 11 12 13-14 + 15 16 17 18 19-15 + + 12 faces: + + (0, 1, 2, 3, 4) (0, 1, 6, 10, 5) (1, 2, 7, 11, 6) + (2, 3, 8, 12, 7) (3, 4, 9, 13, 8) (0, 4, 9, 14, 5) + (5, 10, 16, 15, 14) (6, 10, 16, 17, 11) (7, 11, 17, 18, 12) + (8, 12, 18, 19, 13) (9, 13, 19, 15, 14)(15, 16, 17, 18, 19) + + icosahedron, icosahedron_faces + ------------------------------ + + 12 vertices (face up) net: + + 0 0 0 0 -0 + 1 2 3 4 5 -1 + 6 7 8 9 10 -6 + 11 11 11 11 -11 + + 20 faces: + + (0, 1, 2) (0, 2, 3) (0, 3, 4) + (0, 4, 5) (0, 1, 5) (1, 2, 6) + (2, 3, 7) (3, 4, 8) (4, 5, 9) + (1, 5, 10) (2, 6, 7) (3, 7, 8) + (4, 8, 9) (5, 9, 10) (1, 6, 10) + (6, 7, 11) (7, 8, 11) (8, 9, 11) + (9, 10, 11) (6, 10, 11) + + >>> from sympy.combinatorics.polyhedron import cube + >>> cube.edges + {(0, 1), (0, 3), (0, 4), (1, 2), (1, 5), (2, 3), (2, 6), (3, 7), (4, 5), (4, 7), (5, 6), (6, 7)} + + If you want to use letters or other names for the corners you + can still use the pre-calculated faces: + + >>> corners = list('abcdefgh') + >>> Polyhedron(corners, cube.faces).corners + (a, b, c, d, e, f, g, h) + + References + ========== + + .. [1] www.ocf.berkeley.edu/~wwu/articles/platonicsolids.pdf + + """ + faces = [minlex(f, directed=False, key=default_sort_key) for f in faces] + corners, faces, pgroup = args = \ + [Tuple(*a) for a in (corners, faces, pgroup)] + obj = Basic.__new__(cls, *args) + obj._corners = tuple(corners) # in order given + obj._faces = FiniteSet(*faces) + if pgroup and pgroup[0].size != len(corners): + raise ValueError("Permutation size unequal to number of corners.") + # use the identity permutation if none are given + obj._pgroup = PermutationGroup( + pgroup or [Perm(range(len(corners)))] ) + return obj + + @property + def corners(self): + """ + Get the corners of the Polyhedron. + + The method ``vertices`` is an alias for ``corners``. + + Examples + ======== + + >>> from sympy.combinatorics import Polyhedron + >>> from sympy.abc import a, b, c, d + >>> p = Polyhedron(list('abcd')) + >>> p.corners == p.vertices == (a, b, c, d) + True + + See Also + ======== + + array_form, cyclic_form + """ + return self._corners + vertices = corners + + @property + def array_form(self): + """Return the indices of the corners. + + The indices are given relative to the original position of corners. + + Examples + ======== + + >>> from sympy.combinatorics.polyhedron import tetrahedron + >>> tetrahedron = tetrahedron.copy() + >>> tetrahedron.array_form + [0, 1, 2, 3] + + >>> tetrahedron.rotate(0) + >>> tetrahedron.array_form + [0, 2, 3, 1] + >>> tetrahedron.pgroup[0].array_form + [0, 2, 3, 1] + + See Also + ======== + + corners, cyclic_form + """ + corners = list(self.args[0]) + return [corners.index(c) for c in self.corners] + + @property + def cyclic_form(self): + """Return the indices of the corners in cyclic notation. + + The indices are given relative to the original position of corners. + + See Also + ======== + + corners, array_form + """ + return Perm._af_new(self.array_form).cyclic_form + + @property + def size(self): + """ + Get the number of corners of the Polyhedron. + """ + return len(self._corners) + + @property + def faces(self): + """ + Get the faces of the Polyhedron. + """ + return self._faces + + @property + def pgroup(self): + """ + Get the permutations of the Polyhedron. + """ + return self._pgroup + + @property + def edges(self): + """ + Given the faces of the polyhedra we can get the edges. + + Examples + ======== + + >>> from sympy.combinatorics import Polyhedron + >>> from sympy.abc import a, b, c + >>> corners = (a, b, c) + >>> faces = [(0, 1, 2)] + >>> Polyhedron(corners, faces).edges + {(0, 1), (0, 2), (1, 2)} + + """ + if self._edges is None: + output = set() + for face in self.faces: + for i in range(len(face)): + edge = tuple(sorted([face[i], face[i - 1]])) + output.add(edge) + self._edges = FiniteSet(*output) + return self._edges + + def rotate(self, perm): + """ + Apply a permutation to the polyhedron *in place*. The permutation + may be given as a Permutation instance or an integer indicating + which permutation from pgroup of the Polyhedron should be + applied. + + This is an operation that is analogous to rotation about + an axis by a fixed increment. + + Notes + ===== + + When a Permutation is applied, no check is done to see if that + is a valid permutation for the Polyhedron. For example, a cube + could be given a permutation which effectively swaps only 2 + vertices. A valid permutation (that rotates the object in a + physical way) will be obtained if one only uses + permutations from the ``pgroup`` of the Polyhedron. On the other + hand, allowing arbitrary rotations (applications of permutations) + gives a way to follow named elements rather than indices since + Polyhedron allows vertices to be named while Permutation works + only with indices. + + Examples + ======== + + >>> from sympy.combinatorics import Polyhedron, Permutation + >>> from sympy.combinatorics.polyhedron import cube + >>> cube = cube.copy() + >>> cube.corners + (0, 1, 2, 3, 4, 5, 6, 7) + >>> cube.rotate(0) + >>> cube.corners + (1, 2, 3, 0, 5, 6, 7, 4) + + A non-physical "rotation" that is not prohibited by this method: + + >>> cube.reset() + >>> cube.rotate(Permutation([[1, 2]], size=8)) + >>> cube.corners + (0, 2, 1, 3, 4, 5, 6, 7) + + Polyhedron can be used to follow elements of set that are + identified by letters instead of integers: + + >>> shadow = h5 = Polyhedron(list('abcde')) + >>> p = Permutation([3, 0, 1, 2, 4]) + >>> h5.rotate(p) + >>> h5.corners + (d, a, b, c, e) + >>> _ == shadow.corners + True + >>> copy = h5.copy() + >>> h5.rotate(p) + >>> h5.corners == copy.corners + False + """ + if not isinstance(perm, Perm): + perm = self.pgroup[perm] + # and we know it's valid + else: + if perm.size != self.size: + raise ValueError('Polyhedron and Permutation sizes differ.') + a = perm.array_form + corners = [self.corners[a[i]] for i in range(len(self.corners))] + self._corners = tuple(corners) + + def reset(self): + """Return corners to their original positions. + + Examples + ======== + + >>> from sympy.combinatorics.polyhedron import tetrahedron as T + >>> T = T.copy() + >>> T.corners + (0, 1, 2, 3) + >>> T.rotate(0) + >>> T.corners + (0, 2, 3, 1) + >>> T.reset() + >>> T.corners + (0, 1, 2, 3) + """ + self._corners = self.args[0] + + +def _pgroup_calcs(): + """Return the permutation groups for each of the polyhedra and the face + definitions: tetrahedron, cube, octahedron, dodecahedron, icosahedron, + tetrahedron_faces, cube_faces, octahedron_faces, dodecahedron_faces, + icosahedron_faces + + Explanation + =========== + + (This author did not find and did not know of a better way to do it though + there likely is such a way.) + + Although only 2 permutations are needed for a polyhedron in order to + generate all the possible orientations, a group of permutations is + provided instead. A set of permutations is called a "group" if:: + + a*b = c (for any pair of permutations in the group, a and b, their + product, c, is in the group) + + a*(b*c) = (a*b)*c (for any 3 permutations in the group associativity holds) + + there is an identity permutation, I, such that I*a = a*I for all elements + in the group + + a*b = I (the inverse of each permutation is also in the group) + + None of the polyhedron groups defined follow these definitions of a group. + Instead, they are selected to contain those permutations whose powers + alone will construct all orientations of the polyhedron, i.e. for + permutations ``a``, ``b``, etc... in the group, ``a, a**2, ..., a**o_a``, + ``b, b**2, ..., b**o_b``, etc... (where ``o_i`` is the order of + permutation ``i``) generate all permutations of the polyhedron instead of + mixed products like ``a*b``, ``a*b**2``, etc.... + + Note that for a polyhedron with n vertices, the valid permutations of the + vertices exclude those that do not maintain its faces. e.g. the + permutation BCDE of a square's four corners, ABCD, is a valid + permutation while CBDE is not (because this would twist the square). + + Examples + ======== + + The is_group checks for: closure, the presence of the Identity permutation, + and the presence of the inverse for each of the elements in the group. This + confirms that none of the polyhedra are true groups: + + >>> from sympy.combinatorics.polyhedron import ( + ... tetrahedron, cube, octahedron, dodecahedron, icosahedron) + ... + >>> polyhedra = (tetrahedron, cube, octahedron, dodecahedron, icosahedron) + >>> [h.pgroup.is_group for h in polyhedra] + ... + [True, True, True, True, True] + + Although tests in polyhedron's test suite check that powers of the + permutations in the groups generate all permutations of the vertices + of the polyhedron, here we also demonstrate the powers of the given + permutations create a complete group for the tetrahedron: + + >>> from sympy.combinatorics import Permutation, PermutationGroup + >>> for h in polyhedra[:1]: + ... G = h.pgroup + ... perms = set() + ... for g in G: + ... for e in range(g.order()): + ... p = tuple((g**e).array_form) + ... perms.add(p) + ... + ... perms = [Permutation(p) for p in perms] + ... assert PermutationGroup(perms).is_group + + In addition to doing the above, the tests in the suite confirm that the + faces are all present after the application of each permutation. + + References + ========== + + .. [1] https://dogschool.tripod.com/trianglegroup.html + + """ + def _pgroup_of_double(polyh, ordered_faces, pgroup): + n = len(ordered_faces[0]) + # the vertices of the double which sits inside a give polyhedron + # can be found by tracking the faces of the outer polyhedron. + # A map between face and the vertex of the double is made so that + # after rotation the position of the vertices can be located + fmap = dict(zip(ordered_faces, + range(len(ordered_faces)))) + flat_faces = flatten(ordered_faces) + new_pgroup = [] + for p in pgroup: + h = polyh.copy() + h.rotate(p) + c = h.corners + # reorder corners in the order they should appear when + # enumerating the faces + reorder = unflatten([c[j] for j in flat_faces], n) + # make them canonical + reorder = [tuple(map(as_int, + minlex(f, directed=False))) + for f in reorder] + # map face to vertex: the resulting list of vertices are the + # permutation that we seek for the double + new_pgroup.append(Perm([fmap[f] for f in reorder])) + return new_pgroup + + tetrahedron_faces = [ + (0, 1, 2), (0, 2, 3), (0, 3, 1), # upper 3 + (1, 2, 3), # bottom + ] + + # cw from top + # + _t_pgroup = [ + Perm([[1, 2, 3], [0]]), # cw from top + Perm([[0, 1, 2], [3]]), # cw from front face + Perm([[0, 3, 2], [1]]), # cw from back right face + Perm([[0, 3, 1], [2]]), # cw from back left face + Perm([[0, 1], [2, 3]]), # through front left edge + Perm([[0, 2], [1, 3]]), # through front right edge + Perm([[0, 3], [1, 2]]), # through back edge + ] + + tetrahedron = Polyhedron( + range(4), + tetrahedron_faces, + _t_pgroup) + + cube_faces = [ + (0, 1, 2, 3), # upper + (0, 1, 5, 4), (1, 2, 6, 5), (2, 3, 7, 6), (0, 3, 7, 4), # middle 4 + (4, 5, 6, 7), # lower + ] + + # U, D, F, B, L, R = up, down, front, back, left, right + _c_pgroup = [Perm(p) for p in + [ + [1, 2, 3, 0, 5, 6, 7, 4], # cw from top, U + [4, 0, 3, 7, 5, 1, 2, 6], # cw from F face + [4, 5, 1, 0, 7, 6, 2, 3], # cw from R face + + [1, 0, 4, 5, 2, 3, 7, 6], # cw through UF edge + [6, 2, 1, 5, 7, 3, 0, 4], # cw through UR edge + [6, 7, 3, 2, 5, 4, 0, 1], # cw through UB edge + [3, 7, 4, 0, 2, 6, 5, 1], # cw through UL edge + [4, 7, 6, 5, 0, 3, 2, 1], # cw through FL edge + [6, 5, 4, 7, 2, 1, 0, 3], # cw through FR edge + + [0, 3, 7, 4, 1, 2, 6, 5], # cw through UFL vertex + [5, 1, 0, 4, 6, 2, 3, 7], # cw through UFR vertex + [5, 6, 2, 1, 4, 7, 3, 0], # cw through UBR vertex + [7, 4, 0, 3, 6, 5, 1, 2], # cw through UBL + ]] + + cube = Polyhedron( + range(8), + cube_faces, + _c_pgroup) + + octahedron_faces = [ + (0, 1, 2), (0, 2, 3), (0, 3, 4), (0, 1, 4), # top 4 + (1, 2, 5), (2, 3, 5), (3, 4, 5), (1, 4, 5), # bottom 4 + ] + + octahedron = Polyhedron( + range(6), + octahedron_faces, + _pgroup_of_double(cube, cube_faces, _c_pgroup)) + + dodecahedron_faces = [ + (0, 1, 2, 3, 4), # top + (0, 1, 6, 10, 5), (1, 2, 7, 11, 6), (2, 3, 8, 12, 7), # upper 5 + (3, 4, 9, 13, 8), (0, 4, 9, 14, 5), + (5, 10, 16, 15, 14), (6, 10, 16, 17, 11), (7, 11, 17, 18, + 12), # lower 5 + (8, 12, 18, 19, 13), (9, 13, 19, 15, 14), + (15, 16, 17, 18, 19) # bottom + ] + + def _string_to_perm(s): + rv = [Perm(range(20))] + p = None + for si in s: + if si not in '01': + count = int(si) - 1 + else: + count = 1 + if si == '0': + p = _f0 + elif si == '1': + p = _f1 + rv.extend([p]*count) + return Perm.rmul(*rv) + + # top face cw + _f0 = Perm([ + 1, 2, 3, 4, 0, 6, 7, 8, 9, 5, 11, + 12, 13, 14, 10, 16, 17, 18, 19, 15]) + # front face cw + _f1 = Perm([ + 5, 0, 4, 9, 14, 10, 1, 3, 13, 15, + 6, 2, 8, 19, 16, 17, 11, 7, 12, 18]) + # the strings below, like 0104 are shorthand for F0*F1*F0**4 and are + # the remaining 4 face rotations, 15 edge permutations, and the + # 10 vertex rotations. + _dodeca_pgroup = [_f0, _f1] + [_string_to_perm(s) for s in ''' + 0104 140 014 0410 + 010 1403 03104 04103 102 + 120 1304 01303 021302 03130 + 0412041 041204103 04120410 041204104 041204102 + 10 01 1402 0140 04102 0412 1204 1302 0130 03120'''.strip().split()] + + dodecahedron = Polyhedron( + range(20), + dodecahedron_faces, + _dodeca_pgroup) + + icosahedron_faces = [ + (0, 1, 2), (0, 2, 3), (0, 3, 4), (0, 4, 5), (0, 1, 5), + (1, 6, 7), (1, 2, 7), (2, 7, 8), (2, 3, 8), (3, 8, 9), + (3, 4, 9), (4, 9, 10), (4, 5, 10), (5, 6, 10), (1, 5, 6), + (6, 7, 11), (7, 8, 11), (8, 9, 11), (9, 10, 11), (6, 10, 11)] + + icosahedron = Polyhedron( + range(12), + icosahedron_faces, + _pgroup_of_double( + dodecahedron, dodecahedron_faces, _dodeca_pgroup)) + + return (tetrahedron, cube, octahedron, dodecahedron, icosahedron, + tetrahedron_faces, cube_faces, octahedron_faces, + dodecahedron_faces, icosahedron_faces) + +# ----------------------------------------------------------------------- +# Standard Polyhedron groups +# +# These are generated using _pgroup_calcs() above. However to save +# import time we encode them explicitly here. +# ----------------------------------------------------------------------- + +tetrahedron = Polyhedron( + Tuple(0, 1, 2, 3), + Tuple( + Tuple(0, 1, 2), + Tuple(0, 2, 3), + Tuple(0, 1, 3), + Tuple(1, 2, 3)), + Tuple( + Perm(1, 2, 3), + Perm(3)(0, 1, 2), + Perm(0, 3, 2), + Perm(0, 3, 1), + Perm(0, 1)(2, 3), + Perm(0, 2)(1, 3), + Perm(0, 3)(1, 2) + )) + +cube = Polyhedron( + Tuple(0, 1, 2, 3, 4, 5, 6, 7), + Tuple( + Tuple(0, 1, 2, 3), + Tuple(0, 1, 5, 4), + Tuple(1, 2, 6, 5), + Tuple(2, 3, 7, 6), + Tuple(0, 3, 7, 4), + Tuple(4, 5, 6, 7)), + Tuple( + Perm(0, 1, 2, 3)(4, 5, 6, 7), + Perm(0, 4, 5, 1)(2, 3, 7, 6), + Perm(0, 4, 7, 3)(1, 5, 6, 2), + Perm(0, 1)(2, 4)(3, 5)(6, 7), + Perm(0, 6)(1, 2)(3, 5)(4, 7), + Perm(0, 6)(1, 7)(2, 3)(4, 5), + Perm(0, 3)(1, 7)(2, 4)(5, 6), + Perm(0, 4)(1, 7)(2, 6)(3, 5), + Perm(0, 6)(1, 5)(2, 4)(3, 7), + Perm(1, 3, 4)(2, 7, 5), + Perm(7)(0, 5, 2)(3, 4, 6), + Perm(0, 5, 7)(1, 6, 3), + Perm(0, 7, 2)(1, 4, 6))) + +octahedron = Polyhedron( + Tuple(0, 1, 2, 3, 4, 5), + Tuple( + Tuple(0, 1, 2), + Tuple(0, 2, 3), + Tuple(0, 3, 4), + Tuple(0, 1, 4), + Tuple(1, 2, 5), + Tuple(2, 3, 5), + Tuple(3, 4, 5), + Tuple(1, 4, 5)), + Tuple( + Perm(5)(1, 2, 3, 4), + Perm(0, 4, 5, 2), + Perm(0, 1, 5, 3), + Perm(0, 1)(2, 4)(3, 5), + Perm(0, 2)(1, 3)(4, 5), + Perm(0, 3)(1, 5)(2, 4), + Perm(0, 4)(1, 3)(2, 5), + Perm(0, 5)(1, 4)(2, 3), + Perm(0, 5)(1, 2)(3, 4), + Perm(0, 4, 1)(2, 3, 5), + Perm(0, 1, 2)(3, 4, 5), + Perm(0, 2, 3)(1, 5, 4), + Perm(0, 4, 3)(1, 5, 2))) + +dodecahedron = Polyhedron( + Tuple(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19), + Tuple( + Tuple(0, 1, 2, 3, 4), + Tuple(0, 1, 6, 10, 5), + Tuple(1, 2, 7, 11, 6), + Tuple(2, 3, 8, 12, 7), + Tuple(3, 4, 9, 13, 8), + Tuple(0, 4, 9, 14, 5), + Tuple(5, 10, 16, 15, 14), + Tuple(6, 10, 16, 17, 11), + Tuple(7, 11, 17, 18, 12), + Tuple(8, 12, 18, 19, 13), + Tuple(9, 13, 19, 15, 14), + Tuple(15, 16, 17, 18, 19)), + Tuple( + Perm(0, 1, 2, 3, 4)(5, 6, 7, 8, 9)(10, 11, 12, 13, 14)(15, 16, 17, 18, 19), + Perm(0, 5, 10, 6, 1)(2, 4, 14, 16, 11)(3, 9, 15, 17, 7)(8, 13, 19, 18, 12), + Perm(0, 10, 17, 12, 3)(1, 6, 11, 7, 2)(4, 5, 16, 18, 8)(9, 14, 15, 19, 13), + Perm(0, 6, 17, 19, 9)(1, 11, 18, 13, 4)(2, 7, 12, 8, 3)(5, 10, 16, 15, 14), + Perm(0, 2, 12, 19, 14)(1, 7, 18, 15, 5)(3, 8, 13, 9, 4)(6, 11, 17, 16, 10), + Perm(0, 4, 9, 14, 5)(1, 3, 13, 15, 10)(2, 8, 19, 16, 6)(7, 12, 18, 17, 11), + Perm(0, 1)(2, 5)(3, 10)(4, 6)(7, 14)(8, 16)(9, 11)(12, 15)(13, 17)(18, 19), + Perm(0, 7)(1, 2)(3, 6)(4, 11)(5, 12)(8, 10)(9, 17)(13, 16)(14, 18)(15, 19), + Perm(0, 12)(1, 8)(2, 3)(4, 7)(5, 18)(6, 13)(9, 11)(10, 19)(14, 17)(15, 16), + Perm(0, 8)(1, 13)(2, 9)(3, 4)(5, 12)(6, 19)(7, 14)(10, 18)(11, 15)(16, 17), + Perm(0, 4)(1, 9)(2, 14)(3, 5)(6, 13)(7, 15)(8, 10)(11, 19)(12, 16)(17, 18), + Perm(0, 5)(1, 14)(2, 15)(3, 16)(4, 10)(6, 9)(7, 19)(8, 17)(11, 13)(12, 18), + Perm(0, 11)(1, 6)(2, 10)(3, 16)(4, 17)(5, 7)(8, 15)(9, 18)(12, 14)(13, 19), + Perm(0, 18)(1, 12)(2, 7)(3, 11)(4, 17)(5, 19)(6, 8)(9, 16)(10, 13)(14, 15), + Perm(0, 18)(1, 19)(2, 13)(3, 8)(4, 12)(5, 17)(6, 15)(7, 9)(10, 16)(11, 14), + Perm(0, 13)(1, 19)(2, 15)(3, 14)(4, 9)(5, 8)(6, 18)(7, 16)(10, 12)(11, 17), + Perm(0, 16)(1, 15)(2, 19)(3, 18)(4, 17)(5, 10)(6, 14)(7, 13)(8, 12)(9, 11), + Perm(0, 18)(1, 17)(2, 16)(3, 15)(4, 19)(5, 12)(6, 11)(7, 10)(8, 14)(9, 13), + Perm(0, 15)(1, 19)(2, 18)(3, 17)(4, 16)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10), + Perm(0, 17)(1, 16)(2, 15)(3, 19)(4, 18)(5, 11)(6, 10)(7, 14)(8, 13)(9, 12), + Perm(0, 19)(1, 18)(2, 17)(3, 16)(4, 15)(5, 13)(6, 12)(7, 11)(8, 10)(9, 14), + Perm(1, 4, 5)(2, 9, 10)(3, 14, 6)(7, 13, 16)(8, 15, 11)(12, 19, 17), + Perm(19)(0, 6, 2)(3, 5, 11)(4, 10, 7)(8, 14, 17)(9, 16, 12)(13, 15, 18), + Perm(0, 11, 8)(1, 7, 3)(4, 6, 12)(5, 17, 13)(9, 10, 18)(14, 16, 19), + Perm(0, 7, 13)(1, 12, 9)(2, 8, 4)(5, 11, 19)(6, 18, 14)(10, 17, 15), + Perm(0, 3, 9)(1, 8, 14)(2, 13, 5)(6, 12, 15)(7, 19, 10)(11, 18, 16), + Perm(0, 14, 10)(1, 9, 16)(2, 13, 17)(3, 19, 11)(4, 15, 6)(7, 8, 18), + Perm(0, 16, 7)(1, 10, 11)(2, 5, 17)(3, 14, 18)(4, 15, 12)(8, 9, 19), + Perm(0, 16, 13)(1, 17, 8)(2, 11, 12)(3, 6, 18)(4, 10, 19)(5, 15, 9), + Perm(0, 11, 15)(1, 17, 14)(2, 18, 9)(3, 12, 13)(4, 7, 19)(5, 6, 16), + Perm(0, 8, 15)(1, 12, 16)(2, 18, 10)(3, 19, 5)(4, 13, 14)(6, 7, 17))) + +icosahedron = Polyhedron( + Tuple(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11), + Tuple( + Tuple(0, 1, 2), + Tuple(0, 2, 3), + Tuple(0, 3, 4), + Tuple(0, 4, 5), + Tuple(0, 1, 5), + Tuple(1, 6, 7), + Tuple(1, 2, 7), + Tuple(2, 7, 8), + Tuple(2, 3, 8), + Tuple(3, 8, 9), + Tuple(3, 4, 9), + Tuple(4, 9, 10), + Tuple(4, 5, 10), + Tuple(5, 6, 10), + Tuple(1, 5, 6), + Tuple(6, 7, 11), + Tuple(7, 8, 11), + Tuple(8, 9, 11), + Tuple(9, 10, 11), + Tuple(6, 10, 11)), + Tuple( + Perm(11)(1, 2, 3, 4, 5)(6, 7, 8, 9, 10), + Perm(0, 5, 6, 7, 2)(3, 4, 10, 11, 8), + Perm(0, 1, 7, 8, 3)(4, 5, 6, 11, 9), + Perm(0, 2, 8, 9, 4)(1, 7, 11, 10, 5), + Perm(0, 3, 9, 10, 5)(1, 2, 8, 11, 6), + Perm(0, 4, 10, 6, 1)(2, 3, 9, 11, 7), + Perm(0, 1)(2, 5)(3, 6)(4, 7)(8, 10)(9, 11), + Perm(0, 2)(1, 3)(4, 7)(5, 8)(6, 9)(10, 11), + Perm(0, 3)(1, 9)(2, 4)(5, 8)(6, 11)(7, 10), + Perm(0, 4)(1, 9)(2, 10)(3, 5)(6, 8)(7, 11), + Perm(0, 5)(1, 4)(2, 10)(3, 6)(7, 9)(8, 11), + Perm(0, 6)(1, 5)(2, 10)(3, 11)(4, 7)(8, 9), + Perm(0, 7)(1, 2)(3, 6)(4, 11)(5, 8)(9, 10), + Perm(0, 8)(1, 9)(2, 3)(4, 7)(5, 11)(6, 10), + Perm(0, 9)(1, 11)(2, 10)(3, 4)(5, 8)(6, 7), + Perm(0, 10)(1, 9)(2, 11)(3, 6)(4, 5)(7, 8), + Perm(0, 11)(1, 6)(2, 10)(3, 9)(4, 8)(5, 7), + Perm(0, 11)(1, 8)(2, 7)(3, 6)(4, 10)(5, 9), + Perm(0, 11)(1, 10)(2, 9)(3, 8)(4, 7)(5, 6), + Perm(0, 11)(1, 7)(2, 6)(3, 10)(4, 9)(5, 8), + Perm(0, 11)(1, 9)(2, 8)(3, 7)(4, 6)(5, 10), + Perm(0, 5, 1)(2, 4, 6)(3, 10, 7)(8, 9, 11), + Perm(0, 1, 2)(3, 5, 7)(4, 6, 8)(9, 10, 11), + Perm(0, 2, 3)(1, 8, 4)(5, 7, 9)(6, 11, 10), + Perm(0, 3, 4)(1, 8, 10)(2, 9, 5)(6, 7, 11), + Perm(0, 4, 5)(1, 3, 10)(2, 9, 6)(7, 8, 11), + Perm(0, 10, 7)(1, 5, 6)(2, 4, 11)(3, 9, 8), + Perm(0, 6, 8)(1, 7, 2)(3, 5, 11)(4, 10, 9), + Perm(0, 7, 9)(1, 11, 4)(2, 8, 3)(5, 6, 10), + Perm(0, 8, 10)(1, 7, 6)(2, 11, 5)(3, 9, 4), + Perm(0, 9, 6)(1, 3, 11)(2, 8, 7)(4, 10, 5))) + +tetrahedron_faces = [tuple(arg) for arg in tetrahedron.faces] + +cube_faces = [tuple(arg) for arg in cube.faces] + +octahedron_faces = [tuple(arg) for arg in octahedron.faces] + +dodecahedron_faces = [tuple(arg) for arg in dodecahedron.faces] + +icosahedron_faces = [tuple(arg) for arg in icosahedron.faces] diff --git a/lib/python3.11/site-packages/sympy/combinatorics/prufer.py b/lib/python3.11/site-packages/sympy/combinatorics/prufer.py new file mode 100644 index 0000000000000000000000000000000000000000..e389df87cddc0152b2376e18b9f3df2e94d3d2fb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/prufer.py @@ -0,0 +1,435 @@ +from sympy.core import Basic +from sympy.core.containers import Tuple +from sympy.tensor.array import Array +from sympy.core.sympify import _sympify +from sympy.utilities.iterables import flatten, iterable +from sympy.utilities.misc import as_int + +from collections import defaultdict + + +class Prufer(Basic): + """ + The Prufer correspondence is an algorithm that describes the + bijection between labeled trees and the Prufer code. A Prufer + code of a labeled tree is unique up to isomorphism and has + a length of n - 2. + + Prufer sequences were first used by Heinz Prufer to give a + proof of Cayley's formula. + + References + ========== + + .. [1] https://mathworld.wolfram.com/LabeledTree.html + + """ + _prufer_repr = None + _tree_repr = None + _nodes = None + _rank = None + + @property + def prufer_repr(self): + """Returns Prufer sequence for the Prufer object. + + This sequence is found by removing the highest numbered vertex, + recording the node it was attached to, and continuing until only + two vertices remain. The Prufer sequence is the list of recorded nodes. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).prufer_repr + [3, 3, 3, 4] + >>> Prufer([1, 0, 0]).prufer_repr + [1, 0, 0] + + See Also + ======== + + to_prufer + + """ + if self._prufer_repr is None: + self._prufer_repr = self.to_prufer(self._tree_repr[:], self.nodes) + return self._prufer_repr + + @property + def tree_repr(self): + """Returns the tree representation of the Prufer object. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).tree_repr + [[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]] + >>> Prufer([1, 0, 0]).tree_repr + [[1, 2], [0, 1], [0, 3], [0, 4]] + + See Also + ======== + + to_tree + + """ + if self._tree_repr is None: + self._tree_repr = self.to_tree(self._prufer_repr[:]) + return self._tree_repr + + @property + def nodes(self): + """Returns the number of nodes in the tree. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]).nodes + 6 + >>> Prufer([1, 0, 0]).nodes + 5 + + """ + return self._nodes + + @property + def rank(self): + """Returns the rank of the Prufer sequence. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> p = Prufer([[0, 3], [1, 3], [2, 3], [3, 4], [4, 5]]) + >>> p.rank + 778 + >>> p.next(1).rank + 779 + >>> p.prev().rank + 777 + + See Also + ======== + + prufer_rank, next, prev, size + + """ + if self._rank is None: + self._rank = self.prufer_rank() + return self._rank + + @property + def size(self): + """Return the number of possible trees of this Prufer object. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer([0]*4).size == Prufer([6]*4).size == 1296 + True + + See Also + ======== + + prufer_rank, rank, next, prev + + """ + return self.prev(self.rank).prev().rank + 1 + + @staticmethod + def to_prufer(tree, n): + """Return the Prufer sequence for a tree given as a list of edges where + ``n`` is the number of nodes in the tree. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> a = Prufer([[0, 1], [0, 2], [0, 3]]) + >>> a.prufer_repr + [0, 0] + >>> Prufer.to_prufer([[0, 1], [0, 2], [0, 3]], 4) + [0, 0] + + See Also + ======== + prufer_repr: returns Prufer sequence of a Prufer object. + + """ + d = defaultdict(int) + L = [] + for edge in tree: + # Increment the value of the corresponding + # node in the degree list as we encounter an + # edge involving it. + d[edge[0]] += 1 + d[edge[1]] += 1 + for i in range(n - 2): + # find the smallest leaf + for x in range(n): + if d[x] == 1: + break + # find the node it was connected to + y = None + for edge in tree: + if x == edge[0]: + y = edge[1] + elif x == edge[1]: + y = edge[0] + if y is not None: + break + # record and update + L.append(y) + for j in (x, y): + d[j] -= 1 + if not d[j]: + d.pop(j) + tree.remove(edge) + return L + + @staticmethod + def to_tree(prufer): + """Return the tree (as a list of edges) of the given Prufer sequence. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> a = Prufer([0, 2], 4) + >>> a.tree_repr + [[0, 1], [0, 2], [2, 3]] + >>> Prufer.to_tree([0, 2]) + [[0, 1], [0, 2], [2, 3]] + + References + ========== + + .. [1] https://hamberg.no/erlend/posts/2010-11-06-prufer-sequence-compact-tree-representation.html + + See Also + ======== + tree_repr: returns tree representation of a Prufer object. + + """ + tree = [] + last = [] + n = len(prufer) + 2 + d = defaultdict(lambda: 1) + for p in prufer: + d[p] += 1 + for i in prufer: + for j in range(n): + # find the smallest leaf (degree = 1) + if d[j] == 1: + break + # (i, j) is the new edge that we append to the tree + # and remove from the degree dictionary + d[i] -= 1 + d[j] -= 1 + tree.append(sorted([i, j])) + last = [i for i in range(n) if d[i] == 1] or [0, 1] + tree.append(last) + + return tree + + @staticmethod + def edges(*runs): + """Return a list of edges and the number of nodes from the given runs + that connect nodes in an integer-labelled tree. + + All node numbers will be shifted so that the minimum node is 0. It is + not a problem if edges are repeated in the runs; only unique edges are + returned. There is no assumption made about what the range of the node + labels should be, but all nodes from the smallest through the largest + must be present. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer.edges([1, 2, 3], [2, 4, 5]) # a T + ([[0, 1], [1, 2], [1, 3], [3, 4]], 5) + + Duplicate edges are removed: + + >>> Prufer.edges([0, 1, 2, 3], [1, 4, 5], [1, 4, 6]) # a K + ([[0, 1], [1, 2], [1, 4], [2, 3], [4, 5], [4, 6]], 7) + + """ + e = set() + nmin = runs[0][0] + for r in runs: + for i in range(len(r) - 1): + a, b = r[i: i + 2] + if b < a: + a, b = b, a + e.add((a, b)) + rv = [] + got = set() + nmin = nmax = None + for ei in e: + got.update(ei) + nmin = min(ei[0], nmin) if nmin is not None else ei[0] + nmax = max(ei[1], nmax) if nmax is not None else ei[1] + rv.append(list(ei)) + missing = set(range(nmin, nmax + 1)) - got + if missing: + missing = [i + nmin for i in missing] + if len(missing) == 1: + msg = 'Node %s is missing.' % missing.pop() + else: + msg = 'Nodes %s are missing.' % sorted(missing) + raise ValueError(msg) + if nmin != 0: + for i, ei in enumerate(rv): + rv[i] = [n - nmin for n in ei] + nmax -= nmin + return sorted(rv), nmax + 1 + + def prufer_rank(self): + """Computes the rank of a Prufer sequence. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> a = Prufer([[0, 1], [0, 2], [0, 3]]) + >>> a.prufer_rank() + 0 + + See Also + ======== + + rank, next, prev, size + + """ + r = 0 + p = 1 + for i in range(self.nodes - 3, -1, -1): + r += p*self.prufer_repr[i] + p *= self.nodes + return r + + @classmethod + def unrank(self, rank, n): + """Finds the unranked Prufer sequence. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> Prufer.unrank(0, 4) + Prufer([0, 0]) + + """ + n, rank = as_int(n), as_int(rank) + L = defaultdict(int) + for i in range(n - 3, -1, -1): + L[i] = rank % n + rank = (rank - L[i])//n + return Prufer([L[i] for i in range(len(L))]) + + def __new__(cls, *args, **kw_args): + """The constructor for the Prufer object. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + + A Prufer object can be constructed from a list of edges: + + >>> a = Prufer([[0, 1], [0, 2], [0, 3]]) + >>> a.prufer_repr + [0, 0] + + If the number of nodes is given, no checking of the nodes will + be performed; it will be assumed that nodes 0 through n - 1 are + present: + + >>> Prufer([[0, 1], [0, 2], [0, 3]], 4) + Prufer([[0, 1], [0, 2], [0, 3]], 4) + + A Prufer object can be constructed from a Prufer sequence: + + >>> b = Prufer([1, 3]) + >>> b.tree_repr + [[0, 1], [1, 3], [2, 3]] + + """ + arg0 = Array(args[0]) if args[0] else Tuple() + args = (arg0,) + tuple(_sympify(arg) for arg in args[1:]) + ret_obj = Basic.__new__(cls, *args, **kw_args) + args = [list(args[0])] + if args[0] and iterable(args[0][0]): + if not args[0][0]: + raise ValueError( + 'Prufer expects at least one edge in the tree.') + if len(args) > 1: + nnodes = args[1] + else: + nodes = set(flatten(args[0])) + nnodes = max(nodes) + 1 + if nnodes != len(nodes): + missing = set(range(nnodes)) - nodes + if len(missing) == 1: + msg = 'Node %s is missing.' % missing.pop() + else: + msg = 'Nodes %s are missing.' % sorted(missing) + raise ValueError(msg) + ret_obj._tree_repr = [list(i) for i in args[0]] + ret_obj._nodes = nnodes + else: + ret_obj._prufer_repr = args[0] + ret_obj._nodes = len(ret_obj._prufer_repr) + 2 + return ret_obj + + def next(self, delta=1): + """Generates the Prufer sequence that is delta beyond the current one. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> a = Prufer([[0, 1], [0, 2], [0, 3]]) + >>> b = a.next(1) # == a.next() + >>> b.tree_repr + [[0, 2], [0, 1], [1, 3]] + >>> b.rank + 1 + + See Also + ======== + + prufer_rank, rank, prev, size + + """ + return Prufer.unrank(self.rank + delta, self.nodes) + + def prev(self, delta=1): + """Generates the Prufer sequence that is -delta before the current one. + + Examples + ======== + + >>> from sympy.combinatorics.prufer import Prufer + >>> a = Prufer([[0, 1], [1, 2], [2, 3], [1, 4]]) + >>> a.rank + 36 + >>> b = a.prev() + >>> b + Prufer([1, 2, 0]) + >>> b.rank + 35 + + See Also + ======== + + prufer_rank, rank, next, size + + """ + return Prufer.unrank(self.rank -delta, self.nodes) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem.py b/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem.py new file mode 100644 index 0000000000000000000000000000000000000000..b9e8dfe4c831db6490c987c85a57d0d1a939de61 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem.py @@ -0,0 +1,453 @@ +from collections import deque +from sympy.combinatorics.rewritingsystem_fsm import StateMachine + +class RewritingSystem: + ''' + A class implementing rewriting systems for `FpGroup`s. + + References + ========== + .. [1] Epstein, D., Holt, D. and Rees, S. (1991). + The use of Knuth-Bendix methods to solve the word problem in automatic groups. + Journal of Symbolic Computation, 12(4-5), pp.397-414. + + .. [2] GAP's Manual on its KBMAG package + https://www.gap-system.org/Manuals/pkg/kbmag-1.5.3/doc/manual.pdf + + ''' + def __init__(self, group): + self.group = group + self.alphabet = group.generators + self._is_confluent = None + + # these values are taken from [2] + self.maxeqns = 32767 # max rules + self.tidyint = 100 # rules before tidying + + # _max_exceeded is True if maxeqns is exceeded + # at any point + self._max_exceeded = False + + # Reduction automaton + self.reduction_automaton = None + self._new_rules = {} + + # dictionary of reductions + self.rules = {} + self.rules_cache = deque([], 50) + self._init_rules() + + + # All the transition symbols in the automaton + generators = list(self.alphabet) + generators += [gen**-1 for gen in generators] + # Create a finite state machine as an instance of the StateMachine object + self.reduction_automaton = StateMachine('Reduction automaton for '+ repr(self.group), generators) + self.construct_automaton() + + def set_max(self, n): + ''' + Set the maximum number of rules that can be defined + + ''' + if n > self.maxeqns: + self._max_exceeded = False + self.maxeqns = n + return + + @property + def is_confluent(self): + ''' + Return `True` if the system is confluent + + ''' + if self._is_confluent is None: + self._is_confluent = self._check_confluence() + return self._is_confluent + + def _init_rules(self): + identity = self.group.free_group.identity + for r in self.group.relators: + self.add_rule(r, identity) + self._remove_redundancies() + return + + def _add_rule(self, r1, r2): + ''' + Add the rule r1 -> r2 with no checking or further + deductions + + ''' + if len(self.rules) + 1 > self.maxeqns: + self._is_confluent = self._check_confluence() + self._max_exceeded = True + raise RuntimeError("Too many rules were defined.") + self.rules[r1] = r2 + # Add the newly added rule to the `new_rules` dictionary. + if self.reduction_automaton: + self._new_rules[r1] = r2 + + def add_rule(self, w1, w2, check=False): + new_keys = set() + + if w1 == w2: + return new_keys + + if w1 < w2: + w1, w2 = w2, w1 + + if (w1, w2) in self.rules_cache: + return new_keys + self.rules_cache.append((w1, w2)) + + s1, s2 = w1, w2 + + # The following is the equivalent of checking + # s1 for overlaps with the implicit reductions + # {g*g**-1 -> } and {g**-1*g -> } + # for any generator g without installing the + # redundant rules that would result from processing + # the overlaps. See [1], Section 3 for details. + + if len(s1) - len(s2) < 3: + if s1 not in self.rules: + new_keys.add(s1) + if not check: + self._add_rule(s1, s2) + if s2**-1 > s1**-1 and s2**-1 not in self.rules: + new_keys.add(s2**-1) + if not check: + self._add_rule(s2**-1, s1**-1) + + # overlaps on the right + while len(s1) - len(s2) > -1: + g = s1[len(s1)-1] + s1 = s1.subword(0, len(s1)-1) + s2 = s2*g**-1 + if len(s1) - len(s2) < 0: + if s2 not in self.rules: + if not check: + self._add_rule(s2, s1) + new_keys.add(s2) + elif len(s1) - len(s2) < 3: + new = self.add_rule(s1, s2, check) + new_keys.update(new) + + # overlaps on the left + while len(w1) - len(w2) > -1: + g = w1[0] + w1 = w1.subword(1, len(w1)) + w2 = g**-1*w2 + if len(w1) - len(w2) < 0: + if w2 not in self.rules: + if not check: + self._add_rule(w2, w1) + new_keys.add(w2) + elif len(w1) - len(w2) < 3: + new = self.add_rule(w1, w2, check) + new_keys.update(new) + + return new_keys + + def _remove_redundancies(self, changes=False): + ''' + Reduce left- and right-hand sides of reduction rules + and remove redundant equations (i.e. those for which + lhs == rhs). If `changes` is `True`, return a set + containing the removed keys and a set containing the + added keys + + ''' + removed = set() + added = set() + rules = self.rules.copy() + for r in rules: + v = self.reduce(r, exclude=r) + w = self.reduce(rules[r]) + if v != r: + del self.rules[r] + removed.add(r) + if v > w: + added.add(v) + self.rules[v] = w + elif v < w: + added.add(w) + self.rules[w] = v + else: + self.rules[v] = w + if changes: + return removed, added + return + + def make_confluent(self, check=False): + ''' + Try to make the system confluent using the Knuth-Bendix + completion algorithm + + ''' + if self._max_exceeded: + return self._is_confluent + lhs = list(self.rules.keys()) + + def _overlaps(r1, r2): + len1 = len(r1) + len2 = len(r2) + result = [] + for j in range(1, len1 + len2): + if (r1.subword(len1 - j, len1 + len2 - j, strict=False) + == r2.subword(j - len1, j, strict=False)): + a = r1.subword(0, len1-j, strict=False) + a = a*r2.subword(0, j-len1, strict=False) + b = r2.subword(j-len1, j, strict=False) + c = r2.subword(j, len2, strict=False) + c = c*r1.subword(len1 + len2 - j, len1, strict=False) + result.append(a*b*c) + return result + + def _process_overlap(w, r1, r2, check): + s = w.eliminate_word(r1, self.rules[r1]) + s = self.reduce(s) + t = w.eliminate_word(r2, self.rules[r2]) + t = self.reduce(t) + if s != t: + if check: + # system not confluent + return [0] + try: + new_keys = self.add_rule(t, s, check) + return new_keys + except RuntimeError: + return False + return + + added = 0 + i = 0 + while i < len(lhs): + r1 = lhs[i] + i += 1 + # j could be i+1 to not + # check each pair twice but lhs + # is extended in the loop and the new + # elements have to be checked with the + # preceding ones. there is probably a better way + # to handle this + j = 0 + while j < len(lhs): + r2 = lhs[j] + j += 1 + if r1 == r2: + continue + overlaps = _overlaps(r1, r2) + overlaps.extend(_overlaps(r1**-1, r2)) + if not overlaps: + continue + for w in overlaps: + new_keys = _process_overlap(w, r1, r2, check) + if new_keys: + if check: + return False + lhs.extend(new_keys) + added += len(new_keys) + elif new_keys == False: + # too many rules were added so the process + # couldn't complete + return self._is_confluent + + if added > self.tidyint and not check: + # tidy up + r, a = self._remove_redundancies(changes=True) + added = 0 + if r: + # reset i since some elements were removed + i = min(lhs.index(s) for s in r) + lhs = [l for l in lhs if l not in r] + lhs.extend(a) + if r1 in r: + # r1 was removed as redundant + break + + self._is_confluent = True + if not check: + self._remove_redundancies() + return True + + def _check_confluence(self): + return self.make_confluent(check=True) + + def reduce(self, word, exclude=None): + ''' + Apply reduction rules to `word` excluding the reduction rule + for the lhs equal to `exclude` + + ''' + rules = {r: self.rules[r] for r in self.rules if r != exclude} + # the following is essentially `eliminate_words()` code from the + # `FreeGroupElement` class, the only difference being the first + # "if" statement + again = True + new = word + while again: + again = False + for r in rules: + prev = new + if rules[r]**-1 > r**-1: + new = new.eliminate_word(r, rules[r], _all=True, inverse=False) + else: + new = new.eliminate_word(r, rules[r], _all=True) + if new != prev: + again = True + return new + + def _compute_inverse_rules(self, rules): + ''' + Compute the inverse rules for a given set of rules. + The inverse rules are used in the automaton for word reduction. + + Arguments: + rules (dictionary): Rules for which the inverse rules are to computed. + + Returns: + Dictionary of inverse_rules. + + ''' + inverse_rules = {} + for r in rules: + rule_key_inverse = r**-1 + rule_value_inverse = (rules[r])**-1 + if (rule_value_inverse < rule_key_inverse): + inverse_rules[rule_key_inverse] = rule_value_inverse + else: + inverse_rules[rule_value_inverse] = rule_key_inverse + return inverse_rules + + def construct_automaton(self): + ''' + Construct the automaton based on the set of reduction rules of the system. + + Automata Design: + The accept states of the automaton are the proper prefixes of the left hand side of the rules. + The complete left hand side of the rules are the dead states of the automaton. + + ''' + self._add_to_automaton(self.rules) + + def _add_to_automaton(self, rules): + ''' + Add new states and transitions to the automaton. + + Summary: + States corresponding to the new rules added to the system are computed and added to the automaton. + Transitions in the previously added states are also modified if necessary. + + Arguments: + rules (dictionary) -- Dictionary of the newly added rules. + + ''' + # Automaton variables + automaton_alphabet = [] + proper_prefixes = {} + + # compute the inverses of all the new rules added + all_rules = rules + inverse_rules = self._compute_inverse_rules(all_rules) + all_rules.update(inverse_rules) + + # Keep track of the accept_states. + accept_states = [] + + for rule in all_rules: + # The symbols present in the new rules are the symbols to be verified at each state. + # computes the automaton_alphabet, as the transitions solely depend upon the new states. + automaton_alphabet += rule.letter_form_elm + # Compute the proper prefixes for every rule. + proper_prefixes[rule] = [] + letter_word_array = list(rule.letter_form_elm) + len_letter_word_array = len(letter_word_array) + for i in range (1, len_letter_word_array): + letter_word_array[i] = letter_word_array[i-1]*letter_word_array[i] + # Add accept states. + elem = letter_word_array[i-1] + if elem not in self.reduction_automaton.states: + self.reduction_automaton.add_state(elem, state_type='a') + accept_states.append(elem) + proper_prefixes[rule] = letter_word_array + # Check for overlaps between dead and accept states. + if rule in accept_states: + self.reduction_automaton.states[rule].state_type = 'd' + self.reduction_automaton.states[rule].rh_rule = all_rules[rule] + accept_states.remove(rule) + # Add dead states + if rule not in self.reduction_automaton.states: + self.reduction_automaton.add_state(rule, state_type='d', rh_rule=all_rules[rule]) + + automaton_alphabet = set(automaton_alphabet) + + # Add new transitions for every state. + for state in self.reduction_automaton.states: + current_state_name = state + current_state_type = self.reduction_automaton.states[state].state_type + # Transitions will be modified only when suffixes of the current_state + # belongs to the proper_prefixes of the new rules. + # The rest are ignored if they cannot lead to a dead state after a finite number of transisitons. + if current_state_type == 's': + for letter in automaton_alphabet: + if letter in self.reduction_automaton.states: + self.reduction_automaton.states[state].add_transition(letter, letter) + else: + self.reduction_automaton.states[state].add_transition(letter, current_state_name) + elif current_state_type == 'a': + # Check if the transition to any new state in possible. + for letter in automaton_alphabet: + _next = current_state_name*letter + while len(_next) and _next not in self.reduction_automaton.states: + _next = _next.subword(1, len(_next)) + if not len(_next): + _next = 'start' + self.reduction_automaton.states[state].add_transition(letter, _next) + + # Add transitions for new states. All symbols used in the automaton are considered here. + # Ignore this if `reduction_automaton.automaton_alphabet` = `automaton_alphabet`. + if len(self.reduction_automaton.automaton_alphabet) != len(automaton_alphabet): + for state in accept_states: + current_state_name = state + for letter in self.reduction_automaton.automaton_alphabet: + _next = current_state_name*letter + while len(_next) and _next not in self.reduction_automaton.states: + _next = _next.subword(1, len(_next)) + if not len(_next): + _next = 'start' + self.reduction_automaton.states[state].add_transition(letter, _next) + + def reduce_using_automaton(self, word): + ''' + Reduce a word using an automaton. + + Summary: + All the symbols of the word are stored in an array and are given as the input to the automaton. + If the automaton reaches a dead state that subword is replaced and the automaton is run from the beginning. + The complete word has to be replaced when the word is read and the automaton reaches a dead state. + So, this process is repeated until the word is read completely and the automaton reaches the accept state. + + Arguments: + word (instance of FreeGroupElement) -- Word that needs to be reduced. + + ''' + # Modify the automaton if new rules are found. + if self._new_rules: + self._add_to_automaton(self._new_rules) + self._new_rules = {} + + flag = 1 + while flag: + flag = 0 + current_state = self.reduction_automaton.states['start'] + for i, s in enumerate(word.letter_form_elm): + next_state_name = current_state.transitions[s] + next_state = self.reduction_automaton.states[next_state_name] + if next_state.state_type == 'd': + subst = next_state.rh_rule + word = word.substituted_word(i - len(next_state_name) + 1, i+1, subst) + flag = 1 + break + current_state = next_state + return word diff --git a/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem_fsm.py b/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem_fsm.py new file mode 100644 index 0000000000000000000000000000000000000000..21916530040ac321180692d1a0811da4ae36a056 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/rewritingsystem_fsm.py @@ -0,0 +1,60 @@ +class State: + ''' + A representation of a state managed by a ``StateMachine``. + + Attributes: + name (instance of FreeGroupElement or string) -- State name which is also assigned to the Machine. + transisitons (OrderedDict) -- Represents all the transitions of the state object. + state_type (string) -- Denotes the type (accept/start/dead) of the state. + rh_rule (instance of FreeGroupElement) -- right hand rule for dead state. + state_machine (instance of StateMachine object) -- The finite state machine that the state belongs to. + ''' + + def __init__(self, name, state_machine, state_type=None, rh_rule=None): + self.name = name + self.transitions = {} + self.state_machine = state_machine + self.state_type = state_type[0] + self.rh_rule = rh_rule + + def add_transition(self, letter, state): + ''' + Add a transition from the current state to a new state. + + Keyword Arguments: + letter -- The alphabet element the current state reads to make the state transition. + state -- This will be an instance of the State object which represents a new state after in the transition after the alphabet is read. + + ''' + self.transitions[letter] = state + +class StateMachine: + ''' + Representation of a finite state machine the manages the states and the transitions of the automaton. + + Attributes: + states (dictionary) -- Collection of all registered `State` objects. + name (str) -- Name of the state machine. + ''' + + def __init__(self, name, automaton_alphabet): + self.name = name + self.automaton_alphabet = automaton_alphabet + self.states = {} # Contains all the states in the machine. + self.add_state('start', state_type='s') + + def add_state(self, state_name, state_type=None, rh_rule=None): + ''' + Instantiate a state object and stores it in the 'states' dictionary. + + Arguments: + state_name (instance of FreeGroupElement or string) -- name of the new states. + state_type (string) -- Denotes the type (accept/start/dead) of the state added. + rh_rule (instance of FreeGroupElement) -- right hand rule for dead state. + + ''' + new_state = State(state_name, self, state_type, rh_rule) + self.states[state_name] = new_state + + def __repr__(self): + return "%s" % (self.name) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/schur_number.py b/lib/python3.11/site-packages/sympy/combinatorics/schur_number.py new file mode 100644 index 0000000000000000000000000000000000000000..83aac98e543d4b54d4e6af17adca6e4f4de1b9ac --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/schur_number.py @@ -0,0 +1,160 @@ +""" +The Schur number S(k) is the largest integer n for which the interval [1,n] +can be partitioned into k sum-free sets.(https://mathworld.wolfram.com/SchurNumber.html) +""" +import math +from sympy.core import S +from sympy.core.basic import Basic +from sympy.core.function import Function +from sympy.core.numbers import Integer + + +class SchurNumber(Function): + r""" + This function creates a SchurNumber object + which is evaluated for `k \le 5` otherwise only + the lower bound information can be retrieved. + + Examples + ======== + + >>> from sympy.combinatorics.schur_number import SchurNumber + + Since S(3) = 13, hence the output is a number + >>> SchurNumber(3) + 13 + + We do not know the Schur number for values greater than 5, hence + only the object is returned + >>> SchurNumber(6) + SchurNumber(6) + + Now, the lower bound information can be retrieved using lower_bound() + method + >>> SchurNumber(6).lower_bound() + 536 + + """ + + @classmethod + def eval(cls, k): + if k.is_Number: + if k is S.Infinity: + return S.Infinity + if k.is_zero: + return S.Zero + if not k.is_integer or k.is_negative: + raise ValueError("k should be a positive integer") + first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160} + if k <= 5: + return Integer(first_known_schur_numbers[k]) + + def lower_bound(self): + f_ = self.args[0] + # Improved lower bounds known for S(6) and S(7) + if f_ == 6: + return Integer(536) + if f_ == 7: + return Integer(1680) + # For other cases, use general expression + if f_.is_Integer: + return 3*self.func(f_ - 1).lower_bound() - 1 + return (3**f_ - 1)/2 + + +def _schur_subsets_number(n): + + if n is S.Infinity: + raise ValueError("Input must be finite") + if n <= 0: + raise ValueError("n must be a non-zero positive integer.") + elif n <= 3: + min_k = 1 + else: + min_k = math.ceil(math.log(2*n + 1, 3)) + + return Integer(min_k) + + +def schur_partition(n): + """ + + This function returns the partition in the minimum number of sum-free subsets + according to the lower bound given by the Schur Number. + + Parameters + ========== + + n: a number + n is the upper limit of the range [1, n] for which we need to find and + return the minimum number of free subsets according to the lower bound + of schur number + + Returns + ======= + + List of lists + List of the minimum number of sum-free subsets + + Notes + ===== + + It is possible for some n to make the partition into less + subsets since the only known Schur numbers are: + S(1) = 1, S(2) = 4, S(3) = 13, S(4) = 44. + e.g for n = 44 the lower bound from the function above is 5 subsets but it has been proven + that can be done with 4 subsets. + + Examples + ======== + + For n = 1, 2, 3 the answer is the set itself + + >>> from sympy.combinatorics.schur_number import schur_partition + >>> schur_partition(2) + [[1, 2]] + + For n > 3, the answer is the minimum number of sum-free subsets: + + >>> schur_partition(5) + [[3, 2], [5], [1, 4]] + + >>> schur_partition(8) + [[3, 2], [6, 5, 8], [1, 4, 7]] + """ + + if isinstance(n, Basic) and not n.is_Number: + raise ValueError("Input value must be a number") + + number_of_subsets = _schur_subsets_number(n) + if n == 1: + sum_free_subsets = [[1]] + elif n == 2: + sum_free_subsets = [[1, 2]] + elif n == 3: + sum_free_subsets = [[1, 2, 3]] + else: + sum_free_subsets = [[1, 4], [2, 3]] + + while len(sum_free_subsets) < number_of_subsets: + sum_free_subsets = _generate_next_list(sum_free_subsets, n) + missed_elements = [3*k + 1 for k in range(len(sum_free_subsets), (n-1)//3 + 1)] + sum_free_subsets[-1] += missed_elements + + return sum_free_subsets + + +def _generate_next_list(current_list, n): + new_list = [] + + for item in current_list: + temp_1 = [number*3 for number in item if number*3 <= n] + temp_2 = [number*3 - 1 for number in item if number*3 - 1 <= n] + new_item = temp_1 + temp_2 + new_list.append(new_item) + + last_list = [3*k + 1 for k in range(len(current_list)+1) if 3*k + 1 <= n] + new_list.append(last_list) + current_list = new_list + + return current_list diff --git a/lib/python3.11/site-packages/sympy/combinatorics/subsets.py b/lib/python3.11/site-packages/sympy/combinatorics/subsets.py new file mode 100644 index 0000000000000000000000000000000000000000..e540cb2395cb27e04c9d513831cb834a05ec2abd --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/subsets.py @@ -0,0 +1,619 @@ +from itertools import combinations + +from sympy.combinatorics.graycode import GrayCode + + +class Subset(): + """ + Represents a basic subset object. + + Explanation + =========== + + We generate subsets using essentially two techniques, + binary enumeration and lexicographic enumeration. + The Subset class takes two arguments, the first one + describes the initial subset to consider and the second + describes the superset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.next_binary().subset + ['b'] + >>> a.prev_binary().subset + ['c'] + """ + + _rank_binary = None + _rank_lex = None + _rank_graycode = None + _subset = None + _superset = None + + def __new__(cls, subset, superset): + """ + Default constructor. + + It takes the ``subset`` and its ``superset`` as its parameters. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.subset + ['c', 'd'] + >>> a.superset + ['a', 'b', 'c', 'd'] + >>> a.size + 2 + """ + if len(subset) > len(superset): + raise ValueError('Invalid arguments have been provided. The ' + 'superset must be larger than the subset.') + for elem in subset: + if elem not in superset: + raise ValueError('The superset provided is invalid as it does ' + 'not contain the element {}'.format(elem)) + obj = object.__new__(cls) + obj._subset = subset + obj._superset = superset + return obj + + def __eq__(self, other): + """Return a boolean indicating whether a == b on the basis of + whether both objects are of the class Subset and if the values + of the subset and superset attributes are the same. + """ + if not isinstance(other, Subset): + return NotImplemented + return self.subset == other.subset and self.superset == other.superset + + def iterate_binary(self, k): + """ + This is a helper function. It iterates over the + binary subsets by ``k`` steps. This variable can be + both positive or negative. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.iterate_binary(-2).subset + ['d'] + >>> a = Subset(['a', 'b', 'c'], ['a', 'b', 'c', 'd']) + >>> a.iterate_binary(2).subset + [] + + See Also + ======== + + next_binary, prev_binary + """ + bin_list = Subset.bitlist_from_subset(self.subset, self.superset) + n = (int(''.join(bin_list), 2) + k) % 2**self.superset_size + bits = bin(n)[2:].rjust(self.superset_size, '0') + return Subset.subset_from_bitlist(self.superset, bits) + + def next_binary(self): + """ + Generates the next binary ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.next_binary().subset + ['b'] + >>> a = Subset(['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.next_binary().subset + [] + + See Also + ======== + + prev_binary, iterate_binary + """ + return self.iterate_binary(1) + + def prev_binary(self): + """ + Generates the previous binary ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([], ['a', 'b', 'c', 'd']) + >>> a.prev_binary().subset + ['a', 'b', 'c', 'd'] + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.prev_binary().subset + ['c'] + + See Also + ======== + + next_binary, iterate_binary + """ + return self.iterate_binary(-1) + + def next_lexicographic(self): + """ + Generates the next lexicographically ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.next_lexicographic().subset + ['d'] + >>> a = Subset(['d'], ['a', 'b', 'c', 'd']) + >>> a.next_lexicographic().subset + [] + + See Also + ======== + + prev_lexicographic + """ + i = self.superset_size - 1 + indices = Subset.subset_indices(self.subset, self.superset) + + if i in indices: + if i - 1 in indices: + indices.remove(i - 1) + else: + indices.remove(i) + i = i - 1 + while i >= 0 and i not in indices: + i = i - 1 + if i >= 0: + indices.remove(i) + indices.append(i+1) + else: + while i not in indices and i >= 0: + i = i - 1 + indices.append(i + 1) + + ret_set = [] + super_set = self.superset + for i in indices: + ret_set.append(super_set[i]) + return Subset(ret_set, super_set) + + def prev_lexicographic(self): + """ + Generates the previous lexicographically ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([], ['a', 'b', 'c', 'd']) + >>> a.prev_lexicographic().subset + ['d'] + >>> a = Subset(['c','d'], ['a', 'b', 'c', 'd']) + >>> a.prev_lexicographic().subset + ['c'] + + See Also + ======== + + next_lexicographic + """ + i = self.superset_size - 1 + indices = Subset.subset_indices(self.subset, self.superset) + + while i >= 0 and i not in indices: + i = i - 1 + + if i == 0 or i - 1 in indices: + indices.remove(i) + else: + if i >= 0: + indices.remove(i) + indices.append(i - 1) + indices.append(self.superset_size - 1) + + ret_set = [] + super_set = self.superset + for i in indices: + ret_set.append(super_set[i]) + return Subset(ret_set, super_set) + + def iterate_graycode(self, k): + """ + Helper function used for prev_gray and next_gray. + It performs ``k`` step overs to get the respective Gray codes. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) + >>> a.iterate_graycode(3).subset + [1, 4] + >>> a.iterate_graycode(-2).subset + [1, 2, 4] + + See Also + ======== + + next_gray, prev_gray + """ + unranked_code = GrayCode.unrank(self.superset_size, + (self.rank_gray + k) % self.cardinality) + return Subset.subset_from_bitlist(self.superset, + unranked_code) + + def next_gray(self): + """ + Generates the next Gray code ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) + >>> a.next_gray().subset + [1, 3] + + See Also + ======== + + iterate_graycode, prev_gray + """ + return self.iterate_graycode(1) + + def prev_gray(self): + """ + Generates the previous Gray code ordered subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([2, 3, 4], [1, 2, 3, 4, 5]) + >>> a.prev_gray().subset + [2, 3, 4, 5] + + See Also + ======== + + iterate_graycode, next_gray + """ + return self.iterate_graycode(-1) + + @property + def rank_binary(self): + """ + Computes the binary ordered rank. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset([], ['a','b','c','d']) + >>> a.rank_binary + 0 + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.rank_binary + 3 + + See Also + ======== + + iterate_binary, unrank_binary + """ + if self._rank_binary is None: + self._rank_binary = int("".join( + Subset.bitlist_from_subset(self.subset, + self.superset)), 2) + return self._rank_binary + + @property + def rank_lexicographic(self): + """ + Computes the lexicographic ranking of the subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.rank_lexicographic + 14 + >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) + >>> a.rank_lexicographic + 43 + """ + if self._rank_lex is None: + def _ranklex(self, subset_index, i, n): + if subset_index == [] or i > n: + return 0 + if i in subset_index: + subset_index.remove(i) + return 1 + _ranklex(self, subset_index, i + 1, n) + return 2**(n - i - 1) + _ranklex(self, subset_index, i + 1, n) + indices = Subset.subset_indices(self.subset, self.superset) + self._rank_lex = _ranklex(self, indices, 0, self.superset_size) + return self._rank_lex + + @property + def rank_gray(self): + """ + Computes the Gray code ranking of the subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c','d'], ['a','b','c','d']) + >>> a.rank_gray + 2 + >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) + >>> a.rank_gray + 27 + + See Also + ======== + + iterate_graycode, unrank_gray + """ + if self._rank_graycode is None: + bits = Subset.bitlist_from_subset(self.subset, self.superset) + self._rank_graycode = GrayCode(len(bits), start=bits).rank + return self._rank_graycode + + @property + def subset(self): + """ + Gets the subset represented by the current instance. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.subset + ['c', 'd'] + + See Also + ======== + + superset, size, superset_size, cardinality + """ + return self._subset + + @property + def size(self): + """ + Gets the size of the subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.size + 2 + + See Also + ======== + + subset, superset, superset_size, cardinality + """ + return len(self.subset) + + @property + def superset(self): + """ + Gets the superset of the subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.superset + ['a', 'b', 'c', 'd'] + + See Also + ======== + + subset, size, superset_size, cardinality + """ + return self._superset + + @property + def superset_size(self): + """ + Returns the size of the superset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.superset_size + 4 + + See Also + ======== + + subset, superset, size, cardinality + """ + return len(self.superset) + + @property + def cardinality(self): + """ + Returns the number of all possible subsets. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + >>> a.cardinality + 16 + + See Also + ======== + + subset, superset, size, superset_size + """ + return 2**(self.superset_size) + + @classmethod + def subset_from_bitlist(self, super_set, bitlist): + """ + Gets the subset defined by the bitlist. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> Subset.subset_from_bitlist(['a', 'b', 'c', 'd'], '0011').subset + ['c', 'd'] + + See Also + ======== + + bitlist_from_subset + """ + if len(super_set) != len(bitlist): + raise ValueError("The sizes of the lists are not equal") + ret_set = [] + for i in range(len(bitlist)): + if bitlist[i] == '1': + ret_set.append(super_set[i]) + return Subset(ret_set, super_set) + + @classmethod + def bitlist_from_subset(self, subset, superset): + """ + Gets the bitlist corresponding to a subset. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> Subset.bitlist_from_subset(['c', 'd'], ['a', 'b', 'c', 'd']) + '0011' + + See Also + ======== + + subset_from_bitlist + """ + bitlist = ['0'] * len(superset) + if isinstance(subset, Subset): + subset = subset.subset + for i in Subset.subset_indices(subset, superset): + bitlist[i] = '1' + return ''.join(bitlist) + + @classmethod + def unrank_binary(self, rank, superset): + """ + Gets the binary ordered subset of the specified rank. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> Subset.unrank_binary(4, ['a', 'b', 'c', 'd']).subset + ['b'] + + See Also + ======== + + iterate_binary, rank_binary + """ + bits = bin(rank)[2:].rjust(len(superset), '0') + return Subset.subset_from_bitlist(superset, bits) + + @classmethod + def unrank_gray(self, rank, superset): + """ + Gets the Gray code ordered subset of the specified rank. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> Subset.unrank_gray(4, ['a', 'b', 'c']).subset + ['a', 'b'] + >>> Subset.unrank_gray(0, ['a', 'b', 'c']).subset + [] + + See Also + ======== + + iterate_graycode, rank_gray + """ + graycode_bitlist = GrayCode.unrank(len(superset), rank) + return Subset.subset_from_bitlist(superset, graycode_bitlist) + + @classmethod + def subset_indices(self, subset, superset): + """Return indices of subset in superset in a list; the list is empty + if all elements of ``subset`` are not in ``superset``. + + Examples + ======== + + >>> from sympy.combinatorics import Subset + >>> superset = [1, 3, 2, 5, 4] + >>> Subset.subset_indices([3, 2, 1], superset) + [1, 2, 0] + >>> Subset.subset_indices([1, 6], superset) + [] + >>> Subset.subset_indices([], superset) + [] + + """ + a, b = superset, subset + sb = set(b) + d = {} + for i, ai in enumerate(a): + if ai in sb: + d[ai] = i + sb.remove(ai) + if not sb: + break + else: + return [] + return [d[bi] for bi in b] + + +def ksubsets(superset, k): + """ + Finds the subsets of size ``k`` in lexicographic order. + + This uses the itertools generator. + + Examples + ======== + + >>> from sympy.combinatorics.subsets import ksubsets + >>> list(ksubsets([1, 2, 3], 2)) + [(1, 2), (1, 3), (2, 3)] + >>> list(ksubsets([1, 2, 3, 4, 5], 2)) + [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), \ + (2, 5), (3, 4), (3, 5), (4, 5)] + + See Also + ======== + + Subset + """ + return combinations(superset, k) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tensor_can.py b/lib/python3.11/site-packages/sympy/combinatorics/tensor_can.py new file mode 100644 index 0000000000000000000000000000000000000000..984d69d9ecd2bb7b222e275da14b16dfcc58c3ae --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tensor_can.py @@ -0,0 +1,1190 @@ +from sympy.combinatorics.permutations import Permutation, _af_rmul, \ + _af_invert, _af_new +from sympy.combinatorics.perm_groups import PermutationGroup, _orbit, \ + _orbit_transversal +from sympy.combinatorics.util import _distribute_gens_by_base, \ + _orbits_transversals_from_bsgs + +""" + References for tensor canonicalization: + + [1] R. Portugal "Algorithmic simplification of tensor expressions", + J. Phys. A 32 (1999) 7779-7789 + + [2] R. Portugal, B.F. Svaiter "Group-theoretic Approach for Symbolic + Tensor Manipulation: I. Free Indices" + arXiv:math-ph/0107031v1 + + [3] L.R.U. Manssur, R. Portugal "Group-theoretic Approach for Symbolic + Tensor Manipulation: II. Dummy Indices" + arXiv:math-ph/0107032v1 + + [4] xperm.c part of XPerm written by J. M. Martin-Garcia + http://www.xact.es/index.html +""" + + +def dummy_sgs(dummies, sym, n): + """ + Return the strong generators for dummy indices. + + Parameters + ========== + + dummies : List of dummy indices. + `dummies[2k], dummies[2k+1]` are paired indices. + In base form, the dummy indices are always in + consecutive positions. + sym : symmetry under interchange of contracted dummies:: + * None no symmetry + * 0 commuting + * 1 anticommuting + + n : number of indices + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import dummy_sgs + >>> dummy_sgs(list(range(2, 8)), 0, 8) + [[0, 1, 3, 2, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 5, 4, 6, 7, 8, 9], + [0, 1, 2, 3, 4, 5, 7, 6, 8, 9], [0, 1, 4, 5, 2, 3, 6, 7, 8, 9], + [0, 1, 2, 3, 6, 7, 4, 5, 8, 9]] + """ + if len(dummies) > n: + raise ValueError("List too large") + res = [] + # exchange of contravariant and covariant indices + if sym is not None: + for j in dummies[::2]: + a = list(range(n + 2)) + if sym == 1: + a[n] = n + 1 + a[n + 1] = n + a[j], a[j + 1] = a[j + 1], a[j] + res.append(a) + # rename dummy indices + for j in dummies[:-3:2]: + a = list(range(n + 2)) + a[j:j + 4] = a[j + 2], a[j + 3], a[j], a[j + 1] + res.append(a) + return res + + +def _min_dummies(dummies, sym, indices): + """ + Return list of minima of the orbits of indices in group of dummies. + See ``double_coset_can_rep`` for the description of ``dummies`` and ``sym``. + ``indices`` is the initial list of dummy indices. + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import _min_dummies + >>> _min_dummies([list(range(2, 8))], [0], list(range(10))) + [0, 1, 2, 2, 2, 2, 2, 2, 8, 9] + """ + num_types = len(sym) + m = [min(dx) if dx else None for dx in dummies] + res = indices[:] + for i in range(num_types): + for c, i in enumerate(indices): + for j in range(num_types): + if i in dummies[j]: + res[c] = m[j] + break + return res + + +def _trace_S(s, j, b, S_cosets): + """ + Return the representative h satisfying s[h[b]] == j + + If there is not such a representative return None + """ + for h in S_cosets[b]: + if s[h[b]] == j: + return h + return None + + +def _trace_D(gj, p_i, Dxtrav): + """ + Return the representative h satisfying h[gj] == p_i + + If there is not such a representative return None + """ + for h in Dxtrav: + if h[gj] == p_i: + return h + return None + + +def _dumx_remove(dumx, dumx_flat, p0): + """ + remove p0 from dumx + """ + res = [] + for dx in dumx: + if p0 not in dx: + res.append(dx) + continue + k = dx.index(p0) + if k % 2 == 0: + p0_paired = dx[k + 1] + else: + p0_paired = dx[k - 1] + dx.remove(p0) + dx.remove(p0_paired) + dumx_flat.remove(p0) + dumx_flat.remove(p0_paired) + res.append(dx) + + +def transversal2coset(size, base, transversal): + a = [] + j = 0 + for i in range(size): + if i in base: + a.append(sorted(transversal[j].values())) + j += 1 + else: + a.append([list(range(size))]) + j = len(a) - 1 + while a[j] == [list(range(size))]: + j -= 1 + return a[:j + 1] + + +def double_coset_can_rep(dummies, sym, b_S, sgens, S_transversals, g): + r""" + Butler-Portugal algorithm for tensor canonicalization with dummy indices. + + Parameters + ========== + + dummies + list of lists of dummy indices, + one list for each type of index; + the dummy indices are put in order contravariant, covariant + [d0, -d0, d1, -d1, ...]. + + sym + list of the symmetries of the index metric for each type. + + possible symmetries of the metrics + * 0 symmetric + * 1 antisymmetric + * None no symmetry + + b_S + base of a minimal slot symmetry BSGS. + + sgens + generators of the slot symmetry BSGS. + + S_transversals + transversals for the slot BSGS. + + g + permutation representing the tensor. + + Returns + ======= + + Return 0 if the tensor is zero, else return the array form of + the permutation representing the canonical form of the tensor. + + Notes + ===== + + A tensor with dummy indices can be represented in a number + of equivalent ways which typically grows exponentially with + the number of indices. To be able to establish if two tensors + with many indices are equal becomes computationally very slow + in absence of an efficient algorithm. + + The Butler-Portugal algorithm [3] is an efficient algorithm to + put tensors in canonical form, solving the above problem. + + Portugal observed that a tensor can be represented by a permutation, + and that the class of tensors equivalent to it under slot and dummy + symmetries is equivalent to the double coset `D*g*S` + (Note: in this documentation we use the conventions for multiplication + of permutations p, q with (p*q)(i) = p[q[i]] which is opposite + to the one used in the Permutation class) + + Using the algorithm by Butler to find a representative of the + double coset one can find a canonical form for the tensor. + + To see this correspondence, + let `g` be a permutation in array form; a tensor with indices `ind` + (the indices including both the contravariant and the covariant ones) + can be written as + + `t = T(ind[g[0]], \dots, ind[g[n-1]])`, + + where `n = len(ind)`; + `g` has size `n + 2`, the last two indices for the sign of the tensor + (trick introduced in [4]). + + A slot symmetry transformation `s` is a permutation acting on the slots + `t \rightarrow T(ind[(g*s)[0]], \dots, ind[(g*s)[n-1]])` + + A dummy symmetry transformation acts on `ind` + `t \rightarrow T(ind[(d*g)[0]], \dots, ind[(d*g)[n-1]])` + + Being interested only in the transformations of the tensor under + these symmetries, one can represent the tensor by `g`, which transforms + as + + `g -> d*g*s`, so it belongs to the coset `D*g*S`, or in other words + to the set of all permutations allowed by the slot and dummy symmetries. + + Let us explain the conventions by an example. + + Given a tensor `T^{d3 d2 d1}{}_{d1 d2 d3}` with the slot symmetries + `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}` + + `T^{a0 a1 a2 a3 a4 a5} = -T^{a4 a1 a2 a3 a0 a5}` + + and symmetric metric, find the tensor equivalent to it which + is the lowest under the ordering of indices: + lexicographic ordering `d1, d2, d3` and then contravariant + before covariant index; that is the canonical form of the tensor. + + The canonical form is `-T^{d1 d2 d3}{}_{d1 d2 d3}` + obtained using `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}`. + + To convert this problem in the input for this function, + use the following ordering of the index names + (- for covariant for short) `d1, -d1, d2, -d2, d3, -d3` + + `T^{d3 d2 d1}{}_{d1 d2 d3}` corresponds to `g = [4, 2, 0, 1, 3, 5, 6, 7]` + where the last two indices are for the sign + + `sgens = [Permutation(0, 2)(6, 7), Permutation(0, 4)(6, 7)]` + + sgens[0] is the slot symmetry `-(0, 2)` + `T^{a0 a1 a2 a3 a4 a5} = -T^{a2 a1 a0 a3 a4 a5}` + + sgens[1] is the slot symmetry `-(0, 4)` + `T^{a0 a1 a2 a3 a4 a5} = -T^{a4 a1 a2 a3 a0 a5}` + + The dummy symmetry group D is generated by the strong base generators + `[(0, 1), (2, 3), (4, 5), (0, 2)(1, 3), (0, 4)(1, 5)]` + where the first three interchange covariant and contravariant + positions of the same index (d1 <-> -d1) and the last two interchange + the dummy indices themselves (d1 <-> d2). + + The dummy symmetry acts from the left + `d = [1, 0, 2, 3, 4, 5, 6, 7]` exchange `d1 \leftrightarrow -d1` + `T^{d3 d2 d1}{}_{d1 d2 d3} == T^{d3 d2}{}_{d1}{}^{d1}{}_{d2 d3}` + + `g=[4, 2, 0, 1, 3, 5, 6, 7] -> [4, 2, 1, 0, 3, 5, 6, 7] = _af_rmul(d, g)` + which differs from `_af_rmul(g, d)`. + + The slot symmetry acts from the right + `s = [2, 1, 0, 3, 4, 5, 7, 6]` exchanges slots 0 and 2 and changes sign + `T^{d3 d2 d1}{}_{d1 d2 d3} == -T^{d1 d2 d3}{}_{d1 d2 d3}` + + `g=[4,2,0,1,3,5,6,7] -> [0, 2, 4, 1, 3, 5, 7, 6] = _af_rmul(g, s)` + + Example in which the tensor is zero, same slot symmetries as above: + `T^{d2}{}_{d1 d3}{}^{d1 d3}{}_{d2}` + + `= -T^{d3}{}_{d1 d3}{}^{d1 d2}{}_{d2}` under slot symmetry `-(0,4)`; + + `= T_{d3 d1}{}^{d3}{}^{d1 d2}{}_{d2}` under slot symmetry `-(0,2)`; + + `= T^{d3}{}_{d1 d3}{}^{d1 d2}{}_{d2}` symmetric metric; + + `= 0` since two of these lines have tensors differ only for the sign. + + The double coset D*g*S consists of permutations `h = d*g*s` corresponding + to equivalent tensors; if there are two `h` which are the same apart + from the sign, return zero; otherwise + choose as representative the tensor with indices + ordered lexicographically according to `[d1, -d1, d2, -d2, d3, -d3]` + that is ``rep = min(D*g*S) = min([d*g*s for d in D for s in S])`` + + The indices are fixed one by one; first choose the lowest index + for slot 0, then the lowest remaining index for slot 1, etc. + Doing this one obtains a chain of stabilizers + + `S \rightarrow S_{b0} \rightarrow S_{b0,b1} \rightarrow \dots` and + `D \rightarrow D_{p0} \rightarrow D_{p0,p1} \rightarrow \dots` + + where ``[b0, b1, ...] = range(b)`` is a base of the symmetric group; + the strong base `b_S` of S is an ordered sublist of it; + therefore it is sufficient to compute once the + strong base generators of S using the Schreier-Sims algorithm; + the stabilizers of the strong base generators are the + strong base generators of the stabilizer subgroup. + + ``dbase = [p0, p1, ...]`` is not in general in lexicographic order, + so that one must recompute the strong base generators each time; + however this is trivial, there is no need to use the Schreier-Sims + algorithm for D. + + The algorithm keeps a TAB of elements `(s_i, d_i, h_i)` + where `h_i = d_i \times g \times s_i` satisfying `h_i[j] = p_j` for `0 \le j < i` + starting from `s_0 = id, d_0 = id, h_0 = g`. + + The equations `h_0[0] = p_0, h_1[1] = p_1, \dots` are solved in this order, + choosing each time the lowest possible value of p_i + + For `j < i` + `d_i*g*s_i*S_{b_0, \dots, b_{i-1}}*b_j = D_{p_0, \dots, p_{i-1}}*p_j` + so that for dx in `D_{p_0,\dots,p_{i-1}}` and sx in + `S_{base[0], \dots, base[i-1]}` one has `dx*d_i*g*s_i*sx*b_j = p_j` + + Search for dx, sx such that this equation holds for `j = i`; + it can be written as `s_i*sx*b_j = J, dx*d_i*g*J = p_j` + `sx*b_j = s_i**-1*J; sx = trace(s_i**-1, S_{b_0,...,b_{i-1}})` + `dx**-1*p_j = d_i*g*J; dx = trace(d_i*g*J, D_{p_0,...,p_{i-1}})` + + `s_{i+1} = s_i*trace(s_i**-1*J, S_{b_0,...,b_{i-1}})` + `d_{i+1} = trace(d_i*g*J, D_{p_0,...,p_{i-1}})**-1*d_i` + `h_{i+1}*b_i = d_{i+1}*g*s_{i+1}*b_i = p_i` + + `h_n*b_j = p_j` for all j, so that `h_n` is the solution. + + Add the found `(s, d, h)` to TAB1. + + At the end of the iteration sort TAB1 with respect to the `h`; + if there are two consecutive `h` in TAB1 which differ only for the + sign, the tensor is zero, so return 0; + if there are two consecutive `h` which are equal, keep only one. + + Then stabilize the slot generators under `i` and the dummy generators + under `p_i`. + + Assign `TAB = TAB1` at the end of the iteration step. + + At the end `TAB` contains a unique `(s, d, h)`, since all the slots + of the tensor `h` have been fixed to have the minimum value according + to the symmetries. The algorithm returns `h`. + + It is important that the slot BSGS has lexicographic minimal base, + otherwise there is an `i` which does not belong to the slot base + for which `p_i` is fixed by the dummy symmetry only, while `i` + is not invariant from the slot stabilizer, so `p_i` is not in + general the minimal value. + + This algorithm differs slightly from the original algorithm [3]: + the canonical form is minimal lexicographically, and + the BSGS has minimal base under lexicographic order. + Equal tensors `h` are eliminated from TAB. + + + Examples + ======== + + >>> from sympy.combinatorics.permutations import Permutation + >>> from sympy.combinatorics.tensor_can import double_coset_can_rep, get_transversals + >>> gens = [Permutation(x) for x in [[2, 1, 0, 3, 4, 5, 7, 6], [4, 1, 2, 3, 0, 5, 7, 6]]] + >>> base = [0, 2] + >>> g = Permutation([4, 2, 0, 1, 3, 5, 6, 7]) + >>> transversals = get_transversals(base, gens) + >>> double_coset_can_rep([list(range(6))], [0], base, gens, transversals, g) + [0, 1, 2, 3, 4, 5, 7, 6] + + >>> g = Permutation([4, 1, 3, 0, 5, 2, 6, 7]) + >>> double_coset_can_rep([list(range(6))], [0], base, gens, transversals, g) + 0 + """ + size = g.size + g = g.array_form + num_dummies = size - 2 + indices = list(range(num_dummies)) + all_metrics_with_sym = not any(_ is None for _ in sym) + num_types = len(sym) + dumx = dummies[:] + dumx_flat = [] + for dx in dumx: + dumx_flat.extend(dx) + b_S = b_S[:] + sgensx = [h._array_form for h in sgens] + if b_S: + S_transversals = transversal2coset(size, b_S, S_transversals) + # strong generating set for D + dsgsx = [] + for i in range(num_types): + dsgsx.extend(dummy_sgs(dumx[i], sym[i], num_dummies)) + idn = list(range(size)) + # TAB = list of entries (s, d, h) where h = _af_rmuln(d,g,s) + # for short, in the following d*g*s means _af_rmuln(d,g,s) + TAB = [(idn, idn, g)] + for i in range(size - 2): + b = i + testb = b in b_S and sgensx + if testb: + sgensx1 = [_af_new(_) for _ in sgensx] + deltab = _orbit(size, sgensx1, b) + else: + deltab = {b} + # p1 = min(IMAGES) = min(Union D_p*h*deltab for h in TAB) + if all_metrics_with_sym: + md = _min_dummies(dumx, sym, indices) + else: + md = [min(_orbit(size, [_af_new( + ddx) for ddx in dsgsx], ii)) for ii in range(size - 2)] + + p_i = min(min(md[h[x]] for x in deltab) for s, d, h in TAB) + dsgsx1 = [_af_new(_) for _ in dsgsx] + Dxtrav = _orbit_transversal(size, dsgsx1, p_i, False, af=True) \ + if dsgsx else None + if Dxtrav: + Dxtrav = [_af_invert(x) for x in Dxtrav] + # compute the orbit of p_i + for ii in range(num_types): + if p_i in dumx[ii]: + # the orbit is made by all the indices in dum[ii] + if sym[ii] is not None: + deltap = dumx[ii] + else: + # the orbit is made by all the even indices if p_i + # is even, by all the odd indices if p_i is odd + p_i_index = dumx[ii].index(p_i) % 2 + deltap = dumx[ii][p_i_index::2] + break + else: + deltap = [p_i] + TAB1 = [] + while TAB: + s, d, h = TAB.pop() + if min(md[h[x]] for x in deltab) != p_i: + continue + deltab1 = [x for x in deltab if md[h[x]] == p_i] + # NEXT = s*deltab1 intersection (d*g)**-1*deltap + dg = _af_rmul(d, g) + dginv = _af_invert(dg) + sdeltab = [s[x] for x in deltab1] + gdeltap = [dginv[x] for x in deltap] + NEXT = [x for x in sdeltab if x in gdeltap] + # d, s satisfy + # d*g*s*base[i-1] = p_{i-1}; using the stabilizers + # d*g*s*S_{base[0],...,base[i-1]}*base[i-1] = + # D_{p_0,...,p_{i-1}}*p_{i-1} + # so that to find d1, s1 satisfying d1*g*s1*b = p_i + # one can look for dx in D_{p_0,...,p_{i-1}} and + # sx in S_{base[0],...,base[i-1]} + # d1 = dx*d; s1 = s*sx + # d1*g*s1*b = dx*d*g*s*sx*b = p_i + for j in NEXT: + if testb: + # solve s1*b = j with s1 = s*sx for some element sx + # of the stabilizer of ..., base[i-1] + # sx*b = s**-1*j; sx = _trace_S(s, j,...) + # s1 = s*trace_S(s**-1*j,...) + s1 = _trace_S(s, j, b, S_transversals) + if not s1: + continue + else: + s1 = [s[ix] for ix in s1] + else: + s1 = s + # assert s1[b] == j # invariant + # solve d1*g*j = p_i with d1 = dx*d for some element dg + # of the stabilizer of ..., p_{i-1} + # dx**-1*p_i = d*g*j; dx**-1 = trace_D(d*g*j,...) + # d1 = trace_D(d*g*j,...)**-1*d + # to save an inversion in the inner loop; notice we did + # Dxtrav = [perm_af_invert(x) for x in Dxtrav] out of the loop + if Dxtrav: + d1 = _trace_D(dg[j], p_i, Dxtrav) + if not d1: + continue + else: + if p_i != dg[j]: + continue + d1 = idn + assert d1[dg[j]] == p_i # invariant + d1 = [d1[ix] for ix in d] + h1 = [d1[g[ix]] for ix in s1] + # assert h1[b] == p_i # invariant + TAB1.append((s1, d1, h1)) + + # if TAB contains equal permutations, keep only one of them; + # if TAB contains equal permutations up to the sign, return 0 + TAB1.sort(key=lambda x: x[-1]) + prev = [0] * size + while TAB1: + s, d, h = TAB1.pop() + if h[:-2] == prev[:-2]: + if h[-1] != prev[-1]: + return 0 + else: + TAB.append((s, d, h)) + prev = h + + # stabilize the SGS + sgensx = [h for h in sgensx if h[b] == b] + if b in b_S: + b_S.remove(b) + _dumx_remove(dumx, dumx_flat, p_i) + dsgsx = [] + for i in range(num_types): + dsgsx.extend(dummy_sgs(dumx[i], sym[i], num_dummies)) + return TAB[0][-1] + + +def canonical_free(base, gens, g, num_free): + """ + Canonicalization of a tensor with respect to free indices + choosing the minimum with respect to lexicographical ordering + in the free indices. + + Explanation + =========== + + ``base``, ``gens`` BSGS for slot permutation group + ``g`` permutation representing the tensor + ``num_free`` number of free indices + The indices must be ordered with first the free indices + + See explanation in double_coset_can_rep + The algorithm is a variation of the one given in [2]. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy.combinatorics.tensor_can import canonical_free + >>> gens = [[1, 0, 2, 3, 5, 4], [2, 3, 0, 1, 4, 5],[0, 1, 3, 2, 5, 4]] + >>> gens = [Permutation(h) for h in gens] + >>> base = [0, 2] + >>> g = Permutation([2, 1, 0, 3, 4, 5]) + >>> canonical_free(base, gens, g, 4) + [0, 3, 1, 2, 5, 4] + + Consider the product of Riemann tensors + ``T = R^{a}_{d0}^{d1,d2}*R_{d2,d1}^{d0,b}`` + The order of the indices is ``[a, b, d0, -d0, d1, -d1, d2, -d2]`` + The permutation corresponding to the tensor is + ``g = [0, 3, 4, 6, 7, 5, 2, 1, 8, 9]`` + + In particular ``a`` is position ``0``, ``b`` is in position ``9``. + Use the slot symmetries to get `T` is a form which is the minimal + in lexicographic order in the free indices ``a`` and ``b``, e.g. + ``-R^{a}_{d0}^{d1,d2}*R^{b,d0}_{d2,d1}`` corresponding to + ``[0, 3, 4, 6, 1, 2, 7, 5, 9, 8]`` + + >>> from sympy.combinatorics.tensor_can import riemann_bsgs, tensor_gens + >>> base, gens = riemann_bsgs + >>> size, sbase, sgens = tensor_gens(base, gens, [[], []], 0) + >>> g = Permutation([0, 3, 4, 6, 7, 5, 2, 1, 8, 9]) + >>> canonical_free(sbase, [Permutation(h) for h in sgens], g, 2) + [0, 3, 4, 6, 1, 2, 7, 5, 9, 8] + """ + g = g.array_form + size = len(g) + if not base: + return g[:] + + transversals = get_transversals(base, gens) + for x in sorted(g[:-2]): + if x not in base: + base.append(x) + h = g + for transv in transversals: + h_i = [size]*num_free + # find the element s in transversals[i] such that + # _af_rmul(h, s) has its free elements with the lowest position in h + s = None + for sk in transv.values(): + h1 = _af_rmul(h, sk) + hi = [h1.index(ix) for ix in range(num_free)] + if hi < h_i: + h_i = hi + s = sk + if s: + h = _af_rmul(h, s) + return h + + +def _get_map_slots(size, fixed_slots): + res = list(range(size)) + pos = 0 + for i in range(size): + if i in fixed_slots: + continue + res[i] = pos + pos += 1 + return res + + +def _lift_sgens(size, fixed_slots, free, s): + a = [] + j = k = 0 + fd = list(zip(fixed_slots, free)) + fd = [y for x, y in sorted(fd)] + num_free = len(free) + for i in range(size): + if i in fixed_slots: + a.append(fd[k]) + k += 1 + else: + a.append(s[j] + num_free) + j += 1 + return a + + +def canonicalize(g, dummies, msym, *v): + """ + canonicalize tensor formed by tensors + + Parameters + ========== + + g : permutation representing the tensor + + dummies : list representing the dummy indices + it can be a list of dummy indices of the same type + or a list of lists of dummy indices, one list for each + type of index; + the dummy indices must come after the free indices, + and put in order contravariant, covariant + [d0, -d0, d1,-d1,...] + + msym : symmetry of the metric(s) + it can be an integer or a list; + in the first case it is the symmetry of the dummy index metric; + in the second case it is the list of the symmetries of the + index metric for each type + + v : list, (base_i, gens_i, n_i, sym_i) for tensors of type `i` + + base_i, gens_i : BSGS for tensors of this type. + The BSGS should have minimal base under lexicographic ordering; + if not, an attempt is made do get the minimal BSGS; + in case of failure, + canonicalize_naive is used, which is much slower. + + n_i : number of tensors of type `i`. + + sym_i : symmetry under exchange of component tensors of type `i`. + + Both for msym and sym_i the cases are + * None no symmetry + * 0 commuting + * 1 anticommuting + + Returns + ======= + + 0 if the tensor is zero, else return the array form of + the permutation representing the canonical form of the tensor. + + Algorithm + ========= + + First one uses canonical_free to get the minimum tensor under + lexicographic order, using only the slot symmetries. + If the component tensors have not minimal BSGS, it is attempted + to find it; if the attempt fails canonicalize_naive + is used instead. + + Compute the residual slot symmetry keeping fixed the free indices + using tensor_gens(base, gens, list_free_indices, sym). + + Reduce the problem eliminating the free indices. + + Then use double_coset_can_rep and lift back the result reintroducing + the free indices. + + Examples + ======== + + one type of index with commuting metric; + + `A_{a b}` and `B_{a b}` antisymmetric and commuting + + `T = A_{d0 d1} * B^{d0}{}_{d2} * B^{d2 d1}` + + `ord = [d0,-d0,d1,-d1,d2,-d2]` order of the indices + + g = [1, 3, 0, 5, 4, 2, 6, 7] + + `T_c = 0` + + >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, canonicalize, bsgs_direct_product + >>> from sympy.combinatorics import Permutation + >>> base2a, gens2a = get_symmetric_group_sgs(2, 1) + >>> t0 = (base2a, gens2a, 1, 0) + >>> t1 = (base2a, gens2a, 2, 0) + >>> g = Permutation([1, 3, 0, 5, 4, 2, 6, 7]) + >>> canonicalize(g, range(6), 0, t0, t1) + 0 + + same as above, but with `B_{a b}` anticommuting + + `T_c = -A^{d0 d1} * B_{d0}{}^{d2} * B_{d1 d2}` + + can = [0,2,1,4,3,5,7,6] + + >>> t1 = (base2a, gens2a, 2, 1) + >>> canonicalize(g, range(6), 0, t0, t1) + [0, 2, 1, 4, 3, 5, 7, 6] + + two types of indices `[a,b,c,d,e,f]` and `[m,n]`, in this order, + both with commuting metric + + `f^{a b c}` antisymmetric, commuting + + `A_{m a}` no symmetry, commuting + + `T = f^c{}_{d a} * f^f{}_{e b} * A_m{}^d * A^{m b} * A_n{}^a * A^{n e}` + + ord = [c,f,a,-a,b,-b,d,-d,e,-e,m,-m,n,-n] + + g = [0,7,3, 1,9,5, 11,6, 10,4, 13,2, 12,8, 14,15] + + The canonical tensor is + `T_c = -f^{c a b} * f^{f d e} * A^m{}_a * A_{m d} * A^n{}_b * A_{n e}` + + can = [0,2,4, 1,6,8, 10,3, 11,7, 12,5, 13,9, 15,14] + + >>> base_f, gens_f = get_symmetric_group_sgs(3, 1) + >>> base1, gens1 = get_symmetric_group_sgs(1) + >>> base_A, gens_A = bsgs_direct_product(base1, gens1, base1, gens1) + >>> t0 = (base_f, gens_f, 2, 0) + >>> t1 = (base_A, gens_A, 4, 0) + >>> dummies = [range(2, 10), range(10, 14)] + >>> g = Permutation([0, 7, 3, 1, 9, 5, 11, 6, 10, 4, 13, 2, 12, 8, 14, 15]) + >>> canonicalize(g, dummies, [0, 0], t0, t1) + [0, 2, 4, 1, 6, 8, 10, 3, 11, 7, 12, 5, 13, 9, 15, 14] + """ + from sympy.combinatorics.testutil import canonicalize_naive + if not isinstance(msym, list): + if msym not in (0, 1, None): + raise ValueError('msym must be 0, 1 or None') + num_types = 1 + else: + num_types = len(msym) + if not all(msymx in (0, 1, None) for msymx in msym): + raise ValueError('msym entries must be 0, 1 or None') + if len(dummies) != num_types: + raise ValueError( + 'dummies and msym must have the same number of elements') + size = g.size + num_tensors = 0 + v1 = [] + for base_i, gens_i, n_i, sym_i in v: + # check that the BSGS is minimal; + # this property is used in double_coset_can_rep; + # if it is not minimal use canonicalize_naive + if not _is_minimal_bsgs(base_i, gens_i): + mbsgs = get_minimal_bsgs(base_i, gens_i) + if not mbsgs: + can = canonicalize_naive(g, dummies, msym, *v) + return can + base_i, gens_i = mbsgs + v1.append((base_i, gens_i, [[]] * n_i, sym_i)) + num_tensors += n_i + + if num_types == 1 and not isinstance(msym, list): + dummies = [dummies] + msym = [msym] + flat_dummies = [] + for dumx in dummies: + flat_dummies.extend(dumx) + + if flat_dummies and flat_dummies != list(range(flat_dummies[0], flat_dummies[-1] + 1)): + raise ValueError('dummies is not valid') + + # slot symmetry of the tensor + size1, sbase, sgens = gens_products(*v1) + if size != size1: + raise ValueError( + 'g has size %d, generators have size %d' % (size, size1)) + free = [i for i in range(size - 2) if i not in flat_dummies] + num_free = len(free) + + # g1 minimal tensor under slot symmetry + g1 = canonical_free(sbase, sgens, g, num_free) + if not flat_dummies: + return g1 + # save the sign of g1 + sign = 0 if g1[-1] == size - 1 else 1 + + # the free indices are kept fixed. + # Determine free_i, the list of slots of tensors which are fixed + # since they are occupied by free indices, which are fixed. + start = 0 + for i, (base_i, gens_i, n_i, sym_i) in enumerate(v): + free_i = [] + len_tens = gens_i[0].size - 2 + # for each component tensor get a list od fixed islots + for j in range(n_i): + # get the elements corresponding to the component tensor + h = g1[start:(start + len_tens)] + fr = [] + # get the positions of the fixed elements in h + for k in free: + if k in h: + fr.append(h.index(k)) + free_i.append(fr) + start += len_tens + v1[i] = (base_i, gens_i, free_i, sym_i) + # BSGS of the tensor with fixed free indices + # if tensor_gens fails in gens_product, use canonicalize_naive + size, sbase, sgens = gens_products(*v1) + + # reduce the permutations getting rid of the free indices + pos_free = [g1.index(x) for x in range(num_free)] + size_red = size - num_free + g1_red = [x - num_free for x in g1 if x in flat_dummies] + if sign: + g1_red.extend([size_red - 1, size_red - 2]) + else: + g1_red.extend([size_red - 2, size_red - 1]) + map_slots = _get_map_slots(size, pos_free) + sbase_red = [map_slots[i] for i in sbase if i not in pos_free] + sgens_red = [_af_new([map_slots[i] for i in y._array_form if i not in pos_free]) for y in sgens] + dummies_red = [[x - num_free for x in y] for y in dummies] + transv_red = get_transversals(sbase_red, sgens_red) + g1_red = _af_new(g1_red) + g2 = double_coset_can_rep( + dummies_red, msym, sbase_red, sgens_red, transv_red, g1_red) + if g2 == 0: + return 0 + # lift to the case with the free indices + g3 = _lift_sgens(size, pos_free, free, g2) + return g3 + + +def perm_af_direct_product(gens1, gens2, signed=True): + """ + Direct products of the generators gens1 and gens2. + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import perm_af_direct_product + >>> gens1 = [[1, 0, 2, 3], [0, 1, 3, 2]] + >>> gens2 = [[1, 0]] + >>> perm_af_direct_product(gens1, gens2, False) + [[1, 0, 2, 3, 4, 5], [0, 1, 3, 2, 4, 5], [0, 1, 2, 3, 5, 4]] + >>> gens1 = [[1, 0, 2, 3, 5, 4], [0, 1, 3, 2, 4, 5]] + >>> gens2 = [[1, 0, 2, 3]] + >>> perm_af_direct_product(gens1, gens2, True) + [[1, 0, 2, 3, 4, 5, 7, 6], [0, 1, 3, 2, 4, 5, 6, 7], [0, 1, 2, 3, 5, 4, 6, 7]] + """ + gens1 = [list(x) for x in gens1] + gens2 = [list(x) for x in gens2] + s = 2 if signed else 0 + n1 = len(gens1[0]) - s + n2 = len(gens2[0]) - s + start = list(range(n1)) + end = list(range(n1, n1 + n2)) + if signed: + gens1 = [gen[:-2] + end + [gen[-2] + n2, gen[-1] + n2] + for gen in gens1] + gens2 = [start + [x + n1 for x in gen] for gen in gens2] + else: + gens1 = [gen + end for gen in gens1] + gens2 = [start + [x + n1 for x in gen] for gen in gens2] + + res = gens1 + gens2 + + return res + + +def bsgs_direct_product(base1, gens1, base2, gens2, signed=True): + """ + Direct product of two BSGS. + + Parameters + ========== + + base1 : base of the first BSGS. + + gens1 : strong generating sequence of the first BSGS. + + base2, gens2 : similarly for the second BSGS. + + signed : flag for signed permutations. + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import (get_symmetric_group_sgs, bsgs_direct_product) + >>> base1, gens1 = get_symmetric_group_sgs(1) + >>> base2, gens2 = get_symmetric_group_sgs(2) + >>> bsgs_direct_product(base1, gens1, base2, gens2) + ([1], [(4)(1 2)]) + """ + s = 2 if signed else 0 + n1 = gens1[0].size - s + base = list(base1) + base += [x + n1 for x in base2] + gens1 = [h._array_form for h in gens1] + gens2 = [h._array_form for h in gens2] + gens = perm_af_direct_product(gens1, gens2, signed) + size = len(gens[0]) + id_af = list(range(size)) + gens = [h for h in gens if h != id_af] + if not gens: + gens = [id_af] + return base, [_af_new(h) for h in gens] + + +def get_symmetric_group_sgs(n, antisym=False): + """ + Return base, gens of the minimal BSGS for (anti)symmetric tensor + + Parameters + ========== + + n : rank of the tensor + antisym : bool + ``antisym = False`` symmetric tensor + ``antisym = True`` antisymmetric tensor + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs + >>> get_symmetric_group_sgs(3) + ([0, 1], [(4)(0 1), (4)(1 2)]) + """ + if n == 1: + return [], [_af_new(list(range(3)))] + gens = [Permutation(n - 1)(i, i + 1)._array_form for i in range(n - 1)] + if antisym == 0: + gens = [x + [n, n + 1] for x in gens] + else: + gens = [x + [n + 1, n] for x in gens] + base = list(range(n - 1)) + return base, [_af_new(h) for h in gens] + +riemann_bsgs = [0, 2], [Permutation(0, 1)(4, 5), Permutation(2, 3)(4, 5), + Permutation(5)(0, 2)(1, 3)] + + +def get_transversals(base, gens): + """ + Return transversals for the group with BSGS base, gens + """ + if not base: + return [] + stabs = _distribute_gens_by_base(base, gens) + orbits, transversals = _orbits_transversals_from_bsgs(base, stabs) + transversals = [{x: h._array_form for x, h in y.items()} for y in + transversals] + return transversals + + +def _is_minimal_bsgs(base, gens): + """ + Check if the BSGS has minimal base under lexigographic order. + + base, gens BSGS + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy.combinatorics.tensor_can import riemann_bsgs, _is_minimal_bsgs + >>> _is_minimal_bsgs(*riemann_bsgs) + True + >>> riemann_bsgs1 = ([2, 0], ([Permutation(5)(0, 1)(4, 5), Permutation(5)(0, 2)(1, 3)])) + >>> _is_minimal_bsgs(*riemann_bsgs1) + False + """ + base1 = [] + sgs1 = gens[:] + size = gens[0].size + for i in range(size): + if not all(h._array_form[i] == i for h in sgs1): + base1.append(i) + sgs1 = [h for h in sgs1 if h._array_form[i] == i] + return base1 == base + + +def get_minimal_bsgs(base, gens): + """ + Compute a minimal GSGS + + base, gens BSGS + + If base, gens is a minimal BSGS return it; else return a minimal BSGS + if it fails in finding one, it returns None + + TODO: use baseswap in the case in which if it fails in finding a + minimal BSGS + + Examples + ======== + + >>> from sympy.combinatorics import Permutation + >>> from sympy.combinatorics.tensor_can import get_minimal_bsgs + >>> riemann_bsgs1 = ([2, 0], ([Permutation(5)(0, 1)(4, 5), Permutation(5)(0, 2)(1, 3)])) + >>> get_minimal_bsgs(*riemann_bsgs1) + ([0, 2], [(0 1)(4 5), (5)(0 2)(1 3), (2 3)(4 5)]) + """ + G = PermutationGroup(gens) + base, gens = G.schreier_sims_incremental() + if not _is_minimal_bsgs(base, gens): + return None + return base, gens + + +def tensor_gens(base, gens, list_free_indices, sym=0): + """ + Returns size, res_base, res_gens BSGS for n tensors of the + same type. + + Explanation + =========== + + base, gens BSGS for tensors of this type + list_free_indices list of the slots occupied by fixed indices + for each of the tensors + + sym symmetry under commutation of two tensors + sym None no symmetry + sym 0 commuting + sym 1 anticommuting + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import tensor_gens, get_symmetric_group_sgs + + two symmetric tensors with 3 indices without free indices + + >>> base, gens = get_symmetric_group_sgs(3) + >>> tensor_gens(base, gens, [[], []]) + (8, [0, 1, 3, 4], [(7)(0 1), (7)(1 2), (7)(3 4), (7)(4 5), (7)(0 3)(1 4)(2 5)]) + + two symmetric tensors with 3 indices with free indices in slot 1 and 0 + + >>> tensor_gens(base, gens, [[1], [0]]) + (8, [0, 4], [(7)(0 2), (7)(4 5)]) + + four symmetric tensors with 3 indices, two of which with free indices + + """ + def _get_bsgs(G, base, gens, free_indices): + """ + return the BSGS for G.pointwise_stabilizer(free_indices) + """ + if not free_indices: + return base[:], gens[:] + else: + H = G.pointwise_stabilizer(free_indices) + base, sgs = H.schreier_sims_incremental() + return base, sgs + + # if not base there is no slot symmetry for the component tensors + # if list_free_indices.count([]) < 2 there is no commutation symmetry + # so there is no resulting slot symmetry + if not base and list_free_indices.count([]) < 2: + n = len(list_free_indices) + size = gens[0].size + size = n * (size - 2) + 2 + return size, [], [_af_new(list(range(size)))] + + # if any(list_free_indices) one needs to compute the pointwise + # stabilizer, so G is needed + if any(list_free_indices): + G = PermutationGroup(gens) + else: + G = None + + # no_free list of lists of indices for component tensors without fixed + # indices + no_free = [] + size = gens[0].size + id_af = list(range(size)) + num_indices = size - 2 + if not list_free_indices[0]: + no_free.append(list(range(num_indices))) + res_base, res_gens = _get_bsgs(G, base, gens, list_free_indices[0]) + for i in range(1, len(list_free_indices)): + base1, gens1 = _get_bsgs(G, base, gens, list_free_indices[i]) + res_base, res_gens = bsgs_direct_product(res_base, res_gens, + base1, gens1, 1) + if not list_free_indices[i]: + no_free.append(list(range(size - 2, size - 2 + num_indices))) + size += num_indices + nr = size - 2 + res_gens = [h for h in res_gens if h._array_form != id_af] + # if sym there are no commuting tensors stop here + if sym is None or not no_free: + if not res_gens: + res_gens = [_af_new(id_af)] + return size, res_base, res_gens + + # if the component tensors have moinimal BSGS, so is their direct + # product P; the slot symmetry group is S = P*C, where C is the group + # to (anti)commute the component tensors with no free indices + # a stabilizer has the property S_i = P_i*C_i; + # the BSGS of P*C has SGS_P + SGS_C and the base is + # the ordered union of the bases of P and C. + # If P has minimal BSGS, so has S with this base. + base_comm = [] + for i in range(len(no_free) - 1): + ind1 = no_free[i] + ind2 = no_free[i + 1] + a = list(range(ind1[0])) + a.extend(ind2) + a.extend(ind1) + base_comm.append(ind1[0]) + a.extend(list(range(ind2[-1] + 1, nr))) + if sym == 0: + a.extend([nr, nr + 1]) + else: + a.extend([nr + 1, nr]) + res_gens.append(_af_new(a)) + res_base = list(res_base) + # each base is ordered; order the union of the two bases + for i in base_comm: + if i not in res_base: + res_base.append(i) + res_base.sort() + if not res_gens: + res_gens = [_af_new(id_af)] + + return size, res_base, res_gens + + +def gens_products(*v): + """ + Returns size, res_base, res_gens BSGS for n tensors of different types. + + Explanation + =========== + + v is a sequence of (base_i, gens_i, free_i, sym_i) + where + base_i, gens_i BSGS of tensor of type `i` + free_i list of the fixed slots for each of the tensors + of type `i`; if there are `n_i` tensors of type `i` + and none of them have fixed slots, `free = [[]]*n_i` + sym 0 (1) if the tensors of type `i` (anti)commute among themselves + + Examples + ======== + + >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, gens_products + >>> base, gens = get_symmetric_group_sgs(2) + >>> gens_products((base, gens, [[], []], 0)) + (6, [0, 2], [(5)(0 1), (5)(2 3), (5)(0 2)(1 3)]) + >>> gens_products((base, gens, [[1], []], 0)) + (6, [2], [(5)(2 3)]) + """ + res_size, res_base, res_gens = tensor_gens(*v[0]) + for i in range(1, len(v)): + size, base, gens = tensor_gens(*v[i]) + res_base, res_gens = bsgs_direct_product(res_base, res_gens, base, + gens, 1) + res_size = res_gens[0].size + id_af = list(range(res_size)) + res_gens = [h for h in res_gens if h != id_af] + if not res_gens: + res_gens = [id_af] + return res_size, res_base, res_gens diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/__init__.py 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sympy.combinatorics.coset_table import (CosetTable, + coset_enumeration_r, coset_enumeration_c) +from sympy.combinatorics.coset_table import modified_coset_enumeration_r +from sympy.combinatorics.free_groups import free_group + +from sympy.testing.pytest import slow + +""" +References +========== + +[1] Holt, D., Eick, B., O'Brien, E. +"Handbook of Computational Group Theory" + +[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson +Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490. +"Implementation and Analysis of the Todd-Coxeter Algorithm" + +""" + +def test_scan_1(): + # Example 5.1 from [1] + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + c = CosetTable(f, [x]) + + c.scan_and_fill(0, x) + assert c.table == [[0, 0, None, None]] + assert c.p == [0] + assert c.n == 1 + assert c.omega == [0] + + c.scan_and_fill(0, x**3) + assert c.table == [[0, 0, None, None]] + assert c.p == [0] + assert c.n == 1 + assert c.omega == [0] + + c.scan_and_fill(0, y**3) + assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [None, None, 0, 1]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(0, x**-1*y**-1*x*y) + assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [2, 2, 0, 1]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, x**3) + assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \ + [4, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(1, y**3) + assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \ + [4, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(1, x**-1*y**-1*x*y) + assert c.table == [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1], \ + [None, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 1, 1] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + # Example 5.2 from [1] + f = FpGroup(F, [x**2, y**3, (x*y)**3]) + c = CosetTable(f, [x*y]) + + c.scan_and_fill(0, x*y) + assert c.table == [[1, None, None, 1], [None, 0, 0, None]] + assert c.p == [0, 1] + assert c.n == 2 + assert c.omega == [0, 1] + + c.scan_and_fill(0, x**2) + assert c.table == [[1, 1, None, 1], [0, 0, 0, None]] + assert c.p == [0, 1] + assert c.n == 2 + assert c.omega == [0, 1] + + c.scan_and_fill(0, y**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(0, (x*y)**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, x**2) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, y**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, (x*y)**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 4, 1, 0], [None, 2, 4, None], [2, None, None, 3]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(2, x**2) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 3, 1, 0], [2, 2, 3, 3], [2, None, None, 3]] + assert c.p == [0, 1, 2, 3, 3] + assert c.n == 4 + assert c.omega == [0, 1, 2, 3] + + +@slow +def test_coset_enumeration(): + # this test function contains the combined tests for the two strategies + # i.e. HLT and Felsch strategies. + + # Example 5.1 from [1] + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + C_r = coset_enumeration_r(f, [x]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(f, [x]) + C_c.compress(); C_c.standardize() + table1 = [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]] + assert C_r.table == table1 + assert C_c.table == table1 + + # E1 from [2] Pg. 474 + F, r, s, t = free_group("r, s, t") + E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2]) + C_r = coset_enumeration_r(E1, []) + C_r.compress() + C_c = coset_enumeration_c(E1, []) + C_c.compress() + table2 = [[0, 0, 0, 0, 0, 0]] + assert C_r.table == table2 + # test for issue #11449 + assert C_c.table == table2 + + # Cox group from [2] Pg. 474 + F, a, b = free_group("a, b") + Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5]) + C_r = coset_enumeration_r(Cox, [a]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(Cox, [a]) + C_c.compress(); C_c.standardize() + table3 = [[0, 0, 1, 2], + [2, 3, 4, 0], + [5, 1, 0, 6], + [1, 7, 8, 9], + [9, 10, 11, 1], + [12, 2, 9, 13], + [14, 9, 2, 11], + [3, 12, 15, 16], + [16, 17, 18, 3], + [6, 4, 3, 5], + [4, 19, 20, 21], + [21, 22, 6, 4], + [7, 5, 23, 24], + [25, 23, 5, 18], + [19, 6, 22, 26], + [24, 27, 28, 7], + [29, 8, 7, 30], + [8, 31, 32, 33], + [33, 34, 13, 8], + [10, 14, 35, 35], + [35, 36, 37, 10], + [30, 11, 10, 29], + [11, 38, 39, 14], + [13, 39, 38, 12], + [40, 15, 12, 41], + [42, 13, 34, 43], + [44, 35, 14, 45], + [15, 46, 47, 34], + [34, 48, 49, 15], + [50, 16, 21, 51], + [52, 21, 16, 49], + [17, 50, 53, 54], + [54, 55, 56, 17], + [41, 18, 17, 40], + [18, 28, 27, 25], + [26, 20, 19, 19], + [20, 57, 58, 59], + [59, 60, 51, 20], + [22, 52, 61, 23], + [23, 62, 63, 22], + [64, 24, 33, 65], + [48, 33, 24, 61], + [62, 25, 54, 66], + [67, 54, 25, 68], + [57, 26, 59, 69], + [70, 59, 26, 63], + [27, 64, 71, 72], + [72, 73, 68, 27], + [28, 41, 74, 75], + [75, 76, 30, 28], + [31, 29, 77, 78], + [79, 77, 29, 37], + [38, 30, 76, 80], + [78, 81, 82, 31], + [43, 32, 31, 42], + [32, 83, 84, 85], + [85, 86, 65, 32], + [36, 44, 87, 88], + [88, 89, 90, 36], + [45, 37, 36, 44], + [37, 82, 81, 79], + [80, 74, 41, 38], + [39, 42, 91, 92], + [92, 93, 45, 39], + [46, 40, 94, 95], + [96, 94, 40, 56], + [97, 91, 42, 82], + [83, 43, 98, 99], + [100, 98, 43, 47], + [101, 87, 44, 90], + [82, 45, 93, 97], + [95, 102, 103, 46], + [104, 47, 46, 105], + [47, 106, 107, 100], + [61, 108, 109, 48], + [105, 49, 48, 104], + [49, 110, 111, 52], + [51, 111, 110, 50], + [112, 53, 50, 113], + [114, 51, 60, 115], + [116, 61, 52, 117], + [53, 118, 119, 60], + [60, 70, 66, 53], + [55, 67, 120, 121], + [121, 122, 123, 55], + [113, 56, 55, 112], + [56, 103, 102, 96], + [69, 124, 125, 57], + [115, 58, 57, 114], + [58, 126, 127, 128], + [128, 128, 69, 58], + [66, 129, 130, 62], + [117, 63, 62, 116], + [63, 125, 124, 70], + [65, 109, 108, 64], + [131, 71, 64, 132], + [133, 65, 86, 134], + [135, 66, 70, 136], + [68, 130, 129, 67], + [137, 120, 67, 138], + [132, 68, 73, 131], + [139, 69, 128, 140], + [71, 141, 142, 86], + [86, 143, 144, 71], + [145, 72, 75, 146], + [147, 75, 72, 144], + [73, 145, 148, 120], + [120, 149, 150, 73], + [74, 151, 152, 94], + [94, 153, 146, 74], + [76, 147, 154, 77], + [77, 155, 156, 76], + [157, 78, 85, 158], + [143, 85, 78, 154], + [155, 79, 88, 159], + [160, 88, 79, 161], + [151, 80, 92, 162], + [163, 92, 80, 156], + [81, 157, 164, 165], + [165, 166, 161, 81], + [99, 107, 106, 83], + [134, 84, 83, 133], + [84, 167, 168, 169], + [169, 170, 158, 84], + [87, 171, 172, 93], + [93, 163, 159, 87], + [89, 160, 173, 174], + [174, 175, 176, 89], + [90, 90, 89, 101], + [91, 177, 178, 98], + [98, 179, 162, 91], + [180, 95, 100, 181], + [179, 100, 95, 152], + [153, 96, 121, 148], + [182, 121, 96, 183], + [177, 97, 165, 184], + [185, 165, 97, 172], + [186, 99, 169, 187], + [188, 169, 99, 178], + [171, 101, 174, 189], + [190, 174, 101, 176], + [102, 180, 191, 192], + [192, 193, 183, 102], + [103, 113, 194, 195], + [195, 196, 105, 103], + [106, 104, 197, 198], + [199, 197, 104, 109], + [110, 105, 196, 200], + [198, 201, 133, 106], + [107, 186, 202, 203], + [203, 204, 181, 107], + [108, 116, 205, 206], + [206, 207, 132, 108], + [109, 133, 201, 199], + [200, 194, 113, 110], + [111, 114, 208, 209], + [209, 210, 117, 111], + [118, 112, 211, 212], + [213, 211, 112, 123], + [214, 208, 114, 125], + [126, 115, 215, 216], + [217, 215, 115, 119], + [218, 205, 116, 130], + [125, 117, 210, 214], + [212, 219, 220, 118], + [136, 119, 118, 135], + [119, 221, 222, 217], + [122, 182, 223, 224], + [224, 225, 226, 122], + [138, 123, 122, 137], + [123, 220, 219, 213], + [124, 139, 227, 228], + [228, 229, 136, 124], + [216, 222, 221, 126], + [140, 127, 126, 139], + [127, 230, 231, 232], + [232, 233, 140, 127], + [129, 135, 234, 235], + [235, 236, 138, 129], + [130, 132, 207, 218], + [141, 131, 237, 238], + [239, 237, 131, 150], + [167, 134, 240, 241], + [242, 240, 134, 142], + [243, 234, 135, 220], + [221, 136, 229, 244], + [149, 137, 245, 246], + [247, 245, 137, 226], + [220, 138, 236, 243], + [244, 227, 139, 221], + [230, 140, 233, 248], + [238, 249, 250, 141], + [251, 142, 141, 252], + [142, 253, 254, 242], + [154, 255, 256, 143], + [252, 144, 143, 251], + [144, 257, 258, 147], + [146, 258, 257, 145], + [259, 148, 145, 260], + [261, 146, 153, 262], + [263, 154, 147, 264], + [148, 265, 266, 153], + [246, 267, 268, 149], + [260, 150, 149, 259], + [150, 250, 249, 239], + [162, 269, 270, 151], + [262, 152, 151, 261], + [152, 271, 272, 179], + [159, 273, 274, 155], + [264, 156, 155, 263], + [156, 270, 269, 163], + [158, 256, 255, 157], + [275, 164, 157, 276], + [277, 158, 170, 278], + [279, 159, 163, 280], + [161, 274, 273, 160], + [281, 173, 160, 282], + [276, 161, 166, 275], + [283, 162, 179, 284], + [164, 285, 286, 170], + [170, 188, 184, 164], + [166, 185, 189, 173], + [173, 287, 288, 166], + [241, 254, 253, 167], + [278, 168, 167, 277], + [168, 289, 290, 291], + [291, 292, 187, 168], + [189, 293, 294, 171], + [280, 172, 171, 279], + [172, 295, 296, 185], + [175, 190, 297, 297], + [297, 298, 299, 175], + [282, 176, 175, 281], + [176, 294, 293, 190], + [184, 296, 295, 177], + [284, 178, 177, 283], + [178, 300, 301, 188], + [181, 272, 271, 180], + [302, 191, 180, 303], + [304, 181, 204, 305], + [183, 266, 265, 182], + [306, 223, 182, 307], + [303, 183, 193, 302], + [308, 184, 188, 309], + [310, 189, 185, 311], + [187, 301, 300, 186], + [305, 202, 186, 304], + [312, 187, 292, 313], + [314, 297, 190, 315], + [191, 316, 317, 204], + [204, 318, 319, 191], + [320, 192, 195, 321], + [322, 195, 192, 319], + [193, 320, 323, 223], + [223, 324, 325, 193], + [194, 326, 327, 211], + [211, 328, 321, 194], + [196, 322, 329, 197], + [197, 330, 331, 196], + [332, 198, 203, 333], + [318, 203, 198, 329], + [330, 199, 206, 334], + [335, 206, 199, 336], + [326, 200, 209, 337], + [338, 209, 200, 331], + [201, 332, 339, 240], + [240, 340, 336, 201], + [202, 341, 342, 292], + [292, 343, 333, 202], + [205, 344, 345, 210], + [210, 338, 334, 205], + [207, 335, 346, 237], + [237, 347, 348, 207], + [208, 349, 350, 215], + [215, 351, 337, 208], + [352, 212, 217, 353], + [351, 217, 212, 327], + [328, 213, 224, 323], + [354, 224, 213, 355], + [349, 214, 228, 356], + [357, 228, 214, 345], + [358, 216, 232, 359], + [360, 232, 216, 350], + [344, 218, 235, 361], + [362, 235, 218, 348], + [219, 352, 363, 364], + [364, 365, 355, 219], + [222, 358, 366, 367], + [367, 368, 353, 222], + [225, 354, 369, 370], + [370, 371, 372, 225], + [307, 226, 225, 306], + [226, 268, 267, 247], + [227, 373, 374, 233], + [233, 360, 356, 227], + [229, 357, 361, 234], + [234, 375, 376, 229], + [248, 231, 230, 230], + [231, 377, 378, 379], + [379, 380, 359, 231], + [236, 362, 381, 245], + [245, 382, 383, 236], + [384, 238, 242, 385], + [340, 242, 238, 346], + [347, 239, 246, 381], + [386, 246, 239, 387], + [388, 241, 291, 389], + [343, 291, 241, 339], + [375, 243, 364, 390], + [391, 364, 243, 383], + [373, 244, 367, 392], + [393, 367, 244, 376], + [382, 247, 370, 394], + [395, 370, 247, 396], + [377, 248, 379, 397], + [398, 379, 248, 374], + [249, 384, 399, 400], + [400, 401, 387, 249], + [250, 260, 402, 403], + [403, 404, 252, 250], + [253, 251, 405, 406], + [407, 405, 251, 256], + [257, 252, 404, 408], + [406, 409, 277, 253], + [254, 388, 410, 411], + [411, 412, 385, 254], + [255, 263, 413, 414], + [414, 415, 276, 255], + [256, 277, 409, 407], + [408, 402, 260, 257], + [258, 261, 416, 417], + [417, 418, 264, 258], + [265, 259, 419, 420], + [421, 419, 259, 268], + [422, 416, 261, 270], + [271, 262, 423, 424], + [425, 423, 262, 266], + [426, 413, 263, 274], + [270, 264, 418, 422], + [420, 427, 307, 265], + [266, 303, 428, 425], + [267, 386, 429, 430], + [430, 431, 396, 267], + [268, 307, 427, 421], + [269, 283, 432, 433], + [433, 434, 280, 269], + [424, 428, 303, 271], + [272, 304, 435, 436], + [436, 437, 284, 272], + [273, 279, 438, 439], + [439, 440, 282, 273], + [274, 276, 415, 426], + [285, 275, 441, 442], + [443, 441, 275, 288], + [289, 278, 444, 445], + [446, 444, 278, 286], + [447, 438, 279, 294], + [295, 280, 434, 448], + [287, 281, 449, 450], + [451, 449, 281, 299], + [294, 282, 440, 447], + [448, 432, 283, 295], + [300, 284, 437, 452], + [442, 453, 454, 285], + [309, 286, 285, 308], + [286, 455, 456, 446], + [450, 457, 458, 287], + [311, 288, 287, 310], + [288, 454, 453, 443], + [445, 456, 455, 289], + [313, 290, 289, 312], + [290, 459, 460, 461], + [461, 462, 389, 290], + [293, 310, 463, 464], + [464, 465, 315, 293], + [296, 308, 466, 467], + [467, 468, 311, 296], + [298, 314, 469, 470], + [470, 471, 472, 298], + [315, 299, 298, 314], + [299, 458, 457, 451], + [452, 435, 304, 300], + [301, 312, 473, 474], + [474, 475, 309, 301], + [316, 302, 476, 477], + [478, 476, 302, 325], + [341, 305, 479, 480], + [481, 479, 305, 317], + [324, 306, 482, 483], + [484, 482, 306, 372], + [485, 466, 308, 454], + [455, 309, 475, 486], + [487, 463, 310, 458], + [454, 311, 468, 485], + [486, 473, 312, 455], + [459, 313, 488, 489], + [490, 488, 313, 342], + [491, 469, 314, 472], + [458, 315, 465, 487], + [477, 492, 485, 316], + [463, 317, 316, 468], + [317, 487, 493, 481], + [329, 447, 464, 318], + [468, 319, 318, 463], + [319, 467, 448, 322], + [321, 448, 467, 320], + [475, 323, 320, 466], + [432, 321, 328, 437], + [438, 329, 322, 434], + [323, 474, 452, 328], + [483, 494, 486, 324], + [466, 325, 324, 475], + [325, 485, 492, 478], + [337, 422, 433, 326], + [437, 327, 326, 432], + [327, 436, 424, 351], + [334, 426, 439, 330], + [434, 331, 330, 438], + [331, 433, 422, 338], + [333, 464, 447, 332], + [449, 339, 332, 440], + [465, 333, 343, 469], + [413, 334, 338, 418], + [336, 439, 426, 335], + [441, 346, 335, 415], + [440, 336, 340, 449], + [416, 337, 351, 423], + [339, 451, 470, 343], + [346, 443, 450, 340], + [480, 493, 487, 341], + [469, 342, 341, 465], + [342, 491, 495, 490], + [361, 407, 414, 344], + [418, 345, 344, 413], + [345, 417, 408, 357], + [381, 446, 442, 347], + [415, 348, 347, 441], + [348, 414, 407, 362], + [356, 408, 417, 349], + [423, 350, 349, 416], + [350, 425, 420, 360], + [353, 424, 436, 352], + [479, 363, 352, 435], + [428, 353, 368, 476], + [355, 452, 474, 354], + [488, 369, 354, 473], + [435, 355, 365, 479], + [402, 356, 360, 419], + [405, 361, 357, 404], + [359, 420, 425, 358], + [476, 366, 358, 428], + [427, 359, 380, 482], + [444, 381, 362, 409], + [363, 481, 477, 368], + [368, 393, 390, 363], + [365, 391, 394, 369], + [369, 490, 480, 365], + [366, 478, 483, 380], + [380, 398, 392, 366], + [371, 395, 496, 497], + [497, 498, 489, 371], + [473, 372, 371, 488], + [372, 486, 494, 484], + [392, 400, 403, 373], + [419, 374, 373, 402], + [374, 421, 430, 398], + [390, 411, 406, 375], + [404, 376, 375, 405], + [376, 403, 400, 393], + [397, 430, 421, 377], + [482, 378, 377, 427], + [378, 484, 497, 499], + [499, 499, 397, 378], + [394, 461, 445, 382], + [409, 383, 382, 444], + [383, 406, 411, 391], + [385, 450, 443, 384], + [492, 399, 384, 453], + [457, 385, 412, 493], + [387, 442, 446, 386], + [494, 429, 386, 456], + [453, 387, 401, 492], + [389, 470, 451, 388], + [493, 410, 388, 457], + [471, 389, 462, 495], + [412, 390, 393, 399], + [462, 394, 391, 410], + [401, 392, 398, 429], + [396, 445, 461, 395], + [498, 496, 395, 460], + [456, 396, 431, 494], + [431, 397, 499, 496], + [399, 477, 481, 412], + [429, 483, 478, 401], + [410, 480, 490, 462], + [496, 497, 484, 431], + [489, 495, 491, 459], + [495, 460, 459, 471], + [460, 489, 498, 498], + [472, 472, 471, 491]] + + assert C_r.table == table3 + assert C_c.table == table3 + + # Group denoted by B2,4 from [2] Pg. 474 + F, a, b = free_group("a, b") + B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \ + (a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4]) + C_r = coset_enumeration_r(B_2_4, [a]) + C_c = coset_enumeration_c(B_2_4, [a]) + index_r = 0 + for i in range(len(C_r.p)): + if C_r.p[i] == i: + index_r += 1 + assert index_r == 1024 + + index_c = 0 + for i in range(len(C_c.p)): + if C_c.p[i] == i: + index_c += 1 + assert index_c == 1024 + + # trivial Macdonald group G(2,2) from [2] Pg. 480 + M = FpGroup(F, [b**-1*a**-1*b*a*b**-1*a*b*a**-2, a**-1*b**-1*a*b*a**-1*b*a*b**-2]) + C_r = coset_enumeration_r(M, [a]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(M, [a]) + C_c.compress(); C_c.standardize() + table4 = [[0, 0, 0, 0]] + assert C_r.table == table4 + assert C_c.table == table4 + + +def test_look_ahead(): + # Section 3.2 [Test Example] Example (d) from [2] + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**11, b**5, c**4, (a*c)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b]) + H = [c, b, c**2] + table0 = [[1, 2, 0, 0, 0, 0], + [3, 0, 4, 5, 6, 7], + [0, 8, 9, 10, 11, 12], + [5, 1, 10, 13, 14, 15], + [16, 5, 16, 1, 17, 18], + [4, 3, 1, 8, 19, 20], + [12, 21, 22, 23, 24, 1], + [25, 26, 27, 28, 1, 24], + [2, 10, 5, 16, 22, 28], + [10, 13, 13, 2, 29, 30]] + CosetTable.max_stack_size = 10 + C_c = coset_enumeration_c(f, H) + C_c.compress(); C_c.standardize() + assert C_c.table[: 10] == table0 + +def test_modified_methods(): + ''' + Tests for modified coset table methods. + Example 5.7 from [1] Holt, D., Eick, B., O'Brien + "Handbook of Computational Group Theory". + + ''' + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + C = CosetTable(f, H) + C.modified_define(0, x) + identity = C._grp.identity + a_0 = C._grp.generators[0] + a_1 = C._grp.generators[1] + + assert C.P == [[identity, None, None, None], + [None, identity, None, None]] + assert C.table == [[1, None, None, None], + [None, 0, None, None]] + + C.modified_define(1, x) + assert C.table == [[1, None, None, None], + [2, 0, None, None], + [None, 1, None, None]] + assert C.P == [[identity, None, None, None], + [identity, identity, None, None], + [None, identity, None, None]] + + C.modified_scan(0, x**3, C._grp.identity, fill=False) + assert C.P == [[identity, identity, None, None], + [identity, identity, None, None], + [identity, identity, None, None]] + assert C.table == [[1, 2, None, None], + [2, 0, None, None], + [0, 1, None, None]] + + C.modified_scan(0, x*y, C._grp.generators[0], fill=False) + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, None]] + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, None]] + + C.modified_define(2, y**-1) + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [None, None, 2, None]] + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [None, None, identity, None]] + + C.modified_scan(0, x**-1*y**-1*x*y*x, C._grp.generators[1]) + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [3, 3, 2, None]] + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [a_1, a_1**-1, identity, None]] + + C.modified_scan(2, (x*y)**2, C._grp.identity) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [3, 3, 2, 0]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [a_1, a_1**-1, identity, a_1]] + + C.modified_define(2, y) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, None], + [0, 1, 4, 3], + [3, 3, 2, 0], + [None, None, None, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [None, None, None, identity]] + + C.modified_scan(0, y**5, C._grp.identity) + assert C.table == [[1, 2, 3, 1], [2, 0, 0, 4], [0, 1, 4, 3], [3, 3, 2, 0], [None, None, 1, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, a_0*a_1**-1], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [None, None, a_1*a_0**-1, identity]] + + C.modified_scan(1, (x*y)**2, C._grp.identity) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, 4], + [0, 1, 4, 3], + [3, 3, 2, 0], + [4, 4, 1, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, a_0*a_1**-1], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [a_0*a_1**-1, a_1*a_0**-1, a_1*a_0**-1, identity]] + + # Modified coset enumeration test + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + C = coset_enumeration_r(f, [x]) + C_m = modified_coset_enumeration_r(f, [x]) + assert C_m.table == C.table diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_fp_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_fp_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..3f57bdf8eff92a3022d8e01cd74ce98575987929 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_fp_groups.py @@ -0,0 +1,257 @@ +from sympy.core.singleton import S +from sympy.combinatorics.fp_groups import (FpGroup, low_index_subgroups, + reidemeister_presentation, FpSubgroup, + simplify_presentation) +from sympy.combinatorics.free_groups import (free_group, FreeGroup) + +from sympy.testing.pytest import slow + +""" +References +========== + +[1] Holt, D., Eick, B., O'Brien, E. +"Handbook of Computational Group Theory" + +[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson +Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490. +"Implementation and Analysis of the Todd-Coxeter Algorithm" + +[3] PROC. SECOND INTERNAT. CONF. THEORY OF GROUPS, CANBERRA 1973, +pp. 347-356. "A Reidemeister-Schreier program" by George Havas. +http://staff.itee.uq.edu.au/havas/1973cdhw.pdf + +""" + +def test_low_index_subgroups(): + F, x, y = free_group("x, y") + + # Example 5.10 from [1] Pg. 194 + f = FpGroup(F, [x**2, y**3, (x*y)**4]) + L = low_index_subgroups(f, 4) + t1 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 3, 3]], + [[0, 0, 1, 2], [2, 2, 2, 0], [1, 1, 0, 1]], + [[1, 1, 0, 0], [0, 0, 1, 1]]] + for i in range(len(t1)): + assert L[i].table == t1[i] + + f = FpGroup(F, [x**2, y**3, (x*y)**7]) + L = low_index_subgroups(f, 15) + t2 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [4, 4, 5, 3], [6, 6, 3, 4], [5, 5, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [5, 5, 3, 4], [4, 4, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [9, 9, 6, 8], [12, 12, 11, 7], [8, 8, 7, 10], + [10, 10, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [12, 12, 6, 8], [10, 10, 11, 7], [8, 8, 7, 10], + [9, 9, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [12, 12, 6, 8], [13, 13, 11, 7], [8, 8, 7, 10], + [9, 9, 12, 12], [10, 10, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6] + , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [11, 11, 12, 10], [13, 13, 10, 11], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6] + , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11], + [11, 11, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 4, 4] + , [7, 7, 6, 3], [8, 8, 3, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11], + [11, 11, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [5, 5, 6, 3], [9, 9, 3, 5], [10, 10, 8, 4], [8, 8, 4, 7], + [6, 6, 10, 11], [7, 7, 11, 9], [12, 12, 9, 10], [11, 11, 13, 14], + [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7], + [5, 5, 10, 12], [7, 7, 12, 9], [8, 8, 11, 11], [13, 13, 9, 10], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7], + [5, 5, 12, 11], [7, 7, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7], + [5, 5, 9, 9], [6, 6, 11, 12], [8, 8, 12, 10], [13, 13, 10, 11], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7], + [5, 5, 12, 11], [6, 6, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [11, 11, 8, 4], [12, 12, 4, 7], + [5, 5, 9, 9], [6, 6, 12, 13], [7, 7, 11, 11], [8, 8, 13, 10], + [13, 13, 10, 12]], + [[1, 1, 0, 0], [0, 0, 2, 3], [4, 4, 3, 1], [5, 5, 1, 2], [2, 2, 4, 4] + , [3, 3, 6, 7], [7, 7, 7, 5], [6, 6, 5, 6]]] + for i in range(len(t2)): + assert L[i].table == t2[i] + + f = FpGroup(F, [x**2, y**3, (x*y)**7]) + L = low_index_subgroups(f, 10, [x]) + t3 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [4, 4, 5, 3], + [6, 6, 3, 4], [5, 5, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [6, 6, 5, 3], + [5, 5, 3, 4], [4, 4, 6, 6]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8], + [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]]] + for i in range(len(t3)): + assert L[i].table == t3[i] + + +def test_subgroup_presentations(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + p1 = reidemeister_presentation(f, H) + assert str(p1) == "((y_1, y_2), (y_1**2, y_2**3, y_2*y_1*y_2*y_1*y_2*y_1))" + + H = f.subgroup(H) + assert (H.generators, H.relators) == p1 + + f = FpGroup(F, [x**3, y**3, (x*y)**3]) + H = [x*y, x*y**-1] + p2 = reidemeister_presentation(f, H) + assert str(p2) == "((x_0, y_0), (x_0**3, y_0**3, x_0*y_0*x_0*y_0*x_0*y_0))" + + f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3]) + H = [x] + p3 = reidemeister_presentation(f, H) + assert str(p3) == "((x_0,), (x_0**4,))" + + f = FpGroup(F, [x**3*y**-3, (x*y)**3, (x*y**-1)**2]) + H = [x] + p4 = reidemeister_presentation(f, H) + assert str(p4) == "((x_0,), (x_0**6,))" + + # this presentation can be improved, the most simplified form + # of presentation is + # See [2] Pg 474 group PSL_2(11) + # This is the group PSL_2(11) + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**11, b**5, c**4, (b*c**2)**2, (a*b*c)**3, (a**4*c**2)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b]) + H = [a, b, c**2] + gens, rels = reidemeister_presentation(f, H) + assert str(gens) == "(b_1, c_3)" + assert len(rels) == 18 + + +@slow +def test_order(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert f.order() == 8 + + f = FpGroup(F, [x*y*x**-1*y**-1, y**2]) + assert f.order() is S.Infinity + + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**250, b**2, c*b*c**-1*b, c**4, c**-1*a**-1*c*a, a**-1*b**-1*a*b]) + assert f.order() == 2000 + + F, x = free_group("x") + f = FpGroup(F, []) + assert f.order() is S.Infinity + + f = FpGroup(free_group('')[0], []) + assert f.order() == 1 + +def test_fp_subgroup(): + def _test_subgroup(K, T, S): + _gens = T(K.generators) + assert all(elem in S for elem in _gens) + assert T.is_injective() + assert T.image().order() == S.order() + F, x, y = free_group("x, y") + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + S = FpSubgroup(f, [x*y]) + assert (x*y)**-3 in S + K, T = f.subgroup([x*y], homomorphism=True) + assert T(K.generators) == [y*x**-1] + _test_subgroup(K, T, S) + + S = FpSubgroup(f, [x**-1*y*x]) + assert x**-1*y**4*x in S + assert x**-1*y**4*x**2 not in S + K, T = f.subgroup([x**-1*y*x], homomorphism=True) + assert T(K.generators[0]**3) == y**3 + _test_subgroup(K, T, S) + + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + K, T = f.subgroup(H, homomorphism=True) + S = FpSubgroup(f, H) + _test_subgroup(K, T, S) + +def test_permutation_methods(): + F, x, y = free_group("x, y") + # DihedralGroup(8) + G = FpGroup(F, [x**2, y**8, x*y*x**-1*y]) + T = G._to_perm_group()[1] + assert T.is_isomorphism() + assert G.center() == [y**4] + + # DiheadralGroup(4) + G = FpGroup(F, [x**2, y**4, x*y*x**-1*y]) + S = FpSubgroup(G, G.normal_closure([x])) + assert x in S + assert y**-1*x*y in S + + # Z_5xZ_4 + G = FpGroup(F, [x*y*x**-1*y**-1, y**5, x**4]) + assert G.is_abelian + assert G.is_solvable + + # AlternatingGroup(5) + G = FpGroup(F, [x**3, y**2, (x*y)**5]) + assert not G.is_solvable + + # AlternatingGroup(4) + G = FpGroup(F, [x**3, y**2, (x*y)**3]) + assert len(G.derived_series()) == 3 + S = FpSubgroup(G, G.derived_subgroup()) + assert S.order() == 4 + + +def test_simplify_presentation(): + # ref #16083 + G = simplify_presentation(FpGroup(FreeGroup([]), [])) + assert not G.generators + assert not G.relators + + # CyclicGroup(3) + # The second generator in is trivial due to relators {x^2, x^5} + F, x, y = free_group("x, y") + G = simplify_presentation(FpGroup(F, [x**2, x**5, y**3])) + assert x in G.relators + +def test_cyclic(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x]) + assert f.is_cyclic + f = FpGroup(F, [x*y, x*y**-1]) + assert f.is_cyclic + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert not f.is_cyclic + + +def test_abelian_invariants(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x]) + assert f.abelian_invariants() == [] + f = FpGroup(F, [x*y, x*y**-1]) + assert f.abelian_invariants() == [2] + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert f.abelian_invariants() == [2, 4] diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_free_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_free_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..652dbcd017eb2604506d91f669b708041ac0f3d4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_free_groups.py @@ -0,0 +1,221 @@ +from sympy.combinatorics.free_groups import free_group, FreeGroup +from sympy.core import Symbol +from sympy.testing.pytest import raises +from sympy.core.numbers import oo + +F, x, y, z = free_group("x, y, z") + + +def test_FreeGroup__init__(): + x, y, z = map(Symbol, "xyz") + + assert len(FreeGroup("x, y, z").generators) == 3 + assert len(FreeGroup(x).generators) == 1 + assert len(FreeGroup(("x", "y", "z"))) == 3 + assert len(FreeGroup((x, y, z)).generators) == 3 + + +def test_free_group(): + G, a, b, c = free_group("a, b, c") + assert F.generators == (x, y, z) + assert x*z**2 in F + assert x in F + assert y*z**-1 in F + assert (y*z)**0 in F + assert a not in F + assert a**0 not in F + assert len(F) == 3 + assert str(F) == '' + assert not F == G + assert F.order() is oo + assert F.is_abelian == False + assert F.center() == {F.identity} + + (e,) = free_group("") + assert e.order() == 1 + assert e.generators == () + assert e.elements == {e.identity} + assert e.is_abelian == True + + +def test_FreeGroup__hash__(): + assert hash(F) + + +def test_FreeGroup__eq__(): + assert free_group("x, y, z")[0] == free_group("x, y, z")[0] + assert free_group("x, y, z")[0] is free_group("x, y, z")[0] + + assert free_group("x, y, z")[0] != free_group("a, x, y")[0] + assert free_group("x, y, z")[0] is not free_group("a, x, y")[0] + + assert free_group("x, y")[0] != free_group("x, y, z")[0] + assert free_group("x, y")[0] is not free_group("x, y, z")[0] + + assert free_group("x, y, z")[0] != free_group("x, y")[0] + assert free_group("x, y, z")[0] is not free_group("x, y")[0] + + +def test_FreeGroup__getitem__(): + assert F[0:] == FreeGroup("x, y, z") + assert F[1:] == FreeGroup("y, z") + assert F[2:] == FreeGroup("z") + + +def test_FreeGroupElm__hash__(): + assert hash(x*y*z) + + +def test_FreeGroupElm_copy(): + f = x*y*z**3 + g = f.copy() + h = x*y*z**7 + + assert f == g + assert f != h + + +def test_FreeGroupElm_inverse(): + assert x.inverse() == x**-1 + assert (x*y).inverse() == y**-1*x**-1 + assert (y*x*y**-1).inverse() == y*x**-1*y**-1 + assert (y**2*x**-1).inverse() == x*y**-2 + + +def test_FreeGroupElm_type_error(): + raises(TypeError, lambda: 2/x) + raises(TypeError, lambda: x**2 + y**2) + raises(TypeError, lambda: x/2) + + +def test_FreeGroupElm_methods(): + assert (x**0).order() == 1 + assert (y**2).order() is oo + assert (x**-1*y).commutator(x) == y**-1*x**-1*y*x + assert len(x**2*y**-1) == 3 + assert len(x**-1*y**3*z) == 5 + + +def test_FreeGroupElm_eliminate_word(): + w = x**5*y*x**2*y**-4*x + assert w.eliminate_word( x, x**2 ) == x**10*y*x**4*y**-4*x**2 + w3 = x**2*y**3*x**-1*y + assert w3.eliminate_word(x, x**2) == x**4*y**3*x**-2*y + assert w3.eliminate_word(x, y) == y**5 + assert w3.eliminate_word(x, y**4) == y**8 + assert w3.eliminate_word(y, x**-1) == x**-3 + assert w3.eliminate_word(x, y*z) == y*z*y*z*y**3*z**-1 + assert (y**-3).eliminate_word(y, x**-1*z**-1) == z*x*z*x*z*x + #assert w3.eliminate_word(x, y*x) == y*x*y*x**2*y*x*y*x*y*x*z**3 + #assert w3.eliminate_word(x, x*y) == x*y*x**2*y*x*y*x*y*x*y*z**3 + + +def test_FreeGroupElm_array_form(): + assert (x*z).array_form == ((Symbol('x'), 1), (Symbol('z'), 1)) + assert (x**2*z*y*x**-2).array_form == \ + ((Symbol('x'), 2), (Symbol('z'), 1), (Symbol('y'), 1), (Symbol('x'), -2)) + assert (x**-2*y**-1).array_form == ((Symbol('x'), -2), (Symbol('y'), -1)) + + +def test_FreeGroupElm_letter_form(): + assert (x**3).letter_form == (Symbol('x'), Symbol('x'), Symbol('x')) + assert (x**2*z**-2*x).letter_form == \ + (Symbol('x'), Symbol('x'), -Symbol('z'), -Symbol('z'), Symbol('x')) + + +def test_FreeGroupElm_ext_rep(): + assert (x**2*z**-2*x).ext_rep == \ + (Symbol('x'), 2, Symbol('z'), -2, Symbol('x'), 1) + assert (x**-2*y**-1).ext_rep == (Symbol('x'), -2, Symbol('y'), -1) + assert (x*z).ext_rep == (Symbol('x'), 1, Symbol('z'), 1) + + +def test_FreeGroupElm__mul__pow__(): + x1 = x.group.dtype(((Symbol('x'), 1),)) + assert x**2 == x1*x + + assert (x**2*y*x**-2)**4 == x**2*y**4*x**-2 + assert (x**2)**2 == x**4 + assert (x**-1)**-1 == x + assert (x**-1)**0 == F.identity + assert (y**2)**-2 == y**-4 + + assert x**2*x**-1 == x + assert x**2*y**2*y**-1 == x**2*y + assert x*x**-1 == F.identity + + assert x/x == F.identity + assert x/x**2 == x**-1 + assert (x**2*y)/(x**2*y**-1) == x**2*y**2*x**-2 + assert (x**2*y)/(y**-1*x**2) == x**2*y*x**-2*y + + assert x*(x**-1*y*z*y**-1) == y*z*y**-1 + assert x**2*(x**-2*y**-1*z**2*y) == y**-1*z**2*y + + a = F.identity + for n in range(10): + assert a == x**n + assert a**-1 == x**-n + a *= x + + +def test_FreeGroupElm__len__(): + assert len(x**5*y*x**2*y**-4*x) == 13 + assert len(x**17) == 17 + assert len(y**0) == 0 + + +def test_FreeGroupElm_comparison(): + assert not (x*y == y*x) + assert x**0 == y**0 + + assert x**2 < y**3 + assert not x**3 < y**2 + assert x*y < x**2*y + assert x**2*y**2 < y**4 + assert not y**4 < y**-4 + assert not y**4 < x**-4 + assert y**-2 < y**2 + + assert x**2 <= y**2 + assert x**2 <= x**2 + + assert not y*z > z*y + assert x > x**-1 + + assert not x**2 >= y**2 + + +def test_FreeGroupElm_syllables(): + w = x**5*y*x**2*y**-4*x + assert w.number_syllables() == 5 + assert w.exponent_syllable(2) == 2 + assert w.generator_syllable(3) == Symbol('y') + assert w.sub_syllables(1, 2) == y + assert w.sub_syllables(3, 3) == F.identity + + +def test_FreeGroup_exponents(): + w1 = x**2*y**3 + assert w1.exponent_sum(x) == 2 + assert w1.exponent_sum(x**-1) == -2 + assert w1.generator_count(x) == 2 + + w2 = x**2*y**4*x**-3 + assert w2.exponent_sum(x) == -1 + assert w2.generator_count(x) == 5 + + +def test_FreeGroup_generators(): + assert (x**2*y**4*z**-1).contains_generators() == {x, y, z} + assert (x**-1*y**3).contains_generators() == {x, y} + + +def test_FreeGroupElm_words(): + w = x**5*y*x**2*y**-4*x + assert w.subword(2, 6) == x**3*y + assert w.subword(3, 2) == F.identity + assert w.subword(6, 10) == x**2*y**-2 + + assert w.substituted_word(0, 7, y**-1) == y**-1*x*y**-4*x + assert w.substituted_word(0, 7, y**2*x) == y**2*x**2*y**-4*x diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_galois.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_galois.py new file mode 100644 index 0000000000000000000000000000000000000000..0d2ac29a846db88444d275b72a85ce3debaeaf05 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_galois.py @@ -0,0 +1,82 @@ +"""Test groups defined by the galois module. """ + +from sympy.combinatorics.galois import ( + S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups, + find_transitive_subgroups_of_S6, +) +from sympy.combinatorics.homomorphisms import is_isomorphic +from sympy.combinatorics.named_groups import ( + SymmetricGroup, AlternatingGroup, CyclicGroup, +) + + +def test_four_group(): + G = S4TransitiveSubgroups.V.get_perm_group() + A4 = AlternatingGroup(4) + assert G.is_subgroup(A4) + assert G.degree == 4 + assert G.is_transitive() + assert G.order() == 4 + assert not G.is_cyclic + + +def test_M20(): + G = S5TransitiveSubgroups.M20.get_perm_group() + S5 = SymmetricGroup(5) + A5 = AlternatingGroup(5) + assert G.is_subgroup(S5) + assert not G.is_subgroup(A5) + assert G.degree == 5 + assert G.is_transitive() + assert G.order() == 20 + + +# Setting this True means that for each of the transitive subgroups of S6, +# we run a test not only on the fixed representation, but also on one freshly +# generated by the search procedure. +INCLUDE_SEARCH_REPS = False +S6_randomized = {} +if INCLUDE_SEARCH_REPS: + S6_randomized = find_transitive_subgroups_of_S6(*list(S6TransitiveSubgroups)) + + +def get_versions_of_S6_subgroup(name): + vers = [name.get_perm_group()] + if INCLUDE_SEARCH_REPS: + vers.append(S6_randomized[name]) + return vers + + +def test_S6_transitive_subgroups(): + """ + Test enough characteristics to distinguish all 16 transitive subgroups. + """ + ts = S6TransitiveSubgroups + A6 = AlternatingGroup(6) + for name, alt, order, is_isom, not_isom in [ + (ts.C6, False, 6, CyclicGroup(6), None), + (ts.S3, False, 6, SymmetricGroup(3), None), + (ts.D6, False, 12, None, None), + (ts.A4, True, 12, None, None), + (ts.G18, False, 18, None, None), + (ts.A4xC2, False, 24, None, SymmetricGroup(4)), + (ts.S4m, False, 24, SymmetricGroup(4), None), + (ts.S4p, True, 24, None, None), + (ts.G36m, False, 36, None, None), + (ts.G36p, True, 36, None, None), + (ts.S4xC2, False, 48, None, None), + (ts.PSL2F5, True, 60, None, None), + (ts.G72, False, 72, None, None), + (ts.PGL2F5, False, 120, None, None), + (ts.A6, True, 360, None, None), + (ts.S6, False, 720, None, None), + ]: + for G in get_versions_of_S6_subgroup(name): + assert G.is_transitive() + assert G.degree == 6 + assert G.is_subgroup(A6) is alt + assert G.order() == order + if is_isom: + assert is_isomorphic(G, is_isom) + if not_isom: + assert not is_isomorphic(G, not_isom) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_generators.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_generators.py new file mode 100644 index 0000000000000000000000000000000000000000..795ef8f08f6ec212879f528c6a0c2f0bd73037f0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_generators.py @@ -0,0 +1,105 @@ +from sympy.combinatorics.generators import symmetric, cyclic, alternating, \ + dihedral, rubik +from sympy.combinatorics.permutations import Permutation +from sympy.testing.pytest import raises + +def test_generators(): + + assert list(cyclic(6)) == [ + Permutation([0, 1, 2, 3, 4, 5]), + Permutation([1, 2, 3, 4, 5, 0]), + Permutation([2, 3, 4, 5, 0, 1]), + Permutation([3, 4, 5, 0, 1, 2]), + Permutation([4, 5, 0, 1, 2, 3]), + Permutation([5, 0, 1, 2, 3, 4])] + + assert list(cyclic(10)) == [ + Permutation([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), + Permutation([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]), + Permutation([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]), + Permutation([3, 4, 5, 6, 7, 8, 9, 0, 1, 2]), + Permutation([4, 5, 6, 7, 8, 9, 0, 1, 2, 3]), + Permutation([5, 6, 7, 8, 9, 0, 1, 2, 3, 4]), + Permutation([6, 7, 8, 9, 0, 1, 2, 3, 4, 5]), + Permutation([7, 8, 9, 0, 1, 2, 3, 4, 5, 6]), + Permutation([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]), + Permutation([9, 0, 1, 2, 3, 4, 5, 6, 7, 8])] + + assert list(alternating(4)) == [ + Permutation([0, 1, 2, 3]), + Permutation([0, 2, 3, 1]), + Permutation([0, 3, 1, 2]), + Permutation([1, 0, 3, 2]), + Permutation([1, 2, 0, 3]), + Permutation([1, 3, 2, 0]), + Permutation([2, 0, 1, 3]), + Permutation([2, 1, 3, 0]), + Permutation([2, 3, 0, 1]), + Permutation([3, 0, 2, 1]), + Permutation([3, 1, 0, 2]), + Permutation([3, 2, 1, 0])] + + assert list(symmetric(3)) == [ + Permutation([0, 1, 2]), + Permutation([0, 2, 1]), + Permutation([1, 0, 2]), + Permutation([1, 2, 0]), + Permutation([2, 0, 1]), + Permutation([2, 1, 0])] + + assert list(symmetric(4)) == [ + Permutation([0, 1, 2, 3]), + Permutation([0, 1, 3, 2]), + Permutation([0, 2, 1, 3]), + Permutation([0, 2, 3, 1]), + Permutation([0, 3, 1, 2]), + Permutation([0, 3, 2, 1]), + Permutation([1, 0, 2, 3]), + Permutation([1, 0, 3, 2]), + Permutation([1, 2, 0, 3]), + Permutation([1, 2, 3, 0]), + Permutation([1, 3, 0, 2]), + Permutation([1, 3, 2, 0]), + Permutation([2, 0, 1, 3]), + Permutation([2, 0, 3, 1]), + Permutation([2, 1, 0, 3]), + Permutation([2, 1, 3, 0]), + Permutation([2, 3, 0, 1]), + Permutation([2, 3, 1, 0]), + Permutation([3, 0, 1, 2]), + Permutation([3, 0, 2, 1]), + Permutation([3, 1, 0, 2]), + Permutation([3, 1, 2, 0]), + Permutation([3, 2, 0, 1]), + Permutation([3, 2, 1, 0])] + + assert list(dihedral(1)) == [ + Permutation([0, 1]), Permutation([1, 0])] + + assert list(dihedral(2)) == [ + Permutation([0, 1, 2, 3]), + Permutation([1, 0, 3, 2]), + Permutation([2, 3, 0, 1]), + Permutation([3, 2, 1, 0])] + + assert list(dihedral(3)) == [ + Permutation([0, 1, 2]), + Permutation([2, 1, 0]), + Permutation([1, 2, 0]), + Permutation([0, 2, 1]), + Permutation([2, 0, 1]), + Permutation([1, 0, 2])] + + assert list(dihedral(5)) == [ + Permutation([0, 1, 2, 3, 4]), + Permutation([4, 3, 2, 1, 0]), + Permutation([1, 2, 3, 4, 0]), + Permutation([0, 4, 3, 2, 1]), + Permutation([2, 3, 4, 0, 1]), + Permutation([1, 0, 4, 3, 2]), + Permutation([3, 4, 0, 1, 2]), + Permutation([2, 1, 0, 4, 3]), + Permutation([4, 0, 1, 2, 3]), + Permutation([3, 2, 1, 0, 4])] + + raises(ValueError, lambda: rubik(1)) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_graycode.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_graycode.py new file mode 100644 index 0000000000000000000000000000000000000000..a754a3c401b07c9c12cb9bdeeefdfc94f6cb8b5c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_graycode.py @@ -0,0 +1,72 @@ +from sympy.combinatorics.graycode import (GrayCode, bin_to_gray, + random_bitstring, get_subset_from_bitstring, graycode_subsets, + gray_to_bin) +from sympy.testing.pytest import raises + +def test_graycode(): + g = GrayCode(2) + got = [] + for i in g.generate_gray(): + if i.startswith('0'): + g.skip() + got.append(i) + assert got == '00 11 10'.split() + a = GrayCode(6) + assert a.current == '0'*6 + assert a.rank == 0 + assert len(list(a.generate_gray())) == 64 + codes = ['011001', '011011', '011010', + '011110', '011111', '011101', '011100', '010100', '010101', '010111', + '010110', '010010', '010011', '010001', '010000', '110000', '110001', + '110011', '110010', '110110', '110111', '110101', '110100', '111100', + '111101', '111111', '111110', '111010', '111011', '111001', '111000', + '101000', '101001', '101011', '101010', '101110', '101111', '101101', + '101100', '100100', '100101', '100111', '100110', '100010', '100011', + '100001', '100000'] + assert list(a.generate_gray(start='011001')) == codes + assert list( + a.generate_gray(rank=GrayCode(6, start='011001').rank)) == codes + assert a.next().current == '000001' + assert a.next(2).current == '000011' + assert a.next(-1).current == '100000' + + a = GrayCode(5, start='10010') + assert a.rank == 28 + a = GrayCode(6, start='101000') + assert a.rank == 48 + + assert GrayCode(6, rank=4).current == '000110' + assert GrayCode(6, rank=4).rank == 4 + assert [GrayCode(4, start=s).rank for s in + GrayCode(4).generate_gray()] == [0, 1, 2, 3, 4, 5, 6, 7, 8, + 9, 10, 11, 12, 13, 14, 15] + a = GrayCode(15, rank=15) + assert a.current == '000000000001000' + + assert bin_to_gray('111') == '100' + + a = random_bitstring(5) + assert type(a) is str + assert len(a) == 5 + assert all(i in ['0', '1'] for i in a) + + assert get_subset_from_bitstring( + ['a', 'b', 'c', 'd'], '0011') == ['c', 'd'] + assert get_subset_from_bitstring('abcd', '1001') == ['a', 'd'] + assert list(graycode_subsets(['a', 'b', 'c'])) == \ + [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], + ['a', 'c'], ['a']] + + raises(ValueError, lambda: GrayCode(0)) + raises(ValueError, lambda: GrayCode(2.2)) + raises(ValueError, lambda: GrayCode(2, start=[1, 1, 0])) + raises(ValueError, lambda: GrayCode(2, rank=2.5)) + raises(ValueError, lambda: get_subset_from_bitstring(['c', 'a', 'c'], '1100')) + raises(ValueError, lambda: list(GrayCode(3).generate_gray(start="1111"))) + + +def test_live_issue_117(): + assert bin_to_gray('0100') == '0110' + assert bin_to_gray('0101') == '0111' + for bits in ('0100', '0101'): + assert gray_to_bin(bin_to_gray(bits)) == bits diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_constructs.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_constructs.py new file mode 100644 index 0000000000000000000000000000000000000000..d0f7d6394bbc2e285650ea95d36be8e2ed5ea69e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_constructs.py @@ -0,0 +1,15 @@ +from sympy.combinatorics.group_constructs import DirectProduct +from sympy.combinatorics.named_groups import CyclicGroup, DihedralGroup + + +def test_direct_product_n(): + C = CyclicGroup(4) + D = DihedralGroup(4) + G = DirectProduct(C, C, C) + assert G.order() == 64 + assert G.degree == 12 + assert len(G.orbits()) == 3 + assert G.is_abelian is True + H = DirectProduct(D, C) + assert H.order() == 32 + assert H.is_abelian is False diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_numbers.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..743f1dcc8b642c19706687eeeddf6c9070b59166 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_group_numbers.py @@ -0,0 +1,110 @@ +from sympy.combinatorics.group_numbers import (is_nilpotent_number, + is_abelian_number, is_cyclic_number, _holder_formula, groups_count) +from sympy.ntheory.factor_ import factorint +from sympy.ntheory.generate import prime +from sympy.testing.pytest import raises +from sympy import randprime + + +def test_is_nilpotent_number(): + assert is_nilpotent_number(21) == False + assert is_nilpotent_number(randprime(1, 30)**12) == True + raises(ValueError, lambda: is_nilpotent_number(-5)) + + A056867 = [1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, + 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45, + 47, 49, 51, 53, 59, 61, 64, 65, 67, 69, 71, 73, + 77, 79, 81, 83, 85, 87, 89, 91, 95, 97, 99] + for n in range(1, 100): + assert is_nilpotent_number(n) == (n in A056867) + + +def test_is_abelian_number(): + assert is_abelian_number(4) == True + assert is_abelian_number(randprime(1, 2000)**2) == True + assert is_abelian_number(randprime(1000, 100000)) == True + assert is_abelian_number(60) == False + assert is_abelian_number(24) == False + raises(ValueError, lambda: is_abelian_number(-5)) + + A051532 = [1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, + 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, + 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, + 89, 91, 95, 97, 99] + for n in range(1, 100): + assert is_abelian_number(n) == (n in A051532) + + +A003277 = [1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, + 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61, + 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, + 91, 95, 97] + + +def test_is_cyclic_number(): + assert is_cyclic_number(15) == True + assert is_cyclic_number(randprime(1, 2000)**2) == False + assert is_cyclic_number(randprime(1000, 100000)) == True + assert is_cyclic_number(4) == False + raises(ValueError, lambda: is_cyclic_number(-5)) + + for n in range(1, 100): + assert is_cyclic_number(n) == (n in A003277) + + +def test_holder_formula(): + # semiprime + assert _holder_formula({3, 5}) == 1 + assert _holder_formula({5, 11}) == 2 + # n in A003277 is always 1 + for n in A003277: + assert _holder_formula(set(factorint(n).keys())) == 1 + # otherwise + assert _holder_formula({2, 3, 5, 7}) == 12 + + +def test_groups_count(): + A000001 = [0, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, + 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, + 5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2, + 14, 1, 6, 1, 4, 2, 2, 1, 52, 2, 5, 1, 5, + 1, 15, 2, 13, 2, 2, 1, 13, 1, 2, 4, 267, + 1, 4, 1, 5, 1, 4, 1, 50, 1, 2, 3, 4, 1, + 6, 1, 52, 15, 2, 1, 15, 1, 2, 1, 12, 1, + 10, 1, 4, 2] + for n in range(1, len(A000001)): + try: + assert groups_count(n) == A000001[n] + except ValueError: + pass + + A000679 = [1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289] + for e in range(1, len(A000679)): + assert groups_count(2**e) == A000679[e] + + A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645] + for e in range(1, len(A090091)): + assert groups_count(3**e) == A090091[e] + + A090130 = [1, 1, 2, 5, 15, 77, 684, 34297] + for e in range(1, len(A090130)): + assert groups_count(5**e) == A090130[e] + + A090140 = [1, 1, 2, 5, 15, 83, 860, 113147] + for e in range(1, len(A090140)): + assert groups_count(7**e) == A090140[e] + + A232105 = [51, 67, 77, 83, 87, 97, 101, 107, 111, 125, 131, + 145, 149, 155, 159, 173, 183, 193, 203, 207, 217] + for i in range(len(A232105)): + assert groups_count(prime(i+1)**5) == A232105[i] + + A232106 = [267, 504, 684, 860, 1192, 1476, 1944, 2264, 2876, + 4068, 4540, 6012, 7064, 7664, 8852, 10908, 13136] + for i in range(len(A232106)): + assert groups_count(prime(i+1)**6) == A232106[i] + + A232107 = [2328, 9310, 34297, 113147, 750735, 1600573, + 5546909, 9380741, 23316851, 71271069, 98488755] + for i in range(len(A232107)): + assert groups_count(prime(i+1)**7) == A232107[i] diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_homomorphisms.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_homomorphisms.py new file mode 100644 index 0000000000000000000000000000000000000000..0936bbddf46a16dccdfbaebda8d1c675c131f05a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_homomorphisms.py @@ -0,0 +1,114 @@ +from sympy.combinatorics import Permutation +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.combinatorics.homomorphisms import homomorphism, group_isomorphism, is_isomorphic +from sympy.combinatorics.free_groups import free_group +from sympy.combinatorics.fp_groups import FpGroup +from sympy.combinatorics.named_groups import AlternatingGroup, DihedralGroup, CyclicGroup +from sympy.testing.pytest import raises + +def test_homomorphism(): + # FpGroup -> PermutationGroup + F, a, b = free_group("a, b") + G = FpGroup(F, [a**3, b**3, (a*b)**2]) + + c = Permutation(3)(0, 1, 2) + d = Permutation(3)(1, 2, 3) + A = AlternatingGroup(4) + T = homomorphism(G, A, [a, b], [c, d]) + assert T(a*b**2*a**-1) == c*d**2*c**-1 + assert T.is_isomorphism() + assert T(T.invert(Permutation(3)(0, 2, 3))) == Permutation(3)(0, 2, 3) + + T = homomorphism(G, AlternatingGroup(4), G.generators) + assert T.is_trivial() + assert T.kernel().order() == G.order() + + E, e = free_group("e") + G = FpGroup(E, [e**8]) + P = PermutationGroup([Permutation(0, 1, 2, 3), Permutation(0, 2)]) + T = homomorphism(G, P, [e], [Permutation(0, 1, 2, 3)]) + assert T.image().order() == 4 + assert T(T.invert(Permutation(0, 2)(1, 3))) == Permutation(0, 2)(1, 3) + + T = homomorphism(E, AlternatingGroup(4), E.generators, [c]) + assert T.invert(c**2) == e**-1 #order(c) == 3 so c**2 == c**-1 + + # FreeGroup -> FreeGroup + T = homomorphism(F, E, [a], [e]) + assert T(a**-2*b**4*a**2).is_identity + + # FreeGroup -> FpGroup + G = FpGroup(F, [a*b*a**-1*b**-1]) + T = homomorphism(F, G, F.generators, G.generators) + assert T.invert(a**-1*b**-1*a**2) == a*b**-1 + + # PermutationGroup -> PermutationGroup + D = DihedralGroup(8) + p = Permutation(0, 1, 2, 3, 4, 5, 6, 7) + P = PermutationGroup(p) + T = homomorphism(P, D, [p], [p]) + assert T.is_injective() + assert not T.is_isomorphism() + assert T.invert(p**3) == p**3 + + T2 = homomorphism(F, P, [F.generators[0]], P.generators) + T = T.compose(T2) + assert T.domain == F + assert T.codomain == D + assert T(a*b) == p + + D3 = DihedralGroup(3) + T = homomorphism(D3, D3, D3.generators, D3.generators) + assert T.is_isomorphism() + + +def test_isomorphisms(): + + F, a, b = free_group("a, b") + E, c, d = free_group("c, d") + # Infinite groups with differently ordered relators. + G = FpGroup(F, [a**2, b**3]) + H = FpGroup(F, [b**3, a**2]) + assert is_isomorphic(G, H) + + # Trivial Case + # FpGroup -> FpGroup + H = FpGroup(F, [a**3, b**3, (a*b)**2]) + F, c, d = free_group("c, d") + G = FpGroup(F, [c**3, d**3, (c*d)**2]) + check, T = group_isomorphism(G, H) + assert check + assert T(c**3*d**2) == a**3*b**2 + + # FpGroup -> PermutationGroup + # FpGroup is converted to the equivalent isomorphic group. + F, a, b = free_group("a, b") + G = FpGroup(F, [a**3, b**3, (a*b)**2]) + H = AlternatingGroup(4) + check, T = group_isomorphism(G, H) + assert check + assert T(b*a*b**-1*a**-1*b**-1) == Permutation(0, 2, 3) + assert T(b*a*b*a**-1*b**-1) == Permutation(0, 3, 2) + + # PermutationGroup -> PermutationGroup + D = DihedralGroup(8) + p = Permutation(0, 1, 2, 3, 4, 5, 6, 7) + P = PermutationGroup(p) + assert not is_isomorphic(D, P) + + A = CyclicGroup(5) + B = CyclicGroup(7) + assert not is_isomorphic(A, B) + + # Two groups of the same prime order are isomorphic to each other. + G = FpGroup(F, [a, b**5]) + H = CyclicGroup(5) + assert G.order() == H.order() + assert is_isomorphic(G, H) + + +def test_check_homomorphism(): + a = Permutation(1,2,3,4) + b = Permutation(1,3) + G = PermutationGroup([a, b]) + raises(ValueError, lambda: homomorphism(G, G, [a], [a])) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_named_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_named_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..59bcb6ef3f020335de76d7a72152a0b58cbc6976 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_named_groups.py @@ -0,0 +1,70 @@ +from sympy.combinatorics.named_groups import (SymmetricGroup, CyclicGroup, + DihedralGroup, AlternatingGroup, + AbelianGroup, RubikGroup) +from sympy.testing.pytest import raises + + +def test_SymmetricGroup(): + G = SymmetricGroup(5) + elements = list(G.generate()) + assert (G.generators[0]).size == 5 + assert len(elements) == 120 + assert G.is_solvable is False + assert G.is_abelian is False + assert G.is_nilpotent is False + assert G.is_transitive() is True + H = SymmetricGroup(1) + assert H.order() == 1 + L = SymmetricGroup(2) + assert L.order() == 2 + + +def test_CyclicGroup(): + G = CyclicGroup(10) + elements = list(G.generate()) + assert len(elements) == 10 + assert (G.derived_subgroup()).order() == 1 + assert G.is_abelian is True + assert G.is_solvable is True + assert G.is_nilpotent is True + H = CyclicGroup(1) + assert H.order() == 1 + L = CyclicGroup(2) + assert L.order() == 2 + + +def test_DihedralGroup(): + G = DihedralGroup(6) + elements = list(G.generate()) + assert len(elements) == 12 + assert G.is_transitive() is True + assert G.is_abelian is False + assert G.is_solvable is True + assert G.is_nilpotent is False + H = DihedralGroup(1) + assert H.order() == 2 + L = DihedralGroup(2) + assert L.order() == 4 + assert L.is_abelian is True + assert L.is_nilpotent is True + + +def test_AlternatingGroup(): + G = AlternatingGroup(5) + elements = list(G.generate()) + assert len(elements) == 60 + assert [perm.is_even for perm in elements] == [True]*60 + H = AlternatingGroup(1) + assert H.order() == 1 + L = AlternatingGroup(2) + assert L.order() == 1 + + +def test_AbelianGroup(): + A = AbelianGroup(3, 3, 3) + assert A.order() == 27 + assert A.is_abelian is True + + +def test_RubikGroup(): + raises(ValueError, lambda: RubikGroup(1)) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_partitions.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_partitions.py new file mode 100644 index 0000000000000000000000000000000000000000..32e70e53a53aadbb17c8292bbef8f52d1144d6e0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_partitions.py @@ -0,0 +1,118 @@ +from sympy.core.sorting import ordered, default_sort_key +from sympy.combinatorics.partitions import (Partition, IntegerPartition, + RGS_enum, RGS_unrank, RGS_rank, + random_integer_partition) +from sympy.testing.pytest import raises +from sympy.utilities.iterables import partitions +from sympy.sets.sets import Set, FiniteSet + + +def test_partition_constructor(): + raises(ValueError, lambda: Partition([1, 1, 2])) + raises(ValueError, lambda: Partition([1, 2, 3], [2, 3, 4])) + raises(ValueError, lambda: Partition(1, 2, 3)) + raises(ValueError, lambda: Partition(*list(range(3)))) + + assert Partition([1, 2, 3], [4, 5]) == Partition([4, 5], [1, 2, 3]) + assert Partition({1, 2, 3}, {4, 5}) == Partition([1, 2, 3], [4, 5]) + + a = FiniteSet(1, 2, 3) + b = FiniteSet(4, 5) + assert Partition(a, b) == Partition([1, 2, 3], [4, 5]) + assert Partition({a, b}) == Partition(FiniteSet(a, b)) + assert Partition({a, b}) != Partition(a, b) + +def test_partition(): + from sympy.abc import x + + a = Partition([1, 2, 3], [4]) + b = Partition([1, 2], [3, 4]) + c = Partition([x]) + l = [a, b, c] + l.sort(key=default_sort_key) + assert l == [c, a, b] + l.sort(key=lambda w: default_sort_key(w, order='rev-lex')) + assert l == [c, a, b] + + assert (a == b) is False + assert a <= b + assert (a > b) is False + assert a != b + assert a < b + + assert (a + 2).partition == [[1, 2], [3, 4]] + assert (b - 1).partition == [[1, 2, 4], [3]] + + assert (a - 1).partition == [[1, 2, 3, 4]] + assert (a + 1).partition == [[1, 2, 4], [3]] + assert (b + 1).partition == [[1, 2], [3], [4]] + + assert a.rank == 1 + assert b.rank == 3 + + assert a.RGS == (0, 0, 0, 1) + assert b.RGS == (0, 0, 1, 1) + + +def test_integer_partition(): + # no zeros in partition + raises(ValueError, lambda: IntegerPartition(list(range(3)))) + # check fails since 1 + 2 != 100 + raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3)))) + a = IntegerPartition(8, [1, 3, 4]) + b = a.next_lex() + c = IntegerPartition([1, 3, 4]) + d = IntegerPartition(8, {1: 3, 3: 1, 2: 1}) + assert a == c + assert a.integer == d.integer + assert a.conjugate == [3, 2, 2, 1] + assert (a == b) is False + assert a <= b + assert (a > b) is False + assert a != b + + for i in range(1, 11): + next = set() + prev = set() + a = IntegerPartition([i]) + ans = {IntegerPartition(p) for p in partitions(i)} + n = len(ans) + for j in range(n): + next.add(a) + a = a.next_lex() + IntegerPartition(i, a.partition) # check it by giving i + for j in range(n): + prev.add(a) + a = a.prev_lex() + IntegerPartition(i, a.partition) # check it by giving i + assert next == ans + assert prev == ans + + assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#' + assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no' + assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]' + assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1] + + raises(ValueError, lambda: random_integer_partition(-1)) + assert random_integer_partition(1) == [1] + assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1] + ) == [5, 2, 1, 1, 1] + + +def test_rgs(): + raises(ValueError, lambda: RGS_unrank(-1, 3)) + raises(ValueError, lambda: RGS_unrank(3, 0)) + raises(ValueError, lambda: RGS_unrank(10, 1)) + + raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2)))) + raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2)))) + assert RGS_enum(-1) == 0 + assert RGS_enum(1) == 1 + assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2] + assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2] + assert RGS_rank(RGS_unrank(40, 100)) == 40 + +def test_ordered_partition_9608(): + a = Partition([1, 2, 3], [4]) + b = Partition([1, 2], [3, 4]) + assert list(ordered([a,b], Set._infimum_key)) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_pc_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_pc_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..b0c146279921e1e6499534fe9e33b993348d1503 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_pc_groups.py @@ -0,0 +1,87 @@ +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, DihedralGroup +from sympy.matrices import Matrix + +def test_pc_presentation(): + Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), + SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2), DihedralGroup(10)] + + S = SymmetricGroup(125).sylow_subgroup(5) + G = S.derived_series()[2] + Groups.append(G) + + G = SymmetricGroup(25).sylow_subgroup(5) + Groups.append(G) + + S = SymmetricGroup(11**2).sylow_subgroup(11) + G = S.derived_series()[2] + Groups.append(G) + + for G in Groups: + PcGroup = G.polycyclic_group() + collector = PcGroup.collector + pc_presentation = collector.pc_presentation + + pcgs = PcGroup.pcgs + free_group = collector.free_group + free_to_perm = {} + for s, g in zip(free_group.symbols, pcgs): + free_to_perm[s] = g + + for k, v in pc_presentation.items(): + k_array = k.array_form + if v != (): + v_array = v.array_form + + lhs = Permutation() + for gen in k_array: + s = gen[0] + e = gen[1] + lhs = lhs*free_to_perm[s]**e + + if v == (): + assert lhs.is_identity + continue + + rhs = Permutation() + for gen in v_array: + s = gen[0] + e = gen[1] + rhs = rhs*free_to_perm[s]**e + + assert lhs == rhs + + +def test_exponent_vector(): + + Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), + SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2)] + + for G in Groups: + PcGroup = G.polycyclic_group() + collector = PcGroup.collector + + pcgs = PcGroup.pcgs + # free_group = collector.free_group + + for gen in G.generators: + exp = collector.exponent_vector(gen) + g = Permutation() + for i in range(len(exp)): + g = g*pcgs[i]**exp[i] if exp[i] else g + assert g == gen + + +def test_induced_pcgs(): + G = [SymmetricGroup(9).sylow_subgroup(3), SymmetricGroup(20).sylow_subgroup(2), AlternatingGroup(4), + DihedralGroup(4), DihedralGroup(10), DihedralGroup(9), SymmetricGroup(3), SymmetricGroup(4)] + + for g in G: + PcGroup = g.polycyclic_group() + collector = PcGroup.collector + gens = list(g.generators) + ipcgs = collector.induced_pcgs(gens) + m = [] + for i in ipcgs: + m.append(collector.exponent_vector(i)) + assert Matrix(m).is_upper diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_perm_groups.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_perm_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..1e01e89e9208f2439401ea09f421117a4b9bfda0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_perm_groups.py @@ -0,0 +1,1243 @@ +from sympy.core.containers import Tuple +from sympy.combinatorics.generators import rubik_cube_generators +from sympy.combinatorics.homomorphisms import is_isomorphic +from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup,\ + DihedralGroup, AlternatingGroup, AbelianGroup, RubikGroup +from sympy.combinatorics.perm_groups import (PermutationGroup, + _orbit_transversal, Coset, SymmetricPermutationGroup) +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.polyhedron import tetrahedron as Tetra, cube +from sympy.combinatorics.testutil import _verify_bsgs, _verify_centralizer,\ + _verify_normal_closure +from sympy.testing.pytest import skip, XFAIL, slow + +rmul = Permutation.rmul + + +def test_has(): + a = Permutation([1, 0]) + G = PermutationGroup([a]) + assert G.is_abelian + a = Permutation([2, 0, 1]) + b = Permutation([2, 1, 0]) + G = PermutationGroup([a, b]) + assert not G.is_abelian + + G = PermutationGroup([a]) + assert G.has(a) + assert not G.has(b) + + a = Permutation([2, 0, 1, 3, 4, 5]) + b = Permutation([0, 2, 1, 3, 4]) + assert PermutationGroup(a, b).degree == \ + PermutationGroup(a, b).degree == 6 + + g = PermutationGroup(Permutation(0, 2, 1)) + assert Tuple(1, g).has(g) + + +def test_generate(): + a = Permutation([1, 0]) + g = list(PermutationGroup([a]).generate()) + assert g == [Permutation([0, 1]), Permutation([1, 0])] + assert len(list(PermutationGroup(Permutation((0, 1))).generate())) == 1 + g = PermutationGroup([a]).generate(method='dimino') + assert list(g) == [Permutation([0, 1]), Permutation([1, 0])] + a = Permutation([2, 0, 1]) + b = Permutation([2, 1, 0]) + G = PermutationGroup([a, b]) + g = G.generate() + v1 = [p.array_form for p in list(g)] + v1.sort() + assert v1 == [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, + 1], [2, 1, 0]] + v2 = list(G.generate(method='dimino', af=True)) + assert v1 == sorted(v2) + a = Permutation([2, 0, 1, 3, 4, 5]) + b = Permutation([2, 1, 3, 4, 5, 0]) + g = PermutationGroup([a, b]).generate(af=True) + assert len(list(g)) == 360 + + +def test_order(): + a = Permutation([2, 0, 1, 3, 4, 5, 6, 7, 8, 9]) + b = Permutation([2, 1, 3, 4, 5, 6, 7, 8, 9, 0]) + g = PermutationGroup([a, b]) + assert g.order() == 1814400 + assert PermutationGroup().order() == 1 + + +def test_equality(): + p_1 = Permutation(0, 1, 3) + p_2 = Permutation(0, 2, 3) + p_3 = Permutation(0, 1, 2) + p_4 = Permutation(0, 1, 3) + g_1 = PermutationGroup(p_1, p_2) + g_2 = PermutationGroup(p_3, p_4) + g_3 = PermutationGroup(p_2, p_1) + g_4 = PermutationGroup(p_1, p_2) + + assert g_1 != g_2 + assert g_1.generators != g_2.generators + assert g_1.equals(g_2) + assert g_1 != g_3 + assert g_1.equals(g_3) + assert g_1 == g_4 + + +def test_stabilizer(): + S = SymmetricGroup(2) + H = S.stabilizer(0) + assert H.generators == [Permutation(1)] + a = Permutation([2, 0, 1, 3, 4, 5]) + b = Permutation([2, 1, 3, 4, 5, 0]) + G = PermutationGroup([a, b]) + G0 = G.stabilizer(0) + assert G0.order() == 60 + + gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]] + gens = [Permutation(p) for p in gens_cube] + G = PermutationGroup(gens) + G2 = G.stabilizer(2) + assert G2.order() == 6 + G2_1 = G2.stabilizer(1) + v = list(G2_1.generate(af=True)) + assert v == [[0, 1, 2, 3, 4, 5, 6, 7], [3, 1, 2, 0, 7, 5, 6, 4]] + + gens = ( + (1, 2, 0, 4, 5, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19), + (0, 1, 2, 3, 4, 5, 19, 6, 8, 9, 10, 11, 12, 13, 14, + 15, 16, 7, 17, 18), + (0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 16, 11, 12, 13, 14, 15, 8, 17, 10, 19)) + gens = [Permutation(p) for p in gens] + G = PermutationGroup(gens) + G2 = G.stabilizer(2) + assert G2.order() == 181440 + S = SymmetricGroup(3) + assert [G.order() for G in S.basic_stabilizers] == [6, 2] + + +def test_center(): + # the center of the dihedral group D_n is of order 2 for even n + for i in (4, 6, 10): + D = DihedralGroup(i) + assert (D.center()).order() == 2 + # the center of the dihedral group D_n is of order 1 for odd n>2 + for i in (3, 5, 7): + D = DihedralGroup(i) + assert (D.center()).order() == 1 + # the center of an abelian group is the group itself + for i in (2, 3, 5): + for j in (1, 5, 7): + for k in (1, 1, 11): + G = AbelianGroup(i, j, k) + assert G.center().is_subgroup(G) + # the center of a nonabelian simple group is trivial + for i in(1, 5, 9): + A = AlternatingGroup(i) + assert (A.center()).order() == 1 + # brute-force verifications + D = DihedralGroup(5) + A = AlternatingGroup(3) + C = CyclicGroup(4) + G.is_subgroup(D*A*C) + assert _verify_centralizer(G, G) + + +def test_centralizer(): + # the centralizer of the trivial group is the entire group + S = SymmetricGroup(2) + assert S.centralizer(Permutation(list(range(2)))).is_subgroup(S) + A = AlternatingGroup(5) + assert A.centralizer(Permutation(list(range(5)))).is_subgroup(A) + # a centralizer in the trivial group is the trivial group itself + triv = PermutationGroup([Permutation([0, 1, 2, 3])]) + D = DihedralGroup(4) + assert triv.centralizer(D).is_subgroup(triv) + # brute-force verifications for centralizers of groups + for i in (4, 5, 6): + S = SymmetricGroup(i) + A = AlternatingGroup(i) + C = CyclicGroup(i) + D = DihedralGroup(i) + for gp in (S, A, C, D): + for gp2 in (S, A, C, D): + if not gp2.is_subgroup(gp): + assert _verify_centralizer(gp, gp2) + # verify the centralizer for all elements of several groups + S = SymmetricGroup(5) + elements = list(S.generate_dimino()) + for element in elements: + assert _verify_centralizer(S, element) + A = AlternatingGroup(5) + elements = list(A.generate_dimino()) + for element in elements: + assert _verify_centralizer(A, element) + D = DihedralGroup(7) + elements = list(D.generate_dimino()) + for element in elements: + assert _verify_centralizer(D, element) + # verify centralizers of small groups within small groups + small = [] + for i in (1, 2, 3): + small.append(SymmetricGroup(i)) + small.append(AlternatingGroup(i)) + small.append(DihedralGroup(i)) + small.append(CyclicGroup(i)) + for gp in small: + for gp2 in small: + if gp.degree == gp2.degree: + assert _verify_centralizer(gp, gp2) + + +def test_coset_rank(): + gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]] + gens = [Permutation(p) for p in gens_cube] + G = PermutationGroup(gens) + i = 0 + for h in G.generate(af=True): + rk = G.coset_rank(h) + assert rk == i + h1 = G.coset_unrank(rk, af=True) + assert h == h1 + i += 1 + assert G.coset_unrank(48) is None + assert G.coset_unrank(G.coset_rank(gens[0])) == gens[0] + + +def test_coset_factor(): + a = Permutation([0, 2, 1]) + G = PermutationGroup([a]) + c = Permutation([2, 1, 0]) + assert not G.coset_factor(c) + assert G.coset_rank(c) is None + + a = Permutation([2, 0, 1, 3, 4, 5]) + b = Permutation([2, 1, 3, 4, 5, 0]) + g = PermutationGroup([a, b]) + assert g.order() == 360 + d = Permutation([1, 0, 2, 3, 4, 5]) + assert not g.coset_factor(d.array_form) + assert not g.contains(d) + assert Permutation(2) in G + c = Permutation([1, 0, 2, 3, 5, 4]) + v = g.coset_factor(c, True) + tr = g.basic_transversals + p = Permutation.rmul(*[tr[i][v[i]] for i in range(len(g.base))]) + assert p == c + v = g.coset_factor(c) + p = Permutation.rmul(*v) + assert p == c + assert g.contains(c) + G = PermutationGroup([Permutation([2, 1, 0])]) + p = Permutation([1, 0, 2]) + assert G.coset_factor(p) == [] + + +def test_orbits(): + a = Permutation([2, 0, 1]) + b = Permutation([2, 1, 0]) + g = PermutationGroup([a, b]) + assert g.orbit(0) == {0, 1, 2} + assert g.orbits() == [{0, 1, 2}] + assert g.is_transitive() and g.is_transitive(strict=False) + assert g.orbit_transversal(0) == \ + [Permutation( + [0, 1, 2]), Permutation([2, 0, 1]), Permutation([1, 2, 0])] + assert g.orbit_transversal(0, True) == \ + [(0, Permutation([0, 1, 2])), (2, Permutation([2, 0, 1])), + (1, Permutation([1, 2, 0]))] + + G = DihedralGroup(6) + transversal, slps = _orbit_transversal(G.degree, G.generators, 0, True, slp=True) + for i, t in transversal: + slp = slps[i] + w = G.identity + for s in slp: + w = G.generators[s]*w + assert w == t + + a = Permutation(list(range(1, 100)) + [0]) + G = PermutationGroup([a]) + assert [min(o) for o in G.orbits()] == [0] + G = PermutationGroup(rubik_cube_generators()) + assert [min(o) for o in G.orbits()] == [0, 1] + assert not G.is_transitive() and not G.is_transitive(strict=False) + G = PermutationGroup([Permutation(0, 1, 3), Permutation(3)(0, 1)]) + assert not G.is_transitive() and G.is_transitive(strict=False) + assert PermutationGroup( + Permutation(3)).is_transitive(strict=False) is False + + +def test_is_normal(): + gens_s5 = [Permutation(p) for p in [[1, 2, 3, 4, 0], [2, 1, 4, 0, 3]]] + G1 = PermutationGroup(gens_s5) + assert G1.order() == 120 + gens_a5 = [Permutation(p) for p in [[1, 0, 3, 2, 4], [2, 1, 4, 3, 0]]] + G2 = PermutationGroup(gens_a5) + assert G2.order() == 60 + assert G2.is_normal(G1) + gens3 = [Permutation(p) for p in [[2, 1, 3, 0, 4], [1, 2, 0, 3, 4]]] + G3 = PermutationGroup(gens3) + assert not G3.is_normal(G1) + assert G3.order() == 12 + G4 = G1.normal_closure(G3.generators) + assert G4.order() == 60 + gens5 = [Permutation(p) for p in [[1, 2, 3, 0, 4], [1, 2, 0, 3, 4]]] + G5 = PermutationGroup(gens5) + assert G5.order() == 24 + G6 = G1.normal_closure(G5.generators) + assert G6.order() == 120 + assert G1.is_subgroup(G6) + assert not G1.is_subgroup(G4) + assert G2.is_subgroup(G4) + I5 = PermutationGroup(Permutation(4)) + assert I5.is_normal(G5) + assert I5.is_normal(G6, strict=False) + p1 = Permutation([1, 0, 2, 3, 4]) + p2 = Permutation([0, 1, 2, 4, 3]) + p3 = Permutation([3, 4, 2, 1, 0]) + id_ = Permutation([0, 1, 2, 3, 4]) + H = PermutationGroup([p1, p3]) + H_n1 = PermutationGroup([p1, p2]) + H_n2_1 = PermutationGroup(p1) + H_n2_2 = PermutationGroup(p2) + H_id = PermutationGroup(id_) + assert H_n1.is_normal(H) + assert H_n2_1.is_normal(H_n1) + assert H_n2_2.is_normal(H_n1) + assert H_id.is_normal(H_n2_1) + assert H_id.is_normal(H_n1) + assert H_id.is_normal(H) + assert not H_n2_1.is_normal(H) + assert not H_n2_2.is_normal(H) + + +def test_eq(): + a = [[1, 2, 0, 3, 4, 5], [1, 0, 2, 3, 4, 5], [2, 1, 0, 3, 4, 5], [ + 1, 2, 0, 3, 4, 5]] + a = [Permutation(p) for p in a + [[1, 2, 3, 4, 5, 0]]] + g = Permutation([1, 2, 3, 4, 5, 0]) + G1, G2, G3 = [PermutationGroup(x) for x in [a[:2], a[2:4], [g, g**2]]] + assert G1.order() == G2.order() == G3.order() == 6 + assert G1.is_subgroup(G2) + assert not G1.is_subgroup(G3) + G4 = PermutationGroup([Permutation([0, 1])]) + assert not G1.is_subgroup(G4) + assert G4.is_subgroup(G1, 0) + assert PermutationGroup(g, g).is_subgroup(PermutationGroup(g)) + assert SymmetricGroup(3).is_subgroup(SymmetricGroup(4), 0) + assert SymmetricGroup(3).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0) + assert not CyclicGroup(5).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0) + assert CyclicGroup(3).is_subgroup(SymmetricGroup(3)*CyclicGroup(5), 0) + + +def test_derived_subgroup(): + a = Permutation([1, 0, 2, 4, 3]) + b = Permutation([0, 1, 3, 2, 4]) + G = PermutationGroup([a, b]) + C = G.derived_subgroup() + assert C.order() == 3 + assert C.is_normal(G) + assert C.is_subgroup(G, 0) + assert not G.is_subgroup(C, 0) + gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]] + gens = [Permutation(p) for p in gens_cube] + G = PermutationGroup(gens) + C = G.derived_subgroup() + assert C.order() == 12 + + +def test_is_solvable(): + a = Permutation([1, 2, 0]) + b = Permutation([1, 0, 2]) + G = PermutationGroup([a, b]) + assert G.is_solvable + G = PermutationGroup([a]) + assert G.is_solvable + a = Permutation([1, 2, 3, 4, 0]) + b = Permutation([1, 0, 2, 3, 4]) + G = PermutationGroup([a, b]) + assert not G.is_solvable + P = SymmetricGroup(10) + S = P.sylow_subgroup(3) + assert S.is_solvable + +def test_rubik1(): + gens = rubik_cube_generators() + gens1 = [gens[-1]] + [p**2 for p in gens[1:]] + G1 = PermutationGroup(gens1) + assert G1.order() == 19508428800 + gens2 = [p**2 for p in gens] + G2 = PermutationGroup(gens2) + assert G2.order() == 663552 + assert G2.is_subgroup(G1, 0) + C1 = G1.derived_subgroup() + assert C1.order() == 4877107200 + assert C1.is_subgroup(G1, 0) + assert not G2.is_subgroup(C1, 0) + + G = RubikGroup(2) + assert G.order() == 3674160 + + +@XFAIL +def test_rubik(): + skip('takes too much time') + G = PermutationGroup(rubik_cube_generators()) + assert G.order() == 43252003274489856000 + G1 = PermutationGroup(G[:3]) + assert G1.order() == 170659735142400 + assert not G1.is_normal(G) + G2 = G.normal_closure(G1.generators) + assert G2.is_subgroup(G) + + +def test_direct_product(): + C = CyclicGroup(4) + D = DihedralGroup(4) + G = C*C*C + assert G.order() == 64 + assert G.degree == 12 + assert len(G.orbits()) == 3 + assert G.is_abelian is True + H = D*C + assert H.order() == 32 + assert H.is_abelian is False + + +def test_orbit_rep(): + G = DihedralGroup(6) + assert G.orbit_rep(1, 3) in [Permutation([2, 3, 4, 5, 0, 1]), + Permutation([4, 3, 2, 1, 0, 5])] + H = CyclicGroup(4)*G + assert H.orbit_rep(1, 5) is False + + +def test_schreier_vector(): + G = CyclicGroup(50) + v = [0]*50 + v[23] = -1 + assert G.schreier_vector(23) == v + H = DihedralGroup(8) + assert H.schreier_vector(2) == [0, 1, -1, 0, 0, 1, 0, 0] + L = SymmetricGroup(4) + assert L.schreier_vector(1) == [1, -1, 0, 0] + + +def test_random_pr(): + D = DihedralGroup(6) + r = 11 + n = 3 + _random_prec_n = {} + _random_prec_n[0] = {'s': 7, 't': 3, 'x': 2, 'e': -1} + _random_prec_n[1] = {'s': 5, 't': 5, 'x': 1, 'e': -1} + _random_prec_n[2] = {'s': 3, 't': 4, 'x': 2, 'e': 1} + D._random_pr_init(r, n, _random_prec_n=_random_prec_n) + assert D._random_gens[11] == [0, 1, 2, 3, 4, 5] + _random_prec = {'s': 2, 't': 9, 'x': 1, 'e': -1} + assert D.random_pr(_random_prec=_random_prec) == \ + Permutation([0, 5, 4, 3, 2, 1]) + + +def test_is_alt_sym(): + G = DihedralGroup(10) + assert G.is_alt_sym() is False + assert G._eval_is_alt_sym_naive() is False + assert G._eval_is_alt_sym_naive(only_alt=True) is False + assert G._eval_is_alt_sym_naive(only_sym=True) is False + + S = SymmetricGroup(10) + assert S._eval_is_alt_sym_naive() is True + assert S._eval_is_alt_sym_naive(only_alt=True) is False + assert S._eval_is_alt_sym_naive(only_sym=True) is True + + N_eps = 10 + _random_prec = {'N_eps': N_eps, + 0: Permutation([[2], [1, 4], [0, 6, 7, 8, 9, 3, 5]]), + 1: Permutation([[1, 8, 7, 6, 3, 5, 2, 9], [0, 4]]), + 2: Permutation([[5, 8], [4, 7], [0, 1, 2, 3, 6, 9]]), + 3: Permutation([[3], [0, 8, 2, 7, 4, 1, 6, 9, 5]]), + 4: Permutation([[8], [4, 7, 9], [3, 6], [0, 5, 1, 2]]), + 5: Permutation([[6], [0, 2, 4, 5, 1, 8, 3, 9, 7]]), + 6: Permutation([[6, 9, 8], [4, 5], [1, 3, 7], [0, 2]]), + 7: Permutation([[4], [0, 2, 9, 1, 3, 8, 6, 5, 7]]), + 8: Permutation([[1, 5, 6, 3], [0, 2, 7, 8, 4, 9]]), + 9: Permutation([[8], [6, 7], [2, 3, 4, 5], [0, 1, 9]])} + assert S.is_alt_sym(_random_prec=_random_prec) is True + + A = AlternatingGroup(10) + assert A._eval_is_alt_sym_naive() is True + assert A._eval_is_alt_sym_naive(only_alt=True) is True + assert A._eval_is_alt_sym_naive(only_sym=True) is False + + _random_prec = {'N_eps': N_eps, + 0: Permutation([[1, 6, 4, 2, 7, 8, 5, 9, 3], [0]]), + 1: Permutation([[1], [0, 5, 8, 4, 9, 2, 3, 6, 7]]), + 2: Permutation([[1, 9, 8, 3, 2, 5], [0, 6, 7, 4]]), + 3: Permutation([[6, 8, 9], [4, 5], [1, 3, 7, 2], [0]]), + 4: Permutation([[8], [5], [4], [2, 6, 9, 3], [1], [0, 7]]), + 5: Permutation([[3, 6], [0, 8, 1, 7, 5, 9, 4, 2]]), + 6: Permutation([[5], [2, 9], [1, 8, 3], [0, 4, 7, 6]]), + 7: Permutation([[1, 8, 4, 7, 2, 3], [0, 6, 9, 5]]), + 8: Permutation([[5, 8, 7], [3], [1, 4, 2, 6], [0, 9]]), + 9: Permutation([[4, 9, 6], [3, 8], [1, 2], [0, 5, 7]])} + assert A.is_alt_sym(_random_prec=_random_prec) is False + + G = PermutationGroup( + Permutation(1, 3, size=8)(0, 2, 4, 6), + Permutation(5, 7, size=8)(0, 2, 4, 6)) + assert G.is_alt_sym() is False + + # Tests for monte-carlo c_n parameter setting, and which guarantees + # to give False. + G = DihedralGroup(10) + assert G._eval_is_alt_sym_monte_carlo() is False + G = DihedralGroup(20) + assert G._eval_is_alt_sym_monte_carlo() is False + + # A dry-running test to check if it looks up for the updated cache. + G = DihedralGroup(6) + G.is_alt_sym() + assert G.is_alt_sym() is False + + +def test_minimal_block(): + D = DihedralGroup(6) + block_system = D.minimal_block([0, 3]) + for i in range(3): + assert block_system[i] == block_system[i + 3] + S = SymmetricGroup(6) + assert S.minimal_block([0, 1]) == [0, 0, 0, 0, 0, 0] + + assert Tetra.pgroup.minimal_block([0, 1]) == [0, 0, 0, 0] + + P1 = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5)) + P2 = PermutationGroup(Permutation(0, 1, 2, 3, 4, 5), Permutation(1, 5)(2, 4)) + assert P1.minimal_block([0, 2]) == [0, 1, 0, 1, 0, 1] + assert P2.minimal_block([0, 2]) == [0, 1, 0, 1, 0, 1] + + +def test_minimal_blocks(): + P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5)) + assert P.minimal_blocks() == [[0, 1, 0, 1, 0, 1], [0, 1, 2, 0, 1, 2]] + + P = SymmetricGroup(5) + assert P.minimal_blocks() == [[0]*5] + + P = PermutationGroup(Permutation(0, 3)) + assert P.minimal_blocks() is False + + +def test_max_div(): + S = SymmetricGroup(10) + assert S.max_div == 5 + + +def test_is_primitive(): + S = SymmetricGroup(5) + assert S.is_primitive() is True + C = CyclicGroup(7) + assert C.is_primitive() is True + + a = Permutation(0, 1, 2, size=6) + b = Permutation(3, 4, 5, size=6) + G = PermutationGroup(a, b) + assert G.is_primitive() is False + + +def test_random_stab(): + S = SymmetricGroup(5) + _random_el = Permutation([1, 3, 2, 0, 4]) + _random_prec = {'rand': _random_el} + g = S.random_stab(2, _random_prec=_random_prec) + assert g == Permutation([1, 3, 2, 0, 4]) + h = S.random_stab(1) + assert h(1) == 1 + + +def test_transitivity_degree(): + perm = Permutation([1, 2, 0]) + C = PermutationGroup([perm]) + assert C.transitivity_degree == 1 + gen1 = Permutation([1, 2, 0, 3, 4]) + gen2 = Permutation([1, 2, 3, 4, 0]) + # alternating group of degree 5 + Alt = PermutationGroup([gen1, gen2]) + assert Alt.transitivity_degree == 3 + + +def test_schreier_sims_random(): + assert sorted(Tetra.pgroup.base) == [0, 1] + + S = SymmetricGroup(3) + base = [0, 1] + strong_gens = [Permutation([1, 2, 0]), Permutation([1, 0, 2]), + Permutation([0, 2, 1])] + assert S.schreier_sims_random(base, strong_gens, 5) == (base, strong_gens) + D = DihedralGroup(3) + _random_prec = {'g': [Permutation([2, 0, 1]), Permutation([1, 2, 0]), + Permutation([1, 0, 2])]} + base = [0, 1] + strong_gens = [Permutation([1, 2, 0]), Permutation([2, 1, 0]), + Permutation([0, 2, 1])] + assert D.schreier_sims_random([], D.generators, 2, + _random_prec=_random_prec) == (base, strong_gens) + + +def test_baseswap(): + S = SymmetricGroup(4) + S.schreier_sims() + base = S.base + strong_gens = S.strong_gens + assert base == [0, 1, 2] + deterministic = S.baseswap(base, strong_gens, 1, randomized=False) + randomized = S.baseswap(base, strong_gens, 1) + assert deterministic[0] == [0, 2, 1] + assert _verify_bsgs(S, deterministic[0], deterministic[1]) is True + assert randomized[0] == [0, 2, 1] + assert _verify_bsgs(S, randomized[0], randomized[1]) is True + + +def test_schreier_sims_incremental(): + identity = Permutation([0, 1, 2, 3, 4]) + TrivialGroup = PermutationGroup([identity]) + base, strong_gens = TrivialGroup.schreier_sims_incremental(base=[0, 1, 2]) + assert _verify_bsgs(TrivialGroup, base, strong_gens) is True + S = SymmetricGroup(5) + base, strong_gens = S.schreier_sims_incremental(base=[0, 1, 2]) + assert _verify_bsgs(S, base, strong_gens) is True + D = DihedralGroup(2) + base, strong_gens = D.schreier_sims_incremental(base=[1]) + assert _verify_bsgs(D, base, strong_gens) is True + A = AlternatingGroup(7) + gens = A.generators[:] + gen0 = gens[0] + gen1 = gens[1] + gen1 = rmul(gen1, ~gen0) + gen0 = rmul(gen0, gen1) + gen1 = rmul(gen0, gen1) + base, strong_gens = A.schreier_sims_incremental(base=[0, 1], gens=gens) + assert _verify_bsgs(A, base, strong_gens) is True + C = CyclicGroup(11) + gen = C.generators[0] + base, strong_gens = C.schreier_sims_incremental(gens=[gen**3]) + assert _verify_bsgs(C, base, strong_gens) is True + + +def _subgroup_search(i, j, k): + prop_true = lambda x: True + prop_fix_points = lambda x: [x(point) for point in points] == points + prop_comm_g = lambda x: rmul(x, g) == rmul(g, x) + prop_even = lambda x: x.is_even + for i in range(i, j, k): + S = SymmetricGroup(i) + A = AlternatingGroup(i) + C = CyclicGroup(i) + Sym = S.subgroup_search(prop_true) + assert Sym.is_subgroup(S) + Alt = S.subgroup_search(prop_even) + assert Alt.is_subgroup(A) + Sym = S.subgroup_search(prop_true, init_subgroup=C) + assert Sym.is_subgroup(S) + points = [7] + assert S.stabilizer(7).is_subgroup(S.subgroup_search(prop_fix_points)) + points = [3, 4] + assert S.stabilizer(3).stabilizer(4).is_subgroup( + S.subgroup_search(prop_fix_points)) + points = [3, 5] + fix35 = A.subgroup_search(prop_fix_points) + points = [5] + fix5 = A.subgroup_search(prop_fix_points) + assert A.subgroup_search(prop_fix_points, init_subgroup=fix35 + ).is_subgroup(fix5) + base, strong_gens = A.schreier_sims_incremental() + g = A.generators[0] + comm_g = \ + A.subgroup_search(prop_comm_g, base=base, strong_gens=strong_gens) + assert _verify_bsgs(comm_g, base, comm_g.generators) is True + assert [prop_comm_g(gen) is True for gen in comm_g.generators] + + +def test_subgroup_search(): + _subgroup_search(10, 15, 2) + + +@XFAIL +def test_subgroup_search2(): + skip('takes too much time') + _subgroup_search(16, 17, 1) + + +def test_normal_closure(): + # the normal closure of the trivial group is trivial + S = SymmetricGroup(3) + identity = Permutation([0, 1, 2]) + closure = S.normal_closure(identity) + assert closure.is_trivial + # the normal closure of the entire group is the entire group + A = AlternatingGroup(4) + assert A.normal_closure(A).is_subgroup(A) + # brute-force verifications for subgroups + for i in (3, 4, 5): + S = SymmetricGroup(i) + A = AlternatingGroup(i) + D = DihedralGroup(i) + C = CyclicGroup(i) + for gp in (A, D, C): + assert _verify_normal_closure(S, gp) + # brute-force verifications for all elements of a group + S = SymmetricGroup(5) + elements = list(S.generate_dimino()) + for element in elements: + assert _verify_normal_closure(S, element) + # small groups + small = [] + for i in (1, 2, 3): + small.append(SymmetricGroup(i)) + small.append(AlternatingGroup(i)) + small.append(DihedralGroup(i)) + small.append(CyclicGroup(i)) + for gp in small: + for gp2 in small: + if gp2.is_subgroup(gp, 0) and gp2.degree == gp.degree: + assert _verify_normal_closure(gp, gp2) + + +def test_derived_series(): + # the derived series of the trivial group consists only of the trivial group + triv = PermutationGroup([Permutation([0, 1, 2])]) + assert triv.derived_series()[0].is_subgroup(triv) + # the derived series for a simple group consists only of the group itself + for i in (5, 6, 7): + A = AlternatingGroup(i) + assert A.derived_series()[0].is_subgroup(A) + # the derived series for S_4 is S_4 > A_4 > K_4 > triv + S = SymmetricGroup(4) + series = S.derived_series() + assert series[1].is_subgroup(AlternatingGroup(4)) + assert series[2].is_subgroup(DihedralGroup(2)) + assert series[3].is_trivial + + +def test_lower_central_series(): + # the lower central series of the trivial group consists of the trivial + # group + triv = PermutationGroup([Permutation([0, 1, 2])]) + assert triv.lower_central_series()[0].is_subgroup(triv) + # the lower central series of a simple group consists of the group itself + for i in (5, 6, 7): + A = AlternatingGroup(i) + assert A.lower_central_series()[0].is_subgroup(A) + # GAP-verified example + S = SymmetricGroup(6) + series = S.lower_central_series() + assert len(series) == 2 + assert series[1].is_subgroup(AlternatingGroup(6)) + + +def test_commutator(): + # the commutator of the trivial group and the trivial group is trivial + S = SymmetricGroup(3) + triv = PermutationGroup([Permutation([0, 1, 2])]) + assert S.commutator(triv, triv).is_subgroup(triv) + # the commutator of the trivial group and any other group is again trivial + A = AlternatingGroup(3) + assert S.commutator(triv, A).is_subgroup(triv) + # the commutator is commutative + for i in (3, 4, 5): + S = SymmetricGroup(i) + A = AlternatingGroup(i) + D = DihedralGroup(i) + assert S.commutator(A, D).is_subgroup(S.commutator(D, A)) + # the commutator of an abelian group is trivial + S = SymmetricGroup(7) + A1 = AbelianGroup(2, 5) + A2 = AbelianGroup(3, 4) + triv = PermutationGroup([Permutation([0, 1, 2, 3, 4, 5, 6])]) + assert S.commutator(A1, A1).is_subgroup(triv) + assert S.commutator(A2, A2).is_subgroup(triv) + # examples calculated by hand + S = SymmetricGroup(3) + A = AlternatingGroup(3) + assert S.commutator(A, S).is_subgroup(A) + + +def test_is_nilpotent(): + # every abelian group is nilpotent + for i in (1, 2, 3): + C = CyclicGroup(i) + Ab = AbelianGroup(i, i + 2) + assert C.is_nilpotent + assert Ab.is_nilpotent + Ab = AbelianGroup(5, 7, 10) + assert Ab.is_nilpotent + # A_5 is not solvable and thus not nilpotent + assert AlternatingGroup(5).is_nilpotent is False + + +def test_is_trivial(): + for i in range(5): + triv = PermutationGroup([Permutation(list(range(i)))]) + assert triv.is_trivial + + +def test_pointwise_stabilizer(): + S = SymmetricGroup(2) + stab = S.pointwise_stabilizer([0]) + assert stab.generators == [Permutation(1)] + S = SymmetricGroup(5) + points = [] + stab = S + for point in (2, 0, 3, 4, 1): + stab = stab.stabilizer(point) + points.append(point) + assert S.pointwise_stabilizer(points).is_subgroup(stab) + + +def test_make_perm(): + assert cube.pgroup.make_perm(5, seed=list(range(5))) == \ + Permutation([4, 7, 6, 5, 0, 3, 2, 1]) + assert cube.pgroup.make_perm(7, seed=list(range(7))) == \ + Permutation([6, 7, 3, 2, 5, 4, 0, 1]) + + +def test_elements(): + from sympy.sets.sets import FiniteSet + + p = Permutation(2, 3) + assert set(PermutationGroup(p).elements) == {Permutation(3), Permutation(2, 3)} + assert FiniteSet(*PermutationGroup(p).elements) \ + == FiniteSet(Permutation(2, 3), Permutation(3)) + + +def test_is_group(): + assert PermutationGroup(Permutation(1,2), Permutation(2,4)).is_group is True + assert SymmetricGroup(4).is_group is True + + +def test_PermutationGroup(): + assert PermutationGroup() == PermutationGroup(Permutation()) + assert (PermutationGroup() == 0) is False + + +def test_coset_transvesal(): + G = AlternatingGroup(5) + H = PermutationGroup(Permutation(0,1,2),Permutation(1,2)(3,4)) + assert G.coset_transversal(H) == \ + [Permutation(4), Permutation(2, 3, 4), Permutation(2, 4, 3), + Permutation(1, 2, 4), Permutation(4)(1, 2, 3), Permutation(1, 3)(2, 4), + Permutation(0, 1, 2, 3, 4), Permutation(0, 1, 2, 4, 3), + Permutation(0, 1, 3, 2, 4), Permutation(0, 2, 4, 1, 3)] + + +def test_coset_table(): + G = PermutationGroup(Permutation(0,1,2,3), Permutation(0,1,2), + Permutation(0,4,2,7), Permutation(5,6), Permutation(0,7)); + H = PermutationGroup(Permutation(0,1,2,3), Permutation(0,7)) + assert G.coset_table(H) == \ + [[0, 0, 0, 0, 1, 2, 3, 3, 0, 0], [4, 5, 2, 5, 6, 0, 7, 7, 1, 1], + [5, 4, 5, 1, 0, 6, 8, 8, 6, 6], [3, 3, 3, 3, 7, 8, 0, 0, 3, 3], + [2, 1, 4, 4, 4, 4, 9, 9, 4, 4], [1, 2, 1, 2, 5, 5, 10, 10, 5, 5], + [6, 6, 6, 6, 2, 1, 11, 11, 2, 2], [9, 10, 8, 10, 11, 3, 1, 1, 7, 7], + [10, 9, 10, 7, 3, 11, 2, 2, 11, 11], [8, 7, 9, 9, 9, 9, 4, 4, 9, 9], + [7, 8, 7, 8, 10, 10, 5, 5, 10, 10], [11, 11, 11, 11, 8, 7, 6, 6, 8, 8]] + + +def test_subgroup(): + G = PermutationGroup(Permutation(0,1,2), Permutation(0,2,3)) + H = G.subgroup([Permutation(0,1,3)]) + assert H.is_subgroup(G) + + +def test_generator_product(): + G = SymmetricGroup(5) + p = Permutation(0, 2, 3)(1, 4) + gens = G.generator_product(p) + assert all(g in G.strong_gens for g in gens) + w = G.identity + for g in gens: + w = g*w + assert w == p + + +def test_sylow_subgroup(): + P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5)) + S = P.sylow_subgroup(2) + assert S.order() == 4 + + P = DihedralGroup(12) + S = P.sylow_subgroup(3) + assert S.order() == 3 + + P = PermutationGroup( + Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5), Permutation(0, 2)) + S = P.sylow_subgroup(3) + assert S.order() == 9 + S = P.sylow_subgroup(2) + assert S.order() == 8 + + P = SymmetricGroup(10) + S = P.sylow_subgroup(2) + assert S.order() == 256 + S = P.sylow_subgroup(3) + assert S.order() == 81 + S = P.sylow_subgroup(5) + assert S.order() == 25 + + # the length of the lower central series + # of a p-Sylow subgroup of Sym(n) grows with + # the highest exponent exp of p such + # that n >= p**exp + exp = 1 + length = 0 + for i in range(2, 9): + P = SymmetricGroup(i) + S = P.sylow_subgroup(2) + ls = S.lower_central_series() + if i // 2**exp > 0: + # length increases with exponent + assert len(ls) > length + length = len(ls) + exp += 1 + else: + assert len(ls) == length + + G = SymmetricGroup(100) + S = G.sylow_subgroup(3) + assert G.order() % S.order() == 0 + assert G.order()/S.order() % 3 > 0 + + G = AlternatingGroup(100) + S = G.sylow_subgroup(2) + assert G.order() % S.order() == 0 + assert G.order()/S.order() % 2 > 0 + + G = DihedralGroup(18) + S = G.sylow_subgroup(p=2) + assert S.order() == 4 + + G = DihedralGroup(50) + S = G.sylow_subgroup(p=2) + assert S.order() == 4 + + +@slow +def test_presentation(): + def _test(P): + G = P.presentation() + return G.order() == P.order() + + def _strong_test(P): + G = P.strong_presentation() + chk = len(G.generators) == len(P.strong_gens) + return chk and G.order() == P.order() + + P = PermutationGroup(Permutation(0,1,5,2)(3,7,4,6), Permutation(0,3,5,4)(1,6,2,7)) + assert _test(P) + + P = AlternatingGroup(5) + assert _test(P) + + P = SymmetricGroup(5) + assert _test(P) + + P = PermutationGroup( + [Permutation(0,3,1,2), Permutation(3)(0,1), Permutation(0,1)(2,3)]) + assert _strong_test(P) + + P = DihedralGroup(6) + assert _strong_test(P) + + a = Permutation(0,1)(2,3) + b = Permutation(0,2)(3,1) + c = Permutation(4,5) + P = PermutationGroup(c, a, b) + assert _strong_test(P) + + +def test_polycyclic(): + a = Permutation([0, 1, 2]) + b = Permutation([2, 1, 0]) + G = PermutationGroup([a, b]) + assert G.is_polycyclic is True + + a = Permutation([1, 2, 3, 4, 0]) + b = Permutation([1, 0, 2, 3, 4]) + G = PermutationGroup([a, b]) + assert G.is_polycyclic is False + + +def test_elementary(): + a = Permutation([1, 5, 2, 0, 3, 6, 4]) + G = PermutationGroup([a]) + assert G.is_elementary(7) is False + + a = Permutation(0, 1)(2, 3) + b = Permutation(0, 2)(3, 1) + G = PermutationGroup([a, b]) + assert G.is_elementary(2) is True + c = Permutation(4, 5, 6) + G = PermutationGroup([a, b, c]) + assert G.is_elementary(2) is False + + G = SymmetricGroup(4).sylow_subgroup(2) + assert G.is_elementary(2) is False + H = AlternatingGroup(4).sylow_subgroup(2) + assert H.is_elementary(2) is True + + +def test_perfect(): + G = AlternatingGroup(3) + assert G.is_perfect is False + G = AlternatingGroup(5) + assert G.is_perfect is True + + +def test_index(): + G = PermutationGroup(Permutation(0,1,2), Permutation(0,2,3)) + H = G.subgroup([Permutation(0,1,3)]) + assert G.index(H) == 4 + + +def test_cyclic(): + G = SymmetricGroup(2) + assert G.is_cyclic + G = AbelianGroup(3, 7) + assert G.is_cyclic + G = AbelianGroup(7, 7) + assert not G.is_cyclic + G = AlternatingGroup(3) + assert G.is_cyclic + G = AlternatingGroup(4) + assert not G.is_cyclic + + # Order less than 6 + G = PermutationGroup(Permutation(0, 1, 2), Permutation(0, 2, 1)) + assert G.is_cyclic + G = PermutationGroup( + Permutation(0, 1, 2, 3), + Permutation(0, 2)(1, 3) + ) + assert G.is_cyclic + G = PermutationGroup( + Permutation(3), + Permutation(0, 1)(2, 3), + Permutation(0, 2)(1, 3), + Permutation(0, 3)(1, 2) + ) + assert G.is_cyclic is False + + # Order 15 + G = PermutationGroup( + Permutation(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14), + Permutation(0, 2, 4, 6, 8, 10, 12, 14, 1, 3, 5, 7, 9, 11, 13) + ) + assert G.is_cyclic + + # Distinct prime orders + assert PermutationGroup._distinct_primes_lemma([3, 5]) is True + assert PermutationGroup._distinct_primes_lemma([5, 7]) is True + assert PermutationGroup._distinct_primes_lemma([2, 3]) is None + assert PermutationGroup._distinct_primes_lemma([3, 5, 7]) is None + assert PermutationGroup._distinct_primes_lemma([5, 7, 13]) is True + + G = PermutationGroup( + Permutation(0, 1, 2, 3), + Permutation(0, 2)(1, 3)) + assert G.is_cyclic + assert G._is_abelian + + # Non-abelian and therefore not cyclic + G = PermutationGroup(*SymmetricGroup(3).generators) + assert G.is_cyclic is False + + # Abelian and cyclic + G = PermutationGroup( + Permutation(0, 1, 2, 3), + Permutation(4, 5, 6) + ) + assert G.is_cyclic + + # Abelian but not cyclic + G = PermutationGroup( + Permutation(0, 1), + Permutation(2, 3), + Permutation(4, 5, 6) + ) + assert G.is_cyclic is False + + +def test_dihedral(): + G = SymmetricGroup(2) + assert G.is_dihedral + G = SymmetricGroup(3) + assert G.is_dihedral + + G = AbelianGroup(2, 2) + assert G.is_dihedral + G = CyclicGroup(4) + assert not G.is_dihedral + + G = AbelianGroup(3, 5) + assert not G.is_dihedral + G = AbelianGroup(2) + assert G.is_dihedral + G = AbelianGroup(6) + assert not G.is_dihedral + + # D6, generated by two adjacent flips + G = PermutationGroup( + Permutation(1, 5)(2, 4), + Permutation(0, 1)(3, 4)(2, 5)) + assert G.is_dihedral + + # D7, generated by a flip and a rotation + G = PermutationGroup( + Permutation(1, 6)(2, 5)(3, 4), + Permutation(0, 1, 2, 3, 4, 5, 6)) + assert G.is_dihedral + + # S4, presented by three generators, fails due to having exactly 9 + # elements of order 2: + G = PermutationGroup( + Permutation(0, 1), Permutation(0, 2), + Permutation(0, 3)) + assert not G.is_dihedral + + # D7, given by three generators + G = PermutationGroup( + Permutation(1, 6)(2, 5)(3, 4), + Permutation(2, 0)(3, 6)(4, 5), + Permutation(0, 1, 2, 3, 4, 5, 6)) + assert G.is_dihedral + + +def test_abelian_invariants(): + G = AbelianGroup(2, 3, 4) + assert G.abelian_invariants() == [2, 3, 4] + G=PermutationGroup([Permutation(1, 2, 3, 4), Permutation(1, 2), Permutation(5, 6)]) + assert G.abelian_invariants() == [2, 2] + G = AlternatingGroup(7) + assert G.abelian_invariants() == [] + G = AlternatingGroup(4) + assert G.abelian_invariants() == [3] + G = DihedralGroup(4) + assert G.abelian_invariants() == [2, 2] + + G = PermutationGroup([Permutation(1, 2, 3, 4, 5, 6, 7)]) + assert G.abelian_invariants() == [7] + G = DihedralGroup(12) + S = G.sylow_subgroup(3) + assert S.abelian_invariants() == [3] + G = PermutationGroup(Permutation(0, 1, 2), Permutation(0, 2, 3)) + assert G.abelian_invariants() == [3] + G = PermutationGroup([Permutation(0, 1), Permutation(0, 2, 4, 6)(1, 3, 5, 7)]) + assert G.abelian_invariants() == [2, 4] + G = SymmetricGroup(30) + S = G.sylow_subgroup(2) + assert S.abelian_invariants() == [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] + S = G.sylow_subgroup(3) + assert S.abelian_invariants() == [3, 3, 3, 3] + S = G.sylow_subgroup(5) + assert S.abelian_invariants() == [5, 5, 5] + + +def test_composition_series(): + a = Permutation(1, 2, 3) + b = Permutation(1, 2) + G = PermutationGroup([a, b]) + comp_series = G.composition_series() + assert comp_series == G.derived_series() + # The first group in the composition series is always the group itself and + # the last group in the series is the trivial group. + S = SymmetricGroup(4) + assert S.composition_series()[0] == S + assert len(S.composition_series()) == 5 + A = AlternatingGroup(4) + assert A.composition_series()[0] == A + assert len(A.composition_series()) == 4 + + # the composition series for C_8 is C_8 > C_4 > C_2 > triv + G = CyclicGroup(8) + series = G.composition_series() + assert is_isomorphic(series[1], CyclicGroup(4)) + assert is_isomorphic(series[2], CyclicGroup(2)) + assert series[3].is_trivial + + +def test_is_symmetric(): + a = Permutation(0, 1, 2) + b = Permutation(0, 1, size=3) + assert PermutationGroup(a, b).is_symmetric is True + + a = Permutation(0, 2, 1) + b = Permutation(1, 2, size=3) + assert PermutationGroup(a, b).is_symmetric is True + + a = Permutation(0, 1, 2, 3) + b = Permutation(0, 3)(1, 2) + assert PermutationGroup(a, b).is_symmetric is False + +def test_conjugacy_class(): + S = SymmetricGroup(4) + x = Permutation(1, 2, 3) + C = {Permutation(0, 1, 2, size = 4), Permutation(0, 1, 3), + Permutation(0, 2, 1, size = 4), Permutation(0, 2, 3), + Permutation(0, 3, 1), Permutation(0, 3, 2), + Permutation(1, 2, 3), Permutation(1, 3, 2)} + assert S.conjugacy_class(x) == C + +def test_conjugacy_classes(): + S = SymmetricGroup(3) + expected = [{Permutation(size = 3)}, + {Permutation(0, 1, size = 3), Permutation(0, 2), Permutation(1, 2)}, + {Permutation(0, 1, 2), Permutation(0, 2, 1)}] + computed = S.conjugacy_classes() + + assert len(expected) == len(computed) + assert all(e in computed for e in expected) + +def test_coset_class(): + a = Permutation(1, 2) + b = Permutation(0, 1) + G = PermutationGroup([a, b]) + #Creating right coset + rht_coset = G*a + #Checking whether it is left coset or right coset + assert rht_coset.is_right_coset + assert not rht_coset.is_left_coset + #Creating list representation of coset + list_repr = rht_coset.as_list() + expected = [Permutation(0, 2), Permutation(0, 2, 1), Permutation(1, 2), + Permutation(2), Permutation(2)(0, 1), Permutation(0, 1, 2)] + for ele in list_repr: + assert ele in expected + #Creating left coset + left_coset = a*G + #Checking whether it is left coset or right coset + assert not left_coset.is_right_coset + assert left_coset.is_left_coset + #Creating list representation of Coset + list_repr = left_coset.as_list() + expected = [Permutation(2)(0, 1), Permutation(0, 1, 2), Permutation(1, 2), + Permutation(2), Permutation(0, 2), Permutation(0, 2, 1)] + for ele in list_repr: + assert ele in expected + + G = PermutationGroup(Permutation(1, 2, 3, 4), Permutation(2, 3, 4)) + H = PermutationGroup(Permutation(1, 2, 3, 4)) + g = Permutation(1, 3)(2, 4) + rht_coset = Coset(g, H, G, dir='+') + assert rht_coset.is_right_coset + list_repr = rht_coset.as_list() + expected = [Permutation(1, 2, 3, 4), Permutation(4), Permutation(1, 3)(2, 4), + Permutation(1, 4, 3, 2)] + for ele in list_repr: + assert ele in expected + +def test_symmetricpermutationgroup(): + a = SymmetricPermutationGroup(5) + assert a.degree == 5 + assert a.order() == 120 + assert a.identity() == Permutation(4) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_permutations.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_permutations.py new file mode 100644 index 0000000000000000000000000000000000000000..b52fcfec0e2fb3be872efaa814077760e121c748 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_permutations.py @@ -0,0 +1,564 @@ +from itertools import permutations +from copy import copy + +from sympy.core.expr import unchanged +from sympy.core.numbers import Integer +from sympy.core.relational import Eq +from sympy.core.symbol import Symbol +from sympy.core.singleton import S +from sympy.combinatorics.permutations import \ + Permutation, _af_parity, _af_rmul, _af_rmuln, AppliedPermutation, Cycle +from sympy.printing import sstr, srepr, pretty, latex +from sympy.testing.pytest import raises, warns_deprecated_sympy + + +rmul = Permutation.rmul +a = Symbol('a', integer=True) + + +def test_Permutation(): + # don't auto fill 0 + raises(ValueError, lambda: Permutation([1])) + p = Permutation([0, 1, 2, 3]) + # call as bijective + assert [p(i) for i in range(p.size)] == list(p) + # call as operator + assert p(list(range(p.size))) == list(p) + # call as function + assert list(p(1, 2)) == [0, 2, 1, 3] + raises(TypeError, lambda: p(-1)) + raises(TypeError, lambda: p(5)) + # conversion to list + assert list(p) == list(range(4)) + assert p.copy() == p + assert copy(p) == p + assert Permutation(size=4) == Permutation(3) + assert Permutation(Permutation(3), size=5) == Permutation(4) + # cycle form with size + assert Permutation([[1, 2]], size=4) == Permutation([[1, 2], [0], [3]]) + # random generation + assert Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1])) + + p = Permutation([2, 5, 1, 6, 3, 0, 4]) + q = Permutation([[1], [0, 3, 5, 6, 2, 4]]) + assert len({p, p}) == 1 + r = Permutation([1, 3, 2, 0, 4, 6, 5]) + ans = Permutation(_af_rmuln(*[w.array_form for w in (p, q, r)])).array_form + assert rmul(p, q, r).array_form == ans + # make sure no other permutation of p, q, r could have given + # that answer + for a, b, c in permutations((p, q, r)): + if (a, b, c) == (p, q, r): + continue + assert rmul(a, b, c).array_form != ans + + assert p.support() == list(range(7)) + assert q.support() == [0, 2, 3, 4, 5, 6] + assert Permutation(p.cyclic_form).array_form == p.array_form + assert p.cardinality == 5040 + assert q.cardinality == 5040 + assert q.cycles == 2 + assert rmul(q, p) == Permutation([4, 6, 1, 2, 5, 3, 0]) + assert rmul(p, q) == Permutation([6, 5, 3, 0, 2, 4, 1]) + assert _af_rmul(p.array_form, q.array_form) == \ + [6, 5, 3, 0, 2, 4, 1] + + assert rmul(Permutation([[1, 2, 3], [0, 4]]), + Permutation([[1, 2, 4], [0], [3]])).cyclic_form == \ + [[0, 4, 2], [1, 3]] + assert q.array_form == [3, 1, 4, 5, 0, 6, 2] + assert q.cyclic_form == [[0, 3, 5, 6, 2, 4]] + assert q.full_cyclic_form == [[0, 3, 5, 6, 2, 4], [1]] + assert p.cyclic_form == [[0, 2, 1, 5], [3, 6, 4]] + t = p.transpositions() + assert t == [(0, 5), (0, 1), (0, 2), (3, 4), (3, 6)] + assert Permutation.rmul(*[Permutation(Cycle(*ti)) for ti in (t)]) + assert Permutation([1, 0]).transpositions() == [(0, 1)] + + assert p**13 == p + assert q**0 == Permutation(list(range(q.size))) + assert q**-2 == ~q**2 + assert q**2 == Permutation([5, 1, 0, 6, 3, 2, 4]) + assert q**3 == q**2*q + assert q**4 == q**2*q**2 + + a = Permutation(1, 3) + b = Permutation(2, 0, 3) + I = Permutation(3) + assert ~a == a**-1 + assert a*~a == I + assert a*b**-1 == a*~b + + ans = Permutation(0, 5, 3, 1, 6)(2, 4) + assert (p + q.rank()).rank() == ans.rank() + assert (p + q.rank())._rank == ans.rank() + assert (q + p.rank()).rank() == ans.rank() + raises(TypeError, lambda: p + Permutation(list(range(10)))) + + assert (p - q.rank()).rank() == Permutation(0, 6, 3, 1, 2, 5, 4).rank() + assert p.rank() - q.rank() < 0 # for coverage: make sure mod is used + assert (q - p.rank()).rank() == Permutation(1, 4, 6, 2)(3, 5).rank() + + assert p*q == Permutation(_af_rmuln(*[list(w) for w in (q, p)])) + assert p*Permutation([]) == p + assert Permutation([])*p == p + assert p*Permutation([[0, 1]]) == Permutation([2, 5, 0, 6, 3, 1, 4]) + assert Permutation([[0, 1]])*p == Permutation([5, 2, 1, 6, 3, 0, 4]) + + pq = p ^ q + assert pq == Permutation([5, 6, 0, 4, 1, 2, 3]) + assert pq == rmul(q, p, ~q) + qp = q ^ p + assert qp == Permutation([4, 3, 6, 2, 1, 5, 0]) + assert qp == rmul(p, q, ~p) + raises(ValueError, lambda: p ^ Permutation([])) + + assert p.commutator(q) == Permutation(0, 1, 3, 4, 6, 5, 2) + assert q.commutator(p) == Permutation(0, 2, 5, 6, 4, 3, 1) + assert p.commutator(q) == ~q.commutator(p) + raises(ValueError, lambda: p.commutator(Permutation([]))) + + assert len(p.atoms()) == 7 + assert q.atoms() == {0, 1, 2, 3, 4, 5, 6} + + assert p.inversion_vector() == [2, 4, 1, 3, 1, 0] + assert q.inversion_vector() == [3, 1, 2, 2, 0, 1] + + assert Permutation.from_inversion_vector(p.inversion_vector()) == p + assert Permutation.from_inversion_vector(q.inversion_vector()).array_form\ + == q.array_form + raises(ValueError, lambda: Permutation.from_inversion_vector([0, 2])) + assert Permutation(list(range(500, -1, -1))).inversions() == 125250 + + s = Permutation([0, 4, 1, 3, 2]) + assert s.parity() == 0 + _ = s.cyclic_form # needed to create a value for _cyclic_form + assert len(s._cyclic_form) != s.size and s.parity() == 0 + assert not s.is_odd + assert s.is_even + assert Permutation([0, 1, 4, 3, 2]).parity() == 1 + assert _af_parity([0, 4, 1, 3, 2]) == 0 + assert _af_parity([0, 1, 4, 3, 2]) == 1 + + s = Permutation([0]) + + assert s.is_Singleton + assert Permutation([]).is_Empty + + r = Permutation([3, 2, 1, 0]) + assert (r**2).is_Identity + + assert rmul(~p, p).is_Identity + assert (~p)**13 == Permutation([5, 2, 0, 4, 6, 1, 3]) + assert p.max() == 6 + assert p.min() == 0 + + q = Permutation([[6], [5], [0, 1, 2, 3, 4]]) + + assert q.max() == 4 + assert q.min() == 0 + + p = Permutation([1, 5, 2, 0, 3, 6, 4]) + q = Permutation([[1, 2, 3, 5, 6], [0, 4]]) + + assert p.ascents() == [0, 3, 4] + assert q.ascents() == [1, 2, 4] + assert r.ascents() == [] + + assert p.descents() == [1, 2, 5] + assert q.descents() == [0, 3, 5] + assert Permutation(r.descents()).is_Identity + + assert p.inversions() == 7 + # test the merge-sort with a longer permutation + big = list(p) + list(range(p.max() + 1, p.max() + 130)) + assert Permutation(big).inversions() == 7 + assert p.signature() == -1 + assert q.inversions() == 11 + assert q.signature() == -1 + assert rmul(p, ~p).inversions() == 0 + assert rmul(p, ~p).signature() == 1 + + assert p.order() == 6 + assert q.order() == 10 + assert (p**(p.order())).is_Identity + + assert p.length() == 6 + assert q.length() == 7 + assert r.length() == 4 + + assert p.runs() == [[1, 5], [2], [0, 3, 6], [4]] + assert q.runs() == [[4], [2, 3, 5], [0, 6], [1]] + assert r.runs() == [[3], [2], [1], [0]] + + assert p.index() == 8 + assert q.index() == 8 + assert r.index() == 3 + + assert p.get_precedence_distance(q) == q.get_precedence_distance(p) + assert p.get_adjacency_distance(q) == p.get_adjacency_distance(q) + assert p.get_positional_distance(q) == p.get_positional_distance(q) + p = Permutation([0, 1, 2, 3]) + q = Permutation([3, 2, 1, 0]) + assert p.get_precedence_distance(q) == 6 + assert p.get_adjacency_distance(q) == 3 + assert p.get_positional_distance(q) == 8 + p = Permutation([0, 3, 1, 2, 4]) + q = Permutation.josephus(4, 5, 2) + assert p.get_adjacency_distance(q) == 3 + raises(ValueError, lambda: p.get_adjacency_distance(Permutation([]))) + raises(ValueError, lambda: p.get_positional_distance(Permutation([]))) + raises(ValueError, lambda: p.get_precedence_distance(Permutation([]))) + + a = [Permutation.unrank_nonlex(4, i) for i in range(5)] + iden = Permutation([0, 1, 2, 3]) + for i in range(5): + for j in range(i + 1, 5): + assert a[i].commutes_with(a[j]) == \ + (rmul(a[i], a[j]) == rmul(a[j], a[i])) + if a[i].commutes_with(a[j]): + assert a[i].commutator(a[j]) == iden + assert a[j].commutator(a[i]) == iden + + a = Permutation(3) + b = Permutation(0, 6, 3)(1, 2) + assert a.cycle_structure == {1: 4} + assert b.cycle_structure == {2: 1, 3: 1, 1: 2} + # issue 11130 + raises(ValueError, lambda: Permutation(3, size=3)) + raises(ValueError, lambda: Permutation([1, 2, 0, 3], size=3)) + + +def test_Permutation_subclassing(): + # Subclass that adds permutation application on iterables + class CustomPermutation(Permutation): + def __call__(self, *i): + try: + return super().__call__(*i) + except TypeError: + pass + + try: + perm_obj = i[0] + return [self._array_form[j] for j in perm_obj] + except TypeError: + raise TypeError('unrecognized argument') + + def __eq__(self, other): + if isinstance(other, Permutation): + return self._hashable_content() == other._hashable_content() + else: + return super().__eq__(other) + + def __hash__(self): + return super().__hash__() + + p = CustomPermutation([1, 2, 3, 0]) + q = Permutation([1, 2, 3, 0]) + + assert p == q + raises(TypeError, lambda: q([1, 2])) + assert [2, 3] == p([1, 2]) + + assert type(p * q) == CustomPermutation + assert type(q * p) == Permutation # True because q.__mul__(p) is called! + + # Run all tests for the Permutation class also on the subclass + def wrapped_test_Permutation(): + # Monkeypatch the class definition in the globals + globals()['__Perm'] = globals()['Permutation'] + globals()['Permutation'] = CustomPermutation + test_Permutation() + globals()['Permutation'] = globals()['__Perm'] # Restore + del globals()['__Perm'] + + wrapped_test_Permutation() + + +def test_josephus(): + assert Permutation.josephus(4, 6, 1) == Permutation([3, 1, 0, 2, 5, 4]) + assert Permutation.josephus(1, 5, 1).is_Identity + + +def test_ranking(): + assert Permutation.unrank_lex(5, 10).rank() == 10 + p = Permutation.unrank_lex(15, 225) + assert p.rank() == 225 + p1 = p.next_lex() + assert p1.rank() == 226 + assert Permutation.unrank_lex(15, 225).rank() == 225 + assert Permutation.unrank_lex(10, 0).is_Identity + p = Permutation.unrank_lex(4, 23) + assert p.rank() == 23 + assert p.array_form == [3, 2, 1, 0] + assert p.next_lex() is None + + p = Permutation([1, 5, 2, 0, 3, 6, 4]) + q = Permutation([[1, 2, 3, 5, 6], [0, 4]]) + a = [Permutation.unrank_trotterjohnson(4, i).array_form for i in range(5)] + assert a == [[0, 1, 2, 3], [0, 1, 3, 2], [0, 3, 1, 2], [3, 0, 1, + 2], [3, 0, 2, 1] ] + assert [Permutation(pa).rank_trotterjohnson() for pa in a] == list(range(5)) + assert Permutation([0, 1, 2, 3]).next_trotterjohnson() == \ + Permutation([0, 1, 3, 2]) + + assert q.rank_trotterjohnson() == 2283 + assert p.rank_trotterjohnson() == 3389 + assert Permutation([1, 0]).rank_trotterjohnson() == 1 + a = Permutation(list(range(3))) + b = a + l = [] + tj = [] + for i in range(6): + l.append(a) + tj.append(b) + a = a.next_lex() + b = b.next_trotterjohnson() + assert a == b is None + assert {tuple(a) for a in l} == {tuple(a) for a in tj} + + p = Permutation([2, 5, 1, 6, 3, 0, 4]) + q = Permutation([[6], [5], [0, 1, 2, 3, 4]]) + assert p.rank() == 1964 + assert q.rank() == 870 + assert Permutation([]).rank_nonlex() == 0 + prank = p.rank_nonlex() + assert prank == 1600 + assert Permutation.unrank_nonlex(7, 1600) == p + qrank = q.rank_nonlex() + assert qrank == 41 + assert Permutation.unrank_nonlex(7, 41) == Permutation(q.array_form) + + a = [Permutation.unrank_nonlex(4, i).array_form for i in range(24)] + assert a == [ + [1, 2, 3, 0], [3, 2, 0, 1], [1, 3, 0, 2], [1, 2, 0, 3], [2, 3, 1, 0], + [2, 0, 3, 1], [3, 0, 1, 2], [2, 0, 1, 3], [1, 3, 2, 0], [3, 0, 2, 1], + [1, 0, 3, 2], [1, 0, 2, 3], [2, 1, 3, 0], [2, 3, 0, 1], [3, 1, 0, 2], + [2, 1, 0, 3], [3, 2, 1, 0], [0, 2, 3, 1], [0, 3, 1, 2], [0, 2, 1, 3], + [3, 1, 2, 0], [0, 3, 2, 1], [0, 1, 3, 2], [0, 1, 2, 3]] + + N = 10 + p1 = Permutation(a[0]) + for i in range(1, N+1): + p1 = p1*Permutation(a[i]) + p2 = Permutation.rmul_with_af(*[Permutation(h) for h in a[N::-1]]) + assert p1 == p2 + + ok = [] + p = Permutation([1, 0]) + for i in range(3): + ok.append(p.array_form) + p = p.next_nonlex() + if p is None: + ok.append(None) + break + assert ok == [[1, 0], [0, 1], None] + assert Permutation([3, 2, 0, 1]).next_nonlex() == Permutation([1, 3, 0, 2]) + assert [Permutation(pa).rank_nonlex() for pa in a] == list(range(24)) + + +def test_mul(): + a, b = [0, 2, 1, 3], [0, 1, 3, 2] + assert _af_rmul(a, b) == [0, 2, 3, 1] + assert _af_rmuln(a, b, list(range(4))) == [0, 2, 3, 1] + assert rmul(Permutation(a), Permutation(b)).array_form == [0, 2, 3, 1] + + a = Permutation([0, 2, 1, 3]) + b = (0, 1, 3, 2) + c = (3, 1, 2, 0) + assert Permutation.rmul(a, b, c) == Permutation([1, 2, 3, 0]) + assert Permutation.rmul(a, c) == Permutation([3, 2, 1, 0]) + raises(TypeError, lambda: Permutation.rmul(b, c)) + + n = 6 + m = 8 + a = [Permutation.unrank_nonlex(n, i).array_form for i in range(m)] + h = list(range(n)) + for i in range(m): + h = _af_rmul(h, a[i]) + h2 = _af_rmuln(*a[:i + 1]) + assert h == h2 + + +def test_args(): + p = Permutation([(0, 3, 1, 2), (4, 5)]) + assert p._cyclic_form is None + assert Permutation(p) == p + assert p.cyclic_form == [[0, 3, 1, 2], [4, 5]] + assert p._array_form == [3, 2, 0, 1, 5, 4] + p = Permutation((0, 3, 1, 2)) + assert p._cyclic_form is None + assert p._array_form == [0, 3, 1, 2] + assert Permutation([0]) == Permutation((0, )) + assert Permutation([[0], [1]]) == Permutation(((0, ), (1, ))) == \ + Permutation(((0, ), [1])) + assert Permutation([[1, 2]]) == Permutation([0, 2, 1]) + assert Permutation([[1], [4, 2]]) == Permutation([0, 1, 4, 3, 2]) + assert Permutation([[1], [4, 2]], size=1) == Permutation([0, 1, 4, 3, 2]) + assert Permutation( + [[1], [4, 2]], size=6) == Permutation([0, 1, 4, 3, 2, 5]) + assert Permutation([[0, 1], [0, 2]]) == Permutation(0, 1, 2) + assert Permutation([], size=3) == Permutation([0, 1, 2]) + assert Permutation(3).list(5) == [0, 1, 2, 3, 4] + assert Permutation(3).list(-1) == [] + assert Permutation(5)(1, 2).list(-1) == [0, 2, 1] + assert Permutation(5)(1, 2).list() == [0, 2, 1, 3, 4, 5] + raises(ValueError, lambda: Permutation([1, 2], [0])) + # enclosing brackets needed + raises(ValueError, lambda: Permutation([[1, 2], 0])) + # enclosing brackets needed on 0 + raises(ValueError, lambda: Permutation([1, 1, 0])) + raises(ValueError, lambda: Permutation([4, 5], size=10)) # where are 0-3? + # but this is ok because cycles imply that only those listed moved + assert Permutation(4, 5) == Permutation([0, 1, 2, 3, 5, 4]) + + +def test_Cycle(): + assert str(Cycle()) == '()' + assert Cycle(Cycle(1,2)) == Cycle(1, 2) + assert Cycle(1,2).copy() == Cycle(1,2) + assert list(Cycle(1, 3, 2)) == [0, 3, 1, 2] + assert Cycle(1, 2)(2, 3) == Cycle(1, 3, 2) + assert Cycle(1, 2)(2, 3)(4, 5) == Cycle(1, 3, 2)(4, 5) + assert Permutation(Cycle(1, 2)(2, 1, 0, 3)).cyclic_form, Cycle(0, 2, 1) + raises(ValueError, lambda: Cycle().list()) + assert Cycle(1, 2).list() == [0, 2, 1] + assert Cycle(1, 2).list(4) == [0, 2, 1, 3] + assert Cycle(3).list(2) == [0, 1] + assert Cycle(3).list(6) == [0, 1, 2, 3, 4, 5] + assert Permutation(Cycle(1, 2), size=4) == \ + Permutation([0, 2, 1, 3]) + assert str(Cycle(1, 2)(4, 5)) == '(1 2)(4 5)' + assert str(Cycle(1, 2)) == '(1 2)' + assert Cycle(Permutation(list(range(3)))) == Cycle() + assert Cycle(1, 2).list() == [0, 2, 1] + assert Cycle(1, 2).list(4) == [0, 2, 1, 3] + assert Cycle().size == 0 + raises(ValueError, lambda: Cycle((1, 2))) + raises(ValueError, lambda: Cycle(1, 2, 1)) + raises(TypeError, lambda: Cycle(1, 2)*{}) + raises(ValueError, lambda: Cycle(4)[a]) + raises(ValueError, lambda: Cycle(2, -4, 3)) + + # check round-trip + p = Permutation([[1, 2], [4, 3]], size=5) + assert Permutation(Cycle(p)) == p + + +def test_from_sequence(): + assert Permutation.from_sequence('SymPy') == Permutation(4)(0, 1, 3) + assert Permutation.from_sequence('SymPy', key=lambda x: x.lower()) == \ + Permutation(4)(0, 2)(1, 3) + + +def test_resize(): + p = Permutation(0, 1, 2) + assert p.resize(5) == Permutation(0, 1, 2, size=5) + assert p.resize(4) == Permutation(0, 1, 2, size=4) + assert p.resize(3) == p + raises(ValueError, lambda: p.resize(2)) + + p = Permutation(0, 1, 2)(3, 4)(5, 6) + assert p.resize(3) == Permutation(0, 1, 2) + raises(ValueError, lambda: p.resize(4)) + + +def test_printing_cyclic(): + p1 = Permutation([0, 2, 1]) + assert repr(p1) == 'Permutation(1, 2)' + assert str(p1) == '(1 2)' + p2 = Permutation() + assert repr(p2) == 'Permutation()' + assert str(p2) == '()' + p3 = Permutation([1, 2, 0, 3]) + assert repr(p3) == 'Permutation(3)(0, 1, 2)' + + +def test_printing_non_cyclic(): + p1 = Permutation([0, 1, 2, 3, 4, 5]) + assert srepr(p1, perm_cyclic=False) == 'Permutation([], size=6)' + assert sstr(p1, perm_cyclic=False) == 'Permutation([], size=6)' + p2 = Permutation([0, 1, 2]) + assert srepr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])' + assert sstr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])' + + p3 = Permutation([0, 2, 1]) + assert srepr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])' + assert sstr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])' + p4 = Permutation([0, 1, 3, 2, 4, 5, 6, 7]) + assert srepr(p4, perm_cyclic=False) == 'Permutation([0, 1, 3, 2], size=8)' + + +def test_deprecated_print_cyclic(): + p = Permutation(0, 1, 2) + try: + Permutation.print_cyclic = True + with warns_deprecated_sympy(): + assert sstr(p) == '(0 1 2)' + with warns_deprecated_sympy(): + assert srepr(p) == 'Permutation(0, 1, 2)' + with warns_deprecated_sympy(): + assert pretty(p) == '(0 1 2)' + with warns_deprecated_sympy(): + assert latex(p) == r'\left( 0\; 1\; 2\right)' + + Permutation.print_cyclic = False + with warns_deprecated_sympy(): + assert sstr(p) == 'Permutation([1, 2, 0])' + with warns_deprecated_sympy(): + assert srepr(p) == 'Permutation([1, 2, 0])' + with warns_deprecated_sympy(): + assert pretty(p, use_unicode=False) == '/0 1 2\\\n\\1 2 0/' + with warns_deprecated_sympy(): + assert latex(p) == \ + r'\begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 0 \end{pmatrix}' + finally: + Permutation.print_cyclic = None + + +def test_permutation_equality(): + a = Permutation(0, 1, 2) + b = Permutation(0, 1, 2) + assert Eq(a, b) is S.true + c = Permutation(0, 2, 1) + assert Eq(a, c) is S.false + + d = Permutation(0, 1, 2, size=4) + assert unchanged(Eq, a, d) + e = Permutation(0, 2, 1, size=4) + assert unchanged(Eq, a, e) + + i = Permutation() + assert unchanged(Eq, i, 0) + assert unchanged(Eq, 0, i) + + +def test_issue_17661(): + c1 = Cycle(1,2) + c2 = Cycle(1,2) + assert c1 == c2 + assert repr(c1) == 'Cycle(1, 2)' + assert c1 == c2 + + +def test_permutation_apply(): + x = Symbol('x') + p = Permutation(0, 1, 2) + assert p.apply(0) == 1 + assert isinstance(p.apply(0), Integer) + assert p.apply(x) == AppliedPermutation(p, x) + assert AppliedPermutation(p, x).subs(x, 0) == 1 + + x = Symbol('x', integer=False) + raises(NotImplementedError, lambda: p.apply(x)) + x = Symbol('x', negative=True) + raises(NotImplementedError, lambda: p.apply(x)) + + +def test_AppliedPermutation(): + x = Symbol('x') + p = Permutation(0, 1, 2) + raises(ValueError, lambda: AppliedPermutation((0, 1, 2), x)) + assert AppliedPermutation(p, 1, evaluate=True) == 2 + assert AppliedPermutation(p, 1, evaluate=False).__class__ == \ + AppliedPermutation diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_polyhedron.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_polyhedron.py new file mode 100644 index 0000000000000000000000000000000000000000..abf469bb560eef1f378eff4740a84b80b696035f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_polyhedron.py @@ -0,0 +1,105 @@ +from sympy.core.symbol import symbols +from sympy.sets.sets import FiniteSet +from sympy.combinatorics.polyhedron import (Polyhedron, + tetrahedron, cube as square, octahedron, dodecahedron, icosahedron, + cube_faces) +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.testing.pytest import raises + +rmul = Permutation.rmul + + +def test_polyhedron(): + raises(ValueError, lambda: Polyhedron(list('ab'), + pgroup=[Permutation([0])])) + pgroup = [Permutation([[0, 7, 2, 5], [6, 1, 4, 3]]), + Permutation([[0, 7, 1, 6], [5, 2, 4, 3]]), + Permutation([[3, 6, 0, 5], [4, 1, 7, 2]]), + Permutation([[7, 4, 5], [1, 3, 0], [2], [6]]), + Permutation([[1, 3, 2], [7, 6, 5], [4], [0]]), + Permutation([[4, 7, 6], [2, 0, 3], [1], [5]]), + Permutation([[1, 2, 0], [4, 5, 6], [3], [7]]), + Permutation([[4, 2], [0, 6], [3, 7], [1, 5]]), + Permutation([[3, 5], [7, 1], [2, 6], [0, 4]]), + Permutation([[2, 5], [1, 6], [0, 4], [3, 7]]), + Permutation([[4, 3], [7, 0], [5, 1], [6, 2]]), + Permutation([[4, 1], [0, 5], [6, 2], [7, 3]]), + Permutation([[7, 2], [3, 6], [0, 4], [1, 5]]), + Permutation([0, 1, 2, 3, 4, 5, 6, 7])] + corners = tuple(symbols('A:H')) + faces = cube_faces + cube = Polyhedron(corners, faces, pgroup) + + assert cube.edges == FiniteSet(*( + (0, 1), (6, 7), (1, 2), (5, 6), (0, 3), (2, 3), + (4, 7), (4, 5), (3, 7), (1, 5), (0, 4), (2, 6))) + + for i in range(3): # add 180 degree face rotations + cube.rotate(cube.pgroup[i]**2) + + assert cube.corners == corners + + for i in range(3, 7): # add 240 degree axial corner rotations + cube.rotate(cube.pgroup[i]**2) + + assert cube.corners == corners + cube.rotate(1) + raises(ValueError, lambda: cube.rotate(Permutation([0, 1]))) + assert cube.corners != corners + assert cube.array_form == [7, 6, 4, 5, 3, 2, 0, 1] + assert cube.cyclic_form == [[0, 7, 1, 6], [2, 4, 3, 5]] + cube.reset() + assert cube.corners == corners + + def check(h, size, rpt, target): + + assert len(h.faces) + len(h.vertices) - len(h.edges) == 2 + assert h.size == size + + got = set() + for p in h.pgroup: + # make sure it restores original + P = h.copy() + hit = P.corners + for i in range(rpt): + P.rotate(p) + if P.corners == hit: + break + else: + print('error in permutation', p.array_form) + for i in range(rpt): + P.rotate(p) + got.add(tuple(P.corners)) + c = P.corners + f = [[c[i] for i in f] for f in P.faces] + assert h.faces == Polyhedron(c, f).faces + assert len(got) == target + assert PermutationGroup([Permutation(g) for g in got]).is_group + + for h, size, rpt, target in zip( + (tetrahedron, square, octahedron, dodecahedron, icosahedron), + (4, 8, 6, 20, 12), + (3, 4, 4, 5, 5), + (12, 24, 24, 60, 60)): + check(h, size, rpt, target) + + +def test_pgroups(): + from sympy.combinatorics.polyhedron import (cube, tetrahedron_faces, + octahedron_faces, dodecahedron_faces, icosahedron_faces) + from sympy.combinatorics.polyhedron import _pgroup_calcs + (tetrahedron2, cube2, octahedron2, dodecahedron2, icosahedron2, + tetrahedron_faces2, cube_faces2, octahedron_faces2, + dodecahedron_faces2, icosahedron_faces2) = _pgroup_calcs() + + assert tetrahedron == tetrahedron2 + assert cube == cube2 + assert octahedron == octahedron2 + assert dodecahedron == dodecahedron2 + assert icosahedron == icosahedron2 + assert sorted(map(sorted, tetrahedron_faces)) == sorted(map(sorted, tetrahedron_faces2)) + assert sorted(cube_faces) == sorted(cube_faces2) + assert sorted(octahedron_faces) == sorted(octahedron_faces2) + assert sorted(dodecahedron_faces) == sorted(dodecahedron_faces2) + assert sorted(icosahedron_faces) == sorted(icosahedron_faces2) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_prufer.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_prufer.py new file mode 100644 index 0000000000000000000000000000000000000000..b077c7cf3f023a4c36d7039505e6165ab29f275a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_prufer.py @@ -0,0 +1,74 @@ +from sympy.combinatorics.prufer import Prufer +from sympy.testing.pytest import raises + + +def test_prufer(): + # number of nodes is optional + assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]], 5).nodes == 5 + assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]]).nodes == 5 + + a = Prufer([[0, 1], [0, 2], [0, 3], [0, 4]]) + assert a.rank == 0 + assert a.nodes == 5 + assert a.prufer_repr == [0, 0, 0] + + a = Prufer([[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]]) + assert a.rank == 924 + assert a.nodes == 6 + assert a.tree_repr == [[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]] + assert a.prufer_repr == [4, 1, 4, 0] + + assert Prufer.edges([0, 1, 2, 3], [1, 4, 5], [1, 4, 6]) == \ + ([[0, 1], [1, 2], [1, 4], [2, 3], [4, 5], [4, 6]], 7) + assert Prufer([0]*4).size == Prufer([6]*4).size == 1296 + + # accept iterables but convert to list of lists + tree = [(0, 1), (1, 5), (0, 3), (0, 2), (2, 6), (4, 7), (2, 4)] + tree_lists = [list(t) for t in tree] + assert Prufer(tree).tree_repr == tree_lists + assert sorted(Prufer(set(tree)).tree_repr) == sorted(tree_lists) + + raises(ValueError, lambda: Prufer([[1, 2], [3, 4]])) # 0 is missing + raises(ValueError, lambda: Prufer([[2, 3], [3, 4]])) # 0, 1 are missing + assert Prufer(*Prufer.edges([1, 2], [3, 4])).prufer_repr == [1, 3] + raises(ValueError, lambda: Prufer.edges( + [1, 3], [3, 4])) # a broken tree but edges doesn't care + raises(ValueError, lambda: Prufer.edges([1, 2], [5, 6])) + raises(ValueError, lambda: Prufer([[]])) + + a = Prufer([[0, 1], [0, 2], [0, 3]]) + b = a.next() + assert b.tree_repr == [[0, 2], [0, 1], [1, 3]] + assert b.rank == 1 + + +def test_round_trip(): + def doit(t, b): + e, n = Prufer.edges(*t) + t = Prufer(e, n) + a = sorted(t.tree_repr) + b = [i - 1 for i in b] + assert t.prufer_repr == b + assert sorted(Prufer(b).tree_repr) == a + assert Prufer.unrank(t.rank, n).prufer_repr == b + + doit([[1, 2]], []) + doit([[2, 1, 3]], [1]) + doit([[1, 3, 2]], [3]) + doit([[1, 2, 3]], [2]) + doit([[2, 1, 4], [1, 3]], [1, 1]) + doit([[3, 2, 1, 4]], [2, 1]) + doit([[3, 2, 1], [2, 4]], [2, 2]) + doit([[1, 3, 2, 4]], [3, 2]) + doit([[1, 4, 2, 3]], [4, 2]) + doit([[3, 1, 4, 2]], [4, 1]) + doit([[4, 2, 1, 3]], [1, 2]) + doit([[1, 2, 4, 3]], [2, 4]) + doit([[1, 3, 4, 2]], [3, 4]) + doit([[2, 4, 1], [4, 3]], [4, 4]) + doit([[1, 2, 3, 4]], [2, 3]) + doit([[2, 3, 1], [3, 4]], [3, 3]) + doit([[1, 4, 3, 2]], [4, 3]) + doit([[2, 1, 4, 3]], [1, 4]) + doit([[2, 1, 3, 4]], [1, 3]) + doit([[6, 2, 1, 4], [1, 3, 5, 8], [3, 7]], [1, 2, 1, 3, 3, 5]) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_rewriting.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_rewriting.py new file mode 100644 index 0000000000000000000000000000000000000000..97c562bd57a2cd6318fa1dcb13c6f6278c861cca --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_rewriting.py @@ -0,0 +1,49 @@ +from sympy.combinatorics.fp_groups import FpGroup +from sympy.combinatorics.free_groups import free_group +from sympy.testing.pytest import raises + + +def test_rewriting(): + F, a, b = free_group("a, b") + G = FpGroup(F, [a*b*a**-1*b**-1]) + a, b = G.generators + R = G._rewriting_system + assert R.is_confluent + + assert G.reduce(b**-1*a) == a*b**-1 + assert G.reduce(b**3*a**4*b**-2*a) == a**5*b + assert G.equals(b**2*a**-1*b, b**4*a**-1*b**-1) + + assert R.reduce_using_automaton(b*a*a**2*b**-1) == a**3 + assert R.reduce_using_automaton(b**3*a**4*b**-2*a) == a**5*b + assert R.reduce_using_automaton(b**-1*a) == a*b**-1 + + G = FpGroup(F, [a**3, b**3, (a*b)**2]) + R = G._rewriting_system + R.make_confluent() + # R._is_confluent should be set to True after + # a successful run of make_confluent + assert R.is_confluent + # but also the system should actually be confluent + assert R._check_confluence() + assert G.reduce(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1 + # check for automaton reduction + assert R.reduce_using_automaton(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1 + + G = FpGroup(F, [a**2, b**3, (a*b)**4]) + R = G._rewriting_system + assert G.reduce(a**2*b**-2*a**2*b) == b**-1 + assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1 + assert G.reduce(a**3*b**-2*a**2*b) == a**-1*b**-1 + assert R.reduce_using_automaton(a**3*b**-2*a**2*b) == a**-1*b**-1 + # Check after adding a rule + R.add_rule(a**2, b) + assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1 + assert R.reduce_using_automaton(a**4*b**-2*a**2*b**3) == b + + R.set_max(15) + raises(RuntimeError, lambda: R.add_rule(a**-3, b)) + R.set_max(20) + R.add_rule(a**-3, b) + + assert R.add_rule(a, a) == set() diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_schur_number.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_schur_number.py new file mode 100644 index 0000000000000000000000000000000000000000..e6beb9b11fa993a99b71d89b8485050fc3575b8e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_schur_number.py @@ -0,0 +1,55 @@ +from sympy.core import S, Rational +from sympy.combinatorics.schur_number import schur_partition, SchurNumber +from sympy.core.random import _randint +from sympy.testing.pytest import raises +from sympy.core.symbol import symbols + + +def _sum_free_test(subset): + """ + Checks if subset is sum-free(There are no x,y,z in the subset such that + x + y = z) + """ + for i in subset: + for j in subset: + assert (i + j in subset) is False + + +def test_schur_partition(): + raises(ValueError, lambda: schur_partition(S.Infinity)) + raises(ValueError, lambda: schur_partition(-1)) + raises(ValueError, lambda: schur_partition(0)) + assert schur_partition(2) == [[1, 2]] + + random_number_generator = _randint(1000) + for _ in range(5): + n = random_number_generator(1, 1000) + result = schur_partition(n) + t = 0 + numbers = [] + for item in result: + _sum_free_test(item) + """ + Checks if the occurrence of all numbers is exactly one + """ + t += len(item) + for l in item: + assert (l in numbers) is False + numbers.append(l) + assert n == t + + x = symbols("x") + raises(ValueError, lambda: schur_partition(x)) + +def test_schur_number(): + first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160} + for k in first_known_schur_numbers: + assert SchurNumber(k) == first_known_schur_numbers[k] + + assert SchurNumber(S.Infinity) == S.Infinity + assert SchurNumber(0) == 0 + raises(ValueError, lambda: SchurNumber(0.5)) + + n = symbols("n") + assert SchurNumber(n).lower_bound() == 3**n/2 - Rational(1, 2) + assert SchurNumber(8).lower_bound() == 5039 diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_subsets.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_subsets.py new file mode 100644 index 0000000000000000000000000000000000000000..1d50076da1c685294c2d2561dcc2a6af629eaf83 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_subsets.py @@ -0,0 +1,63 @@ +from sympy.combinatorics.subsets import Subset, ksubsets +from sympy.testing.pytest import raises + + +def test_subset(): + a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) + assert a.next_binary() == Subset(['b'], ['a', 'b', 'c', 'd']) + assert a.prev_binary() == Subset(['c'], ['a', 'b', 'c', 'd']) + assert a.next_lexicographic() == Subset(['d'], ['a', 'b', 'c', 'd']) + assert a.prev_lexicographic() == Subset(['c'], ['a', 'b', 'c', 'd']) + assert a.next_gray() == Subset(['c'], ['a', 'b', 'c', 'd']) + assert a.prev_gray() == Subset(['d'], ['a', 'b', 'c', 'd']) + assert a.rank_binary == 3 + assert a.rank_lexicographic == 14 + assert a.rank_gray == 2 + assert a.cardinality == 16 + assert a.size == 2 + assert Subset.bitlist_from_subset(a, ['a', 'b', 'c', 'd']) == '0011' + + a = Subset([2, 5, 7], [1, 2, 3, 4, 5, 6, 7]) + assert a.next_binary() == Subset([2, 5, 6], [1, 2, 3, 4, 5, 6, 7]) + assert a.prev_binary() == Subset([2, 5], [1, 2, 3, 4, 5, 6, 7]) + assert a.next_lexicographic() == Subset([2, 6], [1, 2, 3, 4, 5, 6, 7]) + assert a.prev_lexicographic() == Subset([2, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]) + assert a.next_gray() == Subset([2, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7]) + assert a.prev_gray() == Subset([2, 5], [1, 2, 3, 4, 5, 6, 7]) + assert a.rank_binary == 37 + assert a.rank_lexicographic == 93 + assert a.rank_gray == 57 + assert a.cardinality == 128 + + superset = ['a', 'b', 'c', 'd'] + assert Subset.unrank_binary(4, superset).rank_binary == 4 + assert Subset.unrank_gray(10, superset).rank_gray == 10 + + superset = [1, 2, 3, 4, 5, 6, 7, 8, 9] + assert Subset.unrank_binary(33, superset).rank_binary == 33 + assert Subset.unrank_gray(25, superset).rank_gray == 25 + + a = Subset([], ['a', 'b', 'c', 'd']) + i = 1 + while a.subset != Subset(['d'], ['a', 'b', 'c', 'd']).subset: + a = a.next_lexicographic() + i = i + 1 + assert i == 16 + + i = 1 + while a.subset != Subset([], ['a', 'b', 'c', 'd']).subset: + a = a.prev_lexicographic() + i = i + 1 + assert i == 16 + + raises(ValueError, lambda: Subset(['a', 'b'], ['a'])) + raises(ValueError, lambda: Subset(['a'], ['b', 'c'])) + raises(ValueError, lambda: Subset.subset_from_bitlist(['a', 'b'], '010')) + + assert Subset(['a'], ['a', 'b']) != Subset(['b'], ['a', 'b']) + assert Subset(['a'], ['a', 'b']) != Subset(['a'], ['a', 'c']) + +def test_ksubsets(): + assert list(ksubsets([1, 2, 3], 2)) == [(1, 2), (1, 3), (2, 3)] + assert list(ksubsets([1, 2, 3, 4, 5], 2)) == [(1, 2), (1, 3), (1, 4), + (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_tensor_can.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_tensor_can.py new file mode 100644 index 0000000000000000000000000000000000000000..3922419f20b92536426bfaae4b7e94df5db671b5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_tensor_can.py @@ -0,0 +1,560 @@ +from sympy.combinatorics.permutations import Permutation, Perm +from sympy.combinatorics.tensor_can import (perm_af_direct_product, dummy_sgs, + riemann_bsgs, get_symmetric_group_sgs, canonicalize, bsgs_direct_product) +from sympy.combinatorics.testutil import canonicalize_naive, graph_certificate +from sympy.testing.pytest import skip, XFAIL + +def test_perm_af_direct_product(): + gens1 = [[1,0,2,3], [0,1,3,2]] + gens2 = [[1,0]] + assert perm_af_direct_product(gens1, gens2, 0) == [[1, 0, 2, 3, 4, 5], [0, 1, 3, 2, 4, 5], [0, 1, 2, 3, 5, 4]] + gens1 = [[1,0,2,3,5,4], [0,1,3,2,4,5]] + gens2 = [[1,0,2,3]] + assert [[1, 0, 2, 3, 4, 5, 7, 6], [0, 1, 3, 2, 4, 5, 6, 7], [0, 1, 2, 3, 5, 4, 6, 7]] + +def test_dummy_sgs(): + a = dummy_sgs([1,2], 0, 4) + assert a == [[0,2,1,3,4,5]] + a = dummy_sgs([2,3,4,5], 0, 8) + assert a == [x._array_form for x in [Perm(9)(2,3), Perm(9)(4,5), + Perm(9)(2,4)(3,5)]] + + a = dummy_sgs([2,3,4,5], 1, 8) + assert a == [x._array_form for x in [Perm(2,3)(8,9), Perm(4,5)(8,9), + Perm(9)(2,4)(3,5)]] + +def test_get_symmetric_group_sgs(): + assert get_symmetric_group_sgs(2) == ([0], [Permutation(3)(0,1)]) + assert get_symmetric_group_sgs(2, 1) == ([0], [Permutation(0,1)(2,3)]) + assert get_symmetric_group_sgs(3) == ([0,1], [Permutation(4)(0,1), Permutation(4)(1,2)]) + assert get_symmetric_group_sgs(3, 1) == ([0,1], [Permutation(0,1)(3,4), Permutation(1,2)(3,4)]) + assert get_symmetric_group_sgs(4) == ([0,1,2], [Permutation(5)(0,1), Permutation(5)(1,2), Permutation(5)(2,3)]) + assert get_symmetric_group_sgs(4, 1) == ([0,1,2], [Permutation(0,1)(4,5), Permutation(1,2)(4,5), Permutation(2,3)(4,5)]) + + +def test_canonicalize_no_slot_sym(): + # cases in which there is no slot symmetry after fixing the + # free indices; here and in the following if the symmetry of the + # metric is not specified, it is assumed to be symmetric. + # If it is not specified, tensors are commuting. + + # A_d0 * B^d0; g = [1,0, 2,3]; T_c = A^d0*B_d0; can = [0,1,2,3] + base1, gens1 = get_symmetric_group_sgs(1) + dummies = [0, 1] + g = Permutation([1,0,2,3]) + can = canonicalize(g, dummies, 0, (base1,gens1,1,0), (base1,gens1,1,0)) + assert can == [0,1,2,3] + # equivalently + can = canonicalize(g, dummies, 0, (base1, gens1, 2, None)) + assert can == [0,1,2,3] + + # with antisymmetric metric; T_c = -A^d0*B_d0; can = [0,1,3,2] + can = canonicalize(g, dummies, 1, (base1,gens1,1,0), (base1,gens1,1,0)) + assert can == [0,1,3,2] + + # A^a * B^b; ord = [a,b]; g = [0,1,2,3]; can = g + g = Permutation([0,1,2,3]) + dummies = [] + t0 = t1 = (base1, gens1, 1, 0) + can = canonicalize(g, dummies, 0, t0, t1) + assert can == [0,1,2,3] + # B^b * A^a + g = Permutation([1,0,2,3]) + can = canonicalize(g, dummies, 0, t0, t1) + assert can == [1,0,2,3] + + # A symmetric + # A^{b}_{d0}*A^{d0, a} order a,b,d0,-d0; T_c = A^{a d0}*A{b}_{d0} + # g = [1,3,2,0,4,5]; can = [0,2,1,3,4,5] + base2, gens2 = get_symmetric_group_sgs(2) + dummies = [2,3] + g = Permutation([1,3,2,0,4,5]) + can = canonicalize(g, dummies, 0, (base2, gens2, 2, 0)) + assert can == [0, 2, 1, 3, 4, 5] + # with antisymmetric metric + can = canonicalize(g, dummies, 1, (base2, gens2, 2, 0)) + assert can == [0, 2, 1, 3, 4, 5] + # A^{a}_{d0}*A^{d0, b} + g = Permutation([0,3,2,1,4,5]) + can = canonicalize(g, dummies, 1, (base2, gens2, 2, 0)) + assert can == [0, 2, 1, 3, 5, 4] + + # A, B symmetric + # A^b_d0*B^{d0,a}; g=[1,3,2,0,4,5] + # T_c = A^{b,d0}*B_{a,d0}; can = [1,2,0,3,4,5] + dummies = [2,3] + g = Permutation([1,3,2,0,4,5]) + can = canonicalize(g, dummies, 0, (base2,gens2,1,0), (base2,gens2,1,0)) + assert can == [1,2,0,3,4,5] + # same with antisymmetric metric + can = canonicalize(g, dummies, 1, (base2,gens2,1,0), (base2,gens2,1,0)) + assert can == [1,2,0,3,5,4] + + # A^{d1}_{d0}*B^d0*C_d1 ord=[d0,-d0,d1,-d1]; g = [2,1,0,3,4,5] + # T_c = A^{d0 d1}*B_d0*C_d1; can = [0,2,1,3,4,5] + base1, gens1 = get_symmetric_group_sgs(1) + base2, gens2 = get_symmetric_group_sgs(2) + g = Permutation([2,1,0,3,4,5]) + dummies = [0,1,2,3] + t0 = (base2, gens2, 1, 0) + t1 = t2 = (base1, gens1, 1, 0) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [0, 2, 1, 3, 4, 5] + + # A without symmetry + # A^{d1}_{d0}*B^d0*C_d1 ord=[d0,-d0,d1,-d1]; g = [2,1,0,3,4,5] + # T_c = A^{d0 d1}*B_d1*C_d0; can = [0,2,3,1,4,5] + g = Permutation([2,1,0,3,4,5]) + dummies = [0,1,2,3] + t0 = ([], [Permutation(list(range(4)))], 1, 0) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [0,2,3,1,4,5] + # A, B without symmetry + # A^{d1}_{d0}*B_{d1}^{d0}; g = [2,1,3,0,4,5] + # T_c = A^{d0 d1}*B_{d0 d1}; can = [0,2,1,3,4,5] + t0 = t1 = ([], [Permutation(list(range(4)))], 1, 0) + dummies = [0,1,2,3] + g = Permutation([2,1,3,0,4,5]) + can = canonicalize(g, dummies, 0, t0, t1) + assert can == [0, 2, 1, 3, 4, 5] + # A_{d0}^{d1}*B_{d1}^{d0}; g = [1,2,3,0,4,5] + # T_c = A^{d0 d1}*B_{d1 d0}; can = [0,2,3,1,4,5] + g = Permutation([1,2,3,0,4,5]) + can = canonicalize(g, dummies, 0, t0, t1) + assert can == [0,2,3,1,4,5] + + # A, B, C without symmetry + # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1] + # g=[4,2,0,3,5,1,6,7] + # T_c=A^{d0 d1}*B_{a d1}*C_{d0 b}; can = [2,4,0,5,3,1,6,7] + t0 = t1 = t2 = ([], [Permutation(list(range(4)))], 1, 0) + dummies = [2,3,4,5] + g = Permutation([4,2,0,3,5,1,6,7]) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [2,4,0,5,3,1,6,7] + + # A symmetric, B and C without symmetry + # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1] + # g=[4,2,0,3,5,1,6,7] + # T_c = A^{d0 d1}*B_{a d0}*C_{d1 b}; can = [2,4,0,3,5,1,6,7] + t0 = (base2,gens2,1,0) + t1 = t2 = ([], [Permutation(list(range(4)))], 1, 0) + dummies = [2,3,4,5] + g = Permutation([4,2,0,3,5,1,6,7]) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [2,4,0,3,5,1,6,7] + + # A and C symmetric, B without symmetry + # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1] + # g=[4,2,0,3,5,1,6,7] + # T_c = A^{d0 d1}*B_{a d0}*C_{b d1}; can = [2,4,0,3,1,5,6,7] + t0 = t2 = (base2,gens2,1,0) + t1 = ([], [Permutation(list(range(4)))], 1, 0) + dummies = [2,3,4,5] + g = Permutation([4,2,0,3,5,1,6,7]) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [2,4,0,3,1,5,6,7] + + # A symmetric, B without symmetry, C antisymmetric + # A^{d1 d0}*B_{a d0}*C_{d1 b} ord=[a,b,d0,-d0,d1,-d1] + # g=[4,2,0,3,5,1,6,7] + # T_c = -A^{d0 d1}*B_{a d0}*C_{b d1}; can = [2,4,0,3,1,5,7,6] + t0 = (base2,gens2, 1, 0) + t1 = ([], [Permutation(list(range(4)))], 1, 0) + base2a, gens2a = get_symmetric_group_sgs(2, 1) + t2 = (base2a, gens2a, 1, 0) + dummies = [2,3,4,5] + g = Permutation([4,2,0,3,5,1,6,7]) + can = canonicalize(g, dummies, 0, t0, t1, t2) + assert can == [2,4,0,3,1,5,7,6] + + +def test_canonicalize_no_dummies(): + base1, gens1 = get_symmetric_group_sgs(1) + base2, gens2 = get_symmetric_group_sgs(2) + base2a, gens2a = get_symmetric_group_sgs(2, 1) + + # A commuting + # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4] + # T_c = A^a A^b A^c; can = list(range(5)) + g = Permutation([2,1,0,3,4]) + can = canonicalize(g, [], 0, (base1, gens1, 3, 0)) + assert can == list(range(5)) + + # A anticommuting + # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4] + # T_c = -A^a A^b A^c; can = [0,1,2,4,3] + g = Permutation([2,1,0,3,4]) + can = canonicalize(g, [], 0, (base1, gens1, 3, 1)) + assert can == [0,1,2,4,3] + + # A commuting and symmetric + # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5] + # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5] + g = Permutation([1,3,2,0,4,5]) + can = canonicalize(g, [], 0, (base2, gens2, 2, 0)) + assert can == [0,2,1,3,4,5] + + # A anticommuting and symmetric + # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5] + # T_c = -A^{a c}*A^{b d}; can = [0,2,1,3,5,4] + g = Permutation([1,3,2,0,4,5]) + can = canonicalize(g, [], 0, (base2, gens2, 2, 1)) + assert can == [0,2,1,3,5,4] + # A^{c,a}*A^{b,d} ; g = [2,0,1,3,4,5] + # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5] + g = Permutation([2,0,1,3,4,5]) + can = canonicalize(g, [], 0, (base2, gens2, 2, 1)) + assert can == [0,2,1,3,4,5] + +def test_no_metric_symmetry(): + # no metric symmetry + # A^d1_d0 * A^d0_d1; ord = [d0,-d0,d1,-d1]; g= [2,1,0,3,4,5] + # T_c = A^d0_d1 * A^d1_d0; can = [0,3,2,1,4,5] + g = Permutation([2,1,0,3,4,5]) + can = canonicalize(g, list(range(4)), None, [[], [Permutation(list(range(4)))], 2, 0]) + assert can == [0,3,2,1,4,5] + + # A^d1_d2 * A^d0_d3 * A^d2_d1 * A^d3_d0 + # ord = [d0,-d0,d1,-d1,d2,-d2,d3,-d3] + # 0 1 2 3 4 5 6 7 + # g = [2,5,0,7,4,3,6,1,8,9] + # T_c = A^d0_d1 * A^d1_d0 * A^d2_d3 * A^d3_d2 + # can = [0,3,2,1,4,7,6,5,8,9] + g = Permutation([2,5,0,7,4,3,6,1,8,9]) + #can = canonicalize(g, list(range(8)), 0, [[], [list(range(4))], 4, 0]) + #assert can == [0, 2, 3, 1, 4, 6, 7, 5, 8, 9] + can = canonicalize(g, list(range(8)), None, [[], [Permutation(list(range(4)))], 4, 0]) + assert can == [0, 3, 2, 1, 4, 7, 6, 5, 8, 9] + + # A^d0_d2 * A^d1_d3 * A^d3_d0 * A^d2_d1 + # g = [0,5,2,7,6,1,4,3,8,9] + # T_c = A^d0_d1 * A^d1_d2 * A^d2_d3 * A^d3_d0 + # can = [0,3,2,5,4,7,6,1,8,9] + g = Permutation([0,5,2,7,6,1,4,3,8,9]) + can = canonicalize(g, list(range(8)), None, [[], [Permutation(list(range(4)))], 4, 0]) + assert can == [0,3,2,5,4,7,6,1,8,9] + + g = Permutation([12,7,10,3,14,13,4,11,6,1,2,9,0,15,8,5,16,17]) + can = canonicalize(g, list(range(16)), None, [[], [Permutation(list(range(4)))], 8, 0]) + assert can == [0,3,2,5,4,7,6,1,8,11,10,13,12,15,14,9,16,17] + +def test_canonical_free(): + # t = A^{d0 a1}*A_d0^a0 + # ord = [a0,a1,d0,-d0]; g = [2,1,3,0,4,5]; dummies = [[2,3]] + # t_c = A_d0^a0*A^{d0 a1} + # can = [3,0, 2,1, 4,5] + g = Permutation([2,1,3,0,4,5]) + dummies = [[2,3]] + can = canonicalize(g, dummies, [None], ([], [Permutation(3)], 2, 0)) + assert can == [3,0, 2,1, 4,5] + +def test_canonicalize1(): + base1, gens1 = get_symmetric_group_sgs(1) + base1a, gens1a = get_symmetric_group_sgs(1, 1) + base2, gens2 = get_symmetric_group_sgs(2) + base3, gens3 = get_symmetric_group_sgs(3) + base2a, gens2a = get_symmetric_group_sgs(2, 1) + base3a, gens3a = get_symmetric_group_sgs(3, 1) + + # A_d0*A^d0; ord = [d0,-d0]; g = [1,0,2,3] + # T_c = A^d0*A_d0; can = [0,1,2,3] + g = Permutation([1,0,2,3]) + can = canonicalize(g, [0, 1], 0, (base1, gens1, 2, 0)) + assert can == list(range(4)) + + # A commuting + # A_d0*A_d1*A_d2*A^d2*A^d1*A^d0; ord=[d0,-d0,d1,-d1,d2,-d2] + # g = [1,3,5,4,2,0,6,7] + # T_c = A^d0*A_d0*A^d1*A_d1*A^d2*A_d2; can = list(range(8)) + g = Permutation([1,3,5,4,2,0,6,7]) + can = canonicalize(g, list(range(6)), 0, (base1, gens1, 6, 0)) + assert can == list(range(8)) + + # A anticommuting + # A_d0*A_d1*A_d2*A^d2*A^d1*A^d0; ord=[d0,-d0,d1,-d1,d2,-d2] + # g = [1,3,5,4,2,0,6,7] + # T_c 0; can = 0 + g = Permutation([1,3,5,4,2,0,6,7]) + can = canonicalize(g, list(range(6)), 0, (base1, gens1, 6, 1)) + assert can == 0 + can1 = canonicalize_naive(g, list(range(6)), 0, (base1, gens1, 6, 1)) + assert can1 == 0 + + # A commuting symmetric + # A^{d0 b}*A^a_d1*A^d1_d0; ord=[a,b,d0,-d0,d1,-d1] + # g = [2,1,0,5,4,3,6,7] + # T_c = A^{a d0}*A^{b d1}*A_{d0 d1}; can = [0,2,1,4,3,5,6,7] + g = Permutation([2,1,0,5,4,3,6,7]) + can = canonicalize(g, list(range(2,6)), 0, (base2, gens2, 3, 0)) + assert can == [0,2,1,4,3,5,6,7] + + # A, B commuting symmetric + # A^{d0 b}*A^d1_d0*B^a_d1; ord=[a,b,d0,-d0,d1,-d1] + # g = [2,1,4,3,0,5,6,7] + # T_c = A^{b d0}*A_d0^d1*B^a_d1; can = [1,2,3,4,0,5,6,7] + g = Permutation([2,1,4,3,0,5,6,7]) + can = canonicalize(g, list(range(2,6)), 0, (base2,gens2,2,0), (base2,gens2,1,0)) + assert can == [1,2,3,4,0,5,6,7] + + # A commuting symmetric + # A^{d1 d0 b}*A^{a}_{d1 d0}; ord=[a,b, d0,-d0,d1,-d1] + # g = [4,2,1,0,5,3,6,7] + # T_c = A^{a d0 d1}*A^{b}_{d0 d1}; can = [0,2,4,1,3,5,6,7] + g = Permutation([4,2,1,0,5,3,6,7]) + can = canonicalize(g, list(range(2,6)), 0, (base3, gens3, 2, 0)) + assert can == [0,2,4,1,3,5,6,7] + + + # A^{d3 d0 d2}*A^a0_{d1 d2}*A^d1_d3^a1*A^{a2 a3}_d0 + # ord = [a0,a1,a2,a3,d0,-d0,d1,-d1,d2,-d2,d3,-d3] + # 0 1 2 3 4 5 6 7 8 9 10 11 + # g = [10,4,8, 0,7,9, 6,11,1, 2,3,5, 12,13] + # T_c = A^{a0 d0 d1}*A^a1_d0^d2*A^{a2 a3 d3}*A_{d1 d2 d3} + # can = [0,4,6, 1,5,8, 2,3,10, 7,9,11, 12,13] + g = Permutation([10,4,8, 0,7,9, 6,11,1, 2,3,5, 12,13]) + can = canonicalize(g, list(range(4,12)), 0, (base3, gens3, 4, 0)) + assert can == [0,4,6, 1,5,8, 2,3,10, 7,9,11, 12,13] + + # A commuting symmetric, B antisymmetric + # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3 + # ord = [d0,-d0,d1,-d1,d2,-d2,d3,-d3] + # g = [0,2,4,5,7,3,1,6,8,9] + # in this esxample and in the next three, + # renaming dummy indices and using symmetry of A, + # T = A^{d0 d1 d2} * A_{d0 d1 d3} * B_d2^d3 + # can = 0 + g = Permutation([0,2,4,5,7,3,1,6,8,9]) + can = canonicalize(g, list(range(8)), 0, (base3, gens3,2,0), (base2a,gens2a,1,0)) + assert can == 0 + # A anticommuting symmetric, B anticommuting + # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3 + # T_c = A^{d0 d1 d2} * A_{d0 d1}^d3 * B_{d2 d3} + # can = [0,2,4, 1,3,6, 5,7, 8,9] + can = canonicalize(g, list(range(8)), 0, (base3, gens3,2,1), (base2a,gens2a,1,0)) + assert can == [0,2,4, 1,3,6, 5,7, 8,9] + # A anticommuting symmetric, B antisymmetric commuting, antisymmetric metric + # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3 + # T_c = -A^{d0 d1 d2} * A_{d0 d1}^d3 * B_{d2 d3} + # can = [0,2,4, 1,3,6, 5,7, 9,8] + can = canonicalize(g, list(range(8)), 1, (base3, gens3,2,1), (base2a,gens2a,1,0)) + assert can == [0,2,4, 1,3,6, 5,7, 9,8] + + # A anticommuting symmetric, B anticommuting anticommuting, + # no metric symmetry + # A^{d0 d1 d2} * A_{d2 d3 d1} * B_d0^d3 + # T_c = A^{d0 d1 d2} * A_{d0 d1 d3} * B_d2^d3 + # can = [0,2,4, 1,3,7, 5,6, 8,9] + can = canonicalize(g, list(range(8)), None, (base3, gens3,2,1), (base2a,gens2a,1,0)) + assert can == [0,2,4,1,3,7,5,6,8,9] + + # Gamma anticommuting + # Gamma_{mu nu} * gamma^rho * Gamma^{nu mu alpha} + # ord = [alpha, rho, mu,-mu,nu,-nu] + # g = [3,5,1,4,2,0,6,7] + # T_c = -Gamma^{mu nu} * gamma^rho * Gamma_{alpha mu nu} + # can = [2,4,1,0,3,5,7,6]] + g = Permutation([3,5,1,4,2,0,6,7]) + t0 = (base2a, gens2a, 1, None) + t1 = (base1, gens1, 1, None) + t2 = (base3a, gens3a, 1, None) + can = canonicalize(g, list(range(2, 6)), 0, t0, t1, t2) + assert can == [2,4,1,0,3,5,7,6] + + # Gamma_{mu nu} * Gamma^{gamma beta} * gamma_rho * Gamma^{nu mu alpha} + # ord = [alpha, beta, gamma, -rho, mu,-mu,nu,-nu] + # 0 1 2 3 4 5 6 7 + # g = [5,7,2,1,3,6,4,0,8,9] + # T_c = Gamma^{mu nu} * Gamma^{beta gamma} * gamma_rho * Gamma^alpha_{mu nu} # can = [4,6,1,2,3,0,5,7,8,9] + t0 = (base2a, gens2a, 2, None) + g = Permutation([5,7,2,1,3,6,4,0,8,9]) + can = canonicalize(g, list(range(4, 8)), 0, t0, t1, t2) + assert can == [4,6,1,2,3,0,5,7,8,9] + + # f^a_{b,c} antisymmetric in b,c; A_mu^a no symmetry + # f^c_{d a} * f_{c e b} * A_mu^d * A_nu^a * A^{nu e} * A^{mu b} + # ord = [mu,-mu,nu,-nu,a,-a,b,-b,c,-c,d,-d, e, -e] + # 0 1 2 3 4 5 6 7 8 9 10 11 12 13 + # g = [8,11,5, 9,13,7, 1,10, 3,4, 2,12, 0,6, 14,15] + # T_c = -f^{a b c} * f_a^{d e} * A^mu_b * A_{mu d} * A^nu_c * A_{nu e} + # can = [4,6,8, 5,10,12, 0,7, 1,11, 2,9, 3,13, 15,14] + g = Permutation([8,11,5, 9,13,7, 1,10, 3,4, 2,12, 0,6, 14,15]) + base_f, gens_f = bsgs_direct_product(base1, gens1, base2a, gens2a) + base_A, gens_A = bsgs_direct_product(base1, gens1, base1, gens1) + t0 = (base_f, gens_f, 2, 0) + t1 = (base_A, gens_A, 4, 0) + can = canonicalize(g, [list(range(4)), list(range(4, 14))], [0, 0], t0, t1) + assert can == [4,6,8, 5,10,12, 0,7, 1,11, 2,9, 3,13, 15,14] + + +def test_riemann_invariants(): + baser, gensr = riemann_bsgs + # R^{d0 d1}_{d1 d0}; ord = [d0,-d0,d1,-d1]; g = [0,2,3,1,4,5] + # T_c = -R^{d0 d1}_{d0 d1}; can = [0,2,1,3,5,4] + g = Permutation([0,2,3,1,4,5]) + can = canonicalize(g, list(range(2, 4)), 0, (baser, gensr, 1, 0)) + assert can == [0,2,1,3,5,4] + # use a non minimal BSGS + can = canonicalize(g, list(range(2, 4)), 0, ([2, 0], [Permutation([1,0,2,3,5,4]), Permutation([2,3,0,1,4,5])], 1, 0)) + assert can == [0,2,1,3,5,4] + + """ + The following tests in test_riemann_invariants and in + test_riemann_invariants1 have been checked using xperm.c from XPerm in + in [1] and with an older version contained in [2] + + [1] xperm.c part of xPerm written by J. M. Martin-Garcia + http://www.xact.es/index.html + [2] test_xperm.cc in cadabra by Kasper Peeters, http://cadabra.phi-sci.com/ + """ + # R_d11^d1_d0^d5 * R^{d6 d4 d0}_d5 * R_{d7 d2 d8 d9} * + # R_{d10 d3 d6 d4} * R^{d2 d7 d11}_d1 * R^{d8 d9 d3 d10} + # ord: contravariant d_k ->2*k, covariant d_k -> 2*k+1 + # T_c = R^{d0 d1 d2 d3} * R_{d0 d1}^{d4 d5} * R_{d2 d3}^{d6 d7} * + # R_{d4 d5}^{d8 d9} * R_{d6 d7}^{d10 d11} * R_{d8 d9 d10 d11} + g = Permutation([23,2,1,10,12,8,0,11,15,5,17,19,21,7,13,9,4,14,22,3,16,18,6,20,24,25]) + can = canonicalize(g, list(range(24)), 0, (baser, gensr, 6, 0)) + assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,21,23,24,25] + + # use a non minimal BSGS + can = canonicalize(g, list(range(24)), 0, ([2, 0], [Permutation([1,0,2,3,5,4]), Permutation([2,3,0,1,4,5])], 6, 0)) + assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,21,23,24,25] + + g = Permutation([0,2,5,7,4,6,9,11,8,10,13,15,12,14,17,19,16,18,21,23,20,22,25,27,24,26,29,31,28,30,33,35,32,34,37,39,36,38,1,3,40,41]) + can = canonicalize(g, list(range(40)), 0, (baser, gensr, 10, 0)) + assert can == [0,2,4,6,1,3,8,10,5,7,12,14,9,11,16,18,13,15,20,22,17,19,24,26,21,23,28,30,25,27,32,34,29,31,36,38,33,35,37,39,40,41] + + +@XFAIL +def test_riemann_invariants1(): + skip('takes too much time') + baser, gensr = riemann_bsgs + g = Permutation([17, 44, 11, 3, 0, 19, 23, 15, 38, 4, 25, 27, 43, 36, 22, 14, 8, 30, 41, 20, 2, 10, 12, 28, 18, 1, 29, 13, 37, 42, 33, 7, 9, 31, 24, 26, 39, 5, 34, 47, 32, 6, 21, 40, 35, 46, 45, 16, 48, 49]) + can = canonicalize(g, list(range(48)), 0, (baser, gensr, 12, 0)) + assert can == [0, 2, 4, 6, 1, 3, 8, 10, 5, 7, 12, 14, 9, 11, 16, 18, 13, 15, 20, 22, 17, 19, 24, 26, 21, 23, 28, 30, 25, 27, 32, 34, 29, 31, 36, 38, 33, 35, 40, 42, 37, 39, 44, 46, 41, 43, 45, 47, 48, 49] + + g = Permutation([0,2,4,6, 7,8,10,12, 14,16,18,20, 19,22,24,26, 5,21,28,30, 32,34,36,38, 40,42,44,46, 13,48,50,52, 15,49,54,56, 17,33,41,58, 9,23,60,62, 29,35,63,64, 3,45,66,68, 25,37,47,57, 11,31,69,70, 27,39,53,72, 1,59,73,74, 55,61,67,76, 43,65,75,78, 51,71,77,79, 80,81]) + can = canonicalize(g, list(range(80)), 0, (baser, gensr, 20, 0)) + assert can == [0,2,4,6, 1,8,10,12, 3,14,16,18, 5,20,22,24, 7,26,28,30, 9,15,32,34, 11,36,23,38, 13,40,42,44, 17,39,29,46, 19,48,43,50, 21,45,52,54, 25,56,33,58, 27,60,53,62, 31,51,64,66, 35,65,47,68, 37,70,49,72, 41,74,57,76, 55,67,59,78, 61,69,71,75, 63,79,73,77, 80,81] + + +def test_riemann_products(): + baser, gensr = riemann_bsgs + base1, gens1 = get_symmetric_group_sgs(1) + base2, gens2 = get_symmetric_group_sgs(2) + base2a, gens2a = get_symmetric_group_sgs(2, 1) + + # R^{a b d0}_d0 = 0 + g = Permutation([0,1,2,3,4,5]) + can = canonicalize(g, list(range(2,4)), 0, (baser, gensr, 1, 0)) + assert can == 0 + + # R^{d0 b a}_d0 ; ord = [a,b,d0,-d0}; g = [2,1,0,3,4,5] + # T_c = -R^{a d0 b}_d0; can = [0,2,1,3,5,4] + g = Permutation([2,1,0,3,4,5]) + can = canonicalize(g, list(range(2, 4)), 0, (baser, gensr, 1, 0)) + assert can == [0,2,1,3,5,4] + + # R^d1_d2^b_d0 * R^{d0 a}_d1^d2; ord=[a,b,d0,-d0,d1,-d1,d2,-d2] + # g = [4,7,1,3,2,0,5,6,8,9] + # T_c = -R^{a d0 d1 d2}* R^b_{d0 d1 d2} + # can = [0,2,4,6,1,3,5,7,9,8] + g = Permutation([4,7,1,3,2,0,5,6,8,9]) + can = canonicalize(g, list(range(2,8)), 0, (baser, gensr, 2, 0)) + assert can == [0,2,4,6,1,3,5,7,9,8] + can1 = canonicalize_naive(g, list(range(2,8)), 0, (baser, gensr, 2, 0)) + assert can == can1 + + # A symmetric commuting + # R^{d6 d5}_d2^d1 * R^{d4 d0 d2 d3} * A_{d6 d0} A_{d3 d1} * A_{d4 d5} + # g = [12,10,5,2, 8,0,4,6, 13,1, 7,3, 9,11,14,15] + # T_c = -R^{d0 d1 d2 d3} * R_d0^{d4 d5 d6} * A_{d1 d4}*A_{d2 d5}*A_{d3 d6} + + g = Permutation([12,10,5,2,8,0,4,6,13,1,7,3,9,11,14,15]) + can = canonicalize(g, list(range(14)), 0, ((baser,gensr,2,0)), (base2,gens2,3,0)) + assert can == [0, 2, 4, 6, 1, 8, 10, 12, 3, 9, 5, 11, 7, 13, 15, 14] + + # R^{d2 a0 a2 d0} * R^d1_d2^{a1 a3} * R^{a4 a5}_{d0 d1} + # ord = [a0,a1,a2,a3,a4,a5,d0,-d0,d1,-d1,d2,-d2] + # 0 1 2 3 4 5 6 7 8 9 10 11 + # can = [0, 6, 2, 8, 1, 3, 7, 10, 4, 5, 9, 11, 12, 13] + # T_c = R^{a0 d0 a2 d1}*R^{a1 a3}_d0^d2*R^{a4 a5}_{d1 d2} + g = Permutation([10,0,2,6,8,11,1,3,4,5,7,9,12,13]) + can = canonicalize(g, list(range(6,12)), 0, (baser, gensr, 3, 0)) + assert can == [0, 6, 2, 8, 1, 3, 7, 10, 4, 5, 9, 11, 12, 13] + #can1 = canonicalize_naive(g, list(range(6,12)), 0, (baser, gensr, 3, 0)) + #assert can == can1 + + # A^n_{i, j} antisymmetric in i,j + # A_m0^d0_a1 * A_m1^a0_d0; ord = [m0,m1,a0,a1,d0,-d0] + # g = [0,4,3,1,2,5,6,7] + # T_c = -A_{m a1}^d0 * A_m1^a0_d0 + # can = [0,3,4,1,2,5,7,6] + base, gens = bsgs_direct_product(base1, gens1, base2a, gens2a) + dummies = list(range(4, 6)) + g = Permutation([0,4,3,1,2,5,6,7]) + can = canonicalize(g, dummies, 0, (base, gens, 2, 0)) + assert can == [0, 3, 4, 1, 2, 5, 7, 6] + + + # A^n_{i, j} symmetric in i,j + # A^m0_a0^d2 * A^n0_d2^d1 * A^n1_d1^d0 * A_{m0 d0}^a1 + # ordering: first the free indices; then first n, then d + # ord=[n0,n1,a0,a1, m0,-m0,d0,-d0,d1,-d1,d2,-d2] + # 0 1 2 3 4 5 6 7 8 9 10 11] + # g = [4,2,10, 0,11,8, 1,9,6, 5,7,3, 12,13] + # if the dummy indices m_i and d_i were separated, + # one gets + # T_c = A^{n0 d0 d1} * A^n1_d0^d2 * A^m0^a0_d1 * A_m0^a1_d2 + # can = [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 12, 13] + # If they are not, so can is + # T_c = A^{n0 m0 d0} A^n1_m0^d1 A^{d2 a0}_d0 A_d2^a1_d1 + # can = [0, 4, 6, 1, 5, 8, 10, 2, 7, 11, 3, 9, 12, 13] + # case with single type of indices + + base, gens = bsgs_direct_product(base1, gens1, base2, gens2) + dummies = list(range(4, 12)) + g = Permutation([4,2,10, 0,11,8, 1,9,6, 5,7,3, 12,13]) + can = canonicalize(g, dummies, 0, (base, gens, 4, 0)) + assert can == [0, 4, 6, 1, 5, 8, 10, 2, 7, 11, 3, 9, 12, 13] + # case with separated indices + dummies = [list(range(4, 6)), list(range(6,12))] + sym = [0, 0] + can = canonicalize(g, dummies, sym, (base, gens, 4, 0)) + assert can == [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 12, 13] + # case with separated indices with the second type of index + # with antisymmetric metric: there is a sign change + sym = [0, 1] + can = canonicalize(g, dummies, sym, (base, gens, 4, 0)) + assert can == [0, 6, 8, 1, 7, 10, 4, 2, 9, 5, 3, 11, 13, 12] + +def test_graph_certificate(): + # test tensor invariants constructed from random regular graphs; + # checked graph isomorphism with networkx + import random + def randomize_graph(size, g): + p = list(range(size)) + random.shuffle(p) + g1a = {} + for k, v in g1.items(): + g1a[p[k]] = [p[i] for i in v] + return g1a + + g1 = {0: [2, 3, 7], 1: [4, 5, 7], 2: [0, 4, 6], 3: [0, 6, 7], 4: [1, 2, 5], 5: [1, 4, 6], 6: [2, 3, 5], 7: [0, 1, 3]} + g2 = {0: [2, 3, 7], 1: [2, 4, 5], 2: [0, 1, 5], 3: [0, 6, 7], 4: [1, 5, 6], 5: [1, 2, 4], 6: [3, 4, 7], 7: [0, 3, 6]} + + c1 = graph_certificate(g1) + c2 = graph_certificate(g2) + assert c1 != c2 + g1a = randomize_graph(8, g1) + c1a = graph_certificate(g1a) + assert c1 == c1a + + g1 = {0: [8, 1, 9, 7], 1: [0, 9, 3, 4], 2: [3, 4, 6, 7], 3: [1, 2, 5, 6], 4: [8, 1, 2, 5], 5: [9, 3, 4, 7], 6: [8, 2, 3, 7], 7: [0, 2, 5, 6], 8: [0, 9, 4, 6], 9: [8, 0, 5, 1]} + g2 = {0: [1, 2, 5, 6], 1: [0, 9, 5, 7], 2: [0, 4, 6, 7], 3: [8, 9, 6, 7], 4: [8, 2, 6, 7], 5: [0, 9, 8, 1], 6: [0, 2, 3, 4], 7: [1, 2, 3, 4], 8: [9, 3, 4, 5], 9: [8, 1, 3, 5]} + c1 = graph_certificate(g1) + c2 = graph_certificate(g2) + assert c1 != c2 + g1a = randomize_graph(10, g1) + c1a = graph_certificate(g1a) + assert c1 == c1a diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_testutil.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_testutil.py new file mode 100644 index 0000000000000000000000000000000000000000..e13f4d5b9913213bac7798c4df77f6665785c9ca --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_testutil.py @@ -0,0 +1,55 @@ +from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup,\ + CyclicGroup +from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists,\ + _naive_list_centralizer, _verify_centralizer,\ + _verify_normal_closure +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.core.random import shuffle + + +def test_cmp_perm_lists(): + S = SymmetricGroup(4) + els = list(S.generate_dimino()) + other = els[:] + shuffle(other) + assert _cmp_perm_lists(els, other) is True + + +def test_naive_list_centralizer(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + assert _naive_list_centralizer(S, S) == [Permutation([0, 1, 2])] + assert PermutationGroup(_naive_list_centralizer(S, A)).is_subgroup(A) + + +def test_verify_bsgs(): + S = SymmetricGroup(5) + S.schreier_sims() + base = S.base + strong_gens = S.strong_gens + assert _verify_bsgs(S, base, strong_gens) is True + assert _verify_bsgs(S, base[:-1], strong_gens) is False + assert _verify_bsgs(S, base, S.generators) is False + + +def test_verify_centralizer(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + triv = PermutationGroup([Permutation([0, 1, 2])]) + assert _verify_centralizer(S, S, centr=triv) + assert _verify_centralizer(S, A, centr=A) + + +def test_verify_normal_closure(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + assert _verify_normal_closure(S, A, closure=A) + S = SymmetricGroup(5) + A = AlternatingGroup(5) + C = CyclicGroup(5) + assert _verify_normal_closure(S, A, closure=A) + assert _verify_normal_closure(S, C, closure=A) diff --git a/lib/python3.11/site-packages/sympy/combinatorics/tests/test_util.py b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_util.py new file mode 100644 index 0000000000000000000000000000000000000000..bca183e81f354e398aee9ae809fe79b20c7f2468 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/tests/test_util.py @@ -0,0 +1,120 @@ +from sympy.combinatorics.named_groups import SymmetricGroup, DihedralGroup,\ + AlternatingGroup +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.util import _check_cycles_alt_sym, _strip,\ + _distribute_gens_by_base, _strong_gens_from_distr,\ + _orbits_transversals_from_bsgs, _handle_precomputed_bsgs, _base_ordering,\ + _remove_gens +from sympy.combinatorics.testutil import _verify_bsgs + + +def test_check_cycles_alt_sym(): + perm1 = Permutation([[0, 1, 2, 3, 4, 5, 6], [7], [8], [9]]) + perm2 = Permutation([[0, 1, 2, 3, 4, 5], [6, 7, 8, 9]]) + perm3 = Permutation([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) + assert _check_cycles_alt_sym(perm1) is True + assert _check_cycles_alt_sym(perm2) is False + assert _check_cycles_alt_sym(perm3) is False + + +def test_strip(): + D = DihedralGroup(5) + D.schreier_sims() + member = Permutation([4, 0, 1, 2, 3]) + not_member1 = Permutation([0, 1, 4, 3, 2]) + not_member2 = Permutation([3, 1, 4, 2, 0]) + identity = Permutation([0, 1, 2, 3, 4]) + res1 = _strip(member, D.base, D.basic_orbits, D.basic_transversals) + res2 = _strip(not_member1, D.base, D.basic_orbits, D.basic_transversals) + res3 = _strip(not_member2, D.base, D.basic_orbits, D.basic_transversals) + assert res1[0] == identity + assert res1[1] == len(D.base) + 1 + assert res2[0] == not_member1 + assert res2[1] == len(D.base) + 1 + assert res3[0] != identity + assert res3[1] == 2 + + +def test_distribute_gens_by_base(): + base = [0, 1, 2] + gens = [Permutation([0, 1, 2, 3]), Permutation([0, 1, 3, 2]), + Permutation([0, 2, 3, 1]), Permutation([3, 2, 1, 0])] + assert _distribute_gens_by_base(base, gens) == [gens, + [Permutation([0, 1, 2, 3]), + Permutation([0, 1, 3, 2]), + Permutation([0, 2, 3, 1])], + [Permutation([0, 1, 2, 3]), + Permutation([0, 1, 3, 2])]] + + +def test_strong_gens_from_distr(): + strong_gens_distr = [[Permutation([0, 2, 1]), Permutation([1, 2, 0]), + Permutation([1, 0, 2])], [Permutation([0, 2, 1])]] + assert _strong_gens_from_distr(strong_gens_distr) == \ + [Permutation([0, 2, 1]), + Permutation([1, 2, 0]), + Permutation([1, 0, 2])] + + +def test_orbits_transversals_from_bsgs(): + S = SymmetricGroup(4) + S.schreier_sims() + base = S.base + strong_gens = S.strong_gens + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + result = _orbits_transversals_from_bsgs(base, strong_gens_distr) + orbits = result[0] + transversals = result[1] + base_len = len(base) + for i in range(base_len): + for el in orbits[i]: + assert transversals[i][el](base[i]) == el + for j in range(i): + assert transversals[i][el](base[j]) == base[j] + order = 1 + for i in range(base_len): + order *= len(orbits[i]) + assert S.order() == order + + +def test_handle_precomputed_bsgs(): + A = AlternatingGroup(5) + A.schreier_sims() + base = A.base + strong_gens = A.strong_gens + result = _handle_precomputed_bsgs(base, strong_gens) + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + assert strong_gens_distr == result[2] + transversals = result[0] + orbits = result[1] + base_len = len(base) + for i in range(base_len): + for el in orbits[i]: + assert transversals[i][el](base[i]) == el + for j in range(i): + assert transversals[i][el](base[j]) == base[j] + order = 1 + for i in range(base_len): + order *= len(orbits[i]) + assert A.order() == order + + +def test_base_ordering(): + base = [2, 4, 5] + degree = 7 + assert _base_ordering(base, degree) == [3, 4, 0, 5, 1, 2, 6] + + +def test_remove_gens(): + S = SymmetricGroup(10) + base, strong_gens = S.schreier_sims_incremental() + new_gens = _remove_gens(base, strong_gens) + assert _verify_bsgs(S, base, new_gens) is True + A = AlternatingGroup(7) + base, strong_gens = A.schreier_sims_incremental() + new_gens = _remove_gens(base, strong_gens) + assert _verify_bsgs(A, base, new_gens) is True + D = DihedralGroup(2) + base, strong_gens = D.schreier_sims_incremental() + new_gens = _remove_gens(base, strong_gens) + assert _verify_bsgs(D, base, new_gens) is True diff --git a/lib/python3.11/site-packages/sympy/combinatorics/testutil.py b/lib/python3.11/site-packages/sympy/combinatorics/testutil.py new file mode 100644 index 0000000000000000000000000000000000000000..9fe664ce9e7437b97feec90f2052eb2987c57a4e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/testutil.py @@ -0,0 +1,357 @@ +from sympy.combinatorics import Permutation +from sympy.combinatorics.util import _distribute_gens_by_base + +rmul = Permutation.rmul + + +def _cmp_perm_lists(first, second): + """ + Compare two lists of permutations as sets. + + Explanation + =========== + + This is used for testing purposes. Since the array form of a + permutation is currently a list, Permutation is not hashable + and cannot be put into a set. + + Examples + ======== + + >>> from sympy.combinatorics.permutations import Permutation + >>> from sympy.combinatorics.testutil import _cmp_perm_lists + >>> a = Permutation([0, 2, 3, 4, 1]) + >>> b = Permutation([1, 2, 0, 4, 3]) + >>> c = Permutation([3, 4, 0, 1, 2]) + >>> ls1 = [a, b, c] + >>> ls2 = [b, c, a] + >>> _cmp_perm_lists(ls1, ls2) + True + + """ + return {tuple(a) for a in first} == \ + {tuple(a) for a in second} + + +def _naive_list_centralizer(self, other, af=False): + from sympy.combinatorics.perm_groups import PermutationGroup + """ + Return a list of elements for the centralizer of a subgroup/set/element. + + Explanation + =========== + + This is a brute force implementation that goes over all elements of the + group and checks for membership in the centralizer. It is used to + test ``.centralizer()`` from ``sympy.combinatorics.perm_groups``. + + Examples + ======== + + >>> from sympy.combinatorics.testutil import _naive_list_centralizer + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> D = DihedralGroup(4) + >>> _naive_list_centralizer(D, D) + [Permutation([0, 1, 2, 3]), Permutation([2, 3, 0, 1])] + + See Also + ======== + + sympy.combinatorics.perm_groups.centralizer + + """ + from sympy.combinatorics.permutations import _af_commutes_with + if hasattr(other, 'generators'): + elements = list(self.generate_dimino(af=True)) + gens = [x._array_form for x in other.generators] + commutes_with_gens = lambda x: all(_af_commutes_with(x, gen) for gen in gens) + centralizer_list = [] + if not af: + for element in elements: + if commutes_with_gens(element): + centralizer_list.append(Permutation._af_new(element)) + else: + for element in elements: + if commutes_with_gens(element): + centralizer_list.append(element) + return centralizer_list + elif hasattr(other, 'getitem'): + return _naive_list_centralizer(self, PermutationGroup(other), af) + elif hasattr(other, 'array_form'): + return _naive_list_centralizer(self, PermutationGroup([other]), af) + + +def _verify_bsgs(group, base, gens): + """ + Verify the correctness of a base and strong generating set. + + Explanation + =========== + + This is a naive implementation using the definition of a base and a strong + generating set relative to it. There are other procedures for + verifying a base and strong generating set, but this one will + serve for more robust testing. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import AlternatingGroup + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> A = AlternatingGroup(4) + >>> A.schreier_sims() + >>> _verify_bsgs(A, A.base, A.strong_gens) + True + + See Also + ======== + + sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims + + """ + from sympy.combinatorics.perm_groups import PermutationGroup + strong_gens_distr = _distribute_gens_by_base(base, gens) + current_stabilizer = group + for i in range(len(base)): + candidate = PermutationGroup(strong_gens_distr[i]) + if current_stabilizer.order() != candidate.order(): + return False + current_stabilizer = current_stabilizer.stabilizer(base[i]) + if current_stabilizer.order() != 1: + return False + return True + + +def _verify_centralizer(group, arg, centr=None): + """ + Verify the centralizer of a group/set/element inside another group. + + This is used for testing ``.centralizer()`` from + ``sympy.combinatorics.perm_groups`` + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... AlternatingGroup) + >>> from sympy.combinatorics.perm_groups import PermutationGroup + >>> from sympy.combinatorics.permutations import Permutation + >>> from sympy.combinatorics.testutil import _verify_centralizer + >>> S = SymmetricGroup(5) + >>> A = AlternatingGroup(5) + >>> centr = PermutationGroup([Permutation([0, 1, 2, 3, 4])]) + >>> _verify_centralizer(S, A, centr) + True + + See Also + ======== + + _naive_list_centralizer, + sympy.combinatorics.perm_groups.PermutationGroup.centralizer, + _cmp_perm_lists + + """ + if centr is None: + centr = group.centralizer(arg) + centr_list = list(centr.generate_dimino(af=True)) + centr_list_naive = _naive_list_centralizer(group, arg, af=True) + return _cmp_perm_lists(centr_list, centr_list_naive) + + +def _verify_normal_closure(group, arg, closure=None): + from sympy.combinatorics.perm_groups import PermutationGroup + """ + Verify the normal closure of a subgroup/subset/element in a group. + + This is used to test + sympy.combinatorics.perm_groups.PermutationGroup.normal_closure + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import (SymmetricGroup, + ... AlternatingGroup) + >>> from sympy.combinatorics.testutil import _verify_normal_closure + >>> S = SymmetricGroup(3) + >>> A = AlternatingGroup(3) + >>> _verify_normal_closure(S, A, closure=A) + True + + See Also + ======== + + sympy.combinatorics.perm_groups.PermutationGroup.normal_closure + + """ + if closure is None: + closure = group.normal_closure(arg) + conjugates = set() + if hasattr(arg, 'generators'): + subgr_gens = arg.generators + elif hasattr(arg, '__getitem__'): + subgr_gens = arg + elif hasattr(arg, 'array_form'): + subgr_gens = [arg] + for el in group.generate_dimino(): + conjugates.update(gen ^ el for gen in subgr_gens) + naive_closure = PermutationGroup(list(conjugates)) + return closure.is_subgroup(naive_closure) + + +def canonicalize_naive(g, dummies, sym, *v): + """ + Canonicalize tensor formed by tensors of the different types. + + Explanation + =========== + + sym_i symmetry under exchange of two component tensors of type `i` + None no symmetry + 0 commuting + 1 anticommuting + + Parameters + ========== + + g : Permutation representing the tensor. + dummies : List of dummy indices. + msym : Symmetry of the metric. + v : A list of (base_i, gens_i, n_i, sym_i) for tensors of type `i`. + base_i, gens_i BSGS for tensors of this type + n_i number of tensors of type `i` + + Returns + ======= + + Returns 0 if the tensor is zero, else returns the array form of + the permutation representing the canonical form of the tensor. + + Examples + ======== + + >>> from sympy.combinatorics.testutil import canonicalize_naive + >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs + >>> from sympy.combinatorics import Permutation + >>> g = Permutation([1, 3, 2, 0, 4, 5]) + >>> base2, gens2 = get_symmetric_group_sgs(2) + >>> canonicalize_naive(g, [2, 3], 0, (base2, gens2, 2, 0)) + [0, 2, 1, 3, 4, 5] + """ + from sympy.combinatorics.perm_groups import PermutationGroup + from sympy.combinatorics.tensor_can import gens_products, dummy_sgs + from sympy.combinatorics.permutations import _af_rmul + v1 = [] + for i in range(len(v)): + base_i, gens_i, n_i, sym_i = v[i] + v1.append((base_i, gens_i, [[]]*n_i, sym_i)) + size, sbase, sgens = gens_products(*v1) + dgens = dummy_sgs(dummies, sym, size-2) + if isinstance(sym, int): + num_types = 1 + dummies = [dummies] + sym = [sym] + else: + num_types = len(sym) + dgens = [] + for i in range(num_types): + dgens.extend(dummy_sgs(dummies[i], sym[i], size - 2)) + S = PermutationGroup(sgens) + D = PermutationGroup([Permutation(x) for x in dgens]) + dlist = list(D.generate(af=True)) + g = g.array_form + st = set() + for s in S.generate(af=True): + h = _af_rmul(g, s) + for d in dlist: + q = tuple(_af_rmul(d, h)) + st.add(q) + a = list(st) + a.sort() + prev = (0,)*size + for h in a: + if h[:-2] == prev[:-2]: + if h[-1] != prev[-1]: + return 0 + prev = h + return list(a[0]) + + +def graph_certificate(gr): + """ + Return a certificate for the graph + + Parameters + ========== + + gr : adjacency list + + Explanation + =========== + + The graph is assumed to be unoriented and without + external lines. + + Associate to each vertex of the graph a symmetric tensor with + number of indices equal to the degree of the vertex; indices + are contracted when they correspond to the same line of the graph. + The canonical form of the tensor gives a certificate for the graph. + + This is not an efficient algorithm to get the certificate of a graph. + + Examples + ======== + + >>> from sympy.combinatorics.testutil import graph_certificate + >>> gr1 = {0:[1, 2, 3, 5], 1:[0, 2, 4], 2:[0, 1, 3, 4], 3:[0, 2, 4], 4:[1, 2, 3, 5], 5:[0, 4]} + >>> gr2 = {0:[1, 5], 1:[0, 2, 3, 4], 2:[1, 3, 5], 3:[1, 2, 4, 5], 4:[1, 3, 5], 5:[0, 2, 3, 4]} + >>> c1 = graph_certificate(gr1) + >>> c2 = graph_certificate(gr2) + >>> c1 + [0, 2, 4, 6, 1, 8, 10, 12, 3, 14, 16, 18, 5, 9, 15, 7, 11, 17, 13, 19, 20, 21] + >>> c1 == c2 + True + """ + from sympy.combinatorics.permutations import _af_invert + from sympy.combinatorics.tensor_can import get_symmetric_group_sgs, canonicalize + items = list(gr.items()) + items.sort(key=lambda x: len(x[1]), reverse=True) + pvert = [x[0] for x in items] + pvert = _af_invert(pvert) + + # the indices of the tensor are twice the number of lines of the graph + num_indices = 0 + for v, neigh in items: + num_indices += len(neigh) + # associate to each vertex its indices; for each line + # between two vertices assign the + # even index to the vertex which comes first in items, + # the odd index to the other vertex + vertices = [[] for i in items] + i = 0 + for v, neigh in items: + for v2 in neigh: + if pvert[v] < pvert[v2]: + vertices[pvert[v]].append(i) + vertices[pvert[v2]].append(i+1) + i += 2 + g = [] + for v in vertices: + g.extend(v) + assert len(g) == num_indices + g += [num_indices, num_indices + 1] + size = num_indices + 2 + assert sorted(g) == list(range(size)) + g = Permutation(g) + vlen = [0]*(len(vertices[0])+1) + for neigh in vertices: + vlen[len(neigh)] += 1 + v = [] + for i in range(len(vlen)): + n = vlen[i] + if n: + base, gens = get_symmetric_group_sgs(i) + v.append((base, gens, n, 0)) + v.reverse() + dummies = list(range(num_indices)) + can = canonicalize(g, dummies, 0, *v) + return can diff --git a/lib/python3.11/site-packages/sympy/combinatorics/util.py b/lib/python3.11/site-packages/sympy/combinatorics/util.py new file mode 100644 index 0000000000000000000000000000000000000000..fc73b02f94f4aae6f1b98bb3f0c837fd5a1d1e6d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/combinatorics/util.py @@ -0,0 +1,532 @@ +from sympy.combinatorics.permutations import Permutation, _af_invert, _af_rmul +from sympy.ntheory import isprime + +rmul = Permutation.rmul +_af_new = Permutation._af_new + +############################################ +# +# Utilities for computational group theory +# +############################################ + + +def _base_ordering(base, degree): + r""" + Order `\{0, 1, \dots, n-1\}` so that base points come first and in order. + + Parameters + ========== + + base : the base + degree : the degree of the associated permutation group + + Returns + ======= + + A list ``base_ordering`` such that ``base_ordering[point]`` is the + number of ``point`` in the ordering. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> from sympy.combinatorics.util import _base_ordering + >>> S = SymmetricGroup(4) + >>> S.schreier_sims() + >>> _base_ordering(S.base, S.degree) + [0, 1, 2, 3] + + Notes + ===== + + This is used in backtrack searches, when we define a relation `\ll` on + the underlying set for a permutation group of degree `n`, + `\{0, 1, \dots, n-1\}`, so that if `(b_1, b_2, \dots, b_k)` is a base we + have `b_i \ll b_j` whenever `i>> from sympy.combinatorics.util import _check_cycles_alt_sym + >>> from sympy.combinatorics import Permutation + >>> a = Permutation([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12]]) + >>> _check_cycles_alt_sym(a) + False + >>> b = Permutation([[0, 1, 2, 3, 4, 5, 6], [7, 8, 9, 10]]) + >>> _check_cycles_alt_sym(b) + True + + See Also + ======== + + sympy.combinatorics.perm_groups.PermutationGroup.is_alt_sym + + """ + n = perm.size + af = perm.array_form + current_len = 0 + total_len = 0 + used = set() + for i in range(n//2): + if i not in used and i < n//2 - total_len: + current_len = 1 + used.add(i) + j = i + while af[j] != i: + current_len += 1 + j = af[j] + used.add(j) + total_len += current_len + if current_len > n//2 and current_len < n - 2 and isprime(current_len): + return True + return False + + +def _distribute_gens_by_base(base, gens): + r""" + Distribute the group elements ``gens`` by membership in basic stabilizers. + + Explanation + =========== + + Notice that for a base `(b_1, b_2, \dots, b_k)`, the basic stabilizers + are defined as `G^{(i)} = G_{b_1, \dots, b_{i-1}}` for + `i \in\{1, 2, \dots, k\}`. + + Parameters + ========== + + base : a sequence of points in `\{0, 1, \dots, n-1\}` + gens : a list of elements of a permutation group of degree `n`. + + Returns + ======= + list + List of length `k`, where `k` is the length of *base*. The `i`-th entry + contains those elements in *gens* which fix the first `i` elements of + *base* (so that the `0`-th entry is equal to *gens* itself). If no + element fixes the first `i` elements of *base*, the `i`-th element is + set to a list containing the identity element. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> from sympy.combinatorics.util import _distribute_gens_by_base + >>> D = DihedralGroup(3) + >>> D.schreier_sims() + >>> D.strong_gens + [(0 1 2), (0 2), (1 2)] + >>> D.base + [0, 1] + >>> _distribute_gens_by_base(D.base, D.strong_gens) + [[(0 1 2), (0 2), (1 2)], + [(1 2)]] + + See Also + ======== + + _strong_gens_from_distr, _orbits_transversals_from_bsgs, + _handle_precomputed_bsgs + + """ + base_len = len(base) + degree = gens[0].size + stabs = [[] for _ in range(base_len)] + max_stab_index = 0 + for gen in gens: + j = 0 + while j < base_len - 1 and gen._array_form[base[j]] == base[j]: + j += 1 + if j > max_stab_index: + max_stab_index = j + for k in range(j + 1): + stabs[k].append(gen) + for i in range(max_stab_index + 1, base_len): + stabs[i].append(_af_new(list(range(degree)))) + return stabs + + +def _handle_precomputed_bsgs(base, strong_gens, transversals=None, + basic_orbits=None, strong_gens_distr=None): + """ + Calculate BSGS-related structures from those present. + + Explanation + =========== + + The base and strong generating set must be provided; if any of the + transversals, basic orbits or distributed strong generators are not + provided, they will be calculated from the base and strong generating set. + + Parameters + ========== + + base : the base + strong_gens : the strong generators + transversals : basic transversals + basic_orbits : basic orbits + strong_gens_distr : strong generators distributed by membership in basic stabilizers + + Returns + ======= + + (transversals, basic_orbits, strong_gens_distr) + where *transversals* are the basic transversals, *basic_orbits* are the + basic orbits, and *strong_gens_distr* are the strong generators distributed + by membership in basic stabilizers. + + Examples + ======== + + >>> from sympy.combinatorics.named_groups import DihedralGroup + >>> from sympy.combinatorics.util import _handle_precomputed_bsgs + >>> D = DihedralGroup(3) + >>> D.schreier_sims() + >>> _handle_precomputed_bsgs(D.base, D.strong_gens, + ... basic_orbits=D.basic_orbits) + ([{0: (2), 1: (0 1 2), 2: (0 2)}, {1: (2), 2: (1 2)}], [[0, 1, 2], [1, 2]], [[(0 1 2), (0 2), (1 2)], [(1 2)]]) + + See Also + ======== + + _orbits_transversals_from_bsgs, _distribute_gens_by_base + + """ + if strong_gens_distr is None: + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + if transversals is None: + if basic_orbits is None: + basic_orbits, transversals = \ + _orbits_transversals_from_bsgs(base, strong_gens_distr) + else: + transversals = \ + _orbits_transversals_from_bsgs(base, strong_gens_distr, + transversals_only=True) + else: + if basic_orbits is None: + base_len = len(base) + basic_orbits = [None]*base_len + for i in range(base_len): + basic_orbits[i] = list(transversals[i].keys()) + return transversals, basic_orbits, strong_gens_distr + + +def _orbits_transversals_from_bsgs(base, strong_gens_distr, + transversals_only=False, slp=False): + """ + Compute basic orbits and transversals from a base and strong generating set. + + Explanation + =========== + + The generators are provided as distributed across the basic stabilizers. + If the optional argument ``transversals_only`` is set to True, only the + transversals are returned. + + Parameters + ========== + + base : The base. + strong_gens_distr : Strong generators distributed by membership in basic stabilizers. + transversals_only : bool, default: False + A flag switching between returning only the + transversals and both orbits and transversals. + slp : bool, default: False + If ``True``, return a list of dictionaries containing the + generator presentations of the elements of the transversals, + i.e. the list of indices of generators from ``strong_gens_distr[i]`` + such that their product is the relevant transversal element. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> from sympy.combinatorics.util import _distribute_gens_by_base + >>> S = SymmetricGroup(3) + >>> S.schreier_sims() + >>> strong_gens_distr = _distribute_gens_by_base(S.base, S.strong_gens) + >>> (S.base, strong_gens_distr) + ([0, 1], [[(0 1 2), (2)(0 1), (1 2)], [(1 2)]]) + + See Also + ======== + + _distribute_gens_by_base, _handle_precomputed_bsgs + + """ + from sympy.combinatorics.perm_groups import _orbit_transversal + base_len = len(base) + degree = strong_gens_distr[0][0].size + transversals = [None]*base_len + slps = [None]*base_len + if transversals_only is False: + basic_orbits = [None]*base_len + for i in range(base_len): + transversals[i], slps[i] = _orbit_transversal(degree, strong_gens_distr[i], + base[i], pairs=True, slp=True) + transversals[i] = dict(transversals[i]) + if transversals_only is False: + basic_orbits[i] = list(transversals[i].keys()) + if transversals_only: + return transversals + else: + if not slp: + return basic_orbits, transversals + return basic_orbits, transversals, slps + + +def _remove_gens(base, strong_gens, basic_orbits=None, strong_gens_distr=None): + """ + Remove redundant generators from a strong generating set. + + Parameters + ========== + + base : a base + strong_gens : a strong generating set relative to *base* + basic_orbits : basic orbits + strong_gens_distr : strong generators distributed by membership in basic stabilizers + + Returns + ======= + + A strong generating set with respect to ``base`` which is a subset of + ``strong_gens``. + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> from sympy.combinatorics.util import _remove_gens + >>> from sympy.combinatorics.testutil import _verify_bsgs + >>> S = SymmetricGroup(15) + >>> base, strong_gens = S.schreier_sims_incremental() + >>> new_gens = _remove_gens(base, strong_gens) + >>> len(new_gens) + 14 + >>> _verify_bsgs(S, base, new_gens) + True + + Notes + ===== + + This procedure is outlined in [1],p.95. + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E. + "Handbook of computational group theory" + + """ + from sympy.combinatorics.perm_groups import _orbit + base_len = len(base) + degree = strong_gens[0].size + if strong_gens_distr is None: + strong_gens_distr = _distribute_gens_by_base(base, strong_gens) + if basic_orbits is None: + basic_orbits = [] + for i in range(base_len): + basic_orbit = _orbit(degree, strong_gens_distr[i], base[i]) + basic_orbits.append(basic_orbit) + strong_gens_distr.append([]) + res = strong_gens[:] + for i in range(base_len - 1, -1, -1): + gens_copy = strong_gens_distr[i][:] + for gen in strong_gens_distr[i]: + if gen not in strong_gens_distr[i + 1]: + temp_gens = gens_copy[:] + temp_gens.remove(gen) + if temp_gens == []: + continue + temp_orbit = _orbit(degree, temp_gens, base[i]) + if temp_orbit == basic_orbits[i]: + gens_copy.remove(gen) + res.remove(gen) + return res + + +def _strip(g, base, orbits, transversals): + """ + Attempt to decompose a permutation using a (possibly partial) BSGS + structure. + + Explanation + =========== + + This is done by treating the sequence ``base`` as an actual base, and + the orbits ``orbits`` and transversals ``transversals`` as basic orbits and + transversals relative to it. + + This process is called "sifting". A sift is unsuccessful when a certain + orbit element is not found or when after the sift the decomposition + does not end with the identity element. + + The argument ``transversals`` is a list of dictionaries that provides + transversal elements for the orbits ``orbits``. + + Parameters + ========== + + g : permutation to be decomposed + base : sequence of points + orbits : list + A list in which the ``i``-th entry is an orbit of ``base[i]`` + under some subgroup of the pointwise stabilizer of ` + `base[0], base[1], ..., base[i - 1]``. The groups themselves are implicit + in this function since the only information we need is encoded in the orbits + and transversals + transversals : list + A list of orbit transversals associated with the orbits *orbits*. + + Examples + ======== + + >>> from sympy.combinatorics import Permutation, SymmetricGroup + >>> from sympy.combinatorics.util import _strip + >>> S = SymmetricGroup(5) + >>> S.schreier_sims() + >>> g = Permutation([0, 2, 3, 1, 4]) + >>> _strip(g, S.base, S.basic_orbits, S.basic_transversals) + ((4), 5) + + Notes + ===== + + The algorithm is described in [1],pp.89-90. The reason for returning + both the current state of the element being decomposed and the level + at which the sifting ends is that they provide important information for + the randomized version of the Schreier-Sims algorithm. + + References + ========== + + .. [1] Holt, D., Eick, B., O'Brien, E."Handbook of computational group theory" + + See Also + ======== + + sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims + sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims_random + + """ + h = g._array_form + base_len = len(base) + for i in range(base_len): + beta = h[base[i]] + if beta == base[i]: + continue + if beta not in orbits[i]: + return _af_new(h), i + 1 + u = transversals[i][beta]._array_form + h = _af_rmul(_af_invert(u), h) + return _af_new(h), base_len + 1 + + +def _strip_af(h, base, orbits, transversals, j, slp=[], slps={}): + """ + optimized _strip, with h, transversals and result in array form + if the stripped elements is the identity, it returns False, base_len + 1 + + j h[base[i]] == base[i] for i <= j + + """ + base_len = len(base) + for i in range(j+1, base_len): + beta = h[base[i]] + if beta == base[i]: + continue + if beta not in orbits[i]: + if not slp: + return h, i + 1 + return h, i + 1, slp + u = transversals[i][beta] + if h == u: + if not slp: + return False, base_len + 1 + return False, base_len + 1, slp + h = _af_rmul(_af_invert(u), h) + if slp: + u_slp = slps[i][beta][:] + u_slp.reverse() + u_slp = [(i, (g,)) for g in u_slp] + slp = u_slp + slp + if not slp: + return h, base_len + 1 + return h, base_len + 1, slp + + +def _strong_gens_from_distr(strong_gens_distr): + """ + Retrieve strong generating set from generators of basic stabilizers. + + This is just the union of the generators of the first and second basic + stabilizers. + + Parameters + ========== + + strong_gens_distr : strong generators distributed by membership in basic stabilizers + + Examples + ======== + + >>> from sympy.combinatorics import SymmetricGroup + >>> from sympy.combinatorics.util import (_strong_gens_from_distr, + ... _distribute_gens_by_base) + >>> S = SymmetricGroup(3) + >>> S.schreier_sims() + >>> S.strong_gens + [(0 1 2), (2)(0 1), (1 2)] + >>> strong_gens_distr = _distribute_gens_by_base(S.base, S.strong_gens) + >>> _strong_gens_from_distr(strong_gens_distr) + [(0 1 2), (2)(0 1), (1 2)] + + See Also + ======== + + _distribute_gens_by_base + + """ + if len(strong_gens_distr) == 1: + return strong_gens_distr[0][:] + else: + result = strong_gens_distr[0] + for gen in strong_gens_distr[1]: + if gen not in result: + result.append(gen) + return result diff --git a/lib/python3.11/site-packages/sympy/concrete/__init__.py b/lib/python3.11/site-packages/sympy/concrete/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..7048bd548cca04780479539339dd8cc49a21990f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/__init__.py @@ -0,0 +1,8 @@ +from .products import product, Product +from .summations import summation, Sum + +__all__ = [ + 'product', 'Product', + + 'summation', 'Sum', +] diff --git a/lib/python3.11/site-packages/sympy/concrete/__pycache__/__init__.cpython-311.pyc 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[1] https://mathworld.wolfram.com/KroneckerDelta.html + +""" +from .products import product +from .summations import Sum, summation +from sympy.core import Add, Mul, S, Dummy +from sympy.core.cache import cacheit +from sympy.core.sorting import default_sort_key +from sympy.functions import KroneckerDelta, Piecewise, piecewise_fold +from sympy.polys.polytools import factor +from sympy.sets.sets import Interval +from sympy.solvers.solvers import solve + + +@cacheit +def _expand_delta(expr, index): + """ + Expand the first Add containing a simple KroneckerDelta. + """ + if not expr.is_Mul: + return expr + delta = None + func = Add + terms = [S.One] + for h in expr.args: + if delta is None and h.is_Add and _has_simple_delta(h, index): + delta = True + func = h.func + terms = [terms[0]*t for t in h.args] + else: + terms = [t*h for t in terms] + return func(*terms) + + +@cacheit +def _extract_delta(expr, index): + """ + Extract a simple KroneckerDelta from the expression. + + Explanation + =========== + + Returns the tuple ``(delta, newexpr)`` where: + + - ``delta`` is a simple KroneckerDelta expression if one was found, + or ``None`` if no simple KroneckerDelta expression was found. + + - ``newexpr`` is a Mul containing the remaining terms; ``expr`` is + returned unchanged if no simple KroneckerDelta expression was found. + + Examples + ======== + + >>> from sympy import KroneckerDelta + >>> from sympy.concrete.delta import _extract_delta + >>> from sympy.abc import x, y, i, j, k + >>> _extract_delta(4*x*y*KroneckerDelta(i, j), i) + (KroneckerDelta(i, j), 4*x*y) + >>> _extract_delta(4*x*y*KroneckerDelta(i, j), k) + (None, 4*x*y*KroneckerDelta(i, j)) + + See Also + ======== + + sympy.functions.special.tensor_functions.KroneckerDelta + deltaproduct + deltasummation + """ + if not _has_simple_delta(expr, index): + return (None, expr) + if isinstance(expr, KroneckerDelta): + return (expr, S.One) + if not expr.is_Mul: + raise ValueError("Incorrect expr") + delta = None + terms = [] + + for arg in expr.args: + if delta is None and _is_simple_delta(arg, index): + delta = arg + else: + terms.append(arg) + return (delta, expr.func(*terms)) + + +@cacheit +def _has_simple_delta(expr, index): + """ + Returns True if ``expr`` is an expression that contains a KroneckerDelta + that is simple in the index ``index``, meaning that this KroneckerDelta + is nonzero for a single value of the index ``index``. + """ + if expr.has(KroneckerDelta): + if _is_simple_delta(expr, index): + return True + if expr.is_Add or expr.is_Mul: + for arg in expr.args: + if _has_simple_delta(arg, index): + return True + return False + + +@cacheit +def _is_simple_delta(delta, index): + """ + Returns True if ``delta`` is a KroneckerDelta and is nonzero for a single + value of the index ``index``. + """ + if isinstance(delta, KroneckerDelta) and delta.has(index): + p = (delta.args[0] - delta.args[1]).as_poly(index) + if p: + return p.degree() == 1 + return False + + +@cacheit +def _remove_multiple_delta(expr): + """ + Evaluate products of KroneckerDelta's. + """ + if expr.is_Add: + return expr.func(*list(map(_remove_multiple_delta, expr.args))) + if not expr.is_Mul: + return expr + eqs = [] + newargs = [] + for arg in expr.args: + if isinstance(arg, KroneckerDelta): + eqs.append(arg.args[0] - arg.args[1]) + else: + newargs.append(arg) + if not eqs: + return expr + solns = solve(eqs, dict=True) + if len(solns) == 0: + return S.Zero + elif len(solns) == 1: + for key in solns[0].keys(): + newargs.append(KroneckerDelta(key, solns[0][key])) + expr2 = expr.func(*newargs) + if expr != expr2: + return _remove_multiple_delta(expr2) + return expr + + +@cacheit +def _simplify_delta(expr): + """ + Rewrite a KroneckerDelta's indices in its simplest form. + """ + if isinstance(expr, KroneckerDelta): + try: + slns = solve(expr.args[0] - expr.args[1], dict=True) + if slns and len(slns) == 1: + return Mul(*[KroneckerDelta(*(key, value)) + for key, value in slns[0].items()]) + except NotImplementedError: + pass + return expr + + +@cacheit +def deltaproduct(f, limit): + """ + Handle products containing a KroneckerDelta. + + See Also + ======== + + deltasummation + sympy.functions.special.tensor_functions.KroneckerDelta + sympy.concrete.products.product + """ + if ((limit[2] - limit[1]) < 0) == True: + return S.One + + if not f.has(KroneckerDelta): + return product(f, limit) + + if f.is_Add: + # Identify the term in the Add that has a simple KroneckerDelta + delta = None + terms = [] + for arg in sorted(f.args, key=default_sort_key): + if delta is None and _has_simple_delta(arg, limit[0]): + delta = arg + else: + terms.append(arg) + newexpr = f.func(*terms) + k = Dummy("kprime", integer=True) + if isinstance(limit[1], int) and isinstance(limit[2], int): + result = deltaproduct(newexpr, limit) + sum(deltaproduct(newexpr, (limit[0], limit[1], ik - 1)) * + delta.subs(limit[0], ik) * + deltaproduct(newexpr, (limit[0], ik + 1, limit[2])) for ik in range(int(limit[1]), int(limit[2] + 1)) + ) + else: + result = deltaproduct(newexpr, limit) + deltasummation( + deltaproduct(newexpr, (limit[0], limit[1], k - 1)) * + delta.subs(limit[0], k) * + deltaproduct(newexpr, (limit[0], k + 1, limit[2])), + (k, limit[1], limit[2]), + no_piecewise=_has_simple_delta(newexpr, limit[0]) + ) + return _remove_multiple_delta(result) + + delta, _ = _extract_delta(f, limit[0]) + + if not delta: + g = _expand_delta(f, limit[0]) + if f != g: + try: + return factor(deltaproduct(g, limit)) + except AssertionError: + return deltaproduct(g, limit) + return product(f, limit) + + return _remove_multiple_delta(f.subs(limit[0], limit[1])*KroneckerDelta(limit[2], limit[1])) + \ + S.One*_simplify_delta(KroneckerDelta(limit[2], limit[1] - 1)) + + +@cacheit +def deltasummation(f, limit, no_piecewise=False): + """ + Handle summations containing a KroneckerDelta. + + Explanation + =========== + + The idea for summation is the following: + + - If we are dealing with a KroneckerDelta expression, i.e. KroneckerDelta(g(x), j), + we try to simplify it. + + If we could simplify it, then we sum the resulting expression. + We already know we can sum a simplified expression, because only + simple KroneckerDelta expressions are involved. + + If we could not simplify it, there are two cases: + + 1) The expression is a simple expression: we return the summation, + taking care if we are dealing with a Derivative or with a proper + KroneckerDelta. + + 2) The expression is not simple (i.e. KroneckerDelta(cos(x))): we can do + nothing at all. + + - If the expr is a multiplication expr having a KroneckerDelta term: + + First we expand it. + + If the expansion did work, then we try to sum the expansion. + + If not, we try to extract a simple KroneckerDelta term, then we have two + cases: + + 1) We have a simple KroneckerDelta term, so we return the summation. + + 2) We did not have a simple term, but we do have an expression with + simplified KroneckerDelta terms, so we sum this expression. + + Examples + ======== + + >>> from sympy import oo, symbols + >>> from sympy.abc import k + >>> i, j = symbols('i, j', integer=True, finite=True) + >>> from sympy.concrete.delta import deltasummation + >>> from sympy import KroneckerDelta + >>> deltasummation(KroneckerDelta(i, k), (k, -oo, oo)) + 1 + >>> deltasummation(KroneckerDelta(i, k), (k, 0, oo)) + Piecewise((1, i >= 0), (0, True)) + >>> deltasummation(KroneckerDelta(i, k), (k, 1, 3)) + Piecewise((1, (i >= 1) & (i <= 3)), (0, True)) + >>> deltasummation(k*KroneckerDelta(i, j)*KroneckerDelta(j, k), (k, -oo, oo)) + j*KroneckerDelta(i, j) + >>> deltasummation(j*KroneckerDelta(i, j), (j, -oo, oo)) + i + >>> deltasummation(i*KroneckerDelta(i, j), (i, -oo, oo)) + j + + See Also + ======== + + deltaproduct + sympy.functions.special.tensor_functions.KroneckerDelta + sympy.concrete.sums.summation + """ + if ((limit[2] - limit[1]) < 0) == True: + return S.Zero + + if not f.has(KroneckerDelta): + return summation(f, limit) + + x = limit[0] + + g = _expand_delta(f, x) + if g.is_Add: + return piecewise_fold( + g.func(*[deltasummation(h, limit, no_piecewise) for h in g.args])) + + # try to extract a simple KroneckerDelta term + delta, expr = _extract_delta(g, x) + + if (delta is not None) and (delta.delta_range is not None): + dinf, dsup = delta.delta_range + if (limit[1] - dinf <= 0) == True and (limit[2] - dsup >= 0) == True: + no_piecewise = True + + if not delta: + return summation(f, limit) + + solns = solve(delta.args[0] - delta.args[1], x) + if len(solns) == 0: + return S.Zero + elif len(solns) != 1: + return Sum(f, limit) + value = solns[0] + if no_piecewise: + return expr.subs(x, value) + return Piecewise( + (expr.subs(x, value), Interval(*limit[1:3]).as_relational(value)), + (S.Zero, True) + ) diff --git a/lib/python3.11/site-packages/sympy/concrete/expr_with_intlimits.py b/lib/python3.11/site-packages/sympy/concrete/expr_with_intlimits.py new file mode 100644 index 0000000000000000000000000000000000000000..8e109913cdb2f3018096972b14651b990f4b985e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/expr_with_intlimits.py @@ -0,0 +1,354 @@ +from sympy.concrete.expr_with_limits import ExprWithLimits +from sympy.core.singleton import S +from sympy.core.relational import Eq + +class ReorderError(NotImplementedError): + """ + Exception raised when trying to reorder dependent limits. + """ + def __init__(self, expr, msg): + super().__init__( + "%s could not be reordered: %s." % (expr, msg)) + +class ExprWithIntLimits(ExprWithLimits): + """ + Superclass for Product and Sum. + + See Also + ======== + + sympy.concrete.expr_with_limits.ExprWithLimits + sympy.concrete.products.Product + sympy.concrete.summations.Sum + """ + __slots__ = () + + def change_index(self, var, trafo, newvar=None): + r""" + Change index of a Sum or Product. + + Perform a linear transformation `x \mapsto a x + b` on the index variable + `x`. For `a` the only values allowed are `\pm 1`. A new variable to be used + after the change of index can also be specified. + + Explanation + =========== + + ``change_index(expr, var, trafo, newvar=None)`` where ``var`` specifies the + index variable `x` to transform. The transformation ``trafo`` must be linear + and given in terms of ``var``. If the optional argument ``newvar`` is + provided then ``var`` gets replaced by ``newvar`` in the final expression. + + Examples + ======== + + >>> from sympy import Sum, Product, simplify + >>> from sympy.abc import x, y, a, b, c, d, u, v, i, j, k, l + + >>> S = Sum(x, (x, a, b)) + >>> S.doit() + -a**2/2 + a/2 + b**2/2 + b/2 + + >>> Sn = S.change_index(x, x + 1, y) + >>> Sn + Sum(y - 1, (y, a + 1, b + 1)) + >>> Sn.doit() + -a**2/2 + a/2 + b**2/2 + b/2 + + >>> Sn = S.change_index(x, -x, y) + >>> Sn + Sum(-y, (y, -b, -a)) + >>> Sn.doit() + -a**2/2 + a/2 + b**2/2 + b/2 + + >>> Sn = S.change_index(x, x+u) + >>> Sn + Sum(-u + x, (x, a + u, b + u)) + >>> Sn.doit() + -a**2/2 - a*u + a/2 + b**2/2 + b*u + b/2 - u*(-a + b + 1) + u + >>> simplify(Sn.doit()) + -a**2/2 + a/2 + b**2/2 + b/2 + + >>> Sn = S.change_index(x, -x - u, y) + >>> Sn + Sum(-u - y, (y, -b - u, -a - u)) + >>> Sn.doit() + -a**2/2 - a*u + a/2 + b**2/2 + b*u + b/2 - u*(-a + b + 1) + u + >>> simplify(Sn.doit()) + -a**2/2 + a/2 + b**2/2 + b/2 + + >>> P = Product(i*j**2, (i, a, b), (j, c, d)) + >>> P + Product(i*j**2, (i, a, b), (j, c, d)) + >>> P2 = P.change_index(i, i+3, k) + >>> P2 + Product(j**2*(k - 3), (k, a + 3, b + 3), (j, c, d)) + >>> P3 = P2.change_index(j, -j, l) + >>> P3 + Product(l**2*(k - 3), (k, a + 3, b + 3), (l, -d, -c)) + + When dealing with symbols only, we can make a + general linear transformation: + + >>> Sn = S.change_index(x, u*x+v, y) + >>> Sn + Sum((-v + y)/u, (y, b*u + v, a*u + v)) + >>> Sn.doit() + -v*(a*u - b*u + 1)/u + (a**2*u**2/2 + a*u*v + a*u/2 - b**2*u**2/2 - b*u*v + b*u/2 + v)/u + >>> simplify(Sn.doit()) + a**2*u/2 + a/2 - b**2*u/2 + b/2 + + However, the last result can be inconsistent with usual + summation where the index increment is always 1. This is + obvious as we get back the original value only for ``u`` + equal +1 or -1. + + See Also + ======== + + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index, + reorder_limit, + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder, + sympy.concrete.summations.Sum.reverse_order, + sympy.concrete.products.Product.reverse_order + """ + if newvar is None: + newvar = var + + limits = [] + for limit in self.limits: + if limit[0] == var: + p = trafo.as_poly(var) + if p.degree() != 1: + raise ValueError("Index transformation is not linear") + alpha = p.coeff_monomial(var) + beta = p.coeff_monomial(S.One) + if alpha.is_number: + if alpha == S.One: + limits.append((newvar, alpha*limit[1] + beta, alpha*limit[2] + beta)) + elif alpha == S.NegativeOne: + limits.append((newvar, alpha*limit[2] + beta, alpha*limit[1] + beta)) + else: + raise ValueError("Linear transformation results in non-linear summation stepsize") + else: + # Note that the case of alpha being symbolic can give issues if alpha < 0. + limits.append((newvar, alpha*limit[2] + beta, alpha*limit[1] + beta)) + else: + limits.append(limit) + + function = self.function.subs(var, (var - beta)/alpha) + function = function.subs(var, newvar) + + return self.func(function, *limits) + + + def index(expr, x): + """ + Return the index of a dummy variable in the list of limits. + + Explanation + =========== + + ``index(expr, x)`` returns the index of the dummy variable ``x`` in the + limits of ``expr``. Note that we start counting with 0 at the inner-most + limits tuple. + + Examples + ======== + + >>> from sympy.abc import x, y, a, b, c, d + >>> from sympy import Sum, Product + >>> Sum(x*y, (x, a, b), (y, c, d)).index(x) + 0 + >>> Sum(x*y, (x, a, b), (y, c, d)).index(y) + 1 + >>> Product(x*y, (x, a, b), (y, c, d)).index(x) + 0 + >>> Product(x*y, (x, a, b), (y, c, d)).index(y) + 1 + + See Also + ======== + + reorder_limit, reorder, sympy.concrete.summations.Sum.reverse_order, + sympy.concrete.products.Product.reverse_order + """ + variables = [limit[0] for limit in expr.limits] + + if variables.count(x) != 1: + raise ValueError(expr, "Number of instances of variable not equal to one") + else: + return variables.index(x) + + def reorder(expr, *arg): + """ + Reorder limits in a expression containing a Sum or a Product. + + Explanation + =========== + + ``expr.reorder(*arg)`` reorders the limits in the expression ``expr`` + according to the list of tuples given by ``arg``. These tuples can + contain numerical indices or index variable names or involve both. + + Examples + ======== + + >>> from sympy import Sum, Product + >>> from sympy.abc import x, y, z, a, b, c, d, e, f + + >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((x, y)) + Sum(x*y, (y, c, d), (x, a, b)) + + >>> Sum(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder((x, y), (x, z), (y, z)) + Sum(x*y*z, (z, e, f), (y, c, d), (x, a, b)) + + >>> P = Product(x*y*z, (x, a, b), (y, c, d), (z, e, f)) + >>> P.reorder((x, y), (x, z), (y, z)) + Product(x*y*z, (z, e, f), (y, c, d), (x, a, b)) + + We can also select the index variables by counting them, starting + with the inner-most one: + + >>> Sum(x**2, (x, a, b), (x, c, d)).reorder((0, 1)) + Sum(x**2, (x, c, d), (x, a, b)) + + And of course we can mix both schemes: + + >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((y, x)) + Sum(x*y, (y, c, d), (x, a, b)) + >>> Sum(x*y, (x, a, b), (y, c, d)).reorder((y, 0)) + Sum(x*y, (y, c, d), (x, a, b)) + + See Also + ======== + + reorder_limit, index, sympy.concrete.summations.Sum.reverse_order, + sympy.concrete.products.Product.reverse_order + """ + new_expr = expr + + for r in arg: + if len(r) != 2: + raise ValueError(r, "Invalid number of arguments") + + index1 = r[0] + index2 = r[1] + + if not isinstance(r[0], int): + index1 = expr.index(r[0]) + if not isinstance(r[1], int): + index2 = expr.index(r[1]) + + new_expr = new_expr.reorder_limit(index1, index2) + + return new_expr + + + def reorder_limit(expr, x, y): + """ + Interchange two limit tuples of a Sum or Product expression. + + Explanation + =========== + + ``expr.reorder_limit(x, y)`` interchanges two limit tuples. The + arguments ``x`` and ``y`` are integers corresponding to the index + variables of the two limits which are to be interchanged. The + expression ``expr`` has to be either a Sum or a Product. + + Examples + ======== + + >>> from sympy.abc import x, y, z, a, b, c, d, e, f + >>> from sympy import Sum, Product + + >>> Sum(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder_limit(0, 2) + Sum(x*y*z, (z, e, f), (y, c, d), (x, a, b)) + >>> Sum(x**2, (x, a, b), (x, c, d)).reorder_limit(1, 0) + Sum(x**2, (x, c, d), (x, a, b)) + + >>> Product(x*y*z, (x, a, b), (y, c, d), (z, e, f)).reorder_limit(0, 2) + Product(x*y*z, (z, e, f), (y, c, d), (x, a, b)) + + See Also + ======== + + index, reorder, sympy.concrete.summations.Sum.reverse_order, + sympy.concrete.products.Product.reverse_order + """ + var = {limit[0] for limit in expr.limits} + limit_x = expr.limits[x] + limit_y = expr.limits[y] + + if (len(set(limit_x[1].free_symbols).intersection(var)) == 0 and + len(set(limit_x[2].free_symbols).intersection(var)) == 0 and + len(set(limit_y[1].free_symbols).intersection(var)) == 0 and + len(set(limit_y[2].free_symbols).intersection(var)) == 0): + + limits = [] + for i, limit in enumerate(expr.limits): + if i == x: + limits.append(limit_y) + elif i == y: + limits.append(limit_x) + else: + limits.append(limit) + + return type(expr)(expr.function, *limits) + else: + raise ReorderError(expr, "could not interchange the two limits specified") + + @property + def has_empty_sequence(self): + """ + Returns True if the Sum or Product is computed for an empty sequence. + + Examples + ======== + + >>> from sympy import Sum, Product, Symbol + >>> m = Symbol('m') + >>> Sum(m, (m, 1, 0)).has_empty_sequence + True + + >>> Sum(m, (m, 1, 1)).has_empty_sequence + False + + >>> M = Symbol('M', integer=True, positive=True) + >>> Product(m, (m, 1, M)).has_empty_sequence + False + + >>> Product(m, (m, 2, M)).has_empty_sequence + + >>> Product(m, (m, M + 1, M)).has_empty_sequence + True + + >>> N = Symbol('N', integer=True, positive=True) + >>> Sum(m, (m, N, M)).has_empty_sequence + + >>> N = Symbol('N', integer=True, negative=True) + >>> Sum(m, (m, N, M)).has_empty_sequence + False + + See Also + ======== + + has_reversed_limits + has_finite_limits + + """ + ret_None = False + for lim in self.limits: + dif = lim[1] - lim[2] + eq = Eq(dif, 1) + if eq == True: + return True + elif eq == False: + continue + else: + ret_None = True + + if ret_None: + return None + return False diff --git a/lib/python3.11/site-packages/sympy/concrete/expr_with_limits.py b/lib/python3.11/site-packages/sympy/concrete/expr_with_limits.py new file mode 100644 index 0000000000000000000000000000000000000000..034e6ab0a7663525632abe0224fbac973c505c08 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/expr_with_limits.py @@ -0,0 +1,603 @@ +from sympy.core.add import Add +from sympy.core.containers import Tuple +from sympy.core.expr import Expr +from sympy.core.function import AppliedUndef, UndefinedFunction +from sympy.core.mul import Mul +from sympy.core.relational import Equality, Relational +from sympy.core.singleton import S +from sympy.core.symbol import Symbol, Dummy +from sympy.core.sympify import sympify +from sympy.functions.elementary.piecewise import (piecewise_fold, + Piecewise) +from sympy.logic.boolalg import BooleanFunction +from sympy.matrices.matrixbase import MatrixBase +from sympy.sets.sets import Interval, Set +from sympy.sets.fancysets import Range +from sympy.tensor.indexed import Idx +from sympy.utilities import flatten +from sympy.utilities.iterables import sift, is_sequence +from sympy.utilities.exceptions import sympy_deprecation_warning + + +def _common_new(cls, function, *symbols, discrete, **assumptions): + """Return either a special return value or the tuple, + (function, limits, orientation). This code is common to + both ExprWithLimits and AddWithLimits.""" + function = sympify(function) + + if isinstance(function, Equality): + # This transforms e.g. Integral(Eq(x, y)) to Eq(Integral(x), Integral(y)) + # but that is only valid for definite integrals. + limits, orientation = _process_limits(*symbols, discrete=discrete) + if not (limits and all(len(limit) == 3 for limit in limits)): + sympy_deprecation_warning( + """ + Creating a indefinite integral with an Eq() argument is + deprecated. + + This is because indefinite integrals do not preserve equality + due to the arbitrary constants. If you want an equality of + indefinite integrals, use Eq(Integral(a, x), Integral(b, x)) + explicitly. + """, + deprecated_since_version="1.6", + active_deprecations_target="deprecated-indefinite-integral-eq", + stacklevel=5, + ) + + lhs = function.lhs + rhs = function.rhs + return Equality(cls(lhs, *symbols, **assumptions), \ + cls(rhs, *symbols, **assumptions)) + + if function is S.NaN: + return S.NaN + + if symbols: + limits, orientation = _process_limits(*symbols, discrete=discrete) + for i, li in enumerate(limits): + if len(li) == 4: + function = function.subs(li[0], li[-1]) + limits[i] = Tuple(*li[:-1]) + else: + # symbol not provided -- we can still try to compute a general form + free = function.free_symbols + if len(free) != 1: + raise ValueError( + "specify dummy variables for %s" % function) + limits, orientation = [Tuple(s) for s in free], 1 + + # denest any nested calls + while cls == type(function): + limits = list(function.limits) + limits + function = function.function + + # Any embedded piecewise functions need to be brought out to the + # top level. We only fold Piecewise that contain the integration + # variable. + reps = {} + symbols_of_integration = {i[0] for i in limits} + for p in function.atoms(Piecewise): + if not p.has(*symbols_of_integration): + reps[p] = Dummy() + # mask off those that don't + function = function.xreplace(reps) + # do the fold + function = piecewise_fold(function) + # remove the masking + function = function.xreplace({v: k for k, v in reps.items()}) + + return function, limits, orientation + + +def _process_limits(*symbols, discrete=None): + """Process the list of symbols and convert them to canonical limits, + storing them as Tuple(symbol, lower, upper). The orientation of + the function is also returned when the upper limit is missing + so (x, 1, None) becomes (x, None, 1) and the orientation is changed. + In the case that a limit is specified as (symbol, Range), a list of + length 4 may be returned if a change of variables is needed; the + expression that should replace the symbol in the expression is + the fourth element in the list. + """ + limits = [] + orientation = 1 + if discrete is None: + err_msg = 'discrete must be True or False' + elif discrete: + err_msg = 'use Range, not Interval or Relational' + else: + err_msg = 'use Interval or Relational, not Range' + for V in symbols: + if isinstance(V, (Relational, BooleanFunction)): + if discrete: + raise TypeError(err_msg) + variable = V.atoms(Symbol).pop() + V = (variable, V.as_set()) + elif isinstance(V, Symbol) or getattr(V, '_diff_wrt', False): + if isinstance(V, Idx): + if V.lower is None or V.upper is None: + limits.append(Tuple(V)) + else: + limits.append(Tuple(V, V.lower, V.upper)) + else: + limits.append(Tuple(V)) + continue + if is_sequence(V) and not isinstance(V, Set): + if len(V) == 2 and isinstance(V[1], Set): + V = list(V) + if isinstance(V[1], Interval): # includes Reals + if discrete: + raise TypeError(err_msg) + V[1:] = V[1].inf, V[1].sup + elif isinstance(V[1], Range): + if not discrete: + raise TypeError(err_msg) + lo = V[1].inf + hi = V[1].sup + dx = abs(V[1].step) # direction doesn't matter + if dx == 1: + V[1:] = [lo, hi] + else: + if lo is not S.NegativeInfinity: + V = [V[0]] + [0, (hi - lo)//dx, dx*V[0] + lo] + else: + V = [V[0]] + [0, S.Infinity, -dx*V[0] + hi] + else: + # more complicated sets would require splitting, e.g. + # Union(Interval(1, 3), interval(6,10)) + raise NotImplementedError( + 'expecting Range' if discrete else + 'Relational or single Interval' ) + V = sympify(flatten(V)) # list of sympified elements/None + if isinstance(V[0], (Symbol, Idx)) or getattr(V[0], '_diff_wrt', False): + newsymbol = V[0] + if len(V) == 3: + # general case + if V[2] is None and V[1] is not None: + orientation *= -1 + V = [newsymbol] + [i for i in V[1:] if i is not None] + + lenV = len(V) + if not isinstance(newsymbol, Idx) or lenV == 3: + if lenV == 4: + limits.append(Tuple(*V)) + continue + if lenV == 3: + if isinstance(newsymbol, Idx): + # Idx represents an integer which may have + # specified values it can take on; if it is + # given such a value, an error is raised here + # if the summation would try to give it a larger + # or smaller value than permitted. None and Symbolic + # values will not raise an error. + lo, hi = newsymbol.lower, newsymbol.upper + try: + if lo is not None and not bool(V[1] >= lo): + raise ValueError("Summation will set Idx value too low.") + except TypeError: + pass + try: + if hi is not None and not bool(V[2] <= hi): + raise ValueError("Summation will set Idx value too high.") + except TypeError: + pass + limits.append(Tuple(*V)) + continue + if lenV == 1 or (lenV == 2 and V[1] is None): + limits.append(Tuple(newsymbol)) + continue + elif lenV == 2: + limits.append(Tuple(newsymbol, V[1])) + continue + + raise ValueError('Invalid limits given: %s' % str(symbols)) + + return limits, orientation + + +class ExprWithLimits(Expr): + __slots__ = ('is_commutative',) + + def __new__(cls, function, *symbols, **assumptions): + from sympy.concrete.products import Product + pre = _common_new(cls, function, *symbols, + discrete=issubclass(cls, Product), **assumptions) + if isinstance(pre, tuple): + function, limits, _ = pre + else: + return pre + + # limits must have upper and lower bounds; the indefinite form + # is not supported. This restriction does not apply to AddWithLimits + if any(len(l) != 3 or None in l for l in limits): + raise ValueError('ExprWithLimits requires values for lower and upper bounds.') + + obj = Expr.__new__(cls, **assumptions) + arglist = [function] + arglist.extend(limits) + obj._args = tuple(arglist) + obj.is_commutative = function.is_commutative # limits already checked + + return obj + + @property + def function(self): + """Return the function applied across limits. + + Examples + ======== + + >>> from sympy import Integral + >>> from sympy.abc import x + >>> Integral(x**2, (x,)).function + x**2 + + See Also + ======== + + limits, variables, free_symbols + """ + return self._args[0] + + @property + def kind(self): + return self.function.kind + + @property + def limits(self): + """Return the limits of expression. + + Examples + ======== + + >>> from sympy import Integral + >>> from sympy.abc import x, i + >>> Integral(x**i, (i, 1, 3)).limits + ((i, 1, 3),) + + See Also + ======== + + function, variables, free_symbols + """ + return self._args[1:] + + @property + def variables(self): + """Return a list of the limit variables. + + >>> from sympy import Sum + >>> from sympy.abc import x, i + >>> Sum(x**i, (i, 1, 3)).variables + [i] + + See Also + ======== + + function, limits, free_symbols + as_dummy : Rename dummy variables + sympy.integrals.integrals.Integral.transform : Perform mapping on the dummy variable + """ + return [l[0] for l in self.limits] + + @property + def bound_symbols(self): + """Return only variables that are dummy variables. + + Examples + ======== + + >>> from sympy import Integral + >>> from sympy.abc import x, i, j, k + >>> Integral(x**i, (i, 1, 3), (j, 2), k).bound_symbols + [i, j] + + See Also + ======== + + function, limits, free_symbols + as_dummy : Rename dummy variables + sympy.integrals.integrals.Integral.transform : Perform mapping on the dummy variable + """ + return [l[0] for l in self.limits if len(l) != 1] + + @property + def free_symbols(self): + """ + This method returns the symbols in the object, excluding those + that take on a specific value (i.e. the dummy symbols). + + Examples + ======== + + >>> from sympy import Sum + >>> from sympy.abc import x, y + >>> Sum(x, (x, y, 1)).free_symbols + {y} + """ + # don't test for any special values -- nominal free symbols + # should be returned, e.g. don't return set() if the + # function is zero -- treat it like an unevaluated expression. + function, limits = self.function, self.limits + # mask off non-symbol integration variables that have + # more than themself as a free symbol + reps = {i[0]: i[0] if i[0].free_symbols == {i[0]} else Dummy() + for i in self.limits} + function = function.xreplace(reps) + isyms = function.free_symbols + for xab in limits: + v = reps[xab[0]] + if len(xab) == 1: + isyms.add(v) + continue + # take out the target symbol + if v in isyms: + isyms.remove(v) + # add in the new symbols + for i in xab[1:]: + isyms.update(i.free_symbols) + reps = {v: k for k, v in reps.items()} + return {reps.get(_, _) for _ in isyms} + + @property + def is_number(self): + """Return True if the Sum has no free symbols, else False.""" + return not self.free_symbols + + def _eval_interval(self, x, a, b): + limits = [(i if i[0] != x else (x, a, b)) for i in self.limits] + integrand = self.function + return self.func(integrand, *limits) + + def _eval_subs(self, old, new): + """ + Perform substitutions over non-dummy variables + of an expression with limits. Also, can be used + to specify point-evaluation of an abstract antiderivative. + + Examples + ======== + + >>> from sympy import Sum, oo + >>> from sympy.abc import s, n + >>> Sum(1/n**s, (n, 1, oo)).subs(s, 2) + Sum(n**(-2), (n, 1, oo)) + + >>> from sympy import Integral + >>> from sympy.abc import x, a + >>> Integral(a*x**2, x).subs(x, 4) + Integral(a*x**2, (x, 4)) + + See Also + ======== + + variables : Lists the integration variables + transform : Perform mapping on the dummy variable for integrals + change_index : Perform mapping on the sum and product dummy variables + + """ + func, limits = self.function, list(self.limits) + + # If one of the expressions we are replacing is used as a func index + # one of two things happens. + # - the old variable first appears as a free variable + # so we perform all free substitutions before it becomes + # a func index. + # - the old variable first appears as a func index, in + # which case we ignore. See change_index. + + # Reorder limits to match standard mathematical practice for scoping + limits.reverse() + + if not isinstance(old, Symbol) or \ + old.free_symbols.intersection(self.free_symbols): + sub_into_func = True + for i, xab in enumerate(limits): + if 1 == len(xab) and old == xab[0]: + if new._diff_wrt: + xab = (new,) + else: + xab = (old, old) + limits[i] = Tuple(xab[0], *[l._subs(old, new) for l in xab[1:]]) + if len(xab[0].free_symbols.intersection(old.free_symbols)) != 0: + sub_into_func = False + break + if isinstance(old, (AppliedUndef, UndefinedFunction)): + sy2 = set(self.variables).intersection(set(new.atoms(Symbol))) + sy1 = set(self.variables).intersection(set(old.args)) + if not sy2.issubset(sy1): + raise ValueError( + "substitution cannot create dummy dependencies") + sub_into_func = True + if sub_into_func: + func = func.subs(old, new) + else: + # old is a Symbol and a dummy variable of some limit + for i, xab in enumerate(limits): + if len(xab) == 3: + limits[i] = Tuple(xab[0], *[l._subs(old, new) for l in xab[1:]]) + if old == xab[0]: + break + # simplify redundant limits (x, x) to (x, ) + for i, xab in enumerate(limits): + if len(xab) == 2 and (xab[0] - xab[1]).is_zero: + limits[i] = Tuple(xab[0], ) + + # Reorder limits back to representation-form + limits.reverse() + + return self.func(func, *limits) + + @property + def has_finite_limits(self): + """ + Returns True if the limits are known to be finite, either by the + explicit bounds, assumptions on the bounds, or assumptions on the + variables. False if known to be infinite, based on the bounds. + None if not enough information is available to determine. + + Examples + ======== + + >>> from sympy import Sum, Integral, Product, oo, Symbol + >>> x = Symbol('x') + >>> Sum(x, (x, 1, 8)).has_finite_limits + True + + >>> Integral(x, (x, 1, oo)).has_finite_limits + False + + >>> M = Symbol('M') + >>> Sum(x, (x, 1, M)).has_finite_limits + + >>> N = Symbol('N', integer=True) + >>> Product(x, (x, 1, N)).has_finite_limits + True + + See Also + ======== + + has_reversed_limits + + """ + + ret_None = False + for lim in self.limits: + if len(lim) == 3: + if any(l.is_infinite for l in lim[1:]): + # Any of the bounds are +/-oo + return False + elif any(l.is_infinite is None for l in lim[1:]): + # Maybe there are assumptions on the variable? + if lim[0].is_infinite is None: + ret_None = True + else: + if lim[0].is_infinite is None: + ret_None = True + + if ret_None: + return None + return True + + @property + def has_reversed_limits(self): + """ + Returns True if the limits are known to be in reversed order, either + by the explicit bounds, assumptions on the bounds, or assumptions on the + variables. False if known to be in normal order, based on the bounds. + None if not enough information is available to determine. + + Examples + ======== + + >>> from sympy import Sum, Integral, Product, oo, Symbol + >>> x = Symbol('x') + >>> Sum(x, (x, 8, 1)).has_reversed_limits + True + + >>> Sum(x, (x, 1, oo)).has_reversed_limits + False + + >>> M = Symbol('M') + >>> Integral(x, (x, 1, M)).has_reversed_limits + + >>> N = Symbol('N', integer=True, positive=True) + >>> Sum(x, (x, 1, N)).has_reversed_limits + False + + >>> Product(x, (x, 2, N)).has_reversed_limits + + >>> Product(x, (x, 2, N)).subs(N, N + 2).has_reversed_limits + False + + See Also + ======== + + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.has_empty_sequence + + """ + ret_None = False + for lim in self.limits: + if len(lim) == 3: + var, a, b = lim + dif = b - a + if dif.is_extended_negative: + return True + elif dif.is_extended_nonnegative: + continue + else: + ret_None = True + else: + return None + if ret_None: + return None + return False + + +class AddWithLimits(ExprWithLimits): + r"""Represents unevaluated oriented additions. + Parent class for Integral and Sum. + """ + + __slots__ = () + + def __new__(cls, function, *symbols, **assumptions): + from sympy.concrete.summations import Sum + pre = _common_new(cls, function, *symbols, + discrete=issubclass(cls, Sum), **assumptions) + if isinstance(pre, tuple): + function, limits, orientation = pre + else: + return pre + + obj = Expr.__new__(cls, **assumptions) + arglist = [orientation*function] # orientation not used in ExprWithLimits + arglist.extend(limits) + obj._args = tuple(arglist) + obj.is_commutative = function.is_commutative # limits already checked + + return obj + + def _eval_adjoint(self): + if all(x.is_real for x in flatten(self.limits)): + return self.func(self.function.adjoint(), *self.limits) + return None + + def _eval_conjugate(self): + if all(x.is_real for x in flatten(self.limits)): + return self.func(self.function.conjugate(), *self.limits) + return None + + def _eval_transpose(self): + if all(x.is_real for x in flatten(self.limits)): + return self.func(self.function.transpose(), *self.limits) + return None + + def _eval_factor(self, **hints): + if 1 == len(self.limits): + summand = self.function.factor(**hints) + if summand.is_Mul: + out = sift(summand.args, lambda w: w.is_commutative \ + and not set(self.variables) & w.free_symbols) + return Mul(*out[True])*self.func(Mul(*out[False]), \ + *self.limits) + else: + summand = self.func(self.function, *self.limits[0:-1]).factor() + if not summand.has(self.variables[-1]): + return self.func(1, [self.limits[-1]]).doit()*summand + elif isinstance(summand, Mul): + return self.func(summand, self.limits[-1]).factor() + return self + + def _eval_expand_basic(self, **hints): + summand = self.function.expand(**hints) + force = hints.get('force', False) + if (summand.is_Add and (force or summand.is_commutative and + self.has_finite_limits is not False)): + return Add(*[self.func(i, *self.limits) for i in summand.args]) + elif isinstance(summand, MatrixBase): + return summand.applyfunc(lambda x: self.func(x, *self.limits)) + elif summand != self.function: + return self.func(summand, *self.limits) + return self diff --git a/lib/python3.11/site-packages/sympy/concrete/gosper.py b/lib/python3.11/site-packages/sympy/concrete/gosper.py new file mode 100644 index 0000000000000000000000000000000000000000..c50bb8051fc0171878b207a1c7680b3ff7e2b1e4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/gosper.py @@ -0,0 +1,227 @@ +"""Gosper's algorithm for hypergeometric summation. """ + +from sympy.core import S, Dummy, symbols +from sympy.polys import Poly, parallel_poly_from_expr, factor +from sympy.utilities.iterables import is_sequence + + +def gosper_normal(f, g, n, polys=True): + r""" + Compute the Gosper's normal form of ``f`` and ``g``. + + Explanation + =========== + + Given relatively prime univariate polynomials ``f`` and ``g``, + rewrite their quotient to a normal form defined as follows: + + .. math:: + \frac{f(n)}{g(n)} = Z \cdot \frac{A(n) C(n+1)}{B(n) C(n)} + + where ``Z`` is an arbitrary constant and ``A``, ``B``, ``C`` are + monic polynomials in ``n`` with the following properties: + + 1. `\gcd(A(n), B(n+h)) = 1 \forall h \in \mathbb{N}` + 2. `\gcd(B(n), C(n+1)) = 1` + 3. `\gcd(A(n), C(n)) = 1` + + This normal form, or rational factorization in other words, is a + crucial step in Gosper's algorithm and in solving of difference + equations. It can be also used to decide if two hypergeometric + terms are similar or not. + + This procedure will return a tuple containing elements of this + factorization in the form ``(Z*A, B, C)``. + + Examples + ======== + + >>> from sympy.concrete.gosper import gosper_normal + >>> from sympy.abc import n + + >>> gosper_normal(4*n+5, 2*(4*n+1)*(2*n+3), n, polys=False) + (1/4, n + 3/2, n + 1/4) + + """ + (p, q), opt = parallel_poly_from_expr( + (f, g), n, field=True, extension=True) + + a, A = p.LC(), p.monic() + b, B = q.LC(), q.monic() + + C, Z = A.one, a/b + h = Dummy('h') + + D = Poly(n + h, n, h, domain=opt.domain) + + R = A.resultant(B.compose(D)) + roots = set(R.ground_roots().keys()) + + for r in set(roots): + if not r.is_Integer or r < 0: + roots.remove(r) + + for i in sorted(roots): + d = A.gcd(B.shift(+i)) + + A = A.quo(d) + B = B.quo(d.shift(-i)) + + for j in range(1, i + 1): + C *= d.shift(-j) + + A = A.mul_ground(Z) + + if not polys: + A = A.as_expr() + B = B.as_expr() + C = C.as_expr() + + return A, B, C + + +def gosper_term(f, n): + r""" + Compute Gosper's hypergeometric term for ``f``. + + Explanation + =========== + + Suppose ``f`` is a hypergeometric term such that: + + .. math:: + s_n = \sum_{k=0}^{n-1} f_k + + and `f_k` does not depend on `n`. Returns a hypergeometric + term `g_n` such that `g_{n+1} - g_n = f_n`. + + Examples + ======== + + >>> from sympy.concrete.gosper import gosper_term + >>> from sympy import factorial + >>> from sympy.abc import n + + >>> gosper_term((4*n + 1)*factorial(n)/factorial(2*n + 1), n) + (-n - 1/2)/(n + 1/4) + + """ + from sympy.simplify import hypersimp + r = hypersimp(f, n) + + if r is None: + return None # 'f' is *not* a hypergeometric term + + p, q = r.as_numer_denom() + + A, B, C = gosper_normal(p, q, n) + B = B.shift(-1) + + N = S(A.degree()) + M = S(B.degree()) + K = S(C.degree()) + + if (N != M) or (A.LC() != B.LC()): + D = {K - max(N, M)} + elif not N: + D = {K - N + 1, S.Zero} + else: + D = {K - N + 1, (B.nth(N - 1) - A.nth(N - 1))/A.LC()} + + for d in set(D): + if not d.is_Integer or d < 0: + D.remove(d) + + if not D: + return None # 'f(n)' is *not* Gosper-summable + + d = max(D) + + coeffs = symbols('c:%s' % (d + 1), cls=Dummy) + domain = A.get_domain().inject(*coeffs) + + x = Poly(coeffs, n, domain=domain) + H = A*x.shift(1) - B*x - C + + from sympy.solvers.solvers import solve + solution = solve(H.coeffs(), coeffs) + + if solution is None: + return None # 'f(n)' is *not* Gosper-summable + + x = x.as_expr().subs(solution) + + for coeff in coeffs: + if coeff not in solution: + x = x.subs(coeff, 0) + + if x.is_zero: + return None # 'f(n)' is *not* Gosper-summable + else: + return B.as_expr()*x/C.as_expr() + + +def gosper_sum(f, k): + r""" + Gosper's hypergeometric summation algorithm. + + Explanation + =========== + + Given a hypergeometric term ``f`` such that: + + .. math :: + s_n = \sum_{k=0}^{n-1} f_k + + and `f(n)` does not depend on `n`, returns `g_{n} - g(0)` where + `g_{n+1} - g_n = f_n`, or ``None`` if `s_n` cannot be expressed + in closed form as a sum of hypergeometric terms. + + Examples + ======== + + >>> from sympy.concrete.gosper import gosper_sum + >>> from sympy import factorial + >>> from sympy.abc import n, k + + >>> f = (4*k + 1)*factorial(k)/factorial(2*k + 1) + >>> gosper_sum(f, (k, 0, n)) + (-factorial(n) + 2*factorial(2*n + 1))/factorial(2*n + 1) + >>> _.subs(n, 2) == sum(f.subs(k, i) for i in [0, 1, 2]) + True + >>> gosper_sum(f, (k, 3, n)) + (-60*factorial(n) + factorial(2*n + 1))/(60*factorial(2*n + 1)) + >>> _.subs(n, 5) == sum(f.subs(k, i) for i in [3, 4, 5]) + True + + References + ========== + + .. [1] Marko Petkovsek, Herbert S. Wilf, Doron Zeilberger, A = B, + AK Peters, Ltd., Wellesley, MA, USA, 1997, pp. 73--100 + + """ + indefinite = False + + if is_sequence(k): + k, a, b = k + else: + indefinite = True + + g = gosper_term(f, k) + + if g is None: + return None + + if indefinite: + result = f*g + else: + result = (f*(g + 1)).subs(k, b) - (f*g).subs(k, a) + + if result is S.NaN: + try: + result = (f*(g + 1)).limit(k, b) - (f*g).limit(k, a) + except NotImplementedError: + result = None + + return factor(result) diff --git a/lib/python3.11/site-packages/sympy/concrete/guess.py b/lib/python3.11/site-packages/sympy/concrete/guess.py new file mode 100644 index 0000000000000000000000000000000000000000..f3974485d7cfe16ca2338797d00acf04c3aadfb6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/guess.py @@ -0,0 +1,473 @@ +"""Various algorithms for helping identifying numbers and sequences.""" + + +from sympy.concrete.products import (Product, product) +from sympy.core import Function, S +from sympy.core.add import Add +from sympy.core.numbers import Integer, Rational +from sympy.core.symbol import Symbol, symbols +from sympy.core.sympify import sympify +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.integers import floor +from sympy.integrals.integrals import integrate +from sympy.polys.polyfuncs import rational_interpolate as rinterp +from sympy.polys.polytools import lcm +from sympy.simplify.radsimp import denom +from sympy.utilities import public + + +@public +def find_simple_recurrence_vector(l): + """ + This function is used internally by other functions from the + sympy.concrete.guess module. While most users may want to rather use the + function find_simple_recurrence when looking for recurrence relations + among rational numbers, the current function may still be useful when + some post-processing has to be done. + + Explanation + =========== + + The function returns a vector of length n when a recurrence relation of + order n is detected in the sequence of rational numbers v. + + If the returned vector has a length 1, then the returned value is always + the list [0], which means that no relation has been found. + + While the functions is intended to be used with rational numbers, it should + work for other kinds of real numbers except for some cases involving + quadratic numbers; for that reason it should be used with some caution when + the argument is not a list of rational numbers. + + Examples + ======== + + >>> from sympy.concrete.guess import find_simple_recurrence_vector + >>> from sympy import fibonacci + >>> find_simple_recurrence_vector([fibonacci(k) for k in range(12)]) + [1, -1, -1] + + See Also + ======== + + See the function sympy.concrete.guess.find_simple_recurrence which is more + user-friendly. + + """ + q1 = [0] + q2 = [1] + b, z = 0, len(l) >> 1 + while len(q2) <= z: + while l[b]==0: + b += 1 + if b == len(l): + c = 1 + for x in q2: + c = lcm(c, denom(x)) + if q2[0]*c < 0: c = -c + for k in range(len(q2)): + q2[k] = int(q2[k]*c) + return q2 + a = S.One/l[b] + m = [a] + for k in range(b+1, len(l)): + m.append(-sum(l[j+1]*m[b-j-1] for j in range(b, k))*a) + l, m = m, [0] * max(len(q2), b+len(q1)) + for k, q in enumerate(q2): + m[k] = a*q + for k, q in enumerate(q1): + m[k+b] += q + while m[-1]==0: m.pop() # because trailing zeros can occur + q1, q2, b = q2, m, 1 + return [0] + +@public +def find_simple_recurrence(v, A=Function('a'), N=Symbol('n')): + """ + Detects and returns a recurrence relation from a sequence of several integer + (or rational) terms. The name of the function in the returned expression is + 'a' by default; the main variable is 'n' by default. The smallest index in + the returned expression is always n (and never n-1, n-2, etc.). + + Examples + ======== + + >>> from sympy.concrete.guess import find_simple_recurrence + >>> from sympy import fibonacci + >>> find_simple_recurrence([fibonacci(k) for k in range(12)]) + -a(n) - a(n + 1) + a(n + 2) + + >>> from sympy import Function, Symbol + >>> a = [1, 1, 1] + >>> for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3]) + >>> find_simple_recurrence(a, A=Function('f'), N=Symbol('i')) + -8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3) + + """ + p = find_simple_recurrence_vector(v) + n = len(p) + if n <= 1: return S.Zero + + return Add(*[A(N+n-1-k)*p[k] for k in range(n)]) + + +@public +def rationalize(x, maxcoeff=10000): + """ + Helps identifying a rational number from a float (or mpmath.mpf) value by + using a continued fraction. The algorithm stops as soon as a large partial + quotient is detected (greater than 10000 by default). + + Examples + ======== + + >>> from sympy.concrete.guess import rationalize + >>> from mpmath import cos, pi + >>> rationalize(cos(pi/3)) + 1/2 + + >>> from mpmath import mpf + >>> rationalize(mpf("0.333333333333333")) + 1/3 + + While the function is rather intended to help 'identifying' rational + values, it may be used in some cases for approximating real numbers. + (Though other functions may be more relevant in that case.) + + >>> rationalize(pi, maxcoeff = 250) + 355/113 + + See Also + ======== + + Several other methods can approximate a real number as a rational, like: + + * fractions.Fraction.from_decimal + * fractions.Fraction.from_float + * mpmath.identify + * mpmath.pslq by using the following syntax: mpmath.pslq([x, 1]) + * mpmath.findpoly by using the following syntax: mpmath.findpoly(x, 1) + * sympy.simplify.nsimplify (which is a more general function) + + The main difference between the current function and all these variants is + that control focuses on magnitude of partial quotients here rather than on + global precision of the approximation. If the real is "known to be" a + rational number, the current function should be able to detect it correctly + with the default settings even when denominator is great (unless its + expansion contains unusually big partial quotients) which may occur + when studying sequences of increasing numbers. If the user cares more + on getting simple fractions, other methods may be more convenient. + + """ + p0, p1 = 0, 1 + q0, q1 = 1, 0 + a = floor(x) + while a < maxcoeff or q1==0: + p = a*p1 + p0 + q = a*q1 + q0 + p0, p1 = p1, p + q0, q1 = q1, q + if x==a: break + x = 1/(x-a) + a = floor(x) + return sympify(p) / q + + +@public +def guess_generating_function_rational(v, X=Symbol('x')): + """ + Tries to "guess" a rational generating function for a sequence of rational + numbers v. + + Examples + ======== + + >>> from sympy.concrete.guess import guess_generating_function_rational + >>> from sympy import fibonacci + >>> l = [fibonacci(k) for k in range(5,15)] + >>> guess_generating_function_rational(l) + (3*x + 5)/(-x**2 - x + 1) + + See Also + ======== + + sympy.series.approximants + mpmath.pade + + """ + # a) compute the denominator as q + q = find_simple_recurrence_vector(v) + n = len(q) + if n <= 1: return None + # b) compute the numerator as p + p = [sum(v[i-k]*q[k] for k in range(min(i+1, n))) + for i in range(len(v)>>1)] + return (sum(p[k]*X**k for k in range(len(p))) + / sum(q[k]*X**k for k in range(n))) + + +@public +def guess_generating_function(v, X=Symbol('x'), types=['all'], maxsqrtn=2): + """ + Tries to "guess" a generating function for a sequence of rational numbers v. + Only a few patterns are implemented yet. + + Explanation + =========== + + The function returns a dictionary where keys are the name of a given type of + generating function. Six types are currently implemented: + + type | formal definition + -------+---------------------------------------------------------------- + ogf | f(x) = Sum( a_k * x^k , k: 0..infinity ) + egf | f(x) = Sum( a_k * x^k / k! , k: 0..infinity ) + lgf | f(x) = Sum( (-1)^(k+1) a_k * x^k / k , k: 1..infinity ) + | (with initial index being hold as 1 rather than 0) + hlgf | f(x) = Sum( a_k * x^k / k , k: 1..infinity ) + | (with initial index being hold as 1 rather than 0) + lgdogf | f(x) = derivate( log(Sum( a_k * x^k, k: 0..infinity )), x) + lgdegf | f(x) = derivate( log(Sum( a_k * x^k / k!, k: 0..infinity )), x) + + In order to spare time, the user can select only some types of generating + functions (default being ['all']). While forgetting to use a list in the + case of a single type may seem to work most of the time as in: types='ogf' + this (convenient) syntax may lead to unexpected extra results in some cases. + + Discarding a type when calling the function does not mean that the type will + not be present in the returned dictionary; it only means that no extra + computation will be performed for that type, but the function may still add + it in the result when it can be easily converted from another type. + + Two generating functions (lgdogf and lgdegf) are not even computed if the + initial term of the sequence is 0; it may be useful in that case to try + again after having removed the leading zeros. + + Examples + ======== + + >>> from sympy.concrete.guess import guess_generating_function as ggf + >>> ggf([k+1 for k in range(12)], types=['ogf', 'lgf', 'hlgf']) + {'hlgf': 1/(1 - x), 'lgf': 1/(x + 1), 'ogf': 1/(x**2 - 2*x + 1)} + + >>> from sympy import sympify + >>> l = sympify("[3/2, 11/2, 0, -121/2, -363/2, 121]") + >>> ggf(l) + {'ogf': (x + 3/2)/(11*x**2 - 3*x + 1)} + + >>> from sympy import fibonacci + >>> ggf([fibonacci(k) for k in range(5, 15)], types=['ogf']) + {'ogf': (3*x + 5)/(-x**2 - x + 1)} + + >>> from sympy import factorial + >>> ggf([factorial(k) for k in range(12)], types=['ogf', 'egf', 'lgf']) + {'egf': 1/(1 - x)} + + >>> ggf([k+1 for k in range(12)], types=['egf']) + {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)} + + N-th root of a rational function can also be detected (below is an example + coming from the sequence A108626 from https://oeis.org). + The greatest n-th root to be tested is specified as maxsqrtn (default 2). + + >>> ggf([1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] + sqrt(1/(x**4 + 2*x**2 - 4*x + 1)) + + References + ========== + + .. [1] "Concrete Mathematics", R.L. Graham, D.E. Knuth, O. Patashnik + .. [2] https://oeis.org/wiki/Generating_functions + + """ + # List of all types of all g.f. known by the algorithm + if 'all' in types: + types = ('ogf', 'egf', 'lgf', 'hlgf', 'lgdogf', 'lgdegf') + + result = {} + + # Ordinary Generating Function (ogf) + if 'ogf' in types: + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(v) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*v[i] for i in range(n+1)) for n in range(len(v))] + g = guess_generating_function_rational(t, X=X) + if g: + result['ogf'] = g**Rational(1, d+1) + break + + # Exponential Generating Function (egf) + if 'egf' in types: + # Transform sequence (division by factorial) + w, f = [], S.One + for i, k in enumerate(v): + f *= i if i else 1 + w.append(k/f) + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(w) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))] + g = guess_generating_function_rational(t, X=X) + if g: + result['egf'] = g**Rational(1, d+1) + break + + # Logarithmic Generating Function (lgf) + if 'lgf' in types: + # Transform sequence (multiplication by (-1)^(n+1) / n) + w, f = [], S.NegativeOne + for i, k in enumerate(v): + f = -f + w.append(f*k/Integer(i+1)) + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(w) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))] + g = guess_generating_function_rational(t, X=X) + if g: + result['lgf'] = g**Rational(1, d+1) + break + + # Hyperbolic logarithmic Generating Function (hlgf) + if 'hlgf' in types: + # Transform sequence (division by n+1) + w = [] + for i, k in enumerate(v): + w.append(k/Integer(i+1)) + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(w) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))] + g = guess_generating_function_rational(t, X=X) + if g: + result['hlgf'] = g**Rational(1, d+1) + break + + # Logarithmic derivative of ordinary generating Function (lgdogf) + if v[0] != 0 and ('lgdogf' in types + or ('ogf' in types and 'ogf' not in result)): + # Transform sequence by computing f'(x)/f(x) + # because log(f(x)) = integrate( f'(x)/f(x) ) + a, w = sympify(v[0]), [] + for n in range(len(v)-1): + w.append( + (v[n+1]*(n+1) - sum(w[-i-1]*v[i+1] for i in range(n)))/a) + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(w) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))] + g = guess_generating_function_rational(t, X=X) + if g: + result['lgdogf'] = g**Rational(1, d+1) + if 'ogf' not in result: + result['ogf'] = exp(integrate(result['lgdogf'], X)) + break + + # Logarithmic derivative of exponential generating Function (lgdegf) + if v[0] != 0 and ('lgdegf' in types + or ('egf' in types and 'egf' not in result)): + # Transform sequence / step 1 (division by factorial) + z, f = [], S.One + for i, k in enumerate(v): + f *= i if i else 1 + z.append(k/f) + # Transform sequence / step 2 by computing f'(x)/f(x) + # because log(f(x)) = integrate( f'(x)/f(x) ) + a, w = z[0], [] + for n in range(len(z)-1): + w.append( + (z[n+1]*(n+1) - sum(w[-i-1]*z[i+1] for i in range(n)))/a) + # Perform some convolutions of the sequence with itself + t = [1] + [0]*(len(w) - 1) + for d in range(max(1, maxsqrtn)): + t = [sum(t[n-i]*w[i] for i in range(n+1)) for n in range(len(w))] + g = guess_generating_function_rational(t, X=X) + if g: + result['lgdegf'] = g**Rational(1, d+1) + if 'egf' not in result: + result['egf'] = exp(integrate(result['lgdegf'], X)) + break + + return result + + +@public +def guess(l, all=False, evaluate=True, niter=2, variables=None): + """ + This function is adapted from the Rate.m package for Mathematica + written by Christian Krattenthaler. + It tries to guess a formula from a given sequence of rational numbers. + + Explanation + =========== + + In order to speed up the process, the 'all' variable is set to False by + default, stopping the computation as some results are returned during an + iteration; the variable can be set to True if more iterations are needed + (other formulas may be found; however they may be equivalent to the first + ones). + + Another option is the 'evaluate' variable (default is True); setting it + to False will leave the involved products unevaluated. + + By default, the number of iterations is set to 2 but a greater value (up + to len(l)-1) can be specified with the optional 'niter' variable. + More and more convoluted results are found when the order of the + iteration gets higher: + + * first iteration returns polynomial or rational functions; + * second iteration returns products of rising factorials and their + inverses; + * third iteration returns products of products of rising factorials + and their inverses; + * etc. + + The returned formulas contain symbols i0, i1, i2, ... where the main + variables is i0 (and auxiliary variables are i1, i2, ...). A list of + other symbols can be provided in the 'variables' option; the length of + the least should be the value of 'niter' (more is acceptable but only + the first symbols will be used); in this case, the main variable will be + the first symbol in the list. + + Examples + ======== + + >>> from sympy.concrete.guess import guess + >>> guess([1,2,6,24,120], evaluate=False) + [Product(i1 + 1, (i1, 1, i0 - 1))] + + >>> from sympy import symbols + >>> r = guess([1,2,7,42,429,7436,218348,10850216], niter=4) + >>> i0 = symbols("i0") + >>> [r[0].subs(i0,n).doit() for n in range(1,10)] + [1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460] + """ + if any(a==0 for a in l[:-1]): + return [] + N = len(l) + niter = min(N-1, niter) + myprod = product if evaluate else Product + g = [] + res = [] + if variables is None: + symb = symbols('i:'+str(niter)) + else: + symb = variables + for k, s in enumerate(symb): + g.append(l) + n, r = len(l), [] + for i in range(n-2-1, -1, -1): + ri = rinterp(enumerate(g[k][:-1], start=1), i, X=s) + if ((denom(ri).subs({s:n}) != 0) + and (ri.subs({s:n}) - g[k][-1] == 0) + and ri not in r): + r.append(ri) + if r: + for i in range(k-1, -1, -1): + r = [g[i][0] + * myprod(v, (symb[i+1], 1, symb[i]-1)) for v in r] + if not all: return r + res += r + l = [Rational(l[i+1], l[i]) for i in range(N-k-1)] + return res diff --git a/lib/python3.11/site-packages/sympy/concrete/products.py b/lib/python3.11/site-packages/sympy/concrete/products.py new file mode 100644 index 0000000000000000000000000000000000000000..c23c7212d7c325e8b5cad02c7ccd822b0c525214 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/products.py @@ -0,0 +1,610 @@ +from typing import Tuple as tTuple + +from .expr_with_intlimits import ExprWithIntLimits +from .summations import Sum, summation, _dummy_with_inherited_properties_concrete +from sympy.core.expr import Expr +from sympy.core.exprtools import factor_terms +from sympy.core.function import Derivative +from sympy.core.mul import Mul +from sympy.core.singleton import S +from sympy.core.symbol import Dummy, Symbol +from sympy.functions.combinatorial.factorials import RisingFactorial +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.polys import quo, roots + + +class Product(ExprWithIntLimits): + r""" + Represents unevaluated products. + + Explanation + =========== + + ``Product`` represents a finite or infinite product, with the first + argument being the general form of terms in the series, and the second + argument being ``(dummy_variable, start, end)``, with ``dummy_variable`` + taking all integer values from ``start`` through ``end``. In accordance + with long-standing mathematical convention, the end term is included in + the product. + + Finite products + =============== + + For finite products (and products with symbolic limits assumed to be finite) + we follow the analogue of the summation convention described by Karr [1], + especially definition 3 of section 1.4. The product: + + .. math:: + + \prod_{m \leq i < n} f(i) + + has *the obvious meaning* for `m < n`, namely: + + .. math:: + + \prod_{m \leq i < n} f(i) = f(m) f(m+1) \cdot \ldots \cdot f(n-2) f(n-1) + + with the upper limit value `f(n)` excluded. The product over an empty set is + one if and only if `m = n`: + + .. math:: + + \prod_{m \leq i < n} f(i) = 1 \quad \mathrm{for} \quad m = n + + Finally, for all other products over empty sets we assume the following + definition: + + .. math:: + + \prod_{m \leq i < n} f(i) = \frac{1}{\prod_{n \leq i < m} f(i)} \quad \mathrm{for} \quad m > n + + It is important to note that above we define all products with the upper + limit being exclusive. This is in contrast to the usual mathematical notation, + but does not affect the product convention. Indeed we have: + + .. math:: + + \prod_{m \leq i < n} f(i) = \prod_{i = m}^{n - 1} f(i) + + where the difference in notation is intentional to emphasize the meaning, + with limits typeset on the top being inclusive. + + Examples + ======== + + >>> from sympy.abc import a, b, i, k, m, n, x + >>> from sympy import Product, oo + >>> Product(k, (k, 1, m)) + Product(k, (k, 1, m)) + >>> Product(k, (k, 1, m)).doit() + factorial(m) + >>> Product(k**2,(k, 1, m)) + Product(k**2, (k, 1, m)) + >>> Product(k**2,(k, 1, m)).doit() + factorial(m)**2 + + Wallis' product for pi: + + >>> W = Product(2*i/(2*i-1) * 2*i/(2*i+1), (i, 1, oo)) + >>> W + Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, oo)) + + Direct computation currently fails: + + >>> W.doit() + Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, oo)) + + But we can approach the infinite product by a limit of finite products: + + >>> from sympy import limit + >>> W2 = Product(2*i/(2*i-1)*2*i/(2*i+1), (i, 1, n)) + >>> W2 + Product(4*i**2/((2*i - 1)*(2*i + 1)), (i, 1, n)) + >>> W2e = W2.doit() + >>> W2e + 4**n*factorial(n)**2/(2**(2*n)*RisingFactorial(1/2, n)*RisingFactorial(3/2, n)) + >>> limit(W2e, n, oo) + pi/2 + + By the same formula we can compute sin(pi/2): + + >>> from sympy import combsimp, pi, gamma, simplify + >>> P = pi * x * Product(1 - x**2/k**2, (k, 1, n)) + >>> P = P.subs(x, pi/2) + >>> P + pi**2*Product(1 - pi**2/(4*k**2), (k, 1, n))/2 + >>> Pe = P.doit() + >>> Pe + pi**2*RisingFactorial(1 - pi/2, n)*RisingFactorial(1 + pi/2, n)/(2*factorial(n)**2) + >>> limit(Pe, n, oo).gammasimp() + sin(pi**2/2) + >>> Pe.rewrite(gamma) + (-1)**n*pi**2*gamma(pi/2)*gamma(n + 1 + pi/2)/(2*gamma(1 + pi/2)*gamma(-n + pi/2)*gamma(n + 1)**2) + + Products with the lower limit being larger than the upper one: + + >>> Product(1/i, (i, 6, 1)).doit() + 120 + >>> Product(i, (i, 2, 5)).doit() + 120 + + The empty product: + + >>> Product(i, (i, n, n-1)).doit() + 1 + + An example showing that the symbolic result of a product is still + valid for seemingly nonsensical values of the limits. Then the Karr + convention allows us to give a perfectly valid interpretation to + those products by interchanging the limits according to the above rules: + + >>> P = Product(2, (i, 10, n)).doit() + >>> P + 2**(n - 9) + >>> P.subs(n, 5) + 1/16 + >>> Product(2, (i, 10, 5)).doit() + 1/16 + >>> 1/Product(2, (i, 6, 9)).doit() + 1/16 + + An explicit example of the Karr summation convention applied to products: + + >>> P1 = Product(x, (i, a, b)).doit() + >>> P1 + x**(-a + b + 1) + >>> P2 = Product(x, (i, b+1, a-1)).doit() + >>> P2 + x**(a - b - 1) + >>> simplify(P1 * P2) + 1 + + And another one: + + >>> P1 = Product(i, (i, b, a)).doit() + >>> P1 + RisingFactorial(b, a - b + 1) + >>> P2 = Product(i, (i, a+1, b-1)).doit() + >>> P2 + RisingFactorial(a + 1, -a + b - 1) + >>> P1 * P2 + RisingFactorial(b, a - b + 1)*RisingFactorial(a + 1, -a + b - 1) + >>> combsimp(P1 * P2) + 1 + + See Also + ======== + + Sum, summation + product + + References + ========== + + .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM, + Volume 28 Issue 2, April 1981, Pages 305-350 + https://dl.acm.org/doi/10.1145/322248.322255 + .. [2] https://en.wikipedia.org/wiki/Multiplication#Capital_Pi_notation + .. [3] https://en.wikipedia.org/wiki/Empty_product + """ + + __slots__ = () + + limits: tTuple[tTuple[Symbol, Expr, Expr]] + + def __new__(cls, function, *symbols, **assumptions): + obj = ExprWithIntLimits.__new__(cls, function, *symbols, **assumptions) + return obj + + def _eval_rewrite_as_Sum(self, *args, **kwargs): + return exp(Sum(log(self.function), *self.limits)) + + @property + def term(self): + return self._args[0] + function = term + + def _eval_is_zero(self): + if self.has_empty_sequence: + return False + + z = self.term.is_zero + if z is True: + return True + if self.has_finite_limits: + # A Product is zero only if its term is zero assuming finite limits. + return z + + def _eval_is_extended_real(self): + if self.has_empty_sequence: + return True + + return self.function.is_extended_real + + def _eval_is_positive(self): + if self.has_empty_sequence: + return True + if self.function.is_positive and self.has_finite_limits: + return True + + def _eval_is_nonnegative(self): + if self.has_empty_sequence: + return True + if self.function.is_nonnegative and self.has_finite_limits: + return True + + def _eval_is_extended_nonnegative(self): + if self.has_empty_sequence: + return True + if self.function.is_extended_nonnegative: + return True + + def _eval_is_extended_nonpositive(self): + if self.has_empty_sequence: + return True + + def _eval_is_finite(self): + if self.has_finite_limits and self.function.is_finite: + return True + + def doit(self, **hints): + # first make sure any definite limits have product + # variables with matching assumptions + reps = {} + for xab in self.limits: + d = _dummy_with_inherited_properties_concrete(xab) + if d: + reps[xab[0]] = d + if reps: + undo = {v: k for k, v in reps.items()} + did = self.xreplace(reps).doit(**hints) + if isinstance(did, tuple): # when separate=True + did = tuple([i.xreplace(undo) for i in did]) + else: + did = did.xreplace(undo) + return did + + from sympy.simplify.powsimp import powsimp + f = self.function + for index, limit in enumerate(self.limits): + i, a, b = limit + dif = b - a + if dif.is_integer and dif.is_negative: + a, b = b + 1, a - 1 + f = 1 / f + + g = self._eval_product(f, (i, a, b)) + if g in (None, S.NaN): + return self.func(powsimp(f), *self.limits[index:]) + else: + f = g + + if hints.get('deep', True): + return f.doit(**hints) + else: + return powsimp(f) + + def _eval_adjoint(self): + if self.is_commutative: + return self.func(self.function.adjoint(), *self.limits) + return None + + def _eval_conjugate(self): + return self.func(self.function.conjugate(), *self.limits) + + def _eval_product(self, term, limits): + + (k, a, n) = limits + + if k not in term.free_symbols: + if (term - 1).is_zero: + return S.One + return term**(n - a + 1) + + if a == n: + return term.subs(k, a) + + from .delta import deltaproduct, _has_simple_delta + if term.has(KroneckerDelta) and _has_simple_delta(term, limits[0]): + return deltaproduct(term, limits) + + dif = n - a + definite = dif.is_Integer + if definite and (dif < 100): + return self._eval_product_direct(term, limits) + + elif term.is_polynomial(k): + poly = term.as_poly(k) + + A = B = Q = S.One + + all_roots = roots(poly) + + M = 0 + for r, m in all_roots.items(): + M += m + A *= RisingFactorial(a - r, n - a + 1)**m + Q *= (n - r)**m + + if M < poly.degree(): + arg = quo(poly, Q.as_poly(k)) + B = self.func(arg, (k, a, n)).doit() + + return poly.LC()**(n - a + 1) * A * B + + elif term.is_Add: + factored = factor_terms(term, fraction=True) + if factored.is_Mul: + return self._eval_product(factored, (k, a, n)) + + elif term.is_Mul: + # Factor in part without the summation variable and part with + without_k, with_k = term.as_coeff_mul(k) + + if len(with_k) >= 2: + # More than one term including k, so still a multiplication + exclude, include = [], [] + for t in with_k: + p = self._eval_product(t, (k, a, n)) + + if p is not None: + exclude.append(p) + else: + include.append(t) + + if not exclude: + return None + else: + arg = term._new_rawargs(*include) + A = Mul(*exclude) + B = self.func(arg, (k, a, n)).doit() + return without_k**(n - a + 1)*A * B + else: + # Just a single term + p = self._eval_product(with_k[0], (k, a, n)) + if p is None: + p = self.func(with_k[0], (k, a, n)).doit() + return without_k**(n - a + 1)*p + + + elif term.is_Pow: + if not term.base.has(k): + s = summation(term.exp, (k, a, n)) + + return term.base**s + elif not term.exp.has(k): + p = self._eval_product(term.base, (k, a, n)) + + if p is not None: + return p**term.exp + + elif isinstance(term, Product): + evaluated = term.doit() + f = self._eval_product(evaluated, limits) + if f is None: + return self.func(evaluated, limits) + else: + return f + + if definite: + return self._eval_product_direct(term, limits) + + def _eval_simplify(self, **kwargs): + from sympy.simplify.simplify import product_simplify + rv = product_simplify(self, **kwargs) + return rv.doit() if kwargs['doit'] else rv + + def _eval_transpose(self): + if self.is_commutative: + return self.func(self.function.transpose(), *self.limits) + return None + + def _eval_product_direct(self, term, limits): + (k, a, n) = limits + return Mul(*[term.subs(k, a + i) for i in range(n - a + 1)]) + + def _eval_derivative(self, x): + if isinstance(x, Symbol) and x not in self.free_symbols: + return S.Zero + f, limits = self.function, list(self.limits) + limit = limits.pop(-1) + if limits: + f = self.func(f, *limits) + i, a, b = limit + if x in a.free_symbols or x in b.free_symbols: + return None + h = Dummy() + rv = Sum( Product(f, (i, a, h - 1)) * Product(f, (i, h + 1, b)) * Derivative(f, x, evaluate=True).subs(i, h), (h, a, b)) + return rv + + def is_convergent(self): + r""" + See docs of :obj:`.Sum.is_convergent()` for explanation of convergence + in SymPy. + + Explanation + =========== + + The infinite product: + + .. math:: + + \prod_{1 \leq i < \infty} f(i) + + is defined by the sequence of partial products: + + .. math:: + + \prod_{i=1}^{n} f(i) = f(1) f(2) \cdots f(n) + + as n increases without bound. The product converges to a non-zero + value if and only if the sum: + + .. math:: + + \sum_{1 \leq i < \infty} \log{f(n)} + + converges. + + Examples + ======== + + >>> from sympy import Product, Symbol, cos, pi, exp, oo + >>> n = Symbol('n', integer=True) + >>> Product(n/(n + 1), (n, 1, oo)).is_convergent() + False + >>> Product(1/n**2, (n, 1, oo)).is_convergent() + False + >>> Product(cos(pi/n), (n, 1, oo)).is_convergent() + True + >>> Product(exp(-n**2), (n, 1, oo)).is_convergent() + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Infinite_product + """ + sequence_term = self.function + log_sum = log(sequence_term) + lim = self.limits + try: + is_conv = Sum(log_sum, *lim).is_convergent() + except NotImplementedError: + if Sum(sequence_term - 1, *lim).is_absolutely_convergent() is S.true: + return S.true + raise NotImplementedError("The algorithm to find the product convergence of %s " + "is not yet implemented" % (sequence_term)) + return is_conv + + def reverse_order(expr, *indices): + """ + Reverse the order of a limit in a Product. + + Explanation + =========== + + ``reverse_order(expr, *indices)`` reverses some limits in the expression + ``expr`` which can be either a ``Sum`` or a ``Product``. The selectors in + the argument ``indices`` specify some indices whose limits get reversed. + These selectors are either variable names or numerical indices counted + starting from the inner-most limit tuple. + + Examples + ======== + + >>> from sympy import gamma, Product, simplify, Sum + >>> from sympy.abc import x, y, a, b, c, d + >>> P = Product(x, (x, a, b)) + >>> Pr = P.reverse_order(x) + >>> Pr + Product(1/x, (x, b + 1, a - 1)) + >>> Pr = Pr.doit() + >>> Pr + 1/RisingFactorial(b + 1, a - b - 1) + >>> simplify(Pr.rewrite(gamma)) + Piecewise((gamma(b + 1)/gamma(a), b > -1), ((-1)**(-a + b + 1)*gamma(1 - a)/gamma(-b), True)) + >>> P = P.doit() + >>> P + RisingFactorial(a, -a + b + 1) + >>> simplify(P.rewrite(gamma)) + Piecewise((gamma(b + 1)/gamma(a), a > 0), ((-1)**(-a + b + 1)*gamma(1 - a)/gamma(-b), True)) + + While one should prefer variable names when specifying which limits + to reverse, the index counting notation comes in handy in case there + are several symbols with the same name. + + >>> S = Sum(x*y, (x, a, b), (y, c, d)) + >>> S + Sum(x*y, (x, a, b), (y, c, d)) + >>> S0 = S.reverse_order(0) + >>> S0 + Sum(-x*y, (x, b + 1, a - 1), (y, c, d)) + >>> S1 = S0.reverse_order(1) + >>> S1 + Sum(x*y, (x, b + 1, a - 1), (y, d + 1, c - 1)) + + Of course we can mix both notations: + + >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + + See Also + ======== + + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index, + reorder_limit, + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder + + References + ========== + + .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM, + Volume 28 Issue 2, April 1981, Pages 305-350 + https://dl.acm.org/doi/10.1145/322248.322255 + + """ + l_indices = list(indices) + + for i, indx in enumerate(l_indices): + if not isinstance(indx, int): + l_indices[i] = expr.index(indx) + + e = 1 + limits = [] + for i, limit in enumerate(expr.limits): + l = limit + if i in l_indices: + e = -e + l = (limit[0], limit[2] + 1, limit[1] - 1) + limits.append(l) + + return Product(expr.function ** e, *limits) + + +def product(*args, **kwargs): + r""" + Compute the product. + + Explanation + =========== + + The notation for symbols is similar to the notation used in Sum or + Integral. product(f, (i, a, b)) computes the product of f with + respect to i from a to b, i.e., + + :: + + b + _____ + product(f(n), (i, a, b)) = | | f(n) + | | + i = a + + If it cannot compute the product, it returns an unevaluated Product object. + Repeated products can be computed by introducing additional symbols tuples:: + + Examples + ======== + + >>> from sympy import product, symbols + >>> i, n, m, k = symbols('i n m k', integer=True) + + >>> product(i, (i, 1, k)) + factorial(k) + >>> product(m, (i, 1, k)) + m**k + >>> product(i, (i, 1, k), (k, 1, n)) + Product(factorial(k), (k, 1, n)) + + """ + + prod = Product(*args, **kwargs) + + if isinstance(prod, Product): + return prod.doit(deep=False) + else: + return prod diff --git a/lib/python3.11/site-packages/sympy/concrete/summations.py b/lib/python3.11/site-packages/sympy/concrete/summations.py new file mode 100644 index 0000000000000000000000000000000000000000..e167c77e462ef85463d49d616e19231989815e45 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/summations.py @@ -0,0 +1,1646 @@ +from typing import Tuple as tTuple + +from sympy.calculus.singularities import is_decreasing +from sympy.calculus.accumulationbounds import AccumulationBounds +from .expr_with_intlimits import ExprWithIntLimits +from .expr_with_limits import AddWithLimits +from .gosper import gosper_sum +from sympy.core.expr import Expr +from sympy.core.add import Add +from sympy.core.containers import Tuple +from sympy.core.function import Derivative, expand +from sympy.core.mul import Mul +from sympy.core.numbers import Float, _illegal +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.sorting import ordered +from sympy.core.symbol import Dummy, Wild, Symbol, symbols +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.combinatorial.numbers import bernoulli, harmonic +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import cot, csc +from sympy.functions.special.hyper import hyper +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.functions.special.zeta_functions import zeta +from sympy.integrals.integrals import Integral +from sympy.logic.boolalg import And +from sympy.polys.partfrac import apart +from sympy.polys.polyerrors import PolynomialError, PolificationFailed +from sympy.polys.polytools import parallel_poly_from_expr, Poly, factor +from sympy.polys.rationaltools import together +from sympy.series.limitseq import limit_seq +from sympy.series.order import O +from sympy.series.residues import residue +from sympy.sets.sets import FiniteSet, Interval +from sympy.utilities.iterables import sift +import itertools + + +class Sum(AddWithLimits, ExprWithIntLimits): + r""" + Represents unevaluated summation. + + Explanation + =========== + + ``Sum`` represents a finite or infinite series, with the first argument + being the general form of terms in the series, and the second argument + being ``(dummy_variable, start, end)``, with ``dummy_variable`` taking + all integer values from ``start`` through ``end``. In accordance with + long-standing mathematical convention, the end term is included in the + summation. + + Finite sums + =========== + + For finite sums (and sums with symbolic limits assumed to be finite) we + follow the summation convention described by Karr [1], especially + definition 3 of section 1.4. The sum: + + .. math:: + + \sum_{m \leq i < n} f(i) + + has *the obvious meaning* for `m < n`, namely: + + .. math:: + + \sum_{m \leq i < n} f(i) = f(m) + f(m+1) + \ldots + f(n-2) + f(n-1) + + with the upper limit value `f(n)` excluded. The sum over an empty set is + zero if and only if `m = n`: + + .. math:: + + \sum_{m \leq i < n} f(i) = 0 \quad \mathrm{for} \quad m = n + + Finally, for all other sums over empty sets we assume the following + definition: + + .. math:: + + \sum_{m \leq i < n} f(i) = - \sum_{n \leq i < m} f(i) \quad \mathrm{for} \quad m > n + + It is important to note that Karr defines all sums with the upper + limit being exclusive. This is in contrast to the usual mathematical notation, + but does not affect the summation convention. Indeed we have: + + .. math:: + + \sum_{m \leq i < n} f(i) = \sum_{i = m}^{n - 1} f(i) + + where the difference in notation is intentional to emphasize the meaning, + with limits typeset on the top being inclusive. + + Examples + ======== + + >>> from sympy.abc import i, k, m, n, x + >>> from sympy import Sum, factorial, oo, IndexedBase, Function + >>> Sum(k, (k, 1, m)) + Sum(k, (k, 1, m)) + >>> Sum(k, (k, 1, m)).doit() + m**2/2 + m/2 + >>> Sum(k**2, (k, 1, m)) + Sum(k**2, (k, 1, m)) + >>> Sum(k**2, (k, 1, m)).doit() + m**3/3 + m**2/2 + m/6 + >>> Sum(x**k, (k, 0, oo)) + Sum(x**k, (k, 0, oo)) + >>> Sum(x**k, (k, 0, oo)).doit() + Piecewise((1/(1 - x), Abs(x) < 1), (Sum(x**k, (k, 0, oo)), True)) + >>> Sum(x**k/factorial(k), (k, 0, oo)).doit() + exp(x) + + Here are examples to do summation with symbolic indices. You + can use either Function of IndexedBase classes: + + >>> f = Function('f') + >>> Sum(f(n), (n, 0, 3)).doit() + f(0) + f(1) + f(2) + f(3) + >>> Sum(f(n), (n, 0, oo)).doit() + Sum(f(n), (n, 0, oo)) + >>> f = IndexedBase('f') + >>> Sum(f[n]**2, (n, 0, 3)).doit() + f[0]**2 + f[1]**2 + f[2]**2 + f[3]**2 + + An example showing that the symbolic result of a summation is still + valid for seemingly nonsensical values of the limits. Then the Karr + convention allows us to give a perfectly valid interpretation to + those sums by interchanging the limits according to the above rules: + + >>> S = Sum(i, (i, 1, n)).doit() + >>> S + n**2/2 + n/2 + >>> S.subs(n, -4) + 6 + >>> Sum(i, (i, 1, -4)).doit() + 6 + >>> Sum(-i, (i, -3, 0)).doit() + 6 + + An explicit example of the Karr summation convention: + + >>> S1 = Sum(i**2, (i, m, m+n-1)).doit() + >>> S1 + m**2*n + m*n**2 - m*n + n**3/3 - n**2/2 + n/6 + >>> S2 = Sum(i**2, (i, m+n, m-1)).doit() + >>> S2 + -m**2*n - m*n**2 + m*n - n**3/3 + n**2/2 - n/6 + >>> S1 + S2 + 0 + >>> S3 = Sum(i, (i, m, m-1)).doit() + >>> S3 + 0 + + See Also + ======== + + summation + Product, sympy.concrete.products.product + + References + ========== + + .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM, + Volume 28 Issue 2, April 1981, Pages 305-350 + https://dl.acm.org/doi/10.1145/322248.322255 + .. [2] https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation + .. [3] https://en.wikipedia.org/wiki/Empty_sum + """ + + __slots__ = () + + limits: tTuple[tTuple[Symbol, Expr, Expr]] + + def __new__(cls, function, *symbols, **assumptions): + obj = AddWithLimits.__new__(cls, function, *symbols, **assumptions) + if not hasattr(obj, 'limits'): + return obj + if any(len(l) != 3 or None in l for l in obj.limits): + raise ValueError('Sum requires values for lower and upper bounds.') + + return obj + + def _eval_is_zero(self): + # a Sum is only zero if its function is zero or if all terms + # cancel out. This only answers whether the summand is zero; if + # not then None is returned since we don't analyze whether all + # terms cancel out. + if self.function.is_zero or self.has_empty_sequence: + return True + + def _eval_is_extended_real(self): + if self.has_empty_sequence: + return True + return self.function.is_extended_real + + def _eval_is_positive(self): + if self.has_finite_limits and self.has_reversed_limits is False: + return self.function.is_positive + + def _eval_is_negative(self): + if self.has_finite_limits and self.has_reversed_limits is False: + return self.function.is_negative + + def _eval_is_finite(self): + if self.has_finite_limits and self.function.is_finite: + return True + + def doit(self, **hints): + if hints.get('deep', True): + f = self.function.doit(**hints) + else: + f = self.function + + # first make sure any definite limits have summation + # variables with matching assumptions + reps = {} + for xab in self.limits: + d = _dummy_with_inherited_properties_concrete(xab) + if d: + reps[xab[0]] = d + if reps: + undo = {v: k for k, v in reps.items()} + did = self.xreplace(reps).doit(**hints) + if isinstance(did, tuple): # when separate=True + did = tuple([i.xreplace(undo) for i in did]) + elif did is not None: + did = did.xreplace(undo) + else: + did = self + return did + + + if self.function.is_Matrix: + expanded = self.expand() + if self != expanded: + return expanded.doit() + return _eval_matrix_sum(self) + + for n, limit in enumerate(self.limits): + i, a, b = limit + dif = b - a + if dif == -1: + # Any summation over an empty set is zero + return S.Zero + if dif.is_integer and dif.is_negative: + a, b = b + 1, a - 1 + f = -f + + newf = eval_sum(f, (i, a, b)) + if newf is None: + if f == self.function: + zeta_function = self.eval_zeta_function(f, (i, a, b)) + if zeta_function is not None: + return zeta_function + return self + else: + return self.func(f, *self.limits[n:]) + f = newf + + if hints.get('deep', True): + # eval_sum could return partially unevaluated + # result with Piecewise. In this case we won't + # doit() recursively. + if not isinstance(f, Piecewise): + return f.doit(**hints) + + return f + + def eval_zeta_function(self, f, limits): + """ + Check whether the function matches with the zeta function. + + If it matches, then return a `Piecewise` expression because + zeta function does not converge unless `s > 1` and `q > 0` + """ + i, a, b = limits + w, y, z = Wild('w', exclude=[i]), Wild('y', exclude=[i]), Wild('z', exclude=[i]) + result = f.match((w * i + y) ** (-z)) + if result is not None and b is S.Infinity: + coeff = 1 / result[w] ** result[z] + s = result[z] + q = result[y] / result[w] + a + return Piecewise((coeff * zeta(s, q), And(q > 0, s > 1)), (self, True)) + + def _eval_derivative(self, x): + """ + Differentiate wrt x as long as x is not in the free symbols of any of + the upper or lower limits. + + Explanation + =========== + + Sum(a*b*x, (x, 1, a)) can be differentiated wrt x or b but not `a` + since the value of the sum is discontinuous in `a`. In a case + involving a limit variable, the unevaluated derivative is returned. + """ + + # diff already confirmed that x is in the free symbols of self, but we + # don't want to differentiate wrt any free symbol in the upper or lower + # limits + # XXX remove this test for free_symbols when the default _eval_derivative is in + if isinstance(x, Symbol) and x not in self.free_symbols: + return S.Zero + + # get limits and the function + f, limits = self.function, list(self.limits) + + limit = limits.pop(-1) + + if limits: # f is the argument to a Sum + f = self.func(f, *limits) + + _, a, b = limit + if x in a.free_symbols or x in b.free_symbols: + return None + df = Derivative(f, x, evaluate=True) + rv = self.func(df, limit) + return rv + + def _eval_difference_delta(self, n, step): + k, _, upper = self.args[-1] + new_upper = upper.subs(n, n + step) + + if len(self.args) == 2: + f = self.args[0] + else: + f = self.func(*self.args[:-1]) + + return Sum(f, (k, upper + 1, new_upper)).doit() + + def _eval_simplify(self, **kwargs): + + function = self.function + + if kwargs.get('deep', True): + function = function.simplify(**kwargs) + + # split the function into adds + terms = Add.make_args(expand(function)) + s_t = [] # Sum Terms + o_t = [] # Other Terms + + for term in terms: + if term.has(Sum): + # if there is an embedded sum here + # it is of the form x * (Sum(whatever)) + # hence we make a Mul out of it, and simplify all interior sum terms + subterms = Mul.make_args(expand(term)) + out_terms = [] + for subterm in subterms: + # go through each term + if isinstance(subterm, Sum): + # if it's a sum, simplify it + out_terms.append(subterm._eval_simplify(**kwargs)) + else: + # otherwise, add it as is + out_terms.append(subterm) + + # turn it back into a Mul + s_t.append(Mul(*out_terms)) + else: + o_t.append(term) + + # next try to combine any interior sums for further simplification + from sympy.simplify.simplify import factor_sum, sum_combine + result = Add(sum_combine(s_t), *o_t) + + return factor_sum(result, limits=self.limits) + + def is_convergent(self): + r""" + Checks for the convergence of a Sum. + + Explanation + =========== + + We divide the study of convergence of infinite sums and products in + two parts. + + First Part: + One part is the question whether all the terms are well defined, i.e., + they are finite in a sum and also non-zero in a product. Zero + is the analogy of (minus) infinity in products as + :math:`e^{-\infty} = 0`. + + Second Part: + The second part is the question of convergence after infinities, + and zeros in products, have been omitted assuming that their number + is finite. This means that we only consider the tail of the sum or + product, starting from some point after which all terms are well + defined. + + For example, in a sum of the form: + + .. math:: + + \sum_{1 \leq i < \infty} \frac{1}{n^2 + an + b} + + where a and b are numbers. The routine will return true, even if there + are infinities in the term sequence (at most two). An analogous + product would be: + + .. math:: + + \prod_{1 \leq i < \infty} e^{\frac{1}{n^2 + an + b}} + + This is how convergence is interpreted. It is concerned with what + happens at the limit. Finding the bad terms is another independent + matter. + + Note: It is responsibility of user to see that the sum or product + is well defined. + + There are various tests employed to check the convergence like + divergence test, root test, integral test, alternating series test, + comparison tests, Dirichlet tests. It returns true if Sum is convergent + and false if divergent and NotImplementedError if it cannot be checked. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Convergence_tests + + Examples + ======== + + >>> from sympy import factorial, S, Sum, Symbol, oo + >>> n = Symbol('n', integer=True) + >>> Sum(n/(n - 1), (n, 4, 7)).is_convergent() + True + >>> Sum(n/(2*n + 1), (n, 1, oo)).is_convergent() + False + >>> Sum(factorial(n)/5**n, (n, 1, oo)).is_convergent() + False + >>> Sum(1/n**(S(6)/5), (n, 1, oo)).is_convergent() + True + + See Also + ======== + + Sum.is_absolutely_convergent + sympy.concrete.products.Product.is_convergent + """ + p, q, r = symbols('p q r', cls=Wild) + + sym = self.limits[0][0] + lower_limit = self.limits[0][1] + upper_limit = self.limits[0][2] + sequence_term = self.function.simplify() + + if len(sequence_term.free_symbols) > 1: + raise NotImplementedError("convergence checking for more than one symbol " + "containing series is not handled") + + if lower_limit.is_finite and upper_limit.is_finite: + return S.true + + # transform sym -> -sym and swap the upper_limit = S.Infinity + # and lower_limit = - upper_limit + if lower_limit is S.NegativeInfinity: + if upper_limit is S.Infinity: + return Sum(sequence_term, (sym, 0, S.Infinity)).is_convergent() and \ + Sum(sequence_term, (sym, S.NegativeInfinity, 0)).is_convergent() + from sympy.simplify.simplify import simplify + sequence_term = simplify(sequence_term.xreplace({sym: -sym})) + lower_limit = -upper_limit + upper_limit = S.Infinity + + sym_ = Dummy(sym.name, integer=True, positive=True) + sequence_term = sequence_term.xreplace({sym: sym_}) + sym = sym_ + + interval = Interval(lower_limit, upper_limit) + + # Piecewise function handle + if sequence_term.is_Piecewise: + for func, cond in sequence_term.args: + # see if it represents something going to oo + if cond == True or cond.as_set().sup is S.Infinity: + s = Sum(func, (sym, lower_limit, upper_limit)) + return s.is_convergent() + return S.true + + ### -------- Divergence test ----------- ### + try: + lim_val = limit_seq(sequence_term, sym) + if lim_val is not None and lim_val.is_zero is False: + return S.false + except NotImplementedError: + pass + + try: + lim_val_abs = limit_seq(abs(sequence_term), sym) + if lim_val_abs is not None and lim_val_abs.is_zero is False: + return S.false + except NotImplementedError: + pass + + order = O(sequence_term, (sym, S.Infinity)) + + ### --------- p-series test (1/n**p) ---------- ### + p_series_test = order.expr.match(sym**p) + if p_series_test is not None: + if p_series_test[p] < -1: + return S.true + if p_series_test[p] >= -1: + return S.false + + ### ------------- comparison test ------------- ### + # 1/(n**p*log(n)**q*log(log(n))**r) comparison + n_log_test = (order.expr.match(1/(sym**p*log(1/sym)**q*log(-log(1/sym))**r)) or + order.expr.match(1/(sym**p*(-log(1/sym))**q*log(-log(1/sym))**r))) + if n_log_test is not None: + if (n_log_test[p] > 1 or + (n_log_test[p] == 1 and n_log_test[q] > 1) or + (n_log_test[p] == n_log_test[q] == 1 and n_log_test[r] > 1)): + return S.true + return S.false + + ### ------------- Limit comparison test -----------### + # (1/n) comparison + try: + lim_comp = limit_seq(sym*sequence_term, sym) + if lim_comp is not None and lim_comp.is_number and lim_comp > 0: + return S.false + except NotImplementedError: + pass + + ### ----------- ratio test ---------------- ### + next_sequence_term = sequence_term.xreplace({sym: sym + 1}) + from sympy.simplify.combsimp import combsimp + from sympy.simplify.powsimp import powsimp + ratio = combsimp(powsimp(next_sequence_term/sequence_term)) + try: + lim_ratio = limit_seq(ratio, sym) + if lim_ratio is not None and lim_ratio.is_number: + if abs(lim_ratio) > 1: + return S.false + if abs(lim_ratio) < 1: + return S.true + except NotImplementedError: + lim_ratio = None + + ### ---------- Raabe's test -------------- ### + if lim_ratio == 1: # ratio test inconclusive + test_val = sym*(sequence_term/ + sequence_term.subs(sym, sym + 1) - 1) + test_val = test_val.gammasimp() + try: + lim_val = limit_seq(test_val, sym) + if lim_val is not None and lim_val.is_number: + if lim_val > 1: + return S.true + if lim_val < 1: + return S.false + except NotImplementedError: + pass + + ### ----------- root test ---------------- ### + # lim = Limit(abs(sequence_term)**(1/sym), sym, S.Infinity) + try: + lim_evaluated = limit_seq(abs(sequence_term)**(1/sym), sym) + if lim_evaluated is not None and lim_evaluated.is_number: + if lim_evaluated < 1: + return S.true + if lim_evaluated > 1: + return S.false + except NotImplementedError: + pass + + ### ------------- alternating series test ----------- ### + dict_val = sequence_term.match(S.NegativeOne**(sym + p)*q) + if not dict_val[p].has(sym) and is_decreasing(dict_val[q], interval): + return S.true + + ### ------------- integral test -------------- ### + check_interval = None + from sympy.solvers.solveset import solveset + maxima = solveset(sequence_term.diff(sym), sym, interval) + if not maxima: + check_interval = interval + elif isinstance(maxima, FiniteSet) and maxima.sup.is_number: + check_interval = Interval(maxima.sup, interval.sup) + if (check_interval is not None and + (is_decreasing(sequence_term, check_interval) or + is_decreasing(-sequence_term, check_interval))): + integral_val = Integral( + sequence_term, (sym, lower_limit, upper_limit)) + try: + integral_val_evaluated = integral_val.doit() + if integral_val_evaluated.is_number: + return S(integral_val_evaluated.is_finite) + except NotImplementedError: + pass + + ### ----- Dirichlet and bounded times convergent tests ----- ### + # TODO + # + # Dirichlet_test + # https://en.wikipedia.org/wiki/Dirichlet%27s_test + # + # Bounded times convergent test + # It is based on comparison theorems for series. + # In particular, if the general term of a series can + # be written as a product of two terms a_n and b_n + # and if a_n is bounded and if Sum(b_n) is absolutely + # convergent, then the original series Sum(a_n * b_n) + # is absolutely convergent and so convergent. + # + # The following code can grows like 2**n where n is the + # number of args in order.expr + # Possibly combined with the potentially slow checks + # inside the loop, could make this test extremely slow + # for larger summation expressions. + + if order.expr.is_Mul: + args = order.expr.args + argset = set(args) + + ### -------------- Dirichlet tests -------------- ### + m = Dummy('m', integer=True) + def _dirichlet_test(g_n): + try: + ing_val = limit_seq(Sum(g_n, (sym, interval.inf, m)).doit(), m) + if ing_val is not None and ing_val.is_finite: + return S.true + except NotImplementedError: + pass + + ### -------- bounded times convergent test ---------### + def _bounded_convergent_test(g1_n, g2_n): + try: + lim_val = limit_seq(g1_n, sym) + if lim_val is not None and (lim_val.is_finite or ( + isinstance(lim_val, AccumulationBounds) + and (lim_val.max - lim_val.min).is_finite)): + if Sum(g2_n, (sym, lower_limit, upper_limit)).is_absolutely_convergent(): + return S.true + except NotImplementedError: + pass + + for n in range(1, len(argset)): + for a_tuple in itertools.combinations(args, n): + b_set = argset - set(a_tuple) + a_n = Mul(*a_tuple) + b_n = Mul(*b_set) + + if is_decreasing(a_n, interval): + dirich = _dirichlet_test(b_n) + if dirich is not None: + return dirich + + bc_test = _bounded_convergent_test(a_n, b_n) + if bc_test is not None: + return bc_test + + _sym = self.limits[0][0] + sequence_term = sequence_term.xreplace({sym: _sym}) + raise NotImplementedError("The algorithm to find the Sum convergence of %s " + "is not yet implemented" % (sequence_term)) + + def is_absolutely_convergent(self): + """ + Checks for the absolute convergence of an infinite series. + + Same as checking convergence of absolute value of sequence_term of + an infinite series. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Absolute_convergence + + Examples + ======== + + >>> from sympy import Sum, Symbol, oo + >>> n = Symbol('n', integer=True) + >>> Sum((-1)**n, (n, 1, oo)).is_absolutely_convergent() + False + >>> Sum((-1)**n/n**2, (n, 1, oo)).is_absolutely_convergent() + True + + See Also + ======== + + Sum.is_convergent + """ + return Sum(abs(self.function), self.limits).is_convergent() + + def euler_maclaurin(self, m=0, n=0, eps=0, eval_integral=True): + """ + Return an Euler-Maclaurin approximation of self, where m is the + number of leading terms to sum directly and n is the number of + terms in the tail. + + With m = n = 0, this is simply the corresponding integral + plus a first-order endpoint correction. + + Returns (s, e) where s is the Euler-Maclaurin approximation + and e is the estimated error (taken to be the magnitude of + the first omitted term in the tail): + + >>> from sympy.abc import k, a, b + >>> from sympy import Sum + >>> Sum(1/k, (k, 2, 5)).doit().evalf() + 1.28333333333333 + >>> s, e = Sum(1/k, (k, 2, 5)).euler_maclaurin() + >>> s + -log(2) + 7/20 + log(5) + >>> from sympy import sstr + >>> print(sstr((s.evalf(), e.evalf()), full_prec=True)) + (1.26629073187415, 0.0175000000000000) + + The endpoints may be symbolic: + + >>> s, e = Sum(1/k, (k, a, b)).euler_maclaurin() + >>> s + -log(a) + log(b) + 1/(2*b) + 1/(2*a) + >>> e + Abs(1/(12*b**2) - 1/(12*a**2)) + + If the function is a polynomial of degree at most 2n+1, the + Euler-Maclaurin formula becomes exact (and e = 0 is returned): + + >>> Sum(k, (k, 2, b)).euler_maclaurin() + (b**2/2 + b/2 - 1, 0) + >>> Sum(k, (k, 2, b)).doit() + b**2/2 + b/2 - 1 + + With a nonzero eps specified, the summation is ended + as soon as the remainder term is less than the epsilon. + """ + m = int(m) + n = int(n) + f = self.function + if len(self.limits) != 1: + raise ValueError("More than 1 limit") + i, a, b = self.limits[0] + if (a > b) == True: + if a - b == 1: + return S.Zero, S.Zero + a, b = b + 1, a - 1 + f = -f + s = S.Zero + if m: + if b.is_Integer and a.is_Integer: + m = min(m, b - a + 1) + if not eps or f.is_polynomial(i): + s = Add(*[f.subs(i, a + k) for k in range(m)]) + else: + term = f.subs(i, a) + if term: + test = abs(term.evalf(3)) < eps + if test == True: + return s, abs(term) + elif not (test == False): + # a symbolic Relational class, can't go further + return term, S.Zero + s = term + for k in range(1, m): + term = f.subs(i, a + k) + if abs(term.evalf(3)) < eps and term != 0: + return s, abs(term) + s += term + if b - a + 1 == m: + return s, S.Zero + a += m + x = Dummy('x') + I = Integral(f.subs(i, x), (x, a, b)) + if eval_integral: + I = I.doit() + s += I + + def fpoint(expr): + if b is S.Infinity: + return expr.subs(i, a), 0 + return expr.subs(i, a), expr.subs(i, b) + fa, fb = fpoint(f) + iterm = (fa + fb)/2 + g = f.diff(i) + for k in range(1, n + 2): + ga, gb = fpoint(g) + term = bernoulli(2*k)/factorial(2*k)*(gb - ga) + if k > n: + break + if eps and term: + term_evalf = term.evalf(3) + if term_evalf is S.NaN: + return S.NaN, S.NaN + if abs(term_evalf) < eps: + break + s += term + g = g.diff(i, 2, simplify=False) + return s + iterm, abs(term) + + + def reverse_order(self, *indices): + """ + Reverse the order of a limit in a Sum. + + Explanation + =========== + + ``reverse_order(self, *indices)`` reverses some limits in the expression + ``self`` which can be either a ``Sum`` or a ``Product``. The selectors in + the argument ``indices`` specify some indices whose limits get reversed. + These selectors are either variable names or numerical indices counted + starting from the inner-most limit tuple. + + Examples + ======== + + >>> from sympy import Sum + >>> from sympy.abc import x, y, a, b, c, d + + >>> Sum(x, (x, 0, 3)).reverse_order(x) + Sum(-x, (x, 4, -1)) + >>> Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(x, y) + Sum(x*y, (x, 6, 0), (y, 7, -1)) + >>> Sum(x, (x, a, b)).reverse_order(x) + Sum(-x, (x, b + 1, a - 1)) + >>> Sum(x, (x, a, b)).reverse_order(0) + Sum(-x, (x, b + 1, a - 1)) + + While one should prefer variable names when specifying which limits + to reverse, the index counting notation comes in handy in case there + are several symbols with the same name. + + >>> S = Sum(x**2, (x, a, b), (x, c, d)) + >>> S + Sum(x**2, (x, a, b), (x, c, d)) + >>> S0 = S.reverse_order(0) + >>> S0 + Sum(-x**2, (x, b + 1, a - 1), (x, c, d)) + >>> S1 = S0.reverse_order(1) + >>> S1 + Sum(x**2, (x, b + 1, a - 1), (x, d + 1, c - 1)) + + Of course we can mix both notations: + + >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + + See Also + ======== + + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.index, reorder_limit, + sympy.concrete.expr_with_intlimits.ExprWithIntLimits.reorder + + References + ========== + + .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM, + Volume 28 Issue 2, April 1981, Pages 305-350 + https://dl.acm.org/doi/10.1145/322248.322255 + """ + l_indices = list(indices) + + for i, indx in enumerate(l_indices): + if not isinstance(indx, int): + l_indices[i] = self.index(indx) + + e = 1 + limits = [] + for i, limit in enumerate(self.limits): + l = limit + if i in l_indices: + e = -e + l = (limit[0], limit[2] + 1, limit[1] - 1) + limits.append(l) + + return Sum(e * self.function, *limits) + + def _eval_rewrite_as_Product(self, *args, **kwargs): + from sympy.concrete.products import Product + if self.function.is_extended_real: + return log(Product(exp(self.function), *self.limits)) + + +def summation(f, *symbols, **kwargs): + r""" + Compute the summation of f with respect to symbols. + + Explanation + =========== + + The notation for symbols is similar to the notation used in Integral. + summation(f, (i, a, b)) computes the sum of f with respect to i from a to b, + i.e., + + :: + + b + ____ + \ ` + summation(f, (i, a, b)) = ) f + /___, + i = a + + If it cannot compute the sum, it returns an unevaluated Sum object. + Repeated sums can be computed by introducing additional symbols tuples:: + + Examples + ======== + + >>> from sympy import summation, oo, symbols, log + >>> i, n, m = symbols('i n m', integer=True) + + >>> summation(2*i - 1, (i, 1, n)) + n**2 + >>> summation(1/2**i, (i, 0, oo)) + 2 + >>> summation(1/log(n)**n, (n, 2, oo)) + Sum(log(n)**(-n), (n, 2, oo)) + >>> summation(i, (i, 0, n), (n, 0, m)) + m**3/6 + m**2/2 + m/3 + + >>> from sympy.abc import x + >>> from sympy import factorial + >>> summation(x**n/factorial(n), (n, 0, oo)) + exp(x) + + See Also + ======== + + Sum + Product, sympy.concrete.products.product + + """ + return Sum(f, *symbols, **kwargs).doit(deep=False) + + +def telescopic_direct(L, R, n, limits): + """ + Returns the direct summation of the terms of a telescopic sum + + Explanation + =========== + + L is the term with lower index + R is the term with higher index + n difference between the indexes of L and R + + Examples + ======== + + >>> from sympy.concrete.summations import telescopic_direct + >>> from sympy.abc import k, a, b + >>> telescopic_direct(1/k, -1/(k+2), 2, (k, a, b)) + -1/(b + 2) - 1/(b + 1) + 1/(a + 1) + 1/a + + """ + (i, a, b) = limits + return Add(*[L.subs(i, a + m) + R.subs(i, b - m) for m in range(n)]) + + +def telescopic(L, R, limits): + ''' + Tries to perform the summation using the telescopic property. + + Return None if not possible. + ''' + (i, a, b) = limits + if L.is_Add or R.is_Add: + return None + + # We want to solve(L.subs(i, i + m) + R, m) + # First we try a simple match since this does things that + # solve doesn't do, e.g. solve(cos(k+m)-cos(k), m) gives + # a more complicated solution than m == 0. + + k = Wild("k") + sol = (-R).match(L.subs(i, i + k)) + s = None + if sol and k in sol: + s = sol[k] + if not (s.is_Integer and L.subs(i, i + s) + R == 0): + # invalid match or match didn't work + s = None + + # But there are things that match doesn't do that solve + # can do, e.g. determine that 1/(x + m) = 1/(1 - x) when m = 1 + + if s is None: + m = Dummy('m') + try: + from sympy.solvers.solvers import solve + sol = solve(L.subs(i, i + m) + R, m) or [] + except NotImplementedError: + return None + sol = [si for si in sol if si.is_Integer and + (L.subs(i, i + si) + R).expand().is_zero] + if len(sol) != 1: + return None + s = sol[0] + + if s < 0: + return telescopic_direct(R, L, abs(s), (i, a, b)) + elif s > 0: + return telescopic_direct(L, R, s, (i, a, b)) + + +def eval_sum(f, limits): + (i, a, b) = limits + if f.is_zero: + return S.Zero + if i not in f.free_symbols: + return f*(b - a + 1) + if a == b: + return f.subs(i, a) + if isinstance(f, Piecewise): + if not any(i in arg.args[1].free_symbols for arg in f.args): + # Piecewise conditions do not depend on the dummy summation variable, + # therefore we can fold: Sum(Piecewise((e, c), ...), limits) + # --> Piecewise((Sum(e, limits), c), ...) + newargs = [] + for arg in f.args: + newexpr = eval_sum(arg.expr, limits) + if newexpr is None: + return None + newargs.append((newexpr, arg.cond)) + return f.func(*newargs) + + if f.has(KroneckerDelta): + from .delta import deltasummation, _has_simple_delta + f = f.replace( + lambda x: isinstance(x, Sum), + lambda x: x.factor() + ) + if _has_simple_delta(f, limits[0]): + return deltasummation(f, limits) + + dif = b - a + definite = dif.is_Integer + # Doing it directly may be faster if there are very few terms. + if definite and (dif < 100): + return eval_sum_direct(f, (i, a, b)) + if isinstance(f, Piecewise): + return None + # Try to do it symbolically. Even when the number of terms is + # known, this can save time when b-a is big. + value = eval_sum_symbolic(f.expand(), (i, a, b)) + if value is not None: + return value + # Do it directly + if definite: + return eval_sum_direct(f, (i, a, b)) + + +def eval_sum_direct(expr, limits): + """ + Evaluate expression directly, but perform some simple checks first + to possibly result in a smaller expression and faster execution. + """ + (i, a, b) = limits + + dif = b - a + # Linearity + if expr.is_Mul: + # Try factor out everything not including i + without_i, with_i = expr.as_independent(i) + if without_i != 1: + s = eval_sum_direct(with_i, (i, a, b)) + if s: + r = without_i*s + if r is not S.NaN: + return r + else: + # Try term by term + L, R = expr.as_two_terms() + + if not L.has(i): + sR = eval_sum_direct(R, (i, a, b)) + if sR: + return L*sR + + if not R.has(i): + sL = eval_sum_direct(L, (i, a, b)) + if sL: + return sL*R + + # do this whether its an Add or Mul + # e.g. apart(1/(25*i**2 + 45*i + 14)) and + # apart(1/((5*i + 2)*(5*i + 7))) -> + # -1/(5*(5*i + 7)) + 1/(5*(5*i + 2)) + try: + expr = apart(expr, i) # see if it becomes an Add + except PolynomialError: + pass + + if expr.is_Add: + # Try factor out everything not including i + without_i, with_i = expr.as_independent(i) + if without_i != 0: + s = eval_sum_direct(with_i, (i, a, b)) + if s: + r = without_i*(dif + 1) + s + if r is not S.NaN: + return r + else: + # Try term by term + L, R = expr.as_two_terms() + lsum = eval_sum_direct(L, (i, a, b)) + rsum = eval_sum_direct(R, (i, a, b)) + + if None not in (lsum, rsum): + r = lsum + rsum + if r is not S.NaN: + return r + + return Add(*[expr.subs(i, a + j) for j in range(dif + 1)]) + + +def eval_sum_symbolic(f, limits): + f_orig = f + (i, a, b) = limits + if not f.has(i): + return f*(b - a + 1) + + # Linearity + if f.is_Mul: + # Try factor out everything not including i + without_i, with_i = f.as_independent(i) + if without_i != 1: + s = eval_sum_symbolic(with_i, (i, a, b)) + if s: + r = without_i*s + if r is not S.NaN: + return r + else: + # Try term by term + L, R = f.as_two_terms() + + if not L.has(i): + sR = eval_sum_symbolic(R, (i, a, b)) + if sR: + return L*sR + + if not R.has(i): + sL = eval_sum_symbolic(L, (i, a, b)) + if sL: + return sL*R + + # do this whether its an Add or Mul + # e.g. apart(1/(25*i**2 + 45*i + 14)) and + # apart(1/((5*i + 2)*(5*i + 7))) -> + # -1/(5*(5*i + 7)) + 1/(5*(5*i + 2)) + try: + f = apart(f, i) + except PolynomialError: + pass + + if f.is_Add: + L, R = f.as_two_terms() + lrsum = telescopic(L, R, (i, a, b)) + + if lrsum: + return lrsum + + # Try factor out everything not including i + without_i, with_i = f.as_independent(i) + if without_i != 0: + s = eval_sum_symbolic(with_i, (i, a, b)) + if s: + r = without_i*(b - a + 1) + s + if r is not S.NaN: + return r + else: + # Try term by term + lsum = eval_sum_symbolic(L, (i, a, b)) + rsum = eval_sum_symbolic(R, (i, a, b)) + + if None not in (lsum, rsum): + r = lsum + rsum + if r is not S.NaN: + return r + + + # Polynomial terms with Faulhaber's formula + n = Wild('n') + result = f.match(i**n) + + if result is not None: + n = result[n] + + if n.is_Integer: + if n >= 0: + if (b is S.Infinity and a is not S.NegativeInfinity) or \ + (a is S.NegativeInfinity and b is not S.Infinity): + return S.Infinity + return ((bernoulli(n + 1, b + 1) - bernoulli(n + 1, a))/(n + 1)).expand() + elif a.is_Integer and a >= 1: + if n == -1: + return harmonic(b) - harmonic(a - 1) + else: + return harmonic(b, abs(n)) - harmonic(a - 1, abs(n)) + + if not (a.has(S.Infinity, S.NegativeInfinity) or + b.has(S.Infinity, S.NegativeInfinity)): + # Geometric terms + c1 = Wild('c1', exclude=[i]) + c2 = Wild('c2', exclude=[i]) + c3 = Wild('c3', exclude=[i]) + wexp = Wild('wexp') + + # Here we first attempt powsimp on f for easier matching with the + # exponential pattern, and attempt expansion on the exponent for easier + # matching with the linear pattern. + e = f.powsimp().match(c1 ** wexp) + if e is not None: + e_exp = e.pop(wexp).expand().match(c2*i + c3) + if e_exp is not None: + e.update(e_exp) + + p = (c1**c3).subs(e) + q = (c1**c2).subs(e) + r = p*(q**a - q**(b + 1))/(1 - q) + l = p*(b - a + 1) + return Piecewise((l, Eq(q, S.One)), (r, True)) + + r = gosper_sum(f, (i, a, b)) + + if isinstance(r, (Mul,Add)): + from sympy.simplify.radsimp import denom + from sympy.solvers.solvers import solve + non_limit = r.free_symbols - Tuple(*limits[1:]).free_symbols + den = denom(together(r)) + den_sym = non_limit & den.free_symbols + args = [] + for v in ordered(den_sym): + try: + s = solve(den, v) + m = Eq(v, s[0]) if s else S.false + if m != False: + args.append((Sum(f_orig.subs(*m.args), limits).doit(), m)) + break + except NotImplementedError: + continue + + args.append((r, True)) + return Piecewise(*args) + + if r not in (None, S.NaN): + return r + + h = eval_sum_hyper(f_orig, (i, a, b)) + if h is not None: + return h + + r = eval_sum_residue(f_orig, (i, a, b)) + if r is not None: + return r + + factored = f_orig.factor() + if factored != f_orig: + return eval_sum_symbolic(factored, (i, a, b)) + + +def _eval_sum_hyper(f, i, a): + """ Returns (res, cond). Sums from a to oo. """ + if a != 0: + return _eval_sum_hyper(f.subs(i, i + a), i, 0) + + if f.subs(i, 0) == 0: + from sympy.simplify.simplify import simplify + if simplify(f.subs(i, Dummy('i', integer=True, positive=True))) == 0: + return S.Zero, True + return _eval_sum_hyper(f.subs(i, i + 1), i, 0) + + from sympy.simplify.simplify import hypersimp + hs = hypersimp(f, i) + if hs is None: + return None + + if isinstance(hs, Float): + from sympy.simplify.simplify import nsimplify + hs = nsimplify(hs) + + from sympy.simplify.combsimp import combsimp + from sympy.simplify.hyperexpand import hyperexpand + from sympy.simplify.radsimp import fraction + numer, denom = fraction(factor(hs)) + top, topl = numer.as_coeff_mul(i) + bot, botl = denom.as_coeff_mul(i) + ab = [top, bot] + factors = [topl, botl] + params = [[], []] + for k in range(2): + for fac in factors[k]: + mul = 1 + if fac.is_Pow: + mul = fac.exp + fac = fac.base + if not mul.is_Integer: + return None + p = Poly(fac, i) + if p.degree() != 1: + return None + m, n = p.all_coeffs() + ab[k] *= m**mul + params[k] += [n/m]*mul + + # Add "1" to numerator parameters, to account for implicit n! in + # hypergeometric series. + ap = params[0] + [1] + bq = params[1] + x = ab[0]/ab[1] + h = hyper(ap, bq, x) + f = combsimp(f) + return f.subs(i, 0)*hyperexpand(h), h.convergence_statement + + +def eval_sum_hyper(f, i_a_b): + i, a, b = i_a_b + + if f.is_hypergeometric(i) is False: + return + + if (b - a).is_Integer: + # We are never going to do better than doing the sum in the obvious way + return None + + old_sum = Sum(f, (i, a, b)) + + if b != S.Infinity: + if a is S.NegativeInfinity: + res = _eval_sum_hyper(f.subs(i, -i), i, -b) + if res is not None: + return Piecewise(res, (old_sum, True)) + else: + n_illegal = lambda x: sum(x.count(_) for _ in _illegal) + had = n_illegal(f) + # check that no extra illegals are introduced + res1 = _eval_sum_hyper(f, i, a) + if res1 is None or n_illegal(res1) > had: + return + res2 = _eval_sum_hyper(f, i, b + 1) + if res2 is None or n_illegal(res2) > had: + return + (res1, cond1), (res2, cond2) = res1, res2 + cond = And(cond1, cond2) + if cond == False: + return None + return Piecewise((res1 - res2, cond), (old_sum, True)) + + if a is S.NegativeInfinity: + res1 = _eval_sum_hyper(f.subs(i, -i), i, 1) + res2 = _eval_sum_hyper(f, i, 0) + if res1 is None or res2 is None: + return None + res1, cond1 = res1 + res2, cond2 = res2 + cond = And(cond1, cond2) + if cond == False or cond.as_set() == S.EmptySet: + return None + return Piecewise((res1 + res2, cond), (old_sum, True)) + + # Now b == oo, a != -oo + res = _eval_sum_hyper(f, i, a) + if res is not None: + r, c = res + if c == False: + if r.is_number: + f = f.subs(i, Dummy('i', integer=True, positive=True) + a) + if f.is_positive or f.is_zero: + return S.Infinity + elif f.is_negative: + return S.NegativeInfinity + return None + return Piecewise(res, (old_sum, True)) + + +def eval_sum_residue(f, i_a_b): + r"""Compute the infinite summation with residues + + Notes + ===== + + If $f(n), g(n)$ are polynomials with $\deg(g(n)) - \deg(f(n)) \ge 2$, + some infinite summations can be computed by the following residue + evaluations. + + .. math:: + \sum_{n=-\infty, g(n) \ne 0}^{\infty} \frac{f(n)}{g(n)} = + -\pi \sum_{\alpha|g(\alpha)=0} + \text{Res}(\cot(\pi x) \frac{f(x)}{g(x)}, \alpha) + + .. math:: + \sum_{n=-\infty, g(n) \ne 0}^{\infty} (-1)^n \frac{f(n)}{g(n)} = + -\pi \sum_{\alpha|g(\alpha)=0} + \text{Res}(\csc(\pi x) \frac{f(x)}{g(x)}, \alpha) + + Examples + ======== + + >>> from sympy import Sum, oo, Symbol + >>> x = Symbol('x') + + Doubly infinite series of rational functions. + + >>> Sum(1 / (x**2 + 1), (x, -oo, oo)).doit() + pi/tanh(pi) + + Doubly infinite alternating series of rational functions. + + >>> Sum((-1)**x / (x**2 + 1), (x, -oo, oo)).doit() + pi/sinh(pi) + + Infinite series of even rational functions. + + >>> Sum(1 / (x**2 + 1), (x, 0, oo)).doit() + 1/2 + pi/(2*tanh(pi)) + + Infinite series of alternating even rational functions. + + >>> Sum((-1)**x / (x**2 + 1), (x, 0, oo)).doit() + pi/(2*sinh(pi)) + 1/2 + + This also have heuristics to transform arbitrarily shifted summand or + arbitrarily shifted summation range to the canonical problem the + formula can handle. + + >>> Sum(1 / (x**2 + 2*x + 2), (x, -1, oo)).doit() + 1/2 + pi/(2*tanh(pi)) + >>> Sum(1 / (x**2 + 4*x + 5), (x, -2, oo)).doit() + 1/2 + pi/(2*tanh(pi)) + >>> Sum(1 / (x**2 + 1), (x, 1, oo)).doit() + -1/2 + pi/(2*tanh(pi)) + >>> Sum(1 / (x**2 + 1), (x, 2, oo)).doit() + -1 + pi/(2*tanh(pi)) + + References + ========== + + .. [#] http://www.supermath.info/InfiniteSeriesandtheResidueTheorem.pdf + + .. [#] Asmar N.H., Grafakos L. (2018) Residue Theory. + In: Complex Analysis with Applications. + Undergraduate Texts in Mathematics. Springer, Cham. + https://doi.org/10.1007/978-3-319-94063-2_5 + """ + i, a, b = i_a_b + + def is_even_function(numer, denom): + """Test if the rational function is an even function""" + numer_even = all(i % 2 == 0 for (i,) in numer.monoms()) + denom_even = all(i % 2 == 0 for (i,) in denom.monoms()) + numer_odd = all(i % 2 == 1 for (i,) in numer.monoms()) + denom_odd = all(i % 2 == 1 for (i,) in denom.monoms()) + return (numer_even and denom_even) or (numer_odd and denom_odd) + + def match_rational(f, i): + numer, denom = f.as_numer_denom() + try: + (numer, denom), opt = parallel_poly_from_expr((numer, denom), i) + except (PolificationFailed, PolynomialError): + return None + return numer, denom + + def get_poles(denom): + roots = denom.sqf_part().all_roots() + roots = sift(roots, lambda x: x.is_integer) + if None in roots: + return None + int_roots, nonint_roots = roots[True], roots[False] + return int_roots, nonint_roots + + def get_shift(denom): + n = denom.degree(i) + a = denom.coeff_monomial(i**n) + b = denom.coeff_monomial(i**(n-1)) + shift = - b / a / n + return shift + + #Need a dummy symbol with no assumptions set for get_residue_factor + z = Dummy('z') + + def get_residue_factor(numer, denom, alternating): + residue_factor = (numer.as_expr() / denom.as_expr()).subs(i, z) + if not alternating: + residue_factor *= cot(S.Pi * z) + else: + residue_factor *= csc(S.Pi * z) + return residue_factor + + # We don't know how to deal with symbolic constants in summand + if f.free_symbols - {i}: + return None + + if not (a.is_Integer or a in (S.Infinity, S.NegativeInfinity)): + return None + if not (b.is_Integer or b in (S.Infinity, S.NegativeInfinity)): + return None + + # Quick exit heuristic for the sums which doesn't have infinite range + if a != S.NegativeInfinity and b != S.Infinity: + return None + + match = match_rational(f, i) + if match: + alternating = False + numer, denom = match + else: + match = match_rational(f / S.NegativeOne**i, i) + if match: + alternating = True + numer, denom = match + else: + return None + + if denom.degree(i) - numer.degree(i) < 2: + return None + + if (a, b) == (S.NegativeInfinity, S.Infinity): + poles = get_poles(denom) + if poles is None: + return None + int_roots, nonint_roots = poles + + if int_roots: + return None + + residue_factor = get_residue_factor(numer, denom, alternating) + residues = [residue(residue_factor, z, root) for root in nonint_roots] + return -S.Pi * sum(residues) + + if not (a.is_finite and b is S.Infinity): + return None + + if not is_even_function(numer, denom): + # Try shifting summation and check if the summand can be made + # and even function from the origin. + # Sum(f(n), (n, a, b)) => Sum(f(n + s), (n, a - s, b - s)) + shift = get_shift(denom) + + if not shift.is_Integer: + return None + if shift == 0: + return None + + numer = numer.shift(shift) + denom = denom.shift(shift) + + if not is_even_function(numer, denom): + return None + + if alternating: + f = S.NegativeOne**i * (S.NegativeOne**shift * numer.as_expr() / denom.as_expr()) + else: + f = numer.as_expr() / denom.as_expr() + return eval_sum_residue(f, (i, a-shift, b-shift)) + + poles = get_poles(denom) + if poles is None: + return None + int_roots, nonint_roots = poles + + if int_roots: + int_roots = [int(root) for root in int_roots] + int_roots_max = max(int_roots) + int_roots_min = min(int_roots) + # Integer valued poles must be next to each other + # and also symmetric from origin (Because the function is even) + if not len(int_roots) == int_roots_max - int_roots_min + 1: + return None + + # Check whether the summation indices contain poles + if a <= max(int_roots): + return None + + residue_factor = get_residue_factor(numer, denom, alternating) + residues = [residue(residue_factor, z, root) for root in int_roots + nonint_roots] + full_sum = -S.Pi * sum(residues) + + if not int_roots: + # Compute Sum(f, (i, 0, oo)) by adding a extraneous evaluation + # at the origin. + half_sum = (full_sum + f.xreplace({i: 0})) / 2 + + # Add and subtract extraneous evaluations + extraneous_neg = [f.xreplace({i: i0}) for i0 in range(int(a), 0)] + extraneous_pos = [f.xreplace({i: i0}) for i0 in range(0, int(a))] + result = half_sum + sum(extraneous_neg) - sum(extraneous_pos) + + return result + + # Compute Sum(f, (i, min(poles) + 1, oo)) + half_sum = full_sum / 2 + + # Subtract extraneous evaluations + extraneous = [f.xreplace({i: i0}) for i0 in range(max(int_roots) + 1, int(a))] + result = half_sum - sum(extraneous) + + return result + + +def _eval_matrix_sum(expression): + f = expression.function + for limit in expression.limits: + i, a, b = limit + dif = b - a + if dif.is_Integer: + if (dif < 0) == True: + a, b = b + 1, a - 1 + f = -f + + newf = eval_sum_direct(f, (i, a, b)) + if newf is not None: + return newf.doit() + + +def _dummy_with_inherited_properties_concrete(limits): + """ + Return a Dummy symbol that inherits as many assumptions as possible + from the provided symbol and limits. + + If the symbol already has all True assumption shared by the limits + then return None. + """ + x, a, b = limits + l = [a, b] + + assumptions_to_consider = ['extended_nonnegative', 'nonnegative', + 'extended_nonpositive', 'nonpositive', + 'extended_positive', 'positive', + 'extended_negative', 'negative', + 'integer', 'rational', 'finite', + 'zero', 'real', 'extended_real'] + + assumptions_to_keep = {} + assumptions_to_add = {} + for assum in assumptions_to_consider: + assum_true = x._assumptions.get(assum, None) + if assum_true: + assumptions_to_keep[assum] = True + elif all(getattr(i, 'is_' + assum) for i in l): + assumptions_to_add[assum] = True + if assumptions_to_add: + assumptions_to_keep.update(assumptions_to_add) + return Dummy('d', **assumptions_to_keep) diff --git a/lib/python3.11/site-packages/sympy/concrete/tests/__init__.py b/lib/python3.11/site-packages/sympy/concrete/tests/__init__.py new file mode 100644 index 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+ +i, j, k, l, m = symbols("i j k l m", integer=True, finite=True) +x, y = symbols("x y", commutative=False) + + +def test_deltaproduct_trivial(): + assert dp(x, (j, 1, 0)) == 1 + assert dp(x, (j, 1, 3)) == x**3 + assert dp(x + y, (j, 1, 3)) == (x + y)**3 + assert dp(x*y, (j, 1, 3)) == (x*y)**3 + assert dp(KD(i, j), (k, 1, 3)) == KD(i, j) + assert dp(x*KD(i, j), (k, 1, 3)) == x**3*KD(i, j) + assert dp(x*y*KD(i, j), (k, 1, 3)) == (x*y)**3*KD(i, j) + + +def test_deltaproduct_basic(): + assert dp(KD(i, j), (j, 1, 3)) == 0 + assert dp(KD(i, j), (j, 1, 1)) == KD(i, 1) + assert dp(KD(i, j), (j, 2, 2)) == KD(i, 2) + assert dp(KD(i, j), (j, 3, 3)) == KD(i, 3) + assert dp(KD(i, j), (j, 1, k)) == KD(i, 1)*KD(k, 1) + KD(k, 0) + assert dp(KD(i, j), (j, k, 3)) == KD(i, 3)*KD(k, 3) + KD(k, 4) + assert dp(KD(i, j), (j, k, l)) == KD(i, l)*KD(k, l) + KD(k, l + 1) + + +def test_deltaproduct_mul_x_kd(): + assert dp(x*KD(i, j), (j, 1, 3)) == 0 + assert dp(x*KD(i, j), (j, 1, 1)) == x*KD(i, 1) + assert dp(x*KD(i, j), (j, 2, 2)) == x*KD(i, 2) + assert dp(x*KD(i, j), (j, 3, 3)) == x*KD(i, 3) + assert dp(x*KD(i, j), (j, 1, k)) == x*KD(i, 1)*KD(k, 1) + KD(k, 0) + assert dp(x*KD(i, j), (j, k, 3)) == x*KD(i, 3)*KD(k, 3) + KD(k, 4) + assert dp(x*KD(i, j), (j, k, l)) == x*KD(i, l)*KD(k, l) + KD(k, l + 1) + + +def test_deltaproduct_mul_add_x_y_kd(): + assert dp((x + y)*KD(i, j), (j, 1, 3)) == 0 + assert dp((x + y)*KD(i, j), (j, 1, 1)) == (x + y)*KD(i, 1) + assert dp((x + y)*KD(i, j), (j, 2, 2)) == (x + y)*KD(i, 2) + assert dp((x + y)*KD(i, j), (j, 3, 3)) == (x + y)*KD(i, 3) + assert dp((x + y)*KD(i, j), (j, 1, k)) == \ + (x + y)*KD(i, 1)*KD(k, 1) + KD(k, 0) + assert dp((x + y)*KD(i, j), (j, k, 3)) == \ + (x + y)*KD(i, 3)*KD(k, 3) + KD(k, 4) + assert dp((x + y)*KD(i, j), (j, k, l)) == \ + (x + y)*KD(i, l)*KD(k, l) + KD(k, l + 1) + + +def test_deltaproduct_add_kd_kd(): + assert dp(KD(i, k) + KD(j, k), (k, 1, 3)) == 0 + assert dp(KD(i, k) + KD(j, k), (k, 1, 1)) == KD(i, 1) + KD(j, 1) + assert dp(KD(i, k) + KD(j, k), (k, 2, 2)) == KD(i, 2) + KD(j, 2) + assert dp(KD(i, k) + KD(j, k), (k, 3, 3)) == KD(i, 3) + KD(j, 3) + assert dp(KD(i, k) + KD(j, k), (k, 1, l)) == KD(l, 0) + \ + KD(i, 1)*KD(l, 1) + KD(j, 1)*KD(l, 1) + \ + KD(i, 1)*KD(j, 2)*KD(l, 2) + KD(j, 1)*KD(i, 2)*KD(l, 2) + assert dp(KD(i, k) + KD(j, k), (k, l, 3)) == KD(l, 4) + \ + KD(i, 3)*KD(l, 3) + KD(j, 3)*KD(l, 3) + \ + KD(i, 2)*KD(j, 3)*KD(l, 2) + KD(i, 3)*KD(j, 2)*KD(l, 2) + assert dp(KD(i, k) + KD(j, k), (k, l, m)) == KD(l, m + 1) + \ + KD(i, m)*KD(l, m) + KD(j, m)*KD(l, m) + \ + KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + + +def test_deltaproduct_mul_x_add_kd_kd(): + assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0 + assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == x*(KD(i, 1) + KD(j, 1)) + assert dp(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == x*(KD(i, 2) + KD(j, 2)) + assert dp(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == x*(KD(i, 3) + KD(j, 3)) + assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \ + x*KD(i, 1)*KD(l, 1) + x*KD(j, 1)*KD(l, 1) + \ + x**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + x**2*KD(j, 1)*KD(i, 2)*KD(l, 2) + assert dp(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \ + x*KD(i, 3)*KD(l, 3) + x*KD(j, 3)*KD(l, 3) + \ + x**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + x**2*KD(i, 3)*KD(j, 2)*KD(l, 2) + assert dp(x*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \ + x*KD(i, m)*KD(l, m) + x*KD(j, m)*KD(l, m) + \ + x**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \ + x**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + + +def test_deltaproduct_mul_add_x_y_add_kd_kd(): + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0 + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 1)) == \ + (x + y)*(KD(i, 1) + KD(j, 1)) + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 2, 2)) == \ + (x + y)*(KD(i, 2) + KD(j, 2)) + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 3, 3)) == \ + (x + y)*(KD(i, 3) + KD(j, 3)) + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \ + (x + y)*KD(i, 1)*KD(l, 1) + (x + y)*KD(j, 1)*KD(l, 1) + \ + (x + y)**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + \ + (x + y)**2*KD(j, 1)*KD(i, 2)*KD(l, 2) + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \ + (x + y)*KD(i, 3)*KD(l, 3) + (x + y)*KD(j, 3)*KD(l, 3) + \ + (x + y)**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + \ + (x + y)**2*KD(i, 3)*KD(j, 2)*KD(l, 2) + assert dp((x + y)*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \ + (x + y)*KD(i, m)*KD(l, m) + (x + y)*KD(j, m)*KD(l, m) + \ + (x + y)**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \ + (x + y)**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + + +def test_deltaproduct_add_mul_x_y_mul_x_kd(): + assert dp(x*y + x*KD(i, j), (j, 1, 3)) == (x*y)**3 + \ + x*(x*y)**2*KD(i, 1) + (x*y)*x*(x*y)*KD(i, 2) + (x*y)**2*x*KD(i, 3) + assert dp(x*y + x*KD(i, j), (j, 1, 1)) == x*y + x*KD(i, 1) + assert dp(x*y + x*KD(i, j), (j, 2, 2)) == x*y + x*KD(i, 2) + assert dp(x*y + x*KD(i, j), (j, 3, 3)) == x*y + x*KD(i, 3) + assert dp(x*y + x*KD(i, j), (j, 1, k)) == \ + (x*y)**k + Piecewise( + ((x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)), + (0, True) + ) + assert dp(x*y + x*KD(i, j), (j, k, 3)) == \ + (x*y)**(-k + 4) + Piecewise( + ((x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)), + (0, True) + ) + assert dp(x*y + x*KD(i, j), (j, k, l)) == \ + (x*y)**(-k + l + 1) + Piecewise( + ((x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)), + (0, True) + ) + + +def test_deltaproduct_mul_x_add_y_kd(): + assert dp(x*(y + KD(i, j)), (j, 1, 3)) == (x*y)**3 + \ + x*(x*y)**2*KD(i, 1) + (x*y)*x*(x*y)*KD(i, 2) + (x*y)**2*x*KD(i, 3) + assert dp(x*(y + KD(i, j)), (j, 1, 1)) == x*(y + KD(i, 1)) + assert dp(x*(y + KD(i, j)), (j, 2, 2)) == x*(y + KD(i, 2)) + assert dp(x*(y + KD(i, j)), (j, 3, 3)) == x*(y + KD(i, 3)) + assert dp(x*(y + KD(i, j)), (j, 1, k)) == \ + (x*y)**k + Piecewise( + ((x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)), + (0, True) + ).expand() + assert dp(x*(y + KD(i, j)), (j, k, 3)) == \ + ((x*y)**(-k + 4) + Piecewise( + ((x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)), + (0, True) + )).expand() + assert dp(x*(y + KD(i, j)), (j, k, l)) == \ + ((x*y)**(-k + l + 1) + Piecewise( + ((x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)), + (0, True) + )).expand() + + +def test_deltaproduct_mul_x_add_y_twokd(): + assert dp(x*(y + 2*KD(i, j)), (j, 1, 3)) == (x*y)**3 + \ + 2*x*(x*y)**2*KD(i, 1) + 2*x*y*x*x*y*KD(i, 2) + 2*(x*y)**2*x*KD(i, 3) + assert dp(x*(y + 2*KD(i, j)), (j, 1, 1)) == x*(y + 2*KD(i, 1)) + assert dp(x*(y + 2*KD(i, j)), (j, 2, 2)) == x*(y + 2*KD(i, 2)) + assert dp(x*(y + 2*KD(i, j)), (j, 3, 3)) == x*(y + 2*KD(i, 3)) + assert dp(x*(y + 2*KD(i, j)), (j, 1, k)) == \ + (x*y)**k + Piecewise( + (2*(x*y)**(i - 1)*x*(x*y)**(k - i), And(1 <= i, i <= k)), + (0, True) + ).expand() + assert dp(x*(y + 2*KD(i, j)), (j, k, 3)) == \ + ((x*y)**(-k + 4) + Piecewise( + (2*(x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)), + (0, True) + )).expand() + assert dp(x*(y + 2*KD(i, j)), (j, k, l)) == \ + ((x*y)**(-k + l + 1) + Piecewise( + (2*(x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)), + (0, True) + )).expand() + + +def test_deltaproduct_mul_add_x_y_add_y_kd(): + assert dp((x + y)*(y + KD(i, j)), (j, 1, 3)) == ((x + y)*y)**3 + \ + (x + y)*((x + y)*y)**2*KD(i, 1) + \ + (x + y)*y*(x + y)**2*y*KD(i, 2) + \ + ((x + y)*y)**2*(x + y)*KD(i, 3) + assert dp((x + y)*(y + KD(i, j)), (j, 1, 1)) == (x + y)*(y + KD(i, 1)) + assert dp((x + y)*(y + KD(i, j)), (j, 2, 2)) == (x + y)*(y + KD(i, 2)) + assert dp((x + y)*(y + KD(i, j)), (j, 3, 3)) == (x + y)*(y + KD(i, 3)) + assert dp((x + y)*(y + KD(i, j)), (j, 1, k)) == \ + ((x + y)*y)**k + Piecewise( + (((x + y)*y)**(-1)*((x + y)*y)**i*(x + y)*((x + y)*y + )**k*((x + y)*y)**(-i), (i >= 1) & (i <= k)), (0, True)) + assert dp((x + y)*(y + KD(i, j)), (j, k, 3)) == ( + (x + y)*y)**4*((x + y)*y)**(-k) + Piecewise((((x + y)*y)**i*( + (x + y)*y)**(-k)*(x + y)*((x + y)*y)**3*((x + y)*y)**(-i), + (i >= k) & (i <= 3)), (0, True)) + assert dp((x + y)*(y + KD(i, j)), (j, k, l)) == \ + (x + y)*y*((x + y)*y)**l*((x + y)*y)**(-k) + Piecewise( + (((x + y)*y)**i*((x + y)*y)**(-k)*(x + y)*((x + y)*y + )**l*((x + y)*y)**(-i), (i >= k) & (i <= l)), (0, True)) + + +def test_deltaproduct_mul_add_x_kd_add_y_kd(): + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == \ + KD(i, 1)*(KD(i, k) + x)*((KD(i, k) + x)*y)**2 + \ + KD(i, 2)*(KD(i, k) + x)*y*(KD(i, k) + x)**2*y + \ + KD(i, 3)*((KD(i, k) + x)*y)**2*(KD(i, k) + x) + \ + ((KD(i, k) + x)*y)**3 + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == \ + (x + KD(i, k))*(y + KD(i, 1)) + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == \ + (x + KD(i, k))*(y + KD(i, 2)) + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == \ + (x + KD(i, k))*(y + KD(i, 3)) + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == \ + ((KD(i, k) + x)*y)**k + Piecewise( + (((KD(i, k) + x)*y)**(-1)*((KD(i, k) + x)*y)**i*(KD(i, k) + x + )*((KD(i, k) + x)*y)**k*((KD(i, k) + x)*y)**(-i), (i >= 1 + ) & (i <= k)), (0, True)) + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == ( + (KD(i, k) + x)*y)**4*((KD(i, k) + x)*y)**(-k) + Piecewise( + (((KD(i, k) + x)*y)**i*((KD(i, k) + x)*y)**(-k)*(KD(i, k) + + x)*((KD(i, k) + x)*y)**3*((KD(i, k) + x)*y)**(-i), + (i >= k) & (i <= 3)), (0, True)) + assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == ( + KD(i, k) + x)*y*((KD(i, k) + x)*y)**l*((KD(i, k) + x)*y + )**(-k) + Piecewise((((KD(i, k) + x)*y)**i*((KD(i, k) + x + )*y)**(-k)*(KD(i, k) + x)*((KD(i, k) + x)*y)**l*((KD(i, k) + x + )*y)**(-i), (i >= k) & (i <= l)), (0, True)) + + +def test_deltasummation_trivial(): + assert ds(x, (j, 1, 0)) == 0 + assert ds(x, (j, 1, 3)) == 3*x + assert ds(x + y, (j, 1, 3)) == 3*(x + y) + assert ds(x*y, (j, 1, 3)) == 3*x*y + assert ds(KD(i, j), (k, 1, 3)) == 3*KD(i, j) + assert ds(x*KD(i, j), (k, 1, 3)) == 3*x*KD(i, j) + assert ds(x*y*KD(i, j), (k, 1, 3)) == 3*x*y*KD(i, j) + + +def test_deltasummation_basic_numerical(): + n = symbols('n', integer=True, nonzero=True) + assert ds(KD(n, 0), (n, 1, 3)) == 0 + + # return unevaluated, until it gets implemented + assert ds(KD(i**2, j**2), (j, -oo, oo)) == \ + Sum(KD(i**2, j**2), (j, -oo, oo)) + + assert Piecewise((KD(i, k), And(1 <= i, i <= 3)), (0, True)) == \ + ds(KD(i, j)*KD(j, k), (j, 1, 3)) == \ + ds(KD(j, k)*KD(i, j), (j, 1, 3)) + + assert ds(KD(i, k), (k, -oo, oo)) == 1 + assert ds(KD(i, k), (k, 0, oo)) == Piecewise((1, S.Zero <= i), (0, True)) + assert ds(KD(i, k), (k, 1, 3)) == \ + Piecewise((1, And(1 <= i, i <= 3)), (0, True)) + assert ds(k*KD(i, j)*KD(j, k), (k, -oo, oo)) == j*KD(i, j) + assert ds(j*KD(i, j), (j, -oo, oo)) == i + assert ds(i*KD(i, j), (i, -oo, oo)) == j + assert ds(x, (i, 1, 3)) == 3*x + assert ds((i + j)*KD(i, j), (j, -oo, oo)) == 2*i + + +def test_deltasummation_basic_symbolic(): + assert ds(KD(i, j), (j, 1, 3)) == \ + Piecewise((1, And(1 <= i, i <= 3)), (0, True)) + assert ds(KD(i, j), (j, 1, 1)) == Piecewise((1, Eq(i, 1)), (0, True)) + assert ds(KD(i, j), (j, 2, 2)) == Piecewise((1, Eq(i, 2)), (0, True)) + assert ds(KD(i, j), (j, 3, 3)) == Piecewise((1, Eq(i, 3)), (0, True)) + assert ds(KD(i, j), (j, 1, k)) == \ + Piecewise((1, And(1 <= i, i <= k)), (0, True)) + assert ds(KD(i, j), (j, k, 3)) == \ + Piecewise((1, And(k <= i, i <= 3)), (0, True)) + assert ds(KD(i, j), (j, k, l)) == \ + Piecewise((1, And(k <= i, i <= l)), (0, True)) + + +def test_deltasummation_mul_x_kd(): + assert ds(x*KD(i, j), (j, 1, 3)) == \ + Piecewise((x, And(1 <= i, i <= 3)), (0, True)) + assert ds(x*KD(i, j), (j, 1, 1)) == Piecewise((x, Eq(i, 1)), (0, True)) + assert ds(x*KD(i, j), (j, 2, 2)) == Piecewise((x, Eq(i, 2)), (0, True)) + assert ds(x*KD(i, j), (j, 3, 3)) == Piecewise((x, Eq(i, 3)), (0, True)) + assert ds(x*KD(i, j), (j, 1, k)) == \ + Piecewise((x, And(1 <= i, i <= k)), (0, True)) + assert ds(x*KD(i, j), (j, k, 3)) == \ + Piecewise((x, And(k <= i, i <= 3)), (0, True)) + assert ds(x*KD(i, j), (j, k, l)) == \ + Piecewise((x, And(k <= i, i <= l)), (0, True)) + + +def test_deltasummation_mul_add_x_y_kd(): + assert ds((x + y)*KD(i, j), (j, 1, 3)) == \ + Piecewise((x + y, And(1 <= i, i <= 3)), (0, True)) + assert ds((x + y)*KD(i, j), (j, 1, 1)) == \ + Piecewise((x + y, Eq(i, 1)), (0, True)) + assert ds((x + y)*KD(i, j), (j, 2, 2)) == \ + Piecewise((x + y, Eq(i, 2)), (0, True)) + assert ds((x + y)*KD(i, j), (j, 3, 3)) == \ + Piecewise((x + y, Eq(i, 3)), (0, True)) + assert ds((x + y)*KD(i, j), (j, 1, k)) == \ + Piecewise((x + y, And(1 <= i, i <= k)), (0, True)) + assert ds((x + y)*KD(i, j), (j, k, 3)) == \ + Piecewise((x + y, And(k <= i, i <= 3)), (0, True)) + assert ds((x + y)*KD(i, j), (j, k, l)) == \ + Piecewise((x + y, And(k <= i, i <= l)), (0, True)) + + +def test_deltasummation_add_kd_kd(): + assert ds(KD(i, k) + KD(j, k), (k, 1, 3)) == piecewise_fold( + Piecewise((1, And(1 <= i, i <= 3)), (0, True)) + + Piecewise((1, And(1 <= j, j <= 3)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, 1, 1)) == piecewise_fold( + Piecewise((1, Eq(i, 1)), (0, True)) + + Piecewise((1, Eq(j, 1)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, 2, 2)) == piecewise_fold( + Piecewise((1, Eq(i, 2)), (0, True)) + + Piecewise((1, Eq(j, 2)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, 3, 3)) == piecewise_fold( + Piecewise((1, Eq(i, 3)), (0, True)) + + Piecewise((1, Eq(j, 3)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, 1, l)) == piecewise_fold( + Piecewise((1, And(1 <= i, i <= l)), (0, True)) + + Piecewise((1, And(1 <= j, j <= l)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, l, 3)) == piecewise_fold( + Piecewise((1, And(l <= i, i <= 3)), (0, True)) + + Piecewise((1, And(l <= j, j <= 3)), (0, True))) + assert ds(KD(i, k) + KD(j, k), (k, l, m)) == piecewise_fold( + Piecewise((1, And(l <= i, i <= m)), (0, True)) + + Piecewise((1, And(l <= j, j <= m)), (0, True))) + + +def test_deltasummation_add_mul_x_kd_kd(): + assert ds(x*KD(i, k) + KD(j, k), (k, 1, 3)) == piecewise_fold( + Piecewise((x, And(1 <= i, i <= 3)), (0, True)) + + Piecewise((1, And(1 <= j, j <= 3)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, 1, 1)) == piecewise_fold( + Piecewise((x, Eq(i, 1)), (0, True)) + + Piecewise((1, Eq(j, 1)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, 2, 2)) == piecewise_fold( + Piecewise((x, Eq(i, 2)), (0, True)) + + Piecewise((1, Eq(j, 2)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, 3, 3)) == piecewise_fold( + Piecewise((x, Eq(i, 3)), (0, True)) + + Piecewise((1, Eq(j, 3)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, 1, l)) == piecewise_fold( + Piecewise((x, And(1 <= i, i <= l)), (0, True)) + + Piecewise((1, And(1 <= j, j <= l)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, l, 3)) == piecewise_fold( + Piecewise((x, And(l <= i, i <= 3)), (0, True)) + + Piecewise((1, And(l <= j, j <= 3)), (0, True))) + assert ds(x*KD(i, k) + KD(j, k), (k, l, m)) == piecewise_fold( + Piecewise((x, And(l <= i, i <= m)), (0, True)) + + Piecewise((1, And(l <= j, j <= m)), (0, True))) + + +def test_deltasummation_mul_x_add_kd_kd(): + assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == piecewise_fold( + Piecewise((x, And(1 <= i, i <= 3)), (0, True)) + + Piecewise((x, And(1 <= j, j <= 3)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == piecewise_fold( + Piecewise((x, Eq(i, 1)), (0, True)) + + Piecewise((x, Eq(j, 1)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == piecewise_fold( + Piecewise((x, Eq(i, 2)), (0, True)) + + Piecewise((x, Eq(j, 2)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == piecewise_fold( + Piecewise((x, Eq(i, 3)), (0, True)) + + Piecewise((x, Eq(j, 3)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == piecewise_fold( + Piecewise((x, And(1 <= i, i <= l)), (0, True)) + + Piecewise((x, And(1 <= j, j <= l)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == piecewise_fold( + Piecewise((x, And(l <= i, i <= 3)), (0, True)) + + Piecewise((x, And(l <= j, j <= 3)), (0, True))) + assert ds(x*(KD(i, k) + KD(j, k)), (k, l, m)) == piecewise_fold( + Piecewise((x, And(l <= i, i <= m)), (0, True)) + + Piecewise((x, And(l <= j, j <= m)), (0, True))) + + +def test_deltasummation_mul_add_x_y_add_kd_kd(): + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 3)) == piecewise_fold( + Piecewise((x + y, And(1 <= i, i <= 3)), (0, True)) + + Piecewise((x + y, And(1 <= j, j <= 3)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, 1)) == piecewise_fold( + Piecewise((x + y, Eq(i, 1)), (0, True)) + + Piecewise((x + y, Eq(j, 1)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 2, 2)) == piecewise_fold( + Piecewise((x + y, Eq(i, 2)), (0, True)) + + Piecewise((x + y, Eq(j, 2)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 3, 3)) == piecewise_fold( + Piecewise((x + y, Eq(i, 3)), (0, True)) + + Piecewise((x + y, Eq(j, 3)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, 1, l)) == piecewise_fold( + Piecewise((x + y, And(1 <= i, i <= l)), (0, True)) + + Piecewise((x + y, And(1 <= j, j <= l)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, l, 3)) == piecewise_fold( + Piecewise((x + y, And(l <= i, i <= 3)), (0, True)) + + Piecewise((x + y, And(l <= j, j <= 3)), (0, True))) + assert ds((x + y)*(KD(i, k) + KD(j, k)), (k, l, m)) == piecewise_fold( + Piecewise((x + y, And(l <= i, i <= m)), (0, True)) + + Piecewise((x + y, And(l <= j, j <= m)), (0, True))) + + +def test_deltasummation_add_mul_x_y_mul_x_kd(): + assert ds(x*y + x*KD(i, j), (j, 1, 3)) == \ + Piecewise((3*x*y + x, And(1 <= i, i <= 3)), (3*x*y, True)) + assert ds(x*y + x*KD(i, j), (j, 1, 1)) == \ + Piecewise((x*y + x, Eq(i, 1)), (x*y, True)) + assert ds(x*y + x*KD(i, j), (j, 2, 2)) == \ + Piecewise((x*y + x, Eq(i, 2)), (x*y, True)) + assert ds(x*y + x*KD(i, j), (j, 3, 3)) == \ + Piecewise((x*y + x, Eq(i, 3)), (x*y, True)) + assert ds(x*y + x*KD(i, j), (j, 1, k)) == \ + Piecewise((k*x*y + x, And(1 <= i, i <= k)), (k*x*y, True)) + assert ds(x*y + x*KD(i, j), (j, k, 3)) == \ + Piecewise(((4 - k)*x*y + x, And(k <= i, i <= 3)), ((4 - k)*x*y, True)) + assert ds(x*y + x*KD(i, j), (j, k, l)) == Piecewise( + ((l - k + 1)*x*y + x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True)) + + +def test_deltasummation_mul_x_add_y_kd(): + assert ds(x*(y + KD(i, j)), (j, 1, 3)) == \ + Piecewise((3*x*y + x, And(1 <= i, i <= 3)), (3*x*y, True)) + assert ds(x*(y + KD(i, j)), (j, 1, 1)) == \ + Piecewise((x*y + x, Eq(i, 1)), (x*y, True)) + assert ds(x*(y + KD(i, j)), (j, 2, 2)) == \ + Piecewise((x*y + x, Eq(i, 2)), (x*y, True)) + assert ds(x*(y + KD(i, j)), (j, 3, 3)) == \ + Piecewise((x*y + x, Eq(i, 3)), (x*y, True)) + assert ds(x*(y + KD(i, j)), (j, 1, k)) == \ + Piecewise((k*x*y + x, And(1 <= i, i <= k)), (k*x*y, True)) + assert ds(x*(y + KD(i, j)), (j, k, 3)) == \ + Piecewise(((4 - k)*x*y + x, And(k <= i, i <= 3)), ((4 - k)*x*y, True)) + assert ds(x*(y + KD(i, j)), (j, k, l)) == Piecewise( + ((l - k + 1)*x*y + x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True)) + + +def test_deltasummation_mul_x_add_y_twokd(): + assert ds(x*(y + 2*KD(i, j)), (j, 1, 3)) == \ + Piecewise((3*x*y + 2*x, And(1 <= i, i <= 3)), (3*x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, 1, 1)) == \ + Piecewise((x*y + 2*x, Eq(i, 1)), (x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, 2, 2)) == \ + Piecewise((x*y + 2*x, Eq(i, 2)), (x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, 3, 3)) == \ + Piecewise((x*y + 2*x, Eq(i, 3)), (x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, 1, k)) == \ + Piecewise((k*x*y + 2*x, And(1 <= i, i <= k)), (k*x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, k, 3)) == Piecewise( + ((4 - k)*x*y + 2*x, And(k <= i, i <= 3)), ((4 - k)*x*y, True)) + assert ds(x*(y + 2*KD(i, j)), (j, k, l)) == Piecewise( + ((l - k + 1)*x*y + 2*x, And(k <= i, i <= l)), ((l - k + 1)*x*y, True)) + + +def test_deltasummation_mul_add_x_y_add_y_kd(): + assert ds((x + y)*(y + KD(i, j)), (j, 1, 3)) == Piecewise( + (3*(x + y)*y + x + y, And(1 <= i, i <= 3)), (3*(x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, 1, 1)) == \ + Piecewise(((x + y)*y + x + y, Eq(i, 1)), ((x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, 2, 2)) == \ + Piecewise(((x + y)*y + x + y, Eq(i, 2)), ((x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, 3, 3)) == \ + Piecewise(((x + y)*y + x + y, Eq(i, 3)), ((x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, 1, k)) == Piecewise( + (k*(x + y)*y + x + y, And(1 <= i, i <= k)), (k*(x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, k, 3)) == Piecewise( + ((4 - k)*(x + y)*y + x + y, And(k <= i, i <= 3)), + ((4 - k)*(x + y)*y, True)) + assert ds((x + y)*(y + KD(i, j)), (j, k, l)) == Piecewise( + ((l - k + 1)*(x + y)*y + x + y, And(k <= i, i <= l)), + ((l - k + 1)*(x + y)*y, True)) + + +def test_deltasummation_mul_add_x_kd_add_y_kd(): + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == piecewise_fold( + Piecewise((KD(i, k) + x, And(1 <= i, i <= 3)), (0, True)) + + 3*(KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == piecewise_fold( + Piecewise((KD(i, k) + x, Eq(i, 1)), (0, True)) + + (KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == piecewise_fold( + Piecewise((KD(i, k) + x, Eq(i, 2)), (0, True)) + + (KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == piecewise_fold( + Piecewise((KD(i, k) + x, Eq(i, 3)), (0, True)) + + (KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == piecewise_fold( + Piecewise((KD(i, k) + x, And(1 <= i, i <= k)), (0, True)) + + k*(KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == piecewise_fold( + Piecewise((KD(i, k) + x, And(k <= i, i <= 3)), (0, True)) + + (4 - k)*(KD(i, k) + x)*y) + assert ds((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == piecewise_fold( + Piecewise((KD(i, k) + x, And(k <= i, i <= l)), (0, True)) + + (l - k + 1)*(KD(i, k) + x)*y) + + +def test_extract_delta(): + raises(ValueError, lambda: _extract_delta(KD(i, j) + KD(k, l), i)) diff --git a/lib/python3.11/site-packages/sympy/concrete/tests/test_gosper.py b/lib/python3.11/site-packages/sympy/concrete/tests/test_gosper.py new file mode 100644 index 0000000000000000000000000000000000000000..77b642a9b7cd55f96840a8e20e517206b6a6f8f0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/tests/test_gosper.py @@ -0,0 +1,204 @@ +"""Tests for Gosper's algorithm for hypergeometric summation. """ + +from sympy.core.numbers import (Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.combinatorial.factorials import (binomial, factorial) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.gamma_functions import gamma +from sympy.polys.polytools import Poly +from sympy.simplify.simplify import simplify +from sympy.concrete.gosper import gosper_normal, gosper_sum, gosper_term +from sympy.abc import a, b, j, k, m, n, r, x + + +def test_gosper_normal(): + eq = 4*n + 5, 2*(4*n + 1)*(2*n + 3), n + assert gosper_normal(*eq) == \ + (Poly(Rational(1, 4), n), Poly(n + Rational(3, 2)), Poly(n + Rational(1, 4))) + assert gosper_normal(*eq, polys=False) == \ + (Rational(1, 4), n + Rational(3, 2), n + Rational(1, 4)) + + +def test_gosper_term(): + assert gosper_term((4*k + 1)*factorial( + k)/factorial(2*k + 1), k) == (-k - S.Half)/(k + Rational(1, 4)) + + +def test_gosper_sum(): + assert gosper_sum(1, (k, 0, n)) == 1 + n + assert gosper_sum(k, (k, 0, n)) == n*(1 + n)/2 + assert gosper_sum(k**2, (k, 0, n)) == n*(1 + n)*(1 + 2*n)/6 + assert gosper_sum(k**3, (k, 0, n)) == n**2*(1 + n)**2/4 + + assert gosper_sum(2**k, (k, 0, n)) == 2*2**n - 1 + + assert gosper_sum(factorial(k), (k, 0, n)) is None + assert gosper_sum(binomial(n, k), (k, 0, n)) is None + + assert gosper_sum(factorial(k)/k**2, (k, 0, n)) is None + assert gosper_sum((k - 3)*factorial(k), (k, 0, n)) is None + + assert gosper_sum(k*factorial(k), k) == factorial(k) + assert gosper_sum( + k*factorial(k), (k, 0, n)) == n*factorial(n) + factorial(n) - 1 + + assert gosper_sum((-1)**k*binomial(n, k), (k, 0, n)) == 0 + assert gosper_sum(( + -1)**k*binomial(n, k), (k, 0, m)) == -(-1)**m*(m - n)*binomial(n, m)/n + + assert gosper_sum((4*k + 1)*factorial(k)/factorial(2*k + 1), (k, 0, n)) == \ + (2*factorial(2*n + 1) - factorial(n))/factorial(2*n + 1) + + # issue 6033: + assert gosper_sum( + n*(n + a + b)*a**n*b**n/(factorial(n + a)*factorial(n + b)), \ + (n, 0, m)).simplify() == -exp(m*log(a) + m*log(b))*gamma(a + 1) \ + *gamma(b + 1)/(gamma(a)*gamma(b)*gamma(a + m + 1)*gamma(b + m + 1)) \ + + 1/(gamma(a)*gamma(b)) + + +def test_gosper_sum_indefinite(): + assert gosper_sum(k, k) == k*(k - 1)/2 + assert gosper_sum(k**2, k) == k*(k - 1)*(2*k - 1)/6 + + assert gosper_sum(1/(k*(k + 1)), k) == -1/k + assert gosper_sum(-(27*k**4 + 158*k**3 + 430*k**2 + 678*k + 445)*gamma(2*k + + 4)/(3*(3*k + 7)*gamma(3*k + 6)), k) == \ + (3*k + 5)*(k**2 + 2*k + 5)*gamma(2*k + 4)/gamma(3*k + 6) + + +def test_gosper_sum_parametric(): + assert gosper_sum(binomial(S.Half, m - j + 1)*binomial(S.Half, m + j), (j, 1, n)) == \ + n*(1 + m - n)*(-1 + 2*m + 2*n)*binomial(S.Half, 1 + m - n)* \ + binomial(S.Half, m + n)/(m*(1 + 2*m)) + + +def test_gosper_sum_algebraic(): + assert gosper_sum( + n**2 + sqrt(2), (n, 0, m)) == (m + 1)*(2*m**2 + m + 6*sqrt(2))/6 + + +def test_gosper_sum_iterated(): + f1 = binomial(2*k, k)/4**k + f2 = (1 + 2*n)*binomial(2*n, n)/4**n + f3 = (1 + 2*n)*(3 + 2*n)*binomial(2*n, n)/(3*4**n) + f4 = (1 + 2*n)*(3 + 2*n)*(5 + 2*n)*binomial(2*n, n)/(15*4**n) + f5 = (1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*binomial(2*n, n)/(105*4**n) + + assert gosper_sum(f1, (k, 0, n)) == f2 + assert gosper_sum(f2, (n, 0, n)) == f3 + assert gosper_sum(f3, (n, 0, n)) == f4 + assert gosper_sum(f4, (n, 0, n)) == f5 + +# the AeqB tests test expressions given in +# www.math.upenn.edu/~wilf/AeqB.pdf + + +def test_gosper_sum_AeqB_part1(): + f1a = n**4 + f1b = n**3*2**n + f1c = 1/(n**2 + sqrt(5)*n - 1) + f1d = n**4*4**n/binomial(2*n, n) + f1e = factorial(3*n)/(factorial(n)*factorial(n + 1)*factorial(n + 2)*27**n) + f1f = binomial(2*n, n)**2/((n + 1)*4**(2*n)) + f1g = (4*n - 1)*binomial(2*n, n)**2/((2*n - 1)**2*4**(2*n)) + f1h = n*factorial(n - S.Half)**2/factorial(n + 1)**2 + + g1a = m*(m + 1)*(2*m + 1)*(3*m**2 + 3*m - 1)/30 + g1b = 26 + 2**(m + 1)*(m**3 - 3*m**2 + 9*m - 13) + g1c = (m + 1)*(m*(m**2 - 7*m + 3)*sqrt(5) - ( + 3*m**3 - 7*m**2 + 19*m - 6))/(2*m**3*sqrt(5) + m**4 + 5*m**2 - 1)/6 + g1d = Rational(-2, 231) + 2*4**m*(m + 1)*(63*m**4 + 112*m**3 + 18*m**2 - + 22*m + 3)/(693*binomial(2*m, m)) + g1e = Rational(-9, 2) + (81*m**2 + 261*m + 200)*factorial( + 3*m + 2)/(40*27**m*factorial(m)*factorial(m + 1)*factorial(m + 2)) + g1f = (2*m + 1)**2*binomial(2*m, m)**2/(4**(2*m)*(m + 1)) + g1g = -binomial(2*m, m)**2/4**(2*m) + g1h = 4*pi -(2*m + 1)**2*(3*m + 4)*factorial(m - S.Half)**2/factorial(m + 1)**2 + + g = gosper_sum(f1a, (n, 0, m)) + assert g is not None and simplify(g - g1a) == 0 + g = gosper_sum(f1b, (n, 0, m)) + assert g is not None and simplify(g - g1b) == 0 + g = gosper_sum(f1c, (n, 0, m)) + assert g is not None and simplify(g - g1c) == 0 + g = gosper_sum(f1d, (n, 0, m)) + assert g is not None and simplify(g - g1d) == 0 + g = gosper_sum(f1e, (n, 0, m)) + assert g is not None and simplify(g - g1e) == 0 + g = gosper_sum(f1f, (n, 0, m)) + assert g is not None and simplify(g - g1f) == 0 + g = gosper_sum(f1g, (n, 0, m)) + assert g is not None and simplify(g - g1g) == 0 + g = gosper_sum(f1h, (n, 0, m)) + # need to call rewrite(gamma) here because we have terms involving + # factorial(1/2) + assert g is not None and simplify(g - g1h).rewrite(gamma) == 0 + + +def test_gosper_sum_AeqB_part2(): + f2a = n**2*a**n + f2b = (n - r/2)*binomial(r, n) + f2c = factorial(n - 1)**2/(factorial(n - x)*factorial(n + x)) + + g2a = -a*(a + 1)/(a - 1)**3 + a**( + m + 1)*(a**2*m**2 - 2*a*m**2 + m**2 - 2*a*m + 2*m + a + 1)/(a - 1)**3 + g2b = (m - r)*binomial(r, m)/2 + ff = factorial(1 - x)*factorial(1 + x) + g2c = 1/ff*( + 1 - 1/x**2) + factorial(m)**2/(x**2*factorial(m - x)*factorial(m + x)) + + g = gosper_sum(f2a, (n, 0, m)) + assert g is not None and simplify(g - g2a) == 0 + g = gosper_sum(f2b, (n, 0, m)) + assert g is not None and simplify(g - g2b) == 0 + g = gosper_sum(f2c, (n, 1, m)) + assert g is not None and simplify(g - g2c) == 0 + + +def test_gosper_nan(): + a = Symbol('a', positive=True) + b = Symbol('b', positive=True) + n = Symbol('n', integer=True) + m = Symbol('m', integer=True) + f2d = n*(n + a + b)*a**n*b**n/(factorial(n + a)*factorial(n + b)) + g2d = 1/(factorial(a - 1)*factorial( + b - 1)) - a**(m + 1)*b**(m + 1)/(factorial(a + m)*factorial(b + m)) + g = gosper_sum(f2d, (n, 0, m)) + assert simplify(g - g2d) == 0 + + +def test_gosper_sum_AeqB_part3(): + f3a = 1/n**4 + f3b = (6*n + 3)/(4*n**4 + 8*n**3 + 8*n**2 + 4*n + 3) + f3c = 2**n*(n**2 - 2*n - 1)/(n**2*(n + 1)**2) + f3d = n**2*4**n/((n + 1)*(n + 2)) + f3e = 2**n/(n + 1) + f3f = 4*(n - 1)*(n**2 - 2*n - 1)/(n**2*(n + 1)**2*(n - 2)**2*(n - 3)**2) + f3g = (n**4 - 14*n**2 - 24*n - 9)*2**n/(n**2*(n + 1)**2*(n + 2)**2* + (n + 3)**2) + + # g3a -> no closed form + g3b = m*(m + 2)/(2*m**2 + 4*m + 3) + g3c = 2**m/m**2 - 2 + g3d = Rational(2, 3) + 4**(m + 1)*(m - 1)/(m + 2)/3 + # g3e -> no closed form + g3f = -(Rational(-1, 16) + 1/((m - 2)**2*(m + 1)**2)) # the AeqB key is wrong + g3g = Rational(-2, 9) + 2**(m + 1)/((m + 1)**2*(m + 3)**2) + + g = gosper_sum(f3a, (n, 1, m)) + assert g is None + g = gosper_sum(f3b, (n, 1, m)) + assert g is not None and simplify(g - g3b) == 0 + g = gosper_sum(f3c, (n, 1, m - 1)) + assert g is not None and simplify(g - g3c) == 0 + g = gosper_sum(f3d, (n, 1, m)) + assert g is not None and simplify(g - g3d) == 0 + g = gosper_sum(f3e, (n, 0, m - 1)) + assert g is None + g = gosper_sum(f3f, (n, 4, m)) + assert g is not None and simplify(g - g3f) == 0 + g = gosper_sum(f3g, (n, 1, m)) + assert g is not None and simplify(g - g3g) == 0 diff --git a/lib/python3.11/site-packages/sympy/concrete/tests/test_guess.py b/lib/python3.11/site-packages/sympy/concrete/tests/test_guess.py new file mode 100644 index 0000000000000000000000000000000000000000..5ac5d02b89ad62a70a29bd450b71b284b6aea76d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/tests/test_guess.py @@ -0,0 +1,82 @@ +from sympy.concrete.guess import ( + find_simple_recurrence_vector, + find_simple_recurrence, + rationalize, + guess_generating_function_rational, + guess_generating_function, + guess + ) +from sympy.concrete.products import Product +from sympy.core.function import Function +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial) +from sympy.functions.combinatorial.numbers import fibonacci +from sympy.functions.elementary.exponential import exp + + +def test_find_simple_recurrence_vector(): + assert find_simple_recurrence_vector( + [fibonacci(k) for k in range(12)]) == [1, -1, -1] + + +def test_find_simple_recurrence(): + a = Function('a') + n = Symbol('n') + assert find_simple_recurrence([fibonacci(k) for k in range(12)]) == ( + -a(n) - a(n + 1) + a(n + 2)) + + f = Function('a') + i = Symbol('n') + a = [1, 1, 1] + for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3]) + assert find_simple_recurrence(a, A=f, N=i) == ( + -8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3)) + assert find_simple_recurrence([0, 2, 15, 74, 12, 3, 0, + 1, 2, 85, 4, 5, 63]) == 0 + + +def test_rationalize(): + from mpmath import cos, pi, mpf + assert rationalize(cos(pi/3)) == S.Half + assert rationalize(mpf("0.333333333333333")) == Rational(1, 3) + assert rationalize(mpf("-0.333333333333333")) == Rational(-1, 3) + assert rationalize(pi, maxcoeff = 250) == Rational(355, 113) + + +def test_guess_generating_function_rational(): + x = Symbol('x') + assert guess_generating_function_rational([fibonacci(k) + for k in range(5, 15)]) == ((3*x + 5)/(-x**2 - x + 1)) + + +def test_guess_generating_function(): + x = Symbol('x') + assert guess_generating_function([fibonacci(k) + for k in range(5, 15)])['ogf'] == ((3*x + 5)/(-x**2 - x + 1)) + assert guess_generating_function( + [1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] == ( + (1/(x**4 + 2*x**2 - 4*x + 1))**S.Half) + assert guess_generating_function(sympify( + "[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]") + )['ogf'] == (x + Rational(3, 2))/(11*x**2 - 3*x + 1) + assert guess_generating_function([factorial(k) for k in range(12)], + types=['egf'])['egf'] == 1/(-x + 1) + assert guess_generating_function([k+1 for k in range(12)], + types=['egf']) == {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)} + + +def test_guess(): + i0, i1 = symbols('i0 i1') + assert guess([1, 2, 6, 24, 120], evaluate=False) == [Product(i1 + 1, (i1, 1, i0 - 1))] + assert guess([1, 2, 6, 24, 120]) == [RisingFactorial(2, i0 - 1)] + assert guess([1, 2, 7, 42, 429, 7436, 218348, 10850216], niter=4) == [ + 2**(i0 - 1)*(Rational(27, 16))**(i0**2/2 - 3*i0/2 + + 1)*Product(RisingFactorial(Rational(5, 3), i1 - 1)*RisingFactorial(Rational(7, 3), i1 + - 1)/(RisingFactorial(Rational(3, 2), i1 - 1)*RisingFactorial(Rational(5, 2), i1 - + 1)), (i1, 1, i0 - 1))] + assert guess([1, 0, 2]) == [] + x, y = symbols('x y') + assert guess([1, 2, 6, 24, 120], variables=[x, y]) == [RisingFactorial(2, x - 1)] diff --git a/lib/python3.11/site-packages/sympy/concrete/tests/test_products.py b/lib/python3.11/site-packages/sympy/concrete/tests/test_products.py new file mode 100644 index 0000000000000000000000000000000000000000..9be053a7040014c6ed38c1279a609fcb2426258e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/tests/test_products.py @@ -0,0 +1,410 @@ +from sympy.concrete.products import (Product, product) +from sympy.concrete.summations import Sum +from sympy.core.function import (Derivative, Function, diff) +from sympy.core.numbers import (Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.combinatorial.factorials import (rf, factorial) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.simplify.combsimp import combsimp +from sympy.simplify.simplify import simplify +from sympy.testing.pytest import raises + +a, k, n, m, x = symbols('a,k,n,m,x', integer=True) +f = Function('f') + + +def test_karr_convention(): + # Test the Karr product convention that we want to hold. + # See his paper "Summation in Finite Terms" for a detailed + # reasoning why we really want exactly this definition. + # The convention is described for sums on page 309 and + # essentially in section 1.4, definition 3. For products + # we can find in analogy: + # + # \prod_{m <= i < n} f(i) 'has the obvious meaning' for m < n + # \prod_{m <= i < n} f(i) = 0 for m = n + # \prod_{m <= i < n} f(i) = 1 / \prod_{n <= i < m} f(i) for m > n + # + # It is important to note that he defines all products with + # the upper limit being *exclusive*. + # In contrast, SymPy and the usual mathematical notation has: + # + # prod_{i = a}^b f(i) = f(a) * f(a+1) * ... * f(b-1) * f(b) + # + # with the upper limit *inclusive*. So translating between + # the two we find that: + # + # \prod_{m <= i < n} f(i) = \prod_{i = m}^{n-1} f(i) + # + # where we intentionally used two different ways to typeset the + # products and its limits. + + i = Symbol("i", integer=True) + k = Symbol("k", integer=True) + j = Symbol("j", integer=True, positive=True) + + # A simple example with a concrete factors and symbolic limits. + + # The normal product: m = k and n = k + j and therefore m < n: + m = k + n = k + j + + a = m + b = n - 1 + S1 = Product(i**2, (i, a, b)).doit() + + # The reversed product: m = k + j and n = k and therefore m > n: + m = k + j + n = k + + a = m + b = n - 1 + S2 = Product(i**2, (i, a, b)).doit() + + assert S1 * S2 == 1 + + # Test the empty product: m = k and n = k and therefore m = n: + m = k + n = k + + a = m + b = n - 1 + Sz = Product(i**2, (i, a, b)).doit() + + assert Sz == 1 + + # Another example this time with an unspecified factor and + # numeric limits. (We can not do both tests in the same example.) + f = Function("f") + + # The normal product with m < n: + m = 2 + n = 11 + + a = m + b = n - 1 + S1 = Product(f(i), (i, a, b)).doit() + + # The reversed product with m > n: + m = 11 + n = 2 + + a = m + b = n - 1 + S2 = Product(f(i), (i, a, b)).doit() + + assert simplify(S1 * S2) == 1 + + # Test the empty product with m = n: + m = 5 + n = 5 + + a = m + b = n - 1 + Sz = Product(f(i), (i, a, b)).doit() + + assert Sz == 1 + + +def test_karr_proposition_2a(): + # Test Karr, page 309, proposition 2, part a + i, u, v = symbols('i u v', integer=True) + + def test_the_product(m, n): + # g + g = i**3 + 2*i**2 - 3*i + # f = Delta g + f = simplify(g.subs(i, i+1) / g) + # The product + a = m + b = n - 1 + P = Product(f, (i, a, b)).doit() + # Test if Product_{m <= i < n} f(i) = g(n) / g(m) + assert combsimp(P / (g.subs(i, n) / g.subs(i, m))) == 1 + + # m < n + test_the_product(u, u + v) + # m = n + test_the_product(u, u) + # m > n + test_the_product(u + v, u) + + +def test_karr_proposition_2b(): + # Test Karr, page 309, proposition 2, part b + i, u, v, w = symbols('i u v w', integer=True) + + def test_the_product(l, n, m): + # Productmand + s = i**3 + # First product + a = l + b = n - 1 + S1 = Product(s, (i, a, b)).doit() + # Second product + a = l + b = m - 1 + S2 = Product(s, (i, a, b)).doit() + # Third product + a = m + b = n - 1 + S3 = Product(s, (i, a, b)).doit() + # Test if S1 = S2 * S3 as required + assert combsimp(S1 / (S2 * S3)) == 1 + + # l < m < n + test_the_product(u, u + v, u + v + w) + # l < m = n + test_the_product(u, u + v, u + v) + # l < m > n + test_the_product(u, u + v + w, v) + # l = m < n + test_the_product(u, u, u + v) + # l = m = n + test_the_product(u, u, u) + # l = m > n + test_the_product(u + v, u + v, u) + # l > m < n + test_the_product(u + v, u, u + w) + # l > m = n + test_the_product(u + v, u, u) + # l > m > n + test_the_product(u + v + w, u + v, u) + + +def test_simple_products(): + assert product(2, (k, a, n)) == 2**(n - a + 1) + assert product(k, (k, 1, n)) == factorial(n) + assert product(k**3, (k, 1, n)) == factorial(n)**3 + + assert product(k + 1, (k, 0, n - 1)) == factorial(n) + assert product(k + 1, (k, a, n - 1)) == rf(1 + a, n - a) + + assert product(cos(k), (k, 0, 5)) == cos(1)*cos(2)*cos(3)*cos(4)*cos(5) + assert product(cos(k), (k, 3, 5)) == cos(3)*cos(4)*cos(5) + assert product(cos(k), (k, 1, Rational(5, 2))) != cos(1)*cos(2) + + assert isinstance(product(k**k, (k, 1, n)), Product) + + assert Product(x**k, (k, 1, n)).variables == [k] + + raises(ValueError, lambda: Product(n)) + raises(ValueError, lambda: Product(n, k)) + raises(ValueError, lambda: Product(n, k, 1)) + raises(ValueError, lambda: Product(n, k, 1, 10)) + raises(ValueError, lambda: Product(n, (k, 1))) + + assert product(1, (n, 1, oo)) == 1 # issue 8301 + assert product(2, (n, 1, oo)) is oo + assert product(-1, (n, 1, oo)).func is Product + + +def test_multiple_products(): + assert product(x, (n, 1, k), (k, 1, m)) == x**(m**2/2 + m/2) + assert product(f(n), ( + n, 1, m), (m, 1, k)) == Product(f(n), (n, 1, m), (m, 1, k)).doit() + assert Product(f(n), (m, 1, k), (n, 1, k)).doit() == \ + Product(Product(f(n), (m, 1, k)), (n, 1, k)).doit() == \ + product(f(n), (m, 1, k), (n, 1, k)) == \ + product(product(f(n), (m, 1, k)), (n, 1, k)) == \ + Product(f(n)**k, (n, 1, k)) + assert Product( + x, (x, 1, k), (k, 1, n)).doit() == Product(factorial(k), (k, 1, n)) + + assert Product(x**k, (n, 1, k), (k, 1, m)).variables == [n, k] + + +def test_rational_products(): + assert product(1 + 1/k, (k, 1, n)) == rf(2, n)/factorial(n) + + +def test_special_products(): + # Wallis product + assert product((4*k)**2 / (4*k**2 - 1), (k, 1, n)) == \ + 4**n*factorial(n)**2/rf(S.Half, n)/rf(Rational(3, 2), n) + + # Euler's product formula for sin + assert product(1 + a/k**2, (k, 1, n)) == \ + rf(1 - sqrt(-a), n)*rf(1 + sqrt(-a), n)/factorial(n)**2 + + +def test__eval_product(): + from sympy.abc import i, n + # issue 4809 + a = Function('a') + assert product(2*a(i), (i, 1, n)) == 2**n * Product(a(i), (i, 1, n)) + # issue 4810 + assert product(2**i, (i, 1, n)) == 2**(n*(n + 1)/2) + k, m = symbols('k m', integer=True) + assert product(2**i, (i, k, m)) == 2**(-k**2/2 + k/2 + m**2/2 + m/2) + n = Symbol('n', negative=True, integer=True) + p = Symbol('p', positive=True, integer=True) + assert product(2**i, (i, n, p)) == 2**(-n**2/2 + n/2 + p**2/2 + p/2) + assert product(2**i, (i, p, n)) == 2**(n**2/2 + n/2 - p**2/2 + p/2) + + +def test_product_pow(): + # issue 4817 + assert product(2**f(k), (k, 1, n)) == 2**Sum(f(k), (k, 1, n)) + assert product(2**(2*f(k)), (k, 1, n)) == 2**Sum(2*f(k), (k, 1, n)) + + +def test_infinite_product(): + # issue 5737 + assert isinstance(Product(2**(1/factorial(n)), (n, 0, oo)), Product) + + +def test_conjugate_transpose(): + p = Product(x**k, (k, 1, 3)) + assert p.adjoint().doit() == p.doit().adjoint() + assert p.conjugate().doit() == p.doit().conjugate() + assert p.transpose().doit() == p.doit().transpose() + + A, B = symbols("A B", commutative=False) + p = Product(A*B**k, (k, 1, 3)) + assert p.adjoint().doit() == p.doit().adjoint() + assert p.conjugate().doit() == p.doit().conjugate() + assert p.transpose().doit() == p.doit().transpose() + + p = Product(B**k*A, (k, 1, 3)) + assert p.adjoint().doit() == p.doit().adjoint() + assert p.conjugate().doit() == p.doit().conjugate() + assert p.transpose().doit() == p.doit().transpose() + + +def test_simplify_prod(): + y, t, b, c, v, d = symbols('y, t, b, c, v, d', integer = True) + + _simplify = lambda e: simplify(e, doit=False) + assert _simplify(Product(x*y, (x, n, m), (y, a, k)) * \ + Product(y, (x, n, m), (y, a, k))) == \ + Product(x*y**2, (x, n, m), (y, a, k)) + assert _simplify(3 * y* Product(x, (x, n, m)) * Product(x, (x, m + 1, a))) \ + == 3 * y * Product(x, (x, n, a)) + assert _simplify(Product(x, (x, k + 1, a)) * Product(x, (x, n, k))) == \ + Product(x, (x, n, a)) + assert _simplify(Product(x, (x, k + 1, a)) * Product(x + 1, (x, n, k))) == \ + Product(x, (x, k + 1, a)) * Product(x + 1, (x, n, k)) + assert _simplify(Product(x, (t, a, b)) * Product(y, (t, a, b)) * \ + Product(x, (t, b+1, c))) == Product(x*y, (t, a, b)) * \ + Product(x, (t, b+1, c)) + assert _simplify(Product(x, (t, a, b)) * Product(x, (t, b+1, c)) * \ + Product(y, (t, a, b))) == Product(x*y, (t, a, b)) * \ + Product(x, (t, b+1, c)) + assert _simplify(Product(sin(t)**2 + cos(t)**2 + 1, (t, a, b))) == \ + Product(2, (t, a, b)) + assert _simplify(Product(sin(t)**2 + cos(t)**2 - 1, (t, a, b))) == \ + Product(0, (t, a, b)) + assert _simplify(Product(v*Product(sin(t)**2 + cos(t)**2, (t, a, b)), + (v, c, d))) == Product(v*Product(1, (t, a, b)), (v, c, d)) + + +def test_change_index(): + b, y, c, d, z = symbols('b, y, c, d, z', integer = True) + + assert Product(x, (x, a, b)).change_index(x, x + 1, y) == \ + Product(y - 1, (y, a + 1, b + 1)) + assert Product(x**2, (x, a, b)).change_index(x, x - 1) == \ + Product((x + 1)**2, (x, a - 1, b - 1)) + assert Product(x**2, (x, a, b)).change_index(x, -x, y) == \ + Product((-y)**2, (y, -b, -a)) + assert Product(x, (x, a, b)).change_index(x, -x - 1) == \ + Product(-x - 1, (x, - b - 1, -a - 1)) + assert Product(x*y, (x, a, b), (y, c, d)).change_index(x, x - 1, z) == \ + Product((z + 1)*y, (z, a - 1, b - 1), (y, c, d)) + + +def test_reorder(): + b, y, c, d, z = symbols('b, y, c, d, z', integer = True) + + assert Product(x*y, (x, a, b), (y, c, d)).reorder((0, 1)) == \ + Product(x*y, (y, c, d), (x, a, b)) + assert Product(x, (x, a, b), (x, c, d)).reorder((0, 1)) == \ + Product(x, (x, c, d), (x, a, b)) + assert Product(x*y + z, (x, a, b), (z, m, n), (y, c, d)).reorder(\ + (2, 0), (0, 1)) == Product(x*y + z, (z, m, n), (y, c, d), (x, a, b)) + assert Product(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\ + (0, 1), (1, 2), (0, 2)) == \ + Product(x*y*z, (x, a, b), (z, m, n), (y, c, d)) + assert Product(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\ + (x, y), (y, z), (x, z)) == \ + Product(x*y*z, (x, a, b), (z, m, n), (y, c, d)) + assert Product(x*y, (x, a, b), (y, c, d)).reorder((x, 1)) == \ + Product(x*y, (y, c, d), (x, a, b)) + assert Product(x*y, (x, a, b), (y, c, d)).reorder((y, x)) == \ + Product(x*y, (y, c, d), (x, a, b)) + + +def test_Product_is_convergent(): + assert Product(1/n**2, (n, 1, oo)).is_convergent() is S.false + assert Product(exp(1/n**2), (n, 1, oo)).is_convergent() is S.true + assert Product(1/n, (n, 1, oo)).is_convergent() is S.false + assert Product(1 + 1/n, (n, 1, oo)).is_convergent() is S.false + assert Product(1 + 1/n**2, (n, 1, oo)).is_convergent() is S.true + + +def test_reverse_order(): + x, y, a, b, c, d= symbols('x, y, a, b, c, d', integer = True) + + assert Product(x, (x, 0, 3)).reverse_order(0) == Product(1/x, (x, 4, -1)) + assert Product(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(0, 1) == \ + Product(x*y, (x, 6, 0), (y, 7, -1)) + assert Product(x, (x, 1, 2)).reverse_order(0) == Product(1/x, (x, 3, 0)) + assert Product(x, (x, 1, 3)).reverse_order(0) == Product(1/x, (x, 4, 0)) + assert Product(x, (x, 1, a)).reverse_order(0) == Product(1/x, (x, a + 1, 0)) + assert Product(x, (x, a, 5)).reverse_order(0) == Product(1/x, (x, 6, a - 1)) + assert Product(x, (x, a + 1, a + 5)).reverse_order(0) == \ + Product(1/x, (x, a + 6, a)) + assert Product(x, (x, a + 1, a + 2)).reverse_order(0) == \ + Product(1/x, (x, a + 3, a)) + assert Product(x, (x, a + 1, a + 1)).reverse_order(0) == \ + Product(1/x, (x, a + 2, a)) + assert Product(x, (x, a, b)).reverse_order(0) == Product(1/x, (x, b + 1, a - 1)) + assert Product(x, (x, a, b)).reverse_order(x) == Product(1/x, (x, b + 1, a - 1)) + assert Product(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) == \ + Product(x*y, (x, b + 1, a - 1), (y, 6, 1)) + assert Product(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) == \ + Product(x*y, (x, b + 1, a - 1), (y, 6, 1)) + + +def test_issue_9983(): + n = Symbol('n', integer=True, positive=True) + p = Product(1 + 1/n**Rational(2, 3), (n, 1, oo)) + assert p.is_convergent() is S.false + assert product(1 + 1/n**Rational(2, 3), (n, 1, oo)) == p.doit() + + +def test_issue_13546(): + n = Symbol('n') + k = Symbol('k') + p = Product(n + 1 / 2**k, (k, 0, n-1)).doit() + assert p.subs(n, 2).doit() == Rational(15, 2) + + +def test_issue_14036(): + a, n = symbols('a n') + assert product(1 - a**2 / (n*pi)**2, [n, 1, oo]) != 0 + + +def test_rewrite_Sum(): + assert Product(1 - S.Half**2/k**2, (k, 1, oo)).rewrite(Sum) == \ + exp(Sum(log(1 - 1/(4*k**2)), (k, 1, oo))) + + +def test_KroneckerDelta_Product(): + y = Symbol('y') + assert Product(x*KroneckerDelta(x, y), (x, 0, 1)).doit() == 0 + + +def test_issue_20848(): + _i = Dummy('i') + t, y, z = symbols('t y z') + assert diff(Product(x, (y, 1, z)), x).as_dummy() == Sum(Product(x, (y, 1, _i - 1))*Product(x, (y, _i + 1, z)), (_i, 1, z)).as_dummy() + assert diff(Product(x, (y, 1, z)), x).doit() == x**(z - 1)*z + assert diff(Product(x, (y, x, z)), x) == Derivative(Product(x, (y, x, z)), x) + assert diff(Product(t, (x, 1, z)), x) == S(0) + assert Product(sin(n*x), (n, -1, 1)).diff(x).doit() == S(0) diff --git a/lib/python3.11/site-packages/sympy/concrete/tests/test_sums_products.py b/lib/python3.11/site-packages/sympy/concrete/tests/test_sums_products.py new file mode 100644 index 0000000000000000000000000000000000000000..806f2edb1c1fa31beee800eb1799cc755bf04f01 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/concrete/tests/test_sums_products.py @@ -0,0 +1,1646 @@ +from math import prod + +from sympy.concrete.expr_with_intlimits import ReorderError +from sympy.concrete.products import (Product, product) +from sympy.concrete.summations import (Sum, summation, telescopic, + eval_sum_residue, _dummy_with_inherited_properties_concrete) +from sympy.core.function import (Derivative, Function) +from sympy.core import (Catalan, EulerGamma) +from sympy.core.facts import InconsistentAssumptions +from sympy.core.mod import Mod +from sympy.core.numbers import (E, I, Rational, nan, oo, pi) +from sympy.core.relational import Eq +from sympy.core.numbers import Float +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import (rf, binomial, factorial) +from sympy.functions.combinatorial.numbers import harmonic +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.hyperbolic import (sinh, tanh) +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.gamma_functions import (gamma, lowergamma) +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.functions.special.zeta_functions import zeta +from sympy.integrals.integrals import Integral +from sympy.logic.boolalg import And, Or +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.matrices.expressions.special import Identity +from sympy.matrices import (Matrix, SparseMatrix, + ImmutableDenseMatrix, ImmutableSparseMatrix, diag) +from sympy.sets.fancysets import Range +from sympy.sets.sets import Interval +from sympy.simplify.combsimp import combsimp +from sympy.simplify.simplify import simplify +from sympy.tensor.indexed import (Idx, Indexed, IndexedBase) +from sympy.testing.pytest import XFAIL, raises, slow +from sympy.abc import a, b, c, d, k, m, x, y, z + +n = Symbol('n', integer=True) +f, g = symbols('f g', cls=Function) + +def test_karr_convention(): + # Test the Karr summation convention that we want to hold. + # See his paper "Summation in Finite Terms" for a detailed + # reasoning why we really want exactly this definition. + # The convention is described on page 309 and essentially + # in section 1.4, definition 3: + # + # \sum_{m <= i < n} f(i) 'has the obvious meaning' for m < n + # \sum_{m <= i < n} f(i) = 0 for m = n + # \sum_{m <= i < n} f(i) = - \sum_{n <= i < m} f(i) for m > n + # + # It is important to note that he defines all sums with + # the upper limit being *exclusive*. + # In contrast, SymPy and the usual mathematical notation has: + # + # sum_{i = a}^b f(i) = f(a) + f(a+1) + ... + f(b-1) + f(b) + # + # with the upper limit *inclusive*. So translating between + # the two we find that: + # + # \sum_{m <= i < n} f(i) = \sum_{i = m}^{n-1} f(i) + # + # where we intentionally used two different ways to typeset the + # sum and its limits. + + i = Symbol("i", integer=True) + k = Symbol("k", integer=True) + j = Symbol("j", integer=True) + + # A simple example with a concrete summand and symbolic limits. + + # The normal sum: m = k and n = k + j and therefore m < n: + m = k + n = k + j + + a = m + b = n - 1 + S1 = Sum(i**2, (i, a, b)).doit() + + # The reversed sum: m = k + j and n = k and therefore m > n: + m = k + j + n = k + + a = m + b = n - 1 + S2 = Sum(i**2, (i, a, b)).doit() + + assert simplify(S1 + S2) == 0 + + # Test the empty sum: m = k and n = k and therefore m = n: + m = k + n = k + + a = m + b = n - 1 + Sz = Sum(i**2, (i, a, b)).doit() + + assert Sz == 0 + + # Another example this time with an unspecified summand and + # numeric limits. (We can not do both tests in the same example.) + + # The normal sum with m < n: + m = 2 + n = 11 + + a = m + b = n - 1 + S1 = Sum(f(i), (i, a, b)).doit() + + # The reversed sum with m > n: + m = 11 + n = 2 + + a = m + b = n - 1 + S2 = Sum(f(i), (i, a, b)).doit() + + assert simplify(S1 + S2) == 0 + + # Test the empty sum with m = n: + m = 5 + n = 5 + + a = m + b = n - 1 + Sz = Sum(f(i), (i, a, b)).doit() + + assert Sz == 0 + + e = Piecewise((exp(-i), Mod(i, 2) > 0), (0, True)) + s = Sum(e, (i, 0, 11)) + assert s.n(3) == s.doit().n(3) + + +def test_karr_proposition_2a(): + # Test Karr, page 309, proposition 2, part a + i = Symbol("i", integer=True) + u = Symbol("u", integer=True) + v = Symbol("v", integer=True) + + def test_the_sum(m, n): + # g + g = i**3 + 2*i**2 - 3*i + # f = Delta g + f = simplify(g.subs(i, i+1) - g) + # The sum + a = m + b = n - 1 + S = Sum(f, (i, a, b)).doit() + # Test if Sum_{m <= i < n} f(i) = g(n) - g(m) + assert simplify(S - (g.subs(i, n) - g.subs(i, m))) == 0 + + # m < n + test_the_sum(u, u+v) + # m = n + test_the_sum(u, u ) + # m > n + test_the_sum(u+v, u ) + + +def test_karr_proposition_2b(): + # Test Karr, page 309, proposition 2, part b + i = Symbol("i", integer=True) + u = Symbol("u", integer=True) + v = Symbol("v", integer=True) + w = Symbol("w", integer=True) + + def test_the_sum(l, n, m): + # Summand + s = i**3 + # First sum + a = l + b = n - 1 + S1 = Sum(s, (i, a, b)).doit() + # Second sum + a = l + b = m - 1 + S2 = Sum(s, (i, a, b)).doit() + # Third sum + a = m + b = n - 1 + S3 = Sum(s, (i, a, b)).doit() + # Test if S1 = S2 + S3 as required + assert S1 - (S2 + S3) == 0 + + # l < m < n + test_the_sum(u, u+v, u+v+w) + # l < m = n + test_the_sum(u, u+v, u+v ) + # l < m > n + test_the_sum(u, u+v+w, v ) + # l = m < n + test_the_sum(u, u, u+v ) + # l = m = n + test_the_sum(u, u, u ) + # l = m > n + test_the_sum(u+v, u+v, u ) + # l > m < n + test_the_sum(u+v, u, u+w ) + # l > m = n + test_the_sum(u+v, u, u ) + # l > m > n + test_the_sum(u+v+w, u+v, u ) + + +def test_arithmetic_sums(): + assert summation(1, (n, a, b)) == b - a + 1 + assert Sum(S.NaN, (n, a, b)) is S.NaN + assert Sum(x, (n, a, a)).doit() == x + assert Sum(x, (x, a, a)).doit() == a + assert Sum(x, (n, 1, a)).doit() == a*x + assert Sum(x, (x, Range(1, 11))).doit() == 55 + assert Sum(x, (x, Range(1, 11, 2))).doit() == 25 + assert Sum(x, (x, Range(1, 10, 2))) == Sum(x, (x, Range(9, 0, -2))) + lo, hi = 1, 2 + s1 = Sum(n, (n, lo, hi)) + s2 = Sum(n, (n, hi, lo)) + assert s1 != s2 + assert s1.doit() == 3 and s2.doit() == 0 + lo, hi = x, x + 1 + s1 = Sum(n, (n, lo, hi)) + s2 = Sum(n, (n, hi, lo)) + assert s1 != s2 + assert s1.doit() == 2*x + 1 and s2.doit() == 0 + assert Sum(Integral(x, (x, 1, y)) + x, (x, 1, 2)).doit() == \ + y**2 + 2 + assert summation(1, (n, 1, 10)) == 10 + assert summation(2*n, (n, 0, 10**10)) == 100000000010000000000 + assert summation(4*n*m, (n, a, 1), (m, 1, d)).expand() == \ + 2*d + 2*d**2 + a*d + a*d**2 - d*a**2 - a**2*d**2 + assert summation(cos(n), (n, -2, 1)) == cos(-2) + cos(-1) + cos(0) + cos(1) + assert summation(cos(n), (n, x, x + 2)) == cos(x) + cos(x + 1) + cos(x + 2) + assert isinstance(summation(cos(n), (n, x, x + S.Half)), Sum) + assert summation(k, (k, 0, oo)) is oo + assert summation(k, (k, Range(1, 11))) == 55 + + +def test_polynomial_sums(): + assert summation(n**2, (n, 3, 8)) == 199 + assert summation(n, (n, a, b)) == \ + ((a + b)*(b - a + 1)/2).expand() + assert summation(n**2, (n, 1, b)) == \ + ((2*b**3 + 3*b**2 + b)/6).expand() + assert summation(n**3, (n, 1, b)) == \ + ((b**4 + 2*b**3 + b**2)/4).expand() + assert summation(n**6, (n, 1, b)) == \ + ((6*b**7 + 21*b**6 + 21*b**5 - 7*b**3 + b)/42).expand() + + +def test_geometric_sums(): + assert summation(pi**n, (n, 0, b)) == (1 - pi**(b + 1)) / (1 - pi) + assert summation(2 * 3**n, (n, 0, b)) == 3**(b + 1) - 1 + assert summation(S.Half**n, (n, 1, oo)) == 1 + assert summation(2**n, (n, 0, b)) == 2**(b + 1) - 1 + assert summation(2**n, (n, 1, oo)) is oo + assert summation(2**(-n), (n, 1, oo)) == 1 + assert summation(3**(-n), (n, 4, oo)) == Rational(1, 54) + assert summation(2**(-4*n + 3), (n, 1, oo)) == Rational(8, 15) + assert summation(2**(n + 1), (n, 1, b)).expand() == 4*(2**b - 1) + + # issue 6664: + assert summation(x**n, (n, 0, oo)) == \ + Piecewise((1/(-x + 1), Abs(x) < 1), (Sum(x**n, (n, 0, oo)), True)) + + assert summation(-2**n, (n, 0, oo)) is -oo + assert summation(I**n, (n, 0, oo)) == Sum(I**n, (n, 0, oo)) + + # issue 6802: + assert summation((-1)**(2*x + 2), (x, 0, n)) == n + 1 + assert summation((-2)**(2*x + 2), (x, 0, n)) == 4*4**(n + 1)/S(3) - Rational(4, 3) + assert summation((-1)**x, (x, 0, n)) == -(-1)**(n + 1)/S(2) + S.Half + assert summation(y**x, (x, a, b)) == \ + Piecewise((-a + b + 1, Eq(y, 1)), ((y**a - y**(b + 1))/(-y + 1), True)) + assert summation((-2)**(y*x + 2), (x, 0, n)) == \ + 4*Piecewise((n + 1, Eq((-2)**y, 1)), + ((-(-2)**(y*(n + 1)) + 1)/(-(-2)**y + 1), True)) + + # issue 8251: + assert summation((1/(n + 1)**2)*n**2, (n, 0, oo)) is oo + + #issue 9908: + assert Sum(1/(n**3 - 1), (n, -oo, -2)).doit() == summation(1/(n**3 - 1), (n, -oo, -2)) + + #issue 11642: + result = Sum(0.5**n, (n, 1, oo)).doit() + assert result == 1.0 + assert result.is_Float + + result = Sum(0.25**n, (n, 1, oo)).doit() + assert result == 1/3. + assert result.is_Float + + result = Sum(0.99999**n, (n, 1, oo)).doit() + assert result == 99999.0 + assert result.is_Float + + result = Sum(S.Half**n, (n, 1, oo)).doit() + assert result == 1 + assert not result.is_Float + + result = Sum(Rational(3, 5)**n, (n, 1, oo)).doit() + assert result == Rational(3, 2) + assert not result.is_Float + + assert Sum(1.0**n, (n, 1, oo)).doit() is oo + assert Sum(2.43**n, (n, 1, oo)).doit() is oo + + # Issue 13979 + i, k, q = symbols('i k q', integer=True) + result = summation( + exp(-2*I*pi*k*i/n) * exp(2*I*pi*q*i/n) / n, (i, 0, n - 1) + ) + assert result.simplify() == Piecewise( + (1, Eq(exp(-2*I*pi*(k - q)/n), 1)), (0, True) + ) + + #Issue 23491 + assert Sum(1/(n**2 + 1), (n, 1, oo)).doit() == S(-1)/2 + pi/(2*tanh(pi)) + +def test_harmonic_sums(): + assert summation(1/k, (k, 0, n)) == Sum(1/k, (k, 0, n)) + assert summation(1/k, (k, 1, n)) == harmonic(n) + assert summation(n/k, (k, 1, n)) == n*harmonic(n) + assert summation(1/k, (k, 5, n)) == harmonic(n) - harmonic(4) + + +def test_composite_sums(): + f = S.Half*(7 - 6*n + Rational(1, 7)*n**3) + s = summation(f, (n, a, b)) + assert not isinstance(s, Sum) + A = 0 + for i in range(-3, 5): + A += f.subs(n, i) + B = s.subs(a, -3).subs(b, 4) + assert A == B + + +def test_hypergeometric_sums(): + assert summation( + binomial(2*k, k)/4**k, (k, 0, n)) == (1 + 2*n)*binomial(2*n, n)/4**n + assert summation(binomial(2*k, k)/5**k, (k, -oo, oo)) == sqrt(5) + + +def test_other_sums(): + f = m**2 + m*exp(m) + g = 3*exp(Rational(3, 2))/2 + exp(S.Half)/2 - exp(Rational(-1, 2))/2 - 3*exp(Rational(-3, 2))/2 + 5 + + assert summation(f, (m, Rational(-3, 2), Rational(3, 2))) == g + assert summation(f, (m, -1.5, 1.5)).evalf().epsilon_eq(g.evalf(), 1e-10) + +fac = factorial + + +def NS(e, n=15, **options): + return str(sympify(e).evalf(n, **options)) + + +def test_evalf_fast_series(): + # Euler transformed series for sqrt(1+x) + assert NS(Sum( + fac(2*n + 1)/fac(n)**2/2**(3*n + 1), (n, 0, oo)), 100) == NS(sqrt(2), 100) + + # Some series for exp(1) + estr = NS(E, 100) + assert NS(Sum(1/fac(n), (n, 0, oo)), 100) == estr + assert NS(1/Sum((1 - 2*n)/fac(2*n), (n, 0, oo)), 100) == estr + assert NS(Sum((2*n + 1)/fac(2*n), (n, 0, oo)), 100) == estr + assert NS(Sum((4*n + 3)/2**(2*n + 1)/fac(2*n + 1), (n, 0, oo))**2, 100) == estr + + pistr = NS(pi, 100) + # Ramanujan series for pi + assert NS(9801/sqrt(8)/Sum(fac( + 4*n)*(1103 + 26390*n)/fac(n)**4/396**(4*n), (n, 0, oo)), 100) == pistr + assert NS(1/Sum( + binomial(2*n, n)**3 * (42*n + 5)/2**(12*n + 4), (n, 0, oo)), 100) == pistr + # Machin's formula for pi + assert NS(16*Sum((-1)**n/(2*n + 1)/5**(2*n + 1), (n, 0, oo)) - + 4*Sum((-1)**n/(2*n + 1)/239**(2*n + 1), (n, 0, oo)), 100) == pistr + + # Apery's constant + astr = NS(zeta(3), 100) + P = 126392*n**5 + 412708*n**4 + 531578*n**3 + 336367*n**2 + 104000* \ + n + 12463 + assert NS(Sum((-1)**n * P / 24 * (fac(2*n + 1)*fac(2*n)*fac( + n))**3 / fac(3*n + 2) / fac(4*n + 3)**3, (n, 0, oo)), 100) == astr + assert NS(Sum((-1)**n * (205*n**2 + 250*n + 77)/64 * fac(n)**10 / + fac(2*n + 1)**5, (n, 0, oo)), 100) == astr + + +def test_evalf_fast_series_issue_4021(): + # Catalan's constant + assert NS(Sum((-1)**(n - 1)*2**(8*n)*(40*n**2 - 24*n + 3)*fac(2*n)**3* + fac(n)**2/n**3/(2*n - 1)/fac(4*n)**2, (n, 1, oo))/64, 100) == \ + NS(Catalan, 100) + astr = NS(zeta(3), 100) + assert NS(5*Sum( + (-1)**(n - 1)*fac(n)**2 / n**3 / fac(2*n), (n, 1, oo))/2, 100) == astr + assert NS(Sum((-1)**(n - 1)*(56*n**2 - 32*n + 5) / (2*n - 1)**2 * fac(n - 1) + **3 / fac(3*n), (n, 1, oo))/4, 100) == astr + + +def test_evalf_slow_series(): + assert NS(Sum((-1)**n / n, (n, 1, oo)), 15) == NS(-log(2), 15) + assert NS(Sum((-1)**n / n, (n, 1, oo)), 50) == NS(-log(2), 50) + assert NS(Sum(1/n**2, (n, 1, oo)), 15) == NS(pi**2/6, 15) + assert NS(Sum(1/n**2, (n, 1, oo)), 100) == NS(pi**2/6, 100) + assert NS(Sum(1/n**2, (n, 1, oo)), 500) == NS(pi**2/6, 500) + assert NS(Sum((-1)**n / (2*n + 1)**3, (n, 0, oo)), 15) == NS(pi**3/32, 15) + assert NS(Sum((-1)**n / (2*n + 1)**3, (n, 0, oo)), 50) == NS(pi**3/32, 50) + + +def test_evalf_oo_to_oo(): + # There used to be an error in certain cases + # Does not evaluate, but at least do not throw an error + # Evaluates symbolically to 0, which is not correct + assert Sum(1/(n**2+1), (n, -oo, oo)).evalf() == Sum(1/(n**2+1), (n, -oo, oo)) + # This evaluates if from 1 to oo and symbolically + assert Sum(1/(factorial(abs(n))), (n, -oo, -1)).evalf() == Sum(1/(factorial(abs(n))), (n, -oo, -1)) + + +def test_euler_maclaurin(): + # Exact polynomial sums with E-M + def check_exact(f, a, b, m, n): + A = Sum(f, (k, a, b)) + s, e = A.euler_maclaurin(m, n) + assert (e == 0) and (s.expand() == A.doit()) + check_exact(k**4, a, b, 0, 2) + check_exact(k**4 + 2*k, a, b, 1, 2) + check_exact(k**4 + k**2, a, b, 1, 5) + check_exact(k**5, 2, 6, 1, 2) + check_exact(k**5, 2, 6, 1, 3) + assert Sum(x-1, (x, 0, 2)).euler_maclaurin(m=30, n=30, eps=2**-15) == (0, 0) + # Not exact + assert Sum(k**6, (k, a, b)).euler_maclaurin(0, 2)[1] != 0 + # Numerical test + for mi, ni in [(2, 4), (2, 20), (10, 20), (18, 20)]: + A = Sum(1/k**3, (k, 1, oo)) + s, e = A.euler_maclaurin(mi, ni) + assert abs((s - zeta(3)).evalf()) < e.evalf() + + raises(ValueError, lambda: Sum(1, (x, 0, 1), (k, 0, 1)).euler_maclaurin()) + + +@slow +def test_evalf_euler_maclaurin(): + assert NS(Sum(1/k**k, (k, 1, oo)), 15) == '1.29128599706266' + assert NS(Sum(1/k**k, (k, 1, oo)), + 50) == '1.2912859970626635404072825905956005414986193682745' + assert NS(Sum(1/k - log(1 + 1/k), (k, 1, oo)), 15) == NS(EulerGamma, 15) + assert NS(Sum(1/k - log(1 + 1/k), (k, 1, oo)), 50) == NS(EulerGamma, 50) + assert NS(Sum(log(k)/k**2, (k, 1, oo)), 15) == '0.937548254315844' + assert NS(Sum(log(k)/k**2, (k, 1, oo)), + 50) == '0.93754825431584375370257409456786497789786028861483' + assert NS(Sum(1/k, (k, 1000000, 2000000)), 15) == '0.693147930560008' + assert NS(Sum(1/k, (k, 1000000, 2000000)), + 50) == '0.69314793056000780941723211364567656807940638436025' + + +def test_evalf_symbolic(): + # issue 6328 + expr = Sum(f(x), (x, 1, 3)) + Sum(g(x), (x, 1, 3)) + assert expr.evalf() == expr + + +def test_evalf_issue_3273(): + assert Sum(0, (k, 1, oo)).evalf() == 0 + + +def test_simple_products(): + assert Product(S.NaN, (x, 1, 3)) is S.NaN + assert product(S.NaN, (x, 1, 3)) is S.NaN + assert Product(x, (n, a, a)).doit() == x + assert Product(x, (x, a, a)).doit() == a + assert Product(x, (y, 1, a)).doit() == x**a + + lo, hi = 1, 2 + s1 = Product(n, (n, lo, hi)) + s2 = Product(n, (n, hi, lo)) + assert s1 != s2 + # This IS correct according to Karr product convention + assert s1.doit() == 2 + assert s2.doit() == 1 + + lo, hi = x, x + 1 + s1 = Product(n, (n, lo, hi)) + s2 = Product(n, (n, hi, lo)) + s3 = 1 / Product(n, (n, hi + 1, lo - 1)) + assert s1 != s2 + # This IS correct according to Karr product convention + assert s1.doit() == x*(x + 1) + assert s2.doit() == 1 + assert s3.doit() == x*(x + 1) + + assert Product(Integral(2*x, (x, 1, y)) + 2*x, (x, 1, 2)).doit() == \ + (y**2 + 1)*(y**2 + 3) + assert product(2, (n, a, b)) == 2**(b - a + 1) + assert product(n, (n, 1, b)) == factorial(b) + assert product(n**3, (n, 1, b)) == factorial(b)**3 + assert product(3**(2 + n), (n, a, b)) \ + == 3**(2*(1 - a + b) + b/2 + (b**2)/2 + a/2 - (a**2)/2) + assert product(cos(n), (n, 3, 5)) == cos(3)*cos(4)*cos(5) + assert product(cos(n), (n, x, x + 2)) == cos(x)*cos(x + 1)*cos(x + 2) + assert isinstance(product(cos(n), (n, x, x + S.Half)), Product) + # If Product managed to evaluate this one, it most likely got it wrong! + assert isinstance(Product(n**n, (n, 1, b)), Product) + + +def test_rational_products(): + assert combsimp(product(1 + 1/n, (n, a, b))) == (1 + b)/a + assert combsimp(product(n + 1, (n, a, b))) == gamma(2 + b)/gamma(1 + a) + assert combsimp(product((n + 1)/(n - 1), (n, a, b))) == b*(1 + b)/(a*(a - 1)) + assert combsimp(product(n/(n + 1)/(n + 2), (n, a, b))) == \ + a*gamma(a + 2)/(b + 1)/gamma(b + 3) + assert combsimp(product(n*(n + 1)/(n - 1)/(n - 2), (n, a, b))) == \ + b**2*(b - 1)*(1 + b)/(a - 1)**2/(a*(a - 2)) + + +def test_wallis_product(): + # Wallis product, given in two different forms to ensure that Product + # can factor simple rational expressions + A = Product(4*n**2 / (4*n**2 - 1), (n, 1, b)) + B = Product((2*n)*(2*n)/(2*n - 1)/(2*n + 1), (n, 1, b)) + R = pi*gamma(b + 1)**2/(2*gamma(b + S.Half)*gamma(b + Rational(3, 2))) + assert simplify(A.doit()) == R + assert simplify(B.doit()) == R + # This one should eventually also be doable (Euler's product formula for sin) + # assert Product(1+x/n**2, (n, 1, b)) == ... + + +def test_telescopic_sums(): + #checks also input 2 of comment 1 issue 4127 + assert Sum(1/k - 1/(k + 1), (k, 1, n)).doit() == 1 - 1/(1 + n) + assert Sum( + f(k) - f(k + 2), (k, m, n)).doit() == -f(1 + n) - f(2 + n) + f(m) + f(1 + m) + assert Sum(cos(k) - cos(k + 3), (k, 1, n)).doit() == -cos(1 + n) - \ + cos(2 + n) - cos(3 + n) + cos(1) + cos(2) + cos(3) + + # dummy variable shouldn't matter + assert telescopic(1/m, -m/(1 + m), (m, n - 1, n)) == \ + telescopic(1/k, -k/(1 + k), (k, n - 1, n)) + + assert Sum(1/x/(x - 1), (x, a, b)).doit() == 1/(a - 1) - 1/b + eq = 1/((5*n + 2)*(5*(n + 1) + 2)) + assert Sum(eq, (n, 0, oo)).doit() == S(1)/10 + nz = symbols('nz', nonzero=True) + v = Sum(eq.subs(5, nz), (n, 0, oo)).doit() + assert v.subs(nz, 5).simplify() == S(1)/10 + # check that apart is being used in non-symbolic case + s = Sum(eq, (n, 0, k)).doit() + v = Sum(eq, (n, 0, 10**100)).doit() + assert v == s.subs(k, 10**100) + + +def test_sum_reconstruct(): + s = Sum(n**2, (n, -1, 1)) + assert s == Sum(*s.args) + raises(ValueError, lambda: Sum(x, x)) + raises(ValueError, lambda: Sum(x, (x, 1))) + + +def test_limit_subs(): + for F in (Sum, Product, Integral): + assert F(a*exp(a), (a, -2, 2)) == F(a*exp(a), (a, -b, b)).subs(b, 2) + assert F(a, (a, F(b, (b, 1, 2)), 4)).subs(F(b, (b, 1, 2)), c) == \ + F(a, (a, c, 4)) + assert F(x, (x, 1, x + y)).subs(x, 1) == F(x, (x, 1, y + 1)) + + +def test_function_subs(): + S = Sum(x*f(y),(x,0,oo),(y,0,oo)) + assert S.subs(f(y),y) == Sum(x*y,(x,0,oo),(y,0,oo)) + assert S.subs(f(x),x) == S + raises(ValueError, lambda: S.subs(f(y),x+y) ) + S = Sum(x*log(y),(x,0,oo),(y,0,oo)) + assert S.subs(log(y),y) == S + S = Sum(x*f(y),(x,0,oo),(y,0,oo)) + assert S.subs(f(y),y) == Sum(x*y,(x,0,oo),(y,0,oo)) + + +def test_equality(): + # if this fails remove special handling below + raises(ValueError, lambda: Sum(x, x)) + r = symbols('x', real=True) + for F in (Sum, Product, Integral): + try: + assert F(x, x) != F(y, y) + assert F(x, (x, 1, 2)) != F(x, x) + assert F(x, (x, x)) != F(x, x) # or else they print the same + assert F(1, x) != F(1, y) + except ValueError: + pass + assert F(a, (x, 1, 2)) != F(a, (x, 1, 3)) # diff limit + assert F(a, (x, 1, x)) != F(a, (y, 1, y)) + assert F(a, (x, 1, 2)) != F(b, (x, 1, 2)) # diff expression + assert F(x, (x, 1, 2)) != F(r, (r, 1, 2)) # diff assumptions + assert F(1, (x, 1, x)) != F(1, (y, 1, x)) # only dummy is diff + assert F(1, (x, 1, x)).dummy_eq(F(1, (y, 1, x))) + + # issue 5265 + assert Sum(x, (x, 1, x)).subs(x, a) == Sum(x, (x, 1, a)) + + +def test_Sum_doit(): + assert Sum(n*Integral(a**2), (n, 0, 2)).doit() == a**3 + assert Sum(n*Integral(a**2), (n, 0, 2)).doit(deep=False) == \ + 3*Integral(a**2) + assert summation(n*Integral(a**2), (n, 0, 2)) == 3*Integral(a**2) + + # test nested sum evaluation + s = Sum( Sum( Sum(2,(z,1,n+1)), (y,x+1,n)), (x,1,n)) + assert 0 == (s.doit() - n*(n+1)*(n-1)).factor() + + # Integer assumes finite + assert Sum(KroneckerDelta(x, y), (x, -oo, oo)).doit() == Piecewise((1, And(-oo < y, y < oo)), (0, True)) + assert Sum(KroneckerDelta(m, n), (m, -oo, oo)).doit() == 1 + assert Sum(m*KroneckerDelta(x, y), (x, -oo, oo)).doit() == Piecewise((m, And(-oo < y, y < oo)), (0, True)) + assert Sum(x*KroneckerDelta(m, n), (m, -oo, oo)).doit() == x + assert Sum(Sum(KroneckerDelta(m, n), (m, 1, 3)), (n, 1, 3)).doit() == 3 + assert Sum(Sum(KroneckerDelta(k, m), (m, 1, 3)), (n, 1, 3)).doit() == \ + 3 * Piecewise((1, And(1 <= k, k <= 3)), (0, True)) + assert Sum(f(n) * Sum(KroneckerDelta(m, n), (m, 0, oo)), (n, 1, 3)).doit() == \ + f(1) + f(2) + f(3) + assert Sum(f(n) * Sum(KroneckerDelta(m, n), (m, 0, oo)), (n, 1, oo)).doit() == \ + Sum(f(n), (n, 1, oo)) + + # issue 2597 + nmax = symbols('N', integer=True, positive=True) + pw = Piecewise((1, And(1 <= n, n <= nmax)), (0, True)) + assert Sum(pw, (n, 1, nmax)).doit() == Sum(Piecewise((1, nmax >= n), + (0, True)), (n, 1, nmax)) + + q, s = symbols('q, s') + assert summation(1/n**(2*s), (n, 1, oo)) == Piecewise((zeta(2*s), 2*s > 1), + (Sum(n**(-2*s), (n, 1, oo)), True)) + assert summation(1/(n+1)**s, (n, 0, oo)) == Piecewise((zeta(s), s > 1), + (Sum((n + 1)**(-s), (n, 0, oo)), True)) + assert summation(1/(n+q)**s, (n, 0, oo)) == Piecewise( + (zeta(s, q), And(q > 0, s > 1)), + (Sum((n + q)**(-s), (n, 0, oo)), True)) + assert summation(1/(n+q)**s, (n, q, oo)) == Piecewise( + (zeta(s, 2*q), And(2*q > 0, s > 1)), + (Sum((n + q)**(-s), (n, q, oo)), True)) + assert summation(1/n**2, (n, 1, oo)) == zeta(2) + assert summation(1/n**s, (n, 0, oo)) == Sum(n**(-s), (n, 0, oo)) + + +def test_Product_doit(): + assert Product(n*Integral(a**2), (n, 1, 3)).doit() == 2 * a**9 / 9 + assert Product(n*Integral(a**2), (n, 1, 3)).doit(deep=False) == \ + 6*Integral(a**2)**3 + assert product(n*Integral(a**2), (n, 1, 3)) == 6*Integral(a**2)**3 + + +def test_Sum_interface(): + assert isinstance(Sum(0, (n, 0, 2)), Sum) + assert Sum(nan, (n, 0, 2)) is nan + assert Sum(nan, (n, 0, oo)) is nan + assert Sum(0, (n, 0, 2)).doit() == 0 + assert isinstance(Sum(0, (n, 0, oo)), Sum) + assert Sum(0, (n, 0, oo)).doit() == 0 + raises(ValueError, lambda: Sum(1)) + raises(ValueError, lambda: summation(1)) + + +def test_diff(): + assert Sum(x, (x, 1, 2)).diff(x) == 0 + assert Sum(x*y, (x, 1, 2)).diff(x) == 0 + assert Sum(x*y, (y, 1, 2)).diff(x) == Sum(y, (y, 1, 2)) + e = Sum(x*y, (x, 1, a)) + assert e.diff(a) == Derivative(e, a) + assert Sum(x*y, (x, 1, 3), (a, 2, 5)).diff(y).doit() == \ + Sum(x*y, (x, 1, 3), (a, 2, 5)).doit().diff(y) == 24 + assert Sum(x, (x, 1, 2)).diff(y) == 0 + + +def test_hypersum(): + assert simplify(summation(x**n/fac(n), (n, 1, oo))) == -1 + exp(x) + assert summation((-1)**n * x**(2*n) / fac(2*n), (n, 0, oo)) == cos(x) + assert simplify(summation((-1)**n*x**(2*n + 1) / + factorial(2*n + 1), (n, 3, oo))) == -x + sin(x) + x**3/6 - x**5/120 + + assert summation(1/(n + 2)**3, (n, 1, oo)) == Rational(-9, 8) + zeta(3) + assert summation(1/n**4, (n, 1, oo)) == pi**4/90 + + s = summation(x**n*n, (n, -oo, 0)) + assert s.is_Piecewise + assert s.args[0].args[0] == -1/(x*(1 - 1/x)**2) + assert s.args[0].args[1] == (abs(1/x) < 1) + + m = Symbol('n', integer=True, positive=True) + assert summation(binomial(m, k), (k, 0, m)) == 2**m + + +def test_issue_4170(): + assert summation(1/factorial(k), (k, 0, oo)) == E + + +def test_is_commutative(): + from sympy.physics.secondquant import NO, F, Fd + m = Symbol('m', commutative=False) + for f in (Sum, Product, Integral): + assert f(z, (z, 1, 1)).is_commutative is True + assert f(z*y, (z, 1, 6)).is_commutative is True + assert f(m*x, (x, 1, 2)).is_commutative is False + + assert f(NO(Fd(x)*F(y))*z, (z, 1, 2)).is_commutative is False + + +def test_is_zero(): + for func in [Sum, Product]: + assert func(0, (x, 1, 1)).is_zero is True + assert func(x, (x, 1, 1)).is_zero is None + + assert Sum(0, (x, 1, 0)).is_zero is True + assert Product(0, (x, 1, 0)).is_zero is False + + +def test_is_number(): + # is number should not rely on evaluation or assumptions, + # it should be equivalent to `not foo.free_symbols` + assert Sum(1, (x, 1, 1)).is_number is True + assert Sum(1, (x, 1, x)).is_number is False + assert Sum(0, (x, y, z)).is_number is False + assert Sum(x, (y, 1, 2)).is_number is False + assert Sum(x, (y, 1, 1)).is_number is False + assert Sum(x, (x, 1, 2)).is_number is True + assert Sum(x*y, (x, 1, 2), (y, 1, 3)).is_number is True + + assert Product(2, (x, 1, 1)).is_number is True + assert Product(2, (x, 1, y)).is_number is False + assert Product(0, (x, y, z)).is_number is False + assert Product(1, (x, y, z)).is_number is False + assert Product(x, (y, 1, x)).is_number is False + assert Product(x, (y, 1, 2)).is_number is False + assert Product(x, (y, 1, 1)).is_number is False + assert Product(x, (x, 1, 2)).is_number is True + + +def test_free_symbols(): + for func in [Sum, Product]: + assert func(1, (x, 1, 2)).free_symbols == set() + assert func(0, (x, 1, y)).free_symbols == {y} + assert func(2, (x, 1, y)).free_symbols == {y} + assert func(x, (x, 1, 2)).free_symbols == set() + assert func(x, (x, 1, y)).free_symbols == {y} + assert func(x, (y, 1, y)).free_symbols == {x, y} + assert func(x, (y, 1, 2)).free_symbols == {x} + assert func(x, (y, 1, 1)).free_symbols == {x} + assert func(x, (y, 1, z)).free_symbols == {x, z} + assert func(x, (x, 1, y), (y, 1, 2)).free_symbols == set() + assert func(x, (x, 1, y), (y, 1, z)).free_symbols == {z} + assert func(x, (x, 1, y), (y, 1, y)).free_symbols == {y} + assert func(x, (y, 1, y), (y, 1, z)).free_symbols == {x, z} + assert Sum(1, (x, 1, y)).free_symbols == {y} + # free_symbols answers whether the object *as written* has free symbols, + # not whether the evaluated expression has free symbols + assert Product(1, (x, 1, y)).free_symbols == {y} + # don't count free symbols that are not independent of integration + # variable(s) + assert func(f(x), (f(x), 1, 2)).free_symbols == set() + assert func(f(x), (f(x), 1, x)).free_symbols == {x} + assert func(f(x), (f(x), 1, y)).free_symbols == {y} + assert func(f(x), (z, 1, y)).free_symbols == {x, y} + + +def test_conjugate_transpose(): + A, B = symbols("A B", commutative=False) + p = Sum(A*B**n, (n, 1, 3)) + assert p.adjoint().doit() == p.doit().adjoint() + assert p.conjugate().doit() == p.doit().conjugate() + assert p.transpose().doit() == p.doit().transpose() + + p = Sum(B**n*A, (n, 1, 3)) + assert p.adjoint().doit() == p.doit().adjoint() + assert p.conjugate().doit() == p.doit().conjugate() + assert p.transpose().doit() == p.doit().transpose() + + +def test_noncommutativity_honoured(): + A, B = symbols("A B", commutative=False) + M = symbols('M', integer=True, positive=True) + p = Sum(A*B**n, (n, 1, M)) + assert p.doit() == A*Piecewise((M, Eq(B, 1)), + ((B - B**(M + 1))*(1 - B)**(-1), True)) + + p = Sum(B**n*A, (n, 1, M)) + assert p.doit() == Piecewise((M, Eq(B, 1)), + ((B - B**(M + 1))*(1 - B)**(-1), True))*A + + p = Sum(B**n*A*B**n, (n, 1, M)) + assert p.doit() == p + + +def test_issue_4171(): + assert summation(factorial(2*k + 1)/factorial(2*k), (k, 0, oo)) is oo + assert summation(2*k + 1, (k, 0, oo)) is oo + + +def test_issue_6273(): + assert Sum(x, (x, 1, n)).n(2, subs={n: 1}) == Float(1, 2) + + +def test_issue_6274(): + assert Sum(x, (x, 1, 0)).doit() == 0 + assert NS(Sum(x, (x, 1, 0))) == '0' + assert Sum(n, (n, 10, 5)).doit() == -30 + assert NS(Sum(n, (n, 10, 5))) == '-30.0000000000000' + + +def test_simplify_sum(): + y, t, v = symbols('y, t, v') + + _simplify = lambda e: simplify(e, doit=False) + assert _simplify(Sum(x*y, (x, n, m), (y, a, k)) + \ + Sum(y, (x, n, m), (y, a, k))) == Sum(y * (x + 1), (x, n, m), (y, a, k)) + assert _simplify(Sum(x, (x, n, m)) + Sum(x, (x, m + 1, a))) == \ + Sum(x, (x, n, a)) + assert _simplify(Sum(x, (x, k + 1, a)) + Sum(x, (x, n, k))) == \ + Sum(x, (x, n, a)) + assert _simplify(Sum(x, (x, k + 1, a)) + Sum(x + 1, (x, n, k))) == \ + Sum(x, (x, n, a)) + Sum(1, (x, n, k)) + assert _simplify(Sum(x, (x, 0, 3)) * 3 + 3 * Sum(x, (x, 4, 6)) + \ + 4 * Sum(z, (z, 0, 1))) == 4*Sum(z, (z, 0, 1)) + 3*Sum(x, (x, 0, 6)) + assert _simplify(3*Sum(x**2, (x, a, b)) + Sum(x, (x, a, b))) == \ + Sum(x*(3*x + 1), (x, a, b)) + assert _simplify(Sum(x**3, (x, n, k)) * 3 + 3 * Sum(x, (x, n, k)) + \ + 4 * y * Sum(z, (z, n, k))) + 1 == \ + 4*y*Sum(z, (z, n, k)) + 3*Sum(x**3 + x, (x, n, k)) + 1 + assert _simplify(Sum(x, (x, a, b)) + 1 + Sum(x, (x, b + 1, c))) == \ + 1 + Sum(x, (x, a, c)) + assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + \ + Sum(x, (t, b+1, c))) == x * Sum(1, (t, a, c)) + y * Sum(1, (t, a, b)) + assert _simplify(Sum(x, (t, a, b)) + Sum(x, (t, b+1, c)) + \ + Sum(y, (t, a, b))) == x * Sum(1, (t, a, c)) + y * Sum(1, (t, a, b)) + assert _simplify(Sum(x, (t, a, b)) + 2 * Sum(x, (t, b+1, c))) == \ + _simplify(Sum(x, (t, a, b)) + Sum(x, (t, b+1, c)) + Sum(x, (t, b+1, c))) + assert _simplify(Sum(x, (x, a, b))*Sum(x**2, (x, a, b))) == \ + Sum(x, (x, a, b)) * Sum(x**2, (x, a, b)) + assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + Sum(z, (t, a, b))) \ + == (x + y + z) * Sum(1, (t, a, b)) # issue 8596 + assert _simplify(Sum(x, (t, a, b)) + Sum(y, (t, a, b)) + Sum(z, (t, a, b)) + \ + Sum(v, (t, a, b))) == (x + y + z + v) * Sum(1, (t, a, b)) # issue 8596 + assert _simplify(Sum(x * y, (x, a, b)) / (3 * y)) == \ + (Sum(x, (x, a, b)) / 3) + assert _simplify(Sum(f(x) * y * z, (x, a, b)) / (y * z)) \ + == Sum(f(x), (x, a, b)) + assert _simplify(Sum(c * x, (x, a, b)) - c * Sum(x, (x, a, b))) == 0 + assert _simplify(c * (Sum(x, (x, a, b)) + y)) == c * (y + Sum(x, (x, a, b))) + assert _simplify(c * (Sum(x, (x, a, b)) + y * Sum(x, (x, a, b)))) == \ + c * (y + 1) * Sum(x, (x, a, b)) + assert _simplify(Sum(Sum(c * x, (x, a, b)), (y, a, b))) == \ + c * Sum(x, (x, a, b), (y, a, b)) + assert _simplify(Sum((3 + y) * Sum(c * x, (x, a, b)), (y, a, b))) == \ + c * Sum((3 + y), (y, a, b)) * Sum(x, (x, a, b)) + assert _simplify(Sum((3 + t) * Sum(c * t, (x, a, b)), (y, a, b))) == \ + c*t*(t + 3)*Sum(1, (x, a, b))*Sum(1, (y, a, b)) + assert _simplify(Sum(Sum(d * t, (x, a, b - 1)) + \ + Sum(d * t, (x, b, c)), (t, a, b))) == \ + d * Sum(1, (x, a, c)) * Sum(t, (t, a, b)) + assert _simplify(Sum(sin(t)**2 + cos(t)**2 + 1, (t, a, b))) == \ + 2 * Sum(1, (t, a, b)) + + +def test_change_index(): + b, v, w = symbols('b, v, w', integer = True) + + assert Sum(x, (x, a, b)).change_index(x, x + 1, y) == \ + Sum(y - 1, (y, a + 1, b + 1)) + assert Sum(x**2, (x, a, b)).change_index( x, x - 1) == \ + Sum((x+1)**2, (x, a - 1, b - 1)) + assert Sum(x**2, (x, a, b)).change_index( x, -x, y) == \ + Sum((-y)**2, (y, -b, -a)) + assert Sum(x, (x, a, b)).change_index( x, -x - 1) == \ + Sum(-x - 1, (x, -b - 1, -a - 1)) + assert Sum(x*y, (x, a, b), (y, c, d)).change_index( x, x - 1, z) == \ + Sum((z + 1)*y, (z, a - 1, b - 1), (y, c, d)) + assert Sum(x, (x, a, b)).change_index( x, x + v) == \ + Sum(-v + x, (x, a + v, b + v)) + assert Sum(x, (x, a, b)).change_index( x, -x - v) == \ + Sum(-v - x, (x, -b - v, -a - v)) + assert Sum(x, (x, a, b)).change_index(x, w*x, v) == \ + Sum(v/w, (v, b*w, a*w)) + raises(ValueError, lambda: Sum(x, (x, a, b)).change_index(x, 2*x)) + + +def test_reorder(): + b, y, c, d, z = symbols('b, y, c, d, z', integer = True) + + assert Sum(x*y, (x, a, b), (y, c, d)).reorder((0, 1)) == \ + Sum(x*y, (y, c, d), (x, a, b)) + assert Sum(x, (x, a, b), (x, c, d)).reorder((0, 1)) == \ + Sum(x, (x, c, d), (x, a, b)) + assert Sum(x*y + z, (x, a, b), (z, m, n), (y, c, d)).reorder(\ + (2, 0), (0, 1)) == Sum(x*y + z, (z, m, n), (y, c, d), (x, a, b)) + assert Sum(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\ + (0, 1), (1, 2), (0, 2)) == Sum(x*y*z, (x, a, b), (z, m, n), (y, c, d)) + assert Sum(x*y*z, (x, a, b), (y, c, d), (z, m, n)).reorder(\ + (x, y), (y, z), (x, z)) == Sum(x*y*z, (x, a, b), (z, m, n), (y, c, d)) + assert Sum(x*y, (x, a, b), (y, c, d)).reorder((x, 1)) == \ + Sum(x*y, (y, c, d), (x, a, b)) + assert Sum(x*y, (x, a, b), (y, c, d)).reorder((y, x)) == \ + Sum(x*y, (y, c, d), (x, a, b)) + + +def test_reverse_order(): + assert Sum(x, (x, 0, 3)).reverse_order(0) == Sum(-x, (x, 4, -1)) + assert Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(0, 1) == \ + Sum(x*y, (x, 6, 0), (y, 7, -1)) + assert Sum(x, (x, 1, 2)).reverse_order(0) == Sum(-x, (x, 3, 0)) + assert Sum(x, (x, 1, 3)).reverse_order(0) == Sum(-x, (x, 4, 0)) + assert Sum(x, (x, 1, a)).reverse_order(0) == Sum(-x, (x, a + 1, 0)) + assert Sum(x, (x, a, 5)).reverse_order(0) == Sum(-x, (x, 6, a - 1)) + assert Sum(x, (x, a + 1, a + 5)).reverse_order(0) == \ + Sum(-x, (x, a + 6, a)) + assert Sum(x, (x, a + 1, a + 2)).reverse_order(0) == \ + Sum(-x, (x, a + 3, a)) + assert Sum(x, (x, a + 1, a + 1)).reverse_order(0) == \ + Sum(-x, (x, a + 2, a)) + assert Sum(x, (x, a, b)).reverse_order(0) == Sum(-x, (x, b + 1, a - 1)) + assert Sum(x, (x, a, b)).reverse_order(x) == Sum(-x, (x, b + 1, a - 1)) + assert Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(x, 1) == \ + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + assert Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order(y, x) == \ + Sum(x*y, (x, b + 1, a - 1), (y, 6, 1)) + + +def test_issue_7097(): + assert sum(x**n/n for n in range(1, 401)) == summation(x**n/n, (n, 1, 400)) + + +def test_factor_expand_subs(): + # test factoring + assert Sum(4 * x, (x, 1, y)).factor() == 4 * Sum(x, (x, 1, y)) + assert Sum(x * a, (x, 1, y)).factor() == a * Sum(x, (x, 1, y)) + assert Sum(4 * x * a, (x, 1, y)).factor() == 4 * a * Sum(x, (x, 1, y)) + assert Sum(4 * x * y, (x, 1, y)).factor() == 4 * y * Sum(x, (x, 1, y)) + + # test expand + _x = Symbol('x', zero=False) + assert Sum(x+1,(x,1,y)).expand() == Sum(x,(x,1,y)) + Sum(1,(x,1,y)) + assert Sum(x+a*x**2,(x,1,y)).expand() == Sum(x,(x,1,y)) + Sum(a*x**2,(x,1,y)) + assert Sum(_x**(n + 1)*(n + 1), (n, -1, oo)).expand() \ + == Sum(n*_x*_x**n + _x*_x**n, (n, -1, oo)) + assert Sum(x**(n + 1)*(n + 1), (n, -1, oo)).expand(power_exp=False) \ + == Sum(n*x**(n + 1) + x**(n + 1), (n, -1, oo)) + assert Sum(x**(n + 1)*(n + 1), (n, -1, oo)).expand(force=True) \ + == Sum(x*x**n, (n, -1, oo)) + Sum(n*x*x**n, (n, -1, oo)) + assert Sum(a*n+a*n**2,(n,0,4)).expand() \ + == Sum(a*n,(n,0,4)) + Sum(a*n**2,(n,0,4)) + assert Sum(_x**a*_x**n,(x,0,3)) \ + == Sum(_x**(a+n),(x,0,3)).expand(power_exp=True) + _a, _n = symbols('a n', positive=True) + assert Sum(x**(_a+_n),(x,0,3)).expand(power_exp=True) \ + == Sum(x**_a*x**_n, (x, 0, 3)) + assert Sum(x**(_a-_n),(x,0,3)).expand(power_exp=True) \ + == Sum(x**(_a-_n),(x,0,3)).expand(power_exp=False) + + # test subs + assert Sum(1/(1+a*x**2),(x,0,3)).subs([(a,3)]) == Sum(1/(1+3*x**2),(x,0,3)) + assert Sum(x*y,(x,0,y),(y,0,x)).subs([(x,3)]) == Sum(x*y,(x,0,y),(y,0,3)) + assert Sum(x,(x,1,10)).subs([(x,y-2)]) == Sum(x,(x,1,10)) + assert Sum(1/x,(x,1,10)).subs([(x,(3+n)**3)]) == Sum(1/x,(x,1,10)) + assert Sum(1/x,(x,1,10)).subs([(x,3*x-2)]) == Sum(1/x,(x,1,10)) + + +def test_distribution_over_equality(): + assert Product(Eq(x*2, f(x)), (x, 1, 3)).doit() == Eq(48, f(1)*f(2)*f(3)) + assert Sum(Eq(f(x), x**2), (x, 0, y)) == \ + Eq(Sum(f(x), (x, 0, y)), Sum(x**2, (x, 0, y))) + + +def test_issue_2787(): + n, k = symbols('n k', positive=True, integer=True) + p = symbols('p', positive=True) + binomial_dist = binomial(n, k)*p**k*(1 - p)**(n - k) + s = Sum(binomial_dist*k, (k, 0, n)) + res = s.doit().simplify() + ans = Piecewise( + (n*p, x), + (Sum(k*p**k*binomial(n, k)*(1 - p)**(n - k), (k, 0, n)), + True)).subs(x, (Eq(n, 1) | (n > 1)) & (p/Abs(p - 1) <= 1)) + ans2 = Piecewise( + (n*p, x), + (factorial(n)*Sum(p**k*(1 - p)**(-k + n)/ + (factorial(-k + n)*factorial(k - 1)), (k, 0, n)), + True)).subs(x, (Eq(n, 1) | (n > 1)) & (p/Abs(p - 1) <= 1)) + assert res in [ans, ans2] # XXX system dependent + # Issue #17165: make sure that another simplify does not complicate + # the result by much. Why didn't first simplify replace + # Eq(n, 1) | (n > 1) with True? + assert res.simplify().count_ops() <= res.count_ops() + 2 + + +def test_issue_4668(): + assert summation(1/n, (n, 2, oo)) is oo + + +def test_matrix_sum(): + A = Matrix([[0, 1], [n, 0]]) + + result = Sum(A, (n, 0, 3)).doit() + assert result == Matrix([[0, 4], [6, 0]]) + assert result.__class__ == ImmutableDenseMatrix + + A = SparseMatrix([[0, 1], [n, 0]]) + + result = Sum(A, (n, 0, 3)).doit() + assert result.__class__ == ImmutableSparseMatrix + + +def test_failing_matrix_sum(): + n = Symbol('n') + # TODO Implement matrix geometric series summation. + A = Matrix([[0, 1, 0], [-1, 0, 0], [0, 0, 0]]) + assert Sum(A ** n, (n, 1, 4)).doit() == \ + Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]]) + # issue sympy/sympy#16989 + assert summation(A**n, (n, 1, 1)) == A + + +def test_indexed_idx_sum(): + i = symbols('i', cls=Idx) + r = Indexed('r', i) + assert Sum(r, (i, 0, 3)).doit() == sum(r.xreplace({i: j}) for j in range(4)) + assert Product(r, (i, 0, 3)).doit() == prod([r.xreplace({i: j}) for j in range(4)]) + + j = symbols('j', integer=True) + assert Sum(r, (i, j, j+2)).doit() == sum(r.xreplace({i: j+k}) for k in range(3)) + assert Product(r, (i, j, j+2)).doit() == prod([r.xreplace({i: j+k}) for k in range(3)]) + + k = Idx('k', range=(1, 3)) + A = IndexedBase('A') + assert Sum(A[k], k).doit() == sum(A[Idx(j, (1, 3))] for j in range(1, 4)) + assert Product(A[k], k).doit() == prod([A[Idx(j, (1, 3))] for j in range(1, 4)]) + + raises(ValueError, lambda: Sum(A[k], (k, 1, 4))) + raises(ValueError, lambda: Sum(A[k], (k, 0, 3))) + raises(ValueError, lambda: Sum(A[k], (k, 2, oo))) + + raises(ValueError, lambda: Product(A[k], (k, 1, 4))) + raises(ValueError, lambda: Product(A[k], (k, 0, 3))) + raises(ValueError, lambda: Product(A[k], (k, 2, oo))) + + +@slow +def test_is_convergent(): + # divergence tests -- + assert Sum(n/(2*n + 1), (n, 1, oo)).is_convergent() is S.false + assert Sum(factorial(n)/5**n, (n, 1, oo)).is_convergent() is S.false + assert Sum(3**(-2*n - 1)*n**n, (n, 1, oo)).is_convergent() is S.false + assert Sum((-1)**n*n, (n, 3, oo)).is_convergent() is S.false + assert Sum((-1)**n, (n, 1, oo)).is_convergent() is S.false + assert Sum(log(1/n), (n, 2, oo)).is_convergent() is S.false + + # Raabe's test -- + assert Sum(Product((3*m),(m,1,n))/Product((3*m+4),(m,1,n)),(n,1,oo)).is_convergent() is S.true + + # root test -- + assert Sum((-12)**n/n, (n, 1, oo)).is_convergent() is S.false + + # integral test -- + + # p-series test -- + assert Sum(1/(n**2 + 1), (n, 1, oo)).is_convergent() is S.true + assert Sum(1/n**Rational(6, 5), (n, 1, oo)).is_convergent() is S.true + assert Sum(2/(n*sqrt(n - 1)), (n, 2, oo)).is_convergent() is S.true + assert Sum(1/(sqrt(n)*sqrt(n)), (n, 2, oo)).is_convergent() is S.false + assert Sum(factorial(n) / factorial(n+2), (n, 1, oo)).is_convergent() is S.true + assert Sum(rf(5,n)/rf(7,n),(n,1,oo)).is_convergent() is S.true + assert Sum((rf(1, n)*rf(2, n))/(rf(3, n)*factorial(n)),(n,1,oo)).is_convergent() is S.false + + # comparison test -- + assert Sum(1/(n + log(n)), (n, 1, oo)).is_convergent() is S.false + assert Sum(1/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true + assert Sum(1/(n*log(n)), (n, 2, oo)).is_convergent() is S.false + assert Sum(2/(n*log(n)*log(log(n))**2), (n, 5, oo)).is_convergent() is S.true + assert Sum(2/(n*log(n)**2), (n, 2, oo)).is_convergent() is S.true + assert Sum((n - 1)/(n**2*log(n)**3), (n, 2, oo)).is_convergent() is S.true + assert Sum(1/(n*log(n)*log(log(n))), (n, 5, oo)).is_convergent() is S.false + assert Sum((n - 1)/(n*log(n)**3), (n, 3, oo)).is_convergent() is S.false + assert Sum(2/(n**2*log(n)), (n, 2, oo)).is_convergent() is S.true + assert Sum(1/(n*sqrt(log(n))*log(log(n))), (n, 100, oo)).is_convergent() is S.false + assert Sum(log(log(n))/(n*log(n)**2), (n, 100, oo)).is_convergent() is S.true + assert Sum(log(n)/n**2, (n, 5, oo)).is_convergent() is S.true + + # alternating series tests -- + assert Sum((-1)**(n - 1)/(n**2 - 1), (n, 3, oo)).is_convergent() is S.true + + # with -negativeInfinite Limits + assert Sum(1/(n**2 + 1), (n, -oo, 1)).is_convergent() is S.true + assert Sum(1/(n - 1), (n, -oo, -1)).is_convergent() is S.false + assert Sum(1/(n**2 - 1), (n, -oo, -5)).is_convergent() is S.true + assert Sum(1/(n**2 - 1), (n, -oo, 2)).is_convergent() is S.true + assert Sum(1/(n**2 - 1), (n, -oo, oo)).is_convergent() is S.true + + # piecewise functions + f = Piecewise((n**(-2), n <= 1), (n**2, n > 1)) + assert Sum(f, (n, 1, oo)).is_convergent() is S.false + assert Sum(f, (n, -oo, oo)).is_convergent() is S.false + assert Sum(f, (n, 1, 100)).is_convergent() is S.true + #assert Sum(f, (n, -oo, 1)).is_convergent() is S.true + + # integral test + + assert Sum(log(n)/n**3, (n, 1, oo)).is_convergent() is S.true + assert Sum(-log(n)/n**3, (n, 1, oo)).is_convergent() is S.true + # the following function has maxima located at (x, y) = + # (1.2, 0.43), (3.0, -0.25) and (6.8, 0.050) + eq = (x - 2)*(x**2 - 6*x + 4)*exp(-x) + assert Sum(eq, (x, 1, oo)).is_convergent() is S.true + assert Sum(eq, (x, 1, 2)).is_convergent() is S.true + assert Sum(1/(x**3), (x, 1, oo)).is_convergent() is S.true + assert Sum(1/(x**S.Half), (x, 1, oo)).is_convergent() is S.false + + # issue 19545 + assert Sum(1/n - 3/(3*n +2), (n, 1, oo)).is_convergent() is S.true + + # issue 19836 + assert Sum(4/(n + 2) - 5/(n + 1) + 1/n,(n, 7, oo)).is_convergent() is S.true + + +def test_is_absolutely_convergent(): + assert Sum((-1)**n, (n, 1, oo)).is_absolutely_convergent() is S.false + assert Sum((-1)**n/n**2, (n, 1, oo)).is_absolutely_convergent() is S.true + + +@XFAIL +def test_convergent_failing(): + # dirichlet tests + assert Sum(sin(n)/n, (n, 1, oo)).is_convergent() is S.true + assert Sum(sin(2*n)/n, (n, 1, oo)).is_convergent() is S.true + + +def test_issue_6966(): + i, k, m = symbols('i k m', integer=True) + z_i, q_i = symbols('z_i q_i') + a_k = Sum(-q_i*z_i/k,(i,1,m)) + b_k = a_k.diff(z_i) + assert isinstance(b_k, Sum) + assert b_k == Sum(-q_i/k,(i,1,m)) + + +def test_issue_10156(): + cx = Sum(2*y**2*x, (x, 1,3)) + e = 2*y*Sum(2*cx*x**2, (x, 1, 9)) + assert e.factor() == \ + 8*y**3*Sum(x, (x, 1, 3))*Sum(x**2, (x, 1, 9)) + + +def test_issue_10973(): + assert Sum((-n + (n**3 + 1)**(S(1)/3))/log(n), (n, 1, oo)).is_convergent() is S.true + + +def test_issue_14129(): + x = Symbol('x', zero=False) + assert Sum( k*x**k, (k, 0, n-1)).doit() == \ + Piecewise((n**2/2 - n/2, Eq(x, 1)), ((n*x*x**n - + n*x**n - x*x**n + x)/(x - 1)**2, True)) + assert Sum( x**k, (k, 0, n-1)).doit() == \ + Piecewise((n, Eq(x, 1)), ((-x**n + 1)/(-x + 1), True)) + assert Sum( k*(x/y+x)**k, (k, 0, n-1)).doit() == \ + Piecewise((n*(n - 1)/2, Eq(x, y/(y + 1))), + (x*(y + 1)*(n*x*y*(x + x/y)**(n - 1) + + n*x*(x + x/y)**(n - 1) - n*y*(x + x/y)**(n - 1) - + x*y*(x + x/y)**(n - 1) - x*(x + x/y)**(n - 1) + y)/ + (x*y + x - y)**2, True)) + + +def test_issue_14112(): + assert Sum((-1)**n/sqrt(n), (n, 1, oo)).is_absolutely_convergent() is S.false + assert Sum((-1)**(2*n)/n, (n, 1, oo)).is_convergent() is S.false + assert Sum((-2)**n + (-3)**n, (n, 1, oo)).is_convergent() is S.false + + +def test_issue_14219(): + A = diag(0, 2, -3) + res = diag(1, 15, -20) + assert Sum(A**n, (n, 0, 3)).doit() == res + + +def test_sin_times_absolutely_convergent(): + assert Sum(sin(n) / n**3, (n, 1, oo)).is_convergent() is S.true + assert Sum(sin(n) * log(n) / n**3, (n, 1, oo)).is_convergent() is S.true + + +def test_issue_14111(): + assert Sum(1/log(log(n)), (n, 22, oo)).is_convergent() is S.false + + +def test_issue_14484(): + assert Sum(sin(n)/log(log(n)), (n, 22, oo)).is_convergent() is S.false + + +def test_issue_14640(): + i, n = symbols("i n", integer=True) + a, b, c = symbols("a b c", zero=False) + + assert Sum(a**-i/(a - b), (i, 0, n)).doit() == Sum( + 1/(a*a**i - a**i*b), (i, 0, n)).doit() == Piecewise( + (n + 1, Eq(1/a, 1)), + ((-a**(-n - 1) + 1)/(1 - 1/a), True))/(a - b) + + assert Sum((b*a**i - c*a**i)**-2, (i, 0, n)).doit() == Piecewise( + (n + 1, Eq(a**(-2), 1)), + ((-a**(-2*n - 2) + 1)/(1 - 1/a**2), True))/(b - c)**2 + + s = Sum(i*(a**(n - i) - b**(n - i))/(a - b), (i, 0, n)).doit() + assert not s.has(Sum) + assert s.subs({a: 2, b: 3, n: 5}) == 122 + + +def test_issue_15943(): + s = Sum(binomial(n, k)*factorial(n - k), (k, 0, n)).doit().rewrite(gamma) + assert s == -E*(n + 1)*gamma(n + 1)*lowergamma(n + 1, 1)/gamma(n + 2 + ) + E*gamma(n + 1) + assert s.simplify() == E*(factorial(n) - lowergamma(n + 1, 1)) + + +def test_Sum_dummy_eq(): + assert not Sum(x, (x, a, b)).dummy_eq(1) + assert not Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, b), (a, 1, 2))) + assert not Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, c))) + assert Sum(x, (x, a, b)).dummy_eq(Sum(x, (x, a, b))) + d = Dummy() + assert Sum(x, (x, a, d)).dummy_eq(Sum(x, (x, a, c)), c) + assert not Sum(x, (x, a, d)).dummy_eq(Sum(x, (x, a, c))) + assert Sum(x, (x, a, c)).dummy_eq(Sum(y, (y, a, c))) + assert Sum(x, (x, a, d)).dummy_eq(Sum(y, (y, a, c)), c) + assert not Sum(x, (x, a, d)).dummy_eq(Sum(y, (y, a, c))) + + +def test_issue_15852(): + assert summation(x**y*y, (y, -oo, oo)).doit() == Sum(x**y*y, (y, -oo, oo)) + + +def test_exceptions(): + S = Sum(x, (x, a, b)) + raises(ValueError, lambda: S.change_index(x, x**2, y)) + S = Sum(x, (x, a, b), (x, 1, 4)) + raises(ValueError, lambda: S.index(x)) + S = Sum(x, (x, a, b), (y, 1, 4)) + raises(ValueError, lambda: S.reorder([x])) + S = Sum(x, (x, y, b), (y, 1, 4)) + raises(ReorderError, lambda: S.reorder_limit(0, 1)) + S = Sum(x*y, (x, a, b), (y, 1, 4)) + raises(NotImplementedError, lambda: S.is_convergent()) + + +def test_sumproducts_assumptions(): + M = Symbol('M', integer=True, positive=True) + + m = Symbol('m', integer=True) + for func in [Sum, Product]: + assert func(m, (m, -M, M)).is_positive is None + assert func(m, (m, -M, M)).is_nonpositive is None + assert func(m, (m, -M, M)).is_negative is None + assert func(m, (m, -M, M)).is_nonnegative is None + assert func(m, (m, -M, M)).is_finite is True + + m = Symbol('m', integer=True, nonnegative=True) + for func in [Sum, Product]: + assert func(m, (m, 0, M)).is_positive is None + assert func(m, (m, 0, M)).is_nonpositive is None + assert func(m, (m, 0, M)).is_negative is False + assert func(m, (m, 0, M)).is_nonnegative is True + assert func(m, (m, 0, M)).is_finite is True + + m = Symbol('m', integer=True, positive=True) + for func in [Sum, Product]: + assert func(m, (m, 1, M)).is_positive is True + assert func(m, (m, 1, M)).is_nonpositive is False + assert func(m, (m, 1, M)).is_negative is False + assert func(m, (m, 1, M)).is_nonnegative is True + assert func(m, (m, 1, M)).is_finite is True + + m = Symbol('m', integer=True, negative=True) + assert Sum(m, (m, -M, -1)).is_positive is False + assert Sum(m, (m, -M, -1)).is_nonpositive is True + assert Sum(m, (m, -M, -1)).is_negative is True + assert Sum(m, (m, -M, -1)).is_nonnegative is False + assert Sum(m, (m, -M, -1)).is_finite is True + assert Product(m, (m, -M, -1)).is_positive is None + assert Product(m, (m, -M, -1)).is_nonpositive is None + assert Product(m, (m, -M, -1)).is_negative is None + assert Product(m, (m, -M, -1)).is_nonnegative is None + assert Product(m, (m, -M, -1)).is_finite is True + + m = Symbol('m', integer=True, nonpositive=True) + assert Sum(m, (m, -M, 0)).is_positive is False + assert Sum(m, (m, -M, 0)).is_nonpositive is True + assert Sum(m, (m, -M, 0)).is_negative is None + assert Sum(m, (m, -M, 0)).is_nonnegative is None + assert Sum(m, (m, -M, 0)).is_finite is True + assert Product(m, (m, -M, 0)).is_positive is None + assert Product(m, (m, -M, 0)).is_nonpositive is None + assert Product(m, (m, -M, 0)).is_negative is None + assert Product(m, (m, -M, 0)).is_nonnegative is None + assert Product(m, (m, -M, 0)).is_finite is True + + m = Symbol('m', integer=True) + assert Sum(2, (m, 0, oo)).is_positive is None + assert Sum(2, (m, 0, oo)).is_nonpositive is None + assert Sum(2, (m, 0, oo)).is_negative is None + assert Sum(2, (m, 0, oo)).is_nonnegative is None + assert Sum(2, (m, 0, oo)).is_finite is None + + assert Product(2, (m, 0, oo)).is_positive is None + assert Product(2, (m, 0, oo)).is_nonpositive is None + assert Product(2, (m, 0, oo)).is_negative is False + assert Product(2, (m, 0, oo)).is_nonnegative is None + assert Product(2, (m, 0, oo)).is_finite is None + + assert Product(0, (x, M, M-1)).is_positive is True + assert Product(0, (x, M, M-1)).is_finite is True + + +def test_expand_with_assumptions(): + M = Symbol('M', integer=True, positive=True) + x = Symbol('x', positive=True) + m = Symbol('m', nonnegative=True) + assert log(Product(x**m, (m, 0, M))).expand() == Sum(m*log(x), (m, 0, M)) + assert log(Product(exp(x**m), (m, 0, M))).expand() == Sum(x**m, (m, 0, M)) + assert log(Product(x**m, (m, 0, M))).rewrite(Sum).expand() == Sum(m*log(x), (m, 0, M)) + assert log(Product(exp(x**m), (m, 0, M))).rewrite(Sum).expand() == Sum(x**m, (m, 0, M)) + + n = Symbol('n', nonnegative=True) + i, j = symbols('i,j', positive=True, integer=True) + x, y = symbols('x,y', positive=True) + assert log(Product(x**i*y**j, (i, 1, n), (j, 1, m))).expand() \ + == Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m)) + + m = Symbol('m', nonnegative=True, integer=True) + s = Sum(x**m, (m, 0, M)) + s_as_product = s.rewrite(Product) + assert s_as_product.has(Product) + assert s_as_product == log(Product(exp(x**m), (m, 0, M))) + assert s_as_product.expand() == s + s5 = s.subs(M, 5) + s5_as_product = s5.rewrite(Product) + assert s5_as_product.has(Product) + assert s5_as_product.doit().expand() == s5.doit() + + +def test_has_finite_limits(): + x = Symbol('x') + assert Sum(1, (x, 1, 9)).has_finite_limits is True + assert Sum(1, (x, 1, oo)).has_finite_limits is False + M = Symbol('M') + assert Sum(1, (x, 1, M)).has_finite_limits is None + M = Symbol('M', positive=True) + assert Sum(1, (x, 1, M)).has_finite_limits is True + x = Symbol('x', positive=True) + M = Symbol('M') + assert Sum(1, (x, 1, M)).has_finite_limits is True + + assert Sum(1, (x, 1, M), (y, -oo, oo)).has_finite_limits is False + +def test_has_reversed_limits(): + assert Sum(1, (x, 1, 1)).has_reversed_limits is False + assert Sum(1, (x, 1, 9)).has_reversed_limits is False + assert Sum(1, (x, 1, -9)).has_reversed_limits is True + assert Sum(1, (x, 1, 0)).has_reversed_limits is True + assert Sum(1, (x, 1, oo)).has_reversed_limits is False + M = Symbol('M') + assert Sum(1, (x, 1, M)).has_reversed_limits is None + M = Symbol('M', positive=True, integer=True) + assert Sum(1, (x, 1, M)).has_reversed_limits is False + assert Sum(1, (x, 1, M), (y, -oo, oo)).has_reversed_limits is False + M = Symbol('M', negative=True) + assert Sum(1, (x, 1, M)).has_reversed_limits is True + + assert Sum(1, (x, 1, M), (y, -oo, oo)).has_reversed_limits is True + assert Sum(1, (x, oo, oo)).has_reversed_limits is None + + +def test_has_empty_sequence(): + assert Sum(1, (x, 1, 1)).has_empty_sequence is False + assert Sum(1, (x, 1, 9)).has_empty_sequence is False + assert Sum(1, (x, 1, -9)).has_empty_sequence is False + assert Sum(1, (x, 1, 0)).has_empty_sequence is True + assert Sum(1, (x, y, y - 1)).has_empty_sequence is True + assert Sum(1, (x, 3, 2), (y, -oo, oo)).has_empty_sequence is True + assert Sum(1, (y, -oo, oo), (x, 3, 2)).has_empty_sequence is True + assert Sum(1, (x, oo, oo)).has_empty_sequence is False + + +def test_empty_sequence(): + assert Product(x*y, (x, -oo, oo), (y, 1, 0)).doit() == 1 + assert Product(x*y, (y, 1, 0), (x, -oo, oo)).doit() == 1 + assert Sum(x, (x, -oo, oo), (y, 1, 0)).doit() == 0 + assert Sum(x, (y, 1, 0), (x, -oo, oo)).doit() == 0 + + +def test_issue_8016(): + k = Symbol('k', integer=True) + n, m = symbols('n, m', integer=True, positive=True) + s = Sum(binomial(m, k)*binomial(m, n - k)*(-1)**k, (k, 0, n)) + assert s.doit().simplify() == \ + cos(pi*n/2)*gamma(m + 1)/gamma(n/2 + 1)/gamma(m - n/2 + 1) + + +def test_issue_14313(): + assert Sum(S.Half**floor(n/2), (n, 1, oo)).is_convergent() + + +def test_issue_14563(): + # The assertion was failing due to no assumptions methods in Sums and Product + assert 1 % Sum(1, (x, 0, 1)) == 1 + + +def test_issue_16735(): + assert Sum(5**n/gamma(n+1), (n, 1, oo)).is_convergent() is S.true + + +def test_issue_14871(): + assert Sum((Rational(1, 10))**n*rf(0, n)/factorial(n), (n, 0, oo)).rewrite(factorial).doit() == 1 + + +def test_issue_17165(): + n = symbols("n", integer=True) + x = symbols('x') + s = (x*Sum(x**n, (n, -1, oo))) + ssimp = s.doit().simplify() + + assert ssimp == Piecewise((-1/(x - 1), (x > -1) & (x < 1)), + (x*Sum(x**n, (n, -1, oo)), True)), ssimp + assert ssimp.simplify() == ssimp + + +def test_issue_19379(): + assert Sum(factorial(n)/factorial(n + 2), (n, 1, oo)).is_convergent() is S.true + + +def test_issue_20777(): + assert Sum(exp(x*sin(n/m)), (n, 1, m)).doit() == Sum(exp(x*sin(n/m)), (n, 1, m)) + + +def test__dummy_with_inherited_properties_concrete(): + x = Symbol('x') + + from sympy.core.containers import Tuple + d = _dummy_with_inherited_properties_concrete(Tuple(x, 0, 5)) + assert d.is_real + assert d.is_integer + assert d.is_nonnegative + assert d.is_extended_nonnegative + + d = _dummy_with_inherited_properties_concrete(Tuple(x, 1, 9)) + assert d.is_real + assert d.is_integer + assert d.is_positive + assert d.is_odd is None + + d = _dummy_with_inherited_properties_concrete(Tuple(x, -5, 5)) + assert d.is_real + assert d.is_integer + assert d.is_positive is None + assert d.is_extended_nonnegative is None + assert d.is_odd is None + + d = _dummy_with_inherited_properties_concrete(Tuple(x, -1.5, 1.5)) + assert d.is_real + assert d.is_integer is None + assert d.is_positive is None + assert d.is_extended_nonnegative is None + + N = Symbol('N', integer=True, positive=True) + d = _dummy_with_inherited_properties_concrete(Tuple(x, 2, N)) + assert d.is_real + assert d.is_positive + assert d.is_integer + + # Return None if no assumptions are added + N = Symbol('N', integer=True, positive=True) + d = _dummy_with_inherited_properties_concrete(Tuple(N, 2, 4)) + assert d is None + + x = Symbol('x', negative=True) + raises(InconsistentAssumptions, + lambda: _dummy_with_inherited_properties_concrete(Tuple(x, 1, 5))) + + +def test_matrixsymbol_summation_numerical_limits(): + A = MatrixSymbol('A', 3, 3) + n = Symbol('n', integer=True) + + assert Sum(A**n, (n, 0, 2)).doit() == Identity(3) + A + A**2 + assert Sum(A, (n, 0, 2)).doit() == 3*A + assert Sum(n*A, (n, 0, 2)).doit() == 3*A + + B = Matrix([[0, n, 0], [-1, 0, 0], [0, 0, 2]]) + ans = Matrix([[0, 6, 0], [-4, 0, 0], [0, 0, 8]]) + 4*A + assert Sum(A+B, (n, 0, 3)).doit() == ans + ans = A*Matrix([[0, 6, 0], [-4, 0, 0], [0, 0, 8]]) + assert Sum(A*B, (n, 0, 3)).doit() == ans + + ans = (A**2*Matrix([[-2, 0, 0], [0,-2, 0], [0, 0, 4]]) + + A**3*Matrix([[0, -9, 0], [3, 0, 0], [0, 0, 8]]) + + A*Matrix([[0, 1, 0], [-1, 0, 0], [0, 0, 2]])) + assert Sum(A**n*B**n, (n, 1, 3)).doit() == ans + + +def test_issue_21651(): + i = Symbol('i') + a = Sum(floor(2*2**(-i)), (i, S.One, 2)) + assert a.doit() == S.One + + +@XFAIL +def test_matrixsymbol_summation_symbolic_limits(): + N = Symbol('N', integer=True, positive=True) + + A = MatrixSymbol('A', 3, 3) + n = Symbol('n', integer=True) + assert Sum(A, (n, 0, N)).doit() == (N+1)*A + assert Sum(n*A, (n, 0, N)).doit() == (N**2/2+N/2)*A + + +def test_summation_by_residues(): + x = Symbol('x') + + # Examples from Nakhle H. Asmar, Loukas Grafakos, + # Complex Analysis with Applications + assert eval_sum_residue(1 / (x**2 + 1), (x, -oo, oo)) == pi/tanh(pi) + assert eval_sum_residue(1 / x**6, (x, S(1), oo)) == pi**6/945 + assert eval_sum_residue(1 / (x**2 + 9), (x, -oo, oo)) == pi/(3*tanh(3*pi)) + assert eval_sum_residue(1 / (x**2 + 1)**2, (x, -oo, oo)).cancel() == \ + (-pi**2*tanh(pi)**2 + pi*tanh(pi) + pi**2)/(2*tanh(pi)**2) + assert eval_sum_residue(x**2 / (x**2 + 1)**2, (x, -oo, oo)).cancel() == \ + (-pi**2 + pi*tanh(pi) + pi**2*tanh(pi)**2)/(2*tanh(pi)**2) + assert eval_sum_residue(1 / (4*x**2 - 1), (x, -oo, oo)) == 0 + assert eval_sum_residue(x**2 / (x**2 - S(1)/4)**2, (x, -oo, oo)) == pi**2/2 + assert eval_sum_residue(1 / (4*x**2 - 1)**2, (x, -oo, oo)) == pi**2/8 + assert eval_sum_residue(1 / ((x - S(1)/2)**2 + 1), (x, -oo, oo)) == pi*tanh(pi) + assert eval_sum_residue(1 / x**2, (x, S(1), oo)) == pi**2/6 + assert eval_sum_residue(1 / x**4, (x, S(1), oo)) == pi**4/90 + assert eval_sum_residue(1 / x**2 / (x**2 + 4), (x, S(1), oo)) == \ + -pi*(-pi/12 - 1/(16*pi) + 1/(8*tanh(2*pi)))/2 + + # Some examples made from 1 / (x**2 + 1) + assert eval_sum_residue(1 / (x**2 + 1), (x, S(0), oo)) == \ + S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue(1 / (x**2 + 1), (x, S(1), oo)) == \ + -S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue(1 / (x**2 + 1), (x, S(-1), oo)) == \ + 1 + pi/(2*tanh(pi)) + assert eval_sum_residue((-1)**x / (x**2 + 1), (x, -oo, oo)) == \ + pi/sinh(pi) + assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(0), oo)) == \ + pi/(2*sinh(pi)) + S(1)/2 + assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(1), oo)) == \ + -S(1)/2 + pi/(2*sinh(pi)) + assert eval_sum_residue((-1)**x / (x**2 + 1), (x, S(-1), oo)) == \ + pi/(2*sinh(pi)) + + # Some examples made from shifting of 1 / (x**2 + 1) + assert eval_sum_residue(1 / (x**2 + 2*x + 2), (x, S(-1), oo)) == S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue(1 / (x**2 + 4*x + 5), (x, S(-2), oo)) == S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue(1 / (x**2 - 2*x + 2), (x, S(1), oo)) == S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue(1 / (x**2 - 4*x + 5), (x, S(2), oo)) == S(1)/2 + pi/(2*tanh(pi)) + assert eval_sum_residue((-1)**x * -1 / (x**2 + 2*x + 2), (x, S(-1), oo)) == S(1)/2 + pi/(2*sinh(pi)) + assert eval_sum_residue((-1)**x * -1 / (x**2 -2*x + 2), (x, S(1), oo)) == S(1)/2 + pi/(2*sinh(pi)) + + # Some examples made from 1 / x**2 + assert eval_sum_residue(1 / x**2, (x, S(2), oo)) == -1 + pi**2/6 + assert eval_sum_residue(1 / x**2, (x, S(3), oo)) == -S(5)/4 + pi**2/6 + assert eval_sum_residue((-1)**x / x**2, (x, S(1), oo)) == -pi**2/12 + assert eval_sum_residue((-1)**x / x**2, (x, S(2), oo)) == 1 - pi**2/12 + + +@slow +def test_summation_by_residues_failing(): + x = Symbol('x') + + # Failing because of the bug in residue computation + assert eval_sum_residue(x**2 / (x**4 + 1), (x, S(1), oo)) + assert eval_sum_residue(1 / ((x - 1)*(x - 2) + 1), (x, -oo, oo)) != 0 + + +def test_process_limits(): + from sympy.concrete.expr_with_limits import _process_limits + + # these should be (x, Range(3)) not Range(3) + raises(ValueError, lambda: _process_limits( + Range(3), discrete=True)) + raises(ValueError, lambda: _process_limits( + Range(3), discrete=False)) + # these should be (x, union) not union + # (but then we would get a TypeError because we don't + # handle non-contiguous sets: see below use of `union`) + union = Or(x < 1, x > 3).as_set() + raises(ValueError, lambda: _process_limits( + union, discrete=True)) + raises(ValueError, lambda: _process_limits( + union, discrete=False)) + + # error not triggered if not needed + assert _process_limits((x, 1, 2)) == ([(x, 1, 2)], 1) + + # this equivalence is used to detect Reals in _process_limits + assert isinstance(S.Reals, Interval) + + C = Integral # continuous limits + assert C(x, x >= 5) == C(x, (x, 5, oo)) + assert C(x, x < 3) == C(x, (x, -oo, 3)) + ans = C(x, (x, 0, 3)) + assert C(x, And(x >= 0, x < 3)) == ans + assert C(x, (x, Interval.Ropen(0, 3))) == ans + raises(TypeError, lambda: C(x, (x, Range(3)))) + + # discrete limits + for D in (Sum, Product): + r, ans = Range(3, 10, 2), D(2*x + 3, (x, 0, 3)) + assert D(x, (x, r)) == ans + assert D(x, (x, r.reversed)) == ans + r, ans = Range(3, oo, 2), D(2*x + 3, (x, 0, oo)) + assert D(x, (x, r)) == ans + assert D(x, (x, r.reversed)) == ans + r, ans = Range(-oo, 5, 2), D(3 - 2*x, (x, 0, oo)) + assert D(x, (x, r)) == ans + assert D(x, (x, r.reversed)) == ans + raises(TypeError, lambda: D(x, x > 0)) + raises(ValueError, lambda: D(x, Interval(1, 3))) + raises(NotImplementedError, lambda: D(x, (x, union))) + + +def test_pr_22677(): + b = Symbol('b', integer=True, positive=True) + assert Sum(1/x**2,(x, 0, b)).doit() == Sum(x**(-2), (x, 0, b)) + assert Sum(1/(x - b)**2,(x, 0, b-1)).doit() == Sum( + (-b + x)**(-2), (x, 0, b - 1)) + + +def test_issue_23952(): + p, q = symbols("p q", real=True, nonnegative=True) + k1, k2 = symbols("k1 k2", integer=True, nonnegative=True) + n = Symbol("n", integer=True, positive=True) + expr = Sum(abs(k1 - k2)*p**k1 *(1 - q)**(n - k2), + (k1, 0, n), (k2, 0, n)) + assert expr.subs(p,0).subs(q,1).subs(n, 3).doit() == 3 diff --git a/lib/python3.11/site-packages/sympy/conftest.py b/lib/python3.11/site-packages/sympy/conftest.py new file mode 100644 index 0000000000000000000000000000000000000000..788ec7ed8a38de422b76c4ac19057513670d2d38 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/conftest.py @@ -0,0 +1,96 @@ +import sys + +sys._running_pytest = True # type: ignore +from sympy.external.importtools import version_tuple + +import pytest +from sympy.core.cache import clear_cache, USE_CACHE +from sympy.external.gmpy import GROUND_TYPES +from sympy.utilities.misc import ARCH +import re + +try: + import hypothesis + + hypothesis.settings.register_profile("sympy_hypothesis_profile", deadline=None) + hypothesis.settings.load_profile("sympy_hypothesis_profile") +except ImportError: + raise ImportError( + "hypothesis is a required dependency to run the SymPy test suite. " + "Install it with 'pip install hypothesis' or 'conda install -c conda-forge hypothesis'" + ) + + +sp = re.compile(r"([0-9]+)/([1-9][0-9]*)") + + +def process_split(config, items): + split = config.getoption("--split") + if not split: + return + m = sp.match(split) + if not m: + raise ValueError( + "split must be a string of the form a/b " "where a and b are ints." + ) + i, t = map(int, m.groups()) + start, end = (i - 1) * len(items) // t, i * len(items) // t + + if i < t: + # remove elements from end of list first + del items[end:] + del items[:start] + + +def pytest_report_header(config): + s = "architecture: %s\n" % ARCH + s += "cache: %s\n" % USE_CACHE + version = "" + if GROUND_TYPES == "gmpy": + import gmpy2 + + version = gmpy2.version() + elif GROUND_TYPES == "flint": + try: + from flint import __version__ + except ImportError: + version = "unknown" + else: + version = f'(python-flint=={__version__})' + s += "ground types: %s %s\n" % (GROUND_TYPES, version) + return s + + +def pytest_terminal_summary(terminalreporter): + if terminalreporter.stats.get("error", None) or terminalreporter.stats.get( + "failed", None + ): + terminalreporter.write_sep(" ", "DO *NOT* COMMIT!", red=True, bold=True) + + +def pytest_addoption(parser): + parser.addoption("--split", action="store", default="", help="split tests") + + +def pytest_collection_modifyitems(config, items): + """pytest hook.""" + # handle splits + process_split(config, items) + + +@pytest.fixture(autouse=True, scope="module") +def file_clear_cache(): + clear_cache() + + +@pytest.fixture(autouse=True, scope="module") +def check_disabled(request): + if getattr(request.module, "disabled", False): + pytest.skip("test requirements not met.") + elif getattr(request.module, "ipython", False): + # need to check version and options for ipython tests + if ( + version_tuple(pytest.__version__) < version_tuple("2.6.3") + and pytest.config.getvalue("-s") != "no" + ): + pytest.skip("run py.test with -s or upgrade to newer version.") diff --git a/lib/python3.11/site-packages/sympy/core/__init__.py b/lib/python3.11/site-packages/sympy/core/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..4c03c9fc11479bb6d93a3bff3dfd0992ef994a19 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/__init__.py @@ -0,0 +1,103 @@ +"""Core module. Provides the basic operations needed in sympy. +""" + +from .sympify import sympify, SympifyError +from .cache import cacheit +from .assumptions import assumptions, check_assumptions, failing_assumptions, common_assumptions +from .basic import Basic, Atom +from .singleton import S +from .expr import Expr, AtomicExpr, UnevaluatedExpr +from .symbol import Symbol, Wild, Dummy, symbols, var +from .numbers import Number, Float, Rational, Integer, NumberSymbol, \ + RealNumber, igcd, ilcm, seterr, E, I, nan, oo, pi, zoo, \ + AlgebraicNumber, comp, mod_inverse +from .power import Pow +from .intfunc import integer_nthroot, integer_log, num_digits, trailing +from .mul import Mul, prod +from .add import Add +from .mod import Mod +from .relational import ( Rel, Eq, Ne, Lt, Le, Gt, Ge, + Equality, GreaterThan, LessThan, Unequality, StrictGreaterThan, + StrictLessThan ) +from .multidimensional import vectorize +from .function import Lambda, WildFunction, Derivative, diff, FunctionClass, \ + Function, Subs, expand, PoleError, count_ops, \ + expand_mul, expand_log, expand_func, \ + expand_trig, expand_complex, expand_multinomial, nfloat, \ + expand_power_base, expand_power_exp, arity +from .evalf import PrecisionExhausted, N +from .containers import Tuple, Dict +from .exprtools import gcd_terms, factor_terms, factor_nc +from .parameters import evaluate +from .kind import UndefinedKind, NumberKind, BooleanKind +from .traversal import preorder_traversal, bottom_up, use, postorder_traversal +from .sorting import default_sort_key, ordered + +# expose singletons +Catalan = S.Catalan +EulerGamma = S.EulerGamma +GoldenRatio = S.GoldenRatio +TribonacciConstant = S.TribonacciConstant + +__all__ = [ + 'sympify', 'SympifyError', + + 'cacheit', + + 'assumptions', 'check_assumptions', 'failing_assumptions', + 'common_assumptions', + + 'Basic', 'Atom', + + 'S', + + 'Expr', 'AtomicExpr', 'UnevaluatedExpr', + + 'Symbol', 'Wild', 'Dummy', 'symbols', 'var', + + 'Number', 'Float', 'Rational', 'Integer', 'NumberSymbol', 'RealNumber', + 'igcd', 'ilcm', 'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo', + 'AlgebraicNumber', 'comp', 'mod_inverse', + + 'Pow', + + 'integer_nthroot', 'integer_log', 'num_digits', 'trailing', + + 'Mul', 'prod', + + 'Add', + + 'Mod', + + 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality', 'GreaterThan', + 'LessThan', 'Unequality', 'StrictGreaterThan', 'StrictLessThan', + + 'vectorize', + + 'Lambda', 'WildFunction', 'Derivative', 'diff', 'FunctionClass', + 'Function', 'Subs', 'expand', 'PoleError', 'count_ops', 'expand_mul', + 'expand_log', 'expand_func', 'expand_trig', 'expand_complex', + 'expand_multinomial', 'nfloat', 'expand_power_base', 'expand_power_exp', + 'arity', + + 'PrecisionExhausted', 'N', + + 'evalf', # The module? + + 'Tuple', 'Dict', + + 'gcd_terms', 'factor_terms', 'factor_nc', + + 'evaluate', + + 'Catalan', + 'EulerGamma', + 'GoldenRatio', + 'TribonacciConstant', + + 'UndefinedKind', 'NumberKind', 'BooleanKind', + + 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Natively Python uses ``repr()`` + even if ``str()`` was explicitly requested. Mix in this trait into + a class to get proper default printing. + + This also adds support for LaTeX printing in jupyter notebooks. + """ + + # Since this class is used as a mixin we set empty slots. That means that + # instances of any subclasses that use slots will not need to have a + # __dict__. + __slots__ = () + + # Note, we always use the default ordering (lex) in __str__ and __repr__, + # regardless of the global setting. See issue 5487. + def __str__(self): + from sympy.printing.str import sstr + return sstr(self, order=None) + + __repr__ = __str__ + + def _repr_disabled(self): + """ + No-op repr function used to disable jupyter display hooks. + + When :func:`sympy.init_printing` is used to disable certain display + formats, this function is copied into the appropriate ``_repr_*_`` + attributes. + + While we could just set the attributes to `None``, doing it this way + allows derived classes to call `super()`. + """ + return None + + # We don't implement _repr_png_ here because it would add a large amount of + # data to any notebook containing SymPy expressions, without adding + # anything useful to the notebook. It can still enabled manually, e.g., + # for the qtconsole, with init_printing(). + _repr_png_ = _repr_disabled + + _repr_svg_ = _repr_disabled + + def _repr_latex_(self): + """ + IPython/Jupyter LaTeX printing + + To change the behavior of this (e.g., pass in some settings to LaTeX), + use init_printing(). init_printing() will also enable LaTeX printing + for built in numeric types like ints and container types that contain + SymPy objects, like lists and dictionaries of expressions. + """ + from sympy.printing.latex import latex + s = latex(self, mode='plain') + return "$\\displaystyle %s$" % s diff --git a/lib/python3.11/site-packages/sympy/core/add.py b/lib/python3.11/site-packages/sympy/core/add.py new file mode 100644 index 0000000000000000000000000000000000000000..43d7fd72c73f1cf9d01e8467f0af2c2cc9947ec7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/add.py @@ -0,0 +1,1284 @@ +from typing import Tuple as tTuple +from collections import defaultdict +from functools import reduce +from operator import attrgetter +from .basic import _args_sortkey +from .parameters import global_parameters +from .logic import _fuzzy_group, fuzzy_or, fuzzy_not +from .singleton import S +from .operations import AssocOp, AssocOpDispatcher +from .cache import cacheit +from .numbers import equal_valued +from .intfunc import ilcm, igcd +from .expr import Expr +from .kind import UndefinedKind +from sympy.utilities.iterables import is_sequence, sift + +def _could_extract_minus_sign(expr): + # assume expr is Add-like + # We choose the one with less arguments with minus signs + negative_args = sum(1 for i in expr.args + if i.could_extract_minus_sign()) + positive_args = len(expr.args) - negative_args + if positive_args > negative_args: + return False + elif positive_args < negative_args: + return True + # choose based on .sort_key() to prefer + # x - 1 instead of 1 - x and + # 3 - sqrt(2) instead of -3 + sqrt(2) + return bool(expr.sort_key() < (-expr).sort_key()) + + +def _addsort(args): + # in-place sorting of args + args.sort(key=_args_sortkey) + + +def _unevaluated_Add(*args): + """Return a well-formed unevaluated Add: Numbers are collected and + put in slot 0 and args are sorted. Use this when args have changed + but you still want to return an unevaluated Add. + + Examples + ======== + + >>> from sympy.core.add import _unevaluated_Add as uAdd + >>> from sympy import S, Add + >>> from sympy.abc import x, y + >>> a = uAdd(*[S(1.0), x, S(2)]) + >>> a.args[0] + 3.00000000000000 + >>> a.args[1] + x + + Beyond the Number being in slot 0, there is no other assurance of + order for the arguments since they are hash sorted. So, for testing + purposes, output produced by this in some other function can only + be tested against the output of this function or as one of several + options: + + >>> opts = (Add(x, y, evaluate=False), Add(y, x, evaluate=False)) + >>> a = uAdd(x, y) + >>> assert a in opts and a == uAdd(x, y) + >>> uAdd(x + 1, x + 2) + x + x + 3 + """ + args = list(args) + newargs = [] + co = S.Zero + while args: + a = args.pop() + if a.is_Add: + # this will keep nesting from building up + # so that x + (x + 1) -> x + x + 1 (3 args) + args.extend(a.args) + elif a.is_Number: + co += a + else: + newargs.append(a) + _addsort(newargs) + if co: + newargs.insert(0, co) + return Add._from_args(newargs) + + +class Add(Expr, AssocOp): + """ + Expression representing addition operation for algebraic group. + + .. deprecated:: 1.7 + + Using arguments that aren't subclasses of :class:`~.Expr` in core + operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is + deprecated. See :ref:`non-expr-args-deprecated` for details. + + Every argument of ``Add()`` must be ``Expr``. Infix operator ``+`` + on most scalar objects in SymPy calls this class. + + Another use of ``Add()`` is to represent the structure of abstract + addition so that its arguments can be substituted to return different + class. Refer to examples section for this. + + ``Add()`` evaluates the argument unless ``evaluate=False`` is passed. + The evaluation logic includes: + + 1. Flattening + ``Add(x, Add(y, z))`` -> ``Add(x, y, z)`` + + 2. Identity removing + ``Add(x, 0, y)`` -> ``Add(x, y)`` + + 3. Coefficient collecting by ``.as_coeff_Mul()`` + ``Add(x, 2*x)`` -> ``Mul(3, x)`` + + 4. Term sorting + ``Add(y, x, 2)`` -> ``Add(2, x, y)`` + + If no argument is passed, identity element 0 is returned. If single + element is passed, that element is returned. + + Note that ``Add(*args)`` is more efficient than ``sum(args)`` because + it flattens the arguments. ``sum(a, b, c, ...)`` recursively adds the + arguments as ``a + (b + (c + ...))``, which has quadratic complexity. + On the other hand, ``Add(a, b, c, d)`` does not assume nested + structure, making the complexity linear. + + Since addition is group operation, every argument should have the + same :obj:`sympy.core.kind.Kind()`. + + Examples + ======== + + >>> from sympy import Add, I + >>> from sympy.abc import x, y + >>> Add(x, 1) + x + 1 + >>> Add(x, x) + 2*x + >>> 2*x**2 + 3*x + I*y + 2*y + 2*x/5 + 1.0*y + 1 + 2*x**2 + 17*x/5 + 3.0*y + I*y + 1 + + If ``evaluate=False`` is passed, result is not evaluated. + + >>> Add(1, 2, evaluate=False) + 1 + 2 + >>> Add(x, x, evaluate=False) + x + x + + ``Add()`` also represents the general structure of addition operation. + + >>> from sympy import MatrixSymbol + >>> A,B = MatrixSymbol('A', 2,2), MatrixSymbol('B', 2,2) + >>> expr = Add(x,y).subs({x:A, y:B}) + >>> expr + A + B + >>> type(expr) + + + Note that the printers do not display in args order. + + >>> Add(x, 1) + x + 1 + >>> Add(x, 1).args + (1, x) + + See Also + ======== + + MatAdd + + """ + + __slots__ = () + + args: tTuple[Expr, ...] + + is_Add = True + + _args_type = Expr + + @classmethod + def flatten(cls, seq): + """ + Takes the sequence "seq" of nested Adds and returns a flatten list. + + Returns: (commutative_part, noncommutative_part, order_symbols) + + Applies associativity, all terms are commutable with respect to + addition. + + NB: the removal of 0 is already handled by AssocOp.__new__ + + See Also + ======== + + sympy.core.mul.Mul.flatten + + """ + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.matrices.expressions import MatrixExpr + from sympy.tensor.tensor import TensExpr + rv = None + if len(seq) == 2: + a, b = seq + if b.is_Rational: + a, b = b, a + if a.is_Rational: + if b.is_Mul: + rv = [a, b], [], None + if rv: + if all(s.is_commutative for s in rv[0]): + return rv + return [], rv[0], None + + terms = {} # term -> coeff + # e.g. x**2 -> 5 for ... + 5*x**2 + ... + + coeff = S.Zero # coefficient (Number or zoo) to always be in slot 0 + # e.g. 3 + ... + order_factors = [] + + extra = [] + + for o in seq: + + # O(x) + if o.is_Order: + if o.expr.is_zero: + continue + for o1 in order_factors: + if o1.contains(o): + o = None + break + if o is None: + continue + order_factors = [o] + [ + o1 for o1 in order_factors if not o.contains(o1)] + continue + + # 3 or NaN + elif o.is_Number: + if (o is S.NaN or coeff is S.ComplexInfinity and + o.is_finite is False) and not extra: + # we know for sure the result will be nan + return [S.NaN], [], None + if coeff.is_Number or isinstance(coeff, AccumBounds): + coeff += o + if coeff is S.NaN and not extra: + # we know for sure the result will be nan + return [S.NaN], [], None + continue + + elif isinstance(o, AccumBounds): + coeff = o.__add__(coeff) + continue + + elif isinstance(o, MatrixExpr): + # can't add 0 to Matrix so make sure coeff is not 0 + extra.append(o) + continue + + elif isinstance(o, TensExpr): + coeff = o.__add__(coeff) if coeff else o + continue + + elif o is S.ComplexInfinity: + if coeff.is_finite is False and not extra: + # we know for sure the result will be nan + return [S.NaN], [], None + coeff = S.ComplexInfinity + continue + + # Add([...]) + elif o.is_Add: + # NB: here we assume Add is always commutative + seq.extend(o.args) # TODO zerocopy? + continue + + # Mul([...]) + elif o.is_Mul: + c, s = o.as_coeff_Mul() + + # check for unevaluated Pow, e.g. 2**3 or 2**(-1/2) + elif o.is_Pow: + b, e = o.as_base_exp() + if b.is_Number and (e.is_Integer or + (e.is_Rational and e.is_negative)): + seq.append(b**e) + continue + c, s = S.One, o + + else: + # everything else + c = S.One + s = o + + # now we have: + # o = c*s, where + # + # c is a Number + # s is an expression with number factor extracted + # let's collect terms with the same s, so e.g. + # 2*x**2 + 3*x**2 -> 5*x**2 + if s in terms: + terms[s] += c + if terms[s] is S.NaN and not extra: + # we know for sure the result will be nan + return [S.NaN], [], None + else: + terms[s] = c + + # now let's construct new args: + # [2*x**2, x**3, 7*x**4, pi, ...] + newseq = [] + noncommutative = False + for s, c in terms.items(): + # 0*s + if c.is_zero: + continue + # 1*s + elif c is S.One: + newseq.append(s) + # c*s + else: + if s.is_Mul: + # Mul, already keeps its arguments in perfect order. + # so we can simply put c in slot0 and go the fast way. + cs = s._new_rawargs(*((c,) + s.args)) + newseq.append(cs) + elif s.is_Add: + # we just re-create the unevaluated Mul + newseq.append(Mul(c, s, evaluate=False)) + else: + # alternatively we have to call all Mul's machinery (slow) + newseq.append(Mul(c, s)) + + noncommutative = noncommutative or not s.is_commutative + + # oo, -oo + if coeff is S.Infinity: + newseq = [f for f in newseq if not (f.is_extended_nonnegative or f.is_real)] + + elif coeff is S.NegativeInfinity: + newseq = [f for f in newseq if not (f.is_extended_nonpositive or f.is_real)] + + if coeff is S.ComplexInfinity: + # zoo might be + # infinite_real + finite_im + # finite_real + infinite_im + # infinite_real + infinite_im + # addition of a finite real or imaginary number won't be able to + # change the zoo nature; adding an infinite qualtity would result + # in a NaN condition if it had sign opposite of the infinite + # portion of zoo, e.g., infinite_real - infinite_real. + newseq = [c for c in newseq if not (c.is_finite and + c.is_extended_real is not None)] + + # process O(x) + if order_factors: + newseq2 = [] + for t in newseq: + for o in order_factors: + # x + O(x) -> O(x) + if o.contains(t): + t = None + break + # x + O(x**2) -> x + O(x**2) + if t is not None: + newseq2.append(t) + newseq = newseq2 + order_factors + # 1 + O(1) -> O(1) + for o in order_factors: + if o.contains(coeff): + coeff = S.Zero + break + + # order args canonically + _addsort(newseq) + + # current code expects coeff to be first + if coeff is not S.Zero: + newseq.insert(0, coeff) + + if extra: + newseq += extra + noncommutative = True + + # we are done + if noncommutative: + return [], newseq, None + else: + return newseq, [], None + + @classmethod + def class_key(cls): + return 3, 1, cls.__name__ + + @property + def kind(self): + k = attrgetter('kind') + kinds = map(k, self.args) + kinds = frozenset(kinds) + if len(kinds) != 1: + # Since addition is group operator, kind must be same. + # We know that this is unexpected signature, so return this. + result = UndefinedKind + else: + result, = kinds + return result + + def could_extract_minus_sign(self): + return _could_extract_minus_sign(self) + + @cacheit + def as_coeff_add(self, *deps): + """ + Returns a tuple (coeff, args) where self is treated as an Add and coeff + is the Number term and args is a tuple of all other terms. + + Examples + ======== + + >>> from sympy.abc import x + >>> (7 + 3*x).as_coeff_add() + (7, (3*x,)) + >>> (7*x).as_coeff_add() + (0, (7*x,)) + """ + if deps: + l1, l2 = sift(self.args, lambda x: x.has_free(*deps), binary=True) + return self._new_rawargs(*l2), tuple(l1) + coeff, notrat = self.args[0].as_coeff_add() + if coeff is not S.Zero: + return coeff, notrat + self.args[1:] + return S.Zero, self.args + + def as_coeff_Add(self, rational=False, deps=None): + """ + Efficiently extract the coefficient of a summation. + """ + coeff, args = self.args[0], self.args[1:] + + if coeff.is_Number and not rational or coeff.is_Rational: + return coeff, self._new_rawargs(*args) + return S.Zero, self + + # Note, we intentionally do not implement Add.as_coeff_mul(). Rather, we + # let Expr.as_coeff_mul() just always return (S.One, self) for an Add. See + # issue 5524. + + def _eval_power(self, e): + from .evalf import pure_complex + from .relational import is_eq + if len(self.args) == 2 and any(_.is_infinite for _ in self.args): + if e.is_zero is False and is_eq(e, S.One) is False: + # looking for literal a + I*b + a, b = self.args + if a.coeff(S.ImaginaryUnit): + a, b = b, a + ico = b.coeff(S.ImaginaryUnit) + if ico and ico.is_extended_real and a.is_extended_real: + if e.is_extended_negative: + return S.Zero + if e.is_extended_positive: + return S.ComplexInfinity + return + if e.is_Rational and self.is_number: + ri = pure_complex(self) + if ri: + r, i = ri + if e.q == 2: + from sympy.functions.elementary.miscellaneous import sqrt + D = sqrt(r**2 + i**2) + if D.is_Rational: + from .exprtools import factor_terms + from sympy.functions.elementary.complexes import sign + from .function import expand_multinomial + # (r, i, D) is a Pythagorean triple + root = sqrt(factor_terms((D - r)/2))**e.p + return root*expand_multinomial(( + # principle value + (D + r)/abs(i) + sign(i)*S.ImaginaryUnit)**e.p) + elif e == -1: + return _unevaluated_Mul( + r - i*S.ImaginaryUnit, + 1/(r**2 + i**2)) + elif e.is_Number and abs(e) != 1: + # handle the Float case: (2.0 + 4*x)**e -> 4**e*(0.5 + x)**e + c, m = zip(*[i.as_coeff_Mul() for i in self.args]) + if any(i.is_Float for i in c): # XXX should this always be done? + big = -1 + for i in c: + if abs(i) >= big: + big = abs(i) + if big > 0 and not equal_valued(big, 1): + from sympy.functions.elementary.complexes import sign + bigs = (big, -big) + c = [sign(i) if i in bigs else i/big for i in c] + addpow = Add(*[c*m for c, m in zip(c, m)])**e + return big**e*addpow + + @cacheit + def _eval_derivative(self, s): + return self.func(*[a.diff(s) for a in self.args]) + + def _eval_nseries(self, x, n, logx, cdir=0): + terms = [t.nseries(x, n=n, logx=logx, cdir=cdir) for t in self.args] + return self.func(*terms) + + def _matches_simple(self, expr, repl_dict): + # handle (w+3).matches('x+5') -> {w: x+2} + coeff, terms = self.as_coeff_add() + if len(terms) == 1: + return terms[0].matches(expr - coeff, repl_dict) + return + + def matches(self, expr, repl_dict=None, old=False): + return self._matches_commutative(expr, repl_dict, old) + + @staticmethod + def _combine_inverse(lhs, rhs): + """ + Returns lhs - rhs, but treats oo like a symbol so oo - oo + returns 0, instead of a nan. + """ + from sympy.simplify.simplify import signsimp + inf = (S.Infinity, S.NegativeInfinity) + if lhs.has(*inf) or rhs.has(*inf): + from .symbol import Dummy + oo = Dummy('oo') + reps = { + S.Infinity: oo, + S.NegativeInfinity: -oo} + ireps = {v: k for k, v in reps.items()} + eq = lhs.xreplace(reps) - rhs.xreplace(reps) + if eq.has(oo): + eq = eq.replace( + lambda x: x.is_Pow and x.base is oo, + lambda x: x.base) + rv = eq.xreplace(ireps) + else: + rv = lhs - rhs + srv = signsimp(rv) + return srv if srv.is_Number else rv + + @cacheit + def as_two_terms(self): + """Return head and tail of self. + + This is the most efficient way to get the head and tail of an + expression. + + - if you want only the head, use self.args[0]; + - if you want to process the arguments of the tail then use + self.as_coef_add() which gives the head and a tuple containing + the arguments of the tail when treated as an Add. + - if you want the coefficient when self is treated as a Mul + then use self.as_coeff_mul()[0] + + >>> from sympy.abc import x, y + >>> (3*x - 2*y + 5).as_two_terms() + (5, 3*x - 2*y) + """ + return self.args[0], self._new_rawargs(*self.args[1:]) + + def as_numer_denom(self): + """ + Decomposes an expression to its numerator part and its + denominator part. + + Examples + ======== + + >>> from sympy.abc import x, y, z + >>> (x*y/z).as_numer_denom() + (x*y, z) + >>> (x*(y + 1)/y**7).as_numer_denom() + (x*(y + 1), y**7) + + See Also + ======== + + sympy.core.expr.Expr.as_numer_denom + """ + # clear rational denominator + content, expr = self.primitive() + if not isinstance(expr, Add): + return Mul(content, expr, evaluate=False).as_numer_denom() + ncon, dcon = content.as_numer_denom() + + # collect numerators and denominators of the terms + nd = defaultdict(list) + for f in expr.args: + ni, di = f.as_numer_denom() + nd[di].append(ni) + + # check for quick exit + if len(nd) == 1: + d, n = nd.popitem() + return self.func( + *[_keep_coeff(ncon, ni) for ni in n]), _keep_coeff(dcon, d) + + # sum up the terms having a common denominator + for d, n in nd.items(): + if len(n) == 1: + nd[d] = n[0] + else: + nd[d] = self.func(*n) + + # assemble single numerator and denominator + denoms, numers = [list(i) for i in zip(*iter(nd.items()))] + n, d = self.func(*[Mul(*(denoms[:i] + [numers[i]] + denoms[i + 1:])) + for i in range(len(numers))]), Mul(*denoms) + + return _keep_coeff(ncon, n), _keep_coeff(dcon, d) + + def _eval_is_polynomial(self, syms): + return all(term._eval_is_polynomial(syms) for term in self.args) + + def _eval_is_rational_function(self, syms): + return all(term._eval_is_rational_function(syms) for term in self.args) + + def _eval_is_meromorphic(self, x, a): + return _fuzzy_group((arg.is_meromorphic(x, a) for arg in self.args), + quick_exit=True) + + def _eval_is_algebraic_expr(self, syms): + return all(term._eval_is_algebraic_expr(syms) for term in self.args) + + # assumption methods + _eval_is_real = lambda self: _fuzzy_group( + (a.is_real for a in self.args), quick_exit=True) + _eval_is_extended_real = lambda self: _fuzzy_group( + (a.is_extended_real for a in self.args), quick_exit=True) + _eval_is_complex = lambda self: _fuzzy_group( + (a.is_complex for a in self.args), quick_exit=True) + _eval_is_antihermitian = lambda self: _fuzzy_group( + (a.is_antihermitian for a in self.args), quick_exit=True) + _eval_is_finite = lambda self: _fuzzy_group( + (a.is_finite for a in self.args), quick_exit=True) + _eval_is_hermitian = lambda self: _fuzzy_group( + (a.is_hermitian for a in self.args), quick_exit=True) + _eval_is_integer = lambda self: _fuzzy_group( + (a.is_integer for a in self.args), quick_exit=True) + _eval_is_rational = lambda self: _fuzzy_group( + (a.is_rational for a in self.args), quick_exit=True) + _eval_is_algebraic = lambda self: _fuzzy_group( + (a.is_algebraic for a in self.args), quick_exit=True) + _eval_is_commutative = lambda self: _fuzzy_group( + a.is_commutative for a in self.args) + + def _eval_is_infinite(self): + sawinf = False + for a in self.args: + ainf = a.is_infinite + if ainf is None: + return None + elif ainf is True: + # infinite+infinite might not be infinite + if sawinf is True: + return None + sawinf = True + return sawinf + + def _eval_is_imaginary(self): + nz = [] + im_I = [] + for a in self.args: + if a.is_extended_real: + if a.is_zero: + pass + elif a.is_zero is False: + nz.append(a) + else: + return + elif a.is_imaginary: + im_I.append(a*S.ImaginaryUnit) + elif a.is_Mul and S.ImaginaryUnit in a.args: + coeff, ai = a.as_coeff_mul(S.ImaginaryUnit) + if ai == (S.ImaginaryUnit,) and coeff.is_extended_real: + im_I.append(-coeff) + else: + return + else: + return + b = self.func(*nz) + if b != self: + if b.is_zero: + return fuzzy_not(self.func(*im_I).is_zero) + elif b.is_zero is False: + return False + + def _eval_is_zero(self): + if self.is_commutative is False: + # issue 10528: there is no way to know if a nc symbol + # is zero or not + return + nz = [] + z = 0 + im_or_z = False + im = 0 + for a in self.args: + if a.is_extended_real: + if a.is_zero: + z += 1 + elif a.is_zero is False: + nz.append(a) + else: + return + elif a.is_imaginary: + im += 1 + elif a.is_Mul and S.ImaginaryUnit in a.args: + coeff, ai = a.as_coeff_mul(S.ImaginaryUnit) + if ai == (S.ImaginaryUnit,) and coeff.is_extended_real: + im_or_z = True + else: + return + else: + return + if z == len(self.args): + return True + if len(nz) in [0, len(self.args)]: + return None + b = self.func(*nz) + if b.is_zero: + if not im_or_z: + if im == 0: + return True + elif im == 1: + return False + if b.is_zero is False: + return False + + def _eval_is_odd(self): + l = [f for f in self.args if not (f.is_even is True)] + if not l: + return False + if l[0].is_odd: + return self._new_rawargs(*l[1:]).is_even + + def _eval_is_irrational(self): + for t in self.args: + a = t.is_irrational + if a: + others = list(self.args) + others.remove(t) + if all(x.is_rational is True for x in others): + return True + return None + if a is None: + return + return False + + def _all_nonneg_or_nonppos(self): + nn = np = 0 + for a in self.args: + if a.is_nonnegative: + if np: + return False + nn = 1 + elif a.is_nonpositive: + if nn: + return False + np = 1 + else: + break + else: + return True + + def _eval_is_extended_positive(self): + if self.is_number: + return super()._eval_is_extended_positive() + c, a = self.as_coeff_Add() + if not c.is_zero: + from .exprtools import _monotonic_sign + v = _monotonic_sign(a) + if v is not None: + s = v + c + if s != self and s.is_extended_positive and a.is_extended_nonnegative: + return True + if len(self.free_symbols) == 1: + v = _monotonic_sign(self) + if v is not None and v != self and v.is_extended_positive: + return True + pos = nonneg = nonpos = unknown_sign = False + saw_INF = set() + args = [a for a in self.args if not a.is_zero] + if not args: + return False + for a in args: + ispos = a.is_extended_positive + infinite = a.is_infinite + if infinite: + saw_INF.add(fuzzy_or((ispos, a.is_extended_nonnegative))) + if True in saw_INF and False in saw_INF: + return + if ispos: + pos = True + continue + elif a.is_extended_nonnegative: + nonneg = True + continue + elif a.is_extended_nonpositive: + nonpos = True + continue + + if infinite is None: + return + unknown_sign = True + + if saw_INF: + if len(saw_INF) > 1: + return + return saw_INF.pop() + elif unknown_sign: + return + elif not nonpos and not nonneg and pos: + return True + elif not nonpos and pos: + return True + elif not pos and not nonneg: + return False + + def _eval_is_extended_nonnegative(self): + if not self.is_number: + c, a = self.as_coeff_Add() + if not c.is_zero and a.is_extended_nonnegative: + from .exprtools import _monotonic_sign + v = _monotonic_sign(a) + if v is not None: + s = v + c + if s != self and s.is_extended_nonnegative: + return True + if len(self.free_symbols) == 1: + v = _monotonic_sign(self) + if v is not None and v != self and v.is_extended_nonnegative: + return True + + def _eval_is_extended_nonpositive(self): + if not self.is_number: + c, a = self.as_coeff_Add() + if not c.is_zero and a.is_extended_nonpositive: + from .exprtools import _monotonic_sign + v = _monotonic_sign(a) + if v is not None: + s = v + c + if s != self and s.is_extended_nonpositive: + return True + if len(self.free_symbols) == 1: + v = _monotonic_sign(self) + if v is not None and v != self and v.is_extended_nonpositive: + return True + + def _eval_is_extended_negative(self): + if self.is_number: + return super()._eval_is_extended_negative() + c, a = self.as_coeff_Add() + if not c.is_zero: + from .exprtools import _monotonic_sign + v = _monotonic_sign(a) + if v is not None: + s = v + c + if s != self and s.is_extended_negative and a.is_extended_nonpositive: + return True + if len(self.free_symbols) == 1: + v = _monotonic_sign(self) + if v is not None and v != self and v.is_extended_negative: + return True + neg = nonpos = nonneg = unknown_sign = False + saw_INF = set() + args = [a for a in self.args if not a.is_zero] + if not args: + return False + for a in args: + isneg = a.is_extended_negative + infinite = a.is_infinite + if infinite: + saw_INF.add(fuzzy_or((isneg, a.is_extended_nonpositive))) + if True in saw_INF and False in saw_INF: + return + if isneg: + neg = True + continue + elif a.is_extended_nonpositive: + nonpos = True + continue + elif a.is_extended_nonnegative: + nonneg = True + continue + + if infinite is None: + return + unknown_sign = True + + if saw_INF: + if len(saw_INF) > 1: + return + return saw_INF.pop() + elif unknown_sign: + return + elif not nonneg and not nonpos and neg: + return True + elif not nonneg and neg: + return True + elif not neg and not nonpos: + return False + + def _eval_subs(self, old, new): + if not old.is_Add: + if old is S.Infinity and -old in self.args: + # foo - oo is foo + (-oo) internally + return self.xreplace({-old: -new}) + return None + + coeff_self, terms_self = self.as_coeff_Add() + coeff_old, terms_old = old.as_coeff_Add() + + if coeff_self.is_Rational and coeff_old.is_Rational: + if terms_self == terms_old: # (2 + a).subs( 3 + a, y) -> -1 + y + return self.func(new, coeff_self, -coeff_old) + if terms_self == -terms_old: # (2 + a).subs(-3 - a, y) -> -1 - y + return self.func(-new, coeff_self, coeff_old) + + if coeff_self.is_Rational and coeff_old.is_Rational \ + or coeff_self == coeff_old: + args_old, args_self = self.func.make_args( + terms_old), self.func.make_args(terms_self) + if len(args_old) < len(args_self): # (a+b+c).subs(b+c,x) -> a+x + self_set = set(args_self) + old_set = set(args_old) + + if old_set < self_set: + ret_set = self_set - old_set + return self.func(new, coeff_self, -coeff_old, + *[s._subs(old, new) for s in ret_set]) + + args_old = self.func.make_args( + -terms_old) # (a+b+c+d).subs(-b-c,x) -> a-x+d + old_set = set(args_old) + if old_set < self_set: + ret_set = self_set - old_set + return self.func(-new, coeff_self, coeff_old, + *[s._subs(old, new) for s in ret_set]) + + def removeO(self): + args = [a for a in self.args if not a.is_Order] + return self._new_rawargs(*args) + + def getO(self): + args = [a for a in self.args if a.is_Order] + if args: + return self._new_rawargs(*args) + + @cacheit + def extract_leading_order(self, symbols, point=None): + """ + Returns the leading term and its order. + + Examples + ======== + + >>> from sympy.abc import x + >>> (x + 1 + 1/x**5).extract_leading_order(x) + ((x**(-5), O(x**(-5))),) + >>> (1 + x).extract_leading_order(x) + ((1, O(1)),) + >>> (x + x**2).extract_leading_order(x) + ((x, O(x)),) + + """ + from sympy.series.order import Order + lst = [] + symbols = list(symbols if is_sequence(symbols) else [symbols]) + if not point: + point = [0]*len(symbols) + seq = [(f, Order(f, *zip(symbols, point))) for f in self.args] + for ef, of in seq: + for e, o in lst: + if o.contains(of) and o != of: + of = None + break + if of is None: + continue + new_lst = [(ef, of)] + for e, o in lst: + if of.contains(o) and o != of: + continue + new_lst.append((e, o)) + lst = new_lst + return tuple(lst) + + def as_real_imag(self, deep=True, **hints): + """ + Return a tuple representing a complex number. + + Examples + ======== + + >>> from sympy import I + >>> (7 + 9*I).as_real_imag() + (7, 9) + >>> ((1 + I)/(1 - I)).as_real_imag() + (0, 1) + >>> ((1 + 2*I)*(1 + 3*I)).as_real_imag() + (-5, 5) + """ + sargs = self.args + re_part, im_part = [], [] + for term in sargs: + re, im = term.as_real_imag(deep=deep) + re_part.append(re) + im_part.append(im) + return (self.func(*re_part), self.func(*im_part)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.core.symbol import Dummy, Symbol + from sympy.series.order import Order + from sympy.functions.elementary.exponential import log + from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold + from .function import expand_mul + + o = self.getO() + if o is None: + o = Order(0) + old = self.removeO() + + if old.has(Piecewise): + old = piecewise_fold(old) + + # This expansion is the last part of expand_log. expand_log also calls + # expand_mul with factor=True, which would be more expensive + if any(isinstance(a, log) for a in self.args): + logflags = {"deep": True, "log": True, "mul": False, "power_exp": False, + "power_base": False, "multinomial": False, "basic": False, "force": False, + "factor": False} + old = old.expand(**logflags) + expr = expand_mul(old) + + if not expr.is_Add: + return expr.as_leading_term(x, logx=logx, cdir=cdir) + + infinite = [t for t in expr.args if t.is_infinite] + + _logx = Dummy('logx') if logx is None else logx + leading_terms = [t.as_leading_term(x, logx=_logx, cdir=cdir) for t in expr.args] + + min, new_expr = Order(0), 0 + + try: + for term in leading_terms: + order = Order(term, x) + if not min or order not in min: + min = order + new_expr = term + elif min in order: + new_expr += term + + except TypeError: + return expr + + if logx is None: + new_expr = new_expr.subs(_logx, log(x)) + + is_zero = new_expr.is_zero + if is_zero is None: + new_expr = new_expr.trigsimp().cancel() + is_zero = new_expr.is_zero + if is_zero is True: + # simple leading term analysis gave us cancelled terms but we have to send + # back a term, so compute the leading term (via series) + try: + n0 = min.getn() + except NotImplementedError: + n0 = S.One + if n0.has(Symbol): + n0 = S.One + res = Order(1) + incr = S.One + while res.is_Order: + res = old._eval_nseries(x, n=n0+incr, logx=logx, cdir=cdir).cancel().powsimp().trigsimp() + incr *= 2 + return res.as_leading_term(x, logx=logx, cdir=cdir) + + elif new_expr is S.NaN: + return old.func._from_args(infinite) + o + + else: + return new_expr + + def _eval_adjoint(self): + return self.func(*[t.adjoint() for t in self.args]) + + def _eval_conjugate(self): + return self.func(*[t.conjugate() for t in self.args]) + + def _eval_transpose(self): + return self.func(*[t.transpose() for t in self.args]) + + def primitive(self): + """ + Return ``(R, self/R)`` where ``R``` is the Rational GCD of ``self```. + + ``R`` is collected only from the leading coefficient of each term. + + Examples + ======== + + >>> from sympy.abc import x, y + + >>> (2*x + 4*y).primitive() + (2, x + 2*y) + + >>> (2*x/3 + 4*y/9).primitive() + (2/9, 3*x + 2*y) + + >>> (2*x/3 + 4.2*y).primitive() + (1/3, 2*x + 12.6*y) + + No subprocessing of term factors is performed: + + >>> ((2 + 2*x)*x + 2).primitive() + (1, x*(2*x + 2) + 2) + + Recursive processing can be done with the ``as_content_primitive()`` + method: + + >>> ((2 + 2*x)*x + 2).as_content_primitive() + (2, x*(x + 1) + 1) + + See also: primitive() function in polytools.py + + """ + + terms = [] + inf = False + for a in self.args: + c, m = a.as_coeff_Mul() + if not c.is_Rational: + c = S.One + m = a + inf = inf or m is S.ComplexInfinity + terms.append((c.p, c.q, m)) + + if not inf: + ngcd = reduce(igcd, [t[0] for t in terms], 0) + dlcm = reduce(ilcm, [t[1] for t in terms], 1) + else: + ngcd = reduce(igcd, [t[0] for t in terms if t[1]], 0) + dlcm = reduce(ilcm, [t[1] for t in terms if t[1]], 1) + + if ngcd == dlcm == 1: + return S.One, self + if not inf: + for i, (p, q, term) in enumerate(terms): + terms[i] = _keep_coeff(Rational((p//ngcd)*(dlcm//q)), term) + else: + for i, (p, q, term) in enumerate(terms): + if q: + terms[i] = _keep_coeff(Rational((p//ngcd)*(dlcm//q)), term) + else: + terms[i] = _keep_coeff(Rational(p, q), term) + + # we don't need a complete re-flattening since no new terms will join + # so we just use the same sort as is used in Add.flatten. When the + # coefficient changes, the ordering of terms may change, e.g. + # (3*x, 6*y) -> (2*y, x) + # + # We do need to make sure that term[0] stays in position 0, however. + # + if terms[0].is_Number or terms[0] is S.ComplexInfinity: + c = terms.pop(0) + else: + c = None + _addsort(terms) + if c: + terms.insert(0, c) + return Rational(ngcd, dlcm), self._new_rawargs(*terms) + + def as_content_primitive(self, radical=False, clear=True): + """Return the tuple (R, self/R) where R is the positive Rational + extracted from self. If radical is True (default is False) then + common radicals will be removed and included as a factor of the + primitive expression. + + Examples + ======== + + >>> from sympy import sqrt + >>> (3 + 3*sqrt(2)).as_content_primitive() + (3, 1 + sqrt(2)) + + Radical content can also be factored out of the primitive: + + >>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive(radical=True) + (2, sqrt(2)*(1 + 2*sqrt(5))) + + See docstring of Expr.as_content_primitive for more examples. + """ + con, prim = self.func(*[_keep_coeff(*a.as_content_primitive( + radical=radical, clear=clear)) for a in self.args]).primitive() + if not clear and not con.is_Integer and prim.is_Add: + con, d = con.as_numer_denom() + _p = prim/d + if any(a.as_coeff_Mul()[0].is_Integer for a in _p.args): + prim = _p + else: + con /= d + if radical and prim.is_Add: + # look for common radicals that can be removed + args = prim.args + rads = [] + common_q = None + for m in args: + term_rads = defaultdict(list) + for ai in Mul.make_args(m): + if ai.is_Pow: + b, e = ai.as_base_exp() + if e.is_Rational and b.is_Integer: + term_rads[e.q].append(abs(int(b))**e.p) + if not term_rads: + break + if common_q is None: + common_q = set(term_rads.keys()) + else: + common_q = common_q & set(term_rads.keys()) + if not common_q: + break + rads.append(term_rads) + else: + # process rads + # keep only those in common_q + for r in rads: + for q in list(r.keys()): + if q not in common_q: + r.pop(q) + for q in r: + r[q] = Mul(*r[q]) + # find the gcd of bases for each q + G = [] + for q in common_q: + g = reduce(igcd, [r[q] for r in rads], 0) + if g != 1: + G.append(g**Rational(1, q)) + if G: + G = Mul(*G) + args = [ai/G for ai in args] + prim = G*prim.func(*args) + + return con, prim + + @property + def _sorted_args(self): + from .sorting import default_sort_key + return tuple(sorted(self.args, key=default_sort_key)) + + def _eval_difference_delta(self, n, step): + from sympy.series.limitseq import difference_delta as dd + return self.func(*[dd(a, n, step) for a in self.args]) + + @property + def _mpc_(self): + """ + Convert self to an mpmath mpc if possible + """ + from .numbers import Float + re_part, rest = self.as_coeff_Add() + im_part, imag_unit = rest.as_coeff_Mul() + if not imag_unit == S.ImaginaryUnit: + # ValueError may seem more reasonable but since it's a @property, + # we need to use AttributeError to keep from confusing things like + # hasattr. + raise AttributeError("Cannot convert Add to mpc. Must be of the form Number + Number*I") + + return (Float(re_part)._mpf_, Float(im_part)._mpf_) + + def __neg__(self): + if not global_parameters.distribute: + return super().__neg__() + return Mul(S.NegativeOne, self) + +add = AssocOpDispatcher('add') + +from .mul import Mul, _keep_coeff, _unevaluated_Mul +from .numbers import Rational diff --git a/lib/python3.11/site-packages/sympy/core/alphabets.py b/lib/python3.11/site-packages/sympy/core/alphabets.py new file mode 100644 index 0000000000000000000000000000000000000000..1ea2ae1c410ccd30e7ec9551f4cd8b19a36cdba1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/alphabets.py @@ -0,0 +1,4 @@ +greeks = ('alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta', + 'eta', 'theta', 'iota', 'kappa', 'lambda', 'mu', 'nu', + 'xi', 'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon', + 'phi', 'chi', 'psi', 'omega') diff --git a/lib/python3.11/site-packages/sympy/core/assumptions.py b/lib/python3.11/site-packages/sympy/core/assumptions.py new file mode 100644 index 0000000000000000000000000000000000000000..677e86c5e39390b0b188a5158dd2fabfbac4c760 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/assumptions.py @@ -0,0 +1,692 @@ +""" +This module contains the machinery handling assumptions. +Do also consider the guide :ref:`assumptions-guide`. + +All symbolic objects have assumption attributes that can be accessed via +``.is_`` attribute. + +Assumptions determine certain properties of symbolic objects and can +have 3 possible values: ``True``, ``False``, ``None``. ``True`` is returned if the +object has the property and ``False`` is returned if it does not or cannot +(i.e. does not make sense): + + >>> from sympy import I + >>> I.is_algebraic + True + >>> I.is_real + False + >>> I.is_prime + False + +When the property cannot be determined (or when a method is not +implemented) ``None`` will be returned. For example, a generic symbol, ``x``, +may or may not be positive so a value of ``None`` is returned for ``x.is_positive``. + +By default, all symbolic values are in the largest set in the given context +without specifying the property. For example, a symbol that has a property +being integer, is also real, complex, etc. + +Here follows a list of possible assumption names: + +.. glossary:: + + commutative + object commutes with any other object with + respect to multiplication operation. See [12]_. + + complex + object can have only values from the set + of complex numbers. See [13]_. + + imaginary + object value is a number that can be written as a real + number multiplied by the imaginary unit ``I``. See + [3]_. Please note that ``0`` is not considered to be an + imaginary number, see + `issue #7649 `_. + + real + object can have only values from the set + of real numbers. + + extended_real + object can have only values from the set + of real numbers, ``oo`` and ``-oo``. + + integer + object can have only values from the set + of integers. + + odd + even + object can have only values from the set of + odd (even) integers [2]_. + + prime + object is a natural number greater than 1 that has + no positive divisors other than 1 and itself. See [6]_. + + composite + object is a positive integer that has at least one positive + divisor other than 1 or the number itself. See [4]_. + + zero + object has the value of 0. + + nonzero + object is a real number that is not zero. + + rational + object can have only values from the set + of rationals. + + algebraic + object can have only values from the set + of algebraic numbers [11]_. + + transcendental + object can have only values from the set + of transcendental numbers [10]_. + + irrational + object value cannot be represented exactly by :class:`~.Rational`, see [5]_. + + finite + infinite + object absolute value is bounded (arbitrarily large). + See [7]_, [8]_, [9]_. + + negative + nonnegative + object can have only negative (nonnegative) + values [1]_. + + positive + nonpositive + object can have only positive (nonpositive) values. + + extended_negative + extended_nonnegative + extended_positive + extended_nonpositive + extended_nonzero + as without the extended part, but also including infinity with + corresponding sign, e.g., extended_positive includes ``oo`` + + hermitian + antihermitian + object belongs to the field of Hermitian + (antihermitian) operators. + +Examples +======== + + >>> from sympy import Symbol + >>> x = Symbol('x', real=True); x + x + >>> x.is_real + True + >>> x.is_complex + True + +See Also +======== + +.. seealso:: + + :py:class:`sympy.core.numbers.ImaginaryUnit` + :py:class:`sympy.core.numbers.Zero` + :py:class:`sympy.core.numbers.One` + :py:class:`sympy.core.numbers.Infinity` + :py:class:`sympy.core.numbers.NegativeInfinity` + :py:class:`sympy.core.numbers.ComplexInfinity` + +Notes +===== + +The fully-resolved assumptions for any SymPy expression +can be obtained as follows: + + >>> from sympy.core.assumptions import assumptions + >>> x = Symbol('x',positive=True) + >>> assumptions(x + I) + {'commutative': True, 'complex': True, 'composite': False, 'even': + False, 'extended_negative': False, 'extended_nonnegative': False, + 'extended_nonpositive': False, 'extended_nonzero': False, + 'extended_positive': False, 'extended_real': False, 'finite': True, + 'imaginary': False, 'infinite': False, 'integer': False, 'irrational': + False, 'negative': False, 'noninteger': False, 'nonnegative': False, + 'nonpositive': False, 'nonzero': False, 'odd': False, 'positive': + False, 'prime': False, 'rational': False, 'real': False, 'zero': + False} + +Developers Notes +================ + +The current (and possibly incomplete) values are stored +in the ``obj._assumptions dictionary``; queries to getter methods +(with property decorators) or attributes of objects/classes +will return values and update the dictionary. + + >>> eq = x**2 + I + >>> eq._assumptions + {} + >>> eq.is_finite + True + >>> eq._assumptions + {'finite': True, 'infinite': False} + +For a :class:`~.Symbol`, there are two locations for assumptions that may +be of interest. The ``assumptions0`` attribute gives the full set of +assumptions derived from a given set of initial assumptions. The +latter assumptions are stored as ``Symbol._assumptions_orig`` + + >>> Symbol('x', prime=True, even=True)._assumptions_orig + {'even': True, 'prime': True} + +The ``_assumptions_orig`` are not necessarily canonical nor are they filtered +in any way: they records the assumptions used to instantiate a Symbol and (for +storage purposes) represent a more compact representation of the assumptions +needed to recreate the full set in ``Symbol.assumptions0``. + + +References +========== + +.. [1] https://en.wikipedia.org/wiki/Negative_number +.. [2] https://en.wikipedia.org/wiki/Parity_%28mathematics%29 +.. [3] https://en.wikipedia.org/wiki/Imaginary_number +.. [4] https://en.wikipedia.org/wiki/Composite_number +.. [5] https://en.wikipedia.org/wiki/Irrational_number +.. [6] https://en.wikipedia.org/wiki/Prime_number +.. [7] https://en.wikipedia.org/wiki/Finite +.. [8] https://docs.python.org/3/library/math.html#math.isfinite +.. [9] https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html +.. [10] https://en.wikipedia.org/wiki/Transcendental_number +.. [11] https://en.wikipedia.org/wiki/Algebraic_number +.. [12] https://en.wikipedia.org/wiki/Commutative_property +.. [13] https://en.wikipedia.org/wiki/Complex_number + +""" + +from sympy.utilities.exceptions import sympy_deprecation_warning + +from .facts import FactRules, FactKB +from .sympify import sympify + +from sympy.core.random import _assumptions_shuffle as shuffle +from sympy.core.assumptions_generated import generated_assumptions as _assumptions + +def _load_pre_generated_assumption_rules() -> FactRules: + """ Load the assumption rules from pre-generated data + + To update the pre-generated data, see :method::`_generate_assumption_rules` + """ + _assume_rules=FactRules._from_python(_assumptions) + return _assume_rules + +def _generate_assumption_rules(): + """ Generate the default assumption rules + + This method should only be called to update the pre-generated + assumption rules. + + To update the pre-generated assumptions run: bin/ask_update.py + + """ + _assume_rules = FactRules([ + + 'integer -> rational', + 'rational -> real', + 'rational -> algebraic', + 'algebraic -> complex', + 'transcendental == complex & !algebraic', + 'real -> hermitian', + 'imaginary -> complex', + 'imaginary -> antihermitian', + 'extended_real -> commutative', + 'complex -> commutative', + 'complex -> finite', + + 'odd == integer & !even', + 'even == integer & !odd', + + 'real -> complex', + 'extended_real -> real | infinite', + 'real == extended_real & finite', + + 'extended_real == extended_negative | zero | extended_positive', + 'extended_negative == extended_nonpositive & extended_nonzero', + 'extended_positive == extended_nonnegative & extended_nonzero', + + 'extended_nonpositive == extended_real & !extended_positive', + 'extended_nonnegative == extended_real & !extended_negative', + + 'real == negative | zero | positive', + 'negative == nonpositive & nonzero', + 'positive == nonnegative & nonzero', + + 'nonpositive == real & !positive', + 'nonnegative == real & !negative', + + 'positive == extended_positive & finite', + 'negative == extended_negative & finite', + 'nonpositive == extended_nonpositive & finite', + 'nonnegative == extended_nonnegative & finite', + 'nonzero == extended_nonzero & finite', + + 'zero -> even & finite', + 'zero == extended_nonnegative & extended_nonpositive', + 'zero == nonnegative & nonpositive', + 'nonzero -> real', + + 'prime -> integer & positive', + 'composite -> integer & positive & !prime', + '!composite -> !positive | !even | prime', + + 'irrational == real & !rational', + + 'imaginary -> !extended_real', + + 'infinite == !finite', + 'noninteger == extended_real & !integer', + 'extended_nonzero == extended_real & !zero', + ]) + return _assume_rules + + +_assume_rules = _load_pre_generated_assumption_rules() +_assume_defined = _assume_rules.defined_facts.copy() +_assume_defined.add('polar') +_assume_defined = frozenset(_assume_defined) + + +def assumptions(expr, _check=None): + """return the T/F assumptions of ``expr``""" + n = sympify(expr) + if n.is_Symbol: + rv = n.assumptions0 # are any important ones missing? + if _check is not None: + rv = {k: rv[k] for k in set(rv) & set(_check)} + return rv + rv = {} + for k in _assume_defined if _check is None else _check: + v = getattr(n, 'is_{}'.format(k)) + if v is not None: + rv[k] = v + return rv + + +def common_assumptions(exprs, check=None): + """return those assumptions which have the same True or False + value for all the given expressions. + + Examples + ======== + + >>> from sympy.core import common_assumptions + >>> from sympy import oo, pi, sqrt + >>> common_assumptions([-4, 0, sqrt(2), 2, pi, oo]) + {'commutative': True, 'composite': False, + 'extended_real': True, 'imaginary': False, 'odd': False} + + By default, all assumptions are tested; pass an iterable of the + assumptions to limit those that are reported: + + >>> common_assumptions([0, 1, 2], ['positive', 'integer']) + {'integer': True} + """ + check = _assume_defined if check is None else set(check) + if not check or not exprs: + return {} + + # get all assumptions for each + assume = [assumptions(i, _check=check) for i in sympify(exprs)] + # focus on those of interest that are True + for i, e in enumerate(assume): + assume[i] = {k: e[k] for k in set(e) & check} + # what assumptions are in common? + common = set.intersection(*[set(i) for i in assume]) + # which ones hold the same value + a = assume[0] + return {k: a[k] for k in common if all(a[k] == b[k] + for b in assume)} + + +def failing_assumptions(expr, **assumptions): + """ + Return a dictionary containing assumptions with values not + matching those of the passed assumptions. + + Examples + ======== + + >>> from sympy import failing_assumptions, Symbol + + >>> x = Symbol('x', positive=True) + >>> y = Symbol('y') + >>> failing_assumptions(6*x + y, positive=True) + {'positive': None} + + >>> failing_assumptions(x**2 - 1, positive=True) + {'positive': None} + + If *expr* satisfies all of the assumptions, an empty dictionary is returned. + + >>> failing_assumptions(x**2, positive=True) + {} + + """ + expr = sympify(expr) + failed = {} + for k in assumptions: + test = getattr(expr, 'is_%s' % k, None) + if test is not assumptions[k]: + failed[k] = test + return failed # {} or {assumption: value != desired} + + +def check_assumptions(expr, against=None, **assume): + """ + Checks whether assumptions of ``expr`` match the T/F assumptions + given (or possessed by ``against``). True is returned if all + assumptions match; False is returned if there is a mismatch and + the assumption in ``expr`` is not None; else None is returned. + + Explanation + =========== + + *assume* is a dict of assumptions with True or False values + + Examples + ======== + + >>> from sympy import Symbol, pi, I, exp, check_assumptions + >>> check_assumptions(-5, integer=True) + True + >>> check_assumptions(pi, real=True, integer=False) + True + >>> check_assumptions(pi, negative=True) + False + >>> check_assumptions(exp(I*pi/7), real=False) + True + >>> x = Symbol('x', positive=True) + >>> check_assumptions(2*x + 1, positive=True) + True + >>> check_assumptions(-2*x - 5, positive=True) + False + + To check assumptions of *expr* against another variable or expression, + pass the expression or variable as ``against``. + + >>> check_assumptions(2*x + 1, x) + True + + To see if a number matches the assumptions of an expression, pass + the number as the first argument, else its specific assumptions + may not have a non-None value in the expression: + + >>> check_assumptions(x, 3) + >>> check_assumptions(3, x) + True + + ``None`` is returned if ``check_assumptions()`` could not conclude. + + >>> check_assumptions(2*x - 1, x) + + >>> z = Symbol('z') + >>> check_assumptions(z, real=True) + + See Also + ======== + + failing_assumptions + + """ + expr = sympify(expr) + if against is not None: + if assume: + raise ValueError( + 'Expecting `against` or `assume`, not both.') + assume = assumptions(against) + known = True + for k, v in assume.items(): + if v is None: + continue + e = getattr(expr, 'is_' + k, None) + if e is None: + known = None + elif v != e: + return False + return known + + +class StdFactKB(FactKB): + """A FactKB specialized for the built-in rules + + This is the only kind of FactKB that Basic objects should use. + """ + def __init__(self, facts=None): + super().__init__(_assume_rules) + # save a copy of the facts dict + if not facts: + self._generator = {} + elif not isinstance(facts, FactKB): + self._generator = facts.copy() + else: + self._generator = facts.generator + if facts: + self.deduce_all_facts(facts) + + def copy(self): + return self.__class__(self) + + @property + def generator(self): + return self._generator.copy() + + +def as_property(fact): + """Convert a fact name to the name of the corresponding property""" + return 'is_%s' % fact + + +def make_property(fact): + """Create the automagic property corresponding to a fact.""" + + def getit(self): + try: + return self._assumptions[fact] + except KeyError: + if self._assumptions is self.default_assumptions: + self._assumptions = self.default_assumptions.copy() + return _ask(fact, self) + + getit.func_name = as_property(fact) + return property(getit) + + +def _ask(fact, obj): + """ + Find the truth value for a property of an object. + + This function is called when a request is made to see what a fact + value is. + + For this we use several techniques: + + First, the fact-evaluation function is tried, if it exists (for + example _eval_is_integer). Then we try related facts. For example + + rational --> integer + + another example is joined rule: + + integer & !odd --> even + + so in the latter case if we are looking at what 'even' value is, + 'integer' and 'odd' facts will be asked. + + In all cases, when we settle on some fact value, its implications are + deduced, and the result is cached in ._assumptions. + """ + # FactKB which is dict-like and maps facts to their known values: + assumptions = obj._assumptions + + # A dict that maps facts to their handlers: + handler_map = obj._prop_handler + + # This is our queue of facts to check: + facts_to_check = [fact] + facts_queued = {fact} + + # Loop over the queue as it extends + for fact_i in facts_to_check: + + # If fact_i has already been determined then we don't need to rerun the + # handler. There is a potential race condition for multithreaded code + # though because it's possible that fact_i was checked in another + # thread. The main logic of the loop below would potentially skip + # checking assumptions[fact] in this case so we check it once after the + # loop to be sure. + if fact_i in assumptions: + continue + + # Now we call the associated handler for fact_i if it exists. + fact_i_value = None + handler_i = handler_map.get(fact_i) + if handler_i is not None: + fact_i_value = handler_i(obj) + + # If we get a new value for fact_i then we should update our knowledge + # of fact_i as well as any related facts that can be inferred using the + # inference rules connecting the fact_i and any other fact values that + # are already known. + if fact_i_value is not None: + assumptions.deduce_all_facts(((fact_i, fact_i_value),)) + + # Usually if assumptions[fact] is now not None then that is because of + # the call to deduce_all_facts above. The handler for fact_i returned + # True or False and knowing fact_i (which is equal to fact in the first + # iteration) implies knowing a value for fact. It is also possible + # though that independent code e.g. called indirectly by the handler or + # called in another thread in a multithreaded context might have + # resulted in assumptions[fact] being set. Either way we return it. + fact_value = assumptions.get(fact) + if fact_value is not None: + return fact_value + + # Extend the queue with other facts that might determine fact_i. Here + # we randomise the order of the facts that are checked. This should not + # lead to any non-determinism if all handlers are logically consistent + # with the inference rules for the facts. Non-deterministic assumptions + # queries can result from bugs in the handlers that are exposed by this + # call to shuffle. These are pushed to the back of the queue meaning + # that the inference graph is traversed in breadth-first order. + new_facts_to_check = list(_assume_rules.prereq[fact_i] - facts_queued) + shuffle(new_facts_to_check) + facts_to_check.extend(new_facts_to_check) + facts_queued.update(new_facts_to_check) + + # The above loop should be able to handle everything fine in a + # single-threaded context but in multithreaded code it is possible that + # this thread skipped computing a particular fact that was computed in + # another thread (due to the continue). In that case it is possible that + # fact was inferred and is now stored in the assumptions dict but it wasn't + # checked for in the body of the loop. This is an obscure case but to make + # sure we catch it we check once here at the end of the loop. + if fact in assumptions: + return assumptions[fact] + + # This query can not be answered. It's possible that e.g. another thread + # has already stored None for fact but assumptions._tell does not mind if + # we call _tell twice setting the same value. If this raises + # InconsistentAssumptions then it probably means that another thread + # attempted to compute this and got a value of True or False rather than + # None. In that case there must be a bug in at least one of the handlers. + # If the handlers are all deterministic and are consistent with the + # inference rules then the same value should be computed for fact in all + # threads. + assumptions._tell(fact, None) + return None + + +def _prepare_class_assumptions(cls): + """Precompute class level assumptions and generate handlers. + + This is called by Basic.__init_subclass__ each time a Basic subclass is + defined. + """ + + local_defs = {} + for k in _assume_defined: + attrname = as_property(k) + v = cls.__dict__.get(attrname, '') + if isinstance(v, (bool, int, type(None))): + if v is not None: + v = bool(v) + local_defs[k] = v + + defs = {} + for base in reversed(cls.__bases__): + assumptions = getattr(base, '_explicit_class_assumptions', None) + if assumptions is not None: + defs.update(assumptions) + defs.update(local_defs) + + cls._explicit_class_assumptions = defs + cls.default_assumptions = StdFactKB(defs) + + cls._prop_handler = {} + for k in _assume_defined: + eval_is_meth = getattr(cls, '_eval_is_%s' % k, None) + if eval_is_meth is not None: + cls._prop_handler[k] = eval_is_meth + + # Put definite results directly into the class dict, for speed + for k, v in cls.default_assumptions.items(): + setattr(cls, as_property(k), v) + + # protection e.g. for Integer.is_even=F <- (Rational.is_integer=F) + derived_from_bases = set() + for base in cls.__bases__: + default_assumptions = getattr(base, 'default_assumptions', None) + # is an assumption-aware class + if default_assumptions is not None: + derived_from_bases.update(default_assumptions) + + for fact in derived_from_bases - set(cls.default_assumptions): + pname = as_property(fact) + if pname not in cls.__dict__: + setattr(cls, pname, make_property(fact)) + + # Finally, add any missing automagic property (e.g. for Basic) + for fact in _assume_defined: + pname = as_property(fact) + if not hasattr(cls, pname): + setattr(cls, pname, make_property(fact)) + + +# XXX: ManagedProperties used to be the metaclass for Basic but now Basic does +# not use a metaclass. We leave this here for backwards compatibility for now +# in case someone has been using the ManagedProperties class in downstream +# code. The reason that it might have been used is that when subclassing a +# class and wanting to use a metaclass the metaclass must be a subclass of the +# metaclass for the class that is being subclassed. Anyone wanting to subclass +# Basic and use a metaclass in their subclass would have needed to subclass +# ManagedProperties. Here ManagedProperties is not the metaclass for Basic any +# more but it should still be usable as a metaclass for Basic subclasses since +# it is a subclass of type which is now the metaclass for Basic. +class ManagedProperties(type): + def __init__(cls, *args, **kwargs): + msg = ("The ManagedProperties metaclass. " + "Basic does not use metaclasses any more") + sympy_deprecation_warning(msg, + deprecated_since_version="1.12", + active_deprecations_target='managedproperties') + + # Here we still call this function in case someone is using + # ManagedProperties for something that is not a Basic subclass. For + # Basic subclasses this function is now called by __init_subclass__ and + # so this metaclass is not needed any more. + _prepare_class_assumptions(cls) diff --git a/lib/python3.11/site-packages/sympy/core/assumptions_generated.py b/lib/python3.11/site-packages/sympy/core/assumptions_generated.py new file mode 100644 index 0000000000000000000000000000000000000000..b4b2597a72b500155370db385b58e61f0f951984 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/assumptions_generated.py @@ -0,0 +1,1615 @@ +""" +Do NOT manually edit this file. +Instead, run ./bin/ask_update.py. +""" + +defined_facts = [ + 'algebraic', + 'antihermitian', + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', +] # defined_facts + + +full_implications = dict( [ + # Implications of algebraic = True: + (('algebraic', True), set( ( + ('commutative', True), + ('complex', True), + ('finite', True), + ('infinite', False), + ('transcendental', False), + ) ), + ), + # Implications of algebraic = False: + (('algebraic', False), set( ( + ('composite', False), + ('even', False), + ('integer', False), + ('odd', False), + ('prime', False), + ('rational', False), + ('zero', False), + ) ), + ), + # Implications of antihermitian = True: + (('antihermitian', True), set( ( + ) ), + ), + # Implications of antihermitian = False: + (('antihermitian', False), set( ( + ('imaginary', False), + ) ), + ), + # Implications of commutative = True: + (('commutative', True), set( ( + ) ), + ), + # Implications of commutative = False: + (('commutative', False), set( ( + ('algebraic', False), + ('complex', False), + ('composite', False), + ('even', False), + ('extended_negative', False), + ('extended_nonnegative', False), + ('extended_nonpositive', False), + ('extended_nonzero', False), + ('extended_positive', False), + ('extended_real', False), + ('imaginary', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of complex = True: + (('complex', True), set( ( + ('commutative', True), + ('finite', True), + ('infinite', False), + ) ), + ), + # Implications of complex = False: + (('complex', False), set( ( + ('algebraic', False), + ('composite', False), + ('even', False), + ('imaginary', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of composite = True: + (('composite', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_nonpositive', False), + ('extended_nonzero', True), + ('extended_positive', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', True), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', True), + ('nonpositive', False), + ('nonzero', True), + ('positive', True), + ('prime', False), + ('rational', True), + ('real', True), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of composite = False: + (('composite', False), set( ( + ) ), + ), + # Implications of even = True: + (('even', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', True), + ('irrational', False), + ('noninteger', False), + ('odd', False), + ('rational', True), + ('real', True), + ('transcendental', False), + ) ), + ), + # Implications of even = False: + (('even', False), set( ( + ('zero', False), + ) ), + ), + # Implications of extended_negative = True: + (('extended_negative', True), set( ( + ('commutative', True), + ('composite', False), + ('extended_nonnegative', False), + ('extended_nonpositive', True), + ('extended_nonzero', True), + ('extended_positive', False), + ('extended_real', True), + ('imaginary', False), + ('nonnegative', False), + ('positive', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of extended_negative = False: + (('extended_negative', False), set( ( + ('negative', False), + ) ), + ), + # Implications of extended_nonnegative = True: + (('extended_nonnegative', True), set( ( + ('commutative', True), + ('extended_negative', False), + ('extended_real', True), + ('imaginary', False), + ('negative', False), + ) ), + ), + # Implications of extended_nonnegative = False: + (('extended_nonnegative', False), set( ( + ('composite', False), + ('extended_positive', False), + ('nonnegative', False), + ('positive', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of extended_nonpositive = True: + (('extended_nonpositive', True), set( ( + ('commutative', True), + ('composite', False), + ('extended_positive', False), + ('extended_real', True), + ('imaginary', False), + ('positive', False), + ('prime', False), + ) ), + ), + # Implications of extended_nonpositive = False: + (('extended_nonpositive', False), set( ( + ('extended_negative', False), + ('negative', False), + ('nonpositive', False), + ('zero', False), + ) ), + ), + # Implications of extended_nonzero = True: + (('extended_nonzero', True), set( ( + ('commutative', True), + ('extended_real', True), + ('imaginary', False), + ('zero', False), + ) ), + ), + # Implications of extended_nonzero = False: + (('extended_nonzero', False), set( ( + ('composite', False), + ('extended_negative', False), + ('extended_positive', False), + ('negative', False), + ('nonzero', False), + ('positive', False), + ('prime', False), + ) ), + ), + # Implications of extended_positive = True: + (('extended_positive', True), set( ( + ('commutative', True), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_nonpositive', False), + ('extended_nonzero', True), + ('extended_real', True), + ('imaginary', False), + ('negative', False), + ('nonpositive', False), + ('zero', False), + ) ), + ), + # Implications of extended_positive = False: + (('extended_positive', False), set( ( + ('composite', False), + ('positive', False), + ('prime', False), + ) ), + ), + # Implications of extended_real = True: + (('extended_real', True), set( ( + ('commutative', True), + ('imaginary', False), + ) ), + ), + # Implications of extended_real = False: + (('extended_real', False), set( ( + ('composite', False), + ('even', False), + ('extended_negative', False), + ('extended_nonnegative', False), + ('extended_nonpositive', False), + ('extended_nonzero', False), + ('extended_positive', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('zero', False), + ) ), + ), + # Implications of finite = True: + (('finite', True), set( ( + ('infinite', False), + ) ), + ), + # Implications of finite = False: + (('finite', False), set( ( + ('algebraic', False), + ('complex', False), + ('composite', False), + ('even', False), + ('imaginary', False), + ('infinite', True), + ('integer', False), + ('irrational', False), + ('negative', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of hermitian = True: + (('hermitian', True), set( ( + ) ), + ), + # Implications of hermitian = False: + (('hermitian', False), set( ( + ('composite', False), + ('even', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('zero', False), + ) ), + ), + # Implications of imaginary = True: + (('imaginary', True), set( ( + ('antihermitian', True), + ('commutative', True), + ('complex', True), + ('composite', False), + ('even', False), + ('extended_negative', False), + ('extended_nonnegative', False), + ('extended_nonpositive', False), + ('extended_nonzero', False), + ('extended_positive', False), + ('extended_real', False), + ('finite', True), + ('infinite', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('zero', False), + ) ), + ), + # Implications of imaginary = False: + (('imaginary', False), set( ( + ) ), + ), + # Implications of infinite = True: + (('infinite', True), set( ( + ('algebraic', False), + ('complex', False), + ('composite', False), + ('even', False), + ('finite', False), + ('imaginary', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('real', False), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of infinite = False: + (('infinite', False), set( ( + ('finite', True), + ) ), + ), + # Implications of integer = True: + (('integer', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('irrational', False), + ('noninteger', False), + ('rational', True), + ('real', True), + ('transcendental', False), + ) ), + ), + # Implications of integer = False: + (('integer', False), set( ( + ('composite', False), + ('even', False), + ('odd', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of irrational = True: + (('irrational', True), set( ( + ('commutative', True), + ('complex', True), + ('composite', False), + ('even', False), + ('extended_nonzero', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', False), + ('noninteger', True), + ('nonzero', True), + ('odd', False), + ('prime', False), + ('rational', False), + ('real', True), + ('zero', False), + ) ), + ), + # Implications of irrational = False: + (('irrational', False), set( ( + ) ), + ), + # Implications of negative = True: + (('negative', True), set( ( + ('commutative', True), + ('complex', True), + ('composite', False), + ('extended_negative', True), + ('extended_nonnegative', False), + ('extended_nonpositive', True), + ('extended_nonzero', True), + ('extended_positive', False), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('nonnegative', False), + ('nonpositive', True), + ('nonzero', True), + ('positive', False), + ('prime', False), + ('real', True), + ('zero', False), + ) ), + ), + # Implications of negative = False: + (('negative', False), set( ( + ) ), + ), + # Implications of noninteger = True: + (('noninteger', True), set( ( + ('commutative', True), + ('composite', False), + ('even', False), + ('extended_nonzero', True), + ('extended_real', True), + ('imaginary', False), + ('integer', False), + ('odd', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of noninteger = False: + (('noninteger', False), set( ( + ) ), + ), + # Implications of nonnegative = True: + (('nonnegative', True), set( ( + ('commutative', True), + ('complex', True), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('negative', False), + ('real', True), + ) ), + ), + # Implications of nonnegative = False: + (('nonnegative', False), set( ( + ('composite', False), + ('positive', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of nonpositive = True: + (('nonpositive', True), set( ( + ('commutative', True), + ('complex', True), + ('composite', False), + ('extended_nonpositive', True), + ('extended_positive', False), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('positive', False), + ('prime', False), + ('real', True), + ) ), + ), + # Implications of nonpositive = False: + (('nonpositive', False), set( ( + ('negative', False), + ('zero', False), + ) ), + ), + # Implications of nonzero = True: + (('nonzero', True), set( ( + ('commutative', True), + ('complex', True), + ('extended_nonzero', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('real', True), + ('zero', False), + ) ), + ), + # Implications of nonzero = False: + (('nonzero', False), set( ( + ('composite', False), + ('negative', False), + ('positive', False), + ('prime', False), + ) ), + ), + # Implications of odd = True: + (('odd', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('even', False), + ('extended_nonzero', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', True), + ('irrational', False), + ('noninteger', False), + ('nonzero', True), + ('rational', True), + ('real', True), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of odd = False: + (('odd', False), set( ( + ) ), + ), + # Implications of positive = True: + (('positive', True), set( ( + ('commutative', True), + ('complex', True), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_nonpositive', False), + ('extended_nonzero', True), + ('extended_positive', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('negative', False), + ('nonnegative', True), + ('nonpositive', False), + ('nonzero', True), + ('real', True), + ('zero', False), + ) ), + ), + # Implications of positive = False: + (('positive', False), set( ( + ('composite', False), + ('prime', False), + ) ), + ), + # Implications of prime = True: + (('prime', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('composite', False), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_nonpositive', False), + ('extended_nonzero', True), + ('extended_positive', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', True), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', True), + ('nonpositive', False), + ('nonzero', True), + ('positive', True), + ('rational', True), + ('real', True), + ('transcendental', False), + ('zero', False), + ) ), + ), + # Implications of prime = False: + (('prime', False), set( ( + ) ), + ), + # Implications of rational = True: + (('rational', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('irrational', False), + ('real', True), + ('transcendental', False), + ) ), + ), + # Implications of rational = False: + (('rational', False), set( ( + ('composite', False), + ('even', False), + ('integer', False), + ('odd', False), + ('prime', False), + ('zero', False), + ) ), + ), + # Implications of real = True: + (('real', True), set( ( + ('commutative', True), + ('complex', True), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ) ), + ), + # Implications of real = False: + (('real', False), set( ( + ('composite', False), + ('even', False), + ('integer', False), + ('irrational', False), + ('negative', False), + ('nonnegative', False), + ('nonpositive', False), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', False), + ('zero', False), + ) ), + ), + # Implications of transcendental = True: + (('transcendental', True), set( ( + ('algebraic', False), + ('commutative', True), + ('complex', True), + ('composite', False), + ('even', False), + ('finite', True), + ('infinite', False), + ('integer', False), + ('odd', False), + ('prime', False), + ('rational', False), + ('zero', False), + ) ), + ), + # Implications of transcendental = False: + (('transcendental', False), set( ( + ) ), + ), + # Implications of zero = True: + (('zero', True), set( ( + ('algebraic', True), + ('commutative', True), + ('complex', True), + ('composite', False), + ('even', True), + ('extended_negative', False), + ('extended_nonnegative', True), + ('extended_nonpositive', True), + ('extended_nonzero', False), + ('extended_positive', False), + ('extended_real', True), + ('finite', True), + ('hermitian', True), + ('imaginary', False), + ('infinite', False), + ('integer', True), + ('irrational', False), + ('negative', False), + ('noninteger', False), + ('nonnegative', True), + ('nonpositive', True), + ('nonzero', False), + ('odd', False), + ('positive', False), + ('prime', False), + ('rational', True), + ('real', True), + ('transcendental', False), + ) ), + ), + # Implications of zero = False: + (('zero', False), set( ( + ) ), + ), + ] ) # full_implications + + +prereq = { + + # facts that could determine the value of algebraic + 'algebraic': { + 'commutative', + 'complex', + 'composite', + 'even', + 'finite', + 'infinite', + 'integer', + 'odd', + 'prime', + 'rational', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of antihermitian + 'antihermitian': { + 'imaginary', + }, + + # facts that could determine the value of commutative + 'commutative': { + 'algebraic', + 'complex', + 'composite', + 'even', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'imaginary', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of complex + 'complex': { + 'algebraic', + 'commutative', + 'composite', + 'even', + 'finite', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of composite + 'composite': { + 'algebraic', + 'commutative', + 'complex', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of even + 'even': { + 'algebraic', + 'commutative', + 'complex', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'noninteger', + 'odd', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of extended_negative + 'extended_negative': { + 'commutative', + 'composite', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'imaginary', + 'negative', + 'nonnegative', + 'positive', + 'prime', + 'zero', + }, + + # facts that could determine the value of extended_nonnegative + 'extended_nonnegative': { + 'commutative', + 'composite', + 'extended_negative', + 'extended_positive', + 'extended_real', + 'imaginary', + 'negative', + 'nonnegative', + 'positive', + 'prime', + 'zero', + }, + + # facts that could determine the value of extended_nonpositive + 'extended_nonpositive': { + 'commutative', + 'composite', + 'extended_negative', + 'extended_positive', + 'extended_real', + 'imaginary', + 'negative', + 'nonpositive', + 'positive', + 'prime', + 'zero', + }, + + # facts that could determine the value of extended_nonzero + 'extended_nonzero': { + 'commutative', + 'composite', + 'extended_negative', + 'extended_positive', + 'extended_real', + 'imaginary', + 'irrational', + 'negative', + 'noninteger', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'zero', + }, + + # facts that could determine the value of extended_positive + 'extended_positive': { + 'commutative', + 'composite', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_real', + 'imaginary', + 'negative', + 'nonpositive', + 'positive', + 'prime', + 'zero', + }, + + # facts that could determine the value of extended_real + 'extended_real': { + 'commutative', + 'composite', + 'even', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'imaginary', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'zero', + }, + + # facts that could determine the value of finite + 'finite': { + 'algebraic', + 'complex', + 'composite', + 'even', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of hermitian + 'hermitian': { + 'composite', + 'even', + 'integer', + 'irrational', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'zero', + }, + + # facts that could determine the value of imaginary + 'imaginary': { + 'antihermitian', + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'zero', + }, + + # facts that could determine the value of infinite + 'infinite': { + 'algebraic', + 'complex', + 'composite', + 'even', + 'finite', + 'imaginary', + 'integer', + 'irrational', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of integer + 'integer': { + 'algebraic', + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'irrational', + 'noninteger', + 'odd', + 'prime', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of irrational + 'irrational': { + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'odd', + 'prime', + 'rational', + 'real', + 'zero', + }, + + # facts that could determine the value of negative + 'negative': { + 'commutative', + 'complex', + 'composite', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'positive', + 'prime', + 'real', + 'zero', + }, + + # facts that could determine the value of noninteger + 'noninteger': { + 'commutative', + 'composite', + 'even', + 'extended_real', + 'imaginary', + 'integer', + 'irrational', + 'odd', + 'prime', + 'zero', + }, + + # facts that could determine the value of nonnegative + 'nonnegative': { + 'commutative', + 'complex', + 'composite', + 'extended_negative', + 'extended_nonnegative', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'negative', + 'positive', + 'prime', + 'real', + 'zero', + }, + + # facts that could determine the value of nonpositive + 'nonpositive': { + 'commutative', + 'complex', + 'composite', + 'extended_nonpositive', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'negative', + 'positive', + 'prime', + 'real', + 'zero', + }, + + # facts that could determine the value of nonzero + 'nonzero': { + 'commutative', + 'complex', + 'composite', + 'extended_nonzero', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'irrational', + 'negative', + 'odd', + 'positive', + 'prime', + 'real', + 'zero', + }, + + # facts that could determine the value of odd + 'odd': { + 'algebraic', + 'commutative', + 'complex', + 'even', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'noninteger', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of positive + 'positive': { + 'commutative', + 'complex', + 'composite', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'prime', + 'real', + 'zero', + }, + + # facts that could determine the value of prime + 'prime': { + 'algebraic', + 'commutative', + 'complex', + 'composite', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'positive', + 'rational', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of rational + 'rational': { + 'algebraic', + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'odd', + 'prime', + 'real', + 'transcendental', + 'zero', + }, + + # facts that could determine the value of real + 'real': { + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'zero', + }, + + # facts that could determine the value of transcendental + 'transcendental': { + 'algebraic', + 'commutative', + 'complex', + 'composite', + 'even', + 'finite', + 'infinite', + 'integer', + 'odd', + 'prime', + 'rational', + 'zero', + }, + + # facts that could determine the value of zero + 'zero': { + 'algebraic', + 'commutative', + 'complex', + 'composite', + 'even', + 'extended_negative', + 'extended_nonnegative', + 'extended_nonpositive', + 'extended_nonzero', + 'extended_positive', + 'extended_real', + 'finite', + 'hermitian', + 'imaginary', + 'infinite', + 'integer', + 'irrational', + 'negative', + 'noninteger', + 'nonnegative', + 'nonpositive', + 'nonzero', + 'odd', + 'positive', + 'prime', + 'rational', + 'real', + 'transcendental', + }, + +} # prereq + + +# Note: the order of the beta rules is used in the beta_triggers +beta_rules = [ + + # Rules implying composite = True + ({('even', True), ('positive', True), ('prime', False)}, + ('composite', True)), + + # Rules implying even = False + ({('composite', False), ('positive', True), ('prime', False)}, + ('even', False)), + + # Rules implying even = True + ({('integer', True), ('odd', False)}, + ('even', True)), + + # Rules implying extended_negative = True + ({('extended_positive', False), ('extended_real', True), ('zero', False)}, + ('extended_negative', True)), + ({('extended_nonpositive', True), ('extended_nonzero', True)}, + ('extended_negative', True)), + + # Rules implying extended_nonnegative = True + ({('extended_negative', False), ('extended_real', True)}, + ('extended_nonnegative', True)), + + # Rules implying extended_nonpositive = True + ({('extended_positive', False), ('extended_real', True)}, + ('extended_nonpositive', True)), + + # Rules implying extended_nonzero = True + ({('extended_real', True), ('zero', False)}, + ('extended_nonzero', True)), + + # Rules implying extended_positive = True + ({('extended_negative', False), ('extended_real', True), ('zero', False)}, + ('extended_positive', True)), + ({('extended_nonnegative', True), ('extended_nonzero', True)}, + ('extended_positive', True)), + + # Rules implying extended_real = False + ({('infinite', False), ('real', False)}, + ('extended_real', False)), + ({('extended_negative', False), ('extended_positive', False), ('zero', False)}, + ('extended_real', False)), + + # Rules implying infinite = True + ({('extended_real', True), ('real', False)}, + ('infinite', True)), + + # Rules implying irrational = True + ({('rational', False), ('real', True)}, + ('irrational', True)), + + # Rules implying negative = True + ({('positive', False), ('real', True), ('zero', False)}, + ('negative', True)), + ({('nonpositive', True), ('nonzero', True)}, + ('negative', True)), + ({('extended_negative', True), ('finite', True)}, + ('negative', True)), + + # Rules implying noninteger = True + ({('extended_real', True), ('integer', False)}, + ('noninteger', True)), + + # Rules implying nonnegative = True + ({('negative', False), ('real', True)}, + ('nonnegative', True)), + ({('extended_nonnegative', True), ('finite', True)}, + ('nonnegative', True)), + + # Rules implying nonpositive = True + ({('positive', False), ('real', True)}, + ('nonpositive', True)), + ({('extended_nonpositive', True), ('finite', True)}, + ('nonpositive', True)), + + # Rules implying nonzero = True + ({('extended_nonzero', True), ('finite', True)}, + ('nonzero', True)), + + # Rules implying odd = True + ({('even', False), ('integer', True)}, + ('odd', True)), + + # Rules implying positive = False + ({('composite', False), ('even', True), ('prime', False)}, + ('positive', False)), + + # Rules implying positive = True + ({('negative', False), ('real', True), ('zero', False)}, + ('positive', True)), + ({('nonnegative', True), ('nonzero', True)}, + ('positive', True)), + ({('extended_positive', True), ('finite', True)}, + ('positive', True)), + + # Rules implying prime = True + ({('composite', False), ('even', True), ('positive', True)}, + ('prime', True)), + + # Rules implying real = False + ({('negative', False), ('positive', False), ('zero', False)}, + ('real', False)), + + # Rules implying real = True + ({('extended_real', True), ('infinite', False)}, + ('real', True)), + ({('extended_real', True), ('finite', True)}, + ('real', True)), + + # Rules implying transcendental = True + ({('algebraic', False), ('complex', True)}, + ('transcendental', True)), + + # Rules implying zero = True + ({('extended_negative', False), ('extended_positive', False), ('extended_real', True)}, + ('zero', True)), + ({('negative', False), ('positive', False), ('real', True)}, + ('zero', True)), + ({('extended_nonnegative', True), ('extended_nonpositive', True)}, + ('zero', True)), + ({('nonnegative', True), ('nonpositive', True)}, + ('zero', True)), + +] # beta_rules +beta_triggers = { + ('algebraic', False): [32, 11, 3, 8, 29, 14, 25, 13, 17, 7], + ('algebraic', True): [10, 30, 31, 27, 16, 21, 19, 22], + ('antihermitian', False): [], + ('commutative', False): [], + ('complex', False): [10, 12, 11, 3, 8, 17, 7], + ('complex', True): [32, 10, 30, 31, 27, 16, 21, 19, 22], + ('composite', False): [1, 28, 24], + ('composite', True): [23, 2], + ('even', False): [23, 11, 3, 8, 29, 14, 25, 7], + ('even', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 0, 28, 24, 7], + ('extended_negative', False): [11, 33, 8, 5, 29, 34, 25, 18], + ('extended_negative', True): [30, 12, 31, 29, 14, 20, 16, 21, 22, 17], + ('extended_nonnegative', False): [11, 3, 6, 29, 14, 20, 7], + ('extended_nonnegative', True): [30, 12, 31, 33, 8, 9, 6, 29, 34, 25, 18, 19, 35, 17, 7], + ('extended_nonpositive', False): [11, 8, 5, 29, 25, 18, 7], + ('extended_nonpositive', True): [30, 12, 31, 3, 33, 4, 5, 29, 14, 34, 20, 21, 35, 17, 7], + ('extended_nonzero', False): [11, 33, 6, 5, 29, 34, 20, 18], + ('extended_nonzero', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22, 17], + ('extended_positive', False): [11, 3, 33, 6, 29, 14, 34, 20], + ('extended_positive', True): [30, 12, 31, 29, 25, 18, 27, 19, 22, 17], + ('extended_real', False): [], + ('extended_real', True): [30, 12, 31, 3, 33, 8, 6, 5, 17, 7], + ('finite', False): [11, 3, 8, 17, 7], + ('finite', True): [10, 30, 31, 27, 16, 21, 19, 22], + ('hermitian', False): [10, 12, 11, 3, 8, 17, 7], + ('imaginary', True): [32], + ('infinite', False): [10, 30, 31, 27, 16, 21, 19, 22], + ('infinite', True): [11, 3, 8, 17, 7], + ('integer', False): [11, 3, 8, 29, 14, 25, 17, 7], + ('integer', True): [23, 2, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 7], + ('irrational', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19], + ('negative', False): [29, 34, 25, 18], + ('negative', True): [32, 13, 17], + ('noninteger', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22], + ('nonnegative', False): [11, 3, 8, 29, 14, 20, 7], + ('nonnegative', True): [32, 33, 8, 9, 6, 34, 25, 26, 20, 27, 21, 22, 35, 36, 13, 17, 7], + ('nonpositive', False): [11, 3, 8, 29, 25, 18, 7], + ('nonpositive', True): [32, 3, 33, 4, 5, 14, 34, 15, 18, 16, 19, 22, 35, 36, 13, 17, 7], + ('nonzero', False): [29, 34, 20, 18], + ('nonzero', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19, 13, 17], + ('odd', False): [2], + ('odd', True): [3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19], + ('positive', False): [29, 14, 34, 20], + ('positive', True): [32, 0, 1, 28, 13, 17], + ('prime', False): [0, 1, 24], + ('prime', True): [23, 2], + ('rational', False): [11, 3, 8, 29, 14, 25, 13, 17, 7], + ('rational', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 17, 7], + ('real', False): [10, 12, 11, 3, 8, 17, 7], + ('real', True): [32, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 13, 17, 7], + ('transcendental', True): [10, 30, 31, 11, 3, 8, 29, 14, 25, 27, 16, 21, 19, 22, 13, 17, 7], + ('zero', False): [11, 3, 8, 29, 14, 25, 7], + ('zero', True): [], +} # beta_triggers + + +generated_assumptions = {'defined_facts': defined_facts, 'full_implications': full_implications, + 'prereq': prereq, 'beta_rules': beta_rules, 'beta_triggers': beta_triggers} diff --git a/lib/python3.11/site-packages/sympy/core/backend.py b/lib/python3.11/site-packages/sympy/core/backend.py new file mode 100644 index 0000000000000000000000000000000000000000..ea801b74df3822d274d4e7f287c68d51619d5889 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/backend.py @@ -0,0 +1,120 @@ +import os +USE_SYMENGINE = os.getenv('USE_SYMENGINE', '0') +USE_SYMENGINE = USE_SYMENGINE.lower() in ('1', 't', 'true') # type: ignore + +if USE_SYMENGINE: + from symengine import (Symbol, Integer, sympify as sympify_symengine, S, + SympifyError, exp, log, gamma, sqrt, I, E, pi, Matrix, + sin, cos, tan, cot, csc, sec, asin, acos, atan, acot, acsc, asec, + sinh, cosh, tanh, coth, asinh, acosh, atanh, acoth, + lambdify, symarray, diff, zeros, eye, diag, ones, + expand, Function, symbols, var, Add, Mul, Derivative, + ImmutableMatrix, MatrixBase, Rational, Basic) + from symengine.lib.symengine_wrapper import gcd as igcd + from symengine import AppliedUndef + + def sympify(a, *, strict=False): + """ + Notes + ===== + + SymEngine's ``sympify`` does not accept keyword arguments and is + therefore not compatible with SymPy's ``sympify`` with ``strict=True`` + (which ensures that only the types for which an explicit conversion has + been defined are converted). This wrapper adds an addiotional parameter + ``strict`` (with default ``False``) that will raise a ``SympifyError`` + if ``strict=True`` and the argument passed to the parameter ``a`` is a + string. + + See Also + ======== + + sympify: Converts an arbitrary expression to a type that can be used + inside SymPy. + + """ + # The parameter ``a`` is used for this function to keep compatibility + # with the SymEngine docstring. + if strict and isinstance(a, str): + raise SympifyError(a) + return sympify_symengine(a) + + # Keep the SymEngine docstring and append the additional "Notes" and "See + # Also" sections. Replacement of spaces is required to correctly format the + # indentation of the combined docstring. + sympify.__doc__ = ( + sympify_symengine.__doc__ + + sympify.__doc__.replace(' ', ' ') # type: ignore + ) +else: + from sympy.core.add import Add + from sympy.core.basic import Basic + from sympy.core.function import (diff, Function, AppliedUndef, + expand, Derivative) + from sympy.core.mul import Mul + from sympy.core.intfunc import igcd + from sympy.core.numbers import pi, I, Integer, Rational, E + from sympy.core.singleton import S + from sympy.core.symbol import Symbol, var, symbols + from sympy.core.sympify import SympifyError, sympify + from sympy.functions.elementary.exponential import log, exp + from sympy.functions.elementary.hyperbolic import (coth, sinh, + acosh, acoth, tanh, asinh, atanh, cosh) + from sympy.functions.elementary.miscellaneous import sqrt + from sympy.functions.elementary.trigonometric import (csc, + asec, cos, atan, sec, acot, asin, tan, sin, cot, acsc, acos) + from sympy.functions.special.gamma_functions import gamma + from sympy.matrices.dense import (eye, zeros, diag, Matrix, + ones, symarray) + from sympy.matrices.immutable import ImmutableMatrix + from sympy.matrices.matrixbase import MatrixBase + from sympy.utilities.lambdify import lambdify + + +# +# XXX: Handling of immutable and mutable matrices in SymEngine is inconsistent +# with SymPy's matrix classes in at least SymEngine version 0.7.0. Until that +# is fixed the function below is needed for consistent behaviour when +# attempting to simplify a matrix. +# +# Expected behaviour of a SymPy mutable/immutable matrix .simplify() method: +# +# Matrix.simplify() : works in place, returns None +# ImmutableMatrix.simplify() : returns a simplified copy +# +# In SymEngine both mutable and immutable matrices simplify in place and return +# None. This is inconsistent with the matrix being "immutable" and also the +# returned None leads to problems in the mechanics module. +# +# The simplify function should not be used because simplify(M) sympifies the +# matrix M and the SymEngine matrices all sympify to SymPy matrices. If we want +# to work with SymEngine matrices then we need to use their .simplify() method +# but that method does not work correctly with immutable matrices. +# +# The _simplify_matrix function can be removed when the SymEngine bug is fixed. +# Since this should be a temporary problem we do not make this function part of +# the public API. +# +# SymEngine issue: https://github.com/symengine/symengine.py/issues/363 +# + +def _simplify_matrix(M): + """Return a simplified copy of the matrix M""" + if not isinstance(M, (Matrix, ImmutableMatrix)): + raise TypeError("The matrix M must be an instance of Matrix or ImmutableMatrix") + Mnew = M.as_mutable() # makes a copy if mutable + Mnew.simplify() + if isinstance(M, ImmutableMatrix): + Mnew = Mnew.as_immutable() + return Mnew + + +__all__ = [ + 'Symbol', 'Integer', 'sympify', 'S', 'SympifyError', 'exp', 'log', + 'gamma', 'sqrt', 'I', 'E', 'pi', 'Matrix', 'sin', 'cos', 'tan', 'cot', + 'csc', 'sec', 'asin', 'acos', 'atan', 'acot', 'acsc', 'asec', 'sinh', + 'cosh', 'tanh', 'coth', 'asinh', 'acosh', 'atanh', 'acoth', 'lambdify', + 'symarray', 'diff', 'zeros', 'eye', 'diag', 'ones', 'expand', 'Function', + 'symbols', 'var', 'Add', 'Mul', 'Derivative', 'ImmutableMatrix', + 'MatrixBase', 'Rational', 'Basic', 'igcd', 'AppliedUndef', +] diff --git a/lib/python3.11/site-packages/sympy/core/basic.py b/lib/python3.11/site-packages/sympy/core/basic.py new file mode 100644 index 0000000000000000000000000000000000000000..caab088cf2663c2ff55f807e085ae95f93a5a5e3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/basic.py @@ -0,0 +1,2339 @@ +"""Base class for all the objects in SymPy""" +from __future__ import annotations + +from collections import defaultdict +from collections.abc import Mapping +from itertools import chain, zip_longest +from functools import cmp_to_key + +from .assumptions import _prepare_class_assumptions +from .cache import cacheit +from .sympify import _sympify, sympify, SympifyError, _external_converter +from .sorting import ordered +from .kind import Kind, UndefinedKind +from ._print_helpers import Printable + +from sympy.utilities.decorator import deprecated +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import iterable, numbered_symbols +from sympy.utilities.misc import filldedent, func_name + +from inspect import getmro + + +def as_Basic(expr): + """Return expr as a Basic instance using strict sympify + or raise a TypeError; this is just a wrapper to _sympify, + raising a TypeError instead of a SympifyError.""" + try: + return _sympify(expr) + except SympifyError: + raise TypeError( + 'Argument must be a Basic object, not `%s`' % func_name( + expr)) + + +# Key for sorting commutative args in canonical order +# by name. This is used for canonical ordering of the +# args for Add and Mul *if* the names of both classes +# being compared appear here. Some things in this list +# are not spelled the same as their name so they do not, +# in effect, appear here. See Basic.compare. +ordering_of_classes = [ + # singleton numbers + 'Zero', 'One', 'Half', 'Infinity', 'NaN', 'NegativeOne', 'NegativeInfinity', + # numbers + 'Integer', 'Rational', 'Float', + # singleton symbols + 'Exp1', 'Pi', 'ImaginaryUnit', + # symbols + 'Symbol', 'Wild', + # arithmetic operations + 'Pow', 'Mul', 'Add', + # function values + 'Derivative', 'Integral', + # defined singleton functions + 'Abs', 'Sign', 'Sqrt', + 'Floor', 'Ceiling', + 'Re', 'Im', 'Arg', + 'Conjugate', + 'Exp', 'Log', + 'Sin', 'Cos', 'Tan', 'Cot', 'ASin', 'ACos', 'ATan', 'ACot', + 'Sinh', 'Cosh', 'Tanh', 'Coth', 'ASinh', 'ACosh', 'ATanh', 'ACoth', + 'RisingFactorial', 'FallingFactorial', + 'factorial', 'binomial', + 'Gamma', 'LowerGamma', 'UpperGamma', 'PolyGamma', + 'Erf', + # special polynomials + 'Chebyshev', 'Chebyshev2', + # undefined functions + 'Function', 'WildFunction', + # anonymous functions + 'Lambda', + # Landau O symbol + 'Order', + # relational operations + 'Equality', 'Unequality', 'StrictGreaterThan', 'StrictLessThan', + 'GreaterThan', 'LessThan', +] + +def _cmp_name(x: type, y: type) -> int: + """return -1, 0, 1 if the name of x is before that of y. + A string comparison is done if either name does not appear + in `ordering_of_classes`. This is the helper for + ``Basic.compare`` + + Examples + ======== + + >>> from sympy import cos, tan, sin + >>> from sympy.core import basic + >>> save = basic.ordering_of_classes + >>> basic.ordering_of_classes = () + >>> basic._cmp_name(cos, tan) + -1 + >>> basic.ordering_of_classes = ["tan", "sin", "cos"] + >>> basic._cmp_name(cos, tan) + 1 + >>> basic._cmp_name(sin, cos) + -1 + >>> basic.ordering_of_classes = save + + """ + # If the other object is not a Basic subclass, then we are not equal to it. + if not issubclass(y, Basic): + return -1 + + n1 = x.__name__ + n2 = y.__name__ + if n1 == n2: + return 0 + + UNKNOWN = len(ordering_of_classes) + 1 + try: + i1 = ordering_of_classes.index(n1) + except ValueError: + i1 = UNKNOWN + try: + i2 = ordering_of_classes.index(n2) + except ValueError: + i2 = UNKNOWN + if i1 == UNKNOWN and i2 == UNKNOWN: + return (n1 > n2) - (n1 < n2) + return (i1 > i2) - (i1 < i2) + + +class Basic(Printable): + """ + Base class for all SymPy objects. + + Notes and conventions + ===================== + + 1) Always use ``.args``, when accessing parameters of some instance: + + >>> from sympy import cot + >>> from sympy.abc import x, y + + >>> cot(x).args + (x,) + + >>> cot(x).args[0] + x + + >>> (x*y).args + (x, y) + + >>> (x*y).args[1] + y + + + 2) Never use internal methods or variables (the ones prefixed with ``_``): + + >>> cot(x)._args # do not use this, use cot(x).args instead + (x,) + + + 3) By "SymPy object" we mean something that can be returned by + ``sympify``. But not all objects one encounters using SymPy are + subclasses of Basic. For example, mutable objects are not: + + >>> from sympy import Basic, Matrix, sympify + >>> A = Matrix([[1, 2], [3, 4]]).as_mutable() + >>> isinstance(A, Basic) + False + + >>> B = sympify(A) + >>> isinstance(B, Basic) + True + """ + __slots__ = ('_mhash', # hash value + '_args', # arguments + '_assumptions' + ) + + _args: tuple[Basic, ...] + _mhash: int | None + + @property + def __sympy__(self): + return True + + def __init_subclass__(cls): + # Initialize the default_assumptions FactKB and also any assumptions + # property methods. This method will only be called for subclasses of + # Basic but not for Basic itself so we call + # _prepare_class_assumptions(Basic) below the class definition. + super().__init_subclass__() + _prepare_class_assumptions(cls) + + # To be overridden with True in the appropriate subclasses + is_number = False + is_Atom = False + is_Symbol = False + is_symbol = False + is_Indexed = False + is_Dummy = False + is_Wild = False + is_Function = False + is_Add = False + is_Mul = False + is_Pow = False + is_Number = False + is_Float = False + is_Rational = False + is_Integer = False + is_NumberSymbol = False + is_Order = False + is_Derivative = False + is_Piecewise = False + is_Poly = False + is_AlgebraicNumber = False + is_Relational = False + is_Equality = False + is_Boolean = False + is_Not = False + is_Matrix = False + is_Vector = False + is_Point = False + is_MatAdd = False + is_MatMul = False + is_real: bool | None + is_extended_real: bool | None + is_zero: bool | None + is_negative: bool | None + is_commutative: bool | None + + kind: Kind = UndefinedKind + + def __new__(cls, *args): + obj = object.__new__(cls) + obj._assumptions = cls.default_assumptions + obj._mhash = None # will be set by __hash__ method. + + obj._args = args # all items in args must be Basic objects + return obj + + def copy(self): + return self.func(*self.args) + + def __getnewargs__(self): + return self.args + + def __getstate__(self): + return None + + def __setstate__(self, state): + for name, value in state.items(): + setattr(self, name, value) + + def __reduce_ex__(self, protocol): + if protocol < 2: + msg = "Only pickle protocol 2 or higher is supported by SymPy" + raise NotImplementedError(msg) + return super().__reduce_ex__(protocol) + + def __hash__(self) -> int: + # hash cannot be cached using cache_it because infinite recurrence + # occurs as hash is needed for setting cache dictionary keys + h = self._mhash + if h is None: + h = hash((type(self).__name__,) + self._hashable_content()) + self._mhash = h + return h + + def _hashable_content(self): + """Return a tuple of information about self that can be used to + compute the hash. If a class defines additional attributes, + like ``name`` in Symbol, then this method should be updated + accordingly to return such relevant attributes. + + Defining more than _hashable_content is necessary if __eq__ has + been defined by a class. See note about this in Basic.__eq__.""" + return self._args + + @property + def assumptions0(self): + """ + Return object `type` assumptions. + + For example: + + Symbol('x', real=True) + Symbol('x', integer=True) + + are different objects. In other words, besides Python type (Symbol in + this case), the initial assumptions are also forming their typeinfo. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.abc import x + >>> x.assumptions0 + {'commutative': True} + >>> x = Symbol("x", positive=True) + >>> x.assumptions0 + {'commutative': True, 'complex': True, 'extended_negative': False, + 'extended_nonnegative': True, 'extended_nonpositive': False, + 'extended_nonzero': True, 'extended_positive': True, 'extended_real': + True, 'finite': True, 'hermitian': True, 'imaginary': False, + 'infinite': False, 'negative': False, 'nonnegative': True, + 'nonpositive': False, 'nonzero': True, 'positive': True, 'real': + True, 'zero': False} + """ + return {} + + def compare(self, other): + """ + Return -1, 0, 1 if the object is less than, equal, + or greater than other in a canonical sense. + Non-Basic are always greater than Basic. + If both names of the classes being compared appear + in the `ordering_of_classes` then the ordering will + depend on the appearance of the names there. + If either does not appear in that list, then the + comparison is based on the class name. + If the names are the same then a comparison is made + on the length of the hashable content. + Items of the equal-lengthed contents are then + successively compared using the same rules. If there + is never a difference then 0 is returned. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> x.compare(y) + -1 + >>> x.compare(x) + 0 + >>> y.compare(x) + 1 + + """ + # all redefinitions of __cmp__ method should start with the + # following lines: + if self is other: + return 0 + n1 = self.__class__ + n2 = other.__class__ + c = _cmp_name(n1, n2) + if c: + return c + # + st = self._hashable_content() + ot = other._hashable_content() + c = (len(st) > len(ot)) - (len(st) < len(ot)) + if c: + return c + for l, r in zip(st, ot): + l = Basic(*l) if isinstance(l, frozenset) else l + r = Basic(*r) if isinstance(r, frozenset) else r + if isinstance(l, Basic): + c = l.compare(r) + else: + c = (l > r) - (l < r) + if c: + return c + return 0 + + @staticmethod + def _compare_pretty(a, b): + """return -1, 0, 1 if a is canonically less, equal or + greater than b. This is used when 'order=old' is selected + for printing. This puts Order last, orders Rationals + according to value, puts terms in order wrt the power of + the last power appearing in a term. Ties are broken using + Basic.compare. + """ + from sympy.series.order import Order + if isinstance(a, Order) and not isinstance(b, Order): + return 1 + if not isinstance(a, Order) and isinstance(b, Order): + return -1 + + if a.is_Rational and b.is_Rational: + l = a.p * b.q + r = b.p * a.q + return (l > r) - (l < r) + else: + from .symbol import Wild + p1, p2, p3 = Wild("p1"), Wild("p2"), Wild("p3") + r_a = a.match(p1 * p2**p3) + if r_a and p3 in r_a: + a3 = r_a[p3] + r_b = b.match(p1 * p2**p3) + if r_b and p3 in r_b: + b3 = r_b[p3] + c = Basic.compare(a3, b3) + if c != 0: + return c + + # break ties + return Basic.compare(a, b) + + @classmethod + def fromiter(cls, args, **assumptions): + """ + Create a new object from an iterable. + + This is a convenience function that allows one to create objects from + any iterable, without having to convert to a list or tuple first. + + Examples + ======== + + >>> from sympy import Tuple + >>> Tuple.fromiter(i for i in range(5)) + (0, 1, 2, 3, 4) + + """ + return cls(*tuple(args), **assumptions) + + @classmethod + def class_key(cls): + """Nice order of classes.""" + return 5, 0, cls.__name__ + + @cacheit + def sort_key(self, order=None): + """ + Return a sort key. + + Examples + ======== + + >>> from sympy import S, I + + >>> sorted([S(1)/2, I, -I], key=lambda x: x.sort_key()) + [1/2, -I, I] + + >>> S("[x, 1/x, 1/x**2, x**2, x**(1/2), x**(1/4), x**(3/2)]") + [x, 1/x, x**(-2), x**2, sqrt(x), x**(1/4), x**(3/2)] + >>> sorted(_, key=lambda x: x.sort_key()) + [x**(-2), 1/x, x**(1/4), sqrt(x), x, x**(3/2), x**2] + + """ + + # XXX: remove this when issue 5169 is fixed + def inner_key(arg): + if isinstance(arg, Basic): + return arg.sort_key(order) + else: + return arg + + args = self._sorted_args + args = len(args), tuple([inner_key(arg) for arg in args]) + return self.class_key(), args, S.One.sort_key(), S.One + + def _do_eq_sympify(self, other): + """Returns a boolean indicating whether a == b when either a + or b is not a Basic. This is only done for types that were either + added to `converter` by a 3rd party or when the object has `_sympy_` + defined. This essentially reuses the code in `_sympify` that is + specific for this use case. Non-user defined types that are meant + to work with SymPy should be handled directly in the __eq__ methods + of the `Basic` classes it could equate to and not be converted. Note + that after conversion, `==` is used again since it is not + necessarily clear whether `self` or `other`'s __eq__ method needs + to be used.""" + for superclass in type(other).__mro__: + conv = _external_converter.get(superclass) + if conv is not None: + return self == conv(other) + if hasattr(other, '_sympy_'): + return self == other._sympy_() + return NotImplemented + + def __eq__(self, other): + """Return a boolean indicating whether a == b on the basis of + their symbolic trees. + + This is the same as a.compare(b) == 0 but faster. + + Notes + ===== + + If a class that overrides __eq__() needs to retain the + implementation of __hash__() from a parent class, the + interpreter must be told this explicitly by setting + __hash__ : Callable[[object], int] = .__hash__. + Otherwise the inheritance of __hash__() will be blocked, + just as if __hash__ had been explicitly set to None. + + References + ========== + + from https://docs.python.org/dev/reference/datamodel.html#object.__hash__ + """ + if self is other: + return True + + if not isinstance(other, Basic): + return self._do_eq_sympify(other) + + # check for pure number expr + if not (self.is_Number and other.is_Number) and ( + type(self) != type(other)): + return False + a, b = self._hashable_content(), other._hashable_content() + if a != b: + return False + # check number *in* an expression + for a, b in zip(a, b): + if not isinstance(a, Basic): + continue + if a.is_Number and type(a) != type(b): + return False + return True + + def __ne__(self, other): + """``a != b`` -> Compare two symbolic trees and see whether they are different + + this is the same as: + + ``a.compare(b) != 0`` + + but faster + """ + return not self == other + + def dummy_eq(self, other, symbol=None): + """ + Compare two expressions and handle dummy symbols. + + Examples + ======== + + >>> from sympy import Dummy + >>> from sympy.abc import x, y + + >>> u = Dummy('u') + + >>> (u**2 + 1).dummy_eq(x**2 + 1) + True + >>> (u**2 + 1) == (x**2 + 1) + False + + >>> (u**2 + y).dummy_eq(x**2 + y, x) + True + >>> (u**2 + y).dummy_eq(x**2 + y, y) + False + + """ + s = self.as_dummy() + o = _sympify(other) + o = o.as_dummy() + + dummy_symbols = [i for i in s.free_symbols if i.is_Dummy] + + if len(dummy_symbols) == 1: + dummy = dummy_symbols.pop() + else: + return s == o + + if symbol is None: + symbols = o.free_symbols + + if len(symbols) == 1: + symbol = symbols.pop() + else: + return s == o + + tmp = dummy.__class__() + + return s.xreplace({dummy: tmp}) == o.xreplace({symbol: tmp}) + + def atoms(self, *types): + """Returns the atoms that form the current object. + + By default, only objects that are truly atomic and cannot + be divided into smaller pieces are returned: symbols, numbers, + and number symbols like I and pi. It is possible to request + atoms of any type, however, as demonstrated below. + + Examples + ======== + + >>> from sympy import I, pi, sin + >>> from sympy.abc import x, y + >>> (1 + x + 2*sin(y + I*pi)).atoms() + {1, 2, I, pi, x, y} + + If one or more types are given, the results will contain only + those types of atoms. + + >>> from sympy import Number, NumberSymbol, Symbol + >>> (1 + x + 2*sin(y + I*pi)).atoms(Symbol) + {x, y} + + >>> (1 + x + 2*sin(y + I*pi)).atoms(Number) + {1, 2} + + >>> (1 + x + 2*sin(y + I*pi)).atoms(Number, NumberSymbol) + {1, 2, pi} + + >>> (1 + x + 2*sin(y + I*pi)).atoms(Number, NumberSymbol, I) + {1, 2, I, pi} + + Note that I (imaginary unit) and zoo (complex infinity) are special + types of number symbols and are not part of the NumberSymbol class. + + The type can be given implicitly, too: + + >>> (1 + x + 2*sin(y + I*pi)).atoms(x) # x is a Symbol + {x, y} + + Be careful to check your assumptions when using the implicit option + since ``S(1).is_Integer = True`` but ``type(S(1))`` is ``One``, a special type + of SymPy atom, while ``type(S(2))`` is type ``Integer`` and will find all + integers in an expression: + + >>> from sympy import S + >>> (1 + x + 2*sin(y + I*pi)).atoms(S(1)) + {1} + + >>> (1 + x + 2*sin(y + I*pi)).atoms(S(2)) + {1, 2} + + Finally, arguments to atoms() can select more than atomic atoms: any + SymPy type (loaded in core/__init__.py) can be listed as an argument + and those types of "atoms" as found in scanning the arguments of the + expression recursively: + + >>> from sympy import Function, Mul + >>> from sympy.core.function import AppliedUndef + >>> f = Function('f') + >>> (1 + f(x) + 2*sin(y + I*pi)).atoms(Function) + {f(x), sin(y + I*pi)} + >>> (1 + f(x) + 2*sin(y + I*pi)).atoms(AppliedUndef) + {f(x)} + + >>> (1 + x + 2*sin(y + I*pi)).atoms(Mul) + {I*pi, 2*sin(y + I*pi)} + + """ + if types: + types = tuple( + [t if isinstance(t, type) else type(t) for t in types]) + nodes = _preorder_traversal(self) + if types: + result = {node for node in nodes if isinstance(node, types)} + else: + result = {node for node in nodes if not node.args} + return result + + @property + def free_symbols(self) -> set[Basic]: + """Return from the atoms of self those which are free symbols. + + Not all free symbols are ``Symbol``. Eg: IndexedBase('I')[0].free_symbols + + For most expressions, all symbols are free symbols. For some classes + this is not true. e.g. Integrals use Symbols for the dummy variables + which are bound variables, so Integral has a method to return all + symbols except those. Derivative keeps track of symbols with respect + to which it will perform a derivative; those are + bound variables, too, so it has its own free_symbols method. + + Any other method that uses bound variables should implement a + free_symbols method.""" + empty: set[Basic] = set() + return empty.union(*(a.free_symbols for a in self.args)) + + @property + def expr_free_symbols(self): + sympy_deprecation_warning(""" + The expr_free_symbols property is deprecated. Use free_symbols to get + the free symbols of an expression. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-expr-free-symbols") + return set() + + def as_dummy(self): + """Return the expression with any objects having structurally + bound symbols replaced with unique, canonical symbols within + the object in which they appear and having only the default + assumption for commutativity being True. When applied to a + symbol a new symbol having only the same commutativity will be + returned. + + Examples + ======== + + >>> from sympy import Integral, Symbol + >>> from sympy.abc import x + >>> r = Symbol('r', real=True) + >>> Integral(r, (r, x)).as_dummy() + Integral(_0, (_0, x)) + >>> _.variables[0].is_real is None + True + >>> r.as_dummy() + _r + + Notes + ===== + + Any object that has structurally bound variables should have + a property, `bound_symbols` that returns those symbols + appearing in the object. + """ + from .symbol import Dummy, Symbol + def can(x): + # mask free that shadow bound + free = x.free_symbols + bound = set(x.bound_symbols) + d = {i: Dummy() for i in bound & free} + x = x.subs(d) + # replace bound with canonical names + x = x.xreplace(x.canonical_variables) + # return after undoing masking + return x.xreplace({v: k for k, v in d.items()}) + if not self.has(Symbol): + return self + return self.replace( + lambda x: hasattr(x, 'bound_symbols'), + can, + simultaneous=False) + + @property + def canonical_variables(self): + """Return a dictionary mapping any variable defined in + ``self.bound_symbols`` to Symbols that do not clash + with any free symbols in the expression. + + Examples + ======== + + >>> from sympy import Lambda + >>> from sympy.abc import x + >>> Lambda(x, 2*x).canonical_variables + {x: _0} + """ + if not hasattr(self, 'bound_symbols'): + return {} + dums = numbered_symbols('_') + reps = {} + # watch out for free symbol that are not in bound symbols; + # those that are in bound symbols are about to get changed + bound = self.bound_symbols + names = {i.name for i in self.free_symbols - set(bound)} + for b in bound: + d = next(dums) + if b.is_Symbol: + while d.name in names: + d = next(dums) + reps[b] = d + return reps + + def rcall(self, *args): + """Apply on the argument recursively through the expression tree. + + This method is used to simulate a common abuse of notation for + operators. For instance, in SymPy the following will not work: + + ``(x+Lambda(y, 2*y))(z) == x+2*z``, + + however, you can use: + + >>> from sympy import Lambda + >>> from sympy.abc import x, y, z + >>> (x + Lambda(y, 2*y)).rcall(z) + x + 2*z + """ + return Basic._recursive_call(self, args) + + @staticmethod + def _recursive_call(expr_to_call, on_args): + """Helper for rcall method.""" + from .symbol import Symbol + def the_call_method_is_overridden(expr): + for cls in getmro(type(expr)): + if '__call__' in cls.__dict__: + return cls != Basic + + if callable(expr_to_call) and the_call_method_is_overridden(expr_to_call): + if isinstance(expr_to_call, Symbol): # XXX When you call a Symbol it is + return expr_to_call # transformed into an UndefFunction + else: + return expr_to_call(*on_args) + elif expr_to_call.args: + args = [Basic._recursive_call( + sub, on_args) for sub in expr_to_call.args] + return type(expr_to_call)(*args) + else: + return expr_to_call + + def is_hypergeometric(self, k): + from sympy.simplify.simplify import hypersimp + from sympy.functions.elementary.piecewise import Piecewise + if self.has(Piecewise): + return None + return hypersimp(self, k) is not None + + @property + def is_comparable(self): + """Return True if self can be computed to a real number + (or already is a real number) with precision, else False. + + Examples + ======== + + >>> from sympy import exp_polar, pi, I + >>> (I*exp_polar(I*pi/2)).is_comparable + True + >>> (I*exp_polar(I*pi*2)).is_comparable + False + + A False result does not mean that `self` cannot be rewritten + into a form that would be comparable. For example, the + difference computed below is zero but without simplification + it does not evaluate to a zero with precision: + + >>> e = 2**pi*(1 + 2**pi) + >>> dif = e - e.expand() + >>> dif.is_comparable + False + >>> dif.n(2)._prec + 1 + + """ + is_extended_real = self.is_extended_real + if is_extended_real is False: + return False + if not self.is_number: + return False + # don't re-eval numbers that are already evaluated since + # this will create spurious precision + n, i = [p.evalf(2) if not p.is_Number else p + for p in self.as_real_imag()] + if not (i.is_Number and n.is_Number): + return False + if i: + # if _prec = 1 we can't decide and if not, + # the answer is False because numbers with + # imaginary parts can't be compared + # so return False + return False + else: + return n._prec != 1 + + @property + def func(self): + """ + The top-level function in an expression. + + The following should hold for all objects:: + + >> x == x.func(*x.args) + + Examples + ======== + + >>> from sympy.abc import x + >>> a = 2*x + >>> a.func + + >>> a.args + (2, x) + >>> a.func(*a.args) + 2*x + >>> a == a.func(*a.args) + True + + """ + return self.__class__ + + @property + def args(self) -> tuple[Basic, ...]: + """Returns a tuple of arguments of 'self'. + + Examples + ======== + + >>> from sympy import cot + >>> from sympy.abc import x, y + + >>> cot(x).args + (x,) + + >>> cot(x).args[0] + x + + >>> (x*y).args + (x, y) + + >>> (x*y).args[1] + y + + Notes + ===== + + Never use self._args, always use self.args. + Only use _args in __new__ when creating a new function. + Do not override .args() from Basic (so that it is easy to + change the interface in the future if needed). + """ + return self._args + + @property + def _sorted_args(self): + """ + The same as ``args``. Derived classes which do not fix an + order on their arguments should override this method to + produce the sorted representation. + """ + return self.args + + def as_content_primitive(self, radical=False, clear=True): + """A stub to allow Basic args (like Tuple) to be skipped when computing + the content and primitive components of an expression. + + See Also + ======== + + sympy.core.expr.Expr.as_content_primitive + """ + return S.One, self + + def subs(self, *args, **kwargs): + """ + Substitutes old for new in an expression after sympifying args. + + `args` is either: + - two arguments, e.g. foo.subs(old, new) + - one iterable argument, e.g. foo.subs(iterable). The iterable may be + o an iterable container with (old, new) pairs. In this case the + replacements are processed in the order given with successive + patterns possibly affecting replacements already made. + o a dict or set whose key/value items correspond to old/new pairs. + In this case the old/new pairs will be sorted by op count and in + case of a tie, by number of args and the default_sort_key. The + resulting sorted list is then processed as an iterable container + (see previous). + + If the keyword ``simultaneous`` is True, the subexpressions will not be + evaluated until all the substitutions have been made. + + Examples + ======== + + >>> from sympy import pi, exp, limit, oo + >>> from sympy.abc import x, y + >>> (1 + x*y).subs(x, pi) + pi*y + 1 + >>> (1 + x*y).subs({x:pi, y:2}) + 1 + 2*pi + >>> (1 + x*y).subs([(x, pi), (y, 2)]) + 1 + 2*pi + >>> reps = [(y, x**2), (x, 2)] + >>> (x + y).subs(reps) + 6 + >>> (x + y).subs(reversed(reps)) + x**2 + 2 + + >>> (x**2 + x**4).subs(x**2, y) + y**2 + y + + To replace only the x**2 but not the x**4, use xreplace: + + >>> (x**2 + x**4).xreplace({x**2: y}) + x**4 + y + + To delay evaluation until all substitutions have been made, + set the keyword ``simultaneous`` to True: + + >>> (x/y).subs([(x, 0), (y, 0)]) + 0 + >>> (x/y).subs([(x, 0), (y, 0)], simultaneous=True) + nan + + This has the added feature of not allowing subsequent substitutions + to affect those already made: + + >>> ((x + y)/y).subs({x + y: y, y: x + y}) + 1 + >>> ((x + y)/y).subs({x + y: y, y: x + y}, simultaneous=True) + y/(x + y) + + In order to obtain a canonical result, unordered iterables are + sorted by count_op length, number of arguments and by the + default_sort_key to break any ties. All other iterables are left + unsorted. + + >>> from sympy import sqrt, sin, cos + >>> from sympy.abc import a, b, c, d, e + + >>> A = (sqrt(sin(2*x)), a) + >>> B = (sin(2*x), b) + >>> C = (cos(2*x), c) + >>> D = (x, d) + >>> E = (exp(x), e) + + >>> expr = sqrt(sin(2*x))*sin(exp(x)*x)*cos(2*x) + sin(2*x) + + >>> expr.subs(dict([A, B, C, D, E])) + a*c*sin(d*e) + b + + The resulting expression represents a literal replacement of the + old arguments with the new arguments. This may not reflect the + limiting behavior of the expression: + + >>> (x**3 - 3*x).subs({x: oo}) + nan + + >>> limit(x**3 - 3*x, x, oo) + oo + + If the substitution will be followed by numerical + evaluation, it is better to pass the substitution to + evalf as + + >>> (1/x).evalf(subs={x: 3.0}, n=21) + 0.333333333333333333333 + + rather than + + >>> (1/x).subs({x: 3.0}).evalf(21) + 0.333333333333333314830 + + as the former will ensure that the desired level of precision is + obtained. + + See Also + ======== + replace: replacement capable of doing wildcard-like matching, + parsing of match, and conditional replacements + xreplace: exact node replacement in expr tree; also capable of + using matching rules + sympy.core.evalf.EvalfMixin.evalf: calculates the given formula to a desired level of precision + + """ + from .containers import Dict + from .symbol import Dummy, Symbol + from .numbers import _illegal + + unordered = False + if len(args) == 1: + + sequence = args[0] + if isinstance(sequence, set): + unordered = True + elif isinstance(sequence, (Dict, Mapping)): + unordered = True + sequence = sequence.items() + elif not iterable(sequence): + raise ValueError(filldedent(""" + When a single argument is passed to subs + it should be a dictionary of old: new pairs or an iterable + of (old, new) tuples.""")) + elif len(args) == 2: + sequence = [args] + else: + raise ValueError("subs accepts either 1 or 2 arguments") + + def sympify_old(old): + if isinstance(old, str): + # Use Symbol rather than parse_expr for old + return Symbol(old) + elif isinstance(old, type): + # Allow a type e.g. Function('f') or sin + return sympify(old, strict=False) + else: + return sympify(old, strict=True) + + def sympify_new(new): + if isinstance(new, (str, type)): + # Allow a type or parse a string input + return sympify(new, strict=False) + else: + return sympify(new, strict=True) + + sequence = [(sympify_old(s1), sympify_new(s2)) for s1, s2 in sequence] + + # skip if there is no change + sequence = [(s1, s2) for s1, s2 in sequence if not _aresame(s1, s2)] + + simultaneous = kwargs.pop('simultaneous', False) + + if unordered: + from .sorting import _nodes, default_sort_key + sequence = dict(sequence) + # order so more complex items are first and items + # of identical complexity are ordered so + # f(x) < f(y) < x < y + # \___ 2 __/ \_1_/ <- number of nodes + # + # For more complex ordering use an unordered sequence. + k = list(ordered(sequence, default=False, keys=( + lambda x: -_nodes(x), + default_sort_key, + ))) + sequence = [(k, sequence[k]) for k in k] + # do infinities first + if not simultaneous: + redo = [i for i, seq in enumerate(sequence) if seq[1] in _illegal] + for i in reversed(redo): + sequence.insert(0, sequence.pop(i)) + + if simultaneous: # XXX should this be the default for dict subs? + reps = {} + rv = self + kwargs['hack2'] = True + m = Dummy('subs_m') + for old, new in sequence: + com = new.is_commutative + if com is None: + com = True + d = Dummy('subs_d', commutative=com) + # using d*m so Subs will be used on dummy variables + # in things like Derivative(f(x, y), x) in which x + # is both free and bound + rv = rv._subs(old, d*m, **kwargs) + if not isinstance(rv, Basic): + break + reps[d] = new + reps[m] = S.One # get rid of m + return rv.xreplace(reps) + else: + rv = self + for old, new in sequence: + rv = rv._subs(old, new, **kwargs) + if not isinstance(rv, Basic): + break + return rv + + @cacheit + def _subs(self, old, new, **hints): + """Substitutes an expression old -> new. + + If self is not equal to old then _eval_subs is called. + If _eval_subs does not want to make any special replacement + then a None is received which indicates that the fallback + should be applied wherein a search for replacements is made + amongst the arguments of self. + + >>> from sympy import Add + >>> from sympy.abc import x, y, z + + Examples + ======== + + Add's _eval_subs knows how to target x + y in the following + so it makes the change: + + >>> (x + y + z).subs(x + y, 1) + z + 1 + + Add's _eval_subs does not need to know how to find x + y in + the following: + + >>> Add._eval_subs(z*(x + y) + 3, x + y, 1) is None + True + + The returned None will cause the fallback routine to traverse the args and + pass the z*(x + y) arg to Mul where the change will take place and the + substitution will succeed: + + >>> (z*(x + y) + 3).subs(x + y, 1) + z + 3 + + ** Developers Notes ** + + An _eval_subs routine for a class should be written if: + + 1) any arguments are not instances of Basic (e.g. bool, tuple); + + 2) some arguments should not be targeted (as in integration + variables); + + 3) if there is something other than a literal replacement + that should be attempted (as in Piecewise where the condition + may be updated without doing a replacement). + + If it is overridden, here are some special cases that might arise: + + 1) If it turns out that no special change was made and all + the original sub-arguments should be checked for + replacements then None should be returned. + + 2) If it is necessary to do substitutions on a portion of + the expression then _subs should be called. _subs will + handle the case of any sub-expression being equal to old + (which usually would not be the case) while its fallback + will handle the recursion into the sub-arguments. For + example, after Add's _eval_subs removes some matching terms + it must process the remaining terms so it calls _subs + on each of the un-matched terms and then adds them + onto the terms previously obtained. + + 3) If the initial expression should remain unchanged then + the original expression should be returned. (Whenever an + expression is returned, modified or not, no further + substitution of old -> new is attempted.) Sum's _eval_subs + routine uses this strategy when a substitution is attempted + on any of its summation variables. + """ + + def fallback(self, old, new): + """ + Try to replace old with new in any of self's arguments. + """ + hit = False + args = list(self.args) + for i, arg in enumerate(args): + if not hasattr(arg, '_eval_subs'): + continue + arg = arg._subs(old, new, **hints) + if not _aresame(arg, args[i]): + hit = True + args[i] = arg + if hit: + rv = self.func(*args) + hack2 = hints.get('hack2', False) + if hack2 and self.is_Mul and not rv.is_Mul: # 2-arg hack + coeff = S.One + nonnumber = [] + for i in args: + if i.is_Number: + coeff *= i + else: + nonnumber.append(i) + nonnumber = self.func(*nonnumber) + if coeff is S.One: + return nonnumber + else: + return self.func(coeff, nonnumber, evaluate=False) + return rv + return self + + if _aresame(self, old): + return new + + rv = self._eval_subs(old, new) + if rv is None: + rv = fallback(self, old, new) + return rv + + def _eval_subs(self, old, new): + """Override this stub if you want to do anything more than + attempt a replacement of old with new in the arguments of self. + + See also + ======== + + _subs + """ + return None + + def xreplace(self, rule): + """ + Replace occurrences of objects within the expression. + + Parameters + ========== + + rule : dict-like + Expresses a replacement rule + + Returns + ======= + + xreplace : the result of the replacement + + Examples + ======== + + >>> from sympy import symbols, pi, exp + >>> x, y, z = symbols('x y z') + >>> (1 + x*y).xreplace({x: pi}) + pi*y + 1 + >>> (1 + x*y).xreplace({x: pi, y: 2}) + 1 + 2*pi + + Replacements occur only if an entire node in the expression tree is + matched: + + >>> (x*y + z).xreplace({x*y: pi}) + z + pi + >>> (x*y*z).xreplace({x*y: pi}) + x*y*z + >>> (2*x).xreplace({2*x: y, x: z}) + y + >>> (2*2*x).xreplace({2*x: y, x: z}) + 4*z + >>> (x + y + 2).xreplace({x + y: 2}) + x + y + 2 + >>> (x + 2 + exp(x + 2)).xreplace({x + 2: y}) + x + exp(y) + 2 + + xreplace does not differentiate between free and bound symbols. In the + following, subs(x, y) would not change x since it is a bound symbol, + but xreplace does: + + >>> from sympy import Integral + >>> Integral(x, (x, 1, 2*x)).xreplace({x: y}) + Integral(y, (y, 1, 2*y)) + + Trying to replace x with an expression raises an error: + + >>> Integral(x, (x, 1, 2*x)).xreplace({x: 2*y}) # doctest: +SKIP + ValueError: Invalid limits given: ((2*y, 1, 4*y),) + + See Also + ======== + replace: replacement capable of doing wildcard-like matching, + parsing of match, and conditional replacements + subs: substitution of subexpressions as defined by the objects + themselves. + + """ + value, _ = self._xreplace(rule) + return value + + def _xreplace(self, rule): + """ + Helper for xreplace. Tracks whether a replacement actually occurred. + """ + if self in rule: + return rule[self], True + elif rule: + args = [] + changed = False + for a in self.args: + _xreplace = getattr(a, '_xreplace', None) + if _xreplace is not None: + a_xr = _xreplace(rule) + args.append(a_xr[0]) + changed |= a_xr[1] + else: + args.append(a) + args = tuple(args) + if changed: + return self.func(*args), True + return self, False + + @cacheit + def has(self, *patterns): + """ + Test whether any subexpression matches any of the patterns. + + Examples + ======== + + >>> from sympy import sin + >>> from sympy.abc import x, y, z + >>> (x**2 + sin(x*y)).has(z) + False + >>> (x**2 + sin(x*y)).has(x, y, z) + True + >>> x.has(x) + True + + Note ``has`` is a structural algorithm with no knowledge of + mathematics. Consider the following half-open interval: + + >>> from sympy import Interval + >>> i = Interval.Lopen(0, 5); i + Interval.Lopen(0, 5) + >>> i.args + (0, 5, True, False) + >>> i.has(4) # there is no "4" in the arguments + False + >>> i.has(0) # there *is* a "0" in the arguments + True + + Instead, use ``contains`` to determine whether a number is in the + interval or not: + + >>> i.contains(4) + True + >>> i.contains(0) + False + + + Note that ``expr.has(*patterns)`` is exactly equivalent to + ``any(expr.has(p) for p in patterns)``. In particular, ``False`` is + returned when the list of patterns is empty. + + >>> x.has() + False + + """ + return self._has(iterargs, *patterns) + + def has_xfree(self, s: set[Basic]): + """Return True if self has any of the patterns in s as a + free argument, else False. This is like `Basic.has_free` + but this will only report exact argument matches. + + Examples + ======== + + >>> from sympy import Function + >>> from sympy.abc import x, y + >>> f = Function('f') + >>> f(x).has_xfree({f}) + False + >>> f(x).has_xfree({f(x)}) + True + >>> f(x + 1).has_xfree({x}) + True + >>> f(x + 1).has_xfree({x + 1}) + True + >>> f(x + y + 1).has_xfree({x + 1}) + False + """ + # protect O(1) containment check by requiring: + if type(s) is not set: + raise TypeError('expecting set argument') + return any(a in s for a in iterfreeargs(self)) + + @cacheit + def has_free(self, *patterns): + """Return True if self has object(s) ``x`` as a free expression + else False. + + Examples + ======== + + >>> from sympy import Integral, Function + >>> from sympy.abc import x, y + >>> f = Function('f') + >>> g = Function('g') + >>> expr = Integral(f(x), (f(x), 1, g(y))) + >>> expr.free_symbols + {y} + >>> expr.has_free(g(y)) + True + >>> expr.has_free(*(x, f(x))) + False + + This works for subexpressions and types, too: + + >>> expr.has_free(g) + True + >>> (x + y + 1).has_free(y + 1) + True + """ + if not patterns: + return False + p0 = patterns[0] + if len(patterns) == 1 and iterable(p0) and not isinstance(p0, Basic): + # Basic can contain iterables (though not non-Basic, ideally) + # but don't encourage mixed passing patterns + raise TypeError(filldedent(''' + Expecting 1 or more Basic args, not a single + non-Basic iterable. Don't forget to unpack + iterables: `eq.has_free(*patterns)`''')) + # try quick test first + s = set(patterns) + rv = self.has_xfree(s) + if rv: + return rv + # now try matching through slower _has + return self._has(iterfreeargs, *patterns) + + def _has(self, iterargs, *patterns): + # separate out types and unhashable objects + type_set = set() # only types + p_set = set() # hashable non-types + for p in patterns: + if isinstance(p, type) and issubclass(p, Basic): + type_set.add(p) + continue + if not isinstance(p, Basic): + try: + p = _sympify(p) + except SympifyError: + continue # Basic won't have this in it + p_set.add(p) # fails if object defines __eq__ but + # doesn't define __hash__ + types = tuple(type_set) # + for i in iterargs(self): # + if i in p_set: # <--- here, too + return True + if isinstance(i, types): + return True + + # use matcher if defined, e.g. operations defines + # matcher that checks for exact subset containment, + # (x + y + 1).has(x + 1) -> True + for i in p_set - type_set: # types don't have matchers + if not hasattr(i, '_has_matcher'): + continue + match = i._has_matcher() + if any(match(arg) for arg in iterargs(self)): + return True + + # no success + return False + + def replace(self, query, value, map=False, simultaneous=True, exact=None): + """ + Replace matching subexpressions of ``self`` with ``value``. + + If ``map = True`` then also return the mapping {old: new} where ``old`` + was a sub-expression found with query and ``new`` is the replacement + value for it. If the expression itself does not match the query, then + the returned value will be ``self.xreplace(map)`` otherwise it should + be ``self.subs(ordered(map.items()))``. + + Traverses an expression tree and performs replacement of matching + subexpressions from the bottom to the top of the tree. The default + approach is to do the replacement in a simultaneous fashion so + changes made are targeted only once. If this is not desired or causes + problems, ``simultaneous`` can be set to False. + + In addition, if an expression containing more than one Wild symbol + is being used to match subexpressions and the ``exact`` flag is None + it will be set to True so the match will only succeed if all non-zero + values are received for each Wild that appears in the match pattern. + Setting this to False accepts a match of 0; while setting it True + accepts all matches that have a 0 in them. See example below for + cautions. + + The list of possible combinations of queries and replacement values + is listed below: + + Examples + ======== + + Initial setup + + >>> from sympy import log, sin, cos, tan, Wild, Mul, Add + >>> from sympy.abc import x, y + >>> f = log(sin(x)) + tan(sin(x**2)) + + 1.1. type -> type + obj.replace(type, newtype) + + When object of type ``type`` is found, replace it with the + result of passing its argument(s) to ``newtype``. + + >>> f.replace(sin, cos) + log(cos(x)) + tan(cos(x**2)) + >>> sin(x).replace(sin, cos, map=True) + (cos(x), {sin(x): cos(x)}) + >>> (x*y).replace(Mul, Add) + x + y + + 1.2. type -> func + obj.replace(type, func) + + When object of type ``type`` is found, apply ``func`` to its + argument(s). ``func`` must be written to handle the number + of arguments of ``type``. + + >>> f.replace(sin, lambda arg: sin(2*arg)) + log(sin(2*x)) + tan(sin(2*x**2)) + >>> (x*y).replace(Mul, lambda *args: sin(2*Mul(*args))) + sin(2*x*y) + + 2.1. pattern -> expr + obj.replace(pattern(wild), expr(wild)) + + Replace subexpressions matching ``pattern`` with the expression + written in terms of the Wild symbols in ``pattern``. + + >>> a, b = map(Wild, 'ab') + >>> f.replace(sin(a), tan(a)) + log(tan(x)) + tan(tan(x**2)) + >>> f.replace(sin(a), tan(a/2)) + log(tan(x/2)) + tan(tan(x**2/2)) + >>> f.replace(sin(a), a) + log(x) + tan(x**2) + >>> (x*y).replace(a*x, a) + y + + Matching is exact by default when more than one Wild symbol + is used: matching fails unless the match gives non-zero + values for all Wild symbols: + + >>> (2*x + y).replace(a*x + b, b - a) + y - 2 + >>> (2*x).replace(a*x + b, b - a) + 2*x + + When set to False, the results may be non-intuitive: + + >>> (2*x).replace(a*x + b, b - a, exact=False) + 2/x + + 2.2. pattern -> func + obj.replace(pattern(wild), lambda wild: expr(wild)) + + All behavior is the same as in 2.1 but now a function in terms of + pattern variables is used rather than an expression: + + >>> f.replace(sin(a), lambda a: sin(2*a)) + log(sin(2*x)) + tan(sin(2*x**2)) + + 3.1. func -> func + obj.replace(filter, func) + + Replace subexpression ``e`` with ``func(e)`` if ``filter(e)`` + is True. + + >>> g = 2*sin(x**3) + >>> g.replace(lambda expr: expr.is_Number, lambda expr: expr**2) + 4*sin(x**9) + + The expression itself is also targeted by the query but is done in + such a fashion that changes are not made twice. + + >>> e = x*(x*y + 1) + >>> e.replace(lambda x: x.is_Mul, lambda x: 2*x) + 2*x*(2*x*y + 1) + + When matching a single symbol, `exact` will default to True, but + this may or may not be the behavior that is desired: + + Here, we want `exact=False`: + + >>> from sympy import Function + >>> f = Function('f') + >>> e = f(1) + f(0) + >>> q = f(a), lambda a: f(a + 1) + >>> e.replace(*q, exact=False) + f(1) + f(2) + >>> e.replace(*q, exact=True) + f(0) + f(2) + + But here, the nature of matching makes selecting + the right setting tricky: + + >>> e = x**(1 + y) + >>> (x**(1 + y)).replace(x**(1 + a), lambda a: x**-a, exact=False) + x + >>> (x**(1 + y)).replace(x**(1 + a), lambda a: x**-a, exact=True) + x**(-x - y + 1) + >>> (x**y).replace(x**(1 + a), lambda a: x**-a, exact=False) + x + >>> (x**y).replace(x**(1 + a), lambda a: x**-a, exact=True) + x**(1 - y) + + It is probably better to use a different form of the query + that describes the target expression more precisely: + + >>> (1 + x**(1 + y)).replace( + ... lambda x: x.is_Pow and x.exp.is_Add and x.exp.args[0] == 1, + ... lambda x: x.base**(1 - (x.exp - 1))) + ... + x**(1 - y) + 1 + + See Also + ======== + + subs: substitution of subexpressions as defined by the objects + themselves. + xreplace: exact node replacement in expr tree; also capable of + using matching rules + + """ + + try: + query = _sympify(query) + except SympifyError: + pass + try: + value = _sympify(value) + except SympifyError: + pass + if isinstance(query, type): + _query = lambda expr: isinstance(expr, query) + + if isinstance(value, type): + _value = lambda expr, result: value(*expr.args) + elif callable(value): + _value = lambda expr, result: value(*expr.args) + else: + raise TypeError( + "given a type, replace() expects another " + "type or a callable") + elif isinstance(query, Basic): + _query = lambda expr: expr.match(query) + if exact is None: + from .symbol import Wild + exact = (len(query.atoms(Wild)) > 1) + + if isinstance(value, Basic): + if exact: + _value = lambda expr, result: (value.subs(result) + if all(result.values()) else expr) + else: + _value = lambda expr, result: value.subs(result) + elif callable(value): + # match dictionary keys get the trailing underscore stripped + # from them and are then passed as keywords to the callable; + # if ``exact`` is True, only accept match if there are no null + # values amongst those matched. + if exact: + _value = lambda expr, result: (value(** + {str(k)[:-1]: v for k, v in result.items()}) + if all(val for val in result.values()) else expr) + else: + _value = lambda expr, result: value(** + {str(k)[:-1]: v for k, v in result.items()}) + else: + raise TypeError( + "given an expression, replace() expects " + "another expression or a callable") + elif callable(query): + _query = query + + if callable(value): + _value = lambda expr, result: value(expr) + else: + raise TypeError( + "given a callable, replace() expects " + "another callable") + else: + raise TypeError( + "first argument to replace() must be a " + "type, an expression or a callable") + + def walk(rv, F): + """Apply ``F`` to args and then to result. + """ + args = getattr(rv, 'args', None) + if args is not None: + if args: + newargs = tuple([walk(a, F) for a in args]) + if args != newargs: + rv = rv.func(*newargs) + if simultaneous: + # if rv is something that was already + # matched (that was changed) then skip + # applying F again + for i, e in enumerate(args): + if rv == e and e != newargs[i]: + return rv + rv = F(rv) + return rv + + mapping = {} # changes that took place + + def rec_replace(expr): + result = _query(expr) + if result or result == {}: + v = _value(expr, result) + if v is not None and v != expr: + if map: + mapping[expr] = v + expr = v + return expr + + rv = walk(self, rec_replace) + return (rv, mapping) if map else rv + + def find(self, query, group=False): + """Find all subexpressions matching a query.""" + query = _make_find_query(query) + results = list(filter(query, _preorder_traversal(self))) + + if not group: + return set(results) + else: + groups = {} + + for result in results: + if result in groups: + groups[result] += 1 + else: + groups[result] = 1 + + return groups + + def count(self, query): + """Count the number of matching subexpressions.""" + query = _make_find_query(query) + return sum(bool(query(sub)) for sub in _preorder_traversal(self)) + + def matches(self, expr, repl_dict=None, old=False): + """ + Helper method for match() that looks for a match between Wild symbols + in self and expressions in expr. + + Examples + ======== + + >>> from sympy import symbols, Wild, Basic + >>> a, b, c = symbols('a b c') + >>> x = Wild('x') + >>> Basic(a + x, x).matches(Basic(a + b, c)) is None + True + >>> Basic(a + x, x).matches(Basic(a + b + c, b + c)) + {x_: b + c} + """ + expr = sympify(expr) + if not isinstance(expr, self.__class__): + return None + + if repl_dict is None: + repl_dict = {} + else: + repl_dict = repl_dict.copy() + + if self == expr: + return repl_dict + + if len(self.args) != len(expr.args): + return None + + d = repl_dict # already a copy + for arg, other_arg in zip(self.args, expr.args): + if arg == other_arg: + continue + if arg.is_Relational: + try: + d = arg.xreplace(d).matches(other_arg, d, old=old) + except TypeError: # Should be InvalidComparisonError when introduced + d = None + else: + d = arg.xreplace(d).matches(other_arg, d, old=old) + if d is None: + return None + return d + + def match(self, pattern, old=False): + """ + Pattern matching. + + Wild symbols match all. + + Return ``None`` when expression (self) does not match + with pattern. Otherwise return a dictionary such that:: + + pattern.xreplace(self.match(pattern)) == self + + Examples + ======== + + >>> from sympy import Wild, Sum + >>> from sympy.abc import x, y + >>> p = Wild("p") + >>> q = Wild("q") + >>> r = Wild("r") + >>> e = (x+y)**(x+y) + >>> e.match(p**p) + {p_: x + y} + >>> e.match(p**q) + {p_: x + y, q_: x + y} + >>> e = (2*x)**2 + >>> e.match(p*q**r) + {p_: 4, q_: x, r_: 2} + >>> (p*q**r).xreplace(e.match(p*q**r)) + 4*x**2 + + Structurally bound symbols are ignored during matching: + + >>> Sum(x, (x, 1, 2)).match(Sum(y, (y, 1, p))) + {p_: 2} + + But they can be identified if desired: + + >>> Sum(x, (x, 1, 2)).match(Sum(q, (q, 1, p))) + {p_: 2, q_: x} + + The ``old`` flag will give the old-style pattern matching where + expressions and patterns are essentially solved to give the + match. Both of the following give None unless ``old=True``: + + >>> (x - 2).match(p - x, old=True) + {p_: 2*x - 2} + >>> (2/x).match(p*x, old=True) + {p_: 2/x**2} + + """ + pattern = sympify(pattern) + # match non-bound symbols + canonical = lambda x: x if x.is_Symbol else x.as_dummy() + m = canonical(pattern).matches(canonical(self), old=old) + if m is None: + return m + from .symbol import Wild + from .function import WildFunction + from ..tensor.tensor import WildTensor, WildTensorIndex, WildTensorHead + wild = pattern.atoms(Wild, WildFunction, WildTensor, WildTensorIndex, WildTensorHead) + # sanity check + if set(m) - wild: + raise ValueError(filldedent(''' + Some `matches` routine did not use a copy of repl_dict + and injected unexpected symbols. Report this as an + error at https://github.com/sympy/sympy/issues''')) + # now see if bound symbols were requested + bwild = wild - set(m) + if not bwild: + return m + # replace free-Wild symbols in pattern with match result + # so they will match but not be in the next match + wpat = pattern.xreplace(m) + # identify remaining bound wild + w = wpat.matches(self, old=old) + # add them to m + if w: + m.update(w) + # done + return m + + def count_ops(self, visual=None): + """Wrapper for count_ops that returns the operation count.""" + from .function import count_ops + return count_ops(self, visual) + + def doit(self, **hints): + """Evaluate objects that are not evaluated by default like limits, + integrals, sums and products. All objects of this kind will be + evaluated recursively, unless some species were excluded via 'hints' + or unless the 'deep' hint was set to 'False'. + + >>> from sympy import Integral + >>> from sympy.abc import x + + >>> 2*Integral(x, x) + 2*Integral(x, x) + + >>> (2*Integral(x, x)).doit() + x**2 + + >>> (2*Integral(x, x)).doit(deep=False) + 2*Integral(x, x) + + """ + if hints.get('deep', True): + terms = [term.doit(**hints) if isinstance(term, Basic) else term + for term in self.args] + return self.func(*terms) + else: + return self + + def simplify(self, **kwargs): + """See the simplify function in sympy.simplify""" + from sympy.simplify.simplify import simplify + return simplify(self, **kwargs) + + def refine(self, assumption=True): + """See the refine function in sympy.assumptions""" + from sympy.assumptions.refine import refine + return refine(self, assumption) + + def _eval_derivative_n_times(self, s, n): + # This is the default evaluator for derivatives (as called by `diff` + # and `Derivative`), it will attempt a loop to derive the expression + # `n` times by calling the corresponding `_eval_derivative` method, + # while leaving the derivative unevaluated if `n` is symbolic. This + # method should be overridden if the object has a closed form for its + # symbolic n-th derivative. + from .numbers import Integer + if isinstance(n, (int, Integer)): + obj = self + for i in range(n): + obj2 = obj._eval_derivative(s) + if obj == obj2 or obj2 is None: + break + obj = obj2 + return obj2 + else: + return None + + def rewrite(self, *args, deep=True, **hints): + """ + Rewrite *self* using a defined rule. + + Rewriting transforms an expression to another, which is mathematically + equivalent but structurally different. For example you can rewrite + trigonometric functions as complex exponentials or combinatorial + functions as gamma function. + + This method takes a *pattern* and a *rule* as positional arguments. + *pattern* is optional parameter which defines the types of expressions + that will be transformed. If it is not passed, all possible expressions + will be rewritten. *rule* defines how the expression will be rewritten. + + Parameters + ========== + + args : Expr + A *rule*, or *pattern* and *rule*. + - *pattern* is a type or an iterable of types. + - *rule* can be any object. + + deep : bool, optional + If ``True``, subexpressions are recursively transformed. Default is + ``True``. + + Examples + ======== + + If *pattern* is unspecified, all possible expressions are transformed. + + >>> from sympy import cos, sin, exp, I + >>> from sympy.abc import x + >>> expr = cos(x) + I*sin(x) + >>> expr.rewrite(exp) + exp(I*x) + + Pattern can be a type or an iterable of types. + + >>> expr.rewrite(sin, exp) + exp(I*x)/2 + cos(x) - exp(-I*x)/2 + >>> expr.rewrite([cos,], exp) + exp(I*x)/2 + I*sin(x) + exp(-I*x)/2 + >>> expr.rewrite([cos, sin], exp) + exp(I*x) + + Rewriting behavior can be implemented by defining ``_eval_rewrite()`` + method. + + >>> from sympy import Expr, sqrt, pi + >>> class MySin(Expr): + ... def _eval_rewrite(self, rule, args, **hints): + ... x, = args + ... if rule == cos: + ... return cos(pi/2 - x, evaluate=False) + ... if rule == sqrt: + ... return sqrt(1 - cos(x)**2) + >>> MySin(MySin(x)).rewrite(cos) + cos(-cos(-x + pi/2) + pi/2) + >>> MySin(x).rewrite(sqrt) + sqrt(1 - cos(x)**2) + + Defining ``_eval_rewrite_as_[...]()`` method is supported for backwards + compatibility reason. This may be removed in the future and using it is + discouraged. + + >>> class MySin(Expr): + ... def _eval_rewrite_as_cos(self, *args, **hints): + ... x, = args + ... return cos(pi/2 - x, evaluate=False) + >>> MySin(x).rewrite(cos) + cos(-x + pi/2) + + """ + if not args: + return self + + hints.update(deep=deep) + + pattern = args[:-1] + rule = args[-1] + + # support old design by _eval_rewrite_as_[...] method + if isinstance(rule, str): + method = "_eval_rewrite_as_%s" % rule + elif hasattr(rule, "__name__"): + # rule is class or function + clsname = rule.__name__ + method = "_eval_rewrite_as_%s" % clsname + else: + # rule is instance + clsname = rule.__class__.__name__ + method = "_eval_rewrite_as_%s" % clsname + + if pattern: + if iterable(pattern[0]): + pattern = pattern[0] + pattern = tuple(p for p in pattern if self.has(p)) + if not pattern: + return self + # hereafter, empty pattern is interpreted as all pattern. + + return self._rewrite(pattern, rule, method, **hints) + + def _rewrite(self, pattern, rule, method, **hints): + deep = hints.pop('deep', True) + if deep: + args = [a._rewrite(pattern, rule, method, **hints) + for a in self.args] + else: + args = self.args + if not pattern or any(isinstance(self, p) for p in pattern): + meth = getattr(self, method, None) + if meth is not None: + rewritten = meth(*args, **hints) + else: + rewritten = self._eval_rewrite(rule, args, **hints) + if rewritten is not None: + return rewritten + if not args: + return self + return self.func(*args) + + def _eval_rewrite(self, rule, args, **hints): + return None + + _constructor_postprocessor_mapping = {} # type: ignore + + @classmethod + def _exec_constructor_postprocessors(cls, obj): + # WARNING: This API is experimental. + + # This is an experimental API that introduces constructor + # postprosessors for SymPy Core elements. If an argument of a SymPy + # expression has a `_constructor_postprocessor_mapping` attribute, it will + # be interpreted as a dictionary containing lists of postprocessing + # functions for matching expression node names. + + clsname = obj.__class__.__name__ + postprocessors = defaultdict(list) + for i in obj.args: + try: + postprocessor_mappings = ( + Basic._constructor_postprocessor_mapping[cls].items() + for cls in type(i).mro() + if cls in Basic._constructor_postprocessor_mapping + ) + for k, v in chain.from_iterable(postprocessor_mappings): + postprocessors[k].extend([j for j in v if j not in postprocessors[k]]) + except TypeError: + pass + + for f in postprocessors.get(clsname, []): + obj = f(obj) + + return obj + + def _sage_(self): + """ + Convert *self* to a symbolic expression of SageMath. + + This version of the method is merely a placeholder. + """ + old_method = self._sage_ + from sage.interfaces.sympy import sympy_init + sympy_init() # may monkey-patch _sage_ method into self's class or superclasses + if old_method == self._sage_: + raise NotImplementedError('conversion to SageMath is not implemented') + else: + # call the freshly monkey-patched method + return self._sage_() + + def could_extract_minus_sign(self): + return False # see Expr.could_extract_minus_sign + + def is_same(a, b, approx=None): + """Return True if a and b are structurally the same, else False. + If `approx` is supplied, it will be used to test whether two + numbers are the same or not. By default, only numbers of the + same type will compare equal, so S.Half != Float(0.5). + + Examples + ======== + + In SymPy (unlike Python) two numbers do not compare the same if they are + not of the same type: + + >>> from sympy import S + >>> 2.0 == S(2) + False + >>> 0.5 == S.Half + False + + By supplying a function with which to compare two numbers, such + differences can be ignored. e.g. `equal_valued` will return True + for decimal numbers having a denominator that is a power of 2, + regardless of precision. + + >>> from sympy import Float + >>> from sympy.core.numbers import equal_valued + >>> (S.Half/4).is_same(Float(0.125, 1), equal_valued) + True + >>> Float(1, 2).is_same(Float(1, 10), equal_valued) + True + + But decimals without a power of 2 denominator will compare + as not being the same. + + >>> Float(0.1, 9).is_same(Float(0.1, 10), equal_valued) + False + + But arbitrary differences can be ignored by supplying a function + to test the equivalence of two numbers: + + >>> import math + >>> Float(0.1, 9).is_same(Float(0.1, 10), math.isclose) + True + + Other objects might compare the same even though types are not the + same. This routine will only return True if two expressions are + identical in terms of class types. + + >>> from sympy import eye, Basic + >>> eye(1) == S(eye(1)) # mutable vs immutable + True + >>> Basic.is_same(eye(1), S(eye(1))) + False + + """ + from .numbers import Number + from .traversal import postorder_traversal as pot + for t in zip_longest(pot(a), pot(b)): + if None in t: + return False + a, b = t + if isinstance(a, Number): + if not isinstance(b, Number): + return False + if approx: + return approx(a, b) + if not (a == b and a.__class__ == b.__class__): + return False + return True + +_aresame = Basic.is_same # for sake of others importing this + +# key used by Mul and Add to make canonical args +_args_sortkey = cmp_to_key(Basic.compare) + +# For all Basic subclasses _prepare_class_assumptions is called by +# Basic.__init_subclass__ but that method is not called for Basic itself so we +# call the function here instead. +_prepare_class_assumptions(Basic) + + +class Atom(Basic): + """ + A parent class for atomic things. An atom is an expression with no subexpressions. + + Examples + ======== + + Symbol, Number, Rational, Integer, ... + But not: Add, Mul, Pow, ... + """ + + is_Atom = True + + __slots__ = () + + def matches(self, expr, repl_dict=None, old=False): + if self == expr: + if repl_dict is None: + return {} + return repl_dict.copy() + + def xreplace(self, rule, hack2=False): + return rule.get(self, self) + + def doit(self, **hints): + return self + + @classmethod + def class_key(cls): + return 2, 0, cls.__name__ + + @cacheit + def sort_key(self, order=None): + return self.class_key(), (1, (str(self),)), S.One.sort_key(), S.One + + def _eval_simplify(self, **kwargs): + return self + + @property + def _sorted_args(self): + # this is here as a safeguard against accidentally using _sorted_args + # on Atoms -- they cannot be rebuilt as atom.func(*atom._sorted_args) + # since there are no args. So the calling routine should be checking + # to see that this property is not called for Atoms. + raise AttributeError('Atoms have no args. It might be necessary' + ' to make a check for Atoms in the calling code.') + + +def _atomic(e, recursive=False): + """Return atom-like quantities as far as substitution is + concerned: Derivatives, Functions and Symbols. Do not + return any 'atoms' that are inside such quantities unless + they also appear outside, too, unless `recursive` is True. + + Examples + ======== + + >>> from sympy import Derivative, Function, cos + >>> from sympy.abc import x, y + >>> from sympy.core.basic import _atomic + >>> f = Function('f') + >>> _atomic(x + y) + {x, y} + >>> _atomic(x + f(y)) + {x, f(y)} + >>> _atomic(Derivative(f(x), x) + cos(x) + y) + {y, cos(x), Derivative(f(x), x)} + + """ + pot = _preorder_traversal(e) + seen = set() + if isinstance(e, Basic): + free = getattr(e, "free_symbols", None) + if free is None: + return {e} + else: + return set() + from .symbol import Symbol + from .function import Derivative, Function + atoms = set() + for p in pot: + if p in seen: + pot.skip() + continue + seen.add(p) + if isinstance(p, Symbol) and p in free: + atoms.add(p) + elif isinstance(p, (Derivative, Function)): + if not recursive: + pot.skip() + atoms.add(p) + return atoms + + +def _make_find_query(query): + """Convert the argument of Basic.find() into a callable""" + try: + query = _sympify(query) + except SympifyError: + pass + if isinstance(query, type): + return lambda expr: isinstance(expr, query) + elif isinstance(query, Basic): + return lambda expr: expr.match(query) is not None + return query + +# Delayed to avoid cyclic import +from .singleton import S +from .traversal import (preorder_traversal as _preorder_traversal, + iterargs, iterfreeargs) + +preorder_traversal = deprecated( + """ + Using preorder_traversal from the sympy.core.basic submodule is + deprecated. + + Instead, use preorder_traversal from the top-level sympy namespace, like + + sympy.preorder_traversal + """, + deprecated_since_version="1.10", + active_deprecations_target="deprecated-traversal-functions-moved", +)(_preorder_traversal) diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/__init__.py b/lib/python3.11/site-packages/sympy/core/benchmarks/__init__.py new file mode 100644 index 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0000000000000000000000000000000000000000..03547b3002cbc027483d58480732993b6c353fb2 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/core/benchmarks/__pycache__/bench_sympify.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_arit.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_arit.py new file mode 100644 index 0000000000000000000000000000000000000000..39860943b763a30cf4f91578dbac37dc7e6e444e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_arit.py @@ -0,0 +1,43 @@ +from sympy.core import Add, Mul, symbols + +x, y, z = symbols('x,y,z') + + +def timeit_neg(): + -x + + +def timeit_Add_x1(): + x + 1 + + +def timeit_Add_1x(): + 1 + x + + +def timeit_Add_x05(): + x + 0.5 + + +def timeit_Add_xy(): + x + y + + +def timeit_Add_xyz(): + Add(*[x, y, z]) + + +def timeit_Mul_xy(): + x*y + + +def timeit_Mul_xyz(): + Mul(*[x, y, z]) + + +def timeit_Div_xy(): + x/y + + +def timeit_Div_2y(): + 2/y diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_assumptions.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_assumptions.py new file mode 100644 index 0000000000000000000000000000000000000000..1a8e47928b76034dd1d7ba8b8f87bd527bb1cdeb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_assumptions.py @@ -0,0 +1,12 @@ +from sympy.core import Symbol, Integer + +x = Symbol('x') +i3 = Integer(3) + + +def timeit_x_is_integer(): + x.is_integer + + +def timeit_Integer_is_irrational(): + i3.is_irrational diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_basic.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_basic.py new file mode 100644 index 0000000000000000000000000000000000000000..df2a382ecbd3cf6eb1f8555577dabb5e07c6643b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_basic.py @@ -0,0 +1,15 @@ +from sympy.core import symbols, S + +x, y = symbols('x,y') + + +def timeit_Symbol_meth_lookup(): + x.diff # no call, just method lookup + + +def timeit_S_lookup(): + S.Exp1 + + +def timeit_Symbol_eq_xy(): + x == y diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_expand.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_expand.py new file mode 100644 index 0000000000000000000000000000000000000000..4f5ac513e368cb7e9b542926bc25a5695de6d914 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_expand.py @@ -0,0 +1,23 @@ +from sympy.core import symbols, I + +x, y, z = symbols('x,y,z') + +p = 3*x**2*y*z**7 + 7*x*y*z**2 + 4*x + x*y**4 +e = (x + y + z + 1)**32 + + +def timeit_expand_nothing_todo(): + p.expand() + + +def bench_expand_32(): + """(x+y+z+1)**32 -> expand""" + e.expand() + + +def timeit_expand_complex_number_1(): + ((2 + 3*I)**1000).expand(complex=True) + + +def timeit_expand_complex_number_2(): + ((2 + 3*I/4)**1000).expand(complex=True) diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_numbers.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..5c7484c389232b3622fb4b6724e4ab8534dde382 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_numbers.py @@ -0,0 +1,92 @@ +from sympy.core.numbers import Integer, Rational, pi, oo +from sympy.core.intfunc import integer_nthroot, igcd +from sympy.core.singleton import S + +i3 = Integer(3) +i4 = Integer(4) +r34 = Rational(3, 4) +q45 = Rational(4, 5) + + +def timeit_Integer_create(): + Integer(2) + + +def timeit_Integer_int(): + int(i3) + + +def timeit_neg_one(): + -S.One + + +def timeit_Integer_neg(): + -i3 + + +def timeit_Integer_abs(): + abs(i3) + + +def timeit_Integer_sub(): + i3 - i3 + + +def timeit_abs_pi(): + abs(pi) + + +def timeit_neg_oo(): + -oo + + +def timeit_Integer_add_i1(): + i3 + 1 + + +def timeit_Integer_add_ij(): + i3 + i4 + + +def timeit_Integer_add_Rational(): + i3 + r34 + + +def timeit_Integer_mul_i4(): + i3*4 + + +def timeit_Integer_mul_ij(): + i3*i4 + + +def timeit_Integer_mul_Rational(): + i3*r34 + + +def timeit_Integer_eq_i3(): + i3 == 3 + + +def timeit_Integer_ed_Rational(): + i3 == r34 + + +def timeit_integer_nthroot(): + integer_nthroot(100, 2) + + +def timeit_number_igcd_23_17(): + igcd(23, 17) + + +def timeit_number_igcd_60_3600(): + igcd(60, 3600) + + +def timeit_Rational_add_r1(): + r34 + 1 + + +def timeit_Rational_add_rq(): + r34 + q45 diff --git a/lib/python3.11/site-packages/sympy/core/benchmarks/bench_sympify.py b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_sympify.py new file mode 100644 index 0000000000000000000000000000000000000000..d8cc0abc1e35439a1a495454abf87769d5b40d04 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/benchmarks/bench_sympify.py @@ -0,0 +1,11 @@ +from sympy.core import sympify, Symbol + +x = Symbol('x') + + +def timeit_sympify_1(): + sympify(1) + + +def timeit_sympify_x(): + sympify(x) diff --git a/lib/python3.11/site-packages/sympy/core/cache.py b/lib/python3.11/site-packages/sympy/core/cache.py new file mode 100644 index 0000000000000000000000000000000000000000..ec11600a5e40ad446a6e5dde8820d46ea915b06a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/cache.py @@ -0,0 +1,210 @@ +""" Caching facility for SymPy """ +from importlib import import_module +from typing import Callable + +class _cache(list): + """ List of cached functions """ + + def print_cache(self): + """print cache info""" + + for item in self: + name = item.__name__ + myfunc = item + while hasattr(myfunc, '__wrapped__'): + if hasattr(myfunc, 'cache_info'): + info = myfunc.cache_info() + break + else: + myfunc = myfunc.__wrapped__ + else: + info = None + + print(name, info) + + def clear_cache(self): + """clear cache content""" + for item in self: + myfunc = item + while hasattr(myfunc, '__wrapped__'): + if hasattr(myfunc, 'cache_clear'): + myfunc.cache_clear() + break + else: + myfunc = myfunc.__wrapped__ + + +# global cache registry: +CACHE = _cache() +# make clear and print methods available +print_cache = CACHE.print_cache +clear_cache = CACHE.clear_cache + +from functools import lru_cache, wraps + +def __cacheit(maxsize): + """caching decorator. + + important: the result of cached function must be *immutable* + + + Examples + ======== + + >>> from sympy import cacheit + >>> @cacheit + ... def f(a, b): + ... return a+b + + >>> @cacheit + ... def f(a, b): # noqa: F811 + ... return [a, b] # <-- WRONG, returns mutable object + + to force cacheit to check returned results mutability and consistency, + set environment variable SYMPY_USE_CACHE to 'debug' + """ + def func_wrapper(func): + cfunc = lru_cache(maxsize, typed=True)(func) + + @wraps(func) + def wrapper(*args, **kwargs): + try: + retval = cfunc(*args, **kwargs) + except TypeError as e: + if not e.args or not e.args[0].startswith('unhashable type:'): + raise + retval = func(*args, **kwargs) + return retval + + wrapper.cache_info = cfunc.cache_info + wrapper.cache_clear = cfunc.cache_clear + + CACHE.append(wrapper) + return wrapper + + return func_wrapper +######################################## + + +def __cacheit_nocache(func): + return func + + +def __cacheit_debug(maxsize): + """cacheit + code to check cache consistency""" + def func_wrapper(func): + cfunc = __cacheit(maxsize)(func) + + @wraps(func) + def wrapper(*args, **kw_args): + # always call function itself and compare it with cached version + r1 = func(*args, **kw_args) + r2 = cfunc(*args, **kw_args) + + # try to see if the result is immutable + # + # this works because: + # + # hash([1,2,3]) -> raise TypeError + # hash({'a':1, 'b':2}) -> raise TypeError + # hash((1,[2,3])) -> raise TypeError + # + # hash((1,2,3)) -> just computes the hash + hash(r1), hash(r2) + + # also see if returned values are the same + if r1 != r2: + raise RuntimeError("Returned values are not the same") + return r1 + return wrapper + return func_wrapper + + +def _getenv(key, default=None): + from os import getenv + return getenv(key, default) + +# SYMPY_USE_CACHE=yes/no/debug +USE_CACHE = _getenv('SYMPY_USE_CACHE', 'yes').lower() +# SYMPY_CACHE_SIZE=some_integer/None +# special cases : +# SYMPY_CACHE_SIZE=0 -> No caching +# SYMPY_CACHE_SIZE=None -> Unbounded caching +scs = _getenv('SYMPY_CACHE_SIZE', '1000') +if scs.lower() == 'none': + SYMPY_CACHE_SIZE = None +else: + try: + SYMPY_CACHE_SIZE = int(scs) + except ValueError: + raise RuntimeError( + 'SYMPY_CACHE_SIZE must be a valid integer or None. ' + \ + 'Got: %s' % SYMPY_CACHE_SIZE) + +if USE_CACHE == 'no': + cacheit = __cacheit_nocache +elif USE_CACHE == 'yes': + cacheit = __cacheit(SYMPY_CACHE_SIZE) +elif USE_CACHE == 'debug': + cacheit = __cacheit_debug(SYMPY_CACHE_SIZE) # a lot slower +else: + raise RuntimeError( + 'unrecognized value for SYMPY_USE_CACHE: %s' % USE_CACHE) + + +def cached_property(func): + '''Decorator to cache property method''' + attrname = '__' + func.__name__ + _cached_property_sentinel = object() + def propfunc(self): + val = getattr(self, attrname, _cached_property_sentinel) + if val is _cached_property_sentinel: + val = func(self) + setattr(self, attrname, val) + return val + return property(propfunc) + + +def lazy_function(module : str, name : str) -> Callable: + """Create a lazy proxy for a function in a module. + + The module containing the function is not imported until the function is used. + + """ + func = None + + def _get_function(): + nonlocal func + if func is None: + func = getattr(import_module(module), name) + return func + + # The metaclass is needed so that help() shows the docstring + class LazyFunctionMeta(type): + @property + def __doc__(self): + docstring = _get_function().__doc__ + docstring += f"\n\nNote: this is a {self.__class__.__name__} wrapper of '{module}.{name}'" + return docstring + + class LazyFunction(metaclass=LazyFunctionMeta): + def __call__(self, *args, **kwargs): + # inline get of function for performance gh-23832 + nonlocal func + if func is None: + func = getattr(import_module(module), name) + return func(*args, **kwargs) + + @property + def __doc__(self): + docstring = _get_function().__doc__ + docstring += f"\n\nNote: this is a {self.__class__.__name__} wrapper of '{module}.{name}'" + return docstring + + def __str__(self): + return _get_function().__str__() + + def __repr__(self): + return f"<{__class__.__name__} object at 0x{id(self):x}>: wrapping '{module}.{name}'" + + return LazyFunction() diff --git a/lib/python3.11/site-packages/sympy/core/compatibility.py b/lib/python3.11/site-packages/sympy/core/compatibility.py new file mode 100644 index 0000000000000000000000000000000000000000..637a2698dbb39a042d3d664404bb0a4cba7fd004 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/compatibility.py @@ -0,0 +1,35 @@ +""" +.. deprecated:: 1.10 + + ``sympy.core.compatibility`` is deprecated. See + :ref:`sympy-core-compatibility`. + +Reimplementations of constructs introduced in later versions of Python than +we support. Also some functions that are needed SymPy-wide and are located +here for easy import. + +""" + + +from sympy.utilities.exceptions import sympy_deprecation_warning + +sympy_deprecation_warning(""" +The sympy.core.compatibility submodule is deprecated. + +This module was only ever intended for internal use. Some of the functions +that were in this module are available from the top-level SymPy namespace, +i.e., + + from sympy import ordered, default_sort_key + +The remaining were only intended for internal SymPy use and should not be used +by user code. +""", + deprecated_since_version="1.10", + active_deprecations_target="deprecated-sympy-core-compatibility", + ) + + +from .sorting import ordered, _nodes, default_sort_key # noqa:F401 +from sympy.utilities.misc import as_int as _as_int # noqa:F401 +from sympy.utilities.iterables import iterable, is_sequence, NotIterable # noqa:F401 diff --git a/lib/python3.11/site-packages/sympy/core/containers.py b/lib/python3.11/site-packages/sympy/core/containers.py new file mode 100644 index 0000000000000000000000000000000000000000..bb03b61869f6929552e614d3fa6b2bfc272f270c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/containers.py @@ -0,0 +1,410 @@ +"""Module for SymPy containers + + (SymPy objects that store other SymPy objects) + + The containers implemented in this module are subclassed to Basic. + They are supposed to work seamlessly within the SymPy framework. +""" + +from collections import OrderedDict +from collections.abc import MutableSet +from typing import Any, Callable + +from .basic import Basic +from .sorting import default_sort_key, ordered +from .sympify import _sympify, sympify, _sympy_converter, SympifyError +from sympy.core.kind import Kind +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import as_int + + +class Tuple(Basic): + """ + Wrapper around the builtin tuple object. + + Explanation + =========== + + The Tuple is a subclass of Basic, so that it works well in the + SymPy framework. The wrapped tuple is available as self.args, but + you can also access elements or slices with [:] syntax. + + Parameters + ========== + + sympify : bool + If ``False``, ``sympify`` is not called on ``args``. This + can be used for speedups for very large tuples where the + elements are known to already be SymPy objects. + + Examples + ======== + + >>> from sympy import Tuple, symbols + >>> a, b, c, d = symbols('a b c d') + >>> Tuple(a, b, c)[1:] + (b, c) + >>> Tuple(a, b, c).subs(a, d) + (d, b, c) + + """ + + def __new__(cls, *args, **kwargs): + if kwargs.get('sympify', True): + args = (sympify(arg) for arg in args) + obj = Basic.__new__(cls, *args) + return obj + + def __getitem__(self, i): + if isinstance(i, slice): + indices = i.indices(len(self)) + return Tuple(*(self.args[j] for j in range(*indices))) + return self.args[i] + + def __len__(self): + return len(self.args) + + def __contains__(self, item): + return item in self.args + + def __iter__(self): + return iter(self.args) + + def __add__(self, other): + if isinstance(other, Tuple): + return Tuple(*(self.args + other.args)) + elif isinstance(other, tuple): + return Tuple(*(self.args + other)) + else: + return NotImplemented + + def __radd__(self, other): + if isinstance(other, Tuple): + return Tuple(*(other.args + self.args)) + elif isinstance(other, tuple): + return Tuple(*(other + self.args)) + else: + return NotImplemented + + def __mul__(self, other): + try: + n = as_int(other) + except ValueError: + raise TypeError("Can't multiply sequence by non-integer of type '%s'" % type(other)) + return self.func(*(self.args*n)) + + __rmul__ = __mul__ + + def __eq__(self, other): + if isinstance(other, Basic): + return super().__eq__(other) + return self.args == other + + def __ne__(self, other): + if isinstance(other, Basic): + return super().__ne__(other) + return self.args != other + + def __hash__(self): + return hash(self.args) + + def _to_mpmath(self, prec): + return tuple(a._to_mpmath(prec) for a in self.args) + + def __lt__(self, other): + return _sympify(self.args < other.args) + + def __le__(self, other): + return _sympify(self.args <= other.args) + + # XXX: Basic defines count() as something different, so we can't + # redefine it here. Originally this lead to cse() test failure. + def tuple_count(self, value) -> int: + """Return number of occurrences of value.""" + return self.args.count(value) + + def index(self, value, start=None, stop=None): + """Searches and returns the first index of the value.""" + # XXX: One would expect: + # + # return self.args.index(value, start, stop) + # + # here. Any trouble with that? Yes: + # + # >>> (1,).index(1, None, None) + # Traceback (most recent call last): + # File "", line 1, in + # TypeError: slice indices must be integers or None or have an __index__ method + # + # See: http://bugs.python.org/issue13340 + + if start is None and stop is None: + return self.args.index(value) + elif stop is None: + return self.args.index(value, start) + else: + return self.args.index(value, start, stop) + + @property + def kind(self): + """ + The kind of a Tuple instance. + + The kind of a Tuple is always of :class:`TupleKind` but + parametrised by the number of elements and the kind of each element. + + Examples + ======== + + >>> from sympy import Tuple, Matrix + >>> Tuple(1, 2).kind + TupleKind(NumberKind, NumberKind) + >>> Tuple(Matrix([1, 2]), 1).kind + TupleKind(MatrixKind(NumberKind), NumberKind) + >>> Tuple(1, 2).kind.element_kind + (NumberKind, NumberKind) + + See Also + ======== + + sympy.matrices.kind.MatrixKind + sympy.core.kind.NumberKind + """ + return TupleKind(*(i.kind for i in self.args)) + +_sympy_converter[tuple] = lambda tup: Tuple(*tup) + + + + + +def tuple_wrapper(method): + """ + Decorator that converts any tuple in the function arguments into a Tuple. + + Explanation + =========== + + The motivation for this is to provide simple user interfaces. The user can + call a function with regular tuples in the argument, and the wrapper will + convert them to Tuples before handing them to the function. + + Explanation + =========== + + >>> from sympy.core.containers import tuple_wrapper + >>> def f(*args): + ... return args + >>> g = tuple_wrapper(f) + + The decorated function g sees only the Tuple argument: + + >>> g(0, (1, 2), 3) + (0, (1, 2), 3) + + """ + def wrap_tuples(*args, **kw_args): + newargs = [] + for arg in args: + if isinstance(arg, tuple): + newargs.append(Tuple(*arg)) + else: + newargs.append(arg) + return method(*newargs, **kw_args) + return wrap_tuples + + +class Dict(Basic): + """ + Wrapper around the builtin dict object. + + Explanation + =========== + + The Dict is a subclass of Basic, so that it works well in the + SymPy framework. Because it is immutable, it may be included + in sets, but its values must all be given at instantiation and + cannot be changed afterwards. Otherwise it behaves identically + to the Python dict. + + Examples + ======== + + >>> from sympy import Dict, Symbol + + >>> D = Dict({1: 'one', 2: 'two'}) + >>> for key in D: + ... if key == 1: + ... print('%s %s' % (key, D[key])) + 1 one + + The args are sympified so the 1 and 2 are Integers and the values + are Symbols. Queries automatically sympify args so the following work: + + >>> 1 in D + True + >>> D.has(Symbol('one')) # searches keys and values + True + >>> 'one' in D # not in the keys + False + >>> D[1] + one + + """ + + def __new__(cls, *args): + if len(args) == 1 and isinstance(args[0], (dict, Dict)): + items = [Tuple(k, v) for k, v in args[0].items()] + elif iterable(args) and all(len(arg) == 2 for arg in args): + items = [Tuple(k, v) for k, v in args] + else: + raise TypeError('Pass Dict args as Dict((k1, v1), ...) or Dict({k1: v1, ...})') + elements = frozenset(items) + obj = Basic.__new__(cls, *ordered(items)) + obj.elements = elements + obj._dict = dict(items) # In case Tuple decides it wants to sympify + return obj + + def __getitem__(self, key): + """x.__getitem__(y) <==> x[y]""" + try: + key = _sympify(key) + except SympifyError: + raise KeyError(key) + + return self._dict[key] + + def __setitem__(self, key, value): + raise NotImplementedError("SymPy Dicts are Immutable") + + def items(self): + '''Returns a set-like object providing a view on dict's items. + ''' + return self._dict.items() + + def keys(self): + '''Returns the list of the dict's keys.''' + return self._dict.keys() + + def values(self): + '''Returns the list of the dict's values.''' + return self._dict.values() + + def __iter__(self): + '''x.__iter__() <==> iter(x)''' + return iter(self._dict) + + def __len__(self): + '''x.__len__() <==> len(x)''' + return self._dict.__len__() + + def get(self, key, default=None): + '''Returns the value for key if the key is in the dictionary.''' + try: + key = _sympify(key) + except SympifyError: + return default + return self._dict.get(key, default) + + def __contains__(self, key): + '''D.__contains__(k) -> True if D has a key k, else False''' + try: + key = _sympify(key) + except SympifyError: + return False + return key in self._dict + + def __lt__(self, other): + return _sympify(self.args < other.args) + + @property + def _sorted_args(self): + return tuple(sorted(self.args, key=default_sort_key)) + + def __eq__(self, other): + if isinstance(other, dict): + return self == Dict(other) + return super().__eq__(other) + + __hash__ : Callable[[Basic], Any] = Basic.__hash__ + +# this handles dict, defaultdict, OrderedDict +_sympy_converter[dict] = lambda d: Dict(*d.items()) + +class OrderedSet(MutableSet): + def __init__(self, iterable=None): + if iterable: + self.map = OrderedDict((item, None) for item in iterable) + else: + self.map = OrderedDict() + + def __len__(self): + return len(self.map) + + def __contains__(self, key): + return key in self.map + + def add(self, key): + self.map[key] = None + + def discard(self, key): + self.map.pop(key) + + def pop(self, last=True): + return self.map.popitem(last=last)[0] + + def __iter__(self): + yield from self.map.keys() + + def __repr__(self): + if not self.map: + return '%s()' % (self.__class__.__name__,) + return '%s(%r)' % (self.__class__.__name__, list(self.map.keys())) + + def intersection(self, other): + return self.__class__([val for val in self if val in other]) + + def difference(self, other): + return self.__class__([val for val in self if val not in other]) + + def update(self, iterable): + for val in iterable: + self.add(val) + +class TupleKind(Kind): + """ + TupleKind is a subclass of Kind, which is used to define Kind of ``Tuple``. + + Parameters of TupleKind will be kinds of all the arguments in Tuples, for + example + + Parameters + ========== + + args : tuple(element_kind) + element_kind is kind of element. + args is tuple of kinds of element + + Examples + ======== + + >>> from sympy import Tuple + >>> Tuple(1, 2).kind + TupleKind(NumberKind, NumberKind) + >>> Tuple(1, 2).kind.element_kind + (NumberKind, NumberKind) + + See Also + ======== + + sympy.core.kind.NumberKind + MatrixKind + sympy.sets.sets.SetKind + """ + def __new__(cls, *args): + obj = super().__new__(cls, *args) + obj.element_kind = args + return obj + + def __repr__(self): + return "TupleKind{}".format(self.element_kind) diff --git a/lib/python3.11/site-packages/sympy/core/core.py b/lib/python3.11/site-packages/sympy/core/core.py new file mode 100644 index 0000000000000000000000000000000000000000..8a45bb06919d7a8ef88e2c9958decac705c0b8ee --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/core.py @@ -0,0 +1,21 @@ +""" The core's core. """ +from __future__ import annotations + + +class Registry: + """ + Base class for registry objects. + + Registries map a name to an object using attribute notation. Registry + classes behave singletonically: all their instances share the same state, + which is stored in the class object. + + All subclasses should set `__slots__ = ()`. + """ + __slots__ = () + + def __setattr__(self, name, obj): + setattr(self.__class__, name, obj) + + def __delattr__(self, name): + delattr(self.__class__, name) diff --git a/lib/python3.11/site-packages/sympy/core/coreerrors.py b/lib/python3.11/site-packages/sympy/core/coreerrors.py new file mode 100644 index 0000000000000000000000000000000000000000..e1af0729533a7ce2ae2a4564d225a03eaed6e333 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/coreerrors.py @@ -0,0 +1,9 @@ +"""Definitions of common exceptions for :mod:`sympy.core` module. """ + + +class BaseCoreError(Exception): + """Base class for core related exceptions. """ + + +class NonCommutativeExpression(BaseCoreError): + """Raised when expression didn't have commutative property. """ diff --git a/lib/python3.11/site-packages/sympy/core/decorators.py b/lib/python3.11/site-packages/sympy/core/decorators.py new file mode 100644 index 0000000000000000000000000000000000000000..1da77d2be6b8351ad16ef142f7add51f316e58ef --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/decorators.py @@ -0,0 +1,238 @@ +""" +SymPy core decorators. + +The purpose of this module is to expose decorators without any other +dependencies, so that they can be easily imported anywhere in sympy/core. +""" + +from functools import wraps +from .sympify import SympifyError, sympify + + +def _sympifyit(arg, retval=None): + """ + decorator to smartly _sympify function arguments + + Explanation + =========== + + @_sympifyit('other', NotImplemented) + def add(self, other): + ... + + In add, other can be thought of as already being a SymPy object. + + If it is not, the code is likely to catch an exception, then other will + be explicitly _sympified, and the whole code restarted. + + if _sympify(arg) fails, NotImplemented will be returned + + See also + ======== + + __sympifyit + """ + def deco(func): + return __sympifyit(func, arg, retval) + + return deco + + +def __sympifyit(func, arg, retval=None): + """Decorator to _sympify `arg` argument for function `func`. + + Do not use directly -- use _sympifyit instead. + """ + + # we support f(a,b) only + if not func.__code__.co_argcount: + raise LookupError("func not found") + # only b is _sympified + assert func.__code__.co_varnames[1] == arg + if retval is None: + @wraps(func) + def __sympifyit_wrapper(a, b): + return func(a, sympify(b, strict=True)) + + else: + @wraps(func) + def __sympifyit_wrapper(a, b): + try: + # If an external class has _op_priority, it knows how to deal + # with SymPy objects. Otherwise, it must be converted. + if not hasattr(b, '_op_priority'): + b = sympify(b, strict=True) + return func(a, b) + except SympifyError: + return retval + + return __sympifyit_wrapper + + +def call_highest_priority(method_name): + """A decorator for binary special methods to handle _op_priority. + + Explanation + =========== + + Binary special methods in Expr and its subclasses use a special attribute + '_op_priority' to determine whose special method will be called to + handle the operation. In general, the object having the highest value of + '_op_priority' will handle the operation. Expr and subclasses that define + custom binary special methods (__mul__, etc.) should decorate those + methods with this decorator to add the priority logic. + + The ``method_name`` argument is the name of the method of the other class + that will be called. Use this decorator in the following manner:: + + # Call other.__rmul__ if other._op_priority > self._op_priority + @call_highest_priority('__rmul__') + def __mul__(self, other): + ... + + # Call other.__mul__ if other._op_priority > self._op_priority + @call_highest_priority('__mul__') + def __rmul__(self, other): + ... + """ + def priority_decorator(func): + @wraps(func) + def binary_op_wrapper(self, other): + if hasattr(other, '_op_priority'): + if other._op_priority > self._op_priority: + f = getattr(other, method_name, None) + if f is not None: + return f(self) + return func(self, other) + return binary_op_wrapper + return priority_decorator + + +def sympify_method_args(cls): + '''Decorator for a class with methods that sympify arguments. + + Explanation + =========== + + The sympify_method_args decorator is to be used with the sympify_return + decorator for automatic sympification of method arguments. This is + intended for the common idiom of writing a class like : + + Examples + ======== + + >>> from sympy import Basic, SympifyError, S + >>> from sympy.core.sympify import _sympify + + >>> class MyTuple(Basic): + ... def __add__(self, other): + ... try: + ... other = _sympify(other) + ... except SympifyError: + ... return NotImplemented + ... if not isinstance(other, MyTuple): + ... return NotImplemented + ... return MyTuple(*(self.args + other.args)) + + >>> MyTuple(S(1), S(2)) + MyTuple(S(3), S(4)) + MyTuple(1, 2, 3, 4) + + In the above it is important that we return NotImplemented when other is + not sympifiable and also when the sympified result is not of the expected + type. This allows the MyTuple class to be used cooperatively with other + classes that overload __add__ and want to do something else in combination + with instance of Tuple. + + Using this decorator the above can be written as + + >>> from sympy.core.decorators import sympify_method_args, sympify_return + + >>> @sympify_method_args + ... class MyTuple(Basic): + ... @sympify_return([('other', 'MyTuple')], NotImplemented) + ... def __add__(self, other): + ... return MyTuple(*(self.args + other.args)) + + >>> MyTuple(S(1), S(2)) + MyTuple(S(3), S(4)) + MyTuple(1, 2, 3, 4) + + The idea here is that the decorators take care of the boiler-plate code + for making this happen in each method that potentially needs to accept + unsympified arguments. Then the body of e.g. the __add__ method can be + written without needing to worry about calling _sympify or checking the + type of the resulting object. + + The parameters for sympify_return are a list of tuples of the form + (parameter_name, expected_type) and the value to return (e.g. + NotImplemented). The expected_type parameter can be a type e.g. Tuple or a + string 'Tuple'. Using a string is useful for specifying a Type within its + class body (as in the above example). + + Notes: Currently sympify_return only works for methods that take a single + argument (not including self). Specifying an expected_type as a string + only works for the class in which the method is defined. + ''' + # Extract the wrapped methods from each of the wrapper objects created by + # the sympify_return decorator. Doing this here allows us to provide the + # cls argument which is used for forward string referencing. + for attrname, obj in cls.__dict__.items(): + if isinstance(obj, _SympifyWrapper): + setattr(cls, attrname, obj.make_wrapped(cls)) + return cls + + +def sympify_return(*args): + '''Function/method decorator to sympify arguments automatically + + See the docstring of sympify_method_args for explanation. + ''' + # Store a wrapper object for the decorated method + def wrapper(func): + return _SympifyWrapper(func, args) + return wrapper + + +class _SympifyWrapper: + '''Internal class used by sympify_return and sympify_method_args''' + + def __init__(self, func, args): + self.func = func + self.args = args + + def make_wrapped(self, cls): + func = self.func + parameters, retval = self.args + + # XXX: Handle more than one parameter? + [(parameter, expectedcls)] = parameters + + # Handle forward references to the current class using strings + if expectedcls == cls.__name__: + expectedcls = cls + + # Raise RuntimeError since this is a failure at import time and should + # not be recoverable. + nargs = func.__code__.co_argcount + # we support f(a, b) only + if nargs != 2: + raise RuntimeError('sympify_return can only be used with 2 argument functions') + # only b is _sympified + if func.__code__.co_varnames[1] != parameter: + raise RuntimeError('parameter name mismatch "%s" in %s' % + (parameter, func.__name__)) + + @wraps(func) + def _func(self, other): + # XXX: The check for _op_priority here should be removed. It is + # needed to stop mutable matrices from being sympified to + # immutable matrices which breaks things in quantum... + if not hasattr(other, '_op_priority'): + try: + other = sympify(other, strict=True) + except SympifyError: + return retval + if not isinstance(other, expectedcls): + return retval + return func(self, other) + + return _func diff --git a/lib/python3.11/site-packages/sympy/core/evalf.py b/lib/python3.11/site-packages/sympy/core/evalf.py new file mode 100644 index 0000000000000000000000000000000000000000..c5337c446be737f079c6dccf7cef08d720c0bde7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/evalf.py @@ -0,0 +1,1802 @@ +""" +Adaptive numerical evaluation of SymPy expressions, using mpmath +for mathematical functions. +""" +from __future__ import annotations +from typing import Tuple as tTuple, Optional, Union as tUnion, Callable, List, Dict as tDict, Type, TYPE_CHECKING, \ + Any, overload + +import math + +import mpmath.libmp as libmp +from mpmath import ( + make_mpc, make_mpf, mp, mpc, mpf, nsum, quadts, quadosc, workprec) +from mpmath import inf as mpmath_inf +from mpmath.libmp import (from_int, from_man_exp, from_rational, fhalf, + fnan, finf, fninf, fnone, fone, fzero, mpf_abs, mpf_add, + mpf_atan, mpf_atan2, mpf_cmp, mpf_cos, mpf_e, mpf_exp, mpf_log, mpf_lt, + mpf_mul, mpf_neg, mpf_pi, mpf_pow, mpf_pow_int, mpf_shift, mpf_sin, + mpf_sqrt, normalize, round_nearest, to_int, to_str) +from mpmath.libmp import bitcount as mpmath_bitcount +from mpmath.libmp.backend import MPZ +from mpmath.libmp.libmpc import _infs_nan +from mpmath.libmp.libmpf import dps_to_prec, prec_to_dps + +from .sympify import sympify +from .singleton import S +from sympy.external.gmpy import SYMPY_INTS +from sympy.utilities.iterables import is_sequence +from sympy.utilities.lambdify import lambdify +from sympy.utilities.misc import as_int + +if TYPE_CHECKING: + from sympy.core.expr import Expr + from sympy.core.add import Add + from sympy.core.mul import Mul + from sympy.core.power import Pow + from sympy.core.symbol import Symbol + from sympy.integrals.integrals import Integral + from sympy.concrete.summations import Sum + from sympy.concrete.products import Product + from sympy.functions.elementary.exponential import exp, log + from sympy.functions.elementary.complexes import Abs, re, im + from sympy.functions.elementary.integers import ceiling, floor + from sympy.functions.elementary.trigonometric import atan + from .numbers import Float, Rational, Integer, AlgebraicNumber, Number + +LG10 = math.log2(10) +rnd = round_nearest + + +def bitcount(n): + """Return smallest integer, b, such that |n|/2**b < 1. + """ + return mpmath_bitcount(abs(int(n))) + +# Used in a few places as placeholder values to denote exponents and +# precision levels, e.g. of exact numbers. Must be careful to avoid +# passing these to mpmath functions or returning them in final results. +INF = float(mpmath_inf) +MINUS_INF = float(-mpmath_inf) + +# ~= 100 digits. Real men set this to INF. +DEFAULT_MAXPREC = 333 + + +class PrecisionExhausted(ArithmeticError): + pass + +#----------------------------------------------------------------------------# +# # +# Helper functions for arithmetic and complex parts # +# # +#----------------------------------------------------------------------------# + +""" +An mpf value tuple is a tuple of integers (sign, man, exp, bc) +representing a floating-point number: [1, -1][sign]*man*2**exp where +sign is 0 or 1 and bc should correspond to the number of bits used to +represent the mantissa (man) in binary notation, e.g. +""" +MPF_TUP = tTuple[int, int, int, int] # mpf value tuple + +""" +Explanation +=========== + +>>> from sympy.core.evalf import bitcount +>>> sign, man, exp, bc = 0, 5, 1, 3 +>>> n = [1, -1][sign]*man*2**exp +>>> n, bitcount(man) +(10, 3) + +A temporary result is a tuple (re, im, re_acc, im_acc) where +re and im are nonzero mpf value tuples representing approximate +numbers, or None to denote exact zeros. + +re_acc, im_acc are integers denoting log2(e) where e is the estimated +relative accuracy of the respective complex part, but may be anything +if the corresponding complex part is None. + +""" +TMP_RES = Any # temporary result, should be some variant of +# tUnion[tTuple[Optional[MPF_TUP], Optional[MPF_TUP], +# Optional[int], Optional[int]], +# 'ComplexInfinity'] +# but mypy reports error because it doesn't know as we know +# 1. re and re_acc are either both None or both MPF_TUP +# 2. sometimes the result can't be zoo + +# type of the "options" parameter in internal evalf functions +OPT_DICT = tDict[str, Any] + + +def fastlog(x: Optional[MPF_TUP]) -> tUnion[int, Any]: + """Fast approximation of log2(x) for an mpf value tuple x. + + Explanation + =========== + + Calculated as exponent + width of mantissa. This is an + approximation for two reasons: 1) it gives the ceil(log2(abs(x))) + value and 2) it is too high by 1 in the case that x is an exact + power of 2. Although this is easy to remedy by testing to see if + the odd mpf mantissa is 1 (indicating that one was dealing with + an exact power of 2) that would decrease the speed and is not + necessary as this is only being used as an approximation for the + number of bits in x. The correct return value could be written as + "x[2] + (x[3] if x[1] != 1 else 0)". + Since mpf tuples always have an odd mantissa, no check is done + to see if the mantissa is a multiple of 2 (in which case the + result would be too large by 1). + + Examples + ======== + + >>> from sympy import log + >>> from sympy.core.evalf import fastlog, bitcount + >>> s, m, e = 0, 5, 1 + >>> bc = bitcount(m) + >>> n = [1, -1][s]*m*2**e + >>> n, (log(n)/log(2)).evalf(2), fastlog((s, m, e, bc)) + (10, 3.3, 4) + """ + + if not x or x == fzero: + return MINUS_INF + return x[2] + x[3] + + +def pure_complex(v: 'Expr', or_real=False) -> tuple['Number', 'Number'] | None: + """Return a and b if v matches a + I*b where b is not zero and + a and b are Numbers, else None. If `or_real` is True then 0 will + be returned for `b` if `v` is a real number. + + Examples + ======== + + >>> from sympy.core.evalf import pure_complex + >>> from sympy import sqrt, I, S + >>> a, b, surd = S(2), S(3), sqrt(2) + >>> pure_complex(a) + >>> pure_complex(a, or_real=True) + (2, 0) + >>> pure_complex(surd) + >>> pure_complex(a + b*I) + (2, 3) + >>> pure_complex(I) + (0, 1) + """ + h, t = v.as_coeff_Add() + if t: + c, i = t.as_coeff_Mul() + if i is S.ImaginaryUnit: + return h, c + elif or_real: + return h, S.Zero + return None + + +# I don't know what this is, see function scaled_zero below +SCALED_ZERO_TUP = tTuple[List[int], int, int, int] + + +@overload +def scaled_zero(mag: SCALED_ZERO_TUP, sign=1) -> MPF_TUP: + ... +@overload +def scaled_zero(mag: int, sign=1) -> tTuple[SCALED_ZERO_TUP, int]: + ... +def scaled_zero(mag: tUnion[SCALED_ZERO_TUP, int], sign=1) -> \ + tUnion[MPF_TUP, tTuple[SCALED_ZERO_TUP, int]]: + """Return an mpf representing a power of two with magnitude ``mag`` + and -1 for precision. Or, if ``mag`` is a scaled_zero tuple, then just + remove the sign from within the list that it was initially wrapped + in. + + Examples + ======== + + >>> from sympy.core.evalf import scaled_zero + >>> from sympy import Float + >>> z, p = scaled_zero(100) + >>> z, p + (([0], 1, 100, 1), -1) + >>> ok = scaled_zero(z) + >>> ok + (0, 1, 100, 1) + >>> Float(ok) + 1.26765060022823e+30 + >>> Float(ok, p) + 0.e+30 + >>> ok, p = scaled_zero(100, -1) + >>> Float(scaled_zero(ok), p) + -0.e+30 + """ + if isinstance(mag, tuple) and len(mag) == 4 and iszero(mag, scaled=True): + return (mag[0][0],) + mag[1:] + elif isinstance(mag, SYMPY_INTS): + if sign not in [-1, 1]: + raise ValueError('sign must be +/-1') + rv, p = mpf_shift(fone, mag), -1 + s = 0 if sign == 1 else 1 + rv = ([s],) + rv[1:] + return rv, p + else: + raise ValueError('scaled zero expects int or scaled_zero tuple.') + + +def iszero(mpf: tUnion[MPF_TUP, SCALED_ZERO_TUP, None], scaled=False) -> Optional[bool]: + if not scaled: + return not mpf or not mpf[1] and not mpf[-1] + return mpf and isinstance(mpf[0], list) and mpf[1] == mpf[-1] == 1 + + +def complex_accuracy(result: TMP_RES) -> tUnion[int, Any]: + """ + Returns relative accuracy of a complex number with given accuracies + for the real and imaginary parts. The relative accuracy is defined + in the complex norm sense as ||z|+|error|| / |z| where error + is equal to (real absolute error) + (imag absolute error)*i. + + The full expression for the (logarithmic) error can be approximated + easily by using the max norm to approximate the complex norm. + + In the worst case (re and im equal), this is wrong by a factor + sqrt(2), or by log2(sqrt(2)) = 0.5 bit. + """ + if result is S.ComplexInfinity: + return INF + re, im, re_acc, im_acc = result + if not im: + if not re: + return INF + return re_acc + if not re: + return im_acc + re_size = fastlog(re) + im_size = fastlog(im) + absolute_error = max(re_size - re_acc, im_size - im_acc) + relative_error = absolute_error - max(re_size, im_size) + return -relative_error + + +def get_abs(expr: 'Expr', prec: int, options: OPT_DICT) -> TMP_RES: + result = evalf(expr, prec + 2, options) + if result is S.ComplexInfinity: + return finf, None, prec, None + re, im, re_acc, im_acc = result + if not re: + re, re_acc, im, im_acc = im, im_acc, re, re_acc + if im: + if expr.is_number: + abs_expr, _, acc, _ = evalf(abs(N(expr, prec + 2)), + prec + 2, options) + return abs_expr, None, acc, None + else: + if 'subs' in options: + return libmp.mpc_abs((re, im), prec), None, re_acc, None + return abs(expr), None, prec, None + elif re: + return mpf_abs(re), None, re_acc, None + else: + return None, None, None, None + + +def get_complex_part(expr: 'Expr', no: int, prec: int, options: OPT_DICT) -> TMP_RES: + """no = 0 for real part, no = 1 for imaginary part""" + workprec = prec + i = 0 + while 1: + res = evalf(expr, workprec, options) + if res is S.ComplexInfinity: + return fnan, None, prec, None + value, accuracy = res[no::2] + # XXX is the last one correct? Consider re((1+I)**2).n() + if (not value) or accuracy >= prec or -value[2] > prec: + return value, None, accuracy, None + workprec += max(30, 2**i) + i += 1 + + +def evalf_abs(expr: 'Abs', prec: int, options: OPT_DICT) -> TMP_RES: + return get_abs(expr.args[0], prec, options) + + +def evalf_re(expr: 're', prec: int, options: OPT_DICT) -> TMP_RES: + return get_complex_part(expr.args[0], 0, prec, options) + + +def evalf_im(expr: 'im', prec: int, options: OPT_DICT) -> TMP_RES: + return get_complex_part(expr.args[0], 1, prec, options) + + +def finalize_complex(re: MPF_TUP, im: MPF_TUP, prec: int) -> TMP_RES: + if re == fzero and im == fzero: + raise ValueError("got complex zero with unknown accuracy") + elif re == fzero: + return None, im, None, prec + elif im == fzero: + return re, None, prec, None + + size_re = fastlog(re) + size_im = fastlog(im) + if size_re > size_im: + re_acc = prec + im_acc = prec + min(-(size_re - size_im), 0) + else: + im_acc = prec + re_acc = prec + min(-(size_im - size_re), 0) + return re, im, re_acc, im_acc + + +def chop_parts(value: TMP_RES, prec: int) -> TMP_RES: + """ + Chop off tiny real or complex parts. + """ + if value is S.ComplexInfinity: + return value + re, im, re_acc, im_acc = value + # Method 1: chop based on absolute value + if re and re not in _infs_nan and (fastlog(re) < -prec + 4): + re, re_acc = None, None + if im and im not in _infs_nan and (fastlog(im) < -prec + 4): + im, im_acc = None, None + # Method 2: chop if inaccurate and relatively small + if re and im: + delta = fastlog(re) - fastlog(im) + if re_acc < 2 and (delta - re_acc <= -prec + 4): + re, re_acc = None, None + if im_acc < 2 and (delta - im_acc >= prec - 4): + im, im_acc = None, None + return re, im, re_acc, im_acc + + +def check_target(expr: 'Expr', result: TMP_RES, prec: int): + a = complex_accuracy(result) + if a < prec: + raise PrecisionExhausted("Failed to distinguish the expression: \n\n%s\n\n" + "from zero. Try simplifying the input, using chop=True, or providing " + "a higher maxn for evalf" % (expr)) + + +def get_integer_part(expr: 'Expr', no: int, options: OPT_DICT, return_ints=False) -> \ + tUnion[TMP_RES, tTuple[int, int]]: + """ + With no = 1, computes ceiling(expr) + With no = -1, computes floor(expr) + + Note: this function either gives the exact result or signals failure. + """ + from sympy.functions.elementary.complexes import re, im + # The expression is likely less than 2^30 or so + assumed_size = 30 + result = evalf(expr, assumed_size, options) + if result is S.ComplexInfinity: + raise ValueError("Cannot get integer part of Complex Infinity") + ire, iim, ire_acc, iim_acc = result + + # We now know the size, so we can calculate how much extra precision + # (if any) is needed to get within the nearest integer + if ire and iim: + gap = max(fastlog(ire) - ire_acc, fastlog(iim) - iim_acc) + elif ire: + gap = fastlog(ire) - ire_acc + elif iim: + gap = fastlog(iim) - iim_acc + else: + # ... or maybe the expression was exactly zero + if return_ints: + return 0, 0 + else: + return None, None, None, None + + margin = 10 + + if gap >= -margin: + prec = margin + assumed_size + gap + ire, iim, ire_acc, iim_acc = evalf( + expr, prec, options) + else: + prec = assumed_size + + # We can now easily find the nearest integer, but to find floor/ceil, we + # must also calculate whether the difference to the nearest integer is + # positive or negative (which may fail if very close). + def calc_part(re_im: 'Expr', nexpr: MPF_TUP): + from .add import Add + _, _, exponent, _ = nexpr + is_int = exponent == 0 + nint = int(to_int(nexpr, rnd)) + if is_int: + # make sure that we had enough precision to distinguish + # between nint and the re or im part (re_im) of expr that + # was passed to calc_part + ire, iim, ire_acc, iim_acc = evalf( + re_im - nint, 10, options) # don't need much precision + assert not iim + size = -fastlog(ire) + 2 # -ve b/c ire is less than 1 + if size > prec: + ire, iim, ire_acc, iim_acc = evalf( + re_im, size, options) + assert not iim + nexpr = ire + nint = int(to_int(nexpr, rnd)) + _, _, new_exp, _ = ire + is_int = new_exp == 0 + if not is_int: + # if there are subs and they all contain integer re/im parts + # then we can (hopefully) safely substitute them into the + # expression + s = options.get('subs', False) + if s: + # use strict=False with as_int because we take + # 2.0 == 2 + def is_int_reim(x): + """Check for integer or integer + I*integer.""" + try: + as_int(x, strict=False) + return True + except ValueError: + try: + [as_int(i, strict=False) for i in x.as_real_imag()] + return True + except ValueError: + return False + + if all(is_int_reim(v) for v in s.values()): + re_im = re_im.subs(s) + + re_im = Add(re_im, -nint, evaluate=False) + x, _, x_acc, _ = evalf(re_im, 10, options) + try: + check_target(re_im, (x, None, x_acc, None), 3) + except PrecisionExhausted: + if not re_im.equals(0): + raise PrecisionExhausted + x = fzero + nint += int(no*(mpf_cmp(x or fzero, fzero) == no)) + nint = from_int(nint) + return nint, INF + + re_, im_, re_acc, im_acc = None, None, None, None + + if ire: + re_, re_acc = calc_part(re(expr, evaluate=False), ire) + if iim: + im_, im_acc = calc_part(im(expr, evaluate=False), iim) + + if return_ints: + return int(to_int(re_ or fzero)), int(to_int(im_ or fzero)) + return re_, im_, re_acc, im_acc + + +def evalf_ceiling(expr: 'ceiling', prec: int, options: OPT_DICT) -> TMP_RES: + return get_integer_part(expr.args[0], 1, options) + + +def evalf_floor(expr: 'floor', prec: int, options: OPT_DICT) -> TMP_RES: + return get_integer_part(expr.args[0], -1, options) + + +def evalf_float(expr: 'Float', prec: int, options: OPT_DICT) -> TMP_RES: + return expr._mpf_, None, prec, None + + +def evalf_rational(expr: 'Rational', prec: int, options: OPT_DICT) -> TMP_RES: + return from_rational(expr.p, expr.q, prec), None, prec, None + + +def evalf_integer(expr: 'Integer', prec: int, options: OPT_DICT) -> TMP_RES: + return from_int(expr.p, prec), None, prec, None + +#----------------------------------------------------------------------------# +# # +# Arithmetic operations # +# # +#----------------------------------------------------------------------------# + + +def add_terms(terms: list, prec: int, target_prec: int) -> \ + tTuple[tUnion[MPF_TUP, SCALED_ZERO_TUP, None], Optional[int]]: + """ + Helper for evalf_add. Adds a list of (mpfval, accuracy) terms. + + Returns + ======= + + - None, None if there are no non-zero terms; + - terms[0] if there is only 1 term; + - scaled_zero if the sum of the terms produces a zero by cancellation + e.g. mpfs representing 1 and -1 would produce a scaled zero which need + special handling since they are not actually zero and they are purposely + malformed to ensure that they cannot be used in anything but accuracy + calculations; + - a tuple that is scaled to target_prec that corresponds to the + sum of the terms. + + The returned mpf tuple will be normalized to target_prec; the input + prec is used to define the working precision. + + XXX explain why this is needed and why one cannot just loop using mpf_add + """ + + terms = [t for t in terms if not iszero(t[0])] + if not terms: + return None, None + elif len(terms) == 1: + return terms[0] + + # see if any argument is NaN or oo and thus warrants a special return + special = [] + from .numbers import Float + for t in terms: + arg = Float._new(t[0], 1) + if arg is S.NaN or arg.is_infinite: + special.append(arg) + if special: + from .add import Add + rv = evalf(Add(*special), prec + 4, {}) + return rv[0], rv[2] + + working_prec = 2*prec + sum_man, sum_exp = 0, 0 + absolute_err: List[int] = [] + + for x, accuracy in terms: + sign, man, exp, bc = x + if sign: + man = -man + absolute_err.append(bc + exp - accuracy) + delta = exp - sum_exp + if exp >= sum_exp: + # x much larger than existing sum? + # first: quick test + if ((delta > working_prec) and + ((not sum_man) or + delta - bitcount(abs(sum_man)) > working_prec)): + sum_man = man + sum_exp = exp + else: + sum_man += (man << delta) + else: + delta = -delta + # x much smaller than existing sum? + if delta - bc > working_prec: + if not sum_man: + sum_man, sum_exp = man, exp + else: + sum_man = (sum_man << delta) + man + sum_exp = exp + absolute_error = max(absolute_err) + if not sum_man: + return scaled_zero(absolute_error) + if sum_man < 0: + sum_sign = 1 + sum_man = -sum_man + else: + sum_sign = 0 + sum_bc = bitcount(sum_man) + sum_accuracy = sum_exp + sum_bc - absolute_error + r = normalize(sum_sign, sum_man, sum_exp, sum_bc, target_prec, + rnd), sum_accuracy + return r + + +def evalf_add(v: 'Add', prec: int, options: OPT_DICT) -> TMP_RES: + res = pure_complex(v) + if res: + h, c = res + re, _, re_acc, _ = evalf(h, prec, options) + im, _, im_acc, _ = evalf(c, prec, options) + return re, im, re_acc, im_acc + + oldmaxprec = options.get('maxprec', DEFAULT_MAXPREC) + + i = 0 + target_prec = prec + while 1: + options['maxprec'] = min(oldmaxprec, 2*prec) + + terms = [evalf(arg, prec + 10, options) for arg in v.args] + n = terms.count(S.ComplexInfinity) + if n >= 2: + return fnan, None, prec, None + re, re_acc = add_terms( + [a[0::2] for a in terms if isinstance(a, tuple) and a[0]], prec, target_prec) + im, im_acc = add_terms( + [a[1::2] for a in terms if isinstance(a, tuple) and a[1]], prec, target_prec) + if n == 1: + if re in (finf, fninf, fnan) or im in (finf, fninf, fnan): + return fnan, None, prec, None + return S.ComplexInfinity + acc = complex_accuracy((re, im, re_acc, im_acc)) + if acc >= target_prec: + if options.get('verbose'): + print("ADD: wanted", target_prec, "accurate bits, got", re_acc, im_acc) + break + else: + if (prec - target_prec) > options['maxprec']: + break + + prec = prec + max(10 + 2**i, target_prec - acc) + i += 1 + if options.get('verbose'): + print("ADD: restarting with prec", prec) + + options['maxprec'] = oldmaxprec + if iszero(re, scaled=True): + re = scaled_zero(re) + if iszero(im, scaled=True): + im = scaled_zero(im) + return re, im, re_acc, im_acc + + +def evalf_mul(v: 'Mul', prec: int, options: OPT_DICT) -> TMP_RES: + res = pure_complex(v) + if res: + # the only pure complex that is a mul is h*I + _, h = res + im, _, im_acc, _ = evalf(h, prec, options) + return None, im, None, im_acc + args = list(v.args) + + # see if any argument is NaN or oo and thus warrants a special return + has_zero = False + special = [] + from .numbers import Float + for arg in args: + result = evalf(arg, prec, options) + if result is S.ComplexInfinity: + special.append(result) + continue + if result[0] is None: + if result[1] is None: + has_zero = True + continue + num = Float._new(result[0], 1) + if num is S.NaN: + return fnan, None, prec, None + if num.is_infinite: + special.append(num) + if special: + if has_zero: + return fnan, None, prec, None + from .mul import Mul + return evalf(Mul(*special), prec + 4, {}) + if has_zero: + return None, None, None, None + + # With guard digits, multiplication in the real case does not destroy + # accuracy. This is also true in the complex case when considering the + # total accuracy; however accuracy for the real or imaginary parts + # separately may be lower. + acc = prec + + # XXX: big overestimate + working_prec = prec + len(args) + 5 + + # Empty product is 1 + start = man, exp, bc = MPZ(1), 0, 1 + + # First, we multiply all pure real or pure imaginary numbers. + # direction tells us that the result should be multiplied by + # I**direction; all other numbers get put into complex_factors + # to be multiplied out after the first phase. + last = len(args) + direction = 0 + args.append(S.One) + complex_factors = [] + + for i, arg in enumerate(args): + if i != last and pure_complex(arg): + args[-1] = (args[-1]*arg).expand() + continue + elif i == last and arg is S.One: + continue + re, im, re_acc, im_acc = evalf(arg, working_prec, options) + if re and im: + complex_factors.append((re, im, re_acc, im_acc)) + continue + elif re: + (s, m, e, b), w_acc = re, re_acc + elif im: + (s, m, e, b), w_acc = im, im_acc + direction += 1 + else: + return None, None, None, None + direction += 2*s + man *= m + exp += e + bc += b + while bc > 3*working_prec: + man >>= working_prec + exp += working_prec + bc -= working_prec + acc = min(acc, w_acc) + sign = (direction & 2) >> 1 + if not complex_factors: + v = normalize(sign, man, exp, bitcount(man), prec, rnd) + # multiply by i + if direction & 1: + return None, v, None, acc + else: + return v, None, acc, None + else: + # initialize with the first term + if (man, exp, bc) != start: + # there was a real part; give it an imaginary part + re, im = (sign, man, exp, bitcount(man)), (0, MPZ(0), 0, 0) + i0 = 0 + else: + # there is no real part to start (other than the starting 1) + wre, wim, wre_acc, wim_acc = complex_factors[0] + acc = min(acc, + complex_accuracy((wre, wim, wre_acc, wim_acc))) + re = wre + im = wim + i0 = 1 + + for wre, wim, wre_acc, wim_acc in complex_factors[i0:]: + # acc is the overall accuracy of the product; we aren't + # computing exact accuracies of the product. + acc = min(acc, + complex_accuracy((wre, wim, wre_acc, wim_acc))) + + use_prec = working_prec + A = mpf_mul(re, wre, use_prec) + B = mpf_mul(mpf_neg(im), wim, use_prec) + C = mpf_mul(re, wim, use_prec) + D = mpf_mul(im, wre, use_prec) + re = mpf_add(A, B, use_prec) + im = mpf_add(C, D, use_prec) + if options.get('verbose'): + print("MUL: wanted", prec, "accurate bits, got", acc) + # multiply by I + if direction & 1: + re, im = mpf_neg(im), re + return re, im, acc, acc + + +def evalf_pow(v: 'Pow', prec: int, options) -> TMP_RES: + + target_prec = prec + base, exp = v.args + + # We handle x**n separately. This has two purposes: 1) it is much + # faster, because we avoid calling evalf on the exponent, and 2) it + # allows better handling of real/imaginary parts that are exactly zero + if exp.is_Integer: + p: int = exp.p # type: ignore + # Exact + if not p: + return fone, None, prec, None + # Exponentiation by p magnifies relative error by |p|, so the + # base must be evaluated with increased precision if p is large + prec += int(math.log2(abs(p))) + result = evalf(base, prec + 5, options) + if result is S.ComplexInfinity: + if p < 0: + return None, None, None, None + return result + re, im, re_acc, im_acc = result + # Real to integer power + if re and not im: + return mpf_pow_int(re, p, target_prec), None, target_prec, None + # (x*I)**n = I**n * x**n + if im and not re: + z = mpf_pow_int(im, p, target_prec) + case = p % 4 + if case == 0: + return z, None, target_prec, None + if case == 1: + return None, z, None, target_prec + if case == 2: + return mpf_neg(z), None, target_prec, None + if case == 3: + return None, mpf_neg(z), None, target_prec + # Zero raised to an integer power + if not re: + if p < 0: + return S.ComplexInfinity + return None, None, None, None + # General complex number to arbitrary integer power + re, im = libmp.mpc_pow_int((re, im), p, prec) + # Assumes full accuracy in input + return finalize_complex(re, im, target_prec) + + result = evalf(base, prec + 5, options) + if result is S.ComplexInfinity: + if exp.is_Rational: + if exp < 0: + return None, None, None, None + return result + raise NotImplementedError + + # Pure square root + if exp is S.Half: + xre, xim, _, _ = result + # General complex square root + if xim: + re, im = libmp.mpc_sqrt((xre or fzero, xim), prec) + return finalize_complex(re, im, prec) + if not xre: + return None, None, None, None + # Square root of a negative real number + if mpf_lt(xre, fzero): + return None, mpf_sqrt(mpf_neg(xre), prec), None, prec + # Positive square root + return mpf_sqrt(xre, prec), None, prec, None + + # We first evaluate the exponent to find its magnitude + # This determines the working precision that must be used + prec += 10 + result = evalf(exp, prec, options) + if result is S.ComplexInfinity: + return fnan, None, prec, None + yre, yim, _, _ = result + # Special cases: x**0 + if not (yre or yim): + return fone, None, prec, None + + ysize = fastlog(yre) + # Restart if too big + # XXX: prec + ysize might exceed maxprec + if ysize > 5: + prec += ysize + yre, yim, _, _ = evalf(exp, prec, options) + + # Pure exponential function; no need to evalf the base + if base is S.Exp1: + if yim: + re, im = libmp.mpc_exp((yre or fzero, yim), prec) + return finalize_complex(re, im, target_prec) + return mpf_exp(yre, target_prec), None, target_prec, None + + xre, xim, _, _ = evalf(base, prec + 5, options) + # 0**y + if not (xre or xim): + if yim: + return fnan, None, prec, None + if yre[0] == 1: # y < 0 + return S.ComplexInfinity + return None, None, None, None + + # (real ** complex) or (complex ** complex) + if yim: + re, im = libmp.mpc_pow( + (xre or fzero, xim or fzero), (yre or fzero, yim), + target_prec) + return finalize_complex(re, im, target_prec) + # complex ** real + if xim: + re, im = libmp.mpc_pow_mpf((xre or fzero, xim), yre, target_prec) + return finalize_complex(re, im, target_prec) + # negative ** real + elif mpf_lt(xre, fzero): + re, im = libmp.mpc_pow_mpf((xre, fzero), yre, target_prec) + return finalize_complex(re, im, target_prec) + # positive ** real + else: + return mpf_pow(xre, yre, target_prec), None, target_prec, None + + +#----------------------------------------------------------------------------# +# # +# Special functions # +# # +#----------------------------------------------------------------------------# + + +def evalf_exp(expr: 'exp', prec: int, options: OPT_DICT) -> TMP_RES: + from .power import Pow + return evalf_pow(Pow(S.Exp1, expr.exp, evaluate=False), prec, options) + + +def evalf_trig(v: 'Expr', prec: int, options: OPT_DICT) -> TMP_RES: + """ + This function handles sin and cos of complex arguments. + + TODO: should also handle tan of complex arguments. + """ + from sympy.functions.elementary.trigonometric import cos, sin + if isinstance(v, cos): + func = mpf_cos + elif isinstance(v, sin): + func = mpf_sin + else: + raise NotImplementedError + arg = v.args[0] + # 20 extra bits is possibly overkill. It does make the need + # to restart very unlikely + xprec = prec + 20 + re, im, re_acc, im_acc = evalf(arg, xprec, options) + if im: + if 'subs' in options: + v = v.subs(options['subs']) + return evalf(v._eval_evalf(prec), prec, options) + if not re: + if isinstance(v, cos): + return fone, None, prec, None + elif isinstance(v, sin): + return None, None, None, None + else: + raise NotImplementedError + # For trigonometric functions, we are interested in the + # fixed-point (absolute) accuracy of the argument. + xsize = fastlog(re) + # Magnitude <= 1.0. OK to compute directly, because there is no + # danger of hitting the first root of cos (with sin, magnitude + # <= 2.0 would actually be ok) + if xsize < 1: + return func(re, prec, rnd), None, prec, None + # Very large + if xsize >= 10: + xprec = prec + xsize + re, im, re_acc, im_acc = evalf(arg, xprec, options) + # Need to repeat in case the argument is very close to a + # multiple of pi (or pi/2), hitting close to a root + while 1: + y = func(re, prec, rnd) + ysize = fastlog(y) + gap = -ysize + accuracy = (xprec - xsize) - gap + if accuracy < prec: + if options.get('verbose'): + print("SIN/COS", accuracy, "wanted", prec, "gap", gap) + print(to_str(y, 10)) + if xprec > options.get('maxprec', DEFAULT_MAXPREC): + return y, None, accuracy, None + xprec += gap + re, im, re_acc, im_acc = evalf(arg, xprec, options) + continue + else: + return y, None, prec, None + + +def evalf_log(expr: 'log', prec: int, options: OPT_DICT) -> TMP_RES: + if len(expr.args)>1: + expr = expr.doit() + return evalf(expr, prec, options) + arg = expr.args[0] + workprec = prec + 10 + result = evalf(arg, workprec, options) + if result is S.ComplexInfinity: + return result + xre, xim, xacc, _ = result + + # evalf can return NoneTypes if chop=True + # issue 18516, 19623 + if xre is xim is None: + # Dear reviewer, I do not know what -inf is; + # it looks to be (1, 0, -789, -3) + # but I'm not sure in general, + # so we just let mpmath figure + # it out by taking log of 0 directly. + # It would be better to return -inf instead. + xre = fzero + + if xim: + from sympy.functions.elementary.complexes import Abs + from sympy.functions.elementary.exponential import log + + # XXX: use get_abs etc instead + re = evalf_log( + log(Abs(arg, evaluate=False), evaluate=False), prec, options) + im = mpf_atan2(xim, xre or fzero, prec) + return re[0], im, re[2], prec + + imaginary_term = (mpf_cmp(xre, fzero) < 0) + + re = mpf_log(mpf_abs(xre), prec, rnd) + size = fastlog(re) + if prec - size > workprec and re != fzero: + from .add import Add + # We actually need to compute 1+x accurately, not x + add = Add(S.NegativeOne, arg, evaluate=False) + xre, xim, _, _ = evalf_add(add, prec, options) + prec2 = workprec - fastlog(xre) + # xre is now x - 1 so we add 1 back here to calculate x + re = mpf_log(mpf_abs(mpf_add(xre, fone, prec2)), prec, rnd) + + re_acc = prec + + if imaginary_term: + return re, mpf_pi(prec), re_acc, prec + else: + return re, None, re_acc, None + + +def evalf_atan(v: 'atan', prec: int, options: OPT_DICT) -> TMP_RES: + arg = v.args[0] + xre, xim, reacc, imacc = evalf(arg, prec + 5, options) + if xre is xim is None: + return (None,)*4 + if xim: + raise NotImplementedError + return mpf_atan(xre, prec, rnd), None, prec, None + + +def evalf_subs(prec: int, subs: dict) -> dict: + """ Change all Float entries in `subs` to have precision prec. """ + newsubs = {} + for a, b in subs.items(): + b = S(b) + if b.is_Float: + b = b._eval_evalf(prec) + newsubs[a] = b + return newsubs + + +def evalf_piecewise(expr: 'Expr', prec: int, options: OPT_DICT) -> TMP_RES: + from .numbers import Float, Integer + if 'subs' in options: + expr = expr.subs(evalf_subs(prec, options['subs'])) + newopts = options.copy() + del newopts['subs'] + if hasattr(expr, 'func'): + return evalf(expr, prec, newopts) + if isinstance(expr, float): + return evalf(Float(expr), prec, newopts) + if isinstance(expr, int): + return evalf(Integer(expr), prec, newopts) + + # We still have undefined symbols + raise NotImplementedError + + +def evalf_alg_num(a: 'AlgebraicNumber', prec: int, options: OPT_DICT) -> TMP_RES: + return evalf(a.to_root(), prec, options) + +#----------------------------------------------------------------------------# +# # +# High-level operations # +# # +#----------------------------------------------------------------------------# + + +def as_mpmath(x: Any, prec: int, options: OPT_DICT) -> tUnion[mpc, mpf]: + from .numbers import Infinity, NegativeInfinity, Zero + x = sympify(x) + if isinstance(x, Zero) or x == 0.0: + return mpf(0) + if isinstance(x, Infinity): + return mpf('inf') + if isinstance(x, NegativeInfinity): + return mpf('-inf') + # XXX + result = evalf(x, prec, options) + return quad_to_mpmath(result) + + +def do_integral(expr: 'Integral', prec: int, options: OPT_DICT) -> TMP_RES: + func = expr.args[0] + x, xlow, xhigh = expr.args[1] + if xlow == xhigh: + xlow = xhigh = 0 + elif x not in func.free_symbols: + # only the difference in limits matters in this case + # so if there is a symbol in common that will cancel + # out when taking the difference, then use that + # difference + if xhigh.free_symbols & xlow.free_symbols: + diff = xhigh - xlow + if diff.is_number: + xlow, xhigh = 0, diff + + oldmaxprec = options.get('maxprec', DEFAULT_MAXPREC) + options['maxprec'] = min(oldmaxprec, 2*prec) + + with workprec(prec + 5): + xlow = as_mpmath(xlow, prec + 15, options) + xhigh = as_mpmath(xhigh, prec + 15, options) + + # Integration is like summation, and we can phone home from + # the integrand function to update accuracy summation style + # Note that this accuracy is inaccurate, since it fails + # to account for the variable quadrature weights, + # but it is better than nothing + + from sympy.functions.elementary.trigonometric import cos, sin + from .symbol import Wild + + have_part = [False, False] + max_real_term: tUnion[float, int] = MINUS_INF + max_imag_term: tUnion[float, int] = MINUS_INF + + def f(t: 'Expr') -> tUnion[mpc, mpf]: + nonlocal max_real_term, max_imag_term + re, im, re_acc, im_acc = evalf(func, mp.prec, {'subs': {x: t}}) + + have_part[0] = re or have_part[0] + have_part[1] = im or have_part[1] + + max_real_term = max(max_real_term, fastlog(re)) + max_imag_term = max(max_imag_term, fastlog(im)) + + if im: + return mpc(re or fzero, im) + return mpf(re or fzero) + + if options.get('quad') == 'osc': + A = Wild('A', exclude=[x]) + B = Wild('B', exclude=[x]) + D = Wild('D') + m = func.match(cos(A*x + B)*D) + if not m: + m = func.match(sin(A*x + B)*D) + if not m: + raise ValueError("An integrand of the form sin(A*x+B)*f(x) " + "or cos(A*x+B)*f(x) is required for oscillatory quadrature") + period = as_mpmath(2*S.Pi/m[A], prec + 15, options) + result = quadosc(f, [xlow, xhigh], period=period) + # XXX: quadosc does not do error detection yet + quadrature_error = MINUS_INF + else: + result, quadrature_err = quadts(f, [xlow, xhigh], error=1) + quadrature_error = fastlog(quadrature_err._mpf_) + + options['maxprec'] = oldmaxprec + + if have_part[0]: + re: Optional[MPF_TUP] = result.real._mpf_ + re_acc: Optional[int] + if re == fzero: + re_s, re_acc = scaled_zero(int(-max(prec, max_real_term, quadrature_error))) + re = scaled_zero(re_s) # handled ok in evalf_integral + else: + re_acc = int(-max(max_real_term - fastlog(re) - prec, quadrature_error)) + else: + re, re_acc = None, None + + if have_part[1]: + im: Optional[MPF_TUP] = result.imag._mpf_ + im_acc: Optional[int] + if im == fzero: + im_s, im_acc = scaled_zero(int(-max(prec, max_imag_term, quadrature_error))) + im = scaled_zero(im_s) # handled ok in evalf_integral + else: + im_acc = int(-max(max_imag_term - fastlog(im) - prec, quadrature_error)) + else: + im, im_acc = None, None + + result = re, im, re_acc, im_acc + return result + + +def evalf_integral(expr: 'Integral', prec: int, options: OPT_DICT) -> TMP_RES: + limits = expr.limits + if len(limits) != 1 or len(limits[0]) != 3: + raise NotImplementedError + workprec = prec + i = 0 + maxprec = options.get('maxprec', INF) + while 1: + result = do_integral(expr, workprec, options) + accuracy = complex_accuracy(result) + if accuracy >= prec: # achieved desired precision + break + if workprec >= maxprec: # can't increase accuracy any more + break + if accuracy == -1: + # maybe the answer really is zero and maybe we just haven't increased + # the precision enough. So increase by doubling to not take too long + # to get to maxprec. + workprec *= 2 + else: + workprec += max(prec, 2**i) + workprec = min(workprec, maxprec) + i += 1 + return result + + +def check_convergence(numer: 'Expr', denom: 'Expr', n: 'Symbol') -> tTuple[int, Any, Any]: + """ + Returns + ======= + + (h, g, p) where + -- h is: + > 0 for convergence of rate 1/factorial(n)**h + < 0 for divergence of rate factorial(n)**(-h) + = 0 for geometric or polynomial convergence or divergence + + -- abs(g) is: + > 1 for geometric convergence of rate 1/h**n + < 1 for geometric divergence of rate h**n + = 1 for polynomial convergence or divergence + + (g < 0 indicates an alternating series) + + -- p is: + > 1 for polynomial convergence of rate 1/n**h + <= 1 for polynomial divergence of rate n**(-h) + + """ + from sympy.polys.polytools import Poly + npol = Poly(numer, n) + dpol = Poly(denom, n) + p = npol.degree() + q = dpol.degree() + rate = q - p + if rate: + return rate, None, None + constant = dpol.LC() / npol.LC() + from .numbers import equal_valued + if not equal_valued(abs(constant), 1): + return rate, constant, None + if npol.degree() == dpol.degree() == 0: + return rate, constant, 0 + pc = npol.all_coeffs()[1] + qc = dpol.all_coeffs()[1] + return rate, constant, (qc - pc)/dpol.LC() + + +def hypsum(expr: 'Expr', n: 'Symbol', start: int, prec: int) -> mpf: + """ + Sum a rapidly convergent infinite hypergeometric series with + given general term, e.g. e = hypsum(1/factorial(n), n). The + quotient between successive terms must be a quotient of integer + polynomials. + """ + from .numbers import Float, equal_valued + from sympy.simplify.simplify import hypersimp + + if prec == float('inf'): + raise NotImplementedError('does not support inf prec') + + if start: + expr = expr.subs(n, n + start) + hs = hypersimp(expr, n) + if hs is None: + raise NotImplementedError("a hypergeometric series is required") + num, den = hs.as_numer_denom() + + func1 = lambdify(n, num) + func2 = lambdify(n, den) + + h, g, p = check_convergence(num, den, n) + + if h < 0: + raise ValueError("Sum diverges like (n!)^%i" % (-h)) + + term = expr.subs(n, 0) + if not term.is_Rational: + raise NotImplementedError("Non rational term functionality is not implemented.") + + # Direct summation if geometric or faster + if h > 0 or (h == 0 and abs(g) > 1): + term = (MPZ(term.p) << prec) // term.q + s = term + k = 1 + while abs(term) > 5: + term *= MPZ(func1(k - 1)) + term //= MPZ(func2(k - 1)) + s += term + k += 1 + return from_man_exp(s, -prec) + else: + alt = g < 0 + if abs(g) < 1: + raise ValueError("Sum diverges like (%i)^n" % abs(1/g)) + if p < 1 or (equal_valued(p, 1) and not alt): + raise ValueError("Sum diverges like n^%i" % (-p)) + # We have polynomial convergence: use Richardson extrapolation + vold = None + ndig = prec_to_dps(prec) + while True: + # Need to use at least quad precision because a lot of cancellation + # might occur in the extrapolation process; we check the answer to + # make sure that the desired precision has been reached, too. + prec2 = 4*prec + term0 = (MPZ(term.p) << prec2) // term.q + + def summand(k, _term=[term0]): + if k: + k = int(k) + _term[0] *= MPZ(func1(k - 1)) + _term[0] //= MPZ(func2(k - 1)) + return make_mpf(from_man_exp(_term[0], -prec2)) + + with workprec(prec): + v = nsum(summand, [0, mpmath_inf], method='richardson') + vf = Float(v, ndig) + if vold is not None and vold == vf: + break + prec += prec # double precision each time + vold = vf + + return v._mpf_ + + +def evalf_prod(expr: 'Product', prec: int, options: OPT_DICT) -> TMP_RES: + if all((l[1] - l[2]).is_Integer for l in expr.limits): + result = evalf(expr.doit(), prec=prec, options=options) + else: + from sympy.concrete.summations import Sum + result = evalf(expr.rewrite(Sum), prec=prec, options=options) + return result + + +def evalf_sum(expr: 'Sum', prec: int, options: OPT_DICT) -> TMP_RES: + from .numbers import Float + if 'subs' in options: + expr = expr.subs(options['subs']) + func = expr.function + limits = expr.limits + if len(limits) != 1 or len(limits[0]) != 3: + raise NotImplementedError + if func.is_zero: + return None, None, prec, None + prec2 = prec + 10 + try: + n, a, b = limits[0] + if b is not S.Infinity or a is S.NegativeInfinity or a != int(a): + raise NotImplementedError + # Use fast hypergeometric summation if possible + v = hypsum(func, n, int(a), prec2) + delta = prec - fastlog(v) + if fastlog(v) < -10: + v = hypsum(func, n, int(a), delta) + return v, None, min(prec, delta), None + except NotImplementedError: + # Euler-Maclaurin summation for general series + eps = Float(2.0)**(-prec) + for i in range(1, 5): + m = n = 2**i * prec + s, err = expr.euler_maclaurin(m=m, n=n, eps=eps, + eval_integral=False) + err = err.evalf() + if err is S.NaN: + raise NotImplementedError + if err <= eps: + break + err = fastlog(evalf(abs(err), 20, options)[0]) + re, im, re_acc, im_acc = evalf(s, prec2, options) + if re_acc is None: + re_acc = -err + if im_acc is None: + im_acc = -err + return re, im, re_acc, im_acc + + +#----------------------------------------------------------------------------# +# # +# Symbolic interface # +# # +#----------------------------------------------------------------------------# + +def evalf_symbol(x: 'Expr', prec: int, options: OPT_DICT) -> TMP_RES: + val = options['subs'][x] + if isinstance(val, mpf): + if not val: + return None, None, None, None + return val._mpf_, None, prec, None + else: + if '_cache' not in options: + options['_cache'] = {} + cache = options['_cache'] + cached, cached_prec = cache.get(x, (None, MINUS_INF)) + if cached_prec >= prec: + return cached + v = evalf(sympify(val), prec, options) + cache[x] = (v, prec) + return v + + +evalf_table: tDict[Type['Expr'], Callable[['Expr', int, OPT_DICT], TMP_RES]] = {} + + +def _create_evalf_table(): + global evalf_table + from sympy.concrete.products import Product + from sympy.concrete.summations import Sum + from .add import Add + from .mul import Mul + from .numbers import Exp1, Float, Half, ImaginaryUnit, Integer, NaN, NegativeOne, One, Pi, Rational, \ + Zero, ComplexInfinity, AlgebraicNumber + from .power import Pow + from .symbol import Dummy, Symbol + from sympy.functions.elementary.complexes import Abs, im, re + from sympy.functions.elementary.exponential import exp, log + from sympy.functions.elementary.integers import ceiling, floor + from sympy.functions.elementary.piecewise import Piecewise + from sympy.functions.elementary.trigonometric import atan, cos, sin + from sympy.integrals.integrals import Integral + evalf_table = { + Symbol: evalf_symbol, + Dummy: evalf_symbol, + Float: evalf_float, + Rational: evalf_rational, + Integer: evalf_integer, + Zero: lambda x, prec, options: (None, None, prec, None), + One: lambda x, prec, options: (fone, None, prec, None), + Half: lambda x, prec, options: (fhalf, None, prec, None), + Pi: lambda x, prec, options: (mpf_pi(prec), None, prec, None), + Exp1: lambda x, prec, options: (mpf_e(prec), None, prec, None), + ImaginaryUnit: lambda x, prec, options: (None, fone, None, prec), + NegativeOne: lambda x, prec, options: (fnone, None, prec, None), + ComplexInfinity: lambda x, prec, options: S.ComplexInfinity, + NaN: lambda x, prec, options: (fnan, None, prec, None), + + exp: evalf_exp, + + cos: evalf_trig, + sin: evalf_trig, + + Add: evalf_add, + Mul: evalf_mul, + Pow: evalf_pow, + + log: evalf_log, + atan: evalf_atan, + Abs: evalf_abs, + + re: evalf_re, + im: evalf_im, + floor: evalf_floor, + ceiling: evalf_ceiling, + + Integral: evalf_integral, + Sum: evalf_sum, + Product: evalf_prod, + Piecewise: evalf_piecewise, + + AlgebraicNumber: evalf_alg_num, + } + + +def evalf(x: 'Expr', prec: int, options: OPT_DICT) -> TMP_RES: + """ + Evaluate the ``Expr`` instance, ``x`` + to a binary precision of ``prec``. This + function is supposed to be used internally. + + Parameters + ========== + + x : Expr + The formula to evaluate to a float. + prec : int + The binary precision that the output should have. + options : dict + A dictionary with the same entries as + ``EvalfMixin.evalf`` and in addition, + ``maxprec`` which is the maximum working precision. + + Returns + ======= + + An optional tuple, ``(re, im, re_acc, im_acc)`` + which are the real, imaginary, real accuracy + and imaginary accuracy respectively. ``re`` is + an mpf value tuple and so is ``im``. ``re_acc`` + and ``im_acc`` are ints. + + NB: all these return values can be ``None``. + If all values are ``None``, then that represents 0. + Note that 0 is also represented as ``fzero = (0, 0, 0, 0)``. + """ + from sympy.functions.elementary.complexes import re as re_, im as im_ + try: + rf = evalf_table[type(x)] + r = rf(x, prec, options) + except KeyError: + # Fall back to ordinary evalf if possible + if 'subs' in options: + x = x.subs(evalf_subs(prec, options['subs'])) + xe = x._eval_evalf(prec) + if xe is None: + raise NotImplementedError + as_real_imag = getattr(xe, "as_real_imag", None) + if as_real_imag is None: + raise NotImplementedError # e.g. FiniteSet(-1.0, 1.0).evalf() + re, im = as_real_imag() + if re.has(re_) or im.has(im_): + raise NotImplementedError + if re == 0.0: + re = None + reprec = None + elif re.is_number: + re = re._to_mpmath(prec, allow_ints=False)._mpf_ + reprec = prec + else: + raise NotImplementedError + if im == 0.0: + im = None + imprec = None + elif im.is_number: + im = im._to_mpmath(prec, allow_ints=False)._mpf_ + imprec = prec + else: + raise NotImplementedError + r = re, im, reprec, imprec + + if options.get("verbose"): + print("### input", x) + print("### output", to_str(r[0] or fzero, 50) if isinstance(r, tuple) else r) + print("### raw", r) # r[0], r[2] + print() + chop = options.get('chop', False) + if chop: + if chop is True: + chop_prec = prec + else: + # convert (approximately) from given tolerance; + # the formula here will will make 1e-i rounds to 0 for + # i in the range +/-27 while 2e-i will not be chopped + chop_prec = int(round(-3.321*math.log10(chop) + 2.5)) + if chop_prec == 3: + chop_prec -= 1 + r = chop_parts(r, chop_prec) + if options.get("strict"): + check_target(x, r, prec) + return r + + +def quad_to_mpmath(q, ctx=None): + """Turn the quad returned by ``evalf`` into an ``mpf`` or ``mpc``. """ + mpc = make_mpc if ctx is None else ctx.make_mpc + mpf = make_mpf if ctx is None else ctx.make_mpf + if q is S.ComplexInfinity: + raise NotImplementedError + re, im, _, _ = q + if im: + if not re: + re = fzero + return mpc((re, im)) + elif re: + return mpf(re) + else: + return mpf(fzero) + + +class EvalfMixin: + """Mixin class adding evalf capability.""" + + __slots__ = () # type: tTuple[str, ...] + + def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False): + """ + Evaluate the given formula to an accuracy of *n* digits. + + Parameters + ========== + + subs : dict, optional + Substitute numerical values for symbols, e.g. + ``subs={x:3, y:1+pi}``. The substitutions must be given as a + dictionary. + + maxn : int, optional + Allow a maximum temporary working precision of maxn digits. + + chop : bool or number, optional + Specifies how to replace tiny real or imaginary parts in + subresults by exact zeros. + + When ``True`` the chop value defaults to standard precision. + + Otherwise the chop value is used to determine the + magnitude of "small" for purposes of chopping. + + >>> from sympy import N + >>> x = 1e-4 + >>> N(x, chop=True) + 0.000100000000000000 + >>> N(x, chop=1e-5) + 0.000100000000000000 + >>> N(x, chop=1e-4) + 0 + + strict : bool, optional + Raise ``PrecisionExhausted`` if any subresult fails to + evaluate to full accuracy, given the available maxprec. + + quad : str, optional + Choose algorithm for numerical quadrature. By default, + tanh-sinh quadrature is used. For oscillatory + integrals on an infinite interval, try ``quad='osc'``. + + verbose : bool, optional + Print debug information. + + Notes + ===== + + When Floats are naively substituted into an expression, + precision errors may adversely affect the result. For example, + adding 1e16 (a Float) to 1 will truncate to 1e16; if 1e16 is + then subtracted, the result will be 0. + That is exactly what happens in the following: + + >>> from sympy.abc import x, y, z + >>> values = {x: 1e16, y: 1, z: 1e16} + >>> (x + y - z).subs(values) + 0 + + Using the subs argument for evalf is the accurate way to + evaluate such an expression: + + >>> (x + y - z).evalf(subs=values) + 1.00000000000000 + """ + from .numbers import Float, Number + n = n if n is not None else 15 + + if subs and is_sequence(subs): + raise TypeError('subs must be given as a dictionary') + + # for sake of sage that doesn't like evalf(1) + if n == 1 and isinstance(self, Number): + from .expr import _mag + rv = self.evalf(2, subs, maxn, chop, strict, quad, verbose) + m = _mag(rv) + rv = rv.round(1 - m) + return rv + + if not evalf_table: + _create_evalf_table() + prec = dps_to_prec(n) + options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop, + 'strict': strict, 'verbose': verbose} + if subs is not None: + options['subs'] = subs + if quad is not None: + options['quad'] = quad + try: + result = evalf(self, prec + 4, options) + except NotImplementedError: + # Fall back to the ordinary evalf + if hasattr(self, 'subs') and subs is not None: # issue 20291 + v = self.subs(subs)._eval_evalf(prec) + else: + v = self._eval_evalf(prec) + if v is None: + return self + elif not v.is_number: + return v + try: + # If the result is numerical, normalize it + result = evalf(v, prec, options) + except NotImplementedError: + # Probably contains symbols or unknown functions + return v + if result is S.ComplexInfinity: + return result + re, im, re_acc, im_acc = result + if re is S.NaN or im is S.NaN: + return S.NaN + if re: + p = max(min(prec, re_acc), 1) + re = Float._new(re, p) + else: + re = S.Zero + if im: + p = max(min(prec, im_acc), 1) + im = Float._new(im, p) + return re + im*S.ImaginaryUnit + else: + return re + + n = evalf + + def _evalf(self, prec): + """Helper for evalf. Does the same thing but takes binary precision""" + r = self._eval_evalf(prec) + if r is None: + r = self + return r + + def _eval_evalf(self, prec): + return + + def _to_mpmath(self, prec, allow_ints=True): + # mpmath functions accept ints as input + errmsg = "cannot convert to mpmath number" + if allow_ints and self.is_Integer: + return self.p + if hasattr(self, '_as_mpf_val'): + return make_mpf(self._as_mpf_val(prec)) + try: + result = evalf(self, prec, {}) + return quad_to_mpmath(result) + except NotImplementedError: + v = self._eval_evalf(prec) + if v is None: + raise ValueError(errmsg) + if v.is_Float: + return make_mpf(v._mpf_) + # Number + Number*I is also fine + re, im = v.as_real_imag() + if allow_ints and re.is_Integer: + re = from_int(re.p) + elif re.is_Float: + re = re._mpf_ + else: + raise ValueError(errmsg) + if allow_ints and im.is_Integer: + im = from_int(im.p) + elif im.is_Float: + im = im._mpf_ + else: + raise ValueError(errmsg) + return make_mpc((re, im)) + + +def N(x, n=15, **options): + r""" + Calls x.evalf(n, \*\*options). + + Explanations + ============ + + Both .n() and N() are equivalent to .evalf(); use the one that you like better. + See also the docstring of .evalf() for information on the options. + + Examples + ======== + + >>> from sympy import Sum, oo, N + >>> from sympy.abc import k + >>> Sum(1/k**k, (k, 1, oo)) + Sum(k**(-k), (k, 1, oo)) + >>> N(_, 4) + 1.291 + + """ + # by using rational=True, any evaluation of a string + # will be done using exact values for the Floats + return sympify(x, rational=True).evalf(n, **options) + + +def _evalf_with_bounded_error(x: 'Expr', eps: 'Optional[Expr]' = None, + m: int = 0, + options: Optional[OPT_DICT] = None) -> TMP_RES: + """ + Evaluate *x* to within a bounded absolute error. + + Parameters + ========== + + x : Expr + The quantity to be evaluated. + eps : Expr, None, optional (default=None) + Positive real upper bound on the acceptable error. + m : int, optional (default=0) + If *eps* is None, then use 2**(-m) as the upper bound on the error. + options: OPT_DICT + As in the ``evalf`` function. + + Returns + ======= + + A tuple ``(re, im, re_acc, im_acc)``, as returned by ``evalf``. + + See Also + ======== + + evalf + + """ + if eps is not None: + if not (eps.is_Rational or eps.is_Float) or not eps > 0: + raise ValueError("eps must be positive") + r, _, _, _ = evalf(1/eps, 1, {}) + m = fastlog(r) + + c, d, _, _ = evalf(x, 1, {}) + # Note: If x = a + b*I, then |a| <= 2|c| and |b| <= 2|d|, with equality + # only in the zero case. + # If a is non-zero, then |c| = 2**nc for some integer nc, and c has + # bitcount 1. Therefore 2**fastlog(c) = 2**(nc+1) = 2|c| is an upper bound + # on |a|. Likewise for b and d. + nr, ni = fastlog(c), fastlog(d) + n = max(nr, ni) + 1 + # If x is 0, then n is MINUS_INF, and p will be 1. Otherwise, + # n - 1 bits get us past the integer parts of a and b, and +1 accounts for + # the factor of <= sqrt(2) that is |x|/max(|a|, |b|). + p = max(1, m + n + 1) + + options = options or {} + return evalf(x, p, options) diff --git a/lib/python3.11/site-packages/sympy/core/expr.py b/lib/python3.11/site-packages/sympy/core/expr.py new file mode 100644 index 0000000000000000000000000000000000000000..c6be21344a60ef7521ee75a5b8e453aaf682f315 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/expr.py @@ -0,0 +1,4163 @@ +from __future__ import annotations + +from typing import TYPE_CHECKING +from collections.abc import Iterable +from functools import reduce +import re + +from .sympify import sympify, _sympify +from .basic import Basic, Atom +from .singleton import S +from .evalf import EvalfMixin, pure_complex, DEFAULT_MAXPREC +from .decorators import call_highest_priority, sympify_method_args, sympify_return +from .cache import cacheit +from .intfunc import mod_inverse +from .sorting import default_sort_key +from .kind import NumberKind +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.misc import as_int, func_name, filldedent +from sympy.utilities.iterables import has_variety, sift +from mpmath.libmp import mpf_log, prec_to_dps +from mpmath.libmp.libintmath import giant_steps + + +if TYPE_CHECKING: + from .numbers import Number + +from collections import defaultdict + + +def _corem(eq, c): # helper for extract_additively + # return co, diff from co*c + diff + co = [] + non = [] + for i in Add.make_args(eq): + ci = i.coeff(c) + if not ci: + non.append(i) + else: + co.append(ci) + return Add(*co), Add(*non) + + +@sympify_method_args +class Expr(Basic, EvalfMixin): + """ + Base class for algebraic expressions. + + Explanation + =========== + + Everything that requires arithmetic operations to be defined + should subclass this class, instead of Basic (which should be + used only for argument storage and expression manipulation, i.e. + pattern matching, substitutions, etc). + + If you want to override the comparisons of expressions: + Should use _eval_is_ge for inequality, or _eval_is_eq, with multiple dispatch. + _eval_is_ge return true if x >= y, false if x < y, and None if the two types + are not comparable or the comparison is indeterminate + + See Also + ======== + + sympy.core.basic.Basic + """ + + __slots__: tuple[str, ...] = () + + is_scalar = True # self derivative is 1 + + @property + def _diff_wrt(self): + """Return True if one can differentiate with respect to this + object, else False. + + Explanation + =========== + + Subclasses such as Symbol, Function and Derivative return True + to enable derivatives wrt them. The implementation in Derivative + separates the Symbol and non-Symbol (_diff_wrt=True) variables and + temporarily converts the non-Symbols into Symbols when performing + the differentiation. By default, any object deriving from Expr + will behave like a scalar with self.diff(self) == 1. If this is + not desired then the object must also set `is_scalar = False` or + else define an _eval_derivative routine. + + Note, see the docstring of Derivative for how this should work + mathematically. In particular, note that expr.subs(yourclass, Symbol) + should be well-defined on a structural level, or this will lead to + inconsistent results. + + Examples + ======== + + >>> from sympy import Expr + >>> e = Expr() + >>> e._diff_wrt + False + >>> class MyScalar(Expr): + ... _diff_wrt = True + ... + >>> MyScalar().diff(MyScalar()) + 1 + >>> class MySymbol(Expr): + ... _diff_wrt = True + ... is_scalar = False + ... + >>> MySymbol().diff(MySymbol()) + Derivative(MySymbol(), MySymbol()) + """ + return False + + @cacheit + def sort_key(self, order=None): + + coeff, expr = self.as_coeff_Mul() + + if expr.is_Pow: + if expr.base is S.Exp1: + # If we remove this, many doctests will go crazy: + # (keeps E**x sorted like the exp(x) function, + # part of exp(x) to E**x transition) + expr, exp = Function("exp")(expr.exp), S.One + else: + expr, exp = expr.args + else: + exp = S.One + + if expr.is_Dummy: + args = (expr.sort_key(),) + elif expr.is_Atom: + args = (str(expr),) + else: + if expr.is_Add: + args = expr.as_ordered_terms(order=order) + elif expr.is_Mul: + args = expr.as_ordered_factors(order=order) + else: + args = expr.args + + args = tuple( + [ default_sort_key(arg, order=order) for arg in args ]) + + args = (len(args), tuple(args)) + exp = exp.sort_key(order=order) + + return expr.class_key(), args, exp, coeff + + def _hashable_content(self): + """Return a tuple of information about self that can be used to + compute the hash. If a class defines additional attributes, + like ``name`` in Symbol, then this method should be updated + accordingly to return such relevant attributes. + Defining more than _hashable_content is necessary if __eq__ has + been defined by a class. See note about this in Basic.__eq__.""" + return self._args + + # *************** + # * Arithmetics * + # *************** + # Expr and its subclasses use _op_priority to determine which object + # passed to a binary special method (__mul__, etc.) will handle the + # operation. In general, the 'call_highest_priority' decorator will choose + # the object with the highest _op_priority to handle the call. + # Custom subclasses that want to define their own binary special methods + # should set an _op_priority value that is higher than the default. + # + # **NOTE**: + # This is a temporary fix, and will eventually be replaced with + # something better and more powerful. See issue 5510. + _op_priority = 10.0 + + @property + def _add_handler(self): + return Add + + @property + def _mul_handler(self): + return Mul + + def __pos__(self): + return self + + def __neg__(self): + # Mul has its own __neg__ routine, so we just + # create a 2-args Mul with the -1 in the canonical + # slot 0. + c = self.is_commutative + return Mul._from_args((S.NegativeOne, self), c) + + def __abs__(self) -> Expr: + from sympy.functions.elementary.complexes import Abs + return Abs(self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__radd__') + def __add__(self, other): + return Add(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__add__') + def __radd__(self, other): + return Add(other, self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rsub__') + def __sub__(self, other): + return Add(self, -other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__sub__') + def __rsub__(self, other): + return Add(other, -self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rmul__') + def __mul__(self, other): + return Mul(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__mul__') + def __rmul__(self, other): + return Mul(other, self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rpow__') + def _pow(self, other): + return Pow(self, other) + + def __pow__(self, other, mod=None) -> Expr: + if mod is None: + return self._pow(other) + try: + _self, other, mod = as_int(self), as_int(other), as_int(mod) + if other >= 0: + return _sympify(pow(_self, other, mod)) + else: + return _sympify(mod_inverse(pow(_self, -other, mod), mod)) + except ValueError: + power = self._pow(other) + try: + return power%mod + except TypeError: + return NotImplemented + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__pow__') + def __rpow__(self, other): + return Pow(other, self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rtruediv__') + def __truediv__(self, other): + denom = Pow(other, S.NegativeOne) + if self is S.One: + return denom + else: + return Mul(self, denom) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__truediv__') + def __rtruediv__(self, other): + denom = Pow(self, S.NegativeOne) + if other is S.One: + return denom + else: + return Mul(other, denom) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rmod__') + def __mod__(self, other): + return Mod(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__mod__') + def __rmod__(self, other): + return Mod(other, self) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rfloordiv__') + def __floordiv__(self, other): + from sympy.functions.elementary.integers import floor + return floor(self / other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__floordiv__') + def __rfloordiv__(self, other): + from sympy.functions.elementary.integers import floor + return floor(other / self) + + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__rdivmod__') + def __divmod__(self, other): + from sympy.functions.elementary.integers import floor + return floor(self / other), Mod(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + @call_highest_priority('__divmod__') + def __rdivmod__(self, other): + from sympy.functions.elementary.integers import floor + return floor(other / self), Mod(other, self) + + def __int__(self): + if not self.is_number: + raise TypeError("Cannot convert symbols to int") + r = self.round(2) + if not r.is_Number: + raise TypeError("Cannot convert complex to int") + if r in (S.NaN, S.Infinity, S.NegativeInfinity): + raise TypeError("Cannot convert %s to int" % r) + i = int(r) + if not i: + return i + if int_valued(r): + # non-integer self should pass one of these tests + if (self > i) is S.true: + return i + if (self < i) is S.true: + return i - 1 + ok = self.equals(i) + if ok is None: + raise TypeError('cannot compute int value accurately') + if ok: + return i + # off by one + return i - (1 if i > 0 else -1) + return i + + def __float__(self): + # Don't bother testing if it's a number; if it's not this is going + # to fail, and if it is we still need to check that it evalf'ed to + # a number. + result = self.evalf() + if result.is_Number: + return float(result) + if result.is_number and result.as_real_imag()[1]: + raise TypeError("Cannot convert complex to float") + raise TypeError("Cannot convert expression to float") + + def __complex__(self): + result = self.evalf() + re, im = result.as_real_imag() + return complex(float(re), float(im)) + + @sympify_return([('other', 'Expr')], NotImplemented) + def __ge__(self, other): + from .relational import GreaterThan + return GreaterThan(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + def __le__(self, other): + from .relational import LessThan + return LessThan(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + def __gt__(self, other): + from .relational import StrictGreaterThan + return StrictGreaterThan(self, other) + + @sympify_return([('other', 'Expr')], NotImplemented) + def __lt__(self, other): + from .relational import StrictLessThan + return StrictLessThan(self, other) + + def __trunc__(self): + if not self.is_number: + raise TypeError("Cannot truncate symbols and expressions") + else: + return Integer(self) + + def __format__(self, format_spec: str): + if self.is_number: + mt = re.match(r'\+?\d*\.(\d+)f', format_spec) + if mt: + prec = int(mt.group(1)) + rounded = self.round(prec) + if rounded.is_Integer: + return format(int(rounded), format_spec) + if rounded.is_Float: + return format(rounded, format_spec) + return super().__format__(format_spec) + + @staticmethod + def _from_mpmath(x, prec): + if hasattr(x, "_mpf_"): + return Float._new(x._mpf_, prec) + elif hasattr(x, "_mpc_"): + re, im = x._mpc_ + re = Float._new(re, prec) + im = Float._new(im, prec)*S.ImaginaryUnit + return re + im + else: + raise TypeError("expected mpmath number (mpf or mpc)") + + @property + def is_number(self): + """Returns True if ``self`` has no free symbols and no + undefined functions (AppliedUndef, to be precise). It will be + faster than ``if not self.free_symbols``, however, since + ``is_number`` will fail as soon as it hits a free symbol + or undefined function. + + Examples + ======== + + >>> from sympy import Function, Integral, cos, sin, pi + >>> from sympy.abc import x + >>> f = Function('f') + + >>> x.is_number + False + >>> f(1).is_number + False + >>> (2*x).is_number + False + >>> (2 + Integral(2, x)).is_number + False + >>> (2 + Integral(2, (x, 1, 2))).is_number + True + + Not all numbers are Numbers in the SymPy sense: + + >>> pi.is_number, pi.is_Number + (True, False) + + If something is a number it should evaluate to a number with + real and imaginary parts that are Numbers; the result may not + be comparable, however, since the real and/or imaginary part + of the result may not have precision. + + >>> cos(1).is_number and cos(1).is_comparable + True + + >>> z = cos(1)**2 + sin(1)**2 - 1 + >>> z.is_number + True + >>> z.is_comparable + False + + See Also + ======== + + sympy.core.basic.Basic.is_comparable + """ + return all(obj.is_number for obj in self.args) + + def _random(self, n=None, re_min=-1, im_min=-1, re_max=1, im_max=1): + """Return self evaluated, if possible, replacing free symbols with + random complex values, if necessary. + + Explanation + =========== + + The random complex value for each free symbol is generated + by the random_complex_number routine giving real and imaginary + parts in the range given by the re_min, re_max, im_min, and im_max + values. The returned value is evaluated to a precision of n + (if given) else the maximum of 15 and the precision needed + to get more than 1 digit of precision. If the expression + could not be evaluated to a number, or could not be evaluated + to more than 1 digit of precision, then None is returned. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.abc import x, y + >>> x._random() # doctest: +SKIP + 0.0392918155679172 + 0.916050214307199*I + >>> x._random(2) # doctest: +SKIP + -0.77 - 0.87*I + >>> (x + y/2)._random(2) # doctest: +SKIP + -0.57 + 0.16*I + >>> sqrt(2)._random(2) + 1.4 + + See Also + ======== + + sympy.core.random.random_complex_number + """ + + free = self.free_symbols + prec = 1 + if free: + from sympy.core.random import random_complex_number + a, c, b, d = re_min, re_max, im_min, im_max + reps = dict(list(zip(free, [random_complex_number(a, b, c, d, rational=True) + for zi in free]))) + try: + nmag = abs(self.evalf(2, subs=reps)) + except (ValueError, TypeError): + # if an out of range value resulted in evalf problems + # then return None -- XXX is there a way to know how to + # select a good random number for a given expression? + # e.g. when calculating n! negative values for n should not + # be used + return None + else: + reps = {} + nmag = abs(self.evalf(2)) + + if not hasattr(nmag, '_prec'): + # e.g. exp_polar(2*I*pi) doesn't evaluate but is_number is True + return None + + if nmag._prec == 1: + # increase the precision up to the default maximum + # precision to see if we can get any significance + + # evaluate + for prec in giant_steps(2, DEFAULT_MAXPREC): + nmag = abs(self.evalf(prec, subs=reps)) + if nmag._prec != 1: + break + + if nmag._prec != 1: + if n is None: + n = max(prec, 15) + return self.evalf(n, subs=reps) + + # never got any significance + return None + + def is_constant(self, *wrt, **flags): + """Return True if self is constant, False if not, or None if + the constancy could not be determined conclusively. + + Explanation + =========== + + If an expression has no free symbols then it is a constant. If + there are free symbols it is possible that the expression is a + constant, perhaps (but not necessarily) zero. To test such + expressions, a few strategies are tried: + + 1) numerical evaluation at two random points. If two such evaluations + give two different values and the values have a precision greater than + 1 then self is not constant. If the evaluations agree or could not be + obtained with any precision, no decision is made. The numerical testing + is done only if ``wrt`` is different than the free symbols. + + 2) differentiation with respect to variables in 'wrt' (or all free + symbols if omitted) to see if the expression is constant or not. This + will not always lead to an expression that is zero even though an + expression is constant (see added test in test_expr.py). If + all derivatives are zero then self is constant with respect to the + given symbols. + + 3) finding out zeros of denominator expression with free_symbols. + It will not be constant if there are zeros. It gives more negative + answers for expression that are not constant. + + If neither evaluation nor differentiation can prove the expression is + constant, None is returned unless two numerical values happened to be + the same and the flag ``failing_number`` is True -- in that case the + numerical value will be returned. + + If flag simplify=False is passed, self will not be simplified; + the default is True since self should be simplified before testing. + + Examples + ======== + + >>> from sympy import cos, sin, Sum, S, pi + >>> from sympy.abc import a, n, x, y + >>> x.is_constant() + False + >>> S(2).is_constant() + True + >>> Sum(x, (x, 1, 10)).is_constant() + True + >>> Sum(x, (x, 1, n)).is_constant() + False + >>> Sum(x, (x, 1, n)).is_constant(y) + True + >>> Sum(x, (x, 1, n)).is_constant(n) + False + >>> Sum(x, (x, 1, n)).is_constant(x) + True + >>> eq = a*cos(x)**2 + a*sin(x)**2 - a + >>> eq.is_constant() + True + >>> eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0 + True + + >>> (0**x).is_constant() + False + >>> x.is_constant() + False + >>> (x**x).is_constant() + False + >>> one = cos(x)**2 + sin(x)**2 + >>> one.is_constant() + True + >>> ((one - 1)**(x + 1)).is_constant() in (True, False) # could be 0 or 1 + True + """ + + def check_denominator_zeros(expression): + from sympy.solvers.solvers import denoms + + retNone = False + for den in denoms(expression): + z = den.is_zero + if z is True: + return True + if z is None: + retNone = True + if retNone: + return None + return False + + simplify = flags.get('simplify', True) + + if self.is_number: + return True + free = self.free_symbols + if not free: + return True # assume f(1) is some constant + + # if we are only interested in some symbols and they are not in the + # free symbols then this expression is constant wrt those symbols + wrt = set(wrt) + if wrt and not wrt & free: + return True + wrt = wrt or free + + # simplify unless this has already been done + expr = self + if simplify: + expr = expr.simplify() + + # is_zero should be a quick assumptions check; it can be wrong for + # numbers (see test_is_not_constant test), giving False when it + # shouldn't, but hopefully it will never give True unless it is sure. + if expr.is_zero: + return True + + # Don't attempt substitution or differentiation with non-number symbols + wrt_number = {sym for sym in wrt if sym.kind is NumberKind} + + # try numerical evaluation to see if we get two different values + failing_number = None + if wrt_number == free: + # try 0 (for a) and 1 (for b) + try: + a = expr.subs(list(zip(free, [0]*len(free))), + simultaneous=True) + if a is S.NaN: + # evaluation may succeed when substitution fails + a = expr._random(None, 0, 0, 0, 0) + except ZeroDivisionError: + a = None + if a is not None and a is not S.NaN: + try: + b = expr.subs(list(zip(free, [1]*len(free))), + simultaneous=True) + if b is S.NaN: + # evaluation may succeed when substitution fails + b = expr._random(None, 1, 0, 1, 0) + except ZeroDivisionError: + b = None + if b is not None and b is not S.NaN and b.equals(a) is False: + return False + # try random real + b = expr._random(None, -1, 0, 1, 0) + if b is not None and b is not S.NaN and b.equals(a) is False: + return False + # try random complex + b = expr._random() + if b is not None and b is not S.NaN: + if b.equals(a) is False: + return False + failing_number = a if a.is_number else b + + # now we will test each wrt symbol (or all free symbols) to see if the + # expression depends on them or not using differentiation. This is + # not sufficient for all expressions, however, so we don't return + # False if we get a derivative other than 0 with free symbols. + for w in wrt_number: + deriv = expr.diff(w) + if simplify: + deriv = deriv.simplify() + if deriv != 0: + if not (pure_complex(deriv, or_real=True)): + if flags.get('failing_number', False): + return failing_number + return False + cd = check_denominator_zeros(self) + if cd is True: + return False + elif cd is None: + return None + return True + + def equals(self, other, failing_expression=False): + """Return True if self == other, False if it does not, or None. If + failing_expression is True then the expression which did not simplify + to a 0 will be returned instead of None. + + Explanation + =========== + + If ``self`` is a Number (or complex number) that is not zero, then + the result is False. + + If ``self`` is a number and has not evaluated to zero, evalf will be + used to test whether the expression evaluates to zero. If it does so + and the result has significance (i.e. the precision is either -1, for + a Rational result, or is greater than 1) then the evalf value will be + used to return True or False. + + """ + from sympy.simplify.simplify import nsimplify, simplify + from sympy.solvers.solvers import solve + from sympy.polys.polyerrors import NotAlgebraic + from sympy.polys.numberfields import minimal_polynomial + + other = sympify(other) + if self == other: + return True + + # they aren't the same so see if we can make the difference 0; + # don't worry about doing simplification steps one at a time + # because if the expression ever goes to 0 then the subsequent + # simplification steps that are done will be very fast. + diff = factor_terms(simplify(self - other), radical=True) + + if not diff: + return True + + if not diff.has(Add, Mod): + # if there is no expanding to be done after simplifying + # then this can't be a zero + return False + + factors = diff.as_coeff_mul()[1] + if len(factors) > 1: # avoid infinity recursion + fac_zero = [fac.equals(0) for fac in factors] + if None not in fac_zero: # every part can be decided + return any(fac_zero) + + constant = diff.is_constant(simplify=False, failing_number=True) + + if constant is False: + return False + + if not diff.is_number: + if constant is None: + # e.g. unless the right simplification is done, a symbolic + # zero is possible (see expression of issue 6829: without + # simplification constant will be None). + return + + if constant is True: + # this gives a number whether there are free symbols or not + ndiff = diff._random() + # is_comparable will work whether the result is real + # or complex; it could be None, however. + if ndiff and ndiff.is_comparable: + return False + + # sometimes we can use a simplified result to give a clue as to + # what the expression should be; if the expression is *not* zero + # then we should have been able to compute that and so now + # we can just consider the cases where the approximation appears + # to be zero -- we try to prove it via minimal_polynomial. + # + # removed + # ns = nsimplify(diff) + # if diff.is_number and (not ns or ns == diff): + # + # The thought was that if it nsimplifies to 0 that's a sure sign + # to try the following to prove it; or if it changed but wasn't + # zero that might be a sign that it's not going to be easy to + # prove. But tests seem to be working without that logic. + # + if diff.is_number: + # try to prove via self-consistency + surds = [s for s in diff.atoms(Pow) if s.args[0].is_Integer] + # it seems to work better to try big ones first + surds.sort(key=lambda x: -x.args[0]) + for s in surds: + try: + # simplify is False here -- this expression has already + # been identified as being hard to identify as zero; + # we will handle the checking ourselves using nsimplify + # to see if we are in the right ballpark or not and if so + # *then* the simplification will be attempted. + sol = solve(diff, s, simplify=False) + if sol: + if s in sol: + # the self-consistent result is present + return True + if all(si.is_Integer for si in sol): + # perfect powers are removed at instantiation + # so surd s cannot be an integer + return False + if all(i.is_algebraic is False for i in sol): + # a surd is algebraic + return False + if any(si in surds for si in sol): + # it wasn't equal to s but it is in surds + # and different surds are not equal + return False + if any(nsimplify(s - si) == 0 and + simplify(s - si) == 0 for si in sol): + return True + if s.is_real: + if any(nsimplify(si, [s]) == s and simplify(si) == s + for si in sol): + return True + except NotImplementedError: + pass + + # try to prove with minimal_polynomial but know when + # *not* to use this or else it can take a long time. e.g. issue 8354 + if True: # change True to condition that assures non-hang + try: + mp = minimal_polynomial(diff) + if mp.is_Symbol: + return True + return False + except (NotAlgebraic, NotImplementedError): + pass + + # diff has not simplified to zero; constant is either None, True + # or the number with significance (is_comparable) that was randomly + # calculated twice as the same value. + if constant not in (True, None) and constant != 0: + return False + + if failing_expression: + return diff + return None + + def _eval_is_extended_positive_negative(self, positive): + from sympy.polys.numberfields import minimal_polynomial + from sympy.polys.polyerrors import NotAlgebraic + if self.is_number: + # check to see that we can get a value + try: + n2 = self._eval_evalf(2) + # XXX: This shouldn't be caught here + # Catches ValueError: hypsum() failed to converge to the requested + # 34 bits of accuracy + except ValueError: + return None + if n2 is None: + return None + if getattr(n2, '_prec', 1) == 1: # no significance + return None + if n2 is S.NaN: + return None + + f = self.evalf(2) + if f.is_Float: + match = f, S.Zero + else: + match = pure_complex(f) + if match is None: + return False + r, i = match + if not (i.is_Number and r.is_Number): + return False + if r._prec != 1 and i._prec != 1: + return bool(not i and ((r > 0) if positive else (r < 0))) + elif r._prec == 1 and (not i or i._prec == 1) and \ + self._eval_is_algebraic() and not self.has(Function): + try: + if minimal_polynomial(self).is_Symbol: + return False + except (NotAlgebraic, NotImplementedError): + pass + + def _eval_is_extended_positive(self): + return self._eval_is_extended_positive_negative(positive=True) + + def _eval_is_extended_negative(self): + return self._eval_is_extended_positive_negative(positive=False) + + def _eval_interval(self, x, a, b): + """ + Returns evaluation over an interval. For most functions this is: + + self.subs(x, b) - self.subs(x, a), + + possibly using limit() if NaN is returned from subs, or if + singularities are found between a and b. + + If b or a is None, it only evaluates -self.subs(x, a) or self.subs(b, x), + respectively. + + """ + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.functions.elementary.exponential import log + from sympy.series.limits import limit, Limit + from sympy.sets.sets import Interval + from sympy.solvers.solveset import solveset + + if (a is None and b is None): + raise ValueError('Both interval ends cannot be None.') + + def _eval_endpoint(left): + c = a if left else b + if c is None: + return S.Zero + else: + C = self.subs(x, c) + if C.has(S.NaN, S.Infinity, S.NegativeInfinity, + S.ComplexInfinity, AccumBounds): + if (a < b) != False: + C = limit(self, x, c, "+" if left else "-") + else: + C = limit(self, x, c, "-" if left else "+") + + if isinstance(C, Limit): + raise NotImplementedError("Could not compute limit") + return C + + if a == b: + return S.Zero + + A = _eval_endpoint(left=True) + if A is S.NaN: + return A + + B = _eval_endpoint(left=False) + + if (a and b) is None: + return B - A + + value = B - A + + if a.is_comparable and b.is_comparable: + if a < b: + domain = Interval(a, b) + else: + domain = Interval(b, a) + # check the singularities of self within the interval + # if singularities is a ConditionSet (not iterable), catch the exception and pass + singularities = solveset(self.cancel().as_numer_denom()[1], x, + domain=domain) + for logterm in self.atoms(log): + singularities = singularities | solveset(logterm.args[0], x, + domain=domain) + try: + for s in singularities: + if value is S.NaN: + # no need to keep adding, it will stay NaN + break + if not s.is_comparable: + continue + if (a < s) == (s < b) == True: + value += -limit(self, x, s, "+") + limit(self, x, s, "-") + elif (b < s) == (s < a) == True: + value += limit(self, x, s, "+") - limit(self, x, s, "-") + except TypeError: + pass + + return value + + def _eval_power(self, other): + # subclass to compute self**other for cases when + # other is not NaN, 0, or 1 + return None + + def _eval_conjugate(self): + if self.is_extended_real: + return self + elif self.is_imaginary: + return -self + + def conjugate(self): + """Returns the complex conjugate of 'self'.""" + from sympy.functions.elementary.complexes import conjugate as c + return c(self) + + def dir(self, x, cdir): + if self.is_zero: + return S.Zero + from sympy.functions.elementary.exponential import log + minexp = S.Zero + arg = self + while arg: + minexp += S.One + arg = arg.diff(x) + coeff = arg.subs(x, 0) + if coeff is S.NaN: + coeff = arg.limit(x, 0) + if coeff is S.ComplexInfinity: + try: + coeff, _ = arg.leadterm(x) + if coeff.has(log(x)): + raise ValueError() + except ValueError: + coeff = arg.limit(x, 0) + if coeff != S.Zero: + break + return coeff*cdir**minexp + + def _eval_transpose(self): + from sympy.functions.elementary.complexes import conjugate + if (self.is_complex or self.is_infinite): + return self + elif self.is_hermitian: + return conjugate(self) + elif self.is_antihermitian: + return -conjugate(self) + + def transpose(self): + from sympy.functions.elementary.complexes import transpose + return transpose(self) + + def _eval_adjoint(self): + from sympy.functions.elementary.complexes import conjugate, transpose + if self.is_hermitian: + return self + elif self.is_antihermitian: + return -self + obj = self._eval_conjugate() + if obj is not None: + return transpose(obj) + obj = self._eval_transpose() + if obj is not None: + return conjugate(obj) + + def adjoint(self): + from sympy.functions.elementary.complexes import adjoint + return adjoint(self) + + @classmethod + def _parse_order(cls, order): + """Parse and configure the ordering of terms. """ + from sympy.polys.orderings import monomial_key + + startswith = getattr(order, "startswith", None) + if startswith is None: + reverse = False + else: + reverse = startswith('rev-') + if reverse: + order = order[4:] + + monom_key = monomial_key(order) + + def neg(monom): + return tuple([neg(m) if isinstance(m, tuple) else -m for m in monom]) + + def key(term): + _, ((re, im), monom, ncpart) = term + + monom = neg(monom_key(monom)) + ncpart = tuple([e.sort_key(order=order) for e in ncpart]) + coeff = ((bool(im), im), (re, im)) + + return monom, ncpart, coeff + + return key, reverse + + def as_ordered_factors(self, order=None): + """Return list of ordered factors (if Mul) else [self].""" + return [self] + + def as_poly(self, *gens, **args): + """Converts ``self`` to a polynomial or returns ``None``. + + Explanation + =========== + + >>> from sympy import sin + >>> from sympy.abc import x, y + + >>> print((x**2 + x*y).as_poly()) + Poly(x**2 + x*y, x, y, domain='ZZ') + + >>> print((x**2 + x*y).as_poly(x, y)) + Poly(x**2 + x*y, x, y, domain='ZZ') + + >>> print((x**2 + sin(y)).as_poly(x, y)) + None + + """ + from sympy.polys.polyerrors import PolynomialError, GeneratorsNeeded + from sympy.polys.polytools import Poly + + try: + poly = Poly(self, *gens, **args) + + if not poly.is_Poly: + return None + else: + return poly + except (PolynomialError, GeneratorsNeeded): + # PolynomialError is caught for e.g. exp(x).as_poly(x) + # GeneratorsNeeded is caught for e.g. S(2).as_poly() + return None + + def as_ordered_terms(self, order=None, data=False): + """ + Transform an expression to an ordered list of terms. + + Examples + ======== + + >>> from sympy import sin, cos + >>> from sympy.abc import x + + >>> (sin(x)**2*cos(x) + sin(x)**2 + 1).as_ordered_terms() + [sin(x)**2*cos(x), sin(x)**2, 1] + + """ + + from .numbers import Number, NumberSymbol + + if order is None and self.is_Add: + # Spot the special case of Add(Number, Mul(Number, expr)) with the + # first number positive and the second number negative + key = lambda x:not isinstance(x, (Number, NumberSymbol)) + add_args = sorted(Add.make_args(self), key=key) + if (len(add_args) == 2 + and isinstance(add_args[0], (Number, NumberSymbol)) + and isinstance(add_args[1], Mul)): + mul_args = sorted(Mul.make_args(add_args[1]), key=key) + if (len(mul_args) == 2 + and isinstance(mul_args[0], Number) + and add_args[0].is_positive + and mul_args[0].is_negative): + return add_args + + key, reverse = self._parse_order(order) + terms, gens = self.as_terms() + + if not any(term.is_Order for term, _ in terms): + ordered = sorted(terms, key=key, reverse=reverse) + else: + _terms, _order = [], [] + + for term, repr in terms: + if not term.is_Order: + _terms.append((term, repr)) + else: + _order.append((term, repr)) + + ordered = sorted(_terms, key=key, reverse=True) \ + + sorted(_order, key=key, reverse=True) + + if data: + return ordered, gens + else: + return [term for term, _ in ordered] + + def as_terms(self): + """Transform an expression to a list of terms. """ + from .exprtools import decompose_power + + gens, terms = set(), [] + + for term in Add.make_args(self): + coeff, _term = term.as_coeff_Mul() + + coeff = complex(coeff) + cpart, ncpart = {}, [] + + if _term is not S.One: + for factor in Mul.make_args(_term): + if factor.is_number: + try: + coeff *= complex(factor) + except (TypeError, ValueError): + pass + else: + continue + + if factor.is_commutative: + base, exp = decompose_power(factor) + + cpart[base] = exp + gens.add(base) + else: + ncpart.append(factor) + + coeff = coeff.real, coeff.imag + ncpart = tuple(ncpart) + + terms.append((term, (coeff, cpart, ncpart))) + + gens = sorted(gens, key=default_sort_key) + + k, indices = len(gens), {} + + for i, g in enumerate(gens): + indices[g] = i + + result = [] + + for term, (coeff, cpart, ncpart) in terms: + monom = [0]*k + + for base, exp in cpart.items(): + monom[indices[base]] = exp + + result.append((term, (coeff, tuple(monom), ncpart))) + + return result, gens + + def removeO(self): + """Removes the additive O(..) symbol if there is one""" + return self + + def getO(self): + """Returns the additive O(..) symbol if there is one, else None.""" + return None + + def getn(self): + """ + Returns the order of the expression. + + Explanation + =========== + + The order is determined either from the O(...) term. If there + is no O(...) term, it returns None. + + Examples + ======== + + >>> from sympy import O + >>> from sympy.abc import x + >>> (1 + x + O(x**2)).getn() + 2 + >>> (1 + x).getn() + + """ + o = self.getO() + if o is None: + return None + elif o.is_Order: + o = o.expr + if o is S.One: + return S.Zero + if o.is_Symbol: + return S.One + if o.is_Pow: + return o.args[1] + if o.is_Mul: # x**n*log(x)**n or x**n/log(x)**n + for oi in o.args: + if oi.is_Symbol: + return S.One + if oi.is_Pow: + from .symbol import Dummy, Symbol + syms = oi.atoms(Symbol) + if len(syms) == 1: + x = syms.pop() + oi = oi.subs(x, Dummy('x', positive=True)) + if oi.base.is_Symbol and oi.exp.is_Rational: + return abs(oi.exp) + + raise NotImplementedError('not sure of order of %s' % o) + + def count_ops(self, visual=None): + from .function import count_ops + return count_ops(self, visual) + + def args_cnc(self, cset=False, warn=True, split_1=True): + """Return [commutative factors, non-commutative factors] of self. + + Explanation + =========== + + self is treated as a Mul and the ordering of the factors is maintained. + If ``cset`` is True the commutative factors will be returned in a set. + If there were repeated factors (as may happen with an unevaluated Mul) + then an error will be raised unless it is explicitly suppressed by + setting ``warn`` to False. + + Note: -1 is always separated from a Number unless split_1 is False. + + Examples + ======== + + >>> from sympy import symbols, oo + >>> A, B = symbols('A B', commutative=0) + >>> x, y = symbols('x y') + >>> (-2*x*y).args_cnc() + [[-1, 2, x, y], []] + >>> (-2.5*x).args_cnc() + [[-1, 2.5, x], []] + >>> (-2*x*A*B*y).args_cnc() + [[-1, 2, x, y], [A, B]] + >>> (-2*x*A*B*y).args_cnc(split_1=False) + [[-2, x, y], [A, B]] + >>> (-2*x*y).args_cnc(cset=True) + [{-1, 2, x, y}, []] + + The arg is always treated as a Mul: + + >>> (-2 + x + A).args_cnc() + [[], [x - 2 + A]] + >>> (-oo).args_cnc() # -oo is a singleton + [[-1, oo], []] + """ + + if self.is_Mul: + args = list(self.args) + else: + args = [self] + for i, mi in enumerate(args): + if not mi.is_commutative: + c = args[:i] + nc = args[i:] + break + else: + c = args + nc = [] + + if c and split_1 and ( + c[0].is_Number and + c[0].is_extended_negative and + c[0] is not S.NegativeOne): + c[:1] = [S.NegativeOne, -c[0]] + + if cset: + clen = len(c) + c = set(c) + if clen and warn and len(c) != clen: + raise ValueError('repeated commutative arguments: %s' % + [ci for ci in c if list(self.args).count(ci) > 1]) + return [c, nc] + + def coeff(self, x, n=1, right=False, _first=True): + """ + Returns the coefficient from the term(s) containing ``x**n``. If ``n`` + is zero then all terms independent of ``x`` will be returned. + + Explanation + =========== + + When ``x`` is noncommutative, the coefficient to the left (default) or + right of ``x`` can be returned. The keyword 'right' is ignored when + ``x`` is commutative. + + Examples + ======== + + >>> from sympy import symbols + >>> from sympy.abc import x, y, z + + You can select terms that have an explicit negative in front of them: + + >>> (-x + 2*y).coeff(-1) + x + >>> (x - 2*y).coeff(-1) + 2*y + + You can select terms with no Rational coefficient: + + >>> (x + 2*y).coeff(1) + x + >>> (3 + 2*x + 4*x**2).coeff(1) + 0 + + You can select terms independent of x by making n=0; in this case + expr.as_independent(x)[0] is returned (and 0 will be returned instead + of None): + + >>> (3 + 2*x + 4*x**2).coeff(x, 0) + 3 + >>> eq = ((x + 1)**3).expand() + 1 + >>> eq + x**3 + 3*x**2 + 3*x + 2 + >>> [eq.coeff(x, i) for i in reversed(range(4))] + [1, 3, 3, 2] + >>> eq -= 2 + >>> [eq.coeff(x, i) for i in reversed(range(4))] + [1, 3, 3, 0] + + You can select terms that have a numerical term in front of them: + + >>> (-x - 2*y).coeff(2) + -y + >>> from sympy import sqrt + >>> (x + sqrt(2)*x).coeff(sqrt(2)) + x + + The matching is exact: + + >>> (3 + 2*x + 4*x**2).coeff(x) + 2 + >>> (3 + 2*x + 4*x**2).coeff(x**2) + 4 + >>> (3 + 2*x + 4*x**2).coeff(x**3) + 0 + >>> (z*(x + y)**2).coeff((x + y)**2) + z + >>> (z*(x + y)**2).coeff(x + y) + 0 + + In addition, no factoring is done, so 1 + z*(1 + y) is not obtained + from the following: + + >>> (x + z*(x + x*y)).coeff(x) + 1 + + If such factoring is desired, factor_terms can be used first: + + >>> from sympy import factor_terms + >>> factor_terms(x + z*(x + x*y)).coeff(x) + z*(y + 1) + 1 + + >>> n, m, o = symbols('n m o', commutative=False) + >>> n.coeff(n) + 1 + >>> (3*n).coeff(n) + 3 + >>> (n*m + m*n*m).coeff(n) # = (1 + m)*n*m + 1 + m + >>> (n*m + m*n*m).coeff(n, right=True) # = (1 + m)*n*m + m + + If there is more than one possible coefficient 0 is returned: + + >>> (n*m + m*n).coeff(n) + 0 + + If there is only one possible coefficient, it is returned: + + >>> (n*m + x*m*n).coeff(m*n) + x + >>> (n*m + x*m*n).coeff(m*n, right=1) + 1 + + See Also + ======== + + as_coefficient: separate the expression into a coefficient and factor + as_coeff_Add: separate the additive constant from an expression + as_coeff_Mul: separate the multiplicative constant from an expression + as_independent: separate x-dependent terms/factors from others + sympy.polys.polytools.Poly.coeff_monomial: efficiently find the single coefficient of a monomial in Poly + sympy.polys.polytools.Poly.nth: like coeff_monomial but powers of monomial terms are used + """ + x = sympify(x) + if not isinstance(x, Basic): + return S.Zero + + n = as_int(n) + + if not x: + return S.Zero + + if x == self: + if n == 1: + return S.One + return S.Zero + + if x is S.One: + co = [a for a in Add.make_args(self) + if a.as_coeff_Mul()[0] is S.One] + if not co: + return S.Zero + return Add(*co) + + if n == 0: + if x.is_Add and self.is_Add: + c = self.coeff(x, right=right) + if not c: + return S.Zero + if not right: + return self - Add(*[a*x for a in Add.make_args(c)]) + return self - Add(*[x*a for a in Add.make_args(c)]) + return self.as_independent(x, as_Add=True)[0] + + # continue with the full method, looking for this power of x: + x = x**n + + def incommon(l1, l2): + if not l1 or not l2: + return [] + n = min(len(l1), len(l2)) + for i in range(n): + if l1[i] != l2[i]: + return l1[:i] + return l1[:] + + def find(l, sub, first=True): + """ Find where list sub appears in list l. When ``first`` is True + the first occurrence from the left is returned, else the last + occurrence is returned. Return None if sub is not in l. + + Examples + ======== + + >> l = range(5)*2 + >> find(l, [2, 3]) + 2 + >> find(l, [2, 3], first=0) + 7 + >> find(l, [2, 4]) + None + + """ + if not sub or not l or len(sub) > len(l): + return None + n = len(sub) + if not first: + l.reverse() + sub.reverse() + for i in range(len(l) - n + 1): + if all(l[i + j] == sub[j] for j in range(n)): + break + else: + i = None + if not first: + l.reverse() + sub.reverse() + if i is not None and not first: + i = len(l) - (i + n) + return i + + co = [] + args = Add.make_args(self) + self_c = self.is_commutative + x_c = x.is_commutative + if self_c and not x_c: + return S.Zero + if _first and self.is_Add and not self_c and not x_c: + # get the part that depends on x exactly + xargs = Mul.make_args(x) + d = Add(*[i for i in Add.make_args(self.as_independent(x)[1]) + if all(xi in Mul.make_args(i) for xi in xargs)]) + rv = d.coeff(x, right=right, _first=False) + if not rv.is_Add or not right: + return rv + c_part, nc_part = zip(*[i.args_cnc() for i in rv.args]) + if has_variety(c_part): + return rv + return Add(*[Mul._from_args(i) for i in nc_part]) + + one_c = self_c or x_c + xargs, nx = x.args_cnc(cset=True, warn=bool(not x_c)) + # find the parts that pass the commutative terms + for a in args: + margs, nc = a.args_cnc(cset=True, warn=bool(not self_c)) + if nc is None: + nc = [] + if len(xargs) > len(margs): + continue + resid = margs.difference(xargs) + if len(resid) + len(xargs) == len(margs): + if one_c: + co.append(Mul(*(list(resid) + nc))) + else: + co.append((resid, nc)) + if one_c: + if co == []: + return S.Zero + elif co: + return Add(*co) + else: # both nc + # now check the non-comm parts + if not co: + return S.Zero + if all(n == co[0][1] for r, n in co): + ii = find(co[0][1], nx, right) + if ii is not None: + if not right: + return Mul(Add(*[Mul(*r) for r, c in co]), Mul(*co[0][1][:ii])) + else: + return Mul(*co[0][1][ii + len(nx):]) + beg = reduce(incommon, (n[1] for n in co)) + if beg: + ii = find(beg, nx, right) + if ii is not None: + if not right: + gcdc = co[0][0] + for i in range(1, len(co)): + gcdc = gcdc.intersection(co[i][0]) + if not gcdc: + break + return Mul(*(list(gcdc) + beg[:ii])) + else: + m = ii + len(nx) + return Add(*[Mul(*(list(r) + n[m:])) for r, n in co]) + end = list(reversed( + reduce(incommon, (list(reversed(n[1])) for n in co)))) + if end: + ii = find(end, nx, right) + if ii is not None: + if not right: + return Add(*[Mul(*(list(r) + n[:-len(end) + ii])) for r, n in co]) + else: + return Mul(*end[ii + len(nx):]) + # look for single match + hit = None + for i, (r, n) in enumerate(co): + ii = find(n, nx, right) + if ii is not None: + if not hit: + hit = ii, r, n + else: + break + else: + if hit: + ii, r, n = hit + if not right: + return Mul(*(list(r) + n[:ii])) + else: + return Mul(*n[ii + len(nx):]) + + return S.Zero + + def as_expr(self, *gens): + """ + Convert a polynomial to a SymPy expression. + + Examples + ======== + + >>> from sympy import sin + >>> from sympy.abc import x, y + + >>> f = (x**2 + x*y).as_poly(x, y) + >>> f.as_expr() + x**2 + x*y + + >>> sin(x).as_expr() + sin(x) + + """ + return self + + def as_coefficient(self, expr): + """ + Extracts symbolic coefficient at the given expression. In + other words, this functions separates 'self' into the product + of 'expr' and 'expr'-free coefficient. If such separation + is not possible it will return None. + + Examples + ======== + + >>> from sympy import E, pi, sin, I, Poly + >>> from sympy.abc import x + + >>> E.as_coefficient(E) + 1 + >>> (2*E).as_coefficient(E) + 2 + >>> (2*sin(E)*E).as_coefficient(E) + + Two terms have E in them so a sum is returned. (If one were + desiring the coefficient of the term exactly matching E then + the constant from the returned expression could be selected. + Or, for greater precision, a method of Poly can be used to + indicate the desired term from which the coefficient is + desired.) + + >>> (2*E + x*E).as_coefficient(E) + x + 2 + >>> _.args[0] # just want the exact match + 2 + >>> p = Poly(2*E + x*E); p + Poly(x*E + 2*E, x, E, domain='ZZ') + >>> p.coeff_monomial(E) + 2 + >>> p.nth(0, 1) + 2 + + Since the following cannot be written as a product containing + E as a factor, None is returned. (If the coefficient ``2*x`` is + desired then the ``coeff`` method should be used.) + + >>> (2*E*x + x).as_coefficient(E) + >>> (2*E*x + x).coeff(E) + 2*x + + >>> (E*(x + 1) + x).as_coefficient(E) + + >>> (2*pi*I).as_coefficient(pi*I) + 2 + >>> (2*I).as_coefficient(pi*I) + + See Also + ======== + + coeff: return sum of terms have a given factor + as_coeff_Add: separate the additive constant from an expression + as_coeff_Mul: separate the multiplicative constant from an expression + as_independent: separate x-dependent terms/factors from others + sympy.polys.polytools.Poly.coeff_monomial: efficiently find the single coefficient of a monomial in Poly + sympy.polys.polytools.Poly.nth: like coeff_monomial but powers of monomial terms are used + + + """ + + r = self.extract_multiplicatively(expr) + if r and not r.has(expr): + return r + + def as_independent(self, *deps, **hint) -> tuple[Expr, Expr]: + """ + A mostly naive separation of a Mul or Add into arguments that are not + are dependent on deps. To obtain as complete a separation of variables + as possible, use a separation method first, e.g.: + + * separatevars() to change Mul, Add and Pow (including exp) into Mul + * .expand(mul=True) to change Add or Mul into Add + * .expand(log=True) to change log expr into an Add + + The only non-naive thing that is done here is to respect noncommutative + ordering of variables and to always return (0, 0) for `self` of zero + regardless of hints. + + For nonzero `self`, the returned tuple (i, d) has the + following interpretation: + + * i will has no variable that appears in deps + * d will either have terms that contain variables that are in deps, or + be equal to 0 (when self is an Add) or 1 (when self is a Mul) + * if self is an Add then self = i + d + * if self is a Mul then self = i*d + * otherwise (self, S.One) or (S.One, self) is returned. + + To force the expression to be treated as an Add, use the hint as_Add=True + + Examples + ======== + + -- self is an Add + + >>> from sympy import sin, cos, exp + >>> from sympy.abc import x, y, z + + >>> (x + x*y).as_independent(x) + (0, x*y + x) + >>> (x + x*y).as_independent(y) + (x, x*y) + >>> (2*x*sin(x) + y + x + z).as_independent(x) + (y + z, 2*x*sin(x) + x) + >>> (2*x*sin(x) + y + x + z).as_independent(x, y) + (z, 2*x*sin(x) + x + y) + + -- self is a Mul + + >>> (x*sin(x)*cos(y)).as_independent(x) + (cos(y), x*sin(x)) + + non-commutative terms cannot always be separated out when self is a Mul + + >>> from sympy import symbols + >>> n1, n2, n3 = symbols('n1 n2 n3', commutative=False) + >>> (n1 + n1*n2).as_independent(n2) + (n1, n1*n2) + >>> (n2*n1 + n1*n2).as_independent(n2) + (0, n1*n2 + n2*n1) + >>> (n1*n2*n3).as_independent(n1) + (1, n1*n2*n3) + >>> (n1*n2*n3).as_independent(n2) + (n1, n2*n3) + >>> ((x-n1)*(x-y)).as_independent(x) + (1, (x - y)*(x - n1)) + + -- self is anything else: + + >>> (sin(x)).as_independent(x) + (1, sin(x)) + >>> (sin(x)).as_independent(y) + (sin(x), 1) + >>> exp(x+y).as_independent(x) + (1, exp(x + y)) + + -- force self to be treated as an Add: + + >>> (3*x).as_independent(x, as_Add=True) + (0, 3*x) + + -- force self to be treated as a Mul: + + >>> (3+x).as_independent(x, as_Add=False) + (1, x + 3) + >>> (-3+x).as_independent(x, as_Add=False) + (1, x - 3) + + Note how the below differs from the above in making the + constant on the dep term positive. + + >>> (y*(-3+x)).as_independent(x) + (y, x - 3) + + -- use .as_independent() for true independence testing instead + of .has(). The former considers only symbols in the free + symbols while the latter considers all symbols + + >>> from sympy import Integral + >>> I = Integral(x, (x, 1, 2)) + >>> I.has(x) + True + >>> x in I.free_symbols + False + >>> I.as_independent(x) == (I, 1) + True + >>> (I + x).as_independent(x) == (I, x) + True + + Note: when trying to get independent terms, a separation method + might need to be used first. In this case, it is important to keep + track of what you send to this routine so you know how to interpret + the returned values + + >>> from sympy import separatevars, log + >>> separatevars(exp(x+y)).as_independent(x) + (exp(y), exp(x)) + >>> (x + x*y).as_independent(y) + (x, x*y) + >>> separatevars(x + x*y).as_independent(y) + (x, y + 1) + >>> (x*(1 + y)).as_independent(y) + (x, y + 1) + >>> (x*(1 + y)).expand(mul=True).as_independent(y) + (x, x*y) + >>> a, b=symbols('a b', positive=True) + >>> (log(a*b).expand(log=True)).as_independent(b) + (log(a), log(b)) + + See Also + ======== + + separatevars + expand_log + sympy.core.add.Add.as_two_terms + sympy.core.mul.Mul.as_two_terms + as_coeff_mul + """ + from .symbol import Symbol + from .add import _unevaluated_Add + from .mul import _unevaluated_Mul + + if self is S.Zero: + return (self, self) + + func = self.func + if hint.get('as_Add', isinstance(self, Add) ): + want = Add + else: + want = Mul + + # sift out deps into symbolic and other and ignore + # all symbols but those that are in the free symbols + sym = set() + other = [] + for d in deps: + if isinstance(d, Symbol): # Symbol.is_Symbol is True + sym.add(d) + else: + other.append(d) + + def has(e): + """return the standard has() if there are no literal symbols, else + check to see that symbol-deps are in the free symbols.""" + has_other = e.has(*other) + if not sym: + return has_other + return has_other or e.has(*(e.free_symbols & sym)) + + if (want is not func or + func is not Add and func is not Mul): + if has(self): + return (want.identity, self) + else: + return (self, want.identity) + else: + if func is Add: + args = list(self.args) + else: + args, nc = self.args_cnc() + + d = sift(args, has) + depend = d[True] + indep = d[False] + if func is Add: # all terms were treated as commutative + return (Add(*indep), _unevaluated_Add(*depend)) + else: # handle noncommutative by stopping at first dependent term + for i, n in enumerate(nc): + if has(n): + depend.extend(nc[i:]) + break + indep.append(n) + return Mul(*indep), ( + Mul(*depend, evaluate=False) if nc else + _unevaluated_Mul(*depend)) + + def as_real_imag(self, deep=True, **hints): + """Performs complex expansion on 'self' and returns a tuple + containing collected both real and imaginary parts. This + method cannot be confused with re() and im() functions, + which does not perform complex expansion at evaluation. + + However it is possible to expand both re() and im() + functions and get exactly the same results as with + a single call to this function. + + >>> from sympy import symbols, I + + >>> x, y = symbols('x,y', real=True) + + >>> (x + y*I).as_real_imag() + (x, y) + + >>> from sympy.abc import z, w + + >>> (z + w*I).as_real_imag() + (re(z) - im(w), re(w) + im(z)) + + """ + if hints.get('ignore') == self: + return None + else: + from sympy.functions.elementary.complexes import im, re + return (re(self), im(self)) + + def as_powers_dict(self): + """Return self as a dictionary of factors with each factor being + treated as a power. The keys are the bases of the factors and the + values, the corresponding exponents. The resulting dictionary should + be used with caution if the expression is a Mul and contains non- + commutative factors since the order that they appeared will be lost in + the dictionary. + + See Also + ======== + as_ordered_factors: An alternative for noncommutative applications, + returning an ordered list of factors. + args_cnc: Similar to as_ordered_factors, but guarantees separation + of commutative and noncommutative factors. + """ + d = defaultdict(int) + d.update([self.as_base_exp()]) + return d + + def as_coefficients_dict(self, *syms): + """Return a dictionary mapping terms to their Rational coefficient. + Since the dictionary is a defaultdict, inquiries about terms which + were not present will return a coefficient of 0. + + If symbols ``syms`` are provided, any multiplicative terms + independent of them will be considered a coefficient and a + regular dictionary of syms-dependent generators as keys and + their corresponding coefficients as values will be returned. + + Examples + ======== + + >>> from sympy.abc import a, x, y + >>> (3*x + a*x + 4).as_coefficients_dict() + {1: 4, x: 3, a*x: 1} + >>> _[a] + 0 + >>> (3*a*x).as_coefficients_dict() + {a*x: 3} + >>> (3*a*x).as_coefficients_dict(x) + {x: 3*a} + >>> (3*a*x).as_coefficients_dict(y) + {1: 3*a*x} + + """ + d = defaultdict(list) + if not syms: + for ai in Add.make_args(self): + c, m = ai.as_coeff_Mul() + d[m].append(c) + for k, v in d.items(): + if len(v) == 1: + d[k] = v[0] + else: + d[k] = Add(*v) + else: + ind, dep = self.as_independent(*syms, as_Add=True) + for i in Add.make_args(dep): + if i.is_Mul: + c, x = i.as_coeff_mul(*syms) + if c is S.One: + d[i].append(c) + else: + d[i._new_rawargs(*x)].append(c) + elif i: + d[i].append(S.One) + d = {k: Add(*d[k]) for k in d} + if ind is not S.Zero: + d.update({S.One: ind}) + di = defaultdict(int) + di.update(d) + return di + + def as_base_exp(self) -> tuple[Expr, Expr]: + # a -> b ** e + return self, S.One + + def as_coeff_mul(self, *deps, **kwargs) -> tuple[Expr, tuple[Expr, ...]]: + """Return the tuple (c, args) where self is written as a Mul, ``m``. + + c should be a Rational multiplied by any factors of the Mul that are + independent of deps. + + args should be a tuple of all other factors of m; args is empty + if self is a Number or if self is independent of deps (when given). + + This should be used when you do not know if self is a Mul or not but + you want to treat self as a Mul or if you want to process the + individual arguments of the tail of self as a Mul. + + - if you know self is a Mul and want only the head, use self.args[0]; + - if you do not want to process the arguments of the tail but need the + tail then use self.as_two_terms() which gives the head and tail; + - if you want to split self into an independent and dependent parts + use ``self.as_independent(*deps)`` + + >>> from sympy import S + >>> from sympy.abc import x, y + >>> (S(3)).as_coeff_mul() + (3, ()) + >>> (3*x*y).as_coeff_mul() + (3, (x, y)) + >>> (3*x*y).as_coeff_mul(x) + (3*y, (x,)) + >>> (3*y).as_coeff_mul(x) + (3*y, ()) + """ + if deps: + if not self.has(*deps): + return self, () + return S.One, (self,) + + def as_coeff_add(self, *deps) -> tuple[Expr, tuple[Expr, ...]]: + """Return the tuple (c, args) where self is written as an Add, ``a``. + + c should be a Rational added to any terms of the Add that are + independent of deps. + + args should be a tuple of all other terms of ``a``; args is empty + if self is a Number or if self is independent of deps (when given). + + This should be used when you do not know if self is an Add or not but + you want to treat self as an Add or if you want to process the + individual arguments of the tail of self as an Add. + + - if you know self is an Add and want only the head, use self.args[0]; + - if you do not want to process the arguments of the tail but need the + tail then use self.as_two_terms() which gives the head and tail. + - if you want to split self into an independent and dependent parts + use ``self.as_independent(*deps)`` + + >>> from sympy import S + >>> from sympy.abc import x, y + >>> (S(3)).as_coeff_add() + (3, ()) + >>> (3 + x).as_coeff_add() + (3, (x,)) + >>> (3 + x + y).as_coeff_add(x) + (y + 3, (x,)) + >>> (3 + y).as_coeff_add(x) + (y + 3, ()) + + """ + if deps: + if not self.has_free(*deps): + return self, () + return S.Zero, (self,) + + def primitive(self): + """Return the positive Rational that can be extracted non-recursively + from every term of self (i.e., self is treated like an Add). This is + like the as_coeff_Mul() method but primitive always extracts a positive + Rational (never a negative or a Float). + + Examples + ======== + + >>> from sympy.abc import x + >>> (3*(x + 1)**2).primitive() + (3, (x + 1)**2) + >>> a = (6*x + 2); a.primitive() + (2, 3*x + 1) + >>> b = (x/2 + 3); b.primitive() + (1/2, x + 6) + >>> (a*b).primitive() == (1, a*b) + True + """ + if not self: + return S.One, S.Zero + c, r = self.as_coeff_Mul(rational=True) + if c.is_negative: + c, r = -c, -r + return c, r + + def as_content_primitive(self, radical=False, clear=True): + """This method should recursively remove a Rational from all arguments + and return that (content) and the new self (primitive). The content + should always be positive and ``Mul(*foo.as_content_primitive()) == foo``. + The primitive need not be in canonical form and should try to preserve + the underlying structure if possible (i.e. expand_mul should not be + applied to self). + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.abc import x, y, z + + >>> eq = 2 + 2*x + 2*y*(3 + 3*y) + + The as_content_primitive function is recursive and retains structure: + + >>> eq.as_content_primitive() + (2, x + 3*y*(y + 1) + 1) + + Integer powers will have Rationals extracted from the base: + + >>> ((2 + 6*x)**2).as_content_primitive() + (4, (3*x + 1)**2) + >>> ((2 + 6*x)**(2*y)).as_content_primitive() + (1, (2*(3*x + 1))**(2*y)) + + Terms may end up joining once their as_content_primitives are added: + + >>> ((5*(x*(1 + y)) + 2*x*(3 + 3*y))).as_content_primitive() + (11, x*(y + 1)) + >>> ((3*(x*(1 + y)) + 2*x*(3 + 3*y))).as_content_primitive() + (9, x*(y + 1)) + >>> ((3*(z*(1 + y)) + 2.0*x*(3 + 3*y))).as_content_primitive() + (1, 6.0*x*(y + 1) + 3*z*(y + 1)) + >>> ((5*(x*(1 + y)) + 2*x*(3 + 3*y))**2).as_content_primitive() + (121, x**2*(y + 1)**2) + >>> ((x*(1 + y) + 0.4*x*(3 + 3*y))**2).as_content_primitive() + (1, 4.84*x**2*(y + 1)**2) + + Radical content can also be factored out of the primitive: + + >>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive(radical=True) + (2, sqrt(2)*(1 + 2*sqrt(5))) + + If clear=False (default is True) then content will not be removed + from an Add if it can be distributed to leave one or more + terms with integer coefficients. + + >>> (x/2 + y).as_content_primitive() + (1/2, x + 2*y) + >>> (x/2 + y).as_content_primitive(clear=False) + (1, x/2 + y) + """ + return S.One, self + + def as_numer_denom(self): + """Return the numerator and the denominator of an expression. + + expression -> a/b -> a, b + + This is just a stub that should be defined by + an object's class methods to get anything else. + + See Also + ======== + + normal: return ``a/b`` instead of ``(a, b)`` + + """ + return self, S.One + + def normal(self): + """Return the expression as a fraction. + + expression -> a/b + + See Also + ======== + + as_numer_denom: return ``(a, b)`` instead of ``a/b`` + + """ + from .mul import _unevaluated_Mul + n, d = self.as_numer_denom() + if d is S.One: + return n + if d.is_Number: + return _unevaluated_Mul(n, 1/d) + else: + return n/d + + def extract_multiplicatively(self, c): + """Return None if it's not possible to make self in the form + c * something in a nice way, i.e. preserving the properties + of arguments of self. + + Examples + ======== + + >>> from sympy import symbols, Rational + + >>> x, y = symbols('x,y', real=True) + + >>> ((x*y)**3).extract_multiplicatively(x**2 * y) + x*y**2 + + >>> ((x*y)**3).extract_multiplicatively(x**4 * y) + + >>> (2*x).extract_multiplicatively(2) + x + + >>> (2*x).extract_multiplicatively(3) + + >>> (Rational(1, 2)*x).extract_multiplicatively(3) + x/6 + + """ + from sympy.functions.elementary.exponential import exp + from .add import _unevaluated_Add + c = sympify(c) + if self is S.NaN: + return None + if c is S.One: + return self + elif c == self: + return S.One + + if c.is_Add: + cc, pc = c.primitive() + if cc is not S.One: + c = Mul(cc, pc, evaluate=False) + + if c.is_Mul: + a, b = c.as_two_terms() + x = self.extract_multiplicatively(a) + if x is not None: + return x.extract_multiplicatively(b) + else: + return x + + quotient = self / c + if self.is_Number: + if self is S.Infinity: + if c.is_positive: + return S.Infinity + elif self is S.NegativeInfinity: + if c.is_negative: + return S.Infinity + elif c.is_positive: + return S.NegativeInfinity + elif self is S.ComplexInfinity: + if not c.is_zero: + return S.ComplexInfinity + elif self.is_Integer: + if not quotient.is_Integer: + return None + elif self.is_positive and quotient.is_negative: + return None + else: + return quotient + elif self.is_Rational: + if not quotient.is_Rational: + return None + elif self.is_positive and quotient.is_negative: + return None + else: + return quotient + elif self.is_Float: + if not quotient.is_Float: + return None + elif self.is_positive and quotient.is_negative: + return None + else: + return quotient + elif self.is_NumberSymbol or self.is_Symbol or self is S.ImaginaryUnit: + if quotient.is_Mul and len(quotient.args) == 2: + if quotient.args[0].is_Integer and quotient.args[0].is_positive and quotient.args[1] == self: + return quotient + elif quotient.is_Integer and c.is_Number: + return quotient + elif self.is_Add: + cs, ps = self.primitive() + # assert cs >= 1 + if c.is_Number and c is not S.NegativeOne: + # assert c != 1 (handled at top) + if cs is not S.One: + if c.is_negative: + xc = -(cs.extract_multiplicatively(-c)) + else: + xc = cs.extract_multiplicatively(c) + if xc is not None: + return xc*ps # rely on 2-arg Mul to restore Add + return # |c| != 1 can only be extracted from cs + if c == ps: + return cs + # check args of ps + newargs = [] + for arg in ps.args: + newarg = arg.extract_multiplicatively(c) + if newarg is None: + return # all or nothing + newargs.append(newarg) + if cs is not S.One: + args = [cs*t for t in newargs] + # args may be in different order + return _unevaluated_Add(*args) + else: + return Add._from_args(newargs) + elif self.is_Mul: + args = list(self.args) + for i, arg in enumerate(args): + newarg = arg.extract_multiplicatively(c) + if newarg is not None: + args[i] = newarg + return Mul(*args) + elif self.is_Pow or isinstance(self, exp): + sb, se = self.as_base_exp() + cb, ce = c.as_base_exp() + if cb == sb: + new_exp = se.extract_additively(ce) + if new_exp is not None: + return Pow(sb, new_exp) + elif c == sb: + new_exp = self.exp.extract_additively(1) + if new_exp is not None: + return Pow(sb, new_exp) + + def extract_additively(self, c): + """Return self - c if it's possible to subtract c from self and + make all matching coefficients move towards zero, else return None. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> e = 2*x + 3 + >>> e.extract_additively(x + 1) + x + 2 + >>> e.extract_additively(3*x) + >>> e.extract_additively(4) + >>> (y*(x + 1)).extract_additively(x + 1) + >>> ((x + 1)*(x + 2*y + 1) + 3).extract_additively(x + 1) + (x + 1)*(x + 2*y) + 3 + + See Also + ======== + extract_multiplicatively + coeff + as_coefficient + + """ + + c = sympify(c) + if self is S.NaN: + return None + if c.is_zero: + return self + elif c == self: + return S.Zero + elif self == S.Zero: + return None + + if self.is_Number: + if not c.is_Number: + return None + co = self + diff = co - c + # XXX should we match types? i.e should 3 - .1 succeed? + if (co > 0 and diff >= 0 and diff < co or + co < 0 and diff <= 0 and diff > co): + return diff + return None + + if c.is_Number: + co, t = self.as_coeff_Add() + xa = co.extract_additively(c) + if xa is None: + return None + return xa + t + + # handle the args[0].is_Number case separately + # since we will have trouble looking for the coeff of + # a number. + if c.is_Add and c.args[0].is_Number: + # whole term as a term factor + co = self.coeff(c) + xa0 = (co.extract_additively(1) or 0)*c + if xa0: + diff = self - co*c + return (xa0 + (diff.extract_additively(c) or diff)) or None + # term-wise + h, t = c.as_coeff_Add() + sh, st = self.as_coeff_Add() + xa = sh.extract_additively(h) + if xa is None: + return None + xa2 = st.extract_additively(t) + if xa2 is None: + return None + return xa + xa2 + + # whole term as a term factor + co, diff = _corem(self, c) + xa0 = (co.extract_additively(1) or 0)*c + if xa0: + return (xa0 + (diff.extract_additively(c) or diff)) or None + # term-wise + coeffs = [] + for a in Add.make_args(c): + ac, at = a.as_coeff_Mul() + co = self.coeff(at) + if not co: + return None + coc, cot = co.as_coeff_Add() + xa = coc.extract_additively(ac) + if xa is None: + return None + self -= co*at + coeffs.append((cot + xa)*at) + coeffs.append(self) + return Add(*coeffs) + + @property + def expr_free_symbols(self): + """ + Like ``free_symbols``, but returns the free symbols only if + they are contained in an expression node. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> (x + y).expr_free_symbols # doctest: +SKIP + {x, y} + + If the expression is contained in a non-expression object, do not return + the free symbols. Compare: + + >>> from sympy import Tuple + >>> t = Tuple(x + y) + >>> t.expr_free_symbols # doctest: +SKIP + set() + >>> t.free_symbols + {x, y} + """ + sympy_deprecation_warning(""" + The expr_free_symbols property is deprecated. Use free_symbols to get + the free symbols of an expression. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-expr-free-symbols") + return {j for i in self.args for j in i.expr_free_symbols} + + def could_extract_minus_sign(self): + """Return True if self has -1 as a leading factor or has + more literal negative signs than positive signs in a sum, + otherwise False. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> e = x - y + >>> {i.could_extract_minus_sign() for i in (e, -e)} + {False, True} + + Though the ``y - x`` is considered like ``-(x - y)``, since it + is in a product without a leading factor of -1, the result is + false below: + + >>> (x*(y - x)).could_extract_minus_sign() + False + + To put something in canonical form wrt to sign, use `signsimp`: + + >>> from sympy import signsimp + >>> signsimp(x*(y - x)) + -x*(x - y) + >>> _.could_extract_minus_sign() + True + """ + return False + + def extract_branch_factor(self, allow_half=False): + """ + Try to write self as ``exp_polar(2*pi*I*n)*z`` in a nice way. + Return (z, n). + + >>> from sympy import exp_polar, I, pi + >>> from sympy.abc import x, y + >>> exp_polar(I*pi).extract_branch_factor() + (exp_polar(I*pi), 0) + >>> exp_polar(2*I*pi).extract_branch_factor() + (1, 1) + >>> exp_polar(-pi*I).extract_branch_factor() + (exp_polar(I*pi), -1) + >>> exp_polar(3*pi*I + x).extract_branch_factor() + (exp_polar(x + I*pi), 1) + >>> (y*exp_polar(-5*pi*I)*exp_polar(3*pi*I + 2*pi*x)).extract_branch_factor() + (y*exp_polar(2*pi*x), -1) + >>> exp_polar(-I*pi/2).extract_branch_factor() + (exp_polar(-I*pi/2), 0) + + If allow_half is True, also extract exp_polar(I*pi): + + >>> exp_polar(I*pi).extract_branch_factor(allow_half=True) + (1, 1/2) + >>> exp_polar(2*I*pi).extract_branch_factor(allow_half=True) + (1, 1) + >>> exp_polar(3*I*pi).extract_branch_factor(allow_half=True) + (1, 3/2) + >>> exp_polar(-I*pi).extract_branch_factor(allow_half=True) + (1, -1/2) + """ + from sympy.functions.elementary.exponential import exp_polar + from sympy.functions.elementary.integers import ceiling + + n = S.Zero + res = S.One + args = Mul.make_args(self) + exps = [] + for arg in args: + if isinstance(arg, exp_polar): + exps += [arg.exp] + else: + res *= arg + piimult = S.Zero + extras = [] + + ipi = S.Pi*S.ImaginaryUnit + while exps: + exp = exps.pop() + if exp.is_Add: + exps += exp.args + continue + if exp.is_Mul: + coeff = exp.as_coefficient(ipi) + if coeff is not None: + piimult += coeff + continue + extras += [exp] + if piimult.is_number: + coeff = piimult + tail = () + else: + coeff, tail = piimult.as_coeff_add(*piimult.free_symbols) + # round down to nearest multiple of 2 + branchfact = ceiling(coeff/2 - S.Half)*2 + n += branchfact/2 + c = coeff - branchfact + if allow_half: + nc = c.extract_additively(1) + if nc is not None: + n += S.Half + c = nc + newexp = ipi*Add(*((c, ) + tail)) + Add(*extras) + if newexp != 0: + res *= exp_polar(newexp) + return res, n + + def is_polynomial(self, *syms): + r""" + Return True if self is a polynomial in syms and False otherwise. + + This checks if self is an exact polynomial in syms. This function + returns False for expressions that are "polynomials" with symbolic + exponents. Thus, you should be able to apply polynomial algorithms to + expressions for which this returns True, and Poly(expr, \*syms) should + work if and only if expr.is_polynomial(\*syms) returns True. The + polynomial does not have to be in expanded form. If no symbols are + given, all free symbols in the expression will be used. + + This is not part of the assumptions system. You cannot do + Symbol('z', polynomial=True). + + Examples + ======== + + >>> from sympy import Symbol, Function + >>> x = Symbol('x') + >>> ((x**2 + 1)**4).is_polynomial(x) + True + >>> ((x**2 + 1)**4).is_polynomial() + True + >>> (2**x + 1).is_polynomial(x) + False + >>> (2**x + 1).is_polynomial(2**x) + True + >>> f = Function('f') + >>> (f(x) + 1).is_polynomial(x) + False + >>> (f(x) + 1).is_polynomial(f(x)) + True + >>> (1/f(x) + 1).is_polynomial(f(x)) + False + + >>> n = Symbol('n', nonnegative=True, integer=True) + >>> (x**n + 1).is_polynomial(x) + False + + This function does not attempt any nontrivial simplifications that may + result in an expression that does not appear to be a polynomial to + become one. + + >>> from sympy import sqrt, factor, cancel + >>> y = Symbol('y', positive=True) + >>> a = sqrt(y**2 + 2*y + 1) + >>> a.is_polynomial(y) + False + >>> factor(a) + y + 1 + >>> factor(a).is_polynomial(y) + True + + >>> b = (y**2 + 2*y + 1)/(y + 1) + >>> b.is_polynomial(y) + False + >>> cancel(b) + y + 1 + >>> cancel(b).is_polynomial(y) + True + + See also .is_rational_function() + + """ + if syms: + syms = set(map(sympify, syms)) + else: + syms = self.free_symbols + if not syms: + return True + + return self._eval_is_polynomial(syms) + + def _eval_is_polynomial(self, syms): + if self in syms: + return True + if not self.has_free(*syms): + # constant polynomial + return True + # subclasses should return True or False + + def is_rational_function(self, *syms): + """ + Test whether function is a ratio of two polynomials in the given + symbols, syms. When syms is not given, all free symbols will be used. + The rational function does not have to be in expanded or in any kind of + canonical form. + + This function returns False for expressions that are "rational + functions" with symbolic exponents. Thus, you should be able to call + .as_numer_denom() and apply polynomial algorithms to the result for + expressions for which this returns True. + + This is not part of the assumptions system. You cannot do + Symbol('z', rational_function=True). + + Examples + ======== + + >>> from sympy import Symbol, sin + >>> from sympy.abc import x, y + + >>> (x/y).is_rational_function() + True + + >>> (x**2).is_rational_function() + True + + >>> (x/sin(y)).is_rational_function(y) + False + + >>> n = Symbol('n', integer=True) + >>> (x**n + 1).is_rational_function(x) + False + + This function does not attempt any nontrivial simplifications that may + result in an expression that does not appear to be a rational function + to become one. + + >>> from sympy import sqrt, factor + >>> y = Symbol('y', positive=True) + >>> a = sqrt(y**2 + 2*y + 1)/y + >>> a.is_rational_function(y) + False + >>> factor(a) + (y + 1)/y + >>> factor(a).is_rational_function(y) + True + + See also is_algebraic_expr(). + + """ + if syms: + syms = set(map(sympify, syms)) + else: + syms = self.free_symbols + if not syms: + return self not in _illegal + + return self._eval_is_rational_function(syms) + + def _eval_is_rational_function(self, syms): + if self in syms: + return True + if not self.has_xfree(syms): + return True + # subclasses should return True or False + + def is_meromorphic(self, x, a): + """ + This tests whether an expression is meromorphic as + a function of the given symbol ``x`` at the point ``a``. + + This method is intended as a quick test that will return + None if no decision can be made without simplification or + more detailed analysis. + + Examples + ======== + + >>> from sympy import zoo, log, sin, sqrt + >>> from sympy.abc import x + + >>> f = 1/x**2 + 1 - 2*x**3 + >>> f.is_meromorphic(x, 0) + True + >>> f.is_meromorphic(x, 1) + True + >>> f.is_meromorphic(x, zoo) + True + + >>> g = x**log(3) + >>> g.is_meromorphic(x, 0) + False + >>> g.is_meromorphic(x, 1) + True + >>> g.is_meromorphic(x, zoo) + False + + >>> h = sin(1/x)*x**2 + >>> h.is_meromorphic(x, 0) + False + >>> h.is_meromorphic(x, 1) + True + >>> h.is_meromorphic(x, zoo) + True + + Multivalued functions are considered meromorphic when their + branches are meromorphic. Thus most functions are meromorphic + everywhere except at essential singularities and branch points. + In particular, they will be meromorphic also on branch cuts + except at their endpoints. + + >>> log(x).is_meromorphic(x, -1) + True + >>> log(x).is_meromorphic(x, 0) + False + >>> sqrt(x).is_meromorphic(x, -1) + True + >>> sqrt(x).is_meromorphic(x, 0) + False + + """ + if not x.is_symbol: + raise TypeError("{} should be of symbol type".format(x)) + a = sympify(a) + + return self._eval_is_meromorphic(x, a) + + def _eval_is_meromorphic(self, x, a): + if self == x: + return True + if not self.has_free(x): + return True + # subclasses should return True or False + + def is_algebraic_expr(self, *syms): + """ + This tests whether a given expression is algebraic or not, in the + given symbols, syms. When syms is not given, all free symbols + will be used. The rational function does not have to be in expanded + or in any kind of canonical form. + + This function returns False for expressions that are "algebraic + expressions" with symbolic exponents. This is a simple extension to the + is_rational_function, including rational exponentiation. + + Examples + ======== + + >>> from sympy import Symbol, sqrt + >>> x = Symbol('x', real=True) + >>> sqrt(1 + x).is_rational_function() + False + >>> sqrt(1 + x).is_algebraic_expr() + True + + This function does not attempt any nontrivial simplifications that may + result in an expression that does not appear to be an algebraic + expression to become one. + + >>> from sympy import exp, factor + >>> a = sqrt(exp(x)**2 + 2*exp(x) + 1)/(exp(x) + 1) + >>> a.is_algebraic_expr(x) + False + >>> factor(a).is_algebraic_expr() + True + + See Also + ======== + + is_rational_function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Algebraic_expression + + """ + if syms: + syms = set(map(sympify, syms)) + else: + syms = self.free_symbols + if not syms: + return True + + return self._eval_is_algebraic_expr(syms) + + def _eval_is_algebraic_expr(self, syms): + if self in syms: + return True + if not self.has_free(*syms): + return True + # subclasses should return True or False + + ################################################################################### + ##################### SERIES, LEADING TERM, LIMIT, ORDER METHODS ################## + ################################################################################### + + def series(self, x=None, x0=0, n=6, dir="+", logx=None, cdir=0): + """ + Series expansion of "self" around ``x = x0`` yielding either terms of + the series one by one (the lazy series given when n=None), else + all the terms at once when n != None. + + Returns the series expansion of "self" around the point ``x = x0`` + with respect to ``x`` up to ``O((x - x0)**n, x, x0)`` (default n is 6). + + If ``x=None`` and ``self`` is univariate, the univariate symbol will + be supplied, otherwise an error will be raised. + + Parameters + ========== + + expr : Expression + The expression whose series is to be expanded. + + x : Symbol + It is the variable of the expression to be calculated. + + x0 : Value + The value around which ``x`` is calculated. Can be any value + from ``-oo`` to ``oo``. + + n : Value + The value used to represent the order in terms of ``x**n``, + up to which the series is to be expanded. + + dir : String, optional + The series-expansion can be bi-directional. If ``dir="+"``, + then (x->x0+). If ``dir="-", then (x->x0-). For infinite + ``x0`` (``oo`` or ``-oo``), the ``dir`` argument is determined + from the direction of the infinity (i.e., ``dir="-"`` for + ``oo``). + + logx : optional + It is used to replace any log(x) in the returned series with a + symbolic value rather than evaluating the actual value. + + cdir : optional + It stands for complex direction, and indicates the direction + from which the expansion needs to be evaluated. + + Examples + ======== + + >>> from sympy import cos, exp, tan + >>> from sympy.abc import x, y + >>> cos(x).series() + 1 - x**2/2 + x**4/24 + O(x**6) + >>> cos(x).series(n=4) + 1 - x**2/2 + O(x**4) + >>> cos(x).series(x, x0=1, n=2) + cos(1) - (x - 1)*sin(1) + O((x - 1)**2, (x, 1)) + >>> e = cos(x + exp(y)) + >>> e.series(y, n=2) + cos(x + 1) - y*sin(x + 1) + O(y**2) + >>> e.series(x, n=2) + cos(exp(y)) - x*sin(exp(y)) + O(x**2) + + If ``n=None`` then a generator of the series terms will be returned. + + >>> term=cos(x).series(n=None) + >>> [next(term) for i in range(2)] + [1, -x**2/2] + + For ``dir=+`` (default) the series is calculated from the right and + for ``dir=-`` the series from the left. For smooth functions this + flag will not alter the results. + + >>> abs(x).series(dir="+") + x + >>> abs(x).series(dir="-") + -x + >>> f = tan(x) + >>> f.series(x, 2, 6, "+") + tan(2) + (1 + tan(2)**2)*(x - 2) + (x - 2)**2*(tan(2)**3 + tan(2)) + + (x - 2)**3*(1/3 + 4*tan(2)**2/3 + tan(2)**4) + (x - 2)**4*(tan(2)**5 + + 5*tan(2)**3/3 + 2*tan(2)/3) + (x - 2)**5*(2/15 + 17*tan(2)**2/15 + + 2*tan(2)**4 + tan(2)**6) + O((x - 2)**6, (x, 2)) + + >>> f.series(x, 2, 3, "-") + tan(2) + (2 - x)*(-tan(2)**2 - 1) + (2 - x)**2*(tan(2)**3 + tan(2)) + + O((x - 2)**3, (x, 2)) + + For rational expressions this method may return original expression without the Order term. + >>> (1/x).series(x, n=8) + 1/x + + Returns + ======= + + Expr : Expression + Series expansion of the expression about x0 + + Raises + ====== + + TypeError + If "n" and "x0" are infinity objects + + PoleError + If "x0" is an infinity object + + """ + if x is None: + syms = self.free_symbols + if not syms: + return self + elif len(syms) > 1: + raise ValueError('x must be given for multivariate functions.') + x = syms.pop() + + from .symbol import Dummy, Symbol + if isinstance(x, Symbol): + dep = x in self.free_symbols + else: + d = Dummy() + dep = d in self.xreplace({x: d}).free_symbols + if not dep: + if n is None: + return (s for s in [self]) + else: + return self + + if len(dir) != 1 or dir not in '+-': + raise ValueError("Dir must be '+' or '-'") + + x0 = sympify(x0) + cdir = sympify(cdir) + from sympy.functions.elementary.complexes import im, sign + + if not cdir.is_zero: + if cdir.is_real: + dir = '+' if cdir.is_positive else '-' + else: + dir = '+' if im(cdir).is_positive else '-' + else: + if x0 and x0.is_infinite: + cdir = sign(x0).simplify() + elif str(dir) == "+": + cdir = S.One + elif str(dir) == "-": + cdir = S.NegativeOne + elif cdir == S.Zero: + cdir = S.One + + cdir = cdir/abs(cdir) + + if x0 and x0.is_infinite: + from .function import PoleError + try: + s = self.subs(x, cdir/x).series(x, n=n, dir='+', cdir=1) + if n is None: + return (si.subs(x, cdir/x) for si in s) + return s.subs(x, cdir/x) + except PoleError: + s = self.subs(x, cdir*x).aseries(x, n=n) + return s.subs(x, cdir*x) + + # use rep to shift origin to x0 and change sign (if dir is negative) + # and undo the process with rep2 + if x0 or cdir != 1: + s = self.subs({x: x0 + cdir*x}).series(x, x0=0, n=n, dir='+', logx=logx, cdir=1) + if n is None: # lseries... + return (si.subs({x: x/cdir - x0/cdir}) for si in s) + return s.subs({x: x/cdir - x0/cdir}) + + # from here on it's x0=0 and dir='+' handling + + if x.is_positive is x.is_negative is None or x.is_Symbol is not True: + # replace x with an x that has a positive assumption + xpos = Dummy('x', positive=True) + rv = self.subs(x, xpos).series(xpos, x0, n, dir, logx=logx, cdir=cdir) + if n is None: + return (s.subs(xpos, x) for s in rv) + else: + return rv.subs(xpos, x) + + from sympy.series.order import Order + if n is not None: # nseries handling + s1 = self._eval_nseries(x, n=n, logx=logx, cdir=cdir) + o = s1.getO() or S.Zero + if o: + # make sure the requested order is returned + ngot = o.getn() + if ngot > n: + # leave o in its current form (e.g. with x*log(x)) so + # it eats terms properly, then replace it below + if n != 0: + s1 += o.subs(x, x**Rational(n, ngot)) + else: + s1 += Order(1, x) + elif ngot < n: + # increase the requested number of terms to get the desired + # number keep increasing (up to 9) until the received order + # is different than the original order and then predict how + # many additional terms are needed + from sympy.functions.elementary.integers import ceiling + for more in range(1, 9): + s1 = self._eval_nseries(x, n=n + more, logx=logx, cdir=cdir) + newn = s1.getn() + if newn != ngot: + ndo = n + ceiling((n - ngot)*more/(newn - ngot)) + s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir) + while s1.getn() < n: + s1 = self._eval_nseries(x, n=ndo, logx=logx, cdir=cdir) + ndo += 1 + break + else: + raise ValueError('Could not calculate %s terms for %s' + % (str(n), self)) + s1 += Order(x**n, x) + o = s1.getO() + s1 = s1.removeO() + elif s1.has(Order): + # asymptotic expansion + return s1 + else: + o = Order(x**n, x) + s1done = s1.doit() + try: + if (s1done + o).removeO() == s1done: + o = S.Zero + except NotImplementedError: + return s1 + + try: + from sympy.simplify.radsimp import collect + return collect(s1, x) + o + except NotImplementedError: + return s1 + o + + else: # lseries handling + def yield_lseries(s): + """Return terms of lseries one at a time.""" + for si in s: + if not si.is_Add: + yield si + continue + # yield terms 1 at a time if possible + # by increasing order until all the + # terms have been returned + yielded = 0 + o = Order(si, x)*x + ndid = 0 + ndo = len(si.args) + while 1: + do = (si - yielded + o).removeO() + o *= x + if not do or do.is_Order: + continue + if do.is_Add: + ndid += len(do.args) + else: + ndid += 1 + yield do + if ndid == ndo: + break + yielded += do + + return yield_lseries(self.removeO()._eval_lseries(x, logx=logx, cdir=cdir)) + + def aseries(self, x=None, n=6, bound=0, hir=False): + """Asymptotic Series expansion of self. + This is equivalent to ``self.series(x, oo, n)``. + + Parameters + ========== + + self : Expression + The expression whose series is to be expanded. + + x : Symbol + It is the variable of the expression to be calculated. + + n : Value + The value used to represent the order in terms of ``x**n``, + up to which the series is to be expanded. + + hir : Boolean + Set this parameter to be True to produce hierarchical series. + It stops the recursion at an early level and may provide nicer + and more useful results. + + bound : Value, Integer + Use the ``bound`` parameter to give limit on rewriting + coefficients in its normalised form. + + Examples + ======== + + >>> from sympy import sin, exp + >>> from sympy.abc import x + + >>> e = sin(1/x + exp(-x)) - sin(1/x) + + >>> e.aseries(x) + (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x) + + >>> e.aseries(x, n=3, hir=True) + -exp(-2*x)*sin(1/x)/2 + exp(-x)*cos(1/x) + O(exp(-3*x), (x, oo)) + + >>> e = exp(exp(x)/(1 - 1/x)) + + >>> e.aseries(x) + exp(exp(x)/(1 - 1/x)) + + >>> e.aseries(x, bound=3) # doctest: +SKIP + exp(exp(x)/x**2)*exp(exp(x)/x)*exp(-exp(x) + exp(x)/(1 - 1/x) - exp(x)/x - exp(x)/x**2)*exp(exp(x)) + + For rational expressions this method may return original expression without the Order term. + >>> (1/x).aseries(x, n=8) + 1/x + + Returns + ======= + + Expr + Asymptotic series expansion of the expression. + + Notes + ===== + + This algorithm is directly induced from the limit computational algorithm provided by Gruntz. + It majorly uses the mrv and rewrite sub-routines. The overall idea of this algorithm is first + to look for the most rapidly varying subexpression w of a given expression f and then expands f + in a series in w. Then same thing is recursively done on the leading coefficient + till we get constant coefficients. + + If the most rapidly varying subexpression of a given expression f is f itself, + the algorithm tries to find a normalised representation of the mrv set and rewrites f + using this normalised representation. + + If the expansion contains an order term, it will be either ``O(x ** (-n))`` or ``O(w ** (-n))`` + where ``w`` belongs to the most rapidly varying expression of ``self``. + + References + ========== + + .. [1] Gruntz, Dominik. A new algorithm for computing asymptotic series. + In: Proc. 1993 Int. Symp. Symbolic and Algebraic Computation. 1993. + pp. 239-244. + .. [2] Gruntz thesis - p90 + .. [3] https://en.wikipedia.org/wiki/Asymptotic_expansion + + See Also + ======== + + Expr.aseries: See the docstring of this function for complete details of this wrapper. + """ + + from .symbol import Dummy + + if x.is_positive is x.is_negative is None: + xpos = Dummy('x', positive=True) + return self.subs(x, xpos).aseries(xpos, n, bound, hir).subs(xpos, x) + + from .function import PoleError + from sympy.series.gruntz import mrv, rewrite + + try: + om, exps = mrv(self, x) + except PoleError: + return self + + # We move one level up by replacing `x` by `exp(x)`, and then + # computing the asymptotic series for f(exp(x)). Then asymptotic series + # can be obtained by moving one-step back, by replacing x by ln(x). + + from sympy.functions.elementary.exponential import exp, log + from sympy.series.order import Order + + if x in om: + s = self.subs(x, exp(x)).aseries(x, n, bound, hir).subs(x, log(x)) + if s.getO(): + return s + Order(1/x**n, (x, S.Infinity)) + return s + + k = Dummy('k', positive=True) + # f is rewritten in terms of omega + func, logw = rewrite(exps, om, x, k) + + if self in om: + if bound <= 0: + return self + s = (self.exp).aseries(x, n, bound=bound) + s = s.func(*[t.removeO() for t in s.args]) + try: + res = exp(s.subs(x, 1/x).as_leading_term(x).subs(x, 1/x)) + except PoleError: + res = self + + func = exp(self.args[0] - res.args[0]) / k + logw = log(1/res) + + s = func.series(k, 0, n) + + # Hierarchical series + if hir: + return s.subs(k, exp(logw)) + + o = s.getO() + terms = sorted(Add.make_args(s.removeO()), key=lambda i: int(i.as_coeff_exponent(k)[1])) + s = S.Zero + has_ord = False + + # Then we recursively expand these coefficients one by one into + # their asymptotic series in terms of their most rapidly varying subexpressions. + for t in terms: + coeff, expo = t.as_coeff_exponent(k) + if coeff.has(x): + # Recursive step + snew = coeff.aseries(x, n, bound=bound-1) + if has_ord and snew.getO(): + break + elif snew.getO(): + has_ord = True + s += (snew * k**expo) + else: + s += t + + if not o or has_ord: + return s.subs(k, exp(logw)) + return (s + o).subs(k, exp(logw)) + + + def taylor_term(self, n, x, *previous_terms): + """General method for the taylor term. + + This method is slow, because it differentiates n-times. Subclasses can + redefine it to make it faster by using the "previous_terms". + """ + from .symbol import Dummy + from sympy.functions.combinatorial.factorials import factorial + + x = sympify(x) + _x = Dummy('x') + return self.subs(x, _x).diff(_x, n).subs(_x, x).subs(x, 0) * x**n / factorial(n) + + def lseries(self, x=None, x0=0, dir='+', logx=None, cdir=0): + """ + Wrapper for series yielding an iterator of the terms of the series. + + Note: an infinite series will yield an infinite iterator. The following, + for exaxmple, will never terminate. It will just keep printing terms + of the sin(x) series:: + + for term in sin(x).lseries(x): + print term + + The advantage of lseries() over nseries() is that many times you are + just interested in the next term in the series (i.e. the first term for + example), but you do not know how many you should ask for in nseries() + using the "n" parameter. + + See also nseries(). + """ + return self.series(x, x0, n=None, dir=dir, logx=logx, cdir=cdir) + + def _eval_lseries(self, x, logx=None, cdir=0): + # default implementation of lseries is using nseries(), and adaptively + # increasing the "n". As you can see, it is not very efficient, because + # we are calculating the series over and over again. Subclasses should + # override this method and implement much more efficient yielding of + # terms. + n = 0 + series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir) + + while series.is_Order: + n += 1 + series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir) + + e = series.removeO() + yield e + if e is S.Zero: + return + + while 1: + while 1: + n += 1 + series = self._eval_nseries(x, n=n, logx=logx, cdir=cdir).removeO() + if e != series: + break + if (series - self).cancel() is S.Zero: + return + yield series - e + e = series + + def nseries(self, x=None, x0=0, n=6, dir='+', logx=None, cdir=0): + """ + Wrapper to _eval_nseries if assumptions allow, else to series. + + If x is given, x0 is 0, dir='+', and self has x, then _eval_nseries is + called. This calculates "n" terms in the innermost expressions and + then builds up the final series just by "cross-multiplying" everything + out. + + The optional ``logx`` parameter can be used to replace any log(x) in the + returned series with a symbolic value to avoid evaluating log(x) at 0. A + symbol to use in place of log(x) should be provided. + + Advantage -- it's fast, because we do not have to determine how many + terms we need to calculate in advance. + + Disadvantage -- you may end up with less terms than you may have + expected, but the O(x**n) term appended will always be correct and + so the result, though perhaps shorter, will also be correct. + + If any of those assumptions is not met, this is treated like a + wrapper to series which will try harder to return the correct + number of terms. + + See also lseries(). + + Examples + ======== + + >>> from sympy import sin, log, Symbol + >>> from sympy.abc import x, y + >>> sin(x).nseries(x, 0, 6) + x - x**3/6 + x**5/120 + O(x**6) + >>> log(x+1).nseries(x, 0, 5) + x - x**2/2 + x**3/3 - x**4/4 + O(x**5) + + Handling of the ``logx`` parameter --- in the following example the + expansion fails since ``sin`` does not have an asymptotic expansion + at -oo (the limit of log(x) as x approaches 0): + + >>> e = sin(log(x)) + >>> e.nseries(x, 0, 6) + Traceback (most recent call last): + ... + PoleError: ... + ... + >>> logx = Symbol('logx') + >>> e.nseries(x, 0, 6, logx=logx) + sin(logx) + + In the following example, the expansion works but only returns self + unless the ``logx`` parameter is used: + + >>> e = x**y + >>> e.nseries(x, 0, 2) + x**y + >>> e.nseries(x, 0, 2, logx=logx) + exp(logx*y) + + """ + if x and x not in self.free_symbols: + return self + if x is None or x0 or dir != '+': # {see XPOS above} or (x.is_positive == x.is_negative == None): + return self.series(x, x0, n, dir, cdir=cdir) + else: + return self._eval_nseries(x, n=n, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir): + """ + Return terms of series for self up to O(x**n) at x=0 + from the positive direction. + + This is a method that should be overridden in subclasses. Users should + never call this method directly (use .nseries() instead), so you do not + have to write docstrings for _eval_nseries(). + """ + raise NotImplementedError(filldedent(""" + The _eval_nseries method should be added to + %s to give terms up to O(x**n) at x=0 + from the positive direction so it is available when + nseries calls it.""" % self.func) + ) + + def limit(self, x, xlim, dir='+'): + """ Compute limit x->xlim. + """ + from sympy.series.limits import limit + return limit(self, x, xlim, dir) + + def compute_leading_term(self, x, logx=None): + """Deprecated function to compute the leading term of a series. + + as_leading_term is only allowed for results of .series() + This is a wrapper to compute a series first. + """ + from sympy.utilities.exceptions import SymPyDeprecationWarning + + SymPyDeprecationWarning( + feature="compute_leading_term", + useinstead="as_leading_term", + issue=21843, + deprecated_since_version="1.12" + ).warn() + + from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold + if self.has(Piecewise): + expr = piecewise_fold(self) + else: + expr = self + if self.removeO() == 0: + return self + + from .symbol import Dummy + from sympy.functions.elementary.exponential import log + from sympy.series.order import Order + + _logx = logx + logx = Dummy('logx') if logx is None else logx + res = Order(1) + incr = S.One + while res.is_Order: + res = expr._eval_nseries(x, n=1+incr, logx=logx).cancel().powsimp().trigsimp() + incr *= 2 + + if _logx is None: + res = res.subs(logx, log(x)) + + return res.as_leading_term(x) + + @cacheit + def as_leading_term(self, *symbols, logx=None, cdir=0): + """ + Returns the leading (nonzero) term of the series expansion of self. + + The _eval_as_leading_term routines are used to do this, and they must + always return a non-zero value. + + Examples + ======== + + >>> from sympy.abc import x + >>> (1 + x + x**2).as_leading_term(x) + 1 + >>> (1/x**2 + x + x**2).as_leading_term(x) + x**(-2) + + """ + if len(symbols) > 1: + c = self + for x in symbols: + c = c.as_leading_term(x, logx=logx, cdir=cdir) + return c + elif not symbols: + return self + x = sympify(symbols[0]) + if not x.is_symbol: + raise ValueError('expecting a Symbol but got %s' % x) + if x not in self.free_symbols: + return self + obj = self._eval_as_leading_term(x, logx=logx, cdir=cdir) + if obj is not None: + from sympy.simplify.powsimp import powsimp + return powsimp(obj, deep=True, combine='exp') + raise NotImplementedError('as_leading_term(%s, %s)' % (self, x)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + return self + + def as_coeff_exponent(self, x) -> tuple[Expr, Expr]: + """ ``c*x**e -> c,e`` where x can be any symbolic expression. + """ + from sympy.simplify.radsimp import collect + s = collect(self, x) + c, p = s.as_coeff_mul(x) + if len(p) == 1: + b, e = p[0].as_base_exp() + if b == x: + return c, e + return s, S.Zero + + def leadterm(self, x, logx=None, cdir=0): + """ + Returns the leading term a*x**b as a tuple (a, b). + + Examples + ======== + + >>> from sympy.abc import x + >>> (1+x+x**2).leadterm(x) + (1, 0) + >>> (1/x**2+x+x**2).leadterm(x) + (1, -2) + + """ + from .symbol import Dummy + from sympy.functions.elementary.exponential import log + l = self.as_leading_term(x, logx=logx, cdir=cdir) + d = Dummy('logx') + if l.has(log(x)): + l = l.subs(log(x), d) + c, e = l.as_coeff_exponent(x) + if x in c.free_symbols: + raise ValueError(filldedent(""" + cannot compute leadterm(%s, %s). The coefficient + should have been free of %s but got %s""" % (self, x, x, c))) + c = c.subs(d, log(x)) + return c, e + + def as_coeff_Mul(self, rational: bool = False) -> tuple['Number', Expr]: + """Efficiently extract the coefficient of a product.""" + return S.One, self + + def as_coeff_Add(self, rational=False) -> tuple['Number', Expr]: + """Efficiently extract the coefficient of a summation.""" + return S.Zero, self + + def fps(self, x=None, x0=0, dir=1, hyper=True, order=4, rational=True, + full=False): + """ + Compute formal power power series of self. + + See the docstring of the :func:`fps` function in sympy.series.formal for + more information. + """ + from sympy.series.formal import fps + + return fps(self, x, x0, dir, hyper, order, rational, full) + + def fourier_series(self, limits=None): + """Compute fourier sine/cosine series of self. + + See the docstring of the :func:`fourier_series` in sympy.series.fourier + for more information. + """ + from sympy.series.fourier import fourier_series + + return fourier_series(self, limits) + + ################################################################################### + ##################### DERIVATIVE, INTEGRAL, FUNCTIONAL METHODS #################### + ################################################################################### + + def diff(self, *symbols, **assumptions): + assumptions.setdefault("evaluate", True) + return _derivative_dispatch(self, *symbols, **assumptions) + + ########################################################################### + ###################### EXPRESSION EXPANSION METHODS ####################### + ########################################################################### + + # Relevant subclasses should override _eval_expand_hint() methods. See + # the docstring of expand() for more info. + + def _eval_expand_complex(self, **hints): + real, imag = self.as_real_imag(**hints) + return real + S.ImaginaryUnit*imag + + @staticmethod + def _expand_hint(expr, hint, deep=True, **hints): + """ + Helper for ``expand()``. Recursively calls ``expr._eval_expand_hint()``. + + Returns ``(expr, hit)``, where expr is the (possibly) expanded + ``expr`` and ``hit`` is ``True`` if ``expr`` was truly expanded and + ``False`` otherwise. + """ + hit = False + # XXX: Hack to support non-Basic args + # | + # V + if deep and getattr(expr, 'args', ()) and not expr.is_Atom: + sargs = [] + for arg in expr.args: + arg, arghit = Expr._expand_hint(arg, hint, **hints) + hit |= arghit + sargs.append(arg) + + if hit: + expr = expr.func(*sargs) + + if hasattr(expr, hint): + newexpr = getattr(expr, hint)(**hints) + if newexpr != expr: + return (newexpr, True) + + return (expr, hit) + + @cacheit + def expand(self, deep=True, modulus=None, power_base=True, power_exp=True, + mul=True, log=True, multinomial=True, basic=True, **hints): + """ + Expand an expression using hints. + + See the docstring of the expand() function in sympy.core.function for + more information. + + """ + from sympy.simplify.radsimp import fraction + + hints.update(power_base=power_base, power_exp=power_exp, mul=mul, + log=log, multinomial=multinomial, basic=basic) + + expr = self + # default matches fraction's default + _fraction = lambda x: fraction(x, hints.get('exact', False)) + if hints.pop('frac', False): + n, d = [a.expand(deep=deep, modulus=modulus, **hints) + for a in _fraction(self)] + return n/d + elif hints.pop('denom', False): + n, d = _fraction(self) + return n/d.expand(deep=deep, modulus=modulus, **hints) + elif hints.pop('numer', False): + n, d = _fraction(self) + return n.expand(deep=deep, modulus=modulus, **hints)/d + + # Although the hints are sorted here, an earlier hint may get applied + # at a given node in the expression tree before another because of how + # the hints are applied. e.g. expand(log(x*(y + z))) -> log(x*y + + # x*z) because while applying log at the top level, log and mul are + # applied at the deeper level in the tree so that when the log at the + # upper level gets applied, the mul has already been applied at the + # lower level. + + # Additionally, because hints are only applied once, the expression + # may not be expanded all the way. For example, if mul is applied + # before multinomial, x*(x + 1)**2 won't be expanded all the way. For + # now, we just use a special case to make multinomial run before mul, + # so that at least polynomials will be expanded all the way. In the + # future, smarter heuristics should be applied. + # TODO: Smarter heuristics + + def _expand_hint_key(hint): + """Make multinomial come before mul""" + if hint == 'mul': + return 'mulz' + return hint + + for hint in sorted(hints.keys(), key=_expand_hint_key): + use_hint = hints[hint] + if use_hint: + hint = '_eval_expand_' + hint + expr, hit = Expr._expand_hint(expr, hint, deep=deep, **hints) + + while True: + was = expr + if hints.get('multinomial', False): + expr, _ = Expr._expand_hint( + expr, '_eval_expand_multinomial', deep=deep, **hints) + if hints.get('mul', False): + expr, _ = Expr._expand_hint( + expr, '_eval_expand_mul', deep=deep, **hints) + if hints.get('log', False): + expr, _ = Expr._expand_hint( + expr, '_eval_expand_log', deep=deep, **hints) + if expr == was: + break + + if modulus is not None: + modulus = sympify(modulus) + + if not modulus.is_Integer or modulus <= 0: + raise ValueError( + "modulus must be a positive integer, got %s" % modulus) + + terms = [] + + for term in Add.make_args(expr): + coeff, tail = term.as_coeff_Mul(rational=True) + + coeff %= modulus + + if coeff: + terms.append(coeff*tail) + + expr = Add(*terms) + + return expr + + ########################################################################### + ################### GLOBAL ACTION VERB WRAPPER METHODS #################### + ########################################################################### + + def integrate(self, *args, **kwargs): + """See the integrate function in sympy.integrals""" + from sympy.integrals.integrals import integrate + return integrate(self, *args, **kwargs) + + def nsimplify(self, constants=(), tolerance=None, full=False): + """See the nsimplify function in sympy.simplify""" + from sympy.simplify.simplify import nsimplify + return nsimplify(self, constants, tolerance, full) + + def separate(self, deep=False, force=False): + """See the separate function in sympy.simplify""" + from .function import expand_power_base + return expand_power_base(self, deep=deep, force=force) + + def collect(self, syms, func=None, evaluate=True, exact=False, distribute_order_term=True): + """See the collect function in sympy.simplify""" + from sympy.simplify.radsimp import collect + return collect(self, syms, func, evaluate, exact, distribute_order_term) + + def together(self, *args, **kwargs): + """See the together function in sympy.polys""" + from sympy.polys.rationaltools import together + return together(self, *args, **kwargs) + + def apart(self, x=None, **args): + """See the apart function in sympy.polys""" + from sympy.polys.partfrac import apart + return apart(self, x, **args) + + def ratsimp(self): + """See the ratsimp function in sympy.simplify""" + from sympy.simplify.ratsimp import ratsimp + return ratsimp(self) + + def trigsimp(self, **args): + """See the trigsimp function in sympy.simplify""" + from sympy.simplify.trigsimp import trigsimp + return trigsimp(self, **args) + + def radsimp(self, **kwargs): + """See the radsimp function in sympy.simplify""" + from sympy.simplify.radsimp import radsimp + return radsimp(self, **kwargs) + + def powsimp(self, *args, **kwargs): + """See the powsimp function in sympy.simplify""" + from sympy.simplify.powsimp import powsimp + return powsimp(self, *args, **kwargs) + + def combsimp(self): + """See the combsimp function in sympy.simplify""" + from sympy.simplify.combsimp import combsimp + return combsimp(self) + + def gammasimp(self): + """See the gammasimp function in sympy.simplify""" + from sympy.simplify.gammasimp import gammasimp + return gammasimp(self) + + def factor(self, *gens, **args): + """See the factor() function in sympy.polys.polytools""" + from sympy.polys.polytools import factor + return factor(self, *gens, **args) + + def cancel(self, *gens, **args): + """See the cancel function in sympy.polys""" + from sympy.polys.polytools import cancel + return cancel(self, *gens, **args) + + def invert(self, g, *gens, **args): + """Return the multiplicative inverse of ``self`` mod ``g`` + where ``self`` (and ``g``) may be symbolic expressions). + + See Also + ======== + sympy.core.intfunc.mod_inverse, sympy.polys.polytools.invert + """ + if self.is_number and getattr(g, 'is_number', True): + return mod_inverse(self, g) + from sympy.polys.polytools import invert + return invert(self, g, *gens, **args) + + def round(self, n=None): + """Return x rounded to the given decimal place. + + If a complex number would results, apply round to the real + and imaginary components of the number. + + Examples + ======== + + >>> from sympy import pi, E, I, S, Number + >>> pi.round() + 3 + >>> pi.round(2) + 3.14 + >>> (2*pi + E*I).round() + 6 + 3*I + + The round method has a chopping effect: + + >>> (2*pi + I/10).round() + 6 + >>> (pi/10 + 2*I).round() + 2*I + >>> (pi/10 + E*I).round(2) + 0.31 + 2.72*I + + Notes + ===== + + The Python ``round`` function uses the SymPy ``round`` method so it + will always return a SymPy number (not a Python float or int): + + >>> isinstance(round(S(123), -2), Number) + True + """ + x = self + + if not x.is_number: + raise TypeError("Cannot round symbolic expression") + if not x.is_Atom: + if not pure_complex(x.n(2), or_real=True): + raise TypeError( + 'Expected a number but got %s:' % func_name(x)) + elif x in _illegal: + return x + if not (xr := x.is_extended_real): + r, i = x.as_real_imag() + if xr is False: + return r.round(n) + S.ImaginaryUnit*i.round(n) + if i.equals(0): + return r.round(n) + if not x: + return S.Zero if n is None else x + + p = as_int(n or 0) + + if x.is_Integer: + return Integer(round(int(x), p)) + + digits_to_decimal = _mag(x) # _mag(12) = 2, _mag(.012) = -1 + allow = digits_to_decimal + p + precs = [f._prec for f in x.atoms(Float)] + dps = prec_to_dps(max(precs)) if precs else None + if dps is None: + # assume everything is exact so use the Python + # float default or whatever was requested + dps = max(15, allow) + else: + allow = min(allow, dps) + # this will shift all digits to right of decimal + # and give us dps to work with as an int + shift = -digits_to_decimal + dps + extra = 1 # how far we look past known digits + # NOTE + # mpmath will calculate the binary representation to + # an arbitrary number of digits but we must base our + # answer on a finite number of those digits, e.g. + # .575 2589569785738035/2**52 in binary. + # mpmath shows us that the first 18 digits are + # >>> Float(.575).n(18) + # 0.574999999999999956 + # The default precision is 15 digits and if we ask + # for 15 we get + # >>> Float(.575).n(15) + # 0.575000000000000 + # mpmath handles rounding at the 15th digit. But we + # need to be careful since the user might be asking + # for rounding at the last digit and our semantics + # are to round toward the even final digit when there + # is a tie. So the extra digit will be used to make + # that decision. In this case, the value is the same + # to 15 digits: + # >>> Float(.575).n(16) + # 0.5750000000000000 + # Now converting this to the 15 known digits gives + # 575000000000000.0 + # which rounds to integer + # 5750000000000000 + # And now we can round to the desired digt, e.g. at + # the second from the left and we get + # 5800000000000000 + # and rescaling that gives + # 0.58 + # as the final result. + # If the value is made slightly less than 0.575 we might + # still obtain the same value: + # >>> Float(.575-1e-16).n(16)*10**15 + # 574999999999999.8 + # What 15 digits best represents the known digits (which are + # to the left of the decimal? 5750000000000000, the same as + # before. The only way we will round down (in this case) is + # if we declared that we had more than 15 digits of precision. + # For example, if we use 16 digits of precision, the integer + # we deal with is + # >>> Float(.575-1e-16).n(17)*10**16 + # 5749999999999998.4 + # and this now rounds to 5749999999999998 and (if we round to + # the 2nd digit from the left) we get 5700000000000000. + # + xf = x.n(dps + extra)*Pow(10, shift) + if xf.is_Number and xf._prec == 1: # xf.is_Add will raise below + # is x == 0? + if x.equals(0): + return Float(0) + raise ValueError('not computing with precision') + xi = Integer(xf) + # use the last digit to select the value of xi + # nearest to x before rounding at the desired digit + sign = 1 if x > 0 else -1 + dif2 = sign*(xf - xi).n(extra) + if dif2 < 0: + raise NotImplementedError( + 'not expecting int(x) to round away from 0') + if dif2 > .5: + xi += sign # round away from 0 + elif dif2 == .5: + xi += sign if xi%2 else -sign # round toward even + # shift p to the new position + ip = p - shift + # let Python handle the int rounding then rescale + xr = round(xi.p, ip) + # restore scale + rv = Rational(xr, Pow(10, shift)) + # return Float or Integer + if rv.is_Integer: + if n is None: # the single-arg case + return rv + # use str or else it won't be a float + return Float(str(rv), dps) # keep same precision + else: + if not allow and rv > self: + allow += 1 + return Float(rv, allow) + + __round__ = round + + def _eval_derivative_matrix_lines(self, x): + from sympy.matrices.expressions.matexpr import _LeftRightArgs + return [_LeftRightArgs([S.One, S.One], higher=self._eval_derivative(x))] + + +class AtomicExpr(Atom, Expr): + """ + A parent class for object which are both atoms and Exprs. + + For example: Symbol, Number, Rational, Integer, ... + But not: Add, Mul, Pow, ... + """ + is_number = False + is_Atom = True + + __slots__ = () + + def _eval_derivative(self, s): + if self == s: + return S.One + return S.Zero + + def _eval_derivative_n_times(self, s, n): + from .containers import Tuple + from sympy.matrices.expressions.matexpr import MatrixExpr + from sympy.matrices.matrixbase import MatrixBase + if isinstance(s, (MatrixBase, Tuple, Iterable, MatrixExpr)): + return super()._eval_derivative_n_times(s, n) + from .relational import Eq + from sympy.functions.elementary.piecewise import Piecewise + if self == s: + return Piecewise((self, Eq(n, 0)), (1, Eq(n, 1)), (0, True)) + else: + return Piecewise((self, Eq(n, 0)), (0, True)) + + def _eval_is_polynomial(self, syms): + return True + + def _eval_is_rational_function(self, syms): + return self not in _illegal + + def _eval_is_meromorphic(self, x, a): + from sympy.calculus.accumulationbounds import AccumBounds + return (not self.is_Number or self.is_finite) and not isinstance(self, AccumBounds) + + def _eval_is_algebraic_expr(self, syms): + return True + + def _eval_nseries(self, x, n, logx, cdir=0): + return self + + @property + def expr_free_symbols(self): + sympy_deprecation_warning(""" + The expr_free_symbols property is deprecated. Use free_symbols to get + the free symbols of an expression. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-expr-free-symbols") + return {self} + + +def _mag(x): + r"""Return integer $i$ such that $0.1 \le x/10^i < 1$ + + Examples + ======== + + >>> from sympy.core.expr import _mag + >>> from sympy import Float + >>> _mag(Float(.1)) + 0 + >>> _mag(Float(.01)) + -1 + >>> _mag(Float(1234)) + 4 + """ + from math import log10, ceil, log + xpos = abs(x.n()) + if not xpos: + return S.Zero + try: + mag_first_dig = int(ceil(log10(xpos))) + except (ValueError, OverflowError): + mag_first_dig = int(ceil(Float(mpf_log(xpos._mpf_, 53))/log(10))) + # check that we aren't off by 1 + if (xpos/10**mag_first_dig) >= 1: + assert 1 <= (xpos/10**mag_first_dig) < 10 + mag_first_dig += 1 + return mag_first_dig + + +class UnevaluatedExpr(Expr): + """ + Expression that is not evaluated unless released. + + Examples + ======== + + >>> from sympy import UnevaluatedExpr + >>> from sympy.abc import x + >>> x*(1/x) + 1 + >>> x*UnevaluatedExpr(1/x) + x*1/x + + """ + + def __new__(cls, arg, **kwargs): + arg = _sympify(arg) + obj = Expr.__new__(cls, arg, **kwargs) + return obj + + def doit(self, **hints): + if hints.get("deep", True): + return self.args[0].doit(**hints) + else: + return self.args[0] + + + +def unchanged(func, *args): + """Return True if `func` applied to the `args` is unchanged. + Can be used instead of `assert foo == foo`. + + Examples + ======== + + >>> from sympy import Piecewise, cos, pi + >>> from sympy.core.expr import unchanged + >>> from sympy.abc import x + + >>> unchanged(cos, 1) # instead of assert cos(1) == cos(1) + True + + >>> unchanged(cos, pi) + False + + Comparison of args uses the builtin capabilities of the object's + arguments to test for equality so args can be defined loosely. Here, + the ExprCondPair arguments of Piecewise compare as equal to the + tuples that can be used to create the Piecewise: + + >>> unchanged(Piecewise, (x, x > 1), (0, True)) + True + """ + f = func(*args) + return f.func == func and f.args == args + + +class ExprBuilder: + def __init__(self, op, args=None, validator=None, check=True): + if not hasattr(op, "__call__"): + raise TypeError("op {} needs to be callable".format(op)) + self.op = op + if args is None: + self.args = [] + else: + self.args = args + self.validator = validator + if (validator is not None) and check: + self.validate() + + @staticmethod + def _build_args(args): + return [i.build() if isinstance(i, ExprBuilder) else i for i in args] + + def validate(self): + if self.validator is None: + return + args = self._build_args(self.args) + self.validator(*args) + + def build(self, check=True): + args = self._build_args(self.args) + if self.validator and check: + self.validator(*args) + return self.op(*args) + + def append_argument(self, arg, check=True): + self.args.append(arg) + if self.validator and check: + self.validate(*self.args) + + def __getitem__(self, item): + if item == 0: + return self.op + else: + return self.args[item-1] + + def __repr__(self): + return str(self.build()) + + def search_element(self, elem): + for i, arg in enumerate(self.args): + if isinstance(arg, ExprBuilder): + ret = arg.search_index(elem) + if ret is not None: + return (i,) + ret + elif id(arg) == id(elem): + return (i,) + return None + + +from .mul import Mul +from .add import Add +from .power import Pow +from .function import Function, _derivative_dispatch +from .mod import Mod +from .exprtools import factor_terms +from .numbers import Float, Integer, Rational, _illegal, int_valued diff --git a/lib/python3.11/site-packages/sympy/core/exprtools.py b/lib/python3.11/site-packages/sympy/core/exprtools.py new file mode 100644 index 0000000000000000000000000000000000000000..869b9d569f4c7e962773337f739136ff271a3897 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/exprtools.py @@ -0,0 +1,1569 @@ +"""Tools for manipulating of large commutative expressions. """ + +from .add import Add +from .mul import Mul, _keep_coeff +from .power import Pow +from .basic import Basic +from .expr import Expr +from .function import expand_power_exp +from .sympify import sympify +from .numbers import Rational, Integer, Number, I, equal_valued +from .singleton import S +from .sorting import default_sort_key, ordered +from .symbol import Dummy +from .traversal import preorder_traversal +from .coreerrors import NonCommutativeExpression +from .containers import Tuple, Dict +from sympy.external.gmpy import SYMPY_INTS +from sympy.utilities.iterables import (common_prefix, common_suffix, + variations, iterable, is_sequence) + +from collections import defaultdict +from typing import Tuple as tTuple + + +_eps = Dummy(positive=True) + + +def _isnumber(i): + return isinstance(i, (SYMPY_INTS, float)) or i.is_Number + + +def _monotonic_sign(self): + """Return the value closest to 0 that ``self`` may have if all symbols + are signed and the result is uniformly the same sign for all values of symbols. + If a symbol is only signed but not known to be an + integer or the result is 0 then a symbol representative of the sign of self + will be returned. Otherwise, None is returned if a) the sign could be positive + or negative or b) self is not in one of the following forms: + + - L(x, y, ...) + A: a function linear in all symbols x, y, ... with an + additive constant; if A is zero then the function can be a monomial whose + sign is monotonic over the range of the variables, e.g. (x + 1)**3 if x is + nonnegative. + - A/L(x, y, ...) + B: the inverse of a function linear in all symbols x, y, ... + that does not have a sign change from positive to negative for any set + of values for the variables. + - M(x, y, ...) + A: a monomial M whose factors are all signed and a constant, A. + - A/M(x, y, ...) + B: the inverse of a monomial and constants A and B. + - P(x): a univariate polynomial + + Examples + ======== + + >>> from sympy.core.exprtools import _monotonic_sign as F + >>> from sympy import Dummy + >>> nn = Dummy(integer=True, nonnegative=True) + >>> p = Dummy(integer=True, positive=True) + >>> p2 = Dummy(integer=True, positive=True) + >>> F(nn + 1) + 1 + >>> F(p - 1) + _nneg + >>> F(nn*p + 1) + 1 + >>> F(p2*p + 1) + 2 + >>> F(nn - 1) # could be negative, zero or positive + """ + if not self.is_extended_real: + return + + if (-self).is_Symbol: + rv = _monotonic_sign(-self) + return rv if rv is None else -rv + + if not self.is_Add and self.as_numer_denom()[1].is_number: + s = self + if s.is_prime: + if s.is_odd: + return Integer(3) + else: + return Integer(2) + elif s.is_composite: + if s.is_odd: + return Integer(9) + else: + return Integer(4) + elif s.is_positive: + if s.is_even: + if s.is_prime is False: + return Integer(4) + else: + return Integer(2) + elif s.is_integer: + return S.One + else: + return _eps + elif s.is_extended_negative: + if s.is_even: + return Integer(-2) + elif s.is_integer: + return S.NegativeOne + else: + return -_eps + if s.is_zero or s.is_extended_nonpositive or s.is_extended_nonnegative: + return S.Zero + return None + + # univariate polynomial + free = self.free_symbols + if len(free) == 1: + if self.is_polynomial(): + from sympy.polys.polytools import real_roots + from sympy.polys.polyroots import roots + from sympy.polys.polyerrors import PolynomialError + x = free.pop() + x0 = _monotonic_sign(x) + if x0 in (_eps, -_eps): + x0 = S.Zero + if x0 is not None: + d = self.diff(x) + if d.is_number: + currentroots = [] + else: + try: + currentroots = real_roots(d) + except (PolynomialError, NotImplementedError): + currentroots = [r for r in roots(d, x) if r.is_extended_real] + y = self.subs(x, x0) + if x.is_nonnegative and all( + (r - x0).is_nonpositive for r in currentroots): + if y.is_nonnegative and d.is_positive: + if y: + return y if y.is_positive else Dummy('pos', positive=True) + else: + return Dummy('nneg', nonnegative=True) + if y.is_nonpositive and d.is_negative: + if y: + return y if y.is_negative else Dummy('neg', negative=True) + else: + return Dummy('npos', nonpositive=True) + elif x.is_nonpositive and all( + (r - x0).is_nonnegative for r in currentroots): + if y.is_nonnegative and d.is_negative: + if y: + return Dummy('pos', positive=True) + else: + return Dummy('nneg', nonnegative=True) + if y.is_nonpositive and d.is_positive: + if y: + return Dummy('neg', negative=True) + else: + return Dummy('npos', nonpositive=True) + else: + n, d = self.as_numer_denom() + den = None + if n.is_number: + den = _monotonic_sign(d) + elif not d.is_number: + if _monotonic_sign(n) is not None: + den = _monotonic_sign(d) + if den is not None and (den.is_positive or den.is_negative): + v = n*den + if v.is_positive: + return Dummy('pos', positive=True) + elif v.is_nonnegative: + return Dummy('nneg', nonnegative=True) + elif v.is_negative: + return Dummy('neg', negative=True) + elif v.is_nonpositive: + return Dummy('npos', nonpositive=True) + return None + + # multivariate + c, a = self.as_coeff_Add() + v = None + if not a.is_polynomial(): + # F/A or A/F where A is a number and F is a signed, rational monomial + n, d = a.as_numer_denom() + if not (n.is_number or d.is_number): + return + if ( + a.is_Mul or a.is_Pow) and \ + a.is_rational and \ + all(p.exp.is_Integer for p in a.atoms(Pow) if p.is_Pow) and \ + (a.is_positive or a.is_negative): + v = S.One + for ai in Mul.make_args(a): + if ai.is_number: + v *= ai + continue + reps = {} + for x in ai.free_symbols: + reps[x] = _monotonic_sign(x) + if reps[x] is None: + return + v *= ai.subs(reps) + elif c: + # signed linear expression + if not any(p for p in a.atoms(Pow) if not p.is_number) and (a.is_nonpositive or a.is_nonnegative): + free = list(a.free_symbols) + p = {} + for i in free: + v = _monotonic_sign(i) + if v is None: + return + p[i] = v or (_eps if i.is_nonnegative else -_eps) + v = a.xreplace(p) + if v is not None: + rv = v + c + if v.is_nonnegative and rv.is_positive: + return rv.subs(_eps, 0) + if v.is_nonpositive and rv.is_negative: + return rv.subs(_eps, 0) + + +def decompose_power(expr: Expr) -> tTuple[Expr, int]: + """ + Decompose power into symbolic base and integer exponent. + + Examples + ======== + + >>> from sympy.core.exprtools import decompose_power + >>> from sympy.abc import x, y + >>> from sympy import exp + + >>> decompose_power(x) + (x, 1) + >>> decompose_power(x**2) + (x, 2) + >>> decompose_power(exp(2*y/3)) + (exp(y/3), 2) + + """ + base, exp = expr.as_base_exp() + + if exp.is_Number: + if exp.is_Rational: + if not exp.is_Integer: + base = Pow(base, Rational(1, exp.q)) # type: ignore + e = exp.p # type: ignore + else: + base, e = expr, 1 + else: + exp, tail = exp.as_coeff_Mul(rational=True) + + if exp is S.NegativeOne: + base, e = Pow(base, tail), -1 + elif exp is not S.One: + # todo: after dropping python 3.7 support, use overload and Literal + # in as_coeff_Mul to make exp Rational, and remove these 2 ignores + tail = _keep_coeff(Rational(1, exp.q), tail) # type: ignore + base, e = Pow(base, tail), exp.p # type: ignore + else: + base, e = expr, 1 + + return base, e + + +def decompose_power_rat(expr: Expr) -> tTuple[Expr, Rational]: + """ + Decompose power into symbolic base and rational exponent; + if the exponent is not a Rational, then separate only the + integer coefficient. + + Examples + ======== + + >>> from sympy.core.exprtools import decompose_power_rat + >>> from sympy.abc import x + >>> from sympy import sqrt, exp + + >>> decompose_power_rat(sqrt(x)) + (x, 1/2) + >>> decompose_power_rat(exp(-3*x/2)) + (exp(x/2), -3) + + """ + _ = base, exp = expr.as_base_exp() + return _ if exp.is_Rational else decompose_power(expr) + + +class Factors: + """Efficient representation of ``f_1*f_2*...*f_n``.""" + + __slots__ = ('factors', 'gens') + + def __init__(self, factors=None): # Factors + """Initialize Factors from dict or expr. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x + >>> from sympy import I + >>> e = 2*x**3 + >>> Factors(e) + Factors({2: 1, x: 3}) + >>> Factors(e.as_powers_dict()) + Factors({2: 1, x: 3}) + >>> f = _ + >>> f.factors # underlying dictionary + {2: 1, x: 3} + >>> f.gens # base of each factor + frozenset({2, x}) + >>> Factors(0) + Factors({0: 1}) + >>> Factors(I) + Factors({I: 1}) + + Notes + ===== + + Although a dictionary can be passed, only minimal checking is + performed: powers of -1 and I are made canonical. + + """ + if isinstance(factors, (SYMPY_INTS, float)): + factors = S(factors) + if isinstance(factors, Factors): + factors = factors.factors.copy() + elif factors in (None, S.One): + factors = {} + elif factors is S.Zero or factors == 0: + factors = {S.Zero: S.One} + elif isinstance(factors, Number): + n = factors + factors = {} + if n < 0: + factors[S.NegativeOne] = S.One + n = -n + if n is not S.One: + if n.is_Float or n.is_Integer or n is S.Infinity: + factors[n] = S.One + elif n.is_Rational: + # since we're processing Numbers, the denominator is + # stored with a negative exponent; all other factors + # are left . + if n.p != 1: + factors[Integer(n.p)] = S.One + factors[Integer(n.q)] = S.NegativeOne + else: + raise ValueError('Expected Float|Rational|Integer, not %s' % n) + elif isinstance(factors, Basic) and not factors.args: + factors = {factors: S.One} + elif isinstance(factors, Expr): + c, nc = factors.args_cnc() + i = c.count(I) + for _ in range(i): + c.remove(I) + factors = dict(Mul._from_args(c).as_powers_dict()) + # Handle all rational Coefficients + for f in list(factors.keys()): + if isinstance(f, Rational) and not isinstance(f, Integer): + p, q = Integer(f.p), Integer(f.q) + factors[p] = (factors[p] if p in factors else S.Zero) + factors[f] + factors[q] = (factors[q] if q in factors else S.Zero) - factors[f] + factors.pop(f) + if i: + factors[I] = factors.get(I, S.Zero) + i + if nc: + factors[Mul(*nc, evaluate=False)] = S.One + else: + factors = factors.copy() # /!\ should be dict-like + + # tidy up -/+1 and I exponents if Rational + + handle = [k for k in factors if k is I or k in (-1, 1)] + if handle: + i1 = S.One + for k in handle: + if not _isnumber(factors[k]): + continue + i1 *= k**factors.pop(k) + if i1 is not S.One: + for a in i1.args if i1.is_Mul else [i1]: # at worst, -1.0*I*(-1)**e + if a is S.NegativeOne: + factors[a] = S.One + elif a is I: + factors[I] = S.One + elif a.is_Pow: + factors[a.base] = factors.get(a.base, S.Zero) + a.exp + elif equal_valued(a, 1): + factors[a] = S.One + elif equal_valued(a, -1): + factors[-a] = S.One + factors[S.NegativeOne] = S.One + else: + raise ValueError('unexpected factor in i1: %s' % a) + + self.factors = factors + keys = getattr(factors, 'keys', None) + if keys is None: + raise TypeError('expecting Expr or dictionary') + self.gens = frozenset(keys()) + + def __hash__(self): # Factors + keys = tuple(ordered(self.factors.keys())) + values = [self.factors[k] for k in keys] + return hash((keys, values)) + + def __repr__(self): # Factors + return "Factors({%s})" % ', '.join( + ['%s: %s' % (k, v) for k, v in ordered(self.factors.items())]) + + @property + def is_zero(self): # Factors + """ + >>> from sympy.core.exprtools import Factors + >>> Factors(0).is_zero + True + """ + f = self.factors + return len(f) == 1 and S.Zero in f + + @property + def is_one(self): # Factors + """ + >>> from sympy.core.exprtools import Factors + >>> Factors(1).is_one + True + """ + return not self.factors + + def as_expr(self): # Factors + """Return the underlying expression. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y + >>> Factors((x*y**2).as_powers_dict()).as_expr() + x*y**2 + + """ + + args = [] + for factor, exp in self.factors.items(): + if exp != 1: + if isinstance(exp, Integer): + b, e = factor.as_base_exp() + e = _keep_coeff(exp, e) + args.append(b**e) + else: + args.append(factor**exp) + else: + args.append(factor) + return Mul(*args) + + def mul(self, other): # Factors + """Return Factors of ``self * other``. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> a = Factors((x*y**2).as_powers_dict()) + >>> b = Factors((x*y/z).as_powers_dict()) + >>> a.mul(b) + Factors({x: 2, y: 3, z: -1}) + >>> a*b + Factors({x: 2, y: 3, z: -1}) + """ + if not isinstance(other, Factors): + other = Factors(other) + if any(f.is_zero for f in (self, other)): + return Factors(S.Zero) + factors = dict(self.factors) + + for factor, exp in other.factors.items(): + if factor in factors: + exp = factors[factor] + exp + + if not exp: + del factors[factor] + continue + + factors[factor] = exp + + return Factors(factors) + + def normal(self, other): + """Return ``self`` and ``other`` with ``gcd`` removed from each. + The only differences between this and method ``div`` is that this + is 1) optimized for the case when there are few factors in common and + 2) this does not raise an error if ``other`` is zero. + + See Also + ======== + div + + """ + if not isinstance(other, Factors): + other = Factors(other) + if other.is_zero: + return (Factors(), Factors(S.Zero)) + if self.is_zero: + return (Factors(S.Zero), Factors()) + + self_factors = dict(self.factors) + other_factors = dict(other.factors) + + for factor, self_exp in self.factors.items(): + try: + other_exp = other.factors[factor] + except KeyError: + continue + + exp = self_exp - other_exp + + if not exp: + del self_factors[factor] + del other_factors[factor] + elif _isnumber(exp): + if exp > 0: + self_factors[factor] = exp + del other_factors[factor] + else: + del self_factors[factor] + other_factors[factor] = -exp + else: + r = self_exp.extract_additively(other_exp) + if r is not None: + if r: + self_factors[factor] = r + del other_factors[factor] + else: # should be handled already + del self_factors[factor] + del other_factors[factor] + else: + sc, sa = self_exp.as_coeff_Add() + if sc: + oc, oa = other_exp.as_coeff_Add() + diff = sc - oc + if diff > 0: + self_factors[factor] -= oc + other_exp = oa + elif diff < 0: + self_factors[factor] -= sc + other_factors[factor] -= sc + other_exp = oa - diff + else: + self_factors[factor] = sa + other_exp = oa + if other_exp: + other_factors[factor] = other_exp + else: + del other_factors[factor] + + return Factors(self_factors), Factors(other_factors) + + def div(self, other): # Factors + """Return ``self`` and ``other`` with ``gcd`` removed from each. + This is optimized for the case when there are many factors in common. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> from sympy import S + + >>> a = Factors((x*y**2).as_powers_dict()) + >>> a.div(a) + (Factors({}), Factors({})) + >>> a.div(x*z) + (Factors({y: 2}), Factors({z: 1})) + + The ``/`` operator only gives ``quo``: + + >>> a/x + Factors({y: 2}) + + Factors treats its factors as though they are all in the numerator, so + if you violate this assumption the results will be correct but will + not strictly correspond to the numerator and denominator of the ratio: + + >>> a.div(x/z) + (Factors({y: 2}), Factors({z: -1})) + + Factors is also naive about bases: it does not attempt any denesting + of Rational-base terms, for example the following does not become + 2**(2*x)/2. + + >>> Factors(2**(2*x + 2)).div(S(8)) + (Factors({2: 2*x + 2}), Factors({8: 1})) + + factor_terms can clean up such Rational-bases powers: + + >>> from sympy import factor_terms + >>> n, d = Factors(2**(2*x + 2)).div(S(8)) + >>> n.as_expr()/d.as_expr() + 2**(2*x + 2)/8 + >>> factor_terms(_) + 2**(2*x)/2 + + """ + quo, rem = dict(self.factors), {} + + if not isinstance(other, Factors): + other = Factors(other) + if other.is_zero: + raise ZeroDivisionError + if self.is_zero: + return (Factors(S.Zero), Factors()) + + for factor, exp in other.factors.items(): + if factor in quo: + d = quo[factor] - exp + if _isnumber(d): + if d <= 0: + del quo[factor] + + if d >= 0: + if d: + quo[factor] = d + + continue + + exp = -d + + else: + r = quo[factor].extract_additively(exp) + if r is not None: + if r: + quo[factor] = r + else: # should be handled already + del quo[factor] + else: + other_exp = exp + sc, sa = quo[factor].as_coeff_Add() + if sc: + oc, oa = other_exp.as_coeff_Add() + diff = sc - oc + if diff > 0: + quo[factor] -= oc + other_exp = oa + elif diff < 0: + quo[factor] -= sc + other_exp = oa - diff + else: + quo[factor] = sa + other_exp = oa + if other_exp: + rem[factor] = other_exp + else: + assert factor not in rem + continue + + rem[factor] = exp + + return Factors(quo), Factors(rem) + + def quo(self, other): # Factors + """Return numerator Factor of ``self / other``. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> a = Factors((x*y**2).as_powers_dict()) + >>> b = Factors((x*y/z).as_powers_dict()) + >>> a.quo(b) # same as a/b + Factors({y: 1}) + """ + return self.div(other)[0] + + def rem(self, other): # Factors + """Return denominator Factors of ``self / other``. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> a = Factors((x*y**2).as_powers_dict()) + >>> b = Factors((x*y/z).as_powers_dict()) + >>> a.rem(b) + Factors({z: -1}) + >>> a.rem(a) + Factors({}) + """ + return self.div(other)[1] + + def pow(self, other): # Factors + """Return self raised to a non-negative integer power. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y + >>> a = Factors((x*y**2).as_powers_dict()) + >>> a**2 + Factors({x: 2, y: 4}) + + """ + if isinstance(other, Factors): + other = other.as_expr() + if other.is_Integer: + other = int(other) + if isinstance(other, SYMPY_INTS) and other >= 0: + factors = {} + + if other: + for factor, exp in self.factors.items(): + factors[factor] = exp*other + + return Factors(factors) + else: + raise ValueError("expected non-negative integer, got %s" % other) + + def gcd(self, other): # Factors + """Return Factors of ``gcd(self, other)``. The keys are + the intersection of factors with the minimum exponent for + each factor. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> a = Factors((x*y**2).as_powers_dict()) + >>> b = Factors((x*y/z).as_powers_dict()) + >>> a.gcd(b) + Factors({x: 1, y: 1}) + """ + if not isinstance(other, Factors): + other = Factors(other) + if other.is_zero: + return Factors(self.factors) + + factors = {} + + for factor, exp in self.factors.items(): + factor, exp = sympify(factor), sympify(exp) + if factor in other.factors: + lt = (exp - other.factors[factor]).is_negative + if lt == True: + factors[factor] = exp + elif lt == False: + factors[factor] = other.factors[factor] + + return Factors(factors) + + def lcm(self, other): # Factors + """Return Factors of ``lcm(self, other)`` which are + the union of factors with the maximum exponent for + each factor. + + Examples + ======== + + >>> from sympy.core.exprtools import Factors + >>> from sympy.abc import x, y, z + >>> a = Factors((x*y**2).as_powers_dict()) + >>> b = Factors((x*y/z).as_powers_dict()) + >>> a.lcm(b) + Factors({x: 1, y: 2, z: -1}) + """ + if not isinstance(other, Factors): + other = Factors(other) + if any(f.is_zero for f in (self, other)): + return Factors(S.Zero) + + factors = dict(self.factors) + + for factor, exp in other.factors.items(): + if factor in factors: + exp = max(exp, factors[factor]) + + factors[factor] = exp + + return Factors(factors) + + def __mul__(self, other): # Factors + return self.mul(other) + + def __divmod__(self, other): # Factors + return self.div(other) + + def __truediv__(self, other): # Factors + return self.quo(other) + + def __mod__(self, other): # Factors + return self.rem(other) + + def __pow__(self, other): # Factors + return self.pow(other) + + def __eq__(self, other): # Factors + if not isinstance(other, Factors): + other = Factors(other) + return self.factors == other.factors + + def __ne__(self, other): # Factors + return not self == other + + +class Term: + """Efficient representation of ``coeff*(numer/denom)``. """ + + __slots__ = ('coeff', 'numer', 'denom') + + def __init__(self, term, numer=None, denom=None): # Term + if numer is None and denom is None: + if not term.is_commutative: + raise NonCommutativeExpression( + 'commutative expression expected') + + coeff, factors = term.as_coeff_mul() + numer, denom = defaultdict(int), defaultdict(int) + + for factor in factors: + base, exp = decompose_power(factor) + + if base.is_Add: + cont, base = base.primitive() + coeff *= cont**exp + + if exp > 0: + numer[base] += exp + else: + denom[base] += -exp + + numer = Factors(numer) + denom = Factors(denom) + else: + coeff = term + + if numer is None: + numer = Factors() + + if denom is None: + denom = Factors() + + self.coeff = coeff + self.numer = numer + self.denom = denom + + def __hash__(self): # Term + return hash((self.coeff, self.numer, self.denom)) + + def __repr__(self): # Term + return "Term(%s, %s, %s)" % (self.coeff, self.numer, self.denom) + + def as_expr(self): # Term + return self.coeff*(self.numer.as_expr()/self.denom.as_expr()) + + def mul(self, other): # Term + coeff = self.coeff*other.coeff + numer = self.numer.mul(other.numer) + denom = self.denom.mul(other.denom) + + numer, denom = numer.normal(denom) + + return Term(coeff, numer, denom) + + def inv(self): # Term + return Term(1/self.coeff, self.denom, self.numer) + + def quo(self, other): # Term + return self.mul(other.inv()) + + def pow(self, other): # Term + if other < 0: + return self.inv().pow(-other) + else: + return Term(self.coeff ** other, + self.numer.pow(other), + self.denom.pow(other)) + + def gcd(self, other): # Term + return Term(self.coeff.gcd(other.coeff), + self.numer.gcd(other.numer), + self.denom.gcd(other.denom)) + + def lcm(self, other): # Term + return Term(self.coeff.lcm(other.coeff), + self.numer.lcm(other.numer), + self.denom.lcm(other.denom)) + + def __mul__(self, other): # Term + if isinstance(other, Term): + return self.mul(other) + else: + return NotImplemented + + def __truediv__(self, other): # Term + if isinstance(other, Term): + return self.quo(other) + else: + return NotImplemented + + def __pow__(self, other): # Term + if isinstance(other, SYMPY_INTS): + return self.pow(other) + else: + return NotImplemented + + def __eq__(self, other): # Term + return (self.coeff == other.coeff and + self.numer == other.numer and + self.denom == other.denom) + + def __ne__(self, other): # Term + return not self == other + + +def _gcd_terms(terms, isprimitive=False, fraction=True): + """Helper function for :func:`gcd_terms`. + + Parameters + ========== + + isprimitive : boolean, optional + If ``isprimitive`` is True then the call to primitive + for an Add will be skipped. This is useful when the + content has already been extracted. + + fraction : boolean, optional + If ``fraction`` is True then the expression will appear over a common + denominator, the lcm of all term denominators. + """ + + if isinstance(terms, Basic) and not isinstance(terms, Tuple): + terms = Add.make_args(terms) + + terms = list(map(Term, [t for t in terms if t])) + + # there is some simplification that may happen if we leave this + # here rather than duplicate it before the mapping of Term onto + # the terms + if len(terms) == 0: + return S.Zero, S.Zero, S.One + + if len(terms) == 1: + cont = terms[0].coeff + numer = terms[0].numer.as_expr() + denom = terms[0].denom.as_expr() + + else: + cont = terms[0] + for term in terms[1:]: + cont = cont.gcd(term) + + for i, term in enumerate(terms): + terms[i] = term.quo(cont) + + if fraction: + denom = terms[0].denom + + for term in terms[1:]: + denom = denom.lcm(term.denom) + + numers = [] + for term in terms: + numer = term.numer.mul(denom.quo(term.denom)) + numers.append(term.coeff*numer.as_expr()) + else: + numers = [t.as_expr() for t in terms] + denom = Term(S.One).numer + + cont = cont.as_expr() + numer = Add(*numers) + denom = denom.as_expr() + + if not isprimitive and numer.is_Add: + _cont, numer = numer.primitive() + cont *= _cont + + return cont, numer, denom + + +def gcd_terms(terms, isprimitive=False, clear=True, fraction=True): + """Compute the GCD of ``terms`` and put them together. + + Parameters + ========== + + terms : Expr + Can be an expression or a non-Basic sequence of expressions + which will be handled as though they are terms from a sum. + + isprimitive : bool, optional + If ``isprimitive`` is True the _gcd_terms will not run the primitive + method on the terms. + + clear : bool, optional + It controls the removal of integers from the denominator of an Add + expression. When True (default), all numerical denominator will be cleared; + when False the denominators will be cleared only if all terms had numerical + denominators other than 1. + + fraction : bool, optional + When True (default), will put the expression over a common + denominator. + + Examples + ======== + + >>> from sympy import gcd_terms + >>> from sympy.abc import x, y + + >>> gcd_terms((x + 1)**2*y + (x + 1)*y**2) + y*(x + 1)*(x + y + 1) + >>> gcd_terms(x/2 + 1) + (x + 2)/2 + >>> gcd_terms(x/2 + 1, clear=False) + x/2 + 1 + >>> gcd_terms(x/2 + y/2, clear=False) + (x + y)/2 + >>> gcd_terms(x/2 + 1/x) + (x**2 + 2)/(2*x) + >>> gcd_terms(x/2 + 1/x, fraction=False) + (x + 2/x)/2 + >>> gcd_terms(x/2 + 1/x, fraction=False, clear=False) + x/2 + 1/x + + >>> gcd_terms(x/2/y + 1/x/y) + (x**2 + 2)/(2*x*y) + >>> gcd_terms(x/2/y + 1/x/y, clear=False) + (x**2/2 + 1)/(x*y) + >>> gcd_terms(x/2/y + 1/x/y, clear=False, fraction=False) + (x/2 + 1/x)/y + + The ``clear`` flag was ignored in this case because the returned + expression was a rational expression, not a simple sum. + + See Also + ======== + + factor_terms, sympy.polys.polytools.terms_gcd + + """ + def mask(terms): + """replace nc portions of each term with a unique Dummy symbols + and return the replacements to restore them""" + args = [(a, []) if a.is_commutative else a.args_cnc() for a in terms] + reps = [] + for i, (c, nc) in enumerate(args): + if nc: + nc = Mul(*nc) + d = Dummy() + reps.append((d, nc)) + c.append(d) + args[i] = Mul(*c) + else: + args[i] = c + return args, dict(reps) + + isadd = isinstance(terms, Add) + addlike = isadd or not isinstance(terms, Basic) and \ + is_sequence(terms, include=set) and \ + not isinstance(terms, Dict) + + if addlike: + if isadd: # i.e. an Add + terms = list(terms.args) + else: + terms = sympify(terms) + terms, reps = mask(terms) + cont, numer, denom = _gcd_terms(terms, isprimitive, fraction) + numer = numer.xreplace(reps) + coeff, factors = cont.as_coeff_Mul() + if not clear: + c, _coeff = coeff.as_coeff_Mul() + if not c.is_Integer and not clear and numer.is_Add: + n, d = c.as_numer_denom() + _numer = numer/d + if any(a.as_coeff_Mul()[0].is_Integer + for a in _numer.args): + numer = _numer + coeff = n*_coeff + return _keep_coeff(coeff, factors*numer/denom, clear=clear) + + if not isinstance(terms, Basic): + return terms + + if terms.is_Atom: + return terms + + if terms.is_Mul: + c, args = terms.as_coeff_mul() + return _keep_coeff(c, Mul(*[gcd_terms(i, isprimitive, clear, fraction) + for i in args]), clear=clear) + + def handle(a): + # don't treat internal args like terms of an Add + if not isinstance(a, Expr): + if isinstance(a, Basic): + if not a.args: + return a + return a.func(*[handle(i) for i in a.args]) + return type(a)([handle(i) for i in a]) + return gcd_terms(a, isprimitive, clear, fraction) + + if isinstance(terms, Dict): + return Dict(*[(k, handle(v)) for k, v in terms.args]) + return terms.func(*[handle(i) for i in terms.args]) + + +def _factor_sum_int(expr, **kwargs): + """Return Sum or Integral object with factors that are not + in the wrt variables removed. In cases where there are additive + terms in the function of the object that are independent, the + object will be separated into two objects. + + Examples + ======== + + >>> from sympy import Sum, factor_terms + >>> from sympy.abc import x, y + >>> factor_terms(Sum(x + y, (x, 1, 3))) + y*Sum(1, (x, 1, 3)) + Sum(x, (x, 1, 3)) + >>> factor_terms(Sum(x*y, (x, 1, 3))) + y*Sum(x, (x, 1, 3)) + + Notes + ===== + + If a function in the summand or integrand is replaced + with a symbol, then this simplification should not be + done or else an incorrect result will be obtained when + the symbol is replaced with an expression that depends + on the variables of summation/integration: + + >>> eq = Sum(y, (x, 1, 3)) + >>> factor_terms(eq).subs(y, x).doit() + 3*x + >>> eq.subs(y, x).doit() + 6 + """ + result = expr.function + if result == 0: + return S.Zero + limits = expr.limits + + # get the wrt variables + wrt = {i.args[0] for i in limits} + + # factor out any common terms that are independent of wrt + f = factor_terms(result, **kwargs) + i, d = f.as_independent(*wrt) + if isinstance(f, Add): + return i * expr.func(1, *limits) + expr.func(d, *limits) + else: + return i * expr.func(d, *limits) + + +def factor_terms(expr, radical=False, clear=False, fraction=False, sign=True): + """Remove common factors from terms in all arguments without + changing the underlying structure of the expr. No expansion or + simplification (and no processing of non-commutatives) is performed. + + Parameters + ========== + + radical: bool, optional + If radical=True then a radical common to all terms will be factored + out of any Add sub-expressions of the expr. + + clear : bool, optional + If clear=False (default) then coefficients will not be separated + from a single Add if they can be distributed to leave one or more + terms with integer coefficients. + + fraction : bool, optional + If fraction=True (default is False) then a common denominator will be + constructed for the expression. + + sign : bool, optional + If sign=True (default) then even if the only factor in common is a -1, + it will be factored out of the expression. + + Examples + ======== + + >>> from sympy import factor_terms, Symbol + >>> from sympy.abc import x, y + >>> factor_terms(x + x*(2 + 4*y)**3) + x*(8*(2*y + 1)**3 + 1) + >>> A = Symbol('A', commutative=False) + >>> factor_terms(x*A + x*A + x*y*A) + x*(y*A + 2*A) + + When ``clear`` is False, a rational will only be factored out of an + Add expression if all terms of the Add have coefficients that are + fractions: + + >>> factor_terms(x/2 + 1, clear=False) + x/2 + 1 + >>> factor_terms(x/2 + 1, clear=True) + (x + 2)/2 + + If a -1 is all that can be factored out, to *not* factor it out, the + flag ``sign`` must be False: + + >>> factor_terms(-x - y) + -(x + y) + >>> factor_terms(-x - y, sign=False) + -x - y + >>> factor_terms(-2*x - 2*y, sign=False) + -2*(x + y) + + See Also + ======== + + gcd_terms, sympy.polys.polytools.terms_gcd + + """ + def do(expr): + from sympy.concrete.summations import Sum + from sympy.integrals.integrals import Integral + is_iterable = iterable(expr) + + if not isinstance(expr, Basic) or expr.is_Atom: + if is_iterable: + return type(expr)([do(i) for i in expr]) + return expr + + if expr.is_Pow or expr.is_Function or \ + is_iterable or not hasattr(expr, 'args_cnc'): + args = expr.args + newargs = tuple([do(i) for i in args]) + if newargs == args: + return expr + return expr.func(*newargs) + + if isinstance(expr, (Sum, Integral)): + return _factor_sum_int(expr, + radical=radical, clear=clear, + fraction=fraction, sign=sign) + + cont, p = expr.as_content_primitive(radical=radical, clear=clear) + if p.is_Add: + list_args = [do(a) for a in Add.make_args(p)] + # get a common negative (if there) which gcd_terms does not remove + if not any(a.as_coeff_Mul()[0].extract_multiplicatively(-1) is None + for a in list_args): + cont = -cont + list_args = [-a for a in list_args] + # watch out for exp(-(x+2)) which gcd_terms will change to exp(-x-2) + special = {} + for i, a in enumerate(list_args): + b, e = a.as_base_exp() + if e.is_Mul and e != Mul(*e.args): + list_args[i] = Dummy() + special[list_args[i]] = a + # rebuild p not worrying about the order which gcd_terms will fix + p = Add._from_args(list_args) + p = gcd_terms(p, + isprimitive=True, + clear=clear, + fraction=fraction).xreplace(special) + elif p.args: + p = p.func( + *[do(a) for a in p.args]) + rv = _keep_coeff(cont, p, clear=clear, sign=sign) + return rv + expr = sympify(expr) + return do(expr) + + +def _mask_nc(eq, name=None): + """ + Return ``eq`` with non-commutative objects replaced with Dummy + symbols. A dictionary that can be used to restore the original + values is returned: if it is None, the expression is noncommutative + and cannot be made commutative. The third value returned is a list + of any non-commutative symbols that appear in the returned equation. + + Explanation + =========== + + All non-commutative objects other than Symbols are replaced with + a non-commutative Symbol. Identical objects will be identified + by identical symbols. + + If there is only 1 non-commutative object in an expression it will + be replaced with a commutative symbol. Otherwise, the non-commutative + entities are retained and the calling routine should handle + replacements in this case since some care must be taken to keep + track of the ordering of symbols when they occur within Muls. + + Parameters + ========== + + name : str + ``name``, if given, is the name that will be used with numbered Dummy + variables that will replace the non-commutative objects and is mainly + used for doctesting purposes. + + Examples + ======== + + >>> from sympy.physics.secondquant import Commutator, NO, F, Fd + >>> from sympy import symbols + >>> from sympy.core.exprtools import _mask_nc + >>> from sympy.abc import x, y + >>> A, B, C = symbols('A,B,C', commutative=False) + + One nc-symbol: + + >>> _mask_nc(A**2 - x**2, 'd') + (_d0**2 - x**2, {_d0: A}, []) + + Multiple nc-symbols: + + >>> _mask_nc(A**2 - B**2, 'd') + (A**2 - B**2, {}, [A, B]) + + An nc-object with nc-symbols but no others outside of it: + + >>> _mask_nc(1 + x*Commutator(A, B), 'd') + (_d0*x + 1, {_d0: Commutator(A, B)}, []) + >>> _mask_nc(NO(Fd(x)*F(y)), 'd') + (_d0, {_d0: NO(CreateFermion(x)*AnnihilateFermion(y))}, []) + + Multiple nc-objects: + + >>> eq = x*Commutator(A, B) + x*Commutator(A, C)*Commutator(A, B) + >>> _mask_nc(eq, 'd') + (x*_d0 + x*_d1*_d0, {_d0: Commutator(A, B), _d1: Commutator(A, C)}, [_d0, _d1]) + + Multiple nc-objects and nc-symbols: + + >>> eq = A*Commutator(A, B) + B*Commutator(A, C) + >>> _mask_nc(eq, 'd') + (A*_d0 + B*_d1, {_d0: Commutator(A, B), _d1: Commutator(A, C)}, [_d0, _d1, A, B]) + + """ + name = name or 'mask' + # Make Dummy() append sequential numbers to the name + + def numbered_names(): + i = 0 + while True: + yield name + str(i) + i += 1 + + names = numbered_names() + + def Dummy(*args, **kwargs): + from .symbol import Dummy + return Dummy(next(names), *args, **kwargs) + + expr = eq + if expr.is_commutative: + return eq, {}, [] + + # identify nc-objects; symbols and other + rep = [] + nc_obj = set() + nc_syms = set() + pot = preorder_traversal(expr, keys=default_sort_key) + for i, a in enumerate(pot): + if any(a == r[0] for r in rep): + pot.skip() + elif not a.is_commutative: + if a.is_symbol: + nc_syms.add(a) + pot.skip() + elif not (a.is_Add or a.is_Mul or a.is_Pow): + nc_obj.add(a) + pot.skip() + + # If there is only one nc symbol or object, it can be factored regularly + # but polys is going to complain, so replace it with a Dummy. + if len(nc_obj) == 1 and not nc_syms: + rep.append((nc_obj.pop(), Dummy())) + elif len(nc_syms) == 1 and not nc_obj: + rep.append((nc_syms.pop(), Dummy())) + + # Any remaining nc-objects will be replaced with an nc-Dummy and + # identified as an nc-Symbol to watch out for + nc_obj = sorted(nc_obj, key=default_sort_key) + for n in nc_obj: + nc = Dummy(commutative=False) + rep.append((n, nc)) + nc_syms.add(nc) + expr = expr.subs(rep) + + nc_syms = list(nc_syms) + nc_syms.sort(key=default_sort_key) + return expr, {v: k for k, v in rep}, nc_syms + + +def factor_nc(expr): + """Return the factored form of ``expr`` while handling non-commutative + expressions. + + Examples + ======== + + >>> from sympy import factor_nc, Symbol + >>> from sympy.abc import x + >>> A = Symbol('A', commutative=False) + >>> B = Symbol('B', commutative=False) + >>> factor_nc((x**2 + 2*A*x + A**2).expand()) + (x + A)**2 + >>> factor_nc(((x + A)*(x + B)).expand()) + (x + A)*(x + B) + """ + expr = sympify(expr) + if not isinstance(expr, Expr) or not expr.args: + return expr + if not expr.is_Add: + return expr.func(*[factor_nc(a) for a in expr.args]) + expr = expr.func(*[expand_power_exp(i) for i in expr.args]) + + from sympy.polys.polytools import gcd, factor + expr, rep, nc_symbols = _mask_nc(expr) + + if rep: + return factor(expr).subs(rep) + else: + args = [a.args_cnc() for a in Add.make_args(expr)] + c = g = l = r = S.One + hit = False + # find any commutative gcd term + for i, a in enumerate(args): + if i == 0: + c = Mul._from_args(a[0]) + elif a[0]: + c = gcd(c, Mul._from_args(a[0])) + else: + c = S.One + if c is not S.One: + hit = True + c, g = c.as_coeff_Mul() + if g is not S.One: + for i, (cc, _) in enumerate(args): + cc = list(Mul.make_args(Mul._from_args(list(cc))/g)) + args[i][0] = cc + for i, (cc, _) in enumerate(args): + if cc: + cc[0] = cc[0]/c + else: + cc = [1/c] + args[i][0] = cc + # find any noncommutative common prefix + for i, a in enumerate(args): + if i == 0: + n = a[1][:] + else: + n = common_prefix(n, a[1]) + if not n: + # is there a power that can be extracted? + if not args[0][1]: + break + b, e = args[0][1][0].as_base_exp() + ok = False + if e.is_Integer: + for t in args: + if not t[1]: + break + bt, et = t[1][0].as_base_exp() + if et.is_Integer and bt == b: + e = min(e, et) + else: + break + else: + ok = hit = True + l = b**e + il = b**-e + for _ in args: + _[1][0] = il*_[1][0] + break + if not ok: + break + else: + hit = True + lenn = len(n) + l = Mul(*n) + for _ in args: + _[1] = _[1][lenn:] + # find any noncommutative common suffix + for i, a in enumerate(args): + if i == 0: + n = a[1][:] + else: + n = common_suffix(n, a[1]) + if not n: + # is there a power that can be extracted? + if not args[0][1]: + break + b, e = args[0][1][-1].as_base_exp() + ok = False + if e.is_Integer: + for t in args: + if not t[1]: + break + bt, et = t[1][-1].as_base_exp() + if et.is_Integer and bt == b: + e = min(e, et) + else: + break + else: + ok = hit = True + r = b**e + il = b**-e + for _ in args: + _[1][-1] = _[1][-1]*il + break + if not ok: + break + else: + hit = True + lenn = len(n) + r = Mul(*n) + for _ in args: + _[1] = _[1][:len(_[1]) - lenn] + if hit: + mid = Add(*[Mul(*cc)*Mul(*nc) for cc, nc in args]) + else: + mid = expr + + from sympy.simplify.powsimp import powsimp + + # sort the symbols so the Dummys would appear in the same + # order as the original symbols, otherwise you may introduce + # a factor of -1, e.g. A**2 - B**2) -- {A:y, B:x} --> y**2 - x**2 + # and the former factors into two terms, (A - B)*(A + B) while the + # latter factors into 3 terms, (-1)*(x - y)*(x + y) + rep1 = [(n, Dummy()) for n in sorted(nc_symbols, key=default_sort_key)] + unrep1 = [(v, k) for k, v in rep1] + unrep1.reverse() + new_mid, r2, _ = _mask_nc(mid.subs(rep1)) + new_mid = powsimp(factor(new_mid)) + + new_mid = new_mid.subs(r2).subs(unrep1) + + if new_mid.is_Pow: + return _keep_coeff(c, g*l*new_mid*r) + + if new_mid.is_Mul: + def _pemexpand(expr): + "Expand with the minimal set of hints necessary to check the result." + return expr.expand(deep=True, mul=True, power_exp=True, + power_base=False, basic=False, multinomial=True, log=False) + # XXX TODO there should be a way to inspect what order the terms + # must be in and just select the plausible ordering without + # checking permutations + cfac = [] + ncfac = [] + for f in new_mid.args: + if f.is_commutative: + cfac.append(f) + else: + b, e = f.as_base_exp() + if e.is_Integer: + ncfac.extend([b]*e) + else: + ncfac.append(f) + pre_mid = g*Mul(*cfac)*l + target = _pemexpand(expr/c) + for s in variations(ncfac, len(ncfac)): + ok = pre_mid*Mul(*s)*r + if _pemexpand(ok) == target: + return _keep_coeff(c, ok) + + # mid was an Add that didn't factor successfully + return _keep_coeff(c, g*l*mid*r) diff --git a/lib/python3.11/site-packages/sympy/core/facts.py b/lib/python3.11/site-packages/sympy/core/facts.py new file mode 100644 index 0000000000000000000000000000000000000000..0b98d9b14bbac661d3c0fd1d1fd87977a792fb74 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/facts.py @@ -0,0 +1,634 @@ +r"""This is rule-based deduction system for SymPy + +The whole thing is split into two parts + + - rules compilation and preparation of tables + - runtime inference + +For rule-based inference engines, the classical work is RETE algorithm [1], +[2] Although we are not implementing it in full (or even significantly) +it's still worth a read to understand the underlying ideas. + +In short, every rule in a system of rules is one of two forms: + + - atom -> ... (alpha rule) + - And(atom1, atom2, ...) -> ... (beta rule) + + +The major complexity is in efficient beta-rules processing and usually for an +expert system a lot of effort goes into code that operates on beta-rules. + + +Here we take minimalistic approach to get something usable first. + + - (preparation) of alpha- and beta- networks, everything except + - (runtime) FactRules.deduce_all_facts + + _____________________________________ + ( Kirr: I've never thought that doing ) + ( logic stuff is that difficult... ) + ------------------------------------- + o ^__^ + o (oo)\_______ + (__)\ )\/\ + ||----w | + || || + + +Some references on the topic +---------------------------- + +[1] https://en.wikipedia.org/wiki/Rete_algorithm +[2] http://reports-archive.adm.cs.cmu.edu/anon/1995/CMU-CS-95-113.pdf + +https://en.wikipedia.org/wiki/Propositional_formula +https://en.wikipedia.org/wiki/Inference_rule +https://en.wikipedia.org/wiki/List_of_rules_of_inference +""" + +from collections import defaultdict +from typing import Iterator + +from .logic import Logic, And, Or, Not + + +def _base_fact(atom): + """Return the literal fact of an atom. + + Effectively, this merely strips the Not around a fact. + """ + if isinstance(atom, Not): + return atom.arg + else: + return atom + + +def _as_pair(atom): + if isinstance(atom, Not): + return (atom.arg, False) + else: + return (atom, True) + +# XXX this prepares forward-chaining rules for alpha-network + + +def transitive_closure(implications): + """ + Computes the transitive closure of a list of implications + + Uses Warshall's algorithm, as described at + http://www.cs.hope.edu/~cusack/Notes/Notes/DiscreteMath/Warshall.pdf. + """ + full_implications = set(implications) + literals = set().union(*map(set, full_implications)) + + for k in literals: + for i in literals: + if (i, k) in full_implications: + for j in literals: + if (k, j) in full_implications: + full_implications.add((i, j)) + + return full_implications + + +def deduce_alpha_implications(implications): + """deduce all implications + + Description by example + ---------------------- + + given set of logic rules: + + a -> b + b -> c + + we deduce all possible rules: + + a -> b, c + b -> c + + + implications: [] of (a,b) + return: {} of a -> set([b, c, ...]) + """ + implications = implications + [(Not(j), Not(i)) for (i, j) in implications] + res = defaultdict(set) + full_implications = transitive_closure(implications) + for a, b in full_implications: + if a == b: + continue # skip a->a cyclic input + + res[a].add(b) + + # Clean up tautologies and check consistency + for a, impl in res.items(): + impl.discard(a) + na = Not(a) + if na in impl: + raise ValueError( + 'implications are inconsistent: %s -> %s %s' % (a, na, impl)) + + return res + + +def apply_beta_to_alpha_route(alpha_implications, beta_rules): + """apply additional beta-rules (And conditions) to already-built + alpha implication tables + + TODO: write about + + - static extension of alpha-chains + - attaching refs to beta-nodes to alpha chains + + + e.g. + + alpha_implications: + + a -> [b, !c, d] + b -> [d] + ... + + + beta_rules: + + &(b,d) -> e + + + then we'll extend a's rule to the following + + a -> [b, !c, d, e] + """ + x_impl = {} + for x in alpha_implications.keys(): + x_impl[x] = (set(alpha_implications[x]), []) + for bcond, bimpl in beta_rules: + for bk in bcond.args: + if bk in x_impl: + continue + x_impl[bk] = (set(), []) + + # static extensions to alpha rules: + # A: x -> a,b B: &(a,b) -> c ==> A: x -> a,b,c + seen_static_extension = True + while seen_static_extension: + seen_static_extension = False + + for bcond, bimpl in beta_rules: + if not isinstance(bcond, And): + raise TypeError("Cond is not And") + bargs = set(bcond.args) + for x, (ximpls, bb) in x_impl.items(): + x_all = ximpls | {x} + # A: ... -> a B: &(...) -> a is non-informative + if bimpl not in x_all and bargs.issubset(x_all): + ximpls.add(bimpl) + + # we introduced new implication - now we have to restore + # completeness of the whole set. + bimpl_impl = x_impl.get(bimpl) + if bimpl_impl is not None: + ximpls |= bimpl_impl[0] + seen_static_extension = True + + # attach beta-nodes which can be possibly triggered by an alpha-chain + for bidx, (bcond, bimpl) in enumerate(beta_rules): + bargs = set(bcond.args) + for x, (ximpls, bb) in x_impl.items(): + x_all = ximpls | {x} + # A: ... -> a B: &(...) -> a (non-informative) + if bimpl in x_all: + continue + # A: x -> a... B: &(!a,...) -> ... (will never trigger) + # A: x -> a... B: &(...) -> !a (will never trigger) + if any(Not(xi) in bargs or Not(xi) == bimpl for xi in x_all): + continue + + if bargs & x_all: + bb.append(bidx) + + return x_impl + + +def rules_2prereq(rules): + """build prerequisites table from rules + + Description by example + ---------------------- + + given set of logic rules: + + a -> b, c + b -> c + + we build prerequisites (from what points something can be deduced): + + b <- a + c <- a, b + + rules: {} of a -> [b, c, ...] + return: {} of c <- [a, b, ...] + + Note however, that this prerequisites may be *not* enough to prove a + fact. An example is 'a -> b' rule, where prereq(a) is b, and prereq(b) + is a. That's because a=T -> b=T, and b=F -> a=F, but a=F -> b=? + """ + prereq = defaultdict(set) + for (a, _), impl in rules.items(): + if isinstance(a, Not): + a = a.args[0] + for (i, _) in impl: + if isinstance(i, Not): + i = i.args[0] + prereq[i].add(a) + return prereq + +################ +# RULES PROVER # +################ + + +class TautologyDetected(Exception): + """(internal) Prover uses it for reporting detected tautology""" + pass + + +class Prover: + """ai - prover of logic rules + + given a set of initial rules, Prover tries to prove all possible rules + which follow from given premises. + + As a result proved_rules are always either in one of two forms: alpha or + beta: + + Alpha rules + ----------- + + This are rules of the form:: + + a -> b & c & d & ... + + + Beta rules + ---------- + + This are rules of the form:: + + &(a,b,...) -> c & d & ... + + + i.e. beta rules are join conditions that say that something follows when + *several* facts are true at the same time. + """ + + def __init__(self): + self.proved_rules = [] + self._rules_seen = set() + + def split_alpha_beta(self): + """split proved rules into alpha and beta chains""" + rules_alpha = [] # a -> b + rules_beta = [] # &(...) -> b + for a, b in self.proved_rules: + if isinstance(a, And): + rules_beta.append((a, b)) + else: + rules_alpha.append((a, b)) + return rules_alpha, rules_beta + + @property + def rules_alpha(self): + return self.split_alpha_beta()[0] + + @property + def rules_beta(self): + return self.split_alpha_beta()[1] + + def process_rule(self, a, b): + """process a -> b rule""" # TODO write more? + if (not a) or isinstance(b, bool): + return + if isinstance(a, bool): + return + if (a, b) in self._rules_seen: + return + else: + self._rules_seen.add((a, b)) + + # this is the core of processing + try: + self._process_rule(a, b) + except TautologyDetected: + pass + + def _process_rule(self, a, b): + # right part first + + # a -> b & c --> a -> b ; a -> c + # (?) FIXME this is only correct when b & c != null ! + + if isinstance(b, And): + sorted_bargs = sorted(b.args, key=str) + for barg in sorted_bargs: + self.process_rule(a, barg) + + # a -> b | c --> !b & !c -> !a + # --> a & !b -> c + # --> a & !c -> b + elif isinstance(b, Or): + sorted_bargs = sorted(b.args, key=str) + # detect tautology first + if not isinstance(a, Logic): # Atom + # tautology: a -> a|c|... + if a in sorted_bargs: + raise TautologyDetected(a, b, 'a -> a|c|...') + self.process_rule(And(*[Not(barg) for barg in b.args]), Not(a)) + + for bidx in range(len(sorted_bargs)): + barg = sorted_bargs[bidx] + brest = sorted_bargs[:bidx] + sorted_bargs[bidx + 1:] + self.process_rule(And(a, Not(barg)), Or(*brest)) + + # left part + + # a & b -> c --> IRREDUCIBLE CASE -- WE STORE IT AS IS + # (this will be the basis of beta-network) + elif isinstance(a, And): + sorted_aargs = sorted(a.args, key=str) + if b in sorted_aargs: + raise TautologyDetected(a, b, 'a & b -> a') + self.proved_rules.append((a, b)) + # XXX NOTE at present we ignore !c -> !a | !b + + elif isinstance(a, Or): + sorted_aargs = sorted(a.args, key=str) + if b in sorted_aargs: + raise TautologyDetected(a, b, 'a | b -> a') + for aarg in sorted_aargs: + self.process_rule(aarg, b) + + else: + # both `a` and `b` are atoms + self.proved_rules.append((a, b)) # a -> b + self.proved_rules.append((Not(b), Not(a))) # !b -> !a + +######################################## + + +class FactRules: + """Rules that describe how to deduce facts in logic space + + When defined, these rules allow implications to quickly be determined + for a set of facts. For this precomputed deduction tables are used. + see `deduce_all_facts` (forward-chaining) + + Also it is possible to gather prerequisites for a fact, which is tried + to be proven. (backward-chaining) + + + Definition Syntax + ----------------- + + a -> b -- a=T -> b=T (and automatically b=F -> a=F) + a -> !b -- a=T -> b=F + a == b -- a -> b & b -> a + a -> b & c -- a=T -> b=T & c=T + # TODO b | c + + + Internals + --------- + + .full_implications[k, v]: all the implications of fact k=v + .beta_triggers[k, v]: beta rules that might be triggered when k=v + .prereq -- {} k <- [] of k's prerequisites + + .defined_facts -- set of defined fact names + """ + + def __init__(self, rules): + """Compile rules into internal lookup tables""" + + if isinstance(rules, str): + rules = rules.splitlines() + + # --- parse and process rules --- + P = Prover() + + for rule in rules: + # XXX `a` is hardcoded to be always atom + a, op, b = rule.split(None, 2) + + a = Logic.fromstring(a) + b = Logic.fromstring(b) + + if op == '->': + P.process_rule(a, b) + elif op == '==': + P.process_rule(a, b) + P.process_rule(b, a) + else: + raise ValueError('unknown op %r' % op) + + # --- build deduction networks --- + self.beta_rules = [] + for bcond, bimpl in P.rules_beta: + self.beta_rules.append( + ({_as_pair(a) for a in bcond.args}, _as_pair(bimpl))) + + # deduce alpha implications + impl_a = deduce_alpha_implications(P.rules_alpha) + + # now: + # - apply beta rules to alpha chains (static extension), and + # - further associate beta rules to alpha chain (for inference + # at runtime) + impl_ab = apply_beta_to_alpha_route(impl_a, P.rules_beta) + + # extract defined fact names + self.defined_facts = {_base_fact(k) for k in impl_ab.keys()} + + # build rels (forward chains) + full_implications = defaultdict(set) + beta_triggers = defaultdict(set) + for k, (impl, betaidxs) in impl_ab.items(): + full_implications[_as_pair(k)] = {_as_pair(i) for i in impl} + beta_triggers[_as_pair(k)] = betaidxs + + self.full_implications = full_implications + self.beta_triggers = beta_triggers + + # build prereq (backward chains) + prereq = defaultdict(set) + rel_prereq = rules_2prereq(full_implications) + for k, pitems in rel_prereq.items(): + prereq[k] |= pitems + self.prereq = prereq + + def _to_python(self) -> str: + """ Generate a string with plain python representation of the instance """ + return '\n'.join(self.print_rules()) + + @classmethod + def _from_python(cls, data : dict): + """ Generate an instance from the plain python representation """ + self = cls('') + for key in ['full_implications', 'beta_triggers', 'prereq']: + d=defaultdict(set) + d.update(data[key]) + setattr(self, key, d) + self.beta_rules = data['beta_rules'] + self.defined_facts = set(data['defined_facts']) + + return self + + def _defined_facts_lines(self): + yield 'defined_facts = [' + for fact in sorted(self.defined_facts): + yield f' {fact!r},' + yield '] # defined_facts' + + def _full_implications_lines(self): + yield 'full_implications = dict( [' + for fact in sorted(self.defined_facts): + for value in (True, False): + yield f' # Implications of {fact} = {value}:' + yield f' (({fact!r}, {value!r}), set( (' + implications = self.full_implications[(fact, value)] + for implied in sorted(implications): + yield f' {implied!r},' + yield ' ) ),' + yield ' ),' + yield ' ] ) # full_implications' + + def _prereq_lines(self): + yield 'prereq = {' + yield '' + for fact in sorted(self.prereq): + yield f' # facts that could determine the value of {fact}' + yield f' {fact!r}: {{' + for pfact in sorted(self.prereq[fact]): + yield f' {pfact!r},' + yield ' },' + yield '' + yield '} # prereq' + + def _beta_rules_lines(self): + reverse_implications = defaultdict(list) + for n, (pre, implied) in enumerate(self.beta_rules): + reverse_implications[implied].append((pre, n)) + + yield '# Note: the order of the beta rules is used in the beta_triggers' + yield 'beta_rules = [' + yield '' + m = 0 + indices = {} + for implied in sorted(reverse_implications): + fact, value = implied + yield f' # Rules implying {fact} = {value}' + for pre, n in reverse_implications[implied]: + indices[n] = m + m += 1 + setstr = ", ".join(map(str, sorted(pre))) + yield f' ({{{setstr}}},' + yield f' {implied!r}),' + yield '' + yield '] # beta_rules' + + yield 'beta_triggers = {' + for query in sorted(self.beta_triggers): + fact, value = query + triggers = [indices[n] for n in self.beta_triggers[query]] + yield f' {query!r}: {triggers!r},' + yield '} # beta_triggers' + + def print_rules(self) -> Iterator[str]: + """ Returns a generator with lines to represent the facts and rules """ + yield from self._defined_facts_lines() + yield '' + yield '' + yield from self._full_implications_lines() + yield '' + yield '' + yield from self._prereq_lines() + yield '' + yield '' + yield from self._beta_rules_lines() + yield '' + yield '' + yield "generated_assumptions = {'defined_facts': defined_facts, 'full_implications': full_implications," + yield " 'prereq': prereq, 'beta_rules': beta_rules, 'beta_triggers': beta_triggers}" + + +class InconsistentAssumptions(ValueError): + def __str__(self): + kb, fact, value = self.args + return "%s, %s=%s" % (kb, fact, value) + + +class FactKB(dict): + """ + A simple propositional knowledge base relying on compiled inference rules. + """ + def __str__(self): + return '{\n%s}' % ',\n'.join( + ["\t%s: %s" % i for i in sorted(self.items())]) + + def __init__(self, rules): + self.rules = rules + + def _tell(self, k, v): + """Add fact k=v to the knowledge base. + + Returns True if the KB has actually been updated, False otherwise. + """ + if k in self and self[k] is not None: + if self[k] == v: + return False + else: + raise InconsistentAssumptions(self, k, v) + else: + self[k] = v + return True + + # ********************************************* + # * This is the workhorse, so keep it *fast*. * + # ********************************************* + def deduce_all_facts(self, facts): + """ + Update the KB with all the implications of a list of facts. + + Facts can be specified as a dictionary or as a list of (key, value) + pairs. + """ + # keep frequently used attributes locally, so we'll avoid extra + # attribute access overhead + full_implications = self.rules.full_implications + beta_triggers = self.rules.beta_triggers + beta_rules = self.rules.beta_rules + + if isinstance(facts, dict): + facts = facts.items() + + while facts: + beta_maytrigger = set() + + # --- alpha chains --- + for k, v in facts: + if not self._tell(k, v) or v is None: + continue + + # lookup routing tables + for key, value in full_implications[k, v]: + self._tell(key, value) + + beta_maytrigger.update(beta_triggers[k, v]) + + # --- beta chains --- + facts = [] + for bidx in beta_maytrigger: + bcond, bimpl = beta_rules[bidx] + if all(self.get(k) is v for k, v in bcond): + facts.append(bimpl) diff --git a/lib/python3.11/site-packages/sympy/core/function.py b/lib/python3.11/site-packages/sympy/core/function.py new file mode 100644 index 0000000000000000000000000000000000000000..62d45d01ad989e8312a39010e9ded363a12c50e6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/function.py @@ -0,0 +1,3393 @@ +""" +There are three types of functions implemented in SymPy: + + 1) defined functions (in the sense that they can be evaluated) like + exp or sin; they have a name and a body: + f = exp + 2) undefined function which have a name but no body. Undefined + functions can be defined using a Function class as follows: + f = Function('f') + (the result will be a Function instance) + 3) anonymous function (or lambda function) which have a body (defined + with dummy variables) but have no name: + f = Lambda(x, exp(x)*x) + f = Lambda((x, y), exp(x)*y) + The fourth type of functions are composites, like (sin + cos)(x); these work in + SymPy core, but are not yet part of SymPy. + + Examples + ======== + + >>> import sympy + >>> f = sympy.Function("f") + >>> from sympy.abc import x + >>> f(x) + f(x) + >>> print(sympy.srepr(f(x).func)) + Function('f') + >>> f(x).args + (x,) + +""" + +from __future__ import annotations +from typing import Any +from collections.abc import Iterable + +from .add import Add +from .basic import Basic, _atomic +from .cache import cacheit +from .containers import Tuple, Dict +from .decorators import _sympifyit +from .evalf import pure_complex +from .expr import Expr, AtomicExpr +from .logic import fuzzy_and, fuzzy_or, fuzzy_not, FuzzyBool +from .mul import Mul +from .numbers import Rational, Float, Integer +from .operations import LatticeOp +from .parameters import global_parameters +from .rules import Transform +from .singleton import S +from .sympify import sympify, _sympify + +from .sorting import default_sort_key, ordered +from sympy.utilities.exceptions import (sympy_deprecation_warning, + SymPyDeprecationWarning, ignore_warnings) +from sympy.utilities.iterables import (has_dups, sift, iterable, + is_sequence, uniq, topological_sort) +from sympy.utilities.lambdify import MPMATH_TRANSLATIONS +from sympy.utilities.misc import as_int, filldedent, func_name + +import mpmath +from mpmath.libmp.libmpf import prec_to_dps + +import inspect +from collections import Counter + +def _coeff_isneg(a): + """Return True if the leading Number is negative. + + Examples + ======== + + >>> from sympy.core.function import _coeff_isneg + >>> from sympy import S, Symbol, oo, pi + >>> _coeff_isneg(-3*pi) + True + >>> _coeff_isneg(S(3)) + False + >>> _coeff_isneg(-oo) + True + >>> _coeff_isneg(Symbol('n', negative=True)) # coeff is 1 + False + + For matrix expressions: + + >>> from sympy import MatrixSymbol, sqrt + >>> A = MatrixSymbol("A", 3, 3) + >>> _coeff_isneg(-sqrt(2)*A) + True + >>> _coeff_isneg(sqrt(2)*A) + False + """ + + if a.is_MatMul: + a = a.args[0] + if a.is_Mul: + a = a.args[0] + return a.is_Number and a.is_extended_negative + + +class PoleError(Exception): + pass + + +class ArgumentIndexError(ValueError): + def __str__(self): + return ("Invalid operation with argument number %s for Function %s" % + (self.args[1], self.args[0])) + + +class BadSignatureError(TypeError): + '''Raised when a Lambda is created with an invalid signature''' + pass + + +class BadArgumentsError(TypeError): + '''Raised when a Lambda is called with an incorrect number of arguments''' + pass + + +# Python 3 version that does not raise a Deprecation warning +def arity(cls): + """Return the arity of the function if it is known, else None. + + Explanation + =========== + + When default values are specified for some arguments, they are + optional and the arity is reported as a tuple of possible values. + + Examples + ======== + + >>> from sympy import arity, log + >>> arity(lambda x: x) + 1 + >>> arity(log) + (1, 2) + >>> arity(lambda *x: sum(x)) is None + True + """ + eval_ = getattr(cls, 'eval', cls) + + parameters = inspect.signature(eval_).parameters.items() + if [p for _, p in parameters if p.kind == p.VAR_POSITIONAL]: + return + p_or_k = [p for _, p in parameters if p.kind == p.POSITIONAL_OR_KEYWORD] + # how many have no default and how many have a default value + no, yes = map(len, sift(p_or_k, + lambda p:p.default == p.empty, binary=True)) + return no if not yes else tuple(range(no, no + yes + 1)) + +class FunctionClass(type): + """ + Base class for function classes. FunctionClass is a subclass of type. + + Use Function('' [ , signature ]) to create + undefined function classes. + """ + _new = type.__new__ + + def __init__(cls, *args, **kwargs): + # honor kwarg value or class-defined value before using + # the number of arguments in the eval function (if present) + nargs = kwargs.pop('nargs', cls.__dict__.get('nargs', arity(cls))) + if nargs is None and 'nargs' not in cls.__dict__: + for supcls in cls.__mro__: + if hasattr(supcls, '_nargs'): + nargs = supcls._nargs + break + else: + continue + + # Canonicalize nargs here; change to set in nargs. + if is_sequence(nargs): + if not nargs: + raise ValueError(filldedent(''' + Incorrectly specified nargs as %s: + if there are no arguments, it should be + `nargs = 0`; + if there are any number of arguments, + it should be + `nargs = None`''' % str(nargs))) + nargs = tuple(ordered(set(nargs))) + elif nargs is not None: + nargs = (as_int(nargs),) + cls._nargs = nargs + + # When __init__ is called from UndefinedFunction it is called with + # just one arg but when it is called from subclassing Function it is + # called with the usual (name, bases, namespace) type() signature. + if len(args) == 3: + namespace = args[2] + if 'eval' in namespace and not isinstance(namespace['eval'], classmethod): + raise TypeError("eval on Function subclasses should be a class method (defined with @classmethod)") + + @property + def __signature__(self): + """ + Allow Python 3's inspect.signature to give a useful signature for + Function subclasses. + """ + # Python 3 only, but backports (like the one in IPython) still might + # call this. + try: + from inspect import signature + except ImportError: + return None + + # TODO: Look at nargs + return signature(self.eval) + + @property + def free_symbols(self): + return set() + + @property + def xreplace(self): + # Function needs args so we define a property that returns + # a function that takes args...and then use that function + # to return the right value + return lambda rule, **_: rule.get(self, self) + + @property + def nargs(self): + """Return a set of the allowed number of arguments for the function. + + Examples + ======== + + >>> from sympy import Function + >>> f = Function('f') + + If the function can take any number of arguments, the set of whole + numbers is returned: + + >>> Function('f').nargs + Naturals0 + + If the function was initialized to accept one or more arguments, a + corresponding set will be returned: + + >>> Function('f', nargs=1).nargs + {1} + >>> Function('f', nargs=(2, 1)).nargs + {1, 2} + + The undefined function, after application, also has the nargs + attribute; the actual number of arguments is always available by + checking the ``args`` attribute: + + >>> f = Function('f') + >>> f(1).nargs + Naturals0 + >>> len(f(1).args) + 1 + """ + from sympy.sets.sets import FiniteSet + # XXX it would be nice to handle this in __init__ but there are import + # problems with trying to import FiniteSet there + return FiniteSet(*self._nargs) if self._nargs else S.Naturals0 + + def _valid_nargs(self, n : int) -> bool: + """ Return True if the specified integer is a valid number of arguments + + The number of arguments n is guaranteed to be an integer and positive + + """ + if self._nargs: + return n in self._nargs + + nargs = self.nargs + return nargs is S.Naturals0 or n in nargs + + def __repr__(cls): + return cls.__name__ + + +class Application(Basic, metaclass=FunctionClass): + """ + Base class for applied functions. + + Explanation + =========== + + Instances of Application represent the result of applying an application of + any type to any object. + """ + + is_Function = True + + @cacheit + def __new__(cls, *args, **options): + from sympy.sets.fancysets import Naturals0 + from sympy.sets.sets import FiniteSet + + args = list(map(sympify, args)) + evaluate = options.pop('evaluate', global_parameters.evaluate) + # WildFunction (and anything else like it) may have nargs defined + # and we throw that value away here + options.pop('nargs', None) + + if options: + raise ValueError("Unknown options: %s" % options) + + if evaluate: + evaluated = cls.eval(*args) + if evaluated is not None: + return evaluated + + obj = super().__new__(cls, *args, **options) + + # make nargs uniform here + sentinel = object() + objnargs = getattr(obj, "nargs", sentinel) + if objnargs is not sentinel: + # things passing through here: + # - functions subclassed from Function (e.g. myfunc(1).nargs) + # - functions like cos(1).nargs + # - AppliedUndef with given nargs like Function('f', nargs=1)(1).nargs + # Canonicalize nargs here + if is_sequence(objnargs): + nargs = tuple(ordered(set(objnargs))) + elif objnargs is not None: + nargs = (as_int(objnargs),) + else: + nargs = None + else: + # things passing through here: + # - WildFunction('f').nargs + # - AppliedUndef with no nargs like Function('f')(1).nargs + nargs = obj._nargs # note the underscore here + # convert to FiniteSet + obj.nargs = FiniteSet(*nargs) if nargs else Naturals0() + return obj + + @classmethod + def eval(cls, *args): + """ + Returns a canonical form of cls applied to arguments args. + + Explanation + =========== + + The ``eval()`` method is called when the class ``cls`` is about to be + instantiated and it should return either some simplified instance + (possible of some other class), or if the class ``cls`` should be + unmodified, return None. + + Examples of ``eval()`` for the function "sign" + + .. code-block:: python + + @classmethod + def eval(cls, arg): + if arg is S.NaN: + return S.NaN + if arg.is_zero: return S.Zero + if arg.is_positive: return S.One + if arg.is_negative: return S.NegativeOne + if isinstance(arg, Mul): + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff is not S.One: + return cls(coeff) * cls(terms) + + """ + return + + @property + def func(self): + return self.__class__ + + def _eval_subs(self, old, new): + if (old.is_Function and new.is_Function and + callable(old) and callable(new) and + old == self.func and len(self.args) in new.nargs): + return new(*[i._subs(old, new) for i in self.args]) + + +class Function(Application, Expr): + r""" + Base class for applied mathematical functions. + + It also serves as a constructor for undefined function classes. + + See the :ref:`custom-functions` guide for details on how to subclass + ``Function`` and what methods can be defined. + + Examples + ======== + + **Undefined Functions** + + To create an undefined function, pass a string of the function name to + ``Function``. + + >>> from sympy import Function, Symbol + >>> x = Symbol('x') + >>> f = Function('f') + >>> g = Function('g')(x) + >>> f + f + >>> f(x) + f(x) + >>> g + g(x) + >>> f(x).diff(x) + Derivative(f(x), x) + >>> g.diff(x) + Derivative(g(x), x) + + Assumptions can be passed to ``Function`` the same as with a + :class:`~.Symbol`. Alternatively, you can use a ``Symbol`` with + assumptions for the function name and the function will inherit the name + and assumptions associated with the ``Symbol``: + + >>> f_real = Function('f', real=True) + >>> f_real(x).is_real + True + >>> f_real_inherit = Function(Symbol('f', real=True)) + >>> f_real_inherit(x).is_real + True + + Note that assumptions on a function are unrelated to the assumptions on + the variables it is called on. If you want to add a relationship, subclass + ``Function`` and define custom assumptions handler methods. See the + :ref:`custom-functions-assumptions` section of the :ref:`custom-functions` + guide for more details. + + **Custom Function Subclasses** + + The :ref:`custom-functions` guide has several + :ref:`custom-functions-complete-examples` of how to subclass ``Function`` + to create a custom function. + + """ + + @property + def _diff_wrt(self): + return False + + @cacheit + def __new__(cls, *args, **options): + # Handle calls like Function('f') + if cls is Function: + return UndefinedFunction(*args, **options) + + n = len(args) + + if not cls._valid_nargs(n): + # XXX: exception message must be in exactly this format to + # make it work with NumPy's functions like vectorize(). See, + # for example, https://github.com/numpy/numpy/issues/1697. + # The ideal solution would be just to attach metadata to + # the exception and change NumPy to take advantage of this. + temp = ('%(name)s takes %(qual)s %(args)s ' + 'argument%(plural)s (%(given)s given)') + raise TypeError(temp % { + 'name': cls, + 'qual': 'exactly' if len(cls.nargs) == 1 else 'at least', + 'args': min(cls.nargs), + 'plural': 's'*(min(cls.nargs) != 1), + 'given': n}) + + evaluate = options.get('evaluate', global_parameters.evaluate) + result = super().__new__(cls, *args, **options) + if evaluate and isinstance(result, cls) and result.args: + _should_evalf = [cls._should_evalf(a) for a in result.args] + pr2 = min(_should_evalf) + if pr2 > 0: + pr = max(_should_evalf) + result = result.evalf(prec_to_dps(pr)) + + return _sympify(result) + + @classmethod + def _should_evalf(cls, arg): + """ + Decide if the function should automatically evalf(). + + Explanation + =========== + + By default (in this implementation), this happens if (and only if) the + ARG is a floating point number (including complex numbers). + This function is used by __new__. + + Returns the precision to evalf to, or -1 if it should not evalf. + """ + if arg.is_Float: + return arg._prec + if not arg.is_Add: + return -1 + m = pure_complex(arg) + if m is None: + return -1 + # the elements of m are of type Number, so have a _prec + return max(m[0]._prec, m[1]._prec) + + @classmethod + def class_key(cls): + from sympy.sets.fancysets import Naturals0 + funcs = { + 'exp': 10, + 'log': 11, + 'sin': 20, + 'cos': 21, + 'tan': 22, + 'cot': 23, + 'sinh': 30, + 'cosh': 31, + 'tanh': 32, + 'coth': 33, + 'conjugate': 40, + 're': 41, + 'im': 42, + 'arg': 43, + } + name = cls.__name__ + + try: + i = funcs[name] + except KeyError: + i = 0 if isinstance(cls.nargs, Naturals0) else 10000 + + return 4, i, name + + def _eval_evalf(self, prec): + + def _get_mpmath_func(fname): + """Lookup mpmath function based on name""" + if isinstance(self, AppliedUndef): + # Shouldn't lookup in mpmath but might have ._imp_ + return None + + if not hasattr(mpmath, fname): + fname = MPMATH_TRANSLATIONS.get(fname, None) + if fname is None: + return None + return getattr(mpmath, fname) + + _eval_mpmath = getattr(self, '_eval_mpmath', None) + if _eval_mpmath is None: + func = _get_mpmath_func(self.func.__name__) + args = self.args + else: + func, args = _eval_mpmath() + + # Fall-back evaluation + if func is None: + imp = getattr(self, '_imp_', None) + if imp is None: + return None + try: + return Float(imp(*[i.evalf(prec) for i in self.args]), prec) + except (TypeError, ValueError): + return None + + # Convert all args to mpf or mpc + # Convert the arguments to *higher* precision than requested for the + # final result. + # XXX + 5 is a guess, it is similar to what is used in evalf.py. Should + # we be more intelligent about it? + try: + args = [arg._to_mpmath(prec + 5) for arg in args] + def bad(m): + from mpmath import mpf, mpc + # the precision of an mpf value is the last element + # if that is 1 (and m[1] is not 1 which would indicate a + # power of 2), then the eval failed; so check that none of + # the arguments failed to compute to a finite precision. + # Note: An mpc value has two parts, the re and imag tuple; + # check each of those parts, too. Anything else is allowed to + # pass + if isinstance(m, mpf): + m = m._mpf_ + return m[1] !=1 and m[-1] == 1 + elif isinstance(m, mpc): + m, n = m._mpc_ + return m[1] !=1 and m[-1] == 1 and \ + n[1] !=1 and n[-1] == 1 + else: + return False + if any(bad(a) for a in args): + raise ValueError # one or more args failed to compute with significance + except ValueError: + return + + with mpmath.workprec(prec): + v = func(*args) + + return Expr._from_mpmath(v, prec) + + def _eval_derivative(self, s): + # f(x).diff(s) -> x.diff(s) * f.fdiff(1)(s) + i = 0 + l = [] + for a in self.args: + i += 1 + da = a.diff(s) + if da.is_zero: + continue + try: + df = self.fdiff(i) + except ArgumentIndexError: + df = Function.fdiff(self, i) + l.append(df * da) + return Add(*l) + + def _eval_is_commutative(self): + return fuzzy_and(a.is_commutative for a in self.args) + + def _eval_is_meromorphic(self, x, a): + if not self.args: + return True + if any(arg.has(x) for arg in self.args[1:]): + return False + + arg = self.args[0] + if not arg._eval_is_meromorphic(x, a): + return None + + return fuzzy_not(type(self).is_singular(arg.subs(x, a))) + + _singularities: FuzzyBool | tuple[Expr, ...] = None + + @classmethod + def is_singular(cls, a): + """ + Tests whether the argument is an essential singularity + or a branch point, or the functions is non-holomorphic. + """ + ss = cls._singularities + if ss in (True, None, False): + return ss + + return fuzzy_or(a.is_infinite if s is S.ComplexInfinity + else (a - s).is_zero for s in ss) + + def as_base_exp(self): + """ + Returns the method as the 2-tuple (base, exponent). + """ + return self, S.One + + def _eval_aseries(self, n, args0, x, logx): + """ + Compute an asymptotic expansion around args0, in terms of self.args. + This function is only used internally by _eval_nseries and should not + be called directly; derived classes can overwrite this to implement + asymptotic expansions. + """ + raise PoleError(filldedent(''' + Asymptotic expansion of %s around %s is + not implemented.''' % (type(self), args0))) + + def _eval_nseries(self, x, n, logx, cdir=0): + """ + This function does compute series for multivariate functions, + but the expansion is always in terms of *one* variable. + + Examples + ======== + + >>> from sympy import atan2 + >>> from sympy.abc import x, y + >>> atan2(x, y).series(x, n=2) + atan2(0, y) + x/y + O(x**2) + >>> atan2(x, y).series(y, n=2) + -y/x + atan2(x, 0) + O(y**2) + + This function also computes asymptotic expansions, if necessary + and possible: + + >>> from sympy import loggamma + >>> loggamma(1/x)._eval_nseries(x,0,None) + -1/x - log(x)/x + log(x)/2 + O(1) + + """ + from .symbol import uniquely_named_symbol + from sympy.series.order import Order + from sympy.sets.sets import FiniteSet + args = self.args + args0 = [t.limit(x, 0) for t in args] + if any(t.is_finite is False for t in args0): + from .numbers import oo, zoo, nan + a = [t.as_leading_term(x, logx=logx) for t in args] + a0 = [t.limit(x, 0) for t in a] + if any(t.has(oo, -oo, zoo, nan) for t in a0): + return self._eval_aseries(n, args0, x, logx) + # Careful: the argument goes to oo, but only logarithmically so. We + # are supposed to do a power series expansion "around the + # logarithmic term". e.g. + # f(1+x+log(x)) + # -> f(1+logx) + x*f'(1+logx) + O(x**2) + # where 'logx' is given in the argument + a = [t._eval_nseries(x, n, logx) for t in args] + z = [r - r0 for (r, r0) in zip(a, a0)] + p = [Dummy() for _ in z] + q = [] + v = None + for ai, zi, pi in zip(a0, z, p): + if zi.has(x): + if v is not None: + raise NotImplementedError + q.append(ai + pi) + v = pi + else: + q.append(ai) + e1 = self.func(*q) + if v is None: + return e1 + s = e1._eval_nseries(v, n, logx) + o = s.getO() + s = s.removeO() + s = s.subs(v, zi).expand() + Order(o.expr.subs(v, zi), x) + return s + if (self.func.nargs is S.Naturals0 + or (self.func.nargs == FiniteSet(1) and args0[0]) + or any(c > 1 for c in self.func.nargs)): + e = self + e1 = e.expand() + if e == e1: + #for example when e = sin(x+1) or e = sin(cos(x)) + #let's try the general algorithm + if len(e.args) == 1: + # issue 14411 + e = e.func(e.args[0].cancel()) + term = e.subs(x, S.Zero) + if term.is_finite is False or term is S.NaN: + raise PoleError("Cannot expand %s around 0" % (self)) + series = term + fact = S.One + + _x = uniquely_named_symbol('xi', self) + e = e.subs(x, _x) + for i in range(1, n): + fact *= Rational(i) + e = e.diff(_x) + subs = e.subs(_x, S.Zero) + if subs is S.NaN: + # try to evaluate a limit if we have to + subs = e.limit(_x, S.Zero) + if subs.is_finite is False: + raise PoleError("Cannot expand %s around 0" % (self)) + term = subs*(x**i)/fact + term = term.expand() + series += term + return series + Order(x**n, x) + return e1.nseries(x, n=n, logx=logx) + arg = self.args[0] + l = [] + g = None + # try to predict a number of terms needed + nterms = n + 2 + cf = Order(arg.as_leading_term(x), x).getn() + if cf != 0: + nterms = (n/cf).ceiling() + for i in range(nterms): + g = self.taylor_term(i, arg, g) + g = g.nseries(x, n=n, logx=logx) + l.append(g) + return Add(*l) + Order(x**n, x) + + def fdiff(self, argindex=1): + """ + Returns the first derivative of the function. + """ + if not (1 <= argindex <= len(self.args)): + raise ArgumentIndexError(self, argindex) + ix = argindex - 1 + A = self.args[ix] + if A._diff_wrt: + if len(self.args) == 1 or not A.is_Symbol: + return _derivative_dispatch(self, A) + for i, v in enumerate(self.args): + if i != ix and A in v.free_symbols: + # it can't be in any other argument's free symbols + # issue 8510 + break + else: + return _derivative_dispatch(self, A) + + # See issue 4624 and issue 4719, 5600 and 8510 + D = Dummy('xi_%i' % argindex, dummy_index=hash(A)) + args = self.args[:ix] + (D,) + self.args[ix + 1:] + return Subs(Derivative(self.func(*args), D), D, A) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + """Stub that should be overridden by new Functions to return + the first non-zero term in a series if ever an x-dependent + argument whose leading term vanishes as x -> 0 might be encountered. + See, for example, cos._eval_as_leading_term. + """ + from sympy.series.order import Order + args = [a.as_leading_term(x, logx=logx) for a in self.args] + o = Order(1, x) + if any(x in a.free_symbols and o.contains(a) for a in args): + # Whereas x and any finite number are contained in O(1, x), + # expressions like 1/x are not. If any arg simplified to a + # vanishing expression as x -> 0 (like x or x**2, but not + # 3, 1/x, etc...) then the _eval_as_leading_term is needed + # to supply the first non-zero term of the series, + # + # e.g. expression leading term + # ---------- ------------ + # cos(1/x) cos(1/x) + # cos(cos(x)) cos(1) + # cos(x) 1 <- _eval_as_leading_term needed + # sin(x) x <- _eval_as_leading_term needed + # + raise NotImplementedError( + '%s has no _eval_as_leading_term routine' % self.func) + else: + return self + + +class AppliedUndef(Function): + """ + Base class for expressions resulting from the application of an undefined + function. + """ + + is_number = False + + def __new__(cls, *args, **options): + args = list(map(sympify, args)) + u = [a.name for a in args if isinstance(a, UndefinedFunction)] + if u: + raise TypeError('Invalid argument: expecting an expression, not UndefinedFunction%s: %s' % ( + 's'*(len(u) > 1), ', '.join(u))) + obj = super().__new__(cls, *args, **options) + return obj + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + return self + + @property + def _diff_wrt(self): + """ + Allow derivatives wrt to undefined functions. + + Examples + ======== + + >>> from sympy import Function, Symbol + >>> f = Function('f') + >>> x = Symbol('x') + >>> f(x)._diff_wrt + True + >>> f(x).diff(x) + Derivative(f(x), x) + """ + return True + + +class UndefSageHelper: + """ + Helper to facilitate Sage conversion. + """ + def __get__(self, ins, typ): + import sage.all as sage + if ins is None: + return lambda: sage.function(typ.__name__) + else: + args = [arg._sage_() for arg in ins.args] + return lambda : sage.function(ins.__class__.__name__)(*args) + +_undef_sage_helper = UndefSageHelper() + +class UndefinedFunction(FunctionClass): + """ + The (meta)class of undefined functions. + """ + def __new__(mcl, name, bases=(AppliedUndef,), __dict__=None, **kwargs): + from .symbol import _filter_assumptions + # Allow Function('f', real=True) + # and/or Function(Symbol('f', real=True)) + assumptions, kwargs = _filter_assumptions(kwargs) + if isinstance(name, Symbol): + assumptions = name._merge(assumptions) + name = name.name + elif not isinstance(name, str): + raise TypeError('expecting string or Symbol for name') + else: + commutative = assumptions.get('commutative', None) + assumptions = Symbol(name, **assumptions).assumptions0 + if commutative is None: + assumptions.pop('commutative') + __dict__ = __dict__ or {} + # put the `is_*` for into __dict__ + __dict__.update({'is_%s' % k: v for k, v in assumptions.items()}) + # You can add other attributes, although they do have to be hashable + # (but seriously, if you want to add anything other than assumptions, + # just subclass Function) + __dict__.update(kwargs) + # add back the sanitized assumptions without the is_ prefix + kwargs.update(assumptions) + # Save these for __eq__ + __dict__.update({'_kwargs': kwargs}) + # do this for pickling + __dict__['__module__'] = None + obj = super().__new__(mcl, name, bases, __dict__) + obj.name = name + obj._sage_ = _undef_sage_helper + return obj + + def __instancecheck__(cls, instance): + return cls in type(instance).__mro__ + + _kwargs: dict[str, bool | None] = {} + + def __hash__(self): + return hash((self.class_key(), frozenset(self._kwargs.items()))) + + def __eq__(self, other): + return (isinstance(other, self.__class__) and + self.class_key() == other.class_key() and + self._kwargs == other._kwargs) + + def __ne__(self, other): + return not self == other + + @property + def _diff_wrt(self): + return False + + +# XXX: The type: ignore on WildFunction is because mypy complains: +# +# sympy/core/function.py:939: error: Cannot determine type of 'sort_key' in +# base class 'Expr' +# +# Somehow this is because of the @cacheit decorator but it is not clear how to +# fix it. + + +class WildFunction(Function, AtomicExpr): # type: ignore + """ + A WildFunction function matches any function (with its arguments). + + Examples + ======== + + >>> from sympy import WildFunction, Function, cos + >>> from sympy.abc import x, y + >>> F = WildFunction('F') + >>> f = Function('f') + >>> F.nargs + Naturals0 + >>> x.match(F) + >>> F.match(F) + {F_: F_} + >>> f(x).match(F) + {F_: f(x)} + >>> cos(x).match(F) + {F_: cos(x)} + >>> f(x, y).match(F) + {F_: f(x, y)} + + To match functions with a given number of arguments, set ``nargs`` to the + desired value at instantiation: + + >>> F = WildFunction('F', nargs=2) + >>> F.nargs + {2} + >>> f(x).match(F) + >>> f(x, y).match(F) + {F_: f(x, y)} + + To match functions with a range of arguments, set ``nargs`` to a tuple + containing the desired number of arguments, e.g. if ``nargs = (1, 2)`` + then functions with 1 or 2 arguments will be matched. + + >>> F = WildFunction('F', nargs=(1, 2)) + >>> F.nargs + {1, 2} + >>> f(x).match(F) + {F_: f(x)} + >>> f(x, y).match(F) + {F_: f(x, y)} + >>> f(x, y, 1).match(F) + + """ + + # XXX: What is this class attribute used for? + include: set[Any] = set() + + def __init__(cls, name, **assumptions): + from sympy.sets.sets import Set, FiniteSet + cls.name = name + nargs = assumptions.pop('nargs', S.Naturals0) + if not isinstance(nargs, Set): + # Canonicalize nargs here. See also FunctionClass. + if is_sequence(nargs): + nargs = tuple(ordered(set(nargs))) + elif nargs is not None: + nargs = (as_int(nargs),) + nargs = FiniteSet(*nargs) + cls.nargs = nargs + + def matches(self, expr, repl_dict=None, old=False): + if not isinstance(expr, (AppliedUndef, Function)): + return None + if len(expr.args) not in self.nargs: + return None + + if repl_dict is None: + repl_dict = {} + else: + repl_dict = repl_dict.copy() + + repl_dict[self] = expr + return repl_dict + + +class Derivative(Expr): + """ + Carries out differentiation of the given expression with respect to symbols. + + Examples + ======== + + >>> from sympy import Derivative, Function, symbols, Subs + >>> from sympy.abc import x, y + >>> f, g = symbols('f g', cls=Function) + + >>> Derivative(x**2, x, evaluate=True) + 2*x + + Denesting of derivatives retains the ordering of variables: + + >>> Derivative(Derivative(f(x, y), y), x) + Derivative(f(x, y), y, x) + + Contiguously identical symbols are merged into a tuple giving + the symbol and the count: + + >>> Derivative(f(x), x, x, y, x) + Derivative(f(x), (x, 2), y, x) + + If the derivative cannot be performed, and evaluate is True, the + order of the variables of differentiation will be made canonical: + + >>> Derivative(f(x, y), y, x, evaluate=True) + Derivative(f(x, y), x, y) + + Derivatives with respect to undefined functions can be calculated: + + >>> Derivative(f(x)**2, f(x), evaluate=True) + 2*f(x) + + Such derivatives will show up when the chain rule is used to + evalulate a derivative: + + >>> f(g(x)).diff(x) + Derivative(f(g(x)), g(x))*Derivative(g(x), x) + + Substitution is used to represent derivatives of functions with + arguments that are not symbols or functions: + + >>> f(2*x + 3).diff(x) == 2*Subs(f(y).diff(y), y, 2*x + 3) + True + + Notes + ===== + + Simplification of high-order derivatives: + + Because there can be a significant amount of simplification that can be + done when multiple differentiations are performed, results will be + automatically simplified in a fairly conservative fashion unless the + keyword ``simplify`` is set to False. + + >>> from sympy import sqrt, diff, Function, symbols + >>> from sympy.abc import x, y, z + >>> f, g = symbols('f,g', cls=Function) + + >>> e = sqrt((x + 1)**2 + x) + >>> diff(e, (x, 5), simplify=False).count_ops() + 136 + >>> diff(e, (x, 5)).count_ops() + 30 + + Ordering of variables: + + If evaluate is set to True and the expression cannot be evaluated, the + list of differentiation symbols will be sorted, that is, the expression is + assumed to have continuous derivatives up to the order asked. + + Derivative wrt non-Symbols: + + For the most part, one may not differentiate wrt non-symbols. + For example, we do not allow differentiation wrt `x*y` because + there are multiple ways of structurally defining where x*y appears + in an expression: a very strict definition would make + (x*y*z).diff(x*y) == 0. Derivatives wrt defined functions (like + cos(x)) are not allowed, either: + + >>> (x*y*z).diff(x*y) + Traceback (most recent call last): + ... + ValueError: Can't calculate derivative wrt x*y. + + To make it easier to work with variational calculus, however, + derivatives wrt AppliedUndef and Derivatives are allowed. + For example, in the Euler-Lagrange method one may write + F(t, u, v) where u = f(t) and v = f'(t). These variables can be + written explicitly as functions of time:: + + >>> from sympy.abc import t + >>> F = Function('F') + >>> U = f(t) + >>> V = U.diff(t) + + The derivative wrt f(t) can be obtained directly: + + >>> direct = F(t, U, V).diff(U) + + When differentiation wrt a non-Symbol is attempted, the non-Symbol + is temporarily converted to a Symbol while the differentiation + is performed and the same answer is obtained: + + >>> indirect = F(t, U, V).subs(U, x).diff(x).subs(x, U) + >>> assert direct == indirect + + The implication of this non-symbol replacement is that all + functions are treated as independent of other functions and the + symbols are independent of the functions that contain them:: + + >>> x.diff(f(x)) + 0 + >>> g(x).diff(f(x)) + 0 + + It also means that derivatives are assumed to depend only + on the variables of differentiation, not on anything contained + within the expression being differentiated:: + + >>> F = f(x) + >>> Fx = F.diff(x) + >>> Fx.diff(F) # derivative depends on x, not F + 0 + >>> Fxx = Fx.diff(x) + >>> Fxx.diff(Fx) # derivative depends on x, not Fx + 0 + + The last example can be made explicit by showing the replacement + of Fx in Fxx with y: + + >>> Fxx.subs(Fx, y) + Derivative(y, x) + + Since that in itself will evaluate to zero, differentiating + wrt Fx will also be zero: + + >>> _.doit() + 0 + + Replacing undefined functions with concrete expressions + + One must be careful to replace undefined functions with expressions + that contain variables consistent with the function definition and + the variables of differentiation or else insconsistent result will + be obtained. Consider the following example: + + >>> eq = f(x)*g(y) + >>> eq.subs(f(x), x*y).diff(x, y).doit() + y*Derivative(g(y), y) + g(y) + >>> eq.diff(x, y).subs(f(x), x*y).doit() + y*Derivative(g(y), y) + + The results differ because `f(x)` was replaced with an expression + that involved both variables of differentiation. In the abstract + case, differentiation of `f(x)` by `y` is 0; in the concrete case, + the presence of `y` made that derivative nonvanishing and produced + the extra `g(y)` term. + + Defining differentiation for an object + + An object must define ._eval_derivative(symbol) method that returns + the differentiation result. This function only needs to consider the + non-trivial case where expr contains symbol and it should call the diff() + method internally (not _eval_derivative); Derivative should be the only + one to call _eval_derivative. + + Any class can allow derivatives to be taken with respect to + itself (while indicating its scalar nature). See the + docstring of Expr._diff_wrt. + + See Also + ======== + _sort_variable_count + """ + + is_Derivative = True + + @property + def _diff_wrt(self): + """An expression may be differentiated wrt a Derivative if + it is in elementary form. + + Examples + ======== + + >>> from sympy import Function, Derivative, cos + >>> from sympy.abc import x + >>> f = Function('f') + + >>> Derivative(f(x), x)._diff_wrt + True + >>> Derivative(cos(x), x)._diff_wrt + False + >>> Derivative(x + 1, x)._diff_wrt + False + + A Derivative might be an unevaluated form of what will not be + a valid variable of differentiation if evaluated. For example, + + >>> Derivative(f(f(x)), x).doit() + Derivative(f(x), x)*Derivative(f(f(x)), f(x)) + + Such an expression will present the same ambiguities as arise + when dealing with any other product, like ``2*x``, so ``_diff_wrt`` + is False: + + >>> Derivative(f(f(x)), x)._diff_wrt + False + """ + return self.expr._diff_wrt and isinstance(self.doit(), Derivative) + + def __new__(cls, expr, *variables, **kwargs): + expr = sympify(expr) + symbols_or_none = getattr(expr, "free_symbols", None) + has_symbol_set = isinstance(symbols_or_none, set) + + if not has_symbol_set: + raise ValueError(filldedent(''' + Since there are no variables in the expression %s, + it cannot be differentiated.''' % expr)) + + # determine value for variables if it wasn't given + if not variables: + variables = expr.free_symbols + if len(variables) != 1: + if expr.is_number: + return S.Zero + if len(variables) == 0: + raise ValueError(filldedent(''' + Since there are no variables in the expression, + the variable(s) of differentiation must be supplied + to differentiate %s''' % expr)) + else: + raise ValueError(filldedent(''' + Since there is more than one variable in the + expression, the variable(s) of differentiation + must be supplied to differentiate %s''' % expr)) + + # Split the list of variables into a list of the variables we are diff + # wrt, where each element of the list has the form (s, count) where + # s is the entity to diff wrt and count is the order of the + # derivative. + variable_count = [] + array_likes = (tuple, list, Tuple) + + from sympy.tensor.array import Array, NDimArray + + for i, v in enumerate(variables): + if isinstance(v, UndefinedFunction): + raise TypeError( + "cannot differentiate wrt " + "UndefinedFunction: %s" % v) + + if isinstance(v, array_likes): + if len(v) == 0: + # Ignore empty tuples: Derivative(expr, ... , (), ... ) + continue + if isinstance(v[0], array_likes): + # Derive by array: Derivative(expr, ... , [[x, y, z]], ... ) + if len(v) == 1: + v = Array(v[0]) + count = 1 + else: + v, count = v + v = Array(v) + else: + v, count = v + if count == 0: + continue + variable_count.append(Tuple(v, count)) + continue + + v = sympify(v) + if isinstance(v, Integer): + if i == 0: + raise ValueError("First variable cannot be a number: %i" % v) + count = v + prev, prevcount = variable_count[-1] + if prevcount != 1: + raise TypeError("tuple {} followed by number {}".format((prev, prevcount), v)) + if count == 0: + variable_count.pop() + else: + variable_count[-1] = Tuple(prev, count) + else: + count = 1 + variable_count.append(Tuple(v, count)) + + # light evaluation of contiguous, identical + # items: (x, 1), (x, 1) -> (x, 2) + merged = [] + for t in variable_count: + v, c = t + if c.is_negative: + raise ValueError( + 'order of differentiation must be nonnegative') + if merged and merged[-1][0] == v: + c += merged[-1][1] + if not c: + merged.pop() + else: + merged[-1] = Tuple(v, c) + else: + merged.append(t) + variable_count = merged + + # sanity check of variables of differentation; we waited + # until the counts were computed since some variables may + # have been removed because the count was 0 + for v, c in variable_count: + # v must have _diff_wrt True + if not v._diff_wrt: + __ = '' # filler to make error message neater + raise ValueError(filldedent(''' + Can't calculate derivative wrt %s.%s''' % (v, + __))) + + # We make a special case for 0th derivative, because there is no + # good way to unambiguously print this. + if len(variable_count) == 0: + return expr + + evaluate = kwargs.get('evaluate', False) + + if evaluate: + if isinstance(expr, Derivative): + expr = expr.canonical + variable_count = [ + (v.canonical if isinstance(v, Derivative) else v, c) + for v, c in variable_count] + + # Look for a quick exit if there are symbols that don't appear in + # expression at all. Note, this cannot check non-symbols like + # Derivatives as those can be created by intermediate + # derivatives. + zero = False + free = expr.free_symbols + from sympy.matrices.expressions.matexpr import MatrixExpr + + for v, c in variable_count: + vfree = v.free_symbols + if c.is_positive and vfree: + if isinstance(v, AppliedUndef): + # these match exactly since + # x.diff(f(x)) == g(x).diff(f(x)) == 0 + # and are not created by differentiation + D = Dummy() + if not expr.xreplace({v: D}).has(D): + zero = True + break + elif isinstance(v, MatrixExpr): + zero = False + break + elif isinstance(v, Symbol) and v not in free: + zero = True + break + else: + if not free & vfree: + # e.g. v is IndexedBase or Matrix + zero = True + break + if zero: + return cls._get_zero_with_shape_like(expr) + + # make the order of symbols canonical + #TODO: check if assumption of discontinuous derivatives exist + variable_count = cls._sort_variable_count(variable_count) + + # denest + if isinstance(expr, Derivative): + variable_count = list(expr.variable_count) + variable_count + expr = expr.expr + return _derivative_dispatch(expr, *variable_count, **kwargs) + + # we return here if evaluate is False or if there is no + # _eval_derivative method + if not evaluate or not hasattr(expr, '_eval_derivative'): + # return an unevaluated Derivative + if evaluate and variable_count == [(expr, 1)] and expr.is_scalar: + # special hack providing evaluation for classes + # that have defined is_scalar=True but have no + # _eval_derivative defined + return S.One + return Expr.__new__(cls, expr, *variable_count) + + # evaluate the derivative by calling _eval_derivative method + # of expr for each variable + # ------------------------------------------------------------- + nderivs = 0 # how many derivatives were performed + unhandled = [] + from sympy.matrices.matrixbase import MatrixBase + for i, (v, count) in enumerate(variable_count): + + old_expr = expr + old_v = None + + is_symbol = v.is_symbol or isinstance(v, + (Iterable, Tuple, MatrixBase, NDimArray)) + + if not is_symbol: + old_v = v + v = Dummy('xi') + expr = expr.xreplace({old_v: v}) + # Derivatives and UndefinedFunctions are independent + # of all others + clashing = not (isinstance(old_v, (Derivative, AppliedUndef))) + if v not in expr.free_symbols and not clashing: + return expr.diff(v) # expr's version of 0 + if not old_v.is_scalar and not hasattr( + old_v, '_eval_derivative'): + # special hack providing evaluation for classes + # that have defined is_scalar=True but have no + # _eval_derivative defined + expr *= old_v.diff(old_v) + + obj = cls._dispatch_eval_derivative_n_times(expr, v, count) + if obj is not None and obj.is_zero: + return obj + + nderivs += count + + if old_v is not None: + if obj is not None: + # remove the dummy that was used + obj = obj.subs(v, old_v) + # restore expr + expr = old_expr + + if obj is None: + # we've already checked for quick-exit conditions + # that give 0 so the remaining variables + # are contained in the expression but the expression + # did not compute a derivative so we stop taking + # derivatives + unhandled = variable_count[i:] + break + + expr = obj + + # what we have so far can be made canonical + expr = expr.replace( + lambda x: isinstance(x, Derivative), + lambda x: x.canonical) + + if unhandled: + if isinstance(expr, Derivative): + unhandled = list(expr.variable_count) + unhandled + expr = expr.expr + expr = Expr.__new__(cls, expr, *unhandled) + + if (nderivs > 1) == True and kwargs.get('simplify', True): + from .exprtools import factor_terms + from sympy.simplify.simplify import signsimp + expr = factor_terms(signsimp(expr)) + return expr + + @property + def canonical(cls): + return cls.func(cls.expr, + *Derivative._sort_variable_count(cls.variable_count)) + + @classmethod + def _sort_variable_count(cls, vc): + """ + Sort (variable, count) pairs into canonical order while + retaining order of variables that do not commute during + differentiation: + + * symbols and functions commute with each other + * derivatives commute with each other + * a derivative does not commute with anything it contains + * any other object is not allowed to commute if it has + free symbols in common with another object + + Examples + ======== + + >>> from sympy import Derivative, Function, symbols + >>> vsort = Derivative._sort_variable_count + >>> x, y, z = symbols('x y z') + >>> f, g, h = symbols('f g h', cls=Function) + + Contiguous items are collapsed into one pair: + + >>> vsort([(x, 1), (x, 1)]) + [(x, 2)] + >>> vsort([(y, 1), (f(x), 1), (y, 1), (f(x), 1)]) + [(y, 2), (f(x), 2)] + + Ordering is canonical. + + >>> def vsort0(*v): + ... # docstring helper to + ... # change vi -> (vi, 0), sort, and return vi vals + ... return [i[0] for i in vsort([(i, 0) for i in v])] + + >>> vsort0(y, x) + [x, y] + >>> vsort0(g(y), g(x), f(y)) + [f(y), g(x), g(y)] + + Symbols are sorted as far to the left as possible but never + move to the left of a derivative having the same symbol in + its variables; the same applies to AppliedUndef which are + always sorted after Symbols: + + >>> dfx = f(x).diff(x) + >>> assert vsort0(dfx, y) == [y, dfx] + >>> assert vsort0(dfx, x) == [dfx, x] + """ + if not vc: + return [] + vc = list(vc) + if len(vc) == 1: + return [Tuple(*vc[0])] + V = list(range(len(vc))) + E = [] + v = lambda i: vc[i][0] + D = Dummy() + def _block(d, v, wrt=False): + # return True if v should not come before d else False + if d == v: + return wrt + if d.is_Symbol: + return False + if isinstance(d, Derivative): + # a derivative blocks if any of it's variables contain + # v; the wrt flag will return True for an exact match + # and will cause an AppliedUndef to block if v is in + # the arguments + if any(_block(k, v, wrt=True) + for k in d._wrt_variables): + return True + return False + if not wrt and isinstance(d, AppliedUndef): + return False + if v.is_Symbol: + return v in d.free_symbols + if isinstance(v, AppliedUndef): + return _block(d.xreplace({v: D}), D) + return d.free_symbols & v.free_symbols + for i in range(len(vc)): + for j in range(i): + if _block(v(j), v(i)): + E.append((j,i)) + # this is the default ordering to use in case of ties + O = dict(zip(ordered(uniq([i for i, c in vc])), range(len(vc)))) + ix = topological_sort((V, E), key=lambda i: O[v(i)]) + # merge counts of contiguously identical items + merged = [] + for v, c in [vc[i] for i in ix]: + if merged and merged[-1][0] == v: + merged[-1][1] += c + else: + merged.append([v, c]) + return [Tuple(*i) for i in merged] + + def _eval_is_commutative(self): + return self.expr.is_commutative + + def _eval_derivative(self, v): + # If v (the variable of differentiation) is not in + # self.variables, we might be able to take the derivative. + if v not in self._wrt_variables: + dedv = self.expr.diff(v) + if isinstance(dedv, Derivative): + return dedv.func(dedv.expr, *(self.variable_count + dedv.variable_count)) + # dedv (d(self.expr)/dv) could have simplified things such that the + # derivative wrt things in self.variables can now be done. Thus, + # we set evaluate=True to see if there are any other derivatives + # that can be done. The most common case is when dedv is a simple + # number so that the derivative wrt anything else will vanish. + return self.func(dedv, *self.variables, evaluate=True) + # In this case v was in self.variables so the derivative wrt v has + # already been attempted and was not computed, either because it + # couldn't be or evaluate=False originally. + variable_count = list(self.variable_count) + variable_count.append((v, 1)) + return self.func(self.expr, *variable_count, evaluate=False) + + def doit(self, **hints): + expr = self.expr + if hints.get('deep', True): + expr = expr.doit(**hints) + hints['evaluate'] = True + rv = self.func(expr, *self.variable_count, **hints) + if rv!= self and rv.has(Derivative): + rv = rv.doit(**hints) + return rv + + @_sympifyit('z0', NotImplementedError) + def doit_numerically(self, z0): + """ + Evaluate the derivative at z numerically. + + When we can represent derivatives at a point, this should be folded + into the normal evalf. For now, we need a special method. + """ + if len(self.free_symbols) != 1 or len(self.variables) != 1: + raise NotImplementedError('partials and higher order derivatives') + z = list(self.free_symbols)[0] + + def eval(x): + f0 = self.expr.subs(z, Expr._from_mpmath(x, prec=mpmath.mp.prec)) + f0 = f0.evalf(prec_to_dps(mpmath.mp.prec)) + return f0._to_mpmath(mpmath.mp.prec) + return Expr._from_mpmath(mpmath.diff(eval, + z0._to_mpmath(mpmath.mp.prec)), + mpmath.mp.prec) + + @property + def expr(self): + return self._args[0] + + @property + def _wrt_variables(self): + # return the variables of differentiation without + # respect to the type of count (int or symbolic) + return [i[0] for i in self.variable_count] + + @property + def variables(self): + # TODO: deprecate? YES, make this 'enumerated_variables' and + # name _wrt_variables as variables + # TODO: support for `d^n`? + rv = [] + for v, count in self.variable_count: + if not count.is_Integer: + raise TypeError(filldedent(''' + Cannot give expansion for symbolic count. If you just + want a list of all variables of differentiation, use + _wrt_variables.''')) + rv.extend([v]*count) + return tuple(rv) + + @property + def variable_count(self): + return self._args[1:] + + @property + def derivative_count(self): + return sum([count for _, count in self.variable_count], 0) + + @property + def free_symbols(self): + ret = self.expr.free_symbols + # Add symbolic counts to free_symbols + for _, count in self.variable_count: + ret.update(count.free_symbols) + return ret + + @property + def kind(self): + return self.args[0].kind + + def _eval_subs(self, old, new): + # The substitution (old, new) cannot be done inside + # Derivative(expr, vars) for a variety of reasons + # as handled below. + if old in self._wrt_variables: + # first handle the counts + expr = self.func(self.expr, *[(v, c.subs(old, new)) + for v, c in self.variable_count]) + if expr != self: + return expr._eval_subs(old, new) + # quick exit case + if not getattr(new, '_diff_wrt', False): + # case (0): new is not a valid variable of + # differentiation + if isinstance(old, Symbol): + # don't introduce a new symbol if the old will do + return Subs(self, old, new) + else: + xi = Dummy('xi') + return Subs(self.xreplace({old: xi}), xi, new) + + # If both are Derivatives with the same expr, check if old is + # equivalent to self or if old is a subderivative of self. + if old.is_Derivative and old.expr == self.expr: + if self.canonical == old.canonical: + return new + + # collections.Counter doesn't have __le__ + def _subset(a, b): + return all((a[i] <= b[i]) == True for i in a) + + old_vars = Counter(dict(reversed(old.variable_count))) + self_vars = Counter(dict(reversed(self.variable_count))) + if _subset(old_vars, self_vars): + return _derivative_dispatch(new, *(self_vars - old_vars).items()).canonical + + args = list(self.args) + newargs = [x._subs(old, new) for x in args] + if args[0] == old: + # complete replacement of self.expr + # we already checked that the new is valid so we know + # it won't be a problem should it appear in variables + return _derivative_dispatch(*newargs) + + if newargs[0] != args[0]: + # case (1) can't change expr by introducing something that is in + # the _wrt_variables if it was already in the expr + # e.g. + # for Derivative(f(x, g(y)), y), x cannot be replaced with + # anything that has y in it; for f(g(x), g(y)).diff(g(y)) + # g(x) cannot be replaced with anything that has g(y) + syms = {vi: Dummy() for vi in self._wrt_variables + if not vi.is_Symbol} + wrt = {syms.get(vi, vi) for vi in self._wrt_variables} + forbidden = args[0].xreplace(syms).free_symbols & wrt + nfree = new.xreplace(syms).free_symbols + ofree = old.xreplace(syms).free_symbols + if (nfree - ofree) & forbidden: + return Subs(self, old, new) + + viter = ((i, j) for ((i, _), (j, _)) in zip(newargs[1:], args[1:])) + if any(i != j for i, j in viter): # a wrt-variable change + # case (2) can't change vars by introducing a variable + # that is contained in expr, e.g. + # for Derivative(f(z, g(h(x), y)), y), y cannot be changed to + # x, h(x), or g(h(x), y) + for a in _atomic(self.expr, recursive=True): + for i in range(1, len(newargs)): + vi, _ = newargs[i] + if a == vi and vi != args[i][0]: + return Subs(self, old, new) + # more arg-wise checks + vc = newargs[1:] + oldv = self._wrt_variables + newe = self.expr + subs = [] + for i, (vi, ci) in enumerate(vc): + if not vi._diff_wrt: + # case (3) invalid differentiation expression so + # create a replacement dummy + xi = Dummy('xi_%i' % i) + # replace the old valid variable with the dummy + # in the expression + newe = newe.xreplace({oldv[i]: xi}) + # and replace the bad variable with the dummy + vc[i] = (xi, ci) + # and record the dummy with the new (invalid) + # differentiation expression + subs.append((xi, vi)) + + if subs: + # handle any residual substitution in the expression + newe = newe._subs(old, new) + # return the Subs-wrapped derivative + return Subs(Derivative(newe, *vc), *zip(*subs)) + + # everything was ok + return _derivative_dispatch(*newargs) + + def _eval_lseries(self, x, logx, cdir=0): + dx = self.variables + for term in self.expr.lseries(x, logx=logx, cdir=cdir): + yield self.func(term, *dx) + + def _eval_nseries(self, x, n, logx, cdir=0): + arg = self.expr.nseries(x, n=n, logx=logx) + o = arg.getO() + dx = self.variables + rv = [self.func(a, *dx) for a in Add.make_args(arg.removeO())] + if o: + rv.append(o/x) + return Add(*rv) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + series_gen = self.expr.lseries(x) + d = S.Zero + for leading_term in series_gen: + d = diff(leading_term, *self.variables) + if d != 0: + break + return d + + def as_finite_difference(self, points=1, x0=None, wrt=None): + """ Expresses a Derivative instance as a finite difference. + + Parameters + ========== + + points : sequence or coefficient, optional + If sequence: discrete values (length >= order+1) of the + independent variable used for generating the finite + difference weights. + If it is a coefficient, it will be used as the step-size + for generating an equidistant sequence of length order+1 + centered around ``x0``. Default: 1 (step-size 1) + + x0 : number or Symbol, optional + the value of the independent variable (``wrt``) at which the + derivative is to be approximated. Default: same as ``wrt``. + + wrt : Symbol, optional + "with respect to" the variable for which the (partial) + derivative is to be approximated for. If not provided it + is required that the derivative is ordinary. Default: ``None``. + + + Examples + ======== + + >>> from sympy import symbols, Function, exp, sqrt, Symbol + >>> x, h = symbols('x h') + >>> f = Function('f') + >>> f(x).diff(x).as_finite_difference() + -f(x - 1/2) + f(x + 1/2) + + The default step size and number of points are 1 and + ``order + 1`` respectively. We can change the step size by + passing a symbol as a parameter: + + >>> f(x).diff(x).as_finite_difference(h) + -f(-h/2 + x)/h + f(h/2 + x)/h + + We can also specify the discretized values to be used in a + sequence: + + >>> f(x).diff(x).as_finite_difference([x, x+h, x+2*h]) + -3*f(x)/(2*h) + 2*f(h + x)/h - f(2*h + x)/(2*h) + + The algorithm is not restricted to use equidistant spacing, nor + do we need to make the approximation around ``x0``, but we can get + an expression estimating the derivative at an offset: + + >>> e, sq2 = exp(1), sqrt(2) + >>> xl = [x-h, x+h, x+e*h] + >>> f(x).diff(x, 1).as_finite_difference(xl, x+h*sq2) # doctest: +ELLIPSIS + 2*h*((h + sqrt(2)*h)/(2*h) - (-sqrt(2)*h + h)/(2*h))*f(E*h + x)/... + + To approximate ``Derivative`` around ``x0`` using a non-equidistant + spacing step, the algorithm supports assignment of undefined + functions to ``points``: + + >>> dx = Function('dx') + >>> f(x).diff(x).as_finite_difference(points=dx(x), x0=x-h) + -f(-h + x - dx(-h + x)/2)/dx(-h + x) + f(-h + x + dx(-h + x)/2)/dx(-h + x) + + Partial derivatives are also supported: + + >>> y = Symbol('y') + >>> d2fdxdy=f(x,y).diff(x,y) + >>> d2fdxdy.as_finite_difference(wrt=x) + -Derivative(f(x - 1/2, y), y) + Derivative(f(x + 1/2, y), y) + + We can apply ``as_finite_difference`` to ``Derivative`` instances in + compound expressions using ``replace``: + + >>> (1 + 42**f(x).diff(x)).replace(lambda arg: arg.is_Derivative, + ... lambda arg: arg.as_finite_difference()) + 42**(-f(x - 1/2) + f(x + 1/2)) + 1 + + + See also + ======== + + sympy.calculus.finite_diff.apply_finite_diff + sympy.calculus.finite_diff.differentiate_finite + sympy.calculus.finite_diff.finite_diff_weights + + """ + from sympy.calculus.finite_diff import _as_finite_diff + return _as_finite_diff(self, points, x0, wrt) + + @classmethod + def _get_zero_with_shape_like(cls, expr): + return S.Zero + + @classmethod + def _dispatch_eval_derivative_n_times(cls, expr, v, count): + # Evaluate the derivative `n` times. If + # `_eval_derivative_n_times` is not overridden by the current + # object, the default in `Basic` will call a loop over + # `_eval_derivative`: + return expr._eval_derivative_n_times(v, count) + + +def _derivative_dispatch(expr, *variables, **kwargs): + from sympy.matrices.matrixbase import MatrixBase + from sympy.matrices.expressions.matexpr import MatrixExpr + from sympy.tensor.array import NDimArray + array_types = (MatrixBase, MatrixExpr, NDimArray, list, tuple, Tuple) + if isinstance(expr, array_types) or any(isinstance(i[0], array_types) if isinstance(i, (tuple, list, Tuple)) else isinstance(i, array_types) for i in variables): + from sympy.tensor.array.array_derivatives import ArrayDerivative + return ArrayDerivative(expr, *variables, **kwargs) + return Derivative(expr, *variables, **kwargs) + + +class Lambda(Expr): + """ + Lambda(x, expr) represents a lambda function similar to Python's + 'lambda x: expr'. A function of several variables is written as + Lambda((x, y, ...), expr). + + Examples + ======== + + A simple example: + + >>> from sympy import Lambda + >>> from sympy.abc import x + >>> f = Lambda(x, x**2) + >>> f(4) + 16 + + For multivariate functions, use: + + >>> from sympy.abc import y, z, t + >>> f2 = Lambda((x, y, z, t), x + y**z + t**z) + >>> f2(1, 2, 3, 4) + 73 + + It is also possible to unpack tuple arguments: + + >>> f = Lambda(((x, y), z), x + y + z) + >>> f((1, 2), 3) + 6 + + A handy shortcut for lots of arguments: + + >>> p = x, y, z + >>> f = Lambda(p, x + y*z) + >>> f(*p) + x + y*z + + """ + is_Function = True + + def __new__(cls, signature, expr): + if iterable(signature) and not isinstance(signature, (tuple, Tuple)): + sympy_deprecation_warning( + """ + Using a non-tuple iterable as the first argument to Lambda + is deprecated. Use Lambda(tuple(args), expr) instead. + """, + deprecated_since_version="1.5", + active_deprecations_target="deprecated-non-tuple-lambda", + ) + signature = tuple(signature) + sig = signature if iterable(signature) else (signature,) + sig = sympify(sig) + cls._check_signature(sig) + + if len(sig) == 1 and sig[0] == expr: + return S.IdentityFunction + + return Expr.__new__(cls, sig, sympify(expr)) + + @classmethod + def _check_signature(cls, sig): + syms = set() + + def rcheck(args): + for a in args: + if a.is_symbol: + if a in syms: + raise BadSignatureError("Duplicate symbol %s" % a) + syms.add(a) + elif isinstance(a, Tuple): + rcheck(a) + else: + raise BadSignatureError("Lambda signature should be only tuples" + " and symbols, not %s" % a) + + if not isinstance(sig, Tuple): + raise BadSignatureError("Lambda signature should be a tuple not %s" % sig) + # Recurse through the signature: + rcheck(sig) + + @property + def signature(self): + """The expected form of the arguments to be unpacked into variables""" + return self._args[0] + + @property + def expr(self): + """The return value of the function""" + return self._args[1] + + @property + def variables(self): + """The variables used in the internal representation of the function""" + def _variables(args): + if isinstance(args, Tuple): + for arg in args: + yield from _variables(arg) + else: + yield args + return tuple(_variables(self.signature)) + + @property + def nargs(self): + from sympy.sets.sets import FiniteSet + return FiniteSet(len(self.signature)) + + bound_symbols = variables + + @property + def free_symbols(self): + return self.expr.free_symbols - set(self.variables) + + def __call__(self, *args): + n = len(args) + if n not in self.nargs: # Lambda only ever has 1 value in nargs + # XXX: exception message must be in exactly this format to + # make it work with NumPy's functions like vectorize(). See, + # for example, https://github.com/numpy/numpy/issues/1697. + # The ideal solution would be just to attach metadata to + # the exception and change NumPy to take advantage of this. + ## XXX does this apply to Lambda? If not, remove this comment. + temp = ('%(name)s takes exactly %(args)s ' + 'argument%(plural)s (%(given)s given)') + raise BadArgumentsError(temp % { + 'name': self, + 'args': list(self.nargs)[0], + 'plural': 's'*(list(self.nargs)[0] != 1), + 'given': n}) + + d = self._match_signature(self.signature, args) + + return self.expr.xreplace(d) + + def _match_signature(self, sig, args): + + symargmap = {} + + def rmatch(pars, args): + for par, arg in zip(pars, args): + if par.is_symbol: + symargmap[par] = arg + elif isinstance(par, Tuple): + if not isinstance(arg, (tuple, Tuple)) or len(args) != len(pars): + raise BadArgumentsError("Can't match %s and %s" % (args, pars)) + rmatch(par, arg) + + rmatch(sig, args) + + return symargmap + + @property + def is_identity(self): + """Return ``True`` if this ``Lambda`` is an identity function. """ + return self.signature == self.expr + + def _eval_evalf(self, prec): + return self.func(self.args[0], self.args[1].evalf(n=prec_to_dps(prec))) + + +class Subs(Expr): + """ + Represents unevaluated substitutions of an expression. + + ``Subs(expr, x, x0)`` represents the expression resulting + from substituting x with x0 in expr. + + Parameters + ========== + + expr : Expr + An expression. + + x : tuple, variable + A variable or list of distinct variables. + + x0 : tuple or list of tuples + A point or list of evaluation points + corresponding to those variables. + + Examples + ======== + + >>> from sympy import Subs, Function, sin, cos + >>> from sympy.abc import x, y, z + >>> f = Function('f') + + Subs are created when a particular substitution cannot be made. The + x in the derivative cannot be replaced with 0 because 0 is not a + valid variables of differentiation: + + >>> f(x).diff(x).subs(x, 0) + Subs(Derivative(f(x), x), x, 0) + + Once f is known, the derivative and evaluation at 0 can be done: + + >>> _.subs(f, sin).doit() == sin(x).diff(x).subs(x, 0) == cos(0) + True + + Subs can also be created directly with one or more variables: + + >>> Subs(f(x)*sin(y) + z, (x, y), (0, 1)) + Subs(z + f(x)*sin(y), (x, y), (0, 1)) + >>> _.doit() + z + f(0)*sin(1) + + Notes + ===== + + ``Subs`` objects are generally useful to represent unevaluated derivatives + calculated at a point. + + The variables may be expressions, but they are subjected to the limitations + of subs(), so it is usually a good practice to use only symbols for + variables, since in that case there can be no ambiguity. + + There's no automatic expansion - use the method .doit() to effect all + possible substitutions of the object and also of objects inside the + expression. + + When evaluating derivatives at a point that is not a symbol, a Subs object + is returned. One is also able to calculate derivatives of Subs objects - in + this case the expression is always expanded (for the unevaluated form, use + Derivative()). + + In order to allow expressions to combine before doit is done, a + representation of the Subs expression is used internally to make + expressions that are superficially different compare the same: + + >>> a, b = Subs(x, x, 0), Subs(y, y, 0) + >>> a + b + 2*Subs(x, x, 0) + + This can lead to unexpected consequences when using methods + like `has` that are cached: + + >>> s = Subs(x, x, 0) + >>> s.has(x), s.has(y) + (True, False) + >>> ss = s.subs(x, y) + >>> ss.has(x), ss.has(y) + (True, False) + >>> s, ss + (Subs(x, x, 0), Subs(y, y, 0)) + """ + def __new__(cls, expr, variables, point, **assumptions): + if not is_sequence(variables, Tuple): + variables = [variables] + variables = Tuple(*variables) + + if has_dups(variables): + repeated = [str(v) for v, i in Counter(variables).items() if i > 1] + __ = ', '.join(repeated) + raise ValueError(filldedent(''' + The following expressions appear more than once: %s + ''' % __)) + + point = Tuple(*(point if is_sequence(point, Tuple) else [point])) + + if len(point) != len(variables): + raise ValueError('Number of point values must be the same as ' + 'the number of variables.') + + if not point: + return sympify(expr) + + # denest + if isinstance(expr, Subs): + variables = expr.variables + variables + point = expr.point + point + expr = expr.expr + else: + expr = sympify(expr) + + # use symbols with names equal to the point value (with prepended _) + # to give a variable-independent expression + pre = "_" + pts = sorted(set(point), key=default_sort_key) + from sympy.printing.str import StrPrinter + class CustomStrPrinter(StrPrinter): + def _print_Dummy(self, expr): + return str(expr) + str(expr.dummy_index) + def mystr(expr, **settings): + p = CustomStrPrinter(settings) + return p.doprint(expr) + while 1: + s_pts = {p: Symbol(pre + mystr(p)) for p in pts} + reps = [(v, s_pts[p]) + for v, p in zip(variables, point)] + # if any underscore-prepended symbol is already a free symbol + # and is a variable with a different point value, then there + # is a clash, e.g. _0 clashes in Subs(_0 + _1, (_0, _1), (1, 0)) + # because the new symbol that would be created is _1 but _1 + # is already mapped to 0 so __0 and __1 are used for the new + # symbols + if any(r in expr.free_symbols and + r in variables and + Symbol(pre + mystr(point[variables.index(r)])) != r + for _, r in reps): + pre += "_" + continue + break + + obj = Expr.__new__(cls, expr, Tuple(*variables), point) + obj._expr = expr.xreplace(dict(reps)) + return obj + + def _eval_is_commutative(self): + return self.expr.is_commutative + + def doit(self, **hints): + e, v, p = self.args + + # remove self mappings + for i, (vi, pi) in enumerate(zip(v, p)): + if vi == pi: + v = v[:i] + v[i + 1:] + p = p[:i] + p[i + 1:] + if not v: + return self.expr + + if isinstance(e, Derivative): + # apply functions first, e.g. f -> cos + undone = [] + for i, vi in enumerate(v): + if isinstance(vi, FunctionClass): + e = e.subs(vi, p[i]) + else: + undone.append((vi, p[i])) + if not isinstance(e, Derivative): + e = e.doit() + if isinstance(e, Derivative): + # do Subs that aren't related to differentiation + undone2 = [] + D = Dummy() + arg = e.args[0] + for vi, pi in undone: + if D not in e.xreplace({vi: D}).free_symbols: + if arg.has(vi): + e = e.subs(vi, pi) + else: + undone2.append((vi, pi)) + undone = undone2 + # differentiate wrt variables that are present + wrt = [] + D = Dummy() + expr = e.expr + free = expr.free_symbols + for vi, ci in e.variable_count: + if isinstance(vi, Symbol) and vi in free: + expr = expr.diff((vi, ci)) + elif D in expr.subs(vi, D).free_symbols: + expr = expr.diff((vi, ci)) + else: + wrt.append((vi, ci)) + # inject remaining subs + rv = expr.subs(undone) + # do remaining differentiation *in order given* + for vc in wrt: + rv = rv.diff(vc) + else: + # inject remaining subs + rv = e.subs(undone) + else: + rv = e.doit(**hints).subs(list(zip(v, p))) + + if hints.get('deep', True) and rv != self: + rv = rv.doit(**hints) + return rv + + def evalf(self, prec=None, **options): + return self.doit().evalf(prec, **options) + + n = evalf # type:ignore + + @property + def variables(self): + """The variables to be evaluated""" + return self._args[1] + + bound_symbols = variables + + @property + def expr(self): + """The expression on which the substitution operates""" + return self._args[0] + + @property + def point(self): + """The values for which the variables are to be substituted""" + return self._args[2] + + @property + def free_symbols(self): + return (self.expr.free_symbols - set(self.variables) | + set(self.point.free_symbols)) + + @property + def expr_free_symbols(self): + sympy_deprecation_warning(""" + The expr_free_symbols property is deprecated. Use free_symbols to get + the free symbols of an expression. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-expr-free-symbols") + # Don't show the warning twice from the recursive call + with ignore_warnings(SymPyDeprecationWarning): + return (self.expr.expr_free_symbols - set(self.variables) | + set(self.point.expr_free_symbols)) + + def __eq__(self, other): + if not isinstance(other, Subs): + return False + return self._hashable_content() == other._hashable_content() + + def __ne__(self, other): + return not(self == other) + + def __hash__(self): + return super().__hash__() + + def _hashable_content(self): + return (self._expr.xreplace(self.canonical_variables), + ) + tuple(ordered([(v, p) for v, p in + zip(self.variables, self.point) if not self.expr.has(v)])) + + def _eval_subs(self, old, new): + # Subs doit will do the variables in order; the semantics + # of subs for Subs is have the following invariant for + # Subs object foo: + # foo.doit().subs(reps) == foo.subs(reps).doit() + pt = list(self.point) + if old in self.variables: + if _atomic(new) == {new} and not any( + i.has(new) for i in self.args): + # the substitution is neutral + return self.xreplace({old: new}) + # any occurrence of old before this point will get + # handled by replacements from here on + i = self.variables.index(old) + for j in range(i, len(self.variables)): + pt[j] = pt[j]._subs(old, new) + return self.func(self.expr, self.variables, pt) + v = [i._subs(old, new) for i in self.variables] + if v != list(self.variables): + return self.func(self.expr, self.variables + (old,), pt + [new]) + expr = self.expr._subs(old, new) + pt = [i._subs(old, new) for i in self.point] + return self.func(expr, v, pt) + + def _eval_derivative(self, s): + # Apply the chain rule of the derivative on the substitution variables: + f = self.expr + vp = V, P = self.variables, self.point + val = Add.fromiter(p.diff(s)*Subs(f.diff(v), *vp).doit() + for v, p in zip(V, P)) + + # these are all the free symbols in the expr + efree = f.free_symbols + # some symbols like IndexedBase include themselves and args + # as free symbols + compound = {i for i in efree if len(i.free_symbols) > 1} + # hide them and see what independent free symbols remain + dums = {Dummy() for i in compound} + masked = f.xreplace(dict(zip(compound, dums))) + ifree = masked.free_symbols - dums + # include the compound symbols + free = ifree | compound + # remove the variables already handled + free -= set(V) + # add back any free symbols of remaining compound symbols + free |= {i for j in free & compound for i in j.free_symbols} + # if symbols of s are in free then there is more to do + if free & s.free_symbols: + val += Subs(f.diff(s), self.variables, self.point).doit() + return val + + def _eval_nseries(self, x, n, logx, cdir=0): + if x in self.point: + # x is the variable being substituted into + apos = self.point.index(x) + other = self.variables[apos] + else: + other = x + arg = self.expr.nseries(other, n=n, logx=logx) + o = arg.getO() + terms = Add.make_args(arg.removeO()) + rv = Add(*[self.func(a, *self.args[1:]) for a in terms]) + if o: + rv += o.subs(other, x) + return rv + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + if x in self.point: + ipos = self.point.index(x) + xvar = self.variables[ipos] + return self.expr.as_leading_term(xvar) + if x in self.variables: + # if `x` is a dummy variable, it means it won't exist after the + # substitution has been performed: + return self + # The variable is independent of the substitution: + return self.expr.as_leading_term(x) + + +def diff(f, *symbols, **kwargs): + """ + Differentiate f with respect to symbols. + + Explanation + =========== + + This is just a wrapper to unify .diff() and the Derivative class; its + interface is similar to that of integrate(). You can use the same + shortcuts for multiple variables as with Derivative. For example, + diff(f(x), x, x, x) and diff(f(x), x, 3) both return the third derivative + of f(x). + + You can pass evaluate=False to get an unevaluated Derivative class. Note + that if there are 0 symbols (such as diff(f(x), x, 0), then the result will + be the function (the zeroth derivative), even if evaluate=False. + + Examples + ======== + + >>> from sympy import sin, cos, Function, diff + >>> from sympy.abc import x, y + >>> f = Function('f') + + >>> diff(sin(x), x) + cos(x) + >>> diff(f(x), x, x, x) + Derivative(f(x), (x, 3)) + >>> diff(f(x), x, 3) + Derivative(f(x), (x, 3)) + >>> diff(sin(x)*cos(y), x, 2, y, 2) + sin(x)*cos(y) + + >>> type(diff(sin(x), x)) + cos + >>> type(diff(sin(x), x, evaluate=False)) + + >>> type(diff(sin(x), x, 0)) + sin + >>> type(diff(sin(x), x, 0, evaluate=False)) + sin + + >>> diff(sin(x)) + cos(x) + >>> diff(sin(x*y)) + Traceback (most recent call last): + ... + ValueError: specify differentiation variables to differentiate sin(x*y) + + Note that ``diff(sin(x))`` syntax is meant only for convenience + in interactive sessions and should be avoided in library code. + + References + ========== + + .. [1] https://reference.wolfram.com/legacy/v5_2/Built-inFunctions/AlgebraicComputation/Calculus/D.html + + See Also + ======== + + Derivative + idiff: computes the derivative implicitly + + """ + if hasattr(f, 'diff'): + return f.diff(*symbols, **kwargs) + kwargs.setdefault('evaluate', True) + return _derivative_dispatch(f, *symbols, **kwargs) + + +def expand(e, deep=True, modulus=None, power_base=True, power_exp=True, + mul=True, log=True, multinomial=True, basic=True, **hints): + r""" + Expand an expression using methods given as hints. + + Explanation + =========== + + Hints evaluated unless explicitly set to False are: ``basic``, ``log``, + ``multinomial``, ``mul``, ``power_base``, and ``power_exp`` The following + hints are supported but not applied unless set to True: ``complex``, + ``func``, and ``trig``. In addition, the following meta-hints are + supported by some or all of the other hints: ``frac``, ``numer``, + ``denom``, ``modulus``, and ``force``. ``deep`` is supported by all + hints. Additionally, subclasses of Expr may define their own hints or + meta-hints. + + The ``basic`` hint is used for any special rewriting of an object that + should be done automatically (along with the other hints like ``mul``) + when expand is called. This is a catch-all hint to handle any sort of + expansion that may not be described by the existing hint names. To use + this hint an object should override the ``_eval_expand_basic`` method. + Objects may also define their own expand methods, which are not run by + default. See the API section below. + + If ``deep`` is set to ``True`` (the default), things like arguments of + functions are recursively expanded. Use ``deep=False`` to only expand on + the top level. + + If the ``force`` hint is used, assumptions about variables will be ignored + in making the expansion. + + Hints + ===== + + These hints are run by default + + mul + --- + + Distributes multiplication over addition: + + >>> from sympy import cos, exp, sin + >>> from sympy.abc import x, y, z + >>> (y*(x + z)).expand(mul=True) + x*y + y*z + + multinomial + ----------- + + Expand (x + y + ...)**n where n is a positive integer. + + >>> ((x + y + z)**2).expand(multinomial=True) + x**2 + 2*x*y + 2*x*z + y**2 + 2*y*z + z**2 + + power_exp + --------- + + Expand addition in exponents into multiplied bases. + + >>> exp(x + y).expand(power_exp=True) + exp(x)*exp(y) + >>> (2**(x + y)).expand(power_exp=True) + 2**x*2**y + + power_base + ---------- + + Split powers of multiplied bases. + + This only happens by default if assumptions allow, or if the + ``force`` meta-hint is used: + + >>> ((x*y)**z).expand(power_base=True) + (x*y)**z + >>> ((x*y)**z).expand(power_base=True, force=True) + x**z*y**z + >>> ((2*y)**z).expand(power_base=True) + 2**z*y**z + + Note that in some cases where this expansion always holds, SymPy performs + it automatically: + + >>> (x*y)**2 + x**2*y**2 + + log + --- + + Pull out power of an argument as a coefficient and split logs products + into sums of logs. + + Note that these only work if the arguments of the log function have the + proper assumptions--the arguments must be positive and the exponents must + be real--or else the ``force`` hint must be True: + + >>> from sympy import log, symbols + >>> log(x**2*y).expand(log=True) + log(x**2*y) + >>> log(x**2*y).expand(log=True, force=True) + 2*log(x) + log(y) + >>> x, y = symbols('x,y', positive=True) + >>> log(x**2*y).expand(log=True) + 2*log(x) + log(y) + + basic + ----- + + This hint is intended primarily as a way for custom subclasses to enable + expansion by default. + + These hints are not run by default: + + complex + ------- + + Split an expression into real and imaginary parts. + + >>> x, y = symbols('x,y') + >>> (x + y).expand(complex=True) + re(x) + re(y) + I*im(x) + I*im(y) + >>> cos(x).expand(complex=True) + -I*sin(re(x))*sinh(im(x)) + cos(re(x))*cosh(im(x)) + + Note that this is just a wrapper around ``as_real_imag()``. Most objects + that wish to redefine ``_eval_expand_complex()`` should consider + redefining ``as_real_imag()`` instead. + + func + ---- + + Expand other functions. + + >>> from sympy import gamma + >>> gamma(x + 1).expand(func=True) + x*gamma(x) + + trig + ---- + + Do trigonometric expansions. + + >>> cos(x + y).expand(trig=True) + -sin(x)*sin(y) + cos(x)*cos(y) + >>> sin(2*x).expand(trig=True) + 2*sin(x)*cos(x) + + Note that the forms of ``sin(n*x)`` and ``cos(n*x)`` in terms of ``sin(x)`` + and ``cos(x)`` are not unique, due to the identity `\sin^2(x) + \cos^2(x) + = 1`. The current implementation uses the form obtained from Chebyshev + polynomials, but this may change. See `this MathWorld article + `_ for more + information. + + Notes + ===== + + - You can shut off unwanted methods:: + + >>> (exp(x + y)*(x + y)).expand() + x*exp(x)*exp(y) + y*exp(x)*exp(y) + >>> (exp(x + y)*(x + y)).expand(power_exp=False) + x*exp(x + y) + y*exp(x + y) + >>> (exp(x + y)*(x + y)).expand(mul=False) + (x + y)*exp(x)*exp(y) + + - Use deep=False to only expand on the top level:: + + >>> exp(x + exp(x + y)).expand() + exp(x)*exp(exp(x)*exp(y)) + >>> exp(x + exp(x + y)).expand(deep=False) + exp(x)*exp(exp(x + y)) + + - Hints are applied in an arbitrary, but consistent order (in the current + implementation, they are applied in alphabetical order, except + multinomial comes before mul, but this may change). Because of this, + some hints may prevent expansion by other hints if they are applied + first. For example, ``mul`` may distribute multiplications and prevent + ``log`` and ``power_base`` from expanding them. Also, if ``mul`` is + applied before ``multinomial`, the expression might not be fully + distributed. The solution is to use the various ``expand_hint`` helper + functions or to use ``hint=False`` to this function to finely control + which hints are applied. Here are some examples:: + + >>> from sympy import expand, expand_mul, expand_power_base + >>> x, y, z = symbols('x,y,z', positive=True) + + >>> expand(log(x*(y + z))) + log(x) + log(y + z) + + Here, we see that ``log`` was applied before ``mul``. To get the mul + expanded form, either of the following will work:: + + >>> expand_mul(log(x*(y + z))) + log(x*y + x*z) + >>> expand(log(x*(y + z)), log=False) + log(x*y + x*z) + + A similar thing can happen with the ``power_base`` hint:: + + >>> expand((x*(y + z))**x) + (x*y + x*z)**x + + To get the ``power_base`` expanded form, either of the following will + work:: + + >>> expand((x*(y + z))**x, mul=False) + x**x*(y + z)**x + >>> expand_power_base((x*(y + z))**x) + x**x*(y + z)**x + + >>> expand((x + y)*y/x) + y + y**2/x + + The parts of a rational expression can be targeted:: + + >>> expand((x + y)*y/x/(x + 1), frac=True) + (x*y + y**2)/(x**2 + x) + >>> expand((x + y)*y/x/(x + 1), numer=True) + (x*y + y**2)/(x*(x + 1)) + >>> expand((x + y)*y/x/(x + 1), denom=True) + y*(x + y)/(x**2 + x) + + - The ``modulus`` meta-hint can be used to reduce the coefficients of an + expression post-expansion:: + + >>> expand((3*x + 1)**2) + 9*x**2 + 6*x + 1 + >>> expand((3*x + 1)**2, modulus=5) + 4*x**2 + x + 1 + + - Either ``expand()`` the function or ``.expand()`` the method can be + used. Both are equivalent:: + + >>> expand((x + 1)**2) + x**2 + 2*x + 1 + >>> ((x + 1)**2).expand() + x**2 + 2*x + 1 + + API + === + + Objects can define their own expand hints by defining + ``_eval_expand_hint()``. The function should take the form:: + + def _eval_expand_hint(self, **hints): + # Only apply the method to the top-level expression + ... + + See also the example below. Objects should define ``_eval_expand_hint()`` + methods only if ``hint`` applies to that specific object. The generic + ``_eval_expand_hint()`` method defined in Expr will handle the no-op case. + + Each hint should be responsible for expanding that hint only. + Furthermore, the expansion should be applied to the top-level expression + only. ``expand()`` takes care of the recursion that happens when + ``deep=True``. + + You should only call ``_eval_expand_hint()`` methods directly if you are + 100% sure that the object has the method, as otherwise you are liable to + get unexpected ``AttributeError``s. Note, again, that you do not need to + recursively apply the hint to args of your object: this is handled + automatically by ``expand()``. ``_eval_expand_hint()`` should + generally not be used at all outside of an ``_eval_expand_hint()`` method. + If you want to apply a specific expansion from within another method, use + the public ``expand()`` function, method, or ``expand_hint()`` functions. + + In order for expand to work, objects must be rebuildable by their args, + i.e., ``obj.func(*obj.args) == obj`` must hold. + + Expand methods are passed ``**hints`` so that expand hints may use + 'metahints'--hints that control how different expand methods are applied. + For example, the ``force=True`` hint described above that causes + ``expand(log=True)`` to ignore assumptions is such a metahint. The + ``deep`` meta-hint is handled exclusively by ``expand()`` and is not + passed to ``_eval_expand_hint()`` methods. + + Note that expansion hints should generally be methods that perform some + kind of 'expansion'. For hints that simply rewrite an expression, use the + .rewrite() API. + + Examples + ======== + + >>> from sympy import Expr, sympify + >>> class MyClass(Expr): + ... def __new__(cls, *args): + ... args = sympify(args) + ... return Expr.__new__(cls, *args) + ... + ... def _eval_expand_double(self, *, force=False, **hints): + ... ''' + ... Doubles the args of MyClass. + ... + ... If there more than four args, doubling is not performed, + ... unless force=True is also used (False by default). + ... ''' + ... if not force and len(self.args) > 4: + ... return self + ... return self.func(*(self.args + self.args)) + ... + >>> a = MyClass(1, 2, MyClass(3, 4)) + >>> a + MyClass(1, 2, MyClass(3, 4)) + >>> a.expand(double=True) + MyClass(1, 2, MyClass(3, 4, 3, 4), 1, 2, MyClass(3, 4, 3, 4)) + >>> a.expand(double=True, deep=False) + MyClass(1, 2, MyClass(3, 4), 1, 2, MyClass(3, 4)) + + >>> b = MyClass(1, 2, 3, 4, 5) + >>> b.expand(double=True) + MyClass(1, 2, 3, 4, 5) + >>> b.expand(double=True, force=True) + MyClass(1, 2, 3, 4, 5, 1, 2, 3, 4, 5) + + See Also + ======== + + expand_log, expand_mul, expand_multinomial, expand_complex, expand_trig, + expand_power_base, expand_power_exp, expand_func, sympy.simplify.hyperexpand.hyperexpand + + """ + # don't modify this; modify the Expr.expand method + hints['power_base'] = power_base + hints['power_exp'] = power_exp + hints['mul'] = mul + hints['log'] = log + hints['multinomial'] = multinomial + hints['basic'] = basic + return sympify(e).expand(deep=deep, modulus=modulus, **hints) + +# This is a special application of two hints + +def _mexpand(expr, recursive=False): + # expand multinomials and then expand products; this may not always + # be sufficient to give a fully expanded expression (see + # test_issue_8247_8354 in test_arit) + if expr is None: + return + was = None + while was != expr: + was, expr = expr, expand_mul(expand_multinomial(expr)) + if not recursive: + break + return expr + + +# These are simple wrappers around single hints. + + +def expand_mul(expr, deep=True): + """ + Wrapper around expand that only uses the mul hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import symbols, expand_mul, exp, log + >>> x, y = symbols('x,y', positive=True) + >>> expand_mul(exp(x+y)*(x+y)*log(x*y**2)) + x*exp(x + y)*log(x*y**2) + y*exp(x + y)*log(x*y**2) + + """ + return sympify(expr).expand(deep=deep, mul=True, power_exp=False, + power_base=False, basic=False, multinomial=False, log=False) + + +def expand_multinomial(expr, deep=True): + """ + Wrapper around expand that only uses the multinomial hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import symbols, expand_multinomial, exp + >>> x, y = symbols('x y', positive=True) + >>> expand_multinomial((x + exp(x + 1))**2) + x**2 + 2*x*exp(x + 1) + exp(2*x + 2) + + """ + return sympify(expr).expand(deep=deep, mul=False, power_exp=False, + power_base=False, basic=False, multinomial=True, log=False) + + +def expand_log(expr, deep=True, force=False, factor=False): + """ + Wrapper around expand that only uses the log hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import symbols, expand_log, exp, log + >>> x, y = symbols('x,y', positive=True) + >>> expand_log(exp(x+y)*(x+y)*log(x*y**2)) + (x + y)*(log(x) + 2*log(y))*exp(x + y) + + """ + from sympy.functions.elementary.exponential import log + from sympy.simplify.radsimp import fraction + if factor is False: + def _handleMul(x): + # look for the simple case of expanded log(b**a)/log(b) -> a in args + n, d = fraction(x) + n = [i for i in n.atoms(log) if i.args[0].is_Integer] + d = [i for i in d.atoms(log) if i.args[0].is_Integer] + if len(n) == 1 and len(d) == 1: + n = n[0] + d = d[0] + from sympy import multiplicity + m = multiplicity(d.args[0], n.args[0]) + if m: + r = m + log(n.args[0]//d.args[0]**m)/d + x = x.subs(n, d*r) + x1 = expand_mul(expand_log(x, deep=deep, force=force, factor=True)) + if x1.count(log) <= x.count(log): + return x1 + return x + + expr = expr.replace( + lambda x: x.is_Mul and all(any(isinstance(i, log) and i.args[0].is_Rational + for i in Mul.make_args(j)) for j in x.as_numer_denom()), + _handleMul) + + return sympify(expr).expand(deep=deep, log=True, mul=False, + power_exp=False, power_base=False, multinomial=False, + basic=False, force=force, factor=factor) + + +def expand_func(expr, deep=True): + """ + Wrapper around expand that only uses the func hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import expand_func, gamma + >>> from sympy.abc import x + >>> expand_func(gamma(x + 2)) + x*(x + 1)*gamma(x) + + """ + return sympify(expr).expand(deep=deep, func=True, basic=False, + log=False, mul=False, power_exp=False, power_base=False, multinomial=False) + + +def expand_trig(expr, deep=True): + """ + Wrapper around expand that only uses the trig hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import expand_trig, sin + >>> from sympy.abc import x, y + >>> expand_trig(sin(x+y)*(x+y)) + (x + y)*(sin(x)*cos(y) + sin(y)*cos(x)) + + """ + return sympify(expr).expand(deep=deep, trig=True, basic=False, + log=False, mul=False, power_exp=False, power_base=False, multinomial=False) + + +def expand_complex(expr, deep=True): + """ + Wrapper around expand that only uses the complex hint. See the expand + docstring for more information. + + Examples + ======== + + >>> from sympy import expand_complex, exp, sqrt, I + >>> from sympy.abc import z + >>> expand_complex(exp(z)) + I*exp(re(z))*sin(im(z)) + exp(re(z))*cos(im(z)) + >>> expand_complex(sqrt(I)) + sqrt(2)/2 + sqrt(2)*I/2 + + See Also + ======== + + sympy.core.expr.Expr.as_real_imag + """ + return sympify(expr).expand(deep=deep, complex=True, basic=False, + log=False, mul=False, power_exp=False, power_base=False, multinomial=False) + + +def expand_power_base(expr, deep=True, force=False): + """ + Wrapper around expand that only uses the power_base hint. + + A wrapper to expand(power_base=True) which separates a power with a base + that is a Mul into a product of powers, without performing any other + expansions, provided that assumptions about the power's base and exponent + allow. + + deep=False (default is True) will only apply to the top-level expression. + + force=True (default is False) will cause the expansion to ignore + assumptions about the base and exponent. When False, the expansion will + only happen if the base is non-negative or the exponent is an integer. + + >>> from sympy.abc import x, y, z + >>> from sympy import expand_power_base, sin, cos, exp, Symbol + + >>> (x*y)**2 + x**2*y**2 + + >>> (2*x)**y + (2*x)**y + >>> expand_power_base(_) + 2**y*x**y + + >>> expand_power_base((x*y)**z) + (x*y)**z + >>> expand_power_base((x*y)**z, force=True) + x**z*y**z + >>> expand_power_base(sin((x*y)**z), deep=False) + sin((x*y)**z) + >>> expand_power_base(sin((x*y)**z), force=True) + sin(x**z*y**z) + + >>> expand_power_base((2*sin(x))**y + (2*cos(x))**y) + 2**y*sin(x)**y + 2**y*cos(x)**y + + >>> expand_power_base((2*exp(y))**x) + 2**x*exp(y)**x + + >>> expand_power_base((2*cos(x))**y) + 2**y*cos(x)**y + + Notice that sums are left untouched. If this is not the desired behavior, + apply full ``expand()`` to the expression: + + >>> expand_power_base(((x+y)*z)**2) + z**2*(x + y)**2 + >>> (((x+y)*z)**2).expand() + x**2*z**2 + 2*x*y*z**2 + y**2*z**2 + + >>> expand_power_base((2*y)**(1+z)) + 2**(z + 1)*y**(z + 1) + >>> ((2*y)**(1+z)).expand() + 2*2**z*y**(z + 1) + + The power that is unexpanded can be expanded safely when + ``y != 0``, otherwise different values might be obtained for the expression: + + >>> prev = _ + + If we indicate that ``y`` is positive but then replace it with + a value of 0 after expansion, the expression becomes 0: + + >>> p = Symbol('p', positive=True) + >>> prev.subs(y, p).expand().subs(p, 0) + 0 + + But if ``z = -1`` the expression would not be zero: + + >>> prev.subs(y, 0).subs(z, -1) + 1 + + See Also + ======== + + expand + + """ + return sympify(expr).expand(deep=deep, log=False, mul=False, + power_exp=False, power_base=True, multinomial=False, + basic=False, force=force) + + +def expand_power_exp(expr, deep=True): + """ + Wrapper around expand that only uses the power_exp hint. + + See the expand docstring for more information. + + Examples + ======== + + >>> from sympy import expand_power_exp, Symbol + >>> from sympy.abc import x, y + >>> expand_power_exp(3**(y + 2)) + 9*3**y + >>> expand_power_exp(x**(y + 2)) + x**(y + 2) + + If ``x = 0`` the value of the expression depends on the + value of ``y``; if the expression were expanded the result + would be 0. So expansion is only done if ``x != 0``: + + >>> expand_power_exp(Symbol('x', zero=False)**(y + 2)) + x**2*x**y + """ + return sympify(expr).expand(deep=deep, complex=False, basic=False, + log=False, mul=False, power_exp=True, power_base=False, multinomial=False) + + +def count_ops(expr, visual=False): + """ + Return a representation (integer or expression) of the operations in expr. + + Parameters + ========== + + expr : Expr + If expr is an iterable, the sum of the op counts of the + items will be returned. + + visual : bool, optional + If ``False`` (default) then the sum of the coefficients of the + visual expression will be returned. + If ``True`` then the number of each type of operation is shown + with the core class types (or their virtual equivalent) multiplied by the + number of times they occur. + + Examples + ======== + + >>> from sympy.abc import a, b, x, y + >>> from sympy import sin, count_ops + + Although there is not a SUB object, minus signs are interpreted as + either negations or subtractions: + + >>> (x - y).count_ops(visual=True) + SUB + >>> (-x).count_ops(visual=True) + NEG + + Here, there are two Adds and a Pow: + + >>> (1 + a + b**2).count_ops(visual=True) + 2*ADD + POW + + In the following, an Add, Mul, Pow and two functions: + + >>> (sin(x)*x + sin(x)**2).count_ops(visual=True) + ADD + MUL + POW + 2*SIN + + for a total of 5: + + >>> (sin(x)*x + sin(x)**2).count_ops(visual=False) + 5 + + Note that "what you type" is not always what you get. The expression + 1/x/y is translated by sympy into 1/(x*y) so it gives a DIV and MUL rather + than two DIVs: + + >>> (1/x/y).count_ops(visual=True) + DIV + MUL + + The visual option can be used to demonstrate the difference in + operations for expressions in different forms. Here, the Horner + representation is compared with the expanded form of a polynomial: + + >>> eq=x*(1 + x*(2 + x*(3 + x))) + >>> count_ops(eq.expand(), visual=True) - count_ops(eq, visual=True) + -MUL + 3*POW + + The count_ops function also handles iterables: + + >>> count_ops([x, sin(x), None, True, x + 2], visual=False) + 2 + >>> count_ops([x, sin(x), None, True, x + 2], visual=True) + ADD + SIN + >>> count_ops({x: sin(x), x + 2: y + 1}, visual=True) + 2*ADD + SIN + + """ + from .relational import Relational + from sympy.concrete.summations import Sum + from sympy.integrals.integrals import Integral + from sympy.logic.boolalg import BooleanFunction + from sympy.simplify.radsimp import fraction + + expr = sympify(expr) + if isinstance(expr, Expr) and not expr.is_Relational: + + ops = [] + args = [expr] + NEG = Symbol('NEG') + DIV = Symbol('DIV') + SUB = Symbol('SUB') + ADD = Symbol('ADD') + EXP = Symbol('EXP') + while args: + a = args.pop() + + # if the following fails because the object is + # not Basic type, then the object should be fixed + # since it is the intention that all args of Basic + # should themselves be Basic + if a.is_Rational: + #-1/3 = NEG + DIV + if a is not S.One: + if a.p < 0: + ops.append(NEG) + if a.q != 1: + ops.append(DIV) + continue + elif a.is_Mul or a.is_MatMul: + if _coeff_isneg(a): + ops.append(NEG) + if a.args[0] is S.NegativeOne: + a = a.as_two_terms()[1] + else: + a = -a + n, d = fraction(a) + if n.is_Integer: + ops.append(DIV) + if n < 0: + ops.append(NEG) + args.append(d) + continue # won't be -Mul but could be Add + elif d is not S.One: + if not d.is_Integer: + args.append(d) + ops.append(DIV) + args.append(n) + continue # could be -Mul + elif a.is_Add or a.is_MatAdd: + aargs = list(a.args) + negs = 0 + for i, ai in enumerate(aargs): + if _coeff_isneg(ai): + negs += 1 + args.append(-ai) + if i > 0: + ops.append(SUB) + else: + args.append(ai) + if i > 0: + ops.append(ADD) + if negs == len(aargs): # -x - y = NEG + SUB + ops.append(NEG) + elif _coeff_isneg(aargs[0]): # -x + y = SUB, but already recorded ADD + ops.append(SUB - ADD) + continue + if a.is_Pow and a.exp is S.NegativeOne: + ops.append(DIV) + args.append(a.base) # won't be -Mul but could be Add + continue + if a == S.Exp1: + ops.append(EXP) + continue + if a.is_Pow and a.base == S.Exp1: + ops.append(EXP) + args.append(a.exp) + continue + if a.is_Mul or isinstance(a, LatticeOp): + o = Symbol(a.func.__name__.upper()) + # count the args + ops.append(o*(len(a.args) - 1)) + elif a.args and ( + a.is_Pow or a.is_Function or isinstance(a, (Derivative, Integral, Sum))): + # if it's not in the list above we don't + # consider a.func something to count, e.g. + # Tuple, MatrixSymbol, etc... + if isinstance(a.func, UndefinedFunction): + o = Symbol("FUNC_" + a.func.__name__.upper()) + else: + o = Symbol(a.func.__name__.upper()) + ops.append(o) + + if not a.is_Symbol: + args.extend(a.args) + + elif isinstance(expr, Dict): + ops = [count_ops(k, visual=visual) + + count_ops(v, visual=visual) for k, v in expr.items()] + elif iterable(expr): + ops = [count_ops(i, visual=visual) for i in expr] + elif isinstance(expr, (Relational, BooleanFunction)): + ops = [] + for arg in expr.args: + ops.append(count_ops(arg, visual=True)) + o = Symbol(func_name(expr, short=True).upper()) + ops.append(o) + elif not isinstance(expr, Basic): + ops = [] + else: # it's Basic not isinstance(expr, Expr): + if not isinstance(expr, Basic): + raise TypeError("Invalid type of expr") + else: + ops = [] + args = [expr] + while args: + a = args.pop() + + if a.args: + o = Symbol(type(a).__name__.upper()) + if a.is_Boolean: + ops.append(o*(len(a.args)-1)) + else: + ops.append(o) + args.extend(a.args) + + if not ops: + if visual: + return S.Zero + return 0 + + ops = Add(*ops) + + if visual: + return ops + + if ops.is_Number: + return int(ops) + + return sum(int((a.args or [1])[0]) for a in Add.make_args(ops)) + + +def nfloat(expr, n=15, exponent=False, dkeys=False): + """Make all Rationals in expr Floats except those in exponents + (unless the exponents flag is set to True) and those in undefined + functions. When processing dictionaries, do not modify the keys + unless ``dkeys=True``. + + Examples + ======== + + >>> from sympy import nfloat, cos, pi, sqrt + >>> from sympy.abc import x, y + >>> nfloat(x**4 + x/2 + cos(pi/3) + 1 + sqrt(y)) + x**4 + 0.5*x + sqrt(y) + 1.5 + >>> nfloat(x**4 + sqrt(y), exponent=True) + x**4.0 + y**0.5 + + Container types are not modified: + + >>> type(nfloat((1, 2))) is tuple + True + """ + from sympy.matrices.matrixbase import MatrixBase + + kw = {"n": n, "exponent": exponent, "dkeys": dkeys} + + if isinstance(expr, MatrixBase): + return expr.applyfunc(lambda e: nfloat(e, **kw)) + + # handling of iterable containers + if iterable(expr, exclude=str): + if isinstance(expr, (dict, Dict)): + if dkeys: + args = [tuple((nfloat(i, **kw) for i in a)) + for a in expr.items()] + else: + args = [(k, nfloat(v, **kw)) for k, v in expr.items()] + if isinstance(expr, dict): + return type(expr)(args) + else: + return expr.func(*args) + elif isinstance(expr, Basic): + return expr.func(*[nfloat(a, **kw) for a in expr.args]) + return type(expr)([nfloat(a, **kw) for a in expr]) + + rv = sympify(expr) + + if rv.is_Number: + return Float(rv, n) + elif rv.is_number: + # evalf doesn't always set the precision + rv = rv.n(n) + if rv.is_Number: + rv = Float(rv.n(n), n) + else: + pass # pure_complex(rv) is likely True + return rv + elif rv.is_Atom: + return rv + elif rv.is_Relational: + args_nfloat = (nfloat(arg, **kw) for arg in rv.args) + return rv.func(*args_nfloat) + + + # watch out for RootOf instances that don't like to have + # their exponents replaced with Dummies and also sometimes have + # problems with evaluating at low precision (issue 6393) + from sympy.polys.rootoftools import RootOf + rv = rv.xreplace({ro: ro.n(n) for ro in rv.atoms(RootOf)}) + + from .power import Pow + if not exponent: + reps = [(p, Pow(p.base, Dummy())) for p in rv.atoms(Pow)] + rv = rv.xreplace(dict(reps)) + rv = rv.n(n) + if not exponent: + rv = rv.xreplace({d.exp: p.exp for p, d in reps}) + else: + # Pow._eval_evalf special cases Integer exponents so if + # exponent is suppose to be handled we have to do so here + rv = rv.xreplace(Transform( + lambda x: Pow(x.base, Float(x.exp, n)), + lambda x: x.is_Pow and x.exp.is_Integer)) + + return rv.xreplace(Transform( + lambda x: x.func(*nfloat(x.args, n, exponent)), + lambda x: isinstance(x, Function) and not isinstance(x, AppliedUndef))) + + +from .symbol import Dummy, Symbol diff --git a/lib/python3.11/site-packages/sympy/core/intfunc.py b/lib/python3.11/site-packages/sympy/core/intfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..112f737ebcb584d41ace39b6a2015b0f05b89aeb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/intfunc.py @@ -0,0 +1,532 @@ +""" +The routines here were removed from numbers.py, power.py, +digits.py and factor_.py so they could be imported into core +without raising circular import errors. + +Although the name 'intfunc' was chosen to represent functions that +work with integers, it can also be thought of as containing +internal/core functions that are needed by the classes of the core. +""" + +import math +import sys +from functools import lru_cache + +from .sympify import sympify +from .singleton import S +from sympy.external.gmpy import (gcd as number_gcd, lcm as number_lcm, sqrt, + iroot, bit_scan1, gcdext) +from sympy.utilities.misc import as_int, filldedent + + +def num_digits(n, base=10): + """Return the number of digits needed to express n in give base. + + Examples + ======== + + >>> from sympy.core.intfunc import num_digits + >>> num_digits(10) + 2 + >>> num_digits(10, 2) # 1010 -> 4 digits + 4 + >>> num_digits(-100, 16) # -64 -> 2 digits + 2 + + + Parameters + ========== + + n: integer + The number whose digits are counted. + + b: integer + The base in which digits are computed. + + See Also + ======== + sympy.ntheory.digits.digits, sympy.ntheory.digits.count_digits + """ + if base < 0: + raise ValueError('base must be int greater than 1') + if not n: + return 1 + e, t = integer_log(abs(n), base) + return 1 + e + + +def integer_log(n, b): + r""" + Returns ``(e, bool)`` where e is the largest nonnegative integer + such that :math:`|n| \geq |b^e|` and ``bool`` is True if $n = b^e$. + + Examples + ======== + + >>> from sympy import integer_log + >>> integer_log(125, 5) + (3, True) + >>> integer_log(17, 9) + (1, False) + + If the base is positive and the number negative the + return value will always be the same except for 2: + + >>> integer_log(-4, 2) + (2, False) + >>> integer_log(-16, 4) + (0, False) + + When the base is negative, the returned value + will only be True if the parity of the exponent is + correct for the sign of the base: + + >>> integer_log(4, -2) + (2, True) + >>> integer_log(8, -2) + (3, False) + >>> integer_log(-8, -2) + (3, True) + >>> integer_log(-4, -2) + (2, False) + + See Also + ======== + integer_nthroot + sympy.ntheory.primetest.is_square + sympy.ntheory.factor_.multiplicity + sympy.ntheory.factor_.perfect_power + """ + n = as_int(n) + b = as_int(b) + + if b < 0: + e, t = integer_log(abs(n), -b) + # (-2)**3 == -8 + # (-2)**2 = 4 + t = t and e % 2 == (n < 0) + return e, t + if b <= 1: + raise ValueError('base must be 2 or more') + if n < 0: + if b != 2: + return 0, False + e, t = integer_log(-n, b) + return e, False + if n == 0: + raise ValueError('n cannot be 0') + + if n < b: + return 0, n == 1 + if b == 2: + e = n.bit_length() - 1 + return e, trailing(n) == e + t = trailing(b) + if 2**t == b: + e = int(n.bit_length() - 1)//t + n_ = 1 << (t*e) + return e, n_ == n + + d = math.floor(math.log10(n) / math.log10(b)) + n_ = b ** d + while n_ <= n: # this will iterate 0, 1 or 2 times + d += 1 + n_ *= b + return d - (n_ > n), (n_ == n or n_//b == n) + + +def trailing(n): + """Count the number of trailing zero digits in the binary + representation of n, i.e. determine the largest power of 2 + that divides n. + + Examples + ======== + + >>> from sympy import trailing + >>> trailing(128) + 7 + >>> trailing(63) + 0 + + See Also + ======== + sympy.ntheory.factor_.multiplicity + + """ + if not n: + return 0 + return bit_scan1(int(n)) + + +@lru_cache(1024) +def igcd(*args): + """Computes nonnegative integer greatest common divisor. + + Explanation + =========== + + The algorithm is based on the well known Euclid's algorithm [1]_. To + improve speed, ``igcd()`` has its own caching mechanism. + If you do not need the cache mechanism, using ``sympy.external.gmpy.gcd``. + + Examples + ======== + + >>> from sympy import igcd + >>> igcd(2, 4) + 2 + >>> igcd(5, 10, 15) + 5 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Euclidean_algorithm + + """ + if len(args) < 2: + raise TypeError("igcd() takes at least 2 arguments (%s given)" % len(args)) + return int(number_gcd(*map(as_int, args))) + + +igcd2 = math.gcd + + +def igcd_lehmer(a, b): + r"""Computes greatest common divisor of two integers. + + Explanation + =========== + + Euclid's algorithm for the computation of the greatest + common divisor ``gcd(a, b)`` of two (positive) integers + $a$ and $b$ is based on the division identity + $$ a = q \times b + r$$, + where the quotient $q$ and the remainder $r$ are integers + and $0 \le r < b$. Then each common divisor of $a$ and $b$ + divides $r$, and it follows that ``gcd(a, b) == gcd(b, r)``. + The algorithm works by constructing the sequence + r0, r1, r2, ..., where r0 = a, r1 = b, and each rn + is the remainder from the division of the two preceding + elements. + + In Python, ``q = a // b`` and ``r = a % b`` are obtained by the + floor division and the remainder operations, respectively. + These are the most expensive arithmetic operations, especially + for large a and b. + + Lehmer's algorithm [1]_ is based on the observation that the quotients + ``qn = r(n-1) // rn`` are in general small integers even + when a and b are very large. Hence the quotients can be + usually determined from a relatively small number of most + significant bits. + + The efficiency of the algorithm is further enhanced by not + computing each long remainder in Euclid's sequence. The remainders + are linear combinations of a and b with integer coefficients + derived from the quotients. The coefficients can be computed + as far as the quotients can be determined from the chosen + most significant parts of a and b. Only then a new pair of + consecutive remainders is computed and the algorithm starts + anew with this pair. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Lehmer%27s_GCD_algorithm + + """ + a, b = abs(as_int(a)), abs(as_int(b)) + if a < b: + a, b = b, a + + # The algorithm works by using one or two digit division + # whenever possible. The outer loop will replace the + # pair (a, b) with a pair of shorter consecutive elements + # of the Euclidean gcd sequence until a and b + # fit into two Python (long) int digits. + nbits = 2 * sys.int_info.bits_per_digit + + while a.bit_length() > nbits and b != 0: + # Quotients are mostly small integers that can + # be determined from most significant bits. + n = a.bit_length() - nbits + x, y = int(a >> n), int(b >> n) # most significant bits + + # Elements of the Euclidean gcd sequence are linear + # combinations of a and b with integer coefficients. + # Compute the coefficients of consecutive pairs + # a' = A*a + B*b, b' = C*a + D*b + # using small integer arithmetic as far as possible. + A, B, C, D = 1, 0, 0, 1 # initial values + + while True: + # The coefficients alternate in sign while looping. + # The inner loop combines two steps to keep track + # of the signs. + + # At this point we have + # A > 0, B <= 0, C <= 0, D > 0, + # x' = x + B <= x < x" = x + A, + # y' = y + C <= y < y" = y + D, + # and + # x'*N <= a' < x"*N, y'*N <= b' < y"*N, + # where N = 2**n. + + # Now, if y' > 0, and x"//y' and x'//y" agree, + # then their common value is equal to q = a'//b'. + # In addition, + # x'%y" = x' - q*y" < x" - q*y' = x"%y', + # and + # (x'%y")*N < a'%b' < (x"%y')*N. + + # On the other hand, we also have x//y == q, + # and therefore + # x'%y" = x + B - q*(y + D) = x%y + B', + # x"%y' = x + A - q*(y + C) = x%y + A', + # where + # B' = B - q*D < 0, A' = A - q*C > 0. + + if y + C <= 0: + break + q = (x + A) // (y + C) + + # Now x'//y" <= q, and equality holds if + # x' - q*y" = (x - q*y) + (B - q*D) >= 0. + # This is a minor optimization to avoid division. + x_qy, B_qD = x - q * y, B - q * D + if x_qy + B_qD < 0: + break + + # Next step in the Euclidean sequence. + x, y = y, x_qy + A, B, C, D = C, D, A - q * C, B_qD + + # At this point the signs of the coefficients + # change and their roles are interchanged. + # A <= 0, B > 0, C > 0, D < 0, + # x' = x + A <= x < x" = x + B, + # y' = y + D < y < y" = y + C. + + if y + D <= 0: + break + q = (x + B) // (y + D) + x_qy, A_qC = x - q * y, A - q * C + if x_qy + A_qC < 0: + break + + x, y = y, x_qy + A, B, C, D = C, D, A_qC, B - q * D + # Now the conditions on top of the loop + # are again satisfied. + # A > 0, B < 0, C < 0, D > 0. + + if B == 0: + # This can only happen when y == 0 in the beginning + # and the inner loop does nothing. + # Long division is forced. + a, b = b, a % b + continue + + # Compute new long arguments using the coefficients. + a, b = A * a + B * b, C * a + D * b + + # Small divisors. Finish with the standard algorithm. + while b: + a, b = b, a % b + + return a + + +def ilcm(*args): + """Computes integer least common multiple. + + Examples + ======== + + >>> from sympy import ilcm + >>> ilcm(5, 10) + 10 + >>> ilcm(7, 3) + 21 + >>> ilcm(5, 10, 15) + 30 + + """ + if len(args) < 2: + raise TypeError("ilcm() takes at least 2 arguments (%s given)" % len(args)) + return int(number_lcm(*map(as_int, args))) + + +def igcdex(a, b): + """Returns x, y, g such that g = x*a + y*b = gcd(a, b). + + Examples + ======== + + >>> from sympy.core.intfunc import igcdex + >>> igcdex(2, 3) + (-1, 1, 1) + >>> igcdex(10, 12) + (-1, 1, 2) + + >>> x, y, g = igcdex(100, 2004) + >>> x, y, g + (-20, 1, 4) + >>> x*100 + y*2004 + 4 + + """ + if (not a) and (not b): + return (0, 1, 0) + g, x, y = gcdext(int(a), int(b)) + return x, y, g + + +def mod_inverse(a, m): + r""" + Return the number $c$ such that, $a \times c = 1 \pmod{m}$ + where $c$ has the same sign as $m$. If no such value exists, + a ValueError is raised. + + Examples + ======== + + >>> from sympy import mod_inverse, S + + Suppose we wish to find multiplicative inverse $x$ of + 3 modulo 11. This is the same as finding $x$ such + that $3x = 1 \pmod{11}$. One value of x that satisfies + this congruence is 4. Because $3 \times 4 = 12$ and $12 = 1 \pmod{11}$. + This is the value returned by ``mod_inverse``: + + >>> mod_inverse(3, 11) + 4 + >>> mod_inverse(-3, 11) + 7 + + When there is a common factor between the numerators of + `a` and `m` the inverse does not exist: + + >>> mod_inverse(2, 4) + Traceback (most recent call last): + ... + ValueError: inverse of 2 mod 4 does not exist + + >>> mod_inverse(S(2)/7, S(5)/2) + 7/2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Modular_multiplicative_inverse + .. [2] https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm + """ + c = None + try: + a, m = as_int(a), as_int(m) + if m != 1 and m != -1: + x, _, g = igcdex(a, m) + if g == 1: + c = x % m + except ValueError: + a, m = sympify(a), sympify(m) + if not (a.is_number and m.is_number): + raise TypeError( + filldedent( + """ + Expected numbers for arguments; symbolic `mod_inverse` + is not implemented + but symbolic expressions can be handled with the + similar function, + sympy.polys.polytools.invert""" + ) + ) + big = m > 1 + if big not in (S.true, S.false): + raise ValueError("m > 1 did not evaluate; try to simplify %s" % m) + elif big: + c = 1 / a + if c is None: + raise ValueError("inverse of %s (mod %s) does not exist" % (a, m)) + return c + + +def isqrt(n): + r""" Return the largest integer less than or equal to `\sqrt{n}`. + + Parameters + ========== + + n : non-negative integer + + Returns + ======= + + int : `\left\lfloor\sqrt{n}\right\rfloor` + + Raises + ====== + + ValueError + If n is negative. + TypeError + If n is of a type that cannot be compared to ``int``. + Therefore, a TypeError is raised for ``str``, but not for ``float``. + + Examples + ======== + + >>> from sympy.core.intfunc import isqrt + >>> isqrt(0) + 0 + >>> isqrt(9) + 3 + >>> isqrt(10) + 3 + >>> isqrt("30") + Traceback (most recent call last): + ... + TypeError: '<' not supported between instances of 'str' and 'int' + >>> from sympy.core.numbers import Rational + >>> isqrt(Rational(-1, 2)) + Traceback (most recent call last): + ... + ValueError: n must be nonnegative + + """ + if n < 0: + raise ValueError("n must be nonnegative") + return int(sqrt(int(n))) + + +def integer_nthroot(y, n): + """ + Return a tuple containing x = floor(y**(1/n)) + and a boolean indicating whether the result is exact (that is, + whether x**n == y). + + Examples + ======== + + >>> from sympy import integer_nthroot + >>> integer_nthroot(16, 2) + (4, True) + >>> integer_nthroot(26, 2) + (5, False) + + To simply determine if a number is a perfect square, the is_square + function should be used: + + >>> from sympy.ntheory.primetest import is_square + >>> is_square(26) + False + + See Also + ======== + sympy.ntheory.primetest.is_square + integer_log + """ + x, b = iroot(as_int(y), as_int(n)) + return int(x), b diff --git a/lib/python3.11/site-packages/sympy/core/kind.py b/lib/python3.11/site-packages/sympy/core/kind.py new file mode 100644 index 0000000000000000000000000000000000000000..83c5929eda14114659f2a5a72eb2d8b91a560f0e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/kind.py @@ -0,0 +1,388 @@ +""" +Module to efficiently partition SymPy objects. + +This system is introduced because class of SymPy object does not always +represent the mathematical classification of the entity. For example, +``Integral(1, x)`` and ``Integral(Matrix([1,2]), x)`` are both instance +of ``Integral`` class. However the former is number and the latter is +matrix. + +One way to resolve this is defining subclass for each mathematical type, +such as ``MatAdd`` for the addition between matrices. Basic algebraic +operation such as addition or multiplication take this approach, but +defining every class for every mathematical object is not scalable. + +Therefore, we define the "kind" of the object and let the expression +infer the kind of itself from its arguments. Function and class can +filter the arguments by their kind, and behave differently according to +the type of itself. + +This module defines basic kinds for core objects. Other kinds such as +``ArrayKind`` or ``MatrixKind`` can be found in corresponding modules. + +.. notes:: + This approach is experimental, and can be replaced or deleted in the future. + See https://github.com/sympy/sympy/pull/20549. +""" + +from collections import defaultdict + +from .cache import cacheit +from sympy.multipledispatch.dispatcher import (Dispatcher, + ambiguity_warn, ambiguity_register_error_ignore_dup, + str_signature, RaiseNotImplementedError) + + +class KindMeta(type): + """ + Metaclass for ``Kind``. + + Assigns empty ``dict`` as class attribute ``_inst`` for every class, + in order to endow singleton-like behavior. + """ + def __new__(cls, clsname, bases, dct): + dct['_inst'] = {} + return super().__new__(cls, clsname, bases, dct) + + +class Kind(object, metaclass=KindMeta): + """ + Base class for kinds. + + Kind of the object represents the mathematical classification that + the entity falls into. It is expected that functions and classes + recognize and filter the argument by its kind. + + Kind of every object must be carefully selected so that it shows the + intention of design. Expressions may have different kind according + to the kind of its arguments. For example, arguments of ``Add`` + must have common kind since addition is group operator, and the + resulting ``Add()`` has the same kind. + + For the performance, each kind is as broad as possible and is not + based on set theory. For example, ``NumberKind`` includes not only + complex number but expression containing ``S.Infinity`` or ``S.NaN`` + which are not strictly number. + + Kind may have arguments as parameter. For example, ``MatrixKind()`` + may be constructed with one element which represents the kind of its + elements. + + ``Kind`` behaves in singleton-like fashion. Same signature will + return the same object. + + """ + def __new__(cls, *args): + if args in cls._inst: + inst = cls._inst[args] + else: + inst = super().__new__(cls) + cls._inst[args] = inst + return inst + + +class _UndefinedKind(Kind): + """ + Default kind for all SymPy object. If the kind is not defined for + the object, or if the object cannot infer the kind from its + arguments, this will be returned. + + Examples + ======== + + >>> from sympy import Expr + >>> Expr().kind + UndefinedKind + """ + def __new__(cls): + return super().__new__(cls) + + def __repr__(self): + return "UndefinedKind" + +UndefinedKind = _UndefinedKind() + + +class _NumberKind(Kind): + """ + Kind for all numeric object. + + This kind represents every number, including complex numbers, + infinity and ``S.NaN``. Other objects such as quaternions do not + have this kind. + + Most ``Expr`` are initially designed to represent the number, so + this will be the most common kind in SymPy core. For example + ``Symbol()``, which represents a scalar, has this kind as long as it + is commutative. + + Numbers form a field. Any operation between number-kind objects will + result this kind as well. + + Examples + ======== + + >>> from sympy import S, oo, Symbol + >>> S.One.kind + NumberKind + >>> (-oo).kind + NumberKind + >>> S.NaN.kind + NumberKind + + Commutative symbol are treated as number. + + >>> x = Symbol('x') + >>> x.kind + NumberKind + >>> Symbol('y', commutative=False).kind + UndefinedKind + + Operation between numbers results number. + + >>> (x+1).kind + NumberKind + + See Also + ======== + + sympy.core.expr.Expr.is_Number : check if the object is strictly + subclass of ``Number`` class. + + sympy.core.expr.Expr.is_number : check if the object is number + without any free symbol. + + """ + def __new__(cls): + return super().__new__(cls) + + def __repr__(self): + return "NumberKind" + +NumberKind = _NumberKind() + + +class _BooleanKind(Kind): + """ + Kind for boolean objects. + + SymPy's ``S.true``, ``S.false``, and built-in ``True`` and ``False`` + have this kind. Boolean number ``1`` and ``0`` are not relevant. + + Examples + ======== + + >>> from sympy import S, Q + >>> S.true.kind + BooleanKind + >>> Q.even(3).kind + BooleanKind + """ + def __new__(cls): + return super().__new__(cls) + + def __repr__(self): + return "BooleanKind" + +BooleanKind = _BooleanKind() + + +class KindDispatcher: + """ + Dispatcher to select a kind from multiple kinds by binary dispatching. + + .. notes:: + This approach is experimental, and can be replaced or deleted in + the future. + + Explanation + =========== + + SymPy object's :obj:`sympy.core.kind.Kind()` vaguely represents the + algebraic structure where the object belongs to. Therefore, with + given operation, we can always find a dominating kind among the + different kinds. This class selects the kind by recursive binary + dispatching. If the result cannot be determined, ``UndefinedKind`` + is returned. + + Examples + ======== + + Multiplication between numbers return number. + + >>> from sympy import NumberKind, Mul + >>> Mul._kind_dispatcher(NumberKind, NumberKind) + NumberKind + + Multiplication between number and unknown-kind object returns unknown kind. + + >>> from sympy import UndefinedKind + >>> Mul._kind_dispatcher(NumberKind, UndefinedKind) + UndefinedKind + + Any number and order of kinds is allowed. + + >>> Mul._kind_dispatcher(UndefinedKind, NumberKind) + UndefinedKind + >>> Mul._kind_dispatcher(NumberKind, UndefinedKind, NumberKind) + UndefinedKind + + Since matrix forms a vector space over scalar field, multiplication + between matrix with numeric element and number returns matrix with + numeric element. + + >>> from sympy.matrices import MatrixKind + >>> Mul._kind_dispatcher(MatrixKind(NumberKind), NumberKind) + MatrixKind(NumberKind) + + If a matrix with number element and another matrix with unknown-kind + element are multiplied, we know that the result is matrix but the + kind of its elements is unknown. + + >>> Mul._kind_dispatcher(MatrixKind(NumberKind), MatrixKind(UndefinedKind)) + MatrixKind(UndefinedKind) + + Parameters + ========== + + name : str + + commutative : bool, optional + If True, binary dispatch will be automatically registered in + reversed order as well. + + doc : str, optional + + """ + def __init__(self, name, commutative=False, doc=None): + self.name = name + self.doc = doc + self.commutative = commutative + self._dispatcher = Dispatcher(name) + + def __repr__(self): + return "" % self.name + + def register(self, *types, **kwargs): + """ + Register the binary dispatcher for two kind classes. + + If *self.commutative* is ``True``, signature in reversed order is + automatically registered as well. + """ + on_ambiguity = kwargs.pop("on_ambiguity", None) + if not on_ambiguity: + if self.commutative: + on_ambiguity = ambiguity_register_error_ignore_dup + else: + on_ambiguity = ambiguity_warn + kwargs.update(on_ambiguity=on_ambiguity) + + if not len(types) == 2: + raise RuntimeError( + "Only binary dispatch is supported, but got %s types: <%s>." % ( + len(types), str_signature(types) + )) + + def _(func): + self._dispatcher.add(types, func, **kwargs) + if self.commutative: + self._dispatcher.add(tuple(reversed(types)), func, **kwargs) + return _ + + def __call__(self, *args, **kwargs): + if self.commutative: + kinds = frozenset(args) + else: + kinds = [] + prev = None + for a in args: + if prev is not a: + kinds.append(a) + prev = a + return self.dispatch_kinds(kinds, **kwargs) + + @cacheit + def dispatch_kinds(self, kinds, **kwargs): + # Quick exit for the case where all kinds are same + if len(kinds) == 1: + result, = kinds + if not isinstance(result, Kind): + raise RuntimeError("%s is not a kind." % result) + return result + + for i,kind in enumerate(kinds): + if not isinstance(kind, Kind): + raise RuntimeError("%s is not a kind." % kind) + + if i == 0: + result = kind + else: + prev_kind = result + + t1, t2 = type(prev_kind), type(kind) + k1, k2 = prev_kind, kind + func = self._dispatcher.dispatch(t1, t2) + if func is None and self.commutative: + # try reversed order + func = self._dispatcher.dispatch(t2, t1) + k1, k2 = k2, k1 + if func is None: + # unregistered kind relation + result = UndefinedKind + else: + result = func(k1, k2) + if not isinstance(result, Kind): + raise RuntimeError( + "Dispatcher for {!r} and {!r} must return a Kind, but got {!r}".format( + prev_kind, kind, result + )) + + return result + + @property + def __doc__(self): + docs = [ + "Kind dispatcher : %s" % self.name, + "Note that support for this is experimental. See the docs for :class:`KindDispatcher` for details" + ] + + if self.doc: + docs.append(self.doc) + + s = "Registered kind classes\n" + s += '=' * len(s) + docs.append(s) + + amb_sigs = [] + + typ_sigs = defaultdict(list) + for sigs in self._dispatcher.ordering[::-1]: + key = self._dispatcher.funcs[sigs] + typ_sigs[key].append(sigs) + + for func, sigs in typ_sigs.items(): + + sigs_str = ', '.join('<%s>' % str_signature(sig) for sig in sigs) + + if isinstance(func, RaiseNotImplementedError): + amb_sigs.append(sigs_str) + continue + + s = 'Inputs: %s\n' % sigs_str + s += '-' * len(s) + '\n' + if func.__doc__: + s += func.__doc__.strip() + else: + s += func.__name__ + docs.append(s) + + if amb_sigs: + s = "Ambiguous kind classes\n" + s += '=' * len(s) + docs.append(s) + + s = '\n'.join(amb_sigs) + docs.append(s) + + return '\n\n'.join(docs) diff --git a/lib/python3.11/site-packages/sympy/core/logic.py b/lib/python3.11/site-packages/sympy/core/logic.py new file mode 100644 index 0000000000000000000000000000000000000000..73b525b4b07cb06de0751340614eff15ca3bb510 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/logic.py @@ -0,0 +1,427 @@ +"""Logic expressions handling + +NOTE +---- + +at present this is mainly needed for facts.py, feel free however to improve +this stuff for general purpose. +""" + +from __future__ import annotations +from typing import Optional + +# Type of a fuzzy bool +FuzzyBool = Optional[bool] + + +def _torf(args): + """Return True if all args are True, False if they + are all False, else None. + + >>> from sympy.core.logic import _torf + >>> _torf((True, True)) + True + >>> _torf((False, False)) + False + >>> _torf((True, False)) + """ + sawT = sawF = False + for a in args: + if a is True: + if sawF: + return + sawT = True + elif a is False: + if sawT: + return + sawF = True + else: + return + return sawT + + +def _fuzzy_group(args, quick_exit=False): + """Return True if all args are True, None if there is any None else False + unless ``quick_exit`` is True (then return None as soon as a second False + is seen. + + ``_fuzzy_group`` is like ``fuzzy_and`` except that it is more + conservative in returning a False, waiting to make sure that all + arguments are True or False and returning None if any arguments are + None. It also has the capability of permiting only a single False and + returning None if more than one is seen. For example, the presence of a + single transcendental amongst rationals would indicate that the group is + no longer rational; but a second transcendental in the group would make the + determination impossible. + + + Examples + ======== + + >>> from sympy.core.logic import _fuzzy_group + + By default, multiple Falses mean the group is broken: + + >>> _fuzzy_group([False, False, True]) + False + + If multiple Falses mean the group status is unknown then set + `quick_exit` to True so None can be returned when the 2nd False is seen: + + >>> _fuzzy_group([False, False, True], quick_exit=True) + + But if only a single False is seen then the group is known to + be broken: + + >>> _fuzzy_group([False, True, True], quick_exit=True) + False + + """ + saw_other = False + for a in args: + if a is True: + continue + if a is None: + return + if quick_exit and saw_other: + return + saw_other = True + return not saw_other + + +def fuzzy_bool(x): + """Return True, False or None according to x. + + Whereas bool(x) returns True or False, fuzzy_bool allows + for the None value and non-false values (which become None), too. + + Examples + ======== + + >>> from sympy.core.logic import fuzzy_bool + >>> from sympy.abc import x + >>> fuzzy_bool(x), fuzzy_bool(None) + (None, None) + >>> bool(x), bool(None) + (True, False) + + """ + if x is None: + return None + if x in (True, False): + return bool(x) + + +def fuzzy_and(args): + """Return True (all True), False (any False) or None. + + Examples + ======== + + >>> from sympy.core.logic import fuzzy_and + >>> from sympy import Dummy + + If you had a list of objects to test the commutivity of + and you want the fuzzy_and logic applied, passing an + iterator will allow the commutativity to only be computed + as many times as necessary. With this list, False can be + returned after analyzing the first symbol: + + >>> syms = [Dummy(commutative=False), Dummy()] + >>> fuzzy_and(s.is_commutative for s in syms) + False + + That False would require less work than if a list of pre-computed + items was sent: + + >>> fuzzy_and([s.is_commutative for s in syms]) + False + """ + + rv = True + for ai in args: + ai = fuzzy_bool(ai) + if ai is False: + return False + if rv: # this will stop updating if a None is ever trapped + rv = ai + return rv + + +def fuzzy_not(v): + """ + Not in fuzzy logic + + Return None if `v` is None else `not v`. + + Examples + ======== + + >>> from sympy.core.logic import fuzzy_not + >>> fuzzy_not(True) + False + >>> fuzzy_not(None) + >>> fuzzy_not(False) + True + + """ + if v is None: + return v + else: + return not v + + +def fuzzy_or(args): + """ + Or in fuzzy logic. Returns True (any True), False (all False), or None + + See the docstrings of fuzzy_and and fuzzy_not for more info. fuzzy_or is + related to the two by the standard De Morgan's law. + + >>> from sympy.core.logic import fuzzy_or + >>> fuzzy_or([True, False]) + True + >>> fuzzy_or([True, None]) + True + >>> fuzzy_or([False, False]) + False + >>> print(fuzzy_or([False, None])) + None + + """ + rv = False + for ai in args: + ai = fuzzy_bool(ai) + if ai is True: + return True + if rv is False: # this will stop updating if a None is ever trapped + rv = ai + return rv + + +def fuzzy_xor(args): + """Return None if any element of args is not True or False, else + True (if there are an odd number of True elements), else False.""" + t = f = 0 + for a in args: + ai = fuzzy_bool(a) + if ai: + t += 1 + elif ai is False: + f += 1 + else: + return + return t % 2 == 1 + + +def fuzzy_nand(args): + """Return False if all args are True, True if they are all False, + else None.""" + return fuzzy_not(fuzzy_and(args)) + + +class Logic: + """Logical expression""" + # {} 'op' -> LogicClass + op_2class: dict[str, type[Logic]] = {} + + def __new__(cls, *args): + obj = object.__new__(cls) + obj.args = args + return obj + + def __getnewargs__(self): + return self.args + + def __hash__(self): + return hash((type(self).__name__,) + tuple(self.args)) + + def __eq__(a, b): + if not isinstance(b, type(a)): + return False + else: + return a.args == b.args + + def __ne__(a, b): + if not isinstance(b, type(a)): + return True + else: + return a.args != b.args + + def __lt__(self, other): + if self.__cmp__(other) == -1: + return True + return False + + def __cmp__(self, other): + if type(self) is not type(other): + a = str(type(self)) + b = str(type(other)) + else: + a = self.args + b = other.args + return (a > b) - (a < b) + + def __str__(self): + return '%s(%s)' % (self.__class__.__name__, + ', '.join(str(a) for a in self.args)) + + __repr__ = __str__ + + @staticmethod + def fromstring(text): + """Logic from string with space around & and | but none after !. + + e.g. + + !a & b | c + """ + lexpr = None # current logical expression + schedop = None # scheduled operation + for term in text.split(): + # operation symbol + if term in '&|': + if schedop is not None: + raise ValueError( + 'double op forbidden: "%s %s"' % (term, schedop)) + if lexpr is None: + raise ValueError( + '%s cannot be in the beginning of expression' % term) + schedop = term + continue + if '&' in term or '|' in term: + raise ValueError('& and | must have space around them') + if term[0] == '!': + if len(term) == 1: + raise ValueError('do not include space after "!"') + term = Not(term[1:]) + + # already scheduled operation, e.g. '&' + if schedop: + lexpr = Logic.op_2class[schedop](lexpr, term) + schedop = None + continue + + # this should be atom + if lexpr is not None: + raise ValueError( + 'missing op between "%s" and "%s"' % (lexpr, term)) + + lexpr = term + + # let's check that we ended up in correct state + if schedop is not None: + raise ValueError('premature end-of-expression in "%s"' % text) + if lexpr is None: + raise ValueError('"%s" is empty' % text) + + # everything looks good now + return lexpr + + +class AndOr_Base(Logic): + + def __new__(cls, *args): + bargs = [] + for a in args: + if a == cls.op_x_notx: + return a + elif a == (not cls.op_x_notx): + continue # skip this argument + bargs.append(a) + + args = sorted(set(cls.flatten(bargs)), key=hash) + + for a in args: + if Not(a) in args: + return cls.op_x_notx + + if len(args) == 1: + return args.pop() + elif len(args) == 0: + return not cls.op_x_notx + + return Logic.__new__(cls, *args) + + @classmethod + def flatten(cls, args): + # quick-n-dirty flattening for And and Or + args_queue = list(args) + res = [] + + while True: + try: + arg = args_queue.pop(0) + except IndexError: + break + if isinstance(arg, Logic): + if isinstance(arg, cls): + args_queue.extend(arg.args) + continue + res.append(arg) + + args = tuple(res) + return args + + +class And(AndOr_Base): + op_x_notx = False + + def _eval_propagate_not(self): + # !(a&b&c ...) == !a | !b | !c ... + return Or(*[Not(a) for a in self.args]) + + # (a|b|...) & c == (a&c) | (b&c) | ... + def expand(self): + + # first locate Or + for i, arg in enumerate(self.args): + if isinstance(arg, Or): + arest = self.args[:i] + self.args[i + 1:] + + orterms = [And(*(arest + (a,))) for a in arg.args] + for j in range(len(orterms)): + if isinstance(orterms[j], Logic): + orterms[j] = orterms[j].expand() + + res = Or(*orterms) + return res + + return self + + +class Or(AndOr_Base): + op_x_notx = True + + def _eval_propagate_not(self): + # !(a|b|c ...) == !a & !b & !c ... + return And(*[Not(a) for a in self.args]) + + +class Not(Logic): + + def __new__(cls, arg): + if isinstance(arg, str): + return Logic.__new__(cls, arg) + + elif isinstance(arg, bool): + return not arg + elif isinstance(arg, Not): + return arg.args[0] + + elif isinstance(arg, Logic): + # XXX this is a hack to expand right from the beginning + arg = arg._eval_propagate_not() + return arg + + else: + raise ValueError('Not: unknown argument %r' % (arg,)) + + @property + def arg(self): + return self.args[0] + + +Logic.op_2class['&'] = And +Logic.op_2class['|'] = Or +Logic.op_2class['!'] = Not diff --git a/lib/python3.11/site-packages/sympy/core/mod.py b/lib/python3.11/site-packages/sympy/core/mod.py new file mode 100644 index 0000000000000000000000000000000000000000..3f0e07a5612c416632d1a0e8e433c09d1053ded8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/mod.py @@ -0,0 +1,260 @@ +from .add import Add +from .exprtools import gcd_terms +from .function import Function +from .kind import NumberKind +from .logic import fuzzy_and, fuzzy_not +from .mul import Mul +from .numbers import equal_valued +from .singleton import S + + +class Mod(Function): + """Represents a modulo operation on symbolic expressions. + + Parameters + ========== + + p : Expr + Dividend. + + q : Expr + Divisor. + + Notes + ===== + + The convention used is the same as Python's: the remainder always has the + same sign as the divisor. + + Many objects can be evaluated modulo ``n`` much faster than they can be + evaluated directly (or at all). For this, ``evaluate=False`` is + necessary to prevent eager evaluation: + + >>> from sympy import binomial, factorial, Mod, Pow + >>> Mod(Pow(2, 10**16, evaluate=False), 97) + 61 + >>> Mod(factorial(10**9, evaluate=False), 10**9 + 9) + 712524808 + >>> Mod(binomial(10**18, 10**12, evaluate=False), (10**5 + 3)**2) + 3744312326 + + Examples + ======== + + >>> from sympy.abc import x, y + >>> x**2 % y + Mod(x**2, y) + >>> _.subs({x: 5, y: 6}) + 1 + + """ + + kind = NumberKind + + @classmethod + def eval(cls, p, q): + def number_eval(p, q): + """Try to return p % q if both are numbers or +/-p is known + to be less than or equal q. + """ + + if q.is_zero: + raise ZeroDivisionError("Modulo by zero") + if p is S.NaN or q is S.NaN or p.is_finite is False or q.is_finite is False: + return S.NaN + if p is S.Zero or p in (q, -q) or (p.is_integer and q == 1): + return S.Zero + + if q.is_Number: + if p.is_Number: + return p%q + if q == 2: + if p.is_even: + return S.Zero + elif p.is_odd: + return S.One + + if hasattr(p, '_eval_Mod'): + rv = getattr(p, '_eval_Mod')(q) + if rv is not None: + return rv + + # by ratio + r = p/q + if r.is_integer: + return S.Zero + try: + d = int(r) + except TypeError: + pass + else: + if isinstance(d, int): + rv = p - d*q + if (rv*q < 0) == True: + rv += q + return rv + + # by difference + # -2|q| < p < 2|q| + d = abs(p) + for _ in range(2): + d -= abs(q) + if d.is_negative: + if q.is_positive: + if p.is_positive: + return d + q + elif p.is_negative: + return -d + elif q.is_negative: + if p.is_positive: + return d + elif p.is_negative: + return -d + q + break + + rv = number_eval(p, q) + if rv is not None: + return rv + + # denest + if isinstance(p, cls): + qinner = p.args[1] + if qinner % q == 0: + return cls(p.args[0], q) + elif (qinner*(q - qinner)).is_nonnegative: + # |qinner| < |q| and have same sign + return p + elif isinstance(-p, cls): + qinner = (-p).args[1] + if qinner % q == 0: + return cls(-(-p).args[0], q) + elif (qinner*(q + qinner)).is_nonpositive: + # |qinner| < |q| and have different sign + return p + elif isinstance(p, Add): + # separating into modulus and non modulus + both_l = non_mod_l, mod_l = [], [] + for arg in p.args: + both_l[isinstance(arg, cls)].append(arg) + # if q same for all + if mod_l and all(inner.args[1] == q for inner in mod_l): + net = Add(*non_mod_l) + Add(*[i.args[0] for i in mod_l]) + return cls(net, q) + + elif isinstance(p, Mul): + # separating into modulus and non modulus + both_l = non_mod_l, mod_l = [], [] + for arg in p.args: + both_l[isinstance(arg, cls)].append(arg) + + if mod_l and all(inner.args[1] == q for inner in mod_l) and all(t.is_integer for t in p.args) and q.is_integer: + # finding distributive term + non_mod_l = [cls(x, q) for x in non_mod_l] + mod = [] + non_mod = [] + for j in non_mod_l: + if isinstance(j, cls): + mod.append(j.args[0]) + else: + non_mod.append(j) + prod_mod = Mul(*mod) + prod_non_mod = Mul(*non_mod) + prod_mod1 = Mul(*[i.args[0] for i in mod_l]) + net = prod_mod1*prod_mod + return prod_non_mod*cls(net, q) + + if q.is_Integer and q is not S.One: + if all(t.is_integer for t in p.args): + non_mod_l = [i % q if i.is_Integer else i for i in p.args] + if any(iq is S.Zero for iq in non_mod_l): + return S.Zero + + p = Mul(*(non_mod_l + mod_l)) + + # XXX other possibilities? + + from sympy.polys.polyerrors import PolynomialError + from sympy.polys.polytools import gcd + + # extract gcd; any further simplification should be done by the user + try: + G = gcd(p, q) + if not equal_valued(G, 1): + p, q = [gcd_terms(i/G, clear=False, fraction=False) + for i in (p, q)] + except PolynomialError: # issue 21373 + G = S.One + pwas, qwas = p, q + + # simplify terms + # (x + y + 2) % x -> Mod(y + 2, x) + if p.is_Add: + args = [] + for i in p.args: + a = cls(i, q) + if a.count(cls) > i.count(cls): + args.append(i) + else: + args.append(a) + if args != list(p.args): + p = Add(*args) + + else: + # handle coefficients if they are not Rational + # since those are not handled by factor_terms + # e.g. Mod(.6*x, .3*y) -> 0.3*Mod(2*x, y) + cp, p = p.as_coeff_Mul() + cq, q = q.as_coeff_Mul() + ok = False + if not cp.is_Rational or not cq.is_Rational: + r = cp % cq + if equal_valued(r, 0): + G *= cq + p *= int(cp/cq) + ok = True + if not ok: + p = cp*p + q = cq*q + + # simple -1 extraction + if p.could_extract_minus_sign() and q.could_extract_minus_sign(): + G, p, q = [-i for i in (G, p, q)] + + # check again to see if p and q can now be handled as numbers + rv = number_eval(p, q) + if rv is not None: + return rv*G + + # put 1.0 from G on inside + if G.is_Float and equal_valued(G, 1): + p *= G + return cls(p, q, evaluate=False) + elif G.is_Mul and G.args[0].is_Float and equal_valued(G.args[0], 1): + p = G.args[0]*p + G = Mul._from_args(G.args[1:]) + return G*cls(p, q, evaluate=(p, q) != (pwas, qwas)) + + def _eval_is_integer(self): + p, q = self.args + if fuzzy_and([p.is_integer, q.is_integer, fuzzy_not(q.is_zero)]): + return True + + def _eval_is_nonnegative(self): + if self.args[1].is_positive: + return True + + def _eval_is_nonpositive(self): + if self.args[1].is_negative: + return True + + def _eval_rewrite_as_floor(self, a, b, **kwargs): + from sympy.functions.elementary.integers import floor + return a - b*floor(a/b) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.functions.elementary.integers import floor + return self.rewrite(floor)._eval_as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.functions.elementary.integers import floor + return self.rewrite(floor)._eval_nseries(x, n, logx=logx, cdir=cdir) diff --git a/lib/python3.11/site-packages/sympy/core/mul.py b/lib/python3.11/site-packages/sympy/core/mul.py new file mode 100644 index 0000000000000000000000000000000000000000..d93dbde7586c87e8076347c4d8062b39a4e13c22 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/mul.py @@ -0,0 +1,2196 @@ +from typing import Tuple as tTuple +from collections import defaultdict +from functools import reduce +from itertools import product +import operator + +from .sympify import sympify +from .basic import Basic, _args_sortkey +from .singleton import S +from .operations import AssocOp, AssocOpDispatcher +from .cache import cacheit +from .intfunc import integer_nthroot, trailing +from .logic import fuzzy_not, _fuzzy_group +from .expr import Expr +from .parameters import global_parameters +from .kind import KindDispatcher +from .traversal import bottom_up + +from sympy.utilities.iterables import sift + +# internal marker to indicate: +# "there are still non-commutative objects -- don't forget to process them" +class NC_Marker: + is_Order = False + is_Mul = False + is_Number = False + is_Poly = False + + is_commutative = False + + +def _mulsort(args): + # in-place sorting of args + args.sort(key=_args_sortkey) + + +def _unevaluated_Mul(*args): + """Return a well-formed unevaluated Mul: Numbers are collected and + put in slot 0, any arguments that are Muls will be flattened, and args + are sorted. Use this when args have changed but you still want to return + an unevaluated Mul. + + Examples + ======== + + >>> from sympy.core.mul import _unevaluated_Mul as uMul + >>> from sympy import S, sqrt, Mul + >>> from sympy.abc import x + >>> a = uMul(*[S(3.0), x, S(2)]) + >>> a.args[0] + 6.00000000000000 + >>> a.args[1] + x + + Two unevaluated Muls with the same arguments will + always compare as equal during testing: + + >>> m = uMul(sqrt(2), sqrt(3)) + >>> m == uMul(sqrt(3), sqrt(2)) + True + >>> u = Mul(sqrt(3), sqrt(2), evaluate=False) + >>> m == uMul(u) + True + >>> m == Mul(*m.args) + False + + """ + args = list(args) + newargs = [] + ncargs = [] + co = S.One + while args: + a = args.pop() + if a.is_Mul: + c, nc = a.args_cnc() + args.extend(c) + if nc: + ncargs.append(Mul._from_args(nc)) + elif a.is_Number: + co *= a + else: + newargs.append(a) + _mulsort(newargs) + if co is not S.One: + newargs.insert(0, co) + if ncargs: + newargs.append(Mul._from_args(ncargs)) + return Mul._from_args(newargs) + + +class Mul(Expr, AssocOp): + """ + Expression representing multiplication operation for algebraic field. + + .. deprecated:: 1.7 + + Using arguments that aren't subclasses of :class:`~.Expr` in core + operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is + deprecated. See :ref:`non-expr-args-deprecated` for details. + + Every argument of ``Mul()`` must be ``Expr``. Infix operator ``*`` + on most scalar objects in SymPy calls this class. + + Another use of ``Mul()`` is to represent the structure of abstract + multiplication so that its arguments can be substituted to return + different class. Refer to examples section for this. + + ``Mul()`` evaluates the argument unless ``evaluate=False`` is passed. + The evaluation logic includes: + + 1. Flattening + ``Mul(x, Mul(y, z))`` -> ``Mul(x, y, z)`` + + 2. Identity removing + ``Mul(x, 1, y)`` -> ``Mul(x, y)`` + + 3. Exponent collecting by ``.as_base_exp()`` + ``Mul(x, x**2)`` -> ``Pow(x, 3)`` + + 4. Term sorting + ``Mul(y, x, 2)`` -> ``Mul(2, x, y)`` + + Since multiplication can be vector space operation, arguments may + have the different :obj:`sympy.core.kind.Kind()`. Kind of the + resulting object is automatically inferred. + + Examples + ======== + + >>> from sympy import Mul + >>> from sympy.abc import x, y + >>> Mul(x, 1) + x + >>> Mul(x, x) + x**2 + + If ``evaluate=False`` is passed, result is not evaluated. + + >>> Mul(1, 2, evaluate=False) + 1*2 + >>> Mul(x, x, evaluate=False) + x*x + + ``Mul()`` also represents the general structure of multiplication + operation. + + >>> from sympy import MatrixSymbol + >>> A = MatrixSymbol('A', 2,2) + >>> expr = Mul(x,y).subs({y:A}) + >>> expr + x*A + >>> type(expr) + + + See Also + ======== + + MatMul + + """ + __slots__ = () + + args: tTuple[Expr, ...] + + is_Mul = True + + _args_type = Expr + _kind_dispatcher = KindDispatcher("Mul_kind_dispatcher", commutative=True) + + @property + def kind(self): + arg_kinds = (a.kind for a in self.args) + return self._kind_dispatcher(*arg_kinds) + + def could_extract_minus_sign(self): + if self == (-self): + return False # e.g. zoo*x == -zoo*x + c = self.args[0] + return c.is_Number and c.is_extended_negative + def __neg__(self): + c, args = self.as_coeff_mul() + if args[0] is not S.ComplexInfinity: + c = -c + if c is not S.One: + if args[0].is_Number: + args = list(args) + if c is S.NegativeOne: + args[0] = -args[0] + else: + args[0] *= c + else: + args = (c,) + args + return self._from_args(args, self.is_commutative) + + @classmethod + def flatten(cls, seq): + """Return commutative, noncommutative and order arguments by + combining related terms. + + Notes + ===== + * In an expression like ``a*b*c``, Python process this through SymPy + as ``Mul(Mul(a, b), c)``. This can have undesirable consequences. + + - Sometimes terms are not combined as one would like: + {c.f. https://github.com/sympy/sympy/issues/4596} + + >>> from sympy import Mul, sqrt + >>> from sympy.abc import x, y, z + >>> 2*(x + 1) # this is the 2-arg Mul behavior + 2*x + 2 + >>> y*(x + 1)*2 + 2*y*(x + 1) + >>> 2*(x + 1)*y # 2-arg result will be obtained first + y*(2*x + 2) + >>> Mul(2, x + 1, y) # all 3 args simultaneously processed + 2*y*(x + 1) + >>> 2*((x + 1)*y) # parentheses can control this behavior + 2*y*(x + 1) + + Powers with compound bases may not find a single base to + combine with unless all arguments are processed at once. + Post-processing may be necessary in such cases. + {c.f. https://github.com/sympy/sympy/issues/5728} + + >>> a = sqrt(x*sqrt(y)) + >>> a**3 + (x*sqrt(y))**(3/2) + >>> Mul(a,a,a) + (x*sqrt(y))**(3/2) + >>> a*a*a + x*sqrt(y)*sqrt(x*sqrt(y)) + >>> _.subs(a.base, z).subs(z, a.base) + (x*sqrt(y))**(3/2) + + - If more than two terms are being multiplied then all the + previous terms will be re-processed for each new argument. + So if each of ``a``, ``b`` and ``c`` were :class:`Mul` + expression, then ``a*b*c`` (or building up the product + with ``*=``) will process all the arguments of ``a`` and + ``b`` twice: once when ``a*b`` is computed and again when + ``c`` is multiplied. + + Using ``Mul(a, b, c)`` will process all arguments once. + + * The results of Mul are cached according to arguments, so flatten + will only be called once for ``Mul(a, b, c)``. If you can + structure a calculation so the arguments are most likely to be + repeats then this can save time in computing the answer. For + example, say you had a Mul, M, that you wished to divide by ``d[i]`` + and multiply by ``n[i]`` and you suspect there are many repeats + in ``n``. It would be better to compute ``M*n[i]/d[i]`` rather + than ``M/d[i]*n[i]`` since every time n[i] is a repeat, the + product, ``M*n[i]`` will be returned without flattening -- the + cached value will be returned. If you divide by the ``d[i]`` + first (and those are more unique than the ``n[i]``) then that will + create a new Mul, ``M/d[i]`` the args of which will be traversed + again when it is multiplied by ``n[i]``. + + {c.f. https://github.com/sympy/sympy/issues/5706} + + This consideration is moot if the cache is turned off. + + NB + -- + The validity of the above notes depends on the implementation + details of Mul and flatten which may change at any time. Therefore, + you should only consider them when your code is highly performance + sensitive. + + Removal of 1 from the sequence is already handled by AssocOp.__new__. + """ + + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.matrices.expressions import MatrixExpr + rv = None + if len(seq) == 2: + a, b = seq + if b.is_Rational: + a, b = b, a + seq = [a, b] + assert a is not S.One + if a.is_Rational and not a.is_zero: + r, b = b.as_coeff_Mul() + if b.is_Add: + if r is not S.One: # 2-arg hack + # leave the Mul as a Mul? + ar = a*r + if ar is S.One: + arb = b + else: + arb = cls(a*r, b, evaluate=False) + rv = [arb], [], None + elif global_parameters.distribute and b.is_commutative: + newb = Add(*[_keep_coeff(a, bi) for bi in b.args]) + rv = [newb], [], None + if rv: + return rv + + # apply associativity, separate commutative part of seq + c_part = [] # out: commutative factors + nc_part = [] # out: non-commutative factors + + nc_seq = [] + + coeff = S.One # standalone term + # e.g. 3 * ... + + c_powers = [] # (base,exp) n + # e.g. (x,n) for x + + num_exp = [] # (num-base, exp) y + # e.g. (3, y) for ... * 3 * ... + + neg1e = S.Zero # exponent on -1 extracted from Number-based Pow and I + + pnum_rat = {} # (num-base, Rat-exp) 1/2 + # e.g. (3, 1/2) for ... * 3 * ... + + order_symbols = None + + # --- PART 1 --- + # + # "collect powers and coeff": + # + # o coeff + # o c_powers + # o num_exp + # o neg1e + # o pnum_rat + # + # NOTE: this is optimized for all-objects-are-commutative case + for o in seq: + # O(x) + if o.is_Order: + o, order_symbols = o.as_expr_variables(order_symbols) + + # Mul([...]) + if o.is_Mul: + if o.is_commutative: + seq.extend(o.args) # XXX zerocopy? + + else: + # NCMul can have commutative parts as well + for q in o.args: + if q.is_commutative: + seq.append(q) + else: + nc_seq.append(q) + + # append non-commutative marker, so we don't forget to + # process scheduled non-commutative objects + seq.append(NC_Marker) + + continue + + # 3 + elif o.is_Number: + if o is S.NaN or coeff is S.ComplexInfinity and o.is_zero: + # we know for sure the result will be nan + return [S.NaN], [], None + elif coeff.is_Number or isinstance(coeff, AccumBounds): # it could be zoo + coeff *= o + if coeff is S.NaN: + # we know for sure the result will be nan + return [S.NaN], [], None + continue + + elif isinstance(o, AccumBounds): + coeff = o.__mul__(coeff) + continue + + elif o is S.ComplexInfinity: + if not coeff: + # 0 * zoo = NaN + return [S.NaN], [], None + coeff = S.ComplexInfinity + continue + + elif o is S.ImaginaryUnit: + neg1e += S.Half + continue + + elif o.is_commutative: + # e + # o = b + b, e = o.as_base_exp() + + # y + # 3 + if o.is_Pow: + if b.is_Number: + + # get all the factors with numeric base so they can be + # combined below, but don't combine negatives unless + # the exponent is an integer + if e.is_Rational: + if e.is_Integer: + coeff *= Pow(b, e) # it is an unevaluated power + continue + elif e.is_negative: # also a sign of an unevaluated power + seq.append(Pow(b, e)) + continue + elif b.is_negative: + neg1e += e + b = -b + if b is not S.One: + pnum_rat.setdefault(b, []).append(e) + continue + elif b.is_positive or e.is_integer: + num_exp.append((b, e)) + continue + + c_powers.append((b, e)) + + # NON-COMMUTATIVE + # TODO: Make non-commutative exponents not combine automatically + else: + if o is not NC_Marker: + nc_seq.append(o) + + # process nc_seq (if any) + while nc_seq: + o = nc_seq.pop(0) + if not nc_part: + nc_part.append(o) + continue + + # b c b+c + # try to combine last terms: a * a -> a + o1 = nc_part.pop() + b1, e1 = o1.as_base_exp() + b2, e2 = o.as_base_exp() + new_exp = e1 + e2 + # Only allow powers to combine if the new exponent is + # not an Add. This allow things like a**2*b**3 == a**5 + # if a.is_commutative == False, but prohibits + # a**x*a**y and x**a*x**b from combining (x,y commute). + if b1 == b2 and (not new_exp.is_Add): + o12 = b1 ** new_exp + + # now o12 could be a commutative object + if o12.is_commutative: + seq.append(o12) + continue + else: + nc_seq.insert(0, o12) + + else: + nc_part.extend([o1, o]) + + # We do want a combined exponent if it would not be an Add, such as + # y 2y 3y + # x * x -> x + # We determine if two exponents have the same term by using + # as_coeff_Mul. + # + # Unfortunately, this isn't smart enough to consider combining into + # exponents that might already be adds, so things like: + # z - y y + # x * x will be left alone. This is because checking every possible + # combination can slow things down. + + # gather exponents of common bases... + def _gather(c_powers): + common_b = {} # b:e + for b, e in c_powers: + co = e.as_coeff_Mul() + common_b.setdefault(b, {}).setdefault( + co[1], []).append(co[0]) + for b, d in common_b.items(): + for di, li in d.items(): + d[di] = Add(*li) + new_c_powers = [] + for b, e in common_b.items(): + new_c_powers.extend([(b, c*t) for t, c in e.items()]) + return new_c_powers + + # in c_powers + c_powers = _gather(c_powers) + + # and in num_exp + num_exp = _gather(num_exp) + + # --- PART 2 --- + # + # o process collected powers (x**0 -> 1; x**1 -> x; otherwise Pow) + # o combine collected powers (2**x * 3**x -> 6**x) + # with numeric base + + # ................................ + # now we have: + # - coeff: + # - c_powers: (b, e) + # - num_exp: (2, e) + # - pnum_rat: {(1/3, [1/3, 2/3, 1/4])} + + # 0 1 + # x -> 1 x -> x + + # this should only need to run twice; if it fails because + # it needs to be run more times, perhaps this should be + # changed to a "while True" loop -- the only reason it + # isn't such now is to allow a less-than-perfect result to + # be obtained rather than raising an error or entering an + # infinite loop + for i in range(2): + new_c_powers = [] + changed = False + for b, e in c_powers: + if e.is_zero: + # canceling out infinities yields NaN + if (b.is_Add or b.is_Mul) and any(infty in b.args + for infty in (S.ComplexInfinity, S.Infinity, + S.NegativeInfinity)): + return [S.NaN], [], None + continue + if e is S.One: + if b.is_Number: + coeff *= b + continue + p = b + if e is not S.One: + p = Pow(b, e) + # check to make sure that the base doesn't change + # after exponentiation; to allow for unevaluated + # Pow, we only do so if b is not already a Pow + if p.is_Pow and not b.is_Pow: + bi = b + b, e = p.as_base_exp() + if b != bi: + changed = True + c_part.append(p) + new_c_powers.append((b, e)) + # there might have been a change, but unless the base + # matches some other base, there is nothing to do + if changed and len({ + b for b, e in new_c_powers}) != len(new_c_powers): + # start over again + c_part = [] + c_powers = _gather(new_c_powers) + else: + break + + # x x x + # 2 * 3 -> 6 + inv_exp_dict = {} # exp:Mul(num-bases) x x + # e.g. x:6 for ... * 2 * 3 * ... + for b, e in num_exp: + inv_exp_dict.setdefault(e, []).append(b) + for e, b in inv_exp_dict.items(): + inv_exp_dict[e] = cls(*b) + c_part.extend([Pow(b, e) for e, b in inv_exp_dict.items() if e]) + + # b, e -> e' = sum(e), b + # {(1/5, [1/3]), (1/2, [1/12, 1/4]} -> {(1/3, [1/5, 1/2])} + comb_e = {} + for b, e in pnum_rat.items(): + comb_e.setdefault(Add(*e), []).append(b) + del pnum_rat + # process them, reducing exponents to values less than 1 + # and updating coeff if necessary else adding them to + # num_rat for further processing + num_rat = [] + for e, b in comb_e.items(): + b = cls(*b) + if e.q == 1: + coeff *= Pow(b, e) + continue + if e.p > e.q: + e_i, ep = divmod(e.p, e.q) + coeff *= Pow(b, e_i) + e = Rational(ep, e.q) + num_rat.append((b, e)) + del comb_e + + # extract gcd of bases in num_rat + # 2**(1/3)*6**(1/4) -> 2**(1/3+1/4)*3**(1/4) + pnew = defaultdict(list) + i = 0 # steps through num_rat which may grow + while i < len(num_rat): + bi, ei = num_rat[i] + if bi == 1: + i += 1 + continue + grow = [] + for j in range(i + 1, len(num_rat)): + bj, ej = num_rat[j] + g = bi.gcd(bj) + if g is not S.One: + # 4**r1*6**r2 -> 2**(r1+r2) * 2**r1 * 3**r2 + # this might have a gcd with something else + e = ei + ej + if e.q == 1: + coeff *= Pow(g, e) + else: + if e.p > e.q: + e_i, ep = divmod(e.p, e.q) # change e in place + coeff *= Pow(g, e_i) + e = Rational(ep, e.q) + grow.append((g, e)) + # update the jth item + num_rat[j] = (bj/g, ej) + # update bi that we are checking with + bi = bi/g + if bi is S.One: + break + if bi is not S.One: + obj = Pow(bi, ei) + if obj.is_Number: + coeff *= obj + else: + # changes like sqrt(12) -> 2*sqrt(3) + for obj in Mul.make_args(obj): + if obj.is_Number: + coeff *= obj + else: + assert obj.is_Pow + bi, ei = obj.args + pnew[ei].append(bi) + + num_rat.extend(grow) + i += 1 + + # combine bases of the new powers + for e, b in pnew.items(): + pnew[e] = cls(*b) + + # handle -1 and I + if neg1e: + # treat I as (-1)**(1/2) and compute -1's total exponent + p, q = neg1e.as_numer_denom() + # if the integer part is odd, extract -1 + n, p = divmod(p, q) + if n % 2: + coeff = -coeff + # if it's a multiple of 1/2 extract I + if q == 2: + c_part.append(S.ImaginaryUnit) + elif p: + # see if there is any positive base this power of + # -1 can join + neg1e = Rational(p, q) + for e, b in pnew.items(): + if e == neg1e and b.is_positive: + pnew[e] = -b + break + else: + # keep it separate; we've already evaluated it as + # much as possible so evaluate=False + c_part.append(Pow(S.NegativeOne, neg1e, evaluate=False)) + + # add all the pnew powers + c_part.extend([Pow(b, e) for e, b in pnew.items()]) + + # oo, -oo + if coeff in (S.Infinity, S.NegativeInfinity): + def _handle_for_oo(c_part, coeff_sign): + new_c_part = [] + for t in c_part: + if t.is_extended_positive: + continue + if t.is_extended_negative: + coeff_sign *= -1 + continue + new_c_part.append(t) + return new_c_part, coeff_sign + c_part, coeff_sign = _handle_for_oo(c_part, 1) + nc_part, coeff_sign = _handle_for_oo(nc_part, coeff_sign) + coeff *= coeff_sign + + # zoo + if coeff is S.ComplexInfinity: + # zoo might be + # infinite_real + bounded_im + # bounded_real + infinite_im + # infinite_real + infinite_im + # and non-zero real or imaginary will not change that status. + c_part = [c for c in c_part if not (fuzzy_not(c.is_zero) and + c.is_extended_real is not None)] + nc_part = [c for c in nc_part if not (fuzzy_not(c.is_zero) and + c.is_extended_real is not None)] + + # 0 + elif coeff.is_zero: + # we know for sure the result will be 0 except the multiplicand + # is infinity or a matrix + if any(isinstance(c, MatrixExpr) for c in nc_part): + return [coeff], nc_part, order_symbols + if any(c.is_finite == False for c in c_part): + return [S.NaN], [], order_symbols + return [coeff], [], order_symbols + + # check for straggling Numbers that were produced + _new = [] + for i in c_part: + if i.is_Number: + coeff *= i + else: + _new.append(i) + c_part = _new + + # order commutative part canonically + _mulsort(c_part) + + # current code expects coeff to be always in slot-0 + if coeff is not S.One: + c_part.insert(0, coeff) + + # we are done + if (global_parameters.distribute and not nc_part and len(c_part) == 2 and + c_part[0].is_Number and c_part[0].is_finite and c_part[1].is_Add): + # 2*(1+a) -> 2 + 2 * a + coeff = c_part[0] + c_part = [Add(*[coeff*f for f in c_part[1].args])] + + return c_part, nc_part, order_symbols + + def _eval_power(self, e): + + # don't break up NC terms: (A*B)**3 != A**3*B**3, it is A*B*A*B*A*B + cargs, nc = self.args_cnc(split_1=False) + + if e.is_Integer: + return Mul(*[Pow(b, e, evaluate=False) for b in cargs]) * \ + Pow(Mul._from_args(nc), e, evaluate=False) + if e.is_Rational and e.q == 2: + if self.is_imaginary: + a = self.as_real_imag()[1] + if a.is_Rational: + n, d = abs(a/2).as_numer_denom() + n, t = integer_nthroot(n, 2) + if t: + d, t = integer_nthroot(d, 2) + if t: + from sympy.functions.elementary.complexes import sign + r = sympify(n)/d + return _unevaluated_Mul(r**e.p, (1 + sign(a)*S.ImaginaryUnit)**e.p) + + p = Pow(self, e, evaluate=False) + + if e.is_Rational or e.is_Float: + return p._eval_expand_power_base() + + return p + + @classmethod + def class_key(cls): + return 3, 0, cls.__name__ + + def _eval_evalf(self, prec): + c, m = self.as_coeff_Mul() + if c is S.NegativeOne: + if m.is_Mul: + rv = -AssocOp._eval_evalf(m, prec) + else: + mnew = m._eval_evalf(prec) + if mnew is not None: + m = mnew + rv = -m + else: + rv = AssocOp._eval_evalf(self, prec) + if rv.is_number: + return rv.expand() + return rv + + @property + def _mpc_(self): + """ + Convert self to an mpmath mpc if possible + """ + from .numbers import Float + im_part, imag_unit = self.as_coeff_Mul() + if imag_unit is not S.ImaginaryUnit: + # ValueError may seem more reasonable but since it's a @property, + # we need to use AttributeError to keep from confusing things like + # hasattr. + raise AttributeError("Cannot convert Mul to mpc. Must be of the form Number*I") + + return (Float(0)._mpf_, Float(im_part)._mpf_) + + @cacheit + def as_two_terms(self): + """Return head and tail of self. + + This is the most efficient way to get the head and tail of an + expression. + + - if you want only the head, use self.args[0]; + - if you want to process the arguments of the tail then use + self.as_coef_mul() which gives the head and a tuple containing + the arguments of the tail when treated as a Mul. + - if you want the coefficient when self is treated as an Add + then use self.as_coeff_add()[0] + + Examples + ======== + + >>> from sympy.abc import x, y + >>> (3*x*y).as_two_terms() + (3, x*y) + """ + args = self.args + + if len(args) == 1: + return S.One, self + elif len(args) == 2: + return args + + else: + return args[0], self._new_rawargs(*args[1:]) + + @cacheit + def as_coeff_mul(self, *deps, rational=True, **kwargs): + if deps: + l1, l2 = sift(self.args, lambda x: x.has(*deps), binary=True) + return self._new_rawargs(*l2), tuple(l1) + args = self.args + if args[0].is_Number: + if not rational or args[0].is_Rational: + return args[0], args[1:] + elif args[0].is_extended_negative: + return S.NegativeOne, (-args[0],) + args[1:] + return S.One, args + + def as_coeff_Mul(self, rational=False): + """ + Efficiently extract the coefficient of a product. + """ + coeff, args = self.args[0], self.args[1:] + + if coeff.is_Number: + if not rational or coeff.is_Rational: + if len(args) == 1: + return coeff, args[0] + else: + return coeff, self._new_rawargs(*args) + elif coeff.is_extended_negative: + return S.NegativeOne, self._new_rawargs(*((-coeff,) + args)) + return S.One, self + + def as_real_imag(self, deep=True, **hints): + from sympy.functions.elementary.complexes import Abs, im, re + other = [] + coeffr = [] + coeffi = [] + addterms = S.One + for a in self.args: + r, i = a.as_real_imag() + if i.is_zero: + coeffr.append(r) + elif r.is_zero: + coeffi.append(i*S.ImaginaryUnit) + elif a.is_commutative: + aconj = a.conjugate() if other else None + # search for complex conjugate pairs: + for i, x in enumerate(other): + if x == aconj: + coeffr.append(Abs(x)**2) + del other[i] + break + else: + if a.is_Add: + addterms *= a + else: + other.append(a) + else: + other.append(a) + m = self.func(*other) + if hints.get('ignore') == m: + return + if len(coeffi) % 2: + imco = im(coeffi.pop(0)) + # all other pairs make a real factor; they will be + # put into reco below + else: + imco = S.Zero + reco = self.func(*(coeffr + coeffi)) + r, i = (reco*re(m), reco*im(m)) + if addterms == 1: + if m == 1: + if imco.is_zero: + return (reco, S.Zero) + else: + return (S.Zero, reco*imco) + if imco is S.Zero: + return (r, i) + return (-imco*i, imco*r) + from .function import expand_mul + addre, addim = expand_mul(addterms, deep=False).as_real_imag() + if imco is S.Zero: + return (r*addre - i*addim, i*addre + r*addim) + else: + r, i = -imco*i, imco*r + return (r*addre - i*addim, r*addim + i*addre) + + @staticmethod + def _expandsums(sums): + """ + Helper function for _eval_expand_mul. + + sums must be a list of instances of Basic. + """ + + L = len(sums) + if L == 1: + return sums[0].args + terms = [] + left = Mul._expandsums(sums[:L//2]) + right = Mul._expandsums(sums[L//2:]) + + terms = [Mul(a, b) for a in left for b in right] + added = Add(*terms) + return Add.make_args(added) # it may have collapsed down to one term + + def _eval_expand_mul(self, **hints): + from sympy.simplify.radsimp import fraction + + # Handle things like 1/(x*(x + 1)), which are automatically converted + # to 1/x*1/(x + 1) + expr = self + # default matches fraction's default + n, d = fraction(expr, hints.get('exact', False)) + if d.is_Mul: + n, d = [i._eval_expand_mul(**hints) if i.is_Mul else i + for i in (n, d)] + expr = n/d + if not expr.is_Mul: + return expr + + plain, sums, rewrite = [], [], False + for factor in expr.args: + if factor.is_Add: + sums.append(factor) + rewrite = True + else: + if factor.is_commutative: + plain.append(factor) + else: + sums.append(Basic(factor)) # Wrapper + + if not rewrite: + return expr + else: + plain = self.func(*plain) + if sums: + deep = hints.get("deep", False) + terms = self.func._expandsums(sums) + args = [] + for term in terms: + t = self.func(plain, term) + if t.is_Mul and any(a.is_Add for a in t.args) and deep: + t = t._eval_expand_mul() + args.append(t) + return Add(*args) + else: + return plain + + @cacheit + def _eval_derivative(self, s): + args = list(self.args) + terms = [] + for i in range(len(args)): + d = args[i].diff(s) + if d: + # Note: reduce is used in step of Mul as Mul is unable to + # handle subtypes and operation priority: + terms.append(reduce(lambda x, y: x*y, (args[:i] + [d] + args[i + 1:]), S.One)) + return Add.fromiter(terms) + + @cacheit + def _eval_derivative_n_times(self, s, n): + from .function import AppliedUndef + from .symbol import Symbol, symbols, Dummy + if not isinstance(s, (AppliedUndef, Symbol)): + # other types of s may not be well behaved, e.g. + # (cos(x)*sin(y)).diff([[x, y, z]]) + return super()._eval_derivative_n_times(s, n) + from .numbers import Integer + args = self.args + m = len(args) + if isinstance(n, (int, Integer)): + # https://en.wikipedia.org/wiki/General_Leibniz_rule#More_than_two_factors + terms = [] + from sympy.ntheory.multinomial import multinomial_coefficients_iterator + for kvals, c in multinomial_coefficients_iterator(m, n): + p = Mul(*[arg.diff((s, k)) for k, arg in zip(kvals, args)]) + terms.append(c * p) + return Add(*terms) + from sympy.concrete.summations import Sum + from sympy.functions.combinatorial.factorials import factorial + from sympy.functions.elementary.miscellaneous import Max + kvals = symbols("k1:%i" % m, cls=Dummy) + klast = n - sum(kvals) + nfact = factorial(n) + e, l = (# better to use the multinomial? + nfact/prod(map(factorial, kvals))/factorial(klast)*\ + Mul(*[args[t].diff((s, kvals[t])) for t in range(m-1)])*\ + args[-1].diff((s, Max(0, klast))), + [(k, 0, n) for k in kvals]) + return Sum(e, *l) + + def _eval_difference_delta(self, n, step): + from sympy.series.limitseq import difference_delta as dd + arg0 = self.args[0] + rest = Mul(*self.args[1:]) + return (arg0.subs(n, n + step) * dd(rest, n, step) + dd(arg0, n, step) * + rest) + + def _matches_simple(self, expr, repl_dict): + # handle (w*3).matches('x*5') -> {w: x*5/3} + coeff, terms = self.as_coeff_Mul() + terms = Mul.make_args(terms) + if len(terms) == 1: + newexpr = self.__class__._combine_inverse(expr, coeff) + return terms[0].matches(newexpr, repl_dict) + return + + def matches(self, expr, repl_dict=None, old=False): + expr = sympify(expr) + if self.is_commutative and expr.is_commutative: + return self._matches_commutative(expr, repl_dict, old) + elif self.is_commutative is not expr.is_commutative: + return None + + # Proceed only if both both expressions are non-commutative + c1, nc1 = self.args_cnc() + c2, nc2 = expr.args_cnc() + c1, c2 = [c or [1] for c in [c1, c2]] + + # TODO: Should these be self.func? + comm_mul_self = Mul(*c1) + comm_mul_expr = Mul(*c2) + + repl_dict = comm_mul_self.matches(comm_mul_expr, repl_dict, old) + + # If the commutative arguments didn't match and aren't equal, then + # then the expression as a whole doesn't match + if not repl_dict and c1 != c2: + return None + + # Now match the non-commutative arguments, expanding powers to + # multiplications + nc1 = Mul._matches_expand_pows(nc1) + nc2 = Mul._matches_expand_pows(nc2) + + repl_dict = Mul._matches_noncomm(nc1, nc2, repl_dict) + + return repl_dict or None + + @staticmethod + def _matches_expand_pows(arg_list): + new_args = [] + for arg in arg_list: + if arg.is_Pow and arg.exp > 0: + new_args.extend([arg.base] * arg.exp) + else: + new_args.append(arg) + return new_args + + @staticmethod + def _matches_noncomm(nodes, targets, repl_dict=None): + """Non-commutative multiplication matcher. + + `nodes` is a list of symbols within the matcher multiplication + expression, while `targets` is a list of arguments in the + multiplication expression being matched against. + """ + if repl_dict is None: + repl_dict = {} + else: + repl_dict = repl_dict.copy() + + # List of possible future states to be considered + agenda = [] + # The current matching state, storing index in nodes and targets + state = (0, 0) + node_ind, target_ind = state + # Mapping between wildcard indices and the index ranges they match + wildcard_dict = {} + + while target_ind < len(targets) and node_ind < len(nodes): + node = nodes[node_ind] + + if node.is_Wild: + Mul._matches_add_wildcard(wildcard_dict, state) + + states_matches = Mul._matches_new_states(wildcard_dict, state, + nodes, targets) + if states_matches: + new_states, new_matches = states_matches + agenda.extend(new_states) + if new_matches: + for match in new_matches: + repl_dict[match] = new_matches[match] + if not agenda: + return None + else: + state = agenda.pop() + node_ind, target_ind = state + + return repl_dict + + @staticmethod + def _matches_add_wildcard(dictionary, state): + node_ind, target_ind = state + if node_ind in dictionary: + begin, end = dictionary[node_ind] + dictionary[node_ind] = (begin, target_ind) + else: + dictionary[node_ind] = (target_ind, target_ind) + + @staticmethod + def _matches_new_states(dictionary, state, nodes, targets): + node_ind, target_ind = state + node = nodes[node_ind] + target = targets[target_ind] + + # Don't advance at all if we've exhausted the targets but not the nodes + if target_ind >= len(targets) - 1 and node_ind < len(nodes) - 1: + return None + + if node.is_Wild: + match_attempt = Mul._matches_match_wilds(dictionary, node_ind, + nodes, targets) + if match_attempt: + # If the same node has been matched before, don't return + # anything if the current match is diverging from the previous + # match + other_node_inds = Mul._matches_get_other_nodes(dictionary, + nodes, node_ind) + for ind in other_node_inds: + other_begin, other_end = dictionary[ind] + curr_begin, curr_end = dictionary[node_ind] + + other_targets = targets[other_begin:other_end + 1] + current_targets = targets[curr_begin:curr_end + 1] + + for curr, other in zip(current_targets, other_targets): + if curr != other: + return None + + # A wildcard node can match more than one target, so only the + # target index is advanced + new_state = [(node_ind, target_ind + 1)] + # Only move on to the next node if there is one + if node_ind < len(nodes) - 1: + new_state.append((node_ind + 1, target_ind + 1)) + return new_state, match_attempt + else: + # If we're not at a wildcard, then make sure we haven't exhausted + # nodes but not targets, since in this case one node can only match + # one target + if node_ind >= len(nodes) - 1 and target_ind < len(targets) - 1: + return None + + match_attempt = node.matches(target) + + if match_attempt: + return [(node_ind + 1, target_ind + 1)], match_attempt + elif node == target: + return [(node_ind + 1, target_ind + 1)], None + else: + return None + + @staticmethod + def _matches_match_wilds(dictionary, wildcard_ind, nodes, targets): + """Determine matches of a wildcard with sub-expression in `target`.""" + wildcard = nodes[wildcard_ind] + begin, end = dictionary[wildcard_ind] + terms = targets[begin:end + 1] + # TODO: Should this be self.func? + mult = Mul(*terms) if len(terms) > 1 else terms[0] + return wildcard.matches(mult) + + @staticmethod + def _matches_get_other_nodes(dictionary, nodes, node_ind): + """Find other wildcards that may have already been matched.""" + ind_node = nodes[node_ind] + return [ind for ind in dictionary if nodes[ind] == ind_node] + + @staticmethod + def _combine_inverse(lhs, rhs): + """ + Returns lhs/rhs, but treats arguments like symbols, so things + like oo/oo return 1 (instead of a nan) and ``I`` behaves like + a symbol instead of sqrt(-1). + """ + from sympy.simplify.simplify import signsimp + from .symbol import Dummy + if lhs == rhs: + return S.One + + def check(l, r): + if l.is_Float and r.is_comparable: + # if both objects are added to 0 they will share the same "normalization" + # and are more likely to compare the same. Since Add(foo, 0) will not allow + # the 0 to pass, we use __add__ directly. + return l.__add__(0) == r.evalf().__add__(0) + return False + if check(lhs, rhs) or check(rhs, lhs): + return S.One + if any(i.is_Pow or i.is_Mul for i in (lhs, rhs)): + # gruntz and limit wants a literal I to not combine + # with a power of -1 + d = Dummy('I') + _i = {S.ImaginaryUnit: d} + i_ = {d: S.ImaginaryUnit} + a = lhs.xreplace(_i).as_powers_dict() + b = rhs.xreplace(_i).as_powers_dict() + blen = len(b) + for bi in tuple(b.keys()): + if bi in a: + a[bi] -= b.pop(bi) + if not a[bi]: + a.pop(bi) + if len(b) != blen: + lhs = Mul(*[k**v for k, v in a.items()]).xreplace(i_) + rhs = Mul(*[k**v for k, v in b.items()]).xreplace(i_) + rv = lhs/rhs + srv = signsimp(rv) + return srv if srv.is_Number else rv + + def as_powers_dict(self): + d = defaultdict(int) + for term in self.args: + for b, e in term.as_powers_dict().items(): + d[b] += e + return d + + def as_numer_denom(self): + # don't use _from_args to rebuild the numerators and denominators + # as the order is not guaranteed to be the same once they have + # been separated from each other + numers, denoms = list(zip(*[f.as_numer_denom() for f in self.args])) + return self.func(*numers), self.func(*denoms) + + def as_base_exp(self): + e1 = None + bases = [] + nc = 0 + for m in self.args: + b, e = m.as_base_exp() + if not b.is_commutative: + nc += 1 + if e1 is None: + e1 = e + elif e != e1 or nc > 1: + return self, S.One + bases.append(b) + return self.func(*bases), e1 + + def _eval_is_polynomial(self, syms): + return all(term._eval_is_polynomial(syms) for term in self.args) + + def _eval_is_rational_function(self, syms): + return all(term._eval_is_rational_function(syms) for term in self.args) + + def _eval_is_meromorphic(self, x, a): + return _fuzzy_group((arg.is_meromorphic(x, a) for arg in self.args), + quick_exit=True) + + def _eval_is_algebraic_expr(self, syms): + return all(term._eval_is_algebraic_expr(syms) for term in self.args) + + _eval_is_commutative = lambda self: _fuzzy_group( + a.is_commutative for a in self.args) + + def _eval_is_complex(self): + comp = _fuzzy_group(a.is_complex for a in self.args) + if comp is False: + if any(a.is_infinite for a in self.args): + if any(a.is_zero is not False for a in self.args): + return None + return False + return comp + + def _eval_is_zero_infinite_helper(self): + # + # Helper used by _eval_is_zero and _eval_is_infinite. + # + # Three-valued logic is tricky so let us reason this carefully. It + # would be nice to say that we just check is_zero/is_infinite in all + # args but we need to be careful about the case that one arg is zero + # and another is infinite like Mul(0, oo) or more importantly a case + # where it is not known if the arguments are zero or infinite like + # Mul(y, 1/x). If either y or x could be zero then there is a + # *possibility* that we have Mul(0, oo) which should give None for both + # is_zero and is_infinite. + # + # We keep track of whether we have seen a zero or infinity but we also + # need to keep track of whether we have *possibly* seen one which + # would be indicated by None. + # + # For each argument there is the possibility that is_zero might give + # True, False or None and likewise that is_infinite might give True, + # False or None, giving 9 combinations. The True cases for is_zero and + # is_infinite are mutually exclusive though so there are 3 main cases: + # + # - is_zero = True + # - is_infinite = True + # - is_zero and is_infinite are both either False or None + # + # At the end seen_zero and seen_infinite can be any of 9 combinations + # of True/False/None. Unless one is False though we cannot return + # anything except None: + # + # - is_zero=True needs seen_zero=True and seen_infinite=False + # - is_zero=False needs seen_zero=False + # - is_infinite=True needs seen_infinite=True and seen_zero=False + # - is_infinite=False needs seen_infinite=False + # - anything else gives both is_zero=None and is_infinite=None + # + # The loop only sets the flags to True or None and never back to False. + # Hence as soon as neither flag is False we exit early returning None. + # In particular as soon as we encounter a single arg that has + # is_zero=is_infinite=None we exit. This is a common case since it is + # the default assumptions for a Symbol and also the case for most + # expressions containing such a symbol. The early exit gives a big + # speedup for something like Mul(*symbols('x:1000')).is_zero. + # + seen_zero = seen_infinite = False + + for a in self.args: + if a.is_zero: + if seen_infinite is not False: + return None, None + seen_zero = True + elif a.is_infinite: + if seen_zero is not False: + return None, None + seen_infinite = True + else: + if seen_zero is False and a.is_zero is None: + if seen_infinite is not False: + return None, None + seen_zero = None + if seen_infinite is False and a.is_infinite is None: + if seen_zero is not False: + return None, None + seen_infinite = None + + return seen_zero, seen_infinite + + def _eval_is_zero(self): + # True iff any arg is zero and no arg is infinite but need to handle + # three valued logic carefully. + seen_zero, seen_infinite = self._eval_is_zero_infinite_helper() + + if seen_zero is False: + return False + elif seen_zero is True and seen_infinite is False: + return True + else: + return None + + def _eval_is_infinite(self): + # True iff any arg is infinite and no arg is zero but need to handle + # three valued logic carefully. + seen_zero, seen_infinite = self._eval_is_zero_infinite_helper() + + if seen_infinite is True and seen_zero is False: + return True + elif seen_infinite is False: + return False + else: + return None + + # We do not need to implement _eval_is_finite because the assumptions + # system can infer it from finite = not infinite. + + def _eval_is_rational(self): + r = _fuzzy_group((a.is_rational for a in self.args), quick_exit=True) + if r: + return r + elif r is False: + # All args except one are rational + if all(a.is_zero is False for a in self.args): + return False + + def _eval_is_algebraic(self): + r = _fuzzy_group((a.is_algebraic for a in self.args), quick_exit=True) + if r: + return r + elif r is False: + # All args except one are algebraic + if all(a.is_zero is False for a in self.args): + return False + + # without involving odd/even checks this code would suffice: + #_eval_is_integer = lambda self: _fuzzy_group( + # (a.is_integer for a in self.args), quick_exit=True) + def _eval_is_integer(self): + is_rational = self._eval_is_rational() + if is_rational is False: + return False + + numerators = [] + denominators = [] + unknown = False + for a in self.args: + hit = False + if a.is_integer: + if abs(a) is not S.One: + numerators.append(a) + elif a.is_Rational: + n, d = a.as_numer_denom() + if abs(n) is not S.One: + numerators.append(n) + if d is not S.One: + denominators.append(d) + elif a.is_Pow: + b, e = a.as_base_exp() + if not b.is_integer or not e.is_integer: + hit = unknown = True + if e.is_negative: + denominators.append(2 if a is S.Half else + Pow(a, S.NegativeOne)) + elif not hit: + # int b and pos int e: a = b**e is integer + assert not e.is_positive + # for rational self and e equal to zero: a = b**e is 1 + assert not e.is_zero + return # sign of e unknown -> self.is_integer unknown + else: + # x**2, 2**x, or x**y with x and y int-unknown -> unknown + return + else: + return + + if not denominators and not unknown: + return True + + allodd = lambda x: all(i.is_odd for i in x) + alleven = lambda x: all(i.is_even for i in x) + anyeven = lambda x: any(i.is_even for i in x) + + from .relational import is_gt + if not numerators and denominators and all( + is_gt(_, S.One) for _ in denominators): + return False + elif unknown: + return + elif allodd(numerators) and anyeven(denominators): + return False + elif anyeven(numerators) and denominators == [2]: + return True + elif alleven(numerators) and allodd(denominators + ) and (Mul(*denominators, evaluate=False) - 1 + ).is_positive: + return False + if len(denominators) == 1: + d = denominators[0] + if d.is_Integer and d.is_even: + # if minimal power of 2 in num vs den is not + # negative then we have an integer + if (Add(*[i.as_base_exp()[1] for i in + numerators if i.is_even]) - trailing(d.p) + ).is_nonnegative: + return True + if len(numerators) == 1: + n = numerators[0] + if n.is_Integer and n.is_even: + # if minimal power of 2 in den vs num is positive + # then we have have a non-integer + if (Add(*[i.as_base_exp()[1] for i in + denominators if i.is_even]) - trailing(n.p) + ).is_positive: + return False + + def _eval_is_polar(self): + has_polar = any(arg.is_polar for arg in self.args) + return has_polar and \ + all(arg.is_polar or arg.is_positive for arg in self.args) + + def _eval_is_extended_real(self): + return self._eval_real_imag(True) + + def _eval_real_imag(self, real): + zero = False + t_not_re_im = None + + for t in self.args: + if (t.is_complex or t.is_infinite) is False and t.is_extended_real is False: + return False + elif t.is_imaginary: # I + real = not real + elif t.is_extended_real: # 2 + if not zero: + z = t.is_zero + if not z and zero is False: + zero = z + elif z: + if all(a.is_finite for a in self.args): + return True + return + elif t.is_extended_real is False: + # symbolic or literal like `2 + I` or symbolic imaginary + if t_not_re_im: + return # complex terms might cancel + t_not_re_im = t + elif t.is_imaginary is False: # symbolic like `2` or `2 + I` + if t_not_re_im: + return # complex terms might cancel + t_not_re_im = t + else: + return + + if t_not_re_im: + if t_not_re_im.is_extended_real is False: + if real: # like 3 + return zero # 3*(smthng like 2 + I or i) is not real + if t_not_re_im.is_imaginary is False: # symbolic 2 or 2 + I + if not real: # like I + return zero # I*(smthng like 2 or 2 + I) is not real + elif zero is False: + return real # can't be trumped by 0 + elif real: + return real # doesn't matter what zero is + + def _eval_is_imaginary(self): + if all(a.is_zero is False and a.is_finite for a in self.args): + return self._eval_real_imag(False) + + def _eval_is_hermitian(self): + return self._eval_herm_antiherm(True) + + def _eval_is_antihermitian(self): + return self._eval_herm_antiherm(False) + + def _eval_herm_antiherm(self, herm): + for t in self.args: + if t.is_hermitian is None or t.is_antihermitian is None: + return + if t.is_hermitian: + continue + elif t.is_antihermitian: + herm = not herm + else: + return + + if herm is not False: + return herm + + is_zero = self._eval_is_zero() + if is_zero: + return True + elif is_zero is False: + return herm + + def _eval_is_irrational(self): + for t in self.args: + a = t.is_irrational + if a: + others = list(self.args) + others.remove(t) + if all((x.is_rational and fuzzy_not(x.is_zero)) is True for x in others): + return True + return + if a is None: + return + if all(x.is_real for x in self.args): + return False + + def _eval_is_extended_positive(self): + """Return True if self is positive, False if not, and None if it + cannot be determined. + + Explanation + =========== + + This algorithm is non-recursive and works by keeping track of the + sign which changes when a negative or nonpositive is encountered. + Whether a nonpositive or nonnegative is seen is also tracked since + the presence of these makes it impossible to return True, but + possible to return False if the end result is nonpositive. e.g. + + pos * neg * nonpositive -> pos or zero -> None is returned + pos * neg * nonnegative -> neg or zero -> False is returned + """ + return self._eval_pos_neg(1) + + def _eval_pos_neg(self, sign): + saw_NON = saw_NOT = False + for t in self.args: + if t.is_extended_positive: + continue + elif t.is_extended_negative: + sign = -sign + elif t.is_zero: + if all(a.is_finite for a in self.args): + return False + return + elif t.is_extended_nonpositive: + sign = -sign + saw_NON = True + elif t.is_extended_nonnegative: + saw_NON = True + # FIXME: is_positive/is_negative is False doesn't take account of + # Symbol('x', infinite=True, extended_real=True) which has + # e.g. is_positive is False but has uncertain sign. + elif t.is_positive is False: + sign = -sign + if saw_NOT: + return + saw_NOT = True + elif t.is_negative is False: + if saw_NOT: + return + saw_NOT = True + else: + return + if sign == 1 and saw_NON is False and saw_NOT is False: + return True + if sign < 0: + return False + + def _eval_is_extended_negative(self): + return self._eval_pos_neg(-1) + + def _eval_is_odd(self): + is_integer = self._eval_is_integer() + if is_integer is not True: + return is_integer + + from sympy.simplify.radsimp import fraction + n, d = fraction(self) + if d.is_Integer and d.is_even: + # if minimal power of 2 in num vs den is + # positive then we have an even number + if (Add(*[i.as_base_exp()[1] for i in + Mul.make_args(n) if i.is_even]) - trailing(d.p) + ).is_positive: + return False + return + r, acc = True, 1 + for t in self.args: + if abs(t) is S.One: + continue + if t.is_even: + return False + if r is False: + pass + elif acc != 1 and (acc + t).is_odd: + r = False + elif t.is_even is None: + r = None + acc = t + return r + + def _eval_is_even(self): + from sympy.simplify.radsimp import fraction + n, d = fraction(self) + if n.is_Integer and n.is_even: + # if minimal power of 2 in den vs num is not + # negative then this is not an integer and + # can't be even + if (Add(*[i.as_base_exp()[1] for i in + Mul.make_args(d) if i.is_even]) - trailing(n.p) + ).is_nonnegative: + return False + + def _eval_is_composite(self): + """ + Here we count the number of arguments that have a minimum value + greater than two. + If there are more than one of such a symbol then the result is composite. + Else, the result cannot be determined. + """ + number_of_args = 0 # count of symbols with minimum value greater than one + for arg in self.args: + if not (arg.is_integer and arg.is_positive): + return None + if (arg-1).is_positive: + number_of_args += 1 + + if number_of_args > 1: + return True + + def _eval_subs(self, old, new): + from sympy.functions.elementary.complexes import sign + from sympy.ntheory.factor_ import multiplicity + from sympy.simplify.powsimp import powdenest + from sympy.simplify.radsimp import fraction + + if not old.is_Mul: + return None + + # try keep replacement literal so -2*x doesn't replace 4*x + if old.args[0].is_Number and old.args[0] < 0: + if self.args[0].is_Number: + if self.args[0] < 0: + return self._subs(-old, -new) + return None + + def base_exp(a): + # if I and -1 are in a Mul, they get both end up with + # a -1 base (see issue 6421); all we want here are the + # true Pow or exp separated into base and exponent + from sympy.functions.elementary.exponential import exp + if a.is_Pow or isinstance(a, exp): + return a.as_base_exp() + return a, S.One + + def breakup(eq): + """break up powers of eq when treated as a Mul: + b**(Rational*e) -> b**e, Rational + commutatives come back as a dictionary {b**e: Rational} + noncommutatives come back as a list [(b**e, Rational)] + """ + + (c, nc) = (defaultdict(int), []) + for a in Mul.make_args(eq): + a = powdenest(a) + (b, e) = base_exp(a) + if e is not S.One: + (co, _) = e.as_coeff_mul() + b = Pow(b, e/co) + e = co + if a.is_commutative: + c[b] += e + else: + nc.append([b, e]) + return (c, nc) + + def rejoin(b, co): + """ + Put rational back with exponent; in general this is not ok, but + since we took it from the exponent for analysis, it's ok to put + it back. + """ + + (b, e) = base_exp(b) + return Pow(b, e*co) + + def ndiv(a, b): + """if b divides a in an extractive way (like 1/4 divides 1/2 + but not vice versa, and 2/5 does not divide 1/3) then return + the integer number of times it divides, else return 0. + """ + if not b.q % a.q or not a.q % b.q: + return int(a/b) + return 0 + + # give Muls in the denominator a chance to be changed (see issue 5651) + # rv will be the default return value + rv = None + n, d = fraction(self) + self2 = self + if d is not S.One: + self2 = n._subs(old, new)/d._subs(old, new) + if not self2.is_Mul: + return self2._subs(old, new) + if self2 != self: + rv = self2 + + # Now continue with regular substitution. + + # handle the leading coefficient and use it to decide if anything + # should even be started; we always know where to find the Rational + # so it's a quick test + + co_self = self2.args[0] + co_old = old.args[0] + co_xmul = None + if co_old.is_Rational and co_self.is_Rational: + # if coeffs are the same there will be no updating to do + # below after breakup() step; so skip (and keep co_xmul=None) + if co_old != co_self: + co_xmul = co_self.extract_multiplicatively(co_old) + elif co_old.is_Rational: + return rv + + # break self and old into factors + + (c, nc) = breakup(self2) + (old_c, old_nc) = breakup(old) + + # update the coefficients if we had an extraction + # e.g. if co_self were 2*(3/35*x)**2 and co_old = 3/5 + # then co_self in c is replaced by (3/5)**2 and co_residual + # is 2*(1/7)**2 + + if co_xmul and co_xmul.is_Rational and abs(co_old) != 1: + mult = S(multiplicity(abs(co_old), co_self)) + c.pop(co_self) + if co_old in c: + c[co_old] += mult + else: + c[co_old] = mult + co_residual = co_self/co_old**mult + else: + co_residual = 1 + + # do quick tests to see if we can't succeed + + ok = True + if len(old_nc) > len(nc): + # more non-commutative terms + ok = False + elif len(old_c) > len(c): + # more commutative terms + ok = False + elif {i[0] for i in old_nc}.difference({i[0] for i in nc}): + # unmatched non-commutative bases + ok = False + elif set(old_c).difference(set(c)): + # unmatched commutative terms + ok = False + elif any(sign(c[b]) != sign(old_c[b]) for b in old_c): + # differences in sign + ok = False + if not ok: + return rv + + if not old_c: + cdid = None + else: + rat = [] + for (b, old_e) in old_c.items(): + c_e = c[b] + rat.append(ndiv(c_e, old_e)) + if not rat[-1]: + return rv + cdid = min(rat) + + if not old_nc: + ncdid = None + for i in range(len(nc)): + nc[i] = rejoin(*nc[i]) + else: + ncdid = 0 # number of nc replacements we did + take = len(old_nc) # how much to look at each time + limit = cdid or S.Infinity # max number that we can take + failed = [] # failed terms will need subs if other terms pass + i = 0 + while limit and i + take <= len(nc): + hit = False + + # the bases must be equivalent in succession, and + # the powers must be extractively compatible on the + # first and last factor but equal in between. + + rat = [] + for j in range(take): + if nc[i + j][0] != old_nc[j][0]: + break + elif j == 0: + rat.append(ndiv(nc[i + j][1], old_nc[j][1])) + elif j == take - 1: + rat.append(ndiv(nc[i + j][1], old_nc[j][1])) + elif nc[i + j][1] != old_nc[j][1]: + break + else: + rat.append(1) + j += 1 + else: + ndo = min(rat) + if ndo: + if take == 1: + if cdid: + ndo = min(cdid, ndo) + nc[i] = Pow(new, ndo)*rejoin(nc[i][0], + nc[i][1] - ndo*old_nc[0][1]) + else: + ndo = 1 + + # the left residual + + l = rejoin(nc[i][0], nc[i][1] - ndo* + old_nc[0][1]) + + # eliminate all middle terms + + mid = new + + # the right residual (which may be the same as the middle if take == 2) + + ir = i + take - 1 + r = (nc[ir][0], nc[ir][1] - ndo* + old_nc[-1][1]) + if r[1]: + if i + take < len(nc): + nc[i:i + take] = [l*mid, r] + else: + r = rejoin(*r) + nc[i:i + take] = [l*mid*r] + else: + + # there was nothing left on the right + + nc[i:i + take] = [l*mid] + + limit -= ndo + ncdid += ndo + hit = True + if not hit: + + # do the subs on this failing factor + + failed.append(i) + i += 1 + else: + + if not ncdid: + return rv + + # although we didn't fail, certain nc terms may have + # failed so we rebuild them after attempting a partial + # subs on them + + failed.extend(range(i, len(nc))) + for i in failed: + nc[i] = rejoin(*nc[i]).subs(old, new) + + # rebuild the expression + + if cdid is None: + do = ncdid + elif ncdid is None: + do = cdid + else: + do = min(ncdid, cdid) + + margs = [] + for b in c: + if b in old_c: + + # calculate the new exponent + + e = c[b] - old_c[b]*do + margs.append(rejoin(b, e)) + else: + margs.append(rejoin(b.subs(old, new), c[b])) + if cdid and not ncdid: + + # in case we are replacing commutative with non-commutative, + # we want the new term to come at the front just like the + # rest of this routine + + margs = [Pow(new, cdid)] + margs + return co_residual*self2.func(*margs)*self2.func(*nc) + + def _eval_nseries(self, x, n, logx, cdir=0): + from .function import PoleError + from sympy.functions.elementary.integers import ceiling + from sympy.series.order import Order + + def coeff_exp(term, x): + lt = term.as_coeff_exponent(x) + if lt[0].has(x): + try: + lt = term.leadterm(x) + except ValueError: + return term, S.Zero + return lt + + ords = [] + + try: + for t in self.args: + coeff, exp = t.leadterm(x) + if not coeff.has(x): + ords.append((t, exp)) + else: + raise ValueError + + n0 = sum(t[1] for t in ords if t[1].is_number) + facs = [] + for t, m in ords: + n1 = ceiling(n - n0 + (m if m.is_number else 0)) + s = t.nseries(x, n=n1, logx=logx, cdir=cdir) + ns = s.getn() + if ns is not None: + if ns < n1: # less than expected + n -= n1 - ns # reduce n + facs.append(s) + + except (ValueError, NotImplementedError, TypeError, PoleError): + # XXX: Catching so many generic exceptions around a large block of + # code will mask bugs. Whatever purpose catching these exceptions + # serves should be handled in a different way. + n0 = sympify(sum(t[1] for t in ords if t[1].is_number)) + if n0.is_nonnegative: + n0 = S.Zero + facs = [t.nseries(x, n=ceiling(n-n0), logx=logx, cdir=cdir) for t in self.args] + from sympy.simplify.powsimp import powsimp + res = powsimp(self.func(*facs).expand(), combine='exp', deep=True) + if res.has(Order): + res += Order(x**n, x) + return res + + res = S.Zero + ords2 = [Add.make_args(factor) for factor in facs] + + for fac in product(*ords2): + ords3 = [coeff_exp(term, x) for term in fac] + coeffs, powers = zip(*ords3) + power = sum(powers) + if (power - n).is_negative: + res += Mul(*coeffs)*(x**power) + + def max_degree(e, x): + if e is x: + return S.One + if e.is_Atom: + return S.Zero + if e.is_Add: + return max(max_degree(a, x) for a in e.args) + if e.is_Mul: + return Add(*[max_degree(a, x) for a in e.args]) + if e.is_Pow: + return max_degree(e.base, x)*e.exp + return S.Zero + + if self.is_polynomial(x): + from sympy.polys.polyerrors import PolynomialError + from sympy.polys.polytools import degree + try: + if max_degree(self, x) >= n or degree(self, x) != degree(res, x): + res += Order(x**n, x) + except PolynomialError: + pass + else: + return res + + if res != self: + if (self - res).subs(x, 0) == S.Zero and n > 0: + lt = self._eval_as_leading_term(x, logx=logx, cdir=cdir) + if lt == S.Zero: + return res + res += Order(x**n, x) + return res + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + return self.func(*[t.as_leading_term(x, logx=logx, cdir=cdir) for t in self.args]) + + def _eval_conjugate(self): + return self.func(*[t.conjugate() for t in self.args]) + + def _eval_transpose(self): + return self.func(*[t.transpose() for t in self.args[::-1]]) + + def _eval_adjoint(self): + return self.func(*[t.adjoint() for t in self.args[::-1]]) + + def as_content_primitive(self, radical=False, clear=True): + """Return the tuple (R, self/R) where R is the positive Rational + extracted from self. + + Examples + ======== + + >>> from sympy import sqrt + >>> (-3*sqrt(2)*(2 - 2*sqrt(2))).as_content_primitive() + (6, -sqrt(2)*(1 - sqrt(2))) + + See docstring of Expr.as_content_primitive for more examples. + """ + + coef = S.One + args = [] + for a in self.args: + c, p = a.as_content_primitive(radical=radical, clear=clear) + coef *= c + if p is not S.One: + args.append(p) + # don't use self._from_args here to reconstruct args + # since there may be identical args now that should be combined + # e.g. (2+2*x)*(3+3*x) should be (6, (1 + x)**2) not (6, (1+x)*(1+x)) + return coef, self.func(*args) + + def as_ordered_factors(self, order=None): + """Transform an expression into an ordered list of factors. + + Examples + ======== + + >>> from sympy import sin, cos + >>> from sympy.abc import x, y + + >>> (2*x*y*sin(x)*cos(x)).as_ordered_factors() + [2, x, y, sin(x), cos(x)] + + """ + cpart, ncpart = self.args_cnc() + cpart.sort(key=lambda expr: expr.sort_key(order=order)) + return cpart + ncpart + + @property + def _sorted_args(self): + return tuple(self.as_ordered_factors()) + +mul = AssocOpDispatcher('mul') + + +def prod(a, start=1): + """Return product of elements of a. Start with int 1 so if only + ints are included then an int result is returned. + + Examples + ======== + + >>> from sympy import prod, S + >>> prod(range(3)) + 0 + >>> type(_) is int + True + >>> prod([S(2), 3]) + 6 + >>> _.is_Integer + True + + You can start the product at something other than 1: + + >>> prod([1, 2], 3) + 6 + + """ + return reduce(operator.mul, a, start) + + +def _keep_coeff(coeff, factors, clear=True, sign=False): + """Return ``coeff*factors`` unevaluated if necessary. + + If ``clear`` is False, do not keep the coefficient as a factor + if it can be distributed on a single factor such that one or + more terms will still have integer coefficients. + + If ``sign`` is True, allow a coefficient of -1 to remain factored out. + + Examples + ======== + + >>> from sympy.core.mul import _keep_coeff + >>> from sympy.abc import x, y + >>> from sympy import S + + >>> _keep_coeff(S.Half, x + 2) + (x + 2)/2 + >>> _keep_coeff(S.Half, x + 2, clear=False) + x/2 + 1 + >>> _keep_coeff(S.Half, (x + 2)*y, clear=False) + y*(x + 2)/2 + >>> _keep_coeff(S(-1), x + y) + -x - y + >>> _keep_coeff(S(-1), x + y, sign=True) + -(x + y) + """ + if not coeff.is_Number: + if factors.is_Number: + factors, coeff = coeff, factors + else: + return coeff*factors + if factors is S.One: + return coeff + if coeff is S.One: + return factors + elif coeff is S.NegativeOne and not sign: + return -factors + elif factors.is_Add: + if not clear and coeff.is_Rational and coeff.q != 1: + args = [i.as_coeff_Mul() for i in factors.args] + args = [(_keep_coeff(c, coeff), m) for c, m in args] + if any(c.is_Integer for c, _ in args): + return Add._from_args([Mul._from_args( + i[1:] if i[0] == 1 else i) for i in args]) + return Mul(coeff, factors, evaluate=False) + elif factors.is_Mul: + margs = list(factors.args) + if margs[0].is_Number: + margs[0] *= coeff + if margs[0] == 1: + margs.pop(0) + else: + margs.insert(0, coeff) + return Mul._from_args(margs) + else: + m = coeff*factors + if m.is_Number and not factors.is_Number: + m = Mul._from_args((coeff, factors)) + return m + +def expand_2arg(e): + def do(e): + if e.is_Mul: + c, r = e.as_coeff_Mul() + if c.is_Number and r.is_Add: + return _unevaluated_Add(*[c*ri for ri in r.args]) + return e + return bottom_up(e, do) + + +from .numbers import Rational +from .power import Pow +from .add import Add, _unevaluated_Add diff --git a/lib/python3.11/site-packages/sympy/core/multidimensional.py b/lib/python3.11/site-packages/sympy/core/multidimensional.py new file mode 100644 index 0000000000000000000000000000000000000000..133e0ab6cba6a87c627feb6f6034a6daed1128c5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/multidimensional.py @@ -0,0 +1,131 @@ +""" +Provides functionality for multidimensional usage of scalar-functions. + +Read the vectorize docstring for more details. +""" + +from functools import wraps + + +def apply_on_element(f, args, kwargs, n): + """ + Returns a structure with the same dimension as the specified argument, + where each basic element is replaced by the function f applied on it. All + other arguments stay the same. + """ + # Get the specified argument. + if isinstance(n, int): + structure = args[n] + is_arg = True + elif isinstance(n, str): + structure = kwargs[n] + is_arg = False + + # Define reduced function that is only dependent on the specified argument. + def f_reduced(x): + if hasattr(x, "__iter__"): + return list(map(f_reduced, x)) + else: + if is_arg: + args[n] = x + else: + kwargs[n] = x + return f(*args, **kwargs) + + # f_reduced will call itself recursively so that in the end f is applied to + # all basic elements. + return list(map(f_reduced, structure)) + + +def iter_copy(structure): + """ + Returns a copy of an iterable object (also copying all embedded iterables). + """ + return [iter_copy(i) if hasattr(i, "__iter__") else i for i in structure] + + +def structure_copy(structure): + """ + Returns a copy of the given structure (numpy-array, list, iterable, ..). + """ + if hasattr(structure, "copy"): + return structure.copy() + return iter_copy(structure) + + +class vectorize: + """ + Generalizes a function taking scalars to accept multidimensional arguments. + + Examples + ======== + + >>> from sympy import vectorize, diff, sin, symbols, Function + >>> x, y, z = symbols('x y z') + >>> f, g, h = list(map(Function, 'fgh')) + + >>> @vectorize(0) + ... def vsin(x): + ... return sin(x) + + >>> vsin([1, x, y]) + [sin(1), sin(x), sin(y)] + + >>> @vectorize(0, 1) + ... def vdiff(f, y): + ... return diff(f, y) + + >>> vdiff([f(x, y, z), g(x, y, z), h(x, y, z)], [x, y, z]) + [[Derivative(f(x, y, z), x), Derivative(f(x, y, z), y), Derivative(f(x, y, z), z)], [Derivative(g(x, y, z), x), Derivative(g(x, y, z), y), Derivative(g(x, y, z), z)], [Derivative(h(x, y, z), x), Derivative(h(x, y, z), y), Derivative(h(x, y, z), z)]] + """ + def __init__(self, *mdargs): + """ + The given numbers and strings characterize the arguments that will be + treated as data structures, where the decorated function will be applied + to every single element. + If no argument is given, everything is treated multidimensional. + """ + for a in mdargs: + if not isinstance(a, (int, str)): + raise TypeError("a is of invalid type") + self.mdargs = mdargs + + def __call__(self, f): + """ + Returns a wrapper for the one-dimensional function that can handle + multidimensional arguments. + """ + @wraps(f) + def wrapper(*args, **kwargs): + # Get arguments that should be treated multidimensional + if self.mdargs: + mdargs = self.mdargs + else: + mdargs = range(len(args)) + kwargs.keys() + + arglength = len(args) + + for n in mdargs: + if isinstance(n, int): + if n >= arglength: + continue + entry = args[n] + is_arg = True + elif isinstance(n, str): + try: + entry = kwargs[n] + except KeyError: + continue + is_arg = False + if hasattr(entry, "__iter__"): + # Create now a copy of the given array and manipulate then + # the entries directly. + if is_arg: + args = list(args) + args[n] = structure_copy(entry) + else: + kwargs[n] = structure_copy(entry) + result = apply_on_element(wrapper, args, kwargs, n) + return result + return f(*args, **kwargs) + return wrapper diff --git a/lib/python3.11/site-packages/sympy/core/numbers.py b/lib/python3.11/site-packages/sympy/core/numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..5b23d74506d93c1560a7ba5430cd2c29db4afba7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/numbers.py @@ -0,0 +1,4378 @@ +from __future__ import annotations + +import numbers +import decimal +import fractions +import math + +from .containers import Tuple +from .sympify import (SympifyError, _sympy_converter, sympify, _convert_numpy_types, + _sympify, _is_numpy_instance) +from .singleton import S, Singleton +from .basic import Basic +from .expr import Expr, AtomicExpr +from .evalf import pure_complex +from .cache import cacheit, clear_cache +from .decorators import _sympifyit +from .intfunc import num_digits, igcd, ilcm, mod_inverse, integer_nthroot +from .logic import fuzzy_not +from .kind import NumberKind +from sympy.external.gmpy import SYMPY_INTS, gmpy, flint +from sympy.multipledispatch import dispatch +import mpmath +import mpmath.libmp as mlib +from mpmath.libmp import bitcount, round_nearest as rnd +from mpmath.libmp.backend import MPZ +from mpmath.libmp import mpf_pow, mpf_pi, mpf_e, phi_fixed +from mpmath.ctx_mp_python import mpnumeric +from mpmath.libmp.libmpf import ( + finf as _mpf_inf, fninf as _mpf_ninf, + fnan as _mpf_nan, fzero, _normalize as mpf_normalize, + prec_to_dps, dps_to_prec) +from sympy.utilities.misc import debug +from .parameters import global_parameters + +_LOG2 = math.log(2) + + +def comp(z1, z2, tol=None): + r"""Return a bool indicating whether the error between z1 and z2 + is $\le$ ``tol``. + + Examples + ======== + + If ``tol`` is ``None`` then ``True`` will be returned if + :math:`|z1 - z2|\times 10^p \le 5` where $p$ is minimum value of the + decimal precision of each value. + + >>> from sympy import comp, pi + >>> pi4 = pi.n(4); pi4 + 3.142 + >>> comp(_, 3.142) + True + >>> comp(pi4, 3.141) + False + >>> comp(pi4, 3.143) + False + + A comparison of strings will be made + if ``z1`` is a Number and ``z2`` is a string or ``tol`` is ''. + + >>> comp(pi4, 3.1415) + True + >>> comp(pi4, 3.1415, '') + False + + When ``tol`` is provided and $z2$ is non-zero and + :math:`|z1| > 1` the error is normalized by :math:`|z1|`: + + >>> abs(pi4 - 3.14)/pi4 + 0.000509791731426756 + >>> comp(pi4, 3.14, .001) # difference less than 0.1% + True + >>> comp(pi4, 3.14, .0005) # difference less than 0.1% + False + + When :math:`|z1| \le 1` the absolute error is used: + + >>> 1/pi4 + 0.3183 + >>> abs(1/pi4 - 0.3183)/(1/pi4) + 3.07371499106316e-5 + >>> abs(1/pi4 - 0.3183) + 9.78393554684764e-6 + >>> comp(1/pi4, 0.3183, 1e-5) + True + + To see if the absolute error between ``z1`` and ``z2`` is less + than or equal to ``tol``, call this as ``comp(z1 - z2, 0, tol)`` + or ``comp(z1 - z2, tol=tol)``: + + >>> abs(pi4 - 3.14) + 0.00160156249999988 + >>> comp(pi4 - 3.14, 0, .002) + True + >>> comp(pi4 - 3.14, 0, .001) + False + """ + if isinstance(z2, str): + if not pure_complex(z1, or_real=True): + raise ValueError('when z2 is a str z1 must be a Number') + return str(z1) == z2 + if not z1: + z1, z2 = z2, z1 + if not z1: + return True + if not tol: + a, b = z1, z2 + if tol == '': + return str(a) == str(b) + if tol is None: + a, b = sympify(a), sympify(b) + if not all(i.is_number for i in (a, b)): + raise ValueError('expecting 2 numbers') + fa = a.atoms(Float) + fb = b.atoms(Float) + if not fa and not fb: + # no floats -- compare exactly + return a == b + # get a to be pure_complex + for _ in range(2): + ca = pure_complex(a, or_real=True) + if not ca: + if fa: + a = a.n(prec_to_dps(min(i._prec for i in fa))) + ca = pure_complex(a, or_real=True) + break + else: + fa, fb = fb, fa + a, b = b, a + cb = pure_complex(b) + if not cb and fb: + b = b.n(prec_to_dps(min(i._prec for i in fb))) + cb = pure_complex(b, or_real=True) + if ca and cb and (ca[1] or cb[1]): + return all(comp(i, j) for i, j in zip(ca, cb)) + tol = 10**prec_to_dps(min(a._prec, getattr(b, '_prec', a._prec))) + return int(abs(a - b)*tol) <= 5 + diff = abs(z1 - z2) + az1 = abs(z1) + if z2 and az1 > 1: + return diff/az1 <= tol + else: + return diff <= tol + + +def mpf_norm(mpf, prec): + """Return the mpf tuple normalized appropriately for the indicated + precision after doing a check to see if zero should be returned or + not when the mantissa is 0. ``mpf_normlize`` always assumes that this + is zero, but it may not be since the mantissa for mpf's values "+inf", + "-inf" and "nan" have a mantissa of zero, too. + + Note: this is not intended to validate a given mpf tuple, so sending + mpf tuples that were not created by mpmath may produce bad results. This + is only a wrapper to ``mpf_normalize`` which provides the check for non- + zero mpfs that have a 0 for the mantissa. + """ + sign, man, expt, bc = mpf + if not man: + # hack for mpf_normalize which does not do this; + # it assumes that if man is zero the result is 0 + # (see issue 6639) + if not bc: + return fzero + else: + # don't change anything; this should already + # be a well formed mpf tuple + return mpf + + # Necessary if mpmath is using the gmpy backend + from mpmath.libmp.backend import MPZ + rv = mpf_normalize(sign, MPZ(man), expt, bc, prec, rnd) + return rv + +# TODO: we should use the warnings module +_errdict = {"divide": False} + + +def seterr(divide=False): + """ + Should SymPy raise an exception on 0/0 or return a nan? + + divide == True .... raise an exception + divide == False ... return nan + """ + if _errdict["divide"] != divide: + clear_cache() + _errdict["divide"] = divide + + +def _as_integer_ratio(p): + neg_pow, man, expt, _ = getattr(p, '_mpf_', mpmath.mpf(p)._mpf_) + p = [1, -1][neg_pow % 2]*man + if expt < 0: + q = 2**-expt + else: + q = 1 + p *= 2**expt + return int(p), int(q) + + +def _decimal_to_Rational_prec(dec): + """Convert an ordinary decimal instance to a Rational.""" + if not dec.is_finite(): + raise TypeError("dec must be finite, got %s." % dec) + s, d, e = dec.as_tuple() + prec = len(d) + if e >= 0: # it's an integer + rv = Integer(int(dec)) + else: + s = (-1)**s + d = sum(di*10**i for i, di in enumerate(reversed(d))) + rv = Rational(s*d, 10**-e) + return rv, prec + +_dig = str.maketrans(dict.fromkeys('1234567890')) + +def _literal_float(s): + """return True if s is space-trimmed number literal else False + + Python allows underscore as digit separators: there must be a + digit on each side. So neither a leading underscore nor a + double underscore are valid as part of a number. A number does + not have to precede the decimal point, but there must be a + digit before the optional "e" or "E" that begins the signs + exponent of the number which must be an integer, perhaps with + underscore separators. + + SymPy allows space as a separator; if the calling routine replaces + them with underscores then the same semantics will be enforced + for them as for underscores: there can only be 1 *between* digits. + + We don't check for error from float(s) because we don't know + whether s is malicious or not. A regex for this could maybe + be written but will it be understood by most who read it? + """ + # mantissa and exponent + parts = s.split('e') + if len(parts) > 2: + return False + if len(parts) == 2: + m, e = parts + if e.startswith(tuple('+-')): + e = e[1:] + if not e: + return False + else: + m, e = s, '1' + # integer and fraction of mantissa + parts = m.split('.') + if len(parts) > 2: + return False + elif len(parts) == 2: + i, f = parts + else: + i, f = m, '1' + if not i and not f: + return False + if i and i[0] in '+-': + i = i[1:] + if not i: # -.3e4 -> -0.3e4 + i = '1' + f = f or '1' + # check that all groups contain only digits and are not null + for n in (i, f, e): + for g in n.split('_'): + if not g or g.translate(_dig): + return False + return True + +# (a,b) -> gcd(a,b) + +# TODO caching with decorator, but not to degrade performance + + +class Number(AtomicExpr): + """Represents atomic numbers in SymPy. + + Explanation + =========== + + Floating point numbers are represented by the Float class. + Rational numbers (of any size) are represented by the Rational class. + Integer numbers (of any size) are represented by the Integer class. + Float and Rational are subclasses of Number; Integer is a subclass + of Rational. + + For example, ``2/3`` is represented as ``Rational(2, 3)`` which is + a different object from the floating point number obtained with + Python division ``2/3``. Even for numbers that are exactly + represented in binary, there is a difference between how two forms, + such as ``Rational(1, 2)`` and ``Float(0.5)``, are used in SymPy. + The rational form is to be preferred in symbolic computations. + + Other kinds of numbers, such as algebraic numbers ``sqrt(2)`` or + complex numbers ``3 + 4*I``, are not instances of Number class as + they are not atomic. + + See Also + ======== + + Float, Integer, Rational + """ + is_commutative = True + is_number = True + is_Number = True + + __slots__ = () + + # Used to make max(x._prec, y._prec) return x._prec when only x is a float + _prec = -1 + + kind = NumberKind + + def __new__(cls, *obj): + if len(obj) == 1: + obj = obj[0] + + if isinstance(obj, Number): + return obj + if isinstance(obj, SYMPY_INTS): + return Integer(obj) + if isinstance(obj, tuple) and len(obj) == 2: + return Rational(*obj) + if isinstance(obj, (float, mpmath.mpf, decimal.Decimal)): + return Float(obj) + if isinstance(obj, str): + _obj = obj.lower() # float('INF') == float('inf') + if _obj == 'nan': + return S.NaN + elif _obj == 'inf': + return S.Infinity + elif _obj == '+inf': + return S.Infinity + elif _obj == '-inf': + return S.NegativeInfinity + val = sympify(obj) + if isinstance(val, Number): + return val + else: + raise ValueError('String "%s" does not denote a Number' % obj) + msg = "expected str|int|long|float|Decimal|Number object but got %r" + raise TypeError(msg % type(obj).__name__) + + def could_extract_minus_sign(self): + return bool(self.is_extended_negative) + + def invert(self, other, *gens, **args): + from sympy.polys.polytools import invert + if getattr(other, 'is_number', True): + return mod_inverse(self, other) + return invert(self, other, *gens, **args) + + def __divmod__(self, other): + from sympy.functions.elementary.complexes import sign + + try: + other = Number(other) + if self.is_infinite or S.NaN in (self, other): + return (S.NaN, S.NaN) + except TypeError: + return NotImplemented + if not other: + raise ZeroDivisionError('modulo by zero') + if self.is_Integer and other.is_Integer: + return Tuple(*divmod(self.p, other.p)) + elif isinstance(other, Float): + rat = self/Rational(other) + else: + rat = self/other + if other.is_finite: + w = int(rat) if rat >= 0 else int(rat) - 1 + r = self - other*w + if r == Float(other): + w += 1 + r = 0 + if isinstance(self, Float) or isinstance(other, Float): + r = Float(r) # in case w or r is 0 + else: + w = 0 if not self or (sign(self) == sign(other)) else -1 + r = other if w else self + return Tuple(w, r) + + def __rdivmod__(self, other): + try: + other = Number(other) + except TypeError: + return NotImplemented + return divmod(other, self) + + def _as_mpf_val(self, prec): + """Evaluation of mpf tuple accurate to at least prec bits.""" + raise NotImplementedError('%s needs ._as_mpf_val() method' % + (self.__class__.__name__)) + + def _eval_evalf(self, prec): + return Float._new(self._as_mpf_val(prec), prec) + + def _as_mpf_op(self, prec): + prec = max(prec, self._prec) + return self._as_mpf_val(prec), prec + + def __float__(self): + return mlib.to_float(self._as_mpf_val(53)) + + def floor(self): + raise NotImplementedError('%s needs .floor() method' % + (self.__class__.__name__)) + + def ceiling(self): + raise NotImplementedError('%s needs .ceiling() method' % + (self.__class__.__name__)) + + def __floor__(self): + return self.floor() + + def __ceil__(self): + return self.ceiling() + + def _eval_conjugate(self): + return self + + def _eval_order(self, *symbols): + from sympy.series.order import Order + # Order(5, x, y) -> Order(1,x,y) + return Order(S.One, *symbols) + + def _eval_subs(self, old, new): + if old == -self: + return -new + return self # there is no other possibility + + @classmethod + def class_key(cls): + return 1, 0, 'Number' + + @cacheit + def sort_key(self, order=None): + return self.class_key(), (0, ()), (), self + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.NaN: + return S.NaN + elif other is S.Infinity: + return S.Infinity + elif other is S.NegativeInfinity: + return S.NegativeInfinity + return AtomicExpr.__add__(self, other) + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.NaN: + return S.NaN + elif other is S.Infinity: + return S.NegativeInfinity + elif other is S.NegativeInfinity: + return S.Infinity + return AtomicExpr.__sub__(self, other) + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.NaN: + return S.NaN + elif other is S.Infinity: + if self.is_zero: + return S.NaN + elif self.is_positive: + return S.Infinity + else: + return S.NegativeInfinity + elif other is S.NegativeInfinity: + if self.is_zero: + return S.NaN + elif self.is_positive: + return S.NegativeInfinity + else: + return S.Infinity + elif isinstance(other, Tuple): + return NotImplemented + return AtomicExpr.__mul__(self, other) + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.NaN: + return S.NaN + elif other in (S.Infinity, S.NegativeInfinity): + return S.Zero + return AtomicExpr.__truediv__(self, other) + + def __eq__(self, other): + raise NotImplementedError('%s needs .__eq__() method' % + (self.__class__.__name__)) + + def __ne__(self, other): + raise NotImplementedError('%s needs .__ne__() method' % + (self.__class__.__name__)) + + def __lt__(self, other): + try: + other = _sympify(other) + except SympifyError: + raise TypeError("Invalid comparison %s < %s" % (self, other)) + raise NotImplementedError('%s needs .__lt__() method' % + (self.__class__.__name__)) + + def __le__(self, other): + try: + other = _sympify(other) + except SympifyError: + raise TypeError("Invalid comparison %s <= %s" % (self, other)) + raise NotImplementedError('%s needs .__le__() method' % + (self.__class__.__name__)) + + def __gt__(self, other): + try: + other = _sympify(other) + except SympifyError: + raise TypeError("Invalid comparison %s > %s" % (self, other)) + return _sympify(other).__lt__(self) + + def __ge__(self, other): + try: + other = _sympify(other) + except SympifyError: + raise TypeError("Invalid comparison %s >= %s" % (self, other)) + return _sympify(other).__le__(self) + + def __hash__(self): + return super().__hash__() + + def is_constant(self, *wrt, **flags): + return True + + def as_coeff_mul(self, *deps, rational=True, **kwargs): + # a -> c*t + if self.is_Rational or not rational: + return self, () + elif self.is_negative: + return S.NegativeOne, (-self,) + return S.One, (self,) + + def as_coeff_add(self, *deps): + # a -> c + t + if self.is_Rational: + return self, () + return S.Zero, (self,) + + def as_coeff_Mul(self, rational=False): + """Efficiently extract the coefficient of a product.""" + if not rational: + return self, S.One + return S.One, self + + def as_coeff_Add(self, rational=False): + """Efficiently extract the coefficient of a summation.""" + if not rational: + return self, S.Zero + return S.Zero, self + + def gcd(self, other): + """Compute GCD of `self` and `other`. """ + from sympy.polys.polytools import gcd + return gcd(self, other) + + def lcm(self, other): + """Compute LCM of `self` and `other`. """ + from sympy.polys.polytools import lcm + return lcm(self, other) + + def cofactors(self, other): + """Compute GCD and cofactors of `self` and `other`. """ + from sympy.polys.polytools import cofactors + return cofactors(self, other) + + +class Float(Number): + """Represent a floating-point number of arbitrary precision. + + Examples + ======== + + >>> from sympy import Float + >>> Float(3.5) + 3.50000000000000 + >>> Float(3) + 3.00000000000000 + + Creating Floats from strings (and Python ``int`` and ``long`` + types) will give a minimum precision of 15 digits, but the + precision will automatically increase to capture all digits + entered. + + >>> Float(1) + 1.00000000000000 + >>> Float(10**20) + 100000000000000000000. + >>> Float('1e20') + 100000000000000000000. + + However, *floating-point* numbers (Python ``float`` types) retain + only 15 digits of precision: + + >>> Float(1e20) + 1.00000000000000e+20 + >>> Float(1.23456789123456789) + 1.23456789123457 + + It may be preferable to enter high-precision decimal numbers + as strings: + + >>> Float('1.23456789123456789') + 1.23456789123456789 + + The desired number of digits can also be specified: + + >>> Float('1e-3', 3) + 0.00100 + >>> Float(100, 4) + 100.0 + + Float can automatically count significant figures if a null string + is sent for the precision; spaces or underscores are also allowed. (Auto- + counting is only allowed for strings, ints and longs). + + >>> Float('123 456 789.123_456', '') + 123456789.123456 + >>> Float('12e-3', '') + 0.012 + >>> Float(3, '') + 3. + + If a number is written in scientific notation, only the digits before the + exponent are considered significant if a decimal appears, otherwise the + "e" signifies only how to move the decimal: + + >>> Float('60.e2', '') # 2 digits significant + 6.0e+3 + >>> Float('60e2', '') # 4 digits significant + 6000. + >>> Float('600e-2', '') # 3 digits significant + 6.00 + + Notes + ===== + + Floats are inexact by their nature unless their value is a binary-exact + value. + + >>> approx, exact = Float(.1, 1), Float(.125, 1) + + For calculation purposes, evalf needs to be able to change the precision + but this will not increase the accuracy of the inexact value. The + following is the most accurate 5-digit approximation of a value of 0.1 + that had only 1 digit of precision: + + >>> approx.evalf(5) + 0.099609 + + By contrast, 0.125 is exact in binary (as it is in base 10) and so it + can be passed to Float or evalf to obtain an arbitrary precision with + matching accuracy: + + >>> Float(exact, 5) + 0.12500 + >>> exact.evalf(20) + 0.12500000000000000000 + + Trying to make a high-precision Float from a float is not disallowed, + but one must keep in mind that the *underlying float* (not the apparent + decimal value) is being obtained with high precision. For example, 0.3 + does not have a finite binary representation. The closest rational is + the fraction 5404319552844595/2**54. So if you try to obtain a Float of + 0.3 to 20 digits of precision you will not see the same thing as 0.3 + followed by 19 zeros: + + >>> Float(0.3, 20) + 0.29999999999999998890 + + If you want a 20-digit value of the decimal 0.3 (not the floating point + approximation of 0.3) you should send the 0.3 as a string. The underlying + representation is still binary but a higher precision than Python's float + is used: + + >>> Float('0.3', 20) + 0.30000000000000000000 + + Although you can increase the precision of an existing Float using Float + it will not increase the accuracy -- the underlying value is not changed: + + >>> def show(f): # binary rep of Float + ... from sympy import Mul, Pow + ... s, m, e, b = f._mpf_ + ... v = Mul(int(m), Pow(2, int(e), evaluate=False), evaluate=False) + ... print('%s at prec=%s' % (v, f._prec)) + ... + >>> t = Float('0.3', 3) + >>> show(t) + 4915/2**14 at prec=13 + >>> show(Float(t, 20)) # higher prec, not higher accuracy + 4915/2**14 at prec=70 + >>> show(Float(t, 2)) # lower prec + 307/2**10 at prec=10 + + The same thing happens when evalf is used on a Float: + + >>> show(t.evalf(20)) + 4915/2**14 at prec=70 + >>> show(t.evalf(2)) + 307/2**10 at prec=10 + + Finally, Floats can be instantiated with an mpf tuple (n, c, p) to + produce the number (-1)**n*c*2**p: + + >>> n, c, p = 1, 5, 0 + >>> (-1)**n*c*2**p + -5 + >>> Float((1, 5, 0)) + -5.00000000000000 + + An actual mpf tuple also contains the number of bits in c as the last + element of the tuple: + + >>> _._mpf_ + (1, 5, 0, 3) + + This is not needed for instantiation and is not the same thing as the + precision. The mpf tuple and the precision are two separate quantities + that Float tracks. + + In SymPy, a Float is a number that can be computed with arbitrary + precision. Although floating point 'inf' and 'nan' are not such + numbers, Float can create these numbers: + + >>> Float('-inf') + -oo + >>> _.is_Float + False + + Zero in Float only has a single value. Values are not separate for + positive and negative zeroes. + """ + __slots__ = ('_mpf_', '_prec') + + _mpf_: tuple[int, int, int, int] + + # A Float, though rational in form, does not behave like + # a rational in all Python expressions so we deal with + # exceptions (where we want to deal with the rational + # form of the Float as a rational) at the source rather + # than assigning a mathematically loaded category of 'rational' + is_rational = None + is_irrational = None + is_number = True + + is_real = True + is_extended_real = True + + is_Float = True + + _remove_non_digits = str.maketrans(dict.fromkeys("-+_.")) + + def __new__(cls, num, dps=None, precision=None): + if dps is not None and precision is not None: + raise ValueError('Both decimal and binary precision supplied. ' + 'Supply only one. ') + + if isinstance(num, str): + _num = num = num.strip() # Python ignores leading and trailing space + num = num.replace(' ', '_').lower() # Float treats spaces as digit sep; E -> e + if num.startswith('.') and len(num) > 1: + num = '0' + num + elif num.startswith('-.') and len(num) > 2: + num = '-0.' + num[2:] + elif num in ('inf', '+inf'): + return S.Infinity + elif num == '-inf': + return S.NegativeInfinity + elif num == 'nan': + return S.NaN + elif not _literal_float(num): + raise ValueError('string-float not recognized: %s' % _num) + elif isinstance(num, float) and num == 0: + num = '0' + elif isinstance(num, float) and num == float('inf'): + return S.Infinity + elif isinstance(num, float) and num == float('-inf'): + return S.NegativeInfinity + elif isinstance(num, float) and math.isnan(num): + return S.NaN + elif isinstance(num, (SYMPY_INTS, Integer)): + num = str(num) + elif num is S.Infinity: + return num + elif num is S.NegativeInfinity: + return num + elif num is S.NaN: + return num + elif _is_numpy_instance(num): # support for numpy datatypes + num = _convert_numpy_types(num) + elif isinstance(num, mpmath.mpf): + if precision is None: + if dps is None: + precision = num.context.prec + num = num._mpf_ + + if dps is None and precision is None: + dps = 15 + if isinstance(num, Float): + return num + if isinstance(num, str): + try: + Num = decimal.Decimal(num) + except decimal.InvalidOperation: + pass + else: + isint = '.' not in num + num, dps = _decimal_to_Rational_prec(Num) + if num.is_Integer and isint: + # 12e3 is shorthand for int, not float; + # 12.e3 would be the float version + dps = max(dps, num_digits(num)) + dps = max(15, dps) + precision = dps_to_prec(dps) + elif precision == '' and dps is None or precision is None and dps == '': + if not isinstance(num, str): + raise ValueError('The null string can only be used when ' + 'the number to Float is passed as a string or an integer.') + try: + Num = decimal.Decimal(num) + except decimal.InvalidOperation: + raise ValueError('string-float not recognized by Decimal: %s' % num) + else: + isint = '.' not in num + num, dps = _decimal_to_Rational_prec(Num) + if num.is_Integer and isint: + # without dec, e-notation is short for int + dps = max(dps, num_digits(num)) + precision = dps_to_prec(dps) + + # decimal precision(dps) is set and maybe binary precision(precision) + # as well.From here on binary precision is used to compute the Float. + # Hence, if supplied use binary precision else translate from decimal + # precision. + + if precision is None or precision == '': + precision = dps_to_prec(dps) + + precision = int(precision) + + if isinstance(num, float): + _mpf_ = mlib.from_float(num, precision, rnd) + elif isinstance(num, str): + _mpf_ = mlib.from_str(num, precision, rnd) + elif isinstance(num, decimal.Decimal): + if num.is_finite(): + _mpf_ = mlib.from_str(str(num), precision, rnd) + elif num.is_nan(): + return S.NaN + elif num.is_infinite(): + if num > 0: + return S.Infinity + return S.NegativeInfinity + else: + raise ValueError("unexpected decimal value %s" % str(num)) + elif isinstance(num, tuple) and len(num) in (3, 4): + if isinstance(num[1], str): + # it's a hexadecimal (coming from a pickled object) + num = list(num) + # If we're loading an object pickled in Python 2 into + # Python 3, we may need to strip a tailing 'L' because + # of a shim for int on Python 3, see issue #13470. + if num[1].endswith('L'): + num[1] = num[1][:-1] + # Strip leading '0x' - gmpy2 only documents such inputs + # with base prefix as valid when the 2nd argument (base) is 0. + # When mpmath uses Sage as the backend, however, it + # ends up including '0x' when preparing the picklable tuple. + # See issue #19690. + if num[1].startswith('0x'): + num[1] = num[1][2:] + # Now we can assume that it is in standard form + num[1] = MPZ(num[1], 16) + _mpf_ = tuple(num) + else: + if len(num) == 4: + # handle normalization hack + return Float._new(num, precision) + else: + if not all(( + num[0] in (0, 1), + num[1] >= 0, + all(type(i) in (int, int) for i in num) + )): + raise ValueError('malformed mpf: %s' % (num,)) + # don't compute number or else it may + # over/underflow + return Float._new( + (num[0], num[1], num[2], bitcount(num[1])), + precision) + elif isinstance(num, (Number, NumberSymbol)): + _mpf_ = num._as_mpf_val(precision) + else: + _mpf_ = mpmath.mpf(num, prec=precision)._mpf_ + + return cls._new(_mpf_, precision, zero=False) + + @classmethod + def _new(cls, _mpf_, _prec, zero=True): + # special cases + if zero and _mpf_ == fzero: + return S.Zero # Float(0) -> 0.0; Float._new((0,0,0,0)) -> 0 + elif _mpf_ == _mpf_nan: + return S.NaN + elif _mpf_ == _mpf_inf: + return S.Infinity + elif _mpf_ == _mpf_ninf: + return S.NegativeInfinity + + obj = Expr.__new__(cls) + obj._mpf_ = mpf_norm(_mpf_, _prec) + obj._prec = _prec + return obj + + def __getnewargs_ex__(self): + sign, man, exp, bc = self._mpf_ + arg = (sign, hex(man)[2:], exp, bc) + kwargs = {'precision': self._prec} + return ((arg,), kwargs) + + def _hashable_content(self): + return (self._mpf_, self._prec) + + def floor(self): + return Integer(int(mlib.to_int( + mlib.mpf_floor(self._mpf_, self._prec)))) + + def ceiling(self): + return Integer(int(mlib.to_int( + mlib.mpf_ceil(self._mpf_, self._prec)))) + + def __floor__(self): + return self.floor() + + def __ceil__(self): + return self.ceiling() + + @property + def num(self): + return mpmath.mpf(self._mpf_) + + def _as_mpf_val(self, prec): + rv = mpf_norm(self._mpf_, prec) + if rv != self._mpf_ and self._prec == prec: + debug(self._mpf_, rv) + return rv + + def _as_mpf_op(self, prec): + return self._mpf_, max(prec, self._prec) + + def _eval_is_finite(self): + if self._mpf_ in (_mpf_inf, _mpf_ninf): + return False + return True + + def _eval_is_infinite(self): + if self._mpf_ in (_mpf_inf, _mpf_ninf): + return True + return False + + def _eval_is_integer(self): + if self._mpf_ == fzero: + return True + if not int_valued(self): + return False + + def _eval_is_negative(self): + if self._mpf_ in (_mpf_ninf, _mpf_inf): + return False + return self.num < 0 + + def _eval_is_positive(self): + if self._mpf_ in (_mpf_ninf, _mpf_inf): + return False + return self.num > 0 + + def _eval_is_extended_negative(self): + if self._mpf_ == _mpf_ninf: + return True + if self._mpf_ == _mpf_inf: + return False + return self.num < 0 + + def _eval_is_extended_positive(self): + if self._mpf_ == _mpf_inf: + return True + if self._mpf_ == _mpf_ninf: + return False + return self.num > 0 + + def _eval_is_zero(self): + return self._mpf_ == fzero + + def __bool__(self): + return self._mpf_ != fzero + + def __neg__(self): + if not self: + return self + return Float._new(mlib.mpf_neg(self._mpf_), self._prec) + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_add(self._mpf_, rhs, prec, rnd), prec) + return Number.__add__(self, other) + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_sub(self._mpf_, rhs, prec, rnd), prec) + return Number.__sub__(self, other) + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_mul(self._mpf_, rhs, prec, rnd), prec) + return Number.__mul__(self, other) + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if isinstance(other, Number) and other != 0 and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_div(self._mpf_, rhs, prec, rnd), prec) + return Number.__truediv__(self, other) + + @_sympifyit('other', NotImplemented) + def __mod__(self, other): + if isinstance(other, Rational) and other.q != 1 and global_parameters.evaluate: + # calculate mod with Rationals, *then* round the result + return Float(Rational.__mod__(Rational(self), other), + precision=self._prec) + if isinstance(other, Float) and global_parameters.evaluate: + r = self/other + if int_valued(r): + return Float(0, precision=max(self._prec, other._prec)) + if isinstance(other, Number) and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_mod(self._mpf_, rhs, prec, rnd), prec) + return Number.__mod__(self, other) + + @_sympifyit('other', NotImplemented) + def __rmod__(self, other): + if isinstance(other, Float) and global_parameters.evaluate: + return other.__mod__(self) + if isinstance(other, Number) and global_parameters.evaluate: + rhs, prec = other._as_mpf_op(self._prec) + return Float._new(mlib.mpf_mod(rhs, self._mpf_, prec, rnd), prec) + return Number.__rmod__(self, other) + + def _eval_power(self, expt): + """ + expt is symbolic object but not equal to 0, 1 + + (-p)**r -> exp(r*log(-p)) -> exp(r*(log(p) + I*Pi)) -> + -> p**r*(sin(Pi*r) + cos(Pi*r)*I) + """ + if equal_valued(self, 0): + if expt.is_extended_positive: + return self + if expt.is_extended_negative: + return S.ComplexInfinity + if isinstance(expt, Number): + if isinstance(expt, Integer): + prec = self._prec + return Float._new( + mlib.mpf_pow_int(self._mpf_, expt.p, prec, rnd), prec) + elif isinstance(expt, Rational) and \ + expt.p == 1 and expt.q % 2 and self.is_negative: + return Pow(S.NegativeOne, expt, evaluate=False)*( + -self)._eval_power(expt) + expt, prec = expt._as_mpf_op(self._prec) + mpfself = self._mpf_ + try: + y = mpf_pow(mpfself, expt, prec, rnd) + return Float._new(y, prec) + except mlib.ComplexResult: + re, im = mlib.mpc_pow( + (mpfself, fzero), (expt, fzero), prec, rnd) + return Float._new(re, prec) + \ + Float._new(im, prec)*S.ImaginaryUnit + + def __abs__(self): + return Float._new(mlib.mpf_abs(self._mpf_), self._prec) + + def __int__(self): + if self._mpf_ == fzero: + return 0 + return int(mlib.to_int(self._mpf_)) # uses round_fast = round_down + + def __eq__(self, other): + if isinstance(other, float): + other = Float(other) + return Basic.__eq__(self, other) + + def __ne__(self, other): + eq = self.__eq__(other) + if eq is NotImplemented: + return eq + else: + return not eq + + def __hash__(self): + float_val = float(self) + if not math.isinf(float_val): + return hash(float_val) + return Basic.__hash__(self) + + def _Frel(self, other, op): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Rational: + # test self*other.q other.p without losing precision + ''' + >>> f = Float(.1,2) + >>> i = 1234567890 + >>> (f*i)._mpf_ + (0, 471, 18, 9) + >>> mlib.mpf_mul(f._mpf_, mlib.from_int(i)) + (0, 505555550955, -12, 39) + ''' + smpf = mlib.mpf_mul(self._mpf_, mlib.from_int(other.q)) + ompf = mlib.from_int(other.p) + return _sympify(bool(op(smpf, ompf))) + elif other.is_Float: + return _sympify(bool( + op(self._mpf_, other._mpf_))) + elif other.is_comparable and other not in ( + S.Infinity, S.NegativeInfinity): + other = other.evalf(prec_to_dps(self._prec)) + if other._prec > 1: + if other.is_Number: + return _sympify(bool( + op(self._mpf_, other._as_mpf_val(self._prec)))) + + def __gt__(self, other): + if isinstance(other, NumberSymbol): + return other.__lt__(self) + rv = self._Frel(other, mlib.mpf_gt) + if rv is None: + return Expr.__gt__(self, other) + return rv + + def __ge__(self, other): + if isinstance(other, NumberSymbol): + return other.__le__(self) + rv = self._Frel(other, mlib.mpf_ge) + if rv is None: + return Expr.__ge__(self, other) + return rv + + def __lt__(self, other): + if isinstance(other, NumberSymbol): + return other.__gt__(self) + rv = self._Frel(other, mlib.mpf_lt) + if rv is None: + return Expr.__lt__(self, other) + return rv + + def __le__(self, other): + if isinstance(other, NumberSymbol): + return other.__ge__(self) + rv = self._Frel(other, mlib.mpf_le) + if rv is None: + return Expr.__le__(self, other) + return rv + + def epsilon_eq(self, other, epsilon="1e-15"): + return abs(self - other) < Float(epsilon) + + def __format__(self, format_spec): + return format(decimal.Decimal(str(self)), format_spec) + + +# Add sympify converters +_sympy_converter[float] = _sympy_converter[decimal.Decimal] = Float + +# this is here to work nicely in Sage +RealNumber = Float + + +class Rational(Number): + """Represents rational numbers (p/q) of any size. + + Examples + ======== + + >>> from sympy import Rational, nsimplify, S, pi + >>> Rational(1, 2) + 1/2 + + Rational is unprejudiced in accepting input. If a float is passed, the + underlying value of the binary representation will be returned: + + >>> Rational(.5) + 1/2 + >>> Rational(.2) + 3602879701896397/18014398509481984 + + If the simpler representation of the float is desired then consider + limiting the denominator to the desired value or convert the float to + a string (which is roughly equivalent to limiting the denominator to + 10**12): + + >>> Rational(str(.2)) + 1/5 + >>> Rational(.2).limit_denominator(10**12) + 1/5 + + An arbitrarily precise Rational is obtained when a string literal is + passed: + + >>> Rational("1.23") + 123/100 + >>> Rational('1e-2') + 1/100 + >>> Rational(".1") + 1/10 + >>> Rational('1e-2/3.2') + 1/320 + + The conversion of other types of strings can be handled by + the sympify() function, and conversion of floats to expressions + or simple fractions can be handled with nsimplify: + + >>> S('.[3]') # repeating digits in brackets + 1/3 + >>> S('3**2/10') # general expressions + 9/10 + >>> nsimplify(.3) # numbers that have a simple form + 3/10 + + But if the input does not reduce to a literal Rational, an error will + be raised: + + >>> Rational(pi) + Traceback (most recent call last): + ... + TypeError: invalid input: pi + + + Low-level + --------- + + Access numerator and denominator as .p and .q: + + >>> r = Rational(3, 4) + >>> r + 3/4 + >>> r.p + 3 + >>> r.q + 4 + + Note that p and q return integers (not SymPy Integers) so some care + is needed when using them in expressions: + + >>> r.p/r.q + 0.75 + + If an unevaluated Rational is desired, ``gcd=1`` can be passed and + this will keep common divisors of the numerator and denominator + from being eliminated. It is not possible, however, to leave a + negative value in the denominator. + + >>> Rational(2, 4, gcd=1) + 2/4 + >>> Rational(2, -4, gcd=1).q + 4 + + See Also + ======== + sympy.core.sympify.sympify, sympy.simplify.simplify.nsimplify + """ + is_real = True + is_integer = False + is_rational = True + is_number = True + + __slots__ = ('p', 'q') + + p: int + q: int + + is_Rational = True + + @cacheit + def __new__(cls, p, q=None, gcd=None): + if q is None: + if isinstance(p, Rational): + return p + + if isinstance(p, SYMPY_INTS): + pass + else: + if isinstance(p, (float, Float)): + return Rational(*_as_integer_ratio(p)) + + if not isinstance(p, str): + try: + p = sympify(p) + except (SympifyError, SyntaxError): + pass # error will raise below + else: + if p.count('/') > 1: + raise TypeError('invalid input: %s' % p) + p = p.replace(' ', '') + pq = p.rsplit('/', 1) + if len(pq) == 2: + p, q = pq + fp = fractions.Fraction(p) + fq = fractions.Fraction(q) + p = fp/fq + try: + p = fractions.Fraction(p) + except ValueError: + pass # error will raise below + else: + return Rational(p.numerator, p.denominator, 1) + + if not isinstance(p, Rational): + raise TypeError('invalid input: %s' % p) + + q = 1 + gcd = 1 + Q = 1 + + if not isinstance(p, SYMPY_INTS): + p = Rational(p) + Q *= p.q + p = p.p + else: + p = int(p) + + if not isinstance(q, SYMPY_INTS): + q = Rational(q) + p *= q.q + Q *= q.p + else: + Q *= int(q) + q = Q + + # p and q are now ints + if q == 0: + if p == 0: + if _errdict["divide"]: + raise ValueError("Indeterminate 0/0") + else: + return S.NaN + return S.ComplexInfinity + if q < 0: + q = -q + p = -p + if not gcd: + gcd = igcd(abs(p), q) + if gcd > 1: + p //= gcd + q //= gcd + if q == 1: + return Integer(p) + if p == 1 and q == 2: + return S.Half + obj = Expr.__new__(cls) + obj.p = p + obj.q = q + return obj + + def limit_denominator(self, max_denominator=1000000): + """Closest Rational to self with denominator at most max_denominator. + + Examples + ======== + + >>> from sympy import Rational + >>> Rational('3.141592653589793').limit_denominator(10) + 22/7 + >>> Rational('3.141592653589793').limit_denominator(100) + 311/99 + + """ + f = fractions.Fraction(self.p, self.q) + return Rational(f.limit_denominator(fractions.Fraction(int(max_denominator)))) + + def __getnewargs__(self): + return (self.p, self.q) + + def _hashable_content(self): + return (self.p, self.q) + + def _eval_is_positive(self): + return self.p > 0 + + def _eval_is_zero(self): + return self.p == 0 + + def __neg__(self): + return Rational(-self.p, self.q) + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + return Rational(self.p + self.q*other.p, self.q, 1) + elif isinstance(other, Rational): + #TODO: this can probably be optimized more + return Rational(self.p*other.q + self.q*other.p, self.q*other.q) + elif isinstance(other, Float): + return other + self + else: + return Number.__add__(self, other) + return Number.__add__(self, other) + __radd__ = __add__ + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + return Rational(self.p - self.q*other.p, self.q, 1) + elif isinstance(other, Rational): + return Rational(self.p*other.q - self.q*other.p, self.q*other.q) + elif isinstance(other, Float): + return -other + self + else: + return Number.__sub__(self, other) + return Number.__sub__(self, other) + @_sympifyit('other', NotImplemented) + def __rsub__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + return Rational(self.q*other.p - self.p, self.q, 1) + elif isinstance(other, Rational): + return Rational(self.q*other.p - self.p*other.q, self.q*other.q) + elif isinstance(other, Float): + return -self + other + else: + return Number.__rsub__(self, other) + return Number.__rsub__(self, other) + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + return Rational(self.p*other.p, self.q, igcd(other.p, self.q)) + elif isinstance(other, Rational): + return Rational(self.p*other.p, self.q*other.q, igcd(self.p, other.q)*igcd(self.q, other.p)) + elif isinstance(other, Float): + return other*self + else: + return Number.__mul__(self, other) + return Number.__mul__(self, other) + __rmul__ = __mul__ + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + if self.p and other.p == S.Zero: + return S.ComplexInfinity + else: + return Rational(self.p, self.q*other.p, igcd(self.p, other.p)) + elif isinstance(other, Rational): + return Rational(self.p*other.q, self.q*other.p, igcd(self.p, other.p)*igcd(self.q, other.q)) + elif isinstance(other, Float): + return self*(1/other) + else: + return Number.__truediv__(self, other) + return Number.__truediv__(self, other) + @_sympifyit('other', NotImplemented) + def __rtruediv__(self, other): + if global_parameters.evaluate: + if isinstance(other, Integer): + return Rational(other.p*self.q, self.p, igcd(self.p, other.p)) + elif isinstance(other, Rational): + return Rational(other.p*self.q, other.q*self.p, igcd(self.p, other.p)*igcd(self.q, other.q)) + elif isinstance(other, Float): + return other*(1/self) + else: + return Number.__rtruediv__(self, other) + return Number.__rtruediv__(self, other) + + @_sympifyit('other', NotImplemented) + def __mod__(self, other): + if global_parameters.evaluate: + if isinstance(other, Rational): + n = (self.p*other.q) // (other.p*self.q) + return Rational(self.p*other.q - n*other.p*self.q, self.q*other.q) + if isinstance(other, Float): + # calculate mod with Rationals, *then* round the answer + return Float(self.__mod__(Rational(other)), + precision=other._prec) + return Number.__mod__(self, other) + return Number.__mod__(self, other) + + @_sympifyit('other', NotImplemented) + def __rmod__(self, other): + if isinstance(other, Rational): + return Rational.__mod__(other, self) + return Number.__rmod__(self, other) + + def _eval_power(self, expt): + if isinstance(expt, Number): + if isinstance(expt, Float): + return self._eval_evalf(expt._prec)**expt + if expt.is_extended_negative: + # (3/4)**-2 -> (4/3)**2 + ne = -expt + if (ne is S.One): + return Rational(self.q, self.p) + if self.is_negative: + return S.NegativeOne**expt*Rational(self.q, -self.p)**ne + else: + return Rational(self.q, self.p)**ne + if expt is S.Infinity: # -oo already caught by test for negative + if self.p > self.q: + # (3/2)**oo -> oo + return S.Infinity + if self.p < -self.q: + # (-3/2)**oo -> oo + I*oo + return S.Infinity + S.Infinity*S.ImaginaryUnit + return S.Zero + if isinstance(expt, Integer): + # (4/3)**2 -> 4**2 / 3**2 + return Rational(self.p**expt.p, self.q**expt.p, 1) + if isinstance(expt, Rational): + intpart = expt.p // expt.q + if intpart: + intpart += 1 + remfracpart = intpart*expt.q - expt.p + ratfracpart = Rational(remfracpart, expt.q) + if self.p != 1: + return Integer(self.p)**expt*Integer(self.q)**ratfracpart*Rational(1, self.q**intpart, 1) + return Integer(self.q)**ratfracpart*Rational(1, self.q**intpart, 1) + else: + remfracpart = expt.q - expt.p + ratfracpart = Rational(remfracpart, expt.q) + if self.p != 1: + return Integer(self.p)**expt*Integer(self.q)**ratfracpart*Rational(1, self.q, 1) + return Integer(self.q)**ratfracpart*Rational(1, self.q, 1) + + if self.is_extended_negative and expt.is_even: + return (-self)**expt + + return + + def _as_mpf_val(self, prec): + return mlib.from_rational(self.p, self.q, prec, rnd) + + def _mpmath_(self, prec, rnd): + return mpmath.make_mpf(mlib.from_rational(self.p, self.q, prec, rnd)) + + def __abs__(self): + return Rational(abs(self.p), self.q) + + def __int__(self): + p, q = self.p, self.q + if p < 0: + return -int(-p//q) + return int(p//q) + + def floor(self): + return Integer(self.p // self.q) + + def ceiling(self): + return -Integer(-self.p // self.q) + + def __floor__(self): + return self.floor() + + def __ceil__(self): + return self.ceiling() + + def __eq__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if not isinstance(other, Number): + # S(0) == S.false is False + # S(0) == False is True + return False + if not self: + return not other + if other.is_NumberSymbol: + if other.is_irrational: + return False + return other.__eq__(self) + if other.is_Rational: + # a Rational is always in reduced form so will never be 2/4 + # so we can just check equivalence of args + return self.p == other.p and self.q == other.q + return False + + def __ne__(self, other): + return not self == other + + def _Rrel(self, other, attr): + # if you want self < other, pass self, other, __gt__ + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Number: + op = None + s, o = self, other + if other.is_NumberSymbol: + op = getattr(o, attr) + elif other.is_Float: + op = getattr(o, attr) + elif other.is_Rational: + s, o = Integer(s.p*o.q), Integer(s.q*o.p) + op = getattr(o, attr) + if op: + return op(s) + if o.is_number and o.is_extended_real: + return Integer(s.p), s.q*o + + def __gt__(self, other): + rv = self._Rrel(other, '__lt__') + if rv is None: + rv = self, other + elif not isinstance(rv, tuple): + return rv + return Expr.__gt__(*rv) + + def __ge__(self, other): + rv = self._Rrel(other, '__le__') + if rv is None: + rv = self, other + elif not isinstance(rv, tuple): + return rv + return Expr.__ge__(*rv) + + def __lt__(self, other): + rv = self._Rrel(other, '__gt__') + if rv is None: + rv = self, other + elif not isinstance(rv, tuple): + return rv + return Expr.__lt__(*rv) + + def __le__(self, other): + rv = self._Rrel(other, '__ge__') + if rv is None: + rv = self, other + elif not isinstance(rv, tuple): + return rv + return Expr.__le__(*rv) + + def __hash__(self): + return super().__hash__() + + def factors(self, limit=None, use_trial=True, use_rho=False, + use_pm1=False, verbose=False, visual=False): + """A wrapper to factorint which return factors of self that are + smaller than limit (or cheap to compute). Special methods of + factoring are disabled by default so that only trial division is used. + """ + from sympy.ntheory.factor_ import factorrat + + return factorrat(self, limit=limit, use_trial=use_trial, + use_rho=use_rho, use_pm1=use_pm1, + verbose=verbose).copy() + + @property + def numerator(self): + return self.p + + @property + def denominator(self): + return self.q + + @_sympifyit('other', NotImplemented) + def gcd(self, other): + if isinstance(other, Rational): + if other == S.Zero: + return other + return Rational( + igcd(self.p, other.p), + ilcm(self.q, other.q)) + return Number.gcd(self, other) + + @_sympifyit('other', NotImplemented) + def lcm(self, other): + if isinstance(other, Rational): + return Rational( + self.p // igcd(self.p, other.p) * other.p, + igcd(self.q, other.q)) + return Number.lcm(self, other) + + def as_numer_denom(self): + return Integer(self.p), Integer(self.q) + + def as_content_primitive(self, radical=False, clear=True): + """Return the tuple (R, self/R) where R is the positive Rational + extracted from self. + + Examples + ======== + + >>> from sympy import S + >>> (S(-3)/2).as_content_primitive() + (3/2, -1) + + See docstring of Expr.as_content_primitive for more examples. + """ + + if self: + if self.is_positive: + return self, S.One + return -self, S.NegativeOne + return S.One, self + + def as_coeff_Mul(self, rational=False): + """Efficiently extract the coefficient of a product.""" + return self, S.One + + def as_coeff_Add(self, rational=False): + """Efficiently extract the coefficient of a summation.""" + return self, S.Zero + + +class Integer(Rational): + """Represents integer numbers of any size. + + Examples + ======== + + >>> from sympy import Integer + >>> Integer(3) + 3 + + If a float or a rational is passed to Integer, the fractional part + will be discarded; the effect is of rounding toward zero. + + >>> Integer(3.8) + 3 + >>> Integer(-3.8) + -3 + + A string is acceptable input if it can be parsed as an integer: + + >>> Integer("9" * 20) + 99999999999999999999 + + It is rarely needed to explicitly instantiate an Integer, because + Python integers are automatically converted to Integer when they + are used in SymPy expressions. + """ + q = 1 + is_integer = True + is_number = True + + is_Integer = True + + __slots__ = () + + def _as_mpf_val(self, prec): + return mlib.from_int(self.p, prec, rnd) + + def _mpmath_(self, prec, rnd): + return mpmath.make_mpf(self._as_mpf_val(prec)) + + @cacheit + def __new__(cls, i): + if isinstance(i, str): + i = i.replace(' ', '') + # whereas we cannot, in general, make a Rational from an + # arbitrary expression, we can make an Integer unambiguously + # (except when a non-integer expression happens to round to + # an integer). So we proceed by taking int() of the input and + # let the int routines determine whether the expression can + # be made into an int or whether an error should be raised. + try: + ival = int(i) + except TypeError: + raise TypeError( + "Argument of Integer should be of numeric type, got %s." % i) + # We only work with well-behaved integer types. This converts, for + # example, numpy.int32 instances. + if ival == 1: + return S.One + if ival == -1: + return S.NegativeOne + if ival == 0: + return S.Zero + obj = Expr.__new__(cls) + obj.p = ival + return obj + + def __getnewargs__(self): + return (self.p,) + + # Arithmetic operations are here for efficiency + def __int__(self): + return self.p + + def floor(self): + return Integer(self.p) + + def ceiling(self): + return Integer(self.p) + + def __floor__(self): + return self.floor() + + def __ceil__(self): + return self.ceiling() + + def __neg__(self): + return Integer(-self.p) + + def __abs__(self): + if self.p >= 0: + return self + else: + return Integer(-self.p) + + def __divmod__(self, other): + if isinstance(other, Integer) and global_parameters.evaluate: + return Tuple(*(divmod(self.p, other.p))) + else: + return Number.__divmod__(self, other) + + def __rdivmod__(self, other): + if isinstance(other, int) and global_parameters.evaluate: + return Tuple(*(divmod(other, self.p))) + else: + try: + other = Number(other) + except TypeError: + msg = "unsupported operand type(s) for divmod(): '%s' and '%s'" + oname = type(other).__name__ + sname = type(self).__name__ + raise TypeError(msg % (oname, sname)) + return Number.__divmod__(other, self) + + # TODO make it decorator + bytecodehacks? + def __add__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(self.p + other) + elif isinstance(other, Integer): + return Integer(self.p + other.p) + elif isinstance(other, Rational): + return Rational(self.p*other.q + other.p, other.q, 1) + return Rational.__add__(self, other) + else: + return Add(self, other) + + def __radd__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(other + self.p) + elif isinstance(other, Rational): + return Rational(other.p + self.p*other.q, other.q, 1) + return Rational.__radd__(self, other) + return Rational.__radd__(self, other) + + def __sub__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(self.p - other) + elif isinstance(other, Integer): + return Integer(self.p - other.p) + elif isinstance(other, Rational): + return Rational(self.p*other.q - other.p, other.q, 1) + return Rational.__sub__(self, other) + return Rational.__sub__(self, other) + + def __rsub__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(other - self.p) + elif isinstance(other, Rational): + return Rational(other.p - self.p*other.q, other.q, 1) + return Rational.__rsub__(self, other) + return Rational.__rsub__(self, other) + + def __mul__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(self.p*other) + elif isinstance(other, Integer): + return Integer(self.p*other.p) + elif isinstance(other, Rational): + return Rational(self.p*other.p, other.q, igcd(self.p, other.q)) + return Rational.__mul__(self, other) + return Rational.__mul__(self, other) + + def __rmul__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(other*self.p) + elif isinstance(other, Rational): + return Rational(other.p*self.p, other.q, igcd(self.p, other.q)) + return Rational.__rmul__(self, other) + return Rational.__rmul__(self, other) + + def __mod__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(self.p % other) + elif isinstance(other, Integer): + return Integer(self.p % other.p) + return Rational.__mod__(self, other) + return Rational.__mod__(self, other) + + def __rmod__(self, other): + if global_parameters.evaluate: + if isinstance(other, int): + return Integer(other % self.p) + elif isinstance(other, Integer): + return Integer(other.p % self.p) + return Rational.__rmod__(self, other) + return Rational.__rmod__(self, other) + + def __eq__(self, other): + if isinstance(other, int): + return (self.p == other) + elif isinstance(other, Integer): + return (self.p == other.p) + return Rational.__eq__(self, other) + + def __ne__(self, other): + return not self == other + + def __gt__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Integer: + return _sympify(self.p > other.p) + return Rational.__gt__(self, other) + + def __lt__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Integer: + return _sympify(self.p < other.p) + return Rational.__lt__(self, other) + + def __ge__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Integer: + return _sympify(self.p >= other.p) + return Rational.__ge__(self, other) + + def __le__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if other.is_Integer: + return _sympify(self.p <= other.p) + return Rational.__le__(self, other) + + def __hash__(self): + return hash(self.p) + + def __index__(self): + return self.p + + ######################################## + + def _eval_is_odd(self): + return bool(self.p % 2) + + def _eval_power(self, expt): + """ + Tries to do some simplifications on self**expt + + Returns None if no further simplifications can be done. + + Explanation + =========== + + When exponent is a fraction (so we have for example a square root), + we try to find a simpler representation by factoring the argument + up to factors of 2**15, e.g. + + - sqrt(4) becomes 2 + - sqrt(-4) becomes 2*I + - (2**(3+7)*3**(6+7))**Rational(1,7) becomes 6*18**(3/7) + + Further simplification would require a special call to factorint on + the argument which is not done here for sake of speed. + + """ + from sympy.ntheory.factor_ import perfect_power + + if expt is S.Infinity: + if self.p > S.One: + return S.Infinity + # cases -1, 0, 1 are done in their respective classes + return S.Infinity + S.ImaginaryUnit*S.Infinity + if expt is S.NegativeInfinity: + return Rational(1, self, 1)**S.Infinity + if not isinstance(expt, Number): + # simplify when expt is even + # (-2)**k --> 2**k + if self.is_negative and expt.is_even: + return (-self)**expt + if isinstance(expt, Float): + # Rational knows how to exponentiate by a Float + return super()._eval_power(expt) + if not isinstance(expt, Rational): + return + if expt is S.Half and self.is_negative: + # we extract I for this special case since everyone is doing so + return S.ImaginaryUnit*Pow(-self, expt) + if expt.is_negative: + # invert base and change sign on exponent + ne = -expt + if self.is_negative: + return S.NegativeOne**expt*Rational(1, -self, 1)**ne + else: + return Rational(1, self.p, 1)**ne + # see if base is a perfect root, sqrt(4) --> 2 + x, xexact = integer_nthroot(abs(self.p), expt.q) + if xexact: + # if it's a perfect root we've finished + result = Integer(x**abs(expt.p)) + if self.is_negative: + result *= S.NegativeOne**expt + return result + + # The following is an algorithm where we collect perfect roots + # from the factors of base. + + # if it's not an nth root, it still might be a perfect power + b_pos = int(abs(self.p)) + p = perfect_power(b_pos) + if p is not False: + dict = {p[0]: p[1]} + else: + dict = Integer(b_pos).factors(limit=2**15) + + # now process the dict of factors + out_int = 1 # integer part + out_rad = 1 # extracted radicals + sqr_int = 1 + sqr_gcd = 0 + sqr_dict = {} + for prime, exponent in dict.items(): + exponent *= expt.p + # remove multiples of expt.q: (2**12)**(1/10) -> 2*(2**2)**(1/10) + div_e, div_m = divmod(exponent, expt.q) + if div_e > 0: + out_int *= prime**div_e + if div_m > 0: + # see if the reduced exponent shares a gcd with e.q + # (2**2)**(1/10) -> 2**(1/5) + g = igcd(div_m, expt.q) + if g != 1: + out_rad *= Pow(prime, Rational(div_m//g, expt.q//g, 1)) + else: + sqr_dict[prime] = div_m + # identify gcd of remaining powers + for p, ex in sqr_dict.items(): + if sqr_gcd == 0: + sqr_gcd = ex + else: + sqr_gcd = igcd(sqr_gcd, ex) + if sqr_gcd == 1: + break + for k, v in sqr_dict.items(): + sqr_int *= k**(v//sqr_gcd) + if sqr_int == b_pos and out_int == 1 and out_rad == 1: + result = None + else: + result = out_int*out_rad*Pow(sqr_int, Rational(sqr_gcd, expt.q)) + if self.is_negative: + result *= Pow(S.NegativeOne, expt) + return result + + def _eval_is_prime(self): + from sympy.ntheory.primetest import isprime + + return isprime(self) + + def _eval_is_composite(self): + if self > 1: + return fuzzy_not(self.is_prime) + else: + return False + + def as_numer_denom(self): + return self, S.One + + @_sympifyit('other', NotImplemented) + def __floordiv__(self, other): + if not isinstance(other, Expr): + return NotImplemented + if isinstance(other, Integer): + return Integer(self.p // other) + return divmod(self, other)[0] + + def __rfloordiv__(self, other): + return Integer(Integer(other).p // self.p) + + # These bitwise operations (__lshift__, __rlshift__, ..., __invert__) are defined + # for Integer only and not for general SymPy expressions. This is to achieve + # compatibility with the numbers.Integral ABC which only defines these operations + # among instances of numbers.Integral. Therefore, these methods check explicitly for + # integer types rather than using sympify because they should not accept arbitrary + # symbolic expressions and there is no symbolic analogue of numbers.Integral's + # bitwise operations. + def __lshift__(self, other): + if isinstance(other, (int, Integer, numbers.Integral)): + return Integer(self.p << int(other)) + else: + return NotImplemented + + def __rlshift__(self, other): + if isinstance(other, (int, numbers.Integral)): + return Integer(int(other) << self.p) + else: + return NotImplemented + + def __rshift__(self, other): + if isinstance(other, (int, Integer, numbers.Integral)): + return Integer(self.p >> int(other)) + else: + return NotImplemented + + def __rrshift__(self, other): + if isinstance(other, (int, numbers.Integral)): + return Integer(int(other) >> self.p) + else: + return NotImplemented + + def __and__(self, other): + if isinstance(other, (int, Integer, numbers.Integral)): + return Integer(self.p & int(other)) + else: + return NotImplemented + + def __rand__(self, other): + if isinstance(other, (int, numbers.Integral)): + return Integer(int(other) & self.p) + else: + return NotImplemented + + def __xor__(self, other): + if isinstance(other, (int, Integer, numbers.Integral)): + return Integer(self.p ^ int(other)) + else: + return NotImplemented + + def __rxor__(self, other): + if isinstance(other, (int, numbers.Integral)): + return Integer(int(other) ^ self.p) + else: + return NotImplemented + + def __or__(self, other): + if isinstance(other, (int, Integer, numbers.Integral)): + return Integer(self.p | int(other)) + else: + return NotImplemented + + def __ror__(self, other): + if isinstance(other, (int, numbers.Integral)): + return Integer(int(other) | self.p) + else: + return NotImplemented + + def __invert__(self): + return Integer(~self.p) + +# Add sympify converters +_sympy_converter[int] = Integer + + +class AlgebraicNumber(Expr): + r""" + Class for representing algebraic numbers in SymPy. + + Symbolically, an instance of this class represents an element + $\alpha \in \mathbb{Q}(\theta) \hookrightarrow \mathbb{C}$. That is, the + algebraic number $\alpha$ is represented as an element of a particular + number field $\mathbb{Q}(\theta)$, with a particular embedding of this + field into the complex numbers. + + Formally, the primitive element $\theta$ is given by two data points: (1) + its minimal polynomial (which defines $\mathbb{Q}(\theta)$), and (2) a + particular complex number that is a root of this polynomial (which defines + the embedding $\mathbb{Q}(\theta) \hookrightarrow \mathbb{C}$). Finally, + the algebraic number $\alpha$ which we represent is then given by the + coefficients of a polynomial in $\theta$. + """ + + __slots__ = ('rep', 'root', 'alias', 'minpoly', '_own_minpoly') + + is_AlgebraicNumber = True + is_algebraic = True + is_number = True + + + kind = NumberKind + + # Optional alias symbol is not free. + # Actually, alias should be a Str, but some methods + # expect that it be an instance of Expr. + free_symbols: set[Basic] = set() + + def __new__(cls, expr, coeffs=None, alias=None, **args): + r""" + Construct a new algebraic number $\alpha$ belonging to a number field + $k = \mathbb{Q}(\theta)$. + + There are four instance attributes to be determined: + + =========== ============================================================================ + Attribute Type/Meaning + =========== ============================================================================ + ``root`` :py:class:`~.Expr` for $\theta$ as a complex number + ``minpoly`` :py:class:`~.Poly`, the minimal polynomial of $\theta$ + ``rep`` :py:class:`~sympy.polys.polyclasses.DMP` giving $\alpha$ as poly in $\theta$ + ``alias`` :py:class:`~.Symbol` for $\theta$, or ``None`` + =========== ============================================================================ + + See Parameters section for how they are determined. + + Parameters + ========== + + expr : :py:class:`~.Expr`, or pair $(m, r)$ + There are three distinct modes of construction, depending on what + is passed as *expr*. + + **(1)** *expr* is an :py:class:`~.AlgebraicNumber`: + In this case we begin by copying all four instance attributes from + *expr*. If *coeffs* were also given, we compose the two coeff + polynomials (see below). If an *alias* was given, it overrides. + + **(2)** *expr* is any other type of :py:class:`~.Expr`: + Then ``root`` will equal *expr*. Therefore it + must express an algebraic quantity, and we will compute its + ``minpoly``. + + **(3)** *expr* is an ordered pair $(m, r)$ giving the + ``minpoly`` $m$, and a ``root`` $r$ thereof, which together + define $\theta$. In this case $m$ may be either a univariate + :py:class:`~.Poly` or any :py:class:`~.Expr` which represents the + same, while $r$ must be some :py:class:`~.Expr` representing a + complex number that is a root of $m$, including both explicit + expressions in radicals, and instances of + :py:class:`~.ComplexRootOf` or :py:class:`~.AlgebraicNumber`. + + coeffs : list, :py:class:`~.ANP`, None, optional (default=None) + This defines ``rep``, giving the algebraic number $\alpha$ as a + polynomial in $\theta$. + + If a list, the elements should be integers or rational numbers. + If an :py:class:`~.ANP`, we take its coefficients (using its + :py:meth:`~.ANP.to_list()` method). If ``None``, then the list of + coefficients defaults to ``[1, 0]``, meaning that $\alpha = \theta$ + is the primitive element of the field. + + If *expr* was an :py:class:`~.AlgebraicNumber`, let $g(x)$ be its + ``rep`` polynomial, and let $f(x)$ be the polynomial defined by + *coeffs*. Then ``self.rep`` will represent the composition + $(f \circ g)(x)$. + + alias : str, :py:class:`~.Symbol`, None, optional (default=None) + This is a way to provide a name for the primitive element. We + described several ways in which the *expr* argument can define the + value of the primitive element, but none of these methods gave it + a name. Here, for example, *alias* could be set as + ``Symbol('theta')``, in order to make this symbol appear when + $\alpha$ is printed, or rendered as a polynomial, using the + :py:meth:`~.as_poly()` method. + + Examples + ======== + + Recall that we are constructing an algebraic number as a field element + $\alpha \in \mathbb{Q}(\theta)$. + + >>> from sympy import AlgebraicNumber, sqrt, CRootOf, S + >>> from sympy.abc import x + + Example (1): $\alpha = \theta = \sqrt{2}$ + + >>> a1 = AlgebraicNumber(sqrt(2)) + >>> a1.minpoly_of_element().as_expr(x) + x**2 - 2 + >>> a1.evalf(10) + 1.414213562 + + Example (2): $\alpha = 3 \sqrt{2} - 5$, $\theta = \sqrt{2}$. We can + either build on the last example: + + >>> a2 = AlgebraicNumber(a1, [3, -5]) + >>> a2.as_expr() + -5 + 3*sqrt(2) + + or start from scratch: + + >>> a2 = AlgebraicNumber(sqrt(2), [3, -5]) + >>> a2.as_expr() + -5 + 3*sqrt(2) + + Example (3): $\alpha = 6 \sqrt{2} - 11$, $\theta = \sqrt{2}$. Again we + can build on the previous example, and we see that the coeff polys are + composed: + + >>> a3 = AlgebraicNumber(a2, [2, -1]) + >>> a3.as_expr() + -11 + 6*sqrt(2) + + reflecting the fact that $(2x - 1) \circ (3x - 5) = 6x - 11$. + + Example (4): $\alpha = \sqrt{2}$, $\theta = \sqrt{2} + \sqrt{3}$. The + easiest way is to use the :py:func:`~.to_number_field()` function: + + >>> from sympy import to_number_field + >>> a4 = to_number_field(sqrt(2), sqrt(2) + sqrt(3)) + >>> a4.minpoly_of_element().as_expr(x) + x**2 - 2 + >>> a4.to_root() + sqrt(2) + >>> a4.primitive_element() + sqrt(2) + sqrt(3) + >>> a4.coeffs() + [1/2, 0, -9/2, 0] + + but if you already knew the right coefficients, you could construct it + directly: + + >>> a4 = AlgebraicNumber(sqrt(2) + sqrt(3), [S(1)/2, 0, S(-9)/2, 0]) + >>> a4.to_root() + sqrt(2) + >>> a4.primitive_element() + sqrt(2) + sqrt(3) + + Example (5): Construct the Golden Ratio as an element of the 5th + cyclotomic field, supposing we already know its coefficients. This time + we introduce the alias $\zeta$ for the primitive element of the field: + + >>> from sympy import cyclotomic_poly + >>> from sympy.abc import zeta + >>> a5 = AlgebraicNumber(CRootOf(cyclotomic_poly(5), -1), + ... [-1, -1, 0, 0], alias=zeta) + >>> a5.as_poly().as_expr() + -zeta**3 - zeta**2 + >>> a5.evalf() + 1.61803398874989 + + (The index ``-1`` to ``CRootOf`` selects the complex root with the + largest real and imaginary parts, which in this case is + $\mathrm{e}^{2i\pi/5}$. See :py:class:`~.ComplexRootOf`.) + + Example (6): Building on the last example, construct the number + $2 \phi \in \mathbb{Q}(\phi)$, where $\phi$ is the Golden Ratio: + + >>> from sympy.abc import phi + >>> a6 = AlgebraicNumber(a5.to_root(), coeffs=[2, 0], alias=phi) + >>> a6.as_poly().as_expr() + 2*phi + >>> a6.primitive_element().evalf() + 1.61803398874989 + + Note that we needed to use ``a5.to_root()``, since passing ``a5`` as + the first argument would have constructed the number $2 \phi$ as an + element of the field $\mathbb{Q}(\zeta)$: + + >>> a6_wrong = AlgebraicNumber(a5, coeffs=[2, 0]) + >>> a6_wrong.as_poly().as_expr() + -2*zeta**3 - 2*zeta**2 + >>> a6_wrong.primitive_element().evalf() + 0.309016994374947 + 0.951056516295154*I + + """ + from sympy.polys.polyclasses import ANP, DMP + from sympy.polys.numberfields import minimal_polynomial + + expr = sympify(expr) + rep0 = None + alias0 = None + + if isinstance(expr, (tuple, Tuple)): + minpoly, root = expr + + if not minpoly.is_Poly: + from sympy.polys.polytools import Poly + minpoly = Poly(minpoly) + elif expr.is_AlgebraicNumber: + minpoly, root, rep0, alias0 = (expr.minpoly, expr.root, + expr.rep, expr.alias) + else: + minpoly, root = minimal_polynomial( + expr, args.get('gen'), polys=True), expr + + dom = minpoly.get_domain() + + if coeffs is not None: + if not isinstance(coeffs, ANP): + rep = DMP.from_sympy_list(sympify(coeffs), 0, dom) + scoeffs = Tuple(*coeffs) + else: + rep = DMP.from_list(coeffs.to_list(), 0, dom) + scoeffs = Tuple(*coeffs.to_list()) + + else: + rep = DMP.from_list([1, 0], 0, dom) + scoeffs = Tuple(1, 0) + + if rep0 is not None: + from sympy.polys.densetools import dup_compose + c = dup_compose(rep.to_list(), rep0.to_list(), dom) + rep = DMP.from_list(c, 0, dom) + scoeffs = Tuple(*c) + + if rep.degree() >= minpoly.degree(): + rep = rep.rem(minpoly.rep) + + sargs = (root, scoeffs) + + alias = alias or alias0 + if alias is not None: + from .symbol import Symbol + if not isinstance(alias, Symbol): + alias = Symbol(alias) + sargs = sargs + (alias,) + + obj = Expr.__new__(cls, *sargs) + + obj.rep = rep + obj.root = root + obj.alias = alias + obj.minpoly = minpoly + + obj._own_minpoly = None + + return obj + + def __hash__(self): + return super().__hash__() + + def _eval_evalf(self, prec): + return self.as_expr()._evalf(prec) + + @property + def is_aliased(self): + """Returns ``True`` if ``alias`` was set. """ + return self.alias is not None + + def as_poly(self, x=None): + """Create a Poly instance from ``self``. """ + from sympy.polys.polytools import Poly, PurePoly + if x is not None: + return Poly.new(self.rep, x) + else: + if self.alias is not None: + return Poly.new(self.rep, self.alias) + else: + from .symbol import Dummy + return PurePoly.new(self.rep, Dummy('x')) + + def as_expr(self, x=None): + """Create a Basic expression from ``self``. """ + return self.as_poly(x or self.root).as_expr().expand() + + def coeffs(self): + """Returns all SymPy coefficients of an algebraic number. """ + return [ self.rep.dom.to_sympy(c) for c in self.rep.all_coeffs() ] + + def native_coeffs(self): + """Returns all native coefficients of an algebraic number. """ + return self.rep.all_coeffs() + + def to_algebraic_integer(self): + """Convert ``self`` to an algebraic integer. """ + from sympy.polys.polytools import Poly + + f = self.minpoly + + if f.LC() == 1: + return self + + coeff = f.LC()**(f.degree() - 1) + poly = f.compose(Poly(f.gen/f.LC())) + + minpoly = poly*coeff + root = f.LC()*self.root + + return AlgebraicNumber((minpoly, root), self.coeffs()) + + def _eval_simplify(self, **kwargs): + from sympy.polys.rootoftools import CRootOf + from sympy.polys import minpoly + measure, ratio = kwargs['measure'], kwargs['ratio'] + for r in [r for r in self.minpoly.all_roots() if r.func != CRootOf]: + if minpoly(self.root - r).is_Symbol: + # use the matching root if it's simpler + if measure(r) < ratio*measure(self.root): + return AlgebraicNumber(r) + return self + + def field_element(self, coeffs): + r""" + Form another element of the same number field. + + Explanation + =========== + + If we represent $\alpha \in \mathbb{Q}(\theta)$, form another element + $\beta \in \mathbb{Q}(\theta)$ of the same number field. + + Parameters + ========== + + coeffs : list, :py:class:`~.ANP` + Like the *coeffs* arg to the class + :py:meth:`constructor<.AlgebraicNumber.__new__>`, defines the + new element as a polynomial in the primitive element. + + If a list, the elements should be integers or rational numbers. + If an :py:class:`~.ANP`, we take its coefficients (using its + :py:meth:`~.ANP.to_list()` method). + + Examples + ======== + + >>> from sympy import AlgebraicNumber, sqrt + >>> a = AlgebraicNumber(sqrt(5), [-1, 1]) + >>> b = a.field_element([3, 2]) + >>> print(a) + 1 - sqrt(5) + >>> print(b) + 2 + 3*sqrt(5) + >>> print(b.primitive_element() == a.primitive_element()) + True + + See Also + ======== + + AlgebraicNumber + """ + return AlgebraicNumber( + (self.minpoly, self.root), coeffs=coeffs, alias=self.alias) + + @property + def is_primitive_element(self): + r""" + Say whether this algebraic number $\alpha \in \mathbb{Q}(\theta)$ is + equal to the primitive element $\theta$ for its field. + """ + c = self.coeffs() + # Second case occurs if self.minpoly is linear: + return c == [1, 0] or c == [self.root] + + def primitive_element(self): + r""" + Get the primitive element $\theta$ for the number field + $\mathbb{Q}(\theta)$ to which this algebraic number $\alpha$ belongs. + + Returns + ======= + + AlgebraicNumber + + """ + if self.is_primitive_element: + return self + return self.field_element([1, 0]) + + def to_primitive_element(self, radicals=True): + r""" + Convert ``self`` to an :py:class:`~.AlgebraicNumber` instance that is + equal to its own primitive element. + + Explanation + =========== + + If we represent $\alpha \in \mathbb{Q}(\theta)$, $\alpha \neq \theta$, + construct a new :py:class:`~.AlgebraicNumber` that represents + $\alpha \in \mathbb{Q}(\alpha)$. + + Examples + ======== + + >>> from sympy import sqrt, to_number_field + >>> from sympy.abc import x + >>> a = to_number_field(sqrt(2), sqrt(2) + sqrt(3)) + + The :py:class:`~.AlgebraicNumber` ``a`` represents the number + $\sqrt{2}$ in the field $\mathbb{Q}(\sqrt{2} + \sqrt{3})$. Rendering + ``a`` as a polynomial, + + >>> a.as_poly().as_expr(x) + x**3/2 - 9*x/2 + + reflects the fact that $\sqrt{2} = \theta^3/2 - 9 \theta/2$, where + $\theta = \sqrt{2} + \sqrt{3}$. + + ``a`` is not equal to its own primitive element. Its minpoly + + >>> a.minpoly.as_poly().as_expr(x) + x**4 - 10*x**2 + 1 + + is that of $\theta$. + + Converting to a primitive element, + + >>> a_prim = a.to_primitive_element() + >>> a_prim.minpoly.as_poly().as_expr(x) + x**2 - 2 + + we obtain an :py:class:`~.AlgebraicNumber` whose ``minpoly`` is that of + the number itself. + + Parameters + ========== + + radicals : boolean, optional (default=True) + If ``True``, then we will try to return an + :py:class:`~.AlgebraicNumber` whose ``root`` is an expression + in radicals. If that is not possible (or if *radicals* is + ``False``), ``root`` will be a :py:class:`~.ComplexRootOf`. + + Returns + ======= + + AlgebraicNumber + + See Also + ======== + + is_primitive_element + + """ + if self.is_primitive_element: + return self + m = self.minpoly_of_element() + r = self.to_root(radicals=radicals) + return AlgebraicNumber((m, r)) + + def minpoly_of_element(self): + r""" + Compute the minimal polynomial for this algebraic number. + + Explanation + =========== + + Recall that we represent an element $\alpha \in \mathbb{Q}(\theta)$. + Our instance attribute ``self.minpoly`` is the minimal polynomial for + our primitive element $\theta$. This method computes the minimal + polynomial for $\alpha$. + + """ + if self._own_minpoly is None: + if self.is_primitive_element: + self._own_minpoly = self.minpoly + else: + from sympy.polys.numberfields.minpoly import minpoly + theta = self.primitive_element() + self._own_minpoly = minpoly(self.as_expr(theta), polys=True) + return self._own_minpoly + + def to_root(self, radicals=True, minpoly=None): + """ + Convert to an :py:class:`~.Expr` that is not an + :py:class:`~.AlgebraicNumber`, specifically, either a + :py:class:`~.ComplexRootOf`, or, optionally and where possible, an + expression in radicals. + + Parameters + ========== + + radicals : boolean, optional (default=True) + If ``True``, then we will try to return the root as an expression + in radicals. If that is not possible, we will return a + :py:class:`~.ComplexRootOf`. + + minpoly : :py:class:`~.Poly` + If the minimal polynomial for `self` has been pre-computed, it can + be passed in order to save time. + + """ + if self.is_primitive_element and not isinstance(self.root, AlgebraicNumber): + return self.root + m = minpoly or self.minpoly_of_element() + roots = m.all_roots(radicals=radicals) + if len(roots) == 1: + return roots[0] + ex = self.as_expr() + for b in roots: + if m.same_root(b, ex): + return b + + +class RationalConstant(Rational): + """ + Abstract base class for rationals with specific behaviors + + Derived classes must define class attributes p and q and should probably all + be singletons. + """ + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + +class IntegerConstant(Integer): + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + +class Zero(IntegerConstant, metaclass=Singleton): + """The number zero. + + Zero is a singleton, and can be accessed by ``S.Zero`` + + Examples + ======== + + >>> from sympy import S, Integer + >>> Integer(0) is S.Zero + True + >>> 1/S.Zero + zoo + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Zero + """ + + p = 0 + q = 1 + is_positive = False + is_negative = False + is_zero = True + is_number = True + is_comparable = True + + __slots__ = () + + def __getnewargs__(self): + return () + + @staticmethod + def __abs__(): + return S.Zero + + @staticmethod + def __neg__(): + return S.Zero + + def _eval_power(self, expt): + if expt.is_extended_positive: + return self + if expt.is_extended_negative: + return S.ComplexInfinity + if expt.is_extended_real is False: + return S.NaN + if expt.is_zero: + return S.One + + # infinities are already handled with pos and neg + # tests above; now throw away leading numbers on Mul + # exponent since 0**-x = zoo**x even when x == 0 + coeff, terms = expt.as_coeff_Mul() + if coeff.is_negative: + return S.ComplexInfinity**terms + if coeff is not S.One: # there is a Number to discard + return self**terms + + def _eval_order(self, *symbols): + # Order(0,x) -> 0 + return self + + def __bool__(self): + return False + + +class One(IntegerConstant, metaclass=Singleton): + """The number one. + + One is a singleton, and can be accessed by ``S.One``. + + Examples + ======== + + >>> from sympy import S, Integer + >>> Integer(1) is S.One + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/1_%28number%29 + """ + is_number = True + is_positive = True + + p = 1 + q = 1 + + __slots__ = () + + def __getnewargs__(self): + return () + + @staticmethod + def __abs__(): + return S.One + + @staticmethod + def __neg__(): + return S.NegativeOne + + def _eval_power(self, expt): + return self + + def _eval_order(self, *symbols): + return + + @staticmethod + def factors(limit=None, use_trial=True, use_rho=False, use_pm1=False, + verbose=False, visual=False): + if visual: + return S.One + else: + return {} + + +class NegativeOne(IntegerConstant, metaclass=Singleton): + """The number negative one. + + NegativeOne is a singleton, and can be accessed by ``S.NegativeOne``. + + Examples + ======== + + >>> from sympy import S, Integer + >>> Integer(-1) is S.NegativeOne + True + + See Also + ======== + + One + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/%E2%88%921_%28number%29 + + """ + is_number = True + + p = -1 + q = 1 + + __slots__ = () + + def __getnewargs__(self): + return () + + @staticmethod + def __abs__(): + return S.One + + @staticmethod + def __neg__(): + return S.One + + def _eval_power(self, expt): + if expt.is_odd: + return S.NegativeOne + if expt.is_even: + return S.One + if isinstance(expt, Number): + if isinstance(expt, Float): + return Float(-1.0)**expt + if expt is S.NaN: + return S.NaN + if expt in (S.Infinity, S.NegativeInfinity): + return S.NaN + if expt is S.Half: + return S.ImaginaryUnit + if isinstance(expt, Rational): + if expt.q == 2: + return S.ImaginaryUnit**Integer(expt.p) + i, r = divmod(expt.p, expt.q) + if i: + return self**i*self**Rational(r, expt.q) + return + + +class Half(RationalConstant, metaclass=Singleton): + """The rational number 1/2. + + Half is a singleton, and can be accessed by ``S.Half``. + + Examples + ======== + + >>> from sympy import S, Rational + >>> Rational(1, 2) is S.Half + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/One_half + """ + is_number = True + + p = 1 + q = 2 + + __slots__ = () + + def __getnewargs__(self): + return () + + @staticmethod + def __abs__(): + return S.Half + + +class Infinity(Number, metaclass=Singleton): + r"""Positive infinite quantity. + + Explanation + =========== + + In real analysis the symbol `\infty` denotes an unbounded + limit: `x\to\infty` means that `x` grows without bound. + + Infinity is often used not only to define a limit but as a value + in the affinely extended real number system. Points labeled `+\infty` + and `-\infty` can be added to the topological space of the real numbers, + producing the two-point compactification of the real numbers. Adding + algebraic properties to this gives us the extended real numbers. + + Infinity is a singleton, and can be accessed by ``S.Infinity``, + or can be imported as ``oo``. + + Examples + ======== + + >>> from sympy import oo, exp, limit, Symbol + >>> 1 + oo + oo + >>> 42/oo + 0 + >>> x = Symbol('x') + >>> limit(exp(x), x, oo) + oo + + See Also + ======== + + NegativeInfinity, NaN + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Infinity + """ + + is_commutative = True + is_number = True + is_complex = False + is_extended_real = True + is_infinite = True + is_comparable = True + is_extended_positive = True + is_prime = False + + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + def _latex(self, printer): + return r"\infty" + + def _eval_subs(self, old, new): + if self == old: + return new + + def _eval_evalf(self, prec=None): + return Float('inf') + + def evalf(self, prec=None, **options): + return self._eval_evalf(prec) + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other in (S.NegativeInfinity, S.NaN): + return S.NaN + return self + return Number.__add__(self, other) + __radd__ = __add__ + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other in (S.Infinity, S.NaN): + return S.NaN + return self + return Number.__sub__(self, other) + + @_sympifyit('other', NotImplemented) + def __rsub__(self, other): + return (-self).__add__(other) + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other.is_zero or other is S.NaN: + return S.NaN + if other.is_extended_positive: + return self + return S.NegativeInfinity + return Number.__mul__(self, other) + __rmul__ = __mul__ + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.Infinity or \ + other is S.NegativeInfinity or \ + other is S.NaN: + return S.NaN + if other.is_extended_nonnegative: + return self + return S.NegativeInfinity + return Number.__truediv__(self, other) + + def __abs__(self): + return S.Infinity + + def __neg__(self): + return S.NegativeInfinity + + def _eval_power(self, expt): + """ + ``expt`` is symbolic object but not equal to 0 or 1. + + ================ ======= ============================== + Expression Result Notes + ================ ======= ============================== + ``oo ** nan`` ``nan`` + ``oo ** -p`` ``0`` ``p`` is number, ``oo`` + ================ ======= ============================== + + See Also + ======== + Pow + NaN + NegativeInfinity + + """ + if expt.is_extended_positive: + return S.Infinity + if expt.is_extended_negative: + return S.Zero + if expt is S.NaN: + return S.NaN + if expt is S.ComplexInfinity: + return S.NaN + if expt.is_extended_real is False and expt.is_number: + from sympy.functions.elementary.complexes import re + expt_real = re(expt) + if expt_real.is_positive: + return S.ComplexInfinity + if expt_real.is_negative: + return S.Zero + if expt_real.is_zero: + return S.NaN + + return self**expt.evalf() + + def _as_mpf_val(self, prec): + return mlib.finf + + def __hash__(self): + return super().__hash__() + + def __eq__(self, other): + return other is S.Infinity or other == float('inf') + + def __ne__(self, other): + return other is not S.Infinity and other != float('inf') + + __gt__ = Expr.__gt__ + __ge__ = Expr.__ge__ + __lt__ = Expr.__lt__ + __le__ = Expr.__le__ + + @_sympifyit('other', NotImplemented) + def __mod__(self, other): + if not isinstance(other, Expr): + return NotImplemented + return S.NaN + + __rmod__ = __mod__ + + def floor(self): + return self + + def ceiling(self): + return self + +oo = S.Infinity + + +class NegativeInfinity(Number, metaclass=Singleton): + """Negative infinite quantity. + + NegativeInfinity is a singleton, and can be accessed + by ``S.NegativeInfinity``. + + See Also + ======== + + Infinity + """ + + is_extended_real = True + is_complex = False + is_commutative = True + is_infinite = True + is_comparable = True + is_extended_negative = True + is_number = True + is_prime = False + + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + def _latex(self, printer): + return r"-\infty" + + def _eval_subs(self, old, new): + if self == old: + return new + + def _eval_evalf(self, prec=None): + return Float('-inf') + + def evalf(self, prec=None, **options): + return self._eval_evalf(prec) + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other in (S.Infinity, S.NaN): + return S.NaN + return self + return Number.__add__(self, other) + __radd__ = __add__ + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other in (S.NegativeInfinity, S.NaN): + return S.NaN + return self + return Number.__sub__(self, other) + + @_sympifyit('other', NotImplemented) + def __rsub__(self, other): + return (-self).__add__(other) + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other.is_zero or other is S.NaN: + return S.NaN + if other.is_extended_positive: + return self + return S.Infinity + return Number.__mul__(self, other) + __rmul__ = __mul__ + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + if isinstance(other, Number) and global_parameters.evaluate: + if other is S.Infinity or \ + other is S.NegativeInfinity or \ + other is S.NaN: + return S.NaN + if other.is_extended_nonnegative: + return self + return S.Infinity + return Number.__truediv__(self, other) + + def __abs__(self): + return S.Infinity + + def __neg__(self): + return S.Infinity + + def _eval_power(self, expt): + """ + ``expt`` is symbolic object but not equal to 0 or 1. + + ================ ======= ============================== + Expression Result Notes + ================ ======= ============================== + ``(-oo) ** nan`` ``nan`` + ``(-oo) ** oo`` ``nan`` + ``(-oo) ** -oo`` ``nan`` + ``(-oo) ** e`` ``oo`` ``e`` is positive even integer + ``(-oo) ** o`` ``-oo`` ``o`` is positive odd integer + ================ ======= ============================== + + See Also + ======== + + Infinity + Pow + NaN + + """ + if expt.is_number: + if expt is S.NaN or \ + expt is S.Infinity or \ + expt is S.NegativeInfinity: + return S.NaN + + if isinstance(expt, Integer) and expt.is_extended_positive: + if expt.is_odd: + return S.NegativeInfinity + else: + return S.Infinity + + inf_part = S.Infinity**expt + s_part = S.NegativeOne**expt + if inf_part == 0 and s_part.is_finite: + return inf_part + if (inf_part is S.ComplexInfinity and + s_part.is_finite and not s_part.is_zero): + return S.ComplexInfinity + return s_part*inf_part + + def _as_mpf_val(self, prec): + return mlib.fninf + + def __hash__(self): + return super().__hash__() + + def __eq__(self, other): + return other is S.NegativeInfinity or other == float('-inf') + + def __ne__(self, other): + return other is not S.NegativeInfinity and other != float('-inf') + + __gt__ = Expr.__gt__ + __ge__ = Expr.__ge__ + __lt__ = Expr.__lt__ + __le__ = Expr.__le__ + + @_sympifyit('other', NotImplemented) + def __mod__(self, other): + if not isinstance(other, Expr): + return NotImplemented + return S.NaN + + __rmod__ = __mod__ + + def floor(self): + return self + + def ceiling(self): + return self + + def as_powers_dict(self): + return {S.NegativeOne: 1, S.Infinity: 1} + + +class NaN(Number, metaclass=Singleton): + """ + Not a Number. + + Explanation + =========== + + This serves as a place holder for numeric values that are indeterminate. + Most operations on NaN, produce another NaN. Most indeterminate forms, + such as ``0/0`` or ``oo - oo` produce NaN. Two exceptions are ``0**0`` + and ``oo**0``, which all produce ``1`` (this is consistent with Python's + float). + + NaN is loosely related to floating point nan, which is defined in the + IEEE 754 floating point standard, and corresponds to the Python + ``float('nan')``. Differences are noted below. + + NaN is mathematically not equal to anything else, even NaN itself. This + explains the initially counter-intuitive results with ``Eq`` and ``==`` in + the examples below. + + NaN is not comparable so inequalities raise a TypeError. This is in + contrast with floating point nan where all inequalities are false. + + NaN is a singleton, and can be accessed by ``S.NaN``, or can be imported + as ``nan``. + + Examples + ======== + + >>> from sympy import nan, S, oo, Eq + >>> nan is S.NaN + True + >>> oo - oo + nan + >>> nan + 1 + nan + >>> Eq(nan, nan) # mathematical equality + False + >>> nan == nan # structural equality + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/NaN + + """ + is_commutative = True + is_extended_real = None + is_real = None + is_rational = None + is_algebraic = None + is_transcendental = None + is_integer = None + is_comparable = False + is_finite = None + is_zero = None + is_prime = None + is_positive = None + is_negative = None + is_number = True + + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + def _latex(self, printer): + return r"\text{NaN}" + + def __neg__(self): + return self + + @_sympifyit('other', NotImplemented) + def __add__(self, other): + return self + + @_sympifyit('other', NotImplemented) + def __sub__(self, other): + return self + + @_sympifyit('other', NotImplemented) + def __mul__(self, other): + return self + + @_sympifyit('other', NotImplemented) + def __truediv__(self, other): + return self + + def floor(self): + return self + + def ceiling(self): + return self + + def _as_mpf_val(self, prec): + return _mpf_nan + + def __hash__(self): + return super().__hash__() + + def __eq__(self, other): + # NaN is structurally equal to another NaN + return other is S.NaN + + def __ne__(self, other): + return other is not S.NaN + + # Expr will _sympify and raise TypeError + __gt__ = Expr.__gt__ + __ge__ = Expr.__ge__ + __lt__ = Expr.__lt__ + __le__ = Expr.__le__ + +nan = S.NaN + +@dispatch(NaN, Expr) # type:ignore +def _eval_is_eq(a, b): # noqa:F811 + return False + + +class ComplexInfinity(AtomicExpr, metaclass=Singleton): + r"""Complex infinity. + + Explanation + =========== + + In complex analysis the symbol `\tilde\infty`, called "complex + infinity", represents a quantity with infinite magnitude, but + undetermined complex phase. + + ComplexInfinity is a singleton, and can be accessed by + ``S.ComplexInfinity``, or can be imported as ``zoo``. + + Examples + ======== + + >>> from sympy import zoo + >>> zoo + 42 + zoo + >>> 42/zoo + 0 + >>> zoo + zoo + nan + >>> zoo*zoo + zoo + + See Also + ======== + + Infinity + """ + + is_commutative = True + is_infinite = True + is_number = True + is_prime = False + is_complex = False + is_extended_real = False + + kind = NumberKind + + __slots__ = () + + def __new__(cls): + return AtomicExpr.__new__(cls) + + def _latex(self, printer): + return r"\tilde{\infty}" + + @staticmethod + def __abs__(): + return S.Infinity + + def floor(self): + return self + + def ceiling(self): + return self + + @staticmethod + def __neg__(): + return S.ComplexInfinity + + def _eval_power(self, expt): + if expt is S.ComplexInfinity: + return S.NaN + + if isinstance(expt, Number): + if expt.is_zero: + return S.NaN + else: + if expt.is_positive: + return S.ComplexInfinity + else: + return S.Zero + + +zoo = S.ComplexInfinity + + +class NumberSymbol(AtomicExpr): + + is_commutative = True + is_finite = True + is_number = True + + __slots__ = () + + is_NumberSymbol = True + + kind = NumberKind + + def __new__(cls): + return AtomicExpr.__new__(cls) + + def approximation(self, number_cls): + """ Return an interval with number_cls endpoints + that contains the value of NumberSymbol. + If not implemented, then return None. + """ + + def _eval_evalf(self, prec): + return Float._new(self._as_mpf_val(prec), prec) + + def __eq__(self, other): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if self is other: + return True + if other.is_Number and self.is_irrational: + return False + + return False # NumberSymbol != non-(Number|self) + + def __ne__(self, other): + return not self == other + + def __le__(self, other): + if self is other: + return S.true + return Expr.__le__(self, other) + + def __ge__(self, other): + if self is other: + return S.true + return Expr.__ge__(self, other) + + def __int__(self): + # subclass with appropriate return value + raise NotImplementedError + + def __hash__(self): + return super().__hash__() + + +class Exp1(NumberSymbol, metaclass=Singleton): + r"""The `e` constant. + + Explanation + =========== + + The transcendental number `e = 2.718281828\ldots` is the base of the + natural logarithm and of the exponential function, `e = \exp(1)`. + Sometimes called Euler's number or Napier's constant. + + Exp1 is a singleton, and can be accessed by ``S.Exp1``, + or can be imported as ``E``. + + Examples + ======== + + >>> from sympy import exp, log, E + >>> E is exp(1) + True + >>> log(E) + 1 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/E_%28mathematical_constant%29 + """ + + is_real = True + is_positive = True + is_negative = False # XXX Forces is_negative/is_nonnegative + is_irrational = True + is_number = True + is_algebraic = False + is_transcendental = True + + __slots__ = () + + def _latex(self, printer): + return r"e" + + @staticmethod + def __abs__(): + return S.Exp1 + + def __int__(self): + return 2 + + def _as_mpf_val(self, prec): + return mpf_e(prec) + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (Integer(2), Integer(3)) + elif issubclass(number_cls, Rational): + pass + + def _eval_power(self, expt): + if global_parameters.exp_is_pow: + return self._eval_power_exp_is_pow(expt) + else: + from sympy.functions.elementary.exponential import exp + return exp(expt) + + def _eval_power_exp_is_pow(self, arg): + if arg.is_Number: + if arg is oo: + return oo + elif arg == -oo: + return S.Zero + from sympy.functions.elementary.exponential import log + if isinstance(arg, log): + return arg.args[0] + + # don't autoexpand Pow or Mul (see the issue 3351): + elif not arg.is_Add: + Ioo = I*oo + if arg in [Ioo, -Ioo]: + return nan + + coeff = arg.coeff(pi*I) + if coeff: + if (2*coeff).is_integer: + if coeff.is_even: + return S.One + elif coeff.is_odd: + return S.NegativeOne + elif (coeff + S.Half).is_even: + return -I + elif (coeff + S.Half).is_odd: + return I + elif coeff.is_Rational: + ncoeff = coeff % 2 # restrict to [0, 2pi) + if ncoeff > 1: # restrict to (-pi, pi] + ncoeff -= 2 + if ncoeff != coeff: + return S.Exp1**(ncoeff*S.Pi*S.ImaginaryUnit) + + # Warning: code in risch.py will be very sensitive to changes + # in this (see DifferentialExtension). + + # look for a single log factor + + coeff, terms = arg.as_coeff_Mul() + + # but it can't be multiplied by oo + if coeff in (oo, -oo): + return + + coeffs, log_term = [coeff], None + for term in Mul.make_args(terms): + if isinstance(term, log): + if log_term is None: + log_term = term.args[0] + else: + return + elif term.is_comparable: + coeffs.append(term) + else: + return + + return log_term**Mul(*coeffs) if log_term else None + elif arg.is_Add: + out = [] + add = [] + argchanged = False + for a in arg.args: + if a is S.One: + add.append(a) + continue + newa = self**a + if isinstance(newa, Pow) and newa.base is self: + if newa.exp != a: + add.append(newa.exp) + argchanged = True + else: + add.append(a) + else: + out.append(newa) + if out or argchanged: + return Mul(*out)*Pow(self, Add(*add), evaluate=False) + elif arg.is_Matrix: + return arg.exp() + + def _eval_rewrite_as_sin(self, **kwargs): + from sympy.functions.elementary.trigonometric import sin + return sin(I + S.Pi/2) - I*sin(I) + + def _eval_rewrite_as_cos(self, **kwargs): + from sympy.functions.elementary.trigonometric import cos + return cos(I) + I*cos(I + S.Pi/2) + +E = S.Exp1 + + +class Pi(NumberSymbol, metaclass=Singleton): + r"""The `\pi` constant. + + Explanation + =========== + + The transcendental number `\pi = 3.141592654\ldots` represents the ratio + of a circle's circumference to its diameter, the area of the unit circle, + the half-period of trigonometric functions, and many other things + in mathematics. + + Pi is a singleton, and can be accessed by ``S.Pi``, or can + be imported as ``pi``. + + Examples + ======== + + >>> from sympy import S, pi, oo, sin, exp, integrate, Symbol + >>> S.Pi + pi + >>> pi > 3 + True + >>> pi.is_irrational + True + >>> x = Symbol('x') + >>> sin(x + 2*pi) + sin(x) + >>> integrate(exp(-x**2), (x, -oo, oo)) + sqrt(pi) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Pi + """ + + is_real = True + is_positive = True + is_negative = False + is_irrational = True + is_number = True + is_algebraic = False + is_transcendental = True + + __slots__ = () + + def _latex(self, printer): + return r"\pi" + + @staticmethod + def __abs__(): + return S.Pi + + def __int__(self): + return 3 + + def _as_mpf_val(self, prec): + return mpf_pi(prec) + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (Integer(3), Integer(4)) + elif issubclass(number_cls, Rational): + return (Rational(223, 71, 1), Rational(22, 7, 1)) + +pi = S.Pi + + +class GoldenRatio(NumberSymbol, metaclass=Singleton): + r"""The golden ratio, `\phi`. + + Explanation + =========== + + `\phi = \frac{1 + \sqrt{5}}{2}` is an algebraic number. Two quantities + are in the golden ratio if their ratio is the same as the ratio of + their sum to the larger of the two quantities, i.e. their maximum. + + GoldenRatio is a singleton, and can be accessed by ``S.GoldenRatio``. + + Examples + ======== + + >>> from sympy import S + >>> S.GoldenRatio > 1 + True + >>> S.GoldenRatio.expand(func=True) + 1/2 + sqrt(5)/2 + >>> S.GoldenRatio.is_irrational + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Golden_ratio + """ + + is_real = True + is_positive = True + is_negative = False + is_irrational = True + is_number = True + is_algebraic = True + is_transcendental = False + + __slots__ = () + + def _latex(self, printer): + return r"\phi" + + def __int__(self): + return 1 + + def _as_mpf_val(self, prec): + # XXX track down why this has to be increased + rv = mlib.from_man_exp(phi_fixed(prec + 10), -prec - 10) + return mpf_norm(rv, prec) + + def _eval_expand_func(self, **hints): + from sympy.functions.elementary.miscellaneous import sqrt + return S.Half + S.Half*sqrt(5) + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (S.One, Rational(2)) + elif issubclass(number_cls, Rational): + pass + + _eval_rewrite_as_sqrt = _eval_expand_func + + +class TribonacciConstant(NumberSymbol, metaclass=Singleton): + r"""The tribonacci constant. + + Explanation + =========== + + The tribonacci numbers are like the Fibonacci numbers, but instead + of starting with two predetermined terms, the sequence starts with + three predetermined terms and each term afterwards is the sum of the + preceding three terms. + + The tribonacci constant is the ratio toward which adjacent tribonacci + numbers tend. It is a root of the polynomial `x^3 - x^2 - x - 1 = 0`, + and also satisfies the equation `x + x^{-3} = 2`. + + TribonacciConstant is a singleton, and can be accessed + by ``S.TribonacciConstant``. + + Examples + ======== + + >>> from sympy import S + >>> S.TribonacciConstant > 1 + True + >>> S.TribonacciConstant.expand(func=True) + 1/3 + (19 - 3*sqrt(33))**(1/3)/3 + (3*sqrt(33) + 19)**(1/3)/3 + >>> S.TribonacciConstant.is_irrational + True + >>> S.TribonacciConstant.n(20) + 1.8392867552141611326 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers + """ + + is_real = True + is_positive = True + is_negative = False + is_irrational = True + is_number = True + is_algebraic = True + is_transcendental = False + + __slots__ = () + + def _latex(self, printer): + return r"\text{TribonacciConstant}" + + def __int__(self): + return 1 + + def _as_mpf_val(self, prec): + return self._eval_evalf(prec)._mpf_ + + def _eval_evalf(self, prec): + rv = self._eval_expand_func(function=True)._eval_evalf(prec + 4) + return Float(rv, precision=prec) + + def _eval_expand_func(self, **hints): + from sympy.functions.elementary.miscellaneous import cbrt, sqrt + return (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3 + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (S.One, Rational(2)) + elif issubclass(number_cls, Rational): + pass + + _eval_rewrite_as_sqrt = _eval_expand_func + + +class EulerGamma(NumberSymbol, metaclass=Singleton): + r"""The Euler-Mascheroni constant. + + Explanation + =========== + + `\gamma = 0.5772157\ldots` (also called Euler's constant) is a mathematical + constant recurring in analysis and number theory. It is defined as the + limiting difference between the harmonic series and the + natural logarithm: + + .. math:: \gamma = \lim\limits_{n\to\infty} + \left(\sum\limits_{k=1}^n\frac{1}{k} - \ln n\right) + + EulerGamma is a singleton, and can be accessed by ``S.EulerGamma``. + + Examples + ======== + + >>> from sympy import S + >>> S.EulerGamma.is_irrational + >>> S.EulerGamma > 0 + True + >>> S.EulerGamma > 1 + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant + """ + + is_real = True + is_positive = True + is_negative = False + is_irrational = None + is_number = True + + __slots__ = () + + def _latex(self, printer): + return r"\gamma" + + def __int__(self): + return 0 + + def _as_mpf_val(self, prec): + # XXX track down why this has to be increased + v = mlib.libhyper.euler_fixed(prec + 10) + rv = mlib.from_man_exp(v, -prec - 10) + return mpf_norm(rv, prec) + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (S.Zero, S.One) + elif issubclass(number_cls, Rational): + return (S.Half, Rational(3, 5, 1)) + + +class Catalan(NumberSymbol, metaclass=Singleton): + r"""Catalan's constant. + + Explanation + =========== + + $G = 0.91596559\ldots$ is given by the infinite series + + .. math:: G = \sum_{k=0}^{\infty} \frac{(-1)^k}{(2k+1)^2} + + Catalan is a singleton, and can be accessed by ``S.Catalan``. + + Examples + ======== + + >>> from sympy import S + >>> S.Catalan.is_irrational + >>> S.Catalan > 0 + True + >>> S.Catalan > 1 + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Catalan%27s_constant + """ + + is_real = True + is_positive = True + is_negative = False + is_irrational = None + is_number = True + + __slots__ = () + + def __int__(self): + return 0 + + def _as_mpf_val(self, prec): + # XXX track down why this has to be increased + v = mlib.catalan_fixed(prec + 10) + rv = mlib.from_man_exp(v, -prec - 10) + return mpf_norm(rv, prec) + + def approximation_interval(self, number_cls): + if issubclass(number_cls, Integer): + return (S.Zero, S.One) + elif issubclass(number_cls, Rational): + return (Rational(9, 10, 1), S.One) + + def _eval_rewrite_as_Sum(self, k_sym=None, symbols=None, **hints): + if (k_sym is not None) or (symbols is not None): + return self + from .symbol import Dummy + from sympy.concrete.summations import Sum + k = Dummy('k', integer=True, nonnegative=True) + return Sum(S.NegativeOne**k / (2*k+1)**2, (k, 0, S.Infinity)) + + def _latex(self, printer): + return "G" + + +class ImaginaryUnit(AtomicExpr, metaclass=Singleton): + r"""The imaginary unit, `i = \sqrt{-1}`. + + I is a singleton, and can be accessed by ``S.I``, or can be + imported as ``I``. + + Examples + ======== + + >>> from sympy import I, sqrt + >>> sqrt(-1) + I + >>> I*I + -1 + >>> 1/I + -I + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Imaginary_unit + """ + + is_commutative = True + is_imaginary = True + is_finite = True + is_number = True + is_algebraic = True + is_transcendental = False + + kind = NumberKind + + __slots__ = () + + def _latex(self, printer): + return printer._settings['imaginary_unit_latex'] + + @staticmethod + def __abs__(): + return S.One + + def _eval_evalf(self, prec): + return self + + def _eval_conjugate(self): + return -S.ImaginaryUnit + + def _eval_power(self, expt): + """ + b is I = sqrt(-1) + e is symbolic object but not equal to 0, 1 + + I**r -> (-1)**(r/2) -> exp(r/2*Pi*I) -> sin(Pi*r/2) + cos(Pi*r/2)*I, r is decimal + I**0 mod 4 -> 1 + I**1 mod 4 -> I + I**2 mod 4 -> -1 + I**3 mod 4 -> -I + """ + + if isinstance(expt, Integer): + expt = expt % 4 + if expt == 0: + return S.One + elif expt == 1: + return S.ImaginaryUnit + elif expt == 2: + return S.NegativeOne + elif expt == 3: + return -S.ImaginaryUnit + if isinstance(expt, Rational): + i, r = divmod(expt, 2) + rv = Pow(S.ImaginaryUnit, r, evaluate=False) + if i % 2: + return Mul(S.NegativeOne, rv, evaluate=False) + return rv + + def as_base_exp(self): + return S.NegativeOne, S.Half + + @property + def _mpc_(self): + return (Float(0)._mpf_, Float(1)._mpf_) + + +I = S.ImaginaryUnit + + +def int_valued(x): + """return True only for a literal Number whose internal + representation as a fraction has a denominator of 1, + else False, i.e. integer, with no fractional part. + """ + if isinstance(x, (SYMPY_INTS, int)): + return True + if type(x) is float: + return x.is_integer() + if isinstance(x, Integer): + return True + if isinstance(x, Float): + # x = s*m*2**p; _mpf_ = s,m,e,p + return x._mpf_[2] >= 0 + return False # or add new types to recognize + + +def equal_valued(x, y): + """Compare expressions treating plain floats as rationals. + + Examples + ======== + + >>> from sympy import S, symbols, Rational, Float + >>> from sympy.core.numbers import equal_valued + >>> equal_valued(1, 2) + False + >>> equal_valued(1, 1) + True + + In SymPy expressions with Floats compare unequal to corresponding + expressions with rationals: + + >>> x = symbols('x') + >>> x**2 == x**2.0 + False + + However an individual Float compares equal to a Rational: + + >>> Rational(1, 2) == Float(0.5) + False + + In a future version of SymPy this might change so that Rational and Float + compare unequal. This function provides the behavior currently expected of + ``==`` so that it could still be used if the behavior of ``==`` were to + change in future. + + >>> equal_valued(1, 1.0) # Float vs Rational + True + >>> equal_valued(S(1).n(3), S(1).n(5)) # Floats of different precision + True + + Explanation + =========== + + In future SymPy verions Float and Rational might compare unequal and floats + with different precisions might compare unequal. In that context a function + is needed that can check if a number is equal to 1 or 0 etc. The idea is + that instead of testing ``if x == 1:`` if we want to accept floats like + ``1.0`` as well then the test can be written as ``if equal_valued(x, 1):`` + or ``if equal_valued(x, 2):``. Since this function is intended to be used + in situations where one or both operands are expected to be concrete + numbers like 1 or 0 the function does not recurse through the args of any + compound expression to compare any nested floats. + + References + ========== + + .. [1] https://github.com/sympy/sympy/pull/20033 + """ + x = _sympify(x) + y = _sympify(y) + + # Handle everything except Float/Rational first + if not x.is_Float and not y.is_Float: + return x == y + elif x.is_Float and y.is_Float: + # Compare values without regard for precision + return x._mpf_ == y._mpf_ + elif x.is_Float: + x, y = y, x + if not x.is_Rational: + return False + + # Now y is Float and x is Rational. A simple approach at this point would + # just be x == Rational(y) but if y has a large exponent creating a + # Rational could be prohibitively expensive. + + sign, man, exp, _ = y._mpf_ + p, q = x.p, x.q + + if sign: + man = -man + + if exp == 0: + # y odd integer + return q == 1 and man == p + elif exp > 0: + # y even integer + if q != 1: + return False + if p.bit_length() != man.bit_length() + exp: + return False + return man << exp == p + else: + # y non-integer. Need p == man and q == 2**-exp + if p != man: + return False + neg_exp = -exp + if q.bit_length() - 1 != neg_exp: + return False + return (1 << neg_exp) == q + + +def all_close(expr1, expr2, rtol=1e-5, atol=1e-8): + """Return True if expr1 and expr2 are numerically close. + + The expressions must have the same structure, but any Rational, Integer, or + Float numbers they contain are compared approximately using rtol and atol. + Any other parts of expressions are compared exactly. + + Relative tolerance is measured with respect to expr2 so when used in + testing expr2 should be the expected correct answer. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.abc import x, y + >>> from sympy.core.numbers import all_close + >>> expr1 = 0.1*exp(x - y) + >>> expr2 = exp(x - y)/10 + >>> expr1 + 0.1*exp(x - y) + >>> expr2 + exp(x - y)/10 + >>> expr1 == expr2 + False + >>> all_close(expr1, expr2) + True + """ + NUM_TYPES = (Rational, Float) + + def _all_close(expr1, expr2, rtol, atol): + num1 = isinstance(expr1, NUM_TYPES) + num2 = isinstance(expr2, NUM_TYPES) + if num1 != num2: + return False + elif num1: + return bool(abs(expr1 - expr2) <= atol + rtol*abs(expr2)) + elif expr1.is_Atom: + return expr1 == expr2 + elif expr1.func != expr2.func or len(expr1.args) != len(expr2.args): + return False + elif expr1.is_Add or expr1.is_Mul: + return _all_close_ac(expr1, expr2, rtol, atol) + else: + args = zip(expr1.args, expr2.args) + return all(_all_close(a1, a2, rtol, atol) for a1, a2 in args) + + def _all_close_ac(expr1, expr2, rtol, atol): + # Compare expressions with associative commutative operators for + # approximate equality. This could be horribly inefficient for large + # expressions e.g. an Add with many terms. + args2 = list(expr2.args) + for arg1 in expr1.args: + for i, arg2 in enumerate(args2): + if _all_close(arg1, arg2, rtol, atol): + args2.pop(i) + break + else: + return False + return True + + return _all_close(_sympify(expr1), _sympify(expr2), rtol, atol) + + +@dispatch(Tuple, Number) # type:ignore +def _eval_is_eq(self, other): # noqa: F811 + return False + + +def sympify_fractions(f): + return Rational(f.numerator, f.denominator, 1) + +_sympy_converter[fractions.Fraction] = sympify_fractions + + +if gmpy is not None: + + def sympify_mpz(x): + return Integer(int(x)) + + def sympify_mpq(x): + return Rational(int(x.numerator), int(x.denominator)) + + _sympy_converter[type(gmpy.mpz(1))] = sympify_mpz + _sympy_converter[type(gmpy.mpq(1, 2))] = sympify_mpq + + +if flint is not None: + + def sympify_fmpz(x): + return Integer(int(x)) + + def sympify_fmpq(x): + return Rational(int(x.numerator), int(x.denominator)) + + _sympy_converter[type(flint.fmpz(1))] = sympify_fmpz + _sympy_converter[type(flint.fmpq(1, 2))] = sympify_fmpq + + +def sympify_mpmath(x): + return Expr._from_mpmath(x, x.context.prec) + +_sympy_converter[mpnumeric] = sympify_mpmath + + +def sympify_complex(a): + real, imag = list(map(sympify, (a.real, a.imag))) + return real + S.ImaginaryUnit*imag + +_sympy_converter[complex] = sympify_complex + +from .power import Pow +from .mul import Mul +Mul.identity = One() +from .add import Add +Add.identity = Zero() + + +def _register_classes(): + numbers.Number.register(Number) + numbers.Real.register(Float) + numbers.Rational.register(Rational) + numbers.Integral.register(Integer) + +_register_classes() + +_illegal = (S.NaN, S.Infinity, S.NegativeInfinity, S.ComplexInfinity) diff --git a/lib/python3.11/site-packages/sympy/core/operations.py b/lib/python3.11/site-packages/sympy/core/operations.py new file mode 100644 index 0000000000000000000000000000000000000000..efd4f6b85de499dad8c30d75cf63ec98bd439998 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/operations.py @@ -0,0 +1,718 @@ +from __future__ import annotations +from operator import attrgetter +from collections import defaultdict + +from sympy.utilities.exceptions import sympy_deprecation_warning + +from .sympify import _sympify as _sympify_, sympify +from .basic import Basic +from .cache import cacheit +from .sorting import ordered +from .logic import fuzzy_and +from .parameters import global_parameters +from sympy.utilities.iterables import sift +from sympy.multipledispatch.dispatcher import (Dispatcher, + ambiguity_register_error_ignore_dup, + str_signature, RaiseNotImplementedError) + + +class AssocOp(Basic): + """ Associative operations, can separate noncommutative and + commutative parts. + + (a op b) op c == a op (b op c) == a op b op c. + + Base class for Add and Mul. + + This is an abstract base class, concrete derived classes must define + the attribute `identity`. + + .. deprecated:: 1.7 + + Using arguments that aren't subclasses of :class:`~.Expr` in core + operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is + deprecated. See :ref:`non-expr-args-deprecated` for details. + + Parameters + ========== + + *args : + Arguments which are operated + + evaluate : bool, optional + Evaluate the operation. If not passed, refer to ``global_parameters.evaluate``. + """ + + # for performance reason, we don't let is_commutative go to assumptions, + # and keep it right here + __slots__: tuple[str, ...] = ('is_commutative',) + + _args_type: type[Basic] | None = None + + @cacheit + def __new__(cls, *args, evaluate=None, _sympify=True): + # Allow faster processing by passing ``_sympify=False``, if all arguments + # are already sympified. + if _sympify: + args = list(map(_sympify_, args)) + + # Disallow non-Expr args in Add/Mul + typ = cls._args_type + if typ is not None: + from .relational import Relational + if any(isinstance(arg, Relational) for arg in args): + raise TypeError("Relational cannot be used in %s" % cls.__name__) + + # This should raise TypeError once deprecation period is over: + for arg in args: + if not isinstance(arg, typ): + sympy_deprecation_warning( + f""" + +Using non-Expr arguments in {cls.__name__} is deprecated (in this case, one of +the arguments has type {type(arg).__name__!r}). + +If you really did intend to use a multiplication or addition operation with +this object, use the * or + operator instead. + + """, + deprecated_since_version="1.7", + active_deprecations_target="non-expr-args-deprecated", + stacklevel=4, + ) + + if evaluate is None: + evaluate = global_parameters.evaluate + if not evaluate: + obj = cls._from_args(args) + obj = cls._exec_constructor_postprocessors(obj) + return obj + + args = [a for a in args if a is not cls.identity] + + if len(args) == 0: + return cls.identity + if len(args) == 1: + return args[0] + + c_part, nc_part, order_symbols = cls.flatten(args) + is_commutative = not nc_part + obj = cls._from_args(c_part + nc_part, is_commutative) + obj = cls._exec_constructor_postprocessors(obj) + + if order_symbols is not None: + from sympy.series.order import Order + return Order(obj, *order_symbols) + return obj + + @classmethod + def _from_args(cls, args, is_commutative=None): + """Create new instance with already-processed args. + If the args are not in canonical order, then a non-canonical + result will be returned, so use with caution. The order of + args may change if the sign of the args is changed.""" + if len(args) == 0: + return cls.identity + elif len(args) == 1: + return args[0] + + obj = super().__new__(cls, *args) + if is_commutative is None: + is_commutative = fuzzy_and(a.is_commutative for a in args) + obj.is_commutative = is_commutative + return obj + + def _new_rawargs(self, *args, reeval=True, **kwargs): + """Create new instance of own class with args exactly as provided by + caller but returning the self class identity if args is empty. + + Examples + ======== + + This is handy when we want to optimize things, e.g. + + >>> from sympy import Mul, S + >>> from sympy.abc import x, y + >>> e = Mul(3, x, y) + >>> e.args + (3, x, y) + >>> Mul(*e.args[1:]) + x*y + >>> e._new_rawargs(*e.args[1:]) # the same as above, but faster + x*y + + Note: use this with caution. There is no checking of arguments at + all. This is best used when you are rebuilding an Add or Mul after + simply removing one or more args. If, for example, modifications, + result in extra 1s being inserted they will show up in the result: + + >>> m = (x*y)._new_rawargs(S.One, x); m + 1*x + >>> m == x + False + >>> m.is_Mul + True + + Another issue to be aware of is that the commutativity of the result + is based on the commutativity of self. If you are rebuilding the + terms that came from a commutative object then there will be no + problem, but if self was non-commutative then what you are + rebuilding may now be commutative. + + Although this routine tries to do as little as possible with the + input, getting the commutativity right is important, so this level + of safety is enforced: commutativity will always be recomputed if + self is non-commutative and kwarg `reeval=False` has not been + passed. + """ + if reeval and self.is_commutative is False: + is_commutative = None + else: + is_commutative = self.is_commutative + return self._from_args(args, is_commutative) + + @classmethod + def flatten(cls, seq): + """Return seq so that none of the elements are of type `cls`. This is + the vanilla routine that will be used if a class derived from AssocOp + does not define its own flatten routine.""" + # apply associativity, no commutativity property is used + new_seq = [] + while seq: + o = seq.pop() + if o.__class__ is cls: # classes must match exactly + seq.extend(o.args) + else: + new_seq.append(o) + new_seq.reverse() + + # c_part, nc_part, order_symbols + return [], new_seq, None + + def _matches_commutative(self, expr, repl_dict=None, old=False): + """ + Matches Add/Mul "pattern" to an expression "expr". + + repl_dict ... a dictionary of (wild: expression) pairs, that get + returned with the results + + This function is the main workhorse for Add/Mul. + + Examples + ======== + + >>> from sympy import symbols, Wild, sin + >>> a = Wild("a") + >>> b = Wild("b") + >>> c = Wild("c") + >>> x, y, z = symbols("x y z") + >>> (a+sin(b)*c)._matches_commutative(x+sin(y)*z) + {a_: x, b_: y, c_: z} + + In the example above, "a+sin(b)*c" is the pattern, and "x+sin(y)*z" is + the expression. + + The repl_dict contains parts that were already matched. For example + here: + + >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z, repl_dict={a: x}) + {a_: x, b_: y, c_: z} + + the only function of the repl_dict is to return it in the + result, e.g. if you omit it: + + >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z) + {b_: y, c_: z} + + the "a: x" is not returned in the result, but otherwise it is + equivalent. + + """ + from .function import _coeff_isneg + # make sure expr is Expr if pattern is Expr + from .expr import Expr + if isinstance(self, Expr) and not isinstance(expr, Expr): + return None + + if repl_dict is None: + repl_dict = {} + + # handle simple patterns + if self == expr: + return repl_dict + + d = self._matches_simple(expr, repl_dict) + if d is not None: + return d + + # eliminate exact part from pattern: (2+a+w1+w2).matches(expr) -> (w1+w2).matches(expr-a-2) + from .function import WildFunction + from .symbol import Wild + wild_part, exact_part = sift(self.args, lambda p: + p.has(Wild, WildFunction) and not expr.has(p), + binary=True) + if not exact_part: + wild_part = list(ordered(wild_part)) + if self.is_Add: + # in addition to normal ordered keys, impose + # sorting on Muls with leading Number to put + # them in order + wild_part = sorted(wild_part, key=lambda x: + x.args[0] if x.is_Mul and x.args[0].is_Number else + 0) + else: + exact = self._new_rawargs(*exact_part) + free = expr.free_symbols + if free and (exact.free_symbols - free): + # there are symbols in the exact part that are not + # in the expr; but if there are no free symbols, let + # the matching continue + return None + newexpr = self._combine_inverse(expr, exact) + if not old and (expr.is_Add or expr.is_Mul): + check = newexpr + if _coeff_isneg(check): + check = -check + if check.count_ops() > expr.count_ops(): + return None + newpattern = self._new_rawargs(*wild_part) + return newpattern.matches(newexpr, repl_dict) + + # now to real work ;) + i = 0 + saw = set() + while expr not in saw: + saw.add(expr) + args = tuple(ordered(self.make_args(expr))) + if self.is_Add and expr.is_Add: + # in addition to normal ordered keys, impose + # sorting on Muls with leading Number to put + # them in order + args = tuple(sorted(args, key=lambda x: + x.args[0] if x.is_Mul and x.args[0].is_Number else + 0)) + expr_list = (self.identity,) + args + for last_op in reversed(expr_list): + for w in reversed(wild_part): + d1 = w.matches(last_op, repl_dict) + if d1 is not None: + d2 = self.xreplace(d1).matches(expr, d1) + if d2 is not None: + return d2 + + if i == 0: + if self.is_Mul: + # make e**i look like Mul + if expr.is_Pow and expr.exp.is_Integer: + from .mul import Mul + if expr.exp > 0: + expr = Mul(*[expr.base, expr.base**(expr.exp - 1)], evaluate=False) + else: + expr = Mul(*[1/expr.base, expr.base**(expr.exp + 1)], evaluate=False) + i += 1 + continue + + elif self.is_Add: + # make i*e look like Add + c, e = expr.as_coeff_Mul() + if abs(c) > 1: + from .add import Add + if c > 0: + expr = Add(*[e, (c - 1)*e], evaluate=False) + else: + expr = Add(*[-e, (c + 1)*e], evaluate=False) + i += 1 + continue + + # try collection on non-Wild symbols + from sympy.simplify.radsimp import collect + was = expr + did = set() + for w in reversed(wild_part): + c, w = w.as_coeff_mul(Wild) + free = c.free_symbols - did + if free: + did.update(free) + expr = collect(expr, free) + if expr != was: + i += 0 + continue + + break # if we didn't continue, there is nothing more to do + + return + + def _has_matcher(self): + """Helper for .has() that checks for containment of + subexpressions within an expr by using sets of args + of similar nodes, e.g. x + 1 in x + y + 1 checks + to see that {x, 1} & {x, y, 1} == {x, 1} + """ + def _ncsplit(expr): + # this is not the same as args_cnc because here + # we don't assume expr is a Mul -- hence deal with args -- + # and always return a set. + cpart, ncpart = sift(expr.args, + lambda arg: arg.is_commutative is True, binary=True) + return set(cpart), ncpart + + c, nc = _ncsplit(self) + cls = self.__class__ + + def is_in(expr): + if isinstance(expr, cls): + if expr == self: + return True + _c, _nc = _ncsplit(expr) + if (c & _c) == c: + if not nc: + return True + elif len(nc) <= len(_nc): + for i in range(len(_nc) - len(nc) + 1): + if _nc[i:i + len(nc)] == nc: + return True + return False + return is_in + + def _eval_evalf(self, prec): + """ + Evaluate the parts of self that are numbers; if the whole thing + was a number with no functions it would have been evaluated, but + it wasn't so we must judiciously extract the numbers and reconstruct + the object. This is *not* simply replacing numbers with evaluated + numbers. Numbers should be handled in the largest pure-number + expression as possible. So the code below separates ``self`` into + number and non-number parts and evaluates the number parts and + walks the args of the non-number part recursively (doing the same + thing). + """ + from .add import Add + from .mul import Mul + from .symbol import Symbol + from .function import AppliedUndef + if isinstance(self, (Mul, Add)): + x, tail = self.as_independent(Symbol, AppliedUndef) + # if x is an AssocOp Function then the _evalf below will + # call _eval_evalf (here) so we must break the recursion + if not (tail is self.identity or + isinstance(x, AssocOp) and x.is_Function or + x is self.identity and isinstance(tail, AssocOp)): + # here, we have a number so we just call to _evalf with prec; + # prec is not the same as n, it is the binary precision so + # that's why we don't call to evalf. + x = x._evalf(prec) if x is not self.identity else self.identity + args = [] + tail_args = tuple(self.func.make_args(tail)) + for a in tail_args: + # here we call to _eval_evalf since we don't know what we + # are dealing with and all other _eval_evalf routines should + # be doing the same thing (i.e. taking binary prec and + # finding the evalf-able args) + newa = a._eval_evalf(prec) + if newa is None: + args.append(a) + else: + args.append(newa) + return self.func(x, *args) + + # this is the same as above, but there were no pure-number args to + # deal with + args = [] + for a in self.args: + newa = a._eval_evalf(prec) + if newa is None: + args.append(a) + else: + args.append(newa) + return self.func(*args) + + @classmethod + def make_args(cls, expr): + """ + Return a sequence of elements `args` such that cls(*args) == expr + + Examples + ======== + + >>> from sympy import Symbol, Mul, Add + >>> x, y = map(Symbol, 'xy') + + >>> Mul.make_args(x*y) + (x, y) + >>> Add.make_args(x*y) + (x*y,) + >>> set(Add.make_args(x*y + y)) == set([y, x*y]) + True + + """ + if isinstance(expr, cls): + return expr.args + else: + return (sympify(expr),) + + def doit(self, **hints): + if hints.get('deep', True): + terms = [term.doit(**hints) for term in self.args] + else: + terms = self.args + return self.func(*terms, evaluate=True) + +class ShortCircuit(Exception): + pass + + +class LatticeOp(AssocOp): + """ + Join/meet operations of an algebraic lattice[1]. + + Explanation + =========== + + These binary operations are associative (op(op(a, b), c) = op(a, op(b, c))), + commutative (op(a, b) = op(b, a)) and idempotent (op(a, a) = op(a) = a). + Common examples are AND, OR, Union, Intersection, max or min. They have an + identity element (op(identity, a) = a) and an absorbing element + conventionally called zero (op(zero, a) = zero). + + This is an abstract base class, concrete derived classes must declare + attributes zero and identity. All defining properties are then respected. + + Examples + ======== + + >>> from sympy import Integer + >>> from sympy.core.operations import LatticeOp + >>> class my_join(LatticeOp): + ... zero = Integer(0) + ... identity = Integer(1) + >>> my_join(2, 3) == my_join(3, 2) + True + >>> my_join(2, my_join(3, 4)) == my_join(2, 3, 4) + True + >>> my_join(0, 1, 4, 2, 3, 4) + 0 + >>> my_join(1, 2) + 2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Lattice_%28order%29 + """ + + is_commutative = True + + def __new__(cls, *args, **options): + args = (_sympify_(arg) for arg in args) + + try: + # /!\ args is a generator and _new_args_filter + # must be careful to handle as such; this + # is done so short-circuiting can be done + # without having to sympify all values + _args = frozenset(cls._new_args_filter(args)) + except ShortCircuit: + return sympify(cls.zero) + if not _args: + return sympify(cls.identity) + elif len(_args) == 1: + return set(_args).pop() + else: + # XXX in almost every other case for __new__, *_args is + # passed along, but the expectation here is for _args + obj = super(AssocOp, cls).__new__(cls, *ordered(_args)) + obj._argset = _args + return obj + + @classmethod + def _new_args_filter(cls, arg_sequence, call_cls=None): + """Generator filtering args""" + ncls = call_cls or cls + for arg in arg_sequence: + if arg == ncls.zero: + raise ShortCircuit(arg) + elif arg == ncls.identity: + continue + elif arg.func == ncls: + yield from arg.args + else: + yield arg + + @classmethod + def make_args(cls, expr): + """ + Return a set of args such that cls(*arg_set) == expr. + """ + if isinstance(expr, cls): + return expr._argset + else: + return frozenset([sympify(expr)]) + + +class AssocOpDispatcher: + """ + Handler dispatcher for associative operators + + .. notes:: + This approach is experimental, and can be replaced or deleted in the future. + See https://github.com/sympy/sympy/pull/19463. + + Explanation + =========== + + If arguments of different types are passed, the classes which handle the operation for each type + are collected. Then, a class which performs the operation is selected by recursive binary dispatching. + Dispatching relation can be registered by ``register_handlerclass`` method. + + Priority registration is unordered. You cannot make ``A*B`` and ``B*A`` refer to + different handler classes. All logic dealing with the order of arguments must be implemented + in the handler class. + + Examples + ======== + + >>> from sympy import Add, Expr, Symbol + >>> from sympy.core.add import add + + >>> class NewExpr(Expr): + ... @property + ... def _add_handler(self): + ... return NewAdd + >>> class NewAdd(NewExpr, Add): + ... pass + >>> add.register_handlerclass((Add, NewAdd), NewAdd) + + >>> a, b = Symbol('a'), NewExpr() + >>> add(a, b) == NewAdd(a, b) + True + + """ + def __init__(self, name, doc=None): + self.name = name + self.doc = doc + self.handlerattr = "_%s_handler" % name + self._handlergetter = attrgetter(self.handlerattr) + self._dispatcher = Dispatcher(name) + + def __repr__(self): + return "" % self.name + + def register_handlerclass(self, classes, typ, on_ambiguity=ambiguity_register_error_ignore_dup): + """ + Register the handler class for two classes, in both straight and reversed order. + + Paramteters + =========== + + classes : tuple of two types + Classes who are compared with each other. + + typ: + Class which is registered to represent *cls1* and *cls2*. + Handler method of *self* must be implemented in this class. + """ + if not len(classes) == 2: + raise RuntimeError( + "Only binary dispatch is supported, but got %s types: <%s>." % ( + len(classes), str_signature(classes) + )) + if len(set(classes)) == 1: + raise RuntimeError( + "Duplicate types <%s> cannot be dispatched." % str_signature(classes) + ) + self._dispatcher.add(tuple(classes), typ, on_ambiguity=on_ambiguity) + self._dispatcher.add(tuple(reversed(classes)), typ, on_ambiguity=on_ambiguity) + + @cacheit + def __call__(self, *args, _sympify=True, **kwargs): + """ + Parameters + ========== + + *args : + Arguments which are operated + """ + if _sympify: + args = tuple(map(_sympify_, args)) + handlers = frozenset(map(self._handlergetter, args)) + + # no need to sympify again + return self.dispatch(handlers)(*args, _sympify=False, **kwargs) + + @cacheit + def dispatch(self, handlers): + """ + Select the handler class, and return its handler method. + """ + + # Quick exit for the case where all handlers are same + if len(handlers) == 1: + h, = handlers + if not isinstance(h, type): + raise RuntimeError("Handler {!r} is not a type.".format(h)) + return h + + # Recursively select with registered binary priority + for i, typ in enumerate(handlers): + + if not isinstance(typ, type): + raise RuntimeError("Handler {!r} is not a type.".format(typ)) + + if i == 0: + handler = typ + else: + prev_handler = handler + handler = self._dispatcher.dispatch(prev_handler, typ) + + if not isinstance(handler, type): + raise RuntimeError( + "Dispatcher for {!r} and {!r} must return a type, but got {!r}".format( + prev_handler, typ, handler + )) + + # return handler class + return handler + + @property + def __doc__(self): + docs = [ + "Multiply dispatched associative operator: %s" % self.name, + "Note that support for this is experimental, see the docs for :class:`AssocOpDispatcher` for details" + ] + + if self.doc: + docs.append(self.doc) + + s = "Registered handler classes\n" + s += '=' * len(s) + docs.append(s) + + amb_sigs = [] + + typ_sigs = defaultdict(list) + for sigs in self._dispatcher.ordering[::-1]: + key = self._dispatcher.funcs[sigs] + typ_sigs[key].append(sigs) + + for typ, sigs in typ_sigs.items(): + + sigs_str = ', '.join('<%s>' % str_signature(sig) for sig in sigs) + + if isinstance(typ, RaiseNotImplementedError): + amb_sigs.append(sigs_str) + continue + + s = 'Inputs: %s\n' % sigs_str + s += '-' * len(s) + '\n' + s += typ.__name__ + docs.append(s) + + if amb_sigs: + s = "Ambiguous handler classes\n" + s += '=' * len(s) + docs.append(s) + + s = '\n'.join(amb_sigs) + docs.append(s) + + return '\n\n'.join(docs) diff --git a/lib/python3.11/site-packages/sympy/core/parameters.py b/lib/python3.11/site-packages/sympy/core/parameters.py new file mode 100644 index 0000000000000000000000000000000000000000..d911a3652bf02fa5b24c43b138035a57be687228 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/parameters.py @@ -0,0 +1,161 @@ +"""Thread-safe global parameters""" + +from .cache import clear_cache +from contextlib import contextmanager +from threading import local + +class _global_parameters(local): + """ + Thread-local global parameters. + + Explanation + =========== + + This class generates thread-local container for SymPy's global parameters. + Every global parameters must be passed as keyword argument when generating + its instance. + A variable, `global_parameters` is provided as default instance for this class. + + WARNING! Although the global parameters are thread-local, SymPy's cache is not + by now. + This may lead to undesired result in multi-threading operations. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.core.cache import clear_cache + >>> from sympy.core.parameters import global_parameters as gp + + >>> gp.evaluate + True + >>> x+x + 2*x + + >>> log = [] + >>> def f(): + ... clear_cache() + ... gp.evaluate = False + ... log.append(x+x) + ... clear_cache() + >>> import threading + >>> thread = threading.Thread(target=f) + >>> thread.start() + >>> thread.join() + + >>> print(log) + [x + x] + + >>> gp.evaluate + True + >>> x+x + 2*x + + References + ========== + + .. [1] https://docs.python.org/3/library/threading.html + + """ + def __init__(self, **kwargs): + self.__dict__.update(kwargs) + + def __setattr__(self, name, value): + if getattr(self, name) != value: + clear_cache() + return super().__setattr__(name, value) + +global_parameters = _global_parameters(evaluate=True, distribute=True, exp_is_pow=False) + +class evaluate: + """ Control automatic evaluation + + Explanation + =========== + + This context manager controls whether or not all SymPy functions evaluate + by default. + + Note that much of SymPy expects evaluated expressions. This functionality + is experimental and is unlikely to function as intended on large + expressions. + + Examples + ======== + + >>> from sympy import evaluate + >>> from sympy.abc import x + >>> print(x + x) + 2*x + >>> with evaluate(False): + ... print(x + x) + x + x + """ + def __init__(self, x): + self.x = x + self.old = [] + + def __enter__(self): + self.old.append(global_parameters.evaluate) + global_parameters.evaluate = self.x + + def __exit__(self, exc_type, exc_val, exc_tb): + global_parameters.evaluate = self.old.pop() + +@contextmanager +def distribute(x): + """ Control automatic distribution of Number over Add + + Explanation + =========== + + This context manager controls whether or not Mul distribute Number over + Add. Plan is to avoid distributing Number over Add in all of sympy. Once + that is done, this contextmanager will be removed. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.core.parameters import distribute + >>> print(2*(x + 1)) + 2*x + 2 + >>> with distribute(False): + ... print(2*(x + 1)) + 2*(x + 1) + """ + + old = global_parameters.distribute + + try: + global_parameters.distribute = x + yield + finally: + global_parameters.distribute = old + + +@contextmanager +def _exp_is_pow(x): + """ + Control whether `e^x` should be represented as ``exp(x)`` or a ``Pow(E, x)``. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.abc import x + >>> from sympy.core.parameters import _exp_is_pow + >>> with _exp_is_pow(True): print(type(exp(x))) + + >>> with _exp_is_pow(False): print(type(exp(x))) + exp + """ + old = global_parameters.exp_is_pow + + clear_cache() + try: + global_parameters.exp_is_pow = x + yield + finally: + clear_cache() + global_parameters.exp_is_pow = old diff --git a/lib/python3.11/site-packages/sympy/core/power.py b/lib/python3.11/site-packages/sympy/core/power.py new file mode 100644 index 0000000000000000000000000000000000000000..02eb307fd65598a6587ffabb52fc404f73622d5f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/power.py @@ -0,0 +1,1844 @@ +from __future__ import annotations +from typing import Callable +from itertools import product + +from .sympify import _sympify +from .cache import cacheit +from .singleton import S +from .expr import Expr +from .evalf import PrecisionExhausted +from .function import (expand_complex, expand_multinomial, + expand_mul, _mexpand, PoleError) +from .logic import fuzzy_bool, fuzzy_not, fuzzy_and, fuzzy_or +from .parameters import global_parameters +from .relational import is_gt, is_lt +from .kind import NumberKind, UndefinedKind +from sympy.utilities.iterables import sift +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.misc import as_int +from sympy.multipledispatch import Dispatcher + + +class Pow(Expr): + """ + Defines the expression x**y as "x raised to a power y" + + .. deprecated:: 1.7 + + Using arguments that aren't subclasses of :class:`~.Expr` in core + operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is + deprecated. See :ref:`non-expr-args-deprecated` for details. + + Singleton definitions involving (0, 1, -1, oo, -oo, I, -I): + + +--------------+---------+-----------------------------------------------+ + | expr | value | reason | + +==============+=========+===============================================+ + | z**0 | 1 | Although arguments over 0**0 exist, see [2]. | + +--------------+---------+-----------------------------------------------+ + | z**1 | z | | + +--------------+---------+-----------------------------------------------+ + | (-oo)**(-1) | 0 | | + +--------------+---------+-----------------------------------------------+ + | (-1)**-1 | -1 | | + +--------------+---------+-----------------------------------------------+ + | S.Zero**-1 | zoo | This is not strictly true, as 0**-1 may be | + | | | undefined, but is convenient in some contexts | + | | | where the base is assumed to be positive. | + +--------------+---------+-----------------------------------------------+ + | 1**-1 | 1 | | + +--------------+---------+-----------------------------------------------+ + | oo**-1 | 0 | | + +--------------+---------+-----------------------------------------------+ + | 0**oo | 0 | Because for all complex numbers z near | + | | | 0, z**oo -> 0. | + +--------------+---------+-----------------------------------------------+ + | 0**-oo | zoo | This is not strictly true, as 0**oo may be | + | | | oscillating between positive and negative | + | | | values or rotating in the complex plane. | + | | | It is convenient, however, when the base | + | | | is positive. | + +--------------+---------+-----------------------------------------------+ + | 1**oo | nan | Because there are various cases where | + | 1**-oo | | lim(x(t),t)=1, lim(y(t),t)=oo (or -oo), | + | | | but lim( x(t)**y(t), t) != 1. See [3]. | + +--------------+---------+-----------------------------------------------+ + | b**zoo | nan | Because b**z has no limit as z -> zoo | + +--------------+---------+-----------------------------------------------+ + | (-1)**oo | nan | Because of oscillations in the limit. | + | (-1)**(-oo) | | | + +--------------+---------+-----------------------------------------------+ + | oo**oo | oo | | + +--------------+---------+-----------------------------------------------+ + | oo**-oo | 0 | | + +--------------+---------+-----------------------------------------------+ + | (-oo)**oo | nan | | + | (-oo)**-oo | | | + +--------------+---------+-----------------------------------------------+ + | oo**I | nan | oo**e could probably be best thought of as | + | (-oo)**I | | the limit of x**e for real x as x tends to | + | | | oo. If e is I, then the limit does not exist | + | | | and nan is used to indicate that. | + +--------------+---------+-----------------------------------------------+ + | oo**(1+I) | zoo | If the real part of e is positive, then the | + | (-oo)**(1+I) | | limit of abs(x**e) is oo. So the limit value | + | | | is zoo. | + +--------------+---------+-----------------------------------------------+ + | oo**(-1+I) | 0 | If the real part of e is negative, then the | + | -oo**(-1+I) | | limit is 0. | + +--------------+---------+-----------------------------------------------+ + + Because symbolic computations are more flexible than floating point + calculations and we prefer to never return an incorrect answer, + we choose not to conform to all IEEE 754 conventions. This helps + us avoid extra test-case code in the calculation of limits. + + See Also + ======== + + sympy.core.numbers.Infinity + sympy.core.numbers.NegativeInfinity + sympy.core.numbers.NaN + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Exponentiation + .. [2] https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero + .. [3] https://en.wikipedia.org/wiki/Indeterminate_forms + + """ + is_Pow = True + + __slots__ = ('is_commutative',) + + args: tuple[Expr, Expr] + _args: tuple[Expr, Expr] + + @cacheit + def __new__(cls, b, e, evaluate=None): + if evaluate is None: + evaluate = global_parameters.evaluate + + b = _sympify(b) + e = _sympify(e) + + # XXX: This can be removed when non-Expr args are disallowed rather + # than deprecated. + from .relational import Relational + if isinstance(b, Relational) or isinstance(e, Relational): + raise TypeError('Relational cannot be used in Pow') + + # XXX: This should raise TypeError once deprecation period is over: + for arg in [b, e]: + if not isinstance(arg, Expr): + sympy_deprecation_warning( + f""" + Using non-Expr arguments in Pow is deprecated (in this case, one of the + arguments is of type {type(arg).__name__!r}). + + If you really did intend to construct a power with this base, use the ** + operator instead.""", + deprecated_since_version="1.7", + active_deprecations_target="non-expr-args-deprecated", + stacklevel=4, + ) + + if evaluate: + if e is S.ComplexInfinity: + return S.NaN + if e is S.Infinity: + if is_gt(b, S.One): + return S.Infinity + if is_gt(b, S.NegativeOne) and is_lt(b, S.One): + return S.Zero + if is_lt(b, S.NegativeOne): + if b.is_finite: + return S.ComplexInfinity + if b.is_finite is False: + return S.NaN + if e is S.Zero: + return S.One + elif e is S.One: + return b + elif e == -1 and not b: + return S.ComplexInfinity + elif e.__class__.__name__ == "AccumulationBounds": + if b == S.Exp1: + from sympy.calculus.accumulationbounds import AccumBounds + return AccumBounds(Pow(b, e.min), Pow(b, e.max)) + # autosimplification if base is a number and exp odd/even + # if base is Number then the base will end up positive; we + # do not do this with arbitrary expressions since symbolic + # cancellation might occur as in (x - 1)/(1 - x) -> -1. If + # we returned Piecewise((-1, Ne(x, 1))) for such cases then + # we could do this...but we don't + elif (e.is_Symbol and e.is_integer or e.is_Integer + ) and (b.is_number and b.is_Mul or b.is_Number + ) and b.could_extract_minus_sign(): + if e.is_even: + b = -b + elif e.is_odd: + return -Pow(-b, e) + if S.NaN in (b, e): # XXX S.NaN**x -> S.NaN under assumption that x != 0 + return S.NaN + elif b is S.One: + if abs(e).is_infinite: + return S.NaN + return S.One + else: + # recognize base as E + from sympy.functions.elementary.exponential import exp_polar + if not e.is_Atom and b is not S.Exp1 and not isinstance(b, exp_polar): + from .exprtools import factor_terms + from sympy.functions.elementary.exponential import log + from sympy.simplify.radsimp import fraction + c, ex = factor_terms(e, sign=False).as_coeff_Mul() + num, den = fraction(ex) + if isinstance(den, log) and den.args[0] == b: + return S.Exp1**(c*num) + elif den.is_Add: + from sympy.functions.elementary.complexes import sign, im + s = sign(im(b)) + if s.is_Number and s and den == \ + log(-factor_terms(b, sign=False)) + s*S.ImaginaryUnit*S.Pi: + return S.Exp1**(c*num) + + obj = b._eval_power(e) + if obj is not None: + return obj + obj = Expr.__new__(cls, b, e) + obj = cls._exec_constructor_postprocessors(obj) + if not isinstance(obj, Pow): + return obj + obj.is_commutative = (b.is_commutative and e.is_commutative) + return obj + + def inverse(self, argindex=1): + if self.base == S.Exp1: + from sympy.functions.elementary.exponential import log + return log + return None + + @property + def base(self) -> Expr: + return self._args[0] + + @property + def exp(self) -> Expr: + return self._args[1] + + @property + def kind(self): + if self.exp.kind is NumberKind: + return self.base.kind + else: + return UndefinedKind + + @classmethod + def class_key(cls): + return 3, 2, cls.__name__ + + def _eval_refine(self, assumptions): + from sympy.assumptions.ask import ask, Q + b, e = self.as_base_exp() + if ask(Q.integer(e), assumptions) and b.could_extract_minus_sign(): + if ask(Q.even(e), assumptions): + return Pow(-b, e) + elif ask(Q.odd(e), assumptions): + return -Pow(-b, e) + + def _eval_power(self, other): + b, e = self.as_base_exp() + if b is S.NaN: + return (b**e)**other # let __new__ handle it + + s = None + if other.is_integer: + s = 1 + elif b.is_polar: # e.g. exp_polar, besselj, var('p', polar=True)... + s = 1 + elif e.is_extended_real is not None: + from sympy.functions.elementary.complexes import arg, im, re, sign + from sympy.functions.elementary.exponential import exp, log + from sympy.functions.elementary.integers import floor + # helper functions =========================== + def _half(e): + """Return True if the exponent has a literal 2 as the + denominator, else None.""" + if getattr(e, 'q', None) == 2: + return True + n, d = e.as_numer_denom() + if n.is_integer and d == 2: + return True + def _n2(e): + """Return ``e`` evaluated to a Number with 2 significant + digits, else None.""" + try: + rv = e.evalf(2, strict=True) + if rv.is_Number: + return rv + except PrecisionExhausted: + pass + # =================================================== + if e.is_extended_real: + # we need _half(other) with constant floor or + # floor(S.Half - e*arg(b)/2/pi) == 0 + + + # handle -1 as special case + if e == -1: + # floor arg. is 1/2 + arg(b)/2/pi + if _half(other): + if b.is_negative is True: + return S.NegativeOne**other*Pow(-b, e*other) + elif b.is_negative is False: # XXX ok if im(b) != 0? + return Pow(b, -other) + elif e.is_even: + if b.is_extended_real: + b = abs(b) + if b.is_imaginary: + b = abs(im(b))*S.ImaginaryUnit + + if (abs(e) < 1) == True or e == 1: + s = 1 # floor = 0 + elif b.is_extended_nonnegative: + s = 1 # floor = 0 + elif re(b).is_extended_nonnegative and (abs(e) < 2) == True: + s = 1 # floor = 0 + elif _half(other): + s = exp(2*S.Pi*S.ImaginaryUnit*other*floor( + S.Half - e*arg(b)/(2*S.Pi))) + if s.is_extended_real and _n2(sign(s) - s) == 0: + s = sign(s) + else: + s = None + else: + # e.is_extended_real is False requires: + # _half(other) with constant floor or + # floor(S.Half - im(e*log(b))/2/pi) == 0 + try: + s = exp(2*S.ImaginaryUnit*S.Pi*other* + floor(S.Half - im(e*log(b))/2/S.Pi)) + # be careful to test that s is -1 or 1 b/c sign(I) == I: + # so check that s is real + if s.is_extended_real and _n2(sign(s) - s) == 0: + s = sign(s) + else: + s = None + except PrecisionExhausted: + s = None + + if s is not None: + return s*Pow(b, e*other) + + def _eval_Mod(self, q): + r"""A dispatched function to compute `b^e \bmod q`, dispatched + by ``Mod``. + + Notes + ===== + + Algorithms: + + 1. For unevaluated integer power, use built-in ``pow`` function + with 3 arguments, if powers are not too large wrt base. + + 2. For very large powers, use totient reduction if $e \ge \log(m)$. + Bound on m, is for safe factorization memory wise i.e. $m^{1/4}$. + For pollard-rho to be faster than built-in pow $\log(e) > m^{1/4}$ + check is added. + + 3. For any unevaluated power found in `b` or `e`, the step 2 + will be recursed down to the base and the exponent + such that the $b \bmod q$ becomes the new base and + $\phi(q) + e \bmod \phi(q)$ becomes the new exponent, and then + the computation for the reduced expression can be done. + """ + + base, exp = self.base, self.exp + + if exp.is_integer and exp.is_positive: + if q.is_integer and base % q == 0: + return S.Zero + + from sympy.functions.combinatorial.numbers import totient + + if base.is_Integer and exp.is_Integer and q.is_Integer: + b, e, m = int(base), int(exp), int(q) + mb = m.bit_length() + if mb <= 80 and e >= mb and e.bit_length()**4 >= m: + phi = int(totient(m)) + return Integer(pow(b, phi + e%phi, m)) + return Integer(pow(b, e, m)) + + from .mod import Mod + + if isinstance(base, Pow) and base.is_integer and base.is_number: + base = Mod(base, q) + return Mod(Pow(base, exp, evaluate=False), q) + + if isinstance(exp, Pow) and exp.is_integer and exp.is_number: + bit_length = int(q).bit_length() + # XXX Mod-Pow actually attempts to do a hanging evaluation + # if this dispatched function returns None. + # May need some fixes in the dispatcher itself. + if bit_length <= 80: + phi = totient(q) + exp = phi + Mod(exp, phi) + return Mod(Pow(base, exp, evaluate=False), q) + + def _eval_is_even(self): + if self.exp.is_integer and self.exp.is_positive: + return self.base.is_even + + def _eval_is_negative(self): + ext_neg = Pow._eval_is_extended_negative(self) + if ext_neg is True: + return self.is_finite + return ext_neg + + def _eval_is_extended_positive(self): + if self.base == self.exp: + if self.base.is_extended_nonnegative: + return True + elif self.base.is_positive: + if self.exp.is_real: + return True + elif self.base.is_extended_negative: + if self.exp.is_even: + return True + if self.exp.is_odd: + return False + elif self.base.is_zero: + if self.exp.is_extended_real: + return self.exp.is_zero + elif self.base.is_extended_nonpositive: + if self.exp.is_odd: + return False + elif self.base.is_imaginary: + if self.exp.is_integer: + m = self.exp % 4 + if m.is_zero: + return True + if m.is_integer and m.is_zero is False: + return False + if self.exp.is_imaginary: + from sympy.functions.elementary.exponential import log + return log(self.base).is_imaginary + + def _eval_is_extended_negative(self): + if self.exp is S.Half: + if self.base.is_complex or self.base.is_extended_real: + return False + if self.base.is_extended_negative: + if self.exp.is_odd and self.base.is_finite: + return True + if self.exp.is_even: + return False + elif self.base.is_extended_positive: + if self.exp.is_extended_real: + return False + elif self.base.is_zero: + if self.exp.is_extended_real: + return False + elif self.base.is_extended_nonnegative: + if self.exp.is_extended_nonnegative: + return False + elif self.base.is_extended_nonpositive: + if self.exp.is_even: + return False + elif self.base.is_extended_real: + if self.exp.is_even: + return False + + def _eval_is_zero(self): + if self.base.is_zero: + if self.exp.is_extended_positive: + return True + elif self.exp.is_extended_nonpositive: + return False + elif self.base == S.Exp1: + return self.exp is S.NegativeInfinity + elif self.base.is_zero is False: + if self.base.is_finite and self.exp.is_finite: + return False + elif self.exp.is_negative: + return self.base.is_infinite + elif self.exp.is_nonnegative: + return False + elif self.exp.is_infinite and self.exp.is_extended_real: + if (1 - abs(self.base)).is_extended_positive: + return self.exp.is_extended_positive + elif (1 - abs(self.base)).is_extended_negative: + return self.exp.is_extended_negative + elif self.base.is_finite and self.exp.is_negative: + # when self.base.is_zero is None + return False + + def _eval_is_integer(self): + b, e = self.args + if b.is_rational: + if b.is_integer is False and e.is_positive: + return False # rat**nonneg + if b.is_integer and e.is_integer: + if b is S.NegativeOne: + return True + if e.is_nonnegative or e.is_positive: + return True + if b.is_integer and e.is_negative and (e.is_finite or e.is_integer): + if fuzzy_not((b - 1).is_zero) and fuzzy_not((b + 1).is_zero): + return False + if b.is_Number and e.is_Number: + check = self.func(*self.args) + return check.is_Integer + if e.is_negative and b.is_positive and (b - 1).is_positive: + return False + if e.is_negative and b.is_negative and (b + 1).is_negative: + return False + + def _eval_is_extended_real(self): + if self.base is S.Exp1: + if self.exp.is_extended_real: + return True + elif self.exp.is_imaginary: + return (2*S.ImaginaryUnit*self.exp/S.Pi).is_even + + from sympy.functions.elementary.exponential import log, exp + real_b = self.base.is_extended_real + if real_b is None: + if self.base.func == exp and self.base.exp.is_imaginary: + return self.exp.is_imaginary + if self.base.func == Pow and self.base.base is S.Exp1 and self.base.exp.is_imaginary: + return self.exp.is_imaginary + return + real_e = self.exp.is_extended_real + if real_e is None: + return + if real_b and real_e: + if self.base.is_extended_positive: + return True + elif self.base.is_extended_nonnegative and self.exp.is_extended_nonnegative: + return True + elif self.exp.is_integer and self.base.is_extended_nonzero: + return True + elif self.exp.is_integer and self.exp.is_nonnegative: + return True + elif self.base.is_extended_negative: + if self.exp.is_Rational: + return False + if real_e and self.exp.is_extended_negative and self.base.is_zero is False: + return Pow(self.base, -self.exp).is_extended_real + im_b = self.base.is_imaginary + im_e = self.exp.is_imaginary + if im_b: + if self.exp.is_integer: + if self.exp.is_even: + return True + elif self.exp.is_odd: + return False + elif im_e and log(self.base).is_imaginary: + return True + elif self.exp.is_Add: + c, a = self.exp.as_coeff_Add() + if c and c.is_Integer: + return Mul( + self.base**c, self.base**a, evaluate=False).is_extended_real + elif self.base in (-S.ImaginaryUnit, S.ImaginaryUnit): + if (self.exp/2).is_integer is False: + return False + if real_b and im_e: + if self.base is S.NegativeOne: + return True + c = self.exp.coeff(S.ImaginaryUnit) + if c: + if self.base.is_rational and c.is_rational: + if self.base.is_nonzero and (self.base - 1).is_nonzero and c.is_nonzero: + return False + ok = (c*log(self.base)/S.Pi).is_integer + if ok is not None: + return ok + + if real_b is False and real_e: # we already know it's not imag + if isinstance(self.exp, Rational) and self.exp.p == 1: + return False + from sympy.functions.elementary.complexes import arg + i = arg(self.base)*self.exp/S.Pi + if i.is_complex: # finite + return i.is_integer + + def _eval_is_complex(self): + + if self.base == S.Exp1: + return fuzzy_or([self.exp.is_complex, self.exp.is_extended_negative]) + + if all(a.is_complex for a in self.args) and self._eval_is_finite(): + return True + + def _eval_is_imaginary(self): + if self.base.is_commutative is False: + return False + + if self.base.is_imaginary: + if self.exp.is_integer: + odd = self.exp.is_odd + if odd is not None: + return odd + return + + if self.base == S.Exp1: + f = 2 * self.exp / (S.Pi*S.ImaginaryUnit) + # exp(pi*integer) = 1 or -1, so not imaginary + if f.is_even: + return False + # exp(pi*integer + pi/2) = I or -I, so it is imaginary + if f.is_odd: + return True + return None + + if self.exp.is_imaginary: + from sympy.functions.elementary.exponential import log + imlog = log(self.base).is_imaginary + if imlog is not None: + return False # I**i -> real; (2*I)**i -> complex ==> not imaginary + + if self.base.is_extended_real and self.exp.is_extended_real: + if self.base.is_positive: + return False + else: + rat = self.exp.is_rational + if not rat: + return rat + if self.exp.is_integer: + return False + else: + half = (2*self.exp).is_integer + if half: + return self.base.is_negative + return half + + if self.base.is_extended_real is False: # we already know it's not imag + from sympy.functions.elementary.complexes import arg + i = arg(self.base)*self.exp/S.Pi + isodd = (2*i).is_odd + if isodd is not None: + return isodd + + def _eval_is_odd(self): + if self.exp.is_integer: + if self.exp.is_positive: + return self.base.is_odd + elif self.exp.is_nonnegative and self.base.is_odd: + return True + elif self.base is S.NegativeOne: + return True + + def _eval_is_finite(self): + if self.exp.is_negative: + if self.base.is_zero: + return False + if self.base.is_infinite or self.base.is_nonzero: + return True + c1 = self.base.is_finite + if c1 is None: + return + c2 = self.exp.is_finite + if c2 is None: + return + if c1 and c2: + if self.exp.is_nonnegative or fuzzy_not(self.base.is_zero): + return True + + def _eval_is_prime(self): + ''' + An integer raised to the n(>=2)-th power cannot be a prime. + ''' + if self.base.is_integer and self.exp.is_integer and (self.exp - 1).is_positive: + return False + + def _eval_is_composite(self): + """ + A power is composite if both base and exponent are greater than 1 + """ + if (self.base.is_integer and self.exp.is_integer and + ((self.base - 1).is_positive and (self.exp - 1).is_positive or + (self.base + 1).is_negative and self.exp.is_positive and self.exp.is_even)): + return True + + def _eval_is_polar(self): + return self.base.is_polar + + def _eval_subs(self, old, new): + from sympy.calculus.accumulationbounds import AccumBounds + + if isinstance(self.exp, AccumBounds): + b = self.base.subs(old, new) + e = self.exp.subs(old, new) + if isinstance(e, AccumBounds): + return e.__rpow__(b) + return self.func(b, e) + + from sympy.functions.elementary.exponential import exp, log + + def _check(ct1, ct2, old): + """Return (bool, pow, remainder_pow) where, if bool is True, then the + exponent of Pow `old` will combine with `pow` so the substitution + is valid, otherwise bool will be False. + + For noncommutative objects, `pow` will be an integer, and a factor + `Pow(old.base, remainder_pow)` needs to be included. If there is + no such factor, None is returned. For commutative objects, + remainder_pow is always None. + + cti are the coefficient and terms of an exponent of self or old + In this _eval_subs routine a change like (b**(2*x)).subs(b**x, y) + will give y**2 since (b**x)**2 == b**(2*x); if that equality does + not hold then the substitution should not occur so `bool` will be + False. + + """ + coeff1, terms1 = ct1 + coeff2, terms2 = ct2 + if terms1 == terms2: + if old.is_commutative: + # Allow fractional powers for commutative objects + pow = coeff1/coeff2 + try: + as_int(pow, strict=False) + combines = True + except ValueError: + b, e = old.as_base_exp() + # These conditions ensure that (b**e)**f == b**(e*f) for any f + combines = b.is_positive and e.is_real or b.is_nonnegative and e.is_nonnegative + + return combines, pow, None + else: + # With noncommutative symbols, substitute only integer powers + if not isinstance(terms1, tuple): + terms1 = (terms1,) + if not all(term.is_integer for term in terms1): + return False, None, None + + try: + # Round pow toward zero + pow, remainder = divmod(as_int(coeff1), as_int(coeff2)) + if pow < 0 and remainder != 0: + pow += 1 + remainder -= as_int(coeff2) + + if remainder == 0: + remainder_pow = None + else: + remainder_pow = Mul(remainder, *terms1) + + return True, pow, remainder_pow + except ValueError: + # Can't substitute + pass + + return False, None, None + + if old == self.base or (old == exp and self.base == S.Exp1): + if new.is_Function and isinstance(new, Callable): + return new(self.exp._subs(old, new)) + else: + return new**self.exp._subs(old, new) + + # issue 10829: (4**x - 3*y + 2).subs(2**x, y) -> y**2 - 3*y + 2 + if isinstance(old, self.func) and self.exp == old.exp: + l = log(self.base, old.base) + if l.is_Number: + return Pow(new, l) + + if isinstance(old, self.func) and self.base == old.base: + if self.exp.is_Add is False: + ct1 = self.exp.as_independent(Symbol, as_Add=False) + ct2 = old.exp.as_independent(Symbol, as_Add=False) + ok, pow, remainder_pow = _check(ct1, ct2, old) + if ok: + # issue 5180: (x**(6*y)).subs(x**(3*y),z)->z**2 + result = self.func(new, pow) + if remainder_pow is not None: + result = Mul(result, Pow(old.base, remainder_pow)) + return result + else: # b**(6*x + a).subs(b**(3*x), y) -> y**2 * b**a + # exp(exp(x) + exp(x**2)).subs(exp(exp(x)), w) -> w * exp(exp(x**2)) + oarg = old.exp + new_l = [] + o_al = [] + ct2 = oarg.as_coeff_mul() + for a in self.exp.args: + newa = a._subs(old, new) + ct1 = newa.as_coeff_mul() + ok, pow, remainder_pow = _check(ct1, ct2, old) + if ok: + new_l.append(new**pow) + if remainder_pow is not None: + o_al.append(remainder_pow) + continue + elif not old.is_commutative and not newa.is_integer: + # If any term in the exponent is non-integer, + # we do not do any substitutions in the noncommutative case + return + o_al.append(newa) + if new_l: + expo = Add(*o_al) + new_l.append(Pow(self.base, expo, evaluate=False) if expo != 1 else self.base) + return Mul(*new_l) + + if (isinstance(old, exp) or (old.is_Pow and old.base is S.Exp1)) and self.exp.is_extended_real and self.base.is_positive: + ct1 = old.exp.as_independent(Symbol, as_Add=False) + ct2 = (self.exp*log(self.base)).as_independent( + Symbol, as_Add=False) + ok, pow, remainder_pow = _check(ct1, ct2, old) + if ok: + result = self.func(new, pow) # (2**x).subs(exp(x*log(2)), z) -> z + if remainder_pow is not None: + result = Mul(result, Pow(old.base, remainder_pow)) + return result + + def as_base_exp(self): + """Return base and exp of self. + + Explanation + =========== + + If base a Rational less than 1, then return 1/Rational, -exp. + If this extra processing is not needed, the base and exp + properties will give the raw arguments. + + Examples + ======== + + >>> from sympy import Pow, S + >>> p = Pow(S.Half, 2, evaluate=False) + >>> p.as_base_exp() + (2, -2) + >>> p.args + (1/2, 2) + >>> p.base, p.exp + (1/2, 2) + + """ + + b, e = self.args + if b.is_Rational and b.p < b.q and b.p > 0: + return 1/b, -e + return b, e + + def _eval_adjoint(self): + from sympy.functions.elementary.complexes import adjoint + i, p = self.exp.is_integer, self.base.is_positive + if i: + return adjoint(self.base)**self.exp + if p: + return self.base**adjoint(self.exp) + if i is False and p is False: + expanded = expand_complex(self) + if expanded != self: + return adjoint(expanded) + + def _eval_conjugate(self): + from sympy.functions.elementary.complexes import conjugate as c + i, p = self.exp.is_integer, self.base.is_positive + if i: + return c(self.base)**self.exp + if p: + return self.base**c(self.exp) + if i is False and p is False: + expanded = expand_complex(self) + if expanded != self: + return c(expanded) + if self.is_extended_real: + return self + + def _eval_transpose(self): + from sympy.functions.elementary.complexes import transpose + if self.base == S.Exp1: + return self.func(S.Exp1, self.exp.transpose()) + i, p = self.exp.is_integer, (self.base.is_complex or self.base.is_infinite) + if p: + return self.base**self.exp + if i: + return transpose(self.base)**self.exp + if i is False and p is False: + expanded = expand_complex(self) + if expanded != self: + return transpose(expanded) + + def _eval_expand_power_exp(self, **hints): + """a**(n + m) -> a**n*a**m""" + b = self.base + e = self.exp + if b == S.Exp1: + from sympy.concrete.summations import Sum + if isinstance(e, Sum) and e.is_commutative: + from sympy.concrete.products import Product + return Product(self.func(b, e.function), *e.limits) + if e.is_Add and (hints.get('force', False) or + b.is_zero is False or e._all_nonneg_or_nonppos()): + if e.is_commutative: + return Mul(*[self.func(b, x) for x in e.args]) + if b.is_commutative: + c, nc = sift(e.args, lambda x: x.is_commutative, binary=True) + if c: + return Mul(*[self.func(b, x) for x in c] + )*b**Add._from_args(nc) + return self + + def _eval_expand_power_base(self, **hints): + """(a*b)**n -> a**n * b**n""" + force = hints.get('force', False) + + b = self.base + e = self.exp + if not b.is_Mul: + return self + + cargs, nc = b.args_cnc(split_1=False) + + # expand each term - this is top-level-only + # expansion but we have to watch out for things + # that don't have an _eval_expand method + if nc: + nc = [i._eval_expand_power_base(**hints) + if hasattr(i, '_eval_expand_power_base') else i + for i in nc] + + if e.is_Integer: + if e.is_positive: + rv = Mul(*nc*e) + else: + rv = Mul(*[i**-1 for i in nc[::-1]]*-e) + if cargs: + rv *= Mul(*cargs)**e + return rv + + if not cargs: + return self.func(Mul(*nc), e, evaluate=False) + + nc = [Mul(*nc)] + + # sift the commutative bases + other, maybe_real = sift(cargs, lambda x: x.is_extended_real is False, + binary=True) + def pred(x): + if x is S.ImaginaryUnit: + return S.ImaginaryUnit + polar = x.is_polar + if polar: + return True + if polar is None: + return fuzzy_bool(x.is_extended_nonnegative) + sifted = sift(maybe_real, pred) + nonneg = sifted[True] + other += sifted[None] + neg = sifted[False] + imag = sifted[S.ImaginaryUnit] + if imag: + I = S.ImaginaryUnit + i = len(imag) % 4 + if i == 0: + pass + elif i == 1: + other.append(I) + elif i == 2: + if neg: + nonn = -neg.pop() + if nonn is not S.One: + nonneg.append(nonn) + else: + neg.append(S.NegativeOne) + else: + if neg: + nonn = -neg.pop() + if nonn is not S.One: + nonneg.append(nonn) + else: + neg.append(S.NegativeOne) + other.append(I) + del imag + + # bring out the bases that can be separated from the base + + if force or e.is_integer: + # treat all commutatives the same and put nc in other + cargs = nonneg + neg + other + other = nc + else: + # this is just like what is happening automatically, except + # that now we are doing it for an arbitrary exponent for which + # no automatic expansion is done + + assert not e.is_Integer + + # handle negatives by making them all positive and putting + # the residual -1 in other + if len(neg) > 1: + o = S.One + if not other and neg[0].is_Number: + o *= neg.pop(0) + if len(neg) % 2: + o = -o + for n in neg: + nonneg.append(-n) + if o is not S.One: + other.append(o) + elif neg and other: + if neg[0].is_Number and neg[0] is not S.NegativeOne: + other.append(S.NegativeOne) + nonneg.append(-neg[0]) + else: + other.extend(neg) + else: + other.extend(neg) + del neg + + cargs = nonneg + other += nc + + rv = S.One + if cargs: + if e.is_Rational: + npow, cargs = sift(cargs, lambda x: x.is_Pow and + x.exp.is_Rational and x.base.is_number, + binary=True) + rv = Mul(*[self.func(b.func(*b.args), e) for b in npow]) + rv *= Mul(*[self.func(b, e, evaluate=False) for b in cargs]) + if other: + rv *= self.func(Mul(*other), e, evaluate=False) + return rv + + def _eval_expand_multinomial(self, **hints): + """(a + b + ..)**n -> a**n + n*a**(n-1)*b + .., n is nonzero integer""" + + base, exp = self.args + result = self + + if exp.is_Rational and exp.p > 0 and base.is_Add: + if not exp.is_Integer: + n = Integer(exp.p // exp.q) + + if not n: + return result + else: + radical, result = self.func(base, exp - n), [] + + expanded_base_n = self.func(base, n) + if expanded_base_n.is_Pow: + expanded_base_n = \ + expanded_base_n._eval_expand_multinomial() + for term in Add.make_args(expanded_base_n): + result.append(term*radical) + + return Add(*result) + + n = int(exp) + + if base.is_commutative: + order_terms, other_terms = [], [] + + for b in base.args: + if b.is_Order: + order_terms.append(b) + else: + other_terms.append(b) + + if order_terms: + # (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n) + f = Add(*other_terms) + o = Add(*order_terms) + + if n == 2: + return expand_multinomial(f**n, deep=False) + n*f*o + else: + g = expand_multinomial(f**(n - 1), deep=False) + return expand_mul(f*g, deep=False) + n*g*o + + if base.is_number: + # Efficiently expand expressions of the form (a + b*I)**n + # where 'a' and 'b' are real numbers and 'n' is integer. + a, b = base.as_real_imag() + + if a.is_Rational and b.is_Rational: + if not a.is_Integer: + if not b.is_Integer: + k = self.func(a.q * b.q, n) + a, b = a.p*b.q, a.q*b.p + else: + k = self.func(a.q, n) + a, b = a.p, a.q*b + elif not b.is_Integer: + k = self.func(b.q, n) + a, b = a*b.q, b.p + else: + k = 1 + + a, b, c, d = int(a), int(b), 1, 0 + + while n: + if n & 1: + c, d = a*c - b*d, b*c + a*d + n -= 1 + a, b = a*a - b*b, 2*a*b + n //= 2 + + I = S.ImaginaryUnit + + if k == 1: + return c + I*d + else: + return Integer(c)/k + I*d/k + + p = other_terms + # (x + y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3 + # in this particular example: + # p = [x,y]; n = 3 + # so now it's easy to get the correct result -- we get the + # coefficients first: + from sympy.ntheory.multinomial import multinomial_coefficients + from sympy.polys.polyutils import basic_from_dict + expansion_dict = multinomial_coefficients(len(p), n) + # in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3} + # and now construct the expression. + return basic_from_dict(expansion_dict, *p) + else: + if n == 2: + return Add(*[f*g for f in base.args for g in base.args]) + else: + multi = (base**(n - 1))._eval_expand_multinomial() + if multi.is_Add: + return Add(*[f*g for f in base.args + for g in multi.args]) + else: + # XXX can this ever happen if base was an Add? + return Add(*[f*multi for f in base.args]) + elif (exp.is_Rational and exp.p < 0 and base.is_Add and + abs(exp.p) > exp.q): + return 1 / self.func(base, -exp)._eval_expand_multinomial() + elif exp.is_Add and base.is_Number and (hints.get('force', False) or + base.is_zero is False or exp._all_nonneg_or_nonppos()): + # a + b a b + # n --> n n, where n, a, b are Numbers + # XXX should be in expand_power_exp? + coeff, tail = [], [] + for term in exp.args: + if term.is_Number: + coeff.append(self.func(base, term)) + else: + tail.append(term) + return Mul(*(coeff + [self.func(base, Add._from_args(tail))])) + else: + return result + + def as_real_imag(self, deep=True, **hints): + if self.exp.is_Integer: + from sympy.polys.polytools import poly + + exp = self.exp + re_e, im_e = self.base.as_real_imag(deep=deep) + if not im_e: + return self, S.Zero + a, b = symbols('a b', cls=Dummy) + if exp >= 0: + if re_e.is_Number and im_e.is_Number: + # We can be more efficient in this case + expr = expand_multinomial(self.base**exp) + if expr != self: + return expr.as_real_imag() + + expr = poly( + (a + b)**exp) # a = re, b = im; expr = (a + b*I)**exp + else: + mag = re_e**2 + im_e**2 + re_e, im_e = re_e/mag, -im_e/mag + if re_e.is_Number and im_e.is_Number: + # We can be more efficient in this case + expr = expand_multinomial((re_e + im_e*S.ImaginaryUnit)**-exp) + if expr != self: + return expr.as_real_imag() + + expr = poly((a + b)**-exp) + + # Terms with even b powers will be real + r = [i for i in expr.terms() if not i[0][1] % 2] + re_part = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r]) + # Terms with odd b powers will be imaginary + r = [i for i in expr.terms() if i[0][1] % 4 == 1] + im_part1 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r]) + r = [i for i in expr.terms() if i[0][1] % 4 == 3] + im_part3 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r]) + + return (re_part.subs({a: re_e, b: S.ImaginaryUnit*im_e}), + im_part1.subs({a: re_e, b: im_e}) + im_part3.subs({a: re_e, b: -im_e})) + + from sympy.functions.elementary.trigonometric import atan2, cos, sin + + if self.exp.is_Rational: + re_e, im_e = self.base.as_real_imag(deep=deep) + + if im_e.is_zero and self.exp is S.Half: + if re_e.is_extended_nonnegative: + return self, S.Zero + if re_e.is_extended_nonpositive: + return S.Zero, (-self.base)**self.exp + + # XXX: This is not totally correct since for x**(p/q) with + # x being imaginary there are actually q roots, but + # only a single one is returned from here. + r = self.func(self.func(re_e, 2) + self.func(im_e, 2), S.Half) + + t = atan2(im_e, re_e) + + rp, tp = self.func(r, self.exp), t*self.exp + + return rp*cos(tp), rp*sin(tp) + elif self.base is S.Exp1: + from sympy.functions.elementary.exponential import exp + re_e, im_e = self.exp.as_real_imag() + if deep: + re_e = re_e.expand(deep, **hints) + im_e = im_e.expand(deep, **hints) + c, s = cos(im_e), sin(im_e) + return exp(re_e)*c, exp(re_e)*s + else: + from sympy.functions.elementary.complexes import im, re + if deep: + hints['complex'] = False + + expanded = self.expand(deep, **hints) + if hints.get('ignore') == expanded: + return None + else: + return (re(expanded), im(expanded)) + else: + return re(self), im(self) + + def _eval_derivative(self, s): + from sympy.functions.elementary.exponential import log + dbase = self.base.diff(s) + dexp = self.exp.diff(s) + return self * (dexp * log(self.base) + dbase * self.exp/self.base) + + def _eval_evalf(self, prec): + base, exp = self.as_base_exp() + if base == S.Exp1: + # Use mpmath function associated to class "exp": + from sympy.functions.elementary.exponential import exp as exp_function + return exp_function(self.exp, evaluate=False)._eval_evalf(prec) + base = base._evalf(prec) + if not exp.is_Integer: + exp = exp._evalf(prec) + if exp.is_negative and base.is_number and base.is_extended_real is False: + base = base.conjugate() / (base * base.conjugate())._evalf(prec) + exp = -exp + return self.func(base, exp).expand() + return self.func(base, exp) + + def _eval_is_polynomial(self, syms): + if self.exp.has(*syms): + return False + + if self.base.has(*syms): + return bool(self.base._eval_is_polynomial(syms) and + self.exp.is_Integer and (self.exp >= 0)) + else: + return True + + def _eval_is_rational(self): + # The evaluation of self.func below can be very expensive in the case + # of integer**integer if the exponent is large. We should try to exit + # before that if possible: + if (self.exp.is_integer and self.base.is_rational + and fuzzy_not(fuzzy_and([self.exp.is_negative, self.base.is_zero]))): + return True + p = self.func(*self.as_base_exp()) # in case it's unevaluated + if not p.is_Pow: + return p.is_rational + b, e = p.as_base_exp() + if e.is_Rational and b.is_Rational: + # we didn't check that e is not an Integer + # because Rational**Integer autosimplifies + return False + if e.is_integer: + if b.is_rational: + if fuzzy_not(b.is_zero) or e.is_nonnegative: + return True + if b == e: # always rational, even for 0**0 + return True + elif b.is_irrational: + return e.is_zero + if b is S.Exp1: + if e.is_rational and e.is_nonzero: + return False + + def _eval_is_algebraic(self): + def _is_one(expr): + try: + return (expr - 1).is_zero + except ValueError: + # when the operation is not allowed + return False + + if self.base.is_zero or _is_one(self.base): + return True + elif self.base is S.Exp1: + s = self.func(*self.args) + if s.func == self.func: + if self.exp.is_nonzero: + if self.exp.is_algebraic: + return False + elif (self.exp/S.Pi).is_rational: + return False + elif (self.exp/(S.ImaginaryUnit*S.Pi)).is_rational: + return True + else: + return s.is_algebraic + elif self.exp.is_rational: + if self.base.is_algebraic is False: + return self.exp.is_zero + if self.base.is_zero is False: + if self.exp.is_nonzero: + return self.base.is_algebraic + elif self.base.is_algebraic: + return True + if self.exp.is_positive: + return self.base.is_algebraic + elif self.base.is_algebraic and self.exp.is_algebraic: + if ((fuzzy_not(self.base.is_zero) + and fuzzy_not(_is_one(self.base))) + or self.base.is_integer is False + or self.base.is_irrational): + return self.exp.is_rational + + def _eval_is_rational_function(self, syms): + if self.exp.has(*syms): + return False + + if self.base.has(*syms): + return self.base._eval_is_rational_function(syms) and \ + self.exp.is_Integer + else: + return True + + def _eval_is_meromorphic(self, x, a): + # f**g is meromorphic if g is an integer and f is meromorphic. + # E**(log(f)*g) is meromorphic if log(f)*g is meromorphic + # and finite. + base_merom = self.base._eval_is_meromorphic(x, a) + exp_integer = self.exp.is_Integer + if exp_integer: + return base_merom + + exp_merom = self.exp._eval_is_meromorphic(x, a) + if base_merom is False: + # f**g = E**(log(f)*g) may be meromorphic if the + # singularities of log(f) and g cancel each other, + # for example, if g = 1/log(f). Hence, + return False if exp_merom else None + elif base_merom is None: + return None + + b = self.base.subs(x, a) + # b is extended complex as base is meromorphic. + # log(base) is finite and meromorphic when b != 0, zoo. + b_zero = b.is_zero + if b_zero: + log_defined = False + else: + log_defined = fuzzy_and((b.is_finite, fuzzy_not(b_zero))) + + if log_defined is False: # zero or pole of base + return exp_integer # False or None + elif log_defined is None: + return None + + if not exp_merom: + return exp_merom # False or None + + return self.exp.subs(x, a).is_finite + + def _eval_is_algebraic_expr(self, syms): + if self.exp.has(*syms): + return False + + if self.base.has(*syms): + return self.base._eval_is_algebraic_expr(syms) and \ + self.exp.is_Rational + else: + return True + + def _eval_rewrite_as_exp(self, base, expo, **kwargs): + from sympy.functions.elementary.exponential import exp, log + + if base.is_zero or base.has(exp) or expo.has(exp): + return base**expo + + evaluate = expo.has(Symbol) + + if base.has(Symbol): + # delay evaluation if expo is non symbolic + # (as exp(x*log(5)) automatically reduces to x**5) + if global_parameters.exp_is_pow: + return Pow(S.Exp1, log(base)*expo, evaluate=evaluate) + else: + return exp(log(base)*expo, evaluate=evaluate) + + else: + from sympy.functions.elementary.complexes import arg, Abs + return exp((log(Abs(base)) + S.ImaginaryUnit*arg(base))*expo) + + def as_numer_denom(self): + if not self.is_commutative: + return self, S.One + base, exp = self.as_base_exp() + n, d = base.as_numer_denom() + # this should be the same as ExpBase.as_numer_denom wrt + # exponent handling + neg_exp = exp.is_negative + if exp.is_Mul and not neg_exp and not exp.is_positive: + neg_exp = exp.could_extract_minus_sign() + int_exp = exp.is_integer + # the denominator cannot be separated from the numerator if + # its sign is unknown unless the exponent is an integer, e.g. + # sqrt(a/b) != sqrt(a)/sqrt(b) when a=1 and b=-1. But if the + # denominator is negative the numerator and denominator can + # be negated and the denominator (now positive) separated. + if not (d.is_extended_real or int_exp): + n = base + d = S.One + dnonpos = d.is_nonpositive + if dnonpos: + n, d = -n, -d + elif dnonpos is None and not int_exp: + n = base + d = S.One + if neg_exp: + n, d = d, n + exp = -exp + if exp.is_infinite: + if n is S.One and d is not S.One: + return n, self.func(d, exp) + if n is not S.One and d is S.One: + return self.func(n, exp), d + return self.func(n, exp), self.func(d, exp) + + def matches(self, expr, repl_dict=None, old=False): + expr = _sympify(expr) + if repl_dict is None: + repl_dict = {} + + # special case, pattern = 1 and expr.exp can match to 0 + if expr is S.One: + d = self.exp.matches(S.Zero, repl_dict) + if d is not None: + return d + + # make sure the expression to be matched is an Expr + if not isinstance(expr, Expr): + return None + + b, e = expr.as_base_exp() + + # special case number + sb, se = self.as_base_exp() + if sb.is_Symbol and se.is_Integer and expr: + if e.is_rational: + return sb.matches(b**(e/se), repl_dict) + return sb.matches(expr**(1/se), repl_dict) + + d = repl_dict.copy() + d = self.base.matches(b, d) + if d is None: + return None + + d = self.exp.xreplace(d).matches(e, d) + if d is None: + return Expr.matches(self, expr, repl_dict) + return d + + def _eval_nseries(self, x, n, logx, cdir=0): + # NOTE! This function is an important part of the gruntz algorithm + # for computing limits. It has to return a generalized power + # series with coefficients in C(log, log(x)). In more detail: + # It has to return an expression + # c_0*x**e_0 + c_1*x**e_1 + ... (finitely many terms) + # where e_i are numbers (not necessarily integers) and c_i are + # expressions involving only numbers, the log function, and log(x). + # The series expansion of b**e is computed as follows: + # 1) We express b as f*(1 + g) where f is the leading term of b. + # g has order O(x**d) where d is strictly positive. + # 2) Then b**e = (f**e)*((1 + g)**e). + # (1 + g)**e is computed using binomial series. + from sympy.functions.elementary.exponential import exp, log + from sympy.series.limits import limit + from sympy.series.order import Order + from sympy.core.sympify import sympify + if self.base is S.Exp1: + e_series = self.exp.nseries(x, n=n, logx=logx) + if e_series.is_Order: + return 1 + e_series + e0 = limit(e_series.removeO(), x, 0) + if e0 is S.NegativeInfinity: + return Order(x**n, x) + if e0 is S.Infinity: + return self + t = e_series - e0 + exp_series = term = exp(e0) + # series of exp(e0 + t) in t + for i in range(1, n): + term *= t/i + term = term.nseries(x, n=n, logx=logx) + exp_series += term + exp_series += Order(t**n, x) + from sympy.simplify.powsimp import powsimp + return powsimp(exp_series, deep=True, combine='exp') + from sympy.simplify.powsimp import powdenest + from .numbers import _illegal + self = powdenest(self, force=True).trigsimp() + b, e = self.as_base_exp() + + if e.has(*_illegal): + raise PoleError() + + if e.has(x): + return exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir) + + if logx is not None and b.has(log): + from .symbol import Wild + c, ex = symbols('c, ex', cls=Wild, exclude=[x]) + b = b.replace(log(c*x**ex), log(c) + ex*logx) + self = b**e + + b = b.removeO() + try: + from sympy.functions.special.gamma_functions import polygamma + if b.has(polygamma, S.EulerGamma) and logx is not None: + raise ValueError() + _, m = b.leadterm(x) + except (ValueError, NotImplementedError, PoleError): + b = b._eval_nseries(x, n=max(2, n), logx=logx, cdir=cdir).removeO() + if b.has(S.NaN, S.ComplexInfinity): + raise NotImplementedError() + _, m = b.leadterm(x) + + if e.has(log): + from sympy.simplify.simplify import logcombine + e = logcombine(e).cancel() + + if not (m.is_zero or e.is_number and e.is_real): + if self == self._eval_as_leading_term(x, logx=logx, cdir=cdir): + res = exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir) + if res == exp(e*log(b)): + return self + return res + + f = b.as_leading_term(x, logx=logx) + g = (b/f - S.One).cancel(expand=False) + if not m.is_number: + raise NotImplementedError() + maxpow = n - m*e + if maxpow.has(Symbol): + maxpow = sympify(n) + + if maxpow.is_negative: + return Order(x**(m*e), x) + + if g.is_zero: + r = f**e + if r != self: + r += Order(x**n, x) + return r + + def coeff_exp(term, x): + coeff, exp = S.One, S.Zero + for factor in Mul.make_args(term): + if factor.has(x): + base, exp = factor.as_base_exp() + if base != x: + try: + return term.leadterm(x) + except ValueError: + return term, S.Zero + else: + coeff *= factor + return coeff, exp + + def mul(d1, d2): + res = {} + for e1, e2 in product(d1, d2): + ex = e1 + e2 + if ex < maxpow: + res[ex] = res.get(ex, S.Zero) + d1[e1]*d2[e2] + return res + + try: + c, d = g.leadterm(x, logx=logx) + except (ValueError, NotImplementedError): + if limit(g/x**maxpow, x, 0) == 0: + # g has higher order zero + return f**e + e*f**e*g # first term of binomial series + else: + raise NotImplementedError() + if c.is_Float and d == S.Zero: + # Convert floats like 0.5 to exact SymPy numbers like S.Half, to + # prevent rounding errors which can induce wrong values of d leading + # to a NotImplementedError being returned from the block below. + from sympy.simplify.simplify import nsimplify + _, d = nsimplify(g).leadterm(x, logx=logx) + if not d.is_positive: + g = g.simplify() + if g.is_zero: + return f**e + _, d = g.leadterm(x, logx=logx) + if not d.is_positive: + g = ((b - f)/f).expand() + _, d = g.leadterm(x, logx=logx) + if not d.is_positive: + raise NotImplementedError() + + from sympy.functions.elementary.integers import ceiling + gpoly = g._eval_nseries(x, n=ceiling(maxpow), logx=logx, cdir=cdir).removeO() + gterms = {} + + for term in Add.make_args(gpoly): + co1, e1 = coeff_exp(term, x) + gterms[e1] = gterms.get(e1, S.Zero) + co1 + + k = S.One + terms = {S.Zero: S.One} + tk = gterms + + from sympy.functions.combinatorial.factorials import factorial, ff + + while (k*d - maxpow).is_negative: + coeff = ff(e, k)/factorial(k) + for ex in tk: + terms[ex] = terms.get(ex, S.Zero) + coeff*tk[ex] + tk = mul(tk, gterms) + k += S.One + + from sympy.functions.elementary.complexes import im + + if not e.is_integer and m.is_zero and f.is_negative: + ndir = (b - f).dir(x, cdir) + if im(ndir).is_negative: + inco, inex = coeff_exp(f**e*(-1)**(-2*e), x) + elif im(ndir).is_zero: + inco, inex = coeff_exp(exp(e*log(b)).as_leading_term(x, logx=logx, cdir=cdir), x) + else: + inco, inex = coeff_exp(f**e, x) + else: + inco, inex = coeff_exp(f**e, x) + res = S.Zero + + for e1 in terms: + ex = e1 + inex + res += terms[e1]*inco*x**(ex) + + if not (e.is_integer and e.is_positive and (e*d - n).is_nonpositive and + res == _mexpand(self)): + try: + res += Order(x**n, x) + except NotImplementedError: + return exp(e*log(b))._eval_nseries(x, n=n, logx=logx, cdir=cdir) + return res + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.functions.elementary.exponential import exp, log + e = self.exp + b = self.base + if self.base is S.Exp1: + arg = e.as_leading_term(x, logx=logx) + arg0 = arg.subs(x, 0) + if arg0 is S.NaN: + arg0 = arg.limit(x, 0) + if arg0.is_infinite is False: + return S.Exp1**arg0 + raise PoleError("Cannot expand %s around 0" % (self)) + elif e.has(x): + lt = exp(e * log(b)) + return lt.as_leading_term(x, logx=logx, cdir=cdir) + else: + from sympy.functions.elementary.complexes import im + try: + f = b.as_leading_term(x, logx=logx, cdir=cdir) + except PoleError: + return self + if not e.is_integer and f.is_negative and not f.has(x): + ndir = (b - f).dir(x, cdir) + if im(ndir).is_negative: + # Normally, f**e would evaluate to exp(e*log(f)) but on branch cuts + # an other value is expected through the following computation + # exp(e*(log(f) - 2*pi*I)) == f**e*exp(-2*e*pi*I) == f**e*(-1)**(-2*e). + return self.func(f, e) * (-1)**(-2*e) + elif im(ndir).is_zero: + log_leadterm = log(b)._eval_as_leading_term(x, logx=logx, cdir=cdir) + if log_leadterm.is_infinite is False: + return exp(e*log_leadterm) + return self.func(f, e) + + @cacheit + def _taylor_term(self, n, x, *previous_terms): # of (1 + x)**e + from sympy.functions.combinatorial.factorials import binomial + return binomial(self.exp, n) * self.func(x, n) + + def taylor_term(self, n, x, *previous_terms): + if self.base is not S.Exp1: + return super().taylor_term(n, x, *previous_terms) + if n < 0: + return S.Zero + if n == 0: + return S.One + from .sympify import sympify + x = sympify(x) + if previous_terms: + p = previous_terms[-1] + if p is not None: + return p * x / n + from sympy.functions.combinatorial.factorials import factorial + return x**n/factorial(n) + + def _eval_rewrite_as_sin(self, base, exp, **hints): + if self.base is S.Exp1: + from sympy.functions.elementary.trigonometric import sin + return sin(S.ImaginaryUnit*self.exp + S.Pi/2) - S.ImaginaryUnit*sin(S.ImaginaryUnit*self.exp) + + def _eval_rewrite_as_cos(self, base, exp, **hints): + if self.base is S.Exp1: + from sympy.functions.elementary.trigonometric import cos + return cos(S.ImaginaryUnit*self.exp) + S.ImaginaryUnit*cos(S.ImaginaryUnit*self.exp + S.Pi/2) + + def _eval_rewrite_as_tanh(self, base, exp, **hints): + if self.base is S.Exp1: + from sympy.functions.elementary.hyperbolic import tanh + return (1 + tanh(self.exp/2))/(1 - tanh(self.exp/2)) + + def _eval_rewrite_as_sqrt(self, base, exp, **kwargs): + from sympy.functions.elementary.trigonometric import sin, cos + if base is not S.Exp1: + return None + if exp.is_Mul: + coeff = exp.coeff(S.Pi * S.ImaginaryUnit) + if coeff and coeff.is_number: + cosine, sine = cos(S.Pi*coeff), sin(S.Pi*coeff) + if not isinstance(cosine, cos) and not isinstance (sine, sin): + return cosine + S.ImaginaryUnit*sine + + def as_content_primitive(self, radical=False, clear=True): + """Return the tuple (R, self/R) where R is the positive Rational + extracted from self. + + Examples + ======== + + >>> from sympy import sqrt + >>> sqrt(4 + 4*sqrt(2)).as_content_primitive() + (2, sqrt(1 + sqrt(2))) + >>> sqrt(3 + 3*sqrt(2)).as_content_primitive() + (1, sqrt(3)*sqrt(1 + sqrt(2))) + + >>> from sympy import expand_power_base, powsimp, Mul + >>> from sympy.abc import x, y + + >>> ((2*x + 2)**2).as_content_primitive() + (4, (x + 1)**2) + >>> (4**((1 + y)/2)).as_content_primitive() + (2, 4**(y/2)) + >>> (3**((1 + y)/2)).as_content_primitive() + (1, 3**((y + 1)/2)) + >>> (3**((5 + y)/2)).as_content_primitive() + (9, 3**((y + 1)/2)) + >>> eq = 3**(2 + 2*x) + >>> powsimp(eq) == eq + True + >>> eq.as_content_primitive() + (9, 3**(2*x)) + >>> powsimp(Mul(*_)) + 3**(2*x + 2) + + >>> eq = (2 + 2*x)**y + >>> s = expand_power_base(eq); s.is_Mul, s + (False, (2*x + 2)**y) + >>> eq.as_content_primitive() + (1, (2*(x + 1))**y) + >>> s = expand_power_base(_[1]); s.is_Mul, s + (True, 2**y*(x + 1)**y) + + See docstring of Expr.as_content_primitive for more examples. + """ + + b, e = self.as_base_exp() + b = _keep_coeff(*b.as_content_primitive(radical=radical, clear=clear)) + ce, pe = e.as_content_primitive(radical=radical, clear=clear) + if b.is_Rational: + #e + #= ce*pe + #= ce*(h + t) + #= ce*h + ce*t + #=> self + #= b**(ce*h)*b**(ce*t) + #= b**(cehp/cehq)*b**(ce*t) + #= b**(iceh + r/cehq)*b**(ce*t) + #= b**(iceh)*b**(r/cehq)*b**(ce*t) + #= b**(iceh)*b**(ce*t + r/cehq) + h, t = pe.as_coeff_Add() + if h.is_Rational and b != S.Zero: + ceh = ce*h + c = self.func(b, ceh) + r = S.Zero + if not c.is_Rational: + iceh, r = divmod(ceh.p, ceh.q) + c = self.func(b, iceh) + return c, self.func(b, _keep_coeff(ce, t + r/ce/ceh.q)) + e = _keep_coeff(ce, pe) + # b**e = (h*t)**e = h**e*t**e = c*m*t**e + if e.is_Rational and b.is_Mul: + h, t = b.as_content_primitive(radical=radical, clear=clear) # h is positive + c, m = self.func(h, e).as_coeff_Mul() # so c is positive + m, me = m.as_base_exp() + if m is S.One or me == e: # probably always true + # return the following, not return c, m*Pow(t, e) + # which would change Pow into Mul; we let SymPy + # decide what to do by using the unevaluated Mul, e.g + # should it stay as sqrt(2 + 2*sqrt(5)) or become + # sqrt(2)*sqrt(1 + sqrt(5)) + return c, self.func(_keep_coeff(m, t), e) + return S.One, self.func(b, e) + + def is_constant(self, *wrt, **flags): + expr = self + if flags.get('simplify', True): + expr = expr.simplify() + b, e = expr.as_base_exp() + bz = b.equals(0) + if bz: # recalculate with assumptions in case it's unevaluated + new = b**e + if new != expr: + return new.is_constant() + econ = e.is_constant(*wrt) + bcon = b.is_constant(*wrt) + if bcon: + if econ: + return True + bz = b.equals(0) + if bz is False: + return False + elif bcon is None: + return None + + return e.equals(0) + + def _eval_difference_delta(self, n, step): + b, e = self.args + if e.has(n) and not b.has(n): + new_e = e.subs(n, n + step) + return (b**(new_e - e) - 1) * self + +power = Dispatcher('power') +power.add((object, object), Pow) + +from .add import Add +from .numbers import Integer, Rational +from .mul import Mul, _keep_coeff +from .symbol import Symbol, Dummy, symbols diff --git a/lib/python3.11/site-packages/sympy/core/random.py b/lib/python3.11/site-packages/sympy/core/random.py new file mode 100644 index 0000000000000000000000000000000000000000..c02986283523b39462a1e2c0b97e3fb230cff100 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/random.py @@ -0,0 +1,227 @@ +""" +When you need to use random numbers in SymPy library code, import from here +so there is only one generator working for SymPy. Imports from here should +behave the same as if they were being imported from Python's random module. +But only the routines currently used in SymPy are included here. To use others +import ``rng`` and access the method directly. For example, to capture the +current state of the generator use ``rng.getstate()``. + +There is intentionally no Random to import from here. If you want +to control the state of the generator, import ``seed`` and call it +with or without an argument to set the state. + +Examples +======== + +>>> from sympy.core.random import random, seed +>>> assert random() < 1 +>>> seed(1); a = random() +>>> b = random() +>>> seed(1); c = random() +>>> assert a == c +>>> assert a != b # remote possibility this will fail + +""" +from sympy.utilities.iterables import is_sequence +from sympy.utilities.misc import as_int + +import random as _random +rng = _random.Random() + +choice = rng.choice +random = rng.random +randint = rng.randint +randrange = rng.randrange +sample = rng.sample +# seed = rng.seed +shuffle = rng.shuffle +uniform = rng.uniform + +_assumptions_rng = _random.Random() +_assumptions_shuffle = _assumptions_rng.shuffle + + +def seed(a=None, version=2): + rng.seed(a=a, version=version) + _assumptions_rng.seed(a=a, version=version) + + +def random_complex_number(a=2, b=-1, c=3, d=1, rational=False, tolerance=None): + """ + Return a random complex number. + + To reduce chance of hitting branch cuts or anything, we guarantee + b <= Im z <= d, a <= Re z <= c + + When rational is True, a rational approximation to a random number + is obtained within specified tolerance, if any. + """ + from sympy.core.numbers import I + from sympy.simplify.simplify import nsimplify + A, B = uniform(a, c), uniform(b, d) + if not rational: + return A + I*B + return (nsimplify(A, rational=True, tolerance=tolerance) + + I*nsimplify(B, rational=True, tolerance=tolerance)) + + +def verify_numerically(f, g, z=None, tol=1.0e-6, a=2, b=-1, c=3, d=1): + """ + Test numerically that f and g agree when evaluated in the argument z. + + If z is None, all symbols will be tested. This routine does not test + whether there are Floats present with precision higher than 15 digits + so if there are, your results may not be what you expect due to round- + off errors. + + Examples + ======== + + >>> from sympy import sin, cos + >>> from sympy.abc import x + >>> from sympy.core.random import verify_numerically as tn + >>> tn(sin(x)**2 + cos(x)**2, 1, x) + True + """ + from sympy.core.symbol import Symbol + from sympy.core.sympify import sympify + from sympy.core.numbers import comp + f, g = (sympify(i) for i in (f, g)) + if z is None: + z = f.free_symbols | g.free_symbols + elif isinstance(z, Symbol): + z = [z] + reps = list(zip(z, [random_complex_number(a, b, c, d) for _ in z])) + z1 = f.subs(reps).n() + z2 = g.subs(reps).n() + return comp(z1, z2, tol) + + +def test_derivative_numerically(f, z, tol=1.0e-6, a=2, b=-1, c=3, d=1): + """ + Test numerically that the symbolically computed derivative of f + with respect to z is correct. + + This routine does not test whether there are Floats present with + precision higher than 15 digits so if there are, your results may + not be what you expect due to round-off errors. + + Examples + ======== + + >>> from sympy import sin + >>> from sympy.abc import x + >>> from sympy.core.random import test_derivative_numerically as td + >>> td(sin(x), x) + True + """ + from sympy.core.numbers import comp + from sympy.core.function import Derivative + z0 = random_complex_number(a, b, c, d) + f1 = f.diff(z).subs(z, z0) + f2 = Derivative(f, z).doit_numerically(z0) + return comp(f1.n(), f2.n(), tol) + + +def _randrange(seed=None): + """Return a randrange generator. + + ``seed`` can be + + * None - return randomly seeded generator + * int - return a generator seeded with the int + * list - the values to be returned will be taken from the list + in the order given; the provided list is not modified. + + Examples + ======== + + >>> from sympy.core.random import _randrange + >>> rr = _randrange() + >>> rr(1000) # doctest: +SKIP + 999 + >>> rr = _randrange(3) + >>> rr(1000) # doctest: +SKIP + 238 + >>> rr = _randrange([0, 5, 1, 3, 4]) + >>> rr(3), rr(3) + (0, 1) + """ + if seed is None: + return randrange + elif isinstance(seed, int): + rng.seed(seed) + return randrange + elif is_sequence(seed): + seed = list(seed) # make a copy + seed.reverse() + + def give(a, b=None, seq=seed): + if b is None: + a, b = 0, a + a, b = as_int(a), as_int(b) + w = b - a + if w < 1: + raise ValueError('_randrange got empty range') + try: + x = seq.pop() + except IndexError: + raise ValueError('_randrange sequence was too short') + if a <= x < b: + return x + else: + return give(a, b, seq) + return give + else: + raise ValueError('_randrange got an unexpected seed') + + +def _randint(seed=None): + """Return a randint generator. + + ``seed`` can be + + * None - return randomly seeded generator + * int - return a generator seeded with the int + * list - the values to be returned will be taken from the list + in the order given; the provided list is not modified. + + Examples + ======== + + >>> from sympy.core.random import _randint + >>> ri = _randint() + >>> ri(1, 1000) # doctest: +SKIP + 999 + >>> ri = _randint(3) + >>> ri(1, 1000) # doctest: +SKIP + 238 + >>> ri = _randint([0, 5, 1, 2, 4]) + >>> ri(1, 3), ri(1, 3) + (1, 2) + """ + if seed is None: + return randint + elif isinstance(seed, int): + rng.seed(seed) + return randint + elif is_sequence(seed): + seed = list(seed) # make a copy + seed.reverse() + + def give(a, b, seq=seed): + a, b = as_int(a), as_int(b) + w = b - a + if w < 0: + raise ValueError('_randint got empty range') + try: + x = seq.pop() + except IndexError: + raise ValueError('_randint sequence was too short') + if a <= x <= b: + return x + else: + return give(a, b, seq) + return give + else: + raise ValueError('_randint got an unexpected seed') diff --git a/lib/python3.11/site-packages/sympy/core/relational.py b/lib/python3.11/site-packages/sympy/core/relational.py new file mode 100644 index 0000000000000000000000000000000000000000..5ccfc7e9632e650def00dab4559b209a1e6099e9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/relational.py @@ -0,0 +1,1615 @@ +from __future__ import annotations + +from .basic import Atom, Basic +from .sorting import ordered +from .evalf import EvalfMixin +from .function import AppliedUndef +from .numbers import int_valued +from .singleton import S +from .sympify import _sympify, SympifyError +from .parameters import global_parameters +from .logic import fuzzy_bool, fuzzy_xor, fuzzy_and, fuzzy_not +from sympy.logic.boolalg import Boolean, BooleanAtom +from sympy.utilities.iterables import sift +from sympy.utilities.misc import filldedent +from sympy.utilities.exceptions import sympy_deprecation_warning + + +__all__ = ( + 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', + 'Relational', 'Equality', 'Unequality', 'StrictLessThan', 'LessThan', + 'StrictGreaterThan', 'GreaterThan', +) + +from .expr import Expr +from sympy.multipledispatch import dispatch +from .containers import Tuple +from .symbol import Symbol + + +def _nontrivBool(side): + return isinstance(side, Boolean) and \ + not isinstance(side, Atom) + + +# Note, see issue 4986. Ideally, we wouldn't want to subclass both Boolean +# and Expr. +# from .. import Expr + + +def _canonical(cond): + # return a condition in which all relationals are canonical + reps = {r: r.canonical for r in cond.atoms(Relational)} + return cond.xreplace(reps) + # XXX: AttributeError was being caught here but it wasn't triggered by any of + # the tests so I've removed it... + + +def _canonical_coeff(rel): + # return -2*x + 1 < 0 as x > 1/2 + # XXX make this part of Relational.canonical? + rel = rel.canonical + if not rel.is_Relational or rel.rhs.is_Boolean: + return rel # Eq(x, True) + b, l = rel.lhs.as_coeff_Add(rational=True) + m, lhs = l.as_coeff_Mul(rational=True) + rhs = (rel.rhs - b)/m + if m < 0: + return rel.reversed.func(lhs, rhs) + return rel.func(lhs, rhs) + + +class Relational(Boolean, EvalfMixin): + """Base class for all relation types. + + Explanation + =========== + + Subclasses of Relational should generally be instantiated directly, but + Relational can be instantiated with a valid ``rop`` value to dispatch to + the appropriate subclass. + + Parameters + ========== + + rop : str or None + Indicates what subclass to instantiate. Valid values can be found + in the keys of Relational.ValidRelationOperator. + + Examples + ======== + + >>> from sympy import Rel + >>> from sympy.abc import x, y + >>> Rel(y, x + x**2, '==') + Eq(y, x**2 + x) + + A relation's type can be defined upon creation using ``rop``. + The relation type of an existing expression can be obtained + using its ``rel_op`` property. + Here is a table of all the relation types, along with their + ``rop`` and ``rel_op`` values: + + +---------------------+----------------------------+------------+ + |Relation |``rop`` |``rel_op`` | + +=====================+============================+============+ + |``Equality`` |``==`` or ``eq`` or ``None``|``==`` | + +---------------------+----------------------------+------------+ + |``Unequality`` |``!=`` or ``ne`` |``!=`` | + +---------------------+----------------------------+------------+ + |``GreaterThan`` |``>=`` or ``ge`` |``>=`` | + +---------------------+----------------------------+------------+ + |``LessThan`` |``<=`` or ``le`` |``<=`` | + +---------------------+----------------------------+------------+ + |``StrictGreaterThan``|``>`` or ``gt`` |``>`` | + +---------------------+----------------------------+------------+ + |``StrictLessThan`` |``<`` or ``lt`` |``<`` | + +---------------------+----------------------------+------------+ + + For example, setting ``rop`` to ``==`` produces an + ``Equality`` relation, ``Eq()``. + So does setting ``rop`` to ``eq``, or leaving ``rop`` unspecified. + That is, the first three ``Rel()`` below all produce the same result. + Using a ``rop`` from a different row in the table produces a + different relation type. + For example, the fourth ``Rel()`` below using ``lt`` for ``rop`` + produces a ``StrictLessThan`` inequality: + + >>> from sympy import Rel + >>> from sympy.abc import x, y + >>> Rel(y, x + x**2, '==') + Eq(y, x**2 + x) + >>> Rel(y, x + x**2, 'eq') + Eq(y, x**2 + x) + >>> Rel(y, x + x**2) + Eq(y, x**2 + x) + >>> Rel(y, x + x**2, 'lt') + y < x**2 + x + + To obtain the relation type of an existing expression, + get its ``rel_op`` property. + For example, ``rel_op`` is ``==`` for the ``Equality`` relation above, + and ``<`` for the strict less than inequality above: + + >>> from sympy import Rel + >>> from sympy.abc import x, y + >>> my_equality = Rel(y, x + x**2, '==') + >>> my_equality.rel_op + '==' + >>> my_inequality = Rel(y, x + x**2, 'lt') + >>> my_inequality.rel_op + '<' + + """ + __slots__ = () + + ValidRelationOperator: dict[str | None, type[Relational]] = {} + + is_Relational = True + + # ValidRelationOperator - Defined below, because the necessary classes + # have not yet been defined + + def __new__(cls, lhs, rhs, rop=None, **assumptions): + # If called by a subclass, do nothing special and pass on to Basic. + if cls is not Relational: + return Basic.__new__(cls, lhs, rhs, **assumptions) + + # XXX: Why do this? There should be a separate function to make a + # particular subclass of Relational from a string. + # + # If called directly with an operator, look up the subclass + # corresponding to that operator and delegate to it + cls = cls.ValidRelationOperator.get(rop, None) + if cls is None: + raise ValueError("Invalid relational operator symbol: %r" % rop) + + if not issubclass(cls, (Eq, Ne)): + # validate that Booleans are not being used in a relational + # other than Eq/Ne; + # Note: Symbol is a subclass of Boolean but is considered + # acceptable here. + if any(map(_nontrivBool, (lhs, rhs))): + raise TypeError(filldedent(''' + A Boolean argument can only be used in + Eq and Ne; all other relationals expect + real expressions. + ''')) + + return cls(lhs, rhs, **assumptions) + + @property + def lhs(self): + """The left-hand side of the relation.""" + return self._args[0] + + @property + def rhs(self): + """The right-hand side of the relation.""" + return self._args[1] + + @property + def reversed(self): + """Return the relationship with sides reversed. + + Examples + ======== + + >>> from sympy import Eq + >>> from sympy.abc import x + >>> Eq(x, 1) + Eq(x, 1) + >>> _.reversed + Eq(1, x) + >>> x < 1 + x < 1 + >>> _.reversed + 1 > x + """ + ops = {Eq: Eq, Gt: Lt, Ge: Le, Lt: Gt, Le: Ge, Ne: Ne} + a, b = self.args + return Relational.__new__(ops.get(self.func, self.func), b, a) + + @property + def reversedsign(self): + """Return the relationship with signs reversed. + + Examples + ======== + + >>> from sympy import Eq + >>> from sympy.abc import x + >>> Eq(x, 1) + Eq(x, 1) + >>> _.reversedsign + Eq(-x, -1) + >>> x < 1 + x < 1 + >>> _.reversedsign + -x > -1 + """ + a, b = self.args + if not (isinstance(a, BooleanAtom) or isinstance(b, BooleanAtom)): + ops = {Eq: Eq, Gt: Lt, Ge: Le, Lt: Gt, Le: Ge, Ne: Ne} + return Relational.__new__(ops.get(self.func, self.func), -a, -b) + else: + return self + + @property + def negated(self): + """Return the negated relationship. + + Examples + ======== + + >>> from sympy import Eq + >>> from sympy.abc import x + >>> Eq(x, 1) + Eq(x, 1) + >>> _.negated + Ne(x, 1) + >>> x < 1 + x < 1 + >>> _.negated + x >= 1 + + Notes + ===== + + This works more or less identical to ``~``/``Not``. The difference is + that ``negated`` returns the relationship even if ``evaluate=False``. + Hence, this is useful in code when checking for e.g. negated relations + to existing ones as it will not be affected by the `evaluate` flag. + + """ + ops = {Eq: Ne, Ge: Lt, Gt: Le, Le: Gt, Lt: Ge, Ne: Eq} + # If there ever will be new Relational subclasses, the following line + # will work until it is properly sorted out + # return ops.get(self.func, lambda a, b, evaluate=False: ~(self.func(a, + # b, evaluate=evaluate)))(*self.args, evaluate=False) + return Relational.__new__(ops.get(self.func), *self.args) + + @property + def weak(self): + """return the non-strict version of the inequality or self + + EXAMPLES + ======== + + >>> from sympy.abc import x + >>> (x < 1).weak + x <= 1 + >>> _.weak + x <= 1 + """ + return self + + @property + def strict(self): + """return the strict version of the inequality or self + + EXAMPLES + ======== + + >>> from sympy.abc import x + >>> (x <= 1).strict + x < 1 + >>> _.strict + x < 1 + """ + return self + + def _eval_evalf(self, prec): + return self.func(*[s._evalf(prec) for s in self.args]) + + @property + def canonical(self): + """Return a canonical form of the relational by putting a + number on the rhs, canonically removing a sign or else + ordering the args canonically. No other simplification is + attempted. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> x < 2 + x < 2 + >>> _.reversed.canonical + x < 2 + >>> (-y < x).canonical + x > -y + >>> (-y > x).canonical + x < -y + >>> (-y < -x).canonical + x < y + + The canonicalization is recursively applied: + + >>> from sympy import Eq + >>> Eq(x < y, y > x).canonical + True + """ + args = tuple([i.canonical if isinstance(i, Relational) else i for i in self.args]) + if args != self.args: + r = self.func(*args) + if not isinstance(r, Relational): + return r + else: + r = self + if r.rhs.is_number: + if r.rhs.is_Number and r.lhs.is_Number and r.lhs > r.rhs: + r = r.reversed + elif r.lhs.is_number: + r = r.reversed + elif tuple(ordered(args)) != args: + r = r.reversed + + LHS_CEMS = getattr(r.lhs, 'could_extract_minus_sign', None) + RHS_CEMS = getattr(r.rhs, 'could_extract_minus_sign', None) + + if isinstance(r.lhs, BooleanAtom) or isinstance(r.rhs, BooleanAtom): + return r + + # Check if first value has negative sign + if LHS_CEMS and LHS_CEMS(): + return r.reversedsign + elif not r.rhs.is_number and RHS_CEMS and RHS_CEMS(): + # Right hand side has a minus, but not lhs. + # How does the expression with reversed signs behave? + # This is so that expressions of the type + # Eq(x, -y) and Eq(-x, y) + # have the same canonical representation + expr1, _ = ordered([r.lhs, -r.rhs]) + if expr1 != r.lhs: + return r.reversed.reversedsign + + return r + + def equals(self, other, failing_expression=False): + """Return True if the sides of the relationship are mathematically + identical and the type of relationship is the same. + If failing_expression is True, return the expression whose truth value + was unknown.""" + if isinstance(other, Relational): + if other in (self, self.reversed): + return True + a, b = self, other + if a.func in (Eq, Ne) or b.func in (Eq, Ne): + if a.func != b.func: + return False + left, right = [i.equals(j, + failing_expression=failing_expression) + for i, j in zip(a.args, b.args)] + if left is True: + return right + if right is True: + return left + lr, rl = [i.equals(j, failing_expression=failing_expression) + for i, j in zip(a.args, b.reversed.args)] + if lr is True: + return rl + if rl is True: + return lr + e = (left, right, lr, rl) + if all(i is False for i in e): + return False + for i in e: + if i not in (True, False): + return i + else: + if b.func != a.func: + b = b.reversed + if a.func != b.func: + return False + left = a.lhs.equals(b.lhs, + failing_expression=failing_expression) + if left is False: + return False + right = a.rhs.equals(b.rhs, + failing_expression=failing_expression) + if right is False: + return False + if left is True: + return right + return left + + def _eval_simplify(self, **kwargs): + from .add import Add + from .expr import Expr + r = self + r = r.func(*[i.simplify(**kwargs) for i in r.args]) + if r.is_Relational: + if not isinstance(r.lhs, Expr) or not isinstance(r.rhs, Expr): + return r + dif = r.lhs - r.rhs + # replace dif with a valid Number that will + # allow a definitive comparison with 0 + v = None + if dif.is_comparable: + v = dif.n(2) + if any(i._prec == 1 for i in v.as_real_imag()): + rv, iv = [i.n(2) for i in dif.as_real_imag()] + v = rv + S.ImaginaryUnit*iv + elif dif.equals(0): # XXX this is expensive + v = S.Zero + if v is not None: + r = r.func._eval_relation(v, S.Zero) + r = r.canonical + # If there is only one symbol in the expression, + # try to write it on a simplified form + free = list(filter(lambda x: x.is_real is not False, r.free_symbols)) + if len(free) == 1: + try: + from sympy.solvers.solveset import linear_coeffs + x = free.pop() + dif = r.lhs - r.rhs + m, b = linear_coeffs(dif, x) + if m.is_zero is False: + if m.is_negative: + # Dividing with a negative number, so change order of arguments + # canonical will put the symbol back on the lhs later + r = r.func(-b / m, x) + else: + r = r.func(x, -b / m) + else: + r = r.func(b, S.Zero) + except ValueError: + # maybe not a linear function, try polynomial + from sympy.polys.polyerrors import PolynomialError + from sympy.polys.polytools import gcd, Poly, poly + try: + p = poly(dif, x) + c = p.all_coeffs() + constant = c[-1] + c[-1] = 0 + scale = gcd(c) + c = [ctmp / scale for ctmp in c] + r = r.func(Poly.from_list(c, x).as_expr(), -constant / scale) + except PolynomialError: + pass + elif len(free) >= 2: + try: + from sympy.solvers.solveset import linear_coeffs + from sympy.polys.polytools import gcd + free = list(ordered(free)) + dif = r.lhs - r.rhs + m = linear_coeffs(dif, *free) + constant = m[-1] + del m[-1] + scale = gcd(m) + m = [mtmp / scale for mtmp in m] + nzm = list(filter(lambda f: f[0] != 0, list(zip(m, free)))) + if scale.is_zero is False: + if constant != 0: + # lhs: expression, rhs: constant + newexpr = Add(*[i * j for i, j in nzm]) + r = r.func(newexpr, -constant / scale) + else: + # keep first term on lhs + lhsterm = nzm[0][0] * nzm[0][1] + del nzm[0] + newexpr = Add(*[i * j for i, j in nzm]) + r = r.func(lhsterm, -newexpr) + + else: + r = r.func(constant, S.Zero) + except ValueError: + pass + # Did we get a simplified result? + r = r.canonical + measure = kwargs['measure'] + if measure(r) < kwargs['ratio'] * measure(self): + return r + else: + return self + + def _eval_trigsimp(self, **opts): + from sympy.simplify.trigsimp import trigsimp + return self.func(trigsimp(self.lhs, **opts), trigsimp(self.rhs, **opts)) + + def expand(self, **kwargs): + args = (arg.expand(**kwargs) for arg in self.args) + return self.func(*args) + + def __bool__(self): + raise TypeError("cannot determine truth value of Relational") + + def _eval_as_set(self): + # self is univariate and periodicity(self, x) in (0, None) + from sympy.solvers.inequalities import solve_univariate_inequality + from sympy.sets.conditionset import ConditionSet + syms = self.free_symbols + assert len(syms) == 1 + x = syms.pop() + try: + xset = solve_univariate_inequality(self, x, relational=False) + except NotImplementedError: + # solve_univariate_inequality raises NotImplementedError for + # unsolvable equations/inequalities. + xset = ConditionSet(x, self, S.Reals) + return xset + + @property + def binary_symbols(self): + # override where necessary + return set() + + +Rel = Relational + + +class Equality(Relational): + """ + An equal relation between two objects. + + Explanation + =========== + + Represents that two objects are equal. If they can be easily shown + to be definitively equal (or unequal), this will reduce to True (or + False). Otherwise, the relation is maintained as an unevaluated + Equality object. Use the ``simplify`` function on this object for + more nontrivial evaluation of the equality relation. + + As usual, the keyword argument ``evaluate=False`` can be used to + prevent any evaluation. + + Examples + ======== + + >>> from sympy import Eq, simplify, exp, cos + >>> from sympy.abc import x, y + >>> Eq(y, x + x**2) + Eq(y, x**2 + x) + >>> Eq(2, 5) + False + >>> Eq(2, 5, evaluate=False) + Eq(2, 5) + >>> _.doit() + False + >>> Eq(exp(x), exp(x).rewrite(cos)) + Eq(exp(x), sinh(x) + cosh(x)) + >>> simplify(_) + True + + See Also + ======== + + sympy.logic.boolalg.Equivalent : for representing equality between two + boolean expressions + + Notes + ===== + + Python treats 1 and True (and 0 and False) as being equal; SymPy + does not. And integer will always compare as unequal to a Boolean: + + >>> Eq(True, 1), True == 1 + (False, True) + + This class is not the same as the == operator. The == operator tests + for exact structural equality between two expressions; this class + compares expressions mathematically. + + If either object defines an ``_eval_Eq`` method, it can be used in place of + the default algorithm. If ``lhs._eval_Eq(rhs)`` or ``rhs._eval_Eq(lhs)`` + returns anything other than None, that return value will be substituted for + the Equality. If None is returned by ``_eval_Eq``, an Equality object will + be created as usual. + + Since this object is already an expression, it does not respond to + the method ``as_expr`` if one tries to create `x - y` from ``Eq(x, y)``. + If ``eq = Eq(x, y)`` then write `eq.lhs - eq.rhs` to get ``x - y``. + + .. deprecated:: 1.5 + + ``Eq(expr)`` with a single argument is a shorthand for ``Eq(expr, 0)``, + but this behavior is deprecated and will be removed in a future version + of SymPy. + + """ + rel_op = '==' + + __slots__ = () + + is_Equality = True + + def __new__(cls, lhs, rhs, **options): + evaluate = options.pop('evaluate', global_parameters.evaluate) + lhs = _sympify(lhs) + rhs = _sympify(rhs) + if evaluate: + val = is_eq(lhs, rhs) + if val is None: + return cls(lhs, rhs, evaluate=False) + else: + return _sympify(val) + + return Relational.__new__(cls, lhs, rhs) + + @classmethod + def _eval_relation(cls, lhs, rhs): + return _sympify(lhs == rhs) + + def _eval_rewrite_as_Add(self, L, R, evaluate=True, **kwargs): + """ + return Eq(L, R) as L - R. To control the evaluation of + the result set pass `evaluate=True` to give L - R; + if `evaluate=None` then terms in L and R will not cancel + but they will be listed in canonical order; otherwise + non-canonical args will be returned. If one side is 0, the + non-zero side will be returned. + + .. deprecated:: 1.13 + + The method ``Eq.rewrite(Add)`` is deprecated. + See :ref:`eq-rewrite-Add` for details. + + Examples + ======== + + >>> from sympy import Eq, Add + >>> from sympy.abc import b, x + >>> eq = Eq(x + b, x - b) + >>> eq.rewrite(Add) #doctest: +SKIP + 2*b + >>> eq.rewrite(Add, evaluate=None).args #doctest: +SKIP + (b, b, x, -x) + >>> eq.rewrite(Add, evaluate=False).args #doctest: +SKIP + (b, x, b, -x) + """ + sympy_deprecation_warning(""" + Eq.rewrite(Add) is deprecated. + + For ``eq = Eq(a, b)`` use ``eq.lhs - eq.rhs`` to obtain + ``a - b``. + """, + deprecated_since_version="1.13", + active_deprecations_target="eq-rewrite-Add", + stacklevel=5, + ) + from .add import _unevaluated_Add, Add + if L == 0: + return R + if R == 0: + return L + if evaluate: + # allow cancellation of args + return L - R + args = Add.make_args(L) + Add.make_args(-R) + if evaluate is None: + # no cancellation, but canonical + return _unevaluated_Add(*args) + # no cancellation, not canonical + return Add._from_args(args) + + @property + def binary_symbols(self): + if S.true in self.args or S.false in self.args: + if self.lhs.is_Symbol: + return {self.lhs} + elif self.rhs.is_Symbol: + return {self.rhs} + return set() + + def _eval_simplify(self, **kwargs): + # standard simplify + e = super()._eval_simplify(**kwargs) + if not isinstance(e, Equality): + return e + from .expr import Expr + if not isinstance(e.lhs, Expr) or not isinstance(e.rhs, Expr): + return e + free = self.free_symbols + if len(free) == 1: + try: + from .add import Add + from sympy.solvers.solveset import linear_coeffs + x = free.pop() + m, b = linear_coeffs( + Add(e.lhs, -e.rhs, evaluate=False), x) + if m.is_zero is False: + enew = e.func(x, -b / m) + else: + enew = e.func(m * x, -b) + measure = kwargs['measure'] + if measure(enew) <= kwargs['ratio'] * measure(e): + e = enew + except ValueError: + pass + return e.canonical + + def integrate(self, *args, **kwargs): + """See the integrate function in sympy.integrals""" + from sympy.integrals.integrals import integrate + return integrate(self, *args, **kwargs) + + def as_poly(self, *gens, **kwargs): + '''Returns lhs-rhs as a Poly + + Examples + ======== + + >>> from sympy import Eq + >>> from sympy.abc import x + >>> Eq(x**2, 1).as_poly(x) + Poly(x**2 - 1, x, domain='ZZ') + ''' + return (self.lhs - self.rhs).as_poly(*gens, **kwargs) + + +Eq = Equality + + +class Unequality(Relational): + """An unequal relation between two objects. + + Explanation + =========== + + Represents that two objects are not equal. If they can be shown to be + definitively equal, this will reduce to False; if definitively unequal, + this will reduce to True. Otherwise, the relation is maintained as an + Unequality object. + + Examples + ======== + + >>> from sympy import Ne + >>> from sympy.abc import x, y + >>> Ne(y, x+x**2) + Ne(y, x**2 + x) + + See Also + ======== + Equality + + Notes + ===== + This class is not the same as the != operator. The != operator tests + for exact structural equality between two expressions; this class + compares expressions mathematically. + + This class is effectively the inverse of Equality. As such, it uses the + same algorithms, including any available `_eval_Eq` methods. + + """ + rel_op = '!=' + + __slots__ = () + + def __new__(cls, lhs, rhs, **options): + lhs = _sympify(lhs) + rhs = _sympify(rhs) + evaluate = options.pop('evaluate', global_parameters.evaluate) + if evaluate: + val = is_neq(lhs, rhs) + if val is None: + return cls(lhs, rhs, evaluate=False) + else: + return _sympify(val) + + return Relational.__new__(cls, lhs, rhs, **options) + + @classmethod + def _eval_relation(cls, lhs, rhs): + return _sympify(lhs != rhs) + + @property + def binary_symbols(self): + if S.true in self.args or S.false in self.args: + if self.lhs.is_Symbol: + return {self.lhs} + elif self.rhs.is_Symbol: + return {self.rhs} + return set() + + def _eval_simplify(self, **kwargs): + # simplify as an equality + eq = Equality(*self.args)._eval_simplify(**kwargs) + if isinstance(eq, Equality): + # send back Ne with the new args + return self.func(*eq.args) + return eq.negated # result of Ne is the negated Eq + + +Ne = Unequality + + +class _Inequality(Relational): + """Internal base class for all *Than types. + + Each subclass must implement _eval_relation to provide the method for + comparing two real numbers. + + """ + __slots__ = () + + def __new__(cls, lhs, rhs, **options): + + try: + lhs = _sympify(lhs) + rhs = _sympify(rhs) + except SympifyError: + return NotImplemented + + evaluate = options.pop('evaluate', global_parameters.evaluate) + if evaluate: + for me in (lhs, rhs): + if me.is_extended_real is False: + raise TypeError("Invalid comparison of non-real %s" % me) + if me is S.NaN: + raise TypeError("Invalid NaN comparison") + # First we invoke the appropriate inequality method of `lhs` + # (e.g., `lhs.__lt__`). That method will try to reduce to + # boolean or raise an exception. It may keep calling + # superclasses until it reaches `Expr` (e.g., `Expr.__lt__`). + # In some cases, `Expr` will just invoke us again (if neither it + # nor a subclass was able to reduce to boolean or raise an + # exception). In that case, it must call us with + # `evaluate=False` to prevent infinite recursion. + return cls._eval_relation(lhs, rhs, **options) + + # make a "non-evaluated" Expr for the inequality + return Relational.__new__(cls, lhs, rhs, **options) + + @classmethod + def _eval_relation(cls, lhs, rhs, **options): + val = cls._eval_fuzzy_relation(lhs, rhs) + if val is None: + return cls(lhs, rhs, evaluate=False) + else: + return _sympify(val) + + +class _Greater(_Inequality): + """Not intended for general use + + _Greater is only used so that GreaterThan and StrictGreaterThan may + subclass it for the .gts and .lts properties. + + """ + __slots__ = () + + @property + def gts(self): + return self._args[0] + + @property + def lts(self): + return self._args[1] + + +class _Less(_Inequality): + """Not intended for general use. + + _Less is only used so that LessThan and StrictLessThan may subclass it for + the .gts and .lts properties. + + """ + __slots__ = () + + @property + def gts(self): + return self._args[1] + + @property + def lts(self): + return self._args[0] + + +class GreaterThan(_Greater): + r"""Class representations of inequalities. + + Explanation + =========== + + The ``*Than`` classes represent inequal relationships, where the left-hand + side is generally bigger or smaller than the right-hand side. For example, + the GreaterThan class represents an inequal relationship where the + left-hand side is at least as big as the right side, if not bigger. In + mathematical notation: + + lhs $\ge$ rhs + + In total, there are four ``*Than`` classes, to represent the four + inequalities: + + +-----------------+--------+ + |Class Name | Symbol | + +=================+========+ + |GreaterThan | ``>=`` | + +-----------------+--------+ + |LessThan | ``<=`` | + +-----------------+--------+ + |StrictGreaterThan| ``>`` | + +-----------------+--------+ + |StrictLessThan | ``<`` | + +-----------------+--------+ + + All classes take two arguments, lhs and rhs. + + +----------------------------+-----------------+ + |Signature Example | Math Equivalent | + +============================+=================+ + |GreaterThan(lhs, rhs) | lhs $\ge$ rhs | + +----------------------------+-----------------+ + |LessThan(lhs, rhs) | lhs $\le$ rhs | + +----------------------------+-----------------+ + |StrictGreaterThan(lhs, rhs) | lhs $>$ rhs | + +----------------------------+-----------------+ + |StrictLessThan(lhs, rhs) | lhs $<$ rhs | + +----------------------------+-----------------+ + + In addition to the normal .lhs and .rhs of Relations, ``*Than`` inequality + objects also have the .lts and .gts properties, which represent the "less + than side" and "greater than side" of the operator. Use of .lts and .gts + in an algorithm rather than .lhs and .rhs as an assumption of inequality + direction will make more explicit the intent of a certain section of code, + and will make it similarly more robust to client code changes: + + >>> from sympy import GreaterThan, StrictGreaterThan + >>> from sympy import LessThan, StrictLessThan + >>> from sympy import And, Ge, Gt, Le, Lt, Rel, S + >>> from sympy.abc import x, y, z + >>> from sympy.core.relational import Relational + + >>> e = GreaterThan(x, 1) + >>> e + x >= 1 + >>> '%s >= %s is the same as %s <= %s' % (e.gts, e.lts, e.lts, e.gts) + 'x >= 1 is the same as 1 <= x' + + Examples + ======== + + One generally does not instantiate these classes directly, but uses various + convenience methods: + + >>> for f in [Ge, Gt, Le, Lt]: # convenience wrappers + ... print(f(x, 2)) + x >= 2 + x > 2 + x <= 2 + x < 2 + + Another option is to use the Python inequality operators (``>=``, ``>``, + ``<=``, ``<``) directly. Their main advantage over the ``Ge``, ``Gt``, + ``Le``, and ``Lt`` counterparts, is that one can write a more + "mathematical looking" statement rather than littering the math with + oddball function calls. However there are certain (minor) caveats of + which to be aware (search for 'gotcha', below). + + >>> x >= 2 + x >= 2 + >>> _ == Ge(x, 2) + True + + However, it is also perfectly valid to instantiate a ``*Than`` class less + succinctly and less conveniently: + + >>> Rel(x, 1, ">") + x > 1 + >>> Relational(x, 1, ">") + x > 1 + + >>> StrictGreaterThan(x, 1) + x > 1 + >>> GreaterThan(x, 1) + x >= 1 + >>> LessThan(x, 1) + x <= 1 + >>> StrictLessThan(x, 1) + x < 1 + + Notes + ===== + + There are a couple of "gotchas" to be aware of when using Python's + operators. + + The first is that what your write is not always what you get: + + >>> 1 < x + x > 1 + + Due to the order that Python parses a statement, it may + not immediately find two objects comparable. When ``1 < x`` + is evaluated, Python recognizes that the number 1 is a native + number and that x is *not*. Because a native Python number does + not know how to compare itself with a SymPy object + Python will try the reflective operation, ``x > 1`` and that is the + form that gets evaluated, hence returned. + + If the order of the statement is important (for visual output to + the console, perhaps), one can work around this annoyance in a + couple ways: + + (1) "sympify" the literal before comparison + + >>> S(1) < x + 1 < x + + (2) use one of the wrappers or less succinct methods described + above + + >>> Lt(1, x) + 1 < x + >>> Relational(1, x, "<") + 1 < x + + The second gotcha involves writing equality tests between relationals + when one or both sides of the test involve a literal relational: + + >>> e = x < 1; e + x < 1 + >>> e == e # neither side is a literal + True + >>> e == x < 1 # expecting True, too + False + >>> e != x < 1 # expecting False + x < 1 + >>> x < 1 != x < 1 # expecting False or the same thing as before + Traceback (most recent call last): + ... + TypeError: cannot determine truth value of Relational + + The solution for this case is to wrap literal relationals in + parentheses: + + >>> e == (x < 1) + True + >>> e != (x < 1) + False + >>> (x < 1) != (x < 1) + False + + The third gotcha involves chained inequalities not involving + ``==`` or ``!=``. Occasionally, one may be tempted to write: + + >>> e = x < y < z + Traceback (most recent call last): + ... + TypeError: symbolic boolean expression has no truth value. + + Due to an implementation detail or decision of Python [1]_, + there is no way for SymPy to create a chained inequality with + that syntax so one must use And: + + >>> e = And(x < y, y < z) + >>> type( e ) + And + >>> e + (x < y) & (y < z) + + Although this can also be done with the '&' operator, it cannot + be done with the 'and' operarator: + + >>> (x < y) & (y < z) + (x < y) & (y < z) + >>> (x < y) and (y < z) + Traceback (most recent call last): + ... + TypeError: cannot determine truth value of Relational + + .. [1] This implementation detail is that Python provides no reliable + method to determine that a chained inequality is being built. + Chained comparison operators are evaluated pairwise, using "and" + logic (see + https://docs.python.org/3/reference/expressions.html#not-in). This + is done in an efficient way, so that each object being compared + is only evaluated once and the comparison can short-circuit. For + example, ``1 > 2 > 3`` is evaluated by Python as ``(1 > 2) and (2 + > 3)``. The ``and`` operator coerces each side into a bool, + returning the object itself when it short-circuits. The bool of + the --Than operators will raise TypeError on purpose, because + SymPy cannot determine the mathematical ordering of symbolic + expressions. Thus, if we were to compute ``x > y > z``, with + ``x``, ``y``, and ``z`` being Symbols, Python converts the + statement (roughly) into these steps: + + (1) x > y > z + (2) (x > y) and (y > z) + (3) (GreaterThanObject) and (y > z) + (4) (GreaterThanObject.__bool__()) and (y > z) + (5) TypeError + + Because of the ``and`` added at step 2, the statement gets turned into a + weak ternary statement, and the first object's ``__bool__`` method will + raise TypeError. Thus, creating a chained inequality is not possible. + + In Python, there is no way to override the ``and`` operator, or to + control how it short circuits, so it is impossible to make something + like ``x > y > z`` work. There was a PEP to change this, + :pep:`335`, but it was officially closed in March, 2012. + + """ + __slots__ = () + + rel_op = '>=' + + @classmethod + def _eval_fuzzy_relation(cls, lhs, rhs): + return is_ge(lhs, rhs) + + @property + def strict(self): + return Gt(*self.args) + +Ge = GreaterThan + + +class LessThan(_Less): + __doc__ = GreaterThan.__doc__ + __slots__ = () + + rel_op = '<=' + + @classmethod + def _eval_fuzzy_relation(cls, lhs, rhs): + return is_le(lhs, rhs) + + @property + def strict(self): + return Lt(*self.args) + +Le = LessThan + + +class StrictGreaterThan(_Greater): + __doc__ = GreaterThan.__doc__ + __slots__ = () + + rel_op = '>' + + @classmethod + def _eval_fuzzy_relation(cls, lhs, rhs): + return is_gt(lhs, rhs) + + @property + def weak(self): + return Ge(*self.args) + + +Gt = StrictGreaterThan + + +class StrictLessThan(_Less): + __doc__ = GreaterThan.__doc__ + __slots__ = () + + rel_op = '<' + + @classmethod + def _eval_fuzzy_relation(cls, lhs, rhs): + return is_lt(lhs, rhs) + + @property + def weak(self): + return Le(*self.args) + +Lt = StrictLessThan + +# A class-specific (not object-specific) data item used for a minor speedup. +# It is defined here, rather than directly in the class, because the classes +# that it references have not been defined until now (e.g. StrictLessThan). +Relational.ValidRelationOperator = { + None: Equality, + '==': Equality, + 'eq': Equality, + '!=': Unequality, + '<>': Unequality, + 'ne': Unequality, + '>=': GreaterThan, + 'ge': GreaterThan, + '<=': LessThan, + 'le': LessThan, + '>': StrictGreaterThan, + 'gt': StrictGreaterThan, + '<': StrictLessThan, + 'lt': StrictLessThan, +} + + +def _n2(a, b): + """Return (a - b).evalf(2) if a and b are comparable, else None. + This should only be used when a and b are already sympified. + """ + # /!\ it is very important (see issue 8245) not to + # use a re-evaluated number in the calculation of dif + if a.is_comparable and b.is_comparable: + dif = (a - b).evalf(2) + if dif.is_comparable: + return dif + + +@dispatch(Expr, Expr) +def _eval_is_ge(lhs, rhs): + return None + + +@dispatch(Basic, Basic) +def _eval_is_eq(lhs, rhs): + return None + + +@dispatch(Tuple, Expr) # type: ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + return False + + +@dispatch(Tuple, AppliedUndef) # type: ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + return None + + +@dispatch(Tuple, Symbol) # type: ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + return None + + +@dispatch(Tuple, Tuple) # type: ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + if len(lhs) != len(rhs): + return False + + return fuzzy_and(fuzzy_bool(is_eq(s, o)) for s, o in zip(lhs, rhs)) + + +def is_lt(lhs, rhs, assumptions=None): + """Fuzzy bool for lhs is strictly less than rhs. + + See the docstring for :func:`~.is_ge` for more. + """ + return fuzzy_not(is_ge(lhs, rhs, assumptions)) + + +def is_gt(lhs, rhs, assumptions=None): + """Fuzzy bool for lhs is strictly greater than rhs. + + See the docstring for :func:`~.is_ge` for more. + """ + return fuzzy_not(is_le(lhs, rhs, assumptions)) + + +def is_le(lhs, rhs, assumptions=None): + """Fuzzy bool for lhs is less than or equal to rhs. + + See the docstring for :func:`~.is_ge` for more. + """ + return is_ge(rhs, lhs, assumptions) + + +def is_ge(lhs, rhs, assumptions=None): + """ + Fuzzy bool for *lhs* is greater than or equal to *rhs*. + + Parameters + ========== + + lhs : Expr + The left-hand side of the expression, must be sympified, + and an instance of expression. Throws an exception if + lhs is not an instance of expression. + + rhs : Expr + The right-hand side of the expression, must be sympified + and an instance of expression. Throws an exception if + lhs is not an instance of expression. + + assumptions: Boolean, optional + Assumptions taken to evaluate the inequality. + + Returns + ======= + + ``True`` if *lhs* is greater than or equal to *rhs*, ``False`` if *lhs* + is less than *rhs*, and ``None`` if the comparison between *lhs* and + *rhs* is indeterminate. + + Explanation + =========== + + This function is intended to give a relatively fast determination and + deliberately does not attempt slow calculations that might help in + obtaining a determination of True or False in more difficult cases. + + The four comparison functions ``is_le``, ``is_lt``, ``is_ge``, and ``is_gt`` are + each implemented in terms of ``is_ge`` in the following way: + + is_ge(x, y) := is_ge(x, y) + is_le(x, y) := is_ge(y, x) + is_lt(x, y) := fuzzy_not(is_ge(x, y)) + is_gt(x, y) := fuzzy_not(is_ge(y, x)) + + Therefore, supporting new type with this function will ensure behavior for + other three functions as well. + + To maintain these equivalences in fuzzy logic it is important that in cases where + either x or y is non-real all comparisons will give None. + + Examples + ======== + + >>> from sympy import S, Q + >>> from sympy.core.relational import is_ge, is_le, is_gt, is_lt + >>> from sympy.abc import x + >>> is_ge(S(2), S(0)) + True + >>> is_ge(S(0), S(2)) + False + >>> is_le(S(0), S(2)) + True + >>> is_gt(S(0), S(2)) + False + >>> is_lt(S(2), S(0)) + False + + Assumptions can be passed to evaluate the quality which is otherwise + indeterminate. + + >>> print(is_ge(x, S(0))) + None + >>> is_ge(x, S(0), assumptions=Q.positive(x)) + True + + New types can be supported by dispatching to ``_eval_is_ge``. + + >>> from sympy import Expr, sympify + >>> from sympy.multipledispatch import dispatch + >>> class MyExpr(Expr): + ... def __new__(cls, arg): + ... return super().__new__(cls, sympify(arg)) + ... @property + ... def value(self): + ... return self.args[0] + >>> @dispatch(MyExpr, MyExpr) + ... def _eval_is_ge(a, b): + ... return is_ge(a.value, b.value) + >>> a = MyExpr(1) + >>> b = MyExpr(2) + >>> is_ge(b, a) + True + >>> is_le(a, b) + True + """ + from sympy.assumptions.wrapper import AssumptionsWrapper, is_extended_nonnegative + + if not (isinstance(lhs, Expr) and isinstance(rhs, Expr)): + raise TypeError("Can only compare inequalities with Expr") + + retval = _eval_is_ge(lhs, rhs) + + if retval is not None: + return retval + else: + n2 = _n2(lhs, rhs) + if n2 is not None: + # use float comparison for infinity. + # otherwise get stuck in infinite recursion + if n2 in (S.Infinity, S.NegativeInfinity): + n2 = float(n2) + return n2 >= 0 + + _lhs = AssumptionsWrapper(lhs, assumptions) + _rhs = AssumptionsWrapper(rhs, assumptions) + if _lhs.is_extended_real and _rhs.is_extended_real: + if (_lhs.is_infinite and _lhs.is_extended_positive) or (_rhs.is_infinite and _rhs.is_extended_negative): + return True + diff = lhs - rhs + if diff is not S.NaN: + rv = is_extended_nonnegative(diff, assumptions) + if rv is not None: + return rv + + +def is_neq(lhs, rhs, assumptions=None): + """Fuzzy bool for lhs does not equal rhs. + + See the docstring for :func:`~.is_eq` for more. + """ + return fuzzy_not(is_eq(lhs, rhs, assumptions)) + + +def is_eq(lhs, rhs, assumptions=None): + """ + Fuzzy bool representing mathematical equality between *lhs* and *rhs*. + + Parameters + ========== + + lhs : Expr + The left-hand side of the expression, must be sympified. + + rhs : Expr + The right-hand side of the expression, must be sympified. + + assumptions: Boolean, optional + Assumptions taken to evaluate the equality. + + Returns + ======= + + ``True`` if *lhs* is equal to *rhs*, ``False`` is *lhs* is not equal to *rhs*, + and ``None`` if the comparison between *lhs* and *rhs* is indeterminate. + + Explanation + =========== + + This function is intended to give a relatively fast determination and + deliberately does not attempt slow calculations that might help in + obtaining a determination of True or False in more difficult cases. + + :func:`~.is_neq` calls this function to return its value, so supporting + new type with this function will ensure correct behavior for ``is_neq`` + as well. + + Examples + ======== + + >>> from sympy import Q, S + >>> from sympy.core.relational import is_eq, is_neq + >>> from sympy.abc import x + >>> is_eq(S(0), S(0)) + True + >>> is_neq(S(0), S(0)) + False + >>> is_eq(S(0), S(2)) + False + >>> is_neq(S(0), S(2)) + True + + Assumptions can be passed to evaluate the equality which is otherwise + indeterminate. + + >>> print(is_eq(x, S(0))) + None + >>> is_eq(x, S(0), assumptions=Q.zero(x)) + True + + New types can be supported by dispatching to ``_eval_is_eq``. + + >>> from sympy import Basic, sympify + >>> from sympy.multipledispatch import dispatch + >>> class MyBasic(Basic): + ... def __new__(cls, arg): + ... return Basic.__new__(cls, sympify(arg)) + ... @property + ... def value(self): + ... return self.args[0] + ... + >>> @dispatch(MyBasic, MyBasic) + ... def _eval_is_eq(a, b): + ... return is_eq(a.value, b.value) + ... + >>> a = MyBasic(1) + >>> b = MyBasic(1) + >>> is_eq(a, b) + True + >>> is_neq(a, b) + False + + """ + # here, _eval_Eq is only called for backwards compatibility + # new code should use is_eq with multiple dispatch as + # outlined in the docstring + for side1, side2 in (lhs, rhs), (rhs, lhs): + eval_func = getattr(side1, '_eval_Eq', None) + if eval_func is not None: + retval = eval_func(side2) + if retval is not None: + return retval + + retval = _eval_is_eq(lhs, rhs) + if retval is not None: + return retval + + if dispatch(type(lhs), type(rhs)) != dispatch(type(rhs), type(lhs)): + retval = _eval_is_eq(rhs, lhs) + if retval is not None: + return retval + + # retval is still None, so go through the equality logic + # If expressions have the same structure, they must be equal. + if lhs == rhs: + return True # e.g. True == True + elif all(isinstance(i, BooleanAtom) for i in (rhs, lhs)): + return False # True != False + elif not (lhs.is_Symbol or rhs.is_Symbol) and ( + isinstance(lhs, Boolean) != + isinstance(rhs, Boolean)): + return False # only Booleans can equal Booleans + + from sympy.assumptions.wrapper import (AssumptionsWrapper, + is_infinite, is_extended_real) + from .add import Add + + _lhs = AssumptionsWrapper(lhs, assumptions) + _rhs = AssumptionsWrapper(rhs, assumptions) + + if _lhs.is_infinite or _rhs.is_infinite: + if fuzzy_xor([_lhs.is_infinite, _rhs.is_infinite]): + return False + if fuzzy_xor([_lhs.is_extended_real, _rhs.is_extended_real]): + return False + if fuzzy_and([_lhs.is_extended_real, _rhs.is_extended_real]): + return fuzzy_xor([_lhs.is_extended_positive, fuzzy_not(_rhs.is_extended_positive)]) + + # Try to split real/imaginary parts and equate them + I = S.ImaginaryUnit + + def split_real_imag(expr): + real_imag = lambda t: ( + 'real' if is_extended_real(t, assumptions) else + 'imag' if is_extended_real(I*t, assumptions) else None) + return sift(Add.make_args(expr), real_imag) + + lhs_ri = split_real_imag(lhs) + if not lhs_ri[None]: + rhs_ri = split_real_imag(rhs) + if not rhs_ri[None]: + eq_real = is_eq(Add(*lhs_ri['real']), Add(*rhs_ri['real']), assumptions) + eq_imag = is_eq(I * Add(*lhs_ri['imag']), I * Add(*rhs_ri['imag']), assumptions) + return fuzzy_and(map(fuzzy_bool, [eq_real, eq_imag])) + + from sympy.functions.elementary.complexes import arg + # Compare e.g. zoo with 1+I*oo by comparing args + arglhs = arg(lhs) + argrhs = arg(rhs) + # Guard against Eq(nan, nan) -> False + if not (arglhs == S.NaN and argrhs == S.NaN): + return fuzzy_bool(is_eq(arglhs, argrhs, assumptions)) + + if all(isinstance(i, Expr) for i in (lhs, rhs)): + # see if the difference evaluates + dif = lhs - rhs + _dif = AssumptionsWrapper(dif, assumptions) + z = _dif.is_zero + if z is not None: + if z is False and _dif.is_commutative: # issue 10728 + return False + if z: + return True + + # is_zero cannot help decide integer/rational with Float + c, t = dif.as_coeff_Add() + if c.is_Float: + if int_valued(c): + if t.is_integer is False: + return False + elif t.is_rational is False: + return False + + n2 = _n2(lhs, rhs) + if n2 is not None: + return _sympify(n2 == 0) + + # see if the ratio evaluates + n, d = dif.as_numer_denom() + rv = None + _n = AssumptionsWrapper(n, assumptions) + _d = AssumptionsWrapper(d, assumptions) + if _n.is_zero: + rv = _d.is_nonzero + elif _n.is_finite: + if _d.is_infinite: + rv = True + elif _n.is_zero is False: + rv = _d.is_infinite + if rv is None: + # if the condition that makes the denominator + # infinite does not make the original expression + # True then False can be returned + from sympy.simplify.simplify import clear_coefficients + l, r = clear_coefficients(d, S.Infinity) + args = [_.subs(l, r) for _ in (lhs, rhs)] + if args != [lhs, rhs]: + rv = fuzzy_bool(is_eq(*args, assumptions)) + if rv is True: + rv = None + elif any(is_infinite(a, assumptions) for a in Add.make_args(n)): + # (inf or nan)/x != 0 + rv = False + if rv is not None: + return rv diff --git a/lib/python3.11/site-packages/sympy/core/rules.py b/lib/python3.11/site-packages/sympy/core/rules.py new file mode 100644 index 0000000000000000000000000000000000000000..5ae331f71b21c8a6ef35f499c5c5c89239349e9c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/rules.py @@ -0,0 +1,66 @@ +""" +Replacement rules. +""" + +class Transform: + """ + Immutable mapping that can be used as a generic transformation rule. + + Parameters + ========== + + transform : callable + Computes the value corresponding to any key. + + filter : callable, optional + If supplied, specifies which objects are in the mapping. + + Examples + ======== + + >>> from sympy.core.rules import Transform + >>> from sympy.abc import x + + This Transform will return, as a value, one more than the key: + + >>> add1 = Transform(lambda x: x + 1) + >>> add1[1] + 2 + >>> add1[x] + x + 1 + + By default, all values are considered to be in the dictionary. If a filter + is supplied, only the objects for which it returns True are considered as + being in the dictionary: + + >>> add1_odd = Transform(lambda x: x + 1, lambda x: x%2 == 1) + >>> 2 in add1_odd + False + >>> add1_odd.get(2, 0) + 0 + >>> 3 in add1_odd + True + >>> add1_odd[3] + 4 + >>> add1_odd.get(3, 0) + 4 + """ + + def __init__(self, transform, filter=lambda x: True): + self._transform = transform + self._filter = filter + + def __contains__(self, item): + return self._filter(item) + + def __getitem__(self, key): + if self._filter(key): + return self._transform(key) + else: + raise KeyError(key) + + def get(self, item, default=None): + if item in self: + return self[item] + else: + return default diff --git a/lib/python3.11/site-packages/sympy/core/singleton.py b/lib/python3.11/site-packages/sympy/core/singleton.py new file mode 100644 index 0000000000000000000000000000000000000000..aedf1885058900eece7061d65c53d5704172a596 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/singleton.py @@ -0,0 +1,174 @@ +"""Singleton mechanism""" + + +from .core import Registry +from .sympify import sympify + + +class SingletonRegistry(Registry): + """ + The registry for the singleton classes (accessible as ``S``). + + Explanation + =========== + + This class serves as two separate things. + + The first thing it is is the ``SingletonRegistry``. Several classes in + SymPy appear so often that they are singletonized, that is, using some + metaprogramming they are made so that they can only be instantiated once + (see the :class:`sympy.core.singleton.Singleton` class for details). For + instance, every time you create ``Integer(0)``, this will return the same + instance, :class:`sympy.core.numbers.Zero`. All singleton instances are + attributes of the ``S`` object, so ``Integer(0)`` can also be accessed as + ``S.Zero``. + + Singletonization offers two advantages: it saves memory, and it allows + fast comparison. It saves memory because no matter how many times the + singletonized objects appear in expressions in memory, they all point to + the same single instance in memory. The fast comparison comes from the + fact that you can use ``is`` to compare exact instances in Python + (usually, you need to use ``==`` to compare things). ``is`` compares + objects by memory address, and is very fast. + + Examples + ======== + + >>> from sympy import S, Integer + >>> a = Integer(0) + >>> a is S.Zero + True + + For the most part, the fact that certain objects are singletonized is an + implementation detail that users should not need to worry about. In SymPy + library code, ``is`` comparison is often used for performance purposes + The primary advantage of ``S`` for end users is the convenient access to + certain instances that are otherwise difficult to type, like ``S.Half`` + (instead of ``Rational(1, 2)``). + + When using ``is`` comparison, make sure the argument is sympified. For + instance, + + >>> x = 0 + >>> x is S.Zero + False + + This problem is not an issue when using ``==``, which is recommended for + most use-cases: + + >>> 0 == S.Zero + True + + The second thing ``S`` is is a shortcut for + :func:`sympy.core.sympify.sympify`. :func:`sympy.core.sympify.sympify` is + the function that converts Python objects such as ``int(1)`` into SymPy + objects such as ``Integer(1)``. It also converts the string form of an + expression into a SymPy expression, like ``sympify("x**2")`` -> + ``Symbol("x")**2``. ``S(1)`` is the same thing as ``sympify(1)`` + (basically, ``S.__call__`` has been defined to call ``sympify``). + + This is for convenience, since ``S`` is a single letter. It's mostly + useful for defining rational numbers. Consider an expression like ``x + + 1/2``. If you enter this directly in Python, it will evaluate the ``1/2`` + and give ``0.5``, because both arguments are ints (see also + :ref:`tutorial-gotchas-final-notes`). However, in SymPy, you usually want + the quotient of two integers to give an exact rational number. The way + Python's evaluation works, at least one side of an operator needs to be a + SymPy object for the SymPy evaluation to take over. You could write this + as ``x + Rational(1, 2)``, but this is a lot more typing. A shorter + version is ``x + S(1)/2``. Since ``S(1)`` returns ``Integer(1)``, the + division will return a ``Rational`` type, since it will call + ``Integer.__truediv__``, which knows how to return a ``Rational``. + + """ + __slots__ = () + + # Also allow things like S(5) + __call__ = staticmethod(sympify) + + def __init__(self): + self._classes_to_install = {} + # Dict of classes that have been registered, but that have not have been + # installed as an attribute of this SingletonRegistry. + # Installation automatically happens at the first attempt to access the + # attribute. + # The purpose of this is to allow registration during class + # initialization during import, but not trigger object creation until + # actual use (which should not happen until after all imports are + # finished). + + def register(self, cls): + # Make sure a duplicate class overwrites the old one + if hasattr(self, cls.__name__): + delattr(self, cls.__name__) + self._classes_to_install[cls.__name__] = cls + + def __getattr__(self, name): + """Python calls __getattr__ if no attribute of that name was installed + yet. + + Explanation + =========== + + This __getattr__ checks whether a class with the requested name was + already registered but not installed; if no, raises an AttributeError. + Otherwise, retrieves the class, calculates its singleton value, installs + it as an attribute of the given name, and unregisters the class.""" + if name not in self._classes_to_install: + raise AttributeError( + "Attribute '%s' was not installed on SymPy registry %s" % ( + name, self)) + class_to_install = self._classes_to_install[name] + value_to_install = class_to_install() + self.__setattr__(name, value_to_install) + del self._classes_to_install[name] + return value_to_install + + def __repr__(self): + return "S" + +S = SingletonRegistry() + + +class Singleton(type): + """ + Metaclass for singleton classes. + + Explanation + =========== + + A singleton class has only one instance which is returned every time the + class is instantiated. Additionally, this instance can be accessed through + the global registry object ``S`` as ``S.``. + + Examples + ======== + + >>> from sympy import S, Basic + >>> from sympy.core.singleton import Singleton + >>> class MySingleton(Basic, metaclass=Singleton): + ... pass + >>> Basic() is Basic() + False + >>> MySingleton() is MySingleton() + True + >>> S.MySingleton is MySingleton() + True + + Notes + ===== + + Instance creation is delayed until the first time the value is accessed. + (SymPy versions before 1.0 would create the instance during class + creation time, which would be prone to import cycles.) + """ + def __init__(cls, *args, **kwargs): + cls._instance = obj = Basic.__new__(cls) + cls.__new__ = lambda cls: obj + cls.__getnewargs__ = lambda obj: () + cls.__getstate__ = lambda obj: None + S.register(cls) + + +# Delayed to avoid cyclic import +from .basic import Basic diff --git a/lib/python3.11/site-packages/sympy/core/sorting.py b/lib/python3.11/site-packages/sympy/core/sorting.py new file mode 100644 index 0000000000000000000000000000000000000000..399a7efa1f6cbe1ebdf6307c14b411df36fc7de0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/sorting.py @@ -0,0 +1,312 @@ +from collections import defaultdict + +from .sympify import sympify, SympifyError +from sympy.utilities.iterables import iterable, uniq + + +__all__ = ['default_sort_key', 'ordered'] + + +def default_sort_key(item, order=None): + """Return a key that can be used for sorting. + + The key has the structure: + + (class_key, (len(args), args), exponent.sort_key(), coefficient) + + This key is supplied by the sort_key routine of Basic objects when + ``item`` is a Basic object or an object (other than a string) that + sympifies to a Basic object. Otherwise, this function produces the + key. + + The ``order`` argument is passed along to the sort_key routine and is + used to determine how the terms *within* an expression are ordered. + (See examples below) ``order`` options are: 'lex', 'grlex', 'grevlex', + and reversed values of the same (e.g. 'rev-lex'). The default order + value is None (which translates to 'lex'). + + Examples + ======== + + >>> from sympy import S, I, default_sort_key, sin, cos, sqrt + >>> from sympy.core.function import UndefinedFunction + >>> from sympy.abc import x + + The following are equivalent ways of getting the key for an object: + + >>> x.sort_key() == default_sort_key(x) + True + + Here are some examples of the key that is produced: + + >>> default_sort_key(UndefinedFunction('f')) + ((0, 0, 'UndefinedFunction'), (1, ('f',)), ((1, 0, 'Number'), + (0, ()), (), 1), 1) + >>> default_sort_key('1') + ((0, 0, 'str'), (1, ('1',)), ((1, 0, 'Number'), (0, ()), (), 1), 1) + >>> default_sort_key(S.One) + ((1, 0, 'Number'), (0, ()), (), 1) + >>> default_sort_key(2) + ((1, 0, 'Number'), (0, ()), (), 2) + + While sort_key is a method only defined for SymPy objects, + default_sort_key will accept anything as an argument so it is + more robust as a sorting key. For the following, using key= + lambda i: i.sort_key() would fail because 2 does not have a sort_key + method; that's why default_sort_key is used. Note, that it also + handles sympification of non-string items likes ints: + + >>> a = [2, I, -I] + >>> sorted(a, key=default_sort_key) + [2, -I, I] + + The returned key can be used anywhere that a key can be specified for + a function, e.g. sort, min, max, etc...: + + >>> a.sort(key=default_sort_key); a[0] + 2 + >>> min(a, key=default_sort_key) + 2 + + Notes + ===== + + The key returned is useful for getting items into a canonical order + that will be the same across platforms. It is not directly useful for + sorting lists of expressions: + + >>> a, b = x, 1/x + + Since ``a`` has only 1 term, its value of sort_key is unaffected by + ``order``: + + >>> a.sort_key() == a.sort_key('rev-lex') + True + + If ``a`` and ``b`` are combined then the key will differ because there + are terms that can be ordered: + + >>> eq = a + b + >>> eq.sort_key() == eq.sort_key('rev-lex') + False + >>> eq.as_ordered_terms() + [x, 1/x] + >>> eq.as_ordered_terms('rev-lex') + [1/x, x] + + But since the keys for each of these terms are independent of ``order``'s + value, they do not sort differently when they appear separately in a list: + + >>> sorted(eq.args, key=default_sort_key) + [1/x, x] + >>> sorted(eq.args, key=lambda i: default_sort_key(i, order='rev-lex')) + [1/x, x] + + The order of terms obtained when using these keys is the order that would + be obtained if those terms were *factors* in a product. + + Although it is useful for quickly putting expressions in canonical order, + it does not sort expressions based on their complexity defined by the + number of operations, power of variables and others: + + >>> sorted([sin(x)*cos(x), sin(x)], key=default_sort_key) + [sin(x)*cos(x), sin(x)] + >>> sorted([x, x**2, sqrt(x), x**3], key=default_sort_key) + [sqrt(x), x, x**2, x**3] + + See Also + ======== + + ordered, sympy.core.expr.Expr.as_ordered_factors, sympy.core.expr.Expr.as_ordered_terms + + """ + from .basic import Basic + from .singleton import S + + if isinstance(item, Basic): + return item.sort_key(order=order) + + if iterable(item, exclude=str): + if isinstance(item, dict): + args = item.items() + unordered = True + elif isinstance(item, set): + args = item + unordered = True + else: + # e.g. tuple, list + args = list(item) + unordered = False + + args = [default_sort_key(arg, order=order) for arg in args] + + if unordered: + # e.g. dict, set + args = sorted(args) + + cls_index, args = 10, (len(args), tuple(args)) + else: + if not isinstance(item, str): + try: + item = sympify(item, strict=True) + except SympifyError: + # e.g. lambda x: x + pass + else: + if isinstance(item, Basic): + # e.g int -> Integer + return default_sort_key(item) + # e.g. UndefinedFunction + + # e.g. str + cls_index, args = 0, (1, (str(item),)) + + return (cls_index, 0, item.__class__.__name__ + ), args, S.One.sort_key(), S.One + + +def _node_count(e): + # this not only counts nodes, it affirms that the + # args are Basic (i.e. have an args property). If + # some object has a non-Basic arg, it needs to be + # fixed since it is intended that all Basic args + # are of Basic type (though this is not easy to enforce). + if e.is_Float: + return 0.5 + return 1 + sum(map(_node_count, e.args)) + + +def _nodes(e): + """ + A helper for ordered() which returns the node count of ``e`` which + for Basic objects is the number of Basic nodes in the expression tree + but for other objects is 1 (unless the object is an iterable or dict + for which the sum of nodes is returned). + """ + from .basic import Basic + from .function import Derivative + + if isinstance(e, Basic): + if isinstance(e, Derivative): + return _nodes(e.expr) + sum(i[1] if i[1].is_Number else + _nodes(i[1]) for i in e.variable_count) + return _node_count(e) + elif iterable(e): + return 1 + sum(_nodes(ei) for ei in e) + elif isinstance(e, dict): + return 1 + sum(_nodes(k) + _nodes(v) for k, v in e.items()) + else: + return 1 + + +def ordered(seq, keys=None, default=True, warn=False): + """Return an iterator of the seq where keys are used to break ties + in a conservative fashion: if, after applying a key, there are no + ties then no other keys will be computed. + + Two default keys will be applied if 1) keys are not provided or + 2) the given keys do not resolve all ties (but only if ``default`` + is True). The two keys are ``_nodes`` (which places smaller + expressions before large) and ``default_sort_key`` which (if the + ``sort_key`` for an object is defined properly) should resolve + any ties. This strategy is similar to sorting done by + ``Basic.compare``, but differs in that ``ordered`` never makes a + decision based on an objects name. + + If ``warn`` is True then an error will be raised if there were no + keys remaining to break ties. This can be used if it was expected that + there should be no ties between items that are not identical. + + Examples + ======== + + >>> from sympy import ordered, count_ops + >>> from sympy.abc import x, y + + The count_ops is not sufficient to break ties in this list and the first + two items appear in their original order (i.e. the sorting is stable): + + >>> list(ordered([y + 2, x + 2, x**2 + y + 3], + ... count_ops, default=False, warn=False)) + ... + [y + 2, x + 2, x**2 + y + 3] + + The default_sort_key allows the tie to be broken: + + >>> list(ordered([y + 2, x + 2, x**2 + y + 3])) + ... + [x + 2, y + 2, x**2 + y + 3] + + Here, sequences are sorted by length, then sum: + + >>> seq, keys = [[[1, 2, 1], [0, 3, 1], [1, 1, 3], [2], [1]], [ + ... lambda x: len(x), + ... lambda x: sum(x)]] + ... + >>> list(ordered(seq, keys, default=False, warn=False)) + [[1], [2], [1, 2, 1], [0, 3, 1], [1, 1, 3]] + + If ``warn`` is True, an error will be raised if there were not + enough keys to break ties: + + >>> list(ordered(seq, keys, default=False, warn=True)) + Traceback (most recent call last): + ... + ValueError: not enough keys to break ties + + + Notes + ===== + + The decorated sort is one of the fastest ways to sort a sequence for + which special item comparison is desired: the sequence is decorated, + sorted on the basis of the decoration (e.g. making all letters lower + case) and then undecorated. If one wants to break ties for items that + have the same decorated value, a second key can be used. But if the + second key is expensive to compute then it is inefficient to decorate + all items with both keys: only those items having identical first key + values need to be decorated. This function applies keys successively + only when needed to break ties. By yielding an iterator, use of the + tie-breaker is delayed as long as possible. + + This function is best used in cases when use of the first key is + expected to be a good hashing function; if there are no unique hashes + from application of a key, then that key should not have been used. The + exception, however, is that even if there are many collisions, if the + first group is small and one does not need to process all items in the + list then time will not be wasted sorting what one was not interested + in. For example, if one were looking for the minimum in a list and + there were several criteria used to define the sort order, then this + function would be good at returning that quickly if the first group + of candidates is small relative to the number of items being processed. + + """ + + d = defaultdict(list) + if keys: + if isinstance(keys, (list, tuple)): + keys = list(keys) + f = keys.pop(0) + else: + f = keys + keys = [] + for a in seq: + d[f(a)].append(a) + else: + if not default: + raise ValueError('if default=False then keys must be provided') + d[None].extend(seq) + + for k, value in sorted(d.items()): + if len(value) > 1: + if keys: + value = ordered(value, keys, default, warn) + elif default: + value = ordered(value, (_nodes, default_sort_key,), + default=False, warn=warn) + elif warn: + u = list(uniq(value)) + if len(u) > 1: + raise ValueError( + 'not enough keys to break ties: %s' % u) + yield from value diff --git a/lib/python3.11/site-packages/sympy/core/symbol.py b/lib/python3.11/site-packages/sympy/core/symbol.py new file mode 100644 index 0000000000000000000000000000000000000000..2b51740dfadb430567c1766f42d5e9d1ebf41dc9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/symbol.py @@ -0,0 +1,979 @@ +from __future__ import annotations + +from .assumptions import StdFactKB, _assume_defined +from .basic import Basic, Atom +from .cache import cacheit +from .containers import Tuple +from .expr import Expr, AtomicExpr +from .function import AppliedUndef, FunctionClass +from .kind import NumberKind, UndefinedKind +from .logic import fuzzy_bool +from .singleton import S +from .sorting import ordered +from .sympify import sympify +from sympy.logic.boolalg import Boolean +from sympy.utilities.iterables import sift, is_sequence +from sympy.utilities.misc import filldedent + +import string +import re as _re +import random +from itertools import product +from typing import Any + + +class Str(Atom): + """ + Represents string in SymPy. + + Explanation + =========== + + Previously, ``Symbol`` was used where string is needed in ``args`` of SymPy + objects, e.g. denoting the name of the instance. However, since ``Symbol`` + represents mathematical scalar, this class should be used instead. + + """ + __slots__ = ('name',) + + def __new__(cls, name, **kwargs): + if not isinstance(name, str): + raise TypeError("name should be a string, not %s" % repr(type(name))) + obj = Expr.__new__(cls, **kwargs) + obj.name = name + return obj + + def __getnewargs__(self): + return (self.name,) + + def _hashable_content(self): + return (self.name,) + + +def _filter_assumptions(kwargs): + """Split the given dict into assumptions and non-assumptions. + Keys are taken as assumptions if they correspond to an + entry in ``_assume_defined``. + """ + assumptions, nonassumptions = map(dict, sift(kwargs.items(), + lambda i: i[0] in _assume_defined, + binary=True)) + Symbol._sanitize(assumptions) + return assumptions, nonassumptions + +def _symbol(s, matching_symbol=None, **assumptions): + """Return s if s is a Symbol, else if s is a string, return either + the matching_symbol if the names are the same or else a new symbol + with the same assumptions as the matching symbol (or the + assumptions as provided). + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy.core.symbol import _symbol + >>> _symbol('y') + y + >>> _.is_real is None + True + >>> _symbol('y', real=True).is_real + True + + >>> x = Symbol('x') + >>> _symbol(x, real=True) + x + >>> _.is_real is None # ignore attribute if s is a Symbol + True + + Below, the variable sym has the name 'foo': + + >>> sym = Symbol('foo', real=True) + + Since 'x' is not the same as sym's name, a new symbol is created: + + >>> _symbol('x', sym).name + 'x' + + It will acquire any assumptions give: + + >>> _symbol('x', sym, real=False).is_real + False + + Since 'foo' is the same as sym's name, sym is returned + + >>> _symbol('foo', sym) + foo + + Any assumptions given are ignored: + + >>> _symbol('foo', sym, real=False).is_real + True + + NB: the symbol here may not be the same as a symbol with the same + name defined elsewhere as a result of different assumptions. + + See Also + ======== + + sympy.core.symbol.Symbol + + """ + if isinstance(s, str): + if matching_symbol and matching_symbol.name == s: + return matching_symbol + return Symbol(s, **assumptions) + elif isinstance(s, Symbol): + return s + else: + raise ValueError('symbol must be string for symbol name or Symbol') + +def uniquely_named_symbol(xname, exprs=(), compare=str, modify=None, **assumptions): + """ + Return a symbol whose name is derivated from *xname* but is unique + from any other symbols in *exprs*. + + *xname* and symbol names in *exprs* are passed to *compare* to be + converted to comparable forms. If ``compare(xname)`` is not unique, + it is recursively passed to *modify* until unique name is acquired. + + Parameters + ========== + + xname : str or Symbol + Base name for the new symbol. + + exprs : Expr or iterable of Expr + Expressions whose symbols are compared to *xname*. + + compare : function + Unary function which transforms *xname* and symbol names from + *exprs* to comparable form. + + modify : function + Unary function which modifies the string. Default is appending + the number, or increasing the number if exists. + + Examples + ======== + + By default, a number is appended to *xname* to generate unique name. + If the number already exists, it is recursively increased. + + >>> from sympy.core.symbol import uniquely_named_symbol, Symbol + >>> uniquely_named_symbol('x', Symbol('x')) + x0 + >>> uniquely_named_symbol('x', (Symbol('x'), Symbol('x0'))) + x1 + >>> uniquely_named_symbol('x0', (Symbol('x1'), Symbol('x0'))) + x2 + + Name generation can be controlled by passing *modify* parameter. + + >>> from sympy.abc import x + >>> uniquely_named_symbol('x', x, modify=lambda s: 2*s) + xx + + """ + def numbered_string_incr(s, start=0): + if not s: + return str(start) + i = len(s) - 1 + while i != -1: + if not s[i].isdigit(): + break + i -= 1 + n = str(int(s[i + 1:] or start - 1) + 1) + return s[:i + 1] + n + + default = None + if is_sequence(xname): + xname, default = xname + x = compare(xname) + if not exprs: + return _symbol(x, default, **assumptions) + if not is_sequence(exprs): + exprs = [exprs] + names = set().union( + [i.name for e in exprs for i in e.atoms(Symbol)] + + [i.func.name for e in exprs for i in e.atoms(AppliedUndef)]) + if modify is None: + modify = numbered_string_incr + while any(x == compare(s) for s in names): + x = modify(x) + return _symbol(x, default, **assumptions) +_uniquely_named_symbol = uniquely_named_symbol + +class Symbol(AtomicExpr, Boolean): + """ + Symbol class is used to create symbolic variables. + + Explanation + =========== + + Symbolic variables are placeholders for mathematical symbols that can represent numbers, constants, or any other mathematical entities and can be used in mathematical expressions and to perform symbolic computations. + + Assumptions: + + commutative = True + positive = True + real = True + imaginary = True + complex = True + complete list of more assumptions- :ref:`predicates` + + You can override the default assumptions in the constructor. + + Examples + ======== + + >>> from sympy import Symbol + >>> x = Symbol("x", positive=True) + >>> x.is_positive + True + >>> x.is_negative + False + + passing in greek letters: + + >>> from sympy import Symbol + >>> alpha = Symbol('alpha') + >>> alpha #doctest: +SKIP + α + + Trailing digits are automatically treated like subscripts of what precedes them in the name. + General format to add subscript to a symbol : + `` = Symbol('_')`` + + >>> from sympy import Symbol + >>> alpha_i = Symbol('alpha_i') + >>> alpha_i #doctest: +SKIP + αᵢ + + Parameters + ========== + + AtomicExpr: variable name + Boolean: Assumption with a boolean value(True or False) + """ + + is_comparable = False + + __slots__ = ('name', '_assumptions_orig', '_assumptions0') + + name: str + + is_Symbol = True + is_symbol = True + + @property + def kind(self): + if self.is_commutative: + return NumberKind + return UndefinedKind + + @property + def _diff_wrt(self): + """Allow derivatives wrt Symbols. + + Examples + ======== + + >>> from sympy import Symbol + >>> x = Symbol('x') + >>> x._diff_wrt + True + """ + return True + + @staticmethod + def _sanitize(assumptions, obj=None): + """Remove None, convert values to bool, check commutativity *in place*. + """ + + # be strict about commutativity: cannot be None + is_commutative = fuzzy_bool(assumptions.get('commutative', True)) + if is_commutative is None: + whose = '%s ' % obj.__name__ if obj else '' + raise ValueError( + '%scommutativity must be True or False.' % whose) + + # sanitize other assumptions so 1 -> True and 0 -> False + for key in list(assumptions.keys()): + v = assumptions[key] + if v is None: + assumptions.pop(key) + continue + assumptions[key] = bool(v) + + def _merge(self, assumptions): + base = self.assumptions0 + for k in set(assumptions) & set(base): + if assumptions[k] != base[k]: + raise ValueError(filldedent(''' + non-matching assumptions for %s: existing value + is %s and new value is %s''' % ( + k, base[k], assumptions[k]))) + base.update(assumptions) + return base + + def __new__(cls, name, **assumptions): + """Symbols are identified by name and assumptions:: + + >>> from sympy import Symbol + >>> Symbol("x") == Symbol("x") + True + >>> Symbol("x", real=True) == Symbol("x", real=False) + False + + """ + cls._sanitize(assumptions, cls) + return Symbol.__xnew_cached_(cls, name, **assumptions) + + @staticmethod + def __xnew__(cls, name, **assumptions): # never cached (e.g. dummy) + if not isinstance(name, str): + raise TypeError("name should be a string, not %s" % repr(type(name))) + + # This is retained purely so that srepr can include commutative=True if + # that was explicitly specified but not if it was not. Ideally srepr + # should not distinguish these cases because the symbols otherwise + # compare equal and are considered equivalent. + # + # See https://github.com/sympy/sympy/issues/8873 + # + assumptions_orig = assumptions.copy() + + # The only assumption that is assumed by default is comutative=True: + assumptions.setdefault('commutative', True) + + assumptions_kb = StdFactKB(assumptions) + assumptions0 = dict(assumptions_kb) + + obj = Expr.__new__(cls) + obj.name = name + + obj._assumptions = assumptions_kb + obj._assumptions_orig = assumptions_orig + obj._assumptions0 = assumptions0 + + # The three assumptions dicts are all a little different: + # + # >>> from sympy import Symbol + # >>> x = Symbol('x', finite=True) + # >>> x.is_positive # query an assumption + # >>> x._assumptions + # {'finite': True, 'infinite': False, 'commutative': True, 'positive': None} + # >>> x._assumptions0 + # {'finite': True, 'infinite': False, 'commutative': True} + # >>> x._assumptions_orig + # {'finite': True} + # + # Two symbols with the same name are equal if their _assumptions0 are + # the same. Arguably it should be _assumptions_orig that is being + # compared because that is more transparent to the user (it is + # what was passed to the constructor modulo changes made by _sanitize). + + return obj + + @staticmethod + @cacheit + def __xnew_cached_(cls, name, **assumptions): # symbols are always cached + return Symbol.__xnew__(cls, name, **assumptions) + + def __getnewargs_ex__(self): + return ((self.name,), self._assumptions_orig) + + # NOTE: __setstate__ is not needed for pickles created by __getnewargs_ex__ + # but was used before Symbol was changed to use __getnewargs_ex__ in v1.9. + # Pickles created in previous SymPy versions will still need __setstate__ + # so that they can be unpickled in SymPy > v1.9. + + def __setstate__(self, state): + for name, value in state.items(): + setattr(self, name, value) + + def _hashable_content(self): + # Note: user-specified assumptions not hashed, just derived ones + return (self.name,) + tuple(sorted(self.assumptions0.items())) + + def _eval_subs(self, old, new): + if old.is_Pow: + from sympy.core.power import Pow + return Pow(self, S.One, evaluate=False)._eval_subs(old, new) + + def _eval_refine(self, assumptions): + return self + + @property + def assumptions0(self): + return self._assumptions0.copy() + + @cacheit + def sort_key(self, order=None): + return self.class_key(), (1, (self.name,)), S.One.sort_key(), S.One + + def as_dummy(self): + # only put commutativity in explicitly if it is False + return Dummy(self.name) if self.is_commutative is not False \ + else Dummy(self.name, commutative=self.is_commutative) + + def as_real_imag(self, deep=True, **hints): + if hints.get('ignore') == self: + return None + else: + from sympy.functions.elementary.complexes import im, re + return (re(self), im(self)) + + def is_constant(self, *wrt, **flags): + if not wrt: + return False + return self not in wrt + + @property + def free_symbols(self): + return {self} + + binary_symbols = free_symbols # in this case, not always + + def as_set(self): + return S.UniversalSet + + +class Dummy(Symbol): + """Dummy symbols are each unique, even if they have the same name: + + Examples + ======== + + >>> from sympy import Dummy + >>> Dummy("x") == Dummy("x") + False + + If a name is not supplied then a string value of an internal count will be + used. This is useful when a temporary variable is needed and the name + of the variable used in the expression is not important. + + >>> Dummy() #doctest: +SKIP + _Dummy_10 + + """ + + # In the rare event that a Dummy object needs to be recreated, both the + # `name` and `dummy_index` should be passed. This is used by `srepr` for + # example: + # >>> d1 = Dummy() + # >>> d2 = eval(srepr(d1)) + # >>> d2 == d1 + # True + # + # If a new session is started between `srepr` and `eval`, there is a very + # small chance that `d2` will be equal to a previously-created Dummy. + + _count = 0 + _prng = random.Random() + _base_dummy_index = _prng.randint(10**6, 9*10**6) + + __slots__ = ('dummy_index',) + + is_Dummy = True + + def __new__(cls, name=None, dummy_index=None, **assumptions): + if dummy_index is not None: + assert name is not None, "If you specify a dummy_index, you must also provide a name" + + if name is None: + name = "Dummy_" + str(Dummy._count) + + if dummy_index is None: + dummy_index = Dummy._base_dummy_index + Dummy._count + Dummy._count += 1 + + cls._sanitize(assumptions, cls) + obj = Symbol.__xnew__(cls, name, **assumptions) + + obj.dummy_index = dummy_index + + return obj + + def __getnewargs_ex__(self): + return ((self.name, self.dummy_index), self._assumptions_orig) + + @cacheit + def sort_key(self, order=None): + return self.class_key(), ( + 2, (self.name, self.dummy_index)), S.One.sort_key(), S.One + + def _hashable_content(self): + return Symbol._hashable_content(self) + (self.dummy_index,) + + +class Wild(Symbol): + """ + A Wild symbol matches anything, or anything + without whatever is explicitly excluded. + + Parameters + ========== + + name : str + Name of the Wild instance. + + exclude : iterable, optional + Instances in ``exclude`` will not be matched. + + properties : iterable of functions, optional + Functions, each taking an expressions as input + and returns a ``bool``. All functions in ``properties`` + need to return ``True`` in order for the Wild instance + to match the expression. + + Examples + ======== + + >>> from sympy import Wild, WildFunction, cos, pi + >>> from sympy.abc import x, y, z + >>> a = Wild('a') + >>> x.match(a) + {a_: x} + >>> pi.match(a) + {a_: pi} + >>> (3*x**2).match(a*x) + {a_: 3*x} + >>> cos(x).match(a) + {a_: cos(x)} + >>> b = Wild('b', exclude=[x]) + >>> (3*x**2).match(b*x) + >>> b.match(a) + {a_: b_} + >>> A = WildFunction('A') + >>> A.match(a) + {a_: A_} + + Tips + ==== + + When using Wild, be sure to use the exclude + keyword to make the pattern more precise. + Without the exclude pattern, you may get matches + that are technically correct, but not what you + wanted. For example, using the above without + exclude: + + >>> from sympy import symbols + >>> a, b = symbols('a b', cls=Wild) + >>> (2 + 3*y).match(a*x + b*y) + {a_: 2/x, b_: 3} + + This is technically correct, because + (2/x)*x + 3*y == 2 + 3*y, but you probably + wanted it to not match at all. The issue is that + you really did not want a and b to include x and y, + and the exclude parameter lets you specify exactly + this. With the exclude parameter, the pattern will + not match. + + >>> a = Wild('a', exclude=[x, y]) + >>> b = Wild('b', exclude=[x, y]) + >>> (2 + 3*y).match(a*x + b*y) + + Exclude also helps remove ambiguity from matches. + + >>> E = 2*x**3*y*z + >>> a, b = symbols('a b', cls=Wild) + >>> E.match(a*b) + {a_: 2*y*z, b_: x**3} + >>> a = Wild('a', exclude=[x, y]) + >>> E.match(a*b) + {a_: z, b_: 2*x**3*y} + >>> a = Wild('a', exclude=[x, y, z]) + >>> E.match(a*b) + {a_: 2, b_: x**3*y*z} + + Wild also accepts a ``properties`` parameter: + + >>> a = Wild('a', properties=[lambda k: k.is_Integer]) + >>> E.match(a*b) + {a_: 2, b_: x**3*y*z} + + """ + is_Wild = True + + __slots__ = ('exclude', 'properties') + + def __new__(cls, name, exclude=(), properties=(), **assumptions): + exclude = tuple([sympify(x) for x in exclude]) + properties = tuple(properties) + cls._sanitize(assumptions, cls) + return Wild.__xnew__(cls, name, exclude, properties, **assumptions) + + def __getnewargs__(self): + return (self.name, self.exclude, self.properties) + + @staticmethod + @cacheit + def __xnew__(cls, name, exclude, properties, **assumptions): + obj = Symbol.__xnew__(cls, name, **assumptions) + obj.exclude = exclude + obj.properties = properties + return obj + + def _hashable_content(self): + return super()._hashable_content() + (self.exclude, self.properties) + + # TODO add check against another Wild + def matches(self, expr, repl_dict=None, old=False): + if any(expr.has(x) for x in self.exclude): + return None + if not all(f(expr) for f in self.properties): + return None + if repl_dict is None: + repl_dict = {} + else: + repl_dict = repl_dict.copy() + repl_dict[self] = expr + return repl_dict + + +_range = _re.compile('([0-9]*:[0-9]+|[a-zA-Z]?:[a-zA-Z])') + + +def symbols(names, *, cls=Symbol, **args) -> Any: + r""" + Transform strings into instances of :class:`Symbol` class. + + :func:`symbols` function returns a sequence of symbols with names taken + from ``names`` argument, which can be a comma or whitespace delimited + string, or a sequence of strings:: + + >>> from sympy import symbols, Function + + >>> x, y, z = symbols('x,y,z') + >>> a, b, c = symbols('a b c') + + The type of output is dependent on the properties of input arguments:: + + >>> symbols('x') + x + >>> symbols('x,') + (x,) + >>> symbols('x,y') + (x, y) + >>> symbols(('a', 'b', 'c')) + (a, b, c) + >>> symbols(['a', 'b', 'c']) + [a, b, c] + >>> symbols({'a', 'b', 'c'}) + {a, b, c} + + If an iterable container is needed for a single symbol, set the ``seq`` + argument to ``True`` or terminate the symbol name with a comma:: + + >>> symbols('x', seq=True) + (x,) + + To reduce typing, range syntax is supported to create indexed symbols. + Ranges are indicated by a colon and the type of range is determined by + the character to the right of the colon. If the character is a digit + then all contiguous digits to the left are taken as the nonnegative + starting value (or 0 if there is no digit left of the colon) and all + contiguous digits to the right are taken as 1 greater than the ending + value:: + + >>> symbols('x:10') + (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) + + >>> symbols('x5:10') + (x5, x6, x7, x8, x9) + >>> symbols('x5(:2)') + (x50, x51) + + >>> symbols('x5:10,y:5') + (x5, x6, x7, x8, x9, y0, y1, y2, y3, y4) + + >>> symbols(('x5:10', 'y:5')) + ((x5, x6, x7, x8, x9), (y0, y1, y2, y3, y4)) + + If the character to the right of the colon is a letter, then the single + letter to the left (or 'a' if there is none) is taken as the start + and all characters in the lexicographic range *through* the letter to + the right are used as the range:: + + >>> symbols('x:z') + (x, y, z) + >>> symbols('x:c') # null range + () + >>> symbols('x(:c)') + (xa, xb, xc) + + >>> symbols(':c') + (a, b, c) + + >>> symbols('a:d, x:z') + (a, b, c, d, x, y, z) + + >>> symbols(('a:d', 'x:z')) + ((a, b, c, d), (x, y, z)) + + Multiple ranges are supported; contiguous numerical ranges should be + separated by parentheses to disambiguate the ending number of one + range from the starting number of the next:: + + >>> symbols('x:2(1:3)') + (x01, x02, x11, x12) + >>> symbols(':3:2') # parsing is from left to right + (00, 01, 10, 11, 20, 21) + + Only one pair of parentheses surrounding ranges are removed, so to + include parentheses around ranges, double them. And to include spaces, + commas, or colons, escape them with a backslash:: + + >>> symbols('x((a:b))') + (x(a), x(b)) + >>> symbols(r'x(:1\,:2)') # or r'x((:1)\,(:2))' + (x(0,0), x(0,1)) + + All newly created symbols have assumptions set according to ``args``:: + + >>> a = symbols('a', integer=True) + >>> a.is_integer + True + + >>> x, y, z = symbols('x,y,z', real=True) + >>> x.is_real and y.is_real and z.is_real + True + + Despite its name, :func:`symbols` can create symbol-like objects like + instances of Function or Wild classes. To achieve this, set ``cls`` + keyword argument to the desired type:: + + >>> symbols('f,g,h', cls=Function) + (f, g, h) + + >>> type(_[0]) + + + """ + result = [] + + if isinstance(names, str): + marker = 0 + splitters = r'\,', r'\:', r'\ ' + literals: list[tuple[str, str]] = [] + for splitter in splitters: + if splitter in names: + while chr(marker) in names: + marker += 1 + lit_char = chr(marker) + marker += 1 + names = names.replace(splitter, lit_char) + literals.append((lit_char, splitter[1:])) + def literal(s): + if literals: + for c, l in literals: + s = s.replace(c, l) + return s + + names = names.strip() + as_seq = names.endswith(',') + if as_seq: + names = names[:-1].rstrip() + if not names: + raise ValueError('no symbols given') + + # split on commas + names = [n.strip() for n in names.split(',')] + if not all(n for n in names): + raise ValueError('missing symbol between commas') + # split on spaces + for i in range(len(names) - 1, -1, -1): + names[i: i + 1] = names[i].split() + + seq = args.pop('seq', as_seq) + + for name in names: + if not name: + raise ValueError('missing symbol') + + if ':' not in name: + symbol = cls(literal(name), **args) + result.append(symbol) + continue + + split: list[str] = _range.split(name) + split_list: list[list[str]] = [] + # remove 1 layer of bounding parentheses around ranges + for i in range(len(split) - 1): + if i and ':' in split[i] and split[i] != ':' and \ + split[i - 1].endswith('(') and \ + split[i + 1].startswith(')'): + split[i - 1] = split[i - 1][:-1] + split[i + 1] = split[i + 1][1:] + for s in split: + if ':' in s: + if s.endswith(':'): + raise ValueError('missing end range') + a, b = s.split(':') + if b[-1] in string.digits: + a_i = 0 if not a else int(a) + b_i = int(b) + split_list.append([str(c) for c in range(a_i, b_i)]) + else: + a = a or 'a' + split_list.append([string.ascii_letters[c] for c in range( + string.ascii_letters.index(a), + string.ascii_letters.index(b) + 1)]) # inclusive + if not split_list[-1]: + break + else: + split_list.append([s]) + else: + seq = True + if len(split_list) == 1: + names = split_list[0] + else: + names = [''.join(s) for s in product(*split_list)] + if literals: + result.extend([cls(literal(s), **args) for s in names]) + else: + result.extend([cls(s, **args) for s in names]) + + if not seq and len(result) <= 1: + if not result: + return () + return result[0] + + return tuple(result) + else: + for name in names: + result.append(symbols(name, cls=cls, **args)) + + return type(names)(result) + + +def var(names, **args): + """ + Create symbols and inject them into the global namespace. + + Explanation + =========== + + This calls :func:`symbols` with the same arguments and puts the results + into the *global* namespace. It's recommended not to use :func:`var` in + library code, where :func:`symbols` has to be used:: + + Examples + ======== + + >>> from sympy import var + + >>> var('x') + x + >>> x # noqa: F821 + x + + >>> var('a,ab,abc') + (a, ab, abc) + >>> abc # noqa: F821 + abc + + >>> var('x,y', real=True) + (x, y) + >>> x.is_real and y.is_real # noqa: F821 + True + + See :func:`symbols` documentation for more details on what kinds of + arguments can be passed to :func:`var`. + + """ + def traverse(symbols, frame): + """Recursively inject symbols to the global namespace. """ + for symbol in symbols: + if isinstance(symbol, Basic): + frame.f_globals[symbol.name] = symbol + elif isinstance(symbol, FunctionClass): + frame.f_globals[symbol.__name__] = symbol + else: + traverse(symbol, frame) + + from inspect import currentframe + frame = currentframe().f_back + + try: + syms = symbols(names, **args) + + if syms is not None: + if isinstance(syms, Basic): + frame.f_globals[syms.name] = syms + elif isinstance(syms, FunctionClass): + frame.f_globals[syms.__name__] = syms + else: + traverse(syms, frame) + finally: + del frame # break cyclic dependencies as stated in inspect docs + + return syms + +def disambiguate(*iter): + """ + Return a Tuple containing the passed expressions with symbols + that appear the same when printed replaced with numerically + subscripted symbols, and all Dummy symbols replaced with Symbols. + + Parameters + ========== + + iter: list of symbols or expressions. + + Examples + ======== + + >>> from sympy.core.symbol import disambiguate + >>> from sympy import Dummy, Symbol, Tuple + >>> from sympy.abc import y + + >>> tup = Symbol('_x'), Dummy('x'), Dummy('x') + >>> disambiguate(*tup) + (x_2, x, x_1) + + >>> eqs = Tuple(Symbol('x')/y, Dummy('x')/y) + >>> disambiguate(*eqs) + (x_1/y, x/y) + + >>> ix = Symbol('x', integer=True) + >>> vx = Symbol('x') + >>> disambiguate(vx + ix) + (x + x_1,) + + To make your own mapping of symbols to use, pass only the free symbols + of the expressions and create a dictionary: + + >>> free = eqs.free_symbols + >>> mapping = dict(zip(free, disambiguate(*free))) + >>> eqs.xreplace(mapping) + (x_1/y, x/y) + + """ + new_iter = Tuple(*iter) + key = lambda x:tuple(sorted(x.assumptions0.items())) + syms = ordered(new_iter.free_symbols, keys=key) + mapping = {} + for s in syms: + mapping.setdefault(str(s).lstrip('_'), []).append(s) + reps = {} + for k in mapping: + # the first or only symbol doesn't get subscripted but make + # sure that it's a Symbol, not a Dummy + mapk0 = Symbol("%s" % (k), **mapping[k][0].assumptions0) + if mapping[k][0] != mapk0: + reps[mapping[k][0]] = mapk0 + # the others get subscripts (and are made into Symbols) + skip = 0 + for i in range(1, len(mapping[k])): + while True: + name = "%s_%i" % (k, i + skip) + if name not in mapping: + break + skip += 1 + ki = mapping[k][i] + reps[ki] = Symbol(name, **ki.assumptions0) + return new_iter.xreplace(reps) diff --git a/lib/python3.11/site-packages/sympy/core/sympify.py b/lib/python3.11/site-packages/sympy/core/sympify.py new file mode 100644 index 0000000000000000000000000000000000000000..c849462799c7f0438b954981bf7c10954dc9d964 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/sympify.py @@ -0,0 +1,620 @@ +"""sympify -- convert objects SymPy internal format""" + +from __future__ import annotations +from typing import Any, Callable + +import mpmath.libmp as mlib + +from inspect import getmro +import string +from sympy.core.random import choice + +from .parameters import global_parameters + +from sympy.utilities.iterables import iterable + + +class SympifyError(ValueError): + def __init__(self, expr, base_exc=None): + self.expr = expr + self.base_exc = base_exc + + def __str__(self): + if self.base_exc is None: + return "SympifyError: %r" % (self.expr,) + + return ("Sympify of expression '%s' failed, because of exception being " + "raised:\n%s: %s" % (self.expr, self.base_exc.__class__.__name__, + str(self.base_exc))) + + +converter: dict[type[Any], Callable[[Any], Basic]] = {} + +#holds the conversions defined in SymPy itself, i.e. non-user defined conversions +_sympy_converter: dict[type[Any], Callable[[Any], Basic]] = {} + +#alias for clearer use in the library +_external_converter = converter + +class CantSympify: + """ + Mix in this trait to a class to disallow sympification of its instances. + + Examples + ======== + + >>> from sympy import sympify + >>> from sympy.core.sympify import CantSympify + + >>> class Something(dict): + ... pass + ... + >>> sympify(Something()) + {} + + >>> class Something(dict, CantSympify): + ... pass + ... + >>> sympify(Something()) + Traceback (most recent call last): + ... + SympifyError: SympifyError: {} + + """ + + __slots__ = () + + +def _is_numpy_instance(a): + """ + Checks if an object is an instance of a type from the numpy module. + """ + # This check avoids unnecessarily importing NumPy. We check the whole + # __mro__ in case any base type is a numpy type. + return any(type_.__module__ == 'numpy' + for type_ in type(a).__mro__) + + +def _convert_numpy_types(a, **sympify_args): + """ + Converts a numpy datatype input to an appropriate SymPy type. + """ + import numpy as np + if not isinstance(a, np.floating): + if np.iscomplex(a): + return _sympy_converter[complex](a.item()) + else: + return sympify(a.item(), **sympify_args) + else: + from .numbers import Float + prec = np.finfo(a).nmant + 1 + # E.g. double precision means prec=53 but nmant=52 + # Leading bit of mantissa is always 1, so is not stored + p, q = a.as_integer_ratio() + a = mlib.from_rational(p, q, prec) + return Float(a, precision=prec) + + +def sympify(a, locals=None, convert_xor=True, strict=False, rational=False, + evaluate=None): + """ + Converts an arbitrary expression to a type that can be used inside SymPy. + + Explanation + =========== + + It will convert Python ints into instances of :class:`~.Integer`, floats + into instances of :class:`~.Float`, etc. It is also able to coerce + symbolic expressions which inherit from :class:`~.Basic`. This can be + useful in cooperation with SAGE. + + .. warning:: + Note that this function uses ``eval``, and thus shouldn't be used on + unsanitized input. + + If the argument is already a type that SymPy understands, it will do + nothing but return that value. This can be used at the beginning of a + function to ensure you are working with the correct type. + + Examples + ======== + + >>> from sympy import sympify + + >>> sympify(2).is_integer + True + >>> sympify(2).is_real + True + + >>> sympify(2.0).is_real + True + >>> sympify("2.0").is_real + True + >>> sympify("2e-45").is_real + True + + If the expression could not be converted, a SympifyError is raised. + + >>> sympify("x***2") + Traceback (most recent call last): + ... + SympifyError: SympifyError: "could not parse 'x***2'" + + When attempting to parse non-Python syntax using ``sympify``, it raises a + ``SympifyError``: + + >>> sympify("2x+1") + Traceback (most recent call last): + ... + SympifyError: Sympify of expression 'could not parse '2x+1'' failed + + To parse non-Python syntax, use ``parse_expr`` from ``sympy.parsing.sympy_parser``. + + >>> from sympy.parsing.sympy_parser import parse_expr + >>> parse_expr("2x+1", transformations="all") + 2*x + 1 + + For more details about ``transformations``: see :func:`~sympy.parsing.sympy_parser.parse_expr` + + Locals + ------ + + The sympification happens with access to everything that is loaded + by ``from sympy import *``; anything used in a string that is not + defined by that import will be converted to a symbol. In the following, + the ``bitcount`` function is treated as a symbol and the ``O`` is + interpreted as the :class:`~.Order` object (used with series) and it raises + an error when used improperly: + + >>> s = 'bitcount(42)' + >>> sympify(s) + bitcount(42) + >>> sympify("O(x)") + O(x) + >>> sympify("O + 1") + Traceback (most recent call last): + ... + TypeError: unbound method... + + In order to have ``bitcount`` be recognized it can be imported into a + namespace dictionary and passed as locals: + + >>> ns = {} + >>> exec('from sympy.core.evalf import bitcount', ns) + >>> sympify(s, locals=ns) + 6 + + In order to have the ``O`` interpreted as a Symbol, identify it as such + in the namespace dictionary. This can be done in a variety of ways; all + three of the following are possibilities: + + >>> from sympy import Symbol + >>> ns["O"] = Symbol("O") # method 1 + >>> exec('from sympy.abc import O', ns) # method 2 + >>> ns.update(dict(O=Symbol("O"))) # method 3 + >>> sympify("O + 1", locals=ns) + O + 1 + + If you want *all* single-letter and Greek-letter variables to be symbols + then you can use the clashing-symbols dictionaries that have been defined + there as private variables: ``_clash1`` (single-letter variables), + ``_clash2`` (the multi-letter Greek names) or ``_clash`` (both single and + multi-letter names that are defined in ``abc``). + + >>> from sympy.abc import _clash1 + >>> set(_clash1) # if this fails, see issue #23903 + {'E', 'I', 'N', 'O', 'Q', 'S'} + >>> sympify('I & Q', _clash1) + I & Q + + Strict + ------ + + If the option ``strict`` is set to ``True``, only the types for which an + explicit conversion has been defined are converted. In the other + cases, a SympifyError is raised. + + >>> print(sympify(None)) + None + >>> sympify(None, strict=True) + Traceback (most recent call last): + ... + SympifyError: SympifyError: None + + .. deprecated:: 1.6 + + ``sympify(obj)`` automatically falls back to ``str(obj)`` when all + other conversion methods fail, but this is deprecated. ``strict=True`` + will disable this deprecated behavior. See + :ref:`deprecated-sympify-string-fallback`. + + Evaluation + ---------- + + If the option ``evaluate`` is set to ``False``, then arithmetic and + operators will be converted into their SymPy equivalents and the + ``evaluate=False`` option will be added. Nested ``Add`` or ``Mul`` will + be denested first. This is done via an AST transformation that replaces + operators with their SymPy equivalents, so if an operand redefines any + of those operations, the redefined operators will not be used. If + argument a is not a string, the mathematical expression is evaluated + before being passed to sympify, so adding ``evaluate=False`` will still + return the evaluated result of expression. + + >>> sympify('2**2 / 3 + 5') + 19/3 + >>> sympify('2**2 / 3 + 5', evaluate=False) + 2**2/3 + 5 + >>> sympify('4/2+7', evaluate=True) + 9 + >>> sympify('4/2+7', evaluate=False) + 4/2 + 7 + >>> sympify(4/2+7, evaluate=False) + 9.00000000000000 + + Extending + --------- + + To extend ``sympify`` to convert custom objects (not derived from ``Basic``), + just define a ``_sympy_`` method to your class. You can do that even to + classes that you do not own by subclassing or adding the method at runtime. + + >>> from sympy import Matrix + >>> class MyList1(object): + ... def __iter__(self): + ... yield 1 + ... yield 2 + ... return + ... def __getitem__(self, i): return list(self)[i] + ... def _sympy_(self): return Matrix(self) + >>> sympify(MyList1()) + Matrix([ + [1], + [2]]) + + If you do not have control over the class definition you could also use the + ``converter`` global dictionary. The key is the class and the value is a + function that takes a single argument and returns the desired SymPy + object, e.g. ``converter[MyList] = lambda x: Matrix(x)``. + + >>> class MyList2(object): # XXX Do not do this if you control the class! + ... def __iter__(self): # Use _sympy_! + ... yield 1 + ... yield 2 + ... return + ... def __getitem__(self, i): return list(self)[i] + >>> from sympy.core.sympify import converter + >>> converter[MyList2] = lambda x: Matrix(x) + >>> sympify(MyList2()) + Matrix([ + [1], + [2]]) + + Notes + ===== + + The keywords ``rational`` and ``convert_xor`` are only used + when the input is a string. + + convert_xor + ----------- + + >>> sympify('x^y',convert_xor=True) + x**y + >>> sympify('x^y',convert_xor=False) + x ^ y + + rational + -------- + + >>> sympify('0.1',rational=False) + 0.1 + >>> sympify('0.1',rational=True) + 1/10 + + Sometimes autosimplification during sympification results in expressions + that are very different in structure than what was entered. Until such + autosimplification is no longer done, the ``kernS`` function might be of + some use. In the example below you can see how an expression reduces to + $-1$ by autosimplification, but does not do so when ``kernS`` is used. + + >>> from sympy.core.sympify import kernS + >>> from sympy.abc import x + >>> -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 + -1 + >>> s = '-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1' + >>> sympify(s) + -1 + >>> kernS(s) + -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1 + + Parameters + ========== + + a : + - any object defined in SymPy + - standard numeric Python types: ``int``, ``long``, ``float``, ``Decimal`` + - strings (like ``"0.09"``, ``"2e-19"`` or ``'sin(x)'``) + - booleans, including ``None`` (will leave ``None`` unchanged) + - dicts, lists, sets or tuples containing any of the above + + convert_xor : bool, optional + If true, treats ``^`` as exponentiation. + If False, treats ``^`` as XOR itself. + Used only when input is a string. + + locals : any object defined in SymPy, optional + In order to have strings be recognized it can be imported + into a namespace dictionary and passed as locals. + + strict : bool, optional + If the option strict is set to ``True``, only the types for which + an explicit conversion has been defined are converted. In the + other cases, a SympifyError is raised. + + rational : bool, optional + If ``True``, converts floats into :class:`~.Rational`. + If ``False``, it lets floats remain as it is. + Used only when input is a string. + + evaluate : bool, optional + If False, then arithmetic and operators will be converted into + their SymPy equivalents. If True the expression will be evaluated + and the result will be returned. + + """ + # XXX: If a is a Basic subclass rather than instance (e.g. sin rather than + # sin(x)) then a.__sympy__ will be the property. Only on the instance will + # a.__sympy__ give the *value* of the property (True). Since sympify(sin) + # was used for a long time we allow it to pass. However if strict=True as + # is the case in internal calls to _sympify then we only allow + # is_sympy=True. + # + # https://github.com/sympy/sympy/issues/20124 + is_sympy = getattr(a, '__sympy__', None) + if is_sympy is True: + return a + elif is_sympy is not None: + if not strict: + return a + else: + raise SympifyError(a) + + if isinstance(a, CantSympify): + raise SympifyError(a) + + cls = getattr(a, "__class__", None) + + #Check if there exists a converter for any of the types in the mro + for superclass in getmro(cls): + #First check for user defined converters + conv = _external_converter.get(superclass) + if conv is None: + #if none exists, check for SymPy defined converters + conv = _sympy_converter.get(superclass) + if conv is not None: + return conv(a) + + if cls is type(None): + if strict: + raise SympifyError(a) + else: + return a + + if evaluate is None: + evaluate = global_parameters.evaluate + + # Support for basic numpy datatypes + if _is_numpy_instance(a): + import numpy as np + if np.isscalar(a): + return _convert_numpy_types(a, locals=locals, + convert_xor=convert_xor, strict=strict, rational=rational, + evaluate=evaluate) + + _sympy_ = getattr(a, "_sympy_", None) + if _sympy_ is not None: + return a._sympy_() + + if not strict: + # Put numpy array conversion _before_ float/int, see + # . + flat = getattr(a, "flat", None) + if flat is not None: + shape = getattr(a, "shape", None) + if shape is not None: + from sympy.tensor.array import Array + return Array(a.flat, a.shape) # works with e.g. NumPy arrays + + if not isinstance(a, str): + if _is_numpy_instance(a): + import numpy as np + assert not isinstance(a, np.number) + if isinstance(a, np.ndarray): + # Scalar arrays (those with zero dimensions) have sympify + # called on the scalar element. + if a.ndim == 0: + try: + return sympify(a.item(), + locals=locals, + convert_xor=convert_xor, + strict=strict, + rational=rational, + evaluate=evaluate) + except SympifyError: + pass + elif hasattr(a, '__float__'): + # float and int can coerce size-one numpy arrays to their lone + # element. See issue https://github.com/numpy/numpy/issues/10404. + return sympify(float(a)) + elif hasattr(a, '__int__'): + return sympify(int(a)) + + if strict: + raise SympifyError(a) + + if iterable(a): + try: + return type(a)([sympify(x, locals=locals, convert_xor=convert_xor, + rational=rational, evaluate=evaluate) for x in a]) + except TypeError: + # Not all iterables are rebuildable with their type. + pass + + if not isinstance(a, str): + raise SympifyError('cannot sympify object of type %r' % type(a)) + + from sympy.parsing.sympy_parser import (parse_expr, TokenError, + standard_transformations) + from sympy.parsing.sympy_parser import convert_xor as t_convert_xor + from sympy.parsing.sympy_parser import rationalize as t_rationalize + + transformations = standard_transformations + + if rational: + transformations += (t_rationalize,) + if convert_xor: + transformations += (t_convert_xor,) + + try: + a = a.replace('\n', '') + expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate) + except (TokenError, SyntaxError) as exc: + raise SympifyError('could not parse %r' % a, exc) + + return expr + + +def _sympify(a): + """ + Short version of :func:`~.sympify` for internal usage for ``__add__`` and + ``__eq__`` methods where it is ok to allow some things (like Python + integers and floats) in the expression. This excludes things (like strings) + that are unwise to allow into such an expression. + + >>> from sympy import Integer + >>> Integer(1) == 1 + True + + >>> Integer(1) == '1' + False + + >>> from sympy.abc import x + >>> x + 1 + x + 1 + + >>> x + '1' + Traceback (most recent call last): + ... + TypeError: unsupported operand type(s) for +: 'Symbol' and 'str' + + see: sympify + + """ + return sympify(a, strict=True) + + +def kernS(s): + """Use a hack to try keep autosimplification from distributing a + a number into an Add; this modification does not + prevent the 2-arg Mul from becoming an Add, however. + + Examples + ======== + + >>> from sympy.core.sympify import kernS + >>> from sympy.abc import x, y + + The 2-arg Mul distributes a number (or minus sign) across the terms + of an expression, but kernS will prevent that: + + >>> 2*(x + y), -(x + 1) + (2*x + 2*y, -x - 1) + >>> kernS('2*(x + y)') + 2*(x + y) + >>> kernS('-(x + 1)') + -(x + 1) + + If use of the hack fails, the un-hacked string will be passed to sympify... + and you get what you get. + + XXX This hack should not be necessary once issue 4596 has been resolved. + """ + hit = False + quoted = '"' in s or "'" in s + if '(' in s and not quoted: + if s.count('(') != s.count(")"): + raise SympifyError('unmatched left parenthesis') + + # strip all space from s + s = ''.join(s.split()) + olds = s + # now use space to represent a symbol that + # will + # step 1. turn potential 2-arg Muls into 3-arg versions + # 1a. *( -> * *( + s = s.replace('*(', '* *(') + # 1b. close up exponentials + s = s.replace('** *', '**') + # 2. handle the implied multiplication of a negated + # parenthesized expression in two steps + # 2a: -(...) --> -( *(...) + target = '-( *(' + s = s.replace('-(', target) + # 2b: double the matching closing parenthesis + # -( *(...) --> -( *(...)) + i = nest = 0 + assert target.endswith('(') # assumption below + while True: + j = s.find(target, i) + if j == -1: + break + j += len(target) - 1 + for j in range(j, len(s)): + if s[j] == "(": + nest += 1 + elif s[j] == ")": + nest -= 1 + if nest == 0: + break + s = s[:j] + ")" + s[j:] + i = j + 2 # the first char after 2nd ) + if ' ' in s: + # get a unique kern + kern = '_' + while kern in s: + kern += choice(string.ascii_letters + string.digits) + s = s.replace(' ', kern) + hit = kern in s + else: + hit = False + + for i in range(2): + try: + expr = sympify(s) + break + except TypeError: # the kern might cause unknown errors... + if hit: + s = olds # maybe it didn't like the kern; use un-kerned s + hit = False + continue + expr = sympify(s) # let original error raise + + if not hit: + return expr + + from .symbol import Symbol + rep = {Symbol(kern): 1} + def _clear(expr): + if isinstance(expr, (list, tuple, set)): + return type(expr)([_clear(e) for e in expr]) + if hasattr(expr, 'subs'): + return expr.subs(rep, hack2=True) + return expr + expr = _clear(expr) + # hope that kern is not there anymore + return expr + + +# Avoid 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b/lib/python3.11/site-packages/sympy/core/tests/test_args.py @@ -0,0 +1,5455 @@ +"""Test whether all elements of cls.args are instances of Basic. """ + +# NOTE: keep tests sorted by (module, class name) key. If a class can't +# be instantiated, add it here anyway with @SKIP("abstract class) (see +# e.g. Function). + +import os +import re + +from sympy.assumptions.ask import Q +from sympy.core.basic import Basic +from sympy.core.function import (Function, Lambda) +from sympy.core.numbers import (Rational, oo, pi) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin + +from sympy.testing.pytest import SKIP + +a, b, c, x, y, z = symbols('a,b,c,x,y,z') + + +whitelist = [ + "sympy.assumptions.predicates", # tested by test_predicates() + "sympy.assumptions.relation.equality", # tested by test_predicates() +] + +def test_all_classes_are_tested(): + this = os.path.split(__file__)[0] + path = os.path.join(this, os.pardir, os.pardir) + sympy_path = os.path.abspath(path) + prefix = os.path.split(sympy_path)[0] + os.sep + + re_cls = re.compile(r"^class ([A-Za-z][A-Za-z0-9_]*)\s*\(", re.MULTILINE) + + modules = {} + + for root, dirs, files in os.walk(sympy_path): + module = root.replace(prefix, "").replace(os.sep, ".") + + for file in files: + if file.startswith(("_", "test_", "bench_")): + continue + if not file.endswith(".py"): + continue + + with open(os.path.join(root, file), encoding='utf-8') as f: + text = f.read() + + submodule = module + '.' + file[:-3] + + if any(submodule.startswith(wpath) for wpath in whitelist): + continue + + names = re_cls.findall(text) + + if not names: + continue + + try: + mod = __import__(submodule, fromlist=names) + except ImportError: + continue + + def is_Basic(name): + cls = getattr(mod, name) + if hasattr(cls, '_sympy_deprecated_func'): + cls = cls._sympy_deprecated_func + if not isinstance(cls, type): + # check instance of singleton class with same name + cls = type(cls) + return issubclass(cls, Basic) + + names = list(filter(is_Basic, names)) + + if names: + modules[submodule] = names + + ns = globals() + failed = [] + + for module, names in modules.items(): + mod = module.replace('.', '__') + + for name in names: + test = 'test_' + mod + '__' + name + + if test not in ns: + failed.append(module + '.' + name) + + assert not failed, "Missing classes: %s. Please add tests for these to sympy/core/tests/test_args.py." % ", ".join(failed) + + +def _test_args(obj): + all_basic = all(isinstance(arg, Basic) for arg in obj.args) + # Ideally obj.func(*obj.args) would always recreate the object, but for + # now, we only require it for objects with non-empty .args + recreatable = not obj.args or obj.func(*obj.args) == obj + return all_basic and recreatable + + +def test_sympy__algebras__quaternion__Quaternion(): + from sympy.algebras.quaternion import Quaternion + assert _test_args(Quaternion(x, 1, 2, 3)) + + +def test_sympy__assumptions__assume__AppliedPredicate(): + from sympy.assumptions.assume import AppliedPredicate, Predicate + assert _test_args(AppliedPredicate(Predicate("test"), 2)) + assert _test_args(Q.is_true(True)) + +@SKIP("abstract class") +def test_sympy__assumptions__assume__Predicate(): + pass + +def test_predicates(): + predicates = [ + getattr(Q, attr) + for attr in Q.__class__.__dict__ + if not attr.startswith('__')] + for p in predicates: + assert _test_args(p) + +def test_sympy__assumptions__assume__UndefinedPredicate(): + from sympy.assumptions.assume import Predicate + assert _test_args(Predicate("test")) + +@SKIP('abstract class') +def test_sympy__assumptions__relation__binrel__BinaryRelation(): + pass + +def test_sympy__assumptions__relation__binrel__AppliedBinaryRelation(): + assert _test_args(Q.eq(1, 2)) + +def test_sympy__assumptions__wrapper__AssumptionsWrapper(): + from sympy.assumptions.wrapper import AssumptionsWrapper + assert _test_args(AssumptionsWrapper(x, Q.positive(x))) + +@SKIP("abstract Class") +def test_sympy__codegen__ast__CodegenAST(): + from sympy.codegen.ast import CodegenAST + assert _test_args(CodegenAST()) + +@SKIP("abstract Class") +def test_sympy__codegen__ast__AssignmentBase(): + from sympy.codegen.ast import AssignmentBase + assert _test_args(AssignmentBase(x, 1)) + +@SKIP("abstract Class") +def test_sympy__codegen__ast__AugmentedAssignment(): + from sympy.codegen.ast import AugmentedAssignment + assert _test_args(AugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__AddAugmentedAssignment(): + from sympy.codegen.ast import AddAugmentedAssignment + assert _test_args(AddAugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__SubAugmentedAssignment(): + from sympy.codegen.ast import SubAugmentedAssignment + assert _test_args(SubAugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__MulAugmentedAssignment(): + from sympy.codegen.ast import MulAugmentedAssignment + assert _test_args(MulAugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__DivAugmentedAssignment(): + from sympy.codegen.ast import DivAugmentedAssignment + assert _test_args(DivAugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__ModAugmentedAssignment(): + from sympy.codegen.ast import ModAugmentedAssignment + assert _test_args(ModAugmentedAssignment(x, 1)) + +def test_sympy__codegen__ast__CodeBlock(): + from sympy.codegen.ast import CodeBlock, Assignment + assert _test_args(CodeBlock(Assignment(x, 1), Assignment(y, 2))) + +def test_sympy__codegen__ast__For(): + from sympy.codegen.ast import For, CodeBlock, AddAugmentedAssignment + from sympy.sets import Range + assert _test_args(For(x, Range(10), CodeBlock(AddAugmentedAssignment(y, 1)))) + + +def test_sympy__codegen__ast__Token(): + from sympy.codegen.ast import Token + assert _test_args(Token()) + + +def test_sympy__codegen__ast__ContinueToken(): + from sympy.codegen.ast import ContinueToken + assert _test_args(ContinueToken()) + +def test_sympy__codegen__ast__BreakToken(): + from sympy.codegen.ast import BreakToken + assert _test_args(BreakToken()) + +def test_sympy__codegen__ast__NoneToken(): + from sympy.codegen.ast import NoneToken + assert _test_args(NoneToken()) + +def test_sympy__codegen__ast__String(): + from sympy.codegen.ast import String + assert _test_args(String('foobar')) + +def test_sympy__codegen__ast__QuotedString(): + from sympy.codegen.ast import QuotedString + assert _test_args(QuotedString('foobar')) + +def test_sympy__codegen__ast__Comment(): + from sympy.codegen.ast import Comment + assert _test_args(Comment('this is a comment')) + +def test_sympy__codegen__ast__Node(): + from sympy.codegen.ast import Node + assert _test_args(Node()) + assert _test_args(Node(attrs={1, 2, 3})) + + +def test_sympy__codegen__ast__Type(): + from sympy.codegen.ast import Type + assert _test_args(Type('float128')) + + +def test_sympy__codegen__ast__IntBaseType(): + from sympy.codegen.ast import IntBaseType + assert _test_args(IntBaseType('bigint')) + + +def test_sympy__codegen__ast___SizedIntType(): + from sympy.codegen.ast import _SizedIntType + assert _test_args(_SizedIntType('int128', 128)) + + +def test_sympy__codegen__ast__SignedIntType(): + from sympy.codegen.ast import SignedIntType + assert _test_args(SignedIntType('int128_with_sign', 128)) + + +def test_sympy__codegen__ast__UnsignedIntType(): + from sympy.codegen.ast import UnsignedIntType + assert _test_args(UnsignedIntType('unt128', 128)) + + +def test_sympy__codegen__ast__FloatBaseType(): + from sympy.codegen.ast import FloatBaseType + assert _test_args(FloatBaseType('positive_real')) + + +def test_sympy__codegen__ast__FloatType(): + from sympy.codegen.ast import FloatType + assert _test_args(FloatType('float242', 242, nmant=142, nexp=99)) + + +def test_sympy__codegen__ast__ComplexBaseType(): + from sympy.codegen.ast import ComplexBaseType + assert _test_args(ComplexBaseType('positive_cmplx')) + +def test_sympy__codegen__ast__ComplexType(): + from sympy.codegen.ast import ComplexType + assert _test_args(ComplexType('complex42', 42, nmant=15, nexp=5)) + + +def test_sympy__codegen__ast__Attribute(): + from sympy.codegen.ast import Attribute + assert _test_args(Attribute('noexcept')) + + +def test_sympy__codegen__ast__Variable(): + from sympy.codegen.ast import Variable, Type, value_const + assert _test_args(Variable(x)) + assert _test_args(Variable(y, Type('float32'), {value_const})) + assert _test_args(Variable(z, type=Type('float64'))) + + +def test_sympy__codegen__ast__Pointer(): + from sympy.codegen.ast import Pointer, Type, pointer_const + assert _test_args(Pointer(x)) + assert _test_args(Pointer(y, type=Type('float32'))) + assert _test_args(Pointer(z, Type('float64'), {pointer_const})) + + +def test_sympy__codegen__ast__Declaration(): + from sympy.codegen.ast import Declaration, Variable, Type + vx = Variable(x, type=Type('float')) + assert _test_args(Declaration(vx)) + + +def test_sympy__codegen__ast__While(): + from sympy.codegen.ast import While, AddAugmentedAssignment + assert _test_args(While(abs(x) < 1, [AddAugmentedAssignment(x, -1)])) + + +def test_sympy__codegen__ast__Scope(): + from sympy.codegen.ast import Scope, AddAugmentedAssignment + assert _test_args(Scope([AddAugmentedAssignment(x, -1)])) + + +def test_sympy__codegen__ast__Stream(): + from sympy.codegen.ast import Stream + assert _test_args(Stream('stdin')) + +def test_sympy__codegen__ast__Print(): + from sympy.codegen.ast import Print + assert _test_args(Print([x, y])) + assert _test_args(Print([x, y], "%d %d")) + + +def test_sympy__codegen__ast__FunctionPrototype(): + from sympy.codegen.ast import FunctionPrototype, real, Declaration, Variable + inp_x = Declaration(Variable(x, type=real)) + assert _test_args(FunctionPrototype(real, 'pwer', [inp_x])) + + +def test_sympy__codegen__ast__FunctionDefinition(): + from sympy.codegen.ast import FunctionDefinition, real, Declaration, Variable, Assignment + inp_x = Declaration(Variable(x, type=real)) + assert _test_args(FunctionDefinition(real, 'pwer', [inp_x], [Assignment(x, x**2)])) + + +def test_sympy__codegen__ast__Raise(): + from sympy.codegen.ast import Raise + assert _test_args(Raise(x)) + + +def test_sympy__codegen__ast__Return(): + from sympy.codegen.ast import Return + assert _test_args(Return(x)) + + +def test_sympy__codegen__ast__RuntimeError_(): + from sympy.codegen.ast import RuntimeError_ + assert _test_args(RuntimeError_('"message"')) + + +def test_sympy__codegen__ast__FunctionCall(): + from sympy.codegen.ast import FunctionCall + assert _test_args(FunctionCall('pwer', [x])) + + +def test_sympy__codegen__ast__Element(): + from sympy.codegen.ast import Element + assert _test_args(Element('x', range(3))) + + +def test_sympy__codegen__cnodes__CommaOperator(): + from sympy.codegen.cnodes import CommaOperator + assert _test_args(CommaOperator(1, 2)) + + +def test_sympy__codegen__cnodes__goto(): + from sympy.codegen.cnodes import goto + assert _test_args(goto('early_exit')) + + +def test_sympy__codegen__cnodes__Label(): + from sympy.codegen.cnodes import Label + assert _test_args(Label('early_exit')) + + +def test_sympy__codegen__cnodes__PreDecrement(): + from sympy.codegen.cnodes import PreDecrement + assert _test_args(PreDecrement(x)) + + +def test_sympy__codegen__cnodes__PostDecrement(): + from sympy.codegen.cnodes import PostDecrement + assert _test_args(PostDecrement(x)) + + +def test_sympy__codegen__cnodes__PreIncrement(): + from sympy.codegen.cnodes import PreIncrement + assert _test_args(PreIncrement(x)) + + +def test_sympy__codegen__cnodes__PostIncrement(): + from sympy.codegen.cnodes import PostIncrement + assert _test_args(PostIncrement(x)) + + +def test_sympy__codegen__cnodes__struct(): + from sympy.codegen.ast import real, Variable + from sympy.codegen.cnodes import struct + assert _test_args(struct(declarations=[ + Variable(x, type=real), + Variable(y, type=real) + ])) + + +def test_sympy__codegen__cnodes__union(): + from sympy.codegen.ast import float32, int32, Variable + from sympy.codegen.cnodes import union + assert _test_args(union(declarations=[ + Variable(x, type=float32), + Variable(y, type=int32) + ])) + + +def test_sympy__codegen__cxxnodes__using(): + from sympy.codegen.cxxnodes import using + assert _test_args(using('std::vector')) + assert _test_args(using('std::vector', 'vec')) + + +def test_sympy__codegen__fnodes__Program(): + from sympy.codegen.fnodes import Program + assert _test_args(Program('foobar', [])) + +def test_sympy__codegen__fnodes__Module(): + from sympy.codegen.fnodes import Module + assert _test_args(Module('foobar', [], [])) + + +def test_sympy__codegen__fnodes__Subroutine(): + from sympy.codegen.fnodes import Subroutine + x = symbols('x', real=True) + assert _test_args(Subroutine('foo', [x], [])) + + +def test_sympy__codegen__fnodes__GoTo(): + from sympy.codegen.fnodes import GoTo + assert _test_args(GoTo([10])) + assert _test_args(GoTo([10, 20], x > 1)) + + +def test_sympy__codegen__fnodes__FortranReturn(): + from sympy.codegen.fnodes import FortranReturn + assert _test_args(FortranReturn(10)) + + +def test_sympy__codegen__fnodes__Extent(): + from sympy.codegen.fnodes import Extent + assert _test_args(Extent()) + assert _test_args(Extent(None)) + assert _test_args(Extent(':')) + assert _test_args(Extent(-3, 4)) + assert _test_args(Extent(x, y)) + + +def test_sympy__codegen__fnodes__use_rename(): + from sympy.codegen.fnodes import use_rename + assert _test_args(use_rename('loc', 'glob')) + + +def test_sympy__codegen__fnodes__use(): + from sympy.codegen.fnodes import use + assert _test_args(use('modfoo', only='bar')) + + +def test_sympy__codegen__fnodes__SubroutineCall(): + from sympy.codegen.fnodes import SubroutineCall + assert _test_args(SubroutineCall('foo', ['bar', 'baz'])) + + +def test_sympy__codegen__fnodes__Do(): + from sympy.codegen.fnodes import Do + assert _test_args(Do([], 'i', 1, 42)) + + +def test_sympy__codegen__fnodes__ImpliedDoLoop(): + from sympy.codegen.fnodes import ImpliedDoLoop + assert _test_args(ImpliedDoLoop('i', 'i', 1, 42)) + + +def test_sympy__codegen__fnodes__ArrayConstructor(): + from sympy.codegen.fnodes import ArrayConstructor + assert _test_args(ArrayConstructor([1, 2, 3])) + from sympy.codegen.fnodes import ImpliedDoLoop + idl = ImpliedDoLoop('i', 'i', 1, 42) + assert _test_args(ArrayConstructor([1, idl, 3])) + + +def test_sympy__codegen__fnodes__sum_(): + from sympy.codegen.fnodes import sum_ + assert _test_args(sum_('arr')) + + +def test_sympy__codegen__fnodes__product_(): + from sympy.codegen.fnodes import product_ + assert _test_args(product_('arr')) + + +def test_sympy__codegen__numpy_nodes__logaddexp(): + from sympy.codegen.numpy_nodes import logaddexp + assert _test_args(logaddexp(x, y)) + + +def test_sympy__codegen__numpy_nodes__logaddexp2(): + from sympy.codegen.numpy_nodes import logaddexp2 + assert _test_args(logaddexp2(x, y)) + + +def test_sympy__codegen__pynodes__List(): + from sympy.codegen.pynodes import List + assert _test_args(List(1, 2, 3)) + + +def test_sympy__codegen__pynodes__NumExprEvaluate(): + from sympy.codegen.pynodes import NumExprEvaluate + assert _test_args(NumExprEvaluate(x)) + + +def test_sympy__codegen__scipy_nodes__cosm1(): + from sympy.codegen.scipy_nodes import cosm1 + assert _test_args(cosm1(x)) + + +def test_sympy__codegen__scipy_nodes__powm1(): + from sympy.codegen.scipy_nodes import powm1 + assert _test_args(powm1(x, y)) + + +def test_sympy__codegen__abstract_nodes__List(): + from sympy.codegen.abstract_nodes import List + assert _test_args(List(1, 2, 3)) + +def test_sympy__combinatorics__graycode__GrayCode(): + from sympy.combinatorics.graycode import GrayCode + # an integer is given and returned from GrayCode as the arg + assert _test_args(GrayCode(3, start='100')) + assert _test_args(GrayCode(3, rank=1)) + + +def test_sympy__combinatorics__permutations__Permutation(): + from sympy.combinatorics.permutations import Permutation + assert _test_args(Permutation([0, 1, 2, 3])) + +def test_sympy__combinatorics__permutations__AppliedPermutation(): + from sympy.combinatorics.permutations import Permutation + from sympy.combinatorics.permutations import AppliedPermutation + p = Permutation([0, 1, 2, 3]) + assert _test_args(AppliedPermutation(p, x)) + +def test_sympy__combinatorics__perm_groups__PermutationGroup(): + from sympy.combinatorics.permutations import Permutation + from sympy.combinatorics.perm_groups import PermutationGroup + assert _test_args(PermutationGroup([Permutation([0, 1])])) + + +def test_sympy__combinatorics__polyhedron__Polyhedron(): + from sympy.combinatorics.permutations import Permutation + from sympy.combinatorics.polyhedron import Polyhedron + from sympy.abc import w, x, y, z + pgroup = [Permutation([[0, 1, 2], [3]]), + Permutation([[0, 1, 3], [2]]), + Permutation([[0, 2, 3], [1]]), + Permutation([[1, 2, 3], [0]]), + Permutation([[0, 1], [2, 3]]), + Permutation([[0, 2], [1, 3]]), + Permutation([[0, 3], [1, 2]]), + Permutation([[0, 1, 2, 3]])] + corners = [w, x, y, z] + faces = [(w, x, y), (w, y, z), (w, z, x), (x, y, z)] + assert _test_args(Polyhedron(corners, faces, pgroup)) + + +def test_sympy__combinatorics__prufer__Prufer(): + from sympy.combinatorics.prufer import Prufer + assert _test_args(Prufer([[0, 1], [0, 2], [0, 3]], 4)) + + +def test_sympy__combinatorics__partitions__Partition(): + from sympy.combinatorics.partitions import Partition + assert _test_args(Partition([1])) + + +def test_sympy__combinatorics__partitions__IntegerPartition(): + from sympy.combinatorics.partitions import IntegerPartition + assert _test_args(IntegerPartition([1])) + + +def test_sympy__concrete__products__Product(): + from sympy.concrete.products import Product + assert _test_args(Product(x, (x, 0, 10))) + assert _test_args(Product(x, (x, 0, y), (y, 0, 10))) + + +@SKIP("abstract Class") +def test_sympy__concrete__expr_with_limits__ExprWithLimits(): + from sympy.concrete.expr_with_limits import ExprWithLimits + assert _test_args(ExprWithLimits(x, (x, 0, 10))) + assert _test_args(ExprWithLimits(x*y, (x, 0, 10.),(y,1.,3))) + + +@SKIP("abstract Class") +def test_sympy__concrete__expr_with_limits__AddWithLimits(): + from sympy.concrete.expr_with_limits import AddWithLimits + assert _test_args(AddWithLimits(x, (x, 0, 10))) + assert _test_args(AddWithLimits(x*y, (x, 0, 10),(y,1,3))) + + +@SKIP("abstract Class") +def test_sympy__concrete__expr_with_intlimits__ExprWithIntLimits(): + from sympy.concrete.expr_with_intlimits import ExprWithIntLimits + assert _test_args(ExprWithIntLimits(x, (x, 0, 10))) + assert _test_args(ExprWithIntLimits(x*y, (x, 0, 10),(y,1,3))) + + +def test_sympy__concrete__summations__Sum(): + from sympy.concrete.summations import Sum + assert _test_args(Sum(x, (x, 0, 10))) + assert _test_args(Sum(x, (x, 0, y), (y, 0, 10))) + + +def test_sympy__core__add__Add(): + from sympy.core.add import Add + assert _test_args(Add(x, y, z, 2)) + + +def test_sympy__core__basic__Atom(): + from sympy.core.basic import Atom + assert _test_args(Atom()) + + +def test_sympy__core__basic__Basic(): + from sympy.core.basic import Basic + assert _test_args(Basic()) + + +def test_sympy__core__containers__Dict(): + from sympy.core.containers import Dict + assert _test_args(Dict({x: y, y: z})) + + +def test_sympy__core__containers__Tuple(): + from sympy.core.containers import Tuple + assert _test_args(Tuple(x, y, z, 2)) + + +def test_sympy__core__expr__AtomicExpr(): + from sympy.core.expr import AtomicExpr + assert _test_args(AtomicExpr()) + + +def test_sympy__core__expr__Expr(): + from sympy.core.expr import Expr + assert _test_args(Expr()) + + +def test_sympy__core__expr__UnevaluatedExpr(): + from sympy.core.expr import UnevaluatedExpr + from sympy.abc import x + assert _test_args(UnevaluatedExpr(x)) + + +def test_sympy__core__function__Application(): + from sympy.core.function import Application + assert _test_args(Application(1, 2, 3)) + + +def test_sympy__core__function__AppliedUndef(): + from sympy.core.function import AppliedUndef + assert _test_args(AppliedUndef(1, 2, 3)) + + +def test_sympy__core__function__Derivative(): + from sympy.core.function import Derivative + assert _test_args(Derivative(2, x, y, 3)) + + +@SKIP("abstract class") +def test_sympy__core__function__Function(): + pass + + +def test_sympy__core__function__Lambda(): + assert _test_args(Lambda((x, y), x + y + z)) + + +def test_sympy__core__function__Subs(): + from sympy.core.function import Subs + assert _test_args(Subs(x + y, x, 2)) + + +def test_sympy__core__function__WildFunction(): + from sympy.core.function import WildFunction + assert _test_args(WildFunction('f')) + + +def test_sympy__core__mod__Mod(): + from sympy.core.mod import Mod + assert _test_args(Mod(x, 2)) + + +def test_sympy__core__mul__Mul(): + from sympy.core.mul import Mul + assert _test_args(Mul(2, x, y, z)) + + +def test_sympy__core__numbers__Catalan(): + from sympy.core.numbers import Catalan + assert _test_args(Catalan()) + + +def test_sympy__core__numbers__ComplexInfinity(): + from sympy.core.numbers import ComplexInfinity + assert _test_args(ComplexInfinity()) + + +def test_sympy__core__numbers__EulerGamma(): + from sympy.core.numbers import EulerGamma + assert _test_args(EulerGamma()) + + +def test_sympy__core__numbers__Exp1(): + from sympy.core.numbers import Exp1 + assert _test_args(Exp1()) + + +def test_sympy__core__numbers__Float(): + from sympy.core.numbers import Float + assert _test_args(Float(1.23)) + + +def test_sympy__core__numbers__GoldenRatio(): + from sympy.core.numbers import GoldenRatio + assert _test_args(GoldenRatio()) + + +def test_sympy__core__numbers__TribonacciConstant(): + from sympy.core.numbers import TribonacciConstant + assert _test_args(TribonacciConstant()) + + +def test_sympy__core__numbers__Half(): + from sympy.core.numbers import Half + assert _test_args(Half()) + + +def test_sympy__core__numbers__ImaginaryUnit(): + from sympy.core.numbers import ImaginaryUnit + assert _test_args(ImaginaryUnit()) + + +def test_sympy__core__numbers__Infinity(): + from sympy.core.numbers import Infinity + assert _test_args(Infinity()) + + +def test_sympy__core__numbers__Integer(): + from sympy.core.numbers import Integer + assert _test_args(Integer(7)) + + +@SKIP("abstract class") +def test_sympy__core__numbers__IntegerConstant(): + pass + + +def test_sympy__core__numbers__NaN(): + from sympy.core.numbers import NaN + assert _test_args(NaN()) + + +def test_sympy__core__numbers__NegativeInfinity(): + from sympy.core.numbers import NegativeInfinity + assert _test_args(NegativeInfinity()) + + +def test_sympy__core__numbers__NegativeOne(): + from sympy.core.numbers import NegativeOne + assert _test_args(NegativeOne()) + + +def test_sympy__core__numbers__Number(): + from sympy.core.numbers import Number + assert _test_args(Number(1, 7)) + + +def test_sympy__core__numbers__NumberSymbol(): + from sympy.core.numbers import NumberSymbol + assert _test_args(NumberSymbol()) + + +def test_sympy__core__numbers__One(): + from sympy.core.numbers import One + assert _test_args(One()) + + +def test_sympy__core__numbers__Pi(): + from sympy.core.numbers import Pi + assert _test_args(Pi()) + + +def test_sympy__core__numbers__Rational(): + from sympy.core.numbers import Rational + assert _test_args(Rational(1, 7)) + + +@SKIP("abstract class") +def test_sympy__core__numbers__RationalConstant(): + pass + + +def test_sympy__core__numbers__Zero(): + from sympy.core.numbers import Zero + assert _test_args(Zero()) + + +@SKIP("abstract class") +def test_sympy__core__operations__AssocOp(): + pass + + +@SKIP("abstract class") +def test_sympy__core__operations__LatticeOp(): + pass + + +def test_sympy__core__power__Pow(): + from sympy.core.power import Pow + assert _test_args(Pow(x, 2)) + + +def test_sympy__core__relational__Equality(): + from sympy.core.relational import Equality + assert _test_args(Equality(x, 2)) + + +def test_sympy__core__relational__GreaterThan(): + from sympy.core.relational import GreaterThan + assert _test_args(GreaterThan(x, 2)) + + +def test_sympy__core__relational__LessThan(): + from sympy.core.relational import LessThan + assert _test_args(LessThan(x, 2)) + + +@SKIP("abstract class") +def test_sympy__core__relational__Relational(): + pass + + +def test_sympy__core__relational__StrictGreaterThan(): + from sympy.core.relational import StrictGreaterThan + assert _test_args(StrictGreaterThan(x, 2)) + + +def test_sympy__core__relational__StrictLessThan(): + from sympy.core.relational import StrictLessThan + assert _test_args(StrictLessThan(x, 2)) + + +def test_sympy__core__relational__Unequality(): + from sympy.core.relational import Unequality + assert _test_args(Unequality(x, 2)) + + +def test_sympy__sandbox__indexed_integrals__IndexedIntegral(): + from sympy.tensor import IndexedBase, Idx + from sympy.sandbox.indexed_integrals import IndexedIntegral + A = IndexedBase('A') + i, j = symbols('i j', integer=True) + a1, a2 = symbols('a1:3', cls=Idx) + assert _test_args(IndexedIntegral(A[a1], A[a2])) + assert _test_args(IndexedIntegral(A[i], A[j])) + + +def test_sympy__calculus__accumulationbounds__AccumulationBounds(): + from sympy.calculus.accumulationbounds import AccumulationBounds + assert _test_args(AccumulationBounds(0, 1)) + + +def test_sympy__sets__ordinals__OmegaPower(): + from sympy.sets.ordinals import OmegaPower + assert _test_args(OmegaPower(1, 1)) + +def test_sympy__sets__ordinals__Ordinal(): + from sympy.sets.ordinals import Ordinal, OmegaPower + assert _test_args(Ordinal(OmegaPower(2, 1))) + +def test_sympy__sets__ordinals__OrdinalOmega(): + from sympy.sets.ordinals import OrdinalOmega + assert _test_args(OrdinalOmega()) + +def test_sympy__sets__ordinals__OrdinalZero(): + from sympy.sets.ordinals import OrdinalZero + assert _test_args(OrdinalZero()) + + +def test_sympy__sets__powerset__PowerSet(): + from sympy.sets.powerset import PowerSet + from sympy.core.singleton import S + assert _test_args(PowerSet(S.EmptySet)) + + +def test_sympy__sets__sets__EmptySet(): + from sympy.sets.sets import EmptySet + assert _test_args(EmptySet()) + + +def test_sympy__sets__sets__UniversalSet(): + from sympy.sets.sets import UniversalSet + assert _test_args(UniversalSet()) + + +def test_sympy__sets__sets__FiniteSet(): + from sympy.sets.sets import FiniteSet + assert _test_args(FiniteSet(x, y, z)) + + +def test_sympy__sets__sets__Interval(): + from sympy.sets.sets import Interval + assert _test_args(Interval(0, 1)) + + +def test_sympy__sets__sets__ProductSet(): + from sympy.sets.sets import ProductSet, Interval + assert _test_args(ProductSet(Interval(0, 1), Interval(0, 1))) + + +@SKIP("does it make sense to test this?") +def test_sympy__sets__sets__Set(): + from sympy.sets.sets import Set + assert _test_args(Set()) + + +def test_sympy__sets__sets__Intersection(): + from sympy.sets.sets import Intersection, Interval + from sympy.core.symbol import Symbol + x = Symbol('x') + y = Symbol('y') + S = Intersection(Interval(0, x), Interval(y, 1)) + assert isinstance(S, Intersection) + assert _test_args(S) + + +def test_sympy__sets__sets__Union(): + from sympy.sets.sets import Union, Interval + assert _test_args(Union(Interval(0, 1), Interval(2, 3))) + + +def test_sympy__sets__sets__Complement(): + from sympy.sets.sets import Complement, Interval + assert _test_args(Complement(Interval(0, 2), Interval(0, 1))) + + +def test_sympy__sets__sets__SymmetricDifference(): + from sympy.sets.sets import FiniteSet, SymmetricDifference + assert _test_args(SymmetricDifference(FiniteSet(1, 2, 3), \ + FiniteSet(2, 3, 4))) + +def test_sympy__sets__sets__DisjointUnion(): + from sympy.sets.sets import FiniteSet, DisjointUnion + assert _test_args(DisjointUnion(FiniteSet(1, 2, 3), \ + FiniteSet(2, 3, 4))) + + +def test_sympy__physics__quantum__trace__Tr(): + from sympy.physics.quantum.trace import Tr + a, b = symbols('a b', commutative=False) + assert _test_args(Tr(a + b)) + + +def test_sympy__sets__setexpr__SetExpr(): + from sympy.sets.setexpr import SetExpr + from sympy.sets.sets import Interval + assert _test_args(SetExpr(Interval(0, 1))) + + +def test_sympy__sets__fancysets__Rationals(): + from sympy.sets.fancysets import Rationals + assert _test_args(Rationals()) + + +def test_sympy__sets__fancysets__Naturals(): + from sympy.sets.fancysets import Naturals + assert _test_args(Naturals()) + + +def test_sympy__sets__fancysets__Naturals0(): + from sympy.sets.fancysets import Naturals0 + assert _test_args(Naturals0()) + + +def test_sympy__sets__fancysets__Integers(): + from sympy.sets.fancysets import Integers + assert _test_args(Integers()) + + +def test_sympy__sets__fancysets__Reals(): + from sympy.sets.fancysets import Reals + assert _test_args(Reals()) + + +def test_sympy__sets__fancysets__Complexes(): + from sympy.sets.fancysets import Complexes + assert _test_args(Complexes()) + + +def test_sympy__sets__fancysets__ComplexRegion(): + from sympy.sets.fancysets import ComplexRegion + from sympy.core.singleton import S + from sympy.sets import Interval + a = Interval(0, 1) + b = Interval(2, 3) + theta = Interval(0, 2*S.Pi) + assert _test_args(ComplexRegion(a*b)) + assert _test_args(ComplexRegion(a*theta, polar=True)) + + +def test_sympy__sets__fancysets__CartesianComplexRegion(): + from sympy.sets.fancysets import CartesianComplexRegion + from sympy.sets import Interval + a = Interval(0, 1) + b = Interval(2, 3) + assert _test_args(CartesianComplexRegion(a*b)) + + +def test_sympy__sets__fancysets__PolarComplexRegion(): + from sympy.sets.fancysets import PolarComplexRegion + from sympy.core.singleton import S + from sympy.sets import Interval + a = Interval(0, 1) + theta = Interval(0, 2*S.Pi) + assert _test_args(PolarComplexRegion(a*theta)) + + +def test_sympy__sets__fancysets__ImageSet(): + from sympy.sets.fancysets import ImageSet + from sympy.core.singleton import S + from sympy.core.symbol import Symbol + x = Symbol('x') + assert _test_args(ImageSet(Lambda(x, x**2), S.Naturals)) + + +def test_sympy__sets__fancysets__Range(): + from sympy.sets.fancysets import Range + assert _test_args(Range(1, 5, 1)) + + +def test_sympy__sets__conditionset__ConditionSet(): + from sympy.sets.conditionset import ConditionSet + from sympy.core.singleton import S + from sympy.core.symbol import Symbol + x = Symbol('x') + assert _test_args(ConditionSet(x, Eq(x**2, 1), S.Reals)) + + +def test_sympy__sets__contains__Contains(): + from sympy.sets.fancysets import Range + from sympy.sets.contains import Contains + assert _test_args(Contains(x, Range(0, 10, 2))) + + +# STATS + + +from sympy.stats.crv_types import NormalDistribution +nd = NormalDistribution(0, 1) +from sympy.stats.frv_types import DieDistribution +die = DieDistribution(6) + + +def test_sympy__stats__crv__ContinuousDomain(): + from sympy.sets.sets import Interval + from sympy.stats.crv import ContinuousDomain + assert _test_args(ContinuousDomain({x}, Interval(-oo, oo))) + + +def test_sympy__stats__crv__SingleContinuousDomain(): + from sympy.sets.sets import Interval + from sympy.stats.crv import SingleContinuousDomain + assert _test_args(SingleContinuousDomain(x, Interval(-oo, oo))) + + +def test_sympy__stats__crv__ProductContinuousDomain(): + from sympy.sets.sets import Interval + from sympy.stats.crv import SingleContinuousDomain, ProductContinuousDomain + D = SingleContinuousDomain(x, Interval(-oo, oo)) + E = SingleContinuousDomain(y, Interval(0, oo)) + assert _test_args(ProductContinuousDomain(D, E)) + + +def test_sympy__stats__crv__ConditionalContinuousDomain(): + from sympy.sets.sets import Interval + from sympy.stats.crv import (SingleContinuousDomain, + ConditionalContinuousDomain) + D = SingleContinuousDomain(x, Interval(-oo, oo)) + assert _test_args(ConditionalContinuousDomain(D, x > 0)) + + +def test_sympy__stats__crv__ContinuousPSpace(): + from sympy.sets.sets import Interval + from sympy.stats.crv import ContinuousPSpace, SingleContinuousDomain + D = SingleContinuousDomain(x, Interval(-oo, oo)) + assert _test_args(ContinuousPSpace(D, nd)) + + +def test_sympy__stats__crv__SingleContinuousPSpace(): + from sympy.stats.crv import SingleContinuousPSpace + assert _test_args(SingleContinuousPSpace(x, nd)) + +@SKIP("abstract class") +def test_sympy__stats__rv__Distribution(): + pass + +@SKIP("abstract class") +def test_sympy__stats__crv__SingleContinuousDistribution(): + pass + + +def test_sympy__stats__drv__SingleDiscreteDomain(): + from sympy.stats.drv import SingleDiscreteDomain + assert _test_args(SingleDiscreteDomain(x, S.Naturals)) + + +def test_sympy__stats__drv__ProductDiscreteDomain(): + from sympy.stats.drv import SingleDiscreteDomain, ProductDiscreteDomain + X = SingleDiscreteDomain(x, S.Naturals) + Y = SingleDiscreteDomain(y, S.Integers) + assert _test_args(ProductDiscreteDomain(X, Y)) + + +def test_sympy__stats__drv__SingleDiscretePSpace(): + from sympy.stats.drv import SingleDiscretePSpace + from sympy.stats.drv_types import PoissonDistribution + assert _test_args(SingleDiscretePSpace(x, PoissonDistribution(1))) + +def test_sympy__stats__drv__DiscretePSpace(): + from sympy.stats.drv import DiscretePSpace, SingleDiscreteDomain + density = Lambda(x, 2**(-x)) + domain = SingleDiscreteDomain(x, S.Naturals) + assert _test_args(DiscretePSpace(domain, density)) + +def test_sympy__stats__drv__ConditionalDiscreteDomain(): + from sympy.stats.drv import ConditionalDiscreteDomain, SingleDiscreteDomain + X = SingleDiscreteDomain(x, S.Naturals0) + assert _test_args(ConditionalDiscreteDomain(X, x > 2)) + +def test_sympy__stats__joint_rv__JointPSpace(): + from sympy.stats.joint_rv import JointPSpace, JointDistribution + assert _test_args(JointPSpace('X', JointDistribution(1))) + +def test_sympy__stats__joint_rv__JointRandomSymbol(): + from sympy.stats.joint_rv import JointRandomSymbol + assert _test_args(JointRandomSymbol(x)) + +def test_sympy__stats__joint_rv_types__JointDistributionHandmade(): + from sympy.tensor.indexed import Indexed + from sympy.stats.joint_rv_types import JointDistributionHandmade + x1, x2 = (Indexed('x', i) for i in (1, 2)) + assert _test_args(JointDistributionHandmade(x1 + x2, S.Reals**2)) + + +def test_sympy__stats__joint_rv__MarginalDistribution(): + from sympy.stats.rv import RandomSymbol + from sympy.stats.joint_rv import MarginalDistribution + r = RandomSymbol(S('r')) + assert _test_args(MarginalDistribution(r, (r,))) + + +def test_sympy__stats__compound_rv__CompoundDistribution(): + from sympy.stats.compound_rv import CompoundDistribution + from sympy.stats.drv_types import PoissonDistribution, Poisson + r = Poisson('r', 10) + assert _test_args(CompoundDistribution(PoissonDistribution(r))) + + +def test_sympy__stats__compound_rv__CompoundPSpace(): + from sympy.stats.compound_rv import CompoundPSpace, CompoundDistribution + from sympy.stats.drv_types import PoissonDistribution, Poisson + r = Poisson('r', 5) + C = CompoundDistribution(PoissonDistribution(r)) + assert _test_args(CompoundPSpace('C', C)) + + +@SKIP("abstract class") +def test_sympy__stats__drv__SingleDiscreteDistribution(): + pass + +@SKIP("abstract class") +def test_sympy__stats__drv__DiscreteDistribution(): + pass + +@SKIP("abstract class") +def test_sympy__stats__drv__DiscreteDomain(): + pass + + +def test_sympy__stats__rv__RandomDomain(): + from sympy.stats.rv import RandomDomain + from sympy.sets.sets import FiniteSet + assert _test_args(RandomDomain(FiniteSet(x), FiniteSet(1, 2, 3))) + + +def test_sympy__stats__rv__SingleDomain(): + from sympy.stats.rv import SingleDomain + from sympy.sets.sets import FiniteSet + assert _test_args(SingleDomain(x, FiniteSet(1, 2, 3))) + + +def test_sympy__stats__rv__ConditionalDomain(): + from sympy.stats.rv import ConditionalDomain, RandomDomain + from sympy.sets.sets import FiniteSet + D = RandomDomain(FiniteSet(x), FiniteSet(1, 2)) + assert _test_args(ConditionalDomain(D, x > 1)) + +def test_sympy__stats__rv__MatrixDomain(): + from sympy.stats.rv import MatrixDomain + from sympy.matrices import MatrixSet + from sympy.core.singleton import S + assert _test_args(MatrixDomain(x, MatrixSet(2, 2, S.Reals))) + +def test_sympy__stats__rv__PSpace(): + from sympy.stats.rv import PSpace, RandomDomain + from sympy.sets.sets import FiniteSet + D = RandomDomain(FiniteSet(x), FiniteSet(1, 2, 3, 4, 5, 6)) + assert _test_args(PSpace(D, die)) + + +@SKIP("abstract Class") +def test_sympy__stats__rv__SinglePSpace(): + pass + + +def test_sympy__stats__rv__RandomSymbol(): + from sympy.stats.rv import RandomSymbol + from sympy.stats.crv import SingleContinuousPSpace + A = SingleContinuousPSpace(x, nd) + assert _test_args(RandomSymbol(x, A)) + + +@SKIP("abstract Class") +def test_sympy__stats__rv__ProductPSpace(): + pass + + +def test_sympy__stats__rv__IndependentProductPSpace(): + from sympy.stats.rv import IndependentProductPSpace + from sympy.stats.crv import SingleContinuousPSpace + A = SingleContinuousPSpace(x, nd) + B = SingleContinuousPSpace(y, nd) + assert _test_args(IndependentProductPSpace(A, B)) + + +def test_sympy__stats__rv__ProductDomain(): + from sympy.sets.sets import Interval + from sympy.stats.rv import ProductDomain, SingleDomain + D = SingleDomain(x, Interval(-oo, oo)) + E = SingleDomain(y, Interval(0, oo)) + assert _test_args(ProductDomain(D, E)) + + +def test_sympy__stats__symbolic_probability__Probability(): + from sympy.stats.symbolic_probability import Probability + from sympy.stats import Normal + X = Normal('X', 0, 1) + assert _test_args(Probability(X > 0)) + + +def test_sympy__stats__symbolic_probability__Expectation(): + from sympy.stats.symbolic_probability import Expectation + from sympy.stats import Normal + X = Normal('X', 0, 1) + assert _test_args(Expectation(X > 0)) + + +def test_sympy__stats__symbolic_probability__Covariance(): + from sympy.stats.symbolic_probability import Covariance + from sympy.stats import Normal + X = Normal('X', 0, 1) + Y = Normal('Y', 0, 3) + assert _test_args(Covariance(X, Y)) + + +def test_sympy__stats__symbolic_probability__Variance(): + from sympy.stats.symbolic_probability import Variance + from sympy.stats import Normal + X = Normal('X', 0, 1) + assert _test_args(Variance(X)) + + +def test_sympy__stats__symbolic_probability__Moment(): + from sympy.stats.symbolic_probability import Moment + from sympy.stats import Normal + X = Normal('X', 0, 1) + assert _test_args(Moment(X, 3, 2, X > 3)) + + +def test_sympy__stats__symbolic_probability__CentralMoment(): + from sympy.stats.symbolic_probability import CentralMoment + from sympy.stats import Normal + X = Normal('X', 0, 1) + assert _test_args(CentralMoment(X, 2, X > 1)) + + +def test_sympy__stats__frv_types__DiscreteUniformDistribution(): + from sympy.stats.frv_types import DiscreteUniformDistribution + from sympy.core.containers import Tuple + assert _test_args(DiscreteUniformDistribution(Tuple(*list(range(6))))) + + +def test_sympy__stats__frv_types__DieDistribution(): + assert _test_args(die) + + +def test_sympy__stats__frv_types__BernoulliDistribution(): + from sympy.stats.frv_types import BernoulliDistribution + assert _test_args(BernoulliDistribution(S.Half, 0, 1)) + + +def test_sympy__stats__frv_types__BinomialDistribution(): + from sympy.stats.frv_types import BinomialDistribution + assert _test_args(BinomialDistribution(5, S.Half, 1, 0)) + +def test_sympy__stats__frv_types__BetaBinomialDistribution(): + from sympy.stats.frv_types import BetaBinomialDistribution + assert _test_args(BetaBinomialDistribution(5, 1, 1)) + + +def test_sympy__stats__frv_types__HypergeometricDistribution(): + from sympy.stats.frv_types import HypergeometricDistribution + assert _test_args(HypergeometricDistribution(10, 5, 3)) + + +def test_sympy__stats__frv_types__RademacherDistribution(): + from sympy.stats.frv_types import RademacherDistribution + assert _test_args(RademacherDistribution()) + +def test_sympy__stats__frv_types__IdealSolitonDistribution(): + from sympy.stats.frv_types import IdealSolitonDistribution + assert _test_args(IdealSolitonDistribution(10)) + +def test_sympy__stats__frv_types__RobustSolitonDistribution(): + from sympy.stats.frv_types import RobustSolitonDistribution + assert _test_args(RobustSolitonDistribution(1000, 0.5, 0.1)) + +def test_sympy__stats__frv__FiniteDomain(): + from sympy.stats.frv import FiniteDomain + assert _test_args(FiniteDomain({(x, 1), (x, 2)})) # x can be 1 or 2 + + +def test_sympy__stats__frv__SingleFiniteDomain(): + from sympy.stats.frv import SingleFiniteDomain + assert _test_args(SingleFiniteDomain(x, {1, 2})) # x can be 1 or 2 + + +def test_sympy__stats__frv__ProductFiniteDomain(): + from sympy.stats.frv import SingleFiniteDomain, ProductFiniteDomain + xd = SingleFiniteDomain(x, {1, 2}) + yd = SingleFiniteDomain(y, {1, 2}) + assert _test_args(ProductFiniteDomain(xd, yd)) + + +def test_sympy__stats__frv__ConditionalFiniteDomain(): + from sympy.stats.frv import SingleFiniteDomain, ConditionalFiniteDomain + xd = SingleFiniteDomain(x, {1, 2}) + assert _test_args(ConditionalFiniteDomain(xd, x > 1)) + + +def test_sympy__stats__frv__FinitePSpace(): + from sympy.stats.frv import FinitePSpace, SingleFiniteDomain + xd = SingleFiniteDomain(x, {1, 2, 3, 4, 5, 6}) + assert _test_args(FinitePSpace(xd, {(x, 1): S.Half, (x, 2): S.Half})) + + xd = SingleFiniteDomain(x, {1, 2}) + assert _test_args(FinitePSpace(xd, {(x, 1): S.Half, (x, 2): S.Half})) + + +def test_sympy__stats__frv__SingleFinitePSpace(): + from sympy.stats.frv import SingleFinitePSpace + from sympy.core.symbol import Symbol + + assert _test_args(SingleFinitePSpace(Symbol('x'), die)) + + +def test_sympy__stats__frv__ProductFinitePSpace(): + from sympy.stats.frv import SingleFinitePSpace, ProductFinitePSpace + from sympy.core.symbol import Symbol + xp = SingleFinitePSpace(Symbol('x'), die) + yp = SingleFinitePSpace(Symbol('y'), die) + assert _test_args(ProductFinitePSpace(xp, yp)) + +@SKIP("abstract class") +def test_sympy__stats__frv__SingleFiniteDistribution(): + pass + +@SKIP("abstract class") +def test_sympy__stats__crv__ContinuousDistribution(): + pass + + +def test_sympy__stats__frv_types__FiniteDistributionHandmade(): + from sympy.stats.frv_types import FiniteDistributionHandmade + from sympy.core.containers import Dict + assert _test_args(FiniteDistributionHandmade(Dict({1: 1}))) + + +def test_sympy__stats__crv_types__ContinuousDistributionHandmade(): + from sympy.stats.crv_types import ContinuousDistributionHandmade + from sympy.core.function import Lambda + from sympy.sets.sets import Interval + from sympy.abc import x + assert _test_args(ContinuousDistributionHandmade(Lambda(x, 2*x), + Interval(0, 1))) + + +def test_sympy__stats__drv_types__DiscreteDistributionHandmade(): + from sympy.stats.drv_types import DiscreteDistributionHandmade + from sympy.core.function import Lambda + from sympy.sets.sets import FiniteSet + from sympy.abc import x + assert _test_args(DiscreteDistributionHandmade(Lambda(x, Rational(1, 10)), + FiniteSet(*range(10)))) + + +def test_sympy__stats__rv__Density(): + from sympy.stats.rv import Density + from sympy.stats.crv_types import Normal + assert _test_args(Density(Normal('x', 0, 1))) + + +def test_sympy__stats__crv_types__ArcsinDistribution(): + from sympy.stats.crv_types import ArcsinDistribution + assert _test_args(ArcsinDistribution(0, 1)) + + +def test_sympy__stats__crv_types__BeniniDistribution(): + from sympy.stats.crv_types import BeniniDistribution + assert _test_args(BeniniDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__BetaDistribution(): + from sympy.stats.crv_types import BetaDistribution + assert _test_args(BetaDistribution(1, 1)) + +def test_sympy__stats__crv_types__BetaNoncentralDistribution(): + from sympy.stats.crv_types import BetaNoncentralDistribution + assert _test_args(BetaNoncentralDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__BetaPrimeDistribution(): + from sympy.stats.crv_types import BetaPrimeDistribution + assert _test_args(BetaPrimeDistribution(1, 1)) + +def test_sympy__stats__crv_types__BoundedParetoDistribution(): + from sympy.stats.crv_types import BoundedParetoDistribution + assert _test_args(BoundedParetoDistribution(1, 1, 2)) + +def test_sympy__stats__crv_types__CauchyDistribution(): + from sympy.stats.crv_types import CauchyDistribution + assert _test_args(CauchyDistribution(0, 1)) + + +def test_sympy__stats__crv_types__ChiDistribution(): + from sympy.stats.crv_types import ChiDistribution + assert _test_args(ChiDistribution(1)) + + +def test_sympy__stats__crv_types__ChiNoncentralDistribution(): + from sympy.stats.crv_types import ChiNoncentralDistribution + assert _test_args(ChiNoncentralDistribution(1,1)) + + +def test_sympy__stats__crv_types__ChiSquaredDistribution(): + from sympy.stats.crv_types import ChiSquaredDistribution + assert _test_args(ChiSquaredDistribution(1)) + + +def test_sympy__stats__crv_types__DagumDistribution(): + from sympy.stats.crv_types import DagumDistribution + assert _test_args(DagumDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__DavisDistribution(): + from sympy.stats.crv_types import DavisDistribution + assert _test_args(DavisDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__ExGaussianDistribution(): + from sympy.stats.crv_types import ExGaussianDistribution + assert _test_args(ExGaussianDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__ExponentialDistribution(): + from sympy.stats.crv_types import ExponentialDistribution + assert _test_args(ExponentialDistribution(1)) + + +def test_sympy__stats__crv_types__ExponentialPowerDistribution(): + from sympy.stats.crv_types import ExponentialPowerDistribution + assert _test_args(ExponentialPowerDistribution(0, 1, 1)) + + +def test_sympy__stats__crv_types__FDistributionDistribution(): + from sympy.stats.crv_types import FDistributionDistribution + assert _test_args(FDistributionDistribution(1, 1)) + + +def test_sympy__stats__crv_types__FisherZDistribution(): + from sympy.stats.crv_types import FisherZDistribution + assert _test_args(FisherZDistribution(1, 1)) + + +def test_sympy__stats__crv_types__FrechetDistribution(): + from sympy.stats.crv_types import FrechetDistribution + assert _test_args(FrechetDistribution(1, 1, 1)) + + +def test_sympy__stats__crv_types__GammaInverseDistribution(): + from sympy.stats.crv_types import GammaInverseDistribution + assert _test_args(GammaInverseDistribution(1, 1)) + + +def test_sympy__stats__crv_types__GammaDistribution(): + from sympy.stats.crv_types import GammaDistribution + assert _test_args(GammaDistribution(1, 1)) + +def test_sympy__stats__crv_types__GumbelDistribution(): + from sympy.stats.crv_types import GumbelDistribution + assert _test_args(GumbelDistribution(1, 1, False)) + +def test_sympy__stats__crv_types__GompertzDistribution(): + from sympy.stats.crv_types import GompertzDistribution + assert _test_args(GompertzDistribution(1, 1)) + +def test_sympy__stats__crv_types__KumaraswamyDistribution(): + from sympy.stats.crv_types import KumaraswamyDistribution + assert _test_args(KumaraswamyDistribution(1, 1)) + +def test_sympy__stats__crv_types__LaplaceDistribution(): + from sympy.stats.crv_types import LaplaceDistribution + assert _test_args(LaplaceDistribution(0, 1)) + +def test_sympy__stats__crv_types__LevyDistribution(): + from sympy.stats.crv_types import LevyDistribution + assert _test_args(LevyDistribution(0, 1)) + +def test_sympy__stats__crv_types__LogCauchyDistribution(): + from sympy.stats.crv_types import LogCauchyDistribution + assert _test_args(LogCauchyDistribution(0, 1)) + +def test_sympy__stats__crv_types__LogisticDistribution(): + from sympy.stats.crv_types import LogisticDistribution + assert _test_args(LogisticDistribution(0, 1)) + +def test_sympy__stats__crv_types__LogLogisticDistribution(): + from sympy.stats.crv_types import LogLogisticDistribution + assert _test_args(LogLogisticDistribution(1, 1)) + +def test_sympy__stats__crv_types__LogitNormalDistribution(): + from sympy.stats.crv_types import LogitNormalDistribution + assert _test_args(LogitNormalDistribution(0, 1)) + +def test_sympy__stats__crv_types__LogNormalDistribution(): + from sympy.stats.crv_types import LogNormalDistribution + assert _test_args(LogNormalDistribution(0, 1)) + +def test_sympy__stats__crv_types__LomaxDistribution(): + from sympy.stats.crv_types import LomaxDistribution + assert _test_args(LomaxDistribution(1, 2)) + +def test_sympy__stats__crv_types__MaxwellDistribution(): + from sympy.stats.crv_types import MaxwellDistribution + assert _test_args(MaxwellDistribution(1)) + +def test_sympy__stats__crv_types__MoyalDistribution(): + from sympy.stats.crv_types import MoyalDistribution + assert _test_args(MoyalDistribution(1,2)) + +def test_sympy__stats__crv_types__NakagamiDistribution(): + from sympy.stats.crv_types import NakagamiDistribution + assert _test_args(NakagamiDistribution(1, 1)) + + +def test_sympy__stats__crv_types__NormalDistribution(): + from sympy.stats.crv_types import NormalDistribution + assert _test_args(NormalDistribution(0, 1)) + +def test_sympy__stats__crv_types__GaussianInverseDistribution(): + from sympy.stats.crv_types import GaussianInverseDistribution + assert _test_args(GaussianInverseDistribution(1, 1)) + + +def test_sympy__stats__crv_types__ParetoDistribution(): + from sympy.stats.crv_types import ParetoDistribution + assert _test_args(ParetoDistribution(1, 1)) + +def test_sympy__stats__crv_types__PowerFunctionDistribution(): + from sympy.stats.crv_types import PowerFunctionDistribution + assert _test_args(PowerFunctionDistribution(2,0,1)) + +def test_sympy__stats__crv_types__QuadraticUDistribution(): + from sympy.stats.crv_types import QuadraticUDistribution + assert _test_args(QuadraticUDistribution(1, 2)) + +def test_sympy__stats__crv_types__RaisedCosineDistribution(): + from sympy.stats.crv_types import RaisedCosineDistribution + assert _test_args(RaisedCosineDistribution(1, 1)) + +def test_sympy__stats__crv_types__RayleighDistribution(): + from sympy.stats.crv_types import RayleighDistribution + assert _test_args(RayleighDistribution(1)) + +def test_sympy__stats__crv_types__ReciprocalDistribution(): + from sympy.stats.crv_types import ReciprocalDistribution + assert _test_args(ReciprocalDistribution(5, 30)) + +def test_sympy__stats__crv_types__ShiftedGompertzDistribution(): + from sympy.stats.crv_types import ShiftedGompertzDistribution + assert _test_args(ShiftedGompertzDistribution(1, 1)) + +def test_sympy__stats__crv_types__StudentTDistribution(): + from sympy.stats.crv_types import StudentTDistribution + assert _test_args(StudentTDistribution(1)) + +def test_sympy__stats__crv_types__TrapezoidalDistribution(): + from sympy.stats.crv_types import TrapezoidalDistribution + assert _test_args(TrapezoidalDistribution(1, 2, 3, 4)) + +def test_sympy__stats__crv_types__TriangularDistribution(): + from sympy.stats.crv_types import TriangularDistribution + assert _test_args(TriangularDistribution(-1, 0, 1)) + + +def test_sympy__stats__crv_types__UniformDistribution(): + from sympy.stats.crv_types import UniformDistribution + assert _test_args(UniformDistribution(0, 1)) + + +def test_sympy__stats__crv_types__UniformSumDistribution(): + from sympy.stats.crv_types import UniformSumDistribution + assert _test_args(UniformSumDistribution(1)) + + +def test_sympy__stats__crv_types__VonMisesDistribution(): + from sympy.stats.crv_types import VonMisesDistribution + assert _test_args(VonMisesDistribution(1, 1)) + + +def test_sympy__stats__crv_types__WeibullDistribution(): + from sympy.stats.crv_types import WeibullDistribution + assert _test_args(WeibullDistribution(1, 1)) + + +def test_sympy__stats__crv_types__WignerSemicircleDistribution(): + from sympy.stats.crv_types import WignerSemicircleDistribution + assert _test_args(WignerSemicircleDistribution(1)) + + +def test_sympy__stats__drv_types__GeometricDistribution(): + from sympy.stats.drv_types import GeometricDistribution + assert _test_args(GeometricDistribution(.5)) + +def test_sympy__stats__drv_types__HermiteDistribution(): + from sympy.stats.drv_types import HermiteDistribution + assert _test_args(HermiteDistribution(1, 2)) + +def test_sympy__stats__drv_types__LogarithmicDistribution(): + from sympy.stats.drv_types import LogarithmicDistribution + assert _test_args(LogarithmicDistribution(.5)) + + +def test_sympy__stats__drv_types__NegativeBinomialDistribution(): + from sympy.stats.drv_types import NegativeBinomialDistribution + assert _test_args(NegativeBinomialDistribution(.5, .5)) + +def test_sympy__stats__drv_types__FlorySchulzDistribution(): + from sympy.stats.drv_types import FlorySchulzDistribution + assert _test_args(FlorySchulzDistribution(.5)) + +def test_sympy__stats__drv_types__PoissonDistribution(): + from sympy.stats.drv_types import PoissonDistribution + assert _test_args(PoissonDistribution(1)) + + +def test_sympy__stats__drv_types__SkellamDistribution(): + from sympy.stats.drv_types import SkellamDistribution + assert _test_args(SkellamDistribution(1, 1)) + + +def test_sympy__stats__drv_types__YuleSimonDistribution(): + from sympy.stats.drv_types import YuleSimonDistribution + assert _test_args(YuleSimonDistribution(.5)) + + +def test_sympy__stats__drv_types__ZetaDistribution(): + from sympy.stats.drv_types import ZetaDistribution + assert _test_args(ZetaDistribution(1.5)) + + +def test_sympy__stats__joint_rv__JointDistribution(): + from sympy.stats.joint_rv import JointDistribution + assert _test_args(JointDistribution(1, 2, 3, 4)) + + +def test_sympy__stats__joint_rv_types__MultivariateNormalDistribution(): + from sympy.stats.joint_rv_types import MultivariateNormalDistribution + assert _test_args( + MultivariateNormalDistribution([0, 1], [[1, 0],[0, 1]])) + +def test_sympy__stats__joint_rv_types__MultivariateLaplaceDistribution(): + from sympy.stats.joint_rv_types import MultivariateLaplaceDistribution + assert _test_args(MultivariateLaplaceDistribution([0, 1], [[1, 0],[0, 1]])) + + +def test_sympy__stats__joint_rv_types__MultivariateTDistribution(): + from sympy.stats.joint_rv_types import MultivariateTDistribution + assert _test_args(MultivariateTDistribution([0, 1], [[1, 0],[0, 1]], 1)) + + +def test_sympy__stats__joint_rv_types__NormalGammaDistribution(): + from sympy.stats.joint_rv_types import NormalGammaDistribution + assert _test_args(NormalGammaDistribution(1, 2, 3, 4)) + +def test_sympy__stats__joint_rv_types__GeneralizedMultivariateLogGammaDistribution(): + from sympy.stats.joint_rv_types import GeneralizedMultivariateLogGammaDistribution + v, l, mu = (4, [1, 2, 3, 4], [1, 2, 3, 4]) + assert _test_args(GeneralizedMultivariateLogGammaDistribution(S.Half, v, l, mu)) + +def test_sympy__stats__joint_rv_types__MultivariateBetaDistribution(): + from sympy.stats.joint_rv_types import MultivariateBetaDistribution + assert _test_args(MultivariateBetaDistribution([1, 2, 3])) + +def test_sympy__stats__joint_rv_types__MultivariateEwensDistribution(): + from sympy.stats.joint_rv_types import MultivariateEwensDistribution + assert _test_args(MultivariateEwensDistribution(5, 1)) + +def test_sympy__stats__joint_rv_types__MultinomialDistribution(): + from sympy.stats.joint_rv_types import MultinomialDistribution + assert _test_args(MultinomialDistribution(5, [0.5, 0.1, 0.3])) + +def test_sympy__stats__joint_rv_types__NegativeMultinomialDistribution(): + from sympy.stats.joint_rv_types import NegativeMultinomialDistribution + assert _test_args(NegativeMultinomialDistribution(5, [0.5, 0.1, 0.3])) + +def test_sympy__stats__rv__RandomIndexedSymbol(): + from sympy.stats.rv import RandomIndexedSymbol, pspace + from sympy.stats.stochastic_process_types import DiscreteMarkovChain + X = DiscreteMarkovChain("X") + assert _test_args(RandomIndexedSymbol(X[0].symbol, pspace(X[0]))) + +def test_sympy__stats__rv__RandomMatrixSymbol(): + from sympy.stats.rv import RandomMatrixSymbol + from sympy.stats.random_matrix import RandomMatrixPSpace + pspace = RandomMatrixPSpace('P') + assert _test_args(RandomMatrixSymbol('M', 3, 3, pspace)) + +def test_sympy__stats__stochastic_process__StochasticPSpace(): + from sympy.stats.stochastic_process import StochasticPSpace + from sympy.stats.stochastic_process_types import StochasticProcess + from sympy.stats.frv_types import BernoulliDistribution + assert _test_args(StochasticPSpace("Y", StochasticProcess("Y", [1, 2, 3]), BernoulliDistribution(S.Half, 1, 0))) + +def test_sympy__stats__stochastic_process_types__StochasticProcess(): + from sympy.stats.stochastic_process_types import StochasticProcess + assert _test_args(StochasticProcess("Y", [1, 2, 3])) + +def test_sympy__stats__stochastic_process_types__MarkovProcess(): + from sympy.stats.stochastic_process_types import MarkovProcess + assert _test_args(MarkovProcess("Y", [1, 2, 3])) + +def test_sympy__stats__stochastic_process_types__DiscreteTimeStochasticProcess(): + from sympy.stats.stochastic_process_types import DiscreteTimeStochasticProcess + assert _test_args(DiscreteTimeStochasticProcess("Y", [1, 2, 3])) + +def test_sympy__stats__stochastic_process_types__ContinuousTimeStochasticProcess(): + from sympy.stats.stochastic_process_types import ContinuousTimeStochasticProcess + assert _test_args(ContinuousTimeStochasticProcess("Y", [1, 2, 3])) + +def test_sympy__stats__stochastic_process_types__TransitionMatrixOf(): + from sympy.stats.stochastic_process_types import TransitionMatrixOf, DiscreteMarkovChain + from sympy.matrices.expressions.matexpr import MatrixSymbol + DMC = DiscreteMarkovChain("Y") + assert _test_args(TransitionMatrixOf(DMC, MatrixSymbol('T', 3, 3))) + +def test_sympy__stats__stochastic_process_types__GeneratorMatrixOf(): + from sympy.stats.stochastic_process_types import GeneratorMatrixOf, ContinuousMarkovChain + from sympy.matrices.expressions.matexpr import MatrixSymbol + DMC = ContinuousMarkovChain("Y") + assert _test_args(GeneratorMatrixOf(DMC, MatrixSymbol('T', 3, 3))) + +def test_sympy__stats__stochastic_process_types__StochasticStateSpaceOf(): + from sympy.stats.stochastic_process_types import StochasticStateSpaceOf, DiscreteMarkovChain + DMC = DiscreteMarkovChain("Y") + assert _test_args(StochasticStateSpaceOf(DMC, [0, 1, 2])) + +def test_sympy__stats__stochastic_process_types__DiscreteMarkovChain(): + from sympy.stats.stochastic_process_types import DiscreteMarkovChain + from sympy.matrices.expressions.matexpr import MatrixSymbol + assert _test_args(DiscreteMarkovChain("Y", [0, 1, 2], MatrixSymbol('T', 3, 3))) + +def test_sympy__stats__stochastic_process_types__ContinuousMarkovChain(): + from sympy.stats.stochastic_process_types import ContinuousMarkovChain + from sympy.matrices.expressions.matexpr import MatrixSymbol + assert _test_args(ContinuousMarkovChain("Y", [0, 1, 2], MatrixSymbol('T', 3, 3))) + +def test_sympy__stats__stochastic_process_types__BernoulliProcess(): + from sympy.stats.stochastic_process_types import BernoulliProcess + assert _test_args(BernoulliProcess("B", 0.5, 1, 0)) + +def test_sympy__stats__stochastic_process_types__CountingProcess(): + from sympy.stats.stochastic_process_types import CountingProcess + assert _test_args(CountingProcess("C")) + +def test_sympy__stats__stochastic_process_types__PoissonProcess(): + from sympy.stats.stochastic_process_types import PoissonProcess + assert _test_args(PoissonProcess("X", 2)) + +def test_sympy__stats__stochastic_process_types__WienerProcess(): + from sympy.stats.stochastic_process_types import WienerProcess + assert _test_args(WienerProcess("X")) + +def test_sympy__stats__stochastic_process_types__GammaProcess(): + from sympy.stats.stochastic_process_types import GammaProcess + assert _test_args(GammaProcess("X", 1, 2)) + +def test_sympy__stats__random_matrix__RandomMatrixPSpace(): + from sympy.stats.random_matrix import RandomMatrixPSpace + from sympy.stats.random_matrix_models import RandomMatrixEnsembleModel + model = RandomMatrixEnsembleModel('R', 3) + assert _test_args(RandomMatrixPSpace('P', model=model)) + +def test_sympy__stats__random_matrix_models__RandomMatrixEnsembleModel(): + from sympy.stats.random_matrix_models import RandomMatrixEnsembleModel + assert _test_args(RandomMatrixEnsembleModel('R', 3)) + +def test_sympy__stats__random_matrix_models__GaussianEnsembleModel(): + from sympy.stats.random_matrix_models import GaussianEnsembleModel + assert _test_args(GaussianEnsembleModel('G', 3)) + +def test_sympy__stats__random_matrix_models__GaussianUnitaryEnsembleModel(): + from sympy.stats.random_matrix_models import GaussianUnitaryEnsembleModel + assert _test_args(GaussianUnitaryEnsembleModel('U', 3)) + +def test_sympy__stats__random_matrix_models__GaussianOrthogonalEnsembleModel(): + from sympy.stats.random_matrix_models import GaussianOrthogonalEnsembleModel + assert _test_args(GaussianOrthogonalEnsembleModel('U', 3)) + +def test_sympy__stats__random_matrix_models__GaussianSymplecticEnsembleModel(): + from sympy.stats.random_matrix_models import GaussianSymplecticEnsembleModel + assert _test_args(GaussianSymplecticEnsembleModel('U', 3)) + +def test_sympy__stats__random_matrix_models__CircularEnsembleModel(): + from sympy.stats.random_matrix_models import CircularEnsembleModel + assert _test_args(CircularEnsembleModel('C', 3)) + +def test_sympy__stats__random_matrix_models__CircularUnitaryEnsembleModel(): + from sympy.stats.random_matrix_models import CircularUnitaryEnsembleModel + assert _test_args(CircularUnitaryEnsembleModel('U', 3)) + +def test_sympy__stats__random_matrix_models__CircularOrthogonalEnsembleModel(): + from sympy.stats.random_matrix_models import CircularOrthogonalEnsembleModel + assert _test_args(CircularOrthogonalEnsembleModel('O', 3)) + +def test_sympy__stats__random_matrix_models__CircularSymplecticEnsembleModel(): + from sympy.stats.random_matrix_models import CircularSymplecticEnsembleModel + assert _test_args(CircularSymplecticEnsembleModel('S', 3)) + +def test_sympy__stats__symbolic_multivariate_probability__ExpectationMatrix(): + from sympy.stats import ExpectationMatrix + from sympy.stats.rv import RandomMatrixSymbol + assert _test_args(ExpectationMatrix(RandomMatrixSymbol('R', 2, 1))) + +def test_sympy__stats__symbolic_multivariate_probability__VarianceMatrix(): + from sympy.stats import VarianceMatrix + from sympy.stats.rv import RandomMatrixSymbol + assert _test_args(VarianceMatrix(RandomMatrixSymbol('R', 3, 1))) + +def test_sympy__stats__symbolic_multivariate_probability__CrossCovarianceMatrix(): + from sympy.stats import CrossCovarianceMatrix + from sympy.stats.rv import RandomMatrixSymbol + assert _test_args(CrossCovarianceMatrix(RandomMatrixSymbol('R', 3, 1), + RandomMatrixSymbol('X', 3, 1))) + +def test_sympy__stats__matrix_distributions__MatrixPSpace(): + from sympy.stats.matrix_distributions import MatrixDistribution, MatrixPSpace + from sympy.matrices.dense import Matrix + M = MatrixDistribution(1, Matrix([[1, 0], [0, 1]])) + assert _test_args(MatrixPSpace('M', M, 2, 2)) + +def test_sympy__stats__matrix_distributions__MatrixDistribution(): + from sympy.stats.matrix_distributions import MatrixDistribution + from sympy.matrices.dense import Matrix + assert _test_args(MatrixDistribution(1, Matrix([[1, 0], [0, 1]]))) + +def test_sympy__stats__matrix_distributions__MatrixGammaDistribution(): + from sympy.stats.matrix_distributions import MatrixGammaDistribution + from sympy.matrices.dense import Matrix + assert _test_args(MatrixGammaDistribution(3, 4, Matrix([[1, 0], [0, 1]]))) + +def test_sympy__stats__matrix_distributions__WishartDistribution(): + from sympy.stats.matrix_distributions import WishartDistribution + from sympy.matrices.dense import Matrix + assert _test_args(WishartDistribution(3, Matrix([[1, 0], [0, 1]]))) + +def test_sympy__stats__matrix_distributions__MatrixNormalDistribution(): + from sympy.stats.matrix_distributions import MatrixNormalDistribution + from sympy.matrices.expressions.matexpr import MatrixSymbol + L = MatrixSymbol('L', 1, 2) + S1 = MatrixSymbol('S1', 1, 1) + S2 = MatrixSymbol('S2', 2, 2) + assert _test_args(MatrixNormalDistribution(L, S1, S2)) + +def test_sympy__stats__matrix_distributions__MatrixStudentTDistribution(): + from sympy.stats.matrix_distributions import MatrixStudentTDistribution + from sympy.matrices.expressions.matexpr import MatrixSymbol + v = symbols('v', positive=True) + Omega = MatrixSymbol('Omega', 3, 3) + Sigma = MatrixSymbol('Sigma', 1, 1) + Location = MatrixSymbol('Location', 1, 3) + assert _test_args(MatrixStudentTDistribution(v, Location, Omega, Sigma)) + +def test_sympy__utilities__matchpy_connector__WildDot(): + from sympy.utilities.matchpy_connector import WildDot + assert _test_args(WildDot("w_")) + + +def test_sympy__utilities__matchpy_connector__WildPlus(): + from sympy.utilities.matchpy_connector import WildPlus + assert _test_args(WildPlus("w__")) + + +def test_sympy__utilities__matchpy_connector__WildStar(): + from sympy.utilities.matchpy_connector import WildStar + assert _test_args(WildStar("w___")) + + +def test_sympy__core__symbol__Str(): + from sympy.core.symbol import Str + assert _test_args(Str('t')) + +def test_sympy__core__symbol__Dummy(): + from sympy.core.symbol import Dummy + assert _test_args(Dummy('t')) + + +def test_sympy__core__symbol__Symbol(): + from sympy.core.symbol import Symbol + assert _test_args(Symbol('t')) + + +def test_sympy__core__symbol__Wild(): + from sympy.core.symbol import Wild + assert _test_args(Wild('x', exclude=[x])) + + +@SKIP("abstract class") +def test_sympy__functions__combinatorial__factorials__CombinatorialFunction(): + pass + + +def test_sympy__functions__combinatorial__factorials__FallingFactorial(): + from sympy.functions.combinatorial.factorials import FallingFactorial + assert _test_args(FallingFactorial(2, x)) + + +def test_sympy__functions__combinatorial__factorials__MultiFactorial(): + from sympy.functions.combinatorial.factorials import MultiFactorial + assert _test_args(MultiFactorial(x)) + + +def test_sympy__functions__combinatorial__factorials__RisingFactorial(): + from sympy.functions.combinatorial.factorials import RisingFactorial + assert _test_args(RisingFactorial(2, x)) + + +def test_sympy__functions__combinatorial__factorials__binomial(): + from sympy.functions.combinatorial.factorials import binomial + assert _test_args(binomial(2, x)) + + +def test_sympy__functions__combinatorial__factorials__subfactorial(): + from sympy.functions.combinatorial.factorials import subfactorial + assert _test_args(subfactorial(x)) + + +def test_sympy__functions__combinatorial__factorials__factorial(): + from sympy.functions.combinatorial.factorials import factorial + assert _test_args(factorial(x)) + + +def test_sympy__functions__combinatorial__factorials__factorial2(): + from sympy.functions.combinatorial.factorials import factorial2 + assert _test_args(factorial2(x)) + + +def test_sympy__functions__combinatorial__numbers__bell(): + from sympy.functions.combinatorial.numbers import bell + assert _test_args(bell(x, y)) + + +def test_sympy__functions__combinatorial__numbers__bernoulli(): + from sympy.functions.combinatorial.numbers import bernoulli + assert _test_args(bernoulli(x)) + + +def test_sympy__functions__combinatorial__numbers__catalan(): + from sympy.functions.combinatorial.numbers import catalan + assert _test_args(catalan(x)) + + +def test_sympy__functions__combinatorial__numbers__genocchi(): + from sympy.functions.combinatorial.numbers import genocchi + assert _test_args(genocchi(x)) + + +def test_sympy__functions__combinatorial__numbers__euler(): + from sympy.functions.combinatorial.numbers import euler + assert _test_args(euler(x)) + + +def test_sympy__functions__combinatorial__numbers__andre(): + from sympy.functions.combinatorial.numbers import andre + assert _test_args(andre(x)) + + +def test_sympy__functions__combinatorial__numbers__carmichael(): + from sympy.functions.combinatorial.numbers import carmichael + assert _test_args(carmichael(x)) + + +def test_sympy__functions__combinatorial__numbers__divisor_sigma(): + from sympy.functions.combinatorial.numbers import divisor_sigma + k = symbols('k', integer=True) + n = symbols('n', integer=True) + t = divisor_sigma(n, k) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__fibonacci(): + from sympy.functions.combinatorial.numbers import fibonacci + assert _test_args(fibonacci(x)) + + +def test_sympy__functions__combinatorial__numbers__jacobi_symbol(): + from sympy.functions.combinatorial.numbers import jacobi_symbol + assert _test_args(jacobi_symbol(2, 3)) + + +def test_sympy__functions__combinatorial__numbers__kronecker_symbol(): + from sympy.functions.combinatorial.numbers import kronecker_symbol + assert _test_args(kronecker_symbol(2, 3)) + + +def test_sympy__functions__combinatorial__numbers__legendre_symbol(): + from sympy.functions.combinatorial.numbers import legendre_symbol + assert _test_args(legendre_symbol(2, 3)) + + +def test_sympy__functions__combinatorial__numbers__mobius(): + from sympy.functions.combinatorial.numbers import mobius + assert _test_args(mobius(2)) + + +def test_sympy__functions__combinatorial__numbers__motzkin(): + from sympy.functions.combinatorial.numbers import motzkin + assert _test_args(motzkin(5)) + + +def test_sympy__functions__combinatorial__numbers__partition(): + from sympy.core.symbol import Symbol + from sympy.functions.combinatorial.numbers import partition + assert _test_args(partition(Symbol('a', integer=True))) + + +def test_sympy__functions__combinatorial__numbers__primenu(): + from sympy.functions.combinatorial.numbers import primenu + n = symbols('n', integer=True) + t = primenu(n) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__primeomega(): + from sympy.functions.combinatorial.numbers import primeomega + n = symbols('n', integer=True) + t = primeomega(n) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__primepi(): + from sympy.functions.combinatorial.numbers import primepi + n = symbols('n') + t = primepi(n) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__reduced_totient(): + from sympy.functions.combinatorial.numbers import reduced_totient + k = symbols('k', integer=True) + t = reduced_totient(k) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__totient(): + from sympy.functions.combinatorial.numbers import totient + k = symbols('k', integer=True) + t = totient(k) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__tribonacci(): + from sympy.functions.combinatorial.numbers import tribonacci + assert _test_args(tribonacci(x)) + + +def test_sympy__functions__combinatorial__numbers__udivisor_sigma(): + from sympy.functions.combinatorial.numbers import udivisor_sigma + k = symbols('k', integer=True) + n = symbols('n', integer=True) + t = udivisor_sigma(n, k) + assert _test_args(t) + + +def test_sympy__functions__combinatorial__numbers__harmonic(): + from sympy.functions.combinatorial.numbers import harmonic + assert _test_args(harmonic(x, 2)) + + +def test_sympy__functions__combinatorial__numbers__lucas(): + from sympy.functions.combinatorial.numbers import lucas + assert _test_args(lucas(x)) + + +def test_sympy__functions__elementary__complexes__Abs(): + from sympy.functions.elementary.complexes import Abs + assert _test_args(Abs(x)) + + +def test_sympy__functions__elementary__complexes__adjoint(): + from sympy.functions.elementary.complexes import adjoint + assert _test_args(adjoint(x)) + + +def test_sympy__functions__elementary__complexes__arg(): + from sympy.functions.elementary.complexes import arg + assert _test_args(arg(x)) + + +def test_sympy__functions__elementary__complexes__conjugate(): + from sympy.functions.elementary.complexes import conjugate + assert _test_args(conjugate(x)) + + +def test_sympy__functions__elementary__complexes__im(): + from sympy.functions.elementary.complexes import im + assert _test_args(im(x)) + + +def test_sympy__functions__elementary__complexes__re(): + from sympy.functions.elementary.complexes import re + assert _test_args(re(x)) + + +def test_sympy__functions__elementary__complexes__sign(): + from sympy.functions.elementary.complexes import sign + assert _test_args(sign(x)) + + +def test_sympy__functions__elementary__complexes__polar_lift(): + from sympy.functions.elementary.complexes import polar_lift + assert _test_args(polar_lift(x)) + + +def test_sympy__functions__elementary__complexes__periodic_argument(): + from sympy.functions.elementary.complexes import periodic_argument + assert _test_args(periodic_argument(x, y)) + + +def test_sympy__functions__elementary__complexes__principal_branch(): + from sympy.functions.elementary.complexes import principal_branch + assert _test_args(principal_branch(x, y)) + + +def test_sympy__functions__elementary__complexes__transpose(): + from sympy.functions.elementary.complexes import transpose + assert _test_args(transpose(x)) + + +def test_sympy__functions__elementary__exponential__LambertW(): + from sympy.functions.elementary.exponential import LambertW + assert _test_args(LambertW(2)) + + +@SKIP("abstract class") +def test_sympy__functions__elementary__exponential__ExpBase(): + pass + + +def test_sympy__functions__elementary__exponential__exp(): + from sympy.functions.elementary.exponential import exp + assert _test_args(exp(2)) + + +def test_sympy__functions__elementary__exponential__exp_polar(): + from sympy.functions.elementary.exponential import exp_polar + assert _test_args(exp_polar(2)) + + +def test_sympy__functions__elementary__exponential__log(): + from sympy.functions.elementary.exponential import log + assert _test_args(log(2)) + + +@SKIP("abstract class") +def test_sympy__functions__elementary__hyperbolic__HyperbolicFunction(): + pass + + +@SKIP("abstract class") +def test_sympy__functions__elementary__hyperbolic__ReciprocalHyperbolicFunction(): + pass + + +@SKIP("abstract class") +def test_sympy__functions__elementary__hyperbolic__InverseHyperbolicFunction(): + pass + + +def test_sympy__functions__elementary__hyperbolic__acosh(): + from sympy.functions.elementary.hyperbolic import acosh + assert _test_args(acosh(2)) + + +def test_sympy__functions__elementary__hyperbolic__acoth(): + from sympy.functions.elementary.hyperbolic import acoth + assert _test_args(acoth(2)) + + +def test_sympy__functions__elementary__hyperbolic__asinh(): + from sympy.functions.elementary.hyperbolic import asinh + assert _test_args(asinh(2)) + + +def test_sympy__functions__elementary__hyperbolic__atanh(): + from sympy.functions.elementary.hyperbolic import atanh + assert _test_args(atanh(2)) + + +def test_sympy__functions__elementary__hyperbolic__asech(): + from sympy.functions.elementary.hyperbolic import asech + assert _test_args(asech(x)) + +def test_sympy__functions__elementary__hyperbolic__acsch(): + from sympy.functions.elementary.hyperbolic import acsch + assert _test_args(acsch(x)) + +def test_sympy__functions__elementary__hyperbolic__cosh(): + from sympy.functions.elementary.hyperbolic import cosh + assert _test_args(cosh(2)) + + +def test_sympy__functions__elementary__hyperbolic__coth(): + from sympy.functions.elementary.hyperbolic import coth + assert _test_args(coth(2)) + + +def test_sympy__functions__elementary__hyperbolic__csch(): + from sympy.functions.elementary.hyperbolic import csch + assert _test_args(csch(2)) + + +def test_sympy__functions__elementary__hyperbolic__sech(): + from sympy.functions.elementary.hyperbolic import sech + assert _test_args(sech(2)) + + +def test_sympy__functions__elementary__hyperbolic__sinh(): + from sympy.functions.elementary.hyperbolic import sinh + assert _test_args(sinh(2)) + + +def test_sympy__functions__elementary__hyperbolic__tanh(): + from sympy.functions.elementary.hyperbolic import tanh + assert _test_args(tanh(2)) + + +@SKIP("abstract class") +def test_sympy__functions__elementary__integers__RoundFunction(): + pass + + +def test_sympy__functions__elementary__integers__ceiling(): + from sympy.functions.elementary.integers import ceiling + assert _test_args(ceiling(x)) + + +def test_sympy__functions__elementary__integers__floor(): + from sympy.functions.elementary.integers import floor + assert _test_args(floor(x)) + + +def test_sympy__functions__elementary__integers__frac(): + from sympy.functions.elementary.integers import frac + assert _test_args(frac(x)) + + +def test_sympy__functions__elementary__miscellaneous__IdentityFunction(): + from sympy.functions.elementary.miscellaneous import IdentityFunction + assert _test_args(IdentityFunction()) + + +def test_sympy__functions__elementary__miscellaneous__Max(): + from sympy.functions.elementary.miscellaneous import Max + assert _test_args(Max(x, 2)) + + +def test_sympy__functions__elementary__miscellaneous__Min(): + from sympy.functions.elementary.miscellaneous import Min + assert _test_args(Min(x, 2)) + + +@SKIP("abstract class") +def test_sympy__functions__elementary__miscellaneous__MinMaxBase(): + pass + + +def test_sympy__functions__elementary__miscellaneous__Rem(): + from sympy.functions.elementary.miscellaneous import Rem + assert _test_args(Rem(x, 2)) + + +def test_sympy__functions__elementary__piecewise__ExprCondPair(): + from sympy.functions.elementary.piecewise import ExprCondPair + assert _test_args(ExprCondPair(1, True)) + + +def test_sympy__functions__elementary__piecewise__Piecewise(): + from sympy.functions.elementary.piecewise import Piecewise + assert _test_args(Piecewise((1, x >= 0), (0, True))) + + +@SKIP("abstract class") +def test_sympy__functions__elementary__trigonometric__TrigonometricFunction(): + pass + +@SKIP("abstract class") +def test_sympy__functions__elementary__trigonometric__ReciprocalTrigonometricFunction(): + pass + +@SKIP("abstract class") +def test_sympy__functions__elementary__trigonometric__InverseTrigonometricFunction(): + pass + +def test_sympy__functions__elementary__trigonometric__acos(): + from sympy.functions.elementary.trigonometric import acos + assert _test_args(acos(2)) + + +def test_sympy__functions__elementary__trigonometric__acot(): + from sympy.functions.elementary.trigonometric import acot + assert _test_args(acot(2)) + + +def test_sympy__functions__elementary__trigonometric__asin(): + from sympy.functions.elementary.trigonometric import asin + assert _test_args(asin(2)) + + +def test_sympy__functions__elementary__trigonometric__asec(): + from sympy.functions.elementary.trigonometric import asec + assert _test_args(asec(x)) + + +def test_sympy__functions__elementary__trigonometric__acsc(): + from sympy.functions.elementary.trigonometric import acsc + assert _test_args(acsc(x)) + + +def test_sympy__functions__elementary__trigonometric__atan(): + from sympy.functions.elementary.trigonometric import atan + assert _test_args(atan(2)) + + +def test_sympy__functions__elementary__trigonometric__atan2(): + from sympy.functions.elementary.trigonometric import atan2 + assert _test_args(atan2(2, 3)) + + +def test_sympy__functions__elementary__trigonometric__cos(): + from sympy.functions.elementary.trigonometric import cos + assert _test_args(cos(2)) + + +def test_sympy__functions__elementary__trigonometric__csc(): + from sympy.functions.elementary.trigonometric import csc + assert _test_args(csc(2)) + + +def test_sympy__functions__elementary__trigonometric__cot(): + from sympy.functions.elementary.trigonometric import cot + assert _test_args(cot(2)) + + +def test_sympy__functions__elementary__trigonometric__sin(): + assert _test_args(sin(2)) + + +def test_sympy__functions__elementary__trigonometric__sinc(): + from sympy.functions.elementary.trigonometric import sinc + assert _test_args(sinc(2)) + + +def test_sympy__functions__elementary__trigonometric__sec(): + from sympy.functions.elementary.trigonometric import sec + assert _test_args(sec(2)) + + +def test_sympy__functions__elementary__trigonometric__tan(): + from sympy.functions.elementary.trigonometric import tan + assert _test_args(tan(2)) + + +@SKIP("abstract class") +def test_sympy__functions__special__bessel__BesselBase(): + pass + + +@SKIP("abstract class") +def test_sympy__functions__special__bessel__SphericalBesselBase(): + pass + + +@SKIP("abstract class") +def test_sympy__functions__special__bessel__SphericalHankelBase(): + pass + + +def test_sympy__functions__special__bessel__besseli(): + from sympy.functions.special.bessel import besseli + assert _test_args(besseli(x, 1)) + + +def test_sympy__functions__special__bessel__besselj(): + from sympy.functions.special.bessel import besselj + assert _test_args(besselj(x, 1)) + + +def test_sympy__functions__special__bessel__besselk(): + from sympy.functions.special.bessel import besselk + assert _test_args(besselk(x, 1)) + + +def test_sympy__functions__special__bessel__bessely(): + from sympy.functions.special.bessel import bessely + assert _test_args(bessely(x, 1)) + + +def test_sympy__functions__special__bessel__hankel1(): + from sympy.functions.special.bessel import hankel1 + assert _test_args(hankel1(x, 1)) + + +def test_sympy__functions__special__bessel__hankel2(): + from sympy.functions.special.bessel import hankel2 + assert _test_args(hankel2(x, 1)) + + +def test_sympy__functions__special__bessel__jn(): + from sympy.functions.special.bessel import jn + assert _test_args(jn(0, x)) + + +def test_sympy__functions__special__bessel__yn(): + from sympy.functions.special.bessel import yn + assert _test_args(yn(0, x)) + + +def test_sympy__functions__special__bessel__hn1(): + from sympy.functions.special.bessel import hn1 + assert _test_args(hn1(0, x)) + + +def test_sympy__functions__special__bessel__hn2(): + from sympy.functions.special.bessel import hn2 + assert _test_args(hn2(0, x)) + + +def test_sympy__functions__special__bessel__AiryBase(): + pass + + +def test_sympy__functions__special__bessel__airyai(): + from sympy.functions.special.bessel import airyai + assert _test_args(airyai(2)) + + +def test_sympy__functions__special__bessel__airybi(): + from sympy.functions.special.bessel import airybi + assert _test_args(airybi(2)) + + +def test_sympy__functions__special__bessel__airyaiprime(): + from sympy.functions.special.bessel import airyaiprime + assert _test_args(airyaiprime(2)) + + +def test_sympy__functions__special__bessel__airybiprime(): + from sympy.functions.special.bessel import airybiprime + assert _test_args(airybiprime(2)) + + +def test_sympy__functions__special__bessel__marcumq(): + from sympy.functions.special.bessel import marcumq + assert _test_args(marcumq(x, y, z)) + + +def test_sympy__functions__special__elliptic_integrals__elliptic_k(): + from sympy.functions.special.elliptic_integrals import elliptic_k as K + assert _test_args(K(x)) + + +def test_sympy__functions__special__elliptic_integrals__elliptic_f(): + from sympy.functions.special.elliptic_integrals import elliptic_f as F + assert _test_args(F(x, y)) + + +def test_sympy__functions__special__elliptic_integrals__elliptic_e(): + from sympy.functions.special.elliptic_integrals import elliptic_e as E + assert _test_args(E(x)) + assert _test_args(E(x, y)) + + +def test_sympy__functions__special__elliptic_integrals__elliptic_pi(): + from sympy.functions.special.elliptic_integrals import elliptic_pi as P + assert _test_args(P(x, y)) + assert _test_args(P(x, y, z)) + + +def test_sympy__functions__special__delta_functions__DiracDelta(): + from sympy.functions.special.delta_functions import DiracDelta + assert _test_args(DiracDelta(x, 1)) + + +def test_sympy__functions__special__singularity_functions__SingularityFunction(): + from sympy.functions.special.singularity_functions import SingularityFunction + assert _test_args(SingularityFunction(x, y, z)) + + +def test_sympy__functions__special__delta_functions__Heaviside(): + from sympy.functions.special.delta_functions import Heaviside + assert _test_args(Heaviside(x)) + + +def test_sympy__functions__special__error_functions__erf(): + from sympy.functions.special.error_functions import erf + assert _test_args(erf(2)) + +def test_sympy__functions__special__error_functions__erfc(): + from sympy.functions.special.error_functions import erfc + assert _test_args(erfc(2)) + +def test_sympy__functions__special__error_functions__erfi(): + from sympy.functions.special.error_functions import erfi + assert _test_args(erfi(2)) + +def test_sympy__functions__special__error_functions__erf2(): + from sympy.functions.special.error_functions import erf2 + assert _test_args(erf2(2, 3)) + +def test_sympy__functions__special__error_functions__erfinv(): + from sympy.functions.special.error_functions import erfinv + assert _test_args(erfinv(2)) + +def test_sympy__functions__special__error_functions__erfcinv(): + from sympy.functions.special.error_functions import erfcinv + assert _test_args(erfcinv(2)) + +def test_sympy__functions__special__error_functions__erf2inv(): + from sympy.functions.special.error_functions import erf2inv + assert _test_args(erf2inv(2, 3)) + +@SKIP("abstract class") +def test_sympy__functions__special__error_functions__FresnelIntegral(): + pass + + +def test_sympy__functions__special__error_functions__fresnels(): + from sympy.functions.special.error_functions import fresnels + assert _test_args(fresnels(2)) + + +def test_sympy__functions__special__error_functions__fresnelc(): + from sympy.functions.special.error_functions import fresnelc + assert _test_args(fresnelc(2)) + + +def test_sympy__functions__special__error_functions__erfs(): + from sympy.functions.special.error_functions import _erfs + assert _test_args(_erfs(2)) + + +def test_sympy__functions__special__error_functions__Ei(): + from sympy.functions.special.error_functions import Ei + assert _test_args(Ei(2)) + + +def test_sympy__functions__special__error_functions__li(): + from sympy.functions.special.error_functions import li + assert _test_args(li(2)) + + +def test_sympy__functions__special__error_functions__Li(): + from sympy.functions.special.error_functions import Li + assert _test_args(Li(5)) + + +@SKIP("abstract class") +def test_sympy__functions__special__error_functions__TrigonometricIntegral(): + pass + + +def test_sympy__functions__special__error_functions__Si(): + from sympy.functions.special.error_functions import Si + assert _test_args(Si(2)) + + +def test_sympy__functions__special__error_functions__Ci(): + from sympy.functions.special.error_functions import Ci + assert _test_args(Ci(2)) + + +def test_sympy__functions__special__error_functions__Shi(): + from sympy.functions.special.error_functions import Shi + assert _test_args(Shi(2)) + + +def test_sympy__functions__special__error_functions__Chi(): + from sympy.functions.special.error_functions import Chi + assert _test_args(Chi(2)) + + +def test_sympy__functions__special__error_functions__expint(): + from sympy.functions.special.error_functions import expint + assert _test_args(expint(y, x)) + + +def test_sympy__functions__special__gamma_functions__gamma(): + from sympy.functions.special.gamma_functions import gamma + assert _test_args(gamma(x)) + + +def test_sympy__functions__special__gamma_functions__loggamma(): + from sympy.functions.special.gamma_functions import loggamma + assert _test_args(loggamma(x)) + + +def test_sympy__functions__special__gamma_functions__lowergamma(): + from sympy.functions.special.gamma_functions import lowergamma + assert _test_args(lowergamma(x, 2)) + + +def test_sympy__functions__special__gamma_functions__polygamma(): + from sympy.functions.special.gamma_functions import polygamma + assert _test_args(polygamma(x, 2)) + +def test_sympy__functions__special__gamma_functions__digamma(): + from sympy.functions.special.gamma_functions import digamma + assert _test_args(digamma(x)) + +def test_sympy__functions__special__gamma_functions__trigamma(): + from sympy.functions.special.gamma_functions import trigamma + assert _test_args(trigamma(x)) + +def test_sympy__functions__special__gamma_functions__uppergamma(): + from sympy.functions.special.gamma_functions import uppergamma + assert _test_args(uppergamma(x, 2)) + +def test_sympy__functions__special__gamma_functions__multigamma(): + from sympy.functions.special.gamma_functions import multigamma + assert _test_args(multigamma(x, 1)) + + +def test_sympy__functions__special__beta_functions__beta(): + from sympy.functions.special.beta_functions import beta + assert _test_args(beta(x)) + assert _test_args(beta(x, x)) + +def test_sympy__functions__special__beta_functions__betainc(): + from sympy.functions.special.beta_functions import betainc + assert _test_args(betainc(a, b, x, y)) + +def test_sympy__functions__special__beta_functions__betainc_regularized(): + from sympy.functions.special.beta_functions import betainc_regularized + assert _test_args(betainc_regularized(a, b, x, y)) + + +def test_sympy__functions__special__mathieu_functions__MathieuBase(): + pass + + +def test_sympy__functions__special__mathieu_functions__mathieus(): + from sympy.functions.special.mathieu_functions import mathieus + assert _test_args(mathieus(1, 1, 1)) + + +def test_sympy__functions__special__mathieu_functions__mathieuc(): + from sympy.functions.special.mathieu_functions import mathieuc + assert _test_args(mathieuc(1, 1, 1)) + + +def test_sympy__functions__special__mathieu_functions__mathieusprime(): + from sympy.functions.special.mathieu_functions import mathieusprime + assert _test_args(mathieusprime(1, 1, 1)) + + +def test_sympy__functions__special__mathieu_functions__mathieucprime(): + from sympy.functions.special.mathieu_functions import mathieucprime + assert _test_args(mathieucprime(1, 1, 1)) + + +@SKIP("abstract class") +def test_sympy__functions__special__hyper__TupleParametersBase(): + pass + + +@SKIP("abstract class") +def test_sympy__functions__special__hyper__TupleArg(): + pass + + +def test_sympy__functions__special__hyper__hyper(): + from sympy.functions.special.hyper import hyper + assert _test_args(hyper([1, 2, 3], [4, 5], x)) + + +def test_sympy__functions__special__hyper__meijerg(): + from sympy.functions.special.hyper import meijerg + assert _test_args(meijerg([1, 2, 3], [4, 5], [6], [], x)) + + +@SKIP("abstract class") +def test_sympy__functions__special__hyper__HyperRep(): + pass + + +def test_sympy__functions__special__hyper__HyperRep_power1(): + from sympy.functions.special.hyper import HyperRep_power1 + assert _test_args(HyperRep_power1(x, y)) + + +def test_sympy__functions__special__hyper__HyperRep_power2(): + from sympy.functions.special.hyper import HyperRep_power2 + assert _test_args(HyperRep_power2(x, y)) + + +def test_sympy__functions__special__hyper__HyperRep_log1(): + from sympy.functions.special.hyper import HyperRep_log1 + assert _test_args(HyperRep_log1(x)) + + +def test_sympy__functions__special__hyper__HyperRep_atanh(): + from sympy.functions.special.hyper import HyperRep_atanh + assert _test_args(HyperRep_atanh(x)) + + +def test_sympy__functions__special__hyper__HyperRep_asin1(): + from sympy.functions.special.hyper import HyperRep_asin1 + assert _test_args(HyperRep_asin1(x)) + + +def test_sympy__functions__special__hyper__HyperRep_asin2(): + from sympy.functions.special.hyper import HyperRep_asin2 + assert _test_args(HyperRep_asin2(x)) + + +def test_sympy__functions__special__hyper__HyperRep_sqrts1(): + from sympy.functions.special.hyper import HyperRep_sqrts1 + assert _test_args(HyperRep_sqrts1(x, y)) + + +def test_sympy__functions__special__hyper__HyperRep_sqrts2(): + from sympy.functions.special.hyper import HyperRep_sqrts2 + assert _test_args(HyperRep_sqrts2(x, y)) + + +def test_sympy__functions__special__hyper__HyperRep_log2(): + from sympy.functions.special.hyper import HyperRep_log2 + assert _test_args(HyperRep_log2(x)) + + +def test_sympy__functions__special__hyper__HyperRep_cosasin(): + from sympy.functions.special.hyper import HyperRep_cosasin + assert _test_args(HyperRep_cosasin(x, y)) + + +def test_sympy__functions__special__hyper__HyperRep_sinasin(): + from sympy.functions.special.hyper import HyperRep_sinasin + assert _test_args(HyperRep_sinasin(x, y)) + +def test_sympy__functions__special__hyper__appellf1(): + from sympy.functions.special.hyper import appellf1 + a, b1, b2, c, x, y = symbols('a b1 b2 c x y') + assert _test_args(appellf1(a, b1, b2, c, x, y)) + +@SKIP("abstract class") +def test_sympy__functions__special__polynomials__OrthogonalPolynomial(): + pass + + +def test_sympy__functions__special__polynomials__jacobi(): + from sympy.functions.special.polynomials import jacobi + assert _test_args(jacobi(x, y, 2, 2)) + + +def test_sympy__functions__special__polynomials__gegenbauer(): + from sympy.functions.special.polynomials import gegenbauer + assert _test_args(gegenbauer(x, 2, 2)) + + +def test_sympy__functions__special__polynomials__chebyshevt(): + from sympy.functions.special.polynomials import chebyshevt + assert _test_args(chebyshevt(x, 2)) + + +def test_sympy__functions__special__polynomials__chebyshevt_root(): + from sympy.functions.special.polynomials import chebyshevt_root + assert _test_args(chebyshevt_root(3, 2)) + + +def test_sympy__functions__special__polynomials__chebyshevu(): + from sympy.functions.special.polynomials import chebyshevu + assert _test_args(chebyshevu(x, 2)) + + +def test_sympy__functions__special__polynomials__chebyshevu_root(): + from sympy.functions.special.polynomials import chebyshevu_root + assert _test_args(chebyshevu_root(3, 2)) + + +def test_sympy__functions__special__polynomials__hermite(): + from sympy.functions.special.polynomials import hermite + assert _test_args(hermite(x, 2)) + + +def test_sympy__functions__special__polynomials__hermite_prob(): + from sympy.functions.special.polynomials import hermite_prob + assert _test_args(hermite_prob(x, 2)) + + +def test_sympy__functions__special__polynomials__legendre(): + from sympy.functions.special.polynomials import legendre + assert _test_args(legendre(x, 2)) + + +def test_sympy__functions__special__polynomials__assoc_legendre(): + from sympy.functions.special.polynomials import assoc_legendre + assert _test_args(assoc_legendre(x, 0, y)) + + +def test_sympy__functions__special__polynomials__laguerre(): + from sympy.functions.special.polynomials import laguerre + assert _test_args(laguerre(x, 2)) + + +def test_sympy__functions__special__polynomials__assoc_laguerre(): + from sympy.functions.special.polynomials import assoc_laguerre + assert _test_args(assoc_laguerre(x, 0, y)) + + +def test_sympy__functions__special__spherical_harmonics__Ynm(): + from sympy.functions.special.spherical_harmonics import Ynm + assert _test_args(Ynm(1, 1, x, y)) + + +def test_sympy__functions__special__spherical_harmonics__Znm(): + from sympy.functions.special.spherical_harmonics import Znm + assert _test_args(Znm(x, y, 1, 1)) + + +def test_sympy__functions__special__tensor_functions__LeviCivita(): + from sympy.functions.special.tensor_functions import LeviCivita + assert _test_args(LeviCivita(x, y, 2)) + + +def test_sympy__functions__special__tensor_functions__KroneckerDelta(): + from sympy.functions.special.tensor_functions import KroneckerDelta + assert _test_args(KroneckerDelta(x, y)) + + +def test_sympy__functions__special__zeta_functions__dirichlet_eta(): + from sympy.functions.special.zeta_functions import dirichlet_eta + assert _test_args(dirichlet_eta(x)) + + +def test_sympy__functions__special__zeta_functions__riemann_xi(): + from sympy.functions.special.zeta_functions import riemann_xi + assert _test_args(riemann_xi(x)) + + +def test_sympy__functions__special__zeta_functions__zeta(): + from sympy.functions.special.zeta_functions import zeta + assert _test_args(zeta(101)) + + +def test_sympy__functions__special__zeta_functions__lerchphi(): + from sympy.functions.special.zeta_functions import lerchphi + assert _test_args(lerchphi(x, y, z)) + + +def test_sympy__functions__special__zeta_functions__polylog(): + from sympy.functions.special.zeta_functions import polylog + assert _test_args(polylog(x, y)) + + +def test_sympy__functions__special__zeta_functions__stieltjes(): + from sympy.functions.special.zeta_functions import stieltjes + assert _test_args(stieltjes(x, y)) + + +def test_sympy__integrals__integrals__Integral(): + from sympy.integrals.integrals import Integral + assert _test_args(Integral(2, (x, 0, 1))) + + +def test_sympy__integrals__risch__NonElementaryIntegral(): + from sympy.integrals.risch import NonElementaryIntegral + assert _test_args(NonElementaryIntegral(exp(-x**2), x)) + + +@SKIP("abstract class") +def test_sympy__integrals__transforms__IntegralTransform(): + pass + + +def test_sympy__integrals__transforms__MellinTransform(): + from sympy.integrals.transforms import MellinTransform + assert _test_args(MellinTransform(2, x, y)) + + +def test_sympy__integrals__transforms__InverseMellinTransform(): + from sympy.integrals.transforms import InverseMellinTransform + assert _test_args(InverseMellinTransform(2, x, y, 0, 1)) + + +def test_sympy__integrals__laplace__LaplaceTransform(): + from sympy.integrals.laplace import LaplaceTransform + assert _test_args(LaplaceTransform(2, x, y)) + + +def test_sympy__integrals__laplace__InverseLaplaceTransform(): + from sympy.integrals.laplace import InverseLaplaceTransform + assert _test_args(InverseLaplaceTransform(2, x, y, 0)) + + +@SKIP("abstract class") +def test_sympy__integrals__transforms__FourierTypeTransform(): + pass + + +def test_sympy__integrals__transforms__InverseFourierTransform(): + from sympy.integrals.transforms import InverseFourierTransform + assert _test_args(InverseFourierTransform(2, x, y)) + + +def test_sympy__integrals__transforms__FourierTransform(): + from sympy.integrals.transforms import FourierTransform + assert _test_args(FourierTransform(2, x, y)) + + +@SKIP("abstract class") +def test_sympy__integrals__transforms__SineCosineTypeTransform(): + pass + + +def test_sympy__integrals__transforms__InverseSineTransform(): + from sympy.integrals.transforms import InverseSineTransform + assert _test_args(InverseSineTransform(2, x, y)) + + +def test_sympy__integrals__transforms__SineTransform(): + from sympy.integrals.transforms import SineTransform + assert _test_args(SineTransform(2, x, y)) + + +def test_sympy__integrals__transforms__InverseCosineTransform(): + from sympy.integrals.transforms import InverseCosineTransform + assert _test_args(InverseCosineTransform(2, x, y)) + + +def test_sympy__integrals__transforms__CosineTransform(): + from sympy.integrals.transforms import CosineTransform + assert _test_args(CosineTransform(2, x, y)) + + +@SKIP("abstract class") +def test_sympy__integrals__transforms__HankelTypeTransform(): + pass + + +def test_sympy__integrals__transforms__InverseHankelTransform(): + from sympy.integrals.transforms import InverseHankelTransform + assert _test_args(InverseHankelTransform(2, x, y, 0)) + + +def test_sympy__integrals__transforms__HankelTransform(): + from sympy.integrals.transforms import HankelTransform + assert _test_args(HankelTransform(2, x, y, 0)) + + +def test_sympy__liealgebras__cartan_type__Standard_Cartan(): + from sympy.liealgebras.cartan_type import Standard_Cartan + assert _test_args(Standard_Cartan("A", 2)) + +def test_sympy__liealgebras__weyl_group__WeylGroup(): + from sympy.liealgebras.weyl_group import WeylGroup + assert _test_args(WeylGroup("B4")) + +def test_sympy__liealgebras__root_system__RootSystem(): + from sympy.liealgebras.root_system import RootSystem + assert _test_args(RootSystem("A2")) + +def test_sympy__liealgebras__type_a__TypeA(): + from sympy.liealgebras.type_a import TypeA + assert _test_args(TypeA(2)) + +def test_sympy__liealgebras__type_b__TypeB(): + from sympy.liealgebras.type_b import TypeB + assert _test_args(TypeB(4)) + +def test_sympy__liealgebras__type_c__TypeC(): + from sympy.liealgebras.type_c import TypeC + assert _test_args(TypeC(4)) + +def test_sympy__liealgebras__type_d__TypeD(): + from sympy.liealgebras.type_d import TypeD + assert _test_args(TypeD(4)) + +def test_sympy__liealgebras__type_e__TypeE(): + from sympy.liealgebras.type_e import TypeE + assert _test_args(TypeE(6)) + +def test_sympy__liealgebras__type_f__TypeF(): + from sympy.liealgebras.type_f import TypeF + assert _test_args(TypeF(4)) + +def test_sympy__liealgebras__type_g__TypeG(): + from sympy.liealgebras.type_g import TypeG + assert _test_args(TypeG(2)) + + +def test_sympy__logic__boolalg__And(): + from sympy.logic.boolalg import And + assert _test_args(And(x, y, 1)) + + +@SKIP("abstract class") +def test_sympy__logic__boolalg__Boolean(): + pass + + +def test_sympy__logic__boolalg__BooleanFunction(): + from sympy.logic.boolalg import BooleanFunction + assert _test_args(BooleanFunction(1, 2, 3)) + +@SKIP("abstract class") +def test_sympy__logic__boolalg__BooleanAtom(): + pass + +def test_sympy__logic__boolalg__BooleanTrue(): + from sympy.logic.boolalg import true + assert _test_args(true) + +def test_sympy__logic__boolalg__BooleanFalse(): + from sympy.logic.boolalg import false + assert _test_args(false) + +def test_sympy__logic__boolalg__Equivalent(): + from sympy.logic.boolalg import Equivalent + assert _test_args(Equivalent(x, 2)) + + +def test_sympy__logic__boolalg__ITE(): + from sympy.logic.boolalg import ITE + assert _test_args(ITE(x, y, 1)) + + +def test_sympy__logic__boolalg__Implies(): + from sympy.logic.boolalg import Implies + assert _test_args(Implies(x, y)) + + +def test_sympy__logic__boolalg__Nand(): + from sympy.logic.boolalg import Nand + assert _test_args(Nand(x, y, 1)) + + +def test_sympy__logic__boolalg__Nor(): + from sympy.logic.boolalg import Nor + assert _test_args(Nor(x, y)) + + +def test_sympy__logic__boolalg__Not(): + from sympy.logic.boolalg import Not + assert _test_args(Not(x)) + + +def test_sympy__logic__boolalg__Or(): + from sympy.logic.boolalg import Or + assert _test_args(Or(x, y)) + + +def test_sympy__logic__boolalg__Xor(): + from sympy.logic.boolalg import Xor + assert _test_args(Xor(x, y, 2)) + +def test_sympy__logic__boolalg__Xnor(): + from sympy.logic.boolalg import Xnor + assert _test_args(Xnor(x, y, 2)) + +def test_sympy__logic__boolalg__Exclusive(): + from sympy.logic.boolalg import Exclusive + assert _test_args(Exclusive(x, y, z)) + + +def test_sympy__matrices__matrixbase__DeferredVector(): + from sympy.matrices.matrixbase import DeferredVector + assert _test_args(DeferredVector("X")) + + +@SKIP("abstract class") +def test_sympy__matrices__expressions__matexpr__MatrixBase(): + pass + + +@SKIP("abstract class") +def test_sympy__matrices__immutable__ImmutableRepMatrix(): + pass + + +def test_sympy__matrices__immutable__ImmutableDenseMatrix(): + from sympy.matrices.immutable import ImmutableDenseMatrix + m = ImmutableDenseMatrix([[1, 2], [3, 4]]) + assert _test_args(m) + assert _test_args(Basic(*list(m))) + m = ImmutableDenseMatrix(1, 1, [1]) + assert _test_args(m) + assert _test_args(Basic(*list(m))) + m = ImmutableDenseMatrix(2, 2, lambda i, j: 1) + assert m[0, 0] is S.One + m = ImmutableDenseMatrix(2, 2, lambda i, j: 1/(1 + i) + 1/(1 + j)) + assert m[1, 1] is S.One # true div. will give 1.0 if i,j not sympified + assert _test_args(m) + assert _test_args(Basic(*list(m))) + + +def test_sympy__matrices__immutable__ImmutableSparseMatrix(): + from sympy.matrices.immutable import ImmutableSparseMatrix + m = ImmutableSparseMatrix([[1, 2], [3, 4]]) + assert _test_args(m) + assert _test_args(Basic(*list(m))) + m = ImmutableSparseMatrix(1, 1, {(0, 0): 1}) + assert _test_args(m) + assert _test_args(Basic(*list(m))) + m = ImmutableSparseMatrix(1, 1, [1]) + assert _test_args(m) + assert _test_args(Basic(*list(m))) + m = ImmutableSparseMatrix(2, 2, lambda i, j: 1) + assert m[0, 0] is S.One + m = ImmutableSparseMatrix(2, 2, lambda i, j: 1/(1 + i) + 1/(1 + j)) + assert m[1, 1] is S.One # true div. will give 1.0 if i,j not sympified + assert _test_args(m) + assert _test_args(Basic(*list(m))) + + +def test_sympy__matrices__expressions__slice__MatrixSlice(): + from sympy.matrices.expressions.slice import MatrixSlice + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', 4, 4) + assert _test_args(MatrixSlice(X, (0, 2), (0, 2))) + + +def test_sympy__matrices__expressions__applyfunc__ElementwiseApplyFunction(): + from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol("X", x, x) + func = Lambda(x, x**2) + assert _test_args(ElementwiseApplyFunction(func, X)) + + +def test_sympy__matrices__expressions__blockmatrix__BlockDiagMatrix(): + from sympy.matrices.expressions.blockmatrix import BlockDiagMatrix + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, x) + Y = MatrixSymbol('Y', y, y) + assert _test_args(BlockDiagMatrix(X, Y)) + + +def test_sympy__matrices__expressions__blockmatrix__BlockMatrix(): + from sympy.matrices.expressions.blockmatrix import BlockMatrix + from sympy.matrices.expressions import MatrixSymbol, ZeroMatrix + X = MatrixSymbol('X', x, x) + Y = MatrixSymbol('Y', y, y) + Z = MatrixSymbol('Z', x, y) + O = ZeroMatrix(y, x) + assert _test_args(BlockMatrix([[X, Z], [O, Y]])) + + +def test_sympy__matrices__expressions__inverse__Inverse(): + from sympy.matrices.expressions.inverse import Inverse + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Inverse(MatrixSymbol('A', 3, 3))) + + +def test_sympy__matrices__expressions__matadd__MatAdd(): + from sympy.matrices.expressions.matadd import MatAdd + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, y) + Y = MatrixSymbol('Y', x, y) + assert _test_args(MatAdd(X, Y)) + + +@SKIP("abstract class") +def test_sympy__matrices__expressions__matexpr__MatrixExpr(): + pass + +def test_sympy__matrices__expressions__matexpr__MatrixElement(): + from sympy.matrices.expressions.matexpr import MatrixSymbol, MatrixElement + from sympy.core.singleton import S + assert _test_args(MatrixElement(MatrixSymbol('A', 3, 5), S(2), S(3))) + +def test_sympy__matrices__expressions__matexpr__MatrixSymbol(): + from sympy.matrices.expressions.matexpr import MatrixSymbol + assert _test_args(MatrixSymbol('A', 3, 5)) + + +def test_sympy__matrices__expressions__special__OneMatrix(): + from sympy.matrices.expressions.special import OneMatrix + assert _test_args(OneMatrix(3, 5)) + + +def test_sympy__matrices__expressions__special__ZeroMatrix(): + from sympy.matrices.expressions.special import ZeroMatrix + assert _test_args(ZeroMatrix(3, 5)) + + +def test_sympy__matrices__expressions__special__GenericZeroMatrix(): + from sympy.matrices.expressions.special import GenericZeroMatrix + assert _test_args(GenericZeroMatrix()) + + +def test_sympy__matrices__expressions__special__Identity(): + from sympy.matrices.expressions.special import Identity + assert _test_args(Identity(3)) + + +def test_sympy__matrices__expressions__special__GenericIdentity(): + from sympy.matrices.expressions.special import GenericIdentity + assert _test_args(GenericIdentity()) + + +def test_sympy__matrices__expressions__sets__MatrixSet(): + from sympy.matrices.expressions.sets import MatrixSet + from sympy.core.singleton import S + assert _test_args(MatrixSet(2, 2, S.Reals)) + +def test_sympy__matrices__expressions__matmul__MatMul(): + from sympy.matrices.expressions.matmul import MatMul + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, y) + Y = MatrixSymbol('Y', y, x) + assert _test_args(MatMul(X, Y)) + + +def test_sympy__matrices__expressions__dotproduct__DotProduct(): + from sympy.matrices.expressions.dotproduct import DotProduct + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, 1) + Y = MatrixSymbol('Y', x, 1) + assert _test_args(DotProduct(X, Y)) + +def test_sympy__matrices__expressions__diagonal__DiagonalMatrix(): + from sympy.matrices.expressions.diagonal import DiagonalMatrix + from sympy.matrices.expressions import MatrixSymbol + x = MatrixSymbol('x', 10, 1) + assert _test_args(DiagonalMatrix(x)) + +def test_sympy__matrices__expressions__diagonal__DiagonalOf(): + from sympy.matrices.expressions.diagonal import DiagonalOf + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('x', 10, 10) + assert _test_args(DiagonalOf(X)) + +def test_sympy__matrices__expressions__diagonal__DiagMatrix(): + from sympy.matrices.expressions.diagonal import DiagMatrix + from sympy.matrices.expressions import MatrixSymbol + x = MatrixSymbol('x', 10, 1) + assert _test_args(DiagMatrix(x)) + +def test_sympy__matrices__expressions__hadamard__HadamardProduct(): + from sympy.matrices.expressions.hadamard import HadamardProduct + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, y) + Y = MatrixSymbol('Y', x, y) + assert _test_args(HadamardProduct(X, Y)) + +def test_sympy__matrices__expressions__hadamard__HadamardPower(): + from sympy.matrices.expressions.hadamard import HadamardPower + from sympy.matrices.expressions import MatrixSymbol + from sympy.core.symbol import Symbol + X = MatrixSymbol('X', x, y) + n = Symbol("n") + assert _test_args(HadamardPower(X, n)) + +def test_sympy__matrices__expressions__kronecker__KroneckerProduct(): + from sympy.matrices.expressions.kronecker import KroneckerProduct + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, y) + Y = MatrixSymbol('Y', x, y) + assert _test_args(KroneckerProduct(X, Y)) + + +def test_sympy__matrices__expressions__matpow__MatPow(): + from sympy.matrices.expressions.matpow import MatPow + from sympy.matrices.expressions import MatrixSymbol + X = MatrixSymbol('X', x, x) + assert _test_args(MatPow(X, 2)) + + +def test_sympy__matrices__expressions__transpose__Transpose(): + from sympy.matrices.expressions.transpose import Transpose + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Transpose(MatrixSymbol('A', 3, 5))) + + +def test_sympy__matrices__expressions__adjoint__Adjoint(): + from sympy.matrices.expressions.adjoint import Adjoint + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Adjoint(MatrixSymbol('A', 3, 5))) + + +def test_sympy__matrices__expressions__trace__Trace(): + from sympy.matrices.expressions.trace import Trace + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Trace(MatrixSymbol('A', 3, 3))) + +def test_sympy__matrices__expressions__determinant__Determinant(): + from sympy.matrices.expressions.determinant import Determinant + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Determinant(MatrixSymbol('A', 3, 3))) + +def test_sympy__matrices__expressions__determinant__Permanent(): + from sympy.matrices.expressions.determinant import Permanent + from sympy.matrices.expressions import MatrixSymbol + assert _test_args(Permanent(MatrixSymbol('A', 3, 4))) + +def test_sympy__matrices__expressions__funcmatrix__FunctionMatrix(): + from sympy.matrices.expressions.funcmatrix import FunctionMatrix + from sympy.core.symbol import symbols + i, j = symbols('i,j') + assert _test_args(FunctionMatrix(3, 3, Lambda((i, j), i - j) )) + +def test_sympy__matrices__expressions__fourier__DFT(): + from sympy.matrices.expressions.fourier import DFT + from sympy.core.singleton import S + assert _test_args(DFT(S(2))) + +def test_sympy__matrices__expressions__fourier__IDFT(): + from sympy.matrices.expressions.fourier import IDFT + from sympy.core.singleton import S + assert _test_args(IDFT(S(2))) + +from sympy.matrices.expressions import MatrixSymbol +X = MatrixSymbol('X', 10, 10) + +def test_sympy__matrices__expressions__factorizations__LofLU(): + from sympy.matrices.expressions.factorizations import LofLU + assert _test_args(LofLU(X)) + +def test_sympy__matrices__expressions__factorizations__UofLU(): + from sympy.matrices.expressions.factorizations import UofLU + assert _test_args(UofLU(X)) + +def test_sympy__matrices__expressions__factorizations__QofQR(): + from sympy.matrices.expressions.factorizations import QofQR + assert _test_args(QofQR(X)) + +def test_sympy__matrices__expressions__factorizations__RofQR(): + from sympy.matrices.expressions.factorizations import RofQR + assert _test_args(RofQR(X)) + +def test_sympy__matrices__expressions__factorizations__LofCholesky(): + from sympy.matrices.expressions.factorizations import LofCholesky + assert _test_args(LofCholesky(X)) + +def test_sympy__matrices__expressions__factorizations__UofCholesky(): + from sympy.matrices.expressions.factorizations import UofCholesky + assert _test_args(UofCholesky(X)) + +def test_sympy__matrices__expressions__factorizations__EigenVectors(): + from sympy.matrices.expressions.factorizations import EigenVectors + assert _test_args(EigenVectors(X)) + +def test_sympy__matrices__expressions__factorizations__EigenValues(): + from sympy.matrices.expressions.factorizations import EigenValues + assert _test_args(EigenValues(X)) + +def test_sympy__matrices__expressions__factorizations__UofSVD(): + from sympy.matrices.expressions.factorizations import UofSVD + assert _test_args(UofSVD(X)) + +def test_sympy__matrices__expressions__factorizations__VofSVD(): + from sympy.matrices.expressions.factorizations import VofSVD + assert _test_args(VofSVD(X)) + +def test_sympy__matrices__expressions__factorizations__SofSVD(): + from sympy.matrices.expressions.factorizations import SofSVD + assert _test_args(SofSVD(X)) + +@SKIP("abstract class") +def test_sympy__matrices__expressions__factorizations__Factorization(): + pass + +def test_sympy__matrices__expressions__permutation__PermutationMatrix(): + from sympy.combinatorics import Permutation + from sympy.matrices.expressions.permutation import PermutationMatrix + assert _test_args(PermutationMatrix(Permutation([2, 0, 1]))) + +def test_sympy__matrices__expressions__permutation__MatrixPermute(): + from sympy.combinatorics import Permutation + from sympy.matrices.expressions.matexpr import MatrixSymbol + from sympy.matrices.expressions.permutation import MatrixPermute + A = MatrixSymbol('A', 3, 3) + assert _test_args(MatrixPermute(A, Permutation([2, 0, 1]))) + +def test_sympy__matrices__expressions__companion__CompanionMatrix(): + from sympy.core.symbol import Symbol + from sympy.matrices.expressions.companion import CompanionMatrix + from sympy.polys.polytools import Poly + + x = Symbol('x') + p = Poly([1, 2, 3], x) + assert _test_args(CompanionMatrix(p)) + +def test_sympy__physics__vector__frame__CoordinateSym(): + from sympy.physics.vector import CoordinateSym + from sympy.physics.vector import ReferenceFrame + assert _test_args(CoordinateSym('R_x', ReferenceFrame('R'), 0)) + + +@SKIP("abstract class") +def test_sympy__physics__biomechanics__curve__CharacteristicCurveFunction(): + pass + + +def test_sympy__physics__biomechanics__curve__TendonForceLengthDeGroote2016(): + from sympy.physics.biomechanics import TendonForceLengthDeGroote2016 + l_T_tilde, c0, c1, c2, c3 = symbols('l_T_tilde, c0, c1, c2, c3') + assert _test_args(TendonForceLengthDeGroote2016(l_T_tilde, c0, c1, c2, c3)) + + +def test_sympy__physics__biomechanics__curve__TendonForceLengthInverseDeGroote2016(): + from sympy.physics.biomechanics import TendonForceLengthInverseDeGroote2016 + fl_T, c0, c1, c2, c3 = symbols('fl_T, c0, c1, c2, c3') + assert _test_args(TendonForceLengthInverseDeGroote2016(fl_T, c0, c1, c2, c3)) + + +def test_sympy__physics__biomechanics__curve__FiberForceLengthPassiveDeGroote2016(): + from sympy.physics.biomechanics import FiberForceLengthPassiveDeGroote2016 + l_M_tilde, c0, c1 = symbols('l_M_tilde, c0, c1') + assert _test_args(FiberForceLengthPassiveDeGroote2016(l_M_tilde, c0, c1)) + + +def test_sympy__physics__biomechanics__curve__FiberForceLengthPassiveInverseDeGroote2016(): + from sympy.physics.biomechanics import FiberForceLengthPassiveInverseDeGroote2016 + fl_M_pas, c0, c1 = symbols('fl_M_pas, c0, c1') + assert _test_args(FiberForceLengthPassiveInverseDeGroote2016(fl_M_pas, c0, c1)) + + +def test_sympy__physics__biomechanics__curve__FiberForceLengthActiveDeGroote2016(): + from sympy.physics.biomechanics import FiberForceLengthActiveDeGroote2016 + l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11 = symbols('l_M_tilde, c0:12') + assert _test_args(FiberForceLengthActiveDeGroote2016(l_M_tilde, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11)) + + +def test_sympy__physics__biomechanics__curve__FiberForceVelocityDeGroote2016(): + from sympy.physics.biomechanics import FiberForceVelocityDeGroote2016 + v_M_tilde, c0, c1, c2, c3 = symbols('v_M_tilde, c0, c1, c2, c3') + assert _test_args(FiberForceVelocityDeGroote2016(v_M_tilde, c0, c1, c2, c3)) + + +def test_sympy__physics__biomechanics__curve__FiberForceVelocityInverseDeGroote2016(): + from sympy.physics.biomechanics import FiberForceVelocityInverseDeGroote2016 + fv_M, c0, c1, c2, c3 = symbols('fv_M, c0, c1, c2, c3') + assert _test_args(FiberForceVelocityInverseDeGroote2016(fv_M, c0, c1, c2, c3)) + + +def test_sympy__physics__paulialgebra__Pauli(): + from sympy.physics.paulialgebra import Pauli + assert _test_args(Pauli(1)) + + +def test_sympy__physics__quantum__anticommutator__AntiCommutator(): + from sympy.physics.quantum.anticommutator import AntiCommutator + assert _test_args(AntiCommutator(x, y)) + + +def test_sympy__physics__quantum__cartesian__PositionBra3D(): + from sympy.physics.quantum.cartesian import PositionBra3D + assert _test_args(PositionBra3D(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__PositionKet3D(): + from sympy.physics.quantum.cartesian import PositionKet3D + assert _test_args(PositionKet3D(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__PositionState3D(): + from sympy.physics.quantum.cartesian import PositionState3D + assert _test_args(PositionState3D(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__PxBra(): + from sympy.physics.quantum.cartesian import PxBra + assert _test_args(PxBra(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__PxKet(): + from sympy.physics.quantum.cartesian import PxKet + assert _test_args(PxKet(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__PxOp(): + from sympy.physics.quantum.cartesian import PxOp + assert _test_args(PxOp(x, y, z)) + + +def test_sympy__physics__quantum__cartesian__XBra(): + from sympy.physics.quantum.cartesian import XBra + assert _test_args(XBra(x)) + + +def test_sympy__physics__quantum__cartesian__XKet(): + from sympy.physics.quantum.cartesian import XKet + assert _test_args(XKet(x)) + + +def test_sympy__physics__quantum__cartesian__XOp(): + from sympy.physics.quantum.cartesian import XOp + assert _test_args(XOp(x)) + + +def test_sympy__physics__quantum__cartesian__YOp(): + from sympy.physics.quantum.cartesian import YOp + assert _test_args(YOp(x)) + + +def test_sympy__physics__quantum__cartesian__ZOp(): + from sympy.physics.quantum.cartesian import ZOp + assert _test_args(ZOp(x)) + + +def test_sympy__physics__quantum__cg__CG(): + from sympy.physics.quantum.cg import CG + from sympy.core.singleton import S + assert _test_args(CG(Rational(3, 2), Rational(3, 2), S.Half, Rational(-1, 2), 1, 1)) + + +def test_sympy__physics__quantum__cg__Wigner3j(): + from sympy.physics.quantum.cg import Wigner3j + assert _test_args(Wigner3j(6, 0, 4, 0, 2, 0)) + + +def test_sympy__physics__quantum__cg__Wigner6j(): + from sympy.physics.quantum.cg import Wigner6j + assert _test_args(Wigner6j(1, 2, 3, 2, 1, 2)) + + +def test_sympy__physics__quantum__cg__Wigner9j(): + from sympy.physics.quantum.cg import Wigner9j + assert _test_args(Wigner9j(2, 1, 1, Rational(3, 2), S.Half, 1, S.Half, S.Half, 0)) + +def test_sympy__physics__quantum__circuitplot__Mz(): + from sympy.physics.quantum.circuitplot import Mz + assert _test_args(Mz(0)) + +def test_sympy__physics__quantum__circuitplot__Mx(): + from sympy.physics.quantum.circuitplot import Mx + assert _test_args(Mx(0)) + +def test_sympy__physics__quantum__commutator__Commutator(): + from sympy.physics.quantum.commutator import Commutator + A, B = symbols('A,B', commutative=False) + assert _test_args(Commutator(A, B)) + + +def test_sympy__physics__quantum__constants__HBar(): + from sympy.physics.quantum.constants import HBar + assert _test_args(HBar()) + + +def test_sympy__physics__quantum__dagger__Dagger(): + from sympy.physics.quantum.dagger import Dagger + from sympy.physics.quantum.state import Ket + assert _test_args(Dagger(Dagger(Ket('psi')))) + + +def test_sympy__physics__quantum__gate__CGate(): + from sympy.physics.quantum.gate import CGate, Gate + assert _test_args(CGate((0, 1), Gate(2))) + + +def test_sympy__physics__quantum__gate__CGateS(): + from sympy.physics.quantum.gate import CGateS, Gate + assert _test_args(CGateS((0, 1), Gate(2))) + + +def test_sympy__physics__quantum__gate__CNotGate(): + from sympy.physics.quantum.gate import CNotGate + assert _test_args(CNotGate(0, 1)) + + +def test_sympy__physics__quantum__gate__Gate(): + from sympy.physics.quantum.gate import Gate + assert _test_args(Gate(0)) + + +def test_sympy__physics__quantum__gate__HadamardGate(): + from sympy.physics.quantum.gate import HadamardGate + assert _test_args(HadamardGate(0)) + + +def test_sympy__physics__quantum__gate__IdentityGate(): + from sympy.physics.quantum.gate import IdentityGate + assert _test_args(IdentityGate(0)) + + +def test_sympy__physics__quantum__gate__OneQubitGate(): + from sympy.physics.quantum.gate import OneQubitGate + assert _test_args(OneQubitGate(0)) + + +def test_sympy__physics__quantum__gate__PhaseGate(): + from sympy.physics.quantum.gate import PhaseGate + assert _test_args(PhaseGate(0)) + + +def test_sympy__physics__quantum__gate__SwapGate(): + from sympy.physics.quantum.gate import SwapGate + assert _test_args(SwapGate(0, 1)) + + +def test_sympy__physics__quantum__gate__TGate(): + from sympy.physics.quantum.gate import TGate + assert _test_args(TGate(0)) + + +def test_sympy__physics__quantum__gate__TwoQubitGate(): + from sympy.physics.quantum.gate import TwoQubitGate + assert _test_args(TwoQubitGate(0)) + + +def test_sympy__physics__quantum__gate__UGate(): + from sympy.physics.quantum.gate import UGate + from sympy.matrices.immutable import ImmutableDenseMatrix + from sympy.core.containers import Tuple + from sympy.core.numbers import Integer + assert _test_args( + UGate(Tuple(Integer(1)), ImmutableDenseMatrix([[1, 0], [0, 2]]))) + + +def test_sympy__physics__quantum__gate__XGate(): + from sympy.physics.quantum.gate import XGate + assert _test_args(XGate(0)) + + +def test_sympy__physics__quantum__gate__YGate(): + from sympy.physics.quantum.gate import YGate + assert _test_args(YGate(0)) + + +def test_sympy__physics__quantum__gate__ZGate(): + from sympy.physics.quantum.gate import ZGate + assert _test_args(ZGate(0)) + + +def test_sympy__physics__quantum__grover__OracleGateFunction(): + from sympy.physics.quantum.grover import OracleGateFunction + @OracleGateFunction + def f(qubit): + return + assert _test_args(f) + +def test_sympy__physics__quantum__grover__OracleGate(): + from sympy.physics.quantum.grover import OracleGate + def f(qubit): + return + assert _test_args(OracleGate(1,f)) + + +def test_sympy__physics__quantum__grover__WGate(): + from sympy.physics.quantum.grover import WGate + assert _test_args(WGate(1)) + + +def test_sympy__physics__quantum__hilbert__ComplexSpace(): + from sympy.physics.quantum.hilbert import ComplexSpace + assert _test_args(ComplexSpace(x)) + + +def test_sympy__physics__quantum__hilbert__DirectSumHilbertSpace(): + from sympy.physics.quantum.hilbert import DirectSumHilbertSpace, ComplexSpace, FockSpace + c = ComplexSpace(2) + f = FockSpace() + assert _test_args(DirectSumHilbertSpace(c, f)) + + +def test_sympy__physics__quantum__hilbert__FockSpace(): + from sympy.physics.quantum.hilbert import FockSpace + assert _test_args(FockSpace()) + + +def test_sympy__physics__quantum__hilbert__HilbertSpace(): + from sympy.physics.quantum.hilbert import HilbertSpace + assert _test_args(HilbertSpace()) + + +def test_sympy__physics__quantum__hilbert__L2(): + from sympy.physics.quantum.hilbert import L2 + from sympy.core.numbers import oo + from sympy.sets.sets import Interval + assert _test_args(L2(Interval(0, oo))) + + +def test_sympy__physics__quantum__hilbert__TensorPowerHilbertSpace(): + from sympy.physics.quantum.hilbert import TensorPowerHilbertSpace, FockSpace + f = FockSpace() + assert _test_args(TensorPowerHilbertSpace(f, 2)) + + +def test_sympy__physics__quantum__hilbert__TensorProductHilbertSpace(): + from sympy.physics.quantum.hilbert import TensorProductHilbertSpace, FockSpace, ComplexSpace + c = ComplexSpace(2) + f = FockSpace() + assert _test_args(TensorProductHilbertSpace(f, c)) + + +def test_sympy__physics__quantum__innerproduct__InnerProduct(): + from sympy.physics.quantum import Bra, Ket, InnerProduct + b = Bra('b') + k = Ket('k') + assert _test_args(InnerProduct(b, k)) + + +def test_sympy__physics__quantum__operator__DifferentialOperator(): + from sympy.physics.quantum.operator import DifferentialOperator + from sympy.core.function import (Derivative, Function) + f = Function('f') + assert _test_args(DifferentialOperator(1/x*Derivative(f(x), x), f(x))) + + +def test_sympy__physics__quantum__operator__HermitianOperator(): + from sympy.physics.quantum.operator import HermitianOperator + assert _test_args(HermitianOperator('H')) + + +def test_sympy__physics__quantum__operator__IdentityOperator(): + from sympy.physics.quantum.operator import IdentityOperator + assert _test_args(IdentityOperator(5)) + + +def test_sympy__physics__quantum__operator__Operator(): + from sympy.physics.quantum.operator import Operator + assert _test_args(Operator('A')) + + +def test_sympy__physics__quantum__operator__OuterProduct(): + from sympy.physics.quantum.operator import OuterProduct + from sympy.physics.quantum import Ket, Bra + b = Bra('b') + k = Ket('k') + assert _test_args(OuterProduct(k, b)) + + +def test_sympy__physics__quantum__operator__UnitaryOperator(): + from sympy.physics.quantum.operator import UnitaryOperator + assert _test_args(UnitaryOperator('U')) + + +def test_sympy__physics__quantum__piab__PIABBra(): + from sympy.physics.quantum.piab import PIABBra + assert _test_args(PIABBra('B')) + + +def test_sympy__physics__quantum__boson__BosonOp(): + from sympy.physics.quantum.boson import BosonOp + assert _test_args(BosonOp('a')) + assert _test_args(BosonOp('a', False)) + + +def test_sympy__physics__quantum__boson__BosonFockKet(): + from sympy.physics.quantum.boson import BosonFockKet + assert _test_args(BosonFockKet(1)) + + +def test_sympy__physics__quantum__boson__BosonFockBra(): + from sympy.physics.quantum.boson import BosonFockBra + assert _test_args(BosonFockBra(1)) + + +def test_sympy__physics__quantum__boson__BosonCoherentKet(): + from sympy.physics.quantum.boson import BosonCoherentKet + assert _test_args(BosonCoherentKet(1)) + + +def test_sympy__physics__quantum__boson__BosonCoherentBra(): + from sympy.physics.quantum.boson import BosonCoherentBra + assert _test_args(BosonCoherentBra(1)) + + +def test_sympy__physics__quantum__fermion__FermionOp(): + from sympy.physics.quantum.fermion import FermionOp + assert _test_args(FermionOp('c')) + assert _test_args(FermionOp('c', False)) + + +def test_sympy__physics__quantum__fermion__FermionFockKet(): + from sympy.physics.quantum.fermion import FermionFockKet + assert _test_args(FermionFockKet(1)) + + +def test_sympy__physics__quantum__fermion__FermionFockBra(): + from sympy.physics.quantum.fermion import FermionFockBra + assert _test_args(FermionFockBra(1)) + + +def test_sympy__physics__quantum__pauli__SigmaOpBase(): + from sympy.physics.quantum.pauli import SigmaOpBase + assert _test_args(SigmaOpBase()) + + +def test_sympy__physics__quantum__pauli__SigmaX(): + from sympy.physics.quantum.pauli import SigmaX + assert _test_args(SigmaX()) + + +def test_sympy__physics__quantum__pauli__SigmaY(): + from sympy.physics.quantum.pauli import SigmaY + assert _test_args(SigmaY()) + + +def test_sympy__physics__quantum__pauli__SigmaZ(): + from sympy.physics.quantum.pauli import SigmaZ + assert _test_args(SigmaZ()) + + +def test_sympy__physics__quantum__pauli__SigmaMinus(): + from sympy.physics.quantum.pauli import SigmaMinus + assert _test_args(SigmaMinus()) + + +def test_sympy__physics__quantum__pauli__SigmaPlus(): + from sympy.physics.quantum.pauli import SigmaPlus + assert _test_args(SigmaPlus()) + + +def test_sympy__physics__quantum__pauli__SigmaZKet(): + from sympy.physics.quantum.pauli import SigmaZKet + assert _test_args(SigmaZKet(0)) + + +def test_sympy__physics__quantum__pauli__SigmaZBra(): + from sympy.physics.quantum.pauli import SigmaZBra + assert _test_args(SigmaZBra(0)) + + +def test_sympy__physics__quantum__piab__PIABHamiltonian(): + from sympy.physics.quantum.piab import PIABHamiltonian + assert _test_args(PIABHamiltonian('P')) + + +def test_sympy__physics__quantum__piab__PIABKet(): + from sympy.physics.quantum.piab import PIABKet + assert _test_args(PIABKet('K')) + + +def test_sympy__physics__quantum__qexpr__QExpr(): + from sympy.physics.quantum.qexpr import QExpr + assert _test_args(QExpr(0)) + + +def test_sympy__physics__quantum__qft__Fourier(): + from sympy.physics.quantum.qft import Fourier + assert _test_args(Fourier(0, 1)) + + +def test_sympy__physics__quantum__qft__IQFT(): + from sympy.physics.quantum.qft import IQFT + assert _test_args(IQFT(0, 1)) + + +def test_sympy__physics__quantum__qft__QFT(): + from sympy.physics.quantum.qft import QFT + assert _test_args(QFT(0, 1)) + + +def test_sympy__physics__quantum__qft__RkGate(): + from sympy.physics.quantum.qft import RkGate + assert _test_args(RkGate(0, 1)) + + +def test_sympy__physics__quantum__qubit__IntQubit(): + from sympy.physics.quantum.qubit import IntQubit + assert _test_args(IntQubit(0)) + + +def test_sympy__physics__quantum__qubit__IntQubitBra(): + from sympy.physics.quantum.qubit import IntQubitBra + assert _test_args(IntQubitBra(0)) + + +def test_sympy__physics__quantum__qubit__IntQubitState(): + from sympy.physics.quantum.qubit import IntQubitState, QubitState + assert _test_args(IntQubitState(QubitState(0, 1))) + + +def test_sympy__physics__quantum__qubit__Qubit(): + from sympy.physics.quantum.qubit import Qubit + assert _test_args(Qubit(0, 0, 0)) + + +def test_sympy__physics__quantum__qubit__QubitBra(): + from sympy.physics.quantum.qubit import QubitBra + assert _test_args(QubitBra('1', 0)) + + +def test_sympy__physics__quantum__qubit__QubitState(): + from sympy.physics.quantum.qubit import QubitState + assert _test_args(QubitState(0, 1)) + + +def test_sympy__physics__quantum__density__Density(): + from sympy.physics.quantum.density import Density + from sympy.physics.quantum.state import Ket + assert _test_args(Density([Ket(0), 0.5], [Ket(1), 0.5])) + + +@SKIP("TODO: sympy.physics.quantum.shor: Cmod Not Implemented") +def test_sympy__physics__quantum__shor__CMod(): + from sympy.physics.quantum.shor import CMod + assert _test_args(CMod()) + + +def test_sympy__physics__quantum__spin__CoupledSpinState(): + from sympy.physics.quantum.spin import CoupledSpinState + assert _test_args(CoupledSpinState(1, 0, (1, 1))) + assert _test_args(CoupledSpinState(1, 0, (1, S.Half, S.Half))) + assert _test_args(CoupledSpinState( + 1, 0, (1, S.Half, S.Half), ((2, 3, S.Half), (1, 2, 1)) )) + j, m, j1, j2, j3, j12, x = symbols('j m j1:4 j12 x') + assert CoupledSpinState( + j, m, (j1, j2, j3)).subs(j2, x) == CoupledSpinState(j, m, (j1, x, j3)) + assert CoupledSpinState(j, m, (j1, j2, j3), ((1, 3, j12), (1, 2, j)) ).subs(j12, x) == \ + CoupledSpinState(j, m, (j1, j2, j3), ((1, 3, x), (1, 2, j)) ) + + +def test_sympy__physics__quantum__spin__J2Op(): + from sympy.physics.quantum.spin import J2Op + assert _test_args(J2Op('J')) + + +def test_sympy__physics__quantum__spin__JminusOp(): + from sympy.physics.quantum.spin import JminusOp + assert _test_args(JminusOp('J')) + + +def test_sympy__physics__quantum__spin__JplusOp(): + from sympy.physics.quantum.spin import JplusOp + assert _test_args(JplusOp('J')) + + +def test_sympy__physics__quantum__spin__JxBra(): + from sympy.physics.quantum.spin import JxBra + assert _test_args(JxBra(1, 0)) + + +def test_sympy__physics__quantum__spin__JxBraCoupled(): + from sympy.physics.quantum.spin import JxBraCoupled + assert _test_args(JxBraCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JxKet(): + from sympy.physics.quantum.spin import JxKet + assert _test_args(JxKet(1, 0)) + + +def test_sympy__physics__quantum__spin__JxKetCoupled(): + from sympy.physics.quantum.spin import JxKetCoupled + assert _test_args(JxKetCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JxOp(): + from sympy.physics.quantum.spin import JxOp + assert _test_args(JxOp('J')) + + +def test_sympy__physics__quantum__spin__JyBra(): + from sympy.physics.quantum.spin import JyBra + assert _test_args(JyBra(1, 0)) + + +def test_sympy__physics__quantum__spin__JyBraCoupled(): + from sympy.physics.quantum.spin import JyBraCoupled + assert _test_args(JyBraCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JyKet(): + from sympy.physics.quantum.spin import JyKet + assert _test_args(JyKet(1, 0)) + + +def test_sympy__physics__quantum__spin__JyKetCoupled(): + from sympy.physics.quantum.spin import JyKetCoupled + assert _test_args(JyKetCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JyOp(): + from sympy.physics.quantum.spin import JyOp + assert _test_args(JyOp('J')) + + +def test_sympy__physics__quantum__spin__JzBra(): + from sympy.physics.quantum.spin import JzBra + assert _test_args(JzBra(1, 0)) + + +def test_sympy__physics__quantum__spin__JzBraCoupled(): + from sympy.physics.quantum.spin import JzBraCoupled + assert _test_args(JzBraCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JzKet(): + from sympy.physics.quantum.spin import JzKet + assert _test_args(JzKet(1, 0)) + + +def test_sympy__physics__quantum__spin__JzKetCoupled(): + from sympy.physics.quantum.spin import JzKetCoupled + assert _test_args(JzKetCoupled(1, 0, (1, 1))) + + +def test_sympy__physics__quantum__spin__JzOp(): + from sympy.physics.quantum.spin import JzOp + assert _test_args(JzOp('J')) + + +def test_sympy__physics__quantum__spin__Rotation(): + from sympy.physics.quantum.spin import Rotation + assert _test_args(Rotation(pi, 0, pi/2)) + + +def test_sympy__physics__quantum__spin__SpinState(): + from sympy.physics.quantum.spin import SpinState + assert _test_args(SpinState(1, 0)) + + +def test_sympy__physics__quantum__spin__WignerD(): + from sympy.physics.quantum.spin import WignerD + assert _test_args(WignerD(0, 1, 2, 3, 4, 5)) + + +def test_sympy__physics__quantum__state__Bra(): + from sympy.physics.quantum.state import Bra + assert _test_args(Bra(0)) + + +def test_sympy__physics__quantum__state__BraBase(): + from sympy.physics.quantum.state import BraBase + assert _test_args(BraBase(0)) + + +def test_sympy__physics__quantum__state__Ket(): + from sympy.physics.quantum.state import Ket + assert _test_args(Ket(0)) + + +def test_sympy__physics__quantum__state__KetBase(): + from sympy.physics.quantum.state import KetBase + assert _test_args(KetBase(0)) + + +def test_sympy__physics__quantum__state__State(): + from sympy.physics.quantum.state import State + assert _test_args(State(0)) + + +def test_sympy__physics__quantum__state__StateBase(): + from sympy.physics.quantum.state import StateBase + assert _test_args(StateBase(0)) + + +def test_sympy__physics__quantum__state__OrthogonalBra(): + from sympy.physics.quantum.state import OrthogonalBra + assert _test_args(OrthogonalBra(0)) + + +def test_sympy__physics__quantum__state__OrthogonalKet(): + from sympy.physics.quantum.state import OrthogonalKet + assert _test_args(OrthogonalKet(0)) + + +def test_sympy__physics__quantum__state__OrthogonalState(): + from sympy.physics.quantum.state import OrthogonalState + assert _test_args(OrthogonalState(0)) + + +def test_sympy__physics__quantum__state__TimeDepBra(): + from sympy.physics.quantum.state import TimeDepBra + assert _test_args(TimeDepBra('psi', 't')) + + +def test_sympy__physics__quantum__state__TimeDepKet(): + from sympy.physics.quantum.state import TimeDepKet + assert _test_args(TimeDepKet('psi', 't')) + + +def test_sympy__physics__quantum__state__TimeDepState(): + from sympy.physics.quantum.state import TimeDepState + assert _test_args(TimeDepState('psi', 't')) + + +def test_sympy__physics__quantum__state__Wavefunction(): + from sympy.physics.quantum.state import Wavefunction + from sympy.functions import sin + from sympy.functions.elementary.piecewise import Piecewise + n = 1 + L = 1 + g = Piecewise((0, x < 0), (0, x > L), (sqrt(2//L)*sin(n*pi*x/L), True)) + assert _test_args(Wavefunction(g, x)) + + +def test_sympy__physics__quantum__tensorproduct__TensorProduct(): + from sympy.physics.quantum.tensorproduct import TensorProduct + x, y = symbols("x y", commutative=False) + assert _test_args(TensorProduct(x, y)) + + +def test_sympy__physics__quantum__identitysearch__GateIdentity(): + from sympy.physics.quantum.gate import X + from sympy.physics.quantum.identitysearch import GateIdentity + assert _test_args(GateIdentity(X(0), X(0))) + + +def test_sympy__physics__quantum__sho1d__SHOOp(): + from sympy.physics.quantum.sho1d import SHOOp + assert _test_args(SHOOp('a')) + + +def test_sympy__physics__quantum__sho1d__RaisingOp(): + from sympy.physics.quantum.sho1d import RaisingOp + assert _test_args(RaisingOp('a')) + + +def test_sympy__physics__quantum__sho1d__LoweringOp(): + from sympy.physics.quantum.sho1d import LoweringOp + assert _test_args(LoweringOp('a')) + + +def test_sympy__physics__quantum__sho1d__NumberOp(): + from sympy.physics.quantum.sho1d import NumberOp + assert _test_args(NumberOp('N')) + + +def test_sympy__physics__quantum__sho1d__Hamiltonian(): + from sympy.physics.quantum.sho1d import Hamiltonian + assert _test_args(Hamiltonian('H')) + + +def test_sympy__physics__quantum__sho1d__SHOState(): + from sympy.physics.quantum.sho1d import SHOState + assert _test_args(SHOState(0)) + + +def test_sympy__physics__quantum__sho1d__SHOKet(): + from sympy.physics.quantum.sho1d import SHOKet + assert _test_args(SHOKet(0)) + + +def test_sympy__physics__quantum__sho1d__SHOBra(): + from sympy.physics.quantum.sho1d import SHOBra + assert _test_args(SHOBra(0)) + + +def test_sympy__physics__secondquant__AnnihilateBoson(): + from sympy.physics.secondquant import AnnihilateBoson + assert _test_args(AnnihilateBoson(0)) + + +def test_sympy__physics__secondquant__AnnihilateFermion(): + from sympy.physics.secondquant import AnnihilateFermion + assert _test_args(AnnihilateFermion(0)) + + +@SKIP("abstract class") +def test_sympy__physics__secondquant__Annihilator(): + pass + + +def test_sympy__physics__secondquant__AntiSymmetricTensor(): + from sympy.physics.secondquant import AntiSymmetricTensor + i, j = symbols('i j', below_fermi=True) + a, b = symbols('a b', above_fermi=True) + assert _test_args(AntiSymmetricTensor('v', (a, i), (b, j))) + + +def test_sympy__physics__secondquant__BosonState(): + from sympy.physics.secondquant import BosonState + assert _test_args(BosonState((0, 1))) + + +@SKIP("abstract class") +def test_sympy__physics__secondquant__BosonicOperator(): + pass + + +def test_sympy__physics__secondquant__Commutator(): + from sympy.physics.secondquant import Commutator + x, y = symbols('x y', commutative=False) + assert _test_args(Commutator(x, y)) + + +def test_sympy__physics__secondquant__CreateBoson(): + from sympy.physics.secondquant import CreateBoson + assert _test_args(CreateBoson(0)) + + +def test_sympy__physics__secondquant__CreateFermion(): + from sympy.physics.secondquant import CreateFermion + assert _test_args(CreateFermion(0)) + + +@SKIP("abstract class") +def test_sympy__physics__secondquant__Creator(): + pass + + +def test_sympy__physics__secondquant__Dagger(): + from sympy.physics.secondquant import Dagger + assert _test_args(Dagger(x)) + + +def test_sympy__physics__secondquant__FermionState(): + from sympy.physics.secondquant import FermionState + assert _test_args(FermionState((0, 1))) + + +def test_sympy__physics__secondquant__FermionicOperator(): + from sympy.physics.secondquant import FermionicOperator + assert _test_args(FermionicOperator(0)) + + +def test_sympy__physics__secondquant__FockState(): + from sympy.physics.secondquant import FockState + assert _test_args(FockState((0, 1))) + + +def test_sympy__physics__secondquant__FockStateBosonBra(): + from sympy.physics.secondquant import FockStateBosonBra + assert _test_args(FockStateBosonBra((0, 1))) + + +def test_sympy__physics__secondquant__FockStateBosonKet(): + from sympy.physics.secondquant import FockStateBosonKet + assert _test_args(FockStateBosonKet((0, 1))) + + +def test_sympy__physics__secondquant__FockStateBra(): + from sympy.physics.secondquant import FockStateBra + assert _test_args(FockStateBra((0, 1))) + + +def test_sympy__physics__secondquant__FockStateFermionBra(): + from sympy.physics.secondquant import FockStateFermionBra + assert _test_args(FockStateFermionBra((0, 1))) + + +def test_sympy__physics__secondquant__FockStateFermionKet(): + from sympy.physics.secondquant import FockStateFermionKet + assert _test_args(FockStateFermionKet((0, 1))) + + +def test_sympy__physics__secondquant__FockStateKet(): + from sympy.physics.secondquant import FockStateKet + assert _test_args(FockStateKet((0, 1))) + + +def test_sympy__physics__secondquant__InnerProduct(): + from sympy.physics.secondquant import InnerProduct + from sympy.physics.secondquant import FockStateKet, FockStateBra + assert _test_args(InnerProduct(FockStateBra((0, 1)), FockStateKet((0, 1)))) + + +def test_sympy__physics__secondquant__NO(): + from sympy.physics.secondquant import NO, F, Fd + assert _test_args(NO(Fd(x)*F(y))) + + +def test_sympy__physics__secondquant__PermutationOperator(): + from sympy.physics.secondquant import PermutationOperator + assert _test_args(PermutationOperator(0, 1)) + + +def test_sympy__physics__secondquant__SqOperator(): + from sympy.physics.secondquant import SqOperator + assert _test_args(SqOperator(0)) + + +def test_sympy__physics__secondquant__TensorSymbol(): + from sympy.physics.secondquant import TensorSymbol + assert _test_args(TensorSymbol(x)) + + +def test_sympy__physics__control__lti__LinearTimeInvariant(): + # Direct instances of LinearTimeInvariant class are not allowed. + # func(*args) tests for its derived classes (TransferFunction, + # Series, Parallel and TransferFunctionMatrix) should pass. + pass + + +def test_sympy__physics__control__lti__SISOLinearTimeInvariant(): + # Direct instances of SISOLinearTimeInvariant class are not allowed. + pass + + +def test_sympy__physics__control__lti__MIMOLinearTimeInvariant(): + # Direct instances of MIMOLinearTimeInvariant class are not allowed. + pass + + +def test_sympy__physics__control__lti__TransferFunction(): + from sympy.physics.control.lti import TransferFunction + assert _test_args(TransferFunction(2, 3, x)) + + +def test_sympy__physics__control__lti__Series(): + from sympy.physics.control import Series, TransferFunction + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + assert _test_args(Series(tf1, tf2)) + + +def test_sympy__physics__control__lti__MIMOSeries(): + from sympy.physics.control import MIMOSeries, TransferFunction, TransferFunctionMatrix + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + tfm_1 = TransferFunctionMatrix([[tf2, tf1]]) + tfm_2 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]]) + tfm_3 = TransferFunctionMatrix([[tf1], [tf2]]) + assert _test_args(MIMOSeries(tfm_3, tfm_2, tfm_1)) + + +def test_sympy__physics__control__lti__Parallel(): + from sympy.physics.control import Parallel, TransferFunction + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + assert _test_args(Parallel(tf1, tf2)) + + +def test_sympy__physics__control__lti__MIMOParallel(): + from sympy.physics.control import MIMOParallel, TransferFunction, TransferFunctionMatrix + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + tfm_1 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]]) + tfm_2 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]]) + assert _test_args(MIMOParallel(tfm_1, tfm_2)) + + +def test_sympy__physics__control__lti__Feedback(): + from sympy.physics.control import TransferFunction, Feedback + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + assert _test_args(Feedback(tf1, tf2)) + assert _test_args(Feedback(tf1, tf2, 1)) + + +def test_sympy__physics__control__lti__MIMOFeedback(): + from sympy.physics.control import TransferFunction, MIMOFeedback, TransferFunctionMatrix + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + tfm_1 = TransferFunctionMatrix([[tf2, tf1], [tf1, tf2]]) + tfm_2 = TransferFunctionMatrix([[tf1, tf2], [tf2, tf1]]) + assert _test_args(MIMOFeedback(tfm_1, tfm_2)) + assert _test_args(MIMOFeedback(tfm_1, tfm_2, 1)) + + +def test_sympy__physics__control__lti__TransferFunctionMatrix(): + from sympy.physics.control import TransferFunction, TransferFunctionMatrix + tf1 = TransferFunction(x**2 - y**3, y - z, x) + tf2 = TransferFunction(y - x, z + y, x) + assert _test_args(TransferFunctionMatrix([[tf1, tf2]])) + + +def test_sympy__physics__control__lti__StateSpace(): + from sympy.matrices.dense import Matrix + from sympy.physics.control import StateSpace + A = Matrix([[-5, -1], [3, -1]]) + B = Matrix([2, 5]) + C = Matrix([[1, 2]]) + D = Matrix([0]) + assert _test_args(StateSpace(A, B, C, D)) + + +def test_sympy__physics__units__dimensions__Dimension(): + from sympy.physics.units.dimensions import Dimension + assert _test_args(Dimension("length", "L")) + + +def test_sympy__physics__units__dimensions__DimensionSystem(): + from sympy.physics.units.dimensions import DimensionSystem + from sympy.physics.units.definitions.dimension_definitions import length, time, velocity + assert _test_args(DimensionSystem((length, time), (velocity,))) + + +def test_sympy__physics__units__quantities__Quantity(): + from sympy.physics.units.quantities import Quantity + assert _test_args(Quantity("dam")) + + +def test_sympy__physics__units__quantities__PhysicalConstant(): + from sympy.physics.units.quantities import PhysicalConstant + assert _test_args(PhysicalConstant("foo")) + + +def test_sympy__physics__units__prefixes__Prefix(): + from sympy.physics.units.prefixes import Prefix + assert _test_args(Prefix('kilo', 'k', 3)) + + +def test_sympy__core__numbers__AlgebraicNumber(): + from sympy.core.numbers import AlgebraicNumber + assert _test_args(AlgebraicNumber(sqrt(2), [1, 2, 3])) + + +def test_sympy__polys__polytools__GroebnerBasis(): + from sympy.polys.polytools import GroebnerBasis + assert _test_args(GroebnerBasis([x, y, z], x, y, z)) + + +def test_sympy__polys__polytools__Poly(): + from sympy.polys.polytools import Poly + assert _test_args(Poly(2, x, y)) + + +def test_sympy__polys__polytools__PurePoly(): + from sympy.polys.polytools import PurePoly + assert _test_args(PurePoly(2, x, y)) + + +@SKIP('abstract class') +def test_sympy__polys__rootoftools__RootOf(): + pass + + +def test_sympy__polys__rootoftools__ComplexRootOf(): + from sympy.polys.rootoftools import ComplexRootOf + assert _test_args(ComplexRootOf(x**3 + x + 1, 0)) + + +def test_sympy__polys__rootoftools__RootSum(): + from sympy.polys.rootoftools import RootSum + assert _test_args(RootSum(x**3 + x + 1, sin)) + + +def test_sympy__series__limits__Limit(): + from sympy.series.limits import Limit + assert _test_args(Limit(x, x, 0, dir='-')) + + +def test_sympy__series__order__Order(): + from sympy.series.order import Order + assert _test_args(Order(1, x, y)) + + +@SKIP('Abstract Class') +def test_sympy__series__sequences__SeqBase(): + pass + + +def test_sympy__series__sequences__EmptySequence(): + # Need to import the instance from series not the class from + # series.sequence + from sympy.series import EmptySequence + assert _test_args(EmptySequence) + + +@SKIP('Abstract Class') +def test_sympy__series__sequences__SeqExpr(): + pass + + +def test_sympy__series__sequences__SeqPer(): + from sympy.series.sequences import SeqPer + assert _test_args(SeqPer((1, 2, 3), (0, 10))) + + +def test_sympy__series__sequences__SeqFormula(): + from sympy.series.sequences import SeqFormula + assert _test_args(SeqFormula(x**2, (0, 10))) + + +def test_sympy__series__sequences__RecursiveSeq(): + from sympy.series.sequences import RecursiveSeq + y = Function("y") + n = symbols("n") + assert _test_args(RecursiveSeq(y(n - 1) + y(n - 2), y(n), n, (0, 1))) + assert _test_args(RecursiveSeq(y(n - 1) + y(n - 2), y(n), n)) + + +def test_sympy__series__sequences__SeqExprOp(): + from sympy.series.sequences import SeqExprOp, sequence + s1 = sequence((1, 2, 3)) + s2 = sequence(x**2) + assert _test_args(SeqExprOp(s1, s2)) + + +def test_sympy__series__sequences__SeqAdd(): + from sympy.series.sequences import SeqAdd, sequence + s1 = sequence((1, 2, 3)) + s2 = sequence(x**2) + assert _test_args(SeqAdd(s1, s2)) + + +def test_sympy__series__sequences__SeqMul(): + from sympy.series.sequences import SeqMul, sequence + s1 = sequence((1, 2, 3)) + s2 = sequence(x**2) + assert _test_args(SeqMul(s1, s2)) + + +@SKIP('Abstract Class') +def test_sympy__series__series_class__SeriesBase(): + pass + + +def test_sympy__series__fourier__FourierSeries(): + from sympy.series.fourier import fourier_series + assert _test_args(fourier_series(x, (x, -pi, pi))) + +def test_sympy__series__fourier__FiniteFourierSeries(): + from sympy.series.fourier import fourier_series + assert _test_args(fourier_series(sin(pi*x), (x, -1, 1))) + + +def test_sympy__series__formal__FormalPowerSeries(): + from sympy.series.formal import fps + assert _test_args(fps(log(1 + x), x)) + + +def test_sympy__series__formal__Coeff(): + from sympy.series.formal import fps + assert _test_args(fps(x**2 + x + 1, x)) + + +@SKIP('Abstract Class') +def test_sympy__series__formal__FiniteFormalPowerSeries(): + pass + + +def test_sympy__series__formal__FormalPowerSeriesProduct(): + from sympy.series.formal import fps + f1, f2 = fps(sin(x)), fps(exp(x)) + assert _test_args(f1.product(f2, x)) + + +def test_sympy__series__formal__FormalPowerSeriesCompose(): + from sympy.series.formal import fps + f1, f2 = fps(exp(x)), fps(sin(x)) + assert _test_args(f1.compose(f2, x)) + + +def test_sympy__series__formal__FormalPowerSeriesInverse(): + from sympy.series.formal import fps + f1 = fps(exp(x)) + assert _test_args(f1.inverse(x)) + + +def test_sympy__simplify__hyperexpand__Hyper_Function(): + from sympy.simplify.hyperexpand import Hyper_Function + assert _test_args(Hyper_Function([2], [1])) + + +def test_sympy__simplify__hyperexpand__G_Function(): + from sympy.simplify.hyperexpand import G_Function + assert _test_args(G_Function([2], [1], [], [])) + + +@SKIP("abstract class") +def test_sympy__tensor__array__ndim_array__ImmutableNDimArray(): + pass + + +def test_sympy__tensor__array__dense_ndim_array__ImmutableDenseNDimArray(): + from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray + densarr = ImmutableDenseNDimArray(range(10, 34), (2, 3, 4)) + assert _test_args(densarr) + + +def test_sympy__tensor__array__sparse_ndim_array__ImmutableSparseNDimArray(): + from sympy.tensor.array.sparse_ndim_array import ImmutableSparseNDimArray + sparr = ImmutableSparseNDimArray(range(10, 34), (2, 3, 4)) + assert _test_args(sparr) + + +def test_sympy__tensor__array__array_comprehension__ArrayComprehension(): + from sympy.tensor.array.array_comprehension import ArrayComprehension + arrcom = ArrayComprehension(x, (x, 1, 5)) + assert _test_args(arrcom) + +def test_sympy__tensor__array__array_comprehension__ArrayComprehensionMap(): + from sympy.tensor.array.array_comprehension import ArrayComprehensionMap + arrcomma = ArrayComprehensionMap(lambda: 0, (x, 1, 5)) + assert _test_args(arrcomma) + + +def test_sympy__tensor__array__array_derivatives__ArrayDerivative(): + from sympy.tensor.array.array_derivatives import ArrayDerivative + A = MatrixSymbol("A", 2, 2) + arrder = ArrayDerivative(A, A, evaluate=False) + assert _test_args(arrder) + +def test_sympy__tensor__array__expressions__array_expressions__ArraySymbol(): + from sympy.tensor.array.expressions.array_expressions import ArraySymbol + m, n, k = symbols("m n k") + array = ArraySymbol("A", (m, n, k, 2)) + assert _test_args(array) + +def test_sympy__tensor__array__expressions__array_expressions__ArrayElement(): + from sympy.tensor.array.expressions.array_expressions import ArrayElement + m, n, k = symbols("m n k") + ae = ArrayElement("A", (m, n, k, 2)) + assert _test_args(ae) + +def test_sympy__tensor__array__expressions__array_expressions__ZeroArray(): + from sympy.tensor.array.expressions.array_expressions import ZeroArray + m, n, k = symbols("m n k") + za = ZeroArray(m, n, k, 2) + assert _test_args(za) + +def test_sympy__tensor__array__expressions__array_expressions__OneArray(): + from sympy.tensor.array.expressions.array_expressions import OneArray + m, n, k = symbols("m n k") + za = OneArray(m, n, k, 2) + assert _test_args(za) + +def test_sympy__tensor__functions__TensorProduct(): + from sympy.tensor.functions import TensorProduct + A = MatrixSymbol('A', 3, 3) + B = MatrixSymbol('B', 3, 3) + tp = TensorProduct(A, B) + assert _test_args(tp) + + +def test_sympy__tensor__indexed__Idx(): + from sympy.tensor.indexed import Idx + assert _test_args(Idx('test')) + assert _test_args(Idx('test', (0, 10))) + assert _test_args(Idx('test', 2)) + assert _test_args(Idx('test', x)) + + +def test_sympy__tensor__indexed__Indexed(): + from sympy.tensor.indexed import Indexed, Idx + assert _test_args(Indexed('A', Idx('i'), Idx('j'))) + + +def test_sympy__tensor__indexed__IndexedBase(): + from sympy.tensor.indexed import IndexedBase + assert _test_args(IndexedBase('A', shape=(x, y))) + assert _test_args(IndexedBase('A', 1)) + assert _test_args(IndexedBase('A')[0, 1]) + + +def test_sympy__tensor__tensor__TensorIndexType(): + from sympy.tensor.tensor import TensorIndexType + assert _test_args(TensorIndexType('Lorentz')) + + +@SKIP("deprecated class") +def test_sympy__tensor__tensor__TensorType(): + pass + + +def test_sympy__tensor__tensor__TensorSymmetry(): + from sympy.tensor.tensor import TensorSymmetry, get_symmetric_group_sgs + assert _test_args(TensorSymmetry(get_symmetric_group_sgs(2))) + + +def test_sympy__tensor__tensor__TensorHead(): + from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, TensorHead + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + sym = TensorSymmetry(get_symmetric_group_sgs(1)) + assert _test_args(TensorHead('p', [Lorentz], sym, 0)) + + +def test_sympy__tensor__tensor__TensorIndex(): + from sympy.tensor.tensor import TensorIndexType, TensorIndex + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + assert _test_args(TensorIndex('i', Lorentz)) + +@SKIP("abstract class") +def test_sympy__tensor__tensor__TensExpr(): + pass + +def test_sympy__tensor__tensor__TensAdd(): + from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, TensAdd, tensor_heads + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + a, b = tensor_indices('a,b', Lorentz) + sym = TensorSymmetry(get_symmetric_group_sgs(1)) + p, q = tensor_heads('p,q', [Lorentz], sym) + t1 = p(a) + t2 = q(a) + assert _test_args(TensAdd(t1, t2)) + + +def test_sympy__tensor__tensor__Tensor(): + from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, TensorHead + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + a, b = tensor_indices('a,b', Lorentz) + sym = TensorSymmetry(get_symmetric_group_sgs(1)) + p = TensorHead('p', [Lorentz], sym) + assert _test_args(p(a)) + + +def test_sympy__tensor__tensor__TensMul(): + from sympy.tensor.tensor import TensorIndexType, TensorSymmetry, get_symmetric_group_sgs, tensor_indices, tensor_heads + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + a, b = tensor_indices('a,b', Lorentz) + sym = TensorSymmetry(get_symmetric_group_sgs(1)) + p, q = tensor_heads('p, q', [Lorentz], sym) + assert _test_args(3*p(a)*q(b)) + + +def test_sympy__tensor__tensor__TensorElement(): + from sympy.tensor.tensor import TensorIndexType, TensorHead, TensorElement + L = TensorIndexType("L") + A = TensorHead("A", [L, L]) + telem = TensorElement(A(x, y), {x: 1}) + assert _test_args(telem) + +def test_sympy__tensor__tensor__WildTensor(): + from sympy.tensor.tensor import TensorIndexType, WildTensorHead, TensorIndex + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + a = TensorIndex('a', Lorentz) + p = WildTensorHead('p') + assert _test_args(p(a)) + +def test_sympy__tensor__tensor__WildTensorHead(): + from sympy.tensor.tensor import WildTensorHead + assert _test_args(WildTensorHead('p')) + +def test_sympy__tensor__tensor__WildTensorIndex(): + from sympy.tensor.tensor import TensorIndexType, WildTensorIndex + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + assert _test_args(WildTensorIndex('i', Lorentz)) + +def test_sympy__tensor__toperators__PartialDerivative(): + from sympy.tensor.tensor import TensorIndexType, tensor_indices, TensorHead + from sympy.tensor.toperators import PartialDerivative + Lorentz = TensorIndexType('Lorentz', dummy_name='L') + a, b = tensor_indices('a,b', Lorentz) + A = TensorHead("A", [Lorentz]) + assert _test_args(PartialDerivative(A(a), A(b))) + + +def test_as_coeff_add(): + assert (7, (3*x, 4*x**2)) == (7 + 3*x + 4*x**2).as_coeff_add() + + +def test_sympy__geometry__curve__Curve(): + from sympy.geometry.curve import Curve + assert _test_args(Curve((x, 1), (x, 0, 1))) + + +def test_sympy__geometry__point__Point(): + from sympy.geometry.point import Point + assert _test_args(Point(0, 1)) + + +def test_sympy__geometry__point__Point2D(): + from sympy.geometry.point import Point2D + assert _test_args(Point2D(0, 1)) + + +def test_sympy__geometry__point__Point3D(): + from sympy.geometry.point import Point3D + assert _test_args(Point3D(0, 1, 2)) + + +def test_sympy__geometry__ellipse__Ellipse(): + from sympy.geometry.ellipse import Ellipse + assert _test_args(Ellipse((0, 1), 2, 3)) + + +def test_sympy__geometry__ellipse__Circle(): + from sympy.geometry.ellipse import Circle + assert _test_args(Circle((0, 1), 2)) + + +def test_sympy__geometry__parabola__Parabola(): + from sympy.geometry.parabola import Parabola + from sympy.geometry.line import Line + assert _test_args(Parabola((0, 0), Line((2, 3), (4, 3)))) + + +@SKIP("abstract class") +def test_sympy__geometry__line__LinearEntity(): + pass + + +def test_sympy__geometry__line__Line(): + from sympy.geometry.line import Line + assert _test_args(Line((0, 1), (2, 3))) + + +def test_sympy__geometry__line__Ray(): + from sympy.geometry.line import Ray + assert _test_args(Ray((0, 1), (2, 3))) + + +def test_sympy__geometry__line__Segment(): + from sympy.geometry.line import Segment + assert _test_args(Segment((0, 1), (2, 3))) + +@SKIP("abstract class") +def test_sympy__geometry__line__LinearEntity2D(): + pass + + +def test_sympy__geometry__line__Line2D(): + from sympy.geometry.line import Line2D + assert _test_args(Line2D((0, 1), (2, 3))) + + +def test_sympy__geometry__line__Ray2D(): + from sympy.geometry.line import Ray2D + assert _test_args(Ray2D((0, 1), (2, 3))) + + +def test_sympy__geometry__line__Segment2D(): + from sympy.geometry.line import Segment2D + assert _test_args(Segment2D((0, 1), (2, 3))) + + +@SKIP("abstract class") +def test_sympy__geometry__line__LinearEntity3D(): + pass + + +def test_sympy__geometry__line__Line3D(): + from sympy.geometry.line import Line3D + assert _test_args(Line3D((0, 1, 1), (2, 3, 4))) + + +def test_sympy__geometry__line__Segment3D(): + from sympy.geometry.line import Segment3D + assert _test_args(Segment3D((0, 1, 1), (2, 3, 4))) + + +def test_sympy__geometry__line__Ray3D(): + from sympy.geometry.line import Ray3D + assert _test_args(Ray3D((0, 1, 1), (2, 3, 4))) + + +def test_sympy__geometry__plane__Plane(): + from sympy.geometry.plane import Plane + assert _test_args(Plane((1, 1, 1), (-3, 4, -2), (1, 2, 3))) + + +def test_sympy__geometry__polygon__Polygon(): + from sympy.geometry.polygon import Polygon + assert _test_args(Polygon((0, 1), (2, 3), (4, 5), (6, 7))) + + +def test_sympy__geometry__polygon__RegularPolygon(): + from sympy.geometry.polygon import RegularPolygon + assert _test_args(RegularPolygon((0, 1), 2, 3, 4)) + + +def test_sympy__geometry__polygon__Triangle(): + from sympy.geometry.polygon import Triangle + assert _test_args(Triangle((0, 1), (2, 3), (4, 5))) + + +def test_sympy__geometry__entity__GeometryEntity(): + from sympy.geometry.entity import GeometryEntity + from sympy.geometry.point import Point + assert _test_args(GeometryEntity(Point(1, 0), 1, [1, 2])) + +@SKIP("abstract class") +def test_sympy__geometry__entity__GeometrySet(): + pass + +def test_sympy__diffgeom__diffgeom__Manifold(): + from sympy.diffgeom import Manifold + assert _test_args(Manifold('name', 3)) + + +def test_sympy__diffgeom__diffgeom__Patch(): + from sympy.diffgeom import Manifold, Patch + assert _test_args(Patch('name', Manifold('name', 3))) + + +def test_sympy__diffgeom__diffgeom__CoordSystem(): + from sympy.diffgeom import Manifold, Patch, CoordSystem + assert _test_args(CoordSystem('name', Patch('name', Manifold('name', 3)))) + assert _test_args(CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c])) + + +def test_sympy__diffgeom__diffgeom__CoordinateSymbol(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, CoordinateSymbol + assert _test_args(CoordinateSymbol(CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]), 0)) + + +def test_sympy__diffgeom__diffgeom__Point(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, Point + assert _test_args(Point( + CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]), [x, y])) + + +def test_sympy__diffgeom__diffgeom__BaseScalarField(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + assert _test_args(BaseScalarField(cs, 0)) + + +def test_sympy__diffgeom__diffgeom__BaseVectorField(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + assert _test_args(BaseVectorField(cs, 0)) + + +def test_sympy__diffgeom__diffgeom__Differential(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + assert _test_args(Differential(BaseScalarField(cs, 0))) + + +def test_sympy__diffgeom__diffgeom__Commutator(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField, Commutator + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + cs1 = CoordSystem('name1', Patch('name', Manifold('name', 3)), [a, b, c]) + v = BaseVectorField(cs, 0) + v1 = BaseVectorField(cs1, 0) + assert _test_args(Commutator(v, v1)) + + +def test_sympy__diffgeom__diffgeom__TensorProduct(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, TensorProduct + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + d = Differential(BaseScalarField(cs, 0)) + assert _test_args(TensorProduct(d, d)) + + +def test_sympy__diffgeom__diffgeom__WedgeProduct(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, WedgeProduct + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + d = Differential(BaseScalarField(cs, 0)) + d1 = Differential(BaseScalarField(cs, 1)) + assert _test_args(WedgeProduct(d, d1)) + + +def test_sympy__diffgeom__diffgeom__LieDerivative(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseScalarField, Differential, BaseVectorField, LieDerivative + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + d = Differential(BaseScalarField(cs, 0)) + v = BaseVectorField(cs, 0) + assert _test_args(LieDerivative(v, d)) + + +def test_sympy__diffgeom__diffgeom__BaseCovarDerivativeOp(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseCovarDerivativeOp + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + assert _test_args(BaseCovarDerivativeOp(cs, 0, [[[0, ]*3, ]*3, ]*3)) + + +def test_sympy__diffgeom__diffgeom__CovarDerivativeOp(): + from sympy.diffgeom import Manifold, Patch, CoordSystem, BaseVectorField, CovarDerivativeOp + cs = CoordSystem('name', Patch('name', Manifold('name', 3)), [a, b, c]) + v = BaseVectorField(cs, 0) + _test_args(CovarDerivativeOp(v, [[[0, ]*3, ]*3, ]*3)) + + +def test_sympy__categories__baseclasses__Class(): + from sympy.categories.baseclasses import Class + assert _test_args(Class()) + + +def test_sympy__categories__baseclasses__Object(): + from sympy.categories import Object + assert _test_args(Object("A")) + + +@SKIP("abstract class") +def test_sympy__categories__baseclasses__Morphism(): + pass + + +def test_sympy__categories__baseclasses__IdentityMorphism(): + from sympy.categories import Object, IdentityMorphism + assert _test_args(IdentityMorphism(Object("A"))) + + +def test_sympy__categories__baseclasses__NamedMorphism(): + from sympy.categories import Object, NamedMorphism + assert _test_args(NamedMorphism(Object("A"), Object("B"), "f")) + + +def test_sympy__categories__baseclasses__CompositeMorphism(): + from sympy.categories import Object, NamedMorphism, CompositeMorphism + A = Object("A") + B = Object("B") + C = Object("C") + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + assert _test_args(CompositeMorphism(f, g)) + + +def test_sympy__categories__baseclasses__Diagram(): + from sympy.categories import Object, NamedMorphism, Diagram + A = Object("A") + B = Object("B") + f = NamedMorphism(A, B, "f") + d = Diagram([f]) + assert _test_args(d) + + +def test_sympy__categories__baseclasses__Category(): + from sympy.categories import Object, NamedMorphism, Diagram, Category + A = Object("A") + B = Object("B") + C = Object("C") + f = NamedMorphism(A, B, "f") + g = NamedMorphism(B, C, "g") + d1 = Diagram([f, g]) + d2 = Diagram([f]) + K = Category("K", commutative_diagrams=[d1, d2]) + assert _test_args(K) + + +def test_sympy__physics__optics__waves__TWave(): + from sympy.physics.optics import TWave + A, f, phi = symbols('A, f, phi') + assert _test_args(TWave(A, f, phi)) + + +def test_sympy__physics__optics__gaussopt__BeamParameter(): + from sympy.physics.optics import BeamParameter + assert _test_args(BeamParameter(530e-9, 1, w=1e-3, n=1)) + + +def test_sympy__physics__optics__medium__Medium(): + from sympy.physics.optics import Medium + assert _test_args(Medium('m')) + + +def test_sympy__physics__optics__medium__MediumN(): + from sympy.physics.optics.medium import Medium + assert _test_args(Medium('m', n=2)) + + +def test_sympy__physics__optics__medium__MediumPP(): + from sympy.physics.optics.medium import Medium + assert _test_args(Medium('m', permittivity=2, permeability=2)) + + +def test_sympy__tensor__array__expressions__array_expressions__ArrayContraction(): + from sympy.tensor.array.expressions.array_expressions import ArrayContraction + from sympy.tensor.indexed import IndexedBase + A = symbols("A", cls=IndexedBase) + assert _test_args(ArrayContraction(A, (0, 1))) + + +def test_sympy__tensor__array__expressions__array_expressions__ArrayDiagonal(): + from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal + from sympy.tensor.indexed import IndexedBase + A = symbols("A", cls=IndexedBase) + assert _test_args(ArrayDiagonal(A, (0, 1))) + + +def test_sympy__tensor__array__expressions__array_expressions__ArrayTensorProduct(): + from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct + from sympy.tensor.indexed import IndexedBase + A, B = symbols("A B", cls=IndexedBase) + assert _test_args(ArrayTensorProduct(A, B)) + + +def test_sympy__tensor__array__expressions__array_expressions__ArrayAdd(): + from sympy.tensor.array.expressions.array_expressions import ArrayAdd + from sympy.tensor.indexed import IndexedBase + A, B = symbols("A B", cls=IndexedBase) + assert _test_args(ArrayAdd(A, B)) + + +def test_sympy__tensor__array__expressions__array_expressions__PermuteDims(): + from sympy.tensor.array.expressions.array_expressions import PermuteDims + A = MatrixSymbol("A", 4, 4) + assert _test_args(PermuteDims(A, (1, 0))) + + +def test_sympy__tensor__array__expressions__array_expressions__ArrayElementwiseApplyFunc(): + from sympy.tensor.array.expressions.array_expressions import ArraySymbol, ArrayElementwiseApplyFunc + A = ArraySymbol("A", (4,)) + assert _test_args(ArrayElementwiseApplyFunc(exp, A)) + + +def test_sympy__tensor__array__expressions__array_expressions__Reshape(): + from sympy.tensor.array.expressions.array_expressions import ArraySymbol, Reshape + A = ArraySymbol("A", (4,)) + assert _test_args(Reshape(A, (2, 2))) + + +def test_sympy__codegen__ast__Assignment(): + from sympy.codegen.ast import Assignment + assert _test_args(Assignment(x, y)) + + +def test_sympy__codegen__cfunctions__expm1(): + from sympy.codegen.cfunctions import expm1 + assert _test_args(expm1(x)) + + +def test_sympy__codegen__cfunctions__log1p(): + from sympy.codegen.cfunctions import log1p + assert _test_args(log1p(x)) + + +def test_sympy__codegen__cfunctions__exp2(): + from sympy.codegen.cfunctions import exp2 + assert _test_args(exp2(x)) + + +def test_sympy__codegen__cfunctions__log2(): + from sympy.codegen.cfunctions import log2 + assert _test_args(log2(x)) + + +def test_sympy__codegen__cfunctions__fma(): + from sympy.codegen.cfunctions import fma + assert _test_args(fma(x, y, z)) + + +def test_sympy__codegen__cfunctions__log10(): + from sympy.codegen.cfunctions import log10 + assert _test_args(log10(x)) + + +def test_sympy__codegen__cfunctions__Sqrt(): + from sympy.codegen.cfunctions import Sqrt + assert _test_args(Sqrt(x)) + +def test_sympy__codegen__cfunctions__Cbrt(): + from sympy.codegen.cfunctions import Cbrt + assert _test_args(Cbrt(x)) + +def test_sympy__codegen__cfunctions__hypot(): + from sympy.codegen.cfunctions import hypot + assert _test_args(hypot(x, y)) + + +def test_sympy__codegen__cfunctions__isnan(): + from sympy.codegen.cfunctions import isnan + assert _test_args(isnan(x)) + + +def test_sympy__codegen__fnodes__FFunction(): + from sympy.codegen.fnodes import FFunction + assert _test_args(FFunction('f')) + + +def test_sympy__codegen__fnodes__F95Function(): + from sympy.codegen.fnodes import F95Function + assert _test_args(F95Function('f')) + + +def test_sympy__codegen__fnodes__isign(): + from sympy.codegen.fnodes import isign + assert _test_args(isign(1, x)) + + +def test_sympy__codegen__fnodes__dsign(): + from sympy.codegen.fnodes import dsign + assert _test_args(dsign(1, x)) + + +def test_sympy__codegen__fnodes__cmplx(): + from sympy.codegen.fnodes import cmplx + assert _test_args(cmplx(x, y)) + + +def test_sympy__codegen__fnodes__kind(): + from sympy.codegen.fnodes import kind + assert _test_args(kind(x)) + + +def test_sympy__codegen__fnodes__merge(): + from sympy.codegen.fnodes import merge + assert _test_args(merge(1, 2, Eq(x, 0))) + + +def test_sympy__codegen__fnodes___literal(): + from sympy.codegen.fnodes import _literal + assert _test_args(_literal(1)) + + +def test_sympy__codegen__fnodes__literal_sp(): + from sympy.codegen.fnodes import literal_sp + assert _test_args(literal_sp(1)) + + +def test_sympy__codegen__fnodes__literal_dp(): + from sympy.codegen.fnodes import literal_dp + assert _test_args(literal_dp(1)) + + +def test_sympy__codegen__matrix_nodes__MatrixSolve(): + from sympy.matrices import MatrixSymbol + from sympy.codegen.matrix_nodes import MatrixSolve + A = MatrixSymbol('A', 3, 3) + v = MatrixSymbol('x', 3, 1) + assert _test_args(MatrixSolve(A, v)) + + +def test_sympy__vector__coordsysrect__CoordSys3D(): + from sympy.vector.coordsysrect import CoordSys3D + assert _test_args(CoordSys3D('C')) + + +def test_sympy__vector__point__Point(): + from sympy.vector.point import Point + assert _test_args(Point('P')) + + +def test_sympy__vector__basisdependent__BasisDependent(): + #from sympy.vector.basisdependent import BasisDependent + #These classes have been created to maintain an OOP hierarchy + #for Vectors and Dyadics. Are NOT meant to be initialized + pass + + +def test_sympy__vector__basisdependent__BasisDependentMul(): + #from sympy.vector.basisdependent import BasisDependentMul + #These classes have been created to maintain an OOP hierarchy + #for Vectors and Dyadics. Are NOT meant to be initialized + pass + + +def test_sympy__vector__basisdependent__BasisDependentAdd(): + #from sympy.vector.basisdependent import BasisDependentAdd + #These classes have been created to maintain an OOP hierarchy + #for Vectors and Dyadics. Are NOT meant to be initialized + pass + + +def test_sympy__vector__basisdependent__BasisDependentZero(): + #from sympy.vector.basisdependent import BasisDependentZero + #These classes have been created to maintain an OOP hierarchy + #for Vectors and Dyadics. Are NOT meant to be initialized + pass + + +def test_sympy__vector__vector__BaseVector(): + from sympy.vector.vector import BaseVector + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(BaseVector(0, C, ' ', ' ')) + + +def test_sympy__vector__vector__VectorAdd(): + from sympy.vector.vector import VectorAdd, VectorMul + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + from sympy.abc import a, b, c, x, y, z + v1 = a*C.i + b*C.j + c*C.k + v2 = x*C.i + y*C.j + z*C.k + assert _test_args(VectorAdd(v1, v2)) + assert _test_args(VectorMul(x, v1)) + + +def test_sympy__vector__vector__VectorMul(): + from sympy.vector.vector import VectorMul + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + from sympy.abc import a + assert _test_args(VectorMul(a, C.i)) + + +def test_sympy__vector__vector__VectorZero(): + from sympy.vector.vector import VectorZero + assert _test_args(VectorZero()) + + +def test_sympy__vector__vector__Vector(): + #from sympy.vector.vector import Vector + #Vector is never to be initialized using args + pass + + +def test_sympy__vector__vector__Cross(): + from sympy.vector.vector import Cross + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + _test_args(Cross(C.i, C.j)) + + +def test_sympy__vector__vector__Dot(): + from sympy.vector.vector import Dot + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + _test_args(Dot(C.i, C.j)) + + +def test_sympy__vector__dyadic__Dyadic(): + #from sympy.vector.dyadic import Dyadic + #Dyadic is never to be initialized using args + pass + + +def test_sympy__vector__dyadic__BaseDyadic(): + from sympy.vector.dyadic import BaseDyadic + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(BaseDyadic(C.i, C.j)) + + +def test_sympy__vector__dyadic__DyadicMul(): + from sympy.vector.dyadic import BaseDyadic, DyadicMul + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(DyadicMul(3, BaseDyadic(C.i, C.j))) + + +def test_sympy__vector__dyadic__DyadicAdd(): + from sympy.vector.dyadic import BaseDyadic, DyadicAdd + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(2 * DyadicAdd(BaseDyadic(C.i, C.i), + BaseDyadic(C.i, C.j))) + + +def test_sympy__vector__dyadic__DyadicZero(): + from sympy.vector.dyadic import DyadicZero + assert _test_args(DyadicZero()) + + +def test_sympy__vector__deloperator__Del(): + from sympy.vector.deloperator import Del + assert _test_args(Del()) + + +def test_sympy__vector__implicitregion__ImplicitRegion(): + from sympy.vector.implicitregion import ImplicitRegion + from sympy.abc import x, y + assert _test_args(ImplicitRegion((x, y), y**3 - 4*x)) + + +def test_sympy__vector__integrals__ParametricIntegral(): + from sympy.vector.integrals import ParametricIntegral + from sympy.vector.parametricregion import ParametricRegion + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(ParametricIntegral(C.y*C.i - 10*C.j,\ + ParametricRegion((x, y), (x, 1, 3), (y, -2, 2)))) + +def test_sympy__vector__operators__Curl(): + from sympy.vector.operators import Curl + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(Curl(C.i)) + + +def test_sympy__vector__operators__Laplacian(): + from sympy.vector.operators import Laplacian + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(Laplacian(C.i)) + + +def test_sympy__vector__operators__Divergence(): + from sympy.vector.operators import Divergence + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(Divergence(C.i)) + + +def test_sympy__vector__operators__Gradient(): + from sympy.vector.operators import Gradient + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(Gradient(C.x)) + + +def test_sympy__vector__orienters__Orienter(): + #from sympy.vector.orienters import Orienter + #Not to be initialized + pass + + +def test_sympy__vector__orienters__ThreeAngleOrienter(): + #from sympy.vector.orienters import ThreeAngleOrienter + #Not to be initialized + pass + + +def test_sympy__vector__orienters__AxisOrienter(): + from sympy.vector.orienters import AxisOrienter + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(AxisOrienter(x, C.i)) + + +def test_sympy__vector__orienters__BodyOrienter(): + from sympy.vector.orienters import BodyOrienter + assert _test_args(BodyOrienter(x, y, z, '123')) + + +def test_sympy__vector__orienters__SpaceOrienter(): + from sympy.vector.orienters import SpaceOrienter + assert _test_args(SpaceOrienter(x, y, z, '123')) + + +def test_sympy__vector__orienters__QuaternionOrienter(): + from sympy.vector.orienters import QuaternionOrienter + a, b, c, d = symbols('a b c d') + assert _test_args(QuaternionOrienter(a, b, c, d)) + + +def test_sympy__vector__parametricregion__ParametricRegion(): + from sympy.abc import t + from sympy.vector.parametricregion import ParametricRegion + assert _test_args(ParametricRegion((t, t**3), (t, 0, 2))) + + +def test_sympy__vector__scalar__BaseScalar(): + from sympy.vector.scalar import BaseScalar + from sympy.vector.coordsysrect import CoordSys3D + C = CoordSys3D('C') + assert _test_args(BaseScalar(0, C, ' ', ' ')) + + +def test_sympy__physics__wigner__Wigner3j(): + from sympy.physics.wigner import Wigner3j + assert _test_args(Wigner3j(0, 0, 0, 0, 0, 0)) + + +def test_sympy__combinatorics__schur_number__SchurNumber(): + from sympy.combinatorics.schur_number import SchurNumber + assert _test_args(SchurNumber(x)) + + +def test_sympy__combinatorics__perm_groups__SymmetricPermutationGroup(): + from sympy.combinatorics.perm_groups import SymmetricPermutationGroup + assert _test_args(SymmetricPermutationGroup(5)) + + +def test_sympy__combinatorics__perm_groups__Coset(): + from sympy.combinatorics.permutations import Permutation + from sympy.combinatorics.perm_groups import PermutationGroup, Coset + a = Permutation(1, 2) + b = Permutation(0, 1) + G = PermutationGroup([a, b]) + assert _test_args(Coset(a, G)) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_arit.py b/lib/python3.11/site-packages/sympy/core/tests/test_arit.py new file mode 100644 index 0000000000000000000000000000000000000000..d9848c39eb8c57580ee925f9d40e5e0a149c3174 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_arit.py @@ -0,0 +1,2472 @@ +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.mod import Mod +from sympy.core.mul import Mul +from sympy.core.numbers import (Float, I, Integer, Rational, comp, nan, + oo, pi, zoo) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import (im, re, sign) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import (Max, sqrt) +from sympy.functions.elementary.trigonometric import (atan, cos, sin) +from sympy.polys.polytools import Poly +from sympy.sets.sets import FiniteSet + +from sympy.core.parameters import distribute, evaluate +from sympy.core.expr import unchanged +from sympy.utilities.iterables import permutations +from sympy.testing.pytest import XFAIL, raises, warns +from sympy.utilities.exceptions import SymPyDeprecationWarning +from sympy.core.random import verify_numerically +from sympy.functions.elementary.trigonometric import asin + +from itertools import product + +a, c, x, y, z = symbols('a,c,x,y,z') +b = Symbol("b", positive=True) + + +def same_and_same_prec(a, b): + # stricter matching for Floats + return a == b and a._prec == b._prec + + +def test_bug1(): + assert re(x) != x + x.series(x, 0, 1) + assert re(x) != x + + +def test_Symbol(): + e = a*b + assert e == a*b + assert a*b*b == a*b**2 + assert a*b*b + c == c + a*b**2 + assert a*b*b - c == -c + a*b**2 + + x = Symbol('x', complex=True, real=False) + assert x.is_imaginary is None # could be I or 1 + I + x = Symbol('x', complex=True, imaginary=False) + assert x.is_real is None # could be 1 or 1 + I + x = Symbol('x', real=True) + assert x.is_complex + x = Symbol('x', imaginary=True) + assert x.is_complex + x = Symbol('x', real=False, imaginary=False) + assert x.is_complex is None # might be a non-number + + +def test_arit0(): + p = Rational(5) + e = a*b + assert e == a*b + e = a*b + b*a + assert e == 2*a*b + e = a*b + b*a + a*b + p*b*a + assert e == 8*a*b + e = a*b + b*a + a*b + p*b*a + a + assert e == a + 8*a*b + e = a + a + assert e == 2*a + e = a + b + a + assert e == b + 2*a + e = a + b*b + a + b*b + assert e == 2*a + 2*b**2 + e = a + Rational(2) + b*b + a + b*b + p + assert e == 7 + 2*a + 2*b**2 + e = (a + b*b + a + b*b)*p + assert e == 5*(2*a + 2*b**2) + e = (a*b*c + c*b*a + b*a*c)*p + assert e == 15*a*b*c + e = (a*b*c + c*b*a + b*a*c)*p - Rational(15)*a*b*c + assert e == Rational(0) + e = Rational(50)*(a - a) + assert e == Rational(0) + e = b*a - b - a*b + b + assert e == Rational(0) + e = a*b + c**p + assert e == a*b + c**5 + e = a/b + assert e == a*b**(-1) + e = a*2*2 + assert e == 4*a + e = 2 + a*2/2 + assert e == 2 + a + e = 2 - a - 2 + assert e == -a + e = 2*a*2 + assert e == 4*a + e = 2/a/2 + assert e == a**(-1) + e = 2**a**2 + assert e == 2**(a**2) + e = -(1 + a) + assert e == -1 - a + e = S.Half*(1 + a) + assert e == S.Half + a/2 + + +def test_div(): + e = a/b + assert e == a*b**(-1) + e = a/b + c/2 + assert e == a*b**(-1) + Rational(1)/2*c + e = (1 - b)/(b - 1) + assert e == (1 + -b)*((-1) + b)**(-1) + + +def test_pow_arit(): + n1 = Rational(1) + n2 = Rational(2) + n5 = Rational(5) + e = a*a + assert e == a**2 + e = a*a*a + assert e == a**3 + e = a*a*a*a**Rational(6) + assert e == a**9 + e = a*a*a*a**Rational(6) - a**Rational(9) + assert e == Rational(0) + e = a**(b - b) + assert e == Rational(1) + e = (a + Rational(1) - a)**b + assert e == Rational(1) + + e = (a + b + c)**n2 + assert e == (a + b + c)**2 + assert e.expand() == 2*b*c + 2*a*c + 2*a*b + a**2 + c**2 + b**2 + + e = (a + b)**n2 + assert e == (a + b)**2 + assert e.expand() == 2*a*b + a**2 + b**2 + + e = (a + b)**(n1/n2) + assert e == sqrt(a + b) + assert e.expand() == sqrt(a + b) + + n = n5**(n1/n2) + assert n == sqrt(5) + e = n*a*b - n*b*a + assert e == Rational(0) + e = n*a*b + n*b*a + assert e == 2*a*b*sqrt(5) + assert e.diff(a) == 2*b*sqrt(5) + assert e.diff(a) == 2*b*sqrt(5) + e = a/b**2 + assert e == a*b**(-2) + + assert sqrt(2*(1 + sqrt(2))) == (2*(1 + 2**S.Half))**S.Half + + x = Symbol('x') + y = Symbol('y') + + assert ((x*y)**3).expand() == y**3 * x**3 + assert ((x*y)**-3).expand() == y**-3 * x**-3 + + assert (x**5*(3*x)**(3)).expand() == 27 * x**8 + assert (x**5*(-3*x)**(3)).expand() == -27 * x**8 + assert (x**5*(3*x)**(-3)).expand() == x**2 * Rational(1, 27) + assert (x**5*(-3*x)**(-3)).expand() == x**2 * Rational(-1, 27) + + # expand_power_exp + _x = Symbol('x', zero=False) + _y = Symbol('y', zero=False) + assert (_x**(y**(x + exp(x + y)) + z)).expand(deep=False) == \ + _x**z*_x**(y**(x + exp(x + y))) + assert (_x**(_y**(x + exp(x + y)) + z)).expand() == \ + _x**z*_x**(_y**x*_y**(exp(x)*exp(y))) + + n = Symbol('n', even=False) + k = Symbol('k', even=True) + o = Symbol('o', odd=True) + + assert unchanged(Pow, -1, x) + assert unchanged(Pow, -1, n) + assert (-2)**k == 2**k + assert (-1)**k == 1 + assert (-1)**o == -1 + + +def test_pow2(): + # x**(2*y) is always (x**y)**2 but is only (x**2)**y if + # x.is_positive or y.is_integer + # let x = 1 to see why the following are not true. + assert (-x)**Rational(2, 3) != x**Rational(2, 3) + assert (-x)**Rational(5, 7) != -x**Rational(5, 7) + assert ((-x)**2)**Rational(1, 3) != ((-x)**Rational(1, 3))**2 + assert sqrt(x**2) != x + + +def test_pow3(): + assert sqrt(2)**3 == 2 * sqrt(2) + assert sqrt(2)**3 == sqrt(8) + + +def test_mod_pow(): + for s, t, u, v in [(4, 13, 497, 445), (4, -3, 497, 365), + (3.2, 2.1, 1.9, 0.1031015682350942), (S(3)/2, 5, S(5)/6, S(3)/32)]: + assert pow(S(s), t, u) == v + assert pow(S(s), S(t), u) == v + assert pow(S(s), t, S(u)) == v + assert pow(S(s), S(t), S(u)) == v + assert pow(S(2), S(10000000000), S(3)) == 1 + assert pow(x, y, z) == x**y%z + raises(TypeError, lambda: pow(S(4), "13", 497)) + raises(TypeError, lambda: pow(S(4), 13, "497")) + + +def test_pow_E(): + assert 2**(y/log(2)) == S.Exp1**y + assert 2**(y/log(2)/3) == S.Exp1**(y/3) + assert 3**(1/log(-3)) != S.Exp1 + assert (3 + 2*I)**(1/(log(-3 - 2*I) + I*pi)) == S.Exp1 + assert (4 + 2*I)**(1/(log(-4 - 2*I) + I*pi)) == S.Exp1 + assert (3 + 2*I)**(1/(log(-3 - 2*I, 3)/2 + I*pi/log(3)/2)) == 9 + assert (3 + 2*I)**(1/(log(3 + 2*I, 3)/2)) == 9 + # every time tests are run they will affirm with a different random + # value that this identity holds + while 1: + b = x._random() + r, i = b.as_real_imag() + if i: + break + assert verify_numerically(b**(1/(log(-b) + sign(i)*I*pi).n()), S.Exp1) + + +def test_pow_issue_3516(): + assert 4**Rational(1, 4) == sqrt(2) + + +def test_pow_im(): + for m in (-2, -1, 2): + for d in (3, 4, 5): + b = m*I + for i in range(1, 4*d + 1): + e = Rational(i, d) + assert (b**e - b.n()**e.n()).n(2, chop=1e-10) == 0 + + e = Rational(7, 3) + assert (2*x*I)**e == 4*2**Rational(1, 3)*(I*x)**e # same as Wolfram Alpha + im = symbols('im', imaginary=True) + assert (2*im*I)**e == 4*2**Rational(1, 3)*(I*im)**e + + args = [I, I, I, I, 2] + e = Rational(1, 3) + ans = 2**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + args = [I, I, I, 2] + e = Rational(1, 3) + ans = 2**e*(-I)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + args.append(-3) + ans = (6*I)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + args.append(-1) + ans = (-6*I)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + + args = [I, I, 2] + e = Rational(1, 3) + ans = (-2)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + args.append(-3) + ans = (6)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + args.append(-1) + ans = (-6)**e + assert Mul(*args, evaluate=False)**e == ans + assert Mul(*args)**e == ans + assert Mul(Pow(-1, Rational(3, 2), evaluate=False), I, I) == I + assert Mul(I*Pow(I, S.Half, evaluate=False)) == sqrt(I)*I + + +def test_real_mul(): + assert Float(0) * pi * x == 0 + assert set((Float(1) * pi * x).args) == {Float(1), pi, x} + + +def test_ncmul(): + A = Symbol("A", commutative=False) + B = Symbol("B", commutative=False) + C = Symbol("C", commutative=False) + assert A*B != B*A + assert A*B*C != C*B*A + assert A*b*B*3*C == 3*b*A*B*C + assert A*b*B*3*C != 3*b*B*A*C + assert A*b*B*3*C == 3*A*B*C*b + + assert A + B == B + A + assert (A + B)*C != C*(A + B) + + assert C*(A + B)*C != C*C*(A + B) + + assert A*A == A**2 + assert (A + B)*(A + B) == (A + B)**2 + + assert A**-1 * A == 1 + assert A/A == 1 + assert A/(A**2) == 1/A + + assert A/(1 + A) == A/(1 + A) + + assert set((A + B + 2*(A + B)).args) == \ + {A, B, 2*(A + B)} + + +def test_mul_add_identity(): + m = Mul(1, 2) + assert isinstance(m, Rational) and m.p == 2 and m.q == 1 + m = Mul(1, 2, evaluate=False) + assert isinstance(m, Mul) and m.args == (1, 2) + m = Mul(0, 1) + assert m is S.Zero + m = Mul(0, 1, evaluate=False) + assert isinstance(m, Mul) and m.args == (0, 1) + m = Add(0, 1) + assert m is S.One + m = Add(0, 1, evaluate=False) + assert isinstance(m, Add) and m.args == (0, 1) + + +def test_ncpow(): + x = Symbol('x', commutative=False) + y = Symbol('y', commutative=False) + z = Symbol('z', commutative=False) + a = Symbol('a') + b = Symbol('b') + c = Symbol('c') + + assert (x**2)*(y**2) != (y**2)*(x**2) + assert (x**-2)*y != y*(x**2) + assert 2**x*2**y != 2**(x + y) + assert 2**x*2**y*2**z != 2**(x + y + z) + assert 2**x*2**(2*x) == 2**(3*x) + assert 2**x*2**(2*x)*2**x == 2**(4*x) + assert exp(x)*exp(y) != exp(y)*exp(x) + assert exp(x)*exp(y)*exp(z) != exp(y)*exp(x)*exp(z) + assert exp(x)*exp(y)*exp(z) != exp(x + y + z) + assert x**a*x**b != x**(a + b) + assert x**a*x**b*x**c != x**(a + b + c) + assert x**3*x**4 == x**7 + assert x**3*x**4*x**2 == x**9 + assert x**a*x**(4*a) == x**(5*a) + assert x**a*x**(4*a)*x**a == x**(6*a) + + +def test_powerbug(): + x = Symbol("x") + assert x**1 != (-x)**1 + assert x**2 == (-x)**2 + assert x**3 != (-x)**3 + assert x**4 == (-x)**4 + assert x**5 != (-x)**5 + assert x**6 == (-x)**6 + + assert x**128 == (-x)**128 + assert x**129 != (-x)**129 + + assert (2*x)**2 == (-2*x)**2 + + +def test_Mul_doesnt_expand_exp(): + x = Symbol('x') + y = Symbol('y') + assert unchanged(Mul, exp(x), exp(y)) + assert unchanged(Mul, 2**x, 2**y) + assert x**2*x**3 == x**5 + assert 2**x*3**x == 6**x + assert x**(y)*x**(2*y) == x**(3*y) + assert sqrt(2)*sqrt(2) == 2 + assert 2**x*2**(2*x) == 2**(3*x) + assert sqrt(2)*2**Rational(1, 4)*5**Rational(3, 4) == 10**Rational(3, 4) + assert (x**(-log(5)/log(3))*x)/(x*x**( - log(5)/log(3))) == sympify(1) + + +def test_Mul_is_integer(): + k = Symbol('k', integer=True) + n = Symbol('n', integer=True) + nr = Symbol('nr', rational=False) + ir = Symbol('ir', irrational=True) + nz = Symbol('nz', integer=True, zero=False) + e = Symbol('e', even=True) + o = Symbol('o', odd=True) + i2 = Symbol('2', prime=True, even=True) + + assert (k/3).is_integer is None + assert (nz/3).is_integer is None + assert (nr/3).is_integer is False + assert (ir/3).is_integer is False + assert (x*k*n).is_integer is None + assert (e/2).is_integer is True + assert (e**2/2).is_integer is True + assert (2/k).is_integer is None + assert (2/k**2).is_integer is None + assert ((-1)**k*n).is_integer is True + assert (3*k*e/2).is_integer is True + assert (2*k*e/3).is_integer is None + assert (e/o).is_integer is None + assert (o/e).is_integer is False + assert (o/i2).is_integer is False + assert Mul(k, 1/k, evaluate=False).is_integer is None + assert Mul(2., S.Half, evaluate=False).is_integer is None + assert (2*sqrt(k)).is_integer is None + assert (2*k**n).is_integer is None + + s = 2**2**2**Pow(2, 1000, evaluate=False) + m = Mul(s, s, evaluate=False) + assert m.is_integer + + # broken in 1.6 and before, see #20161 + xq = Symbol('xq', rational=True) + yq = Symbol('yq', rational=True) + assert (xq*yq).is_integer is None + e_20161 = Mul(-1,Mul(1,Pow(2,-1,evaluate=False),evaluate=False),evaluate=False) + assert e_20161.is_integer is not True # expand(e_20161) -> -1/2, but no need to see that in the assumption without evaluation + + +def test_Add_Mul_is_integer(): + x = Symbol('x') + + k = Symbol('k', integer=True) + n = Symbol('n', integer=True) + nk = Symbol('nk', integer=False) + nr = Symbol('nr', rational=False) + nz = Symbol('nz', integer=True, zero=False) + + assert (-nk).is_integer is None + assert (-nr).is_integer is False + assert (2*k).is_integer is True + assert (-k).is_integer is True + + assert (k + nk).is_integer is False + assert (k + n).is_integer is True + assert (k + x).is_integer is None + assert (k + n*x).is_integer is None + assert (k + n/3).is_integer is None + assert (k + nz/3).is_integer is None + assert (k + nr/3).is_integer is False + + assert ((1 + sqrt(3))*(-sqrt(3) + 1)).is_integer is not False + assert (1 + (1 + sqrt(3))*(-sqrt(3) + 1)).is_integer is not False + + +def test_Add_Mul_is_finite(): + x = Symbol('x', extended_real=True, finite=False) + + assert sin(x).is_finite is True + assert (x*sin(x)).is_finite is None + assert (x*atan(x)).is_finite is False + assert (1024*sin(x)).is_finite is True + assert (sin(x)*exp(x)).is_finite is None + assert (sin(x)*cos(x)).is_finite is True + assert (x*sin(x)*exp(x)).is_finite is None + + assert (sin(x) - 67).is_finite is True + assert (sin(x) + exp(x)).is_finite is not True + assert (1 + x).is_finite is False + assert (1 + x**2 + (1 + x)*(1 - x)).is_finite is None + assert (sqrt(2)*(1 + x)).is_finite is False + assert (sqrt(2)*(1 + x)*(1 - x)).is_finite is False + + +def test_Mul_is_even_odd(): + x = Symbol('x', integer=True) + y = Symbol('y', integer=True) + + k = Symbol('k', odd=True) + n = Symbol('n', odd=True) + m = Symbol('m', even=True) + + assert (2*x).is_even is True + assert (2*x).is_odd is False + + assert (3*x).is_even is None + assert (3*x).is_odd is None + + assert (k/3).is_integer is None + assert (k/3).is_even is None + assert (k/3).is_odd is None + + assert (2*n).is_even is True + assert (2*n).is_odd is False + + assert (2*m).is_even is True + assert (2*m).is_odd is False + + assert (-n).is_even is False + assert (-n).is_odd is True + + assert (k*n).is_even is False + assert (k*n).is_odd is True + + assert (k*m).is_even is True + assert (k*m).is_odd is False + + assert (k*n*m).is_even is True + assert (k*n*m).is_odd is False + + assert (k*m*x).is_even is True + assert (k*m*x).is_odd is False + + # issue 6791: + assert (x/2).is_integer is None + assert (k/2).is_integer is False + assert (m/2).is_integer is True + + assert (x*y).is_even is None + assert (x*x).is_even is None + assert (x*(x + k)).is_even is True + assert (x*(x + m)).is_even is None + + assert (x*y).is_odd is None + assert (x*x).is_odd is None + assert (x*(x + k)).is_odd is False + assert (x*(x + m)).is_odd is None + + # issue 8648 + assert (m**2/2).is_even + assert (m**2/3).is_even is False + assert (2/m**2).is_odd is False + assert (2/m).is_odd is None + + +@XFAIL +def test_evenness_in_ternary_integer_product_with_odd(): + # Tests that oddness inference is independent of term ordering. + # Term ordering at the point of testing depends on SymPy's symbol order, so + # we try to force a different order by modifying symbol names. + x = Symbol('x', integer=True) + y = Symbol('y', integer=True) + k = Symbol('k', odd=True) + assert (x*y*(y + k)).is_even is True + assert (y*x*(x + k)).is_even is True + + +def test_evenness_in_ternary_integer_product_with_even(): + x = Symbol('x', integer=True) + y = Symbol('y', integer=True) + m = Symbol('m', even=True) + assert (x*y*(y + m)).is_even is None + + +@XFAIL +def test_oddness_in_ternary_integer_product_with_odd(): + # Tests that oddness inference is independent of term ordering. + # Term ordering at the point of testing depends on SymPy's symbol order, so + # we try to force a different order by modifying symbol names. + x = Symbol('x', integer=True) + y = Symbol('y', integer=True) + k = Symbol('k', odd=True) + assert (x*y*(y + k)).is_odd is False + assert (y*x*(x + k)).is_odd is False + + +def test_oddness_in_ternary_integer_product_with_even(): + x = Symbol('x', integer=True) + y = Symbol('y', integer=True) + m = Symbol('m', even=True) + assert (x*y*(y + m)).is_odd is None + + +def test_Mul_is_rational(): + x = Symbol('x') + n = Symbol('n', integer=True) + m = Symbol('m', integer=True, nonzero=True) + + assert (n/m).is_rational is True + assert (x/pi).is_rational is None + assert (x/n).is_rational is None + assert (m/pi).is_rational is False + + r = Symbol('r', rational=True) + assert (pi*r).is_rational is None + + # issue 8008 + z = Symbol('z', zero=True) + i = Symbol('i', imaginary=True) + assert (z*i).is_rational is True + bi = Symbol('i', imaginary=True, finite=True) + assert (z*bi).is_zero is True + + +def test_Add_is_rational(): + x = Symbol('x') + n = Symbol('n', rational=True) + m = Symbol('m', rational=True) + + assert (n + m).is_rational is True + assert (x + pi).is_rational is None + assert (x + n).is_rational is None + assert (n + pi).is_rational is False + + +def test_Add_is_even_odd(): + x = Symbol('x', integer=True) + + k = Symbol('k', odd=True) + n = Symbol('n', odd=True) + m = Symbol('m', even=True) + + assert (k + 7).is_even is True + assert (k + 7).is_odd is False + + assert (-k + 7).is_even is True + assert (-k + 7).is_odd is False + + assert (k - 12).is_even is False + assert (k - 12).is_odd is True + + assert (-k - 12).is_even is False + assert (-k - 12).is_odd is True + + assert (k + n).is_even is True + assert (k + n).is_odd is False + + assert (k + m).is_even is False + assert (k + m).is_odd is True + + assert (k + n + m).is_even is True + assert (k + n + m).is_odd is False + + assert (k + n + x + m).is_even is None + assert (k + n + x + m).is_odd is None + + +def test_Mul_is_negative_positive(): + x = Symbol('x', real=True) + y = Symbol('y', extended_real=False, complex=True) + z = Symbol('z', zero=True) + + e = 2*z + assert e.is_Mul and e.is_positive is False and e.is_negative is False + + neg = Symbol('neg', negative=True) + pos = Symbol('pos', positive=True) + nneg = Symbol('nneg', nonnegative=True) + npos = Symbol('npos', nonpositive=True) + + assert neg.is_negative is True + assert (-neg).is_negative is False + assert (2*neg).is_negative is True + + assert (2*pos)._eval_is_extended_negative() is False + assert (2*pos).is_negative is False + + assert pos.is_negative is False + assert (-pos).is_negative is True + assert (2*pos).is_negative is False + + assert (pos*neg).is_negative is True + assert (2*pos*neg).is_negative is True + assert (-pos*neg).is_negative is False + assert (pos*neg*y).is_negative is False # y.is_real=F; !real -> !neg + + assert nneg.is_negative is False + assert (-nneg).is_negative is None + assert (2*nneg).is_negative is False + + assert npos.is_negative is None + assert (-npos).is_negative is False + assert (2*npos).is_negative is None + + assert (nneg*npos).is_negative is None + + assert (neg*nneg).is_negative is None + assert (neg*npos).is_negative is False + + assert (pos*nneg).is_negative is False + assert (pos*npos).is_negative is None + + assert (npos*neg*nneg).is_negative is False + assert (npos*pos*nneg).is_negative is None + + assert (-npos*neg*nneg).is_negative is None + assert (-npos*pos*nneg).is_negative is False + + assert (17*npos*neg*nneg).is_negative is False + assert (17*npos*pos*nneg).is_negative is None + + assert (neg*npos*pos*nneg).is_negative is False + + assert (x*neg).is_negative is None + assert (nneg*npos*pos*x*neg).is_negative is None + + assert neg.is_positive is False + assert (-neg).is_positive is True + assert (2*neg).is_positive is False + + assert pos.is_positive is True + assert (-pos).is_positive is False + assert (2*pos).is_positive is True + + assert (pos*neg).is_positive is False + assert (2*pos*neg).is_positive is False + assert (-pos*neg).is_positive is True + assert (-pos*neg*y).is_positive is False # y.is_real=F; !real -> !neg + + assert nneg.is_positive is None + assert (-nneg).is_positive is False + assert (2*nneg).is_positive is None + + assert npos.is_positive is False + assert (-npos).is_positive is None + assert (2*npos).is_positive is False + + assert (nneg*npos).is_positive is False + + assert (neg*nneg).is_positive is False + assert (neg*npos).is_positive is None + + assert (pos*nneg).is_positive is None + assert (pos*npos).is_positive is False + + assert (npos*neg*nneg).is_positive is None + assert (npos*pos*nneg).is_positive is False + + assert (-npos*neg*nneg).is_positive is False + assert (-npos*pos*nneg).is_positive is None + + assert (17*npos*neg*nneg).is_positive is None + assert (17*npos*pos*nneg).is_positive is False + + assert (neg*npos*pos*nneg).is_positive is None + + assert (x*neg).is_positive is None + assert (nneg*npos*pos*x*neg).is_positive is None + + +def test_Mul_is_negative_positive_2(): + a = Symbol('a', nonnegative=True) + b = Symbol('b', nonnegative=True) + c = Symbol('c', nonpositive=True) + d = Symbol('d', nonpositive=True) + + assert (a*b).is_nonnegative is True + assert (a*b).is_negative is False + assert (a*b).is_zero is None + assert (a*b).is_positive is None + + assert (c*d).is_nonnegative is True + assert (c*d).is_negative is False + assert (c*d).is_zero is None + assert (c*d).is_positive is None + + assert (a*c).is_nonpositive is True + assert (a*c).is_positive is False + assert (a*c).is_zero is None + assert (a*c).is_negative is None + + +def test_Mul_is_nonpositive_nonnegative(): + x = Symbol('x', real=True) + + k = Symbol('k', negative=True) + n = Symbol('n', positive=True) + u = Symbol('u', nonnegative=True) + v = Symbol('v', nonpositive=True) + + assert k.is_nonpositive is True + assert (-k).is_nonpositive is False + assert (2*k).is_nonpositive is True + + assert n.is_nonpositive is False + assert (-n).is_nonpositive is True + assert (2*n).is_nonpositive is False + + assert (n*k).is_nonpositive is True + assert (2*n*k).is_nonpositive is True + assert (-n*k).is_nonpositive is False + + assert u.is_nonpositive is None + assert (-u).is_nonpositive is True + assert (2*u).is_nonpositive is None + + assert v.is_nonpositive is True + assert (-v).is_nonpositive is None + assert (2*v).is_nonpositive is True + + assert (u*v).is_nonpositive is True + + assert (k*u).is_nonpositive is True + assert (k*v).is_nonpositive is None + + assert (n*u).is_nonpositive is None + assert (n*v).is_nonpositive is True + + assert (v*k*u).is_nonpositive is None + assert (v*n*u).is_nonpositive is True + + assert (-v*k*u).is_nonpositive is True + assert (-v*n*u).is_nonpositive is None + + assert (17*v*k*u).is_nonpositive is None + assert (17*v*n*u).is_nonpositive is True + + assert (k*v*n*u).is_nonpositive is None + + assert (x*k).is_nonpositive is None + assert (u*v*n*x*k).is_nonpositive is None + + assert k.is_nonnegative is False + assert (-k).is_nonnegative is True + assert (2*k).is_nonnegative is False + + assert n.is_nonnegative is True + assert (-n).is_nonnegative is False + assert (2*n).is_nonnegative is True + + assert (n*k).is_nonnegative is False + assert (2*n*k).is_nonnegative is False + assert (-n*k).is_nonnegative is True + + assert u.is_nonnegative is True + assert (-u).is_nonnegative is None + assert (2*u).is_nonnegative is True + + assert v.is_nonnegative is None + assert (-v).is_nonnegative is True + assert (2*v).is_nonnegative is None + + assert (u*v).is_nonnegative is None + + assert (k*u).is_nonnegative is None + assert (k*v).is_nonnegative is True + + assert (n*u).is_nonnegative is True + assert (n*v).is_nonnegative is None + + assert (v*k*u).is_nonnegative is True + assert (v*n*u).is_nonnegative is None + + assert (-v*k*u).is_nonnegative is None + assert (-v*n*u).is_nonnegative is True + + assert (17*v*k*u).is_nonnegative is True + assert (17*v*n*u).is_nonnegative is None + + assert (k*v*n*u).is_nonnegative is True + + assert (x*k).is_nonnegative is None + assert (u*v*n*x*k).is_nonnegative is None + + +def test_Add_is_negative_positive(): + x = Symbol('x', real=True) + + k = Symbol('k', negative=True) + n = Symbol('n', positive=True) + u = Symbol('u', nonnegative=True) + v = Symbol('v', nonpositive=True) + + assert (k - 2).is_negative is True + assert (k + 17).is_negative is None + assert (-k - 5).is_negative is None + assert (-k + 123).is_negative is False + + assert (k - n).is_negative is True + assert (k + n).is_negative is None + assert (-k - n).is_negative is None + assert (-k + n).is_negative is False + + assert (k - n - 2).is_negative is True + assert (k + n + 17).is_negative is None + assert (-k - n - 5).is_negative is None + assert (-k + n + 123).is_negative is False + + assert (-2*k + 123*n + 17).is_negative is False + + assert (k + u).is_negative is None + assert (k + v).is_negative is True + assert (n + u).is_negative is False + assert (n + v).is_negative is None + + assert (u - v).is_negative is False + assert (u + v).is_negative is None + assert (-u - v).is_negative is None + assert (-u + v).is_negative is None + + assert (u - v + n + 2).is_negative is False + assert (u + v + n + 2).is_negative is None + assert (-u - v + n + 2).is_negative is None + assert (-u + v + n + 2).is_negative is None + + assert (k + x).is_negative is None + assert (k + x - n).is_negative is None + + assert (k - 2).is_positive is False + assert (k + 17).is_positive is None + assert (-k - 5).is_positive is None + assert (-k + 123).is_positive is True + + assert (k - n).is_positive is False + assert (k + n).is_positive is None + assert (-k - n).is_positive is None + assert (-k + n).is_positive is True + + assert (k - n - 2).is_positive is False + assert (k + n + 17).is_positive is None + assert (-k - n - 5).is_positive is None + assert (-k + n + 123).is_positive is True + + assert (-2*k + 123*n + 17).is_positive is True + + assert (k + u).is_positive is None + assert (k + v).is_positive is False + assert (n + u).is_positive is True + assert (n + v).is_positive is None + + assert (u - v).is_positive is None + assert (u + v).is_positive is None + assert (-u - v).is_positive is None + assert (-u + v).is_positive is False + + assert (u - v - n - 2).is_positive is None + assert (u + v - n - 2).is_positive is None + assert (-u - v - n - 2).is_positive is None + assert (-u + v - n - 2).is_positive is False + + assert (n + x).is_positive is None + assert (n + x - k).is_positive is None + + z = (-3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2) + assert z.is_zero + z = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3)) + assert z.is_zero + + +def test_Add_is_nonpositive_nonnegative(): + x = Symbol('x', real=True) + + k = Symbol('k', negative=True) + n = Symbol('n', positive=True) + u = Symbol('u', nonnegative=True) + v = Symbol('v', nonpositive=True) + + assert (u - 2).is_nonpositive is None + assert (u + 17).is_nonpositive is False + assert (-u - 5).is_nonpositive is True + assert (-u + 123).is_nonpositive is None + + assert (u - v).is_nonpositive is None + assert (u + v).is_nonpositive is None + assert (-u - v).is_nonpositive is None + assert (-u + v).is_nonpositive is True + + assert (u - v - 2).is_nonpositive is None + assert (u + v + 17).is_nonpositive is None + assert (-u - v - 5).is_nonpositive is None + assert (-u + v - 123).is_nonpositive is True + + assert (-2*u + 123*v - 17).is_nonpositive is True + + assert (k + u).is_nonpositive is None + assert (k + v).is_nonpositive is True + assert (n + u).is_nonpositive is False + assert (n + v).is_nonpositive is None + + assert (k - n).is_nonpositive is True + assert (k + n).is_nonpositive is None + assert (-k - n).is_nonpositive is None + assert (-k + n).is_nonpositive is False + + assert (k - n + u + 2).is_nonpositive is None + assert (k + n + u + 2).is_nonpositive is None + assert (-k - n + u + 2).is_nonpositive is None + assert (-k + n + u + 2).is_nonpositive is False + + assert (u + x).is_nonpositive is None + assert (v - x - n).is_nonpositive is None + + assert (u - 2).is_nonnegative is None + assert (u + 17).is_nonnegative is True + assert (-u - 5).is_nonnegative is False + assert (-u + 123).is_nonnegative is None + + assert (u - v).is_nonnegative is True + assert (u + v).is_nonnegative is None + assert (-u - v).is_nonnegative is None + assert (-u + v).is_nonnegative is None + + assert (u - v + 2).is_nonnegative is True + assert (u + v + 17).is_nonnegative is None + assert (-u - v - 5).is_nonnegative is None + assert (-u + v - 123).is_nonnegative is False + + assert (2*u - 123*v + 17).is_nonnegative is True + + assert (k + u).is_nonnegative is None + assert (k + v).is_nonnegative is False + assert (n + u).is_nonnegative is True + assert (n + v).is_nonnegative is None + + assert (k - n).is_nonnegative is False + assert (k + n).is_nonnegative is None + assert (-k - n).is_nonnegative is None + assert (-k + n).is_nonnegative is True + + assert (k - n - u - 2).is_nonnegative is False + assert (k + n - u - 2).is_nonnegative is None + assert (-k - n - u - 2).is_nonnegative is None + assert (-k + n - u - 2).is_nonnegative is None + + assert (u - x).is_nonnegative is None + assert (v + x + n).is_nonnegative is None + + +def test_Pow_is_integer(): + x = Symbol('x') + + k = Symbol('k', integer=True) + n = Symbol('n', integer=True, nonnegative=True) + m = Symbol('m', integer=True, positive=True) + + assert (k**2).is_integer is True + assert (k**(-2)).is_integer is None + assert ((m + 1)**(-2)).is_integer is False + assert (m**(-1)).is_integer is None # issue 8580 + + assert (2**k).is_integer is None + assert (2**(-k)).is_integer is None + + assert (2**n).is_integer is True + assert (2**(-n)).is_integer is None + + assert (2**m).is_integer is True + assert (2**(-m)).is_integer is False + + assert (x**2).is_integer is None + assert (2**x).is_integer is None + + assert (k**n).is_integer is True + assert (k**(-n)).is_integer is None + + assert (k**x).is_integer is None + assert (x**k).is_integer is None + + assert (k**(n*m)).is_integer is True + assert (k**(-n*m)).is_integer is None + + assert sqrt(3).is_integer is False + assert sqrt(.3).is_integer is False + assert Pow(3, 2, evaluate=False).is_integer is True + assert Pow(3, 0, evaluate=False).is_integer is True + assert Pow(3, -2, evaluate=False).is_integer is False + assert Pow(S.Half, 3, evaluate=False).is_integer is False + # decided by re-evaluating + assert Pow(3, S.Half, evaluate=False).is_integer is False + assert Pow(3, S.Half, evaluate=False).is_integer is False + assert Pow(4, S.Half, evaluate=False).is_integer is True + assert Pow(S.Half, -2, evaluate=False).is_integer is True + + assert ((-1)**k).is_integer + + # issue 8641 + x = Symbol('x', real=True, integer=False) + assert (x**2).is_integer is None + + # issue 10458 + x = Symbol('x', positive=True) + assert (1/(x + 1)).is_integer is False + assert (1/(-x - 1)).is_integer is False + assert (-1/(x + 1)).is_integer is False + # issue 23287 + assert (x**2/2).is_integer is None + + # issue 8648-like + k = Symbol('k', even=True) + assert (k**3/2).is_integer + assert (k**3/8).is_integer + assert (k**3/16).is_integer is None + assert (2/k).is_integer is None + assert (2/k**2).is_integer is False + o = Symbol('o', odd=True) + assert (k/o).is_integer is None + o = Symbol('o', odd=True, prime=True) + assert (k/o).is_integer is False + + +def test_Pow_is_real(): + x = Symbol('x', real=True) + y = Symbol('y', positive=True) + + assert (x**2).is_real is True + assert (x**3).is_real is True + assert (x**x).is_real is None + assert (y**x).is_real is True + + assert (x**Rational(1, 3)).is_real is None + assert (y**Rational(1, 3)).is_real is True + + assert sqrt(-1 - sqrt(2)).is_real is False + + i = Symbol('i', imaginary=True) + assert (i**i).is_real is None + assert (I**i).is_extended_real is True + assert ((-I)**i).is_extended_real is True + assert (2**i).is_real is None # (2**(pi/log(2) * I)) is real, 2**I is not + assert (2**I).is_real is False + assert (2**-I).is_real is False + assert (i**2).is_extended_real is True + assert (i**3).is_extended_real is False + assert (i**x).is_real is None # could be (-I)**(2/3) + e = Symbol('e', even=True) + o = Symbol('o', odd=True) + k = Symbol('k', integer=True) + assert (i**e).is_extended_real is True + assert (i**o).is_extended_real is False + assert (i**k).is_real is None + assert (i**(4*k)).is_extended_real is True + + x = Symbol("x", nonnegative=True) + y = Symbol("y", nonnegative=True) + assert im(x**y).expand(complex=True) is S.Zero + assert (x**y).is_real is True + i = Symbol('i', imaginary=True) + assert (exp(i)**I).is_extended_real is True + assert log(exp(i)).is_imaginary is None # i could be 2*pi*I + c = Symbol('c', complex=True) + assert log(c).is_real is None # c could be 0 or 2, too + assert log(exp(c)).is_real is None # log(0), log(E), ... + n = Symbol('n', negative=False) + assert log(n).is_real is None + n = Symbol('n', nonnegative=True) + assert log(n).is_real is None + + assert sqrt(-I).is_real is False # issue 7843 + + i = Symbol('i', integer=True) + assert (1/(i-1)).is_real is None + assert (1/(i-1)).is_extended_real is None + + # test issue 20715 + from sympy.core.parameters import evaluate + x = S(-1) + with evaluate(False): + assert x.is_negative is True + + f = Pow(x, -1) + with evaluate(False): + assert f.is_imaginary is False + + +def test_real_Pow(): + k = Symbol('k', integer=True, nonzero=True) + assert (k**(I*pi/log(k))).is_real + + +def test_Pow_is_finite(): + xe = Symbol('xe', extended_real=True) + xr = Symbol('xr', real=True) + p = Symbol('p', positive=True) + n = Symbol('n', negative=True) + i = Symbol('i', integer=True) + + assert (xe**2).is_finite is None # xe could be oo + assert (xr**2).is_finite is True + + assert (xe**xe).is_finite is None + assert (xr**xe).is_finite is None + assert (xe**xr).is_finite is None + # FIXME: The line below should be True rather than None + # assert (xr**xr).is_finite is True + assert (xr**xr).is_finite is None + + assert (p**xe).is_finite is None + assert (p**xr).is_finite is True + + assert (n**xe).is_finite is None + assert (n**xr).is_finite is True + + assert (sin(xe)**2).is_finite is True + assert (sin(xr)**2).is_finite is True + + assert (sin(xe)**xe).is_finite is None # xe, xr could be -pi + assert (sin(xr)**xr).is_finite is None + + # FIXME: Should the line below be True rather than None? + assert (sin(xe)**exp(xe)).is_finite is None + assert (sin(xr)**exp(xr)).is_finite is True + + assert (1/sin(xe)).is_finite is None # if zero, no, otherwise yes + assert (1/sin(xr)).is_finite is None + + assert (1/exp(xe)).is_finite is None # xe could be -oo + assert (1/exp(xr)).is_finite is True + + assert (1/S.Pi).is_finite is True + + assert (1/(i-1)).is_finite is None + + +def test_Pow_is_even_odd(): + x = Symbol('x') + + k = Symbol('k', even=True) + n = Symbol('n', odd=True) + m = Symbol('m', integer=True, nonnegative=True) + p = Symbol('p', integer=True, positive=True) + + assert ((-1)**n).is_odd + assert ((-1)**k).is_odd + assert ((-1)**(m - p)).is_odd + + assert (k**2).is_even is True + assert (n**2).is_even is False + assert (2**k).is_even is None + assert (x**2).is_even is None + + assert (k**m).is_even is None + assert (n**m).is_even is False + + assert (k**p).is_even is True + assert (n**p).is_even is False + + assert (m**k).is_even is None + assert (p**k).is_even is None + + assert (m**n).is_even is None + assert (p**n).is_even is None + + assert (k**x).is_even is None + assert (n**x).is_even is None + + assert (k**2).is_odd is False + assert (n**2).is_odd is True + assert (3**k).is_odd is None + + assert (k**m).is_odd is None + assert (n**m).is_odd is True + + assert (k**p).is_odd is False + assert (n**p).is_odd is True + + assert (m**k).is_odd is None + assert (p**k).is_odd is None + + assert (m**n).is_odd is None + assert (p**n).is_odd is None + + assert (k**x).is_odd is None + assert (n**x).is_odd is None + + +def test_Pow_is_negative_positive(): + r = Symbol('r', real=True) + + k = Symbol('k', integer=True, positive=True) + n = Symbol('n', even=True) + m = Symbol('m', odd=True) + + x = Symbol('x') + + assert (2**r).is_positive is True + assert ((-2)**r).is_positive is None + assert ((-2)**n).is_positive is True + assert ((-2)**m).is_positive is False + + assert (k**2).is_positive is True + assert (k**(-2)).is_positive is True + + assert (k**r).is_positive is True + assert ((-k)**r).is_positive is None + assert ((-k)**n).is_positive is True + assert ((-k)**m).is_positive is False + + assert (2**r).is_negative is False + assert ((-2)**r).is_negative is None + assert ((-2)**n).is_negative is False + assert ((-2)**m).is_negative is True + + assert (k**2).is_negative is False + assert (k**(-2)).is_negative is False + + assert (k**r).is_negative is False + assert ((-k)**r).is_negative is None + assert ((-k)**n).is_negative is False + assert ((-k)**m).is_negative is True + + assert (2**x).is_positive is None + assert (2**x).is_negative is None + + +def test_Pow_is_zero(): + z = Symbol('z', zero=True) + e = z**2 + assert e.is_zero + assert e.is_positive is False + assert e.is_negative is False + + assert Pow(0, 0, evaluate=False).is_zero is False + assert Pow(0, 3, evaluate=False).is_zero + assert Pow(0, oo, evaluate=False).is_zero + assert Pow(0, -3, evaluate=False).is_zero is False + assert Pow(0, -oo, evaluate=False).is_zero is False + assert Pow(2, 2, evaluate=False).is_zero is False + + a = Symbol('a', zero=False) + assert Pow(a, 3).is_zero is False # issue 7965 + + assert Pow(2, oo, evaluate=False).is_zero is False + assert Pow(2, -oo, evaluate=False).is_zero + assert Pow(S.Half, oo, evaluate=False).is_zero + assert Pow(S.Half, -oo, evaluate=False).is_zero is False + + # All combinations of real/complex base/exponent + h = S.Half + T = True + F = False + N = None + + pow_iszero = [ + ['**', 0, h, 1, 2, -h, -1,-2,-2*I,-I/2,I/2,1+I,oo,-oo,zoo], + [ 0, F, T, T, T, F, F, F, F, F, F, N, T, F, N], + [ h, F, F, F, F, F, F, F, F, F, F, F, T, F, N], + [ 1, F, F, F, F, F, F, F, F, F, F, F, F, F, N], + [ 2, F, F, F, F, F, F, F, F, F, F, F, F, T, N], + [ -h, F, F, F, F, F, F, F, F, F, F, F, T, F, N], + [ -1, F, F, F, F, F, F, F, F, F, F, F, F, F, N], + [ -2, F, F, F, F, F, F, F, F, F, F, F, F, T, N], + [-2*I, F, F, F, F, F, F, F, F, F, F, F, F, T, N], + [-I/2, F, F, F, F, F, F, F, F, F, F, F, T, F, N], + [ I/2, F, F, F, F, F, F, F, F, F, F, F, T, F, N], + [ 1+I, F, F, F, F, F, F, F, F, F, F, F, F, T, N], + [ oo, F, F, F, F, T, T, T, F, F, F, F, F, T, N], + [ -oo, F, F, F, F, T, T, T, F, F, F, F, F, T, N], + [ zoo, F, F, F, F, T, T, T, N, N, N, N, F, T, N] + ] + + def test_table(table): + n = len(table[0]) + for row in range(1, n): + base = table[row][0] + for col in range(1, n): + exp = table[0][col] + is_zero = table[row][col] + # The actual test here: + assert Pow(base, exp, evaluate=False).is_zero is is_zero + + test_table(pow_iszero) + + # A zero symbol... + zo, zo2 = symbols('zo, zo2', zero=True) + + # All combinations of finite symbols + zf, zf2 = symbols('zf, zf2', finite=True) + wf, wf2 = symbols('wf, wf2', nonzero=True) + xf, xf2 = symbols('xf, xf2', real=True) + yf, yf2 = symbols('yf, yf2', nonzero=True) + af, af2 = symbols('af, af2', positive=True) + bf, bf2 = symbols('bf, bf2', nonnegative=True) + cf, cf2 = symbols('cf, cf2', negative=True) + df, df2 = symbols('df, df2', nonpositive=True) + + # Without finiteness: + zi, zi2 = symbols('zi, zi2') + wi, wi2 = symbols('wi, wi2', zero=False) + xi, xi2 = symbols('xi, xi2', extended_real=True) + yi, yi2 = symbols('yi, yi2', zero=False, extended_real=True) + ai, ai2 = symbols('ai, ai2', extended_positive=True) + bi, bi2 = symbols('bi, bi2', extended_nonnegative=True) + ci, ci2 = symbols('ci, ci2', extended_negative=True) + di, di2 = symbols('di, di2', extended_nonpositive=True) + + pow_iszero_sym = [ + ['**',zo,wf,yf,af,cf,zf,xf,bf,df,zi,wi,xi,yi,ai,bi,ci,di], + [ zo2, F, N, N, T, F, N, N, N, F, N, N, N, N, T, N, F, F], + [ wf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N], + [ yf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N], + [ af2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N], + [ cf2, F, F, F, F, F, F, F, F, F, N, N, N, N, N, N, N, N], + [ zf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N], + [ xf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N], + [ bf2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N], + [ df2, N, N, N, N, F, N, N, N, N, N, N, N, N, N, N, N, N], + [ zi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N], + [ wi2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N], + [ xi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N], + [ yi2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N], + [ ai2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N], + [ bi2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N], + [ ci2, F, N, N, F, N, N, N, F, N, N, N, N, N, N, N, N, N], + [ di2, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N, N] + ] + + test_table(pow_iszero_sym) + + # In some cases (x**x).is_zero is different from (x**y).is_zero even if y + # has the same assumptions as x. + assert (zo ** zo).is_zero is False + assert (wf ** wf).is_zero is False + assert (yf ** yf).is_zero is False + assert (af ** af).is_zero is False + assert (cf ** cf).is_zero is False + assert (zf ** zf).is_zero is None + assert (xf ** xf).is_zero is None + assert (bf ** bf).is_zero is False # None in table + assert (df ** df).is_zero is None + assert (zi ** zi).is_zero is None + assert (wi ** wi).is_zero is None + assert (xi ** xi).is_zero is None + assert (yi ** yi).is_zero is None + assert (ai ** ai).is_zero is False # None in table + assert (bi ** bi).is_zero is False # None in table + assert (ci ** ci).is_zero is None + assert (di ** di).is_zero is None + + +def test_Pow_is_nonpositive_nonnegative(): + x = Symbol('x', real=True) + + k = Symbol('k', integer=True, nonnegative=True) + l = Symbol('l', integer=True, positive=True) + n = Symbol('n', even=True) + m = Symbol('m', odd=True) + + assert (x**(4*k)).is_nonnegative is True + assert (2**x).is_nonnegative is True + assert ((-2)**x).is_nonnegative is None + assert ((-2)**n).is_nonnegative is True + assert ((-2)**m).is_nonnegative is False + + assert (k**2).is_nonnegative is True + assert (k**(-2)).is_nonnegative is None + assert (k**k).is_nonnegative is True + + assert (k**x).is_nonnegative is None # NOTE (0**x).is_real = U + assert (l**x).is_nonnegative is True + assert (l**x).is_positive is True + assert ((-k)**x).is_nonnegative is None + + assert ((-k)**m).is_nonnegative is None + + assert (2**x).is_nonpositive is False + assert ((-2)**x).is_nonpositive is None + assert ((-2)**n).is_nonpositive is False + assert ((-2)**m).is_nonpositive is True + + assert (k**2).is_nonpositive is None + assert (k**(-2)).is_nonpositive is None + + assert (k**x).is_nonpositive is None + assert ((-k)**x).is_nonpositive is None + assert ((-k)**n).is_nonpositive is None + + + assert (x**2).is_nonnegative is True + i = symbols('i', imaginary=True) + assert (i**2).is_nonpositive is True + assert (i**4).is_nonpositive is False + assert (i**3).is_nonpositive is False + assert (I**i).is_nonnegative is True + assert (exp(I)**i).is_nonnegative is True + + assert ((-l)**n).is_nonnegative is True + assert ((-l)**m).is_nonpositive is True + assert ((-k)**n).is_nonnegative is None + assert ((-k)**m).is_nonpositive is None + + +def test_Mul_is_imaginary_real(): + r = Symbol('r', real=True) + p = Symbol('p', positive=True) + i1 = Symbol('i1', imaginary=True) + i2 = Symbol('i2', imaginary=True) + x = Symbol('x') + + assert I.is_imaginary is True + assert I.is_real is False + assert (-I).is_imaginary is True + assert (-I).is_real is False + assert (3*I).is_imaginary is True + assert (3*I).is_real is False + assert (I*I).is_imaginary is False + assert (I*I).is_real is True + + e = (p + p*I) + j = Symbol('j', integer=True, zero=False) + assert (e**j).is_real is None + assert (e**(2*j)).is_real is None + assert (e**j).is_imaginary is None + assert (e**(2*j)).is_imaginary is None + + assert (e**-1).is_imaginary is False + assert (e**2).is_imaginary + assert (e**3).is_imaginary is False + assert (e**4).is_imaginary is False + assert (e**5).is_imaginary is False + assert (e**-1).is_real is False + assert (e**2).is_real is False + assert (e**3).is_real is False + assert (e**4).is_real is True + assert (e**5).is_real is False + assert (e**3).is_complex + + assert (r*i1).is_imaginary is None + assert (r*i1).is_real is None + + assert (x*i1).is_imaginary is None + assert (x*i1).is_real is None + + assert (i1*i2).is_imaginary is False + assert (i1*i2).is_real is True + + assert (r*i1*i2).is_imaginary is False + assert (r*i1*i2).is_real is True + + # Github's issue 5874: + nr = Symbol('nr', real=False, complex=True) # e.g. I or 1 + I + a = Symbol('a', real=True, nonzero=True) + b = Symbol('b', real=True) + assert (i1*nr).is_real is None + assert (a*nr).is_real is False + assert (b*nr).is_real is None + + ni = Symbol('ni', imaginary=False, complex=True) # e.g. 2 or 1 + I + a = Symbol('a', real=True, nonzero=True) + b = Symbol('b', real=True) + assert (i1*ni).is_real is False + assert (a*ni).is_real is None + assert (b*ni).is_real is None + + +def test_Mul_hermitian_antihermitian(): + xz, yz = symbols('xz, yz', zero=True, antihermitian=True) + xf, yf = symbols('xf, yf', hermitian=False, antihermitian=False, finite=True) + xh, yh = symbols('xh, yh', hermitian=True, antihermitian=False, nonzero=True) + xa, ya = symbols('xa, ya', hermitian=False, antihermitian=True, zero=False, finite=True) + assert (xz*xh).is_hermitian is True + assert (xz*xh).is_antihermitian is True + assert (xz*xa).is_hermitian is True + assert (xz*xa).is_antihermitian is True + assert (xf*yf).is_hermitian is None + assert (xf*yf).is_antihermitian is None + assert (xh*yh).is_hermitian is True + assert (xh*yh).is_antihermitian is False + assert (xh*ya).is_hermitian is False + assert (xh*ya).is_antihermitian is True + assert (xa*ya).is_hermitian is True + assert (xa*ya).is_antihermitian is False + + a = Symbol('a', hermitian=True, zero=False) + b = Symbol('b', hermitian=True) + c = Symbol('c', hermitian=False) + d = Symbol('d', antihermitian=True) + e1 = Mul(a, b, c, evaluate=False) + e2 = Mul(b, a, c, evaluate=False) + e3 = Mul(a, b, c, d, evaluate=False) + e4 = Mul(b, a, c, d, evaluate=False) + e5 = Mul(a, c, evaluate=False) + e6 = Mul(a, c, d, evaluate=False) + assert e1.is_hermitian is None + assert e2.is_hermitian is None + assert e1.is_antihermitian is None + assert e2.is_antihermitian is None + assert e3.is_antihermitian is None + assert e4.is_antihermitian is None + assert e5.is_antihermitian is None + assert e6.is_antihermitian is None + + +def test_Add_is_comparable(): + assert (x + y).is_comparable is False + assert (x + 1).is_comparable is False + assert (Rational(1, 3) - sqrt(8)).is_comparable is True + + +def test_Mul_is_comparable(): + assert (x*y).is_comparable is False + assert (x*2).is_comparable is False + assert (sqrt(2)*Rational(1, 3)).is_comparable is True + + +def test_Pow_is_comparable(): + assert (x**y).is_comparable is False + assert (x**2).is_comparable is False + assert (sqrt(Rational(1, 3))).is_comparable is True + + +def test_Add_is_positive_2(): + e = Rational(1, 3) - sqrt(8) + assert e.is_positive is False + assert e.is_negative is True + + e = pi - 1 + assert e.is_positive is True + assert e.is_negative is False + + +def test_Add_is_irrational(): + i = Symbol('i', irrational=True) + + assert i.is_irrational is True + assert i.is_rational is False + + assert (i + 1).is_irrational is True + assert (i + 1).is_rational is False + + +def test_Mul_is_irrational(): + expr = Mul(1, 2, 3, evaluate=False) + assert expr.is_irrational is False + expr = Mul(1, I, I, evaluate=False) + assert expr.is_rational is None # I * I = -1 but *no evaluation allowed* + # sqrt(2) * I * I = -sqrt(2) is irrational but + # this can't be determined without evaluating the + # expression and the eval_is routines shouldn't do that + expr = Mul(sqrt(2), I, I, evaluate=False) + assert expr.is_irrational is None + + +def test_issue_3531(): + # https://github.com/sympy/sympy/issues/3531 + # https://github.com/sympy/sympy/pull/18116 + class MightyNumeric(tuple): + def __rtruediv__(self, other): + return "something" + + assert sympify(1)/MightyNumeric((1, 2)) == "something" + + +def test_issue_3531b(): + class Foo: + def __init__(self): + self.field = 1.0 + + def __mul__(self, other): + self.field = self.field * other + + def __rmul__(self, other): + self.field = other * self.field + f = Foo() + x = Symbol("x") + assert f*x == x*f + + +def test_bug3(): + a = Symbol("a") + b = Symbol("b", positive=True) + e = 2*a + b + f = b + 2*a + assert e == f + + +def test_suppressed_evaluation(): + a = Add(0, 3, 2, evaluate=False) + b = Mul(1, 3, 2, evaluate=False) + c = Pow(3, 2, evaluate=False) + assert a != 6 + assert a.func is Add + assert a.args == (0, 3, 2) + assert b != 6 + assert b.func is Mul + assert b.args == (1, 3, 2) + assert c != 9 + assert c.func is Pow + assert c.args == (3, 2) + + +def test_AssocOp_doit(): + a = Add(x,x, evaluate=False) + b = Mul(y,y, evaluate=False) + c = Add(b,b, evaluate=False) + d = Mul(a,a, evaluate=False) + assert c.doit(deep=False).func == Mul + assert c.doit(deep=False).args == (2,y,y) + assert c.doit().func == Mul + assert c.doit().args == (2, Pow(y,2)) + assert d.doit(deep=False).func == Pow + assert d.doit(deep=False).args == (a, 2*S.One) + assert d.doit().func == Mul + assert d.doit().args == (4*S.One, Pow(x,2)) + + +def test_Add_Mul_Expr_args(): + nonexpr = [Basic(), Poly(x, x), FiniteSet(x)] + for typ in [Add, Mul]: + for obj in nonexpr: + # The cache can mess with the stacklevel check + with warns(SymPyDeprecationWarning, test_stacklevel=False): + typ(obj, 1) + + +def test_Add_as_coeff_mul(): + # issue 5524. These should all be (1, self) + assert (x + 1).as_coeff_mul() == (1, (x + 1,)) + assert (x + 2).as_coeff_mul() == (1, (x + 2,)) + assert (x + 3).as_coeff_mul() == (1, (x + 3,)) + + assert (x - 1).as_coeff_mul() == (1, (x - 1,)) + assert (x - 2).as_coeff_mul() == (1, (x - 2,)) + assert (x - 3).as_coeff_mul() == (1, (x - 3,)) + + n = Symbol('n', integer=True) + assert (n + 1).as_coeff_mul() == (1, (n + 1,)) + assert (n + 2).as_coeff_mul() == (1, (n + 2,)) + assert (n + 3).as_coeff_mul() == (1, (n + 3,)) + + assert (n - 1).as_coeff_mul() == (1, (n - 1,)) + assert (n - 2).as_coeff_mul() == (1, (n - 2,)) + assert (n - 3).as_coeff_mul() == (1, (n - 3,)) + + +def test_Pow_as_coeff_mul_doesnt_expand(): + assert exp(x + y).as_coeff_mul() == (1, (exp(x + y),)) + assert exp(x + exp(x + y)) != exp(x + exp(x)*exp(y)) + +def test_issue_24751(): + expr = Add(-2, -3, evaluate=False) + expr1 = Add(-1, expr, evaluate=False) + assert int(expr1) == int((-3 - 2) - 1) + + +def test_issue_3514_18626(): + assert sqrt(S.Half) * sqrt(6) == 2 * sqrt(3)/2 + assert S.Half*sqrt(6)*sqrt(2) == sqrt(3) + assert sqrt(6)/2*sqrt(2) == sqrt(3) + assert sqrt(6)*sqrt(2)/2 == sqrt(3) + assert sqrt(8)**Rational(2, 3) == 2 + + +def test_make_args(): + assert Add.make_args(x) == (x,) + assert Mul.make_args(x) == (x,) + + assert Add.make_args(x*y*z) == (x*y*z,) + assert Mul.make_args(x*y*z) == (x*y*z).args + + assert Add.make_args(x + y + z) == (x + y + z).args + assert Mul.make_args(x + y + z) == (x + y + z,) + + assert Add.make_args((x + y)**z) == ((x + y)**z,) + assert Mul.make_args((x + y)**z) == ((x + y)**z,) + + +def test_issue_5126(): + assert (-2)**x*(-3)**x != 6**x + i = Symbol('i', integer=1) + assert (-2)**i*(-3)**i == 6**i + + +def test_Rational_as_content_primitive(): + c, p = S.One, S.Zero + assert (c*p).as_content_primitive() == (c, p) + c, p = S.Half, S.One + assert (c*p).as_content_primitive() == (c, p) + + +def test_Add_as_content_primitive(): + assert (x + 2).as_content_primitive() == (1, x + 2) + + assert (3*x + 2).as_content_primitive() == (1, 3*x + 2) + assert (3*x + 3).as_content_primitive() == (3, x + 1) + assert (3*x + 6).as_content_primitive() == (3, x + 2) + + assert (3*x + 2*y).as_content_primitive() == (1, 3*x + 2*y) + assert (3*x + 3*y).as_content_primitive() == (3, x + y) + assert (3*x + 6*y).as_content_primitive() == (3, x + 2*y) + + assert (3/x + 2*x*y*z**2).as_content_primitive() == (1, 3/x + 2*x*y*z**2) + assert (3/x + 3*x*y*z**2).as_content_primitive() == (3, 1/x + x*y*z**2) + assert (3/x + 6*x*y*z**2).as_content_primitive() == (3, 1/x + 2*x*y*z**2) + + assert (2*x/3 + 4*y/9).as_content_primitive() == \ + (Rational(2, 9), 3*x + 2*y) + assert (2*x/3 + 2.5*y).as_content_primitive() == \ + (Rational(1, 3), 2*x + 7.5*y) + + # the coefficient may sort to a position other than 0 + p = 3 + x + y + assert (2*p).expand().as_content_primitive() == (2, p) + assert (2.0*p).expand().as_content_primitive() == (1, 2.*p) + p *= -1 + assert (2*p).expand().as_content_primitive() == (2, p) + + +def test_Mul_as_content_primitive(): + assert (2*x).as_content_primitive() == (2, x) + assert (x*(2 + 2*x)).as_content_primitive() == (2, x*(1 + x)) + assert (x*(2 + 2*y)*(3*x + 3)**2).as_content_primitive() == \ + (18, x*(1 + y)*(x + 1)**2) + assert ((2 + 2*x)**2*(3 + 6*x) + S.Half).as_content_primitive() == \ + (S.Half, 24*(x + 1)**2*(2*x + 1) + 1) + + +def test_Pow_as_content_primitive(): + assert (x**y).as_content_primitive() == (1, x**y) + assert ((2*x + 2)**y).as_content_primitive() == \ + (1, (Mul(2, (x + 1), evaluate=False))**y) + assert ((2*x + 2)**3).as_content_primitive() == (8, (x + 1)**3) + + +def test_issue_5460(): + u = Mul(2, (1 + x), evaluate=False) + assert (2 + u).args == (2, u) + + +def test_product_irrational(): + assert (I*pi).is_irrational is False + # The following used to be deduced from the above bug: + assert (I*pi).is_positive is False + + +def test_issue_5919(): + assert (x/(y*(1 + y))).expand() == x/(y**2 + y) + + +def test_Mod(): + assert Mod(x, 1).func is Mod + assert pi % pi is S.Zero + assert Mod(5, 3) == 2 + assert Mod(-5, 3) == 1 + assert Mod(5, -3) == -1 + assert Mod(-5, -3) == -2 + assert type(Mod(3.2, 2, evaluate=False)) == Mod + assert 5 % x == Mod(5, x) + assert x % 5 == Mod(x, 5) + assert x % y == Mod(x, y) + assert (x % y).subs({x: 5, y: 3}) == 2 + assert Mod(nan, 1) is nan + assert Mod(1, nan) is nan + assert Mod(nan, nan) is nan + + assert Mod(0, x) == 0 + with raises(ZeroDivisionError): + Mod(x, 0) + + k = Symbol('k', integer=True) + m = Symbol('m', integer=True, positive=True) + assert (x**m % x).func is Mod + assert (k**(-m) % k).func is Mod + assert k**m % k == 0 + assert (-2*k)**m % k == 0 + + # Float handling + point3 = Float(3.3) % 1 + assert (x - 3.3) % 1 == Mod(1.*x + 1 - point3, 1) + assert Mod(-3.3, 1) == 1 - point3 + assert Mod(0.7, 1) == Float(0.7) + e = Mod(1.3, 1) + assert comp(e, .3) and e.is_Float + e = Mod(1.3, .7) + assert comp(e, .6) and e.is_Float + e = Mod(1.3, Rational(7, 10)) + assert comp(e, .6) and e.is_Float + e = Mod(Rational(13, 10), 0.7) + assert comp(e, .6) and e.is_Float + e = Mod(Rational(13, 10), Rational(7, 10)) + assert comp(e, .6) and e.is_Rational + + # check that sign is right + r2 = sqrt(2) + r3 = sqrt(3) + for i in [-r3, -r2, r2, r3]: + for j in [-r3, -r2, r2, r3]: + assert verify_numerically(i % j, i.n() % j.n()) + for _x in range(4): + for _y in range(9): + reps = [(x, _x), (y, _y)] + assert Mod(3*x + y, 9).subs(reps) == (3*_x + _y) % 9 + + # denesting + t = Symbol('t', real=True) + assert Mod(Mod(x, t), t) == Mod(x, t) + assert Mod(-Mod(x, t), t) == Mod(-x, t) + assert Mod(Mod(x, 2*t), t) == Mod(x, t) + assert Mod(-Mod(x, 2*t), t) == Mod(-x, t) + assert Mod(Mod(x, t), 2*t) == Mod(x, t) + assert Mod(-Mod(x, t), -2*t) == -Mod(x, t) + for i in [-4, -2, 2, 4]: + for j in [-4, -2, 2, 4]: + for k in range(4): + assert Mod(Mod(x, i), j).subs({x: k}) == (k % i) % j + assert Mod(-Mod(x, i), j).subs({x: k}) == -(k % i) % j + + # known difference + assert Mod(5*sqrt(2), sqrt(5)) == 5*sqrt(2) - 3*sqrt(5) + p = symbols('p', positive=True) + assert Mod(2, p + 3) == 2 + assert Mod(-2, p + 3) == p + 1 + assert Mod(2, -p - 3) == -p - 1 + assert Mod(-2, -p - 3) == -2 + assert Mod(p + 5, p + 3) == 2 + assert Mod(-p - 5, p + 3) == p + 1 + assert Mod(p + 5, -p - 3) == -p - 1 + assert Mod(-p - 5, -p - 3) == -2 + assert Mod(p + 1, p - 1).func is Mod + + # handling sums + assert (x + 3) % 1 == Mod(x, 1) + assert (x + 3.0) % 1 == Mod(1.*x, 1) + assert (x - S(33)/10) % 1 == Mod(x + S(7)/10, 1) + + a = Mod(.6*x + y, .3*y) + b = Mod(0.1*y + 0.6*x, 0.3*y) + # Test that a, b are equal, with 1e-14 accuracy in coefficients + eps = 1e-14 + assert abs((a.args[0] - b.args[0]).subs({x: 1, y: 1})) < eps + assert abs((a.args[1] - b.args[1]).subs({x: 1, y: 1})) < eps + + assert (x + 1) % x == 1 % x + assert (x + y) % x == y % x + assert (x + y + 2) % x == (y + 2) % x + assert (a + 3*x + 1) % (2*x) == Mod(a + x + 1, 2*x) + assert (12*x + 18*y) % (3*x) == 3*Mod(6*y, x) + + # gcd extraction + assert (-3*x) % (-2*y) == -Mod(3*x, 2*y) + assert (.6*pi) % (.3*x*pi) == 0.3*pi*Mod(2, x) + assert (.6*pi) % (.31*x*pi) == pi*Mod(0.6, 0.31*x) + assert (6*pi) % (.3*x*pi) == 0.3*pi*Mod(20, x) + assert (6*pi) % (.31*x*pi) == pi*Mod(6, 0.31*x) + assert (6*pi) % (.42*x*pi) == pi*Mod(6, 0.42*x) + assert (12*x) % (2*y) == 2*Mod(6*x, y) + assert (12*x) % (3*5*y) == 3*Mod(4*x, 5*y) + assert (12*x) % (15*x*y) == 3*x*Mod(4, 5*y) + assert (-2*pi) % (3*pi) == pi + assert (2*x + 2) % (x + 1) == 0 + assert (x*(x + 1)) % (x + 1) == (x + 1)*Mod(x, 1) + assert Mod(5.0*x, 0.1*y) == 0.1*Mod(50*x, y) + i = Symbol('i', integer=True) + assert (3*i*x) % (2*i*y) == i*Mod(3*x, 2*y) + assert Mod(4*i, 4) == 0 + + # issue 8677 + n = Symbol('n', integer=True, positive=True) + assert factorial(n) % n == 0 + assert factorial(n + 2) % n == 0 + assert (factorial(n + 4) % (n + 5)).func is Mod + + # Wilson's theorem + assert factorial(18042, evaluate=False) % 18043 == 18042 + p = Symbol('n', prime=True) + assert factorial(p - 1) % p == p - 1 + assert factorial(p - 1) % -p == -1 + assert (factorial(3, evaluate=False) % 4).doit() == 2 + n = Symbol('n', composite=True, odd=True) + assert factorial(n - 1) % n == 0 + + # symbolic with known parity + n = Symbol('n', even=True) + assert Mod(n, 2) == 0 + n = Symbol('n', odd=True) + assert Mod(n, 2) == 1 + + # issue 10963 + assert (x**6000%400).args[1] == 400 + + #issue 13543 + assert Mod(Mod(x + 1, 2) + 1, 2) == Mod(x, 2) + + x1 = Symbol('x1', integer=True) + assert Mod(Mod(x1 + 2, 4)*(x1 + 4), 4) == Mod(x1*(x1 + 2), 4) + assert Mod(Mod(x1 + 2, 4)*4, 4) == 0 + + # issue 15493 + i, j = symbols('i j', integer=True, positive=True) + assert Mod(3*i, 2) == Mod(i, 2) + assert Mod(8*i/j, 4) == 4*Mod(2*i/j, 1) + assert Mod(8*i, 4) == 0 + + # rewrite + assert Mod(x, y).rewrite(floor) == x - y*floor(x/y) + assert ((x - Mod(x, y))/y).rewrite(floor) == floor(x/y) + + # issue 21373 + from sympy.functions.elementary.hyperbolic import sinh + from sympy.functions.elementary.piecewise import Piecewise + + x_r, y_r = symbols('x_r y_r', real=True) + assert (Piecewise((x_r, y_r > x_r), (y_r, True)) / z) % 1 + expr = exp(sinh(Piecewise((x_r, y_r > x_r), (y_r, True)) / z)) + expr.subs({1: 1.0}) + sinh(Piecewise((x_r, y_r > x_r), (y_r, True)) * z ** -1.0).is_zero + + # issue 24215 + from sympy.abc import phi + assert Mod(4.0*Mod(phi, 1) , 2) == 2.0*(Mod(2*(Mod(phi, 1)), 1)) + + xi = symbols('x', integer=True) + assert unchanged(Mod, xi, 2) + assert Mod(3*xi, 2) == Mod(xi, 2) + assert unchanged(Mod, 3*x, 2) + + +def test_Mod_Pow(): + # modular exponentiation + assert isinstance(Mod(Pow(2, 2, evaluate=False), 3), Integer) + + assert Mod(Pow(4, 13, evaluate=False), 497) == Mod(Pow(4, 13), 497) + assert Mod(Pow(2, 10000000000, evaluate=False), 3) == 1 + assert Mod(Pow(32131231232, 9**10**6, evaluate=False),10**12) == \ + pow(32131231232,9**10**6,10**12) + assert Mod(Pow(33284959323, 123**999, evaluate=False),11**13) == \ + pow(33284959323,123**999,11**13) + assert Mod(Pow(78789849597, 333**555, evaluate=False),12**9) == \ + pow(78789849597,333**555,12**9) + + # modular nested exponentiation + expr = Pow(2, 2, evaluate=False) + expr = Pow(2, expr, evaluate=False) + assert Mod(expr, 3**10) == 16 + expr = Pow(2, expr, evaluate=False) + assert Mod(expr, 3**10) == 6487 + expr = Pow(2, expr, evaluate=False) + assert Mod(expr, 3**10) == 32191 + expr = Pow(2, expr, evaluate=False) + assert Mod(expr, 3**10) == 18016 + expr = Pow(2, expr, evaluate=False) + assert Mod(expr, 3**10) == 5137 + + expr = Pow(2, 2, evaluate=False) + expr = Pow(expr, 2, evaluate=False) + assert Mod(expr, 3**10) == 16 + expr = Pow(expr, 2, evaluate=False) + assert Mod(expr, 3**10) == 256 + expr = Pow(expr, 2, evaluate=False) + assert Mod(expr, 3**10) == 6487 + expr = Pow(expr, 2, evaluate=False) + assert Mod(expr, 3**10) == 38281 + expr = Pow(expr, 2, evaluate=False) + assert Mod(expr, 3**10) == 15928 + + expr = Pow(2, 2, evaluate=False) + expr = Pow(expr, expr, evaluate=False) + assert Mod(expr, 3**10) == 256 + expr = Pow(expr, expr, evaluate=False) + assert Mod(expr, 3**10) == 9229 + expr = Pow(expr, expr, evaluate=False) + assert Mod(expr, 3**10) == 25708 + expr = Pow(expr, expr, evaluate=False) + assert Mod(expr, 3**10) == 26608 + expr = Pow(expr, expr, evaluate=False) + # XXX This used to fail in a nondeterministic way because of overflow + # error. + assert Mod(expr, 3**10) == 1966 + + +def test_Mod_is_integer(): + p = Symbol('p', integer=True) + q1 = Symbol('q1', integer=True) + q2 = Symbol('q2', integer=True, nonzero=True) + assert Mod(x, y).is_integer is None + assert Mod(p, q1).is_integer is None + assert Mod(x, q2).is_integer is None + assert Mod(p, q2).is_integer + + +def test_Mod_is_nonposneg(): + n = Symbol('n', integer=True) + k = Symbol('k', integer=True, positive=True) + assert (n%3).is_nonnegative + assert Mod(n, -3).is_nonpositive + assert Mod(n, k).is_nonnegative + assert Mod(n, -k).is_nonpositive + assert Mod(k, n).is_nonnegative is None + + +def test_issue_6001(): + A = Symbol("A", commutative=False) + eq = A + A**2 + # it doesn't matter whether it's True or False; they should + # just all be the same + assert ( + eq.is_commutative == + (eq + 1).is_commutative == + (A + 1).is_commutative) + + B = Symbol("B", commutative=False) + # Although commutative terms could cancel we return True + # meaning "there are non-commutative symbols; aftersubstitution + # that definition can change, e.g. (A*B).subs(B,A**-1) -> 1 + assert (sqrt(2)*A).is_commutative is False + assert (sqrt(2)*A*B).is_commutative is False + + +def test_polar(): + from sympy.functions.elementary.complexes import polar_lift + p = Symbol('p', polar=True) + x = Symbol('x') + assert p.is_polar + assert x.is_polar is None + assert S.One.is_polar is None + assert (p**x).is_polar is True + assert (x**p).is_polar is None + assert ((2*p)**x).is_polar is True + assert (2*p).is_polar is True + assert (-2*p).is_polar is not True + assert (polar_lift(-2)*p).is_polar is True + + q = Symbol('q', polar=True) + assert (p*q)**2 == p**2 * q**2 + assert (2*q)**2 == 4 * q**2 + assert ((p*q)**x).expand() == p**x * q**x + + +def test_issue_6040(): + a, b = Pow(1, 2, evaluate=False), S.One + assert a != b + assert b != a + assert not (a == b) + assert not (b == a) + + +def test_issue_6082(): + # Comparison is symmetric + assert Basic.compare(Max(x, 1), Max(x, 2)) == \ + - Basic.compare(Max(x, 2), Max(x, 1)) + # Equal expressions compare equal + assert Basic.compare(Max(x, 1), Max(x, 1)) == 0 + # Basic subtypes (such as Max) compare different than standard types + assert Basic.compare(Max(1, x), frozenset((1, x))) != 0 + + +def test_issue_6077(): + assert x**2.0/x == x**1.0 + assert x/x**2.0 == x**-1.0 + assert x*x**2.0 == x**3.0 + assert x**1.5*x**2.5 == x**4.0 + + assert 2**(2.0*x)/2**x == 2**(1.0*x) + assert 2**x/2**(2.0*x) == 2**(-1.0*x) + assert 2**x*2**(2.0*x) == 2**(3.0*x) + assert 2**(1.5*x)*2**(2.5*x) == 2**(4.0*x) + + +def test_mul_flatten_oo(): + p = symbols('p', positive=True) + n, m = symbols('n,m', negative=True) + x_im = symbols('x_im', imaginary=True) + assert n*oo is -oo + assert n*m*oo is oo + assert p*oo is oo + assert x_im*oo != I*oo # i could be +/- 3*I -> +/-oo + + +def test_add_flatten(): + # see https://github.com/sympy/sympy/issues/2633#issuecomment-29545524 + a = oo + I*oo + b = oo - I*oo + assert a + b is nan + assert a - b is nan + # FIXME: This evaluates as: + # >>> 1/a + # 0*(oo + oo*I) + # which should not simplify to 0. Should be fixed in Pow.eval + #assert (1/a).simplify() == (1/b).simplify() == 0 + + a = Pow(2, 3, evaluate=False) + assert a + a == 16 + + +def test_issue_5160_6087_6089_6090(): + # issue 6087 + assert ((-2*x*y**y)**3.2).n(2) == (2**3.2*(-x*y**y)**3.2).n(2) + # issue 6089 + A, B, C = symbols('A,B,C', commutative=False) + assert (2.*B*C)**3 == 8.0*(B*C)**3 + assert (-2.*B*C)**3 == -8.0*(B*C)**3 + assert (-2*B*C)**2 == 4*(B*C)**2 + # issue 5160 + assert sqrt(-1.0*x) == 1.0*sqrt(-x) + assert sqrt(1.0*x) == 1.0*sqrt(x) + # issue 6090 + assert (-2*x*y*A*B)**2 == 4*x**2*y**2*(A*B)**2 + + +def test_float_int_round(): + assert int(float(sqrt(10))) == int(sqrt(10)) + assert int(pi**1000) % 10 == 2 + assert int(Float('1.123456789012345678901234567890e20', '')) == \ + int(112345678901234567890) + assert int(Float('1.123456789012345678901234567890e25', '')) == \ + int(11234567890123456789012345) + # decimal forces float so it's not an exact integer ending in 000000 + assert int(Float('1.123456789012345678901234567890e35', '')) == \ + 112345678901234567890123456789000192 + assert int(Float('123456789012345678901234567890e5', '')) == \ + 12345678901234567890123456789000000 + assert Integer(Float('1.123456789012345678901234567890e20', '')) == \ + 112345678901234567890 + assert Integer(Float('1.123456789012345678901234567890e25', '')) == \ + 11234567890123456789012345 + # decimal forces float so it's not an exact integer ending in 000000 + assert Integer(Float('1.123456789012345678901234567890e35', '')) == \ + 112345678901234567890123456789000192 + assert Integer(Float('123456789012345678901234567890e5', '')) == \ + 12345678901234567890123456789000000 + assert same_and_same_prec(Float('123000e-2',''), Float('1230.00', '')) + assert same_and_same_prec(Float('123000e2',''), Float('12300000', '')) + + assert int(1 + Rational('.9999999999999999999999999')) == 1 + assert int(pi/1e20) == 0 + assert int(1 + pi/1e20) == 1 + assert int(Add(1.2, -2, evaluate=False)) == int(1.2 - 2) + assert int(Add(1.2, +2, evaluate=False)) == int(1.2 + 2) + assert int(Add(1 + Float('.99999999999999999', ''), evaluate=False)) == 1 + raises(TypeError, lambda: float(x)) + raises(TypeError, lambda: float(sqrt(-1))) + + assert int(12345678901234567890 + cos(1)**2 + sin(1)**2) == \ + 12345678901234567891 + + +def test_issue_6611a(): + assert Mul.flatten([3**Rational(1, 3), + Pow(-Rational(1, 9), Rational(2, 3), evaluate=False)]) == \ + ([Rational(1, 3), (-1)**Rational(2, 3)], [], None) + + +def test_denest_add_mul(): + # when working with evaluated expressions make sure they denest + eq = x + 1 + eq = Add(eq, 2, evaluate=False) + eq = Add(eq, 2, evaluate=False) + assert Add(*eq.args) == x + 5 + eq = x*2 + eq = Mul(eq, 2, evaluate=False) + eq = Mul(eq, 2, evaluate=False) + assert Mul(*eq.args) == 8*x + # but don't let them denest unnecessarily + eq = Mul(-2, x - 2, evaluate=False) + assert 2*eq == Mul(-4, x - 2, evaluate=False) + assert -eq == Mul(2, x - 2, evaluate=False) + + +def test_mul_coeff(): + # It is important that all Numbers be removed from the seq; + # This can be tricky when powers combine to produce those numbers + p = exp(I*pi/3) + assert p**2*x*p*y*p*x*p**2 == x**2*y + + +def test_mul_zero_detection(): + nz = Dummy(real=True, zero=False) + r = Dummy(extended_real=True) + c = Dummy(real=False, complex=True) + c2 = Dummy(real=False, complex=True) + i = Dummy(imaginary=True) + e = nz*r*c + assert e.is_imaginary is None + assert e.is_extended_real is None + e = nz*c + assert e.is_imaginary is None + assert e.is_extended_real is False + e = nz*i*c + assert e.is_imaginary is False + assert e.is_extended_real is None + # check for more than one complex; it is important to use + # uniquely named Symbols to ensure that two factors appear + # e.g. if the symbols have the same name they just become + # a single factor, a power. + e = nz*i*c*c2 + assert e.is_imaginary is None + assert e.is_extended_real is None + + # _eval_is_extended_real and _eval_is_zero both employ trapping of the + # zero value so args should be tested in both directions and + # TO AVOID GETTING THE CACHED RESULT, Dummy MUST BE USED + + # real is unknown + def test(z, b, e): + if z.is_zero and b.is_finite: + assert e.is_extended_real and e.is_zero + else: + assert e.is_extended_real is None + if b.is_finite: + if z.is_zero: + assert e.is_zero + else: + assert e.is_zero is None + elif b.is_finite is False: + if z.is_zero is None: + assert e.is_zero is None + else: + assert e.is_zero is False + + + for iz, ib in product(*[[True, False, None]]*2): + z = Dummy('z', nonzero=iz) + b = Dummy('f', finite=ib) + e = Mul(z, b, evaluate=False) + test(z, b, e) + z = Dummy('nz', nonzero=iz) + b = Dummy('f', finite=ib) + e = Mul(b, z, evaluate=False) + test(z, b, e) + + # real is True + def test(z, b, e): + if z.is_zero and not b.is_finite: + assert e.is_extended_real is None + else: + assert e.is_extended_real is True + + for iz, ib in product(*[[True, False, None]]*2): + z = Dummy('z', nonzero=iz, extended_real=True) + b = Dummy('b', finite=ib, extended_real=True) + e = Mul(z, b, evaluate=False) + test(z, b, e) + z = Dummy('z', nonzero=iz, extended_real=True) + b = Dummy('b', finite=ib, extended_real=True) + e = Mul(b, z, evaluate=False) + test(z, b, e) + + +def test_Mul_with_zero_infinite(): + zer = Dummy(zero=True) + inf = Dummy(finite=False) + + e = Mul(zer, inf, evaluate=False) + assert e.is_extended_positive is None + assert e.is_hermitian is None + + e = Mul(inf, zer, evaluate=False) + assert e.is_extended_positive is None + assert e.is_hermitian is None + + +def test_Mul_does_not_cancel_infinities(): + a, b = symbols('a b') + assert ((zoo + 3*a)/(3*a + zoo)) is nan + assert ((b - oo)/(b - oo)) is nan + # issue 13904 + expr = (1/(a+b) + 1/(a-b))/(1/(a+b) - 1/(a-b)) + assert expr.subs(b, a) is nan + + +def test_Mul_does_not_distribute_infinity(): + a, b = symbols('a b') + assert ((1 + I)*oo).is_Mul + assert ((a + b)*(-oo)).is_Mul + assert ((a + 1)*zoo).is_Mul + assert ((1 + I)*oo).is_finite is False + z = (1 + I)*oo + assert ((1 - I)*z).expand() is oo + + +def test_issue_8247_8354(): + from sympy.functions.elementary.trigonometric import tan + z = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3)) + assert z.is_positive is False # it's 0 + z = S('''-2**(1/3)*(3*sqrt(93) + 29)**2 - 4*(3*sqrt(93) + 29)**(4/3) + + 12*sqrt(93)*(3*sqrt(93) + 29)**(1/3) + 116*(3*sqrt(93) + 29)**(1/3) + + 174*2**(1/3)*sqrt(93) + 1678*2**(1/3)''') + assert z.is_positive is False # it's 0 + z = 2*(-3*tan(19*pi/90) + sqrt(3))*cos(11*pi/90)*cos(19*pi/90) - \ + sqrt(3)*(-3 + 4*cos(19*pi/90)**2) + assert z.is_positive is not True # it's zero and it shouldn't hang + z = S('''9*(3*sqrt(93) + 29)**(2/3)*((3*sqrt(93) + + 29)**(1/3)*(-2**(2/3)*(3*sqrt(93) + 29)**(1/3) - 2) - 2*2**(1/3))**3 + + 72*(3*sqrt(93) + 29)**(2/3)*(81*sqrt(93) + 783) + (162*sqrt(93) + + 1566)*((3*sqrt(93) + 29)**(1/3)*(-2**(2/3)*(3*sqrt(93) + 29)**(1/3) - + 2) - 2*2**(1/3))**2''') + assert z.is_positive is False # it's 0 (and a single _mexpand isn't enough) + + +def test_Add_is_zero(): + x, y = symbols('x y', zero=True) + assert (x + y).is_zero + + # Issue 15873 + e = -2*I + (1 + I)**2 + assert e.is_zero is None + + +def test_issue_14392(): + assert (sin(zoo)**2).as_real_imag() == (nan, nan) + + +def test_divmod(): + assert divmod(x, y) == (x//y, x % y) + assert divmod(x, 3) == (x//3, x % 3) + assert divmod(3, x) == (3//x, 3 % x) + + +def test__neg__(): + assert -(x*y) == -x*y + assert -(-x*y) == x*y + assert -(1.*x) == -1.*x + assert -(-1.*x) == 1.*x + assert -(2.*x) == -2.*x + assert -(-2.*x) == 2.*x + with distribute(False): + eq = -(x + y) + assert eq.is_Mul and eq.args == (-1, x + y) + with evaluate(False): + eq = -(x + y) + assert eq.is_Mul and eq.args == (-1, x + y) + + +def test_issue_18507(): + assert Mul(zoo, zoo, 0) is nan + + +def test_issue_17130(): + e = Add(b, -b, I, -I, evaluate=False) + assert e.is_zero is None # ideally this would be True + + +def test_issue_21034(): + e = -I*log((re(asin(5)) + I*im(asin(5)))/sqrt(re(asin(5))**2 + im(asin(5))**2))/pi + assert e.round(2) + + +def test_issue_22021(): + from sympy.calculus.accumulationbounds import AccumBounds + # these objects are special cases in Mul + from sympy.tensor.tensor import TensorIndexType, tensor_indices, tensor_heads + L = TensorIndexType("L") + i = tensor_indices("i", L) + A, B = tensor_heads("A B", [L]) + e = A(i) + B(i) + assert -e == -1*e + e = zoo + x + assert -e == -1*e + a = AccumBounds(1, 2) + e = a + x + assert -e == -1*e + for args in permutations((zoo, a, x)): + e = Add(*args, evaluate=False) + assert -e == -1*e + assert 2*Add(1, x, x, evaluate=False) == 4*x + 2 + + +def test_issue_22244(): + assert -(zoo*x) == zoo*x + + +def test_issue_22453(): + from sympy.utilities.iterables import cartes + e = Symbol('e', extended_positive=True) + for a, b in cartes(*[[oo, -oo, 3]]*2): + if a == b == 3: + continue + i = a + I*b + assert i**(1 + e) is S.ComplexInfinity + assert i**-e is S.Zero + assert unchanged(Pow, i, e) + assert 1/(oo + I*oo) is S.Zero + r, i = [Dummy(infinite=True, extended_real=True) for _ in range(2)] + assert 1/(r + I*i) is S.Zero + assert 1/(3 + I*i) is S.Zero + assert 1/(r + I*3) is S.Zero + + +def test_issue_22613(): + assert (0**(x - 2)).as_content_primitive() == (1, 0**(x - 2)) + assert (0**(x + 2)).as_content_primitive() == (1, 0**(x + 2)) + + +def test_issue_25176(): + assert sqrt(-4*3**(S(3)/4)*I/3) == 2*3**(S(7)/8)*sqrt(-I)/3 diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_assumptions.py b/lib/python3.11/site-packages/sympy/core/tests/test_assumptions.py new file mode 100644 index 0000000000000000000000000000000000000000..574e90178fb489fe99c99ea0c72df57ceec4b249 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_assumptions.py @@ -0,0 +1,1335 @@ +from sympy.core.mod import Mod +from sympy.core.numbers import (I, oo, pi) +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (asin, sin) +from sympy.simplify.simplify import simplify +from sympy.core import Symbol, S, Rational, Integer, Dummy, Wild, Pow +from sympy.core.assumptions import (assumptions, check_assumptions, + failing_assumptions, common_assumptions, _generate_assumption_rules, + _load_pre_generated_assumption_rules) +from sympy.core.facts import InconsistentAssumptions +from sympy.core.random import seed +from sympy.combinatorics import Permutation +from sympy.combinatorics.perm_groups import PermutationGroup + +from sympy.testing.pytest import raises, XFAIL + + +def test_symbol_unset(): + x = Symbol('x', real=True, integer=True) + assert x.is_real is True + assert x.is_integer is True + assert x.is_imaginary is False + assert x.is_noninteger is False + assert x.is_number is False + + +def test_zero(): + z = Integer(0) + assert z.is_commutative is True + assert z.is_integer is True + assert z.is_rational is True + assert z.is_algebraic is True + assert z.is_transcendental is False + assert z.is_real is True + assert z.is_complex is True + assert z.is_noninteger is False + assert z.is_irrational is False + assert z.is_imaginary is False + assert z.is_positive is False + assert z.is_negative is False + assert z.is_nonpositive is True + assert z.is_nonnegative is True + assert z.is_even is True + assert z.is_odd is False + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is True + assert z.is_prime is False + assert z.is_composite is False + assert z.is_number is True + + +def test_one(): + z = Integer(1) + assert z.is_commutative is True + assert z.is_integer is True + assert z.is_rational is True + assert z.is_algebraic is True + assert z.is_transcendental is False + assert z.is_real is True + assert z.is_complex is True + assert z.is_noninteger is False + assert z.is_irrational is False + assert z.is_imaginary is False + assert z.is_positive is True + assert z.is_negative is False + assert z.is_nonpositive is False + assert z.is_nonnegative is True + assert z.is_even is False + assert z.is_odd is True + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is True + assert z.is_prime is False + assert z.is_number is True + assert z.is_composite is False # issue 8807 + + +def test_negativeone(): + z = Integer(-1) + assert z.is_commutative is True + assert z.is_integer is True + assert z.is_rational is True + assert z.is_algebraic is True + assert z.is_transcendental is False + assert z.is_real is True + assert z.is_complex is True + assert z.is_noninteger is False + assert z.is_irrational is False + assert z.is_imaginary is False + assert z.is_positive is False + assert z.is_negative is True + assert z.is_nonpositive is True + assert z.is_nonnegative is False + assert z.is_even is False + assert z.is_odd is True + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is True + assert z.is_prime is False + assert z.is_composite is False + assert z.is_number is True + + +def test_infinity(): + oo = S.Infinity + + assert oo.is_commutative is True + assert oo.is_integer is False + assert oo.is_rational is False + assert oo.is_algebraic is False + assert oo.is_transcendental is False + assert oo.is_extended_real is True + assert oo.is_real is False + assert oo.is_complex is False + assert oo.is_noninteger is True + assert oo.is_irrational is False + assert oo.is_imaginary is False + assert oo.is_nonzero is False + assert oo.is_positive is False + assert oo.is_negative is False + assert oo.is_nonpositive is False + assert oo.is_nonnegative is False + assert oo.is_extended_nonzero is True + assert oo.is_extended_positive is True + assert oo.is_extended_negative is False + assert oo.is_extended_nonpositive is False + assert oo.is_extended_nonnegative is True + assert oo.is_even is False + assert oo.is_odd is False + assert oo.is_finite is False + assert oo.is_infinite is True + assert oo.is_comparable is True + assert oo.is_prime is False + assert oo.is_composite is False + assert oo.is_number is True + + +def test_neg_infinity(): + mm = S.NegativeInfinity + + assert mm.is_commutative is True + assert mm.is_integer is False + assert mm.is_rational is False + assert mm.is_algebraic is False + assert mm.is_transcendental is False + assert mm.is_extended_real is True + assert mm.is_real is False + assert mm.is_complex is False + assert mm.is_noninteger is True + assert mm.is_irrational is False + assert mm.is_imaginary is False + assert mm.is_nonzero is False + assert mm.is_positive is False + assert mm.is_negative is False + assert mm.is_nonpositive is False + assert mm.is_nonnegative is False + assert mm.is_extended_nonzero is True + assert mm.is_extended_positive is False + assert mm.is_extended_negative is True + assert mm.is_extended_nonpositive is True + assert mm.is_extended_nonnegative is False + assert mm.is_even is False + assert mm.is_odd is False + assert mm.is_finite is False + assert mm.is_infinite is True + assert mm.is_comparable is True + assert mm.is_prime is False + assert mm.is_composite is False + assert mm.is_number is True + + +def test_zoo(): + zoo = S.ComplexInfinity + assert zoo.is_complex is False + assert zoo.is_real is False + assert zoo.is_prime is False + + +def test_nan(): + nan = S.NaN + + assert nan.is_commutative is True + assert nan.is_integer is None + assert nan.is_rational is None + assert nan.is_algebraic is None + assert nan.is_transcendental is None + assert nan.is_real is None + assert nan.is_complex is None + assert nan.is_noninteger is None + assert nan.is_irrational is None + assert nan.is_imaginary is None + assert nan.is_positive is None + assert nan.is_negative is None + assert nan.is_nonpositive is None + assert nan.is_nonnegative is None + assert nan.is_even is None + assert nan.is_odd is None + assert nan.is_finite is None + assert nan.is_infinite is None + assert nan.is_comparable is False + assert nan.is_prime is None + assert nan.is_composite is None + assert nan.is_number is True + + +def test_pos_rational(): + r = Rational(3, 4) + assert r.is_commutative is True + assert r.is_integer is False + assert r.is_rational is True + assert r.is_algebraic is True + assert r.is_transcendental is False + assert r.is_real is True + assert r.is_complex is True + assert r.is_noninteger is True + assert r.is_irrational is False + assert r.is_imaginary is False + assert r.is_positive is True + assert r.is_negative is False + assert r.is_nonpositive is False + assert r.is_nonnegative is True + assert r.is_even is False + assert r.is_odd is False + assert r.is_finite is True + assert r.is_infinite is False + assert r.is_comparable is True + assert r.is_prime is False + assert r.is_composite is False + + r = Rational(1, 4) + assert r.is_nonpositive is False + assert r.is_positive is True + assert r.is_negative is False + assert r.is_nonnegative is True + r = Rational(5, 4) + assert r.is_negative is False + assert r.is_positive is True + assert r.is_nonpositive is False + assert r.is_nonnegative is True + r = Rational(5, 3) + assert r.is_nonnegative is True + assert r.is_positive is True + assert r.is_negative is False + assert r.is_nonpositive is False + + +def test_neg_rational(): + r = Rational(-3, 4) + assert r.is_positive is False + assert r.is_nonpositive is True + assert r.is_negative is True + assert r.is_nonnegative is False + r = Rational(-1, 4) + assert r.is_nonpositive is True + assert r.is_positive is False + assert r.is_negative is True + assert r.is_nonnegative is False + r = Rational(-5, 4) + assert r.is_negative is True + assert r.is_positive is False + assert r.is_nonpositive is True + assert r.is_nonnegative is False + r = Rational(-5, 3) + assert r.is_nonnegative is False + assert r.is_positive is False + assert r.is_negative is True + assert r.is_nonpositive is True + + +def test_pi(): + z = S.Pi + assert z.is_commutative is True + assert z.is_integer is False + assert z.is_rational is False + assert z.is_algebraic is False + assert z.is_transcendental is True + assert z.is_real is True + assert z.is_complex is True + assert z.is_noninteger is True + assert z.is_irrational is True + assert z.is_imaginary is False + assert z.is_positive is True + assert z.is_negative is False + assert z.is_nonpositive is False + assert z.is_nonnegative is True + assert z.is_even is False + assert z.is_odd is False + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is True + assert z.is_prime is False + assert z.is_composite is False + + +def test_E(): + z = S.Exp1 + assert z.is_commutative is True + assert z.is_integer is False + assert z.is_rational is False + assert z.is_algebraic is False + assert z.is_transcendental is True + assert z.is_real is True + assert z.is_complex is True + assert z.is_noninteger is True + assert z.is_irrational is True + assert z.is_imaginary is False + assert z.is_positive is True + assert z.is_negative is False + assert z.is_nonpositive is False + assert z.is_nonnegative is True + assert z.is_even is False + assert z.is_odd is False + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is True + assert z.is_prime is False + assert z.is_composite is False + + +def test_I(): + z = S.ImaginaryUnit + assert z.is_commutative is True + assert z.is_integer is False + assert z.is_rational is False + assert z.is_algebraic is True + assert z.is_transcendental is False + assert z.is_real is False + assert z.is_complex is True + assert z.is_noninteger is False + assert z.is_irrational is False + assert z.is_imaginary is True + assert z.is_positive is False + assert z.is_negative is False + assert z.is_nonpositive is False + assert z.is_nonnegative is False + assert z.is_even is False + assert z.is_odd is False + assert z.is_finite is True + assert z.is_infinite is False + assert z.is_comparable is False + assert z.is_prime is False + assert z.is_composite is False + + +def test_symbol_real_false(): + # issue 3848 + a = Symbol('a', real=False) + + assert a.is_real is False + assert a.is_integer is False + assert a.is_zero is False + + assert a.is_negative is False + assert a.is_positive is False + assert a.is_nonnegative is False + assert a.is_nonpositive is False + assert a.is_nonzero is False + + assert a.is_extended_negative is None + assert a.is_extended_positive is None + assert a.is_extended_nonnegative is None + assert a.is_extended_nonpositive is None + assert a.is_extended_nonzero is None + + +def test_symbol_extended_real_false(): + # issue 3848 + a = Symbol('a', extended_real=False) + + assert a.is_real is False + assert a.is_integer is False + assert a.is_zero is False + + assert a.is_negative is False + assert a.is_positive is False + assert a.is_nonnegative is False + assert a.is_nonpositive is False + assert a.is_nonzero is False + + assert a.is_extended_negative is False + assert a.is_extended_positive is False + assert a.is_extended_nonnegative is False + assert a.is_extended_nonpositive is False + assert a.is_extended_nonzero is False + + +def test_symbol_imaginary(): + a = Symbol('a', imaginary=True) + + assert a.is_real is False + assert a.is_integer is False + assert a.is_negative is False + assert a.is_positive is False + assert a.is_nonnegative is False + assert a.is_nonpositive is False + assert a.is_zero is False + assert a.is_nonzero is False # since nonzero -> real + + +def test_symbol_zero(): + x = Symbol('x', zero=True) + assert x.is_positive is False + assert x.is_nonpositive + assert x.is_negative is False + assert x.is_nonnegative + assert x.is_zero is True + # TODO Change to x.is_nonzero is None + # See https://github.com/sympy/sympy/pull/9583 + assert x.is_nonzero is False + assert x.is_finite is True + + +def test_symbol_positive(): + x = Symbol('x', positive=True) + assert x.is_positive is True + assert x.is_nonpositive is False + assert x.is_negative is False + assert x.is_nonnegative is True + assert x.is_zero is False + assert x.is_nonzero is True + + +def test_neg_symbol_positive(): + x = -Symbol('x', positive=True) + assert x.is_positive is False + assert x.is_nonpositive is True + assert x.is_negative is True + assert x.is_nonnegative is False + assert x.is_zero is False + assert x.is_nonzero is True + + +def test_symbol_nonpositive(): + x = Symbol('x', nonpositive=True) + assert x.is_positive is False + assert x.is_nonpositive is True + assert x.is_negative is None + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_neg_symbol_nonpositive(): + x = -Symbol('x', nonpositive=True) + assert x.is_positive is None + assert x.is_nonpositive is None + assert x.is_negative is False + assert x.is_nonnegative is True + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_symbol_falsepositive(): + x = Symbol('x', positive=False) + assert x.is_positive is False + assert x.is_nonpositive is None + assert x.is_negative is None + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_symbol_falsepositive_mul(): + # To test pull request 9379 + # Explicit handling of arg.is_positive=False was added to Mul._eval_is_positive + x = 2*Symbol('x', positive=False) + assert x.is_positive is False # This was None before + assert x.is_nonpositive is None + assert x.is_negative is None + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +@XFAIL +def test_symbol_infinitereal_mul(): + ix = Symbol('ix', infinite=True, extended_real=True) + assert (-ix).is_extended_positive is None + + +def test_neg_symbol_falsepositive(): + x = -Symbol('x', positive=False) + assert x.is_positive is None + assert x.is_nonpositive is None + assert x.is_negative is False + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_neg_symbol_falsenegative(): + # To test pull request 9379 + # Explicit handling of arg.is_negative=False was added to Mul._eval_is_positive + x = -Symbol('x', negative=False) + assert x.is_positive is False # This was None before + assert x.is_nonpositive is None + assert x.is_negative is None + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_symbol_falsepositive_real(): + x = Symbol('x', positive=False, real=True) + assert x.is_positive is False + assert x.is_nonpositive is True + assert x.is_negative is None + assert x.is_nonnegative is None + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_neg_symbol_falsepositive_real(): + x = -Symbol('x', positive=False, real=True) + assert x.is_positive is None + assert x.is_nonpositive is None + assert x.is_negative is False + assert x.is_nonnegative is True + assert x.is_zero is None + assert x.is_nonzero is None + + +def test_symbol_falsenonnegative(): + x = Symbol('x', nonnegative=False) + assert x.is_positive is False + assert x.is_nonpositive is None + assert x.is_negative is None + assert x.is_nonnegative is False + assert x.is_zero is False + assert x.is_nonzero is None + + +@XFAIL +def test_neg_symbol_falsenonnegative(): + x = -Symbol('x', nonnegative=False) + assert x.is_positive is None + assert x.is_nonpositive is False # this currently returns None + assert x.is_negative is False # this currently returns None + assert x.is_nonnegative is None + assert x.is_zero is False # this currently returns None + assert x.is_nonzero is True # this currently returns None + + +def test_symbol_falsenonnegative_real(): + x = Symbol('x', nonnegative=False, real=True) + assert x.is_positive is False + assert x.is_nonpositive is True + assert x.is_negative is True + assert x.is_nonnegative is False + assert x.is_zero is False + assert x.is_nonzero is True + + +def test_neg_symbol_falsenonnegative_real(): + x = -Symbol('x', nonnegative=False, real=True) + assert x.is_positive is True + assert x.is_nonpositive is False + assert x.is_negative is False + assert x.is_nonnegative is True + assert x.is_zero is False + assert x.is_nonzero is True + + +def test_prime(): + assert S.NegativeOne.is_prime is False + assert S(-2).is_prime is False + assert S(-4).is_prime is False + assert S.Zero.is_prime is False + assert S.One.is_prime is False + assert S(2).is_prime is True + assert S(17).is_prime is True + assert S(4).is_prime is False + + +def test_composite(): + assert S.NegativeOne.is_composite is False + assert S(-2).is_composite is False + assert S(-4).is_composite is False + assert S.Zero.is_composite is False + assert S(2).is_composite is False + assert S(17).is_composite is False + assert S(4).is_composite is True + x = Dummy(integer=True, positive=True, prime=False) + assert x.is_composite is None # x could be 1 + assert (x + 1).is_composite is None + x = Dummy(positive=True, even=True, prime=False) + assert x.is_integer is True + assert x.is_composite is True + + +def test_prime_symbol(): + x = Symbol('x', prime=True) + assert x.is_prime is True + assert x.is_integer is True + assert x.is_positive is True + assert x.is_negative is False + assert x.is_nonpositive is False + assert x.is_nonnegative is True + + x = Symbol('x', prime=False) + assert x.is_prime is False + assert x.is_integer is None + assert x.is_positive is None + assert x.is_negative is None + assert x.is_nonpositive is None + assert x.is_nonnegative is None + + +def test_symbol_noncommutative(): + x = Symbol('x', commutative=True) + assert x.is_complex is None + + x = Symbol('x', commutative=False) + assert x.is_integer is False + assert x.is_rational is False + assert x.is_algebraic is False + assert x.is_irrational is False + assert x.is_real is False + assert x.is_complex is False + + +def test_other_symbol(): + x = Symbol('x', integer=True) + assert x.is_integer is True + assert x.is_real is True + assert x.is_finite is True + + x = Symbol('x', integer=True, nonnegative=True) + assert x.is_integer is True + assert x.is_nonnegative is True + assert x.is_negative is False + assert x.is_positive is None + assert x.is_finite is True + + x = Symbol('x', integer=True, nonpositive=True) + assert x.is_integer is True + assert x.is_nonpositive is True + assert x.is_positive is False + assert x.is_negative is None + assert x.is_finite is True + + x = Symbol('x', odd=True) + assert x.is_odd is True + assert x.is_even is False + assert x.is_integer is True + assert x.is_finite is True + + x = Symbol('x', odd=False) + assert x.is_odd is False + assert x.is_even is None + assert x.is_integer is None + assert x.is_finite is None + + x = Symbol('x', even=True) + assert x.is_even is True + assert x.is_odd is False + assert x.is_integer is True + assert x.is_finite is True + + x = Symbol('x', even=False) + assert x.is_even is False + assert x.is_odd is None + assert x.is_integer is None + assert x.is_finite is None + + x = Symbol('x', integer=True, nonnegative=True) + assert x.is_integer is True + assert x.is_nonnegative is True + assert x.is_finite is True + + x = Symbol('x', integer=True, nonpositive=True) + assert x.is_integer is True + assert x.is_nonpositive is True + assert x.is_finite is True + + x = Symbol('x', rational=True) + assert x.is_real is True + assert x.is_finite is True + + x = Symbol('x', rational=False) + assert x.is_real is None + assert x.is_finite is None + + x = Symbol('x', irrational=True) + assert x.is_real is True + assert x.is_finite is True + + x = Symbol('x', irrational=False) + assert x.is_real is None + assert x.is_finite is None + + with raises(AttributeError): + x.is_real = False + + x = Symbol('x', algebraic=True) + assert x.is_transcendental is False + x = Symbol('x', transcendental=True) + assert x.is_algebraic is False + assert x.is_rational is False + assert x.is_integer is False + + +def test_evaluate_false(): + # Previously this failed because the assumptions query would make new + # expressions and some of the evaluation logic would fail under + # evaluate(False). + from sympy.core.parameters import evaluate + from sympy.abc import x, h + f = 2**x**7 + with evaluate(False): + fh = f.xreplace({x: x+h}) + assert fh.exp.is_rational is None + + +def test_issue_3825(): + """catch: hash instability""" + x = Symbol("x") + y = Symbol("y") + a1 = x + y + a2 = y + x + a2.is_comparable + + h1 = hash(a1) + h2 = hash(a2) + assert h1 == h2 + + +def test_issue_4822(): + z = (-1)**Rational(1, 3)*(1 - I*sqrt(3)) + assert z.is_real in [True, None] + + +def test_hash_vs_typeinfo(): + """seemingly different typeinfo, but in fact equal""" + + # the following two are semantically equal + x1 = Symbol('x', even=True) + x2 = Symbol('x', integer=True, odd=False) + + assert hash(x1) == hash(x2) + assert x1 == x2 + + +def test_hash_vs_typeinfo_2(): + """different typeinfo should mean !eq""" + # the following two are semantically different + x = Symbol('x') + x1 = Symbol('x', even=True) + + assert x != x1 + assert hash(x) != hash(x1) # This might fail with very low probability + + +def test_hash_vs_eq(): + """catch: different hash for equal objects""" + a = 1 + S.Pi # important: do not fold it into a Number instance + ha = hash(a) # it should be Add/Mul/... to trigger the bug + + a.is_positive # this uses .evalf() and deduces it is positive + assert a.is_positive is True + + # be sure that hash stayed the same + assert ha == hash(a) + + # now b should be the same expression + b = a.expand(trig=True) + hb = hash(b) + + assert a == b + assert ha == hb + + +def test_Add_is_pos_neg(): + # these cover lines not covered by the rest of tests in core + n = Symbol('n', extended_negative=True, infinite=True) + nn = Symbol('n', extended_nonnegative=True, infinite=True) + np = Symbol('n', extended_nonpositive=True, infinite=True) + p = Symbol('p', extended_positive=True, infinite=True) + r = Dummy(extended_real=True, finite=False) + x = Symbol('x') + xf = Symbol('xf', finite=True) + assert (n + p).is_extended_positive is None + assert (n + x).is_extended_positive is None + assert (p + x).is_extended_positive is None + assert (n + p).is_extended_negative is None + assert (n + x).is_extended_negative is None + assert (p + x).is_extended_negative is None + + assert (n + xf).is_extended_positive is False + assert (p + xf).is_extended_positive is True + assert (n + xf).is_extended_negative is True + assert (p + xf).is_extended_negative is False + + assert (x - S.Infinity).is_extended_negative is None # issue 7798 + # issue 8046, 16.2 + assert (p + nn).is_extended_positive + assert (n + np).is_extended_negative + assert (p + r).is_extended_positive is None + + +def test_Add_is_imaginary(): + nn = Dummy(nonnegative=True) + assert (I*nn + I).is_imaginary # issue 8046, 17 + + +def test_Add_is_algebraic(): + a = Symbol('a', algebraic=True) + b = Symbol('a', algebraic=True) + na = Symbol('na', algebraic=False) + nb = Symbol('nb', algebraic=False) + x = Symbol('x') + assert (a + b).is_algebraic + assert (na + nb).is_algebraic is None + assert (a + na).is_algebraic is False + assert (a + x).is_algebraic is None + assert (na + x).is_algebraic is None + + +def test_Mul_is_algebraic(): + a = Symbol('a', algebraic=True) + b = Symbol('b', algebraic=True) + na = Symbol('na', algebraic=False) + an = Symbol('an', algebraic=True, nonzero=True) + nb = Symbol('nb', algebraic=False) + x = Symbol('x') + assert (a*b).is_algebraic is True + assert (na*nb).is_algebraic is None + assert (a*na).is_algebraic is None + assert (an*na).is_algebraic is False + assert (a*x).is_algebraic is None + assert (na*x).is_algebraic is None + + +def test_Pow_is_algebraic(): + e = Symbol('e', algebraic=True) + + assert Pow(1, e, evaluate=False).is_algebraic + assert Pow(0, e, evaluate=False).is_algebraic + + a = Symbol('a', algebraic=True) + azf = Symbol('azf', algebraic=True, zero=False) + na = Symbol('na', algebraic=False) + ia = Symbol('ia', algebraic=True, irrational=True) + ib = Symbol('ib', algebraic=True, irrational=True) + r = Symbol('r', rational=True) + x = Symbol('x') + assert (a**2).is_algebraic is True + assert (a**r).is_algebraic is None + assert (azf**r).is_algebraic is True + assert (a**x).is_algebraic is None + assert (na**r).is_algebraic is None + assert (ia**r).is_algebraic is True + assert (ia**ib).is_algebraic is False + + assert (a**e).is_algebraic is None + + # Gelfond-Schneider constant: + assert Pow(2, sqrt(2), evaluate=False).is_algebraic is False + + assert Pow(S.GoldenRatio, sqrt(3), evaluate=False).is_algebraic is False + + # issue 8649 + t = Symbol('t', real=True, transcendental=True) + n = Symbol('n', integer=True) + assert (t**n).is_algebraic is None + assert (t**n).is_integer is None + + assert (pi**3).is_algebraic is False + r = Symbol('r', zero=True) + assert (pi**r).is_algebraic is True + + +def test_Mul_is_prime_composite(): + x = Symbol('x', positive=True, integer=True) + y = Symbol('y', positive=True, integer=True) + assert (x*y).is_prime is None + assert ( (x+1)*(y+1) ).is_prime is False + assert ( (x+1)*(y+1) ).is_composite is True + + x = Symbol('x', positive=True) + assert ( (x+1)*(y+1) ).is_prime is None + assert ( (x+1)*(y+1) ).is_composite is None + + +def test_Pow_is_pos_neg(): + z = Symbol('z', real=True) + w = Symbol('w', nonpositive=True) + + assert (S.NegativeOne**S(2)).is_positive is True + assert (S.One**z).is_positive is True + assert (S.NegativeOne**S(3)).is_positive is False + assert (S.Zero**S.Zero).is_positive is True # 0**0 is 1 + assert (w**S(3)).is_positive is False + assert (w**S(2)).is_positive is None + assert (I**2).is_positive is False + assert (I**4).is_positive is True + + # tests emerging from #16332 issue + p = Symbol('p', zero=True) + q = Symbol('q', zero=False, real=True) + j = Symbol('j', zero=False, even=True) + x = Symbol('x', zero=True) + y = Symbol('y', zero=True) + assert (p**q).is_positive is False + assert (p**q).is_negative is False + assert (p**j).is_positive is False + assert (x**y).is_positive is True # 0**0 + assert (x**y).is_negative is False + + +def test_Pow_is_prime_composite(): + x = Symbol('x', positive=True, integer=True) + y = Symbol('y', positive=True, integer=True) + assert (x**y).is_prime is None + assert ( x**(y+1) ).is_prime is False + assert ( x**(y+1) ).is_composite is None + assert ( (x+1)**(y+1) ).is_composite is True + assert ( (-x-1)**(2*y) ).is_composite is True + + x = Symbol('x', positive=True) + assert (x**y).is_prime is None + + +def test_Mul_is_infinite(): + x = Symbol('x') + f = Symbol('f', finite=True) + i = Symbol('i', infinite=True) + z = Dummy(zero=True) + nzf = Dummy(finite=True, zero=False) + from sympy.core.mul import Mul + assert (x*f).is_finite is None + assert (x*i).is_finite is None + assert (f*i).is_finite is None + assert (x*f*i).is_finite is None + assert (z*i).is_finite is None + assert (nzf*i).is_finite is False + assert (z*f).is_finite is True + assert Mul(0, f, evaluate=False).is_finite is True + assert Mul(0, i, evaluate=False).is_finite is None + + assert (x*f).is_infinite is None + assert (x*i).is_infinite is None + assert (f*i).is_infinite is None + assert (x*f*i).is_infinite is None + assert (z*i).is_infinite is S.NaN.is_infinite + assert (nzf*i).is_infinite is True + assert (z*f).is_infinite is False + assert Mul(0, f, evaluate=False).is_infinite is False + assert Mul(0, i, evaluate=False).is_infinite is S.NaN.is_infinite + + +def test_Add_is_infinite(): + x = Symbol('x') + f = Symbol('f', finite=True) + i = Symbol('i', infinite=True) + i2 = Symbol('i2', infinite=True) + z = Dummy(zero=True) + nzf = Dummy(finite=True, zero=False) + from sympy.core.add import Add + assert (x+f).is_finite is None + assert (x+i).is_finite is None + assert (f+i).is_finite is False + assert (x+f+i).is_finite is None + assert (z+i).is_finite is False + assert (nzf+i).is_finite is False + assert (z+f).is_finite is True + assert (i+i2).is_finite is None + assert Add(0, f, evaluate=False).is_finite is True + assert Add(0, i, evaluate=False).is_finite is False + + assert (x+f).is_infinite is None + assert (x+i).is_infinite is None + assert (f+i).is_infinite is True + assert (x+f+i).is_infinite is None + assert (z+i).is_infinite is True + assert (nzf+i).is_infinite is True + assert (z+f).is_infinite is False + assert (i+i2).is_infinite is None + assert Add(0, f, evaluate=False).is_infinite is False + assert Add(0, i, evaluate=False).is_infinite is True + + +def test_special_is_rational(): + i = Symbol('i', integer=True) + i2 = Symbol('i2', integer=True) + ni = Symbol('ni', integer=True, nonzero=True) + r = Symbol('r', rational=True) + rn = Symbol('r', rational=True, nonzero=True) + nr = Symbol('nr', irrational=True) + x = Symbol('x') + assert sqrt(3).is_rational is False + assert (3 + sqrt(3)).is_rational is False + assert (3*sqrt(3)).is_rational is False + assert exp(3).is_rational is False + assert exp(ni).is_rational is False + assert exp(rn).is_rational is False + assert exp(x).is_rational is None + assert exp(log(3), evaluate=False).is_rational is True + assert log(exp(3), evaluate=False).is_rational is True + assert log(3).is_rational is False + assert log(ni + 1).is_rational is False + assert log(rn + 1).is_rational is False + assert log(x).is_rational is None + assert (sqrt(3) + sqrt(5)).is_rational is None + assert (sqrt(3) + S.Pi).is_rational is False + assert (x**i).is_rational is None + assert (i**i).is_rational is True + assert (i**i2).is_rational is None + assert (r**i).is_rational is None + assert (r**r).is_rational is None + assert (r**x).is_rational is None + assert (nr**i).is_rational is None # issue 8598 + assert (nr**Symbol('z', zero=True)).is_rational + assert sin(1).is_rational is False + assert sin(ni).is_rational is False + assert sin(rn).is_rational is False + assert sin(x).is_rational is None + assert asin(r).is_rational is False + assert sin(asin(3), evaluate=False).is_rational is True + + +@XFAIL +def test_issue_6275(): + x = Symbol('x') + # both zero or both Muls...but neither "change would be very appreciated. + # This is similar to x/x => 1 even though if x = 0, it is really nan. + assert isinstance(x*0, type(0*S.Infinity)) + if 0*S.Infinity is S.NaN: + b = Symbol('b', finite=None) + assert (b*0).is_zero is None + + +def test_sanitize_assumptions(): + # issue 6666 + for cls in (Symbol, Dummy, Wild): + x = cls('x', real=1, positive=0) + assert x.is_real is True + assert x.is_positive is False + assert cls('', real=True, positive=None).is_positive is None + raises(ValueError, lambda: cls('', commutative=None)) + raises(ValueError, lambda: Symbol._sanitize({"commutative": None})) + + +def test_special_assumptions(): + e = -3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2 + assert simplify(e < 0) is S.false + assert simplify(e > 0) is S.false + assert (e == 0) is False # it's not a literal 0 + assert e.equals(0) is True + + +def test_inconsistent(): + # cf. issues 5795 and 5545 + raises(InconsistentAssumptions, lambda: Symbol('x', real=True, + commutative=False)) + + +def test_issue_6631(): + assert ((-1)**(I)).is_real is True + assert ((-1)**(I*2)).is_real is True + assert ((-1)**(I/2)).is_real is True + assert ((-1)**(I*S.Pi)).is_real is True + assert (I**(I + 2)).is_real is True + + +def test_issue_2730(): + assert (1/(1 + I)).is_real is False + + +def test_issue_4149(): + assert (3 + I).is_complex + assert (3 + I).is_imaginary is False + assert (3*I + S.Pi*I).is_imaginary + # as Zero.is_imaginary is False, see issue 7649 + y = Symbol('y', real=True) + assert (3*I + S.Pi*I + y*I).is_imaginary is None + p = Symbol('p', positive=True) + assert (3*I + S.Pi*I + p*I).is_imaginary + n = Symbol('n', negative=True) + assert (-3*I - S.Pi*I + n*I).is_imaginary + + i = Symbol('i', imaginary=True) + assert ([(i**a).is_imaginary for a in range(4)] == + [False, True, False, True]) + + # tests from the PR #7887: + e = S("-sqrt(3)*I/2 + 0.866025403784439*I") + assert e.is_real is False + assert e.is_imaginary + + +def test_issue_2920(): + n = Symbol('n', negative=True) + assert sqrt(n).is_imaginary + + +def test_issue_7899(): + x = Symbol('x', real=True) + assert (I*x).is_real is None + assert ((x - I)*(x - 1)).is_zero is None + assert ((x - I)*(x - 1)).is_real is None + + +@XFAIL +def test_issue_7993(): + x = Dummy(integer=True) + y = Dummy(noninteger=True) + assert (x - y).is_zero is False + + +def test_issue_8075(): + raises(InconsistentAssumptions, lambda: Dummy(zero=True, finite=False)) + raises(InconsistentAssumptions, lambda: Dummy(zero=True, infinite=True)) + + +def test_issue_8642(): + x = Symbol('x', real=True, integer=False) + assert (x*2).is_integer is None, (x*2).is_integer + + +def test_issues_8632_8633_8638_8675_8992(): + p = Dummy(integer=True, positive=True) + nn = Dummy(integer=True, nonnegative=True) + assert (p - S.Half).is_positive + assert (p - 1).is_nonnegative + assert (nn + 1).is_positive + assert (-p + 1).is_nonpositive + assert (-nn - 1).is_negative + prime = Dummy(prime=True) + assert (prime - 2).is_nonnegative + assert (prime - 3).is_nonnegative is None + even = Dummy(positive=True, even=True) + assert (even - 2).is_nonnegative + + p = Dummy(positive=True) + assert (p/(p + 1) - 1).is_negative + assert ((p + 2)**3 - S.Half).is_positive + n = Dummy(negative=True) + assert (n - 3).is_nonpositive + + +def test_issue_9115_9150(): + n = Dummy('n', integer=True, nonnegative=True) + assert (factorial(n) >= 1) == True + assert (factorial(n) < 1) == False + + assert factorial(n + 1).is_even is None + assert factorial(n + 2).is_even is True + assert factorial(n + 2) >= 2 + + +def test_issue_9165(): + z = Symbol('z', zero=True) + f = Symbol('f', finite=False) + assert 0/z is S.NaN + assert 0*(1/z) is S.NaN + assert 0*f is S.NaN + + +def test_issue_10024(): + x = Dummy('x') + assert Mod(x, 2*pi).is_zero is None + + +def test_issue_10302(): + x = Symbol('x') + r = Symbol('r', real=True) + u = -(3*2**pi)**(1/pi) + 2*3**(1/pi) + i = u + u*I + + assert i.is_real is None # w/o simplification this should fail + assert (u + i).is_zero is None + assert (1 + i).is_zero is False + + a = Dummy('a', zero=True) + assert (a + I).is_zero is False + assert (a + r*I).is_zero is None + assert (a + I).is_imaginary + assert (a + x + I).is_imaginary is None + assert (a + r*I + I).is_imaginary is None + + +def test_complex_reciprocal_imaginary(): + assert (1 / (4 + 3*I)).is_imaginary is False + + +def test_issue_16313(): + x = Symbol('x', extended_real=False) + k = Symbol('k', real=True) + l = Symbol('l', real=True, zero=False) + assert (-x).is_real is False + assert (k*x).is_real is None # k can be zero also + assert (l*x).is_real is False + assert (l*x*x).is_real is None # since x*x can be a real number + assert (-x).is_positive is False + + +def test_issue_16579(): + # extended_real -> finite | infinite + x = Symbol('x', extended_real=True, infinite=False) + y = Symbol('y', extended_real=True, finite=False) + assert x.is_finite is True + assert y.is_infinite is True + + # With PR 16978, complex now implies finite + c = Symbol('c', complex=True) + assert c.is_finite is True + raises(InconsistentAssumptions, lambda: Dummy(complex=True, finite=False)) + + # Now infinite == !finite + nf = Symbol('nf', finite=False) + assert nf.is_infinite is True + + +def test_issue_17556(): + z = I*oo + assert z.is_imaginary is False + assert z.is_finite is False + + +def test_issue_21651(): + k = Symbol('k', positive=True, integer=True) + exp = 2*2**(-k) + assert exp.is_integer is None + + +def test_assumptions_copy(): + assert assumptions(Symbol('x'), {"commutative": True} + ) == {'commutative': True} + assert assumptions(Symbol('x'), ['integer']) == {} + assert assumptions(Symbol('x'), ['commutative'] + ) == {'commutative': True} + assert assumptions(Symbol('x')) == {'commutative': True} + assert assumptions(1)['positive'] + assert assumptions(3 + I) == { + 'algebraic': True, + 'commutative': True, + 'complex': True, + 'composite': False, + 'even': False, + 'extended_negative': False, + 'extended_nonnegative': False, + 'extended_nonpositive': False, + 'extended_nonzero': False, + 'extended_positive': False, + 'extended_real': False, + 'finite': True, + 'imaginary': False, + 'infinite': False, + 'integer': False, + 'irrational': False, + 'negative': False, + 'noninteger': False, + 'nonnegative': False, + 'nonpositive': False, + 'nonzero': False, + 'odd': False, + 'positive': False, + 'prime': False, + 'rational': False, + 'real': False, + 'transcendental': False, + 'zero': False} + + +def test_check_assumptions(): + assert check_assumptions(1, 0) is False + x = Symbol('x', positive=True) + assert check_assumptions(1, x) is True + assert check_assumptions(1, 1) is True + assert check_assumptions(-1, 1) is False + i = Symbol('i', integer=True) + # don't know if i is positive (or prime, etc...) + assert check_assumptions(i, 1) is None + assert check_assumptions(Dummy(integer=None), integer=True) is None + assert check_assumptions(Dummy(integer=None), integer=False) is None + assert check_assumptions(Dummy(integer=False), integer=True) is False + assert check_assumptions(Dummy(integer=True), integer=False) is False + # no T/F assumptions to check + assert check_assumptions(Dummy(integer=False), integer=None) is True + raises(ValueError, lambda: check_assumptions(2*x, x, positive=True)) + + +def test_failing_assumptions(): + x = Symbol('x', positive=True) + y = Symbol('y') + assert failing_assumptions(6*x + y, **x.assumptions0) == \ + {'real': None, 'imaginary': None, 'complex': None, 'hermitian': None, + 'positive': None, 'nonpositive': None, 'nonnegative': None, 'nonzero': None, + 'negative': None, 'zero': None, 'extended_real': None, 'finite': None, + 'infinite': None, 'extended_negative': None, 'extended_nonnegative': None, + 'extended_nonpositive': None, 'extended_nonzero': None, + 'extended_positive': None } + + +def test_common_assumptions(): + assert common_assumptions([0, 1, 2] + ) == {'algebraic': True, 'irrational': False, 'hermitian': + True, 'extended_real': True, 'real': True, 'extended_negative': + False, 'extended_nonnegative': True, 'integer': True, + 'rational': True, 'imaginary': False, 'complex': True, + 'commutative': True,'noninteger': False, 'composite': False, + 'infinite': False, 'nonnegative': True, 'finite': True, + 'transcendental': False,'negative': False} + assert common_assumptions([0, 1, 2], 'positive integer'.split() + ) == {'integer': True} + assert common_assumptions([0, 1, 2], []) == {} + assert common_assumptions([], ['integer']) == {} + assert common_assumptions([0], ['integer']) == {'integer': True} + +def test_pre_generated_assumption_rules_are_valid(): + # check the pre-generated assumptions match freshly generated assumptions + # if this check fails, consider updating the assumptions + # see sympy.core.assumptions._generate_assumption_rules + pre_generated_assumptions =_load_pre_generated_assumption_rules() + generated_assumptions =_generate_assumption_rules() + assert pre_generated_assumptions._to_python() == generated_assumptions._to_python(), "pre-generated assumptions are invalid, see sympy.core.assumptions._generate_assumption_rules" + + +def test_ask_shuffle(): + grp = PermutationGroup(Permutation(1, 0, 2), Permutation(2, 1, 3)) + + seed(123) + first = grp.random() + seed(123) + simplify(I) + second = grp.random() + seed(123) + simplify(-I) + third = grp.random() + + assert first == second == third diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_basic.py b/lib/python3.11/site-packages/sympy/core/tests/test_basic.py new file mode 100644 index 0000000000000000000000000000000000000000..44faf93162f0df8bd7d749d99f21c98d79a1ef41 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_basic.py @@ -0,0 +1,333 @@ +"""This tests sympy/core/basic.py with (ideally) no reference to subclasses +of Basic or Atom.""" +import collections +from typing import TypeVar, Generic + +from sympy.assumptions.ask import Q +from sympy.core.basic import (Basic, Atom, as_Basic, + _atomic, _aresame) +from sympy.core.containers import Tuple +from sympy.core.function import Function, Lambda +from sympy.core.numbers import I, pi, Float +from sympy.core.singleton import S +from sympy.core.symbol import symbols, Symbol, Dummy +from sympy.concrete.summations import Sum +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.gamma_functions import gamma +from sympy.integrals.integrals import Integral +from sympy.functions.elementary.exponential import exp +from sympy.testing.pytest import raises, warns_deprecated_sympy + +b1 = Basic() +b2 = Basic(b1) +b3 = Basic(b2) +b21 = Basic(b2, b1) +T = TypeVar('T') + + +def test__aresame(): + assert not _aresame(Basic(Tuple()), Basic()) + for i, j in [(S(2), S(2.)), (1., Float(1))]: + for do in range(2): + assert not _aresame(Basic(i), Basic(j)) + assert not _aresame(i, j) + i, j = j, i + + +def test_structure(): + assert b21.args == (b2, b1) + assert b21.func(*b21.args) == b21 + assert bool(b1) + + +def test_immutable(): + assert not hasattr(b1, '__dict__') + with raises(AttributeError): + b1.x = 1 + + +def test_equality(): + instances = [b1, b2, b3, b21, Basic(b1, b1, b1), Basic] + for i, b_i in enumerate(instances): + for j, b_j in enumerate(instances): + assert (b_i == b_j) == (i == j) + assert (b_i != b_j) == (i != j) + + assert Basic() != [] + assert not(Basic() == []) + assert Basic() != 0 + assert not(Basic() == 0) + + class Foo: + """ + Class that is unaware of Basic, and relies on both classes returning + the NotImplemented singleton for equivalence to evaluate to False. + + """ + + b = Basic() + foo = Foo() + + assert b != foo + assert foo != b + assert not b == foo + assert not foo == b + + class Bar: + """ + Class that considers itself equal to any instance of Basic, and relies + on Basic returning the NotImplemented singleton in order to achieve + a symmetric equivalence relation. + + """ + def __eq__(self, other): + if isinstance(other, Basic): + return True + return NotImplemented + + def __ne__(self, other): + return not self == other + + bar = Bar() + + assert b == bar + assert bar == b + assert not b != bar + assert not bar != b + + +def test_matches_basic(): + instances = [Basic(b1, b1, b2), Basic(b1, b2, b1), Basic(b2, b1, b1), + Basic(b1, b2), Basic(b2, b1), b2, b1] + for i, b_i in enumerate(instances): + for j, b_j in enumerate(instances): + if i == j: + assert b_i.matches(b_j) == {} + else: + assert b_i.matches(b_j) is None + assert b1.match(b1) == {} + + +def test_has(): + assert b21.has(b1) + assert b21.has(b3, b1) + assert b21.has(Basic) + assert not b1.has(b21, b3) + assert not b21.has() + assert not b21.has(str) + assert not Symbol("x").has("x") + + +def test_subs(): + assert b21.subs(b2, b1) == Basic(b1, b1) + assert b21.subs(b2, b21) == Basic(b21, b1) + assert b3.subs(b2, b1) == b2 + + assert b21.subs([(b2, b1), (b1, b2)]) == Basic(b2, b2) + + assert b21.subs({b1: b2, b2: b1}) == Basic(b2, b2) + assert b21.subs(collections.ChainMap({b1: b2}, {b2: b1})) == Basic(b2, b2) + assert b21.subs(collections.OrderedDict([(b2, b1), (b1, b2)])) == Basic(b2, b2) + + raises(ValueError, lambda: b21.subs('bad arg')) + raises(ValueError, lambda: b21.subs(b1, b2, b3)) + # dict(b1=foo) creates a string 'b1' but leaves foo unchanged; subs + # will convert the first to a symbol but will raise an error if foo + # cannot be sympified; sympification is strict if foo is not string + raises(ValueError, lambda: b21.subs(b1='bad arg')) + + assert Symbol("text").subs({"text": b1}) == b1 + assert Symbol("s").subs({"s": 1}) == 1 + + +def test_subs_with_unicode_symbols(): + expr = Symbol('var1') + replaced = expr.subs('var1', 'x') + assert replaced.name == 'x' + + replaced = expr.subs('var1', 'x') + assert replaced.name == 'x' + + +def test_atoms(): + assert b21.atoms() == {Basic()} + + +def test_free_symbols_empty(): + assert b21.free_symbols == set() + + +def test_doit(): + assert b21.doit() == b21 + assert b21.doit(deep=False) == b21 + + +def test_S(): + assert repr(S) == 'S' + + +def test_xreplace(): + assert b21.xreplace({b2: b1}) == Basic(b1, b1) + assert b21.xreplace({b2: b21}) == Basic(b21, b1) + assert b3.xreplace({b2: b1}) == b2 + assert Basic(b1, b2).xreplace({b1: b2, b2: b1}) == Basic(b2, b1) + assert Atom(b1).xreplace({b1: b2}) == Atom(b1) + assert Atom(b1).xreplace({Atom(b1): b2}) == b2 + raises(TypeError, lambda: b1.xreplace()) + raises(TypeError, lambda: b1.xreplace([b1, b2])) + for f in (exp, Function('f')): + assert f.xreplace({}) == f + assert f.xreplace({}, hack2=True) == f + assert f.xreplace({f: b1}) == b1 + assert f.xreplace({f: b1}, hack2=True) == b1 + + +def test_sorted_args(): + x = symbols('x') + assert b21._sorted_args == b21.args + raises(AttributeError, lambda: x._sorted_args) + +def test_call(): + x, y = symbols('x y') + # See the long history of this in issues 5026 and 5105. + + raises(TypeError, lambda: sin(x)({ x : 1, sin(x) : 2})) + raises(TypeError, lambda: sin(x)(1)) + + # No effect as there are no callables + assert sin(x).rcall(1) == sin(x) + assert (1 + sin(x)).rcall(1) == 1 + sin(x) + + # Effect in the pressence of callables + l = Lambda(x, 2*x) + assert (l + x).rcall(y) == 2*y + x + assert (x**l).rcall(2) == x**4 + # TODO UndefinedFunction does not subclass Expr + #f = Function('f') + #assert (2*f)(x) == 2*f(x) + + assert (Q.real & Q.positive).rcall(x) == Q.real(x) & Q.positive(x) + + +def test_rewrite(): + x, y, z = symbols('x y z') + a, b = symbols('a b') + f1 = sin(x) + cos(x) + assert f1.rewrite(cos,exp) == exp(I*x)/2 + sin(x) + exp(-I*x)/2 + assert f1.rewrite([cos],sin) == sin(x) + sin(x + pi/2, evaluate=False) + f2 = sin(x) + cos(y)/gamma(z) + assert f2.rewrite(sin,exp) == -I*(exp(I*x) - exp(-I*x))/2 + cos(y)/gamma(z) + + assert f1.rewrite() == f1 + +def test_literal_evalf_is_number_is_zero_is_comparable(): + x = symbols('x') + f = Function('f') + + # issue 5033 + assert f.is_number is False + # issue 6646 + assert f(1).is_number is False + i = Integral(0, (x, x, x)) + # expressions that are symbolically 0 can be difficult to prove + # so in case there is some easy way to know if something is 0 + # it should appear in the is_zero property for that object; + # if is_zero is true evalf should always be able to compute that + # zero + assert i.n() == 0 + assert i.is_zero + assert i.is_number is False + assert i.evalf(2, strict=False) == 0 + + # issue 10268 + n = sin(1)**2 + cos(1)**2 - 1 + assert n.is_comparable is False + assert n.n(2).is_comparable is False + assert n.n(2).n(2).is_comparable + + +def test_as_Basic(): + assert as_Basic(1) is S.One + assert as_Basic(()) == Tuple() + raises(TypeError, lambda: as_Basic([])) + + +def test_atomic(): + g, h = map(Function, 'gh') + x = symbols('x') + assert _atomic(g(x + h(x))) == {g(x + h(x))} + assert _atomic(g(x + h(x)), recursive=True) == {h(x), x, g(x + h(x))} + assert _atomic(1) == set() + assert _atomic(Basic(S(1), S(2))) == set() + + +def test_as_dummy(): + u, v, x, y, z, _0, _1 = symbols('u v x y z _0 _1') + assert Lambda(x, x + 1).as_dummy() == Lambda(_0, _0 + 1) + assert Lambda(x, x + _0).as_dummy() == Lambda(_1, _0 + _1) + eq = (1 + Sum(x, (x, 1, x))) + ans = 1 + Sum(_0, (_0, 1, x)) + once = eq.as_dummy() + assert once == ans + twice = once.as_dummy() + assert twice == ans + assert Integral(x + _0, (x, x + 1), (_0, 1, 2) + ).as_dummy() == Integral(_0 + _1, (_0, x + 1), (_1, 1, 2)) + for T in (Symbol, Dummy): + d = T('x', real=True) + D = d.as_dummy() + assert D != d and D.func == Dummy and D.is_real is None + assert Dummy().as_dummy().is_commutative + assert Dummy(commutative=False).as_dummy().is_commutative is False + + +def test_canonical_variables(): + x, i0, i1 = symbols('x _:2') + assert Integral(x, (x, x + 1)).canonical_variables == {x: i0} + assert Integral(x, (x, x + 1), (i0, 1, 2)).canonical_variables == { + x: i0, i0: i1} + assert Integral(x, (x, x + i0)).canonical_variables == {x: i1} + + +def test_replace_exceptions(): + from sympy.core.symbol import Wild + x, y = symbols('x y') + e = (x**2 + x*y) + raises(TypeError, lambda: e.replace(sin, 2)) + b = Wild('b') + c = Wild('c') + raises(TypeError, lambda: e.replace(b*c, c.is_real)) + raises(TypeError, lambda: e.replace(b.is_real, 1)) + raises(TypeError, lambda: e.replace(lambda d: d.is_Number, 1)) + + +def test_ManagedProperties(): + # ManagedProperties is now deprecated. Here we do our best to check that if + # someone is using it then it does work in the way that it previously did + # but gives a deprecation warning. + from sympy.core.assumptions import ManagedProperties + + myclasses = [] + + class MyMeta(ManagedProperties): + def __init__(cls, *args, **kwargs): + myclasses.append('executed') + super().__init__(*args, **kwargs) + + code = """ +class MySubclass(Basic, metaclass=MyMeta): + pass +""" + with warns_deprecated_sympy(): + exec(code) + + assert myclasses == ['executed'] + + +def test_generic(): + # https://github.com/sympy/sympy/issues/25399 + class A(Symbol, Generic[T]): + pass + + class B(A[T]): + pass diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_cache.py b/lib/python3.11/site-packages/sympy/core/tests/test_cache.py new file mode 100644 index 0000000000000000000000000000000000000000..9124fca70718299252929a9923f335dde25256eb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_cache.py @@ -0,0 +1,91 @@ +import sys +from sympy.core.cache import cacheit, cached_property, lazy_function +from sympy.testing.pytest import raises + +def test_cacheit_doc(): + @cacheit + def testfn(): + "test docstring" + pass + + assert testfn.__doc__ == "test docstring" + assert testfn.__name__ == "testfn" + +def test_cacheit_unhashable(): + @cacheit + def testit(x): + return x + + assert testit(1) == 1 + assert testit(1) == 1 + a = {} + assert testit(a) == {} + a[1] = 2 + assert testit(a) == {1: 2} + +def test_cachit_exception(): + # Make sure the cache doesn't call functions multiple times when they + # raise TypeError + + a = [] + + @cacheit + def testf(x): + a.append(0) + raise TypeError + + raises(TypeError, lambda: testf(1)) + assert len(a) == 1 + + a.clear() + # Unhashable type + raises(TypeError, lambda: testf([])) + assert len(a) == 1 + + @cacheit + def testf2(x): + a.append(0) + raise TypeError("Error") + + a.clear() + raises(TypeError, lambda: testf2(1)) + assert len(a) == 1 + + a.clear() + # Unhashable type + raises(TypeError, lambda: testf2([])) + assert len(a) == 1 + +def test_cached_property(): + class A: + def __init__(self, value): + self.value = value + self.calls = 0 + + @cached_property + def prop(self): + self.calls = self.calls + 1 + return self.value + + a = A(2) + assert a.calls == 0 + assert a.prop == 2 + assert a.calls == 1 + assert a.prop == 2 + assert a.calls == 1 + b = A(None) + assert b.prop == None + + +def test_lazy_function(): + module_name='xmlrpc.client' + function_name = 'gzip_decode' + lazy = lazy_function(module_name, function_name) + assert lazy(b'') == b'' + assert module_name in sys.modules + assert function_name in str(lazy) + repr_lazy = repr(lazy) + assert 'LazyFunction' in repr_lazy + assert function_name in repr_lazy + + lazy = lazy_function('sympy.core.cache', 'cheap') diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_compatibility.py b/lib/python3.11/site-packages/sympy/core/tests/test_compatibility.py new file mode 100644 index 0000000000000000000000000000000000000000..31d2bed07b21aa2fa489273dca9edfc9993cfd86 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_compatibility.py @@ -0,0 +1,6 @@ +from sympy.testing.pytest import warns_deprecated_sympy + +def test_compatibility_submodule(): + # Test the sympy.core.compatibility deprecation warning + with warns_deprecated_sympy(): + import sympy.core.compatibility # noqa:F401 diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_complex.py b/lib/python3.11/site-packages/sympy/core/tests/test_complex.py new file mode 100644 index 0000000000000000000000000000000000000000..a607e0bdb4db859336aa30aa61f43bfb57d5df88 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_complex.py @@ -0,0 +1,226 @@ +from sympy.core.function import expand_complex +from sympy.core.numbers import (I, Integer, Rational, pi) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (Abs, conjugate, im, re, sign) +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.hyperbolic import (cosh, coth, sinh, tanh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, cot, sin, tan) + +def test_complex(): + a = Symbol("a", real=True) + b = Symbol("b", real=True) + e = (a + I*b)*(a - I*b) + assert e.expand() == a**2 + b**2 + assert sqrt(I) == Pow(I, S.Half) + + +def test_conjugate(): + a = Symbol("a", real=True) + b = Symbol("b", real=True) + c = Symbol("c", imaginary=True) + d = Symbol("d", imaginary=True) + x = Symbol('x') + z = a + I*b + c + I*d + zc = a - I*b - c + I*d + assert conjugate(z) == zc + assert conjugate(exp(z)) == exp(zc) + assert conjugate(exp(I*x)) == exp(-I*conjugate(x)) + assert conjugate(z**5) == zc**5 + assert conjugate(abs(x)) == abs(x) + assert conjugate(sign(z)) == sign(zc) + assert conjugate(sin(z)) == sin(zc) + assert conjugate(cos(z)) == cos(zc) + assert conjugate(tan(z)) == tan(zc) + assert conjugate(cot(z)) == cot(zc) + assert conjugate(sinh(z)) == sinh(zc) + assert conjugate(cosh(z)) == cosh(zc) + assert conjugate(tanh(z)) == tanh(zc) + assert conjugate(coth(z)) == coth(zc) + + +def test_abs1(): + a = Symbol("a", real=True) + b = Symbol("b", real=True) + assert abs(a) == Abs(a) + assert abs(-a) == abs(a) + assert abs(a + I*b) == sqrt(a**2 + b**2) + + +def test_abs2(): + a = Symbol("a", real=False) + b = Symbol("b", real=False) + assert abs(a) != a + assert abs(-a) != a + assert abs(a + I*b) != sqrt(a**2 + b**2) + + +def test_evalc(): + x = Symbol("x", real=True) + y = Symbol("y", real=True) + z = Symbol("z") + assert ((x + I*y)**2).expand(complex=True) == x**2 + 2*I*x*y - y**2 + assert expand_complex(z**(2*I)) == (re((re(z) + I*im(z))**(2*I)) + + I*im((re(z) + I*im(z))**(2*I))) + assert expand_complex( + z**(2*I), deep=False) == I*im(z**(2*I)) + re(z**(2*I)) + + assert exp(I*x) != cos(x) + I*sin(x) + assert exp(I*x).expand(complex=True) == cos(x) + I*sin(x) + assert exp(I*x + y).expand(complex=True) == exp(y)*cos(x) + I*sin(x)*exp(y) + + assert sin(I*x).expand(complex=True) == I * sinh(x) + assert sin(x + I*y).expand(complex=True) == sin(x)*cosh(y) + \ + I * sinh(y) * cos(x) + + assert cos(I*x).expand(complex=True) == cosh(x) + assert cos(x + I*y).expand(complex=True) == cos(x)*cosh(y) - \ + I * sinh(y) * sin(x) + + assert tan(I*x).expand(complex=True) == tanh(x) * I + assert tan(x + I*y).expand(complex=True) == ( + sin(2*x)/(cos(2*x) + cosh(2*y)) + + I*sinh(2*y)/(cos(2*x) + cosh(2*y))) + + assert sinh(I*x).expand(complex=True) == I * sin(x) + assert sinh(x + I*y).expand(complex=True) == sinh(x)*cos(y) + \ + I * sin(y) * cosh(x) + + assert cosh(I*x).expand(complex=True) == cos(x) + assert cosh(x + I*y).expand(complex=True) == cosh(x)*cos(y) + \ + I * sin(y) * sinh(x) + + assert tanh(I*x).expand(complex=True) == tan(x) * I + assert tanh(x + I*y).expand(complex=True) == ( + (sinh(x)*cosh(x) + I*cos(y)*sin(y)) / + (sinh(x)**2 + cos(y)**2)).expand() + + +def test_pythoncomplex(): + x = Symbol("x") + assert 4j*x != 4*x*I + assert 4j*x == 4.0*x*I + assert 4.1j*x != 4*x*I + + +def test_rootcomplex(): + R = Rational + assert ((+1 + I)**R(1, 2)).expand( + complex=True) == 2**R(1, 4)*cos( pi/8) + 2**R(1, 4)*sin( pi/8)*I + assert ((-1 - I)**R(1, 2)).expand( + complex=True) == 2**R(1, 4)*cos(3*pi/8) - 2**R(1, 4)*sin(3*pi/8)*I + assert (sqrt(-10)*I).as_real_imag() == (-sqrt(10), 0) + + +def test_expand_inverse(): + assert (1/(1 + I)).expand(complex=True) == (1 - I)/2 + assert ((1 + 2*I)**(-2)).expand(complex=True) == (-3 - 4*I)/25 + assert ((1 + I)**(-8)).expand(complex=True) == Rational(1, 16) + + +def test_expand_complex(): + assert ((2 + 3*I)**10).expand(complex=True) == -341525 - 145668*I + # the following two tests are to ensure the SymPy uses an efficient + # algorithm for calculating powers of complex numbers. They should execute + # in something like 0.01s. + assert ((2 + 3*I)**1000).expand(complex=True) == \ + -81079464736246615951519029367296227340216902563389546989376269312984127074385455204551402940331021387412262494620336565547972162814110386834027871072723273110439771695255662375718498785908345629702081336606863762777939617745464755635193139022811989314881997210583159045854968310911252660312523907616129080027594310008539817935736331124833163907518549408018652090650537035647520296539436440394920287688149200763245475036722326561143851304795139005599209239350981457301460233967137708519975586996623552182807311159141501424576682074392689622074945519232029999 + \ + 46938745946789557590804551905243206242164799136976022474337918748798900569942573265747576032611189047943842446167719177749107138603040963603119861476016947257034472364028585381714774667326478071264878108114128915685688115488744955550920239128462489496563930809677159214598114273887061533057125164518549173898349061972857446844052995037423459472376202251620778517659247970283904820245958198842631651569984310559418135975795868314764489884749573052997832686979294085577689571149679540256349988338406458116270429842222666345146926395233040564229555893248370000*I + assert ((2 + 3*I/4)**1000).expand(complex=True) == \ + Integer(1)*37079892761199059751745775382463070250205990218394308874593455293485167797989691280095867197640410033222367257278387021789651672598831503296531725827158233077451476545928116965316544607115843772405184272449644892857783761260737279675075819921259597776770965829089907990486964515784097181964312256560561065607846661496055417619388874421218472707497847700629822858068783288579581649321248495739224020822198695759609598745114438265083593711851665996586461937988748911532242908776883696631067311443171682974330675406616373422505939887984366289623091300746049101284856530270685577940283077888955692921951247230006346681086274961362500646889925803654263491848309446197554307105991537357310209426736453173441104334496173618419659521888945605315751089087820455852582920963561495787655250624781448951403353654348109893478206364632640344111022531861683064175862889459084900614967785405977231549003280842218501570429860550379522498497412180001/114813069527425452423283320117768198402231770208869520047764273682576626139237031385665948631650626991844596463898746277344711896086305533142593135616665318539129989145312280000688779148240044871428926990063486244781615463646388363947317026040466353970904996558162398808944629605623311649536164221970332681344168908984458505602379484807914058900934776500429002716706625830522008132236281291761267883317206598995396418127021779858404042159853183251540889433902091920554957783589672039160081957216630582755380425583726015528348786419432054508915275783882625175435528800822842770817965453762184851149029376 + \ + I*421638390580169706973991429333213477486930178424989246669892530737775352519112934278994501272111385966211392610029433824534634841747911783746811994443436271013377059560245191441549885048056920190833693041257216263519792201852046825443439142932464031501882145407459174948712992271510309541474392303461939389368955986650538525895866713074543004916049550090364398070215427272240155060576252568700906004691224321432509053286859100920489253598392100207663785243368195857086816912514025693453058403158416856847185079684216151337200057494966741268925263085619240941610301610538225414050394612058339070756009433535451561664522479191267503989904464718368605684297071150902631208673621618217106272361061676184840810762902463998065947687814692402219182668782278472952758690939877465065070481351343206840649517150634973307937551168752642148704904383991876969408056379195860410677814566225456558230131911142229028179902418223009651437985670625/1793954211366022694113801876840128100034871409513586250746316776290259783425578615401030447369541046747571819748417910583511123376348523955353017744010395602173906080395504375010762174191250701116076984219741972574712741619474818186676828531882286780795390571221287481389759837587864244524002565968286448146002639202882164150037179450123657170327105882819203167448541028601906377066191895183769810676831353109303069033234715310287563158747705988305326397404720186258671215368588625611876280581509852855552819149745718992630449787803625851701801184123166018366180137512856918294030710215034138299203584 + assert ((2 + 3*I)**-1000).expand(complex=True) == \ + Integer(1)*-81079464736246615951519029367296227340216902563389546989376269312984127074385455204551402940331021387412262494620336565547972162814110386834027871072723273110439771695255662375718498785908345629702081336606863762777939617745464755635193139022811989314881997210583159045854968310911252660312523907616129080027594310008539817935736331124833163907518549408018652090650537035647520296539436440394920287688149200763245475036722326561143851304795139005599209239350981457301460233967137708519975586996623552182807311159141501424576682074392689622074945519232029999/8777125472973511649630750050295188683351430110097915876250894978429797369155961290321829625004920141758416719066805645579710744290541337680113772670040386863849283653078324415471816788604945889094925784900885812724984087843737442111926413818245854362613018058774368703971604921858023116665586358870612944209398056562604561248859926344335598822815885851096698226775053153403320782439987679978321289537645645163767251396759519805603090332694449553371530571613352311006350058217982509738362083094920649452123351717366337410243853659113315547584871655479914439219520157174729130746351059075207407866012574386726064196992865627149566238044625779078186624347183905913357718850537058578084932880569701242598663149911276357125355850792073635533676541250531086757377369962506979378337216411188347761901006460813413505861461267545723590468627854202034450569581626648934062198718362303420281555886394558137408159453103395918783625713213314350531051312551733021627153081075080140680608080529736975658786227362251632725009435866547613598753584705455955419696609282059191031962604169242974038517575645939316377801594539335940001 - Integer(1)*46938745946789557590804551905243206242164799136976022474337918748798900569942573265747576032611189047943842446167719177749107138603040963603119861476016947257034472364028585381714774667326478071264878108114128915685688115488744955550920239128462489496563930809677159214598114273887061533057125164518549173898349061972857446844052995037423459472376202251620778517659247970283904820245958198842631651569984310559418135975795868314764489884749573052997832686979294085577689571149679540256349988338406458116270429842222666345146926395233040564229555893248370000*I/8777125472973511649630750050295188683351430110097915876250894978429797369155961290321829625004920141758416719066805645579710744290541337680113772670040386863849283653078324415471816788604945889094925784900885812724984087843737442111926413818245854362613018058774368703971604921858023116665586358870612944209398056562604561248859926344335598822815885851096698226775053153403320782439987679978321289537645645163767251396759519805603090332694449553371530571613352311006350058217982509738362083094920649452123351717366337410243853659113315547584871655479914439219520157174729130746351059075207407866012574386726064196992865627149566238044625779078186624347183905913357718850537058578084932880569701242598663149911276357125355850792073635533676541250531086757377369962506979378337216411188347761901006460813413505861461267545723590468627854202034450569581626648934062198718362303420281555886394558137408159453103395918783625713213314350531051312551733021627153081075080140680608080529736975658786227362251632725009435866547613598753584705455955419696609282059191031962604169242974038517575645939316377801594539335940001 + assert ((2 + 3*I/4)**-1000).expand(complex=True) == \ + Integer(1)*4257256305661027385394552848555894604806501409793288342610746813288539790051927148781268212212078237301273165351052934681382567968787279534591114913777456610214738290619922068269909423637926549603264174216950025398244509039145410016404821694746262142525173737175066432954496592560621330313807235750500564940782099283410261748370262433487444897446779072067625787246390824312580440138770014838135245148574339248259670887549732495841810961088930810608893772914812838358159009303794863047635845688453859317690488124382253918725010358589723156019888846606295866740117645571396817375322724096486161308083462637370825829567578309445855481578518239186117686659177284332344643124760453112513611749309168470605289172320376911472635805822082051716625171429727162039621902266619821870482519063133136820085579315127038372190224739238686708451840610064871885616258831386810233957438253532027049148030157164346719204500373766157143311767338973363806106967439378604898250533766359989107510507493549529158818602327525235240510049484816090584478644771183158342479140194633579061295740839490629457435283873180259847394582069479062820225159699506175855369539201399183443253793905149785994830358114153241481884290274629611529758663543080724574566578220908907477622643689220814376054314972190402285121776593824615083669045183404206291739005554569305329760211752815718335731118664756831942466773261465213581616104242113894521054475516019456867271362053692785300826523328020796670205463390909136593859765912483565093461468865534470710132881677639651348709376/2103100954337624833663208713697737151593634525061637972297915388685604042449504336765884978184588688426595940401280828953096857809292320006227881797146858511436638446932833617514351442216409828605662238790280753075176269765767010004889778647709740770757817960711900340755635772183674511158570690702969774966791073165467918123298694584729211212414462628433370481195120564586361368504153395406845170075275051749019600057116719726628746724489572189061061036426955163696859127711110719502594479795200686212257570291758725259007379710596548777812659422174199194837355646482046783616494013289495563083118517507178847555801163089723056310287760875135196081975602765511153122381201303871673391366630940702817360340900568748719988954847590748960761446218262344767250783946365392689256634180417145926390656439421745644011831124277463643383712803287985472471755648426749842410972650924240795946699346613614779460399530274263580007672855851663196114585312432954432654691485867618908420370875753749297487803461900447407917655296784879220450937110470920633595689721819488638484547259978337741496090602390463594556401615298457456112485536498177883358587125449801777718900375736758266215245325999241624148841915093787519330809347240990363802360596034171167818310322276373120180985148650099673289383722502488957717848531612020897298448601714154586319660314294591620415272119454982220034319689607295960162971300417552364254983071768070124456169427638371140064235083443242844616326538396503937972586505546495649094344512270582463639152160238137952390380581401171977159154009407415523525096743009110916334144716516647041176989758534635251844947906038080852185583742296318878233394998111078843229681030277039104786225656992262073797524057992347971177720807155842376332851559276430280477639539393920006008737472164850104411971830120295750221200029811143140323763349636629725073624360001 - Integer(1)*3098214262599218784594285246258841485430681674561917573155883806818465520660668045042109232930382494608383663464454841313154390741655282039877410154577448327874989496074260116195788919037407420625081798124301494353693248757853222257918294662198297114746822817460991242508743651430439120439020484502408313310689912381846149597061657483084652685283853595100434135149479564507015504022249330340259111426799121454516345905101620532787348293877485702600390665276070250119465888154331218827342488849948540687659846652377277250614246402784754153678374932540789808703029043827352976139228402417432199779415751301480406673762521987999573209628597459357964214510139892316208670927074795773830798600837815329291912002136924506221066071242281626618211060464126372574400100990746934953437169840312584285942093951405864225230033279614235191326102697164613004299868695519642598882914862568516635347204441042798206770888274175592401790040170576311989738272102077819127459014286741435419468254146418098278519775722104890854275995510700298782146199325790002255362719776098816136732897323406228294203133323296591166026338391813696715894870956511298793595675308998014158717167429941371979636895553724830981754579086664608880698350866487717403917070872269853194118364230971216854931998642990452908852258008095741042117326241406479532880476938937997238098399302185675832474590293188864060116934035867037219176916416481757918864533515526389079998129329045569609325290897577497835388451456680707076072624629697883854217331728051953671643278797380171857920000*I/2103100954337624833663208713697737151593634525061637972297915388685604042449504336765884978184588688426595940401280828953096857809292320006227881797146858511436638446932833617514351442216409828605662238790280753075176269765767010004889778647709740770757817960711900340755635772183674511158570690702969774966791073165467918123298694584729211212414462628433370481195120564586361368504153395406845170075275051749019600057116719726628746724489572189061061036426955163696859127711110719502594479795200686212257570291758725259007379710596548777812659422174199194837355646482046783616494013289495563083118517507178847555801163089723056310287760875135196081975602765511153122381201303871673391366630940702817360340900568748719988954847590748960761446218262344767250783946365392689256634180417145926390656439421745644011831124277463643383712803287985472471755648426749842410972650924240795946699346613614779460399530274263580007672855851663196114585312432954432654691485867618908420370875753749297487803461900447407917655296784879220450937110470920633595689721819488638484547259978337741496090602390463594556401615298457456112485536498177883358587125449801777718900375736758266215245325999241624148841915093787519330809347240990363802360596034171167818310322276373120180985148650099673289383722502488957717848531612020897298448601714154586319660314294591620415272119454982220034319689607295960162971300417552364254983071768070124456169427638371140064235083443242844616326538396503937972586505546495649094344512270582463639152160238137952390380581401171977159154009407415523525096743009110916334144716516647041176989758534635251844947906038080852185583742296318878233394998111078843229681030277039104786225656992262073797524057992347971177720807155842376332851559276430280477639539393920006008737472164850104411971830120295750221200029811143140323763349636629725073624360001 + + a = Symbol('a', real=True) + b = Symbol('b', real=True) + assert exp(a*(2 + I*b)).expand(complex=True) == \ + I*exp(2*a)*sin(a*b) + exp(2*a)*cos(a*b) + + +def test_expand(): + f = (16 - 2*sqrt(29))**2 + assert f.expand() == 372 - 64*sqrt(29) + f = (Integer(1)/2 + I/2)**10 + assert f.expand() == I/32 + f = (Integer(1)/2 + I)**10 + assert f.expand() == Integer(237)/1024 - 779*I/256 + + +def test_re_im1652(): + x = Symbol('x') + assert re(x) == re(conjugate(x)) + assert im(x) == - im(conjugate(x)) + assert im(x)*re(conjugate(x)) + im(conjugate(x)) * re(x) == 0 + + +def test_issue_5084(): + x = Symbol('x') + assert ((x + x*I)/(1 + I)).as_real_imag() == (re((x + I*x)/(1 + I) + ), im((x + I*x)/(1 + I))) + + +def test_issue_5236(): + assert (cos(1 + I)**3).as_real_imag() == (-3*sin(1)**2*sinh(1)**2*cos(1)*cosh(1) + + cos(1)**3*cosh(1)**3, -3*cos(1)**2*cosh(1)**2*sin(1)*sinh(1) + sin(1)**3*sinh(1)**3) + + +def test_real_imag(): + x, y, z = symbols('x, y, z') + X, Y, Z = symbols('X, Y, Z', commutative=False) + a = Symbol('a', real=True) + assert (2*a*x).as_real_imag() == (2*a*re(x), 2*a*im(x)) + + # issue 5395: + assert (x*x.conjugate()).as_real_imag() == (Abs(x)**2, 0) + assert im(x*x.conjugate()) == 0 + assert im(x*y.conjugate()*z*y) == im(x*z)*Abs(y)**2 + assert im(x*y.conjugate()*x*y) == im(x**2)*Abs(y)**2 + assert im(Z*y.conjugate()*X*y) == im(Z*X)*Abs(y)**2 + assert im(X*X.conjugate()) == im(X*X.conjugate(), evaluate=False) + assert (sin(x)*sin(x).conjugate()).as_real_imag() == \ + (Abs(sin(x))**2, 0) + + # issue 6573: + assert (x**2).as_real_imag() == (re(x)**2 - im(x)**2, 2*re(x)*im(x)) + + # issue 6428: + r = Symbol('r', real=True) + i = Symbol('i', imaginary=True) + assert (i*r*x).as_real_imag() == (I*i*r*im(x), -I*i*r*re(x)) + assert (i*r*x*(y + 2)).as_real_imag() == ( + I*i*r*(re(y) + 2)*im(x) + I*i*r*re(x)*im(y), + -I*i*r*(re(y) + 2)*re(x) + I*i*r*im(x)*im(y)) + + # issue 7106: + assert ((1 + I)/(1 - I)).as_real_imag() == (0, 1) + assert ((1 + 2*I)*(1 + 3*I)).as_real_imag() == (-5, 5) + + +def test_pow_issue_1724(): + e = ((S.NegativeOne)**(S.One/3)) + assert e.conjugate().n() == e.n().conjugate() + e = S('-2/3 - (-29/54 + sqrt(93)/18)**(1/3) - 1/(9*(-29/54 + sqrt(93)/18)**(1/3))') + assert e.conjugate().n() == e.n().conjugate() + e = 2**I + assert e.conjugate().n() == e.n().conjugate() + + +def test_issue_5429(): + assert sqrt(I).conjugate() != sqrt(I) + +def test_issue_4124(): + from sympy.core.numbers import oo + assert expand_complex(I*oo) == oo*I + +def test_issue_11518(): + x = Symbol("x", real=True) + y = Symbol("y", real=True) + r = sqrt(x**2 + y**2) + assert conjugate(r) == r + s = abs(x + I * y) + assert conjugate(s) == r diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_constructor_postprocessor.py b/lib/python3.11/site-packages/sympy/core/tests/test_constructor_postprocessor.py new file mode 100644 index 0000000000000000000000000000000000000000..c199e24eddf8ef7c2a14e38d1ad2dc95e4acc0cc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_constructor_postprocessor.py @@ -0,0 +1,87 @@ +from sympy.core.basic import Basic +from sympy.core.mul import Mul +from sympy.core.symbol import (Symbol, symbols) + +from sympy.testing.pytest import XFAIL + +class SymbolInMulOnce(Symbol): + # Test class for a symbol that can only appear once in a `Mul` expression. + pass + + +Basic._constructor_postprocessor_mapping[SymbolInMulOnce] = { + "Mul": [lambda x: x], + "Pow": [lambda x: x.base if isinstance(x.base, SymbolInMulOnce) else x], + "Add": [lambda x: x], +} + + +def _postprocess_SymbolRemovesOtherSymbols(expr): + args = tuple(i for i in expr.args if not isinstance(i, Symbol) or isinstance(i, SymbolRemovesOtherSymbols)) + if args == expr.args: + return expr + return Mul.fromiter(args) + + +class SymbolRemovesOtherSymbols(Symbol): + # Test class for a symbol that removes other symbols in `Mul`. + pass + +Basic._constructor_postprocessor_mapping[SymbolRemovesOtherSymbols] = { + "Mul": [_postprocess_SymbolRemovesOtherSymbols], +} + +class SubclassSymbolInMulOnce(SymbolInMulOnce): + pass + +class SubclassSymbolRemovesOtherSymbols(SymbolRemovesOtherSymbols): + pass + + +def test_constructor_postprocessors1(): + x = SymbolInMulOnce("x") + y = SymbolInMulOnce("y") + assert isinstance(3*x, Mul) + assert (3*x).args == (3, x) + assert x*x == x + assert 3*x*x == 3*x + assert 2*x*x + x == 3*x + assert x**3*y*y == x*y + assert x**5 + y*x**3 == x + x*y + + w = SymbolRemovesOtherSymbols("w") + assert x*w == w + assert (3*w).args == (3, w) + assert set((w + x).args) == {x, w} + +def test_constructor_postprocessors2(): + x = SubclassSymbolInMulOnce("x") + y = SubclassSymbolInMulOnce("y") + assert isinstance(3*x, Mul) + assert (3*x).args == (3, x) + assert x*x == x + assert 3*x*x == 3*x + assert 2*x*x + x == 3*x + assert x**3*y*y == x*y + assert x**5 + y*x**3 == x + x*y + + w = SubclassSymbolRemovesOtherSymbols("w") + assert x*w == w + assert (3*w).args == (3, w) + assert set((w + x).args) == {x, w} + + +@XFAIL +def test_subexpression_postprocessors(): + # The postprocessors used to work with subexpressions, but the + # functionality was removed. See #15948. + a = symbols("a") + x = SymbolInMulOnce("x") + w = SymbolRemovesOtherSymbols("w") + assert 3*a*w**2 == 3*w**2 + assert 3*a*x**3*w**2 == 3*w**2 + + x = SubclassSymbolInMulOnce("x") + w = SubclassSymbolRemovesOtherSymbols("w") + assert 3*a*w**2 == 3*w**2 + assert 3*a*x**3*w**2 == 3*w**2 diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_containers.py b/lib/python3.11/site-packages/sympy/core/tests/test_containers.py new file mode 100644 index 0000000000000000000000000000000000000000..23357b9f667fffc82d93b2b1adb42b495114c67e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_containers.py @@ -0,0 +1,217 @@ +from collections import defaultdict + +from sympy.core.basic import Basic +from sympy.core.containers import (Dict, Tuple) +from sympy.core.numbers import Integer +from sympy.core.kind import NumberKind +from sympy.matrices.kind import MatrixKind +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.core.sympify import sympify +from sympy.matrices.dense import Matrix +from sympy.sets.sets import FiniteSet +from sympy.core.containers import tuple_wrapper, TupleKind +from sympy.core.expr import unchanged +from sympy.core.function import Function, Lambda +from sympy.core.relational import Eq +from sympy.testing.pytest import raises +from sympy.utilities.iterables import is_sequence, iterable + +from sympy.abc import x, y + + +def test_Tuple(): + t = (1, 2, 3, 4) + st = Tuple(*t) + assert set(sympify(t)) == set(st) + assert len(t) == len(st) + assert set(sympify(t[:2])) == set(st[:2]) + assert isinstance(st[:], Tuple) + assert st == Tuple(1, 2, 3, 4) + assert st.func(*st.args) == st + p, q, r, s = symbols('p q r s') + t2 = (p, q, r, s) + st2 = Tuple(*t2) + assert st2.atoms() == set(t2) + assert st == st2.subs({p: 1, q: 2, r: 3, s: 4}) + # issue 5505 + assert all(isinstance(arg, Basic) for arg in st.args) + assert Tuple(p, 1).subs(p, 0) == Tuple(0, 1) + assert Tuple(p, Tuple(p, 1)).subs(p, 0) == Tuple(0, Tuple(0, 1)) + + assert Tuple(t2) == Tuple(Tuple(*t2)) + assert Tuple.fromiter(t2) == Tuple(*t2) + assert Tuple.fromiter(x for x in range(4)) == Tuple(0, 1, 2, 3) + assert st2.fromiter(st2.args) == st2 + + +def test_Tuple_contains(): + t1, t2 = Tuple(1), Tuple(2) + assert t1 in Tuple(1, 2, 3, t1, Tuple(t2)) + assert t2 not in Tuple(1, 2, 3, t1, Tuple(t2)) + + +def test_Tuple_concatenation(): + assert Tuple(1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4) + assert (1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4) + assert Tuple(1, 2) + (3, 4) == Tuple(1, 2, 3, 4) + raises(TypeError, lambda: Tuple(1, 2) + 3) + raises(TypeError, lambda: 1 + Tuple(2, 3)) + + #the Tuple case in __radd__ is only reached when a subclass is involved + class Tuple2(Tuple): + def __radd__(self, other): + return Tuple.__radd__(self, other + other) + assert Tuple(1, 2) + Tuple2(3, 4) == Tuple(1, 2, 1, 2, 3, 4) + assert Tuple2(1, 2) + Tuple(3, 4) == Tuple(1, 2, 3, 4) + + +def test_Tuple_equality(): + assert not isinstance(Tuple(1, 2), tuple) + assert (Tuple(1, 2) == (1, 2)) is True + assert (Tuple(1, 2) != (1, 2)) is False + assert (Tuple(1, 2) == (1, 3)) is False + assert (Tuple(1, 2) != (1, 3)) is True + assert (Tuple(1, 2) == Tuple(1, 2)) is True + assert (Tuple(1, 2) != Tuple(1, 2)) is False + assert (Tuple(1, 2) == Tuple(1, 3)) is False + assert (Tuple(1, 2) != Tuple(1, 3)) is True + + +def test_Tuple_Eq(): + assert Eq(Tuple(), Tuple()) is S.true + assert Eq(Tuple(1), 1) is S.false + assert Eq(Tuple(1, 2), Tuple(1)) is S.false + assert Eq(Tuple(1), Tuple(1)) is S.true + assert Eq(Tuple(1, 2), Tuple(1, 3)) is S.false + assert Eq(Tuple(1, 2), Tuple(1, 2)) is S.true + assert unchanged(Eq, Tuple(1, x), Tuple(1, 2)) + assert Eq(Tuple(1, x), Tuple(1, 2)).subs(x, 2) is S.true + assert unchanged(Eq, Tuple(1, 2), x) + f = Function('f') + assert unchanged(Eq, Tuple(1), f(x)) + assert Eq(Tuple(1), f(x)).subs(x, 1).subs(f, Lambda(y, (y,))) is S.true + + +def test_Tuple_comparision(): + assert (Tuple(1, 3) >= Tuple(-10, 30)) is S.true + assert (Tuple(1, 3) <= Tuple(-10, 30)) is S.false + assert (Tuple(1, 3) >= Tuple(1, 3)) is S.true + assert (Tuple(1, 3) <= Tuple(1, 3)) is S.true + + +def test_Tuple_tuple_count(): + assert Tuple(0, 1, 2, 3).tuple_count(4) == 0 + assert Tuple(0, 4, 1, 2, 3).tuple_count(4) == 1 + assert Tuple(0, 4, 1, 4, 2, 3).tuple_count(4) == 2 + assert Tuple(0, 4, 1, 4, 2, 4, 3).tuple_count(4) == 3 + + +def test_Tuple_index(): + assert Tuple(4, 0, 1, 2, 3).index(4) == 0 + assert Tuple(0, 4, 1, 2, 3).index(4) == 1 + assert Tuple(0, 1, 4, 2, 3).index(4) == 2 + assert Tuple(0, 1, 2, 4, 3).index(4) == 3 + assert Tuple(0, 1, 2, 3, 4).index(4) == 4 + + raises(ValueError, lambda: Tuple(0, 1, 2, 3).index(4)) + raises(ValueError, lambda: Tuple(4, 0, 1, 2, 3).index(4, 1)) + raises(ValueError, lambda: Tuple(0, 1, 2, 3, 4).index(4, 1, 4)) + + +def test_Tuple_mul(): + assert Tuple(1, 2, 3)*2 == Tuple(1, 2, 3, 1, 2, 3) + assert 2*Tuple(1, 2, 3) == Tuple(1, 2, 3, 1, 2, 3) + assert Tuple(1, 2, 3)*Integer(2) == Tuple(1, 2, 3, 1, 2, 3) + assert Integer(2)*Tuple(1, 2, 3) == Tuple(1, 2, 3, 1, 2, 3) + + raises(TypeError, lambda: Tuple(1, 2, 3)*S.Half) + raises(TypeError, lambda: S.Half*Tuple(1, 2, 3)) + + +def test_tuple_wrapper(): + + @tuple_wrapper + def wrap_tuples_and_return(*t): + return t + + p = symbols('p') + assert wrap_tuples_and_return(p, 1) == (p, 1) + assert wrap_tuples_and_return((p, 1)) == (Tuple(p, 1),) + assert wrap_tuples_and_return(1, (p, 2), 3) == (1, Tuple(p, 2), 3) + + +def test_iterable_is_sequence(): + ordered = [[], (), Tuple(), Matrix([[]])] + unordered = [set()] + not_sympy_iterable = [{}, '', ''] + assert all(is_sequence(i) for i in ordered) + assert all(not is_sequence(i) for i in unordered) + assert all(iterable(i) for i in ordered + unordered) + assert all(not iterable(i) for i in not_sympy_iterable) + assert all(iterable(i, exclude=None) for i in not_sympy_iterable) + + +def test_TupleKind(): + kind = TupleKind(NumberKind, MatrixKind(NumberKind)) + assert Tuple(1, Matrix([1, 2])).kind is kind + assert Tuple(1, 2).kind is TupleKind(NumberKind, NumberKind) + assert Tuple(1, 2).kind.element_kind == (NumberKind, NumberKind) + + +def test_Dict(): + x, y, z = symbols('x y z') + d = Dict({x: 1, y: 2, z: 3}) + assert d[x] == 1 + assert d[y] == 2 + raises(KeyError, lambda: d[2]) + raises(KeyError, lambda: d['2']) + assert len(d) == 3 + assert set(d.keys()) == {x, y, z} + assert set(d.values()) == {S.One, S(2), S(3)} + assert d.get(5, 'default') == 'default' + assert d.get('5', 'default') == 'default' + assert x in d and z in d and 5 not in d and '5' not in d + assert d.has(x) and d.has(1) # SymPy Basic .has method + + # Test input types + # input - a Python dict + # input - items as args - SymPy style + assert (Dict({x: 1, y: 2, z: 3}) == + Dict((x, 1), (y, 2), (z, 3))) + + raises(TypeError, lambda: Dict(((x, 1), (y, 2), (z, 3)))) + with raises(NotImplementedError): + d[5] = 6 # assert immutability + + assert set( + d.items()) == {Tuple(x, S.One), Tuple(y, S(2)), Tuple(z, S(3))} + assert set(d) == {x, y, z} + assert str(d) == '{x: 1, y: 2, z: 3}' + assert d.__repr__() == '{x: 1, y: 2, z: 3}' + + # Test creating a Dict from a Dict. + d = Dict({x: 1, y: 2, z: 3}) + assert d == Dict(d) + + # Test for supporting defaultdict + d = defaultdict(int) + assert d[x] == 0 + assert d[y] == 0 + assert d[z] == 0 + assert Dict(d) + d = Dict(d) + assert len(d) == 3 + assert set(d.keys()) == {x, y, z} + assert set(d.values()) == {S.Zero, S.Zero, S.Zero} + + +def test_issue_5788(): + args = [(1, 2), (2, 1)] + for o in [Dict, Tuple, FiniteSet]: + # __eq__ and arg handling + if o != Tuple: + assert o(*args) == o(*reversed(args)) + pair = [o(*args), o(*reversed(args))] + assert sorted(pair) == sorted(pair) + assert set(o(*args)) # doesn't fail diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_count_ops.py b/lib/python3.11/site-packages/sympy/core/tests/test_count_ops.py new file mode 100644 index 0000000000000000000000000000000000000000..bc95004ef5ba4421927289a049a9197d208c30d0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_count_ops.py @@ -0,0 +1,155 @@ +from sympy.concrete.summations import Sum +from sympy.core.basic import Basic +from sympy.core.function import (Derivative, Function, count_ops) +from sympy.core.numbers import (I, Rational, pi) +from sympy.core.relational import (Eq, Rel) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.integrals.integrals import Integral +from sympy.logic.boolalg import (And, Equivalent, ITE, Implies, Nand, + Nor, Not, Or, Xor) +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.core.containers import Tuple + +x, y, z = symbols('x,y,z') +a, b, c = symbols('a,b,c') + +def test_count_ops_non_visual(): + def count(val): + return count_ops(val, visual=False) + assert count(x) == 0 + assert count(x) is not S.Zero + assert count(x + y) == 1 + assert count(x + y) is not S.One + assert count(x + y*x + 2*y) == 4 + assert count({x + y: x}) == 1 + assert count({x + y: S(2) + x}) is not S.One + assert count(x < y) == 1 + assert count(Or(x,y)) == 1 + assert count(And(x,y)) == 1 + assert count(Not(x)) == 1 + assert count(Nor(x,y)) == 2 + assert count(Nand(x,y)) == 2 + assert count(Xor(x,y)) == 1 + assert count(Implies(x,y)) == 1 + assert count(Equivalent(x,y)) == 1 + assert count(ITE(x,y,z)) == 1 + assert count(ITE(True,x,y)) == 0 + + +def test_count_ops_visual(): + ADD, MUL, POW, SIN, COS, EXP, AND, D, G, M = symbols( + 'Add Mul Pow sin cos exp And Derivative Integral Sum'.upper()) + DIV, SUB, NEG = symbols('DIV SUB NEG') + LT, LE, GT, GE, EQ, NE = symbols('LT LE GT GE EQ NE') + NOT, OR, AND, XOR, IMPLIES, EQUIVALENT, _ITE, BASIC, TUPLE = symbols( + 'Not Or And Xor Implies Equivalent ITE Basic Tuple'.upper()) + + def count(val): + return count_ops(val, visual=True) + + assert count(7) is S.Zero + assert count(S(7)) is S.Zero + assert count(-1) == NEG + assert count(-2) == NEG + assert count(S(2)/3) == DIV + assert count(Rational(2, 3)) == DIV + assert count(pi/3) == DIV + assert count(-pi/3) == DIV + NEG + assert count(I - 1) == SUB + assert count(1 - I) == SUB + assert count(1 - 2*I) == SUB + MUL + + assert count(x) is S.Zero + assert count(-x) == NEG + assert count(-2*x/3) == NEG + DIV + MUL + assert count(Rational(-2, 3)*x) == NEG + DIV + MUL + assert count(1/x) == DIV + assert count(1/(x*y)) == DIV + MUL + assert count(-1/x) == NEG + DIV + assert count(-2/x) == NEG + DIV + assert count(x/y) == DIV + assert count(-x/y) == NEG + DIV + + assert count(x**2) == POW + assert count(-x**2) == POW + NEG + assert count(-2*x**2) == POW + MUL + NEG + + assert count(x + pi/3) == ADD + DIV + assert count(x + S.One/3) == ADD + DIV + assert count(x + Rational(1, 3)) == ADD + DIV + assert count(x + y) == ADD + assert count(x - y) == SUB + assert count(y - x) == SUB + assert count(-1/(x - y)) == DIV + NEG + SUB + assert count(-1/(y - x)) == DIV + NEG + SUB + assert count(1 + x**y) == ADD + POW + assert count(1 + x + y) == 2*ADD + assert count(1 + x + y + z) == 3*ADD + assert count(1 + x**y + 2*x*y + y**2) == 3*ADD + 2*POW + 2*MUL + assert count(2*z + y + x + 1) == 3*ADD + MUL + assert count(2*z + y**17 + x + 1) == 3*ADD + MUL + POW + assert count(2*z + y**17 + x + sin(x)) == 3*ADD + POW + MUL + SIN + assert count(2*z + y**17 + x + sin(x**2)) == 3*ADD + MUL + 2*POW + SIN + assert count(2*z + y**17 + x + sin( + x**2) + exp(cos(x))) == 4*ADD + MUL + 2*POW + EXP + COS + SIN + + assert count(Derivative(x, x)) == D + assert count(Integral(x, x) + 2*x/(1 + x)) == G + DIV + MUL + 2*ADD + assert count(Sum(x, (x, 1, x + 1)) + 2*x/(1 + x)) == M + DIV + MUL + 3*ADD + assert count(Basic()) is S.Zero + + assert count({x + 1: sin(x)}) == ADD + SIN + assert count([x + 1, sin(x) + y, None]) == ADD + SIN + ADD + assert count({x + 1: sin(x), y: cos(x) + 1}) == SIN + COS + 2*ADD + assert count({}) is S.Zero + assert count([x + 1, sin(x)*y, None]) == SIN + ADD + MUL + assert count([]) is S.Zero + + assert count(Basic()) == 0 + assert count(Basic(Basic(),Basic(x,x+y))) == ADD + 2*BASIC + assert count(Basic(x, x + y)) == ADD + BASIC + assert [count(Rel(x, y, op)) for op in '< <= > >= == <> !='.split() + ] == [LT, LE, GT, GE, EQ, NE, NE] + assert count(Or(x, y)) == OR + assert count(And(x, y)) == AND + assert count(Or(x, Or(y, And(z, a)))) == AND + OR + assert count(Nor(x, y)) == NOT + OR + assert count(Nand(x, y)) == NOT + AND + assert count(Xor(x, y)) == XOR + assert count(Implies(x, y)) == IMPLIES + assert count(Equivalent(x, y)) == EQUIVALENT + assert count(ITE(x, y, z)) == _ITE + assert count([Or(x, y), And(x, y), Basic(x + y)] + ) == ADD + AND + BASIC + OR + + assert count(Basic(Tuple(x))) == BASIC + TUPLE + #It checks that TUPLE is counted as an operation. + + assert count(Eq(x + y, S(2))) == ADD + EQ + + +def test_issue_9324(): + def count(val): + return count_ops(val, visual=False) + + M = MatrixSymbol('M', 10, 10) + assert count(M[0, 0]) == 0 + assert count(2 * M[0, 0] + M[5, 7]) == 2 + P = MatrixSymbol('P', 3, 3) + Q = MatrixSymbol('Q', 3, 3) + assert count(P + Q) == 1 + m = Symbol('m', integer=True) + n = Symbol('n', integer=True) + M = MatrixSymbol('M', m + n, m * m) + assert count(M[0, 1]) == 2 + + +def test_issue_21532(): + f = Function('f') + g = Function('g') + FUNC_F, FUNC_G = symbols('FUNC_F, FUNC_G') + assert f(x).count_ops(visual=True) == FUNC_F + assert g(x).count_ops(visual=True) == FUNC_G diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_diff.py b/lib/python3.11/site-packages/sympy/core/tests/test_diff.py new file mode 100644 index 0000000000000000000000000000000000000000..effc9cd91d2e7b6f8f8e5fd04bb667ed71c0ffaf --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_diff.py @@ -0,0 +1,160 @@ +from sympy.concrete.summations import Sum +from sympy.core.expr import Expr +from sympy.core.function import (Derivative, Function, diff, Subs) +from sympy.core.numbers import (I, Rational, pi) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import (im, re) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import Max +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (cos, cot, sin, tan) +from sympy.tensor.array.ndim_array import NDimArray +from sympy.testing.pytest import raises +from sympy.abc import a, b, c, x, y, z + +def test_diff(): + assert Rational(1, 3).diff(x) is S.Zero + assert I.diff(x) is S.Zero + assert pi.diff(x) is S.Zero + assert x.diff(x, 0) == x + assert (x**2).diff(x, 2, x) == 0 + assert (x**2).diff((x, 2), x) == 0 + assert (x**2).diff((x, 1), x) == 2 + assert (x**2).diff((x, 1), (x, 1)) == 2 + assert (x**2).diff((x, 2)) == 2 + assert (x**2).diff(x, y, 0) == 2*x + assert (x**2).diff(x, (y, 0)) == 2*x + assert (x**2).diff(x, y) == 0 + raises(ValueError, lambda: x.diff(1, x)) + + p = Rational(5) + e = a*b + b**p + assert e.diff(a) == b + assert e.diff(b) == a + 5*b**4 + assert e.diff(b).diff(a) == Rational(1) + e = a*(b + c) + assert e.diff(a) == b + c + assert e.diff(b) == a + assert e.diff(b).diff(a) == Rational(1) + e = c**p + assert e.diff(c, 6) == Rational(0) + assert e.diff(c, 5) == Rational(120) + e = c**Rational(2) + assert e.diff(c) == 2*c + e = a*b*c + assert e.diff(c) == a*b + + +def test_diff2(): + n3 = Rational(3) + n2 = Rational(2) + n6 = Rational(6) + + e = n3*(-n2 + x**n2)*cos(x) + x*(-n6 + x**n2)*sin(x) + assert e == 3*(-2 + x**2)*cos(x) + x*(-6 + x**2)*sin(x) + assert e.diff(x).expand() == x**3*cos(x) + + e = (x + 1)**3 + assert e.diff(x) == 3*(x + 1)**2 + e = x*(x + 1)**3 + assert e.diff(x) == (x + 1)**3 + 3*x*(x + 1)**2 + e = 2*exp(x*x)*x + assert e.diff(x) == 2*exp(x**2) + 4*x**2*exp(x**2) + + +def test_diff3(): + p = Rational(5) + e = a*b + sin(b**p) + assert e == a*b + sin(b**5) + assert e.diff(a) == b + assert e.diff(b) == a + 5*b**4*cos(b**5) + e = tan(c) + assert e == tan(c) + assert e.diff(c) in [cos(c)**(-2), 1 + sin(c)**2/cos(c)**2, 1 + tan(c)**2] + e = c*log(c) - c + assert e == -c + c*log(c) + assert e.diff(c) == log(c) + e = log(sin(c)) + assert e == log(sin(c)) + assert e.diff(c) in [sin(c)**(-1)*cos(c), cot(c)] + e = (Rational(2)**a/log(Rational(2))) + assert e == 2**a*log(Rational(2))**(-1) + assert e.diff(a) == 2**a + + +def test_diff_no_eval_derivative(): + class My(Expr): + def __new__(cls, x): + return Expr.__new__(cls, x) + + # My doesn't have its own _eval_derivative method + assert My(x).diff(x).func is Derivative + assert My(x).diff(x, 3).func is Derivative + assert re(x).diff(x, 2) == Derivative(re(x), (x, 2)) # issue 15518 + assert diff(NDimArray([re(x), im(x)]), (x, 2)) == NDimArray( + [Derivative(re(x), (x, 2)), Derivative(im(x), (x, 2))]) + # it doesn't have y so it shouldn't need a method for this case + assert My(x).diff(y) == 0 + + +def test_speed(): + # this should return in 0.0s. If it takes forever, it's wrong. + assert x.diff(x, 10**8) == 0 + + +def test_deriv_noncommutative(): + A = Symbol("A", commutative=False) + f = Function("f") + assert A*f(x)*A == f(x)*A**2 + assert A*f(x).diff(x)*A == f(x).diff(x) * A**2 + + +def test_diff_nth_derivative(): + f = Function("f") + n = Symbol("n", integer=True) + + expr = diff(sin(x), (x, n)) + expr2 = diff(f(x), (x, 2)) + expr3 = diff(f(x), (x, n)) + + assert expr.subs(sin(x), cos(-x)) == Derivative(cos(-x), (x, n)) + assert expr.subs(n, 1).doit() == cos(x) + assert expr.subs(n, 2).doit() == -sin(x) + + assert expr2.subs(Derivative(f(x), x), y) == Derivative(y, x) + # Currently not supported (cannot determine if `n > 1`): + #assert expr3.subs(Derivative(f(x), x), y) == Derivative(y, (x, n-1)) + assert expr3 == Derivative(f(x), (x, n)) + + assert diff(x, (x, n)) == Piecewise((x, Eq(n, 0)), (1, Eq(n, 1)), (0, True)) + assert diff(2*x, (x, n)).dummy_eq( + Sum(Piecewise((2*x*factorial(n)/(factorial(y)*factorial(-y + n)), + Eq(y, 0) & Eq(Max(0, -y + n), 0)), + (2*factorial(n)/(factorial(y)*factorial(-y + n)), Eq(y, 0) & Eq(Max(0, + -y + n), 1)), (0, True)), (y, 0, n))) + # TODO: assert diff(x**2, (x, n)) == x**(2-n)*ff(2, n) + exprm = x*sin(x) + mul_diff = diff(exprm, (x, n)) + assert isinstance(mul_diff, Sum) + for i in range(5): + assert mul_diff.subs(n, i).doit() == exprm.diff((x, i)).expand() + + exprm2 = 2*y*x*sin(x)*cos(x)*log(x)*exp(x) + dex = exprm2.diff((x, n)) + assert isinstance(dex, Sum) + for i in range(7): + assert dex.subs(n, i).doit().expand() == \ + exprm2.diff((x, i)).expand() + + assert (cos(x)*sin(y)).diff([[x, y, z]]) == NDimArray([ + -sin(x)*sin(y), cos(x)*cos(y), 0]) + + +def test_issue_16160(): + assert Derivative(x**3, (x, x)).subs(x, 2) == Subs( + Derivative(x**3, (x, 2)), x, 2) + assert Derivative(1 + x**3, (x, x)).subs(x, 0 + ) == Derivative(1 + y**3, (y, 0)).subs(y, 0) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_equal.py b/lib/python3.11/site-packages/sympy/core/tests/test_equal.py new file mode 100644 index 0000000000000000000000000000000000000000..82213b757cda5fbd80310e387bdf00cc1c9c25fe --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_equal.py @@ -0,0 +1,89 @@ +from sympy.core.numbers import Rational +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.elementary.exponential import exp + + +def test_equal(): + b = Symbol("b") + a = Symbol("a") + e1 = a + b + e2 = 2*a*b + e3 = a**3*b**2 + e4 = a*b + b*a + assert not e1 == e2 + assert not e1 == e2 + assert e1 != e2 + assert e2 == e4 + assert e2 != e3 + assert not e2 == e3 + + x = Symbol("x") + e1 = exp(x + 1/x) + y = Symbol("x") + e2 = exp(y + 1/y) + assert e1 == e2 + assert not e1 != e2 + y = Symbol("y") + e2 = exp(y + 1/y) + assert not e1 == e2 + assert e1 != e2 + + e5 = Rational(3) + 2*x - x - x + assert e5 == 3 + assert 3 == e5 + assert e5 != 4 + assert 4 != e5 + assert e5 != 3 + x + assert 3 + x != e5 + + +def test_expevalbug(): + x = Symbol("x") + e1 = exp(1*x) + e3 = exp(x) + assert e1 == e3 + + +def test_cmp_bug1(): + class T: + pass + + t = T() + x = Symbol("x") + + assert not (x == t) + assert (x != t) + + +def test_cmp_bug2(): + class T: + pass + + t = T() + + assert not (Symbol == t) + assert (Symbol != t) + + +def test_cmp_issue_4357(): + """ Check that Basic subclasses can be compared with sympifiable objects. + + https://github.com/sympy/sympy/issues/4357 + """ + assert not (Symbol == 1) + assert (Symbol != 1) + assert not (Symbol == 'x') + assert (Symbol != 'x') + + +def test_dummy_eq(): + x = Symbol('x') + y = Symbol('y') + + u = Dummy('u') + + assert (u**2 + 1).dummy_eq(x**2 + 1) is True + assert ((u**2 + 1) == (x**2 + 1)) is False + + assert (u**2 + y).dummy_eq(x**2 + y, x) is True + assert (u**2 + y).dummy_eq(x**2 + y, y) is False diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_eval.py b/lib/python3.11/site-packages/sympy/core/tests/test_eval.py new file mode 100644 index 0000000000000000000000000000000000000000..9c1633f77b50483afee21c6d9fca232b1279d2b9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_eval.py @@ -0,0 +1,95 @@ +from sympy.core.function import Function +from sympy.core.numbers import (I, Rational) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, tan) +from sympy.testing.pytest import XFAIL + + +def test_add_eval(): + a = Symbol("a") + b = Symbol("b") + c = Rational(1) + p = Rational(5) + assert a*b + c + p == a*b + 6 + assert c + a + p == a + 6 + assert c + a - p == a + (-4) + assert a + a == 2*a + assert a + p + a == 2*a + 5 + assert c + p == Rational(6) + assert b + a - b == a + + +def test_addmul_eval(): + a = Symbol("a") + b = Symbol("b") + c = Rational(1) + p = Rational(5) + assert c + a + b*c + a - p == 2*a + b + (-4) + assert a*2 + p + a == a*2 + 5 + a + assert a*2 + p + a == 3*a + 5 + assert a*2 + a == 3*a + + +def test_pow_eval(): + # XXX Pow does not fully support conversion of negative numbers + # to their complex equivalent + + assert sqrt(-1) == I + + assert sqrt(-4) == 2*I + assert sqrt( 4) == 2 + assert (8)**Rational(1, 3) == 2 + assert (-8)**Rational(1, 3) == 2*((-1)**Rational(1, 3)) + + assert sqrt(-2) == I*sqrt(2) + assert (-1)**Rational(1, 3) != I + assert (-10)**Rational(1, 3) != I*((10)**Rational(1, 3)) + assert (-2)**Rational(1, 4) != (2)**Rational(1, 4) + + assert 64**Rational(1, 3) == 4 + assert 64**Rational(2, 3) == 16 + assert 24/sqrt(64) == 3 + assert (-27)**Rational(1, 3) == 3*(-1)**Rational(1, 3) + + assert (cos(2) / tan(2))**2 == (cos(2) / tan(2))**2 + + +@XFAIL +def test_pow_eval_X1(): + assert (-1)**Rational(1, 3) == S.Half + S.Half*I*sqrt(3) + + +def test_mulpow_eval(): + x = Symbol('x') + assert sqrt(50)/(sqrt(2)*x) == 5/x + assert sqrt(27)/sqrt(3) == 3 + + +def test_evalpow_bug(): + x = Symbol("x") + assert 1/(1/x) == x + assert 1/(-1/x) == -x + + +def test_symbol_expand(): + x = Symbol('x') + y = Symbol('y') + + f = x**4*y**4 + assert f == x**4*y**4 + assert f == f.expand() + + g = (x*y)**4 + assert g == f + assert g.expand() == f + assert g.expand() == g.expand().expand() + + +def test_function(): + f, l = map(Function, 'fl') + x = Symbol('x') + assert exp(l(x))*l(x)/exp(l(x)) == l(x) + assert exp(f(x))*f(x)/exp(f(x)) == f(x) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_evalf.py b/lib/python3.11/site-packages/sympy/core/tests/test_evalf.py new file mode 100644 index 0000000000000000000000000000000000000000..05d0fd0b58b756570c954d7d7e35e0c2cb589746 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_evalf.py @@ -0,0 +1,734 @@ +import math + +from sympy.concrete.products import (Product, product) +from sympy.concrete.summations import Sum +from sympy.core.add import Add +from sympy.core.evalf import N +from sympy.core.function import (Function, nfloat) +from sympy.core.mul import Mul +from sympy.core import (GoldenRatio) +from sympy.core.numbers import (AlgebraicNumber, E, Float, I, Rational, + oo, zoo, nan, pi) +from sympy.core.power import Pow +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.combinatorial.numbers import fibonacci +from sympy.functions.elementary.complexes import (Abs, re, im) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.hyperbolic import (acosh, cosh) +from sympy.functions.elementary.integers import (ceiling, floor) +from sympy.functions.elementary.miscellaneous import (Max, sqrt) +from sympy.functions.elementary.trigonometric import (acos, atan, cos, sin, tan) +from sympy.integrals.integrals import (Integral, integrate) +from sympy.polys.polytools import factor +from sympy.polys.rootoftools import CRootOf +from sympy.polys.specialpolys import cyclotomic_poly +from sympy.printing import srepr +from sympy.printing.str import sstr +from sympy.simplify.simplify import simplify +from sympy.core.numbers import comp +from sympy.core.evalf import (complex_accuracy, PrecisionExhausted, + scaled_zero, get_integer_part, as_mpmath, evalf, _evalf_with_bounded_error) +from mpmath import inf, ninf, make_mpc +from mpmath.libmp.libmpf import from_float, fzero +from sympy.core.expr import unchanged +from sympy.testing.pytest import raises, XFAIL +from sympy.abc import n, x, y + + +def NS(e, n=15, **options): + return sstr(sympify(e).evalf(n, **options), full_prec=True) + + +def test_evalf_helpers(): + from mpmath.libmp import finf + assert complex_accuracy((from_float(2.0), None, 35, None)) == 35 + assert complex_accuracy((from_float(2.0), from_float(10.0), 35, 100)) == 37 + assert complex_accuracy( + (from_float(2.0), from_float(1000.0), 35, 100)) == 43 + assert complex_accuracy((from_float(2.0), from_float(10.0), 100, 35)) == 35 + assert complex_accuracy( + (from_float(2.0), from_float(1000.0), 100, 35)) == 35 + assert complex_accuracy(finf) == math.inf + assert complex_accuracy(zoo) == math.inf + raises(ValueError, lambda: get_integer_part(zoo, 1, {})) + + +def test_evalf_basic(): + assert NS('pi', 15) == '3.14159265358979' + assert NS('2/3', 10) == '0.6666666667' + assert NS('355/113-pi', 6) == '2.66764e-7' + assert NS('16*atan(1/5)-4*atan(1/239)', 15) == '3.14159265358979' + + +def test_cancellation(): + assert NS(Add(pi, Rational(1, 10**1000), -pi, evaluate=False), 15, + maxn=1200) == '1.00000000000000e-1000' + + +def test_evalf_powers(): + assert NS('pi**(10**20)', 10) == '1.339148777e+49714987269413385435' + assert NS(pi**(10**100), 10) == ('4.946362032e+4971498726941338543512682882' + '9089887365167832438044244613405349992494711208' + '95526746555473864642912223') + assert NS('2**(1/10**50)', 15) == '1.00000000000000' + assert NS('2**(1/10**50)-1', 15) == '6.93147180559945e-51' + +# Evaluation of Rump's ill-conditioned polynomial + + +def test_evalf_rump(): + a = 1335*y**6/4 + x**2*(11*x**2*y**2 - y**6 - 121*y**4 - 2) + 11*y**8/2 + x/(2*y) + assert NS(a, 15, subs={x: 77617, y: 33096}) == '-0.827396059946821' + + +def test_evalf_complex(): + assert NS('2*sqrt(pi)*I', 10) == '3.544907702*I' + assert NS('3+3*I', 15) == '3.00000000000000 + 3.00000000000000*I' + assert NS('E+pi*I', 15) == '2.71828182845905 + 3.14159265358979*I' + assert NS('pi * (3+4*I)', 15) == '9.42477796076938 + 12.5663706143592*I' + assert NS('I*(2+I)', 15) == '-1.00000000000000 + 2.00000000000000*I' + + +@XFAIL +def test_evalf_complex_bug(): + assert NS('(pi+E*I)*(E+pi*I)', 15) in ('0.e-15 + 17.25866050002*I', + '0.e-17 + 17.25866050002*I', '-0.e-17 + 17.25866050002*I') + + +def test_evalf_complex_powers(): + assert NS('(E+pi*I)**100000000000000000') == \ + '-3.58896782867793e+61850354284995199 + 4.58581754997159e+61850354284995199*I' + # XXX: rewrite if a+a*I simplification introduced in SymPy + #assert NS('(pi + pi*I)**2') in ('0.e-15 + 19.7392088021787*I', '0.e-16 + 19.7392088021787*I') + assert NS('(pi + pi*I)**2', chop=True) == '19.7392088021787*I' + assert NS( + '(pi + 1/10**8 + pi*I)**2') == '6.2831853e-8 + 19.7392088650106*I' + assert NS('(pi + 1/10**12 + pi*I)**2') == '6.283e-12 + 19.7392088021850*I' + assert NS('(pi + pi*I)**4', chop=True) == '-389.636364136010' + assert NS( + '(pi + 1/10**8 + pi*I)**4') == '-389.636366616512 + 2.4805021e-6*I' + assert NS('(pi + 1/10**12 + pi*I)**4') == '-389.636364136258 + 2.481e-10*I' + assert NS( + '(10000*pi + 10000*pi*I)**4', chop=True) == '-3.89636364136010e+18' + + +@XFAIL +def test_evalf_complex_powers_bug(): + assert NS('(pi + pi*I)**4') == '-389.63636413601 + 0.e-14*I' + + +def test_evalf_exponentiation(): + assert NS(sqrt(-pi)) == '1.77245385090552*I' + assert NS(Pow(pi*I, Rational( + 1, 2), evaluate=False)) == '1.25331413731550 + 1.25331413731550*I' + assert NS(pi**I) == '0.413292116101594 + 0.910598499212615*I' + assert NS(pi**(E + I/3)) == '20.8438653991931 + 8.36343473930031*I' + assert NS((pi + I/3)**(E + I/3)) == '17.2442906093590 + 13.6839376767037*I' + assert NS(exp(pi)) == '23.1406926327793' + assert NS(exp(pi + E*I)) == '-21.0981542849657 + 9.50576358282422*I' + assert NS(pi**pi) == '36.4621596072079' + assert NS((-pi)**pi) == '-32.9138577418939 - 15.6897116534332*I' + assert NS((-pi)**(-pi)) == '-0.0247567717232697 + 0.0118013091280262*I' + +# An example from Smith, "Multiple Precision Complex Arithmetic and Functions" + + +def test_evalf_complex_cancellation(): + A = Rational('63287/100000') + B = Rational('52498/100000') + C = Rational('69301/100000') + D = Rational('83542/100000') + F = Rational('2231321613/2500000000') + # XXX: the number of returned mantissa digits in the real part could + # change with the implementation. What matters is that the returned digits are + # correct; those that are showing now are correct. + # >>> ((A+B*I)*(C+D*I)).expand() + # 64471/10000000000 + 2231321613*I/2500000000 + # >>> 2231321613*4 + # 8925286452L + assert NS((A + B*I)*(C + D*I), 6) == '6.44710e-6 + 0.892529*I' + assert NS((A + B*I)*(C + D*I), 10) == '6.447100000e-6 + 0.8925286452*I' + assert NS((A + B*I)*( + C + D*I) - F*I, 5) in ('6.4471e-6 + 0.e-14*I', '6.4471e-6 - 0.e-14*I') + + +def test_evalf_logs(): + assert NS("log(3+pi*I)", 15) == '1.46877619736226 + 0.808448792630022*I' + assert NS("log(pi*I)", 15) == '1.14472988584940 + 1.57079632679490*I' + assert NS('log(-1 + 0.00001)', 2) == '-1.0e-5 + 3.1*I' + assert NS('log(100, 10, evaluate=False)', 15) == '2.00000000000000' + assert NS('-2*I*log(-(-1)**(S(1)/9))', 15) == '-5.58505360638185' + + +def test_evalf_trig(): + assert NS('sin(1)', 15) == '0.841470984807897' + assert NS('cos(1)', 15) == '0.540302305868140' + assert NS('sin(10**-6)', 15) == '9.99999999999833e-7' + assert NS('cos(10**-6)', 15) == '0.999999999999500' + assert NS('sin(E*10**100)', 15) == '0.409160531722613' + # Some input near roots + assert NS(sin(exp(pi*sqrt(163))*pi), 15) == '-2.35596641936785e-12' + assert NS(sin(pi*10**100 + Rational(7, 10**5), evaluate=False), 15, maxn=120) == \ + '6.99999999428333e-5' + assert NS(sin(Rational(7, 10**5), evaluate=False), 15) == \ + '6.99999999428333e-5' + +# Check detection of various false identities + + +def test_evalf_near_integers(): + # Binet's formula + f = lambda n: ((1 + sqrt(5))**n)/(2**n * sqrt(5)) + assert NS(f(5000) - fibonacci(5000), 10, maxn=1500) == '5.156009964e-1046' + # Some near-integer identities from + # http://mathworld.wolfram.com/AlmostInteger.html + assert NS('sin(2017*2**(1/5))', 15) == '-1.00000000000000' + assert NS('sin(2017*2**(1/5))', 20) == '-0.99999999999999997857' + assert NS('1+sin(2017*2**(1/5))', 15) == '2.14322287389390e-17' + assert NS('45 - 613*E/37 + 35/991', 15) == '6.03764498766326e-11' + + +def test_evalf_ramanujan(): + assert NS(exp(pi*sqrt(163)) - 640320**3 - 744, 10) == '-7.499274028e-13' + # A related identity + A = 262537412640768744*exp(-pi*sqrt(163)) + B = 196884*exp(-2*pi*sqrt(163)) + C = 103378831900730205293632*exp(-3*pi*sqrt(163)) + assert NS(1 - A - B + C, 10) == '1.613679005e-59' + +# Input that for various reasons have failed at some point + + +def test_evalf_bugs(): + assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10) + assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10) + assert NS('expand_log(log(1+1/10**50))', 20) == '1.0000000000000000000e-50' + assert NS('log(10**100,10)', 10) == '100.0000000' + assert NS('log(2)', 10) == '0.6931471806' + assert NS( + '(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667' + assert NS(sin(1) + Rational( + 1, 10**100)*I, 15) == '0.841470984807897 + 1.00000000000000e-100*I' + assert x.evalf() == x + assert NS((1 + I)**2*I, 6) == '-2.00000' + d = {n: ( + -1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)} + assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I' + assert NS(((-I - sqrt(2)*I)**2).evalf()) == '-5.82842712474619' + assert NS((1 + I)**2*I, 15) == '-2.00000000000000' + # issue 4758 (1/2): + assert NS(pi.evalf(69) - pi) == '-4.43863937855894e-71' + # issue 4758 (2/2): With the bug present, this still only fails if the + # terms are in the order given here. This is not generally the case, + # because the order depends on the hashes of the terms. + assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n, + subs={n: .01}) == '19.8100000000000' + assert NS(((x - 1)*(1 - x)**1000).n() + ) == '(1.00000000000000 - x)**1000*(x - 1.00000000000000)' + assert NS((-x).n()) == '-x' + assert NS((-2*x).n()) == '-2.00000000000000*x' + assert NS((-2*x*y).n()) == '-2.00000000000000*x*y' + assert cos(x).n(subs={x: 1+I}) == cos(x).subs(x, 1+I).n() + # issue 6660. Also NaN != mpmath.nan + # In this order: + # 0*nan, 0/nan, 0*inf, 0/inf + # 0+nan, 0-nan, 0+inf, 0-inf + # >>> n = Some Number + # n*nan, n/nan, n*inf, n/inf + # n+nan, n-nan, n+inf, n-inf + assert (0*E**(oo)).n() is S.NaN + assert (0/E**(oo)).n() is S.Zero + + assert (0+E**(oo)).n() is S.Infinity + assert (0-E**(oo)).n() is S.NegativeInfinity + + assert (5*E**(oo)).n() is S.Infinity + assert (5/E**(oo)).n() is S.Zero + + assert (5+E**(oo)).n() is S.Infinity + assert (5-E**(oo)).n() is S.NegativeInfinity + + #issue 7416 + assert as_mpmath(0.0, 10, {'chop': True}) == 0 + + #issue 5412 + assert ((oo*I).n() == S.Infinity*I) + assert ((oo+oo*I).n() == S.Infinity + S.Infinity*I) + + #issue 11518 + assert NS(2*x**2.5, 5) == '2.0000*x**2.5000' + + #issue 13076 + assert NS(Mul(Max(0, y), x, evaluate=False).evalf()) == 'x*Max(0, y)' + + #issue 18516 + assert NS(log(S(3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376)/36360291795869936842385267079543319118023385026001623040346035832580600191583895484198508262979388783308179702534403855752855931517013066142992430916562025780021771247847643450125342836565813209972590371590152578728008385990139795377610001).evalf(15, chop=True)) == '-oo' + + +def test_evalf_integer_parts(): + a = floor(log(8)/log(2) - exp(-1000), evaluate=False) + b = floor(log(8)/log(2), evaluate=False) + assert a.evalf() == 3.0 + assert b.evalf() == 3.0 + # equals, as a fallback, can still fail but it might succeed as here + assert ceiling(10*(sin(1)**2 + cos(1)**2)) == 10 + + assert int(floor(factorial(50)/E, evaluate=False).evalf(70)) == \ + int(11188719610782480504630258070757734324011354208865721592720336800) + assert int(ceiling(factorial(50)/E, evaluate=False).evalf(70)) == \ + int(11188719610782480504630258070757734324011354208865721592720336801) + assert int(floor(GoldenRatio**999 / sqrt(5) + S.Half) + .evalf(1000)) == fibonacci(999) + assert int(floor(GoldenRatio**1000 / sqrt(5) + S.Half) + .evalf(1000)) == fibonacci(1000) + + assert ceiling(x).evalf(subs={x: 3}) == 3.0 + assert ceiling(x).evalf(subs={x: 3*I}) == 3.0*I + assert ceiling(x).evalf(subs={x: 2 + 3*I}) == 2.0 + 3.0*I + assert ceiling(x).evalf(subs={x: 3.}) == 3.0 + assert ceiling(x).evalf(subs={x: 3.*I}) == 3.0*I + assert ceiling(x).evalf(subs={x: 2. + 3*I}) == 2.0 + 3.0*I + + assert float((floor(1.5, evaluate=False)+1/9).evalf()) == 1 + 1/9 + assert float((floor(0.5, evaluate=False)+20).evalf()) == 20 + + # issue 19991 + n = 1169809367327212570704813632106852886389036911 + r = 744723773141314414542111064094745678855643068 + + assert floor(n / (pi / 2)) == r + assert floor(80782 * sqrt(2)) == 114242 + + # issue 20076 + assert 260515 - floor(260515/pi + 1/2) * pi == atan(tan(260515)) + + assert floor(x).evalf(subs={x: sqrt(2)}) == 1.0 + + +def test_evalf_trig_zero_detection(): + a = sin(160*pi, evaluate=False) + t = a.evalf(maxn=100) + assert abs(t) < 1e-100 + assert t._prec < 2 + assert a.evalf(chop=True) == 0 + raises(PrecisionExhausted, lambda: a.evalf(strict=True)) + + +def test_evalf_sum(): + assert Sum(n,(n,1,2)).evalf() == 3. + assert Sum(n,(n,1,2)).doit().evalf() == 3. + # the next test should return instantly + assert Sum(1/n,(n,1,2)).evalf() == 1.5 + + # issue 8219 + assert Sum(E/factorial(n), (n, 0, oo)).evalf() == (E*E).evalf() + # issue 8254 + assert Sum(2**n*n/factorial(n), (n, 0, oo)).evalf() == (2*E*E).evalf() + # issue 8411 + s = Sum(1/x**2, (x, 100, oo)) + assert s.n() == s.doit().n() + + +def test_evalf_divergent_series(): + raises(ValueError, lambda: Sum(1/n, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum(n/(n**2 + 1), (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum((-1)**n, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum((-1)**n, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum(n**2, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum(2**n, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum((-2)**n, (n, 1, oo)).evalf()) + raises(ValueError, lambda: Sum((2*n + 3)/(3*n**2 + 4), (n, 0, oo)).evalf()) + raises(ValueError, lambda: Sum((0.5*n**3)/(n**4 + 1), (n, 0, oo)).evalf()) + + +def test_evalf_product(): + assert Product(n, (n, 1, 10)).evalf() == 3628800. + assert comp(Product(1 - S.Half**2/n**2, (n, 1, oo)).n(5), 0.63662) + assert Product(n, (n, -1, 3)).evalf() == 0 + + +def test_evalf_py_methods(): + assert abs(float(pi + 1) - 4.1415926535897932) < 1e-10 + assert abs(complex(pi + 1) - 4.1415926535897932) < 1e-10 + assert abs( + complex(pi + E*I) - (3.1415926535897931 + 2.7182818284590451j)) < 1e-10 + raises(TypeError, lambda: float(pi + x)) + + +def test_evalf_power_subs_bugs(): + assert (x**2).evalf(subs={x: 0}) == 0 + assert sqrt(x).evalf(subs={x: 0}) == 0 + assert (x**Rational(2, 3)).evalf(subs={x: 0}) == 0 + assert (x**x).evalf(subs={x: 0}) == 1.0 + assert (3**x).evalf(subs={x: 0}) == 1.0 + assert exp(x).evalf(subs={x: 0}) == 1.0 + assert ((2 + I)**x).evalf(subs={x: 0}) == 1.0 + assert (0**x).evalf(subs={x: 0}) == 1.0 + + +def test_evalf_arguments(): + raises(TypeError, lambda: pi.evalf(method="garbage")) + + +def test_implemented_function_evalf(): + from sympy.utilities.lambdify import implemented_function + f = Function('f') + f = implemented_function(f, lambda x: x + 1) + assert str(f(x)) == "f(x)" + assert str(f(2)) == "f(2)" + assert f(2).evalf() == 3.0 + assert f(x).evalf() == f(x) + f = implemented_function(Function('sin'), lambda x: x + 1) + assert f(2).evalf() != sin(2) + del f._imp_ # XXX: due to caching _imp_ would influence all other tests + + +def test_evaluate_false(): + for no in [0, False]: + assert Add(3, 2, evaluate=no).is_Add + assert Mul(3, 2, evaluate=no).is_Mul + assert Pow(3, 2, evaluate=no).is_Pow + assert Pow(y, 2, evaluate=True) - Pow(y, 2, evaluate=True) == 0 + + +def test_evalf_relational(): + assert Eq(x/5, y/10).evalf() == Eq(0.2*x, 0.1*y) + # if this first assertion fails it should be replaced with + # one that doesn't + assert unchanged(Eq, (3 - I)**2/2 + I, 0) + assert Eq((3 - I)**2/2 + I, 0).n() is S.false + assert nfloat(Eq((3 - I)**2 + I, 0)) == S.false + + +def test_issue_5486(): + assert not cos(sqrt(0.5 + I)).n().is_Function + + +def test_issue_5486_bug(): + from sympy.core.expr import Expr + from sympy.core.numbers import I + assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15 + + +def test_bugs(): + from sympy.functions.elementary.complexes import (polar_lift, re) + + assert abs(re((1 + I)**2)) < 1e-15 + + # anything that evalf's to 0 will do in place of polar_lift + assert abs(polar_lift(0)).n() == 0 + + +def test_subs(): + assert NS('besseli(-x, y) - besseli(x, y)', subs={x: 3.5, y: 20.0}) == \ + '-4.92535585957223e-10' + assert NS('Piecewise((x, x>0)) + Piecewise((1-x, x>0))', subs={x: 0.1}) == \ + '1.00000000000000' + raises(TypeError, lambda: x.evalf(subs=(x, 1))) + + +def test_issue_4956_5204(): + # issue 4956 + v = S('''(-27*12**(1/3)*sqrt(31)*I + + 27*2**(2/3)*3**(1/3)*sqrt(31)*I)/(-2511*2**(2/3)*3**(1/3) + + (29*18**(1/3) + 9*2**(1/3)*3**(2/3)*sqrt(31)*I + + 87*2**(1/3)*3**(1/6)*I)**2)''') + assert NS(v, 1) == '0.e-118 - 0.e-118*I' + + # issue 5204 + v = S('''-(357587765856 + 18873261792*249**(1/2) + 56619785376*I*83**(1/2) + + 108755765856*I*3**(1/2) + 41281887168*6**(1/3)*(1422 + + 54*249**(1/2))**(1/3) - 1239810624*6**(1/3)*249**(1/2)*(1422 + + 54*249**(1/2))**(1/3) - 3110400000*I*6**(1/3)*83**(1/2)*(1422 + + 54*249**(1/2))**(1/3) + 13478400000*I*3**(1/2)*6**(1/3)*(1422 + + 54*249**(1/2))**(1/3) + 1274950152*6**(2/3)*(1422 + + 54*249**(1/2))**(2/3) + 32347944*6**(2/3)*249**(1/2)*(1422 + + 54*249**(1/2))**(2/3) - 1758790152*I*3**(1/2)*6**(2/3)*(1422 + + 54*249**(1/2))**(2/3) - 304403832*I*6**(2/3)*83**(1/2)*(1422 + + 4*249**(1/2))**(2/3))/(175732658352 + (1106028 + 25596*249**(1/2) + + 76788*I*83**(1/2))**2)''') + assert NS(v, 5) == '0.077284 + 1.1104*I' + assert NS(v, 1) == '0.08 + 1.*I' + + +def test_old_docstring(): + a = (E + pi*I)*(E - pi*I) + assert NS(a) == '17.2586605000200' + assert a.n() == 17.25866050002001 + + +def test_issue_4806(): + assert integrate(atan(x)**2, (x, -1, 1)).evalf().round(1) == Float(0.5, 1) + assert atan(0, evaluate=False).n() == 0 + + +def test_evalf_mul(): + # SymPy should not try to expand this; it should be handled term-wise + # in evalf through mpmath + assert NS(product(1 + sqrt(n)*I, (n, 1, 500)), 1) == '5.e+567 + 2.e+568*I' + + +def test_scaled_zero(): + a, b = (([0], 1, 100, 1), -1) + assert scaled_zero(100) == (a, b) + assert scaled_zero(a) == (0, 1, 100, 1) + a, b = (([1], 1, 100, 1), -1) + assert scaled_zero(100, -1) == (a, b) + assert scaled_zero(a) == (1, 1, 100, 1) + raises(ValueError, lambda: scaled_zero(scaled_zero(100))) + raises(ValueError, lambda: scaled_zero(100, 2)) + raises(ValueError, lambda: scaled_zero(100, 0)) + raises(ValueError, lambda: scaled_zero((1, 5, 1, 3))) + + +def test_chop_value(): + for i in range(-27, 28): + assert (Pow(10, i)*2).n(chop=10**i) and not (Pow(10, i)).n(chop=10**i) + + +def test_infinities(): + assert oo.evalf(chop=True) == inf + assert (-oo).evalf(chop=True) == ninf + + +def test_to_mpmath(): + assert sqrt(3)._to_mpmath(20)._mpf_ == (0, int(908093), -19, 20) + assert S(3.2)._to_mpmath(20)._mpf_ == (0, int(838861), -18, 20) + + +def test_issue_6632_evalf(): + add = (-100000*sqrt(2500000001) + 5000000001) + assert add.n() == 9.999999998e-11 + assert (add*add).n() == 9.999999996e-21 + + +def test_issue_4945(): + from sympy.abc import H + assert (H/0).evalf(subs={H:1}) == zoo + + +def test_evalf_integral(): + # test that workprec has to increase in order to get a result other than 0 + eps = Rational(1, 1000000) + assert Integral(sin(x), (x, -pi, pi + eps)).n(2)._prec == 10 + + +def test_issue_8821_highprec_from_str(): + s = str(pi.evalf(128)) + p = N(s) + assert Abs(sin(p)) < 1e-15 + p = N(s, 64) + assert Abs(sin(p)) < 1e-64 + + +def test_issue_8853(): + p = Symbol('x', even=True, positive=True) + assert floor(-p - S.Half).is_even == False + assert floor(-p + S.Half).is_even == True + assert ceiling(p - S.Half).is_even == True + assert ceiling(p + S.Half).is_even == False + + assert get_integer_part(S.Half, -1, {}, True) == (0, 0) + assert get_integer_part(S.Half, 1, {}, True) == (1, 0) + assert get_integer_part(Rational(-1, 2), -1, {}, True) == (-1, 0) + assert get_integer_part(Rational(-1, 2), 1, {}, True) == (0, 0) + + +def test_issue_17681(): + class identity_func(Function): + + def _eval_evalf(self, *args, **kwargs): + return self.args[0].evalf(*args, **kwargs) + + assert floor(identity_func(S(0))) == 0 + assert get_integer_part(S(0), 1, {}, True) == (0, 0) + + +def test_issue_9326(): + from sympy.core.symbol import Dummy + d1 = Dummy('d') + d2 = Dummy('d') + e = d1 + d2 + assert e.evalf(subs = {d1: 1, d2: 2}) == 3.0 + + +def test_issue_10323(): + assert ceiling(sqrt(2**30 + 1)) == 2**15 + 1 + + +def test_AssocOp_Function(): + # the first arg of Min is not comparable in the imaginary part + raises(ValueError, lambda: S(''' + Min(-sqrt(3)*cos(pi/18)/6 + re(1/((-1/2 - sqrt(3)*I/2)*(1/6 + + sqrt(3)*I/18)**(1/3)))/3 + sin(pi/18)/2 + 2 + I*(-cos(pi/18)/2 - + sqrt(3)*sin(pi/18)/6 + im(1/((-1/2 - sqrt(3)*I/2)*(1/6 + + sqrt(3)*I/18)**(1/3)))/3), re(1/((-1/2 + sqrt(3)*I/2)*(1/6 + + sqrt(3)*I/18)**(1/3)))/3 - sqrt(3)*cos(pi/18)/6 - sin(pi/18)/2 + 2 + + I*(im(1/((-1/2 + sqrt(3)*I/2)*(1/6 + sqrt(3)*I/18)**(1/3)))/3 - + sqrt(3)*sin(pi/18)/6 + cos(pi/18)/2))''')) + # if that is changed so a non-comparable number remains as + # an arg, then the Min/Max instantiation needs to be changed + # to watch out for non-comparable args when making simplifications + # and the following test should be added instead (with e being + # the sympified expression above): + # raises(ValueError, lambda: e._eval_evalf(2)) + + +def test_issue_10395(): + eq = x*Max(0, y) + assert nfloat(eq) == eq + eq = x*Max(y, -1.1) + assert nfloat(eq) == eq + assert Max(y, 4).n() == Max(4.0, y) + + +def test_issue_13098(): + assert floor(log(S('9.'+'9'*20), 10)) == 0 + assert ceiling(log(S('9.'+'9'*20), 10)) == 1 + assert floor(log(20 - S('9.'+'9'*20), 10)) == 1 + assert ceiling(log(20 - S('9.'+'9'*20), 10)) == 2 + + +def test_issue_14601(): + e = 5*x*y/2 - y*(35*(x**3)/2 - 15*x/2) + subst = {x:0.0, y:0.0} + e2 = e.evalf(subs=subst) + assert float(e2) == 0.0 + assert float((x + x*(x**2 + x)).evalf(subs={x: 0.0})) == 0.0 + + +def test_issue_11151(): + z = S.Zero + e = Sum(z, (x, 1, 2)) + assert e != z # it shouldn't evaluate + # when it does evaluate, this is what it should give + assert evalf(e, 15, {}) == \ + evalf(z, 15, {}) == (None, None, 15, None) + # so this shouldn't fail + assert (e/2).n() == 0 + # this was where the issue appeared + expr0 = Sum(x**2 + x, (x, 1, 2)) + expr1 = Sum(0, (x, 1, 2)) + expr2 = expr1/expr0 + assert simplify(factor(expr2) - expr2) == 0 + + +def test_issue_13425(): + assert N('2**.5', 30) == N('sqrt(2)', 30) + assert N('x - x', 30) == 0 + assert abs((N('pi*.1', 22)*10 - pi).n()) < 1e-22 + + +def test_issue_17421(): + assert N(acos(-I + acosh(cosh(cosh(1) + I)))) == 1.0*I + + +def test_issue_20291(): + from sympy.sets import EmptySet, Reals + from sympy.sets.sets import (Complement, FiniteSet, Intersection) + a = Symbol('a') + b = Symbol('b') + A = FiniteSet(a, b) + assert A.evalf(subs={a: 1, b: 2}) == FiniteSet(1.0, 2.0) + B = FiniteSet(a-b, 1) + assert B.evalf(subs={a: 1, b: 2}) == FiniteSet(-1.0, 1.0) + + sol = Complement(Intersection(FiniteSet(-b/2 - sqrt(b**2-4*pi)/2), Reals), FiniteSet(0)) + assert sol.evalf(subs={b: 1}) == EmptySet + + +def test_evalf_with_zoo(): + assert (1/x).evalf(subs={x: 0}) == zoo # issue 8242 + assert (-1/x).evalf(subs={x: 0}) == zoo # PR 16150 + assert (0 ** x).evalf(subs={x: -1}) == zoo # PR 16150 + assert (0 ** x).evalf(subs={x: -1 + I}) == nan + assert Mul(2, Pow(0, -1, evaluate=False), evaluate=False).evalf() == zoo # issue 21147 + assert Mul(x, 1/x, evaluate=False).evalf(subs={x: 0}) == Mul(x, 1/x, evaluate=False).subs(x, 0) == nan + assert Mul(1/x, 1/x, evaluate=False).evalf(subs={x: 0}) == zoo + assert Mul(1/x, Abs(1/x), evaluate=False).evalf(subs={x: 0}) == zoo + assert Abs(zoo, evaluate=False).evalf() == oo + assert re(zoo, evaluate=False).evalf() == nan + assert im(zoo, evaluate=False).evalf() == nan + assert Add(zoo, zoo, evaluate=False).evalf() == nan + assert Add(oo, zoo, evaluate=False).evalf() == nan + assert Pow(zoo, -1, evaluate=False).evalf() == 0 + assert Pow(zoo, Rational(-1, 3), evaluate=False).evalf() == 0 + assert Pow(zoo, Rational(1, 3), evaluate=False).evalf() == zoo + assert Pow(zoo, S.Half, evaluate=False).evalf() == zoo + assert Pow(zoo, 2, evaluate=False).evalf() == zoo + assert Pow(0, zoo, evaluate=False).evalf() == nan + assert log(zoo, evaluate=False).evalf() == zoo + assert zoo.evalf(chop=True) == zoo + assert x.evalf(subs={x: zoo}) == zoo + + +def test_evalf_with_bounded_error(): + cases = [ + # zero + (Rational(0), None, 1), + # zero im part + (pi, None, 10), + # zero real part + (pi*I, None, 10), + # re and im nonzero + (2-3*I, None, 5), + # similar tests again, but using eps instead of m + (Rational(0), Rational(1, 2), None), + (pi, Rational(1, 1000), None), + (pi * I, Rational(1, 1000), None), + (2 - 3 * I, Rational(1, 1000), None), + # very large eps + (2 - 3 * I, Rational(1000), None), + # case where x already small, hence some cancellation in p = m + n - 1 + (Rational(1234, 10**8), Rational(1, 10**12), None), + ] + for x0, eps, m in cases: + a, b, _, _ = evalf(x0, 53, {}) + c, d, _, _ = _evalf_with_bounded_error(x0, eps, m) + if eps is None: + eps = 2**(-m) + z = make_mpc((a or fzero, b or fzero)) + w = make_mpc((c or fzero, d or fzero)) + assert abs(w - z) < eps + + # eps must be positive + raises(ValueError, lambda: _evalf_with_bounded_error(pi, Rational(0))) + raises(ValueError, lambda: _evalf_with_bounded_error(pi, -pi)) + raises(ValueError, lambda: _evalf_with_bounded_error(pi, I)) + + +def test_issue_22849(): + a = -8 + 3 * sqrt(3) + x = AlgebraicNumber(a) + assert evalf(a, 1, {}) == evalf(x, 1, {}) + + +def test_evalf_real_alg_num(): + # This test demonstrates why the entry for `AlgebraicNumber` in + # `sympy.core.evalf._create_evalf_table()` has to use `x.to_root()`, + # instead of `x.as_expr()`. If the latter is used, then `z` will be + # a complex number with `0.e-20` for imaginary part, even though `a5` + # is a real number. + zeta = Symbol('zeta') + a5 = AlgebraicNumber(CRootOf(cyclotomic_poly(5), -1), [-1, -1, 0, 0], alias=zeta) + z = a5.evalf() + assert isinstance(z, Float) + assert not hasattr(z, '_mpc_') + assert hasattr(z, '_mpf_') + + +def test_issue_20733(): + expr = 1/((x - 9)*(x - 8)*(x - 7)*(x - 4)**2*(x - 3)**3*(x - 2)) + assert str(expr.evalf(1, subs={x:1})) == '-4.e-5' + assert str(expr.evalf(2, subs={x:1})) == '-4.1e-5' + assert str(expr.evalf(11, subs={x:1})) == '-4.1335978836e-5' + assert str(expr.evalf(20, subs={x:1})) == '-0.000041335978835978835979' + + expr = Mul(*((x - i) for i in range(2, 1000))) + assert srepr(expr.evalf(2, subs={x: 1})) == "Float('4.0271e+2561', precision=10)" + assert srepr(expr.evalf(10, subs={x: 1})) == "Float('4.02790050126e+2561', precision=37)" + assert srepr(expr.evalf(53, subs={x: 1})) == "Float('4.0279005012722099453824067459760158730668154575647110393e+2561', precision=179)" diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_expand.py b/lib/python3.11/site-packages/sympy/core/tests/test_expand.py new file mode 100644 index 0000000000000000000000000000000000000000..e7abb5daacebbe81664b3de3a7ac35a490ab31bc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_expand.py @@ -0,0 +1,364 @@ +from sympy.core.expr import unchanged +from sympy.core.mul import Mul +from sympy.core.numbers import (I, Rational as R, pi) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.series.order import O +from sympy.simplify.radsimp import expand_numer +from sympy.core.function import (expand, expand_multinomial, + expand_power_base, expand_log) + +from sympy.testing.pytest import raises +from sympy.core.random import verify_numerically + +from sympy.abc import x, y, z + + +def test_expand_no_log(): + assert ( + (1 + log(x**4))**2).expand(log=False) == 1 + 2*log(x**4) + log(x**4)**2 + assert ((1 + log(x**4))*(1 + log(x**3))).expand( + log=False) == 1 + log(x**4) + log(x**3) + log(x**4)*log(x**3) + + +def test_expand_no_multinomial(): + assert ((1 + x)*(1 + (1 + x)**4)).expand(multinomial=False) == \ + 1 + x + (1 + x)**4 + x*(1 + x)**4 + + +def test_expand_negative_integer_powers(): + expr = (x + y)**(-2) + assert expr.expand() == 1 / (2*x*y + x**2 + y**2) + assert expr.expand(multinomial=False) == (x + y)**(-2) + expr = (x + y)**(-3) + assert expr.expand() == 1 / (3*x*x*y + 3*x*y*y + x**3 + y**3) + assert expr.expand(multinomial=False) == (x + y)**(-3) + expr = (x + y)**(2) * (x + y)**(-4) + assert expr.expand() == 1 / (2*x*y + x**2 + y**2) + assert expr.expand(multinomial=False) == (x + y)**(-2) + + +def test_expand_non_commutative(): + A = Symbol('A', commutative=False) + B = Symbol('B', commutative=False) + C = Symbol('C', commutative=False) + a = Symbol('a') + b = Symbol('b') + i = Symbol('i', integer=True) + n = Symbol('n', negative=True) + m = Symbol('m', negative=True) + p = Symbol('p', polar=True) + np = Symbol('p', polar=False) + + assert (C*(A + B)).expand() == C*A + C*B + assert (C*(A + B)).expand() != A*C + B*C + assert ((A + B)**2).expand() == A**2 + A*B + B*A + B**2 + assert ((A + B)**3).expand() == (A**2*B + B**2*A + A*B**2 + B*A**2 + + A**3 + B**3 + A*B*A + B*A*B) + # issue 6219 + assert ((a*A*B*A**-1)**2).expand() == a**2*A*B**2/A + # Note that (a*A*B*A**-1)**2 is automatically converted to a**2*(A*B*A**-1)**2 + assert ((a*A*B*A**-1)**2).expand(deep=False) == a**2*(A*B*A**-1)**2 + assert ((a*A*B*A**-1)**2).expand() == a**2*(A*B**2*A**-1) + assert ((a*A*B*A**-1)**2).expand(force=True) == a**2*A*B**2*A**(-1) + assert ((a*A*B)**2).expand() == a**2*A*B*A*B + assert ((a*A)**2).expand() == a**2*A**2 + assert ((a*A*B)**i).expand() == a**i*(A*B)**i + assert ((a*A*(B*(A*B/A)**2))**i).expand() == a**i*(A*B*A*B**2/A)**i + # issue 6558 + assert (A*B*(A*B)**-1).expand() == 1 + assert ((a*A)**i).expand() == a**i*A**i + assert ((a*A*B*A**-1)**3).expand() == a**3*A*B**3/A + assert ((a*A*B*A*B/A)**3).expand() == \ + a**3*A*B*(A*B**2)*(A*B**2)*A*B*A**(-1) + assert ((a*A*B*A*B/A)**-2).expand() == \ + A*B**-1*A**-1*B**-2*A**-1*B**-1*A**-1/a**2 + assert ((a*b*A*B*A**-1)**i).expand() == a**i*b**i*(A*B/A)**i + assert ((a*(a*b)**i)**i).expand() == a**i*a**(i**2)*b**(i**2) + e = Pow(Mul(a, 1/a, A, B, evaluate=False), S(2), evaluate=False) + assert e.expand() == A*B*A*B + assert sqrt(a*(A*b)**i).expand() == sqrt(a*b**i*A**i) + assert (sqrt(-a)**a).expand() == sqrt(-a)**a + assert expand((-2*n)**(i/3)) == 2**(i/3)*(-n)**(i/3) + assert expand((-2*n*m)**(i/a)) == (-2)**(i/a)*(-n)**(i/a)*(-m)**(i/a) + assert expand((-2*a*p)**b) == 2**b*p**b*(-a)**b + assert expand((-2*a*np)**b) == 2**b*(-a*np)**b + assert expand(sqrt(A*B)) == sqrt(A*B) + assert expand(sqrt(-2*a*b)) == sqrt(2)*sqrt(-a*b) + + +def test_expand_radicals(): + a = (x + y)**R(1, 2) + + assert (a**1).expand() == a + assert (a**3).expand() == x*a + y*a + assert (a**5).expand() == x**2*a + 2*x*y*a + y**2*a + + assert (1/a**1).expand() == 1/a + assert (1/a**3).expand() == 1/(x*a + y*a) + assert (1/a**5).expand() == 1/(x**2*a + 2*x*y*a + y**2*a) + + a = (x + y)**R(1, 3) + + assert (a**1).expand() == a + assert (a**2).expand() == a**2 + assert (a**4).expand() == x*a + y*a + assert (a**5).expand() == x*a**2 + y*a**2 + assert (a**7).expand() == x**2*a + 2*x*y*a + y**2*a + + +def test_expand_modulus(): + assert ((x + y)**11).expand(modulus=11) == x**11 + y**11 + assert ((x + sqrt(2)*y)**11).expand(modulus=11) == x**11 + 10*sqrt(2)*y**11 + assert (x + y/2).expand(modulus=1) == y/2 + + raises(ValueError, lambda: ((x + y)**11).expand(modulus=0)) + raises(ValueError, lambda: ((x + y)**11).expand(modulus=x)) + + +def test_issue_5743(): + assert (x*sqrt( + x + y)*(1 + sqrt(x + y))).expand() == x**2 + x*y + x*sqrt(x + y) + assert (x*sqrt( + x + y)*(1 + x*sqrt(x + y))).expand() == x**3 + x**2*y + x*sqrt(x + y) + + +def test_expand_frac(): + assert expand((x + y)*y/x/(x + 1), frac=True) == \ + (x*y + y**2)/(x**2 + x) + assert expand((x + y)*y/x/(x + 1), numer=True) == \ + (x*y + y**2)/(x*(x + 1)) + assert expand((x + y)*y/x/(x + 1), denom=True) == \ + y*(x + y)/(x**2 + x) + eq = (x + 1)**2/y + assert expand_numer(eq, multinomial=False) == eq + # issue 26329 + eq = (exp(x*z) - exp(y*z))/exp(z*(x + y)) + ans = exp(-y*z) - exp(-x*z) + assert eq.expand(numer=True) != ans + assert eq.expand(numer=True, exact=True) == ans + assert expand_numer(eq) != ans + assert expand_numer(eq, exact=True) == ans + + +def test_issue_6121(): + eq = -I*exp(-3*I*pi/4)/(4*pi**(S(3)/2)*sqrt(x)) + assert eq.expand(complex=True) # does not give oo recursion + eq = -I*exp(-3*I*pi/4)/(4*pi**(R(3, 2))*sqrt(x)) + assert eq.expand(complex=True) # does not give oo recursion + + +def test_expand_power_base(): + assert expand_power_base((x*y*z)**4) == x**4*y**4*z**4 + assert expand_power_base((x*y*z)**x).is_Pow + assert expand_power_base((x*y*z)**x, force=True) == x**x*y**x*z**x + assert expand_power_base((x*(y*z)**2)**3) == x**3*y**6*z**6 + + assert expand_power_base((sin((x*y)**2)*y)**z).is_Pow + assert expand_power_base( + (sin((x*y)**2)*y)**z, force=True) == sin((x*y)**2)**z*y**z + assert expand_power_base( + (sin((x*y)**2)*y)**z, deep=True) == (sin(x**2*y**2)*y)**z + + assert expand_power_base(exp(x)**2) == exp(2*x) + assert expand_power_base((exp(x)*exp(y))**2) == exp(2*x)*exp(2*y) + + assert expand_power_base( + (exp((x*y)**z)*exp(y))**2) == exp(2*(x*y)**z)*exp(2*y) + assert expand_power_base((exp((x*y)**z)*exp( + y))**2, deep=True, force=True) == exp(2*x**z*y**z)*exp(2*y) + + assert expand_power_base((exp(x)*exp(y))**z).is_Pow + assert expand_power_base( + (exp(x)*exp(y))**z, force=True) == exp(x)**z*exp(y)**z + + +def test_expand_arit(): + a = Symbol("a") + b = Symbol("b", positive=True) + c = Symbol("c") + + p = R(5) + e = (a + b)*c + assert e == c*(a + b) + assert (e.expand() - a*c - b*c) == R(0) + e = (a + b)*(a + b) + assert e == (a + b)**2 + assert e.expand() == 2*a*b + a**2 + b**2 + e = (a + b)*(a + b)**R(2) + assert e == (a + b)**3 + assert e.expand() == 3*b*a**2 + 3*a*b**2 + a**3 + b**3 + assert e.expand() == 3*b*a**2 + 3*a*b**2 + a**3 + b**3 + e = (a + b)*(a + c)*(b + c) + assert e == (a + c)*(a + b)*(b + c) + assert e.expand() == 2*a*b*c + b*a**2 + c*a**2 + b*c**2 + a*c**2 + c*b**2 + a*b**2 + e = (a + R(1))**p + assert e == (1 + a)**5 + assert e.expand() == 1 + 5*a + 10*a**2 + 10*a**3 + 5*a**4 + a**5 + e = (a + b + c)*(a + c + p) + assert e == (5 + a + c)*(a + b + c) + assert e.expand() == 5*a + 5*b + 5*c + 2*a*c + b*c + a*b + a**2 + c**2 + x = Symbol("x") + s = exp(x*x) - 1 + e = s.nseries(x, 0, 6)/x**2 + assert e.expand() == 1 + x**2/2 + O(x**4) + + e = (x*(y + z))**(x*(y + z))*(x + y) + assert e.expand(power_exp=False, power_base=False) == x*(x*y + x* + z)**(x*y + x*z) + y*(x*y + x*z)**(x*y + x*z) + assert e.expand(power_exp=False, power_base=False, deep=False) == x* \ + (x*(y + z))**(x*(y + z)) + y*(x*(y + z))**(x*(y + z)) + e = x * (x + (y + 1)**2) + assert e.expand(deep=False) == x**2 + x*(y + 1)**2 + e = (x*(y + z))**z + assert e.expand(power_base=True, mul=True, deep=True) in [x**z*(y + + z)**z, (x*y + x*z)**z] + assert ((2*y)**z).expand() == 2**z*y**z + p = Symbol('p', positive=True) + assert sqrt(-x).expand().is_Pow + assert sqrt(-x).expand(force=True) == I*sqrt(x) + assert ((2*y*p)**z).expand() == 2**z*p**z*y**z + assert ((2*y*p*x)**z).expand() == 2**z*p**z*(x*y)**z + assert ((2*y*p*x)**z).expand(force=True) == 2**z*p**z*x**z*y**z + assert ((2*y*p*-pi)**z).expand() == 2**z*pi**z*p**z*(-y)**z + assert ((2*y*p*-pi*x)**z).expand() == 2**z*pi**z*p**z*(-x*y)**z + n = Symbol('n', negative=True) + m = Symbol('m', negative=True) + assert ((-2*x*y*n)**z).expand() == 2**z*(-n)**z*(x*y)**z + assert ((-2*x*y*n*m)**z).expand() == 2**z*(-m)**z*(-n)**z*(-x*y)**z + # issue 5482 + assert sqrt(-2*x*n) == sqrt(2)*sqrt(-n)*sqrt(x) + # issue 5605 (2) + assert (cos(x + y)**2).expand(trig=True) in [ + (-sin(x)*sin(y) + cos(x)*cos(y))**2, + sin(x)**2*sin(y)**2 - 2*sin(x)*sin(y)*cos(x)*cos(y) + cos(x)**2*cos(y)**2 + ] + + # Check that this isn't too slow + x = Symbol('x') + W = 1 + for i in range(1, 21): + W = W * (x - i) + W = W.expand() + assert W.has(-1672280820*x**15) + +def test_expand_mul(): + # part of issue 20597 + e = Mul(2, 3, evaluate=False) + assert e.expand() == 6 + + e = Mul(2, 3, 1/x, evaluate=False) + assert e.expand() == 6/x + e = Mul(2, R(1, 3), evaluate=False) + assert e.expand() == R(2, 3) + +def test_power_expand(): + """Test for Pow.expand()""" + a = Symbol('a') + b = Symbol('b') + p = (a + b)**2 + assert p.expand() == a**2 + b**2 + 2*a*b + + p = (1 + 2*(1 + a))**2 + assert p.expand() == 9 + 4*(a**2) + 12*a + + p = 2**(a + b) + assert p.expand() == 2**a*2**b + + A = Symbol('A', commutative=False) + B = Symbol('B', commutative=False) + assert (2**(A + B)).expand() == 2**(A + B) + assert (A**(a + b)).expand() != A**(a + b) + + +def test_issues_5919_6830(): + # issue 5919 + n = -1 + 1/x + z = n/x/(-n)**2 - 1/n/x + assert expand(z) == 1/(x**2 - 2*x + 1) - 1/(x - 2 + 1/x) - 1/(-x + 1) + + # issue 6830 + p = (1 + x)**2 + assert expand_multinomial((1 + x*p)**2) == ( + x**2*(x**4 + 4*x**3 + 6*x**2 + 4*x + 1) + 2*x*(x**2 + 2*x + 1) + 1) + assert expand_multinomial((1 + (y + x)*p)**2) == ( + 2*((x + y)*(x**2 + 2*x + 1)) + (x**2 + 2*x*y + y**2)* + (x**4 + 4*x**3 + 6*x**2 + 4*x + 1) + 1) + A = Symbol('A', commutative=False) + p = (1 + A)**2 + assert expand_multinomial((1 + x*p)**2) == ( + x**2*(1 + 4*A + 6*A**2 + 4*A**3 + A**4) + 2*x*(1 + 2*A + A**2) + 1) + assert expand_multinomial((1 + (y + x)*p)**2) == ( + (x + y)*(1 + 2*A + A**2)*2 + (x**2 + 2*x*y + y**2)* + (1 + 4*A + 6*A**2 + 4*A**3 + A**4) + 1) + assert expand_multinomial((1 + (y + x)*p)**3) == ( + (x + y)*(1 + 2*A + A**2)*3 + (x**2 + 2*x*y + y**2)*(1 + 4*A + + 6*A**2 + 4*A**3 + A**4)*3 + (x**3 + 3*x**2*y + 3*x*y**2 + y**3)*(1 + 6*A + + 15*A**2 + 20*A**3 + 15*A**4 + 6*A**5 + A**6) + 1) + # unevaluate powers + eq = (Pow((x + 1)*((A + 1)**2), 2, evaluate=False)) + # - in this case the base is not an Add so no further + # expansion is done + assert expand_multinomial(eq) == \ + (x**2 + 2*x + 1)*(1 + 4*A + 6*A**2 + 4*A**3 + A**4) + # - but here, the expanded base *is* an Add so it gets expanded + eq = (Pow(((A + 1)**2), 2, evaluate=False)) + assert expand_multinomial(eq) == 1 + 4*A + 6*A**2 + 4*A**3 + A**4 + + # coverage + def ok(a, b, n): + e = (a + I*b)**n + return verify_numerically(e, expand_multinomial(e)) + + for a in [2, S.Half]: + for b in [3, R(1, 3)]: + for n in range(2, 6): + assert ok(a, b, n) + + assert expand_multinomial((x + 1 + O(z))**2) == \ + 1 + 2*x + x**2 + O(z) + assert expand_multinomial((x + 1 + O(z))**3) == \ + 1 + 3*x + 3*x**2 + x**3 + O(z) + + assert expand_multinomial(3**(x + y + 3)) == 27*3**(x + y) + +def test_expand_log(): + t = Symbol('t', positive=True) + # after first expansion, -2*log(2) + log(4); then 0 after second + assert expand(log(t**2) - log(t**2/4) - 2*log(2)) == 0 + assert expand_log(log(7*6)/log(6)) == 1 + log(7)/log(6) + b = factorial(10) + assert expand_log(log(7*b**4)/log(b) + ) == 4 + log(7)/log(b) + + +def test_issue_23952(): + assert (x**(y + z)).expand(force=True) == x**y*x**z + one = Symbol('1', integer=True, prime=True, odd=True, positive=True) + two = Symbol('2', integer=True, prime=True, even=True) + e = two - one + for b in (0, x): + # 0**e = 0, 0**-e = zoo; but if expanded then nan + assert unchanged(Pow, b, e) # power_exp + assert unchanged(Pow, b, -e) # power_exp + assert unchanged(Pow, b, y - x) # power_exp + assert unchanged(Pow, b, 3 - x) # multinomial + assert (b**e).expand().is_Pow # power_exp + assert (b**-e).expand().is_Pow # power_exp + assert (b**(y - x)).expand().is_Pow # power_exp + assert (b**(3 - x)).expand().is_Pow # multinomial + nn1 = Symbol('nn1', nonnegative=True) + nn2 = Symbol('nn2', nonnegative=True) + nn3 = Symbol('nn3', nonnegative=True) + assert (x**(nn1 + nn2)).expand() == x**nn1*x**nn2 + assert (x**(-nn1 - nn2)).expand() == x**-nn1*x**-nn2 + assert unchanged(Pow, x, nn1 + nn2 - nn3) + assert unchanged(Pow, x, 1 + nn2 - nn3) + assert unchanged(Pow, x, nn1 - nn2) + assert unchanged(Pow, x, 1 - nn2) + assert unchanged(Pow, x, -1 + nn2) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_expr.py b/lib/python3.11/site-packages/sympy/core/tests/test_expr.py new file mode 100644 index 0000000000000000000000000000000000000000..8299ca312cad03d68064c592e4f4e5adc7a96fcc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_expr.py @@ -0,0 +1,2288 @@ +from sympy.assumptions.refine import refine +from sympy.concrete.summations import Sum +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.expr import (ExprBuilder, unchanged, Expr, + UnevaluatedExpr) +from sympy.core.function import (Function, expand, WildFunction, + AppliedUndef, Derivative, diff, Subs) +from sympy.core.mul import Mul +from sympy.core.numbers import (NumberSymbol, E, zoo, oo, Float, I, + Rational, nan, Integer, Number, pi, _illegal) +from sympy.core.power import Pow +from sympy.core.relational import Ge, Lt, Gt, Le +from sympy.core.singleton import S +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import Symbol, symbols, Dummy, Wild +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.exponential import exp_polar, exp, log +from sympy.functions.elementary.miscellaneous import sqrt, Max +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import tan, sin, cos +from sympy.functions.special.delta_functions import (Heaviside, + DiracDelta) +from sympy.functions.special.error_functions import Si +from sympy.functions.special.gamma_functions import gamma +from sympy.integrals.integrals import integrate, Integral +from sympy.physics.secondquant import FockState +from sympy.polys.partfrac import apart +from sympy.polys.polytools import factor, cancel, Poly +from sympy.polys.rationaltools import together +from sympy.series.order import O +from sympy.sets.sets import FiniteSet +from sympy.simplify.combsimp import combsimp +from sympy.simplify.gammasimp import gammasimp +from sympy.simplify.powsimp import powsimp +from sympy.simplify.radsimp import collect, radsimp +from sympy.simplify.ratsimp import ratsimp +from sympy.simplify.simplify import simplify, nsimplify +from sympy.simplify.trigsimp import trigsimp +from sympy.tensor.indexed import Indexed +from sympy.physics.units import meter + +from sympy.testing.pytest import raises, XFAIL + +from sympy.abc import a, b, c, n, t, u, x, y, z + + +f, g, h = symbols('f,g,h', cls=Function) + + +class DummyNumber: + """ + Minimal implementation of a number that works with SymPy. + + If one has a Number class (e.g. Sage Integer, or some other custom class) + that one wants to work well with SymPy, one has to implement at least the + methods of this class DummyNumber, resp. its subclasses I5 and F1_1. + + Basically, one just needs to implement either __int__() or __float__() and + then one needs to make sure that the class works with Python integers and + with itself. + """ + + def __radd__(self, a): + if isinstance(a, (int, float)): + return a + self.number + return NotImplemented + + def __add__(self, a): + if isinstance(a, (int, float, DummyNumber)): + return self.number + a + return NotImplemented + + def __rsub__(self, a): + if isinstance(a, (int, float)): + return a - self.number + return NotImplemented + + def __sub__(self, a): + if isinstance(a, (int, float, DummyNumber)): + return self.number - a + return NotImplemented + + def __rmul__(self, a): + if isinstance(a, (int, float)): + return a * self.number + return NotImplemented + + def __mul__(self, a): + if isinstance(a, (int, float, DummyNumber)): + return self.number * a + return NotImplemented + + def __rtruediv__(self, a): + if isinstance(a, (int, float)): + return a / self.number + return NotImplemented + + def __truediv__(self, a): + if isinstance(a, (int, float, DummyNumber)): + return self.number / a + return NotImplemented + + def __rpow__(self, a): + if isinstance(a, (int, float)): + return a ** self.number + return NotImplemented + + def __pow__(self, a): + if isinstance(a, (int, float, DummyNumber)): + return self.number ** a + return NotImplemented + + def __pos__(self): + return self.number + + def __neg__(self): + return - self.number + + +class I5(DummyNumber): + number = 5 + + def __int__(self): + return self.number + + +class F1_1(DummyNumber): + number = 1.1 + + def __float__(self): + return self.number + +i5 = I5() +f1_1 = F1_1() + +# basic SymPy objects +basic_objs = [ + Rational(2), + Float("1.3"), + x, + y, + pow(x, y)*y, +] + +# all supported objects +all_objs = basic_objs + [ + 5, + 5.5, + i5, + f1_1 +] + + +def dotest(s): + for xo in all_objs: + for yo in all_objs: + s(xo, yo) + return True + + +def test_basic(): + def j(a, b): + x = a + x = +a + x = -a + x = a + b + x = a - b + x = a*b + x = a/b + x = a**b + del x + assert dotest(j) + + +def test_ibasic(): + def s(a, b): + x = a + x += b + x = a + x -= b + x = a + x *= b + x = a + x /= b + assert dotest(s) + + +class NonBasic: + '''This class represents an object that knows how to implement binary + operations like +, -, etc with Expr but is not a subclass of Basic itself. + The NonExpr subclass below does subclass Basic but not Expr. + + For both NonBasic and NonExpr it should be possible for them to override + Expr.__add__ etc because Expr.__add__ should be returning NotImplemented + for non Expr classes. Otherwise Expr.__add__ would create meaningless + objects like Add(Integer(1), FiniteSet(2)) and it wouldn't be possible for + other classes to override these operations when interacting with Expr. + ''' + def __add__(self, other): + return SpecialOp('+', self, other) + + def __radd__(self, other): + return SpecialOp('+', other, self) + + def __sub__(self, other): + return SpecialOp('-', self, other) + + def __rsub__(self, other): + return SpecialOp('-', other, self) + + def __mul__(self, other): + return SpecialOp('*', self, other) + + def __rmul__(self, other): + return SpecialOp('*', other, self) + + def __truediv__(self, other): + return SpecialOp('/', self, other) + + def __rtruediv__(self, other): + return SpecialOp('/', other, self) + + def __floordiv__(self, other): + return SpecialOp('//', self, other) + + def __rfloordiv__(self, other): + return SpecialOp('//', other, self) + + def __mod__(self, other): + return SpecialOp('%', self, other) + + def __rmod__(self, other): + return SpecialOp('%', other, self) + + def __divmod__(self, other): + return SpecialOp('divmod', self, other) + + def __rdivmod__(self, other): + return SpecialOp('divmod', other, self) + + def __pow__(self, other): + return SpecialOp('**', self, other) + + def __rpow__(self, other): + return SpecialOp('**', other, self) + + def __lt__(self, other): + return SpecialOp('<', self, other) + + def __gt__(self, other): + return SpecialOp('>', self, other) + + def __le__(self, other): + return SpecialOp('<=', self, other) + + def __ge__(self, other): + return SpecialOp('>=', self, other) + + +class NonExpr(Basic, NonBasic): + '''Like NonBasic above except this is a subclass of Basic but not Expr''' + pass + + +class SpecialOp(): + '''Represents the results of operations with NonBasic and NonExpr''' + def __new__(cls, op, arg1, arg2): + obj = object.__new__(cls) + obj.args = (op, arg1, arg2) + return obj + + +class NonArithmetic(Basic): + '''Represents a Basic subclass that does not support arithmetic operations''' + pass + + +def test_cooperative_operations(): + '''Tests that Expr uses binary operations cooperatively. + + In particular it should be possible for non-Expr classes to override + binary operators like +, - etc when used with Expr instances. This should + work for non-Expr classes whether they are Basic subclasses or not. Also + non-Expr classes that do not define binary operators with Expr should give + TypeError. + ''' + # A bunch of instances of Expr subclasses + exprs = [ + Expr(), + S.Zero, + S.One, + S.Infinity, + S.NegativeInfinity, + S.ComplexInfinity, + S.Half, + Float(0.5), + Integer(2), + Symbol('x'), + Mul(2, Symbol('x')), + Add(2, Symbol('x')), + Pow(2, Symbol('x')), + ] + + for e in exprs: + # Test that these classes can override arithmetic operations in + # combination with various Expr types. + for ne in [NonBasic(), NonExpr()]: + + results = [ + (ne + e, ('+', ne, e)), + (e + ne, ('+', e, ne)), + (ne - e, ('-', ne, e)), + (e - ne, ('-', e, ne)), + (ne * e, ('*', ne, e)), + (e * ne, ('*', e, ne)), + (ne / e, ('/', ne, e)), + (e / ne, ('/', e, ne)), + (ne // e, ('//', ne, e)), + (e // ne, ('//', e, ne)), + (ne % e, ('%', ne, e)), + (e % ne, ('%', e, ne)), + (divmod(ne, e), ('divmod', ne, e)), + (divmod(e, ne), ('divmod', e, ne)), + (ne ** e, ('**', ne, e)), + (e ** ne, ('**', e, ne)), + (e < ne, ('>', ne, e)), + (ne < e, ('<', ne, e)), + (e > ne, ('<', ne, e)), + (ne > e, ('>', ne, e)), + (e <= ne, ('>=', ne, e)), + (ne <= e, ('<=', ne, e)), + (e >= ne, ('<=', ne, e)), + (ne >= e, ('>=', ne, e)), + ] + + for res, args in results: + assert type(res) is SpecialOp and res.args == args + + # These classes do not support binary operators with Expr. Every + # operation should raise in combination with any of the Expr types. + for na in [NonArithmetic(), object()]: + + raises(TypeError, lambda : e + na) + raises(TypeError, lambda : na + e) + raises(TypeError, lambda : e - na) + raises(TypeError, lambda : na - e) + raises(TypeError, lambda : e * na) + raises(TypeError, lambda : na * e) + raises(TypeError, lambda : e / na) + raises(TypeError, lambda : na / e) + raises(TypeError, lambda : e // na) + raises(TypeError, lambda : na // e) + raises(TypeError, lambda : e % na) + raises(TypeError, lambda : na % e) + raises(TypeError, lambda : divmod(e, na)) + raises(TypeError, lambda : divmod(na, e)) + raises(TypeError, lambda : e ** na) + raises(TypeError, lambda : na ** e) + raises(TypeError, lambda : e > na) + raises(TypeError, lambda : na > e) + raises(TypeError, lambda : e < na) + raises(TypeError, lambda : na < e) + raises(TypeError, lambda : e >= na) + raises(TypeError, lambda : na >= e) + raises(TypeError, lambda : e <= na) + raises(TypeError, lambda : na <= e) + + +def test_relational(): + from sympy.core.relational import Lt + assert (pi < 3) is S.false + assert (pi <= 3) is S.false + assert (pi > 3) is S.true + assert (pi >= 3) is S.true + assert (-pi < 3) is S.true + assert (-pi <= 3) is S.true + assert (-pi > 3) is S.false + assert (-pi >= 3) is S.false + r = Symbol('r', real=True) + assert (r - 2 < r - 3) is S.false + assert Lt(x + I, x + I + 2).func == Lt # issue 8288 + + +def test_relational_assumptions(): + m1 = Symbol("m1", nonnegative=False) + m2 = Symbol("m2", positive=False) + m3 = Symbol("m3", nonpositive=False) + m4 = Symbol("m4", negative=False) + assert (m1 < 0) == Lt(m1, 0) + assert (m2 <= 0) == Le(m2, 0) + assert (m3 > 0) == Gt(m3, 0) + assert (m4 >= 0) == Ge(m4, 0) + m1 = Symbol("m1", nonnegative=False, real=True) + m2 = Symbol("m2", positive=False, real=True) + m3 = Symbol("m3", nonpositive=False, real=True) + m4 = Symbol("m4", negative=False, real=True) + assert (m1 < 0) is S.true + assert (m2 <= 0) is S.true + assert (m3 > 0) is S.true + assert (m4 >= 0) is S.true + m1 = Symbol("m1", negative=True) + m2 = Symbol("m2", nonpositive=True) + m3 = Symbol("m3", positive=True) + m4 = Symbol("m4", nonnegative=True) + assert (m1 < 0) is S.true + assert (m2 <= 0) is S.true + assert (m3 > 0) is S.true + assert (m4 >= 0) is S.true + m1 = Symbol("m1", negative=False, real=True) + m2 = Symbol("m2", nonpositive=False, real=True) + m3 = Symbol("m3", positive=False, real=True) + m4 = Symbol("m4", nonnegative=False, real=True) + assert (m1 < 0) is S.false + assert (m2 <= 0) is S.false + assert (m3 > 0) is S.false + assert (m4 >= 0) is S.false + + +# See https://github.com/sympy/sympy/issues/17708 +#def test_relational_noncommutative(): +# from sympy import Lt, Gt, Le, Ge +# A, B = symbols('A,B', commutative=False) +# assert (A < B) == Lt(A, B) +# assert (A <= B) == Le(A, B) +# assert (A > B) == Gt(A, B) +# assert (A >= B) == Ge(A, B) + + +def test_basic_nostr(): + for obj in basic_objs: + raises(TypeError, lambda: obj + '1') + raises(TypeError, lambda: obj - '1') + if obj == 2: + assert obj * '1' == '11' + else: + raises(TypeError, lambda: obj * '1') + raises(TypeError, lambda: obj / '1') + raises(TypeError, lambda: obj ** '1') + + +def test_series_expansion_for_uniform_order(): + assert (1/x + y + x).series(x, 0, 0) == 1/x + O(1, x) + assert (1/x + y + x).series(x, 0, 1) == 1/x + y + O(x) + assert (1/x + 1 + x).series(x, 0, 0) == 1/x + O(1, x) + assert (1/x + 1 + x).series(x, 0, 1) == 1/x + 1 + O(x) + assert (1/x + x).series(x, 0, 0) == 1/x + O(1, x) + assert (1/x + y + y*x + x).series(x, 0, 0) == 1/x + O(1, x) + assert (1/x + y + y*x + x).series(x, 0, 1) == 1/x + y + O(x) + + +def test_leadterm(): + assert (3 + 2*x**(log(3)/log(2) - 1)).leadterm(x) == (3, 0) + + assert (1/x**2 + 1 + x + x**2).leadterm(x)[1] == -2 + assert (1/x + 1 + x + x**2).leadterm(x)[1] == -1 + assert (x**2 + 1/x).leadterm(x)[1] == -1 + assert (1 + x**2).leadterm(x)[1] == 0 + assert (x + 1).leadterm(x)[1] == 0 + assert (x + x**2).leadterm(x)[1] == 1 + assert (x**2).leadterm(x)[1] == 2 + + +def test_as_leading_term(): + assert (3 + 2*x**(log(3)/log(2) - 1)).as_leading_term(x) == 3 + assert (1/x**2 + 1 + x + x**2).as_leading_term(x) == 1/x**2 + assert (1/x + 1 + x + x**2).as_leading_term(x) == 1/x + assert (x**2 + 1/x).as_leading_term(x) == 1/x + assert (1 + x**2).as_leading_term(x) == 1 + assert (x + 1).as_leading_term(x) == 1 + assert (x + x**2).as_leading_term(x) == x + assert (x**2).as_leading_term(x) == x**2 + assert (x + oo).as_leading_term(x) is oo + + raises(ValueError, lambda: (x + 1).as_leading_term(1)) + + # https://github.com/sympy/sympy/issues/21177 + e = -3*x + (x + Rational(3, 2) - sqrt(3)*S.ImaginaryUnit/2)**2\ + - Rational(3, 2) + 3*sqrt(3)*S.ImaginaryUnit/2 + assert e.as_leading_term(x) == \ + (12*sqrt(3)*x - 12*S.ImaginaryUnit*x)/(4*sqrt(3) + 12*S.ImaginaryUnit) + + # https://github.com/sympy/sympy/issues/21245 + e = 1 - x - x**2 + d = (1 + sqrt(5))/2 + assert e.subs(x, y + 1/d).as_leading_term(y) == \ + (-576*sqrt(5)*y - 1280*y)/(256*sqrt(5) + 576) + + +def test_leadterm2(): + assert (x*cos(1)*cos(1 + sin(1)) + sin(1 + sin(1))).leadterm(x) == \ + (sin(1 + sin(1)), 0) + + +def test_leadterm3(): + assert (y + z + x).leadterm(x) == (y + z, 0) + + +def test_as_leading_term2(): + assert (x*cos(1)*cos(1 + sin(1)) + sin(1 + sin(1))).as_leading_term(x) == \ + sin(1 + sin(1)) + + +def test_as_leading_term3(): + assert (2 + pi + x).as_leading_term(x) == 2 + pi + assert (2*x + pi*x + x**2).as_leading_term(x) == 2*x + pi*x + + +def test_as_leading_term4(): + # see issue 6843 + n = Symbol('n', integer=True, positive=True) + r = -n**3/(2*n**2 + 4*n + 2) - n**2/(n**2 + 2*n + 1) + \ + n**2/(n + 1) - n/(2*n**2 + 4*n + 2) + n/(n*x + x) + 2*n/(n + 1) - \ + 1 + 1/(n*x + x) + 1/(n + 1) - 1/x + assert r.as_leading_term(x).cancel() == n/2 + + +def test_as_leading_term_stub(): + class foo(Function): + pass + assert foo(1/x).as_leading_term(x) == foo(1/x) + assert foo(1).as_leading_term(x) == foo(1) + raises(NotImplementedError, lambda: foo(x).as_leading_term(x)) + + +def test_as_leading_term_deriv_integral(): + # related to issue 11313 + assert Derivative(x ** 3, x).as_leading_term(x) == 3*x**2 + assert Derivative(x ** 3, y).as_leading_term(x) == 0 + + assert Integral(x ** 3, x).as_leading_term(x) == x**4/4 + assert Integral(x ** 3, y).as_leading_term(x) == y*x**3 + + assert Derivative(exp(x), x).as_leading_term(x) == 1 + assert Derivative(log(x), x).as_leading_term(x) == (1/x).as_leading_term(x) + + +def test_atoms(): + assert x.atoms() == {x} + assert (1 + x).atoms() == {x, S.One} + + assert (1 + 2*cos(x)).atoms(Symbol) == {x} + assert (1 + 2*cos(x)).atoms(Symbol, Number) == {S.One, S(2), x} + + assert (2*(x**(y**x))).atoms() == {S(2), x, y} + + assert S.Half.atoms() == {S.Half} + assert S.Half.atoms(Symbol) == set() + + assert sin(oo).atoms(oo) == set() + + assert Poly(0, x).atoms() == {S.Zero, x} + assert Poly(1, x).atoms() == {S.One, x} + + assert Poly(x, x).atoms() == {x} + assert Poly(x, x, y).atoms() == {x, y} + assert Poly(x + y, x, y).atoms() == {x, y} + assert Poly(x + y, x, y, z).atoms() == {x, y, z} + assert Poly(x + y*t, x, y, z).atoms() == {t, x, y, z} + + assert (I*pi).atoms(NumberSymbol) == {pi} + assert (I*pi).atoms(NumberSymbol, I) == \ + (I*pi).atoms(I, NumberSymbol) == {pi, I} + + assert exp(exp(x)).atoms(exp) == {exp(exp(x)), exp(x)} + assert (1 + x*(2 + y) + exp(3 + z)).atoms(Add) == \ + {1 + x*(2 + y) + exp(3 + z), 2 + y, 3 + z} + + # issue 6132 + e = (f(x) + sin(x) + 2) + assert e.atoms(AppliedUndef) == \ + {f(x)} + assert e.atoms(AppliedUndef, Function) == \ + {f(x), sin(x)} + assert e.atoms(Function) == \ + {f(x), sin(x)} + assert e.atoms(AppliedUndef, Number) == \ + {f(x), S(2)} + assert e.atoms(Function, Number) == \ + {S(2), sin(x), f(x)} + + +def test_is_polynomial(): + k = Symbol('k', nonnegative=True, integer=True) + + assert Rational(2).is_polynomial(x, y, z) is True + assert (S.Pi).is_polynomial(x, y, z) is True + + assert x.is_polynomial(x) is True + assert x.is_polynomial(y) is True + + assert (x**2).is_polynomial(x) is True + assert (x**2).is_polynomial(y) is True + + assert (x**(-2)).is_polynomial(x) is False + assert (x**(-2)).is_polynomial(y) is True + + assert (2**x).is_polynomial(x) is False + assert (2**x).is_polynomial(y) is True + + assert (x**k).is_polynomial(x) is False + assert (x**k).is_polynomial(k) is False + assert (x**x).is_polynomial(x) is False + assert (k**k).is_polynomial(k) is False + assert (k**x).is_polynomial(k) is False + + assert (x**(-k)).is_polynomial(x) is False + assert ((2*x)**k).is_polynomial(x) is False + + assert (x**2 + 3*x - 8).is_polynomial(x) is True + assert (x**2 + 3*x - 8).is_polynomial(y) is True + + assert (x**2 + 3*x - 8).is_polynomial() is True + + assert sqrt(x).is_polynomial(x) is False + assert (sqrt(x)**3).is_polynomial(x) is False + + assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(x) is True + assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(y) is False + + assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial() is True + assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial() is False + + assert ( + (x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial(x, y) is True + assert ( + (x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial(x, y) is False + + assert (1/f(x) + 1).is_polynomial(f(x)) is False + + +def test_is_rational_function(): + assert Integer(1).is_rational_function() is True + assert Integer(1).is_rational_function(x) is True + + assert Rational(17, 54).is_rational_function() is True + assert Rational(17, 54).is_rational_function(x) is True + + assert (12/x).is_rational_function() is True + assert (12/x).is_rational_function(x) is True + + assert (x/y).is_rational_function() is True + assert (x/y).is_rational_function(x) is True + assert (x/y).is_rational_function(x, y) is True + + assert (x**2 + 1/x/y).is_rational_function() is True + assert (x**2 + 1/x/y).is_rational_function(x) is True + assert (x**2 + 1/x/y).is_rational_function(x, y) is True + + assert (sin(y)/x).is_rational_function() is False + assert (sin(y)/x).is_rational_function(y) is False + assert (sin(y)/x).is_rational_function(x) is True + assert (sin(y)/x).is_rational_function(x, y) is False + + for i in _illegal: + assert not i.is_rational_function() + for d in (1, x): + assert not (i/d).is_rational_function() + + +def test_is_meromorphic(): + f = a/x**2 + b + x + c*x**2 + assert f.is_meromorphic(x, 0) is True + assert f.is_meromorphic(x, 1) is True + assert f.is_meromorphic(x, zoo) is True + + g = 3 + 2*x**(log(3)/log(2) - 1) + assert g.is_meromorphic(x, 0) is False + assert g.is_meromorphic(x, 1) is True + assert g.is_meromorphic(x, zoo) is False + + n = Symbol('n', integer=True) + e = sin(1/x)**n*x + assert e.is_meromorphic(x, 0) is False + assert e.is_meromorphic(x, 1) is True + assert e.is_meromorphic(x, zoo) is False + + e = log(x)**pi + assert e.is_meromorphic(x, 0) is False + assert e.is_meromorphic(x, 1) is False + assert e.is_meromorphic(x, 2) is True + assert e.is_meromorphic(x, zoo) is False + + assert (log(x)**a).is_meromorphic(x, 0) is False + assert (log(x)**a).is_meromorphic(x, 1) is False + assert (a**log(x)).is_meromorphic(x, 0) is None + assert (3**log(x)).is_meromorphic(x, 0) is False + assert (3**log(x)).is_meromorphic(x, 1) is True + +def test_is_algebraic_expr(): + assert sqrt(3).is_algebraic_expr(x) is True + assert sqrt(3).is_algebraic_expr() is True + + eq = ((1 + x**2)/(1 - y**2))**(S.One/3) + assert eq.is_algebraic_expr(x) is True + assert eq.is_algebraic_expr(y) is True + + assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr(x) is True + assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr(y) is True + assert (sqrt(x) + y**(S(2)/3)).is_algebraic_expr() is True + + assert (cos(y)/sqrt(x)).is_algebraic_expr() is False + assert (cos(y)/sqrt(x)).is_algebraic_expr(x) is True + assert (cos(y)/sqrt(x)).is_algebraic_expr(y) is False + assert (cos(y)/sqrt(x)).is_algebraic_expr(x, y) is False + + +def test_SAGE1(): + #see https://github.com/sympy/sympy/issues/3346 + class MyInt: + def _sympy_(self): + return Integer(5) + m = MyInt() + e = Rational(2)*m + assert e == 10 + + raises(TypeError, lambda: Rational(2)*MyInt) + + +def test_SAGE2(): + class MyInt: + def __int__(self): + return 5 + assert sympify(MyInt()) == 5 + e = Rational(2)*MyInt() + assert e == 10 + + raises(TypeError, lambda: Rational(2)*MyInt) + + +def test_SAGE3(): + class MySymbol: + def __rmul__(self, other): + return ('mys', other, self) + + o = MySymbol() + e = x*o + + assert e == ('mys', x, o) + + +def test_len(): + e = x*y + assert len(e.args) == 2 + e = x + y + z + assert len(e.args) == 3 + + +def test_doit(): + a = Integral(x**2, x) + + assert isinstance(a.doit(), Integral) is False + + assert isinstance(a.doit(integrals=True), Integral) is False + assert isinstance(a.doit(integrals=False), Integral) is True + + assert (2*Integral(x, x)).doit() == x**2 + + +def test_attribute_error(): + raises(AttributeError, lambda: x.cos()) + raises(AttributeError, lambda: x.sin()) + raises(AttributeError, lambda: x.exp()) + + +def test_args(): + assert (x*y).args in ((x, y), (y, x)) + assert (x + y).args in ((x, y), (y, x)) + assert (x*y + 1).args in ((x*y, 1), (1, x*y)) + assert sin(x*y).args == (x*y,) + assert sin(x*y).args[0] == x*y + assert (x**y).args == (x, y) + assert (x**y).args[0] == x + assert (x**y).args[1] == y + + +def test_noncommutative_expand_issue_3757(): + A, B, C = symbols('A,B,C', commutative=False) + assert A*B - B*A != 0 + assert (A*(A + B)*B).expand() == A**2*B + A*B**2 + assert (A*(A + B + C)*B).expand() == A**2*B + A*B**2 + A*C*B + + +def test_as_numer_denom(): + a, b, c = symbols('a, b, c') + + assert nan.as_numer_denom() == (nan, 1) + assert oo.as_numer_denom() == (oo, 1) + assert (-oo).as_numer_denom() == (-oo, 1) + assert zoo.as_numer_denom() == (zoo, 1) + assert (-zoo).as_numer_denom() == (zoo, 1) + + assert x.as_numer_denom() == (x, 1) + assert (1/x).as_numer_denom() == (1, x) + assert (x/y).as_numer_denom() == (x, y) + assert (x/2).as_numer_denom() == (x, 2) + assert (x*y/z).as_numer_denom() == (x*y, z) + assert (x/(y*z)).as_numer_denom() == (x, y*z) + assert S.Half.as_numer_denom() == (1, 2) + assert (1/y**2).as_numer_denom() == (1, y**2) + assert (x/y**2).as_numer_denom() == (x, y**2) + assert ((x**2 + 1)/y).as_numer_denom() == (x**2 + 1, y) + assert (x*(y + 1)/y**7).as_numer_denom() == (x*(y + 1), y**7) + assert (x**-2).as_numer_denom() == (1, x**2) + assert (a/x + b/2/x + c/3/x).as_numer_denom() == \ + (6*a + 3*b + 2*c, 6*x) + assert (a/x + b/2/x + c/3/y).as_numer_denom() == \ + (2*c*x + y*(6*a + 3*b), 6*x*y) + assert (a/x + b/2/x + c/.5/x).as_numer_denom() == \ + (2*a + b + 4.0*c, 2*x) + # this should take no more than a few seconds + assert int(log(Add(*[Dummy()/i/x for i in range(1, 705)] + ).as_numer_denom()[1]/x).n(4)) == 705 + for i in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]: + assert (i + x/3).as_numer_denom() == \ + (x + i, 3) + assert (S.Infinity + x/3 + y/4).as_numer_denom() == \ + (4*x + 3*y + S.Infinity, 12) + assert (oo*x + zoo*y).as_numer_denom() == \ + (zoo*y + oo*x, 1) + + A, B, C = symbols('A,B,C', commutative=False) + + assert (A*B*C**-1).as_numer_denom() == (A*B*C**-1, 1) + assert (A*B*C**-1/x).as_numer_denom() == (A*B*C**-1, x) + assert (C**-1*A*B).as_numer_denom() == (C**-1*A*B, 1) + assert (C**-1*A*B/x).as_numer_denom() == (C**-1*A*B, x) + assert ((A*B*C)**-1).as_numer_denom() == ((A*B*C)**-1, 1) + assert ((A*B*C)**-1/x).as_numer_denom() == ((A*B*C)**-1, x) + + # the following morphs from Add to Mul during processing + assert Add(0, (x + y)/z/-2, evaluate=False).as_numer_denom( + ) == (-x - y, 2*z) + + +def test_trunc(): + import math + x, y = symbols('x y') + assert math.trunc(2) == 2 + assert math.trunc(4.57) == 4 + assert math.trunc(-5.79) == -5 + assert math.trunc(pi) == 3 + assert math.trunc(log(7)) == 1 + assert math.trunc(exp(5)) == 148 + assert math.trunc(cos(pi)) == -1 + assert math.trunc(sin(5)) == 0 + + raises(TypeError, lambda: math.trunc(x)) + raises(TypeError, lambda: math.trunc(x + y**2)) + raises(TypeError, lambda: math.trunc(oo)) + + +def test_as_independent(): + assert S.Zero.as_independent(x, as_Add=True) == (0, 0) + assert S.Zero.as_independent(x, as_Add=False) == (0, 0) + assert (2*x*sin(x) + y + x).as_independent(x) == (y, x + 2*x*sin(x)) + assert (2*x*sin(x) + y + x).as_independent(y) == (x + 2*x*sin(x), y) + + assert (2*x*sin(x) + y + x).as_independent(x, y) == (0, y + x + 2*x*sin(x)) + + assert (x*sin(x)*cos(y)).as_independent(x) == (cos(y), x*sin(x)) + assert (x*sin(x)*cos(y)).as_independent(y) == (x*sin(x), cos(y)) + + assert (x*sin(x)*cos(y)).as_independent(x, y) == (1, x*sin(x)*cos(y)) + + assert (sin(x)).as_independent(x) == (1, sin(x)) + assert (sin(x)).as_independent(y) == (sin(x), 1) + + assert (2*sin(x)).as_independent(x) == (2, sin(x)) + assert (2*sin(x)).as_independent(y) == (2*sin(x), 1) + + # issue 4903 = 1766b + n1, n2, n3 = symbols('n1 n2 n3', commutative=False) + assert (n1 + n1*n2).as_independent(n2) == (n1, n1*n2) + assert (n2*n1 + n1*n2).as_independent(n2) == (0, n1*n2 + n2*n1) + assert (n1*n2*n1).as_independent(n2) == (n1, n2*n1) + assert (n1*n2*n1).as_independent(n1) == (1, n1*n2*n1) + + assert (3*x).as_independent(x, as_Add=True) == (0, 3*x) + assert (3*x).as_independent(x, as_Add=False) == (3, x) + assert (3 + x).as_independent(x, as_Add=True) == (3, x) + assert (3 + x).as_independent(x, as_Add=False) == (1, 3 + x) + + # issue 5479 + assert (3*x).as_independent(Symbol) == (3, x) + + # issue 5648 + assert (n1*x*y).as_independent(x) == (n1*y, x) + assert ((x + n1)*(x - y)).as_independent(x) == (1, (x + n1)*(x - y)) + assert ((x + n1)*(x - y)).as_independent(y) == (x + n1, x - y) + assert (DiracDelta(x - n1)*DiracDelta(x - y)).as_independent(x) \ + == (1, DiracDelta(x - n1)*DiracDelta(x - y)) + assert (x*y*n1*n2*n3).as_independent(n2) == (x*y*n1, n2*n3) + assert (x*y*n1*n2*n3).as_independent(n1) == (x*y, n1*n2*n3) + assert (x*y*n1*n2*n3).as_independent(n3) == (x*y*n1*n2, n3) + assert (DiracDelta(x - n1)*DiracDelta(y - n1)*DiracDelta(x - n2)).as_independent(y) == \ + (DiracDelta(x - n1)*DiracDelta(x - n2), DiracDelta(y - n1)) + + # issue 5784 + assert (x + Integral(x, (x, 1, 2))).as_independent(x, strict=True) == \ + (Integral(x, (x, 1, 2)), x) + + eq = Add(x, -x, 2, -3, evaluate=False) + assert eq.as_independent(x) == (-1, Add(x, -x, evaluate=False)) + eq = Mul(x, 1/x, 2, -3, evaluate=False) + assert eq.as_independent(x) == (-6, Mul(x, 1/x, evaluate=False)) + + assert (x*y).as_independent(z, as_Add=True) == (x*y, 0) + +@XFAIL +def test_call_2(): + # TODO UndefinedFunction does not subclass Expr + assert (2*f)(x) == 2*f(x) + + +def test_replace(): + e = log(sin(x)) + tan(sin(x**2)) + + assert e.replace(sin, cos) == log(cos(x)) + tan(cos(x**2)) + assert e.replace( + sin, lambda a: sin(2*a)) == log(sin(2*x)) + tan(sin(2*x**2)) + + a = Wild('a') + b = Wild('b') + + assert e.replace(sin(a), cos(a)) == log(cos(x)) + tan(cos(x**2)) + assert e.replace( + sin(a), lambda a: sin(2*a)) == log(sin(2*x)) + tan(sin(2*x**2)) + # test exact + assert (2*x).replace(a*x + b, b - a, exact=True) == 2*x + assert (2*x).replace(a*x + b, b - a) == 2*x + assert (2*x).replace(a*x + b, b - a, exact=False) == 2/x + assert (2*x).replace(a*x + b, lambda a, b: b - a, exact=True) == 2*x + assert (2*x).replace(a*x + b, lambda a, b: b - a) == 2*x + assert (2*x).replace(a*x + b, lambda a, b: b - a, exact=False) == 2/x + + g = 2*sin(x**3) + + assert g.replace( + lambda expr: expr.is_Number, lambda expr: expr**2) == 4*sin(x**9) + + assert cos(x).replace(cos, sin, map=True) == (sin(x), {cos(x): sin(x)}) + assert sin(x).replace(cos, sin) == sin(x) + + cond, func = lambda x: x.is_Mul, lambda x: 2*x + assert (x*y).replace(cond, func, map=True) == (2*x*y, {x*y: 2*x*y}) + assert (x*(1 + x*y)).replace(cond, func, map=True) == \ + (2*x*(2*x*y + 1), {x*(2*x*y + 1): 2*x*(2*x*y + 1), x*y: 2*x*y}) + assert (y*sin(x)).replace(sin, lambda expr: sin(expr)/y, map=True) == \ + (sin(x), {sin(x): sin(x)/y}) + # if not simultaneous then y*sin(x) -> y*sin(x)/y = sin(x) -> sin(x)/y + assert (y*sin(x)).replace(sin, lambda expr: sin(expr)/y, + simultaneous=False) == sin(x)/y + assert (x**2 + O(x**3)).replace(Pow, lambda b, e: b**e/e + ) == x**2/2 + O(x**3) + assert (x**2 + O(x**3)).replace(Pow, lambda b, e: b**e/e, + simultaneous=False) == x**2/2 + O(x**3) + assert (x*(x*y + 3)).replace(lambda x: x.is_Mul, lambda x: 2 + x) == \ + x*(x*y + 5) + 2 + e = (x*y + 1)*(2*x*y + 1) + 1 + assert e.replace(cond, func, map=True) == ( + 2*((2*x*y + 1)*(4*x*y + 1)) + 1, + {2*x*y: 4*x*y, x*y: 2*x*y, (2*x*y + 1)*(4*x*y + 1): + 2*((2*x*y + 1)*(4*x*y + 1))}) + assert x.replace(x, y) == y + assert (x + 1).replace(1, 2) == x + 2 + + # https://groups.google.com/forum/#!topic/sympy/8wCgeC95tz0 + n1, n2, n3 = symbols('n1:4', commutative=False) + assert (n1*f(n2)).replace(f, lambda x: x) == n1*n2 + assert (n3*f(n2)).replace(f, lambda x: x) == n3*n2 + + # issue 16725 + assert S.Zero.replace(Wild('x'), 1) == 1 + # let the user override the default decision of False + assert S.Zero.replace(Wild('x'), 1, exact=True) == 0 + + +def test_find(): + expr = (x + y + 2 + sin(3*x)) + + assert expr.find(lambda u: u.is_Integer) == {S(2), S(3)} + assert expr.find(lambda u: u.is_Symbol) == {x, y} + + assert expr.find(lambda u: u.is_Integer, group=True) == {S(2): 1, S(3): 1} + assert expr.find(lambda u: u.is_Symbol, group=True) == {x: 2, y: 1} + + assert expr.find(Integer) == {S(2), S(3)} + assert expr.find(Symbol) == {x, y} + + assert expr.find(Integer, group=True) == {S(2): 1, S(3): 1} + assert expr.find(Symbol, group=True) == {x: 2, y: 1} + + a = Wild('a') + + expr = sin(sin(x)) + sin(x) + cos(x) + x + + assert expr.find(lambda u: type(u) is sin) == {sin(x), sin(sin(x))} + assert expr.find( + lambda u: type(u) is sin, group=True) == {sin(x): 2, sin(sin(x)): 1} + + assert expr.find(sin(a)) == {sin(x), sin(sin(x))} + assert expr.find(sin(a), group=True) == {sin(x): 2, sin(sin(x)): 1} + + assert expr.find(sin) == {sin(x), sin(sin(x))} + assert expr.find(sin, group=True) == {sin(x): 2, sin(sin(x)): 1} + + +def test_count(): + expr = (x + y + 2 + sin(3*x)) + + assert expr.count(lambda u: u.is_Integer) == 2 + assert expr.count(lambda u: u.is_Symbol) == 3 + + assert expr.count(Integer) == 2 + assert expr.count(Symbol) == 3 + assert expr.count(2) == 1 + + a = Wild('a') + + assert expr.count(sin) == 1 + assert expr.count(sin(a)) == 1 + assert expr.count(lambda u: type(u) is sin) == 1 + + assert f(x).count(f(x)) == 1 + assert f(x).diff(x).count(f(x)) == 1 + assert f(x).diff(x).count(x) == 2 + + +def test_has_basics(): + p = Wild('p') + + assert sin(x).has(x) + assert sin(x).has(sin) + assert not sin(x).has(y) + assert not sin(x).has(cos) + assert f(x).has(x) + assert f(x).has(f) + assert not f(x).has(y) + assert not f(x).has(g) + + assert f(x).diff(x).has(x) + assert f(x).diff(x).has(f) + assert f(x).diff(x).has(Derivative) + assert not f(x).diff(x).has(y) + assert not f(x).diff(x).has(g) + assert not f(x).diff(x).has(sin) + + assert (x**2).has(Symbol) + assert not (x**2).has(Wild) + assert (2*p).has(Wild) + + assert not x.has() + + # see issue at https://github.com/sympy/sympy/issues/5190 + assert not S(1).has(Wild) + assert not x.has(Wild) + + +def test_has_multiple(): + f = x**2*y + sin(2**t + log(z)) + + assert f.has(x) + assert f.has(y) + assert f.has(z) + assert f.has(t) + + assert not f.has(u) + + assert f.has(x, y, z, t) + assert f.has(x, y, z, t, u) + + i = Integer(4400) + + assert not i.has(x) + + assert (i*x**i).has(x) + assert not (i*y**i).has(x) + assert (i*y**i).has(x, y) + assert not (i*y**i).has(x, z) + + +def test_has_piecewise(): + f = (x*y + 3/y)**(3 + 2) + p = Piecewise((g(x), x < -1), (1, x <= 1), (f, True)) + + assert p.has(x) + assert p.has(y) + assert not p.has(z) + assert p.has(1) + assert p.has(3) + assert not p.has(4) + assert p.has(f) + assert p.has(g) + assert not p.has(h) + + +def test_has_iterative(): + A, B, C = symbols('A,B,C', commutative=False) + f = x*gamma(x)*sin(x)*exp(x*y)*A*B*C*cos(x*A*B) + + assert f.has(x) + assert f.has(x*y) + assert f.has(x*sin(x)) + assert not f.has(x*sin(y)) + assert f.has(x*A) + assert f.has(x*A*B) + assert not f.has(x*A*C) + assert f.has(x*A*B*C) + assert not f.has(x*A*C*B) + assert f.has(x*sin(x)*A*B*C) + assert not f.has(x*sin(x)*A*C*B) + assert not f.has(x*sin(y)*A*B*C) + assert f.has(x*gamma(x)) + assert not f.has(x + sin(x)) + + assert (x & y & z).has(x & z) + + +def test_has_integrals(): + f = Integral(x**2 + sin(x*y*z), (x, 0, x + y + z)) + + assert f.has(x + y) + assert f.has(x + z) + assert f.has(y + z) + + assert f.has(x*y) + assert f.has(x*z) + assert f.has(y*z) + + assert not f.has(2*x + y) + assert not f.has(2*x*y) + + +def test_has_tuple(): + assert Tuple(x, y).has(x) + assert not Tuple(x, y).has(z) + assert Tuple(f(x), g(x)).has(x) + assert not Tuple(f(x), g(x)).has(y) + assert Tuple(f(x), g(x)).has(f) + assert Tuple(f(x), g(x)).has(f(x)) + # XXX to be deprecated + #assert not Tuple(f, g).has(x) + #assert Tuple(f, g).has(f) + #assert not Tuple(f, g).has(h) + assert Tuple(True).has(True) + assert Tuple(True).has(S.true) + assert not Tuple(True).has(1) + + +def test_has_units(): + from sympy.physics.units import m, s + + assert (x*m/s).has(x) + assert (x*m/s).has(y, z) is False + + +def test_has_polys(): + poly = Poly(x**2 + x*y*sin(z), x, y, t) + + assert poly.has(x) + assert poly.has(x, y, z) + assert poly.has(x, y, z, t) + + +def test_has_physics(): + assert FockState((x, y)).has(x) + + +def test_as_poly_as_expr(): + f = x**2 + 2*x*y + + assert f.as_poly().as_expr() == f + assert f.as_poly(x, y).as_expr() == f + + assert (f + sin(x)).as_poly(x, y) is None + + p = Poly(f, x, y) + + assert p.as_poly() == p + + # https://github.com/sympy/sympy/issues/20610 + assert S(2).as_poly() is None + assert sqrt(2).as_poly(extension=True) is None + + raises(AttributeError, lambda: Tuple(x, x).as_poly(x)) + raises(AttributeError, lambda: Tuple(x ** 2, x, y).as_poly(x)) + + +def test_nonzero(): + assert bool(S.Zero) is False + assert bool(S.One) is True + assert bool(x) is True + assert bool(x + y) is True + assert bool(x - x) is False + assert bool(x*y) is True + assert bool(x*1) is True + assert bool(x*0) is False + + +def test_is_number(): + assert Float(3.14).is_number is True + assert Integer(737).is_number is True + assert Rational(3, 2).is_number is True + assert Rational(8).is_number is True + assert x.is_number is False + assert (2*x).is_number is False + assert (x + y).is_number is False + assert log(2).is_number is True + assert log(x).is_number is False + assert (2 + log(2)).is_number is True + assert (8 + log(2)).is_number is True + assert (2 + log(x)).is_number is False + assert (8 + log(2) + x).is_number is False + assert (1 + x**2/x - x).is_number is True + assert Tuple(Integer(1)).is_number is False + assert Add(2, x).is_number is False + assert Mul(3, 4).is_number is True + assert Pow(log(2), 2).is_number is True + assert oo.is_number is True + g = WildFunction('g') + assert g.is_number is False + assert (2*g).is_number is False + assert (x**2).subs(x, 3).is_number is True + + # test extensibility of .is_number + # on subinstances of Basic + class A(Basic): + pass + a = A() + assert a.is_number is False + + +def test_as_coeff_add(): + assert S(2).as_coeff_add() == (2, ()) + assert S(3.0).as_coeff_add() == (0, (S(3.0),)) + assert S(-3.0).as_coeff_add() == (0, (S(-3.0),)) + assert x.as_coeff_add() == (0, (x,)) + assert (x - 1).as_coeff_add() == (-1, (x,)) + assert (x + 1).as_coeff_add() == (1, (x,)) + assert (x + 2).as_coeff_add() == (2, (x,)) + assert (x + y).as_coeff_add(y) == (x, (y,)) + assert (3*x).as_coeff_add(y) == (3*x, ()) + # don't do expansion + e = (x + y)**2 + assert e.as_coeff_add(y) == (0, (e,)) + + +def test_as_coeff_mul(): + assert S(2).as_coeff_mul() == (2, ()) + assert S(3.0).as_coeff_mul() == (1, (S(3.0),)) + assert S(-3.0).as_coeff_mul() == (-1, (S(3.0),)) + assert S(-3.0).as_coeff_mul(rational=False) == (-S(3.0), ()) + assert x.as_coeff_mul() == (1, (x,)) + assert (-x).as_coeff_mul() == (-1, (x,)) + assert (2*x).as_coeff_mul() == (2, (x,)) + assert (x*y).as_coeff_mul(y) == (x, (y,)) + assert (3 + x).as_coeff_mul() == (1, (3 + x,)) + assert (3 + x).as_coeff_mul(y) == (3 + x, ()) + # don't do expansion + e = exp(x + y) + assert e.as_coeff_mul(y) == (1, (e,)) + e = 2**(x + y) + assert e.as_coeff_mul(y) == (1, (e,)) + assert (1.1*x).as_coeff_mul(rational=False) == (1.1, (x,)) + assert (1.1*x).as_coeff_mul() == (1, (1.1, x)) + assert (-oo*x).as_coeff_mul(rational=True) == (-1, (oo, x)) + + +def test_as_coeff_exponent(): + assert (3*x**4).as_coeff_exponent(x) == (3, 4) + assert (2*x**3).as_coeff_exponent(x) == (2, 3) + assert (4*x**2).as_coeff_exponent(x) == (4, 2) + assert (6*x**1).as_coeff_exponent(x) == (6, 1) + assert (3*x**0).as_coeff_exponent(x) == (3, 0) + assert (2*x**0).as_coeff_exponent(x) == (2, 0) + assert (1*x**0).as_coeff_exponent(x) == (1, 0) + assert (0*x**0).as_coeff_exponent(x) == (0, 0) + assert (-1*x**0).as_coeff_exponent(x) == (-1, 0) + assert (-2*x**0).as_coeff_exponent(x) == (-2, 0) + assert (2*x**3 + pi*x**3).as_coeff_exponent(x) == (2 + pi, 3) + assert (x*log(2)/(2*x + pi*x)).as_coeff_exponent(x) == \ + (log(2)/(2 + pi), 0) + # issue 4784 + D = Derivative + fx = D(f(x), x) + assert fx.as_coeff_exponent(f(x)) == (fx, 0) + + +def test_extractions(): + for base in (2, S.Exp1): + assert Pow(base**x, 3, evaluate=False + ).extract_multiplicatively(base**x) == base**(2*x) + assert (base**(5*x)).extract_multiplicatively( + base**(3*x)) == base**(2*x) + assert ((x*y)**3).extract_multiplicatively(x**2 * y) == x*y**2 + assert ((x*y)**3).extract_multiplicatively(x**4 * y) is None + assert (2*x).extract_multiplicatively(2) == x + assert (2*x).extract_multiplicatively(3) is None + assert (2*x).extract_multiplicatively(-1) is None + assert (S.Half*x).extract_multiplicatively(3) == x/6 + assert (sqrt(x)).extract_multiplicatively(x) is None + assert (sqrt(x)).extract_multiplicatively(1/x) is None + assert x.extract_multiplicatively(-x) is None + assert (-2 - 4*I).extract_multiplicatively(-2) == 1 + 2*I + assert (-2 - 4*I).extract_multiplicatively(3) is None + assert (-2*x - 4*y - 8).extract_multiplicatively(-2) == x + 2*y + 4 + assert (-2*x*y - 4*x**2*y).extract_multiplicatively(-2*y) == 2*x**2 + x + assert (2*x*y + 4*x**2*y).extract_multiplicatively(2*y) == 2*x**2 + x + assert (-4*y**2*x).extract_multiplicatively(-3*y) is None + assert (2*x).extract_multiplicatively(1) == 2*x + assert (-oo).extract_multiplicatively(5) is -oo + assert (oo).extract_multiplicatively(5) is oo + + assert ((x*y)**3).extract_additively(1) is None + assert (x + 1).extract_additively(x) == 1 + assert (x + 1).extract_additively(2*x) is None + assert (x + 1).extract_additively(-x) is None + assert (-x + 1).extract_additively(2*x) is None + assert (2*x + 3).extract_additively(x) == x + 3 + assert (2*x + 3).extract_additively(2) == 2*x + 1 + assert (2*x + 3).extract_additively(3) == 2*x + assert (2*x + 3).extract_additively(-2) is None + assert (2*x + 3).extract_additively(3*x) is None + assert (2*x + 3).extract_additively(2*x) == 3 + assert x.extract_additively(0) == x + assert S(2).extract_additively(x) is None + assert S(2.).extract_additively(2.) is S.Zero + assert S(2.).extract_additively(2) is S.Zero + assert S(2*x + 3).extract_additively(x + 1) == x + 2 + assert S(2*x + 3).extract_additively(y + 1) is None + assert S(2*x - 3).extract_additively(x + 1) is None + assert S(2*x - 3).extract_additively(y + z) is None + assert ((a + 1)*x*4 + y).extract_additively(x).expand() == \ + 4*a*x + 3*x + y + assert ((a + 1)*x*4 + 3*y).extract_additively(x + 2*y).expand() == \ + 4*a*x + 3*x + y + assert (y*(x + 1)).extract_additively(x + 1) is None + assert ((y + 1)*(x + 1) + 3).extract_additively(x + 1) == \ + y*(x + 1) + 3 + assert ((x + y)*(x + 1) + x + y + 3).extract_additively(x + y) == \ + x*(x + y) + 3 + assert (x + y + 2*((x + y)*(x + 1)) + 3).extract_additively((x + y)*(x + 1)) == \ + x + y + (x + 1)*(x + y) + 3 + assert ((y + 1)*(x + 2*y + 1) + 3).extract_additively(y + 1) == \ + (x + 2*y)*(y + 1) + 3 + assert (-x - x*I).extract_additively(-x) == -I*x + # extraction does not leave artificats, now + assert (4*x*(y + 1) + y).extract_additively(x) == x*(4*y + 3) + y + + n = Symbol("n", integer=True) + assert (Integer(-3)).could_extract_minus_sign() is True + assert (-n*x + x).could_extract_minus_sign() != \ + (n*x - x).could_extract_minus_sign() + assert (x - y).could_extract_minus_sign() != \ + (-x + y).could_extract_minus_sign() + assert (1 - x - y).could_extract_minus_sign() is True + assert (1 - x + y).could_extract_minus_sign() is False + assert ((-x - x*y)/y).could_extract_minus_sign() is False + assert ((x + x*y)/(-y)).could_extract_minus_sign() is True + assert ((x + x*y)/y).could_extract_minus_sign() is False + assert ((-x - y)/(x + y)).could_extract_minus_sign() is False + + class sign_invariant(Function, Expr): + nargs = 1 + def __neg__(self): + return self + foo = sign_invariant(x) + assert foo == -foo + assert foo.could_extract_minus_sign() is False + assert (x - y).could_extract_minus_sign() is False + assert (-x + y).could_extract_minus_sign() is True + assert (x - 1).could_extract_minus_sign() is False + assert (1 - x).could_extract_minus_sign() is True + assert (sqrt(2) - 1).could_extract_minus_sign() is True + assert (1 - sqrt(2)).could_extract_minus_sign() is False + # check that result is canonical + eq = (3*x + 15*y).extract_multiplicatively(3) + assert eq.args == eq.func(*eq.args).args + + +def test_nan_extractions(): + for r in (1, 0, I, nan): + assert nan.extract_additively(r) is None + assert nan.extract_multiplicatively(r) is None + + +def test_coeff(): + assert (x + 1).coeff(x + 1) == 1 + assert (3*x).coeff(0) == 0 + assert (z*(1 + x)*x**2).coeff(1 + x) == z*x**2 + assert (1 + 2*x*x**(1 + x)).coeff(x*x**(1 + x)) == 2 + assert (1 + 2*x**(y + z)).coeff(x**(y + z)) == 2 + assert (3 + 2*x + 4*x**2).coeff(1) == 0 + assert (3 + 2*x + 4*x**2).coeff(-1) == 0 + assert (3 + 2*x + 4*x**2).coeff(x) == 2 + assert (3 + 2*x + 4*x**2).coeff(x**2) == 4 + assert (3 + 2*x + 4*x**2).coeff(x**3) == 0 + + assert (-x/8 + x*y).coeff(x) == Rational(-1, 8) + y + assert (-x/8 + x*y).coeff(-x) == S.One/8 + assert (4*x).coeff(2*x) == 0 + assert (2*x).coeff(2*x) == 1 + assert (-oo*x).coeff(x*oo) == -1 + assert (10*x).coeff(x, 0) == 0 + assert (10*x).coeff(10*x, 0) == 0 + + n1, n2 = symbols('n1 n2', commutative=False) + assert (n1*n2).coeff(n1) == 1 + assert (n1*n2).coeff(n2) == n1 + assert (n1*n2 + x*n1).coeff(n1) == 1 # 1*n1*(n2+x) + assert (n2*n1 + x*n1).coeff(n1) == n2 + x + assert (n2*n1 + x*n1**2).coeff(n1) == n2 + assert (n1**x).coeff(n1) == 0 + assert (n1*n2 + n2*n1).coeff(n1) == 0 + assert (2*(n1 + n2)*n2).coeff(n1 + n2, right=1) == n2 + assert (2*(n1 + n2)*n2).coeff(n1 + n2, right=0) == 2 + + assert (2*f(x) + 3*f(x).diff(x)).coeff(f(x)) == 2 + + expr = z*(x + y)**2 + expr2 = z*(x + y)**2 + z*(2*x + 2*y)**2 + assert expr.coeff(z) == (x + y)**2 + assert expr.coeff(x + y) == 0 + assert expr2.coeff(z) == (x + y)**2 + (2*x + 2*y)**2 + + assert (x + y + 3*z).coeff(1) == x + y + assert (-x + 2*y).coeff(-1) == x + assert (x - 2*y).coeff(-1) == 2*y + assert (3 + 2*x + 4*x**2).coeff(1) == 0 + assert (-x - 2*y).coeff(2) == -y + assert (x + sqrt(2)*x).coeff(sqrt(2)) == x + assert (3 + 2*x + 4*x**2).coeff(x) == 2 + assert (3 + 2*x + 4*x**2).coeff(x**2) == 4 + assert (3 + 2*x + 4*x**2).coeff(x**3) == 0 + assert (z*(x + y)**2).coeff((x + y)**2) == z + assert (z*(x + y)**2).coeff(x + y) == 0 + assert (2 + 2*x + (x + 1)*y).coeff(x + 1) == y + + assert (x + 2*y + 3).coeff(1) == x + assert (x + 2*y + 3).coeff(x, 0) == 2*y + 3 + assert (x**2 + 2*y + 3*x).coeff(x**2, 0) == 2*y + 3*x + assert x.coeff(0, 0) == 0 + assert x.coeff(x, 0) == 0 + + n, m, o, l = symbols('n m o l', commutative=False) + assert n.coeff(n) == 1 + assert y.coeff(n) == 0 + assert (3*n).coeff(n) == 3 + assert (2 + n).coeff(x*m) == 0 + assert (2*x*n*m).coeff(x) == 2*n*m + assert (2 + n).coeff(x*m*n + y) == 0 + assert (2*x*n*m).coeff(3*n) == 0 + assert (n*m + m*n*m).coeff(n) == 1 + m + assert (n*m + m*n*m).coeff(n, right=True) == m # = (1 + m)*n*m + assert (n*m + m*n).coeff(n) == 0 + assert (n*m + o*m*n).coeff(m*n) == o + assert (n*m + o*m*n).coeff(m*n, right=True) == 1 + assert (n*m + n*m*n).coeff(n*m, right=True) == 1 + n # = n*m*(n + 1) + + assert (x*y).coeff(z, 0) == x*y + + assert (x*n + y*n + z*m).coeff(n) == x + y + assert (n*m + n*o + o*l).coeff(n, right=True) == m + o + assert (x*n*m*n + y*n*m*o + z*l).coeff(m, right=True) == x*n + y*o + assert (x*n*m*n + x*n*m*o + z*l).coeff(m, right=True) == n + o + assert (x*n*m*n + x*n*m*o + z*l).coeff(m) == x*n + + +def test_coeff2(): + r, kappa = symbols('r, kappa') + psi = Function("psi") + g = 1/r**2 * (2*r*psi(r).diff(r, 1) + r**2 * psi(r).diff(r, 2)) + g = g.expand() + assert g.coeff(psi(r).diff(r)) == 2/r + + +def test_coeff2_0(): + r, kappa = symbols('r, kappa') + psi = Function("psi") + g = 1/r**2 * (2*r*psi(r).diff(r, 1) + r**2 * psi(r).diff(r, 2)) + g = g.expand() + + assert g.coeff(psi(r).diff(r, 2)) == 1 + + +def test_coeff_expand(): + expr = z*(x + y)**2 + expr2 = z*(x + y)**2 + z*(2*x + 2*y)**2 + assert expr.coeff(z) == (x + y)**2 + assert expr2.coeff(z) == (x + y)**2 + (2*x + 2*y)**2 + + +def test_integrate(): + assert x.integrate(x) == x**2/2 + assert x.integrate((x, 0, 1)) == S.Half + + +def test_as_base_exp(): + assert x.as_base_exp() == (x, S.One) + assert (x*y*z).as_base_exp() == (x*y*z, S.One) + assert (x + y + z).as_base_exp() == (x + y + z, S.One) + assert ((x + y)**z).as_base_exp() == (x + y, z) + + +def test_issue_4963(): + assert hasattr(Mul(x, y), "is_commutative") + assert hasattr(Mul(x, y, evaluate=False), "is_commutative") + assert hasattr(Pow(x, y), "is_commutative") + assert hasattr(Pow(x, y, evaluate=False), "is_commutative") + expr = Mul(Pow(2, 2, evaluate=False), 3, evaluate=False) + 1 + assert hasattr(expr, "is_commutative") + + +def test_action_verbs(): + assert nsimplify(1/(exp(3*pi*x/5) + 1)) == \ + (1/(exp(3*pi*x/5) + 1)).nsimplify() + assert ratsimp(1/x + 1/y) == (1/x + 1/y).ratsimp() + assert trigsimp(log(x), deep=True) == (log(x)).trigsimp(deep=True) + assert radsimp(1/(2 + sqrt(2))) == (1/(2 + sqrt(2))).radsimp() + assert radsimp(1/(a + b*sqrt(c)), symbolic=False) == \ + (1/(a + b*sqrt(c))).radsimp(symbolic=False) + assert powsimp(x**y*x**z*y**z, combine='all') == \ + (x**y*x**z*y**z).powsimp(combine='all') + assert (x**t*y**t).powsimp(force=True) == (x*y)**t + assert simplify(x**y*x**z*y**z) == (x**y*x**z*y**z).simplify() + assert together(1/x + 1/y) == (1/x + 1/y).together() + assert collect(a*x**2 + b*x**2 + a*x - b*x + c, x) == \ + (a*x**2 + b*x**2 + a*x - b*x + c).collect(x) + assert apart(y/(y + 2)/(y + 1), y) == (y/(y + 2)/(y + 1)).apart(y) + assert combsimp(y/(x + 2)/(x + 1)) == (y/(x + 2)/(x + 1)).combsimp() + assert gammasimp(gamma(x)/gamma(x-5)) == (gamma(x)/gamma(x-5)).gammasimp() + assert factor(x**2 + 5*x + 6) == (x**2 + 5*x + 6).factor() + assert refine(sqrt(x**2)) == sqrt(x**2).refine() + assert cancel((x**2 + 5*x + 6)/(x + 2)) == ((x**2 + 5*x + 6)/(x + 2)).cancel() + + +def test_as_powers_dict(): + assert x.as_powers_dict() == {x: 1} + assert (x**y*z).as_powers_dict() == {x: y, z: 1} + assert Mul(2, 2, evaluate=False).as_powers_dict() == {S(2): S(2)} + assert (x*y).as_powers_dict()[z] == 0 + assert (x + y).as_powers_dict()[z] == 0 + + +def test_as_coefficients_dict(): + check = [S.One, x, y, x*y, 1] + assert [Add(3*x, 2*x, y, 3).as_coefficients_dict()[i] for i in check] == \ + [3, 5, 1, 0, 3] + assert [Add(3*x, 2*x, y, 3, evaluate=False).as_coefficients_dict()[i] + for i in check] == [3, 5, 1, 0, 3] + assert [(3*x*y).as_coefficients_dict()[i] for i in check] == \ + [0, 0, 0, 3, 0] + assert [(3.0*x*y).as_coefficients_dict()[i] for i in check] == \ + [0, 0, 0, 3.0, 0] + assert (3.0*x*y).as_coefficients_dict()[3.0*x*y] == 0 + eq = x*(x + 1)*a + x*b + c/x + assert eq.as_coefficients_dict(x) == {x: b, 1/x: c, + x*(x + 1): a} + assert eq.expand().as_coefficients_dict(x) == {x**2: a, x: a + b, 1/x: c} + assert x.as_coefficients_dict() == {x: S.One} + + +def test_args_cnc(): + A = symbols('A', commutative=False) + assert (x + A).args_cnc() == \ + [[], [x + A]] + assert (x + a).args_cnc() == \ + [[a + x], []] + assert (x*a).args_cnc() == \ + [[a, x], []] + assert (x*y*A*(A + 1)).args_cnc(cset=True) == \ + [{x, y}, [A, 1 + A]] + assert Mul(x, x, evaluate=False).args_cnc(cset=True, warn=False) == \ + [{x}, []] + assert Mul(x, x**2, evaluate=False).args_cnc(cset=True, warn=False) == \ + [{x, x**2}, []] + raises(ValueError, lambda: Mul(x, x, evaluate=False).args_cnc(cset=True)) + assert Mul(x, y, x, evaluate=False).args_cnc() == \ + [[x, y, x], []] + # always split -1 from leading number + assert (-1.*x).args_cnc() == [[-1, 1.0, x], []] + + +def test_new_rawargs(): + n = Symbol('n', commutative=False) + a = x + n + assert a.is_commutative is False + assert a._new_rawargs(x).is_commutative + assert a._new_rawargs(x, y).is_commutative + assert a._new_rawargs(x, n).is_commutative is False + assert a._new_rawargs(x, y, n).is_commutative is False + m = x*n + assert m.is_commutative is False + assert m._new_rawargs(x).is_commutative + assert m._new_rawargs(n).is_commutative is False + assert m._new_rawargs(x, y).is_commutative + assert m._new_rawargs(x, n).is_commutative is False + assert m._new_rawargs(x, y, n).is_commutative is False + + assert m._new_rawargs(x, n, reeval=False).is_commutative is False + assert m._new_rawargs(S.One) is S.One + + +def test_issue_5226(): + assert Add(evaluate=False) == 0 + assert Mul(evaluate=False) == 1 + assert Mul(x + y, evaluate=False).is_Add + + +def test_free_symbols(): + # free_symbols should return the free symbols of an object + assert S.One.free_symbols == set() + assert x.free_symbols == {x} + assert Integral(x, (x, 1, y)).free_symbols == {y} + assert (-Integral(x, (x, 1, y))).free_symbols == {y} + assert meter.free_symbols == set() + assert (meter**x).free_symbols == {x} + + +def test_has_free(): + assert x.has_free(x) + assert not x.has_free(y) + assert (x + y).has_free(x) + assert (x + y).has_free(*(x, z)) + assert f(x).has_free(x) + assert f(x).has_free(f(x)) + assert Integral(f(x), (f(x), 1, y)).has_free(y) + assert not Integral(f(x), (f(x), 1, y)).has_free(x) + assert not Integral(f(x), (f(x), 1, y)).has_free(f(x)) + # simple extraction + assert (x + 1 + y).has_free(x + 1) + assert not (x + 2 + y).has_free(x + 1) + assert (2 + 3*x*y).has_free(3*x) + raises(TypeError, lambda: x.has_free({x, y})) + s = FiniteSet(1, 2) + assert Piecewise((s, x > 3), (4, True)).has_free(s) + assert not Piecewise((1, x > 3), (4, True)).has_free(s) + # can't make set of these, but fallback will handle + raises(TypeError, lambda: x.has_free(y, [])) + + +def test_has_xfree(): + assert (x + 1).has_xfree({x}) + assert ((x + 1)**2).has_xfree({x + 1}) + assert not (x + y + 1).has_xfree({x + 1}) + raises(TypeError, lambda: x.has_xfree(x)) + raises(TypeError, lambda: x.has_xfree([x])) + + +def test_issue_5300(): + x = Symbol('x', commutative=False) + assert x*sqrt(2)/sqrt(6) == x*sqrt(3)/3 + + +def test_floordiv(): + from sympy.functions.elementary.integers import floor + assert x // y == floor(x / y) + + +def test_as_coeff_Mul(): + assert Integer(3).as_coeff_Mul() == (Integer(3), Integer(1)) + assert Rational(3, 4).as_coeff_Mul() == (Rational(3, 4), Integer(1)) + assert Float(5.0).as_coeff_Mul() == (Float(5.0), Integer(1)) + assert Float(0.0).as_coeff_Mul() == (Float(0.0), Integer(1)) + + assert (Integer(3)*x).as_coeff_Mul() == (Integer(3), x) + assert (Rational(3, 4)*x).as_coeff_Mul() == (Rational(3, 4), x) + assert (Float(5.0)*x).as_coeff_Mul() == (Float(5.0), x) + + assert (Integer(3)*x*y).as_coeff_Mul() == (Integer(3), x*y) + assert (Rational(3, 4)*x*y).as_coeff_Mul() == (Rational(3, 4), x*y) + assert (Float(5.0)*x*y).as_coeff_Mul() == (Float(5.0), x*y) + + assert (x).as_coeff_Mul() == (S.One, x) + assert (x*y).as_coeff_Mul() == (S.One, x*y) + assert (-oo*x).as_coeff_Mul(rational=True) == (-1, oo*x) + + +def test_as_coeff_Add(): + assert Integer(3).as_coeff_Add() == (Integer(3), Integer(0)) + assert Rational(3, 4).as_coeff_Add() == (Rational(3, 4), Integer(0)) + assert Float(5.0).as_coeff_Add() == (Float(5.0), Integer(0)) + + assert (Integer(3) + x).as_coeff_Add() == (Integer(3), x) + assert (Rational(3, 4) + x).as_coeff_Add() == (Rational(3, 4), x) + assert (Float(5.0) + x).as_coeff_Add() == (Float(5.0), x) + assert (Float(5.0) + x).as_coeff_Add(rational=True) == (0, Float(5.0) + x) + + assert (Integer(3) + x + y).as_coeff_Add() == (Integer(3), x + y) + assert (Rational(3, 4) + x + y).as_coeff_Add() == (Rational(3, 4), x + y) + assert (Float(5.0) + x + y).as_coeff_Add() == (Float(5.0), x + y) + + assert (x).as_coeff_Add() == (S.Zero, x) + assert (x*y).as_coeff_Add() == (S.Zero, x*y) + + +def test_expr_sorting(): + + exprs = [1/x**2, 1/x, sqrt(sqrt(x)), sqrt(x), x, sqrt(x)**3, x**2] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [x, 2*x, 2*x**2, 2*x**3, x**n, 2*x**n, sin(x), sin(x)**n, + sin(x**2), cos(x), cos(x**2), tan(x)] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [x + 1, x**2 + x + 1, x**3 + x**2 + x + 1] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [S(4), x - 3*I/2, x + 3*I/2, x - 4*I + 1, x + 4*I + 1] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [f(x), g(x), exp(x), sin(x), cos(x), factorial(x)] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [Tuple(x, y), Tuple(x, z), Tuple(x, y, z)] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [[3], [1, 2]] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [[1, 2], [2, 3]] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [[1, 2], [1, 2, 3]] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [{x: -y}, {x: y}] + assert sorted(exprs, key=default_sort_key) == exprs + + exprs = [{1}, {1, 2}] + assert sorted(exprs, key=default_sort_key) == exprs + + a, b = exprs = [Dummy('x'), Dummy('x')] + assert sorted([b, a], key=default_sort_key) == exprs + + +def test_as_ordered_factors(): + + assert x.as_ordered_factors() == [x] + assert (2*x*x**n*sin(x)*cos(x)).as_ordered_factors() \ + == [Integer(2), x, x**n, sin(x), cos(x)] + + args = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)] + expr = Mul(*args) + + assert expr.as_ordered_factors() == args + + A, B = symbols('A,B', commutative=False) + + assert (A*B).as_ordered_factors() == [A, B] + assert (B*A).as_ordered_factors() == [B, A] + + +def test_as_ordered_terms(): + + assert x.as_ordered_terms() == [x] + assert (sin(x)**2*cos(x) + sin(x)*cos(x)**2 + 1).as_ordered_terms() \ + == [sin(x)**2*cos(x), sin(x)*cos(x)**2, 1] + + args = [f(1), f(2), f(3), f(1, 2, 3), g(1), g(2), g(3), g(1, 2, 3)] + expr = Add(*args) + + assert expr.as_ordered_terms() == args + + assert (1 + 4*sqrt(3)*pi*x).as_ordered_terms() == [4*pi*x*sqrt(3), 1] + + assert ( 2 + 3*I).as_ordered_terms() == [2, 3*I] + assert (-2 + 3*I).as_ordered_terms() == [-2, 3*I] + assert ( 2 - 3*I).as_ordered_terms() == [2, -3*I] + assert (-2 - 3*I).as_ordered_terms() == [-2, -3*I] + + assert ( 4 + 3*I).as_ordered_terms() == [4, 3*I] + assert (-4 + 3*I).as_ordered_terms() == [-4, 3*I] + assert ( 4 - 3*I).as_ordered_terms() == [4, -3*I] + assert (-4 - 3*I).as_ordered_terms() == [-4, -3*I] + + e = x**2*y**2 + x*y**4 + y + 2 + + assert e.as_ordered_terms(order="lex") == [x**2*y**2, x*y**4, y, 2] + assert e.as_ordered_terms(order="grlex") == [x*y**4, x**2*y**2, y, 2] + assert e.as_ordered_terms(order="rev-lex") == [2, y, x*y**4, x**2*y**2] + assert e.as_ordered_terms(order="rev-grlex") == [2, y, x**2*y**2, x*y**4] + + k = symbols('k') + assert k.as_ordered_terms(data=True) == ([(k, ((1.0, 0.0), (1,), ()))], [k]) + + +def test_sort_key_atomic_expr(): + from sympy.physics.units import m, s + assert sorted([-m, s], key=lambda arg: arg.sort_key()) == [-m, s] + + +def test_eval_interval(): + assert exp(x)._eval_interval(*Tuple(x, 0, 1)) == exp(1) - exp(0) + + # issue 4199 + a = x/y + raises(NotImplementedError, lambda: a._eval_interval(x, S.Zero, oo)._eval_interval(y, oo, S.Zero)) + raises(NotImplementedError, lambda: a._eval_interval(x, S.Zero, oo)._eval_interval(y, S.Zero, oo)) + a = x - y + raises(NotImplementedError, lambda: a._eval_interval(x, S.One, oo)._eval_interval(y, oo, S.One)) + raises(ValueError, lambda: x._eval_interval(x, None, None)) + a = -y*Heaviside(x - y) + assert a._eval_interval(x, -oo, oo) == -y + assert a._eval_interval(x, oo, -oo) == y + + +def test_eval_interval_zoo(): + # Test that limit is used when zoo is returned + assert Si(1/x)._eval_interval(x, S.Zero, S.One) == -pi/2 + Si(1) + + +def test_primitive(): + assert (3*(x + 1)**2).primitive() == (3, (x + 1)**2) + assert (6*x + 2).primitive() == (2, 3*x + 1) + assert (x/2 + 3).primitive() == (S.Half, x + 6) + eq = (6*x + 2)*(x/2 + 3) + assert eq.primitive()[0] == 1 + eq = (2 + 2*x)**2 + assert eq.primitive()[0] == 1 + assert (4.0*x).primitive() == (1, 4.0*x) + assert (4.0*x + y/2).primitive() == (S.Half, 8.0*x + y) + assert (-2*x).primitive() == (2, -x) + assert Add(5*z/7, 0.5*x, 3*y/2, evaluate=False).primitive() == \ + (S.One/14, 7.0*x + 21*y + 10*z) + for i in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]: + assert (i + x/3).primitive() == \ + (S.One/3, i + x) + assert (S.Infinity + 2*x/3 + 4*y/7).primitive() == \ + (S.One/21, 14*x + 12*y + oo) + assert S.Zero.primitive() == (S.One, S.Zero) + + +def test_issue_5843(): + a = 1 + x + assert (2*a).extract_multiplicatively(a) == 2 + assert (4*a).extract_multiplicatively(2*a) == 2 + assert ((3*a)*(2*a)).extract_multiplicatively(a) == 6*a + + +def test_is_constant(): + from sympy.solvers.solvers import checksol + assert Sum(x, (x, 1, 10)).is_constant() is True + assert Sum(x, (x, 1, n)).is_constant() is False + assert Sum(x, (x, 1, n)).is_constant(y) is True + assert Sum(x, (x, 1, n)).is_constant(n) is False + assert Sum(x, (x, 1, n)).is_constant(x) is True + eq = a*cos(x)**2 + a*sin(x)**2 - a + assert eq.is_constant() is True + assert eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0 + assert x.is_constant() is False + assert x.is_constant(y) is True + assert log(x/y).is_constant() is False + + assert checksol(x, x, Sum(x, (x, 1, n))) is False + assert checksol(x, x, Sum(x, (x, 1, n))) is False + assert f(1).is_constant + assert checksol(x, x, f(x)) is False + + assert Pow(x, S.Zero, evaluate=False).is_constant() is True # == 1 + assert Pow(S.Zero, x, evaluate=False).is_constant() is False # == 0 or 1 + assert (2**x).is_constant() is False + assert Pow(S(2), S(3), evaluate=False).is_constant() is True + + z1, z2 = symbols('z1 z2', zero=True) + assert (z1 + 2*z2).is_constant() is True + + assert meter.is_constant() is True + assert (3*meter).is_constant() is True + assert (x*meter).is_constant() is False + + +def test_equals(): + assert (-3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2).equals(0) + assert (x**2 - 1).equals((x + 1)*(x - 1)) + assert (cos(x)**2 + sin(x)**2).equals(1) + assert (a*cos(x)**2 + a*sin(x)**2).equals(a) + r = sqrt(2) + assert (-1/(r + r*x) + 1/r/(1 + x)).equals(0) + assert factorial(x + 1).equals((x + 1)*factorial(x)) + assert sqrt(3).equals(2*sqrt(3)) is False + assert (sqrt(5)*sqrt(3)).equals(sqrt(3)) is False + assert (sqrt(5) + sqrt(3)).equals(0) is False + assert (sqrt(5) + pi).equals(0) is False + assert meter.equals(0) is False + assert (3*meter**2).equals(0) is False + eq = -(-1)**(S(3)/4)*6**(S.One/4) + (-6)**(S.One/4)*I + if eq != 0: # if canonicalization makes this zero, skip the test + assert eq.equals(0) + assert sqrt(x).equals(0) is False + + # from integrate(x*sqrt(1 + 2*x), x); + # diff is zero only when assumptions allow + i = 2*sqrt(2)*x**(S(5)/2)*(1 + 1/(2*x))**(S(5)/2)/5 + \ + 2*sqrt(2)*x**(S(3)/2)*(1 + 1/(2*x))**(S(5)/2)/(-6 - 3/x) + ans = sqrt(2*x + 1)*(6*x**2 + x - 1)/15 + diff = i - ans + assert diff.equals(0) is None # should be False, but previously this was False due to wrong intermediate result + assert diff.subs(x, Rational(-1, 2)/2) == 7*sqrt(2)/120 + # there are regions for x for which the expression is True, for + # example, when x < -1/2 or x > 0 the expression is zero + p = Symbol('p', positive=True) + assert diff.subs(x, p).equals(0) is True + assert diff.subs(x, -1).equals(0) is True + + # prove via minimal_polynomial or self-consistency + eq = sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) - sqrt(10 + 6*sqrt(3)) + assert eq.equals(0) + q = 3**Rational(1, 3) + 3 + p = expand(q**3)**Rational(1, 3) + assert (p - q).equals(0) + + # issue 6829 + # eq = q*x + q/4 + x**4 + x**3 + 2*x**2 - S.One/3 + # z = eq.subs(x, solve(eq, x)[0]) + q = symbols('q') + z = (q*(-sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/12)/2 - sqrt((2*q - S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - + S(2197)/13824)**(S.One/3) - S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - + S(2197)/13824)**(S.One/3) - S(13)/6)/2 - S.One/4) + q/4 + (-sqrt(-2*(-(q + - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q + - S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/6)/2 - S.One/4)**4 + (-sqrt(-2*(-(q - S(7)/8)**S(2)/8 - + S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q - + S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/6)/2 - S.One/4)**3 + 2*(-sqrt(-2*(-(q - S(7)/8)**S(2)/8 - + S(2197)/13824)**(S.One/3) - S(13)/12)/2 - sqrt((2*q - + S(7)/4)/sqrt(-2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/12) + 2*(-(q - S(7)/8)**S(2)/8 - S(2197)/13824)**(S.One/3) - + S(13)/6)/2 - S.One/4)**2 - Rational(1, 3)) + assert z.equals(0) + + +def test_random(): + from sympy.functions.combinatorial.numbers import lucas + from sympy.simplify.simplify import posify + assert posify(x)[0]._random() is not None + assert lucas(n)._random(2, -2, 0, -1, 1) is None + + # issue 8662 + assert Piecewise((Max(x, y), z))._random() is None + + +def test_round(): + assert str(Float('0.1249999').round(2)) == '0.12' + d20 = 12345678901234567890 + ans = S(d20).round(2) + assert ans.is_Integer and ans == d20 + ans = S(d20).round(-2) + assert ans.is_Integer and ans == 12345678901234567900 + assert str(S('1/7').round(4)) == '0.1429' + assert str(S('.[12345]').round(4)) == '0.1235' + assert str(S('.1349').round(2)) == '0.13' + n = S(12345) + ans = n.round() + assert ans.is_Integer + assert ans == n + ans = n.round(1) + assert ans.is_Integer + assert ans == n + ans = n.round(4) + assert ans.is_Integer + assert ans == n + assert n.round(-1) == 12340 + + r = Float(str(n)).round(-4) + assert r == 10000.0 + + assert n.round(-5) == 0 + + assert str((pi + sqrt(2)).round(2)) == '4.56' + assert (10*(pi + sqrt(2))).round(-1) == 50.0 + raises(TypeError, lambda: round(x + 2, 2)) + assert str(S(2.3).round(1)) == '2.3' + # rounding in SymPy (as in Decimal) should be + # exact for the given precision; we check here + # that when a 5 follows the last digit that + # the rounded digit will be even. + for i in range(-99, 100): + # construct a decimal that ends in 5, e.g. 123 -> 0.1235 + s = str(abs(i)) + p = len(s) # we are going to round to the last digit of i + n = '0.%s5' % s # put a 5 after i's digits + j = p + 2 # 2 for '0.' + if i < 0: # 1 for '-' + j += 1 + n = '-' + n + v = str(Float(n).round(p))[:j] # pertinent digits + if v.endswith('.'): + continue # it ends with 0 which is even + L = int(v[-1]) # last digit + assert L % 2 == 0, (n, '->', v) + + assert (Float(.3, 3) + 2*pi).round() == 7 + assert (Float(.3, 3) + 2*pi*100).round() == 629 + assert (pi + 2*E*I).round() == 3 + 5*I + # don't let request for extra precision give more than + # what is known (in this case, only 3 digits) + assert str((Float(.03, 3) + 2*pi/100).round(5)) == '0.0928' + assert str((Float(.03, 3) + 2*pi/100).round(4)) == '0.0928' + + assert S.Zero.round() == 0 + + a = (Add(1, Float('1.' + '9'*27, ''), evaluate=0)) + assert a.round(10) == Float('3.000000000000000000000000000', '') + assert a.round(25) == Float('3.000000000000000000000000000', '') + assert a.round(26) == Float('3.000000000000000000000000000', '') + assert a.round(27) == Float('2.999999999999999999999999999', '') + assert a.round(30) == Float('2.999999999999999999999999999', '') + #assert a.round(10) == Float('3.0000000000', '') + #assert a.round(25) == Float('3.0000000000000000000000000', '') + #assert a.round(26) == Float('3.00000000000000000000000000', '') + #assert a.round(27) == Float('2.999999999999999999999999999', '') + #assert a.round(30) == Float('2.999999999999999999999999999', '') + + # XXX: Should round set the precision of the result? + # The previous version of the tests above is this but they only pass + # because Floats with unequal precision compare equal: + # + # assert a.round(10) == Float('3.0000000000', '') + # assert a.round(25) == Float('3.0000000000000000000000000', '') + # assert a.round(26) == Float('3.00000000000000000000000000', '') + # assert a.round(27) == Float('2.999999999999999999999999999', '') + # assert a.round(30) == Float('2.999999999999999999999999999', '') + + raises(TypeError, lambda: x.round()) + raises(TypeError, lambda: f(1).round()) + + # exact magnitude of 10 + assert str(S.One.round()) == '1' + assert str(S(100).round()) == '100' + + # applied to real and imaginary portions + assert (2*pi + E*I).round() == 6 + 3*I + assert (2*pi + I/10).round() == 6 + assert (pi/10 + 2*I).round() == 2*I + # the lhs re and im parts are Float with dps of 2 + # and those on the right have dps of 15 so they won't compare + # equal unless we use string or compare components (which will + # then coerce the floats to the same precision) or re-create + # the floats + assert str((pi/10 + E*I).round(2)) == '0.31 + 2.72*I' + assert str((pi/10 + E*I).round(2).as_real_imag()) == '(0.31, 2.72)' + assert str((pi/10 + E*I).round(2)) == '0.31 + 2.72*I' + + # issue 6914 + assert (I**(I + 3)).round(3) == Float('-0.208', '')*I + + # issue 8720 + assert S(-123.6).round() == -124 + assert S(-1.5).round() == -2 + assert S(-100.5).round() == -100 + assert S(-1.5 - 10.5*I).round() == -2 - 10*I + + # issue 7961 + assert str(S(0.006).round(2)) == '0.01' + assert str(S(0.00106).round(4)) == '0.0011' + + # issue 8147 + assert S.NaN.round() is S.NaN + assert S.Infinity.round() is S.Infinity + assert S.NegativeInfinity.round() is S.NegativeInfinity + assert S.ComplexInfinity.round() is S.ComplexInfinity + + # check that types match + for i in range(2): + fi = float(i) + # 2 args + assert all(type(round(i, p)) is int for p in (-1, 0, 1)) + assert all(S(i).round(p).is_Integer for p in (-1, 0, 1)) + assert all(type(round(fi, p)) is float for p in (-1, 0, 1)) + assert all(S(fi).round(p).is_Float for p in (-1, 0, 1)) + # 1 arg (p is None) + assert type(round(i)) is int + assert S(i).round().is_Integer + assert type(round(fi)) is int + assert S(fi).round().is_Integer + + # issue 25698 + n = 6000002 + assert int(n*(log(n) + log(log(n)))) == 110130079 + one = cos(2)**2 + sin(2)**2 + eq = exp(one*I*pi) + qr, qi = eq.as_real_imag() + assert qi.round(2) == 0.0 + assert eq.round(2) == -1.0 + eq = one - 1/S(10**120) + assert S.true not in (eq > 1, eq < 1) + assert int(eq) == int(.9) == 0 + assert int(-eq) == int(-.9) == 0 + + +def test_held_expression_UnevaluatedExpr(): + x = symbols("x") + he = UnevaluatedExpr(1/x) + e1 = x*he + + assert isinstance(e1, Mul) + assert e1.args == (x, he) + assert e1.doit() == 1 + assert UnevaluatedExpr(Derivative(x, x)).doit(deep=False + ) == Derivative(x, x) + assert UnevaluatedExpr(Derivative(x, x)).doit() == 1 + + xx = Mul(x, x, evaluate=False) + assert xx != x**2 + + ue2 = UnevaluatedExpr(xx) + assert isinstance(ue2, UnevaluatedExpr) + assert ue2.args == (xx,) + assert ue2.doit() == x**2 + assert ue2.doit(deep=False) == xx + + x2 = UnevaluatedExpr(2)*2 + assert type(x2) is Mul + assert x2.args == (2, UnevaluatedExpr(2)) + +def test_round_exception_nostr(): + # Don't use the string form of the expression in the round exception, as + # it's too slow + s = Symbol('bad') + try: + s.round() + except TypeError as e: + assert 'bad' not in str(e) + else: + # Did not raise + raise AssertionError("Did not raise") + + +def test_extract_branch_factor(): + assert exp_polar(2.0*I*pi).extract_branch_factor() == (1, 1) + + +def test_identity_removal(): + assert Add.make_args(x + 0) == (x,) + assert Mul.make_args(x*1) == (x,) + + +def test_float_0(): + assert Float(0.0) + 1 == Float(1.0) + + +@XFAIL +def test_float_0_fail(): + assert Float(0.0)*x == Float(0.0) + assert (x + Float(0.0)).is_Add + + +def test_issue_6325(): + ans = (b**2 + z**2 - (b*(a + b*t) + z*(c + t*z))**2/( + (a + b*t)**2 + (c + t*z)**2))/sqrt((a + b*t)**2 + (c + t*z)**2) + e = sqrt((a + b*t)**2 + (c + z*t)**2) + assert diff(e, t, 2) == ans + assert e.diff(t, 2) == ans + assert diff(e, t, 2, simplify=False) != ans + + +def test_issue_7426(): + f1 = a % c + f2 = x % z + assert f1.equals(f2) is None + + +def test_issue_11122(): + x = Symbol('x', extended_positive=False) + assert unchanged(Gt, x, 0) # (x > 0) + # (x > 0) should remain unevaluated after PR #16956 + + x = Symbol('x', positive=False, real=True) + assert (x > 0) is S.false + + +def test_issue_10651(): + x = Symbol('x', real=True) + e1 = (-1 + x)/(1 - x) + e3 = (4*x**2 - 4)/((1 - x)*(1 + x)) + e4 = 1/(cos(x)**2) - (tan(x))**2 + x = Symbol('x', positive=True) + e5 = (1 + x)/x + assert e1.is_constant() is None + assert e3.is_constant() is None + assert e4.is_constant() is None + assert e5.is_constant() is False + + +def test_issue_10161(): + x = symbols('x', real=True) + assert x*abs(x)*abs(x) == x**3 + + +def test_issue_10755(): + x = symbols('x') + raises(TypeError, lambda: int(log(x))) + raises(TypeError, lambda: log(x).round(2)) + + +def test_issue_11877(): + x = symbols('x') + assert integrate(log(S.Half - x), (x, 0, S.Half)) == Rational(-1, 2) -log(2)/2 + + +def test_normal(): + x = symbols('x') + e = Mul(S.Half, 1 + x, evaluate=False) + assert e.normal() == e + + +def test_expr(): + x = symbols('x') + raises(TypeError, lambda: tan(x).series(x, 2, oo, "+")) + + +def test_ExprBuilder(): + eb = ExprBuilder(Mul) + eb.args.extend([x, x]) + assert eb.build() == x**2 + + +def test_issue_22020(): + from sympy.parsing.sympy_parser import parse_expr + x = parse_expr("log((2*V/3-V)/C)/-(R+r)*C") + y = parse_expr("log((2*V/3-V)/C)/-(R+r)*2") + assert x.equals(y) is False + + +def test_non_string_equality(): + # Expressions should not compare equal to strings + x = symbols('x') + one = sympify(1) + assert (x == 'x') is False + assert (x != 'x') is True + assert (one == '1') is False + assert (one != '1') is True + assert (x + 1 == 'x + 1') is False + assert (x + 1 != 'x + 1') is True + + # Make sure == doesn't try to convert the resulting expression to a string + # (e.g., by calling sympify() instead of _sympify()) + + class BadRepr: + def __repr__(self): + raise RuntimeError + + assert (x == BadRepr()) is False + assert (x != BadRepr()) is True + + +def test_21494(): + from sympy.testing.pytest import warns_deprecated_sympy + + with warns_deprecated_sympy(): + assert x.expr_free_symbols == {x} + + with warns_deprecated_sympy(): + assert Basic().expr_free_symbols == set() + + with warns_deprecated_sympy(): + assert S(2).expr_free_symbols == {S(2)} + + with warns_deprecated_sympy(): + assert Indexed("A", x).expr_free_symbols == {Indexed("A", x)} + + with warns_deprecated_sympy(): + assert Subs(x, x, 0).expr_free_symbols == set() + + +def test_Expr__eq__iterable_handling(): + assert x != range(3) + + +def test_format(): + assert '{:1.2f}'.format(S.Zero) == '0.00' + assert '{:+3.0f}'.format(S(3)) == ' +3' + assert '{:23.20f}'.format(pi) == ' 3.14159265358979323846' + assert '{:50.48f}'.format(exp(sin(1))) == '2.319776824715853173956590377503266813254904772376' + + +def test_issue_24045(): + assert powsimp(exp(a)/((c*a - c*b)*(Float(1.0)*c*a - Float(1.0)*c*b))) # doesn't raise diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_exprtools.py b/lib/python3.11/site-packages/sympy/core/tests/test_exprtools.py new file mode 100644 index 0000000000000000000000000000000000000000..b550db1606866fb76442980ea2139aaf61219525 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_exprtools.py @@ -0,0 +1,493 @@ +"""Tests for tools for manipulating of large commutative expressions. """ + +from sympy.concrete.summations import Sum +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.containers import (Dict, Tuple) +from sympy.core.function import Function +from sympy.core.mul import Mul +from sympy.core.numbers import (I, Rational, oo) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import (root, sqrt) +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.integrals.integrals import Integral +from sympy.series.order import O +from sympy.sets.sets import Interval +from sympy.simplify.radsimp import collect +from sympy.simplify.simplify import simplify +from sympy.core.exprtools import (decompose_power, Factors, Term, _gcd_terms, + gcd_terms, factor_terms, factor_nc, _mask_nc, + _monotonic_sign) +from sympy.core.mul import _keep_coeff as _keep_coeff +from sympy.simplify.cse_opts import sub_pre +from sympy.testing.pytest import raises + +from sympy.abc import a, b, t, x, y, z + + +def test_decompose_power(): + assert decompose_power(x) == (x, 1) + assert decompose_power(x**2) == (x, 2) + assert decompose_power(x**(2*y)) == (x**y, 2) + assert decompose_power(x**(2*y/3)) == (x**(y/3), 2) + assert decompose_power(x**(y*Rational(2, 3))) == (x**(y/3), 2) + + +def test_Factors(): + assert Factors() == Factors({}) == Factors(S.One) + assert Factors().as_expr() is S.One + assert Factors({x: 2, y: 3, sin(x): 4}).as_expr() == x**2*y**3*sin(x)**4 + assert Factors(S.Infinity) == Factors({oo: 1}) + assert Factors(S.NegativeInfinity) == Factors({oo: 1, -1: 1}) + # issue #18059: + assert Factors((x**2)**S.Half).as_expr() == (x**2)**S.Half + + a = Factors({x: 5, y: 3, z: 7}) + b = Factors({ y: 4, z: 3, t: 10}) + + assert a.mul(b) == a*b == Factors({x: 5, y: 7, z: 10, t: 10}) + + assert a.div(b) == divmod(a, b) == \ + (Factors({x: 5, z: 4}), Factors({y: 1, t: 10})) + assert a.quo(b) == a/b == Factors({x: 5, z: 4}) + assert a.rem(b) == a % b == Factors({y: 1, t: 10}) + + assert a.pow(3) == a**3 == Factors({x: 15, y: 9, z: 21}) + assert b.pow(3) == b**3 == Factors({y: 12, z: 9, t: 30}) + + assert a.gcd(b) == Factors({y: 3, z: 3}) + assert a.lcm(b) == Factors({x: 5, y: 4, z: 7, t: 10}) + + a = Factors({x: 4, y: 7, t: 7}) + b = Factors({z: 1, t: 3}) + + assert a.normal(b) == (Factors({x: 4, y: 7, t: 4}), Factors({z: 1})) + + assert Factors(sqrt(2)*x).as_expr() == sqrt(2)*x + + assert Factors(-I)*I == Factors() + assert Factors({S.NegativeOne: S(3)})*Factors({S.NegativeOne: S.One, I: S(5)}) == \ + Factors(I) + assert Factors(sqrt(I)*I) == Factors(I**(S(3)/2)) == Factors({I: S(3)/2}) + assert Factors({I: S(3)/2}).as_expr() == I**(S(3)/2) + + assert Factors(S(2)**x).div(S(3)**x) == \ + (Factors({S(2): x}), Factors({S(3): x})) + assert Factors(2**(2*x + 2)).div(S(8)) == \ + (Factors({S(2): 2*x + 2}), Factors({S(8): S.One})) + + # coverage + # /!\ things break if this is not True + assert Factors({S.NegativeOne: Rational(3, 2)}) == Factors({I: S.One, S.NegativeOne: S.One}) + assert Factors({I: S.One, S.NegativeOne: Rational(1, 3)}).as_expr() == I*(-1)**Rational(1, 3) + + assert Factors(-1.) == Factors({S.NegativeOne: S.One, S(1.): 1}) + assert Factors(-2.) == Factors({S.NegativeOne: S.One, S(2.): 1}) + assert Factors((-2.)**x) == Factors({S(-2.): x}) + assert Factors(S(-2)) == Factors({S.NegativeOne: S.One, S(2): 1}) + assert Factors(S.Half) == Factors({S(2): -S.One}) + assert Factors(Rational(3, 2)) == Factors({S(3): S.One, S(2): S.NegativeOne}) + assert Factors({I: S.One}) == Factors(I) + assert Factors({-1.0: 2, I: 1}) == Factors({S(1.0): 1, I: 1}) + assert Factors({S.NegativeOne: Rational(-3, 2)}).as_expr() == I + A = symbols('A', commutative=False) + assert Factors(2*A**2) == Factors({S(2): 1, A**2: 1}) + assert Factors(I) == Factors({I: S.One}) + assert Factors(x).normal(S(2)) == (Factors(x), Factors(S(2))) + assert Factors(x).normal(S.Zero) == (Factors(), Factors(S.Zero)) + raises(ZeroDivisionError, lambda: Factors(x).div(S.Zero)) + assert Factors(x).mul(S(2)) == Factors(2*x) + assert Factors(x).mul(S.Zero).is_zero + assert Factors(x).mul(1/x).is_one + assert Factors(x**sqrt(2)**3).as_expr() == x**(2*sqrt(2)) + assert Factors(x)**Factors(S(2)) == Factors(x**2) + assert Factors(x).gcd(S.Zero) == Factors(x) + assert Factors(x).lcm(S.Zero).is_zero + assert Factors(S.Zero).div(x) == (Factors(S.Zero), Factors()) + assert Factors(x).div(x) == (Factors(), Factors()) + assert Factors({x: .2})/Factors({x: .2}) == Factors() + assert Factors(x) != Factors() + assert Factors(S.Zero).normal(x) == (Factors(S.Zero), Factors()) + n, d = x**(2 + y), x**2 + f = Factors(n) + assert f.div(d) == f.normal(d) == (Factors(x**y), Factors()) + assert f.gcd(d) == Factors() + d = x**y + assert f.div(d) == f.normal(d) == (Factors(x**2), Factors()) + assert f.gcd(d) == Factors(d) + n = d = 2**x + f = Factors(n) + assert f.div(d) == f.normal(d) == (Factors(), Factors()) + assert f.gcd(d) == Factors(d) + n, d = 2**x, 2**y + f = Factors(n) + assert f.div(d) == f.normal(d) == (Factors({S(2): x}), Factors({S(2): y})) + assert f.gcd(d) == Factors() + + # extraction of constant only + n = x**(x + 3) + assert Factors(n).normal(x**-3) == (Factors({x: x + 6}), Factors({})) + assert Factors(n).normal(x**3) == (Factors({x: x}), Factors({})) + assert Factors(n).normal(x**4) == (Factors({x: x}), Factors({x: 1})) + assert Factors(n).normal(x**(y - 3)) == \ + (Factors({x: x + 6}), Factors({x: y})) + assert Factors(n).normal(x**(y + 3)) == (Factors({x: x}), Factors({x: y})) + assert Factors(n).normal(x**(y + 4)) == \ + (Factors({x: x}), Factors({x: y + 1})) + + assert Factors(n).div(x**-3) == (Factors({x: x + 6}), Factors({})) + assert Factors(n).div(x**3) == (Factors({x: x}), Factors({})) + assert Factors(n).div(x**4) == (Factors({x: x}), Factors({x: 1})) + assert Factors(n).div(x**(y - 3)) == \ + (Factors({x: x + 6}), Factors({x: y})) + assert Factors(n).div(x**(y + 3)) == (Factors({x: x}), Factors({x: y})) + assert Factors(n).div(x**(y + 4)) == \ + (Factors({x: x}), Factors({x: y + 1})) + + assert Factors(3 * x / 2) == Factors({3: 1, 2: -1, x: 1}) + assert Factors(x * x / y) == Factors({x: 2, y: -1}) + assert Factors(27 * x / y**9) == Factors({27: 1, x: 1, y: -9}) + + +def test_Term(): + a = Term(4*x*y**2/z/t**3) + b = Term(2*x**3*y**5/t**3) + + assert a == Term(4, Factors({x: 1, y: 2}), Factors({z: 1, t: 3})) + assert b == Term(2, Factors({x: 3, y: 5}), Factors({t: 3})) + + assert a.as_expr() == 4*x*y**2/z/t**3 + assert b.as_expr() == 2*x**3*y**5/t**3 + + assert a.inv() == \ + Term(S.One/4, Factors({z: 1, t: 3}), Factors({x: 1, y: 2})) + assert b.inv() == Term(S.Half, Factors({t: 3}), Factors({x: 3, y: 5})) + + assert a.mul(b) == a*b == \ + Term(8, Factors({x: 4, y: 7}), Factors({z: 1, t: 6})) + assert a.quo(b) == a/b == Term(2, Factors({}), Factors({x: 2, y: 3, z: 1})) + + assert a.pow(3) == a**3 == \ + Term(64, Factors({x: 3, y: 6}), Factors({z: 3, t: 9})) + assert b.pow(3) == b**3 == Term(8, Factors({x: 9, y: 15}), Factors({t: 9})) + + assert a.pow(-3) == a**(-3) == \ + Term(S.One/64, Factors({z: 3, t: 9}), Factors({x: 3, y: 6})) + assert b.pow(-3) == b**(-3) == \ + Term(S.One/8, Factors({t: 9}), Factors({x: 9, y: 15})) + + assert a.gcd(b) == Term(2, Factors({x: 1, y: 2}), Factors({t: 3})) + assert a.lcm(b) == Term(4, Factors({x: 3, y: 5}), Factors({z: 1, t: 3})) + + a = Term(4*x*y**2/z/t**3) + b = Term(2*x**3*y**5*t**7) + + assert a.mul(b) == Term(8, Factors({x: 4, y: 7, t: 4}), Factors({z: 1})) + + assert Term((2*x + 2)**3) == Term(8, Factors({x + 1: 3}), Factors({})) + assert Term((2*x + 2)*(3*x + 6)**2) == \ + Term(18, Factors({x + 1: 1, x + 2: 2}), Factors({})) + + +def test_gcd_terms(): + f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \ + (2*x + 2)*(x + 6)/(5*x**2 + 5) + + assert _gcd_terms(f) == ((Rational(6, 5))*((1 + x)/(1 + x**2)), 5 + x, 1) + assert _gcd_terms(Add.make_args(f)) == \ + ((Rational(6, 5))*((1 + x)/(1 + x**2)), 5 + x, 1) + + newf = (Rational(6, 5))*((1 + x)*(5 + x)/(1 + x**2)) + assert gcd_terms(f) == newf + args = Add.make_args(f) + # non-Basic sequences of terms treated as terms of Add + assert gcd_terms(list(args)) == newf + assert gcd_terms(tuple(args)) == newf + assert gcd_terms(set(args)) == newf + # but a Basic sequence is treated as a container + assert gcd_terms(Tuple(*args)) != newf + assert gcd_terms(Basic(Tuple(S(1), 3*y + 3*x*y), Tuple(S(1), S(3)))) == \ + Basic(Tuple(S(1), 3*y*(x + 1)), Tuple(S(1), S(3))) + # but we shouldn't change keys of a dictionary or some may be lost + assert gcd_terms(Dict((x*(1 + y), S(2)), (x + x*y, y + x*y))) == \ + Dict({x*(y + 1): S(2), x + x*y: y*(1 + x)}) + + assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3) + + assert gcd_terms(0) == 0 + assert gcd_terms(1) == 1 + assert gcd_terms(x) == x + assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False) + arg = x*(2*x + 4*y) + garg = 2*x*(x + 2*y) + assert gcd_terms(arg) == garg + assert gcd_terms(sin(arg)) == sin(garg) + + # issue 6139-like + alpha, alpha1, alpha2, alpha3 = symbols('alpha:4') + a = alpha**2 - alpha*x**2 + alpha + x**3 - x*(alpha + 1) + rep = (alpha, (1 + sqrt(5))/2 + alpha1*x + alpha2*x**2 + alpha3*x**3) + s = (a/(x - alpha)).subs(*rep).series(x, 0, 1) + assert simplify(collect(s, x)) == -sqrt(5)/2 - Rational(3, 2) + O(x) + + # issue 5917 + assert _gcd_terms([S.Zero, S.Zero]) == (0, 0, 1) + assert _gcd_terms([2*x + 4]) == (2, x + 2, 1) + + eq = x/(x + 1/x) + assert gcd_terms(eq, fraction=False) == eq + eq = x/2/y + 1/x/y + assert gcd_terms(eq, fraction=True, clear=True) == \ + (x**2 + 2)/(2*x*y) + assert gcd_terms(eq, fraction=True, clear=False) == \ + (x**2/2 + 1)/(x*y) + assert gcd_terms(eq, fraction=False, clear=True) == \ + (x + 2/x)/(2*y) + assert gcd_terms(eq, fraction=False, clear=False) == \ + (x/2 + 1/x)/y + + +def test_factor_terms(): + A = Symbol('A', commutative=False) + assert factor_terms(9*(x + x*y + 1) + (3*x + 3)**(2 + 2*x)) == \ + 9*x*y + 9*x + _keep_coeff(S(3), x + 1)**_keep_coeff(S(2), x + 1) + 9 + assert factor_terms(9*(x + x*y + 1) + (3)**(2 + 2*x)) == \ + _keep_coeff(S(9), 3**(2*x) + x*y + x + 1) + assert factor_terms(3**(2 + 2*x) + a*3**(2 + 2*x)) == \ + 9*3**(2*x)*(a + 1) + assert factor_terms(x + x*A) == \ + x*(1 + A) + assert factor_terms(sin(x + x*A)) == \ + sin(x*(1 + A)) + assert factor_terms((3*x + 3)**((2 + 2*x)/3)) == \ + _keep_coeff(S(3), x + 1)**_keep_coeff(Rational(2, 3), x + 1) + assert factor_terms(x + (x*y + x)**(3*x + 3)) == \ + x + (x*(y + 1))**_keep_coeff(S(3), x + 1) + assert factor_terms(a*(x + x*y) + b*(x*2 + y*x*2)) == \ + x*(a + 2*b)*(y + 1) + i = Integral(x, (x, 0, oo)) + assert factor_terms(i) == i + + assert factor_terms(x/2 + y) == x/2 + y + # fraction doesn't apply to integer denominators + assert factor_terms(x/2 + y, fraction=True) == x/2 + y + # clear *does* apply to the integer denominators + assert factor_terms(x/2 + y, clear=True) == Mul(S.Half, x + 2*y, evaluate=False) + + # check radical extraction + eq = sqrt(2) + sqrt(10) + assert factor_terms(eq) == eq + assert factor_terms(eq, radical=True) == sqrt(2)*(1 + sqrt(5)) + eq = root(-6, 3) + root(6, 3) + assert factor_terms(eq, radical=True) == 6**(S.One/3)*(1 + (-1)**(S.One/3)) + + eq = [x + x*y] + ans = [x*(y + 1)] + for c in [list, tuple, set]: + assert factor_terms(c(eq)) == c(ans) + assert factor_terms(Tuple(x + x*y)) == Tuple(x*(y + 1)) + assert factor_terms(Interval(0, 1)) == Interval(0, 1) + e = 1/sqrt(a/2 + 1) + assert factor_terms(e, clear=False) == 1/sqrt(a/2 + 1) + assert factor_terms(e, clear=True) == sqrt(2)/sqrt(a + 2) + + eq = x/(x + 1/x) + 1/(x**2 + 1) + assert factor_terms(eq, fraction=False) == eq + assert factor_terms(eq, fraction=True) == 1 + + assert factor_terms((1/(x**3 + x**2) + 2/x**2)*y) == \ + y*(2 + 1/(x + 1))/x**2 + + # if not True, then processesing for this in factor_terms is not necessary + assert gcd_terms(-x - y) == -x - y + assert factor_terms(-x - y) == Mul(-1, x + y, evaluate=False) + + # if not True, then "special" processesing in factor_terms is not necessary + assert gcd_terms(exp(Mul(-1, x + 1))) == exp(-x - 1) + e = exp(-x - 2) + x + assert factor_terms(e) == exp(Mul(-1, x + 2, evaluate=False)) + x + assert factor_terms(e, sign=False) == e + assert factor_terms(exp(-4*x - 2) - x) == -x + exp(Mul(-2, 2*x + 1, evaluate=False)) + + # sum/integral tests + for F in (Sum, Integral): + assert factor_terms(F(x, (y, 1, 10))) == x * F(1, (y, 1, 10)) + assert factor_terms(F(x, (y, 1, 10)) + x) == x * (1 + F(1, (y, 1, 10))) + assert factor_terms(F(x*y + x*y**2, (y, 1, 10))) == x*F(y*(y + 1), (y, 1, 10)) + + # expressions involving Pow terms with base 0 + assert factor_terms(0**(x - 2) - 1) == 0**(x - 2) - 1 + assert factor_terms(0**(x + 2) - 1) == 0**(x + 2) - 1 + assert factor_terms((0**(x + 2) - 1).subs(x,-2)) == 0 + + +def test_xreplace(): + e = Mul(2, 1 + x, evaluate=False) + assert e.xreplace({}) == e + assert e.xreplace({y: x}) == e + + +def test_factor_nc(): + x, y = symbols('x,y') + k = symbols('k', integer=True) + n, m, o = symbols('n,m,o', commutative=False) + + # mul and multinomial expansion is needed + from sympy.core.function import _mexpand + e = x*(1 + y)**2 + assert _mexpand(e) == x + x*2*y + x*y**2 + + def factor_nc_test(e): + ex = _mexpand(e) + assert ex.is_Add + f = factor_nc(ex) + assert not f.is_Add and _mexpand(f) == ex + + factor_nc_test(x*(1 + y)) + factor_nc_test(n*(x + 1)) + factor_nc_test(n*(x + m)) + factor_nc_test((x + m)*n) + factor_nc_test(n*m*(x*o + n*o*m)*n) + s = Sum(x, (x, 1, 2)) + factor_nc_test(x*(1 + s)) + factor_nc_test(x*(1 + s)*s) + factor_nc_test(x*(1 + sin(s))) + factor_nc_test((1 + n)**2) + + factor_nc_test((x + n)*(x + m)*(x + y)) + factor_nc_test(x*(n*m + 1)) + factor_nc_test(x*(n*m + x)) + factor_nc_test(x*(x*n*m + 1)) + factor_nc_test(n*(m/x + o)) + factor_nc_test(m*(n + o/2)) + factor_nc_test(x*n*(x*m + 1)) + factor_nc_test(x*(m*n + x*n*m)) + factor_nc_test(n*(1 - m)*n**2) + + factor_nc_test((n + m)**2) + factor_nc_test((n - m)*(n + m)**2) + factor_nc_test((n + m)**2*(n - m)) + factor_nc_test((m - n)*(n + m)**2*(n - m)) + + assert factor_nc(n*(n + n*m)) == n**2*(1 + m) + assert factor_nc(m*(m*n + n*m*n**2)) == m*(m + n*m*n)*n + eq = m*sin(n) - sin(n)*m + assert factor_nc(eq) == eq + + # for coverage: + from sympy.physics.secondquant import Commutator + from sympy.polys.polytools import factor + eq = 1 + x*Commutator(m, n) + assert factor_nc(eq) == eq + eq = x*Commutator(m, n) + x*Commutator(m, o)*Commutator(m, n) + assert factor(eq) == x*(1 + Commutator(m, o))*Commutator(m, n) + + # issue 6534 + assert (2*n + 2*m).factor() == 2*(n + m) + + # issue 6701 + _n = symbols('nz', zero=False, commutative=False) + assert factor_nc(_n**k + _n**(k + 1)) == _n**k*(1 + _n) + assert factor_nc((m*n)**k + (m*n)**(k + 1)) == (1 + m*n)*(m*n)**k + + # issue 6918 + assert factor_nc(-n*(2*x**2 + 2*x)) == -2*n*x*(x + 1) + + +def test_issue_6360(): + a, b = symbols("a b") + apb = a + b + eq = apb + apb**2*(-2*a - 2*b) + assert factor_terms(sub_pre(eq)) == a + b - 2*(a + b)**3 + + +def test_issue_7903(): + a = symbols(r'a', real=True) + t = exp(I*cos(a)) + exp(-I*sin(a)) + assert t.simplify() + +def test_issue_8263(): + F, G = symbols('F, G', commutative=False, cls=Function) + x, y = symbols('x, y') + expr, dummies, _ = _mask_nc(F(x)*G(y) - G(y)*F(x)) + for v in dummies.values(): + assert not v.is_commutative + assert not expr.is_zero + +def test_monotonic_sign(): + F = _monotonic_sign + x = symbols('x') + assert F(x) is None + assert F(-x) is None + assert F(Dummy(prime=True)) == 2 + assert F(Dummy(prime=True, odd=True)) == 3 + assert F(Dummy(composite=True)) == 4 + assert F(Dummy(composite=True, odd=True)) == 9 + assert F(Dummy(positive=True, integer=True)) == 1 + assert F(Dummy(positive=True, even=True)) == 2 + assert F(Dummy(positive=True, even=True, prime=False)) == 4 + assert F(Dummy(negative=True, integer=True)) == -1 + assert F(Dummy(negative=True, even=True)) == -2 + assert F(Dummy(zero=True)) == 0 + assert F(Dummy(nonnegative=True)) == 0 + assert F(Dummy(nonpositive=True)) == 0 + + assert F(Dummy(positive=True) + 1).is_positive + assert F(Dummy(positive=True, integer=True) - 1).is_nonnegative + assert F(Dummy(positive=True) - 1) is None + assert F(Dummy(negative=True) + 1) is None + assert F(Dummy(negative=True, integer=True) - 1).is_nonpositive + assert F(Dummy(negative=True) - 1).is_negative + assert F(-Dummy(positive=True) + 1) is None + assert F(-Dummy(positive=True, integer=True) - 1).is_negative + assert F(-Dummy(positive=True) - 1).is_negative + assert F(-Dummy(negative=True) + 1).is_positive + assert F(-Dummy(negative=True, integer=True) - 1).is_nonnegative + assert F(-Dummy(negative=True) - 1) is None + x = Dummy(negative=True) + assert F(x**3).is_nonpositive + assert F(x**3 + log(2)*x - 1).is_negative + x = Dummy(positive=True) + assert F(-x**3).is_nonpositive + + p = Dummy(positive=True) + assert F(1/p).is_positive + assert F(p/(p + 1)).is_positive + p = Dummy(nonnegative=True) + assert F(p/(p + 1)).is_nonnegative + p = Dummy(positive=True) + assert F(-1/p).is_negative + p = Dummy(nonpositive=True) + assert F(p/(-p + 1)).is_nonpositive + + p = Dummy(positive=True, integer=True) + q = Dummy(positive=True, integer=True) + assert F(-2/p/q).is_negative + assert F(-2/(p - 1)/q) is None + + assert F((p - 1)*q + 1).is_positive + assert F(-(p - 1)*q - 1).is_negative + +def test_issue_17256(): + from sympy.sets.fancysets import Range + x = Symbol('x') + s1 = Sum(x + 1, (x, 1, 9)) + s2 = Sum(x + 1, (x, Range(1, 10))) + a = Symbol('a') + r1 = s1.xreplace({x:a}) + r2 = s2.xreplace({x:a}) + + assert r1.doit() == r2.doit() + s1 = Sum(x + 1, (x, 0, 9)) + s2 = Sum(x + 1, (x, Range(10))) + a = Symbol('a') + r1 = s1.xreplace({x:a}) + r2 = s2.xreplace({x:a}) + assert r1 == r2 + +def test_issue_21623(): + from sympy.matrices.expressions.matexpr import MatrixSymbol + M = MatrixSymbol('X', 2, 2) + assert gcd_terms(M[0,0], 1) == M[0,0] diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_facts.py b/lib/python3.11/site-packages/sympy/core/tests/test_facts.py new file mode 100644 index 0000000000000000000000000000000000000000..7ca04877d0bdaf8124258ea1d25a10bcfa0f5f3a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_facts.py @@ -0,0 +1,312 @@ +from sympy.core.facts import (deduce_alpha_implications, + apply_beta_to_alpha_route, rules_2prereq, FactRules, FactKB) +from sympy.core.logic import And, Not +from sympy.testing.pytest import raises + +T = True +F = False +U = None + + +def test_deduce_alpha_implications(): + def D(i): + I = deduce_alpha_implications(i) + P = rules_2prereq({ + (k, True): {(v, True) for v in S} for k, S in I.items()}) + return I, P + + # transitivity + I, P = D([('a', 'b'), ('b', 'c')]) + assert I == {'a': {'b', 'c'}, 'b': {'c'}, Not('b'): + {Not('a')}, Not('c'): {Not('a'), Not('b')}} + assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}} + + # Duplicate entry + I, P = D([('a', 'b'), ('b', 'c'), ('b', 'c')]) + assert I == {'a': {'b', 'c'}, 'b': {'c'}, Not('b'): {Not('a')}, Not('c'): {Not('a'), Not('b')}} + assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}} + + # see if it is tolerant to cycles + assert D([('a', 'a'), ('a', 'a')]) == ({}, {}) + assert D([('a', 'b'), ('b', 'a')]) == ( + {'a': {'b'}, 'b': {'a'}, Not('a'): {Not('b')}, Not('b'): {Not('a')}}, + {'a': {'b'}, 'b': {'a'}}) + + # see if it catches inconsistency + raises(ValueError, lambda: D([('a', Not('a'))])) + raises(ValueError, lambda: D([('a', 'b'), ('b', Not('a'))])) + raises(ValueError, lambda: D([('a', 'b'), ('b', 'c'), ('b', 'na'), + ('na', Not('a'))])) + + # see if it handles implications with negations + I, P = D([('a', Not('b')), ('c', 'b')]) + assert I == {'a': {Not('b'), Not('c')}, 'b': {Not('a')}, 'c': {'b', Not('a')}, Not('b'): {Not('c')}} + assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}} + I, P = D([(Not('a'), 'b'), ('a', 'c')]) + assert I == {'a': {'c'}, Not('a'): {'b'}, Not('b'): {'a', + 'c'}, Not('c'): {Not('a'), 'b'},} + assert P == {'a': {'b', 'c'}, 'b': {'a', 'c'}, 'c': {'a', 'b'}} + + + # Long deductions + I, P = D([('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'e')]) + assert I == {'a': {'b', 'c', 'd', 'e'}, 'b': {'c', 'd', 'e'}, + 'c': {'d', 'e'}, 'd': {'e'}, Not('b'): {Not('a')}, + Not('c'): {Not('a'), Not('b')}, Not('d'): {Not('a'), Not('b'), + Not('c')}, Not('e'): {Not('a'), Not('b'), Not('c'), Not('d')}} + assert P == {'a': {'b', 'c', 'd', 'e'}, 'b': {'a', 'c', 'd', + 'e'}, 'c': {'a', 'b', 'd', 'e'}, 'd': {'a', 'b', 'c', 'e'}, + 'e': {'a', 'b', 'c', 'd'}} + + # something related to real-world + I, P = D([('rat', 'real'), ('int', 'rat')]) + + assert I == {'int': {'rat', 'real'}, 'rat': {'real'}, + Not('real'): {Not('rat'), Not('int')}, Not('rat'): {Not('int')}} + assert P == {'rat': {'int', 'real'}, 'real': {'int', 'rat'}, + 'int': {'rat', 'real'}} + + +# TODO move me to appropriate place +def test_apply_beta_to_alpha_route(): + APPLY = apply_beta_to_alpha_route + + # indicates empty alpha-chain with attached beta-rule #bidx + def Q(bidx): + return (set(), [bidx]) + + # x -> a &(a,b) -> x -- x -> a + A = {'x': {'a'}} + B = [(And('a', 'b'), 'x')] + assert APPLY(A, B) == {'x': ({'a'}, []), 'a': Q(0), 'b': Q(0)} + + # x -> a &(a,!x) -> b -- x -> a + A = {'x': {'a'}} + B = [(And('a', Not('x')), 'b')] + assert APPLY(A, B) == {'x': ({'a'}, []), Not('x'): Q(0), 'a': Q(0)} + + # x -> a b &(a,b) -> c -- x -> a b c + A = {'x': {'a', 'b'}} + B = [(And('a', 'b'), 'c')] + assert APPLY(A, B) == \ + {'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)} + + # x -> a &(a,b) -> y -- x -> a [#0] + A = {'x': {'a'}} + B = [(And('a', 'b'), 'y')] + assert APPLY(A, B) == {'x': ({'a'}, [0]), 'a': Q(0), 'b': Q(0)} + + # x -> a b c &(a,b) -> c -- x -> a b c + A = {'x': {'a', 'b', 'c'}} + B = [(And('a', 'b'), 'c')] + assert APPLY(A, B) == \ + {'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)} + + # x -> a b &(a,b,c) -> y -- x -> a b [#0] + A = {'x': {'a', 'b'}} + B = [(And('a', 'b', 'c'), 'y')] + assert APPLY(A, B) == \ + {'x': ({'a', 'b'}, [0]), 'a': Q(0), 'b': Q(0), 'c': Q(0)} + + # x -> a b &(a,b) -> c -- x -> a b c d + # c -> d c -> d + A = {'x': {'a', 'b'}, 'c': {'d'}} + B = [(And('a', 'b'), 'c')] + assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'd'}, []), + 'c': ({'d'}, []), 'a': Q(0), 'b': Q(0)} + + # x -> a b &(a,b) -> c -- x -> a b c d e + # c -> d &(c,d) -> e c -> d e + A = {'x': {'a', 'b'}, 'c': {'d'}} + B = [(And('a', 'b'), 'c'), (And('c', 'd'), 'e')] + assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'd', 'e'}, []), + 'c': ({'d', 'e'}, []), 'a': Q(0), 'b': Q(0), 'd': Q(1)} + + # x -> a b &(a,y) -> z -- x -> a b y z + # &(a,b) -> y + A = {'x': {'a', 'b'}} + B = [(And('a', 'y'), 'z'), (And('a', 'b'), 'y')] + assert APPLY(A, B) == {'x': ({'a', 'b', 'y', 'z'}, []), + 'a': (set(), [0, 1]), 'y': Q(0), 'b': Q(1)} + + # x -> a b &(a,!b) -> c -- x -> a b + A = {'x': {'a', 'b'}} + B = [(And('a', Not('b')), 'c')] + assert APPLY(A, B) == \ + {'x': ({'a', 'b'}, []), 'a': Q(0), Not('b'): Q(0)} + + # !x -> !a !b &(!a,b) -> c -- !x -> !a !b + A = {Not('x'): {Not('a'), Not('b')}} + B = [(And(Not('a'), 'b'), 'c')] + assert APPLY(A, B) == \ + {Not('x'): ({Not('a'), Not('b')}, []), Not('a'): Q(0), 'b': Q(0)} + + # x -> a b &(b,c) -> !a -- x -> a b + A = {'x': {'a', 'b'}} + B = [(And('b', 'c'), Not('a'))] + assert APPLY(A, B) == {'x': ({'a', 'b'}, []), 'b': Q(0), 'c': Q(0)} + + # x -> a b &(a, b) -> c -- x -> a b c p + # c -> p a + A = {'x': {'a', 'b'}, 'c': {'p', 'a'}} + B = [(And('a', 'b'), 'c')] + assert APPLY(A, B) == {'x': ({'a', 'b', 'c', 'p'}, []), + 'c': ({'p', 'a'}, []), 'a': Q(0), 'b': Q(0)} + + +def test_FactRules_parse(): + f = FactRules('a -> b') + assert f.prereq == {'b': {'a'}, 'a': {'b'}} + + f = FactRules('a -> !b') + assert f.prereq == {'b': {'a'}, 'a': {'b'}} + + f = FactRules('!a -> b') + assert f.prereq == {'b': {'a'}, 'a': {'b'}} + + f = FactRules('!a -> !b') + assert f.prereq == {'b': {'a'}, 'a': {'b'}} + + f = FactRules('!z == nz') + assert f.prereq == {'z': {'nz'}, 'nz': {'z'}} + + +def test_FactRules_parse2(): + raises(ValueError, lambda: FactRules('a -> !a')) + + +def test_FactRules_deduce(): + f = FactRules(['a -> b', 'b -> c', 'b -> d', 'c -> e']) + + def D(facts): + kb = FactKB(f) + kb.deduce_all_facts(facts) + return kb + + assert D({'a': T}) == {'a': T, 'b': T, 'c': T, 'd': T, 'e': T} + assert D({'b': T}) == { 'b': T, 'c': T, 'd': T, 'e': T} + assert D({'c': T}) == { 'c': T, 'e': T} + assert D({'d': T}) == { 'd': T } + assert D({'e': T}) == { 'e': T} + + assert D({'a': F}) == {'a': F } + assert D({'b': F}) == {'a': F, 'b': F } + assert D({'c': F}) == {'a': F, 'b': F, 'c': F } + assert D({'d': F}) == {'a': F, 'b': F, 'd': F } + + assert D({'a': U}) == {'a': U} # XXX ok? + + +def test_FactRules_deduce2(): + # pos/neg/zero, but the rules are not sufficient to derive all relations + f = FactRules(['pos -> !neg', 'pos -> !z']) + + def D(facts): + kb = FactKB(f) + kb.deduce_all_facts(facts) + return kb + + assert D({'pos': T}) == {'pos': T, 'neg': F, 'z': F} + assert D({'pos': F}) == {'pos': F } + assert D({'neg': T}) == {'pos': F, 'neg': T } + assert D({'neg': F}) == { 'neg': F } + assert D({'z': T}) == {'pos': F, 'z': T} + assert D({'z': F}) == { 'z': F} + + # pos/neg/zero. rules are sufficient to derive all relations + f = FactRules(['pos -> !neg', 'neg -> !pos', 'pos -> !z', 'neg -> !z']) + + assert D({'pos': T}) == {'pos': T, 'neg': F, 'z': F} + assert D({'pos': F}) == {'pos': F } + assert D({'neg': T}) == {'pos': F, 'neg': T, 'z': F} + assert D({'neg': F}) == { 'neg': F } + assert D({'z': T}) == {'pos': F, 'neg': F, 'z': T} + assert D({'z': F}) == { 'z': F} + + +def test_FactRules_deduce_multiple(): + # deduction that involves _several_ starting points + f = FactRules(['real == pos | npos']) + + def D(facts): + kb = FactKB(f) + kb.deduce_all_facts(facts) + return kb + + assert D({'real': T}) == {'real': T} + assert D({'real': F}) == {'real': F, 'pos': F, 'npos': F} + assert D({'pos': T}) == {'real': T, 'pos': T} + assert D({'npos': T}) == {'real': T, 'npos': T} + + # --- key tests below --- + assert D({'pos': F, 'npos': F}) == {'real': F, 'pos': F, 'npos': F} + assert D({'real': T, 'pos': F}) == {'real': T, 'pos': F, 'npos': T} + assert D({'real': T, 'npos': F}) == {'real': T, 'pos': T, 'npos': F} + + assert D({'pos': T, 'npos': F}) == {'real': T, 'pos': T, 'npos': F} + assert D({'pos': F, 'npos': T}) == {'real': T, 'pos': F, 'npos': T} + + +def test_FactRules_deduce_multiple2(): + f = FactRules(['real == neg | zero | pos']) + + def D(facts): + kb = FactKB(f) + kb.deduce_all_facts(facts) + return kb + + assert D({'real': T}) == {'real': T} + assert D({'real': F}) == {'real': F, 'neg': F, 'zero': F, 'pos': F} + assert D({'neg': T}) == {'real': T, 'neg': T} + assert D({'zero': T}) == {'real': T, 'zero': T} + assert D({'pos': T}) == {'real': T, 'pos': T} + + # --- key tests below --- + assert D({'neg': F, 'zero': F, 'pos': F}) == {'real': F, 'neg': F, + 'zero': F, 'pos': F} + assert D({'real': T, 'neg': F}) == {'real': T, 'neg': F} + assert D({'real': T, 'zero': F}) == {'real': T, 'zero': F} + assert D({'real': T, 'pos': F}) == {'real': T, 'pos': F} + + assert D({'real': T, 'zero': F, 'pos': F}) == {'real': T, + 'neg': T, 'zero': F, 'pos': F} + assert D({'real': T, 'neg': F, 'pos': F}) == {'real': T, + 'neg': F, 'zero': T, 'pos': F} + assert D({'real': T, 'neg': F, 'zero': F }) == {'real': T, + 'neg': F, 'zero': F, 'pos': T} + + assert D({'neg': T, 'zero': F, 'pos': F}) == {'real': T, 'neg': T, + 'zero': F, 'pos': F} + assert D({'neg': F, 'zero': T, 'pos': F}) == {'real': T, 'neg': F, + 'zero': T, 'pos': F} + assert D({'neg': F, 'zero': F, 'pos': T}) == {'real': T, 'neg': F, + 'zero': F, 'pos': T} + + +def test_FactRules_deduce_base(): + # deduction that starts from base + + f = FactRules(['real == neg | zero | pos', + 'neg -> real & !zero & !pos', + 'pos -> real & !zero & !neg']) + base = FactKB(f) + + base.deduce_all_facts({'real': T, 'neg': F}) + assert base == {'real': T, 'neg': F} + + base.deduce_all_facts({'zero': F}) + assert base == {'real': T, 'neg': F, 'zero': F, 'pos': T} + + +def test_FactRules_deduce_staticext(): + # verify that static beta-extensions deduction takes place + f = FactRules(['real == neg | zero | pos', + 'neg -> real & !zero & !pos', + 'pos -> real & !zero & !neg', + 'nneg == real & !neg', + 'npos == real & !pos']) + + assert ('npos', True) in f.full_implications[('neg', True)] + assert ('nneg', True) in f.full_implications[('pos', True)] + assert ('nneg', True) in f.full_implications[('zero', True)] + assert ('npos', True) in f.full_implications[('zero', True)] diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_function.py b/lib/python3.11/site-packages/sympy/core/tests/test_function.py new file mode 100644 index 0000000000000000000000000000000000000000..7cc5df95f2399a96329f1111d3ef2cc9aa1342f8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_function.py @@ -0,0 +1,1455 @@ +from sympy.concrete.summations import Sum +from sympy.core.basic import Basic, _aresame +from sympy.core.cache import clear_cache +from sympy.core.containers import Dict, Tuple +from sympy.core.expr import Expr, unchanged +from sympy.core.function import (Subs, Function, diff, Lambda, expand, + nfloat, Derivative) +from sympy.core.numbers import E, Float, zoo, Rational, pi, I, oo, nan +from sympy.core.power import Pow +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import symbols, Dummy, Symbol +from sympy.functions.elementary.complexes import im, re +from sympy.functions.elementary.exponential import log, exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import sin, cos, acos +from sympy.functions.special.error_functions import expint +from sympy.functions.special.gamma_functions import loggamma, polygamma +from sympy.matrices.dense import Matrix +from sympy.printing.str import sstr +from sympy.series.order import O +from sympy.tensor.indexed import Indexed +from sympy.core.function import (PoleError, _mexpand, arity, + BadSignatureError, BadArgumentsError) +from sympy.core.parameters import _exp_is_pow +from sympy.core.sympify import sympify, SympifyError +from sympy.matrices import MutableMatrix, ImmutableMatrix +from sympy.sets.sets import FiniteSet +from sympy.solvers.solveset import solveset +from sympy.tensor.array import NDimArray +from sympy.utilities.iterables import subsets, variations +from sympy.testing.pytest import XFAIL, raises, warns_deprecated_sympy, _both_exp_pow + +from sympy.abc import t, w, x, y, z +f, g, h = symbols('f g h', cls=Function) +_xi_1, _xi_2, _xi_3 = [Dummy() for i in range(3)] + +def test_f_expand_complex(): + x = Symbol('x', real=True) + + assert f(x).expand(complex=True) == I*im(f(x)) + re(f(x)) + assert exp(x).expand(complex=True) == exp(x) + assert exp(I*x).expand(complex=True) == cos(x) + I*sin(x) + assert exp(z).expand(complex=True) == cos(im(z))*exp(re(z)) + \ + I*sin(im(z))*exp(re(z)) + + +def test_bug1(): + e = sqrt(-log(w)) + assert e.subs(log(w), -x) == sqrt(x) + + e = sqrt(-5*log(w)) + assert e.subs(log(w), -x) == sqrt(5*x) + + +def test_general_function(): + nu = Function('nu') + + e = nu(x) + edx = e.diff(x) + edy = e.diff(y) + edxdx = e.diff(x).diff(x) + edxdy = e.diff(x).diff(y) + assert e == nu(x) + assert edx != nu(x) + assert edx == diff(nu(x), x) + assert edy == 0 + assert edxdx == diff(diff(nu(x), x), x) + assert edxdy == 0 + +def test_general_function_nullary(): + nu = Function('nu') + + e = nu() + edx = e.diff(x) + edxdx = e.diff(x).diff(x) + assert e == nu() + assert edx != nu() + assert edx == 0 + assert edxdx == 0 + + +def test_derivative_subs_bug(): + e = diff(g(x), x) + assert e.subs(g(x), f(x)) != e + assert e.subs(g(x), f(x)) == Derivative(f(x), x) + assert e.subs(g(x), -f(x)) == Derivative(-f(x), x) + + assert e.subs(x, y) == Derivative(g(y), y) + + +def test_derivative_subs_self_bug(): + d = diff(f(x), x) + + assert d.subs(d, y) == y + + +def test_derivative_linearity(): + assert diff(-f(x), x) == -diff(f(x), x) + assert diff(8*f(x), x) == 8*diff(f(x), x) + assert diff(8*f(x), x) != 7*diff(f(x), x) + assert diff(8*f(x)*x, x) == 8*f(x) + 8*x*diff(f(x), x) + assert diff(8*f(x)*y*x, x).expand() == 8*y*f(x) + 8*y*x*diff(f(x), x) + + +def test_derivative_evaluate(): + assert Derivative(sin(x), x) != diff(sin(x), x) + assert Derivative(sin(x), x).doit() == diff(sin(x), x) + + assert Derivative(Derivative(f(x), x), x) == diff(f(x), x, x) + assert Derivative(sin(x), x, 0) == sin(x) + assert Derivative(sin(x), (x, y), (x, -y)) == sin(x) + + +def test_diff_symbols(): + assert diff(f(x, y, z), x, y, z) == Derivative(f(x, y, z), x, y, z) + assert diff(f(x, y, z), x, x, x) == Derivative(f(x, y, z), x, x, x) == Derivative(f(x, y, z), (x, 3)) + assert diff(f(x, y, z), x, 3) == Derivative(f(x, y, z), x, 3) + + # issue 5028 + assert [diff(-z + x/y, sym) for sym in (z, x, y)] == [-1, 1/y, -x/y**2] + assert diff(f(x, y, z), x, y, z, 2) == Derivative(f(x, y, z), x, y, z, z) + assert diff(f(x, y, z), x, y, z, 2, evaluate=False) == \ + Derivative(f(x, y, z), x, y, z, z) + assert Derivative(f(x, y, z), x, y, z)._eval_derivative(z) == \ + Derivative(f(x, y, z), x, y, z, z) + assert Derivative(Derivative(f(x, y, z), x), y)._eval_derivative(z) == \ + Derivative(f(x, y, z), x, y, z) + + raises(TypeError, lambda: cos(x).diff((x, y)).variables) + assert cos(x).diff((x, y))._wrt_variables == [x] + + # issue 23222 + assert sympify("a*x+b").diff("x") == sympify("a") + +def test_Function(): + class myfunc(Function): + @classmethod + def eval(cls): # zero args + return + + assert myfunc.nargs == FiniteSet(0) + assert myfunc().nargs == FiniteSet(0) + raises(TypeError, lambda: myfunc(x).nargs) + + class myfunc(Function): + @classmethod + def eval(cls, x): # one arg + return + + assert myfunc.nargs == FiniteSet(1) + assert myfunc(x).nargs == FiniteSet(1) + raises(TypeError, lambda: myfunc(x, y).nargs) + + class myfunc(Function): + @classmethod + def eval(cls, *x): # star args + return + + assert myfunc.nargs == S.Naturals0 + assert myfunc(x).nargs == S.Naturals0 + + +def test_nargs(): + f = Function('f') + assert f.nargs == S.Naturals0 + assert f(1).nargs == S.Naturals0 + assert Function('f', nargs=2)(1, 2).nargs == FiniteSet(2) + assert sin.nargs == FiniteSet(1) + assert sin(2).nargs == FiniteSet(1) + assert log.nargs == FiniteSet(1, 2) + assert log(2).nargs == FiniteSet(1, 2) + assert Function('f', nargs=2).nargs == FiniteSet(2) + assert Function('f', nargs=0).nargs == FiniteSet(0) + assert Function('f', nargs=(0, 1)).nargs == FiniteSet(0, 1) + assert Function('f', nargs=None).nargs == S.Naturals0 + raises(ValueError, lambda: Function('f', nargs=())) + +def test_nargs_inheritance(): + class f1(Function): + nargs = 2 + class f2(f1): + pass + class f3(f2): + pass + class f4(f3): + nargs = 1,2 + class f5(f4): + pass + class f6(f5): + pass + class f7(f6): + nargs=None + class f8(f7): + pass + class f9(f8): + pass + class f10(f9): + nargs = 1 + class f11(f10): + pass + assert f1.nargs == FiniteSet(2) + assert f2.nargs == FiniteSet(2) + assert f3.nargs == FiniteSet(2) + assert f4.nargs == FiniteSet(1, 2) + assert f5.nargs == FiniteSet(1, 2) + assert f6.nargs == FiniteSet(1, 2) + assert f7.nargs == S.Naturals0 + assert f8.nargs == S.Naturals0 + assert f9.nargs == S.Naturals0 + assert f10.nargs == FiniteSet(1) + assert f11.nargs == FiniteSet(1) + +def test_arity(): + f = lambda x, y: 1 + assert arity(f) == 2 + def f(x, y, z=None): + pass + assert arity(f) == (2, 3) + assert arity(lambda *x: x) is None + assert arity(log) == (1, 2) + + +def test_Lambda(): + e = Lambda(x, x**2) + assert e(4) == 16 + assert e(x) == x**2 + assert e(y) == y**2 + + assert Lambda((), 42)() == 42 + assert unchanged(Lambda, (), 42) + assert Lambda((), 42) != Lambda((), 43) + assert Lambda((), f(x))() == f(x) + assert Lambda((), 42).nargs == FiniteSet(0) + + assert unchanged(Lambda, (x,), x**2) + assert Lambda(x, x**2) == Lambda((x,), x**2) + assert Lambda(x, x**2) != Lambda(x, x**2 + 1) + assert Lambda((x, y), x**y) != Lambda((y, x), y**x) + assert Lambda((x, y), x**y) != Lambda((x, y), y**x) + + assert Lambda((x, y), x**y)(x, y) == x**y + assert Lambda((x, y), x**y)(3, 3) == 3**3 + assert Lambda((x, y), x**y)(x, 3) == x**3 + assert Lambda((x, y), x**y)(3, y) == 3**y + assert Lambda(x, f(x))(x) == f(x) + assert Lambda(x, x**2)(e(x)) == x**4 + assert e(e(x)) == x**4 + + x1, x2 = (Indexed('x', i) for i in (1, 2)) + assert Lambda((x1, x2), x1 + x2)(x, y) == x + y + + assert Lambda((x, y), x + y).nargs == FiniteSet(2) + + p = x, y, z, t + assert Lambda(p, t*(x + y + z))(*p) == t * (x + y + z) + + eq = Lambda(x, 2*x) + Lambda(y, 2*y) + assert eq != 2*Lambda(x, 2*x) + assert eq.as_dummy() == 2*Lambda(x, 2*x).as_dummy() + assert Lambda(x, 2*x) not in [ Lambda(x, x) ] + raises(BadSignatureError, lambda: Lambda(1, x)) + assert Lambda(x, 1)(1) is S.One + + raises(BadSignatureError, lambda: Lambda((x, x), x + 2)) + raises(BadSignatureError, lambda: Lambda(((x, x), y), x)) + raises(BadSignatureError, lambda: Lambda(((y, x), x), x)) + raises(BadSignatureError, lambda: Lambda(((y, 1), 2), x)) + + with warns_deprecated_sympy(): + assert Lambda([x, y], x+y) == Lambda((x, y), x+y) + + flam = Lambda(((x, y),), x + y) + assert flam((2, 3)) == 5 + flam = Lambda(((x, y), z), x + y + z) + assert flam((2, 3), 1) == 6 + flam = Lambda((((x, y), z),), x + y + z) + assert flam(((2, 3), 1)) == 6 + raises(BadArgumentsError, lambda: flam(1, 2, 3)) + flam = Lambda( (x,), (x, x)) + assert flam(1,) == (1, 1) + assert flam((1,)) == ((1,), (1,)) + flam = Lambda( ((x,),), (x, x)) + raises(BadArgumentsError, lambda: flam(1)) + assert flam((1,)) == (1, 1) + + # Previously TypeError was raised so this is potentially needed for + # backwards compatibility. + assert issubclass(BadSignatureError, TypeError) + assert issubclass(BadArgumentsError, TypeError) + + # These are tested to see they don't raise: + hash(Lambda(x, 2*x)) + hash(Lambda(x, x)) # IdentityFunction subclass + + +def test_IdentityFunction(): + assert Lambda(x, x) is Lambda(y, y) is S.IdentityFunction + assert Lambda(x, 2*x) is not S.IdentityFunction + assert Lambda((x, y), x) is not S.IdentityFunction + + +def test_Lambda_symbols(): + assert Lambda(x, 2*x).free_symbols == set() + assert Lambda(x, x*y).free_symbols == {y} + assert Lambda((), 42).free_symbols == set() + assert Lambda((), x*y).free_symbols == {x,y} + + +def test_functionclas_symbols(): + assert f.free_symbols == set() + + +def test_Lambda_arguments(): + raises(TypeError, lambda: Lambda(x, 2*x)(x, y)) + raises(TypeError, lambda: Lambda((x, y), x + y)(x)) + raises(TypeError, lambda: Lambda((), 42)(x)) + + +def test_Lambda_equality(): + assert Lambda((x, y), 2*x) == Lambda((x, y), 2*x) + # these, of course, should never be equal + assert Lambda(x, 2*x) != Lambda((x, y), 2*x) + assert Lambda(x, 2*x) != 2*x + # But it is tempting to want expressions that differ only + # in bound symbols to compare the same. But this is not what + # Python's `==` is intended to do; two objects that compare + # as equal means that they are indistibguishable and cache to the + # same value. We wouldn't want to expression that are + # mathematically the same but written in different variables to be + # interchanged else what is the point of allowing for different + # variable names? + assert Lambda(x, 2*x) != Lambda(y, 2*y) + + +def test_Subs(): + assert Subs(1, (), ()) is S.One + # check null subs influence on hashing + assert Subs(x, y, z) != Subs(x, y, 1) + # neutral subs works + assert Subs(x, x, 1).subs(x, y).has(y) + # self mapping var/point + assert Subs(Derivative(f(x), (x, 2)), x, x).doit() == f(x).diff(x, x) + assert Subs(x, x, 0).has(x) # it's a structural answer + assert not Subs(x, x, 0).free_symbols + assert Subs(Subs(x + y, x, 2), y, 1) == Subs(x + y, (x, y), (2, 1)) + assert Subs(x, (x,), (0,)) == Subs(x, x, 0) + assert Subs(x, x, 0) == Subs(y, y, 0) + assert Subs(x, x, 0).subs(x, 1) == Subs(x, x, 0) + assert Subs(y, x, 0).subs(y, 1) == Subs(1, x, 0) + assert Subs(f(x), x, 0).doit() == f(0) + assert Subs(f(x**2), x**2, 0).doit() == f(0) + assert Subs(f(x, y, z), (x, y, z), (0, 1, 1)) != \ + Subs(f(x, y, z), (x, y, z), (0, 0, 1)) + assert Subs(x, y, 2).subs(x, y).doit() == 2 + assert Subs(f(x, y), (x, y, z), (0, 1, 1)) != \ + Subs(f(x, y) + z, (x, y, z), (0, 1, 0)) + assert Subs(f(x, y), (x, y), (0, 1)).doit() == f(0, 1) + assert Subs(Subs(f(x, y), x, 0), y, 1).doit() == f(0, 1) + raises(ValueError, lambda: Subs(f(x, y), (x, y), (0, 0, 1))) + raises(ValueError, lambda: Subs(f(x, y), (x, x, y), (0, 0, 1))) + + assert len(Subs(f(x, y), (x, y), (0, 1)).variables) == 2 + assert Subs(f(x, y), (x, y), (0, 1)).point == Tuple(0, 1) + + assert Subs(f(x), x, 0) == Subs(f(y), y, 0) + assert Subs(f(x, y), (x, y), (0, 1)) == Subs(f(x, y), (y, x), (1, 0)) + assert Subs(f(x)*y, (x, y), (0, 1)) == Subs(f(y)*x, (y, x), (0, 1)) + assert Subs(f(x)*y, (x, y), (1, 1)) == Subs(f(y)*x, (x, y), (1, 1)) + + assert Subs(f(x), x, 0).subs(x, 1).doit() == f(0) + assert Subs(f(x), x, y).subs(y, 0) == Subs(f(x), x, 0) + assert Subs(y*f(x), x, y).subs(y, 2) == Subs(2*f(x), x, 2) + assert (2 * Subs(f(x), x, 0)).subs(Subs(f(x), x, 0), y) == 2*y + + assert Subs(f(x), x, 0).free_symbols == set() + assert Subs(f(x, y), x, z).free_symbols == {y, z} + + assert Subs(f(x).diff(x), x, 0).doit(), Subs(f(x).diff(x), x, 0) + assert Subs(1 + f(x).diff(x), x, 0).doit(), 1 + Subs(f(x).diff(x), x, 0) + assert Subs(y*f(x, y).diff(x), (x, y), (0, 2)).doit() == \ + 2*Subs(Derivative(f(x, 2), x), x, 0) + assert Subs(y**2*f(x), x, 0).diff(y) == 2*y*f(0) + + e = Subs(y**2*f(x), x, y) + assert e.diff(y) == e.doit().diff(y) == y**2*Derivative(f(y), y) + 2*y*f(y) + + assert Subs(f(x), x, 0) + Subs(f(x), x, 0) == 2*Subs(f(x), x, 0) + e1 = Subs(z*f(x), x, 1) + e2 = Subs(z*f(y), y, 1) + assert e1 + e2 == 2*e1 + assert e1.__hash__() == e2.__hash__() + assert Subs(z*f(x + 1), x, 1) not in [ e1, e2 ] + assert Derivative(f(x), x).subs(x, g(x)) == Derivative(f(g(x)), g(x)) + assert Derivative(f(x), x).subs(x, x + y) == Subs(Derivative(f(x), x), + x, x + y) + assert Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).n(2) == \ + Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).evalf(2) == \ + z + Rational('1/2').n(2)*f(0) + + assert f(x).diff(x).subs(x, 0).subs(x, y) == f(x).diff(x).subs(x, 0) + assert (x*f(x).diff(x).subs(x, 0)).subs(x, y) == y*f(x).diff(x).subs(x, 0) + assert Subs(Derivative(g(x)**2, g(x), x), g(x), exp(x) + ).doit() == 2*exp(x) + assert Subs(Derivative(g(x)**2, g(x), x), g(x), exp(x) + ).doit(deep=False) == 2*Derivative(exp(x), x) + assert Derivative(f(x, g(x)), x).doit() == Derivative( + f(x, g(x)), g(x))*Derivative(g(x), x) + Subs(Derivative( + f(y, g(x)), y), y, x) + +def test_doitdoit(): + done = Derivative(f(x, g(x)), x, g(x)).doit() + assert done == done.doit() + + +@XFAIL +def test_Subs2(): + # this reflects a limitation of subs(), probably won't fix + assert Subs(f(x), x**2, x).doit() == f(sqrt(x)) + + +def test_expand_function(): + assert expand(x + y) == x + y + assert expand(x + y, complex=True) == I*im(x) + I*im(y) + re(x) + re(y) + assert expand((x + y)**11, modulus=11) == x**11 + y**11 + + +def test_function_comparable(): + assert sin(x).is_comparable is False + assert cos(x).is_comparable is False + + assert sin(Float('0.1')).is_comparable is True + assert cos(Float('0.1')).is_comparable is True + + assert sin(E).is_comparable is True + assert cos(E).is_comparable is True + + assert sin(Rational(1, 3)).is_comparable is True + assert cos(Rational(1, 3)).is_comparable is True + + +def test_function_comparable_infinities(): + assert sin(oo).is_comparable is False + assert sin(-oo).is_comparable is False + assert sin(zoo).is_comparable is False + assert sin(nan).is_comparable is False + + +def test_deriv1(): + # These all require derivatives evaluated at a point (issue 4719) to work. + # See issue 4624 + assert f(2*x).diff(x) == 2*Subs(Derivative(f(x), x), x, 2*x) + assert (f(x)**3).diff(x) == 3*f(x)**2*f(x).diff(x) + assert (f(2*x)**3).diff(x) == 6*f(2*x)**2*Subs( + Derivative(f(x), x), x, 2*x) + + assert f(2 + x).diff(x) == Subs(Derivative(f(x), x), x, x + 2) + assert f(2 + 3*x).diff(x) == 3*Subs( + Derivative(f(x), x), x, 3*x + 2) + assert f(3*sin(x)).diff(x) == 3*cos(x)*Subs( + Derivative(f(x), x), x, 3*sin(x)) + + # See issue 8510 + assert f(x, x + z).diff(x) == ( + Subs(Derivative(f(y, x + z), y), y, x) + + Subs(Derivative(f(x, y), y), y, x + z)) + assert f(x, x**2).diff(x) == ( + 2*x*Subs(Derivative(f(x, y), y), y, x**2) + + Subs(Derivative(f(y, x**2), y), y, x)) + # but Subs is not always necessary + assert f(x, g(y)).diff(g(y)) == Derivative(f(x, g(y)), g(y)) + + +def test_deriv2(): + assert (x**3).diff(x) == 3*x**2 + assert (x**3).diff(x, evaluate=False) != 3*x**2 + assert (x**3).diff(x, evaluate=False) == Derivative(x**3, x) + + assert diff(x**3, x) == 3*x**2 + assert diff(x**3, x, evaluate=False) != 3*x**2 + assert diff(x**3, x, evaluate=False) == Derivative(x**3, x) + + +def test_func_deriv(): + assert f(x).diff(x) == Derivative(f(x), x) + # issue 4534 + assert f(x, y).diff(x, y) - f(x, y).diff(y, x) == 0 + assert Derivative(f(x, y), x, y).args[1:] == ((x, 1), (y, 1)) + assert Derivative(f(x, y), y, x).args[1:] == ((y, 1), (x, 1)) + assert (Derivative(f(x, y), x, y) - Derivative(f(x, y), y, x)).doit() == 0 + + +def test_suppressed_evaluation(): + a = sin(0, evaluate=False) + assert a != 0 + assert a.func is sin + assert a.args == (0,) + + +def test_function_evalf(): + def eq(a, b, eps): + return abs(a - b) < eps + assert eq(sin(1).evalf(15), Float("0.841470984807897"), 1e-13) + assert eq( + sin(2).evalf(25), Float("0.9092974268256816953960199", 25), 1e-23) + assert eq(sin(1 + I).evalf( + 15), Float("1.29845758141598") + Float("0.634963914784736")*I, 1e-13) + assert eq(exp(1 + I).evalf(15), Float( + "1.46869393991588") + Float("2.28735528717884239")*I, 1e-13) + assert eq(exp(-0.5 + 1.5*I).evalf(15), Float( + "0.0429042815937374") + Float("0.605011292285002")*I, 1e-13) + assert eq(log(pi + sqrt(2)*I).evalf( + 15), Float("1.23699044022052") + Float("0.422985442737893")*I, 1e-13) + assert eq(cos(100).evalf(15), Float("0.86231887228768"), 1e-13) + + +def test_extensibility_eval(): + class MyFunc(Function): + @classmethod + def eval(cls, *args): + return (0, 0, 0) + assert MyFunc(0) == (0, 0, 0) + + +@_both_exp_pow +def test_function_non_commutative(): + x = Symbol('x', commutative=False) + assert f(x).is_commutative is False + assert sin(x).is_commutative is False + assert exp(x).is_commutative is False + assert log(x).is_commutative is False + assert f(x).is_complex is False + assert sin(x).is_complex is False + assert exp(x).is_complex is False + assert log(x).is_complex is False + + +def test_function_complex(): + x = Symbol('x', complex=True) + xzf = Symbol('x', complex=True, zero=False) + assert f(x).is_commutative is True + assert sin(x).is_commutative is True + assert exp(x).is_commutative is True + assert log(x).is_commutative is True + assert f(x).is_complex is None + assert sin(x).is_complex is True + assert exp(x).is_complex is True + assert log(x).is_complex is None + assert log(xzf).is_complex is True + + +def test_function__eval_nseries(): + n = Symbol('n') + + assert sin(x)._eval_nseries(x, 2, None) == x + O(x**2) + assert sin(x + 1)._eval_nseries(x, 2, None) == x*cos(1) + sin(1) + O(x**2) + assert sin(pi*(1 - x))._eval_nseries(x, 2, None) == pi*x + O(x**2) + assert acos(1 - x**2)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(x**2) + O(x**2) + assert polygamma(n, x + 1)._eval_nseries(x, 2, None) == \ + polygamma(n, 1) + polygamma(n + 1, 1)*x + O(x**2) + raises(PoleError, lambda: sin(1/x)._eval_nseries(x, 2, None)) + assert acos(1 - x)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(x) + sqrt(2)*x**(S(3)/2)/12 + O(x**2) + assert acos(1 + x)._eval_nseries(x, 2, None) == sqrt(2)*sqrt(-x) + sqrt(2)*(-x)**(S(3)/2)/12 + O(x**2) + assert loggamma(1/x)._eval_nseries(x, 0, None) == \ + log(x)/2 - log(x)/x - 1/x + O(1, x) + assert loggamma(log(1/x)).nseries(x, n=1, logx=y) == loggamma(-y) + + # issue 6725: + assert expint(Rational(3, 2), -x)._eval_nseries(x, 5, None) == \ + 2 - 2*sqrt(pi)*sqrt(-x) - 2*x + x**2 + x**3/3 + x**4/12 + 4*I*x**(S(3)/2)*sqrt(-x)/3 + \ + 2*I*x**(S(5)/2)*sqrt(-x)/5 + 2*I*x**(S(7)/2)*sqrt(-x)/21 + O(x**5) + assert sin(sqrt(x))._eval_nseries(x, 3, None) == \ + sqrt(x) - x**Rational(3, 2)/6 + x**Rational(5, 2)/120 + O(x**3) + + # issue 19065: + s1 = f(x,y).series(y, n=2) + assert {i.name for i in s1.atoms(Symbol)} == {'x', 'xi', 'y'} + xi = Symbol('xi') + s2 = f(xi, y).series(y, n=2) + assert {i.name for i in s2.atoms(Symbol)} == {'xi', 'xi0', 'y'} + +def test_doit(): + n = Symbol('n', integer=True) + f = Sum(2 * n * x, (n, 1, 3)) + d = Derivative(f, x) + assert d.doit() == 12 + assert d.doit(deep=False) == Sum(2*n, (n, 1, 3)) + + +def test_evalf_default(): + from sympy.functions.special.gamma_functions import polygamma + assert type(sin(4.0)) == Float + assert type(re(sin(I + 1.0))) == Float + assert type(im(sin(I + 1.0))) == Float + assert type(sin(4)) == sin + assert type(polygamma(2.0, 4.0)) == Float + assert type(sin(Rational(1, 4))) == sin + + +def test_issue_5399(): + args = [x, y, S(2), S.Half] + + def ok(a): + """Return True if the input args for diff are ok""" + if not a: + return False + if a[0].is_Symbol is False: + return False + s_at = [i for i in range(len(a)) if a[i].is_Symbol] + n_at = [i for i in range(len(a)) if not a[i].is_Symbol] + # every symbol is followed by symbol or int + # every number is followed by a symbol + return (all(a[i + 1].is_Symbol or a[i + 1].is_Integer + for i in s_at if i + 1 < len(a)) and + all(a[i + 1].is_Symbol + for i in n_at if i + 1 < len(a))) + eq = x**10*y**8 + for a in subsets(args): + for v in variations(a, len(a)): + if ok(v): + eq.diff(*v) # does not raise + else: + raises(ValueError, lambda: eq.diff(*v)) + + +def test_derivative_numerically(): + z0 = x._random() + assert abs(Derivative(sin(x), x).doit_numerically(z0) - cos(z0)) < 1e-15 + + +def test_fdiff_argument_index_error(): + from sympy.core.function import ArgumentIndexError + + class myfunc(Function): + nargs = 1 # define since there is no eval routine + + def fdiff(self, idx): + raise ArgumentIndexError + mf = myfunc(x) + assert mf.diff(x) == Derivative(mf, x) + raises(TypeError, lambda: myfunc(x, x)) + + +def test_deriv_wrt_function(): + x = f(t) + xd = diff(x, t) + xdd = diff(xd, t) + y = g(t) + yd = diff(y, t) + + assert diff(x, t) == xd + assert diff(2 * x + 4, t) == 2 * xd + assert diff(2 * x + 4 + y, t) == 2 * xd + yd + assert diff(2 * x + 4 + y * x, t) == 2 * xd + x * yd + xd * y + assert diff(2 * x + 4 + y * x, x) == 2 + y + assert (diff(4 * x**2 + 3 * x + x * y, t) == 3 * xd + x * yd + xd * y + + 8 * x * xd) + assert (diff(4 * x**2 + 3 * xd + x * y, t) == 3 * xdd + x * yd + xd * y + + 8 * x * xd) + assert diff(4 * x**2 + 3 * xd + x * y, xd) == 3 + assert diff(4 * x**2 + 3 * xd + x * y, xdd) == 0 + assert diff(sin(x), t) == xd * cos(x) + assert diff(exp(x), t) == xd * exp(x) + assert diff(sqrt(x), t) == xd / (2 * sqrt(x)) + + +def test_diff_wrt_value(): + assert Expr()._diff_wrt is False + assert x._diff_wrt is True + assert f(x)._diff_wrt is True + assert Derivative(f(x), x)._diff_wrt is True + assert Derivative(x**2, x)._diff_wrt is False + + +def test_diff_wrt(): + fx = f(x) + dfx = diff(f(x), x) + ddfx = diff(f(x), x, x) + + assert diff(sin(fx) + fx**2, fx) == cos(fx) + 2*fx + assert diff(sin(dfx) + dfx**2, dfx) == cos(dfx) + 2*dfx + assert diff(sin(ddfx) + ddfx**2, ddfx) == cos(ddfx) + 2*ddfx + assert diff(fx**2, dfx) == 0 + assert diff(fx**2, ddfx) == 0 + assert diff(dfx**2, fx) == 0 + assert diff(dfx**2, ddfx) == 0 + assert diff(ddfx**2, dfx) == 0 + + assert diff(fx*dfx*ddfx, fx) == dfx*ddfx + assert diff(fx*dfx*ddfx, dfx) == fx*ddfx + assert diff(fx*dfx*ddfx, ddfx) == fx*dfx + + assert diff(f(x), x).diff(f(x)) == 0 + assert (sin(f(x)) - cos(diff(f(x), x))).diff(f(x)) == cos(f(x)) + + assert diff(sin(fx), fx, x) == diff(sin(fx), x, fx) + + # Chain rule cases + assert f(g(x)).diff(x) == \ + Derivative(g(x), x)*Derivative(f(g(x)), g(x)) + assert diff(f(g(x), h(y)), x) == \ + Derivative(g(x), x)*Derivative(f(g(x), h(y)), g(x)) + assert diff(f(g(x), h(x)), x) == ( + Derivative(f(g(x), h(x)), g(x))*Derivative(g(x), x) + + Derivative(f(g(x), h(x)), h(x))*Derivative(h(x), x)) + assert f( + sin(x)).diff(x) == cos(x)*Subs(Derivative(f(x), x), x, sin(x)) + + assert diff(f(g(x)), g(x)) == Derivative(f(g(x)), g(x)) + + +def test_diff_wrt_func_subs(): + assert f(g(x)).diff(x).subs(g, Lambda(x, 2*x)).doit() == f(2*x).diff(x) + + +def test_subs_in_derivative(): + expr = sin(x*exp(y)) + u = Function('u') + v = Function('v') + assert Derivative(expr, y).subs(expr, y) == Derivative(y, y) + assert Derivative(expr, y).subs(y, x).doit() == \ + Derivative(expr, y).doit().subs(y, x) + assert Derivative(f(x, y), y).subs(y, x) == Subs(Derivative(f(x, y), y), y, x) + assert Derivative(f(x, y), y).subs(x, y) == Subs(Derivative(f(x, y), y), x, y) + assert Derivative(f(x, y), y).subs(y, g(x, y)) == Subs(Derivative(f(x, y), y), y, g(x, y)).doit() + assert Derivative(f(x, y), y).subs(x, g(x, y)) == Subs(Derivative(f(x, y), y), x, g(x, y)) + assert Derivative(f(x, y), g(y)).subs(x, g(x, y)) == Derivative(f(g(x, y), y), g(y)) + assert Derivative(f(u(x), h(y)), h(y)).subs(h(y), g(x, y)) == \ + Subs(Derivative(f(u(x), h(y)), h(y)), h(y), g(x, y)).doit() + assert Derivative(f(x, y), y).subs(y, z) == Derivative(f(x, z), z) + assert Derivative(f(x, y), y).subs(y, g(y)) == Derivative(f(x, g(y)), g(y)) + assert Derivative(f(g(x), h(y)), h(y)).subs(h(y), u(y)) == \ + Derivative(f(g(x), u(y)), u(y)) + assert Derivative(f(x, f(x, x)), f(x, x)).subs( + f, Lambda((x, y), x + y)) == Subs( + Derivative(z + x, z), z, 2*x) + assert Subs(Derivative(f(f(x)), x), f, cos).doit() == sin(x)*sin(cos(x)) + assert Subs(Derivative(f(f(x)), f(x)), f, cos).doit() == -sin(cos(x)) + # Issue 13791. No comparison (it's a long formula) but this used to raise an exception. + assert isinstance(v(x, y, u(x, y)).diff(y).diff(x).diff(y), Expr) + # This is also related to issues 13791 and 13795; issue 15190 + F = Lambda((x, y), exp(2*x + 3*y)) + abstract = f(x, f(x, x)).diff(x, 2) + concrete = F(x, F(x, x)).diff(x, 2) + assert (abstract.subs(f, F).doit() - concrete).simplify() == 0 + # don't introduce a new symbol if not necessary + assert x in f(x).diff(x).subs(x, 0).atoms() + # case (4) + assert Derivative(f(x,f(x,y)), x, y).subs(x, g(y) + ) == Subs(Derivative(f(x, f(x, y)), x, y), x, g(y)) + + assert Derivative(f(x, x), x).subs(x, 0 + ) == Subs(Derivative(f(x, x), x), x, 0) + # issue 15194 + assert Derivative(f(y, g(x)), (x, z)).subs(z, x + ) == Derivative(f(y, g(x)), (x, x)) + + df = f(x).diff(x) + assert df.subs(df, 1) is S.One + assert df.diff(df) is S.One + dxy = Derivative(f(x, y), x, y) + dyx = Derivative(f(x, y), y, x) + assert dxy.subs(Derivative(f(x, y), y, x), 1) is S.One + assert dxy.diff(dyx) is S.One + assert Derivative(f(x, y), x, 2, y, 3).subs( + dyx, g(x, y)) == Derivative(g(x, y), x, 1, y, 2) + assert Derivative(f(x, x - y), y).subs(x, x + y) == Subs( + Derivative(f(x, x - y), y), x, x + y) + + +def test_diff_wrt_not_allowed(): + # issue 7027 included + for wrt in ( + cos(x), re(x), x**2, x*y, 1 + x, + Derivative(cos(x), x), Derivative(f(f(x)), x)): + raises(ValueError, lambda: diff(f(x), wrt)) + # if we don't differentiate wrt then don't raise error + assert diff(exp(x*y), x*y, 0) == exp(x*y) + + +def test_diff_wrt_intlike(): + class Two: + def __int__(self): + return 2 + + assert cos(x).diff(x, Two()) == -cos(x) + + +def test_klein_gordon_lagrangian(): + m = Symbol('m') + phi = f(x, t) + + L = -(diff(phi, t)**2 - diff(phi, x)**2 - m**2*phi**2)/2 + eqna = Eq( + diff(L, phi) - diff(L, diff(phi, x), x) - diff(L, diff(phi, t), t), 0) + eqnb = Eq(diff(phi, t, t) - diff(phi, x, x) + m**2*phi, 0) + assert eqna == eqnb + + +def test_sho_lagrangian(): + m = Symbol('m') + k = Symbol('k') + x = f(t) + + L = m*diff(x, t)**2/2 - k*x**2/2 + eqna = Eq(diff(L, x), diff(L, diff(x, t), t)) + eqnb = Eq(-k*x, m*diff(x, t, t)) + assert eqna == eqnb + + assert diff(L, x, t) == diff(L, t, x) + assert diff(L, diff(x, t), t) == m*diff(x, t, 2) + assert diff(L, t, diff(x, t)) == -k*x + m*diff(x, t, 2) + + +def test_straight_line(): + F = f(x) + Fd = F.diff(x) + L = sqrt(1 + Fd**2) + assert diff(L, F) == 0 + assert diff(L, Fd) == Fd/sqrt(1 + Fd**2) + + +def test_sort_variable(): + vsort = Derivative._sort_variable_count + def vsort0(*v, reverse=False): + return [i[0] for i in vsort([(i, 0) for i in ( + reversed(v) if reverse else v)])] + + for R in range(2): + assert vsort0(y, x, reverse=R) == [x, y] + assert vsort0(f(x), x, reverse=R) == [x, f(x)] + assert vsort0(f(y), f(x), reverse=R) == [f(x), f(y)] + assert vsort0(g(x), f(y), reverse=R) == [f(y), g(x)] + assert vsort0(f(x, y), f(x), reverse=R) == [f(x), f(x, y)] + fx = f(x).diff(x) + assert vsort0(fx, y, reverse=R) == [y, fx] + fy = f(y).diff(y) + assert vsort0(fy, fx, reverse=R) == [fx, fy] + fxx = fx.diff(x) + assert vsort0(fxx, fx, reverse=R) == [fx, fxx] + assert vsort0(Basic(x), f(x), reverse=R) == [f(x), Basic(x)] + assert vsort0(Basic(y), Basic(x), reverse=R) == [Basic(x), Basic(y)] + assert vsort0(Basic(y, z), Basic(x), reverse=R) == [ + Basic(x), Basic(y, z)] + assert vsort0(fx, x, reverse=R) == [ + x, fx] if R else [fx, x] + assert vsort0(Basic(x), x, reverse=R) == [ + x, Basic(x)] if R else [Basic(x), x] + assert vsort0(Basic(f(x)), f(x), reverse=R) == [ + f(x), Basic(f(x))] if R else [Basic(f(x)), f(x)] + assert vsort0(Basic(x, z), Basic(x), reverse=R) == [ + Basic(x), Basic(x, z)] if R else [Basic(x, z), Basic(x)] + assert vsort([]) == [] + assert _aresame(vsort([(x, 1)]), [Tuple(x, 1)]) + assert vsort([(x, y), (x, z)]) == [(x, y + z)] + assert vsort([(y, 1), (x, 1 + y)]) == [(x, 1 + y), (y, 1)] + # coverage complete; legacy tests below + assert vsort([(x, 3), (y, 2), (z, 1)]) == [(x, 3), (y, 2), (z, 1)] + assert vsort([(h(x), 1), (g(x), 1), (f(x), 1)]) == [ + (f(x), 1), (g(x), 1), (h(x), 1)] + assert vsort([(z, 1), (y, 2), (x, 3), (h(x), 1), (g(x), 1), + (f(x), 1)]) == [(x, 3), (y, 2), (z, 1), (f(x), 1), (g(x), 1), + (h(x), 1)] + assert vsort([(x, 1), (f(x), 1), (y, 1), (f(y), 1)]) == [(x, 1), + (y, 1), (f(x), 1), (f(y), 1)] + assert vsort([(y, 1), (x, 2), (g(x), 1), (f(x), 1), (z, 1), + (h(x), 1), (y, 2), (x, 1)]) == [(x, 3), (y, 3), (z, 1), + (f(x), 1), (g(x), 1), (h(x), 1)] + assert vsort([(z, 1), (y, 1), (f(x), 1), (x, 1), (f(x), 1), + (g(x), 1)]) == [(x, 1), (y, 1), (z, 1), (f(x), 2), (g(x), 1)] + assert vsort([(z, 1), (y, 2), (f(x), 1), (x, 2), (f(x), 2), + (g(x), 1), (z, 2), (z, 1), (y, 1), (x, 1)]) == [(x, 3), (y, 3), + (z, 4), (f(x), 3), (g(x), 1)] + assert vsort(((y, 2), (x, 1), (y, 1), (x, 1))) == [(x, 2), (y, 3)] + assert isinstance(vsort([(x, 3), (y, 2), (z, 1)])[0], Tuple) + assert vsort([(x, 1), (f(x), 1), (x, 1)]) == [(x, 2), (f(x), 1)] + assert vsort([(y, 2), (x, 3), (z, 1)]) == [(x, 3), (y, 2), (z, 1)] + assert vsort([(h(y), 1), (g(x), 1), (f(x), 1)]) == [ + (f(x), 1), (g(x), 1), (h(y), 1)] + assert vsort([(x, 1), (y, 1), (x, 1)]) == [(x, 2), (y, 1)] + assert vsort([(f(x), 1), (f(y), 1), (f(x), 1)]) == [ + (f(x), 2), (f(y), 1)] + dfx = f(x).diff(x) + self = [(dfx, 1), (x, 1)] + assert vsort(self) == self + assert vsort([ + (dfx, 1), (y, 1), (f(x), 1), (x, 1), (f(y), 1), (x, 1)]) == [ + (y, 1), (f(x), 1), (f(y), 1), (dfx, 1), (x, 2)] + dfy = f(y).diff(y) + assert vsort([(dfy, 1), (dfx, 1)]) == [(dfx, 1), (dfy, 1)] + d2fx = dfx.diff(x) + assert vsort([(d2fx, 1), (dfx, 1)]) == [(dfx, 1), (d2fx, 1)] + + +def test_multiple_derivative(): + # Issue #15007 + assert f(x, y).diff(y, y, x, y, x + ) == Derivative(f(x, y), (x, 2), (y, 3)) + + +def test_unhandled(): + class MyExpr(Expr): + def _eval_derivative(self, s): + if not s.name.startswith('xi'): + return self + else: + return None + + eq = MyExpr(f(x), y, z) + assert diff(eq, x, y, f(x), z) == Derivative(eq, f(x)) + assert diff(eq, f(x), x) == Derivative(eq, f(x)) + assert f(x, y).diff(x,(y, z)) == Derivative(f(x, y), x, (y, z)) + assert f(x, y).diff(x,(y, 0)) == Derivative(f(x, y), x) + + +def test_nfloat(): + from sympy.core.basic import _aresame + from sympy.polys.rootoftools import rootof + + x = Symbol("x") + eq = x**Rational(4, 3) + 4*x**(S.One/3)/3 + assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0/3)*x**(S.One/3)) + assert _aresame(nfloat(eq, exponent=True), x**(4.0/3) + (4.0/3)*x**(1.0/3)) + eq = x**Rational(4, 3) + 4*x**(x/3)/3 + assert _aresame(nfloat(eq), x**Rational(4, 3) + (4.0/3)*x**(x/3)) + big = 12345678901234567890 + # specify precision to match value used in nfloat + Float_big = Float(big, 15) + assert _aresame(nfloat(big), Float_big) + assert _aresame(nfloat(big*x), Float_big*x) + assert _aresame(nfloat(x**big, exponent=True), x**Float_big) + assert nfloat(cos(x + sqrt(2))) == cos(x + nfloat(sqrt(2))) + + # issue 6342 + f = S('x*lamda + lamda**3*(x/2 + 1/2) + lamda**2 + 1/4') + assert not any(a.free_symbols for a in solveset(f.subs(x, -0.139))) + + # issue 6632 + assert nfloat(-100000*sqrt(2500000001) + 5000000001) == \ + 9.99999999800000e-11 + + # issue 7122 + eq = cos(3*x**4 + y)*rootof(x**5 + 3*x**3 + 1, 0) + assert str(nfloat(eq, exponent=False, n=1)) == '-0.7*cos(3.0*x**4 + y)' + + # issue 10933 + for ti in (dict, Dict): + d = ti({S.Half: S.Half}) + n = nfloat(d) + assert isinstance(n, ti) + assert _aresame(list(n.items()).pop(), (S.Half, Float(.5))) + for ti in (dict, Dict): + d = ti({S.Half: S.Half}) + n = nfloat(d, dkeys=True) + assert isinstance(n, ti) + assert _aresame(list(n.items()).pop(), (Float(.5), Float(.5))) + d = [S.Half] + n = nfloat(d) + assert type(n) is list + assert _aresame(n[0], Float(.5)) + assert _aresame(nfloat(Eq(x, S.Half)).rhs, Float(.5)) + assert _aresame(nfloat(S(True)), S(True)) + assert _aresame(nfloat(Tuple(S.Half))[0], Float(.5)) + assert nfloat(Eq((3 - I)**2/2 + I, 0)) == S.false + # pass along kwargs + assert nfloat([{S.Half: x}], dkeys=True) == [{Float(0.5): x}] + + # Issue 17706 + A = MutableMatrix([[1, 2], [3, 4]]) + B = MutableMatrix( + [[Float('1.0', precision=53), Float('2.0', precision=53)], + [Float('3.0', precision=53), Float('4.0', precision=53)]]) + assert _aresame(nfloat(A), B) + A = ImmutableMatrix([[1, 2], [3, 4]]) + B = ImmutableMatrix( + [[Float('1.0', precision=53), Float('2.0', precision=53)], + [Float('3.0', precision=53), Float('4.0', precision=53)]]) + assert _aresame(nfloat(A), B) + + # issue 22524 + f = Function('f') + assert not nfloat(f(2)).atoms(Float) + + +def test_issue_7068(): + from sympy.abc import a, b + f = Function('f') + y1 = Dummy('y') + y2 = Dummy('y') + func1 = f(a + y1 * b) + func2 = f(a + y2 * b) + func1_y = func1.diff(y1) + func2_y = func2.diff(y2) + assert func1_y != func2_y + z1 = Subs(f(a), a, y1) + z2 = Subs(f(a), a, y2) + assert z1 != z2 + + +def test_issue_7231(): + from sympy.abc import a + ans1 = f(x).series(x, a) + res = (f(a) + (-a + x)*Subs(Derivative(f(y), y), y, a) + + (-a + x)**2*Subs(Derivative(f(y), y, y), y, a)/2 + + (-a + x)**3*Subs(Derivative(f(y), y, y, y), + y, a)/6 + + (-a + x)**4*Subs(Derivative(f(y), y, y, y, y), + y, a)/24 + + (-a + x)**5*Subs(Derivative(f(y), y, y, y, y, y), + y, a)/120 + O((-a + x)**6, (x, a))) + assert res == ans1 + ans2 = f(x).series(x, a) + assert res == ans2 + + +def test_issue_7687(): + from sympy.core.function import Function + from sympy.abc import x + f = Function('f')(x) + ff = Function('f')(x) + match_with_cache = ff.matches(f) + assert isinstance(f, type(ff)) + clear_cache() + ff = Function('f')(x) + assert isinstance(f, type(ff)) + assert match_with_cache == ff.matches(f) + + +def test_issue_7688(): + from sympy.core.function import Function, UndefinedFunction + + f = Function('f') # actually an UndefinedFunction + clear_cache() + class A(UndefinedFunction): + pass + a = A('f') + assert isinstance(a, type(f)) + + +def test_mexpand(): + from sympy.abc import x + assert _mexpand(None) is None + assert _mexpand(1) is S.One + assert _mexpand(x*(x + 1)**2) == (x*(x + 1)**2).expand() + + +def test_issue_8469(): + # This should not take forever to run + N = 40 + def g(w, theta): + return 1/(1+exp(w-theta)) + + ws = symbols(['w%i'%i for i in range(N)]) + import functools + expr = functools.reduce(g, ws) + assert isinstance(expr, Pow) + + +def test_issue_12996(): + # foo=True imitates the sort of arguments that Derivative can get + # from Integral when it passes doit to the expression + assert Derivative(im(x), x).doit(foo=True) == Derivative(im(x), x) + + +def test_should_evalf(): + # This should not take forever to run (see #8506) + assert isinstance(sin((1.0 + 1.0*I)**10000 + 1), sin) + + +def test_Derivative_as_finite_difference(): + # Central 1st derivative at gridpoint + x, h = symbols('x h', real=True) + dfdx = f(x).diff(x) + assert (dfdx.as_finite_difference([x-2, x-1, x, x+1, x+2]) - + (S.One/12*(f(x-2)-f(x+2)) + Rational(2, 3)*(f(x+1)-f(x-1)))).simplify() == 0 + + # Central 1st derivative "half-way" + assert (dfdx.as_finite_difference() - + (f(x + S.Half)-f(x - S.Half))).simplify() == 0 + assert (dfdx.as_finite_difference(h) - + (f(x + h/S(2))-f(x - h/S(2)))/h).simplify() == 0 + assert (dfdx.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) - + (S(9)/(8*2*h)*(f(x+h) - f(x-h)) + + S.One/(24*2*h)*(f(x - 3*h) - f(x + 3*h)))).simplify() == 0 + + # One sided 1st derivative at gridpoint + assert (dfdx.as_finite_difference([0, 1, 2], 0) - + (Rational(-3, 2)*f(0) + 2*f(1) - f(2)/2)).simplify() == 0 + assert (dfdx.as_finite_difference([x, x+h], x) - + (f(x+h) - f(x))/h).simplify() == 0 + assert (dfdx.as_finite_difference([x-h, x, x+h], x-h) - + (-S(3)/(2*h)*f(x-h) + 2/h*f(x) - + S.One/(2*h)*f(x+h))).simplify() == 0 + + # One sided 1st derivative "half-way" + assert (dfdx.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h, x + 7*h]) + - 1/(2*h)*(-S(11)/(12)*f(x-h) + S(17)/(24)*f(x+h) + + Rational(3, 8)*f(x + 3*h) - Rational(5, 24)*f(x + 5*h) + + S.One/24*f(x + 7*h))).simplify() == 0 + + d2fdx2 = f(x).diff(x, 2) + # Central 2nd derivative at gridpoint + assert (d2fdx2.as_finite_difference([x-h, x, x+h]) - + h**-2 * (f(x-h) + f(x+h) - 2*f(x))).simplify() == 0 + + assert (d2fdx2.as_finite_difference([x - 2*h, x-h, x, x+h, x + 2*h]) - + h**-2 * (Rational(-1, 12)*(f(x - 2*h) + f(x + 2*h)) + + Rational(4, 3)*(f(x+h) + f(x-h)) - Rational(5, 2)*f(x))).simplify() == 0 + + # Central 2nd derivative "half-way" + assert (d2fdx2.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) - + (2*h)**-2 * (S.Half*(f(x - 3*h) + f(x + 3*h)) - + S.Half*(f(x+h) + f(x-h)))).simplify() == 0 + + # One sided 2nd derivative at gridpoint + assert (d2fdx2.as_finite_difference([x, x+h, x + 2*h, x + 3*h]) - + h**-2 * (2*f(x) - 5*f(x+h) + + 4*f(x+2*h) - f(x+3*h))).simplify() == 0 + + # One sided 2nd derivative at "half-way" + assert (d2fdx2.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h]) - + (2*h)**-2 * (Rational(3, 2)*f(x-h) - Rational(7, 2)*f(x+h) + Rational(5, 2)*f(x + 3*h) - + S.Half*f(x + 5*h))).simplify() == 0 + + d3fdx3 = f(x).diff(x, 3) + # Central 3rd derivative at gridpoint + assert (d3fdx3.as_finite_difference() - + (-f(x - Rational(3, 2)) + 3*f(x - S.Half) - + 3*f(x + S.Half) + f(x + Rational(3, 2)))).simplify() == 0 + + assert (d3fdx3.as_finite_difference( + [x - 3*h, x - 2*h, x-h, x, x+h, x + 2*h, x + 3*h]) - + h**-3 * (S.One/8*(f(x - 3*h) - f(x + 3*h)) - f(x - 2*h) + + f(x + 2*h) + Rational(13, 8)*(f(x-h) - f(x+h)))).simplify() == 0 + + # Central 3rd derivative at "half-way" + assert (d3fdx3.as_finite_difference([x - 3*h, x-h, x+h, x + 3*h]) - + (2*h)**-3 * (f(x + 3*h)-f(x - 3*h) + + 3*(f(x-h)-f(x+h)))).simplify() == 0 + + # One sided 3rd derivative at gridpoint + assert (d3fdx3.as_finite_difference([x, x+h, x + 2*h, x + 3*h]) - + h**-3 * (f(x + 3*h)-f(x) + 3*(f(x+h)-f(x + 2*h)))).simplify() == 0 + + # One sided 3rd derivative at "half-way" + assert (d3fdx3.as_finite_difference([x-h, x+h, x + 3*h, x + 5*h]) - + (2*h)**-3 * (f(x + 5*h)-f(x-h) + + 3*(f(x+h)-f(x + 3*h)))).simplify() == 0 + + # issue 11007 + y = Symbol('y', real=True) + d2fdxdy = f(x, y).diff(x, y) + + ref0 = Derivative(f(x + S.Half, y), y) - Derivative(f(x - S.Half, y), y) + assert (d2fdxdy.as_finite_difference(wrt=x) - ref0).simplify() == 0 + + half = S.Half + xm, xp, ym, yp = x-half, x+half, y-half, y+half + ref2 = f(xm, ym) + f(xp, yp) - f(xp, ym) - f(xm, yp) + assert (d2fdxdy.as_finite_difference() - ref2).simplify() == 0 + + +def test_issue_11159(): + # Tests Application._eval_subs + with _exp_is_pow(False): + expr1 = E + expr0 = expr1 * expr1 + expr1 = expr0.subs(expr1,expr0) + assert expr0 == expr1 + with _exp_is_pow(True): + expr1 = E + expr0 = expr1 * expr1 + expr2 = expr0.subs(expr1, expr0) + assert expr2 == E ** 4 + + +def test_issue_12005(): + e1 = Subs(Derivative(f(x), x), x, x) + assert e1.diff(x) == Derivative(f(x), x, x) + e2 = Subs(Derivative(f(x), x), x, x**2 + 1) + assert e2.diff(x) == 2*x*Subs(Derivative(f(x), x, x), x, x**2 + 1) + e3 = Subs(Derivative(f(x) + y**2 - y, y), y, y**2) + assert e3.diff(y) == 4*y + e4 = Subs(Derivative(f(x + y), y), y, (x**2)) + assert e4.diff(y) is S.Zero + e5 = Subs(Derivative(f(x), x), (y, z), (y, z)) + assert e5.diff(x) == Derivative(f(x), x, x) + assert f(g(x)).diff(g(x), g(x)) == Derivative(f(g(x)), g(x), g(x)) + + +def test_issue_13843(): + x = symbols('x') + f = Function('f') + m, n = symbols('m n', integer=True) + assert Derivative(Derivative(f(x), (x, m)), (x, n)) == Derivative(f(x), (x, m + n)) + assert Derivative(Derivative(f(x), (x, m+5)), (x, n+3)) == Derivative(f(x), (x, m + n + 8)) + + assert Derivative(f(x), (x, n)).doit() == Derivative(f(x), (x, n)) + + +def test_order_could_be_zero(): + x, y = symbols('x, y') + n = symbols('n', integer=True, nonnegative=True) + m = symbols('m', integer=True, positive=True) + assert diff(y, (x, n)) == Piecewise((y, Eq(n, 0)), (0, True)) + assert diff(y, (x, n + 1)) is S.Zero + assert diff(y, (x, m)) is S.Zero + + +def test_undefined_function_eq(): + f = Function('f') + f2 = Function('f') + g = Function('g') + f_real = Function('f', is_real=True) + + # This test may only be meaningful if the cache is turned off + assert f == f2 + assert hash(f) == hash(f2) + assert f == f + + assert f != g + + assert f != f_real + + +def test_function_assumptions(): + x = Symbol('x') + f = Function('f') + f_real = Function('f', real=True) + f_real1 = Function('f', real=1) + f_real_inherit = Function(Symbol('f', real=True)) + + assert f_real == f_real1 # assumptions are sanitized + assert f != f_real + assert f(x) != f_real(x) + + assert f(x).is_real is None + assert f_real(x).is_real is True + assert f_real_inherit(x).is_real is True and f_real_inherit.name == 'f' + + # Can also do it this way, but it won't be equal to f_real because of the + # way UndefinedFunction.__new__ works. Any non-recognized assumptions + # are just added literally as something which is used in the hash + f_real2 = Function('f', is_real=True) + assert f_real2(x).is_real is True + + +def test_undef_fcn_float_issue_6938(): + f = Function('ceil') + assert not f(0.3).is_number + f = Function('sin') + assert not f(0.3).is_number + assert not f(pi).evalf().is_number + x = Symbol('x') + assert not f(x).evalf(subs={x:1.2}).is_number + + +def test_undefined_function_eval(): + # Issue 15170. Make sure UndefinedFunction with eval defined works + # properly. + + fdiff = lambda self, argindex=1: cos(self.args[argindex - 1]) + eval = classmethod(lambda cls, t: None) + _imp_ = classmethod(lambda cls, t: sin(t)) + + temp = Function('temp', fdiff=fdiff, eval=eval, _imp_=_imp_) + + expr = temp(t) + assert sympify(expr) == expr + assert type(sympify(expr)).fdiff.__name__ == "" + assert expr.diff(t) == cos(t) + + +def test_issue_15241(): + F = f(x) + Fx = F.diff(x) + assert (F + x*Fx).diff(x, Fx) == 2 + assert (F + x*Fx).diff(Fx, x) == 1 + assert (x*F + x*Fx*F).diff(F, x) == x*Fx.diff(x) + Fx + 1 + assert (x*F + x*Fx*F).diff(x, F) == x*Fx.diff(x) + Fx + 1 + y = f(x) + G = f(y) + Gy = G.diff(y) + assert (G + y*Gy).diff(y, Gy) == 2 + assert (G + y*Gy).diff(Gy, y) == 1 + assert (y*G + y*Gy*G).diff(G, y) == y*Gy.diff(y) + Gy + 1 + assert (y*G + y*Gy*G).diff(y, G) == y*Gy.diff(y) + Gy + 1 + + +def test_issue_15226(): + assert Subs(Derivative(f(y), x, y), y, g(x)).doit() != 0 + + +def test_issue_7027(): + for wrt in (cos(x), re(x), Derivative(cos(x), x)): + raises(ValueError, lambda: diff(f(x), wrt)) + + +def test_derivative_quick_exit(): + assert f(x).diff(y) == 0 + assert f(x).diff(y, f(x)) == 0 + assert f(x).diff(x, f(y)) == 0 + assert f(f(x)).diff(x, f(x), f(y)) == 0 + assert f(f(x)).diff(x, f(x), y) == 0 + assert f(x).diff(g(x)) == 0 + assert f(x).diff(x, f(x).diff(x)) == 1 + df = f(x).diff(x) + assert f(x).diff(df) == 0 + dg = g(x).diff(x) + assert dg.diff(df).doit() == 0 + + +def test_issue_15084_13166(): + eq = f(x, g(x)) + assert eq.diff((g(x), y)) == Derivative(f(x, g(x)), (g(x), y)) + # issue 13166 + assert eq.diff(x, 2).doit() == ( + (Derivative(f(x, g(x)), (g(x), 2))*Derivative(g(x), x) + + Subs(Derivative(f(x, _xi_2), _xi_2, x), _xi_2, g(x)))*Derivative(g(x), + x) + Derivative(f(x, g(x)), g(x))*Derivative(g(x), (x, 2)) + + Derivative(g(x), x)*Subs(Derivative(f(_xi_1, g(x)), _xi_1, g(x)), + _xi_1, x) + Subs(Derivative(f(_xi_1, g(x)), (_xi_1, 2)), _xi_1, x)) + # issue 6681 + assert diff(f(x, t, g(x, t)), x).doit() == ( + Derivative(f(x, t, g(x, t)), g(x, t))*Derivative(g(x, t), x) + + Subs(Derivative(f(_xi_1, t, g(x, t)), _xi_1), _xi_1, x)) + # make sure the order doesn't matter when using diff + assert eq.diff(x, g(x)) == eq.diff(g(x), x) + + +def test_negative_counts(): + # issue 13873 + raises(ValueError, lambda: sin(x).diff(x, -1)) + + +def test_Derivative__new__(): + raises(TypeError, lambda: f(x).diff((x, 2), 0)) + assert f(x, y).diff([(x, y), 0]) == f(x, y) + assert f(x, y).diff([(x, y), 1]) == NDimArray([ + Derivative(f(x, y), x), Derivative(f(x, y), y)]) + assert f(x,y).diff(y, (x, z), y, x) == Derivative( + f(x, y), (x, z + 1), (y, 2)) + assert Matrix([x]).diff(x, 2) == Matrix([0]) # is_zero exit + + +def test_issue_14719_10150(): + class V(Expr): + _diff_wrt = True + is_scalar = False + assert V().diff(V()) == Derivative(V(), V()) + assert (2*V()).diff(V()) == 2*Derivative(V(), V()) + class X(Expr): + _diff_wrt = True + assert X().diff(X()) == 1 + assert (2*X()).diff(X()) == 2 + + +def test_noncommutative_issue_15131(): + x = Symbol('x', commutative=False) + t = Symbol('t', commutative=False) + fx = Function('Fx', commutative=False)(x) + ft = Function('Ft', commutative=False)(t) + A = Symbol('A', commutative=False) + eq = fx * A * ft + eqdt = eq.diff(t) + assert eqdt.args[-1] == ft.diff(t) + + +def test_Subs_Derivative(): + a = Derivative(f(g(x), h(x)), g(x), h(x),x) + b = Derivative(Derivative(f(g(x), h(x)), g(x), h(x)),x) + c = f(g(x), h(x)).diff(g(x), h(x), x) + d = f(g(x), h(x)).diff(g(x), h(x)).diff(x) + e = Derivative(f(g(x), h(x)), x) + eqs = (a, b, c, d, e) + subs = lambda arg: arg.subs(f, Lambda((x, y), exp(x + y)) + ).subs(g(x), 1/x).subs(h(x), x**3) + ans = 3*x**2*exp(1/x)*exp(x**3) - exp(1/x)*exp(x**3)/x**2 + assert all(subs(i).doit().expand() == ans for i in eqs) + assert all(subs(i.doit()).doit().expand() == ans for i in eqs) + +def test_issue_15360(): + f = Function('f') + assert f.name == 'f' + + +def test_issue_15947(): + assert f._diff_wrt is False + raises(TypeError, lambda: f(f)) + raises(TypeError, lambda: f(x).diff(f)) + + +def test_Derivative_free_symbols(): + f = Function('f') + n = Symbol('n', integer=True, positive=True) + assert diff(f(x), (x, n)).free_symbols == {n, x} + + +def test_issue_20683(): + x = Symbol('x') + y = Symbol('y') + z = Symbol('z') + y = Derivative(z, x).subs(x,0) + assert y.doit() == 0 + y = Derivative(8, x).subs(x,0) + assert y.doit() == 0 + + +def test_issue_10503(): + f = exp(x**3)*cos(x**6) + assert f.series(x, 0, 14) == 1 + x**3 + x**6/2 + x**9/6 - 11*x**12/24 + O(x**14) + + +def test_issue_17382(): + # copied from sympy/core/tests/test_evalf.py + def NS(e, n=15, **options): + return sstr(sympify(e).evalf(n, **options), full_prec=True) + + x = Symbol('x') + expr = solveset(2 * cos(x) * cos(2 * x) - 1, x, S.Reals) + expected = "Union(" \ + "ImageSet(Lambda(_n, 6.28318530717959*_n + 5.79812359592087), Integers), " \ + "ImageSet(Lambda(_n, 6.28318530717959*_n + 0.485061711258717), Integers))" + assert NS(expr) == expected + +def test_eval_sympified(): + # Check both arguments and return types from eval are sympified + + class F(Function): + @classmethod + def eval(cls, x): + assert x is S.One + return 1 + + assert F(1) is S.One + + # String arguments are not allowed + class F2(Function): + @classmethod + def eval(cls, x): + if x == 0: + return '1' + + raises(SympifyError, lambda: F2(0)) + F2(1) # Doesn't raise + + # TODO: Disable string inputs (https://github.com/sympy/sympy/issues/11003) + # raises(SympifyError, lambda: F2('2')) + +def test_eval_classmethod_check(): + with raises(TypeError): + class F(Function): + def eval(self, x): + pass diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_kind.py b/lib/python3.11/site-packages/sympy/core/tests/test_kind.py new file mode 100644 index 0000000000000000000000000000000000000000..cbfdffb9304b49488756752ca198fd4067087437 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_kind.py @@ -0,0 +1,57 @@ +from sympy.core.add import Add +from sympy.core.kind import NumberKind, UndefinedKind +from sympy.core.mul import Mul +from sympy.core.numbers import pi, zoo, I, AlgebraicNumber +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.integrals.integrals import Integral +from sympy.core.function import Derivative +from sympy.matrices import (Matrix, SparseMatrix, ImmutableMatrix, + ImmutableSparseMatrix, MatrixSymbol, MatrixKind, MatMul) + +comm_x = Symbol('x') +noncomm_x = Symbol('x', commutative=False) + +def test_NumberKind(): + assert S.One.kind is NumberKind + assert pi.kind is NumberKind + assert S.NaN.kind is NumberKind + assert zoo.kind is NumberKind + assert I.kind is NumberKind + assert AlgebraicNumber(1).kind is NumberKind + +def test_Add_kind(): + assert Add(2, 3, evaluate=False).kind is NumberKind + assert Add(2,comm_x).kind is NumberKind + assert Add(2,noncomm_x).kind is UndefinedKind + +def test_mul_kind(): + assert Mul(2,comm_x, evaluate=False).kind is NumberKind + assert Mul(2,3, evaluate=False).kind is NumberKind + assert Mul(noncomm_x,2, evaluate=False).kind is UndefinedKind + assert Mul(2,noncomm_x, evaluate=False).kind is UndefinedKind + +def test_Symbol_kind(): + assert comm_x.kind is NumberKind + assert noncomm_x.kind is UndefinedKind + +def test_Integral_kind(): + A = MatrixSymbol('A', 2,2) + assert Integral(comm_x, comm_x).kind is NumberKind + assert Integral(A, comm_x).kind is MatrixKind(NumberKind) + +def test_Derivative_kind(): + A = MatrixSymbol('A', 2,2) + assert Derivative(comm_x, comm_x).kind is NumberKind + assert Derivative(A, comm_x).kind is MatrixKind(NumberKind) + +def test_Matrix_kind(): + classes = (Matrix, SparseMatrix, ImmutableMatrix, ImmutableSparseMatrix) + for cls in classes: + m = cls.zeros(3, 2) + assert m.kind is MatrixKind(NumberKind) + +def test_MatMul_kind(): + M = Matrix([[1,2],[3,4]]) + assert MatMul(2, M).kind is MatrixKind(NumberKind) + assert MatMul(comm_x, M).kind is MatrixKind(NumberKind) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_logic.py b/lib/python3.11/site-packages/sympy/core/tests/test_logic.py new file mode 100644 index 0000000000000000000000000000000000000000..df5647f32ea7c4e326eb4e3aec6a7b2987f32aee --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_logic.py @@ -0,0 +1,198 @@ +from sympy.core.logic import (fuzzy_not, Logic, And, Or, Not, fuzzy_and, + fuzzy_or, _fuzzy_group, _torf, fuzzy_nand, fuzzy_xor) +from sympy.testing.pytest import raises + +from itertools import product + +T = True +F = False +U = None + + + +def test_torf(): + v = [T, F, U] + for i in product(*[v]*3): + assert _torf(i) is (True if all(j for j in i) else + (False if all(j is False for j in i) else None)) + + +def test_fuzzy_group(): + v = [T, F, U] + for i in product(*[v]*3): + assert _fuzzy_group(i) is (None if None in i else + (True if all(j for j in i) else False)) + assert _fuzzy_group(i, quick_exit=True) is \ + (None if (i.count(False) > 1) else + (None if None in i else (True if all(j for j in i) else False))) + it = (True if (i == 0) else None for i in range(2)) + assert _torf(it) is None + it = (True if (i == 1) else None for i in range(2)) + assert _torf(it) is None + + +def test_fuzzy_not(): + assert fuzzy_not(T) == F + assert fuzzy_not(F) == T + assert fuzzy_not(U) == U + + +def test_fuzzy_and(): + assert fuzzy_and([T, T]) == T + assert fuzzy_and([T, F]) == F + assert fuzzy_and([T, U]) == U + assert fuzzy_and([F, F]) == F + assert fuzzy_and([F, U]) == F + assert fuzzy_and([U, U]) == U + assert [fuzzy_and([w]) for w in [U, T, F]] == [U, T, F] + assert fuzzy_and([T, F, U]) == F + assert fuzzy_and([]) == T + raises(TypeError, lambda: fuzzy_and()) + + +def test_fuzzy_or(): + assert fuzzy_or([T, T]) == T + assert fuzzy_or([T, F]) == T + assert fuzzy_or([T, U]) == T + assert fuzzy_or([F, F]) == F + assert fuzzy_or([F, U]) == U + assert fuzzy_or([U, U]) == U + assert [fuzzy_or([w]) for w in [U, T, F]] == [U, T, F] + assert fuzzy_or([T, F, U]) == T + assert fuzzy_or([]) == F + raises(TypeError, lambda: fuzzy_or()) + + +def test_logic_cmp(): + l1 = And('a', Not('b')) + l2 = And('a', Not('b')) + + assert hash(l1) == hash(l2) + assert (l1 == l2) == T + assert (l1 != l2) == F + + assert And('a', 'b', 'c') == And('b', 'a', 'c') + assert And('a', 'b', 'c') == And('c', 'b', 'a') + assert And('a', 'b', 'c') == And('c', 'a', 'b') + + assert Not('a') < Not('b') + assert (Not('b') < Not('a')) is False + assert (Not('a') < 2) is False + + +def test_logic_onearg(): + assert And() is True + assert Or() is False + + assert And(T) == T + assert And(F) == F + assert Or(T) == T + assert Or(F) == F + + assert And('a') == 'a' + assert Or('a') == 'a' + + +def test_logic_xnotx(): + assert And('a', Not('a')) == F + assert Or('a', Not('a')) == T + + +def test_logic_eval_TF(): + assert And(F, F) == F + assert And(F, T) == F + assert And(T, F) == F + assert And(T, T) == T + + assert Or(F, F) == F + assert Or(F, T) == T + assert Or(T, F) == T + assert Or(T, T) == T + + assert And('a', T) == 'a' + assert And('a', F) == F + assert Or('a', T) == T + assert Or('a', F) == 'a' + + +def test_logic_combine_args(): + assert And('a', 'b', 'a') == And('a', 'b') + assert Or('a', 'b', 'a') == Or('a', 'b') + + assert And(And('a', 'b'), And('c', 'd')) == And('a', 'b', 'c', 'd') + assert Or(Or('a', 'b'), Or('c', 'd')) == Or('a', 'b', 'c', 'd') + + assert Or('t', And('n', 'p', 'r'), And('n', 'r'), And('n', 'p', 'r'), 't', + And('n', 'r')) == Or('t', And('n', 'p', 'r'), And('n', 'r')) + + +def test_logic_expand(): + t = And(Or('a', 'b'), 'c') + assert t.expand() == Or(And('a', 'c'), And('b', 'c')) + + t = And(Or('a', Not('b')), 'b') + assert t.expand() == And('a', 'b') + + t = And(Or('a', 'b'), Or('c', 'd')) + assert t.expand() == \ + Or(And('a', 'c'), And('a', 'd'), And('b', 'c'), And('b', 'd')) + + +def test_logic_fromstring(): + S = Logic.fromstring + + assert S('a') == 'a' + assert S('!a') == Not('a') + assert S('a & b') == And('a', 'b') + assert S('a | b') == Or('a', 'b') + assert S('a | b & c') == And(Or('a', 'b'), 'c') + assert S('a & b | c') == Or(And('a', 'b'), 'c') + assert S('a & b & c') == And('a', 'b', 'c') + assert S('a | b | c') == Or('a', 'b', 'c') + + raises(ValueError, lambda: S('| a')) + raises(ValueError, lambda: S('& a')) + raises(ValueError, lambda: S('a | | b')) + raises(ValueError, lambda: S('a | & b')) + raises(ValueError, lambda: S('a & & b')) + raises(ValueError, lambda: S('a |')) + raises(ValueError, lambda: S('a|b')) + raises(ValueError, lambda: S('!')) + raises(ValueError, lambda: S('! a')) + raises(ValueError, lambda: S('!(a + 1)')) + raises(ValueError, lambda: S('')) + + +def test_logic_not(): + assert Not('a') != '!a' + assert Not('!a') != 'a' + assert Not(True) == False + assert Not(False) == True + + # NOTE: we may want to change default Not behaviour and put this + # functionality into some method. + assert Not(And('a', 'b')) == Or(Not('a'), Not('b')) + assert Not(Or('a', 'b')) == And(Not('a'), Not('b')) + + raises(ValueError, lambda: Not(1)) + + +def test_formatting(): + S = Logic.fromstring + raises(ValueError, lambda: S('a&b')) + raises(ValueError, lambda: S('a|b')) + raises(ValueError, lambda: S('! a')) + + +def test_fuzzy_xor(): + assert fuzzy_xor((None,)) is None + assert fuzzy_xor((None, True)) is None + assert fuzzy_xor((None, False)) is None + assert fuzzy_xor((True, False)) is True + assert fuzzy_xor((True, True)) is False + assert fuzzy_xor((True, True, False)) is False + assert fuzzy_xor((True, True, False, True)) is True + +def test_fuzzy_nand(): + for args in [(1, 0), (1, 1), (0, 0)]: + assert fuzzy_nand(args) == fuzzy_not(fuzzy_and(args)) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_match.py b/lib/python3.11/site-packages/sympy/core/tests/test_match.py new file mode 100644 index 0000000000000000000000000000000000000000..caa25e3c9dc1233e4566484f38a6b002ed4e72bd --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_match.py @@ -0,0 +1,766 @@ +from sympy import abc +from sympy.concrete.summations import Sum +from sympy.core.add import Add +from sympy.core.function import (Derivative, Function, diff) +from sympy.core.mul import Mul +from sympy.core.numbers import (Float, I, Integer, Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, Wild, symbols) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.hyper import meijerg +from sympy.polys.polytools import Poly +from sympy.simplify.radsimp import collect +from sympy.simplify.simplify import signsimp + +from sympy.testing.pytest import XFAIL + + +def test_symbol(): + x = Symbol('x') + a, b, c, p, q = map(Wild, 'abcpq') + + e = x + assert e.match(x) == {} + assert e.matches(x) == {} + assert e.match(a) == {a: x} + + e = Rational(5) + assert e.match(c) == {c: 5} + assert e.match(e) == {} + assert e.match(e + 1) is None + + +def test_add(): + x, y, a, b, c = map(Symbol, 'xyabc') + p, q, r = map(Wild, 'pqr') + + e = a + b + assert e.match(p + b) == {p: a} + assert e.match(p + a) == {p: b} + + e = 1 + b + assert e.match(p + b) == {p: 1} + + e = a + b + c + assert e.match(a + p + c) == {p: b} + assert e.match(b + p + c) == {p: a} + + e = a + b + c + x + assert e.match(a + p + x + c) == {p: b} + assert e.match(b + p + c + x) == {p: a} + assert e.match(b) is None + assert e.match(b + p) == {p: a + c + x} + assert e.match(a + p + c) == {p: b + x} + assert e.match(b + p + c) == {p: a + x} + + e = 4*x + 5 + assert e.match(4*x + p) == {p: 5} + assert e.match(3*x + p) == {p: x + 5} + assert e.match(p*x + 5) == {p: 4} + + +def test_power(): + x, y, a, b, c = map(Symbol, 'xyabc') + p, q, r = map(Wild, 'pqr') + + e = (x + y)**a + assert e.match(p**q) == {p: x + y, q: a} + assert e.match(p**p) is None + + e = (x + y)**(x + y) + assert e.match(p**p) == {p: x + y} + assert e.match(p**q) == {p: x + y, q: x + y} + + e = (2*x)**2 + assert e.match(p*q**r) == {p: 4, q: x, r: 2} + + e = Integer(1) + assert e.match(x**p) == {p: 0} + + +def test_match_exclude(): + x = Symbol('x') + y = Symbol('y') + p = Wild("p") + q = Wild("q") + r = Wild("r") + + e = Rational(6) + assert e.match(2*p) == {p: 3} + + e = 3/(4*x + 5) + assert e.match(3/(p*x + q)) == {p: 4, q: 5} + + e = 3/(4*x + 5) + assert e.match(p/(q*x + r)) == {p: 3, q: 4, r: 5} + + e = 2/(x + 1) + assert e.match(p/(q*x + r)) == {p: 2, q: 1, r: 1} + + e = 1/(x + 1) + assert e.match(p/(q*x + r)) == {p: 1, q: 1, r: 1} + + e = 4*x + 5 + assert e.match(p*x + q) == {p: 4, q: 5} + + e = 4*x + 5*y + 6 + assert e.match(p*x + q*y + r) == {p: 4, q: 5, r: 6} + + a = Wild('a', exclude=[x]) + + e = 3*x + assert e.match(p*x) == {p: 3} + assert e.match(a*x) == {a: 3} + + e = 3*x**2 + assert e.match(p*x) == {p: 3*x} + assert e.match(a*x) is None + + e = 3*x + 3 + 6/x + assert e.match(p*x**2 + p*x + 2*p) == {p: 3/x} + assert e.match(a*x**2 + a*x + 2*a) is None + + +def test_mul(): + x, y, a, b, c = map(Symbol, 'xyabc') + p, q = map(Wild, 'pq') + + e = 4*x + assert e.match(p*x) == {p: 4} + assert e.match(p*y) is None + assert e.match(e + p*y) == {p: 0} + + e = a*x*b*c + assert e.match(p*x) == {p: a*b*c} + assert e.match(c*p*x) == {p: a*b} + + e = (a + b)*(a + c) + assert e.match((p + b)*(p + c)) == {p: a} + + e = x + assert e.match(p*x) == {p: 1} + + e = exp(x) + assert e.match(x**p*exp(x*q)) == {p: 0, q: 1} + + e = I*Poly(x, x) + assert e.match(I*p) == {p: x} + + +def test_mul_noncommutative(): + x, y = symbols('x y') + A, B, C = symbols('A B C', commutative=False) + u, v = symbols('u v', cls=Wild) + w, z = symbols('w z', cls=Wild, commutative=False) + + assert (u*v).matches(x) in ({v: x, u: 1}, {u: x, v: 1}) + assert (u*v).matches(x*y) in ({v: y, u: x}, {u: y, v: x}) + assert (u*v).matches(A) is None + assert (u*v).matches(A*B) is None + assert (u*v).matches(x*A) is None + assert (u*v).matches(x*y*A) is None + assert (u*v).matches(x*A*B) is None + assert (u*v).matches(x*y*A*B) is None + + assert (v*w).matches(x) is None + assert (v*w).matches(x*y) is None + assert (v*w).matches(A) == {w: A, v: 1} + assert (v*w).matches(A*B) == {w: A*B, v: 1} + assert (v*w).matches(x*A) == {w: A, v: x} + assert (v*w).matches(x*y*A) == {w: A, v: x*y} + assert (v*w).matches(x*A*B) == {w: A*B, v: x} + assert (v*w).matches(x*y*A*B) == {w: A*B, v: x*y} + + assert (v*w).matches(-x) is None + assert (v*w).matches(-x*y) is None + assert (v*w).matches(-A) == {w: A, v: -1} + assert (v*w).matches(-A*B) == {w: A*B, v: -1} + assert (v*w).matches(-x*A) == {w: A, v: -x} + assert (v*w).matches(-x*y*A) == {w: A, v: -x*y} + assert (v*w).matches(-x*A*B) == {w: A*B, v: -x} + assert (v*w).matches(-x*y*A*B) == {w: A*B, v: -x*y} + + assert (w*z).matches(x) is None + assert (w*z).matches(x*y) is None + assert (w*z).matches(A) is None + assert (w*z).matches(A*B) == {w: A, z: B} + assert (w*z).matches(B*A) == {w: B, z: A} + assert (w*z).matches(A*B*C) in [{w: A, z: B*C}, {w: A*B, z: C}] + assert (w*z).matches(x*A) is None + assert (w*z).matches(x*y*A) is None + assert (w*z).matches(x*A*B) is None + assert (w*z).matches(x*y*A*B) is None + + assert (w*A).matches(A) is None + assert (A*w*B).matches(A*B) is None + + assert (u*w*z).matches(x) is None + assert (u*w*z).matches(x*y) is None + assert (u*w*z).matches(A) is None + assert (u*w*z).matches(A*B) == {u: 1, w: A, z: B} + assert (u*w*z).matches(B*A) == {u: 1, w: B, z: A} + assert (u*w*z).matches(x*A) is None + assert (u*w*z).matches(x*y*A) is None + assert (u*w*z).matches(x*A*B) == {u: x, w: A, z: B} + assert (u*w*z).matches(x*B*A) == {u: x, w: B, z: A} + assert (u*w*z).matches(x*y*A*B) == {u: x*y, w: A, z: B} + assert (u*w*z).matches(x*y*B*A) == {u: x*y, w: B, z: A} + + assert (u*A).matches(x*A) == {u: x} + assert (u*A).matches(x*A*B) is None + assert (u*B).matches(x*A) is None + assert (u*A*B).matches(x*A*B) == {u: x} + assert (u*A*B).matches(x*B*A) is None + assert (u*A*B).matches(x*A) is None + + assert (u*w*A).matches(x*A*B) is None + assert (u*w*B).matches(x*A*B) == {u: x, w: A} + + assert (u*v*A*B).matches(x*A*B) in [{u: x, v: 1}, {v: x, u: 1}] + assert (u*v*A*B).matches(x*B*A) is None + assert (u*v*A*B).matches(u*v*A*C) is None + + +def test_mul_noncommutative_mismatch(): + A, B, C = symbols('A B C', commutative=False) + w = symbols('w', cls=Wild, commutative=False) + + assert (w*B*w).matches(A*B*A) == {w: A} + assert (w*B*w).matches(A*C*B*A*C) == {w: A*C} + assert (w*B*w).matches(A*C*B*A*B) is None + assert (w*B*w).matches(A*B*C) is None + assert (w*w*C).matches(A*B*C) is None + + +def test_mul_noncommutative_pow(): + A, B, C = symbols('A B C', commutative=False) + w = symbols('w', cls=Wild, commutative=False) + + assert (A*B*w).matches(A*B**2) == {w: B} + assert (A*(B**2)*w*(B**3)).matches(A*B**8) == {w: B**3} + assert (A*B*w*C).matches(A*(B**4)*C) == {w: B**3} + + assert (A*B*(w**(-1))).matches(A*B*(C**(-1))) == {w: C} + assert (A*(B*w)**(-1)*C).matches(A*(B*C)**(-1)*C) == {w: C} + + assert ((w**2)*B*C).matches((A**2)*B*C) == {w: A} + assert ((w**2)*B*(w**3)).matches((A**2)*B*(A**3)) == {w: A} + assert ((w**2)*B*(w**4)).matches((A**2)*B*(A**2)) is None + +def test_complex(): + a, b, c = map(Symbol, 'abc') + x, y = map(Wild, 'xy') + + assert (1 + I).match(x + I) == {x: 1} + assert (a + I).match(x + I) == {x: a} + assert (2*I).match(x*I) == {x: 2} + assert (a*I).match(x*I) == {x: a} + assert (a*I).match(x*y) == {x: I, y: a} + assert (2*I).match(x*y) == {x: 2, y: I} + assert (a + b*I).match(x + y*I) == {x: a, y: b} + + +def test_functions(): + from sympy.core.function import WildFunction + x = Symbol('x') + g = WildFunction('g') + p = Wild('p') + q = Wild('q') + + f = cos(5*x) + notf = x + assert f.match(p*cos(q*x)) == {p: 1, q: 5} + assert f.match(p*g) == {p: 1, g: cos(5*x)} + assert notf.match(g) is None + + +@XFAIL +def test_functions_X1(): + from sympy.core.function import WildFunction + x = Symbol('x') + g = WildFunction('g') + p = Wild('p') + q = Wild('q') + + f = cos(5*x) + assert f.match(p*g(q*x)) == {p: 1, g: cos, q: 5} + + +def test_interface(): + x, y = map(Symbol, 'xy') + p, q = map(Wild, 'pq') + + assert (x + 1).match(p + 1) == {p: x} + assert (x*3).match(p*3) == {p: x} + assert (x**3).match(p**3) == {p: x} + assert (x*cos(y)).match(p*cos(q)) == {p: x, q: y} + + assert (x*y).match(p*q) in [{p:x, q:y}, {p:y, q:x}] + assert (x + y).match(p + q) in [{p:x, q:y}, {p:y, q:x}] + assert (x*y + 1).match(p*q) in [{p:1, q:1 + x*y}, {p:1 + x*y, q:1}] + + +def test_derivative1(): + x, y = map(Symbol, 'xy') + p, q = map(Wild, 'pq') + + f = Function('f', nargs=1) + fd = Derivative(f(x), x) + + assert fd.match(p) == {p: fd} + assert (fd + 1).match(p + 1) == {p: fd} + assert (fd).match(fd) == {} + assert (3*fd).match(p*fd) is not None + assert (3*fd - 1).match(p*fd + q) == {p: 3, q: -1} + + +def test_derivative_bug1(): + f = Function("f") + x = Symbol("x") + a = Wild("a", exclude=[f, x]) + b = Wild("b", exclude=[f]) + pattern = a * Derivative(f(x), x, x) + b + expr = Derivative(f(x), x) + x**2 + d1 = {b: x**2} + d2 = pattern.xreplace(d1).matches(expr, d1) + assert d2 is None + + +def test_derivative2(): + f = Function("f") + x = Symbol("x") + a = Wild("a", exclude=[f, x]) + b = Wild("b", exclude=[f]) + e = Derivative(f(x), x) + assert e.match(Derivative(f(x), x)) == {} + assert e.match(Derivative(f(x), x, x)) is None + e = Derivative(f(x), x, x) + assert e.match(Derivative(f(x), x)) is None + assert e.match(Derivative(f(x), x, x)) == {} + e = Derivative(f(x), x) + x**2 + assert e.match(a*Derivative(f(x), x) + b) == {a: 1, b: x**2} + assert e.match(a*Derivative(f(x), x, x) + b) is None + e = Derivative(f(x), x, x) + x**2 + assert e.match(a*Derivative(f(x), x) + b) is None + assert e.match(a*Derivative(f(x), x, x) + b) == {a: 1, b: x**2} + + +def test_match_deriv_bug1(): + n = Function('n') + l = Function('l') + + x = Symbol('x') + p = Wild('p') + + e = diff(l(x), x)/x - diff(diff(n(x), x), x)/2 - \ + diff(n(x), x)**2/4 + diff(n(x), x)*diff(l(x), x)/4 + e = e.subs(n(x), -l(x)).doit() + t = x*exp(-l(x)) + t2 = t.diff(x, x)/t + assert e.match( (p*t2).expand() ) == {p: Rational(-1, 2)} + + +def test_match_bug2(): + x, y = map(Symbol, 'xy') + p, q, r = map(Wild, 'pqr') + res = (x + y).match(p + q + r) + assert (p + q + r).subs(res) == x + y + + +def test_match_bug3(): + x, a, b = map(Symbol, 'xab') + p = Wild('p') + assert (b*x*exp(a*x)).match(x*exp(p*x)) is None + + +def test_match_bug4(): + x = Symbol('x') + p = Wild('p') + e = x + assert e.match(-p*x) == {p: -1} + + +def test_match_bug5(): + x = Symbol('x') + p = Wild('p') + e = -x + assert e.match(-p*x) == {p: 1} + + +def test_match_bug6(): + x = Symbol('x') + p = Wild('p') + e = x + assert e.match(3*p*x) == {p: Rational(1)/3} + + +def test_match_polynomial(): + x = Symbol('x') + a = Wild('a', exclude=[x]) + b = Wild('b', exclude=[x]) + c = Wild('c', exclude=[x]) + d = Wild('d', exclude=[x]) + + eq = 4*x**3 + 3*x**2 + 2*x + 1 + pattern = a*x**3 + b*x**2 + c*x + d + assert eq.match(pattern) == {a: 4, b: 3, c: 2, d: 1} + assert (eq - 3*x**2).match(pattern) == {a: 4, b: 0, c: 2, d: 1} + assert (x + sqrt(2) + 3).match(a + b*x + c*x**2) == \ + {b: 1, a: sqrt(2) + 3, c: 0} + + +def test_exclude(): + x, y, a = map(Symbol, 'xya') + p = Wild('p', exclude=[1, x]) + q = Wild('q') + r = Wild('r', exclude=[sin, y]) + + assert sin(x).match(r) is None + assert cos(y).match(r) is None + + e = 3*x**2 + y*x + a + assert e.match(p*x**2 + q*x + r) == {p: 3, q: y, r: a} + + e = x + 1 + assert e.match(x + p) is None + assert e.match(p + 1) is None + assert e.match(x + 1 + p) == {p: 0} + + e = cos(x) + 5*sin(y) + assert e.match(r) is None + assert e.match(cos(y) + r) is None + assert e.match(r + p*sin(q)) == {r: cos(x), p: 5, q: y} + + +def test_floats(): + a, b = map(Wild, 'ab') + + e = cos(0.12345, evaluate=False)**2 + r = e.match(a*cos(b)**2) + assert r == {a: 1, b: Float(0.12345)} + + +def test_Derivative_bug1(): + f = Function("f") + x = abc.x + a = Wild("a", exclude=[f(x)]) + b = Wild("b", exclude=[f(x)]) + eq = f(x).diff(x) + assert eq.match(a*Derivative(f(x), x) + b) == {a: 1, b: 0} + + +def test_match_wild_wild(): + p = Wild('p') + q = Wild('q') + r = Wild('r') + + assert p.match(q + r) in [ {q: p, r: 0}, {q: 0, r: p} ] + assert p.match(q*r) in [ {q: p, r: 1}, {q: 1, r: p} ] + + p = Wild('p') + q = Wild('q', exclude=[p]) + r = Wild('r') + + assert p.match(q + r) == {q: 0, r: p} + assert p.match(q*r) == {q: 1, r: p} + + p = Wild('p') + q = Wild('q', exclude=[p]) + r = Wild('r', exclude=[p]) + + assert p.match(q + r) is None + assert p.match(q*r) is None + + +def test__combine_inverse(): + x, y = symbols("x y") + assert Mul._combine_inverse(x*I*y, x*I) == y + assert Mul._combine_inverse(x*x**(1 + y), x**(1 + y)) == x + assert Mul._combine_inverse(x*I*y, y*I) == x + assert Mul._combine_inverse(oo*I*y, y*I) is oo + assert Mul._combine_inverse(oo*I*y, oo*I) == y + assert Mul._combine_inverse(oo*I*y, oo*I) == y + assert Mul._combine_inverse(oo*y, -oo) == -y + assert Mul._combine_inverse(-oo*y, oo) == -y + assert Mul._combine_inverse((1-exp(x/y)),(exp(x/y)-1)) == -1 + assert Add._combine_inverse(oo, oo) is S.Zero + assert Add._combine_inverse(oo*I, oo*I) is S.Zero + assert Add._combine_inverse(x*oo, x*oo) is S.Zero + assert Add._combine_inverse(-x*oo, -x*oo) is S.Zero + assert Add._combine_inverse((x - oo)*(x + oo), -oo) + + +def test_issue_3773(): + x = symbols('x') + z, phi, r = symbols('z phi r') + c, A, B, N = symbols('c A B N', cls=Wild) + l = Wild('l', exclude=(0,)) + + eq = z * sin(2*phi) * r**7 + matcher = c * sin(phi*N)**l * r**A * log(r)**B + + assert eq.match(matcher) == {c: z, l: 1, N: 2, A: 7, B: 0} + assert (-eq).match(matcher) == {c: -z, l: 1, N: 2, A: 7, B: 0} + assert (x*eq).match(matcher) == {c: x*z, l: 1, N: 2, A: 7, B: 0} + assert (-7*x*eq).match(matcher) == {c: -7*x*z, l: 1, N: 2, A: 7, B: 0} + + matcher = c*sin(phi*N)**l * r**A + + assert eq.match(matcher) == {c: z, l: 1, N: 2, A: 7} + assert (-eq).match(matcher) == {c: -z, l: 1, N: 2, A: 7} + assert (x*eq).match(matcher) == {c: x*z, l: 1, N: 2, A: 7} + assert (-7*x*eq).match(matcher) == {c: -7*x*z, l: 1, N: 2, A: 7} + + +def test_issue_3883(): + from sympy.abc import gamma, mu, x + f = (-gamma * (x - mu)**2 - log(gamma) + log(2*pi))/2 + a, b, c = symbols('a b c', cls=Wild, exclude=(gamma,)) + + assert f.match(a * log(gamma) + b * gamma + c) == \ + {a: Rational(-1, 2), b: -(-mu + x)**2/2, c: log(2*pi)/2} + assert f.expand().collect(gamma).match(a * log(gamma) + b * gamma + c) == \ + {a: Rational(-1, 2), b: (-(x - mu)**2/2).expand(), c: (log(2*pi)/2).expand()} + g1 = Wild('g1', exclude=[gamma]) + g2 = Wild('g2', exclude=[gamma]) + g3 = Wild('g3', exclude=[gamma]) + assert f.expand().match(g1 * log(gamma) + g2 * gamma + g3) == \ + {g3: log(2)/2 + log(pi)/2, g1: Rational(-1, 2), g2: -mu**2/2 + mu*x - x**2/2} + + +def test_issue_4418(): + x = Symbol('x') + a, b, c = symbols('a b c', cls=Wild, exclude=(x,)) + f, g = symbols('f g', cls=Function) + + eq = diff(g(x)*f(x).diff(x), x) + + assert eq.match( + g(x).diff(x)*f(x).diff(x) + g(x)*f(x).diff(x, x) + c) == {c: 0} + assert eq.match(a*g(x).diff( + x)*f(x).diff(x) + b*g(x)*f(x).diff(x, x) + c) == {a: 1, b: 1, c: 0} + + +def test_issue_4700(): + f = Function('f') + x = Symbol('x') + a, b = symbols('a b', cls=Wild, exclude=(f(x),)) + + p = a*f(x) + b + eq1 = sin(x) + eq2 = f(x) + sin(x) + eq3 = f(x) + x + sin(x) + eq4 = x + sin(x) + + assert eq1.match(p) == {a: 0, b: sin(x)} + assert eq2.match(p) == {a: 1, b: sin(x)} + assert eq3.match(p) == {a: 1, b: x + sin(x)} + assert eq4.match(p) == {a: 0, b: x + sin(x)} + + +def test_issue_5168(): + a, b, c = symbols('a b c', cls=Wild) + x = Symbol('x') + f = Function('f') + + assert x.match(a) == {a: x} + assert x.match(a*f(x)**c) == {a: x, c: 0} + assert x.match(a*b) == {a: 1, b: x} + assert x.match(a*b*f(x)**c) == {a: 1, b: x, c: 0} + + assert (-x).match(a) == {a: -x} + assert (-x).match(a*f(x)**c) == {a: -x, c: 0} + assert (-x).match(a*b) == {a: -1, b: x} + assert (-x).match(a*b*f(x)**c) == {a: -1, b: x, c: 0} + + assert (2*x).match(a) == {a: 2*x} + assert (2*x).match(a*f(x)**c) == {a: 2*x, c: 0} + assert (2*x).match(a*b) == {a: 2, b: x} + assert (2*x).match(a*b*f(x)**c) == {a: 2, b: x, c: 0} + + assert (-2*x).match(a) == {a: -2*x} + assert (-2*x).match(a*f(x)**c) == {a: -2*x, c: 0} + assert (-2*x).match(a*b) == {a: -2, b: x} + assert (-2*x).match(a*b*f(x)**c) == {a: -2, b: x, c: 0} + + +def test_issue_4559(): + x = Symbol('x') + e = Symbol('e') + w = Wild('w', exclude=[x]) + y = Wild('y') + + # this is as it should be + + assert (3/x).match(w/y) == {w: 3, y: x} + assert (3*x).match(w*y) == {w: 3, y: x} + assert (x/3).match(y/w) == {w: 3, y: x} + assert (3*x).match(y/w) == {w: S.One/3, y: x} + assert (3*x).match(y/w) == {w: Rational(1, 3), y: x} + + # these could be allowed to fail + + assert (x/3).match(w/y) == {w: S.One/3, y: 1/x} + assert (3*x).match(w/y) == {w: 3, y: 1/x} + assert (3/x).match(w*y) == {w: 3, y: 1/x} + + # Note that solve will give + # multiple roots but match only gives one: + # + # >>> solve(x**r-y**2,y) + # [-x**(r/2), x**(r/2)] + + r = Symbol('r', rational=True) + assert (x**r).match(y**2) == {y: x**(r/2)} + assert (x**e).match(y**2) == {y: sqrt(x**e)} + + # since (x**i = y) -> x = y**(1/i) where i is an integer + # the following should also be valid as long as y is not + # zero when i is negative. + + a = Wild('a') + + e = S.Zero + assert e.match(a) == {a: e} + assert e.match(1/a) is None + assert e.match(a**.3) is None + + e = S(3) + assert e.match(1/a) == {a: 1/e} + assert e.match(1/a**2) == {a: 1/sqrt(e)} + e = pi + assert e.match(1/a) == {a: 1/e} + assert e.match(1/a**2) == {a: 1/sqrt(e)} + assert (-e).match(sqrt(a)) is None + assert (-e).match(a**2) == {a: I*sqrt(pi)} + +# The pattern matcher doesn't know how to handle (x - a)**2 == (a - x)**2. To +# avoid ambiguity in actual applications, don't put a coefficient (including a +# minus sign) in front of a wild. +@XFAIL +def test_issue_4883(): + a = Wild('a') + x = Symbol('x') + + e = [i**2 for i in (x - 2, 2 - x)] + p = [i**2 for i in (x - a, a- x)] + for eq in e: + for pat in p: + assert eq.match(pat) == {a: 2} + + +def test_issue_4319(): + x, y = symbols('x y') + + p = -x*(S.One/8 - y) + ans = {S.Zero, y - S.One/8} + + def ok(pat): + assert set(p.match(pat).values()) == ans + + ok(Wild("coeff", exclude=[x])*x + Wild("rest")) + ok(Wild("w", exclude=[x])*x + Wild("rest")) + ok(Wild("coeff", exclude=[x])*x + Wild("rest")) + ok(Wild("w", exclude=[x])*x + Wild("rest")) + ok(Wild("e", exclude=[x])*x + Wild("rest")) + ok(Wild("ress", exclude=[x])*x + Wild("rest")) + ok(Wild("resu", exclude=[x])*x + Wild("rest")) + + +def test_issue_3778(): + p, c, q = symbols('p c q', cls=Wild) + x = Symbol('x') + + assert (sin(x)**2).match(sin(p)*sin(q)*c) == {q: x, c: 1, p: x} + assert (2*sin(x)).match(sin(p) + sin(q) + c) == {q: x, c: 0, p: x} + + +def test_issue_6103(): + x = Symbol('x') + a = Wild('a') + assert (-I*x*oo).match(I*a*oo) == {a: -x} + + +def test_issue_3539(): + a = Wild('a') + x = Symbol('x') + assert (x - 2).match(a - x) is None + assert (6/x).match(a*x) is None + assert (6/x**2).match(a/x) == {a: 6/x} + +def test_gh_issue_2711(): + x = Symbol('x') + f = meijerg(((), ()), ((0,), ()), x) + a = Wild('a') + b = Wild('b') + + assert f.find(a) == {(S.Zero,), ((), ()), ((S.Zero,), ()), x, S.Zero, + (), meijerg(((), ()), ((S.Zero,), ()), x)} + assert f.find(a + b) == \ + {meijerg(((), ()), ((S.Zero,), ()), x), x, S.Zero} + assert f.find(a**2) == {meijerg(((), ()), ((S.Zero,), ()), x), x} + + +def test_issue_17354(): + from sympy.core.symbol import (Wild, symbols) + x, y = symbols("x y", real=True) + a, b = symbols("a b", cls=Wild) + assert ((0 <= x).reversed | (y <= x)).match((1/a <= b) | (a <= b)) is None + + +def test_match_issue_17397(): + f = Function("f") + x = Symbol("x") + a3 = Wild('a3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)]) + b3 = Wild('b3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)]) + c3 = Wild('c3', exclude=[f(x), f(x).diff(x), f(x).diff(x, 2)]) + deq = a3*(f(x).diff(x, 2)) + b3*f(x).diff(x) + c3*f(x) + + eq = (x-2)**2*(f(x).diff(x, 2)) + (x-2)*(f(x).diff(x)) + ((x-2)**2 - 4)*f(x) + r = collect(eq, [f(x).diff(x, 2), f(x).diff(x), f(x)]).match(deq) + assert r == {a3: (x - 2)**2, c3: (x - 2)**2 - 4, b3: x - 2} + + eq =x*f(x) + x*Derivative(f(x), (x, 2)) - 4*f(x) + Derivative(f(x), x) \ + - 4*Derivative(f(x), (x, 2)) - 2*Derivative(f(x), x)/x + 4*Derivative(f(x), (x, 2))/x + r = collect(eq, [f(x).diff(x, 2), f(x).diff(x), f(x)]).match(deq) + assert r == {a3: x - 4 + 4/x, b3: 1 - 2/x, c3: x - 4} + + +def test_match_issue_21942(): + a, r, w = symbols('a, r, w', nonnegative=True) + p = symbols('p', positive=True) + g_ = Wild('g') + pattern = g_ ** (1 / (1 - p)) + eq = (a * r ** (1 - p) + w ** (1 - p) * (1 - a)) ** (1 / (1 - p)) + m = {g_: a * r ** (1 - p) + w ** (1 - p) * (1 - a)} + assert pattern.matches(eq) == m + assert (-pattern).matches(-eq) == m + assert pattern.matches(signsimp(eq)) is None + + +def test_match_terms(): + X, Y = map(Wild, "XY") + x, y, z = symbols('x y z') + assert (5*y - x).match(5*X - Y) == {X: y, Y: x} + # 15907 + assert (x + (y - 1)*z).match(x + X*z) == {X: y - 1} + # 20747 + assert (x - log(x/y)*(1-exp(x/y))).match(x - log(X/y)*(1-exp(x/y))) == {X: x} + + +def test_match_bound(): + V, W = map(Wild, "VW") + x, y = symbols('x y') + assert Sum(x, (x, 1, 2)).match(Sum(y, (y, 1, W))) == {W: 2} + assert Sum(x, (x, 1, 2)).match(Sum(V, (V, 1, W))) == {W: 2, V:x} + assert Sum(x, (x, 1, 2)).match(Sum(V, (V, 1, 2))) == {V:x} + + +def test_issue_22462(): + x, f = symbols('x'), Function('f') + n, Q = symbols('n Q', cls=Wild) + pattern = -Q*f(x)**n + eq = 5*f(x)**2 + assert pattern.matches(eq) == {n: 2, Q: -5} diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_multidimensional.py b/lib/python3.11/site-packages/sympy/core/tests/test_multidimensional.py new file mode 100644 index 0000000000000000000000000000000000000000..765c78adf8dbed2ead43721ca4ab9510dbeeb282 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_multidimensional.py @@ -0,0 +1,24 @@ +from sympy.core.function import (Derivative, Function, diff) +from sympy.core.symbol import symbols +from sympy.functions.elementary.trigonometric import sin +from sympy.core.multidimensional import vectorize +x, y, z = symbols('x y z') +f, g, h = list(map(Function, 'fgh')) + + +def test_vectorize(): + @vectorize(0) + def vsin(x): + return sin(x) + + assert vsin([1, x, y]) == [sin(1), sin(x), sin(y)] + + @vectorize(0, 1) + def vdiff(f, y): + return diff(f, y) + + assert vdiff([f(x, y, z), g(x, y, z), h(x, y, z)], [x, y, z]) == \ + [[Derivative(f(x, y, z), x), Derivative(f(x, y, z), y), + Derivative(f(x, y, z), z)], [Derivative(g(x, y, z), x), + Derivative(g(x, y, z), y), Derivative(g(x, y, z), z)], + [Derivative(h(x, y, z), x), Derivative(h(x, y, z), y), Derivative(h(x, y, z), z)]] diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_noncommutative.py b/lib/python3.11/site-packages/sympy/core/tests/test_noncommutative.py new file mode 100644 index 0000000000000000000000000000000000000000..b3d3a3cec2ef64aa500aad08b438c90cc8987581 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_noncommutative.py @@ -0,0 +1,140 @@ +"""Tests for noncommutative symbols and expressions.""" + +from sympy.core.function import expand +from sympy.core.numbers import I +from sympy.core.symbol import symbols +from sympy.functions.elementary.complexes import (adjoint, conjugate, transpose) +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.polys.polytools import (cancel, factor) +from sympy.simplify.combsimp import combsimp +from sympy.simplify.gammasimp import gammasimp +from sympy.simplify.radsimp import (collect, radsimp, rcollect) +from sympy.simplify.ratsimp import ratsimp +from sympy.simplify.simplify import (posify, simplify) +from sympy.simplify.trigsimp import trigsimp +from sympy.abc import x, y, z +from sympy.testing.pytest import XFAIL + +A, B, C = symbols("A B C", commutative=False) +X = symbols("X", commutative=False, hermitian=True) +Y = symbols("Y", commutative=False, antihermitian=True) + + +def test_adjoint(): + assert adjoint(A).is_commutative is False + assert adjoint(A*A) == adjoint(A)**2 + assert adjoint(A*B) == adjoint(B)*adjoint(A) + assert adjoint(A*B**2) == adjoint(B)**2*adjoint(A) + assert adjoint(A*B - B*A) == adjoint(B)*adjoint(A) - adjoint(A)*adjoint(B) + assert adjoint(A + I*B) == adjoint(A) - I*adjoint(B) + + assert adjoint(X) == X + assert adjoint(-I*X) == I*X + assert adjoint(Y) == -Y + assert adjoint(-I*Y) == -I*Y + + assert adjoint(X) == conjugate(transpose(X)) + assert adjoint(Y) == conjugate(transpose(Y)) + assert adjoint(X) == transpose(conjugate(X)) + assert adjoint(Y) == transpose(conjugate(Y)) + + +def test_cancel(): + assert cancel(A*B - B*A) == A*B - B*A + assert cancel(A*B*(x - 1)) == A*B*(x - 1) + assert cancel(A*B*(x**2 - 1)/(x + 1)) == A*B*(x - 1) + assert cancel(A*B*(x**2 - 1)/(x + 1) - B*A*(x - 1)) == A*B*(x - 1) + (1 - x)*B*A + + +@XFAIL +def test_collect(): + assert collect(A*B - B*A, A) == A*B - B*A + assert collect(A*B - B*A, B) == A*B - B*A + assert collect(A*B - B*A, x) == A*B - B*A + + +def test_combsimp(): + assert combsimp(A*B - B*A) == A*B - B*A + + +def test_gammasimp(): + assert gammasimp(A*B - B*A) == A*B - B*A + + +def test_conjugate(): + assert conjugate(A).is_commutative is False + assert (A*A).conjugate() == conjugate(A)**2 + assert (A*B).conjugate() == conjugate(A)*conjugate(B) + assert (A*B**2).conjugate() == conjugate(A)*conjugate(B)**2 + assert (A*B - B*A).conjugate() == \ + conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A) + assert (A*B).conjugate() - (B*A).conjugate() == \ + conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A) + assert (A + I*B).conjugate() == conjugate(A) - I*conjugate(B) + + +def test_expand(): + assert expand((A*B)**2) == A*B*A*B + assert expand(A*B - B*A) == A*B - B*A + assert expand((A*B/A)**2) == A*B*B/A + assert expand(B*A*(A + B)*B) == B*A**2*B + B*A*B**2 + assert expand(B*A*(A + C)*B) == B*A**2*B + B*A*C*B + + +def test_factor(): + assert factor(A*B - B*A) == A*B - B*A + + +def test_posify(): + assert posify(A)[0].is_commutative is False + for q in (A*B/A, (A*B/A)**2, (A*B)**2, A*B - B*A): + p = posify(q) + assert p[0].subs(p[1]) == q + + +def test_radsimp(): + assert radsimp(A*B - B*A) == A*B - B*A + + +@XFAIL +def test_ratsimp(): + assert ratsimp(A*B - B*A) == A*B - B*A + + +@XFAIL +def test_rcollect(): + assert rcollect(A*B - B*A, A) == A*B - B*A + assert rcollect(A*B - B*A, B) == A*B - B*A + assert rcollect(A*B - B*A, x) == A*B - B*A + + +def test_simplify(): + assert simplify(A*B - B*A) == A*B - B*A + + +def test_subs(): + assert (x*y*A).subs(x*y, z) == A*z + assert (x*A*B).subs(x*A, C) == C*B + assert (x*A*x*x).subs(x**2*A, C) == x*C + assert (x*A*x*B).subs(x**2*A, C) == C*B + assert (A**2*B**2).subs(A*B**2, C) == A*C + assert (A*A*A + A*B*A).subs(A*A*A, C) == C + A*B*A + + +def test_transpose(): + assert transpose(A).is_commutative is False + assert transpose(A*A) == transpose(A)**2 + assert transpose(A*B) == transpose(B)*transpose(A) + assert transpose(A*B**2) == transpose(B)**2*transpose(A) + assert transpose(A*B - B*A) == \ + transpose(B)*transpose(A) - transpose(A)*transpose(B) + assert transpose(A + I*B) == transpose(A) + I*transpose(B) + + assert transpose(X) == conjugate(X) + assert transpose(-I*X) == -I*conjugate(X) + assert transpose(Y) == -conjugate(Y) + assert transpose(-I*Y) == I*conjugate(Y) + + +def test_trigsimp(): + assert trigsimp(A*sin(x)**2 + A*cos(x)**2) == A diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_numbers.py b/lib/python3.11/site-packages/sympy/core/tests/test_numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..054fd7591b28d352b648c98d78cdda10a4fe2cb1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_numbers.py @@ -0,0 +1,2300 @@ +import numbers as nums +import decimal +from sympy.concrete.summations import Sum +from sympy.core import (EulerGamma, Catalan, TribonacciConstant, + GoldenRatio) +from sympy.core.containers import Tuple +from sympy.core.expr import unchanged +from sympy.core.logic import fuzzy_not +from sympy.core.mul import Mul +from sympy.core.numbers import (mpf_norm, seterr, + Integer, I, pi, comp, Rational, E, nan, + oo, AlgebraicNumber, Number, Float, zoo, equal_valued, + int_valued, all_close) +from sympy.core.intfunc import (igcd, igcdex, igcd2, igcd_lehmer, + ilcm, integer_nthroot, isqrt, integer_log, mod_inverse) +from sympy.core.power import Pow +from sympy.core.relational import Ge, Gt, Le, Lt +from sympy.core.singleton import S +from sympy.core.symbol import Dummy, Symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.integers import floor +from sympy.functions.combinatorial.numbers import fibonacci +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.miscellaneous import sqrt, cbrt +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.polys.domains.realfield import RealField +from sympy.printing.latex import latex +from sympy.printing.repr import srepr +from sympy.simplify import simplify +from sympy.polys.domains.groundtypes import PythonRational +from sympy.utilities.decorator import conserve_mpmath_dps +from sympy.utilities.iterables import permutations +from sympy.testing.pytest import XFAIL, raises, _both_exp_pow +from sympy import Add + +from mpmath import mpf +import mpmath +from sympy.core import numbers +t = Symbol('t', real=False) + +_ninf = float(-oo) +_inf = float(oo) + + +def same_and_same_prec(a, b): + # stricter matching for Floats + return a == b and a._prec == b._prec + + +def test_seterr(): + seterr(divide=True) + raises(ValueError, lambda: S.Zero/S.Zero) + seterr(divide=False) + assert S.Zero / S.Zero is S.NaN + + +def test_mod(): + x = S.Half + y = Rational(3, 4) + z = Rational(5, 18043) + + assert x % x == 0 + assert x % y == S.Half + assert x % z == Rational(3, 36086) + assert y % x == Rational(1, 4) + assert y % y == 0 + assert y % z == Rational(9, 72172) + assert z % x == Rational(5, 18043) + assert z % y == Rational(5, 18043) + assert z % z == 0 + + a = Float(2.6) + + assert (a % .2) == 0.0 + assert (a % 2).round(15) == 0.6 + assert (a % 0.5).round(15) == 0.1 + + p = Symbol('p', infinite=True) + + assert oo % oo is nan + assert zoo % oo is nan + assert 5 % oo is nan + assert p % 5 is nan + + # In these two tests, if the precision of m does + # not match the precision of the ans, then it is + # likely that the change made now gives an answer + # with degraded accuracy. + r = Rational(500, 41) + f = Float('.36', 3) + m = r % f + ans = Float(r % Rational(f), 3) + assert m == ans and m._prec == ans._prec + f = Float('8.36', 3) + m = f % r + ans = Float(Rational(f) % r, 3) + assert m == ans and m._prec == ans._prec + + s = S.Zero + + assert s % float(1) == 0.0 + + # No rounding required since these numbers can be represented + # exactly. + assert Rational(3, 4) % Float(1.1) == 0.75 + assert Float(1.5) % Rational(5, 4) == 0.25 + assert Rational(5, 4).__rmod__(Float('1.5')) == 0.25 + assert Float('1.5').__rmod__(Float('2.75')) == Float('1.25') + assert 2.75 % Float('1.5') == Float('1.25') + + a = Integer(7) + b = Integer(4) + + assert type(a % b) == Integer + assert a % b == Integer(3) + assert Integer(1) % Rational(2, 3) == Rational(1, 3) + assert Rational(7, 5) % Integer(1) == Rational(2, 5) + assert Integer(2) % 1.5 == 0.5 + + assert Integer(3).__rmod__(Integer(10)) == Integer(1) + assert Integer(10) % 4 == Integer(2) + assert 15 % Integer(4) == Integer(3) + + +def test_divmod(): + x = Symbol("x") + assert divmod(S(12), S(8)) == Tuple(1, 4) + assert divmod(-S(12), S(8)) == Tuple(-2, 4) + assert divmod(S.Zero, S.One) == Tuple(0, 0) + raises(ZeroDivisionError, lambda: divmod(S.Zero, S.Zero)) + raises(ZeroDivisionError, lambda: divmod(S.One, S.Zero)) + assert divmod(S(12), 8) == Tuple(1, 4) + assert divmod(12, S(8)) == Tuple(1, 4) + assert S(1024)//x == 1024//x == floor(1024/x) + + assert divmod(S("2"), S("3/2")) == Tuple(S("1"), S("1/2")) + assert divmod(S("3/2"), S("2")) == Tuple(S("0"), S("3/2")) + assert divmod(S("2"), S("3.5")) == Tuple(S("0"), S("2.")) + assert divmod(S("3.5"), S("2")) == Tuple(S("1"), S("1.5")) + assert divmod(S("2"), S("1/3")) == Tuple(S("6"), S("0")) + assert divmod(S("1/3"), S("2")) == Tuple(S("0"), S("1/3")) + assert divmod(S("2"), S("1/10")) == Tuple(S("20"), S("0")) + assert divmod(S("2"), S(".1"))[0] == 19 + assert divmod(S("0.1"), S("2")) == Tuple(S("0"), S("0.1")) + assert divmod(S("2"), 2) == Tuple(S("1"), S("0")) + assert divmod(2, S("2")) == Tuple(S("1"), S("0")) + assert divmod(S("2"), 1.5) == Tuple(S("1"), S("0.5")) + assert divmod(1.5, S("2")) == Tuple(S("0"), S("1.5")) + assert divmod(0.3, S("2")) == Tuple(S("0"), S("0.3")) + assert divmod(S("3/2"), S("3.5")) == Tuple(S("0"), S(3/2)) + assert divmod(S("3.5"), S("3/2")) == Tuple(S("2"), S("0.5")) + assert divmod(S("3/2"), S("1/3")) == Tuple(S("4"), S("1/6")) + assert divmod(S("1/3"), S("3/2")) == Tuple(S("0"), S("1/3")) + assert divmod(S("3/2"), S("0.1"))[0] == 14 + assert divmod(S("0.1"), S("3/2")) == Tuple(S("0"), S("0.1")) + assert divmod(S("3/2"), 2) == Tuple(S("0"), S("3/2")) + assert divmod(2, S("3/2")) == Tuple(S("1"), S("1/2")) + assert divmod(S("3/2"), 1.5) == Tuple(S("1"), S("0.")) + assert divmod(1.5, S("3/2")) == Tuple(S("1"), S("0.")) + assert divmod(S("3/2"), 0.3) == Tuple(S("5"), S("0.")) + assert divmod(0.3, S("3/2")) == Tuple(S("0"), S("0.3")) + assert divmod(S("1/3"), S("3.5")) == (0, 1/3) + assert divmod(S("3.5"), S("0.1")) == Tuple(S("35"), S("0.")) + assert divmod(S("0.1"), S("3.5")) == Tuple(S("0"), S("0.1")) + assert divmod(S("3.5"), 2) == Tuple(S("1"), S("1.5")) + assert divmod(2, S("3.5")) == Tuple(S("0"), S("2.")) + assert divmod(S("3.5"), 1.5) == Tuple(S("2"), S("0.5")) + assert divmod(1.5, S("3.5")) == Tuple(S("0"), S("1.5")) + assert divmod(0.3, S("3.5")) == Tuple(S("0"), S("0.3")) + assert divmod(S("0.1"), S("1/3")) == Tuple(S("0"), S("0.1")) + assert divmod(S("1/3"), 2) == Tuple(S("0"), S("1/3")) + assert divmod(2, S("1/3")) == Tuple(S("6"), S("0")) + assert divmod(S("1/3"), 1.5) == (0, 1/3) + assert divmod(0.3, S("1/3")) == (0, 0.3) + assert divmod(S("0.1"), 2) == (0, 0.1) + assert divmod(2, S("0.1"))[0] == 19 + assert divmod(S("0.1"), 1.5) == (0, 0.1) + assert divmod(1.5, S("0.1")) == Tuple(S("15"), S("0.")) + assert divmod(S("0.1"), 0.3) == Tuple(S("0"), S("0.1")) + + assert str(divmod(S("2"), 0.3)) == '(6, 0.2)' + assert str(divmod(S("3.5"), S("1/3"))) == '(10, 0.166666666666667)' + assert str(divmod(S("3.5"), 0.3)) == '(11, 0.2)' + assert str(divmod(S("1/3"), S("0.1"))) == '(3, 0.0333333333333333)' + assert str(divmod(1.5, S("1/3"))) == '(4, 0.166666666666667)' + assert str(divmod(S("1/3"), 0.3)) == '(1, 0.0333333333333333)' + assert str(divmod(0.3, S("0.1"))) == '(2, 0.1)' + + assert divmod(-3, S(2)) == (-2, 1) + assert divmod(S(-3), S(2)) == (-2, 1) + assert divmod(S(-3), 2) == (-2, 1) + + assert divmod(oo, 1) == (S.NaN, S.NaN) + assert divmod(S.NaN, 1) == (S.NaN, S.NaN) + assert divmod(1, S.NaN) == (S.NaN, S.NaN) + ans = [(-1, oo), (-1, oo), (0, 0), (0, 1), (0, 2)] + OO = float('inf') + ANS = [tuple(map(float, i)) for i in ans] + assert [divmod(i, oo) for i in range(-2, 3)] == ans + ans = [(0, -2), (0, -1), (0, 0), (-1, -oo), (-1, -oo)] + ANS = [tuple(map(float, i)) for i in ans] + assert [divmod(i, -oo) for i in range(-2, 3)] == ans + assert [divmod(i, -OO) for i in range(-2, 3)] == ANS + + # sympy's divmod gives an Integer for the quotient rather than a float + dmod = lambda a, b: tuple([j if i else int(j) for i, j in enumerate(divmod(a, b))]) + for a in (4, 4., 4.25, 0, 0., -4, -4. -4.25): + for b in (2, 2., 2.5, -2, -2., -2.5): + assert divmod(S(a), S(b)) == dmod(a, b) + + +def test_igcd(): + assert igcd(0, 0) == 0 + assert igcd(0, 1) == 1 + assert igcd(1, 0) == 1 + assert igcd(0, 7) == 7 + assert igcd(7, 0) == 7 + assert igcd(7, 1) == 1 + assert igcd(1, 7) == 1 + assert igcd(-1, 0) == 1 + assert igcd(0, -1) == 1 + assert igcd(-1, -1) == 1 + assert igcd(-1, 7) == 1 + assert igcd(7, -1) == 1 + assert igcd(8, 2) == 2 + assert igcd(4, 8) == 4 + assert igcd(8, 16) == 8 + assert igcd(7, -3) == 1 + assert igcd(-7, 3) == 1 + assert igcd(-7, -3) == 1 + assert igcd(*[10, 20, 30]) == 10 + raises(TypeError, lambda: igcd()) + raises(TypeError, lambda: igcd(2)) + raises(ValueError, lambda: igcd(0, None)) + raises(ValueError, lambda: igcd(1, 2.2)) + for args in permutations((45.1, 1, 30)): + raises(ValueError, lambda: igcd(*args)) + for args in permutations((1, 2, None)): + raises(ValueError, lambda: igcd(*args)) + + +def test_igcd_lehmer(): + a, b = fibonacci(10001), fibonacci(10000) + # len(str(a)) == 2090 + # small divisors, long Euclidean sequence + assert igcd_lehmer(a, b) == 1 + c = fibonacci(100) + assert igcd_lehmer(a*c, b*c) == c + # big divisor + assert igcd_lehmer(a, 10**1000) == 1 + # swapping argument + assert igcd_lehmer(1, 2) == igcd_lehmer(2, 1) + + +def test_igcd2(): + # short loop + assert igcd2(2**100 - 1, 2**99 - 1) == 1 + # Lehmer's algorithm + a, b = int(fibonacci(10001)), int(fibonacci(10000)) + assert igcd2(a, b) == 1 + + +def test_ilcm(): + assert ilcm(0, 0) == 0 + assert ilcm(1, 0) == 0 + assert ilcm(0, 1) == 0 + assert ilcm(1, 1) == 1 + assert ilcm(2, 1) == 2 + assert ilcm(8, 2) == 8 + assert ilcm(8, 6) == 24 + assert ilcm(8, 7) == 56 + assert ilcm(*[10, 20, 30]) == 60 + raises(ValueError, lambda: ilcm(8.1, 7)) + raises(ValueError, lambda: ilcm(8, 7.1)) + raises(TypeError, lambda: ilcm(8)) + + +def test_igcdex(): + assert igcdex(2, 3) == (-1, 1, 1) + assert igcdex(10, 12) == (-1, 1, 2) + assert igcdex(100, 2004) == (-20, 1, 4) + assert igcdex(0, 0) == (0, 1, 0) + assert igcdex(1, 0) == (1, 0, 1) + + +def _strictly_equal(a, b): + return (a.p, a.q, type(a.p), type(a.q)) == \ + (b.p, b.q, type(b.p), type(b.q)) + + +def _test_rational_new(cls): + """ + Tests that are common between Integer and Rational. + """ + assert cls(0) is S.Zero + assert cls(1) is S.One + assert cls(-1) is S.NegativeOne + # These look odd, but are similar to int(): + assert cls('1') is S.One + assert cls('-1') is S.NegativeOne + + i = Integer(10) + assert _strictly_equal(i, cls('10')) + assert _strictly_equal(i, cls('10')) + assert _strictly_equal(i, cls(int(10))) + assert _strictly_equal(i, cls(i)) + + raises(TypeError, lambda: cls(Symbol('x'))) + + +def test_Integer_new(): + """ + Test for Integer constructor + """ + _test_rational_new(Integer) + + assert _strictly_equal(Integer(0.9), S.Zero) + assert _strictly_equal(Integer(10.5), Integer(10)) + raises(ValueError, lambda: Integer("10.5")) + assert Integer(Rational('1.' + '9'*20)) == 1 + + +def test_Rational_new(): + """" + Test for Rational constructor + """ + _test_rational_new(Rational) + + n1 = S.Half + assert n1 == Rational(Integer(1), 2) + assert n1 == Rational(Integer(1), Integer(2)) + assert n1 == Rational(1, Integer(2)) + assert n1 == Rational(S.Half) + assert 1 == Rational(n1, n1) + assert Rational(3, 2) == Rational(S.Half, Rational(1, 3)) + assert Rational(3, 1) == Rational(1, Rational(1, 3)) + n3_4 = Rational(3, 4) + assert Rational('3/4') == n3_4 + assert -Rational('-3/4') == n3_4 + assert Rational('.76').limit_denominator(4) == n3_4 + assert Rational(19, 25).limit_denominator(4) == n3_4 + assert Rational('19/25').limit_denominator(4) == n3_4 + assert Rational(1.0, 3) == Rational(1, 3) + assert Rational(1, 3.0) == Rational(1, 3) + assert Rational(Float(0.5)) == S.Half + assert Rational('1e2/1e-2') == Rational(10000) + assert Rational('1 234') == Rational(1234) + assert Rational('1/1 234') == Rational(1, 1234) + assert Rational(-1, 0) is S.ComplexInfinity + assert Rational(1, 0) is S.ComplexInfinity + # Make sure Rational doesn't lose precision on Floats + assert Rational(pi.evalf(100)).evalf(100) == pi.evalf(100) + raises(TypeError, lambda: Rational('3**3')) + raises(TypeError, lambda: Rational('1/2 + 2/3')) + + # handle fractions.Fraction instances + try: + import fractions + assert Rational(fractions.Fraction(1, 2)) == S.Half + except ImportError: + pass + + assert Rational(PythonRational(2, 6)) == Rational(1, 3) + + assert Rational(2, 4, gcd=1).q == 4 + n = Rational(2, -4, gcd=1) + assert n.q == 4 + assert n.p == -2 + +def test_issue_24543(): + for p in ('1.5', 1.5, 2): + for q in ('1.5', 1.5, 2): + assert Rational(p, q).as_numer_denom() == Rational('%s/%s'%(p,q)).as_numer_denom() + + assert Rational('0.5', '100') == Rational(1, 200) + + +def test_Number_new(): + """" + Test for Number constructor + """ + # Expected behavior on numbers and strings + assert Number(1) is S.One + assert Number(2).__class__ is Integer + assert Number(-622).__class__ is Integer + assert Number(5, 3).__class__ is Rational + assert Number(5.3).__class__ is Float + assert Number('1') is S.One + assert Number('2').__class__ is Integer + assert Number('-622').__class__ is Integer + assert Number('5/3').__class__ is Rational + assert Number('5.3').__class__ is Float + raises(ValueError, lambda: Number('cos')) + raises(TypeError, lambda: Number(cos)) + a = Rational(3, 5) + assert Number(a) is a # Check idempotence on Numbers + u = ['inf', '-inf', 'nan', 'iNF', '+inf'] + v = [oo, -oo, nan, oo, oo] + for i, a in zip(u, v): + assert Number(i) is a, (i, Number(i), a) + + +def test_Number_cmp(): + n1 = Number(1) + n2 = Number(2) + n3 = Number(-3) + + assert n1 < n2 + assert n1 <= n2 + assert n3 < n1 + assert n2 > n3 + assert n2 >= n3 + + raises(TypeError, lambda: n1 < S.NaN) + raises(TypeError, lambda: n1 <= S.NaN) + raises(TypeError, lambda: n1 > S.NaN) + raises(TypeError, lambda: n1 >= S.NaN) + + +def test_Rational_cmp(): + n1 = Rational(1, 4) + n2 = Rational(1, 3) + n3 = Rational(2, 4) + n4 = Rational(2, -4) + n5 = Rational(0) + n6 = Rational(1) + n7 = Rational(3) + n8 = Rational(-3) + + assert n8 < n5 + assert n5 < n6 + assert n6 < n7 + assert n8 < n7 + assert n7 > n8 + assert (n1 + 1)**n2 < 2 + assert ((n1 + n6)/n7) < 1 + + assert n4 < n3 + assert n2 < n3 + assert n1 < n2 + assert n3 > n1 + assert not n3 < n1 + assert not (Rational(-1) > 0) + assert Rational(-1) < 0 + + raises(TypeError, lambda: n1 < S.NaN) + raises(TypeError, lambda: n1 <= S.NaN) + raises(TypeError, lambda: n1 > S.NaN) + raises(TypeError, lambda: n1 >= S.NaN) + + +def test_Float(): + def eq(a, b): + t = Float("1.0E-15") + return (-t < a - b < t) + + zeros = (0, S.Zero, 0., Float(0)) + for i, j in permutations(zeros[:-1], 2): + assert i == j + for i, j in permutations(zeros[-2:], 2): + assert i == j + for z in zeros: + assert z in zeros + assert S.Zero.is_zero + + a = Float(2) ** Float(3) + assert eq(a.evalf(), Float(8)) + assert eq((pi ** -1).evalf(), Float("0.31830988618379067")) + a = Float(2) ** Float(4) + assert eq(a.evalf(), Float(16)) + assert (S(.3) == S(.5)) is False + + mpf = (0, 5404319552844595, -52, 53) + x_str = Float((0, '13333333333333', -52, 53)) + x_0xstr = Float((0, '0x13333333333333', -52, 53)) + x2_str = Float((0, '26666666666666', -53, 54)) + x_hex = Float((0, int(0x13333333333333), -52, 53)) + x_dec = Float(mpf) + assert x_str == x_0xstr == x_hex == x_dec == Float(1.2) + # x2_str was entered slightly malformed in that the mantissa + # was even -- it should be odd and the even part should be + # included with the exponent, but this is resolved by normalization + # ONLY IF REQUIREMENTS of mpf_norm are met: the bitcount must + # be exact: double the mantissa ==> increase bc by 1 + assert Float(1.2)._mpf_ == mpf + assert x2_str._mpf_ == mpf + + assert Float((0, int(0), -123, -1)) is S.NaN + assert Float((0, int(0), -456, -2)) is S.Infinity + assert Float((1, int(0), -789, -3)) is S.NegativeInfinity + # if you don't give the full signature, it's not special + assert Float((0, int(0), -123)) == Float(0) + assert Float((0, int(0), -456)) == Float(0) + assert Float((1, int(0), -789)) == Float(0) + + raises(ValueError, lambda: Float((0, 7, 1, 3), '')) + + assert Float('0.0').is_finite is True + assert Float('0.0').is_negative is False + assert Float('0.0').is_positive is False + assert Float('0.0').is_infinite is False + assert Float('0.0').is_zero is True + + # rationality properties + # if the integer test fails then the use of intlike + # should be removed from gamma_functions.py + assert Float(1).is_integer is None + assert Float(1).is_rational is None + assert Float(1).is_irrational is None + assert sqrt(2).n(15).is_rational is None + assert sqrt(2).n(15).is_irrational is None + + # do not automatically evalf + def teq(a): + assert (a.evalf() == a) is False + assert (a.evalf() != a) is True + assert (a == a.evalf()) is False + assert (a != a.evalf()) is True + + teq(pi) + teq(2*pi) + teq(cos(0.1, evaluate=False)) + + # long integer + i = 12345678901234567890 + assert same_and_same_prec(Float(12, ''), Float('12', '')) + assert same_and_same_prec(Float(Integer(i), ''), Float(i, '')) + assert same_and_same_prec(Float(i, ''), Float(str(i), 20)) + assert same_and_same_prec(Float(str(i)), Float(i, '')) + assert same_and_same_prec(Float(i), Float(i, '')) + + # inexact floats (repeating binary = denom not multiple of 2) + # cannot have precision greater than 15 + assert Float(.125, 22)._prec == 76 + assert Float(2.0, 22)._prec == 76 + # only default prec is equal, even for exactly representable float + assert Float(.125, 22) != .125 + #assert Float(2.0, 22) == 2 + assert float(Float('.12500000000000001', '')) == .125 + raises(ValueError, lambda: Float(.12500000000000001, '')) + + # allow spaces + assert Float('123 456.123 456') == Float('123456.123456') + assert Integer('123 456') == Integer('123456') + assert Rational('123 456.123 456') == Rational('123456.123456') + assert Float(' .3e2') == Float('0.3e2') + # but treat them as strictly ass underscore between digits: only 1 + raises(ValueError, lambda: Float('1 2')) + + # allow underscore between digits + assert Float('1_23.4_56') == Float('123.456') + # assert Float('1_23.4_5_6', 12) == Float('123.456', 12) + # ...but not in all cases (per Py 3.6) + raises(ValueError, lambda: Float('1_')) + raises(ValueError, lambda: Float('1__2')) + raises(ValueError, lambda: Float('_1')) + raises(ValueError, lambda: Float('_inf')) + + # allow auto precision detection + assert Float('.1', '') == Float(.1, 1) + assert Float('.125', '') == Float(.125, 3) + assert Float('.100', '') == Float(.1, 3) + assert Float('2.0', '') == Float('2', 2) + + raises(ValueError, lambda: Float("12.3d-4", "")) + raises(ValueError, lambda: Float(12.3, "")) + raises(ValueError, lambda: Float('.')) + raises(ValueError, lambda: Float('-.')) + + zero = Float('0.0') + assert Float('-0') == zero + assert Float('.0') == zero + assert Float('-.0') == zero + assert Float('-0.0') == zero + assert Float(0.0) == zero + assert Float(0) == zero + assert Float(0, '') == Float('0', '') + assert Float(1) == Float(1.0) + assert Float(S.Zero) == zero + assert Float(S.One) == Float(1.0) + + assert Float(decimal.Decimal('0.1'), 3) == Float('.1', 3) + assert Float(decimal.Decimal('nan')) is S.NaN + assert Float(decimal.Decimal('Infinity')) is S.Infinity + assert Float(decimal.Decimal('-Infinity')) is S.NegativeInfinity + + assert '{:.3f}'.format(Float(4.236622)) == '4.237' + assert '{:.35f}'.format(Float(pi.n(40), 40)) == \ + '3.14159265358979323846264338327950288' + + # unicode + assert Float('0.73908513321516064100000000') == \ + Float('0.73908513321516064100000000') + assert Float('0.73908513321516064100000000', 28) == \ + Float('0.73908513321516064100000000', 28) + + # binary precision + # Decimal value 0.1 cannot be expressed precisely as a base 2 fraction + a = Float(S.One/10, dps=15) + b = Float(S.One/10, dps=16) + p = Float(S.One/10, precision=53) + q = Float(S.One/10, precision=54) + assert a._mpf_ == p._mpf_ + assert not a._mpf_ == q._mpf_ + assert not b._mpf_ == q._mpf_ + + # Precision specifying errors + raises(ValueError, lambda: Float("1.23", dps=3, precision=10)) + raises(ValueError, lambda: Float("1.23", dps="", precision=10)) + raises(ValueError, lambda: Float("1.23", dps=3, precision="")) + raises(ValueError, lambda: Float("1.23", dps="", precision="")) + + # from NumberSymbol + assert same_and_same_prec(Float(pi, 32), pi.evalf(32)) + assert same_and_same_prec(Float(Catalan), Catalan.evalf()) + + # oo and nan + u = ['inf', '-inf', 'nan', 'iNF', '+inf'] + v = [oo, -oo, nan, oo, oo] + for i, a in zip(u, v): + assert Float(i) is a + + +def test_zero_not_false(): + # https://github.com/sympy/sympy/issues/20796 + assert (S(0.0) == S.false) is False + assert (S.false == S(0.0)) is False + assert (S(0) == S.false) is False + assert (S.false == S(0)) is False + + +@conserve_mpmath_dps +def test_float_mpf(): + import mpmath + mpmath.mp.dps = 100 + mp_pi = mpmath.pi() + + assert Float(mp_pi, 100) == Float(mp_pi._mpf_, 100) == pi.evalf(100) + + mpmath.mp.dps = 15 + + assert Float(mp_pi, 100) == Float(mp_pi._mpf_, 100) == pi.evalf(100) + + +def test_Float_RealElement(): + repi = RealField(dps=100)(pi.evalf(100)) + # We still have to pass the precision because Float doesn't know what + # RealElement is, but make sure it keeps full precision from the result. + assert Float(repi, 100) == pi.evalf(100) + + +def test_Float_default_to_highprec_from_str(): + s = str(pi.evalf(128)) + assert same_and_same_prec(Float(s), Float(s, '')) + + +def test_Float_eval(): + a = Float(3.2) + assert (a**2).is_Float + + +def test_Float_issue_2107(): + a = Float(0.1, 10) + b = Float("0.1", 10) + + assert a - a == 0 + assert a + (-a) == 0 + assert S.Zero + a - a == 0 + assert S.Zero + a + (-a) == 0 + + assert b - b == 0 + assert b + (-b) == 0 + assert S.Zero + b - b == 0 + assert S.Zero + b + (-b) == 0 + + +def test_issue_14289(): + from sympy.polys.numberfields import to_number_field + + a = 1 - sqrt(2) + b = to_number_field(a) + assert b.as_expr() == a + assert b.minpoly(a).expand() == 0 + + +def test_Float_from_tuple(): + a = Float((0, '1L', 0, 1)) + b = Float((0, '1', 0, 1)) + assert a == b + + +def test_Infinity(): + assert oo != 1 + assert 1*oo is oo + assert 1 != oo + assert oo != -oo + assert oo != Symbol("x")**3 + assert oo + 1 is oo + assert 2 + oo is oo + assert 3*oo + 2 is oo + assert S.Half**oo == 0 + assert S.Half**(-oo) is oo + assert -oo*3 is -oo + assert oo + oo is oo + assert -oo + oo*(-5) is -oo + assert 1/oo == 0 + assert 1/(-oo) == 0 + assert 8/oo == 0 + assert oo % 2 is nan + assert 2 % oo is nan + assert oo/oo is nan + assert oo/-oo is nan + assert -oo/oo is nan + assert -oo/-oo is nan + assert oo - oo is nan + assert oo - -oo is oo + assert -oo - oo is -oo + assert -oo - -oo is nan + assert oo + -oo is nan + assert -oo + oo is nan + assert oo + oo is oo + assert -oo + oo is nan + assert oo + -oo is nan + assert -oo + -oo is -oo + assert oo*oo is oo + assert -oo*oo is -oo + assert oo*-oo is -oo + assert -oo*-oo is oo + assert oo/0 is oo + assert -oo/0 is -oo + assert 0/oo == 0 + assert 0/-oo == 0 + assert oo*0 is nan + assert -oo*0 is nan + assert 0*oo is nan + assert 0*-oo is nan + assert oo + 0 is oo + assert -oo + 0 is -oo + assert 0 + oo is oo + assert 0 + -oo is -oo + assert oo - 0 is oo + assert -oo - 0 is -oo + assert 0 - oo is -oo + assert 0 - -oo is oo + assert oo/2 is oo + assert -oo/2 is -oo + assert oo/-2 is -oo + assert -oo/-2 is oo + assert oo*2 is oo + assert -oo*2 is -oo + assert oo*-2 is -oo + assert 2/oo == 0 + assert 2/-oo == 0 + assert -2/oo == 0 + assert -2/-oo == 0 + assert 2*oo is oo + assert 2*-oo is -oo + assert -2*oo is -oo + assert -2*-oo is oo + assert 2 + oo is oo + assert 2 - oo is -oo + assert -2 + oo is oo + assert -2 - oo is -oo + assert 2 + -oo is -oo + assert 2 - -oo is oo + assert -2 + -oo is -oo + assert -2 - -oo is oo + assert S(2) + oo is oo + assert S(2) - oo is -oo + assert oo/I == -oo*I + assert -oo/I == oo*I + assert oo*float(1) == _inf and (oo*float(1)) is oo + assert -oo*float(1) == _ninf and (-oo*float(1)) is -oo + assert oo/float(1) == _inf and (oo/float(1)) is oo + assert -oo/float(1) == _ninf and (-oo/float(1)) is -oo + assert oo*float(-1) == _ninf and (oo*float(-1)) is -oo + assert -oo*float(-1) == _inf and (-oo*float(-1)) is oo + assert oo/float(-1) == _ninf and (oo/float(-1)) is -oo + assert -oo/float(-1) == _inf and (-oo/float(-1)) is oo + assert oo + float(1) == _inf and (oo + float(1)) is oo + assert -oo + float(1) == _ninf and (-oo + float(1)) is -oo + assert oo - float(1) == _inf and (oo - float(1)) is oo + assert -oo - float(1) == _ninf and (-oo - float(1)) is -oo + assert float(1)*oo == _inf and (float(1)*oo) is oo + assert float(1)*-oo == _ninf and (float(1)*-oo) is -oo + assert float(1)/oo == 0 + assert float(1)/-oo == 0 + assert float(-1)*oo == _ninf and (float(-1)*oo) is -oo + assert float(-1)*-oo == _inf and (float(-1)*-oo) is oo + assert float(-1)/oo == 0 + assert float(-1)/-oo == 0 + assert float(1) + oo is oo + assert float(1) + -oo is -oo + assert float(1) - oo is -oo + assert float(1) - -oo is oo + assert oo == float(oo) + assert (oo != float(oo)) is False + assert type(float(oo)) is float + assert -oo == float(-oo) + assert (-oo != float(-oo)) is False + assert type(float(-oo)) is float + + assert Float('nan') is nan + assert nan*1.0 is nan + assert -1.0*nan is nan + assert nan*oo is nan + assert nan*-oo is nan + assert nan/oo is nan + assert nan/-oo is nan + assert nan + oo is nan + assert nan + -oo is nan + assert nan - oo is nan + assert nan - -oo is nan + assert -oo * S.Zero is nan + + assert oo*nan is nan + assert -oo*nan is nan + assert oo/nan is nan + assert -oo/nan is nan + assert oo + nan is nan + assert -oo + nan is nan + assert oo - nan is nan + assert -oo - nan is nan + assert S.Zero * oo is nan + assert oo.is_Rational is False + assert isinstance(oo, Rational) is False + + assert S.One/oo == 0 + assert -S.One/oo == 0 + assert S.One/-oo == 0 + assert -S.One/-oo == 0 + assert S.One*oo is oo + assert -S.One*oo is -oo + assert S.One*-oo is -oo + assert -S.One*-oo is oo + assert S.One/nan is nan + assert S.One - -oo is oo + assert S.One + nan is nan + assert S.One - nan is nan + assert nan - S.One is nan + assert nan/S.One is nan + assert -oo - S.One is -oo + + +def test_Infinity_2(): + x = Symbol('x') + assert oo*x != oo + assert oo*(pi - 1) is oo + assert oo*(1 - pi) is -oo + + assert (-oo)*x != -oo + assert (-oo)*(pi - 1) is -oo + assert (-oo)*(1 - pi) is oo + + assert (-1)**S.NaN is S.NaN + assert oo - _inf is S.NaN + assert oo + _ninf is S.NaN + assert oo*0 is S.NaN + assert oo/_inf is S.NaN + assert oo/_ninf is S.NaN + assert oo**S.NaN is S.NaN + assert -oo + _inf is S.NaN + assert -oo - _ninf is S.NaN + assert -oo*S.NaN is S.NaN + assert -oo*0 is S.NaN + assert -oo/_inf is S.NaN + assert -oo/_ninf is S.NaN + assert -oo/S.NaN is S.NaN + assert abs(-oo) is oo + assert all((-oo)**i is S.NaN for i in (oo, -oo, S.NaN)) + assert (-oo)**3 is -oo + assert (-oo)**2 is oo + assert abs(S.ComplexInfinity) is oo + + +def test_Mul_Infinity_Zero(): + assert Float(0)*_inf is nan + assert Float(0)*_ninf is nan + assert Float(0)*_inf is nan + assert Float(0)*_ninf is nan + assert _inf*Float(0) is nan + assert _ninf*Float(0) is nan + assert _inf*Float(0) is nan + assert _ninf*Float(0) is nan + + +def test_Div_By_Zero(): + assert 1/S.Zero is zoo + assert 1/Float(0) is zoo + assert 0/S.Zero is nan + assert 0/Float(0) is nan + assert S.Zero/0 is nan + assert Float(0)/0 is nan + assert -1/S.Zero is zoo + assert -1/Float(0) is zoo + + +@_both_exp_pow +def test_Infinity_inequations(): + assert oo > pi + assert not (oo < pi) + assert exp(-3) < oo + + assert _inf > pi + assert not (_inf < pi) + assert exp(-3) < _inf + + raises(TypeError, lambda: oo < I) + raises(TypeError, lambda: oo <= I) + raises(TypeError, lambda: oo > I) + raises(TypeError, lambda: oo >= I) + raises(TypeError, lambda: -oo < I) + raises(TypeError, lambda: -oo <= I) + raises(TypeError, lambda: -oo > I) + raises(TypeError, lambda: -oo >= I) + + raises(TypeError, lambda: I < oo) + raises(TypeError, lambda: I <= oo) + raises(TypeError, lambda: I > oo) + raises(TypeError, lambda: I >= oo) + raises(TypeError, lambda: I < -oo) + raises(TypeError, lambda: I <= -oo) + raises(TypeError, lambda: I > -oo) + raises(TypeError, lambda: I >= -oo) + + assert oo > -oo and oo >= -oo + assert (oo < -oo) == False and (oo <= -oo) == False + assert -oo < oo and -oo <= oo + assert (-oo > oo) == False and (-oo >= oo) == False + + assert (oo < oo) == False # issue 7775 + assert (oo > oo) == False + assert (-oo > -oo) == False and (-oo < -oo) == False + assert oo >= oo and oo <= oo and -oo >= -oo and -oo <= -oo + assert (-oo < -_inf) == False + assert (oo > _inf) == False + assert -oo >= -_inf + assert oo <= _inf + + x = Symbol('x') + b = Symbol('b', finite=True, real=True) + assert (x < oo) == Lt(x, oo) # issue 7775 + assert b < oo and b > -oo and b <= oo and b >= -oo + assert oo > b and oo >= b and (oo < b) == False and (oo <= b) == False + assert (-oo > b) == False and (-oo >= b) == False and -oo < b and -oo <= b + assert (oo < x) == Lt(oo, x) and (oo > x) == Gt(oo, x) + assert (oo <= x) == Le(oo, x) and (oo >= x) == Ge(oo, x) + assert (-oo < x) == Lt(-oo, x) and (-oo > x) == Gt(-oo, x) + assert (-oo <= x) == Le(-oo, x) and (-oo >= x) == Ge(-oo, x) + + +def test_NaN(): + assert nan is nan + assert nan != 1 + assert 1*nan is nan + assert 1 != nan + assert -nan is nan + assert oo != Symbol("x")**3 + assert 2 + nan is nan + assert 3*nan + 2 is nan + assert -nan*3 is nan + assert nan + nan is nan + assert -nan + nan*(-5) is nan + assert 8/nan is nan + raises(TypeError, lambda: nan > 0) + raises(TypeError, lambda: nan < 0) + raises(TypeError, lambda: nan >= 0) + raises(TypeError, lambda: nan <= 0) + raises(TypeError, lambda: 0 < nan) + raises(TypeError, lambda: 0 > nan) + raises(TypeError, lambda: 0 <= nan) + raises(TypeError, lambda: 0 >= nan) + assert nan**0 == 1 # as per IEEE 754 + assert 1**nan is nan # IEEE 754 is not the best choice for symbolic work + # test Pow._eval_power's handling of NaN + assert Pow(nan, 0, evaluate=False)**2 == 1 + for n in (1, 1., S.One, S.NegativeOne, Float(1)): + assert n + nan is nan + assert n - nan is nan + assert nan + n is nan + assert nan - n is nan + assert n/nan is nan + assert nan/n is nan + + +def test_special_numbers(): + assert isinstance(S.NaN, Number) is True + assert isinstance(S.Infinity, Number) is True + assert isinstance(S.NegativeInfinity, Number) is True + + assert S.NaN.is_number is True + assert S.Infinity.is_number is True + assert S.NegativeInfinity.is_number is True + assert S.ComplexInfinity.is_number is True + + assert isinstance(S.NaN, Rational) is False + assert isinstance(S.Infinity, Rational) is False + assert isinstance(S.NegativeInfinity, Rational) is False + + assert S.NaN.is_rational is not True + assert S.Infinity.is_rational is not True + assert S.NegativeInfinity.is_rational is not True + + +def test_powers(): + assert integer_nthroot(1, 2) == (1, True) + assert integer_nthroot(1, 5) == (1, True) + assert integer_nthroot(2, 1) == (2, True) + assert integer_nthroot(2, 2) == (1, False) + assert integer_nthroot(2, 5) == (1, False) + assert integer_nthroot(4, 2) == (2, True) + assert integer_nthroot(123**25, 25) == (123, True) + assert integer_nthroot(123**25 + 1, 25) == (123, False) + assert integer_nthroot(123**25 - 1, 25) == (122, False) + assert integer_nthroot(1, 1) == (1, True) + assert integer_nthroot(0, 1) == (0, True) + assert integer_nthroot(0, 3) == (0, True) + assert integer_nthroot(10000, 1) == (10000, True) + assert integer_nthroot(4, 2) == (2, True) + assert integer_nthroot(16, 2) == (4, True) + assert integer_nthroot(26, 2) == (5, False) + assert integer_nthroot(1234567**7, 7) == (1234567, True) + assert integer_nthroot(1234567**7 + 1, 7) == (1234567, False) + assert integer_nthroot(1234567**7 - 1, 7) == (1234566, False) + b = 25**1000 + assert integer_nthroot(b, 1000) == (25, True) + assert integer_nthroot(b + 1, 1000) == (25, False) + assert integer_nthroot(b - 1, 1000) == (24, False) + c = 10**400 + c2 = c**2 + assert integer_nthroot(c2, 2) == (c, True) + assert integer_nthroot(c2 + 1, 2) == (c, False) + assert integer_nthroot(c2 - 1, 2) == (c - 1, False) + assert integer_nthroot(2, 10**10) == (1, False) + + p, r = integer_nthroot(int(factorial(10000)), 100) + assert p % (10**10) == 5322420655 + assert not r + + # Test that this is fast + assert integer_nthroot(2, 10**10) == (1, False) + + # output should be int if possible + assert type(integer_nthroot(2**61, 2)[0]) is int + + +def test_integer_nthroot_overflow(): + assert integer_nthroot(10**(50*50), 50) == (10**50, True) + assert integer_nthroot(10**100000, 10000) == (10**10, True) + + +def test_integer_log(): + raises(ValueError, lambda: integer_log(2, 1)) + raises(ValueError, lambda: integer_log(0, 2)) + raises(ValueError, lambda: integer_log(1.1, 2)) + raises(ValueError, lambda: integer_log(1, 2.2)) + + assert integer_log(1, 2) == (0, True) + assert integer_log(1, 3) == (0, True) + assert integer_log(2, 3) == (0, False) + assert integer_log(3, 3) == (1, True) + assert integer_log(3*2, 3) == (1, False) + assert integer_log(3**2, 3) == (2, True) + assert integer_log(3*4, 3) == (2, False) + assert integer_log(3**3, 3) == (3, True) + assert integer_log(27, 5) == (2, False) + assert integer_log(2, 3) == (0, False) + assert integer_log(-4, 2) == (2, False) + assert integer_log(-16, 4) == (0, False) + assert integer_log(-4, -2) == (2, False) + assert integer_log(4, -2) == (2, True) + assert integer_log(-8, -2) == (3, True) + assert integer_log(8, -2) == (3, False) + assert integer_log(-9, 3) == (0, False) + assert integer_log(-9, -3) == (2, False) + assert integer_log(9, -3) == (2, True) + assert integer_log(-27, -3) == (3, True) + assert integer_log(27, -3) == (3, False) + + +def test_isqrt(): + from math import sqrt as _sqrt + limit = 4503599761588223 + assert int(_sqrt(limit)) == integer_nthroot(limit, 2)[0] + assert int(_sqrt(limit + 1)) != integer_nthroot(limit + 1, 2)[0] + assert isqrt(limit + 1) == integer_nthroot(limit + 1, 2)[0] + assert isqrt(limit + S.Half) == integer_nthroot(limit, 2)[0] + assert isqrt(limit + 1 + S.Half) == integer_nthroot(limit + 1, 2)[0] + assert isqrt(limit + 2 + S.Half) == integer_nthroot(limit + 2, 2)[0] + + # Regression tests for https://github.com/sympy/sympy/issues/17034 + assert isqrt(4503599761588224) == 67108864 + assert isqrt(9999999999999999) == 99999999 + + # Other corner cases, especially involving non-integers. + raises(ValueError, lambda: isqrt(-1)) + raises(ValueError, lambda: isqrt(-10**1000)) + raises(ValueError, lambda: isqrt(Rational(-1, 2))) + + tiny = Rational(1, 10**1000) + raises(ValueError, lambda: isqrt(-tiny)) + assert isqrt(1-tiny) == 0 + assert isqrt(4503599761588224-tiny) == 67108864 + assert isqrt(10**100 - tiny) == 10**50 - 1 + + +def test_powers_Integer(): + """Test Integer._eval_power""" + # check infinity + assert S.One ** S.Infinity is S.NaN + assert S.NegativeOne** S.Infinity is S.NaN + assert S(2) ** S.Infinity is S.Infinity + assert S(-2)** S.Infinity == zoo + assert S(0) ** S.Infinity is S.Zero + + # check Nan + assert S.One ** S.NaN is S.NaN + assert S.NegativeOne ** S.NaN is S.NaN + + # check for exact roots + assert S.NegativeOne ** Rational(6, 5) == - (-1)**(S.One/5) + assert sqrt(S(4)) == 2 + assert sqrt(S(-4)) == I * 2 + assert S(16) ** Rational(1, 4) == 2 + assert S(-16) ** Rational(1, 4) == 2 * (-1)**Rational(1, 4) + assert S(9) ** Rational(3, 2) == 27 + assert S(-9) ** Rational(3, 2) == -27*I + assert S(27) ** Rational(2, 3) == 9 + assert S(-27) ** Rational(2, 3) == 9 * (S.NegativeOne ** Rational(2, 3)) + assert (-2) ** Rational(-2, 1) == Rational(1, 4) + + # not exact roots + assert sqrt(-3) == I*sqrt(3) + assert (3) ** (Rational(3, 2)) == 3 * sqrt(3) + assert (-3) ** (Rational(3, 2)) == - 3 * sqrt(-3) + assert (-3) ** (Rational(5, 2)) == 9 * I * sqrt(3) + assert (-3) ** (Rational(7, 2)) == - I * 27 * sqrt(3) + assert (2) ** (Rational(3, 2)) == 2 * sqrt(2) + assert (2) ** (Rational(-3, 2)) == sqrt(2) / 4 + assert (81) ** (Rational(2, 3)) == 9 * (S(3) ** (Rational(2, 3))) + assert (-81) ** (Rational(2, 3)) == 9 * (S(-3) ** (Rational(2, 3))) + assert (-3) ** Rational(-7, 3) == \ + -(-1)**Rational(2, 3)*3**Rational(2, 3)/27 + assert (-3) ** Rational(-2, 3) == \ + -(-1)**Rational(1, 3)*3**Rational(1, 3)/3 + + # join roots + assert sqrt(6) + sqrt(24) == 3*sqrt(6) + assert sqrt(2) * sqrt(3) == sqrt(6) + + # separate symbols & constansts + x = Symbol("x") + assert sqrt(49 * x) == 7 * sqrt(x) + assert sqrt((3 - sqrt(pi)) ** 2) == 3 - sqrt(pi) + + # check that it is fast for big numbers + assert (2**64 + 1) ** Rational(4, 3) + assert (2**64 + 1) ** Rational(17, 25) + + # negative rational power and negative base + assert (-3) ** Rational(-7, 3) == \ + -(-1)**Rational(2, 3)*3**Rational(2, 3)/27 + assert (-3) ** Rational(-2, 3) == \ + -(-1)**Rational(1, 3)*3**Rational(1, 3)/3 + assert (-2) ** Rational(-10, 3) == \ + (-1)**Rational(2, 3)*2**Rational(2, 3)/16 + assert abs(Pow(-2, Rational(-10, 3)).n() - + Pow(-2, Rational(-10, 3), evaluate=False).n()) < 1e-16 + + # negative base and rational power with some simplification + assert (-8) ** Rational(2, 5) == \ + 2*(-1)**Rational(2, 5)*2**Rational(1, 5) + assert (-4) ** Rational(9, 5) == \ + -8*(-1)**Rational(4, 5)*2**Rational(3, 5) + + assert S(1234).factors() == {617: 1, 2: 1} + assert Rational(2*3, 3*5*7).factors() == {2: 1, 5: -1, 7: -1} + + # test that eval_power factors numbers bigger than + # the current limit in factor_trial_division (2**15) + from sympy.ntheory.generate import nextprime + n = nextprime(2**15) + assert sqrt(n**2) == n + assert sqrt(n**3) == n*sqrt(n) + assert sqrt(4*n) == 2*sqrt(n) + + # check that factors of base with powers sharing gcd with power are removed + assert (2**4*3)**Rational(1, 6) == 2**Rational(2, 3)*3**Rational(1, 6) + assert (2**4*3)**Rational(5, 6) == 8*2**Rational(1, 3)*3**Rational(5, 6) + + # check that bases sharing a gcd are exptracted + assert 2**Rational(1, 3)*3**Rational(1, 4)*6**Rational(1, 5) == \ + 2**Rational(8, 15)*3**Rational(9, 20) + assert sqrt(8)*24**Rational(1, 3)*6**Rational(1, 5) == \ + 4*2**Rational(7, 10)*3**Rational(8, 15) + assert sqrt(8)*(-24)**Rational(1, 3)*(-6)**Rational(1, 5) == \ + 4*(-3)**Rational(8, 15)*2**Rational(7, 10) + assert 2**Rational(1, 3)*2**Rational(8, 9) == 2*2**Rational(2, 9) + assert 2**Rational(2, 3)*6**Rational(1, 3) == 2*3**Rational(1, 3) + assert 2**Rational(2, 3)*6**Rational(8, 9) == \ + 2*2**Rational(5, 9)*3**Rational(8, 9) + assert (-2)**Rational(2, S(3))*(-4)**Rational(1, S(3)) == -2*2**Rational(1, 3) + assert 3*Pow(3, 2, evaluate=False) == 3**3 + assert 3*Pow(3, Rational(-1, 3), evaluate=False) == 3**Rational(2, 3) + assert (-2)**Rational(1, 3)*(-3)**Rational(1, 4)*(-5)**Rational(5, 6) == \ + -(-1)**Rational(5, 12)*2**Rational(1, 3)*3**Rational(1, 4) * \ + 5**Rational(5, 6) + + assert Integer(-2)**Symbol('', even=True) == \ + Integer(2)**Symbol('', even=True) + assert (-1)**Float(.5) == 1.0*I + + +def test_powers_Rational(): + """Test Rational._eval_power""" + # check infinity + assert S.Half ** S.Infinity == 0 + assert Rational(3, 2) ** S.Infinity is S.Infinity + assert Rational(-1, 2) ** S.Infinity == 0 + assert Rational(-3, 2) ** S.Infinity == zoo + + # check Nan + assert Rational(3, 4) ** S.NaN is S.NaN + assert Rational(-2, 3) ** S.NaN is S.NaN + + # exact roots on numerator + assert sqrt(Rational(4, 3)) == 2 * sqrt(3) / 3 + assert Rational(4, 3) ** Rational(3, 2) == 8 * sqrt(3) / 9 + assert sqrt(Rational(-4, 3)) == I * 2 * sqrt(3) / 3 + assert Rational(-4, 3) ** Rational(3, 2) == - I * 8 * sqrt(3) / 9 + assert Rational(27, 2) ** Rational(1, 3) == 3 * (2 ** Rational(2, 3)) / 2 + assert Rational(5**3, 8**3) ** Rational(4, 3) == Rational(5**4, 8**4) + + # exact root on denominator + assert sqrt(Rational(1, 4)) == S.Half + assert sqrt(Rational(1, -4)) == I * S.Half + assert sqrt(Rational(3, 4)) == sqrt(3) / 2 + assert sqrt(Rational(3, -4)) == I * sqrt(3) / 2 + assert Rational(5, 27) ** Rational(1, 3) == (5 ** Rational(1, 3)) / 3 + + # not exact roots + assert sqrt(S.Half) == sqrt(2) / 2 + assert sqrt(Rational(-4, 7)) == I * sqrt(Rational(4, 7)) + assert Rational(-3, 2)**Rational(-7, 3) == \ + -4*(-1)**Rational(2, 3)*2**Rational(1, 3)*3**Rational(2, 3)/27 + assert Rational(-3, 2)**Rational(-2, 3) == \ + -(-1)**Rational(1, 3)*2**Rational(2, 3)*3**Rational(1, 3)/3 + assert Rational(-3, 2)**Rational(-10, 3) == \ + 8*(-1)**Rational(2, 3)*2**Rational(1, 3)*3**Rational(2, 3)/81 + assert abs(Pow(Rational(-2, 3), Rational(-7, 4)).n() - + Pow(Rational(-2, 3), Rational(-7, 4), evaluate=False).n()) < 1e-16 + + # negative integer power and negative rational base + assert Rational(-2, 3) ** Rational(-2, 1) == Rational(9, 4) + + a = Rational(1, 10) + assert a**Float(a, 2) == Float(a, 2)**Float(a, 2) + assert Rational(-2, 3)**Symbol('', even=True) == \ + Rational(2, 3)**Symbol('', even=True) + + +def test_powers_Float(): + assert str((S('-1/10')**S('3/10')).n()) == str(Float(-.1)**(.3)) + + +def test_lshift_Integer(): + assert Integer(0) << Integer(2) == Integer(0) + assert Integer(0) << 2 == Integer(0) + assert 0 << Integer(2) == Integer(0) + + assert Integer(0b11) << Integer(0) == Integer(0b11) + assert Integer(0b11) << 0 == Integer(0b11) + assert 0b11 << Integer(0) == Integer(0b11) + + assert Integer(0b11) << Integer(2) == Integer(0b11 << 2) + assert Integer(0b11) << 2 == Integer(0b11 << 2) + assert 0b11 << Integer(2) == Integer(0b11 << 2) + + assert Integer(-0b11) << Integer(2) == Integer(-0b11 << 2) + assert Integer(-0b11) << 2 == Integer(-0b11 << 2) + assert -0b11 << Integer(2) == Integer(-0b11 << 2) + + raises(TypeError, lambda: Integer(2) << 0.0) + raises(TypeError, lambda: 0.0 << Integer(2)) + raises(ValueError, lambda: Integer(1) << Integer(-1)) + + +def test_rshift_Integer(): + assert Integer(0) >> Integer(2) == Integer(0) + assert Integer(0) >> 2 == Integer(0) + assert 0 >> Integer(2) == Integer(0) + + assert Integer(0b11) >> Integer(0) == Integer(0b11) + assert Integer(0b11) >> 0 == Integer(0b11) + assert 0b11 >> Integer(0) == Integer(0b11) + + assert Integer(0b11) >> Integer(2) == Integer(0) + assert Integer(0b11) >> 2 == Integer(0) + assert 0b11 >> Integer(2) == Integer(0) + + assert Integer(-0b11) >> Integer(2) == Integer(-1) + assert Integer(-0b11) >> 2 == Integer(-1) + assert -0b11 >> Integer(2) == Integer(-1) + + assert Integer(0b1100) >> Integer(2) == Integer(0b1100 >> 2) + assert Integer(0b1100) >> 2 == Integer(0b1100 >> 2) + assert 0b1100 >> Integer(2) == Integer(0b1100 >> 2) + + assert Integer(-0b1100) >> Integer(2) == Integer(-0b1100 >> 2) + assert Integer(-0b1100) >> 2 == Integer(-0b1100 >> 2) + assert -0b1100 >> Integer(2) == Integer(-0b1100 >> 2) + + raises(TypeError, lambda: Integer(0b10) >> 0.0) + raises(TypeError, lambda: 0.0 >> Integer(2)) + raises(ValueError, lambda: Integer(1) >> Integer(-1)) + + +def test_and_Integer(): + assert Integer(0b01010101) & Integer(0b10101010) == Integer(0) + assert Integer(0b01010101) & 0b10101010 == Integer(0) + assert 0b01010101 & Integer(0b10101010) == Integer(0) + + assert Integer(0b01010101) & Integer(0b11011011) == Integer(0b01010001) + assert Integer(0b01010101) & 0b11011011 == Integer(0b01010001) + assert 0b01010101 & Integer(0b11011011) == Integer(0b01010001) + + assert -Integer(0b01010101) & Integer(0b11011011) == Integer(-0b01010101 & 0b11011011) + assert Integer(-0b01010101) & 0b11011011 == Integer(-0b01010101 & 0b11011011) + assert -0b01010101 & Integer(0b11011011) == Integer(-0b01010101 & 0b11011011) + + assert Integer(0b01010101) & -Integer(0b11011011) == Integer(0b01010101 & -0b11011011) + assert Integer(0b01010101) & -0b11011011 == Integer(0b01010101 & -0b11011011) + assert 0b01010101 & Integer(-0b11011011) == Integer(0b01010101 & -0b11011011) + + raises(TypeError, lambda: Integer(2) & 0.0) + raises(TypeError, lambda: 0.0 & Integer(2)) + + +def test_xor_Integer(): + assert Integer(0b01010101) ^ Integer(0b11111111) == Integer(0b10101010) + assert Integer(0b01010101) ^ 0b11111111 == Integer(0b10101010) + assert 0b01010101 ^ Integer(0b11111111) == Integer(0b10101010) + + assert Integer(0b01010101) ^ Integer(0b11011011) == Integer(0b10001110) + assert Integer(0b01010101) ^ 0b11011011 == Integer(0b10001110) + assert 0b01010101 ^ Integer(0b11011011) == Integer(0b10001110) + + assert -Integer(0b01010101) ^ Integer(0b11011011) == Integer(-0b01010101 ^ 0b11011011) + assert Integer(-0b01010101) ^ 0b11011011 == Integer(-0b01010101 ^ 0b11011011) + assert -0b01010101 ^ Integer(0b11011011) == Integer(-0b01010101 ^ 0b11011011) + + assert Integer(0b01010101) ^ -Integer(0b11011011) == Integer(0b01010101 ^ -0b11011011) + assert Integer(0b01010101) ^ -0b11011011 == Integer(0b01010101 ^ -0b11011011) + assert 0b01010101 ^ Integer(-0b11011011) == Integer(0b01010101 ^ -0b11011011) + + raises(TypeError, lambda: Integer(2) ^ 0.0) + raises(TypeError, lambda: 0.0 ^ Integer(2)) + + +def test_or_Integer(): + assert Integer(0b01010101) | Integer(0b10101010) == Integer(0b11111111) + assert Integer(0b01010101) | 0b10101010 == Integer(0b11111111) + assert 0b01010101 | Integer(0b10101010) == Integer(0b11111111) + + assert Integer(0b01010101) | Integer(0b11011011) == Integer(0b11011111) + assert Integer(0b01010101) | 0b11011011 == Integer(0b11011111) + assert 0b01010101 | Integer(0b11011011) == Integer(0b11011111) + + assert -Integer(0b01010101) | Integer(0b11011011) == Integer(-0b01010101 | 0b11011011) + assert Integer(-0b01010101) | 0b11011011 == Integer(-0b01010101 | 0b11011011) + assert -0b01010101 | Integer(0b11011011) == Integer(-0b01010101 | 0b11011011) + + assert Integer(0b01010101) | -Integer(0b11011011) == Integer(0b01010101 | -0b11011011) + assert Integer(0b01010101) | -0b11011011 == Integer(0b01010101 | -0b11011011) + assert 0b01010101 | Integer(-0b11011011) == Integer(0b01010101 | -0b11011011) + + raises(TypeError, lambda: Integer(2) | 0.0) + raises(TypeError, lambda: 0.0 | Integer(2)) + + +def test_invert_Integer(): + assert ~Integer(0b01010101) == Integer(-0b01010110) + assert ~Integer(0b01010101) == Integer(~0b01010101) + assert ~(~Integer(0b01010101)) == Integer(0b01010101) + + +def test_abs1(): + assert Rational(1, 6) != Rational(-1, 6) + assert abs(Rational(1, 6)) == abs(Rational(-1, 6)) + + +def test_accept_int(): + assert not Float(4) == 4 + assert Float(4) != 4 + assert Float(4) == 4.0 + + +def test_dont_accept_str(): + assert Float("0.2") != "0.2" + assert not (Float("0.2") == "0.2") + + +def test_int(): + a = Rational(5) + assert int(a) == 5 + a = Rational(9, 10) + assert int(a) == int(-a) == 0 + assert 1/(-1)**Rational(2, 3) == -(-1)**Rational(1, 3) + # issue 10368 + a = Rational(32442016954, 78058255275) + assert type(int(a)) is type(int(-a)) is int + + +def test_int_NumberSymbols(): + assert int(Catalan) == 0 + assert int(EulerGamma) == 0 + assert int(pi) == 3 + assert int(E) == 2 + assert int(GoldenRatio) == 1 + assert int(TribonacciConstant) == 1 + for i in [Catalan, E, EulerGamma, GoldenRatio, TribonacciConstant, pi]: + a, b = i.approximation_interval(Integer) + ia = int(i) + assert ia == a + assert isinstance(ia, int) + assert b == a + 1 + assert a.is_Integer and b.is_Integer + + +def test_real_bug(): + x = Symbol("x") + assert str(2.0*x*x) in ["(2.0*x)*x", "2.0*x**2", "2.00000000000000*x**2"] + assert str(2.1*x*x) != "(2.0*x)*x" + + +def test_bug_sqrt(): + assert ((sqrt(Rational(2)) + 1)*(sqrt(Rational(2)) - 1)).expand() == 1 + + +def test_pi_Pi(): + "Test that pi (instance) is imported, but Pi (class) is not" + from sympy import pi # noqa + with raises(ImportError): + from sympy import Pi # noqa + + +def test_no_len(): + # there should be no len for numbers + raises(TypeError, lambda: len(Rational(2))) + raises(TypeError, lambda: len(Rational(2, 3))) + raises(TypeError, lambda: len(Integer(2))) + + +def test_issue_3321(): + assert sqrt(Rational(1, 5)) == Rational(1, 5)**S.Half + assert 5 * sqrt(Rational(1, 5)) == sqrt(5) + + +def test_issue_3692(): + assert ((-1)**Rational(1, 6)).expand(complex=True) == I/2 + sqrt(3)/2 + assert ((-5)**Rational(1, 6)).expand(complex=True) == \ + 5**Rational(1, 6)*I/2 + 5**Rational(1, 6)*sqrt(3)/2 + assert ((-64)**Rational(1, 6)).expand(complex=True) == I + sqrt(3) + + +def test_issue_3423(): + x = Symbol("x") + assert sqrt(x - 1).as_base_exp() == (x - 1, S.Half) + assert sqrt(x - 1) != I*sqrt(1 - x) + + +def test_issue_3449(): + x = Symbol("x") + assert sqrt(x - 1).subs(x, 5) == 2 + + +def test_issue_13890(): + x = Symbol("x") + e = (-x/4 - S.One/12)**x - 1 + f = simplify(e) + a = Rational(9, 5) + assert abs(e.subs(x,a).evalf() - f.subs(x,a).evalf()) < 1e-15 + + +def test_Integer_factors(): + def F(i): + return Integer(i).factors() + + assert F(1) == {} + assert F(2) == {2: 1} + assert F(3) == {3: 1} + assert F(4) == {2: 2} + assert F(5) == {5: 1} + assert F(6) == {2: 1, 3: 1} + assert F(7) == {7: 1} + assert F(8) == {2: 3} + assert F(9) == {3: 2} + assert F(10) == {2: 1, 5: 1} + assert F(11) == {11: 1} + assert F(12) == {2: 2, 3: 1} + assert F(13) == {13: 1} + assert F(14) == {2: 1, 7: 1} + assert F(15) == {3: 1, 5: 1} + assert F(16) == {2: 4} + assert F(17) == {17: 1} + assert F(18) == {2: 1, 3: 2} + assert F(19) == {19: 1} + assert F(20) == {2: 2, 5: 1} + assert F(21) == {3: 1, 7: 1} + assert F(22) == {2: 1, 11: 1} + assert F(23) == {23: 1} + assert F(24) == {2: 3, 3: 1} + assert F(25) == {5: 2} + assert F(26) == {2: 1, 13: 1} + assert F(27) == {3: 3} + assert F(28) == {2: 2, 7: 1} + assert F(29) == {29: 1} + assert F(30) == {2: 1, 3: 1, 5: 1} + assert F(31) == {31: 1} + assert F(32) == {2: 5} + assert F(33) == {3: 1, 11: 1} + assert F(34) == {2: 1, 17: 1} + assert F(35) == {5: 1, 7: 1} + assert F(36) == {2: 2, 3: 2} + assert F(37) == {37: 1} + assert F(38) == {2: 1, 19: 1} + assert F(39) == {3: 1, 13: 1} + assert F(40) == {2: 3, 5: 1} + assert F(41) == {41: 1} + assert F(42) == {2: 1, 3: 1, 7: 1} + assert F(43) == {43: 1} + assert F(44) == {2: 2, 11: 1} + assert F(45) == {3: 2, 5: 1} + assert F(46) == {2: 1, 23: 1} + assert F(47) == {47: 1} + assert F(48) == {2: 4, 3: 1} + assert F(49) == {7: 2} + assert F(50) == {2: 1, 5: 2} + assert F(51) == {3: 1, 17: 1} + + +def test_Rational_factors(): + def F(p, q, visual=None): + return Rational(p, q).factors(visual=visual) + + assert F(2, 3) == {2: 1, 3: -1} + assert F(2, 9) == {2: 1, 3: -2} + assert F(2, 15) == {2: 1, 3: -1, 5: -1} + assert F(6, 10) == {3: 1, 5: -1} + + +def test_issue_4107(): + assert pi*(E + 10) + pi*(-E - 10) != 0 + assert pi*(E + 10**10) + pi*(-E - 10**10) != 0 + assert pi*(E + 10**20) + pi*(-E - 10**20) != 0 + assert pi*(E + 10**80) + pi*(-E - 10**80) != 0 + + assert (pi*(E + 10) + pi*(-E - 10)).expand() == 0 + assert (pi*(E + 10**10) + pi*(-E - 10**10)).expand() == 0 + assert (pi*(E + 10**20) + pi*(-E - 10**20)).expand() == 0 + assert (pi*(E + 10**80) + pi*(-E - 10**80)).expand() == 0 + + +def test_IntegerInteger(): + a = Integer(4) + b = Integer(a) + + assert a == b + + +def test_Rational_gcd_lcm_cofactors(): + assert Integer(4).gcd(2) == Integer(2) + assert Integer(4).lcm(2) == Integer(4) + assert Integer(4).gcd(Integer(2)) == Integer(2) + assert Integer(4).lcm(Integer(2)) == Integer(4) + a, b = 720**99911, 480**12342 + assert Integer(a).lcm(b) == a*b/Integer(a).gcd(b) + + assert Integer(4).gcd(3) == Integer(1) + assert Integer(4).lcm(3) == Integer(12) + assert Integer(4).gcd(Integer(3)) == Integer(1) + assert Integer(4).lcm(Integer(3)) == Integer(12) + + assert Rational(4, 3).gcd(2) == Rational(2, 3) + assert Rational(4, 3).lcm(2) == Integer(4) + assert Rational(4, 3).gcd(Integer(2)) == Rational(2, 3) + assert Rational(4, 3).lcm(Integer(2)) == Integer(4) + + assert Integer(4).gcd(Rational(2, 9)) == Rational(2, 9) + assert Integer(4).lcm(Rational(2, 9)) == Integer(4) + + assert Rational(4, 3).gcd(Rational(2, 9)) == Rational(2, 9) + assert Rational(4, 3).lcm(Rational(2, 9)) == Rational(4, 3) + assert Rational(4, 5).gcd(Rational(2, 9)) == Rational(2, 45) + assert Rational(4, 5).lcm(Rational(2, 9)) == Integer(4) + assert Rational(5, 9).lcm(Rational(3, 7)) == Rational(Integer(5).lcm(3),Integer(9).gcd(7)) + + assert Integer(4).cofactors(2) == (Integer(2), Integer(2), Integer(1)) + assert Integer(4).cofactors(Integer(2)) == \ + (Integer(2), Integer(2), Integer(1)) + + assert Integer(4).gcd(Float(2.0)) == Float(1.0) + assert Integer(4).lcm(Float(2.0)) == Float(8.0) + assert Integer(4).cofactors(Float(2.0)) == (Float(1.0), Float(4.0), Float(2.0)) + + assert S.Half.gcd(Float(2.0)) == Float(1.0) + assert S.Half.lcm(Float(2.0)) == Float(1.0) + assert S.Half.cofactors(Float(2.0)) == \ + (Float(1.0), Float(0.5), Float(2.0)) + + +def test_Float_gcd_lcm_cofactors(): + assert Float(2.0).gcd(Integer(4)) == Float(1.0) + assert Float(2.0).lcm(Integer(4)) == Float(8.0) + assert Float(2.0).cofactors(Integer(4)) == (Float(1.0), Float(2.0), Float(4.0)) + + assert Float(2.0).gcd(S.Half) == Float(1.0) + assert Float(2.0).lcm(S.Half) == Float(1.0) + assert Float(2.0).cofactors(S.Half) == \ + (Float(1.0), Float(2.0), Float(0.5)) + + +def test_issue_4611(): + assert abs(pi._evalf(50) - 3.14159265358979) < 1e-10 + assert abs(E._evalf(50) - 2.71828182845905) < 1e-10 + assert abs(Catalan._evalf(50) - 0.915965594177219) < 1e-10 + assert abs(EulerGamma._evalf(50) - 0.577215664901533) < 1e-10 + assert abs(GoldenRatio._evalf(50) - 1.61803398874989) < 1e-10 + assert abs(TribonacciConstant._evalf(50) - 1.83928675521416) < 1e-10 + + x = Symbol("x") + assert (pi + x).evalf() == pi.evalf() + x + assert (E + x).evalf() == E.evalf() + x + assert (Catalan + x).evalf() == Catalan.evalf() + x + assert (EulerGamma + x).evalf() == EulerGamma.evalf() + x + assert (GoldenRatio + x).evalf() == GoldenRatio.evalf() + x + assert (TribonacciConstant + x).evalf() == TribonacciConstant.evalf() + x + + +@conserve_mpmath_dps +def test_conversion_to_mpmath(): + assert mpmath.mpmathify(Integer(1)) == mpmath.mpf(1) + assert mpmath.mpmathify(S.Half) == mpmath.mpf(0.5) + assert mpmath.mpmathify(Float('1.23', 15)) == mpmath.mpf('1.23') + + assert mpmath.mpmathify(I) == mpmath.mpc(1j) + + assert mpmath.mpmathify(1 + 2*I) == mpmath.mpc(1 + 2j) + assert mpmath.mpmathify(1.0 + 2*I) == mpmath.mpc(1 + 2j) + assert mpmath.mpmathify(1 + 2.0*I) == mpmath.mpc(1 + 2j) + assert mpmath.mpmathify(1.0 + 2.0*I) == mpmath.mpc(1 + 2j) + assert mpmath.mpmathify(S.Half + S.Half*I) == mpmath.mpc(0.5 + 0.5j) + + assert mpmath.mpmathify(2*I) == mpmath.mpc(2j) + assert mpmath.mpmathify(2.0*I) == mpmath.mpc(2j) + assert mpmath.mpmathify(S.Half*I) == mpmath.mpc(0.5j) + + mpmath.mp.dps = 100 + assert mpmath.mpmathify(pi.evalf(100) + pi.evalf(100)*I) == mpmath.pi + mpmath.pi*mpmath.j + assert mpmath.mpmathify(pi.evalf(100)*I) == mpmath.pi*mpmath.j + + +def test_relational(): + # real + x = S(.1) + assert (x != cos) is True + assert (x == cos) is False + + # rational + x = Rational(1, 3) + assert (x != cos) is True + assert (x == cos) is False + + # integer defers to rational so these tests are omitted + + # number symbol + x = pi + assert (x != cos) is True + assert (x == cos) is False + + +def test_Integer_as_index(): + assert 'hello'[Integer(2):] == 'llo' + + +def test_Rational_int(): + assert int( Rational(7, 5)) == 1 + assert int( S.Half) == 0 + assert int(Rational(-1, 2)) == 0 + assert int(-Rational(7, 5)) == -1 + + +def test_zoo(): + b = Symbol('b', finite=True) + nz = Symbol('nz', nonzero=True) + p = Symbol('p', positive=True) + n = Symbol('n', negative=True) + im = Symbol('i', imaginary=True) + c = Symbol('c', complex=True) + pb = Symbol('pb', positive=True) + nb = Symbol('nb', negative=True) + imb = Symbol('ib', imaginary=True, finite=True) + for i in [I, S.Infinity, S.NegativeInfinity, S.Zero, S.One, S.Pi, S.Half, S(3), log(3), + b, nz, p, n, im, pb, nb, imb, c]: + if i.is_finite and (i.is_real or i.is_imaginary): + assert i + zoo is zoo + assert i - zoo is zoo + assert zoo + i is zoo + assert zoo - i is zoo + elif i.is_finite is not False: + assert (i + zoo).is_Add + assert (i - zoo).is_Add + assert (zoo + i).is_Add + assert (zoo - i).is_Add + else: + assert (i + zoo) is S.NaN + assert (i - zoo) is S.NaN + assert (zoo + i) is S.NaN + assert (zoo - i) is S.NaN + + if fuzzy_not(i.is_zero) and (i.is_extended_real or i.is_imaginary): + assert i*zoo is zoo + assert zoo*i is zoo + elif i.is_zero: + assert i*zoo is S.NaN + assert zoo*i is S.NaN + else: + assert (i*zoo).is_Mul + assert (zoo*i).is_Mul + + if fuzzy_not((1/i).is_zero) and (i.is_real or i.is_imaginary): + assert zoo/i is zoo + elif (1/i).is_zero: + assert zoo/i is S.NaN + elif i.is_zero: + assert zoo/i is zoo + else: + assert (zoo/i).is_Mul + + assert (I*oo).is_Mul # allow directed infinity + assert zoo + zoo is S.NaN + assert zoo * zoo is zoo + assert zoo - zoo is S.NaN + assert zoo/zoo is S.NaN + assert zoo**zoo is S.NaN + assert zoo**0 is S.One + assert zoo**2 is zoo + assert 1/zoo is S.Zero + + assert Mul.flatten([S.NegativeOne, oo, S(0)]) == ([S.NaN], [], None) + + +def test_issue_4122(): + x = Symbol('x', nonpositive=True) + assert oo + x is oo + x = Symbol('x', extended_nonpositive=True) + assert (oo + x).is_Add + x = Symbol('x', finite=True) + assert (oo + x).is_Add # x could be imaginary + x = Symbol('x', nonnegative=True) + assert oo + x is oo + x = Symbol('x', extended_nonnegative=True) + assert oo + x is oo + x = Symbol('x', finite=True, real=True) + assert oo + x is oo + + # similarly for negative infinity + x = Symbol('x', nonnegative=True) + assert -oo + x is -oo + x = Symbol('x', extended_nonnegative=True) + assert (-oo + x).is_Add + x = Symbol('x', finite=True) + assert (-oo + x).is_Add + x = Symbol('x', nonpositive=True) + assert -oo + x is -oo + x = Symbol('x', extended_nonpositive=True) + assert -oo + x is -oo + x = Symbol('x', finite=True, real=True) + assert -oo + x is -oo + + +def test_GoldenRatio_expand(): + assert GoldenRatio.expand(func=True) == S.Half + sqrt(5)/2 + + +def test_TribonacciConstant_expand(): + assert TribonacciConstant.expand(func=True) == \ + (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3 + + +def test_as_content_primitive(): + assert S.Zero.as_content_primitive() == (1, 0) + assert S.Half.as_content_primitive() == (S.Half, 1) + assert (Rational(-1, 2)).as_content_primitive() == (S.Half, -1) + assert S(3).as_content_primitive() == (3, 1) + assert S(3.1).as_content_primitive() == (1, 3.1) + + +def test_hashing_sympy_integers(): + # Test for issue 5072 + assert {Integer(3)} == {int(3)} + assert hash(Integer(4)) == hash(int(4)) + + +def test_rounding_issue_4172(): + assert int((E**100).round()) == \ + 26881171418161354484126255515800135873611119 + assert int((pi**100).round()) == \ + 51878483143196131920862615246303013562686760680406 + assert int((Rational(1)/EulerGamma**100).round()) == \ + 734833795660954410469466 + + +@XFAIL +def test_mpmath_issues(): + from mpmath.libmp.libmpf import _normalize + import mpmath.libmp as mlib + rnd = mlib.round_nearest + mpf = (0, int(0), -123, -1, 53, rnd) # nan + assert _normalize(mpf, 53) != (0, int(0), 0, 0) + mpf = (0, int(0), -456, -2, 53, rnd) # +inf + assert _normalize(mpf, 53) != (0, int(0), 0, 0) + mpf = (1, int(0), -789, -3, 53, rnd) # -inf + assert _normalize(mpf, 53) != (0, int(0), 0, 0) + + from mpmath.libmp.libmpf import fnan + assert mlib.mpf_eq(fnan, fnan) + + +def test_Catalan_EulerGamma_prec(): + n = GoldenRatio + f = Float(n.n(), 5) + assert f._mpf_ == (0, int(212079), -17, 18) + assert f._prec == 20 + assert n._as_mpf_val(20) == f._mpf_ + + n = EulerGamma + f = Float(n.n(), 5) + assert f._mpf_ == (0, int(302627), -19, 19) + assert f._prec == 20 + assert n._as_mpf_val(20) == f._mpf_ + + +def test_Catalan_rewrite(): + k = Dummy('k', integer=True, nonnegative=True) + assert Catalan.rewrite(Sum).dummy_eq( + Sum((-1)**k/(2*k + 1)**2, (k, 0, oo))) + assert Catalan.rewrite() == Catalan + + +def test_bool_eq(): + assert 0 == False + assert S(0) == False + assert S(0) != S.false + assert 1 == True + assert S.One == True + assert S.One != S.true + + +def test_Float_eq(): + # Floats with different precision should not compare equal + assert Float(.5, 10) != Float(.5, 11) != Float(.5, 1) + # but floats that aren't exact in base-2 still + # don't compare the same because they have different + # underlying mpf values + assert Float(.12, 3) != Float(.12, 4) + assert Float(.12, 3) != .12 + assert 0.12 != Float(.12, 3) + assert Float('.12', 22) != .12 + # issue 11707 + # but Float/Rational -- except for 0 -- + # are exact so Rational(x) = Float(y) only if + # Rational(x) == Rational(Float(y)) + assert Float('1.1') != Rational(11, 10) + assert Rational(11, 10) != Float('1.1') + # coverage + assert not Float(3) == 2 + assert not Float(3) == Float(2) + assert not Float(3) == 3 + assert not Float(2**2) == S.Half + assert Float(2**2) == 4.0 + assert not Float(2**-2) == 1 + assert Float(2**-1) == 0.5 + assert not Float(2*3) == 3 + assert not Float(2*3) == 0.5 + assert Float(2*3) == 6.0 + assert not Float(2*3) == 6 + assert not Float(2*3) == 8 + assert not Float(.75) == Rational(3, 4) + assert Float(.75) == 0.75 + assert Float(5/18) == 5/18 + # 4473 + assert Float(2.) != 3 + assert not Float((0,1,-3)) == S.One/8 + assert Float((0,1,-3)) == 1/8 + assert Float((0,1,-3)) != S.One/9 + # 16196 + assert not 2 == Float(2) # unlike Python + assert t**2 != t**2.0 + + +def test_issue_6640(): + from mpmath.libmp.libmpf import finf, fninf + # fnan is not included because Float no longer returns fnan, + # but otherwise, the same sort of test could apply + assert Float(finf).is_zero is False + assert Float(fninf).is_zero is False + assert bool(Float(0)) is False + + +def test_issue_6349(): + assert Float('23.e3', '')._prec == 10 + assert Float('23e3', '')._prec == 20 + assert Float('23000', '')._prec == 20 + assert Float('-23000', '')._prec == 20 + + +def test_mpf_norm(): + assert mpf_norm((1, 0, 1, 0), 10) == mpf('0')._mpf_ + assert Float._new((1, 0, 1, 0), 10)._mpf_ == mpf('0')._mpf_ + + +def test_latex(): + assert latex(pi) == r"\pi" + assert latex(E) == r"e" + assert latex(GoldenRatio) == r"\phi" + assert latex(TribonacciConstant) == r"\text{TribonacciConstant}" + assert latex(EulerGamma) == r"\gamma" + assert latex(oo) == r"\infty" + assert latex(-oo) == r"-\infty" + assert latex(zoo) == r"\tilde{\infty}" + assert latex(nan) == r"\text{NaN}" + assert latex(I) == r"i" + + +def test_issue_7742(): + assert -oo % 1 is nan + + +def test_simplify_AlgebraicNumber(): + A = AlgebraicNumber + e = 3**(S.One/6)*(3 + (135 + 78*sqrt(3))**Rational(2, 3))/(45 + 26*sqrt(3))**(S.One/3) + assert simplify(A(e)) == A(12) # wester test_C20 + + e = (41 + 29*sqrt(2))**(S.One/5) + assert simplify(A(e)) == A(1 + sqrt(2)) # wester test_C21 + + e = (3 + 4*I)**Rational(3, 2) + assert simplify(A(e)) == A(2 + 11*I) # issue 4401 + + +def test_Float_idempotence(): + x = Float('1.23', '') + y = Float(x) + z = Float(x, 15) + assert same_and_same_prec(y, x) + assert not same_and_same_prec(z, x) + x = Float(10**20) + y = Float(x) + z = Float(x, 15) + assert same_and_same_prec(y, x) + assert not same_and_same_prec(z, x) + + +def test_comp1(): + # sqrt(2) = 1.414213 5623730950... + a = sqrt(2).n(7) + assert comp(a, 1.4142129) is False + assert comp(a, 1.4142130) + # ... + assert comp(a, 1.4142141) + assert comp(a, 1.4142142) is False + assert comp(sqrt(2).n(2), '1.4') + assert comp(sqrt(2).n(2), Float(1.4, 2), '') + assert comp(sqrt(2).n(2), 1.4, '') + assert comp(sqrt(2).n(2), Float(1.4, 3), '') is False + assert comp(sqrt(2) + sqrt(3)*I, 1.4 + 1.7*I, .1) + assert not comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*0.89, .1) + assert comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*0.90, .1) + assert comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*1.07, .1) + assert not comp(sqrt(2) + sqrt(3)*I, (1.5 + 1.7*I)*1.08, .1) + assert [(i, j) + for i in range(130, 150) + for j in range(170, 180) + if comp((sqrt(2)+ I*sqrt(3)).n(3), i/100. + I*j/100.)] == [ + (141, 173), (142, 173)] + raises(ValueError, lambda: comp(t, '1')) + raises(ValueError, lambda: comp(t, 1)) + assert comp(0, 0.0) + assert comp(.5, S.Half) + assert comp(2 + sqrt(2), 2.0 + sqrt(2)) + assert not comp(0, 1) + assert not comp(2, sqrt(2)) + assert not comp(2 + I, 2.0 + sqrt(2)) + assert not comp(2.0 + sqrt(2), 2 + I) + assert not comp(2.0 + sqrt(2), sqrt(3)) + assert comp(1/pi.n(4), 0.3183, 1e-5) + assert not comp(1/pi.n(4), 0.3183, 8e-6) + + +def test_issue_9491(): + assert oo**zoo is nan + + +def test_issue_10063(): + assert 2**Float(3) == Float(8) + + +def test_issue_10020(): + assert oo**I is S.NaN + assert oo**(1 + I) is S.ComplexInfinity + assert oo**(-1 + I) is S.Zero + assert (-oo)**I is S.NaN + assert (-oo)**(-1 + I) is S.Zero + assert oo**t == Pow(oo, t, evaluate=False) + assert (-oo)**t == Pow(-oo, t, evaluate=False) + + +def test_invert_numbers(): + assert S(2).invert(5) == 3 + assert S(2).invert(Rational(5, 2)) == S.Half + assert S(2).invert(5.) == S.Half + assert S(2).invert(S(5)) == 3 + assert S(2.).invert(5) == 0.5 + assert S(sqrt(2)).invert(5) == 1/sqrt(2) + assert S(sqrt(2)).invert(sqrt(3)) == 1/sqrt(2) + + +def test_mod_inverse(): + assert mod_inverse(3, 11) == 4 + assert mod_inverse(5, 11) == 9 + assert mod_inverse(21124921, 521512) == 7713 + assert mod_inverse(124215421, 5125) == 2981 + assert mod_inverse(214, 12515) == 1579 + assert mod_inverse(5823991, 3299) == 1442 + assert mod_inverse(123, 44) == 39 + assert mod_inverse(2, 5) == 3 + assert mod_inverse(-2, 5) == 2 + assert mod_inverse(2, -5) == -2 + assert mod_inverse(-2, -5) == -3 + assert mod_inverse(-3, -7) == -5 + x = Symbol('x') + assert S(2).invert(x) == S.Half + raises(TypeError, lambda: mod_inverse(2, x)) + raises(ValueError, lambda: mod_inverse(2, S.Half)) + raises(ValueError, lambda: mod_inverse(2, cos(1)**2 + sin(1)**2)) + + +def test_golden_ratio_rewrite_as_sqrt(): + assert GoldenRatio.rewrite(sqrt) == S.Half + sqrt(5)*S.Half + + +def test_tribonacci_constant_rewrite_as_sqrt(): + assert TribonacciConstant.rewrite(sqrt) == \ + (1 + cbrt(19 - 3*sqrt(33)) + cbrt(19 + 3*sqrt(33))) / 3 + + +def test_comparisons_with_unknown_type(): + class Foo: + """ + Class that is unaware of Basic, and relies on both classes returning + the NotImplemented singleton for equivalence to evaluate to False. + + """ + + ni, nf, nr = Integer(3), Float(1.0), Rational(1, 3) + foo = Foo() + + for n in ni, nf, nr, oo, -oo, zoo, nan: + assert n != foo + assert foo != n + assert not n == foo + assert not foo == n + raises(TypeError, lambda: n < foo) + raises(TypeError, lambda: foo > n) + raises(TypeError, lambda: n > foo) + raises(TypeError, lambda: foo < n) + raises(TypeError, lambda: n <= foo) + raises(TypeError, lambda: foo >= n) + raises(TypeError, lambda: n >= foo) + raises(TypeError, lambda: foo <= n) + + class Bar: + """ + Class that considers itself equal to any instance of Number except + infinities and nans, and relies on SymPy types returning the + NotImplemented singleton for symmetric equality relations. + + """ + def __eq__(self, other): + if other in (oo, -oo, zoo, nan): + return False + if isinstance(other, Number): + return True + return NotImplemented + + def __ne__(self, other): + return not self == other + + bar = Bar() + + for n in ni, nf, nr: + assert n == bar + assert bar == n + assert not n != bar + assert not bar != n + + for n in oo, -oo, zoo, nan: + assert n != bar + assert bar != n + assert not n == bar + assert not bar == n + + for n in ni, nf, nr, oo, -oo, zoo, nan: + raises(TypeError, lambda: n < bar) + raises(TypeError, lambda: bar > n) + raises(TypeError, lambda: n > bar) + raises(TypeError, lambda: bar < n) + raises(TypeError, lambda: n <= bar) + raises(TypeError, lambda: bar >= n) + raises(TypeError, lambda: n >= bar) + raises(TypeError, lambda: bar <= n) + + +def test_NumberSymbol_comparison(): + from sympy.core.tests.test_relational import rel_check + rpi = Rational('905502432259640373/288230376151711744') + fpi = Float(float(pi)) + assert rel_check(rpi, fpi) + + +def test_Integer_precision(): + # Make sure Integer inputs for keyword args work + assert Float('1.0', dps=Integer(15))._prec == 53 + assert Float('1.0', precision=Integer(15))._prec == 15 + assert type(Float('1.0', precision=Integer(15))._prec) == int + assert sympify(srepr(Float('1.0', precision=15))) == Float('1.0', precision=15) + + +def test_numpy_to_float(): + from sympy.testing.pytest import skip + from sympy.external import import_module + np = import_module('numpy') + if not np: + skip('numpy not installed. Abort numpy tests.') + + def check_prec_and_relerr(npval, ratval): + prec = np.finfo(npval).nmant + 1 + x = Float(npval) + assert x._prec == prec + y = Float(ratval, precision=prec) + assert abs((x - y)/y) < 2**(-(prec + 1)) + + check_prec_and_relerr(np.float16(2.0/3), Rational(2, 3)) + check_prec_and_relerr(np.float32(2.0/3), Rational(2, 3)) + check_prec_and_relerr(np.float64(2.0/3), Rational(2, 3)) + # extended precision, on some arch/compilers: + x = np.longdouble(2)/3 + check_prec_and_relerr(x, Rational(2, 3)) + y = Float(x, precision=10) + assert same_and_same_prec(y, Float(Rational(2, 3), precision=10)) + + raises(TypeError, lambda: Float(np.complex64(1+2j))) + raises(TypeError, lambda: Float(np.complex128(1+2j))) + + +def test_Integer_ceiling_floor(): + a = Integer(4) + + assert a.floor() == a + assert a.ceiling() == a + + +def test_ComplexInfinity(): + assert zoo.floor() is zoo + assert zoo.ceiling() is zoo + assert zoo**zoo is S.NaN + + +def test_Infinity_floor_ceiling_power(): + assert oo.floor() is oo + assert oo.ceiling() is oo + assert oo**S.NaN is S.NaN + assert oo**zoo is S.NaN + + +def test_One_power(): + assert S.One**12 is S.One + assert S.NegativeOne**S.NaN is S.NaN + + +def test_NegativeInfinity(): + assert (-oo).floor() is -oo + assert (-oo).ceiling() is -oo + assert (-oo)**11 is -oo + assert (-oo)**12 is oo + + +def test_issue_6133(): + raises(TypeError, lambda: (-oo < None)) + raises(TypeError, lambda: (S(-2) < None)) + raises(TypeError, lambda: (oo < None)) + raises(TypeError, lambda: (oo > None)) + raises(TypeError, lambda: (S(2) < None)) + + +def test_abc(): + x = numbers.Float(5) + assert(isinstance(x, nums.Number)) + assert(isinstance(x, numbers.Number)) + assert(isinstance(x, nums.Real)) + y = numbers.Rational(1, 3) + assert(isinstance(y, nums.Number)) + assert(y.numerator == 1) + assert(y.denominator == 3) + assert(isinstance(y, nums.Rational)) + z = numbers.Integer(3) + assert(isinstance(z, nums.Number)) + assert(isinstance(z, numbers.Number)) + assert(isinstance(z, nums.Rational)) + assert(isinstance(z, numbers.Rational)) + assert(isinstance(z, nums.Integral)) + + +def test_floordiv(): + assert S(2)//S.Half == 4 + + +def test_negation(): + assert -S.Zero is S.Zero + assert -Float(0) is not S.Zero and -Float(0) == 0.0 + + +def test_exponentiation_of_0(): + x = Symbol('x') + assert 0**-x == zoo**x + assert unchanged(Pow, 0, x) + x = Symbol('x', zero=True) + assert 0**-x == S.One + assert 0**x == S.One + + +def test_int_valued(): + x = Symbol('x') + assert int_valued(x) == False + assert int_valued(S.Half) == False + assert int_valued(S.One) == True + assert int_valued(Float(1)) == True + assert int_valued(Float(1.1)) == False + assert int_valued(pi) == False + + +def test_equal_valued(): + x = Symbol('x') + + equal_values = [ + [1, 1.0, S(1), S(1.0), S(1).n(5)], + [2, 2.0, S(2), S(2.0), S(2).n(5)], + [-1, -1.0, -S(1), -S(1.0), -S(1).n(5)], + [0.5, S(0.5), S(1)/2], + [-0.5, -S(0.5), -S(1)/2], + [0, 0.0, S(0), S(0.0), S(0).n()], + [pi], [pi.n()], # <-- not equal + [S(1)/10], [0.1, S(0.1)], # <-- not equal + [S(0.1).n(5)], + [oo], + [cos(x/2)], [cos(0.5*x)], # <-- no recursion + ] + + for m, values_m in enumerate(equal_values): + for value_i in values_m: + + # All values in same list equal + for value_j in values_m: + assert equal_valued(value_i, value_j) is True + + # Not equal to anything in any other list: + for n, values_n in enumerate(equal_values): + if n == m: + continue + for value_j in values_n: + assert equal_valued(value_i, value_j) is False + + +def test_all_close(): + x = Symbol('x') + assert all_close(2, 2) is True + assert all_close(2, 2.0000) is True + assert all_close(2, 2.0001) is False + assert all_close(1/3, 1/3.0001) is False + assert all_close(1/3, 1/3.0001, 1e-3, 1e-3) is True + assert all_close(1/3, Rational(1, 3)) is True + assert all_close(0.1*exp(0.2*x), exp(x/5)/10) is True + # The expressions should be structurally the same: + assert all_close(1.4142135623730951, sqrt(2)) is False + assert all_close(1.4142135623730951, sqrt(2).evalf()) is True + assert all_close(x + 1e-20, x) is False + # We should be able to match terms of an Add/Mul in any order + assert all_close(Add(1, 2, evaluate=False), Add(2, 1, evaluate=False)) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_operations.py b/lib/python3.11/site-packages/sympy/core/tests/test_operations.py new file mode 100644 index 0000000000000000000000000000000000000000..c60d691ef00ee9601ada04ef68e2db37794a81ad --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_operations.py @@ -0,0 +1,110 @@ +from sympy.core.expr import Expr +from sympy.core.numbers import Integer +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.core.operations import AssocOp, LatticeOp +from sympy.testing.pytest import raises +from sympy.core.sympify import SympifyError +from sympy.core.add import Add, add +from sympy.core.mul import Mul, mul + +# create the simplest possible Lattice class + + +class join(LatticeOp): + zero = Integer(0) + identity = Integer(1) + + +def test_lattice_simple(): + assert join(join(2, 3), 4) == join(2, join(3, 4)) + assert join(2, 3) == join(3, 2) + assert join(0, 2) == 0 + assert join(1, 2) == 2 + assert join(2, 2) == 2 + + assert join(join(2, 3), 4) == join(2, 3, 4) + assert join() == 1 + assert join(4) == 4 + assert join(1, 4, 2, 3, 1, 3, 2) == join(2, 3, 4) + + +def test_lattice_shortcircuit(): + raises(SympifyError, lambda: join(object)) + assert join(0, object) == 0 + + +def test_lattice_print(): + assert str(join(5, 4, 3, 2)) == 'join(2, 3, 4, 5)' + + +def test_lattice_make_args(): + assert join.make_args(join(2, 3, 4)) == {S(2), S(3), S(4)} + assert join.make_args(0) == {0} + assert list(join.make_args(0))[0] is S.Zero + assert Add.make_args(0)[0] is S.Zero + + +def test_issue_14025(): + a, b, c, d = symbols('a,b,c,d', commutative=False) + assert Mul(a, b, c).has(c*b) == False + assert Mul(a, b, c).has(b*c) == True + assert Mul(a, b, c, d).has(b*c*d) == True + + +def test_AssocOp_flatten(): + a, b, c, d = symbols('a,b,c,d') + + class MyAssoc(AssocOp): + identity = S.One + + assert MyAssoc(a, MyAssoc(b, c)).args == \ + MyAssoc(MyAssoc(a, b), c).args == \ + MyAssoc(MyAssoc(a, b, c)).args == \ + MyAssoc(a, b, c).args == \ + (a, b, c) + u = MyAssoc(b, c) + v = MyAssoc(u, d, evaluate=False) + assert v.args == (u, d) + # like Add, any unevaluated outer call will flatten inner args + assert MyAssoc(a, v).args == (a, b, c, d) + + +def test_add_dispatcher(): + + class NewBase(Expr): + @property + def _add_handler(self): + return NewAdd + class NewAdd(NewBase, Add): + pass + add.register_handlerclass((Add, NewAdd), NewAdd) + + a, b = Symbol('a'), NewBase() + + # Add called as fallback + assert add(1, 2) == Add(1, 2) + assert add(a, a) == Add(a, a) + + # selection by registered priority + assert add(a,b,a) == NewAdd(2*a, b) + + +def test_mul_dispatcher(): + + class NewBase(Expr): + @property + def _mul_handler(self): + return NewMul + class NewMul(NewBase, Mul): + pass + mul.register_handlerclass((Mul, NewMul), NewMul) + + a, b = Symbol('a'), NewBase() + + # Mul called as fallback + assert mul(1, 2) == Mul(1, 2) + assert mul(a, a) == Mul(a, a) + + # selection by registered priority + assert mul(a,b,a) == NewMul(a**2, b) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_parameters.py b/lib/python3.11/site-packages/sympy/core/tests/test_parameters.py new file mode 100644 index 0000000000000000000000000000000000000000..21e03d717872a9a8165ceeebf7ef58e9842702c0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_parameters.py @@ -0,0 +1,126 @@ +from sympy.abc import x, y +from sympy.core.parameters import evaluate +from sympy.core import Mul, Add, Pow, S +from sympy.core.numbers import oo +from sympy.functions.elementary.miscellaneous import sqrt + +def test_add(): + with evaluate(False): + p = oo - oo + assert isinstance(p, Add) and p.args == (oo, -oo) + p = 5 - oo + assert isinstance(p, Add) and p.args == (-oo, 5) + p = oo - 5 + assert isinstance(p, Add) and p.args == (oo, -5) + p = oo + 5 + assert isinstance(p, Add) and p.args == (oo, 5) + p = 5 + oo + assert isinstance(p, Add) and p.args == (oo, 5) + p = -oo + 5 + assert isinstance(p, Add) and p.args == (-oo, 5) + p = -5 - oo + assert isinstance(p, Add) and p.args == (-oo, -5) + + with evaluate(False): + expr = x + x + assert isinstance(expr, Add) + assert expr.args == (x, x) + + with evaluate(True): + assert (x + x).args == (2, x) + + assert (x + x).args == (x, x) + + assert isinstance(x + x, Mul) + + with evaluate(False): + assert S.One + 1 == Add(1, 1) + assert 1 + S.One == Add(1, 1) + + assert S(4) - 3 == Add(4, -3) + assert -3 + S(4) == Add(4, -3) + + assert S(2) * 4 == Mul(2, 4) + assert 4 * S(2) == Mul(2, 4) + + assert S(6) / 3 == Mul(6, Pow(3, -1)) + assert S.One / 3 * 6 == Mul(S.One / 3, 6) + + assert 9 ** S(2) == Pow(9, 2) + assert S(2) ** 9 == Pow(2, 9) + + assert S(2) / 2 == Mul(2, Pow(2, -1)) + assert S.One / 2 * 2 == Mul(S.One / 2, 2) + + assert S(2) / 3 + 1 == Add(S(2) / 3, 1) + assert 1 + S(2) / 3 == Add(1, S(2) / 3) + + assert S(4) / 7 - 3 == Add(S(4) / 7, -3) + assert -3 + S(4) / 7 == Add(-3, S(4) / 7) + + assert S(2) / 4 * 4 == Mul(S(2) / 4, 4) + assert 4 * (S(2) / 4) == Mul(4, S(2) / 4) + + assert S(6) / 3 == Mul(6, Pow(3, -1)) + assert S.One / 3 * 6 == Mul(S.One / 3, 6) + + assert S.One / 3 + sqrt(3) == Add(S.One / 3, sqrt(3)) + assert sqrt(3) + S.One / 3 == Add(sqrt(3), S.One / 3) + + assert S.One / 2 * 10.333 == Mul(S.One / 2, 10.333) + assert 10.333 * (S.One / 2) == Mul(10.333, S.One / 2) + + assert sqrt(2) * sqrt(2) == Mul(sqrt(2), sqrt(2)) + + assert S.One / 2 + x == Add(S.One / 2, x) + assert x + S.One / 2 == Add(x, S.One / 2) + + assert S.One / x * x == Mul(S.One / x, x) + assert x * (S.One / x) == Mul(x, Pow(x, -1)) + + assert S.One / 3 == Pow(3, -1) + assert S.One / x == Pow(x, -1) + assert 1 / S(3) == Pow(3, -1) + assert 1 / x == Pow(x, -1) + +def test_nested(): + with evaluate(False): + expr = (x + x) + (y + y) + assert expr.args == ((x + x), (y + y)) + assert expr.args[0].args == (x, x) + +def test_reentrantcy(): + with evaluate(False): + expr = x + x + assert expr.args == (x, x) + with evaluate(True): + expr = x + x + assert expr.args == (2, x) + expr = x + x + assert expr.args == (x, x) + +def test_reusability(): + f = evaluate(False) + + with f: + expr = x + x + assert expr.args == (x, x) + + expr = x + x + assert expr.args == (2, x) + + with f: + expr = x + x + assert expr.args == (x, x) + + # Assure reentrancy with reusability + ctx = evaluate(False) + with ctx: + expr = x + x + assert expr.args == (x, x) + with ctx: + expr = x + x + assert expr.args == (x, x) + + expr = x + x + assert expr.args == (2, x) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_power.py b/lib/python3.11/site-packages/sympy/core/tests/test_power.py new file mode 100644 index 0000000000000000000000000000000000000000..9dcc828d854c75cebc8177663035e976ae10f9e5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_power.py @@ -0,0 +1,663 @@ +from sympy.core import ( + Basic, Rational, Symbol, S, Float, Integer, Mul, Number, Pow, + Expr, I, nan, pi, symbols, oo, zoo, N) +from sympy.core.parameters import global_parameters +from sympy.core.tests.test_evalf import NS +from sympy.core.function import expand_multinomial +from sympy.functions.elementary.miscellaneous import sqrt, cbrt +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.special.error_functions import erf +from sympy.functions.elementary.trigonometric import ( + sin, cos, tan, sec, csc, atan) +from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh +from sympy.polys import Poly +from sympy.series.order import O +from sympy.sets import FiniteSet +from sympy.core.power import power +from sympy.core.intfunc import integer_nthroot +from sympy.testing.pytest import warns, _both_exp_pow +from sympy.utilities.exceptions import SymPyDeprecationWarning +from sympy.abc import a, b, c, x, y + +def test_rational(): + a = Rational(1, 5) + + r = sqrt(5)/5 + assert sqrt(a) == r + assert 2*sqrt(a) == 2*r + + r = a*a**S.Half + assert a**Rational(3, 2) == r + assert 2*a**Rational(3, 2) == 2*r + + r = a**5*a**Rational(2, 3) + assert a**Rational(17, 3) == r + assert 2 * a**Rational(17, 3) == 2*r + + +def test_large_rational(): + e = (Rational(123712**12 - 1, 7) + Rational(1, 7))**Rational(1, 3) + assert e == 234232585392159195136 * (Rational(1, 7)**Rational(1, 3)) + + +def test_negative_real(): + def feq(a, b): + return abs(a - b) < 1E-10 + + assert feq(S.One / Float(-0.5), -Integer(2)) + + +def test_expand(): + assert (2**(-1 - x)).expand() == S.Half*2**(-x) + + +def test_issue_3449(): + #test if powers are simplified correctly + #see also issue 3995 + assert ((x**Rational(1, 3))**Rational(2)) == x**Rational(2, 3) + assert ( + (x**Rational(3))**Rational(2, 5)) == (x**Rational(3))**Rational(2, 5) + + a = Symbol('a', real=True) + b = Symbol('b', real=True) + assert (a**2)**b == (abs(a)**b)**2 + assert sqrt(1/a) != 1/sqrt(a) # e.g. for a = -1 + assert (a**3)**Rational(1, 3) != a + assert (x**a)**b != x**(a*b) # e.g. x = -1, a=2, b=1/2 + assert (x**.5)**b == x**(.5*b) + assert (x**.5)**.5 == x**.25 + assert (x**2.5)**.5 != x**1.25 # e.g. for x = 5*I + + k = Symbol('k', integer=True) + m = Symbol('m', integer=True) + assert (x**k)**m == x**(k*m) + assert Number(5)**Rational(2, 3) == Number(25)**Rational(1, 3) + + assert (x**.5)**2 == x**1.0 + assert (x**2)**k == (x**k)**2 == x**(2*k) + + a = Symbol('a', positive=True) + assert (a**3)**Rational(2, 5) == a**Rational(6, 5) + assert (a**2)**b == (a**b)**2 + assert (a**Rational(2, 3))**x == a**(x*Rational(2, 3)) != (a**x)**Rational(2, 3) + + +def test_issue_3866(): + assert --sqrt(sqrt(5) - 1) == sqrt(sqrt(5) - 1) + + +def test_negative_one(): + x = Symbol('x', complex=True) + y = Symbol('y', complex=True) + assert 1/x**y == x**(-y) + + +def test_issue_4362(): + neg = Symbol('neg', negative=True) + nonneg = Symbol('nonneg', nonnegative=True) + any = Symbol('any') + num, den = sqrt(1/neg).as_numer_denom() + assert num == sqrt(-1) + assert den == sqrt(-neg) + num, den = sqrt(1/nonneg).as_numer_denom() + assert num == 1 + assert den == sqrt(nonneg) + num, den = sqrt(1/any).as_numer_denom() + assert num == sqrt(1/any) + assert den == 1 + + def eqn(num, den, pow): + return (num/den)**pow + npos = 1 + nneg = -1 + dpos = 2 - sqrt(3) + dneg = 1 - sqrt(3) + assert dpos > 0 and dneg < 0 and npos > 0 and nneg < 0 + # pos or neg integer + eq = eqn(npos, dpos, 2) + assert eq.is_Pow and eq.as_numer_denom() == (1, dpos**2) + eq = eqn(npos, dneg, 2) + assert eq.is_Pow and eq.as_numer_denom() == (1, dneg**2) + eq = eqn(nneg, dpos, 2) + assert eq.is_Pow and eq.as_numer_denom() == (1, dpos**2) + eq = eqn(nneg, dneg, 2) + assert eq.is_Pow and eq.as_numer_denom() == (1, dneg**2) + eq = eqn(npos, dpos, -2) + assert eq.is_Pow and eq.as_numer_denom() == (dpos**2, 1) + eq = eqn(npos, dneg, -2) + assert eq.is_Pow and eq.as_numer_denom() == (dneg**2, 1) + eq = eqn(nneg, dpos, -2) + assert eq.is_Pow and eq.as_numer_denom() == (dpos**2, 1) + eq = eqn(nneg, dneg, -2) + assert eq.is_Pow and eq.as_numer_denom() == (dneg**2, 1) + # pos or neg rational + pow = S.Half + eq = eqn(npos, dpos, pow) + assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow) + eq = eqn(npos, dneg, pow) + assert eq.is_Pow is False and eq.as_numer_denom() == ((-npos)**pow, (-dneg)**pow) + eq = eqn(nneg, dpos, pow) + assert not eq.is_Pow or eq.as_numer_denom() == (nneg**pow, dpos**pow) + eq = eqn(nneg, dneg, pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-nneg)**pow, (-dneg)**pow) + eq = eqn(npos, dpos, -pow) + assert eq.is_Pow and eq.as_numer_denom() == (dpos**pow, npos**pow) + eq = eqn(npos, dneg, -pow) + assert eq.is_Pow is False and eq.as_numer_denom() == (-(-npos)**pow*(-dneg)**pow, npos) + eq = eqn(nneg, dpos, -pow) + assert not eq.is_Pow or eq.as_numer_denom() == (dpos**pow, nneg**pow) + eq = eqn(nneg, dneg, -pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-nneg)**pow) + # unknown exponent + pow = 2*any + eq = eqn(npos, dpos, pow) + assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow) + eq = eqn(npos, dneg, pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-npos)**pow, (-dneg)**pow) + eq = eqn(nneg, dpos, pow) + assert eq.is_Pow and eq.as_numer_denom() == (nneg**pow, dpos**pow) + eq = eqn(nneg, dneg, pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-nneg)**pow, (-dneg)**pow) + eq = eqn(npos, dpos, -pow) + assert eq.as_numer_denom() == (dpos**pow, npos**pow) + eq = eqn(npos, dneg, -pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-npos)**pow) + eq = eqn(nneg, dpos, -pow) + assert eq.is_Pow and eq.as_numer_denom() == (dpos**pow, nneg**pow) + eq = eqn(nneg, dneg, -pow) + assert eq.is_Pow and eq.as_numer_denom() == ((-dneg)**pow, (-nneg)**pow) + + assert ((1/(1 + x/3))**(-S.One)).as_numer_denom() == (3 + x, 3) + notp = Symbol('notp', positive=False) # not positive does not imply real + b = ((1 + x/notp)**-2) + assert (b**(-y)).as_numer_denom() == (1, b**y) + assert (b**(-S.One)).as_numer_denom() == ((notp + x)**2, notp**2) + nonp = Symbol('nonp', nonpositive=True) + assert (((1 + x/nonp)**-2)**(-S.One)).as_numer_denom() == ((-nonp - + x)**2, nonp**2) + + n = Symbol('n', negative=True) + assert (x**n).as_numer_denom() == (1, x**-n) + assert sqrt(1/n).as_numer_denom() == (S.ImaginaryUnit, sqrt(-n)) + n = Symbol('0 or neg', nonpositive=True) + # if x and n are split up without negating each term and n is negative + # then the answer might be wrong; if n is 0 it won't matter since + # 1/oo and 1/zoo are both zero as is sqrt(0)/sqrt(-x) unless x is also + # zero (in which case the negative sign doesn't matter): + # 1/sqrt(1/-1) = -I but sqrt(-1)/sqrt(1) = I + assert (1/sqrt(x/n)).as_numer_denom() == (sqrt(-n), sqrt(-x)) + c = Symbol('c', complex=True) + e = sqrt(1/c) + assert e.as_numer_denom() == (e, 1) + i = Symbol('i', integer=True) + assert ((1 + x/y)**i).as_numer_denom() == ((x + y)**i, y**i) + + +def test_Pow_Expr_args(): + bases = [Basic(), Poly(x, x), FiniteSet(x)] + for base in bases: + # The cache can mess with the stacklevel test + with warns(SymPyDeprecationWarning, test_stacklevel=False): + Pow(base, S.One) + + +def test_Pow_signs(): + """Cf. issues 4595 and 5250""" + n = Symbol('n', even=True) + assert (3 - y)**2 != (y - 3)**2 + assert (3 - y)**n != (y - 3)**n + assert (-3 + y - x)**2 != (3 - y + x)**2 + assert (y - 3)**3 != -(3 - y)**3 + + +def test_power_with_noncommutative_mul_as_base(): + x = Symbol('x', commutative=False) + y = Symbol('y', commutative=False) + assert not (x*y)**3 == x**3*y**3 + assert (2*x*y)**3 == 8*(x*y)**3 + + +@_both_exp_pow +def test_power_rewrite_exp(): + assert (I**I).rewrite(exp) == exp(-pi/2) + + expr = (2 + 3*I)**(4 + 5*I) + assert expr.rewrite(exp) == exp((4 + 5*I)*(log(sqrt(13)) + I*atan(Rational(3, 2)))) + assert expr.rewrite(exp).expand() == \ + 169*exp(5*I*log(13)/2)*exp(4*I*atan(Rational(3, 2)))*exp(-5*atan(Rational(3, 2))) + + assert ((6 + 7*I)**5).rewrite(exp) == 7225*sqrt(85)*exp(5*I*atan(Rational(7, 6))) + + expr = 5**(6 + 7*I) + assert expr.rewrite(exp) == exp((6 + 7*I)*log(5)) + assert expr.rewrite(exp).expand() == 15625*exp(7*I*log(5)) + + assert Pow(123, 789, evaluate=False).rewrite(exp) == 123**789 + assert (1**I).rewrite(exp) == 1**I + assert (0**I).rewrite(exp) == 0**I + + expr = (-2)**(2 + 5*I) + assert expr.rewrite(exp) == exp((2 + 5*I)*(log(2) + I*pi)) + assert expr.rewrite(exp).expand() == 4*exp(-5*pi)*exp(5*I*log(2)) + + assert ((-2)**S(-5)).rewrite(exp) == (-2)**S(-5) + + x, y = symbols('x y') + assert (x**y).rewrite(exp) == exp(y*log(x)) + if global_parameters.exp_is_pow: + assert (7**x).rewrite(exp) == Pow(S.Exp1, x*log(7), evaluate=False) + else: + assert (7**x).rewrite(exp) == exp(x*log(7), evaluate=False) + assert ((2 + 3*I)**x).rewrite(exp) == exp(x*(log(sqrt(13)) + I*atan(Rational(3, 2)))) + assert (y**(5 + 6*I)).rewrite(exp) == exp(log(y)*(5 + 6*I)) + + assert all((1/func(x)).rewrite(exp) == 1/(func(x).rewrite(exp)) for func in + (sin, cos, tan, sec, csc, sinh, cosh, tanh)) + + +def test_zero(): + assert 0**x != 0 + assert 0**(2*x) == 0**x + assert 0**(1.0*x) == 0**x + assert 0**(2.0*x) == 0**x + assert (0**(2 - x)).as_base_exp() == (0, 2 - x) + assert 0**(x - 2) != S.Infinity**(2 - x) + assert 0**(2*x*y) == 0**(x*y) + assert 0**(-2*x*y) == S.ComplexInfinity**(x*y) + assert Float(0)**2 is not S.Zero + assert Float(0)**2 == 0.0 + assert Float(0)**-2 is zoo + assert Float(0)**oo is S.Zero + + #Test issue 19572 + assert 0 ** -oo is zoo + assert power(0, -oo) is zoo + assert Float(0)**-oo is zoo + +def test_pow_as_base_exp(): + assert (S.Infinity**(2 - x)).as_base_exp() == (S.Infinity, 2 - x) + assert (S.Infinity**(x - 2)).as_base_exp() == (S.Infinity, x - 2) + p = S.Half**x + assert p.base, p.exp == p.as_base_exp() == (S(2), -x) + p = (S(3)/2)**x + assert p.base, p.exp == p.as_base_exp() == (3*S.Half, x) + p = (S(2)/3)**x + assert p.as_base_exp() == (S(3)/2, -x) + assert p.base, p.exp == (S(2)/3, x) + # issue 8344: + assert Pow(1, 2, evaluate=False).as_base_exp() == (S.One, S(2)) + + +def test_nseries(): + assert sqrt(I*x - 1)._eval_nseries(x, 4, None, 1) == I + x/2 + I*x**2/8 - x**3/16 + O(x**4) + assert sqrt(I*x - 1)._eval_nseries(x, 4, None, -1) == -I - x/2 - I*x**2/8 + x**3/16 + O(x**4) + assert cbrt(I*x - 1)._eval_nseries(x, 4, None, 1) == (-1)**(S(1)/3) - (-1)**(S(5)/6)*x/3 + \ + (-1)**(S(1)/3)*x**2/9 + 5*(-1)**(S(5)/6)*x**3/81 + O(x**4) + assert cbrt(I*x - 1)._eval_nseries(x, 4, None, -1) == -(-1)**(S(2)/3) - (-1)**(S(1)/6)*x/3 - \ + (-1)**(S(2)/3)*x**2/9 + 5*(-1)**(S(1)/6)*x**3/81 + O(x**4) + assert (1 / (exp(-1/x) + 1/x))._eval_nseries(x, 2, None) == x + O(x**2) + # test issue 23752 + assert sqrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, 1) == -sqrt(3)*I + sqrt(3)*I*x/6 - \ + sqrt(3)*I*x**2*(-S(1)/72 + I/6) - sqrt(3)*I*x**3*(-S(1)/432 + I/36) + O(x**4) + assert sqrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, -1) == -sqrt(3)*I + sqrt(3)*I*x/6 - \ + sqrt(3)*I*x**2*(-S(1)/72 + I/6) - sqrt(3)*I*x**3*(-S(1)/432 + I/36) + O(x**4) + assert cbrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, 1) == -(-1)**(S(2)/3)*3**(S(1)/3) + \ + (-1)**(S(2)/3)*3**(S(1)/3)*x/9 - (-1)**(S(2)/3)*3**(S(1)/3)*x**2*(-S(1)/81 + I/9) - \ + (-1)**(S(2)/3)*3**(S(1)/3)*x**3*(-S(5)/2187 + 2*I/81) + O(x**4) + assert cbrt(-I*x**2 + x - 3)._eval_nseries(x, 4, None, -1) == -(-1)**(S(2)/3)*3**(S(1)/3) + \ + (-1)**(S(2)/3)*3**(S(1)/3)*x/9 - (-1)**(S(2)/3)*3**(S(1)/3)*x**2*(-S(1)/81 + I/9) - \ + (-1)**(S(2)/3)*3**(S(1)/3)*x**3*(-S(5)/2187 + 2*I/81) + O(x**4) + + +def test_issue_6100_12942_4473(): + assert x**1.0 != x + assert x != x**1.0 + assert True != x**1.0 + assert x**1.0 is not True + assert x is not True + assert x*y != (x*y)**1.0 + # Pow != Symbol + assert (x**1.0)**1.0 != x + assert (x**1.0)**2.0 != x**2 + b = Expr() + assert Pow(b, 1.0, evaluate=False) != b + # if the following gets distributed as a Mul (x**1.0*y**1.0 then + # __eq__ methods could be added to Symbol and Pow to detect the + # power-of-1.0 case. + assert ((x*y)**1.0).func is Pow + + +def test_issue_6208(): + from sympy.functions.elementary.miscellaneous import root + assert sqrt(33**(I*9/10)) == -33**(I*9/20) + assert root((6*I)**(2*I), 3).as_base_exp()[1] == Rational(1, 3) # != 2*I/3 + assert root((6*I)**(I/3), 3).as_base_exp()[1] == I/9 + assert sqrt(exp(3*I)) == exp(3*I/2) + assert sqrt(-sqrt(3)*(1 + 2*I)) == sqrt(sqrt(3))*sqrt(-1 - 2*I) + assert sqrt(exp(5*I)) == -exp(5*I/2) + assert root(exp(5*I), 3).exp == Rational(1, 3) + + +def test_issue_6990(): + assert (sqrt(a + b*x + x**2)).series(x, 0, 3).removeO() == \ + sqrt(a)*x**2*(1/(2*a) - b**2/(8*a**2)) + sqrt(a) + b*x/(2*sqrt(a)) + + +def test_issue_6068(): + assert sqrt(sin(x)).series(x, 0, 7) == \ + sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \ + x**Rational(13, 2)/24192 + O(x**7) + assert sqrt(sin(x)).series(x, 0, 9) == \ + sqrt(x) - x**Rational(5, 2)/12 + x**Rational(9, 2)/1440 - \ + x**Rational(13, 2)/24192 - 67*x**Rational(17, 2)/29030400 + O(x**9) + assert sqrt(sin(x**3)).series(x, 0, 19) == \ + x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 + O(x**19) + assert sqrt(sin(x**3)).series(x, 0, 20) == \ + x**Rational(3, 2) - x**Rational(15, 2)/12 + x**Rational(27, 2)/1440 - \ + x**Rational(39, 2)/24192 + O(x**20) + + +def test_issue_6782(): + assert sqrt(sin(x**3)).series(x, 0, 7) == x**Rational(3, 2) + O(x**7) + assert sqrt(sin(x**4)).series(x, 0, 3) == x**2 + O(x**3) + + +def test_issue_6653(): + assert (1 / sqrt(1 + sin(x**2))).series(x, 0, 3) == 1 - x**2/2 + O(x**3) + + +def test_issue_6429(): + f = (c**2 + x)**(0.5) + assert f.series(x, x0=0, n=1) == (c**2)**0.5 + O(x) + assert f.taylor_term(0, x) == (c**2)**0.5 + assert f.taylor_term(1, x) == 0.5*x*(c**2)**(-0.5) + assert f.taylor_term(2, x) == -0.125*x**2*(c**2)**(-1.5) + + +def test_issue_7638(): + f = pi/log(sqrt(2)) + assert ((1 + I)**(I*f/2))**0.3 == (1 + I)**(0.15*I*f) + # if 1/3 -> 1.0/3 this should fail since it cannot be shown that the + # sign will be +/-1; for the previous "small arg" case, it didn't matter + # that this could not be proved + assert (1 + I)**(4*I*f) == ((1 + I)**(12*I*f))**Rational(1, 3) + + assert (((1 + I)**(I*(1 + 7*f)))**Rational(1, 3)).exp == Rational(1, 3) + r = symbols('r', real=True) + assert sqrt(r**2) == abs(r) + assert cbrt(r**3) != r + assert sqrt(Pow(2*I, 5*S.Half)) != (2*I)**Rational(5, 4) + p = symbols('p', positive=True) + assert cbrt(p**2) == p**Rational(2, 3) + assert NS(((0.2 + 0.7*I)**(0.7 + 1.0*I))**(0.5 - 0.1*I), 1) == '0.4 + 0.2*I' + assert sqrt(1/(1 + I)) == sqrt(1 - I)/sqrt(2) # or 1/sqrt(1 + I) + e = 1/(1 - sqrt(2)) + assert sqrt(e) == I/sqrt(-1 + sqrt(2)) + assert e**Rational(-1, 2) == -I*sqrt(-1 + sqrt(2)) + assert sqrt((cos(1)**2 + sin(1)**2 - 1)**(3 + I)).exp in [S.Half, + Rational(3, 2) + I/2] + assert sqrt(r**Rational(4, 3)) != r**Rational(2, 3) + assert sqrt((p + I)**Rational(4, 3)) == (p + I)**Rational(2, 3) + + for q in 1+I, 1-I: + assert sqrt(q**2) == q + for q in -1+I, -1-I: + assert sqrt(q**2) == -q + + assert sqrt((p + r*I)**2) != p + r*I + e = (1 + I/5) + assert sqrt(e**5) == e**(5*S.Half) + assert sqrt(e**6) == e**3 + assert sqrt((1 + I*r)**6) != (1 + I*r)**3 + + +def test_issue_8582(): + assert 1**oo is nan + assert 1**(-oo) is nan + assert 1**zoo is nan + assert 1**(oo + I) is nan + assert 1**(1 + I*oo) is nan + assert 1**(oo + I*oo) is nan + + +def test_issue_8650(): + n = Symbol('n', integer=True, nonnegative=True) + assert (n**n).is_positive is True + x = 5*n + 5 + assert (x**(5*(n + 1))).is_positive is True + + +def test_issue_13914(): + b = Symbol('b') + assert (-1)**zoo is nan + assert 2**zoo is nan + assert (S.Half)**(1 + zoo) is nan + assert I**(zoo + I) is nan + assert b**(I + zoo) is nan + + +def test_better_sqrt(): + n = Symbol('n', integer=True, nonnegative=True) + assert sqrt(3 + 4*I) == 2 + I + assert sqrt(3 - 4*I) == 2 - I + assert sqrt(-3 - 4*I) == 1 - 2*I + assert sqrt(-3 + 4*I) == 1 + 2*I + assert sqrt(32 + 24*I) == 6 + 2*I + assert sqrt(32 - 24*I) == 6 - 2*I + assert sqrt(-32 - 24*I) == 2 - 6*I + assert sqrt(-32 + 24*I) == 2 + 6*I + + # triple (3, 4, 5): + # parity of 3 matches parity of 5 and + # den, 4, is a square + assert sqrt((3 + 4*I)/4) == 1 + I/2 + # triple (8, 15, 17) + # parity of 8 doesn't match parity of 17 but + # den/2, 8/2, is a square + assert sqrt((8 + 15*I)/8) == (5 + 3*I)/4 + # handle the denominator + assert sqrt((3 - 4*I)/25) == (2 - I)/5 + assert sqrt((3 - 4*I)/26) == (2 - I)/sqrt(26) + # mul + # issue #12739 + assert sqrt((3 + 4*I)/(3 - 4*I)) == (3 + 4*I)/5 + assert sqrt(2/(3 + 4*I)) == sqrt(2)/5*(2 - I) + assert sqrt(n/(3 + 4*I)).subs(n, 2) == sqrt(2)/5*(2 - I) + assert sqrt(-2/(3 + 4*I)) == sqrt(2)/5*(1 + 2*I) + assert sqrt(-n/(3 + 4*I)).subs(n, 2) == sqrt(2)/5*(1 + 2*I) + # power + assert sqrt(1/(3 + I*4)) == (2 - I)/5 + assert sqrt(1/(3 - I)) == sqrt(10)*sqrt(3 + I)/10 + # symbolic + i = symbols('i', imaginary=True) + assert sqrt(3/i) == Mul(sqrt(3), 1/sqrt(i), evaluate=False) + # multiples of 1/2; don't make this too automatic + assert sqrt(3 + 4*I)**3 == (2 + I)**3 + assert Pow(3 + 4*I, Rational(3, 2)) == 2 + 11*I + assert Pow(6 + 8*I, Rational(3, 2)) == 2*sqrt(2)*(2 + 11*I) + n, d = (3 + 4*I), (3 - 4*I)**3 + a = n/d + assert a.args == (1/d, n) + eq = sqrt(a) + assert eq.args == (a, S.Half) + assert expand_multinomial(eq) == sqrt((-117 + 44*I)*(3 + 4*I))/125 + assert eq.expand() == (7 - 24*I)/125 + + # issue 12775 + # pos im part + assert sqrt(2*I) == (1 + I) + assert sqrt(2*9*I) == Mul(3, 1 + I, evaluate=False) + assert Pow(2*I, 3*S.Half) == (1 + I)**3 + # neg im part + assert sqrt(-I/2) == Mul(S.Half, 1 - I, evaluate=False) + # fractional im part + assert Pow(Rational(-9, 2)*I, Rational(3, 2)) == 27*(1 - I)**3/8 + + +def test_issue_2993(): + assert str((2.3*x - 4)**0.3) == '1.5157165665104*(0.575*x - 1)**0.3' + assert str((2.3*x + 4)**0.3) == '1.5157165665104*(0.575*x + 1)**0.3' + assert str((-2.3*x + 4)**0.3) == '1.5157165665104*(1 - 0.575*x)**0.3' + assert str((-2.3*x - 4)**0.3) == '1.5157165665104*(-0.575*x - 1)**0.3' + assert str((2.3*x - 2)**0.3) == '1.28386201800527*(x - 0.869565217391304)**0.3' + assert str((-2.3*x - 2)**0.3) == '1.28386201800527*(-x - 0.869565217391304)**0.3' + assert str((-2.3*x + 2)**0.3) == '1.28386201800527*(0.869565217391304 - x)**0.3' + assert str((2.3*x + 2)**0.3) == '1.28386201800527*(x + 0.869565217391304)**0.3' + assert str((2.3*x - 4)**Rational(1, 3)) == '2**(2/3)*(0.575*x - 1)**(1/3)' + eq = (2.3*x + 4) + assert eq**2 == 16*(0.575*x + 1)**2 + assert (1/eq).args == (eq, -1) # don't change trivial power + # issue 17735 + q=.5*exp(x) - .5*exp(-x) + 0.1 + assert int((q**2).subs(x, 1)) == 1 + # issue 17756 + y = Symbol('y') + assert len(sqrt(x/(x + y)**2 + Float('0.008', 30)).subs(y, pi.n(25)).atoms(Float)) == 2 + # issue 17756 + a, b, c, d, e, f, g = symbols('a:g') + expr = sqrt(1 + a*(c**4 + g*d - 2*g*e - f*(-g + d))**2/ + (c**3*b**2*(d - 3*e + 2*f)**2))/2 + r = [ + (a, N('0.0170992456333788667034850458615', 30)), + (b, N('0.0966594956075474769169134801223', 30)), + (c, N('0.390911862903463913632151616184', 30)), + (d, N('0.152812084558656566271750185933', 30)), + (e, N('0.137562344465103337106561623432', 30)), + (f, N('0.174259178881496659302933610355', 30)), + (g, N('0.220745448491223779615401870086', 30))] + tru = expr.n(30, subs=dict(r)) + seq = expr.subs(r) + # although `tru` is the right way to evaluate + # expr with numerical values, `seq` will have + # significant loss of precision if extraction of + # the largest coefficient of a power's base's terms + # is done improperly + assert seq == tru + +def test_issue_17450(): + assert (erf(cosh(1)**7)**I).is_real is None + assert (erf(cosh(1)**7)**I).is_imaginary is False + assert (Pow(exp(1+sqrt(2)), ((1-sqrt(2))*I*pi), evaluate=False)).is_real is None + assert ((-10)**(10*I*pi/3)).is_real is False + assert ((-5)**(4*I*pi)).is_real is False + + +def test_issue_18190(): + assert sqrt(1 / tan(1 + I)) == 1 / sqrt(tan(1 + I)) + + +def test_issue_14815(): + x = Symbol('x', real=True) + assert sqrt(x).is_extended_negative is False + x = Symbol('x', real=False) + assert sqrt(x).is_extended_negative is None + x = Symbol('x', complex=True) + assert sqrt(x).is_extended_negative is False + x = Symbol('x', extended_real=True) + assert sqrt(x).is_extended_negative is False + assert sqrt(zoo, evaluate=False).is_extended_negative is False + assert sqrt(nan, evaluate=False).is_extended_negative is None + + +def test_issue_18509(): + x = Symbol('x', prime=True) + assert x**oo is oo + assert (1/x)**oo is S.Zero + assert (-1/x)**oo is S.Zero + assert (-x)**oo is zoo + assert (-oo)**(-1 + I) is S.Zero + assert (-oo)**(1 + I) is zoo + assert (oo)**(-1 + I) is S.Zero + assert (oo)**(1 + I) is zoo + + +def test_issue_18762(): + e, p = symbols('e p') + g0 = sqrt(1 + e**2 - 2*e*cos(p)) + assert len(g0.series(e, 1, 3).args) == 4 + + +def test_issue_21860(): + e = 3*2**Rational(66666666667,200000000000)*3**Rational(16666666667,50000000000)*x**Rational(66666666667, 200000000000) + ans = Mul(Rational(3, 2), + Pow(Integer(2), Rational(33333333333, 100000000000)), + Pow(Integer(3), Rational(26666666667, 40000000000))) + assert e.xreplace({x: Rational(3,8)}) == ans + + +def test_issue_21647(): + e = log((Integer(567)/500)**(811*(Integer(567)/500)**x/100)) + ans = log(Mul(Rational(64701150190720499096094005280169087619821081527, + 76293945312500000000000000000000000000000000000), + Pow(Integer(2), Rational(396204892125479941, 781250000000000000)), + Pow(Integer(3), Rational(385045107874520059, 390625000000000000)), + Pow(Integer(5), Rational(407364676376439823, 1562500000000000000)), + Pow(Integer(7), Rational(385045107874520059, 1562500000000000000)))) + assert e.xreplace({x: 6}) == ans + + +def test_issue_21762(): + e = (x**2 + 6)**(Integer(33333333333333333)/50000000000000000) + ans = Mul(Rational(5, 4), + Pow(Integer(2), Rational(16666666666666667, 25000000000000000)), + Pow(Integer(5), Rational(8333333333333333, 25000000000000000))) + assert e.xreplace({x: S.Half}) == ans + + +def test_issue_14704(): + a = 144**144 + x, xexact = integer_nthroot(a,a) + assert x == 1 and xexact is False + + +def test_rational_powers_larger_than_one(): + assert Rational(2, 3)**Rational(3, 2) == 2*sqrt(6)/9 + assert Rational(1, 6)**Rational(9, 4) == 6**Rational(3, 4)/216 + assert Rational(3, 7)**Rational(7, 3) == 9*3**Rational(1, 3)*7**Rational(2, 3)/343 + + +def test_power_dispatcher(): + + class NewBase(Expr): + pass + class NewPow(NewBase, Pow): + pass + a, b = Symbol('a'), NewBase() + + @power.register(Expr, NewBase) + @power.register(NewBase, Expr) + @power.register(NewBase, NewBase) + def _(a, b): + return NewPow(a, b) + + # Pow called as fallback + assert power(2, 3) == 8*S.One + assert power(a, 2) == Pow(a, 2) + assert power(a, a) == Pow(a, a) + + # NewPow called by dispatch + assert power(a, b) == NewPow(a, b) + assert power(b, a) == NewPow(b, a) + assert power(b, b) == NewPow(b, b) + + +def test_powers_of_I(): + assert [sqrt(I)**i for i in range(13)] == [ + 1, sqrt(I), I, sqrt(I)**3, -1, -sqrt(I), -I, -sqrt(I)**3, + 1, sqrt(I), I, sqrt(I)**3, -1] + assert sqrt(I)**(S(9)/2) == -I**(S(1)/4) + + +def test_issue_23918(): + b = S(2)/3 + assert (b**x).as_base_exp() == (1/b, -x) + + +def test_issue_26546(): + x = Symbol('x', real=True) + assert x.is_extended_real is True + assert sqrt(x+I).is_extended_real is False + assert Pow(x+I, S.Half).is_extended_real is False + assert Pow(x+I, Rational(1,2)).is_extended_real is False + assert Pow(x+I, Rational(1,13)).is_extended_real is False + assert Pow(x+I, Rational(2,3)).is_extended_real is None diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_priority.py b/lib/python3.11/site-packages/sympy/core/tests/test_priority.py new file mode 100644 index 0000000000000000000000000000000000000000..7be30f24033698e43ed68bdbaa0f3566465de173 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_priority.py @@ -0,0 +1,144 @@ +from sympy.core.decorators import call_highest_priority +from sympy.core.expr import Expr +from sympy.core.mod import Mod +from sympy.core.numbers import Integer +from sympy.core.symbol import Symbol +from sympy.functions.elementary.integers import floor + + +class Higher(Integer): + ''' + Integer of value 1 and _op_priority 20 + + Operations handled by this class return 1 and reverse operations return 2 + ''' + + _op_priority = 20.0 + result = 1 + + def __new__(cls): + obj = Expr.__new__(cls) + obj.p = 1 + return obj + + @call_highest_priority('__rmul__') + def __mul__(self, other): + return self.result + + @call_highest_priority('__mul__') + def __rmul__(self, other): + return 2*self.result + + @call_highest_priority('__radd__') + def __add__(self, other): + return self.result + + @call_highest_priority('__add__') + def __radd__(self, other): + return 2*self.result + + @call_highest_priority('__rsub__') + def __sub__(self, other): + return self.result + + @call_highest_priority('__sub__') + def __rsub__(self, other): + return 2*self.result + + @call_highest_priority('__rpow__') + def __pow__(self, other): + return self.result + + @call_highest_priority('__pow__') + def __rpow__(self, other): + return 2*self.result + + @call_highest_priority('__rtruediv__') + def __truediv__(self, other): + return self.result + + @call_highest_priority('__truediv__') + def __rtruediv__(self, other): + return 2*self.result + + @call_highest_priority('__rmod__') + def __mod__(self, other): + return self.result + + @call_highest_priority('__mod__') + def __rmod__(self, other): + return 2*self.result + + @call_highest_priority('__rfloordiv__') + def __floordiv__(self, other): + return self.result + + @call_highest_priority('__floordiv__') + def __rfloordiv__(self, other): + return 2*self.result + + +class Lower(Higher): + ''' + Integer of value -1 and _op_priority 5 + + Operations handled by this class return -1 and reverse operations return -2 + ''' + + _op_priority = 5.0 + result = -1 + + def __new__(cls): + obj = Expr.__new__(cls) + obj.p = -1 + return obj + + +x = Symbol('x') +h = Higher() +l = Lower() + + +def test_mul(): + assert h*l == h*x == 1 + assert l*h == x*h == 2 + assert x*l == l*x == -x + + +def test_add(): + assert h + l == h + x == 1 + assert l + h == x + h == 2 + assert x + l == l + x == x - 1 + + +def test_sub(): + assert h - l == h - x == 1 + assert l - h == x - h == 2 + assert x - l == -(l - x) == x + 1 + + +def test_pow(): + assert h**l == h**x == 1 + assert l**h == x**h == 2 + assert (x**l).args == (1/x).args and (x**l).is_Pow + assert (l**x).args == ((-1)**x).args and (l**x).is_Pow + + +def test_div(): + assert h/l == h/x == 1 + assert l/h == x/h == 2 + assert x/l == 1/(l/x) == -x + + +def test_mod(): + assert h%l == h%x == 1 + assert l%h == x%h == 2 + assert x%l == Mod(x, -1) + assert l%x == Mod(-1, x) + + +def test_floordiv(): + assert h//l == h//x == 1 + assert l//h == x//h == 2 + assert x//l == floor(-x) + assert l//x == floor(-1/x) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_random.py b/lib/python3.11/site-packages/sympy/core/tests/test_random.py new file mode 100644 index 0000000000000000000000000000000000000000..01c677126285eb66349253368b94b3270fb97793 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_random.py @@ -0,0 +1,61 @@ +import random +from sympy.core.random import random as rand, seed, shuffle, _assumptions_shuffle +from sympy.core.symbol import Symbol, symbols +from sympy.functions.elementary.trigonometric import sin, acos +from sympy.abc import x + + +def test_random(): + random.seed(42) + a = random.random() + random.seed(42) + Symbol('z').is_finite + b = random.random() + assert a == b + + got = set() + for i in range(2): + random.seed(28) + m0, m1 = symbols('m_0 m_1', real=True) + _ = acos(-m0/m1) + got.add(random.uniform(0,1)) + assert len(got) == 1 + + random.seed(10) + y = 0 + for i in range(4): + y += sin(random.uniform(-10,10) * x) + random.seed(10) + z = 0 + for i in range(4): + z += sin(random.uniform(-10,10) * x) + assert y == z + + +def test_seed(): + assert rand() < 1 + seed(1) + a = rand() + b = rand() + seed(1) + c = rand() + d = rand() + assert a == c + if not c == d: + assert a != b + else: + assert a == b + + abc = 'abc' + first = list(abc) + second = list(abc) + third = list(abc) + + seed(123) + shuffle(first) + + seed(123) + shuffle(second) + _assumptions_shuffle(third) + + assert first == second == third diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_relational.py b/lib/python3.11/site-packages/sympy/core/tests/test_relational.py new file mode 100644 index 0000000000000000000000000000000000000000..6ab6405c49db677b2c0cbdec7892d46cda841428 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_relational.py @@ -0,0 +1,1271 @@ +from sympy.core.logic import fuzzy_and +from sympy.core.sympify import _sympify +from sympy.multipledispatch import dispatch +from sympy.testing.pytest import XFAIL, raises +from sympy.assumptions.ask import Q +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.expr import Expr, unchanged +from sympy.core.function import Function +from sympy.core.mul import Mul +from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import sign, Abs +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.integers import (ceiling, floor) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.logic.boolalg import (And, Implies, Not, Or, Xor) +from sympy.sets import Reals +from sympy.simplify.simplify import simplify +from sympy.simplify.trigsimp import trigsimp +from sympy.core.relational import (Relational, Equality, Unequality, + GreaterThan, LessThan, StrictGreaterThan, + StrictLessThan, Rel, Eq, Lt, Le, + Gt, Ge, Ne, is_le, is_gt, is_ge, is_lt, is_eq, is_neq) +from sympy.sets.sets import Interval, FiniteSet + +from itertools import combinations + +x, y, z, t = symbols('x,y,z,t') + + +def rel_check(a, b): + from sympy.testing.pytest import raises + assert a.is_number and b.is_number + for do in range(len({type(a), type(b)})): + if S.NaN in (a, b): + v = [(a == b), (a != b)] + assert len(set(v)) == 1 and v[0] == False + assert not (a != b) and not (a == b) + assert raises(TypeError, lambda: a < b) + assert raises(TypeError, lambda: a <= b) + assert raises(TypeError, lambda: a > b) + assert raises(TypeError, lambda: a >= b) + else: + E = [(a == b), (a != b)] + assert len(set(E)) == 2 + v = [ + (a < b), (a <= b), (a > b), (a >= b)] + i = [ + [True, True, False, False], + [False, True, False, True], # <-- i == 1 + [False, False, True, True]].index(v) + if i == 1: + assert E[0] or (a.is_Float != b.is_Float) # ugh + else: + assert E[1] + a, b = b, a + return True + + +def test_rel_ne(): + assert Relational(x, y, '!=') == Ne(x, y) + + # issue 6116 + p = Symbol('p', positive=True) + assert Ne(p, 0) is S.true + + +def test_rel_subs(): + e = Relational(x, y, '==') + e = e.subs(x, z) + + assert isinstance(e, Equality) + assert e.lhs == z + assert e.rhs == y + + e = Relational(x, y, '>=') + e = e.subs(x, z) + + assert isinstance(e, GreaterThan) + assert e.lhs == z + assert e.rhs == y + + e = Relational(x, y, '<=') + e = e.subs(x, z) + + assert isinstance(e, LessThan) + assert e.lhs == z + assert e.rhs == y + + e = Relational(x, y, '>') + e = e.subs(x, z) + + assert isinstance(e, StrictGreaterThan) + assert e.lhs == z + assert e.rhs == y + + e = Relational(x, y, '<') + e = e.subs(x, z) + + assert isinstance(e, StrictLessThan) + assert e.lhs == z + assert e.rhs == y + + e = Eq(x, 0) + assert e.subs(x, 0) is S.true + assert e.subs(x, 1) is S.false + + +def test_wrappers(): + e = x + x**2 + + res = Relational(y, e, '==') + assert Rel(y, x + x**2, '==') == res + assert Eq(y, x + x**2) == res + + res = Relational(y, e, '<') + assert Lt(y, x + x**2) == res + + res = Relational(y, e, '<=') + assert Le(y, x + x**2) == res + + res = Relational(y, e, '>') + assert Gt(y, x + x**2) == res + + res = Relational(y, e, '>=') + assert Ge(y, x + x**2) == res + + res = Relational(y, e, '!=') + assert Ne(y, x + x**2) == res + + +def test_Eq_Ne(): + + assert Eq(x, x) # issue 5719 + + # issue 6116 + p = Symbol('p', positive=True) + assert Eq(p, 0) is S.false + + # issue 13348; 19048 + # SymPy is strict about 0 and 1 not being + # interpreted as Booleans + assert Eq(True, 1) is S.false + assert Eq(False, 0) is S.false + assert Eq(~x, 0) is S.false + assert Eq(~x, 1) is S.false + assert Ne(True, 1) is S.true + assert Ne(False, 0) is S.true + assert Ne(~x, 0) is S.true + assert Ne(~x, 1) is S.true + + assert Eq((), 1) is S.false + assert Ne((), 1) is S.true + + +def test_as_poly(): + from sympy.polys.polytools import Poly + # Only Eq should have an as_poly method: + assert Eq(x, 1).as_poly() == Poly(x - 1, x, domain='ZZ') + raises(AttributeError, lambda: Ne(x, 1).as_poly()) + raises(AttributeError, lambda: Ge(x, 1).as_poly()) + raises(AttributeError, lambda: Gt(x, 1).as_poly()) + raises(AttributeError, lambda: Le(x, 1).as_poly()) + raises(AttributeError, lambda: Lt(x, 1).as_poly()) + + +def test_rel_Infinity(): + # NOTE: All of these are actually handled by sympy.core.Number, and do + # not create Relational objects. + assert (oo > oo) is S.false + assert (oo > -oo) is S.true + assert (oo > 1) is S.true + assert (oo < oo) is S.false + assert (oo < -oo) is S.false + assert (oo < 1) is S.false + assert (oo >= oo) is S.true + assert (oo >= -oo) is S.true + assert (oo >= 1) is S.true + assert (oo <= oo) is S.true + assert (oo <= -oo) is S.false + assert (oo <= 1) is S.false + assert (-oo > oo) is S.false + assert (-oo > -oo) is S.false + assert (-oo > 1) is S.false + assert (-oo < oo) is S.true + assert (-oo < -oo) is S.false + assert (-oo < 1) is S.true + assert (-oo >= oo) is S.false + assert (-oo >= -oo) is S.true + assert (-oo >= 1) is S.false + assert (-oo <= oo) is S.true + assert (-oo <= -oo) is S.true + assert (-oo <= 1) is S.true + + +def test_infinite_symbol_inequalities(): + x = Symbol('x', extended_positive=True, infinite=True) + y = Symbol('y', extended_positive=True, infinite=True) + z = Symbol('z', extended_negative=True, infinite=True) + w = Symbol('w', extended_negative=True, infinite=True) + + inf_set = (x, y, oo) + ninf_set = (z, w, -oo) + + for inf1 in inf_set: + assert (inf1 < 1) is S.false + assert (inf1 > 1) is S.true + assert (inf1 <= 1) is S.false + assert (inf1 >= 1) is S.true + + for inf2 in inf_set: + assert (inf1 < inf2) is S.false + assert (inf1 > inf2) is S.false + assert (inf1 <= inf2) is S.true + assert (inf1 >= inf2) is S.true + + for ninf1 in ninf_set: + assert (inf1 < ninf1) is S.false + assert (inf1 > ninf1) is S.true + assert (inf1 <= ninf1) is S.false + assert (inf1 >= ninf1) is S.true + assert (ninf1 < inf1) is S.true + assert (ninf1 > inf1) is S.false + assert (ninf1 <= inf1) is S.true + assert (ninf1 >= inf1) is S.false + + for ninf1 in ninf_set: + assert (ninf1 < 1) is S.true + assert (ninf1 > 1) is S.false + assert (ninf1 <= 1) is S.true + assert (ninf1 >= 1) is S.false + + for ninf2 in ninf_set: + assert (ninf1 < ninf2) is S.false + assert (ninf1 > ninf2) is S.false + assert (ninf1 <= ninf2) is S.true + assert (ninf1 >= ninf2) is S.true + + +def test_bool(): + assert Eq(0, 0) is S.true + assert Eq(1, 0) is S.false + assert Ne(0, 0) is S.false + assert Ne(1, 0) is S.true + assert Lt(0, 1) is S.true + assert Lt(1, 0) is S.false + assert Le(0, 1) is S.true + assert Le(1, 0) is S.false + assert Le(0, 0) is S.true + assert Gt(1, 0) is S.true + assert Gt(0, 1) is S.false + assert Ge(1, 0) is S.true + assert Ge(0, 1) is S.false + assert Ge(1, 1) is S.true + assert Eq(I, 2) is S.false + assert Ne(I, 2) is S.true + raises(TypeError, lambda: Gt(I, 2)) + raises(TypeError, lambda: Ge(I, 2)) + raises(TypeError, lambda: Lt(I, 2)) + raises(TypeError, lambda: Le(I, 2)) + a = Float('.000000000000000000001', '') + b = Float('.0000000000000000000001', '') + assert Eq(pi + a, pi + b) is S.false + + +def test_rich_cmp(): + assert (x < y) == Lt(x, y) + assert (x <= y) == Le(x, y) + assert (x > y) == Gt(x, y) + assert (x >= y) == Ge(x, y) + + +def test_doit(): + from sympy.core.symbol import Symbol + p = Symbol('p', positive=True) + n = Symbol('n', negative=True) + np = Symbol('np', nonpositive=True) + nn = Symbol('nn', nonnegative=True) + + assert Gt(p, 0).doit() is S.true + assert Gt(p, 1).doit() == Gt(p, 1) + assert Ge(p, 0).doit() is S.true + assert Le(p, 0).doit() is S.false + assert Lt(n, 0).doit() is S.true + assert Le(np, 0).doit() is S.true + assert Gt(nn, 0).doit() == Gt(nn, 0) + assert Lt(nn, 0).doit() is S.false + + assert Eq(x, 0).doit() == Eq(x, 0) + + +def test_new_relational(): + x = Symbol('x') + + assert Eq(x, 0) == Relational(x, 0) # None ==> Equality + assert Eq(x, 0) == Relational(x, 0, '==') + assert Eq(x, 0) == Relational(x, 0, 'eq') + assert Eq(x, 0) == Equality(x, 0) + + assert Eq(x, 0) != Relational(x, 1) # None ==> Equality + assert Eq(x, 0) != Relational(x, 1, '==') + assert Eq(x, 0) != Relational(x, 1, 'eq') + assert Eq(x, 0) != Equality(x, 1) + + assert Eq(x, -1) == Relational(x, -1) # None ==> Equality + assert Eq(x, -1) == Relational(x, -1, '==') + assert Eq(x, -1) == Relational(x, -1, 'eq') + assert Eq(x, -1) == Equality(x, -1) + assert Eq(x, -1) != Relational(x, 1) # None ==> Equality + assert Eq(x, -1) != Relational(x, 1, '==') + assert Eq(x, -1) != Relational(x, 1, 'eq') + assert Eq(x, -1) != Equality(x, 1) + + assert Ne(x, 0) == Relational(x, 0, '!=') + assert Ne(x, 0) == Relational(x, 0, '<>') + assert Ne(x, 0) == Relational(x, 0, 'ne') + assert Ne(x, 0) == Unequality(x, 0) + assert Ne(x, 0) != Relational(x, 1, '!=') + assert Ne(x, 0) != Relational(x, 1, '<>') + assert Ne(x, 0) != Relational(x, 1, 'ne') + assert Ne(x, 0) != Unequality(x, 1) + + assert Ge(x, 0) == Relational(x, 0, '>=') + assert Ge(x, 0) == Relational(x, 0, 'ge') + assert Ge(x, 0) == GreaterThan(x, 0) + assert Ge(x, 1) != Relational(x, 0, '>=') + assert Ge(x, 1) != Relational(x, 0, 'ge') + assert Ge(x, 1) != GreaterThan(x, 0) + assert (x >= 1) == Relational(x, 1, '>=') + assert (x >= 1) == Relational(x, 1, 'ge') + assert (x >= 1) == GreaterThan(x, 1) + assert (x >= 0) != Relational(x, 1, '>=') + assert (x >= 0) != Relational(x, 1, 'ge') + assert (x >= 0) != GreaterThan(x, 1) + + assert Le(x, 0) == Relational(x, 0, '<=') + assert Le(x, 0) == Relational(x, 0, 'le') + assert Le(x, 0) == LessThan(x, 0) + assert Le(x, 1) != Relational(x, 0, '<=') + assert Le(x, 1) != Relational(x, 0, 'le') + assert Le(x, 1) != LessThan(x, 0) + assert (x <= 1) == Relational(x, 1, '<=') + assert (x <= 1) == Relational(x, 1, 'le') + assert (x <= 1) == LessThan(x, 1) + assert (x <= 0) != Relational(x, 1, '<=') + assert (x <= 0) != Relational(x, 1, 'le') + assert (x <= 0) != LessThan(x, 1) + + assert Gt(x, 0) == Relational(x, 0, '>') + assert Gt(x, 0) == Relational(x, 0, 'gt') + assert Gt(x, 0) == StrictGreaterThan(x, 0) + assert Gt(x, 1) != Relational(x, 0, '>') + assert Gt(x, 1) != Relational(x, 0, 'gt') + assert Gt(x, 1) != StrictGreaterThan(x, 0) + assert (x > 1) == Relational(x, 1, '>') + assert (x > 1) == Relational(x, 1, 'gt') + assert (x > 1) == StrictGreaterThan(x, 1) + assert (x > 0) != Relational(x, 1, '>') + assert (x > 0) != Relational(x, 1, 'gt') + assert (x > 0) != StrictGreaterThan(x, 1) + + assert Lt(x, 0) == Relational(x, 0, '<') + assert Lt(x, 0) == Relational(x, 0, 'lt') + assert Lt(x, 0) == StrictLessThan(x, 0) + assert Lt(x, 1) != Relational(x, 0, '<') + assert Lt(x, 1) != Relational(x, 0, 'lt') + assert Lt(x, 1) != StrictLessThan(x, 0) + assert (x < 1) == Relational(x, 1, '<') + assert (x < 1) == Relational(x, 1, 'lt') + assert (x < 1) == StrictLessThan(x, 1) + assert (x < 0) != Relational(x, 1, '<') + assert (x < 0) != Relational(x, 1, 'lt') + assert (x < 0) != StrictLessThan(x, 1) + + # finally, some fuzz testing + from sympy.core.random import randint + for i in range(100): + while 1: + strtype, length = (chr, 65535) if randint(0, 1) else (chr, 255) + relation_type = strtype(randint(0, length)) + if randint(0, 1): + relation_type += strtype(randint(0, length)) + if relation_type not in ('==', 'eq', '!=', '<>', 'ne', '>=', 'ge', + '<=', 'le', '>', 'gt', '<', 'lt', ':=', + '+=', '-=', '*=', '/=', '%='): + break + + raises(ValueError, lambda: Relational(x, 1, relation_type)) + assert all(Relational(x, 0, op).rel_op == '==' for op in ('eq', '==')) + assert all(Relational(x, 0, op).rel_op == '!=' + for op in ('ne', '<>', '!=')) + assert all(Relational(x, 0, op).rel_op == '>' for op in ('gt', '>')) + assert all(Relational(x, 0, op).rel_op == '<' for op in ('lt', '<')) + assert all(Relational(x, 0, op).rel_op == '>=' for op in ('ge', '>=')) + assert all(Relational(x, 0, op).rel_op == '<=' for op in ('le', '<=')) + + +def test_relational_arithmetic(): + for cls in [Eq, Ne, Le, Lt, Ge, Gt]: + rel = cls(x, y) + raises(TypeError, lambda: 0+rel) + raises(TypeError, lambda: 1*rel) + raises(TypeError, lambda: 1**rel) + raises(TypeError, lambda: rel**1) + raises(TypeError, lambda: Add(0, rel)) + raises(TypeError, lambda: Mul(1, rel)) + raises(TypeError, lambda: Pow(1, rel)) + raises(TypeError, lambda: Pow(rel, 1)) + + +def test_relational_bool_output(): + # https://github.com/sympy/sympy/issues/5931 + raises(TypeError, lambda: bool(x > 3)) + raises(TypeError, lambda: bool(x >= 3)) + raises(TypeError, lambda: bool(x < 3)) + raises(TypeError, lambda: bool(x <= 3)) + raises(TypeError, lambda: bool(Eq(x, 3))) + raises(TypeError, lambda: bool(Ne(x, 3))) + + +def test_relational_logic_symbols(): + # See issue 6204 + assert (x < y) & (z < t) == And(x < y, z < t) + assert (x < y) | (z < t) == Or(x < y, z < t) + assert ~(x < y) == Not(x < y) + assert (x < y) >> (z < t) == Implies(x < y, z < t) + assert (x < y) << (z < t) == Implies(z < t, x < y) + assert (x < y) ^ (z < t) == Xor(x < y, z < t) + + assert isinstance((x < y) & (z < t), And) + assert isinstance((x < y) | (z < t), Or) + assert isinstance(~(x < y), GreaterThan) + assert isinstance((x < y) >> (z < t), Implies) + assert isinstance((x < y) << (z < t), Implies) + assert isinstance((x < y) ^ (z < t), (Or, Xor)) + + +def test_univariate_relational_as_set(): + assert (x > 0).as_set() == Interval(0, oo, True, True) + assert (x >= 0).as_set() == Interval(0, oo) + assert (x < 0).as_set() == Interval(-oo, 0, True, True) + assert (x <= 0).as_set() == Interval(-oo, 0) + assert Eq(x, 0).as_set() == FiniteSet(0) + assert Ne(x, 0).as_set() == Interval(-oo, 0, True, True) + \ + Interval(0, oo, True, True) + + assert (x**2 >= 4).as_set() == Interval(-oo, -2) + Interval(2, oo) + + +@XFAIL +def test_multivariate_relational_as_set(): + assert (x*y >= 0).as_set() == Interval(0, oo)*Interval(0, oo) + \ + Interval(-oo, 0)*Interval(-oo, 0) + + +def test_Not(): + assert Not(Equality(x, y)) == Unequality(x, y) + assert Not(Unequality(x, y)) == Equality(x, y) + assert Not(StrictGreaterThan(x, y)) == LessThan(x, y) + assert Not(StrictLessThan(x, y)) == GreaterThan(x, y) + assert Not(GreaterThan(x, y)) == StrictLessThan(x, y) + assert Not(LessThan(x, y)) == StrictGreaterThan(x, y) + + +def test_evaluate(): + assert str(Eq(x, x, evaluate=False)) == 'Eq(x, x)' + assert Eq(x, x, evaluate=False).doit() == S.true + assert str(Ne(x, x, evaluate=False)) == 'Ne(x, x)' + assert Ne(x, x, evaluate=False).doit() == S.false + + assert str(Ge(x, x, evaluate=False)) == 'x >= x' + assert str(Le(x, x, evaluate=False)) == 'x <= x' + assert str(Gt(x, x, evaluate=False)) == 'x > x' + assert str(Lt(x, x, evaluate=False)) == 'x < x' + + +def assert_all_ineq_raise_TypeError(a, b): + raises(TypeError, lambda: a > b) + raises(TypeError, lambda: a >= b) + raises(TypeError, lambda: a < b) + raises(TypeError, lambda: a <= b) + raises(TypeError, lambda: b > a) + raises(TypeError, lambda: b >= a) + raises(TypeError, lambda: b < a) + raises(TypeError, lambda: b <= a) + + +def assert_all_ineq_give_class_Inequality(a, b): + """All inequality operations on `a` and `b` result in class Inequality.""" + from sympy.core.relational import _Inequality as Inequality + assert isinstance(a > b, Inequality) + assert isinstance(a >= b, Inequality) + assert isinstance(a < b, Inequality) + assert isinstance(a <= b, Inequality) + assert isinstance(b > a, Inequality) + assert isinstance(b >= a, Inequality) + assert isinstance(b < a, Inequality) + assert isinstance(b <= a, Inequality) + + +def test_imaginary_compare_raises_TypeError(): + # See issue #5724 + assert_all_ineq_raise_TypeError(I, x) + + +def test_complex_compare_not_real(): + # two cases which are not real + y = Symbol('y', imaginary=True) + z = Symbol('z', complex=True, extended_real=False) + for w in (y, z): + assert_all_ineq_raise_TypeError(2, w) + # some cases which should remain un-evaluated + t = Symbol('t') + x = Symbol('x', real=True) + z = Symbol('z', complex=True) + for w in (x, z, t): + assert_all_ineq_give_class_Inequality(2, w) + + +def test_imaginary_and_inf_compare_raises_TypeError(): + # See pull request #7835 + y = Symbol('y', imaginary=True) + assert_all_ineq_raise_TypeError(oo, y) + assert_all_ineq_raise_TypeError(-oo, y) + + +def test_complex_pure_imag_not_ordered(): + raises(TypeError, lambda: 2*I < 3*I) + + # more generally + x = Symbol('x', real=True, nonzero=True) + y = Symbol('y', imaginary=True) + z = Symbol('z', complex=True) + assert_all_ineq_raise_TypeError(I, y) + + t = I*x # an imaginary number, should raise errors + assert_all_ineq_raise_TypeError(2, t) + + t = -I*y # a real number, so no errors + assert_all_ineq_give_class_Inequality(2, t) + + t = I*z # unknown, should be unevaluated + assert_all_ineq_give_class_Inequality(2, t) + + +def test_x_minus_y_not_same_as_x_lt_y(): + """ + A consequence of pull request #7792 is that `x - y < 0` and `x < y` + are not synonymous. + """ + x = I + 2 + y = I + 3 + raises(TypeError, lambda: x < y) + assert x - y < 0 + + ineq = Lt(x, y, evaluate=False) + raises(TypeError, lambda: ineq.doit()) + assert ineq.lhs - ineq.rhs < 0 + + t = Symbol('t', imaginary=True) + x = 2 + t + y = 3 + t + ineq = Lt(x, y, evaluate=False) + raises(TypeError, lambda: ineq.doit()) + assert ineq.lhs - ineq.rhs < 0 + + # this one should give error either way + x = I + 2 + y = 2*I + 3 + raises(TypeError, lambda: x < y) + raises(TypeError, lambda: x - y < 0) + + +def test_nan_equality_exceptions(): + # See issue #7774 + import random + assert Equality(nan, nan) is S.false + assert Unequality(nan, nan) is S.true + + # See issue #7773 + A = (x, S.Zero, S.One/3, pi, oo, -oo) + assert Equality(nan, random.choice(A)) is S.false + assert Equality(random.choice(A), nan) is S.false + assert Unequality(nan, random.choice(A)) is S.true + assert Unequality(random.choice(A), nan) is S.true + + +def test_nan_inequality_raise_errors(): + # See discussion in pull request #7776. We test inequalities with + # a set including examples of various classes. + for q in (x, S.Zero, S(10), S.One/3, pi, S(1.3), oo, -oo, nan): + assert_all_ineq_raise_TypeError(q, nan) + + +def test_nan_complex_inequalities(): + # Comparisons of NaN with non-real raise errors, we're not too + # fussy whether its the NaN error or complex error. + for r in (I, zoo, Symbol('z', imaginary=True)): + assert_all_ineq_raise_TypeError(r, nan) + + +def test_complex_infinity_inequalities(): + raises(TypeError, lambda: zoo > 0) + raises(TypeError, lambda: zoo >= 0) + raises(TypeError, lambda: zoo < 0) + raises(TypeError, lambda: zoo <= 0) + + +def test_inequalities_symbol_name_same(): + """Using the operator and functional forms should give same results.""" + # We test all combinations from a set + # FIXME: could replace with random selection after test passes + A = (x, y, S.Zero, S.One/3, pi, oo, -oo) + for a in A: + for b in A: + assert Gt(a, b) == (a > b) + assert Lt(a, b) == (a < b) + assert Ge(a, b) == (a >= b) + assert Le(a, b) == (a <= b) + + for b in (y, S.Zero, S.One/3, pi, oo, -oo): + assert Gt(x, b, evaluate=False) == (x > b) + assert Lt(x, b, evaluate=False) == (x < b) + assert Ge(x, b, evaluate=False) == (x >= b) + assert Le(x, b, evaluate=False) == (x <= b) + + for b in (y, S.Zero, S.One/3, pi, oo, -oo): + assert Gt(b, x, evaluate=False) == (b > x) + assert Lt(b, x, evaluate=False) == (b < x) + assert Ge(b, x, evaluate=False) == (b >= x) + assert Le(b, x, evaluate=False) == (b <= x) + + +def test_inequalities_symbol_name_same_complex(): + """Using the operator and functional forms should give same results. + With complex non-real numbers, both should raise errors. + """ + # FIXME: could replace with random selection after test passes + for a in (x, S.Zero, S.One/3, pi, oo, Rational(1, 3)): + raises(TypeError, lambda: Gt(a, I)) + raises(TypeError, lambda: a > I) + raises(TypeError, lambda: Lt(a, I)) + raises(TypeError, lambda: a < I) + raises(TypeError, lambda: Ge(a, I)) + raises(TypeError, lambda: a >= I) + raises(TypeError, lambda: Le(a, I)) + raises(TypeError, lambda: a <= I) + + +def test_inequalities_cant_sympify_other(): + # see issue 7833 + from operator import gt, lt, ge, le + + bar = "foo" + + for a in (x, S.Zero, S.One/3, pi, I, zoo, oo, -oo, nan, Rational(1, 3)): + for op in (lt, gt, le, ge): + raises(TypeError, lambda: op(a, bar)) + + +def test_ineq_avoid_wild_symbol_flip(): + # see issue #7951, we try to avoid this internally, e.g., by using + # __lt__ instead of "<". + from sympy.core.symbol import Wild + p = symbols('p', cls=Wild) + # x > p might flip, but Gt should not: + assert Gt(x, p) == Gt(x, p, evaluate=False) + # Previously failed as 'p > x': + e = Lt(x, y).subs({y: p}) + assert e == Lt(x, p, evaluate=False) + # Previously failed as 'p <= x': + e = Ge(x, p).doit() + assert e == Ge(x, p, evaluate=False) + + +def test_issue_8245(): + a = S("6506833320952669167898688709329/5070602400912917605986812821504") + assert rel_check(a, a.n(10)) + assert rel_check(a, a.n(20)) + assert rel_check(a, a.n()) + # prec of 31 is enough to fully capture a as mpf + assert Float(a, 31) == Float(str(a.p), '')/Float(str(a.q), '') + for i in range(31): + r = Rational(Float(a, i)) + f = Float(r) + assert (f < a) == (Rational(f) < a) + # test sign handling + assert (-f < -a) == (Rational(-f) < -a) + # test equivalence handling + isa = Float(a.p,'')/Float(a.q,'') + assert isa <= a + assert not isa < a + assert isa >= a + assert not isa > a + assert isa > 0 + + a = sqrt(2) + r = Rational(str(a.n(30))) + assert rel_check(a, r) + + a = sqrt(2) + r = Rational(str(a.n(29))) + assert rel_check(a, r) + + assert Eq(log(cos(2)**2 + sin(2)**2), 0) is S.true + + +def test_issue_8449(): + p = Symbol('p', nonnegative=True) + assert Lt(-oo, p) + assert Ge(-oo, p) is S.false + assert Gt(oo, -p) + assert Le(oo, -p) is S.false + + +def test_simplify_relational(): + assert simplify(x*(y + 1) - x*y - x + 1 < x) == (x > 1) + assert simplify(x*(y + 1) - x*y - x - 1 < x) == (x > -1) + assert simplify(x < x*(y + 1) - x*y - x + 1) == (x < 1) + q, r = symbols("q r") + assert (((-q + r) - (q - r)) <= 0).simplify() == (q >= r) + root2 = sqrt(2) + equation = ((root2 * (-q + r) - root2 * (q - r)) <= 0).simplify() + assert equation == (q >= r) + r = S.One < x + # canonical operations are not the same as simplification, + # so if there is no simplification, canonicalization will + # be done unless the measure forbids it + assert simplify(r) == r.canonical + assert simplify(r, ratio=0) != r.canonical + # this is not a random test; in _eval_simplify + # this will simplify to S.false and that is the + # reason for the 'if r.is_Relational' in Relational's + # _eval_simplify routine + assert simplify(-(2**(pi*Rational(3, 2)) + 6**pi)**(1/pi) + + 2*(2**(pi/2) + 3**pi)**(1/pi) < 0) is S.false + # canonical at least + assert Eq(y, x).simplify() == Eq(x, y) + assert Eq(x - 1, 0).simplify() == Eq(x, 1) + assert Eq(x - 1, x).simplify() == S.false + assert Eq(2*x - 1, x).simplify() == Eq(x, 1) + assert Eq(2*x, 4).simplify() == Eq(x, 2) + z = cos(1)**2 + sin(1)**2 - 1 # z.is_zero is None + assert Eq(z*x, 0).simplify() == S.true + + assert Ne(y, x).simplify() == Ne(x, y) + assert Ne(x - 1, 0).simplify() == Ne(x, 1) + assert Ne(x - 1, x).simplify() == S.true + assert Ne(2*x - 1, x).simplify() == Ne(x, 1) + assert Ne(2*x, 4).simplify() == Ne(x, 2) + assert Ne(z*x, 0).simplify() == S.false + + # No real-valued assumptions + assert Ge(y, x).simplify() == Le(x, y) + assert Ge(x - 1, 0).simplify() == Ge(x, 1) + assert Ge(x - 1, x).simplify() == S.false + assert Ge(2*x - 1, x).simplify() == Ge(x, 1) + assert Ge(2*x, 4).simplify() == Ge(x, 2) + assert Ge(z*x, 0).simplify() == S.true + assert Ge(x, -2).simplify() == Ge(x, -2) + assert Ge(-x, -2).simplify() == Le(x, 2) + assert Ge(x, 2).simplify() == Ge(x, 2) + assert Ge(-x, 2).simplify() == Le(x, -2) + + assert Le(y, x).simplify() == Ge(x, y) + assert Le(x - 1, 0).simplify() == Le(x, 1) + assert Le(x - 1, x).simplify() == S.true + assert Le(2*x - 1, x).simplify() == Le(x, 1) + assert Le(2*x, 4).simplify() == Le(x, 2) + assert Le(z*x, 0).simplify() == S.true + assert Le(x, -2).simplify() == Le(x, -2) + assert Le(-x, -2).simplify() == Ge(x, 2) + assert Le(x, 2).simplify() == Le(x, 2) + assert Le(-x, 2).simplify() == Ge(x, -2) + + assert Gt(y, x).simplify() == Lt(x, y) + assert Gt(x - 1, 0).simplify() == Gt(x, 1) + assert Gt(x - 1, x).simplify() == S.false + assert Gt(2*x - 1, x).simplify() == Gt(x, 1) + assert Gt(2*x, 4).simplify() == Gt(x, 2) + assert Gt(z*x, 0).simplify() == S.false + assert Gt(x, -2).simplify() == Gt(x, -2) + assert Gt(-x, -2).simplify() == Lt(x, 2) + assert Gt(x, 2).simplify() == Gt(x, 2) + assert Gt(-x, 2).simplify() == Lt(x, -2) + + assert Lt(y, x).simplify() == Gt(x, y) + assert Lt(x - 1, 0).simplify() == Lt(x, 1) + assert Lt(x - 1, x).simplify() == S.true + assert Lt(2*x - 1, x).simplify() == Lt(x, 1) + assert Lt(2*x, 4).simplify() == Lt(x, 2) + assert Lt(z*x, 0).simplify() == S.false + assert Lt(x, -2).simplify() == Lt(x, -2) + assert Lt(-x, -2).simplify() == Gt(x, 2) + assert Lt(x, 2).simplify() == Lt(x, 2) + assert Lt(-x, 2).simplify() == Gt(x, -2) + + # Test particular branches of _eval_simplify + m = exp(1) - exp_polar(1) + assert simplify(m*x > 1) is S.false + # These two test the same branch + assert simplify(m*x + 2*m*y > 1) is S.false + assert simplify(m*x + y > 1 + y) is S.false + + +def test_equals(): + w, x, y, z = symbols('w:z') + f = Function('f') + assert Eq(x, 1).equals(Eq(x*(y + 1) - x*y - x + 1, x)) + assert Eq(x, y).equals(x < y, True) == False + assert Eq(x, f(1)).equals(Eq(x, f(2)), True) == f(1) - f(2) + assert Eq(f(1), y).equals(Eq(f(2), y), True) == f(1) - f(2) + assert Eq(x, f(1)).equals(Eq(f(2), x), True) == f(1) - f(2) + assert Eq(f(1), x).equals(Eq(x, f(2)), True) == f(1) - f(2) + assert Eq(w, x).equals(Eq(y, z), True) == False + assert Eq(f(1), f(2)).equals(Eq(f(3), f(4)), True) == f(1) - f(3) + assert (x < y).equals(y > x, True) == True + assert (x < y).equals(y >= x, True) == False + assert (x < y).equals(z < y, True) == False + assert (x < y).equals(x < z, True) == False + assert (x < f(1)).equals(x < f(2), True) == f(1) - f(2) + assert (f(1) < x).equals(f(2) < x, True) == f(1) - f(2) + + +def test_reversed(): + assert (x < y).reversed == (y > x) + assert (x <= y).reversed == (y >= x) + assert Eq(x, y, evaluate=False).reversed == Eq(y, x, evaluate=False) + assert Ne(x, y, evaluate=False).reversed == Ne(y, x, evaluate=False) + assert (x >= y).reversed == (y <= x) + assert (x > y).reversed == (y < x) + + +def test_canonical(): + c = [i.canonical for i in ( + x + y < z, + x + 2 > 3, + x < 2, + S(2) > x, + x**2 > -x/y, + Gt(3, 2, evaluate=False) + )] + assert [i.canonical for i in c] == c + assert [i.reversed.canonical for i in c] == c + assert not any(i.lhs.is_Number and not i.rhs.is_Number for i in c) + + c = [i.reversed.func(i.rhs, i.lhs, evaluate=False).canonical for i in c] + assert [i.canonical for i in c] == c + assert [i.reversed.canonical for i in c] == c + assert not any(i.lhs.is_Number and not i.rhs.is_Number for i in c) + assert Eq(y < x, x > y).canonical is S.true + + +@XFAIL +def test_issue_8444_nonworkingtests(): + x = symbols('x', real=True) + assert (x <= oo) == (x >= -oo) == True + + x = symbols('x') + assert x >= floor(x) + assert (x < floor(x)) == False + assert x <= ceiling(x) + assert (x > ceiling(x)) == False + + +def test_issue_8444_workingtests(): + x = symbols('x') + assert Gt(x, floor(x)) == Gt(x, floor(x), evaluate=False) + assert Ge(x, floor(x)) == Ge(x, floor(x), evaluate=False) + assert Lt(x, ceiling(x)) == Lt(x, ceiling(x), evaluate=False) + assert Le(x, ceiling(x)) == Le(x, ceiling(x), evaluate=False) + i = symbols('i', integer=True) + assert (i > floor(i)) == False + assert (i < ceiling(i)) == False + + +def test_issue_10304(): + d = cos(1)**2 + sin(1)**2 - 1 + assert d.is_comparable is False # if this fails, find a new d + e = 1 + d*I + assert simplify(Eq(e, 0)) is S.false + + +def test_issue_18412(): + d = (Rational(1, 6) + z / 4 / y) + assert Eq(x, pi * y**3 * d).replace(y**3, z) == Eq(x, pi * z * d) + + +def test_issue_10401(): + x = symbols('x') + fin = symbols('inf', finite=True) + inf = symbols('inf', infinite=True) + inf2 = symbols('inf2', infinite=True) + infx = symbols('infx', infinite=True, extended_real=True) + # Used in the commented tests below: + #infx2 = symbols('infx2', infinite=True, extended_real=True) + infnx = symbols('inf~x', infinite=True, extended_real=False) + infnx2 = symbols('inf~x2', infinite=True, extended_real=False) + infp = symbols('infp', infinite=True, extended_positive=True) + infp1 = symbols('infp1', infinite=True, extended_positive=True) + infn = symbols('infn', infinite=True, extended_negative=True) + zero = symbols('z', zero=True) + nonzero = symbols('nz', zero=False, finite=True) + + assert Eq(1/(1/x + 1), 1).func is Eq + assert Eq(1/(1/x + 1), 1).subs(x, S.ComplexInfinity) is S.true + assert Eq(1/(1/fin + 1), 1) is S.false + + T, F = S.true, S.false + assert Eq(fin, inf) is F + assert Eq(inf, inf2) not in (T, F) and inf != inf2 + assert Eq(1 + inf, 2 + inf2) not in (T, F) and inf != inf2 + assert Eq(infp, infp1) is T + assert Eq(infp, infn) is F + assert Eq(1 + I*oo, I*oo) is F + assert Eq(I*oo, 1 + I*oo) is F + assert Eq(1 + I*oo, 2 + I*oo) is F + assert Eq(1 + I*oo, 2 + I*infx) is F + assert Eq(1 + I*oo, 2 + infx) is F + # FIXME: The test below fails because (-infx).is_extended_positive is True + # (should be None) + #assert Eq(1 + I*infx, 1 + I*infx2) not in (T, F) and infx != infx2 + # + assert Eq(zoo, sqrt(2) + I*oo) is F + assert Eq(zoo, oo) is F + r = Symbol('r', real=True) + i = Symbol('i', imaginary=True) + assert Eq(i*I, r) not in (T, F) + assert Eq(infx, infnx) is F + assert Eq(infnx, infnx2) not in (T, F) and infnx != infnx2 + assert Eq(zoo, oo) is F + assert Eq(inf/inf2, 0) is F + assert Eq(inf/fin, 0) is F + assert Eq(fin/inf, 0) is T + assert Eq(zero/nonzero, 0) is T and ((zero/nonzero) != 0) + # The commented out test below is incorrect because: + assert zoo == -zoo + assert Eq(zoo, -zoo) is T + assert Eq(oo, -oo) is F + assert Eq(inf, -inf) not in (T, F) + + assert Eq(fin/(fin + 1), 1) is S.false + + o = symbols('o', odd=True) + assert Eq(o, 2*o) is S.false + + p = symbols('p', positive=True) + assert Eq(p/(p - 1), 1) is F + + +def test_issue_10633(): + assert Eq(True, False) == False + assert Eq(False, True) == False + assert Eq(True, True) == True + assert Eq(False, False) == True + + +def test_issue_10927(): + x = symbols('x') + assert str(Eq(x, oo)) == 'Eq(x, oo)' + assert str(Eq(x, -oo)) == 'Eq(x, -oo)' + + +def test_issues_13081_12583_12534(): + # 13081 + r = Rational('905502432259640373/288230376151711744') + assert (r < pi) is S.false + assert (r > pi) is S.true + # 12583 + v = sqrt(2) + u = sqrt(v) + 2/sqrt(10 - 8/sqrt(2 - v) + 4*v*(1/sqrt(2 - v) - 1)) + assert (u >= 0) is S.true + # 12534; Rational vs NumberSymbol + # here are some precisions for which Rational forms + # at a lower and higher precision bracket the value of pi + # e.g. for p = 20: + # Rational(pi.n(p + 1)).n(25) = 3.14159265358979323846 2834 + # pi.n(25) = 3.14159265358979323846 2643 + # Rational(pi.n(p )).n(25) = 3.14159265358979323846 1987 + assert [p for p in range(20, 50) if + (Rational(pi.n(p)) < pi) and + (pi < Rational(pi.n(p + 1)))] == [20, 24, 27, 33, 37, 43, 48] + # pick one such precision and affirm that the reversed operation + # gives the opposite result, i.e. if x < y is true then x > y + # must be false + for i in (20, 21): + v = pi.n(i) + assert rel_check(Rational(v), pi) + assert rel_check(v, pi) + assert rel_check(pi.n(20), pi.n(21)) + # Float vs Rational + # the rational form is less than the floating representation + # at the same precision + assert [i for i in range(15, 50) if Rational(pi.n(i)) > pi.n(i)] == [] + # this should be the same if we reverse the relational + assert [i for i in range(15, 50) if pi.n(i) < Rational(pi.n(i))] == [] + +def test_issue_18188(): + from sympy.sets.conditionset import ConditionSet + result1 = Eq(x*cos(x) - 3*sin(x), 0) + assert result1.as_set() == ConditionSet(x, Eq(x*cos(x) - 3*sin(x), 0), Reals) + + result2 = Eq(x**2 + sqrt(x*2) + sin(x), 0) + assert result2.as_set() == ConditionSet(x, Eq(sqrt(2)*sqrt(x) + x**2 + sin(x), 0), Reals) + +def test_binary_symbols(): + ans = {x} + for f in Eq, Ne: + for t in S.true, S.false: + eq = f(x, S.true) + assert eq.binary_symbols == ans + assert eq.reversed.binary_symbols == ans + assert f(x, 1).binary_symbols == set() + + +def test_rel_args(): + # can't have Boolean args; this is automatic for True/False + # with Python 3 and we confirm that SymPy does the same + # for true/false + for op in ['<', '<=', '>', '>=']: + for b in (S.true, x < 1, And(x, y)): + for v in (0.1, 1, 2**32, t, S.One): + raises(TypeError, lambda: Relational(b, v, op)) + + +def test_nothing_happens_to_Eq_condition_during_simplify(): + # issue 25701 + r = symbols('r', real=True) + assert Eq(2*sign(r + 3)/(5*Abs(r + 3)**Rational(3, 5)), 0 + ).simplify() == Eq(Piecewise( + (0, Eq(r, -3)), ((r + 3)/(5*Abs((r + 3)**Rational(8, 5)))*2, True)), 0) + + +def test_issue_15847(): + a = Ne(x*(x + y), x**2 + x*y) + assert simplify(a) == False + + +def test_negated_property(): + eq = Eq(x, y) + assert eq.negated == Ne(x, y) + + eq = Ne(x, y) + assert eq.negated == Eq(x, y) + + eq = Ge(x + y, y - x) + assert eq.negated == Lt(x + y, y - x) + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(x, y).negated.negated == f(x, y) + + +def test_reversedsign_property(): + eq = Eq(x, y) + assert eq.reversedsign == Eq(-x, -y) + + eq = Ne(x, y) + assert eq.reversedsign == Ne(-x, -y) + + eq = Ge(x + y, y - x) + assert eq.reversedsign == Le(-x - y, x - y) + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(x, y).reversedsign.reversedsign == f(x, y) + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(-x, y).reversedsign.reversedsign == f(-x, y) + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(x, -y).reversedsign.reversedsign == f(x, -y) + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(-x, -y).reversedsign.reversedsign == f(-x, -y) + + +def test_reversed_reversedsign_property(): + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(x, y).reversed.reversedsign == f(x, y).reversedsign.reversed + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(-x, y).reversed.reversedsign == f(-x, y).reversedsign.reversed + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(x, -y).reversed.reversedsign == f(x, -y).reversedsign.reversed + + for f in (Eq, Ne, Ge, Gt, Le, Lt): + assert f(-x, -y).reversed.reversedsign == \ + f(-x, -y).reversedsign.reversed + + +def test_improved_canonical(): + def test_different_forms(listofforms): + for form1, form2 in combinations(listofforms, 2): + assert form1.canonical == form2.canonical + + def generate_forms(expr): + return [expr, expr.reversed, expr.reversedsign, + expr.reversed.reversedsign] + + test_different_forms(generate_forms(x > -y)) + test_different_forms(generate_forms(x >= -y)) + test_different_forms(generate_forms(Eq(x, -y))) + test_different_forms(generate_forms(Ne(x, -y))) + test_different_forms(generate_forms(pi < x)) + test_different_forms(generate_forms(pi - 5*y < -x + 2*y**2 - 7)) + + assert (pi >= x).canonical == (x <= pi) + + +def test_set_equality_canonical(): + a, b, c = symbols('a b c') + + A = Eq(FiniteSet(a, b, c), FiniteSet(1, 2, 3)) + B = Ne(FiniteSet(a, b, c), FiniteSet(4, 5, 6)) + + assert A.canonical == A.reversed + assert B.canonical == B.reversed + + +def test_trigsimp(): + # issue 16736 + s, c = sin(2*x), cos(2*x) + eq = Eq(s, c) + assert trigsimp(eq) == eq # no rearrangement of sides + # simplification of sides might result in + # an unevaluated Eq + changed = trigsimp(Eq(s + c, sqrt(2))) + assert isinstance(changed, Eq) + assert changed.subs(x, pi/8) is S.true + # or an evaluated one + assert trigsimp(Eq(cos(x)**2 + sin(x)**2, 1)) is S.true + + +def test_polynomial_relation_simplification(): + assert Ge(3*x*(x + 1) + 4, 3*x).simplify() in [Ge(x**2, -Rational(4,3)), Le(-x**2, Rational(4, 3))] + assert Le(-(3*x*(x + 1) + 4), -3*x).simplify() in [Ge(x**2, -Rational(4,3)), Le(-x**2, Rational(4, 3))] + assert ((x**2+3)*(x**2-1)+3*x >= 2*x**2).simplify() in [(x**4 + 3*x >= 3), (-x**4 - 3*x <= -3)] + + +def test_multivariate_linear_function_simplification(): + assert Ge(x + y, x - y).simplify() == Ge(y, 0) + assert Le(-x + y, -x - y).simplify() == Le(y, 0) + assert Eq(2*x + y, 2*x + y - 3).simplify() == False + assert (2*x + y > 2*x + y - 3).simplify() == True + assert (2*x + y < 2*x + y - 3).simplify() == False + assert (2*x + y < 2*x + y + 3).simplify() == True + a, b, c, d, e, f, g = symbols('a b c d e f g') + assert Lt(a + b + c + 2*d, 3*d - f + g). simplify() == Lt(a, -b - c + d - f + g) + + +def test_nonpolymonial_relations(): + assert Eq(cos(x), 0).simplify() == Eq(cos(x), 0) + +def test_18778(): + raises(TypeError, lambda: is_le(Basic(), Basic())) + raises(TypeError, lambda: is_gt(Basic(), Basic())) + raises(TypeError, lambda: is_ge(Basic(), Basic())) + raises(TypeError, lambda: is_lt(Basic(), Basic())) + +def test_EvalEq(): + """ + + This test exists to ensure backwards compatibility. + The method to use is _eval_is_eq + """ + from sympy.core.expr import Expr + + class PowTest(Expr): + def __new__(cls, base, exp): + return Basic.__new__(PowTest, _sympify(base), _sympify(exp)) + + def _eval_Eq(lhs, rhs): + if type(lhs) == PowTest and type(rhs) == PowTest: + return lhs.args[0] == rhs.args[0] and lhs.args[1] == rhs.args[1] + + assert is_eq(PowTest(3, 4), PowTest(3,4)) + assert is_eq(PowTest(3, 4), _sympify(4)) is None + assert is_neq(PowTest(3, 4), PowTest(3,7)) + + +def test_is_eq(): + # test assumptions + assert is_eq(x, y, Q.infinite(x) & Q.finite(y)) is False + assert is_eq(x, y, Q.infinite(x) & Q.infinite(y) & Q.extended_real(x) & ~Q.extended_real(y)) is False + assert is_eq(x, y, Q.infinite(x) & Q.infinite(y) & Q.extended_positive(x) & Q.extended_negative(y)) is False + + assert is_eq(x+I, y+I, Q.infinite(x) & Q.finite(y)) is False + assert is_eq(1+x*I, 1+y*I, Q.infinite(x) & Q.finite(y)) is False + + assert is_eq(x, S(0), assumptions=Q.zero(x)) + assert is_eq(x, S(0), assumptions=~Q.zero(x)) is False + assert is_eq(x, S(0), assumptions=Q.nonzero(x)) is False + assert is_neq(x, S(0), assumptions=Q.zero(x)) is False + assert is_neq(x, S(0), assumptions=~Q.zero(x)) + assert is_neq(x, S(0), assumptions=Q.nonzero(x)) + + # test registration + class PowTest(Expr): + def __new__(cls, base, exp): + return Basic.__new__(cls, _sympify(base), _sympify(exp)) + + @dispatch(PowTest, PowTest) + def _eval_is_eq(lhs, rhs): + if type(lhs) == PowTest and type(rhs) == PowTest: + return fuzzy_and([is_eq(lhs.args[0], rhs.args[0]), is_eq(lhs.args[1], rhs.args[1])]) + + assert is_eq(PowTest(3, 4), PowTest(3,4)) + assert is_eq(PowTest(3, 4), _sympify(4)) is None + assert is_neq(PowTest(3, 4), PowTest(3,7)) + + +def test_is_ge_le(): + # test assumptions + assert is_ge(x, S(0), Q.nonnegative(x)) is True + assert is_ge(x, S(0), Q.negative(x)) is False + + # test registration + class PowTest(Expr): + def __new__(cls, base, exp): + return Basic.__new__(cls, _sympify(base), _sympify(exp)) + + @dispatch(PowTest, PowTest) + def _eval_is_ge(lhs, rhs): + if type(lhs) == PowTest and type(rhs) == PowTest: + return fuzzy_and([is_ge(lhs.args[0], rhs.args[0]), is_ge(lhs.args[1], rhs.args[1])]) + + assert is_ge(PowTest(3, 9), PowTest(3,2)) + assert is_gt(PowTest(3, 9), PowTest(3,2)) + assert is_le(PowTest(3, 2), PowTest(3,9)) + assert is_lt(PowTest(3, 2), PowTest(3,9)) + + +def test_weak_strict(): + for func in (Eq, Ne): + eq = func(x, 1) + assert eq.strict == eq.weak == eq + eq = Gt(x, 1) + assert eq.weak == Ge(x, 1) + assert eq.strict == eq + eq = Lt(x, 1) + assert eq.weak == Le(x, 1) + assert eq.strict == eq + eq = Ge(x, 1) + assert eq.strict == Gt(x, 1) + assert eq.weak == eq + eq = Le(x, 1) + assert eq.strict == Lt(x, 1) + assert eq.weak == eq + + +def test_issue_23731(): + i = symbols('i', integer=True) + assert unchanged(Eq, i, 1.0) + assert unchanged(Eq, i/2, 0.5) + ni = symbols('ni', integer=False) + assert Eq(ni, 1) == False + assert unchanged(Eq, ni, .1) + assert Eq(ni, 1.0) == False + nr = symbols('nr', rational=False) + assert Eq(nr, .1) == False + + +def test_rewrite_Add(): + from sympy.testing.pytest import warns_deprecated_sympy + with warns_deprecated_sympy(): + assert Eq(x, y).rewrite(Add) == x - y diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_rules.py b/lib/python3.11/site-packages/sympy/core/tests/test_rules.py new file mode 100644 index 0000000000000000000000000000000000000000..31cb88b52db21f39653033b4567526e992be99f0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_rules.py @@ -0,0 +1,14 @@ +from sympy.core.rules import Transform + +from sympy.testing.pytest import raises + + +def test_Transform(): + add1 = Transform(lambda x: x + 1, lambda x: x % 2 == 1) + assert add1[1] == 2 + assert (1 in add1) is True + assert add1.get(1) == 2 + + raises(KeyError, lambda: add1[2]) + assert (2 in add1) is False + assert add1.get(2) is None diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_singleton.py b/lib/python3.11/site-packages/sympy/core/tests/test_singleton.py new file mode 100644 index 0000000000000000000000000000000000000000..893713f27d74b884391ad800d186eafe5337ab1c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_singleton.py @@ -0,0 +1,76 @@ +from sympy.core.basic import Basic +from sympy.core.numbers import Rational +from sympy.core.singleton import S, Singleton + +def test_Singleton(): + + class MySingleton(Basic, metaclass=Singleton): + pass + + MySingleton() # force instantiation + assert MySingleton() is not Basic() + assert MySingleton() is MySingleton() + assert S.MySingleton is MySingleton() + + class MySingleton_sub(MySingleton): + pass + + MySingleton_sub() + assert MySingleton_sub() is not MySingleton() + assert MySingleton_sub() is MySingleton_sub() + +def test_singleton_redefinition(): + class TestSingleton(Basic, metaclass=Singleton): + pass + + assert TestSingleton() is S.TestSingleton + + class TestSingleton(Basic, metaclass=Singleton): + pass + + assert TestSingleton() is S.TestSingleton + +def test_names_in_namespace(): + # Every singleton name should be accessible from the 'from sympy import *' + # namespace in addition to the S object. However, it does not need to be + # by the same name (e.g., oo instead of S.Infinity). + + # As a general rule, things should only be added to the singleton registry + # if they are used often enough that code can benefit either from the + # performance benefit of being able to use 'is' (this only matters in very + # tight loops), or from the memory savings of having exactly one instance + # (this matters for the numbers singletons, but very little else). The + # singleton registry is already a bit overpopulated, and things cannot be + # removed from it without breaking backwards compatibility. So if you got + # here by adding something new to the singletons, ask yourself if it + # really needs to be singletonized. Note that SymPy classes compare to one + # another just fine, so Class() == Class() will give True even if each + # Class() returns a new instance. Having unique instances is only + # necessary for the above noted performance gains. It should not be needed + # for any behavioral purposes. + + # If you determine that something really should be a singleton, it must be + # accessible to sympify() without using 'S' (hence this test). Also, its + # str printer should print a form that does not use S. This is because + # sympify() disables attribute lookups by default for safety purposes. + d = {} + exec('from sympy import *', d) + + for name in dir(S) + list(S._classes_to_install): + if name.startswith('_'): + continue + if name == 'register': + continue + if isinstance(getattr(S, name), Rational): + continue + if getattr(S, name).__module__.startswith('sympy.physics'): + continue + if name in ['MySingleton', 'MySingleton_sub', 'TestSingleton']: + # From the tests above + continue + if name == 'NegativeInfinity': + # Accessible by -oo + continue + + # Use is here to ensure it is the exact same object + assert any(getattr(S, name) is i for i in d.values()), name diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_sorting.py b/lib/python3.11/site-packages/sympy/core/tests/test_sorting.py new file mode 100644 index 0000000000000000000000000000000000000000..a18dbfb624552cf2fa11bb7f3c3a9e865caeb0c4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_sorting.py @@ -0,0 +1,28 @@ +from sympy.core.sorting import default_sort_key, ordered +from sympy.testing.pytest import raises + +from sympy.abc import x + + +def test_default_sort_key(): + func = lambda x: x + assert sorted([func, x, func], key=default_sort_key) == [func, func, x] + + class C: + def __repr__(self): + return 'x.y' + func = C() + assert sorted([x, func], key=default_sort_key) == [func, x] + + +def test_ordered(): + # Issue 7210 - this had been failing with python2/3 problems + assert (list(ordered([{1:3, 2:4, 9:10}, {1:3}])) == \ + [{1: 3}, {1: 3, 2: 4, 9: 10}]) + # warnings should not be raised for identical items + l = [1, 1] + assert list(ordered(l, warn=True)) == l + l = [[1], [2], [1]] + assert list(ordered(l, warn=True)) == [[1], [1], [2]] + raises(ValueError, lambda: list(ordered(['a', 'ab'], keys=[lambda x: x[0]], + default=False, warn=True))) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_subs.py b/lib/python3.11/site-packages/sympy/core/tests/test_subs.py new file mode 100644 index 0000000000000000000000000000000000000000..0803a4b1b5e93b8a35f43516ccef3ab9a16f08ec --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_subs.py @@ -0,0 +1,895 @@ +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.containers import (Dict, Tuple) +from sympy.core.function import (Derivative, Function, Lambda, Subs) +from sympy.core.mul import Mul +from sympy.core.numbers import (Float, I, Integer, Rational, oo, pi, zoo) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, Wild, symbols) +from sympy.core.sympify import SympifyError +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (atan2, cos, cot, sin, tan) +from sympy.matrices.dense import (Matrix, zeros) +from sympy.matrices.expressions.special import ZeroMatrix +from sympy.polys.polytools import factor +from sympy.polys.rootoftools import RootOf +from sympy.simplify.cse_main import cse +from sympy.simplify.simplify import nsimplify +from sympy.core.basic import _aresame +from sympy.testing.pytest import XFAIL, raises +from sympy.abc import a, x, y, z, t + + +def test_subs(): + n3 = Rational(3) + e = x + e = e.subs(x, n3) + assert e == Rational(3) + + e = 2*x + assert e == 2*x + e = e.subs(x, n3) + assert e == Rational(6) + + +def test_subs_Matrix(): + z = zeros(2) + z1 = ZeroMatrix(2, 2) + assert (x*y).subs({x:z, y:0}) in [z, z1] + assert (x*y).subs({y:z, x:0}) == 0 + assert (x*y).subs({y:z, x:0}, simultaneous=True) in [z, z1] + assert (x + y).subs({x: z, y: z}, simultaneous=True) in [z, z1] + assert (x + y).subs({x: z, y: z}) in [z, z1] + + # Issue #15528 + assert Mul(Matrix([[3]]), x).subs(x, 2.0) == Matrix([[6.0]]) + # Does not raise a TypeError, see comment on the MatAdd postprocessor + assert Add(Matrix([[3]]), x).subs(x, 2.0) == Add(Matrix([[3]]), 2.0) + + +def test_subs_AccumBounds(): + e = x + e = e.subs(x, AccumBounds(1, 3)) + assert e == AccumBounds(1, 3) + + e = 2*x + e = e.subs(x, AccumBounds(1, 3)) + assert e == AccumBounds(2, 6) + + e = x + x**2 + e = e.subs(x, AccumBounds(-1, 1)) + assert e == AccumBounds(-1, 2) + + +def test_trigonometric(): + n3 = Rational(3) + e = (sin(x)**2).diff(x) + assert e == 2*sin(x)*cos(x) + e = e.subs(x, n3) + assert e == 2*cos(n3)*sin(n3) + + e = (sin(x)**2).diff(x) + assert e == 2*sin(x)*cos(x) + e = e.subs(sin(x), cos(x)) + assert e == 2*cos(x)**2 + + assert exp(pi).subs(exp, sin) == 0 + assert cos(exp(pi)).subs(exp, sin) == 1 + + i = Symbol('i', integer=True) + zoo = S.ComplexInfinity + assert tan(x).subs(x, pi/2) is zoo + assert cot(x).subs(x, pi) is zoo + assert cot(i*x).subs(x, pi) is zoo + assert tan(i*x).subs(x, pi/2) == tan(i*pi/2) + assert tan(i*x).subs(x, pi/2).subs(i, 1) is zoo + o = Symbol('o', odd=True) + assert tan(o*x).subs(x, pi/2) == tan(o*pi/2) + + +def test_powers(): + assert sqrt(1 - sqrt(x)).subs(x, 4) == I + assert (sqrt(1 - x**2)**3).subs(x, 2) == - 3*I*sqrt(3) + assert (x**Rational(1, 3)).subs(x, 27) == 3 + assert (x**Rational(1, 3)).subs(x, -27) == 3*(-1)**Rational(1, 3) + assert ((-x)**Rational(1, 3)).subs(x, 27) == 3*(-1)**Rational(1, 3) + n = Symbol('n', negative=True) + assert (x**n).subs(x, 0) is S.ComplexInfinity + assert exp(-1).subs(S.Exp1, 0) is S.ComplexInfinity + assert (x**(4.0*y)).subs(x**(2.0*y), n) == n**2.0 + assert (2**(x + 2)).subs(2, 3) == 3**(x + 3) + + +def test_logexppow(): # no eval() + x = Symbol('x', real=True) + w = Symbol('w') + e = (3**(1 + x) + 2**(1 + x))/(3**x + 2**x) + assert e.subs(2**x, w) != e + assert e.subs(exp(x*log(Rational(2))), w) != e + + +def test_bug(): + x1 = Symbol('x1') + x2 = Symbol('x2') + y = x1*x2 + assert y.subs(x1, Float(3.0)) == Float(3.0)*x2 + + +def test_subbug1(): + # see that they don't fail + (x**x).subs(x, 1) + (x**x).subs(x, 1.0) + + +def test_subbug2(): + # Ensure this does not cause infinite recursion + assert Float(7.7).epsilon_eq(abs(x).subs(x, -7.7)) + + +def test_dict_set(): + a, b, c = map(Wild, 'abc') + + f = 3*cos(4*x) + r = f.match(a*cos(b*x)) + assert r == {a: 3, b: 4} + e = a/b*sin(b*x) + assert e.subs(r) == r[a]/r[b]*sin(r[b]*x) + assert e.subs(r) == 3*sin(4*x) / 4 + s = set(r.items()) + assert e.subs(s) == r[a]/r[b]*sin(r[b]*x) + assert e.subs(s) == 3*sin(4*x) / 4 + + assert e.subs(r) == r[a]/r[b]*sin(r[b]*x) + assert e.subs(r) == 3*sin(4*x) / 4 + assert x.subs(Dict((x, 1))) == 1 + + +def test_dict_ambigous(): # see issue 3566 + f = x*exp(x) + g = z*exp(z) + + df = {x: y, exp(x): y} + dg = {z: y, exp(z): y} + + assert f.subs(df) == y**2 + assert g.subs(dg) == y**2 + + # and this is how order can affect the result + assert f.subs(x, y).subs(exp(x), y) == y*exp(y) + assert f.subs(exp(x), y).subs(x, y) == y**2 + + # length of args and count_ops are the same so + # default_sort_key resolves ordering...if one + # doesn't want this result then an unordered + # sequence should not be used. + e = 1 + x*y + assert e.subs({x: y, y: 2}) == 5 + # here, there are no obviously clashing keys or values + # but the results depend on the order + assert exp(x/2 + y).subs({exp(y + 1): 2, x: 2}) == exp(y + 1) + + +def test_deriv_sub_bug3(): + f = Function('f') + pat = Derivative(f(x), x, x) + assert pat.subs(y, y**2) == Derivative(f(x), x, x) + assert pat.subs(y, y**2) != Derivative(f(x), x) + + +def test_equality_subs1(): + f = Function('f') + eq = Eq(f(x)**2, x) + res = Eq(Integer(16), x) + assert eq.subs(f(x), 4) == res + + +def test_equality_subs2(): + f = Function('f') + eq = Eq(f(x)**2, 16) + assert bool(eq.subs(f(x), 3)) is False + assert bool(eq.subs(f(x), 4)) is True + + +def test_issue_3742(): + e = sqrt(x)*exp(y) + assert e.subs(sqrt(x), 1) == exp(y) + + +def test_subs_dict1(): + assert (1 + x*y).subs(x, pi) == 1 + pi*y + assert (1 + x*y).subs({x: pi, y: 2}) == 1 + 2*pi + + c2, c3, q1p, q2p, c1, s1, s2, s3 = symbols('c2 c3 q1p q2p c1 s1 s2 s3') + test = (c2**2*q2p*c3 + c1**2*s2**2*q2p*c3 + s1**2*s2**2*q2p*c3 + - c1**2*q1p*c2*s3 - s1**2*q1p*c2*s3) + assert (test.subs({c1**2: 1 - s1**2, c2**2: 1 - s2**2, c3**3: 1 - s3**2}) + == c3*q2p*(1 - s2**2) + c3*q2p*s2**2*(1 - s1**2) + - c2*q1p*s3*(1 - s1**2) + c3*q2p*s1**2*s2**2 - c2*q1p*s3*s1**2) + + +def test_mul(): + x, y, z, a, b, c = symbols('x y z a b c') + A, B, C = symbols('A B C', commutative=0) + assert (x*y*z).subs(z*x, y) == y**2 + assert (z*x).subs(1/x, z) == 1 + assert (x*y/z).subs(1/z, a) == a*x*y + assert (x*y/z).subs(x/z, a) == a*y + assert (x*y/z).subs(y/z, a) == a*x + assert (x*y/z).subs(x/z, 1/a) == y/a + assert (x*y/z).subs(x, 1/a) == y/(z*a) + assert (2*x*y).subs(5*x*y, z) != z*Rational(2, 5) + assert (x*y*A).subs(x*y, a) == a*A + assert (x**2*y**(x*Rational(3, 2))).subs(x*y**(x/2), 2) == 4*y**(x/2) + assert (x*exp(x*2)).subs(x*exp(x), 2) == 2*exp(x) + assert ((x**(2*y))**3).subs(x**y, 2) == 64 + assert (x*A*B).subs(x*A, y) == y*B + assert (x*y*(1 + x)*(1 + x*y)).subs(x*y, 2) == 6*(1 + x) + assert ((1 + A*B)*A*B).subs(A*B, x*A*B) + assert (x*a/z).subs(x/z, A) == a*A + assert (x**3*A).subs(x**2*A, a) == a*x + assert (x**2*A*B).subs(x**2*B, a) == a*A + assert (x**2*A*B).subs(x**2*A, a) == a*B + assert (b*A**3/(a**3*c**3)).subs(a**4*c**3*A**3/b**4, z) == \ + b*A**3/(a**3*c**3) + assert (6*x).subs(2*x, y) == 3*y + assert (y*exp(x*Rational(3, 2))).subs(y*exp(x), 2) == 2*exp(x/2) + assert (y*exp(x*Rational(3, 2))).subs(y*exp(x), 2) == 2*exp(x/2) + assert (A**2*B*A**2*B*A**2).subs(A*B*A, C) == A*C**2*A + assert (x*A**3).subs(x*A, y) == y*A**2 + assert (x**2*A**3).subs(x*A, y) == y**2*A + assert (x*A**3).subs(x*A, B) == B*A**2 + assert (x*A*B*A*exp(x*A*B)).subs(x*A, B) == B**2*A*exp(B*B) + assert (x**2*A*B*A*exp(x*A*B)).subs(x*A, B) == B**3*exp(B**2) + assert (x**3*A*exp(x*A*B)*A*exp(x*A*B)).subs(x*A, B) == \ + x*B*exp(B**2)*B*exp(B**2) + assert (x*A*B*C*A*B).subs(x*A*B, C) == C**2*A*B + assert (-I*a*b).subs(a*b, 2) == -2*I + + # issue 6361 + assert (-8*I*a).subs(-2*a, 1) == 4*I + assert (-I*a).subs(-a, 1) == I + + # issue 6441 + assert (4*x**2).subs(2*x, y) == y**2 + assert (2*4*x**2).subs(2*x, y) == 2*y**2 + assert (-x**3/9).subs(-x/3, z) == -z**2*x + assert (-x**3/9).subs(x/3, z) == -z**2*x + assert (-2*x**3/9).subs(x/3, z) == -2*x*z**2 + assert (-2*x**3/9).subs(-x/3, z) == -2*x*z**2 + assert (-2*x**3/9).subs(-2*x, z) == z*x**2/9 + assert (-2*x**3/9).subs(2*x, z) == -z*x**2/9 + assert (2*(3*x/5/7)**2).subs(3*x/5, z) == 2*(Rational(1, 7))**2*z**2 + assert (4*x).subs(-2*x, z) == 4*x # try keep subs literal + + +def test_subs_simple(): + a = symbols('a', commutative=True) + x = symbols('x', commutative=False) + + assert (2*a).subs(1, 3) == 2*a + assert (2*a).subs(2, 3) == 3*a + assert (2*a).subs(a, 3) == 6 + assert sin(2).subs(1, 3) == sin(2) + assert sin(2).subs(2, 3) == sin(3) + assert sin(a).subs(a, 3) == sin(3) + + assert (2*x).subs(1, 3) == 2*x + assert (2*x).subs(2, 3) == 3*x + assert (2*x).subs(x, 3) == 6 + assert sin(x).subs(x, 3) == sin(3) + + +def test_subs_constants(): + a, b = symbols('a b', commutative=True) + x, y = symbols('x y', commutative=False) + + assert (a*b).subs(2*a, 1) == a*b + assert (1.5*a*b).subs(a, 1) == 1.5*b + assert (2*a*b).subs(2*a, 1) == b + assert (2*a*b).subs(4*a, 1) == 2*a*b + + assert (x*y).subs(2*x, 1) == x*y + assert (1.5*x*y).subs(x, 1) == 1.5*y + assert (2*x*y).subs(2*x, 1) == y + assert (2*x*y).subs(4*x, 1) == 2*x*y + + +def test_subs_commutative(): + a, b, c, d, K = symbols('a b c d K', commutative=True) + + assert (a*b).subs(a*b, K) == K + assert (a*b*a*b).subs(a*b, K) == K**2 + assert (a*a*b*b).subs(a*b, K) == K**2 + assert (a*b*c*d).subs(a*b*c, K) == d*K + assert (a*b**c).subs(a, K) == K*b**c + assert (a*b**c).subs(b, K) == a*K**c + assert (a*b**c).subs(c, K) == a*b**K + assert (a*b*c*b*a).subs(a*b, K) == c*K**2 + assert (a**3*b**2*a).subs(a*b, K) == a**2*K**2 + + +def test_subs_noncommutative(): + w, x, y, z, L = symbols('w x y z L', commutative=False) + alpha = symbols('alpha', commutative=True) + someint = symbols('someint', commutative=True, integer=True) + + assert (x*y).subs(x*y, L) == L + assert (w*y*x).subs(x*y, L) == w*y*x + assert (w*x*y*z).subs(x*y, L) == w*L*z + assert (x*y*x*y).subs(x*y, L) == L**2 + assert (x*x*y).subs(x*y, L) == x*L + assert (x*x*y*y).subs(x*y, L) == x*L*y + assert (w*x*y).subs(x*y*z, L) == w*x*y + assert (x*y**z).subs(x, L) == L*y**z + assert (x*y**z).subs(y, L) == x*L**z + assert (x*y**z).subs(z, L) == x*y**L + assert (w*x*y*z*x*y).subs(x*y*z, L) == w*L*x*y + assert (w*x*y*y*w*x*x*y*x*y*y*x*y).subs(x*y, L) == w*L*y*w*x*L**2*y*L + + # Check fractional power substitutions. It should not do + # substitutions that choose a value for noncommutative log, + # or inverses that don't already appear in the expressions. + assert (x*x*x).subs(x*x, L) == L*x + assert (x*x*x*y*x*x*x*x).subs(x*x, L) == L*x*y*L**2 + for p in range(1, 5): + for k in range(10): + assert (y * x**k).subs(x**p, L) == y * L**(k//p) * x**(k % p) + assert (x**Rational(3, 2)).subs(x**S.Half, L) == x**Rational(3, 2) + assert (x**S.Half).subs(x**S.Half, L) == L + assert (x**Rational(-1, 2)).subs(x**S.Half, L) == x**Rational(-1, 2) + assert (x**Rational(-1, 2)).subs(x**Rational(-1, 2), L) == L + + assert (x**(2*someint)).subs(x**someint, L) == L**2 + assert (x**(2*someint + 3)).subs(x**someint, L) == L**2*x**3 + assert (x**(3*someint + 3)).subs(x**someint, L) == L**3*x**3 + assert (x**(3*someint)).subs(x**(2*someint), L) == L * x**someint + assert (x**(4*someint)).subs(x**(2*someint), L) == L**2 + assert (x**(4*someint + 1)).subs(x**(2*someint), L) == L**2 * x + assert (x**(4*someint)).subs(x**(3*someint), L) == L * x**someint + assert (x**(4*someint + 1)).subs(x**(3*someint), L) == L * x**(someint + 1) + + assert (x**(2*alpha)).subs(x**alpha, L) == x**(2*alpha) + assert (x**(2*alpha + 2)).subs(x**2, L) == x**(2*alpha + 2) + assert ((2*z)**alpha).subs(z**alpha, y) == (2*z)**alpha + assert (x**(2*someint*alpha)).subs(x**someint, L) == x**(2*someint*alpha) + assert (x**(2*someint + alpha)).subs(x**someint, L) == x**(2*someint + alpha) + + # This could in principle be substituted, but is not currently + # because it requires recognizing that someint**2 is divisible by + # someint. + assert (x**(someint**2 + 3)).subs(x**someint, L) == x**(someint**2 + 3) + + # alpha**z := exp(log(alpha) z) is usually well-defined + assert (4**z).subs(2**z, y) == y**2 + + # Negative powers + assert (x**(-1)).subs(x**3, L) == x**(-1) + assert (x**(-2)).subs(x**3, L) == x**(-2) + assert (x**(-3)).subs(x**3, L) == L**(-1) + assert (x**(-4)).subs(x**3, L) == L**(-1) * x**(-1) + assert (x**(-5)).subs(x**3, L) == L**(-1) * x**(-2) + + assert (x**(-1)).subs(x**(-3), L) == x**(-1) + assert (x**(-2)).subs(x**(-3), L) == x**(-2) + assert (x**(-3)).subs(x**(-3), L) == L + assert (x**(-4)).subs(x**(-3), L) == L * x**(-1) + assert (x**(-5)).subs(x**(-3), L) == L * x**(-2) + + assert (x**1).subs(x**(-3), L) == x + assert (x**2).subs(x**(-3), L) == x**2 + assert (x**3).subs(x**(-3), L) == L**(-1) + assert (x**4).subs(x**(-3), L) == L**(-1) * x + assert (x**5).subs(x**(-3), L) == L**(-1) * x**2 + + +def test_subs_basic_funcs(): + a, b, c, d, K = symbols('a b c d K', commutative=True) + w, x, y, z, L = symbols('w x y z L', commutative=False) + + assert (x + y).subs(x + y, L) == L + assert (x - y).subs(x - y, L) == L + assert (x/y).subs(x, L) == L/y + assert (x**y).subs(x, L) == L**y + assert (x**y).subs(y, L) == x**L + assert ((a - c)/b).subs(b, K) == (a - c)/K + assert (exp(x*y - z)).subs(x*y, L) == exp(L - z) + assert (a*exp(x*y - w*z) + b*exp(x*y + w*z)).subs(z, 0) == \ + a*exp(x*y) + b*exp(x*y) + assert ((a - b)/(c*d - a*b)).subs(c*d - a*b, K) == (a - b)/K + assert (w*exp(a*b - c)*x*y/4).subs(x*y, L) == w*exp(a*b - c)*L/4 + + +def test_subs_wild(): + R, S, T, U = symbols('R S T U', cls=Wild) + + assert (R*S).subs(R*S, T) == T + assert (S*R).subs(R*S, T) == T + assert (R + S).subs(R + S, T) == T + assert (R**S).subs(R, T) == T**S + assert (R**S).subs(S, T) == R**T + assert (R*S**T).subs(R, U) == U*S**T + assert (R*S**T).subs(S, U) == R*U**T + assert (R*S**T).subs(T, U) == R*S**U + + +def test_subs_mixed(): + a, b, c, d, K = symbols('a b c d K', commutative=True) + w, x, y, z, L = symbols('w x y z L', commutative=False) + R, S, T, U = symbols('R S T U', cls=Wild) + + assert (a*x*y).subs(x*y, L) == a*L + assert (a*b*x*y*x).subs(x*y, L) == a*b*L*x + assert (R*x*y*exp(x*y)).subs(x*y, L) == R*L*exp(L) + assert (a*x*y*y*x - x*y*z*exp(a*b)).subs(x*y, L) == a*L*y*x - L*z*exp(a*b) + e = c*y*x*y*x**(R*S - a*b) - T*(a*R*b*S) + assert e.subs(x*y, L).subs(a*b, K).subs(R*S, U) == \ + c*y*L*x**(U - K) - T*(U*K) + + +def test_division(): + a, b, c = symbols('a b c', commutative=True) + x, y, z = symbols('x y z', commutative=True) + + assert (1/a).subs(a, c) == 1/c + assert (1/a**2).subs(a, c) == 1/c**2 + assert (1/a**2).subs(a, -2) == Rational(1, 4) + assert (-(1/a**2)).subs(a, -2) == Rational(-1, 4) + + assert (1/x).subs(x, z) == 1/z + assert (1/x**2).subs(x, z) == 1/z**2 + assert (1/x**2).subs(x, -2) == Rational(1, 4) + assert (-(1/x**2)).subs(x, -2) == Rational(-1, 4) + + #issue 5360 + assert (1/x).subs(x, 0) == 1/S.Zero + + +def test_add(): + a, b, c, d, x, y, t = symbols('a b c d x y t') + + assert (a**2 - b - c).subs(a**2 - b, d) in [d - c, a**2 - b - c] + assert (a**2 - c).subs(a**2 - c, d) == d + assert (a**2 - b - c).subs(a**2 - c, d) in [d - b, a**2 - b - c] + assert (a**2 - x - c).subs(a**2 - c, d) in [d - x, a**2 - x - c] + assert (a**2 - b - sqrt(a)).subs(a**2 - sqrt(a), c) == c - b + assert (a + b + exp(a + b)).subs(a + b, c) == c + exp(c) + assert (c + b + exp(c + b)).subs(c + b, a) == a + exp(a) + assert (a + b + c + d).subs(b + c, x) == a + d + x + assert (a + b + c + d).subs(-b - c, x) == a + d - x + assert ((x + 1)*y).subs(x + 1, t) == t*y + assert ((-x - 1)*y).subs(x + 1, t) == -t*y + assert ((x - 1)*y).subs(x + 1, t) == y*(t - 2) + assert ((-x + 1)*y).subs(x + 1, t) == y*(-t + 2) + + # this should work every time: + e = a**2 - b - c + assert e.subs(Add(*e.args[:2]), d) == d + e.args[2] + assert e.subs(a**2 - c, d) == d - b + + # the fallback should recognize when a change has + # been made; while .1 == Rational(1, 10) they are not the same + # and the change should be made + assert (0.1 + a).subs(0.1, Rational(1, 10)) == Rational(1, 10) + a + + e = (-x*(-y + 1) - y*(y - 1)) + ans = (-x*(x) - y*(-x)).expand() + assert e.subs(-y + 1, x) == ans + + #Test issue 18747 + assert (exp(x) + cos(x)).subs(x, oo) == oo + assert Add(*[AccumBounds(-1, 1), oo]) == oo + assert Add(*[oo, AccumBounds(-1, 1)]) == oo + + +def test_subs_issue_4009(): + assert (I*Symbol('a')).subs(1, 2) == I*Symbol('a') + + +def test_functions_subs(): + f, g = symbols('f g', cls=Function) + l = Lambda((x, y), sin(x) + y) + assert (g(y, x) + cos(x)).subs(g, l) == sin(y) + x + cos(x) + assert (f(x)**2).subs(f, sin) == sin(x)**2 + assert (f(x, y)).subs(f, log) == log(x, y) + assert (f(x, y)).subs(f, sin) == f(x, y) + assert (sin(x) + atan2(x, y)).subs([[atan2, f], [sin, g]]) == \ + f(x, y) + g(x) + assert (g(f(x + y, x))).subs([[f, l], [g, exp]]) == exp(x + sin(x + y)) + + +def test_derivative_subs(): + f = Function('f') + g = Function('g') + assert Derivative(f(x), x).subs(f(x), y) != 0 + # need xreplace to put the function back, see #13803 + assert Derivative(f(x), x).subs(f(x), y).xreplace({y: f(x)}) == \ + Derivative(f(x), x) + # issues 5085, 5037 + assert cse(Derivative(f(x), x) + f(x))[1][0].has(Derivative) + assert cse(Derivative(f(x, y), x) + + Derivative(f(x, y), y))[1][0].has(Derivative) + eq = Derivative(g(x), g(x)) + assert eq.subs(g, f) == Derivative(f(x), f(x)) + assert eq.subs(g(x), f(x)) == Derivative(f(x), f(x)) + assert eq.subs(g, cos) == Subs(Derivative(y, y), y, cos(x)) + + +def test_derivative_subs2(): + f_func, g_func = symbols('f g', cls=Function) + f, g = f_func(x, y, z), g_func(x, y, z) + assert Derivative(f, x, y).subs(Derivative(f, x, y), g) == g + assert Derivative(f, y, x).subs(Derivative(f, x, y), g) == g + assert Derivative(f, x, y).subs(Derivative(f, x), g) == Derivative(g, y) + assert Derivative(f, x, y).subs(Derivative(f, y), g) == Derivative(g, x) + assert (Derivative(f, x, y, z).subs( + Derivative(f, x, z), g) == Derivative(g, y)) + assert (Derivative(f, x, y, z).subs( + Derivative(f, z, y), g) == Derivative(g, x)) + assert (Derivative(f, x, y, z).subs( + Derivative(f, z, y, x), g) == g) + + # Issue 9135 + assert (Derivative(f, x, x, y).subs( + Derivative(f, y, y), g) == Derivative(f, x, x, y)) + assert (Derivative(f, x, y, y, z).subs( + Derivative(f, x, y, y, y), g) == Derivative(f, x, y, y, z)) + + assert Derivative(f, x, y).subs(Derivative(f_func(x), x, y), g) == Derivative(f, x, y) + + +def test_derivative_subs3(): + dex = Derivative(exp(x), x) + assert Derivative(dex, x).subs(dex, exp(x)) == dex + assert dex.subs(exp(x), dex) == Derivative(exp(x), x, x) + + +def test_issue_5284(): + A, B = symbols('A B', commutative=False) + assert (x*A).subs(x**2*A, B) == x*A + assert (A**2).subs(A**3, B) == A**2 + assert (A**6).subs(A**3, B) == B**2 + + +def test_subs_iter(): + assert x.subs(reversed([[x, y]])) == y + it = iter([[x, y]]) + assert x.subs(it) == y + assert x.subs(Tuple((x, y))) == y + + +def test_subs_dict(): + a, b, c, d, e = symbols('a b c d e') + + assert (2*x + y + z).subs({"x": 1, "y": 2}) == 4 + z + + l = [(sin(x), 2), (x, 1)] + assert (sin(x)).subs(l) == \ + (sin(x)).subs(dict(l)) == 2 + assert sin(x).subs(reversed(l)) == sin(1) + + expr = sin(2*x) + sqrt(sin(2*x))*cos(2*x)*sin(exp(x)*x) + reps = {sin(2*x): c, + sqrt(sin(2*x)): a, + cos(2*x): b, + exp(x): e, + x: d,} + assert expr.subs(reps) == c + a*b*sin(d*e) + + l = [(x, 3), (y, x**2)] + assert (x + y).subs(l) == 3 + x**2 + assert (x + y).subs(reversed(l)) == 12 + + # If changes are made to convert lists into dictionaries and do + # a dictionary-lookup replacement, these tests will help to catch + # some logical errors that might occur + l = [(y, z + 2), (1 + z, 5), (z, 2)] + assert (y - 1 + 3*x).subs(l) == 5 + 3*x + l = [(y, z + 2), (z, 3)] + assert (y - 2).subs(l) == 3 + + +def test_no_arith_subs_on_floats(): + assert (x + 3).subs(x + 3, a) == a + assert (x + 3).subs(x + 2, a) == a + 1 + + assert (x + y + 3).subs(x + 3, a) == a + y + assert (x + y + 3).subs(x + 2, a) == a + y + 1 + + assert (x + 3.0).subs(x + 3.0, a) == a + assert (x + 3.0).subs(x + 2.0, a) == x + 3.0 + + assert (x + y + 3.0).subs(x + 3.0, a) == a + y + assert (x + y + 3.0).subs(x + 2.0, a) == x + y + 3.0 + + +def test_issue_5651(): + a, b, c, K = symbols('a b c K', commutative=True) + assert (a/(b*c)).subs(b*c, K) == a/K + assert (a/(b**2*c**3)).subs(b*c, K) == a/(c*K**2) + assert (1/(x*y)).subs(x*y, 2) == S.Half + assert ((1 + x*y)/(x*y)).subs(x*y, 1) == 2 + assert (x*y*z).subs(x*y, 2) == 2*z + assert ((1 + x*y)/(x*y)/z).subs(x*y, 1) == 2/z + + +def test_issue_6075(): + assert Tuple(1, True).subs(1, 2) == Tuple(2, True) + + +def test_issue_6079(): + # since x + 2.0 == x + 2 we can't do a simple equality test + assert _aresame((x + 2.0).subs(2, 3), x + 2.0) + assert _aresame((x + 2.0).subs(2.0, 3), x + 3) + assert not _aresame(x + 2, x + 2.0) + assert not _aresame(Basic(cos(x), S(1)), Basic(cos(x), S(1.))) + assert _aresame(cos, cos) + assert not _aresame(1, S.One) + assert not _aresame(x, symbols('x', positive=True)) + + +def test_issue_4680(): + N = Symbol('N') + assert N.subs({"N": 3}) == 3 + + +def test_issue_6158(): + assert (x - 1).subs(1, y) == x - y + assert (x - 1).subs(-1, y) == x + y + assert (x - oo).subs(oo, y) == x - y + assert (x - oo).subs(-oo, y) == x + y + + +def test_Function_subs(): + f, g, h, i = symbols('f g h i', cls=Function) + p = Piecewise((g(f(x, y)), x < -1), (g(x), x <= 1)) + assert p.subs(g, h) == Piecewise((h(f(x, y)), x < -1), (h(x), x <= 1)) + assert (f(y) + g(x)).subs({f: h, g: i}) == i(x) + h(y) + + +def test_simultaneous_subs(): + reps = {x: 0, y: 0} + assert (x/y).subs(reps) != (y/x).subs(reps) + assert (x/y).subs(reps, simultaneous=True) == \ + (y/x).subs(reps, simultaneous=True) + reps = reps.items() + assert (x/y).subs(reps) != (y/x).subs(reps) + assert (x/y).subs(reps, simultaneous=True) == \ + (y/x).subs(reps, simultaneous=True) + assert Derivative(x, y, z).subs(reps, simultaneous=True) == \ + Subs(Derivative(0, y, z), y, 0) + + +def test_issue_6419_6421(): + assert (1/(1 + x/y)).subs(x/y, x) == 1/(1 + x) + assert (-2*I).subs(2*I, x) == -x + assert (-I*x).subs(I*x, x) == -x + assert (-3*I*y**4).subs(3*I*y**2, x) == -x*y**2 + + +def test_issue_6559(): + assert (-12*x + y).subs(-x, 1) == 12 + y + # though this involves cse it generated a failure in Mul._eval_subs + x0, x1 = symbols('x0 x1') + e = -log(-12*sqrt(2) + 17)/24 - log(-2*sqrt(2) + 3)/12 + sqrt(2)/3 + # XXX modify cse so x1 is eliminated and x0 = -sqrt(2)? + assert cse(e) == ( + [(x0, sqrt(2))], [x0/3 - log(-12*x0 + 17)/24 - log(-2*x0 + 3)/12]) + + +def test_issue_5261(): + x = symbols('x', real=True) + e = I*x + assert exp(e).subs(exp(x), y) == y**I + assert (2**e).subs(2**x, y) == y**I + eq = (-2)**e + assert eq.subs((-2)**x, y) == eq + + +def test_issue_6923(): + assert (-2*x*sqrt(2)).subs(2*x, y) == -sqrt(2)*y + + +def test_2arg_hack(): + N = Symbol('N', commutative=False) + ans = Mul(2, y + 1, evaluate=False) + assert (2*x*(y + 1)).subs(x, 1, hack2=True) == ans + assert (2*(y + 1 + N)).subs(N, 0, hack2=True) == ans + + +@XFAIL +def test_mul2(): + """When this fails, remove things labelled "2-arg hack" + 1) remove special handling in the fallback of subs that + was added in the same commit as this test + 2) remove the special handling in Mul.flatten + """ + assert (2*(x + 1)).is_Mul + + +def test_noncommutative_subs(): + x,y = symbols('x,y', commutative=False) + assert (x*y*x).subs([(x, x*y), (y, x)], simultaneous=True) == (x*y*x**2*y) + + +def test_issue_2877(): + f = Float(2.0) + assert (x + f).subs({f: 2}) == x + 2 + + def r(a, b, c): + return factor(a*x**2 + b*x + c) + e = r(5.0/6, 10, 5) + assert nsimplify(e) == 5*x**2/6 + 10*x + 5 + + +def test_issue_5910(): + t = Symbol('t') + assert (1/(1 - t)).subs(t, 1) is zoo + n = t + d = t - 1 + assert (n/d).subs(t, 1) is zoo + assert (-n/-d).subs(t, 1) is zoo + + +def test_issue_5217(): + s = Symbol('s') + z = (1 - 2*x*x) + w = (1 + 2*x*x) + q = 2*x*x*2*y*y + sub = {2*x*x: s} + assert w.subs(sub) == 1 + s + assert z.subs(sub) == 1 - s + assert q == 4*x**2*y**2 + assert q.subs(sub) == 2*y**2*s + + +def test_issue_10829(): + assert (4**x).subs(2**x, y) == y**2 + assert (9**x).subs(3**x, y) == y**2 + + +def test_pow_eval_subs_no_cache(): + # Tests pull request 9376 is working + from sympy.core.cache import clear_cache + + s = 1/sqrt(x**2) + # This bug only appeared when the cache was turned off. + # We need to approximate running this test without the cache. + # This creates approximately the same situation. + clear_cache() + + # This used to fail with a wrong result. + # It incorrectly returned 1/sqrt(x**2) before this pull request. + result = s.subs(sqrt(x**2), y) + assert result == 1/y + + +def test_RootOf_issue_10092(): + x = Symbol('x', real=True) + eq = x**3 - 17*x**2 + 81*x - 118 + r = RootOf(eq, 0) + assert (x < r).subs(x, r) is S.false + + +def test_issue_8886(): + from sympy.physics.mechanics import ReferenceFrame as R + # if something can't be sympified we assume that it + # doesn't play well with SymPy and disallow the + # substitution + v = R('A').x + raises(SympifyError, lambda: x.subs(x, v)) + raises(SympifyError, lambda: v.subs(v, x)) + assert v.__eq__(x) is False + + +def test_issue_12657(): + # treat -oo like the atom that it is + reps = [(-oo, 1), (oo, 2)] + assert (x < -oo).subs(reps) == (x < 1) + assert (x < -oo).subs(list(reversed(reps))) == (x < 1) + reps = [(-oo, 2), (oo, 1)] + assert (x < oo).subs(reps) == (x < 1) + assert (x < oo).subs(list(reversed(reps))) == (x < 1) + + +def test_recurse_Application_args(): + F = Lambda((x, y), exp(2*x + 3*y)) + f = Function('f') + A = f(x, f(x, x)) + C = F(x, F(x, x)) + assert A.subs(f, F) == A.replace(f, F) == C + + +def test_Subs_subs(): + assert Subs(x*y, x, x).subs(x, y) == Subs(x*y, x, y) + assert Subs(x*y, x, x + 1).subs(x, y) == \ + Subs(x*y, x, y + 1) + assert Subs(x*y, y, x + 1).subs(x, y) == \ + Subs(y**2, y, y + 1) + a = Subs(x*y*z, (y, x, z), (x + 1, x + z, x)) + b = Subs(x*y*z, (y, x, z), (x + 1, y + z, y)) + assert a.subs(x, y) == b and \ + a.doit().subs(x, y) == a.subs(x, y).doit() + f = Function('f') + g = Function('g') + assert Subs(2*f(x, y) + g(x), f(x, y), 1).subs(y, 2) == Subs( + 2*f(x, y) + g(x), (f(x, y), y), (1, 2)) + + +def test_issue_13333(): + eq = 1/x + assert eq.subs({"x": '1/2'}) == 2 + assert eq.subs({"x": '(1/2)'}) == 2 + + +def test_issue_15234(): + x, y = symbols('x y', real=True) + p = 6*x**5 + x**4 - 4*x**3 + 4*x**2 - 2*x + 3 + p_subbed = 6*x**5 - 4*x**3 - 2*x + y**4 + 4*y**2 + 3 + assert p.subs([(x**i, y**i) for i in [2, 4]]) == p_subbed + x, y = symbols('x y', complex=True) + p = 6*x**5 + x**4 - 4*x**3 + 4*x**2 - 2*x + 3 + p_subbed = 6*x**5 - 4*x**3 - 2*x + y**4 + 4*y**2 + 3 + assert p.subs([(x**i, y**i) for i in [2, 4]]) == p_subbed + + +def test_issue_6976(): + x, y = symbols('x y') + assert (sqrt(x)**3 + sqrt(x) + x + x**2).subs(sqrt(x), y) == \ + y**4 + y**3 + y**2 + y + assert (x**4 + x**3 + x**2 + x + sqrt(x)).subs(x**2, y) == \ + sqrt(x) + x**3 + x + y**2 + y + assert x.subs(x**3, y) == x + assert x.subs(x**Rational(1, 3), y) == y**3 + + # More substitutions are possible with nonnegative symbols + x, y = symbols('x y', nonnegative=True) + assert (x**4 + x**3 + x**2 + x + sqrt(x)).subs(x**2, y) == \ + y**Rational(1, 4) + y**Rational(3, 2) + sqrt(y) + y**2 + y + assert x.subs(x**3, y) == y**Rational(1, 3) + + +def test_issue_11746(): + assert (1/x).subs(x**2, 1) == 1/x + assert (1/(x**3)).subs(x**2, 1) == x**(-3) + assert (1/(x**4)).subs(x**2, 1) == 1 + assert (1/(x**3)).subs(x**4, 1) == x**(-3) + assert (1/(y**5)).subs(x**5, 1) == y**(-5) + + +def test_issue_17823(): + from sympy.physics.mechanics import dynamicsymbols + q1, q2 = dynamicsymbols('q1, q2') + expr = q1.diff().diff()**2*q1 + q1.diff()*q2.diff() + reps={q1: a, q1.diff(): a*x*y, q1.diff().diff(): z} + assert expr.subs(reps) == a*x*y*Derivative(q2, t) + a*z**2 + + +def test_issue_19326(): + x, y = [i(t) for i in map(Function, 'xy')] + assert (x*y).subs({x: 1 + x, y: x}) == (1 + x)*x + + +def test_issue_19558(): + e = (7*x*cos(x) - 12*log(x)**3)*(-log(x)**4 + 2*sin(x) + 1)**2/ \ + (2*(x*cos(x) - 2*log(x)**3)*(3*log(x)**4 - 7*sin(x) + 3)**2) + + assert e.subs(x, oo) == AccumBounds(-oo, oo) + assert (sin(x) + cos(x)).subs(x, oo) == AccumBounds(-2, 2) + + +def test_issue_22033(): + xr = Symbol('xr', real=True) + e = (1/xr) + assert e.subs(xr**2, y) == e + + +def test_guard_against_indeterminate_evaluation(): + eq = x**y + assert eq.subs([(x, 1), (y, oo)]) == 1 # because 1**y == 1 + assert eq.subs([(y, oo), (x, 1)]) is S.NaN + assert eq.subs({x: 1, y: oo}) is S.NaN + assert eq.subs([(x, 1), (y, oo)], simultaneous=True) is S.NaN diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_symbol.py b/lib/python3.11/site-packages/sympy/core/tests/test_symbol.py new file mode 100644 index 0000000000000000000000000000000000000000..acf27700825c4822456207afe95108480505ce2c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_symbol.py @@ -0,0 +1,421 @@ +import threading + +from sympy.core.function import Function, UndefinedFunction +from sympy.core.numbers import (I, Rational, pi) +from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan) +from sympy.core.symbol import (Dummy, Symbol, Wild, symbols) +from sympy.core.sympify import sympify # can't import as S yet +from sympy.core.symbol import uniquely_named_symbol, _symbol, Str + +from sympy.testing.pytest import raises, skip_under_pyodide +from sympy.core.symbol import disambiguate + + +def test_Str(): + a1 = Str('a') + a2 = Str('a') + b = Str('b') + assert a1 == a2 != b + raises(TypeError, lambda: Str()) + + +def test_Symbol(): + a = Symbol("a") + x1 = Symbol("x") + x2 = Symbol("x") + xdummy1 = Dummy("x") + xdummy2 = Dummy("x") + + assert a != x1 + assert a != x2 + assert x1 == x2 + assert x1 != xdummy1 + assert xdummy1 != xdummy2 + + assert Symbol("x") == Symbol("x") + assert Dummy("x") != Dummy("x") + d = symbols('d', cls=Dummy) + assert isinstance(d, Dummy) + c, d = symbols('c,d', cls=Dummy) + assert isinstance(c, Dummy) + assert isinstance(d, Dummy) + raises(TypeError, lambda: Symbol()) + + +def test_Dummy(): + assert Dummy() != Dummy() + + +def test_Dummy_force_dummy_index(): + raises(AssertionError, lambda: Dummy(dummy_index=1)) + assert Dummy('d', dummy_index=2) == Dummy('d', dummy_index=2) + assert Dummy('d1', dummy_index=2) != Dummy('d2', dummy_index=2) + d1 = Dummy('d', dummy_index=3) + d2 = Dummy('d') + # might fail if d1 were created with dummy_index >= 10**6 + assert d1 != d2 + d3 = Dummy('d', dummy_index=3) + assert d1 == d3 + assert Dummy()._count == Dummy('d', dummy_index=3)._count + + +def test_lt_gt(): + S = sympify + x, y = Symbol('x'), Symbol('y') + + assert (x >= y) == GreaterThan(x, y) + assert (x >= 0) == GreaterThan(x, 0) + assert (x <= y) == LessThan(x, y) + assert (x <= 0) == LessThan(x, 0) + + assert (0 <= x) == GreaterThan(x, 0) + assert (0 >= x) == LessThan(x, 0) + assert (S(0) >= x) == GreaterThan(0, x) + assert (S(0) <= x) == LessThan(0, x) + + assert (x > y) == StrictGreaterThan(x, y) + assert (x > 0) == StrictGreaterThan(x, 0) + assert (x < y) == StrictLessThan(x, y) + assert (x < 0) == StrictLessThan(x, 0) + + assert (0 < x) == StrictGreaterThan(x, 0) + assert (0 > x) == StrictLessThan(x, 0) + assert (S(0) > x) == StrictGreaterThan(0, x) + assert (S(0) < x) == StrictLessThan(0, x) + + e = x**2 + 4*x + 1 + assert (e >= 0) == GreaterThan(e, 0) + assert (0 <= e) == GreaterThan(e, 0) + assert (e > 0) == StrictGreaterThan(e, 0) + assert (0 < e) == StrictGreaterThan(e, 0) + + assert (e <= 0) == LessThan(e, 0) + assert (0 >= e) == LessThan(e, 0) + assert (e < 0) == StrictLessThan(e, 0) + assert (0 > e) == StrictLessThan(e, 0) + + assert (S(0) >= e) == GreaterThan(0, e) + assert (S(0) <= e) == LessThan(0, e) + assert (S(0) < e) == StrictLessThan(0, e) + assert (S(0) > e) == StrictGreaterThan(0, e) + + +def test_no_len(): + # there should be no len for numbers + x = Symbol('x') + raises(TypeError, lambda: len(x)) + + +def test_ineq_unequal(): + S = sympify + x, y, z = symbols('x,y,z') + + e = ( + S(-1) >= x, S(-1) >= y, S(-1) >= z, + S(-1) > x, S(-1) > y, S(-1) > z, + S(-1) <= x, S(-1) <= y, S(-1) <= z, + S(-1) < x, S(-1) < y, S(-1) < z, + S(0) >= x, S(0) >= y, S(0) >= z, + S(0) > x, S(0) > y, S(0) > z, + S(0) <= x, S(0) <= y, S(0) <= z, + S(0) < x, S(0) < y, S(0) < z, + S('3/7') >= x, S('3/7') >= y, S('3/7') >= z, + S('3/7') > x, S('3/7') > y, S('3/7') > z, + S('3/7') <= x, S('3/7') <= y, S('3/7') <= z, + S('3/7') < x, S('3/7') < y, S('3/7') < z, + S(1.5) >= x, S(1.5) >= y, S(1.5) >= z, + S(1.5) > x, S(1.5) > y, S(1.5) > z, + S(1.5) <= x, S(1.5) <= y, S(1.5) <= z, + S(1.5) < x, S(1.5) < y, S(1.5) < z, + S(2) >= x, S(2) >= y, S(2) >= z, + S(2) > x, S(2) > y, S(2) > z, + S(2) <= x, S(2) <= y, S(2) <= z, + S(2) < x, S(2) < y, S(2) < z, + x >= -1, y >= -1, z >= -1, + x > -1, y > -1, z > -1, + x <= -1, y <= -1, z <= -1, + x < -1, y < -1, z < -1, + x >= 0, y >= 0, z >= 0, + x > 0, y > 0, z > 0, + x <= 0, y <= 0, z <= 0, + x < 0, y < 0, z < 0, + x >= 1.5, y >= 1.5, z >= 1.5, + x > 1.5, y > 1.5, z > 1.5, + x <= 1.5, y <= 1.5, z <= 1.5, + x < 1.5, y < 1.5, z < 1.5, + x >= 2, y >= 2, z >= 2, + x > 2, y > 2, z > 2, + x <= 2, y <= 2, z <= 2, + x < 2, y < 2, z < 2, + + x >= y, x >= z, y >= x, y >= z, z >= x, z >= y, + x > y, x > z, y > x, y > z, z > x, z > y, + x <= y, x <= z, y <= x, y <= z, z <= x, z <= y, + x < y, x < z, y < x, y < z, z < x, z < y, + + x - pi >= y + z, y - pi >= x + z, z - pi >= x + y, + x - pi > y + z, y - pi > x + z, z - pi > x + y, + x - pi <= y + z, y - pi <= x + z, z - pi <= x + y, + x - pi < y + z, y - pi < x + z, z - pi < x + y, + True, False + ) + + left_e = e[:-1] + for i, e1 in enumerate( left_e ): + for e2 in e[i + 1:]: + assert e1 != e2 + + +def test_Wild_properties(): + S = sympify + # these tests only include Atoms + x = Symbol("x") + y = Symbol("y") + p = Symbol("p", positive=True) + k = Symbol("k", integer=True) + n = Symbol("n", integer=True, positive=True) + + given_patterns = [ x, y, p, k, -k, n, -n, S(-3), S(3), + pi, Rational(3, 2), I ] + + integerp = lambda k: k.is_integer + positivep = lambda k: k.is_positive + symbolp = lambda k: k.is_Symbol + realp = lambda k: k.is_extended_real + + S = Wild("S", properties=[symbolp]) + R = Wild("R", properties=[realp]) + Y = Wild("Y", exclude=[x, p, k, n]) + P = Wild("P", properties=[positivep]) + K = Wild("K", properties=[integerp]) + N = Wild("N", properties=[positivep, integerp]) + + given_wildcards = [ S, R, Y, P, K, N ] + + goodmatch = { + S: (x, y, p, k, n), + R: (p, k, -k, n, -n, -3, 3, pi, Rational(3, 2)), + Y: (y, -3, 3, pi, Rational(3, 2), I ), + P: (p, n, 3, pi, Rational(3, 2)), + K: (k, -k, n, -n, -3, 3), + N: (n, 3)} + + for A in given_wildcards: + for pat in given_patterns: + d = pat.match(A) + if pat in goodmatch[A]: + assert d[A] in goodmatch[A] + else: + assert d is None + + +def test_symbols(): + x = Symbol('x') + y = Symbol('y') + z = Symbol('z') + + assert symbols('x') == x + assert symbols('x ') == x + assert symbols(' x ') == x + assert symbols('x,') == (x,) + assert symbols('x, ') == (x,) + assert symbols('x ,') == (x,) + + assert symbols('x , y') == (x, y) + + assert symbols('x,y,z') == (x, y, z) + assert symbols('x y z') == (x, y, z) + + assert symbols('x,y,z,') == (x, y, z) + assert symbols('x y z ') == (x, y, z) + + xyz = Symbol('xyz') + abc = Symbol('abc') + + assert symbols('xyz') == xyz + assert symbols('xyz,') == (xyz,) + assert symbols('xyz,abc') == (xyz, abc) + + assert symbols(('xyz',)) == (xyz,) + assert symbols(('xyz,',)) == ((xyz,),) + assert symbols(('x,y,z,',)) == ((x, y, z),) + assert symbols(('xyz', 'abc')) == (xyz, abc) + assert symbols(('xyz,abc',)) == ((xyz, abc),) + assert symbols(('xyz,abc', 'x,y,z')) == ((xyz, abc), (x, y, z)) + + assert symbols(('x', 'y', 'z')) == (x, y, z) + assert symbols(['x', 'y', 'z']) == [x, y, z] + assert symbols({'x', 'y', 'z'}) == {x, y, z} + + raises(ValueError, lambda: symbols('')) + raises(ValueError, lambda: symbols(',')) + raises(ValueError, lambda: symbols('x,,y,,z')) + raises(ValueError, lambda: symbols(('x', '', 'y', '', 'z'))) + + a, b = symbols('x,y', real=True) + assert a.is_real and b.is_real + + x0 = Symbol('x0') + x1 = Symbol('x1') + x2 = Symbol('x2') + + y0 = Symbol('y0') + y1 = Symbol('y1') + + assert symbols('x0:0') == () + assert symbols('x0:1') == (x0,) + assert symbols('x0:2') == (x0, x1) + assert symbols('x0:3') == (x0, x1, x2) + + assert symbols('x:0') == () + assert symbols('x:1') == (x0,) + assert symbols('x:2') == (x0, x1) + assert symbols('x:3') == (x0, x1, x2) + + assert symbols('x1:1') == () + assert symbols('x1:2') == (x1,) + assert symbols('x1:3') == (x1, x2) + + assert symbols('x1:3,x,y,z') == (x1, x2, x, y, z) + + assert symbols('x:3,y:2') == (x0, x1, x2, y0, y1) + assert symbols(('x:3', 'y:2')) == ((x0, x1, x2), (y0, y1)) + + a = Symbol('a') + b = Symbol('b') + c = Symbol('c') + d = Symbol('d') + + assert symbols('x:z') == (x, y, z) + assert symbols('a:d,x:z') == (a, b, c, d, x, y, z) + assert symbols(('a:d', 'x:z')) == ((a, b, c, d), (x, y, z)) + + aa = Symbol('aa') + ab = Symbol('ab') + ac = Symbol('ac') + ad = Symbol('ad') + + assert symbols('aa:d') == (aa, ab, ac, ad) + assert symbols('aa:d,x:z') == (aa, ab, ac, ad, x, y, z) + assert symbols(('aa:d','x:z')) == ((aa, ab, ac, ad), (x, y, z)) + + assert type(symbols(('q:2', 'u:2'), cls=Function)[0][0]) == UndefinedFunction # issue 23532 + + # issue 6675 + def sym(s): + return str(symbols(s)) + assert sym('a0:4') == '(a0, a1, a2, a3)' + assert sym('a2:4,b1:3') == '(a2, a3, b1, b2)' + assert sym('a1(2:4)') == '(a12, a13)' + assert sym('a0:2.0:2') == '(a0.0, a0.1, a1.0, a1.1)' + assert sym('aa:cz') == '(aaz, abz, acz)' + assert sym('aa:c0:2') == '(aa0, aa1, ab0, ab1, ac0, ac1)' + assert sym('aa:ba:b') == '(aaa, aab, aba, abb)' + assert sym('a:3b') == '(a0b, a1b, a2b)' + assert sym('a-1:3b') == '(a-1b, a-2b)' + assert sym(r'a:2\,:2' + chr(0)) == '(a0,0%s, a0,1%s, a1,0%s, a1,1%s)' % ( + (chr(0),)*4) + assert sym('x(:a:3)') == '(x(a0), x(a1), x(a2))' + assert sym('x(:c):1') == '(xa0, xb0, xc0)' + assert sym('x((:a)):3') == '(x(a)0, x(a)1, x(a)2)' + assert sym('x(:a:3') == '(x(a0, x(a1, x(a2)' + assert sym(':2') == '(0, 1)' + assert sym(':b') == '(a, b)' + assert sym(':b:2') == '(a0, a1, b0, b1)' + assert sym(':2:2') == '(00, 01, 10, 11)' + assert sym(':b:b') == '(aa, ab, ba, bb)' + + raises(ValueError, lambda: symbols(':')) + raises(ValueError, lambda: symbols('a:')) + raises(ValueError, lambda: symbols('::')) + raises(ValueError, lambda: symbols('a::')) + raises(ValueError, lambda: symbols(':a:')) + raises(ValueError, lambda: symbols('::a')) + + +def test_symbols_become_functions_issue_3539(): + from sympy.abc import alpha, phi, beta, t + raises(TypeError, lambda: beta(2)) + raises(TypeError, lambda: beta(2.5)) + raises(TypeError, lambda: phi(2.5)) + raises(TypeError, lambda: alpha(2.5)) + raises(TypeError, lambda: phi(t)) + + +def test_unicode(): + xu = Symbol('x') + x = Symbol('x') + assert x == xu + + raises(TypeError, lambda: Symbol(1)) + + +def test_uniquely_named_symbol_and_Symbol(): + F = uniquely_named_symbol + x = Symbol('x') + assert F(x) == x + assert F('x') == x + assert str(F('x', x)) == 'x0' + assert str(F('x', (x + 1, 1/x))) == 'x0' + _x = Symbol('x', real=True) + assert F(('x', _x)) == _x + assert F((x, _x)) == _x + assert F('x', real=True).is_real + y = Symbol('y') + assert F(('x', y), real=True).is_real + r = Symbol('x', real=True) + assert F(('x', r)).is_real + assert F(('x', r), real=False).is_real + assert F('x1', Symbol('x1'), + compare=lambda i: str(i).rstrip('1')).name == 'x0' + assert F('x1', Symbol('x1'), + modify=lambda i: i + '_').name == 'x1_' + assert _symbol(x, _x) == x + + +def test_disambiguate(): + x, y, y_1, _x, x_1, x_2 = symbols('x y y_1 _x x_1 x_2') + t1 = Dummy('y'), _x, Dummy('x'), Dummy('x') + t2 = Dummy('x'), Dummy('x') + t3 = Dummy('x'), Dummy('y') + t4 = x, Dummy('x') + t5 = Symbol('x', integer=True), x, Symbol('x_1') + + assert disambiguate(*t1) == (y, x_2, x, x_1) + assert disambiguate(*t2) == (x, x_1) + assert disambiguate(*t3) == (x, y) + assert disambiguate(*t4) == (x_1, x) + assert disambiguate(*t5) == (t5[0], x_2, x_1) + assert disambiguate(*t5)[0] != x # assumptions are retained + + t6 = _x, Dummy('x')/y + t7 = y*Dummy('y'), y + + assert disambiguate(*t6) == (x_1, x/y) + assert disambiguate(*t7) == (y*y_1, y_1) + assert disambiguate(Dummy('x_1'), Dummy('x_1') + ) == (x_1, Symbol('x_1_1')) + + +@skip_under_pyodide("Cannot create threads under pyodide.") +def test_issue_gh_16734(): + # https://github.com/sympy/sympy/issues/16734 + + syms = list(symbols('x, y')) + + def thread1(): + for n in range(1000): + syms[0], syms[1] = symbols(f'x{n}, y{n}') + syms[0].is_positive # Check an assumption in this thread. + syms[0] = None + + def thread2(): + while syms[0] is not None: + # Compare the symbol in this thread. + result = (syms[0] == syms[1]) # noqa + + # Previously this would be very likely to raise an exception: + thread = threading.Thread(target=thread1) + thread.start() + thread2() + thread.join() diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_sympify.py b/lib/python3.11/site-packages/sympy/core/tests/test_sympify.py new file mode 100644 index 0000000000000000000000000000000000000000..8cd0787bc6f5320c6be1cf3279c82cbff3ab97ce --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_sympify.py @@ -0,0 +1,885 @@ +from sympy.core.add import Add +from sympy.core.containers import Tuple +from sympy.core.function import (Function, Lambda) +from sympy.core.mul import Mul +from sympy.core.numbers import (Float, I, Integer, Rational, pi, oo) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.logic.boolalg import (false, Or, true, Xor) +from sympy.matrices.dense import Matrix +from sympy.parsing.sympy_parser import null +from sympy.polys.polytools import Poly +from sympy.printing.repr import srepr +from sympy.sets.fancysets import Range +from sympy.sets.sets import Interval +from sympy.abc import x, y +from sympy.core.sympify import (sympify, _sympify, SympifyError, kernS, + CantSympify, converter) +from sympy.core.decorators import _sympifyit +from sympy.external import import_module +from sympy.testing.pytest import raises, XFAIL, skip +from sympy.utilities.decorator import conserve_mpmath_dps +from sympy.geometry import Point, Line +from sympy.functions.combinatorial.factorials import factorial, factorial2 +from sympy.abc import _clash, _clash1, _clash2 +from sympy.external.gmpy import gmpy as _gmpy, flint as _flint +from sympy.sets import FiniteSet, EmptySet +from sympy.tensor.array.dense_ndim_array import ImmutableDenseNDimArray + +import mpmath +from collections import defaultdict, OrderedDict + + +numpy = import_module('numpy') + + +def test_issue_3538(): + v = sympify("exp(x)") + assert v == exp(x) + assert type(v) == type(exp(x)) + assert str(type(v)) == str(type(exp(x))) + + +def test_sympify1(): + assert sympify("x") == Symbol("x") + assert sympify(" x") == Symbol("x") + assert sympify(" x ") == Symbol("x") + # issue 4877 + assert sympify('--.5') == 0.5 + assert sympify('-1/2') == -S.Half + assert sympify('-+--.5') == -0.5 + assert sympify('-.[3]') == Rational(-1, 3) + assert sympify('.[3]') == Rational(1, 3) + assert sympify('+.[3]') == Rational(1, 3) + assert sympify('+0.[3]*10**-2') == Rational(1, 300) + assert sympify('.[052631578947368421]') == Rational(1, 19) + assert sympify('.0[526315789473684210]') == Rational(1, 19) + assert sympify('.034[56]') == Rational(1711, 49500) + # options to make reals into rationals + assert sympify('1.22[345]', rational=True) == \ + 1 + Rational(22, 100) + Rational(345, 99900) + assert sympify('2/2.6', rational=True) == Rational(10, 13) + assert sympify('2.6/2', rational=True) == Rational(13, 10) + assert sympify('2.6e2/17', rational=True) == Rational(260, 17) + assert sympify('2.6e+2/17', rational=True) == Rational(260, 17) + assert sympify('2.6e-2/17', rational=True) == Rational(26, 17000) + assert sympify('2.1+3/4', rational=True) == \ + Rational(21, 10) + Rational(3, 4) + assert sympify('2.234456', rational=True) == Rational(279307, 125000) + assert sympify('2.234456e23', rational=True) == 223445600000000000000000 + assert sympify('2.234456e-23', rational=True) == \ + Rational(279307, 12500000000000000000000000000) + assert sympify('-2.234456e-23', rational=True) == \ + Rational(-279307, 12500000000000000000000000000) + assert sympify('12345678901/17', rational=True) == \ + Rational(12345678901, 17) + assert sympify('1/.3 + x', rational=True) == Rational(10, 3) + x + # make sure longs in fractions work + assert sympify('222222222222/11111111111') == \ + Rational(222222222222, 11111111111) + # ... even if they come from repetend notation + assert sympify('1/.2[123456789012]') == Rational(333333333333, 70781892967) + # ... or from high precision reals + assert sympify('.1234567890123456', rational=True) == \ + Rational(19290123283179, 156250000000000) + + +def test_sympify_Fraction(): + try: + import fractions + except ImportError: + pass + else: + value = sympify(fractions.Fraction(101, 127)) + assert value == Rational(101, 127) and type(value) is Rational + + +def test_sympify_gmpy(): + if _gmpy is not None: + import gmpy2 + + value = sympify(gmpy2.mpz(1000001)) + assert value == Integer(1000001) and type(value) is Integer + + value = sympify(gmpy2.mpq(101, 127)) + assert value == Rational(101, 127) and type(value) is Rational + + +def test_sympify_flint(): + if _flint is not None: + import flint + + value = sympify(flint.fmpz(1000001)) + assert value == Integer(1000001) and type(value) is Integer + + value = sympify(flint.fmpq(101, 127)) + assert value == Rational(101, 127) and type(value) is Rational + + +@conserve_mpmath_dps +def test_sympify_mpmath(): + value = sympify(mpmath.mpf(1.0)) + assert value == Float(1.0) and type(value) is Float + + mpmath.mp.dps = 12 + assert sympify( + mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-12")) == True + assert sympify( + mpmath.pi).epsilon_eq(Float("3.14159265359"), Float("1e-13")) == False + + mpmath.mp.dps = 6 + assert sympify( + mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-5")) == True + assert sympify( + mpmath.pi).epsilon_eq(Float("3.14159"), Float("1e-6")) == False + + mpmath.mp.dps = 15 + assert sympify(mpmath.mpc(1.0 + 2.0j)) == Float(1.0) + Float(2.0)*I + + +def test_sympify2(): + class A: + def _sympy_(self): + return Symbol("x")**3 + + a = A() + + assert _sympify(a) == x**3 + assert sympify(a) == x**3 + assert a == x**3 + + +def test_sympify3(): + assert sympify("x**3") == x**3 + assert sympify("x^3") == x**3 + assert sympify("1/2") == Integer(1)/2 + + raises(SympifyError, lambda: _sympify('x**3')) + raises(SympifyError, lambda: _sympify('1/2')) + + +def test_sympify_keywords(): + raises(SympifyError, lambda: sympify('if')) + raises(SympifyError, lambda: sympify('for')) + raises(SympifyError, lambda: sympify('while')) + raises(SympifyError, lambda: sympify('lambda')) + + +def test_sympify_float(): + assert sympify("1e-64") != 0 + assert sympify("1e-20000") != 0 + + +def test_sympify_bool(): + assert sympify(True) is true + assert sympify(False) is false + + +def test_sympyify_iterables(): + ans = [Rational(3, 10), Rational(1, 5)] + assert sympify(['.3', '.2'], rational=True) == ans + assert sympify({"x": 0, "y": 1}) == {x: 0, y: 1} + assert sympify(['1', '2', ['3', '4']]) == [S(1), S(2), [S(3), S(4)]] + + +@XFAIL +def test_issue_16772(): + # because there is a converter for tuple, the + # args are only sympified without the flags being passed + # along; list, on the other hand, is not converted + # with a converter so its args are traversed later + ans = [Rational(3, 10), Rational(1, 5)] + assert sympify(('.3', '.2'), rational=True) == Tuple(*ans) + + +def test_issue_16859(): + class no(float, CantSympify): + pass + raises(SympifyError, lambda: sympify(no(1.2))) + + +def test_sympify4(): + class A: + def _sympy_(self): + return Symbol("x") + + a = A() + + assert _sympify(a)**3 == x**3 + assert sympify(a)**3 == x**3 + assert a == x + + +def test_sympify_text(): + assert sympify('some') == Symbol('some') + assert sympify('core') == Symbol('core') + + assert sympify('True') is True + assert sympify('False') is False + + assert sympify('Poly') == Poly + assert sympify('sin') == sin + + +def test_sympify_function(): + assert sympify('factor(x**2-1, x)') == -(1 - x)*(x + 1) + assert sympify('sin(pi/2)*cos(pi)') == -Integer(1) + + +def test_sympify_poly(): + p = Poly(x**2 + x + 1, x) + + assert _sympify(p) is p + assert sympify(p) is p + + +def test_sympify_factorial(): + assert sympify('x!') == factorial(x) + assert sympify('(x+1)!') == factorial(x + 1) + assert sympify('(1 + y*(x + 1))!') == factorial(1 + y*(x + 1)) + assert sympify('(1 + y*(x + 1)!)^2') == (1 + y*factorial(x + 1))**2 + assert sympify('y*x!') == y*factorial(x) + assert sympify('x!!') == factorial2(x) + assert sympify('(x+1)!!') == factorial2(x + 1) + assert sympify('(1 + y*(x + 1))!!') == factorial2(1 + y*(x + 1)) + assert sympify('(1 + y*(x + 1)!!)^2') == (1 + y*factorial2(x + 1))**2 + assert sympify('y*x!!') == y*factorial2(x) + assert sympify('factorial2(x)!') == factorial(factorial2(x)) + + raises(SympifyError, lambda: sympify("+!!")) + raises(SympifyError, lambda: sympify(")!!")) + raises(SympifyError, lambda: sympify("!")) + raises(SympifyError, lambda: sympify("(!)")) + raises(SympifyError, lambda: sympify("x!!!")) + + +def test_issue_3595(): + assert sympify("a_") == Symbol("a_") + assert sympify("_a") == Symbol("_a") + + +def test_lambda(): + x = Symbol('x') + assert sympify('lambda: 1') == Lambda((), 1) + assert sympify('lambda x: x') == Lambda(x, x) + assert sympify('lambda x: 2*x') == Lambda(x, 2*x) + assert sympify('lambda x, y: 2*x+y') == Lambda((x, y), 2*x + y) + + +def test_lambda_raises(): + raises(SympifyError, lambda: sympify("lambda *args: args")) # args argument error + raises(SympifyError, lambda: sympify("lambda **kwargs: kwargs[0]")) # kwargs argument error + raises(SympifyError, lambda: sympify("lambda x = 1: x")) # Keyword argument error + with raises(SympifyError): + _sympify('lambda: 1') + + +def test_sympify_raises(): + raises(SympifyError, lambda: sympify("fx)")) + + class A: + def __str__(self): + return 'x' + + raises(SympifyError, lambda: sympify(A())) + + +def test__sympify(): + x = Symbol('x') + f = Function('f') + + # positive _sympify + assert _sympify(x) is x + assert _sympify(1) == Integer(1) + assert _sympify(0.5) == Float("0.5") + assert _sympify(1 + 1j) == 1.0 + I*1.0 + + # Function f is not Basic and can't sympify to Basic. We allow it to pass + # with sympify but not with _sympify. + # https://github.com/sympy/sympy/issues/20124 + assert sympify(f) is f + raises(SympifyError, lambda: _sympify(f)) + + class A: + def _sympy_(self): + return Integer(5) + + a = A() + assert _sympify(a) == Integer(5) + + # negative _sympify + raises(SympifyError, lambda: _sympify('1')) + raises(SympifyError, lambda: _sympify([1, 2, 3])) + + +def test_sympifyit(): + x = Symbol('x') + y = Symbol('y') + + @_sympifyit('b', NotImplemented) + def add(a, b): + return a + b + + assert add(x, 1) == x + 1 + assert add(x, 0.5) == x + Float('0.5') + assert add(x, y) == x + y + + assert add(x, '1') == NotImplemented + + @_sympifyit('b') + def add_raises(a, b): + return a + b + + assert add_raises(x, 1) == x + 1 + assert add_raises(x, 0.5) == x + Float('0.5') + assert add_raises(x, y) == x + y + + raises(SympifyError, lambda: add_raises(x, '1')) + + +def test_int_float(): + class F1_1: + def __float__(self): + return 1.1 + + class F1_1b: + """ + This class is still a float, even though it also implements __int__(). + """ + def __float__(self): + return 1.1 + + def __int__(self): + return 1 + + class F1_1c: + """ + This class is still a float, because it implements _sympy_() + """ + def __float__(self): + return 1.1 + + def __int__(self): + return 1 + + def _sympy_(self): + return Float(1.1) + + class I5: + def __int__(self): + return 5 + + class I5b: + """ + This class implements both __int__() and __float__(), so it will be + treated as Float in SymPy. One could change this behavior, by using + float(a) == int(a), but deciding that integer-valued floats represent + exact numbers is arbitrary and often not correct, so we do not do it. + If, in the future, we decide to do it anyway, the tests for I5b need to + be changed. + """ + def __float__(self): + return 5.0 + + def __int__(self): + return 5 + + class I5c: + """ + This class implements both __int__() and __float__(), but also + a _sympy_() method, so it will be Integer. + """ + def __float__(self): + return 5.0 + + def __int__(self): + return 5 + + def _sympy_(self): + return Integer(5) + + i5 = I5() + i5b = I5b() + i5c = I5c() + f1_1 = F1_1() + f1_1b = F1_1b() + f1_1c = F1_1c() + assert sympify(i5) == 5 + assert isinstance(sympify(i5), Integer) + assert sympify(i5b) == 5.0 + assert isinstance(sympify(i5b), Float) + assert sympify(i5c) == 5 + assert isinstance(sympify(i5c), Integer) + assert abs(sympify(f1_1) - 1.1) < 1e-5 + assert abs(sympify(f1_1b) - 1.1) < 1e-5 + assert abs(sympify(f1_1c) - 1.1) < 1e-5 + + assert _sympify(i5) == 5 + assert isinstance(_sympify(i5), Integer) + assert _sympify(i5b) == 5.0 + assert isinstance(_sympify(i5b), Float) + assert _sympify(i5c) == 5 + assert isinstance(_sympify(i5c), Integer) + assert abs(_sympify(f1_1) - 1.1) < 1e-5 + assert abs(_sympify(f1_1b) - 1.1) < 1e-5 + assert abs(_sympify(f1_1c) - 1.1) < 1e-5 + + +def test_evaluate_false(): + cases = { + '2 + 3': Add(2, 3, evaluate=False), + '2**2 / 3': Mul(Pow(2, 2, evaluate=False), Pow(3, -1, evaluate=False), evaluate=False), + '2 + 3 * 5': Add(2, Mul(3, 5, evaluate=False), evaluate=False), + '2 - 3 * 5': Add(2, Mul(-1, Mul(3, 5,evaluate=False), evaluate=False), evaluate=False), + '1 / 3': Mul(1, Pow(3, -1, evaluate=False), evaluate=False), + 'True | False': Or(True, False, evaluate=False), + '1 + 2 + 3 + 5*3 + integrate(x)': Add(1, 2, 3, Mul(5, 3, evaluate=False), x**2/2, evaluate=False), + '2 * 4 * 6 + 8': Add(Mul(2, 4, 6, evaluate=False), 8, evaluate=False), + '2 - 8 / 4': Add(2, Mul(-1, Mul(8, Pow(4, -1, evaluate=False), evaluate=False), evaluate=False), evaluate=False), + '2 - 2**2': Add(2, Mul(-1, Pow(2, 2, evaluate=False), evaluate=False), evaluate=False), + } + for case, result in cases.items(): + assert sympify(case, evaluate=False) == result + + +def test_issue_4133(): + a = sympify('Integer(4)') + + assert a == Integer(4) + assert a.is_Integer + + +def test_issue_3982(): + a = [3, 2.0] + assert sympify(a) == [Integer(3), Float(2.0)] + assert sympify(tuple(a)) == Tuple(Integer(3), Float(2.0)) + assert sympify(set(a)) == FiniteSet(Integer(3), Float(2.0)) + + +def test_S_sympify(): + assert S(1)/2 == sympify(1)/2 == S.Half + assert (-2)**(S(1)/2) == sqrt(2)*I + + +def test_issue_4788(): + assert srepr(S(1.0 + 0J)) == srepr(S(1.0)) == srepr(Float(1.0)) + + +def test_issue_4798_None(): + assert S(None) is None + + +def test_issue_3218(): + assert sympify("x+\ny") == x + y + +def test_issue_19399(): + if not numpy: + skip("numpy not installed.") + + a = numpy.array(Rational(1, 2)) + b = Rational(1, 3) + assert (a * b, type(a * b)) == (b * a, type(b * a)) + + +def test_issue_4988_builtins(): + C = Symbol('C') + vars = {'C': C} + exp1 = sympify('C') + assert exp1 == C # Make sure it did not get mixed up with sympy.C + + exp2 = sympify('C', vars) + assert exp2 == C # Make sure it did not get mixed up with sympy.C + + +def test_geometry(): + p = sympify(Point(0, 1)) + assert p == Point(0, 1) and isinstance(p, Point) + L = sympify(Line(p, (1, 0))) + assert L == Line((0, 1), (1, 0)) and isinstance(L, Line) + + +def test_kernS(): + s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))' + # when 1497 is fixed, this no longer should pass: the expression + # should be unchanged + assert -1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) == -1 + # sympification should not allow the constant to enter a Mul + # or else the structure can change dramatically + ss = kernS(s) + assert ss != -1 and ss.simplify() == -1 + s = '-1 - 2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x)))'.replace( + 'x', '_kern') + ss = kernS(s) + assert ss != -1 and ss.simplify() == -1 + # issue 6687 + assert (kernS('Interval(-1,-2 - 4*(-3))') + == Interval(-1, Add(-2, Mul(12, 1, evaluate=False), evaluate=False))) + assert kernS('_kern') == Symbol('_kern') + assert kernS('E**-(x)') == exp(-x) + e = 2*(x + y)*y + assert kernS(['2*(x + y)*y', ('2*(x + y)*y',)]) == [e, (e,)] + assert kernS('-(2*sin(x)**2 + 2*sin(x)*cos(x))*y/2') == \ + -y*(2*sin(x)**2 + 2*sin(x)*cos(x))/2 + # issue 15132 + assert kernS('(1 - x)/(1 - x*(1-y))') == kernS('(1-x)/(1-(1-y)*x)') + assert kernS('(1-2**-(4+1)*(1-y)*x)') == (1 - x*(1 - y)/32) + assert kernS('(1-2**(4+1)*(1-y)*x)') == (1 - 32*x*(1 - y)) + assert kernS('(1-2.*(1-y)*x)') == 1 - 2.*x*(1 - y) + one = kernS('x - (x - 1)') + assert one != 1 and one.expand() == 1 + assert kernS("(2*x)/(x-1)") == 2*x/(x-1) + + +def test_issue_6540_6552(): + assert S('[[1/3,2], (2/5,)]') == [[Rational(1, 3), 2], (Rational(2, 5),)] + assert S('[[2/6,2], (2/4,)]') == [[Rational(1, 3), 2], (S.Half,)] + assert S('[[[2*(1)]]]') == [[[2]]] + assert S('Matrix([2*(1)])') == Matrix([2]) + + +def test_issue_6046(): + assert str(S("Q & C", locals=_clash1)) == 'C & Q' + assert str(S('pi(x)', locals=_clash2)) == 'pi(x)' + locals = {} + exec("from sympy.abc import Q, C", locals) + assert str(S('C&Q', locals)) == 'C & Q' + # clash can act as Symbol or Function + assert str(S('pi(C, Q)', locals=_clash)) == 'pi(C, Q)' + assert len(S('pi + x', locals=_clash2).free_symbols) == 2 + # but not both + raises(TypeError, lambda: S('pi + pi(x)', locals=_clash2)) + assert all(set(i.values()) == {null} for i in ( + _clash, _clash1, _clash2)) + + +def test_issue_8821_highprec_from_str(): + s = str(pi.evalf(128)) + p = sympify(s) + assert Abs(sin(p)) < 1e-127 + + +def test_issue_10295(): + if not numpy: + skip("numpy not installed.") + + A = numpy.array([[1, 3, -1], + [0, 1, 7]]) + sA = S(A) + assert sA.shape == (2, 3) + for (ri, ci), val in numpy.ndenumerate(A): + assert sA[ri, ci] == val + + B = numpy.array([-7, x, 3*y**2]) + sB = S(B) + assert sB.shape == (3,) + assert B[0] == sB[0] == -7 + assert B[1] == sB[1] == x + assert B[2] == sB[2] == 3*y**2 + + C = numpy.arange(0, 24) + C.resize(2,3,4) + sC = S(C) + assert sC[0, 0, 0].is_integer + assert sC[0, 0, 0] == 0 + + a1 = numpy.array([1, 2, 3]) + a2 = numpy.array(list(range(24))) + a2.resize(2, 4, 3) + assert sympify(a1) == ImmutableDenseNDimArray([1, 2, 3]) + assert sympify(a2) == ImmutableDenseNDimArray(list(range(24)), (2, 4, 3)) + + +def test_Range(): + # Only works in Python 3 where range returns a range type + assert sympify(range(10)) == Range(10) + assert _sympify(range(10)) == Range(10) + + +def test_sympify_set(): + n = Symbol('n') + assert sympify({n}) == FiniteSet(n) + assert sympify(set()) == EmptySet + + +def test_sympify_numpy(): + if not numpy: + skip('numpy not installed. Abort numpy tests.') + np = numpy + + def equal(x, y): + return x == y and type(x) == type(y) + + assert sympify(np.bool_(1)) is S(True) + try: + assert equal( + sympify(np.int_(1234567891234567891)), S(1234567891234567891)) + assert equal( + sympify(np.intp(1234567891234567891)), S(1234567891234567891)) + except OverflowError: + # May fail on 32-bit systems: Python int too large to convert to C long + pass + assert equal(sympify(np.intc(1234567891)), S(1234567891)) + assert equal(sympify(np.int8(-123)), S(-123)) + assert equal(sympify(np.int16(-12345)), S(-12345)) + assert equal(sympify(np.int32(-1234567891)), S(-1234567891)) + assert equal( + sympify(np.int64(-1234567891234567891)), S(-1234567891234567891)) + assert equal(sympify(np.uint8(123)), S(123)) + assert equal(sympify(np.uint16(12345)), S(12345)) + assert equal(sympify(np.uint32(1234567891)), S(1234567891)) + assert equal( + sympify(np.uint64(1234567891234567891)), S(1234567891234567891)) + assert equal(sympify(np.float32(1.123456)), Float(1.123456, precision=24)) + assert equal(sympify(np.float64(1.1234567891234)), + Float(1.1234567891234, precision=53)) + + # The exact precision of np.longdouble, npfloat128 and other extended + # precision dtypes is platform dependent. + ldprec = np.finfo(np.longdouble(1)).nmant + 1 + assert equal(sympify(np.longdouble(1.123456789)), + Float(1.123456789, precision=ldprec)) + + assert equal(sympify(np.complex64(1 + 2j)), S(1.0 + 2.0*I)) + assert equal(sympify(np.complex128(1 + 2j)), S(1.0 + 2.0*I)) + + lcprec = np.finfo(np.clongdouble(1)).nmant + 1 + assert equal(sympify(np.clongdouble(1 + 2j)), + Float(1.0, precision=lcprec) + Float(2.0, precision=lcprec)*I) + + #float96 does not exist on all platforms + if hasattr(np, 'float96'): + f96prec = np.finfo(np.float96(1)).nmant + 1 + assert equal(sympify(np.float96(1.123456789)), + Float(1.123456789, precision=f96prec)) + + #float128 does not exist on all platforms + if hasattr(np, 'float128'): + f128prec = np.finfo(np.float128(1)).nmant + 1 + assert equal(sympify(np.float128(1.123456789123)), + Float(1.123456789123, precision=f128prec)) + + +@XFAIL +def test_sympify_rational_numbers_set(): + ans = [Rational(3, 10), Rational(1, 5)] + assert sympify({'.3', '.2'}, rational=True) == FiniteSet(*ans) + + +def test_sympify_mro(): + """Tests the resolution order for classes that implement _sympy_""" + class a: + def _sympy_(self): + return Integer(1) + class b(a): + def _sympy_(self): + return Integer(2) + class c(a): + pass + + assert sympify(a()) == Integer(1) + assert sympify(b()) == Integer(2) + assert sympify(c()) == Integer(1) + + +def test_sympify_converter(): + """Tests the resolution order for classes in converter""" + class a: + pass + class b(a): + pass + class c(a): + pass + + converter[a] = lambda x: Integer(1) + converter[b] = lambda x: Integer(2) + + assert sympify(a()) == Integer(1) + assert sympify(b()) == Integer(2) + assert sympify(c()) == Integer(1) + + class MyInteger(Integer): + pass + + if int in converter: + int_converter = converter[int] + else: + int_converter = None + + try: + converter[int] = MyInteger + assert sympify(1) == MyInteger(1) + finally: + if int_converter is None: + del converter[int] + else: + converter[int] = int_converter + + +def test_issue_13924(): + if not numpy: + skip("numpy not installed.") + + a = sympify(numpy.array([1])) + assert isinstance(a, ImmutableDenseNDimArray) + assert a[0] == 1 + + +def test_numpy_sympify_args(): + # Issue 15098. Make sure sympify args work with numpy types (like numpy.str_) + if not numpy: + skip("numpy not installed.") + + a = sympify(numpy.str_('a')) + assert type(a) is Symbol + assert a == Symbol('a') + + class CustomSymbol(Symbol): + pass + + a = sympify(numpy.str_('a'), {"Symbol": CustomSymbol}) + assert isinstance(a, CustomSymbol) + + a = sympify(numpy.str_('x^y')) + assert a == x**y + a = sympify(numpy.str_('x^y'), convert_xor=False) + assert a == Xor(x, y) + + raises(SympifyError, lambda: sympify(numpy.str_('x'), strict=True)) + + a = sympify(numpy.str_('1.1')) + assert isinstance(a, Float) + assert a == 1.1 + + a = sympify(numpy.str_('1.1'), rational=True) + assert isinstance(a, Rational) + assert a == Rational(11, 10) + + a = sympify(numpy.str_('x + x')) + assert isinstance(a, Mul) + assert a == 2*x + + a = sympify(numpy.str_('x + x'), evaluate=False) + assert isinstance(a, Add) + assert a == Add(x, x, evaluate=False) + + +def test_issue_5939(): + a = Symbol('a') + b = Symbol('b') + assert sympify('''a+\nb''') == a + b + + +def test_issue_16759(): + d = sympify({.5: 1}) + assert S.Half not in d + assert Float(.5) in d + assert d[.5] is S.One + d = sympify(OrderedDict({.5: 1})) + assert S.Half not in d + assert Float(.5) in d + assert d[.5] is S.One + d = sympify(defaultdict(int, {.5: 1})) + assert S.Half not in d + assert Float(.5) in d + assert d[.5] is S.One + + +def test_issue_17811(): + a = Function('a') + assert sympify('a(x)*5', evaluate=False) == Mul(a(x), 5, evaluate=False) + + +def test_issue_8439(): + assert sympify(float('inf')) == oo + assert x + float('inf') == x + oo + assert S(float('inf')) == oo + + +def test_issue_14706(): + if not numpy: + skip("numpy not installed.") + + z1 = numpy.zeros((1, 1), dtype=numpy.float64) + z2 = numpy.zeros((2, 2), dtype=numpy.float64) + z3 = numpy.zeros((), dtype=numpy.float64) + + y1 = numpy.ones((1, 1), dtype=numpy.float64) + y2 = numpy.ones((2, 2), dtype=numpy.float64) + y3 = numpy.ones((), dtype=numpy.float64) + + assert numpy.all(x + z1 == numpy.full((1, 1), x)) + assert numpy.all(x + z2 == numpy.full((2, 2), x)) + assert numpy.all(z1 + x == numpy.full((1, 1), x)) + assert numpy.all(z2 + x == numpy.full((2, 2), x)) + for z in [z3, + numpy.int64(0), + numpy.float64(0), + numpy.complex64(0)]: + assert x + z == x + assert z + x == x + assert isinstance(x + z, Symbol) + assert isinstance(z + x, Symbol) + + # If these tests fail, then it means that numpy has finally + # fixed the issue of scalar conversion for rank>0 arrays + # which is mentioned in numpy/numpy#10404. In that case, + # some changes have to be made in sympify.py. + # Note: For future reference, for anyone who takes up this + # issue when numpy has finally fixed their side of the problem, + # the changes for this temporary fix were introduced in PR 18651 + assert numpy.all(x + y1 == numpy.full((1, 1), x + 1.0)) + assert numpy.all(x + y2 == numpy.full((2, 2), x + 1.0)) + assert numpy.all(y1 + x == numpy.full((1, 1), x + 1.0)) + assert numpy.all(y2 + x == numpy.full((2, 2), x + 1.0)) + for y_ in [y3, + numpy.int64(1), + numpy.float64(1), + numpy.complex64(1)]: + assert x + y_ == y_ + x + assert isinstance(x + y_, Add) + assert isinstance(y_ + x, Add) + + assert x + numpy.array(x) == 2 * x + assert x + numpy.array([x]) == numpy.array([2*x], dtype=object) + + assert sympify(numpy.array([1])) == ImmutableDenseNDimArray([1], 1) + assert sympify(numpy.array([[[1]]])) == ImmutableDenseNDimArray([1], (1, 1, 1)) + assert sympify(z1) == ImmutableDenseNDimArray([0.0], (1, 1)) + assert sympify(z2) == ImmutableDenseNDimArray([0.0, 0.0, 0.0, 0.0], (2, 2)) + assert sympify(z3) == ImmutableDenseNDimArray([0.0], ()) + assert sympify(z3, strict=True) == 0.0 + + raises(SympifyError, lambda: sympify(numpy.array([1]), strict=True)) + raises(SympifyError, lambda: sympify(z1, strict=True)) + raises(SympifyError, lambda: sympify(z2, strict=True)) + + +def test_issue_21536(): + #test to check evaluate=False in case of iterable input + u = sympify("x+3*x+2", evaluate=False) + v = sympify("2*x+4*x+2+4", evaluate=False) + + assert u.is_Add and set(u.args) == {x, 3*x, 2} + assert v.is_Add and set(v.args) == {2*x, 4*x, 2, 4} + assert sympify(["x+3*x+2", "2*x+4*x+2+4"], evaluate=False) == [u, v] + + #test to check evaluate=True in case of iterable input + u = sympify("x+3*x+2", evaluate=True) + v = sympify("2*x+4*x+2+4", evaluate=True) + + assert u.is_Add and set(u.args) == {4*x, 2} + assert v.is_Add and set(v.args) == {6*x, 6} + assert sympify(["x+3*x+2", "2*x+4*x+2+4"], evaluate=True) == [u, v] + + #test to check evaluate with no input in case of iterable input + u = sympify("x+3*x+2") + v = sympify("2*x+4*x+2+4") + + assert u.is_Add and set(u.args) == {4*x, 2} + assert v.is_Add and set(v.args) == {6*x, 6} + assert sympify(["x+3*x+2", "2*x+4*x+2+4"]) == [u, v] diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_traversal.py b/lib/python3.11/site-packages/sympy/core/tests/test_traversal.py new file mode 100644 index 0000000000000000000000000000000000000000..8bf067283eaba5d4a073a73feb07aac199055a7f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_traversal.py @@ -0,0 +1,119 @@ +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import symbols +from sympy.core.singleton import S +from sympy.core.function import expand, Function +from sympy.core.numbers import I +from sympy.integrals.integrals import Integral +from sympy.polys.polytools import factor +from sympy.core.traversal import preorder_traversal, use, postorder_traversal, iterargs, iterfreeargs +from sympy.functions.elementary.piecewise import ExprCondPair, Piecewise +from sympy.testing.pytest import warns_deprecated_sympy +from sympy.utilities.iterables import capture + +b1 = Basic() +b2 = Basic(b1) +b3 = Basic(b2) +b21 = Basic(b2, b1) + + +def test_preorder_traversal(): + expr = Basic(b21, b3) + assert list( + preorder_traversal(expr)) == [expr, b21, b2, b1, b1, b3, b2, b1] + assert list(preorder_traversal(('abc', ('d', 'ef')))) == [ + ('abc', ('d', 'ef')), 'abc', ('d', 'ef'), 'd', 'ef'] + + result = [] + pt = preorder_traversal(expr) + for i in pt: + result.append(i) + if i == b2: + pt.skip() + assert result == [expr, b21, b2, b1, b3, b2] + + w, x, y, z = symbols('w:z') + expr = z + w*(x + y) + assert list(preorder_traversal([expr], keys=default_sort_key)) == \ + [[w*(x + y) + z], w*(x + y) + z, z, w*(x + y), w, x + y, x, y] + assert list(preorder_traversal((x + y)*z, keys=True)) == \ + [z*(x + y), z, x + y, x, y] + + +def test_use(): + x, y = symbols('x y') + + assert use(0, expand) == 0 + + f = (x + y)**2*x + 1 + + assert use(f, expand, level=0) == x**3 + 2*x**2*y + x*y**2 + + 1 + assert use(f, expand, level=1) == x**3 + 2*x**2*y + x*y**2 + + 1 + assert use(f, expand, level=2) == 1 + x*(2*x*y + x**2 + y**2) + assert use(f, expand, level=3) == (x + y)**2*x + 1 + + f = (x**2 + 1)**2 - 1 + kwargs = {'gaussian': True} + + assert use(f, factor, level=0, kwargs=kwargs) == x**2*(x**2 + 2) + assert use(f, factor, level=1, kwargs=kwargs) == (x + I)**2*(x - I)**2 - 1 + assert use(f, factor, level=2, kwargs=kwargs) == (x + I)**2*(x - I)**2 - 1 + assert use(f, factor, level=3, kwargs=kwargs) == (x**2 + 1)**2 - 1 + + +def test_postorder_traversal(): + x, y, z, w = symbols('x y z w') + expr = z + w*(x + y) + expected = [z, w, x, y, x + y, w*(x + y), w*(x + y) + z] + assert list(postorder_traversal(expr, keys=default_sort_key)) == expected + assert list(postorder_traversal(expr, keys=True)) == expected + + expr = Piecewise((x, x < 1), (x**2, True)) + expected = [ + x, 1, x, x < 1, ExprCondPair(x, x < 1), + 2, x, x**2, S.true, + ExprCondPair(x**2, True), Piecewise((x, x < 1), (x**2, True)) + ] + assert list(postorder_traversal(expr, keys=default_sort_key)) == expected + assert list(postorder_traversal( + [expr], keys=default_sort_key)) == expected + [[expr]] + + assert list(postorder_traversal(Integral(x**2, (x, 0, 1)), + keys=default_sort_key)) == [ + 2, x, x**2, 0, 1, x, Tuple(x, 0, 1), + Integral(x**2, Tuple(x, 0, 1)) + ] + assert list(postorder_traversal(('abc', ('d', 'ef')))) == [ + 'abc', 'd', 'ef', ('d', 'ef'), ('abc', ('d', 'ef'))] + + +def test_iterargs(): + f = Function('f') + x = symbols('x') + assert list(iterfreeargs(Integral(f(x), (f(x), 1)))) == [ + Integral(f(x), (f(x), 1)), 1] + assert list(iterargs(Integral(f(x), (f(x), 1)))) == [ + Integral(f(x), (f(x), 1)), f(x), (f(x), 1), x, f(x), 1, x] + +def test_deprecated_imports(): + x = symbols('x') + + with warns_deprecated_sympy(): + from sympy.core.basic import preorder_traversal + preorder_traversal(x) + with warns_deprecated_sympy(): + from sympy.simplify.simplify import bottom_up + bottom_up(x, lambda x: x) + with warns_deprecated_sympy(): + from sympy.simplify.simplify import walk + walk(x, lambda x: x) + with warns_deprecated_sympy(): + from sympy.simplify.traversaltools import use + use(x, lambda x: x) + with warns_deprecated_sympy(): + from sympy.utilities.iterables import postorder_traversal + postorder_traversal(x) + with warns_deprecated_sympy(): + from sympy.utilities.iterables import interactive_traversal + capture(lambda: interactive_traversal(x)) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_truediv.py b/lib/python3.11/site-packages/sympy/core/tests/test_truediv.py new file mode 100644 index 0000000000000000000000000000000000000000..1fcf9e1ab754d05a3b47e7ec0c2be5ea9929da02 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_truediv.py @@ -0,0 +1,54 @@ +#this module tests that SymPy works with true division turned on + +from sympy.core.numbers import (Float, Rational) +from sympy.core.symbol import Symbol + + +def test_truediv(): + assert 1/2 != 0 + assert Rational(1)/2 != 0 + + +def dotest(s): + x = Symbol("x") + y = Symbol("y") + l = [ + Rational(2), + Float("1.3"), + x, + y, + pow(x, y)*y, + 5, + 5.5 + ] + for x in l: + for y in l: + s(x, y) + return True + + +def test_basic(): + def s(a, b): + x = a + x = +a + x = -a + x = a + b + x = a - b + x = a*b + x = a/b + x = a**b + del x + assert dotest(s) + + +def test_ibasic(): + def s(a, b): + x = a + x += b + x = a + x -= b + x = a + x *= b + x = a + x /= b + assert dotest(s) diff --git a/lib/python3.11/site-packages/sympy/core/tests/test_var.py b/lib/python3.11/site-packages/sympy/core/tests/test_var.py new file mode 100644 index 0000000000000000000000000000000000000000..a02709464c9878082fecaf70fa47067ac8838ac6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/tests/test_var.py @@ -0,0 +1,62 @@ +from sympy.core.function import (Function, FunctionClass) +from sympy.core.symbol import (Symbol, var) +from sympy.testing.pytest import raises + +def test_var(): + ns = {"var": var, "raises": raises} + eval("var('a')", ns) + assert ns["a"] == Symbol("a") + + eval("var('b bb cc zz _x')", ns) + assert ns["b"] == Symbol("b") + assert ns["bb"] == Symbol("bb") + assert ns["cc"] == Symbol("cc") + assert ns["zz"] == Symbol("zz") + assert ns["_x"] == Symbol("_x") + + v = eval("var(['d', 'e', 'fg'])", ns) + assert ns['d'] == Symbol('d') + assert ns['e'] == Symbol('e') + assert ns['fg'] == Symbol('fg') + +# check return value + assert v != ['d', 'e', 'fg'] + assert v == [Symbol('d'), Symbol('e'), Symbol('fg')] + + +def test_var_return(): + ns = {"var": var, "raises": raises} + "raises(ValueError, lambda: var(''))" + v2 = eval("var('q')", ns) + v3 = eval("var('q p')", ns) + + assert v2 == Symbol('q') + assert v3 == (Symbol('q'), Symbol('p')) + + +def test_var_accepts_comma(): + ns = {"var": var} + v1 = eval("var('x y z')", ns) + v2 = eval("var('x,y,z')", ns) + v3 = eval("var('x,y z')", ns) + + assert v1 == v2 + assert v1 == v3 + + +def test_var_keywords(): + ns = {"var": var} + eval("var('x y', real=True)", ns) + assert ns['x'].is_real and ns['y'].is_real + + +def test_var_cls(): + ns = {"var": var, "Function": Function} + eval("var('f', cls=Function)", ns) + + assert isinstance(ns['f'], FunctionClass) + + eval("var('g,h', cls=Function)", ns) + + assert isinstance(ns['g'], FunctionClass) + assert isinstance(ns['h'], FunctionClass) diff --git a/lib/python3.11/site-packages/sympy/core/trace.py b/lib/python3.11/site-packages/sympy/core/trace.py new file mode 100644 index 0000000000000000000000000000000000000000..58326ce1fdd5038f0b5805afe7c453314a22cb6a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/trace.py @@ -0,0 +1,12 @@ +from sympy.utilities.exceptions import sympy_deprecation_warning + +sympy_deprecation_warning( + """ + sympy.core.trace is deprecated. Use sympy.physics.quantum.trace + instead. + """, + deprecated_since_version="1.10", + active_deprecations_target="sympy-core-trace-deprecated", +) + +from sympy.physics.quantum.trace import Tr # noqa:F401 diff --git a/lib/python3.11/site-packages/sympy/core/traversal.py b/lib/python3.11/site-packages/sympy/core/traversal.py new file mode 100644 index 0000000000000000000000000000000000000000..6574b12d98a54b8fedb705e3ca674948534f20c2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/core/traversal.py @@ -0,0 +1,300 @@ +from .basic import Basic +from .sorting import ordered +from .sympify import sympify +from sympy.utilities.iterables import iterable + + + +def iterargs(expr): + """Yield the args of a Basic object in a breadth-first traversal. + Depth-traversal stops if `arg.args` is either empty or is not + an iterable. + + Examples + ======== + + >>> from sympy import Integral, Function + >>> from sympy.abc import x + >>> f = Function('f') + >>> from sympy.core.traversal import iterargs + >>> list(iterargs(Integral(f(x), (f(x), 1)))) + [Integral(f(x), (f(x), 1)), f(x), (f(x), 1), x, f(x), 1, x] + + See Also + ======== + iterfreeargs, preorder_traversal + """ + args = [expr] + for i in args: + yield i + args.extend(i.args) + + +def iterfreeargs(expr, _first=True): + """Yield the args of a Basic object in a breadth-first traversal. + Depth-traversal stops if `arg.args` is either empty or is not + an iterable. The bound objects of an expression will be returned + as canonical variables. + + Examples + ======== + + >>> from sympy import Integral, Function + >>> from sympy.abc import x + >>> f = Function('f') + >>> from sympy.core.traversal import iterfreeargs + >>> list(iterfreeargs(Integral(f(x), (f(x), 1)))) + [Integral(f(x), (f(x), 1)), 1] + + See Also + ======== + iterargs, preorder_traversal + """ + args = [expr] + for i in args: + yield i + if _first and hasattr(i, 'bound_symbols'): + void = i.canonical_variables.values() + for i in iterfreeargs(i.as_dummy(), _first=False): + if not i.has(*void): + yield i + args.extend(i.args) + + +class preorder_traversal: + """ + Do a pre-order traversal of a tree. + + This iterator recursively yields nodes that it has visited in a pre-order + fashion. That is, it yields the current node then descends through the + tree breadth-first to yield all of a node's children's pre-order + traversal. + + + For an expression, the order of the traversal depends on the order of + .args, which in many cases can be arbitrary. + + Parameters + ========== + node : SymPy expression + The expression to traverse. + keys : (default None) sort key(s) + The key(s) used to sort args of Basic objects. When None, args of Basic + objects are processed in arbitrary order. If key is defined, it will + be passed along to ordered() as the only key(s) to use to sort the + arguments; if ``key`` is simply True then the default keys of ordered + will be used. + + Yields + ====== + subtree : SymPy expression + All of the subtrees in the tree. + + Examples + ======== + + >>> from sympy import preorder_traversal, symbols + >>> x, y, z = symbols('x y z') + + The nodes are returned in the order that they are encountered unless key + is given; simply passing key=True will guarantee that the traversal is + unique. + + >>> list(preorder_traversal((x + y)*z, keys=None)) # doctest: +SKIP + [z*(x + y), z, x + y, y, x] + >>> list(preorder_traversal((x + y)*z, keys=True)) + [z*(x + y), z, x + y, x, y] + + """ + def __init__(self, node, keys=None): + self._skip_flag = False + self._pt = self._preorder_traversal(node, keys) + + def _preorder_traversal(self, node, keys): + yield node + if self._skip_flag: + self._skip_flag = False + return + if isinstance(node, Basic): + if not keys and hasattr(node, '_argset'): + # LatticeOp keeps args as a set. We should use this if we + # don't care about the order, to prevent unnecessary sorting. + args = node._argset + else: + args = node.args + if keys: + if keys != True: + args = ordered(args, keys, default=False) + else: + args = ordered(args) + for arg in args: + yield from self._preorder_traversal(arg, keys) + elif iterable(node): + for item in node: + yield from self._preorder_traversal(item, keys) + + def skip(self): + """ + Skip yielding current node's (last yielded node's) subtrees. + + Examples + ======== + + >>> from sympy import preorder_traversal, symbols + >>> x, y, z = symbols('x y z') + >>> pt = preorder_traversal((x + y*z)*z) + >>> for i in pt: + ... print(i) + ... if i == x + y*z: + ... pt.skip() + z*(x + y*z) + z + x + y*z + """ + self._skip_flag = True + + def __next__(self): + return next(self._pt) + + def __iter__(self): + return self + + +def use(expr, func, level=0, args=(), kwargs={}): + """ + Use ``func`` to transform ``expr`` at the given level. + + Examples + ======== + + >>> from sympy import use, expand + >>> from sympy.abc import x, y + + >>> f = (x + y)**2*x + 1 + + >>> use(f, expand, level=2) + x*(x**2 + 2*x*y + y**2) + 1 + >>> expand(f) + x**3 + 2*x**2*y + x*y**2 + 1 + + """ + def _use(expr, level): + if not level: + return func(expr, *args, **kwargs) + else: + if expr.is_Atom: + return expr + else: + level -= 1 + _args = [_use(arg, level) for arg in expr.args] + return expr.__class__(*_args) + + return _use(sympify(expr), level) + + +def walk(e, *target): + """Iterate through the args that are the given types (target) and + return a list of the args that were traversed; arguments + that are not of the specified types are not traversed. + + Examples + ======== + + >>> from sympy.core.traversal import walk + >>> from sympy import Min, Max + >>> from sympy.abc import x, y, z + >>> list(walk(Min(x, Max(y, Min(1, z))), Min)) + [Min(x, Max(y, Min(1, z)))] + >>> list(walk(Min(x, Max(y, Min(1, z))), Min, Max)) + [Min(x, Max(y, Min(1, z))), Max(y, Min(1, z)), Min(1, z)] + + See Also + ======== + + bottom_up + """ + if isinstance(e, target): + yield e + for i in e.args: + yield from walk(i, *target) + + +def bottom_up(rv, F, atoms=False, nonbasic=False): + """Apply ``F`` to all expressions in an expression tree from the + bottom up. If ``atoms`` is True, apply ``F`` even if there are no args; + if ``nonbasic`` is True, try to apply ``F`` to non-Basic objects. + """ + args = getattr(rv, 'args', None) + if args is not None: + if args: + args = tuple([bottom_up(a, F, atoms, nonbasic) for a in args]) + if args != rv.args: + rv = rv.func(*args) + rv = F(rv) + elif atoms: + rv = F(rv) + else: + if nonbasic: + try: + rv = F(rv) + except TypeError: + pass + + return rv + + +def postorder_traversal(node, keys=None): + """ + Do a postorder traversal of a tree. + + This generator recursively yields nodes that it has visited in a postorder + fashion. That is, it descends through the tree depth-first to yield all of + a node's children's postorder traversal before yielding the node itself. + + Parameters + ========== + + node : SymPy expression + The expression to traverse. + keys : (default None) sort key(s) + The key(s) used to sort args of Basic objects. When None, args of Basic + objects are processed in arbitrary order. If key is defined, it will + be passed along to ordered() as the only key(s) to use to sort the + arguments; if ``key`` is simply True then the default keys of + ``ordered`` will be used (node count and default_sort_key). + + Yields + ====== + subtree : SymPy expression + All of the subtrees in the tree. + + Examples + ======== + + >>> from sympy import postorder_traversal + >>> from sympy.abc import w, x, y, z + + The nodes are returned in the order that they are encountered unless key + is given; simply passing key=True will guarantee that the traversal is + unique. + + >>> list(postorder_traversal(w + (x + y)*z)) # doctest: +SKIP + [z, y, x, x + y, z*(x + y), w, w + z*(x + y)] + >>> list(postorder_traversal(w + (x + y)*z, keys=True)) + [w, z, x, y, x + y, z*(x + y), w + z*(x + y)] + + + """ + if isinstance(node, Basic): + args = node.args + if keys: + if keys != True: + args = ordered(args, keys, default=False) + else: + args = ordered(args) + for arg in args: + yield from postorder_traversal(arg, keys) + elif iterable(node): + for item in node: + yield from postorder_traversal(item, keys) + yield node diff --git a/lib/python3.11/site-packages/sympy/crypto/__init__.py b/lib/python3.11/site-packages/sympy/crypto/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..2b27b4b036e5f2ed93a1ea88cd7d7144eb5615d4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/crypto/__init__.py @@ -0,0 +1,35 @@ +from sympy.crypto.crypto import (cycle_list, + encipher_shift, encipher_affine, encipher_substitution, + check_and_join, encipher_vigenere, decipher_vigenere, bifid5_square, + bifid6_square, encipher_hill, decipher_hill, + encipher_bifid5, encipher_bifid6, decipher_bifid5, + decipher_bifid6, encipher_kid_rsa, decipher_kid_rsa, + kid_rsa_private_key, kid_rsa_public_key, decipher_rsa, rsa_private_key, + rsa_public_key, encipher_rsa, lfsr_connection_polynomial, + lfsr_autocorrelation, lfsr_sequence, encode_morse, decode_morse, + elgamal_private_key, elgamal_public_key, decipher_elgamal, + encipher_elgamal, dh_private_key, dh_public_key, dh_shared_key, + padded_key, encipher_bifid, decipher_bifid, bifid_square, bifid5, + bifid6, bifid10, decipher_gm, encipher_gm, gm_public_key, + gm_private_key, bg_private_key, bg_public_key, encipher_bg, decipher_bg, + encipher_rot13, decipher_rot13, encipher_atbash, decipher_atbash, + encipher_railfence, decipher_railfence) + +__all__ = [ + 'cycle_list', 'encipher_shift', 'encipher_affine', + 'encipher_substitution', 'check_and_join', 'encipher_vigenere', + 'decipher_vigenere', 'bifid5_square', 'bifid6_square', 'encipher_hill', + 'decipher_hill', 'encipher_bifid5', 'encipher_bifid6', 'decipher_bifid5', + 'decipher_bifid6', 'encipher_kid_rsa', 'decipher_kid_rsa', + 'kid_rsa_private_key', 'kid_rsa_public_key', 'decipher_rsa', + 'rsa_private_key', 'rsa_public_key', 'encipher_rsa', + 'lfsr_connection_polynomial', 'lfsr_autocorrelation', 'lfsr_sequence', + 'encode_morse', 'decode_morse', 'elgamal_private_key', + 'elgamal_public_key', 'decipher_elgamal', 'encipher_elgamal', + 'dh_private_key', 'dh_public_key', 'dh_shared_key', 'padded_key', + 'encipher_bifid', 'decipher_bifid', 'bifid_square', 'bifid5', 'bifid6', + 'bifid10', 'decipher_gm', 'encipher_gm', 'gm_public_key', + 'gm_private_key', 'bg_private_key', 'bg_public_key', 'encipher_bg', + 'decipher_bg', 'encipher_rot13', 'decipher_rot13', 'encipher_atbash', + 'decipher_atbash', 'encipher_railfence', 'decipher_railfence', +] diff --git a/lib/python3.11/site-packages/sympy/crypto/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/crypto/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..321d60f4c686873b2a2e3ce20593e45cb96fd94a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/crypto/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/crypto/crypto.py b/lib/python3.11/site-packages/sympy/crypto/crypto.py new file mode 100644 index 0000000000000000000000000000000000000000..62c50072ca1aa36123de87700fb9d5ebae0a9f27 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/crypto/crypto.py @@ -0,0 +1,3367 @@ +""" +This file contains some classical ciphers and routines +implementing a linear-feedback shift register (LFSR) +and the Diffie-Hellman key exchange. + +.. warning:: + + This module is intended for educational purposes only. Do not use the + functions in this module for real cryptographic applications. If you wish + to encrypt real data, we recommend using something like the `cryptography + `_ module. + +""" + +from string import whitespace, ascii_uppercase as uppercase, printable +from functools import reduce +import warnings + +from itertools import cycle + +from sympy.external.gmpy import GROUND_TYPES +from sympy.core import Symbol +from sympy.core.numbers import Rational +from sympy.core.random import _randrange, _randint +from sympy.external.gmpy import gcd, invert +from sympy.functions.combinatorial.numbers import (totient as _euler, + reduced_totient as _carmichael) +from sympy.matrices import Matrix +from sympy.ntheory import isprime, primitive_root, factorint +from sympy.ntheory.generate import nextprime +from sympy.ntheory.modular import crt +from sympy.polys.domains import FF +from sympy.polys.polytools import Poly +from sympy.utilities.misc import as_int, filldedent, translate +from sympy.utilities.iterables import uniq, multiset +from sympy.utilities.decorator import doctest_depends_on + + +if GROUND_TYPES == 'flint': + __doctest_skip__ = ['lfsr_sequence'] + + +class NonInvertibleCipherWarning(RuntimeWarning): + """A warning raised if the cipher is not invertible.""" + def __init__(self, msg): + self.fullMessage = msg + + def __str__(self): + return '\n\t' + self.fullMessage + + def warn(self, stacklevel=3): + warnings.warn(self, stacklevel=stacklevel) + + +def AZ(s=None): + """Return the letters of ``s`` in uppercase. In case more than + one string is passed, each of them will be processed and a list + of upper case strings will be returned. + + Examples + ======== + + >>> from sympy.crypto.crypto import AZ + >>> AZ('Hello, world!') + 'HELLOWORLD' + >>> AZ('Hello, world!'.split()) + ['HELLO', 'WORLD'] + + See Also + ======== + + check_and_join + + """ + if not s: + return uppercase + t = isinstance(s, str) + if t: + s = [s] + rv = [check_and_join(i.upper().split(), uppercase, filter=True) + for i in s] + if t: + return rv[0] + return rv + +bifid5 = AZ().replace('J', '') +bifid6 = AZ() + '0123456789' +bifid10 = printable + + +def padded_key(key, symbols): + """Return a string of the distinct characters of ``symbols`` with + those of ``key`` appearing first. A ValueError is raised if + a) there are duplicate characters in ``symbols`` or + b) there are characters in ``key`` that are not in ``symbols``. + + Examples + ======== + + >>> from sympy.crypto.crypto import padded_key + >>> padded_key('PUPPY', 'OPQRSTUVWXY') + 'PUYOQRSTVWX' + >>> padded_key('RSA', 'ARTIST') + Traceback (most recent call last): + ... + ValueError: duplicate characters in symbols: T + + """ + syms = list(uniq(symbols)) + if len(syms) != len(symbols): + extra = ''.join(sorted({ + i for i in symbols if symbols.count(i) > 1})) + raise ValueError('duplicate characters in symbols: %s' % extra) + extra = set(key) - set(syms) + if extra: + raise ValueError( + 'characters in key but not symbols: %s' % ''.join( + sorted(extra))) + key0 = ''.join(list(uniq(key))) + # remove from syms characters in key0 + return key0 + translate(''.join(syms), None, key0) + + +def check_and_join(phrase, symbols=None, filter=None): + """ + Joins characters of ``phrase`` and if ``symbols`` is given, raises + an error if any character in ``phrase`` is not in ``symbols``. + + Parameters + ========== + + phrase + String or list of strings to be returned as a string. + + symbols + Iterable of characters allowed in ``phrase``. + + If ``symbols`` is ``None``, no checking is performed. + + Examples + ======== + + >>> from sympy.crypto.crypto import check_and_join + >>> check_and_join('a phrase') + 'a phrase' + >>> check_and_join('a phrase'.upper().split()) + 'APHRASE' + >>> check_and_join('a phrase!'.upper().split(), 'ARE', filter=True) + 'ARAE' + >>> check_and_join('a phrase!'.upper().split(), 'ARE') + Traceback (most recent call last): + ... + ValueError: characters in phrase but not symbols: "!HPS" + + """ + rv = ''.join(''.join(phrase)) + if symbols is not None: + symbols = check_and_join(symbols) + missing = ''.join(sorted(set(rv) - set(symbols))) + if missing: + if not filter: + raise ValueError( + 'characters in phrase but not symbols: "%s"' % missing) + rv = translate(rv, None, missing) + return rv + + +def _prep(msg, key, alp, default=None): + if not alp: + if not default: + alp = AZ() + msg = AZ(msg) + key = AZ(key) + else: + alp = default + else: + alp = ''.join(alp) + key = check_and_join(key, alp, filter=True) + msg = check_and_join(msg, alp, filter=True) + return msg, key, alp + + +def cycle_list(k, n): + """ + Returns the elements of the list ``range(n)`` shifted to the + left by ``k`` (so the list starts with ``k`` (mod ``n``)). + + Examples + ======== + + >>> from sympy.crypto.crypto import cycle_list + >>> cycle_list(3, 10) + [3, 4, 5, 6, 7, 8, 9, 0, 1, 2] + + """ + k = k % n + return list(range(k, n)) + list(range(k)) + + +######## shift cipher examples ############ + + +def encipher_shift(msg, key, symbols=None): + """ + Performs shift cipher encryption on plaintext msg, and returns the + ciphertext. + + Parameters + ========== + + key : int + The secret key. + + msg : str + Plaintext of upper-case letters. + + Returns + ======= + + str + Ciphertext of upper-case letters. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_shift, decipher_shift + >>> msg = "GONAVYBEATARMY" + >>> ct = encipher_shift(msg, 1); ct + 'HPOBWZCFBUBSNZ' + + To decipher the shifted text, change the sign of the key: + + >>> encipher_shift(ct, -1) + 'GONAVYBEATARMY' + + There is also a convenience function that does this with the + original key: + + >>> decipher_shift(ct, 1) + 'GONAVYBEATARMY' + + Notes + ===== + + ALGORITHM: + + STEPS: + 0. Number the letters of the alphabet from 0, ..., N + 1. Compute from the string ``msg`` a list ``L1`` of + corresponding integers. + 2. Compute from the list ``L1`` a new list ``L2``, given by + adding ``(k mod 26)`` to each element in ``L1``. + 3. Compute from the list ``L2`` a string ``ct`` of + corresponding letters. + + The shift cipher is also called the Caesar cipher, after + Julius Caesar, who, according to Suetonius, used it with a + shift of three to protect messages of military significance. + Caesar's nephew Augustus reportedly used a similar cipher, but + with a right shift of 1. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Caesar_cipher + .. [2] https://mathworld.wolfram.com/CaesarsMethod.html + + See Also + ======== + + decipher_shift + + """ + msg, _, A = _prep(msg, '', symbols) + shift = len(A) - key % len(A) + key = A[shift:] + A[:shift] + return translate(msg, key, A) + + +def decipher_shift(msg, key, symbols=None): + """ + Return the text by shifting the characters of ``msg`` to the + left by the amount given by ``key``. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_shift, decipher_shift + >>> msg = "GONAVYBEATARMY" + >>> ct = encipher_shift(msg, 1); ct + 'HPOBWZCFBUBSNZ' + + To decipher the shifted text, change the sign of the key: + + >>> encipher_shift(ct, -1) + 'GONAVYBEATARMY' + + Or use this function with the original key: + + >>> decipher_shift(ct, 1) + 'GONAVYBEATARMY' + + """ + return encipher_shift(msg, -key, symbols) + +def encipher_rot13(msg, symbols=None): + """ + Performs the ROT13 encryption on a given plaintext ``msg``. + + Explanation + =========== + + ROT13 is a substitution cipher which substitutes each letter + in the plaintext message for the letter furthest away from it + in the English alphabet. + + Equivalently, it is just a Caeser (shift) cipher with a shift + key of 13 (midway point of the alphabet). + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/ROT13 + + See Also + ======== + + decipher_rot13 + encipher_shift + + """ + return encipher_shift(msg, 13, symbols) + +def decipher_rot13(msg, symbols=None): + """ + Performs the ROT13 decryption on a given plaintext ``msg``. + + Explanation + ============ + + ``decipher_rot13`` is equivalent to ``encipher_rot13`` as both + ``decipher_shift`` with a key of 13 and ``encipher_shift`` key with a + key of 13 will return the same results. Nonetheless, + ``decipher_rot13`` has nonetheless been explicitly defined here for + consistency. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_rot13, decipher_rot13 + >>> msg = 'GONAVYBEATARMY' + >>> ciphertext = encipher_rot13(msg);ciphertext + 'TBANILORNGNEZL' + >>> decipher_rot13(ciphertext) + 'GONAVYBEATARMY' + >>> encipher_rot13(msg) == decipher_rot13(msg) + True + >>> msg == decipher_rot13(ciphertext) + True + + """ + return decipher_shift(msg, 13, symbols) + +######## affine cipher examples ############ + + +def encipher_affine(msg, key, symbols=None, _inverse=False): + r""" + Performs the affine cipher encryption on plaintext ``msg``, and + returns the ciphertext. + + Explanation + =========== + + Encryption is based on the map `x \rightarrow ax+b` (mod `N`) + where ``N`` is the number of characters in the alphabet. + Decryption is based on the map `x \rightarrow cx+d` (mod `N`), + where `c = a^{-1}` (mod `N`) and `d = -a^{-1}b` (mod `N`). + In particular, for the map to be invertible, we need + `\mathrm{gcd}(a, N) = 1` and an error will be raised if this is + not true. + + Parameters + ========== + + msg : str + Characters that appear in ``symbols``. + + a, b : int, int + A pair integers, with ``gcd(a, N) = 1`` (the secret key). + + symbols + String of characters (default = uppercase letters). + + When no symbols are given, ``msg`` is converted to upper case + letters and all other characters are ignored. + + Returns + ======= + + ct + String of characters (the ciphertext message) + + Notes + ===== + + ALGORITHM: + + STEPS: + 0. Number the letters of the alphabet from 0, ..., N + 1. Compute from the string ``msg`` a list ``L1`` of + corresponding integers. + 2. Compute from the list ``L1`` a new list ``L2``, given by + replacing ``x`` by ``a*x + b (mod N)``, for each element + ``x`` in ``L1``. + 3. Compute from the list ``L2`` a string ``ct`` of + corresponding letters. + + This is a straightforward generalization of the shift cipher with + the added complexity of requiring 2 characters to be deciphered in + order to recover the key. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Affine_cipher + + See Also + ======== + + decipher_affine + + """ + msg, _, A = _prep(msg, '', symbols) + N = len(A) + a, b = key + assert gcd(a, N) == 1 + if _inverse: + c = invert(a, N) + d = -b*c + a, b = c, d + B = ''.join([A[(a*i + b) % N] for i in range(N)]) + return translate(msg, A, B) + + +def decipher_affine(msg, key, symbols=None): + r""" + Return the deciphered text that was made from the mapping, + `x \rightarrow ax+b` (mod `N`), where ``N`` is the + number of characters in the alphabet. Deciphering is done by + reciphering with a new key: `x \rightarrow cx+d` (mod `N`), + where `c = a^{-1}` (mod `N`) and `d = -a^{-1}b` (mod `N`). + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_affine, decipher_affine + >>> msg = "GO NAVY BEAT ARMY" + >>> key = (3, 1) + >>> encipher_affine(msg, key) + 'TROBMVENBGBALV' + >>> decipher_affine(_, key) + 'GONAVYBEATARMY' + + See Also + ======== + + encipher_affine + + """ + return encipher_affine(msg, key, symbols, _inverse=True) + + +def encipher_atbash(msg, symbols=None): + r""" + Enciphers a given ``msg`` into its Atbash ciphertext and returns it. + + Explanation + =========== + + Atbash is a substitution cipher originally used to encrypt the Hebrew + alphabet. Atbash works on the principle of mapping each alphabet to its + reverse / counterpart (i.e. a would map to z, b to y etc.) + + Atbash is functionally equivalent to the affine cipher with ``a = 25`` + and ``b = 25`` + + See Also + ======== + + decipher_atbash + + """ + return encipher_affine(msg, (25, 25), symbols) + + +def decipher_atbash(msg, symbols=None): + r""" + Deciphers a given ``msg`` using Atbash cipher and returns it. + + Explanation + =========== + + ``decipher_atbash`` is functionally equivalent to ``encipher_atbash``. + However, it has still been added as a separate function to maintain + consistency. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_atbash, decipher_atbash + >>> msg = 'GONAVYBEATARMY' + >>> encipher_atbash(msg) + 'TLMZEBYVZGZINB' + >>> decipher_atbash(msg) + 'TLMZEBYVZGZINB' + >>> encipher_atbash(msg) == decipher_atbash(msg) + True + >>> msg == encipher_atbash(encipher_atbash(msg)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Atbash + + See Also + ======== + + encipher_atbash + + """ + return decipher_affine(msg, (25, 25), symbols) + +#################### substitution cipher ########################### + + +def encipher_substitution(msg, old, new=None): + r""" + Returns the ciphertext obtained by replacing each character that + appears in ``old`` with the corresponding character in ``new``. + If ``old`` is a mapping, then new is ignored and the replacements + defined by ``old`` are used. + + Explanation + =========== + + This is a more general than the affine cipher in that the key can + only be recovered by determining the mapping for each symbol. + Though in practice, once a few symbols are recognized the mappings + for other characters can be quickly guessed. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_substitution, AZ + >>> old = 'OEYAG' + >>> new = '034^6' + >>> msg = AZ("go navy! beat army!") + >>> ct = encipher_substitution(msg, old, new); ct + '60N^V4B3^T^RM4' + + To decrypt a substitution, reverse the last two arguments: + + >>> encipher_substitution(ct, new, old) + 'GONAVYBEATARMY' + + In the special case where ``old`` and ``new`` are a permutation of + order 2 (representing a transposition of characters) their order + is immaterial: + + >>> old = 'NAVY' + >>> new = 'ANYV' + >>> encipher = lambda x: encipher_substitution(x, old, new) + >>> encipher('NAVY') + 'ANYV' + >>> encipher(_) + 'NAVY' + + The substitution cipher, in general, is a method + whereby "units" (not necessarily single characters) of plaintext + are replaced with ciphertext according to a regular system. + + >>> ords = dict(zip('abc', ['\\%i' % ord(i) for i in 'abc'])) + >>> print(encipher_substitution('abc', ords)) + \97\98\99 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Substitution_cipher + + """ + return translate(msg, old, new) + + +###################################################################### +#################### Vigenere cipher examples ######################## +###################################################################### + +def encipher_vigenere(msg, key, symbols=None): + """ + Performs the Vigenere cipher encryption on plaintext ``msg``, and + returns the ciphertext. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_vigenere, AZ + >>> key = "encrypt" + >>> msg = "meet me on monday" + >>> encipher_vigenere(msg, key) + 'QRGKKTHRZQEBPR' + + Section 1 of the Kryptos sculpture at the CIA headquarters + uses this cipher and also changes the order of the + alphabet [2]_. Here is the first line of that section of + the sculpture: + + >>> from sympy.crypto.crypto import decipher_vigenere, padded_key + >>> alp = padded_key('KRYPTOS', AZ()) + >>> key = 'PALIMPSEST' + >>> msg = 'EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJ' + >>> decipher_vigenere(msg, key, alp) + 'BETWEENSUBTLESHADINGANDTHEABSENC' + + Explanation + =========== + + The Vigenere cipher is named after Blaise de Vigenere, a sixteenth + century diplomat and cryptographer, by a historical accident. + Vigenere actually invented a different and more complicated cipher. + The so-called *Vigenere cipher* was actually invented + by Giovan Batista Belaso in 1553. + + This cipher was used in the 1800's, for example, during the American + Civil War. The Confederacy used a brass cipher disk to implement the + Vigenere cipher (now on display in the NSA Museum in Fort + Meade) [1]_. + + The Vigenere cipher is a generalization of the shift cipher. + Whereas the shift cipher shifts each letter by the same amount + (that amount being the key of the shift cipher) the Vigenere + cipher shifts a letter by an amount determined by the key (which is + a word or phrase known only to the sender and receiver). + + For example, if the key was a single letter, such as "C", then the + so-called Vigenere cipher is actually a shift cipher with a + shift of `2` (since "C" is the 2nd letter of the alphabet, if + you start counting at `0`). If the key was a word with two + letters, such as "CA", then the so-called Vigenere cipher will + shift letters in even positions by `2` and letters in odd positions + are left alone (shifted by `0`, since "A" is the 0th letter, if + you start counting at `0`). + + + ALGORITHM: + + INPUT: + + ``msg``: string of characters that appear in ``symbols`` + (the plaintext) + + ``key``: a string of characters that appear in ``symbols`` + (the secret key) + + ``symbols``: a string of letters defining the alphabet + + + OUTPUT: + + ``ct``: string of characters (the ciphertext message) + + STEPS: + 0. Number the letters of the alphabet from 0, ..., N + 1. Compute from the string ``key`` a list ``L1`` of + corresponding integers. Let ``n1 = len(L1)``. + 2. Compute from the string ``msg`` a list ``L2`` of + corresponding integers. Let ``n2 = len(L2)``. + 3. Break ``L2`` up sequentially into sublists of size + ``n1``; the last sublist may be smaller than ``n1`` + 4. For each of these sublists ``L`` of ``L2``, compute a + new list ``C`` given by ``C[i] = L[i] + L1[i] (mod N)`` + to the ``i``-th element in the sublist, for each ``i``. + 5. Assemble these lists ``C`` by concatenation into a new + list of length ``n2``. + 6. Compute from the new list a string ``ct`` of + corresponding letters. + + Once it is known that the key is, say, `n` characters long, + frequency analysis can be applied to every `n`-th letter of + the ciphertext to determine the plaintext. This method is + called *Kasiski examination* (although it was first discovered + by Babbage). If they key is as long as the message and is + comprised of randomly selected characters -- a one-time pad -- the + message is theoretically unbreakable. + + The cipher Vigenere actually discovered is an "auto-key" cipher + described as follows. + + ALGORITHM: + + INPUT: + + ``key``: a string of letters (the secret key) + + ``msg``: string of letters (the plaintext message) + + OUTPUT: + + ``ct``: string of upper-case letters (the ciphertext message) + + STEPS: + 0. Number the letters of the alphabet from 0, ..., N + 1. Compute from the string ``msg`` a list ``L2`` of + corresponding integers. Let ``n2 = len(L2)``. + 2. Let ``n1`` be the length of the key. Append to the + string ``key`` the first ``n2 - n1`` characters of + the plaintext message. Compute from this string (also of + length ``n2``) a list ``L1`` of integers corresponding + to the letter numbers in the first step. + 3. Compute a new list ``C`` given by + ``C[i] = L1[i] + L2[i] (mod N)``. + 4. Compute from the new list a string ``ct`` of letters + corresponding to the new integers. + + To decipher the auto-key ciphertext, the key is used to decipher + the first ``n1`` characters and then those characters become the + key to decipher the next ``n1`` characters, etc...: + + >>> m = AZ('go navy, beat army! yes you can'); m + 'GONAVYBEATARMYYESYOUCAN' + >>> key = AZ('gold bug'); n1 = len(key); n2 = len(m) + >>> auto_key = key + m[:n2 - n1]; auto_key + 'GOLDBUGGONAVYBEATARMYYE' + >>> ct = encipher_vigenere(m, auto_key); ct + 'MCYDWSHKOGAMKZCELYFGAYR' + >>> n1 = len(key) + >>> pt = [] + >>> while ct: + ... part, ct = ct[:n1], ct[n1:] + ... pt.append(decipher_vigenere(part, key)) + ... key = pt[-1] + ... + >>> ''.join(pt) == m + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Vigenere_cipher + .. [2] https://web.archive.org/web/20071116100808/https://filebox.vt.edu/users/batman/kryptos.html + (short URL: https://goo.gl/ijr22d) + + """ + msg, key, A = _prep(msg, key, symbols) + map = {c: i for i, c in enumerate(A)} + key = [map[c] for c in key] + N = len(map) + k = len(key) + rv = [] + for i, m in enumerate(msg): + rv.append(A[(map[m] + key[i % k]) % N]) + rv = ''.join(rv) + return rv + + +def decipher_vigenere(msg, key, symbols=None): + """ + Decode using the Vigenere cipher. + + Examples + ======== + + >>> from sympy.crypto.crypto import decipher_vigenere + >>> key = "encrypt" + >>> ct = "QRGK kt HRZQE BPR" + >>> decipher_vigenere(ct, key) + 'MEETMEONMONDAY' + + """ + msg, key, A = _prep(msg, key, symbols) + map = {c: i for i, c in enumerate(A)} + N = len(A) # normally, 26 + K = [map[c] for c in key] + n = len(K) + C = [map[c] for c in msg] + rv = ''.join([A[(-K[i % n] + c) % N] for i, c in enumerate(C)]) + return rv + + +#################### Hill cipher ######################## + + +def encipher_hill(msg, key, symbols=None, pad="Q"): + r""" + Return the Hill cipher encryption of ``msg``. + + Explanation + =========== + + The Hill cipher [1]_, invented by Lester S. Hill in the 1920's [2]_, + was the first polygraphic cipher in which it was practical + (though barely) to operate on more than three symbols at once. + The following discussion assumes an elementary knowledge of + matrices. + + First, each letter is first encoded as a number starting with 0. + Suppose your message `msg` consists of `n` capital letters, with no + spaces. This may be regarded an `n`-tuple M of elements of + `Z_{26}` (if the letters are those of the English alphabet). A key + in the Hill cipher is a `k x k` matrix `K`, all of whose entries + are in `Z_{26}`, such that the matrix `K` is invertible (i.e., the + linear transformation `K: Z_{N}^k \rightarrow Z_{N}^k` + is one-to-one). + + + Parameters + ========== + + msg + Plaintext message of `n` upper-case letters. + + key + A `k \times k` invertible matrix `K`, all of whose entries are + in `Z_{26}` (or whatever number of symbols are being used). + + pad + Character (default "Q") to use to make length of text be a + multiple of ``k``. + + Returns + ======= + + ct + Ciphertext of upper-case letters. + + Notes + ===== + + ALGORITHM: + + STEPS: + 0. Number the letters of the alphabet from 0, ..., N + 1. Compute from the string ``msg`` a list ``L`` of + corresponding integers. Let ``n = len(L)``. + 2. Break the list ``L`` up into ``t = ceiling(n/k)`` + sublists ``L_1``, ..., ``L_t`` of size ``k`` (with + the last list "padded" to ensure its size is + ``k``). + 3. Compute new list ``C_1``, ..., ``C_t`` given by + ``C[i] = K*L_i`` (arithmetic is done mod N), for each + ``i``. + 4. Concatenate these into a list ``C = C_1 + ... + C_t``. + 5. Compute from ``C`` a string ``ct`` of corresponding + letters. This has length ``k*t``. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hill_cipher + .. [2] Lester S. Hill, Cryptography in an Algebraic Alphabet, + The American Mathematical Monthly Vol.36, June-July 1929, + pp.306-312. + + See Also + ======== + + decipher_hill + + """ + assert key.is_square + assert len(pad) == 1 + msg, pad, A = _prep(msg, pad, symbols) + map = {c: i for i, c in enumerate(A)} + P = [map[c] for c in msg] + N = len(A) + k = key.cols + n = len(P) + m, r = divmod(n, k) + if r: + P = P + [map[pad]]*(k - r) + m += 1 + rv = ''.join([A[c % N] for j in range(m) for c in + list(key*Matrix(k, 1, [P[i] + for i in range(k*j, k*(j + 1))]))]) + return rv + + +def decipher_hill(msg, key, symbols=None): + """ + Deciphering is the same as enciphering but using the inverse of the + key matrix. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_hill, decipher_hill + >>> from sympy import Matrix + + >>> key = Matrix([[1, 2], [3, 5]]) + >>> encipher_hill("meet me on monday", key) + 'UEQDUEODOCTCWQ' + >>> decipher_hill(_, key) + 'MEETMEONMONDAY' + + When the length of the plaintext (stripped of invalid characters) + is not a multiple of the key dimension, extra characters will + appear at the end of the enciphered and deciphered text. In order to + decipher the text, those characters must be included in the text to + be deciphered. In the following, the key has a dimension of 4 but + the text is 2 short of being a multiple of 4 so two characters will + be added. + + >>> key = Matrix([[1, 1, 1, 2], [0, 1, 1, 0], + ... [2, 2, 3, 4], [1, 1, 0, 1]]) + >>> msg = "ST" + >>> encipher_hill(msg, key) + 'HJEB' + >>> decipher_hill(_, key) + 'STQQ' + >>> encipher_hill(msg, key, pad="Z") + 'ISPK' + >>> decipher_hill(_, key) + 'STZZ' + + If the last two characters of the ciphertext were ignored in + either case, the wrong plaintext would be recovered: + + >>> decipher_hill("HD", key) + 'ORMV' + >>> decipher_hill("IS", key) + 'UIKY' + + See Also + ======== + + encipher_hill + + """ + assert key.is_square + msg, _, A = _prep(msg, '', symbols) + map = {c: i for i, c in enumerate(A)} + C = [map[c] for c in msg] + N = len(A) + k = key.cols + n = len(C) + m, r = divmod(n, k) + if r: + C = C + [0]*(k - r) + m += 1 + key_inv = key.inv_mod(N) + rv = ''.join([A[p % N] for j in range(m) for p in + list(key_inv*Matrix( + k, 1, [C[i] for i in range(k*j, k*(j + 1))]))]) + return rv + + +#################### Bifid cipher ######################## + + +def encipher_bifid(msg, key, symbols=None): + r""" + Performs the Bifid cipher encryption on plaintext ``msg``, and + returns the ciphertext. + + This is the version of the Bifid cipher that uses an `n \times n` + Polybius square. + + Parameters + ========== + + msg + Plaintext string. + + key + Short string for key. + + Duplicate characters are ignored and then it is padded with the + characters in ``symbols`` that were not in the short key. + + symbols + `n \times n` characters defining the alphabet. + + (default is string.printable) + + Returns + ======= + + ciphertext + Ciphertext using Bifid5 cipher without spaces. + + See Also + ======== + + decipher_bifid, encipher_bifid5, encipher_bifid6 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Bifid_cipher + + """ + msg, key, A = _prep(msg, key, symbols, bifid10) + long_key = ''.join(uniq(key)) or A + + n = len(A)**.5 + if n != int(n): + raise ValueError( + 'Length of alphabet (%s) is not a square number.' % len(A)) + N = int(n) + if len(long_key) < N**2: + long_key = list(long_key) + [x for x in A if x not in long_key] + + # the fractionalization + row_col = {ch: divmod(i, N) for i, ch in enumerate(long_key)} + r, c = zip(*[row_col[x] for x in msg]) + rc = r + c + ch = {i: ch for ch, i in row_col.items()} + rv = ''.join(ch[i] for i in zip(rc[::2], rc[1::2])) + return rv + + +def decipher_bifid(msg, key, symbols=None): + r""" + Performs the Bifid cipher decryption on ciphertext ``msg``, and + returns the plaintext. + + This is the version of the Bifid cipher that uses the `n \times n` + Polybius square. + + Parameters + ========== + + msg + Ciphertext string. + + key + Short string for key. + + Duplicate characters are ignored and then it is padded with the + characters in symbols that were not in the short key. + + symbols + `n \times n` characters defining the alphabet. + + (default=string.printable, a `10 \times 10` matrix) + + Returns + ======= + + deciphered + Deciphered text. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... encipher_bifid, decipher_bifid, AZ) + + Do an encryption using the bifid5 alphabet: + + >>> alp = AZ().replace('J', '') + >>> ct = AZ("meet me on monday!") + >>> key = AZ("gold bug") + >>> encipher_bifid(ct, key, alp) + 'IEILHHFSTSFQYE' + + When entering the text or ciphertext, spaces are ignored so it + can be formatted as desired. Re-entering the ciphertext from the + preceding, putting 4 characters per line and padding with an extra + J, does not cause problems for the deciphering: + + >>> decipher_bifid(''' + ... IEILH + ... HFSTS + ... FQYEJ''', key, alp) + 'MEETMEONMONDAY' + + When no alphabet is given, all 100 printable characters will be + used: + + >>> key = '' + >>> encipher_bifid('hello world!', key) + 'bmtwmg-bIo*w' + >>> decipher_bifid(_, key) + 'hello world!' + + If the key is changed, a different encryption is obtained: + + >>> key = 'gold bug' + >>> encipher_bifid('hello world!', 'gold_bug') + 'hg2sfuei7t}w' + + And if the key used to decrypt the message is not exact, the + original text will not be perfectly obtained: + + >>> decipher_bifid(_, 'gold pug') + 'heldo~wor6d!' + + """ + msg, _, A = _prep(msg, '', symbols, bifid10) + long_key = ''.join(uniq(key)) or A + + n = len(A)**.5 + if n != int(n): + raise ValueError( + 'Length of alphabet (%s) is not a square number.' % len(A)) + N = int(n) + if len(long_key) < N**2: + long_key = list(long_key) + [x for x in A if x not in long_key] + + # the reverse fractionalization + row_col = { + ch: divmod(i, N) for i, ch in enumerate(long_key)} + rc = [i for c in msg for i in row_col[c]] + n = len(msg) + rc = zip(*(rc[:n], rc[n:])) + ch = {i: ch for ch, i in row_col.items()} + rv = ''.join(ch[i] for i in rc) + return rv + + +def bifid_square(key): + """Return characters of ``key`` arranged in a square. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... bifid_square, AZ, padded_key, bifid5) + >>> bifid_square(AZ().replace('J', '')) + Matrix([ + [A, B, C, D, E], + [F, G, H, I, K], + [L, M, N, O, P], + [Q, R, S, T, U], + [V, W, X, Y, Z]]) + + >>> bifid_square(padded_key(AZ('gold bug!'), bifid5)) + Matrix([ + [G, O, L, D, B], + [U, A, C, E, F], + [H, I, K, M, N], + [P, Q, R, S, T], + [V, W, X, Y, Z]]) + + See Also + ======== + + padded_key + + """ + A = ''.join(uniq(''.join(key))) + n = len(A)**.5 + if n != int(n): + raise ValueError( + 'Length of alphabet (%s) is not a square number.' % len(A)) + n = int(n) + f = lambda i, j: Symbol(A[n*i + j]) + rv = Matrix(n, n, f) + return rv + + +def encipher_bifid5(msg, key): + r""" + Performs the Bifid cipher encryption on plaintext ``msg``, and + returns the ciphertext. + + Explanation + =========== + + This is the version of the Bifid cipher that uses the `5 \times 5` + Polybius square. The letter "J" is ignored so it must be replaced + with something else (traditionally an "I") before encryption. + + ALGORITHM: (5x5 case) + + STEPS: + 0. Create the `5 \times 5` Polybius square ``S`` associated + to ``key`` as follows: + + a) moving from left-to-right, top-to-bottom, + place the letters of the key into a `5 \times 5` + matrix, + b) if the key has less than 25 letters, add the + letters of the alphabet not in the key until the + `5 \times 5` square is filled. + + 1. Create a list ``P`` of pairs of numbers which are the + coordinates in the Polybius square of the letters in + ``msg``. + 2. Let ``L1`` be the list of all first coordinates of ``P`` + (length of ``L1 = n``), let ``L2`` be the list of all + second coordinates of ``P`` (so the length of ``L2`` + is also ``n``). + 3. Let ``L`` be the concatenation of ``L1`` and ``L2`` + (length ``L = 2*n``), except that consecutive numbers + are paired ``(L[2*i], L[2*i + 1])``. You can regard + ``L`` as a list of pairs of length ``n``. + 4. Let ``C`` be the list of all letters which are of the + form ``S[i, j]``, for all ``(i, j)`` in ``L``. As a + string, this is the ciphertext of ``msg``. + + Parameters + ========== + + msg : str + Plaintext string. + + Converted to upper case and filtered of anything but all letters + except J. + + key + Short string for key; non-alphabetic letters, J and duplicated + characters are ignored and then, if the length is less than 25 + characters, it is padded with other letters of the alphabet + (in alphabetical order). + + Returns + ======= + + ct + Ciphertext (all caps, no spaces). + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... encipher_bifid5, decipher_bifid5) + + "J" will be omitted unless it is replaced with something else: + + >>> round_trip = lambda m, k: \ + ... decipher_bifid5(encipher_bifid5(m, k), k) + >>> key = 'a' + >>> msg = "JOSIE" + >>> round_trip(msg, key) + 'OSIE' + >>> round_trip(msg.replace("J", "I"), key) + 'IOSIE' + >>> j = "QIQ" + >>> round_trip(msg.replace("J", j), key).replace(j, "J") + 'JOSIE' + + + Notes + ===== + + The Bifid cipher was invented around 1901 by Felix Delastelle. + It is a *fractional substitution* cipher, where letters are + replaced by pairs of symbols from a smaller alphabet. The + cipher uses a `5 \times 5` square filled with some ordering of the + alphabet, except that "J" is replaced with "I" (this is a so-called + Polybius square; there is a `6 \times 6` analog if you add back in + "J" and also append onto the usual 26 letter alphabet, the digits + 0, 1, ..., 9). + According to Helen Gaines' book *Cryptanalysis*, this type of cipher + was used in the field by the German Army during World War I. + + See Also + ======== + + decipher_bifid5, encipher_bifid + + """ + msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid5) + key = padded_key(key, bifid5) + return encipher_bifid(msg, '', key) + + +def decipher_bifid5(msg, key): + r""" + Return the Bifid cipher decryption of ``msg``. + + Explanation + =========== + + This is the version of the Bifid cipher that uses the `5 \times 5` + Polybius square; the letter "J" is ignored unless a ``key`` of + length 25 is used. + + Parameters + ========== + + msg + Ciphertext string. + + key + Short string for key; duplicated characters are ignored and if + the length is less then 25 characters, it will be padded with + other letters from the alphabet omitting "J". + Non-alphabetic characters are ignored. + + Returns + ======= + + plaintext + Plaintext from Bifid5 cipher (all caps, no spaces). + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_bifid5, decipher_bifid5 + >>> key = "gold bug" + >>> encipher_bifid5('meet me on friday', key) + 'IEILEHFSTSFXEE' + >>> encipher_bifid5('meet me on monday', key) + 'IEILHHFSTSFQYE' + >>> decipher_bifid5(_, key) + 'MEETMEONMONDAY' + + """ + msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid5) + key = padded_key(key, bifid5) + return decipher_bifid(msg, '', key) + + +def bifid5_square(key=None): + r""" + 5x5 Polybius square. + + Produce the Polybius square for the `5 \times 5` Bifid cipher. + + Examples + ======== + + >>> from sympy.crypto.crypto import bifid5_square + >>> bifid5_square("gold bug") + Matrix([ + [G, O, L, D, B], + [U, A, C, E, F], + [H, I, K, M, N], + [P, Q, R, S, T], + [V, W, X, Y, Z]]) + + """ + if not key: + key = bifid5 + else: + _, key, _ = _prep('', key.upper(), None, bifid5) + key = padded_key(key, bifid5) + return bifid_square(key) + + +def encipher_bifid6(msg, key): + r""" + Performs the Bifid cipher encryption on plaintext ``msg``, and + returns the ciphertext. + + This is the version of the Bifid cipher that uses the `6 \times 6` + Polybius square. + + Parameters + ========== + + msg + Plaintext string (digits okay). + + key + Short string for key (digits okay). + + If ``key`` is less than 36 characters long, the square will be + filled with letters A through Z and digits 0 through 9. + + Returns + ======= + + ciphertext + Ciphertext from Bifid cipher (all caps, no spaces). + + See Also + ======== + + decipher_bifid6, encipher_bifid + + """ + msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid6) + key = padded_key(key, bifid6) + return encipher_bifid(msg, '', key) + + +def decipher_bifid6(msg, key): + r""" + Performs the Bifid cipher decryption on ciphertext ``msg``, and + returns the plaintext. + + This is the version of the Bifid cipher that uses the `6 \times 6` + Polybius square. + + Parameters + ========== + + msg + Ciphertext string (digits okay); converted to upper case + + key + Short string for key (digits okay). + + If ``key`` is less than 36 characters long, the square will be + filled with letters A through Z and digits 0 through 9. + All letters are converted to uppercase. + + Returns + ======= + + plaintext + Plaintext from Bifid cipher (all caps, no spaces). + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_bifid6, decipher_bifid6 + >>> key = "gold bug" + >>> encipher_bifid6('meet me on monday at 8am', key) + 'KFKLJJHF5MMMKTFRGPL' + >>> decipher_bifid6(_, key) + 'MEETMEONMONDAYAT8AM' + + """ + msg, key, _ = _prep(msg.upper(), key.upper(), None, bifid6) + key = padded_key(key, bifid6) + return decipher_bifid(msg, '', key) + + +def bifid6_square(key=None): + r""" + 6x6 Polybius square. + + Produces the Polybius square for the `6 \times 6` Bifid cipher. + Assumes alphabet of symbols is "A", ..., "Z", "0", ..., "9". + + Examples + ======== + + >>> from sympy.crypto.crypto import bifid6_square + >>> key = "gold bug" + >>> bifid6_square(key) + Matrix([ + [G, O, L, D, B, U], + [A, C, E, F, H, I], + [J, K, M, N, P, Q], + [R, S, T, V, W, X], + [Y, Z, 0, 1, 2, 3], + [4, 5, 6, 7, 8, 9]]) + + """ + if not key: + key = bifid6 + else: + _, key, _ = _prep('', key.upper(), None, bifid6) + key = padded_key(key, bifid6) + return bifid_square(key) + + +#################### RSA ############################# + +def _decipher_rsa_crt(i, d, factors): + """Decipher RSA using chinese remainder theorem from the information + of the relatively-prime factors of the modulus. + + Parameters + ========== + + i : integer + Ciphertext + + d : integer + The exponent component. + + factors : list of relatively-prime integers + The integers given must be coprime and the product must equal + the modulus component of the original RSA key. + + Examples + ======== + + How to decrypt RSA with CRT: + + >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key + >>> primes = [61, 53] + >>> e = 17 + >>> args = primes + [e] + >>> puk = rsa_public_key(*args) + >>> prk = rsa_private_key(*args) + + >>> from sympy.crypto.crypto import encipher_rsa, _decipher_rsa_crt + >>> msg = 65 + >>> crt_primes = primes + >>> encrypted = encipher_rsa(msg, puk) + >>> decrypted = _decipher_rsa_crt(encrypted, prk[1], primes) + >>> decrypted + 65 + """ + moduluses = [pow(i, d, p) for p in factors] + + result = crt(factors, moduluses) + if not result: + raise ValueError("CRT failed") + return result[0] + + +def _rsa_key(*args, public=True, private=True, totient='Euler', index=None, multipower=None): + r"""A private subroutine to generate RSA key + + Parameters + ========== + + public, private : bool, optional + Flag to generate either a public key, a private key. + + totient : 'Euler' or 'Carmichael' + Different notation used for totient. + + multipower : bool, optional + Flag to bypass warning for multipower RSA. + """ + + if len(args) < 2: + return False + + if totient not in ('Euler', 'Carmichael'): + raise ValueError( + "The argument totient={} should either be " \ + "'Euler', 'Carmichalel'." \ + .format(totient)) + + if totient == 'Euler': + _totient = _euler + else: + _totient = _carmichael + + if index is not None: + index = as_int(index) + if totient != 'Carmichael': + raise ValueError( + "Setting the 'index' keyword argument requires totient" + "notation to be specified as 'Carmichael'.") + + primes, e = args[:-1], args[-1] + + if not all(isprime(p) for p in primes): + new_primes = [] + for i in primes: + new_primes.extend(factorint(i, multiple=True)) + primes = new_primes + + n = reduce(lambda i, j: i*j, primes) + + tally = multiset(primes) + if all(v == 1 for v in tally.values()): + phi = int(_totient(tally)) + + else: + if not multipower: + NonInvertibleCipherWarning( + 'Non-distinctive primes found in the factors {}. ' + 'The cipher may not be decryptable for some numbers ' + 'in the complete residue system Z[{}], but the cipher ' + 'can still be valid if you restrict the domain to be ' + 'the reduced residue system Z*[{}]. You can pass ' + 'the flag multipower=True if you want to suppress this ' + 'warning.' + .format(primes, n, n) + # stacklevel=4 because most users will call a function that + # calls this function + ).warn(stacklevel=4) + phi = int(_totient(tally)) + + if gcd(e, phi) == 1: + if public and not private: + if isinstance(index, int): + e = e % phi + e += index * phi + return n, e + + if private and not public: + d = invert(e, phi) + if isinstance(index, int): + d += index * phi + return n, d + + return False + + +def rsa_public_key(*args, **kwargs): + r"""Return the RSA *public key* pair, `(n, e)` + + Parameters + ========== + + args : naturals + If specified as `p, q, e` where `p` and `q` are distinct primes + and `e` is a desired public exponent of the RSA, `n = p q` and + `e` will be verified against the totient + `\phi(n)` (Euler totient) or `\lambda(n)` (Carmichael totient) + to be `\gcd(e, \phi(n)) = 1` or `\gcd(e, \lambda(n)) = 1`. + + If specified as `p_1, p_2, \dots, p_n, e` where + `p_1, p_2, \dots, p_n` are specified as primes, + and `e` is specified as a desired public exponent of the RSA, + it will be able to form a multi-prime RSA, which is a more + generalized form of the popular 2-prime RSA. + + It can also be possible to form a single-prime RSA by specifying + the argument as `p, e`, which can be considered a trivial case + of a multiprime RSA. + + Furthermore, it can be possible to form a multi-power RSA by + specifying two or more pairs of the primes to be same. + However, unlike the two-distinct prime RSA or multi-prime + RSA, not every numbers in the complete residue system + (`\mathbb{Z}_n`) will be decryptable since the mapping + `\mathbb{Z}_{n} \rightarrow \mathbb{Z}_{n}` + will not be bijective. + (Only except for the trivial case when + `e = 1` + or more generally, + + .. math:: + e \in \left \{ 1 + k \lambda(n) + \mid k \in \mathbb{Z} \land k \geq 0 \right \} + + when RSA reduces to the identity.) + However, the RSA can still be decryptable for the numbers in the + reduced residue system (`\mathbb{Z}_n^{\times}`), since the + mapping + `\mathbb{Z}_{n}^{\times} \rightarrow \mathbb{Z}_{n}^{\times}` + can still be bijective. + + If you pass a non-prime integer to the arguments + `p_1, p_2, \dots, p_n`, the particular number will be + prime-factored and it will become either a multi-prime RSA or a + multi-power RSA in its canonical form, depending on whether the + product equals its radical or not. + `p_1 p_2 \dots p_n = \text{rad}(p_1 p_2 \dots p_n)` + + totient : bool, optional + If ``'Euler'``, it uses Euler's totient `\phi(n)` which is + :meth:`sympy.functions.combinatorial.numbers.totient` in SymPy. + + If ``'Carmichael'``, it uses Carmichael's totient `\lambda(n)` + which is :meth:`sympy.functions.combinatorial.numbers.reduced_totient` in SymPy. + + Unlike private key generation, this is a trivial keyword for + public key generation because + `\gcd(e, \phi(n)) = 1 \iff \gcd(e, \lambda(n)) = 1`. + + index : nonnegative integer, optional + Returns an arbitrary solution of a RSA public key at the index + specified at `0, 1, 2, \dots`. This parameter needs to be + specified along with ``totient='Carmichael'``. + + Similarly to the non-uniquenss of a RSA private key as described + in the ``index`` parameter documentation in + :meth:`rsa_private_key`, RSA public key is also not unique and + there is an infinite number of RSA public exponents which + can behave in the same manner. + + From any given RSA public exponent `e`, there are can be an + another RSA public exponent `e + k \lambda(n)` where `k` is an + integer, `\lambda` is a Carmichael's totient function. + + However, considering only the positive cases, there can be + a principal solution of a RSA public exponent `e_0` in + `0 < e_0 < \lambda(n)`, and all the other solutions + can be canonicalzed in a form of `e_0 + k \lambda(n)`. + + ``index`` specifies the `k` notation to yield any possible value + an RSA public key can have. + + An example of computing any arbitrary RSA public key: + + >>> from sympy.crypto.crypto import rsa_public_key + >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=0) + (3233, 17) + >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=1) + (3233, 797) + >>> rsa_public_key(61, 53, 17, totient='Carmichael', index=2) + (3233, 1577) + + multipower : bool, optional + Any pair of non-distinct primes found in the RSA specification + will restrict the domain of the cryptosystem, as noted in the + explanation of the parameter ``args``. + + SymPy RSA key generator may give a warning before dispatching it + as a multi-power RSA, however, you can disable the warning if + you pass ``True`` to this keyword. + + Returns + ======= + + (n, e) : int, int + `n` is a product of any arbitrary number of primes given as + the argument. + + `e` is relatively prime (coprime) to the Euler totient + `\phi(n)`. + + False + Returned if less than two arguments are given, or `e` is + not relatively prime to the modulus. + + Examples + ======== + + >>> from sympy.crypto.crypto import rsa_public_key + + A public key of a two-prime RSA: + + >>> p, q, e = 3, 5, 7 + >>> rsa_public_key(p, q, e) + (15, 7) + >>> rsa_public_key(p, q, 30) + False + + A public key of a multiprime RSA: + + >>> primes = [2, 3, 5, 7, 11, 13] + >>> e = 7 + >>> args = primes + [e] + >>> rsa_public_key(*args) + (30030, 7) + + Notes + ===== + + Although the RSA can be generalized over any modulus `n`, using + two large primes had became the most popular specification because a + product of two large primes is usually the hardest to factor + relatively to the digits of `n` can have. + + However, it may need further understanding of the time complexities + of each prime-factoring algorithms to verify the claim. + + See Also + ======== + + rsa_private_key + encipher_rsa + decipher_rsa + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29 + + .. [2] https://cacr.uwaterloo.ca/techreports/2006/cacr2006-16.pdf + + .. [3] https://link.springer.com/content/pdf/10.1007/BFb0055738.pdf + + .. [4] https://www.itiis.org/digital-library/manuscript/1381 + """ + return _rsa_key(*args, public=True, private=False, **kwargs) + + +def rsa_private_key(*args, **kwargs): + r"""Return the RSA *private key* pair, `(n, d)` + + Parameters + ========== + + args : naturals + The keyword is identical to the ``args`` in + :meth:`rsa_public_key`. + + totient : bool, optional + If ``'Euler'``, it uses Euler's totient convention `\phi(n)` + which is :meth:`sympy.functions.combinatorial.numbers.totient` in SymPy. + + If ``'Carmichael'``, it uses Carmichael's totient convention + `\lambda(n)` which is + :meth:`sympy.functions.combinatorial.numbers.reduced_totient` in SymPy. + + There can be some output differences for private key generation + as examples below. + + Example using Euler's totient: + + >>> from sympy.crypto.crypto import rsa_private_key + >>> rsa_private_key(61, 53, 17, totient='Euler') + (3233, 2753) + + Example using Carmichael's totient: + + >>> from sympy.crypto.crypto import rsa_private_key + >>> rsa_private_key(61, 53, 17, totient='Carmichael') + (3233, 413) + + index : nonnegative integer, optional + Returns an arbitrary solution of a RSA private key at the index + specified at `0, 1, 2, \dots`. This parameter needs to be + specified along with ``totient='Carmichael'``. + + RSA private exponent is a non-unique solution of + `e d \mod \lambda(n) = 1` and it is possible in any form of + `d + k \lambda(n)`, where `d` is an another + already-computed private exponent, and `\lambda` is a + Carmichael's totient function, and `k` is any integer. + + However, considering only the positive cases, there can be + a principal solution of a RSA private exponent `d_0` in + `0 < d_0 < \lambda(n)`, and all the other solutions + can be canonicalzed in a form of `d_0 + k \lambda(n)`. + + ``index`` specifies the `k` notation to yield any possible value + an RSA private key can have. + + An example of computing any arbitrary RSA private key: + + >>> from sympy.crypto.crypto import rsa_private_key + >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=0) + (3233, 413) + >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=1) + (3233, 1193) + >>> rsa_private_key(61, 53, 17, totient='Carmichael', index=2) + (3233, 1973) + + multipower : bool, optional + The keyword is identical to the ``multipower`` in + :meth:`rsa_public_key`. + + Returns + ======= + + (n, d) : int, int + `n` is a product of any arbitrary number of primes given as + the argument. + + `d` is the inverse of `e` (mod `\phi(n)`) where `e` is the + exponent given, and `\phi` is a Euler totient. + + False + Returned if less than two arguments are given, or `e` is + not relatively prime to the totient of the modulus. + + Examples + ======== + + >>> from sympy.crypto.crypto import rsa_private_key + + A private key of a two-prime RSA: + + >>> p, q, e = 3, 5, 7 + >>> rsa_private_key(p, q, e) + (15, 7) + >>> rsa_private_key(p, q, 30) + False + + A private key of a multiprime RSA: + + >>> primes = [2, 3, 5, 7, 11, 13] + >>> e = 7 + >>> args = primes + [e] + >>> rsa_private_key(*args) + (30030, 823) + + See Also + ======== + + rsa_public_key + encipher_rsa + decipher_rsa + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29 + + .. [2] https://cacr.uwaterloo.ca/techreports/2006/cacr2006-16.pdf + + .. [3] https://link.springer.com/content/pdf/10.1007/BFb0055738.pdf + + .. [4] https://www.itiis.org/digital-library/manuscript/1381 + """ + return _rsa_key(*args, public=False, private=True, **kwargs) + + +def _encipher_decipher_rsa(i, key, factors=None): + n, d = key + if not factors: + return pow(i, d, n) + + def _is_coprime_set(l): + is_coprime_set = True + for i in range(len(l)): + for j in range(i+1, len(l)): + if gcd(l[i], l[j]) != 1: + is_coprime_set = False + break + return is_coprime_set + + prod = reduce(lambda i, j: i*j, factors) + if prod == n and _is_coprime_set(factors): + return _decipher_rsa_crt(i, d, factors) + return _encipher_decipher_rsa(i, key, factors=None) + + +def encipher_rsa(i, key, factors=None): + r"""Encrypt the plaintext with RSA. + + Parameters + ========== + + i : integer + The plaintext to be encrypted for. + + key : (n, e) where n, e are integers + `n` is the modulus of the key and `e` is the exponent of the + key. The encryption is computed by `i^e \bmod n`. + + The key can either be a public key or a private key, however, + the message encrypted by a public key can only be decrypted by + a private key, and vice versa, as RSA is an asymmetric + cryptography system. + + factors : list of coprime integers + This is identical to the keyword ``factors`` in + :meth:`decipher_rsa`. + + Notes + ===== + + Some specifications may make the RSA not cryptographically + meaningful. + + For example, `0`, `1` will remain always same after taking any + number of exponentiation, thus, should be avoided. + + Furthermore, if `i^e < n`, `i` may easily be figured out by taking + `e` th root. + + And also, specifying the exponent as `1` or in more generalized form + as `1 + k \lambda(n)` where `k` is an nonnegative integer, + `\lambda` is a carmichael totient, the RSA becomes an identity + mapping. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_rsa + >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key + + Public Key Encryption: + + >>> p, q, e = 3, 5, 7 + >>> puk = rsa_public_key(p, q, e) + >>> msg = 12 + >>> encipher_rsa(msg, puk) + 3 + + Private Key Encryption: + + >>> p, q, e = 3, 5, 7 + >>> prk = rsa_private_key(p, q, e) + >>> msg = 12 + >>> encipher_rsa(msg, prk) + 3 + + Encryption using chinese remainder theorem: + + >>> encipher_rsa(msg, prk, factors=[p, q]) + 3 + """ + return _encipher_decipher_rsa(i, key, factors=factors) + + +def decipher_rsa(i, key, factors=None): + r"""Decrypt the ciphertext with RSA. + + Parameters + ========== + + i : integer + The ciphertext to be decrypted for. + + key : (n, d) where n, d are integers + `n` is the modulus of the key and `d` is the exponent of the + key. The decryption is computed by `i^d \bmod n`. + + The key can either be a public key or a private key, however, + the message encrypted by a public key can only be decrypted by + a private key, and vice versa, as RSA is an asymmetric + cryptography system. + + factors : list of coprime integers + As the modulus `n` created from RSA key generation is composed + of arbitrary prime factors + `n = {p_1}^{k_1}{p_2}^{k_2}\dots{p_n}^{k_n}` where + `p_1, p_2, \dots, p_n` are distinct primes and + `k_1, k_2, \dots, k_n` are positive integers, chinese remainder + theorem can be used to compute `i^d \bmod n` from the + fragmented modulo operations like + + .. math:: + i^d \bmod {p_1}^{k_1}, i^d \bmod {p_2}^{k_2}, \dots, + i^d \bmod {p_n}^{k_n} + + or like + + .. math:: + i^d \bmod {p_1}^{k_1}{p_2}^{k_2}, + i^d \bmod {p_3}^{k_3}, \dots , + i^d \bmod {p_n}^{k_n} + + as long as every moduli does not share any common divisor each + other. + + The raw primes used in generating the RSA key pair can be a good + option. + + Note that the speed advantage of using this is only viable for + very large cases (Like 2048-bit RSA keys) since the + overhead of using pure Python implementation of + :meth:`sympy.ntheory.modular.crt` may overcompensate the + theoretical speed advantage. + + Notes + ===== + + See the ``Notes`` section in the documentation of + :meth:`encipher_rsa` + + Examples + ======== + + >>> from sympy.crypto.crypto import decipher_rsa, encipher_rsa + >>> from sympy.crypto.crypto import rsa_public_key, rsa_private_key + + Public Key Encryption and Decryption: + + >>> p, q, e = 3, 5, 7 + >>> prk = rsa_private_key(p, q, e) + >>> puk = rsa_public_key(p, q, e) + >>> msg = 12 + >>> new_msg = encipher_rsa(msg, prk) + >>> new_msg + 3 + >>> decipher_rsa(new_msg, puk) + 12 + + Private Key Encryption and Decryption: + + >>> p, q, e = 3, 5, 7 + >>> prk = rsa_private_key(p, q, e) + >>> puk = rsa_public_key(p, q, e) + >>> msg = 12 + >>> new_msg = encipher_rsa(msg, puk) + >>> new_msg + 3 + >>> decipher_rsa(new_msg, prk) + 12 + + Decryption using chinese remainder theorem: + + >>> decipher_rsa(new_msg, prk, factors=[p, q]) + 12 + + See Also + ======== + + encipher_rsa + """ + return _encipher_decipher_rsa(i, key, factors=factors) + + +#################### kid krypto (kid RSA) ############################# + + +def kid_rsa_public_key(a, b, A, B): + r""" + Kid RSA is a version of RSA useful to teach grade school children + since it does not involve exponentiation. + + Explanation + =========== + + Alice wants to talk to Bob. Bob generates keys as follows. + Key generation: + + * Select positive integers `a, b, A, B` at random. + * Compute `M = a b - 1`, `e = A M + a`, `d = B M + b`, + `n = (e d - 1)//M`. + * The *public key* is `(n, e)`. Bob sends these to Alice. + * The *private key* is `(n, d)`, which Bob keeps secret. + + Encryption: If `p` is the plaintext message then the + ciphertext is `c = p e \pmod n`. + + Decryption: If `c` is the ciphertext message then the + plaintext is `p = c d \pmod n`. + + Examples + ======== + + >>> from sympy.crypto.crypto import kid_rsa_public_key + >>> a, b, A, B = 3, 4, 5, 6 + >>> kid_rsa_public_key(a, b, A, B) + (369, 58) + + """ + M = a*b - 1 + e = A*M + a + d = B*M + b + n = (e*d - 1)//M + return n, e + + +def kid_rsa_private_key(a, b, A, B): + """ + Compute `M = a b - 1`, `e = A M + a`, `d = B M + b`, + `n = (e d - 1) / M`. The *private key* is `d`, which Bob + keeps secret. + + Examples + ======== + + >>> from sympy.crypto.crypto import kid_rsa_private_key + >>> a, b, A, B = 3, 4, 5, 6 + >>> kid_rsa_private_key(a, b, A, B) + (369, 70) + + """ + M = a*b - 1 + e = A*M + a + d = B*M + b + n = (e*d - 1)//M + return n, d + + +def encipher_kid_rsa(msg, key): + """ + Here ``msg`` is the plaintext and ``key`` is the public key. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... encipher_kid_rsa, kid_rsa_public_key) + >>> msg = 200 + >>> a, b, A, B = 3, 4, 5, 6 + >>> key = kid_rsa_public_key(a, b, A, B) + >>> encipher_kid_rsa(msg, key) + 161 + + """ + n, e = key + return (msg*e) % n + + +def decipher_kid_rsa(msg, key): + """ + Here ``msg`` is the plaintext and ``key`` is the private key. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... kid_rsa_public_key, kid_rsa_private_key, + ... decipher_kid_rsa, encipher_kid_rsa) + >>> a, b, A, B = 3, 4, 5, 6 + >>> d = kid_rsa_private_key(a, b, A, B) + >>> msg = 200 + >>> pub = kid_rsa_public_key(a, b, A, B) + >>> pri = kid_rsa_private_key(a, b, A, B) + >>> ct = encipher_kid_rsa(msg, pub) + >>> decipher_kid_rsa(ct, pri) + 200 + + """ + n, d = key + return (msg*d) % n + + +#################### Morse Code ###################################### + +morse_char = { + ".-": "A", "-...": "B", + "-.-.": "C", "-..": "D", + ".": "E", "..-.": "F", + "--.": "G", "....": "H", + "..": "I", ".---": "J", + "-.-": "K", ".-..": "L", + "--": "M", "-.": "N", + "---": "O", ".--.": "P", + "--.-": "Q", ".-.": "R", + "...": "S", "-": "T", + "..-": "U", "...-": "V", + ".--": "W", "-..-": "X", + "-.--": "Y", "--..": "Z", + "-----": "0", ".----": "1", + "..---": "2", "...--": "3", + "....-": "4", ".....": "5", + "-....": "6", "--...": "7", + "---..": "8", "----.": "9", + ".-.-.-": ".", "--..--": ",", + "---...": ":", "-.-.-.": ";", + "..--..": "?", "-....-": "-", + "..--.-": "_", "-.--.": "(", + "-.--.-": ")", ".----.": "'", + "-...-": "=", ".-.-.": "+", + "-..-.": "/", ".--.-.": "@", + "...-..-": "$", "-.-.--": "!"} +char_morse = {v: k for k, v in morse_char.items()} + + +def encode_morse(msg, sep='|', mapping=None): + """ + Encodes a plaintext into popular Morse Code with letters + separated by ``sep`` and words by a double ``sep``. + + Examples + ======== + + >>> from sympy.crypto.crypto import encode_morse + >>> msg = 'ATTACK RIGHT FLANK' + >>> encode_morse(msg) + '.-|-|-|.-|-.-.|-.-||.-.|..|--.|....|-||..-.|.-..|.-|-.|-.-' + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Morse_code + + """ + + mapping = mapping or char_morse + assert sep not in mapping + word_sep = 2*sep + mapping[" "] = word_sep + suffix = msg and msg[-1] in whitespace + + # normalize whitespace + msg = (' ' if word_sep else '').join(msg.split()) + # omit unmapped chars + chars = set(''.join(msg.split())) + ok = set(mapping.keys()) + msg = translate(msg, None, ''.join(chars - ok)) + + morsestring = [] + words = msg.split() + for word in words: + morseword = [] + for letter in word: + morseletter = mapping[letter] + morseword.append(morseletter) + + word = sep.join(morseword) + morsestring.append(word) + + return word_sep.join(morsestring) + (word_sep if suffix else '') + + +def decode_morse(msg, sep='|', mapping=None): + """ + Decodes a Morse Code with letters separated by ``sep`` + (default is '|') and words by `word_sep` (default is '||) + into plaintext. + + Examples + ======== + + >>> from sympy.crypto.crypto import decode_morse + >>> mc = '--|---|...-|.||.|.-|...|-' + >>> decode_morse(mc) + 'MOVE EAST' + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Morse_code + + """ + + mapping = mapping or morse_char + word_sep = 2*sep + characterstring = [] + words = msg.strip(word_sep).split(word_sep) + for word in words: + letters = word.split(sep) + chars = [mapping[c] for c in letters] + word = ''.join(chars) + characterstring.append(word) + rv = " ".join(characterstring) + return rv + + +#################### LFSRs ########################################## + + +@doctest_depends_on(ground_types=['python', 'gmpy']) +def lfsr_sequence(key, fill, n): + r""" + This function creates an LFSR sequence. + + Parameters + ========== + + key : list + A list of finite field elements, `[c_0, c_1, \ldots, c_k].` + + fill : list + The list of the initial terms of the LFSR sequence, + `[x_0, x_1, \ldots, x_k].` + + n + Number of terms of the sequence that the function returns. + + Returns + ======= + + L + The LFSR sequence defined by + `x_{n+1} = c_k x_n + \ldots + c_0 x_{n-k}`, for + `n \leq k`. + + Notes + ===== + + S. Golomb [G]_ gives a list of three statistical properties a + sequence of numbers `a = \{a_n\}_{n=1}^\infty`, + `a_n \in \{0,1\}`, should display to be considered + "random". Define the autocorrelation of `a` to be + + .. math:: + + C(k) = C(k,a) = \lim_{N\rightarrow \infty} {1\over N}\sum_{n=1}^N (-1)^{a_n + a_{n+k}}. + + In the case where `a` is periodic with period + `P` then this reduces to + + .. math:: + + C(k) = {1\over P}\sum_{n=1}^P (-1)^{a_n + a_{n+k}}. + + Assume `a` is periodic with period `P`. + + - balance: + + .. math:: + + \left|\sum_{n=1}^P(-1)^{a_n}\right| \leq 1. + + - low autocorrelation: + + .. math:: + + C(k) = \left\{ \begin{array}{cc} 1,& k = 0,\\ \epsilon, & k \ne 0. \end{array} \right. + + (For sequences satisfying these first two properties, it is known + that `\epsilon = -1/P` must hold.) + + - proportional runs property: In each period, half the runs have + length `1`, one-fourth have length `2`, etc. + Moreover, there are as many runs of `1`'s as there are of + `0`'s. + + Examples + ======== + + >>> from sympy.crypto.crypto import lfsr_sequence + >>> from sympy.polys.domains import FF + >>> F = FF(2) + >>> fill = [F(1), F(1), F(0), F(1)] + >>> key = [F(1), F(0), F(0), F(1)] + >>> lfsr_sequence(key, fill, 10) + [1 mod 2, 1 mod 2, 0 mod 2, 1 mod 2, 0 mod 2, + 1 mod 2, 1 mod 2, 0 mod 2, 0 mod 2, 1 mod 2] + + References + ========== + + .. [G] Solomon Golomb, Shift register sequences, Aegean Park Press, + Laguna Hills, Ca, 1967 + + """ + if not isinstance(key, list): + raise TypeError("key must be a list") + if not isinstance(fill, list): + raise TypeError("fill must be a list") + p = key[0].modulus() + F = FF(p) + s = fill + k = len(fill) + L = [] + for i in range(n): + s0 = s[:] + L.append(s[0]) + s = s[1:k] + x = sum(int(key[i]*s0[i]) for i in range(k)) + s.append(F(x)) + return L # use [int(x) for x in L] for int version + + +def lfsr_autocorrelation(L, P, k): + """ + This function computes the LFSR autocorrelation function. + + Parameters + ========== + + L + A periodic sequence of elements of `GF(2)`. + L must have length larger than P. + + P + The period of L. + + k : int + An integer `k` (`0 < k < P`). + + Returns + ======= + + autocorrelation + The k-th value of the autocorrelation of the LFSR L. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... lfsr_sequence, lfsr_autocorrelation) + >>> from sympy.polys.domains import FF + >>> F = FF(2) + >>> fill = [F(1), F(1), F(0), F(1)] + >>> key = [F(1), F(0), F(0), F(1)] + >>> s = lfsr_sequence(key, fill, 20) + >>> lfsr_autocorrelation(s, 15, 7) + -1/15 + >>> lfsr_autocorrelation(s, 15, 0) + 1 + + """ + if not isinstance(L, list): + raise TypeError("L (=%s) must be a list" % L) + P = int(P) + k = int(k) + L0 = L[:P] # slices makes a copy + L1 = L0 + L0[:k] + L2 = [(-1)**(int(L1[i]) + int(L1[i + k])) for i in range(P)] + tot = sum(L2) + return Rational(tot, P) + + +def lfsr_connection_polynomial(s): + """ + This function computes the LFSR connection polynomial. + + Parameters + ========== + + s + A sequence of elements of even length, with entries in a finite + field. + + Returns + ======= + + C(x) + The connection polynomial of a minimal LFSR yielding s. + + This implements the algorithm in section 3 of J. L. Massey's + article [M]_. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... lfsr_sequence, lfsr_connection_polynomial) + >>> from sympy.polys.domains import FF + >>> F = FF(2) + >>> fill = [F(1), F(1), F(0), F(1)] + >>> key = [F(1), F(0), F(0), F(1)] + >>> s = lfsr_sequence(key, fill, 20) + >>> lfsr_connection_polynomial(s) + x**4 + x + 1 + >>> fill = [F(1), F(0), F(0), F(1)] + >>> key = [F(1), F(1), F(0), F(1)] + >>> s = lfsr_sequence(key, fill, 20) + >>> lfsr_connection_polynomial(s) + x**3 + 1 + >>> fill = [F(1), F(0), F(1)] + >>> key = [F(1), F(1), F(0)] + >>> s = lfsr_sequence(key, fill, 20) + >>> lfsr_connection_polynomial(s) + x**3 + x**2 + 1 + >>> fill = [F(1), F(0), F(1)] + >>> key = [F(1), F(0), F(1)] + >>> s = lfsr_sequence(key, fill, 20) + >>> lfsr_connection_polynomial(s) + x**3 + x + 1 + + References + ========== + + .. [M] James L. Massey, "Shift-Register Synthesis and BCH Decoding." + IEEE Trans. on Information Theory, vol. 15(1), pp. 122-127, + Jan 1969. + + """ + # Initialization: + p = s[0].modulus() + x = Symbol("x") + C = 1*x**0 + B = 1*x**0 + m = 1 + b = 1*x**0 + L = 0 + N = 0 + while N < len(s): + if L > 0: + dC = Poly(C).degree() + r = min(L + 1, dC + 1) + coeffsC = [C.subs(x, 0)] + [C.coeff(x**i) + for i in range(1, dC + 1)] + d = (int(s[N]) + sum(coeffsC[i]*int(s[N - i]) + for i in range(1, r))) % p + if L == 0: + d = int(s[N])*x**0 + if d == 0: + m += 1 + N += 1 + if d > 0: + if 2*L > N: + C = (C - d*((b**(p - 2)) % p)*x**m*B).expand() + m += 1 + N += 1 + else: + T = C + C = (C - d*((b**(p - 2)) % p)*x**m*B).expand() + L = N + 1 - L + m = 1 + b = d + B = T + N += 1 + dC = Poly(C).degree() + coeffsC = [C.subs(x, 0)] + [C.coeff(x**i) for i in range(1, dC + 1)] + return sum(coeffsC[i] % p*x**i for i in range(dC + 1) + if coeffsC[i] is not None) + + +#################### ElGamal ############################# + + +def elgamal_private_key(digit=10, seed=None): + r""" + Return three number tuple as private key. + + Explanation + =========== + + Elgamal encryption is based on the mathematical problem + called the Discrete Logarithm Problem (DLP). For example, + + `a^{b} \equiv c \pmod p` + + In general, if ``a`` and ``b`` are known, ``ct`` is easily + calculated. If ``b`` is unknown, it is hard to use + ``a`` and ``ct`` to get ``b``. + + Parameters + ========== + + digit : int + Minimum number of binary digits for key. + + Returns + ======= + + tuple : (p, r, d) + p = prime number. + + r = primitive root. + + d = random number. + + Notes + ===== + + For testing purposes, the ``seed`` parameter may be set to control + the output of this routine. See sympy.core.random._randrange. + + Examples + ======== + + >>> from sympy.crypto.crypto import elgamal_private_key + >>> from sympy.ntheory import is_primitive_root, isprime + >>> a, b, _ = elgamal_private_key() + >>> isprime(a) + True + >>> is_primitive_root(b, a) + True + + """ + randrange = _randrange(seed) + p = nextprime(2**digit) + return p, primitive_root(p), randrange(2, p) + + +def elgamal_public_key(key): + r""" + Return three number tuple as public key. + + Parameters + ========== + + key : (p, r, e) + Tuple generated by ``elgamal_private_key``. + + Returns + ======= + + tuple : (p, r, e) + `e = r**d \bmod p` + + `d` is a random number in private key. + + Examples + ======== + + >>> from sympy.crypto.crypto import elgamal_public_key + >>> elgamal_public_key((1031, 14, 636)) + (1031, 14, 212) + + """ + p, r, e = key + return p, r, pow(r, e, p) + + +def encipher_elgamal(i, key, seed=None): + r""" + Encrypt message with public key. + + Explanation + =========== + + ``i`` is a plaintext message expressed as an integer. + ``key`` is public key (p, r, e). In order to encrypt + a message, a random number ``a`` in ``range(2, p)`` + is generated and the encryped message is returned as + `c_{1}` and `c_{2}` where: + + `c_{1} \equiv r^{a} \pmod p` + + `c_{2} \equiv m e^{a} \pmod p` + + Parameters + ========== + + msg + int of encoded message. + + key + Public key. + + Returns + ======= + + tuple : (c1, c2) + Encipher into two number. + + Notes + ===== + + For testing purposes, the ``seed`` parameter may be set to control + the output of this routine. See sympy.core.random._randrange. + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_elgamal, elgamal_private_key, elgamal_public_key + >>> pri = elgamal_private_key(5, seed=[3]); pri + (37, 2, 3) + >>> pub = elgamal_public_key(pri); pub + (37, 2, 8) + >>> msg = 36 + >>> encipher_elgamal(msg, pub, seed=[3]) + (8, 6) + + """ + p, r, e = key + if i < 0 or i >= p: + raise ValueError( + 'Message (%s) should be in range(%s)' % (i, p)) + randrange = _randrange(seed) + a = randrange(2, p) + return pow(r, a, p), i*pow(e, a, p) % p + + +def decipher_elgamal(msg, key): + r""" + Decrypt message with private key. + + `msg = (c_{1}, c_{2})` + + `key = (p, r, d)` + + According to extended Eucliden theorem, + `u c_{1}^{d} + p n = 1` + + `u \equiv 1/{{c_{1}}^d} \pmod p` + + `u c_{2} \equiv \frac{1}{c_{1}^d} c_{2} \equiv \frac{1}{r^{ad}} c_{2} \pmod p` + + `\frac{1}{r^{ad}} m e^a \equiv \frac{1}{r^{ad}} m {r^{d a}} \equiv m \pmod p` + + Examples + ======== + + >>> from sympy.crypto.crypto import decipher_elgamal + >>> from sympy.crypto.crypto import encipher_elgamal + >>> from sympy.crypto.crypto import elgamal_private_key + >>> from sympy.crypto.crypto import elgamal_public_key + + >>> pri = elgamal_private_key(5, seed=[3]) + >>> pub = elgamal_public_key(pri); pub + (37, 2, 8) + >>> msg = 17 + >>> decipher_elgamal(encipher_elgamal(msg, pub), pri) == msg + True + + """ + p, _, d = key + c1, c2 = msg + u = pow(c1, -d, p) + return u * c2 % p + + +################ Diffie-Hellman Key Exchange ######################### + +def dh_private_key(digit=10, seed=None): + r""" + Return three integer tuple as private key. + + Explanation + =========== + + Diffie-Hellman key exchange is based on the mathematical problem + called the Discrete Logarithm Problem (see ElGamal). + + Diffie-Hellman key exchange is divided into the following steps: + + * Alice and Bob agree on a base that consist of a prime ``p`` + and a primitive root of ``p`` called ``g`` + * Alice choses a number ``a`` and Bob choses a number ``b`` where + ``a`` and ``b`` are random numbers in range `[2, p)`. These are + their private keys. + * Alice then publicly sends Bob `g^{a} \pmod p` while Bob sends + Alice `g^{b} \pmod p` + * They both raise the received value to their secretly chosen + number (``a`` or ``b``) and now have both as their shared key + `g^{ab} \pmod p` + + Parameters + ========== + + digit + Minimum number of binary digits required in key. + + Returns + ======= + + tuple : (p, g, a) + p = prime number. + + g = primitive root of p. + + a = random number from 2 through p - 1. + + Notes + ===== + + For testing purposes, the ``seed`` parameter may be set to control + the output of this routine. See sympy.core.random._randrange. + + Examples + ======== + + >>> from sympy.crypto.crypto import dh_private_key + >>> from sympy.ntheory import isprime, is_primitive_root + >>> p, g, _ = dh_private_key() + >>> isprime(p) + True + >>> is_primitive_root(g, p) + True + >>> p, g, _ = dh_private_key(5) + >>> isprime(p) + True + >>> is_primitive_root(g, p) + True + + """ + p = nextprime(2**digit) + g = primitive_root(p) + randrange = _randrange(seed) + a = randrange(2, p) + return p, g, a + + +def dh_public_key(key): + r""" + Return three number tuple as public key. + + This is the tuple that Alice sends to Bob. + + Parameters + ========== + + key : (p, g, a) + A tuple generated by ``dh_private_key``. + + Returns + ======= + + tuple : int, int, int + A tuple of `(p, g, g^a \mod p)` with `p`, `g` and `a` given as + parameters.s + + Examples + ======== + + >>> from sympy.crypto.crypto import dh_private_key, dh_public_key + >>> p, g, a = dh_private_key(); + >>> _p, _g, x = dh_public_key((p, g, a)) + >>> p == _p and g == _g + True + >>> x == pow(g, a, p) + True + + """ + p, g, a = key + return p, g, pow(g, a, p) + + +def dh_shared_key(key, b): + """ + Return an integer that is the shared key. + + This is what Bob and Alice can both calculate using the public + keys they received from each other and their private keys. + + Parameters + ========== + + key : (p, g, x) + Tuple `(p, g, x)` generated by ``dh_public_key``. + + b + Random number in the range of `2` to `p - 1` + (Chosen by second key exchange member (Bob)). + + Returns + ======= + + int + A shared key. + + Examples + ======== + + >>> from sympy.crypto.crypto import ( + ... dh_private_key, dh_public_key, dh_shared_key) + >>> prk = dh_private_key(); + >>> p, g, x = dh_public_key(prk); + >>> sk = dh_shared_key((p, g, x), 1000) + >>> sk == pow(x, 1000, p) + True + + """ + p, _, x = key + if 1 >= b or b >= p: + raise ValueError(filldedent(''' + Value of b should be greater 1 and less + than prime %s.''' % p)) + + return pow(x, b, p) + + +################ Goldwasser-Micali Encryption ######################### + + +def _legendre(a, p): + """ + Returns the legendre symbol of a and p + assuming that p is a prime. + + i.e. 1 if a is a quadratic residue mod p + -1 if a is not a quadratic residue mod p + 0 if a is divisible by p + + Parameters + ========== + + a : int + The number to test. + + p : prime + The prime to test ``a`` against. + + Returns + ======= + + int + Legendre symbol (a / p). + + """ + sig = pow(a, (p - 1)//2, p) + if sig == 1: + return 1 + elif sig == 0: + return 0 + else: + return -1 + + +def _random_coprime_stream(n, seed=None): + randrange = _randrange(seed) + while True: + y = randrange(n) + if gcd(y, n) == 1: + yield y + + +def gm_private_key(p, q, a=None): + r""" + Check if ``p`` and ``q`` can be used as private keys for + the Goldwasser-Micali encryption. The method works + roughly as follows. + + Explanation + =========== + + #. Pick two large primes $p$ and $q$. + #. Call their product $N$. + #. Given a message as an integer $i$, write $i$ in its bit representation $b_0, \dots, b_n$. + #. For each $k$, + + if $b_k = 0$: + let $a_k$ be a random square + (quadratic residue) modulo $p q$ + such that ``jacobi_symbol(a, p*q) = 1`` + if $b_k = 1$: + let $a_k$ be a random non-square + (non-quadratic residue) modulo $p q$ + such that ``jacobi_symbol(a, p*q) = 1`` + + returns $\left[a_1, a_2, \dots\right]$ + + $b_k$ can be recovered by checking whether or not + $a_k$ is a residue. And from the $b_k$'s, the message + can be reconstructed. + + The idea is that, while ``jacobi_symbol(a, p*q)`` + can be easily computed (and when it is equal to $-1$ will + tell you that $a$ is not a square mod $p q$), quadratic + residuosity modulo a composite number is hard to compute + without knowing its factorization. + + Moreover, approximately half the numbers coprime to $p q$ have + :func:`~.jacobi_symbol` equal to $1$ . And among those, approximately half + are residues and approximately half are not. This maximizes the + entropy of the code. + + Parameters + ========== + + p, q, a + Initialization variables. + + Returns + ======= + + tuple : (p, q) + The input value ``p`` and ``q``. + + Raises + ====== + + ValueError + If ``p`` and ``q`` are not distinct odd primes. + + """ + if p == q: + raise ValueError("expected distinct primes, " + "got two copies of %i" % p) + elif not isprime(p) or not isprime(q): + raise ValueError("first two arguments must be prime, " + "got %i of %i" % (p, q)) + elif p == 2 or q == 2: + raise ValueError("first two arguments must not be even, " + "got %i of %i" % (p, q)) + return p, q + + +def gm_public_key(p, q, a=None, seed=None): + """ + Compute public keys for ``p`` and ``q``. + Note that in Goldwasser-Micali Encryption, + public keys are randomly selected. + + Parameters + ========== + + p, q, a : int, int, int + Initialization variables. + + Returns + ======= + + tuple : (a, N) + ``a`` is the input ``a`` if it is not ``None`` otherwise + some random integer coprime to ``p`` and ``q``. + + ``N`` is the product of ``p`` and ``q``. + + """ + + p, q = gm_private_key(p, q) + N = p * q + + if a is None: + randrange = _randrange(seed) + while True: + a = randrange(N) + if _legendre(a, p) == _legendre(a, q) == -1: + break + else: + if _legendre(a, p) != -1 or _legendre(a, q) != -1: + return False + return (a, N) + + +def encipher_gm(i, key, seed=None): + """ + Encrypt integer 'i' using public_key 'key' + Note that gm uses random encryption. + + Parameters + ========== + + i : int + The message to encrypt. + + key : (a, N) + The public key. + + Returns + ======= + + list : list of int + The randomized encrypted message. + + """ + if i < 0: + raise ValueError( + "message must be a non-negative " + "integer: got %d instead" % i) + a, N = key + bits = [] + while i > 0: + bits.append(i % 2) + i //= 2 + + gen = _random_coprime_stream(N, seed) + rev = reversed(bits) + encode = lambda b: next(gen)**2*pow(a, b) % N + return [ encode(b) for b in rev ] + + + +def decipher_gm(message, key): + """ + Decrypt message 'message' using public_key 'key'. + + Parameters + ========== + + message : list of int + The randomized encrypted message. + + key : (p, q) + The private key. + + Returns + ======= + + int + The encrypted message. + + """ + p, q = key + res = lambda m, p: _legendre(m, p) > 0 + bits = [res(m, p) * res(m, q) for m in message] + m = 0 + for b in bits: + m <<= 1 + m += not b + return m + + + +########### RailFence Cipher ############# + +def encipher_railfence(message,rails): + """ + Performs Railfence Encryption on plaintext and returns ciphertext + + Examples + ======== + + >>> from sympy.crypto.crypto import encipher_railfence + >>> message = "hello world" + >>> encipher_railfence(message,3) + 'horel ollwd' + + Parameters + ========== + + message : string, the message to encrypt. + rails : int, the number of rails. + + Returns + ======= + + The Encrypted string message. + + References + ========== + .. [1] https://en.wikipedia.org/wiki/Rail_fence_cipher + + """ + r = list(range(rails)) + p = cycle(r + r[-2:0:-1]) + return ''.join(sorted(message, key=lambda i: next(p))) + + +def decipher_railfence(ciphertext,rails): + """ + Decrypt the message using the given rails + + Examples + ======== + + >>> from sympy.crypto.crypto import decipher_railfence + >>> decipher_railfence("horel ollwd",3) + 'hello world' + + Parameters + ========== + + message : string, the message to encrypt. + rails : int, the number of rails. + + Returns + ======= + + The Decrypted string message. + + """ + r = list(range(rails)) + p = cycle(r + r[-2:0:-1]) + + idx = sorted(range(len(ciphertext)), key=lambda i: next(p)) + res = [''] * len(ciphertext) + for i, c in zip(idx, ciphertext): + res[i] = c + return ''.join(res) + + +################ Blum-Goldwasser cryptosystem ######################### + +def bg_private_key(p, q): + """ + Check if p and q can be used as private keys for + the Blum-Goldwasser cryptosystem. + + Explanation + =========== + + The three necessary checks for p and q to pass + so that they can be used as private keys: + + 1. p and q must both be prime + 2. p and q must be distinct + 3. p and q must be congruent to 3 mod 4 + + Parameters + ========== + + p, q + The keys to be checked. + + Returns + ======= + + p, q + Input values. + + Raises + ====== + + ValueError + If p and q do not pass the above conditions. + + """ + + if not isprime(p) or not isprime(q): + raise ValueError("the two arguments must be prime, " + "got %i and %i" %(p, q)) + elif p == q: + raise ValueError("the two arguments must be distinct, " + "got two copies of %i. " %p) + elif (p - 3) % 4 != 0 or (q - 3) % 4 != 0: + raise ValueError("the two arguments must be congruent to 3 mod 4, " + "got %i and %i" %(p, q)) + return p, q + +def bg_public_key(p, q): + """ + Calculates public keys from private keys. + + Explanation + =========== + + The function first checks the validity of + private keys passed as arguments and + then returns their product. + + Parameters + ========== + + p, q + The private keys. + + Returns + ======= + + N + The public key. + + """ + p, q = bg_private_key(p, q) + N = p * q + return N + +def encipher_bg(i, key, seed=None): + """ + Encrypts the message using public key and seed. + + Explanation + =========== + + ALGORITHM: + 1. Encodes i as a string of L bits, m. + 2. Select a random element r, where 1 < r < key, and computes + x = r^2 mod key. + 3. Use BBS pseudo-random number generator to generate L random bits, b, + using the initial seed as x. + 4. Encrypted message, c_i = m_i XOR b_i, 1 <= i <= L. + 5. x_L = x^(2^L) mod key. + 6. Return (c, x_L) + + Parameters + ========== + + i + Message, a non-negative integer + + key + The public key + + Returns + ======= + + Tuple + (encrypted_message, x_L) + + Raises + ====== + + ValueError + If i is negative. + + """ + + if i < 0: + raise ValueError( + "message must be a non-negative " + "integer: got %d instead" % i) + + enc_msg = [] + while i > 0: + enc_msg.append(i % 2) + i //= 2 + enc_msg.reverse() + L = len(enc_msg) + + r = _randint(seed)(2, key - 1) + x = r**2 % key + x_L = pow(int(x), int(2**L), int(key)) + + rand_bits = [] + for _ in range(L): + rand_bits.append(x % 2) + x = x**2 % key + + encrypt_msg = [m ^ b for (m, b) in zip(enc_msg, rand_bits)] + + return (encrypt_msg, x_L) + +def decipher_bg(message, key): + """ + Decrypts the message using private keys. + + Explanation + =========== + + ALGORITHM: + 1. Let, c be the encrypted message, y the second number received, + and p and q be the private keys. + 2. Compute, r_p = y^((p+1)/4 ^ L) mod p and + r_q = y^((q+1)/4 ^ L) mod q. + 3. Compute x_0 = (q(q^-1 mod p)r_p + p(p^-1 mod q)r_q) mod N. + 4. From, recompute the bits using the BBS generator, as in the + encryption algorithm. + 5. Compute original message by XORing c and b. + + Parameters + ========== + + message + Tuple of encrypted message and a non-negative integer. + + key + Tuple of private keys. + + Returns + ======= + + orig_msg + The original message + + """ + + p, q = key + encrypt_msg, y = message + public_key = p * q + L = len(encrypt_msg) + p_t = ((p + 1)/4)**L + q_t = ((q + 1)/4)**L + r_p = pow(int(y), int(p_t), int(p)) + r_q = pow(int(y), int(q_t), int(q)) + + x = (q * invert(q, p) * r_p + p * invert(p, q) * r_q) % public_key + + orig_bits = [] + for _ in range(L): + orig_bits.append(x % 2) + x = x**2 % public_key + + orig_msg = 0 + for (m, b) in zip(encrypt_msg, orig_bits): + orig_msg = orig_msg * 2 + orig_msg += (m ^ b) + + return orig_msg diff --git a/lib/python3.11/site-packages/sympy/crypto/tests/__init__.py b/lib/python3.11/site-packages/sympy/crypto/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git 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0000000000000000000000000000000000000000..c671138f9a61325f6e65cc7cafddc7cd46f19229 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/crypto/tests/test_crypto.py @@ -0,0 +1,562 @@ +from sympy.core import symbols +from sympy.crypto.crypto import (cycle_list, + encipher_shift, encipher_affine, encipher_substitution, + check_and_join, encipher_vigenere, decipher_vigenere, + encipher_hill, decipher_hill, encipher_bifid5, encipher_bifid6, + bifid5_square, bifid6_square, bifid5, bifid6, + decipher_bifid5, decipher_bifid6, encipher_kid_rsa, + decipher_kid_rsa, kid_rsa_private_key, kid_rsa_public_key, + decipher_rsa, rsa_private_key, rsa_public_key, encipher_rsa, + lfsr_connection_polynomial, lfsr_autocorrelation, lfsr_sequence, + encode_morse, decode_morse, elgamal_private_key, elgamal_public_key, + encipher_elgamal, decipher_elgamal, dh_private_key, dh_public_key, + dh_shared_key, decipher_shift, decipher_affine, encipher_bifid, + decipher_bifid, bifid_square, padded_key, uniq, decipher_gm, + encipher_gm, gm_public_key, gm_private_key, encipher_bg, decipher_bg, + bg_private_key, bg_public_key, encipher_rot13, decipher_rot13, + encipher_atbash, decipher_atbash, NonInvertibleCipherWarning, + encipher_railfence, decipher_railfence) +from sympy.external.gmpy import gcd +from sympy.matrices import Matrix +from sympy.ntheory import isprime, is_primitive_root +from sympy.polys.domains import FF + +from sympy.testing.pytest import raises, warns + +from sympy.core.random import randrange + +def test_encipher_railfence(): + assert encipher_railfence("hello world",2) == "hlowrdel ol" + assert encipher_railfence("hello world",3) == "horel ollwd" + assert encipher_railfence("hello world",4) == "hwe olordll" + +def test_decipher_railfence(): + assert decipher_railfence("hlowrdel ol",2) == "hello world" + assert decipher_railfence("horel ollwd",3) == "hello world" + assert decipher_railfence("hwe olordll",4) == "hello world" + + +def test_cycle_list(): + assert cycle_list(3, 4) == [3, 0, 1, 2] + assert cycle_list(-1, 4) == [3, 0, 1, 2] + assert cycle_list(1, 4) == [1, 2, 3, 0] + + +def test_encipher_shift(): + assert encipher_shift("ABC", 0) == "ABC" + assert encipher_shift("ABC", 1) == "BCD" + assert encipher_shift("ABC", -1) == "ZAB" + assert decipher_shift("ZAB", -1) == "ABC" + +def test_encipher_rot13(): + assert encipher_rot13("ABC") == "NOP" + assert encipher_rot13("NOP") == "ABC" + assert decipher_rot13("ABC") == "NOP" + assert decipher_rot13("NOP") == "ABC" + + +def test_encipher_affine(): + assert encipher_affine("ABC", (1, 0)) == "ABC" + assert encipher_affine("ABC", (1, 1)) == "BCD" + assert encipher_affine("ABC", (-1, 0)) == "AZY" + assert encipher_affine("ABC", (-1, 1), symbols="ABCD") == "BAD" + assert encipher_affine("123", (-1, 1), symbols="1234") == "214" + assert encipher_affine("ABC", (3, 16)) == "QTW" + assert decipher_affine("QTW", (3, 16)) == "ABC" + +def test_encipher_atbash(): + assert encipher_atbash("ABC") == "ZYX" + assert encipher_atbash("ZYX") == "ABC" + assert decipher_atbash("ABC") == "ZYX" + assert decipher_atbash("ZYX") == "ABC" + +def test_encipher_substitution(): + assert encipher_substitution("ABC", "BAC", "ABC") == "BAC" + assert encipher_substitution("123", "1243", "1234") == "124" + + +def test_check_and_join(): + assert check_and_join("abc") == "abc" + assert check_and_join(uniq("aaabc")) == "abc" + assert check_and_join("ab c".split()) == "abc" + assert check_and_join("abc", "a", filter=True) == "a" + raises(ValueError, lambda: check_and_join('ab', 'a')) + + +def test_encipher_vigenere(): + assert encipher_vigenere("ABC", "ABC") == "ACE" + assert encipher_vigenere("ABC", "ABC", symbols="ABCD") == "ACA" + assert encipher_vigenere("ABC", "AB", symbols="ABCD") == "ACC" + assert encipher_vigenere("AB", "ABC", symbols="ABCD") == "AC" + assert encipher_vigenere("A", "ABC", symbols="ABCD") == "A" + + +def test_decipher_vigenere(): + assert decipher_vigenere("ABC", "ABC") == "AAA" + assert decipher_vigenere("ABC", "ABC", symbols="ABCD") == "AAA" + assert decipher_vigenere("ABC", "AB", symbols="ABCD") == "AAC" + assert decipher_vigenere("AB", "ABC", symbols="ABCD") == "AA" + assert decipher_vigenere("A", "ABC", symbols="ABCD") == "A" + + +def test_encipher_hill(): + A = Matrix(2, 2, [1, 2, 3, 5]) + assert encipher_hill("ABCD", A) == "CFIV" + A = Matrix(2, 2, [1, 0, 0, 1]) + assert encipher_hill("ABCD", A) == "ABCD" + assert encipher_hill("ABCD", A, symbols="ABCD") == "ABCD" + A = Matrix(2, 2, [1, 2, 3, 5]) + assert encipher_hill("ABCD", A, symbols="ABCD") == "CBAB" + assert encipher_hill("AB", A, symbols="ABCD") == "CB" + # message length, n, does not need to be a multiple of k; + # it is padded + assert encipher_hill("ABA", A) == "CFGC" + assert encipher_hill("ABA", A, pad="Z") == "CFYV" + + +def test_decipher_hill(): + A = Matrix(2, 2, [1, 2, 3, 5]) + assert decipher_hill("CFIV", A) == "ABCD" + A = Matrix(2, 2, [1, 0, 0, 1]) + assert decipher_hill("ABCD", A) == "ABCD" + assert decipher_hill("ABCD", A, symbols="ABCD") == "ABCD" + A = Matrix(2, 2, [1, 2, 3, 5]) + assert decipher_hill("CBAB", A, symbols="ABCD") == "ABCD" + assert decipher_hill("CB", A, symbols="ABCD") == "AB" + # n does not need to be a multiple of k + assert decipher_hill("CFA", A) == "ABAA" + + +def test_encipher_bifid5(): + assert encipher_bifid5("AB", "AB") == "AB" + assert encipher_bifid5("AB", "CD") == "CO" + assert encipher_bifid5("ab", "c") == "CH" + assert encipher_bifid5("a bc", "b") == "BAC" + + +def test_bifid5_square(): + A = bifid5 + f = lambda i, j: symbols(A[5*i + j]) + M = Matrix(5, 5, f) + assert bifid5_square("") == M + + +def test_decipher_bifid5(): + assert decipher_bifid5("AB", "AB") == "AB" + assert decipher_bifid5("CO", "CD") == "AB" + assert decipher_bifid5("ch", "c") == "AB" + assert decipher_bifid5("b ac", "b") == "ABC" + + +def test_encipher_bifid6(): + assert encipher_bifid6("AB", "AB") == "AB" + assert encipher_bifid6("AB", "CD") == "CP" + assert encipher_bifid6("ab", "c") == "CI" + assert encipher_bifid6("a bc", "b") == "BAC" + + +def test_decipher_bifid6(): + assert decipher_bifid6("AB", "AB") == "AB" + assert decipher_bifid6("CP", "CD") == "AB" + assert decipher_bifid6("ci", "c") == "AB" + assert decipher_bifid6("b ac", "b") == "ABC" + + +def test_bifid6_square(): + A = bifid6 + f = lambda i, j: symbols(A[6*i + j]) + M = Matrix(6, 6, f) + assert bifid6_square("") == M + + +def test_rsa_public_key(): + assert rsa_public_key(2, 3, 1) == (6, 1) + assert rsa_public_key(5, 3, 3) == (15, 3) + + with warns(NonInvertibleCipherWarning): + assert rsa_public_key(2, 2, 1) == (4, 1) + assert rsa_public_key(8, 8, 8) is False + + +def test_rsa_private_key(): + assert rsa_private_key(2, 3, 1) == (6, 1) + assert rsa_private_key(5, 3, 3) == (15, 3) + assert rsa_private_key(23,29,5) == (667,493) + + with warns(NonInvertibleCipherWarning): + assert rsa_private_key(2, 2, 1) == (4, 1) + assert rsa_private_key(8, 8, 8) is False + + +def test_rsa_large_key(): + # Sample from + # http://www.herongyang.com/Cryptography/JCE-Public-Key-RSA-Private-Public-Key-Pair-Sample.html + p = int('101565610013301240713207239558950144682174355406589305284428666'\ + '903702505233009') + q = int('894687191887545488935455605955948413812376003053143521429242133'\ + '12069293984003') + e = int('65537') + d = int('893650581832704239530398858744759129594796235440844479456143566'\ + '6999402846577625762582824202269399672579058991442587406384754958587'\ + '400493169361356902030209') + assert rsa_public_key(p, q, e) == (p*q, e) + assert rsa_private_key(p, q, e) == (p*q, d) + + +def test_encipher_rsa(): + puk = rsa_public_key(2, 3, 1) + assert encipher_rsa(2, puk) == 2 + puk = rsa_public_key(5, 3, 3) + assert encipher_rsa(2, puk) == 8 + + with warns(NonInvertibleCipherWarning): + puk = rsa_public_key(2, 2, 1) + assert encipher_rsa(2, puk) == 2 + + +def test_decipher_rsa(): + prk = rsa_private_key(2, 3, 1) + assert decipher_rsa(2, prk) == 2 + prk = rsa_private_key(5, 3, 3) + assert decipher_rsa(8, prk) == 2 + + with warns(NonInvertibleCipherWarning): + prk = rsa_private_key(2, 2, 1) + assert decipher_rsa(2, prk) == 2 + + +def test_mutltiprime_rsa_full_example(): + # Test example from + # https://iopscience.iop.org/article/10.1088/1742-6596/995/1/012030 + puk = rsa_public_key(2, 3, 5, 7, 11, 13, 7) + prk = rsa_private_key(2, 3, 5, 7, 11, 13, 7) + assert puk == (30030, 7) + assert prk == (30030, 823) + + msg = 10 + encrypted = encipher_rsa(2 * msg - 15, puk) + assert encrypted == 18065 + decrypted = (decipher_rsa(encrypted, prk) + 15) / 2 + assert decrypted == msg + + # Test example from + # https://www.scirp.org/pdf/JCC_2018032215502008.pdf + puk1 = rsa_public_key(53, 41, 43, 47, 41) + prk1 = rsa_private_key(53, 41, 43, 47, 41) + puk2 = rsa_public_key(53, 41, 43, 47, 97) + prk2 = rsa_private_key(53, 41, 43, 47, 97) + + assert puk1 == (4391633, 41) + assert prk1 == (4391633, 294041) + assert puk2 == (4391633, 97) + assert prk2 == (4391633, 455713) + + msg = 12321 + encrypted = encipher_rsa(encipher_rsa(msg, puk1), puk2) + assert encrypted == 1081588 + decrypted = decipher_rsa(decipher_rsa(encrypted, prk2), prk1) + assert decrypted == msg + + +def test_rsa_crt_extreme(): + p = int( + '10177157607154245068023861503693082120906487143725062283406501' \ + '54082258226204046999838297167140821364638180697194879500245557' \ + '65445186962893346463841419427008800341257468600224049986260471' \ + '92257248163014468841725476918639415726709736077813632961290911' \ + '0256421232977833028677441206049309220354796014376698325101693') + + q = int( + '28752342353095132872290181526607275886182793241660805077850801' \ + '75689512797754286972952273553128181861830576836289738668745250' \ + '34028199691128870676414118458442900035778874482624765513861643' \ + '27966696316822188398336199002306588703902894100476186823849595' \ + '103239410527279605442148285816149368667083114802852804976893') + + r = int( + '17698229259868825776879500736350186838850961935956310134378261' \ + '89771862186717463067541369694816245225291921138038800171125596' \ + '07315449521981157084370187887650624061033066022458512942411841' \ + '18747893789972315277160085086164119879536041875335384844820566' \ + '0287479617671726408053319619892052000850883994343378882717849') + + s = int( + '68925428438585431029269182233502611027091755064643742383515623' \ + '64321310582896893395529367074942808353187138794422745718419645' \ + '28291231865157212604266903677599180789896916456120289112752835' \ + '98502265889669730331688206825220074713977607415178738015831030' \ + '364290585369150502819743827343552098197095520550865360159439' + ) + + t = int( + '69035483433453632820551311892368908779778144568711455301541094' \ + '31487047642322695357696860925747923189635033183069823820910521' \ + '71172909106797748883261493224162414050106920442445896819806600' \ + '15448444826108008217972129130625571421904893252804729877353352' \ + '739420480574842850202181462656251626522910618936534699566291' + ) + + e = 65537 + puk = rsa_public_key(p, q, r, s, t, e) + prk = rsa_private_key(p, q, r, s, t, e) + + plaintext = 1000 + ciphertext_1 = encipher_rsa(plaintext, puk) + ciphertext_2 = encipher_rsa(plaintext, puk, [p, q, r, s, t]) + assert ciphertext_1 == ciphertext_2 + assert decipher_rsa(ciphertext_1, prk) == \ + decipher_rsa(ciphertext_1, prk, [p, q, r, s, t]) + + +def test_rsa_exhaustive(): + p, q = 61, 53 + e = 17 + puk = rsa_public_key(p, q, e, totient='Carmichael') + prk = rsa_private_key(p, q, e, totient='Carmichael') + + for msg in range(puk[0]): + encrypted = encipher_rsa(msg, puk) + decrypted = decipher_rsa(encrypted, prk) + try: + assert decrypted == msg + except AssertionError: + raise AssertionError( + "The RSA is not correctly decrypted " \ + "(Original : {}, Encrypted : {}, Decrypted : {})" \ + .format(msg, encrypted, decrypted) + ) + + +def test_rsa_multiprime_exhanstive(): + primes = [3, 5, 7, 11] + e = 7 + args = primes + [e] + puk = rsa_public_key(*args, totient='Carmichael') + prk = rsa_private_key(*args, totient='Carmichael') + n = puk[0] + + for msg in range(n): + encrypted = encipher_rsa(msg, puk) + decrypted = decipher_rsa(encrypted, prk) + try: + assert decrypted == msg + except AssertionError: + raise AssertionError( + "The RSA is not correctly decrypted " \ + "(Original : {}, Encrypted : {}, Decrypted : {})" \ + .format(msg, encrypted, decrypted) + ) + + +def test_rsa_multipower_exhanstive(): + primes = [5, 5, 7] + e = 7 + args = primes + [e] + puk = rsa_public_key(*args, multipower=True) + prk = rsa_private_key(*args, multipower=True) + n = puk[0] + + for msg in range(n): + if gcd(msg, n) != 1: + continue + + encrypted = encipher_rsa(msg, puk) + decrypted = decipher_rsa(encrypted, prk) + try: + assert decrypted == msg + except AssertionError: + raise AssertionError( + "The RSA is not correctly decrypted " \ + "(Original : {}, Encrypted : {}, Decrypted : {})" \ + .format(msg, encrypted, decrypted) + ) + + +def test_kid_rsa_public_key(): + assert kid_rsa_public_key(1, 2, 1, 1) == (5, 2) + assert kid_rsa_public_key(1, 2, 2, 1) == (8, 3) + assert kid_rsa_public_key(1, 2, 1, 2) == (7, 2) + + +def test_kid_rsa_private_key(): + assert kid_rsa_private_key(1, 2, 1, 1) == (5, 3) + assert kid_rsa_private_key(1, 2, 2, 1) == (8, 3) + assert kid_rsa_private_key(1, 2, 1, 2) == (7, 4) + + +def test_encipher_kid_rsa(): + assert encipher_kid_rsa(1, (5, 2)) == 2 + assert encipher_kid_rsa(1, (8, 3)) == 3 + assert encipher_kid_rsa(1, (7, 2)) == 2 + + +def test_decipher_kid_rsa(): + assert decipher_kid_rsa(2, (5, 3)) == 1 + assert decipher_kid_rsa(3, (8, 3)) == 1 + assert decipher_kid_rsa(2, (7, 4)) == 1 + + +def test_encode_morse(): + assert encode_morse('ABC') == '.-|-...|-.-.' + assert encode_morse('SMS ') == '...|--|...||' + assert encode_morse('SMS\n') == '...|--|...||' + assert encode_morse('') == '' + assert encode_morse(' ') == '||' + assert encode_morse(' ', sep='`') == '``' + assert encode_morse(' ', sep='``') == '````' + assert encode_morse('!@#$%^&*()_+') == '-.-.--|.--.-.|...-..-|-.--.|-.--.-|..--.-|.-.-.' + assert encode_morse('12345') == '.----|..---|...--|....-|.....' + assert encode_morse('67890') == '-....|--...|---..|----.|-----' + + +def test_decode_morse(): + assert decode_morse('-.-|.|-.--') == 'KEY' + assert decode_morse('.-.|..-|-.||') == 'RUN' + raises(KeyError, lambda: decode_morse('.....----')) + + +def test_lfsr_sequence(): + raises(TypeError, lambda: lfsr_sequence(1, [1], 1)) + raises(TypeError, lambda: lfsr_sequence([1], 1, 1)) + F = FF(2) + assert lfsr_sequence([F(1)], [F(1)], 2) == [F(1), F(1)] + assert lfsr_sequence([F(0)], [F(1)], 2) == [F(1), F(0)] + F = FF(3) + assert lfsr_sequence([F(1)], [F(1)], 2) == [F(1), F(1)] + assert lfsr_sequence([F(0)], [F(2)], 2) == [F(2), F(0)] + assert lfsr_sequence([F(1)], [F(2)], 2) == [F(2), F(2)] + + +def test_lfsr_autocorrelation(): + raises(TypeError, lambda: lfsr_autocorrelation(1, 2, 3)) + F = FF(2) + s = lfsr_sequence([F(1), F(0)], [F(0), F(1)], 5) + assert lfsr_autocorrelation(s, 2, 0) == 1 + assert lfsr_autocorrelation(s, 2, 1) == -1 + + +def test_lfsr_connection_polynomial(): + F = FF(2) + x = symbols("x") + s = lfsr_sequence([F(1), F(0)], [F(0), F(1)], 5) + assert lfsr_connection_polynomial(s) == x**2 + 1 + s = lfsr_sequence([F(1), F(1)], [F(0), F(1)], 5) + assert lfsr_connection_polynomial(s) == x**2 + x + 1 + + +def test_elgamal_private_key(): + a, b, _ = elgamal_private_key(digit=100) + assert isprime(a) + assert is_primitive_root(b, a) + assert len(bin(a)) >= 102 + + +def test_elgamal(): + dk = elgamal_private_key(5) + ek = elgamal_public_key(dk) + P = ek[0] + assert P - 1 == decipher_elgamal(encipher_elgamal(P - 1, ek), dk) + raises(ValueError, lambda: encipher_elgamal(P, dk)) + raises(ValueError, lambda: encipher_elgamal(-1, dk)) + + +def test_dh_private_key(): + p, g, _ = dh_private_key(digit = 100) + assert isprime(p) + assert is_primitive_root(g, p) + assert len(bin(p)) >= 102 + + +def test_dh_public_key(): + p1, g1, a = dh_private_key(digit = 100) + p2, g2, ga = dh_public_key((p1, g1, a)) + assert p1 == p2 + assert g1 == g2 + assert ga == pow(g1, a, p1) + + +def test_dh_shared_key(): + prk = dh_private_key(digit = 100) + p, _, ga = dh_public_key(prk) + b = randrange(2, p) + sk = dh_shared_key((p, _, ga), b) + assert sk == pow(ga, b, p) + raises(ValueError, lambda: dh_shared_key((1031, 14, 565), 2000)) + + +def test_padded_key(): + assert padded_key('b', 'ab') == 'ba' + raises(ValueError, lambda: padded_key('ab', 'ace')) + raises(ValueError, lambda: padded_key('ab', 'abba')) + + +def test_bifid(): + raises(ValueError, lambda: encipher_bifid('abc', 'b', 'abcde')) + assert encipher_bifid('abc', 'b', 'abcd') == 'bdb' + raises(ValueError, lambda: decipher_bifid('bdb', 'b', 'abcde')) + assert encipher_bifid('bdb', 'b', 'abcd') == 'abc' + raises(ValueError, lambda: bifid_square('abcde')) + assert bifid5_square("B") == \ + bifid5_square('BACDEFGHIKLMNOPQRSTUVWXYZ') + assert bifid6_square('B0') == \ + bifid6_square('B0ACDEFGHIJKLMNOPQRSTUVWXYZ123456789') + + +def test_encipher_decipher_gm(): + ps = [131, 137, 139, 149, 151, 157, 163, 167, + 173, 179, 181, 191, 193, 197, 199] + qs = [89, 97, 101, 103, 107, 109, 113, 127, + 131, 137, 139, 149, 151, 157, 47] + messages = [ + 0, 32855, 34303, 14805, 1280, 75859, 38368, + 724, 60356, 51675, 76697, 61854, 18661, + ] + for p, q in zip(ps, qs): + pri = gm_private_key(p, q) + for msg in messages: + pub = gm_public_key(p, q) + enc = encipher_gm(msg, pub) + dec = decipher_gm(enc, pri) + assert dec == msg + + +def test_gm_private_key(): + raises(ValueError, lambda: gm_public_key(13, 15)) + raises(ValueError, lambda: gm_public_key(0, 0)) + raises(ValueError, lambda: gm_public_key(0, 5)) + assert 17, 19 == gm_public_key(17, 19) + + +def test_gm_public_key(): + assert 323 == gm_public_key(17, 19)[1] + assert 15 == gm_public_key(3, 5)[1] + raises(ValueError, lambda: gm_public_key(15, 19)) + +def test_encipher_decipher_bg(): + ps = [67, 7, 71, 103, 11, 43, 107, 47, + 79, 19, 83, 23, 59, 127, 31] + qs = qs = [7, 71, 103, 11, 43, 107, 47, + 79, 19, 83, 23, 59, 127, 31, 67] + messages = [ + 0, 328, 343, 148, 1280, 758, 383, + 724, 603, 516, 766, 618, 186, + ] + + for p, q in zip(ps, qs): + pri = bg_private_key(p, q) + for msg in messages: + pub = bg_public_key(p, q) + enc = encipher_bg(msg, pub) + dec = decipher_bg(enc, pri) + assert dec == msg + +def test_bg_private_key(): + raises(ValueError, lambda: bg_private_key(8, 16)) + raises(ValueError, lambda: bg_private_key(8, 8)) + raises(ValueError, lambda: bg_private_key(13, 17)) + assert 23, 31 == bg_private_key(23, 31) + +def test_bg_public_key(): + assert 5293 == bg_public_key(67, 79) + assert 713 == bg_public_key(23, 31) + raises(ValueError, lambda: bg_private_key(13, 17)) diff --git a/lib/python3.11/site-packages/sympy/diffgeom/__init__.py b/lib/python3.11/site-packages/sympy/diffgeom/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..8846a99510601c9675103e21ef5a0a1e839fdd11 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/__init__.py @@ -0,0 +1,19 @@ +from .diffgeom import ( + BaseCovarDerivativeOp, BaseScalarField, BaseVectorField, Commutator, + contravariant_order, CoordSystem, CoordinateSymbol, + CovarDerivativeOp, covariant_order, Differential, intcurve_diffequ, + intcurve_series, LieDerivative, Manifold, metric_to_Christoffel_1st, + metric_to_Christoffel_2nd, metric_to_Ricci_components, + metric_to_Riemann_components, Patch, Point, TensorProduct, twoform_to_matrix, + vectors_in_basis, WedgeProduct, +) + +__all__ = [ + 'BaseCovarDerivativeOp', 'BaseScalarField', 'BaseVectorField', 'Commutator', + 'contravariant_order', 'CoordSystem', 'CoordinateSymbol', + 'CovarDerivativeOp', 'covariant_order', 'Differential', 'intcurve_diffequ', + 'intcurve_series', 'LieDerivative', 'Manifold', 'metric_to_Christoffel_1st', + 'metric_to_Christoffel_2nd', 'metric_to_Ricci_components', + 'metric_to_Riemann_components', 'Patch', 'Point', 'TensorProduct', + 'twoform_to_matrix', 'vectors_in_basis', 'WedgeProduct', +] diff --git a/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1be4b5b8b04318246dd37267044f3f776533fe9b Binary files /dev/null and b/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/rn.cpython-311.pyc b/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/rn.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..c465b1aeac7154fea813c8d04d28369ea2f08724 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/diffgeom/__pycache__/rn.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/diffgeom/diffgeom.py b/lib/python3.11/site-packages/sympy/diffgeom/diffgeom.py new file mode 100644 index 0000000000000000000000000000000000000000..c66d9686fe6f78977c75fae481fc3fb719f9bcdd --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/diffgeom.py @@ -0,0 +1,2270 @@ +from __future__ import annotations +from typing import Any + +from functools import reduce +from itertools import permutations + +from sympy.combinatorics import Permutation +from sympy.core import ( + Basic, Expr, Function, diff, + Pow, Mul, Add, Lambda, S, Tuple, Dict +) +from sympy.core.cache import cacheit + +from sympy.core.symbol import Symbol, Dummy +from sympy.core.symbol import Str +from sympy.core.sympify import _sympify +from sympy.functions import factorial +from sympy.matrices import ImmutableDenseMatrix as Matrix +from sympy.solvers import solve + +from sympy.utilities.exceptions import (sympy_deprecation_warning, + SymPyDeprecationWarning, + ignore_warnings) + + +# TODO you are a bit excessive in the use of Dummies +# TODO dummy point, literal field +# TODO too often one needs to call doit or simplify on the output, check the +# tests and find out why +from sympy.tensor.array import ImmutableDenseNDimArray + + +class Manifold(Basic): + """ + A mathematical manifold. + + Explanation + =========== + + A manifold is a topological space that locally resembles + Euclidean space near each point [1]. + This class does not provide any means to study the topological + characteristics of the manifold that it represents, though. + + Parameters + ========== + + name : str + The name of the manifold. + + dim : int + The dimension of the manifold. + + Examples + ======== + + >>> from sympy.diffgeom import Manifold + >>> m = Manifold('M', 2) + >>> m + M + >>> m.dim + 2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Manifold + """ + + def __new__(cls, name, dim, **kwargs): + if not isinstance(name, Str): + name = Str(name) + dim = _sympify(dim) + obj = super().__new__(cls, name, dim) + + obj.patches = _deprecated_list( + """ + Manifold.patches is deprecated. The Manifold object is now + immutable. Instead use a separate list to keep track of the + patches. + """, []) + return obj + + @property + def name(self): + return self.args[0] + + @property + def dim(self): + return self.args[1] + + +class Patch(Basic): + """ + A patch on a manifold. + + Explanation + =========== + + Coordinate patch, or patch in short, is a simply-connected open set around + a point in the manifold [1]. On a manifold one can have many patches that + do not always include the whole manifold. On these patches coordinate + charts can be defined that permit the parameterization of any point on the + patch in terms of a tuple of real numbers (the coordinates). + + This class does not provide any means to study the topological + characteristics of the patch that it represents. + + Parameters + ========== + + name : str + The name of the patch. + + manifold : Manifold + The manifold on which the patch is defined. + + Examples + ======== + + >>> from sympy.diffgeom import Manifold, Patch + >>> m = Manifold('M', 2) + >>> p = Patch('P', m) + >>> p + P + >>> p.dim + 2 + + References + ========== + + .. [1] G. Sussman, J. Wisdom, W. Farr, Functional Differential Geometry + (2013) + + """ + def __new__(cls, name, manifold, **kwargs): + if not isinstance(name, Str): + name = Str(name) + obj = super().__new__(cls, name, manifold) + + obj.manifold.patches.append(obj) # deprecated + obj.coord_systems = _deprecated_list( + """ + Patch.coord_systms is deprecated. The Patch class is now + immutable. Instead use a separate list to keep track of coordinate + systems. + """, []) + return obj + + @property + def name(self): + return self.args[0] + + @property + def manifold(self): + return self.args[1] + + @property + def dim(self): + return self.manifold.dim + + +class CoordSystem(Basic): + """ + A coordinate system defined on the patch. + + Explanation + =========== + + Coordinate system is a system that uses one or more coordinates to uniquely + determine the position of the points or other geometric elements on a + manifold [1]. + + By passing ``Symbols`` to *symbols* parameter, user can define the name and + assumptions of coordinate symbols of the coordinate system. If not passed, + these symbols are generated automatically and are assumed to be real valued. + + By passing *relations* parameter, user can define the transform relations of + coordinate systems. Inverse transformation and indirect transformation can + be found automatically. If this parameter is not passed, coordinate + transformation cannot be done. + + Parameters + ========== + + name : str + The name of the coordinate system. + + patch : Patch + The patch where the coordinate system is defined. + + symbols : list of Symbols, optional + Defines the names and assumptions of coordinate symbols. + + relations : dict, optional + Key is a tuple of two strings, who are the names of the systems where + the coordinates transform from and transform to. + Value is a tuple of the symbols before transformation and a tuple of + the expressions after transformation. + + Examples + ======== + + We define two-dimensional Cartesian coordinate system and polar coordinate + system. + + >>> from sympy import symbols, pi, sqrt, atan2, cos, sin + >>> from sympy.diffgeom import Manifold, Patch, CoordSystem + >>> m = Manifold('M', 2) + >>> p = Patch('P', m) + >>> x, y = symbols('x y', real=True) + >>> r, theta = symbols('r theta', nonnegative=True) + >>> relation_dict = { + ... ('Car2D', 'Pol'): [(x, y), (sqrt(x**2 + y**2), atan2(y, x))], + ... ('Pol', 'Car2D'): [(r, theta), (r*cos(theta), r*sin(theta))] + ... } + >>> Car2D = CoordSystem('Car2D', p, (x, y), relation_dict) + >>> Pol = CoordSystem('Pol', p, (r, theta), relation_dict) + + ``symbols`` property returns ``CoordinateSymbol`` instances. These symbols + are not same with the symbols used to construct the coordinate system. + + >>> Car2D + Car2D + >>> Car2D.dim + 2 + >>> Car2D.symbols + (x, y) + >>> _[0].func + + + ``transformation()`` method returns the transformation function from + one coordinate system to another. ``transform()`` method returns the + transformed coordinates. + + >>> Car2D.transformation(Pol) + Lambda((x, y), Matrix([ + [sqrt(x**2 + y**2)], + [ atan2(y, x)]])) + >>> Car2D.transform(Pol) + Matrix([ + [sqrt(x**2 + y**2)], + [ atan2(y, x)]]) + >>> Car2D.transform(Pol, [1, 2]) + Matrix([ + [sqrt(5)], + [atan(2)]]) + + ``jacobian()`` method returns the Jacobian matrix of coordinate + transformation between two systems. ``jacobian_determinant()`` method + returns the Jacobian determinant of coordinate transformation between two + systems. + + >>> Pol.jacobian(Car2D) + Matrix([ + [cos(theta), -r*sin(theta)], + [sin(theta), r*cos(theta)]]) + >>> Pol.jacobian(Car2D, [1, pi/2]) + Matrix([ + [0, -1], + [1, 0]]) + >>> Car2D.jacobian_determinant(Pol) + 1/sqrt(x**2 + y**2) + >>> Car2D.jacobian_determinant(Pol, [1,0]) + 1 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Coordinate_system + + """ + def __new__(cls, name, patch, symbols=None, relations={}, **kwargs): + if not isinstance(name, Str): + name = Str(name) + + # canonicallize the symbols + if symbols is None: + names = kwargs.get('names', None) + if names is None: + symbols = Tuple( + *[Symbol('%s_%s' % (name.name, i), real=True) + for i in range(patch.dim)] + ) + else: + sympy_deprecation_warning( + f""" +The 'names' argument to CoordSystem is deprecated. Use 'symbols' instead. That +is, replace + + CoordSystem(..., names={names}) + +with + + CoordSystem(..., symbols=[{', '.join(["Symbol(" + repr(n) + ", real=True)" for n in names])}]) + """, + deprecated_since_version="1.7", + active_deprecations_target="deprecated-diffgeom-mutable", + ) + symbols = Tuple( + *[Symbol(n, real=True) for n in names] + ) + else: + syms = [] + for s in symbols: + if isinstance(s, Symbol): + syms.append(Symbol(s.name, **s._assumptions.generator)) + elif isinstance(s, str): + sympy_deprecation_warning( + f""" + +Passing a string as the coordinate symbol name to CoordSystem is deprecated. +Pass a Symbol with the appropriate name and assumptions instead. + +That is, replace {s} with Symbol({s!r}, real=True). + """, + + deprecated_since_version="1.7", + active_deprecations_target="deprecated-diffgeom-mutable", + ) + syms.append(Symbol(s, real=True)) + symbols = Tuple(*syms) + + # canonicallize the relations + rel_temp = {} + for k,v in relations.items(): + s1, s2 = k + if not isinstance(s1, Str): + s1 = Str(s1) + if not isinstance(s2, Str): + s2 = Str(s2) + key = Tuple(s1, s2) + + # Old version used Lambda as a value. + if isinstance(v, Lambda): + v = (tuple(v.signature), tuple(v.expr)) + else: + v = (tuple(v[0]), tuple(v[1])) + rel_temp[key] = v + relations = Dict(rel_temp) + + # construct the object + obj = super().__new__(cls, name, patch, symbols, relations) + + # Add deprecated attributes + obj.transforms = _deprecated_dict( + """ + CoordSystem.transforms is deprecated. The CoordSystem class is now + immutable. Use the 'relations' keyword argument to the + CoordSystems() constructor to specify relations. + """, {}) + obj._names = [str(n) for n in symbols] + obj.patch.coord_systems.append(obj) # deprecated + obj._dummies = [Dummy(str(n)) for n in symbols] # deprecated + obj._dummy = Dummy() + + return obj + + @property + def name(self): + return self.args[0] + + @property + def patch(self): + return self.args[1] + + @property + def manifold(self): + return self.patch.manifold + + @property + def symbols(self): + return tuple(CoordinateSymbol(self, i, **s._assumptions.generator) + for i,s in enumerate(self.args[2])) + + @property + def relations(self): + return self.args[3] + + @property + def dim(self): + return self.patch.dim + + ########################################################################## + # Finding transformation relation + ########################################################################## + + def transformation(self, sys): + """ + Return coordinate transformation function from *self* to *sys*. + + Parameters + ========== + + sys : CoordSystem + + Returns + ======= + + sympy.Lambda + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> R2_r.transformation(R2_p) + Lambda((x, y), Matrix([ + [sqrt(x**2 + y**2)], + [ atan2(y, x)]])) + + """ + signature = self.args[2] + + key = Tuple(self.name, sys.name) + if self == sys: + expr = Matrix(self.symbols) + elif key in self.relations: + expr = Matrix(self.relations[key][1]) + elif key[::-1] in self.relations: + expr = Matrix(self._inverse_transformation(sys, self)) + else: + expr = Matrix(self._indirect_transformation(self, sys)) + return Lambda(signature, expr) + + @staticmethod + def _solve_inverse(sym1, sym2, exprs, sys1_name, sys2_name): + ret = solve( + [t[0] - t[1] for t in zip(sym2, exprs)], + list(sym1), dict=True) + + if len(ret) == 0: + temp = "Cannot solve inverse relation from {} to {}." + raise NotImplementedError(temp.format(sys1_name, sys2_name)) + elif len(ret) > 1: + temp = "Obtained multiple inverse relation from {} to {}." + raise ValueError(temp.format(sys1_name, sys2_name)) + + return ret[0] + + @classmethod + def _inverse_transformation(cls, sys1, sys2): + # Find the transformation relation from sys2 to sys1 + forward = sys1.transform(sys2) + inv_results = cls._solve_inverse(sys1.symbols, sys2.symbols, forward, + sys1.name, sys2.name) + signature = tuple(sys1.symbols) + return [inv_results[s] for s in signature] + + @classmethod + @cacheit + def _indirect_transformation(cls, sys1, sys2): + # Find the transformation relation between two indirectly connected + # coordinate systems + rel = sys1.relations + path = cls._dijkstra(sys1, sys2) + + transforms = [] + for s1, s2 in zip(path, path[1:]): + if (s1, s2) in rel: + transforms.append(rel[(s1, s2)]) + else: + sym2, inv_exprs = rel[(s2, s1)] + sym1 = tuple(Dummy() for i in sym2) + ret = cls._solve_inverse(sym2, sym1, inv_exprs, s2, s1) + ret = tuple(ret[s] for s in sym2) + transforms.append((sym1, ret)) + syms = sys1.args[2] + exprs = syms + for newsyms, newexprs in transforms: + exprs = tuple(e.subs(zip(newsyms, exprs)) for e in newexprs) + return exprs + + @staticmethod + def _dijkstra(sys1, sys2): + # Use Dijkstra algorithm to find the shortest path between two indirectly-connected + # coordinate systems + # return value is the list of the names of the systems. + relations = sys1.relations + graph = {} + for s1, s2 in relations.keys(): + if s1 not in graph: + graph[s1] = {s2} + else: + graph[s1].add(s2) + if s2 not in graph: + graph[s2] = {s1} + else: + graph[s2].add(s1) + + path_dict = {sys:[0, [], 0] for sys in graph} # minimum distance, path, times of visited + + def visit(sys): + path_dict[sys][2] = 1 + for newsys in graph[sys]: + distance = path_dict[sys][0] + 1 + if path_dict[newsys][0] >= distance or not path_dict[newsys][1]: + path_dict[newsys][0] = distance + path_dict[newsys][1] = list(path_dict[sys][1]) + path_dict[newsys][1].append(sys) + + visit(sys1.name) + + while True: + min_distance = max(path_dict.values(), key=lambda x:x[0])[0] + newsys = None + for sys, lst in path_dict.items(): + if 0 < lst[0] <= min_distance and not lst[2]: + min_distance = lst[0] + newsys = sys + if newsys is None: + break + visit(newsys) + + result = path_dict[sys2.name][1] + result.append(sys2.name) + + if result == [sys2.name]: + raise KeyError("Two coordinate systems are not connected.") + return result + + def connect_to(self, to_sys, from_coords, to_exprs, inverse=True, fill_in_gaps=False): + sympy_deprecation_warning( + """ + The CoordSystem.connect_to() method is deprecated. Instead, + generate a new instance of CoordSystem with the 'relations' + keyword argument (CoordSystem classes are now immutable). + """, + deprecated_since_version="1.7", + active_deprecations_target="deprecated-diffgeom-mutable", + ) + + from_coords, to_exprs = dummyfy(from_coords, to_exprs) + self.transforms[to_sys] = Matrix(from_coords), Matrix(to_exprs) + + if inverse: + to_sys.transforms[self] = self._inv_transf(from_coords, to_exprs) + + if fill_in_gaps: + self._fill_gaps_in_transformations() + + @staticmethod + def _inv_transf(from_coords, to_exprs): + # Will be removed when connect_to is removed + inv_from = [i.as_dummy() for i in from_coords] + inv_to = solve( + [t[0] - t[1] for t in zip(inv_from, to_exprs)], + list(from_coords), dict=True)[0] + inv_to = [inv_to[fc] for fc in from_coords] + return Matrix(inv_from), Matrix(inv_to) + + @staticmethod + def _fill_gaps_in_transformations(): + # Will be removed when connect_to is removed + raise NotImplementedError + + ########################################################################## + # Coordinate transformations + ########################################################################## + + def transform(self, sys, coordinates=None): + """ + Return the result of coordinate transformation from *self* to *sys*. + If coordinates are not given, coordinate symbols of *self* are used. + + Parameters + ========== + + sys : CoordSystem + + coordinates : Any iterable, optional. + + Returns + ======= + + sympy.ImmutableDenseMatrix containing CoordinateSymbol + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> R2_r.transform(R2_p) + Matrix([ + [sqrt(x**2 + y**2)], + [ atan2(y, x)]]) + >>> R2_r.transform(R2_p, [0, 1]) + Matrix([ + [ 1], + [pi/2]]) + + """ + if coordinates is None: + coordinates = self.symbols + if self != sys: + transf = self.transformation(sys) + coordinates = transf(*coordinates) + else: + coordinates = Matrix(coordinates) + return coordinates + + def coord_tuple_transform_to(self, to_sys, coords): + """Transform ``coords`` to coord system ``to_sys``.""" + sympy_deprecation_warning( + """ + The CoordSystem.coord_tuple_transform_to() method is deprecated. + Use the CoordSystem.transform() method instead. + """, + deprecated_since_version="1.7", + active_deprecations_target="deprecated-diffgeom-mutable", + ) + + coords = Matrix(coords) + if self != to_sys: + with ignore_warnings(SymPyDeprecationWarning): + transf = self.transforms[to_sys] + coords = transf[1].subs(list(zip(transf[0], coords))) + return coords + + def jacobian(self, sys, coordinates=None): + """ + Return the jacobian matrix of a transformation on given coordinates. + If coordinates are not given, coordinate symbols of *self* are used. + + Parameters + ========== + + sys : CoordSystem + + coordinates : Any iterable, optional. + + Returns + ======= + + sympy.ImmutableDenseMatrix + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> R2_p.jacobian(R2_r) + Matrix([ + [cos(theta), -rho*sin(theta)], + [sin(theta), rho*cos(theta)]]) + >>> R2_p.jacobian(R2_r, [1, 0]) + Matrix([ + [1, 0], + [0, 1]]) + + """ + result = self.transform(sys).jacobian(self.symbols) + if coordinates is not None: + result = result.subs(list(zip(self.symbols, coordinates))) + return result + jacobian_matrix = jacobian + + def jacobian_determinant(self, sys, coordinates=None): + """ + Return the jacobian determinant of a transformation on given + coordinates. If coordinates are not given, coordinate symbols of *self* + are used. + + Parameters + ========== + + sys : CoordSystem + + coordinates : Any iterable, optional. + + Returns + ======= + + sympy.Expr + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> R2_r.jacobian_determinant(R2_p) + 1/sqrt(x**2 + y**2) + >>> R2_r.jacobian_determinant(R2_p, [1, 0]) + 1 + + """ + return self.jacobian(sys, coordinates).det() + + + ########################################################################## + # Points + ########################################################################## + + def point(self, coords): + """Create a ``Point`` with coordinates given in this coord system.""" + return Point(self, coords) + + def point_to_coords(self, point): + """Calculate the coordinates of a point in this coord system.""" + return point.coords(self) + + ########################################################################## + # Base fields. + ########################################################################## + + def base_scalar(self, coord_index): + """Return ``BaseScalarField`` that takes a point and returns one of the coordinates.""" + return BaseScalarField(self, coord_index) + coord_function = base_scalar + + def base_scalars(self): + """Returns a list of all coordinate functions. + For more details see the ``base_scalar`` method of this class.""" + return [self.base_scalar(i) for i in range(self.dim)] + coord_functions = base_scalars + + def base_vector(self, coord_index): + """Return a basis vector field. + The basis vector field for this coordinate system. It is also an + operator on scalar fields.""" + return BaseVectorField(self, coord_index) + + def base_vectors(self): + """Returns a list of all base vectors. + For more details see the ``base_vector`` method of this class.""" + return [self.base_vector(i) for i in range(self.dim)] + + def base_oneform(self, coord_index): + """Return a basis 1-form field. + The basis one-form field for this coordinate system. It is also an + operator on vector fields.""" + return Differential(self.coord_function(coord_index)) + + def base_oneforms(self): + """Returns a list of all base oneforms. + For more details see the ``base_oneform`` method of this class.""" + return [self.base_oneform(i) for i in range(self.dim)] + + +class CoordinateSymbol(Symbol): + """A symbol which denotes an abstract value of i-th coordinate of + the coordinate system with given context. + + Explanation + =========== + + Each coordinates in coordinate system are represented by unique symbol, + such as x, y, z in Cartesian coordinate system. + + You may not construct this class directly. Instead, use `symbols` method + of CoordSystem. + + Parameters + ========== + + coord_sys : CoordSystem + + index : integer + + Examples + ======== + + >>> from sympy import symbols, Lambda, Matrix, sqrt, atan2, cos, sin + >>> from sympy.diffgeom import Manifold, Patch, CoordSystem + >>> m = Manifold('M', 2) + >>> p = Patch('P', m) + >>> x, y = symbols('x y', real=True) + >>> r, theta = symbols('r theta', nonnegative=True) + >>> relation_dict = { + ... ('Car2D', 'Pol'): Lambda((x, y), Matrix([sqrt(x**2 + y**2), atan2(y, x)])), + ... ('Pol', 'Car2D'): Lambda((r, theta), Matrix([r*cos(theta), r*sin(theta)])) + ... } + >>> Car2D = CoordSystem('Car2D', p, [x, y], relation_dict) + >>> Pol = CoordSystem('Pol', p, [r, theta], relation_dict) + >>> x, y = Car2D.symbols + + ``CoordinateSymbol`` contains its coordinate symbol and index. + + >>> x.name + 'x' + >>> x.coord_sys == Car2D + True + >>> x.index + 0 + >>> x.is_real + True + + You can transform ``CoordinateSymbol`` into other coordinate system using + ``rewrite()`` method. + + >>> x.rewrite(Pol) + r*cos(theta) + >>> sqrt(x**2 + y**2).rewrite(Pol).simplify() + r + + """ + def __new__(cls, coord_sys, index, **assumptions): + name = coord_sys.args[2][index].name + obj = super().__new__(cls, name, **assumptions) + obj.coord_sys = coord_sys + obj.index = index + return obj + + def __getnewargs__(self): + return (self.coord_sys, self.index) + + def _hashable_content(self): + return ( + self.coord_sys, self.index + ) + tuple(sorted(self.assumptions0.items())) + + def _eval_rewrite(self, rule, args, **hints): + if isinstance(rule, CoordSystem): + return rule.transform(self.coord_sys)[self.index] + return super()._eval_rewrite(rule, args, **hints) + + +class Point(Basic): + """Point defined in a coordinate system. + + Explanation + =========== + + Mathematically, point is defined in the manifold and does not have any coordinates + by itself. Coordinate system is what imbues the coordinates to the point by coordinate + chart. However, due to the difficulty of realizing such logic, you must supply + a coordinate system and coordinates to define a Point here. + + The usage of this object after its definition is independent of the + coordinate system that was used in order to define it, however due to + limitations in the simplification routines you can arrive at complicated + expressions if you use inappropriate coordinate systems. + + Parameters + ========== + + coord_sys : CoordSystem + + coords : list + The coordinates of the point. + + Examples + ======== + + >>> from sympy import pi + >>> from sympy.diffgeom import Point + >>> from sympy.diffgeom.rn import R2, R2_r, R2_p + >>> rho, theta = R2_p.symbols + + >>> p = Point(R2_p, [rho, 3*pi/4]) + + >>> p.manifold == R2 + True + + >>> p.coords() + Matrix([ + [ rho], + [3*pi/4]]) + >>> p.coords(R2_r) + Matrix([ + [-sqrt(2)*rho/2], + [ sqrt(2)*rho/2]]) + + """ + + def __new__(cls, coord_sys, coords, **kwargs): + coords = Matrix(coords) + obj = super().__new__(cls, coord_sys, coords) + obj._coord_sys = coord_sys + obj._coords = coords + return obj + + @property + def patch(self): + return self._coord_sys.patch + + @property + def manifold(self): + return self._coord_sys.manifold + + @property + def dim(self): + return self.manifold.dim + + def coords(self, sys=None): + """ + Coordinates of the point in given coordinate system. If coordinate system + is not passed, it returns the coordinates in the coordinate system in which + the poin was defined. + """ + if sys is None: + return self._coords + else: + return self._coord_sys.transform(sys, self._coords) + + @property + def free_symbols(self): + return self._coords.free_symbols + + +class BaseScalarField(Expr): + """Base scalar field over a manifold for a given coordinate system. + + Explanation + =========== + + A scalar field takes a point as an argument and returns a scalar. + A base scalar field of a coordinate system takes a point and returns one of + the coordinates of that point in the coordinate system in question. + + To define a scalar field you need to choose the coordinate system and the + index of the coordinate. + + The use of the scalar field after its definition is independent of the + coordinate system in which it was defined, however due to limitations in + the simplification routines you may arrive at more complicated + expression if you use unappropriate coordinate systems. + You can build complicated scalar fields by just building up SymPy + expressions containing ``BaseScalarField`` instances. + + Parameters + ========== + + coord_sys : CoordSystem + + index : integer + + Examples + ======== + + >>> from sympy import Function, pi + >>> from sympy.diffgeom import BaseScalarField + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> rho, _ = R2_p.symbols + >>> point = R2_p.point([rho, 0]) + >>> fx, fy = R2_r.base_scalars() + >>> ftheta = BaseScalarField(R2_r, 1) + + >>> fx(point) + rho + >>> fy(point) + 0 + + >>> (fx**2+fy**2).rcall(point) + rho**2 + + >>> g = Function('g') + >>> fg = g(ftheta-pi) + >>> fg.rcall(point) + g(-pi) + + """ + + is_commutative = True + + def __new__(cls, coord_sys, index, **kwargs): + index = _sympify(index) + obj = super().__new__(cls, coord_sys, index) + obj._coord_sys = coord_sys + obj._index = index + return obj + + @property + def coord_sys(self): + return self.args[0] + + @property + def index(self): + return self.args[1] + + @property + def patch(self): + return self.coord_sys.patch + + @property + def manifold(self): + return self.coord_sys.manifold + + @property + def dim(self): + return self.manifold.dim + + def __call__(self, *args): + """Evaluating the field at a point or doing nothing. + If the argument is a ``Point`` instance, the field is evaluated at that + point. The field is returned itself if the argument is any other + object. It is so in order to have working recursive calling mechanics + for all fields (check the ``__call__`` method of ``Expr``). + """ + point = args[0] + if len(args) != 1 or not isinstance(point, Point): + return self + coords = point.coords(self._coord_sys) + # XXX Calling doit is necessary with all the Subs expressions + # XXX Calling simplify is necessary with all the trig expressions + return simplify(coords[self._index]).doit() + + # XXX Workaround for limitations on the content of args + free_symbols: set[Any] = set() + + +class BaseVectorField(Expr): + r"""Base vector field over a manifold for a given coordinate system. + + Explanation + =========== + + A vector field is an operator taking a scalar field and returning a + directional derivative (which is also a scalar field). + A base vector field is the same type of operator, however the derivation is + specifically done with respect to a chosen coordinate. + + To define a base vector field you need to choose the coordinate system and + the index of the coordinate. + + The use of the vector field after its definition is independent of the + coordinate system in which it was defined, however due to limitations in the + simplification routines you may arrive at more complicated expression if you + use unappropriate coordinate systems. + + Parameters + ========== + coord_sys : CoordSystem + + index : integer + + Examples + ======== + + >>> from sympy import Function + >>> from sympy.diffgeom.rn import R2_p, R2_r + >>> from sympy.diffgeom import BaseVectorField + >>> from sympy import pprint + + >>> x, y = R2_r.symbols + >>> rho, theta = R2_p.symbols + >>> fx, fy = R2_r.base_scalars() + >>> point_p = R2_p.point([rho, theta]) + >>> point_r = R2_r.point([x, y]) + + >>> g = Function('g') + >>> s_field = g(fx, fy) + + >>> v = BaseVectorField(R2_r, 1) + >>> pprint(v(s_field)) + / d \| + |---(g(x, xi))|| + \dxi /|xi=y + >>> pprint(v(s_field).rcall(point_r).doit()) + d + --(g(x, y)) + dy + >>> pprint(v(s_field).rcall(point_p)) + / d \| + |---(g(rho*cos(theta), xi))|| + \dxi /|xi=rho*sin(theta) + + """ + + is_commutative = False + + def __new__(cls, coord_sys, index, **kwargs): + index = _sympify(index) + obj = super().__new__(cls, coord_sys, index) + obj._coord_sys = coord_sys + obj._index = index + return obj + + @property + def coord_sys(self): + return self.args[0] + + @property + def index(self): + return self.args[1] + + @property + def patch(self): + return self.coord_sys.patch + + @property + def manifold(self): + return self.coord_sys.manifold + + @property + def dim(self): + return self.manifold.dim + + def __call__(self, scalar_field): + """Apply on a scalar field. + The action of a vector field on a scalar field is a directional + differentiation. + If the argument is not a scalar field an error is raised. + """ + if covariant_order(scalar_field) or contravariant_order(scalar_field): + raise ValueError('Only scalar fields can be supplied as arguments to vector fields.') + + if scalar_field is None: + return self + + base_scalars = list(scalar_field.atoms(BaseScalarField)) + + # First step: e_x(x+r**2) -> e_x(x) + 2*r*e_x(r) + d_var = self._coord_sys._dummy + # TODO: you need a real dummy function for the next line + d_funcs = [Function('_#_%s' % i)(d_var) for i, + b in enumerate(base_scalars)] + d_result = scalar_field.subs(list(zip(base_scalars, d_funcs))) + d_result = d_result.diff(d_var) + + # Second step: e_x(x) -> 1 and e_x(r) -> cos(atan2(x, y)) + coords = self._coord_sys.symbols + d_funcs_deriv = [f.diff(d_var) for f in d_funcs] + d_funcs_deriv_sub = [] + for b in base_scalars: + jac = self._coord_sys.jacobian(b._coord_sys, coords) + d_funcs_deriv_sub.append(jac[b._index, self._index]) + d_result = d_result.subs(list(zip(d_funcs_deriv, d_funcs_deriv_sub))) + + # Remove the dummies + result = d_result.subs(list(zip(d_funcs, base_scalars))) + result = result.subs(list(zip(coords, self._coord_sys.coord_functions()))) + return result.doit() + + +def _find_coords(expr): + # Finds CoordinateSystems existing in expr + fields = expr.atoms(BaseScalarField, BaseVectorField) + return {f._coord_sys for f in fields} + + +class Commutator(Expr): + r"""Commutator of two vector fields. + + Explanation + =========== + + The commutator of two vector fields `v_1` and `v_2` is defined as the + vector field `[v_1, v_2]` that evaluated on each scalar field `f` is equal + to `v_1(v_2(f)) - v_2(v_1(f))`. + + Examples + ======== + + + >>> from sympy.diffgeom.rn import R2_p, R2_r + >>> from sympy.diffgeom import Commutator + >>> from sympy import simplify + + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> e_r = R2_p.base_vector(0) + + >>> c_xy = Commutator(e_x, e_y) + >>> c_xr = Commutator(e_x, e_r) + >>> c_xy + 0 + + Unfortunately, the current code is not able to compute everything: + + >>> c_xr + Commutator(e_x, e_rho) + >>> simplify(c_xr(fy**2)) + -2*cos(theta)*y**2/(x**2 + y**2) + + """ + def __new__(cls, v1, v2): + if (covariant_order(v1) or contravariant_order(v1) != 1 + or covariant_order(v2) or contravariant_order(v2) != 1): + raise ValueError( + 'Only commutators of vector fields are supported.') + if v1 == v2: + return S.Zero + coord_sys = set().union(*[_find_coords(v) for v in (v1, v2)]) + if len(coord_sys) == 1: + # Only one coordinate systems is used, hence it is easy enough to + # actually evaluate the commutator. + if all(isinstance(v, BaseVectorField) for v in (v1, v2)): + return S.Zero + bases_1, bases_2 = [list(v.atoms(BaseVectorField)) + for v in (v1, v2)] + coeffs_1 = [v1.expand().coeff(b) for b in bases_1] + coeffs_2 = [v2.expand().coeff(b) for b in bases_2] + res = 0 + for c1, b1 in zip(coeffs_1, bases_1): + for c2, b2 in zip(coeffs_2, bases_2): + res += c1*b1(c2)*b2 - c2*b2(c1)*b1 + return res + else: + obj = super().__new__(cls, v1, v2) + obj._v1 = v1 # deprecated assignment + obj._v2 = v2 # deprecated assignment + return obj + + @property + def v1(self): + return self.args[0] + + @property + def v2(self): + return self.args[1] + + def __call__(self, scalar_field): + """Apply on a scalar field. + If the argument is not a scalar field an error is raised. + """ + return self.v1(self.v2(scalar_field)) - self.v2(self.v1(scalar_field)) + + +class Differential(Expr): + r"""Return the differential (exterior derivative) of a form field. + + Explanation + =========== + + The differential of a form (i.e. the exterior derivative) has a complicated + definition in the general case. + The differential `df` of the 0-form `f` is defined for any vector field `v` + as `df(v) = v(f)`. + + Examples + ======== + + >>> from sympy import Function + >>> from sympy.diffgeom.rn import R2_r + >>> from sympy.diffgeom import Differential + >>> from sympy import pprint + + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> g = Function('g') + >>> s_field = g(fx, fy) + >>> dg = Differential(s_field) + + >>> dg + d(g(x, y)) + >>> pprint(dg(e_x)) + / d \| + |---(g(xi, y))|| + \dxi /|xi=x + >>> pprint(dg(e_y)) + / d \| + |---(g(x, xi))|| + \dxi /|xi=y + + Applying the exterior derivative operator twice always results in: + + >>> Differential(dg) + 0 + """ + + is_commutative = False + + def __new__(cls, form_field): + if contravariant_order(form_field): + raise ValueError( + 'A vector field was supplied as an argument to Differential.') + if isinstance(form_field, Differential): + return S.Zero + else: + obj = super().__new__(cls, form_field) + obj._form_field = form_field # deprecated assignment + return obj + + @property + def form_field(self): + return self.args[0] + + def __call__(self, *vector_fields): + """Apply on a list of vector_fields. + + Explanation + =========== + + If the number of vector fields supplied is not equal to 1 + the order of + the form field inside the differential the result is undefined. + + For 1-forms (i.e. differentials of scalar fields) the evaluation is + done as `df(v)=v(f)`. However if `v` is ``None`` instead of a vector + field, the differential is returned unchanged. This is done in order to + permit partial contractions for higher forms. + + In the general case the evaluation is done by applying the form field + inside the differential on a list with one less elements than the number + of elements in the original list. Lowering the number of vector fields + is achieved through replacing each pair of fields by their + commutator. + + If the arguments are not vectors or ``None``s an error is raised. + """ + if any((contravariant_order(a) != 1 or covariant_order(a)) and a is not None + for a in vector_fields): + raise ValueError('The arguments supplied to Differential should be vector fields or Nones.') + k = len(vector_fields) + if k == 1: + if vector_fields[0]: + return vector_fields[0].rcall(self._form_field) + return self + else: + # For higher form it is more complicated: + # Invariant formula: + # https://en.wikipedia.org/wiki/Exterior_derivative#Invariant_formula + # df(v1, ... vn) = +/- vi(f(v1..no i..vn)) + # +/- f([vi,vj],v1..no i, no j..vn) + f = self._form_field + v = vector_fields + ret = 0 + for i in range(k): + t = v[i].rcall(f.rcall(*v[:i] + v[i + 1:])) + ret += (-1)**i*t + for j in range(i + 1, k): + c = Commutator(v[i], v[j]) + if c: # TODO this is ugly - the Commutator can be Zero and + # this causes the next line to fail + t = f.rcall(*(c,) + v[:i] + v[i + 1:j] + v[j + 1:]) + ret += (-1)**(i + j)*t + return ret + + +class TensorProduct(Expr): + """Tensor product of forms. + + Explanation + =========== + + The tensor product permits the creation of multilinear functionals (i.e. + higher order tensors) out of lower order fields (e.g. 1-forms and vector + fields). However, the higher tensors thus created lack the interesting + features provided by the other type of product, the wedge product, namely + they are not antisymmetric and hence are not form fields. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r + >>> from sympy.diffgeom import TensorProduct + + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> dx, dy = R2_r.base_oneforms() + + >>> TensorProduct(dx, dy)(e_x, e_y) + 1 + >>> TensorProduct(dx, dy)(e_y, e_x) + 0 + >>> TensorProduct(dx, fx*dy)(fx*e_x, e_y) + x**2 + >>> TensorProduct(e_x, e_y)(fx**2, fy**2) + 4*x*y + >>> TensorProduct(e_y, dx)(fy) + dx + + You can nest tensor products. + + >>> tp1 = TensorProduct(dx, dy) + >>> TensorProduct(tp1, dx)(e_x, e_y, e_x) + 1 + + You can make partial contraction for instance when 'raising an index'. + Putting ``None`` in the second argument of ``rcall`` means that the + respective position in the tensor product is left as it is. + + >>> TP = TensorProduct + >>> metric = TP(dx, dx) + 3*TP(dy, dy) + >>> metric.rcall(e_y, None) + 3*dy + + Or automatically pad the args with ``None`` without specifying them. + + >>> metric.rcall(e_y) + 3*dy + + """ + def __new__(cls, *args): + scalar = Mul(*[m for m in args if covariant_order(m) + contravariant_order(m) == 0]) + multifields = [m for m in args if covariant_order(m) + contravariant_order(m)] + if multifields: + if len(multifields) == 1: + return scalar*multifields[0] + return scalar*super().__new__(cls, *multifields) + else: + return scalar + + def __call__(self, *fields): + """Apply on a list of fields. + + If the number of input fields supplied is not equal to the order of + the tensor product field, the list of arguments is padded with ``None``'s. + + The list of arguments is divided in sublists depending on the order of + the forms inside the tensor product. The sublists are provided as + arguments to these forms and the resulting expressions are given to the + constructor of ``TensorProduct``. + + """ + tot_order = covariant_order(self) + contravariant_order(self) + tot_args = len(fields) + if tot_args != tot_order: + fields = list(fields) + [None]*(tot_order - tot_args) + orders = [covariant_order(f) + contravariant_order(f) for f in self._args] + indices = [sum(orders[:i + 1]) for i in range(len(orders) - 1)] + fields = [fields[i:j] for i, j in zip([0] + indices, indices + [None])] + multipliers = [t[0].rcall(*t[1]) for t in zip(self._args, fields)] + return TensorProduct(*multipliers) + + +class WedgeProduct(TensorProduct): + """Wedge product of forms. + + Explanation + =========== + + In the context of integration only completely antisymmetric forms make + sense. The wedge product permits the creation of such forms. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r + >>> from sympy.diffgeom import WedgeProduct + + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> dx, dy = R2_r.base_oneforms() + + >>> WedgeProduct(dx, dy)(e_x, e_y) + 1 + >>> WedgeProduct(dx, dy)(e_y, e_x) + -1 + >>> WedgeProduct(dx, fx*dy)(fx*e_x, e_y) + x**2 + >>> WedgeProduct(e_x, e_y)(fy, None) + -e_x + + You can nest wedge products. + + >>> wp1 = WedgeProduct(dx, dy) + >>> WedgeProduct(wp1, dx)(e_x, e_y, e_x) + 0 + + """ + # TODO the calculation of signatures is slow + # TODO you do not need all these permutations (neither the prefactor) + def __call__(self, *fields): + """Apply on a list of vector_fields. + The expression is rewritten internally in terms of tensor products and evaluated.""" + orders = (covariant_order(e) + contravariant_order(e) for e in self.args) + mul = 1/Mul(*(factorial(o) for o in orders)) + perms = permutations(fields) + perms_par = (Permutation( + p).signature() for p in permutations(range(len(fields)))) + tensor_prod = TensorProduct(*self.args) + return mul*Add(*[tensor_prod(*p[0])*p[1] for p in zip(perms, perms_par)]) + + +class LieDerivative(Expr): + """Lie derivative with respect to a vector field. + + Explanation + =========== + + The transport operator that defines the Lie derivative is the pushforward of + the field to be derived along the integral curve of the field with respect + to which one derives. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r, R2_p + >>> from sympy.diffgeom import (LieDerivative, TensorProduct) + + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> e_rho, e_theta = R2_p.base_vectors() + >>> dx, dy = R2_r.base_oneforms() + + >>> LieDerivative(e_x, fy) + 0 + >>> LieDerivative(e_x, fx) + 1 + >>> LieDerivative(e_x, e_x) + 0 + + The Lie derivative of a tensor field by another tensor field is equal to + their commutator: + + >>> LieDerivative(e_x, e_rho) + Commutator(e_x, e_rho) + >>> LieDerivative(e_x + e_y, fx) + 1 + + >>> tp = TensorProduct(dx, dy) + >>> LieDerivative(e_x, tp) + LieDerivative(e_x, TensorProduct(dx, dy)) + >>> LieDerivative(e_x, tp) + LieDerivative(e_x, TensorProduct(dx, dy)) + + """ + def __new__(cls, v_field, expr): + expr_form_ord = covariant_order(expr) + if contravariant_order(v_field) != 1 or covariant_order(v_field): + raise ValueError('Lie derivatives are defined only with respect to' + ' vector fields. The supplied argument was not a ' + 'vector field.') + if expr_form_ord > 0: + obj = super().__new__(cls, v_field, expr) + # deprecated assignments + obj._v_field = v_field + obj._expr = expr + return obj + if expr.atoms(BaseVectorField): + return Commutator(v_field, expr) + else: + return v_field.rcall(expr) + + @property + def v_field(self): + return self.args[0] + + @property + def expr(self): + return self.args[1] + + def __call__(self, *args): + v = self.v_field + expr = self.expr + lead_term = v(expr(*args)) + rest = Add(*[Mul(*args[:i] + (Commutator(v, args[i]),) + args[i + 1:]) + for i in range(len(args))]) + return lead_term - rest + + +class BaseCovarDerivativeOp(Expr): + """Covariant derivative operator with respect to a base vector. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r + >>> from sympy.diffgeom import BaseCovarDerivativeOp + >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct + + >>> TP = TensorProduct + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> dx, dy = R2_r.base_oneforms() + + >>> ch = metric_to_Christoffel_2nd(TP(dx, dx) + TP(dy, dy)) + >>> ch + [[[0, 0], [0, 0]], [[0, 0], [0, 0]]] + >>> cvd = BaseCovarDerivativeOp(R2_r, 0, ch) + >>> cvd(fx) + 1 + >>> cvd(fx*e_x) + e_x + """ + + def __new__(cls, coord_sys, index, christoffel): + index = _sympify(index) + christoffel = ImmutableDenseNDimArray(christoffel) + obj = super().__new__(cls, coord_sys, index, christoffel) + # deprecated assignments + obj._coord_sys = coord_sys + obj._index = index + obj._christoffel = christoffel + return obj + + @property + def coord_sys(self): + return self.args[0] + + @property + def index(self): + return self.args[1] + + @property + def christoffel(self): + return self.args[2] + + def __call__(self, field): + """Apply on a scalar field. + + The action of a vector field on a scalar field is a directional + differentiation. + If the argument is not a scalar field the behaviour is undefined. + """ + if covariant_order(field) != 0: + raise NotImplementedError() + + field = vectors_in_basis(field, self._coord_sys) + + wrt_vector = self._coord_sys.base_vector(self._index) + wrt_scalar = self._coord_sys.coord_function(self._index) + vectors = list(field.atoms(BaseVectorField)) + + # First step: replace all vectors with something susceptible to + # derivation and do the derivation + # TODO: you need a real dummy function for the next line + d_funcs = [Function('_#_%s' % i)(wrt_scalar) for i, + b in enumerate(vectors)] + d_result = field.subs(list(zip(vectors, d_funcs))) + d_result = wrt_vector(d_result) + + # Second step: backsubstitute the vectors in + d_result = d_result.subs(list(zip(d_funcs, vectors))) + + # Third step: evaluate the derivatives of the vectors + derivs = [] + for v in vectors: + d = Add(*[(self._christoffel[k, wrt_vector._index, v._index] + *v._coord_sys.base_vector(k)) + for k in range(v._coord_sys.dim)]) + derivs.append(d) + to_subs = [wrt_vector(d) for d in d_funcs] + # XXX: This substitution can fail when there are Dummy symbols and the + # cache is disabled: https://github.com/sympy/sympy/issues/17794 + result = d_result.subs(list(zip(to_subs, derivs))) + + # Remove the dummies + result = result.subs(list(zip(d_funcs, vectors))) + return result.doit() + + +class CovarDerivativeOp(Expr): + """Covariant derivative operator. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2_r + >>> from sympy.diffgeom import CovarDerivativeOp + >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct + >>> TP = TensorProduct + >>> fx, fy = R2_r.base_scalars() + >>> e_x, e_y = R2_r.base_vectors() + >>> dx, dy = R2_r.base_oneforms() + >>> ch = metric_to_Christoffel_2nd(TP(dx, dx) + TP(dy, dy)) + + >>> ch + [[[0, 0], [0, 0]], [[0, 0], [0, 0]]] + >>> cvd = CovarDerivativeOp(fx*e_x, ch) + >>> cvd(fx) + x + >>> cvd(fx*e_x) + x*e_x + + """ + + def __new__(cls, wrt, christoffel): + if len({v._coord_sys for v in wrt.atoms(BaseVectorField)}) > 1: + raise NotImplementedError() + if contravariant_order(wrt) != 1 or covariant_order(wrt): + raise ValueError('Covariant derivatives are defined only with ' + 'respect to vector fields. The supplied argument ' + 'was not a vector field.') + christoffel = ImmutableDenseNDimArray(christoffel) + obj = super().__new__(cls, wrt, christoffel) + # deprecated assignments + obj._wrt = wrt + obj._christoffel = christoffel + return obj + + @property + def wrt(self): + return self.args[0] + + @property + def christoffel(self): + return self.args[1] + + def __call__(self, field): + vectors = list(self._wrt.atoms(BaseVectorField)) + base_ops = [BaseCovarDerivativeOp(v._coord_sys, v._index, self._christoffel) + for v in vectors] + return self._wrt.subs(list(zip(vectors, base_ops))).rcall(field) + + +############################################################################### +# Integral curves on vector fields +############################################################################### +def intcurve_series(vector_field, param, start_point, n=6, coord_sys=None, coeffs=False): + r"""Return the series expansion for an integral curve of the field. + + Explanation + =========== + + Integral curve is a function `\gamma` taking a parameter in `R` to a point + in the manifold. It verifies the equation: + + `V(f)\big(\gamma(t)\big) = \frac{d}{dt}f\big(\gamma(t)\big)` + + where the given ``vector_field`` is denoted as `V`. This holds for any + value `t` for the parameter and any scalar field `f`. + + This equation can also be decomposed of a basis of coordinate functions + `V(f_i)\big(\gamma(t)\big) = \frac{d}{dt}f_i\big(\gamma(t)\big) \quad \forall i` + + This function returns a series expansion of `\gamma(t)` in terms of the + coordinate system ``coord_sys``. The equations and expansions are necessarily + done in coordinate-system-dependent way as there is no other way to + represent movement between points on the manifold (i.e. there is no such + thing as a difference of points for a general manifold). + + Parameters + ========== + vector_field + the vector field for which an integral curve will be given + + param + the argument of the function `\gamma` from R to the curve + + start_point + the point which corresponds to `\gamma(0)` + + n + the order to which to expand + + coord_sys + the coordinate system in which to expand + coeffs (default False) - if True return a list of elements of the expansion + + Examples + ======== + + Use the predefined R2 manifold: + + >>> from sympy.abc import t, x, y + >>> from sympy.diffgeom.rn import R2_p, R2_r + >>> from sympy.diffgeom import intcurve_series + + Specify a starting point and a vector field: + + >>> start_point = R2_r.point([x, y]) + >>> vector_field = R2_r.e_x + + Calculate the series: + + >>> intcurve_series(vector_field, t, start_point, n=3) + Matrix([ + [t + x], + [ y]]) + + Or get the elements of the expansion in a list: + + >>> series = intcurve_series(vector_field, t, start_point, n=3, coeffs=True) + >>> series[0] + Matrix([ + [x], + [y]]) + >>> series[1] + Matrix([ + [t], + [0]]) + >>> series[2] + Matrix([ + [0], + [0]]) + + The series in the polar coordinate system: + + >>> series = intcurve_series(vector_field, t, start_point, + ... n=3, coord_sys=R2_p, coeffs=True) + >>> series[0] + Matrix([ + [sqrt(x**2 + y**2)], + [ atan2(y, x)]]) + >>> series[1] + Matrix([ + [t*x/sqrt(x**2 + y**2)], + [ -t*y/(x**2 + y**2)]]) + >>> series[2] + Matrix([ + [t**2*(-x**2/(x**2 + y**2)**(3/2) + 1/sqrt(x**2 + y**2))/2], + [ t**2*x*y/(x**2 + y**2)**2]]) + + See Also + ======== + + intcurve_diffequ + + """ + if contravariant_order(vector_field) != 1 or covariant_order(vector_field): + raise ValueError('The supplied field was not a vector field.') + + def iter_vfield(scalar_field, i): + """Return ``vector_field`` called `i` times on ``scalar_field``.""" + return reduce(lambda s, v: v.rcall(s), [vector_field, ]*i, scalar_field) + + def taylor_terms_per_coord(coord_function): + """Return the series for one of the coordinates.""" + return [param**i*iter_vfield(coord_function, i).rcall(start_point)/factorial(i) + for i in range(n)] + coord_sys = coord_sys if coord_sys else start_point._coord_sys + coord_functions = coord_sys.coord_functions() + taylor_terms = [taylor_terms_per_coord(f) for f in coord_functions] + if coeffs: + return [Matrix(t) for t in zip(*taylor_terms)] + else: + return Matrix([sum(c) for c in taylor_terms]) + + +def intcurve_diffequ(vector_field, param, start_point, coord_sys=None): + r"""Return the differential equation for an integral curve of the field. + + Explanation + =========== + + Integral curve is a function `\gamma` taking a parameter in `R` to a point + in the manifold. It verifies the equation: + + `V(f)\big(\gamma(t)\big) = \frac{d}{dt}f\big(\gamma(t)\big)` + + where the given ``vector_field`` is denoted as `V`. This holds for any + value `t` for the parameter and any scalar field `f`. + + This function returns the differential equation of `\gamma(t)` in terms of the + coordinate system ``coord_sys``. The equations and expansions are necessarily + done in coordinate-system-dependent way as there is no other way to + represent movement between points on the manifold (i.e. there is no such + thing as a difference of points for a general manifold). + + Parameters + ========== + + vector_field + the vector field for which an integral curve will be given + + param + the argument of the function `\gamma` from R to the curve + + start_point + the point which corresponds to `\gamma(0)` + + coord_sys + the coordinate system in which to give the equations + + Returns + ======= + + a tuple of (equations, initial conditions) + + Examples + ======== + + Use the predefined R2 manifold: + + >>> from sympy.abc import t + >>> from sympy.diffgeom.rn import R2, R2_p, R2_r + >>> from sympy.diffgeom import intcurve_diffequ + + Specify a starting point and a vector field: + + >>> start_point = R2_r.point([0, 1]) + >>> vector_field = -R2.y*R2.e_x + R2.x*R2.e_y + + Get the equation: + + >>> equations, init_cond = intcurve_diffequ(vector_field, t, start_point) + >>> equations + [f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)] + >>> init_cond + [f_0(0), f_1(0) - 1] + + The series in the polar coordinate system: + + >>> equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p) + >>> equations + [Derivative(f_0(t), t), Derivative(f_1(t), t) - 1] + >>> init_cond + [f_0(0) - 1, f_1(0) - pi/2] + + See Also + ======== + + intcurve_series + + """ + if contravariant_order(vector_field) != 1 or covariant_order(vector_field): + raise ValueError('The supplied field was not a vector field.') + coord_sys = coord_sys if coord_sys else start_point._coord_sys + gammas = [Function('f_%d' % i)(param) for i in range( + start_point._coord_sys.dim)] + arbitrary_p = Point(coord_sys, gammas) + coord_functions = coord_sys.coord_functions() + equations = [simplify(diff(cf.rcall(arbitrary_p), param) - vector_field.rcall(cf).rcall(arbitrary_p)) + for cf in coord_functions] + init_cond = [simplify(cf.rcall(arbitrary_p).subs(param, 0) - cf.rcall(start_point)) + for cf in coord_functions] + return equations, init_cond + + +############################################################################### +# Helpers +############################################################################### +def dummyfy(args, exprs): + # TODO Is this a good idea? + d_args = Matrix([s.as_dummy() for s in args]) + reps = dict(zip(args, d_args)) + d_exprs = Matrix([_sympify(expr).subs(reps) for expr in exprs]) + return d_args, d_exprs + +############################################################################### +# Helpers +############################################################################### +def contravariant_order(expr, _strict=False): + """Return the contravariant order of an expression. + + Examples + ======== + + >>> from sympy.diffgeom import contravariant_order + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.abc import a + + >>> contravariant_order(a) + 0 + >>> contravariant_order(a*R2.x + 2) + 0 + >>> contravariant_order(a*R2.x*R2.e_y + R2.e_x) + 1 + + """ + # TODO move some of this to class methods. + # TODO rewrite using the .as_blah_blah methods + if isinstance(expr, Add): + orders = [contravariant_order(e) for e in expr.args] + if len(set(orders)) != 1: + raise ValueError('Misformed expression containing contravariant fields of varying order.') + return orders[0] + elif isinstance(expr, Mul): + orders = [contravariant_order(e) for e in expr.args] + not_zero = [o for o in orders if o != 0] + if len(not_zero) > 1: + raise ValueError('Misformed expression containing multiplication between vectors.') + return 0 if not not_zero else not_zero[0] + elif isinstance(expr, Pow): + if covariant_order(expr.base) or covariant_order(expr.exp): + raise ValueError( + 'Misformed expression containing a power of a vector.') + return 0 + elif isinstance(expr, BaseVectorField): + return 1 + elif isinstance(expr, TensorProduct): + return sum(contravariant_order(a) for a in expr.args) + elif not _strict or expr.atoms(BaseScalarField): + return 0 + else: # If it does not contain anything related to the diffgeom module and it is _strict + return -1 + + +def covariant_order(expr, _strict=False): + """Return the covariant order of an expression. + + Examples + ======== + + >>> from sympy.diffgeom import covariant_order + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.abc import a + + >>> covariant_order(a) + 0 + >>> covariant_order(a*R2.x + 2) + 0 + >>> covariant_order(a*R2.x*R2.dy + R2.dx) + 1 + + """ + # TODO move some of this to class methods. + # TODO rewrite using the .as_blah_blah methods + if isinstance(expr, Add): + orders = [covariant_order(e) for e in expr.args] + if len(set(orders)) != 1: + raise ValueError('Misformed expression containing form fields of varying order.') + return orders[0] + elif isinstance(expr, Mul): + orders = [covariant_order(e) for e in expr.args] + not_zero = [o for o in orders if o != 0] + if len(not_zero) > 1: + raise ValueError('Misformed expression containing multiplication between forms.') + return 0 if not not_zero else not_zero[0] + elif isinstance(expr, Pow): + if covariant_order(expr.base) or covariant_order(expr.exp): + raise ValueError( + 'Misformed expression containing a power of a form.') + return 0 + elif isinstance(expr, Differential): + return covariant_order(*expr.args) + 1 + elif isinstance(expr, TensorProduct): + return sum(covariant_order(a) for a in expr.args) + elif not _strict or expr.atoms(BaseScalarField): + return 0 + else: # If it does not contain anything related to the diffgeom module and it is _strict + return -1 + + +############################################################################### +# Coordinate transformation functions +############################################################################### +def vectors_in_basis(expr, to_sys): + """Transform all base vectors in base vectors of a specified coord basis. + While the new base vectors are in the new coordinate system basis, any + coefficients are kept in the old system. + + Examples + ======== + + >>> from sympy.diffgeom import vectors_in_basis + >>> from sympy.diffgeom.rn import R2_r, R2_p + + >>> vectors_in_basis(R2_r.e_x, R2_p) + -y*e_theta/(x**2 + y**2) + x*e_rho/sqrt(x**2 + y**2) + >>> vectors_in_basis(R2_p.e_r, R2_r) + sin(theta)*e_y + cos(theta)*e_x + + """ + vectors = list(expr.atoms(BaseVectorField)) + new_vectors = [] + for v in vectors: + cs = v._coord_sys + jac = cs.jacobian(to_sys, cs.coord_functions()) + new = (jac.T*Matrix(to_sys.base_vectors()))[v._index] + new_vectors.append(new) + return expr.subs(list(zip(vectors, new_vectors))) + + +############################################################################### +# Coordinate-dependent functions +############################################################################### +def twoform_to_matrix(expr): + """Return the matrix representing the twoform. + + For the twoform `w` return the matrix `M` such that `M[i,j]=w(e_i, e_j)`, + where `e_i` is the i-th base vector field for the coordinate system in + which the expression of `w` is given. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.diffgeom import twoform_to_matrix, TensorProduct + >>> TP = TensorProduct + + >>> twoform_to_matrix(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + Matrix([ + [1, 0], + [0, 1]]) + >>> twoform_to_matrix(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + Matrix([ + [x, 0], + [0, 1]]) + >>> twoform_to_matrix(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy) - TP(R2.dx, R2.dy)/2) + Matrix([ + [ 1, 0], + [-1/2, 1]]) + + """ + if covariant_order(expr) != 2 or contravariant_order(expr): + raise ValueError('The input expression is not a two-form.') + coord_sys = _find_coords(expr) + if len(coord_sys) != 1: + raise ValueError('The input expression concerns more than one ' + 'coordinate systems, hence there is no unambiguous ' + 'way to choose a coordinate system for the matrix.') + coord_sys = coord_sys.pop() + vectors = coord_sys.base_vectors() + expr = expr.expand() + matrix_content = [[expr.rcall(v1, v2) for v1 in vectors] + for v2 in vectors] + return Matrix(matrix_content) + + +def metric_to_Christoffel_1st(expr): + """Return the nested list of Christoffel symbols for the given metric. + This returns the Christoffel symbol of first kind that represents the + Levi-Civita connection for the given metric. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.diffgeom import metric_to_Christoffel_1st, TensorProduct + >>> TP = TensorProduct + + >>> metric_to_Christoffel_1st(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[[0, 0], [0, 0]], [[0, 0], [0, 0]]] + >>> metric_to_Christoffel_1st(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[[1/2, 0], [0, 0]], [[0, 0], [0, 0]]] + + """ + matrix = twoform_to_matrix(expr) + if not matrix.is_symmetric(): + raise ValueError( + 'The two-form representing the metric is not symmetric.') + coord_sys = _find_coords(expr).pop() + deriv_matrices = [matrix.applyfunc(d) for d in coord_sys.base_vectors()] + indices = list(range(coord_sys.dim)) + christoffel = [[[(deriv_matrices[k][i, j] + deriv_matrices[j][i, k] - deriv_matrices[i][j, k])/2 + for k in indices] + for j in indices] + for i in indices] + return ImmutableDenseNDimArray(christoffel) + + +def metric_to_Christoffel_2nd(expr): + """Return the nested list of Christoffel symbols for the given metric. + This returns the Christoffel symbol of second kind that represents the + Levi-Civita connection for the given metric. + + Examples + ======== + + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.diffgeom import metric_to_Christoffel_2nd, TensorProduct + >>> TP = TensorProduct + + >>> metric_to_Christoffel_2nd(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[[0, 0], [0, 0]], [[0, 0], [0, 0]]] + >>> metric_to_Christoffel_2nd(R2.x*TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[[1/(2*x), 0], [0, 0]], [[0, 0], [0, 0]]] + + """ + ch_1st = metric_to_Christoffel_1st(expr) + coord_sys = _find_coords(expr).pop() + indices = list(range(coord_sys.dim)) + # XXX workaround, inverting a matrix does not work if it contains non + # symbols + #matrix = twoform_to_matrix(expr).inv() + matrix = twoform_to_matrix(expr) + s_fields = set() + for e in matrix: + s_fields.update(e.atoms(BaseScalarField)) + s_fields = list(s_fields) + dums = coord_sys.symbols + matrix = matrix.subs(list(zip(s_fields, dums))).inv().subs(list(zip(dums, s_fields))) + # XXX end of workaround + christoffel = [[[Add(*[matrix[i, l]*ch_1st[l, j, k] for l in indices]) + for k in indices] + for j in indices] + for i in indices] + return ImmutableDenseNDimArray(christoffel) + + +def metric_to_Riemann_components(expr): + """Return the components of the Riemann tensor expressed in a given basis. + + Given a metric it calculates the components of the Riemann tensor in the + canonical basis of the coordinate system in which the metric expression is + given. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.diffgeom import metric_to_Riemann_components, TensorProduct + >>> TP = TensorProduct + + >>> metric_to_Riemann_components(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[[[0, 0], [0, 0]], [[0, 0], [0, 0]]], [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]] + >>> non_trivial_metric = exp(2*R2.r)*TP(R2.dr, R2.dr) + \ + R2.r**2*TP(R2.dtheta, R2.dtheta) + >>> non_trivial_metric + exp(2*rho)*TensorProduct(drho, drho) + rho**2*TensorProduct(dtheta, dtheta) + >>> riemann = metric_to_Riemann_components(non_trivial_metric) + >>> riemann[0, :, :, :] + [[[0, 0], [0, 0]], [[0, exp(-2*rho)*rho], [-exp(-2*rho)*rho, 0]]] + >>> riemann[1, :, :, :] + [[[0, -1/rho], [1/rho, 0]], [[0, 0], [0, 0]]] + + """ + ch_2nd = metric_to_Christoffel_2nd(expr) + coord_sys = _find_coords(expr).pop() + indices = list(range(coord_sys.dim)) + deriv_ch = [[[[d(ch_2nd[i, j, k]) + for d in coord_sys.base_vectors()] + for k in indices] + for j in indices] + for i in indices] + riemann_a = [[[[deriv_ch[rho][sig][nu][mu] - deriv_ch[rho][sig][mu][nu] + for nu in indices] + for mu in indices] + for sig in indices] + for rho in indices] + riemann_b = [[[[Add(*[ch_2nd[rho, l, mu]*ch_2nd[l, sig, nu] - ch_2nd[rho, l, nu]*ch_2nd[l, sig, mu] for l in indices]) + for nu in indices] + for mu in indices] + for sig in indices] + for rho in indices] + riemann = [[[[riemann_a[rho][sig][mu][nu] + riemann_b[rho][sig][mu][nu] + for nu in indices] + for mu in indices] + for sig in indices] + for rho in indices] + return ImmutableDenseNDimArray(riemann) + + +def metric_to_Ricci_components(expr): + + """Return the components of the Ricci tensor expressed in a given basis. + + Given a metric it calculates the components of the Ricci tensor in the + canonical basis of the coordinate system in which the metric expression is + given. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.diffgeom.rn import R2 + >>> from sympy.diffgeom import metric_to_Ricci_components, TensorProduct + >>> TP = TensorProduct + + >>> metric_to_Ricci_components(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + [[0, 0], [0, 0]] + >>> non_trivial_metric = exp(2*R2.r)*TP(R2.dr, R2.dr) + \ + R2.r**2*TP(R2.dtheta, R2.dtheta) + >>> non_trivial_metric + exp(2*rho)*TensorProduct(drho, drho) + rho**2*TensorProduct(dtheta, dtheta) + >>> metric_to_Ricci_components(non_trivial_metric) + [[1/rho, 0], [0, exp(-2*rho)*rho]] + + """ + riemann = metric_to_Riemann_components(expr) + coord_sys = _find_coords(expr).pop() + indices = list(range(coord_sys.dim)) + ricci = [[Add(*[riemann[k, i, k, j] for k in indices]) + for j in indices] + for i in indices] + return ImmutableDenseNDimArray(ricci) + +############################################################################### +# Classes for deprecation +############################################################################### + +class _deprecated_container: + # This class gives deprecation warning. + # When deprecated features are completely deleted, this should be removed as well. + # See https://github.com/sympy/sympy/pull/19368 + def __init__(self, message, data): + super().__init__(data) + self.message = message + + def warn(self): + sympy_deprecation_warning( + self.message, + deprecated_since_version="1.7", + active_deprecations_target="deprecated-diffgeom-mutable", + stacklevel=4 + ) + + def __iter__(self): + self.warn() + return super().__iter__() + + def __getitem__(self, key): + self.warn() + return super().__getitem__(key) + + def __contains__(self, key): + self.warn() + return super().__contains__(key) + + +class _deprecated_list(_deprecated_container, list): + pass + + +class _deprecated_dict(_deprecated_container, dict): + pass + + +# Import at end to avoid cyclic imports +from sympy.simplify.simplify import simplify diff --git a/lib/python3.11/site-packages/sympy/diffgeom/rn.py b/lib/python3.11/site-packages/sympy/diffgeom/rn.py new file mode 100644 index 0000000000000000000000000000000000000000..897c7e82bc804d260612f79c820af92632f3b281 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/rn.py @@ -0,0 +1,143 @@ +"""Predefined R^n manifolds together with common coord. systems. + +Coordinate systems are predefined as well as the transformation laws between +them. + +Coordinate functions can be accessed as attributes of the manifold (eg `R2.x`), +as attributes of the coordinate systems (eg `R2_r.x` and `R2_p.theta`), or by +using the usual `coord_sys.coord_function(index, name)` interface. +""" + +from typing import Any +import warnings + +from sympy.core.symbol import (Dummy, symbols) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, atan2, cos, sin) +from .diffgeom import Manifold, Patch, CoordSystem + +__all__ = [ + 'R2', 'R2_origin', 'relations_2d', 'R2_r', 'R2_p', + 'R3', 'R3_origin', 'relations_3d', 'R3_r', 'R3_c', 'R3_s' +] + +############################################################################### +# R2 +############################################################################### +R2: Any = Manifold('R^2', 2) + +R2_origin: Any = Patch('origin', R2) + +x, y = symbols('x y', real=True) +r, theta = symbols('rho theta', nonnegative=True) + +relations_2d = { + ('rectangular', 'polar'): [(x, y), (sqrt(x**2 + y**2), atan2(y, x))], + ('polar', 'rectangular'): [(r, theta), (r*cos(theta), r*sin(theta))], +} + +R2_r: Any = CoordSystem('rectangular', R2_origin, (x, y), relations_2d) +R2_p: Any = CoordSystem('polar', R2_origin, (r, theta), relations_2d) + +# support deprecated feature +with warnings.catch_warnings(): + warnings.simplefilter("ignore") + x, y, r, theta = symbols('x y r theta', cls=Dummy) + R2_r.connect_to(R2_p, [x, y], + [sqrt(x**2 + y**2), atan2(y, x)], + inverse=False, fill_in_gaps=False) + R2_p.connect_to(R2_r, [r, theta], + [r*cos(theta), r*sin(theta)], + inverse=False, fill_in_gaps=False) + +# Defining the basis coordinate functions and adding shortcuts for them to the +# manifold and the patch. +R2.x, R2.y = R2_origin.x, R2_origin.y = R2_r.x, R2_r.y = R2_r.coord_functions() +R2.r, R2.theta = R2_origin.r, R2_origin.theta = R2_p.r, R2_p.theta = R2_p.coord_functions() + +# Defining the basis vector fields and adding shortcuts for them to the +# manifold and the patch. +R2.e_x, R2.e_y = R2_origin.e_x, R2_origin.e_y = R2_r.e_x, R2_r.e_y = R2_r.base_vectors() +R2.e_r, R2.e_theta = R2_origin.e_r, R2_origin.e_theta = R2_p.e_r, R2_p.e_theta = R2_p.base_vectors() + +# Defining the basis oneform fields and adding shortcuts for them to the +# manifold and the patch. +R2.dx, R2.dy = R2_origin.dx, R2_origin.dy = R2_r.dx, R2_r.dy = R2_r.base_oneforms() +R2.dr, R2.dtheta = R2_origin.dr, R2_origin.dtheta = R2_p.dr, R2_p.dtheta = R2_p.base_oneforms() + +############################################################################### +# R3 +############################################################################### +R3: Any = Manifold('R^3', 3) + +R3_origin: Any = Patch('origin', R3) + +x, y, z = symbols('x y z', real=True) +rho, psi, r, theta, phi = symbols('rho psi r theta phi', nonnegative=True) + +relations_3d = { + ('rectangular', 'cylindrical'): [(x, y, z), + (sqrt(x**2 + y**2), atan2(y, x), z)], + ('cylindrical', 'rectangular'): [(rho, psi, z), + (rho*cos(psi), rho*sin(psi), z)], + ('rectangular', 'spherical'): [(x, y, z), + (sqrt(x**2 + y**2 + z**2), + acos(z/sqrt(x**2 + y**2 + z**2)), + atan2(y, x))], + ('spherical', 'rectangular'): [(r, theta, phi), + (r*sin(theta)*cos(phi), + r*sin(theta)*sin(phi), + r*cos(theta))], + ('cylindrical', 'spherical'): [(rho, psi, z), + (sqrt(rho**2 + z**2), + acos(z/sqrt(rho**2 + z**2)), + psi)], + ('spherical', 'cylindrical'): [(r, theta, phi), + (r*sin(theta), phi, r*cos(theta))], +} + +R3_r: Any = CoordSystem('rectangular', R3_origin, (x, y, z), relations_3d) +R3_c: Any = CoordSystem('cylindrical', R3_origin, (rho, psi, z), relations_3d) +R3_s: Any = CoordSystem('spherical', R3_origin, (r, theta, phi), relations_3d) + +# support deprecated feature +with warnings.catch_warnings(): + warnings.simplefilter("ignore") + x, y, z, rho, psi, r, theta, phi = symbols('x y z rho psi r theta phi', cls=Dummy) + R3_r.connect_to(R3_c, [x, y, z], + [sqrt(x**2 + y**2), atan2(y, x), z], + inverse=False, fill_in_gaps=False) + R3_c.connect_to(R3_r, [rho, psi, z], + [rho*cos(psi), rho*sin(psi), z], + inverse=False, fill_in_gaps=False) + ## rectangular <-> spherical + R3_r.connect_to(R3_s, [x, y, z], + [sqrt(x**2 + y**2 + z**2), acos(z/ + sqrt(x**2 + y**2 + z**2)), atan2(y, x)], + inverse=False, fill_in_gaps=False) + R3_s.connect_to(R3_r, [r, theta, phi], + [r*sin(theta)*cos(phi), r*sin( + theta)*sin(phi), r*cos(theta)], + inverse=False, fill_in_gaps=False) + ## cylindrical <-> spherical + R3_c.connect_to(R3_s, [rho, psi, z], + [sqrt(rho**2 + z**2), acos(z/sqrt(rho**2 + z**2)), psi], + inverse=False, fill_in_gaps=False) + R3_s.connect_to(R3_c, [r, theta, phi], + [r*sin(theta), phi, r*cos(theta)], + inverse=False, fill_in_gaps=False) + +# Defining the basis coordinate functions. +R3_r.x, R3_r.y, R3_r.z = R3_r.coord_functions() +R3_c.rho, R3_c.psi, R3_c.z = R3_c.coord_functions() +R3_s.r, R3_s.theta, R3_s.phi = R3_s.coord_functions() + +# Defining the basis vector fields. +R3_r.e_x, R3_r.e_y, R3_r.e_z = R3_r.base_vectors() +R3_c.e_rho, R3_c.e_psi, R3_c.e_z = R3_c.base_vectors() +R3_s.e_r, R3_s.e_theta, R3_s.e_phi = R3_s.base_vectors() + +# Defining the basis oneform fields. +R3_r.dx, R3_r.dy, R3_r.dz = R3_r.base_oneforms() +R3_c.drho, R3_c.dpsi, R3_c.dz = R3_c.base_oneforms() +R3_s.dr, R3_s.dtheta, R3_s.dphi = R3_s.base_oneforms() diff --git a/lib/python3.11/site-packages/sympy/diffgeom/tests/__init__.py b/lib/python3.11/site-packages/sympy/diffgeom/tests/__init__.py new file mode 100644 index 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a/lib/python3.11/site-packages/sympy/diffgeom/tests/__pycache__/test_hyperbolic_space.cpython-311.pyc b/lib/python3.11/site-packages/sympy/diffgeom/tests/__pycache__/test_hyperbolic_space.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f5070e0c6e6447ce711601ea9f66c689a96410ee Binary files /dev/null and b/lib/python3.11/site-packages/sympy/diffgeom/tests/__pycache__/test_hyperbolic_space.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/diffgeom/tests/test_class_structure.py b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_class_structure.py new file mode 100644 index 0000000000000000000000000000000000000000..c649fd9fcb9acdf1f410a021966c6e0fee62cc2b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_class_structure.py @@ -0,0 +1,33 @@ +from sympy.diffgeom import Manifold, Patch, CoordSystem, Point +from sympy.core.function import Function +from sympy.core.symbol import symbols +from sympy.testing.pytest import warns_deprecated_sympy + +m = Manifold('m', 2) +p = Patch('p', m) +a, b = symbols('a b') +cs = CoordSystem('cs', p, [a, b]) +x, y = symbols('x y') +f = Function('f') +s1, s2 = cs.coord_functions() +v1, v2 = cs.base_vectors() +f1, f2 = cs.base_oneforms() + +def test_point(): + point = Point(cs, [x, y]) + assert point != Point(cs, [2, y]) + #TODO assert point.subs(x, 2) == Point(cs, [2, y]) + #TODO assert point.free_symbols == set([x, y]) + +def test_subs(): + assert s1.subs(s1, s2) == s2 + assert v1.subs(v1, v2) == v2 + assert f1.subs(f1, f2) == f2 + assert (x*f(s1) + y).subs(s1, s2) == x*f(s2) + y + assert (f(s1)*v1).subs(v1, v2) == f(s1)*v2 + assert (y*f(s1)*f1).subs(f1, f2) == y*f(s1)*f2 + +def test_deprecated(): + with warns_deprecated_sympy(): + cs_wname = CoordSystem('cs', p, ['a', 'b']) + assert cs_wname == cs_wname.func(*cs_wname.args) diff --git a/lib/python3.11/site-packages/sympy/diffgeom/tests/test_diffgeom.py b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_diffgeom.py new file mode 100644 index 0000000000000000000000000000000000000000..7c3c9265785896b8f4ffa3a2b41816ca90579758 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_diffgeom.py @@ -0,0 +1,342 @@ +from sympy.core import Lambda, Symbol, symbols +from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r, R3_c, R3_s, R2_origin +from sympy.diffgeom import (Manifold, Patch, CoordSystem, Commutator, Differential, TensorProduct, + WedgeProduct, BaseCovarDerivativeOp, CovarDerivativeOp, LieDerivative, + covariant_order, contravariant_order, twoform_to_matrix, metric_to_Christoffel_1st, + metric_to_Christoffel_2nd, metric_to_Riemann_components, + metric_to_Ricci_components, intcurve_diffequ, intcurve_series) +from sympy.simplify import trigsimp, simplify +from sympy.functions import sqrt, atan2, sin +from sympy.matrices import Matrix +from sympy.testing.pytest import raises, nocache_fail +from sympy.testing.pytest import warns_deprecated_sympy + +TP = TensorProduct + + +def test_coordsys_transform(): + # test inverse transforms + p, q, r, s = symbols('p q r s') + rel = {('first', 'second'): [(p, q), (q, -p)]} + R2_pq = CoordSystem('first', R2_origin, [p, q], rel) + R2_rs = CoordSystem('second', R2_origin, [r, s], rel) + r, s = R2_rs.symbols + assert R2_rs.transform(R2_pq) == Matrix([[-s], [r]]) + + # inverse transform impossible case + a, b = symbols('a b', positive=True) + rel = {('first', 'second'): [(a,), (-a,)]} + R2_a = CoordSystem('first', R2_origin, [a], rel) + R2_b = CoordSystem('second', R2_origin, [b], rel) + # This transformation is uninvertible because there is no positive a, b satisfying a = -b + with raises(NotImplementedError): + R2_b.transform(R2_a) + + # inverse transform ambiguous case + c, d = symbols('c d') + rel = {('first', 'second'): [(c,), (c**2,)]} + R2_c = CoordSystem('first', R2_origin, [c], rel) + R2_d = CoordSystem('second', R2_origin, [d], rel) + # The transform method should throw if it finds multiple inverses for a coordinate transformation. + with raises(ValueError): + R2_d.transform(R2_c) + + # test indirect transformation + a, b, c, d, e, f = symbols('a, b, c, d, e, f') + rel = {('C1', 'C2'): [(a, b), (2*a, 3*b)], + ('C2', 'C3'): [(c, d), (3*c, 2*d)]} + C1 = CoordSystem('C1', R2_origin, (a, b), rel) + C2 = CoordSystem('C2', R2_origin, (c, d), rel) + C3 = CoordSystem('C3', R2_origin, (e, f), rel) + a, b = C1.symbols + c, d = C2.symbols + e, f = C3.symbols + assert C2.transform(C1) == Matrix([c/2, d/3]) + assert C1.transform(C3) == Matrix([6*a, 6*b]) + assert C3.transform(C1) == Matrix([e/6, f/6]) + assert C3.transform(C2) == Matrix([e/3, f/2]) + + a, b, c, d, e, f = symbols('a, b, c, d, e, f') + rel = {('C1', 'C2'): [(a, b), (2*a, 3*b + 1)], + ('C3', 'C2'): [(e, f), (-e - 2, 2*f)]} + C1 = CoordSystem('C1', R2_origin, (a, b), rel) + C2 = CoordSystem('C2', R2_origin, (c, d), rel) + C3 = CoordSystem('C3', R2_origin, (e, f), rel) + a, b = C1.symbols + c, d = C2.symbols + e, f = C3.symbols + assert C2.transform(C1) == Matrix([c/2, (d - 1)/3]) + assert C1.transform(C3) == Matrix([-2*a - 2, (3*b + 1)/2]) + assert C3.transform(C1) == Matrix([-e/2 - 1, (2*f - 1)/3]) + assert C3.transform(C2) == Matrix([-e - 2, 2*f]) + + # old signature uses Lambda + a, b, c, d, e, f = symbols('a, b, c, d, e, f') + rel = {('C1', 'C2'): Lambda((a, b), (2*a, 3*b + 1)), + ('C3', 'C2'): Lambda((e, f), (-e - 2, 2*f))} + C1 = CoordSystem('C1', R2_origin, (a, b), rel) + C2 = CoordSystem('C2', R2_origin, (c, d), rel) + C3 = CoordSystem('C3', R2_origin, (e, f), rel) + a, b = C1.symbols + c, d = C2.symbols + e, f = C3.symbols + assert C2.transform(C1) == Matrix([c/2, (d - 1)/3]) + assert C1.transform(C3) == Matrix([-2*a - 2, (3*b + 1)/2]) + assert C3.transform(C1) == Matrix([-e/2 - 1, (2*f - 1)/3]) + assert C3.transform(C2) == Matrix([-e - 2, 2*f]) + + +def test_R2(): + x0, y0, r0, theta0 = symbols('x0, y0, r0, theta0', real=True) + point_r = R2_r.point([x0, y0]) + point_p = R2_p.point([r0, theta0]) + + # r**2 = x**2 + y**2 + assert (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_r) == 0 + assert trigsimp( (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_p) ) == 0 + assert trigsimp(R2.e_r(R2.x**2 + R2.y**2).rcall(point_p).doit()) == 2*r0 + + # polar->rect->polar == Id + a, b = symbols('a b', positive=True) + m = Matrix([[a], [b]]) + + #TODO assert m == R2_r.transform(R2_p, R2_p.transform(R2_r, [a, b])).applyfunc(simplify) + assert m == R2_p.transform(R2_r, R2_r.transform(R2_p, m)).applyfunc(simplify) + + # deprecated method + with warns_deprecated_sympy(): + assert m == R2_p.coord_tuple_transform_to( + R2_r, R2_r.coord_tuple_transform_to(R2_p, m)).applyfunc(simplify) + + +def test_R3(): + a, b, c = symbols('a b c', positive=True) + m = Matrix([[a], [b], [c]]) + + assert m == R3_c.transform(R3_r, R3_r.transform(R3_c, m)).applyfunc(simplify) + #TODO assert m == R3_r.transform(R3_c, R3_c.transform(R3_r, m)).applyfunc(simplify) + assert m == R3_s.transform( + R3_r, R3_r.transform(R3_s, m)).applyfunc(simplify) + #TODO assert m == R3_r.transform(R3_s, R3_s.transform(R3_r, m)).applyfunc(simplify) + assert m == R3_s.transform( + R3_c, R3_c.transform(R3_s, m)).applyfunc(simplify) + #TODO assert m == R3_c.transform(R3_s, R3_s.transform(R3_c, m)).applyfunc(simplify) + + with warns_deprecated_sympy(): + assert m == R3_c.coord_tuple_transform_to( + R3_r, R3_r.coord_tuple_transform_to(R3_c, m)).applyfunc(simplify) + #TODO assert m == R3_r.coord_tuple_transform_to(R3_c, R3_c.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify) + assert m == R3_s.coord_tuple_transform_to( + R3_r, R3_r.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify) + #TODO assert m == R3_r.coord_tuple_transform_to(R3_s, R3_s.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify) + assert m == R3_s.coord_tuple_transform_to( + R3_c, R3_c.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify) + #TODO assert m == R3_c.coord_tuple_transform_to(R3_s, R3_s.coord_tuple_transform_to(R3_c, m)).applyfunc(simplify) + + +def test_CoordinateSymbol(): + x, y = R2_r.symbols + r, theta = R2_p.symbols + assert y.rewrite(R2_p) == r*sin(theta) + + +def test_point(): + x, y = symbols('x, y') + p = R2_r.point([x, y]) + assert p.free_symbols == {x, y} + assert p.coords(R2_r) == p.coords() == Matrix([x, y]) + assert p.coords(R2_p) == Matrix([sqrt(x**2 + y**2), atan2(y, x)]) + + +def test_commutator(): + assert Commutator(R2.e_x, R2.e_y) == 0 + assert Commutator(R2.x*R2.e_x, R2.x*R2.e_x) == 0 + assert Commutator(R2.x*R2.e_x, R2.x*R2.e_y) == R2.x*R2.e_y + c = Commutator(R2.e_x, R2.e_r) + assert c(R2.x) == R2.y*(R2.x**2 + R2.y**2)**(-1)*sin(R2.theta) + + +def test_differential(): + xdy = R2.x*R2.dy + dxdy = Differential(xdy) + assert xdy.rcall(None) == xdy + assert dxdy(R2.e_x, R2.e_y) == 1 + assert dxdy(R2.e_x, R2.x*R2.e_y) == R2.x + assert Differential(dxdy) == 0 + + +def test_products(): + assert TensorProduct( + R2.dx, R2.dy)(R2.e_x, R2.e_y) == R2.dx(R2.e_x)*R2.dy(R2.e_y) == 1 + assert TensorProduct(R2.dx, R2.dy)(None, R2.e_y) == R2.dx + assert TensorProduct(R2.dx, R2.dy)(R2.e_x, None) == R2.dy + assert TensorProduct(R2.dx, R2.dy)(R2.e_x) == R2.dy + assert TensorProduct(R2.x, R2.dx) == R2.x*R2.dx + assert TensorProduct( + R2.e_x, R2.e_y)(R2.x, R2.y) == R2.e_x(R2.x) * R2.e_y(R2.y) == 1 + assert TensorProduct(R2.e_x, R2.e_y)(None, R2.y) == R2.e_x + assert TensorProduct(R2.e_x, R2.e_y)(R2.x, None) == R2.e_y + assert TensorProduct(R2.e_x, R2.e_y)(R2.x) == R2.e_y + assert TensorProduct(R2.x, R2.e_x) == R2.x * R2.e_x + assert TensorProduct( + R2.dx, R2.e_y)(R2.e_x, R2.y) == R2.dx(R2.e_x) * R2.e_y(R2.y) == 1 + assert TensorProduct(R2.dx, R2.e_y)(None, R2.y) == R2.dx + assert TensorProduct(R2.dx, R2.e_y)(R2.e_x, None) == R2.e_y + assert TensorProduct(R2.dx, R2.e_y)(R2.e_x) == R2.e_y + assert TensorProduct(R2.x, R2.e_x) == R2.x * R2.e_x + assert TensorProduct( + R2.e_x, R2.dy)(R2.x, R2.e_y) == R2.e_x(R2.x) * R2.dy(R2.e_y) == 1 + assert TensorProduct(R2.e_x, R2.dy)(None, R2.e_y) == R2.e_x + assert TensorProduct(R2.e_x, R2.dy)(R2.x, None) == R2.dy + assert TensorProduct(R2.e_x, R2.dy)(R2.x) == R2.dy + assert TensorProduct(R2.e_y,R2.e_x)(R2.x**2 + R2.y**2,R2.x**2 + R2.y**2) == 4*R2.x*R2.y + + assert WedgeProduct(R2.dx, R2.dy)(R2.e_x, R2.e_y) == 1 + assert WedgeProduct(R2.e_x, R2.e_y)(R2.x, R2.y) == 1 + + +def test_lie_derivative(): + assert LieDerivative(R2.e_x, R2.y) == R2.e_x(R2.y) == 0 + assert LieDerivative(R2.e_x, R2.x) == R2.e_x(R2.x) == 1 + assert LieDerivative(R2.e_x, R2.e_x) == Commutator(R2.e_x, R2.e_x) == 0 + assert LieDerivative(R2.e_x, R2.e_r) == Commutator(R2.e_x, R2.e_r) + assert LieDerivative(R2.e_x + R2.e_y, R2.x) == 1 + assert LieDerivative( + R2.e_x, TensorProduct(R2.dx, R2.dy))(R2.e_x, R2.e_y) == 0 + + +@nocache_fail +def test_covar_deriv(): + ch = metric_to_Christoffel_2nd(TP(R2.dx, R2.dx) + TP(R2.dy, R2.dy)) + cvd = BaseCovarDerivativeOp(R2_r, 0, ch) + assert cvd(R2.x) == 1 + # This line fails if the cache is disabled: + assert cvd(R2.x*R2.e_x) == R2.e_x + cvd = CovarDerivativeOp(R2.x*R2.e_x, ch) + assert cvd(R2.x) == R2.x + assert cvd(R2.x*R2.e_x) == R2.x*R2.e_x + + +def test_intcurve_diffequ(): + t = symbols('t') + start_point = R2_r.point([1, 0]) + vector_field = -R2.y*R2.e_x + R2.x*R2.e_y + equations, init_cond = intcurve_diffequ(vector_field, t, start_point) + assert str(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]' + assert str(init_cond) == '[f_0(0) - 1, f_1(0)]' + equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p) + assert str( + equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]' + assert str(init_cond) == '[f_0(0) - 1, f_1(0)]' + + +def test_helpers_and_coordinate_dependent(): + one_form = R2.dr + R2.dx + two_form = Differential(R2.x*R2.dr + R2.r*R2.dx) + three_form = Differential( + R2.y*two_form) + Differential(R2.x*Differential(R2.r*R2.dr)) + metric = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dy, R2.dy) + metric_ambig = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dr, R2.dr) + misform_a = TensorProduct(R2.dr, R2.dr) + R2.dr + misform_b = R2.dr**4 + misform_c = R2.dx*R2.dy + twoform_not_sym = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dx, R2.dy) + twoform_not_TP = WedgeProduct(R2.dx, R2.dy) + + one_vector = R2.e_x + R2.e_y + two_vector = TensorProduct(R2.e_x, R2.e_y) + three_vector = TensorProduct(R2.e_x, R2.e_y, R2.e_x) + two_wp = WedgeProduct(R2.e_x,R2.e_y) + + assert covariant_order(one_form) == 1 + assert covariant_order(two_form) == 2 + assert covariant_order(three_form) == 3 + assert covariant_order(two_form + metric) == 2 + assert covariant_order(two_form + metric_ambig) == 2 + assert covariant_order(two_form + twoform_not_sym) == 2 + assert covariant_order(two_form + twoform_not_TP) == 2 + + assert contravariant_order(one_vector) == 1 + assert contravariant_order(two_vector) == 2 + assert contravariant_order(three_vector) == 3 + assert contravariant_order(two_vector + two_wp) == 2 + + raises(ValueError, lambda: covariant_order(misform_a)) + raises(ValueError, lambda: covariant_order(misform_b)) + raises(ValueError, lambda: covariant_order(misform_c)) + + assert twoform_to_matrix(metric) == Matrix([[1, 0], [0, 1]]) + assert twoform_to_matrix(twoform_not_sym) == Matrix([[1, 0], [1, 0]]) + assert twoform_to_matrix(twoform_not_TP) == Matrix([[0, -1], [1, 0]]) + + raises(ValueError, lambda: twoform_to_matrix(one_form)) + raises(ValueError, lambda: twoform_to_matrix(three_form)) + raises(ValueError, lambda: twoform_to_matrix(metric_ambig)) + + raises(ValueError, lambda: metric_to_Christoffel_1st(twoform_not_sym)) + raises(ValueError, lambda: metric_to_Christoffel_2nd(twoform_not_sym)) + raises(ValueError, lambda: metric_to_Riemann_components(twoform_not_sym)) + raises(ValueError, lambda: metric_to_Ricci_components(twoform_not_sym)) + + +def test_correct_arguments(): + raises(ValueError, lambda: R2.e_x(R2.e_x)) + raises(ValueError, lambda: R2.e_x(R2.dx)) + + raises(ValueError, lambda: Commutator(R2.e_x, R2.x)) + raises(ValueError, lambda: Commutator(R2.dx, R2.e_x)) + + raises(ValueError, lambda: Differential(Differential(R2.e_x))) + + raises(ValueError, lambda: R2.dx(R2.x)) + + raises(ValueError, lambda: LieDerivative(R2.dx, R2.dx)) + raises(ValueError, lambda: LieDerivative(R2.x, R2.dx)) + + raises(ValueError, lambda: CovarDerivativeOp(R2.dx, [])) + raises(ValueError, lambda: CovarDerivativeOp(R2.x, [])) + + a = Symbol('a') + raises(ValueError, lambda: intcurve_series(R2.dx, a, R2_r.point([1, 2]))) + raises(ValueError, lambda: intcurve_series(R2.x, a, R2_r.point([1, 2]))) + + raises(ValueError, lambda: intcurve_diffequ(R2.dx, a, R2_r.point([1, 2]))) + raises(ValueError, lambda: intcurve_diffequ(R2.x, a, R2_r.point([1, 2]))) + + raises(ValueError, lambda: contravariant_order(R2.e_x + R2.dx)) + raises(ValueError, lambda: covariant_order(R2.e_x + R2.dx)) + + raises(ValueError, lambda: contravariant_order(R2.e_x*R2.e_y)) + raises(ValueError, lambda: covariant_order(R2.dx*R2.dy)) + +def test_simplify(): + x, y = R2_r.coord_functions() + dx, dy = R2_r.base_oneforms() + ex, ey = R2_r.base_vectors() + assert simplify(x) == x + assert simplify(x*y) == x*y + assert simplify(dx*dy) == dx*dy + assert simplify(ex*ey) == ex*ey + assert ((1-x)*dx)/(1-x)**2 == dx/(1-x) + + +def test_issue_17917(): + X = R2.x*R2.e_x - R2.y*R2.e_y + Y = (R2.x**2 + R2.y**2)*R2.e_x - R2.x*R2.y*R2.e_y + assert LieDerivative(X, Y).expand() == ( + R2.x**2*R2.e_x - 3*R2.y**2*R2.e_x - R2.x*R2.y*R2.e_y) + +def test_deprecations(): + m = Manifold('M', 2) + p = Patch('P', m) + with warns_deprecated_sympy(): + CoordSystem('Car2d', p, names=['x', 'y']) + + with warns_deprecated_sympy(): + c = CoordSystem('Car2d', p, ['x', 'y']) + + with warns_deprecated_sympy(): + list(m.patches) + + with warns_deprecated_sympy(): + list(c.transforms) diff --git a/lib/python3.11/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py new file mode 100644 index 0000000000000000000000000000000000000000..44d9623bc34ab73c7d575d9d9fd5b6d84f8e4a94 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_function_diffgeom_book.py @@ -0,0 +1,145 @@ +from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r +from sympy.diffgeom import intcurve_series, Differential, WedgeProduct +from sympy.core import symbols, Function, Derivative +from sympy.simplify import trigsimp, simplify +from sympy.functions import sqrt, atan2, sin, cos +from sympy.matrices import Matrix + +# Most of the functionality is covered in the +# test_functional_diffgeom_ch* tests which are based on the +# example from the paper of Sussman and Wisdom. +# If they do not cover something, additional tests are added in other test +# functions. + +# From "Functional Differential Geometry" as of 2011 +# by Sussman and Wisdom. + + +def test_functional_diffgeom_ch2(): + x0, y0, r0, theta0 = symbols('x0, y0, r0, theta0', real=True) + x, y = symbols('x, y', real=True) + f = Function('f') + + assert (R2_p.point_to_coords(R2_r.point([x0, y0])) == + Matrix([sqrt(x0**2 + y0**2), atan2(y0, x0)])) + assert (R2_r.point_to_coords(R2_p.point([r0, theta0])) == + Matrix([r0*cos(theta0), r0*sin(theta0)])) + + assert R2_p.jacobian(R2_r, [r0, theta0]) == Matrix( + [[cos(theta0), -r0*sin(theta0)], [sin(theta0), r0*cos(theta0)]]) + + field = f(R2.x, R2.y) + p1_in_rect = R2_r.point([x0, y0]) + p1_in_polar = R2_p.point([sqrt(x0**2 + y0**2), atan2(y0, x0)]) + assert field.rcall(p1_in_rect) == f(x0, y0) + assert field.rcall(p1_in_polar) == f(x0, y0) + + p_r = R2_r.point([x0, y0]) + p_p = R2_p.point([r0, theta0]) + assert R2.x(p_r) == x0 + assert R2.x(p_p) == r0*cos(theta0) + assert R2.r(p_p) == r0 + assert R2.r(p_r) == sqrt(x0**2 + y0**2) + assert R2.theta(p_r) == atan2(y0, x0) + + h = R2.x*R2.r**2 + R2.y**3 + assert h.rcall(p_r) == x0*(x0**2 + y0**2) + y0**3 + assert h.rcall(p_p) == r0**3*sin(theta0)**3 + r0**3*cos(theta0) + + +def test_functional_diffgeom_ch3(): + x0, y0 = symbols('x0, y0', real=True) + x, y, t = symbols('x, y, t', real=True) + f = Function('f') + b1 = Function('b1') + b2 = Function('b2') + p_r = R2_r.point([x0, y0]) + + s_field = f(R2.x, R2.y) + v_field = b1(R2.x)*R2.e_x + b2(R2.y)*R2.e_y + assert v_field.rcall(s_field).rcall(p_r).doit() == b1( + x0)*Derivative(f(x0, y0), x0) + b2(y0)*Derivative(f(x0, y0), y0) + + assert R2.e_x(R2.r**2).rcall(p_r) == 2*x0 + v = R2.e_x + 2*R2.e_y + s = R2.r**2 + 3*R2.x + assert v.rcall(s).rcall(p_r).doit() == 2*x0 + 4*y0 + 3 + + circ = -R2.y*R2.e_x + R2.x*R2.e_y + series = intcurve_series(circ, t, R2_r.point([1, 0]), coeffs=True) + series_x, series_y = zip(*series) + assert all( + term == cos(t).taylor_term(i, t) for i, term in enumerate(series_x)) + assert all( + term == sin(t).taylor_term(i, t) for i, term in enumerate(series_y)) + + +def test_functional_diffgeom_ch4(): + x0, y0, theta0 = symbols('x0, y0, theta0', real=True) + x, y, r, theta = symbols('x, y, r, theta', real=True) + r0 = symbols('r0', positive=True) + f = Function('f') + b1 = Function('b1') + b2 = Function('b2') + p_r = R2_r.point([x0, y0]) + p_p = R2_p.point([r0, theta0]) + + f_field = b1(R2.x, R2.y)*R2.dx + b2(R2.x, R2.y)*R2.dy + assert f_field.rcall(R2.e_x).rcall(p_r) == b1(x0, y0) + assert f_field.rcall(R2.e_y).rcall(p_r) == b2(x0, y0) + + s_field_r = f(R2.x, R2.y) + df = Differential(s_field_r) + assert df(R2.e_x).rcall(p_r).doit() == Derivative(f(x0, y0), x0) + assert df(R2.e_y).rcall(p_r).doit() == Derivative(f(x0, y0), y0) + + s_field_p = f(R2.r, R2.theta) + df = Differential(s_field_p) + assert trigsimp(df(R2.e_x).rcall(p_p).doit()) == ( + cos(theta0)*Derivative(f(r0, theta0), r0) - + sin(theta0)*Derivative(f(r0, theta0), theta0)/r0) + assert trigsimp(df(R2.e_y).rcall(p_p).doit()) == ( + sin(theta0)*Derivative(f(r0, theta0), r0) + + cos(theta0)*Derivative(f(r0, theta0), theta0)/r0) + + assert R2.dx(R2.e_x).rcall(p_r) == 1 + assert R2.dx(R2.e_x) == 1 + assert R2.dx(R2.e_y).rcall(p_r) == 0 + assert R2.dx(R2.e_y) == 0 + + circ = -R2.y*R2.e_x + R2.x*R2.e_y + assert R2.dx(circ).rcall(p_r).doit() == -y0 + assert R2.dy(circ).rcall(p_r) == x0 + assert R2.dr(circ).rcall(p_r) == 0 + assert simplify(R2.dtheta(circ).rcall(p_r)) == 1 + + assert (circ - R2.e_theta).rcall(s_field_r).rcall(p_r) == 0 + + +def test_functional_diffgeom_ch6(): + u0, u1, u2, v0, v1, v2, w0, w1, w2 = symbols('u0:3, v0:3, w0:3', real=True) + + u = u0*R2.e_x + u1*R2.e_y + v = v0*R2.e_x + v1*R2.e_y + wp = WedgeProduct(R2.dx, R2.dy) + assert wp(u, v) == u0*v1 - u1*v0 + + u = u0*R3_r.e_x + u1*R3_r.e_y + u2*R3_r.e_z + v = v0*R3_r.e_x + v1*R3_r.e_y + v2*R3_r.e_z + w = w0*R3_r.e_x + w1*R3_r.e_y + w2*R3_r.e_z + wp = WedgeProduct(R3_r.dx, R3_r.dy, R3_r.dz) + assert wp( + u, v, w) == Matrix(3, 3, [u0, u1, u2, v0, v1, v2, w0, w1, w2]).det() + + a, b, c = symbols('a, b, c', cls=Function) + a_f = a(R3_r.x, R3_r.y, R3_r.z) + b_f = b(R3_r.x, R3_r.y, R3_r.z) + c_f = c(R3_r.x, R3_r.y, R3_r.z) + theta = a_f*R3_r.dx + b_f*R3_r.dy + c_f*R3_r.dz + dtheta = Differential(theta) + da = Differential(a_f) + db = Differential(b_f) + dc = Differential(c_f) + expr = dtheta - WedgeProduct( + da, R3_r.dx) - WedgeProduct(db, R3_r.dy) - WedgeProduct(dc, R3_r.dz) + assert expr.rcall(R3_r.e_x, R3_r.e_y) == 0 diff --git a/lib/python3.11/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py new file mode 100644 index 0000000000000000000000000000000000000000..48ddc7f8065f2b69bcd8eca4726a21c5901514ec --- /dev/null +++ b/lib/python3.11/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.py @@ -0,0 +1,91 @@ +r''' +unit test describing the hyperbolic half-plane with the Poincare metric. This +is a basic model of hyperbolic geometry on the (positive) half-space + +{(x,y) \in R^2 | y > 0} + +with the Riemannian metric + +ds^2 = (dx^2 + dy^2)/y^2 + +It has constant negative scalar curvature = -2 + +https://en.wikipedia.org/wiki/Poincare_half-plane_model +''' +from sympy.matrices.dense import diag +from sympy.diffgeom import (twoform_to_matrix, + metric_to_Christoffel_1st, metric_to_Christoffel_2nd, + metric_to_Riemann_components, metric_to_Ricci_components) +import sympy.diffgeom.rn +from sympy.tensor.array import ImmutableDenseNDimArray + + +def test_H2(): + TP = sympy.diffgeom.TensorProduct + R2 = sympy.diffgeom.rn.R2 + y = R2.y + dy = R2.dy + dx = R2.dx + g = (TP(dx, dx) + TP(dy, dy))*y**(-2) + automat = twoform_to_matrix(g) + mat = diag(y**(-2), y**(-2)) + assert mat == automat + + gamma1 = metric_to_Christoffel_1st(g) + assert gamma1[0, 0, 0] == 0 + assert gamma1[0, 0, 1] == -y**(-3) + assert gamma1[0, 1, 0] == -y**(-3) + assert gamma1[0, 1, 1] == 0 + + assert gamma1[1, 1, 1] == -y**(-3) + assert gamma1[1, 1, 0] == 0 + assert gamma1[1, 0, 1] == 0 + assert gamma1[1, 0, 0] == y**(-3) + + gamma2 = metric_to_Christoffel_2nd(g) + assert gamma2[0, 0, 0] == 0 + assert gamma2[0, 0, 1] == -y**(-1) + assert gamma2[0, 1, 0] == -y**(-1) + assert gamma2[0, 1, 1] == 0 + + assert gamma2[1, 1, 1] == -y**(-1) + assert gamma2[1, 1, 0] == 0 + assert gamma2[1, 0, 1] == 0 + assert gamma2[1, 0, 0] == y**(-1) + + Rm = metric_to_Riemann_components(g) + assert Rm[0, 0, 0, 0] == 0 + assert Rm[0, 0, 0, 1] == 0 + assert Rm[0, 0, 1, 0] == 0 + assert Rm[0, 0, 1, 1] == 0 + + assert Rm[0, 1, 0, 0] == 0 + assert Rm[0, 1, 0, 1] == -y**(-2) + assert Rm[0, 1, 1, 0] == y**(-2) + assert Rm[0, 1, 1, 1] == 0 + + assert Rm[1, 0, 0, 0] == 0 + assert Rm[1, 0, 0, 1] == y**(-2) + assert Rm[1, 0, 1, 0] == -y**(-2) + assert Rm[1, 0, 1, 1] == 0 + + assert Rm[1, 1, 0, 0] == 0 + assert Rm[1, 1, 0, 1] == 0 + assert Rm[1, 1, 1, 0] == 0 + assert Rm[1, 1, 1, 1] == 0 + + Ric = metric_to_Ricci_components(g) + assert Ric[0, 0] == -y**(-2) + assert Ric[0, 1] == 0 + assert Ric[1, 0] == 0 + assert Ric[0, 0] == -y**(-2) + + assert Ric == ImmutableDenseNDimArray([-y**(-2), 0, 0, -y**(-2)], (2, 2)) + + ## scalar curvature is -2 + #TODO - it would be nice to have index contraction built-in + R = (Ric[0, 0] + Ric[1, 1])*y**2 + assert R == -2 + + ## Gauss curvature is -1 + assert R/2 == -1 diff --git a/lib/python3.11/site-packages/sympy/discrete/__init__.py b/lib/python3.11/site-packages/sympy/discrete/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..968c4caa0d4562b71285f414bfb70f43d0b35111 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/__init__.py @@ -0,0 +1,20 @@ +"""This module contains functions which operate on discrete sequences. + +Transforms - ``fft``, ``ifft``, ``ntt``, ``intt``, ``fwht``, ``ifwht``, + ``mobius_transform``, ``inverse_mobius_transform`` + +Convolutions - ``convolution``, ``convolution_fft``, ``convolution_ntt``, + ``convolution_fwht``, ``convolution_subset``, + ``covering_product``, ``intersecting_product`` +""" + +from .transforms import (fft, ifft, ntt, intt, fwht, ifwht, + mobius_transform, inverse_mobius_transform) +from .convolutions import convolution, covering_product, intersecting_product + +__all__ = [ + 'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform', + 'inverse_mobius_transform', + + 'convolution', 'covering_product', 'intersecting_product', +] diff --git a/lib/python3.11/site-packages/sympy/discrete/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/discrete/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..dd4040485ba4c98fd263b93be7edf395a4229788 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/discrete/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/discrete/__pycache__/convolutions.cpython-311.pyc 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0000000000000000000000000000000000000000..a7251640ac1b0673f4bd1eca949550db06de6e00 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/discrete/__pycache__/transforms.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/discrete/convolutions.py b/lib/python3.11/site-packages/sympy/discrete/convolutions.py new file mode 100644 index 0000000000000000000000000000000000000000..ac9a3dbbb26b8b117ea1ee99cf7ebabbd21322cc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/convolutions.py @@ -0,0 +1,597 @@ +""" +Convolution (using **FFT**, **NTT**, **FWHT**), Subset Convolution, +Covering Product, Intersecting Product +""" + +from sympy.core import S, sympify, Rational +from sympy.core.function import expand_mul +from sympy.discrete.transforms import ( + fft, ifft, ntt, intt, fwht, ifwht, + mobius_transform, inverse_mobius_transform) +from sympy.external.gmpy import MPZ, lcm +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import as_int + + +def convolution(a, b, cycle=0, dps=None, prime=None, dyadic=None, subset=None): + """ + Performs convolution by determining the type of desired + convolution using hints. + + Exactly one of ``dps``, ``prime``, ``dyadic``, ``subset`` arguments + should be specified explicitly for identifying the type of convolution, + and the argument ``cycle`` can be specified optionally. + + For the default arguments, linear convolution is performed using **FFT**. + + Parameters + ========== + + a, b : iterables + The sequences for which convolution is performed. + cycle : Integer + Specifies the length for doing cyclic convolution. + dps : Integer + Specifies the number of decimal digits for precision for + performing **FFT** on the sequence. + prime : Integer + Prime modulus of the form `(m 2^k + 1)` to be used for + performing **NTT** on the sequence. + dyadic : bool + Identifies the convolution type as dyadic (*bitwise-XOR*) + convolution, which is performed using **FWHT**. + subset : bool + Identifies the convolution type as subset convolution. + + Examples + ======== + + >>> from sympy import convolution, symbols, S, I + >>> u, v, w, x, y, z = symbols('u v w x y z') + + >>> convolution([1 + 2*I, 4 + 3*I], [S(5)/4, 6], dps=3) + [1.25 + 2.5*I, 11.0 + 15.8*I, 24.0 + 18.0*I] + >>> convolution([1, 2, 3], [4, 5, 6], cycle=3) + [31, 31, 28] + + >>> convolution([111, 777], [888, 444], prime=19*2**10 + 1) + [1283, 19351, 14219] + >>> convolution([111, 777], [888, 444], prime=19*2**10 + 1, cycle=2) + [15502, 19351] + + >>> convolution([u, v], [x, y, z], dyadic=True) + [u*x + v*y, u*y + v*x, u*z, v*z] + >>> convolution([u, v], [x, y, z], dyadic=True, cycle=2) + [u*x + u*z + v*y, u*y + v*x + v*z] + + >>> convolution([u, v, w], [x, y, z], subset=True) + [u*x, u*y + v*x, u*z + w*x, v*z + w*y] + >>> convolution([u, v, w], [x, y, z], subset=True, cycle=3) + [u*x + v*z + w*y, u*y + v*x, u*z + w*x] + + """ + + c = as_int(cycle) + if c < 0: + raise ValueError("The length for cyclic convolution " + "must be non-negative") + + dyadic = True if dyadic else None + subset = True if subset else None + if sum(x is not None for x in (prime, dps, dyadic, subset)) > 1: + raise TypeError("Ambiguity in determining the type of convolution") + + if prime is not None: + ls = convolution_ntt(a, b, prime=prime) + return ls if not c else [sum(ls[i::c]) % prime for i in range(c)] + + if dyadic: + ls = convolution_fwht(a, b) + elif subset: + ls = convolution_subset(a, b) + else: + def loop(a): + dens = [] + for i in a: + if isinstance(i, Rational) and i.q - 1: + dens.append(i.q) + elif not isinstance(i, int): + return + if dens: + l = lcm(*dens) + return [i*l if type(i) is int else i.p*(l//i.q) for i in a], l + # no lcm of den to deal with + return a, 1 + ls = None + da = loop(a) + if da is not None: + db = loop(b) + if db is not None: + (ia, ma), (ib, mb) = da, db + den = ma*mb + ls = convolution_int(ia, ib) + if den != 1: + ls = [Rational(i, den) for i in ls] + if ls is None: + ls = convolution_fft(a, b, dps) + + return ls if not c else [sum(ls[i::c]) for i in range(c)] + + +#----------------------------------------------------------------------------# +# # +# Convolution for Complex domain # +# # +#----------------------------------------------------------------------------# + +def convolution_fft(a, b, dps=None): + """ + Performs linear convolution using Fast Fourier Transform. + + Parameters + ========== + + a, b : iterables + The sequences for which convolution is performed. + dps : Integer + Specifies the number of decimal digits for precision. + + Examples + ======== + + >>> from sympy import S, I + >>> from sympy.discrete.convolutions import convolution_fft + + >>> convolution_fft([2, 3], [4, 5]) + [8, 22, 15] + >>> convolution_fft([2, 5], [6, 7, 3]) + [12, 44, 41, 15] + >>> convolution_fft([1 + 2*I, 4 + 3*I], [S(5)/4, 6]) + [5/4 + 5*I/2, 11 + 63*I/4, 24 + 18*I] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Convolution_theorem + .. [2] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29 + + """ + + a, b = a[:], b[:] + n = m = len(a) + len(b) - 1 # convolution size + + if n > 0 and n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [S.Zero]*(n - len(a)) + b += [S.Zero]*(n - len(b)) + + a, b = fft(a, dps), fft(b, dps) + a = [expand_mul(x*y) for x, y in zip(a, b)] + a = ifft(a, dps)[:m] + + return a + + +#----------------------------------------------------------------------------# +# # +# Convolution for GF(p) # +# # +#----------------------------------------------------------------------------# + +def convolution_ntt(a, b, prime): + """ + Performs linear convolution using Number Theoretic Transform. + + Parameters + ========== + + a, b : iterables + The sequences for which convolution is performed. + prime : Integer + Prime modulus of the form `(m 2^k + 1)` to be used for performing + **NTT** on the sequence. + + Examples + ======== + + >>> from sympy.discrete.convolutions import convolution_ntt + >>> convolution_ntt([2, 3], [4, 5], prime=19*2**10 + 1) + [8, 22, 15] + >>> convolution_ntt([2, 5], [6, 7, 3], prime=19*2**10 + 1) + [12, 44, 41, 15] + >>> convolution_ntt([333, 555], [222, 666], prime=19*2**10 + 1) + [15555, 14219, 19404] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Convolution_theorem + .. [2] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29 + + """ + + a, b, p = a[:], b[:], as_int(prime) + n = m = len(a) + len(b) - 1 # convolution size + + if n > 0 and n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [0]*(n - len(a)) + b += [0]*(n - len(b)) + + a, b = ntt(a, p), ntt(b, p) + a = [x*y % p for x, y in zip(a, b)] + a = intt(a, p)[:m] + + return a + + +#----------------------------------------------------------------------------# +# # +# Convolution for 2**n-group # +# # +#----------------------------------------------------------------------------# + +def convolution_fwht(a, b): + """ + Performs dyadic (*bitwise-XOR*) convolution using Fast Walsh Hadamard + Transform. + + The convolution is automatically padded to the right with zeros, as the + *radix-2 FWHT* requires the number of sample points to be a power of 2. + + Parameters + ========== + + a, b : iterables + The sequences for which convolution is performed. + + Examples + ======== + + >>> from sympy import symbols, S, I + >>> from sympy.discrete.convolutions import convolution_fwht + + >>> u, v, x, y = symbols('u v x y') + >>> convolution_fwht([u, v], [x, y]) + [u*x + v*y, u*y + v*x] + + >>> convolution_fwht([2, 3], [4, 5]) + [23, 22] + >>> convolution_fwht([2, 5 + 4*I, 7], [6*I, 7, 3 + 4*I]) + [56 + 68*I, -10 + 30*I, 6 + 50*I, 48 + 32*I] + + >>> convolution_fwht([S(33)/7, S(55)/6, S(7)/4], [S(2)/3, 5]) + [2057/42, 1870/63, 7/6, 35/4] + + References + ========== + + .. [1] https://www.radioeng.cz/fulltexts/2002/02_03_40_42.pdf + .. [2] https://en.wikipedia.org/wiki/Hadamard_transform + + """ + + if not a or not b: + return [] + + a, b = a[:], b[:] + n = max(len(a), len(b)) + + if n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [S.Zero]*(n - len(a)) + b += [S.Zero]*(n - len(b)) + + a, b = fwht(a), fwht(b) + a = [expand_mul(x*y) for x, y in zip(a, b)] + a = ifwht(a) + + return a + + +#----------------------------------------------------------------------------# +# # +# Subset Convolution # +# # +#----------------------------------------------------------------------------# + +def convolution_subset(a, b): + """ + Performs Subset Convolution of given sequences. + + The indices of each argument, considered as bit strings, correspond to + subsets of a finite set. + + The sequence is automatically padded to the right with zeros, as the + definition of subset based on bitmasks (indices) requires the size of + sequence to be a power of 2. + + Parameters + ========== + + a, b : iterables + The sequences for which convolution is performed. + + Examples + ======== + + >>> from sympy import symbols, S + >>> from sympy.discrete.convolutions import convolution_subset + >>> u, v, x, y, z = symbols('u v x y z') + + >>> convolution_subset([u, v], [x, y]) + [u*x, u*y + v*x] + >>> convolution_subset([u, v, x], [y, z]) + [u*y, u*z + v*y, x*y, x*z] + + >>> convolution_subset([1, S(2)/3], [3, 4]) + [3, 6] + >>> convolution_subset([1, 3, S(5)/7], [7]) + [7, 21, 5, 0] + + References + ========== + + .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf + + """ + + if not a or not b: + return [] + + if not iterable(a) or not iterable(b): + raise TypeError("Expected a sequence of coefficients for convolution") + + a = [sympify(arg) for arg in a] + b = [sympify(arg) for arg in b] + n = max(len(a), len(b)) + + if n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [S.Zero]*(n - len(a)) + b += [S.Zero]*(n - len(b)) + + c = [S.Zero]*n + + for mask in range(n): + smask = mask + while smask > 0: + c[mask] += expand_mul(a[smask] * b[mask^smask]) + smask = (smask - 1)&mask + + c[mask] += expand_mul(a[smask] * b[mask^smask]) + + return c + + +#----------------------------------------------------------------------------# +# # +# Covering Product # +# # +#----------------------------------------------------------------------------# + +def covering_product(a, b): + """ + Returns the covering product of given sequences. + + The indices of each argument, considered as bit strings, correspond to + subsets of a finite set. + + The covering product of given sequences is a sequence which contains + the sum of products of the elements of the given sequences grouped by + the *bitwise-OR* of the corresponding indices. + + The sequence is automatically padded to the right with zeros, as the + definition of subset based on bitmasks (indices) requires the size of + sequence to be a power of 2. + + Parameters + ========== + + a, b : iterables + The sequences for which covering product is to be obtained. + + Examples + ======== + + >>> from sympy import symbols, S, I, covering_product + >>> u, v, x, y, z = symbols('u v x y z') + + >>> covering_product([u, v], [x, y]) + [u*x, u*y + v*x + v*y] + >>> covering_product([u, v, x], [y, z]) + [u*y, u*z + v*y + v*z, x*y, x*z] + + >>> covering_product([1, S(2)/3], [3, 4 + 5*I]) + [3, 26/3 + 25*I/3] + >>> covering_product([1, 3, S(5)/7], [7, 8]) + [7, 53, 5, 40/7] + + References + ========== + + .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf + + """ + + if not a or not b: + return [] + + a, b = a[:], b[:] + n = max(len(a), len(b)) + + if n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [S.Zero]*(n - len(a)) + b += [S.Zero]*(n - len(b)) + + a, b = mobius_transform(a), mobius_transform(b) + a = [expand_mul(x*y) for x, y in zip(a, b)] + a = inverse_mobius_transform(a) + + return a + + +#----------------------------------------------------------------------------# +# # +# Intersecting Product # +# # +#----------------------------------------------------------------------------# + +def intersecting_product(a, b): + """ + Returns the intersecting product of given sequences. + + The indices of each argument, considered as bit strings, correspond to + subsets of a finite set. + + The intersecting product of given sequences is the sequence which + contains the sum of products of the elements of the given sequences + grouped by the *bitwise-AND* of the corresponding indices. + + The sequence is automatically padded to the right with zeros, as the + definition of subset based on bitmasks (indices) requires the size of + sequence to be a power of 2. + + Parameters + ========== + + a, b : iterables + The sequences for which intersecting product is to be obtained. + + Examples + ======== + + >>> from sympy import symbols, S, I, intersecting_product + >>> u, v, x, y, z = symbols('u v x y z') + + >>> intersecting_product([u, v], [x, y]) + [u*x + u*y + v*x, v*y] + >>> intersecting_product([u, v, x], [y, z]) + [u*y + u*z + v*y + x*y + x*z, v*z, 0, 0] + + >>> intersecting_product([1, S(2)/3], [3, 4 + 5*I]) + [9 + 5*I, 8/3 + 10*I/3] + >>> intersecting_product([1, 3, S(5)/7], [7, 8]) + [327/7, 24, 0, 0] + + References + ========== + + .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf + + """ + + if not a or not b: + return [] + + a, b = a[:], b[:] + n = max(len(a), len(b)) + + if n&(n - 1): # not a power of 2 + n = 2**n.bit_length() + + # padding with zeros + a += [S.Zero]*(n - len(a)) + b += [S.Zero]*(n - len(b)) + + a, b = mobius_transform(a, subset=False), mobius_transform(b, subset=False) + a = [expand_mul(x*y) for x, y in zip(a, b)] + a = inverse_mobius_transform(a, subset=False) + + return a + + +#----------------------------------------------------------------------------# +# # +# Integer Convolutions # +# # +#----------------------------------------------------------------------------# + +def convolution_int(a, b): + """Return the convolution of two sequences as a list. + + The iterables must consist solely of integers. + + Parameters + ========== + + a, b : Sequence + The sequences for which convolution is performed. + + Explanation + =========== + + This function performs the convolution of ``a`` and ``b`` by packing + each into a single integer, multiplying them together, and then + unpacking the result from the product. The intuition behind this is + that if we evaluate some polynomial [1]: + + .. math :: + 1156x^6 + 3808x^5 + 8440x^4 + 14856x^3 + 16164x^2 + 14040x + 8100 + + at say $x = 10^5$ we obtain $1156038080844014856161641404008100$. + Note we can read of the coefficients for each term every five digits. + If the $x$ we chose to evaluate at is large enough, the same will hold + for the product. + + The idea now is since big integer multiplication in libraries such + as GMP is highly optimised, this will be reasonably fast. + + Examples + ======== + + >>> from sympy.discrete.convolutions import convolution_int + + >>> convolution_int([2, 3], [4, 5]) + [8, 22, 15] + >>> convolution_int([1, 1, -1], [1, 1]) + [1, 2, 0, -1] + + References + ========== + + .. [1] Fateman, Richard J. + Can you save time in multiplying polynomials by encoding them as integers? + University of California, Berkeley, California (2004). + https://people.eecs.berkeley.edu/~fateman/papers/polysbyGMP.pdf + """ + # An upper bound on the largest coefficient in p(x)q(x) is given by (1 + min(dp, dq))N(p)N(q) + # where dp = deg(p), dq = deg(q), N(f) denotes the coefficient of largest modulus in f [1] + B = max(abs(c) for c in a)*max(abs(c) for c in b)*(1 + min(len(a) - 1, len(b) - 1)) + x, power = MPZ(1), 0 + while x <= (2*B): # multiply by two for negative coefficients, see [1] + x <<= 1 + power += 1 + + def to_integer(poly): + n, mul = MPZ(0), 0 + for c in reversed(poly): + if c and not mul: mul = -1 if c < 0 else 1 + n <<= power + n += mul*int(c) + return mul, n + + # Perform packing and multiplication + (a_mul, a_packed), (b_mul, b_packed) = to_integer(a), to_integer(b) + result = a_packed * b_packed + + # Perform unpacking + mul = a_mul * b_mul + mask, half, borrow, poly = x - 1, x >> 1, 0, [] + while result or borrow: + coeff = (result & mask) + borrow + result >>= power + borrow = coeff >= half + poly.append(mul * int(coeff if coeff < half else coeff - x)) + return poly or [0] diff --git a/lib/python3.11/site-packages/sympy/discrete/recurrences.py b/lib/python3.11/site-packages/sympy/discrete/recurrences.py new file mode 100644 index 0000000000000000000000000000000000000000..0b0ed80d304161cf9ca298321aedc094c8cae1b3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/recurrences.py @@ -0,0 +1,166 @@ +""" +Recurrences +""" + +from sympy.core import S, sympify +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import as_int + + +def linrec(coeffs, init, n): + r""" + Evaluation of univariate linear recurrences of homogeneous type + having coefficients independent of the recurrence variable. + + Parameters + ========== + + coeffs : iterable + Coefficients of the recurrence + init : iterable + Initial values of the recurrence + n : Integer + Point of evaluation for the recurrence + + Notes + ===== + + Let `y(n)` be the recurrence of given type, ``c`` be the sequence + of coefficients, ``b`` be the sequence of initial/base values of the + recurrence and ``k`` (equal to ``len(c)``) be the order of recurrence. + Then, + + .. math :: y(n) = \begin{cases} b_n & 0 \le n < k \\ + c_0 y(n-1) + c_1 y(n-2) + \cdots + c_{k-1} y(n-k) & n \ge k + \end{cases} + + Let `x_0, x_1, \ldots, x_n` be a sequence and consider the transformation + that maps each polynomial `f(x)` to `T(f(x))` where each power `x^i` is + replaced by the corresponding value `x_i`. The sequence is then a solution + of the recurrence if and only if `T(x^i p(x)) = 0` for each `i \ge 0` where + `p(x) = x^k - c_0 x^(k-1) - \cdots - c_{k-1}` is the characteristic + polynomial. + + Then `T(f(x)p(x)) = 0` for each polynomial `f(x)` (as it is a linear + combination of powers `x^i`). Now, if `x^n` is congruent to + `g(x) = a_0 x^0 + a_1 x^1 + \cdots + a_{k-1} x^{k-1}` modulo `p(x)`, then + `T(x^n) = x_n` is equal to + `T(g(x)) = a_0 x_0 + a_1 x_1 + \cdots + a_{k-1} x_{k-1}`. + + Computation of `x^n`, + given `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}` + is performed using exponentiation by squaring (refer to [1_]) with + an additional reduction step performed to retain only first `k` powers + of `x` in the representation of `x^n`. + + Examples + ======== + + >>> from sympy.discrete.recurrences import linrec + >>> from sympy.abc import x, y, z + + >>> linrec(coeffs=[1, 1], init=[0, 1], n=10) + 55 + + >>> linrec(coeffs=[1, 1], init=[x, y], n=10) + 34*x + 55*y + + >>> linrec(coeffs=[x, y], init=[0, 1], n=5) + x**2*y + x*(x**3 + 2*x*y) + y**2 + + >>> linrec(coeffs=[1, 2, 3, 0, 0, 4], init=[x, y, z], n=16) + 13576*x + 5676*y + 2356*z + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Exponentiation_by_squaring + .. [2] https://en.wikipedia.org/w/index.php?title=Modular_exponentiation§ion=6#Matrices + + See Also + ======== + + sympy.polys.agca.extensions.ExtensionElement.__pow__ + + """ + + if not coeffs: + return S.Zero + + if not iterable(coeffs): + raise TypeError("Expected a sequence of coefficients for" + " the recurrence") + + if not iterable(init): + raise TypeError("Expected a sequence of values for the initialization" + " of the recurrence") + + n = as_int(n) + if n < 0: + raise ValueError("Point of evaluation of recurrence must be a " + "non-negative integer") + + c = [sympify(arg) for arg in coeffs] + b = [sympify(arg) for arg in init] + k = len(c) + + if len(b) > k: + raise TypeError("Count of initial values should not exceed the " + "order of the recurrence") + else: + b += [S.Zero]*(k - len(b)) # remaining initial values default to zero + + if n < k: + return b[n] + terms = [u*v for u, v in zip(linrec_coeffs(c, n), b)] + return sum(terms[:-1], terms[-1]) + + +def linrec_coeffs(c, n): + r""" + Compute the coefficients of n'th term in linear recursion + sequence defined by c. + + `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}`. + + It computes the coefficients by using binary exponentiation. + This function is used by `linrec` and `_eval_pow_by_cayley`. + + Parameters + ========== + + c = coefficients of the divisor polynomial + n = exponent of x, so dividend is x^n + + """ + + k = len(c) + + def _square_and_reduce(u, offset): + # squares `(u_0 + u_1 x + u_2 x^2 + \cdots + u_{k-1} x^k)` (and + # multiplies by `x` if offset is 1) and reduces the above result of + # length upto `2k` to `k` using the characteristic equation of the + # recurrence given by, `x^k = c_0 x^{k-1} + c_1 x^{k-2} + \cdots + c_{k-1}` + + w = [S.Zero]*(2*len(u) - 1 + offset) + for i, p in enumerate(u): + for j, q in enumerate(u): + w[offset + i + j] += p*q + + for j in range(len(w) - 1, k - 1, -1): + for i in range(k): + w[j - i - 1] += w[j]*c[i] + + return w[:k] + + def _final_coeffs(n): + # computes the final coefficient list - `cf` corresponding to the + # point at which recurrence is to be evalauted - `n`, such that, + # `y(n) = cf_0 y(k-1) + cf_1 y(k-2) + \cdots + cf_{k-1} y(0)` + + if n < k: + return [S.Zero]*n + [S.One] + [S.Zero]*(k - n - 1) + else: + return _square_and_reduce(_final_coeffs(n // 2), n % 2) + + return _final_coeffs(n) diff --git a/lib/python3.11/site-packages/sympy/discrete/tests/__init__.py b/lib/python3.11/site-packages/sympy/discrete/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/discrete/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/discrete/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..10184a1ebe644f43c508303a93a098b9274a572e Binary files /dev/null and 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--git a/lib/python3.11/site-packages/sympy/discrete/tests/__pycache__/test_transforms.cpython-311.pyc b/lib/python3.11/site-packages/sympy/discrete/tests/__pycache__/test_transforms.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..fdabf2eb702c87f4dc83f382b657dd762efe383a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/discrete/tests/__pycache__/test_transforms.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/discrete/tests/test_convolutions.py b/lib/python3.11/site-packages/sympy/discrete/tests/test_convolutions.py new file mode 100644 index 0000000000000000000000000000000000000000..96e5fc801ac63f95c01eb18d48143ae3a1ac6222 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/tests/test_convolutions.py @@ -0,0 +1,392 @@ +from sympy.core.numbers import (E, Rational, pi) +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.core import S, symbols, I +from sympy.discrete.convolutions import ( + convolution, convolution_fft, convolution_ntt, convolution_fwht, + convolution_subset, covering_product, intersecting_product, + convolution_int) +from sympy.testing.pytest import raises +from sympy.abc import x, y + +def test_convolution(): + # fft + a = [1, Rational(5, 3), sqrt(3), Rational(7, 5)] + b = [9, 5, 5, 4, 3, 2] + c = [3, 5, 3, 7, 8] + d = [1422, 6572, 3213, 5552] + e = [-1, Rational(5, 3), Rational(7, 5)] + + assert convolution(a, b) == convolution_fft(a, b) + assert convolution(a, b, dps=9) == convolution_fft(a, b, dps=9) + assert convolution(a, d, dps=7) == convolution_fft(d, a, dps=7) + assert convolution(a, d[1:], dps=3) == convolution_fft(d[1:], a, dps=3) + + # prime moduli of the form (m*2**k + 1), sequence length + # should be a divisor of 2**k + p = 7*17*2**23 + 1 + q = 19*2**10 + 1 + + # ntt + assert convolution(d, b, prime=q) == convolution_ntt(b, d, prime=q) + assert convolution(c, b, prime=p) == convolution_ntt(b, c, prime=p) + assert convolution(d, c, prime=p) == convolution_ntt(c, d, prime=p) + raises(TypeError, lambda: convolution(b, d, dps=5, prime=q)) + raises(TypeError, lambda: convolution(b, d, dps=6, prime=q)) + + # fwht + assert convolution(a, b, dyadic=True) == convolution_fwht(a, b) + assert convolution(a, b, dyadic=False) == convolution(a, b) + raises(TypeError, lambda: convolution(b, d, dps=2, dyadic=True)) + raises(TypeError, lambda: convolution(b, d, prime=p, dyadic=True)) + raises(TypeError, lambda: convolution(a, b, dps=2, dyadic=True)) + raises(TypeError, lambda: convolution(b, c, prime=p, dyadic=True)) + + # subset + assert convolution(a, b, subset=True) == convolution_subset(a, b) == \ + convolution(a, b, subset=True, dyadic=False) == \ + convolution(a, b, subset=True) + assert convolution(a, b, subset=False) == convolution(a, b) + raises(TypeError, lambda: convolution(a, b, subset=True, dyadic=True)) + raises(TypeError, lambda: convolution(c, d, subset=True, dps=6)) + raises(TypeError, lambda: convolution(a, c, subset=True, prime=q)) + + # integer + assert convolution([0], [0]) == convolution_int([0], [0]) + assert convolution(b, c) == convolution_int(b, c) + + # rational + assert convolution([Rational(1,2)], [Rational(1,2)]) == [Rational(1, 4)] + assert convolution(b, e) == [-9, 10, Rational(239, 15), Rational(34, 3), + Rational(32, 3), Rational(43, 5), Rational(113, 15), + Rational(14, 5)] + + +def test_cyclic_convolution(): + # fft + a = [1, Rational(5, 3), sqrt(3), Rational(7, 5)] + b = [9, 5, 5, 4, 3, 2] + + assert convolution([1, 2, 3], [4, 5, 6], cycle=0) == \ + convolution([1, 2, 3], [4, 5, 6], cycle=5) == \ + convolution([1, 2, 3], [4, 5, 6]) + + assert convolution([1, 2, 3], [4, 5, 6], cycle=3) == [31, 31, 28] + + a = [Rational(1, 3), Rational(7, 3), Rational(5, 9), Rational(2, 7), Rational(5, 8)] + b = [Rational(3, 5), Rational(4, 7), Rational(7, 8), Rational(8, 9)] + + assert convolution(a, b, cycle=0) == \ + convolution(a, b, cycle=len(a) + len(b) - 1) + + assert convolution(a, b, cycle=4) == [Rational(87277, 26460), Rational(30521, 11340), + Rational(11125, 4032), Rational(3653, 1080)] + + assert convolution(a, b, cycle=6) == [Rational(20177, 20160), Rational(676, 315), Rational(47, 24), + Rational(3053, 1080), Rational(16397, 5292), Rational(2497, 2268)] + + assert convolution(a, b, cycle=9) == \ + convolution(a, b, cycle=0) + [S.Zero] + + # ntt + a = [2313, 5323532, S(3232), 42142, 42242421] + b = [S(33456), 56757, 45754, 432423] + + assert convolution(a, b, prime=19*2**10 + 1, cycle=0) == \ + convolution(a, b, prime=19*2**10 + 1, cycle=8) == \ + convolution(a, b, prime=19*2**10 + 1) + + assert convolution(a, b, prime=19*2**10 + 1, cycle=5) == [96, 17146, 2664, + 15534, 3517] + + assert convolution(a, b, prime=19*2**10 + 1, cycle=7) == [4643, 3458, 1260, + 15534, 3517, 16314, 13688] + + assert convolution(a, b, prime=19*2**10 + 1, cycle=9) == \ + convolution(a, b, prime=19*2**10 + 1) + [0] + + # fwht + u, v, w, x, y = symbols('u v w x y') + p, q, r, s, t = symbols('p q r s t') + c = [u, v, w, x, y] + d = [p, q, r, s, t] + + assert convolution(a, b, dyadic=True, cycle=3) == \ + [2499522285783, 19861417974796, 4702176579021] + + assert convolution(a, b, dyadic=True, cycle=5) == [2718149225143, + 2114320852171, 20571217906407, 246166418903, 1413262436976] + + assert convolution(c, d, dyadic=True, cycle=4) == \ + [p*u + p*y + q*v + r*w + s*x + t*u + t*y, + p*v + q*u + q*y + r*x + s*w + t*v, + p*w + q*x + r*u + r*y + s*v + t*w, + p*x + q*w + r*v + s*u + s*y + t*x] + + assert convolution(c, d, dyadic=True, cycle=6) == \ + [p*u + q*v + r*w + r*y + s*x + t*w + t*y, + p*v + q*u + r*x + s*w + s*y + t*x, + p*w + q*x + r*u + s*v, + p*x + q*w + r*v + s*u, + p*y + t*u, + q*y + t*v] + + # subset + assert convolution(a, b, subset=True, cycle=7) == [18266671799811, + 178235365533, 213958794, 246166418903, 1413262436976, + 2397553088697, 1932759730434] + + assert convolution(a[1:], b, subset=True, cycle=4) == \ + [178104086592, 302255835516, 244982785880, 3717819845434] + + assert convolution(a, b[:-1], subset=True, cycle=6) == [1932837114162, + 178235365533, 213958794, 245166224504, 1413262436976, 2397553088697] + + assert convolution(c, d, subset=True, cycle=3) == \ + [p*u + p*x + q*w + r*v + r*y + s*u + t*w, + p*v + p*y + q*u + s*y + t*u + t*x, + p*w + q*y + r*u + t*v] + + assert convolution(c, d, subset=True, cycle=5) == \ + [p*u + q*y + t*v, + p*v + q*u + r*y + t*w, + p*w + r*u + s*y + t*x, + p*x + q*w + r*v + s*u, + p*y + t*u] + + raises(ValueError, lambda: convolution([1, 2, 3], [4, 5, 6], cycle=-1)) + + +def test_convolution_fft(): + assert all(convolution_fft([], x, dps=y) == [] for x in ([], [1]) for y in (None, 3)) + assert convolution_fft([1, 2, 3], [4, 5, 6]) == [4, 13, 28, 27, 18] + assert convolution_fft([1], [5, 6, 7]) == [5, 6, 7] + assert convolution_fft([1, 3], [5, 6, 7]) == [5, 21, 25, 21] + + assert convolution_fft([1 + 2*I], [2 + 3*I]) == [-4 + 7*I] + assert convolution_fft([1 + 2*I, 3 + 4*I, 5 + 3*I/5], [Rational(2, 5) + 4*I/7]) == \ + [Rational(-26, 35) + I*48/35, Rational(-38, 35) + I*116/35, Rational(58, 35) + I*542/175] + + assert convolution_fft([Rational(3, 4), Rational(5, 6)], [Rational(7, 8), Rational(1, 3), Rational(2, 5)]) == \ + [Rational(21, 32), Rational(47, 48), Rational(26, 45), Rational(1, 3)] + + assert convolution_fft([Rational(1, 9), Rational(2, 3), Rational(3, 5)], [Rational(2, 5), Rational(3, 7), Rational(4, 9)]) == \ + [Rational(2, 45), Rational(11, 35), Rational(8152, 14175), Rational(523, 945), Rational(4, 15)] + + assert convolution_fft([pi, E, sqrt(2)], [sqrt(3), 1/pi, 1/E]) == \ + [sqrt(3)*pi, 1 + sqrt(3)*E, E/pi + pi*exp(-1) + sqrt(6), + sqrt(2)/pi + 1, sqrt(2)*exp(-1)] + + assert convolution_fft([2321, 33123], [5321, 6321, 71323]) == \ + [12350041, 190918524, 374911166, 2362431729] + + assert convolution_fft([312313, 31278232], [32139631, 319631]) == \ + [10037624576503, 1005370659728895, 9997492572392] + + raises(TypeError, lambda: convolution_fft(x, y)) + raises(ValueError, lambda: convolution_fft([x, y], [y, x])) + + +def test_convolution_ntt(): + # prime moduli of the form (m*2**k + 1), sequence length + # should be a divisor of 2**k + p = 7*17*2**23 + 1 + q = 19*2**10 + 1 + r = 2*500000003 + 1 # only for sequences of length 1 or 2 + # s = 2*3*5*7 # composite modulus + + assert all(convolution_ntt([], x, prime=y) == [] for x in ([], [1]) for y in (p, q, r)) + assert convolution_ntt([2], [3], r) == [6] + assert convolution_ntt([2, 3], [4], r) == [8, 12] + + assert convolution_ntt([32121, 42144, 4214, 4241], [32132, 3232, 87242], p) == [33867619, + 459741727, 79180879, 831885249, 381344700, 369993322] + assert convolution_ntt([121913, 3171831, 31888131, 12], [17882, 21292, 29921, 312], q) == \ + [8158, 3065, 3682, 7090, 1239, 2232, 3744] + + assert convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], p) == \ + convolution_ntt([12, 19, 21, 98, 67], [2, 6, 7, 8, 9], q) + assert convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], p) == \ + convolution_ntt([12, 19, 21, 98, 67], [21, 76, 17, 78, 69], q) + + raises(ValueError, lambda: convolution_ntt([2, 3], [4, 5], r)) + raises(ValueError, lambda: convolution_ntt([x, y], [y, x], q)) + raises(TypeError, lambda: convolution_ntt(x, y, p)) + + +def test_convolution_fwht(): + assert convolution_fwht([], []) == [] + assert convolution_fwht([], [1]) == [] + assert convolution_fwht([1, 2, 3], [4, 5, 6]) == [32, 13, 18, 27] + + assert convolution_fwht([Rational(5, 7), Rational(6, 8), Rational(7, 3)], [2, 4, Rational(6, 7)]) == \ + [Rational(45, 7), Rational(61, 14), Rational(776, 147), Rational(419, 42)] + + a = [1, Rational(5, 3), sqrt(3), Rational(7, 5), 4 + 5*I] + b = [94, 51, 53, 45, 31, 27, 13] + c = [3 + 4*I, 5 + 7*I, 3, Rational(7, 6), 8] + + assert convolution_fwht(a, b) == [53*sqrt(3) + 366 + 155*I, + 45*sqrt(3) + Rational(5848, 15) + 135*I, + 94*sqrt(3) + Rational(1257, 5) + 65*I, + 51*sqrt(3) + Rational(3974, 15), + 13*sqrt(3) + 452 + 470*I, + Rational(4513, 15) + 255*I, + 31*sqrt(3) + Rational(1314, 5) + 265*I, + 27*sqrt(3) + Rational(3676, 15) + 225*I] + + assert convolution_fwht(b, c) == [Rational(1993, 2) + 733*I, Rational(6215, 6) + 862*I, + Rational(1659, 2) + 527*I, Rational(1988, 3) + 551*I, 1019 + 313*I, Rational(3955, 6) + 325*I, + Rational(1175, 2) + 52*I, Rational(3253, 6) + 91*I] + + assert convolution_fwht(a[3:], c) == [Rational(-54, 5) + I*293/5, -1 + I*204/5, + Rational(133, 15) + I*35/6, Rational(409, 30) + 15*I, Rational(56, 5), 32 + 40*I, 0, 0] + + u, v, w, x, y, z = symbols('u v w x y z') + + assert convolution_fwht([u, v], [x, y]) == [u*x + v*y, u*y + v*x] + + assert convolution_fwht([u, v, w], [x, y]) == \ + [u*x + v*y, u*y + v*x, w*x, w*y] + + assert convolution_fwht([u, v, w], [x, y, z]) == \ + [u*x + v*y + w*z, u*y + v*x, u*z + w*x, v*z + w*y] + + raises(TypeError, lambda: convolution_fwht(x, y)) + raises(TypeError, lambda: convolution_fwht(x*y, u + v)) + + +def test_convolution_subset(): + assert convolution_subset([], []) == [] + assert convolution_subset([], [Rational(1, 3)]) == [] + assert convolution_subset([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7] + + a = [1, Rational(5, 3), sqrt(3), 4 + 5*I] + b = [64, 71, 55, 47, 33, 29, 15] + c = [3 + I*2/3, 5 + 7*I, 7, Rational(7, 5), 9] + + assert convolution_subset(a, b) == [64, Rational(533, 3), 55 + 64*sqrt(3), + 71*sqrt(3) + Rational(1184, 3) + 320*I, 33, 84, + 15 + 33*sqrt(3), 29*sqrt(3) + 157 + 165*I] + + assert convolution_subset(b, c) == [192 + I*128/3, 533 + I*1486/3, + 613 + I*110/3, Rational(5013, 5) + I*1249/3, + 675 + 22*I, 891 + I*751/3, + 771 + 10*I, Rational(3736, 5) + 105*I] + + assert convolution_subset(a, c) == convolution_subset(c, a) + assert convolution_subset(a[:2], b) == \ + [64, Rational(533, 3), 55, Rational(416, 3), 33, 84, 15, 25] + + assert convolution_subset(a[:2], c) == \ + [3 + I*2/3, 10 + I*73/9, 7, Rational(196, 15), 9, 15, 0, 0] + + u, v, w, x, y, z = symbols('u v w x y z') + + assert convolution_subset([u, v, w], [x, y]) == [u*x, u*y + v*x, w*x, w*y] + assert convolution_subset([u, v, w, x], [y, z]) == \ + [u*y, u*z + v*y, w*y, w*z + x*y] + + assert convolution_subset([u, v], [x, y, z]) == \ + convolution_subset([x, y, z], [u, v]) + + raises(TypeError, lambda: convolution_subset(x, z)) + raises(TypeError, lambda: convolution_subset(Rational(7, 3), u)) + + +def test_covering_product(): + assert covering_product([], []) == [] + assert covering_product([], [Rational(1, 3)]) == [] + assert covering_product([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7] + + a = [1, Rational(5, 8), sqrt(7), 4 + 9*I] + b = [66, 81, 95, 49, 37, 89, 17] + c = [3 + I*2/3, 51 + 72*I, 7, Rational(7, 15), 91] + + assert covering_product(a, b) == [66, Rational(1383, 8), 95 + 161*sqrt(7), + 130*sqrt(7) + 1303 + 2619*I, 37, + Rational(671, 4), 17 + 54*sqrt(7), + 89*sqrt(7) + Rational(4661, 8) + 1287*I] + + assert covering_product(b, c) == [198 + 44*I, 7740 + 10638*I, + 1412 + I*190/3, Rational(42684, 5) + I*31202/3, + 9484 + I*74/3, 22163 + I*27394/3, + 10621 + I*34/3, Rational(90236, 15) + 1224*I] + + assert covering_product(a, c) == covering_product(c, a) + assert covering_product(b, c[:-1]) == [198 + 44*I, 7740 + 10638*I, + 1412 + I*190/3, Rational(42684, 5) + I*31202/3, + 111 + I*74/3, 6693 + I*27394/3, + 429 + I*34/3, Rational(23351, 15) + 1224*I] + + assert covering_product(a, c[:-1]) == [3 + I*2/3, + Rational(339, 4) + I*1409/12, 7 + 10*sqrt(7) + 2*sqrt(7)*I/3, + -403 + 772*sqrt(7)/15 + 72*sqrt(7)*I + I*12658/15] + + u, v, w, x, y, z = symbols('u v w x y z') + + assert covering_product([u, v, w], [x, y]) == \ + [u*x, u*y + v*x + v*y, w*x, w*y] + + assert covering_product([u, v, w, x], [y, z]) == \ + [u*y, u*z + v*y + v*z, w*y, w*z + x*y + x*z] + + assert covering_product([u, v], [x, y, z]) == \ + covering_product([x, y, z], [u, v]) + + raises(TypeError, lambda: covering_product(x, z)) + raises(TypeError, lambda: covering_product(Rational(7, 3), u)) + + +def test_intersecting_product(): + assert intersecting_product([], []) == [] + assert intersecting_product([], [Rational(1, 3)]) == [] + assert intersecting_product([6 + I*3/7], [Rational(2, 3)]) == [4 + I*2/7] + + a = [1, sqrt(5), Rational(3, 8) + 5*I, 4 + 7*I] + b = [67, 51, 65, 48, 36, 79, 27] + c = [3 + I*2/5, 5 + 9*I, 7, Rational(7, 19), 13] + + assert intersecting_product(a, b) == [195*sqrt(5) + Rational(6979, 8) + 1886*I, + 178*sqrt(5) + 520 + 910*I, Rational(841, 2) + 1344*I, + 192 + 336*I, 0, 0, 0, 0] + + assert intersecting_product(b, c) == [Rational(128553, 19) + I*9521/5, + Rational(17820, 19) + 1602*I, Rational(19264, 19), Rational(336, 19), 1846, 0, 0, 0] + + assert intersecting_product(a, c) == intersecting_product(c, a) + assert intersecting_product(b[1:], c[:-1]) == [Rational(64788, 19) + I*8622/5, + Rational(12804, 19) + 1152*I, Rational(11508, 19), Rational(252, 19), 0, 0, 0, 0] + + assert intersecting_product(a, c[:-2]) == \ + [Rational(-99, 5) + 10*sqrt(5) + 2*sqrt(5)*I/5 + I*3021/40, + -43 + 5*sqrt(5) + 9*sqrt(5)*I + 71*I, Rational(245, 8) + 84*I, 0] + + u, v, w, x, y, z = symbols('u v w x y z') + + assert intersecting_product([u, v, w], [x, y]) == \ + [u*x + u*y + v*x + w*x + w*y, v*y, 0, 0] + + assert intersecting_product([u, v, w, x], [y, z]) == \ + [u*y + u*z + v*y + w*y + w*z + x*y, v*z + x*z, 0, 0] + + assert intersecting_product([u, v], [x, y, z]) == \ + intersecting_product([x, y, z], [u, v]) + + raises(TypeError, lambda: intersecting_product(x, z)) + raises(TypeError, lambda: intersecting_product(u, Rational(8, 3))) + + +def test_convolution_int(): + assert convolution_int([1], [1]) == [1] + assert convolution_int([1, 1], [0]) == [0] + assert convolution_int([1, 2, 3], [4, 5, 6]) == [4, 13, 28, 27, 18] + assert convolution_int([1], [5, 6, 7]) == [5, 6, 7] + assert convolution_int([1, 3], [5, 6, 7]) == [5, 21, 25, 21] + assert convolution_int([10, -5, 1, 3], [-5, 6, 7]) == [-50, 85, 35, -44, 25, 21] + assert convolution_int([0, 1, 0, -1], [1, 0, -1, 0]) == [0, 1, 0, -2, 0, 1] + assert convolution_int( + [-341, -5, 1, 3, -71, -99, 43, 87], + [5, 6, 7, 12, 345, 21, -78, -7, -89] + ) == [-1705, -2071, -2412, -4106, -118035, -9774, 25998, 2981, 5509, + -34317, 19228, 38870, 5485, 1724, -4436, -7743] diff --git a/lib/python3.11/site-packages/sympy/discrete/tests/test_recurrences.py b/lib/python3.11/site-packages/sympy/discrete/tests/test_recurrences.py new file mode 100644 index 0000000000000000000000000000000000000000..2c2186ca525b6680350a03edbe44ca88f8f95c3c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/tests/test_recurrences.py @@ -0,0 +1,59 @@ +from sympy.core.numbers import Rational +from sympy.functions.combinatorial.numbers import fibonacci +from sympy.core import S, symbols +from sympy.testing.pytest import raises +from sympy.discrete.recurrences import linrec + +def test_linrec(): + assert linrec(coeffs=[1, 1], init=[1, 1], n=20) == 10946 + assert linrec(coeffs=[1, 2, 3, 4, 5], init=[1, 1, 0, 2], n=10) == 1040 + assert linrec(coeffs=[0, 0, 11, 13], init=[23, 27], n=25) == 59628567384 + assert linrec(coeffs=[0, 0, 1, 1, 2], init=[1, 5, 3], n=15) == 165 + assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=70) == \ + 56889923441670659718376223533331214868804815612050381493741233489928913241 + assert linrec(coeffs=[0]*55 + [1, 1, 2, 3], init=[0]*50 + [1, 2, 3], n=4000) == \ + 702633573874937994980598979769135096432444135301118916539 + + assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**4) + assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**5) + + assert all(linrec(coeffs=[1, 1], init=[0, 1], n=n) == fibonacci(n) + for n in range(95, 115)) + + assert all(linrec(coeffs=[1, 1], init=[1, 1], n=n) == fibonacci(n + 1) + for n in range(595, 615)) + + a = [S.Half, Rational(3, 4), Rational(5, 6), 7, Rational(8, 9), Rational(3, 5)] + b = [1, 2, 8, Rational(5, 7), Rational(3, 7), Rational(2, 9), 6] + x, y, z = symbols('x y z') + + assert linrec(coeffs=a[:5], init=b[:4], n=80) == \ + Rational(1726244235456268979436592226626304376013002142588105090705187189, + 1960143456748895967474334873705475211264) + + assert linrec(coeffs=a[:4], init=b[:4], n=50) == \ + Rational(368949940033050147080268092104304441, 504857282956046106624) + + assert linrec(coeffs=a[3:], init=b[:3], n=35) == \ + Rational(97409272177295731943657945116791049305244422833125109, + 814315512679031689453125) + + assert linrec(coeffs=[0]*60 + [Rational(2, 3), Rational(4, 5)], init=b, n=3000) == \ + Rational(26777668739896791448594650497024, 48084516708184142230517578125) + + raises(TypeError, lambda: linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4, 5], n=1)) + raises(TypeError, lambda: linrec(coeffs=a[:4], init=b[:5], n=10000)) + raises(ValueError, lambda: linrec(coeffs=a[:4], init=b[:4], n=-10000)) + raises(TypeError, lambda: linrec(x, b, n=10000)) + raises(TypeError, lambda: linrec(a, y, n=10000)) + + assert linrec(coeffs=[x, y, z], init=[1, 1, 1], n=4) == \ + x**2 + x*y + x*z + y + z + assert linrec(coeffs=[1, 2, 1], init=[x, y, z], n=20) == \ + 269542*x + 664575*y + 578949*z + assert linrec(coeffs=[0, 3, 1, 2], init=[x, y], n=30) == \ + 58516436*x + 56372788*y + assert linrec(coeffs=[0]*50 + [1, 2, 3], init=[x, y, z], n=1000) == \ + 11477135884896*x + 25999077948732*y + 41975630244216*z + assert linrec(coeffs=[], init=[1, 1], n=20) == 0 + assert linrec(coeffs=[x, y, z], init=[1, 2, 3], n=2) == 3 diff --git a/lib/python3.11/site-packages/sympy/discrete/tests/test_transforms.py b/lib/python3.11/site-packages/sympy/discrete/tests/test_transforms.py new file mode 100644 index 0000000000000000000000000000000000000000..385514be4cdec2f19cf3a750bdbe0f4f6e21cc6e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/tests/test_transforms.py @@ -0,0 +1,154 @@ +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.core import S, Symbol, symbols, I, Rational +from sympy.discrete import (fft, ifft, ntt, intt, fwht, ifwht, + mobius_transform, inverse_mobius_transform) +from sympy.testing.pytest import raises + + +def test_fft_ifft(): + assert all(tf(ls) == ls for tf in (fft, ifft) + for ls in ([], [Rational(5, 3)])) + + ls = list(range(6)) + fls = [15, -7*sqrt(2)/2 - 4 - sqrt(2)*I/2 + 2*I, 2 + 3*I, + -4 + 7*sqrt(2)/2 - 2*I - sqrt(2)*I/2, -3, + -4 + 7*sqrt(2)/2 + sqrt(2)*I/2 + 2*I, + 2 - 3*I, -7*sqrt(2)/2 - 4 - 2*I + sqrt(2)*I/2] + + assert fft(ls) == fls + assert ifft(fls) == ls + [S.Zero]*2 + + ls = [1 + 2*I, 3 + 4*I, 5 + 6*I] + ifls = [Rational(9, 4) + 3*I, I*Rational(-7, 4), Rational(3, 4) + I, -2 - I/4] + + assert ifft(ls) == ifls + assert fft(ifls) == ls + [S.Zero] + + x = Symbol('x', real=True) + raises(TypeError, lambda: fft(x)) + raises(ValueError, lambda: ifft([x, 2*x, 3*x**2, 4*x**3])) + + +def test_ntt_intt(): + # prime moduli of the form (m*2**k + 1), sequence length + # should be a divisor of 2**k + p = 7*17*2**23 + 1 + q = 2*500000003 + 1 # only for sequences of length 1 or 2 + r = 2*3*5*7 # composite modulus + + assert all(tf(ls, p) == ls for tf in (ntt, intt) + for ls in ([], [5])) + + ls = list(range(6)) + nls = [15, 801133602, 738493201, 334102277, 998244350, 849020224, + 259751156, 12232587] + + assert ntt(ls, p) == nls + assert intt(nls, p) == ls + [0]*2 + + ls = [1 + 2*I, 3 + 4*I, 5 + 6*I] + x = Symbol('x', integer=True) + + raises(TypeError, lambda: ntt(x, p)) + raises(ValueError, lambda: intt([x, 2*x, 3*x**2, 4*x**3], p)) + raises(ValueError, lambda: intt(ls, p)) + raises(ValueError, lambda: ntt([1.2, 2.1, 3.5], p)) + raises(ValueError, lambda: ntt([3, 5, 6], q)) + raises(ValueError, lambda: ntt([4, 5, 7], r)) + raises(ValueError, lambda: ntt([1.0, 2.0, 3.0], p)) + + +def test_fwht_ifwht(): + assert all(tf(ls) == ls for tf in (fwht, ifwht) \ + for ls in ([], [Rational(7, 4)])) + + ls = [213, 321, 43235, 5325, 312, 53] + fls = [49459, 38061, -47661, -37759, 48729, 37543, -48391, -38277] + + assert fwht(ls) == fls + assert ifwht(fls) == ls + [S.Zero]*2 + + ls = [S.Half + 2*I, Rational(3, 7) + 4*I, Rational(5, 6) + 6*I, Rational(7, 3), Rational(9, 4)] + ifls = [Rational(533, 672) + I*3/2, Rational(23, 224) + I/2, Rational(1, 672), Rational(107, 224) - I, + Rational(155, 672) + I*3/2, Rational(-103, 224) + I/2, Rational(-377, 672), Rational(-19, 224) - I] + + assert ifwht(ls) == ifls + assert fwht(ifls) == ls + [S.Zero]*3 + + x, y = symbols('x y') + + raises(TypeError, lambda: fwht(x)) + + ls = [x, 2*x, 3*x**2, 4*x**3] + ifls = [x**3 + 3*x**2/4 + x*Rational(3, 4), + -x**3 + 3*x**2/4 - x/4, + -x**3 - 3*x**2/4 + x*Rational(3, 4), + x**3 - 3*x**2/4 - x/4] + + assert ifwht(ls) == ifls + assert fwht(ifls) == ls + + ls = [x, y, x**2, y**2, x*y] + fls = [x**2 + x*y + x + y**2 + y, + x**2 + x*y + x - y**2 - y, + -x**2 + x*y + x - y**2 + y, + -x**2 + x*y + x + y**2 - y, + x**2 - x*y + x + y**2 + y, + x**2 - x*y + x - y**2 - y, + -x**2 - x*y + x - y**2 + y, + -x**2 - x*y + x + y**2 - y] + + assert fwht(ls) == fls + assert ifwht(fls) == ls + [S.Zero]*3 + + ls = list(range(6)) + + assert fwht(ls) == [x*8 for x in ifwht(ls)] + + +def test_mobius_transform(): + assert all(tf(ls, subset=subset) == ls + for ls in ([], [Rational(7, 4)]) for subset in (True, False) + for tf in (mobius_transform, inverse_mobius_transform)) + + w, x, y, z = symbols('w x y z') + + assert mobius_transform([x, y]) == [x, x + y] + assert inverse_mobius_transform([x, x + y]) == [x, y] + assert mobius_transform([x, y], subset=False) == [x + y, y] + assert inverse_mobius_transform([x + y, y], subset=False) == [x, y] + + assert mobius_transform([w, x, y, z]) == [w, w + x, w + y, w + x + y + z] + assert inverse_mobius_transform([w, w + x, w + y, w + x + y + z]) == \ + [w, x, y, z] + assert mobius_transform([w, x, y, z], subset=False) == \ + [w + x + y + z, x + z, y + z, z] + assert inverse_mobius_transform([w + x + y + z, x + z, y + z, z], subset=False) == \ + [w, x, y, z] + + ls = [Rational(2, 3), Rational(6, 7), Rational(5, 8), 9, Rational(5, 3) + 7*I] + mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168), + Rational(7, 3) + 7*I, Rational(67, 21) + 7*I, Rational(71, 24) + 7*I, + Rational(2153, 168) + 7*I] + + assert mobius_transform(ls) == mls + assert inverse_mobius_transform(mls) == ls + [S.Zero]*3 + + mls = [Rational(2153, 168) + 7*I, Rational(69, 7), Rational(77, 8), 9, Rational(5, 3) + 7*I, 0, 0, 0] + + assert mobius_transform(ls, subset=False) == mls + assert inverse_mobius_transform(mls, subset=False) == ls + [S.Zero]*3 + + ls = ls[:-1] + mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168)] + + assert mobius_transform(ls) == mls + assert inverse_mobius_transform(mls) == ls + + mls = [Rational(1873, 168), Rational(69, 7), Rational(77, 8), 9] + + assert mobius_transform(ls, subset=False) == mls + assert inverse_mobius_transform(mls, subset=False) == ls + + raises(TypeError, lambda: mobius_transform(x, subset=True)) + raises(TypeError, lambda: inverse_mobius_transform(y, subset=False)) diff --git a/lib/python3.11/site-packages/sympy/discrete/transforms.py b/lib/python3.11/site-packages/sympy/discrete/transforms.py new file mode 100644 index 0000000000000000000000000000000000000000..cb3550837021a4cf99e38c6b15f89ce8bb69b25a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/discrete/transforms.py @@ -0,0 +1,425 @@ +""" +Discrete Fourier Transform, Number Theoretic Transform, +Walsh Hadamard Transform, Mobius Transform +""" + +from sympy.core import S, Symbol, sympify +from sympy.core.function import expand_mul +from sympy.core.numbers import pi, I +from sympy.functions.elementary.trigonometric import sin, cos +from sympy.ntheory import isprime, primitive_root +from sympy.utilities.iterables import ibin, iterable +from sympy.utilities.misc import as_int + + +#----------------------------------------------------------------------------# +# # +# Discrete Fourier Transform # +# # +#----------------------------------------------------------------------------# + +def _fourier_transform(seq, dps, inverse=False): + """Utility function for the Discrete Fourier Transform""" + + if not iterable(seq): + raise TypeError("Expected a sequence of numeric coefficients " + "for Fourier Transform") + + a = [sympify(arg) for arg in seq] + if any(x.has(Symbol) for x in a): + raise ValueError("Expected non-symbolic coefficients") + + n = len(a) + if n < 2: + return a + + b = n.bit_length() - 1 + if n&(n - 1): # not a power of 2 + b += 1 + n = 2**b + + a += [S.Zero]*(n - len(a)) + for i in range(1, n): + j = int(ibin(i, b, str=True)[::-1], 2) + if i < j: + a[i], a[j] = a[j], a[i] + + ang = -2*pi/n if inverse else 2*pi/n + + if dps is not None: + ang = ang.evalf(dps + 2) + + w = [cos(ang*i) + I*sin(ang*i) for i in range(n // 2)] + + h = 2 + while h <= n: + hf, ut = h // 2, n // h + for i in range(0, n, h): + for j in range(hf): + u, v = a[i + j], expand_mul(a[i + j + hf]*w[ut * j]) + a[i + j], a[i + j + hf] = u + v, u - v + h *= 2 + + if inverse: + a = [(x/n).evalf(dps) for x in a] if dps is not None \ + else [x/n for x in a] + + return a + + +def fft(seq, dps=None): + r""" + Performs the Discrete Fourier Transform (**DFT**) in the complex domain. + + The sequence is automatically padded to the right with zeros, as the + *radix-2 FFT* requires the number of sample points to be a power of 2. + + This method should be used with default arguments only for short sequences + as the complexity of expressions increases with the size of the sequence. + + Parameters + ========== + + seq : iterable + The sequence on which **DFT** is to be applied. + dps : Integer + Specifies the number of decimal digits for precision. + + Examples + ======== + + >>> from sympy import fft, ifft + + >>> fft([1, 2, 3, 4]) + [10, -2 - 2*I, -2, -2 + 2*I] + >>> ifft(_) + [1, 2, 3, 4] + + >>> ifft([1, 2, 3, 4]) + [5/2, -1/2 + I/2, -1/2, -1/2 - I/2] + >>> fft(_) + [1, 2, 3, 4] + + >>> ifft([1, 7, 3, 4], dps=15) + [3.75, -0.5 - 0.75*I, -1.75, -0.5 + 0.75*I] + >>> fft(_) + [1.0, 7.0, 3.0, 4.0] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm + .. [2] https://mathworld.wolfram.com/FastFourierTransform.html + + """ + + return _fourier_transform(seq, dps=dps) + + +def ifft(seq, dps=None): + return _fourier_transform(seq, dps=dps, inverse=True) + +ifft.__doc__ = fft.__doc__ + + +#----------------------------------------------------------------------------# +# # +# Number Theoretic Transform # +# # +#----------------------------------------------------------------------------# + +def _number_theoretic_transform(seq, prime, inverse=False): + """Utility function for the Number Theoretic Transform""" + + if not iterable(seq): + raise TypeError("Expected a sequence of integer coefficients " + "for Number Theoretic Transform") + + p = as_int(prime) + if not isprime(p): + raise ValueError("Expected prime modulus for " + "Number Theoretic Transform") + + a = [as_int(x) % p for x in seq] + + n = len(a) + if n < 1: + return a + + b = n.bit_length() - 1 + if n&(n - 1): + b += 1 + n = 2**b + + if (p - 1) % n: + raise ValueError("Expected prime modulus of the form (m*2**k + 1)") + + a += [0]*(n - len(a)) + for i in range(1, n): + j = int(ibin(i, b, str=True)[::-1], 2) + if i < j: + a[i], a[j] = a[j], a[i] + + pr = primitive_root(p) + + rt = pow(pr, (p - 1) // n, p) + if inverse: + rt = pow(rt, p - 2, p) + + w = [1]*(n // 2) + for i in range(1, n // 2): + w[i] = w[i - 1]*rt % p + + h = 2 + while h <= n: + hf, ut = h // 2, n // h + for i in range(0, n, h): + for j in range(hf): + u, v = a[i + j], a[i + j + hf]*w[ut * j] + a[i + j], a[i + j + hf] = (u + v) % p, (u - v) % p + h *= 2 + + if inverse: + rv = pow(n, p - 2, p) + a = [x*rv % p for x in a] + + return a + + +def ntt(seq, prime): + r""" + Performs the Number Theoretic Transform (**NTT**), which specializes the + Discrete Fourier Transform (**DFT**) over quotient ring `Z/pZ` for prime + `p` instead of complex numbers `C`. + + The sequence is automatically padded to the right with zeros, as the + *radix-2 NTT* requires the number of sample points to be a power of 2. + + Parameters + ========== + + seq : iterable + The sequence on which **DFT** is to be applied. + prime : Integer + Prime modulus of the form `(m 2^k + 1)` to be used for performing + **NTT** on the sequence. + + Examples + ======== + + >>> from sympy import ntt, intt + >>> ntt([1, 2, 3, 4], prime=3*2**8 + 1) + [10, 643, 767, 122] + >>> intt(_, 3*2**8 + 1) + [1, 2, 3, 4] + >>> intt([1, 2, 3, 4], prime=3*2**8 + 1) + [387, 415, 384, 353] + >>> ntt(_, prime=3*2**8 + 1) + [1, 2, 3, 4] + + References + ========== + + .. [1] http://www.apfloat.org/ntt.html + .. [2] https://mathworld.wolfram.com/NumberTheoreticTransform.html + .. [3] https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general%29 + + """ + + return _number_theoretic_transform(seq, prime=prime) + + +def intt(seq, prime): + return _number_theoretic_transform(seq, prime=prime, inverse=True) + +intt.__doc__ = ntt.__doc__ + + +#----------------------------------------------------------------------------# +# # +# Walsh Hadamard Transform # +# # +#----------------------------------------------------------------------------# + +def _walsh_hadamard_transform(seq, inverse=False): + """Utility function for the Walsh Hadamard Transform""" + + if not iterable(seq): + raise TypeError("Expected a sequence of coefficients " + "for Walsh Hadamard Transform") + + a = [sympify(arg) for arg in seq] + n = len(a) + if n < 2: + return a + + if n&(n - 1): + n = 2**n.bit_length() + + a += [S.Zero]*(n - len(a)) + h = 2 + while h <= n: + hf = h // 2 + for i in range(0, n, h): + for j in range(hf): + u, v = a[i + j], a[i + j + hf] + a[i + j], a[i + j + hf] = u + v, u - v + h *= 2 + + if inverse: + a = [x/n for x in a] + + return a + + +def fwht(seq): + r""" + Performs the Walsh Hadamard Transform (**WHT**), and uses Hadamard + ordering for the sequence. + + The sequence is automatically padded to the right with zeros, as the + *radix-2 FWHT* requires the number of sample points to be a power of 2. + + Parameters + ========== + + seq : iterable + The sequence on which WHT is to be applied. + + Examples + ======== + + >>> from sympy import fwht, ifwht + >>> fwht([4, 2, 2, 0, 0, 2, -2, 0]) + [8, 0, 8, 0, 8, 8, 0, 0] + >>> ifwht(_) + [4, 2, 2, 0, 0, 2, -2, 0] + + >>> ifwht([19, -1, 11, -9, -7, 13, -15, 5]) + [2, 0, 4, 0, 3, 10, 0, 0] + >>> fwht(_) + [19, -1, 11, -9, -7, 13, -15, 5] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hadamard_transform + .. [2] https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform + + """ + + return _walsh_hadamard_transform(seq) + + +def ifwht(seq): + return _walsh_hadamard_transform(seq, inverse=True) + +ifwht.__doc__ = fwht.__doc__ + + +#----------------------------------------------------------------------------# +# # +# Mobius Transform for Subset Lattice # +# # +#----------------------------------------------------------------------------# + +def _mobius_transform(seq, sgn, subset): + r"""Utility function for performing Mobius Transform using + Yate's Dynamic Programming method""" + + if not iterable(seq): + raise TypeError("Expected a sequence of coefficients") + + a = [sympify(arg) for arg in seq] + + n = len(a) + if n < 2: + return a + + if n&(n - 1): + n = 2**n.bit_length() + + a += [S.Zero]*(n - len(a)) + + if subset: + i = 1 + while i < n: + for j in range(n): + if j & i: + a[j] += sgn*a[j ^ i] + i *= 2 + + else: + i = 1 + while i < n: + for j in range(n): + if j & i: + continue + a[j] += sgn*a[j ^ i] + i *= 2 + + return a + + +def mobius_transform(seq, subset=True): + r""" + Performs the Mobius Transform for subset lattice with indices of + sequence as bitmasks. + + The indices of each argument, considered as bit strings, correspond + to subsets of a finite set. + + The sequence is automatically padded to the right with zeros, as the + definition of subset/superset based on bitmasks (indices) requires + the size of sequence to be a power of 2. + + Parameters + ========== + + seq : iterable + The sequence on which Mobius Transform is to be applied. + subset : bool + Specifies if Mobius Transform is applied by enumerating subsets + or supersets of the given set. + + Examples + ======== + + >>> from sympy import symbols + >>> from sympy import mobius_transform, inverse_mobius_transform + >>> x, y, z = symbols('x y z') + + >>> mobius_transform([x, y, z]) + [x, x + y, x + z, x + y + z] + >>> inverse_mobius_transform(_) + [x, y, z, 0] + + >>> mobius_transform([x, y, z], subset=False) + [x + y + z, y, z, 0] + >>> inverse_mobius_transform(_, subset=False) + [x, y, z, 0] + + >>> mobius_transform([1, 2, 3, 4]) + [1, 3, 4, 10] + >>> inverse_mobius_transform(_) + [1, 2, 3, 4] + >>> mobius_transform([1, 2, 3, 4], subset=False) + [10, 6, 7, 4] + >>> inverse_mobius_transform(_, subset=False) + [1, 2, 3, 4] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula + .. [2] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf + .. [3] https://arxiv.org/pdf/1211.0189.pdf + + """ + + return _mobius_transform(seq, sgn=+1, subset=subset) + +def inverse_mobius_transform(seq, subset=True): + return _mobius_transform(seq, sgn=-1, subset=subset) + +inverse_mobius_transform.__doc__ = mobius_transform.__doc__ diff --git a/lib/python3.11/site-packages/sympy/external/__init__.py b/lib/python3.11/site-packages/sympy/external/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..549b4b96cdce0ee4d31960e89cb9dc26af0e105d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/__init__.py @@ -0,0 +1,20 @@ +""" +Unified place for determining if external dependencies are installed or not. + +You should import all external modules using the import_module() function. + +For example + +>>> from sympy.external import import_module +>>> numpy = import_module('numpy') + +If the resulting library is not installed, or if the installed version +is less than a given minimum version, the function will return None. +Otherwise, it will return the library. See the docstring of +import_module() for more information. + +""" + +from sympy.external.importtools import import_module + +__all__ = ['import_module'] diff --git a/lib/python3.11/site-packages/sympy/external/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..b065ce6a319454e628bf93b7b77136c39ddb250e Binary files /dev/null and b/lib/python3.11/site-packages/sympy/external/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/external/__pycache__/gmpy.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/__pycache__/gmpy.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..2cc463a6e02d998e9906c3e0b87a39348308a388 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/external/__pycache__/gmpy.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/external/__pycache__/importtools.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/__pycache__/importtools.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..3fd91990ee6b73f64a1a8525ea5f283d7c43694d Binary files /dev/null and b/lib/python3.11/site-packages/sympy/external/__pycache__/importtools.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/external/__pycache__/ntheory.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/__pycache__/ntheory.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..05a0e8ef86f60516ab4e9d4a4b8c6b650a118e1d Binary files /dev/null and b/lib/python3.11/site-packages/sympy/external/__pycache__/ntheory.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/external/__pycache__/pythonmpq.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/__pycache__/pythonmpq.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..49668928769db3195631e8cc3ae1a9287050044a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/external/__pycache__/pythonmpq.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/external/gmpy.py b/lib/python3.11/site-packages/sympy/external/gmpy.py new file mode 100644 index 0000000000000000000000000000000000000000..b28da521a620b6c04e5302b5e7f360e00b3099cc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/gmpy.py @@ -0,0 +1,341 @@ +import os +from ctypes import c_long, sizeof +from functools import reduce +from typing import Tuple as tTuple, Type +from warnings import warn + +from sympy.external import import_module + +from .pythonmpq import PythonMPQ + +from .ntheory import ( + bit_scan1 as python_bit_scan1, + bit_scan0 as python_bit_scan0, + remove as python_remove, + factorial as python_factorial, + sqrt as python_sqrt, + sqrtrem as python_sqrtrem, + gcd as python_gcd, + lcm as python_lcm, + gcdext as python_gcdext, + is_square as python_is_square, + invert as python_invert, + legendre as python_legendre, + jacobi as python_jacobi, + kronecker as python_kronecker, + iroot as python_iroot, + is_fermat_prp as python_is_fermat_prp, + is_euler_prp as python_is_euler_prp, + is_strong_prp as python_is_strong_prp, + is_fibonacci_prp as python_is_fibonacci_prp, + is_lucas_prp as python_is_lucas_prp, + is_selfridge_prp as python_is_selfridge_prp, + is_strong_lucas_prp as python_is_strong_lucas_prp, + is_strong_selfridge_prp as python_is_strong_selfridge_prp, + is_bpsw_prp as python_is_bpsw_prp, + is_strong_bpsw_prp as python_is_strong_bpsw_prp, +) + + +__all__ = [ + # GROUND_TYPES is either 'gmpy' or 'python' depending on which is used. If + # gmpy is installed then it will be used unless the environment variable + # SYMPY_GROUND_TYPES is set to something other than 'auto', 'gmpy', or + # 'gmpy2'. + 'GROUND_TYPES', + + # If HAS_GMPY is 0, no supported version of gmpy is available. Otherwise, + # HAS_GMPY will be 2 for gmpy2 if GROUND_TYPES is 'gmpy'. It used to be + # possible for HAS_GMPY to be 1 for gmpy but gmpy is no longer supported. + 'HAS_GMPY', + + # SYMPY_INTS is a tuple containing the base types for valid integer types. + # This is either (int,) or (int, type(mpz(0))) depending on GROUND_TYPES. + 'SYMPY_INTS', + + # MPQ is either gmpy.mpq or the Python equivalent from + # sympy.external.pythonmpq + 'MPQ', + + # MPZ is either gmpy.mpz or int. + 'MPZ', + + 'bit_scan1', + 'bit_scan0', + 'remove', + 'factorial', + 'sqrt', + 'is_square', + 'sqrtrem', + 'gcd', + 'lcm', + 'gcdext', + 'invert', + 'legendre', + 'jacobi', + 'kronecker', + 'iroot', + 'is_fermat_prp', + 'is_euler_prp', + 'is_strong_prp', + 'is_fibonacci_prp', + 'is_lucas_prp', + 'is_selfridge_prp', + 'is_strong_lucas_prp', + 'is_strong_selfridge_prp', + 'is_bpsw_prp', + 'is_strong_bpsw_prp', +] + + +# +# Tested python-flint version. Future versions might work but we will only use +# them if explicitly requested by SYMPY_GROUND_TYPES=flint. +# +_PYTHON_FLINT_VERSION_NEEDED = ["0.6", "0.7", "0.8", "0.9"] + + +def _flint_version_okay(flint_version): + major, minor = flint_version.split('.')[:2] + flint_ver = f'{major}.{minor}' + return flint_ver in _PYTHON_FLINT_VERSION_NEEDED + +# +# We will only use gmpy2 >= 2.0.0 +# +_GMPY2_MIN_VERSION = '2.0.0' + + +def _get_flint(sympy_ground_types): + if sympy_ground_types not in ('auto', 'flint'): + return None + + try: + import flint + # Earlier versions of python-flint may not have __version__. + from flint import __version__ as _flint_version + except ImportError: + if sympy_ground_types == 'flint': + warn("SYMPY_GROUND_TYPES was set to flint but python-flint is not " + "installed. Falling back to other ground types.") + return None + + if _flint_version_okay(_flint_version): + return flint + elif sympy_ground_types == 'auto': + return None + else: + warn(f"Using python-flint {_flint_version} because SYMPY_GROUND_TYPES " + f"is set to flint but this version of SymPy is only tested " + f"with python-flint versions {_PYTHON_FLINT_VERSION_NEEDED}.") + return flint + + +def _get_gmpy2(sympy_ground_types): + if sympy_ground_types not in ('auto', 'gmpy', 'gmpy2'): + return None + + gmpy = import_module('gmpy2', min_module_version=_GMPY2_MIN_VERSION, + module_version_attr='version', module_version_attr_call_args=()) + + if sympy_ground_types != 'auto' and gmpy is None: + warn("gmpy2 library is not installed, switching to 'python' ground types") + + return gmpy + + +# +# SYMPY_GROUND_TYPES can be flint, gmpy, gmpy2, python or auto (default) +# +_SYMPY_GROUND_TYPES = os.environ.get('SYMPY_GROUND_TYPES', 'auto').lower() +_flint = None +_gmpy = None + +# +# First handle auto-detection of flint/gmpy2. We will prefer flint if available +# or otherwise gmpy2 if available and then lastly the python types. +# +if _SYMPY_GROUND_TYPES in ('auto', 'flint'): + _flint = _get_flint(_SYMPY_GROUND_TYPES) + if _flint is not None: + _SYMPY_GROUND_TYPES = 'flint' + else: + _SYMPY_GROUND_TYPES = 'auto' + +if _SYMPY_GROUND_TYPES in ('auto', 'gmpy', 'gmpy2'): + _gmpy = _get_gmpy2(_SYMPY_GROUND_TYPES) + if _gmpy is not None: + _SYMPY_GROUND_TYPES = 'gmpy' + else: + _SYMPY_GROUND_TYPES = 'python' + +if _SYMPY_GROUND_TYPES not in ('flint', 'gmpy', 'python'): + warn("SYMPY_GROUND_TYPES environment variable unrecognised. " + "Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.") + _SYMPY_GROUND_TYPES = 'python' + +# +# At this point _SYMPY_GROUND_TYPES is either flint, gmpy or python. The blocks +# below define the values exported by this module in each case. +# + +# +# In gmpy2 and flint, there are functions that take a long (or unsigned long) +# argument. That is, it is not possible to input a value larger than that. +# +LONG_MAX = (1 << (8*sizeof(c_long) - 1)) - 1 + +# +# Type checkers are confused by what SYMPY_INTS is. There may be a better type +# hint for this like Type[Integral] or something. +# +SYMPY_INTS: tTuple[Type, ...] + +if _SYMPY_GROUND_TYPES == 'gmpy': + + assert _gmpy is not None + + flint = None + gmpy = _gmpy + + HAS_GMPY = 2 + GROUND_TYPES = 'gmpy' + SYMPY_INTS = (int, type(gmpy.mpz(0))) + MPZ = gmpy.mpz + MPQ = gmpy.mpq + + bit_scan1 = gmpy.bit_scan1 + bit_scan0 = gmpy.bit_scan0 + remove = gmpy.remove + factorial = gmpy.fac + sqrt = gmpy.isqrt + is_square = gmpy.is_square + sqrtrem = gmpy.isqrt_rem + gcd = gmpy.gcd + lcm = gmpy.lcm + gcdext = gmpy.gcdext + invert = gmpy.invert + legendre = gmpy.legendre + jacobi = gmpy.jacobi + kronecker = gmpy.kronecker + + def iroot(x, n): + # In the latest gmpy2, the threshold for n is ULONG_MAX, + # but adjust to the older one. + if n <= LONG_MAX: + return gmpy.iroot(x, n) + return python_iroot(x, n) + + is_fermat_prp = gmpy.is_fermat_prp + is_euler_prp = gmpy.is_euler_prp + is_strong_prp = gmpy.is_strong_prp + is_fibonacci_prp = gmpy.is_fibonacci_prp + is_lucas_prp = gmpy.is_lucas_prp + is_selfridge_prp = gmpy.is_selfridge_prp + is_strong_lucas_prp = gmpy.is_strong_lucas_prp + is_strong_selfridge_prp = gmpy.is_strong_selfridge_prp + is_bpsw_prp = gmpy.is_bpsw_prp + is_strong_bpsw_prp = gmpy.is_strong_bpsw_prp + +elif _SYMPY_GROUND_TYPES == 'flint': + + assert _flint is not None + + flint = _flint + gmpy = None + + HAS_GMPY = 0 + GROUND_TYPES = 'flint' + SYMPY_INTS = (int, flint.fmpz) # type: ignore + MPZ = flint.fmpz # type: ignore + MPQ = flint.fmpq # type: ignore + + bit_scan1 = python_bit_scan1 + bit_scan0 = python_bit_scan0 + remove = python_remove + factorial = python_factorial + + def sqrt(x): + return flint.fmpz(x).isqrt() + + def is_square(x): + if x < 0: + return False + return flint.fmpz(x).sqrtrem()[1] == 0 + + def sqrtrem(x): + return flint.fmpz(x).sqrtrem() + + def gcd(*args): + return reduce(flint.fmpz.gcd, args, flint.fmpz(0)) + + def lcm(*args): + return reduce(flint.fmpz.lcm, args, flint.fmpz(1)) + + gcdext = python_gcdext + invert = python_invert + legendre = python_legendre + + def jacobi(x, y): + if y <= 0 or not y % 2: + raise ValueError("y should be an odd positive integer") + return flint.fmpz(x).jacobi(y) + + kronecker = python_kronecker + + def iroot(x, n): + if n <= LONG_MAX: + y = flint.fmpz(x).root(n) + return y, y**n == x + return python_iroot(x, n) + + is_fermat_prp = python_is_fermat_prp + is_euler_prp = python_is_euler_prp + is_strong_prp = python_is_strong_prp + is_fibonacci_prp = python_is_fibonacci_prp + is_lucas_prp = python_is_lucas_prp + is_selfridge_prp = python_is_selfridge_prp + is_strong_lucas_prp = python_is_strong_lucas_prp + is_strong_selfridge_prp = python_is_strong_selfridge_prp + is_bpsw_prp = python_is_bpsw_prp + is_strong_bpsw_prp = python_is_strong_bpsw_prp + +elif _SYMPY_GROUND_TYPES == 'python': + + flint = None + gmpy = None + + HAS_GMPY = 0 + GROUND_TYPES = 'python' + SYMPY_INTS = (int,) + MPZ = int + MPQ = PythonMPQ + + bit_scan1 = python_bit_scan1 + bit_scan0 = python_bit_scan0 + remove = python_remove + factorial = python_factorial + sqrt = python_sqrt + is_square = python_is_square + sqrtrem = python_sqrtrem + gcd = python_gcd + lcm = python_lcm + gcdext = python_gcdext + invert = python_invert + legendre = python_legendre + jacobi = python_jacobi + kronecker = python_kronecker + iroot = python_iroot + is_fermat_prp = python_is_fermat_prp + is_euler_prp = python_is_euler_prp + is_strong_prp = python_is_strong_prp + is_fibonacci_prp = python_is_fibonacci_prp + is_lucas_prp = python_is_lucas_prp + is_selfridge_prp = python_is_selfridge_prp + is_strong_lucas_prp = python_is_strong_lucas_prp + is_strong_selfridge_prp = python_is_strong_selfridge_prp + is_bpsw_prp = python_is_bpsw_prp + is_strong_bpsw_prp = python_is_strong_bpsw_prp + +else: + assert False diff --git a/lib/python3.11/site-packages/sympy/external/importtools.py b/lib/python3.11/site-packages/sympy/external/importtools.py new file mode 100644 index 0000000000000000000000000000000000000000..5008b3dd4634d3cee10744a0a92b1204051f07cc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/importtools.py @@ -0,0 +1,187 @@ +"""Tools to assist importing optional external modules.""" + +import sys +import re + +# Override these in the module to change the default warning behavior. +# For example, you might set both to False before running the tests so that +# warnings are not printed to the console, or set both to True for debugging. + +WARN_NOT_INSTALLED = None # Default is False +WARN_OLD_VERSION = None # Default is True + + +def __sympy_debug(): + # helper function from sympy/__init__.py + # We don't just import SYMPY_DEBUG from that file because we don't want to + # import all of SymPy just to use this module. + import os + debug_str = os.getenv('SYMPY_DEBUG', 'False') + if debug_str in ('True', 'False'): + return eval(debug_str) + else: + raise RuntimeError("unrecognized value for SYMPY_DEBUG: %s" % + debug_str) + +if __sympy_debug(): + WARN_OLD_VERSION = True + WARN_NOT_INSTALLED = True + + +_component_re = re.compile(r'(\d+ | [a-z]+ | \.)', re.VERBOSE) + +def version_tuple(vstring): + # Parse a version string to a tuple e.g. '1.2' -> (1, 2) + # Simplified from distutils.version.LooseVersion which was deprecated in + # Python 3.10. + components = [] + for x in _component_re.split(vstring): + if x and x != '.': + try: + x = int(x) + except ValueError: + pass + components.append(x) + return tuple(components) + + +def import_module(module, min_module_version=None, min_python_version=None, + warn_not_installed=None, warn_old_version=None, + module_version_attr='__version__', module_version_attr_call_args=None, + import_kwargs={}, catch=()): + """ + Import and return a module if it is installed. + + If the module is not installed, it returns None. + + A minimum version for the module can be given as the keyword argument + min_module_version. This should be comparable against the module version. + By default, module.__version__ is used to get the module version. To + override this, set the module_version_attr keyword argument. If the + attribute of the module to get the version should be called (e.g., + module.version()), then set module_version_attr_call_args to the args such + that module.module_version_attr(*module_version_attr_call_args) returns the + module's version. + + If the module version is less than min_module_version using the Python < + comparison, None will be returned, even if the module is installed. You can + use this to keep from importing an incompatible older version of a module. + + You can also specify a minimum Python version by using the + min_python_version keyword argument. This should be comparable against + sys.version_info. + + If the keyword argument warn_not_installed is set to True, the function will + emit a UserWarning when the module is not installed. + + If the keyword argument warn_old_version is set to True, the function will + emit a UserWarning when the library is installed, but cannot be imported + because of the min_module_version or min_python_version options. + + Note that because of the way warnings are handled, a warning will be + emitted for each module only once. You can change the default warning + behavior by overriding the values of WARN_NOT_INSTALLED and WARN_OLD_VERSION + in sympy.external.importtools. By default, WARN_NOT_INSTALLED is False and + WARN_OLD_VERSION is True. + + This function uses __import__() to import the module. To pass additional + options to __import__(), use the import_kwargs keyword argument. For + example, to import a submodule A.B, you must pass a nonempty fromlist option + to __import__. See the docstring of __import__(). + + This catches ImportError to determine if the module is not installed. To + catch additional errors, pass them as a tuple to the catch keyword + argument. + + Examples + ======== + + >>> from sympy.external import import_module + + >>> numpy = import_module('numpy') + + >>> numpy = import_module('numpy', min_python_version=(2, 7), + ... warn_old_version=False) + + >>> numpy = import_module('numpy', min_module_version='1.5', + ... warn_old_version=False) # numpy.__version__ is a string + + >>> # gmpy does not have __version__, but it does have gmpy.version() + + >>> gmpy = import_module('gmpy', min_module_version='1.14', + ... module_version_attr='version', module_version_attr_call_args=(), + ... warn_old_version=False) + + >>> # To import a submodule, you must pass a nonempty fromlist to + >>> # __import__(). The values do not matter. + >>> p3 = import_module('mpl_toolkits.mplot3d', + ... import_kwargs={'fromlist':['something']}) + + >>> # matplotlib.pyplot can raise RuntimeError when the display cannot be opened + >>> matplotlib = import_module('matplotlib', + ... import_kwargs={'fromlist':['pyplot']}, catch=(RuntimeError,)) + + """ + # keyword argument overrides default, and global variable overrides + # keyword argument. + warn_old_version = (WARN_OLD_VERSION if WARN_OLD_VERSION is not None + else warn_old_version or True) + warn_not_installed = (WARN_NOT_INSTALLED if WARN_NOT_INSTALLED is not None + else warn_not_installed or False) + + import warnings + + # Check Python first so we don't waste time importing a module we can't use + if min_python_version: + if sys.version_info < min_python_version: + if warn_old_version: + warnings.warn("Python version is too old to use %s " + "(%s or newer required)" % ( + module, '.'.join(map(str, min_python_version))), + UserWarning, stacklevel=2) + return + + try: + mod = __import__(module, **import_kwargs) + + ## there's something funny about imports with matplotlib and py3k. doing + ## from matplotlib import collections + ## gives python's stdlib collections module. explicitly re-importing + ## the module fixes this. + from_list = import_kwargs.get('fromlist', ()) + for submod in from_list: + if submod == 'collections' and mod.__name__ == 'matplotlib': + __import__(module + '.' + submod) + except ImportError: + if warn_not_installed: + warnings.warn("%s module is not installed" % module, UserWarning, + stacklevel=2) + return + except catch as e: + if warn_not_installed: + warnings.warn( + "%s module could not be used (%s)" % (module, repr(e)), + stacklevel=2) + return + + if min_module_version: + modversion = getattr(mod, module_version_attr) + if module_version_attr_call_args is not None: + modversion = modversion(*module_version_attr_call_args) + if version_tuple(modversion) < version_tuple(min_module_version): + if warn_old_version: + # Attempt to create a pretty string version of the version + if isinstance(min_module_version, str): + verstr = min_module_version + elif isinstance(min_module_version, (tuple, list)): + verstr = '.'.join(map(str, min_module_version)) + else: + # Either don't know what this is. Hopefully + # it's something that has a nice str version, like an int. + verstr = str(min_module_version) + warnings.warn("%s version is too old to use " + "(%s or newer required)" % (module, verstr), + UserWarning, stacklevel=2) + return + + return mod diff --git a/lib/python3.11/site-packages/sympy/external/ntheory.py b/lib/python3.11/site-packages/sympy/external/ntheory.py new file mode 100644 index 0000000000000000000000000000000000000000..296b1331a9e05cd7df386f8e0bfecb1a103aba79 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/ntheory.py @@ -0,0 +1,637 @@ +# sympy.external.ntheory +# +# This module provides pure Python implementations of some number theory +# functions that are alternately used from gmpy2 if it is installed. + +import sys +import math + +import mpmath.libmp as mlib + + +_small_trailing = [0] * 256 +for j in range(1, 8): + _small_trailing[1 << j :: 1 << (j + 1)] = [j] * (1 << (7 - j)) + + +def bit_scan1(x, n=0): + if not x: + return + x = abs(x >> n) + low_byte = x & 0xFF + if low_byte: + return _small_trailing[low_byte] + n + + t = 8 + n + x >>= 8 + # 2**m is quick for z up through 2**30 + z = x.bit_length() - 1 + if x == 1 << z: + return z + t + + if z < 300: + # fixed 8-byte reduction + while not x & 0xFF: + x >>= 8 + t += 8 + else: + # binary reduction important when there might be a large + # number of trailing 0s + p = z >> 1 + while not x & 0xFF: + while x & ((1 << p) - 1): + p >>= 1 + x >>= p + t += p + return t + _small_trailing[x & 0xFF] + + +def bit_scan0(x, n=0): + return bit_scan1(x + (1 << n), n) + + +def remove(x, f): + if f < 2: + raise ValueError("factor must be > 1") + if x == 0: + return 0, 0 + if f == 2: + b = bit_scan1(x) + return x >> b, b + m = 0 + y, rem = divmod(x, f) + while not rem: + x = y + m += 1 + if m > 5: + pow_list = [f**2] + while pow_list: + _f = pow_list[-1] + y, rem = divmod(x, _f) + if not rem: + m += 1 << len(pow_list) + x = y + pow_list.append(_f**2) + else: + pow_list.pop() + y, rem = divmod(x, f) + return x, m + + +def factorial(x): + """Return x!.""" + return int(mlib.ifac(int(x))) + + +def sqrt(x): + """Integer square root of x.""" + return int(mlib.isqrt(int(x))) + + +def sqrtrem(x): + """Integer square root of x and remainder.""" + s, r = mlib.sqrtrem(int(x)) + return (int(s), int(r)) + + +if sys.version_info[:2] >= (3, 9): + # As of Python 3.9 these can take multiple arguments + gcd = math.gcd + lcm = math.lcm + +else: + # Until python 3.8 is no longer supported + from functools import reduce + + + def gcd(*args): + """gcd of multiple integers.""" + return reduce(math.gcd, args, 0) + + + def lcm(*args): + """lcm of multiple integers.""" + if 0 in args: + return 0 + return reduce(lambda x, y: x*y//math.gcd(x, y), args, 1) + + +def _sign(n): + if n < 0: + return -1, -n + return 1, n + + +def gcdext(a, b): + if not a or not b: + g = abs(a) or abs(b) + if not g: + return (0, 0, 0) + return (g, a // g, b // g) + + x_sign, a = _sign(a) + y_sign, b = _sign(b) + x, r = 1, 0 + y, s = 0, 1 + + while b: + q, c = divmod(a, b) + a, b = b, c + x, r = r, x - q*r + y, s = s, y - q*s + + return (a, x * x_sign, y * y_sign) + + +def is_square(x): + """Return True if x is a square number.""" + if x < 0: + return False + + # Note that the possible values of y**2 % n for a given n are limited. + # For example, when n=4, y**2 % n can only take 0 or 1. + # In other words, if x % 4 is 2 or 3, then x is not a square number. + # Mathematically, it determines if it belongs to the set {y**2 % n}, + # but implementationally, it can be realized as a logical conjunction + # with an n-bit integer. + # see https://mersenneforum.org/showpost.php?p=110896 + # def magic(n): + # s = {y**2 % n for y in range(n)} + # s = set(range(n)) - s + # return sum(1 << bit for bit in s) + # >>> print(hex(magic(128))) + # 0xfdfdfdedfdfdfdecfdfdfdedfdfcfdec + # >>> print(hex(magic(99))) + # 0x5f6f9ffb6fb7ddfcb75befdec + # >>> print(hex(magic(91))) + # 0x6fd1bfcfed5f3679d3ebdec + # >>> print(hex(magic(85))) + # 0xdef9ae771ffe3b9d67dec + if 0xfdfdfdedfdfdfdecfdfdfdedfdfcfdec & (1 << (x & 127)): + return False # e.g. 2, 3 + m = x % 765765 # 765765 = 99 * 91 * 85 + if 0x5f6f9ffb6fb7ddfcb75befdec & (1 << (m % 99)): + return False # e.g. 17, 68 + if 0x6fd1bfcfed5f3679d3ebdec & (1 << (m % 91)): + return False # e.g. 97, 388 + if 0xdef9ae771ffe3b9d67dec & (1 << (m % 85)): + return False # e.g. 793, 1408 + return mlib.sqrtrem(int(x))[1] == 0 + + +def invert(x, m): + """Modular inverse of x modulo m. + + Returns y such that x*y == 1 mod m. + + Uses ``math.pow`` but reproduces the behaviour of ``gmpy2.invert`` + which raises ZeroDivisionError if no inverse exists. + """ + try: + return pow(x, -1, m) + except ValueError: + raise ZeroDivisionError("invert() no inverse exists") + + +def legendre(x, y): + """Legendre symbol (x / y). + + Following the implementation of gmpy2, + the error is raised only when y is an even number. + """ + if y <= 0 or not y % 2: + raise ValueError("y should be an odd prime") + x %= y + if not x: + return 0 + if pow(x, (y - 1) // 2, y) == 1: + return 1 + return -1 + + +def jacobi(x, y): + """Jacobi symbol (x / y).""" + if y <= 0 or not y % 2: + raise ValueError("y should be an odd positive integer") + x %= y + if not x: + return int(y == 1) + if y == 1 or x == 1: + return 1 + if gcd(x, y) != 1: + return 0 + j = 1 + while x != 0: + while x % 2 == 0 and x > 0: + x >>= 1 + if y % 8 in [3, 5]: + j = -j + x, y = y, x + if x % 4 == y % 4 == 3: + j = -j + x %= y + return j + + +def kronecker(x, y): + """Kronecker symbol (x / y).""" + if gcd(x, y) != 1: + return 0 + if y == 0: + return 1 + sign = -1 if y < 0 and x < 0 else 1 + y = abs(y) + s = bit_scan1(y) + y >>= s + if s % 2 and x % 8 in [3, 5]: + sign = -sign + return sign * jacobi(x, y) + + +def iroot(y, n): + if y < 0: + raise ValueError("y must be nonnegative") + if n < 1: + raise ValueError("n must be positive") + if y in (0, 1): + return y, True + if n == 1: + return y, True + if n == 2: + x, rem = mlib.sqrtrem(y) + return int(x), not rem + if n >= y.bit_length(): + return 1, False + # Get initial estimate for Newton's method. Care must be taken to + # avoid overflow + try: + guess = int(y**(1./n) + 0.5) + except OverflowError: + exp = math.log2(y)/n + if exp > 53: + shift = int(exp - 53) + guess = int(2.0**(exp - shift) + 1) << shift + else: + guess = int(2.0**exp) + if guess > 2**50: + # Newton iteration + xprev, x = -1, guess + while 1: + t = x**(n - 1) + xprev, x = x, ((n - 1)*x + y//t)//n + if abs(x - xprev) < 2: + break + else: + x = guess + # Compensate + t = x**n + while t < y: + x += 1 + t = x**n + while t > y: + x -= 1 + t = x**n + return x, t == y + + +def is_fermat_prp(n, a): + if a < 2: + raise ValueError("is_fermat_prp() requires 'a' greater than or equal to 2") + if n < 1: + raise ValueError("is_fermat_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + a %= n + if gcd(n, a) != 1: + raise ValueError("is_fermat_prp() requires gcd(n,a) == 1") + return pow(a, n - 1, n) == 1 + + +def is_euler_prp(n, a): + if a < 2: + raise ValueError("is_euler_prp() requires 'a' greater than or equal to 2") + if n < 1: + raise ValueError("is_euler_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + a %= n + if gcd(n, a) != 1: + raise ValueError("is_euler_prp() requires gcd(n,a) == 1") + return pow(a, n >> 1, n) == jacobi(a, n) % n + + +def _is_strong_prp(n, a): + s = bit_scan1(n - 1) + a = pow(a, n >> s, n) + if a == 1 or a == n - 1: + return True + for _ in range(s - 1): + a = pow(a, 2, n) + if a == n - 1: + return True + if a == 1: + return False + return False + + +def is_strong_prp(n, a): + if a < 2: + raise ValueError("is_strong_prp() requires 'a' greater than or equal to 2") + if n < 1: + raise ValueError("is_strong_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + a %= n + if gcd(n, a) != 1: + raise ValueError("is_strong_prp() requires gcd(n,a) == 1") + return _is_strong_prp(n, a) + + +def _lucas_sequence(n, P, Q, k): + r"""Return the modular Lucas sequence (U_k, V_k, Q_k). + + Explanation + =========== + + Given a Lucas sequence defined by P, Q, returns the kth values for + U and V, along with Q^k, all modulo n. This is intended for use with + possibly very large values of n and k, where the combinatorial functions + would be completely unusable. + + .. math :: + U_k = \begin{cases} + 0 & \text{if } k = 0\\ + 1 & \text{if } k = 1\\ + PU_{k-1} - QU_{k-2} & \text{if } k > 1 + \end{cases}\\ + V_k = \begin{cases} + 2 & \text{if } k = 0\\ + P & \text{if } k = 1\\ + PV_{k-1} - QV_{k-2} & \text{if } k > 1 + \end{cases} + + The modular Lucas sequences are used in numerous places in number theory, + especially in the Lucas compositeness tests and the various n + 1 proofs. + + Parameters + ========== + + n : int + n is an odd number greater than or equal to 3 + P : int + Q : int + D determined by D = P**2 - 4*Q is non-zero + k : int + k is a nonnegative integer + + Returns + ======= + + U, V, Qk : (int, int, int) + `(U_k \bmod{n}, V_k \bmod{n}, Q^k \bmod{n})` + + Examples + ======== + + >>> from sympy.external.ntheory import _lucas_sequence + >>> N = 10**2000 + 4561 + >>> sol = U, V, Qk = _lucas_sequence(N, 3, 1, N//2); sol + (0, 2, 1) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Lucas_sequence + + """ + if k == 0: + return (0, 2, 1) + D = P**2 - 4*Q + U = 1 + V = P + Qk = Q % n + if Q == 1: + # Optimization for extra strong tests. + for b in bin(k)[3:]: + U = (U*V) % n + V = (V*V - 2) % n + if b == "1": + U, V = U*P + V, V*P + U*D + if U & 1: + U += n + if V & 1: + V += n + U, V = U >> 1, V >> 1 + elif P == 1 and Q == -1: + # Small optimization for 50% of Selfridge parameters. + for b in bin(k)[3:]: + U = (U*V) % n + if Qk == 1: + V = (V*V - 2) % n + else: + V = (V*V + 2) % n + Qk = 1 + if b == "1": + # new_U = (U + V) // 2 + # new_V = (5*U + V) // 2 = 2*U + new_U + U, V = U + V, U << 1 + if U & 1: + U += n + U >>= 1 + V += U + Qk = -1 + Qk %= n + elif P == 1: + for b in bin(k)[3:]: + U = (U*V) % n + V = (V*V - 2*Qk) % n + Qk *= Qk + if b == "1": + # new_U = (U + V) // 2 + # new_V = new_U - 2*Q*U + U, V = U + V, (Q*U) << 1 + if U & 1: + U += n + U >>= 1 + V = U - V + Qk *= Q + Qk %= n + else: + # The general case with any P and Q. + for b in bin(k)[3:]: + U = (U*V) % n + V = (V*V - 2*Qk) % n + Qk *= Qk + if b == "1": + U, V = U*P + V, V*P + U*D + if U & 1: + U += n + if V & 1: + V += n + U, V = U >> 1, V >> 1 + Qk *= Q + Qk %= n + return (U % n, V % n, Qk) + + +def is_fibonacci_prp(n, p, q): + d = p**2 - 4*q + if d == 0 or p <= 0 or q not in [1, -1]: + raise ValueError("invalid values for p,q in is_fibonacci_prp()") + if n < 1: + raise ValueError("is_fibonacci_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + return _lucas_sequence(n, p, q, n)[1] == p % n + + +def is_lucas_prp(n, p, q): + d = p**2 - 4*q + if d == 0: + raise ValueError("invalid values for p,q in is_lucas_prp()") + if n < 1: + raise ValueError("is_lucas_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + if gcd(n, q*d) not in [1, n]: + raise ValueError("is_lucas_prp() requires gcd(n,2*q*D) == 1") + return _lucas_sequence(n, p, q, n - jacobi(d, n))[0] == 0 + + +def _is_selfridge_prp(n): + """Lucas compositeness test with the Selfridge parameters for n. + + Explanation + =========== + + The Lucas compositeness test checks whether n is a prime number. + The test can be run with arbitrary parameters ``P`` and ``Q``, which also change the performance of the test. + So, which parameters are most effective for running the Lucas compositeness test? + As an algorithm for determining ``P`` and ``Q``, Selfridge proposed method A [1]_ page 1401 + (Since two methods were proposed, referred to simply as A and B in the paper, + we will refer to one of them as "method A"). + + method A fixes ``P = 1``. Then, ``D`` defined by ``D = P**2 - 4Q`` is varied from 5, -7, 9, -11, 13, and so on, + with the first ``D`` being ``jacobi(D, n) == -1``. Once ``D`` is determined, + ``Q`` is determined to be ``(P**2 - D)//4``. + + References + ========== + + .. [1] Robert Baillie, Samuel S. Wagstaff, Lucas Pseudoprimes, + Math. Comp. Vol 35, Number 152 (1980), pp. 1391-1417, + https://doi.org/10.1090%2FS0025-5718-1980-0583518-6 + http://mpqs.free.fr/LucasPseudoprimes.pdf + + """ + for D in range(5, 1_000_000, 2): + if D & 2: # if D % 4 == 3 + D = -D + j = jacobi(D, n) + if j == -1: + return _lucas_sequence(n, 1, (1-D) // 4, n + 1)[0] == 0 + if j == 0 and D % n: + return False + # When j == -1 is hard to find, suspect a square number + if D == 13 and is_square(n): + return False + raise ValueError("appropriate value for D cannot be found in is_selfridge_prp()") + + +def is_selfridge_prp(n): + if n < 1: + raise ValueError("is_selfridge_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + return _is_selfridge_prp(n) + + +def is_strong_lucas_prp(n, p, q): + D = p**2 - 4*q + if D == 0: + raise ValueError("invalid values for p,q in is_strong_lucas_prp()") + if n < 1: + raise ValueError("is_selfridge_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + if gcd(n, q*D) not in [1, n]: + raise ValueError("is_strong_lucas_prp() requires gcd(n,2*q*D) == 1") + j = jacobi(D, n) + s = bit_scan1(n - j) + U, V, Qk = _lucas_sequence(n, p, q, (n - j) >> s) + if U == 0 or V == 0: + return True + for _ in range(s - 1): + V = (V*V - 2*Qk) % n + if V == 0: + return True + Qk = pow(Qk, 2, n) + return False + + +def _is_strong_selfridge_prp(n): + for D in range(5, 1_000_000, 2): + if D & 2: # if D % 4 == 3 + D = -D + j = jacobi(D, n) + if j == -1: + s = bit_scan1(n + 1) + U, V, Qk = _lucas_sequence(n, 1, (1-D) // 4, (n + 1) >> s) + if U == 0 or V == 0: + return True + for _ in range(s - 1): + V = (V*V - 2*Qk) % n + if V == 0: + return True + Qk = pow(Qk, 2, n) + return False + if j == 0 and D % n: + return False + # When j == -1 is hard to find, suspect a square number + if D == 13 and is_square(n): + return False + raise ValueError("appropriate value for D cannot be found in is_strong_selfridge_prp()") + + +def is_strong_selfridge_prp(n): + if n < 1: + raise ValueError("is_strong_selfridge_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + return _is_strong_selfridge_prp(n) + + +def is_bpsw_prp(n): + if n < 1: + raise ValueError("is_bpsw_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + return _is_strong_prp(n, 2) and _is_selfridge_prp(n) + + +def is_strong_bpsw_prp(n): + if n < 1: + raise ValueError("is_strong_bpsw_prp() requires 'n' be greater than 0") + if n == 1: + return False + if n % 2 == 0: + return n == 2 + return _is_strong_prp(n, 2) and _is_strong_selfridge_prp(n) diff --git a/lib/python3.11/site-packages/sympy/external/pythonmpq.py b/lib/python3.11/site-packages/sympy/external/pythonmpq.py new file mode 100644 index 0000000000000000000000000000000000000000..b8efd18a40a75b8a4f4de444b0c10d6347dbca6a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/pythonmpq.py @@ -0,0 +1,341 @@ +""" +PythonMPQ: Rational number type based on Python integers. + +This class is intended as a pure Python fallback for when gmpy2 is not +installed. If gmpy2 is installed then its mpq type will be used instead. The +mpq type is around 20x faster. We could just use the stdlib Fraction class +here but that is slower: + + from fractions import Fraction + from sympy.external.pythonmpq import PythonMPQ + nums = range(1000) + dens = range(5, 1005) + rats = [Fraction(n, d) for n, d in zip(nums, dens)] + sum(rats) # <--- 24 milliseconds + rats = [PythonMPQ(n, d) for n, d in zip(nums, dens)] + sum(rats) # <--- 7 milliseconds + +Both mpq and Fraction have some awkward features like the behaviour of +division with // and %: + + >>> from fractions import Fraction + >>> Fraction(2, 3) % Fraction(1, 4) + 1/6 + +For the QQ domain we do not want this behaviour because there should be no +remainder when dividing rational numbers. SymPy does not make use of this +aspect of mpq when gmpy2 is installed. Since this class is a fallback for that +case we do not bother implementing e.g. __mod__ so that we can be sure we +are not using it when gmpy2 is installed either. +""" + + +import operator +from math import gcd +from decimal import Decimal +from fractions import Fraction +import sys +from typing import Tuple as tTuple, Type + + +# Used for __hash__ +_PyHASH_MODULUS = sys.hash_info.modulus +_PyHASH_INF = sys.hash_info.inf + + +class PythonMPQ: + """Rational number implementation that is intended to be compatible with + gmpy2's mpq. + + Also slightly faster than fractions.Fraction. + + PythonMPQ should be treated as immutable although no effort is made to + prevent mutation (since that might slow down calculations). + """ + __slots__ = ('numerator', 'denominator') + + def __new__(cls, numerator, denominator=None): + """Construct PythonMPQ with gcd computation and checks""" + if denominator is not None: + # + # PythonMPQ(n, d): require n and d to be int and d != 0 + # + if isinstance(numerator, int) and isinstance(denominator, int): + # This is the slow part: + divisor = gcd(numerator, denominator) + numerator //= divisor + denominator //= divisor + return cls._new_check(numerator, denominator) + else: + # + # PythonMPQ(q) + # + # Here q can be PythonMPQ, int, Decimal, float, Fraction or str + # + if isinstance(numerator, int): + return cls._new(numerator, 1) + elif isinstance(numerator, PythonMPQ): + return cls._new(numerator.numerator, numerator.denominator) + + # Let Fraction handle Decimal/float conversion and str parsing + if isinstance(numerator, (Decimal, float, str)): + numerator = Fraction(numerator) + if isinstance(numerator, Fraction): + return cls._new(numerator.numerator, numerator.denominator) + # + # Reject everything else. This is more strict than mpq which allows + # things like mpq(Fraction, Fraction) or mpq(Decimal, any). The mpq + # behaviour is somewhat inconsistent so we choose to accept only a + # more strict subset of what mpq allows. + # + raise TypeError("PythonMPQ() requires numeric or string argument") + + @classmethod + def _new_check(cls, numerator, denominator): + """Construct PythonMPQ, check divide by zero and canonicalize signs""" + if not denominator: + raise ZeroDivisionError(f'Zero divisor {numerator}/{denominator}') + elif denominator < 0: + numerator = -numerator + denominator = -denominator + return cls._new(numerator, denominator) + + @classmethod + def _new(cls, numerator, denominator): + """Construct PythonMPQ efficiently (no checks)""" + obj = super().__new__(cls) + obj.numerator = numerator + obj.denominator = denominator + return obj + + def __int__(self): + """Convert to int (truncates towards zero)""" + p, q = self.numerator, self.denominator + if p < 0: + return -(-p//q) + return p//q + + def __float__(self): + """Convert to float (approximately)""" + return self.numerator / self.denominator + + def __bool__(self): + """True/False if nonzero/zero""" + return bool(self.numerator) + + def __eq__(self, other): + """Compare equal with PythonMPQ, int, float, Decimal or Fraction""" + if isinstance(other, PythonMPQ): + return (self.numerator == other.numerator + and self.denominator == other.denominator) + elif isinstance(other, self._compatible_types): + return self.__eq__(PythonMPQ(other)) + else: + return NotImplemented + + def __hash__(self): + """hash - same as mpq/Fraction""" + try: + dinv = pow(self.denominator, -1, _PyHASH_MODULUS) + except ValueError: + hash_ = _PyHASH_INF + else: + hash_ = hash(hash(abs(self.numerator)) * dinv) + result = hash_ if self.numerator >= 0 else -hash_ + return -2 if result == -1 else result + + def __reduce__(self): + """Deconstruct for pickling""" + return type(self), (self.numerator, self.denominator) + + def __str__(self): + """Convert to string""" + if self.denominator != 1: + return f"{self.numerator}/{self.denominator}" + else: + return f"{self.numerator}" + + def __repr__(self): + """Convert to string""" + return f"MPQ({self.numerator},{self.denominator})" + + def _cmp(self, other, op): + """Helper for lt/le/gt/ge""" + if not isinstance(other, self._compatible_types): + return NotImplemented + lhs = self.numerator * other.denominator + rhs = other.numerator * self.denominator + return op(lhs, rhs) + + def __lt__(self, other): + """self < other""" + return self._cmp(other, operator.lt) + + def __le__(self, other): + """self <= other""" + return self._cmp(other, operator.le) + + def __gt__(self, other): + """self > other""" + return self._cmp(other, operator.gt) + + def __ge__(self, other): + """self >= other""" + return self._cmp(other, operator.ge) + + def __abs__(self): + """abs(q)""" + return self._new(abs(self.numerator), self.denominator) + + def __pos__(self): + """+q""" + return self + + def __neg__(self): + """-q""" + return self._new(-self.numerator, self.denominator) + + def __add__(self, other): + """q1 + q2""" + if isinstance(other, PythonMPQ): + # + # This is much faster than the naive method used in the stdlib + # fractions module. Not sure where this method comes from + # though... + # + # Compare timings for something like: + # nums = range(1000) + # rats = [PythonMPQ(n, d) for n, d in zip(nums[:-5], nums[5:])] + # sum(rats) # <-- time this + # + ap, aq = self.numerator, self.denominator + bp, bq = other.numerator, other.denominator + g = gcd(aq, bq) + if g == 1: + p = ap*bq + aq*bp + q = bq*aq + else: + q1, q2 = aq//g, bq//g + p, q = ap*q2 + bp*q1, q1*q2 + g2 = gcd(p, g) + p, q = (p // g2), q * (g // g2) + + elif isinstance(other, int): + p = self.numerator + self.denominator * other + q = self.denominator + else: + return NotImplemented + + return self._new(p, q) + + def __radd__(self, other): + """z1 + q2""" + if isinstance(other, int): + p = self.numerator + self.denominator * other + q = self.denominator + return self._new(p, q) + else: + return NotImplemented + + def __sub__(self ,other): + """q1 - q2""" + if isinstance(other, PythonMPQ): + ap, aq = self.numerator, self.denominator + bp, bq = other.numerator, other.denominator + g = gcd(aq, bq) + if g == 1: + p = ap*bq - aq*bp + q = bq*aq + else: + q1, q2 = aq//g, bq//g + p, q = ap*q2 - bp*q1, q1*q2 + g2 = gcd(p, g) + p, q = (p // g2), q * (g // g2) + elif isinstance(other, int): + p = self.numerator - self.denominator*other + q = self.denominator + else: + return NotImplemented + + return self._new(p, q) + + def __rsub__(self, other): + """z1 - q2""" + if isinstance(other, int): + p = self.denominator * other - self.numerator + q = self.denominator + return self._new(p, q) + else: + return NotImplemented + + def __mul__(self, other): + """q1 * q2""" + if isinstance(other, PythonMPQ): + ap, aq = self.numerator, self.denominator + bp, bq = other.numerator, other.denominator + x1 = gcd(ap, bq) + x2 = gcd(bp, aq) + p, q = ((ap//x1)*(bp//x2), (aq//x2)*(bq//x1)) + elif isinstance(other, int): + x = gcd(other, self.denominator) + p = self.numerator*(other//x) + q = self.denominator//x + else: + return NotImplemented + + return self._new(p, q) + + def __rmul__(self, other): + """z1 * q2""" + if isinstance(other, int): + x = gcd(self.denominator, other) + p = self.numerator*(other//x) + q = self.denominator//x + return self._new(p, q) + else: + return NotImplemented + + def __pow__(self, exp): + """q ** z""" + p, q = self.numerator, self.denominator + + if exp < 0: + p, q, exp = q, p, -exp + + return self._new_check(p**exp, q**exp) + + def __truediv__(self, other): + """q1 / q2""" + if isinstance(other, PythonMPQ): + ap, aq = self.numerator, self.denominator + bp, bq = other.numerator, other.denominator + x1 = gcd(ap, bp) + x2 = gcd(bq, aq) + p, q = ((ap//x1)*(bq//x2), (aq//x2)*(bp//x1)) + elif isinstance(other, int): + x = gcd(other, self.numerator) + p = self.numerator//x + q = self.denominator*(other//x) + else: + return NotImplemented + + return self._new_check(p, q) + + def __rtruediv__(self, other): + """z / q""" + if isinstance(other, int): + x = gcd(self.numerator, other) + p = self.denominator*(other//x) + q = self.numerator//x + return self._new_check(p, q) + else: + return NotImplemented + + _compatible_types: tTuple[Type, ...] = () + +# +# These are the types that PythonMPQ will interoperate with for operations +# and comparisons such as ==, + etc. We define this down here so that we can +# include PythonMPQ in the list as well. +# +PythonMPQ._compatible_types = (PythonMPQ, int, Decimal, Fraction) diff --git a/lib/python3.11/site-packages/sympy/external/tests/__init__.py b/lib/python3.11/site-packages/sympy/external/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/external/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/external/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..6220bd65604ab39f1e6a49dd25cfb3ea7949523e Binary files 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@@ +import sympy +import tempfile +import os +from sympy.core.mod import Mod +from sympy.core.relational import Eq +from sympy.core.symbol import symbols +from sympy.external import import_module +from sympy.tensor import IndexedBase, Idx +from sympy.utilities.autowrap import autowrap, ufuncify, CodeWrapError +from sympy.testing.pytest import skip + +numpy = import_module('numpy', min_module_version='1.6.1') +Cython = import_module('Cython', min_module_version='0.15.1') +f2py = import_module('numpy.f2py', import_kwargs={'fromlist': ['f2py']}) + +f2pyworks = False +if f2py: + try: + autowrap(symbols('x'), 'f95', 'f2py') + except (CodeWrapError, ImportError, OSError): + f2pyworks = False + else: + f2pyworks = True + +a, b, c = symbols('a b c') +n, m, d = symbols('n m d', integer=True) +A, B, C = symbols('A B C', cls=IndexedBase) +i = Idx('i', m) +j = Idx('j', n) +k = Idx('k', d) + + +def has_module(module): + """ + Return True if module exists, otherwise run skip(). + + module should be a string. + """ + # To give a string of the module name to skip(), this function takes a + # string. So we don't waste time running import_module() more than once, + # just map the three modules tested here in this dict. + modnames = {'numpy': numpy, 'Cython': Cython, 'f2py': f2py} + + if modnames[module]: + if module == 'f2py' and not f2pyworks: + skip("Couldn't run f2py.") + return True + skip("Couldn't import %s." % module) + +# +# test runners used by several language-backend combinations +# + +def runtest_autowrap_twice(language, backend): + f = autowrap((((a + b)/c)**5).expand(), language, backend) + g = autowrap((((a + b)/c)**4).expand(), language, backend) + + # check that autowrap updates the module name. Else, g gives the same as f + assert f(1, -2, 1) == -1.0 + assert g(1, -2, 1) == 1.0 + + +def runtest_autowrap_trace(language, backend): + has_module('numpy') + trace = autowrap(A[i, i], language, backend) + assert trace(numpy.eye(100)) == 100 + + +def runtest_autowrap_matrix_vector(language, backend): + has_module('numpy') + x, y = symbols('x y', cls=IndexedBase) + expr = Eq(y[i], A[i, j]*x[j]) + mv = autowrap(expr, language, backend) + + # compare with numpy's dot product + M = numpy.random.rand(10, 20) + x = numpy.random.rand(20) + y = numpy.dot(M, x) + assert numpy.sum(numpy.abs(y - mv(M, x))) < 1e-13 + + +def runtest_autowrap_matrix_matrix(language, backend): + has_module('numpy') + expr = Eq(C[i, j], A[i, k]*B[k, j]) + matmat = autowrap(expr, language, backend) + + # compare with numpy's dot product + M1 = numpy.random.rand(10, 20) + M2 = numpy.random.rand(20, 15) + M3 = numpy.dot(M1, M2) + assert numpy.sum(numpy.abs(M3 - matmat(M1, M2))) < 1e-13 + + +def runtest_ufuncify(language, backend): + has_module('numpy') + a, b, c = symbols('a b c') + fabc = ufuncify([a, b, c], a*b + c, backend=backend) + facb = ufuncify([a, c, b], a*b + c, backend=backend) + grid = numpy.linspace(-2, 2, 50) + b = numpy.linspace(-5, 4, 50) + c = numpy.linspace(-1, 1, 50) + expected = grid*b + c + numpy.testing.assert_allclose(fabc(grid, b, c), expected) + numpy.testing.assert_allclose(facb(grid, c, b), expected) + + +def runtest_issue_10274(language, backend): + expr = (a - b + c)**(13) + tmp = tempfile.mkdtemp() + f = autowrap(expr, language, backend, tempdir=tmp, + helpers=('helper', a - b + c, (a, b, c))) + assert f(1, 1, 1) == 1 + + for file in os.listdir(tmp): + if not (file.startswith("wrapped_code_") and file.endswith(".c")): + continue + + with open(tmp + '/' + file) as fil: + lines = fil.readlines() + assert lines[0] == "/******************************************************************************\n" + assert "Code generated with SymPy " + sympy.__version__ in lines[1] + assert lines[2:] == [ + " * *\n", + " * See http://www.sympy.org/ for more information. *\n", + " * *\n", + " * This file is part of 'autowrap' *\n", + " ******************************************************************************/\n", + "#include " + '"' + file[:-1]+ 'h"' + "\n", + "#include \n", + "\n", + "double helper(double a, double b, double c) {\n", + "\n", + " double helper_result;\n", + " helper_result = a - b + c;\n", + " return helper_result;\n", + "\n", + "}\n", + "\n", + "double autofunc(double a, double b, double c) {\n", + "\n", + " double autofunc_result;\n", + " autofunc_result = pow(helper(a, b, c), 13);\n", + " return autofunc_result;\n", + "\n", + "}\n", + ] + + +def runtest_issue_15337(language, backend): + has_module('numpy') + # NOTE : autowrap was originally designed to only accept an iterable for + # the kwarg "helpers", but in issue 10274 the user mistakenly thought that + # if there was only a single helper it did not need to be passed via an + # iterable that wrapped the helper tuple. There were no tests for this + # behavior so when the code was changed to accept a single tuple it broke + # the original behavior. These tests below ensure that both now work. + a, b, c, d, e = symbols('a, b, c, d, e') + expr = (a - b + c - d + e)**13 + exp_res = (1. - 2. + 3. - 4. + 5.)**13 + + f = autowrap(expr, language, backend, args=(a, b, c, d, e), + helpers=('f1', a - b + c, (a, b, c))) + numpy.testing.assert_allclose(f(1, 2, 3, 4, 5), exp_res) + + f = autowrap(expr, language, backend, args=(a, b, c, d, e), + helpers=(('f1', a - b, (a, b)), ('f2', c - d, (c, d)))) + numpy.testing.assert_allclose(f(1, 2, 3, 4, 5), exp_res) + + +def test_issue_15230(): + has_module('f2py') + + x, y = symbols('x, y') + expr = Mod(x, 3.0) - Mod(y, -2.0) + f = autowrap(expr, args=[x, y], language='F95') + exp_res = float(expr.xreplace({x: 3.5, y: 2.7}).evalf()) + assert abs(f(3.5, 2.7) - exp_res) < 1e-14 + + x, y = symbols('x, y', integer=True) + expr = Mod(x, 3) - Mod(y, -2) + f = autowrap(expr, args=[x, y], language='F95') + assert f(3, 2) == expr.xreplace({x: 3, y: 2}) + +# +# tests of language-backend combinations +# + +# f2py + + +def test_wrap_twice_f95_f2py(): + has_module('f2py') + runtest_autowrap_twice('f95', 'f2py') + + +def test_autowrap_trace_f95_f2py(): + has_module('f2py') + runtest_autowrap_trace('f95', 'f2py') + + +def test_autowrap_matrix_vector_f95_f2py(): + has_module('f2py') + runtest_autowrap_matrix_vector('f95', 'f2py') + + +def test_autowrap_matrix_matrix_f95_f2py(): + has_module('f2py') + runtest_autowrap_matrix_matrix('f95', 'f2py') + + +def test_ufuncify_f95_f2py(): + has_module('f2py') + runtest_ufuncify('f95', 'f2py') + + +def test_issue_15337_f95_f2py(): + has_module('f2py') + runtest_issue_15337('f95', 'f2py') + +# Cython + + +def test_wrap_twice_c_cython(): + has_module('Cython') + runtest_autowrap_twice('C', 'cython') + + +def test_autowrap_trace_C_Cython(): + has_module('Cython') + runtest_autowrap_trace('C99', 'cython') + + +def test_autowrap_matrix_vector_C_cython(): + has_module('Cython') + runtest_autowrap_matrix_vector('C99', 'cython') + + +def test_autowrap_matrix_matrix_C_cython(): + has_module('Cython') + runtest_autowrap_matrix_matrix('C99', 'cython') + + +def test_ufuncify_C_Cython(): + has_module('Cython') + runtest_ufuncify('C99', 'cython') + + +def test_issue_10274_C_cython(): + has_module('Cython') + runtest_issue_10274('C89', 'cython') + + +def test_issue_15337_C_cython(): + has_module('Cython') + runtest_issue_15337('C89', 'cython') + + +def test_autowrap_custom_printer(): + has_module('Cython') + + from sympy.core.numbers import pi + from sympy.utilities.codegen import C99CodeGen + from sympy.printing.c import C99CodePrinter + + class PiPrinter(C99CodePrinter): + def _print_Pi(self, expr): + return "S_PI" + + printer = PiPrinter() + gen = C99CodeGen(printer=printer) + gen.preprocessor_statements.append('#include "shortpi.h"') + + expr = pi * a + + expected = ( + '#include "%s"\n' + '#include \n' + '#include "shortpi.h"\n' + '\n' + 'double autofunc(double a) {\n' + '\n' + ' double autofunc_result;\n' + ' autofunc_result = S_PI*a;\n' + ' return autofunc_result;\n' + '\n' + '}\n' + ) + + tmpdir = tempfile.mkdtemp() + # write a trivial header file to use in the generated code + with open(os.path.join(tmpdir, 'shortpi.h'), 'w') as f: + f.write('#define S_PI 3.14') + + func = autowrap(expr, backend='cython', tempdir=tmpdir, code_gen=gen) + + assert func(4.2) == 3.14 * 4.2 + + # check that the generated code is correct + for filename in os.listdir(tmpdir): + if filename.startswith('wrapped_code') and filename.endswith('.c'): + with open(os.path.join(tmpdir, filename)) as f: + lines = f.readlines() + expected = expected % filename.replace('.c', '.h') + assert ''.join(lines[7:]) == expected + + +# Numpy + +def test_ufuncify_numpy(): + # This test doesn't use Cython, but if Cython works, then there is a valid + # C compiler, which is needed. + has_module('Cython') + runtest_ufuncify('C99', 'numpy') diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_codegen.py b/lib/python3.11/site-packages/sympy/external/tests/test_codegen.py new file mode 100644 index 0000000000000000000000000000000000000000..5449531a1217753c3c9d68cfec4d38852aeb0f8c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_codegen.py @@ -0,0 +1,379 @@ +# This tests the compilation and execution of the source code generated with +# utilities.codegen. The compilation takes place in a temporary directory that +# is removed after the test. By default the test directory is always removed, +# but this behavior can be changed by setting the environment variable +# SYMPY_TEST_CLEAN_TEMP to: +# export SYMPY_TEST_CLEAN_TEMP=always : the default behavior. +# export SYMPY_TEST_CLEAN_TEMP=success : only remove the directories of working tests. +# export SYMPY_TEST_CLEAN_TEMP=never : never remove the directories with the test code. +# When a directory is not removed, the necessary information is printed on +# screen to find the files that belong to the (failed) tests. If a test does +# not fail, py.test captures all the output and you will not see the directories +# corresponding to the successful tests. Use the --nocapture option to see all +# the output. + +# All tests below have a counterpart in utilities/test/test_codegen.py. In the +# latter file, the resulting code is compared with predefined strings, without +# compilation or execution. + +# All the generated Fortran code should conform with the Fortran 95 standard, +# and all the generated C code should be ANSI C, which facilitates the +# incorporation in various projects. The tests below assume that the binary cc +# is somewhere in the path and that it can compile ANSI C code. + +from sympy.abc import x, y, z +from sympy.external import import_module +from sympy.testing.pytest import skip +from sympy.utilities.codegen import codegen, make_routine, get_code_generator +import sys +import os +import tempfile +import subprocess + + +pyodide_js = import_module('pyodide_js') + +# templates for the main program that will test the generated code. + +main_template = {} +main_template['F95'] = """ +program main + include "codegen.h" + integer :: result; + result = 0 + + %(statements)s + + call exit(result) +end program +""" + +main_template['C89'] = """ +#include "codegen.h" +#include +#include + +int main() { + int result = 0; + + %(statements)s + + return result; +} +""" +main_template['C99'] = main_template['C89'] +# templates for the numerical tests + +numerical_test_template = {} +numerical_test_template['C89'] = """ + if (fabs(%(call)s)>%(threshold)s) { + printf("Numerical validation failed: %(call)s=%%e threshold=%(threshold)s\\n", %(call)s); + result = -1; + } +""" +numerical_test_template['C99'] = numerical_test_template['C89'] + +numerical_test_template['F95'] = """ + if (abs(%(call)s)>%(threshold)s) then + write(6,"('Numerical validation failed:')") + write(6,"('%(call)s=',e15.5,'threshold=',e15.5)") %(call)s, %(threshold)s + result = -1; + end if +""" +# command sequences for supported compilers + +compile_commands = {} +compile_commands['cc'] = [ + "cc -c codegen.c -o codegen.o", + "cc -c main.c -o main.o", + "cc main.o codegen.o -lm -o test.exe" +] + +compile_commands['gfortran'] = [ + "gfortran -c codegen.f90 -o codegen.o", + "gfortran -ffree-line-length-none -c main.f90 -o main.o", + "gfortran main.o codegen.o -o test.exe" +] + +compile_commands['g95'] = [ + "g95 -c codegen.f90 -o codegen.o", + "g95 -ffree-line-length-huge -c main.f90 -o main.o", + "g95 main.o codegen.o -o test.exe" +] + +compile_commands['ifort'] = [ + "ifort -c codegen.f90 -o codegen.o", + "ifort -c main.f90 -o main.o", + "ifort main.o codegen.o -o test.exe" +] + +combinations_lang_compiler = [ + ('C89', 'cc'), + ('C99', 'cc'), + ('F95', 'ifort'), + ('F95', 'gfortran'), + ('F95', 'g95') +] + + +def try_run(commands): + """Run a series of commands and only return True if all ran fine.""" + if pyodide_js: + return False + with open(os.devnull, 'w') as null: + for command in commands: + retcode = subprocess.call(command, stdout=null, shell=True, + stderr=subprocess.STDOUT) + if retcode != 0: + return False + return True + + +def run_test(label, routines, numerical_tests, language, commands, friendly=True): + """A driver for the codegen tests. + + This driver assumes that a compiler ifort is present in the PATH and that + ifort is (at least) a Fortran 90 compiler. The generated code is written in + a temporary directory, together with a main program that validates the + generated code. The test passes when the compilation and the validation + run correctly. + """ + + # Check input arguments before touching the file system + language = language.upper() + assert language in main_template + assert language in numerical_test_template + + # Check that environment variable makes sense + clean = os.getenv('SYMPY_TEST_CLEAN_TEMP', 'always').lower() + if clean not in ('always', 'success', 'never'): + raise ValueError("SYMPY_TEST_CLEAN_TEMP must be one of the following: 'always', 'success' or 'never'.") + + # Do all the magic to compile, run and validate the test code + # 1) prepare the temporary working directory, switch to that dir + work = tempfile.mkdtemp("_sympy_%s_test" % language, "%s_" % label) + oldwork = os.getcwd() + os.chdir(work) + + # 2) write the generated code + if friendly: + # interpret the routines as a name_expr list and call the friendly + # function codegen + codegen(routines, language, "codegen", to_files=True) + else: + code_gen = get_code_generator(language, "codegen") + code_gen.write(routines, "codegen", to_files=True) + + # 3) write a simple main program that links to the generated code, and that + # includes the numerical tests + test_strings = [] + for fn_name, args, expected, threshold in numerical_tests: + call_string = "%s(%s)-(%s)" % ( + fn_name, ",".join(str(arg) for arg in args), expected) + if language == "F95": + call_string = fortranize_double_constants(call_string) + threshold = fortranize_double_constants(str(threshold)) + test_strings.append(numerical_test_template[language] % { + "call": call_string, + "threshold": threshold, + }) + + if language == "F95": + f_name = "main.f90" + elif language.startswith("C"): + f_name = "main.c" + else: + raise NotImplementedError( + "FIXME: filename extension unknown for language: %s" % language) + + with open(f_name, "w") as f: + f.write( + main_template[language] % {'statements': "".join(test_strings)}) + + # 4) Compile and link + compiled = try_run(commands) + + # 5) Run if compiled + if compiled: + executed = try_run(["./test.exe"]) + else: + executed = False + + # 6) Clean up stuff + if clean == 'always' or (clean == 'success' and compiled and executed): + def safe_remove(filename): + if os.path.isfile(filename): + os.remove(filename) + safe_remove("codegen.f90") + safe_remove("codegen.c") + safe_remove("codegen.h") + safe_remove("codegen.o") + safe_remove("main.f90") + safe_remove("main.c") + safe_remove("main.o") + safe_remove("test.exe") + os.chdir(oldwork) + os.rmdir(work) + else: + print("TEST NOT REMOVED: %s" % work, file=sys.stderr) + os.chdir(oldwork) + + # 7) Do the assertions in the end + assert compiled, "failed to compile %s code with:\n%s" % ( + language, "\n".join(commands)) + assert executed, "failed to execute %s code from:\n%s" % ( + language, "\n".join(commands)) + + +def fortranize_double_constants(code_string): + """ + Replaces every literal float with literal doubles + """ + import re + pattern_exp = re.compile(r'\d+(\.)?\d*[eE]-?\d+') + pattern_float = re.compile(r'\d+\.\d*(?!\d*d)') + + def subs_exp(matchobj): + return re.sub('[eE]', 'd', matchobj.group(0)) + + def subs_float(matchobj): + return "%sd0" % matchobj.group(0) + + code_string = pattern_exp.sub(subs_exp, code_string) + code_string = pattern_float.sub(subs_float, code_string) + + return code_string + + +def is_feasible(language, commands): + # This test should always work, otherwise the compiler is not present. + routine = make_routine("test", x) + numerical_tests = [ + ("test", ( 1.0,), 1.0, 1e-15), + ("test", (-1.0,), -1.0, 1e-15), + ] + try: + run_test("is_feasible", [routine], numerical_tests, language, commands, + friendly=False) + return True + except AssertionError: + return False + +valid_lang_commands = [] +invalid_lang_compilers = [] +for lang, compiler in combinations_lang_compiler: + commands = compile_commands[compiler] + if is_feasible(lang, commands): + valid_lang_commands.append((lang, commands)) + else: + invalid_lang_compilers.append((lang, compiler)) + +# We test all language-compiler combinations, just to report what is skipped + +def test_C89_cc(): + if ("C89", 'cc') in invalid_lang_compilers: + skip("`cc' command didn't work as expected (C89)") + + +def test_C99_cc(): + if ("C99", 'cc') in invalid_lang_compilers: + skip("`cc' command didn't work as expected (C99)") + + +def test_F95_ifort(): + if ("F95", 'ifort') in invalid_lang_compilers: + skip("`ifort' command didn't work as expected") + + +def test_F95_gfortran(): + if ("F95", 'gfortran') in invalid_lang_compilers: + skip("`gfortran' command didn't work as expected") + + +def test_F95_g95(): + if ("F95", 'g95') in invalid_lang_compilers: + skip("`g95' command didn't work as expected") + +# Here comes the actual tests + + +def test_basic_codegen(): + numerical_tests = [ + ("test", (1.0, 6.0, 3.0), 21.0, 1e-15), + ("test", (-1.0, 2.0, -2.5), -2.5, 1e-15), + ] + name_expr = [("test", (x + y)*z)] + for lang, commands in valid_lang_commands: + run_test("basic_codegen", name_expr, numerical_tests, lang, commands) + + +def test_intrinsic_math1_codegen(): + # not included: log10 + from sympy.core.evalf import N + from sympy.functions import ln + from sympy.functions.elementary.exponential import log + from sympy.functions.elementary.hyperbolic import (cosh, sinh, tanh) + from sympy.functions.elementary.integers import (ceiling, floor) + from sympy.functions.elementary.miscellaneous import sqrt + from sympy.functions.elementary.trigonometric import (acos, asin, atan, cos, sin, tan) + name_expr = [ + ("test_fabs", abs(x)), + ("test_acos", acos(x)), + ("test_asin", asin(x)), + ("test_atan", atan(x)), + ("test_cos", cos(x)), + ("test_cosh", cosh(x)), + ("test_log", log(x)), + ("test_ln", ln(x)), + ("test_sin", sin(x)), + ("test_sinh", sinh(x)), + ("test_sqrt", sqrt(x)), + ("test_tan", tan(x)), + ("test_tanh", tanh(x)), + ] + numerical_tests = [] + for name, expr in name_expr: + for xval in 0.2, 0.5, 0.8: + expected = N(expr.subs(x, xval)) + numerical_tests.append((name, (xval,), expected, 1e-14)) + for lang, commands in valid_lang_commands: + if lang.startswith("C"): + name_expr_C = [("test_floor", floor(x)), ("test_ceil", ceiling(x))] + else: + name_expr_C = [] + run_test("intrinsic_math1", name_expr + name_expr_C, + numerical_tests, lang, commands) + + +def test_instrinsic_math2_codegen(): + # not included: frexp, ldexp, modf, fmod + from sympy.core.evalf import N + from sympy.functions.elementary.trigonometric import atan2 + name_expr = [ + ("test_atan2", atan2(x, y)), + ("test_pow", x**y), + ] + numerical_tests = [] + for name, expr in name_expr: + for xval, yval in (0.2, 1.3), (0.5, -0.2), (0.8, 0.8): + expected = N(expr.subs(x, xval).subs(y, yval)) + numerical_tests.append((name, (xval, yval), expected, 1e-14)) + for lang, commands in valid_lang_commands: + run_test("intrinsic_math2", name_expr, numerical_tests, lang, commands) + + +def test_complicated_codegen(): + from sympy.core.evalf import N + from sympy.functions.elementary.trigonometric import (cos, sin, tan) + name_expr = [ + ("test1", ((sin(x) + cos(y) + tan(z))**7).expand()), + ("test2", cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))), + ] + numerical_tests = [] + for name, expr in name_expr: + for xval, yval, zval in (0.2, 1.3, -0.3), (0.5, -0.2, 0.0), (0.8, 2.1, 0.8): + expected = N(expr.subs(x, xval).subs(y, yval).subs(z, zval)) + numerical_tests.append((name, (xval, yval, zval), expected, 1e-12)) + for lang, commands in valid_lang_commands: + run_test( + "complicated_codegen", name_expr, numerical_tests, lang, commands) diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_gmpy.py b/lib/python3.11/site-packages/sympy/external/tests/test_gmpy.py new file mode 100644 index 0000000000000000000000000000000000000000..d88f9da0c6c26c15f529ce485fff5b72342170ea --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_gmpy.py @@ -0,0 +1,12 @@ +from sympy.external.gmpy import LONG_MAX, iroot +from sympy.testing.pytest import raises + + +def test_iroot(): + assert iroot(2, LONG_MAX) == (1, False) + assert iroot(2, LONG_MAX + 1) == (1, False) + for x in range(3): + assert iroot(x, 1) == (x, True) + raises(ValueError, lambda: iroot(-1, 1)) + raises(ValueError, lambda: iroot(0, 0)) + raises(ValueError, lambda: iroot(0, -1)) diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_importtools.py b/lib/python3.11/site-packages/sympy/external/tests/test_importtools.py new file mode 100644 index 0000000000000000000000000000000000000000..0b954070c179282ed2bcf5735d802c5f22a3a261 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_importtools.py @@ -0,0 +1,40 @@ +from sympy.external import import_module +from sympy.testing.pytest import warns + +# fixes issue that arose in addressing issue 6533 +def test_no_stdlib_collections(): + ''' + make sure we get the right collections when it is not part of a + larger list + ''' + import collections + matplotlib = import_module('matplotlib', + import_kwargs={'fromlist': ['cm', 'collections']}, + min_module_version='1.1.0', catch=(RuntimeError,)) + if matplotlib: + assert collections != matplotlib.collections + +def test_no_stdlib_collections2(): + ''' + make sure we get the right collections when it is not part of a + larger list + ''' + import collections + matplotlib = import_module('matplotlib', + import_kwargs={'fromlist': ['collections']}, + min_module_version='1.1.0', catch=(RuntimeError,)) + if matplotlib: + assert collections != matplotlib.collections + +def test_no_stdlib_collections3(): + '''make sure we get the right collections with no catch''' + import collections + matplotlib = import_module('matplotlib', + import_kwargs={'fromlist': ['cm', 'collections']}, + min_module_version='1.1.0') + if matplotlib: + assert collections != matplotlib.collections + +def test_min_module_version_python3_basestring_error(): + with warns(UserWarning): + import_module('mpmath', min_module_version='1000.0.1') diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_ntheory.py b/lib/python3.11/site-packages/sympy/external/tests/test_ntheory.py new file mode 100644 index 0000000000000000000000000000000000000000..00824481ad27aa9071ea5801fb3bde75cacbc3c8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_ntheory.py @@ -0,0 +1,307 @@ +from itertools import permutations + +from sympy.external.ntheory import (bit_scan1, remove, bit_scan0, is_fermat_prp, + is_euler_prp, is_strong_prp, gcdext, _lucas_sequence, + is_fibonacci_prp, is_lucas_prp, is_selfridge_prp, + is_strong_lucas_prp, is_strong_selfridge_prp, + is_bpsw_prp, is_strong_bpsw_prp) +from sympy.testing.pytest import raises + + +def test_bit_scan1(): + assert bit_scan1(0) is None + assert bit_scan1(1) == 0 + assert bit_scan1(-1) == 0 + assert bit_scan1(2) == 1 + assert bit_scan1(7) == 0 + assert bit_scan1(-7) == 0 + for i in range(100): + assert bit_scan1(1 << i) == i + assert bit_scan1((1 << i) * 31337) == i + for i in range(500): + n = (1 << 500) + (1 << i) + assert bit_scan1(n) == i + assert bit_scan1(1 << 1000001) == 1000001 + assert bit_scan1((1 << 273956)*7**37) == 273956 + # issue 12709 + for i in range(1, 10): + big = 1 << i + assert bit_scan1(-big) == bit_scan1(big) + + +def test_bit_scan0(): + assert bit_scan0(-1) is None + assert bit_scan0(0) == 0 + assert bit_scan0(1) == 1 + assert bit_scan0(-2) == 0 + + +def test_remove(): + raises(ValueError, lambda: remove(1, 1)) + assert remove(0, 3) == (0, 0) + for f in range(2, 10): + for y in range(2, 1000): + for z in [1, 17, 101, 1009]: + assert remove(z*f**y, f) == (z, y) + + +def test_gcdext(): + assert gcdext(0, 0) == (0, 0, 0) + assert gcdext(3, 0) == (3, 1, 0) + assert gcdext(0, 4) == (4, 0, 1) + + for n in range(1, 10): + assert gcdext(n, 1) == gcdext(-n, 1) == (1, 0, 1) + assert gcdext(n, -1) == gcdext(-n, -1) == (1, 0, -1) + assert gcdext(n, n) == gcdext(-n, n) == (n, 0, 1) + assert gcdext(n, -n) == gcdext(-n, -n) == (n, 0, -1) + + for n in range(2, 10): + assert gcdext(1, n) == gcdext(1, -n) == (1, 1, 0) + assert gcdext(-1, n) == gcdext(-1, -n) == (1, -1, 0) + + for a, b in permutations([2**5, 3, 5, 7**2, 11], 2): + g, x, y = gcdext(a, b) + assert g == a*x + b*y == 1 + + +def test_is_fermat_prp(): + # invalid input + raises(ValueError, lambda: is_fermat_prp(0, 10)) + raises(ValueError, lambda: is_fermat_prp(5, 1)) + + # n = 1 + assert not is_fermat_prp(1, 3) + + # n is prime + assert is_fermat_prp(2, 4) + assert is_fermat_prp(3, 2) + assert is_fermat_prp(11, 3) + assert is_fermat_prp(2**31-1, 5) + + # A001567 + pseudorpime = [341, 561, 645, 1105, 1387, 1729, 1905, 2047, + 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681] + for n in pseudorpime: + assert is_fermat_prp(n, 2) + + # A020136 + pseudorpime = [15, 85, 91, 341, 435, 451, 561, 645, 703, 1105, + 1247, 1271, 1387, 1581, 1695, 1729, 1891, 1905] + for n in pseudorpime: + assert is_fermat_prp(n, 4) + + +def test_is_euler_prp(): + # invalid input + raises(ValueError, lambda: is_euler_prp(0, 10)) + raises(ValueError, lambda: is_euler_prp(5, 1)) + + # n = 1 + assert not is_euler_prp(1, 3) + + # n is prime + assert is_euler_prp(2, 4) + assert is_euler_prp(3, 2) + assert is_euler_prp(11, 3) + assert is_euler_prp(2**31-1, 5) + + # A047713 + pseudorpime = [561, 1105, 1729, 1905, 2047, 2465, 3277, 4033, + 4681, 6601, 8321, 8481, 10585, 12801, 15841] + for n in pseudorpime: + assert is_euler_prp(n, 2) + + # A048950 + pseudorpime = [121, 703, 1729, 1891, 2821, 3281, 7381, 8401, + 8911, 10585, 12403, 15457, 15841, 16531, 18721] + for n in pseudorpime: + assert is_euler_prp(n, 3) + + +def test_is_strong_prp(): + # invalid input + raises(ValueError, lambda: is_strong_prp(0, 10)) + raises(ValueError, lambda: is_strong_prp(5, 1)) + + # n = 1 + assert not is_strong_prp(1, 3) + + # n is prime + assert is_strong_prp(2, 4) + assert is_strong_prp(3, 2) + assert is_strong_prp(11, 3) + assert is_strong_prp(2**31-1, 5) + + # A001262 + pseudorpime = [2047, 3277, 4033, 4681, 8321, 15841, 29341, + 42799, 49141, 52633, 65281, 74665, 80581] + for n in pseudorpime: + assert is_strong_prp(n, 2) + + # A020229 + pseudorpime = [121, 703, 1891, 3281, 8401, 8911, 10585, 12403, + 16531, 18721, 19345, 23521, 31621, 44287, 47197] + for n in pseudorpime: + assert is_strong_prp(n, 3) + + +def test_lucas_sequence(): + def lucas_u(P, Q, length): + array = [0] * length + array[1] = 1 + for k in range(2, length): + array[k] = P * array[k - 1] - Q * array[k - 2] + return array + + def lucas_v(P, Q, length): + array = [0] * length + array[0] = 2 + array[1] = P + for k in range(2, length): + array[k] = P * array[k - 1] - Q * array[k - 2] + return array + + length = 20 + for P in range(-10, 10): + for Q in range(-10, 10): + D = P**2 - 4*Q + if D == 0: + continue + us = lucas_u(P, Q, length) + vs = lucas_v(P, Q, length) + for n in range(3, 100, 2): + for k in range(length): + U, V, Qk = _lucas_sequence(n, P, Q, k) + assert U == us[k] % n + assert V == vs[k] % n + assert pow(Q, k, n) == Qk + + +def test_is_fibonacci_prp(): + # invalid input + raises(ValueError, lambda: is_fibonacci_prp(3, 2, 1)) + raises(ValueError, lambda: is_fibonacci_prp(3, -5, 1)) + raises(ValueError, lambda: is_fibonacci_prp(3, 5, 2)) + raises(ValueError, lambda: is_fibonacci_prp(0, 5, -1)) + + # n = 1 + assert not is_fibonacci_prp(1, 3, 1) + + # n is prime + assert is_fibonacci_prp(2, 5, 1) + assert is_fibonacci_prp(3, 6, -1) + assert is_fibonacci_prp(11, 7, 1) + assert is_fibonacci_prp(2**31-1, 8, -1) + + # A005845 + pseudorpime = [705, 2465, 2737, 3745, 4181, 5777, 6721, + 10877, 13201, 15251, 24465, 29281, 34561] + for n in pseudorpime: + assert is_fibonacci_prp(n, 1, -1) + + +def test_is_lucas_prp(): + # invalid input + raises(ValueError, lambda: is_lucas_prp(3, 2, 1)) + raises(ValueError, lambda: is_lucas_prp(0, 5, -1)) + raises(ValueError, lambda: is_lucas_prp(15, 3, 1)) + + # n = 1 + assert not is_lucas_prp(1, 3, 1) + + # n is prime + assert is_lucas_prp(2, 5, 2) + assert is_lucas_prp(3, 6, -1) + assert is_lucas_prp(11, 7, 5) + assert is_lucas_prp(2**31-1, 8, -3) + + # A081264 + pseudorpime = [323, 377, 1891, 3827, 4181, 5777, 6601, 6721, + 8149, 10877, 11663, 13201, 13981, 15251, 17119] + for n in pseudorpime: + assert is_lucas_prp(n, 1, -1) + + +def test_is_selfridge_prp(): + # invalid input + raises(ValueError, lambda: is_selfridge_prp(0)) + + # n = 1 + assert not is_selfridge_prp(1) + + # n is prime + assert is_selfridge_prp(2) + assert is_selfridge_prp(3) + assert is_selfridge_prp(11) + assert is_selfridge_prp(2**31-1) + + # A217120 + pseudorpime = [323, 377, 1159, 1829, 3827, 5459, 5777, 9071, + 9179, 10877, 11419, 11663, 13919, 14839, 16109] + for n in pseudorpime: + assert is_selfridge_prp(n) + + +def test_is_strong_lucas_prp(): + # invalid input + raises(ValueError, lambda: is_strong_lucas_prp(3, 2, 1)) + raises(ValueError, lambda: is_strong_lucas_prp(0, 5, -1)) + raises(ValueError, lambda: is_strong_lucas_prp(15, 3, 1)) + + # n = 1 + assert not is_strong_lucas_prp(1, 3, 1) + + # n is prime + assert is_strong_lucas_prp(2, 5, 2) + assert is_strong_lucas_prp(3, 6, -1) + assert is_strong_lucas_prp(11, 7, 5) + assert is_strong_lucas_prp(2**31-1, 8, -3) + + +def test_is_strong_selfridge_prp(): + # invalid input + raises(ValueError, lambda: is_strong_selfridge_prp(0)) + + # n = 1 + assert not is_strong_selfridge_prp(1) + + # n is prime + assert is_strong_selfridge_prp(2) + assert is_strong_selfridge_prp(3) + assert is_strong_selfridge_prp(11) + assert is_strong_selfridge_prp(2**31-1) + + # A217255 + pseudorpime = [5459, 5777, 10877, 16109, 18971, 22499, 24569, + 25199, 40309, 58519, 75077, 97439, 100127, 113573] + for n in pseudorpime: + assert is_strong_selfridge_prp(n) + + +def test_is_bpsw_prp(): + # invalid input + raises(ValueError, lambda: is_bpsw_prp(0)) + + # n = 1 + assert not is_bpsw_prp(1) + + # n is prime + assert is_bpsw_prp(2) + assert is_bpsw_prp(3) + assert is_bpsw_prp(11) + assert is_bpsw_prp(2**31-1) + + +def test_is_strong_bpsw_prp(): + # invalid input + raises(ValueError, lambda: is_strong_bpsw_prp(0)) + + # n = 1 + assert not is_strong_bpsw_prp(1) + + # n is prime + assert is_strong_bpsw_prp(2) + assert is_strong_bpsw_prp(3) + assert is_strong_bpsw_prp(11) + assert is_strong_bpsw_prp(2**31-1) diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_numpy.py b/lib/python3.11/site-packages/sympy/external/tests/test_numpy.py new file mode 100644 index 0000000000000000000000000000000000000000..cd456d0d6cc49138c29d7ab28ee02694448d578f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_numpy.py @@ -0,0 +1,335 @@ +# This testfile tests SymPy <-> NumPy compatibility + +# Don't test any SymPy features here. Just pure interaction with NumPy. +# Always write regular SymPy tests for anything, that can be tested in pure +# Python (without numpy). Here we test everything, that a user may need when +# using SymPy with NumPy +from sympy.external.importtools import version_tuple +from sympy.external import import_module + +numpy = import_module('numpy') +if numpy: + array, matrix, ndarray = numpy.array, numpy.matrix, numpy.ndarray +else: + #bin/test will not execute any tests now + disabled = True + + +from sympy.core.numbers import (Float, Integer, Rational) +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.trigonometric import sin +from sympy.matrices.dense import (Matrix, list2numpy, matrix2numpy, symarray) +from sympy.utilities.lambdify import lambdify +import sympy + +import mpmath +from sympy.abc import x, y, z +from sympy.utilities.decorator import conserve_mpmath_dps +from sympy.utilities.exceptions import ignore_warnings +from sympy.testing.pytest import raises + + +# first, systematically check, that all operations are implemented and don't +# raise an exception + + +def test_systematic_basic(): + def s(sympy_object, numpy_array): + _ = [sympy_object + numpy_array, + numpy_array + sympy_object, + sympy_object - numpy_array, + numpy_array - sympy_object, + sympy_object * numpy_array, + numpy_array * sympy_object, + sympy_object / numpy_array, + numpy_array / sympy_object, + sympy_object ** numpy_array, + numpy_array ** sympy_object] + x = Symbol("x") + y = Symbol("y") + sympy_objs = [ + Rational(2, 3), + Float("1.3"), + x, + y, + pow(x, y)*y, + Integer(5), + Float(5.5), + ] + numpy_objs = [ + array([1]), + array([3, 8, -1]), + array([x, x**2, Rational(5)]), + array([x/y*sin(y), 5, Rational(5)]), + ] + for x in sympy_objs: + for y in numpy_objs: + s(x, y) + + +# now some random tests, that test particular problems and that also +# check that the results of the operations are correct + +def test_basics(): + one = Rational(1) + zero = Rational(0) + assert array(1) == array(one) + assert array([one]) == array([one]) + assert array([x]) == array([x]) + assert array(x) == array(Symbol("x")) + assert array(one + x) == array(1 + x) + + X = array([one, zero, zero]) + assert (X == array([one, zero, zero])).all() + assert (X == array([one, 0, 0])).all() + + +def test_arrays(): + one = Rational(1) + zero = Rational(0) + X = array([one, zero, zero]) + Y = one*X + X = array([Symbol("a") + Rational(1, 2)]) + Y = X + X + assert Y == array([1 + 2*Symbol("a")]) + Y = Y + 1 + assert Y == array([2 + 2*Symbol("a")]) + Y = X - X + assert Y == array([0]) + + +def test_conversion1(): + a = list2numpy([x**2, x]) + #looks like an array? + assert isinstance(a, ndarray) + assert a[0] == x**2 + assert a[1] == x + assert len(a) == 2 + #yes, it's the array + + +def test_conversion2(): + a = 2*list2numpy([x**2, x]) + b = list2numpy([2*x**2, 2*x]) + assert (a == b).all() + + one = Rational(1) + zero = Rational(0) + X = list2numpy([one, zero, zero]) + Y = one*X + X = list2numpy([Symbol("a") + Rational(1, 2)]) + Y = X + X + assert Y == array([1 + 2*Symbol("a")]) + Y = Y + 1 + assert Y == array([2 + 2*Symbol("a")]) + Y = X - X + assert Y == array([0]) + + +def test_list2numpy(): + assert (array([x**2, x]) == list2numpy([x**2, x])).all() + + +def test_Matrix1(): + m = Matrix([[x, x**2], [5, 2/x]]) + assert (array(m.subs(x, 2)) == array([[2, 4], [5, 1]])).all() + m = Matrix([[sin(x), x**2], [5, 2/x]]) + assert (array(m.subs(x, 2)) == array([[sin(2), 4], [5, 1]])).all() + + +def test_Matrix2(): + m = Matrix([[x, x**2], [5, 2/x]]) + with ignore_warnings(PendingDeprecationWarning): + assert (matrix(m.subs(x, 2)) == matrix([[2, 4], [5, 1]])).all() + m = Matrix([[sin(x), x**2], [5, 2/x]]) + with ignore_warnings(PendingDeprecationWarning): + assert (matrix(m.subs(x, 2)) == matrix([[sin(2), 4], [5, 1]])).all() + + +def test_Matrix3(): + a = array([[2, 4], [5, 1]]) + assert Matrix(a) == Matrix([[2, 4], [5, 1]]) + assert Matrix(a) != Matrix([[2, 4], [5, 2]]) + a = array([[sin(2), 4], [5, 1]]) + assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]]) + assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]]) + + +def test_Matrix4(): + with ignore_warnings(PendingDeprecationWarning): + a = matrix([[2, 4], [5, 1]]) + assert Matrix(a) == Matrix([[2, 4], [5, 1]]) + assert Matrix(a) != Matrix([[2, 4], [5, 2]]) + with ignore_warnings(PendingDeprecationWarning): + a = matrix([[sin(2), 4], [5, 1]]) + assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]]) + assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]]) + + +def test_Matrix_sum(): + M = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]]) + with ignore_warnings(PendingDeprecationWarning): + m = matrix([[2, 3, 4], [x, 5, 6], [x, y, z**2]]) + assert M + m == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]]) + assert m + M == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]]) + assert M + m == M.add(m) + + +def test_Matrix_mul(): + M = Matrix([[1, 2, 3], [x, y, x]]) + with ignore_warnings(PendingDeprecationWarning): + m = matrix([[2, 4], [x, 6], [x, z**2]]) + assert M*m == Matrix([ + [ 2 + 5*x, 16 + 3*z**2], + [2*x + x*y + x**2, 4*x + 6*y + x*z**2], + ]) + + assert m*M == Matrix([ + [ 2 + 4*x, 4 + 4*y, 6 + 4*x], + [ 7*x, 2*x + 6*y, 9*x], + [x + x*z**2, 2*x + y*z**2, 3*x + x*z**2], + ]) + a = array([2]) + assert a[0] * M == 2 * M + assert M * a[0] == 2 * M + + +def test_Matrix_array(): + class matarray: + def __array__(self, dtype=object, copy=None): + if copy is not None and not copy: + raise TypeError("Cannot implement copy=False when converting Matrix to ndarray") + from numpy import array + return array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + matarr = matarray() + assert Matrix(matarr) == Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + + +def test_matrix2numpy(): + a = matrix2numpy(Matrix([[1, x**2], [3*sin(x), 0]])) + assert isinstance(a, ndarray) + assert a.shape == (2, 2) + assert a[0, 0] == 1 + assert a[0, 1] == x**2 + assert a[1, 0] == 3*sin(x) + assert a[1, 1] == 0 + + +def test_matrix2numpy_conversion(): + a = Matrix([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]]) + b = array([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]]) + assert (matrix2numpy(a) == b).all() + assert matrix2numpy(a).dtype == numpy.dtype('object') + + c = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='int8') + d = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='float64') + assert c.dtype == numpy.dtype('int8') + assert d.dtype == numpy.dtype('float64') + + +def test_issue_3728(): + assert (Rational(1, 2)*array([2*x, 0]) == array([x, 0])).all() + assert (Rational(1, 2) + array( + [2*x, 0]) == array([2*x + Rational(1, 2), Rational(1, 2)])).all() + assert (Float("0.5")*array([2*x, 0]) == array([Float("1.0")*x, 0])).all() + assert (Float("0.5") + array( + [2*x, 0]) == array([2*x + Float("0.5"), Float("0.5")])).all() + + +@conserve_mpmath_dps +def test_lambdify(): + mpmath.mp.dps = 16 + sin02 = mpmath.mpf("0.198669330795061215459412627") + f = lambdify(x, sin(x), "numpy") + prec = 1e-15 + assert -prec < f(0.2) - sin02 < prec + + # if this succeeds, it can't be a numpy function + + if version_tuple(numpy.__version__) >= version_tuple('1.17'): + with raises(TypeError): + f(x) + else: + with raises(AttributeError): + f(x) + + +def test_lambdify_matrix(): + f = lambdify(x, Matrix([[x, 2*x], [1, 2]]), [{'ImmutableMatrix': numpy.array}, "numpy"]) + assert (f(1) == array([[1, 2], [1, 2]])).all() + + +def test_lambdify_matrix_multi_input(): + M = sympy.Matrix([[x**2, x*y, x*z], + [y*x, y**2, y*z], + [z*x, z*y, z**2]]) + f = lambdify((x, y, z), M, [{'ImmutableMatrix': numpy.array}, "numpy"]) + + xh, yh, zh = 1.0, 2.0, 3.0 + expected = array([[xh**2, xh*yh, xh*zh], + [yh*xh, yh**2, yh*zh], + [zh*xh, zh*yh, zh**2]]) + actual = f(xh, yh, zh) + assert numpy.allclose(actual, expected) + + +def test_lambdify_matrix_vec_input(): + X = sympy.DeferredVector('X') + M = Matrix([ + [X[0]**2, X[0]*X[1], X[0]*X[2]], + [X[1]*X[0], X[1]**2, X[1]*X[2]], + [X[2]*X[0], X[2]*X[1], X[2]**2]]) + f = lambdify(X, M, [{'ImmutableMatrix': numpy.array}, "numpy"]) + + Xh = array([1.0, 2.0, 3.0]) + expected = array([[Xh[0]**2, Xh[0]*Xh[1], Xh[0]*Xh[2]], + [Xh[1]*Xh[0], Xh[1]**2, Xh[1]*Xh[2]], + [Xh[2]*Xh[0], Xh[2]*Xh[1], Xh[2]**2]]) + actual = f(Xh) + assert numpy.allclose(actual, expected) + + +def test_lambdify_transl(): + from sympy.utilities.lambdify import NUMPY_TRANSLATIONS + for sym, mat in NUMPY_TRANSLATIONS.items(): + assert sym in sympy.__dict__ + assert mat in numpy.__dict__ + + +def test_symarray(): + """Test creation of numpy arrays of SymPy symbols.""" + + import numpy as np + import numpy.testing as npt + + syms = symbols('_0,_1,_2') + s1 = symarray("", 3) + s2 = symarray("", 3) + npt.assert_array_equal(s1, np.array(syms, dtype=object)) + assert s1[0] == s2[0] + + a = symarray('a', 3) + b = symarray('b', 3) + assert not(a[0] == b[0]) + + asyms = symbols('a_0,a_1,a_2') + npt.assert_array_equal(a, np.array(asyms, dtype=object)) + + # Multidimensional checks + a2d = symarray('a', (2, 3)) + assert a2d.shape == (2, 3) + a00, a12 = symbols('a_0_0,a_1_2') + assert a2d[0, 0] == a00 + assert a2d[1, 2] == a12 + + a3d = symarray('a', (2, 3, 2)) + assert a3d.shape == (2, 3, 2) + a000, a120, a121 = symbols('a_0_0_0,a_1_2_0,a_1_2_1') + assert a3d[0, 0, 0] == a000 + assert a3d[1, 2, 0] == a120 + assert a3d[1, 2, 1] == a121 + + +def test_vectorize(): + assert (numpy.vectorize( + sin)([1, 2, 3]) == numpy.array([sin(1), sin(2), sin(3)])).all() diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_pythonmpq.py b/lib/python3.11/site-packages/sympy/external/tests/test_pythonmpq.py new file mode 100644 index 0000000000000000000000000000000000000000..137cfdf5c858544f0811ae666f000cfb368787a0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_pythonmpq.py @@ -0,0 +1,176 @@ +""" +test_pythonmpq.py + +Test the PythonMPQ class for consistency with gmpy2's mpq type. If gmpy2 is +installed run the same tests for both. +""" +from fractions import Fraction +from decimal import Decimal +import pickle +from typing import Callable, List, Tuple, Type + +from sympy.testing.pytest import raises + +from sympy.external.pythonmpq import PythonMPQ + +# +# If gmpy2 is installed then run the tests for both mpq and PythonMPQ. +# That should ensure consistency between the implementation here and mpq. +# +rational_types: List[Tuple[Callable, Type, Callable, Type]] +rational_types = [(PythonMPQ, PythonMPQ, int, int)] +try: + from gmpy2 import mpq, mpz + rational_types.append((mpq, type(mpq(1)), mpz, type(mpz(1)))) +except ImportError: + pass + + +def test_PythonMPQ(): + # + # Test PythonMPQ and also mpq if gmpy/gmpy2 is installed. + # + for Q, TQ, Z, TZ in rational_types: + + def check_Q(q): + assert isinstance(q, TQ) + assert isinstance(q.numerator, TZ) + assert isinstance(q.denominator, TZ) + return q.numerator, q.denominator + + # Check construction from different types + assert check_Q(Q(3)) == (3, 1) + assert check_Q(Q(3, 5)) == (3, 5) + assert check_Q(Q(Q(3, 5))) == (3, 5) + assert check_Q(Q(0.5)) == (1, 2) + assert check_Q(Q('0.5')) == (1, 2) + assert check_Q(Q(Fraction(3, 5))) == (3, 5) + + # https://github.com/aleaxit/gmpy/issues/327 + if Q is PythonMPQ: + assert check_Q(Q(Decimal('0.6'))) == (3, 5) + + # Invalid types + raises(TypeError, lambda: Q([])) + raises(TypeError, lambda: Q([], [])) + + # Check normalisation of signs + assert check_Q(Q(2, 3)) == (2, 3) + assert check_Q(Q(-2, 3)) == (-2, 3) + assert check_Q(Q(2, -3)) == (-2, 3) + assert check_Q(Q(-2, -3)) == (2, 3) + + # Check gcd calculation + assert check_Q(Q(12, 8)) == (3, 2) + + # __int__/__float__ + assert int(Q(5, 3)) == 1 + assert int(Q(-5, 3)) == -1 + assert float(Q(5, 2)) == 2.5 + assert float(Q(-5, 2)) == -2.5 + + # __str__/__repr__ + assert str(Q(2, 1)) == "2" + assert str(Q(1, 2)) == "1/2" + if Q is PythonMPQ: + assert repr(Q(2, 1)) == "MPQ(2,1)" + assert repr(Q(1, 2)) == "MPQ(1,2)" + else: + assert repr(Q(2, 1)) == "mpq(2,1)" + assert repr(Q(1, 2)) == "mpq(1,2)" + + # __bool__ + assert bool(Q(1, 2)) is True + assert bool(Q(0)) is False + + # __eq__/__ne__ + assert (Q(2, 3) == Q(2, 3)) is True + assert (Q(2, 3) == Q(2, 5)) is False + assert (Q(2, 3) != Q(2, 3)) is False + assert (Q(2, 3) != Q(2, 5)) is True + + # __hash__ + assert hash(Q(3, 5)) == hash(Fraction(3, 5)) + + # __reduce__ + q = Q(2, 3) + assert pickle.loads(pickle.dumps(q)) == q + + # __ge__/__gt__/__le__/__lt__ + assert (Q(1, 3) < Q(2, 3)) is True + assert (Q(2, 3) < Q(2, 3)) is False + assert (Q(2, 3) < Q(1, 3)) is False + assert (Q(-2, 3) < Q(1, 3)) is True + assert (Q(1, 3) < Q(-2, 3)) is False + + assert (Q(1, 3) <= Q(2, 3)) is True + assert (Q(2, 3) <= Q(2, 3)) is True + assert (Q(2, 3) <= Q(1, 3)) is False + assert (Q(-2, 3) <= Q(1, 3)) is True + assert (Q(1, 3) <= Q(-2, 3)) is False + + assert (Q(1, 3) > Q(2, 3)) is False + assert (Q(2, 3) > Q(2, 3)) is False + assert (Q(2, 3) > Q(1, 3)) is True + assert (Q(-2, 3) > Q(1, 3)) is False + assert (Q(1, 3) > Q(-2, 3)) is True + + assert (Q(1, 3) >= Q(2, 3)) is False + assert (Q(2, 3) >= Q(2, 3)) is True + assert (Q(2, 3) >= Q(1, 3)) is True + assert (Q(-2, 3) >= Q(1, 3)) is False + assert (Q(1, 3) >= Q(-2, 3)) is True + + # __abs__/__pos__/__neg__ + assert abs(Q(2, 3)) == abs(Q(-2, 3)) == Q(2, 3) + assert +Q(2, 3) == Q(2, 3) + assert -Q(2, 3) == Q(-2, 3) + + # __add__/__radd__ + assert Q(2, 3) + Q(5, 7) == Q(29, 21) + assert Q(2, 3) + 1 == Q(5, 3) + assert 1 + Q(2, 3) == Q(5, 3) + raises(TypeError, lambda: [] + Q(1)) + raises(TypeError, lambda: Q(1) + []) + + # __sub__/__rsub__ + assert Q(2, 3) - Q(5, 7) == Q(-1, 21) + assert Q(2, 3) - 1 == Q(-1, 3) + assert 1 - Q(2, 3) == Q(1, 3) + raises(TypeError, lambda: [] - Q(1)) + raises(TypeError, lambda: Q(1) - []) + + # __mul__/__rmul__ + assert Q(2, 3) * Q(5, 7) == Q(10, 21) + assert Q(2, 3) * 1 == Q(2, 3) + assert 1 * Q(2, 3) == Q(2, 3) + raises(TypeError, lambda: [] * Q(1)) + raises(TypeError, lambda: Q(1) * []) + + # __pow__/__rpow__ + assert Q(2, 3) ** 2 == Q(4, 9) + assert Q(2, 3) ** 1 == Q(2, 3) + assert Q(-2, 3) ** 2 == Q(4, 9) + assert Q(-2, 3) ** -1 == Q(-3, 2) + if Q is PythonMPQ: + raises(TypeError, lambda: 1 ** Q(2, 3)) + raises(TypeError, lambda: Q(1, 4) ** Q(1, 2)) + raises(TypeError, lambda: [] ** Q(1)) + raises(TypeError, lambda: Q(1) ** []) + + # __div__/__rdiv__ + assert Q(2, 3) / Q(5, 7) == Q(14, 15) + assert Q(2, 3) / 1 == Q(2, 3) + assert 1 / Q(2, 3) == Q(3, 2) + raises(TypeError, lambda: [] / Q(1)) + raises(TypeError, lambda: Q(1) / []) + raises(ZeroDivisionError, lambda: Q(1, 2) / Q(0)) + + # __divmod__ + if Q is PythonMPQ: + raises(TypeError, lambda: Q(2, 3) // Q(1, 3)) + raises(TypeError, lambda: Q(2, 3) % Q(1, 3)) + raises(TypeError, lambda: 1 // Q(1, 3)) + raises(TypeError, lambda: 1 % Q(1, 3)) + raises(TypeError, lambda: Q(2, 3) // 1) + raises(TypeError, lambda: Q(2, 3) % 1) diff --git a/lib/python3.11/site-packages/sympy/external/tests/test_scipy.py b/lib/python3.11/site-packages/sympy/external/tests/test_scipy.py new file mode 100644 index 0000000000000000000000000000000000000000..3746d1a311eb68bb1af16e18ab152c7236b42bb5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/external/tests/test_scipy.py @@ -0,0 +1,35 @@ +# This testfile tests SymPy <-> SciPy compatibility + +# Don't test any SymPy features here. Just pure interaction with SciPy. +# Always write regular SymPy tests for anything, that can be tested in pure +# Python (without scipy). Here we test everything, that a user may need when +# using SymPy with SciPy + +from sympy.external import import_module + +scipy = import_module('scipy') +if not scipy: + #bin/test will not execute any tests now + disabled = True + +from sympy.functions.special.bessel import jn_zeros + + +def eq(a, b, tol=1e-6): + for x, y in zip(a, b): + if not (abs(x - y) < tol): + return False + return True + + +def test_jn_zeros(): + assert eq(jn_zeros(0, 4, method="scipy"), + [3.141592, 6.283185, 9.424777, 12.566370]) + assert eq(jn_zeros(1, 4, method="scipy"), + [4.493409, 7.725251, 10.904121, 14.066193]) + assert eq(jn_zeros(2, 4, method="scipy"), + [5.763459, 9.095011, 12.322940, 15.514603]) + assert eq(jn_zeros(3, 4, method="scipy"), + [6.987932, 10.417118, 13.698023, 16.923621]) + assert eq(jn_zeros(4, 4, method="scipy"), + [8.182561, 11.704907, 15.039664, 18.301255]) diff --git a/lib/python3.11/site-packages/sympy/functions/__init__.py b/lib/python3.11/site-packages/sympy/functions/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..ed93b2a11754aa26af5eef3932d177374b3ddfd6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/__init__.py @@ -0,0 +1,115 @@ +"""A functions module, includes all the standard functions. + +Combinatorial - factorial, fibonacci, harmonic, bernoulli... +Elementary - hyperbolic, trigonometric, exponential, floor and ceiling, sqrt... +Special - gamma, zeta,spherical harmonics... +""" + +from sympy.functions.combinatorial.factorials import (factorial, factorial2, + rf, ff, binomial, RisingFactorial, FallingFactorial, subfactorial) +from sympy.functions.combinatorial.numbers import (carmichael, fibonacci, lucas, tribonacci, + harmonic, bernoulli, bell, euler, catalan, genocchi, andre, partition, divisor_sigma, + udivisor_sigma, legendre_symbol, jacobi_symbol, kronecker_symbol, mobius, + primenu, primeomega, totient, reduced_totient, primepi, motzkin) +from sympy.functions.elementary.miscellaneous import (sqrt, root, Min, Max, + Id, real_root, cbrt, Rem) +from sympy.functions.elementary.complexes import (re, im, sign, Abs, + conjugate, arg, polar_lift, periodic_argument, unbranched_argument, + principal_branch, transpose, adjoint, polarify, unpolarify) +from sympy.functions.elementary.trigonometric import (sin, cos, tan, + sec, csc, cot, sinc, asin, acos, atan, asec, acsc, acot, atan2) +from sympy.functions.elementary.exponential import (exp_polar, exp, log, + LambertW) +from sympy.functions.elementary.hyperbolic import (sinh, cosh, tanh, coth, + sech, csch, asinh, acosh, atanh, acoth, asech, acsch) +from sympy.functions.elementary.integers import floor, ceiling, frac +from sympy.functions.elementary.piecewise import (Piecewise, piecewise_fold, + piecewise_exclusive) +from sympy.functions.special.error_functions import (erf, erfc, erfi, erf2, + erfinv, erfcinv, erf2inv, Ei, expint, E1, li, Li, Si, Ci, Shi, Chi, + fresnels, fresnelc) +from sympy.functions.special.gamma_functions import (gamma, lowergamma, + uppergamma, polygamma, loggamma, digamma, trigamma, multigamma) +from sympy.functions.special.zeta_functions import (dirichlet_eta, zeta, + lerchphi, polylog, stieltjes, riemann_xi) +from sympy.functions.special.tensor_functions import (Eijk, LeviCivita, + KroneckerDelta) +from sympy.functions.special.singularity_functions import SingularityFunction +from sympy.functions.special.delta_functions import DiracDelta, Heaviside +from sympy.functions.special.bsplines import bspline_basis, bspline_basis_set, interpolating_spline +from sympy.functions.special.bessel import (besselj, bessely, besseli, besselk, + hankel1, hankel2, jn, yn, jn_zeros, hn1, hn2, airyai, airybi, airyaiprime, airybiprime, marcumq) +from sympy.functions.special.hyper import hyper, meijerg, appellf1 +from sympy.functions.special.polynomials import (legendre, assoc_legendre, + hermite, hermite_prob, chebyshevt, chebyshevu, chebyshevu_root, + chebyshevt_root, laguerre, assoc_laguerre, gegenbauer, jacobi, jacobi_normalized) +from sympy.functions.special.spherical_harmonics import Ynm, Ynm_c, Znm +from sympy.functions.special.elliptic_integrals import (elliptic_k, + elliptic_f, elliptic_e, elliptic_pi) +from sympy.functions.special.beta_functions import beta, betainc, betainc_regularized +from sympy.functions.special.mathieu_functions import (mathieus, mathieuc, + mathieusprime, mathieucprime) +ln = log + +__all__ = [ + 'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial', + 'FallingFactorial', 'subfactorial', + + 'carmichael', 'fibonacci', 'lucas', 'motzkin', 'tribonacci', 'harmonic', + 'bernoulli', 'bell', 'euler', 'catalan', 'genocchi', 'andre', 'partition', + 'divisor_sigma', 'udivisor_sigma', 'legendre_symbol', 'jacobi_symbol', 'kronecker_symbol', + 'mobius', 'primenu', 'primeomega', 'totient', 'reduced_totient', 'primepi', + + 'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root', 'cbrt', 'Rem', + + 're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift', + 'periodic_argument', 'unbranched_argument', 'principal_branch', + 'transpose', 'adjoint', 'polarify', 'unpolarify', + + 'sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan', + 'asec', 'acsc', 'acot', 'atan2', + + 'exp_polar', 'exp', 'ln', 'log', 'LambertW', + + 'sinh', 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh', + 'acoth', 'asech', 'acsch', + + 'floor', 'ceiling', 'frac', + + 'Piecewise', 'piecewise_fold', 'piecewise_exclusive', + + 'erf', 'erfc', 'erfi', 'erf2', 'erfinv', 'erfcinv', 'erf2inv', 'Ei', + 'expint', 'E1', 'li', 'Li', 'Si', 'Ci', 'Shi', 'Chi', 'fresnels', + 'fresnelc', + + 'gamma', 'lowergamma', 'uppergamma', 'polygamma', 'loggamma', 'digamma', + 'trigamma', 'multigamma', + + 'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'riemann_xi', + + 'Eijk', 'LeviCivita', 'KroneckerDelta', + + 'SingularityFunction', + + 'DiracDelta', 'Heaviside', + + 'bspline_basis', 'bspline_basis_set', 'interpolating_spline', + + 'besselj', 'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn', + 'yn', 'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime', + 'airybiprime', 'marcumq', + + 'hyper', 'meijerg', 'appellf1', + + 'legendre', 'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt', + 'chebyshevu', 'chebyshevu_root', 'chebyshevt_root', 'laguerre', + 'assoc_laguerre', 'gegenbauer', 'jacobi', 'jacobi_normalized', + + 'Ynm', 'Ynm_c', 'Znm', + + 'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi', + + 'beta', 'betainc', 'betainc_regularized', + + 'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime', +] diff --git a/lib/python3.11/site-packages/sympy/functions/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ec7ea276678d79d7e4a1f07063e67ce54d7bba45 Binary files /dev/null and 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a/lib/python3.11/site-packages/sympy/functions/combinatorial/__pycache__/factorials.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/combinatorial/__pycache__/factorials.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1b845e4d6c04d79e5a12d166d27ebb286218508f Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/combinatorial/__pycache__/factorials.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/functions/combinatorial/factorials.py b/lib/python3.11/site-packages/sympy/functions/combinatorial/factorials.py new file mode 100644 index 0000000000000000000000000000000000000000..97e5052408bc9d0cc68749f85bc2901ace05f803 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/combinatorial/factorials.py @@ -0,0 +1,1133 @@ +from __future__ import annotations +from functools import reduce + +from sympy.core import S, sympify, Dummy, Mod +from sympy.core.cache import cacheit +from sympy.core.function import Function, ArgumentIndexError, PoleError +from sympy.core.logic import fuzzy_and +from sympy.core.numbers import Integer, pi, I +from sympy.core.relational import Eq +from sympy.external.gmpy import gmpy as _gmpy +from sympy.ntheory import sieve +from sympy.ntheory.residue_ntheory import binomial_mod +from sympy.polys.polytools import Poly + +from math import factorial as _factorial, prod, sqrt as _sqrt + +class CombinatorialFunction(Function): + """Base class for combinatorial functions. """ + + def _eval_simplify(self, **kwargs): + from sympy.simplify.combsimp import combsimp + # combinatorial function with non-integer arguments is + # automatically passed to gammasimp + expr = combsimp(self) + measure = kwargs['measure'] + if measure(expr) <= kwargs['ratio']*measure(self): + return expr + return self + + +############################################################################### +######################## FACTORIAL and MULTI-FACTORIAL ######################## +############################################################################### + + +class factorial(CombinatorialFunction): + r"""Implementation of factorial function over nonnegative integers. + By convention (consistent with the gamma function and the binomial + coefficients), factorial of a negative integer is complex infinity. + + The factorial is very important in combinatorics where it gives + the number of ways in which `n` objects can be permuted. It also + arises in calculus, probability, number theory, etc. + + There is strict relation of factorial with gamma function. In + fact `n! = gamma(n+1)` for nonnegative integers. Rewrite of this + kind is very useful in case of combinatorial simplification. + + Computation of the factorial is done using two algorithms. For + small arguments a precomputed look up table is used. However for bigger + input algorithm Prime-Swing is used. It is the fastest algorithm + known and computes `n!` via prime factorization of special class + of numbers, called here the 'Swing Numbers'. + + Examples + ======== + + >>> from sympy import Symbol, factorial, S + >>> n = Symbol('n', integer=True) + + >>> factorial(0) + 1 + + >>> factorial(7) + 5040 + + >>> factorial(-2) + zoo + + >>> factorial(n) + factorial(n) + + >>> factorial(2*n) + factorial(2*n) + + >>> factorial(S(1)/2) + factorial(1/2) + + See Also + ======== + + factorial2, RisingFactorial, FallingFactorial + """ + + def fdiff(self, argindex=1): + from sympy.functions.special.gamma_functions import (gamma, polygamma) + if argindex == 1: + return gamma(self.args[0] + 1)*polygamma(0, self.args[0] + 1) + else: + raise ArgumentIndexError(self, argindex) + + _small_swing = [ + 1, 1, 1, 3, 3, 15, 5, 35, 35, 315, 63, 693, 231, 3003, 429, 6435, 6435, 109395, + 12155, 230945, 46189, 969969, 88179, 2028117, 676039, 16900975, 1300075, + 35102025, 5014575, 145422675, 9694845, 300540195, 300540195 + ] + + _small_factorials: list[int] = [] + + @classmethod + def _swing(cls, n): + if n < 33: + return cls._small_swing[n] + else: + N, primes = int(_sqrt(n)), [] + + for prime in sieve.primerange(3, N + 1): + p, q = 1, n + + while True: + q //= prime + + if q > 0: + if q & 1 == 1: + p *= prime + else: + break + + if p > 1: + primes.append(p) + + for prime in sieve.primerange(N + 1, n//3 + 1): + if (n // prime) & 1 == 1: + primes.append(prime) + + L_product = prod(sieve.primerange(n//2 + 1, n + 1)) + R_product = prod(primes) + + return L_product*R_product + + @classmethod + def _recursive(cls, n): + if n < 2: + return 1 + else: + return (cls._recursive(n//2)**2)*cls._swing(n) + + @classmethod + def eval(cls, n): + n = sympify(n) + + if n.is_Number: + if n.is_zero: + return S.One + elif n is S.Infinity: + return S.Infinity + elif n.is_Integer: + if n.is_negative: + return S.ComplexInfinity + else: + n = n.p + + if n < 20: + if not cls._small_factorials: + result = 1 + for i in range(1, 20): + result *= i + cls._small_factorials.append(result) + result = cls._small_factorials[n-1] + + # GMPY factorial is faster, use it when available + # + # XXX: There is a sympy.external.gmpy.factorial function + # which provides gmpy.fac if available or the flint version + # if flint is used. It could be used here to avoid the + # conditional logic but it needs to be checked whether the + # pure Python fallback used there is as fast as the + # fallback used here (perhaps the fallback here should be + # moved to sympy.external.ntheory). + elif _gmpy is not None: + result = _gmpy.fac(n) + + else: + bits = bin(n).count('1') + result = cls._recursive(n)*2**(n - bits) + + return Integer(result) + + def _facmod(self, n, q): + res, N = 1, int(_sqrt(n)) + + # Exponent of prime p in n! is e_p(n) = [n/p] + [n/p**2] + ... + # for p > sqrt(n), e_p(n) < sqrt(n), the primes with [n/p] = m, + # occur consecutively and are grouped together in pw[m] for + # simultaneous exponentiation at a later stage + pw = [1]*N + + m = 2 # to initialize the if condition below + for prime in sieve.primerange(2, n + 1): + if m > 1: + m, y = 0, n // prime + while y: + m += y + y //= prime + if m < N: + pw[m] = pw[m]*prime % q + else: + res = res*pow(prime, m, q) % q + + for ex, bs in enumerate(pw): + if ex == 0 or bs == 1: + continue + if bs == 0: + return 0 + res = res*pow(bs, ex, q) % q + + return res + + def _eval_Mod(self, q): + n = self.args[0] + if n.is_integer and n.is_nonnegative and q.is_integer: + aq = abs(q) + d = aq - n + if d.is_nonpositive: + return S.Zero + else: + isprime = aq.is_prime + if d == 1: + # Apply Wilson's theorem (if a natural number n > 1 + # is a prime number, then (n-1)! = -1 mod n) and + # its inverse (if n > 4 is a composite number, then + # (n-1)! = 0 mod n) + if isprime: + return -1 % q + elif isprime is False and (aq - 6).is_nonnegative: + return S.Zero + elif n.is_Integer and q.is_Integer: + n, d, aq = map(int, (n, d, aq)) + if isprime and (d - 1 < n): + fc = self._facmod(d - 1, aq) + fc = pow(fc, aq - 2, aq) + if d%2: + fc = -fc + else: + fc = self._facmod(n, aq) + + return fc % q + + def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs): + from sympy.functions.special.gamma_functions import gamma + return gamma(n + 1) + + def _eval_rewrite_as_Product(self, n, **kwargs): + from sympy.concrete.products import Product + if n.is_nonnegative and n.is_integer: + i = Dummy('i', integer=True) + return Product(i, (i, 1, n)) + + def _eval_is_integer(self): + if self.args[0].is_integer and self.args[0].is_nonnegative: + return True + + def _eval_is_positive(self): + if self.args[0].is_integer and self.args[0].is_nonnegative: + return True + + def _eval_is_even(self): + x = self.args[0] + if x.is_integer and x.is_nonnegative: + return (x - 2).is_nonnegative + + def _eval_is_composite(self): + x = self.args[0] + if x.is_integer and x.is_nonnegative: + return (x - 3).is_nonnegative + + def _eval_is_real(self): + x = self.args[0] + if x.is_nonnegative or x.is_noninteger: + return True + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x) + arg0 = arg.subs(x, 0) + if arg0.is_zero: + return S.One + elif not arg0.is_infinite: + return self.func(arg) + raise PoleError("Cannot expand %s around 0" % (self)) + +class MultiFactorial(CombinatorialFunction): + pass + + +class subfactorial(CombinatorialFunction): + r"""The subfactorial counts the derangements of $n$ items and is + defined for non-negative integers as: + + .. math:: !n = \begin{cases} 1 & n = 0 \\ 0 & n = 1 \\ + (n-1)(!(n-1) + !(n-2)) & n > 1 \end{cases} + + It can also be written as ``int(round(n!/exp(1)))`` but the + recursive definition with caching is implemented for this function. + + An interesting analytic expression is the following [2]_ + + .. math:: !x = \Gamma(x + 1, -1)/e + + which is valid for non-negative integers `x`. The above formula + is not very useful in case of non-integers. `\Gamma(x + 1, -1)` is + single-valued only for integral arguments `x`, elsewhere on the positive + real axis it has an infinite number of branches none of which are real. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Subfactorial + .. [2] https://mathworld.wolfram.com/Subfactorial.html + + Examples + ======== + + >>> from sympy import subfactorial + >>> from sympy.abc import n + >>> subfactorial(n + 1) + subfactorial(n + 1) + >>> subfactorial(5) + 44 + + See Also + ======== + + factorial, uppergamma, + sympy.utilities.iterables.generate_derangements + """ + + @classmethod + @cacheit + def _eval(self, n): + if not n: + return S.One + elif n == 1: + return S.Zero + else: + z1, z2 = 1, 0 + for i in range(2, n + 1): + z1, z2 = z2, (i - 1)*(z2 + z1) + return z2 + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg.is_Integer and arg.is_nonnegative: + return cls._eval(arg) + elif arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + + def _eval_is_even(self): + if self.args[0].is_odd and self.args[0].is_nonnegative: + return True + + def _eval_is_integer(self): + if self.args[0].is_integer and self.args[0].is_nonnegative: + return True + + def _eval_rewrite_as_factorial(self, arg, **kwargs): + from sympy.concrete.summations import summation + i = Dummy('i') + f = S.NegativeOne**i / factorial(i) + return factorial(arg) * summation(f, (i, 0, arg)) + + def _eval_rewrite_as_gamma(self, arg, piecewise=True, **kwargs): + from sympy.functions.elementary.exponential import exp + from sympy.functions.special.gamma_functions import (gamma, lowergamma) + return (S.NegativeOne**(arg + 1)*exp(-I*pi*arg)*lowergamma(arg + 1, -1) + + gamma(arg + 1))*exp(-1) + + def _eval_rewrite_as_uppergamma(self, arg, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return uppergamma(arg + 1, -1)/S.Exp1 + + def _eval_is_nonnegative(self): + if self.args[0].is_integer and self.args[0].is_nonnegative: + return True + + def _eval_is_odd(self): + if self.args[0].is_even and self.args[0].is_nonnegative: + return True + + +class factorial2(CombinatorialFunction): + r"""The double factorial `n!!`, not to be confused with `(n!)!` + + The double factorial is defined for nonnegative integers and for odd + negative integers as: + + .. math:: n!! = \begin{cases} 1 & n = 0 \\ + n(n-2)(n-4) \cdots 1 & n\ \text{positive odd} \\ + n(n-2)(n-4) \cdots 2 & n\ \text{positive even} \\ + (n+2)!!/(n+2) & n\ \text{negative odd} \end{cases} + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Double_factorial + + Examples + ======== + + >>> from sympy import factorial2, var + >>> n = var('n') + >>> n + n + >>> factorial2(n + 1) + factorial2(n + 1) + >>> factorial2(5) + 15 + >>> factorial2(-1) + 1 + >>> factorial2(-5) + 1/3 + + See Also + ======== + + factorial, RisingFactorial, FallingFactorial + """ + + @classmethod + def eval(cls, arg): + # TODO: extend this to complex numbers? + + if arg.is_Number: + if not arg.is_Integer: + raise ValueError("argument must be nonnegative integer " + "or negative odd integer") + + # This implementation is faster than the recursive one + # It also avoids "maximum recursion depth exceeded" runtime error + if arg.is_nonnegative: + if arg.is_even: + k = arg / 2 + return 2**k * factorial(k) + return factorial(arg) / factorial2(arg - 1) + + + if arg.is_odd: + return arg*(S.NegativeOne)**((1 - arg)/2) / factorial2(-arg) + raise ValueError("argument must be nonnegative integer " + "or negative odd integer") + + + def _eval_is_even(self): + # Double factorial is even for every positive even input + n = self.args[0] + if n.is_integer: + if n.is_odd: + return False + if n.is_even: + if n.is_positive: + return True + if n.is_zero: + return False + + def _eval_is_integer(self): + # Double factorial is an integer for every nonnegative input, and for + # -1 and -3 + n = self.args[0] + if n.is_integer: + if (n + 1).is_nonnegative: + return True + if n.is_odd: + return (n + 3).is_nonnegative + + def _eval_is_odd(self): + # Double factorial is odd for every odd input not smaller than -3, and + # for 0 + n = self.args[0] + if n.is_odd: + return (n + 3).is_nonnegative + if n.is_even: + if n.is_positive: + return False + if n.is_zero: + return True + + def _eval_is_positive(self): + # Double factorial is positive for every nonnegative input, and for + # every odd negative input which is of the form -1-4k for an + # nonnegative integer k + n = self.args[0] + if n.is_integer: + if (n + 1).is_nonnegative: + return True + if n.is_odd: + return ((n + 1) / 2).is_even + + def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs): + from sympy.functions.elementary.miscellaneous import sqrt + from sympy.functions.elementary.piecewise import Piecewise + from sympy.functions.special.gamma_functions import gamma + return 2**(n/2)*gamma(n/2 + 1) * Piecewise((1, Eq(Mod(n, 2), 0)), + (sqrt(2/pi), Eq(Mod(n, 2), 1))) + + +############################################################################### +######################## RISING and FALLING FACTORIALS ######################## +############################################################################### + + +class RisingFactorial(CombinatorialFunction): + r""" + Rising factorial (also called Pochhammer symbol [1]_) is a double valued + function arising in concrete mathematics, hypergeometric functions + and series expansions. It is defined by: + + .. math:: \texttt{rf(y, k)} = (x)^k = x \cdot (x+1) \cdots (x+k-1) + + where `x` can be arbitrary expression and `k` is an integer. For + more information check "Concrete mathematics" by Graham, pp. 66 + or visit https://mathworld.wolfram.com/RisingFactorial.html page. + + When `x` is a `~.Poly` instance of degree $\ge 1$ with a single variable, + `(x)^k = x(y) \cdot x(y+1) \cdots x(y+k-1)`, where `y` is the + variable of `x`. This is as described in [2]_. + + Examples + ======== + + >>> from sympy import rf, Poly + >>> from sympy.abc import x + >>> rf(x, 0) + 1 + >>> rf(1, 5) + 120 + >>> rf(x, 5) == x*(1 + x)*(2 + x)*(3 + x)*(4 + x) + True + >>> rf(Poly(x**3, x), 2) + Poly(x**6 + 3*x**5 + 3*x**4 + x**3, x, domain='ZZ') + + Rewriting is complicated unless the relationship between + the arguments is known, but rising factorial can + be rewritten in terms of gamma, factorial, binomial, + and falling factorial. + + >>> from sympy import Symbol, factorial, ff, binomial, gamma + >>> n = Symbol('n', integer=True, positive=True) + >>> R = rf(n, n + 2) + >>> for i in (rf, ff, factorial, binomial, gamma): + ... R.rewrite(i) + ... + RisingFactorial(n, n + 2) + FallingFactorial(2*n + 1, n + 2) + factorial(2*n + 1)/factorial(n - 1) + binomial(2*n + 1, n + 2)*factorial(n + 2) + gamma(2*n + 2)/gamma(n) + + See Also + ======== + + factorial, factorial2, FallingFactorial + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Pochhammer_symbol + .. [2] Peter Paule, "Greatest Factorial Factorization and Symbolic + Summation", Journal of Symbolic Computation, vol. 20, pp. 235-268, + 1995. + + """ + + @classmethod + def eval(cls, x, k): + x = sympify(x) + k = sympify(k) + + if x is S.NaN or k is S.NaN: + return S.NaN + elif x is S.One: + return factorial(k) + elif k.is_Integer: + if k.is_zero: + return S.One + else: + if k.is_positive: + if x is S.Infinity: + return S.Infinity + elif x is S.NegativeInfinity: + if k.is_odd: + return S.NegativeInfinity + else: + return S.Infinity + else: + if isinstance(x, Poly): + gens = x.gens + if len(gens)!= 1: + raise ValueError("rf only defined for " + "polynomials on one generator") + else: + return reduce(lambda r, i: + r*(x.shift(i)), + range(int(k)), 1) + else: + return reduce(lambda r, i: r*(x + i), + range(int(k)), 1) + + else: + if x is S.Infinity: + return S.Infinity + elif x is S.NegativeInfinity: + return S.Infinity + else: + if isinstance(x, Poly): + gens = x.gens + if len(gens)!= 1: + raise ValueError("rf only defined for " + "polynomials on one generator") + else: + return 1/reduce(lambda r, i: + r*(x.shift(-i)), + range(1, abs(int(k)) + 1), 1) + else: + return 1/reduce(lambda r, i: + r*(x - i), + range(1, abs(int(k)) + 1), 1) + + if k.is_integer == False: + if x.is_integer and x.is_negative: + return S.Zero + + def _eval_rewrite_as_gamma(self, x, k, piecewise=True, **kwargs): + from sympy.functions.elementary.piecewise import Piecewise + from sympy.functions.special.gamma_functions import gamma + if not piecewise: + if (x <= 0) == True: + return S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1) + return gamma(x + k) / gamma(x) + return Piecewise( + (gamma(x + k) / gamma(x), x > 0), + (S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1), True)) + + def _eval_rewrite_as_FallingFactorial(self, x, k, **kwargs): + return FallingFactorial(x + k - 1, k) + + def _eval_rewrite_as_factorial(self, x, k, **kwargs): + from sympy.functions.elementary.piecewise import Piecewise + if x.is_integer and k.is_integer: + return Piecewise( + (factorial(k + x - 1)/factorial(x - 1), x > 0), + (S.NegativeOne**k*factorial(-x)/factorial(-k - x), True)) + + def _eval_rewrite_as_binomial(self, x, k, **kwargs): + if k.is_integer: + return factorial(k) * binomial(x + k - 1, k) + + def _eval_rewrite_as_tractable(self, x, k, limitvar=None, **kwargs): + from sympy.functions.special.gamma_functions import gamma + if limitvar: + k_lim = k.subs(limitvar, S.Infinity) + if k_lim is S.Infinity: + return (gamma(x + k).rewrite('tractable', deep=True) / gamma(x)) + elif k_lim is S.NegativeInfinity: + return (S.NegativeOne**k*gamma(1 - x) / gamma(-k - x + 1).rewrite('tractable', deep=True)) + return self.rewrite(gamma).rewrite('tractable', deep=True) + + def _eval_is_integer(self): + return fuzzy_and((self.args[0].is_integer, self.args[1].is_integer, + self.args[1].is_nonnegative)) + + +class FallingFactorial(CombinatorialFunction): + r""" + Falling factorial (related to rising factorial) is a double valued + function arising in concrete mathematics, hypergeometric functions + and series expansions. It is defined by + + .. math:: \texttt{ff(x, k)} = (x)_k = x \cdot (x-1) \cdots (x-k+1) + + where `x` can be arbitrary expression and `k` is an integer. For + more information check "Concrete mathematics" by Graham, pp. 66 + or [1]_. + + When `x` is a `~.Poly` instance of degree $\ge 1$ with single variable, + `(x)_k = x(y) \cdot x(y-1) \cdots x(y-k+1)`, where `y` is the + variable of `x`. This is as described in + + >>> from sympy import ff, Poly, Symbol + >>> from sympy.abc import x + >>> n = Symbol('n', integer=True) + + >>> ff(x, 0) + 1 + >>> ff(5, 5) + 120 + >>> ff(x, 5) == x*(x - 1)*(x - 2)*(x - 3)*(x - 4) + True + >>> ff(Poly(x**2, x), 2) + Poly(x**4 - 2*x**3 + x**2, x, domain='ZZ') + >>> ff(n, n) + factorial(n) + + Rewriting is complicated unless the relationship between + the arguments is known, but falling factorial can + be rewritten in terms of gamma, factorial and binomial + and rising factorial. + + >>> from sympy import factorial, rf, gamma, binomial, Symbol + >>> n = Symbol('n', integer=True, positive=True) + >>> F = ff(n, n - 2) + >>> for i in (rf, ff, factorial, binomial, gamma): + ... F.rewrite(i) + ... + RisingFactorial(3, n - 2) + FallingFactorial(n, n - 2) + factorial(n)/2 + binomial(n, n - 2)*factorial(n - 2) + gamma(n + 1)/2 + + See Also + ======== + + factorial, factorial2, RisingFactorial + + References + ========== + + .. [1] https://mathworld.wolfram.com/FallingFactorial.html + .. [2] Peter Paule, "Greatest Factorial Factorization and Symbolic + Summation", Journal of Symbolic Computation, vol. 20, pp. 235-268, + 1995. + + """ + + @classmethod + def eval(cls, x, k): + x = sympify(x) + k = sympify(k) + + if x is S.NaN or k is S.NaN: + return S.NaN + elif k.is_integer and x == k: + return factorial(x) + elif k.is_Integer: + if k.is_zero: + return S.One + else: + if k.is_positive: + if x is S.Infinity: + return S.Infinity + elif x is S.NegativeInfinity: + if k.is_odd: + return S.NegativeInfinity + else: + return S.Infinity + else: + if isinstance(x, Poly): + gens = x.gens + if len(gens)!= 1: + raise ValueError("ff only defined for " + "polynomials on one generator") + else: + return reduce(lambda r, i: + r*(x.shift(-i)), + range(int(k)), 1) + else: + return reduce(lambda r, i: r*(x - i), + range(int(k)), 1) + else: + if x is S.Infinity: + return S.Infinity + elif x is S.NegativeInfinity: + return S.Infinity + else: + if isinstance(x, Poly): + gens = x.gens + if len(gens)!= 1: + raise ValueError("rf only defined for " + "polynomials on one generator") + else: + return 1/reduce(lambda r, i: + r*(x.shift(i)), + range(1, abs(int(k)) + 1), 1) + else: + return 1/reduce(lambda r, i: r*(x + i), + range(1, abs(int(k)) + 1), 1) + + def _eval_rewrite_as_gamma(self, x, k, piecewise=True, **kwargs): + from sympy.functions.elementary.piecewise import Piecewise + from sympy.functions.special.gamma_functions import gamma + if not piecewise: + if (x < 0) == True: + return S.NegativeOne**k*gamma(k - x) / gamma(-x) + return gamma(x + 1) / gamma(x - k + 1) + return Piecewise( + (gamma(x + 1) / gamma(x - k + 1), x >= 0), + (S.NegativeOne**k*gamma(k - x) / gamma(-x), True)) + + def _eval_rewrite_as_RisingFactorial(self, x, k, **kwargs): + return rf(x - k + 1, k) + + def _eval_rewrite_as_binomial(self, x, k, **kwargs): + if k.is_integer: + return factorial(k) * binomial(x, k) + + def _eval_rewrite_as_factorial(self, x, k, **kwargs): + from sympy.functions.elementary.piecewise import Piecewise + if x.is_integer and k.is_integer: + return Piecewise( + (factorial(x)/factorial(-k + x), x >= 0), + (S.NegativeOne**k*factorial(k - x - 1)/factorial(-x - 1), True)) + + def _eval_rewrite_as_tractable(self, x, k, limitvar=None, **kwargs): + from sympy.functions.special.gamma_functions import gamma + if limitvar: + k_lim = k.subs(limitvar, S.Infinity) + if k_lim is S.Infinity: + return (S.NegativeOne**k*gamma(k - x).rewrite('tractable', deep=True) / gamma(-x)) + elif k_lim is S.NegativeInfinity: + return (gamma(x + 1) / gamma(x - k + 1).rewrite('tractable', deep=True)) + return self.rewrite(gamma).rewrite('tractable', deep=True) + + def _eval_is_integer(self): + return fuzzy_and((self.args[0].is_integer, self.args[1].is_integer, + self.args[1].is_nonnegative)) + + +rf = RisingFactorial +ff = FallingFactorial + +############################################################################### +########################### BINOMIAL COEFFICIENTS ############################# +############################################################################### + + +class binomial(CombinatorialFunction): + r"""Implementation of the binomial coefficient. It can be defined + in two ways depending on its desired interpretation: + + .. math:: \binom{n}{k} = \frac{n!}{k!(n-k)!}\ \text{or}\ + \binom{n}{k} = \frac{(n)_k}{k!} + + First, in a strict combinatorial sense it defines the + number of ways we can choose `k` elements from a set of + `n` elements. In this case both arguments are nonnegative + integers and binomial is computed using an efficient + algorithm based on prime factorization. + + The other definition is generalization for arbitrary `n`, + however `k` must also be nonnegative. This case is very + useful when evaluating summations. + + For the sake of convenience, for negative integer `k` this function + will return zero no matter the other argument. + + To expand the binomial when `n` is a symbol, use either + ``expand_func()`` or ``expand(func=True)``. The former will keep + the polynomial in factored form while the latter will expand the + polynomial itself. See examples for details. + + Examples + ======== + + >>> from sympy import Symbol, Rational, binomial, expand_func + >>> n = Symbol('n', integer=True, positive=True) + + >>> binomial(15, 8) + 6435 + + >>> binomial(n, -1) + 0 + + Rows of Pascal's triangle can be generated with the binomial function: + + >>> for N in range(8): + ... print([binomial(N, i) for i in range(N + 1)]) + ... + [1] + [1, 1] + [1, 2, 1] + [1, 3, 3, 1] + [1, 4, 6, 4, 1] + [1, 5, 10, 10, 5, 1] + [1, 6, 15, 20, 15, 6, 1] + [1, 7, 21, 35, 35, 21, 7, 1] + + As can a given diagonal, e.g. the 4th diagonal: + + >>> N = -4 + >>> [binomial(N, i) for i in range(1 - N)] + [1, -4, 10, -20, 35] + + >>> binomial(Rational(5, 4), 3) + -5/128 + >>> binomial(Rational(-5, 4), 3) + -195/128 + + >>> binomial(n, 3) + binomial(n, 3) + + >>> binomial(n, 3).expand(func=True) + n**3/6 - n**2/2 + n/3 + + >>> expand_func(binomial(n, 3)) + n*(n - 2)*(n - 1)/6 + + In many cases, we can also compute binomial coefficients modulo a + prime p quickly using Lucas' Theorem [2]_, though we need to include + `evaluate=False` to postpone evaluation: + + >>> from sympy import Mod + >>> Mod(binomial(156675, 4433, evaluate=False), 10**5 + 3) + 28625 + + Using a generalisation of Lucas's Theorem given by Granville [3]_, + we can extend this to arbitrary n: + + >>> Mod(binomial(10**18, 10**12, evaluate=False), (10**5 + 3)**2) + 3744312326 + + References + ========== + + .. [1] https://www.johndcook.com/blog/binomial_coefficients/ + .. [2] https://en.wikipedia.org/wiki/Lucas%27s_theorem + .. [3] Binomial coefficients modulo prime powers, Andrew Granville, + Available: https://web.archive.org/web/20170202003812/http://www.dms.umontreal.ca/~andrew/PDF/BinCoeff.pdf + """ + + def fdiff(self, argindex=1): + from sympy.functions.special.gamma_functions import polygamma + if argindex == 1: + # https://functions.wolfram.com/GammaBetaErf/Binomial/20/01/01/ + n, k = self.args + return binomial(n, k)*(polygamma(0, n + 1) - \ + polygamma(0, n - k + 1)) + elif argindex == 2: + # https://functions.wolfram.com/GammaBetaErf/Binomial/20/01/02/ + n, k = self.args + return binomial(n, k)*(polygamma(0, n - k + 1) - \ + polygamma(0, k + 1)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def _eval(self, n, k): + # n.is_Number and k.is_Integer and k != 1 and n != k + + if k.is_Integer: + if n.is_Integer and n >= 0: + n, k = int(n), int(k) + + if k > n: + return S.Zero + elif k > n // 2: + k = n - k + + # XXX: This conditional logic should be moved to + # sympy.external.gmpy and the pure Python version of bincoef + # should be moved to sympy.external.ntheory. + if _gmpy is not None: + return Integer(_gmpy.bincoef(n, k)) + + d, result = n - k, 1 + for i in range(1, k + 1): + d += 1 + result = result * d // i + return Integer(result) + else: + d, result = n - k, 1 + for i in range(1, k + 1): + d += 1 + result *= d + return result / _factorial(k) + + @classmethod + def eval(cls, n, k): + n, k = map(sympify, (n, k)) + d = n - k + n_nonneg, n_isint = n.is_nonnegative, n.is_integer + if k.is_zero or ((n_nonneg or n_isint is False) + and d.is_zero): + return S.One + if (k - 1).is_zero or ((n_nonneg or n_isint is False) + and (d - 1).is_zero): + return n + if k.is_integer: + if k.is_negative or (n_nonneg and n_isint and d.is_negative): + return S.Zero + elif n.is_number: + res = cls._eval(n, k) + return res.expand(basic=True) if res else res + elif n_nonneg is False and n_isint: + # a special case when binomial evaluates to complex infinity + return S.ComplexInfinity + elif k.is_number: + from sympy.functions.special.gamma_functions import gamma + return gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1)) + + def _eval_Mod(self, q): + n, k = self.args + + if any(x.is_integer is False for x in (n, k, q)): + raise ValueError("Integers expected for binomial Mod") + + if all(x.is_Integer for x in (n, k, q)): + n, k = map(int, (n, k)) + aq, res = abs(q), 1 + + # handle negative integers k or n + if k < 0: + return S.Zero + if n < 0: + n = -n + k - 1 + res = -1 if k%2 else 1 + + # non negative integers k and n + if k > n: + return S.Zero + + isprime = aq.is_prime + aq = int(aq) + if isprime: + if aq < n: + # use Lucas Theorem + N, K = n, k + while N or K: + res = res*binomial(N % aq, K % aq) % aq + N, K = N // aq, K // aq + + else: + # use Factorial Modulo + d = n - k + if k > d: + k, d = d, k + kf = 1 + for i in range(2, k + 1): + kf = kf*i % aq + df = kf + for i in range(k + 1, d + 1): + df = df*i % aq + res *= df + for i in range(d + 1, n + 1): + res = res*i % aq + + res *= pow(kf*df % aq, aq - 2, aq) + res %= aq + + elif _sqrt(q) < k and q != 1: + res = binomial_mod(n, k, q) + + else: + # Binomial Factorization is performed by calculating the + # exponents of primes <= n in `n! /(k! (n - k)!)`, + # for non-negative integers n and k. As the exponent of + # prime in n! is e_p(n) = [n/p] + [n/p**2] + ... + # the exponent of prime in binomial(n, k) would be + # e_p(n) - e_p(k) - e_p(n - k) + M = int(_sqrt(n)) + for prime in sieve.primerange(2, n + 1): + if prime > n - k: + res = res*prime % aq + elif prime > n // 2: + continue + elif prime > M: + if n % prime < k % prime: + res = res*prime % aq + else: + N, K = n, k + exp = a = 0 + + while N > 0: + a = int((N % prime) < (K % prime + a)) + N, K = N // prime, K // prime + exp += a + + if exp > 0: + res *= pow(prime, exp, aq) + res %= aq + + return S(res % q) + + def _eval_expand_func(self, **hints): + """ + Function to expand binomial(n, k) when m is positive integer + Also, + n is self.args[0] and k is self.args[1] while using binomial(n, k) + """ + n = self.args[0] + if n.is_Number: + return binomial(*self.args) + + k = self.args[1] + if (n-k).is_Integer: + k = n - k + + if k.is_Integer: + if k.is_zero: + return S.One + elif k.is_negative: + return S.Zero + else: + n, result = self.args[0], 1 + for i in range(1, k + 1): + result *= n - k + i + return result / _factorial(k) + else: + return binomial(*self.args) + + def _eval_rewrite_as_factorial(self, n, k, **kwargs): + return factorial(n)/(factorial(k)*factorial(n - k)) + + def _eval_rewrite_as_gamma(self, n, k, piecewise=True, **kwargs): + from sympy.functions.special.gamma_functions import gamma + return gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1)) + + def _eval_rewrite_as_tractable(self, n, k, limitvar=None, **kwargs): + return self._eval_rewrite_as_gamma(n, k).rewrite('tractable') + + def _eval_rewrite_as_FallingFactorial(self, n, k, **kwargs): + if k.is_integer: + return ff(n, k) / factorial(k) + + def _eval_is_integer(self): + n, k = self.args + if n.is_integer and k.is_integer: + return True + elif k.is_integer is False: + return False + + def _eval_is_nonnegative(self): + n, k = self.args + if n.is_integer and k.is_integer: + if n.is_nonnegative or k.is_negative or k.is_even: + return True + elif k.is_even is False: + return False + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.functions.special.gamma_functions import gamma + return self.rewrite(gamma)._eval_as_leading_term(x, logx=logx, cdir=cdir) diff --git a/lib/python3.11/site-packages/sympy/functions/combinatorial/numbers.py b/lib/python3.11/site-packages/sympy/functions/combinatorial/numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..a70d7ac7394c7dd6eb03c48b4936ef67aabebf8e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/combinatorial/numbers.py @@ -0,0 +1,3169 @@ +""" +This module implements some special functions that commonly appear in +combinatorial contexts (e.g. in power series); in particular, +sequences of rational numbers such as Bernoulli and Fibonacci numbers. + +Factorials, binomial coefficients and related functions are located in +the separate 'factorials' module. +""" +from math import prod +from collections import defaultdict +from typing import Tuple as tTuple + +from sympy.core import S, Symbol, Add, Dummy +from sympy.core.cache import cacheit +from sympy.core.containers import Dict +from sympy.core.expr import Expr +from sympy.core.function import ArgumentIndexError, Function, expand_mul +from sympy.core.logic import fuzzy_not +from sympy.core.mul import Mul +from sympy.core.numbers import E, I, pi, oo, Rational, Integer +from sympy.core.relational import Eq, is_le, is_gt, is_lt +from sympy.external.gmpy import SYMPY_INTS, remove, lcm, legendre, jacobi, kronecker +from sympy.functions.combinatorial.factorials import (binomial, + factorial, subfactorial) +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.piecewise import Piecewise +from sympy.ntheory.factor_ import (factorint, _divisor_sigma, is_carmichael, + find_carmichael_numbers_in_range, find_first_n_carmichaels) +from sympy.ntheory.generate import _primepi +from sympy.ntheory.partitions_ import _partition, _partition_rec +from sympy.ntheory.primetest import isprime, is_square +from sympy.polys.appellseqs import bernoulli_poly, euler_poly, genocchi_poly +from sympy.polys.polytools import cancel +from sympy.utilities.enumerative import MultisetPartitionTraverser +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import multiset, multiset_derangements, iterable +from sympy.utilities.memoization import recurrence_memo +from sympy.utilities.misc import as_int + +from mpmath import mp, workprec +from mpmath.libmp import ifib as _ifib + + +def _product(a, b): + return prod(range(a, b + 1)) + + +# Dummy symbol used for computing polynomial sequences +_sym = Symbol('x') + + +#----------------------------------------------------------------------------# +# # +# Carmichael numbers # +# # +#----------------------------------------------------------------------------# + +class carmichael(Function): + r""" + Carmichael Numbers: + + Certain cryptographic algorithms make use of big prime numbers. + However, checking whether a big number is prime is not so easy. + Randomized prime number checking tests exist that offer a high degree of + confidence of accurate determination at low cost, such as the Fermat test. + + Let 'a' be a random number between $2$ and $n - 1$, where $n$ is the + number whose primality we are testing. Then, $n$ is probably prime if it + satisfies the modular arithmetic congruence relation: + + .. math :: a^{n-1} = 1 \pmod{n} + + (where mod refers to the modulo operation) + + If a number passes the Fermat test several times, then it is prime with a + high probability. + + Unfortunately, certain composite numbers (non-primes) still pass the Fermat + test with every number smaller than themselves. + These numbers are called Carmichael numbers. + + A Carmichael number will pass a Fermat primality test to every base $b$ + relatively prime to the number, even though it is not actually prime. + This makes tests based on Fermat's Little Theorem less effective than + strong probable prime tests such as the Baillie-PSW primality test and + the Miller-Rabin primality test. + + Examples + ======== + + >>> from sympy.ntheory.factor_ import find_first_n_carmichaels, find_carmichael_numbers_in_range + >>> find_first_n_carmichaels(5) + [561, 1105, 1729, 2465, 2821] + >>> find_carmichael_numbers_in_range(0, 562) + [561] + >>> find_carmichael_numbers_in_range(0,1000) + [561] + >>> find_carmichael_numbers_in_range(0,2000) + [561, 1105, 1729] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Carmichael_number + .. [2] https://en.wikipedia.org/wiki/Fermat_primality_test + .. [3] https://www.jstor.org/stable/23248683?seq=1#metadata_info_tab_contents + """ + + @staticmethod + def is_perfect_square(n): + sympy_deprecation_warning( + """ +is_perfect_square is just a wrapper around sympy.ntheory.primetest.is_square +so use that directly instead. + """, + deprecated_since_version="1.11", + active_deprecations_target='deprecated-carmichael-static-methods', + ) + return is_square(n) + + @staticmethod + def divides(p, n): + sympy_deprecation_warning( + """ + divides can be replaced by directly testing n % p == 0. + """, + deprecated_since_version="1.11", + active_deprecations_target='deprecated-carmichael-static-methods', + ) + return n % p == 0 + + @staticmethod + def is_prime(n): + sympy_deprecation_warning( + """ +is_prime is just a wrapper around sympy.ntheory.primetest.isprime so use that +directly instead. + """, + deprecated_since_version="1.11", + active_deprecations_target='deprecated-carmichael-static-methods', + ) + return isprime(n) + + @staticmethod + def is_carmichael(n): + sympy_deprecation_warning( + """ +is_carmichael is just a wrapper around sympy.ntheory.factor_.is_carmichael so use that +directly instead. + """, + deprecated_since_version="1.13", + active_deprecations_target='deprecated-ntheory-symbolic-functions', + ) + return is_carmichael(n) + + @staticmethod + def find_carmichael_numbers_in_range(x, y): + sympy_deprecation_warning( + """ +find_carmichael_numbers_in_range is just a wrapper around sympy.ntheory.factor_.find_carmichael_numbers_in_range so use that +directly instead. + """, + deprecated_since_version="1.13", + active_deprecations_target='deprecated-ntheory-symbolic-functions', + ) + return find_carmichael_numbers_in_range(x, y) + + @staticmethod + def find_first_n_carmichaels(n): + sympy_deprecation_warning( + """ +find_first_n_carmichaels is just a wrapper around sympy.ntheory.factor_.find_first_n_carmichaels so use that +directly instead. + """, + deprecated_since_version="1.13", + active_deprecations_target='deprecated-ntheory-symbolic-functions', + ) + return find_first_n_carmichaels(n) + + +#----------------------------------------------------------------------------# +# # +# Fibonacci numbers # +# # +#----------------------------------------------------------------------------# + + +class fibonacci(Function): + r""" + Fibonacci numbers / Fibonacci polynomials + + The Fibonacci numbers are the integer sequence defined by the + initial terms `F_0 = 0`, `F_1 = 1` and the two-term recurrence + relation `F_n = F_{n-1} + F_{n-2}`. This definition + extended to arbitrary real and complex arguments using + the formula + + .. math :: F_z = \frac{\phi^z - \cos(\pi z) \phi^{-z}}{\sqrt 5} + + The Fibonacci polynomials are defined by `F_1(x) = 1`, + `F_2(x) = x`, and `F_n(x) = x*F_{n-1}(x) + F_{n-2}(x)` for `n > 2`. + For all positive integers `n`, `F_n(1) = F_n`. + + * ``fibonacci(n)`` gives the `n^{th}` Fibonacci number, `F_n` + * ``fibonacci(n, x)`` gives the `n^{th}` Fibonacci polynomial in `x`, `F_n(x)` + + Examples + ======== + + >>> from sympy import fibonacci, Symbol + + >>> [fibonacci(x) for x in range(11)] + [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55] + >>> fibonacci(5, Symbol('t')) + t**4 + 3*t**2 + 1 + + See Also + ======== + + bell, bernoulli, catalan, euler, harmonic, lucas, genocchi, partition, tribonacci + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Fibonacci_number + .. [2] https://mathworld.wolfram.com/FibonacciNumber.html + + """ + + @staticmethod + def _fib(n): + return _ifib(n) + + @staticmethod + @recurrence_memo([None, S.One, _sym]) + def _fibpoly(n, prev): + return (prev[-2] + _sym*prev[-1]).expand() + + @classmethod + def eval(cls, n, sym=None): + if n is S.Infinity: + return S.Infinity + + if n.is_Integer: + if sym is None: + n = int(n) + if n < 0: + return S.NegativeOne**(n + 1) * fibonacci(-n) + else: + return Integer(cls._fib(n)) + else: + if n < 1: + raise ValueError("Fibonacci polynomials are defined " + "only for positive integer indices.") + return cls._fibpoly(n).subs(_sym, sym) + + def _eval_rewrite_as_tractable(self, n, **kwargs): + from sympy.functions import sqrt, cos + return (S.GoldenRatio**n - cos(S.Pi*n)/S.GoldenRatio**n)/sqrt(5) + + def _eval_rewrite_as_sqrt(self, n, **kwargs): + from sympy.functions.elementary.miscellaneous import sqrt + return 2**(-n)*sqrt(5)*((1 + sqrt(5))**n - (-sqrt(5) + 1)**n) / 5 + + def _eval_rewrite_as_GoldenRatio(self,n, **kwargs): + return (S.GoldenRatio**n - 1/(-S.GoldenRatio)**n)/(2*S.GoldenRatio-1) + + +#----------------------------------------------------------------------------# +# # +# Lucas numbers # +# # +#----------------------------------------------------------------------------# + + +class lucas(Function): + """ + Lucas numbers + + Lucas numbers satisfy a recurrence relation similar to that of + the Fibonacci sequence, in which each term is the sum of the + preceding two. They are generated by choosing the initial + values `L_0 = 2` and `L_1 = 1`. + + * ``lucas(n)`` gives the `n^{th}` Lucas number + + Examples + ======== + + >>> from sympy import lucas + + >>> [lucas(x) for x in range(11)] + [2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123] + + See Also + ======== + + bell, bernoulli, catalan, euler, fibonacci, harmonic, genocchi, partition, tribonacci + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Lucas_number + .. [2] https://mathworld.wolfram.com/LucasNumber.html + + """ + + @classmethod + def eval(cls, n): + if n is S.Infinity: + return S.Infinity + + if n.is_Integer: + return fibonacci(n + 1) + fibonacci(n - 1) + + def _eval_rewrite_as_sqrt(self, n, **kwargs): + from sympy.functions.elementary.miscellaneous import sqrt + return 2**(-n)*((1 + sqrt(5))**n + (-sqrt(5) + 1)**n) + + +#----------------------------------------------------------------------------# +# # +# Tribonacci numbers # +# # +#----------------------------------------------------------------------------# + + +class tribonacci(Function): + r""" + Tribonacci numbers / Tribonacci polynomials + + The Tribonacci numbers are the integer sequence defined by the + initial terms `T_0 = 0`, `T_1 = 1`, `T_2 = 1` and the three-term + recurrence relation `T_n = T_{n-1} + T_{n-2} + T_{n-3}`. + + The Tribonacci polynomials are defined by `T_0(x) = 0`, `T_1(x) = 1`, + `T_2(x) = x^2`, and `T_n(x) = x^2 T_{n-1}(x) + x T_{n-2}(x) + T_{n-3}(x)` + for `n > 2`. For all positive integers `n`, `T_n(1) = T_n`. + + * ``tribonacci(n)`` gives the `n^{th}` Tribonacci number, `T_n` + * ``tribonacci(n, x)`` gives the `n^{th}` Tribonacci polynomial in `x`, `T_n(x)` + + Examples + ======== + + >>> from sympy import tribonacci, Symbol + + >>> [tribonacci(x) for x in range(11)] + [0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149] + >>> tribonacci(5, Symbol('t')) + t**8 + 3*t**5 + 3*t**2 + + See Also + ======== + + bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, partition + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers + .. [2] https://mathworld.wolfram.com/TribonacciNumber.html + .. [3] https://oeis.org/A000073 + + """ + + @staticmethod + @recurrence_memo([S.Zero, S.One, S.One]) + def _trib(n, prev): + return (prev[-3] + prev[-2] + prev[-1]) + + @staticmethod + @recurrence_memo([S.Zero, S.One, _sym**2]) + def _tribpoly(n, prev): + return (prev[-3] + _sym*prev[-2] + _sym**2*prev[-1]).expand() + + @classmethod + def eval(cls, n, sym=None): + if n is S.Infinity: + return S.Infinity + + if n.is_Integer: + n = int(n) + if n < 0: + raise ValueError("Tribonacci polynomials are defined " + "only for non-negative integer indices.") + if sym is None: + return Integer(cls._trib(n)) + else: + return cls._tribpoly(n).subs(_sym, sym) + + def _eval_rewrite_as_sqrt(self, n, **kwargs): + from sympy.functions.elementary.miscellaneous import cbrt, sqrt + w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2 + a = (1 + cbrt(19 + 3*sqrt(33)) + cbrt(19 - 3*sqrt(33))) / 3 + b = (1 + w*cbrt(19 + 3*sqrt(33)) + w**2*cbrt(19 - 3*sqrt(33))) / 3 + c = (1 + w**2*cbrt(19 + 3*sqrt(33)) + w*cbrt(19 - 3*sqrt(33))) / 3 + Tn = (a**(n + 1)/((a - b)*(a - c)) + + b**(n + 1)/((b - a)*(b - c)) + + c**(n + 1)/((c - a)*(c - b))) + return Tn + + def _eval_rewrite_as_TribonacciConstant(self, n, **kwargs): + from sympy.functions.elementary.integers import floor + from sympy.functions.elementary.miscellaneous import cbrt, sqrt + b = cbrt(586 + 102*sqrt(33)) + Tn = 3 * b * S.TribonacciConstant**n / (b**2 - 2*b + 4) + return floor(Tn + S.Half) + + +#----------------------------------------------------------------------------# +# # +# Bernoulli numbers # +# # +#----------------------------------------------------------------------------# + + +class bernoulli(Function): + r""" + Bernoulli numbers / Bernoulli polynomials / Bernoulli function + + The Bernoulli numbers are a sequence of rational numbers + defined by `B_0 = 1` and the recursive relation (`n > 0`): + + .. math :: n+1 = \sum_{k=0}^n \binom{n+1}{k} B_k + + They are also commonly defined by their exponential generating + function, which is `\frac{x}{1 - e^{-x}}`. For odd indices > 1, + the Bernoulli numbers are zero. + + The Bernoulli polynomials satisfy the analogous formula: + + .. math :: B_n(x) = \sum_{k=0}^n (-1)^k \binom{n}{k} B_k x^{n-k} + + Bernoulli numbers and Bernoulli polynomials are related as + `B_n(1) = B_n`. + + The generalized Bernoulli function `\operatorname{B}(s, a)` + is defined for any complex `s` and `a`, except where `a` is a + nonpositive integer and `s` is not a nonnegative integer. It is + an entire function of `s` for fixed `a`, related to the Hurwitz + zeta function by + + .. math:: \operatorname{B}(s, a) = \begin{cases} + -s \zeta(1-s, a) & s \ne 0 \\ 1 & s = 0 \end{cases} + + When `s` is a nonnegative integer this function reduces to the + Bernoulli polynomials: `\operatorname{B}(n, x) = B_n(x)`. When + `a` is omitted it is assumed to be 1, yielding the (ordinary) + Bernoulli function which interpolates the Bernoulli numbers and is + related to the Riemann zeta function. + + We compute Bernoulli numbers using Ramanujan's formula: + + .. math :: B_n = \frac{A(n) - S(n)}{\binom{n+3}{n}} + + where: + + .. math :: A(n) = \begin{cases} \frac{n+3}{3} & + n \equiv 0\ \text{or}\ 2 \pmod{6} \\ + -\frac{n+3}{6} & n \equiv 4 \pmod{6} \end{cases} + + and: + + .. math :: S(n) = \sum_{k=1}^{[n/6]} \binom{n+3}{n-6k} B_{n-6k} + + This formula is similar to the sum given in the definition, but + cuts `\frac{2}{3}` of the terms. For Bernoulli polynomials, we use + Appell sequences. + + For `n` a nonnegative integer and `s`, `a`, `x` arbitrary complex numbers, + + * ``bernoulli(n)`` gives the nth Bernoulli number, `B_n` + * ``bernoulli(s)`` gives the Bernoulli function `\operatorname{B}(s)` + * ``bernoulli(n, x)`` gives the nth Bernoulli polynomial in `x`, `B_n(x)` + * ``bernoulli(s, a)`` gives the generalized Bernoulli function + `\operatorname{B}(s, a)` + + .. versionchanged:: 1.12 + ``bernoulli(1)`` gives `+\frac{1}{2}` instead of `-\frac{1}{2}`. + This choice of value confers several theoretical advantages [5]_, + including the extension to complex parameters described above + which this function now implements. The previous behavior, defined + only for nonnegative integers `n`, can be obtained with + ``(-1)**n*bernoulli(n)``. + + Examples + ======== + + >>> from sympy import bernoulli + >>> from sympy.abc import x + >>> [bernoulli(n) for n in range(11)] + [1, 1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66] + >>> bernoulli(1000001) + 0 + >>> bernoulli(3, x) + x**3 - 3*x**2/2 + x/2 + + See Also + ======== + + andre, bell, catalan, euler, fibonacci, harmonic, lucas, genocchi, + partition, tribonacci, sympy.polys.appellseqs.bernoulli_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Bernoulli_number + .. [2] https://en.wikipedia.org/wiki/Bernoulli_polynomial + .. [3] https://mathworld.wolfram.com/BernoulliNumber.html + .. [4] https://mathworld.wolfram.com/BernoulliPolynomial.html + .. [5] Peter Luschny, "The Bernoulli Manifesto", + https://luschny.de/math/zeta/The-Bernoulli-Manifesto.html + .. [6] Peter Luschny, "An introduction to the Bernoulli function", + https://arxiv.org/abs/2009.06743 + + """ + + args: tTuple[Integer] + + # Calculates B_n for positive even n + @staticmethod + def _calc_bernoulli(n): + s = 0 + a = int(binomial(n + 3, n - 6)) + for j in range(1, n//6 + 1): + s += a * bernoulli(n - 6*j) + # Avoid computing each binomial coefficient from scratch + a *= _product(n - 6 - 6*j + 1, n - 6*j) + a //= _product(6*j + 4, 6*j + 9) + if n % 6 == 4: + s = -Rational(n + 3, 6) - s + else: + s = Rational(n + 3, 3) - s + return s / binomial(n + 3, n) + + # We implement a specialized memoization scheme to handle each + # case modulo 6 separately + _cache = {0: S.One, 1: Rational(1, 2), 2: Rational(1, 6), 4: Rational(-1, 30)} + _highest = {0: 0, 1: 1, 2: 2, 4: 4} + + @classmethod + def eval(cls, n, x=None): + if x is S.One: + return cls(n) + elif n.is_zero: + return S.One + elif n.is_integer is False or n.is_nonnegative is False: + if x is not None and x.is_Integer and x.is_nonpositive: + return S.NaN + return + # Bernoulli numbers + elif x is None: + if n is S.One: + return S.Half + elif n.is_odd and (n-1).is_positive: + return S.Zero + elif n.is_Number: + n = int(n) + # Use mpmath for enormous Bernoulli numbers + if n > 500: + p, q = mp.bernfrac(n) + return Rational(int(p), int(q)) + case = n % 6 + highest_cached = cls._highest[case] + if n <= highest_cached: + return cls._cache[n] + # To avoid excessive recursion when, say, bernoulli(1000) is + # requested, calculate and cache the entire sequence ... B_988, + # B_994, B_1000 in increasing order + for i in range(highest_cached + 6, n + 6, 6): + b = cls._calc_bernoulli(i) + cls._cache[i] = b + cls._highest[case] = i + return b + # Bernoulli polynomials + elif n.is_Number: + return bernoulli_poly(n, x) + + def _eval_rewrite_as_zeta(self, n, x=1, **kwargs): + from sympy.functions.special.zeta_functions import zeta + return Piecewise((1, Eq(n, 0)), (-n * zeta(1-n, x), True)) + + def _eval_evalf(self, prec): + if not all(x.is_number for x in self.args): + return + n = self.args[0]._to_mpmath(prec) + x = (self.args[1] if len(self.args) > 1 else S.One)._to_mpmath(prec) + with workprec(prec): + if n == 0: + res = mp.mpf(1) + elif n == 1: + res = x - mp.mpf(0.5) + elif mp.isint(n) and n >= 0: + res = mp.bernoulli(n) if x == 1 else mp.bernpoly(n, x) + else: + res = -n * mp.zeta(1-n, x) + return Expr._from_mpmath(res, prec) + + +#----------------------------------------------------------------------------# +# # +# Bell numbers # +# # +#----------------------------------------------------------------------------# + + +class bell(Function): + r""" + Bell numbers / Bell polynomials + + The Bell numbers satisfy `B_0 = 1` and + + .. math:: B_n = \sum_{k=0}^{n-1} \binom{n-1}{k} B_k. + + They are also given by: + + .. math:: B_n = \frac{1}{e} \sum_{k=0}^{\infty} \frac{k^n}{k!}. + + The Bell polynomials are given by `B_0(x) = 1` and + + .. math:: B_n(x) = x \sum_{k=1}^{n-1} \binom{n-1}{k-1} B_{k-1}(x). + + The second kind of Bell polynomials (are sometimes called "partial" Bell + polynomials or incomplete Bell polynomials) are defined as + + .. math:: B_{n,k}(x_1, x_2,\dotsc x_{n-k+1}) = + \sum_{j_1+j_2+j_2+\dotsb=k \atop j_1+2j_2+3j_2+\dotsb=n} + \frac{n!}{j_1!j_2!\dotsb j_{n-k+1}!} + \left(\frac{x_1}{1!} \right)^{j_1} + \left(\frac{x_2}{2!} \right)^{j_2} \dotsb + \left(\frac{x_{n-k+1}}{(n-k+1)!} \right) ^{j_{n-k+1}}. + + * ``bell(n)`` gives the `n^{th}` Bell number, `B_n`. + * ``bell(n, x)`` gives the `n^{th}` Bell polynomial, `B_n(x)`. + * ``bell(n, k, (x1, x2, ...))`` gives Bell polynomials of the second kind, + `B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1})`. + + Notes + ===== + + Not to be confused with Bernoulli numbers and Bernoulli polynomials, + which use the same notation. + + Examples + ======== + + >>> from sympy import bell, Symbol, symbols + + >>> [bell(n) for n in range(11)] + [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975] + >>> bell(30) + 846749014511809332450147 + >>> bell(4, Symbol('t')) + t**4 + 6*t**3 + 7*t**2 + t + >>> bell(6, 2, symbols('x:6')[1:]) + 6*x1*x5 + 15*x2*x4 + 10*x3**2 + + See Also + ======== + + bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, partition, tribonacci + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Bell_number + .. [2] https://mathworld.wolfram.com/BellNumber.html + .. [3] https://mathworld.wolfram.com/BellPolynomial.html + + """ + + @staticmethod + @recurrence_memo([1, 1]) + def _bell(n, prev): + s = 1 + a = 1 + for k in range(1, n): + a = a * (n - k) // k + s += a * prev[k] + return s + + @staticmethod + @recurrence_memo([S.One, _sym]) + def _bell_poly(n, prev): + s = 1 + a = 1 + for k in range(2, n + 1): + a = a * (n - k + 1) // (k - 1) + s += a * prev[k - 1] + return expand_mul(_sym * s) + + @staticmethod + def _bell_incomplete_poly(n, k, symbols): + r""" + The second kind of Bell polynomials (incomplete Bell polynomials). + + Calculated by recurrence formula: + + .. math:: B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1}) = + \sum_{m=1}^{n-k+1} + \x_m \binom{n-1}{m-1} B_{n-m,k-1}(x_1, x_2, \dotsc, x_{n-m-k}) + + where + `B_{0,0} = 1;` + `B_{n,0} = 0; for n \ge 1` + `B_{0,k} = 0; for k \ge 1` + + """ + if (n == 0) and (k == 0): + return S.One + elif (n == 0) or (k == 0): + return S.Zero + s = S.Zero + a = S.One + for m in range(1, n - k + 2): + s += a * bell._bell_incomplete_poly( + n - m, k - 1, symbols) * symbols[m - 1] + a = a * (n - m) / m + return expand_mul(s) + + @classmethod + def eval(cls, n, k_sym=None, symbols=None): + if n is S.Infinity: + if k_sym is None: + return S.Infinity + else: + raise ValueError("Bell polynomial is not defined") + + if n.is_negative or n.is_integer is False: + raise ValueError("a non-negative integer expected") + + if n.is_Integer and n.is_nonnegative: + if k_sym is None: + return Integer(cls._bell(int(n))) + elif symbols is None: + return cls._bell_poly(int(n)).subs(_sym, k_sym) + else: + r = cls._bell_incomplete_poly(int(n), int(k_sym), symbols) + return r + + def _eval_rewrite_as_Sum(self, n, k_sym=None, symbols=None, **kwargs): + from sympy.concrete.summations import Sum + if (k_sym is not None) or (symbols is not None): + return self + + # Dobinski's formula + if not n.is_nonnegative: + return self + k = Dummy('k', integer=True, nonnegative=True) + return 1 / E * Sum(k**n / factorial(k), (k, 0, S.Infinity)) + + +#----------------------------------------------------------------------------# +# # +# Harmonic numbers # +# # +#----------------------------------------------------------------------------# + + +class harmonic(Function): + r""" + Harmonic numbers + + The nth harmonic number is given by `\operatorname{H}_{n} = + 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}`. + + More generally: + + .. math:: \operatorname{H}_{n,m} = \sum_{k=1}^{n} \frac{1}{k^m} + + As `n \rightarrow \infty`, `\operatorname{H}_{n,m} \rightarrow \zeta(m)`, + the Riemann zeta function. + + * ``harmonic(n)`` gives the nth harmonic number, `\operatorname{H}_n` + + * ``harmonic(n, m)`` gives the nth generalized harmonic number + of order `m`, `\operatorname{H}_{n,m}`, where + ``harmonic(n) == harmonic(n, 1)`` + + This function can be extended to complex `n` and `m` where `n` is not a + negative integer or `m` is a nonpositive integer as + + .. math:: \operatorname{H}_{n,m} = \begin{cases} \zeta(m) - \zeta(m, n+1) + & m \ne 1 \\ \psi(n+1) + \gamma & m = 1 \end{cases} + + Examples + ======== + + >>> from sympy import harmonic, oo + + >>> [harmonic(n) for n in range(6)] + [0, 1, 3/2, 11/6, 25/12, 137/60] + >>> [harmonic(n, 2) for n in range(6)] + [0, 1, 5/4, 49/36, 205/144, 5269/3600] + >>> harmonic(oo, 2) + pi**2/6 + + >>> from sympy import Symbol, Sum + >>> n = Symbol("n") + + >>> harmonic(n).rewrite(Sum) + Sum(1/_k, (_k, 1, n)) + + We can evaluate harmonic numbers for all integral and positive + rational arguments: + + >>> from sympy import S, expand_func, simplify + >>> harmonic(8) + 761/280 + >>> harmonic(11) + 83711/27720 + + >>> H = harmonic(1/S(3)) + >>> H + harmonic(1/3) + >>> He = expand_func(H) + >>> He + -log(6) - sqrt(3)*pi/6 + 2*Sum(log(sin(_k*pi/3))*cos(2*_k*pi/3), (_k, 1, 1)) + + 3*Sum(1/(3*_k + 1), (_k, 0, 0)) + >>> He.doit() + -log(6) - sqrt(3)*pi/6 - log(sqrt(3)/2) + 3 + >>> H = harmonic(25/S(7)) + >>> He = simplify(expand_func(H).doit()) + >>> He + log(sin(2*pi/7)**(2*cos(16*pi/7))/(14*sin(pi/7)**(2*cos(pi/7))*cos(pi/14)**(2*sin(pi/14)))) + pi*tan(pi/14)/2 + 30247/9900 + >>> He.n(40) + 1.983697455232980674869851942390639915940 + >>> harmonic(25/S(7)).n(40) + 1.983697455232980674869851942390639915940 + + We can rewrite harmonic numbers in terms of polygamma functions: + + >>> from sympy import digamma, polygamma + >>> m = Symbol("m", integer=True, positive=True) + + >>> harmonic(n).rewrite(digamma) + polygamma(0, n + 1) + EulerGamma + + >>> harmonic(n).rewrite(polygamma) + polygamma(0, n + 1) + EulerGamma + + >>> harmonic(n,3).rewrite(polygamma) + polygamma(2, n + 1)/2 + zeta(3) + + >>> simplify(harmonic(n,m).rewrite(polygamma)) + Piecewise((polygamma(0, n + 1) + EulerGamma, Eq(m, 1)), + (-(-1)**m*polygamma(m - 1, n + 1)/factorial(m - 1) + zeta(m), True)) + + Integer offsets in the argument can be pulled out: + + >>> from sympy import expand_func + + >>> expand_func(harmonic(n+4)) + harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1) + + >>> expand_func(harmonic(n-4)) + harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n + + Some limits can be computed as well: + + >>> from sympy import limit, oo + + >>> limit(harmonic(n), n, oo) + oo + + >>> limit(harmonic(n, 2), n, oo) + pi**2/6 + + >>> limit(harmonic(n, 3), n, oo) + zeta(3) + + For `m > 1`, `H_{n,m}` tends to `\zeta(m)` in the limit of infinite `n`: + + >>> m = Symbol("m", positive=True) + >>> limit(harmonic(n, m+1), n, oo) + zeta(m + 1) + + See Also + ======== + + bell, bernoulli, catalan, euler, fibonacci, lucas, genocchi, partition, tribonacci + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Harmonic_number + .. [2] https://functions.wolfram.com/GammaBetaErf/HarmonicNumber/ + .. [3] https://functions.wolfram.com/GammaBetaErf/HarmonicNumber2/ + + """ + + @classmethod + def eval(cls, n, m=None): + from sympy.functions.special.zeta_functions import zeta + if m is S.One: + return cls(n) + if m is None: + m = S.One + if n.is_zero: + return S.Zero + elif m.is_zero: + return n + elif n is S.Infinity: + if m.is_negative: + return S.NaN + elif is_le(m, S.One): + return S.Infinity + elif is_gt(m, S.One): + return zeta(m) + elif m.is_Integer and m.is_nonpositive: + return (bernoulli(1-m, n+1) - bernoulli(1-m)) / (1-m) + elif n.is_Integer: + if n.is_negative and (m.is_integer is False or m.is_nonpositive is False): + return S.ComplexInfinity if m is S.One else S.NaN + if n.is_nonnegative: + return Add(*(k**(-m) for k in range(1, int(n)+1))) + + def _eval_rewrite_as_polygamma(self, n, m=S.One, **kwargs): + from sympy.functions.special.gamma_functions import gamma, polygamma + if m.is_integer and m.is_positive: + return Piecewise((polygamma(0, n+1) + S.EulerGamma, Eq(m, 1)), + (S.NegativeOne**m * (polygamma(m-1, 1) - polygamma(m-1, n+1)) / + gamma(m), True)) + + def _eval_rewrite_as_digamma(self, n, m=1, **kwargs): + from sympy.functions.special.gamma_functions import polygamma + return self.rewrite(polygamma) + + def _eval_rewrite_as_trigamma(self, n, m=1, **kwargs): + from sympy.functions.special.gamma_functions import polygamma + return self.rewrite(polygamma) + + def _eval_rewrite_as_Sum(self, n, m=None, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k", integer=True) + if m is None: + m = S.One + return Sum(k**(-m), (k, 1, n)) + + def _eval_rewrite_as_zeta(self, n, m=S.One, **kwargs): + from sympy.functions.special.zeta_functions import zeta + from sympy.functions.special.gamma_functions import digamma + return Piecewise((digamma(n + 1) + S.EulerGamma, Eq(m, 1)), + (zeta(m) - zeta(m, n+1), True)) + + def _eval_expand_func(self, **hints): + from sympy.concrete.summations import Sum + n = self.args[0] + m = self.args[1] if len(self.args) == 2 else 1 + + if m == S.One: + if n.is_Add: + off = n.args[0] + nnew = n - off + if off.is_Integer and off.is_positive: + result = [S.One/(nnew + i) for i in range(off, 0, -1)] + [harmonic(nnew)] + return Add(*result) + elif off.is_Integer and off.is_negative: + result = [-S.One/(nnew + i) for i in range(0, off, -1)] + [harmonic(nnew)] + return Add(*result) + + if n.is_Rational: + # Expansions for harmonic numbers at general rational arguments (u + p/q) + # Split n as u + p/q with p < q + p, q = n.as_numer_denom() + u = p // q + p = p - u * q + if u.is_nonnegative and p.is_positive and q.is_positive and p < q: + from sympy.functions.elementary.exponential import log + from sympy.functions.elementary.integers import floor + from sympy.functions.elementary.trigonometric import sin, cos, cot + k = Dummy("k") + t1 = q * Sum(1 / (q * k + p), (k, 0, u)) + t2 = 2 * Sum(cos((2 * pi * p * k) / S(q)) * + log(sin((pi * k) / S(q))), + (k, 1, floor((q - 1) / S(2)))) + t3 = (pi / 2) * cot((pi * p) / q) + log(2 * q) + return t1 + t2 - t3 + + return self + + def _eval_rewrite_as_tractable(self, n, m=1, limitvar=None, **kwargs): + from sympy.functions.special.zeta_functions import zeta + from sympy.functions.special.gamma_functions import polygamma + pg = self.rewrite(polygamma) + if not isinstance(pg, harmonic): + return pg.rewrite("tractable", deep=True) + arg = m - S.One + if arg.is_nonzero: + return (zeta(m) - zeta(m, n+1)).rewrite("tractable", deep=True) + + def _eval_evalf(self, prec): + if not all(x.is_number for x in self.args): + return + n = self.args[0]._to_mpmath(prec) + m = (self.args[1] if len(self.args) > 1 else S.One)._to_mpmath(prec) + if mp.isint(n) and n < 0: + return S.NaN + with workprec(prec): + if m == 1: + res = mp.harmonic(n) + else: + res = mp.zeta(m) - mp.zeta(m, n+1) + return Expr._from_mpmath(res, prec) + + def fdiff(self, argindex=1): + from sympy.functions.special.zeta_functions import zeta + if len(self.args) == 2: + n, m = self.args + else: + n, m = self.args + (1,) + if argindex == 1: + return m * zeta(m+1, n+1) + else: + raise ArgumentIndexError + + +#----------------------------------------------------------------------------# +# # +# Euler numbers # +# # +#----------------------------------------------------------------------------# + + +class euler(Function): + r""" + Euler numbers / Euler polynomials / Euler function + + The Euler numbers are given by: + + .. math:: E_{2n} = I \sum_{k=1}^{2n+1} \sum_{j=0}^k \binom{k}{j} + \frac{(-1)^j (k-2j)^{2n+1}}{2^k I^k k} + + .. math:: E_{2n+1} = 0 + + Euler numbers and Euler polynomials are related by + + .. math:: E_n = 2^n E_n\left(\frac{1}{2}\right). + + We compute symbolic Euler polynomials using Appell sequences, + but numerical evaluation of the Euler polynomial is computed + more efficiently (and more accurately) using the mpmath library. + + The Euler polynomials are special cases of the generalized Euler function, + related to the Genocchi function as + + .. math:: \operatorname{E}(s, a) = -\frac{\operatorname{G}(s+1, a)}{s+1} + + with the limit of `\psi\left(\frac{a+1}{2}\right) - \psi\left(\frac{a}{2}\right)` + being taken when `s = -1`. The (ordinary) Euler function interpolating + the Euler numbers is then obtained as + `\operatorname{E}(s) = 2^s \operatorname{E}\left(s, \frac{1}{2}\right)`. + + * ``euler(n)`` gives the nth Euler number `E_n`. + * ``euler(s)`` gives the Euler function `\operatorname{E}(s)`. + * ``euler(n, x)`` gives the nth Euler polynomial `E_n(x)`. + * ``euler(s, a)`` gives the generalized Euler function `\operatorname{E}(s, a)`. + + Examples + ======== + + >>> from sympy import euler, Symbol, S + >>> [euler(n) for n in range(10)] + [1, 0, -1, 0, 5, 0, -61, 0, 1385, 0] + >>> [2**n*euler(n,1) for n in range(10)] + [1, 1, 0, -2, 0, 16, 0, -272, 0, 7936] + >>> n = Symbol("n") + >>> euler(n + 2*n) + euler(3*n) + + >>> x = Symbol("x") + >>> euler(n, x) + euler(n, x) + + >>> euler(0, x) + 1 + >>> euler(1, x) + x - 1/2 + >>> euler(2, x) + x**2 - x + >>> euler(3, x) + x**3 - 3*x**2/2 + 1/4 + >>> euler(4, x) + x**4 - 2*x**3 + x + + >>> euler(12, S.Half) + 2702765/4096 + >>> euler(12) + 2702765 + + See Also + ======== + + andre, bell, bernoulli, catalan, fibonacci, harmonic, lucas, genocchi, + partition, tribonacci, sympy.polys.appellseqs.euler_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Euler_numbers + .. [2] https://mathworld.wolfram.com/EulerNumber.html + .. [3] https://en.wikipedia.org/wiki/Alternating_permutation + .. [4] https://mathworld.wolfram.com/AlternatingPermutation.html + + """ + + @classmethod + def eval(cls, n, x=None): + if n.is_zero: + return S.One + elif n is S.NegativeOne: + if x is None: + return S.Pi/2 + from sympy.functions.special.gamma_functions import digamma + return digamma((x+1)/2) - digamma(x/2) + elif n.is_integer is False or n.is_nonnegative is False: + return + # Euler numbers + elif x is None: + if n.is_odd and n.is_positive: + return S.Zero + elif n.is_Number: + from mpmath import mp + n = n._to_mpmath(mp.prec) + res = mp.eulernum(n, exact=True) + return Integer(res) + # Euler polynomials + elif n.is_Number: + return euler_poly(n, x) + + def _eval_rewrite_as_Sum(self, n, x=None, **kwargs): + from sympy.concrete.summations import Sum + if x is None and n.is_even: + k = Dummy("k", integer=True) + j = Dummy("j", integer=True) + n = n / 2 + Em = (S.ImaginaryUnit * Sum(Sum(binomial(k, j) * (S.NegativeOne**j * + (k - 2*j)**(2*n + 1)) / + (2**k*S.ImaginaryUnit**k * k), (j, 0, k)), (k, 1, 2*n + 1))) + return Em + if x: + k = Dummy("k", integer=True) + return Sum(binomial(n, k)*euler(k)/2**k*(x - S.Half)**(n - k), (k, 0, n)) + + def _eval_rewrite_as_genocchi(self, n, x=None, **kwargs): + if x is None: + return Piecewise((S.Pi/2, Eq(n, -1)), + (-2**n * genocchi(n+1, S.Half) / (n+1), True)) + from sympy.functions.special.gamma_functions import digamma + return Piecewise((digamma((x+1)/2) - digamma(x/2), Eq(n, -1)), + (-genocchi(n+1, x) / (n+1), True)) + + def _eval_evalf(self, prec): + if not all(i.is_number for i in self.args): + return + from mpmath import mp + m, x = (self.args[0], None) if len(self.args) == 1 else self.args + m = m._to_mpmath(prec) + if x is not None: + x = x._to_mpmath(prec) + with workprec(prec): + if mp.isint(m) and m >= 0: + res = mp.eulernum(m) if x is None else mp.eulerpoly(m, x) + else: + if m == -1: + res = mp.pi if x is None else mp.digamma((x+1)/2) - mp.digamma(x/2) + else: + y = 0.5 if x is None else x + res = 2 * (mp.zeta(-m, y) - 2**(m+1) * mp.zeta(-m, (y+1)/2)) + if x is None: + res *= 2**m + return Expr._from_mpmath(res, prec) + + +#----------------------------------------------------------------------------# +# # +# Catalan numbers # +# # +#----------------------------------------------------------------------------# + + +class catalan(Function): + r""" + Catalan numbers + + The `n^{th}` catalan number is given by: + + .. math :: C_n = \frac{1}{n+1} \binom{2n}{n} + + * ``catalan(n)`` gives the `n^{th}` Catalan number, `C_n` + + Examples + ======== + + >>> from sympy import (Symbol, binomial, gamma, hyper, + ... catalan, diff, combsimp, Rational, I) + + >>> [catalan(i) for i in range(1,10)] + [1, 2, 5, 14, 42, 132, 429, 1430, 4862] + + >>> n = Symbol("n", integer=True) + + >>> catalan(n) + catalan(n) + + Catalan numbers can be transformed into several other, identical + expressions involving other mathematical functions + + >>> catalan(n).rewrite(binomial) + binomial(2*n, n)/(n + 1) + + >>> catalan(n).rewrite(gamma) + 4**n*gamma(n + 1/2)/(sqrt(pi)*gamma(n + 2)) + + >>> catalan(n).rewrite(hyper) + hyper((-n, 1 - n), (2,), 1) + + For some non-integer values of n we can get closed form + expressions by rewriting in terms of gamma functions: + + >>> catalan(Rational(1, 2)).rewrite(gamma) + 8/(3*pi) + + We can differentiate the Catalan numbers C(n) interpreted as a + continuous real function in n: + + >>> diff(catalan(n), n) + (polygamma(0, n + 1/2) - polygamma(0, n + 2) + log(4))*catalan(n) + + As a more advanced example consider the following ratio + between consecutive numbers: + + >>> combsimp((catalan(n + 1)/catalan(n)).rewrite(binomial)) + 2*(2*n + 1)/(n + 2) + + The Catalan numbers can be generalized to complex numbers: + + >>> catalan(I).rewrite(gamma) + 4**I*gamma(1/2 + I)/(sqrt(pi)*gamma(2 + I)) + + and evaluated with arbitrary precision: + + >>> catalan(I).evalf(20) + 0.39764993382373624267 - 0.020884341620842555705*I + + See Also + ======== + + andre, bell, bernoulli, euler, fibonacci, harmonic, lucas, genocchi, + partition, tribonacci, sympy.functions.combinatorial.factorials.binomial + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Catalan_number + .. [2] https://mathworld.wolfram.com/CatalanNumber.html + .. [3] https://functions.wolfram.com/GammaBetaErf/CatalanNumber/ + .. [4] http://geometer.org/mathcircles/catalan.pdf + + """ + + @classmethod + def eval(cls, n): + from sympy.functions.special.gamma_functions import gamma + if (n.is_Integer and n.is_nonnegative) or \ + (n.is_noninteger and n.is_negative): + return 4**n*gamma(n + S.Half)/(gamma(S.Half)*gamma(n + 2)) + + if (n.is_integer and n.is_negative): + if (n + 1).is_negative: + return S.Zero + if (n + 1).is_zero: + return Rational(-1, 2) + + def fdiff(self, argindex=1): + from sympy.functions.elementary.exponential import log + from sympy.functions.special.gamma_functions import polygamma + n = self.args[0] + return catalan(n)*(polygamma(0, n + S.Half) - polygamma(0, n + 2) + log(4)) + + def _eval_rewrite_as_binomial(self, n, **kwargs): + return binomial(2*n, n)/(n + 1) + + def _eval_rewrite_as_factorial(self, n, **kwargs): + return factorial(2*n) / (factorial(n+1) * factorial(n)) + + def _eval_rewrite_as_gamma(self, n, piecewise=True, **kwargs): + from sympy.functions.special.gamma_functions import gamma + # The gamma function allows to generalize Catalan numbers to complex n + return 4**n*gamma(n + S.Half)/(gamma(S.Half)*gamma(n + 2)) + + def _eval_rewrite_as_hyper(self, n, **kwargs): + from sympy.functions.special.hyper import hyper + return hyper([1 - n, -n], [2], 1) + + def _eval_rewrite_as_Product(self, n, **kwargs): + from sympy.concrete.products import Product + if not (n.is_integer and n.is_nonnegative): + return self + k = Dummy('k', integer=True, positive=True) + return Product((n + k) / k, (k, 2, n)) + + def _eval_is_integer(self): + if self.args[0].is_integer and self.args[0].is_nonnegative: + return True + + def _eval_is_positive(self): + if self.args[0].is_nonnegative: + return True + + def _eval_is_composite(self): + if self.args[0].is_integer and (self.args[0] - 3).is_positive: + return True + + def _eval_evalf(self, prec): + from sympy.functions.special.gamma_functions import gamma + if self.args[0].is_number: + return self.rewrite(gamma)._eval_evalf(prec) + + +#----------------------------------------------------------------------------# +# # +# Genocchi numbers # +# # +#----------------------------------------------------------------------------# + + +class genocchi(Function): + r""" + Genocchi numbers / Genocchi polynomials / Genocchi function + + The Genocchi numbers are a sequence of integers `G_n` that satisfy the + relation: + + .. math:: \frac{-2t}{1 + e^{-t}} = \sum_{n=0}^\infty \frac{G_n t^n}{n!} + + They are related to the Bernoulli numbers by + + .. math:: G_n = 2 (1 - 2^n) B_n + + and generalize like the Bernoulli numbers to the Genocchi polynomials and + function as + + .. math:: \operatorname{G}(s, a) = 2 \left(\operatorname{B}(s, a) - + 2^s \operatorname{B}\left(s, \frac{a+1}{2}\right)\right) + + .. versionchanged:: 1.12 + ``genocchi(1)`` gives `-1` instead of `1`. + + Examples + ======== + + >>> from sympy import genocchi, Symbol + >>> [genocchi(n) for n in range(9)] + [0, -1, -1, 0, 1, 0, -3, 0, 17] + >>> n = Symbol('n', integer=True, positive=True) + >>> genocchi(2*n + 1) + 0 + >>> x = Symbol('x') + >>> genocchi(4, x) + -4*x**3 + 6*x**2 - 1 + + See Also + ======== + + bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, partition, tribonacci + sympy.polys.appellseqs.genocchi_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Genocchi_number + .. [2] https://mathworld.wolfram.com/GenocchiNumber.html + .. [3] Peter Luschny, "An introduction to the Bernoulli function", + https://arxiv.org/abs/2009.06743 + + """ + + @classmethod + def eval(cls, n, x=None): + if x is S.One: + return cls(n) + elif n.is_integer is False or n.is_nonnegative is False: + return + # Genocchi numbers + elif x is None: + if n.is_odd and (n-1).is_positive: + return S.Zero + elif n.is_Number: + return 2 * (1-S(2)**n) * bernoulli(n) + # Genocchi polynomials + elif n.is_Number: + return genocchi_poly(n, x) + + def _eval_rewrite_as_bernoulli(self, n, x=1, **kwargs): + if x == 1 and n.is_integer and n.is_nonnegative: + return 2 * (1-S(2)**n) * bernoulli(n) + return 2 * (bernoulli(n, x) - 2**n * bernoulli(n, (x+1) / 2)) + + def _eval_rewrite_as_dirichlet_eta(self, n, x=1, **kwargs): + from sympy.functions.special.zeta_functions import dirichlet_eta + return -2*n * dirichlet_eta(1-n, x) + + def _eval_is_integer(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + if n.is_integer and n.is_nonnegative: + return True + + def _eval_is_negative(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + if n.is_integer and n.is_nonnegative: + if n.is_odd: + return fuzzy_not((n-1).is_positive) + return (n/2).is_odd + + def _eval_is_positive(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + if n.is_integer and n.is_nonnegative: + if n.is_zero or n.is_odd: + return False + return (n/2).is_even + + def _eval_is_even(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + if n.is_integer and n.is_nonnegative: + if n.is_even: + return n.is_zero + return (n-1).is_positive + + def _eval_is_odd(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + if n.is_integer and n.is_nonnegative: + if n.is_even: + return fuzzy_not(n.is_zero) + return fuzzy_not((n-1).is_positive) + + def _eval_is_prime(self): + if len(self.args) > 1 and self.args[1] != 1: + return + n = self.args[0] + # only G_6 = -3 and G_8 = 17 are prime, + # but SymPy does not consider negatives as prime + # so only n=8 is tested + return (n-8).is_zero + + def _eval_evalf(self, prec): + if all(i.is_number for i in self.args): + return self.rewrite(bernoulli)._eval_evalf(prec) + + +#----------------------------------------------------------------------------# +# # +# Andre numbers # +# # +#----------------------------------------------------------------------------# + + +class andre(Function): + r""" + Andre numbers / Andre function + + The Andre number `\mathcal{A}_n` is Luschny's name for half the number of + *alternating permutations* on `n` elements, where a permutation is alternating + if adjacent elements alternately compare "greater" and "smaller" going from + left to right. For example, `2 < 3 > 1 < 4` is an alternating permutation. + + This sequence is A000111 in the OEIS, which assigns the names *up/down numbers* + and *Euler zigzag numbers*. It satisfies a recurrence relation similar to that + for the Catalan numbers, with `\mathcal{A}_0 = 1` and + + .. math:: 2 \mathcal{A}_{n+1} = \sum_{k=0}^n \binom{n}{k} \mathcal{A}_k \mathcal{A}_{n-k} + + The Bernoulli and Euler numbers are signed transformations of the odd- and + even-indexed elements of this sequence respectively: + + .. math :: \operatorname{B}_{2k} = \frac{2k \mathcal{A}_{2k-1}}{(-4)^k - (-16)^k} + + .. math :: \operatorname{E}_{2k} = (-1)^k \mathcal{A}_{2k} + + Like the Bernoulli and Euler numbers, the Andre numbers are interpolated by the + entire Andre function: + + .. math :: \mathcal{A}(s) = (-i)^{s+1} \operatorname{Li}_{-s}(i) + + i^{s+1} \operatorname{Li}_{-s}(-i) = \\ \frac{2 \Gamma(s+1)}{(2\pi)^{s+1}} + (\zeta(s+1, 1/4) - \zeta(s+1, 3/4) \cos{\pi s}) + + Examples + ======== + + >>> from sympy import andre, euler, bernoulli + >>> [andre(n) for n in range(11)] + [1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521] + >>> [(-1)**k * andre(2*k) for k in range(7)] + [1, -1, 5, -61, 1385, -50521, 2702765] + >>> [euler(2*k) for k in range(7)] + [1, -1, 5, -61, 1385, -50521, 2702765] + >>> [andre(2*k-1) * (2*k) / ((-4)**k - (-16)**k) for k in range(1, 8)] + [1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6] + >>> [bernoulli(2*k) for k in range(1, 8)] + [1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6] + + See Also + ======== + + bernoulli, catalan, euler, sympy.polys.appellseqs.andre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Alternating_permutation + .. [2] https://mathworld.wolfram.com/EulerZigzagNumber.html + .. [3] Peter Luschny, "An introduction to the Bernoulli function", + https://arxiv.org/abs/2009.06743 + """ + + @classmethod + def eval(cls, n): + if n is S.NaN: + return S.NaN + elif n is S.Infinity: + return S.Infinity + if n.is_zero: + return S.One + elif n == -1: + return -log(2) + elif n == -2: + return -2*S.Catalan + elif n.is_Integer: + if n.is_nonnegative and n.is_even: + return abs(euler(n)) + elif n.is_odd: + from sympy.functions.special.zeta_functions import zeta + m = -n-1 + return I**m * Rational(1-2**m, 4**m) * zeta(-n) + + def _eval_rewrite_as_zeta(self, s, **kwargs): + from sympy.functions.elementary.trigonometric import cos + from sympy.functions.special.gamma_functions import gamma + from sympy.functions.special.zeta_functions import zeta + return 2 * gamma(s+1) / (2*pi)**(s+1) * \ + (zeta(s+1, S.One/4) - cos(pi*s) * zeta(s+1, S(3)/4)) + + def _eval_rewrite_as_polylog(self, s, **kwargs): + from sympy.functions.special.zeta_functions import polylog + return (-I)**(s+1) * polylog(-s, I) + I**(s+1) * polylog(-s, -I) + + def _eval_is_integer(self): + n = self.args[0] + if n.is_integer and n.is_nonnegative: + return True + + def _eval_is_positive(self): + if self.args[0].is_nonnegative: + return True + + def _eval_evalf(self, prec): + if not self.args[0].is_number: + return + s = self.args[0]._to_mpmath(prec+12) + with workprec(prec+12): + sp, cp = mp.sinpi(s/2), mp.cospi(s/2) + res = 2*mp.dirichlet(-s, (-sp, cp, sp, -cp)) + return Expr._from_mpmath(res, prec) + + +#----------------------------------------------------------------------------# +# # +# Partition numbers # +# # +#----------------------------------------------------------------------------# + + +class partition(Function): + r""" + Partition numbers + + The Partition numbers are a sequence of integers `p_n` that represent the + number of distinct ways of representing `n` as a sum of natural numbers + (with order irrelevant). The generating function for `p_n` is given by: + + .. math:: \sum_{n=0}^\infty p_n x^n = \prod_{k=1}^\infty (1 - x^k)^{-1} + + Examples + ======== + + >>> from sympy import partition, Symbol + >>> [partition(n) for n in range(9)] + [1, 1, 2, 3, 5, 7, 11, 15, 22] + >>> n = Symbol('n', integer=True, negative=True) + >>> partition(n) + 0 + + See Also + ======== + + bell, bernoulli, catalan, euler, fibonacci, harmonic, lucas, genocchi, tribonacci + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Partition_(number_theory%29 + .. [2] https://en.wikipedia.org/wiki/Pentagonal_number_theorem + + """ + is_integer = True + is_nonnegative = True + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_negative is True: + return S.Zero + if n.is_zero is True or n is S.One: + return S.One + if n.is_Integer is True: + return S(_partition(as_int(n))) + + def _eval_is_positive(self): + if self.args[0].is_nonnegative is True: + return True + + +class divisor_sigma(Function): + r""" + Calculate the divisor function `\sigma_k(n)` for positive integer n + + ``divisor_sigma(n, k)`` is equal to ``sum([x**k for x in divisors(n)])`` + + If n's prime factorization is: + + .. math :: + n = \prod_{i=1}^\omega p_i^{m_i}, + + then + + .. math :: + \sigma_k(n) = \prod_{i=1}^\omega (1+p_i^k+p_i^{2k}+\cdots + + p_i^{m_ik}). + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import divisor_sigma + >>> divisor_sigma(18, 0) + 6 + >>> divisor_sigma(39, 1) + 56 + >>> divisor_sigma(12, 2) + 210 + >>> divisor_sigma(37) + 38 + + See Also + ======== + + sympy.ntheory.factor_.divisor_count, totient, sympy.ntheory.factor_.divisors, sympy.ntheory.factor_.factorint + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Divisor_function + + """ + is_integer = True + is_positive = True + + @classmethod + def eval(cls, n, k=S.One): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if k.is_integer is False: + raise TypeError("k should be an integer") + if k.is_nonnegative is False: + raise ValueError("k should be a nonnegative integer") + if n.is_prime is True: + return 1 + n**k + if n is S.One: + return S.One + if n.is_Integer is True: + if k.is_zero is True: + return Mul(*[e + 1 for e in factorint(n).values()]) + if k.is_Integer is True: + return S(_divisor_sigma(as_int(n), as_int(k))) + if k.is_zero is False: + return Mul(*[cancel((p**(k*(e + 1)) - 1) / (p**k - 1)) for p, e in factorint(n).items()]) + + +class udivisor_sigma(Function): + r""" + Calculate the unitary divisor function `\sigma_k^*(n)` for positive integer n + + ``udivisor_sigma(n, k)`` is equal to ``sum([x**k for x in udivisors(n)])`` + + If n's prime factorization is: + + .. math :: + n = \prod_{i=1}^\omega p_i^{m_i}, + + then + + .. math :: + \sigma_k^*(n) = \prod_{i=1}^\omega (1+ p_i^{m_ik}). + + Parameters + ========== + + k : power of divisors in the sum + + for k = 0, 1: + ``udivisor_sigma(n, 0)`` is equal to ``udivisor_count(n)`` + ``udivisor_sigma(n, 1)`` is equal to ``sum(udivisors(n))`` + + Default for k is 1. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import udivisor_sigma + >>> udivisor_sigma(18, 0) + 4 + >>> udivisor_sigma(74, 1) + 114 + >>> udivisor_sigma(36, 3) + 47450 + >>> udivisor_sigma(111) + 152 + + See Also + ======== + + sympy.ntheory.factor_.divisor_count, totient, sympy.ntheory.factor_.divisors, + sympy.ntheory.factor_.udivisors, sympy.ntheory.factor_.udivisor_count, divisor_sigma, + sympy.ntheory.factor_.factorint + + References + ========== + + .. [1] https://mathworld.wolfram.com/UnitaryDivisorFunction.html + + """ + is_integer = True + is_positive = True + + @classmethod + def eval(cls, n, k=S.One): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if k.is_integer is False: + raise TypeError("k should be an integer") + if k.is_nonnegative is False: + raise ValueError("k should be a nonnegative integer") + if n.is_prime is True: + return 1 + n**k + if n.is_Integer: + return Mul(*[1+p**(k*e) for p, e in factorint(n).items()]) + + +class legendre_symbol(Function): + r""" + Returns the Legendre symbol `(a / p)`. + + For an integer ``a`` and an odd prime ``p``, the Legendre symbol is + defined as + + .. math :: + \genfrac(){}{}{a}{p} = \begin{cases} + 0 & \text{if } p \text{ divides } a\\ + 1 & \text{if } a \text{ is a quadratic residue modulo } p\\ + -1 & \text{if } a \text{ is a quadratic nonresidue modulo } p + \end{cases} + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import legendre_symbol + >>> [legendre_symbol(i, 7) for i in range(7)] + [0, 1, 1, -1, 1, -1, -1] + >>> sorted(set([i**2 % 7 for i in range(7)])) + [0, 1, 2, 4] + + See Also + ======== + + sympy.ntheory.residue_ntheory.is_quad_residue, jacobi_symbol + + """ + is_integer = True + is_prime = False + + @classmethod + def eval(cls, a, p): + if a.is_integer is False: + raise TypeError("a should be an integer") + if p.is_integer is False: + raise TypeError("p should be an integer") + if p.is_prime is False or p.is_odd is False: + raise ValueError("p should be an odd prime integer") + if (a % p).is_zero is True: + return S.Zero + if a is S.One: + return S.One + if a.is_Integer is True and p.is_Integer is True: + return S(legendre(as_int(a), as_int(p))) + + +class jacobi_symbol(Function): + r""" + Returns the Jacobi symbol `(m / n)`. + + For any integer ``m`` and any positive odd integer ``n`` the Jacobi symbol + is defined as the product of the Legendre symbols corresponding to the + prime factors of ``n``: + + .. math :: + \genfrac(){}{}{m}{n} = + \genfrac(){}{}{m}{p^{1}}^{\alpha_1} + \genfrac(){}{}{m}{p^{2}}^{\alpha_2} + ... + \genfrac(){}{}{m}{p^{k}}^{\alpha_k} + \text{ where } n = + p_1^{\alpha_1} + p_2^{\alpha_2} + ... + p_k^{\alpha_k} + + Like the Legendre symbol, if the Jacobi symbol `\genfrac(){}{}{m}{n} = -1` + then ``m`` is a quadratic nonresidue modulo ``n``. + + But, unlike the Legendre symbol, if the Jacobi symbol + `\genfrac(){}{}{m}{n} = 1` then ``m`` may or may not be a quadratic residue + modulo ``n``. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import jacobi_symbol, legendre_symbol + >>> from sympy import S + >>> jacobi_symbol(45, 77) + -1 + >>> jacobi_symbol(60, 121) + 1 + + The relationship between the ``jacobi_symbol`` and ``legendre_symbol`` can + be demonstrated as follows: + + >>> L = legendre_symbol + >>> S(45).factors() + {3: 2, 5: 1} + >>> jacobi_symbol(7, 45) == L(7, 3)**2 * L(7, 5)**1 + True + + See Also + ======== + + sympy.ntheory.residue_ntheory.is_quad_residue, legendre_symbol + + """ + is_integer = True + is_prime = False + + @classmethod + def eval(cls, m, n): + if m.is_integer is False: + raise TypeError("m should be an integer") + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False or n.is_odd is False: + raise ValueError("n should be an odd positive integer") + if m is S.One or n is S.One: + return S.One + if (m % n).is_zero is True: + return S.Zero + if m.is_Integer is True and n.is_Integer is True: + return S(jacobi(as_int(m), as_int(n))) + + +class kronecker_symbol(Function): + r""" + Returns the Kronecker symbol `(a / n)`. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import kronecker_symbol + >>> kronecker_symbol(45, 77) + -1 + >>> kronecker_symbol(13, -120) + 1 + + See Also + ======== + + jacobi_symbol, legendre_symbol + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Kronecker_symbol + + """ + is_integer = True + is_prime = False + + @classmethod + def eval(cls, a, n): + if a.is_integer is False: + raise TypeError("a should be an integer") + if n.is_integer is False: + raise TypeError("n should be an integer") + if a is S.One or n is S.One: + return S.One + if a.is_Integer is True and n.is_Integer is True: + return S(kronecker(as_int(a), as_int(n))) + + +class mobius(Function): + """ + Mobius function maps natural number to {-1, 0, 1} + + It is defined as follows: + 1) `1` if `n = 1`. + 2) `0` if `n` has a squared prime factor. + 3) `(-1)^k` if `n` is a square-free positive integer with `k` + number of prime factors. + + It is an important multiplicative function in number theory + and combinatorics. It has applications in mathematical series, + algebraic number theory and also physics (Fermion operator has very + concrete realization with Mobius Function model). + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import mobius + >>> mobius(13*7) + 1 + >>> mobius(1) + 1 + >>> mobius(13*7*5) + -1 + >>> mobius(13**2) + 0 + + Even in the case of a symbol, if it clearly contains a squared prime factor, it will be zero. + + >>> from sympy import Symbol + >>> n = Symbol("n", integer=True, positive=True) + >>> mobius(4*n) + 0 + >>> mobius(n**2) + 0 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/M%C3%B6bius_function + .. [2] Thomas Koshy "Elementary Number Theory with Applications" + .. [3] https://oeis.org/A008683 + + """ + is_integer = True + is_prime = False + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if n.is_prime is True: + return S.NegativeOne + if n is S.One: + return S.One + result = None + for m, e in (_.as_base_exp() for _ in Mul.make_args(n)): + if m.is_integer is True and m.is_positive is True and \ + e.is_integer is True and e.is_positive is True: + lt = is_lt(S.One, e) # 1 < e + if lt is True: + result = S.Zero + elif m.is_Integer is True: + factors = factorint(m) + if any(v > 1 for v in factors.values()): + result = S.Zero + elif lt is False: + s = S.NegativeOne if len(factors) % 2 else S.One + if result is None: + result = s + else: + result *= s + else: + return + return result + + +class primenu(Function): + r""" + Calculate the number of distinct prime factors for a positive integer n. + + If n's prime factorization is: + + .. math :: + n = \prod_{i=1}^k p_i^{m_i}, + + then ``primenu(n)`` or `\nu(n)` is: + + .. math :: + \nu(n) = k. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import primenu + >>> primenu(1) + 0 + >>> primenu(30) + 3 + + See Also + ======== + + sympy.ntheory.factor_.factorint + + References + ========== + + .. [1] https://mathworld.wolfram.com/PrimeFactor.html + .. [2] https://oeis.org/A001221 + + """ + is_integer = True + is_nonnegative = True + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if n.is_prime is True: + return S.One + if n is S.One: + return S.Zero + if n.is_Integer is True: + return S(len(factorint(n))) + + +class primeomega(Function): + r""" + Calculate the number of prime factors counting multiplicities for a + positive integer n. + + If n's prime factorization is: + + .. math :: + n = \prod_{i=1}^k p_i^{m_i}, + + then ``primeomega(n)`` or `\Omega(n)` is: + + .. math :: + \Omega(n) = \sum_{i=1}^k m_i. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import primeomega + >>> primeomega(1) + 0 + >>> primeomega(20) + 3 + + See Also + ======== + + sympy.ntheory.factor_.factorint + + References + ========== + + .. [1] https://mathworld.wolfram.com/PrimeFactor.html + .. [2] https://oeis.org/A001222 + + """ + is_integer = True + is_nonnegative = True + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if n.is_prime is True: + return S.One + if n is S.One: + return S.Zero + if n.is_Integer is True: + return S(sum(factorint(n).values())) + + +class totient(Function): + r""" + Calculate the Euler totient function phi(n) + + ``totient(n)`` or `\phi(n)` is the number of positive integers `\leq` n + that are relatively prime to n. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import totient + >>> totient(1) + 1 + >>> totient(25) + 20 + >>> totient(45) == totient(5)*totient(9) + True + + See Also + ======== + + sympy.ntheory.factor_.divisor_count + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Euler%27s_totient_function + .. [2] https://mathworld.wolfram.com/TotientFunction.html + .. [3] https://oeis.org/A000010 + + """ + is_integer = True + is_positive = True + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if n is S.One: + return S.One + if n.is_prime is True: + return n - 1 + if isinstance(n, Dict): + return S(prod(p**(k-1)*(p-1) for p, k in n.items())) + if n.is_Integer is True: + return S(prod(p**(k-1)*(p-1) for p, k in factorint(n).items())) + + +class reduced_totient(Function): + r""" + Calculate the Carmichael reduced totient function lambda(n) + + ``reduced_totient(n)`` or `\lambda(n)` is the smallest m > 0 such that + `k^m \equiv 1 \mod n` for all k relatively prime to n. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import reduced_totient + >>> reduced_totient(1) + 1 + >>> reduced_totient(8) + 2 + >>> reduced_totient(30) + 4 + + See Also + ======== + + totient + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Carmichael_function + .. [2] https://mathworld.wolfram.com/CarmichaelFunction.html + .. [3] https://oeis.org/A002322 + + """ + is_integer = True + is_positive = True + + @classmethod + def eval(cls, n): + if n.is_integer is False: + raise TypeError("n should be an integer") + if n.is_positive is False: + raise ValueError("n should be a positive integer") + if n is S.One: + return S.One + if n.is_prime is True: + return n - 1 + if isinstance(n, Dict): + t = 1 + if 2 in n: + t = (1 << (n[2] - 2)) if 2 < n[2] else n[2] + return S(lcm(int(t), *(int(p-1)*int(p)**int(k-1) for p, k in n.items() if p != 2))) + if n.is_Integer is True: + n, t = remove(int(n), 2) + if not t: + t = 1 + elif 2 < t: + t = 1 << (t - 2) + return S(lcm(t, *((p-1)*p**(k-1) for p, k in factorint(n).items()))) + + +class primepi(Function): + r""" Represents the prime counting function pi(n) = the number + of prime numbers less than or equal to n. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import primepi + >>> from sympy import prime, prevprime, isprime + >>> primepi(25) + 9 + + So there are 9 primes less than or equal to 25. Is 25 prime? + + >>> isprime(25) + False + + It is not. So the first prime less than 25 must be the + 9th prime: + + >>> prevprime(25) == prime(9) + True + + See Also + ======== + + sympy.ntheory.primetest.isprime : Test if n is prime + sympy.ntheory.generate.primerange : Generate all primes in a given range + sympy.ntheory.generate.prime : Return the nth prime + + References + ========== + + .. [1] https://oeis.org/A000720 + + """ + is_integer = True + is_nonnegative = True + + @classmethod + def eval(cls, n): + if n is S.Infinity: + return S.Infinity + if n is S.NegativeInfinity: + return S.Zero + if n.is_real is False: + raise TypeError("n should be a real") + if is_lt(n, S(2)) is True: + return S.Zero + try: + n = int(n) + except TypeError: + return + return S(_primepi(n)) + + +####################################################################### +### +### Functions for enumerating partitions, permutations and combinations +### +####################################################################### + + +class _MultisetHistogram(tuple): + pass + + +_N = -1 +_ITEMS = -2 +_M = slice(None, _ITEMS) + + +def _multiset_histogram(n): + """Return tuple used in permutation and combination counting. Input + is a dictionary giving items with counts as values or a sequence of + items (which need not be sorted). + + The data is stored in a class deriving from tuple so it is easily + recognized and so it can be converted easily to a list. + """ + if isinstance(n, dict): # item: count + if not all(isinstance(v, int) and v >= 0 for v in n.values()): + raise ValueError + tot = sum(n.values()) + items = sum(1 for k in n if n[k] > 0) + return _MultisetHistogram([n[k] for k in n if n[k] > 0] + [items, tot]) + else: + n = list(n) + s = set(n) + lens = len(s) + lenn = len(n) + if lens == lenn: + n = [1]*lenn + [lenn, lenn] + return _MultisetHistogram(n) + m = dict(zip(s, range(lens))) + d = dict(zip(range(lens), (0,)*lens)) + for i in n: + d[m[i]] += 1 + return _multiset_histogram(d) + + +def nP(n, k=None, replacement=False): + """Return the number of permutations of ``n`` items taken ``k`` at a time. + + Possible values for ``n``: + + integer - set of length ``n`` + + sequence - converted to a multiset internally + + multiset - {element: multiplicity} + + If ``k`` is None then the total of all permutations of length 0 + through the number of items represented by ``n`` will be returned. + + If ``replacement`` is True then a given item can appear more than once + in the ``k`` items. (For example, for 'ab' permutations of 2 would + include 'aa', 'ab', 'ba' and 'bb'.) The multiplicity of elements in + ``n`` is ignored when ``replacement`` is True but the total number + of elements is considered since no element can appear more times than + the number of elements in ``n``. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import nP + >>> from sympy.utilities.iterables import multiset_permutations, multiset + >>> nP(3, 2) + 6 + >>> nP('abc', 2) == nP(multiset('abc'), 2) == 6 + True + >>> nP('aab', 2) + 3 + >>> nP([1, 2, 2], 2) + 3 + >>> [nP(3, i) for i in range(4)] + [1, 3, 6, 6] + >>> nP(3) == sum(_) + True + + When ``replacement`` is True, each item can have multiplicity + equal to the length represented by ``n``: + + >>> nP('aabc', replacement=True) + 121 + >>> [len(list(multiset_permutations('aaaabbbbcccc', i))) for i in range(5)] + [1, 3, 9, 27, 81] + >>> sum(_) + 121 + + See Also + ======== + sympy.utilities.iterables.multiset_permutations + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Permutation + + """ + try: + n = as_int(n) + except ValueError: + return Integer(_nP(_multiset_histogram(n), k, replacement)) + return Integer(_nP(n, k, replacement)) + + +@cacheit +def _nP(n, k=None, replacement=False): + + if k == 0: + return 1 + if isinstance(n, SYMPY_INTS): # n different items + # assert n >= 0 + if k is None: + return sum(_nP(n, i, replacement) for i in range(n + 1)) + elif replacement: + return n**k + elif k > n: + return 0 + elif k == n: + return factorial(k) + elif k == 1: + return n + else: + # assert k >= 0 + return _product(n - k + 1, n) + elif isinstance(n, _MultisetHistogram): + if k is None: + return sum(_nP(n, i, replacement) for i in range(n[_N] + 1)) + elif replacement: + return n[_ITEMS]**k + elif k == n[_N]: + return factorial(k)/prod([factorial(i) for i in n[_M] if i > 1]) + elif k > n[_N]: + return 0 + elif k == 1: + return n[_ITEMS] + else: + # assert k >= 0 + tot = 0 + n = list(n) + for i in range(len(n[_M])): + if not n[i]: + continue + n[_N] -= 1 + if n[i] == 1: + n[i] = 0 + n[_ITEMS] -= 1 + tot += _nP(_MultisetHistogram(n), k - 1) + n[_ITEMS] += 1 + n[i] = 1 + else: + n[i] -= 1 + tot += _nP(_MultisetHistogram(n), k - 1) + n[i] += 1 + n[_N] += 1 + return tot + + +@cacheit +def _AOP_product(n): + """for n = (m1, m2, .., mk) return the coefficients of the polynomial, + prod(sum(x**i for i in range(nj + 1)) for nj in n); i.e. the coefficients + of the product of AOPs (all-one polynomials) or order given in n. The + resulting coefficient corresponding to x**r is the number of r-length + combinations of sum(n) elements with multiplicities given in n. + The coefficients are given as a default dictionary (so if a query is made + for a key that is not present, 0 will be returned). + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import _AOP_product + >>> from sympy.abc import x + >>> n = (2, 2, 3) # e.g. aabbccc + >>> prod = ((x**2 + x + 1)*(x**2 + x + 1)*(x**3 + x**2 + x + 1)).expand() + >>> c = _AOP_product(n); dict(c) + {0: 1, 1: 3, 2: 6, 3: 8, 4: 8, 5: 6, 6: 3, 7: 1} + >>> [c[i] for i in range(8)] == [prod.coeff(x, i) for i in range(8)] + True + + The generating poly used here is the same as that listed in + https://tinyurl.com/cep849r, but in a refactored form. + + """ + + n = list(n) + ord = sum(n) + need = (ord + 2)//2 + rv = [1]*(n.pop() + 1) + rv.extend((0,) * (need - len(rv))) + rv = rv[:need] + while n: + ni = n.pop() + N = ni + 1 + was = rv[:] + for i in range(1, min(N, len(rv))): + rv[i] += rv[i - 1] + for i in range(N, need): + rv[i] += rv[i - 1] - was[i - N] + rev = list(reversed(rv)) + if ord % 2: + rv = rv + rev + else: + rv[-1:] = rev + d = defaultdict(int) + for i, r in enumerate(rv): + d[i] = r + return d + + +def nC(n, k=None, replacement=False): + """Return the number of combinations of ``n`` items taken ``k`` at a time. + + Possible values for ``n``: + + integer - set of length ``n`` + + sequence - converted to a multiset internally + + multiset - {element: multiplicity} + + If ``k`` is None then the total of all combinations of length 0 + through the number of items represented in ``n`` will be returned. + + If ``replacement`` is True then a given item can appear more than once + in the ``k`` items. (For example, for 'ab' sets of 2 would include 'aa', + 'ab', and 'bb'.) The multiplicity of elements in ``n`` is ignored when + ``replacement`` is True but the total number of elements is considered + since no element can appear more times than the number of elements in + ``n``. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import nC + >>> from sympy.utilities.iterables import multiset_combinations + >>> nC(3, 2) + 3 + >>> nC('abc', 2) + 3 + >>> nC('aab', 2) + 2 + + When ``replacement`` is True, each item can have multiplicity + equal to the length represented by ``n``: + + >>> nC('aabc', replacement=True) + 35 + >>> [len(list(multiset_combinations('aaaabbbbcccc', i))) for i in range(5)] + [1, 3, 6, 10, 15] + >>> sum(_) + 35 + + If there are ``k`` items with multiplicities ``m_1, m_2, ..., m_k`` + then the total of all combinations of length 0 through ``k`` is the + product, ``(m_1 + 1)*(m_2 + 1)*...*(m_k + 1)``. When the multiplicity + of each item is 1 (i.e., k unique items) then there are 2**k + combinations. For example, if there are 4 unique items, the total number + of combinations is 16: + + >>> sum(nC(4, i) for i in range(5)) + 16 + + See Also + ======== + + sympy.utilities.iterables.multiset_combinations + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Combination + .. [2] https://tinyurl.com/cep849r + + """ + + if isinstance(n, SYMPY_INTS): + if k is None: + if not replacement: + return 2**n + return sum(nC(n, i, replacement) for i in range(n + 1)) + if k < 0: + raise ValueError("k cannot be negative") + if replacement: + return binomial(n + k - 1, k) + return binomial(n, k) + if isinstance(n, _MultisetHistogram): + N = n[_N] + if k is None: + if not replacement: + return prod(m + 1 for m in n[_M]) + return sum(nC(n, i, replacement) for i in range(N + 1)) + elif replacement: + return nC(n[_ITEMS], k, replacement) + # assert k >= 0 + elif k in (1, N - 1): + return n[_ITEMS] + elif k in (0, N): + return 1 + return _AOP_product(tuple(n[_M]))[k] + else: + return nC(_multiset_histogram(n), k, replacement) + + +def _eval_stirling1(n, k): + if n == k == 0: + return S.One + if 0 in (n, k): + return S.Zero + + # some special values + if n == k: + return S.One + elif k == n - 1: + return binomial(n, 2) + elif k == n - 2: + return (3*n - 1)*binomial(n, 3)/4 + elif k == n - 3: + return binomial(n, 2)*binomial(n, 4) + + return _stirling1(n, k) + + +@cacheit +def _stirling1(n, k): + row = [0, 1]+[0]*(k-1) # for n = 1 + for i in range(2, n+1): + for j in range(min(k,i), 0, -1): + row[j] = (i-1) * row[j] + row[j-1] + return Integer(row[k]) + + +def _eval_stirling2(n, k): + if n == k == 0: + return S.One + if 0 in (n, k): + return S.Zero + + # some special values + if n == k: + return S.One + elif k == n - 1: + return binomial(n, 2) + elif k == 1: + return S.One + elif k == 2: + return Integer(2**(n - 1) - 1) + + return _stirling2(n, k) + + +@cacheit +def _stirling2(n, k): + row = [0, 1]+[0]*(k-1) # for n = 1 + for i in range(2, n+1): + for j in range(min(k,i), 0, -1): + row[j] = j * row[j] + row[j-1] + return Integer(row[k]) + + +def stirling(n, k, d=None, kind=2, signed=False): + r"""Return Stirling number $S(n, k)$ of the first or second (default) kind. + + The sum of all Stirling numbers of the second kind for $k = 1$ + through $n$ is ``bell(n)``. The recurrence relationship for these numbers + is: + + .. math :: {0 \brace 0} = 1; {n \brace 0} = {0 \brace k} = 0; + + .. math :: {{n+1} \brace k} = j {n \brace k} + {n \brace {k-1}} + + where $j$ is: + $n$ for Stirling numbers of the first kind, + $-n$ for signed Stirling numbers of the first kind, + $k$ for Stirling numbers of the second kind. + + The first kind of Stirling number counts the number of permutations of + ``n`` distinct items that have ``k`` cycles; the second kind counts the + ways in which ``n`` distinct items can be partitioned into ``k`` parts. + If ``d`` is given, the "reduced Stirling number of the second kind" is + returned: $S^{d}(n, k) = S(n - d + 1, k - d + 1)$ with $n \ge k \ge d$. + (This counts the ways to partition $n$ consecutive integers into $k$ + groups with no pairwise difference less than $d$. See example below.) + + To obtain the signed Stirling numbers of the first kind, use keyword + ``signed=True``. Using this keyword automatically sets ``kind`` to 1. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import stirling, bell + >>> from sympy.combinatorics import Permutation + >>> from sympy.utilities.iterables import multiset_partitions, permutations + + First kind (unsigned by default): + + >>> [stirling(6, i, kind=1) for i in range(7)] + [0, 120, 274, 225, 85, 15, 1] + >>> perms = list(permutations(range(4))) + >>> [sum(Permutation(p).cycles == i for p in perms) for i in range(5)] + [0, 6, 11, 6, 1] + >>> [stirling(4, i, kind=1) for i in range(5)] + [0, 6, 11, 6, 1] + + First kind (signed): + + >>> [stirling(4, i, signed=True) for i in range(5)] + [0, -6, 11, -6, 1] + + Second kind: + + >>> [stirling(10, i) for i in range(12)] + [0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1, 0] + >>> sum(_) == bell(10) + True + >>> len(list(multiset_partitions(range(4), 2))) == stirling(4, 2) + True + + Reduced second kind: + + >>> from sympy import subsets, oo + >>> def delta(p): + ... if len(p) == 1: + ... return oo + ... return min(abs(i[0] - i[1]) for i in subsets(p, 2)) + >>> parts = multiset_partitions(range(5), 3) + >>> d = 2 + >>> sum(1 for p in parts if all(delta(i) >= d for i in p)) + 7 + >>> stirling(5, 3, 2) + 7 + + See Also + ======== + sympy.utilities.iterables.multiset_partitions + + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind + .. [2] https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind + + """ + # TODO: make this a class like bell() + + n = as_int(n) + k = as_int(k) + if n < 0: + raise ValueError('n must be nonnegative') + if k > n: + return S.Zero + if d: + # assert k >= d + # kind is ignored -- only kind=2 is supported + return _eval_stirling2(n - d + 1, k - d + 1) + elif signed: + # kind is ignored -- only kind=1 is supported + return S.NegativeOne**(n - k)*_eval_stirling1(n, k) + + if kind == 1: + return _eval_stirling1(n, k) + elif kind == 2: + return _eval_stirling2(n, k) + else: + raise ValueError('kind must be 1 or 2, not %s' % k) + + +@cacheit +def _nT(n, k): + """Return the partitions of ``n`` items into ``k`` parts. This + is used by ``nT`` for the case when ``n`` is an integer.""" + # really quick exits + if k > n or k < 0: + return 0 + if k in (1, n): + return 1 + if k == 0: + return 0 + # exits that could be done below but this is quicker + if k == 2: + return n//2 + d = n - k + if d <= 3: + return d + # quick exit + if 3*k >= n: # or, equivalently, 2*k >= d + # all the information needed in this case + # will be in the cache needed to calculate + # partition(d), so... + # update cache + tot = _partition_rec(d) + # and correct for values not needed + if d - k > 0: + tot -= sum(_partition_rec.fetch_item(slice(d - k))) + return tot + # regular exit + # nT(n, k) = Sum(nT(n - k, m), (m, 1, k)); + # calculate needed nT(i, j) values + p = [1]*d + for i in range(2, k + 1): + for m in range(i + 1, d): + p[m] += p[m - i] + d -= 1 + # if p[0] were appended to the end of p then the last + # k values of p are the nT(n, j) values for 0 < j < k in reverse + # order p[-1] = nT(n, 1), p[-2] = nT(n, 2), etc.... Instead of + # putting the 1 from p[0] there, however, it is simply added to + # the sum below which is valid for 1 < k <= n//2 + return (1 + sum(p[1 - k:])) + + +def nT(n, k=None): + """Return the number of ``k``-sized partitions of ``n`` items. + + Possible values for ``n``: + + integer - ``n`` identical items + + sequence - converted to a multiset internally + + multiset - {element: multiplicity} + + Note: the convention for ``nT`` is different than that of ``nC`` and + ``nP`` in that + here an integer indicates ``n`` *identical* items instead of a set of + length ``n``; this is in keeping with the ``partitions`` function which + treats its integer-``n`` input like a list of ``n`` 1s. One can use + ``range(n)`` for ``n`` to indicate ``n`` distinct items. + + If ``k`` is None then the total number of ways to partition the elements + represented in ``n`` will be returned. + + Examples + ======== + + >>> from sympy.functions.combinatorial.numbers import nT + + Partitions of the given multiset: + + >>> [nT('aabbc', i) for i in range(1, 7)] + [1, 8, 11, 5, 1, 0] + >>> nT('aabbc') == sum(_) + True + + >>> [nT("mississippi", i) for i in range(1, 12)] + [1, 74, 609, 1521, 1768, 1224, 579, 197, 50, 9, 1] + + Partitions when all items are identical: + + >>> [nT(5, i) for i in range(1, 6)] + [1, 2, 2, 1, 1] + >>> nT('1'*5) == sum(_) + True + + When all items are different: + + >>> [nT(range(5), i) for i in range(1, 6)] + [1, 15, 25, 10, 1] + >>> nT(range(5)) == sum(_) + True + + Partitions of an integer expressed as a sum of positive integers: + + >>> from sympy import partition + >>> partition(4) + 5 + >>> nT(4, 1) + nT(4, 2) + nT(4, 3) + nT(4, 4) + 5 + >>> nT('1'*4) + 5 + + See Also + ======== + sympy.utilities.iterables.partitions + sympy.utilities.iterables.multiset_partitions + sympy.functions.combinatorial.numbers.partition + + References + ========== + + .. [1] https://web.archive.org/web/20210507012732/https://teaching.csse.uwa.edu.au/units/CITS7209/partition.pdf + + """ + + if isinstance(n, SYMPY_INTS): + # n identical items + if k is None: + return partition(n) + if isinstance(k, SYMPY_INTS): + n = as_int(n) + k = as_int(k) + return Integer(_nT(n, k)) + if not isinstance(n, _MultisetHistogram): + try: + # if n contains hashable items there is some + # quick handling that can be done + u = len(set(n)) + if u <= 1: + return nT(len(n), k) + elif u == len(n): + n = range(u) + raise TypeError + except TypeError: + n = _multiset_histogram(n) + N = n[_N] + if k is None and N == 1: + return 1 + if k in (1, N): + return 1 + if k == 2 or N == 2 and k is None: + m, r = divmod(N, 2) + rv = sum(nC(n, i) for i in range(1, m + 1)) + if not r: + rv -= nC(n, m)//2 + if k is None: + rv += 1 # for k == 1 + return rv + if N == n[_ITEMS]: + # all distinct + if k is None: + return bell(N) + return stirling(N, k) + m = MultisetPartitionTraverser() + if k is None: + return m.count_partitions(n[_M]) + # MultisetPartitionTraverser does not have a range-limited count + # method, so need to enumerate and count + tot = 0 + for discard in m.enum_range(n[_M], k-1, k): + tot += 1 + return tot + + +#-----------------------------------------------------------------------------# +# # +# Motzkin numbers # +# # +#-----------------------------------------------------------------------------# + + +class motzkin(Function): + """ + The nth Motzkin number is the number + of ways of drawing non-intersecting chords + between n points on a circle (not necessarily touching + every point by a chord). The Motzkin numbers are named + after Theodore Motzkin and have diverse applications + in geometry, combinatorics and number theory. + + Motzkin numbers are the integer sequence defined by the + initial terms `M_0 = 1`, `M_1 = 1` and the two-term recurrence relation + `M_n = \frac{2*n + 1}{n + 2} * M_{n-1} + \frac{3n - 3}{n + 2} * M_{n-2}`. + + + Examples + ======== + + >>> from sympy import motzkin + + >>> motzkin.is_motzkin(5) + False + >>> motzkin.find_motzkin_numbers_in_range(2,300) + [2, 4, 9, 21, 51, 127] + >>> motzkin.find_motzkin_numbers_in_range(2,900) + [2, 4, 9, 21, 51, 127, 323, 835] + >>> motzkin.find_first_n_motzkins(10) + [1, 1, 2, 4, 9, 21, 51, 127, 323, 835] + + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Motzkin_number + .. [2] https://mathworld.wolfram.com/MotzkinNumber.html + + """ + + @staticmethod + def is_motzkin(n): + try: + n = as_int(n) + except ValueError: + return False + if n > 0: + if n in (1, 2): + return True + + tn1 = 1 + tn = 2 + i = 3 + while tn < n: + a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2) + i += 1 + tn1 = tn + tn = a + + if tn == n: + return True + else: + return False + + else: + return False + + @staticmethod + def find_motzkin_numbers_in_range(x, y): + if 0 <= x <= y: + motzkins = [] + if x <= 1 <= y: + motzkins.append(1) + tn1 = 1 + tn = 2 + i = 3 + while tn <= y: + if tn >= x: + motzkins.append(tn) + a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2) + i += 1 + tn1 = tn + tn = int(a) + + return motzkins + + else: + raise ValueError('The provided range is not valid. This condition should satisfy x <= y') + + @staticmethod + def find_first_n_motzkins(n): + try: + n = as_int(n) + except ValueError: + raise ValueError('The provided number must be a positive integer') + if n < 0: + raise ValueError('The provided number must be a positive integer') + motzkins = [1] + if n >= 1: + motzkins.append(1) + tn1 = 1 + tn = 2 + i = 3 + while i <= n: + motzkins.append(tn) + a = ((2*i + 1)*tn + (3*i - 3)*tn1)/(i + 2) + i += 1 + tn1 = tn + tn = int(a) + + return motzkins + + @staticmethod + @recurrence_memo([S.One, S.One]) + def _motzkin(n, prev): + return ((2*n + 1)*prev[-1] + (3*n - 3)*prev[-2]) // (n + 2) + + @classmethod + def eval(cls, n): + try: + n = as_int(n) + except ValueError: + raise ValueError('The provided number must be a positive integer') + if n < 0: + raise ValueError('The provided number must be a positive integer') + return Integer(cls._motzkin(n - 1)) + + +def nD(i=None, brute=None, *, n=None, m=None): + """return the number of derangements for: ``n`` unique items, ``i`` + items (as a sequence or multiset), or multiplicities, ``m`` given + as a sequence or multiset. + + Examples + ======== + + >>> from sympy.utilities.iterables import generate_derangements as enum + >>> from sympy.functions.combinatorial.numbers import nD + + A derangement ``d`` of sequence ``s`` has all ``d[i] != s[i]``: + + >>> set([''.join(i) for i in enum('abc')]) + {'bca', 'cab'} + >>> nD('abc') + 2 + + Input as iterable or dictionary (multiset form) is accepted: + + >>> assert nD([1, 2, 2, 3, 3, 3]) == nD({1: 1, 2: 2, 3: 3}) + + By default, a brute-force enumeration and count of multiset permutations + is only done if there are fewer than 9 elements. There may be cases when + there is high multiplicity with few unique elements that will benefit + from a brute-force enumeration, too. For this reason, the `brute` + keyword (default None) is provided. When False, the brute-force + enumeration will never be used. When True, it will always be used. + + >>> nD('1111222233', brute=True) + 44 + + For convenience, one may specify ``n`` distinct items using the + ``n`` keyword: + + >>> assert nD(n=3) == nD('abc') == 2 + + Since the number of derangments depends on the multiplicity of the + elements and not the elements themselves, it may be more convenient + to give a list or multiset of multiplicities using keyword ``m``: + + >>> assert nD('abc') == nD(m=(1,1,1)) == nD(m={1:3}) == 2 + + """ + from sympy.integrals.integrals import integrate + from sympy.functions.special.polynomials import laguerre + from sympy.abc import x + def ok(x): + if not isinstance(x, SYMPY_INTS): + raise TypeError('expecting integer values') + if x < 0: + raise ValueError('value must not be negative') + return True + + if (i, n, m).count(None) != 2: + raise ValueError('enter only 1 of i, n, or m') + if i is not None: + if isinstance(i, SYMPY_INTS): + raise TypeError('items must be a list or dictionary') + if not i: + return S.Zero + if type(i) is not dict: + s = list(i) + ms = multiset(s) + elif type(i) is dict: + all(ok(_) for _ in i.values()) + ms = {k: v for k, v in i.items() if v} + s = None + if not ms: + return S.Zero + N = sum(ms.values()) + counts = multiset(ms.values()) + nkey = len(ms) + elif n is not None: + ok(n) + if not n: + return S.Zero + return subfactorial(n) + elif m is not None: + if isinstance(m, dict): + all(ok(i) and ok(j) for i, j in m.items()) + counts = {k: v for k, v in m.items() if k*v} + elif iterable(m) or isinstance(m, str): + m = list(m) + all(ok(i) for i in m) + counts = multiset([i for i in m if i]) + else: + raise TypeError('expecting iterable') + if not counts: + return S.Zero + N = sum(k*v for k, v in counts.items()) + nkey = sum(counts.values()) + s = None + big = int(max(counts)) + if big == 1: # no repetition + return subfactorial(nkey) + nval = len(counts) + if big*2 > N: + return S.Zero + if big*2 == N: + if nkey == 2 and nval == 1: + return S.One # aaabbb + if nkey - 1 == big: # one element repeated + return factorial(big) # e.g. abc part of abcddd + if N < 9 and brute is None or brute: + # for all possibilities, this was found to be faster + if s is None: + s = [] + i = 0 + for m, v in counts.items(): + for j in range(v): + s.extend([i]*m) + i += 1 + return Integer(sum(1 for i in multiset_derangements(s))) + from sympy.functions.elementary.exponential import exp + return Integer(abs(integrate(exp(-x)*Mul(*[ + laguerre(i, x)**m for i, m in counts.items()]), (x, 0, oo)))) diff --git a/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/__init__.py b/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/__pycache__/__init__.cpython-311.pyc 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b/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/test_comb_factorials.py new file mode 100644 index 0000000000000000000000000000000000000000..bf56945e760886bd86b0e5c637d720a3a85513bb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/test_comb_factorials.py @@ -0,0 +1,653 @@ +from sympy.concrete.products import Product +from sympy.core.function import expand_func +from sympy.core.mod import Mod +from sympy.core.mul import Mul +from sympy.core import EulerGamma +from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.combinatorial.factorials import (ff, rf, binomial, factorial, factorial2) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.gamma_functions import (gamma, polygamma) +from sympy.polys.polytools import Poly +from sympy.series.order import O +from sympy.simplify.simplify import simplify +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.functions.combinatorial.factorials import subfactorial +from sympy.functions.special.gamma_functions import uppergamma +from sympy.testing.pytest import XFAIL, raises, slow + +#Solves and Fixes Issue #10388 - This is the updated test for the same solved issue + +def test_rf_eval_apply(): + x, y = symbols('x,y') + n, k = symbols('n k', integer=True) + m = Symbol('m', integer=True, nonnegative=True) + + assert rf(nan, y) is nan + assert rf(x, nan) is nan + + assert unchanged(rf, x, y) + + assert rf(oo, 0) == 1 + assert rf(-oo, 0) == 1 + + assert rf(oo, 6) is oo + assert rf(-oo, 7) is -oo + assert rf(-oo, 6) is oo + + assert rf(oo, -6) is oo + assert rf(-oo, -7) is oo + + assert rf(-1, pi) == 0 + assert rf(-5, 1 + I) == 0 + + assert unchanged(rf, -3, k) + assert unchanged(rf, x, Symbol('k', integer=False)) + assert rf(-3, Symbol('k', integer=False)) == 0 + assert rf(Symbol('x', negative=True, integer=True), Symbol('k', integer=False)) == 0 + + assert rf(x, 0) == 1 + assert rf(x, 1) == x + assert rf(x, 2) == x*(x + 1) + assert rf(x, 3) == x*(x + 1)*(x + 2) + assert rf(x, 5) == x*(x + 1)*(x + 2)*(x + 3)*(x + 4) + + assert rf(x, -1) == 1/(x - 1) + assert rf(x, -2) == 1/((x - 1)*(x - 2)) + assert rf(x, -3) == 1/((x - 1)*(x - 2)*(x - 3)) + + assert rf(1, 100) == factorial(100) + + assert rf(x**2 + 3*x, 2) == (x**2 + 3*x)*(x**2 + 3*x + 1) + assert isinstance(rf(x**2 + 3*x, 2), Mul) + assert rf(x**3 + x, -2) == 1/((x**3 + x - 1)*(x**3 + x - 2)) + + assert rf(Poly(x**2 + 3*x, x), 2) == Poly(x**4 + 8*x**3 + 19*x**2 + 12*x, x) + assert isinstance(rf(Poly(x**2 + 3*x, x), 2), Poly) + raises(ValueError, lambda: rf(Poly(x**2 + 3*x, x, y), 2)) + assert rf(Poly(x**3 + x, x), -2) == 1/(x**6 - 9*x**5 + 35*x**4 - 75*x**3 + 94*x**2 - 66*x + 20) + raises(ValueError, lambda: rf(Poly(x**3 + x, x, y), -2)) + + assert rf(x, m).is_integer is None + assert rf(n, k).is_integer is None + assert rf(n, m).is_integer is True + assert rf(n, k + pi).is_integer is False + assert rf(n, m + pi).is_integer is False + assert rf(pi, m).is_integer is False + + def check(x, k, o, n): + a, b = Dummy(), Dummy() + r = lambda x, k: o(a, b).rewrite(n).subs({a:x,b:k}) + for i in range(-5,5): + for j in range(-5,5): + assert o(i, j) == r(i, j), (o, n, i, j) + check(x, k, rf, ff) + check(x, k, rf, binomial) + check(n, k, rf, factorial) + check(x, y, rf, factorial) + check(x, y, rf, binomial) + + assert rf(x, k).rewrite(ff) == ff(x + k - 1, k) + assert rf(x, k).rewrite(gamma) == Piecewise( + (gamma(k + x)/gamma(x), x > 0), + ((-1)**k*gamma(1 - x)/gamma(-k - x + 1), True)) + assert rf(5, k).rewrite(gamma) == gamma(k + 5)/24 + assert rf(x, k).rewrite(binomial) == factorial(k)*binomial(x + k - 1, k) + assert rf(n, k).rewrite(factorial) == Piecewise( + (factorial(k + n - 1)/factorial(n - 1), n > 0), + ((-1)**k*factorial(-n)/factorial(-k - n), True)) + assert rf(5, k).rewrite(factorial) == factorial(k + 4)/24 + assert rf(x, y).rewrite(factorial) == rf(x, y) + assert rf(x, y).rewrite(binomial) == rf(x, y) + + import random + from mpmath import rf as mpmath_rf + for i in range(100): + x = -500 + 500 * random.random() + k = -500 + 500 * random.random() + assert (abs(mpmath_rf(x, k) - rf(x, k)) < 10**(-15)) + + +def test_ff_eval_apply(): + x, y = symbols('x,y') + n, k = symbols('n k', integer=True) + m = Symbol('m', integer=True, nonnegative=True) + + assert ff(nan, y) is nan + assert ff(x, nan) is nan + + assert unchanged(ff, x, y) + + assert ff(oo, 0) == 1 + assert ff(-oo, 0) == 1 + + assert ff(oo, 6) is oo + assert ff(-oo, 7) is -oo + assert ff(-oo, 6) is oo + + assert ff(oo, -6) is oo + assert ff(-oo, -7) is oo + + assert ff(x, 0) == 1 + assert ff(x, 1) == x + assert ff(x, 2) == x*(x - 1) + assert ff(x, 3) == x*(x - 1)*(x - 2) + assert ff(x, 5) == x*(x - 1)*(x - 2)*(x - 3)*(x - 4) + + assert ff(x, -1) == 1/(x + 1) + assert ff(x, -2) == 1/((x + 1)*(x + 2)) + assert ff(x, -3) == 1/((x + 1)*(x + 2)*(x + 3)) + + assert ff(100, 100) == factorial(100) + + assert ff(2*x**2 - 5*x, 2) == (2*x**2 - 5*x)*(2*x**2 - 5*x - 1) + assert isinstance(ff(2*x**2 - 5*x, 2), Mul) + assert ff(x**2 + 3*x, -2) == 1/((x**2 + 3*x + 1)*(x**2 + 3*x + 2)) + + assert ff(Poly(2*x**2 - 5*x, x), 2) == Poly(4*x**4 - 28*x**3 + 59*x**2 - 35*x, x) + assert isinstance(ff(Poly(2*x**2 - 5*x, x), 2), Poly) + raises(ValueError, lambda: ff(Poly(2*x**2 - 5*x, x, y), 2)) + assert ff(Poly(x**2 + 3*x, x), -2) == 1/(x**4 + 12*x**3 + 49*x**2 + 78*x + 40) + raises(ValueError, lambda: ff(Poly(x**2 + 3*x, x, y), -2)) + + + assert ff(x, m).is_integer is None + assert ff(n, k).is_integer is None + assert ff(n, m).is_integer is True + assert ff(n, k + pi).is_integer is False + assert ff(n, m + pi).is_integer is False + assert ff(pi, m).is_integer is False + + assert isinstance(ff(x, x), ff) + assert ff(n, n) == factorial(n) + + def check(x, k, o, n): + a, b = Dummy(), Dummy() + r = lambda x, k: o(a, b).rewrite(n).subs({a:x,b:k}) + for i in range(-5,5): + for j in range(-5,5): + assert o(i, j) == r(i, j), (o, n) + check(x, k, ff, rf) + check(x, k, ff, gamma) + check(n, k, ff, factorial) + check(x, k, ff, binomial) + check(x, y, ff, factorial) + check(x, y, ff, binomial) + + assert ff(x, k).rewrite(rf) == rf(x - k + 1, k) + assert ff(x, k).rewrite(gamma) == Piecewise( + (gamma(x + 1)/gamma(-k + x + 1), x >= 0), + ((-1)**k*gamma(k - x)/gamma(-x), True)) + assert ff(5, k).rewrite(gamma) == 120/gamma(6 - k) + assert ff(n, k).rewrite(factorial) == Piecewise( + (factorial(n)/factorial(-k + n), n >= 0), + ((-1)**k*factorial(k - n - 1)/factorial(-n - 1), True)) + assert ff(5, k).rewrite(factorial) == 120/factorial(5 - k) + assert ff(x, k).rewrite(binomial) == factorial(k) * binomial(x, k) + assert ff(x, y).rewrite(factorial) == ff(x, y) + assert ff(x, y).rewrite(binomial) == ff(x, y) + + import random + from mpmath import ff as mpmath_ff + for i in range(100): + x = -500 + 500 * random.random() + k = -500 + 500 * random.random() + a = mpmath_ff(x, k) + b = ff(x, k) + assert (abs(a - b) < abs(a) * 10**(-15)) + + +def test_rf_ff_eval_hiprec(): + maple = Float('6.9109401292234329956525265438452') + us = ff(18, Rational(2, 3)).evalf(32) + assert abs(us - maple)/us < 1e-31 + + maple = Float('6.8261540131125511557924466355367') + us = rf(18, Rational(2, 3)).evalf(32) + assert abs(us - maple)/us < 1e-31 + + maple = Float('34.007346127440197150854651814225') + us = rf(Float('4.4', 32), Float('2.2', 32)); + assert abs(us - maple)/us < 1e-31 + + +def test_rf_lambdify_mpmath(): + from sympy.utilities.lambdify import lambdify + x, y = symbols('x,y') + f = lambdify((x,y), rf(x, y), 'mpmath') + maple = Float('34.007346127440197') + us = f(4.4, 2.2) + assert abs(us - maple)/us < 1e-15 + + +def test_factorial(): + x = Symbol('x') + n = Symbol('n', integer=True) + k = Symbol('k', integer=True, nonnegative=True) + r = Symbol('r', integer=False) + s = Symbol('s', integer=False, negative=True) + t = Symbol('t', nonnegative=True) + u = Symbol('u', noninteger=True) + + assert factorial(-2) is zoo + assert factorial(0) == 1 + assert factorial(7) == 5040 + assert factorial(19) == 121645100408832000 + assert factorial(31) == 8222838654177922817725562880000000 + assert factorial(n).func == factorial + assert factorial(2*n).func == factorial + + assert factorial(x).is_integer is None + assert factorial(n).is_integer is None + assert factorial(k).is_integer + assert factorial(r).is_integer is None + + assert factorial(n).is_positive is None + assert factorial(k).is_positive + + assert factorial(x).is_real is None + assert factorial(n).is_real is None + assert factorial(k).is_real is True + assert factorial(r).is_real is None + assert factorial(s).is_real is True + assert factorial(t).is_real is True + assert factorial(u).is_real is True + + assert factorial(x).is_composite is None + assert factorial(n).is_composite is None + assert factorial(k).is_composite is None + assert factorial(k + 3).is_composite is True + assert factorial(r).is_composite is None + assert factorial(s).is_composite is None + assert factorial(t).is_composite is None + assert factorial(u).is_composite is None + + assert factorial(oo) is oo + + +def test_factorial_Mod(): + pr = Symbol('pr', prime=True) + p, q = 10**9 + 9, 10**9 + 33 # prime modulo + r, s = 10**7 + 5, 33333333 # composite modulo + assert Mod(factorial(pr - 1), pr) == pr - 1 + assert Mod(factorial(pr - 1), -pr) == -1 + assert Mod(factorial(r - 1, evaluate=False), r) == 0 + assert Mod(factorial(s - 1, evaluate=False), s) == 0 + assert Mod(factorial(p - 1, evaluate=False), p) == p - 1 + assert Mod(factorial(q - 1, evaluate=False), q) == q - 1 + assert Mod(factorial(p - 50, evaluate=False), p) == 854928834 + assert Mod(factorial(q - 1800, evaluate=False), q) == 905504050 + assert Mod(factorial(153, evaluate=False), r) == Mod(factorial(153), r) + assert Mod(factorial(255, evaluate=False), s) == Mod(factorial(255), s) + assert Mod(factorial(4, evaluate=False), 3) == S.Zero + assert Mod(factorial(5, evaluate=False), 6) == S.Zero + + +def test_factorial_diff(): + n = Symbol('n', integer=True) + + assert factorial(n).diff(n) == \ + gamma(1 + n)*polygamma(0, 1 + n) + assert factorial(n**2).diff(n) == \ + 2*n*gamma(1 + n**2)*polygamma(0, 1 + n**2) + raises(ArgumentIndexError, lambda: factorial(n**2).fdiff(2)) + + +def test_factorial_series(): + n = Symbol('n', integer=True) + + assert factorial(n).series(n, 0, 3) == \ + 1 - n*EulerGamma + n**2*(EulerGamma**2/2 + pi**2/12) + O(n**3) + + +def test_factorial_rewrite(): + n = Symbol('n', integer=True) + k = Symbol('k', integer=True, nonnegative=True) + + assert factorial(n).rewrite(gamma) == gamma(n + 1) + _i = Dummy('i') + assert factorial(k).rewrite(Product).dummy_eq(Product(_i, (_i, 1, k))) + assert factorial(n).rewrite(Product) == factorial(n) + + +def test_factorial2(): + n = Symbol('n', integer=True) + + assert factorial2(-1) == 1 + assert factorial2(0) == 1 + assert factorial2(7) == 105 + assert factorial2(8) == 384 + + # The following is exhaustive + tt = Symbol('tt', integer=True, nonnegative=True) + tte = Symbol('tte', even=True, nonnegative=True) + tpe = Symbol('tpe', even=True, positive=True) + tto = Symbol('tto', odd=True, nonnegative=True) + tf = Symbol('tf', integer=True, nonnegative=False) + tfe = Symbol('tfe', even=True, nonnegative=False) + tfo = Symbol('tfo', odd=True, nonnegative=False) + ft = Symbol('ft', integer=False, nonnegative=True) + ff = Symbol('ff', integer=False, nonnegative=False) + fn = Symbol('fn', integer=False) + nt = Symbol('nt', nonnegative=True) + nf = Symbol('nf', nonnegative=False) + nn = Symbol('nn') + z = Symbol('z', zero=True) + #Solves and Fixes Issue #10388 - This is the updated test for the same solved issue + raises(ValueError, lambda: factorial2(oo)) + raises(ValueError, lambda: factorial2(Rational(5, 2))) + raises(ValueError, lambda: factorial2(-4)) + assert factorial2(n).is_integer is None + assert factorial2(tt - 1).is_integer + assert factorial2(tte - 1).is_integer + assert factorial2(tpe - 3).is_integer + assert factorial2(tto - 4).is_integer + assert factorial2(tto - 2).is_integer + assert factorial2(tf).is_integer is None + assert factorial2(tfe).is_integer is None + assert factorial2(tfo).is_integer is None + assert factorial2(ft).is_integer is None + assert factorial2(ff).is_integer is None + assert factorial2(fn).is_integer is None + assert factorial2(nt).is_integer is None + assert factorial2(nf).is_integer is None + assert factorial2(nn).is_integer is None + + assert factorial2(n).is_positive is None + assert factorial2(tt - 1).is_positive is True + assert factorial2(tte - 1).is_positive is True + assert factorial2(tpe - 3).is_positive is True + assert factorial2(tpe - 1).is_positive is True + assert factorial2(tto - 2).is_positive is True + assert factorial2(tto - 1).is_positive is True + assert factorial2(tf).is_positive is None + assert factorial2(tfe).is_positive is None + assert factorial2(tfo).is_positive is None + assert factorial2(ft).is_positive is None + assert factorial2(ff).is_positive is None + assert factorial2(fn).is_positive is None + assert factorial2(nt).is_positive is None + assert factorial2(nf).is_positive is None + assert factorial2(nn).is_positive is None + + assert factorial2(tt).is_even is None + assert factorial2(tt).is_odd is None + assert factorial2(tte).is_even is None + assert factorial2(tte).is_odd is None + assert factorial2(tte + 2).is_even is True + assert factorial2(tpe).is_even is True + assert factorial2(tpe).is_odd is False + assert factorial2(tto).is_odd is True + assert factorial2(tf).is_even is None + assert factorial2(tf).is_odd is None + assert factorial2(tfe).is_even is None + assert factorial2(tfe).is_odd is None + assert factorial2(tfo).is_even is False + assert factorial2(tfo).is_odd is None + assert factorial2(z).is_even is False + assert factorial2(z).is_odd is True + + +def test_factorial2_rewrite(): + n = Symbol('n', integer=True) + assert factorial2(n).rewrite(gamma) == \ + 2**(n/2)*Piecewise((1, Eq(Mod(n, 2), 0)), (sqrt(2)/sqrt(pi), Eq(Mod(n, 2), 1)))*gamma(n/2 + 1) + assert factorial2(2*n).rewrite(gamma) == 2**n*gamma(n + 1) + assert factorial2(2*n + 1).rewrite(gamma) == \ + sqrt(2)*2**(n + S.Half)*gamma(n + Rational(3, 2))/sqrt(pi) + + +def test_binomial(): + x = Symbol('x') + n = Symbol('n', integer=True) + nz = Symbol('nz', integer=True, nonzero=True) + k = Symbol('k', integer=True) + kp = Symbol('kp', integer=True, positive=True) + kn = Symbol('kn', integer=True, negative=True) + u = Symbol('u', negative=True) + v = Symbol('v', nonnegative=True) + p = Symbol('p', positive=True) + z = Symbol('z', zero=True) + nt = Symbol('nt', integer=False) + kt = Symbol('kt', integer=False) + a = Symbol('a', integer=True, nonnegative=True) + b = Symbol('b', integer=True, nonnegative=True) + + assert binomial(0, 0) == 1 + assert binomial(1, 1) == 1 + assert binomial(10, 10) == 1 + assert binomial(n, z) == 1 + assert binomial(1, 2) == 0 + assert binomial(-1, 2) == 1 + assert binomial(1, -1) == 0 + assert binomial(-1, 1) == -1 + assert binomial(-1, -1) == 0 + assert binomial(S.Half, S.Half) == 1 + assert binomial(-10, 1) == -10 + assert binomial(-10, 7) == -11440 + assert binomial(n, -1) == 0 # holds for all integers (negative, zero, positive) + assert binomial(kp, -1) == 0 + assert binomial(nz, 0) == 1 + assert expand_func(binomial(n, 1)) == n + assert expand_func(binomial(n, 2)) == n*(n - 1)/2 + assert expand_func(binomial(n, n - 2)) == n*(n - 1)/2 + assert expand_func(binomial(n, n - 1)) == n + assert binomial(n, 3).func == binomial + assert binomial(n, 3).expand(func=True) == n**3/6 - n**2/2 + n/3 + assert expand_func(binomial(n, 3)) == n*(n - 2)*(n - 1)/6 + assert binomial(n, n).func == binomial # e.g. (-1, -1) == 0, (2, 2) == 1 + assert binomial(n, n + 1).func == binomial # e.g. (-1, 0) == 1 + assert binomial(kp, kp + 1) == 0 + assert binomial(kn, kn) == 0 # issue #14529 + assert binomial(n, u).func == binomial + assert binomial(kp, u).func == binomial + assert binomial(n, p).func == binomial + assert binomial(n, k).func == binomial + assert binomial(n, n + p).func == binomial + assert binomial(kp, kp + p).func == binomial + + assert expand_func(binomial(n, n - 3)) == n*(n - 2)*(n - 1)/6 + + assert binomial(n, k).is_integer + assert binomial(nt, k).is_integer is None + assert binomial(x, nt).is_integer is False + + assert binomial(gamma(25), 6) == 79232165267303928292058750056084441948572511312165380965440075720159859792344339983120618959044048198214221915637090855535036339620413440000 + assert binomial(1324, 47) == 906266255662694632984994480774946083064699457235920708992926525848438478406790323869952 + assert binomial(1735, 43) == 190910140420204130794758005450919715396159959034348676124678207874195064798202216379800 + assert binomial(2512, 53) == 213894469313832631145798303740098720367984955243020898718979538096223399813295457822575338958939834177325304000 + assert binomial(3383, 52) == 27922807788818096863529701501764372757272890613101645521813434902890007725667814813832027795881839396839287659777235 + assert binomial(4321, 51) == 124595639629264868916081001263541480185227731958274383287107643816863897851139048158022599533438936036467601690983780576 + + assert binomial(a, b).is_nonnegative is True + assert binomial(-1, 2, evaluate=False).is_nonnegative is True + assert binomial(10, 5, evaluate=False).is_nonnegative is True + assert binomial(10, -3, evaluate=False).is_nonnegative is True + assert binomial(-10, -3, evaluate=False).is_nonnegative is True + assert binomial(-10, 2, evaluate=False).is_nonnegative is True + assert binomial(-10, 1, evaluate=False).is_nonnegative is False + assert binomial(-10, 7, evaluate=False).is_nonnegative is False + + # issue #14625 + for _ in (pi, -pi, nt, v, a): + assert binomial(_, _) == 1 + assert binomial(_, _ - 1) == _ + assert isinstance(binomial(u, u), binomial) + assert isinstance(binomial(u, u - 1), binomial) + assert isinstance(binomial(x, x), binomial) + assert isinstance(binomial(x, x - 1), binomial) + + #issue #18802 + assert expand_func(binomial(x + 1, x)) == x + 1 + assert expand_func(binomial(x, x - 1)) == x + assert expand_func(binomial(x + 1, x - 1)) == x*(x + 1)/2 + assert expand_func(binomial(x**2 + 1, x**2)) == x**2 + 1 + + # issue #13980 and #13981 + assert binomial(-7, -5) == 0 + assert binomial(-23, -12) == 0 + assert binomial(Rational(13, 2), -10) == 0 + assert binomial(-49, -51) == 0 + + assert binomial(19, Rational(-7, 2)) == S(-68719476736)/(911337863661225*pi) + assert binomial(0, Rational(3, 2)) == S(-2)/(3*pi) + assert binomial(-3, Rational(-7, 2)) is zoo + assert binomial(kn, kt) is zoo + + assert binomial(nt, kt).func == binomial + assert binomial(nt, Rational(15, 6)) == 8*gamma(nt + 1)/(15*sqrt(pi)*gamma(nt - Rational(3, 2))) + assert binomial(Rational(20, 3), Rational(-10, 8)) == gamma(Rational(23, 3))/(gamma(Rational(-1, 4))*gamma(Rational(107, 12))) + assert binomial(Rational(19, 2), Rational(-7, 2)) == Rational(-1615, 8388608) + assert binomial(Rational(-13, 5), Rational(-7, 8)) == gamma(Rational(-8, 5))/(gamma(Rational(-29, 40))*gamma(Rational(1, 8))) + assert binomial(Rational(-19, 8), Rational(-13, 5)) == gamma(Rational(-11, 8))/(gamma(Rational(-8, 5))*gamma(Rational(49, 40))) + + # binomial for complexes + assert binomial(I, Rational(-89, 8)) == gamma(1 + I)/(gamma(Rational(-81, 8))*gamma(Rational(97, 8) + I)) + assert binomial(I, 2*I) == gamma(1 + I)/(gamma(1 - I)*gamma(1 + 2*I)) + assert binomial(-7, I) is zoo + assert binomial(Rational(-7, 6), I) == gamma(Rational(-1, 6))/(gamma(Rational(-1, 6) - I)*gamma(1 + I)) + assert binomial((1+2*I), (1+3*I)) == gamma(2 + 2*I)/(gamma(1 - I)*gamma(2 + 3*I)) + assert binomial(I, 5) == Rational(1, 3) - I/S(12) + assert binomial((2*I + 3), 7) == -13*I/S(63) + assert isinstance(binomial(I, n), binomial) + assert expand_func(binomial(3, 2, evaluate=False)) == 3 + assert expand_func(binomial(n, 0, evaluate=False)) == 1 + assert expand_func(binomial(n, -2, evaluate=False)) == 0 + assert expand_func(binomial(n, k)) == binomial(n, k) + + +def test_binomial_Mod(): + p, q = 10**5 + 3, 10**9 + 33 # prime modulo + r = 10**7 + 5 # composite modulo + + # A few tests to get coverage + # Lucas Theorem + assert Mod(binomial(156675, 4433, evaluate=False), p) == Mod(binomial(156675, 4433), p) + + # factorial Mod + assert Mod(binomial(1234, 432, evaluate=False), q) == Mod(binomial(1234, 432), q) + + # binomial factorize + assert Mod(binomial(253, 113, evaluate=False), r) == Mod(binomial(253, 113), r) + + # using Granville's generalisation of Lucas' Theorem + assert Mod(binomial(10**18, 10**12, evaluate=False), p*p) == 3744312326 + + +@slow +def test_binomial_Mod_slow(): + p, q = 10**5 + 3, 10**9 + 33 # prime modulo + r, s = 10**7 + 5, 33333333 # composite modulo + + n, k, m = symbols('n k m') + assert (binomial(n, k) % q).subs({n: s, k: p}) == Mod(binomial(s, p), q) + assert (binomial(n, k) % m).subs({n: 8, k: 5, m: 13}) == 4 + assert (binomial(9, k) % 7).subs(k, 2) == 1 + + # Lucas Theorem + assert Mod(binomial(123456, 43253, evaluate=False), p) == Mod(binomial(123456, 43253), p) + assert Mod(binomial(-178911, 237, evaluate=False), p) == Mod(-binomial(178911 + 237 - 1, 237), p) + assert Mod(binomial(-178911, 238, evaluate=False), p) == Mod(binomial(178911 + 238 - 1, 238), p) + + # factorial Mod + assert Mod(binomial(9734, 451, evaluate=False), q) == Mod(binomial(9734, 451), q) + assert Mod(binomial(-10733, 4459, evaluate=False), q) == Mod(binomial(-10733, 4459), q) + assert Mod(binomial(-15733, 4458, evaluate=False), q) == Mod(binomial(-15733, 4458), q) + assert Mod(binomial(23, -38, evaluate=False), q) is S.Zero + assert Mod(binomial(23, 38, evaluate=False), q) is S.Zero + + # binomial factorize + assert Mod(binomial(753, 119, evaluate=False), r) == Mod(binomial(753, 119), r) + assert Mod(binomial(3781, 948, evaluate=False), s) == Mod(binomial(3781, 948), s) + assert Mod(binomial(25773, 1793, evaluate=False), s) == Mod(binomial(25773, 1793), s) + assert Mod(binomial(-753, 118, evaluate=False), r) == Mod(binomial(-753, 118), r) + assert Mod(binomial(-25773, 1793, evaluate=False), s) == Mod(binomial(-25773, 1793), s) + + +def test_binomial_diff(): + n = Symbol('n', integer=True) + k = Symbol('k', integer=True) + + assert binomial(n, k).diff(n) == \ + (-polygamma(0, 1 + n - k) + polygamma(0, 1 + n))*binomial(n, k) + assert binomial(n**2, k**3).diff(n) == \ + 2*n*(-polygamma( + 0, 1 + n**2 - k**3) + polygamma(0, 1 + n**2))*binomial(n**2, k**3) + + assert binomial(n, k).diff(k) == \ + (-polygamma(0, 1 + k) + polygamma(0, 1 + n - k))*binomial(n, k) + assert binomial(n**2, k**3).diff(k) == \ + 3*k**2*(-polygamma( + 0, 1 + k**3) + polygamma(0, 1 + n**2 - k**3))*binomial(n**2, k**3) + raises(ArgumentIndexError, lambda: binomial(n, k).fdiff(3)) + + +def test_binomial_rewrite(): + n = Symbol('n', integer=True) + k = Symbol('k', integer=True) + x = Symbol('x') + + assert binomial(n, k).rewrite( + factorial) == factorial(n)/(factorial(k)*factorial(n - k)) + assert binomial( + n, k).rewrite(gamma) == gamma(n + 1)/(gamma(k + 1)*gamma(n - k + 1)) + assert binomial(n, k).rewrite(ff) == ff(n, k) / factorial(k) + assert binomial(n, x).rewrite(ff) == binomial(n, x) + + +@XFAIL +def test_factorial_simplify_fail(): + # simplify(factorial(x + 1).diff(x) - ((x + 1)*factorial(x)).diff(x))) == 0 + from sympy.abc import x + assert simplify(x*polygamma(0, x + 1) - x*polygamma(0, x + 2) + + polygamma(0, x + 1) - polygamma(0, x + 2) + 1) == 0 + + +def test_subfactorial(): + assert all(subfactorial(i) == ans for i, ans in enumerate( + [1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496])) + assert subfactorial(oo) is oo + assert subfactorial(nan) is nan + assert subfactorial(23) == 9510425471055777937262 + assert unchanged(subfactorial, 2.2) + + x = Symbol('x') + assert subfactorial(x).rewrite(uppergamma) == uppergamma(x + 1, -1)/S.Exp1 + + tt = Symbol('tt', integer=True, nonnegative=True) + tf = Symbol('tf', integer=True, nonnegative=False) + tn = Symbol('tf', integer=True) + ft = Symbol('ft', integer=False, nonnegative=True) + ff = Symbol('ff', integer=False, nonnegative=False) + fn = Symbol('ff', integer=False) + nt = Symbol('nt', nonnegative=True) + nf = Symbol('nf', nonnegative=False) + nn = Symbol('nf') + te = Symbol('te', even=True, nonnegative=True) + to = Symbol('to', odd=True, nonnegative=True) + assert subfactorial(tt).is_integer + assert subfactorial(tf).is_integer is None + assert subfactorial(tn).is_integer is None + assert subfactorial(ft).is_integer is None + assert subfactorial(ff).is_integer is None + assert subfactorial(fn).is_integer is None + assert subfactorial(nt).is_integer is None + assert subfactorial(nf).is_integer is None + assert subfactorial(nn).is_integer is None + assert subfactorial(tt).is_nonnegative + assert subfactorial(tf).is_nonnegative is None + assert subfactorial(tn).is_nonnegative is None + assert subfactorial(ft).is_nonnegative is None + assert subfactorial(ff).is_nonnegative is None + assert subfactorial(fn).is_nonnegative is None + assert subfactorial(nt).is_nonnegative is None + assert subfactorial(nf).is_nonnegative is None + assert subfactorial(nn).is_nonnegative is None + assert subfactorial(tt).is_even is None + assert subfactorial(tt).is_odd is None + assert subfactorial(te).is_odd is True + assert subfactorial(to).is_even is True diff --git a/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py b/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py new file mode 100644 index 0000000000000000000000000000000000000000..e521c2f63bb7ea0864155707e34f2d105bd35806 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/combinatorial/tests/test_comb_numbers.py @@ -0,0 +1,1241 @@ +import string + +from sympy.concrete.products import Product +from sympy.concrete.summations import Sum +from sympy.core.function import (diff, expand_func) +from sympy.core import (EulerGamma, TribonacciConstant) +from sympy.core.numbers import (Float, I, Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.combinatorial.numbers import carmichael +from sympy.functions.elementary.complexes import (im, re) +from sympy.functions.elementary.integers import floor +from sympy.polys.polytools import cancel +from sympy.series.limits import limit, Limit +from sympy.series.order import O +from sympy.functions import ( + bernoulli, harmonic, bell, fibonacci, tribonacci, lucas, euler, catalan, + genocchi, andre, partition, divisor_sigma, udivisor_sigma, legendre_symbol, + jacobi_symbol, kronecker_symbol, mobius, + primenu, primeomega, totient, reduced_totient, primepi, + motzkin, binomial, gamma, sqrt, cbrt, hyper, log, digamma, + trigamma, polygamma, factorial, sin, cos, cot, polylog, zeta, dirichlet_eta) +from sympy.functions.combinatorial.numbers import _nT +from sympy.ntheory.factor_ import factorint + +from sympy.core.expr import unchanged +from sympy.core.numbers import GoldenRatio, Integer + +from sympy.testing.pytest import raises, nocache_fail, warns_deprecated_sympy +from sympy.abc import x + + +def test_carmichael(): + with warns_deprecated_sympy(): + assert carmichael.is_prime(2821) == False + + +def test_bernoulli(): + assert bernoulli(0) == 1 + assert bernoulli(1) == Rational(1, 2) + assert bernoulli(2) == Rational(1, 6) + assert bernoulli(3) == 0 + assert bernoulli(4) == Rational(-1, 30) + assert bernoulli(5) == 0 + assert bernoulli(6) == Rational(1, 42) + assert bernoulli(7) == 0 + assert bernoulli(8) == Rational(-1, 30) + assert bernoulli(10) == Rational(5, 66) + assert bernoulli(1000001) == 0 + + assert bernoulli(0, x) == 1 + assert bernoulli(1, x) == x - S.Half + assert bernoulli(2, x) == x**2 - x + Rational(1, 6) + assert bernoulli(3, x) == x**3 - (3*x**2)/2 + x/2 + + # Should be fast; computed with mpmath + b = bernoulli(1000) + assert b.p % 10**10 == 7950421099 + assert b.q == 342999030 + + b = bernoulli(10**6, evaluate=False).evalf() + assert str(b) == '-2.23799235765713e+4767529' + + # Issue #8527 + l = Symbol('l', integer=True) + m = Symbol('m', integer=True, nonnegative=True) + n = Symbol('n', integer=True, positive=True) + assert isinstance(bernoulli(2 * l + 1), bernoulli) + assert isinstance(bernoulli(2 * m + 1), bernoulli) + assert bernoulli(2 * n + 1) == 0 + + assert bernoulli(x, 1) == bernoulli(x) + + assert str(bernoulli(0.0, 2.3).evalf(n=10)) == '1.000000000' + assert str(bernoulli(1.0).evalf(n=10)) == '0.5000000000' + assert str(bernoulli(1.2).evalf(n=10)) == '0.4195995367' + assert str(bernoulli(1.2, 0.8).evalf(n=10)) == '0.2144830348' + assert str(bernoulli(1.2, -0.8).evalf(n=10)) == '-1.158865646 - 0.6745558744*I' + assert str(bernoulli(3.0, 1j).evalf(n=10)) == '1.5 - 0.5*I' + assert str(bernoulli(I).evalf(n=10)) == '0.9268485643 - 0.5821580598*I' + assert str(bernoulli(I, I).evalf(n=10)) == '0.1267792071 + 0.01947413152*I' + assert bernoulli(x).evalf() == bernoulli(x) + + +def test_bernoulli_rewrite(): + from sympy.functions.elementary.piecewise import Piecewise + n = Symbol('n', integer=True, nonnegative=True) + + assert bernoulli(-1).rewrite(zeta) == pi**2/6 + assert bernoulli(-2).rewrite(zeta) == 2*zeta(3) + assert not bernoulli(n, -3).rewrite(zeta).has(harmonic) + assert bernoulli(-4, x).rewrite(zeta) == 4*zeta(5, x) + assert isinstance(bernoulli(n, x).rewrite(zeta), Piecewise) + assert bernoulli(n+1, x).rewrite(zeta) == -(n+1) * zeta(-n, x) + + +def test_fibonacci(): + assert [fibonacci(n) for n in range(-3, 5)] == [2, -1, 1, 0, 1, 1, 2, 3] + assert fibonacci(100) == 354224848179261915075 + assert [lucas(n) for n in range(-3, 5)] == [-4, 3, -1, 2, 1, 3, 4, 7] + assert lucas(100) == 792070839848372253127 + + assert fibonacci(1, x) == 1 + assert fibonacci(2, x) == x + assert fibonacci(3, x) == x**2 + 1 + assert fibonacci(4, x) == x**3 + 2*x + + # issue #8800 + n = Dummy('n') + assert fibonacci(n).limit(n, S.Infinity) is S.Infinity + assert lucas(n).limit(n, S.Infinity) is S.Infinity + + assert fibonacci(n).rewrite(sqrt) == \ + 2**(-n)*sqrt(5)*((1 + sqrt(5))**n - (-sqrt(5) + 1)**n) / 5 + assert fibonacci(n).rewrite(sqrt).subs(n, 10).expand() == fibonacci(10) + assert fibonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \ + Float(fibonacci(10)) + assert lucas(n).rewrite(sqrt) == \ + (fibonacci(n-1).rewrite(sqrt) + fibonacci(n+1).rewrite(sqrt)).simplify() + assert lucas(n).rewrite(sqrt).subs(n, 10).expand() == lucas(10) + raises(ValueError, lambda: fibonacci(-3, x)) + + +def test_tribonacci(): + assert [tribonacci(n) for n in range(8)] == [0, 1, 1, 2, 4, 7, 13, 24] + assert tribonacci(100) == 98079530178586034536500564 + + assert tribonacci(0, x) == 0 + assert tribonacci(1, x) == 1 + assert tribonacci(2, x) == x**2 + assert tribonacci(3, x) == x**4 + x + assert tribonacci(4, x) == x**6 + 2*x**3 + 1 + assert tribonacci(5, x) == x**8 + 3*x**5 + 3*x**2 + + n = Dummy('n') + assert tribonacci(n).limit(n, S.Infinity) is S.Infinity + + w = (-1 + S.ImaginaryUnit * sqrt(3)) / 2 + a = (1 + cbrt(19 + 3*sqrt(33)) + cbrt(19 - 3*sqrt(33))) / 3 + b = (1 + w*cbrt(19 + 3*sqrt(33)) + w**2*cbrt(19 - 3*sqrt(33))) / 3 + c = (1 + w**2*cbrt(19 + 3*sqrt(33)) + w*cbrt(19 - 3*sqrt(33))) / 3 + assert tribonacci(n).rewrite(sqrt) == \ + (a**(n + 1)/((a - b)*(a - c)) + + b**(n + 1)/((b - a)*(b - c)) + + c**(n + 1)/((c - a)*(c - b))) + assert tribonacci(n).rewrite(sqrt).subs(n, 4).simplify() == tribonacci(4) + assert tribonacci(n).rewrite(GoldenRatio).subs(n,10).evalf() == \ + Float(tribonacci(10)) + assert tribonacci(n).rewrite(TribonacciConstant) == floor( + 3*TribonacciConstant**n*(102*sqrt(33) + 586)**Rational(1, 3)/ + (-2*(102*sqrt(33) + 586)**Rational(1, 3) + 4 + (102*sqrt(33) + + 586)**Rational(2, 3)) + S.Half) + raises(ValueError, lambda: tribonacci(-1, x)) + + +@nocache_fail +def test_bell(): + assert [bell(n) for n in range(8)] == [1, 1, 2, 5, 15, 52, 203, 877] + + assert bell(0, x) == 1 + assert bell(1, x) == x + assert bell(2, x) == x**2 + x + assert bell(5, x) == x**5 + 10*x**4 + 25*x**3 + 15*x**2 + x + assert bell(oo) is S.Infinity + raises(ValueError, lambda: bell(oo, x)) + + raises(ValueError, lambda: bell(-1)) + raises(ValueError, lambda: bell(S.Half)) + + X = symbols('x:6') + # X = (x0, x1, .. x5) + # at the same time: X[1] = x1, X[2] = x2 for standard readablity. + # but we must supply zero-based indexed object X[1:] = (x1, .. x5) + + assert bell(6, 2, X[1:]) == 6*X[5]*X[1] + 15*X[4]*X[2] + 10*X[3]**2 + assert bell( + 6, 3, X[1:]) == 15*X[4]*X[1]**2 + 60*X[3]*X[2]*X[1] + 15*X[2]**3 + + X = (1, 10, 100, 1000, 10000) + assert bell(6, 2, X) == (6 + 15 + 10)*10000 + + X = (1, 2, 3, 3, 5) + assert bell(6, 2, X) == 6*5 + 15*3*2 + 10*3**2 + + X = (1, 2, 3, 5) + assert bell(6, 3, X) == 15*5 + 60*3*2 + 15*2**3 + + # Dobinski's formula + n = Symbol('n', integer=True, nonnegative=True) + # For large numbers, this is too slow + # For nonintegers, there are significant precision errors + for i in [0, 2, 3, 7, 13, 42, 55]: + # Running without the cache this is either very slow or goes into an + # infinite loop. + assert bell(i).evalf() == bell(n).rewrite(Sum).evalf(subs={n: i}) + + m = Symbol("m") + assert bell(m).rewrite(Sum) == bell(m) + assert bell(n, m).rewrite(Sum) == bell(n, m) + # issue 9184 + n = Dummy('n') + assert bell(n).limit(n, S.Infinity) is S.Infinity + + +def test_harmonic(): + n = Symbol("n") + m = Symbol("m") + + assert harmonic(n, 0) == n + assert harmonic(n).evalf() == harmonic(n) + assert harmonic(n, 1) == harmonic(n) + assert harmonic(1, n) == 1 + + assert harmonic(0, 1) == 0 + assert harmonic(1, 1) == 1 + assert harmonic(2, 1) == Rational(3, 2) + assert harmonic(3, 1) == Rational(11, 6) + assert harmonic(4, 1) == Rational(25, 12) + assert harmonic(0, 2) == 0 + assert harmonic(1, 2) == 1 + assert harmonic(2, 2) == Rational(5, 4) + assert harmonic(3, 2) == Rational(49, 36) + assert harmonic(4, 2) == Rational(205, 144) + assert harmonic(0, 3) == 0 + assert harmonic(1, 3) == 1 + assert harmonic(2, 3) == Rational(9, 8) + assert harmonic(3, 3) == Rational(251, 216) + assert harmonic(4, 3) == Rational(2035, 1728) + + assert harmonic(oo, -1) is S.NaN + assert harmonic(oo, 0) is oo + assert harmonic(oo, S.Half) is oo + assert harmonic(oo, 1) is oo + assert harmonic(oo, 2) == (pi**2)/6 + assert harmonic(oo, 3) == zeta(3) + assert harmonic(oo, Dummy(negative=True)) is S.NaN + ip = Dummy(integer=True, positive=True) + if (1/ip <= 1) is True: #---------------------------------+ + assert None, 'delete this if-block and the next line' #| + ip = Dummy(even=True, positive=True) #--------------------+ + assert harmonic(oo, 1/ip) is oo + assert harmonic(oo, 1 + ip) is zeta(1 + ip) + + assert harmonic(0, m) == 0 + assert harmonic(-1, -1) == 0 + assert harmonic(-1, 0) == -1 + assert harmonic(-1, 1) is S.ComplexInfinity + assert harmonic(-1, 2) is S.NaN + assert harmonic(-3, -2) == -5 + assert harmonic(-3, -3) == 9 + + +def test_harmonic_rational(): + ne = S(6) + no = S(5) + pe = S(8) + po = S(9) + qe = S(10) + qo = S(13) + + Heee = harmonic(ne + pe/qe) + Aeee = (-log(10) + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8))) + + pi*sqrt(2*sqrt(5)/5 + 1)/2 + Rational(13944145, 4720968)) + + Heeo = harmonic(ne + pe/qo) + Aeeo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(4, 13)) + 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(32, 13)) + + 2*log(sin(pi*Rational(5, 13)))*cos(pi*Rational(80, 13)) - 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(5, 13)) + - 2*log(sin(pi*Rational(4, 13)))*cos(pi/13) + pi*cot(pi*Rational(5, 13))/2 - 2*log(sin(pi/13))*cos(pi*Rational(3, 13)) + + Rational(2422020029, 702257080)) + + Heoe = harmonic(ne + po/qe) + Aeoe = (-log(20) + 2*(Rational(1, 4) + sqrt(5)/4)*log(Rational(-1, 4) + sqrt(5)/4) + + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 + Rational(1, 4))*log(Rational(1, 4) + sqrt(5)/4) + + Rational(11818877030, 4286604231) + pi*sqrt(2*sqrt(5) + 5)/2) + + Heoo = harmonic(ne + po/qo) + Aeoo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(54, 13)) + 2*log(sin(pi*Rational(4, 13)))*cos(pi*Rational(6, 13)) + + 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(108, 13)) - 2*log(sin(pi*Rational(5, 13)))*cos(pi/13) + - 2*log(sin(pi/13))*cos(pi*Rational(5, 13)) + pi*cot(pi*Rational(4, 13))/2 + - 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(3, 13)) + Rational(11669332571, 3628714320)) + + Hoee = harmonic(no + pe/qe) + Aoee = (-log(10) + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8))) + + pi*sqrt(2*sqrt(5)/5 + 1)/2 + Rational(779405, 277704)) + + Hoeo = harmonic(no + pe/qo) + Aoeo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(4, 13)) + 2*log(sin(pi*Rational(2, 13)))*cos(pi*Rational(32, 13)) + + 2*log(sin(pi*Rational(5, 13)))*cos(pi*Rational(80, 13)) - 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(5, 13)) + - 2*log(sin(pi*Rational(4, 13)))*cos(pi/13) + pi*cot(pi*Rational(5, 13))/2 + - 2*log(sin(pi/13))*cos(pi*Rational(3, 13)) + Rational(53857323, 16331560)) + + Hooe = harmonic(no + po/qe) + Aooe = (-log(20) + 2*(Rational(1, 4) + sqrt(5)/4)*log(Rational(-1, 4) + sqrt(5)/4) + + 2*(Rational(-1, 4) + sqrt(5)/4)*log(sqrt(-sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 - Rational(1, 4))*log(sqrt(sqrt(5)/8 + Rational(5, 8))) + + 2*(-sqrt(5)/4 + Rational(1, 4))*log(Rational(1, 4) + sqrt(5)/4) + + Rational(486853480, 186374097) + pi*sqrt(2*sqrt(5) + 5)/2) + + Hooo = harmonic(no + po/qo) + Aooo = (-log(26) + 2*log(sin(pi*Rational(3, 13)))*cos(pi*Rational(54, 13)) + 2*log(sin(pi*Rational(4, 13)))*cos(pi*Rational(6, 13)) + + 2*log(sin(pi*Rational(6, 13)))*cos(pi*Rational(108, 13)) - 2*log(sin(pi*Rational(5, 13)))*cos(pi/13) + - 2*log(sin(pi/13))*cos(pi*Rational(5, 13)) + pi*cot(pi*Rational(4, 13))/2 + - 2*log(sin(pi*Rational(2, 13)))*cos(3*pi/13) + Rational(383693479, 125128080)) + + H = [Heee, Heeo, Heoe, Heoo, Hoee, Hoeo, Hooe, Hooo] + A = [Aeee, Aeeo, Aeoe, Aeoo, Aoee, Aoeo, Aooe, Aooo] + for h, a in zip(H, A): + e = expand_func(h).doit() + assert cancel(e/a) == 1 + assert abs(h.n() - a.n()) < 1e-12 + + +def test_harmonic_evalf(): + assert str(harmonic(1.5).evalf(n=10)) == '1.280372306' + assert str(harmonic(1.5, 2).evalf(n=10)) == '1.154576311' # issue 7443 + assert str(harmonic(4.0, -3).evalf(n=10)) == '100.0000000' + assert str(harmonic(7.0, 1.0).evalf(n=10)) == '2.592857143' + assert str(harmonic(1, pi).evalf(n=10)) == '1.000000000' + assert str(harmonic(2, pi).evalf(n=10)) == '1.113314732' + assert str(harmonic(1000.0, pi).evalf(n=10)) == '1.176241563' + assert str(harmonic(I).evalf(n=10)) == '0.6718659855 + 1.076674047*I' + assert str(harmonic(I, I).evalf(n=10)) == '-0.3970915266 + 1.9629689*I' + + assert harmonic(-1.0, 1).evalf() is S.NaN + assert harmonic(-2.0, 2.0).evalf() is S.NaN + +def test_harmonic_rewrite(): + from sympy.functions.elementary.piecewise import Piecewise + n = Symbol("n") + m = Symbol("m", integer=True, positive=True) + x1 = Symbol("x1", positive=True) + x2 = Symbol("x2", negative=True) + + assert harmonic(n).rewrite(digamma) == polygamma(0, n + 1) + EulerGamma + assert harmonic(n).rewrite(trigamma) == polygamma(0, n + 1) + EulerGamma + assert harmonic(n).rewrite(polygamma) == polygamma(0, n + 1) + EulerGamma + + assert harmonic(n,3).rewrite(polygamma) == polygamma(2, n + 1)/2 - polygamma(2, 1)/2 + assert isinstance(harmonic(n,m).rewrite(polygamma), Piecewise) + + assert expand_func(harmonic(n+4)) == harmonic(n) + 1/(n + 4) + 1/(n + 3) + 1/(n + 2) + 1/(n + 1) + assert expand_func(harmonic(n-4)) == harmonic(n) - 1/(n - 1) - 1/(n - 2) - 1/(n - 3) - 1/n + + assert harmonic(n, m).rewrite("tractable") == harmonic(n, m).rewrite(polygamma) + assert harmonic(n, x1).rewrite("tractable") == harmonic(n, x1) + assert harmonic(n, x1 + 1).rewrite("tractable") == zeta(x1 + 1) - zeta(x1 + 1, n + 1) + assert harmonic(n, x2).rewrite("tractable") == zeta(x2) - zeta(x2, n + 1) + + _k = Dummy("k") + assert harmonic(n).rewrite(Sum).dummy_eq(Sum(1/_k, (_k, 1, n))) + assert harmonic(n, m).rewrite(Sum).dummy_eq(Sum(_k**(-m), (_k, 1, n))) + + +def test_harmonic_calculus(): + y = Symbol("y", positive=True) + z = Symbol("z", negative=True) + assert harmonic(x, 1).limit(x, 0) == 0 + assert harmonic(x, y).limit(x, 0) == 0 + assert harmonic(x, 1).series(x, y, 2) == \ + harmonic(y) + (x - y)*zeta(2, y + 1) + O((x - y)**2, (x, y)) + assert limit(harmonic(x, y), x, oo) == harmonic(oo, y) + assert limit(harmonic(x, y + 1), x, oo) == zeta(y + 1) + assert limit(harmonic(x, y - 1), x, oo) == harmonic(oo, y - 1) + assert limit(harmonic(x, z), x, oo) == Limit(harmonic(x, z), x, oo, dir='-') + assert limit(harmonic(x, z + 1), x, oo) == oo + assert limit(harmonic(x, z + 2), x, oo) == harmonic(oo, z + 2) + assert limit(harmonic(x, z - 1), x, oo) == Limit(harmonic(x, z - 1), x, oo, dir='-') + + +def test_euler(): + assert euler(0) == 1 + assert euler(1) == 0 + assert euler(2) == -1 + assert euler(3) == 0 + assert euler(4) == 5 + assert euler(6) == -61 + assert euler(8) == 1385 + + assert euler(20, evaluate=False) != 370371188237525 + + n = Symbol('n', integer=True) + assert euler(n) != -1 + assert euler(n).subs(n, 2) == -1 + + assert euler(-1) == S.Pi / 2 + assert euler(-1, 1) == 2*log(2) + assert euler(-2).evalf() == (2*S.Catalan).evalf() + assert euler(-3).evalf() == (S.Pi**3 / 16).evalf() + assert str(euler(2.3).evalf(n=10)) == '-1.052850274' + assert str(euler(1.2, 3.4).evalf(n=10)) == '3.575613489' + assert str(euler(I).evalf(n=10)) == '1.248446443 - 0.7675445124*I' + assert str(euler(I, I).evalf(n=10)) == '0.04812930469 + 0.01052411008*I' + + assert euler(20).evalf() == 370371188237525.0 + assert euler(20, evaluate=False).evalf() == 370371188237525.0 + + assert euler(n).rewrite(Sum) == euler(n) + n = Symbol('n', integer=True, nonnegative=True) + assert euler(2*n + 1).rewrite(Sum) == 0 + _j = Dummy('j') + _k = Dummy('k') + assert euler(2*n).rewrite(Sum).dummy_eq( + I*Sum((-1)**_j*2**(-_k)*I**(-_k)*(-2*_j + _k)**(2*n + 1)* + binomial(_k, _j)/_k, (_j, 0, _k), (_k, 1, 2*n + 1))) + + +def test_euler_odd(): + n = Symbol('n', odd=True, positive=True) + assert euler(n) == 0 + n = Symbol('n', odd=True) + assert euler(n) != 0 + + +def test_euler_polynomials(): + assert euler(0, x) == 1 + assert euler(1, x) == x - S.Half + assert euler(2, x) == x**2 - x + assert euler(3, x) == x**3 - (3*x**2)/2 + Rational(1, 4) + m = Symbol('m') + assert isinstance(euler(m, x), euler) + from sympy.core.numbers import Float + A = Float('-0.46237208575048694923364757452876131e8') # from Maple + B = euler(19, S.Pi).evalf(32) + assert abs((A - B)/A) < 1e-31 + + +def test_euler_polynomial_rewrite(): + m = Symbol('m') + A = euler(m, x).rewrite('Sum'); + assert A.subs({m:3, x:5}).doit() == euler(3, 5) + + +def test_catalan(): + n = Symbol('n', integer=True) + m = Symbol('m', integer=True, positive=True) + k = Symbol('k', integer=True, nonnegative=True) + p = Symbol('p', nonnegative=True) + + catalans = [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786] + for i, c in enumerate(catalans): + assert catalan(i) == c + assert catalan(n).rewrite(factorial).subs(n, i) == c + assert catalan(n).rewrite(Product).subs(n, i).doit() == c + + assert unchanged(catalan, x) + assert catalan(2*x).rewrite(binomial) == binomial(4*x, 2*x)/(2*x + 1) + assert catalan(S.Half).rewrite(gamma) == 8/(3*pi) + assert catalan(S.Half).rewrite(factorial).rewrite(gamma) ==\ + 8 / (3 * pi) + assert catalan(3*x).rewrite(gamma) == 4**( + 3*x)*gamma(3*x + S.Half)/(sqrt(pi)*gamma(3*x + 2)) + assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2,), 1) + + assert catalan(n).rewrite(factorial) == factorial(2*n) / (factorial(n + 1) + * factorial(n)) + assert isinstance(catalan(n).rewrite(Product), catalan) + assert isinstance(catalan(m).rewrite(Product), Product) + + assert diff(catalan(x), x) == (polygamma( + 0, x + S.Half) - polygamma(0, x + 2) + log(4))*catalan(x) + + assert catalan(x).evalf() == catalan(x) + c = catalan(S.Half).evalf() + assert str(c) == '0.848826363156775' + c = catalan(I).evalf(3) + assert str((re(c), im(c))) == '(0.398, -0.0209)' + + # Assumptions + assert catalan(p).is_positive is True + assert catalan(k).is_integer is True + assert catalan(m+3).is_composite is True + + +def test_genocchi(): + genocchis = [0, -1, -1, 0, 1, 0, -3, 0, 17] + for n, g in enumerate(genocchis): + assert genocchi(n) == g + + m = Symbol('m', integer=True) + n = Symbol('n', integer=True, positive=True) + assert unchanged(genocchi, m) + assert genocchi(2*n + 1) == 0 + gn = 2 * (1 - 2**n) * bernoulli(n) + assert genocchi(n).rewrite(bernoulli).factor() == gn.factor() + gnx = 2 * (bernoulli(n, x) - 2**n * bernoulli(n, (x+1) / 2)) + assert genocchi(n, x).rewrite(bernoulli).factor() == gnx.factor() + assert genocchi(2 * n).is_odd + assert genocchi(2 * n).is_even is False + assert genocchi(2 * n + 1).is_even + assert genocchi(n).is_integer + assert genocchi(4 * n).is_positive + # these are the only 2 prime Genocchi numbers + assert genocchi(6, evaluate=False).is_prime == S(-3).is_prime + assert genocchi(8, evaluate=False).is_prime + assert genocchi(4 * n + 2).is_negative + assert genocchi(4 * n + 1).is_negative is False + assert genocchi(4 * n - 2).is_negative + + g0 = genocchi(0, evaluate=False) + assert g0.is_positive is False + assert g0.is_negative is False + assert g0.is_even is True + assert g0.is_odd is False + + assert genocchi(0, x) == 0 + assert genocchi(1, x) == -1 + assert genocchi(2, x) == 1 - 2*x + assert genocchi(3, x) == 3*x - 3*x**2 + assert genocchi(4, x) == -1 + 6*x**2 - 4*x**3 + y = Symbol("y") + assert genocchi(5, (x+y)**100) == -5*(x+y)**400 + 10*(x+y)**300 - 5*(x+y)**100 + + assert str(genocchi(5.0, 4.0).evalf(n=10)) == '-660.0000000' + assert str(genocchi(Rational(5, 4)).evalf(n=10)) == '-1.104286457' + assert str(genocchi(-2).evalf(n=10)) == '3.606170709' + assert str(genocchi(1.3, 3.7).evalf(n=10)) == '-1.847375373' + assert str(genocchi(I, 1.0).evalf(n=10)) == '-0.3161917278 - 1.45311955*I' + + n = Symbol('n') + assert genocchi(n, x).rewrite(dirichlet_eta) == -2*n * dirichlet_eta(1-n, x) + + +def test_andre(): + nums = [1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521] + for n, a in enumerate(nums): + assert andre(n) == a + assert andre(S.Infinity) == S.Infinity + assert andre(-1) == -log(2) + assert andre(-2) == -2*S.Catalan + assert andre(-3) == 3*zeta(3)/16 + assert andre(-5) == -15*zeta(5)/256 + # In fact andre(-2*n) is related to the Dirichlet *beta* function + # at 2*n, but SymPy doesn't implement that (or general L-functions) + assert unchanged(andre, -4) + + n = Symbol('n', integer=True, nonnegative=True) + assert unchanged(andre, n) + assert andre(n).is_integer is True + assert andre(n).is_positive is True + + assert str(andre(10, evaluate=False).evalf(n=10)) == '50521.00000' + assert str(andre(-1, evaluate=False).evalf(n=10)) == '-0.6931471806' + assert str(andre(-2, evaluate=False).evalf(n=10)) == '-1.831931188' + assert str(andre(-4, evaluate=False).evalf(n=10)) == '1.977889103' + assert str(andre(I, evaluate=False).evalf(n=10)) == '2.378417833 + 0.6343322845*I' + + assert andre(x).rewrite(polylog) == \ + (-I)**(x+1) * polylog(-x, I) + I**(x+1) * polylog(-x, -I) + assert andre(x).rewrite(zeta) == \ + 2 * gamma(x+1) / (2*pi)**(x+1) * \ + (zeta(x+1, Rational(1,4)) - cos(pi*x) * zeta(x+1, Rational(3,4))) + + +@nocache_fail +def test_partition(): + partition_nums = [1, 1, 2, 3, 5, 7, 11, 15, 22] + for n, p in enumerate(partition_nums): + assert partition(n) == p + + x = Symbol('x') + y = Symbol('y', real=True) + m = Symbol('m', integer=True) + n = Symbol('n', integer=True, negative=True) + p = Symbol('p', integer=True, nonnegative=True) + assert partition(m).is_integer + assert not partition(m).is_negative + assert partition(m).is_nonnegative + assert partition(n).is_zero + assert partition(p).is_positive + assert partition(x).subs(x, 7) == 15 + assert partition(y).subs(y, 8) == 22 + raises(TypeError, lambda: partition(Rational(5, 4))) + + +def test_divisor_sigma(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: divisor_sigma(m)) + raises(TypeError, lambda: divisor_sigma(4.5)) + raises(TypeError, lambda: divisor_sigma(1, m)) + raises(TypeError, lambda: divisor_sigma(1, 4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: divisor_sigma(m)) + raises(ValueError, lambda: divisor_sigma(0)) + m = Symbol('m', negative=True) + raises(ValueError, lambda: divisor_sigma(1, m)) + raises(ValueError, lambda: divisor_sigma(1, -1)) + + # special case + p = Symbol('p', prime=True) + k = Symbol('k', integer=True) + assert divisor_sigma(p, 1) == p + 1 + assert divisor_sigma(p, k) == p**k + 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert divisor_sigma(n).is_integer is True + assert divisor_sigma(n).is_positive is True + + # symbolic + k = Symbol('k', integer=True, zero=False) + assert divisor_sigma(4, k) == 2**(2*k) + 2**k + 1 + assert divisor_sigma(6, k) == (2**k + 1) * (3**k + 1) + + # Integer + assert divisor_sigma(23450) == 50592 + assert divisor_sigma(23450, 0) == 24 + assert divisor_sigma(23450, 1) == 50592 + assert divisor_sigma(23450, 2) == 730747500 + assert divisor_sigma(23450, 3) == 14666785333344 + + +def test_udivisor_sigma(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: udivisor_sigma(m)) + raises(TypeError, lambda: udivisor_sigma(4.5)) + raises(TypeError, lambda: udivisor_sigma(1, m)) + raises(TypeError, lambda: udivisor_sigma(1, 4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: udivisor_sigma(m)) + raises(ValueError, lambda: udivisor_sigma(0)) + m = Symbol('m', negative=True) + raises(ValueError, lambda: udivisor_sigma(1, m)) + raises(ValueError, lambda: udivisor_sigma(1, -1)) + + # special case + p = Symbol('p', prime=True) + k = Symbol('k', integer=True) + assert udivisor_sigma(p, 1) == p + 1 + assert udivisor_sigma(p, k) == p**k + 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert udivisor_sigma(n).is_integer is True + assert udivisor_sigma(n).is_positive is True + + # Integer + A034444 = [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, + 4, 4, 2, 4, 2, 4, 2, 4, 2, 8, 2, 2, 4, 4, 4, 4, 2, 4, 4, 4, + 2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 8] + for n, val in enumerate(A034444, 1): + assert udivisor_sigma(n, 0) == val + A034448 = [1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, 17, 18, + 30, 20, 30, 32, 36, 24, 36, 26, 42, 28, 40, 30, 72, 32, 33, + 48, 54, 48, 50, 38, 60, 56, 54, 42, 96, 44, 60, 60, 72, 48] + for n, val in enumerate(A034448, 1): + assert udivisor_sigma(n, 1) == val + A034676 = [1, 5, 10, 17, 26, 50, 50, 65, 82, 130, 122, 170, 170, 250, + 260, 257, 290, 410, 362, 442, 500, 610, 530, 650, 626, 850, + 730, 850, 842, 1300, 962, 1025, 1220, 1450, 1300, 1394, 1370] + for n, val in enumerate(A034676, 1): + assert udivisor_sigma(n, 2) == val + + +def test_legendre_symbol(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: legendre_symbol(m, 3)) + raises(TypeError, lambda: legendre_symbol(4.5, 3)) + raises(TypeError, lambda: legendre_symbol(1, m)) + raises(TypeError, lambda: legendre_symbol(1, 4.5)) + m = Symbol('m', prime=False) + raises(ValueError, lambda: legendre_symbol(1, m)) + raises(ValueError, lambda: legendre_symbol(1, 6)) + m = Symbol('m', odd=False) + raises(ValueError, lambda: legendre_symbol(1, m)) + raises(ValueError, lambda: legendre_symbol(1, 2)) + + # special case + p = Symbol('p', prime=True) + k = Symbol('k', integer=True) + assert legendre_symbol(p*k, p) == 0 + assert legendre_symbol(1, p) == 1 + + # property + n = Symbol('n') + m = Symbol('m') + assert legendre_symbol(m, n).is_integer is True + assert legendre_symbol(m, n).is_prime is False + + # Integer + assert legendre_symbol(5, 11) == 1 + assert legendre_symbol(25, 41) == 1 + assert legendre_symbol(67, 101) == -1 + assert legendre_symbol(0, 13) == 0 + assert legendre_symbol(9, 3) == 0 + + +def test_jacobi_symbol(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: jacobi_symbol(m, 3)) + raises(TypeError, lambda: jacobi_symbol(4.5, 3)) + raises(TypeError, lambda: jacobi_symbol(1, m)) + raises(TypeError, lambda: jacobi_symbol(1, 4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: jacobi_symbol(1, m)) + raises(ValueError, lambda: jacobi_symbol(1, -6)) + m = Symbol('m', odd=False) + raises(ValueError, lambda: jacobi_symbol(1, m)) + raises(ValueError, lambda: jacobi_symbol(1, 2)) + + # special case + p = Symbol('p', integer=True) + k = Symbol('k', integer=True) + assert jacobi_symbol(p*k, p) == 0 + assert jacobi_symbol(1, p) == 1 + assert jacobi_symbol(1, 1) == 1 + assert jacobi_symbol(0, 1) == 1 + + # property + n = Symbol('n') + m = Symbol('m') + assert jacobi_symbol(m, n).is_integer is True + assert jacobi_symbol(m, n).is_prime is False + + # Integer + assert jacobi_symbol(25, 41) == 1 + assert jacobi_symbol(-23, 83) == -1 + assert jacobi_symbol(3, 9) == 0 + assert jacobi_symbol(42, 97) == -1 + assert jacobi_symbol(3, 5) == -1 + assert jacobi_symbol(7, 9) == 1 + assert jacobi_symbol(0, 3) == 0 + assert jacobi_symbol(0, 1) == 1 + assert jacobi_symbol(2, 1) == 1 + assert jacobi_symbol(1, 3) == 1 + + +def test_kronecker_symbol(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: kronecker_symbol(m, 3)) + raises(TypeError, lambda: kronecker_symbol(4.5, 3)) + raises(TypeError, lambda: kronecker_symbol(1, m)) + raises(TypeError, lambda: kronecker_symbol(1, 4.5)) + + # special case + p = Symbol('p', integer=True) + assert kronecker_symbol(1, p) == 1 + assert kronecker_symbol(1, 1) == 1 + assert kronecker_symbol(0, 1) == 1 + + # property + n = Symbol('n') + m = Symbol('m') + assert kronecker_symbol(m, n).is_integer is True + assert kronecker_symbol(m, n).is_prime is False + + # Integer + for n in range(3, 10, 2): + for a in range(-n, n): + val = kronecker_symbol(a, n) + assert val == jacobi_symbol(a, n) + minus = kronecker_symbol(a, -n) + if a < 0: + assert -minus == val + else: + assert minus == val + even = kronecker_symbol(a, 2 * n) + if a % 2 == 0: + assert even == 0 + elif a % 8 in [1, 7]: + assert even == val + else: + assert -even == val + assert kronecker_symbol(1, 0) == kronecker_symbol(-1, 0) == 1 + assert kronecker_symbol(0, 0) == 0 + + +def test_mobius(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: mobius(m)) + raises(TypeError, lambda: mobius(4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: mobius(m)) + raises(ValueError, lambda: mobius(-3)) + + # special case + p = Symbol('p', prime=True) + assert mobius(p) == -1 + + # property + n = Symbol('n', integer=True, positive=True) + assert mobius(n).is_integer is True + assert mobius(n).is_prime is False + + # symbolic + n = Symbol('n', integer=True, positive=True) + k = Symbol('k', integer=True, positive=True) + assert mobius(n**2) == 0 + assert mobius(4*n) == 0 + assert isinstance(mobius(n**k), mobius) + assert mobius(n**(k+1)) == 0 + assert isinstance(mobius(3**k), mobius) + assert mobius(3**(k+1)) == 0 + m = Symbol('m') + assert isinstance(mobius(4*m), mobius) + + # Integer + assert mobius(13*7) == 1 + assert mobius(1) == 1 + assert mobius(13*7*5) == -1 + assert mobius(13**2) == 0 + A008683 = [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, + -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, + 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0] + for n, val in enumerate(A008683, 1): + assert mobius(n) == val + + +def test_primenu(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: primenu(m)) + raises(TypeError, lambda: primenu(4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: primenu(m)) + raises(ValueError, lambda: primenu(0)) + + # special case + p = Symbol('p', prime=True) + assert primenu(p) == 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert primenu(n).is_integer is True + assert primenu(n).is_nonnegative is True + + # Integer + assert primenu(7*13) == 2 + assert primenu(2*17*19) == 3 + assert primenu(2**3 * 17 * 19**2) == 3 + A001221 = [0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, + 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2] + for n, val in enumerate(A001221, 1): + assert primenu(n) == val + + +def test_primeomega(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: primeomega(m)) + raises(TypeError, lambda: primeomega(4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: primeomega(m)) + raises(ValueError, lambda: primeomega(0)) + + # special case + p = Symbol('p', prime=True) + assert primeomega(p) == 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert primeomega(n).is_integer is True + assert primeomega(n).is_nonnegative is True + + # Integer + assert primeomega(7*13) == 2 + assert primeomega(2*17*19) == 3 + assert primeomega(2**3 * 17 * 19**2) == 6 + A001222 = [0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, + 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4] + for n, val in enumerate(A001222, 1): + assert primeomega(n) == val + + +def test_totient(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: totient(m)) + raises(TypeError, lambda: totient(4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: totient(m)) + raises(ValueError, lambda: totient(0)) + + # special case + p = Symbol('p', prime=True) + assert totient(p) == p - 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert totient(n).is_integer is True + assert totient(n).is_positive is True + + # Integer + assert totient(7*13) == totient(factorint(7*13)) == (7-1)*(13-1) + assert totient(2*17*19) == totient(factorint(2*17*19)) == (17-1)*(19-1) + assert totient(2**3 * 17 * 19**2) == totient({2: 3, 17: 1, 19: 2}) == 2**2 * (17-1) * 19*(19-1) + A000010 = [1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, + 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, + 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22] + for n, val in enumerate(A000010, 1): + assert totient(n) == val + + +def test_reduced_totient(): + # error + m = Symbol('m', integer=False) + raises(TypeError, lambda: reduced_totient(m)) + raises(TypeError, lambda: reduced_totient(4.5)) + m = Symbol('m', positive=False) + raises(ValueError, lambda: reduced_totient(m)) + raises(ValueError, lambda: reduced_totient(0)) + + # special case + p = Symbol('p', prime=True) + assert reduced_totient(p) == p - 1 + + # property + n = Symbol('n', integer=True, positive=True) + assert reduced_totient(n).is_integer is True + assert reduced_totient(n).is_positive is True + + # Integer + assert reduced_totient(7*13) == reduced_totient(factorint(7*13)) == 12 + assert reduced_totient(2*17*19) == reduced_totient(factorint(2*17*19)) == 144 + assert reduced_totient(2**2 * 11) == reduced_totient({2: 2, 11: 1}) == 10 + assert reduced_totient(2**3 * 17 * 19**2) == reduced_totient({2: 3, 17: 1, 19: 2}) == 2736 + A002322 = [1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4, 4, 16, 6, + 18, 4, 6, 10, 22, 2, 20, 12, 18, 6, 28, 4, 30, 8, 10, 16, + 12, 6, 36, 18, 12, 4, 40, 6, 42, 10, 12, 22, 46, 4, 42] + for n, val in enumerate(A002322, 1): + assert reduced_totient(n) == val + + +def test_primepi(): + # error + z = Symbol('z', real=False) + raises(TypeError, lambda: primepi(z)) + raises(TypeError, lambda: primepi(I)) + + # property + n = Symbol('n', integer=True, positive=True) + assert primepi(n).is_integer is True + assert primepi(n).is_nonnegative is True + + # infinity + assert primepi(oo) == oo + assert primepi(-oo) == 0 + + # symbol + x = Symbol('x') + assert isinstance(primepi(x), primepi) + + # Integer + assert primepi(0) == 0 + A000720 = [0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, + 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, + 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15] + for n, val in enumerate(A000720, 1): + assert primepi(n) == primepi(n + 0.5) == val + + +def test__nT(): + assert [_nT(i, j) for i in range(5) for j in range(i + 2)] == [ + 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0] + check = [_nT(10, i) for i in range(11)] + assert check == [0, 1, 5, 8, 9, 7, 5, 3, 2, 1, 1] + assert all(type(i) is int for i in check) + assert _nT(10, 5) == 7 + assert _nT(100, 98) == 2 + assert _nT(100, 100) == 1 + assert _nT(10, 3) == 8 + + +def test_nC_nP_nT(): + from sympy.utilities.iterables import ( + multiset_permutations, multiset_combinations, multiset_partitions, + partitions, subsets, permutations) + from sympy.functions.combinatorial.numbers import ( + nP, nC, nT, stirling, _stirling1, _stirling2, _multiset_histogram, _AOP_product) + + from sympy.combinatorics.permutations import Permutation + from sympy.core.random import choice + + c = string.ascii_lowercase + for i in range(100): + s = ''.join(choice(c) for i in range(7)) + u = len(s) == len(set(s)) + try: + tot = 0 + for i in range(8): + check = nP(s, i) + tot += check + assert len(list(multiset_permutations(s, i))) == check + if u: + assert nP(len(s), i) == check + assert nP(s) == tot + except AssertionError: + print(s, i, 'failed perm test') + raise ValueError() + + for i in range(100): + s = ''.join(choice(c) for i in range(7)) + u = len(s) == len(set(s)) + try: + tot = 0 + for i in range(8): + check = nC(s, i) + tot += check + assert len(list(multiset_combinations(s, i))) == check + if u: + assert nC(len(s), i) == check + assert nC(s) == tot + if u: + assert nC(len(s)) == tot + except AssertionError: + print(s, i, 'failed combo test') + raise ValueError() + + for i in range(1, 10): + tot = 0 + for j in range(1, i + 2): + check = nT(i, j) + assert check.is_Integer + tot += check + assert sum(1 for p in partitions(i, j, size=True) if p[0] == j) == check + assert nT(i) == tot + + for i in range(1, 10): + tot = 0 + for j in range(1, i + 2): + check = nT(range(i), j) + tot += check + assert len(list(multiset_partitions(list(range(i)), j))) == check + assert nT(range(i)) == tot + + for i in range(100): + s = ''.join(choice(c) for i in range(7)) + u = len(s) == len(set(s)) + try: + tot = 0 + for i in range(1, 8): + check = nT(s, i) + tot += check + assert len(list(multiset_partitions(s, i))) == check + if u: + assert nT(range(len(s)), i) == check + if u: + assert nT(range(len(s))) == tot + assert nT(s) == tot + except AssertionError: + print(s, i, 'failed partition test') + raise ValueError() + + # tests for Stirling numbers of the first kind that are not tested in the + # above + assert [stirling(9, i, kind=1) for i in range(11)] == [ + 0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1, 0] + perms = list(permutations(range(4))) + assert [sum(1 for p in perms if Permutation(p).cycles == i) + for i in range(5)] == [0, 6, 11, 6, 1] == [ + stirling(4, i, kind=1) for i in range(5)] + # http://oeis.org/A008275 + assert [stirling(n, k, signed=1) + for n in range(10) for k in range(1, n + 1)] == [ + 1, -1, + 1, 2, -3, + 1, -6, 11, -6, + 1, 24, -50, 35, -10, + 1, -120, 274, -225, 85, -15, + 1, 720, -1764, 1624, -735, 175, -21, + 1, -5040, 13068, -13132, 6769, -1960, 322, -28, + 1, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1] + # https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind + assert [stirling(n, k, kind=1) + for n in range(10) for k in range(n+1)] == [ + 1, + 0, 1, + 0, 1, 1, + 0, 2, 3, 1, + 0, 6, 11, 6, 1, + 0, 24, 50, 35, 10, 1, + 0, 120, 274, 225, 85, 15, 1, + 0, 720, 1764, 1624, 735, 175, 21, 1, + 0, 5040, 13068, 13132, 6769, 1960, 322, 28, 1, + 0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1] + # https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind + assert [stirling(n, k, kind=2) + for n in range(10) for k in range(n+1)] == [ + 1, + 0, 1, + 0, 1, 1, + 0, 1, 3, 1, + 0, 1, 7, 6, 1, + 0, 1, 15, 25, 10, 1, + 0, 1, 31, 90, 65, 15, 1, + 0, 1, 63, 301, 350, 140, 21, 1, + 0, 1, 127, 966, 1701, 1050, 266, 28, 1, + 0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1] + assert stirling(3, 4, kind=1) == stirling(3, 4, kind=1) == 0 + raises(ValueError, lambda: stirling(-2, 2)) + + # Assertion that the return type is SymPy Integer. + assert isinstance(_stirling1(6, 3), Integer) + assert isinstance(_stirling2(6, 3), Integer) + + def delta(p): + if len(p) == 1: + return oo + return min(abs(i[0] - i[1]) for i in subsets(p, 2)) + parts = multiset_partitions(range(5), 3) + d = 2 + assert (sum(1 for p in parts if all(delta(i) >= d for i in p)) == + stirling(5, 3, d=d) == 7) + + # other coverage tests + assert nC('abb', 2) == nC('aab', 2) == 2 + assert nP(3, 3, replacement=True) == nP('aabc', 3, replacement=True) == 27 + assert nP(3, 4) == 0 + assert nP('aabc', 5) == 0 + assert nC(4, 2, replacement=True) == nC('abcdd', 2, replacement=True) == \ + len(list(multiset_combinations('aabbccdd', 2))) == 10 + assert nC('abcdd') == sum(nC('abcdd', i) for i in range(6)) == 24 + assert nC(list('abcdd'), 4) == 4 + assert nT('aaaa') == nT(4) == len(list(partitions(4))) == 5 + assert nT('aaab') == len(list(multiset_partitions('aaab'))) == 7 + assert nC('aabb'*3, 3) == 4 # aaa, bbb, abb, baa + assert dict(_AOP_product((4,1,1,1))) == { + 0: 1, 1: 4, 2: 7, 3: 8, 4: 8, 5: 7, 6: 4, 7: 1} + # the following was the first t that showed a problem in a previous form of + # the function, so it's not as random as it may appear + t = (3, 9, 4, 6, 6, 5, 5, 2, 10, 4) + assert sum(_AOP_product(t)[i] for i in range(55)) == 58212000 + raises(ValueError, lambda: _multiset_histogram({1:'a'})) + + +def test_PR_14617(): + from sympy.functions.combinatorial.numbers import nT + for n in (0, []): + for k in (-1, 0, 1): + if k == 0: + assert nT(n, k) == 1 + else: + assert nT(n, k) == 0 + + +def test_issue_8496(): + n = Symbol("n") + k = Symbol("k") + + raises(TypeError, lambda: catalan(n, k)) + + +def test_issue_8601(): + n = Symbol('n', integer=True, negative=True) + + assert catalan(n - 1) is S.Zero + assert catalan(Rational(-1, 2)) is S.ComplexInfinity + assert catalan(-S.One) == Rational(-1, 2) + c1 = catalan(-5.6).evalf() + assert str(c1) == '6.93334070531408e-5' + c2 = catalan(-35.4).evalf() + assert str(c2) == '-4.14189164517449e-24' + + +def test_motzkin(): + assert motzkin.is_motzkin(4) == True + assert motzkin.is_motzkin(9) == True + assert motzkin.is_motzkin(10) == False + assert motzkin.find_motzkin_numbers_in_range(10,200) == [21, 51, 127] + assert motzkin.find_motzkin_numbers_in_range(10,400) == [21, 51, 127, 323] + assert motzkin.find_motzkin_numbers_in_range(10,1600) == [21, 51, 127, 323, 835] + assert motzkin.find_first_n_motzkins(5) == [1, 1, 2, 4, 9] + assert motzkin.find_first_n_motzkins(7) == [1, 1, 2, 4, 9, 21, 51] + assert motzkin.find_first_n_motzkins(10) == [1, 1, 2, 4, 9, 21, 51, 127, 323, 835] + raises(ValueError, lambda: motzkin.eval(77.58)) + raises(ValueError, lambda: motzkin.eval(-8)) + raises(ValueError, lambda: motzkin.find_motzkin_numbers_in_range(-2,7)) + raises(ValueError, lambda: motzkin.find_motzkin_numbers_in_range(13,7)) + raises(ValueError, lambda: motzkin.find_first_n_motzkins(112.8)) + + +def test_nD_derangements(): + from sympy.utilities.iterables import (partitions, multiset, + multiset_derangements, multiset_permutations) + from sympy.functions.combinatorial.numbers import nD + + got = [] + for i in partitions(8, k=4): + s = [] + it = 0 + for k, v in i.items(): + for i in range(v): + s.extend([it]*k) + it += 1 + ms = multiset(s) + c1 = sum(1 for i in multiset_permutations(s) if + all(i != j for i, j in zip(i, s))) + assert c1 == nD(ms) == nD(ms, 0) == nD(ms, 1) + v = [tuple(i) for i in multiset_derangements(s)] + c2 = len(v) + assert c2 == len(set(v)) + assert c1 == c2 + got.append(c1) + assert got == [1, 4, 6, 12, 24, 24, 61, 126, 315, 780, 297, 772, + 2033, 5430, 14833] + + assert nD('1112233456', brute=True) == nD('1112233456') == 16356 + assert nD('') == nD([]) == nD({}) == 0 + assert nD({1: 0}) == 0 + raises(ValueError, lambda: nD({1: -1})) + assert nD('112') == 0 + assert nD(i='112') == 0 + assert [nD(n=i) for i in range(6)] == [0, 0, 1, 2, 9, 44] + assert nD((i for i in range(4))) == nD('0123') == 9 + assert nD(m=(i for i in range(4))) == 3 + assert nD(m={0: 1, 1: 1, 2: 1, 3: 1}) == 3 + assert nD(m=[0, 1, 2, 3]) == 3 + raises(TypeError, lambda: nD(m=0)) + raises(TypeError, lambda: nD(-1)) + assert nD({-1: 1, -2: 1}) == 1 + assert nD(m={0: 3}) == 0 + raises(ValueError, lambda: nD(i='123', n=3)) + raises(ValueError, lambda: nD(i='123', m=(1,2))) + raises(ValueError, lambda: nD(n=0, m=(1,2))) + raises(ValueError, lambda: nD({1: -1})) + raises(ValueError, lambda: nD(m={-1: 1, 2: 1})) + raises(ValueError, lambda: nD(m={1: -1, 2: 1})) + raises(ValueError, lambda: nD(m=[-1, 2])) + raises(TypeError, lambda: nD({1: x})) + raises(TypeError, lambda: nD(m={1: x})) + raises(TypeError, lambda: nD(m={x: 1})) + + +def test_deprecated_ntheory_symbolic_functions(): + from sympy.testing.pytest import warns_deprecated_sympy + + with warns_deprecated_sympy(): + assert not carmichael.is_carmichael(3) + with warns_deprecated_sympy(): + assert carmichael.find_carmichael_numbers_in_range(10, 20) == [] + with warns_deprecated_sympy(): + assert carmichael.find_first_n_carmichaels(1) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/__init__.py b/lib/python3.11/site-packages/sympy/functions/elementary/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..78034e72ef2ed722c3ae685a87cf4df618a982b0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/__init__.py @@ -0,0 +1 @@ +# Stub __init__.py for sympy.functions.elementary diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/elementary/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9ea94778cc09946641729df8c090195c0342e474 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/elementary/__pycache__/__init__.cpython-311.pyc differ diff --git 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0000000000000000000000000000000000000000..fdf8c9d06241b46e791afe76836ea33e6d4fb1c8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/_trigonometric_special.py @@ -0,0 +1,261 @@ +r"""A module for special angle formulas for trigonometric functions + +TODO +==== + +This module should be developed in the future to contain direct square root +representation of + +.. math + F(\frac{n}{m} \pi) + +for every + +- $m \in \{ 3, 5, 17, 257, 65537 \}$ +- $n \in \mathbb{N}$, $0 \le n < m$ +- $F \in \{\sin, \cos, \tan, \csc, \sec, \cot\}$ + +Without multi-step rewrites +(e.g. $\tan \to \cos/\sin \to \cos/\sqrt \to \ sqrt$) +or using chebyshev identities +(e.g. $\cos \to \cos + \cos^2 + \cdots \to \sqrt{} + \sqrt{}^2 + \cdots $), +which are trivial to implement in sympy, +and had used to give overly complicated expressions. + +The reference can be found below, if anyone may need help implementing them. + +References +========== + +.. [*] Gottlieb, Christian. (1999). The Simple and straightforward construction + of the regular 257-gon. The Mathematical Intelligencer. 21. 31-37. + 10.1007/BF03024829. +.. [*] https://resources.wolframcloud.com/FunctionRepository/resources/Cos2PiOverFermatPrime +""" +from __future__ import annotations +from typing import Callable +from functools import reduce +from sympy.core.expr import Expr +from sympy.core.singleton import S +from sympy.core.intfunc import igcdex +from sympy.core.numbers import Integer +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.core.cache import cacheit + + +def migcdex(*x: int) -> tuple[tuple[int, ...], int]: + r"""Compute extended gcd for multiple integers. + + Explanation + =========== + + Given the integers $x_1, \cdots, x_n$ and + an extended gcd for multiple arguments are defined as a solution + $(y_1, \cdots, y_n), g$ for the diophantine equation + $x_1 y_1 + \cdots + x_n y_n = g$ such that + $g = \gcd(x_1, \cdots, x_n)$. + + Examples + ======== + + >>> from sympy.functions.elementary._trigonometric_special import migcdex + >>> migcdex() + ((), 0) + >>> migcdex(4) + ((1,), 4) + >>> migcdex(4, 6) + ((-1, 1), 2) + >>> migcdex(6, 10, 15) + ((1, 1, -1), 1) + """ + if not x: + return (), 0 + + if len(x) == 1: + return (1,), x[0] + + if len(x) == 2: + u, v, h = igcdex(x[0], x[1]) + return (u, v), h + + y, g = migcdex(*x[1:]) + u, v, h = igcdex(x[0], g) + return (u, *(v * i for i in y)), h + + +def ipartfrac(*denoms: int) -> tuple[int, ...]: + r"""Compute the partial fraction decomposition. + + Explanation + =========== + + Given a rational number $\frac{1}{q_1 \cdots q_n}$ where all + $q_1, \cdots, q_n$ are pairwise coprime, + + A partial fraction decomposition is defined as + + .. math:: + \frac{1}{q_1 \cdots q_n} = \frac{p_1}{q_1} + \cdots + \frac{p_n}{q_n} + + And it can be derived from solving the following diophantine equation for + the $p_1, \cdots, p_n$ + + .. math:: + 1 = p_1 \prod_{i \ne 1}q_i + \cdots + p_n \prod_{i \ne n}q_i + + Where $q_1, \cdots, q_n$ being pairwise coprime implies + $\gcd(\prod_{i \ne 1}q_i, \cdots, \prod_{i \ne n}q_i) = 1$, + which guarantees the existence of the solution. + + It is sufficient to compute partial fraction decomposition only + for numerator $1$ because partial fraction decomposition for any + $\frac{n}{q_1 \cdots q_n}$ can be easily computed by multiplying + the result by $n$ afterwards. + + Parameters + ========== + + denoms : int + The pairwise coprime integer denominators $q_i$ which defines the + rational number $\frac{1}{q_1 \cdots q_n}$ + + Returns + ======= + + tuple[int, ...] + The list of numerators which semantically corresponds to $p_i$ of the + partial fraction decomposition + $\frac{1}{q_1 \cdots q_n} = \frac{p_1}{q_1} + \cdots + \frac{p_n}{q_n}$ + + Examples + ======== + + >>> from sympy import Rational, Mul + >>> from sympy.functions.elementary._trigonometric_special import ipartfrac + + >>> denoms = 2, 3, 5 + >>> numers = ipartfrac(2, 3, 5) + >>> numers + (1, 7, -14) + + >>> Rational(1, Mul(*denoms)) + 1/30 + >>> out = 0 + >>> for n, d in zip(numers, denoms): + ... out += Rational(n, d) + >>> out + 1/30 + """ + if not denoms: + return () + + def mul(x: int, y: int) -> int: + return x * y + + denom = reduce(mul, denoms) + a = [denom // x for x in denoms] + h, _ = migcdex(*a) + return h + + +def fermat_coords(n: int) -> list[int] | None: + """If n can be factored in terms of Fermat primes with + multiplicity of each being 1, return those primes, else + None + """ + primes = [] + for p in [3, 5, 17, 257, 65537]: + quotient, remainder = divmod(n, p) + if remainder == 0: + n = quotient + primes.append(p) + if n == 1: + return primes + return None + + +@cacheit +def cos_3() -> Expr: + r"""Computes $\cos \frac{\pi}{3}$ in square roots""" + return S.Half + + +@cacheit +def cos_5() -> Expr: + r"""Computes $\cos \frac{\pi}{5}$ in square roots""" + return (sqrt(5) + 1) / 4 + + +@cacheit +def cos_17() -> Expr: + r"""Computes $\cos \frac{\pi}{17}$ in square roots""" + return sqrt( + (15 + sqrt(17)) / 32 + sqrt(2) * (sqrt(17 - sqrt(17)) + + sqrt(sqrt(2) * (-8 * sqrt(17 + sqrt(17)) - (1 - sqrt(17)) + * sqrt(17 - sqrt(17))) + 6 * sqrt(17) + 34)) / 32) + + +@cacheit +def cos_257() -> Expr: + r"""Computes $\cos \frac{\pi}{257}$ in square roots + + References + ========== + + .. [*] https://math.stackexchange.com/questions/516142/how-does-cos2-pi-257-look-like-in-real-radicals + .. [*] https://r-knott.surrey.ac.uk/Fibonacci/simpleTrig.html + """ + def f1(a: Expr, b: Expr) -> tuple[Expr, Expr]: + return (a + sqrt(a**2 + b)) / 2, (a - sqrt(a**2 + b)) / 2 + + def f2(a: Expr, b: Expr) -> Expr: + return (a - sqrt(a**2 + b))/2 + + t1, t2 = f1(S.NegativeOne, Integer(256)) + z1, z3 = f1(t1, Integer(64)) + z2, z4 = f1(t2, Integer(64)) + y1, y5 = f1(z1, 4*(5 + t1 + 2*z1)) + y6, y2 = f1(z2, 4*(5 + t2 + 2*z2)) + y3, y7 = f1(z3, 4*(5 + t1 + 2*z3)) + y8, y4 = f1(z4, 4*(5 + t2 + 2*z4)) + x1, x9 = f1(y1, -4*(t1 + y1 + y3 + 2*y6)) + x2, x10 = f1(y2, -4*(t2 + y2 + y4 + 2*y7)) + x3, x11 = f1(y3, -4*(t1 + y3 + y5 + 2*y8)) + x4, x12 = f1(y4, -4*(t2 + y4 + y6 + 2*y1)) + x5, x13 = f1(y5, -4*(t1 + y5 + y7 + 2*y2)) + x6, x14 = f1(y6, -4*(t2 + y6 + y8 + 2*y3)) + x15, x7 = f1(y7, -4*(t1 + y7 + y1 + 2*y4)) + x8, x16 = f1(y8, -4*(t2 + y8 + y2 + 2*y5)) + v1 = f2(x1, -4*(x1 + x2 + x3 + x6)) + v2 = f2(x2, -4*(x2 + x3 + x4 + x7)) + v3 = f2(x8, -4*(x8 + x9 + x10 + x13)) + v4 = f2(x9, -4*(x9 + x10 + x11 + x14)) + v5 = f2(x10, -4*(x10 + x11 + x12 + x15)) + v6 = f2(x16, -4*(x16 + x1 + x2 + x5)) + u1 = -f2(-v1, -4*(v2 + v3)) + u2 = -f2(-v4, -4*(v5 + v6)) + w1 = -2*f2(-u1, -4*u2) + return sqrt(sqrt(2)*sqrt(w1 + 4)/8 + S.Half) + + +def cos_table() -> dict[int, Callable[[], Expr]]: + r"""Lazily evaluated table for $\cos \frac{\pi}{n}$ in square roots for + $n \in \{3, 5, 17, 257, 65537\}$. + + Notes + ===== + + 65537 is the only other known Fermat prime and it is nearly impossible to + build in the current SymPy due to performance issues. + + References + ========== + + https://r-knott.surrey.ac.uk/Fibonacci/simpleTrig.html + """ + return { + 3: cos_3, + 5: cos_5, + 17: cos_17, + 257: cos_257 + } diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__init__.py b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..66b46f0278ec7608e3213f3f2710fcaad9537182 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/bench_exp.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/bench_exp.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9fc5d412e51556d5d147f73f1793224a80e0b94d Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/__pycache__/bench_exp.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py new file mode 100644 index 0000000000000000000000000000000000000000..fa18d29f87bcd249baec1d278a030fa7a133c3ba --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/benchmarks/bench_exp.py @@ -0,0 +1,11 @@ +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import exp + +x, y = symbols('x,y') + +e = exp(2*x) +q = exp(3*x) + + +def timeit_exp_subs(): + e.subs(q, y) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/complexes.py b/lib/python3.11/site-packages/sympy/functions/elementary/complexes.py new file mode 100644 index 0000000000000000000000000000000000000000..c615a3613d07f345e5b02275347ffe820c914019 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/complexes.py @@ -0,0 +1,1473 @@ +from typing import Tuple as tTuple + +from sympy.core import S, Add, Mul, sympify, Symbol, Dummy, Basic +from sympy.core.expr import Expr +from sympy.core.exprtools import factor_terms +from sympy.core.function import (Function, Derivative, ArgumentIndexError, + AppliedUndef, expand_mul) +from sympy.core.logic import fuzzy_not, fuzzy_or +from sympy.core.numbers import pi, I, oo +from sympy.core.power import Pow +from sympy.core.relational import Eq +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise + +############################################################################### +######################### REAL and IMAGINARY PARTS ############################ +############################################################################### + + +class re(Function): + """ + Returns real part of expression. This function performs only + elementary analysis and so it will fail to decompose properly + more complicated expressions. If completely simplified result + is needed then use ``Basic.as_real_imag()`` or perform complex + expansion on instance of this function. + + Examples + ======== + + >>> from sympy import re, im, I, E, symbols + >>> x, y = symbols('x y', real=True) + >>> re(2*E) + 2*E + >>> re(2*I + 17) + 17 + >>> re(2*I) + 0 + >>> re(im(x) + x*I + 2) + 2 + >>> re(5 + I + 2) + 7 + + Parameters + ========== + + arg : Expr + Real or complex expression. + + Returns + ======= + + expr : Expr + Real part of expression. + + See Also + ======== + + im + """ + + args: tTuple[Expr] + + is_extended_real = True + unbranched = True # implicitly works on the projection to C + _singularities = True # non-holomorphic + + @classmethod + def eval(cls, arg): + if arg is S.NaN: + return S.NaN + elif arg is S.ComplexInfinity: + return S.NaN + elif arg.is_extended_real: + return arg + elif arg.is_imaginary or (I*arg).is_extended_real: + return S.Zero + elif arg.is_Matrix: + return arg.as_real_imag()[0] + elif arg.is_Function and isinstance(arg, conjugate): + return re(arg.args[0]) + else: + + included, reverted, excluded = [], [], [] + args = Add.make_args(arg) + for term in args: + coeff = term.as_coefficient(I) + + if coeff is not None: + if not coeff.is_extended_real: + reverted.append(coeff) + elif not term.has(I) and term.is_extended_real: + excluded.append(term) + else: + # Try to do some advanced expansion. If + # impossible, don't try to do re(arg) again + # (because this is what we are trying to do now). + real_imag = term.as_real_imag(ignore=arg) + if real_imag: + excluded.append(real_imag[0]) + else: + included.append(term) + + if len(args) != len(included): + a, b, c = (Add(*xs) for xs in [included, reverted, excluded]) + + return cls(a) - im(b) + c + + def as_real_imag(self, deep=True, **hints): + """ + Returns the real number with a zero imaginary part. + + """ + return (self, S.Zero) + + def _eval_derivative(self, x): + if x.is_extended_real or self.args[0].is_extended_real: + return re(Derivative(self.args[0], x, evaluate=True)) + if x.is_imaginary or self.args[0].is_imaginary: + return -I \ + * im(Derivative(self.args[0], x, evaluate=True)) + + def _eval_rewrite_as_im(self, arg, **kwargs): + return self.args[0] - I*im(self.args[0]) + + def _eval_is_algebraic(self): + return self.args[0].is_algebraic + + def _eval_is_zero(self): + # is_imaginary implies nonzero + return fuzzy_or([self.args[0].is_imaginary, self.args[0].is_zero]) + + def _eval_is_finite(self): + if self.args[0].is_finite: + return True + + def _eval_is_complex(self): + if self.args[0].is_finite: + return True + + +class im(Function): + """ + Returns imaginary part of expression. This function performs only + elementary analysis and so it will fail to decompose properly more + complicated expressions. If completely simplified result is needed then + use ``Basic.as_real_imag()`` or perform complex expansion on instance of + this function. + + Examples + ======== + + >>> from sympy import re, im, E, I + >>> from sympy.abc import x, y + >>> im(2*E) + 0 + >>> im(2*I + 17) + 2 + >>> im(x*I) + re(x) + >>> im(re(x) + y) + im(y) + >>> im(2 + 3*I) + 3 + + Parameters + ========== + + arg : Expr + Real or complex expression. + + Returns + ======= + + expr : Expr + Imaginary part of expression. + + See Also + ======== + + re + """ + + args: tTuple[Expr] + + is_extended_real = True + unbranched = True # implicitly works on the projection to C + _singularities = True # non-holomorphic + + @classmethod + def eval(cls, arg): + if arg is S.NaN: + return S.NaN + elif arg is S.ComplexInfinity: + return S.NaN + elif arg.is_extended_real: + return S.Zero + elif arg.is_imaginary or (I*arg).is_extended_real: + return -I * arg + elif arg.is_Matrix: + return arg.as_real_imag()[1] + elif arg.is_Function and isinstance(arg, conjugate): + return -im(arg.args[0]) + else: + included, reverted, excluded = [], [], [] + args = Add.make_args(arg) + for term in args: + coeff = term.as_coefficient(I) + + if coeff is not None: + if not coeff.is_extended_real: + reverted.append(coeff) + else: + excluded.append(coeff) + elif term.has(I) or not term.is_extended_real: + # Try to do some advanced expansion. If + # impossible, don't try to do im(arg) again + # (because this is what we are trying to do now). + real_imag = term.as_real_imag(ignore=arg) + if real_imag: + excluded.append(real_imag[1]) + else: + included.append(term) + + if len(args) != len(included): + a, b, c = (Add(*xs) for xs in [included, reverted, excluded]) + + return cls(a) + re(b) + c + + def as_real_imag(self, deep=True, **hints): + """ + Return the imaginary part with a zero real part. + + """ + return (self, S.Zero) + + def _eval_derivative(self, x): + if x.is_extended_real or self.args[0].is_extended_real: + return im(Derivative(self.args[0], x, evaluate=True)) + if x.is_imaginary or self.args[0].is_imaginary: + return -I \ + * re(Derivative(self.args[0], x, evaluate=True)) + + def _eval_rewrite_as_re(self, arg, **kwargs): + return -I*(self.args[0] - re(self.args[0])) + + def _eval_is_algebraic(self): + return self.args[0].is_algebraic + + def _eval_is_zero(self): + return self.args[0].is_extended_real + + def _eval_is_finite(self): + if self.args[0].is_finite: + return True + + def _eval_is_complex(self): + if self.args[0].is_finite: + return True + +############################################################################### +############### SIGN, ABSOLUTE VALUE, ARGUMENT and CONJUGATION ################ +############################################################################### + +class sign(Function): + """ + Returns the complex sign of an expression: + + Explanation + =========== + + If the expression is real the sign will be: + + * $1$ if expression is positive + * $0$ if expression is equal to zero + * $-1$ if expression is negative + + If the expression is imaginary the sign will be: + + * $I$ if im(expression) is positive + * $-I$ if im(expression) is negative + + Otherwise an unevaluated expression will be returned. When evaluated, the + result (in general) will be ``cos(arg(expr)) + I*sin(arg(expr))``. + + Examples + ======== + + >>> from sympy import sign, I + + >>> sign(-1) + -1 + >>> sign(0) + 0 + >>> sign(-3*I) + -I + >>> sign(1 + I) + sign(1 + I) + >>> _.evalf() + 0.707106781186548 + 0.707106781186548*I + + Parameters + ========== + + arg : Expr + Real or imaginary expression. + + Returns + ======= + + expr : Expr + Complex sign of expression. + + See Also + ======== + + Abs, conjugate + """ + + is_complex = True + _singularities = True + + def doit(self, **hints): + s = super().doit() + if s == self and self.args[0].is_zero is False: + return self.args[0] / Abs(self.args[0]) + return s + + @classmethod + def eval(cls, arg): + # handle what we can + if arg.is_Mul: + c, args = arg.as_coeff_mul() + unk = [] + s = sign(c) + for a in args: + if a.is_extended_negative: + s = -s + elif a.is_extended_positive: + pass + else: + if a.is_imaginary: + ai = im(a) + if ai.is_comparable: # i.e. a = I*real + s *= I + if ai.is_extended_negative: + # can't use sign(ai) here since ai might not be + # a Number + s = -s + else: + unk.append(a) + else: + unk.append(a) + if c is S.One and len(unk) == len(args): + return None + return s * cls(arg._new_rawargs(*unk)) + if arg is S.NaN: + return S.NaN + if arg.is_zero: # it may be an Expr that is zero + return S.Zero + if arg.is_extended_positive: + return S.One + if arg.is_extended_negative: + return S.NegativeOne + if arg.is_Function: + if isinstance(arg, sign): + return arg + if arg.is_imaginary: + if arg.is_Pow and arg.exp is S.Half: + # we catch this because non-trivial sqrt args are not expanded + # e.g. sqrt(1-sqrt(2)) --x--> to I*sqrt(sqrt(2) - 1) + return I + arg2 = -I * arg + if arg2.is_extended_positive: + return I + if arg2.is_extended_negative: + return -I + + def _eval_Abs(self): + if fuzzy_not(self.args[0].is_zero): + return S.One + + def _eval_conjugate(self): + return sign(conjugate(self.args[0])) + + def _eval_derivative(self, x): + if self.args[0].is_extended_real: + from sympy.functions.special.delta_functions import DiracDelta + return 2 * Derivative(self.args[0], x, evaluate=True) \ + * DiracDelta(self.args[0]) + elif self.args[0].is_imaginary: + from sympy.functions.special.delta_functions import DiracDelta + return 2 * Derivative(self.args[0], x, evaluate=True) \ + * DiracDelta(-I * self.args[0]) + + def _eval_is_nonnegative(self): + if self.args[0].is_nonnegative: + return True + + def _eval_is_nonpositive(self): + if self.args[0].is_nonpositive: + return True + + def _eval_is_imaginary(self): + return self.args[0].is_imaginary + + def _eval_is_integer(self): + return self.args[0].is_extended_real + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_power(self, other): + if ( + fuzzy_not(self.args[0].is_zero) and + other.is_integer and + other.is_even + ): + return S.One + + def _eval_nseries(self, x, n, logx, cdir=0): + arg0 = self.args[0] + x0 = arg0.subs(x, 0) + if x0 != 0: + return self.func(x0) + if cdir != 0: + cdir = arg0.dir(x, cdir) + return -S.One if re(cdir) < 0 else S.One + + def _eval_rewrite_as_Piecewise(self, arg, **kwargs): + if arg.is_extended_real: + return Piecewise((1, arg > 0), (-1, arg < 0), (0, True)) + + def _eval_rewrite_as_Heaviside(self, arg, **kwargs): + from sympy.functions.special.delta_functions import Heaviside + if arg.is_extended_real: + return Heaviside(arg) * 2 - 1 + + def _eval_rewrite_as_Abs(self, arg, **kwargs): + return Piecewise((0, Eq(arg, 0)), (arg / Abs(arg), True)) + + def _eval_simplify(self, **kwargs): + return self.func(factor_terms(self.args[0])) # XXX include doit? + + +class Abs(Function): + """ + Return the absolute value of the argument. + + Explanation + =========== + + This is an extension of the built-in function ``abs()`` to accept symbolic + values. If you pass a SymPy expression to the built-in ``abs()``, it will + pass it automatically to ``Abs()``. + + Examples + ======== + + >>> from sympy import Abs, Symbol, S, I + >>> Abs(-1) + 1 + >>> x = Symbol('x', real=True) + >>> Abs(-x) + Abs(x) + >>> Abs(x**2) + x**2 + >>> abs(-x) # The Python built-in + Abs(x) + >>> Abs(3*x + 2*I) + sqrt(9*x**2 + 4) + >>> Abs(8*I) + 8 + + Note that the Python built-in will return either an Expr or int depending on + the argument:: + + >>> type(abs(-1)) + <... 'int'> + >>> type(abs(S.NegativeOne)) + + + Abs will always return a SymPy object. + + Parameters + ========== + + arg : Expr + Real or complex expression. + + Returns + ======= + + expr : Expr + Absolute value returned can be an expression or integer depending on + input arg. + + See Also + ======== + + sign, conjugate + """ + + args: tTuple[Expr] + + is_extended_real = True + is_extended_negative = False + is_extended_nonnegative = True + unbranched = True + _singularities = True # non-holomorphic + + def fdiff(self, argindex=1): + """ + Get the first derivative of the argument to Abs(). + + """ + if argindex == 1: + return sign(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + from sympy.simplify.simplify import signsimp + + if hasattr(arg, '_eval_Abs'): + obj = arg._eval_Abs() + if obj is not None: + return obj + if not isinstance(arg, Expr): + raise TypeError("Bad argument type for Abs(): %s" % type(arg)) + + # handle what we can + arg = signsimp(arg, evaluate=False) + n, d = arg.as_numer_denom() + if d.free_symbols and not n.free_symbols: + return cls(n)/cls(d) + + if arg.is_Mul: + known = [] + unk = [] + for t in arg.args: + if t.is_Pow and t.exp.is_integer and t.exp.is_negative: + bnew = cls(t.base) + if isinstance(bnew, cls): + unk.append(t) + else: + known.append(Pow(bnew, t.exp)) + else: + tnew = cls(t) + if isinstance(tnew, cls): + unk.append(t) + else: + known.append(tnew) + known = Mul(*known) + unk = cls(Mul(*unk), evaluate=False) if unk else S.One + return known*unk + if arg is S.NaN: + return S.NaN + if arg is S.ComplexInfinity: + return oo + from sympy.functions.elementary.exponential import exp, log + + if arg.is_Pow: + base, exponent = arg.as_base_exp() + if base.is_extended_real: + if exponent.is_integer: + if exponent.is_even: + return arg + if base is S.NegativeOne: + return S.One + return Abs(base)**exponent + if base.is_extended_nonnegative: + return base**re(exponent) + if base.is_extended_negative: + return (-base)**re(exponent)*exp(-pi*im(exponent)) + return + elif not base.has(Symbol): # complex base + # express base**exponent as exp(exponent*log(base)) + a, b = log(base).as_real_imag() + z = a + I*b + return exp(re(exponent*z)) + if isinstance(arg, exp): + return exp(re(arg.args[0])) + if isinstance(arg, AppliedUndef): + if arg.is_positive: + return arg + elif arg.is_negative: + return -arg + return + if arg.is_Add and arg.has(oo, S.NegativeInfinity): + if any(a.is_infinite for a in arg.as_real_imag()): + return oo + if arg.is_zero: + return S.Zero + if arg.is_extended_nonnegative: + return arg + if arg.is_extended_nonpositive: + return -arg + if arg.is_imaginary: + arg2 = -I * arg + if arg2.is_extended_nonnegative: + return arg2 + if arg.is_extended_real: + return + # reject result if all new conjugates are just wrappers around + # an expression that was already in the arg + conj = signsimp(arg.conjugate(), evaluate=False) + new_conj = conj.atoms(conjugate) - arg.atoms(conjugate) + if new_conj and all(arg.has(i.args[0]) for i in new_conj): + return + if arg != conj and arg != -conj: + ignore = arg.atoms(Abs) + abs_free_arg = arg.xreplace({i: Dummy(real=True) for i in ignore}) + unk = [a for a in abs_free_arg.free_symbols if a.is_extended_real is None] + if not unk or not all(conj.has(conjugate(u)) for u in unk): + return sqrt(expand_mul(arg*conj)) + + def _eval_is_real(self): + if self.args[0].is_finite: + return True + + def _eval_is_integer(self): + if self.args[0].is_extended_real: + return self.args[0].is_integer + + def _eval_is_extended_nonzero(self): + return fuzzy_not(self._args[0].is_zero) + + def _eval_is_zero(self): + return self._args[0].is_zero + + def _eval_is_extended_positive(self): + return fuzzy_not(self._args[0].is_zero) + + def _eval_is_rational(self): + if self.args[0].is_extended_real: + return self.args[0].is_rational + + def _eval_is_even(self): + if self.args[0].is_extended_real: + return self.args[0].is_even + + def _eval_is_odd(self): + if self.args[0].is_extended_real: + return self.args[0].is_odd + + def _eval_is_algebraic(self): + return self.args[0].is_algebraic + + def _eval_power(self, exponent): + if self.args[0].is_extended_real and exponent.is_integer: + if exponent.is_even: + return self.args[0]**exponent + elif exponent is not S.NegativeOne and exponent.is_Integer: + return self.args[0]**(exponent - 1)*self + return + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.functions.elementary.exponential import log + direction = self.args[0].leadterm(x)[0] + if direction.has(log(x)): + direction = direction.subs(log(x), logx) + s = self.args[0]._eval_nseries(x, n=n, logx=logx) + return (sign(direction)*s).expand() + + def _eval_derivative(self, x): + if self.args[0].is_extended_real or self.args[0].is_imaginary: + return Derivative(self.args[0], x, evaluate=True) \ + * sign(conjugate(self.args[0])) + rv = (re(self.args[0]) * Derivative(re(self.args[0]), x, + evaluate=True) + im(self.args[0]) * Derivative(im(self.args[0]), + x, evaluate=True)) / Abs(self.args[0]) + return rv.rewrite(sign) + + def _eval_rewrite_as_Heaviside(self, arg, **kwargs): + # Note this only holds for real arg (since Heaviside is not defined + # for complex arguments). + from sympy.functions.special.delta_functions import Heaviside + if arg.is_extended_real: + return arg*(Heaviside(arg) - Heaviside(-arg)) + + def _eval_rewrite_as_Piecewise(self, arg, **kwargs): + if arg.is_extended_real: + return Piecewise((arg, arg >= 0), (-arg, True)) + elif arg.is_imaginary: + return Piecewise((I*arg, I*arg >= 0), (-I*arg, True)) + + def _eval_rewrite_as_sign(self, arg, **kwargs): + return arg/sign(arg) + + def _eval_rewrite_as_conjugate(self, arg, **kwargs): + return sqrt(arg*conjugate(arg)) + + +class arg(Function): + r""" + Returns the argument (in radians) of a complex number. The argument is + evaluated in consistent convention with ``atan2`` where the branch-cut is + taken along the negative real axis and ``arg(z)`` is in the interval + $(-\pi,\pi]$. For a positive number, the argument is always 0; the + argument of a negative number is $\pi$; and the argument of 0 + is undefined and returns ``nan``. So the ``arg`` function will never nest + greater than 3 levels since at the 4th application, the result must be + nan; for a real number, nan is returned on the 3rd application. + + Examples + ======== + + >>> from sympy import arg, I, sqrt, Dummy + >>> from sympy.abc import x + >>> arg(2.0) + 0 + >>> arg(I) + pi/2 + >>> arg(sqrt(2) + I*sqrt(2)) + pi/4 + >>> arg(sqrt(3)/2 + I/2) + pi/6 + >>> arg(4 + 3*I) + atan(3/4) + >>> arg(0.8 + 0.6*I) + 0.643501108793284 + >>> arg(arg(arg(arg(x)))) + nan + >>> real = Dummy(real=True) + >>> arg(arg(arg(real))) + nan + + Parameters + ========== + + arg : Expr + Real or complex expression. + + Returns + ======= + + value : Expr + Returns arc tangent of arg measured in radians. + + """ + + is_extended_real = True + is_real = True + is_finite = True + _singularities = True # non-holomorphic + + @classmethod + def eval(cls, arg): + a = arg + for i in range(3): + if isinstance(a, cls): + a = a.args[0] + else: + if i == 2 and a.is_extended_real: + return S.NaN + break + else: + return S.NaN + from sympy.functions.elementary.exponential import exp, exp_polar + if isinstance(arg, exp_polar): + return periodic_argument(arg, oo) + elif isinstance(arg, exp): + i_ = im(arg.args[0]) + if i_.is_comparable: + i_ %= 2*S.Pi + if i_ > S.Pi: + i_ -= 2*S.Pi + return i_ + + if not arg.is_Atom: + c, arg_ = factor_terms(arg).as_coeff_Mul() + if arg_.is_Mul: + arg_ = Mul(*[a if (sign(a) not in (-1, 1)) else + sign(a) for a in arg_.args]) + arg_ = sign(c)*arg_ + else: + arg_ = arg + if any(i.is_extended_positive is None for i in arg_.atoms(AppliedUndef)): + return + from sympy.functions.elementary.trigonometric import atan2 + x, y = arg_.as_real_imag() + rv = atan2(y, x) + if rv.is_number: + return rv + if arg_ != arg: + return cls(arg_, evaluate=False) + + def _eval_derivative(self, t): + x, y = self.args[0].as_real_imag() + return (x * Derivative(y, t, evaluate=True) - y * + Derivative(x, t, evaluate=True)) / (x**2 + y**2) + + def _eval_rewrite_as_atan2(self, arg, **kwargs): + from sympy.functions.elementary.trigonometric import atan2 + x, y = self.args[0].as_real_imag() + return atan2(y, x) + + +class conjugate(Function): + """ + Returns the *complex conjugate* [1]_ of an argument. + In mathematics, the complex conjugate of a complex number + is given by changing the sign of the imaginary part. + + Thus, the conjugate of the complex number + :math:`a + ib` (where $a$ and $b$ are real numbers) is :math:`a - ib` + + Examples + ======== + + >>> from sympy import conjugate, I + >>> conjugate(2) + 2 + >>> conjugate(I) + -I + >>> conjugate(3 + 2*I) + 3 - 2*I + >>> conjugate(5 - I) + 5 + I + + Parameters + ========== + + arg : Expr + Real or complex expression. + + Returns + ======= + + arg : Expr + Complex conjugate of arg as real, imaginary or mixed expression. + + See Also + ======== + + sign, Abs + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Complex_conjugation + """ + _singularities = True # non-holomorphic + + @classmethod + def eval(cls, arg): + obj = arg._eval_conjugate() + if obj is not None: + return obj + + def inverse(self): + return conjugate + + def _eval_Abs(self): + return Abs(self.args[0], evaluate=True) + + def _eval_adjoint(self): + return transpose(self.args[0]) + + def _eval_conjugate(self): + return self.args[0] + + def _eval_derivative(self, x): + if x.is_real: + return conjugate(Derivative(self.args[0], x, evaluate=True)) + elif x.is_imaginary: + return -conjugate(Derivative(self.args[0], x, evaluate=True)) + + def _eval_transpose(self): + return adjoint(self.args[0]) + + def _eval_is_algebraic(self): + return self.args[0].is_algebraic + + +class transpose(Function): + """ + Linear map transposition. + + Examples + ======== + + >>> from sympy import transpose, Matrix, MatrixSymbol + >>> A = MatrixSymbol('A', 25, 9) + >>> transpose(A) + A.T + >>> B = MatrixSymbol('B', 9, 22) + >>> transpose(B) + B.T + >>> transpose(A*B) + B.T*A.T + >>> M = Matrix([[4, 5], [2, 1], [90, 12]]) + >>> M + Matrix([ + [ 4, 5], + [ 2, 1], + [90, 12]]) + >>> transpose(M) + Matrix([ + [4, 2, 90], + [5, 1, 12]]) + + Parameters + ========== + + arg : Matrix + Matrix or matrix expression to take the transpose of. + + Returns + ======= + + value : Matrix + Transpose of arg. + + """ + + @classmethod + def eval(cls, arg): + obj = arg._eval_transpose() + if obj is not None: + return obj + + def _eval_adjoint(self): + return conjugate(self.args[0]) + + def _eval_conjugate(self): + return adjoint(self.args[0]) + + def _eval_transpose(self): + return self.args[0] + + +class adjoint(Function): + """ + Conjugate transpose or Hermite conjugation. + + Examples + ======== + + >>> from sympy import adjoint, MatrixSymbol + >>> A = MatrixSymbol('A', 10, 5) + >>> adjoint(A) + Adjoint(A) + + Parameters + ========== + + arg : Matrix + Matrix or matrix expression to take the adjoint of. + + Returns + ======= + + value : Matrix + Represents the conjugate transpose or Hermite + conjugation of arg. + + """ + + @classmethod + def eval(cls, arg): + obj = arg._eval_adjoint() + if obj is not None: + return obj + obj = arg._eval_transpose() + if obj is not None: + return conjugate(obj) + + def _eval_adjoint(self): + return self.args[0] + + def _eval_conjugate(self): + return transpose(self.args[0]) + + def _eval_transpose(self): + return conjugate(self.args[0]) + + def _latex(self, printer, exp=None, *args): + arg = printer._print(self.args[0]) + tex = r'%s^{\dagger}' % arg + if exp: + tex = r'\left(%s\right)^{%s}' % (tex, exp) + return tex + + def _pretty(self, printer, *args): + from sympy.printing.pretty.stringpict import prettyForm + pform = printer._print(self.args[0], *args) + if printer._use_unicode: + pform = pform**prettyForm('\N{DAGGER}') + else: + pform = pform**prettyForm('+') + return pform + +############################################################################### +############### HANDLING OF POLAR NUMBERS ##################################### +############################################################################### + + +class polar_lift(Function): + """ + Lift argument to the Riemann surface of the logarithm, using the + standard branch. + + Examples + ======== + + >>> from sympy import Symbol, polar_lift, I + >>> p = Symbol('p', polar=True) + >>> x = Symbol('x') + >>> polar_lift(4) + 4*exp_polar(0) + >>> polar_lift(-4) + 4*exp_polar(I*pi) + >>> polar_lift(-I) + exp_polar(-I*pi/2) + >>> polar_lift(I + 2) + polar_lift(2 + I) + + >>> polar_lift(4*x) + 4*polar_lift(x) + >>> polar_lift(4*p) + 4*p + + Parameters + ========== + + arg : Expr + Real or complex expression. + + See Also + ======== + + sympy.functions.elementary.exponential.exp_polar + periodic_argument + """ + + is_polar = True + is_comparable = False # Cannot be evalf'd. + + @classmethod + def eval(cls, arg): + from sympy.functions.elementary.complexes import arg as argument + if arg.is_number: + ar = argument(arg) + # In general we want to affirm that something is known, + # e.g. `not ar.has(argument) and not ar.has(atan)` + # but for now we will just be more restrictive and + # see that it has evaluated to one of the known values. + if ar in (0, pi/2, -pi/2, pi): + from sympy.functions.elementary.exponential import exp_polar + return exp_polar(I*ar)*abs(arg) + + if arg.is_Mul: + args = arg.args + else: + args = [arg] + included = [] + excluded = [] + positive = [] + for arg in args: + if arg.is_polar: + included += [arg] + elif arg.is_positive: + positive += [arg] + else: + excluded += [arg] + if len(excluded) < len(args): + if excluded: + return Mul(*(included + positive))*polar_lift(Mul(*excluded)) + elif included: + return Mul(*(included + positive)) + else: + from sympy.functions.elementary.exponential import exp_polar + return Mul(*positive)*exp_polar(0) + + def _eval_evalf(self, prec): + """ Careful! any evalf of polar numbers is flaky """ + return self.args[0]._eval_evalf(prec) + + def _eval_Abs(self): + return Abs(self.args[0], evaluate=True) + + +class periodic_argument(Function): + r""" + Represent the argument on a quotient of the Riemann surface of the + logarithm. That is, given a period $P$, always return a value in + $(-P/2, P/2]$, by using $\exp(PI) = 1$. + + Examples + ======== + + >>> from sympy import exp_polar, periodic_argument + >>> from sympy import I, pi + >>> periodic_argument(exp_polar(10*I*pi), 2*pi) + 0 + >>> periodic_argument(exp_polar(5*I*pi), 4*pi) + pi + >>> from sympy import exp_polar, periodic_argument + >>> from sympy import I, pi + >>> periodic_argument(exp_polar(5*I*pi), 2*pi) + pi + >>> periodic_argument(exp_polar(5*I*pi), 3*pi) + -pi + >>> periodic_argument(exp_polar(5*I*pi), pi) + 0 + + Parameters + ========== + + ar : Expr + A polar number. + + period : Expr + The period $P$. + + See Also + ======== + + sympy.functions.elementary.exponential.exp_polar + polar_lift : Lift argument to the Riemann surface of the logarithm + principal_branch + """ + + @classmethod + def _getunbranched(cls, ar): + from sympy.functions.elementary.exponential import exp_polar, log + if ar.is_Mul: + args = ar.args + else: + args = [ar] + unbranched = 0 + for a in args: + if not a.is_polar: + unbranched += arg(a) + elif isinstance(a, exp_polar): + unbranched += a.exp.as_real_imag()[1] + elif a.is_Pow: + re, im = a.exp.as_real_imag() + unbranched += re*unbranched_argument( + a.base) + im*log(abs(a.base)) + elif isinstance(a, polar_lift): + unbranched += arg(a.args[0]) + else: + return None + return unbranched + + @classmethod + def eval(cls, ar, period): + # Our strategy is to evaluate the argument on the Riemann surface of the + # logarithm, and then reduce. + # NOTE evidently this means it is a rather bad idea to use this with + # period != 2*pi and non-polar numbers. + if not period.is_extended_positive: + return None + if period == oo and isinstance(ar, principal_branch): + return periodic_argument(*ar.args) + if isinstance(ar, polar_lift) and period >= 2*pi: + return periodic_argument(ar.args[0], period) + if ar.is_Mul: + newargs = [x for x in ar.args if not x.is_positive] + if len(newargs) != len(ar.args): + return periodic_argument(Mul(*newargs), period) + unbranched = cls._getunbranched(ar) + if unbranched is None: + return None + from sympy.functions.elementary.trigonometric import atan, atan2 + if unbranched.has(periodic_argument, atan2, atan): + return None + if period == oo: + return unbranched + if period != oo: + from sympy.functions.elementary.integers import ceiling + n = ceiling(unbranched/period - S.Half)*period + if not n.has(ceiling): + return unbranched - n + + def _eval_evalf(self, prec): + z, period = self.args + if period == oo: + unbranched = periodic_argument._getunbranched(z) + if unbranched is None: + return self + return unbranched._eval_evalf(prec) + ub = periodic_argument(z, oo)._eval_evalf(prec) + from sympy.functions.elementary.integers import ceiling + return (ub - ceiling(ub/period - S.Half)*period)._eval_evalf(prec) + + +def unbranched_argument(arg): + ''' + Returns periodic argument of arg with period as infinity. + + Examples + ======== + + >>> from sympy import exp_polar, unbranched_argument + >>> from sympy import I, pi + >>> unbranched_argument(exp_polar(15*I*pi)) + 15*pi + >>> unbranched_argument(exp_polar(7*I*pi)) + 7*pi + + See also + ======== + + periodic_argument + ''' + return periodic_argument(arg, oo) + + +class principal_branch(Function): + """ + Represent a polar number reduced to its principal branch on a quotient + of the Riemann surface of the logarithm. + + Explanation + =========== + + This is a function of two arguments. The first argument is a polar + number `z`, and the second one a positive real number or infinity, `p`. + The result is ``z mod exp_polar(I*p)``. + + Examples + ======== + + >>> from sympy import exp_polar, principal_branch, oo, I, pi + >>> from sympy.abc import z + >>> principal_branch(z, oo) + z + >>> principal_branch(exp_polar(2*pi*I)*3, 2*pi) + 3*exp_polar(0) + >>> principal_branch(exp_polar(2*pi*I)*3*z, 2*pi) + 3*principal_branch(z, 2*pi) + + Parameters + ========== + + x : Expr + A polar number. + + period : Expr + Positive real number or infinity. + + See Also + ======== + + sympy.functions.elementary.exponential.exp_polar + polar_lift : Lift argument to the Riemann surface of the logarithm + periodic_argument + """ + + is_polar = True + is_comparable = False # cannot always be evalf'd + + @classmethod + def eval(self, x, period): + from sympy.functions.elementary.exponential import exp_polar + if isinstance(x, polar_lift): + return principal_branch(x.args[0], period) + if period == oo: + return x + ub = periodic_argument(x, oo) + barg = periodic_argument(x, period) + if ub != barg and not ub.has(periodic_argument) \ + and not barg.has(periodic_argument): + pl = polar_lift(x) + + def mr(expr): + if not isinstance(expr, Symbol): + return polar_lift(expr) + return expr + pl = pl.replace(polar_lift, mr) + # Recompute unbranched argument + ub = periodic_argument(pl, oo) + if not pl.has(polar_lift): + if ub != barg: + res = exp_polar(I*(barg - ub))*pl + else: + res = pl + if not res.is_polar and not res.has(exp_polar): + res *= exp_polar(0) + return res + + if not x.free_symbols: + c, m = x, () + else: + c, m = x.as_coeff_mul(*x.free_symbols) + others = [] + for y in m: + if y.is_positive: + c *= y + else: + others += [y] + m = tuple(others) + arg = periodic_argument(c, period) + if arg.has(periodic_argument): + return None + if arg.is_number and (unbranched_argument(c) != arg or + (arg == 0 and m != () and c != 1)): + if arg == 0: + return abs(c)*principal_branch(Mul(*m), period) + return principal_branch(exp_polar(I*arg)*Mul(*m), period)*abs(c) + if arg.is_number and ((abs(arg) < period/2) == True or arg == period/2) \ + and m == (): + return exp_polar(arg*I)*abs(c) + + def _eval_evalf(self, prec): + z, period = self.args + p = periodic_argument(z, period)._eval_evalf(prec) + if abs(p) > pi or p == -pi: + return self # Cannot evalf for this argument. + from sympy.functions.elementary.exponential import exp + return (abs(z)*exp(I*p))._eval_evalf(prec) + + +def _polarify(eq, lift, pause=False): + from sympy.integrals.integrals import Integral + if eq.is_polar: + return eq + if eq.is_number and not pause: + return polar_lift(eq) + if isinstance(eq, Symbol) and not pause and lift: + return polar_lift(eq) + elif eq.is_Atom: + return eq + elif eq.is_Add: + r = eq.func(*[_polarify(arg, lift, pause=True) for arg in eq.args]) + if lift: + return polar_lift(r) + return r + elif eq.is_Pow and eq.base == S.Exp1: + return eq.func(S.Exp1, _polarify(eq.exp, lift, pause=False)) + elif eq.is_Function: + return eq.func(*[_polarify(arg, lift, pause=False) for arg in eq.args]) + elif isinstance(eq, Integral): + # Don't lift the integration variable + func = _polarify(eq.function, lift, pause=pause) + limits = [] + for limit in eq.args[1:]: + var = _polarify(limit[0], lift=False, pause=pause) + rest = _polarify(limit[1:], lift=lift, pause=pause) + limits.append((var,) + rest) + return Integral(*((func,) + tuple(limits))) + else: + return eq.func(*[_polarify(arg, lift, pause=pause) + if isinstance(arg, Expr) else arg for arg in eq.args]) + + +def polarify(eq, subs=True, lift=False): + """ + Turn all numbers in eq into their polar equivalents (under the standard + choice of argument). + + Note that no attempt is made to guess a formal convention of adding + polar numbers, expressions like $1 + x$ will generally not be altered. + + Note also that this function does not promote ``exp(x)`` to ``exp_polar(x)``. + + If ``subs`` is ``True``, all symbols which are not already polar will be + substituted for polar dummies; in this case the function behaves much + like :func:`~.posify`. + + If ``lift`` is ``True``, both addition statements and non-polar symbols are + changed to their ``polar_lift()``ed versions. + Note that ``lift=True`` implies ``subs=False``. + + Examples + ======== + + >>> from sympy import polarify, sin, I + >>> from sympy.abc import x, y + >>> expr = (-x)**y + >>> expr.expand() + (-x)**y + >>> polarify(expr) + ((_x*exp_polar(I*pi))**_y, {_x: x, _y: y}) + >>> polarify(expr)[0].expand() + _x**_y*exp_polar(_y*I*pi) + >>> polarify(x, lift=True) + polar_lift(x) + >>> polarify(x*(1+y), lift=True) + polar_lift(x)*polar_lift(y + 1) + + Adds are treated carefully: + + >>> polarify(1 + sin((1 + I)*x)) + (sin(_x*polar_lift(1 + I)) + 1, {_x: x}) + """ + if lift: + subs = False + eq = _polarify(sympify(eq), lift) + if not subs: + return eq + reps = {s: Dummy(s.name, polar=True) for s in eq.free_symbols} + eq = eq.subs(reps) + return eq, {r: s for s, r in reps.items()} + + +def _unpolarify(eq, exponents_only, pause=False): + if not isinstance(eq, Basic) or eq.is_Atom: + return eq + + if not pause: + from sympy.functions.elementary.exponential import exp, exp_polar + if isinstance(eq, exp_polar): + return exp(_unpolarify(eq.exp, exponents_only)) + if isinstance(eq, principal_branch) and eq.args[1] == 2*pi: + return _unpolarify(eq.args[0], exponents_only) + if ( + eq.is_Add or eq.is_Mul or eq.is_Boolean or + eq.is_Relational and ( + eq.rel_op in ('==', '!=') and 0 in eq.args or + eq.rel_op not in ('==', '!=')) + ): + return eq.func(*[_unpolarify(x, exponents_only) for x in eq.args]) + if isinstance(eq, polar_lift): + return _unpolarify(eq.args[0], exponents_only) + + if eq.is_Pow: + expo = _unpolarify(eq.exp, exponents_only) + base = _unpolarify(eq.base, exponents_only, + not (expo.is_integer and not pause)) + return base**expo + + if eq.is_Function and getattr(eq.func, 'unbranched', False): + return eq.func(*[_unpolarify(x, exponents_only, exponents_only) + for x in eq.args]) + + return eq.func(*[_unpolarify(x, exponents_only, True) for x in eq.args]) + + +def unpolarify(eq, subs=None, exponents_only=False): + """ + If `p` denotes the projection from the Riemann surface of the logarithm to + the complex line, return a simplified version `eq'` of `eq` such that + `p(eq') = p(eq)`. + Also apply the substitution subs in the end. (This is a convenience, since + ``unpolarify``, in a certain sense, undoes :func:`polarify`.) + + Examples + ======== + + >>> from sympy import unpolarify, polar_lift, sin, I + >>> unpolarify(polar_lift(I + 2)) + 2 + I + >>> unpolarify(sin(polar_lift(I + 7))) + sin(7 + I) + """ + if isinstance(eq, bool): + return eq + + eq = sympify(eq) + if subs is not None: + return unpolarify(eq.subs(subs)) + changed = True + pause = False + if exponents_only: + pause = True + while changed: + changed = False + res = _unpolarify(eq, exponents_only, pause) + if res != eq: + changed = True + eq = res + if isinstance(res, bool): + return res + # Finally, replacing Exp(0) by 1 is always correct. + # So is polar_lift(0) -> 0. + from sympy.functions.elementary.exponential import exp_polar + return res.subs({exp_polar(0): 1, polar_lift(0): 0}) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/exponential.py b/lib/python3.11/site-packages/sympy/functions/elementary/exponential.py new file mode 100644 index 0000000000000000000000000000000000000000..3f4f462150e62d24f5145900f3a1e7143b285005 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/exponential.py @@ -0,0 +1,1306 @@ +from itertools import product +from typing import Tuple as tTuple + +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.expr import Expr +from sympy.core.function import (Function, ArgumentIndexError, expand_log, + expand_mul, FunctionClass, PoleError, expand_multinomial, expand_complex) +from sympy.core.logic import fuzzy_and, fuzzy_not, fuzzy_or +from sympy.core.mul import Mul +from sympy.core.numbers import Integer, Rational, pi, I +from sympy.core.parameters import global_parameters +from sympy.core.power import Pow +from sympy.core.relational import Ge +from sympy.core.singleton import S +from sympy.core.symbol import Wild, Dummy +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import arg, unpolarify, im, re, Abs +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.ntheory import multiplicity, perfect_power +from sympy.ntheory.factor_ import factorint + +# NOTE IMPORTANT +# The series expansion code in this file is an important part of the gruntz +# algorithm for determining limits. _eval_nseries has to return a generalized +# power series with coefficients in C(log(x), log). +# In more detail, the result of _eval_nseries(self, x, n) must be +# c_0*x**e_0 + ... (finitely many terms) +# where e_i are numbers (not necessarily integers) and c_i involve only +# numbers, the function log, and log(x). [This also means it must not contain +# log(x(1+p)), this *has* to be expanded to log(x)+log(1+p) if x.is_positive and +# p.is_positive.] + + +class ExpBase(Function): + + unbranched = True + _singularities = (S.ComplexInfinity,) + + @property + def kind(self): + return self.exp.kind + + def inverse(self, argindex=1): + """ + Returns the inverse function of ``exp(x)``. + """ + return log + + def as_numer_denom(self): + """ + Returns this with a positive exponent as a 2-tuple (a fraction). + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.abc import x + >>> exp(-x).as_numer_denom() + (1, exp(x)) + >>> exp(x).as_numer_denom() + (exp(x), 1) + """ + # this should be the same as Pow.as_numer_denom wrt + # exponent handling + if not self.is_commutative: + return self, S.One + exp = self.exp + neg_exp = exp.is_negative + if not neg_exp and not (-exp).is_negative: + neg_exp = exp.could_extract_minus_sign() + if neg_exp: + return S.One, self.func(-exp) + return self, S.One + + @property + def exp(self): + """ + Returns the exponent of the function. + """ + return self.args[0] + + def as_base_exp(self): + """ + Returns the 2-tuple (base, exponent). + """ + return self.func(1), Mul(*self.args) + + def _eval_adjoint(self): + return self.func(self.exp.adjoint()) + + def _eval_conjugate(self): + return self.func(self.exp.conjugate()) + + def _eval_transpose(self): + return self.func(self.exp.transpose()) + + def _eval_is_finite(self): + arg = self.exp + if arg.is_infinite: + if arg.is_extended_negative: + return True + if arg.is_extended_positive: + return False + if arg.is_finite: + return True + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + z = s.exp.is_zero + if z: + return True + elif s.exp.is_rational and fuzzy_not(z): + return False + else: + return s.is_rational + + def _eval_is_zero(self): + return self.exp is S.NegativeInfinity + + def _eval_power(self, other): + """exp(arg)**e -> exp(arg*e) if assumptions allow it. + """ + b, e = self.as_base_exp() + return Pow._eval_power(Pow(b, e, evaluate=False), other) + + def _eval_expand_power_exp(self, **hints): + from sympy.concrete.products import Product + from sympy.concrete.summations import Sum + arg = self.args[0] + if arg.is_Add and arg.is_commutative: + return Mul.fromiter(self.func(x) for x in arg.args) + elif isinstance(arg, Sum) and arg.is_commutative: + return Product(self.func(arg.function), *arg.limits) + return self.func(arg) + + +class exp_polar(ExpBase): + r""" + Represent a *polar number* (see g-function Sphinx documentation). + + Explanation + =========== + + ``exp_polar`` represents the function + `Exp: \mathbb{C} \rightarrow \mathcal{S}`, sending the complex number + `z = a + bi` to the polar number `r = exp(a), \theta = b`. It is one of + the main functions to construct polar numbers. + + Examples + ======== + + >>> from sympy import exp_polar, pi, I, exp + + The main difference is that polar numbers do not "wrap around" at `2 \pi`: + + >>> exp(2*pi*I) + 1 + >>> exp_polar(2*pi*I) + exp_polar(2*I*pi) + + apart from that they behave mostly like classical complex numbers: + + >>> exp_polar(2)*exp_polar(3) + exp_polar(5) + + See Also + ======== + + sympy.simplify.powsimp.powsimp + polar_lift + periodic_argument + principal_branch + """ + + is_polar = True + is_comparable = False # cannot be evalf'd + + def _eval_Abs(self): # Abs is never a polar number + return exp(re(self.args[0])) + + def _eval_evalf(self, prec): + """ Careful! any evalf of polar numbers is flaky """ + i = im(self.args[0]) + try: + bad = (i <= -pi or i > pi) + except TypeError: + bad = True + if bad: + return self # cannot evalf for this argument + res = exp(self.args[0])._eval_evalf(prec) + if i > 0 and im(res) < 0: + # i ~ pi, but exp(I*i) evaluated to argument slightly bigger than pi + return re(res) + return res + + def _eval_power(self, other): + return self.func(self.args[0]*other) + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + + def as_base_exp(self): + # XXX exp_polar(0) is special! + if self.args[0] == 0: + return self, S.One + return ExpBase.as_base_exp(self) + + +class ExpMeta(FunctionClass): + def __instancecheck__(cls, instance): + if exp in instance.__class__.__mro__: + return True + return isinstance(instance, Pow) and instance.base is S.Exp1 + + +class exp(ExpBase, metaclass=ExpMeta): + """ + The exponential function, :math:`e^x`. + + Examples + ======== + + >>> from sympy import exp, I, pi + >>> from sympy.abc import x + >>> exp(x) + exp(x) + >>> exp(x).diff(x) + exp(x) + >>> exp(I*pi) + -1 + + Parameters + ========== + + arg : Expr + + See Also + ======== + + log + """ + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return self + else: + raise ArgumentIndexError(self, argindex) + + def _eval_refine(self, assumptions): + from sympy.assumptions import ask, Q + arg = self.args[0] + if arg.is_Mul: + Ioo = I*S.Infinity + if arg in [Ioo, -Ioo]: + return S.NaN + + coeff = arg.as_coefficient(pi*I) + if coeff: + if ask(Q.integer(2*coeff)): + if ask(Q.even(coeff)): + return S.One + elif ask(Q.odd(coeff)): + return S.NegativeOne + elif ask(Q.even(coeff + S.Half)): + return -I + elif ask(Q.odd(coeff + S.Half)): + return I + + @classmethod + def eval(cls, arg): + from sympy.calculus import AccumBounds + from sympy.matrices.matrixbase import MatrixBase + from sympy.sets.setexpr import SetExpr + from sympy.simplify.simplify import logcombine + if isinstance(arg, MatrixBase): + return arg.exp() + elif global_parameters.exp_is_pow: + return Pow(S.Exp1, arg) + elif arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg.is_zero: + return S.One + elif arg is S.One: + return S.Exp1 + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Zero + elif arg is S.ComplexInfinity: + return S.NaN + elif isinstance(arg, log): + return arg.args[0] + elif isinstance(arg, AccumBounds): + return AccumBounds(exp(arg.min), exp(arg.max)) + elif isinstance(arg, SetExpr): + return arg._eval_func(cls) + elif arg.is_Mul: + coeff = arg.as_coefficient(pi*I) + if coeff: + if (2*coeff).is_integer: + if coeff.is_even: + return S.One + elif coeff.is_odd: + return S.NegativeOne + elif (coeff + S.Half).is_even: + return -I + elif (coeff + S.Half).is_odd: + return I + elif coeff.is_Rational: + ncoeff = coeff % 2 # restrict to [0, 2pi) + if ncoeff > 1: # restrict to (-pi, pi] + ncoeff -= 2 + if ncoeff != coeff: + return cls(ncoeff*pi*I) + + # Warning: code in risch.py will be very sensitive to changes + # in this (see DifferentialExtension). + + # look for a single log factor + + coeff, terms = arg.as_coeff_Mul() + + # but it can't be multiplied by oo + if coeff in [S.NegativeInfinity, S.Infinity]: + if terms.is_number: + if coeff is S.NegativeInfinity: + terms = -terms + if re(terms).is_zero and terms is not S.Zero: + return S.NaN + if re(terms).is_positive and im(terms) is not S.Zero: + return S.ComplexInfinity + if re(terms).is_negative: + return S.Zero + return None + + coeffs, log_term = [coeff], None + for term in Mul.make_args(terms): + term_ = logcombine(term) + if isinstance(term_, log): + if log_term is None: + log_term = term_.args[0] + else: + return None + elif term.is_comparable: + coeffs.append(term) + else: + return None + + return log_term**Mul(*coeffs) if log_term else None + + elif arg.is_Add: + out = [] + add = [] + argchanged = False + for a in arg.args: + if a is S.One: + add.append(a) + continue + newa = cls(a) + if isinstance(newa, cls): + if newa.args[0] != a: + add.append(newa.args[0]) + argchanged = True + else: + add.append(a) + else: + out.append(newa) + if out or argchanged: + return Mul(*out)*cls(Add(*add), evaluate=False) + + if arg.is_zero: + return S.One + + @property + def base(self): + """ + Returns the base of the exponential function. + """ + return S.Exp1 + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + """ + Calculates the next term in the Taylor series expansion. + """ + if n < 0: + return S.Zero + if n == 0: + return S.One + x = sympify(x) + if previous_terms: + p = previous_terms[-1] + if p is not None: + return p * x / n + return x**n/factorial(n) + + def as_real_imag(self, deep=True, **hints): + """ + Returns this function as a 2-tuple representing a complex number. + + Examples + ======== + + >>> from sympy import exp, I + >>> from sympy.abc import x + >>> exp(x).as_real_imag() + (exp(re(x))*cos(im(x)), exp(re(x))*sin(im(x))) + >>> exp(1).as_real_imag() + (E, 0) + >>> exp(I).as_real_imag() + (cos(1), sin(1)) + >>> exp(1+I).as_real_imag() + (E*cos(1), E*sin(1)) + + See Also + ======== + + sympy.functions.elementary.complexes.re + sympy.functions.elementary.complexes.im + """ + from sympy.functions.elementary.trigonometric import cos, sin + re, im = self.args[0].as_real_imag() + if deep: + re = re.expand(deep, **hints) + im = im.expand(deep, **hints) + cos, sin = cos(im), sin(im) + return (exp(re)*cos, exp(re)*sin) + + def _eval_subs(self, old, new): + # keep processing of power-like args centralized in Pow + if old.is_Pow: # handle (exp(3*log(x))).subs(x**2, z) -> z**(3/2) + old = exp(old.exp*log(old.base)) + elif old is S.Exp1 and new.is_Function: + old = exp + if isinstance(old, exp) or old is S.Exp1: + f = lambda a: Pow(*a.as_base_exp(), evaluate=False) if ( + a.is_Pow or isinstance(a, exp)) else a + return Pow._eval_subs(f(self), f(old), new) + + if old is exp and not new.is_Function: + return new**self.exp._subs(old, new) + return Function._eval_subs(self, old, new) + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + elif self.args[0].is_imaginary: + arg2 = -S(2) * I * self.args[0] / pi + return arg2.is_even + + def _eval_is_complex(self): + def complex_extended_negative(arg): + yield arg.is_complex + yield arg.is_extended_negative + return fuzzy_or(complex_extended_negative(self.args[0])) + + def _eval_is_algebraic(self): + if (self.exp / pi / I).is_rational: + return True + if fuzzy_not(self.exp.is_zero): + if self.exp.is_algebraic: + return False + elif (self.exp / pi).is_rational: + return False + + def _eval_is_extended_positive(self): + if self.exp.is_extended_real: + return self.args[0] is not S.NegativeInfinity + elif self.exp.is_imaginary: + arg2 = -I * self.args[0] / pi + return arg2.is_even + + def _eval_nseries(self, x, n, logx, cdir=0): + # NOTE Please see the comment at the beginning of this file, labelled + # IMPORTANT. + from sympy.functions.elementary.complexes import sign + from sympy.functions.elementary.integers import ceiling + from sympy.series.limits import limit + from sympy.series.order import Order + from sympy.simplify.powsimp import powsimp + arg = self.exp + arg_series = arg._eval_nseries(x, n=n, logx=logx) + if arg_series.is_Order: + return 1 + arg_series + arg0 = limit(arg_series.removeO(), x, 0) + if arg0 is S.NegativeInfinity: + return Order(x**n, x) + if arg0 is S.Infinity: + return self + if arg0.is_infinite: + raise PoleError("Cannot expand %s around 0" % (self)) + # checking for indecisiveness/ sign terms in arg0 + if any(isinstance(arg, sign) for arg in arg0.args): + return self + t = Dummy("t") + nterms = n + try: + cf = Order(arg.as_leading_term(x, logx=logx), x).getn() + except (NotImplementedError, PoleError): + cf = 0 + if cf and cf > 0: + nterms = ceiling(n/cf) + exp_series = exp(t)._taylor(t, nterms) + r = exp(arg0)*exp_series.subs(t, arg_series - arg0) + rep = {logx: log(x)} if logx is not None else {} + if r.subs(rep) == self: + return r + if cf and cf > 1: + r += Order((arg_series - arg0)**n, x)/x**((cf-1)*n) + else: + r += Order((arg_series - arg0)**n, x) + r = r.expand() + r = powsimp(r, deep=True, combine='exp') + # powsimp may introduce unexpanded (-1)**Rational; see PR #17201 + simplerat = lambda x: x.is_Rational and x.q in [3, 4, 6] + w = Wild('w', properties=[simplerat]) + r = r.replace(S.NegativeOne**w, expand_complex(S.NegativeOne**w)) + return r + + def _taylor(self, x, n): + l = [] + g = None + for i in range(n): + g = self.taylor_term(i, self.args[0], g) + g = g.nseries(x, n=n) + l.append(g.removeO()) + return Add(*l) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.util import AccumBounds + arg = self.args[0].cancel().as_leading_term(x, logx=logx) + arg0 = arg.subs(x, 0) + if arg is S.NaN: + return S.NaN + if isinstance(arg0, AccumBounds): + # This check addresses a corner case involving AccumBounds. + # if isinstance(arg, AccumBounds) is True, then arg0 can either be 0, + # AccumBounds(-oo, 0) or AccumBounds(-oo, oo). + # Check out function: test_issue_18473() in test_exponential.py and + # test_limits.py for more information. + if re(cdir) < S.Zero: + return exp(-arg0) + return exp(arg0) + if arg0 is S.NaN: + arg0 = arg.limit(x, 0) + if arg0.is_infinite is False: + return exp(arg0) + raise PoleError("Cannot expand %s around 0" % (self)) + + def _eval_rewrite_as_sin(self, arg, **kwargs): + from sympy.functions.elementary.trigonometric import sin + return sin(I*arg + pi/2) - I*sin(I*arg) + + def _eval_rewrite_as_cos(self, arg, **kwargs): + from sympy.functions.elementary.trigonometric import cos + return cos(I*arg) + I*cos(I*arg + pi/2) + + def _eval_rewrite_as_tanh(self, arg, **kwargs): + from sympy.functions.elementary.hyperbolic import tanh + return (1 + tanh(arg/2))/(1 - tanh(arg/2)) + + def _eval_rewrite_as_sqrt(self, arg, **kwargs): + from sympy.functions.elementary.trigonometric import sin, cos + if arg.is_Mul: + coeff = arg.coeff(pi*I) + if coeff and coeff.is_number: + cosine, sine = cos(pi*coeff), sin(pi*coeff) + if not isinstance(cosine, cos) and not isinstance (sine, sin): + return cosine + I*sine + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + if arg.is_Mul: + logs = [a for a in arg.args if isinstance(a, log) and len(a.args) == 1] + if logs: + return Pow(logs[0].args[0], arg.coeff(logs[0])) + + +def match_real_imag(expr): + r""" + Try to match expr with $a + Ib$ for real $a$ and $b$. + + ``match_real_imag`` returns a tuple containing the real and imaginary + parts of expr or ``(None, None)`` if direct matching is not possible. Contrary + to :func:`~.re()`, :func:`~.im()``, and ``as_real_imag()``, this helper will not force things + by returning expressions themselves containing ``re()`` or ``im()`` and it + does not expand its argument either. + + """ + r_, i_ = expr.as_independent(I, as_Add=True) + if i_ == 0 and r_.is_real: + return (r_, i_) + i_ = i_.as_coefficient(I) + if i_ and i_.is_real and r_.is_real: + return (r_, i_) + else: + return (None, None) # simpler to check for than None + + +class log(Function): + r""" + The natural logarithm function `\ln(x)` or `\log(x)`. + + Explanation + =========== + + Logarithms are taken with the natural base, `e`. To get + a logarithm of a different base ``b``, use ``log(x, b)``, + which is essentially short-hand for ``log(x)/log(b)``. + + ``log`` represents the principal branch of the natural + logarithm. As such it has a branch cut along the negative + real axis and returns values having a complex argument in + `(-\pi, \pi]`. + + Examples + ======== + + >>> from sympy import log, sqrt, S, I + >>> log(8, 2) + 3 + >>> log(S(8)/3, 2) + -log(3)/log(2) + 3 + >>> log(-1 + I*sqrt(3)) + log(2) + 2*I*pi/3 + + See Also + ======== + + exp + + """ + + args: tTuple[Expr] + + _singularities = (S.Zero, S.ComplexInfinity) + + def fdiff(self, argindex=1): + """ + Returns the first derivative of the function. + """ + if argindex == 1: + return 1/self.args[0] + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + r""" + Returns `e^x`, the inverse function of `\log(x)`. + """ + return exp + + @classmethod + def eval(cls, arg, base=None): + from sympy.calculus import AccumBounds + from sympy.sets.setexpr import SetExpr + + arg = sympify(arg) + + if base is not None: + base = sympify(base) + if base == 1: + if arg == 1: + return S.NaN + else: + return S.ComplexInfinity + try: + # handle extraction of powers of the base now + # or else expand_log in Mul would have to handle this + n = multiplicity(base, arg) + if n: + return n + log(arg / base**n) / log(base) + else: + return log(arg)/log(base) + except ValueError: + pass + if base is not S.Exp1: + return cls(arg)/cls(base) + else: + return cls(arg) + + if arg.is_Number: + if arg.is_zero: + return S.ComplexInfinity + elif arg is S.One: + return S.Zero + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Infinity + elif arg is S.NaN: + return S.NaN + elif arg.is_Rational and arg.p == 1: + return -cls(arg.q) + + if arg.is_Pow and arg.base is S.Exp1 and arg.exp.is_extended_real: + return arg.exp + if isinstance(arg, exp) and arg.exp.is_extended_real: + return arg.exp + elif isinstance(arg, exp) and arg.exp.is_number: + r_, i_ = match_real_imag(arg.exp) + if i_ and i_.is_comparable: + i_ %= 2*pi + if i_ > pi: + i_ -= 2*pi + return r_ + expand_mul(i_ * I, deep=False) + elif isinstance(arg, exp_polar): + return unpolarify(arg.exp) + elif isinstance(arg, AccumBounds): + if arg.min.is_positive: + return AccumBounds(log(arg.min), log(arg.max)) + elif arg.min.is_zero: + return AccumBounds(S.NegativeInfinity, log(arg.max)) + else: + return S.NaN + elif isinstance(arg, SetExpr): + return arg._eval_func(cls) + + if arg.is_number: + if arg.is_negative: + return pi * I + cls(-arg) + elif arg is S.ComplexInfinity: + return S.ComplexInfinity + elif arg is S.Exp1: + return S.One + + if arg.is_zero: + return S.ComplexInfinity + + # don't autoexpand Pow or Mul (see the issue 3351): + if not arg.is_Add: + coeff = arg.as_coefficient(I) + + if coeff is not None: + if coeff is S.Infinity: + return S.Infinity + elif coeff is S.NegativeInfinity: + return S.Infinity + elif coeff.is_Rational: + if coeff.is_nonnegative: + return pi * I * S.Half + cls(coeff) + else: + return -pi * I * S.Half + cls(-coeff) + + if arg.is_number and arg.is_algebraic: + # Match arg = coeff*(r_ + i_*I) with coeff>0, r_ and i_ real. + coeff, arg_ = arg.as_independent(I, as_Add=False) + if coeff.is_negative: + coeff *= -1 + arg_ *= -1 + arg_ = expand_mul(arg_, deep=False) + r_, i_ = arg_.as_independent(I, as_Add=True) + i_ = i_.as_coefficient(I) + if coeff.is_real and i_ and i_.is_real and r_.is_real: + if r_.is_zero: + if i_.is_positive: + return pi * I * S.Half + cls(coeff * i_) + elif i_.is_negative: + return -pi * I * S.Half + cls(coeff * -i_) + else: + from sympy.simplify import ratsimp + # Check for arguments involving rational multiples of pi + t = (i_/r_).cancel() + t1 = (-t).cancel() + atan_table = _log_atan_table() + if t in atan_table: + modulus = ratsimp(coeff * Abs(arg_)) + if r_.is_positive: + return cls(modulus) + I * atan_table[t] + else: + return cls(modulus) + I * (atan_table[t] - pi) + elif t1 in atan_table: + modulus = ratsimp(coeff * Abs(arg_)) + if r_.is_positive: + return cls(modulus) + I * (-atan_table[t1]) + else: + return cls(modulus) + I * (pi - atan_table[t1]) + + def as_base_exp(self): + """ + Returns this function in the form (base, exponent). + """ + return self, S.One + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): # of log(1+x) + r""" + Returns the next term in the Taylor series expansion of `\log(1+x)`. + """ + from sympy.simplify.powsimp import powsimp + if n < 0: + return S.Zero + x = sympify(x) + if n == 0: + return x + if previous_terms: + p = previous_terms[-1] + if p is not None: + return powsimp((-n) * p * x / (n + 1), deep=True, combine='exp') + return (1 - 2*(n % 2)) * x**(n + 1)/(n + 1) + + def _eval_expand_log(self, deep=True, **hints): + from sympy.concrete import Sum, Product + force = hints.get('force', False) + factor = hints.get('factor', False) + if (len(self.args) == 2): + return expand_log(self.func(*self.args), deep=deep, force=force) + arg = self.args[0] + if arg.is_Integer: + # remove perfect powers + p = perfect_power(arg) + logarg = None + coeff = 1 + if p is not False: + arg, coeff = p + logarg = self.func(arg) + # expand as product of its prime factors if factor=True + if factor: + p = factorint(arg) + if arg not in p.keys(): + logarg = sum(n*log(val) for val, n in p.items()) + if logarg is not None: + return coeff*logarg + elif arg.is_Rational: + return log(arg.p) - log(arg.q) + elif arg.is_Mul: + expr = [] + nonpos = [] + for x in arg.args: + if force or x.is_positive or x.is_polar: + a = self.func(x) + if isinstance(a, log): + expr.append(self.func(x)._eval_expand_log(**hints)) + else: + expr.append(a) + elif x.is_negative: + a = self.func(-x) + expr.append(a) + nonpos.append(S.NegativeOne) + else: + nonpos.append(x) + return Add(*expr) + log(Mul(*nonpos)) + elif arg.is_Pow or isinstance(arg, exp): + if force or (arg.exp.is_extended_real and (arg.base.is_positive or ((arg.exp+1) + .is_positive and (arg.exp-1).is_nonpositive))) or arg.base.is_polar: + b = arg.base + e = arg.exp + a = self.func(b) + if isinstance(a, log): + return unpolarify(e) * a._eval_expand_log(**hints) + else: + return unpolarify(e) * a + elif isinstance(arg, Product): + if force or arg.function.is_positive: + return Sum(log(arg.function), *arg.limits) + + return self.func(arg) + + def _eval_simplify(self, **kwargs): + from sympy.simplify.simplify import expand_log, simplify, inversecombine + if len(self.args) == 2: # it's unevaluated + return simplify(self.func(*self.args), **kwargs) + + expr = self.func(simplify(self.args[0], **kwargs)) + if kwargs['inverse']: + expr = inversecombine(expr) + expr = expand_log(expr, deep=True) + return min([expr, self], key=kwargs['measure']) + + def as_real_imag(self, deep=True, **hints): + """ + Returns this function as a complex coordinate. + + Examples + ======== + + >>> from sympy import I, log + >>> from sympy.abc import x + >>> log(x).as_real_imag() + (log(Abs(x)), arg(x)) + >>> log(I).as_real_imag() + (0, pi/2) + >>> log(1 + I).as_real_imag() + (log(sqrt(2)), pi/4) + >>> log(I*x).as_real_imag() + (log(Abs(x)), arg(I*x)) + + """ + sarg = self.args[0] + if deep: + sarg = self.args[0].expand(deep, **hints) + sarg_abs = Abs(sarg) + if sarg_abs == sarg: + return self, S.Zero + sarg_arg = arg(sarg) + if hints.get('log', False): # Expand the log + hints['complex'] = False + return (log(sarg_abs).expand(deep, **hints), sarg_arg) + else: + return log(sarg_abs), sarg_arg + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if (self.args[0] - 1).is_zero: + return True + if s.args[0].is_rational and fuzzy_not((self.args[0] - 1).is_zero): + return False + else: + return s.is_rational + + def _eval_is_algebraic(self): + s = self.func(*self.args) + if s.func == self.func: + if (self.args[0] - 1).is_zero: + return True + elif fuzzy_not((self.args[0] - 1).is_zero): + if self.args[0].is_algebraic: + return False + else: + return s.is_algebraic + + def _eval_is_extended_real(self): + return self.args[0].is_extended_positive + + def _eval_is_complex(self): + z = self.args[0] + return fuzzy_and([z.is_complex, fuzzy_not(z.is_zero)]) + + def _eval_is_finite(self): + arg = self.args[0] + if arg.is_zero: + return False + return arg.is_finite + + def _eval_is_extended_positive(self): + return (self.args[0] - 1).is_extended_positive + + def _eval_is_zero(self): + return (self.args[0] - 1).is_zero + + def _eval_is_extended_nonnegative(self): + return (self.args[0] - 1).is_extended_nonnegative + + def _eval_nseries(self, x, n, logx, cdir=0): + # NOTE Please see the comment at the beginning of this file, labelled + # IMPORTANT. + from sympy.series.order import Order + from sympy.simplify.simplify import logcombine + from sympy.core.symbol import Dummy + + if self.args[0] == x: + return log(x) if logx is None else logx + arg = self.args[0] + t = Dummy('t', positive=True) + if cdir == 0: + cdir = 1 + z = arg.subs(x, cdir*t) + + k, l = Wild("k"), Wild("l") + r = z.match(k*t**l) + if r is not None: + k, l = r[k], r[l] + if l != 0 and not l.has(t) and not k.has(t): + r = l*log(x) if logx is None else l*logx + r += log(k) - l*log(cdir) # XXX true regardless of assumptions? + return r + + def coeff_exp(term, x): + coeff, exp = S.One, S.Zero + for factor in Mul.make_args(term): + if factor.has(x): + base, exp = factor.as_base_exp() + if base != x: + try: + return term.leadterm(x) + except ValueError: + return term, S.Zero + else: + coeff *= factor + return coeff, exp + + # TODO new and probably slow + try: + a, b = z.leadterm(t, logx=logx, cdir=1) + except (ValueError, NotImplementedError, PoleError): + s = z._eval_nseries(t, n=n, logx=logx, cdir=1) + while s.is_Order: + n += 1 + s = z._eval_nseries(t, n=n, logx=logx, cdir=1) + try: + a, b = s.removeO().leadterm(t, cdir=1) + except ValueError: + a, b = s.removeO().as_leading_term(t, cdir=1), S.Zero + + p = (z/(a*t**b) - 1)._eval_nseries(t, n=n, logx=logx, cdir=1) + if p.has(exp): + p = logcombine(p) + if isinstance(p, Order): + n = p.getn() + _, d = coeff_exp(p, t) + logx = log(x) if logx is None else logx + + if not d.is_positive: + res = log(a) - b*log(cdir) + b*logx + _res = res + logflags = {"deep": True, "log": True, "mul": False, "power_exp": False, + "power_base": False, "multinomial": False, "basic": False, "force": True, + "factor": False} + expr = self.expand(**logflags) + if (not a.could_extract_minus_sign() and + logx.could_extract_minus_sign()): + _res = _res.subs(-logx, -log(x)).expand(**logflags) + else: + _res = _res.subs(logx, log(x)).expand(**logflags) + if _res == expr: + return res + return res + Order(x**n, x) + + def mul(d1, d2): + res = {} + for e1, e2 in product(d1, d2): + ex = e1 + e2 + if ex < n: + res[ex] = res.get(ex, S.Zero) + d1[e1]*d2[e2] + return res + + pterms = {} + + for term in Add.make_args(p.removeO()): + co1, e1 = coeff_exp(term, t) + pterms[e1] = pterms.get(e1, S.Zero) + co1 + + k = S.One + terms = {} + pk = pterms + + while k*d < n: + coeff = -S.NegativeOne**k/k + for ex in pk: + _ = terms.get(ex, S.Zero) + coeff*pk[ex] + terms[ex] = _.nsimplify() + pk = mul(pk, pterms) + k += S.One + + res = log(a) - b*log(cdir) + b*logx + for ex in terms: + res += terms[ex]*t**(ex) + + if a.is_negative and im(z) != 0: + from sympy.functions.special.delta_functions import Heaviside + for i, term in enumerate(z.lseries(t)): + if not term.is_real or i == 5: + break + if i < 5: + coeff, _ = term.as_coeff_exponent(t) + res += -2*I*pi*Heaviside(-im(coeff), 0) + + res = res.subs(t, x/cdir) + return res + Order(x**n, x) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + # NOTE + # Refer https://github.com/sympy/sympy/pull/23592 for more information + # on each of the following steps involved in this method. + arg0 = self.args[0].together() + + # STEP 1 + t = Dummy('t', positive=True) + if cdir == 0: + cdir = 1 + z = arg0.subs(x, cdir*t) + + # STEP 2 + try: + c, e = z.leadterm(t, logx=logx, cdir=1) + except ValueError: + arg = arg0.as_leading_term(x, logx=logx, cdir=cdir) + return log(arg) + if c.has(t): + c = c.subs(t, x/cdir) + if e != 0: + raise PoleError("Cannot expand %s around 0" % (self)) + return log(c) + + # STEP 3 + if c == S.One and e == S.Zero: + return (arg0 - S.One).as_leading_term(x, logx=logx) + + # STEP 4 + res = log(c) - e*log(cdir) + logx = log(x) if logx is None else logx + res += e*logx + + # STEP 5 + if c.is_negative and im(z) != 0: + from sympy.functions.special.delta_functions import Heaviside + for i, term in enumerate(z.lseries(t)): + if not term.is_real or i == 5: + break + if i < 5: + coeff, _ = term.as_coeff_exponent(t) + res += -2*I*pi*Heaviside(-im(coeff), 0) + return res + + +class LambertW(Function): + r""" + The Lambert W function $W(z)$ is defined as the inverse + function of $w \exp(w)$ [1]_. + + Explanation + =========== + + In other words, the value of $W(z)$ is such that $z = W(z) \exp(W(z))$ + for any complex number $z$. The Lambert W function is a multivalued + function with infinitely many branches $W_k(z)$, indexed by + $k \in \mathbb{Z}$. Each branch gives a different solution $w$ + of the equation $z = w \exp(w)$. + + The Lambert W function has two partially real branches: the + principal branch ($k = 0$) is real for real $z > -1/e$, and the + $k = -1$ branch is real for $-1/e < z < 0$. All branches except + $k = 0$ have a logarithmic singularity at $z = 0$. + + Examples + ======== + + >>> from sympy import LambertW + >>> LambertW(1.2) + 0.635564016364870 + >>> LambertW(1.2, -1).n() + -1.34747534407696 - 4.41624341514535*I + >>> LambertW(-1).is_real + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Lambert_W_function + """ + _singularities = (-Pow(S.Exp1, -1, evaluate=False), S.ComplexInfinity) + + @classmethod + def eval(cls, x, k=None): + if k == S.Zero: + return cls(x) + elif k is None: + k = S.Zero + + if k.is_zero: + if x.is_zero: + return S.Zero + if x is S.Exp1: + return S.One + w = Wild('w') + # W(x*log(x)) = log(x) for x >= 1/e + # e.g., W(-1/e) = -1, W(2*log(2)) = log(2) + result = x.match(w*log(w)) + if result is not None and Ge(result[w]*S.Exp1, S.One) is S.true: + return log(result[w]) + if x == -log(2)/2: + return -log(2) + # W(x**(x+1)*log(x)) = x*log(x) for x > 0 + # e.g., W(81*log(3)) = 3*log(3) + result = x.match(w**(w+1)*log(w)) + if result is not None and result[w].is_positive is True: + return result[w]*log(result[w]) + # W(e**(1/n)/n) = 1/n + # e.g., W(sqrt(e)/2) = 1/2 + result = x.match(S.Exp1**(1/w)/w) + if result is not None: + return 1 / result[w] + if x == -pi/2: + return I*pi/2 + if x == exp(1 + S.Exp1): + return S.Exp1 + if x is S.Infinity: + return S.Infinity + + if fuzzy_not(k.is_zero): + if x.is_zero: + return S.NegativeInfinity + if k is S.NegativeOne: + if x == -pi/2: + return -I*pi/2 + elif x == -1/S.Exp1: + return S.NegativeOne + elif x == -2*exp(-2): + return -Integer(2) + + def fdiff(self, argindex=1): + """ + Return the first derivative of this function. + """ + x = self.args[0] + + if len(self.args) == 1: + if argindex == 1: + return LambertW(x)/(x*(1 + LambertW(x))) + else: + k = self.args[1] + if argindex == 1: + return LambertW(x, k)/(x*(1 + LambertW(x, k))) + + raise ArgumentIndexError(self, argindex) + + def _eval_is_extended_real(self): + x = self.args[0] + if len(self.args) == 1: + k = S.Zero + else: + k = self.args[1] + if k.is_zero: + if (x + 1/S.Exp1).is_positive: + return True + elif (x + 1/S.Exp1).is_nonpositive: + return False + elif (k + 1).is_zero: + if x.is_negative and (x + 1/S.Exp1).is_positive: + return True + elif x.is_nonpositive or (x + 1/S.Exp1).is_nonnegative: + return False + elif fuzzy_not(k.is_zero) and fuzzy_not((k + 1).is_zero): + if x.is_extended_real: + return False + + def _eval_is_finite(self): + return self.args[0].is_finite + + def _eval_is_algebraic(self): + s = self.func(*self.args) + if s.func == self.func: + if fuzzy_not(self.args[0].is_zero) and self.args[0].is_algebraic: + return False + else: + return s.is_algebraic + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + if len(self.args) == 1: + arg = self.args[0] + arg0 = arg.subs(x, 0).cancel() + if not arg0.is_zero: + return self.func(arg0) + return arg.as_leading_term(x) + + def _eval_nseries(self, x, n, logx, cdir=0): + if len(self.args) == 1: + from sympy.functions.elementary.integers import ceiling + from sympy.series.order import Order + arg = self.args[0].nseries(x, n=n, logx=logx) + lt = arg.as_leading_term(x, logx=logx) + lte = 1 + if lt.is_Pow: + lte = lt.exp + if ceiling(n/lte) >= 1: + s = Add(*[(-S.One)**(k - 1)*Integer(k)**(k - 2)/ + factorial(k - 1)*arg**k for k in range(1, ceiling(n/lte))]) + s = expand_multinomial(s) + else: + s = S.Zero + + return s + Order(x**n, x) + return super()._eval_nseries(x, n, logx) + + def _eval_is_zero(self): + x = self.args[0] + if len(self.args) == 1: + return x.is_zero + else: + return fuzzy_and([x.is_zero, self.args[1].is_zero]) + + +@cacheit +def _log_atan_table(): + return { + # first quadrant only + sqrt(3): pi / 3, + 1: pi / 4, + sqrt(5 - 2 * sqrt(5)): pi / 5, + sqrt(2) * sqrt(5 - sqrt(5)) / (1 + sqrt(5)): pi / 5, + sqrt(5 + 2 * sqrt(5)): pi * Rational(2, 5), + sqrt(2) * sqrt(sqrt(5) + 5) / (-1 + sqrt(5)): pi * Rational(2, 5), + sqrt(3) / 3: pi / 6, + sqrt(2) - 1: pi / 8, + sqrt(2 - sqrt(2)) / sqrt(sqrt(2) + 2): pi / 8, + sqrt(2) + 1: pi * Rational(3, 8), + sqrt(sqrt(2) + 2) / sqrt(2 - sqrt(2)): pi * Rational(3, 8), + sqrt(1 - 2 * sqrt(5) / 5): pi / 10, + (-sqrt(2) + sqrt(10)) / (2 * sqrt(sqrt(5) + 5)): pi / 10, + sqrt(1 + 2 * sqrt(5) / 5): pi * Rational(3, 10), + (sqrt(2) + sqrt(10)) / (2 * sqrt(5 - sqrt(5))): pi * Rational(3, 10), + 2 - sqrt(3): pi / 12, + (-1 + sqrt(3)) / (1 + sqrt(3)): pi / 12, + 2 + sqrt(3): pi * Rational(5, 12), + (1 + sqrt(3)) / (-1 + sqrt(3)): pi * Rational(5, 12) + } diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/hyperbolic.py b/lib/python3.11/site-packages/sympy/functions/elementary/hyperbolic.py new file mode 100644 index 0000000000000000000000000000000000000000..845fe5912897836c1bafe3f0a7a79e1842bd0f29 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/hyperbolic.py @@ -0,0 +1,2285 @@ +from sympy.core import S, sympify, cacheit +from sympy.core.add import Add +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.logic import fuzzy_or, fuzzy_and, fuzzy_not, FuzzyBool +from sympy.core.numbers import I, pi, Rational +from sympy.core.symbol import Dummy +from sympy.functions.combinatorial.factorials import (binomial, factorial, + RisingFactorial) +from sympy.functions.combinatorial.numbers import bernoulli, euler, nC +from sympy.functions.elementary.complexes import Abs, im, re +from sympy.functions.elementary.exponential import exp, log, match_real_imag +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import ( + acos, acot, asin, atan, cos, cot, csc, sec, sin, tan, + _imaginary_unit_as_coefficient) +from sympy.polys.specialpolys import symmetric_poly + + +def _rewrite_hyperbolics_as_exp(expr): + return expr.xreplace({h: h.rewrite(exp) + for h in expr.atoms(HyperbolicFunction)}) + + +@cacheit +def _acosh_table(): + return { + I: log(I*(1 + sqrt(2))), + -I: log(-I*(1 + sqrt(2))), + S.Half: pi/3, + Rational(-1, 2): pi*Rational(2, 3), + sqrt(2)/2: pi/4, + -sqrt(2)/2: pi*Rational(3, 4), + 1/sqrt(2): pi/4, + -1/sqrt(2): pi*Rational(3, 4), + sqrt(3)/2: pi/6, + -sqrt(3)/2: pi*Rational(5, 6), + (sqrt(3) - 1)/sqrt(2**3): pi*Rational(5, 12), + -(sqrt(3) - 1)/sqrt(2**3): pi*Rational(7, 12), + sqrt(2 + sqrt(2))/2: pi/8, + -sqrt(2 + sqrt(2))/2: pi*Rational(7, 8), + sqrt(2 - sqrt(2))/2: pi*Rational(3, 8), + -sqrt(2 - sqrt(2))/2: pi*Rational(5, 8), + (1 + sqrt(3))/(2*sqrt(2)): pi/12, + -(1 + sqrt(3))/(2*sqrt(2)): pi*Rational(11, 12), + (sqrt(5) + 1)/4: pi/5, + -(sqrt(5) + 1)/4: pi*Rational(4, 5) + } + + +@cacheit +def _acsch_table(): + return { + I: -pi / 2, + I*(sqrt(2) + sqrt(6)): -pi / 12, + I*(1 + sqrt(5)): -pi / 10, + I*2 / sqrt(2 - sqrt(2)): -pi / 8, + I*2: -pi / 6, + I*sqrt(2 + 2/sqrt(5)): -pi / 5, + I*sqrt(2): -pi / 4, + I*(sqrt(5)-1): -3*pi / 10, + I*2 / sqrt(3): -pi / 3, + I*2 / sqrt(2 + sqrt(2)): -3*pi / 8, + I*sqrt(2 - 2/sqrt(5)): -2*pi / 5, + I*(sqrt(6) - sqrt(2)): -5*pi / 12, + S(2): -I*log((1+sqrt(5))/2), + } + + +@cacheit +def _asech_table(): + return { + I: - (pi*I / 2) + log(1 + sqrt(2)), + -I: (pi*I / 2) + log(1 + sqrt(2)), + (sqrt(6) - sqrt(2)): pi / 12, + (sqrt(2) - sqrt(6)): 11*pi / 12, + sqrt(2 - 2/sqrt(5)): pi / 10, + -sqrt(2 - 2/sqrt(5)): 9*pi / 10, + 2 / sqrt(2 + sqrt(2)): pi / 8, + -2 / sqrt(2 + sqrt(2)): 7*pi / 8, + 2 / sqrt(3): pi / 6, + -2 / sqrt(3): 5*pi / 6, + (sqrt(5) - 1): pi / 5, + (1 - sqrt(5)): 4*pi / 5, + sqrt(2): pi / 4, + -sqrt(2): 3*pi / 4, + sqrt(2 + 2/sqrt(5)): 3*pi / 10, + -sqrt(2 + 2/sqrt(5)): 7*pi / 10, + S(2): pi / 3, + -S(2): 2*pi / 3, + sqrt(2*(2 + sqrt(2))): 3*pi / 8, + -sqrt(2*(2 + sqrt(2))): 5*pi / 8, + (1 + sqrt(5)): 2*pi / 5, + (-1 - sqrt(5)): 3*pi / 5, + (sqrt(6) + sqrt(2)): 5*pi / 12, + (-sqrt(6) - sqrt(2)): 7*pi / 12, + I*S.Infinity: -pi*I / 2, + I*S.NegativeInfinity: pi*I / 2, + } + +############################################################################### +########################### HYPERBOLIC FUNCTIONS ############################## +############################################################################### + + +class HyperbolicFunction(Function): + """ + Base class for hyperbolic functions. + + See Also + ======== + + sinh, cosh, tanh, coth + """ + + unbranched = True + + +def _peeloff_ipi(arg): + r""" + Split ARG into two parts, a "rest" and a multiple of $I\pi$. + This assumes ARG to be an ``Add``. + The multiple of $I\pi$ returned in the second position is always a ``Rational``. + + Examples + ======== + + >>> from sympy.functions.elementary.hyperbolic import _peeloff_ipi as peel + >>> from sympy import pi, I + >>> from sympy.abc import x, y + >>> peel(x + I*pi/2) + (x, 1/2) + >>> peel(x + I*2*pi/3 + I*pi*y) + (x + I*pi*y + I*pi/6, 1/2) + """ + ipi = pi*I + for a in Add.make_args(arg): + if a == ipi: + K = S.One + break + elif a.is_Mul: + K, p = a.as_two_terms() + if p == ipi and K.is_Rational: + break + else: + return arg, S.Zero + + m1 = (K % S.Half) + m2 = K - m1 + return arg - m2*ipi, m2 + + +class sinh(HyperbolicFunction): + r""" + ``sinh(x)`` is the hyperbolic sine of ``x``. + + The hyperbolic sine function is $\frac{e^x - e^{-x}}{2}$. + + Examples + ======== + + >>> from sympy import sinh + >>> from sympy.abc import x + >>> sinh(x) + sinh(x) + + See Also + ======== + + cosh, tanh, asinh + """ + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return cosh(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return asinh + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.NegativeInfinity + elif arg.is_zero: + return S.Zero + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.NaN + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + return I * sin(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_Add: + x, m = _peeloff_ipi(arg) + if m: + m = m*pi*I + return sinh(m)*cosh(x) + cosh(m)*sinh(x) + + if arg.is_zero: + return S.Zero + + if arg.func == asinh: + return arg.args[0] + + if arg.func == acosh: + x = arg.args[0] + return sqrt(x - 1) * sqrt(x + 1) + + if arg.func == atanh: + x = arg.args[0] + return x/sqrt(1 - x**2) + + if arg.func == acoth: + x = arg.args[0] + return 1/(sqrt(x - 1) * sqrt(x + 1)) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + """ + Returns the next term in the Taylor series expansion. + """ + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + if len(previous_terms) > 2: + p = previous_terms[-2] + return p * x**2 / (n*(n - 1)) + else: + return x**(n) / factorial(n) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + """ + Returns this function as a complex coordinate. + """ + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.expand(deep, **hints), S.Zero) + else: + return (self, S.Zero) + if deep: + re, im = self.args[0].expand(deep, **hints).as_real_imag() + else: + re, im = self.args[0].as_real_imag() + return (sinh(re)*cos(im), cosh(re)*sin(im)) + + def _eval_expand_complex(self, deep=True, **hints): + re_part, im_part = self.as_real_imag(deep=deep, **hints) + return re_part + im_part*I + + def _eval_expand_trig(self, deep=True, **hints): + if deep: + arg = self.args[0].expand(deep, **hints) + else: + arg = self.args[0] + x = None + if arg.is_Add: # TODO, implement more if deep stuff here + x, y = arg.as_two_terms() + else: + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff is not S.One and coeff.is_Integer and terms is not S.One: + x = terms + y = (coeff - 1)*x + if x is not None: + return (sinh(x)*cosh(y) + sinh(y)*cosh(x)).expand(trig=True) + return sinh(arg) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + return (exp(arg) - exp(-arg)) / 2 + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return (exp(arg) - exp(-arg)) / 2 + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return -I * sin(I * arg) + + def _eval_rewrite_as_csc(self, arg, **kwargs): + return -I / csc(I * arg) + + def _eval_rewrite_as_cosh(self, arg, **kwargs): + return -I*cosh(arg + pi*I/2) + + def _eval_rewrite_as_tanh(self, arg, **kwargs): + tanh_half = tanh(S.Half*arg) + return 2*tanh_half/(1 - tanh_half**2) + + def _eval_rewrite_as_coth(self, arg, **kwargs): + coth_half = coth(S.Half*arg) + return 2*coth_half/(coth_half**2 - 1) + + def _eval_rewrite_as_csch(self, arg, **kwargs): + return 1 / csch(arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if cdir.is_negative else '+') + if arg0.is_zero: + return arg + elif arg0.is_finite: + return self.func(arg0) + else: + return self + + def _eval_is_real(self): + arg = self.args[0] + if arg.is_real: + return True + + # if `im` is of the form n*pi + # else, check if it is a number + re, im = arg.as_real_imag() + return (im%pi).is_zero + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + + def _eval_is_positive(self): + if self.args[0].is_extended_real: + return self.args[0].is_positive + + def _eval_is_negative(self): + if self.args[0].is_extended_real: + return self.args[0].is_negative + + def _eval_is_finite(self): + arg = self.args[0] + return arg.is_finite + + def _eval_is_zero(self): + rest, ipi_mult = _peeloff_ipi(self.args[0]) + if rest.is_zero: + return ipi_mult.is_integer + + +class cosh(HyperbolicFunction): + r""" + ``cosh(x)`` is the hyperbolic cosine of ``x``. + + The hyperbolic cosine function is $\frac{e^x + e^{-x}}{2}$. + + Examples + ======== + + >>> from sympy import cosh + >>> from sympy.abc import x + >>> cosh(x) + cosh(x) + + See Also + ======== + + sinh, tanh, acosh + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return sinh(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + from sympy.functions.elementary.trigonometric import cos + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Infinity + elif arg.is_zero: + return S.One + elif arg.is_negative: + return cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.NaN + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + return cos(i_coeff) + else: + if arg.could_extract_minus_sign(): + return cls(-arg) + + if arg.is_Add: + x, m = _peeloff_ipi(arg) + if m: + m = m*pi*I + return cosh(m)*cosh(x) + sinh(m)*sinh(x) + + if arg.is_zero: + return S.One + + if arg.func == asinh: + return sqrt(1 + arg.args[0]**2) + + if arg.func == acosh: + return arg.args[0] + + if arg.func == atanh: + return 1/sqrt(1 - arg.args[0]**2) + + if arg.func == acoth: + x = arg.args[0] + return x/(sqrt(x - 1) * sqrt(x + 1)) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + + if len(previous_terms) > 2: + p = previous_terms[-2] + return p * x**2 / (n*(n - 1)) + else: + return x**(n)/factorial(n) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.expand(deep, **hints), S.Zero) + else: + return (self, S.Zero) + if deep: + re, im = self.args[0].expand(deep, **hints).as_real_imag() + else: + re, im = self.args[0].as_real_imag() + + return (cosh(re)*cos(im), sinh(re)*sin(im)) + + def _eval_expand_complex(self, deep=True, **hints): + re_part, im_part = self.as_real_imag(deep=deep, **hints) + return re_part + im_part*I + + def _eval_expand_trig(self, deep=True, **hints): + if deep: + arg = self.args[0].expand(deep, **hints) + else: + arg = self.args[0] + x = None + if arg.is_Add: # TODO, implement more if deep stuff here + x, y = arg.as_two_terms() + else: + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff is not S.One and coeff.is_Integer and terms is not S.One: + x = terms + y = (coeff - 1)*x + if x is not None: + return (cosh(x)*cosh(y) + sinh(x)*sinh(y)).expand(trig=True) + return cosh(arg) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + return (exp(arg) + exp(-arg)) / 2 + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return (exp(arg) + exp(-arg)) / 2 + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return cos(I * arg, evaluate=False) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + return 1 / sec(I * arg, evaluate=False) + + def _eval_rewrite_as_sinh(self, arg, **kwargs): + return -I*sinh(arg + pi*I/2, evaluate=False) + + def _eval_rewrite_as_tanh(self, arg, **kwargs): + tanh_half = tanh(S.Half*arg)**2 + return (1 + tanh_half)/(1 - tanh_half) + + def _eval_rewrite_as_coth(self, arg, **kwargs): + coth_half = coth(S.Half*arg)**2 + return (coth_half + 1)/(coth_half - 1) + + def _eval_rewrite_as_sech(self, arg, **kwargs): + return 1 / sech(arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if cdir.is_negative else '+') + if arg0.is_zero: + return S.One + elif arg0.is_finite: + return self.func(arg0) + else: + return self + + def _eval_is_real(self): + arg = self.args[0] + + # `cosh(x)` is real for real OR purely imaginary `x` + if arg.is_real or arg.is_imaginary: + return True + + # cosh(a+ib) = cos(b)*cosh(a) + i*sin(b)*sinh(a) + # the imaginary part can be an expression like n*pi + # if not, check if the imaginary part is a number + re, im = arg.as_real_imag() + return (im%pi).is_zero + + def _eval_is_positive(self): + # cosh(x+I*y) = cos(y)*cosh(x) + I*sin(y)*sinh(x) + # cosh(z) is positive iff it is real and the real part is positive. + # So we need sin(y)*sinh(x) = 0 which gives x=0 or y=n*pi + # Case 1 (y=n*pi): cosh(z) = (-1)**n * cosh(x) -> positive for n even + # Case 2 (x=0): cosh(z) = cos(y) -> positive when cos(y) is positive + z = self.args[0] + + x, y = z.as_real_imag() + ymod = y % (2*pi) + + yzero = ymod.is_zero + # shortcut if ymod is zero + if yzero: + return True + + xzero = x.is_zero + # shortcut x is not zero + if xzero is False: + return yzero + + return fuzzy_or([ + # Case 1: + yzero, + # Case 2: + fuzzy_and([ + xzero, + fuzzy_or([ymod < pi/2, ymod > 3*pi/2]) + ]) + ]) + + + def _eval_is_nonnegative(self): + z = self.args[0] + + x, y = z.as_real_imag() + ymod = y % (2*pi) + + yzero = ymod.is_zero + # shortcut if ymod is zero + if yzero: + return True + + xzero = x.is_zero + # shortcut x is not zero + if xzero is False: + return yzero + + return fuzzy_or([ + # Case 1: + yzero, + # Case 2: + fuzzy_and([ + xzero, + fuzzy_or([ymod <= pi/2, ymod >= 3*pi/2]) + ]) + ]) + + def _eval_is_finite(self): + arg = self.args[0] + return arg.is_finite + + def _eval_is_zero(self): + rest, ipi_mult = _peeloff_ipi(self.args[0]) + if ipi_mult and rest.is_zero: + return (ipi_mult - S.Half).is_integer + + +class tanh(HyperbolicFunction): + r""" + ``tanh(x)`` is the hyperbolic tangent of ``x``. + + The hyperbolic tangent function is $\frac{\sinh(x)}{\cosh(x)}$. + + Examples + ======== + + >>> from sympy import tanh + >>> from sympy.abc import x + >>> tanh(x) + tanh(x) + + See Also + ======== + + sinh, cosh, atanh + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return S.One - tanh(self.args[0])**2 + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return atanh + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.One + elif arg is S.NegativeInfinity: + return S.NegativeOne + elif arg.is_zero: + return S.Zero + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.NaN + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + if i_coeff.could_extract_minus_sign(): + return -I * tan(-i_coeff) + return I * tan(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_Add: + x, m = _peeloff_ipi(arg) + if m: + tanhm = tanh(m*pi*I) + if tanhm is S.ComplexInfinity: + return coth(x) + else: # tanhm == 0 + return tanh(x) + + if arg.is_zero: + return S.Zero + + if arg.func == asinh: + x = arg.args[0] + return x/sqrt(1 + x**2) + + if arg.func == acosh: + x = arg.args[0] + return sqrt(x - 1) * sqrt(x + 1) / x + + if arg.func == atanh: + return arg.args[0] + + if arg.func == acoth: + return 1/arg.args[0] + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + a = 2**(n + 1) + + B = bernoulli(n + 1) + F = factorial(n + 1) + + return a*(a - 1) * B/F * x**n + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.expand(deep, **hints), S.Zero) + else: + return (self, S.Zero) + if deep: + re, im = self.args[0].expand(deep, **hints).as_real_imag() + else: + re, im = self.args[0].as_real_imag() + denom = sinh(re)**2 + cos(im)**2 + return (sinh(re)*cosh(re)/denom, sin(im)*cos(im)/denom) + + def _eval_expand_trig(self, **hints): + arg = self.args[0] + if arg.is_Add: + n = len(arg.args) + TX = [tanh(x, evaluate=False)._eval_expand_trig() + for x in arg.args] + p = [0, 0] # [den, num] + for i in range(n + 1): + p[i % 2] += symmetric_poly(i, TX) + return p[1]/p[0] + elif arg.is_Mul: + coeff, terms = arg.as_coeff_Mul() + if coeff.is_Integer and coeff > 1: + T = tanh(terms) + n = [nC(range(coeff), k)*T**k for k in range(1, coeff + 1, 2)] + d = [nC(range(coeff), k)*T**k for k in range(0, coeff + 1, 2)] + return Add(*n)/Add(*d) + return tanh(arg) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + neg_exp, pos_exp = exp(-arg), exp(arg) + return (pos_exp - neg_exp)/(pos_exp + neg_exp) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + neg_exp, pos_exp = exp(-arg), exp(arg) + return (pos_exp - neg_exp)/(pos_exp + neg_exp) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + return -I * tan(I * arg, evaluate=False) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + return -I / cot(I * arg, evaluate=False) + + def _eval_rewrite_as_sinh(self, arg, **kwargs): + return I*sinh(arg)/sinh(pi*I/2 - arg, evaluate=False) + + def _eval_rewrite_as_cosh(self, arg, **kwargs): + return I*cosh(pi*I/2 - arg, evaluate=False)/cosh(arg) + + def _eval_rewrite_as_coth(self, arg, **kwargs): + return 1/coth(arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.series.order import Order + arg = self.args[0].as_leading_term(x) + + if x in arg.free_symbols and Order(1, x).contains(arg): + return arg + else: + return self.func(arg) + + def _eval_is_real(self): + arg = self.args[0] + if arg.is_real: + return True + + re, im = arg.as_real_imag() + + # if denom = 0, tanh(arg) = zoo + if re == 0 and im % pi == pi/2: + return None + + # check if im is of the form n*pi/2 to make sin(2*im) = 0 + # if not, im could be a number, return False in that case + return (im % (pi/2)).is_zero + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + + def _eval_is_positive(self): + if self.args[0].is_extended_real: + return self.args[0].is_positive + + def _eval_is_negative(self): + if self.args[0].is_extended_real: + return self.args[0].is_negative + + def _eval_is_finite(self): + arg = self.args[0] + + re, im = arg.as_real_imag() + denom = cos(im)**2 + sinh(re)**2 + if denom == 0: + return False + elif denom.is_number: + return True + if arg.is_extended_real: + return True + + def _eval_is_zero(self): + arg = self.args[0] + if arg.is_zero: + return True + + +class coth(HyperbolicFunction): + r""" + ``coth(x)`` is the hyperbolic cotangent of ``x``. + + The hyperbolic cotangent function is $\frac{\cosh(x)}{\sinh(x)}$. + + Examples + ======== + + >>> from sympy import coth + >>> from sympy.abc import x + >>> coth(x) + coth(x) + + See Also + ======== + + sinh, cosh, acoth + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return -1/sinh(self.args[0])**2 + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return acoth + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.One + elif arg is S.NegativeInfinity: + return S.NegativeOne + elif arg.is_zero: + return S.ComplexInfinity + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.NaN + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + if i_coeff.could_extract_minus_sign(): + return I * cot(-i_coeff) + return -I * cot(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_Add: + x, m = _peeloff_ipi(arg) + if m: + cothm = coth(m*pi*I) + if cothm is S.ComplexInfinity: + return coth(x) + else: # cothm == 0 + return tanh(x) + + if arg.is_zero: + return S.ComplexInfinity + + if arg.func == asinh: + x = arg.args[0] + return sqrt(1 + x**2)/x + + if arg.func == acosh: + x = arg.args[0] + return x/(sqrt(x - 1) * sqrt(x + 1)) + + if arg.func == atanh: + return 1/arg.args[0] + + if arg.func == acoth: + return arg.args[0] + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return 1 / sympify(x) + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + B = bernoulli(n + 1) + F = factorial(n + 1) + + return 2**(n + 1) * B/F * x**n + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + from sympy.functions.elementary.trigonometric import (cos, sin) + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.expand(deep, **hints), S.Zero) + else: + return (self, S.Zero) + if deep: + re, im = self.args[0].expand(deep, **hints).as_real_imag() + else: + re, im = self.args[0].as_real_imag() + denom = sinh(re)**2 + sin(im)**2 + return (sinh(re)*cosh(re)/denom, -sin(im)*cos(im)/denom) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + neg_exp, pos_exp = exp(-arg), exp(arg) + return (pos_exp + neg_exp)/(pos_exp - neg_exp) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + neg_exp, pos_exp = exp(-arg), exp(arg) + return (pos_exp + neg_exp)/(pos_exp - neg_exp) + + def _eval_rewrite_as_sinh(self, arg, **kwargs): + return -I*sinh(pi*I/2 - arg, evaluate=False)/sinh(arg) + + def _eval_rewrite_as_cosh(self, arg, **kwargs): + return -I*cosh(arg)/cosh(pi*I/2 - arg, evaluate=False) + + def _eval_rewrite_as_tanh(self, arg, **kwargs): + return 1/tanh(arg) + + def _eval_is_positive(self): + if self.args[0].is_extended_real: + return self.args[0].is_positive + + def _eval_is_negative(self): + if self.args[0].is_extended_real: + return self.args[0].is_negative + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.series.order import Order + arg = self.args[0].as_leading_term(x) + + if x in arg.free_symbols and Order(1, x).contains(arg): + return 1/arg + else: + return self.func(arg) + + def _eval_expand_trig(self, **hints): + arg = self.args[0] + if arg.is_Add: + CX = [coth(x, evaluate=False)._eval_expand_trig() for x in arg.args] + p = [[], []] + n = len(arg.args) + for i in range(n, -1, -1): + p[(n - i) % 2].append(symmetric_poly(i, CX)) + return Add(*p[0])/Add(*p[1]) + elif arg.is_Mul: + coeff, x = arg.as_coeff_Mul(rational=True) + if coeff.is_Integer and coeff > 1: + c = coth(x, evaluate=False) + p = [[], []] + for i in range(coeff, -1, -1): + p[(coeff - i) % 2].append(binomial(coeff, i)*c**i) + return Add(*p[0])/Add(*p[1]) + return coth(arg) + + +class ReciprocalHyperbolicFunction(HyperbolicFunction): + """Base class for reciprocal functions of hyperbolic functions. """ + + #To be defined in class + _reciprocal_of = None + _is_even: FuzzyBool = None + _is_odd: FuzzyBool = None + + @classmethod + def eval(cls, arg): + if arg.could_extract_minus_sign(): + if cls._is_even: + return cls(-arg) + if cls._is_odd: + return -cls(-arg) + + t = cls._reciprocal_of.eval(arg) + if hasattr(arg, 'inverse') and arg.inverse() == cls: + return arg.args[0] + return 1/t if t is not None else t + + def _call_reciprocal(self, method_name, *args, **kwargs): + # Calls method_name on _reciprocal_of + o = self._reciprocal_of(self.args[0]) + return getattr(o, method_name)(*args, **kwargs) + + def _calculate_reciprocal(self, method_name, *args, **kwargs): + # If calling method_name on _reciprocal_of returns a value != None + # then return the reciprocal of that value + t = self._call_reciprocal(method_name, *args, **kwargs) + return 1/t if t is not None else t + + def _rewrite_reciprocal(self, method_name, arg): + # Special handling for rewrite functions. If reciprocal rewrite returns + # unmodified expression, then return None + t = self._call_reciprocal(method_name, arg) + if t is not None and t != self._reciprocal_of(arg): + return 1/t + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_exp", arg) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_tractable", arg) + + def _eval_rewrite_as_tanh(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_tanh", arg) + + def _eval_rewrite_as_coth(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_coth", arg) + + def as_real_imag(self, deep = True, **hints): + return (1 / self._reciprocal_of(self.args[0])).as_real_imag(deep, **hints) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_expand_complex(self, deep=True, **hints): + re_part, im_part = self.as_real_imag(deep=True, **hints) + return re_part + I*im_part + + def _eval_expand_trig(self, **hints): + return self._calculate_reciprocal("_eval_expand_trig", **hints) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + return (1/self._reciprocal_of(self.args[0]))._eval_as_leading_term(x) + + def _eval_is_extended_real(self): + return self._reciprocal_of(self.args[0]).is_extended_real + + def _eval_is_finite(self): + return (1/self._reciprocal_of(self.args[0])).is_finite + + +class csch(ReciprocalHyperbolicFunction): + r""" + ``csch(x)`` is the hyperbolic cosecant of ``x``. + + The hyperbolic cosecant function is $\frac{2}{e^x - e^{-x}}$ + + Examples + ======== + + >>> from sympy import csch + >>> from sympy.abc import x + >>> csch(x) + csch(x) + + See Also + ======== + + sinh, cosh, tanh, sech, asinh, acosh + """ + + _reciprocal_of = sinh + _is_odd = True + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function + """ + if argindex == 1: + return -coth(self.args[0]) * csch(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + """ + Returns the next term in the Taylor series expansion + """ + if n == 0: + return 1/sympify(x) + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + B = bernoulli(n + 1) + F = factorial(n + 1) + + return 2 * (1 - 2**n) * B/F * x**n + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return I / sin(I * arg, evaluate=False) + + def _eval_rewrite_as_csc(self, arg, **kwargs): + return I * csc(I * arg, evaluate=False) + + def _eval_rewrite_as_cosh(self, arg, **kwargs): + return I / cosh(arg + I * pi / 2, evaluate=False) + + def _eval_rewrite_as_sinh(self, arg, **kwargs): + return 1 / sinh(arg) + + def _eval_is_positive(self): + if self.args[0].is_extended_real: + return self.args[0].is_positive + + def _eval_is_negative(self): + if self.args[0].is_extended_real: + return self.args[0].is_negative + + +class sech(ReciprocalHyperbolicFunction): + r""" + ``sech(x)`` is the hyperbolic secant of ``x``. + + The hyperbolic secant function is $\frac{2}{e^x + e^{-x}}$ + + Examples + ======== + + >>> from sympy import sech + >>> from sympy.abc import x + >>> sech(x) + sech(x) + + See Also + ======== + + sinh, cosh, tanh, coth, csch, asinh, acosh + """ + + _reciprocal_of = cosh + _is_even = True + + def fdiff(self, argindex=1): + if argindex == 1: + return - tanh(self.args[0])*sech(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + return euler(n) / factorial(n) * x**(n) + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return 1 / cos(I * arg, evaluate=False) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + return sec(I * arg, evaluate=False) + + def _eval_rewrite_as_sinh(self, arg, **kwargs): + return I / sinh(arg + I * pi /2, evaluate=False) + + def _eval_rewrite_as_cosh(self, arg, **kwargs): + return 1 / cosh(arg) + + def _eval_is_positive(self): + if self.args[0].is_extended_real: + return True + + +############################################################################### +############################# HYPERBOLIC INVERSES ############################# +############################################################################### + +class InverseHyperbolicFunction(Function): + """Base class for inverse hyperbolic functions.""" + + pass + + +class asinh(InverseHyperbolicFunction): + """ + ``asinh(x)`` is the inverse hyperbolic sine of ``x``. + + The inverse hyperbolic sine function. + + Examples + ======== + + >>> from sympy import asinh + >>> from sympy.abc import x + >>> asinh(x).diff(x) + 1/sqrt(x**2 + 1) + >>> asinh(1) + log(1 + sqrt(2)) + + See Also + ======== + + acosh, atanh, sinh + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/sqrt(self.args[0]**2 + 1) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.NegativeInfinity + elif arg.is_zero: + return S.Zero + elif arg is S.One: + return log(sqrt(2) + 1) + elif arg is S.NegativeOne: + return log(sqrt(2) - 1) + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.ComplexInfinity + + if arg.is_zero: + return S.Zero + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + return I * asin(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if isinstance(arg, sinh) and arg.args[0].is_number: + z = arg.args[0] + if z.is_real: + return z + r, i = match_real_imag(z) + if r is not None and i is not None: + f = floor((i + pi/2)/pi) + m = z - I*pi*f + even = f.is_even + if even is True: + return m + elif even is False: + return -m + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) >= 2 and n > 2: + p = previous_terms[-2] + return -p * (n - 2)**2/(n*(n - 1)) * x**2 + else: + k = (n - 1) // 2 + R = RisingFactorial(S.Half, k) + F = factorial(k) + return S.NegativeOne**k * R / F * x**n / n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # asinh + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0.is_zero: + return arg.as_leading_term(x) + + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + # Handling branch points + if x0 in (-I, I, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo) + if (1 + x0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if re(ndir).is_positive: + if im(x0).is_negative: + return -self.func(x0) - I*pi + elif re(ndir).is_negative: + if im(x0).is_positive: + return -self.func(x0) + I*pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # asinh + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 in (I, -I): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo) + if (1 + arg0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if re(ndir).is_positive: + if im(arg0).is_negative: + return -res - I*pi + elif re(ndir).is_negative: + if im(arg0).is_positive: + return -res + I*pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return log(x + sqrt(x**2 + 1)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_atanh(self, x, **kwargs): + return atanh(x/sqrt(1 + x**2)) + + def _eval_rewrite_as_acosh(self, x, **kwargs): + ix = I*x + return I*(sqrt(1 - ix)/sqrt(ix - 1) * acosh(ix) - pi/2) + + def _eval_rewrite_as_asin(self, x, **kwargs): + return -I * asin(I * x, evaluate=False) + + def _eval_rewrite_as_acos(self, x, **kwargs): + return I * acos(I * x, evaluate=False) - I*pi/2 + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return sinh + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + def _eval_is_finite(self): + return self.args[0].is_finite + + +class acosh(InverseHyperbolicFunction): + """ + ``acosh(x)`` is the inverse hyperbolic cosine of ``x``. + + The inverse hyperbolic cosine function. + + Examples + ======== + + >>> from sympy import acosh + >>> from sympy.abc import x + >>> acosh(x).diff(x) + 1/(sqrt(x - 1)*sqrt(x + 1)) + >>> acosh(1) + 0 + + See Also + ======== + + asinh, atanh, cosh + """ + + def fdiff(self, argindex=1): + if argindex == 1: + arg = self.args[0] + return 1/(sqrt(arg - 1)*sqrt(arg + 1)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Infinity + elif arg.is_zero: + return pi*I / 2 + elif arg is S.One: + return S.Zero + elif arg is S.NegativeOne: + return pi*I + + if arg.is_number: + cst_table = _acosh_table() + + if arg in cst_table: + if arg.is_extended_real: + return cst_table[arg]*I + return cst_table[arg] + + if arg is S.ComplexInfinity: + return S.ComplexInfinity + if arg == I*S.Infinity: + return S.Infinity + I*pi/2 + if arg == -I*S.Infinity: + return S.Infinity - I*pi/2 + + if arg.is_zero: + return pi*I*S.Half + + if isinstance(arg, cosh) and arg.args[0].is_number: + z = arg.args[0] + if z.is_real: + return Abs(z) + r, i = match_real_imag(z) + if r is not None and i is not None: + f = floor(i/pi) + m = z - I*pi*f + even = f.is_even + if even is True: + if r.is_nonnegative: + return m + elif r.is_negative: + return -m + elif even is False: + m -= I*pi + if r.is_nonpositive: + return -m + elif r.is_positive: + return m + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return I*pi/2 + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) >= 2 and n > 2: + p = previous_terms[-2] + return p * (n - 2)**2/(n*(n - 1)) * x**2 + else: + k = (n - 1) // 2 + R = RisingFactorial(S.Half, k) + F = factorial(k) + return -R / F * I * x**n / n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acosh + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + # Handling branch points + if x0 in (-S.One, S.Zero, S.One, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + # Handling points lying on branch cuts (-oo, 1) + if (x0 - 1).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if (x0 + 1).is_negative: + return self.func(x0) - 2*I*pi + return -self.func(x0) + elif not im(ndir).is_positive: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # acosh + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 in (S.One, S.NegativeOne): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts (-oo, 1) + if (arg0 - 1).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if (arg0 + 1).is_negative: + return res - 2*I*pi + return -res + elif not im(ndir).is_positive: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return log(x + sqrt(x + 1) * sqrt(x - 1)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_acos(self, x, **kwargs): + return sqrt(x - 1)/sqrt(1 - x) * acos(x) + + def _eval_rewrite_as_asin(self, x, **kwargs): + return sqrt(x - 1)/sqrt(1 - x) * (pi/2 - asin(x)) + + def _eval_rewrite_as_asinh(self, x, **kwargs): + return sqrt(x - 1)/sqrt(1 - x) * (pi/2 + I*asinh(I*x, evaluate=False)) + + def _eval_rewrite_as_atanh(self, x, **kwargs): + sxm1 = sqrt(x - 1) + s1mx = sqrt(1 - x) + sx2m1 = sqrt(x**2 - 1) + return (pi/2*sxm1/s1mx*(1 - x * sqrt(1/x**2)) + + sxm1*sqrt(x + 1)/sx2m1 * atanh(sx2m1/x)) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return cosh + + def _eval_is_zero(self): + if (self.args[0] - 1).is_zero: + return True + + def _eval_is_extended_real(self): + return fuzzy_and([self.args[0].is_extended_real, (self.args[0] - 1).is_extended_nonnegative]) + + def _eval_is_finite(self): + return self.args[0].is_finite + + +class atanh(InverseHyperbolicFunction): + """ + ``atanh(x)`` is the inverse hyperbolic tangent of ``x``. + + The inverse hyperbolic tangent function. + + Examples + ======== + + >>> from sympy import atanh + >>> from sympy.abc import x + >>> atanh(x).diff(x) + 1/(1 - x**2) + + See Also + ======== + + asinh, acosh, tanh + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/(1 - self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg.is_zero: + return S.Zero + elif arg is S.One: + return S.Infinity + elif arg is S.NegativeOne: + return S.NegativeInfinity + elif arg is S.Infinity: + return -I * atan(arg) + elif arg is S.NegativeInfinity: + return I * atan(-arg) + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + from sympy.calculus.accumulationbounds import AccumBounds + return I*AccumBounds(-pi/2, pi/2) + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + return I * atan(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_zero: + return S.Zero + + if isinstance(arg, tanh) and arg.args[0].is_number: + z = arg.args[0] + if z.is_real: + return z + r, i = match_real_imag(z) + if r is not None and i is not None: + f = floor(2*i/pi) + even = f.is_even + m = z - I*f*pi/2 + if even is True: + return m + elif even is False: + return m - I*pi/2 + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + return x**n / n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # atanh + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0.is_zero: + return arg.as_leading_term(x) + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + # Handling branch points + if x0 in (-S.One, S.One, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + # Handling points lying on branch cuts (-oo, -1] U [1, oo) + if (1 - x0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_negative: + return self.func(x0) - I*pi + elif im(ndir).is_positive: + if x0.is_positive: + return self.func(x0) + I*pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # atanh + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 in (S.One, S.NegativeOne): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts (-oo, -1] U [1, oo) + if (1 - arg0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_negative: + return res - I*pi + elif im(ndir).is_positive: + if arg0.is_positive: + return res + I*pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return (log(1 + x) - log(1 - x)) / 2 + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_asinh(self, x, **kwargs): + f = sqrt(1/(x**2 - 1)) + return (pi*x/(2*sqrt(-x**2)) - + sqrt(-x)*sqrt(1 - x**2)/sqrt(x)*f*asinh(f)) + + def _eval_is_zero(self): + if self.args[0].is_zero: + return True + + def _eval_is_extended_real(self): + return fuzzy_and([self.args[0].is_extended_real, (1 - self.args[0]).is_nonnegative, (self.args[0] + 1).is_nonnegative]) + + def _eval_is_finite(self): + return fuzzy_not(fuzzy_or([(self.args[0] - 1).is_zero, (self.args[0] + 1).is_zero])) + + def _eval_is_imaginary(self): + return self.args[0].is_imaginary + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return tanh + + +class acoth(InverseHyperbolicFunction): + """ + ``acoth(x)`` is the inverse hyperbolic cotangent of ``x``. + + The inverse hyperbolic cotangent function. + + Examples + ======== + + >>> from sympy import acoth + >>> from sympy.abc import x + >>> acoth(x).diff(x) + 1/(1 - x**2) + + See Also + ======== + + asinh, acosh, coth + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/(1 - self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return pi*I / 2 + elif arg is S.One: + return S.Infinity + elif arg is S.NegativeOne: + return S.NegativeInfinity + elif arg.is_negative: + return -cls(-arg) + else: + if arg is S.ComplexInfinity: + return S.Zero + + i_coeff = _imaginary_unit_as_coefficient(arg) + + if i_coeff is not None: + return -I * acot(i_coeff) + else: + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_zero: + return pi*I*S.Half + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return -I*pi/2 + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + return x**n / n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acoth + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.ComplexInfinity: + return (1/arg).as_leading_term(x) + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + # Handling branch points + if x0 in (-S.One, S.One, S.Zero): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + # Handling points lying on branch cuts [-1, 1] + if x0.is_real and (1 - x0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_positive: + return self.func(x0) + I*pi + elif im(ndir).is_positive: + if x0.is_negative: + return self.func(x0) - I*pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # acoth + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 in (S.One, S.NegativeOne): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts [-1, 1] + if arg0.is_real and (1 - arg0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_positive: + return res + I*pi + elif im(ndir).is_positive: + if arg0.is_negative: + return res - I*pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return (log(1 + 1/x) - log(1 - 1/x)) / 2 + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_atanh(self, x, **kwargs): + return atanh(1/x) + + def _eval_rewrite_as_asinh(self, x, **kwargs): + return (pi*I/2*(sqrt((x - 1)/x)*sqrt(x/(x - 1)) - sqrt(1 + 1/x)*sqrt(x/(x + 1))) + + x*sqrt(1/x**2)*asinh(sqrt(1/(x**2 - 1)))) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return coth + + def _eval_is_extended_real(self): + return fuzzy_and([self.args[0].is_extended_real, fuzzy_or([(self.args[0] - 1).is_extended_nonnegative, (self.args[0] + 1).is_extended_nonpositive])]) + + def _eval_is_finite(self): + return fuzzy_not(fuzzy_or([(self.args[0] - 1).is_zero, (self.args[0] + 1).is_zero])) + + +class asech(InverseHyperbolicFunction): + """ + ``asech(x)`` is the inverse hyperbolic secant of ``x``. + + The inverse hyperbolic secant function. + + Examples + ======== + + >>> from sympy import asech, sqrt, S + >>> from sympy.abc import x + >>> asech(x).diff(x) + -1/(x*sqrt(1 - x**2)) + >>> asech(1).diff(x) + 0 + >>> asech(1) + 0 + >>> asech(S(2)) + I*pi/3 + >>> asech(-sqrt(2)) + 3*I*pi/4 + >>> asech((sqrt(6) - sqrt(2))) + I*pi/12 + + See Also + ======== + + asinh, atanh, cosh, acoth + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function + .. [2] https://dlmf.nist.gov/4.37 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSech/ + + """ + + def fdiff(self, argindex=1): + if argindex == 1: + z = self.args[0] + return -1/(z*sqrt(1 - z**2)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return pi*I / 2 + elif arg is S.NegativeInfinity: + return pi*I / 2 + elif arg.is_zero: + return S.Infinity + elif arg is S.One: + return S.Zero + elif arg is S.NegativeOne: + return pi*I + + if arg.is_number: + cst_table = _asech_table() + + if arg in cst_table: + if arg.is_extended_real: + return cst_table[arg]*I + return cst_table[arg] + + if arg is S.ComplexInfinity: + from sympy.calculus.accumulationbounds import AccumBounds + return I*AccumBounds(-pi/2, pi/2) + + if arg.is_zero: + return S.Infinity + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return log(2 / x) + elif n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 2 and n > 2: + p = previous_terms[-2] + return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2) + else: + k = n // 2 + R = RisingFactorial(S.Half, k) * n + F = factorial(k) * n // 2 * n // 2 + return -1 * R / F * x**n / 4 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # asech + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + # Handling branch points + if x0 in (-S.One, S.Zero, S.One, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + # Handling points lying on branch cuts (-oo, 0] U (1, oo) + if x0.is_negative or (1 - x0).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_positive: + if x0.is_positive or (x0 + 1).is_negative: + return -self.func(x0) + return self.func(x0) - 2*I*pi + elif not im(ndir).is_negative: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # asech + from sympy.series.order import O + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 is S.One: + t = Dummy('t', positive=True) + ser = asech(S.One - t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One - self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + if arg0 is S.NegativeOne: + t = Dummy('t', positive=True) + ser = asech(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else I*pi + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts (-oo, 0] U (1, oo) + if arg0.is_negative or (1 - arg0).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_positive: + if arg0.is_positive or (arg0 + 1).is_negative: + return -res + return res - 2*I*pi + elif not im(ndir).is_negative: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return sech + + def _eval_rewrite_as_log(self, arg, **kwargs): + return log(1/arg + sqrt(1/arg - 1) * sqrt(1/arg + 1)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_acosh(self, arg, **kwargs): + return acosh(1/arg) + + def _eval_rewrite_as_asinh(self, arg, **kwargs): + return sqrt(1/arg - 1)/sqrt(1 - 1/arg)*(I*asinh(I/arg, evaluate=False) + + pi*S.Half) + + def _eval_rewrite_as_atanh(self, x, **kwargs): + return (I*pi*(1 - sqrt(x)*sqrt(1/x) - I/2*sqrt(-x)/sqrt(x) - I/2*sqrt(x**2)/sqrt(-x**2)) + + sqrt(1/(x + 1))*sqrt(x + 1)*atanh(sqrt(1 - x**2))) + + def _eval_rewrite_as_acsch(self, x, **kwargs): + return sqrt(1/x - 1)/sqrt(1 - 1/x)*(pi/2 - I*acsch(I*x, evaluate=False)) + + def _eval_is_extended_real(self): + return fuzzy_and([self.args[0].is_extended_real, self.args[0].is_nonnegative, (1 - self.args[0]).is_nonnegative]) + + def _eval_is_finite(self): + return fuzzy_not(self.args[0].is_zero) + + +class acsch(InverseHyperbolicFunction): + """ + ``acsch(x)`` is the inverse hyperbolic cosecant of ``x``. + + The inverse hyperbolic cosecant function. + + Examples + ======== + + >>> from sympy import acsch, sqrt, I + >>> from sympy.abc import x + >>> acsch(x).diff(x) + -1/(x**2*sqrt(1 + x**(-2))) + >>> acsch(1).diff(x) + 0 + >>> acsch(1) + log(1 + sqrt(2)) + >>> acsch(I) + -I*pi/2 + >>> acsch(-2*I) + I*pi/6 + >>> acsch(I*(sqrt(6) - sqrt(2))) + -5*I*pi/12 + + See Also + ======== + + asinh + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hyperbolic_function + .. [2] https://dlmf.nist.gov/4.37 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCsch/ + + """ + + def fdiff(self, argindex=1): + if argindex == 1: + z = self.args[0] + return -1/(z**2*sqrt(1 + 1/z**2)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return S.ComplexInfinity + elif arg is S.One: + return log(1 + sqrt(2)) + elif arg is S.NegativeOne: + return - log(1 + sqrt(2)) + + if arg.is_number: + cst_table = _acsch_table() + + if arg in cst_table: + return cst_table[arg]*I + + if arg is S.ComplexInfinity: + return S.Zero + + if arg.is_infinite: + return S.Zero + + if arg.is_zero: + return S.ComplexInfinity + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return log(2 / x) + elif n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 2 and n > 2: + p = previous_terms[-2] + return -p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2) + else: + k = n // 2 + R = RisingFactorial(S.Half, k) * n + F = factorial(k) * n // 2 * n // 2 + return S.NegativeOne**(k +1) * R / F * x**n / 4 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acsch + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + # Handling branch points + if x0 in (-I, I, S.Zero): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + + if x0 is S.NaN: + expr = self.func(arg.as_leading_term(x)) + if expr.is_finite: + return expr + else: + return self + + if x0 is S.ComplexInfinity: + return (1/arg).as_leading_term(x) + # Handling points lying on branch cuts (-I, I) + if x0.is_imaginary and (1 + x0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if re(ndir).is_positive: + if im(x0).is_positive: + return -self.func(x0) - I*pi + elif re(ndir).is_negative: + if im(x0).is_negative: + return -self.func(x0) + I*pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # acsch + from sympy.series.order import O + arg = self.args[0] + arg0 = arg.subs(x, 0) + + # Handling branch points + if arg0 is I: + t = Dummy('t', positive=True) + ser = acsch(I + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = -I + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else -I*pi/2 + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + res = ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + return res + + if arg0 == S.NegativeOne*I: + t = Dummy('t', positive=True) + ser = acsch(-I + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = I + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else I*pi/2 + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + + # Handling points lying on branch cuts (-I, I) + if arg0.is_imaginary and (1 + arg0**2).is_positive: + ndir = self.args[0].dir(x, cdir if cdir else 1) + if re(ndir).is_positive: + if im(arg0).is_positive: + return -res - I*pi + elif re(ndir).is_negative: + if im(arg0).is_negative: + return -res + I*pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return csch + + def _eval_rewrite_as_log(self, arg, **kwargs): + return log(1/arg + sqrt(1/arg**2 + 1)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_asinh(self, arg, **kwargs): + return asinh(1/arg) + + def _eval_rewrite_as_acosh(self, arg, **kwargs): + return I*(sqrt(1 - I/arg)/sqrt(I/arg - 1)* + acosh(I/arg, evaluate=False) - pi*S.Half) + + def _eval_rewrite_as_atanh(self, arg, **kwargs): + arg2 = arg**2 + arg2p1 = arg2 + 1 + return sqrt(-arg2)/arg*(pi*S.Half - + sqrt(-arg2p1**2)/arg2p1*atanh(sqrt(arg2p1))) + + def _eval_is_zero(self): + return self.args[0].is_infinite + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + def _eval_is_finite(self): + return fuzzy_not(self.args[0].is_zero) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/integers.py b/lib/python3.11/site-packages/sympy/functions/elementary/integers.py new file mode 100644 index 0000000000000000000000000000000000000000..bbbc7113c9c69e6b28e24296ad1073f37a1e193b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/integers.py @@ -0,0 +1,645 @@ +from typing import Tuple as tTuple + +from sympy.core.basic import Basic +from sympy.core.expr import Expr + +from sympy.core import Add, S +from sympy.core.evalf import get_integer_part, PrecisionExhausted +from sympy.core.function import Function +from sympy.core.logic import fuzzy_or +from sympy.core.numbers import Integer, int_valued +from sympy.core.relational import Gt, Lt, Ge, Le, Relational, is_eq +from sympy.core.sympify import _sympify +from sympy.functions.elementary.complexes import im, re +from sympy.multipledispatch import dispatch + +############################################################################### +######################### FLOOR and CEILING FUNCTIONS ######################### +############################################################################### + + +class RoundFunction(Function): + """Abstract base class for rounding functions.""" + + args: tTuple[Expr] + + @classmethod + def eval(cls, arg): + v = cls._eval_number(arg) + if v is not None: + return v + + if arg.is_integer or arg.is_finite is False: + return arg + if arg.is_imaginary or (S.ImaginaryUnit*arg).is_real: + i = im(arg) + if not i.has(S.ImaginaryUnit): + return cls(i)*S.ImaginaryUnit + return cls(arg, evaluate=False) + + # Integral, numerical, symbolic part + ipart = npart = spart = S.Zero + + # Extract integral (or complex integral) terms + intof = lambda x: int(x) if int_valued(x) else ( + x if x.is_integer else None) + for t in Add.make_args(arg): + if t.is_imaginary and (i := intof(im(t))) is not None: + ipart += i*S.ImaginaryUnit + elif (i := intof(t)) is not None: + ipart += i + elif t.is_number: + npart += t + else: + spart += t + + if not (npart or spart): + return ipart + + # Evaluate npart numerically if independent of spart + if npart and ( + not spart or + npart.is_real and (spart.is_imaginary or (S.ImaginaryUnit*spart).is_real) or + npart.is_imaginary and spart.is_real): + try: + r, i = get_integer_part( + npart, cls._dir, {}, return_ints=True) + ipart += Integer(r) + Integer(i)*S.ImaginaryUnit + npart = S.Zero + except (PrecisionExhausted, NotImplementedError): + pass + + spart += npart + if not spart: + return ipart + elif spart.is_imaginary or (S.ImaginaryUnit*spart).is_real: + return ipart + cls(im(spart), evaluate=False)*S.ImaginaryUnit + elif isinstance(spart, (floor, ceiling)): + return ipart + spart + else: + return ipart + cls(spart, evaluate=False) + + @classmethod + def _eval_number(cls, arg): + raise NotImplementedError() + + def _eval_is_finite(self): + return self.args[0].is_finite + + def _eval_is_real(self): + return self.args[0].is_real + + def _eval_is_integer(self): + return self.args[0].is_real + + +class floor(RoundFunction): + """ + Floor is a univariate function which returns the largest integer + value not greater than its argument. This implementation + generalizes floor to complex numbers by taking the floor of the + real and imaginary parts separately. + + Examples + ======== + + >>> from sympy import floor, E, I, S, Float, Rational + >>> floor(17) + 17 + >>> floor(Rational(23, 10)) + 2 + >>> floor(2*E) + 5 + >>> floor(-Float(0.567)) + -1 + >>> floor(-I/2) + -I + >>> floor(S(5)/2 + 5*I/2) + 2 + 2*I + + See Also + ======== + + sympy.functions.elementary.integers.ceiling + + References + ========== + + .. [1] "Concrete mathematics" by Graham, pp. 87 + .. [2] https://mathworld.wolfram.com/FloorFunction.html + + """ + _dir = -1 + + @classmethod + def _eval_number(cls, arg): + if arg.is_Number: + return arg.floor() + elif any(isinstance(i, j) + for i in (arg, -arg) for j in (floor, ceiling)): + return arg + if arg.is_NumberSymbol: + return arg.approximation_interval(Integer)[0] + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + if arg0 is S.NaN or isinstance(arg0, AccumBounds): + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + r = floor(arg0) + if arg0.is_finite: + if arg0 == r: + ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1) + if ndir.is_negative: + return r - 1 + elif ndir.is_positive: + return r + else: + raise NotImplementedError("Not sure of sign of %s" % ndir) + else: + return r + return arg.as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + r = floor(arg0) + if arg0.is_infinite: + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.series.order import Order + s = arg._eval_nseries(x, n, logx, cdir) + o = Order(1, (x, 0)) if n <= 0 else AccumBounds(-1, 0) + return s + o + if arg0 == r: + ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1) + if ndir.is_negative: + return r - 1 + elif ndir.is_positive: + return r + else: + raise NotImplementedError("Not sure of sign of %s" % ndir) + else: + return r + + def _eval_is_negative(self): + return self.args[0].is_negative + + def _eval_is_nonnegative(self): + return self.args[0].is_nonnegative + + def _eval_rewrite_as_ceiling(self, arg, **kwargs): + return -ceiling(-arg) + + def _eval_rewrite_as_frac(self, arg, **kwargs): + return arg - frac(arg) + + def __le__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] < other + 1 + if other.is_number and other.is_real: + return self.args[0] < ceiling(other) + if self.args[0] == other and other.is_real: + return S.true + if other is S.Infinity and self.is_finite: + return S.true + + return Le(self, other, evaluate=False) + + def __ge__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] >= other + if other.is_number and other.is_real: + return self.args[0] >= ceiling(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.NegativeInfinity and self.is_finite: + return S.true + + return Ge(self, other, evaluate=False) + + def __gt__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] >= other + 1 + if other.is_number and other.is_real: + return self.args[0] >= ceiling(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.NegativeInfinity and self.is_finite: + return S.true + + return Gt(self, other, evaluate=False) + + def __lt__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] < other + if other.is_number and other.is_real: + return self.args[0] < ceiling(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.Infinity and self.is_finite: + return S.true + + return Lt(self, other, evaluate=False) + + +@dispatch(floor, Expr) +def _eval_is_eq(lhs, rhs): # noqa:F811 + return is_eq(lhs.rewrite(ceiling), rhs) or \ + is_eq(lhs.rewrite(frac),rhs) + + +class ceiling(RoundFunction): + """ + Ceiling is a univariate function which returns the smallest integer + value not less than its argument. This implementation + generalizes ceiling to complex numbers by taking the ceiling of the + real and imaginary parts separately. + + Examples + ======== + + >>> from sympy import ceiling, E, I, S, Float, Rational + >>> ceiling(17) + 17 + >>> ceiling(Rational(23, 10)) + 3 + >>> ceiling(2*E) + 6 + >>> ceiling(-Float(0.567)) + 0 + >>> ceiling(I/2) + I + >>> ceiling(S(5)/2 + 5*I/2) + 3 + 3*I + + See Also + ======== + + sympy.functions.elementary.integers.floor + + References + ========== + + .. [1] "Concrete mathematics" by Graham, pp. 87 + .. [2] https://mathworld.wolfram.com/CeilingFunction.html + + """ + _dir = 1 + + @classmethod + def _eval_number(cls, arg): + if arg.is_Number: + return arg.ceiling() + elif any(isinstance(i, j) + for i in (arg, -arg) for j in (floor, ceiling)): + return arg + if arg.is_NumberSymbol: + return arg.approximation_interval(Integer)[1] + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + if arg0 is S.NaN or isinstance(arg0, AccumBounds): + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + r = ceiling(arg0) + if arg0.is_finite: + if arg0 == r: + ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1) + if ndir.is_negative: + return r + elif ndir.is_positive: + return r + 1 + else: + raise NotImplementedError("Not sure of sign of %s" % ndir) + else: + return r + return arg.as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + r = ceiling(arg0) + if arg0.is_infinite: + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.series.order import Order + s = arg._eval_nseries(x, n, logx, cdir) + o = Order(1, (x, 0)) if n <= 0 else AccumBounds(0, 1) + return s + o + if arg0 == r: + ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1) + if ndir.is_negative: + return r + elif ndir.is_positive: + return r + 1 + else: + raise NotImplementedError("Not sure of sign of %s" % ndir) + else: + return r + + def _eval_rewrite_as_floor(self, arg, **kwargs): + return -floor(-arg) + + def _eval_rewrite_as_frac(self, arg, **kwargs): + return arg + frac(-arg) + + def _eval_is_positive(self): + return self.args[0].is_positive + + def _eval_is_nonpositive(self): + return self.args[0].is_nonpositive + + def __lt__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] <= other - 1 + if other.is_number and other.is_real: + return self.args[0] <= floor(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.Infinity and self.is_finite: + return S.true + + return Lt(self, other, evaluate=False) + + def __gt__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] > other + if other.is_number and other.is_real: + return self.args[0] > floor(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.NegativeInfinity and self.is_finite: + return S.true + + return Gt(self, other, evaluate=False) + + def __ge__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] > other - 1 + if other.is_number and other.is_real: + return self.args[0] > floor(other) + if self.args[0] == other and other.is_real: + return S.true + if other is S.NegativeInfinity and self.is_finite: + return S.true + + return Ge(self, other, evaluate=False) + + def __le__(self, other): + other = S(other) + if self.args[0].is_real: + if other.is_integer: + return self.args[0] <= other + if other.is_number and other.is_real: + return self.args[0] <= floor(other) + if self.args[0] == other and other.is_real: + return S.false + if other is S.Infinity and self.is_finite: + return S.true + + return Le(self, other, evaluate=False) + + +@dispatch(ceiling, Basic) # type:ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + return is_eq(lhs.rewrite(floor), rhs) or is_eq(lhs.rewrite(frac),rhs) + + +class frac(Function): + r"""Represents the fractional part of x + + For real numbers it is defined [1]_ as + + .. math:: + x - \left\lfloor{x}\right\rfloor + + Examples + ======== + + >>> from sympy import Symbol, frac, Rational, floor, I + >>> frac(Rational(4, 3)) + 1/3 + >>> frac(-Rational(4, 3)) + 2/3 + + returns zero for integer arguments + + >>> n = Symbol('n', integer=True) + >>> frac(n) + 0 + + rewrite as floor + + >>> x = Symbol('x') + >>> frac(x).rewrite(floor) + x - floor(x) + + for complex arguments + + >>> r = Symbol('r', real=True) + >>> t = Symbol('t', real=True) + >>> frac(t + I*r) + I*frac(r) + frac(t) + + See Also + ======== + + sympy.functions.elementary.integers.floor + sympy.functions.elementary.integers.ceiling + + References + =========== + + .. [1] https://en.wikipedia.org/wiki/Fractional_part + .. [2] https://mathworld.wolfram.com/FractionalPart.html + + """ + @classmethod + def eval(cls, arg): + from sympy.calculus.accumulationbounds import AccumBounds + + def _eval(arg): + if arg in (S.Infinity, S.NegativeInfinity): + return AccumBounds(0, 1) + if arg.is_integer: + return S.Zero + if arg.is_number: + if arg is S.NaN: + return S.NaN + elif arg is S.ComplexInfinity: + return S.NaN + else: + return arg - floor(arg) + return cls(arg, evaluate=False) + + real, imag = S.Zero, S.Zero + for t in Add.make_args(arg): + # Two checks are needed for complex arguments + # see issue-7649 for details + if t.is_imaginary or (S.ImaginaryUnit*t).is_real: + i = im(t) + if not i.has(S.ImaginaryUnit): + imag += i + else: + real += t + else: + real += t + + real = _eval(real) + imag = _eval(imag) + return real + S.ImaginaryUnit*imag + + def _eval_rewrite_as_floor(self, arg, **kwargs): + return arg - floor(arg) + + def _eval_rewrite_as_ceiling(self, arg, **kwargs): + return arg + ceiling(-arg) + + def _eval_is_finite(self): + return True + + def _eval_is_real(self): + return self.args[0].is_extended_real + + def _eval_is_imaginary(self): + return self.args[0].is_imaginary + + def _eval_is_integer(self): + return self.args[0].is_integer + + def _eval_is_zero(self): + return fuzzy_or([self.args[0].is_zero, self.args[0].is_integer]) + + def _eval_is_negative(self): + return False + + def __ge__(self, other): + if self.is_extended_real: + other = _sympify(other) + # Check if other <= 0 + if other.is_extended_nonpositive: + return S.true + # Check if other >= 1 + res = self._value_one_or_more(other) + if res is not None: + return not(res) + return Ge(self, other, evaluate=False) + + def __gt__(self, other): + if self.is_extended_real: + other = _sympify(other) + # Check if other < 0 + res = self._value_one_or_more(other) + if res is not None: + return not(res) + # Check if other >= 1 + if other.is_extended_negative: + return S.true + return Gt(self, other, evaluate=False) + + def __le__(self, other): + if self.is_extended_real: + other = _sympify(other) + # Check if other < 0 + if other.is_extended_negative: + return S.false + # Check if other >= 1 + res = self._value_one_or_more(other) + if res is not None: + return res + return Le(self, other, evaluate=False) + + def __lt__(self, other): + if self.is_extended_real: + other = _sympify(other) + # Check if other <= 0 + if other.is_extended_nonpositive: + return S.false + # Check if other >= 1 + res = self._value_one_or_more(other) + if res is not None: + return res + return Lt(self, other, evaluate=False) + + def _value_one_or_more(self, other): + if other.is_extended_real: + if other.is_number: + res = other >= 1 + if res and not isinstance(res, Relational): + return S.true + if other.is_integer and other.is_positive: + return S.true + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + + if arg0.is_finite: + if r.is_zero: + ndir = arg.dir(x, cdir=cdir) + if ndir.is_negative: + return S.One + return (arg - arg0).as_leading_term(x, logx=logx, cdir=cdir) + else: + return r + elif arg0 in (S.ComplexInfinity, S.Infinity, S.NegativeInfinity): + return AccumBounds(0, 1) + return arg.as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.series.order import Order + arg = self.args[0] + arg0 = arg.subs(x, 0) + r = self.subs(x, 0) + + if arg0.is_infinite: + from sympy.calculus.accumulationbounds import AccumBounds + o = Order(1, (x, 0)) if n <= 0 else AccumBounds(0, 1) + Order(x**n, (x, 0)) + return o + else: + res = (arg - arg0)._eval_nseries(x, n, logx=logx, cdir=cdir) + if r.is_zero: + ndir = arg.dir(x, cdir=cdir) + res += S.One if ndir.is_negative else S.Zero + else: + res += r + return res + + +@dispatch(frac, Basic) # type:ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + if (lhs.rewrite(floor) == rhs) or \ + (lhs.rewrite(ceiling) == rhs): + return True + # Check if other < 0 + if rhs.is_extended_negative: + return False + # Check if other >= 1 + res = lhs._value_one_or_more(rhs) + if res is not None: + return False diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/miscellaneous.py b/lib/python3.11/site-packages/sympy/functions/elementary/miscellaneous.py new file mode 100644 index 0000000000000000000000000000000000000000..a59f0c9b525f1d19c32bdf9fe51fdd01aaf172e9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/miscellaneous.py @@ -0,0 +1,915 @@ +from sympy.core import Function, S, sympify, NumberKind +from sympy.utilities.iterables import sift +from sympy.core.add import Add +from sympy.core.containers import Tuple +from sympy.core.operations import LatticeOp, ShortCircuit +from sympy.core.function import (Application, Lambda, + ArgumentIndexError) +from sympy.core.expr import Expr +from sympy.core.exprtools import factor_terms +from sympy.core.mod import Mod +from sympy.core.mul import Mul +from sympy.core.numbers import Rational +from sympy.core.power import Pow +from sympy.core.relational import Eq, Relational +from sympy.core.singleton import Singleton +from sympy.core.sorting import ordered +from sympy.core.symbol import Dummy +from sympy.core.rules import Transform +from sympy.core.logic import fuzzy_and, fuzzy_or, _torf +from sympy.core.traversal import walk +from sympy.core.numbers import Integer +from sympy.logic.boolalg import And, Or + + +def _minmax_as_Piecewise(op, *args): + # helper for Min/Max rewrite as Piecewise + from sympy.functions.elementary.piecewise import Piecewise + ec = [] + for i, a in enumerate(args): + c = [Relational(a, args[j], op) for j in range(i + 1, len(args))] + ec.append((a, And(*c))) + return Piecewise(*ec) + + +class IdentityFunction(Lambda, metaclass=Singleton): + """ + The identity function + + Examples + ======== + + >>> from sympy import Id, Symbol + >>> x = Symbol('x') + >>> Id(x) + x + + """ + + _symbol = Dummy('x') + + @property + def signature(self): + return Tuple(self._symbol) + + @property + def expr(self): + return self._symbol + + +Id = S.IdentityFunction + +############################################################################### +############################# ROOT and SQUARE ROOT FUNCTION ################### +############################################################################### + + +def sqrt(arg, evaluate=None): + """Returns the principal square root. + + Parameters + ========== + + evaluate : bool, optional + The parameter determines if the expression should be evaluated. + If ``None``, its value is taken from + ``global_parameters.evaluate``. + + Examples + ======== + + >>> from sympy import sqrt, Symbol, S + >>> x = Symbol('x') + + >>> sqrt(x) + sqrt(x) + + >>> sqrt(x)**2 + x + + Note that sqrt(x**2) does not simplify to x. + + >>> sqrt(x**2) + sqrt(x**2) + + This is because the two are not equal to each other in general. + For example, consider x == -1: + + >>> from sympy import Eq + >>> Eq(sqrt(x**2), x).subs(x, -1) + False + + This is because sqrt computes the principal square root, so the square may + put the argument in a different branch. This identity does hold if x is + positive: + + >>> y = Symbol('y', positive=True) + >>> sqrt(y**2) + y + + You can force this simplification by using the powdenest() function with + the force option set to True: + + >>> from sympy import powdenest + >>> sqrt(x**2) + sqrt(x**2) + >>> powdenest(sqrt(x**2), force=True) + x + + To get both branches of the square root you can use the rootof function: + + >>> from sympy import rootof + + >>> [rootof(x**2-3,i) for i in (0,1)] + [-sqrt(3), sqrt(3)] + + Although ``sqrt`` is printed, there is no ``sqrt`` function so looking for + ``sqrt`` in an expression will fail: + + >>> from sympy.utilities.misc import func_name + >>> func_name(sqrt(x)) + 'Pow' + >>> sqrt(x).has(sqrt) + False + + To find ``sqrt`` look for ``Pow`` with an exponent of ``1/2``: + + >>> (x + 1/sqrt(x)).find(lambda i: i.is_Pow and abs(i.exp) is S.Half) + {1/sqrt(x)} + + See Also + ======== + + sympy.polys.rootoftools.rootof, root, real_root + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Square_root + .. [2] https://en.wikipedia.org/wiki/Principal_value + """ + # arg = sympify(arg) is handled by Pow + return Pow(arg, S.Half, evaluate=evaluate) + + +def cbrt(arg, evaluate=None): + """Returns the principal cube root. + + Parameters + ========== + + evaluate : bool, optional + The parameter determines if the expression should be evaluated. + If ``None``, its value is taken from + ``global_parameters.evaluate``. + + Examples + ======== + + >>> from sympy import cbrt, Symbol + >>> x = Symbol('x') + + >>> cbrt(x) + x**(1/3) + + >>> cbrt(x)**3 + x + + Note that cbrt(x**3) does not simplify to x. + + >>> cbrt(x**3) + (x**3)**(1/3) + + This is because the two are not equal to each other in general. + For example, consider `x == -1`: + + >>> from sympy import Eq + >>> Eq(cbrt(x**3), x).subs(x, -1) + False + + This is because cbrt computes the principal cube root, this + identity does hold if `x` is positive: + + >>> y = Symbol('y', positive=True) + >>> cbrt(y**3) + y + + See Also + ======== + + sympy.polys.rootoftools.rootof, root, real_root + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Cube_root + .. [2] https://en.wikipedia.org/wiki/Principal_value + + """ + return Pow(arg, Rational(1, 3), evaluate=evaluate) + + +def root(arg, n, k=0, evaluate=None): + r"""Returns the *k*-th *n*-th root of ``arg``. + + Parameters + ========== + + k : int, optional + Should be an integer in $\{0, 1, ..., n-1\}$. + Defaults to the principal root if $0$. + + evaluate : bool, optional + The parameter determines if the expression should be evaluated. + If ``None``, its value is taken from + ``global_parameters.evaluate``. + + Examples + ======== + + >>> from sympy import root, Rational + >>> from sympy.abc import x, n + + >>> root(x, 2) + sqrt(x) + + >>> root(x, 3) + x**(1/3) + + >>> root(x, n) + x**(1/n) + + >>> root(x, -Rational(2, 3)) + x**(-3/2) + + To get the k-th n-th root, specify k: + + >>> root(-2, 3, 2) + -(-1)**(2/3)*2**(1/3) + + To get all n n-th roots you can use the rootof function. + The following examples show the roots of unity for n + equal 2, 3 and 4: + + >>> from sympy import rootof + + >>> [rootof(x**2 - 1, i) for i in range(2)] + [-1, 1] + + >>> [rootof(x**3 - 1,i) for i in range(3)] + [1, -1/2 - sqrt(3)*I/2, -1/2 + sqrt(3)*I/2] + + >>> [rootof(x**4 - 1,i) for i in range(4)] + [-1, 1, -I, I] + + SymPy, like other symbolic algebra systems, returns the + complex root of negative numbers. This is the principal + root and differs from the text-book result that one might + be expecting. For example, the cube root of -8 does not + come back as -2: + + >>> root(-8, 3) + 2*(-1)**(1/3) + + The real_root function can be used to either make the principal + result real (or simply to return the real root directly): + + >>> from sympy import real_root + >>> real_root(_) + -2 + >>> real_root(-32, 5) + -2 + + Alternatively, the n//2-th n-th root of a negative number can be + computed with root: + + >>> root(-32, 5, 5//2) + -2 + + See Also + ======== + + sympy.polys.rootoftools.rootof + sympy.core.intfunc.integer_nthroot + sqrt, real_root + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Square_root + .. [2] https://en.wikipedia.org/wiki/Real_root + .. [3] https://en.wikipedia.org/wiki/Root_of_unity + .. [4] https://en.wikipedia.org/wiki/Principal_value + .. [5] https://mathworld.wolfram.com/CubeRoot.html + + """ + n = sympify(n) + if k: + return Mul(Pow(arg, S.One/n, evaluate=evaluate), S.NegativeOne**(2*k/n), evaluate=evaluate) + return Pow(arg, 1/n, evaluate=evaluate) + + +def real_root(arg, n=None, evaluate=None): + r"""Return the real *n*'th-root of *arg* if possible. + + Parameters + ========== + + n : int or None, optional + If *n* is ``None``, then all instances of + $(-n)^{1/\text{odd}}$ will be changed to $-n^{1/\text{odd}}$. + This will only create a real root of a principal root. + The presence of other factors may cause the result to not be + real. + + evaluate : bool, optional + The parameter determines if the expression should be evaluated. + If ``None``, its value is taken from + ``global_parameters.evaluate``. + + Examples + ======== + + >>> from sympy import root, real_root + + >>> real_root(-8, 3) + -2 + >>> root(-8, 3) + 2*(-1)**(1/3) + >>> real_root(_) + -2 + + If one creates a non-principal root and applies real_root, the + result will not be real (so use with caution): + + >>> root(-8, 3, 2) + -2*(-1)**(2/3) + >>> real_root(_) + -2*(-1)**(2/3) + + See Also + ======== + + sympy.polys.rootoftools.rootof + sympy.core.intfunc.integer_nthroot + root, sqrt + """ + from sympy.functions.elementary.complexes import Abs, im, sign + from sympy.functions.elementary.piecewise import Piecewise + if n is not None: + return Piecewise( + (root(arg, n, evaluate=evaluate), Or(Eq(n, S.One), Eq(n, S.NegativeOne))), + (Mul(sign(arg), root(Abs(arg), n, evaluate=evaluate), evaluate=evaluate), + And(Eq(im(arg), S.Zero), Eq(Mod(n, 2), S.One))), + (root(arg, n, evaluate=evaluate), True)) + rv = sympify(arg) + n1pow = Transform(lambda x: -(-x.base)**x.exp, + lambda x: + x.is_Pow and + x.base.is_negative and + x.exp.is_Rational and + x.exp.p == 1 and x.exp.q % 2) + return rv.xreplace(n1pow) + +############################################################################### +############################# MINIMUM and MAXIMUM ############################# +############################################################################### + + +class MinMaxBase(Expr, LatticeOp): + def __new__(cls, *args, **assumptions): + from sympy.core.parameters import global_parameters + evaluate = assumptions.pop('evaluate', global_parameters.evaluate) + args = (sympify(arg) for arg in args) + + # first standard filter, for cls.zero and cls.identity + # also reshape Max(a, Max(b, c)) to Max(a, b, c) + + if evaluate: + try: + args = frozenset(cls._new_args_filter(args)) + except ShortCircuit: + return cls.zero + # remove redundant args that are easily identified + args = cls._collapse_arguments(args, **assumptions) + # find local zeros + args = cls._find_localzeros(args, **assumptions) + args = frozenset(args) + + if not args: + return cls.identity + + if len(args) == 1: + return list(args).pop() + + # base creation + obj = Expr.__new__(cls, *ordered(args), **assumptions) + obj._argset = args + return obj + + @classmethod + def _collapse_arguments(cls, args, **assumptions): + """Remove redundant args. + + Examples + ======== + + >>> from sympy import Min, Max + >>> from sympy.abc import a, b, c, d, e + + Any arg in parent that appears in any + parent-like function in any of the flat args + of parent can be removed from that sub-arg: + + >>> Min(a, Max(b, Min(a, c, d))) + Min(a, Max(b, Min(c, d))) + + If the arg of parent appears in an opposite-than parent + function in any of the flat args of parent that function + can be replaced with the arg: + + >>> Min(a, Max(b, Min(c, d, Max(a, e)))) + Min(a, Max(b, Min(a, c, d))) + """ + if not args: + return args + args = list(ordered(args)) + if cls == Min: + other = Max + else: + other = Min + + # find global comparable max of Max and min of Min if a new + # value is being introduced in these args at position 0 of + # the ordered args + if args[0].is_number: + sifted = mins, maxs = [], [] + for i in args: + for v in walk(i, Min, Max): + if v.args[0].is_comparable: + sifted[isinstance(v, Max)].append(v) + small = Min.identity + for i in mins: + v = i.args[0] + if v.is_number and (v < small) == True: + small = v + big = Max.identity + for i in maxs: + v = i.args[0] + if v.is_number and (v > big) == True: + big = v + # at the point when this function is called from __new__, + # there may be more than one numeric arg present since + # local zeros have not been handled yet, so look through + # more than the first arg + if cls == Min: + for arg in args: + if not arg.is_number: + break + if (arg < small) == True: + small = arg + elif cls == Max: + for arg in args: + if not arg.is_number: + break + if (arg > big) == True: + big = arg + T = None + if cls == Min: + if small != Min.identity: + other = Max + T = small + elif big != Max.identity: + other = Min + T = big + if T is not None: + # remove numerical redundancy + for i in range(len(args)): + a = args[i] + if isinstance(a, other): + a0 = a.args[0] + if ((a0 > T) if other == Max else (a0 < T)) == True: + args[i] = cls.identity + + # remove redundant symbolic args + def do(ai, a): + if not isinstance(ai, (Min, Max)): + return ai + cond = a in ai.args + if not cond: + return ai.func(*[do(i, a) for i in ai.args], + evaluate=False) + if isinstance(ai, cls): + return ai.func(*[do(i, a) for i in ai.args if i != a], + evaluate=False) + return a + for i, a in enumerate(args): + args[i + 1:] = [do(ai, a) for ai in args[i + 1:]] + + # factor out common elements as for + # Min(Max(x, y), Max(x, z)) -> Max(x, Min(y, z)) + # and vice versa when swapping Min/Max -- do this only for the + # easy case where all functions contain something in common; + # trying to find some optimal subset of args to modify takes + # too long + + def factor_minmax(args): + is_other = lambda arg: isinstance(arg, other) + other_args, remaining_args = sift(args, is_other, binary=True) + if not other_args: + return args + + # Min(Max(x, y, z), Max(x, y, u, v)) -> {x,y}, ({z}, {u,v}) + arg_sets = [set(arg.args) for arg in other_args] + common = set.intersection(*arg_sets) + if not common: + return args + + new_other_args = list(common) + arg_sets_diff = [arg_set - common for arg_set in arg_sets] + + # If any set is empty after removing common then all can be + # discarded e.g. Min(Max(a, b, c), Max(a, b)) -> Max(a, b) + if all(arg_sets_diff): + other_args_diff = [other(*s, evaluate=False) for s in arg_sets_diff] + new_other_args.append(cls(*other_args_diff, evaluate=False)) + + other_args_factored = other(*new_other_args, evaluate=False) + return remaining_args + [other_args_factored] + + if len(args) > 1: + args = factor_minmax(args) + + return args + + @classmethod + def _new_args_filter(cls, arg_sequence): + """ + Generator filtering args. + + first standard filter, for cls.zero and cls.identity. + Also reshape ``Max(a, Max(b, c))`` to ``Max(a, b, c)``, + and check arguments for comparability + """ + for arg in arg_sequence: + # pre-filter, checking comparability of arguments + if not isinstance(arg, Expr) or arg.is_extended_real is False or ( + arg.is_number and + not arg.is_comparable): + raise ValueError("The argument '%s' is not comparable." % arg) + + if arg == cls.zero: + raise ShortCircuit(arg) + elif arg == cls.identity: + continue + elif arg.func == cls: + yield from arg.args + else: + yield arg + + @classmethod + def _find_localzeros(cls, values, **options): + """ + Sequentially allocate values to localzeros. + + When a value is identified as being more extreme than another member it + replaces that member; if this is never true, then the value is simply + appended to the localzeros. + """ + localzeros = set() + for v in values: + is_newzero = True + localzeros_ = list(localzeros) + for z in localzeros_: + if id(v) == id(z): + is_newzero = False + else: + con = cls._is_connected(v, z) + if con: + is_newzero = False + if con is True or con == cls: + localzeros.remove(z) + localzeros.update([v]) + if is_newzero: + localzeros.update([v]) + return localzeros + + @classmethod + def _is_connected(cls, x, y): + """ + Check if x and y are connected somehow. + """ + for i in range(2): + if x == y: + return True + t, f = Max, Min + for op in "><": + for j in range(2): + try: + if op == ">": + v = x >= y + else: + v = x <= y + except TypeError: + return False # non-real arg + if not v.is_Relational: + return t if v else f + t, f = f, t + x, y = y, x + x, y = y, x # run next pass with reversed order relative to start + # simplification can be expensive, so be conservative + # in what is attempted + x = factor_terms(x - y) + y = S.Zero + + return False + + def _eval_derivative(self, s): + # f(x).diff(s) -> x.diff(s) * f.fdiff(1)(s) + i = 0 + l = [] + for a in self.args: + i += 1 + da = a.diff(s) + if da.is_zero: + continue + try: + df = self.fdiff(i) + except ArgumentIndexError: + df = Function.fdiff(self, i) + l.append(df * da) + return Add(*l) + + def _eval_rewrite_as_Abs(self, *args, **kwargs): + from sympy.functions.elementary.complexes import Abs + s = (args[0] + self.func(*args[1:]))/2 + d = abs(args[0] - self.func(*args[1:]))/2 + return (s + d if isinstance(self, Max) else s - d).rewrite(Abs) + + def evalf(self, n=15, **options): + return self.func(*[a.evalf(n, **options) for a in self.args]) + + def n(self, *args, **kwargs): + return self.evalf(*args, **kwargs) + + _eval_is_algebraic = lambda s: _torf(i.is_algebraic for i in s.args) + _eval_is_antihermitian = lambda s: _torf(i.is_antihermitian for i in s.args) + _eval_is_commutative = lambda s: _torf(i.is_commutative for i in s.args) + _eval_is_complex = lambda s: _torf(i.is_complex for i in s.args) + _eval_is_composite = lambda s: _torf(i.is_composite for i in s.args) + _eval_is_even = lambda s: _torf(i.is_even for i in s.args) + _eval_is_finite = lambda s: _torf(i.is_finite for i in s.args) + _eval_is_hermitian = lambda s: _torf(i.is_hermitian for i in s.args) + _eval_is_imaginary = lambda s: _torf(i.is_imaginary for i in s.args) + _eval_is_infinite = lambda s: _torf(i.is_infinite for i in s.args) + _eval_is_integer = lambda s: _torf(i.is_integer for i in s.args) + _eval_is_irrational = lambda s: _torf(i.is_irrational for i in s.args) + _eval_is_negative = lambda s: _torf(i.is_negative for i in s.args) + _eval_is_noninteger = lambda s: _torf(i.is_noninteger for i in s.args) + _eval_is_nonnegative = lambda s: _torf(i.is_nonnegative for i in s.args) + _eval_is_nonpositive = lambda s: _torf(i.is_nonpositive for i in s.args) + _eval_is_nonzero = lambda s: _torf(i.is_nonzero for i in s.args) + _eval_is_odd = lambda s: _torf(i.is_odd for i in s.args) + _eval_is_polar = lambda s: _torf(i.is_polar for i in s.args) + _eval_is_positive = lambda s: _torf(i.is_positive for i in s.args) + _eval_is_prime = lambda s: _torf(i.is_prime for i in s.args) + _eval_is_rational = lambda s: _torf(i.is_rational for i in s.args) + _eval_is_real = lambda s: _torf(i.is_real for i in s.args) + _eval_is_extended_real = lambda s: _torf(i.is_extended_real for i in s.args) + _eval_is_transcendental = lambda s: _torf(i.is_transcendental for i in s.args) + _eval_is_zero = lambda s: _torf(i.is_zero for i in s.args) + + +class Max(MinMaxBase, Application): + r""" + Return, if possible, the maximum value of the list. + + When number of arguments is equal one, then + return this argument. + + When number of arguments is equal two, then + return, if possible, the value from (a, b) that is $\ge$ the other. + + In common case, when the length of list greater than 2, the task + is more complicated. Return only the arguments, which are greater + than others, if it is possible to determine directional relation. + + If is not possible to determine such a relation, return a partially + evaluated result. + + Assumptions are used to make the decision too. + + Also, only comparable arguments are permitted. + + It is named ``Max`` and not ``max`` to avoid conflicts + with the built-in function ``max``. + + + Examples + ======== + + >>> from sympy import Max, Symbol, oo + >>> from sympy.abc import x, y, z + >>> p = Symbol('p', positive=True) + >>> n = Symbol('n', negative=True) + + >>> Max(x, -2) + Max(-2, x) + >>> Max(x, -2).subs(x, 3) + 3 + >>> Max(p, -2) + p + >>> Max(x, y) + Max(x, y) + >>> Max(x, y) == Max(y, x) + True + >>> Max(x, Max(y, z)) + Max(x, y, z) + >>> Max(n, 8, p, 7, -oo) + Max(8, p) + >>> Max (1, x, oo) + oo + + * Algorithm + + The task can be considered as searching of supremums in the + directed complete partial orders [1]_. + + The source values are sequentially allocated by the isolated subsets + in which supremums are searched and result as Max arguments. + + If the resulted supremum is single, then it is returned. + + The isolated subsets are the sets of values which are only the comparable + with each other in the current set. E.g. natural numbers are comparable with + each other, but not comparable with the `x` symbol. Another example: the + symbol `x` with negative assumption is comparable with a natural number. + + Also there are "least" elements, which are comparable with all others, + and have a zero property (maximum or minimum for all elements). + For example, in case of $\infty$, the allocation operation is terminated + and only this value is returned. + + Assumption: + - if $A > B > C$ then $A > C$ + - if $A = B$ then $B$ can be removed + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Directed_complete_partial_order + .. [2] https://en.wikipedia.org/wiki/Lattice_%28order%29 + + See Also + ======== + + Min : find minimum values + """ + zero = S.Infinity + identity = S.NegativeInfinity + + def fdiff( self, argindex ): + from sympy.functions.special.delta_functions import Heaviside + n = len(self.args) + if 0 < argindex and argindex <= n: + argindex -= 1 + if n == 2: + return Heaviside(self.args[argindex] - self.args[1 - argindex]) + newargs = tuple([self.args[i] for i in range(n) if i != argindex]) + return Heaviside(self.args[argindex] - Max(*newargs)) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Heaviside(self, *args, **kwargs): + from sympy.functions.special.delta_functions import Heaviside + return Add(*[j*Mul(*[Heaviside(j - i) for i in args if i!=j]) \ + for j in args]) + + def _eval_rewrite_as_Piecewise(self, *args, **kwargs): + return _minmax_as_Piecewise('>=', *args) + + def _eval_is_positive(self): + return fuzzy_or(a.is_positive for a in self.args) + + def _eval_is_nonnegative(self): + return fuzzy_or(a.is_nonnegative for a in self.args) + + def _eval_is_negative(self): + return fuzzy_and(a.is_negative for a in self.args) + + +class Min(MinMaxBase, Application): + """ + Return, if possible, the minimum value of the list. + It is named ``Min`` and not ``min`` to avoid conflicts + with the built-in function ``min``. + + Examples + ======== + + >>> from sympy import Min, Symbol, oo + >>> from sympy.abc import x, y + >>> p = Symbol('p', positive=True) + >>> n = Symbol('n', negative=True) + + >>> Min(x, -2) + Min(-2, x) + >>> Min(x, -2).subs(x, 3) + -2 + >>> Min(p, -3) + -3 + >>> Min(x, y) + Min(x, y) + >>> Min(n, 8, p, -7, p, oo) + Min(-7, n) + + See Also + ======== + + Max : find maximum values + """ + zero = S.NegativeInfinity + identity = S.Infinity + + def fdiff( self, argindex ): + from sympy.functions.special.delta_functions import Heaviside + n = len(self.args) + if 0 < argindex and argindex <= n: + argindex -= 1 + if n == 2: + return Heaviside( self.args[1-argindex] - self.args[argindex] ) + newargs = tuple([ self.args[i] for i in range(n) if i != argindex]) + return Heaviside( Min(*newargs) - self.args[argindex] ) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Heaviside(self, *args, **kwargs): + from sympy.functions.special.delta_functions import Heaviside + return Add(*[j*Mul(*[Heaviside(i-j) for i in args if i!=j]) \ + for j in args]) + + def _eval_rewrite_as_Piecewise(self, *args, **kwargs): + return _minmax_as_Piecewise('<=', *args) + + def _eval_is_positive(self): + return fuzzy_and(a.is_positive for a in self.args) + + def _eval_is_nonnegative(self): + return fuzzy_and(a.is_nonnegative for a in self.args) + + def _eval_is_negative(self): + return fuzzy_or(a.is_negative for a in self.args) + + +class Rem(Function): + """Returns the remainder when ``p`` is divided by ``q`` where ``p`` is finite + and ``q`` is not equal to zero. The result, ``p - int(p/q)*q``, has the same sign + as the divisor. + + Parameters + ========== + + p : Expr + Dividend. + + q : Expr + Divisor. + + Notes + ===== + + ``Rem`` corresponds to the ``%`` operator in C. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import Rem + >>> Rem(x**3, y) + Rem(x**3, y) + >>> Rem(x**3, y).subs({x: -5, y: 3}) + -2 + + See Also + ======== + + Mod + """ + kind = NumberKind + + @classmethod + def eval(cls, p, q): + """Return the function remainder if both p, q are numbers and q is not + zero. + """ + + if q.is_zero: + raise ZeroDivisionError("Division by zero") + if p is S.NaN or q is S.NaN or p.is_finite is False or q.is_finite is False: + return S.NaN + if p is S.Zero or p in (q, -q) or (p.is_integer and q == 1): + return S.Zero + + if q.is_Number: + if p.is_Number: + return p - Integer(p/q)*q diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/piecewise.py b/lib/python3.11/site-packages/sympy/functions/elementary/piecewise.py new file mode 100644 index 0000000000000000000000000000000000000000..016fe3f4e75a5de8ed40db984c0133685dc95745 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/piecewise.py @@ -0,0 +1,1516 @@ +from sympy.core import S, Function, diff, Tuple, Dummy, Mul +from sympy.core.basic import Basic, as_Basic +from sympy.core.numbers import Rational, NumberSymbol, _illegal +from sympy.core.parameters import global_parameters +from sympy.core.relational import (Lt, Gt, Eq, Ne, Relational, + _canonical, _canonical_coeff) +from sympy.core.sorting import ordered +from sympy.functions.elementary.miscellaneous import Max, Min +from sympy.logic.boolalg import (And, Boolean, distribute_and_over_or, Not, + true, false, Or, ITE, simplify_logic, to_cnf, distribute_or_over_and) +from sympy.utilities.iterables import uniq, sift, common_prefix +from sympy.utilities.misc import filldedent, func_name + +from itertools import product + +Undefined = S.NaN # Piecewise() + +class ExprCondPair(Tuple): + """Represents an expression, condition pair.""" + + def __new__(cls, expr, cond): + expr = as_Basic(expr) + if cond == True: + return Tuple.__new__(cls, expr, true) + elif cond == False: + return Tuple.__new__(cls, expr, false) + elif isinstance(cond, Basic) and cond.has(Piecewise): + cond = piecewise_fold(cond) + if isinstance(cond, Piecewise): + cond = cond.rewrite(ITE) + + if not isinstance(cond, Boolean): + raise TypeError(filldedent(''' + Second argument must be a Boolean, + not `%s`''' % func_name(cond))) + return Tuple.__new__(cls, expr, cond) + + @property + def expr(self): + """ + Returns the expression of this pair. + """ + return self.args[0] + + @property + def cond(self): + """ + Returns the condition of this pair. + """ + return self.args[1] + + @property + def is_commutative(self): + return self.expr.is_commutative + + def __iter__(self): + yield self.expr + yield self.cond + + def _eval_simplify(self, **kwargs): + return self.func(*[a.simplify(**kwargs) for a in self.args]) + + +class Piecewise(Function): + """ + Represents a piecewise function. + + Usage: + + Piecewise( (expr,cond), (expr,cond), ... ) + - Each argument is a 2-tuple defining an expression and condition + - The conds are evaluated in turn returning the first that is True. + If any of the evaluated conds are not explicitly False, + e.g. ``x < 1``, the function is returned in symbolic form. + - If the function is evaluated at a place where all conditions are False, + nan will be returned. + - Pairs where the cond is explicitly False, will be removed and no pair + appearing after a True condition will ever be retained. If a single + pair with a True condition remains, it will be returned, even when + evaluation is False. + + Examples + ======== + + >>> from sympy import Piecewise, log, piecewise_fold + >>> from sympy.abc import x, y + >>> f = x**2 + >>> g = log(x) + >>> p = Piecewise((0, x < -1), (f, x <= 1), (g, True)) + >>> p.subs(x,1) + 1 + >>> p.subs(x,5) + log(5) + + Booleans can contain Piecewise elements: + + >>> cond = (x < y).subs(x, Piecewise((2, x < 0), (3, True))); cond + Piecewise((2, x < 0), (3, True)) < y + + The folded version of this results in a Piecewise whose + expressions are Booleans: + + >>> folded_cond = piecewise_fold(cond); folded_cond + Piecewise((2 < y, x < 0), (3 < y, True)) + + When a Boolean containing Piecewise (like cond) or a Piecewise + with Boolean expressions (like folded_cond) is used as a condition, + it is converted to an equivalent :class:`~.ITE` object: + + >>> Piecewise((1, folded_cond)) + Piecewise((1, ITE(x < 0, y > 2, y > 3))) + + When a condition is an ``ITE``, it will be converted to a simplified + Boolean expression: + + >>> piecewise_fold(_) + Piecewise((1, ((x >= 0) | (y > 2)) & ((y > 3) | (x < 0)))) + + See Also + ======== + + piecewise_fold + piecewise_exclusive + ITE + """ + + nargs = None + is_Piecewise = True + + def __new__(cls, *args, **options): + if len(args) == 0: + raise TypeError("At least one (expr, cond) pair expected.") + # (Try to) sympify args first + newargs = [] + for ec in args: + # ec could be a ExprCondPair or a tuple + pair = ExprCondPair(*getattr(ec, 'args', ec)) + cond = pair.cond + if cond is false: + continue + newargs.append(pair) + if cond is true: + break + + eval = options.pop('evaluate', global_parameters.evaluate) + if eval: + r = cls.eval(*newargs) + if r is not None: + return r + elif len(newargs) == 1 and newargs[0].cond == True: + return newargs[0].expr + + return Basic.__new__(cls, *newargs, **options) + + @classmethod + def eval(cls, *_args): + """Either return a modified version of the args or, if no + modifications were made, return None. + + Modifications that are made here: + + 1. relationals are made canonical + 2. any False conditions are dropped + 3. any repeat of a previous condition is ignored + 4. any args past one with a true condition are dropped + + If there are no args left, nan will be returned. + If there is a single arg with a True condition, its + corresponding expression will be returned. + + EXAMPLES + ======== + + >>> from sympy import Piecewise + >>> from sympy.abc import x + >>> cond = -x < -1 + >>> args = [(1, cond), (4, cond), (3, False), (2, True), (5, x < 1)] + >>> Piecewise(*args, evaluate=False) + Piecewise((1, -x < -1), (4, -x < -1), (2, True)) + >>> Piecewise(*args) + Piecewise((1, x > 1), (2, True)) + """ + if not _args: + return Undefined + + if len(_args) == 1 and _args[0][-1] == True: + return _args[0][0] + + newargs = _piecewise_collapse_arguments(_args) + + # some conditions may have been redundant + missing = len(newargs) != len(_args) + # some conditions may have changed + same = all(a == b for a, b in zip(newargs, _args)) + # if either change happened we return the expr with the + # updated args + if not newargs: + raise ValueError(filldedent(''' + There are no conditions (or none that + are not trivially false) to define an + expression.''')) + if missing or not same: + return cls(*newargs) + + def doit(self, **hints): + """ + Evaluate this piecewise function. + """ + newargs = [] + for e, c in self.args: + if hints.get('deep', True): + if isinstance(e, Basic): + newe = e.doit(**hints) + if newe != self: + e = newe + if isinstance(c, Basic): + c = c.doit(**hints) + newargs.append((e, c)) + return self.func(*newargs) + + def _eval_simplify(self, **kwargs): + return piecewise_simplify(self, **kwargs) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + for e, c in self.args: + if c == True or c.subs(x, 0) == True: + return e.as_leading_term(x) + + def _eval_adjoint(self): + return self.func(*[(e.adjoint(), c) for e, c in self.args]) + + def _eval_conjugate(self): + return self.func(*[(e.conjugate(), c) for e, c in self.args]) + + def _eval_derivative(self, x): + return self.func(*[(diff(e, x), c) for e, c in self.args]) + + def _eval_evalf(self, prec): + return self.func(*[(e._evalf(prec), c) for e, c in self.args]) + + def _eval_is_meromorphic(self, x, a): + # Conditions often implicitly assume that the argument is real. + # Hence, there needs to be some check for as_set. + if not a.is_real: + return None + + # Then, scan ExprCondPairs in the given order to find a piece that would contain a, + # possibly as a boundary point. + for e, c in self.args: + cond = c.subs(x, a) + + if cond.is_Relational: + return None + if a in c.as_set().boundary: + return None + # Apply expression if a is an interior point of the domain of e. + if cond: + return e._eval_is_meromorphic(x, a) + + def piecewise_integrate(self, x, **kwargs): + """Return the Piecewise with each expression being + replaced with its antiderivative. To obtain a continuous + antiderivative, use the :func:`~.integrate` function or method. + + Examples + ======== + + >>> from sympy import Piecewise + >>> from sympy.abc import x + >>> p = Piecewise((0, x < 0), (1, x < 1), (2, True)) + >>> p.piecewise_integrate(x) + Piecewise((0, x < 0), (x, x < 1), (2*x, True)) + + Note that this does not give a continuous function, e.g. + at x = 1 the 3rd condition applies and the antiderivative + there is 2*x so the value of the antiderivative is 2: + + >>> anti = _ + >>> anti.subs(x, 1) + 2 + + The continuous derivative accounts for the integral *up to* + the point of interest, however: + + >>> p.integrate(x) + Piecewise((0, x < 0), (x, x < 1), (2*x - 1, True)) + >>> _.subs(x, 1) + 1 + + See Also + ======== + Piecewise._eval_integral + """ + from sympy.integrals import integrate + return self.func(*[(integrate(e, x, **kwargs), c) for e, c in self.args]) + + def _handle_irel(self, x, handler): + """Return either None (if the conditions of self depend only on x) else + a Piecewise expression whose expressions (handled by the handler that + was passed) are paired with the governing x-independent relationals, + e.g. Piecewise((A, a(x) & b(y)), (B, c(x) | c(y)) -> + Piecewise( + (handler(Piecewise((A, a(x) & True), (B, c(x) | True)), b(y) & c(y)), + (handler(Piecewise((A, a(x) & True), (B, c(x) | False)), b(y)), + (handler(Piecewise((A, a(x) & False), (B, c(x) | True)), c(y)), + (handler(Piecewise((A, a(x) & False), (B, c(x) | False)), True)) + """ + # identify governing relationals + rel = self.atoms(Relational) + irel = list(ordered([r for r in rel if x not in r.free_symbols + and r not in (S.true, S.false)])) + if irel: + args = {} + exprinorder = [] + for truth in product((1, 0), repeat=len(irel)): + reps = dict(zip(irel, truth)) + # only store the true conditions since the false are implied + # when they appear lower in the Piecewise args + if 1 not in truth: + cond = None # flag this one so it doesn't get combined + else: + andargs = Tuple(*[i for i in reps if reps[i]]) + free = list(andargs.free_symbols) + if len(free) == 1: + from sympy.solvers.inequalities import ( + reduce_inequalities, _solve_inequality) + try: + t = reduce_inequalities(andargs, free[0]) + # ValueError when there are potentially + # nonvanishing imaginary parts + except (ValueError, NotImplementedError): + # at least isolate free symbol on left + t = And(*[_solve_inequality( + a, free[0], linear=True) + for a in andargs]) + else: + t = And(*andargs) + if t is S.false: + continue # an impossible combination + cond = t + expr = handler(self.xreplace(reps)) + if isinstance(expr, self.func) and len(expr.args) == 1: + expr, econd = expr.args[0] + cond = And(econd, True if cond is None else cond) + # the ec pairs are being collected since all possibilities + # are being enumerated, but don't put the last one in since + # its expr might match a previous expression and it + # must appear last in the args + if cond is not None: + args.setdefault(expr, []).append(cond) + # but since we only store the true conditions we must maintain + # the order so that the expression with the most true values + # comes first + exprinorder.append(expr) + # convert collected conditions as args of Or + for k in args: + args[k] = Or(*args[k]) + # take them in the order obtained + args = [(e, args[e]) for e in uniq(exprinorder)] + # add in the last arg + args.append((expr, True)) + return Piecewise(*args) + + def _eval_integral(self, x, _first=True, **kwargs): + """Return the indefinite integral of the + Piecewise such that subsequent substitution of x with a + value will give the value of the integral (not including + the constant of integration) up to that point. To only + integrate the individual parts of Piecewise, use the + ``piecewise_integrate`` method. + + Examples + ======== + + >>> from sympy import Piecewise + >>> from sympy.abc import x + >>> p = Piecewise((0, x < 0), (1, x < 1), (2, True)) + >>> p.integrate(x) + Piecewise((0, x < 0), (x, x < 1), (2*x - 1, True)) + >>> p.piecewise_integrate(x) + Piecewise((0, x < 0), (x, x < 1), (2*x, True)) + + See Also + ======== + Piecewise.piecewise_integrate + """ + from sympy.integrals.integrals import integrate + + if _first: + def handler(ipw): + if isinstance(ipw, self.func): + return ipw._eval_integral(x, _first=False, **kwargs) + else: + return ipw.integrate(x, **kwargs) + irv = self._handle_irel(x, handler) + if irv is not None: + return irv + + # handle a Piecewise from -oo to oo with and no x-independent relationals + # ----------------------------------------------------------------------- + ok, abei = self._intervals(x) + if not ok: + from sympy.integrals.integrals import Integral + return Integral(self, x) # unevaluated + + pieces = [(a, b) for a, b, _, _ in abei] + oo = S.Infinity + done = [(-oo, oo, -1)] + for k, p in enumerate(pieces): + if p == (-oo, oo): + # all undone intervals will get this key + for j, (a, b, i) in enumerate(done): + if i == -1: + done[j] = a, b, k + break # nothing else to consider + N = len(done) - 1 + for j, (a, b, i) in enumerate(reversed(done)): + if i == -1: + j = N - j + done[j: j + 1] = _clip(p, (a, b), k) + done = [(a, b, i) for a, b, i in done if a != b] + + # append an arg if there is a hole so a reference to + # argument -1 will give Undefined + if any(i == -1 for (a, b, i) in done): + abei.append((-oo, oo, Undefined, -1)) + + # return the sum of the intervals + args = [] + sum = None + for a, b, i in done: + anti = integrate(abei[i][-2], x, **kwargs) + if sum is None: + sum = anti + else: + sum = sum.subs(x, a) + e = anti._eval_interval(x, a, x) + if sum.has(*_illegal) or e.has(*_illegal): + sum = anti + else: + sum += e + # see if we know whether b is contained in original + # condition + if b is S.Infinity: + cond = True + elif self.args[abei[i][-1]].cond.subs(x, b) == False: + cond = (x < b) + else: + cond = (x <= b) + args.append((sum, cond)) + return Piecewise(*args) + + def _eval_interval(self, sym, a, b, _first=True): + """Evaluates the function along the sym in a given interval [a, b]""" + # FIXME: Currently complex intervals are not supported. A possible + # replacement algorithm, discussed in issue 5227, can be found in the + # following papers; + # http://portal.acm.org/citation.cfm?id=281649 + # http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.4127&rep=rep1&type=pdf + + if a is None or b is None: + # In this case, it is just simple substitution + return super()._eval_interval(sym, a, b) + else: + x, lo, hi = map(as_Basic, (sym, a, b)) + + if _first: # get only x-dependent relationals + def handler(ipw): + if isinstance(ipw, self.func): + return ipw._eval_interval(x, lo, hi, _first=None) + else: + return ipw._eval_interval(x, lo, hi) + irv = self._handle_irel(x, handler) + if irv is not None: + return irv + + if (lo < hi) is S.false or ( + lo is S.Infinity or hi is S.NegativeInfinity): + rv = self._eval_interval(x, hi, lo, _first=False) + if isinstance(rv, Piecewise): + rv = Piecewise(*[(-e, c) for e, c in rv.args]) + else: + rv = -rv + return rv + + if (lo < hi) is S.true or ( + hi is S.Infinity or lo is S.NegativeInfinity): + pass + else: + _a = Dummy('lo') + _b = Dummy('hi') + a = lo if lo.is_comparable else _a + b = hi if hi.is_comparable else _b + pos = self._eval_interval(x, a, b, _first=False) + if a == _a and b == _b: + # it's purely symbolic so just swap lo and hi and + # change the sign to get the value for when lo > hi + neg, pos = (-pos.xreplace({_a: hi, _b: lo}), + pos.xreplace({_a: lo, _b: hi})) + else: + # at least one of the bounds was comparable, so allow + # _eval_interval to use that information when computing + # the interval with lo and hi reversed + neg, pos = (-self._eval_interval(x, hi, lo, _first=False), + pos.xreplace({_a: lo, _b: hi})) + + # allow simplification based on ordering of lo and hi + p = Dummy('', positive=True) + if lo.is_Symbol: + pos = pos.xreplace({lo: hi - p}).xreplace({p: hi - lo}) + neg = neg.xreplace({lo: hi + p}).xreplace({p: lo - hi}) + elif hi.is_Symbol: + pos = pos.xreplace({hi: lo + p}).xreplace({p: hi - lo}) + neg = neg.xreplace({hi: lo - p}).xreplace({p: lo - hi}) + # evaluate limits that may have unevaluate Min/Max + touch = lambda _: _.replace( + lambda x: isinstance(x, (Min, Max)), + lambda x: x.func(*x.args)) + neg = touch(neg) + pos = touch(pos) + # assemble return expression; make the first condition be Lt + # b/c then the first expression will look the same whether + # the lo or hi limit is symbolic + if a == _a: # the lower limit was symbolic + rv = Piecewise( + (pos, + lo < hi), + (neg, + True)) + else: + rv = Piecewise( + (neg, + hi < lo), + (pos, + True)) + + if rv == Undefined: + raise ValueError("Can't integrate across undefined region.") + if any(isinstance(i, Piecewise) for i in (pos, neg)): + rv = piecewise_fold(rv) + return rv + + # handle a Piecewise with lo <= hi and no x-independent relationals + # ----------------------------------------------------------------- + ok, abei = self._intervals(x) + if not ok: + from sympy.integrals.integrals import Integral + # not being able to do the interval of f(x) can + # be stated as not being able to do the integral + # of f'(x) over the same range + return Integral(self.diff(x), (x, lo, hi)) # unevaluated + + pieces = [(a, b) for a, b, _, _ in abei] + done = [(lo, hi, -1)] + oo = S.Infinity + for k, p in enumerate(pieces): + if p[:2] == (-oo, oo): + # all undone intervals will get this key + for j, (a, b, i) in enumerate(done): + if i == -1: + done[j] = a, b, k + break # nothing else to consider + N = len(done) - 1 + for j, (a, b, i) in enumerate(reversed(done)): + if i == -1: + j = N - j + done[j: j + 1] = _clip(p, (a, b), k) + done = [(a, b, i) for a, b, i in done if a != b] + + # return the sum of the intervals + sum = S.Zero + upto = None + for a, b, i in done: + if i == -1: + if upto is None: + return Undefined + # TODO simplify hi <= upto + return Piecewise((sum, hi <= upto), (Undefined, True)) + sum += abei[i][-2]._eval_interval(x, a, b) + upto = b + return sum + + def _intervals(self, sym, err_on_Eq=False): + r"""Return a bool and a message (when bool is False), else a + list of unique tuples, (a, b, e, i), where a and b + are the lower and upper bounds in which the expression e of + argument i in self is defined and $a < b$ (when involving + numbers) or $a \le b$ when involving symbols. + + If there are any relationals not involving sym, or any + relational cannot be solved for sym, the bool will be False + a message be given as the second return value. The calling + routine should have removed such relationals before calling + this routine. + + The evaluated conditions will be returned as ranges. + Discontinuous ranges will be returned separately with + identical expressions. The first condition that evaluates to + True will be returned as the last tuple with a, b = -oo, oo. + """ + from sympy.solvers.inequalities import _solve_inequality + + assert isinstance(self, Piecewise) + + def nonsymfail(cond): + return False, filldedent(''' + A condition not involving + %s appeared: %s''' % (sym, cond)) + + def _solve_relational(r): + if sym not in r.free_symbols: + return nonsymfail(r) + try: + rv = _solve_inequality(r, sym) + except NotImplementedError: + return False, 'Unable to solve relational %s for %s.' % (r, sym) + if isinstance(rv, Relational): + free = rv.args[1].free_symbols + if rv.args[0] != sym or sym in free: + return False, 'Unable to solve relational %s for %s.' % (r, sym) + if rv.rel_op == '==': + # this equality has been affirmed to have the form + # Eq(sym, rhs) where rhs is sym-free; it represents + # a zero-width interval which will be ignored + # whether it is an isolated condition or contained + # within an And or an Or + rv = S.false + elif rv.rel_op == '!=': + try: + rv = Or(sym < rv.rhs, sym > rv.rhs) + except TypeError: + # e.g. x != I ==> all real x satisfy + rv = S.true + elif rv == (S.NegativeInfinity < sym) & (sym < S.Infinity): + rv = S.true + return True, rv + + args = list(self.args) + # make self canonical wrt Relationals + keys = self.atoms(Relational) + reps = {} + for r in keys: + ok, s = _solve_relational(r) + if ok != True: + return False, ok + reps[r] = s + # process args individually so if any evaluate, their position + # in the original Piecewise will be known + args = [i.xreplace(reps) for i in self.args] + + # precondition args + expr_cond = [] + default = idefault = None + for i, (expr, cond) in enumerate(args): + if cond is S.false: + continue + if cond is S.true: + default = expr + idefault = i + break + if isinstance(cond, Eq): + # unanticipated condition, but it is here in case a + # replacement caused an Eq to appear + if err_on_Eq: + return False, 'encountered Eq condition: %s' % cond + continue # zero width interval + + cond = to_cnf(cond) + if isinstance(cond, And): + cond = distribute_or_over_and(cond) + + if isinstance(cond, Or): + expr_cond.extend( + [(i, expr, o) for o in cond.args + if not isinstance(o, Eq)]) + elif cond is not S.false: + expr_cond.append((i, expr, cond)) + elif cond is S.true: + default = expr + idefault = i + break + + # determine intervals represented by conditions + int_expr = [] + for iarg, expr, cond in expr_cond: + if isinstance(cond, And): + lower = S.NegativeInfinity + upper = S.Infinity + exclude = [] + for cond2 in cond.args: + if not isinstance(cond2, Relational): + return False, 'expecting only Relationals' + if isinstance(cond2, Eq): + lower = upper # ignore + if err_on_Eq: + return False, 'encountered secondary Eq condition' + break + elif isinstance(cond2, Ne): + l, r = cond2.args + if l == sym: + exclude.append(r) + elif r == sym: + exclude.append(l) + else: + return nonsymfail(cond2) + continue + elif cond2.lts == sym: + upper = Min(cond2.gts, upper) + elif cond2.gts == sym: + lower = Max(cond2.lts, lower) + else: + return nonsymfail(cond2) # should never get here + if exclude: + exclude = list(ordered(exclude)) + newcond = [] + for i, e in enumerate(exclude): + if e < lower == True or e > upper == True: + continue + if not newcond: + newcond.append((None, lower)) # add a primer + newcond.append((newcond[-1][1], e)) + newcond.append((newcond[-1][1], upper)) + newcond.pop(0) # remove the primer + expr_cond.extend([(iarg, expr, And(i[0] < sym, sym < i[1])) for i in newcond]) + continue + elif isinstance(cond, Relational) and cond.rel_op != '!=': + lower, upper = cond.lts, cond.gts # part 1: initialize with givens + if cond.lts == sym: # part 1a: expand the side ... + lower = S.NegativeInfinity # e.g. x <= 0 ---> -oo <= 0 + elif cond.gts == sym: # part 1a: ... that can be expanded + upper = S.Infinity # e.g. x >= 0 ---> oo >= 0 + else: + return nonsymfail(cond) + else: + return False, 'unrecognized condition: %s' % cond + + lower, upper = lower, Max(lower, upper) + if err_on_Eq and lower == upper: + return False, 'encountered Eq condition' + if (lower >= upper) is not S.true: + int_expr.append((lower, upper, expr, iarg)) + + if default is not None: + int_expr.append( + (S.NegativeInfinity, S.Infinity, default, idefault)) + + return True, list(uniq(int_expr)) + + def _eval_nseries(self, x, n, logx, cdir=0): + args = [(ec.expr._eval_nseries(x, n, logx), ec.cond) for ec in self.args] + return self.func(*args) + + def _eval_power(self, s): + return self.func(*[(e**s, c) for e, c in self.args]) + + def _eval_subs(self, old, new): + # this is strictly not necessary, but we can keep track + # of whether True or False conditions arise and be + # somewhat more efficient by avoiding other substitutions + # and avoiding invalid conditions that appear after a + # True condition + args = list(self.args) + args_exist = False + for i, (e, c) in enumerate(args): + c = c._subs(old, new) + if c != False: + args_exist = True + e = e._subs(old, new) + args[i] = (e, c) + if c == True: + break + if not args_exist: + args = ((Undefined, True),) + return self.func(*args) + + def _eval_transpose(self): + return self.func(*[(e.transpose(), c) for e, c in self.args]) + + def _eval_template_is_attr(self, is_attr): + b = None + for expr, _ in self.args: + a = getattr(expr, is_attr) + if a is None: + return + if b is None: + b = a + elif b is not a: + return + return b + + _eval_is_finite = lambda self: self._eval_template_is_attr( + 'is_finite') + _eval_is_complex = lambda self: self._eval_template_is_attr('is_complex') + _eval_is_even = lambda self: self._eval_template_is_attr('is_even') + _eval_is_imaginary = lambda self: self._eval_template_is_attr( + 'is_imaginary') + _eval_is_integer = lambda self: self._eval_template_is_attr('is_integer') + _eval_is_irrational = lambda self: self._eval_template_is_attr( + 'is_irrational') + _eval_is_negative = lambda self: self._eval_template_is_attr('is_negative') + _eval_is_nonnegative = lambda self: self._eval_template_is_attr( + 'is_nonnegative') + _eval_is_nonpositive = lambda self: self._eval_template_is_attr( + 'is_nonpositive') + _eval_is_nonzero = lambda self: self._eval_template_is_attr( + 'is_nonzero') + _eval_is_odd = lambda self: self._eval_template_is_attr('is_odd') + _eval_is_polar = lambda self: self._eval_template_is_attr('is_polar') + _eval_is_positive = lambda self: self._eval_template_is_attr('is_positive') + _eval_is_extended_real = lambda self: self._eval_template_is_attr( + 'is_extended_real') + _eval_is_extended_positive = lambda self: self._eval_template_is_attr( + 'is_extended_positive') + _eval_is_extended_negative = lambda self: self._eval_template_is_attr( + 'is_extended_negative') + _eval_is_extended_nonzero = lambda self: self._eval_template_is_attr( + 'is_extended_nonzero') + _eval_is_extended_nonpositive = lambda self: self._eval_template_is_attr( + 'is_extended_nonpositive') + _eval_is_extended_nonnegative = lambda self: self._eval_template_is_attr( + 'is_extended_nonnegative') + _eval_is_real = lambda self: self._eval_template_is_attr('is_real') + _eval_is_zero = lambda self: self._eval_template_is_attr( + 'is_zero') + + @classmethod + def __eval_cond(cls, cond): + """Return the truth value of the condition.""" + if cond == True: + return True + if isinstance(cond, Eq): + try: + diff = cond.lhs - cond.rhs + if diff.is_commutative: + return diff.is_zero + except TypeError: + pass + + def as_expr_set_pairs(self, domain=None): + """Return tuples for each argument of self that give + the expression and the interval in which it is valid + which is contained within the given domain. + If a condition cannot be converted to a set, an error + will be raised. The variable of the conditions is + assumed to be real; sets of real values are returned. + + Examples + ======== + + >>> from sympy import Piecewise, Interval + >>> from sympy.abc import x + >>> p = Piecewise( + ... (1, x < 2), + ... (2,(x > 0) & (x < 4)), + ... (3, True)) + >>> p.as_expr_set_pairs() + [(1, Interval.open(-oo, 2)), + (2, Interval.Ropen(2, 4)), + (3, Interval(4, oo))] + >>> p.as_expr_set_pairs(Interval(0, 3)) + [(1, Interval.Ropen(0, 2)), + (2, Interval(2, 3))] + """ + if domain is None: + domain = S.Reals + exp_sets = [] + U = domain + complex = not domain.is_subset(S.Reals) + cond_free = set() + for expr, cond in self.args: + cond_free |= cond.free_symbols + if len(cond_free) > 1: + raise NotImplementedError(filldedent(''' + multivariate conditions are not handled.''')) + if complex: + for i in cond.atoms(Relational): + if not isinstance(i, (Eq, Ne)): + raise ValueError(filldedent(''' + Inequalities in the complex domain are + not supported. Try the real domain by + setting domain=S.Reals''')) + cond_int = U.intersect(cond.as_set()) + U = U - cond_int + if cond_int != S.EmptySet: + exp_sets.append((expr, cond_int)) + return exp_sets + + def _eval_rewrite_as_ITE(self, *args, **kwargs): + byfree = {} + args = list(args) + default = any(c == True for b, c in args) + for i, (b, c) in enumerate(args): + if not isinstance(b, Boolean) and b != True: + raise TypeError(filldedent(''' + Expecting Boolean or bool but got `%s` + ''' % func_name(b))) + if c == True: + break + # loop over independent conditions for this b + for c in c.args if isinstance(c, Or) else [c]: + free = c.free_symbols + x = free.pop() + try: + byfree[x] = byfree.setdefault( + x, S.EmptySet).union(c.as_set()) + except NotImplementedError: + if not default: + raise NotImplementedError(filldedent(''' + A method to determine whether a multivariate + conditional is consistent with a complete coverage + of all variables has not been implemented so the + rewrite is being stopped after encountering `%s`. + This error would not occur if a default expression + like `(foo, True)` were given. + ''' % c)) + if byfree[x] in (S.UniversalSet, S.Reals): + # collapse the ith condition to True and break + args[i] = list(args[i]) + c = args[i][1] = True + break + if c == True: + break + if c != True: + raise ValueError(filldedent(''' + Conditions must cover all reals or a final default + condition `(foo, True)` must be given. + ''')) + last, _ = args[i] # ignore all past ith arg + for a, c in reversed(args[:i]): + last = ITE(c, a, last) + return _canonical(last) + + def _eval_rewrite_as_KroneckerDelta(self, *args, **kwargs): + from sympy.functions.special.tensor_functions import KroneckerDelta + + rules = { + And: [False, False], + Or: [True, True], + Not: [True, False], + Eq: [None, None], + Ne: [None, None] + } + + class UnrecognizedCondition(Exception): + pass + + def rewrite(cond): + if isinstance(cond, Eq): + return KroneckerDelta(*cond.args) + if isinstance(cond, Ne): + return 1 - KroneckerDelta(*cond.args) + + cls, args = type(cond), cond.args + if cls not in rules: + raise UnrecognizedCondition(cls) + + b1, b2 = rules[cls] + k = Mul(*[1 - rewrite(c) for c in args]) if b1 else Mul(*[rewrite(c) for c in args]) + + if b2: + return 1 - k + return k + + conditions = [] + true_value = None + for value, cond in args: + if type(cond) in rules: + conditions.append((value, cond)) + elif cond is S.true: + if true_value is None: + true_value = value + else: + return + + if true_value is not None: + result = true_value + + for value, cond in conditions[::-1]: + try: + k = rewrite(cond) + result = k * value + (1 - k) * result + except UnrecognizedCondition: + return + + return result + + +def piecewise_fold(expr, evaluate=True): + """ + Takes an expression containing a piecewise function and returns the + expression in piecewise form. In addition, any ITE conditions are + rewritten in negation normal form and simplified. + + The final Piecewise is evaluated (default) but if the raw form + is desired, send ``evaluate=False``; if trivial evaluation is + desired, send ``evaluate=None`` and duplicate conditions and + processing of True and False will be handled. + + Examples + ======== + + >>> from sympy import Piecewise, piecewise_fold, S + >>> from sympy.abc import x + >>> p = Piecewise((x, x < 1), (1, S(1) <= x)) + >>> piecewise_fold(x*p) + Piecewise((x**2, x < 1), (x, True)) + + See Also + ======== + + Piecewise + piecewise_exclusive + """ + if not isinstance(expr, Basic) or not expr.has(Piecewise): + return expr + + new_args = [] + if isinstance(expr, (ExprCondPair, Piecewise)): + for e, c in expr.args: + if not isinstance(e, Piecewise): + e = piecewise_fold(e) + # we don't keep Piecewise in condition because + # it has to be checked to see that it's complete + # and we convert it to ITE at that time + assert not c.has(Piecewise) # pragma: no cover + if isinstance(c, ITE): + c = c.to_nnf() + c = simplify_logic(c, form='cnf') + if isinstance(e, Piecewise): + new_args.extend([(piecewise_fold(ei), And(ci, c)) + for ei, ci in e.args]) + else: + new_args.append((e, c)) + else: + # Given + # P1 = Piecewise((e11, c1), (e12, c2), A) + # P2 = Piecewise((e21, c1), (e22, c2), B) + # ... + # the folding of f(P1, P2) is trivially + # Piecewise( + # (f(e11, e21), c1), + # (f(e12, e22), c2), + # (f(Piecewise(A), Piecewise(B)), True)) + # Certain objects end up rewriting themselves as thus, so + # we do that grouping before the more generic folding. + # The following applies this idea when f = Add or f = Mul + # (and the expression is commutative). + if expr.is_Add or expr.is_Mul and expr.is_commutative: + p, args = sift(expr.args, lambda x: x.is_Piecewise, binary=True) + pc = sift(p, lambda x: tuple([c for e,c in x.args])) + for c in list(ordered(pc)): + if len(pc[c]) > 1: + pargs = [list(i.args) for i in pc[c]] + # the first one is the same; there may be more + com = common_prefix(*[ + [i.cond for i in j] for j in pargs]) + n = len(com) + collected = [] + for i in range(n): + collected.append(( + expr.func(*[ai[i].expr for ai in pargs]), + com[i])) + remains = [] + for a in pargs: + if n == len(a): # no more args + continue + if a[n].cond == True: # no longer Piecewise + remains.append(a[n].expr) + else: # restore the remaining Piecewise + remains.append( + Piecewise(*a[n:], evaluate=False)) + if remains: + collected.append((expr.func(*remains), True)) + args.append(Piecewise(*collected, evaluate=False)) + continue + args.extend(pc[c]) + else: + args = expr.args + # fold + folded = list(map(piecewise_fold, args)) + for ec in product(*[ + (i.args if isinstance(i, Piecewise) else + [(i, true)]) for i in folded]): + e, c = zip(*ec) + new_args.append((expr.func(*e), And(*c))) + + if evaluate is None: + # don't return duplicate conditions, otherwise don't evaluate + new_args = list(reversed([(e, c) for c, e in { + c: e for e, c in reversed(new_args)}.items()])) + rv = Piecewise(*new_args, evaluate=evaluate) + if evaluate is None and len(rv.args) == 1 and rv.args[0].cond == True: + return rv.args[0].expr + if any(s.expr.has(Piecewise) for p in rv.atoms(Piecewise) for s in p.args): + return piecewise_fold(rv) + return rv + + +def _clip(A, B, k): + """Return interval B as intervals that are covered by A (keyed + to k) and all other intervals of B not covered by A keyed to -1. + + The reference point of each interval is the rhs; if the lhs is + greater than the rhs then an interval of zero width interval will + result, e.g. (4, 1) is treated like (1, 1). + + Examples + ======== + + >>> from sympy.functions.elementary.piecewise import _clip + >>> from sympy import Tuple + >>> A = Tuple(1, 3) + >>> B = Tuple(2, 4) + >>> _clip(A, B, 0) + [(2, 3, 0), (3, 4, -1)] + + Interpretation: interval portion (2, 3) of interval (2, 4) is + covered by interval (1, 3) and is keyed to 0 as requested; + interval (3, 4) was not covered by (1, 3) and is keyed to -1. + """ + a, b = B + c, d = A + c, d = Min(Max(c, a), b), Min(Max(d, a), b) + a, b = Min(a, b), b + p = [] + if a != c: + p.append((a, c, -1)) + else: + pass + if c != d: + p.append((c, d, k)) + else: + pass + if b != d: + if d == c and p and p[-1][-1] == -1: + p[-1] = p[-1][0], b, -1 + else: + p.append((d, b, -1)) + else: + pass + + return p + + +def piecewise_simplify_arguments(expr, **kwargs): + from sympy.simplify.simplify import simplify + + # simplify conditions + f1 = expr.args[0].cond.free_symbols + args = None + if len(f1) == 1 and not expr.atoms(Eq): + x = f1.pop() + # this won't return intervals involving Eq + # and it won't handle symbols treated as + # booleans + ok, abe_ = expr._intervals(x, err_on_Eq=True) + def include(c, x, a): + "return True if c.subs(x, a) is True, else False" + try: + return c.subs(x, a) == True + except TypeError: + return False + if ok: + args = [] + covered = S.EmptySet + from sympy.sets.sets import Interval + for a, b, e, i in abe_: + c = expr.args[i].cond + incl_a = include(c, x, a) + incl_b = include(c, x, b) + iv = Interval(a, b, not incl_a, not incl_b) + cset = iv - covered + if not cset: + continue + try: + a = cset.inf + except NotImplementedError: + pass # continue with the given `a` + else: + incl_a = include(c, x, a) + if incl_a and incl_b: + if a.is_infinite and b.is_infinite: + c = S.true + elif b.is_infinite: + c = (x > a) if a in covered else (x >= a) + elif a.is_infinite: + c = (x <= b) + elif a in covered: + c = And(a < x, x <= b) + else: + c = And(a <= x, x <= b) + elif incl_a: + if a.is_infinite: + c = (x < b) + elif a in covered: + c = And(a < x, x < b) + else: + c = And(a <= x, x < b) + elif incl_b: + if b.is_infinite: + c = (x > a) + else: + c = And(a < x, x <= b) + else: + if a in covered: + c = (x < b) + else: + c = And(a < x, x < b) + covered |= iv + if a is S.NegativeInfinity and incl_a: + covered |= {S.NegativeInfinity} + if b is S.Infinity and incl_b: + covered |= {S.Infinity} + args.append((e, c)) + if not S.Reals.is_subset(covered): + args.append((Undefined, True)) + if args is None: + args = list(expr.args) + for i in range(len(args)): + e, c = args[i] + if isinstance(c, Basic): + c = simplify(c, **kwargs) + args[i] = (e, c) + + # simplify expressions + doit = kwargs.pop('doit', None) + for i in range(len(args)): + e, c = args[i] + if isinstance(e, Basic): + # Skip doit to avoid growth at every call for some integrals + # and sums, see sympy/sympy#17165 + newe = simplify(e, doit=False, **kwargs) + if newe != e: + e = newe + args[i] = (e, c) + + # restore kwargs flag + if doit is not None: + kwargs['doit'] = doit + + return Piecewise(*args) + + +def _piecewise_collapse_arguments(_args): + newargs = [] # the unevaluated conditions + current_cond = set() # the conditions up to a given e, c pair + for expr, cond in _args: + cond = cond.replace( + lambda _: _.is_Relational, _canonical_coeff) + # Check here if expr is a Piecewise and collapse if one of + # the conds in expr matches cond. This allows the collapsing + # of Piecewise((Piecewise((x,x<0)),x<0)) to Piecewise((x,x<0)). + # This is important when using piecewise_fold to simplify + # multiple Piecewise instances having the same conds. + # Eventually, this code should be able to collapse Piecewise's + # having different intervals, but this will probably require + # using the new assumptions. + if isinstance(expr, Piecewise): + unmatching = [] + for i, (e, c) in enumerate(expr.args): + if c in current_cond: + # this would already have triggered + continue + if c == cond: + if c != True: + # nothing past this condition will ever + # trigger and only those args before this + # that didn't match a previous condition + # could possibly trigger + if unmatching: + expr = Piecewise(*( + unmatching + [(e, c)])) + else: + expr = e + break + else: + unmatching.append((e, c)) + + # check for condition repeats + got = False + # -- if an And contains a condition that was + # already encountered, then the And will be + # False: if the previous condition was False + # then the And will be False and if the previous + # condition is True then then we wouldn't get to + # this point. In either case, we can skip this condition. + for i in ([cond] + + (list(cond.args) if isinstance(cond, And) else + [])): + if i in current_cond: + got = True + break + if got: + continue + + # -- if not(c) is already in current_cond then c is + # a redundant condition in an And. This does not + # apply to Or, however: (e1, c), (e2, Or(~c, d)) + # is not (e1, c), (e2, d) because if c and d are + # both False this would give no results when the + # true answer should be (e2, True) + if isinstance(cond, And): + nonredundant = [] + for c in cond.args: + if isinstance(c, Relational): + if c.negated.canonical in current_cond: + continue + # if a strict inequality appears after + # a non-strict one, then the condition is + # redundant + if isinstance(c, (Lt, Gt)) and ( + c.weak in current_cond): + cond = False + break + nonredundant.append(c) + else: + cond = cond.func(*nonredundant) + elif isinstance(cond, Relational): + if cond.negated.canonical in current_cond: + cond = S.true + + current_cond.add(cond) + + # collect successive e,c pairs when exprs or cond match + if newargs: + if newargs[-1].expr == expr: + orcond = Or(cond, newargs[-1].cond) + if isinstance(orcond, (And, Or)): + orcond = distribute_and_over_or(orcond) + newargs[-1] = ExprCondPair(expr, orcond) + continue + elif newargs[-1].cond == cond: + continue + newargs.append(ExprCondPair(expr, cond)) + return newargs + + +_blessed = lambda e: getattr(e.lhs, '_diff_wrt', False) and ( + getattr(e.rhs, '_diff_wrt', None) or + isinstance(e.rhs, (Rational, NumberSymbol))) + + +def piecewise_simplify(expr, **kwargs): + expr = piecewise_simplify_arguments(expr, **kwargs) + if not isinstance(expr, Piecewise): + return expr + args = list(expr.args) + + args = _piecewise_simplify_eq_and(args) + args = _piecewise_simplify_equal_to_next_segment(args) + return Piecewise(*args) + + +def _piecewise_simplify_equal_to_next_segment(args): + """ + See if expressions valid for an Equal expression happens to evaluate + to the same function as in the next piecewise segment, see: + https://github.com/sympy/sympy/issues/8458 + """ + prevexpr = None + for i, (expr, cond) in reversed(list(enumerate(args))): + if prevexpr is not None: + if isinstance(cond, And): + eqs, other = sift(cond.args, + lambda i: isinstance(i, Eq), binary=True) + elif isinstance(cond, Eq): + eqs, other = [cond], [] + else: + eqs = other = [] + _prevexpr = prevexpr + _expr = expr + if eqs and not other: + eqs = list(ordered(eqs)) + for e in eqs: + # allow 2 args to collapse into 1 for any e + # otherwise limit simplification to only simple-arg + # Eq instances + if len(args) == 2 or _blessed(e): + _prevexpr = _prevexpr.subs(*e.args) + _expr = _expr.subs(*e.args) + # Did it evaluate to the same? + if _prevexpr == _expr: + # Set the expression for the Not equal section to the same + # as the next. These will be merged when creating the new + # Piecewise + args[i] = args[i].func(args[i + 1][0], cond) + else: + # Update the expression that we compare against + prevexpr = expr + else: + prevexpr = expr + return args + + +def _piecewise_simplify_eq_and(args): + """ + Try to simplify conditions and the expression for + equalities that are part of the condition, e.g. + Piecewise((n, And(Eq(n,0), Eq(n + m, 0))), (1, True)) + -> Piecewise((0, And(Eq(n, 0), Eq(m, 0))), (1, True)) + """ + for i, (expr, cond) in enumerate(args): + if isinstance(cond, And): + eqs, other = sift(cond.args, + lambda i: isinstance(i, Eq), binary=True) + elif isinstance(cond, Eq): + eqs, other = [cond], [] + else: + eqs = other = [] + if eqs: + eqs = list(ordered(eqs)) + for j, e in enumerate(eqs): + # these blessed lhs objects behave like Symbols + # and the rhs are simple replacements for the "symbols" + if _blessed(e): + expr = expr.subs(*e.args) + eqs[j + 1:] = [ei.subs(*e.args) for ei in eqs[j + 1:]] + other = [ei.subs(*e.args) for ei in other] + cond = And(*(eqs + other)) + args[i] = args[i].func(expr, cond) + return args + + +def piecewise_exclusive(expr, *, skip_nan=False, deep=True): + """ + Rewrite :class:`Piecewise` with mutually exclusive conditions. + + Explanation + =========== + + SymPy represents the conditions of a :class:`Piecewise` in an + "if-elif"-fashion, allowing more than one condition to be simultaneously + True. The interpretation is that the first condition that is True is the + case that holds. While this is a useful representation computationally it + is not how a piecewise formula is typically shown in a mathematical text. + The :func:`piecewise_exclusive` function can be used to rewrite any + :class:`Piecewise` with more typical mutually exclusive conditions. + + Note that further manipulation of the resulting :class:`Piecewise`, e.g. + simplifying it, will most likely make it non-exclusive. Hence, this is + primarily a function to be used in conjunction with printing the Piecewise + or if one would like to reorder the expression-condition pairs. + + If it is not possible to determine that all possibilities are covered by + the different cases of the :class:`Piecewise` then a final + :class:`~sympy.core.numbers.NaN` case will be included explicitly. This + can be prevented by passing ``skip_nan=True``. + + Examples + ======== + + >>> from sympy import piecewise_exclusive, Symbol, Piecewise, S + >>> x = Symbol('x', real=True) + >>> p = Piecewise((0, x < 0), (S.Half, x <= 0), (1, True)) + >>> piecewise_exclusive(p) + Piecewise((0, x < 0), (1/2, Eq(x, 0)), (1, x > 0)) + >>> piecewise_exclusive(Piecewise((2, x > 1))) + Piecewise((2, x > 1), (nan, x <= 1)) + >>> piecewise_exclusive(Piecewise((2, x > 1)), skip_nan=True) + Piecewise((2, x > 1)) + + Parameters + ========== + + expr: a SymPy expression. + Any :class:`Piecewise` in the expression will be rewritten. + skip_nan: ``bool`` (default ``False``) + If ``skip_nan`` is set to ``True`` then a final + :class:`~sympy.core.numbers.NaN` case will not be included. + deep: ``bool`` (default ``True``) + If ``deep`` is ``True`` then :func:`piecewise_exclusive` will rewrite + any :class:`Piecewise` subexpressions in ``expr`` rather than just + rewriting ``expr`` itself. + + Returns + ======= + + An expression equivalent to ``expr`` but where all :class:`Piecewise` have + been rewritten with mutually exclusive conditions. + + See Also + ======== + + Piecewise + piecewise_fold + """ + + def make_exclusive(*pwargs): + + cumcond = false + newargs = [] + + # Handle the first n-1 cases + for expr_i, cond_i in pwargs[:-1]: + cancond = And(cond_i, Not(cumcond)).simplify() + cumcond = Or(cond_i, cumcond).simplify() + newargs.append((expr_i, cancond)) + + # For the nth case defer simplification of cumcond + expr_n, cond_n = pwargs[-1] + cancond_n = And(cond_n, Not(cumcond)).simplify() + newargs.append((expr_n, cancond_n)) + + if not skip_nan: + cumcond = Or(cond_n, cumcond).simplify() + if cumcond is not true: + newargs.append((Undefined, Not(cumcond).simplify())) + + return Piecewise(*newargs, evaluate=False) + + if deep: + return expr.replace(Piecewise, make_exclusive) + elif isinstance(expr, Piecewise): + return make_exclusive(*expr.args) + else: + return expr diff --git 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0000000000000000000000000000000000000000..a6c65cf9d08c5fb61fc26b745a652cf4fea1c1b4 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/elementary/tests/__pycache__/test_miscellaneous.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_complexes.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_complexes.py new file mode 100644 index 0000000000000000000000000000000000000000..9fd2a0edaa7bd602ca0e111ccb0556d44dd79a26 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_complexes.py @@ -0,0 +1,1028 @@ +from sympy.core.expr import Expr +from sympy.core.function import (Derivative, Function, Lambda, expand) +from sympy.core.numbers import (E, I, Rational, comp, nan, oo, pi, zoo) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (Abs, adjoint, arg, conjugate, im, re, sign, transpose) +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (acos, atan, atan2, cos, sin) +from sympy.functions.elementary.hyperbolic import sinh +from sympy.functions.special.delta_functions import (DiracDelta, Heaviside) +from sympy.integrals.integrals import Integral +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions.funcmatrix import FunctionMatrix +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.matrices.immutable import (ImmutableMatrix, ImmutableSparseMatrix) +from sympy.matrices import SparseMatrix +from sympy.sets.sets import Interval +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.testing.pytest import XFAIL, raises, _both_exp_pow + + +def N_equals(a, b): + """Check whether two complex numbers are numerically close""" + return comp(a.n(), b.n(), 1.e-6) + + +def test_re(): + x, y = symbols('x,y') + a, b = symbols('a,b', real=True) + + r = Symbol('r', real=True) + i = Symbol('i', imaginary=True) + + assert re(nan) is nan + + assert re(oo) is oo + assert re(-oo) is -oo + + assert re(0) == 0 + + assert re(1) == 1 + assert re(-1) == -1 + + assert re(E) == E + assert re(-E) == -E + + assert unchanged(re, x) + assert re(x*I) == -im(x) + assert re(r*I) == 0 + assert re(r) == r + assert re(i*I) == I * i + assert re(i) == 0 + + assert re(x + y) == re(x) + re(y) + assert re(x + r) == re(x) + r + + assert re(re(x)) == re(x) + + assert re(2 + I) == 2 + assert re(x + I) == re(x) + + assert re(x + y*I) == re(x) - im(y) + assert re(x + r*I) == re(x) + + assert re(log(2*I)) == log(2) + + assert re((2 + I)**2).expand(complex=True) == 3 + + assert re(conjugate(x)) == re(x) + assert conjugate(re(x)) == re(x) + + assert re(x).as_real_imag() == (re(x), 0) + + assert re(i*r*x).diff(r) == re(i*x) + assert re(i*r*x).diff(i) == I*r*im(x) + + assert re( + sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2) + assert re(a * (2 + b*I)) == 2*a + + assert re((1 + sqrt(a + b*I))/2) == \ + (a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2)/2 + S.Half + + assert re(x).rewrite(im) == x - S.ImaginaryUnit*im(x) + assert (x + re(y)).rewrite(re, im) == x + y - S.ImaginaryUnit*im(y) + + a = Symbol('a', algebraic=True) + t = Symbol('t', transcendental=True) + x = Symbol('x') + assert re(a).is_algebraic + assert re(x).is_algebraic is None + assert re(t).is_algebraic is False + + assert re(S.ComplexInfinity) is S.NaN + + n, m, l = symbols('n m l') + A = MatrixSymbol('A',n,m) + assert re(A) == (S.Half) * (A + conjugate(A)) + + A = Matrix([[1 + 4*I,2],[0, -3*I]]) + assert re(A) == Matrix([[1, 2],[0, 0]]) + + A = ImmutableMatrix([[1 + 3*I, 3-2*I],[0, 2*I]]) + assert re(A) == ImmutableMatrix([[1, 3],[0, 0]]) + + X = SparseMatrix([[2*j + i*I for i in range(5)] for j in range(5)]) + assert re(X) - Matrix([[0, 0, 0, 0, 0], + [2, 2, 2, 2, 2], + [4, 4, 4, 4, 4], + [6, 6, 6, 6, 6], + [8, 8, 8, 8, 8]]) == Matrix.zeros(5) + + assert im(X) - Matrix([[0, 1, 2, 3, 4], + [0, 1, 2, 3, 4], + [0, 1, 2, 3, 4], + [0, 1, 2, 3, 4], + [0, 1, 2, 3, 4]]) == Matrix.zeros(5) + + X = FunctionMatrix(3, 3, Lambda((n, m), n + m*I)) + assert re(X) == Matrix([[0, 0, 0], [1, 1, 1], [2, 2, 2]]) + + +def test_im(): + x, y = symbols('x,y') + a, b = symbols('a,b', real=True) + + r = Symbol('r', real=True) + i = Symbol('i', imaginary=True) + + assert im(nan) is nan + + assert im(oo*I) is oo + assert im(-oo*I) is -oo + + assert im(0) == 0 + + assert im(1) == 0 + assert im(-1) == 0 + + assert im(E*I) == E + assert im(-E*I) == -E + + assert unchanged(im, x) + assert im(x*I) == re(x) + assert im(r*I) == r + assert im(r) == 0 + assert im(i*I) == 0 + assert im(i) == -I * i + + assert im(x + y) == im(x) + im(y) + assert im(x + r) == im(x) + assert im(x + r*I) == im(x) + r + + assert im(im(x)*I) == im(x) + + assert im(2 + I) == 1 + assert im(x + I) == im(x) + 1 + + assert im(x + y*I) == im(x) + re(y) + assert im(x + r*I) == im(x) + r + + assert im(log(2*I)) == pi/2 + + assert im((2 + I)**2).expand(complex=True) == 4 + + assert im(conjugate(x)) == -im(x) + assert conjugate(im(x)) == im(x) + + assert im(x).as_real_imag() == (im(x), 0) + + assert im(i*r*x).diff(r) == im(i*x) + assert im(i*r*x).diff(i) == -I * re(r*x) + + assert im( + sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2) + assert im(a * (2 + b*I)) == a*b + + assert im((1 + sqrt(a + b*I))/2) == \ + (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2 + + assert im(x).rewrite(re) == -S.ImaginaryUnit * (x - re(x)) + assert (x + im(y)).rewrite(im, re) == x - S.ImaginaryUnit * (y - re(y)) + + a = Symbol('a', algebraic=True) + t = Symbol('t', transcendental=True) + x = Symbol('x') + assert re(a).is_algebraic + assert re(x).is_algebraic is None + assert re(t).is_algebraic is False + + assert im(S.ComplexInfinity) is S.NaN + + n, m, l = symbols('n m l') + A = MatrixSymbol('A',n,m) + + assert im(A) == (S.One/(2*I)) * (A - conjugate(A)) + + A = Matrix([[1 + 4*I, 2],[0, -3*I]]) + assert im(A) == Matrix([[4, 0],[0, -3]]) + + A = ImmutableMatrix([[1 + 3*I, 3-2*I],[0, 2*I]]) + assert im(A) == ImmutableMatrix([[3, -2],[0, 2]]) + + X = ImmutableSparseMatrix( + [[i*I + i for i in range(5)] for i in range(5)]) + Y = SparseMatrix([list(range(5)) for i in range(5)]) + assert im(X).as_immutable() == Y + + X = FunctionMatrix(3, 3, Lambda((n, m), n + m*I)) + assert im(X) == Matrix([[0, 1, 2], [0, 1, 2], [0, 1, 2]]) + +def test_sign(): + assert sign(1.2) == 1 + assert sign(-1.2) == -1 + assert sign(3*I) == I + assert sign(-3*I) == -I + assert sign(0) == 0 + assert sign(0, evaluate=False).doit() == 0 + assert sign(oo, evaluate=False).doit() == 1 + assert sign(nan) is nan + assert sign(2 + 2*I).doit() == sqrt(2)*(2 + 2*I)/4 + assert sign(2 + 3*I).simplify() == sign(2 + 3*I) + assert sign(2 + 2*I).simplify() == sign(1 + I) + assert sign(im(sqrt(1 - sqrt(3)))) == 1 + assert sign(sqrt(1 - sqrt(3))) == I + + x = Symbol('x') + assert sign(x).is_finite is True + assert sign(x).is_complex is True + assert sign(x).is_imaginary is None + assert sign(x).is_integer is None + assert sign(x).is_real is None + assert sign(x).is_zero is None + assert sign(x).doit() == sign(x) + assert sign(1.2*x) == sign(x) + assert sign(2*x) == sign(x) + assert sign(I*x) == I*sign(x) + assert sign(-2*I*x) == -I*sign(x) + assert sign(conjugate(x)) == conjugate(sign(x)) + + p = Symbol('p', positive=True) + n = Symbol('n', negative=True) + m = Symbol('m', negative=True) + assert sign(2*p*x) == sign(x) + assert sign(n*x) == -sign(x) + assert sign(n*m*x) == sign(x) + + x = Symbol('x', imaginary=True) + assert sign(x).is_imaginary is True + assert sign(x).is_integer is False + assert sign(x).is_real is False + assert sign(x).is_zero is False + assert sign(x).diff(x) == 2*DiracDelta(-I*x) + assert sign(x).doit() == x / Abs(x) + assert conjugate(sign(x)) == -sign(x) + + x = Symbol('x', real=True) + assert sign(x).is_imaginary is False + assert sign(x).is_integer is True + assert sign(x).is_real is True + assert sign(x).is_zero is None + assert sign(x).diff(x) == 2*DiracDelta(x) + assert sign(x).doit() == sign(x) + assert conjugate(sign(x)) == sign(x) + + x = Symbol('x', nonzero=True) + assert sign(x).is_imaginary is False + assert sign(x).is_integer is True + assert sign(x).is_real is True + assert sign(x).is_zero is False + assert sign(x).doit() == x / Abs(x) + assert sign(Abs(x)) == 1 + assert Abs(sign(x)) == 1 + + x = Symbol('x', positive=True) + assert sign(x).is_imaginary is False + assert sign(x).is_integer is True + assert sign(x).is_real is True + assert sign(x).is_zero is False + assert sign(x).doit() == x / Abs(x) + assert sign(Abs(x)) == 1 + assert Abs(sign(x)) == 1 + + x = 0 + assert sign(x).is_imaginary is False + assert sign(x).is_integer is True + assert sign(x).is_real is True + assert sign(x).is_zero is True + assert sign(x).doit() == 0 + assert sign(Abs(x)) == 0 + assert Abs(sign(x)) == 0 + + nz = Symbol('nz', nonzero=True, integer=True) + assert sign(nz).is_imaginary is False + assert sign(nz).is_integer is True + assert sign(nz).is_real is True + assert sign(nz).is_zero is False + assert sign(nz)**2 == 1 + assert (sign(nz)**3).args == (sign(nz), 3) + + assert sign(Symbol('x', nonnegative=True)).is_nonnegative + assert sign(Symbol('x', nonnegative=True)).is_nonpositive is None + assert sign(Symbol('x', nonpositive=True)).is_nonnegative is None + assert sign(Symbol('x', nonpositive=True)).is_nonpositive + assert sign(Symbol('x', real=True)).is_nonnegative is None + assert sign(Symbol('x', real=True)).is_nonpositive is None + assert sign(Symbol('x', real=True, zero=False)).is_nonpositive is None + + x, y = Symbol('x', real=True), Symbol('y') + f = Function('f') + assert sign(x).rewrite(Piecewise) == \ + Piecewise((1, x > 0), (-1, x < 0), (0, True)) + assert sign(y).rewrite(Piecewise) == sign(y) + assert sign(x).rewrite(Heaviside) == 2*Heaviside(x, H0=S(1)/2) - 1 + assert sign(y).rewrite(Heaviside) == sign(y) + assert sign(y).rewrite(Abs) == Piecewise((0, Eq(y, 0)), (y/Abs(y), True)) + assert sign(f(y)).rewrite(Abs) == Piecewise((0, Eq(f(y), 0)), (f(y)/Abs(f(y)), True)) + + # evaluate what can be evaluated + assert sign(exp_polar(I*pi)*pi) is S.NegativeOne + + eq = -sqrt(10 + 6*sqrt(3)) + sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) + # if there is a fast way to know when and when you cannot prove an + # expression like this is zero then the equality to zero is ok + assert sign(eq).func is sign or sign(eq) == 0 + # but sometimes it's hard to do this so it's better not to load + # abs down with tests that will be very slow + q = 1 + sqrt(2) - 2*sqrt(3) + 1331*sqrt(6) + p = expand(q**3)**Rational(1, 3) + d = p - q + assert sign(d).func is sign or sign(d) == 0 + + +def test_as_real_imag(): + n = pi**1000 + # the special code for working out the real + # and complex parts of a power with Integer exponent + # should not run if there is no imaginary part, hence + # this should not hang + assert n.as_real_imag() == (n, 0) + + # issue 6261 + x = Symbol('x') + assert sqrt(x).as_real_imag() == \ + ((re(x)**2 + im(x)**2)**Rational(1, 4)*cos(atan2(im(x), re(x))/2), + (re(x)**2 + im(x)**2)**Rational(1, 4)*sin(atan2(im(x), re(x))/2)) + + # issue 3853 + a, b = symbols('a,b', real=True) + assert ((1 + sqrt(a + b*I))/2).as_real_imag() == \ + ( + (a**2 + b**2)**Rational( + 1, 4)*cos(atan2(b, a)/2)/2 + S.Half, + (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2) + + assert sqrt(a**2).as_real_imag() == (sqrt(a**2), 0) + i = symbols('i', imaginary=True) + assert sqrt(i**2).as_real_imag() == (0, abs(i)) + + assert ((1 + I)/(1 - I)).as_real_imag() == (0, 1) + assert ((1 + I)**3/(1 - I)).as_real_imag() == (-2, 0) + + +@XFAIL +def test_sign_issue_3068(): + n = pi**1000 + i = int(n) + x = Symbol('x') + assert (n - i).round() == 1 # doesn't hang + assert sign(n - i) == 1 + # perhaps it's not possible to get the sign right when + # only 1 digit is being requested for this situation; + # 2 digits works + assert (n - x).n(1, subs={x: i}) > 0 + assert (n - x).n(2, subs={x: i}) > 0 + + +def test_Abs(): + raises(TypeError, lambda: Abs(Interval(2, 3))) # issue 8717 + + x, y = symbols('x,y') + assert sign(sign(x)) == sign(x) + assert sign(x*y).func is sign + assert Abs(0) == 0 + assert Abs(1) == 1 + assert Abs(-1) == 1 + assert Abs(I) == 1 + assert Abs(-I) == 1 + assert Abs(nan) is nan + assert Abs(zoo) is oo + assert Abs(I * pi) == pi + assert Abs(-I * pi) == pi + assert Abs(I * x) == Abs(x) + assert Abs(-I * x) == Abs(x) + assert Abs(-2*x) == 2*Abs(x) + assert Abs(-2.0*x) == 2.0*Abs(x) + assert Abs(2*pi*x*y) == 2*pi*Abs(x*y) + assert Abs(conjugate(x)) == Abs(x) + assert conjugate(Abs(x)) == Abs(x) + assert Abs(x).expand(complex=True) == sqrt(re(x)**2 + im(x)**2) + + a = Symbol('a', positive=True) + assert Abs(2*pi*x*a) == 2*pi*a*Abs(x) + assert Abs(2*pi*I*x*a) == 2*pi*a*Abs(x) + + x = Symbol('x', real=True) + n = Symbol('n', integer=True) + assert Abs((-1)**n) == 1 + assert x**(2*n) == Abs(x)**(2*n) + assert Abs(x).diff(x) == sign(x) + assert abs(x) == Abs(x) # Python built-in + assert Abs(x)**3 == x**2*Abs(x) + assert Abs(x)**4 == x**4 + assert ( + Abs(x)**(3*n)).args == (Abs(x), 3*n) # leave symbolic odd unchanged + assert (1/Abs(x)).args == (Abs(x), -1) + assert 1/Abs(x)**3 == 1/(x**2*Abs(x)) + assert Abs(x)**-3 == Abs(x)/(x**4) + assert Abs(x**3) == x**2*Abs(x) + assert Abs(I**I) == exp(-pi/2) + assert Abs((4 + 5*I)**(6 + 7*I)) == 68921*exp(-7*atan(Rational(5, 4))) + y = Symbol('y', real=True) + assert Abs(I**y) == 1 + y = Symbol('y') + assert Abs(I**y) == exp(-pi*im(y)/2) + + x = Symbol('x', imaginary=True) + assert Abs(x).diff(x) == -sign(x) + + eq = -sqrt(10 + 6*sqrt(3)) + sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) + # if there is a fast way to know when you can and when you cannot prove an + # expression like this is zero then the equality to zero is ok + assert abs(eq).func is Abs or abs(eq) == 0 + # but sometimes it's hard to do this so it's better not to load + # abs down with tests that will be very slow + q = 1 + sqrt(2) - 2*sqrt(3) + 1331*sqrt(6) + p = expand(q**3)**Rational(1, 3) + d = p - q + assert abs(d).func is Abs or abs(d) == 0 + + assert Abs(4*exp(pi*I/4)) == 4 + assert Abs(3**(2 + I)) == 9 + assert Abs((-3)**(1 - I)) == 3*exp(pi) + + assert Abs(oo) is oo + assert Abs(-oo) is oo + assert Abs(oo + I) is oo + assert Abs(oo + I*oo) is oo + + a = Symbol('a', algebraic=True) + t = Symbol('t', transcendental=True) + x = Symbol('x') + assert re(a).is_algebraic + assert re(x).is_algebraic is None + assert re(t).is_algebraic is False + assert Abs(x).fdiff() == sign(x) + raises(ArgumentIndexError, lambda: Abs(x).fdiff(2)) + + # doesn't have recursion error + arg = sqrt(acos(1 - I)*acos(1 + I)) + assert abs(arg) == arg + + # special handling to put Abs in denom + assert abs(1/x) == 1/Abs(x) + e = abs(2/x**2) + assert e.is_Mul and e == 2/Abs(x**2) + assert unchanged(Abs, y/x) + assert unchanged(Abs, x/(x + 1)) + assert unchanged(Abs, x*y) + p = Symbol('p', positive=True) + assert abs(x/p) == abs(x)/p + + # coverage + assert unchanged(Abs, Symbol('x', real=True)**y) + # issue 19627 + f = Function('f', positive=True) + assert sqrt(f(x)**2) == f(x) + # issue 21625 + assert unchanged(Abs, S("im(acos(-i + acosh(-g + i)))")) + + +def test_Abs_rewrite(): + x = Symbol('x', real=True) + a = Abs(x).rewrite(Heaviside).expand() + assert a == x*Heaviside(x) - x*Heaviside(-x) + for i in [-2, -1, 0, 1, 2]: + assert a.subs(x, i) == abs(i) + y = Symbol('y') + assert Abs(y).rewrite(Heaviside) == Abs(y) + + x, y = Symbol('x', real=True), Symbol('y') + assert Abs(x).rewrite(Piecewise) == Piecewise((x, x >= 0), (-x, True)) + assert Abs(y).rewrite(Piecewise) == Abs(y) + assert Abs(y).rewrite(sign) == y/sign(y) + + i = Symbol('i', imaginary=True) + assert abs(i).rewrite(Piecewise) == Piecewise((I*i, I*i >= 0), (-I*i, True)) + + + assert Abs(y).rewrite(conjugate) == sqrt(y*conjugate(y)) + assert Abs(i).rewrite(conjugate) == sqrt(-i**2) # == -I*i + + y = Symbol('y', extended_real=True) + assert (Abs(exp(-I*x)-exp(-I*y))**2).rewrite(conjugate) == \ + -exp(I*x)*exp(-I*y) + 2 - exp(-I*x)*exp(I*y) + + +def test_Abs_real(): + # test some properties of abs that only apply + # to real numbers + x = Symbol('x', complex=True) + assert sqrt(x**2) != Abs(x) + assert Abs(x**2) != x**2 + + x = Symbol('x', real=True) + assert sqrt(x**2) == Abs(x) + assert Abs(x**2) == x**2 + + # if the symbol is zero, the following will still apply + nn = Symbol('nn', nonnegative=True, real=True) + np = Symbol('np', nonpositive=True, real=True) + assert Abs(nn) == nn + assert Abs(np) == -np + + +def test_Abs_properties(): + x = Symbol('x') + assert Abs(x).is_real is None + assert Abs(x).is_extended_real is True + assert Abs(x).is_rational is None + assert Abs(x).is_positive is None + assert Abs(x).is_nonnegative is None + assert Abs(x).is_extended_positive is None + assert Abs(x).is_extended_nonnegative is True + + f = Symbol('x', finite=True) + assert Abs(f).is_real is True + assert Abs(f).is_extended_real is True + assert Abs(f).is_rational is None + assert Abs(f).is_positive is None + assert Abs(f).is_nonnegative is True + assert Abs(f).is_extended_positive is None + assert Abs(f).is_extended_nonnegative is True + + z = Symbol('z', complex=True, zero=False) + assert Abs(z).is_real is True # since complex implies finite + assert Abs(z).is_extended_real is True + assert Abs(z).is_rational is None + assert Abs(z).is_positive is True + assert Abs(z).is_extended_positive is True + assert Abs(z).is_zero is False + + p = Symbol('p', positive=True) + assert Abs(p).is_real is True + assert Abs(p).is_extended_real is True + assert Abs(p).is_rational is None + assert Abs(p).is_positive is True + assert Abs(p).is_zero is False + + q = Symbol('q', rational=True) + assert Abs(q).is_real is True + assert Abs(q).is_rational is True + assert Abs(q).is_integer is None + assert Abs(q).is_positive is None + assert Abs(q).is_nonnegative is True + + i = Symbol('i', integer=True) + assert Abs(i).is_real is True + assert Abs(i).is_integer is True + assert Abs(i).is_positive is None + assert Abs(i).is_nonnegative is True + + e = Symbol('n', even=True) + ne = Symbol('ne', real=True, even=False) + assert Abs(e).is_even is True + assert Abs(ne).is_even is False + assert Abs(i).is_even is None + + o = Symbol('n', odd=True) + no = Symbol('no', real=True, odd=False) + assert Abs(o).is_odd is True + assert Abs(no).is_odd is False + assert Abs(i).is_odd is None + + +def test_abs(): + # this tests that abs calls Abs; don't rename to + # test_Abs since that test is already above + a = Symbol('a', positive=True) + assert abs(I*(1 + a)**2) == (1 + a)**2 + + +def test_arg(): + assert arg(0) is nan + assert arg(1) == 0 + assert arg(-1) == pi + assert arg(I) == pi/2 + assert arg(-I) == -pi/2 + assert arg(1 + I) == pi/4 + assert arg(-1 + I) == pi*Rational(3, 4) + assert arg(1 - I) == -pi/4 + assert arg(exp_polar(4*pi*I)) == 4*pi + assert arg(exp_polar(-7*pi*I)) == -7*pi + assert arg(exp_polar(5 - 3*pi*I/4)) == pi*Rational(-3, 4) + + assert arg(exp(I*pi/7)) == pi/7 # issue 17300 + assert arg(exp(16*I)) == 16 - 6*pi + assert arg(exp(13*I*pi/12)) == -11*pi/12 + assert arg(exp(123 - 5*I)) == -5 + 2*pi + assert arg(exp(sin(1 + 3*I))) == -2*pi + cos(1)*sinh(3) + r = Symbol('r', real=True) + assert arg(exp(r - 2*I)) == -2 + + f = Function('f') + assert not arg(f(0) + I*f(1)).atoms(re) + + # check nesting + x = Symbol('x') + assert arg(arg(arg(x))) is not S.NaN + assert arg(arg(arg(arg(x)))) is S.NaN + r = Symbol('r', extended_real=True) + assert arg(arg(r)) is not S.NaN + assert arg(arg(arg(r))) is S.NaN + + p = Function('p', extended_positive=True) + assert arg(p(x)) == 0 + assert arg((3 + I)*p(x)) == arg(3 + I) + + p = Symbol('p', positive=True) + assert arg(p) == 0 + assert arg(p*I) == pi/2 + + n = Symbol('n', negative=True) + assert arg(n) == pi + assert arg(n*I) == -pi/2 + + x = Symbol('x') + assert conjugate(arg(x)) == arg(x) + + e = p + I*p**2 + assert arg(e) == arg(1 + p*I) + # make sure sign doesn't swap + e = -2*p + 4*I*p**2 + assert arg(e) == arg(-1 + 2*p*I) + # make sure sign isn't lost + x = symbols('x', real=True) # could be zero + e = x + I*x + assert arg(e) == arg(x*(1 + I)) + assert arg(e/p) == arg(x*(1 + I)) + e = p*cos(p) + I*log(p)*exp(p) + assert arg(e).args[0] == e + # keep it simple -- let the user do more advanced cancellation + e = (p + 1) + I*(p**2 - 1) + assert arg(e).args[0] == e + + f = Function('f') + e = 2*x*(f(0) - 1) - 2*x*f(0) + assert arg(e) == arg(-2*x) + assert arg(f(0)).func == arg and arg(f(0)).args == (f(0),) + + +def test_arg_rewrite(): + assert arg(1 + I) == atan2(1, 1) + + x = Symbol('x', real=True) + y = Symbol('y', real=True) + assert arg(x + I*y).rewrite(atan2) == atan2(y, x) + + +def test_adjoint(): + a = Symbol('a', antihermitian=True) + b = Symbol('b', hermitian=True) + assert adjoint(a) == -a + assert adjoint(I*a) == I*a + assert adjoint(b) == b + assert adjoint(I*b) == -I*b + assert adjoint(a*b) == -b*a + assert adjoint(I*a*b) == I*b*a + + x, y = symbols('x y') + assert adjoint(adjoint(x)) == x + assert adjoint(x + y) == adjoint(x) + adjoint(y) + assert adjoint(x - y) == adjoint(x) - adjoint(y) + assert adjoint(x * y) == adjoint(x) * adjoint(y) + assert adjoint(x / y) == adjoint(x) / adjoint(y) + assert adjoint(-x) == -adjoint(x) + + x, y = symbols('x y', commutative=False) + assert adjoint(adjoint(x)) == x + assert adjoint(x + y) == adjoint(x) + adjoint(y) + assert adjoint(x - y) == adjoint(x) - adjoint(y) + assert adjoint(x * y) == adjoint(y) * adjoint(x) + assert adjoint(x / y) == 1 / adjoint(y) * adjoint(x) + assert adjoint(-x) == -adjoint(x) + + +def test_conjugate(): + a = Symbol('a', real=True) + b = Symbol('b', imaginary=True) + assert conjugate(a) == a + assert conjugate(I*a) == -I*a + assert conjugate(b) == -b + assert conjugate(I*b) == I*b + assert conjugate(a*b) == -a*b + assert conjugate(I*a*b) == I*a*b + + x, y = symbols('x y') + assert conjugate(conjugate(x)) == x + assert conjugate(x).inverse() == conjugate + assert conjugate(x + y) == conjugate(x) + conjugate(y) + assert conjugate(x - y) == conjugate(x) - conjugate(y) + assert conjugate(x * y) == conjugate(x) * conjugate(y) + assert conjugate(x / y) == conjugate(x) / conjugate(y) + assert conjugate(-x) == -conjugate(x) + + a = Symbol('a', algebraic=True) + t = Symbol('t', transcendental=True) + assert re(a).is_algebraic + assert re(x).is_algebraic is None + assert re(t).is_algebraic is False + + +def test_conjugate_transpose(): + x = Symbol('x') + assert conjugate(transpose(x)) == adjoint(x) + assert transpose(conjugate(x)) == adjoint(x) + assert adjoint(transpose(x)) == conjugate(x) + assert transpose(adjoint(x)) == conjugate(x) + assert adjoint(conjugate(x)) == transpose(x) + assert conjugate(adjoint(x)) == transpose(x) + + class Symmetric(Expr): + def _eval_adjoint(self): + return None + + def _eval_conjugate(self): + return None + + def _eval_transpose(self): + return self + x = Symmetric() + assert conjugate(x) == adjoint(x) + assert transpose(x) == x + + +def test_transpose(): + a = Symbol('a', complex=True) + assert transpose(a) == a + assert transpose(I*a) == I*a + + x, y = symbols('x y') + assert transpose(transpose(x)) == x + assert transpose(x + y) == transpose(x) + transpose(y) + assert transpose(x - y) == transpose(x) - transpose(y) + assert transpose(x * y) == transpose(x) * transpose(y) + assert transpose(x / y) == transpose(x) / transpose(y) + assert transpose(-x) == -transpose(x) + + x, y = symbols('x y', commutative=False) + assert transpose(transpose(x)) == x + assert transpose(x + y) == transpose(x) + transpose(y) + assert transpose(x - y) == transpose(x) - transpose(y) + assert transpose(x * y) == transpose(y) * transpose(x) + assert transpose(x / y) == 1 / transpose(y) * transpose(x) + assert transpose(-x) == -transpose(x) + + +@_both_exp_pow +def test_polarify(): + from sympy.functions.elementary.complexes import (polar_lift, polarify) + x = Symbol('x') + z = Symbol('z', polar=True) + f = Function('f') + ES = {} + + assert polarify(-1) == (polar_lift(-1), ES) + assert polarify(1 + I) == (polar_lift(1 + I), ES) + + assert polarify(exp(x), subs=False) == exp(x) + assert polarify(1 + x, subs=False) == 1 + x + assert polarify(f(I) + x, subs=False) == f(polar_lift(I)) + x + + assert polarify(x, lift=True) == polar_lift(x) + assert polarify(z, lift=True) == z + assert polarify(f(x), lift=True) == f(polar_lift(x)) + assert polarify(1 + x, lift=True) == polar_lift(1 + x) + assert polarify(1 + f(x), lift=True) == polar_lift(1 + f(polar_lift(x))) + + newex, subs = polarify(f(x) + z) + assert newex.subs(subs) == f(x) + z + + mu = Symbol("mu") + sigma = Symbol("sigma", positive=True) + + # Make sure polarify(lift=True) doesn't try to lift the integration + # variable + assert polarify( + Integral(sqrt(2)*x*exp(-(-mu + x)**2/(2*sigma**2))/(2*sqrt(pi)*sigma), + (x, -oo, oo)), lift=True) == Integral(sqrt(2)*(sigma*exp_polar(0))**exp_polar(I*pi)* + exp((sigma*exp_polar(0))**(2*exp_polar(I*pi))*exp_polar(I*pi)*polar_lift(-mu + x)** + (2*exp_polar(0))/2)*exp_polar(0)*polar_lift(x)/(2*sqrt(pi)), (x, -oo, oo)) + + +def test_unpolarify(): + from sympy.functions.elementary.complexes import (polar_lift, principal_branch, unpolarify) + from sympy.core.relational import Ne + from sympy.functions.elementary.hyperbolic import tanh + from sympy.functions.special.error_functions import erf + from sympy.functions.special.gamma_functions import (gamma, uppergamma) + from sympy.abc import x + p = exp_polar(7*I) + 1 + u = exp(7*I) + 1 + + assert unpolarify(1) == 1 + assert unpolarify(p) == u + assert unpolarify(p**2) == u**2 + assert unpolarify(p**x) == p**x + assert unpolarify(p*x) == u*x + assert unpolarify(p + x) == u + x + assert unpolarify(sqrt(sin(p))) == sqrt(sin(u)) + + # Test reduction to principal branch 2*pi. + t = principal_branch(x, 2*pi) + assert unpolarify(t) == x + assert unpolarify(sqrt(t)) == sqrt(t) + + # Test exponents_only. + assert unpolarify(p**p, exponents_only=True) == p**u + assert unpolarify(uppergamma(x, p**p)) == uppergamma(x, p**u) + + # Test functions. + assert unpolarify(sin(p)) == sin(u) + assert unpolarify(tanh(p)) == tanh(u) + assert unpolarify(gamma(p)) == gamma(u) + assert unpolarify(erf(p)) == erf(u) + assert unpolarify(uppergamma(x, p)) == uppergamma(x, p) + + assert unpolarify(uppergamma(sin(p), sin(p + exp_polar(0)))) == \ + uppergamma(sin(u), sin(u + 1)) + assert unpolarify(uppergamma(polar_lift(0), 2*exp_polar(0))) == \ + uppergamma(0, 2) + + assert unpolarify(Eq(p, 0)) == Eq(u, 0) + assert unpolarify(Ne(p, 0)) == Ne(u, 0) + assert unpolarify(polar_lift(x) > 0) == (x > 0) + + # Test bools + assert unpolarify(True) is True + + +def test_issue_4035(): + x = Symbol('x') + assert Abs(x).expand(trig=True) == Abs(x) + assert sign(x).expand(trig=True) == sign(x) + assert arg(x).expand(trig=True) == arg(x) + + +def test_issue_3206(): + x = Symbol('x') + assert Abs(Abs(x)) == Abs(x) + + +def test_issue_4754_derivative_conjugate(): + x = Symbol('x', real=True) + y = Symbol('y', imaginary=True) + f = Function('f') + assert (f(x).conjugate()).diff(x) == (f(x).diff(x)).conjugate() + assert (f(y).conjugate()).diff(y) == -(f(y).diff(y)).conjugate() + + +def test_derivatives_issue_4757(): + x = Symbol('x', real=True) + y = Symbol('y', imaginary=True) + f = Function('f') + assert re(f(x)).diff(x) == re(f(x).diff(x)) + assert im(f(x)).diff(x) == im(f(x).diff(x)) + assert re(f(y)).diff(y) == -I*im(f(y).diff(y)) + assert im(f(y)).diff(y) == -I*re(f(y).diff(y)) + assert Abs(f(x)).diff(x).subs(f(x), 1 + I*x).doit() == x/sqrt(1 + x**2) + assert arg(f(x)).diff(x).subs(f(x), 1 + I*x**2).doit() == 2*x/(1 + x**4) + assert Abs(f(y)).diff(y).subs(f(y), 1 + y).doit() == -y/sqrt(1 - y**2) + assert arg(f(y)).diff(y).subs(f(y), I + y**2).doit() == 2*y/(1 + y**4) + + +def test_issue_11413(): + from sympy.simplify.simplify import simplify + v0 = Symbol('v0') + v1 = Symbol('v1') + v2 = Symbol('v2') + V = Matrix([[v0],[v1],[v2]]) + U = V.normalized() + assert U == Matrix([ + [v0/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)], + [v1/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)], + [v2/sqrt(Abs(v0)**2 + Abs(v1)**2 + Abs(v2)**2)]]) + U.norm = sqrt(v0**2/(v0**2 + v1**2 + v2**2) + v1**2/(v0**2 + v1**2 + v2**2) + v2**2/(v0**2 + v1**2 + v2**2)) + assert simplify(U.norm) == 1 + + +def test_periodic_argument(): + from sympy.functions.elementary.complexes import (periodic_argument, polar_lift, principal_branch, unbranched_argument) + x = Symbol('x') + p = Symbol('p', positive=True) + + assert unbranched_argument(2 + I) == periodic_argument(2 + I, oo) + assert unbranched_argument(1 + x) == periodic_argument(1 + x, oo) + assert N_equals(unbranched_argument((1 + I)**2), pi/2) + assert N_equals(unbranched_argument((1 - I)**2), -pi/2) + assert N_equals(periodic_argument((1 + I)**2, 3*pi), pi/2) + assert N_equals(periodic_argument((1 - I)**2, 3*pi), -pi/2) + + assert unbranched_argument(principal_branch(x, pi)) == \ + periodic_argument(x, pi) + + assert unbranched_argument(polar_lift(2 + I)) == unbranched_argument(2 + I) + assert periodic_argument(polar_lift(2 + I), 2*pi) == \ + periodic_argument(2 + I, 2*pi) + assert periodic_argument(polar_lift(2 + I), 3*pi) == \ + periodic_argument(2 + I, 3*pi) + assert periodic_argument(polar_lift(2 + I), pi) == \ + periodic_argument(polar_lift(2 + I), pi) + + assert unbranched_argument(polar_lift(1 + I)) == pi/4 + assert periodic_argument(2*p, p) == periodic_argument(p, p) + assert periodic_argument(pi*p, p) == periodic_argument(p, p) + + assert Abs(polar_lift(1 + I)) == Abs(1 + I) + + +@XFAIL +def test_principal_branch_fail(): + # TODO XXX why does abs(x)._eval_evalf() not fall back to global evalf? + from sympy.functions.elementary.complexes import principal_branch + assert N_equals(principal_branch((1 + I)**2, pi/2), 0) + + +def test_principal_branch(): + from sympy.functions.elementary.complexes import (polar_lift, principal_branch) + p = Symbol('p', positive=True) + x = Symbol('x') + neg = Symbol('x', negative=True) + + assert principal_branch(polar_lift(x), p) == principal_branch(x, p) + assert principal_branch(polar_lift(2 + I), p) == principal_branch(2 + I, p) + assert principal_branch(2*x, p) == 2*principal_branch(x, p) + assert principal_branch(1, pi) == exp_polar(0) + assert principal_branch(-1, 2*pi) == exp_polar(I*pi) + assert principal_branch(-1, pi) == exp_polar(0) + assert principal_branch(exp_polar(3*pi*I)*x, 2*pi) == \ + principal_branch(exp_polar(I*pi)*x, 2*pi) + assert principal_branch(neg*exp_polar(pi*I), 2*pi) == neg*exp_polar(-I*pi) + # related to issue #14692 + assert principal_branch(exp_polar(-I*pi/2)/polar_lift(neg), 2*pi) == \ + exp_polar(-I*pi/2)/neg + + assert N_equals(principal_branch((1 + I)**2, 2*pi), 2*I) + assert N_equals(principal_branch((1 + I)**2, 3*pi), 2*I) + assert N_equals(principal_branch((1 + I)**2, 1*pi), 2*I) + + # test argument sanitization + assert principal_branch(x, I).func is principal_branch + assert principal_branch(x, -4).func is principal_branch + assert principal_branch(x, -oo).func is principal_branch + assert principal_branch(x, zoo).func is principal_branch + + +@XFAIL +def test_issue_6167_6151(): + n = pi**1000 + i = int(n) + assert sign(n - i) == 1 + assert abs(n - i) == n - i + x = Symbol('x') + eps = pi**-1500 + big = pi**1000 + one = cos(x)**2 + sin(x)**2 + e = big*one - big + eps + from sympy.simplify.simplify import simplify + assert sign(simplify(e)) == 1 + for xi in (111, 11, 1, Rational(1, 10)): + assert sign(e.subs(x, xi)) == 1 + + +def test_issue_14216(): + from sympy.functions.elementary.complexes import unpolarify + A = MatrixSymbol("A", 2, 2) + assert unpolarify(A[0, 0]) == A[0, 0] + assert unpolarify(A[0, 0]*A[1, 0]) == A[0, 0]*A[1, 0] + + +def test_issue_14238(): + # doesn't cause recursion error + r = Symbol('r', real=True) + assert Abs(r + Piecewise((0, r > 0), (1 - r, True))) + + +def test_issue_22189(): + x = Symbol('x') + for a in (sqrt(7 - 2*x) - 2, 1 - x): + assert Abs(a) - Abs(-a) == 0, a + + +def test_zero_assumptions(): + nr = Symbol('nonreal', real=False, finite=True) + ni = Symbol('nonimaginary', imaginary=False) + # imaginary implies not zero + nzni = Symbol('nonzerononimaginary', zero=False, imaginary=False) + + assert re(nr).is_zero is None + assert im(nr).is_zero is False + + assert re(ni).is_zero is None + assert im(ni).is_zero is None + + assert re(nzni).is_zero is False + assert im(nzni).is_zero is None + + +@_both_exp_pow +def test_issue_15893(): + f = Function('f', real=True) + x = Symbol('x', real=True) + eq = Derivative(Abs(f(x)), f(x)) + assert eq.doit() == sign(f(x)) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_exponential.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_exponential.py new file mode 100644 index 0000000000000000000000000000000000000000..686ae3b363f14d333dbedd1ff801f2ad4594893a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_exponential.py @@ -0,0 +1,813 @@ +from sympy.assumptions.refine import refine +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.concrete.products import Product +from sympy.concrete.summations import Sum +from sympy.core.function import expand_log +from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (adjoint, conjugate, re, sign, transpose) +from sympy.functions.elementary.exponential import (LambertW, exp, exp_polar, log) +from sympy.functions.elementary.hyperbolic import (cosh, sinh, tanh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin, tan) +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.polys.polytools import gcd +from sympy.series.order import O +from sympy.simplify.simplify import simplify +from sympy.core.parameters import global_parameters +from sympy.functions.elementary.exponential import match_real_imag +from sympy.abc import x, y, z +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.testing.pytest import raises, XFAIL, _both_exp_pow + + +@_both_exp_pow +def test_exp_values(): + if global_parameters.exp_is_pow: + assert type(exp(x)) is Pow + else: + assert type(exp(x)) is exp + + k = Symbol('k', integer=True) + + assert exp(nan) is nan + + assert exp(oo) is oo + assert exp(-oo) == 0 + + assert exp(0) == 1 + assert exp(1) == E + assert exp(-1 + x).as_base_exp() == (S.Exp1, x - 1) + assert exp(1 + x).as_base_exp() == (S.Exp1, x + 1) + + assert exp(pi*I/2) == I + assert exp(pi*I) == -1 + assert exp(pi*I*Rational(3, 2)) == -I + assert exp(2*pi*I) == 1 + + assert refine(exp(pi*I*2*k)) == 1 + assert refine(exp(pi*I*2*(k + S.Half))) == -1 + assert refine(exp(pi*I*2*(k + Rational(1, 4)))) == I + assert refine(exp(pi*I*2*(k + Rational(3, 4)))) == -I + + assert exp(log(x)) == x + assert exp(2*log(x)) == x**2 + assert exp(pi*log(x)) == x**pi + + assert exp(17*log(x) + E*log(y)) == x**17 * y**E + + assert exp(x*log(x)) != x**x + assert exp(sin(x)*log(x)) != x + + assert exp(3*log(x) + oo*x) == exp(oo*x) * x**3 + assert exp(4*log(x)*log(y) + 3*log(x)) == x**3 * exp(4*log(x)*log(y)) + + assert exp(-oo, evaluate=False).is_finite is True + assert exp(oo, evaluate=False).is_finite is False + + +@_both_exp_pow +def test_exp_period(): + assert exp(I*pi*Rational(9, 4)) == exp(I*pi/4) + assert exp(I*pi*Rational(46, 18)) == exp(I*pi*Rational(5, 9)) + assert exp(I*pi*Rational(25, 7)) == exp(I*pi*Rational(-3, 7)) + assert exp(I*pi*Rational(-19, 3)) == exp(-I*pi/3) + assert exp(I*pi*Rational(37, 8)) - exp(I*pi*Rational(-11, 8)) == 0 + assert exp(I*pi*Rational(-5, 3)) / exp(I*pi*Rational(11, 5)) * exp(I*pi*Rational(148, 15)) == 1 + + assert exp(2 - I*pi*Rational(17, 5)) == exp(2 + I*pi*Rational(3, 5)) + assert exp(log(3) + I*pi*Rational(29, 9)) == 3 * exp(I*pi*Rational(-7, 9)) + + n = Symbol('n', integer=True) + e = Symbol('e', even=True) + assert exp(e*I*pi) == 1 + assert exp((e + 1)*I*pi) == -1 + assert exp((1 + 4*n)*I*pi/2) == I + assert exp((-1 + 4*n)*I*pi/2) == -I + + +@_both_exp_pow +def test_exp_log(): + x = Symbol("x", real=True) + assert log(exp(x)) == x + assert exp(log(x)) == x + + if not global_parameters.exp_is_pow: + assert log(x).inverse() == exp + assert exp(x).inverse() == log + + y = Symbol("y", polar=True) + assert log(exp_polar(z)) == z + assert exp(log(y)) == y + + +@_both_exp_pow +def test_exp_expand(): + e = exp(log(Rational(2))*(1 + x) - log(Rational(2))*x) + assert e.expand() == 2 + assert exp(x + y) != exp(x)*exp(y) + assert exp(x + y).expand() == exp(x)*exp(y) + + +@_both_exp_pow +def test_exp__as_base_exp(): + assert exp(x).as_base_exp() == (E, x) + assert exp(2*x).as_base_exp() == (E, 2*x) + assert exp(x*y).as_base_exp() == (E, x*y) + assert exp(-x).as_base_exp() == (E, -x) + + # Pow( *expr.as_base_exp() ) == expr invariant should hold + assert E**x == exp(x) + assert E**(2*x) == exp(2*x) + assert E**(x*y) == exp(x*y) + + assert exp(x).base is S.Exp1 + assert exp(x).exp == x + + +@_both_exp_pow +def test_exp_infinity(): + assert exp(I*y) != nan + assert refine(exp(I*oo)) is nan + assert refine(exp(-I*oo)) is nan + assert exp(y*I*oo) != nan + assert exp(zoo) is nan + x = Symbol('x', extended_real=True, finite=False) + assert exp(x).is_complex is None + + +@_both_exp_pow +def test_exp_subs(): + x = Symbol('x') + e = (exp(3*log(x), evaluate=False)) # evaluates to x**3 + assert e.subs(x**3, y**3) == e + assert e.subs(x**2, 5) == e + assert (x**3).subs(x**2, y) != y**Rational(3, 2) + assert exp(exp(x) + exp(x**2)).subs(exp(exp(x)), y) == y * exp(exp(x**2)) + assert exp(x).subs(E, y) == y**x + x = symbols('x', real=True) + assert exp(5*x).subs(exp(7*x), y) == y**Rational(5, 7) + assert exp(2*x + 7).subs(exp(3*x), y) == y**Rational(2, 3) * exp(7) + x = symbols('x', positive=True) + assert exp(3*log(x)).subs(x**2, y) == y**Rational(3, 2) + # differentiate between E and exp + assert exp(exp(x + E)).subs(exp, 3) == 3**(3**(x + E)) + assert exp(exp(x + E)).subs(exp, sin) == sin(sin(x + E)) + assert exp(exp(x + E)).subs(E, 3) == 3**(3**(x + 3)) + assert exp(3).subs(E, sin) == sin(3) + + +def test_exp_adjoint(): + assert adjoint(exp(x)) == exp(adjoint(x)) + + +def test_exp_conjugate(): + assert conjugate(exp(x)) == exp(conjugate(x)) + + +@_both_exp_pow +def test_exp_transpose(): + assert transpose(exp(x)) == exp(transpose(x)) + + +@_both_exp_pow +def test_exp_rewrite(): + assert exp(x).rewrite(sin) == sinh(x) + cosh(x) + assert exp(x*I).rewrite(cos) == cos(x) + I*sin(x) + assert exp(1).rewrite(cos) == sinh(1) + cosh(1) + assert exp(1).rewrite(sin) == sinh(1) + cosh(1) + assert exp(1).rewrite(sin) == sinh(1) + cosh(1) + assert exp(x).rewrite(tanh) == (1 + tanh(x/2))/(1 - tanh(x/2)) + assert exp(pi*I/4).rewrite(sqrt) == sqrt(2)/2 + sqrt(2)*I/2 + assert exp(pi*I/3).rewrite(sqrt) == S.Half + sqrt(3)*I/2 + if not global_parameters.exp_is_pow: + assert exp(x*log(y)).rewrite(Pow) == y**x + assert exp(log(x)*log(y)).rewrite(Pow) in [x**log(y), y**log(x)] + assert exp(log(log(x))*y).rewrite(Pow) == log(x)**y + + n = Symbol('n', integer=True) + + assert Sum((exp(pi*I/2)/2)**n, (n, 0, oo)).rewrite(sqrt).doit() == Rational(4, 5) + I*2/5 + assert Sum((exp(pi*I/4)/2)**n, (n, 0, oo)).rewrite(sqrt).doit() == 1/(1 - sqrt(2)*(1 + I)/4) + assert (Sum((exp(pi*I/3)/2)**n, (n, 0, oo)).rewrite(sqrt).doit().cancel() + == 4*I/(sqrt(3) + 3*I)) + + +@_both_exp_pow +def test_exp_leading_term(): + assert exp(x).as_leading_term(x) == 1 + assert exp(2 + x).as_leading_term(x) == exp(2) + assert exp((2*x + 3) / (x+1)).as_leading_term(x) == exp(3) + + # The following tests are commented, since now SymPy returns the + # original function when the leading term in the series expansion does + # not exist. + # raises(NotImplementedError, lambda: exp(1/x).as_leading_term(x)) + # raises(NotImplementedError, lambda: exp((x + 1) / x**2).as_leading_term(x)) + # raises(NotImplementedError, lambda: exp(x + 1/x).as_leading_term(x)) + + +@_both_exp_pow +def test_exp_taylor_term(): + x = symbols('x') + assert exp(x).taylor_term(1, x) == x + assert exp(x).taylor_term(3, x) == x**3/6 + assert exp(x).taylor_term(4, x) == x**4/24 + assert exp(x).taylor_term(-1, x) is S.Zero + + +def test_exp_MatrixSymbol(): + A = MatrixSymbol("A", 2, 2) + assert exp(A).has(exp) + + +def test_exp_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: exp(x).fdiff(2)) + + +def test_log_values(): + assert log(nan) is nan + + assert log(oo) is oo + assert log(-oo) is oo + + assert log(zoo) is zoo + assert log(-zoo) is zoo + + assert log(0) is zoo + + assert log(1) == 0 + assert log(-1) == I*pi + + assert log(E) == 1 + assert log(-E).expand() == 1 + I*pi + + assert unchanged(log, pi) + assert log(-pi).expand() == log(pi) + I*pi + + assert unchanged(log, 17) + assert log(-17) == log(17) + I*pi + + assert log(I) == I*pi/2 + assert log(-I) == -I*pi/2 + + assert log(17*I) == I*pi/2 + log(17) + assert log(-17*I).expand() == -I*pi/2 + log(17) + + assert log(oo*I) is oo + assert log(-oo*I) is oo + assert log(0, 2) is zoo + assert log(0, 5) is zoo + + assert exp(-log(3))**(-1) == 3 + + assert log(S.Half) == -log(2) + assert log(2*3).func is log + assert log(2*3**2).func is log + + +def test_match_real_imag(): + x, y = symbols('x,y', real=True) + i = Symbol('i', imaginary=True) + assert match_real_imag(S.One) == (1, 0) + assert match_real_imag(I) == (0, 1) + assert match_real_imag(3 - 5*I) == (3, -5) + assert match_real_imag(-sqrt(3) + S.Half*I) == (-sqrt(3), S.Half) + assert match_real_imag(x + y*I) == (x, y) + assert match_real_imag(x*I + y*I) == (0, x + y) + assert match_real_imag((x + y)*I) == (0, x + y) + assert match_real_imag(Rational(-2, 3)*i*I) == (None, None) + assert match_real_imag(1 - 2*i) == (None, None) + assert match_real_imag(sqrt(2)*(3 - 5*I)) == (None, None) + + +def test_log_exact(): + # check for pi/2, pi/3, pi/4, pi/6, pi/8, pi/12; pi/5, pi/10: + for n in range(-23, 24): + if gcd(n, 24) != 1: + assert log(exp(n*I*pi/24).rewrite(sqrt)) == n*I*pi/24 + for n in range(-9, 10): + assert log(exp(n*I*pi/10).rewrite(sqrt)) == n*I*pi/10 + + assert log(S.Half - I*sqrt(3)/2) == -I*pi/3 + assert log(Rational(-1, 2) + I*sqrt(3)/2) == I*pi*Rational(2, 3) + assert log(-sqrt(2)/2 - I*sqrt(2)/2) == -I*pi*Rational(3, 4) + assert log(-sqrt(3)/2 - I*S.Half) == -I*pi*Rational(5, 6) + + assert log(Rational(-1, 4) + sqrt(5)/4 - I*sqrt(sqrt(5)/8 + Rational(5, 8))) == -I*pi*Rational(2, 5) + assert log(sqrt(Rational(5, 8) - sqrt(5)/8) + I*(Rational(1, 4) + sqrt(5)/4)) == I*pi*Rational(3, 10) + assert log(-sqrt(sqrt(2)/4 + S.Half) + I*sqrt(S.Half - sqrt(2)/4)) == I*pi*Rational(7, 8) + assert log(-sqrt(6)/4 - sqrt(2)/4 + I*(-sqrt(6)/4 + sqrt(2)/4)) == -I*pi*Rational(11, 12) + + assert log(-1 + I*sqrt(3)) == log(2) + I*pi*Rational(2, 3) + assert log(5 + 5*I) == log(5*sqrt(2)) + I*pi/4 + assert log(sqrt(-12)) == log(2*sqrt(3)) + I*pi/2 + assert log(-sqrt(6) + sqrt(2) - I*sqrt(6) - I*sqrt(2)) == log(4) - I*pi*Rational(7, 12) + assert log(-sqrt(6-3*sqrt(2)) - I*sqrt(6+3*sqrt(2))) == log(2*sqrt(3)) - I*pi*Rational(5, 8) + assert log(1 + I*sqrt(2-sqrt(2))/sqrt(2+sqrt(2))) == log(2/sqrt(sqrt(2) + 2)) + I*pi/8 + assert log(cos(pi*Rational(7, 12)) + I*sin(pi*Rational(7, 12))) == I*pi*Rational(7, 12) + assert log(cos(pi*Rational(6, 5)) + I*sin(pi*Rational(6, 5))) == I*pi*Rational(-4, 5) + + assert log(5*(1 + I)/sqrt(2)) == log(5) + I*pi/4 + assert log(sqrt(2)*(-sqrt(3) + 1 - sqrt(3)*I - I)) == log(4) - I*pi*Rational(7, 12) + assert log(-sqrt(2)*(1 - I*sqrt(3))) == log(2*sqrt(2)) + I*pi*Rational(2, 3) + assert log(sqrt(3)*I*(-sqrt(6 - 3*sqrt(2)) - I*sqrt(3*sqrt(2) + 6))) == log(6) - I*pi/8 + + zero = (1 + sqrt(2))**2 - 3 - 2*sqrt(2) + assert log(zero - I*sqrt(3)) == log(sqrt(3)) - I*pi/2 + assert unchanged(log, zero + I*zero) or log(zero + zero*I) is zoo + + # bail quickly if no obvious simplification is possible: + assert unchanged(log, (sqrt(2)-1/sqrt(sqrt(3)+I))**1000) + # beware of non-real coefficients + assert unchanged(log, sqrt(2-sqrt(5))*(1 + I)) + + +def test_log_base(): + assert log(1, 2) == 0 + assert log(2, 2) == 1 + assert log(3, 2) == log(3)/log(2) + assert log(6, 2) == 1 + log(3)/log(2) + assert log(6, 3) == 1 + log(2)/log(3) + assert log(2**3, 2) == 3 + assert log(3**3, 3) == 3 + assert log(5, 1) is zoo + assert log(1, 1) is nan + assert log(Rational(2, 3), 10) == log(Rational(2, 3))/log(10) + assert log(Rational(2, 3), Rational(1, 3)) == -log(2)/log(3) + 1 + assert log(Rational(2, 3), Rational(2, 5)) == \ + log(Rational(2, 3))/log(Rational(2, 5)) + # issue 17148 + assert log(Rational(8, 3), 2) == -log(3)/log(2) + 3 + + +def test_log_symbolic(): + assert log(x, exp(1)) == log(x) + assert log(exp(x)) != x + + assert log(x, exp(1)) == log(x) + assert log(x*y) != log(x) + log(y) + assert log(x/y).expand() != log(x) - log(y) + assert log(x/y).expand(force=True) == log(x) - log(y) + assert log(x**y).expand() != y*log(x) + assert log(x**y).expand(force=True) == y*log(x) + + assert log(x, 2) == log(x)/log(2) + assert log(E, 2) == 1/log(2) + + p, q = symbols('p,q', positive=True) + r = Symbol('r', real=True) + + assert log(p**2) != 2*log(p) + assert log(p**2).expand() == 2*log(p) + assert log(x**2).expand() != 2*log(x) + assert log(p**q) != q*log(p) + assert log(exp(p)) == p + assert log(p*q) != log(p) + log(q) + assert log(p*q).expand() == log(p) + log(q) + + assert log(-sqrt(3)) == log(sqrt(3)) + I*pi + assert log(-exp(p)) != p + I*pi + assert log(-exp(x)).expand() != x + I*pi + assert log(-exp(r)).expand() == r + I*pi + + assert log(x**y) != y*log(x) + + assert (log(x**-5)**-1).expand() != -1/log(x)/5 + assert (log(p**-5)**-1).expand() == -1/log(p)/5 + assert log(-x).func is log and log(-x).args[0] == -x + assert log(-p).func is log and log(-p).args[0] == -p + + +def test_log_exp(): + assert log(exp(4*I*pi)) == 0 # exp evaluates + assert log(exp(-5*I*pi)) == I*pi # exp evaluates + assert log(exp(I*pi*Rational(19, 4))) == I*pi*Rational(3, 4) + assert log(exp(I*pi*Rational(25, 7))) == I*pi*Rational(-3, 7) + assert log(exp(-5*I)) == -5*I + 2*I*pi + + +@_both_exp_pow +def test_exp_assumptions(): + r = Symbol('r', real=True) + i = Symbol('i', imaginary=True) + for e in exp, exp_polar: + assert e(x).is_real is None + assert e(x).is_imaginary is None + assert e(i).is_real is None + assert e(i).is_imaginary is None + assert e(r).is_real is True + assert e(r).is_imaginary is False + assert e(re(x)).is_extended_real is True + assert e(re(x)).is_imaginary is False + + assert Pow(E, I*pi, evaluate=False).is_imaginary == False + assert Pow(E, 2*I*pi, evaluate=False).is_imaginary == False + assert Pow(E, I*pi/2, evaluate=False).is_imaginary == True + assert Pow(E, I*pi/3, evaluate=False).is_imaginary is None + + assert exp(0, evaluate=False).is_algebraic + + a = Symbol('a', algebraic=True) + an = Symbol('an', algebraic=True, nonzero=True) + r = Symbol('r', rational=True) + rn = Symbol('rn', rational=True, nonzero=True) + assert exp(a).is_algebraic is None + assert exp(an).is_algebraic is False + assert exp(pi*r).is_algebraic is None + assert exp(pi*rn).is_algebraic is False + + assert exp(0, evaluate=False).is_algebraic is True + assert exp(I*pi/3, evaluate=False).is_algebraic is True + assert exp(I*pi*r, evaluate=False).is_algebraic is True + + +@_both_exp_pow +def test_exp_AccumBounds(): + assert exp(AccumBounds(1, 2)) == AccumBounds(E, E**2) + + +def test_log_assumptions(): + p = symbols('p', positive=True) + n = symbols('n', negative=True) + z = symbols('z', zero=True) + x = symbols('x', infinite=True, extended_positive=True) + + assert log(z).is_positive is False + assert log(x).is_extended_positive is True + assert log(2) > 0 + assert log(1, evaluate=False).is_zero + assert log(1 + z).is_zero + assert log(p).is_zero is None + assert log(n).is_zero is False + assert log(0.5).is_negative is True + assert log(exp(p) + 1).is_positive + + assert log(1, evaluate=False).is_algebraic + assert log(42, evaluate=False).is_algebraic is False + + assert log(1 + z).is_rational + + +def test_log_hashing(): + assert x != log(log(x)) + assert hash(x) != hash(log(log(x))) + assert log(x) != log(log(log(x))) + + e = 1/log(log(x) + log(log(x))) + assert e.base.func is log + e = 1/log(log(x) + log(log(log(x)))) + assert e.base.func is log + + e = log(log(x)) + assert e.func is log + assert x.func is not log + assert hash(log(log(x))) != hash(x) + assert e != x + + +def test_log_sign(): + assert sign(log(2)) == 1 + + +def test_log_expand_complex(): + assert log(1 + I).expand(complex=True) == log(2)/2 + I*pi/4 + assert log(1 - sqrt(2)).expand(complex=True) == log(sqrt(2) - 1) + I*pi + + +def test_log_apply_evalf(): + value = (log(3)/log(2) - 1).evalf() + assert value.epsilon_eq(Float("0.58496250072115618145373")) + + +def test_log_leading_term(): + p = Symbol('p') + + # Test for STEP 3 + assert log(1 + x + x**2).as_leading_term(x, cdir=1) == x + # Test for STEP 4 + assert log(2*x).as_leading_term(x, cdir=1) == log(x) + log(2) + assert log(2*x).as_leading_term(x, cdir=-1) == log(x) + log(2) + assert log(-2*x).as_leading_term(x, cdir=1, logx=p) == p + log(2) + I*pi + assert log(-2*x).as_leading_term(x, cdir=-1, logx=p) == p + log(2) - I*pi + # Test for STEP 5 + assert log(-2*x + (3 - I)*x**2).as_leading_term(x, cdir=1) == log(x) + log(2) - I*pi + assert log(-2*x + (3 - I)*x**2).as_leading_term(x, cdir=-1) == log(x) + log(2) - I*pi + assert log(2*x + (3 - I)*x**2).as_leading_term(x, cdir=1) == log(x) + log(2) + assert log(2*x + (3 - I)*x**2).as_leading_term(x, cdir=-1) == log(x) + log(2) - 2*I*pi + assert log(-1 + x - I*x**2 + I*x**3).as_leading_term(x, cdir=1) == -I*pi + assert log(-1 + x - I*x**2 + I*x**3).as_leading_term(x, cdir=-1) == -I*pi + assert log(-1/(1 - x)).as_leading_term(x, cdir=1) == I*pi + assert log(-1/(1 - x)).as_leading_term(x, cdir=-1) == I*pi + + +def test_log_nseries(): + p = Symbol('p') + assert log(1/x)._eval_nseries(x, 4, logx=-p, cdir=1) == p + assert log(1/x)._eval_nseries(x, 4, logx=-p, cdir=-1) == p + 2*I*pi + assert log(x - 1)._eval_nseries(x, 4, None, I) == I*pi - x - x**2/2 - x**3/3 + O(x**4) + assert log(x - 1)._eval_nseries(x, 4, None, -I) == -I*pi - x - x**2/2 - x**3/3 + O(x**4) + assert log(I*x + I*x**3 - 1)._eval_nseries(x, 3, None, 1) == I*pi - I*x + x**2/2 + O(x**3) + assert log(I*x + I*x**3 - 1)._eval_nseries(x, 3, None, -1) == -I*pi - I*x + x**2/2 + O(x**3) + assert log(I*x**2 + I*x**3 - 1)._eval_nseries(x, 3, None, 1) == I*pi - I*x**2 + O(x**3) + assert log(I*x**2 + I*x**3 - 1)._eval_nseries(x, 3, None, -1) == I*pi - I*x**2 + O(x**3) + assert log(2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, 1) == log(2) + log(x) + \ + x*(S(3)/2 - I/2) + x**2*(-1 + 3*I/4) + O(x**3) + assert log(2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, -1) == -2*I*pi + log(2) + \ + log(x) - x*(-S(3)/2 + I/2) + x**2*(-1 + 3*I/4) + O(x**3) + assert log(-2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, 1) == -I*pi + log(2) + log(x) + \ + x*(-S(3)/2 + I/2) + x**2*(-1 + 3*I/4) + O(x**3) + assert log(-2*x + (3 - I)*x**2)._eval_nseries(x, 3, None, -1) == -I*pi + log(2) + log(x) - \ + x*(S(3)/2 - I/2) + x**2*(-1 + 3*I/4) + O(x**3) + assert log(sqrt(-I*x**2 - 3)*sqrt(-I*x**2 - 1) - 2)._eval_nseries(x, 3, None, 1) == -I*pi + \ + log(sqrt(3) + 2) + I*x**2*(-2 + 4*sqrt(3)/3) + O(x**3) + assert log(-1/(1 - x))._eval_nseries(x, 3, None, 1) == I*pi + x + x**2/2 + O(x**3) + assert log(-1/(1 - x))._eval_nseries(x, 3, None, -1) == I*pi + x + x**2/2 + O(x**3) + + +def test_log_series(): + # Note Series at infinities other than oo/-oo were introduced as a part of + # pull request 23798. Refer https://github.com/sympy/sympy/pull/23798 for + # more information. + expr1 = log(1 + x) + expr2 = log(x + sqrt(x**2 + 1)) + + assert expr1.series(x, x0=I*oo, n=4) == 1/(3*x**3) - 1/(2*x**2) + 1/x + \ + I*pi/2 - log(I/x) + O(x**(-4), (x, oo*I)) + assert expr1.series(x, x0=-I*oo, n=4) == 1/(3*x**3) - 1/(2*x**2) + 1/x - \ + I*pi/2 - log(-I/x) + O(x**(-4), (x, -oo*I)) + assert expr2.series(x, x0=I*oo, n=4) == 1/(4*x**2) + I*pi/2 + log(2) - \ + log(I/x) + O(x**(-4), (x, oo*I)) + assert expr2.series(x, x0=-I*oo, n=4) == -1/(4*x**2) - I*pi/2 - log(2) + \ + log(-I/x) + O(x**(-4), (x, -oo*I)) + + +def test_log_expand(): + w = Symbol("w", positive=True) + e = log(w**(log(5)/log(3))) + assert e.expand() == log(5)/log(3) * log(w) + x, y, z = symbols('x,y,z', positive=True) + assert log(x*(y + z)).expand(mul=False) == log(x) + log(y + z) + assert log(log(x**2)*log(y*z)).expand() in [log(2*log(x)*log(y) + + 2*log(x)*log(z)), log(log(x)*log(z) + log(y)*log(x)) + log(2), + log((log(y) + log(z))*log(x)) + log(2)] + assert log(x**log(x**2)).expand(deep=False) == log(x)*log(x**2) + assert log(x**log(x**2)).expand() == 2*log(x)**2 + x, y = symbols('x,y') + assert log(x*y).expand(force=True) == log(x) + log(y) + assert log(x**y).expand(force=True) == y*log(x) + assert log(exp(x)).expand(force=True) == x + + # there's generally no need to expand out logs since this requires + # factoring and if simplification is sought, it's cheaper to put + # logs together than it is to take them apart. + assert log(2*3**2).expand() != 2*log(3) + log(2) + + +@XFAIL +def test_log_expand_fail(): + x, y, z = symbols('x,y,z', positive=True) + assert (log(x*(y + z))*(x + y)).expand(mul=True, log=True) == y*log( + x) + y*log(y + z) + z*log(x) + z*log(y + z) + + +def test_log_simplify(): + x = Symbol("x", positive=True) + assert log(x**2).expand() == 2*log(x) + assert expand_log(log(x**(2 + log(2)))) == (2 + log(2))*log(x) + + z = Symbol('z') + assert log(sqrt(z)).expand() == log(z)/2 + assert expand_log(log(z**(log(2) - 1))) == (log(2) - 1)*log(z) + assert log(z**(-1)).expand() != -log(z) + assert log(z**(x/(x+1))).expand() == x*log(z)/(x + 1) + + +def test_log_AccumBounds(): + assert log(AccumBounds(1, E)) == AccumBounds(0, 1) + assert log(AccumBounds(0, E)) == AccumBounds(-oo, 1) + assert log(AccumBounds(-1, E)) == S.NaN + assert log(AccumBounds(0, oo)) == AccumBounds(-oo, oo) + assert log(AccumBounds(-oo, 0)) == S.NaN + assert log(AccumBounds(-oo, oo)) == S.NaN + + +@_both_exp_pow +def test_lambertw(): + k = Symbol('k') + + assert LambertW(x, 0) == LambertW(x) + assert LambertW(x, 0, evaluate=False) != LambertW(x) + assert LambertW(0) == 0 + assert LambertW(E) == 1 + assert LambertW(-1/E) == -1 + assert LambertW(100*log(100)) == log(100) + assert LambertW(-log(2)/2) == -log(2) + assert LambertW(81*log(3)) == 3*log(3) + assert LambertW(sqrt(E)/2) == S.Half + assert LambertW(oo) is oo + assert LambertW(0, 1) is -oo + assert LambertW(0, 42) is -oo + assert LambertW(-pi/2, -1) == -I*pi/2 + assert LambertW(-1/E, -1) == -1 + assert LambertW(-2*exp(-2), -1) == -2 + assert LambertW(2*log(2)) == log(2) + assert LambertW(-pi/2) == I*pi/2 + assert LambertW(exp(1 + E)) == E + + assert LambertW(x**2).diff(x) == 2*LambertW(x**2)/x/(1 + LambertW(x**2)) + assert LambertW(x, k).diff(x) == LambertW(x, k)/x/(1 + LambertW(x, k)) + + assert LambertW(sqrt(2)).evalf(30).epsilon_eq( + Float("0.701338383413663009202120278965", 30), 1e-29) + assert re(LambertW(2, -1)).evalf().epsilon_eq(Float("-0.834310366631110")) + + assert LambertW(-1).is_real is False # issue 5215 + assert LambertW(2, evaluate=False).is_real + p = Symbol('p', positive=True) + assert LambertW(p, evaluate=False).is_real + assert LambertW(p**(p+1)*log(p)) == p*log(p) + assert LambertW(p - 1, evaluate=False).is_real is None + assert LambertW(-p - 2/S.Exp1, evaluate=False).is_real is False + assert LambertW(S.Half, -1, evaluate=False).is_real is False + assert LambertW(Rational(-1, 10), -1, evaluate=False).is_real + assert LambertW(-10, -1, evaluate=False).is_real is False + assert LambertW(-2, 2, evaluate=False).is_real is False + + assert LambertW(0, evaluate=False).is_algebraic + na = Symbol('na', nonzero=True, algebraic=True) + assert LambertW(na).is_algebraic is False + assert LambertW(p).is_zero is False + n = Symbol('n', negative=True) + assert LambertW(n).is_zero is False + + +def test_issue_5673(): + e = LambertW(-1) + assert e.is_comparable is False + assert e.is_positive is not True + e2 = 1 - 1/(1 - exp(-1000)) + assert e2.is_positive is not True + e3 = -2 + exp(exp(LambertW(log(2)))*LambertW(log(2))) + assert e3.is_nonzero is not True + + +def test_log_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: log(x).fdiff(2)) + + +def test_log_taylor_term(): + x = symbols('x') + assert log(x).taylor_term(0, x) == x + assert log(x).taylor_term(1, x) == -x**2/2 + assert log(x).taylor_term(4, x) == x**5/5 + assert log(x).taylor_term(-1, x) is S.Zero + + +def test_exp_expand_NC(): + A, B, C = symbols('A,B,C', commutative=False) + + assert exp(A + B).expand() == exp(A + B) + assert exp(A + B + C).expand() == exp(A + B + C) + assert exp(x + y).expand() == exp(x)*exp(y) + assert exp(x + y + z).expand() == exp(x)*exp(y)*exp(z) + + +@_both_exp_pow +def test_as_numer_denom(): + n = symbols('n', negative=True) + assert exp(x).as_numer_denom() == (exp(x), 1) + assert exp(-x).as_numer_denom() == (1, exp(x)) + assert exp(-2*x).as_numer_denom() == (1, exp(2*x)) + assert exp(-2).as_numer_denom() == (1, exp(2)) + assert exp(n).as_numer_denom() == (1, exp(-n)) + assert exp(-n).as_numer_denom() == (exp(-n), 1) + assert exp(-I*x).as_numer_denom() == (1, exp(I*x)) + assert exp(-I*n).as_numer_denom() == (1, exp(I*n)) + assert exp(-n).as_numer_denom() == (exp(-n), 1) + # Check noncommutativity + a = symbols('a', commutative=False) + assert exp(-a).as_numer_denom() == (exp(-a), 1) + + +@_both_exp_pow +def test_polar(): + x, y = symbols('x y', polar=True) + + assert abs(exp_polar(I*4)) == 1 + assert abs(exp_polar(0)) == 1 + assert abs(exp_polar(2 + 3*I)) == exp(2) + assert exp_polar(I*10).n() == exp_polar(I*10) + + assert log(exp_polar(z)) == z + assert log(x*y).expand() == log(x) + log(y) + assert log(x**z).expand() == z*log(x) + + assert exp_polar(3).exp == 3 + + # Compare exp(1.0*pi*I). + assert (exp_polar(1.0*pi*I).n(n=5)).as_real_imag()[1] >= 0 + + assert exp_polar(0).is_rational is True # issue 8008 + + +def test_exp_summation(): + w = symbols("w") + m, n, i, j = symbols("m n i j") + expr = exp(Sum(w*i, (i, 0, n), (j, 0, m))) + assert expr.expand() == Product(exp(w*i), (i, 0, n), (j, 0, m)) + + +def test_log_product(): + from sympy.abc import n, m + + i, j = symbols('i,j', positive=True, integer=True) + x, y = symbols('x,y', positive=True) + z = symbols('z', real=True) + w = symbols('w') + + expr = log(Product(x**i, (i, 1, n))) + assert simplify(expr) == expr + assert expr.expand() == Sum(i*log(x), (i, 1, n)) + expr = log(Product(x**i*y**j, (i, 1, n), (j, 1, m))) + assert simplify(expr) == expr + assert expr.expand() == Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m)) + + expr = log(Product(-2, (n, 0, 4))) + assert simplify(expr) == expr + assert expr.expand() == expr + assert expr.expand(force=True) == Sum(log(-2), (n, 0, 4)) + + expr = log(Product(exp(z*i), (i, 0, n))) + assert expr.expand() == Sum(z*i, (i, 0, n)) + + expr = log(Product(exp(w*i), (i, 0, n))) + assert expr.expand() == expr + assert expr.expand(force=True) == Sum(w*i, (i, 0, n)) + + expr = log(Product(i**2*abs(j), (i, 1, n), (j, 1, m))) + assert expr.expand() == Sum(2*log(i) + log(j), (i, 1, n), (j, 1, m)) + + +@XFAIL +def test_log_product_simplify_to_sum(): + from sympy.abc import n, m + i, j = symbols('i,j', positive=True, integer=True) + x, y = symbols('x,y', positive=True) + assert simplify(log(Product(x**i, (i, 1, n)))) == Sum(i*log(x), (i, 1, n)) + assert simplify(log(Product(x**i*y**j, (i, 1, n), (j, 1, m)))) == \ + Sum(i*log(x) + j*log(y), (i, 1, n), (j, 1, m)) + + +def test_issue_8866(): + assert simplify(log(x, 10, evaluate=False)) == simplify(log(x, 10)) + assert expand_log(log(x, 10, evaluate=False)) == expand_log(log(x, 10)) + + y = Symbol('y', positive=True) + l1 = log(exp(y), exp(10)) + b1 = log(exp(y), exp(5)) + l2 = log(exp(y), exp(10), evaluate=False) + b2 = log(exp(y), exp(5), evaluate=False) + assert simplify(log(l1, b1)) == simplify(log(l2, b2)) + assert expand_log(log(l1, b1)) == expand_log(log(l2, b2)) + + +def test_log_expand_factor(): + assert (log(18)/log(3) - 2).expand(factor=True) == log(2)/log(3) + assert (log(12)/log(2)).expand(factor=True) == log(3)/log(2) + 2 + assert (log(15)/log(3)).expand(factor=True) == 1 + log(5)/log(3) + assert (log(2)/(-log(12) + log(24))).expand(factor=True) == 1 + + assert expand_log(log(12), factor=True) == log(3) + 2*log(2) + assert expand_log(log(21)/log(7), factor=False) == log(3)/log(7) + 1 + assert expand_log(log(45)/log(5) + log(20), factor=False) == \ + 1 + 2*log(3)/log(5) + log(20) + assert expand_log(log(45)/log(5) + log(26), factor=True) == \ + log(2) + log(13) + (log(5) + 2*log(3))/log(5) + + +def test_issue_9116(): + n = Symbol('n', positive=True, integer=True) + assert log(n).is_nonnegative is True + + +def test_issue_18473(): + assert exp(x*log(cos(1/x))).as_leading_term(x) == S.NaN + assert exp(x*log(tan(1/x))).as_leading_term(x) == S.NaN + assert log(cos(1/x)).as_leading_term(x) == S.NaN + assert log(tan(1/x)).as_leading_term(x) == S.NaN + assert log(cos(1/x) + 2).as_leading_term(x) == AccumBounds(0, log(3)) + assert exp(x*log(cos(1/x) + 2)).as_leading_term(x) == 1 + assert log(cos(1/x) - 2).as_leading_term(x) == S.NaN + assert exp(x*log(cos(1/x) - 2)).as_leading_term(x) == S.NaN + assert log(cos(1/x) + 1).as_leading_term(x) == AccumBounds(-oo, log(2)) + assert exp(x*log(cos(1/x) + 1)).as_leading_term(x) == AccumBounds(0, 1) + assert log(sin(1/x)**2).as_leading_term(x) == AccumBounds(-oo, 0) + assert exp(x*log(sin(1/x)**2)).as_leading_term(x) == AccumBounds(0, 1) + assert log(tan(1/x)**2).as_leading_term(x) == AccumBounds(-oo, oo) + assert exp(2*x*(log(tan(1/x)**2))).as_leading_term(x) == AccumBounds(0, oo) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py new file mode 100644 index 0000000000000000000000000000000000000000..5b4365d8217d4489b347e6cea7b9b4158732f309 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_hyperbolic.py @@ -0,0 +1,1542 @@ +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.core.function import (expand_mul, expand_trig) +from sympy.core.numbers import (E, I, Integer, Rational, nan, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (im, re) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.hyperbolic import (acosh, acoth, acsch, asech, asinh, atanh, cosh, coth, csch, sech, sinh, tanh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, asin, cos, cot, sec, sin, tan) +from sympy.series.order import O + +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError, PoleError +from sympy.testing.pytest import raises + + +def test_sinh(): + x, y = symbols('x,y') + + k = Symbol('k', integer=True) + + assert sinh(nan) is nan + assert sinh(zoo) is nan + + assert sinh(oo) is oo + assert sinh(-oo) is -oo + + assert sinh(0) == 0 + + assert unchanged(sinh, 1) + assert sinh(-1) == -sinh(1) + + assert unchanged(sinh, x) + assert sinh(-x) == -sinh(x) + + assert unchanged(sinh, pi) + assert sinh(-pi) == -sinh(pi) + + assert unchanged(sinh, 2**1024 * E) + assert sinh(-2**1024 * E) == -sinh(2**1024 * E) + + assert sinh(pi*I) == 0 + assert sinh(-pi*I) == 0 + assert sinh(2*pi*I) == 0 + assert sinh(-2*pi*I) == 0 + assert sinh(-3*10**73*pi*I) == 0 + assert sinh(7*10**103*pi*I) == 0 + + assert sinh(pi*I/2) == I + assert sinh(-pi*I/2) == -I + assert sinh(pi*I*Rational(5, 2)) == I + assert sinh(pi*I*Rational(7, 2)) == -I + + assert sinh(pi*I/3) == S.Half*sqrt(3)*I + assert sinh(pi*I*Rational(-2, 3)) == Rational(-1, 2)*sqrt(3)*I + + assert sinh(pi*I/4) == S.Half*sqrt(2)*I + assert sinh(-pi*I/4) == Rational(-1, 2)*sqrt(2)*I + assert sinh(pi*I*Rational(17, 4)) == S.Half*sqrt(2)*I + assert sinh(pi*I*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2)*I + + assert sinh(pi*I/6) == S.Half*I + assert sinh(-pi*I/6) == Rational(-1, 2)*I + assert sinh(pi*I*Rational(7, 6)) == Rational(-1, 2)*I + assert sinh(pi*I*Rational(-5, 6)) == Rational(-1, 2)*I + + assert sinh(pi*I/105) == sin(pi/105)*I + assert sinh(-pi*I/105) == -sin(pi/105)*I + + assert unchanged(sinh, 2 + 3*I) + + assert sinh(x*I) == sin(x)*I + + assert sinh(k*pi*I) == 0 + assert sinh(17*k*pi*I) == 0 + + assert sinh(k*pi*I/2) == sin(k*pi/2)*I + + assert sinh(x).as_real_imag(deep=False) == (cos(im(x))*sinh(re(x)), + sin(im(x))*cosh(re(x))) + x = Symbol('x', extended_real=True) + assert sinh(x).as_real_imag(deep=False) == (sinh(x), 0) + + x = Symbol('x', real=True) + assert sinh(I*x).is_finite is True + assert sinh(x).is_real is True + assert sinh(I).is_real is False + p = Symbol('p', positive=True) + assert sinh(p).is_zero is False + assert sinh(0, evaluate=False).is_zero is True + assert sinh(2*pi*I, evaluate=False).is_zero is True + + +def test_sinh_series(): + x = Symbol('x') + assert sinh(x).series(x, 0, 10) == \ + x + x**3/6 + x**5/120 + x**7/5040 + x**9/362880 + O(x**10) + + +def test_sinh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: sinh(x).fdiff(2)) + + +def test_cosh(): + x, y = symbols('x,y') + + k = Symbol('k', integer=True) + + assert cosh(nan) is nan + assert cosh(zoo) is nan + + assert cosh(oo) is oo + assert cosh(-oo) is oo + + assert cosh(0) == 1 + + assert unchanged(cosh, 1) + assert cosh(-1) == cosh(1) + + assert unchanged(cosh, x) + assert cosh(-x) == cosh(x) + + assert cosh(pi*I) == cos(pi) + assert cosh(-pi*I) == cos(pi) + + assert unchanged(cosh, 2**1024 * E) + assert cosh(-2**1024 * E) == cosh(2**1024 * E) + + assert cosh(pi*I/2) == 0 + assert cosh(-pi*I/2) == 0 + assert cosh((-3*10**73 + 1)*pi*I/2) == 0 + assert cosh((7*10**103 + 1)*pi*I/2) == 0 + + assert cosh(pi*I) == -1 + assert cosh(-pi*I) == -1 + assert cosh(5*pi*I) == -1 + assert cosh(8*pi*I) == 1 + + assert cosh(pi*I/3) == S.Half + assert cosh(pi*I*Rational(-2, 3)) == Rational(-1, 2) + + assert cosh(pi*I/4) == S.Half*sqrt(2) + assert cosh(-pi*I/4) == S.Half*sqrt(2) + assert cosh(pi*I*Rational(11, 4)) == Rational(-1, 2)*sqrt(2) + assert cosh(pi*I*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2) + + assert cosh(pi*I/6) == S.Half*sqrt(3) + assert cosh(-pi*I/6) == S.Half*sqrt(3) + assert cosh(pi*I*Rational(7, 6)) == Rational(-1, 2)*sqrt(3) + assert cosh(pi*I*Rational(-5, 6)) == Rational(-1, 2)*sqrt(3) + + assert cosh(pi*I/105) == cos(pi/105) + assert cosh(-pi*I/105) == cos(pi/105) + + assert unchanged(cosh, 2 + 3*I) + + assert cosh(x*I) == cos(x) + + assert cosh(k*pi*I) == cos(k*pi) + assert cosh(17*k*pi*I) == cos(17*k*pi) + + assert unchanged(cosh, k*pi) + + assert cosh(x).as_real_imag(deep=False) == (cos(im(x))*cosh(re(x)), + sin(im(x))*sinh(re(x))) + x = Symbol('x', extended_real=True) + assert cosh(x).as_real_imag(deep=False) == (cosh(x), 0) + + x = Symbol('x', real=True) + assert cosh(I*x).is_finite is True + assert cosh(I*x).is_real is True + assert cosh(I*2 + 1).is_real is False + assert cosh(5*I*S.Pi/2, evaluate=False).is_zero is True + assert cosh(x).is_zero is False + + +def test_cosh_series(): + x = Symbol('x') + assert cosh(x).series(x, 0, 10) == \ + 1 + x**2/2 + x**4/24 + x**6/720 + x**8/40320 + O(x**10) + + +def test_cosh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: cosh(x).fdiff(2)) + + +def test_tanh(): + x, y = symbols('x,y') + + k = Symbol('k', integer=True) + + assert tanh(nan) is nan + assert tanh(zoo) is nan + + assert tanh(oo) == 1 + assert tanh(-oo) == -1 + + assert tanh(0) == 0 + + assert unchanged(tanh, 1) + assert tanh(-1) == -tanh(1) + + assert unchanged(tanh, x) + assert tanh(-x) == -tanh(x) + + assert unchanged(tanh, pi) + assert tanh(-pi) == -tanh(pi) + + assert unchanged(tanh, 2**1024 * E) + assert tanh(-2**1024 * E) == -tanh(2**1024 * E) + + assert tanh(pi*I) == 0 + assert tanh(-pi*I) == 0 + assert tanh(2*pi*I) == 0 + assert tanh(-2*pi*I) == 0 + assert tanh(-3*10**73*pi*I) == 0 + assert tanh(7*10**103*pi*I) == 0 + + assert tanh(pi*I/2) is zoo + assert tanh(-pi*I/2) is zoo + assert tanh(pi*I*Rational(5, 2)) is zoo + assert tanh(pi*I*Rational(7, 2)) is zoo + + assert tanh(pi*I/3) == sqrt(3)*I + assert tanh(pi*I*Rational(-2, 3)) == sqrt(3)*I + + assert tanh(pi*I/4) == I + assert tanh(-pi*I/4) == -I + assert tanh(pi*I*Rational(17, 4)) == I + assert tanh(pi*I*Rational(-3, 4)) == I + + assert tanh(pi*I/6) == I/sqrt(3) + assert tanh(-pi*I/6) == -I/sqrt(3) + assert tanh(pi*I*Rational(7, 6)) == I/sqrt(3) + assert tanh(pi*I*Rational(-5, 6)) == I/sqrt(3) + + assert tanh(pi*I/105) == tan(pi/105)*I + assert tanh(-pi*I/105) == -tan(pi/105)*I + + assert unchanged(tanh, 2 + 3*I) + + assert tanh(x*I) == tan(x)*I + + assert tanh(k*pi*I) == 0 + assert tanh(17*k*pi*I) == 0 + + assert tanh(k*pi*I/2) == tan(k*pi/2)*I + + assert tanh(x).as_real_imag(deep=False) == (sinh(re(x))*cosh(re(x))/(cos(im(x))**2 + + sinh(re(x))**2), + sin(im(x))*cos(im(x))/(cos(im(x))**2 + sinh(re(x))**2)) + x = Symbol('x', extended_real=True) + assert tanh(x).as_real_imag(deep=False) == (tanh(x), 0) + assert tanh(I*pi/3 + 1).is_real is False + assert tanh(x).is_real is True + assert tanh(I*pi*x/2).is_real is None + + +def test_tanh_series(): + x = Symbol('x') + assert tanh(x).series(x, 0, 10) == \ + x - x**3/3 + 2*x**5/15 - 17*x**7/315 + 62*x**9/2835 + O(x**10) + + +def test_tanh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: tanh(x).fdiff(2)) + + +def test_coth(): + x, y = symbols('x,y') + + k = Symbol('k', integer=True) + + assert coth(nan) is nan + assert coth(zoo) is nan + + assert coth(oo) == 1 + assert coth(-oo) == -1 + + assert coth(0) is zoo + assert unchanged(coth, 1) + assert coth(-1) == -coth(1) + + assert unchanged(coth, x) + assert coth(-x) == -coth(x) + + assert coth(pi*I) == -I*cot(pi) + assert coth(-pi*I) == cot(pi)*I + + assert unchanged(coth, 2**1024 * E) + assert coth(-2**1024 * E) == -coth(2**1024 * E) + + assert coth(pi*I) == -I*cot(pi) + assert coth(-pi*I) == I*cot(pi) + assert coth(2*pi*I) == -I*cot(2*pi) + assert coth(-2*pi*I) == I*cot(2*pi) + assert coth(-3*10**73*pi*I) == I*cot(3*10**73*pi) + assert coth(7*10**103*pi*I) == -I*cot(7*10**103*pi) + + assert coth(pi*I/2) == 0 + assert coth(-pi*I/2) == 0 + assert coth(pi*I*Rational(5, 2)) == 0 + assert coth(pi*I*Rational(7, 2)) == 0 + + assert coth(pi*I/3) == -I/sqrt(3) + assert coth(pi*I*Rational(-2, 3)) == -I/sqrt(3) + + assert coth(pi*I/4) == -I + assert coth(-pi*I/4) == I + assert coth(pi*I*Rational(17, 4)) == -I + assert coth(pi*I*Rational(-3, 4)) == -I + + assert coth(pi*I/6) == -sqrt(3)*I + assert coth(-pi*I/6) == sqrt(3)*I + assert coth(pi*I*Rational(7, 6)) == -sqrt(3)*I + assert coth(pi*I*Rational(-5, 6)) == -sqrt(3)*I + + assert coth(pi*I/105) == -cot(pi/105)*I + assert coth(-pi*I/105) == cot(pi/105)*I + + assert unchanged(coth, 2 + 3*I) + + assert coth(x*I) == -cot(x)*I + + assert coth(k*pi*I) == -cot(k*pi)*I + assert coth(17*k*pi*I) == -cot(17*k*pi)*I + + assert coth(k*pi*I) == -cot(k*pi)*I + + assert coth(log(tan(2))) == coth(log(-tan(2))) + assert coth(1 + I*pi/2) == tanh(1) + + assert coth(x).as_real_imag(deep=False) == (sinh(re(x))*cosh(re(x))/(sin(im(x))**2 + + sinh(re(x))**2), + -sin(im(x))*cos(im(x))/(sin(im(x))**2 + sinh(re(x))**2)) + x = Symbol('x', extended_real=True) + assert coth(x).as_real_imag(deep=False) == (coth(x), 0) + + assert expand_trig(coth(2*x)) == (coth(x)**2 + 1)/(2*coth(x)) + assert expand_trig(coth(3*x)) == (coth(x)**3 + 3*coth(x))/(1 + 3*coth(x)**2) + + assert expand_trig(coth(x + y)) == (1 + coth(x)*coth(y))/(coth(x) + coth(y)) + + +def test_coth_series(): + x = Symbol('x') + assert coth(x).series(x, 0, 8) == \ + 1/x + x/3 - x**3/45 + 2*x**5/945 - x**7/4725 + O(x**8) + + +def test_coth_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: coth(x).fdiff(2)) + + +def test_csch(): + x, y = symbols('x,y') + + k = Symbol('k', integer=True) + n = Symbol('n', positive=True) + + assert csch(nan) is nan + assert csch(zoo) is nan + + assert csch(oo) == 0 + assert csch(-oo) == 0 + + assert csch(0) is zoo + + assert csch(-1) == -csch(1) + + assert csch(-x) == -csch(x) + assert csch(-pi) == -csch(pi) + assert csch(-2**1024 * E) == -csch(2**1024 * E) + + assert csch(pi*I) is zoo + assert csch(-pi*I) is zoo + assert csch(2*pi*I) is zoo + assert csch(-2*pi*I) is zoo + assert csch(-3*10**73*pi*I) is zoo + assert csch(7*10**103*pi*I) is zoo + + assert csch(pi*I/2) == -I + assert csch(-pi*I/2) == I + assert csch(pi*I*Rational(5, 2)) == -I + assert csch(pi*I*Rational(7, 2)) == I + + assert csch(pi*I/3) == -2/sqrt(3)*I + assert csch(pi*I*Rational(-2, 3)) == 2/sqrt(3)*I + + assert csch(pi*I/4) == -sqrt(2)*I + assert csch(-pi*I/4) == sqrt(2)*I + assert csch(pi*I*Rational(7, 4)) == sqrt(2)*I + assert csch(pi*I*Rational(-3, 4)) == sqrt(2)*I + + assert csch(pi*I/6) == -2*I + assert csch(-pi*I/6) == 2*I + assert csch(pi*I*Rational(7, 6)) == 2*I + assert csch(pi*I*Rational(-7, 6)) == -2*I + assert csch(pi*I*Rational(-5, 6)) == 2*I + + assert csch(pi*I/105) == -1/sin(pi/105)*I + assert csch(-pi*I/105) == 1/sin(pi/105)*I + + assert csch(x*I) == -1/sin(x)*I + + assert csch(k*pi*I) is zoo + assert csch(17*k*pi*I) is zoo + + assert csch(k*pi*I/2) == -1/sin(k*pi/2)*I + + assert csch(n).is_real is True + + assert expand_trig(csch(x + y)) == 1/(sinh(x)*cosh(y) + cosh(x)*sinh(y)) + + +def test_csch_series(): + x = Symbol('x') + assert csch(x).series(x, 0, 10) == \ + 1/ x - x/6 + 7*x**3/360 - 31*x**5/15120 + 127*x**7/604800 \ + - 73*x**9/3421440 + O(x**10) + + +def test_csch_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: csch(x).fdiff(2)) + + +def test_sech(): + x, y = symbols('x, y') + + k = Symbol('k', integer=True) + n = Symbol('n', positive=True) + + assert sech(nan) is nan + assert sech(zoo) is nan + + assert sech(oo) == 0 + assert sech(-oo) == 0 + + assert sech(0) == 1 + + assert sech(-1) == sech(1) + assert sech(-x) == sech(x) + + assert sech(pi*I) == sec(pi) + + assert sech(-pi*I) == sec(pi) + assert sech(-2**1024 * E) == sech(2**1024 * E) + + assert sech(pi*I/2) is zoo + assert sech(-pi*I/2) is zoo + assert sech((-3*10**73 + 1)*pi*I/2) is zoo + assert sech((7*10**103 + 1)*pi*I/2) is zoo + + assert sech(pi*I) == -1 + assert sech(-pi*I) == -1 + assert sech(5*pi*I) == -1 + assert sech(8*pi*I) == 1 + + assert sech(pi*I/3) == 2 + assert sech(pi*I*Rational(-2, 3)) == -2 + + assert sech(pi*I/4) == sqrt(2) + assert sech(-pi*I/4) == sqrt(2) + assert sech(pi*I*Rational(5, 4)) == -sqrt(2) + assert sech(pi*I*Rational(-5, 4)) == -sqrt(2) + + assert sech(pi*I/6) == 2/sqrt(3) + assert sech(-pi*I/6) == 2/sqrt(3) + assert sech(pi*I*Rational(7, 6)) == -2/sqrt(3) + assert sech(pi*I*Rational(-5, 6)) == -2/sqrt(3) + + assert sech(pi*I/105) == 1/cos(pi/105) + assert sech(-pi*I/105) == 1/cos(pi/105) + + assert sech(x*I) == 1/cos(x) + + assert sech(k*pi*I) == 1/cos(k*pi) + assert sech(17*k*pi*I) == 1/cos(17*k*pi) + + assert sech(n).is_real is True + + assert expand_trig(sech(x + y)) == 1/(cosh(x)*cosh(y) + sinh(x)*sinh(y)) + + +def test_sech_series(): + x = Symbol('x') + assert sech(x).series(x, 0, 10) == \ + 1 - x**2/2 + 5*x**4/24 - 61*x**6/720 + 277*x**8/8064 + O(x**10) + + +def test_sech_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: sech(x).fdiff(2)) + + +def test_asinh(): + x, y = symbols('x,y') + assert unchanged(asinh, x) + assert asinh(-x) == -asinh(x) + + # at specific points + assert asinh(nan) is nan + assert asinh( 0) == 0 + assert asinh(+1) == log(sqrt(2) + 1) + + assert asinh(-1) == log(sqrt(2) - 1) + assert asinh(I) == pi*I/2 + assert asinh(-I) == -pi*I/2 + assert asinh(I/2) == pi*I/6 + assert asinh(-I/2) == -pi*I/6 + + # at infinites + assert asinh(oo) is oo + assert asinh(-oo) is -oo + + assert asinh(I*oo) is oo + assert asinh(-I *oo) is -oo + + assert asinh(zoo) is zoo + + # properties + assert asinh(I *(sqrt(3) - 1)/(2**Rational(3, 2))) == pi*I/12 + assert asinh(-I *(sqrt(3) - 1)/(2**Rational(3, 2))) == -pi*I/12 + + assert asinh(I*(sqrt(5) - 1)/4) == pi*I/10 + assert asinh(-I*(sqrt(5) - 1)/4) == -pi*I/10 + + assert asinh(I*(sqrt(5) + 1)/4) == pi*I*Rational(3, 10) + assert asinh(-I*(sqrt(5) + 1)/4) == pi*I*Rational(-3, 10) + + # reality + assert asinh(S(2)).is_real is True + assert asinh(S(2)).is_finite is True + assert asinh(S(-2)).is_real is True + assert asinh(S(oo)).is_extended_real is True + assert asinh(-S(oo)).is_real is False + assert (asinh(2) - oo) == -oo + assert asinh(symbols('y', real=True)).is_real is True + + # Symmetry + assert asinh(Rational(-1, 2)) == -asinh(S.Half) + + # inverse composition + assert unchanged(asinh, sinh(Symbol('v1'))) + + assert asinh(sinh(0, evaluate=False)) == 0 + assert asinh(sinh(-3, evaluate=False)) == -3 + assert asinh(sinh(2, evaluate=False)) == 2 + assert asinh(sinh(I, evaluate=False)) == I + assert asinh(sinh(-I, evaluate=False)) == -I + assert asinh(sinh(5*I, evaluate=False)) == -2*I*pi + 5*I + assert asinh(sinh(15 + 11*I)) == 15 - 4*I*pi + 11*I + assert asinh(sinh(-73 + 97*I)) == 73 - 97*I + 31*I*pi + assert asinh(sinh(-7 - 23*I)) == 7 - 7*I*pi + 23*I + assert asinh(sinh(13 - 3*I)) == -13 - I*pi + 3*I + p = Symbol('p', positive=True) + assert asinh(p).is_zero is False + assert asinh(sinh(0, evaluate=False), evaluate=False).is_zero is True + + +def test_asinh_rewrite(): + x = Symbol('x') + assert asinh(x).rewrite(log) == log(x + sqrt(x**2 + 1)) + assert asinh(x).rewrite(atanh) == atanh(x/sqrt(1 + x**2)) + assert asinh(x).rewrite(asin) == -I*asin(I*x, evaluate=False) + assert asinh(x*(1 + I)).rewrite(asin) == -I*asin(I*x*(1+I)) + assert asinh(x).rewrite(acos) == I*acos(I*x, evaluate=False) - I*pi/2 + + +def test_asinh_leading_term(): + x = Symbol('x') + assert asinh(x).as_leading_term(x, cdir=1) == x + # Tests concerning branch points + assert asinh(x + I).as_leading_term(x, cdir=1) == I*pi/2 + assert asinh(x - I).as_leading_term(x, cdir=1) == -I*pi/2 + assert asinh(1/x).as_leading_term(x, cdir=1) == -log(x) + log(2) + assert asinh(1/x).as_leading_term(x, cdir=-1) == log(x) - log(2) - I*pi + # Tests concerning points lying on branch cuts + assert asinh(x + 2*I).as_leading_term(x, cdir=1) == I*asin(2) + assert asinh(x + 2*I).as_leading_term(x, cdir=-1) == -I*asin(2) + I*pi + assert asinh(x - 2*I).as_leading_term(x, cdir=1) == -I*pi + I*asin(2) + assert asinh(x - 2*I).as_leading_term(x, cdir=-1) == -I*asin(2) + # Tests concerning re(ndir) == 0 + assert asinh(2*I + I*x - x**2).as_leading_term(x, cdir=1) == log(2 - sqrt(3)) + I*pi/2 + assert asinh(2*I + I*x - x**2).as_leading_term(x, cdir=-1) == log(2 - sqrt(3)) + I*pi/2 + + +def test_asinh_series(): + x = Symbol('x') + assert asinh(x).series(x, 0, 8) == \ + x - x**3/6 + 3*x**5/40 - 5*x**7/112 + O(x**8) + t5 = asinh(x).taylor_term(5, x) + assert t5 == 3*x**5/40 + assert asinh(x).taylor_term(7, x, t5, 0) == -5*x**7/112 + + +def test_asinh_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert asinh(x + I)._eval_nseries(x, 4, None) == I*pi/2 + \ + sqrt(x)*(1 - I) + x**(S(3)/2)*(S(1)/12 + I/12) + x**(S(5)/2)*(-S(3)/160 + 3*I/160) + \ + x**(S(7)/2)*(-S(5)/896 - 5*I/896) + O(x**4) + assert asinh(x - I)._eval_nseries(x, 4, None) == -I*pi/2 + \ + sqrt(x)*(1 + I) + x**(S(3)/2)*(S(1)/12 - I/12) + x**(S(5)/2)*(-S(3)/160 - 3*I/160) + \ + x**(S(7)/2)*(-S(5)/896 + 5*I/896) + O(x**4) + # Tests concerning points lying on branch cuts + assert asinh(x + 2*I)._eval_nseries(x, 4, None, cdir=1) == I*asin(2) - \ + sqrt(3)*I*x/3 + sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + assert asinh(x + 2*I)._eval_nseries(x, 4, None, cdir=-1) == I*pi - I*asin(2) + \ + sqrt(3)*I*x/3 - sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert asinh(x - 2*I)._eval_nseries(x, 4, None, cdir=1) == I*asin(2) - I*pi + \ + sqrt(3)*I*x/3 + sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert asinh(x - 2*I)._eval_nseries(x, 4, None, cdir=-1) == -I*asin(2) - \ + sqrt(3)*I*x/3 - sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + # Tests concerning re(ndir) == 0 + assert asinh(2*I + I*x - x**2)._eval_nseries(x, 4, None) == I*pi/2 + log(2 - sqrt(3)) - \ + sqrt(3)*x/3 + x**2*(sqrt(3)/9 - sqrt(3)*I/3) + x**3*(-sqrt(3)/18 + 2*sqrt(3)*I/9) + O(x**4) + + +def test_asinh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: asinh(x).fdiff(2)) + + +def test_acosh(): + x = Symbol('x') + + assert unchanged(acosh, -x) + + #at specific points + assert acosh(1) == 0 + assert acosh(-1) == pi*I + assert acosh(0) == I*pi/2 + assert acosh(S.Half) == I*pi/3 + assert acosh(Rational(-1, 2)) == pi*I*Rational(2, 3) + assert acosh(nan) is nan + + # at infinites + assert acosh(oo) is oo + assert acosh(-oo) is oo + + assert acosh(I*oo) == oo + I*pi/2 + assert acosh(-I*oo) == oo - I*pi/2 + + assert acosh(zoo) is zoo + + assert acosh(I) == log(I*(1 + sqrt(2))) + assert acosh(-I) == log(-I*(1 + sqrt(2))) + assert acosh((sqrt(3) - 1)/(2*sqrt(2))) == pi*I*Rational(5, 12) + assert acosh(-(sqrt(3) - 1)/(2*sqrt(2))) == pi*I*Rational(7, 12) + assert acosh(sqrt(2)/2) == I*pi/4 + assert acosh(-sqrt(2)/2) == I*pi*Rational(3, 4) + assert acosh(sqrt(3)/2) == I*pi/6 + assert acosh(-sqrt(3)/2) == I*pi*Rational(5, 6) + assert acosh(sqrt(2 + sqrt(2))/2) == I*pi/8 + assert acosh(-sqrt(2 + sqrt(2))/2) == I*pi*Rational(7, 8) + assert acosh(sqrt(2 - sqrt(2))/2) == I*pi*Rational(3, 8) + assert acosh(-sqrt(2 - sqrt(2))/2) == I*pi*Rational(5, 8) + assert acosh((1 + sqrt(3))/(2*sqrt(2))) == I*pi/12 + assert acosh(-(1 + sqrt(3))/(2*sqrt(2))) == I*pi*Rational(11, 12) + assert acosh((sqrt(5) + 1)/4) == I*pi/5 + assert acosh(-(sqrt(5) + 1)/4) == I*pi*Rational(4, 5) + + assert str(acosh(5*I).n(6)) == '2.31244 + 1.5708*I' + assert str(acosh(-5*I).n(6)) == '2.31244 - 1.5708*I' + + # inverse composition + assert unchanged(acosh, Symbol('v1')) + + assert acosh(cosh(-3, evaluate=False)) == 3 + assert acosh(cosh(3, evaluate=False)) == 3 + assert acosh(cosh(0, evaluate=False)) == 0 + assert acosh(cosh(I, evaluate=False)) == I + assert acosh(cosh(-I, evaluate=False)) == I + assert acosh(cosh(7*I, evaluate=False)) == -2*I*pi + 7*I + assert acosh(cosh(1 + I)) == 1 + I + assert acosh(cosh(3 - 3*I)) == 3 - 3*I + assert acosh(cosh(-3 + 2*I)) == 3 - 2*I + assert acosh(cosh(-5 - 17*I)) == 5 - 6*I*pi + 17*I + assert acosh(cosh(-21 + 11*I)) == 21 - 11*I + 4*I*pi + assert acosh(cosh(cosh(1) + I)) == cosh(1) + I + assert acosh(1, evaluate=False).is_zero is True + + # Reality + assert acosh(S(2)).is_real is True + assert acosh(S(2)).is_extended_real is True + assert acosh(oo).is_extended_real is True + assert acosh(S(2)).is_finite is True + assert acosh(S(1) / 5).is_real is False + assert (acosh(2) - oo) == -oo + assert acosh(symbols('y', real=True)).is_real is None + + +def test_acosh_rewrite(): + x = Symbol('x') + assert acosh(x).rewrite(log) == log(x + sqrt(x - 1)*sqrt(x + 1)) + assert acosh(x).rewrite(asin) == sqrt(x - 1)*(-asin(x) + pi/2)/sqrt(1 - x) + assert acosh(x).rewrite(asinh) == sqrt(x - 1)*(I*asinh(I*x, evaluate=False) + pi/2)/sqrt(1 - x) + assert acosh(x).rewrite(atanh) == \ + (sqrt(x - 1)*sqrt(x + 1)*atanh(sqrt(x**2 - 1)/x)/sqrt(x**2 - 1) + + pi*sqrt(x - 1)*(-x*sqrt(x**(-2)) + 1)/(2*sqrt(1 - x))) + x = Symbol('x', positive=True) + assert acosh(x).rewrite(atanh) == \ + sqrt(x - 1)*sqrt(x + 1)*atanh(sqrt(x**2 - 1)/x)/sqrt(x**2 - 1) + + +def test_acosh_leading_term(): + x = Symbol('x') + # Tests concerning branch points + assert acosh(x).as_leading_term(x) == I*pi/2 + assert acosh(x + 1).as_leading_term(x) == sqrt(2)*sqrt(x) + assert acosh(x - 1).as_leading_term(x) == I*pi + assert acosh(1/x).as_leading_term(x, cdir=1) == -log(x) + log(2) + assert acosh(1/x).as_leading_term(x, cdir=-1) == -log(x) + log(2) + 2*I*pi + # Tests concerning points lying on branch cuts + assert acosh(I*x - 2).as_leading_term(x, cdir=1) == acosh(-2) + assert acosh(-I*x - 2).as_leading_term(x, cdir=1) == -2*I*pi + acosh(-2) + assert acosh(x**2 - I*x + S(1)/3).as_leading_term(x, cdir=1) == -acosh(S(1)/3) + assert acosh(x**2 - I*x + S(1)/3).as_leading_term(x, cdir=-1) == acosh(S(1)/3) + assert acosh(1/(I*x - 3)).as_leading_term(x, cdir=1) == -acosh(-S(1)/3) + assert acosh(1/(I*x - 3)).as_leading_term(x, cdir=-1) == acosh(-S(1)/3) + # Tests concerning im(ndir) == 0 + assert acosh(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == log(sqrt(3) + 2) - I*pi + assert acosh(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == log(sqrt(3) + 2) - I*pi + + +def test_acosh_series(): + x = Symbol('x') + assert acosh(x).series(x, 0, 8) == \ + -I*x + pi*I/2 - I*x**3/6 - 3*I*x**5/40 - 5*I*x**7/112 + O(x**8) + t5 = acosh(x).taylor_term(5, x) + assert t5 == - 3*I*x**5/40 + assert acosh(x).taylor_term(7, x, t5, 0) == - 5*I*x**7/112 + + +def test_acosh_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert acosh(x + 1)._eval_nseries(x, 4, None) == sqrt(2)*sqrt(x) - \ + sqrt(2)*x**(S(3)/2)/12 + 3*sqrt(2)*x**(S(5)/2)/160 - 5*sqrt(2)*x**(S(7)/2)/896 + O(x**4) + # Tests concerning points lying on branch cuts + assert acosh(x - 1)._eval_nseries(x, 4, None) == I*pi - \ + sqrt(2)*I*sqrt(x) - sqrt(2)*I*x**(S(3)/2)/12 - 3*sqrt(2)*I*x**(S(5)/2)/160 - \ + 5*sqrt(2)*I*x**(S(7)/2)/896 + O(x**4) + assert acosh(I*x - 2)._eval_nseries(x, 4, None, cdir=1) == acosh(-2) - \ + sqrt(3)*I*x/3 + sqrt(3)*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + assert acosh(-I*x - 2)._eval_nseries(x, 4, None, cdir=1) == acosh(-2) - \ + 2*I*pi + sqrt(3)*I*x/3 + sqrt(3)*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert acosh(1/(I*x - 3))._eval_nseries(x, 4, None, cdir=1) == -acosh(-S(1)/3) + \ + sqrt(2)*x/12 + 17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4) + assert acosh(1/(I*x - 3))._eval_nseries(x, 4, None, cdir=-1) == acosh(-S(1)/3) - \ + sqrt(2)*x/12 - 17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4) + # Tests concerning im(ndir) == 0 + assert acosh(-I*x**2 + x - 2)._eval_nseries(x, 4, None) == -I*pi + log(sqrt(3) + 2) - \ + sqrt(3)*x/3 + x**2*(-sqrt(3)/9 + sqrt(3)*I/3) + x**3*(-sqrt(3)/18 + 2*sqrt(3)*I/9) + O(x**4) + + +def test_acosh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: acosh(x).fdiff(2)) + + +def test_asech(): + x = Symbol('x') + + assert unchanged(asech, -x) + + # values at fixed points + assert asech(1) == 0 + assert asech(-1) == pi*I + assert asech(0) is oo + assert asech(2) == I*pi/3 + assert asech(-2) == 2*I*pi / 3 + assert asech(nan) is nan + + # at infinites + assert asech(oo) == I*pi/2 + assert asech(-oo) == I*pi/2 + assert asech(zoo) == I*AccumBounds(-pi/2, pi/2) + + assert asech(I) == log(1 + sqrt(2)) - I*pi/2 + assert asech(-I) == log(1 + sqrt(2)) + I*pi/2 + assert asech(sqrt(2) - sqrt(6)) == 11*I*pi / 12 + assert asech(sqrt(2 - 2/sqrt(5))) == I*pi / 10 + assert asech(-sqrt(2 - 2/sqrt(5))) == 9*I*pi / 10 + assert asech(2 / sqrt(2 + sqrt(2))) == I*pi / 8 + assert asech(-2 / sqrt(2 + sqrt(2))) == 7*I*pi / 8 + assert asech(sqrt(5) - 1) == I*pi / 5 + assert asech(1 - sqrt(5)) == 4*I*pi / 5 + assert asech(-sqrt(2*(2 + sqrt(2)))) == 5*I*pi / 8 + + # properties + # asech(x) == acosh(1/x) + assert asech(sqrt(2)) == acosh(1/sqrt(2)) + assert asech(2/sqrt(3)) == acosh(sqrt(3)/2) + assert asech(2/sqrt(2 + sqrt(2))) == acosh(sqrt(2 + sqrt(2))/2) + assert asech(2) == acosh(S.Half) + + # reality + assert asech(S(2)).is_real is False + assert asech(-S(1) / 3).is_real is False + assert asech(S(2) / 3).is_finite is True + assert asech(S(0)).is_real is False + assert asech(S(0)).is_extended_real is True + assert asech(symbols('y', real=True)).is_real is None + + # asech(x) == I*acos(1/x) + # (Note: the exact formula is asech(x) == +/- I*acos(1/x)) + assert asech(-sqrt(2)) == I*acos(-1/sqrt(2)) + assert asech(-2/sqrt(3)) == I*acos(-sqrt(3)/2) + assert asech(-S(2)) == I*acos(Rational(-1, 2)) + assert asech(-2/sqrt(2)) == I*acos(-sqrt(2)/2) + + # sech(asech(x)) / x == 1 + assert expand_mul(sech(asech(sqrt(6) - sqrt(2))) / (sqrt(6) - sqrt(2))) == 1 + assert expand_mul(sech(asech(sqrt(6) + sqrt(2))) / (sqrt(6) + sqrt(2))) == 1 + assert (sech(asech(sqrt(2 + 2/sqrt(5)))) / (sqrt(2 + 2/sqrt(5)))).simplify() == 1 + assert (sech(asech(-sqrt(2 + 2/sqrt(5)))) / (-sqrt(2 + 2/sqrt(5)))).simplify() == 1 + assert (sech(asech(sqrt(2*(2 + sqrt(2))))) / (sqrt(2*(2 + sqrt(2))))).simplify() == 1 + assert expand_mul(sech(asech(1 + sqrt(5))) / (1 + sqrt(5))) == 1 + assert expand_mul(sech(asech(-1 - sqrt(5))) / (-1 - sqrt(5))) == 1 + assert expand_mul(sech(asech(-sqrt(6) - sqrt(2))) / (-sqrt(6) - sqrt(2))) == 1 + + # numerical evaluation + assert str(asech(5*I).n(6)) == '0.19869 - 1.5708*I' + assert str(asech(-5*I).n(6)) == '0.19869 + 1.5708*I' + + +def test_asech_leading_term(): + x = Symbol('x') + # Tests concerning branch points + assert asech(x).as_leading_term(x, cdir=1) == -log(x) + log(2) + assert asech(x).as_leading_term(x, cdir=-1) == -log(x) + log(2) + 2*I*pi + assert asech(x + 1).as_leading_term(x, cdir=1) == sqrt(2)*I*sqrt(x) + assert asech(1/x).as_leading_term(x, cdir=1) == I*pi/2 + # Tests concerning points lying on branch cuts + assert asech(x - 1).as_leading_term(x, cdir=1) == I*pi + assert asech(I*x + 3).as_leading_term(x, cdir=1) == -asech(3) + assert asech(-I*x + 3).as_leading_term(x, cdir=1) == asech(3) + assert asech(I*x - 3).as_leading_term(x, cdir=1) == -asech(-3) + assert asech(-I*x - 3).as_leading_term(x, cdir=1) == asech(-3) + assert asech(I*x - S(1)/3).as_leading_term(x, cdir=1) == -2*I*pi + asech(-S(1)/3) + assert asech(I*x - S(1)/3).as_leading_term(x, cdir=-1) == asech(-S(1)/3) + # Tests concerning im(ndir) == 0 + assert asech(-I*x**2 + x - 3).as_leading_term(x, cdir=1) == log(-S(1)/3 + 2*sqrt(2)*I/3) + assert asech(-I*x**2 + x - 3).as_leading_term(x, cdir=-1) == log(-S(1)/3 + 2*sqrt(2)*I/3) + + +def test_asech_series(): + x = Symbol('x') + assert asech(x).series(x, 0, 9, cdir=1) == log(2) - log(x) - x**2/4 - 3*x**4/32 \ + - 5*x**6/96 - 35*x**8/1024 + O(x**9) + assert asech(x).series(x, 0, 9, cdir=-1) == I*pi + log(2) - log(-x) - x**2/4 - \ + 3*x**4/32 - 5*x**6/96 - 35*x**8/1024 + O(x**9) + t6 = asech(x).taylor_term(6, x) + assert t6 == -5*x**6/96 + assert asech(x).taylor_term(8, x, t6, 0) == -35*x**8/1024 + + +def test_asech_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert asech(x + 1)._eval_nseries(x, 4, None) == sqrt(2)*sqrt(-x) + 5*sqrt(2)*(-x)**(S(3)/2)/12 + \ + 43*sqrt(2)*(-x)**(S(5)/2)/160 + 177*sqrt(2)*(-x)**(S(7)/2)/896 + O(x**4) + # Tests concerning points lying on branch cuts + assert asech(x - 1)._eval_nseries(x, 4, None) == I*pi + sqrt(2)*sqrt(x) + \ + 5*sqrt(2)*x**(S(3)/2)/12 + 43*sqrt(2)*x**(S(5)/2)/160 + 177*sqrt(2)*x**(S(7)/2)/896 + O(x**4) + assert asech(I*x + 3)._eval_nseries(x, 4, None) == -asech(3) + sqrt(2)*x/12 - \ + 17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4) + assert asech(-I*x + 3)._eval_nseries(x, 4, None) == asech(3) + sqrt(2)*x/12 + \ + 17*sqrt(2)*I*x**2/576 - 443*sqrt(2)*x**3/41472 + O(x**4) + assert asech(I*x - 3)._eval_nseries(x, 4, None) == -asech(-3) - sqrt(2)*x/12 - \ + 17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4) + assert asech(-I*x - 3)._eval_nseries(x, 4, None) == asech(-3) - sqrt(2)*x/12 + \ + 17*sqrt(2)*I*x**2/576 + 443*sqrt(2)*x**3/41472 + O(x**4) + # Tests concerning im(ndir) == 0 + assert asech(-I*x**2 + x - 2)._eval_nseries(x, 3, None) == 2*I*pi/3 + sqrt(3)*I*x/6 + \ + x**2*(sqrt(3)/6 + 7*sqrt(3)*I/72) + O(x**3) + + +def test_asech_rewrite(): + x = Symbol('x') + assert asech(x).rewrite(log) == log(1/x + sqrt(1/x - 1) * sqrt(1/x + 1)) + assert asech(x).rewrite(acosh) == acosh(1/x) + assert asech(x).rewrite(asinh) == sqrt(-1 + 1/x)*(I*asinh(I/x, evaluate=False) + pi/2)/sqrt(1 - 1/x) + assert asech(x).rewrite(atanh) == \ + sqrt(x + 1)*sqrt(1/(x + 1))*atanh(sqrt(1 - x**2)) + I*pi*(-sqrt(x)*sqrt(1/x) + 1 - I*sqrt(x**2)/(2*sqrt(-x**2)) - I*sqrt(-x)/(2*sqrt(x))) + + +def test_asech_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: asech(x).fdiff(2)) + + +def test_acsch(): + x = Symbol('x') + + assert unchanged(acsch, x) + assert acsch(-x) == -acsch(x) + + # values at fixed points + assert acsch(1) == log(1 + sqrt(2)) + assert acsch(-1) == - log(1 + sqrt(2)) + assert acsch(0) is zoo + assert acsch(2) == log((1+sqrt(5))/2) + assert acsch(-2) == - log((1+sqrt(5))/2) + + assert acsch(I) == - I*pi/2 + assert acsch(-I) == I*pi/2 + assert acsch(-I*(sqrt(6) + sqrt(2))) == I*pi / 12 + assert acsch(I*(sqrt(2) + sqrt(6))) == -I*pi / 12 + assert acsch(-I*(1 + sqrt(5))) == I*pi / 10 + assert acsch(I*(1 + sqrt(5))) == -I*pi / 10 + assert acsch(-I*2 / sqrt(2 - sqrt(2))) == I*pi / 8 + assert acsch(I*2 / sqrt(2 - sqrt(2))) == -I*pi / 8 + assert acsch(-I*2) == I*pi / 6 + assert acsch(I*2) == -I*pi / 6 + assert acsch(-I*sqrt(2 + 2/sqrt(5))) == I*pi / 5 + assert acsch(I*sqrt(2 + 2/sqrt(5))) == -I*pi / 5 + assert acsch(-I*sqrt(2)) == I*pi / 4 + assert acsch(I*sqrt(2)) == -I*pi / 4 + assert acsch(-I*(sqrt(5)-1)) == 3*I*pi / 10 + assert acsch(I*(sqrt(5)-1)) == -3*I*pi / 10 + assert acsch(-I*2 / sqrt(3)) == I*pi / 3 + assert acsch(I*2 / sqrt(3)) == -I*pi / 3 + assert acsch(-I*2 / sqrt(2 + sqrt(2))) == 3*I*pi / 8 + assert acsch(I*2 / sqrt(2 + sqrt(2))) == -3*I*pi / 8 + assert acsch(-I*sqrt(2 - 2/sqrt(5))) == 2*I*pi / 5 + assert acsch(I*sqrt(2 - 2/sqrt(5))) == -2*I*pi / 5 + assert acsch(-I*(sqrt(6) - sqrt(2))) == 5*I*pi / 12 + assert acsch(I*(sqrt(6) - sqrt(2))) == -5*I*pi / 12 + assert acsch(nan) is nan + + # properties + # acsch(x) == asinh(1/x) + assert acsch(-I*sqrt(2)) == asinh(I/sqrt(2)) + assert acsch(-I*2 / sqrt(3)) == asinh(I*sqrt(3) / 2) + + # reality + assert acsch(S(2)).is_real is True + assert acsch(S(2)).is_finite is True + assert acsch(S(-2)).is_real is True + assert acsch(S(oo)).is_extended_real is True + assert acsch(-S(oo)).is_real is True + assert (acsch(2) - oo) == -oo + assert acsch(symbols('y', extended_real=True)).is_extended_real is True + + # acsch(x) == -I*asin(I/x) + assert acsch(-I*sqrt(2)) == -I*asin(-1/sqrt(2)) + assert acsch(-I*2 / sqrt(3)) == -I*asin(-sqrt(3)/2) + + # csch(acsch(x)) / x == 1 + assert expand_mul(csch(acsch(-I*(sqrt(6) + sqrt(2)))) / (-I*(sqrt(6) + sqrt(2)))) == 1 + assert expand_mul(csch(acsch(I*(1 + sqrt(5)))) / (I*(1 + sqrt(5)))) == 1 + assert (csch(acsch(I*sqrt(2 - 2/sqrt(5)))) / (I*sqrt(2 - 2/sqrt(5)))).simplify() == 1 + assert (csch(acsch(-I*sqrt(2 - 2/sqrt(5)))) / (-I*sqrt(2 - 2/sqrt(5)))).simplify() == 1 + + # numerical evaluation + assert str(acsch(5*I+1).n(6)) == '0.0391819 - 0.193363*I' + assert str(acsch(-5*I+1).n(6)) == '0.0391819 + 0.193363*I' + + +def test_acsch_infinities(): + assert acsch(oo) == 0 + assert acsch(-oo) == 0 + assert acsch(zoo) == 0 + + +def test_acsch_leading_term(): + x = Symbol('x') + assert acsch(1/x).as_leading_term(x) == x + # Tests concerning branch points + assert acsch(x + I).as_leading_term(x) == -I*pi/2 + assert acsch(x - I).as_leading_term(x) == I*pi/2 + # Tests concerning points lying on branch cuts + assert acsch(x).as_leading_term(x, cdir=1) == -log(x) + log(2) + assert acsch(x).as_leading_term(x, cdir=-1) == log(x) - log(2) - I*pi + assert acsch(x + I/2).as_leading_term(x, cdir=1) == -I*pi - acsch(I/2) + assert acsch(x + I/2).as_leading_term(x, cdir=-1) == acsch(I/2) + assert acsch(x - I/2).as_leading_term(x, cdir=1) == -acsch(I/2) + assert acsch(x - I/2).as_leading_term(x, cdir=-1) == acsch(I/2) + I*pi + # Tests concerning re(ndir) == 0 + assert acsch(I/2 + I*x - x**2).as_leading_term(x, cdir=1) == log(2 - sqrt(3)) - I*pi/2 + assert acsch(I/2 + I*x - x**2).as_leading_term(x, cdir=-1) == log(2 - sqrt(3)) - I*pi/2 + + +def test_acsch_series(): + x = Symbol('x') + assert acsch(x).series(x, 0, 9) == log(2) - log(x) + x**2/4 - 3*x**4/32 \ + + 5*x**6/96 - 35*x**8/1024 + O(x**9) + t4 = acsch(x).taylor_term(4, x) + assert t4 == -3*x**4/32 + assert acsch(x).taylor_term(6, x, t4, 0) == 5*x**6/96 + + +def test_acsch_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert acsch(x + I)._eval_nseries(x, 4, None) == -I*pi/2 + I*sqrt(x) + \ + sqrt(x) + 5*I*x**(S(3)/2)/12 - 5*x**(S(3)/2)/12 - 43*I*x**(S(5)/2)/160 - \ + 43*x**(S(5)/2)/160 - 177*I*x**(S(7)/2)/896 + 177*x**(S(7)/2)/896 + O(x**4) + assert acsch(x - I)._eval_nseries(x, 4, None) == I*pi/2 - I*sqrt(x) + \ + sqrt(x) - 5*I*x**(S(3)/2)/12 - 5*x**(S(3)/2)/12 + 43*I*x**(S(5)/2)/160 - \ + 43*x**(S(5)/2)/160 + 177*I*x**(S(7)/2)/896 + 177*x**(S(7)/2)/896 + O(x**4) + # Tests concerning points lying on branch cuts + assert acsch(x + I/2)._eval_nseries(x, 4, None, cdir=1) == -acsch(I/2) - \ + I*pi + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsch(x + I/2)._eval_nseries(x, 4, None, cdir=-1) == acsch(I/2) - \ + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsch(x - I/2)._eval_nseries(x, 4, None, cdir=1) == -acsch(I/2) - \ + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsch(x - I/2)._eval_nseries(x, 4, None, cdir=-1) == I*pi + \ + acsch(I/2) + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + # TODO: Tests concerning re(ndir) == 0 + assert acsch(I/2 + I*x - x**2)._eval_nseries(x, 4, None) == -I*pi/2 + \ + log(2 - sqrt(3)) + 4*sqrt(3)*x/3 + x**2*(-8*sqrt(3)/9 + 4*sqrt(3)*I/3) + \ + x**3*(16*sqrt(3)/9 - 16*sqrt(3)*I/9) + O(x**4) + + +def test_acsch_rewrite(): + x = Symbol('x') + assert acsch(x).rewrite(log) == log(1/x + sqrt(1/x**2 + 1)) + assert acsch(x).rewrite(asinh) == asinh(1/x) + assert acsch(x).rewrite(atanh) == (sqrt(-x**2)*(-sqrt(-(x**2 + 1)**2) + *atanh(sqrt(x**2 + 1))/(x**2 + 1) + + pi/2)/x) + + +def test_acsch_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: acsch(x).fdiff(2)) + + +def test_atanh(): + x = Symbol('x') + + # at specific points + assert atanh(0) == 0 + assert atanh(I) == I*pi/4 + assert atanh(-I) == -I*pi/4 + assert atanh(1) is oo + assert atanh(-1) is -oo + assert atanh(nan) is nan + + # at infinites + assert atanh(oo) == -I*pi/2 + assert atanh(-oo) == I*pi/2 + + assert atanh(I*oo) == I*pi/2 + assert atanh(-I*oo) == -I*pi/2 + + assert atanh(zoo) == I*AccumBounds(-pi/2, pi/2) + + # properties + assert atanh(-x) == -atanh(x) + + # reality + assert atanh(S(2)).is_real is False + assert atanh(S(-1)/5).is_real is True + assert atanh(symbols('y', extended_real=True)).is_real is None + assert atanh(S(1)).is_real is False + assert atanh(S(1)).is_extended_real is True + assert atanh(S(-1)).is_real is False + + # special values + assert atanh(I/sqrt(3)) == I*pi/6 + assert atanh(-I/sqrt(3)) == -I*pi/6 + assert atanh(I*sqrt(3)) == I*pi/3 + assert atanh(-I*sqrt(3)) == -I*pi/3 + assert atanh(I*(1 + sqrt(2))) == pi*I*Rational(3, 8) + assert atanh(I*(sqrt(2) - 1)) == pi*I/8 + assert atanh(I*(1 - sqrt(2))) == -pi*I/8 + assert atanh(-I*(1 + sqrt(2))) == pi*I*Rational(-3, 8) + assert atanh(I*sqrt(5 + 2*sqrt(5))) == I*pi*Rational(2, 5) + assert atanh(-I*sqrt(5 + 2*sqrt(5))) == I*pi*Rational(-2, 5) + assert atanh(I*(2 - sqrt(3))) == pi*I/12 + assert atanh(I*(sqrt(3) - 2)) == -pi*I/12 + assert atanh(oo) == -I*pi/2 + + # Symmetry + assert atanh(Rational(-1, 2)) == -atanh(S.Half) + + # inverse composition + assert unchanged(atanh, tanh(Symbol('v1'))) + + assert atanh(tanh(-5, evaluate=False)) == -5 + assert atanh(tanh(0, evaluate=False)) == 0 + assert atanh(tanh(7, evaluate=False)) == 7 + assert atanh(tanh(I, evaluate=False)) == I + assert atanh(tanh(-I, evaluate=False)) == -I + assert atanh(tanh(-11*I, evaluate=False)) == -11*I + 4*I*pi + assert atanh(tanh(3 + I)) == 3 + I + assert atanh(tanh(4 + 5*I)) == 4 - 2*I*pi + 5*I + assert atanh(tanh(pi/2)) == pi/2 + assert atanh(tanh(pi)) == pi + assert atanh(tanh(-3 + 7*I)) == -3 - 2*I*pi + 7*I + assert atanh(tanh(9 - I*2/3)) == 9 - I*2/3 + assert atanh(tanh(-32 - 123*I)) == -32 - 123*I + 39*I*pi + + +def test_atanh_rewrite(): + x = Symbol('x') + assert atanh(x).rewrite(log) == (log(1 + x) - log(1 - x)) / 2 + assert atanh(x).rewrite(asinh) == \ + pi*x/(2*sqrt(-x**2)) - sqrt(-x)*sqrt(1 - x**2)*sqrt(1/(x**2 - 1))*asinh(sqrt(1/(x**2 - 1)))/sqrt(x) + + +def test_atanh_leading_term(): + x = Symbol('x') + assert atanh(x).as_leading_term(x) == x + # Tests concerning branch points + assert atanh(x + 1).as_leading_term(x, cdir=1) == -log(x)/2 + log(2)/2 - I*pi/2 + assert atanh(x + 1).as_leading_term(x, cdir=-1) == -log(x)/2 + log(2)/2 + I*pi/2 + assert atanh(x - 1).as_leading_term(x, cdir=1) == log(x)/2 - log(2)/2 + assert atanh(x - 1).as_leading_term(x, cdir=-1) == log(x)/2 - log(2)/2 + assert atanh(1/x).as_leading_term(x, cdir=1) == -I*pi/2 + assert atanh(1/x).as_leading_term(x, cdir=-1) == I*pi/2 + # Tests concerning points lying on branch cuts + assert atanh(I*x + 2).as_leading_term(x, cdir=1) == atanh(2) + I*pi + assert atanh(-I*x + 2).as_leading_term(x, cdir=1) == atanh(2) + assert atanh(I*x - 2).as_leading_term(x, cdir=1) == -atanh(2) + assert atanh(-I*x - 2).as_leading_term(x, cdir=1) == -I*pi - atanh(2) + # Tests concerning im(ndir) == 0 + assert atanh(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == -log(3)/2 - I*pi/2 + assert atanh(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == -log(3)/2 - I*pi/2 + + +def test_atanh_series(): + x = Symbol('x') + assert atanh(x).series(x, 0, 10) == \ + x + x**3/3 + x**5/5 + x**7/7 + x**9/9 + O(x**10) + + +def test_atanh_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert atanh(x + 1)._eval_nseries(x, 4, None, cdir=1) == -I*pi/2 + log(2)/2 - \ + log(x)/2 + x/4 - x**2/16 + x**3/48 + O(x**4) + assert atanh(x + 1)._eval_nseries(x, 4, None, cdir=-1) == I*pi/2 + log(2)/2 - \ + log(x)/2 + x/4 - x**2/16 + x**3/48 + O(x**4) + assert atanh(x - 1)._eval_nseries(x, 4, None, cdir=1) == -log(2)/2 + log(x)/2 + \ + x/4 + x**2/16 + x**3/48 + O(x**4) + assert atanh(x - 1)._eval_nseries(x, 4, None, cdir=-1) == -log(2)/2 + log(x)/2 + \ + x/4 + x**2/16 + x**3/48 + O(x**4) + # Tests concerning points lying on branch cuts + assert atanh(I*x + 2)._eval_nseries(x, 4, None, cdir=1) == I*pi + atanh(2) - \ + I*x/3 - 2*x**2/9 + 13*I*x**3/81 + O(x**4) + assert atanh(I*x + 2)._eval_nseries(x, 4, None, cdir=-1) == atanh(2) - I*x/3 - \ + 2*x**2/9 + 13*I*x**3/81 + O(x**4) + assert atanh(I*x - 2)._eval_nseries(x, 4, None, cdir=1) == -atanh(2) - I*x/3 + \ + 2*x**2/9 + 13*I*x**3/81 + O(x**4) + assert atanh(I*x - 2)._eval_nseries(x, 4, None, cdir=-1) == -atanh(2) - I*pi - \ + I*x/3 + 2*x**2/9 + 13*I*x**3/81 + O(x**4) + # Tests concerning im(ndir) == 0 + assert atanh(-I*x**2 + x - 2)._eval_nseries(x, 4, None) == -I*pi/2 - log(3)/2 - x/3 + \ + x**2*(-S(1)/4 + I/2) + x**2*(S(1)/36 - I/6) + x**3*(-S(1)/6 + I/2) + x**3*(S(1)/162 - I/18) + O(x**4) + + +def test_atanh_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: atanh(x).fdiff(2)) + + +def test_acoth(): + x = Symbol('x') + + #at specific points + assert acoth(0) == I*pi/2 + assert acoth(I) == -I*pi/4 + assert acoth(-I) == I*pi/4 + assert acoth(1) is oo + assert acoth(-1) is -oo + assert acoth(nan) is nan + + # at infinites + assert acoth(oo) == 0 + assert acoth(-oo) == 0 + assert acoth(I*oo) == 0 + assert acoth(-I*oo) == 0 + assert acoth(zoo) == 0 + + #properties + assert acoth(-x) == -acoth(x) + + assert acoth(I/sqrt(3)) == -I*pi/3 + assert acoth(-I/sqrt(3)) == I*pi/3 + assert acoth(I*sqrt(3)) == -I*pi/6 + assert acoth(-I*sqrt(3)) == I*pi/6 + assert acoth(I*(1 + sqrt(2))) == -pi*I/8 + assert acoth(-I*(sqrt(2) + 1)) == pi*I/8 + assert acoth(I*(1 - sqrt(2))) == pi*I*Rational(3, 8) + assert acoth(I*(sqrt(2) - 1)) == pi*I*Rational(-3, 8) + assert acoth(I*sqrt(5 + 2*sqrt(5))) == -I*pi/10 + assert acoth(-I*sqrt(5 + 2*sqrt(5))) == I*pi/10 + assert acoth(I*(2 + sqrt(3))) == -pi*I/12 + assert acoth(-I*(2 + sqrt(3))) == pi*I/12 + assert acoth(I*(2 - sqrt(3))) == pi*I*Rational(-5, 12) + assert acoth(I*(sqrt(3) - 2)) == pi*I*Rational(5, 12) + + # reality + assert acoth(S(2)).is_real is True + assert acoth(S(2)).is_finite is True + assert acoth(S(2)).is_extended_real is True + assert acoth(S(-2)).is_real is True + assert acoth(S(1)).is_real is False + assert acoth(S(1)).is_extended_real is True + assert acoth(S(-1)).is_real is False + assert acoth(symbols('y', real=True)).is_real is None + + # Symmetry + assert acoth(Rational(-1, 2)) == -acoth(S.Half) + + +def test_acoth_rewrite(): + x = Symbol('x') + assert acoth(x).rewrite(log) == (log(1 + 1/x) - log(1 - 1/x)) / 2 + assert acoth(x).rewrite(atanh) == atanh(1/x) + assert acoth(x).rewrite(asinh) == \ + x*sqrt(x**(-2))*asinh(sqrt(1/(x**2 - 1))) + I*pi*(sqrt((x - 1)/x)*sqrt(x/(x - 1)) - sqrt(x/(x + 1))*sqrt(1 + 1/x))/2 + + +def test_acoth_leading_term(): + x = Symbol('x') + # Tests concerning branch points + assert acoth(x + 1).as_leading_term(x, cdir=1) == -log(x)/2 + log(2)/2 + assert acoth(x + 1).as_leading_term(x, cdir=-1) == -log(x)/2 + log(2)/2 + assert acoth(x - 1).as_leading_term(x, cdir=1) == log(x)/2 - log(2)/2 + I*pi/2 + assert acoth(x - 1).as_leading_term(x, cdir=-1) == log(x)/2 - log(2)/2 - I*pi/2 + # Tests concerning points lying on branch cuts + assert acoth(x).as_leading_term(x, cdir=-1) == I*pi/2 + assert acoth(x).as_leading_term(x, cdir=1) == -I*pi/2 + assert acoth(I*x + 1/2).as_leading_term(x, cdir=1) == acoth(1/2) + assert acoth(-I*x + 1/2).as_leading_term(x, cdir=1) == acoth(1/2) + I*pi + assert acoth(I*x - 1/2).as_leading_term(x, cdir=1) == -I*pi - acoth(1/2) + assert acoth(-I*x - 1/2).as_leading_term(x, cdir=1) == -acoth(1/2) + # Tests concerning im(ndir) == 0 + assert acoth(-I*x**2 - x - S(1)/2).as_leading_term(x, cdir=1) == -log(3)/2 + I*pi/2 + assert acoth(-I*x**2 - x - S(1)/2).as_leading_term(x, cdir=-1) == -log(3)/2 + I*pi/2 + + +def test_acoth_series(): + x = Symbol('x') + assert acoth(x).series(x, 0, 10) == \ + -I*pi/2 + x + x**3/3 + x**5/5 + x**7/7 + x**9/9 + O(x**10) + + +def test_acoth_nseries(): + x = Symbol('x') + # Tests concerning branch points + assert acoth(x + 1)._eval_nseries(x, 4, None) == log(2)/2 - log(x)/2 + x/4 - \ + x**2/16 + x**3/48 + O(x**4) + assert acoth(x - 1)._eval_nseries(x, 4, None, cdir=1) == I*pi/2 - log(2)/2 + \ + log(x)/2 + x/4 + x**2/16 + x**3/48 + O(x**4) + assert acoth(x - 1)._eval_nseries(x, 4, None, cdir=-1) == -I*pi/2 - log(2)/2 + \ + log(x)/2 + x/4 + x**2/16 + x**3/48 + O(x**4) + # Tests concerning points lying on branch cuts + assert acoth(I*x + S(1)/2)._eval_nseries(x, 4, None, cdir=1) == acoth(S(1)/2) + \ + 4*I*x/3 - 8*x**2/9 - 112*I*x**3/81 + O(x**4) + assert acoth(I*x + S(1)/2)._eval_nseries(x, 4, None, cdir=-1) == I*pi + \ + acoth(S(1)/2) + 4*I*x/3 - 8*x**2/9 - 112*I*x**3/81 + O(x**4) + assert acoth(I*x - S(1)/2)._eval_nseries(x, 4, None, cdir=1) == -acoth(S(1)/2) - \ + I*pi + 4*I*x/3 + 8*x**2/9 - 112*I*x**3/81 + O(x**4) + assert acoth(I*x - S(1)/2)._eval_nseries(x, 4, None, cdir=-1) == -acoth(S(1)/2) + \ + 4*I*x/3 + 8*x**2/9 - 112*I*x**3/81 + O(x**4) + # Tests concerning im(ndir) == 0 + assert acoth(-I*x**2 - x - S(1)/2)._eval_nseries(x, 4, None) == I*pi/2 - log(3)/2 - \ + 4*x/3 + x**2*(-S(8)/9 + 2*I/3) - 2*I*x**2 + x**3*(S(104)/81 - 16*I/9) - 8*x**3/3 + O(x**4) + + +def test_acoth_fdiff(): + x = Symbol('x') + raises(ArgumentIndexError, lambda: acoth(x).fdiff(2)) + + +def test_inverses(): + x = Symbol('x') + assert sinh(x).inverse() == asinh + raises(AttributeError, lambda: cosh(x).inverse()) + assert tanh(x).inverse() == atanh + assert coth(x).inverse() == acoth + assert asinh(x).inverse() == sinh + assert acosh(x).inverse() == cosh + assert atanh(x).inverse() == tanh + assert acoth(x).inverse() == coth + assert asech(x).inverse() == sech + assert acsch(x).inverse() == csch + + +def test_leading_term(): + x = Symbol('x') + assert cosh(x).as_leading_term(x) == 1 + assert coth(x).as_leading_term(x) == 1/x + for func in [sinh, tanh]: + assert func(x).as_leading_term(x) == x + for func in [sinh, cosh, tanh, coth]: + for ar in (1/x, S.Half): + eq = func(ar) + assert eq.as_leading_term(x) == eq + for func in [csch, sech]: + eq = func(S.Half) + assert eq.as_leading_term(x) == eq + + +def test_complex(): + a, b = symbols('a,b', real=True) + z = a + b*I + for func in [sinh, cosh, tanh, coth, sech, csch]: + assert func(z).conjugate() == func(a - b*I) + for deep in [True, False]: + assert sinh(z).expand( + complex=True, deep=deep) == sinh(a)*cos(b) + I*cosh(a)*sin(b) + assert cosh(z).expand( + complex=True, deep=deep) == cosh(a)*cos(b) + I*sinh(a)*sin(b) + assert tanh(z).expand(complex=True, deep=deep) == sinh(a)*cosh( + a)/(cos(b)**2 + sinh(a)**2) + I*sin(b)*cos(b)/(cos(b)**2 + sinh(a)**2) + assert coth(z).expand(complex=True, deep=deep) == sinh(a)*cosh( + a)/(sin(b)**2 + sinh(a)**2) - I*sin(b)*cos(b)/(sin(b)**2 + sinh(a)**2) + assert csch(z).expand(complex=True, deep=deep) == cos(b) * sinh(a) / (sin(b)**2\ + *cosh(a)**2 + cos(b)**2 * sinh(a)**2) - I*sin(b) * cosh(a) / (sin(b)**2\ + *cosh(a)**2 + cos(b)**2 * sinh(a)**2) + assert sech(z).expand(complex=True, deep=deep) == cos(b) * cosh(a) / (sin(b)**2\ + *sinh(a)**2 + cos(b)**2 * cosh(a)**2) - I*sin(b) * sinh(a) / (sin(b)**2\ + *sinh(a)**2 + cos(b)**2 * cosh(a)**2) + + +def test_complex_2899(): + a, b = symbols('a,b', real=True) + for deep in [True, False]: + for func in [sinh, cosh, tanh, coth]: + assert func(a).expand(complex=True, deep=deep) == func(a) + + +def test_simplifications(): + x = Symbol('x') + assert sinh(asinh(x)) == x + assert sinh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1) + assert sinh(atanh(x)) == x/sqrt(1 - x**2) + assert sinh(acoth(x)) == 1/(sqrt(x - 1) * sqrt(x + 1)) + + assert cosh(asinh(x)) == sqrt(1 + x**2) + assert cosh(acosh(x)) == x + assert cosh(atanh(x)) == 1/sqrt(1 - x**2) + assert cosh(acoth(x)) == x/(sqrt(x - 1) * sqrt(x + 1)) + + assert tanh(asinh(x)) == x/sqrt(1 + x**2) + assert tanh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1) / x + assert tanh(atanh(x)) == x + assert tanh(acoth(x)) == 1/x + + assert coth(asinh(x)) == sqrt(1 + x**2)/x + assert coth(acosh(x)) == x/(sqrt(x - 1) * sqrt(x + 1)) + assert coth(atanh(x)) == 1/x + assert coth(acoth(x)) == x + + assert csch(asinh(x)) == 1/x + assert csch(acosh(x)) == 1/(sqrt(x - 1) * sqrt(x + 1)) + assert csch(atanh(x)) == sqrt(1 - x**2)/x + assert csch(acoth(x)) == sqrt(x - 1) * sqrt(x + 1) + + assert sech(asinh(x)) == 1/sqrt(1 + x**2) + assert sech(acosh(x)) == 1/x + assert sech(atanh(x)) == sqrt(1 - x**2) + assert sech(acoth(x)) == sqrt(x - 1) * sqrt(x + 1)/x + + +def test_issue_4136(): + assert cosh(asinh(Integer(3)/2)) == sqrt(Integer(13)/4) + + +def test_sinh_rewrite(): + x = Symbol('x') + assert sinh(x).rewrite(exp) == (exp(x) - exp(-x))/2 \ + == sinh(x).rewrite('tractable') + assert sinh(x).rewrite(cosh) == -I*cosh(x + I*pi/2) + tanh_half = tanh(S.Half*x) + assert sinh(x).rewrite(tanh) == 2*tanh_half/(1 - tanh_half**2) + coth_half = coth(S.Half*x) + assert sinh(x).rewrite(coth) == 2*coth_half/(coth_half**2 - 1) + + +def test_cosh_rewrite(): + x = Symbol('x') + assert cosh(x).rewrite(exp) == (exp(x) + exp(-x))/2 \ + == cosh(x).rewrite('tractable') + assert cosh(x).rewrite(sinh) == -I*sinh(x + I*pi/2, evaluate=False) + tanh_half = tanh(S.Half*x)**2 + assert cosh(x).rewrite(tanh) == (1 + tanh_half)/(1 - tanh_half) + coth_half = coth(S.Half*x)**2 + assert cosh(x).rewrite(coth) == (coth_half + 1)/(coth_half - 1) + + +def test_tanh_rewrite(): + x = Symbol('x') + assert tanh(x).rewrite(exp) == (exp(x) - exp(-x))/(exp(x) + exp(-x)) \ + == tanh(x).rewrite('tractable') + assert tanh(x).rewrite(sinh) == I*sinh(x)/sinh(I*pi/2 - x, evaluate=False) + assert tanh(x).rewrite(cosh) == I*cosh(I*pi/2 - x, evaluate=False)/cosh(x) + assert tanh(x).rewrite(coth) == 1/coth(x) + + +def test_coth_rewrite(): + x = Symbol('x') + assert coth(x).rewrite(exp) == (exp(x) + exp(-x))/(exp(x) - exp(-x)) \ + == coth(x).rewrite('tractable') + assert coth(x).rewrite(sinh) == -I*sinh(I*pi/2 - x, evaluate=False)/sinh(x) + assert coth(x).rewrite(cosh) == -I*cosh(x)/cosh(I*pi/2 - x, evaluate=False) + assert coth(x).rewrite(tanh) == 1/tanh(x) + + +def test_csch_rewrite(): + x = Symbol('x') + assert csch(x).rewrite(exp) == 1 / (exp(x)/2 - exp(-x)/2) \ + == csch(x).rewrite('tractable') + assert csch(x).rewrite(cosh) == I/cosh(x + I*pi/2, evaluate=False) + tanh_half = tanh(S.Half*x) + assert csch(x).rewrite(tanh) == (1 - tanh_half**2)/(2*tanh_half) + coth_half = coth(S.Half*x) + assert csch(x).rewrite(coth) == (coth_half**2 - 1)/(2*coth_half) + + +def test_sech_rewrite(): + x = Symbol('x') + assert sech(x).rewrite(exp) == 1 / (exp(x)/2 + exp(-x)/2) \ + == sech(x).rewrite('tractable') + assert sech(x).rewrite(sinh) == I/sinh(x + I*pi/2, evaluate=False) + tanh_half = tanh(S.Half*x)**2 + assert sech(x).rewrite(tanh) == (1 - tanh_half)/(1 + tanh_half) + coth_half = coth(S.Half*x)**2 + assert sech(x).rewrite(coth) == (coth_half - 1)/(coth_half + 1) + + +def test_derivs(): + x = Symbol('x') + assert coth(x).diff(x) == -sinh(x)**(-2) + assert sinh(x).diff(x) == cosh(x) + assert cosh(x).diff(x) == sinh(x) + assert tanh(x).diff(x) == -tanh(x)**2 + 1 + assert csch(x).diff(x) == -coth(x)*csch(x) + assert sech(x).diff(x) == -tanh(x)*sech(x) + assert acoth(x).diff(x) == 1/(-x**2 + 1) + assert asinh(x).diff(x) == 1/sqrt(x**2 + 1) + assert acosh(x).diff(x) == 1/(sqrt(x - 1)*sqrt(x + 1)) + assert acosh(x).diff(x) == acosh(x).rewrite(log).diff(x).together() + assert atanh(x).diff(x) == 1/(-x**2 + 1) + assert asech(x).diff(x) == -1/(x*sqrt(1 - x**2)) + assert acsch(x).diff(x) == -1/(x**2*sqrt(1 + x**(-2))) + + +def test_sinh_expansion(): + x, y = symbols('x,y') + assert sinh(x+y).expand(trig=True) == sinh(x)*cosh(y) + cosh(x)*sinh(y) + assert sinh(2*x).expand(trig=True) == 2*sinh(x)*cosh(x) + assert sinh(3*x).expand(trig=True).expand() == \ + sinh(x)**3 + 3*sinh(x)*cosh(x)**2 + + +def test_cosh_expansion(): + x, y = symbols('x,y') + assert cosh(x+y).expand(trig=True) == cosh(x)*cosh(y) + sinh(x)*sinh(y) + assert cosh(2*x).expand(trig=True) == cosh(x)**2 + sinh(x)**2 + assert cosh(3*x).expand(trig=True).expand() == \ + 3*sinh(x)**2*cosh(x) + cosh(x)**3 + +def test_cosh_positive(): + # See issue 11721 + # cosh(x) is positive for real values of x + k = symbols('k', real=True) + n = symbols('n', integer=True) + + assert cosh(k, evaluate=False).is_positive is True + assert cosh(k + 2*n*pi*I, evaluate=False).is_positive is True + assert cosh(I*pi/4, evaluate=False).is_positive is True + assert cosh(3*I*pi/4, evaluate=False).is_positive is False + +def test_cosh_nonnegative(): + k = symbols('k', real=True) + n = symbols('n', integer=True) + + assert cosh(k, evaluate=False).is_nonnegative is True + assert cosh(k + 2*n*pi*I, evaluate=False).is_nonnegative is True + assert cosh(I*pi/4, evaluate=False).is_nonnegative is True + assert cosh(3*I*pi/4, evaluate=False).is_nonnegative is False + assert cosh(S.Zero, evaluate=False).is_nonnegative is True + +def test_real_assumptions(): + z = Symbol('z', real=False) + assert sinh(z).is_real is None + assert cosh(z).is_real is None + assert tanh(z).is_real is None + assert sech(z).is_real is None + assert csch(z).is_real is None + assert coth(z).is_real is None + +def test_sign_assumptions(): + p = Symbol('p', positive=True) + n = Symbol('n', negative=True) + assert sinh(n).is_negative is True + assert sinh(p).is_positive is True + assert cosh(n).is_positive is True + assert cosh(p).is_positive is True + assert tanh(n).is_negative is True + assert tanh(p).is_positive is True + assert csch(n).is_negative is True + assert csch(p).is_positive is True + assert sech(n).is_positive is True + assert sech(p).is_positive is True + assert coth(n).is_negative is True + assert coth(p).is_positive is True + + +def test_issue_25847(): + x = Symbol('x') + + #atanh + assert atanh(sin(x)/x).as_leading_term(x) == atanh(sin(x)/x) + raises(PoleError, lambda: atanh(exp(1/x)).as_leading_term(x)) + + #asinh + assert asinh(sin(x)/x).as_leading_term(x) == log(1 + sqrt(2)) + raises(PoleError, lambda: asinh(exp(1/x)).as_leading_term(x)) + + #acosh + assert acosh(sin(x)/x).as_leading_term(x) == 0 + raises(PoleError, lambda: acosh(exp(1/x)).as_leading_term(x)) + + #acoth + assert acoth(sin(x)/x).as_leading_term(x) == acoth(sin(x)/x) + raises(PoleError, lambda: acoth(exp(1/x)).as_leading_term(x)) + + #asech + assert asech(sinh(x)/x).as_leading_term(x) == 0 + raises(PoleError, lambda: asech(exp(1/x)).as_leading_term(x)) + + #acsch + assert acsch(sin(x)/x).as_leading_term(x) == log(1 + sqrt(2)) + raises(PoleError, lambda: acsch(exp(1/x)).as_leading_term(x)) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_integers.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_integers.py new file mode 100644 index 0000000000000000000000000000000000000000..1ac681a6783d0ebd9c70617085e9fb73603ff0db --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_integers.py @@ -0,0 +1,662 @@ +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.relational import (Eq, Ge, Gt, Le, Lt, Ne) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.integers import (ceiling, floor, frac) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin, cos, tan +from sympy.polys.rootoftools import RootOf, CRootOf +from sympy import Integers +from sympy.sets.sets import Interval +from sympy.sets.fancysets import ImageSet +from sympy.core.function import Lambda + +from sympy.core.expr import unchanged +from sympy.testing.pytest import XFAIL, raises + +x = Symbol('x') +i = Symbol('i', imaginary=True) +y = Symbol('y', real=True) +k, n = symbols('k,n', integer=True) + + +def test_floor(): + + assert floor(nan) is nan + + assert floor(oo) is oo + assert floor(-oo) is -oo + assert floor(zoo) is zoo + + assert floor(0) == 0 + + assert floor(1) == 1 + assert floor(-1) == -1 + + assert floor(E) == 2 + assert floor(-E) == -3 + + assert floor(2*E) == 5 + assert floor(-2*E) == -6 + + assert floor(pi) == 3 + assert floor(-pi) == -4 + + assert floor(S.Half) == 0 + assert floor(Rational(-1, 2)) == -1 + + assert floor(Rational(7, 3)) == 2 + assert floor(Rational(-7, 3)) == -3 + assert floor(-Rational(7, 3)) == -3 + + assert floor(Float(17.0)) == 17 + assert floor(-Float(17.0)) == -17 + + assert floor(Float(7.69)) == 7 + assert floor(-Float(7.69)) == -8 + + assert floor(I) == I + assert floor(-I) == -I + e = floor(i) + assert e.func is floor and e.args[0] == i + + assert floor(oo*I) == oo*I + assert floor(-oo*I) == -oo*I + assert floor(exp(I*pi/4)*oo) == exp(I*pi/4)*oo + + assert floor(2*I) == 2*I + assert floor(-2*I) == -2*I + + assert floor(I/2) == 0 + assert floor(-I/2) == -I + + assert floor(E + 17) == 19 + assert floor(pi + 2) == 5 + + assert floor(E + pi) == 5 + assert floor(I + pi) == 3 + I + + assert floor(floor(pi)) == 3 + assert floor(floor(y)) == floor(y) + assert floor(floor(x)) == floor(x) + + assert unchanged(floor, x) + assert unchanged(floor, 2*x) + assert unchanged(floor, k*x) + + assert floor(k) == k + assert floor(2*k) == 2*k + assert floor(k*n) == k*n + + assert unchanged(floor, k/2) + + assert unchanged(floor, x + y) + + assert floor(x + 3) == floor(x) + 3 + assert floor(x + k) == floor(x) + k + + assert floor(y + 3) == floor(y) + 3 + assert floor(y + k) == floor(y) + k + + assert floor(3 + I*y + pi) == 6 + floor(y)*I + + assert floor(k + n) == k + n + + assert unchanged(floor, x*I) + assert floor(k*I) == k*I + + assert floor(Rational(23, 10) - E*I) == 2 - 3*I + + assert floor(sin(1)) == 0 + assert floor(sin(-1)) == -1 + + assert floor(exp(2)) == 7 + + assert floor(log(8)/log(2)) != 2 + assert int(floor(log(8)/log(2)).evalf(chop=True)) == 3 + + assert floor(factorial(50)/exp(1)) == \ + 11188719610782480504630258070757734324011354208865721592720336800 + + assert (floor(y) < y) == False + assert (floor(y) <= y) == True + assert (floor(y) > y) == False + assert (floor(y) >= y) == False + assert (floor(x) <= x).is_Relational # x could be non-real + assert (floor(x) > x).is_Relational + assert (floor(x) <= y).is_Relational # arg is not same as rhs + assert (floor(x) > y).is_Relational + assert (floor(y) <= oo) == True + assert (floor(y) < oo) == True + assert (floor(y) >= -oo) == True + assert (floor(y) > -oo) == True + + assert floor(y).rewrite(frac) == y - frac(y) + assert floor(y).rewrite(ceiling) == -ceiling(-y) + assert floor(y).rewrite(frac).subs(y, -pi) == floor(-pi) + assert floor(y).rewrite(frac).subs(y, E) == floor(E) + assert floor(y).rewrite(ceiling).subs(y, E) == -ceiling(-E) + assert floor(y).rewrite(ceiling).subs(y, -pi) == -ceiling(pi) + + assert Eq(floor(y), y - frac(y)) + assert Eq(floor(y), -ceiling(-y)) + + neg = Symbol('neg', negative=True) + nn = Symbol('nn', nonnegative=True) + pos = Symbol('pos', positive=True) + np = Symbol('np', nonpositive=True) + + assert (floor(neg) < 0) == True + assert (floor(neg) <= 0) == True + assert (floor(neg) > 0) == False + assert (floor(neg) >= 0) == False + assert (floor(neg) <= -1) == True + assert (floor(neg) >= -3) == (neg >= -3) + assert (floor(neg) < 5) == (neg < 5) + + assert (floor(nn) < 0) == False + assert (floor(nn) >= 0) == True + + assert (floor(pos) < 0) == False + assert (floor(pos) <= 0) == (pos < 1) + assert (floor(pos) > 0) == (pos >= 1) + assert (floor(pos) >= 0) == True + assert (floor(pos) >= 3) == (pos >= 3) + + assert (floor(np) <= 0) == True + assert (floor(np) > 0) == False + + assert floor(neg).is_negative == True + assert floor(neg).is_nonnegative == False + assert floor(nn).is_negative == False + assert floor(nn).is_nonnegative == True + assert floor(pos).is_negative == False + assert floor(pos).is_nonnegative == True + assert floor(np).is_negative is None + assert floor(np).is_nonnegative is None + + assert (floor(7, evaluate=False) >= 7) == True + assert (floor(7, evaluate=False) > 7) == False + assert (floor(7, evaluate=False) <= 7) == True + assert (floor(7, evaluate=False) < 7) == False + + assert (floor(7, evaluate=False) >= 6) == True + assert (floor(7, evaluate=False) > 6) == True + assert (floor(7, evaluate=False) <= 6) == False + assert (floor(7, evaluate=False) < 6) == False + + assert (floor(7, evaluate=False) >= 8) == False + assert (floor(7, evaluate=False) > 8) == False + assert (floor(7, evaluate=False) <= 8) == True + assert (floor(7, evaluate=False) < 8) == True + + assert (floor(x) <= 5.5) == Le(floor(x), 5.5, evaluate=False) + assert (floor(x) >= -3.2) == Ge(floor(x), -3.2, evaluate=False) + assert (floor(x) < 2.9) == Lt(floor(x), 2.9, evaluate=False) + assert (floor(x) > -1.7) == Gt(floor(x), -1.7, evaluate=False) + + assert (floor(y) <= 5.5) == (y < 6) + assert (floor(y) >= -3.2) == (y >= -3) + assert (floor(y) < 2.9) == (y < 3) + assert (floor(y) > -1.7) == (y >= -1) + + assert (floor(y) <= n) == (y < n + 1) + assert (floor(y) >= n) == (y >= n) + assert (floor(y) < n) == (y < n) + assert (floor(y) > n) == (y >= n + 1) + + assert floor(RootOf(x**3 - 27*x, 2)) == 5 + + +def test_ceiling(): + + assert ceiling(nan) is nan + + assert ceiling(oo) is oo + assert ceiling(-oo) is -oo + assert ceiling(zoo) is zoo + + assert ceiling(0) == 0 + + assert ceiling(1) == 1 + assert ceiling(-1) == -1 + + assert ceiling(E) == 3 + assert ceiling(-E) == -2 + + assert ceiling(2*E) == 6 + assert ceiling(-2*E) == -5 + + assert ceiling(pi) == 4 + assert ceiling(-pi) == -3 + + assert ceiling(S.Half) == 1 + assert ceiling(Rational(-1, 2)) == 0 + + assert ceiling(Rational(7, 3)) == 3 + assert ceiling(-Rational(7, 3)) == -2 + + assert ceiling(Float(17.0)) == 17 + assert ceiling(-Float(17.0)) == -17 + + assert ceiling(Float(7.69)) == 8 + assert ceiling(-Float(7.69)) == -7 + + assert ceiling(I) == I + assert ceiling(-I) == -I + e = ceiling(i) + assert e.func is ceiling and e.args[0] == i + + assert ceiling(oo*I) == oo*I + assert ceiling(-oo*I) == -oo*I + assert ceiling(exp(I*pi/4)*oo) == exp(I*pi/4)*oo + + assert ceiling(2*I) == 2*I + assert ceiling(-2*I) == -2*I + + assert ceiling(I/2) == I + assert ceiling(-I/2) == 0 + + assert ceiling(E + 17) == 20 + assert ceiling(pi + 2) == 6 + + assert ceiling(E + pi) == 6 + assert ceiling(I + pi) == I + 4 + + assert ceiling(ceiling(pi)) == 4 + assert ceiling(ceiling(y)) == ceiling(y) + assert ceiling(ceiling(x)) == ceiling(x) + + assert unchanged(ceiling, x) + assert unchanged(ceiling, 2*x) + assert unchanged(ceiling, k*x) + + assert ceiling(k) == k + assert ceiling(2*k) == 2*k + assert ceiling(k*n) == k*n + + assert unchanged(ceiling, k/2) + + assert unchanged(ceiling, x + y) + + assert ceiling(x + 3) == ceiling(x) + 3 + assert ceiling(x + 3.0) == ceiling(x) + 3 + assert ceiling(x + 3.0*I) == ceiling(x) + 3*I + assert ceiling(x + k) == ceiling(x) + k + + assert ceiling(y + 3) == ceiling(y) + 3 + assert ceiling(y + k) == ceiling(y) + k + + assert ceiling(3 + pi + y*I) == 7 + ceiling(y)*I + + assert ceiling(k + n) == k + n + + assert unchanged(ceiling, x*I) + assert ceiling(k*I) == k*I + + assert ceiling(Rational(23, 10) - E*I) == 3 - 2*I + + assert ceiling(sin(1)) == 1 + assert ceiling(sin(-1)) == 0 + + assert ceiling(exp(2)) == 8 + + assert ceiling(-log(8)/log(2)) != -2 + assert int(ceiling(-log(8)/log(2)).evalf(chop=True)) == -3 + + assert ceiling(factorial(50)/exp(1)) == \ + 11188719610782480504630258070757734324011354208865721592720336801 + + assert (ceiling(y) >= y) == True + assert (ceiling(y) > y) == False + assert (ceiling(y) < y) == False + assert (ceiling(y) <= y) == False + assert (ceiling(x) >= x).is_Relational # x could be non-real + assert (ceiling(x) < x).is_Relational + assert (ceiling(x) >= y).is_Relational # arg is not same as rhs + assert (ceiling(x) < y).is_Relational + assert (ceiling(y) >= -oo) == True + assert (ceiling(y) > -oo) == True + assert (ceiling(y) <= oo) == True + assert (ceiling(y) < oo) == True + + assert ceiling(y).rewrite(floor) == -floor(-y) + assert ceiling(y).rewrite(frac) == y + frac(-y) + assert ceiling(y).rewrite(floor).subs(y, -pi) == -floor(pi) + assert ceiling(y).rewrite(floor).subs(y, E) == -floor(-E) + assert ceiling(y).rewrite(frac).subs(y, pi) == ceiling(pi) + assert ceiling(y).rewrite(frac).subs(y, -E) == ceiling(-E) + + assert Eq(ceiling(y), y + frac(-y)) + assert Eq(ceiling(y), -floor(-y)) + + neg = Symbol('neg', negative=True) + nn = Symbol('nn', nonnegative=True) + pos = Symbol('pos', positive=True) + np = Symbol('np', nonpositive=True) + + assert (ceiling(neg) <= 0) == True + assert (ceiling(neg) < 0) == (neg <= -1) + assert (ceiling(neg) > 0) == False + assert (ceiling(neg) >= 0) == (neg > -1) + assert (ceiling(neg) > -3) == (neg > -3) + assert (ceiling(neg) <= 10) == (neg <= 10) + + assert (ceiling(nn) < 0) == False + assert (ceiling(nn) >= 0) == True + + assert (ceiling(pos) < 0) == False + assert (ceiling(pos) <= 0) == False + assert (ceiling(pos) > 0) == True + assert (ceiling(pos) >= 0) == True + assert (ceiling(pos) >= 1) == True + assert (ceiling(pos) > 5) == (pos > 5) + + assert (ceiling(np) <= 0) == True + assert (ceiling(np) > 0) == False + + assert ceiling(neg).is_positive == False + assert ceiling(neg).is_nonpositive == True + assert ceiling(nn).is_positive is None + assert ceiling(nn).is_nonpositive is None + assert ceiling(pos).is_positive == True + assert ceiling(pos).is_nonpositive == False + assert ceiling(np).is_positive == False + assert ceiling(np).is_nonpositive == True + + assert (ceiling(7, evaluate=False) >= 7) == True + assert (ceiling(7, evaluate=False) > 7) == False + assert (ceiling(7, evaluate=False) <= 7) == True + assert (ceiling(7, evaluate=False) < 7) == False + + assert (ceiling(7, evaluate=False) >= 6) == True + assert (ceiling(7, evaluate=False) > 6) == True + assert (ceiling(7, evaluate=False) <= 6) == False + assert (ceiling(7, evaluate=False) < 6) == False + + assert (ceiling(7, evaluate=False) >= 8) == False + assert (ceiling(7, evaluate=False) > 8) == False + assert (ceiling(7, evaluate=False) <= 8) == True + assert (ceiling(7, evaluate=False) < 8) == True + + assert (ceiling(x) <= 5.5) == Le(ceiling(x), 5.5, evaluate=False) + assert (ceiling(x) >= -3.2) == Ge(ceiling(x), -3.2, evaluate=False) + assert (ceiling(x) < 2.9) == Lt(ceiling(x), 2.9, evaluate=False) + assert (ceiling(x) > -1.7) == Gt(ceiling(x), -1.7, evaluate=False) + + assert (ceiling(y) <= 5.5) == (y <= 5) + assert (ceiling(y) >= -3.2) == (y > -4) + assert (ceiling(y) < 2.9) == (y <= 2) + assert (ceiling(y) > -1.7) == (y > -2) + + assert (ceiling(y) <= n) == (y <= n) + assert (ceiling(y) >= n) == (y > n - 1) + assert (ceiling(y) < n) == (y <= n - 1) + assert (ceiling(y) > n) == (y > n) + + assert ceiling(RootOf(x**3 - 27*x, 2)) == 6 + s = ImageSet(Lambda(n, n + (CRootOf(x**5 - x**2 + 1, 0))), Integers) + f = CRootOf(x**5 - x**2 + 1, 0) + s = ImageSet(Lambda(n, n + f), Integers) + assert s.intersect(Interval(-10, 10)) == {i + f for i in range(-9, 11)} + + +def test_frac(): + assert isinstance(frac(x), frac) + assert frac(oo) == AccumBounds(0, 1) + assert frac(-oo) == AccumBounds(0, 1) + assert frac(zoo) is nan + + assert frac(n) == 0 + assert frac(nan) is nan + assert frac(Rational(4, 3)) == Rational(1, 3) + assert frac(-Rational(4, 3)) == Rational(2, 3) + assert frac(Rational(-4, 3)) == Rational(2, 3) + + r = Symbol('r', real=True) + assert frac(I*r) == I*frac(r) + assert frac(1 + I*r) == I*frac(r) + assert frac(0.5 + I*r) == 0.5 + I*frac(r) + assert frac(n + I*r) == I*frac(r) + assert frac(n + I*k) == 0 + assert unchanged(frac, x + I*x) + assert frac(x + I*n) == frac(x) + + assert frac(x).rewrite(floor) == x - floor(x) + assert frac(x).rewrite(ceiling) == x + ceiling(-x) + assert frac(y).rewrite(floor).subs(y, pi) == frac(pi) + assert frac(y).rewrite(floor).subs(y, -E) == frac(-E) + assert frac(y).rewrite(ceiling).subs(y, -pi) == frac(-pi) + assert frac(y).rewrite(ceiling).subs(y, E) == frac(E) + + assert Eq(frac(y), y - floor(y)) + assert Eq(frac(y), y + ceiling(-y)) + + r = Symbol('r', real=True) + p_i = Symbol('p_i', integer=True, positive=True) + n_i = Symbol('p_i', integer=True, negative=True) + np_i = Symbol('np_i', integer=True, nonpositive=True) + nn_i = Symbol('nn_i', integer=True, nonnegative=True) + p_r = Symbol('p_r', positive=True) + n_r = Symbol('n_r', negative=True) + np_r = Symbol('np_r', real=True, nonpositive=True) + nn_r = Symbol('nn_r', real=True, nonnegative=True) + + # Real frac argument, integer rhs + assert frac(r) <= p_i + assert not frac(r) <= n_i + assert (frac(r) <= np_i).has(Le) + assert (frac(r) <= nn_i).has(Le) + assert frac(r) < p_i + assert not frac(r) < n_i + assert not frac(r) < np_i + assert (frac(r) < nn_i).has(Lt) + assert not frac(r) >= p_i + assert frac(r) >= n_i + assert frac(r) >= np_i + assert (frac(r) >= nn_i).has(Ge) + assert not frac(r) > p_i + assert frac(r) > n_i + assert (frac(r) > np_i).has(Gt) + assert (frac(r) > nn_i).has(Gt) + + assert not Eq(frac(r), p_i) + assert not Eq(frac(r), n_i) + assert Eq(frac(r), np_i).has(Eq) + assert Eq(frac(r), nn_i).has(Eq) + + assert Ne(frac(r), p_i) + assert Ne(frac(r), n_i) + assert Ne(frac(r), np_i).has(Ne) + assert Ne(frac(r), nn_i).has(Ne) + + + # Real frac argument, real rhs + assert (frac(r) <= p_r).has(Le) + assert not frac(r) <= n_r + assert (frac(r) <= np_r).has(Le) + assert (frac(r) <= nn_r).has(Le) + assert (frac(r) < p_r).has(Lt) + assert not frac(r) < n_r + assert not frac(r) < np_r + assert (frac(r) < nn_r).has(Lt) + assert (frac(r) >= p_r).has(Ge) + assert frac(r) >= n_r + assert frac(r) >= np_r + assert (frac(r) >= nn_r).has(Ge) + assert (frac(r) > p_r).has(Gt) + assert frac(r) > n_r + assert (frac(r) > np_r).has(Gt) + assert (frac(r) > nn_r).has(Gt) + + assert not Eq(frac(r), n_r) + assert Eq(frac(r), p_r).has(Eq) + assert Eq(frac(r), np_r).has(Eq) + assert Eq(frac(r), nn_r).has(Eq) + + assert Ne(frac(r), p_r).has(Ne) + assert Ne(frac(r), n_r) + assert Ne(frac(r), np_r).has(Ne) + assert Ne(frac(r), nn_r).has(Ne) + + # Real frac argument, +/- oo rhs + assert frac(r) < oo + assert frac(r) <= oo + assert not frac(r) > oo + assert not frac(r) >= oo + + assert not frac(r) < -oo + assert not frac(r) <= -oo + assert frac(r) > -oo + assert frac(r) >= -oo + + assert frac(r) < 1 + assert frac(r) <= 1 + assert not frac(r) > 1 + assert not frac(r) >= 1 + + assert not frac(r) < 0 + assert (frac(r) <= 0).has(Le) + assert (frac(r) > 0).has(Gt) + assert frac(r) >= 0 + + # Some test for numbers + assert frac(r) <= sqrt(2) + assert (frac(r) <= sqrt(3) - sqrt(2)).has(Le) + assert not frac(r) <= sqrt(2) - sqrt(3) + assert not frac(r) >= sqrt(2) + assert (frac(r) >= sqrt(3) - sqrt(2)).has(Ge) + assert frac(r) >= sqrt(2) - sqrt(3) + + assert not Eq(frac(r), sqrt(2)) + assert Eq(frac(r), sqrt(3) - sqrt(2)).has(Eq) + assert not Eq(frac(r), sqrt(2) - sqrt(3)) + assert Ne(frac(r), sqrt(2)) + assert Ne(frac(r), sqrt(3) - sqrt(2)).has(Ne) + assert Ne(frac(r), sqrt(2) - sqrt(3)) + + assert frac(p_i, evaluate=False).is_zero + assert frac(p_i, evaluate=False).is_finite + assert frac(p_i, evaluate=False).is_integer + assert frac(p_i, evaluate=False).is_real + assert frac(r).is_finite + assert frac(r).is_real + assert frac(r).is_zero is None + assert frac(r).is_integer is None + + assert frac(oo).is_finite + assert frac(oo).is_real + + +def test_series(): + x, y = symbols('x,y') + assert floor(x).nseries(x, y, 100) == floor(y) + assert ceiling(x).nseries(x, y, 100) == ceiling(y) + assert floor(x).nseries(x, pi, 100) == 3 + assert ceiling(x).nseries(x, pi, 100) == 4 + assert floor(x).nseries(x, 0, 100) == 0 + assert ceiling(x).nseries(x, 0, 100) == 1 + assert floor(-x).nseries(x, 0, 100) == -1 + assert ceiling(-x).nseries(x, 0, 100) == 0 + + +def test_issue_14355(): + # This test checks the leading term and series for the floor and ceil + # function when arg0 evaluates to S.NaN. + assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -2 + assert floor((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == -1 + assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == -1 + assert floor((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 0 + assert floor(sin(x)/x).as_leading_term(x, cdir = 1) == 0 + assert floor(sin(x)/x).as_leading_term(x, cdir = -1) == 0 + assert floor(-tan(x)/x).as_leading_term(x, cdir = 1) == -2 + assert floor(-tan(x)/x).as_leading_term(x, cdir = -1) == -2 + assert floor(sin(x)/x/3).as_leading_term(x, cdir = 1) == 0 + assert floor(sin(x)/x/3).as_leading_term(x, cdir = -1) == 0 + assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = 1) == -1 + assert ceiling((x**3 + x)/(x**2 - x)).as_leading_term(x, cdir = -1) == 0 + assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = 1) == 0 + assert ceiling((cos(x) - 1)/x).as_leading_term(x, cdir = -1) == 1 + assert ceiling(sin(x)/x).as_leading_term(x, cdir = 1) == 1 + assert ceiling(sin(x)/x).as_leading_term(x, cdir = -1) == 1 + assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1 + assert ceiling(-tan(x)/x).as_leading_term(x, cdir = 1) == -1 + assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = 1) == 1 + assert ceiling(sin(x)/x/3).as_leading_term(x, cdir = -1) == 1 + # test for series + assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0 + assert floor(sin(x)/x).series(x, 0, 100, cdir = 1) == 0 + assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -2 + assert floor((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == -1 + assert ceiling(sin(x)/x).series(x, 0, 100, cdir = 1) == 1 + assert ceiling(sin(x)/x).series(x, 0, 100, cdir = -1) == 1 + assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = 1) == -1 + assert ceiling((x**3 + x)/(x**2 - x)).series(x, 0, 100, cdir = -1) == 0 + + +def test_frac_leading_term(): + assert frac(x).as_leading_term(x) == x + assert frac(x).as_leading_term(x, cdir = 1) == x + assert frac(x).as_leading_term(x, cdir = -1) == 1 + assert frac(x + S.Half).as_leading_term(x, cdir = 1) == S.Half + assert frac(x + S.Half).as_leading_term(x, cdir = -1) == S.Half + assert frac(-2*x + 1).as_leading_term(x, cdir = 1) == S.One + assert frac(-2*x + 1).as_leading_term(x, cdir = -1) == -2*x + assert frac(sin(x) + 5).as_leading_term(x, cdir = 1) == x + assert frac(sin(x) + 5).as_leading_term(x, cdir = -1) == S.One + assert frac(sin(x**2) + 5).as_leading_term(x, cdir = 1) == x**2 + assert frac(sin(x**2) + 5).as_leading_term(x, cdir = -1) == x**2 + + +@XFAIL +def test_issue_4149(): + assert floor(3 + pi*I + y*I) == 3 + floor(pi + y)*I + assert floor(3*I + pi*I + y*I) == floor(3 + pi + y)*I + assert floor(3 + E + pi*I + y*I) == 5 + floor(pi + y)*I + + +def test_issue_21651(): + k = Symbol('k', positive=True, integer=True) + exp = 2*2**(-k) + assert isinstance(floor(exp), floor) + + +def test_issue_11207(): + assert floor(floor(x)) == floor(x) + assert floor(ceiling(x)) == ceiling(x) + assert ceiling(floor(x)) == floor(x) + assert ceiling(ceiling(x)) == ceiling(x) + + +def test_nested_floor_ceiling(): + assert floor(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y) + assert ceiling(-floor(ceiling(x**3)/y)) == -floor(ceiling(x**3)/y) + assert floor(ceiling(-floor(x**Rational(7, 2)/y))) == -floor(x**Rational(7, 2)/y) + assert -ceiling(-ceiling(floor(x)/y)) == ceiling(floor(x)/y) + +def test_issue_18689(): + assert floor(floor(floor(x)) + 3) == floor(x) + 3 + assert ceiling(ceiling(ceiling(x)) + 1) == ceiling(x) + 1 + assert ceiling(ceiling(floor(x)) + 3) == floor(x) + 3 + +def test_issue_18421(): + assert floor(float(0)) is S.Zero + assert ceiling(float(0)) is S.Zero + +def test_issue_25230(): + a = Symbol('a', real = True) + b = Symbol('b', positive = True) + c = Symbol('c', negative = True) + raises(NotImplementedError, lambda: floor(x/a).as_leading_term(x, cdir = 1)) + raises(NotImplementedError, lambda: ceiling(x/a).as_leading_term(x, cdir = 1)) + assert floor(x/b).as_leading_term(x, cdir = 1) == 0 + assert floor(x/b).as_leading_term(x, cdir = -1) == -1 + assert floor(x/c).as_leading_term(x, cdir = 1) == -1 + assert floor(x/c).as_leading_term(x, cdir = -1) == 0 + assert ceiling(x/b).as_leading_term(x, cdir = 1) == 1 + assert ceiling(x/b).as_leading_term(x, cdir = -1) == 0 + assert ceiling(x/c).as_leading_term(x, cdir = 1) == 0 + assert ceiling(x/c).as_leading_term(x, cdir = -1) == 1 diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_interface.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_interface.py new file mode 100644 index 0000000000000000000000000000000000000000..4ef784378cc90fe03cf8b4de78dbde4765caaf79 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_interface.py @@ -0,0 +1,72 @@ +# This test file tests the SymPy function interface, that people use to create +# their own new functions. It should be as easy as possible. +from sympy.core.function import Function +from sympy.core.sympify import sympify +from sympy.functions.elementary.hyperbolic import tanh +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.series.limits import limit +from sympy.abc import x + + +def test_function_series1(): + """Create our new "sin" function.""" + + class my_function(Function): + + def fdiff(self, argindex=1): + return cos(self.args[0]) + + @classmethod + def eval(cls, arg): + arg = sympify(arg) + if arg == 0: + return sympify(0) + + #Test that the taylor series is correct + assert my_function(x).series(x, 0, 10) == sin(x).series(x, 0, 10) + assert limit(my_function(x)/x, x, 0) == 1 + + +def test_function_series2(): + """Create our new "cos" function.""" + + class my_function2(Function): + + def fdiff(self, argindex=1): + return -sin(self.args[0]) + + @classmethod + def eval(cls, arg): + arg = sympify(arg) + if arg == 0: + return sympify(1) + + #Test that the taylor series is correct + assert my_function2(x).series(x, 0, 10) == cos(x).series(x, 0, 10) + + +def test_function_series3(): + """ + Test our easy "tanh" function. + + This test tests two things: + * that the Function interface works as expected and it's easy to use + * that the general algorithm for the series expansion works even when the + derivative is defined recursively in terms of the original function, + since tanh(x).diff(x) == 1-tanh(x)**2 + """ + + class mytanh(Function): + + def fdiff(self, argindex=1): + return 1 - mytanh(self.args[0])**2 + + @classmethod + def eval(cls, arg): + arg = sympify(arg) + if arg == 0: + return sympify(0) + + e = tanh(x) + f = mytanh(x) + assert e.series(x, 0, 6) == f.series(x, 0, 6) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py new file mode 100644 index 0000000000000000000000000000000000000000..374c4fb50eaae54a9884015c124c245385e1761e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py @@ -0,0 +1,504 @@ +import itertools as it + +from sympy.core.expr import unchanged +from sympy.core.function import Function +from sympy.core.numbers import I, oo, Rational +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.external import import_module +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.integers import floor, ceiling +from sympy.functions.elementary.miscellaneous import (sqrt, cbrt, root, Min, + Max, real_root, Rem) +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.functions.special.delta_functions import Heaviside + +from sympy.utilities.lambdify import lambdify +from sympy.testing.pytest import raises, skip, ignore_warnings + +def test_Min(): + from sympy.abc import x, y, z + n = Symbol('n', negative=True) + n_ = Symbol('n_', negative=True) + nn = Symbol('nn', nonnegative=True) + nn_ = Symbol('nn_', nonnegative=True) + p = Symbol('p', positive=True) + p_ = Symbol('p_', positive=True) + np = Symbol('np', nonpositive=True) + np_ = Symbol('np_', nonpositive=True) + r = Symbol('r', real=True) + + assert Min(5, 4) == 4 + assert Min(-oo, -oo) is -oo + assert Min(-oo, n) is -oo + assert Min(n, -oo) is -oo + assert Min(-oo, np) is -oo + assert Min(np, -oo) is -oo + assert Min(-oo, 0) is -oo + assert Min(0, -oo) is -oo + assert Min(-oo, nn) is -oo + assert Min(nn, -oo) is -oo + assert Min(-oo, p) is -oo + assert Min(p, -oo) is -oo + assert Min(-oo, oo) is -oo + assert Min(oo, -oo) is -oo + assert Min(n, n) == n + assert unchanged(Min, n, np) + assert Min(np, n) == Min(n, np) + assert Min(n, 0) == n + assert Min(0, n) == n + assert Min(n, nn) == n + assert Min(nn, n) == n + assert Min(n, p) == n + assert Min(p, n) == n + assert Min(n, oo) == n + assert Min(oo, n) == n + assert Min(np, np) == np + assert Min(np, 0) == np + assert Min(0, np) == np + assert Min(np, nn) == np + assert Min(nn, np) == np + assert Min(np, p) == np + assert Min(p, np) == np + assert Min(np, oo) == np + assert Min(oo, np) == np + assert Min(0, 0) == 0 + assert Min(0, nn) == 0 + assert Min(nn, 0) == 0 + assert Min(0, p) == 0 + assert Min(p, 0) == 0 + assert Min(0, oo) == 0 + assert Min(oo, 0) == 0 + assert Min(nn, nn) == nn + assert unchanged(Min, nn, p) + assert Min(p, nn) == Min(nn, p) + assert Min(nn, oo) == nn + assert Min(oo, nn) == nn + assert Min(p, p) == p + assert Min(p, oo) == p + assert Min(oo, p) == p + assert Min(oo, oo) is oo + + assert Min(n, n_).func is Min + assert Min(nn, nn_).func is Min + assert Min(np, np_).func is Min + assert Min(p, p_).func is Min + + # lists + assert Min() is S.Infinity + assert Min(x) == x + assert Min(x, y) == Min(y, x) + assert Min(x, y, z) == Min(z, y, x) + assert Min(x, Min(y, z)) == Min(z, y, x) + assert Min(x, Max(y, -oo)) == Min(x, y) + assert Min(p, oo, n, p, p, p_) == n + assert Min(p_, n_, p) == n_ + assert Min(n, oo, -7, p, p, 2) == Min(n, -7) + assert Min(2, x, p, n, oo, n_, p, 2, -2, -2) == Min(-2, x, n, n_) + assert Min(0, x, 1, y) == Min(0, x, y) + assert Min(1000, 100, -100, x, p, n) == Min(n, x, -100) + assert unchanged(Min, sin(x), cos(x)) + assert Min(sin(x), cos(x)) == Min(cos(x), sin(x)) + assert Min(cos(x), sin(x)).subs(x, 1) == cos(1) + assert Min(cos(x), sin(x)).subs(x, S.Half) == sin(S.Half) + raises(ValueError, lambda: Min(cos(x), sin(x)).subs(x, I)) + raises(ValueError, lambda: Min(I)) + raises(ValueError, lambda: Min(I, x)) + raises(ValueError, lambda: Min(S.ComplexInfinity, x)) + + assert Min(1, x).diff(x) == Heaviside(1 - x) + assert Min(x, 1).diff(x) == Heaviside(1 - x) + assert Min(0, -x, 1 - 2*x).diff(x) == -Heaviside(x + Min(0, -2*x + 1)) \ + - 2*Heaviside(2*x + Min(0, -x) - 1) + + # issue 7619 + f = Function('f') + assert Min(1, 2*Min(f(1), 2)) # doesn't fail + + # issue 7233 + e = Min(0, x) + assert e.n().args == (0, x) + + # issue 8643 + m = Min(n, p_, n_, r) + assert m.is_positive is False + assert m.is_nonnegative is False + assert m.is_negative is True + + m = Min(p, p_) + assert m.is_positive is True + assert m.is_nonnegative is True + assert m.is_negative is False + + m = Min(p, nn_, p_) + assert m.is_positive is None + assert m.is_nonnegative is True + assert m.is_negative is False + + m = Min(nn, p, r) + assert m.is_positive is None + assert m.is_nonnegative is None + assert m.is_negative is None + + +def test_Max(): + from sympy.abc import x, y, z + n = Symbol('n', negative=True) + n_ = Symbol('n_', negative=True) + nn = Symbol('nn', nonnegative=True) + p = Symbol('p', positive=True) + p_ = Symbol('p_', positive=True) + r = Symbol('r', real=True) + + assert Max(5, 4) == 5 + + # lists + + assert Max() is S.NegativeInfinity + assert Max(x) == x + assert Max(x, y) == Max(y, x) + assert Max(x, y, z) == Max(z, y, x) + assert Max(x, Max(y, z)) == Max(z, y, x) + assert Max(x, Min(y, oo)) == Max(x, y) + assert Max(n, -oo, n_, p, 2) == Max(p, 2) + assert Max(n, -oo, n_, p) == p + assert Max(2, x, p, n, -oo, S.NegativeInfinity, n_, p, 2) == Max(2, x, p) + assert Max(0, x, 1, y) == Max(1, x, y) + assert Max(r, r + 1, r - 1) == 1 + r + assert Max(1000, 100, -100, x, p, n) == Max(p, x, 1000) + assert Max(cos(x), sin(x)) == Max(sin(x), cos(x)) + assert Max(cos(x), sin(x)).subs(x, 1) == sin(1) + assert Max(cos(x), sin(x)).subs(x, S.Half) == cos(S.Half) + raises(ValueError, lambda: Max(cos(x), sin(x)).subs(x, I)) + raises(ValueError, lambda: Max(I)) + raises(ValueError, lambda: Max(I, x)) + raises(ValueError, lambda: Max(S.ComplexInfinity, 1)) + assert Max(n, -oo, n_, p, 2) == Max(p, 2) + assert Max(n, -oo, n_, p, 1000) == Max(p, 1000) + + assert Max(1, x).diff(x) == Heaviside(x - 1) + assert Max(x, 1).diff(x) == Heaviside(x - 1) + assert Max(x**2, 1 + x, 1).diff(x) == \ + 2*x*Heaviside(x**2 - Max(1, x + 1)) \ + + Heaviside(x - Max(1, x**2) + 1) + + e = Max(0, x) + assert e.n().args == (0, x) + + # issue 8643 + m = Max(p, p_, n, r) + assert m.is_positive is True + assert m.is_nonnegative is True + assert m.is_negative is False + + m = Max(n, n_) + assert m.is_positive is False + assert m.is_nonnegative is False + assert m.is_negative is True + + m = Max(n, n_, r) + assert m.is_positive is None + assert m.is_nonnegative is None + assert m.is_negative is None + + m = Max(n, nn, r) + assert m.is_positive is None + assert m.is_nonnegative is True + assert m.is_negative is False + + +def test_minmax_assumptions(): + r = Symbol('r', real=True) + a = Symbol('a', real=True, algebraic=True) + t = Symbol('t', real=True, transcendental=True) + q = Symbol('q', rational=True) + p = Symbol('p', irrational=True) + n = Symbol('n', rational=True, integer=False) + i = Symbol('i', integer=True) + o = Symbol('o', odd=True) + e = Symbol('e', even=True) + k = Symbol('k', prime=True) + reals = [r, a, t, q, p, n, i, o, e, k] + + for ext in (Max, Min): + for x, y in it.product(reals, repeat=2): + + # Must be real + assert ext(x, y).is_real + + # Algebraic? + if x.is_algebraic and y.is_algebraic: + assert ext(x, y).is_algebraic + elif x.is_transcendental and y.is_transcendental: + assert ext(x, y).is_transcendental + else: + assert ext(x, y).is_algebraic is None + + # Rational? + if x.is_rational and y.is_rational: + assert ext(x, y).is_rational + elif x.is_irrational and y.is_irrational: + assert ext(x, y).is_irrational + else: + assert ext(x, y).is_rational is None + + # Integer? + if x.is_integer and y.is_integer: + assert ext(x, y).is_integer + elif x.is_noninteger and y.is_noninteger: + assert ext(x, y).is_noninteger + else: + assert ext(x, y).is_integer is None + + # Odd? + if x.is_odd and y.is_odd: + assert ext(x, y).is_odd + elif x.is_odd is False and y.is_odd is False: + assert ext(x, y).is_odd is False + else: + assert ext(x, y).is_odd is None + + # Even? + if x.is_even and y.is_even: + assert ext(x, y).is_even + elif x.is_even is False and y.is_even is False: + assert ext(x, y).is_even is False + else: + assert ext(x, y).is_even is None + + # Prime? + if x.is_prime and y.is_prime: + assert ext(x, y).is_prime + elif x.is_prime is False and y.is_prime is False: + assert ext(x, y).is_prime is False + else: + assert ext(x, y).is_prime is None + + +def test_issue_8413(): + x = Symbol('x', real=True) + # we can't evaluate in general because non-reals are not + # comparable: Min(floor(3.2 + I), 3.2 + I) -> ValueError + assert Min(floor(x), x) == floor(x) + assert Min(ceiling(x), x) == x + assert Max(floor(x), x) == x + assert Max(ceiling(x), x) == ceiling(x) + + +def test_root(): + from sympy.abc import x + n = Symbol('n', integer=True) + k = Symbol('k', integer=True) + + assert root(2, 2) == sqrt(2) + assert root(2, 1) == 2 + assert root(2, 3) == 2**Rational(1, 3) + assert root(2, 3) == cbrt(2) + assert root(2, -5) == 2**Rational(4, 5)/2 + + assert root(-2, 1) == -2 + + assert root(-2, 2) == sqrt(2)*I + assert root(-2, 1) == -2 + + assert root(x, 2) == sqrt(x) + assert root(x, 1) == x + assert root(x, 3) == x**Rational(1, 3) + assert root(x, 3) == cbrt(x) + assert root(x, -5) == x**Rational(-1, 5) + + assert root(x, n) == x**(1/n) + assert root(x, -n) == x**(-1/n) + + assert root(x, n, k) == (-1)**(2*k/n)*x**(1/n) + + +def test_real_root(): + assert real_root(-8, 3) == -2 + assert real_root(-16, 4) == root(-16, 4) + r = root(-7, 4) + assert real_root(r) == r + r1 = root(-1, 3) + r2 = r1**2 + r3 = root(-1, 4) + assert real_root(r1 + r2 + r3) == -1 + r2 + r3 + assert real_root(root(-2, 3)) == -root(2, 3) + assert real_root(-8., 3) == -2.0 + x = Symbol('x') + n = Symbol('n') + g = real_root(x, n) + assert g.subs({"x": -8, "n": 3}) == -2 + assert g.subs({"x": 8, "n": 3}) == 2 + # give principle root if there is no real root -- if this is not desired + # then maybe a Root class is needed to raise an error instead + assert g.subs({"x": I, "n": 3}) == cbrt(I) + assert g.subs({"x": -8, "n": 2}) == sqrt(-8) + assert g.subs({"x": I, "n": 2}) == sqrt(I) + + +def test_issue_11463(): + numpy = import_module('numpy') + if not numpy: + skip("numpy not installed.") + x = Symbol('x') + f = lambdify(x, real_root((log(x/(x-2))), 3), 'numpy') + # numpy.select evaluates all options before considering conditions, + # so it raises a warning about root of negative number which does + # not affect the outcome. This warning is suppressed here + with ignore_warnings(RuntimeWarning): + assert f(numpy.array(-1)) < -1 + + +def test_rewrite_MaxMin_as_Heaviside(): + from sympy.abc import x + assert Max(0, x).rewrite(Heaviside) == x*Heaviside(x) + assert Max(3, x).rewrite(Heaviside) == x*Heaviside(x - 3) + \ + 3*Heaviside(-x + 3) + assert Max(0, x+2, 2*x).rewrite(Heaviside) == \ + 2*x*Heaviside(2*x)*Heaviside(x - 2) + \ + (x + 2)*Heaviside(-x + 2)*Heaviside(x + 2) + + assert Min(0, x).rewrite(Heaviside) == x*Heaviside(-x) + assert Min(3, x).rewrite(Heaviside) == x*Heaviside(-x + 3) + \ + 3*Heaviside(x - 3) + assert Min(x, -x, -2).rewrite(Heaviside) == \ + x*Heaviside(-2*x)*Heaviside(-x - 2) - \ + x*Heaviside(2*x)*Heaviside(x - 2) \ + - 2*Heaviside(-x + 2)*Heaviside(x + 2) + + +def test_rewrite_MaxMin_as_Piecewise(): + from sympy.core.symbol import symbols + from sympy.functions.elementary.piecewise import Piecewise + x, y, z, a, b = symbols('x y z a b', real=True) + vx, vy, va = symbols('vx vy va') + assert Max(a, b).rewrite(Piecewise) == Piecewise((a, a >= b), (b, True)) + assert Max(x, y, z).rewrite(Piecewise) == Piecewise((x, (x >= y) & (x >= z)), (y, y >= z), (z, True)) + assert Max(x, y, a, b).rewrite(Piecewise) == Piecewise((a, (a >= b) & (a >= x) & (a >= y)), + (b, (b >= x) & (b >= y)), (x, x >= y), (y, True)) + assert Min(a, b).rewrite(Piecewise) == Piecewise((a, a <= b), (b, True)) + assert Min(x, y, z).rewrite(Piecewise) == Piecewise((x, (x <= y) & (x <= z)), (y, y <= z), (z, True)) + assert Min(x, y, a, b).rewrite(Piecewise) == Piecewise((a, (a <= b) & (a <= x) & (a <= y)), + (b, (b <= x) & (b <= y)), (x, x <= y), (y, True)) + + # Piecewise rewriting of Min/Max does also takes place for not explicitly real arguments + assert Max(vx, vy).rewrite(Piecewise) == Piecewise((vx, vx >= vy), (vy, True)) + assert Min(va, vx, vy).rewrite(Piecewise) == Piecewise((va, (va <= vx) & (va <= vy)), (vx, vx <= vy), (vy, True)) + + +def test_issue_11099(): + from sympy.abc import x, y + # some fixed value tests + fixed_test_data = {x: -2, y: 3} + assert Min(x, y).evalf(subs=fixed_test_data) == \ + Min(x, y).subs(fixed_test_data).evalf() + assert Max(x, y).evalf(subs=fixed_test_data) == \ + Max(x, y).subs(fixed_test_data).evalf() + # randomly generate some test data + from sympy.core.random import randint + for i in range(20): + random_test_data = {x: randint(-100, 100), y: randint(-100, 100)} + assert Min(x, y).evalf(subs=random_test_data) == \ + Min(x, y).subs(random_test_data).evalf() + assert Max(x, y).evalf(subs=random_test_data) == \ + Max(x, y).subs(random_test_data).evalf() + + +def test_issue_12638(): + from sympy.abc import a, b, c + assert Min(a, b, c, Max(a, b)) == Min(a, b, c) + assert Min(a, b, Max(a, b, c)) == Min(a, b) + assert Min(a, b, Max(a, c)) == Min(a, b) + +def test_issue_21399(): + from sympy.abc import a, b, c + assert Max(Min(a, b), Min(a, b, c)) == Min(a, b) + + +def test_instantiation_evaluation(): + from sympy.abc import v, w, x, y, z + assert Min(1, Max(2, x)) == 1 + assert Max(3, Min(2, x)) == 3 + assert Min(Max(x, y), Max(x, z)) == Max(x, Min(y, z)) + assert set(Min(Max(w, x), Max(y, z)).args) == { + Max(w, x), Max(y, z)} + assert Min(Max(x, y), Max(x, z), w) == Min( + w, Max(x, Min(y, z))) + A, B = Min, Max + for i in range(2): + assert A(x, B(x, y)) == x + assert A(x, B(y, A(x, w, z))) == A(x, B(y, A(w, z))) + A, B = B, A + assert Min(w, Max(x, y), Max(v, x, z)) == Min( + w, Max(x, Min(y, Max(v, z)))) + +def test_rewrite_as_Abs(): + from itertools import permutations + from sympy.functions.elementary.complexes import Abs + from sympy.abc import x, y, z, w + def test(e): + free = e.free_symbols + a = e.rewrite(Abs) + assert not a.has(Min, Max) + for i in permutations(range(len(free))): + reps = dict(zip(free, i)) + assert a.xreplace(reps) == e.xreplace(reps) + test(Min(x, y)) + test(Max(x, y)) + test(Min(x, y, z)) + test(Min(Max(w, x), Max(y, z))) + +def test_issue_14000(): + assert isinstance(sqrt(4, evaluate=False), Pow) == True + assert isinstance(cbrt(3.5, evaluate=False), Pow) == True + assert isinstance(root(16, 4, evaluate=False), Pow) == True + + assert sqrt(4, evaluate=False) == Pow(4, S.Half, evaluate=False) + assert cbrt(3.5, evaluate=False) == Pow(3.5, Rational(1, 3), evaluate=False) + assert root(4, 2, evaluate=False) == Pow(4, S.Half, evaluate=False) + + assert root(16, 4, 2, evaluate=False).has(Pow) == True + assert real_root(-8, 3, evaluate=False).has(Pow) == True + +def test_issue_6899(): + from sympy.core.function import Lambda + x = Symbol('x') + eqn = Lambda(x, x) + assert eqn.func(*eqn.args) == eqn + +def test_Rem(): + from sympy.abc import x, y + assert Rem(5, 3) == 2 + assert Rem(-5, 3) == -2 + assert Rem(5, -3) == 2 + assert Rem(-5, -3) == -2 + assert Rem(x**3, y) == Rem(x**3, y) + assert Rem(Rem(-5, 3) + 3, 3) == 1 + + +def test_minmax_no_evaluate(): + from sympy import evaluate + p = Symbol('p', positive=True) + + assert Max(1, 3) == 3 + assert Max(1, 3).args == () + assert Max(0, p) == p + assert Max(0, p).args == () + assert Min(0, p) == 0 + assert Min(0, p).args == () + + assert Max(1, 3, evaluate=False) != 3 + assert Max(1, 3, evaluate=False).args == (1, 3) + assert Max(0, p, evaluate=False) != p + assert Max(0, p, evaluate=False).args == (0, p) + assert Min(0, p, evaluate=False) != 0 + assert Min(0, p, evaluate=False).args == (0, p) + + with evaluate(False): + assert Max(1, 3) != 3 + assert Max(1, 3).args == (1, 3) + assert Max(0, p) != p + assert Max(0, p).args == (0, p) + assert Min(0, p) != 0 + assert Min(0, p).args == (0, p) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_piecewise.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_piecewise.py new file mode 100644 index 0000000000000000000000000000000000000000..631cf8f06660cec7d16a442de0284a378064d3e9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_piecewise.py @@ -0,0 +1,1628 @@ +from sympy.concrete.summations import Sum +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.expr import unchanged +from sympy.core.function import (Function, diff, expand) +from sympy.core.mul import Mul +from sympy.core.mod import Mod +from sympy.core.numbers import (Float, I, Rational, oo, pi, zoo) +from sympy.core.relational import (Eq, Ge, Gt, Ne) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import (Abs, adjoint, arg, conjugate, im, re, transpose) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt) +from sympy.functions.elementary.piecewise import (Piecewise, + piecewise_fold, piecewise_exclusive, Undefined, ExprCondPair) +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.delta_functions import (DiracDelta, Heaviside) +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.integrals.integrals import (Integral, integrate) +from sympy.logic.boolalg import (And, ITE, Not, Or) +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.printing import srepr +from sympy.sets.contains import Contains +from sympy.sets.sets import Interval +from sympy.solvers.solvers import solve +from sympy.testing.pytest import raises, slow +from sympy.utilities.lambdify import lambdify + +a, b, c, d, x, y = symbols('a:d, x, y') +z = symbols('z', nonzero=True) + + +def test_piecewise1(): + + # Test canonicalization + assert Piecewise((x, x < 1.)).has(1.0) # doesn't get changed to x < 1 + assert unchanged(Piecewise, ExprCondPair(x, x < 1), ExprCondPair(0, True)) + assert Piecewise((x, x < 1), (0, True)) == Piecewise(ExprCondPair(x, x < 1), + ExprCondPair(0, True)) + assert Piecewise((x, x < 1), (0, True), (1, True)) == \ + Piecewise((x, x < 1), (0, True)) + assert Piecewise((x, x < 1), (0, False), (-1, 1 > 2)) == \ + Piecewise((x, x < 1)) + assert Piecewise((x, x < 1), (0, x < 1), (0, True)) == \ + Piecewise((x, x < 1), (0, True)) + assert Piecewise((x, x < 1), (0, x < 2), (0, True)) == \ + Piecewise((x, x < 1), (0, True)) + assert Piecewise((x, x < 1), (x, x < 2), (0, True)) == \ + Piecewise((x, Or(x < 1, x < 2)), (0, True)) + assert Piecewise((x, x < 1), (x, x < 2), (x, True)) == x + assert Piecewise((x, True)) == x + # Explicitly constructed empty Piecewise not accepted + raises(TypeError, lambda: Piecewise()) + # False condition is never retained + assert Piecewise((2*x, x < 0), (x, False)) == \ + Piecewise((2*x, x < 0), (x, False), evaluate=False) == \ + Piecewise((2*x, x < 0)) + assert Piecewise((x, False)) == Undefined + raises(TypeError, lambda: Piecewise(x)) + assert Piecewise((x, 1)) == x # 1 and 0 are accepted as True/False + raises(TypeError, lambda: Piecewise((x, 2))) + raises(TypeError, lambda: Piecewise((x, x**2))) + raises(TypeError, lambda: Piecewise(([1], True))) + assert Piecewise(((1, 2), True)) == Tuple(1, 2) + cond = (Piecewise((1, x < 0), (2, True)) < y) + assert Piecewise((1, cond) + ) == Piecewise((1, ITE(x < 0, y > 1, y > 2))) + + assert Piecewise((1, x > 0), (2, And(x <= 0, x > -1)) + ) == Piecewise((1, x > 0), (2, x > -1)) + assert Piecewise((1, x <= 0), (2, (x < 0) & (x > -1)) + ) == Piecewise((1, x <= 0)) + + # test for supporting Contains in Piecewise + pwise = Piecewise( + (1, And(x <= 6, x > 1, Contains(x, S.Integers))), + (0, True)) + assert pwise.subs(x, pi) == 0 + assert pwise.subs(x, 2) == 1 + assert pwise.subs(x, 7) == 0 + + # Test subs + p = Piecewise((-1, x < -1), (x**2, x < 0), (log(x), x >= 0)) + p_x2 = Piecewise((-1, x**2 < -1), (x**4, x**2 < 0), (log(x**2), x**2 >= 0)) + assert p.subs(x, x**2) == p_x2 + assert p.subs(x, -5) == -1 + assert p.subs(x, -1) == 1 + assert p.subs(x, 1) == log(1) + + # More subs tests + p2 = Piecewise((1, x < pi), (-1, x < 2*pi), (0, x > 2*pi)) + p3 = Piecewise((1, Eq(x, 0)), (1/x, True)) + p4 = Piecewise((1, Eq(x, 0)), (2, 1/x>2)) + assert p2.subs(x, 2) == 1 + assert p2.subs(x, 4) == -1 + assert p2.subs(x, 10) == 0 + assert p3.subs(x, 0.0) == 1 + assert p4.subs(x, 0.0) == 1 + + + f, g, h = symbols('f,g,h', cls=Function) + pf = Piecewise((f(x), x < -1), (f(x) + h(x) + 2, x <= 1)) + pg = Piecewise((g(x), x < -1), (g(x) + h(x) + 2, x <= 1)) + assert pg.subs(g, f) == pf + + assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 0) == 1 + assert Piecewise((1, Eq(x, 0)), (0, True)).subs(x, 1) == 0 + assert Piecewise((1, Eq(x, y)), (0, True)).subs(x, y) == 1 + assert Piecewise((1, Eq(x, z)), (0, True)).subs(x, z) == 1 + assert Piecewise((1, Eq(exp(x), cos(z))), (0, True)).subs(x, z) == \ + Piecewise((1, Eq(exp(z), cos(z))), (0, True)) + + p5 = Piecewise( (0, Eq(cos(x) + y, 0)), (1, True)) + assert p5.subs(y, 0) == Piecewise( (0, Eq(cos(x), 0)), (1, True)) + + assert Piecewise((-1, y < 1), (0, x < 0), (1, Eq(x, 0)), (2, True) + ).subs(x, 1) == Piecewise((-1, y < 1), (2, True)) + assert Piecewise((1, Eq(x**2, -1)), (2, x < 0)).subs(x, I) == 1 + + p6 = Piecewise((x, x > 0)) + n = symbols('n', negative=True) + assert p6.subs(x, n) == Undefined + + # Test evalf + assert p.evalf() == Piecewise((-1.0, x < -1), (x**2, x < 0), (log(x), True)) + assert p.evalf(subs={x: -2}) == -1.0 + assert p.evalf(subs={x: -1}) == 1.0 + assert p.evalf(subs={x: 1}) == log(1) + assert p6.evalf(subs={x: -5}) == Undefined + + # Test doit + f_int = Piecewise((Integral(x, (x, 0, 1)), x < 1)) + assert f_int.doit() == Piecewise( (S.Half, x < 1) ) + + # Test differentiation + f = x + fp = x*p + dp = Piecewise((0, x < -1), (2*x, x < 0), (1/x, x >= 0)) + fp_dx = x*dp + p + assert diff(p, x) == dp + assert diff(f*p, x) == fp_dx + + # Test simple arithmetic + assert x*p == fp + assert x*p + p == p + x*p + assert p + f == f + p + assert p + dp == dp + p + assert p - dp == -(dp - p) + + # Test power + dp2 = Piecewise((0, x < -1), (4*x**2, x < 0), (1/x**2, x >= 0)) + assert dp**2 == dp2 + + # Test _eval_interval + f1 = x*y + 2 + f2 = x*y**2 + 3 + peval = Piecewise((f1, x < 0), (f2, x > 0)) + peval_interval = f1.subs( + x, 0) - f1.subs(x, -1) + f2.subs(x, 1) - f2.subs(x, 0) + assert peval._eval_interval(x, 0, 0) == 0 + assert peval._eval_interval(x, -1, 1) == peval_interval + peval2 = Piecewise((f1, x < 0), (f2, True)) + assert peval2._eval_interval(x, 0, 0) == 0 + assert peval2._eval_interval(x, 1, -1) == -peval_interval + assert peval2._eval_interval(x, -1, -2) == f1.subs(x, -2) - f1.subs(x, -1) + assert peval2._eval_interval(x, -1, 1) == peval_interval + assert peval2._eval_interval(x, None, 0) == peval2.subs(x, 0) + assert peval2._eval_interval(x, -1, None) == -peval2.subs(x, -1) + + # Test integration + assert p.integrate() == Piecewise( + (-x, x < -1), + (x**3/3 + Rational(4, 3), x < 0), + (x*log(x) - x + Rational(4, 3), True)) + p = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x)) + assert integrate(p, (x, -2, 2)) == Rational(5, 6) + assert integrate(p, (x, 2, -2)) == Rational(-5, 6) + p = Piecewise((0, x < 0), (1, x < 1), (0, x < 2), (1, x < 3), (0, True)) + assert integrate(p, (x, -oo, oo)) == 2 + p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x)) + assert integrate(p, (x, -2, 2)) == Undefined + + # Test commutativity + assert isinstance(p, Piecewise) and p.is_commutative is True + + +def test_piecewise_free_symbols(): + f = Piecewise((x, a < 0), (y, True)) + assert f.free_symbols == {x, y, a} + + +def test_piecewise_integrate1(): + x, y = symbols('x y', real=True) + + f = Piecewise(((x - 2)**2, x >= 0), (1, True)) + assert integrate(f, (x, -2, 2)) == Rational(14, 3) + + g = Piecewise(((x - 5)**5, x >= 4), (f, True)) + assert integrate(g, (x, -2, 2)) == Rational(14, 3) + assert integrate(g, (x, -2, 5)) == Rational(43, 6) + + assert g == Piecewise(((x - 5)**5, x >= 4), (f, x < 4)) + + g = Piecewise(((x - 5)**5, 2 <= x), (f, x < 2)) + assert integrate(g, (x, -2, 2)) == Rational(14, 3) + assert integrate(g, (x, -2, 5)) == Rational(-701, 6) + + assert g == Piecewise(((x - 5)**5, 2 <= x), (f, True)) + + g = Piecewise(((x - 5)**5, 2 <= x), (2*f, True)) + assert integrate(g, (x, -2, 2)) == Rational(28, 3) + assert integrate(g, (x, -2, 5)) == Rational(-673, 6) + + +def test_piecewise_integrate1b(): + g = Piecewise((1, x > 0), (0, Eq(x, 0)), (-1, x < 0)) + assert integrate(g, (x, -1, 1)) == 0 + + g = Piecewise((1, x - y < 0), (0, True)) + assert integrate(g, (y, -oo, 0)) == -Min(0, x) + assert g.subs(x, -3).integrate((y, -oo, 0)) == 3 + assert integrate(g, (y, 0, -oo)) == Min(0, x) + assert integrate(g, (y, 0, oo)) == -Max(0, x) + oo + assert integrate(g, (y, -oo, 42)) == -Min(42, x) + 42 + assert integrate(g, (y, -oo, oo)) == -x + oo + + g = Piecewise((0, x < 0), (x, x <= 1), (1, True)) + gy1 = g.integrate((x, y, 1)) + g1y = g.integrate((x, 1, y)) + for yy in (-1, S.Half, 2): + assert g.integrate((x, yy, 1)) == gy1.subs(y, yy) + assert g.integrate((x, 1, yy)) == g1y.subs(y, yy) + assert gy1 == Piecewise( + (-Min(1, Max(0, y))**2/2 + S.Half, y < 1), + (-y + 1, True)) + assert g1y == Piecewise( + (Min(1, Max(0, y))**2/2 - S.Half, y < 1), + (y - 1, True)) + + +@slow +def test_piecewise_integrate1ca(): + y = symbols('y', real=True) + g = Piecewise( + (1 - x, Interval(0, 1).contains(x)), + (1 + x, Interval(-1, 0).contains(x)), + (0, True) + ) + gy1 = g.integrate((x, y, 1)) + g1y = g.integrate((x, 1, y)) + + assert g.integrate((x, -2, 1)) == gy1.subs(y, -2) + assert g.integrate((x, 1, -2)) == g1y.subs(y, -2) + assert g.integrate((x, 0, 1)) == gy1.subs(y, 0) + assert g.integrate((x, 1, 0)) == g1y.subs(y, 0) + assert g.integrate((x, 2, 1)) == gy1.subs(y, 2) + assert g.integrate((x, 1, 2)) == g1y.subs(y, 2) + assert piecewise_fold(gy1.rewrite(Piecewise) + ).simplify() == Piecewise( + (1, y <= -1), + (-y**2/2 - y + S.Half, y <= 0), + (y**2/2 - y + S.Half, y < 1), + (0, True)) + assert piecewise_fold(g1y.rewrite(Piecewise) + ).simplify() == Piecewise( + (-1, y <= -1), + (y**2/2 + y - S.Half, y <= 0), + (-y**2/2 + y - S.Half, y < 1), + (0, True)) + assert gy1 == Piecewise( + ( + -Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) + + Min(1, Max(0, y))**2 + S.Half, y < 1), + (0, True) + ) + assert g1y == Piecewise( + ( + Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) - + Min(1, Max(0, y))**2 - S.Half, y < 1), + (0, True)) + + +@slow +def test_piecewise_integrate1cb(): + y = symbols('y', real=True) + g = Piecewise( + (0, Or(x <= -1, x >= 1)), + (1 - x, x > 0), + (1 + x, True) + ) + gy1 = g.integrate((x, y, 1)) + g1y = g.integrate((x, 1, y)) + + assert g.integrate((x, -2, 1)) == gy1.subs(y, -2) + assert g.integrate((x, 1, -2)) == g1y.subs(y, -2) + assert g.integrate((x, 0, 1)) == gy1.subs(y, 0) + assert g.integrate((x, 1, 0)) == g1y.subs(y, 0) + assert g.integrate((x, 2, 1)) == gy1.subs(y, 2) + assert g.integrate((x, 1, 2)) == g1y.subs(y, 2) + + assert piecewise_fold(gy1.rewrite(Piecewise) + ).simplify() == Piecewise( + (1, y <= -1), + (-y**2/2 - y + S.Half, y <= 0), + (y**2/2 - y + S.Half, y < 1), + (0, True)) + assert piecewise_fold(g1y.rewrite(Piecewise) + ).simplify() == Piecewise( + (-1, y <= -1), + (y**2/2 + y - S.Half, y <= 0), + (-y**2/2 + y - S.Half, y < 1), + (0, True)) + + # g1y and gy1 should simplify if the condition that y < 1 + # is applied, e.g. Min(1, Max(-1, y)) --> Max(-1, y) + assert gy1 == Piecewise( + ( + -Min(1, Max(-1, y))**2/2 - Min(1, Max(-1, y)) + + Min(1, Max(0, y))**2 + S.Half, y < 1), + (0, True) + ) + assert g1y == Piecewise( + ( + Min(1, Max(-1, y))**2/2 + Min(1, Max(-1, y)) - + Min(1, Max(0, y))**2 - S.Half, y < 1), + (0, True)) + + +def test_piecewise_integrate2(): + from itertools import permutations + lim = Tuple(x, c, d) + p = Piecewise((1, x < a), (2, x > b), (3, True)) + q = p.integrate(lim) + assert q == Piecewise( + (-c + 2*d - 2*Min(d, Max(a, c)) + Min(d, Max(a, b, c)), c < d), + (-2*c + d + 2*Min(c, Max(a, d)) - Min(c, Max(a, b, d)), True)) + for v in permutations((1, 2, 3, 4)): + r = dict(zip((a, b, c, d), v)) + assert p.subs(r).integrate(lim.subs(r)) == q.subs(r) + + +def test_meijer_bypass(): + # totally bypass meijerg machinery when dealing + # with Piecewise in integrate + assert Piecewise((1, x < 4), (0, True)).integrate((x, oo, 1)) == -3 + + +def test_piecewise_integrate3_inequality_conditions(): + from sympy.utilities.iterables import cartes + lim = (x, 0, 5) + # set below includes two pts below range, 2 pts in range, + # 2 pts above range, and the boundaries + N = (-2, -1, 0, 1, 2, 5, 6, 7) + + p = Piecewise((1, x > a), (2, x > b), (0, True)) + ans = p.integrate(lim) + for i, j in cartes(N, repeat=2): + reps = dict(zip((a, b), (i, j))) + assert ans.subs(reps) == p.subs(reps).integrate(lim) + assert ans.subs(a, 4).subs(b, 1) == 0 + 2*3 + 1 + + p = Piecewise((1, x > a), (2, x < b), (0, True)) + ans = p.integrate(lim) + for i, j in cartes(N, repeat=2): + reps = dict(zip((a, b), (i, j))) + assert ans.subs(reps) == p.subs(reps).integrate(lim) + + # delete old tests that involved c1 and c2 since those + # reduce to the above except that a value of 0 was used + # for two expressions whereas the above uses 3 different + # values + + +@slow +def test_piecewise_integrate4_symbolic_conditions(): + a = Symbol('a', real=True) + b = Symbol('b', real=True) + x = Symbol('x', real=True) + y = Symbol('y', real=True) + p0 = Piecewise((0, Or(x < a, x > b)), (1, True)) + p1 = Piecewise((0, x < a), (0, x > b), (1, True)) + p2 = Piecewise((0, x > b), (0, x < a), (1, True)) + p3 = Piecewise((0, x < a), (1, x < b), (0, True)) + p4 = Piecewise((0, x > b), (1, x > a), (0, True)) + p5 = Piecewise((1, And(a < x, x < b)), (0, True)) + + # check values of a=1, b=3 (and reversed) with values + # of y of 0, 1, 2, 3, 4 + lim = Tuple(x, -oo, y) + for p in (p0, p1, p2, p3, p4, p5): + ans = p.integrate(lim) + for i in range(5): + reps = {a:1, b:3, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + reps = {a: 3, b:1, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + lim = Tuple(x, y, oo) + for p in (p0, p1, p2, p3, p4, p5): + ans = p.integrate(lim) + for i in range(5): + reps = {a:1, b:3, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + reps = {a:3, b:1, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + + ans = Piecewise( + (0, x <= Min(a, b)), + (x - Min(a, b), x <= b), + (b - Min(a, b), True)) + for i in (p0, p1, p2, p4): + assert i.integrate(x) == ans + assert p3.integrate(x) == Piecewise( + (0, x < a), + (-a + x, x <= Max(a, b)), + (-a + Max(a, b), True)) + assert p5.integrate(x) == Piecewise( + (0, x <= a), + (-a + x, x <= Max(a, b)), + (-a + Max(a, b), True)) + + p1 = Piecewise((0, x < a), (S.Half, x > b), (1, True)) + p2 = Piecewise((S.Half, x > b), (0, x < a), (1, True)) + p3 = Piecewise((0, x < a), (1, x < b), (S.Half, True)) + p4 = Piecewise((S.Half, x > b), (1, x > a), (0, True)) + p5 = Piecewise((1, And(a < x, x < b)), (S.Half, x > b), (0, True)) + + # check values of a=1, b=3 (and reversed) with values + # of y of 0, 1, 2, 3, 4 + lim = Tuple(x, -oo, y) + for p in (p1, p2, p3, p4, p5): + ans = p.integrate(lim) + for i in range(5): + reps = {a:1, b:3, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + reps = {a: 3, b:1, y:i} + assert ans.subs(reps) == p.subs(reps).integrate(lim.subs(reps)) + + +def test_piecewise_integrate5_independent_conditions(): + p = Piecewise((0, Eq(y, 0)), (x*y, True)) + assert integrate(p, (x, 1, 3)) == Piecewise((0, Eq(y, 0)), (4*y, True)) + + +def test_issue_22917(): + p = (Piecewise((0, ITE((x - y > 1) | (2 * x - 2 * y > 1), False, + ITE(x - y > 1, 2 * y - 2 < -1, 2 * x - 2 * y > 1))), + (Piecewise((0, ITE(x - y > 1, True, 2 * x - 2 * y > 1)), + (2 * Piecewise((0, x - y > 1), (y, True)), True)), True)) + + 2 * Piecewise((1, ITE((x - y > 1) | (2 * x - 2 * y > 1), False, + ITE(x - y > 1, 2 * y - 2 < -1, 2 * x - 2 * y > 1))), + (Piecewise((1, ITE(x - y > 1, True, 2 * x - 2 * y > 1)), + (2 * Piecewise((1, x - y > 1), (x, True)), True)), True))) + assert piecewise_fold(p) == Piecewise((2, (x - y > S.Half) | (x - y > 1)), + (2*y + 4, x - y > 1), + (4*x + 2*y, True)) + assert piecewise_fold(p > 1).rewrite(ITE) == ITE((x - y > S.Half) | (x - y > 1), True, + ITE(x - y > 1, 2*y + 4 > 1, 4*x + 2*y > 1)) + + +def test_piecewise_simplify(): + p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)), + ((-1)**x*(-1), True)) + assert p.simplify() == \ + Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True)) + # simplify when there are Eq in conditions + assert Piecewise( + (a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify( + ) == Piecewise( + (0, And(Eq(a, 0), Eq(b, 0))), (1, True)) + assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)), + Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y + + a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify( + ) == Piecewise( + (2*x, And(Eq(a, 0), Eq(y, 0))), + (2, And(Eq(a, 1), Eq(y, 0))), + (0, True)) + args = (2, And(Eq(x, 2), Ge(y, 0))), (x, True) + assert Piecewise(*args).simplify() == Piecewise(*args) + args = (1, Eq(x, 0)), (sin(x)/x, True) + assert Piecewise(*args).simplify() == Piecewise(*args) + assert Piecewise((2 + y, And(Eq(x, 2), Eq(y, 0))), (x, True) + ).simplify() == x + # check that x or f(x) are recognized as being Symbol-like for lhs + args = Tuple((1, Eq(x, 0)), (sin(x) + 1 + x, True)) + ans = x + sin(x) + 1 + f = Function('f') + assert Piecewise(*args).simplify() == ans + assert Piecewise(*args.subs(x, f(x))).simplify() == ans.subs(x, f(x)) + + # issue 18634 + d = Symbol("d", integer=True) + n = Symbol("n", integer=True) + t = Symbol("t", positive=True) + expr = Piecewise((-d + 2*n, Eq(1/t, 1)), (t**(1 - 4*n)*t**(4*n - 1)*(-d + 2*n), True)) + assert expr.simplify() == -d + 2*n + + # issue 22747 + p = Piecewise((0, (t < -2) & (t < -1) & (t < 0)), ((t/2 + 1)*(t + + 1)*(t + 2), (t < -1) & (t < 0)), ((S.Half - t/2)*(1 - t)*(t + 1), + (t < -2) & (t < -1) & (t < 1)), ((t + 1)*(-t*(t/2 + 1) + (S.Half + - t/2)*(1 - t)), (t < -2) & (t < -1) & (t < 0) & (t < 1)), ((t + + 1)*((S.Half - t/2)*(1 - t) + (t/2 + 1)*(t + 2)), (t < -1) & (t < + 1)), ((t + 1)*(-t*(t/2 + 1) + (S.Half - t/2)*(1 - t)), (t < -1) & + (t < 0) & (t < 1)), (0, (t < -2) & (t < -1)), ((t/2 + 1)*(t + + 1)*(t + 2), t < -1), ((t + 1)*(-t*(t/2 + 1) + (S.Half - t/2)*(t + + 1)), (t < 0) & ((t < -2) | (t < 0))), ((S.Half - t/2)*(1 - t)*(t + + 1), (t < 1) & ((t < -2) | (t < 1))), (0, True)) + Piecewise((0, + (t < -1) & (t < 0) & (t < 1)), ((1 - t)*(t/2 + S.Half)*(t + 1), + (t < 0) & (t < 1)), ((1 - t)*(1 - t/2)*(2 - t), (t < -1) & (t < + 0) & (t < 2)), ((1 - t)*((1 - t)*(t/2 + S.Half) + (1 - t/2)*(2 - + t)), (t < -1) & (t < 0) & (t < 1) & (t < 2)), ((1 - t)*((1 - + t/2)*(2 - t) + (t/2 + S.Half)*(t + 1)), (t < 0) & (t < 2)), ((1 - + t)*((1 - t)*(t/2 + S.Half) + (1 - t/2)*(2 - t)), (t < 0) & (t < + 1) & (t < 2)), (0, (t < -1) & (t < 0)), ((1 - t)*(t/2 + + S.Half)*(t + 1), t < 0), ((1 - t)*(t*(1 - t/2) + (1 - t)*(t/2 + + S.Half)), (t < 1) & ((t < -1) | (t < 1))), ((1 - t)*(1 - t/2)*(2 + - t), (t < 2) & ((t < -1) | (t < 2))), (0, True)) + assert p.simplify() == Piecewise( + (0, t < -2), ((t + 1)*(t + 2)**2/2, t < -1), (-3*t**3/2 + - 5*t**2/2 + 1, t < 0), (3*t**3/2 - 5*t**2/2 + 1, t < 1), ((1 - + t)*(t - 2)**2/2, t < 2), (0, True)) + + # coverage + nan = Undefined + assert Piecewise((1, x > 3), (2, x < 2), (3, x > 1)).simplify( + ) == Piecewise((1, x > 3), (2, x < 2), (3, True)) + assert Piecewise((1, x < 2), (2, x < 1), (3, True)).simplify( + ) == Piecewise((1, x < 2), (3, True)) + assert Piecewise((1, x > 2)).simplify() == Piecewise((1, x > 2), + (nan, True)) + assert Piecewise((1, (x >= 2) & (x < oo)) + ).simplify() == Piecewise((1, (x >= 2) & (x < oo)), (nan, True)) + assert Piecewise((1, x < 2), (2, (x > 1) & (x < 3)), (3, True) + ). simplify() == Piecewise((1, x < 2), (2, x < 3), (3, True)) + assert Piecewise((1, x < 2), (2, (x <= 3) & (x > 1)), (3, True) + ).simplify() == Piecewise((1, x < 2), (2, x <= 3), (3, True)) + assert Piecewise((1, x < 2), (2, (x > 2) & (x < 3)), (3, True) + ).simplify() == Piecewise((1, x < 2), (2, (x > 2) & (x < 3)), + (3, True)) + assert Piecewise((1, x < 2), (2, (x >= 1) & (x <= 3)), (3, True) + ).simplify() == Piecewise((1, x < 2), (2, x <= 3), (3, True)) + assert Piecewise((1, x < 1), (2, (x >= 2) & (x <= 3)), (3, True) + ).simplify() == Piecewise((1, x < 1), (2, (x >= 2) & (x <= 3)), + (3, True)) + # https://github.com/sympy/sympy/issues/25603 + assert Piecewise((log(x), (x <= 5) & (x > 3)), (x, True) + ).simplify() == Piecewise((log(x), (x <= 5) & (x > 3)), (x, True)) + + assert Piecewise((1, (x >= 1) & (x < 3)), (2, (x > 2) & (x < 4)) + ).simplify() == Piecewise((1, (x >= 1) & (x < 3)), ( + 2, (x >= 3) & (x < 4)), (nan, True)) + assert Piecewise((1, (x >= 1) & (x <= 3)), (2, (x > 2) & (x < 4)) + ).simplify() == Piecewise((1, (x >= 1) & (x <= 3)), ( + 2, (x > 3) & (x < 4)), (nan, True)) + + # involves a symbolic range so cset.inf fails + L = Symbol('L', nonnegative=True) + p = Piecewise((nan, x <= 0), (0, (x >= 0) & (L > x) & (L - x <= 0)), + (x - L/2, (L > x) & (L - x <= 0)), + (L/2 - x, (x >= 0) & (L > x)), + (0, L > x), (nan, True)) + assert p.simplify() == Piecewise( + (nan, x <= 0), (L/2 - x, L > x), (nan, True)) + assert p.subs(L, y).simplify() == Piecewise( + (nan, x <= 0), (-x + y/2, x < Max(0, y)), (0, x < y), (nan, True)) + + +def test_piecewise_solve(): + abs2 = Piecewise((-x, x <= 0), (x, x > 0)) + f = abs2.subs(x, x - 2) + assert solve(f, x) == [2] + assert solve(f - 1, x) == [1, 3] + + f = Piecewise(((x - 2)**2, x >= 0), (1, True)) + assert solve(f, x) == [2] + + g = Piecewise(((x - 5)**5, x >= 4), (f, True)) + assert solve(g, x) == [2, 5] + + g = Piecewise(((x - 5)**5, x >= 4), (f, x < 4)) + assert solve(g, x) == [2, 5] + + g = Piecewise(((x - 5)**5, x >= 2), (f, x < 2)) + assert solve(g, x) == [5] + + g = Piecewise(((x - 5)**5, x >= 2), (f, True)) + assert solve(g, x) == [5] + + g = Piecewise(((x - 5)**5, x >= 2), (f, True), (10, False)) + assert solve(g, x) == [5] + + g = Piecewise(((x - 5)**5, x >= 2), + (-x + 2, x - 2 <= 0), (x - 2, x - 2 > 0)) + assert solve(g, x) == [5] + + # if no symbol is given the piecewise detection must still work + assert solve(Piecewise((x - 2, x > 2), (2 - x, True)) - 3) == [-1, 5] + + f = Piecewise(((x - 2)**2, x >= 0), (0, True)) + raises(NotImplementedError, lambda: solve(f, x)) + + def nona(ans): + return list(filter(lambda x: x is not S.NaN, ans)) + p = Piecewise((x**2 - 4, x < y), (x - 2, True)) + ans = solve(p, x) + assert nona([i.subs(y, -2) for i in ans]) == [2] + assert nona([i.subs(y, 2) for i in ans]) == [-2, 2] + assert nona([i.subs(y, 3) for i in ans]) == [-2, 2] + assert ans == [ + Piecewise((-2, y > -2), (S.NaN, True)), + Piecewise((2, y <= 2), (S.NaN, True)), + Piecewise((2, y > 2), (S.NaN, True))] + + # issue 6060 + absxm3 = Piecewise( + (x - 3, 0 <= x - 3), + (3 - x, 0 > x - 3) + ) + assert solve(absxm3 - y, x) == [ + Piecewise((-y + 3, -y < 0), (S.NaN, True)), + Piecewise((y + 3, y >= 0), (S.NaN, True))] + p = Symbol('p', positive=True) + assert solve(absxm3 - p, x) == [-p + 3, p + 3] + + # issue 6989 + f = Function('f') + assert solve(Eq(-f(x), Piecewise((1, x > 0), (0, True))), f(x)) == \ + [Piecewise((-1, x > 0), (0, True))] + + # issue 8587 + f = Piecewise((2*x**2, And(0 < x, x < 1)), (2, True)) + assert solve(f - 1) == [1/sqrt(2)] + + +def test_piecewise_fold(): + p = Piecewise((x, x < 1), (1, 1 <= x)) + + assert piecewise_fold(x*p) == Piecewise((x**2, x < 1), (x, 1 <= x)) + assert piecewise_fold(p + p) == Piecewise((2*x, x < 1), (2, 1 <= x)) + assert piecewise_fold(Piecewise((1, x < 0), (2, True)) + + Piecewise((10, x < 0), (-10, True))) == \ + Piecewise((11, x < 0), (-8, True)) + + p1 = Piecewise((0, x < 0), (x, x <= 1), (0, True)) + p2 = Piecewise((0, x < 0), (1 - x, x <= 1), (0, True)) + + p = 4*p1 + 2*p2 + assert integrate( + piecewise_fold(p), (x, -oo, oo)) == integrate(2*x + 2, (x, 0, 1)) + + assert piecewise_fold( + Piecewise((1, y <= 0), (-Piecewise((2, y >= 0)), True) + )) == Piecewise((1, y <= 0), (-2, y >= 0)) + + assert piecewise_fold(Piecewise((x, ITE(x > 0, y < 1, y > 1))) + ) == Piecewise((x, ((x <= 0) | (y < 1)) & ((x > 0) | (y > 1)))) + + a, b = (Piecewise((2, Eq(x, 0)), (0, True)), + Piecewise((x, Eq(-x + y, 0)), (1, Eq(-x + y, 1)), (0, True))) + assert piecewise_fold(Mul(a, b, evaluate=False) + ) == piecewise_fold(Mul(b, a, evaluate=False)) + + +def test_piecewise_fold_piecewise_in_cond(): + p1 = Piecewise((cos(x), x < 0), (0, True)) + p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True)) + assert p2.subs(x, -pi/2) == 0 + assert p2.subs(x, 1) == 0 + assert p2.subs(x, -pi/4) == 1 + p4 = Piecewise((0, Eq(p1, 0)), (1,True)) + ans = piecewise_fold(p4) + for i in range(-1, 1): + assert ans.subs(x, i) == p4.subs(x, i) + + r1 = 1 < Piecewise((1, x < 1), (3, True)) + ans = piecewise_fold(r1) + for i in range(2): + assert ans.subs(x, i) == r1.subs(x, i) + + p5 = Piecewise((1, x < 0), (3, True)) + p6 = Piecewise((1, x < 1), (3, True)) + p7 = Piecewise((1, p5 < p6), (0, True)) + ans = piecewise_fold(p7) + for i in range(-1, 2): + assert ans.subs(x, i) == p7.subs(x, i) + + +def test_piecewise_fold_piecewise_in_cond_2(): + p1 = Piecewise((cos(x), x < 0), (0, True)) + p2 = Piecewise((0, Eq(p1, 0)), (1 / p1, True)) + p3 = Piecewise( + (0, (x >= 0) | Eq(cos(x), 0)), + (1/cos(x), x < 0), + (zoo, True)) # redundant b/c all x are already covered + assert(piecewise_fold(p2) == p3) + + +def test_piecewise_fold_expand(): + p1 = Piecewise((1, Interval(0, 1, False, True).contains(x)), (0, True)) + + p2 = piecewise_fold(expand((1 - x)*p1)) + cond = ((x >= 0) & (x < 1)) + assert piecewise_fold(expand((1 - x)*p1), evaluate=False + ) == Piecewise((1 - x, cond), (-x, cond), (1, cond), (0, True), evaluate=False) + assert piecewise_fold(expand((1 - x)*p1), evaluate=None + ) == Piecewise((1 - x, cond), (0, True)) + assert p2 == Piecewise((1 - x, cond), (0, True)) + assert p2 == expand(piecewise_fold((1 - x)*p1)) + + +def test_piecewise_duplicate(): + p = Piecewise((x, x < -10), (x**2, x <= -1), (x, 1 < x)) + assert p == Piecewise(*p.args) + + +def test_doit(): + p1 = Piecewise((x, x < 1), (x**2, -1 <= x), (x, 3 < x)) + p2 = Piecewise((x, x < 1), (Integral(2 * x), -1 <= x), (x, 3 < x)) + assert p2.doit() == p1 + assert p2.doit(deep=False) == p2 + # issue 17165 + p1 = Sum(y**x, (x, -1, oo)).doit() + assert p1.doit() == p1 + + +def test_piecewise_interval(): + p1 = Piecewise((x, Interval(0, 1).contains(x)), (0, True)) + assert p1.subs(x, -0.5) == 0 + assert p1.subs(x, 0.5) == 0.5 + assert p1.diff(x) == Piecewise((1, Interval(0, 1).contains(x)), (0, True)) + assert integrate(p1, x) == Piecewise( + (0, x <= 0), + (x**2/2, x <= 1), + (S.Half, True)) + + +def test_piecewise_exclusive(): + p = Piecewise((0, x < 0), (S.Half, x <= 0), (1, True)) + assert piecewise_exclusive(p) == Piecewise((0, x < 0), (S.Half, Eq(x, 0)), + (1, x > 0), evaluate=False) + assert piecewise_exclusive(p + 2) == Piecewise((0, x < 0), (S.Half, Eq(x, 0)), + (1, x > 0), evaluate=False) + 2 + assert piecewise_exclusive(Piecewise((1, y <= 0), + (-Piecewise((2, y >= 0)), True))) == \ + Piecewise((1, y <= 0), + (-Piecewise((2, y >= 0), + (S.NaN, y < 0), evaluate=False), y > 0), evaluate=False) + assert piecewise_exclusive(Piecewise((1, x > y))) == Piecewise((1, x > y), + (S.NaN, x <= y), + evaluate=False) + assert piecewise_exclusive(Piecewise((1, x > y)), + skip_nan=True) == Piecewise((1, x > y)) + + xr, yr = symbols('xr, yr', real=True) + + p1 = Piecewise((1, xr < 0), (2, True), evaluate=False) + p1x = Piecewise((1, xr < 0), (2, xr >= 0), evaluate=False) + + p2 = Piecewise((p1, yr < 0), (3, True), evaluate=False) + p2x = Piecewise((p1, yr < 0), (3, yr >= 0), evaluate=False) + p2xx = Piecewise((p1x, yr < 0), (3, yr >= 0), evaluate=False) + + assert piecewise_exclusive(p2) == p2xx + assert piecewise_exclusive(p2, deep=False) == p2x + + +def test_piecewise_collapse(): + assert Piecewise((x, True)) == x + a = x < 1 + assert Piecewise((x, a), (x + 1, a)) == Piecewise((x, a)) + assert Piecewise((x, a), (x + 1, a.reversed)) == Piecewise((x, a)) + b = x < 5 + def canonical(i): + if isinstance(i, Piecewise): + return Piecewise(*i.args) + return i + for args in [ + ((1, a), (Piecewise((2, a), (3, b)), b)), + ((1, a), (Piecewise((2, a), (3, b.reversed)), b)), + ((1, a), (Piecewise((2, a), (3, b)), b), (4, True)), + ((1, a), (Piecewise((2, a), (3, b), (4, True)), b)), + ((1, a), (Piecewise((2, a), (3, b), (4, True)), b), (5, True))]: + for i in (0, 2, 10): + assert canonical( + Piecewise(*args, evaluate=False).subs(x, i) + ) == canonical(Piecewise(*args).subs(x, i)) + r1, r2, r3, r4 = symbols('r1:5') + a = x < r1 + b = x < r2 + c = x < r3 + d = x < r4 + assert Piecewise((1, a), (Piecewise( + (2, a), (3, b), (4, c)), b), (5, c) + ) == Piecewise((1, a), (3, b), (5, c)) + assert Piecewise((1, a), (Piecewise( + (2, a), (3, b), (4, c), (6, True)), c), (5, d) + ) == Piecewise((1, a), (Piecewise( + (3, b), (4, c)), c), (5, d)) + assert Piecewise((1, Or(a, d)), (Piecewise( + (2, d), (3, b), (4, c)), b), (5, c) + ) == Piecewise((1, Or(a, d)), (Piecewise( + (2, d), (3, b)), b), (5, c)) + assert Piecewise((1, c), (2, ~c), (3, S.true) + ) == Piecewise((1, c), (2, S.true)) + assert Piecewise((1, c), (2, And(~c, b)), (3,True) + ) == Piecewise((1, c), (2, b), (3, True)) + assert Piecewise((1, c), (2, Or(~c, b)), (3,True) + ).subs(dict(zip((r1, r2, r3, r4, x), (1, 2, 3, 4, 3.5)))) == 2 + assert Piecewise((1, c), (2, ~c)) == Piecewise((1, c), (2, True)) + + +def test_piecewise_lambdify(): + p = Piecewise( + (x**2, x < 0), + (x, Interval(0, 1, False, True).contains(x)), + (2 - x, x >= 1), + (0, True) + ) + + f = lambdify(x, p) + assert f(-2.0) == 4.0 + assert f(0.0) == 0.0 + assert f(0.5) == 0.5 + assert f(2.0) == 0.0 + + +def test_piecewise_series(): + from sympy.series.order import O + p1 = Piecewise((sin(x), x < 0), (cos(x), x > 0)) + p2 = Piecewise((x + O(x**2), x < 0), (1 + O(x**2), x > 0)) + assert p1.nseries(x, n=2) == p2 + + +def test_piecewise_as_leading_term(): + p1 = Piecewise((1/x, x > 1), (0, True)) + p2 = Piecewise((x, x > 1), (0, True)) + p3 = Piecewise((1/x, x > 1), (x, True)) + p4 = Piecewise((x, x > 1), (1/x, True)) + p5 = Piecewise((1/x, x > 1), (x, True)) + p6 = Piecewise((1/x, x < 1), (x, True)) + p7 = Piecewise((x, x < 1), (1/x, True)) + p8 = Piecewise((x, x > 1), (1/x, True)) + assert p1.as_leading_term(x) == 0 + assert p2.as_leading_term(x) == 0 + assert p3.as_leading_term(x) == x + assert p4.as_leading_term(x) == 1/x + assert p5.as_leading_term(x) == x + assert p6.as_leading_term(x) == 1/x + assert p7.as_leading_term(x) == x + assert p8.as_leading_term(x) == 1/x + + +def test_piecewise_complex(): + p1 = Piecewise((2, x < 0), (1, 0 <= x)) + p2 = Piecewise((2*I, x < 0), (I, 0 <= x)) + p3 = Piecewise((I*x, x > 1), (1 + I, True)) + p4 = Piecewise((-I*conjugate(x), x > 1), (1 - I, True)) + + assert conjugate(p1) == p1 + assert conjugate(p2) == piecewise_fold(-p2) + assert conjugate(p3) == p4 + + assert p1.is_imaginary is False + assert p1.is_real is True + assert p2.is_imaginary is True + assert p2.is_real is False + assert p3.is_imaginary is None + assert p3.is_real is None + + assert p1.as_real_imag() == (p1, 0) + assert p2.as_real_imag() == (0, -I*p2) + + +def test_conjugate_transpose(): + A, B = symbols("A B", commutative=False) + p = Piecewise((A*B**2, x > 0), (A**2*B, True)) + assert p.adjoint() == \ + Piecewise((adjoint(A*B**2), x > 0), (adjoint(A**2*B), True)) + assert p.conjugate() == \ + Piecewise((conjugate(A*B**2), x > 0), (conjugate(A**2*B), True)) + assert p.transpose() == \ + Piecewise((transpose(A*B**2), x > 0), (transpose(A**2*B), True)) + + +def test_piecewise_evaluate(): + assert Piecewise((x, True)) == x + assert Piecewise((x, True), evaluate=True) == x + assert Piecewise((1, Eq(1, x))).args == ((1, Eq(x, 1)),) + assert Piecewise((1, Eq(1, x)), evaluate=False).args == ( + (1, Eq(1, x)),) + # like the additive and multiplicative identities that + # cannot be kept in Add/Mul, we also do not keep a single True + p = Piecewise((x, True), evaluate=False) + assert p == x + + +def test_as_expr_set_pairs(): + assert Piecewise((x, x > 0), (-x, x <= 0)).as_expr_set_pairs() == \ + [(x, Interval(0, oo, True, True)), (-x, Interval(-oo, 0))] + + assert Piecewise(((x - 2)**2, x >= 0), (0, True)).as_expr_set_pairs() == \ + [((x - 2)**2, Interval(0, oo)), (0, Interval(-oo, 0, True, True))] + + +def test_S_srepr_is_identity(): + p = Piecewise((10, Eq(x, 0)), (12, True)) + q = S(srepr(p)) + assert p == q + + +def test_issue_12587(): + # sort holes into intervals + p = Piecewise((1, x > 4), (2, Not((x <= 3) & (x > -1))), (3, True)) + assert p.integrate((x, -5, 5)) == 23 + p = Piecewise((1, x > 1), (2, x < y), (3, True)) + lim = x, -3, 3 + ans = p.integrate(lim) + for i in range(-1, 3): + assert ans.subs(y, i) == p.subs(y, i).integrate(lim) + + +def test_issue_11045(): + assert integrate(1/(x*sqrt(x**2 - 1)), (x, 1, 2)) == pi/3 + + # handle And with Or arguments + assert Piecewise((1, And(Or(x < 1, x > 3), x < 2)), (0, True) + ).integrate((x, 0, 3)) == 1 + + # hidden false + assert Piecewise((1, x > 1), (2, x > x + 1), (3, True) + ).integrate((x, 0, 3)) == 5 + # targetcond is Eq + assert Piecewise((1, x > 1), (2, Eq(1, x)), (3, True) + ).integrate((x, 0, 4)) == 6 + # And has Relational needing to be solved + assert Piecewise((1, And(2*x > x + 1, x < 2)), (0, True) + ).integrate((x, 0, 3)) == 1 + # Or has Relational needing to be solved + assert Piecewise((1, Or(2*x > x + 2, x < 1)), (0, True) + ).integrate((x, 0, 3)) == 2 + # ignore hidden false (handled in canonicalization) + assert Piecewise((1, x > 1), (2, x > x + 1), (3, True) + ).integrate((x, 0, 3)) == 5 + # watch for hidden True Piecewise + assert Piecewise((2, Eq(1 - x, x*(1/x - 1))), (0, True) + ).integrate((x, 0, 3)) == 6 + + # overlapping conditions of targetcond are recognized and ignored; + # the condition x > 3 will be pre-empted by the first condition + assert Piecewise((1, Or(x < 1, x > 2)), (2, x > 3), (3, True) + ).integrate((x, 0, 4)) == 6 + + # convert Ne to Or + assert Piecewise((1, Ne(x, 0)), (2, True) + ).integrate((x, -1, 1)) == 2 + + # no default but well defined + assert Piecewise((x, (x > 1) & (x < 3)), (1, (x < 4)) + ).integrate((x, 1, 4)) == 5 + + p = Piecewise((x, (x > 1) & (x < 3)), (1, (x < 4))) + nan = Undefined + i = p.integrate((x, 1, y)) + assert i == Piecewise( + (y - 1, y < 1), + (Min(3, y)**2/2 - Min(3, y) + Min(4, y) - S.Half, + y <= Min(4, y)), + (nan, True)) + assert p.integrate((x, 1, -1)) == i.subs(y, -1) + assert p.integrate((x, 1, 4)) == 5 + assert p.integrate((x, 1, 5)) is nan + + # handle Not + p = Piecewise((1, x > 1), (2, Not(And(x > 1, x< 3))), (3, True)) + assert p.integrate((x, 0, 3)) == 4 + + # handle updating of int_expr when there is overlap + p = Piecewise( + (1, And(5 > x, x > 1)), + (2, Or(x < 3, x > 7)), + (4, x < 8)) + assert p.integrate((x, 0, 10)) == 20 + + # And with Eq arg handling + assert Piecewise((1, x < 1), (2, And(Eq(x, 3), x > 1)) + ).integrate((x, 0, 3)) is S.NaN + assert Piecewise((1, x < 1), (2, And(Eq(x, 3), x > 1)), (3, True) + ).integrate((x, 0, 3)) == 7 + assert Piecewise((1, x < 0), (2, And(Eq(x, 3), x < 1)), (3, True) + ).integrate((x, -1, 1)) == 4 + # middle condition doesn't matter: it's a zero width interval + assert Piecewise((1, x < 1), (2, Eq(x, 3) & (y < x)), (3, True) + ).integrate((x, 0, 3)) == 7 + + +def test_holes(): + nan = Undefined + assert Piecewise((1, x < 2)).integrate(x) == Piecewise( + (x, x < 2), (nan, True)) + assert Piecewise((1, And(x > 1, x < 2))).integrate(x) == Piecewise( + (nan, x < 1), (x, x < 2), (nan, True)) + assert Piecewise((1, And(x > 1, x < 2))).integrate((x, 0, 3)) is nan + assert Piecewise((1, And(x > 0, x < 4))).integrate((x, 1, 3)) == 2 + + # this also tests that the integrate method is used on non-Piecwise + # arguments in _eval_integral + A, B = symbols("A B") + a, b = symbols('a b', real=True) + assert Piecewise((A, And(x < 0, a < 1)), (B, Or(x < 1, a > 2)) + ).integrate(x) == Piecewise( + (B*x, (a > 2)), + (Piecewise((A*x, x < 0), (B*x, x < 1), (nan, True)), a < 1), + (Piecewise((B*x, x < 1), (nan, True)), True)) + + +def test_issue_11922(): + def f(x): + return Piecewise((0, x < -1), (1 - x**2, x < 1), (0, True)) + autocorr = lambda k: ( + f(x) * f(x + k)).integrate((x, -1, 1)) + assert autocorr(1.9) > 0 + k = symbols('k') + good_autocorr = lambda k: ( + (1 - x**2) * f(x + k)).integrate((x, -1, 1)) + a = good_autocorr(k) + assert a.subs(k, 3) == 0 + k = symbols('k', positive=True) + a = good_autocorr(k) + assert a.subs(k, 3) == 0 + assert Piecewise((0, x < 1), (10, (x >= 1)) + ).integrate() == Piecewise((0, x < 1), (10*x - 10, True)) + + +def test_issue_5227(): + f = 0.0032513612725229*Piecewise((0, x < -80.8461538461539), + (-0.0160799238820171*x + 1.33215984776403, x < 2), + (Piecewise((0.3, x > 123), (0.7, True)) + + Piecewise((0.4, x > 2), (0.6, True)), x <= + 123), (-0.00817409766454352*x + 2.10541401273885, x < + 380.571428571429), (0, True)) + i = integrate(f, (x, -oo, oo)) + assert i == Integral(f, (x, -oo, oo)).doit() + assert str(i) == '1.00195081676351' + assert Piecewise((1, x - y < 0), (0, True) + ).integrate(y) == Piecewise((0, y <= x), (-x + y, True)) + + +def test_issue_10137(): + a = Symbol('a', real=True) + b = Symbol('b', real=True) + x = Symbol('x', real=True) + y = Symbol('y', real=True) + p0 = Piecewise((0, Or(x < a, x > b)), (1, True)) + p1 = Piecewise((0, Or(a > x, b < x)), (1, True)) + assert integrate(p0, (x, y, oo)) == integrate(p1, (x, y, oo)) + p3 = Piecewise((1, And(0 < x, x < a)), (0, True)) + p4 = Piecewise((1, And(a > x, x > 0)), (0, True)) + ip3 = integrate(p3, x) + assert ip3 == Piecewise( + (0, x <= 0), + (x, x <= Max(0, a)), + (Max(0, a), True)) + ip4 = integrate(p4, x) + assert ip4 == ip3 + assert p3.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2 + assert p4.integrate((x, 2, 4)) == Min(4, Max(2, a)) - 2 + + +def test_stackoverflow_43852159(): + f = lambda x: Piecewise((1, (x >= -1) & (x <= 1)), (0, True)) + Conv = lambda x: integrate(f(x - y)*f(y), (y, -oo, +oo)) + cx = Conv(x) + assert cx.subs(x, -1.5) == cx.subs(x, 1.5) + assert cx.subs(x, 3) == 0 + assert piecewise_fold(f(x - y)*f(y)) == Piecewise( + (1, (y >= -1) & (y <= 1) & (x - y >= -1) & (x - y <= 1)), + (0, True)) + + +def test_issue_12557(): + ''' + # 3200 seconds to compute the fourier part of issue + import sympy as sym + x,y,z,t = sym.symbols('x y z t') + k = sym.symbols("k", integer=True) + fourier = sym.fourier_series(sym.cos(k*x)*sym.sqrt(x**2), + (x, -sym.pi, sym.pi)) + assert fourier == FourierSeries( + sqrt(x**2)*cos(k*x), (x, -pi, pi), (Piecewise((pi**2, + Eq(k, 0)), (2*(-1)**k/k**2 - 2/k**2, True))/(2*pi), + SeqFormula(Piecewise((pi**2, (Eq(_n, 0) & Eq(k, 0)) | (Eq(_n, 0) & + Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) & Eq(k, 0) & Eq(_n, -k)) | (Eq(_n, + 0) & Eq(_n, k) & Eq(k, 0) & Eq(_n, -k))), (pi**2/2, Eq(_n, k) | Eq(_n, + -k) | (Eq(_n, 0) & Eq(_n, k)) | (Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) & + Eq(_n, -k)) | (Eq(_n, k) & Eq(_n, -k)) | (Eq(k, 0) & Eq(_n, -k)) | + (Eq(_n, 0) & Eq(_n, k) & Eq(_n, -k)) | (Eq(_n, k) & Eq(k, 0) & Eq(_n, + -k))), ((-1)**k*pi**2*_n**3*sin(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 + + pi*k**4) - (-1)**k*pi**2*_n**3*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 + - pi*k**4) + (-1)**k*pi*_n**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 + + pi*k**4) - (-1)**k*pi*_n**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 - + pi*k**4) - (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(pi*_n**4 - + 2*pi*_n**2*k**2 + pi*k**4) + + (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 - + pi*k**4) + (-1)**k*pi*k**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 + + pi*k**4) - (-1)**k*pi*k**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 - + pi*k**4) - (2*_n**2 + 2*k**2)/(_n**4 - 2*_n**2*k**2 + k**4), + True))*cos(_n*x)/pi, (_n, 1, oo)), SeqFormula(0, (_k, 1, oo)))) + ''' + x = symbols("x", real=True) + k = symbols('k', integer=True, finite=True) + abs2 = lambda x: Piecewise((-x, x <= 0), (x, x > 0)) + assert integrate(abs2(x), (x, -pi, pi)) == pi**2 + func = cos(k*x)*sqrt(x**2) + assert integrate(func, (x, -pi, pi)) == Piecewise( + (2*(-1)**k/k**2 - 2/k**2, Ne(k, 0)), (pi**2, True)) + +def test_issue_6900(): + from itertools import permutations + t0, t1, T, t = symbols('t0, t1 T t') + f = Piecewise((0, t < t0), (x, And(t0 <= t, t < t1)), (0, t >= t1)) + g = f.integrate(t) + assert g == Piecewise( + (0, t <= t0), + (t*x - t0*x, t <= Max(t0, t1)), + (-t0*x + x*Max(t0, t1), True)) + for i in permutations(range(2)): + reps = dict(zip((t0,t1), i)) + for tt in range(-1,3): + assert (g.xreplace(reps).subs(t,tt) == + f.xreplace(reps).integrate(t).subs(t,tt)) + lim = Tuple(t, t0, T) + g = f.integrate(lim) + ans = Piecewise( + (-t0*x + x*Min(T, Max(t0, t1)), T > t0), + (0, True)) + for i in permutations(range(3)): + reps = dict(zip((t0,t1,T), i)) + tru = f.xreplace(reps).integrate(lim.xreplace(reps)) + assert tru == ans.xreplace(reps) + assert g == ans + + +def test_issue_10122(): + assert solve(abs(x) + abs(x - 1) - 1 > 0, x + ) == Or(And(-oo < x, x < S.Zero), And(S.One < x, x < oo)) + + +def test_issue_4313(): + u = Piecewise((0, x <= 0), (1, x >= a), (x/a, True)) + e = (u - u.subs(x, y))**2/(x - y)**2 + M = Max(0, a) + assert integrate(e, x).expand() == Piecewise( + (Piecewise( + (0, x <= 0), + (-y**2/(a**2*x - a**2*y) + x/a**2 - 2*y*log(-y)/a**2 + + 2*y*log(x - y)/a**2 - y/a**2, x <= M), + (-y**2/(-a**2*y + a**2*M) + 1/(-y + M) - + 1/(x - y) - 2*y*log(-y)/a**2 + 2*y*log(-y + + M)/a**2 - y/a**2 + M/a**2, True)), + ((a <= y) & (y <= 0)) | ((y <= 0) & (y > -oo))), + (Piecewise( + (-1/(x - y), x <= 0), + (-a**2/(a**2*x - a**2*y) + 2*a*y/(a**2*x - a**2*y) - + y**2/(a**2*x - a**2*y) + 2*log(-y)/a - 2*log(x - y)/a + + 2/a + x/a**2 - 2*y*log(-y)/a**2 + 2*y*log(x - y)/a**2 - + y/a**2, x <= M), + (-a**2/(-a**2*y + a**2*M) + 2*a*y/(-a**2*y + + a**2*M) - y**2/(-a**2*y + a**2*M) + + 2*log(-y)/a - 2*log(-y + M)/a + 2/a - + 2*y*log(-y)/a**2 + 2*y*log(-y + M)/a**2 - + y/a**2 + M/a**2, True)), + a <= y), + (Piecewise( + (-y**2/(a**2*x - a**2*y), x <= 0), + (x/a**2 + y/a**2, x <= M), + (a**2/(-a**2*y + a**2*M) - + a**2/(a**2*x - a**2*y) - 2*a*y/(-a**2*y + a**2*M) + + 2*a*y/(a**2*x - a**2*y) + y**2/(-a**2*y + a**2*M) - + y**2/(a**2*x - a**2*y) + y/a**2 + M/a**2, True)), + True)) + + +def test__intervals(): + assert Piecewise((x + 2, Eq(x, 3)))._intervals(x) == (True, []) + assert Piecewise( + (1, x > x + 1), + (Piecewise((1, x < x + 1)), 2*x < 2*x + 1), + (1, True))._intervals(x) == (True, [(-oo, oo, 1, 1)]) + assert Piecewise((1, Ne(x, I)), (0, True))._intervals(x) == (True, + [(-oo, oo, 1, 0)]) + assert Piecewise((-cos(x), sin(x) >= 0), (cos(x), True) + )._intervals(x) == (True, + [(0, pi, -cos(x), 0), (-oo, oo, cos(x), 1)]) + # the following tests that duplicates are removed and that non-Eq + # generated zero-width intervals are removed + assert Piecewise((1, Abs(x**(-2)) > 1), (0, True) + )._intervals(x) == (True, + [(-1, 0, 1, 0), (0, 1, 1, 0), (-oo, oo, 0, 1)]) + + +def test_containment(): + a, b, c, d, e = [1, 2, 3, 4, 5] + p = (Piecewise((d, x > 1), (e, True))* + Piecewise((a, Abs(x - 1) < 1), (b, Abs(x - 2) < 2), (c, True))) + assert p.integrate(x).diff(x) == Piecewise( + (c*e, x <= 0), + (a*e, x <= 1), + (a*d, x < 2), # this is what we want to get right + (b*d, x < 4), + (c*d, True)) + + +def test_piecewise_with_DiracDelta(): + d1 = DiracDelta(x - 1) + assert integrate(d1, (x, -oo, oo)) == 1 + assert integrate(d1, (x, 0, 2)) == 1 + assert Piecewise((d1, Eq(x, 2)), (0, True)).integrate(x) == 0 + assert Piecewise((d1, x < 2), (0, True)).integrate(x) == Piecewise( + (Heaviside(x - 1), x < 2), (1, True)) + # TODO raise error if function is discontinuous at limit of + # integration, e.g. integrate(d1, (x, -2, 1)) or Piecewise( + # (d1, Eq(x, 1) + + +def test_issue_10258(): + assert Piecewise((0, x < 1), (1, True)).is_zero is None + assert Piecewise((-1, x < 1), (1, True)).is_zero is False + a = Symbol('a', zero=True) + assert Piecewise((0, x < 1), (a, True)).is_zero + assert Piecewise((1, x < 1), (a, x < 3)).is_zero is None + a = Symbol('a') + assert Piecewise((0, x < 1), (a, True)).is_zero is None + assert Piecewise((0, x < 1), (1, True)).is_nonzero is None + assert Piecewise((1, x < 1), (2, True)).is_nonzero + assert Piecewise((0, x < 1), (oo, True)).is_finite is None + assert Piecewise((0, x < 1), (1, True)).is_finite + b = Basic() + assert Piecewise((b, x < 1)).is_finite is None + + # 10258 + c = Piecewise((1, x < 0), (2, True)) < 3 + assert c != True + assert piecewise_fold(c) == True + + +def test_issue_10087(): + a, b = Piecewise((x, x > 1), (2, True)), Piecewise((x, x > 3), (3, True)) + m = a*b + f = piecewise_fold(m) + for i in (0, 2, 4): + assert m.subs(x, i) == f.subs(x, i) + m = a + b + f = piecewise_fold(m) + for i in (0, 2, 4): + assert m.subs(x, i) == f.subs(x, i) + + +def test_issue_8919(): + c = symbols('c:5') + x = symbols("x") + f1 = Piecewise((c[1], x < 1), (c[2], True)) + f2 = Piecewise((c[3], x < Rational(1, 3)), (c[4], True)) + assert integrate(f1*f2, (x, 0, 2) + ) == c[1]*c[3]/3 + 2*c[1]*c[4]/3 + c[2]*c[4] + f1 = Piecewise((0, x < 1), (2, True)) + f2 = Piecewise((3, x < 2), (0, True)) + assert integrate(f1*f2, (x, 0, 3)) == 6 + + y = symbols("y", positive=True) + a, b, c, x, z = symbols("a,b,c,x,z", real=True) + I = Integral(Piecewise( + (0, (x >= y) | (x < 0) | (b > c)), + (a, True)), (x, 0, z)) + ans = I.doit() + assert ans == Piecewise((0, b > c), (a*Min(y, z) - a*Min(0, z), True)) + for cond in (True, False): + for yy in range(1, 3): + for zz in range(-yy, 0, yy): + reps = [(b > c, cond), (y, yy), (z, zz)] + assert ans.subs(reps) == I.subs(reps).doit() + + +def test_unevaluated_integrals(): + f = Function('f') + p = Piecewise((1, Eq(f(x) - 1, 0)), (2, x - 10 < 0), (0, True)) + assert p.integrate(x) == Integral(p, x) + assert p.integrate((x, 0, 5)) == Integral(p, (x, 0, 5)) + # test it by replacing f(x) with x%2 which will not + # affect the answer: the integrand is essentially 2 over + # the domain of integration + assert Integral(p, (x, 0, 5)).subs(f(x), x%2).n() == 10.0 + + # this is a test of using _solve_inequality when + # solve_univariate_inequality fails + assert p.integrate(y) == Piecewise( + (y, Eq(f(x), 1) | ((x < 10) & Eq(f(x), 1))), + (2*y, (x > -oo) & (x < 10)), (0, True)) + + +def test_conditions_as_alternate_booleans(): + a, b, c = symbols('a:c') + assert Piecewise((x, Piecewise((y < 1, x > 0), (y > 1, True))) + ) == Piecewise((x, ITE(x > 0, y < 1, y > 1))) + + +def test_Piecewise_rewrite_as_ITE(): + a, b, c, d = symbols('a:d') + + def _ITE(*args): + return Piecewise(*args).rewrite(ITE) + + assert _ITE((a, x < 1), (b, x >= 1)) == ITE(x < 1, a, b) + assert _ITE((a, x < 1), (b, x < oo)) == ITE(x < 1, a, b) + assert _ITE((a, x < 1), (b, Or(y < 1, x < oo)), (c, y > 0) + ) == ITE(x < 1, a, b) + assert _ITE((a, x < 1), (b, True)) == ITE(x < 1, a, b) + assert _ITE((a, x < 1), (b, x < 2), (c, True) + ) == ITE(x < 1, a, ITE(x < 2, b, c)) + assert _ITE((a, x < 1), (b, y < 2), (c, True) + ) == ITE(x < 1, a, ITE(y < 2, b, c)) + assert _ITE((a, x < 1), (b, x < oo), (c, y < 1) + ) == ITE(x < 1, a, b) + assert _ITE((a, x < 1), (c, y < 1), (b, x < oo), (d, True) + ) == ITE(x < 1, a, ITE(y < 1, c, b)) + assert _ITE((a, x < 0), (b, Or(x < oo, y < 1)) + ) == ITE(x < 0, a, b) + raises(TypeError, lambda: _ITE((x + 1, x < 1), (x, True))) + # if `a` in the following were replaced with y then the coverage + # is complete but something other than as_set would need to be + # used to detect this + raises(NotImplementedError, lambda: _ITE((x, x < y), (y, x >= a))) + raises(ValueError, lambda: _ITE((a, x < 2), (b, x > 3))) + + +def test_issue_14052(): + assert integrate(abs(sin(x)), (x, 0, 2*pi)) == 4 + + +def test_issue_14240(): + assert piecewise_fold( + Piecewise((1, a), (2, b), (4, True)) + + Piecewise((8, a), (16, True)) + ) == Piecewise((9, a), (18, b), (20, True)) + assert piecewise_fold( + Piecewise((2, a), (3, b), (5, True)) * + Piecewise((7, a), (11, True)) + ) == Piecewise((14, a), (33, b), (55, True)) + # these will hang if naive folding is used + assert piecewise_fold(Add(*[ + Piecewise((i, a), (0, True)) for i in range(40)]) + ) == Piecewise((780, a), (0, True)) + assert piecewise_fold(Mul(*[ + Piecewise((i, a), (0, True)) for i in range(1, 41)]) + ) == Piecewise((factorial(40), a), (0, True)) + + +def test_issue_14787(): + x = Symbol('x') + f = Piecewise((x, x < 1), ((S(58) / 7), True)) + assert str(f.evalf()) == "Piecewise((x, x < 1), (8.28571428571429, True))" + +def test_issue_21481(): + b, e = symbols('b e') + C = Piecewise( + (2, + ((b > 1) & (e > 0)) | + ((b > 0) & (b < 1) & (e < 0)) | + ((e >= 2) & (b < -1) & Eq(Mod(e, 2), 0)) | + ((e <= -2) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 0))), + (S.Half, + ((b > 1) & (e < 0)) | + ((b > 0) & (e > 0) & (b < 1)) | + ((e <= -2) & (b < -1) & Eq(Mod(e, 2), 0)) | + ((e >= 2) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 0))), + (-S.Half, + Eq(Mod(e, 2), 1) & + (((e <= -1) & (b < -1)) | ((e >= 1) & (b > -1) & (b < 0)))), + (-2, + ((e >= 1) & (b < -1) & Eq(Mod(e, 2), 1)) | + ((e <= -1) & (b > -1) & (b < 0) & Eq(Mod(e, 2), 1))) + ) + A = Piecewise( + (1, Eq(b, 1) | Eq(e, 0) | (Eq(b, -1) & Eq(Mod(e, 2), 0))), + (0, Eq(b, 0) & (e > 0)), + (-1, Eq(b, -1) & Eq(Mod(e, 2), 1)), + (C, Eq(im(b), 0) & Eq(im(e), 0)) + ) + + B = piecewise_fold(A) + sa = A.simplify() + sb = B.simplify() + v = (-2, -1, -S.Half, 0, S.Half, 1, 2) + for i in v: + for j in v: + r = {b:i, e:j} + ok = [k.xreplace(r) for k in (A, B, sa, sb)] + assert len(set(ok)) == 1 + + +def test_issue_8458(): + x, y = symbols('x y') + # Original issue + p1 = Piecewise((0, Eq(x, 0)), (sin(x), True)) + assert p1.simplify() == sin(x) + # Slightly larger variant + p2 = Piecewise((x, Eq(x, 0)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True)) + assert p2.simplify() == sin(x) + # Test for problem highlighted during review + p3 = Piecewise((x+1, Eq(x, -1)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True)) + assert p3.simplify() == Piecewise((0, Eq(x, -1)), (sin(x), True)) + + +def test_issue_16417(): + z = Symbol('z') + assert unchanged(Piecewise, (1, Or(Eq(im(z), 0), Gt(re(z), 0))), (2, True)) + + x = Symbol('x') + assert unchanged(Piecewise, (S.Pi, re(x) < 0), + (0, Or(re(x) > 0, Ne(im(x), 0))), + (S.NaN, True)) + r = Symbol('r', real=True) + p = Piecewise((S.Pi, re(r) < 0), + (0, Or(re(r) > 0, Ne(im(r), 0))), + (S.NaN, True)) + assert p == Piecewise((S.Pi, r < 0), + (0, r > 0), + (S.NaN, True), evaluate=False) + # Does not work since imaginary != 0... + #i = Symbol('i', imaginary=True) + #p = Piecewise((S.Pi, re(i) < 0), + # (0, Or(re(i) > 0, Ne(im(i), 0))), + # (S.NaN, True)) + #assert p == Piecewise((0, Ne(im(i), 0)), + # (S.NaN, True), evaluate=False) + i = I*r + p = Piecewise((S.Pi, re(i) < 0), + (0, Or(re(i) > 0, Ne(im(i), 0))), + (S.NaN, True)) + assert p == Piecewise((0, Ne(im(i), 0)), + (S.NaN, True), evaluate=False) + assert p == Piecewise((0, Ne(r, 0)), + (S.NaN, True), evaluate=False) + + +def test_eval_rewrite_as_KroneckerDelta(): + x, y, z, n, t, m = symbols('x y z n t m') + K = KroneckerDelta + f = lambda p: expand(p.rewrite(K)) + + p1 = Piecewise((0, Eq(x, y)), (1, True)) + assert f(p1) == 1 - K(x, y) + + p2 = Piecewise((x, Eq(y,0)), (z, Eq(t,0)), (n, True)) + assert f(p2) == n*K(0, t)*K(0, y) - n*K(0, t) - n*K(0, y) + n + \ + x*K(0, y) - z*K(0, t)*K(0, y) + z*K(0, t) + + p3 = Piecewise((1, Ne(x, y)), (0, True)) + assert f(p3) == 1 - K(x, y) + + p4 = Piecewise((1, Eq(x, 3)), (4, True), (5, True)) + assert f(p4) == 4 - 3*K(3, x) + + p5 = Piecewise((3, Ne(x, 2)), (4, Eq(y, 2)), (5, True)) + assert f(p5) == -K(2, x)*K(2, y) + 2*K(2, x) + 3 + + p6 = Piecewise((0, Ne(x, 1) & Ne(y, 4)), (1, True)) + assert f(p6) == -K(1, x)*K(4, y) + K(1, x) + K(4, y) + + p7 = Piecewise((2, Eq(y, 3) & Ne(x, 2)), (1, True)) + assert f(p7) == -K(2, x)*K(3, y) + K(3, y) + 1 + + p8 = Piecewise((4, Eq(x, 3) & Ne(y, 2)), (1, True)) + assert f(p8) == -3*K(2, y)*K(3, x) + 3*K(3, x) + 1 + + p9 = Piecewise((6, Eq(x, 4) & Eq(y, 1)), (1, True)) + assert f(p9) == 5 * K(1, y) * K(4, x) + 1 + + p10 = Piecewise((4, Ne(x, -4) | Ne(y, 1)), (1, True)) + assert f(p10) == -3 * K(-4, x) * K(1, y) + 4 + + p11 = Piecewise((1, Eq(y, 2) | Ne(x, -3)), (2, True)) + assert f(p11) == -K(-3, x)*K(2, y) + K(-3, x) + 1 + + p12 = Piecewise((-1, Eq(x, 1) | Ne(y, 3)), (1, True)) + assert f(p12) == -2*K(1, x)*K(3, y) + 2*K(3, y) - 1 + + p13 = Piecewise((3, Eq(x, 2) | Eq(y, 4)), (1, True)) + assert f(p13) == -2*K(2, x)*K(4, y) + 2*K(2, x) + 2*K(4, y) + 1 + + p14 = Piecewise((1, Ne(x, 0) | Ne(y, 1)), (3, True)) + assert f(p14) == 2 * K(0, x) * K(1, y) + 1 + + p15 = Piecewise((2, Eq(x, 3) | Ne(y, 2)), (3, Eq(x, 4) & Eq(y, 5)), (1, True)) + assert f(p15) == -2*K(2, y)*K(3, x)*K(4, x)*K(5, y) + K(2, y)*K(3, x) + \ + 2*K(2, y)*K(4, x)*K(5, y) - K(2, y) + 2 + + p16 = Piecewise((0, Ne(m, n)), (1, True))*Piecewise((0, Ne(n, t)), (1, True))\ + *Piecewise((0, Ne(n, x)), (1, True)) - Piecewise((0, Ne(t, x)), (1, True)) + assert f(p16) == K(m, n)*K(n, t)*K(n, x) - K(t, x) + + p17 = Piecewise((0, Ne(t, x) & (Ne(m, n) | Ne(n, t) | Ne(n, x))), + (1, Ne(t, x)), (-1, Ne(m, n) | Ne(n, t) | Ne(n, x)), (0, True)) + assert f(p17) == K(m, n)*K(n, t)*K(n, x) - K(t, x) + + p18 = Piecewise((-4, Eq(y, 1) | (Eq(x, -5) & Eq(x, z))), (4, True)) + assert f(p18) == 8*K(-5, x)*K(1, y)*K(x, z) - 8*K(-5, x)*K(x, z) - 8*K(1, y) + 4 + + p19 = Piecewise((0, x > 2), (1, True)) + assert f(p19) == p19 + + p20 = Piecewise((0, And(x < 2, x > -5)), (1, True)) + assert f(p20) == p20 + + p21 = Piecewise((0, Or(x > 1, x < 0)), (1, True)) + assert f(p21) == p21 + + p22 = Piecewise((0, ~((Eq(y, -1) | Ne(x, 0)) & (Ne(x, 1) | Ne(y, -1)))), (1, True)) + assert f(p22) == K(-1, y)*K(0, x) - K(-1, y)*K(1, x) - K(0, x) + 1 + + +@slow +def test_identical_conds_issue(): + from sympy.stats import Uniform, density + u1 = Uniform('u1', 0, 1) + u2 = Uniform('u2', 0, 1) + # Result is quite big, so not really important here (and should ideally be + # simpler). Should not give an exception though. + density(u1 + u2) + + +def test_issue_7370(): + f = Piecewise((1, x <= 2400)) + v = integrate(f, (x, 0, Float("252.4", 30))) + assert str(v) == '252.400000000000000000000000000' + + +def test_issue_14933(): + x = Symbol('x') + y = Symbol('y') + + inp = MatrixSymbol('inp', 1, 1) + rep_dict = {y: inp[0, 0], x: inp[0, 0]} + + p = Piecewise((1, ITE(y > 0, x < 0, True))) + assert p.xreplace(rep_dict) == Piecewise((1, ITE(inp[0, 0] > 0, inp[0, 0] < 0, True))) + + +def test_issue_16715(): + raises(NotImplementedError, lambda: Piecewise((x, x<0), (0, y>1)).as_expr_set_pairs()) + + +def test_issue_20360(): + t, tau = symbols("t tau", real=True) + n = symbols("n", integer=True) + lam = pi * (n - S.Half) + eq = integrate(exp(lam * tau), (tau, 0, t)) + assert eq.simplify() == (2*exp(pi*t*(2*n - 1)/2) - 2)/(pi*(2*n - 1)) + + +def test_piecewise_eval(): + # XXX these tests might need modification if this + # simplification is moved out of eval and into + # boolalg or Piecewise simplification functions + f = lambda x: x.args[0].cond + # unsimplified + assert f(Piecewise((x, (x > -oo) & (x < 3))) + ) == ((x > -oo) & (x < 3)) + assert f(Piecewise((x, (x > -oo) & (x < oo))) + ) == ((x > -oo) & (x < oo)) + assert f(Piecewise((x, (x > -3) & (x < 3))) + ) == ((x > -3) & (x < 3)) + assert f(Piecewise((x, (x > -3) & (x < oo))) + ) == ((x > -3) & (x < oo)) + assert f(Piecewise((x, (x <= 3) & (x > -oo))) + ) == ((x <= 3) & (x > -oo)) + assert f(Piecewise((x, (x <= 3) & (x > -3))) + ) == ((x <= 3) & (x > -3)) + assert f(Piecewise((x, (x >= -3) & (x < 3))) + ) == ((x >= -3) & (x < 3)) + assert f(Piecewise((x, (x >= -3) & (x < oo))) + ) == ((x >= -3) & (x < oo)) + assert f(Piecewise((x, (x >= -3) & (x <= 3))) + ) == ((x >= -3) & (x <= 3)) + # could simplify by keeping only the first + # arg of result + assert f(Piecewise((x, (x <= oo) & (x > -oo))) + ) == (x > -oo) & (x <= oo) + assert f(Piecewise((x, (x <= oo) & (x > -3))) + ) == (x > -3) & (x <= oo) + assert f(Piecewise((x, (x >= -oo) & (x < 3))) + ) == (x < 3) & (x >= -oo) + assert f(Piecewise((x, (x >= -oo) & (x < oo))) + ) == (x < oo) & (x >= -oo) + assert f(Piecewise((x, (x >= -oo) & (x <= 3))) + ) == (x <= 3) & (x >= -oo) + assert f(Piecewise((x, (x >= -oo) & (x <= oo))) + ) == (x <= oo) & (x >= -oo) # but cannot be True unless x is real + assert f(Piecewise((x, (x >= -3) & (x <= oo))) + ) == (x >= -3) & (x <= oo) + assert f(Piecewise((x, (Abs(arg(a)) <= 1) | (Abs(arg(a)) < 1))) + ) == (Abs(arg(a)) <= 1) | (Abs(arg(a)) < 1) + + +def test_issue_22533(): + x = Symbol('x', real=True) + f = Piecewise((-1 / x, x <= 0), (1 / x, True)) + assert integrate(f, x) == Piecewise((-log(x), x <= 0), (log(x), True)) + + +def test_issue_24072(): + assert Piecewise((1, x > 1), (2, x <= 1), (3, x <= 1) + ) == Piecewise((1, x > 1), (2, True)) + + +def test_piecewise__eval_is_meromorphic(): + """ Issue 24127: Tests eval_is_meromorphic auxiliary method """ + x = symbols('x', real=True) + f = Piecewise((1, x < 0), (sqrt(1 - x), True)) + assert f.is_meromorphic(x, I) is None + assert f.is_meromorphic(x, -1) == True + assert f.is_meromorphic(x, 0) == None + assert f.is_meromorphic(x, 1) == False + assert f.is_meromorphic(x, 2) == True + assert f.is_meromorphic(x, Symbol('a')) == None + assert f.is_meromorphic(x, Symbol('a', real=True)) == None diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_trigonometric.py b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_trigonometric.py new file mode 100644 index 0000000000000000000000000000000000000000..37cda80f984c6f59cdb44d608f85e6b2623f97d9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_trigonometric.py @@ -0,0 +1,2233 @@ +from sympy.calculus.accumulationbounds import AccumBounds +from sympy.core.add import Add +from sympy.core.function import (Lambda, diff) +from sympy.core.mod import Mod +from sympy.core.mul import Mul +from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (arg, conjugate, im, re) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.hyperbolic import (acoth, asinh, atanh, cosh, coth, sinh, tanh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, acot, acsc, asec, asin, atan, atan2, + cos, cot, csc, sec, sin, sinc, tan) +from sympy.functions.special.bessel import (besselj, jn) +from sympy.functions.special.delta_functions import Heaviside +from sympy.matrices.dense import Matrix +from sympy.polys.polytools import (cancel, gcd) +from sympy.series.limits import limit +from sympy.series.order import O +from sympy.series.series import series +from sympy.sets.fancysets import ImageSet +from sympy.sets.sets import (FiniteSet, Interval) +from sympy.simplify.simplify import simplify +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError, PoleError +from sympy.core.relational import Ne, Eq +from sympy.functions.elementary.piecewise import Piecewise +from sympy.sets.setexpr import SetExpr +from sympy.testing.pytest import XFAIL, slow, raises + + +x, y, z = symbols('x y z') +r = Symbol('r', real=True) +k, m = symbols('k m', integer=True) +p = Symbol('p', positive=True) +n = Symbol('n', negative=True) +np = Symbol('p', nonpositive=True) +nn = Symbol('n', nonnegative=True) +nz = Symbol('nz', nonzero=True) +ep = Symbol('ep', extended_positive=True) +en = Symbol('en', extended_negative=True) +enp = Symbol('ep', extended_nonpositive=True) +enn = Symbol('en', extended_nonnegative=True) +enz = Symbol('enz', extended_nonzero=True) +a = Symbol('a', algebraic=True) +na = Symbol('na', nonzero=True, algebraic=True) + + +def test_sin(): + x, y = symbols('x y') + z = symbols('z', imaginary=True) + + assert sin.nargs == FiniteSet(1) + assert sin(nan) is nan + assert sin(zoo) is nan + + assert sin(oo) == AccumBounds(-1, 1) + assert sin(oo) - sin(oo) == AccumBounds(-2, 2) + assert sin(oo*I) == oo*I + assert sin(-oo*I) == -oo*I + assert 0*sin(oo) is S.Zero + assert 0/sin(oo) is S.Zero + assert 0 + sin(oo) == AccumBounds(-1, 1) + assert 5 + sin(oo) == AccumBounds(4, 6) + + assert sin(0) == 0 + + assert sin(z*I) == I*sinh(z) + assert sin(asin(x)) == x + assert sin(atan(x)) == x / sqrt(1 + x**2) + assert sin(acos(x)) == sqrt(1 - x**2) + assert sin(acot(x)) == 1 / (sqrt(1 + 1 / x**2) * x) + assert sin(acsc(x)) == 1 / x + assert sin(asec(x)) == sqrt(1 - 1 / x**2) + assert sin(atan2(y, x)) == y / sqrt(x**2 + y**2) + + assert sin(pi*I) == sinh(pi)*I + assert sin(-pi*I) == -sinh(pi)*I + assert sin(-2*I) == -sinh(2)*I + + assert sin(pi) == 0 + assert sin(-pi) == 0 + assert sin(2*pi) == 0 + assert sin(-2*pi) == 0 + assert sin(-3*10**73*pi) == 0 + assert sin(7*10**103*pi) == 0 + + assert sin(pi/2) == 1 + assert sin(-pi/2) == -1 + assert sin(pi*Rational(5, 2)) == 1 + assert sin(pi*Rational(7, 2)) == -1 + + ne = symbols('ne', integer=True, even=False) + e = symbols('e', even=True) + assert sin(pi*ne/2) == (-1)**(ne/2 - S.Half) + assert sin(pi*k/2).func == sin + assert sin(pi*e/2) == 0 + assert sin(pi*k) == 0 + assert sin(pi*k).subs(k, 3) == sin(pi*k/2).subs(k, 6) # issue 8298 + + assert sin(pi/3) == S.Half*sqrt(3) + assert sin(pi*Rational(-2, 3)) == Rational(-1, 2)*sqrt(3) + + assert sin(pi/4) == S.Half*sqrt(2) + assert sin(-pi/4) == Rational(-1, 2)*sqrt(2) + assert sin(pi*Rational(17, 4)) == S.Half*sqrt(2) + assert sin(pi*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2) + + assert sin(pi/6) == S.Half + assert sin(-pi/6) == Rational(-1, 2) + assert sin(pi*Rational(7, 6)) == Rational(-1, 2) + assert sin(pi*Rational(-5, 6)) == Rational(-1, 2) + + assert sin(pi*Rational(1, 5)) == sqrt((5 - sqrt(5)) / 8) + assert sin(pi*Rational(2, 5)) == sqrt((5 + sqrt(5)) / 8) + assert sin(pi*Rational(3, 5)) == sin(pi*Rational(2, 5)) + assert sin(pi*Rational(4, 5)) == sin(pi*Rational(1, 5)) + assert sin(pi*Rational(6, 5)) == -sin(pi*Rational(1, 5)) + assert sin(pi*Rational(8, 5)) == -sin(pi*Rational(2, 5)) + + assert sin(pi*Rational(-1273, 5)) == -sin(pi*Rational(2, 5)) + + assert sin(pi/8) == sqrt((2 - sqrt(2))/4) + + assert sin(pi/10) == Rational(-1, 4) + sqrt(5)/4 + + assert sin(pi/12) == -sqrt(2)/4 + sqrt(6)/4 + assert sin(pi*Rational(5, 12)) == sqrt(2)/4 + sqrt(6)/4 + assert sin(pi*Rational(-7, 12)) == -sqrt(2)/4 - sqrt(6)/4 + assert sin(pi*Rational(-11, 12)) == sqrt(2)/4 - sqrt(6)/4 + + assert sin(pi*Rational(104, 105)) == sin(pi/105) + assert sin(pi*Rational(106, 105)) == -sin(pi/105) + + assert sin(pi*Rational(-104, 105)) == -sin(pi/105) + assert sin(pi*Rational(-106, 105)) == sin(pi/105) + + assert sin(x*I) == sinh(x)*I + + assert sin(k*pi) == 0 + assert sin(17*k*pi) == 0 + assert sin(2*k*pi + 4) == sin(4) + assert sin(2*k*pi + m*pi + 1) == (-1)**(m + 2*k)*sin(1) + + assert sin(k*pi*I) == sinh(k*pi)*I + + assert sin(r).is_real is True + + assert sin(0, evaluate=False).is_algebraic + assert sin(a).is_algebraic is None + assert sin(na).is_algebraic is False + q = Symbol('q', rational=True) + assert sin(pi*q).is_algebraic + qn = Symbol('qn', rational=True, nonzero=True) + assert sin(qn).is_rational is False + assert sin(q).is_rational is None # issue 8653 + + assert isinstance(sin( re(x) - im(y)), sin) is True + assert isinstance(sin(-re(x) + im(y)), sin) is False + + assert sin(SetExpr(Interval(0, 1))) == SetExpr(ImageSet(Lambda(x, sin(x)), + Interval(0, 1))) + + for d in list(range(1, 22)) + [60, 85]: + for n in range(d*2 + 1): + x = n*pi/d + e = abs( float(sin(x)) - sin(float(x)) ) + assert e < 1e-12 + + assert sin(0, evaluate=False).is_zero is True + assert sin(k*pi, evaluate=False).is_zero is True + + assert sin(Add(1, -1, evaluate=False), evaluate=False).is_zero is True + + +def test_sin_cos(): + for d in [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 24, 30, 40, 60, 120]: # list is not exhaustive... + for n in range(-2*d, d*2): + x = n*pi/d + assert sin(x + pi/2) == cos(x), "fails for %d*pi/%d" % (n, d) + assert sin(x - pi/2) == -cos(x), "fails for %d*pi/%d" % (n, d) + assert sin(x) == cos(x - pi/2), "fails for %d*pi/%d" % (n, d) + assert -sin(x) == cos(x + pi/2), "fails for %d*pi/%d" % (n, d) + + +def test_sin_series(): + assert sin(x).series(x, 0, 9) == \ + x - x**3/6 + x**5/120 - x**7/5040 + O(x**9) + + +def test_sin_rewrite(): + assert sin(x).rewrite(exp) == -I*(exp(I*x) - exp(-I*x))/2 + assert sin(x).rewrite(tan) == 2*tan(x/2)/(1 + tan(x/2)**2) + assert sin(x).rewrite(cot) == \ + Piecewise((0, Eq(im(x), 0) & Eq(Mod(x, pi), 0)), + (2*cot(x/2)/(cot(x/2)**2 + 1), True)) + assert sin(sinh(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, sinh(3)).n() + assert sin(cosh(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cosh(3)).n() + assert sin(tanh(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, tanh(3)).n() + assert sin(coth(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, coth(3)).n() + assert sin(sin(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, sin(3)).n() + assert sin(cos(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cos(3)).n() + assert sin(tan(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, tan(3)).n() + assert sin(cot(x)).rewrite( + exp).subs(x, 3).n() == sin(x).rewrite(exp).subs(x, cot(3)).n() + assert sin(log(x)).rewrite(Pow) == I*x**-I / 2 - I*x**I /2 + assert sin(x).rewrite(csc) == 1/csc(x) + assert sin(x).rewrite(cos) == cos(x - pi / 2, evaluate=False) + assert sin(x).rewrite(sec) == 1 / sec(x - pi / 2, evaluate=False) + assert sin(cos(x)).rewrite(Pow) == sin(cos(x)) + assert sin(x).rewrite(besselj) == sqrt(pi*x/2)*besselj(S.Half, x) + assert sin(x).rewrite(besselj).subs(x, 0) == sin(0) + + +def _test_extrig(f, i, e): + from sympy.core.function import expand_trig + assert unchanged(f, i) + assert expand_trig(f(i)) == f(i) + # testing directly instead of with .expand(trig=True) + # because the other expansions undo the unevaluated Mul + assert expand_trig(f(Mul(i, 1, evaluate=False))) == e + assert abs(f(i) - e).n() < 1e-10 + + +def test_sin_expansion(): + # Note: these formulas are not unique. The ones here come from the + # Chebyshev formulas. + assert sin(x + y).expand(trig=True) == sin(x)*cos(y) + cos(x)*sin(y) + assert sin(x - y).expand(trig=True) == sin(x)*cos(y) - cos(x)*sin(y) + assert sin(y - x).expand(trig=True) == cos(x)*sin(y) - sin(x)*cos(y) + assert sin(2*x).expand(trig=True) == 2*sin(x)*cos(x) + assert sin(3*x).expand(trig=True) == -4*sin(x)**3 + 3*sin(x) + assert sin(4*x).expand(trig=True) == -8*sin(x)**3*cos(x) + 4*sin(x)*cos(x) + assert sin(2*pi/17).expand(trig=True) == sin(2*pi/17, evaluate=False) + assert sin(x+pi/17).expand(trig=True) == sin(pi/17)*cos(x) + cos(pi/17)*sin(x) + _test_extrig(sin, 2, 2*sin(1)*cos(1)) + _test_extrig(sin, 3, -4*sin(1)**3 + 3*sin(1)) + + +def test_sin_AccumBounds(): + assert sin(AccumBounds(-oo, oo)) == AccumBounds(-1, 1) + assert sin(AccumBounds(0, oo)) == AccumBounds(-1, 1) + assert sin(AccumBounds(-oo, 0)) == AccumBounds(-1, 1) + assert sin(AccumBounds(0, 2*S.Pi)) == AccumBounds(-1, 1) + assert sin(AccumBounds(0, S.Pi*Rational(3, 4))) == AccumBounds(0, 1) + assert sin(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(7, 4))) == AccumBounds(-1, sin(S.Pi*Rational(3, 4))) + assert sin(AccumBounds(S.Pi/4, S.Pi/3)) == AccumBounds(sin(S.Pi/4), sin(S.Pi/3)) + assert sin(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(5, 6))) == AccumBounds(sin(S.Pi*Rational(5, 6)), sin(S.Pi*Rational(3, 4))) + + +def test_sin_fdiff(): + assert sin(x).fdiff() == cos(x) + raises(ArgumentIndexError, lambda: sin(x).fdiff(2)) + + +def test_trig_symmetry(): + assert sin(-x) == -sin(x) + assert cos(-x) == cos(x) + assert tan(-x) == -tan(x) + assert cot(-x) == -cot(x) + assert sin(x + pi) == -sin(x) + assert sin(x + 2*pi) == sin(x) + assert sin(x + 3*pi) == -sin(x) + assert sin(x + 4*pi) == sin(x) + assert sin(x - 5*pi) == -sin(x) + assert cos(x + pi) == -cos(x) + assert cos(x + 2*pi) == cos(x) + assert cos(x + 3*pi) == -cos(x) + assert cos(x + 4*pi) == cos(x) + assert cos(x - 5*pi) == -cos(x) + assert tan(x + pi) == tan(x) + assert tan(x - 3*pi) == tan(x) + assert cot(x + pi) == cot(x) + assert cot(x - 3*pi) == cot(x) + assert sin(pi/2 - x) == cos(x) + assert sin(pi*Rational(3, 2) - x) == -cos(x) + assert sin(pi*Rational(5, 2) - x) == cos(x) + assert cos(pi/2 - x) == sin(x) + assert cos(pi*Rational(3, 2) - x) == -sin(x) + assert cos(pi*Rational(5, 2) - x) == sin(x) + assert tan(pi/2 - x) == cot(x) + assert tan(pi*Rational(3, 2) - x) == cot(x) + assert tan(pi*Rational(5, 2) - x) == cot(x) + assert cot(pi/2 - x) == tan(x) + assert cot(pi*Rational(3, 2) - x) == tan(x) + assert cot(pi*Rational(5, 2) - x) == tan(x) + assert sin(pi/2 + x) == cos(x) + assert cos(pi/2 + x) == -sin(x) + assert tan(pi/2 + x) == -cot(x) + assert cot(pi/2 + x) == -tan(x) + + +def test_cos(): + x, y = symbols('x y') + + assert cos.nargs == FiniteSet(1) + assert cos(nan) is nan + + assert cos(oo) == AccumBounds(-1, 1) + assert cos(oo) - cos(oo) == AccumBounds(-2, 2) + assert cos(oo*I) is oo + assert cos(-oo*I) is oo + assert cos(zoo) is nan + + assert cos(0) == 1 + + assert cos(acos(x)) == x + assert cos(atan(x)) == 1 / sqrt(1 + x**2) + assert cos(asin(x)) == sqrt(1 - x**2) + assert cos(acot(x)) == 1 / sqrt(1 + 1 / x**2) + assert cos(acsc(x)) == sqrt(1 - 1 / x**2) + assert cos(asec(x)) == 1 / x + assert cos(atan2(y, x)) == x / sqrt(x**2 + y**2) + + assert cos(pi*I) == cosh(pi) + assert cos(-pi*I) == cosh(pi) + assert cos(-2*I) == cosh(2) + + assert cos(pi/2) == 0 + assert cos(-pi/2) == 0 + assert cos(pi/2) == 0 + assert cos(-pi/2) == 0 + assert cos((-3*10**73 + 1)*pi/2) == 0 + assert cos((7*10**103 + 1)*pi/2) == 0 + + n = symbols('n', integer=True, even=False) + e = symbols('e', even=True) + assert cos(pi*n/2) == 0 + assert cos(pi*e/2) == (-1)**(e/2) + + assert cos(pi) == -1 + assert cos(-pi) == -1 + assert cos(2*pi) == 1 + assert cos(5*pi) == -1 + assert cos(8*pi) == 1 + + assert cos(pi/3) == S.Half + assert cos(pi*Rational(-2, 3)) == Rational(-1, 2) + + assert cos(pi/4) == S.Half*sqrt(2) + assert cos(-pi/4) == S.Half*sqrt(2) + assert cos(pi*Rational(11, 4)) == Rational(-1, 2)*sqrt(2) + assert cos(pi*Rational(-3, 4)) == Rational(-1, 2)*sqrt(2) + + assert cos(pi/6) == S.Half*sqrt(3) + assert cos(-pi/6) == S.Half*sqrt(3) + assert cos(pi*Rational(7, 6)) == Rational(-1, 2)*sqrt(3) + assert cos(pi*Rational(-5, 6)) == Rational(-1, 2)*sqrt(3) + + assert cos(pi*Rational(1, 5)) == (sqrt(5) + 1)/4 + assert cos(pi*Rational(2, 5)) == (sqrt(5) - 1)/4 + assert cos(pi*Rational(3, 5)) == -cos(pi*Rational(2, 5)) + assert cos(pi*Rational(4, 5)) == -cos(pi*Rational(1, 5)) + assert cos(pi*Rational(6, 5)) == -cos(pi*Rational(1, 5)) + assert cos(pi*Rational(8, 5)) == cos(pi*Rational(2, 5)) + + assert cos(pi*Rational(-1273, 5)) == -cos(pi*Rational(2, 5)) + + assert cos(pi/8) == sqrt((2 + sqrt(2))/4) + + assert cos(pi/12) == sqrt(2)/4 + sqrt(6)/4 + assert cos(pi*Rational(5, 12)) == -sqrt(2)/4 + sqrt(6)/4 + assert cos(pi*Rational(7, 12)) == sqrt(2)/4 - sqrt(6)/4 + assert cos(pi*Rational(11, 12)) == -sqrt(2)/4 - sqrt(6)/4 + + assert cos(pi*Rational(104, 105)) == -cos(pi/105) + assert cos(pi*Rational(106, 105)) == -cos(pi/105) + + assert cos(pi*Rational(-104, 105)) == -cos(pi/105) + assert cos(pi*Rational(-106, 105)) == -cos(pi/105) + + assert cos(x*I) == cosh(x) + assert cos(k*pi*I) == cosh(k*pi) + + assert cos(r).is_real is True + + assert cos(0, evaluate=False).is_algebraic + assert cos(a).is_algebraic is None + assert cos(na).is_algebraic is False + q = Symbol('q', rational=True) + assert cos(pi*q).is_algebraic + assert cos(pi*Rational(2, 7)).is_algebraic + + assert cos(k*pi) == (-1)**k + assert cos(2*k*pi) == 1 + assert cos(0, evaluate=False).is_zero is False + assert cos(Rational(1, 2)).is_zero is False + # The following test will return None as the result, but really it should + # be True even if it is not always possible to resolve an assumptions query. + assert cos(asin(-1, evaluate=False), evaluate=False).is_zero is None + for d in list(range(1, 22)) + [60, 85]: + for n in range(2*d + 1): + x = n*pi/d + e = abs( float(cos(x)) - cos(float(x)) ) + assert e < 1e-12 + + +def test_issue_6190(): + c = Float('123456789012345678901234567890.25', '') + for cls in [sin, cos, tan, cot]: + assert cls(c*pi) == cls(pi/4) + assert cls(4.125*pi) == cls(pi/8) + assert cls(4.7*pi) == cls((4.7 % 2)*pi) + + +def test_cos_series(): + assert cos(x).series(x, 0, 9) == \ + 1 - x**2/2 + x**4/24 - x**6/720 + x**8/40320 + O(x**9) + + +def test_cos_rewrite(): + assert cos(x).rewrite(exp) == exp(I*x)/2 + exp(-I*x)/2 + assert cos(x).rewrite(tan) == (1 - tan(x/2)**2)/(1 + tan(x/2)**2) + assert cos(x).rewrite(cot) == \ + Piecewise((1, Eq(im(x), 0) & Eq(Mod(x, 2*pi), 0)), + ((cot(x/2)**2 - 1)/(cot(x/2)**2 + 1), True)) + assert cos(sinh(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, sinh(3)).n() + assert cos(cosh(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cosh(3)).n() + assert cos(tanh(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, tanh(3)).n() + assert cos(coth(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, coth(3)).n() + assert cos(sin(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, sin(3)).n() + assert cos(cos(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cos(3)).n() + assert cos(tan(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, tan(3)).n() + assert cos(cot(x)).rewrite( + exp).subs(x, 3).n() == cos(x).rewrite(exp).subs(x, cot(3)).n() + assert cos(log(x)).rewrite(Pow) == x**I/2 + x**-I/2 + assert cos(x).rewrite(sec) == 1/sec(x) + assert cos(x).rewrite(sin) == sin(x + pi/2, evaluate=False) + assert cos(x).rewrite(csc) == 1/csc(-x + pi/2, evaluate=False) + assert cos(sin(x)).rewrite(Pow) == cos(sin(x)) + assert cos(x).rewrite(besselj) == Piecewise( + (sqrt(pi*x/2)*besselj(-S.Half, x), Ne(x, 0)), + (1, True) + ) + assert cos(x).rewrite(besselj).subs(x, 0) == cos(0) + + +def test_cos_expansion(): + assert cos(x + y).expand(trig=True) == cos(x)*cos(y) - sin(x)*sin(y) + assert cos(x - y).expand(trig=True) == cos(x)*cos(y) + sin(x)*sin(y) + assert cos(y - x).expand(trig=True) == cos(x)*cos(y) + sin(x)*sin(y) + assert cos(2*x).expand(trig=True) == 2*cos(x)**2 - 1 + assert cos(3*x).expand(trig=True) == 4*cos(x)**3 - 3*cos(x) + assert cos(4*x).expand(trig=True) == 8*cos(x)**4 - 8*cos(x)**2 + 1 + assert cos(2*pi/17).expand(trig=True) == cos(2*pi/17, evaluate=False) + assert cos(x+pi/17).expand(trig=True) == cos(pi/17)*cos(x) - sin(pi/17)*sin(x) + _test_extrig(cos, 2, 2*cos(1)**2 - 1) + _test_extrig(cos, 3, 4*cos(1)**3 - 3*cos(1)) + + +def test_cos_AccumBounds(): + assert cos(AccumBounds(-oo, oo)) == AccumBounds(-1, 1) + assert cos(AccumBounds(0, oo)) == AccumBounds(-1, 1) + assert cos(AccumBounds(-oo, 0)) == AccumBounds(-1, 1) + assert cos(AccumBounds(0, 2*S.Pi)) == AccumBounds(-1, 1) + assert cos(AccumBounds(-S.Pi/3, S.Pi/4)) == AccumBounds(cos(-S.Pi/3), 1) + assert cos(AccumBounds(S.Pi*Rational(3, 4), S.Pi*Rational(5, 4))) == AccumBounds(-1, cos(S.Pi*Rational(3, 4))) + assert cos(AccumBounds(S.Pi*Rational(5, 4), S.Pi*Rational(4, 3))) == AccumBounds(cos(S.Pi*Rational(5, 4)), cos(S.Pi*Rational(4, 3))) + assert cos(AccumBounds(S.Pi/4, S.Pi/3)) == AccumBounds(cos(S.Pi/3), cos(S.Pi/4)) + + +def test_cos_fdiff(): + assert cos(x).fdiff() == -sin(x) + raises(ArgumentIndexError, lambda: cos(x).fdiff(2)) + + +def test_tan(): + assert tan(nan) is nan + + assert tan(zoo) is nan + assert tan(oo) == AccumBounds(-oo, oo) + assert tan(oo) - tan(oo) == AccumBounds(-oo, oo) + assert tan.nargs == FiniteSet(1) + assert tan(oo*I) == I + assert tan(-oo*I) == -I + + assert tan(0) == 0 + + assert tan(atan(x)) == x + assert tan(asin(x)) == x / sqrt(1 - x**2) + assert tan(acos(x)) == sqrt(1 - x**2) / x + assert tan(acot(x)) == 1 / x + assert tan(acsc(x)) == 1 / (sqrt(1 - 1 / x**2) * x) + assert tan(asec(x)) == sqrt(1 - 1 / x**2) * x + assert tan(atan2(y, x)) == y/x + + assert tan(pi*I) == tanh(pi)*I + assert tan(-pi*I) == -tanh(pi)*I + assert tan(-2*I) == -tanh(2)*I + + assert tan(pi) == 0 + assert tan(-pi) == 0 + assert tan(2*pi) == 0 + assert tan(-2*pi) == 0 + assert tan(-3*10**73*pi) == 0 + + assert tan(pi/2) is zoo + assert tan(pi*Rational(3, 2)) is zoo + + assert tan(pi/3) == sqrt(3) + assert tan(pi*Rational(-2, 3)) == sqrt(3) + + assert tan(pi/4) is S.One + assert tan(-pi/4) is S.NegativeOne + assert tan(pi*Rational(17, 4)) is S.One + assert tan(pi*Rational(-3, 4)) is S.One + + assert tan(pi/5) == sqrt(5 - 2*sqrt(5)) + assert tan(pi*Rational(2, 5)) == sqrt(5 + 2*sqrt(5)) + assert tan(pi*Rational(18, 5)) == -sqrt(5 + 2*sqrt(5)) + assert tan(pi*Rational(-16, 5)) == -sqrt(5 - 2*sqrt(5)) + + assert tan(pi/6) == 1/sqrt(3) + assert tan(-pi/6) == -1/sqrt(3) + assert tan(pi*Rational(7, 6)) == 1/sqrt(3) + assert tan(pi*Rational(-5, 6)) == 1/sqrt(3) + + assert tan(pi/8) == -1 + sqrt(2) + assert tan(pi*Rational(3, 8)) == 1 + sqrt(2) # issue 15959 + assert tan(pi*Rational(5, 8)) == -1 - sqrt(2) + assert tan(pi*Rational(7, 8)) == 1 - sqrt(2) + + assert tan(pi/10) == sqrt(1 - 2*sqrt(5)/5) + assert tan(pi*Rational(3, 10)) == sqrt(1 + 2*sqrt(5)/5) + assert tan(pi*Rational(17, 10)) == -sqrt(1 + 2*sqrt(5)/5) + assert tan(pi*Rational(-31, 10)) == -sqrt(1 - 2*sqrt(5)/5) + + assert tan(pi/12) == -sqrt(3) + 2 + assert tan(pi*Rational(5, 12)) == sqrt(3) + 2 + assert tan(pi*Rational(7, 12)) == -sqrt(3) - 2 + assert tan(pi*Rational(11, 12)) == sqrt(3) - 2 + + assert tan(pi/24).radsimp() == -2 - sqrt(3) + sqrt(2) + sqrt(6) + assert tan(pi*Rational(5, 24)).radsimp() == -2 + sqrt(3) - sqrt(2) + sqrt(6) + assert tan(pi*Rational(7, 24)).radsimp() == 2 - sqrt(3) - sqrt(2) + sqrt(6) + assert tan(pi*Rational(11, 24)).radsimp() == 2 + sqrt(3) + sqrt(2) + sqrt(6) + assert tan(pi*Rational(13, 24)).radsimp() == -2 - sqrt(3) - sqrt(2) - sqrt(6) + assert tan(pi*Rational(17, 24)).radsimp() == -2 + sqrt(3) + sqrt(2) - sqrt(6) + assert tan(pi*Rational(19, 24)).radsimp() == 2 - sqrt(3) + sqrt(2) - sqrt(6) + assert tan(pi*Rational(23, 24)).radsimp() == 2 + sqrt(3) - sqrt(2) - sqrt(6) + + assert tan(x*I) == tanh(x)*I + + assert tan(k*pi) == 0 + assert tan(17*k*pi) == 0 + + assert tan(k*pi*I) == tanh(k*pi)*I + + assert tan(r).is_real is None + assert tan(r).is_extended_real is True + + assert tan(0, evaluate=False).is_algebraic + assert tan(a).is_algebraic is None + assert tan(na).is_algebraic is False + + assert tan(pi*Rational(10, 7)) == tan(pi*Rational(3, 7)) + assert tan(pi*Rational(11, 7)) == -tan(pi*Rational(3, 7)) + assert tan(pi*Rational(-11, 7)) == tan(pi*Rational(3, 7)) + + assert tan(pi*Rational(15, 14)) == tan(pi/14) + assert tan(pi*Rational(-15, 14)) == -tan(pi/14) + + assert tan(r).is_finite is None + assert tan(I*r).is_finite is True + + # https://github.com/sympy/sympy/issues/21177 + f = tan(pi*(x + S(3)/2))/(3*x) + assert f.as_leading_term(x) == -1/(3*pi*x**2) + + +def test_tan_series(): + assert tan(x).series(x, 0, 9) == \ + x + x**3/3 + 2*x**5/15 + 17*x**7/315 + O(x**9) + + +def test_tan_rewrite(): + neg_exp, pos_exp = exp(-x*I), exp(x*I) + assert tan(x).rewrite(exp) == I*(neg_exp - pos_exp)/(neg_exp + pos_exp) + assert tan(x).rewrite(sin) == 2*sin(x)**2/sin(2*x) + assert tan(x).rewrite(cos) == cos(x - S.Pi/2, evaluate=False)/cos(x) + assert tan(x).rewrite(cot) == 1/cot(x) + assert tan(sinh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sinh(3)).n() + assert tan(cosh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cosh(3)).n() + assert tan(tanh(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tanh(3)).n() + assert tan(coth(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, coth(3)).n() + assert tan(sin(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sin(3)).n() + assert tan(cos(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cos(3)).n() + assert tan(tan(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tan(3)).n() + assert tan(cot(x)).rewrite(exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cot(3)).n() + assert tan(log(x)).rewrite(Pow) == I*(x**-I - x**I)/(x**-I + x**I) + assert tan(x).rewrite(sec) == sec(x)/sec(x - pi/2, evaluate=False) + assert tan(x).rewrite(csc) == csc(-x + pi/2, evaluate=False)/csc(x) + assert tan(sin(x)).rewrite(Pow) == tan(sin(x)) + assert tan(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == sqrt(sqrt(5)/8 + + Rational(5, 8))/(Rational(-1, 4) + sqrt(5)/4) + assert tan(x).rewrite(besselj) == besselj(S.Half, x)/besselj(-S.Half, x) + assert tan(x).rewrite(besselj).subs(x, 0) == tan(0) + + +@slow +def test_tan_rewrite_slow(): + assert 0 == (cos(pi/34)*tan(pi/34) - sin(pi/34)).rewrite(pow) + assert 0 == (cos(pi/17)*tan(pi/17) - sin(pi/17)).rewrite(pow) + assert tan(pi/19).rewrite(pow) == tan(pi/19) + assert tan(pi*Rational(8, 19)).rewrite(sqrt) == tan(pi*Rational(8, 19)) + assert tan(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == sqrt(sqrt(5)/8 + + Rational(5, 8))/(Rational(-1, 4) + sqrt(5)/4) + + +def test_tan_subs(): + assert tan(x).subs(tan(x), y) == y + assert tan(x).subs(x, y) == tan(y) + assert tan(x).subs(x, S.Pi/2) is zoo + assert tan(x).subs(x, S.Pi*Rational(3, 2)) is zoo + + +def test_tan_expansion(): + assert tan(x + y).expand(trig=True) == ((tan(x) + tan(y))/(1 - tan(x)*tan(y))).expand() + assert tan(x - y).expand(trig=True) == ((tan(x) - tan(y))/(1 + tan(x)*tan(y))).expand() + assert tan(x + y + z).expand(trig=True) == ( + (tan(x) + tan(y) + tan(z) - tan(x)*tan(y)*tan(z))/ + (1 - tan(x)*tan(y) - tan(x)*tan(z) - tan(y)*tan(z))).expand() + assert 0 == tan(2*x).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 7))])*24 - 7 + assert 0 == tan(3*x).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 5))])*55 - 37 + assert 0 == tan(4*x - pi/4).expand(trig=True).rewrite(tan).subs([(tan(x), Rational(1, 5))])*239 - 1 + _test_extrig(tan, 2, 2*tan(1)/(1 - tan(1)**2)) + _test_extrig(tan, 3, (-tan(1)**3 + 3*tan(1))/(1 - 3*tan(1)**2)) + + +def test_tan_AccumBounds(): + assert tan(AccumBounds(-oo, oo)) == AccumBounds(-oo, oo) + assert tan(AccumBounds(S.Pi/3, S.Pi*Rational(2, 3))) == AccumBounds(-oo, oo) + assert tan(AccumBounds(S.Pi/6, S.Pi/3)) == AccumBounds(tan(S.Pi/6), tan(S.Pi/3)) + + +def test_tan_fdiff(): + assert tan(x).fdiff() == tan(x)**2 + 1 + raises(ArgumentIndexError, lambda: tan(x).fdiff(2)) + + +def test_cot(): + assert cot(nan) is nan + + assert cot.nargs == FiniteSet(1) + assert cot(oo*I) == -I + assert cot(-oo*I) == I + assert cot(zoo) is nan + + assert cot(0) is zoo + assert cot(2*pi) is zoo + + assert cot(acot(x)) == x + assert cot(atan(x)) == 1 / x + assert cot(asin(x)) == sqrt(1 - x**2) / x + assert cot(acos(x)) == x / sqrt(1 - x**2) + assert cot(acsc(x)) == sqrt(1 - 1 / x**2) * x + assert cot(asec(x)) == 1 / (sqrt(1 - 1 / x**2) * x) + assert cot(atan2(y, x)) == x/y + + assert cot(pi*I) == -coth(pi)*I + assert cot(-pi*I) == coth(pi)*I + assert cot(-2*I) == coth(2)*I + + assert cot(pi) == cot(2*pi) == cot(3*pi) + assert cot(-pi) == cot(-2*pi) == cot(-3*pi) + + assert cot(pi/2) == 0 + assert cot(-pi/2) == 0 + assert cot(pi*Rational(5, 2)) == 0 + assert cot(pi*Rational(7, 2)) == 0 + + assert cot(pi/3) == 1/sqrt(3) + assert cot(pi*Rational(-2, 3)) == 1/sqrt(3) + + assert cot(pi/4) is S.One + assert cot(-pi/4) is S.NegativeOne + assert cot(pi*Rational(17, 4)) is S.One + assert cot(pi*Rational(-3, 4)) is S.One + + assert cot(pi/6) == sqrt(3) + assert cot(-pi/6) == -sqrt(3) + assert cot(pi*Rational(7, 6)) == sqrt(3) + assert cot(pi*Rational(-5, 6)) == sqrt(3) + + assert cot(pi/8) == 1 + sqrt(2) + assert cot(pi*Rational(3, 8)) == -1 + sqrt(2) + assert cot(pi*Rational(5, 8)) == 1 - sqrt(2) + assert cot(pi*Rational(7, 8)) == -1 - sqrt(2) + + assert cot(pi/12) == sqrt(3) + 2 + assert cot(pi*Rational(5, 12)) == -sqrt(3) + 2 + assert cot(pi*Rational(7, 12)) == sqrt(3) - 2 + assert cot(pi*Rational(11, 12)) == -sqrt(3) - 2 + + assert cot(pi/24).radsimp() == sqrt(2) + sqrt(3) + 2 + sqrt(6) + assert cot(pi*Rational(5, 24)).radsimp() == -sqrt(2) - sqrt(3) + 2 + sqrt(6) + assert cot(pi*Rational(7, 24)).radsimp() == -sqrt(2) + sqrt(3) - 2 + sqrt(6) + assert cot(pi*Rational(11, 24)).radsimp() == sqrt(2) - sqrt(3) - 2 + sqrt(6) + assert cot(pi*Rational(13, 24)).radsimp() == -sqrt(2) + sqrt(3) + 2 - sqrt(6) + assert cot(pi*Rational(17, 24)).radsimp() == sqrt(2) - sqrt(3) + 2 - sqrt(6) + assert cot(pi*Rational(19, 24)).radsimp() == sqrt(2) + sqrt(3) - 2 - sqrt(6) + assert cot(pi*Rational(23, 24)).radsimp() == -sqrt(2) - sqrt(3) - 2 - sqrt(6) + + assert cot(x*I) == -coth(x)*I + assert cot(k*pi*I) == -coth(k*pi)*I + + assert cot(r).is_real is None + assert cot(r).is_extended_real is True + + assert cot(a).is_algebraic is None + assert cot(na).is_algebraic is False + + assert cot(pi*Rational(10, 7)) == cot(pi*Rational(3, 7)) + assert cot(pi*Rational(11, 7)) == -cot(pi*Rational(3, 7)) + assert cot(pi*Rational(-11, 7)) == cot(pi*Rational(3, 7)) + + assert cot(pi*Rational(39, 34)) == cot(pi*Rational(5, 34)) + assert cot(pi*Rational(-41, 34)) == -cot(pi*Rational(7, 34)) + + assert cot(x).is_finite is None + assert cot(r).is_finite is None + i = Symbol('i', imaginary=True) + assert cot(i).is_finite is True + + assert cot(x).subs(x, 3*pi) is zoo + + # https://github.com/sympy/sympy/issues/21177 + f = cot(pi*(x + 4))/(3*x) + assert f.as_leading_term(x) == 1/(3*pi*x**2) + + +def test_tan_cot_sin_cos_evalf(): + assert abs((tan(pi*Rational(8, 15))*cos(pi*Rational(8, 15))/sin(pi*Rational(8, 15)) - 1).evalf()) < 1e-14 + assert abs((cot(pi*Rational(4, 15))*sin(pi*Rational(4, 15))/cos(pi*Rational(4, 15)) - 1).evalf()) < 1e-14 + +@XFAIL +def test_tan_cot_sin_cos_ratsimp(): + assert 1 == (tan(pi*Rational(8, 15))*cos(pi*Rational(8, 15))/sin(pi*Rational(8, 15))).ratsimp() + assert 1 == (cot(pi*Rational(4, 15))*sin(pi*Rational(4, 15))/cos(pi*Rational(4, 15))).ratsimp() + + +def test_cot_series(): + assert cot(x).series(x, 0, 9) == \ + 1/x - x/3 - x**3/45 - 2*x**5/945 - x**7/4725 + O(x**9) + # issue 6210 + assert cot(x**4 + x**5).series(x, 0, 1) == \ + x**(-4) - 1/x**3 + x**(-2) - 1/x + 1 + O(x) + assert cot(pi*(1-x)).series(x, 0, 3) == -1/(pi*x) + pi*x/3 + O(x**3) + assert cot(x).taylor_term(0, x) == 1/x + assert cot(x).taylor_term(2, x) is S.Zero + assert cot(x).taylor_term(3, x) == -x**3/45 + + +def test_cot_rewrite(): + neg_exp, pos_exp = exp(-x*I), exp(x*I) + assert cot(x).rewrite(exp) == I*(pos_exp + neg_exp)/(pos_exp - neg_exp) + assert cot(x).rewrite(sin) == sin(2*x)/(2*(sin(x)**2)) + assert cot(x).rewrite(cos) == cos(x)/cos(x - pi/2, evaluate=False) + assert cot(x).rewrite(tan) == 1/tan(x) + def check(func): + z = cot(func(x)).rewrite(exp) - cot(x).rewrite(exp).subs(x, func(x)) + assert z.rewrite(exp).expand() == 0 + check(sinh) + check(cosh) + check(tanh) + check(coth) + check(sin) + check(cos) + check(tan) + assert cot(log(x)).rewrite(Pow) == -I*(x**-I + x**I)/(x**-I - x**I) + assert cot(x).rewrite(sec) == sec(x - pi / 2, evaluate=False) / sec(x) + assert cot(x).rewrite(csc) == csc(x) / csc(- x + pi / 2, evaluate=False) + assert cot(sin(x)).rewrite(Pow) == cot(sin(x)) + assert cot(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == (Rational(-1, 4) + sqrt(5)/4)/\ + sqrt(sqrt(5)/8 + Rational(5, 8)) + assert cot(x).rewrite(besselj) == besselj(-S.Half, x)/besselj(S.Half, x) + assert cot(x).rewrite(besselj).subs(x, 0) == cot(0) + + +@slow +def test_cot_rewrite_slow(): + assert cot(pi*Rational(4, 34)).rewrite(pow).ratsimp() == \ + (cos(pi*Rational(4, 34))/sin(pi*Rational(4, 34))).rewrite(pow).ratsimp() + assert cot(pi*Rational(4, 17)).rewrite(pow) == \ + (cos(pi*Rational(4, 17))/sin(pi*Rational(4, 17))).rewrite(pow) + assert cot(pi/19).rewrite(pow) == cot(pi/19) + assert cot(pi/19).rewrite(sqrt) == cot(pi/19) + assert cot(pi*Rational(2, 5), evaluate=False).rewrite(sqrt) == \ + (Rational(-1, 4) + sqrt(5)/4) / sqrt(sqrt(5)/8 + Rational(5, 8)) + + +def test_cot_subs(): + assert cot(x).subs(cot(x), y) == y + assert cot(x).subs(x, y) == cot(y) + assert cot(x).subs(x, 0) is zoo + assert cot(x).subs(x, S.Pi) is zoo + + +def test_cot_expansion(): + assert cot(x + y).expand(trig=True).together() == ( + (cot(x)*cot(y) - 1)/(cot(x) + cot(y))) + assert cot(x - y).expand(trig=True).together() == ( + cot(x)*cot(-y) - 1)/(cot(x) + cot(-y)) + assert cot(x + y + z).expand(trig=True).together() == ( + (cot(x)*cot(y)*cot(z) - cot(x) - cot(y) - cot(z))/ + (-1 + cot(x)*cot(y) + cot(x)*cot(z) + cot(y)*cot(z))) + assert cot(3*x).expand(trig=True).together() == ( + (cot(x)**2 - 3)*cot(x)/(3*cot(x)**2 - 1)) + assert cot(2*x).expand(trig=True) == cot(x)/2 - 1/(2*cot(x)) + assert cot(3*x).expand(trig=True).together() == ( + cot(x)**2 - 3)*cot(x)/(3*cot(x)**2 - 1) + assert cot(4*x - pi/4).expand(trig=True).cancel() == ( + -tan(x)**4 + 4*tan(x)**3 + 6*tan(x)**2 - 4*tan(x) - 1 + )/(tan(x)**4 + 4*tan(x)**3 - 6*tan(x)**2 - 4*tan(x) + 1) + _test_extrig(cot, 2, (-1 + cot(1)**2)/(2*cot(1))) + _test_extrig(cot, 3, (-3*cot(1) + cot(1)**3)/(-1 + 3*cot(1)**2)) + + +def test_cot_AccumBounds(): + assert cot(AccumBounds(-oo, oo)) == AccumBounds(-oo, oo) + assert cot(AccumBounds(-S.Pi/3, S.Pi/3)) == AccumBounds(-oo, oo) + assert cot(AccumBounds(S.Pi/6, S.Pi/3)) == AccumBounds(cot(S.Pi/3), cot(S.Pi/6)) + + +def test_cot_fdiff(): + assert cot(x).fdiff() == -cot(x)**2 - 1 + raises(ArgumentIndexError, lambda: cot(x).fdiff(2)) + + +def test_sinc(): + assert isinstance(sinc(x), sinc) + + s = Symbol('s', zero=True) + assert sinc(s) is S.One + assert sinc(S.Infinity) is S.Zero + assert sinc(S.NegativeInfinity) is S.Zero + assert sinc(S.NaN) is S.NaN + assert sinc(S.ComplexInfinity) is S.NaN + + n = Symbol('n', integer=True, nonzero=True) + assert sinc(n*pi) is S.Zero + assert sinc(-n*pi) is S.Zero + assert sinc(pi/2) == 2 / pi + assert sinc(-pi/2) == 2 / pi + assert sinc(pi*Rational(5, 2)) == 2 / (5*pi) + assert sinc(pi*Rational(7, 2)) == -2 / (7*pi) + + assert sinc(-x) == sinc(x) + + assert sinc(x).diff(x) == cos(x)/x - sin(x)/x**2 + assert sinc(x).diff(x) == (sin(x)/x).diff(x) + assert sinc(x).diff(x, x) == (-sin(x) - 2*cos(x)/x + 2*sin(x)/x**2)/x + assert sinc(x).diff(x, x) == (sin(x)/x).diff(x, x) + assert limit(sinc(x).diff(x), x, 0) == 0 + assert limit(sinc(x).diff(x, x), x, 0) == -S(1)/3 + + # https://github.com/sympy/sympy/issues/11402 + # + # assert sinc(x).diff(x) == Piecewise(((x*cos(x) - sin(x)) / x**2, Ne(x, 0)), (0, True)) + # + # assert sinc(x).diff(x).equals(sinc(x).rewrite(sin).diff(x)) + # + # assert sinc(x).diff(x).subs(x, 0) is S.Zero + + assert sinc(x).series() == 1 - x**2/6 + x**4/120 + O(x**6) + + assert sinc(x).rewrite(jn) == jn(0, x) + assert sinc(x).rewrite(sin) == Piecewise((sin(x)/x, Ne(x, 0)), (1, True)) + assert sinc(pi, evaluate=False).is_zero is True + assert sinc(0, evaluate=False).is_zero is False + assert sinc(n*pi, evaluate=False).is_zero is True + assert sinc(x).is_zero is None + xr = Symbol('xr', real=True, nonzero=True) + assert sinc(x).is_real is None + assert sinc(xr).is_real is True + assert sinc(I*xr).is_real is True + assert sinc(I*100).is_real is True + assert sinc(x).is_finite is None + assert sinc(xr).is_finite is True + + +def test_asin(): + assert asin(nan) is nan + + assert asin.nargs == FiniteSet(1) + assert asin(oo) == -I*oo + assert asin(-oo) == I*oo + assert asin(zoo) is zoo + + # Note: asin(-x) = - asin(x) + assert asin(0) == 0 + assert asin(1) == pi/2 + assert asin(-1) == -pi/2 + assert asin(sqrt(3)/2) == pi/3 + assert asin(-sqrt(3)/2) == -pi/3 + assert asin(sqrt(2)/2) == pi/4 + assert asin(-sqrt(2)/2) == -pi/4 + assert asin(sqrt((5 - sqrt(5))/8)) == pi/5 + assert asin(-sqrt((5 - sqrt(5))/8)) == -pi/5 + assert asin(S.Half) == pi/6 + assert asin(Rational(-1, 2)) == -pi/6 + assert asin((sqrt(2 - sqrt(2)))/2) == pi/8 + assert asin(-(sqrt(2 - sqrt(2)))/2) == -pi/8 + assert asin((sqrt(5) - 1)/4) == pi/10 + assert asin(-(sqrt(5) - 1)/4) == -pi/10 + assert asin((sqrt(3) - 1)/sqrt(2**3)) == pi/12 + assert asin(-(sqrt(3) - 1)/sqrt(2**3)) == -pi/12 + + # check round-trip for exact values: + for d in [5, 6, 8, 10, 12]: + for n in range(-(d//2), d//2 + 1): + if gcd(n, d) == 1: + assert asin(sin(n*pi/d)) == n*pi/d + + assert asin(x).diff(x) == 1/sqrt(1 - x**2) + + assert asin(0.2, evaluate=False).is_real is True + assert asin(-2).is_real is False + assert asin(r).is_real is None + + assert asin(-2*I) == -I*asinh(2) + + assert asin(Rational(1, 7), evaluate=False).is_positive is True + assert asin(Rational(-1, 7), evaluate=False).is_positive is False + assert asin(p).is_positive is None + assert asin(sin(Rational(7, 2))) == Rational(-7, 2) + pi + assert asin(sin(Rational(-7, 4))) == Rational(7, 4) - pi + assert unchanged(asin, cos(x)) + + +def test_asin_series(): + assert asin(x).series(x, 0, 9) == \ + x + x**3/6 + 3*x**5/40 + 5*x**7/112 + O(x**9) + t5 = asin(x).taylor_term(5, x) + assert t5 == 3*x**5/40 + assert asin(x).taylor_term(7, x, t5, 0) == 5*x**7/112 + + +def test_asin_leading_term(): + assert asin(x).as_leading_term(x) == x + # Tests concerning branch points + assert asin(x + 1).as_leading_term(x) == pi/2 + assert asin(x - 1).as_leading_term(x) == -pi/2 + assert asin(1/x).as_leading_term(x, cdir=1) == I*log(x) + pi/2 - I*log(2) + assert asin(1/x).as_leading_term(x, cdir=-1) == -I*log(x) - 3*pi/2 + I*log(2) + # Tests concerning points lying on branch cuts + assert asin(I*x + 2).as_leading_term(x, cdir=1) == pi - asin(2) + assert asin(-I*x + 2).as_leading_term(x, cdir=1) == asin(2) + assert asin(I*x - 2).as_leading_term(x, cdir=1) == -asin(2) + assert asin(-I*x - 2).as_leading_term(x, cdir=1) == -pi + asin(2) + # Tests concerning im(ndir) == 0 + assert asin(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == -pi/2 + I*log(2 - sqrt(3)) + assert asin(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(2 - sqrt(3)) + + +def test_asin_rewrite(): + assert asin(x).rewrite(log) == -I*log(I*x + sqrt(1 - x**2)) + assert asin(x).rewrite(atan) == 2*atan(x/(1 + sqrt(1 - x**2))) + assert asin(x).rewrite(acos) == S.Pi/2 - acos(x) + assert asin(x).rewrite(acot) == 2*acot((sqrt(-x**2 + 1) + 1)/x) + assert asin(x).rewrite(asec) == -asec(1/x) + pi/2 + assert asin(x).rewrite(acsc) == acsc(1/x) + + +def test_asin_fdiff(): + assert asin(x).fdiff() == 1/sqrt(1 - x**2) + raises(ArgumentIndexError, lambda: asin(x).fdiff(2)) + + +def test_acos(): + assert acos(nan) is nan + assert acos(zoo) is zoo + + assert acos.nargs == FiniteSet(1) + assert acos(oo) == I*oo + assert acos(-oo) == -I*oo + + # Note: acos(-x) = pi - acos(x) + assert acos(0) == pi/2 + assert acos(S.Half) == pi/3 + assert acos(Rational(-1, 2)) == pi*Rational(2, 3) + assert acos(1) == 0 + assert acos(-1) == pi + assert acos(sqrt(2)/2) == pi/4 + assert acos(-sqrt(2)/2) == pi*Rational(3, 4) + + # check round-trip for exact values: + for d in [5, 6, 8, 10, 12]: + for num in range(d): + if gcd(num, d) == 1: + assert acos(cos(num*pi/d)) == num*pi/d + + assert acos(2*I) == pi/2 - asin(2*I) + + assert acos(x).diff(x) == -1/sqrt(1 - x**2) + + assert acos(0.2).is_real is True + assert acos(-2).is_real is False + assert acos(r).is_real is None + + assert acos(Rational(1, 7), evaluate=False).is_positive is True + assert acos(Rational(-1, 7), evaluate=False).is_positive is True + assert acos(Rational(3, 2), evaluate=False).is_positive is False + assert acos(p).is_positive is None + + assert acos(2 + p).conjugate() != acos(10 + p) + assert acos(-3 + n).conjugate() != acos(-3 + n) + assert acos(Rational(1, 3)).conjugate() == acos(Rational(1, 3)) + assert acos(Rational(-1, 3)).conjugate() == acos(Rational(-1, 3)) + assert acos(p + n*I).conjugate() == acos(p - n*I) + assert acos(z).conjugate() != acos(conjugate(z)) + + +def test_acos_leading_term(): + assert acos(x).as_leading_term(x) == pi/2 + # Tests concerning branch points + assert acos(x + 1).as_leading_term(x) == sqrt(2)*sqrt(-x) + assert acos(x - 1).as_leading_term(x) == pi + assert acos(1/x).as_leading_term(x, cdir=1) == -I*log(x) + I*log(2) + assert acos(1/x).as_leading_term(x, cdir=-1) == I*log(x) + 2*pi - I*log(2) + # Tests concerning points lying on branch cuts + assert acos(I*x + 2).as_leading_term(x, cdir=1) == -acos(2) + assert acos(-I*x + 2).as_leading_term(x, cdir=1) == acos(2) + assert acos(I*x - 2).as_leading_term(x, cdir=1) == acos(-2) + assert acos(-I*x - 2).as_leading_term(x, cdir=1) == 2*pi - acos(-2) + # Tests concerning im(ndir) == 0 + assert acos(-I*x**2 + x - 2).as_leading_term(x, cdir=1) == pi + I*log(sqrt(3) + 2) + assert acos(-I*x**2 + x - 2).as_leading_term(x, cdir=-1) == pi + I*log(sqrt(3) + 2) + + +def test_acos_series(): + assert acos(x).series(x, 0, 8) == \ + pi/2 - x - x**3/6 - 3*x**5/40 - 5*x**7/112 + O(x**8) + assert acos(x).series(x, 0, 8) == pi/2 - asin(x).series(x, 0, 8) + t5 = acos(x).taylor_term(5, x) + assert t5 == -3*x**5/40 + assert acos(x).taylor_term(7, x, t5, 0) == -5*x**7/112 + assert acos(x).taylor_term(0, x) == pi/2 + assert acos(x).taylor_term(2, x) is S.Zero + + +def test_acos_rewrite(): + assert acos(x).rewrite(log) == pi/2 + I*log(I*x + sqrt(1 - x**2)) + assert acos(x).rewrite(atan) == pi*(-x*sqrt(x**(-2)) + 1)/2 + atan(sqrt(1 - x**2)/x) + assert acos(0).rewrite(atan) == S.Pi/2 + assert acos(0.5).rewrite(atan) == acos(0.5).rewrite(log) + assert acos(x).rewrite(asin) == S.Pi/2 - asin(x) + assert acos(x).rewrite(acot) == -2*acot((sqrt(-x**2 + 1) + 1)/x) + pi/2 + assert acos(x).rewrite(asec) == asec(1/x) + assert acos(x).rewrite(acsc) == -acsc(1/x) + pi/2 + + +def test_acos_fdiff(): + assert acos(x).fdiff() == -1/sqrt(1 - x**2) + raises(ArgumentIndexError, lambda: acos(x).fdiff(2)) + + +def test_atan(): + assert atan(nan) is nan + + assert atan.nargs == FiniteSet(1) + assert atan(oo) == pi/2 + assert atan(-oo) == -pi/2 + assert atan(zoo) == AccumBounds(-pi/2, pi/2) + + assert atan(0) == 0 + assert atan(1) == pi/4 + assert atan(sqrt(3)) == pi/3 + assert atan(-(1 + sqrt(2))) == pi*Rational(-3, 8) + assert atan(sqrt(5 - 2 * sqrt(5))) == pi/5 + assert atan(-sqrt(1 - 2 * sqrt(5)/ 5)) == -pi/10 + assert atan(sqrt(1 + 2 * sqrt(5) / 5)) == pi*Rational(3, 10) + assert atan(-2 + sqrt(3)) == -pi/12 + assert atan(2 + sqrt(3)) == pi*Rational(5, 12) + assert atan(-2 - sqrt(3)) == pi*Rational(-5, 12) + + # check round-trip for exact values: + for d in [5, 6, 8, 10, 12]: + for num in range(-(d//2), d//2 + 1): + if gcd(num, d) == 1: + assert atan(tan(num*pi/d)) == num*pi/d + + assert atan(oo) == pi/2 + assert atan(x).diff(x) == 1/(1 + x**2) + + assert atan(r).is_real is True + + assert atan(-2*I) == -I*atanh(2) + assert unchanged(atan, cot(x)) + assert atan(cot(Rational(1, 4))) == Rational(-1, 4) + pi/2 + assert acot(Rational(1, 4)).is_rational is False + + for s in (x, p, n, np, nn, nz, ep, en, enp, enn, enz): + if s.is_real or s.is_extended_real is None: + assert s.is_nonzero is atan(s).is_nonzero + assert s.is_positive is atan(s).is_positive + assert s.is_negative is atan(s).is_negative + assert s.is_nonpositive is atan(s).is_nonpositive + assert s.is_nonnegative is atan(s).is_nonnegative + else: + assert s.is_extended_nonzero is atan(s).is_nonzero + assert s.is_extended_positive is atan(s).is_positive + assert s.is_extended_negative is atan(s).is_negative + assert s.is_extended_nonpositive is atan(s).is_nonpositive + assert s.is_extended_nonnegative is atan(s).is_nonnegative + assert s.is_extended_nonzero is atan(s).is_extended_nonzero + assert s.is_extended_positive is atan(s).is_extended_positive + assert s.is_extended_negative is atan(s).is_extended_negative + assert s.is_extended_nonpositive is atan(s).is_extended_nonpositive + assert s.is_extended_nonnegative is atan(s).is_extended_nonnegative + + +def test_atan_rewrite(): + assert atan(x).rewrite(log) == I*(log(1 - I*x)-log(1 + I*x))/2 + assert atan(x).rewrite(asin) == (-asin(1/sqrt(x**2 + 1)) + pi/2)*sqrt(x**2)/x + assert atan(x).rewrite(acos) == sqrt(x**2)*acos(1/sqrt(x**2 + 1))/x + assert atan(x).rewrite(acot) == acot(1/x) + assert atan(x).rewrite(asec) == sqrt(x**2)*asec(sqrt(x**2 + 1))/x + assert atan(x).rewrite(acsc) == (-acsc(sqrt(x**2 + 1)) + pi/2)*sqrt(x**2)/x + + assert atan(-5*I).evalf() == atan(x).rewrite(log).evalf(subs={x:-5*I}) + assert atan(5*I).evalf() == atan(x).rewrite(log).evalf(subs={x:5*I}) + + +def test_atan_fdiff(): + assert atan(x).fdiff() == 1/(x**2 + 1) + raises(ArgumentIndexError, lambda: atan(x).fdiff(2)) + + +def test_atan_leading_term(): + assert atan(x).as_leading_term(x) == x + assert atan(1/x).as_leading_term(x, cdir=1) == pi/2 + assert atan(1/x).as_leading_term(x, cdir=-1) == -pi/2 + # Tests concerning branch points + assert atan(x + I).as_leading_term(x, cdir=1) == -I*log(x)/2 + pi/4 + I*log(2)/2 + assert atan(x + I).as_leading_term(x, cdir=-1) == -I*log(x)/2 - 3*pi/4 + I*log(2)/2 + assert atan(x - I).as_leading_term(x, cdir=1) == I*log(x)/2 + pi/4 - I*log(2)/2 + assert atan(x - I).as_leading_term(x, cdir=-1) == I*log(x)/2 + pi/4 - I*log(2)/2 + # Tests concerning points lying on branch cuts + assert atan(x + 2*I).as_leading_term(x, cdir=1) == I*atanh(2) + assert atan(x + 2*I).as_leading_term(x, cdir=-1) == -pi + I*atanh(2) + assert atan(x - 2*I).as_leading_term(x, cdir=1) == pi - I*atanh(2) + assert atan(x - 2*I).as_leading_term(x, cdir=-1) == -I*atanh(2) + # Tests concerning re(ndir) == 0 + assert atan(2*I - I*x - x**2).as_leading_term(x, cdir=1) == -pi/2 + I*log(3)/2 + assert atan(2*I - I*x - x**2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(3)/2 + + +def test_atan2(): + assert atan2.nargs == FiniteSet(2) + assert atan2(0, 0) is S.NaN + assert atan2(0, 1) == 0 + assert atan2(1, 1) == pi/4 + assert atan2(1, 0) == pi/2 + assert atan2(1, -1) == pi*Rational(3, 4) + assert atan2(0, -1) == pi + assert atan2(-1, -1) == pi*Rational(-3, 4) + assert atan2(-1, 0) == -pi/2 + assert atan2(-1, 1) == -pi/4 + i = symbols('i', imaginary=True) + r = symbols('r', real=True) + eq = atan2(r, i) + ans = -I*log((i + I*r)/sqrt(i**2 + r**2)) + reps = ((r, 2), (i, I)) + assert eq.subs(reps) == ans.subs(reps) + + x = Symbol('x', negative=True) + y = Symbol('y', negative=True) + assert atan2(y, x) == atan(y/x) - pi + y = Symbol('y', nonnegative=True) + assert atan2(y, x) == atan(y/x) + pi + y = Symbol('y') + assert atan2(y, x) == atan2(y, x, evaluate=False) + + u = Symbol("u", positive=True) + assert atan2(0, u) == 0 + u = Symbol("u", negative=True) + assert atan2(0, u) == pi + + assert atan2(y, oo) == 0 + assert atan2(y, -oo)== 2*pi*Heaviside(re(y), S.Half) - pi + + assert atan2(y, x).rewrite(log) == -I*log((x + I*y)/sqrt(x**2 + y**2)) + assert atan2(0, 0) is S.NaN + + ex = atan2(y, x) - arg(x + I*y) + assert ex.subs({x:2, y:3}).rewrite(arg) == 0 + assert ex.subs({x:2, y:3*I}).rewrite(arg) == -pi - I*log(sqrt(5)*I/5) + assert ex.subs({x:2*I, y:3}).rewrite(arg) == -pi/2 - I*log(sqrt(5)*I) + assert ex.subs({x:2*I, y:3*I}).rewrite(arg) == -pi + atan(Rational(2, 3)) + atan(Rational(3, 2)) + i = symbols('i', imaginary=True) + r = symbols('r', real=True) + e = atan2(i, r) + rewrite = e.rewrite(arg) + reps = {i: I, r: -2} + assert rewrite == -I*log(abs(I*i + r)/sqrt(abs(i**2 + r**2))) + arg((I*i + r)/sqrt(i**2 + r**2)) + assert (e - rewrite).subs(reps).equals(0) + + assert atan2(0, x).rewrite(atan) == Piecewise((pi, re(x) < 0), + (0, Ne(x, 0)), + (nan, True)) + assert atan2(0, r).rewrite(atan) == Piecewise((pi, r < 0), (0, Ne(r, 0)), (S.NaN, True)) + assert atan2(0, i),rewrite(atan) == 0 + assert atan2(0, r + i).rewrite(atan) == Piecewise((pi, r < 0), (0, True)) + + assert atan2(y, x).rewrite(atan) == Piecewise( + (2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)), + (pi, re(x) < 0), + (0, (re(x) > 0) | Ne(im(x), 0)), + (nan, True)) + assert conjugate(atan2(x, y)) == atan2(conjugate(x), conjugate(y)) + + assert diff(atan2(y, x), x) == -y/(x**2 + y**2) + assert diff(atan2(y, x), y) == x/(x**2 + y**2) + + assert simplify(diff(atan2(y, x).rewrite(log), x)) == -y/(x**2 + y**2) + assert simplify(diff(atan2(y, x).rewrite(log), y)) == x/(x**2 + y**2) + + assert str(atan2(1, 2).evalf(5)) == '0.46365' + raises(ArgumentIndexError, lambda: atan2(x, y).fdiff(3)) + +def test_issue_17461(): + class A(Symbol): + is_extended_real = True + + def _eval_evalf(self, prec): + return Float(5.0) + + x = A('X') + y = A('Y') + assert abs(atan2(x, y).evalf() - 0.785398163397448) <= 1e-10 + +def test_acot(): + assert acot(nan) is nan + + assert acot.nargs == FiniteSet(1) + assert acot(-oo) == 0 + assert acot(oo) == 0 + assert acot(zoo) == 0 + assert acot(1) == pi/4 + assert acot(0) == pi/2 + assert acot(sqrt(3)/3) == pi/3 + assert acot(1/sqrt(3)) == pi/3 + assert acot(-1/sqrt(3)) == -pi/3 + assert acot(x).diff(x) == -1/(1 + x**2) + + assert acot(r).is_extended_real is True + + assert acot(I*pi) == -I*acoth(pi) + assert acot(-2*I) == I*acoth(2) + assert acot(x).is_positive is None + assert acot(n).is_positive is False + assert acot(p).is_positive is True + assert acot(I).is_positive is False + assert acot(Rational(1, 4)).is_rational is False + assert unchanged(acot, cot(x)) + assert unchanged(acot, tan(x)) + assert acot(cot(Rational(1, 4))) == Rational(1, 4) + assert acot(tan(Rational(-1, 4))) == Rational(1, 4) - pi/2 + + +def test_acot_rewrite(): + assert acot(x).rewrite(log) == I*(log(1 - I/x)-log(1 + I/x))/2 + assert acot(x).rewrite(asin) == x*(-asin(sqrt(-x**2)/sqrt(-x**2 - 1)) + pi/2)*sqrt(x**(-2)) + assert acot(x).rewrite(acos) == x*sqrt(x**(-2))*acos(sqrt(-x**2)/sqrt(-x**2 - 1)) + assert acot(x).rewrite(atan) == atan(1/x) + assert acot(x).rewrite(asec) == x*sqrt(x**(-2))*asec(sqrt((x**2 + 1)/x**2)) + assert acot(x).rewrite(acsc) == x*(-acsc(sqrt((x**2 + 1)/x**2)) + pi/2)*sqrt(x**(-2)) + + assert acot(-I/5).evalf() == acot(x).rewrite(log).evalf(subs={x:-I/5}) + assert acot(I/5).evalf() == acot(x).rewrite(log).evalf(subs={x:I/5}) + + +def test_acot_fdiff(): + assert acot(x).fdiff() == -1/(x**2 + 1) + raises(ArgumentIndexError, lambda: acot(x).fdiff(2)) + +def test_acot_leading_term(): + assert acot(1/x).as_leading_term(x) == x + # Tests concerning branch points + assert acot(x + I).as_leading_term(x, cdir=1) == I*log(x)/2 + pi/4 - I*log(2)/2 + assert acot(x + I).as_leading_term(x, cdir=-1) == I*log(x)/2 + pi/4 - I*log(2)/2 + assert acot(x - I).as_leading_term(x, cdir=1) == -I*log(x)/2 + pi/4 + I*log(2)/2 + assert acot(x - I).as_leading_term(x, cdir=-1) == -I*log(x)/2 - 3*pi/4 + I*log(2)/2 + # Tests concerning points lying on branch cuts + assert acot(x).as_leading_term(x, cdir=1) == pi/2 + assert acot(x).as_leading_term(x, cdir=-1) == -pi/2 + assert acot(x + I/2).as_leading_term(x, cdir=1) == pi - I*acoth(S(1)/2) + assert acot(x + I/2).as_leading_term(x, cdir=-1) == -I*acoth(S(1)/2) + assert acot(x - I/2).as_leading_term(x, cdir=1) == I*acoth(S(1)/2) + assert acot(x - I/2).as_leading_term(x, cdir=-1) == -pi + I*acoth(S(1)/2) + # Tests concerning re(ndir) == 0 + assert acot(I/2 - I*x - x**2).as_leading_term(x, cdir=1) == -pi/2 - I*log(3)/2 + assert acot(I/2 - I*x - x**2).as_leading_term(x, cdir=-1) == -pi/2 - I*log(3)/2 + + +def test_attributes(): + assert sin(x).args == (x,) + + +def test_sincos_rewrite(): + assert sin(pi/2 - x) == cos(x) + assert sin(pi - x) == sin(x) + assert cos(pi/2 - x) == sin(x) + assert cos(pi - x) == -cos(x) + + +def _check_even_rewrite(func, arg): + """Checks that the expr has been rewritten using f(-x) -> f(x) + arg : -x + """ + return func(arg).args[0] == -arg + + +def _check_odd_rewrite(func, arg): + """Checks that the expr has been rewritten using f(-x) -> -f(x) + arg : -x + """ + return func(arg).func.is_Mul + + +def _check_no_rewrite(func, arg): + """Checks that the expr is not rewritten""" + return func(arg).args[0] == arg + + +def test_evenodd_rewrite(): + a = cos(2) # negative + b = sin(1) # positive + even = [cos] + odd = [sin, tan, cot, asin, atan, acot] + with_minus = [-1, -2**1024 * E, -pi/105, -x*y, -x - y] + for func in even: + for expr in with_minus: + assert _check_even_rewrite(func, expr) + assert _check_no_rewrite(func, a*b) + assert func( + x - y) == func(y - x) # it doesn't matter which form is canonical + for func in odd: + for expr in with_minus: + assert _check_odd_rewrite(func, expr) + assert _check_no_rewrite(func, a*b) + assert func( + x - y) == -func(y - x) # it doesn't matter which form is canonical + + +def test_as_leading_term_issue_5272(): + assert sin(x).as_leading_term(x) == x + assert cos(x).as_leading_term(x) == 1 + assert tan(x).as_leading_term(x) == x + assert cot(x).as_leading_term(x) == 1/x + + +def test_leading_terms(): + assert sin(1/x).as_leading_term(x) == AccumBounds(-1, 1) + assert sin(S.Half).as_leading_term(x) == sin(S.Half) + assert cos(1/x).as_leading_term(x) == AccumBounds(-1, 1) + assert cos(S.Half).as_leading_term(x) == cos(S.Half) + assert sec(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity) + assert csc(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity) + assert tan(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity) + assert cot(1/x).as_leading_term(x) == AccumBounds(S.NegativeInfinity, S.Infinity) + + # https://github.com/sympy/sympy/issues/21038 + f = sin(pi*(x + 4))/(3*x) + assert f.as_leading_term(x) == pi/3 + + +def test_atan2_expansion(): + assert cancel(atan2(x**2, x + 1).diff(x) - atan(x**2/(x + 1)).diff(x)) == 0 + assert cancel(atan(y/x).series(y, 0, 5) - atan2(y, x).series(y, 0, 5) + + atan2(0, x) - atan(0)) == O(y**5) + assert cancel(atan(y/x).series(x, 1, 4) - atan2(y, x).series(x, 1, 4) + + atan2(y, 1) - atan(y)) == O((x - 1)**4, (x, 1)) + assert cancel(atan((y + x)/x).series(x, 1, 3) - atan2(y + x, x).series(x, 1, 3) + + atan2(1 + y, 1) - atan(1 + y)) == O((x - 1)**3, (x, 1)) + assert Matrix([atan2(y, x)]).jacobian([y, x]) == \ + Matrix([[x/(y**2 + x**2), -y/(y**2 + x**2)]]) + + +def test_aseries(): + def t(n, v, d, e): + assert abs( + n(1/v).evalf() - n(1/x).series(x, dir=d).removeO().subs(x, v)) < e + t(atan, 0.1, '+', 1e-5) + t(atan, -0.1, '-', 1e-5) + t(acot, 0.1, '+', 1e-5) + t(acot, -0.1, '-', 1e-5) + + +def test_issue_4420(): + i = Symbol('i', integer=True) + e = Symbol('e', even=True) + o = Symbol('o', odd=True) + + # unknown parity for variable + assert cos(4*i*pi) == 1 + assert sin(4*i*pi) == 0 + assert tan(4*i*pi) == 0 + assert cot(4*i*pi) is zoo + + assert cos(3*i*pi) == cos(pi*i) # +/-1 + assert sin(3*i*pi) == 0 + assert tan(3*i*pi) == 0 + assert cot(3*i*pi) is zoo + + assert cos(4.0*i*pi) == 1 + assert sin(4.0*i*pi) == 0 + assert tan(4.0*i*pi) == 0 + assert cot(4.0*i*pi) is zoo + + assert cos(3.0*i*pi) == cos(pi*i) # +/-1 + assert sin(3.0*i*pi) == 0 + assert tan(3.0*i*pi) == 0 + assert cot(3.0*i*pi) is zoo + + assert cos(4.5*i*pi) == cos(0.5*pi*i) + assert sin(4.5*i*pi) == sin(0.5*pi*i) + assert tan(4.5*i*pi) == tan(0.5*pi*i) + assert cot(4.5*i*pi) == cot(0.5*pi*i) + + # parity of variable is known + assert cos(4*e*pi) == 1 + assert sin(4*e*pi) == 0 + assert tan(4*e*pi) == 0 + assert cot(4*e*pi) is zoo + + assert cos(3*e*pi) == 1 + assert sin(3*e*pi) == 0 + assert tan(3*e*pi) == 0 + assert cot(3*e*pi) is zoo + + assert cos(4.0*e*pi) == 1 + assert sin(4.0*e*pi) == 0 + assert tan(4.0*e*pi) == 0 + assert cot(4.0*e*pi) is zoo + + assert cos(3.0*e*pi) == 1 + assert sin(3.0*e*pi) == 0 + assert tan(3.0*e*pi) == 0 + assert cot(3.0*e*pi) is zoo + + assert cos(4.5*e*pi) == cos(0.5*pi*e) + assert sin(4.5*e*pi) == sin(0.5*pi*e) + assert tan(4.5*e*pi) == tan(0.5*pi*e) + assert cot(4.5*e*pi) == cot(0.5*pi*e) + + assert cos(4*o*pi) == 1 + assert sin(4*o*pi) == 0 + assert tan(4*o*pi) == 0 + assert cot(4*o*pi) is zoo + + assert cos(3*o*pi) == -1 + assert sin(3*o*pi) == 0 + assert tan(3*o*pi) == 0 + assert cot(3*o*pi) is zoo + + assert cos(4.0*o*pi) == 1 + assert sin(4.0*o*pi) == 0 + assert tan(4.0*o*pi) == 0 + assert cot(4.0*o*pi) is zoo + + assert cos(3.0*o*pi) == -1 + assert sin(3.0*o*pi) == 0 + assert tan(3.0*o*pi) == 0 + assert cot(3.0*o*pi) is zoo + + assert cos(4.5*o*pi) == cos(0.5*pi*o) + assert sin(4.5*o*pi) == sin(0.5*pi*o) + assert tan(4.5*o*pi) == tan(0.5*pi*o) + assert cot(4.5*o*pi) == cot(0.5*pi*o) + + # x could be imaginary + assert cos(4*x*pi) == cos(4*pi*x) + assert sin(4*x*pi) == sin(4*pi*x) + assert tan(4*x*pi) == tan(4*pi*x) + assert cot(4*x*pi) == cot(4*pi*x) + + assert cos(3*x*pi) == cos(3*pi*x) + assert sin(3*x*pi) == sin(3*pi*x) + assert tan(3*x*pi) == tan(3*pi*x) + assert cot(3*x*pi) == cot(3*pi*x) + + assert cos(4.0*x*pi) == cos(4.0*pi*x) + assert sin(4.0*x*pi) == sin(4.0*pi*x) + assert tan(4.0*x*pi) == tan(4.0*pi*x) + assert cot(4.0*x*pi) == cot(4.0*pi*x) + + assert cos(3.0*x*pi) == cos(3.0*pi*x) + assert sin(3.0*x*pi) == sin(3.0*pi*x) + assert tan(3.0*x*pi) == tan(3.0*pi*x) + assert cot(3.0*x*pi) == cot(3.0*pi*x) + + assert cos(4.5*x*pi) == cos(4.5*pi*x) + assert sin(4.5*x*pi) == sin(4.5*pi*x) + assert tan(4.5*x*pi) == tan(4.5*pi*x) + assert cot(4.5*x*pi) == cot(4.5*pi*x) + + +def test_inverses(): + raises(AttributeError, lambda: sin(x).inverse()) + raises(AttributeError, lambda: cos(x).inverse()) + assert tan(x).inverse() == atan + assert cot(x).inverse() == acot + raises(AttributeError, lambda: csc(x).inverse()) + raises(AttributeError, lambda: sec(x).inverse()) + assert asin(x).inverse() == sin + assert acos(x).inverse() == cos + assert atan(x).inverse() == tan + assert acot(x).inverse() == cot + + +def test_real_imag(): + a, b = symbols('a b', real=True) + z = a + b*I + for deep in [True, False]: + assert sin( + z).as_real_imag(deep=deep) == (sin(a)*cosh(b), cos(a)*sinh(b)) + assert cos( + z).as_real_imag(deep=deep) == (cos(a)*cosh(b), -sin(a)*sinh(b)) + assert tan(z).as_real_imag(deep=deep) == (sin(2*a)/(cos(2*a) + + cosh(2*b)), sinh(2*b)/(cos(2*a) + cosh(2*b))) + assert cot(z).as_real_imag(deep=deep) == (-sin(2*a)/(cos(2*a) - + cosh(2*b)), sinh(2*b)/(cos(2*a) - cosh(2*b))) + assert sin(a).as_real_imag(deep=deep) == (sin(a), 0) + assert cos(a).as_real_imag(deep=deep) == (cos(a), 0) + assert tan(a).as_real_imag(deep=deep) == (tan(a), 0) + assert cot(a).as_real_imag(deep=deep) == (cot(a), 0) + + +@XFAIL +def test_sin_cos_with_infinity(): + # Test for issue 5196 + # https://github.com/sympy/sympy/issues/5196 + assert sin(oo) is S.NaN + assert cos(oo) is S.NaN + + +@slow +def test_sincos_rewrite_sqrt(): + # equivalent to testing rewrite(pow) + for p in [1, 3, 5, 17]: + for t in [1, 8]: + n = t*p + # The vertices `exp(i*pi/n)` of a regular `n`-gon can + # be expressed by means of nested square roots if and + # only if `n` is a product of Fermat primes, `p`, and + # powers of 2, `t'. The code aims to check all vertices + # not belonging to an `m`-gon for `m < n`(`gcd(i, n) == 1`). + # For large `n` this makes the test too slow, therefore + # the vertices are limited to those of index `i < 10`. + for i in range(1, min((n + 1)//2 + 1, 10)): + if 1 == gcd(i, n): + x = i*pi/n + s1 = sin(x).rewrite(sqrt) + c1 = cos(x).rewrite(sqrt) + assert not s1.has(cos, sin), "fails for %d*pi/%d" % (i, n) + assert not c1.has(cos, sin), "fails for %d*pi/%d" % (i, n) + assert 1e-3 > abs(sin(x.evalf(5)) - s1.evalf(2)), "fails for %d*pi/%d" % (i, n) + assert 1e-3 > abs(cos(x.evalf(5)) - c1.evalf(2)), "fails for %d*pi/%d" % (i, n) + assert cos(pi/14).rewrite(sqrt) == sqrt(cos(pi/7)/2 + S.Half) + assert cos(pi*Rational(-15, 2)/11, evaluate=False).rewrite( + sqrt) == -sqrt(-cos(pi*Rational(4, 11))/2 + S.Half) + assert cos(Mul(2, pi, S.Half, evaluate=False), evaluate=False).rewrite( + sqrt) == -1 + e = cos(pi/3/17) # don't use pi/15 since that is caught at instantiation + a = ( + -3*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17) + 17)/64 - + 3*sqrt(34)*sqrt(sqrt(17) + 17)/128 - sqrt(sqrt(17) + + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 - sqrt(-sqrt(17) + + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/128 - Rational(1, 32) + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 + + 3*sqrt(2)*sqrt(sqrt(17) + 17)/128 + sqrt(34)*sqrt(-sqrt(17) + 17)/128 + + 13*sqrt(2)*sqrt(-sqrt(17) + 17)/128 + sqrt(17)*sqrt(-sqrt(17) + + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/128 + 5*sqrt(17)/32 + + sqrt(3)*sqrt(-sqrt(2)*sqrt(sqrt(17) + 17)*sqrt(sqrt(17)/32 + + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/8 - + 5*sqrt(2)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + + Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 - + 3*sqrt(2)*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 + + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/32 + + sqrt(34)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + + Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/64 + + sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + Rational(15, 32))/2 + + S.Half + sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 + sqrt(2)*sqrt(-sqrt(17) + + 17)/32 + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - + sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + + 6*sqrt(17) + 34)/32 + Rational(15, 32))*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - + sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + + 6*sqrt(17) + 34)/32 + sqrt(34)*sqrt(-sqrt(17) + 17)*sqrt(sqrt(17)/32 + + sqrt(2)*sqrt(-sqrt(17) + 17)/32 + + sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34)/32 + + Rational(15, 32))/32)/2) + assert e.rewrite(sqrt) == a + assert e.n() == a.n() + # coverage of fermatCoords: multiplicity > 1; the following could be + # different but that portion of the code should be tested in some way + assert cos(pi/9/17).rewrite(sqrt) == \ + sin(pi/9)*sin(pi*Rational(2, 17)) + cos(pi/9)*cos(pi*Rational(2, 17)) + + +@slow +def test_sincos_rewrite_sqrt_257(): + assert cos(pi/257).rewrite(sqrt).evalf(64) == cos(pi/257).evalf(64) + + +@slow +def test_tancot_rewrite_sqrt(): + # equivalent to testing rewrite(pow) + for p in [1, 3, 5, 17]: + for t in [1, 8]: + n = t*p + for i in range(1, min((n + 1)//2 + 1, 10)): + if 1 == gcd(i, n): + x = i*pi/n + if 2*i != n and 3*i != 2*n: + t1 = tan(x).rewrite(sqrt) + assert not t1.has(cot, tan), "fails for %d*pi/%d" % (i, n) + assert 1e-3 > abs( tan(x.evalf(7)) - t1.evalf(4) ), "fails for %d*pi/%d" % (i, n) + if i != 0 and i != n: + c1 = cot(x).rewrite(sqrt) + assert not c1.has(cot, tan), "fails for %d*pi/%d" % (i, n) + assert 1e-3 > abs( cot(x.evalf(7)) - c1.evalf(4) ), "fails for %d*pi/%d" % (i, n) + + +def test_sec(): + x = symbols('x', real=True) + z = symbols('z') + + assert sec.nargs == FiniteSet(1) + + assert sec(zoo) is nan + assert sec(0) == 1 + assert sec(pi) == -1 + assert sec(pi/2) is zoo + assert sec(-pi/2) is zoo + assert sec(pi/6) == 2*sqrt(3)/3 + assert sec(pi/3) == 2 + assert sec(pi*Rational(5, 2)) is zoo + assert sec(pi*Rational(9, 7)) == -sec(pi*Rational(2, 7)) + assert sec(pi*Rational(3, 4)) == -sqrt(2) # issue 8421 + assert sec(I) == 1/cosh(1) + assert sec(x*I) == 1/cosh(x) + assert sec(-x) == sec(x) + + assert sec(asec(x)) == x + + assert sec(z).conjugate() == sec(conjugate(z)) + + assert (sec(z).as_real_imag() == + (cos(re(z))*cosh(im(z))/(sin(re(z))**2*sinh(im(z))**2 + + cos(re(z))**2*cosh(im(z))**2), + sin(re(z))*sinh(im(z))/(sin(re(z))**2*sinh(im(z))**2 + + cos(re(z))**2*cosh(im(z))**2))) + + assert sec(x).expand(trig=True) == 1/cos(x) + assert sec(2*x).expand(trig=True) == 1/(2*cos(x)**2 - 1) + + assert sec(x).is_extended_real == True + assert sec(z).is_real == None + + assert sec(a).is_algebraic is None + assert sec(na).is_algebraic is False + + assert sec(x).as_leading_term() == sec(x) + + assert sec(0, evaluate=False).is_finite == True + assert sec(x).is_finite == None + assert sec(pi/2, evaluate=False).is_finite == False + + assert series(sec(x), x, x0=0, n=6) == 1 + x**2/2 + 5*x**4/24 + O(x**6) + + # https://github.com/sympy/sympy/issues/7166 + assert series(sqrt(sec(x))) == 1 + x**2/4 + 7*x**4/96 + O(x**6) + + # https://github.com/sympy/sympy/issues/7167 + assert (series(sqrt(sec(x)), x, x0=pi*3/2, n=4) == + 1/sqrt(x - pi*Rational(3, 2)) + (x - pi*Rational(3, 2))**Rational(3, 2)/12 + + (x - pi*Rational(3, 2))**Rational(7, 2)/160 + O((x - pi*Rational(3, 2))**4, (x, pi*Rational(3, 2)))) + + assert sec(x).diff(x) == tan(x)*sec(x) + + # Taylor Term checks + assert sec(z).taylor_term(4, z) == 5*z**4/24 + assert sec(z).taylor_term(6, z) == 61*z**6/720 + assert sec(z).taylor_term(5, z) == 0 + + +def test_sec_rewrite(): + assert sec(x).rewrite(exp) == 1/(exp(I*x)/2 + exp(-I*x)/2) + assert sec(x).rewrite(cos) == 1/cos(x) + assert sec(x).rewrite(tan) == (tan(x/2)**2 + 1)/(-tan(x/2)**2 + 1) + assert sec(x).rewrite(pow) == sec(x) + assert sec(x).rewrite(sqrt) == sec(x) + assert sec(z).rewrite(cot) == (cot(z/2)**2 + 1)/(cot(z/2)**2 - 1) + assert sec(x).rewrite(sin) == 1 / sin(x + pi / 2, evaluate=False) + assert sec(x).rewrite(tan) == (tan(x / 2)**2 + 1) / (-tan(x / 2)**2 + 1) + assert sec(x).rewrite(csc) == csc(-x + pi/2, evaluate=False) + assert sec(x).rewrite(besselj) == Piecewise( + (sqrt(2)/(sqrt(pi*x)*besselj(-S.Half, x)), Ne(x, 0)), + (1, True) + ) + assert sec(x).rewrite(besselj).subs(x, 0) == sec(0) + + +def test_sec_fdiff(): + assert sec(x).fdiff() == tan(x)*sec(x) + raises(ArgumentIndexError, lambda: sec(x).fdiff(2)) + + +def test_csc(): + x = symbols('x', real=True) + z = symbols('z') + + # https://github.com/sympy/sympy/issues/6707 + cosecant = csc('x') + alternate = 1/sin('x') + assert cosecant.equals(alternate) == True + assert alternate.equals(cosecant) == True + + assert csc.nargs == FiniteSet(1) + + assert csc(0) is zoo + assert csc(pi) is zoo + assert csc(zoo) is nan + + assert csc(pi/2) == 1 + assert csc(-pi/2) == -1 + assert csc(pi/6) == 2 + assert csc(pi/3) == 2*sqrt(3)/3 + assert csc(pi*Rational(5, 2)) == 1 + assert csc(pi*Rational(9, 7)) == -csc(pi*Rational(2, 7)) + assert csc(pi*Rational(3, 4)) == sqrt(2) # issue 8421 + assert csc(I) == -I/sinh(1) + assert csc(x*I) == -I/sinh(x) + assert csc(-x) == -csc(x) + + assert csc(acsc(x)) == x + + assert csc(z).conjugate() == csc(conjugate(z)) + + assert (csc(z).as_real_imag() == + (sin(re(z))*cosh(im(z))/(sin(re(z))**2*cosh(im(z))**2 + + cos(re(z))**2*sinh(im(z))**2), + -cos(re(z))*sinh(im(z))/(sin(re(z))**2*cosh(im(z))**2 + + cos(re(z))**2*sinh(im(z))**2))) + + assert csc(x).expand(trig=True) == 1/sin(x) + assert csc(2*x).expand(trig=True) == 1/(2*sin(x)*cos(x)) + + assert csc(x).is_extended_real == True + assert csc(z).is_real == None + + assert csc(a).is_algebraic is None + assert csc(na).is_algebraic is False + + assert csc(x).as_leading_term() == csc(x) + + assert csc(0, evaluate=False).is_finite == False + assert csc(x).is_finite == None + assert csc(pi/2, evaluate=False).is_finite == True + + assert series(csc(x), x, x0=pi/2, n=6) == \ + 1 + (x - pi/2)**2/2 + 5*(x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2)) + assert series(csc(x), x, x0=0, n=6) == \ + 1/x + x/6 + 7*x**3/360 + 31*x**5/15120 + O(x**6) + + assert csc(x).diff(x) == -cot(x)*csc(x) + + assert csc(x).taylor_term(2, x) == 0 + assert csc(x).taylor_term(3, x) == 7*x**3/360 + assert csc(x).taylor_term(5, x) == 31*x**5/15120 + raises(ArgumentIndexError, lambda: csc(x).fdiff(2)) + + +def test_asec(): + z = Symbol('z', zero=True) + assert asec(z) is zoo + assert asec(nan) is nan + assert asec(1) == 0 + assert asec(-1) == pi + assert asec(oo) == pi/2 + assert asec(-oo) == pi/2 + assert asec(zoo) == pi/2 + + assert asec(sec(pi*Rational(13, 4))) == pi*Rational(3, 4) + assert asec(1 + sqrt(5)) == pi*Rational(2, 5) + assert asec(2/sqrt(3)) == pi/6 + assert asec(sqrt(4 - 2*sqrt(2))) == pi/8 + assert asec(-sqrt(4 + 2*sqrt(2))) == pi*Rational(5, 8) + assert asec(sqrt(2 + 2*sqrt(5)/5)) == pi*Rational(3, 10) + assert asec(-sqrt(2 + 2*sqrt(5)/5)) == pi*Rational(7, 10) + assert asec(sqrt(2) - sqrt(6)) == pi*Rational(11, 12) + + assert asec(x).diff(x) == 1/(x**2*sqrt(1 - 1/x**2)) + + assert asec(x).rewrite(log) == I*log(sqrt(1 - 1/x**2) + I/x) + pi/2 + assert asec(x).rewrite(asin) == -asin(1/x) + pi/2 + assert asec(x).rewrite(acos) == acos(1/x) + assert asec(x).rewrite(atan) == \ + pi*(1 - sqrt(x**2)/x)/2 + sqrt(x**2)*atan(sqrt(x**2 - 1))/x + assert asec(x).rewrite(acot) == \ + pi*(1 - sqrt(x**2)/x)/2 + sqrt(x**2)*acot(1/sqrt(x**2 - 1))/x + assert asec(x).rewrite(acsc) == -acsc(x) + pi/2 + raises(ArgumentIndexError, lambda: asec(x).fdiff(2)) + + +def test_asec_is_real(): + assert asec(S.Half).is_real is False + n = Symbol('n', positive=True, integer=True) + assert asec(n).is_extended_real is True + assert asec(x).is_real is None + assert asec(r).is_real is None + t = Symbol('t', real=False, finite=True) + assert asec(t).is_real is False + + +def test_asec_leading_term(): + assert asec(1/x).as_leading_term(x) == pi/2 + # Tests concerning branch points + assert asec(x + 1).as_leading_term(x) == sqrt(2)*sqrt(x) + assert asec(x - 1).as_leading_term(x) == pi + # Tests concerning points lying on branch cuts + assert asec(x).as_leading_term(x, cdir=1) == -I*log(x) + I*log(2) + assert asec(x).as_leading_term(x, cdir=-1) == I*log(x) + 2*pi - I*log(2) + assert asec(I*x + 1/2).as_leading_term(x, cdir=1) == asec(1/2) + assert asec(-I*x + 1/2).as_leading_term(x, cdir=1) == -asec(1/2) + assert asec(I*x - 1/2).as_leading_term(x, cdir=1) == 2*pi - asec(-1/2) + assert asec(-I*x - 1/2).as_leading_term(x, cdir=1) == asec(-1/2) + # Tests concerning im(ndir) == 0 + assert asec(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=1) == pi + I*log(2 - sqrt(3)) + assert asec(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=-1) == pi + I*log(2 - sqrt(3)) + + +def test_asec_series(): + assert asec(x).series(x, 0, 9) == \ + I*log(2) - I*log(x) - I*x**2/4 - 3*I*x**4/32 \ + - 5*I*x**6/96 - 35*I*x**8/1024 + O(x**9) + t4 = asec(x).taylor_term(4, x) + assert t4 == -3*I*x**4/32 + assert asec(x).taylor_term(6, x, t4, 0) == -5*I*x**6/96 + + +def test_acsc(): + assert acsc(nan) is nan + assert acsc(1) == pi/2 + assert acsc(-1) == -pi/2 + assert acsc(oo) == 0 + assert acsc(-oo) == 0 + assert acsc(zoo) == 0 + assert acsc(0) is zoo + + assert acsc(csc(3)) == -3 + pi + assert acsc(csc(4)) == -4 + pi + assert acsc(csc(6)) == 6 - 2*pi + assert unchanged(acsc, csc(x)) + assert unchanged(acsc, sec(x)) + + assert acsc(2/sqrt(3)) == pi/3 + assert acsc(csc(pi*Rational(13, 4))) == -pi/4 + assert acsc(sqrt(2 + 2*sqrt(5)/5)) == pi/5 + assert acsc(-sqrt(2 + 2*sqrt(5)/5)) == -pi/5 + assert acsc(-2) == -pi/6 + assert acsc(-sqrt(4 + 2*sqrt(2))) == -pi/8 + assert acsc(sqrt(4 - 2*sqrt(2))) == pi*Rational(3, 8) + assert acsc(1 + sqrt(5)) == pi/10 + assert acsc(sqrt(2) - sqrt(6)) == pi*Rational(-5, 12) + + assert acsc(x).diff(x) == -1/(x**2*sqrt(1 - 1/x**2)) + + assert acsc(x).rewrite(log) == -I*log(sqrt(1 - 1/x**2) + I/x) + assert acsc(x).rewrite(asin) == asin(1/x) + assert acsc(x).rewrite(acos) == -acos(1/x) + pi/2 + assert acsc(x).rewrite(atan) == \ + (-atan(sqrt(x**2 - 1)) + pi/2)*sqrt(x**2)/x + assert acsc(x).rewrite(acot) == (-acot(1/sqrt(x**2 - 1)) + pi/2)*sqrt(x**2)/x + assert acsc(x).rewrite(asec) == -asec(x) + pi/2 + raises(ArgumentIndexError, lambda: acsc(x).fdiff(2)) + + +def test_csc_rewrite(): + assert csc(x).rewrite(pow) == csc(x) + assert csc(x).rewrite(sqrt) == csc(x) + + assert csc(x).rewrite(exp) == 2*I/(exp(I*x) - exp(-I*x)) + assert csc(x).rewrite(sin) == 1/sin(x) + assert csc(x).rewrite(tan) == (tan(x/2)**2 + 1)/(2*tan(x/2)) + assert csc(x).rewrite(cot) == (cot(x/2)**2 + 1)/(2*cot(x/2)) + assert csc(x).rewrite(cos) == 1/cos(x - pi/2, evaluate=False) + assert csc(x).rewrite(sec) == sec(-x + pi/2, evaluate=False) + + # issue 17349 + assert csc(1 - exp(-besselj(I, I))).rewrite(cos) == \ + -1/cos(-pi/2 - 1 + cos(I*besselj(I, I)) + + I*cos(-pi/2 + I*besselj(I, I), evaluate=False), evaluate=False) + assert csc(x).rewrite(besselj) == sqrt(2)/(sqrt(pi*x)*besselj(S.Half, x)) + assert csc(x).rewrite(besselj).subs(x, 0) == csc(0) + + +def test_acsc_leading_term(): + assert acsc(1/x).as_leading_term(x) == x + # Tests concerning branch points + assert acsc(x + 1).as_leading_term(x) == pi/2 + assert acsc(x - 1).as_leading_term(x) == -pi/2 + # Tests concerning points lying on branch cuts + assert acsc(x).as_leading_term(x, cdir=1) == I*log(x) + pi/2 - I*log(2) + assert acsc(x).as_leading_term(x, cdir=-1) == -I*log(x) - 3*pi/2 + I*log(2) + assert acsc(I*x + 1/2).as_leading_term(x, cdir=1) == acsc(1/2) + assert acsc(-I*x + 1/2).as_leading_term(x, cdir=1) == pi - acsc(1/2) + assert acsc(I*x - 1/2).as_leading_term(x, cdir=1) == -pi - acsc(-1/2) + assert acsc(-I*x - 1/2).as_leading_term(x, cdir=1) == -acsc(1/2) + # Tests concerning im(ndir) == 0 + assert acsc(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=1) == -pi/2 + I*log(sqrt(3) + 2) + assert acsc(-I*x**2 + x - S(1)/2).as_leading_term(x, cdir=-1) == -pi/2 + I*log(sqrt(3) + 2) + + +def test_acsc_series(): + assert acsc(x).series(x, 0, 9) == \ + -I*log(2) + pi/2 + I*log(x) + I*x**2/4 \ + + 3*I*x**4/32 + 5*I*x**6/96 + 35*I*x**8/1024 + O(x**9) + t6 = acsc(x).taylor_term(6, x) + assert t6 == 5*I*x**6/96 + assert acsc(x).taylor_term(8, x, t6, 0) == 35*I*x**8/1024 + + +def test_asin_nseries(): + assert asin(x + 2)._eval_nseries(x, 4, None, I) == -asin(2) + pi + \ + sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + assert asin(x + 2)._eval_nseries(x, 4, None, -I) == asin(2) - \ + sqrt(3)*I*x/3 + sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert asin(x - 2)._eval_nseries(x, 4, None, I) == -asin(2) - \ + sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert asin(x - 2)._eval_nseries(x, 4, None, -I) == asin(2) - pi + \ + sqrt(3)*I*x/3 + sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + # testing nseries for asin at branch points + assert asin(1 + x)._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(-x) - \ + sqrt(2)*(-x)**(S(3)/2)/12 - 3*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3) + assert asin(-1 + x)._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(x) + \ + sqrt(2)*x**(S(3)/2)/12 + 3*sqrt(2)*x**(S(5)/2)/160 + O(x**3) + assert asin(exp(x))._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(-x) + \ + sqrt(2)*(-x)**(S(3)/2)/6 - sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3) + assert asin(-exp(x))._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(-x) - \ + sqrt(2)*(-x)**(S(3)/2)/6 + sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3) + + +def test_acos_nseries(): + assert acos(x + 2)._eval_nseries(x, 4, None, I) == -acos(2) - sqrt(3)*I*x/3 + \ + sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + assert acos(x + 2)._eval_nseries(x, 4, None, -I) == acos(2) + sqrt(3)*I*x/3 - \ + sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + assert acos(x - 2)._eval_nseries(x, 4, None, I) == acos(-2) + sqrt(3)*I*x/3 + \ + sqrt(3)*I*x**2/9 + sqrt(3)*I*x**3/18 + O(x**4) + assert acos(x - 2)._eval_nseries(x, 4, None, -I) == -acos(-2) + 2*pi - \ + sqrt(3)*I*x/3 - sqrt(3)*I*x**2/9 - sqrt(3)*I*x**3/18 + O(x**4) + # testing nseries for acos at branch points + assert acos(1 + x)._eval_nseries(x, 3, None) == sqrt(2)*sqrt(-x) + \ + sqrt(2)*(-x)**(S(3)/2)/12 + 3*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3) + assert acos(-1 + x)._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(x) - \ + sqrt(2)*x**(S(3)/2)/12 - 3*sqrt(2)*x**(S(5)/2)/160 + O(x**3) + assert acos(exp(x))._eval_nseries(x, 3, None) == sqrt(2)*sqrt(-x) - \ + sqrt(2)*(-x)**(S(3)/2)/6 + sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3) + assert acos(-exp(x))._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(-x) + \ + sqrt(2)*(-x)**(S(3)/2)/6 - sqrt(2)*(-x)**(S(5)/2)/120 + O(x**3) + + +def test_atan_nseries(): + assert atan(x + 2*I)._eval_nseries(x, 4, None, 1) == I*atanh(2) - x/3 - \ + 2*I*x**2/9 + 13*x**3/81 + O(x**4) + assert atan(x + 2*I)._eval_nseries(x, 4, None, -1) == I*atanh(2) - pi - \ + x/3 - 2*I*x**2/9 + 13*x**3/81 + O(x**4) + assert atan(x - 2*I)._eval_nseries(x, 4, None, 1) == -I*atanh(2) + pi - \ + x/3 + 2*I*x**2/9 + 13*x**3/81 + O(x**4) + assert atan(x - 2*I)._eval_nseries(x, 4, None, -1) == -I*atanh(2) - x/3 + \ + 2*I*x**2/9 + 13*x**3/81 + O(x**4) + assert atan(1/x)._eval_nseries(x, 2, None, 1) == pi/2 - x + O(x**2) + assert atan(1/x)._eval_nseries(x, 2, None, -1) == -pi/2 - x + O(x**2) + # testing nseries for atan at branch points + assert atan(x + I)._eval_nseries(x, 4, None) == I*log(2)/2 + pi/4 - \ + I*log(x)/2 + x/4 + I*x**2/16 - x**3/48 + O(x**4) + assert atan(x - I)._eval_nseries(x, 4, None) == -I*log(2)/2 + pi/4 + \ + I*log(x)/2 + x/4 - I*x**2/16 - x**3/48 + O(x**4) + + +def test_acot_nseries(): + assert acot(x + S(1)/2*I)._eval_nseries(x, 4, None, 1) == -I*acoth(S(1)/2) + \ + pi - 4*x/3 + 8*I*x**2/9 + 112*x**3/81 + O(x**4) + assert acot(x + S(1)/2*I)._eval_nseries(x, 4, None, -1) == -I*acoth(S(1)/2) - \ + 4*x/3 + 8*I*x**2/9 + 112*x**3/81 + O(x**4) + assert acot(x - S(1)/2*I)._eval_nseries(x, 4, None, 1) == I*acoth(S(1)/2) - \ + 4*x/3 - 8*I*x**2/9 + 112*x**3/81 + O(x**4) + assert acot(x - S(1)/2*I)._eval_nseries(x, 4, None, -1) == I*acoth(S(1)/2) - \ + pi - 4*x/3 - 8*I*x**2/9 + 112*x**3/81 + O(x**4) + assert acot(x)._eval_nseries(x, 2, None, 1) == pi/2 - x + O(x**2) + assert acot(x)._eval_nseries(x, 2, None, -1) == -pi/2 - x + O(x**2) + # testing nseries for acot at branch points + assert acot(x + I)._eval_nseries(x, 4, None) == -I*log(2)/2 + pi/4 + \ + I*log(x)/2 - x/4 - I*x**2/16 + x**3/48 + O(x**4) + assert acot(x - I)._eval_nseries(x, 4, None) == I*log(2)/2 + pi/4 - \ + I*log(x)/2 - x/4 + I*x**2/16 + x**3/48 + O(x**4) + + +def test_asec_nseries(): + assert asec(x + S(1)/2)._eval_nseries(x, 4, None, I) == asec(S(1)/2) - \ + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + assert asec(x + S(1)/2)._eval_nseries(x, 4, None, -I) == -asec(S(1)/2) + \ + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + assert asec(x - S(1)/2)._eval_nseries(x, 4, None, I) == -asec(-S(1)/2) + \ + 2*pi + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + assert asec(x - S(1)/2)._eval_nseries(x, 4, None, -I) == asec(-S(1)/2) - \ + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + # testing nseries for asec at branch points + assert asec(1 + x)._eval_nseries(x, 3, None) == sqrt(2)*sqrt(x) - \ + 5*sqrt(2)*x**(S(3)/2)/12 + 43*sqrt(2)*x**(S(5)/2)/160 + O(x**3) + assert asec(-1 + x)._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(-x) + \ + 5*sqrt(2)*(-x)**(S(3)/2)/12 - 43*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3) + assert asec(exp(x))._eval_nseries(x, 3, None) == sqrt(2)*sqrt(x) - \ + sqrt(2)*x**(S(3)/2)/6 + sqrt(2)*x**(S(5)/2)/120 + O(x**3) + assert asec(-exp(x))._eval_nseries(x, 3, None) == pi - sqrt(2)*sqrt(x) + \ + sqrt(2)*x**(S(3)/2)/6 - sqrt(2)*x**(S(5)/2)/120 + O(x**3) + + +def test_acsc_nseries(): + assert acsc(x + S(1)/2)._eval_nseries(x, 4, None, I) == acsc(S(1)/2) + \ + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsc(x + S(1)/2)._eval_nseries(x, 4, None, -I) == -acsc(S(1)/2) + \ + pi - 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsc(x - S(1)/2)._eval_nseries(x, 4, None, I) == acsc(S(1)/2) - pi -\ + 4*sqrt(3)*I*x/3 - 8*sqrt(3)*I*x**2/9 - 16*sqrt(3)*I*x**3/9 + O(x**4) + assert acsc(x - S(1)/2)._eval_nseries(x, 4, None, -I) == -acsc(S(1)/2) + \ + 4*sqrt(3)*I*x/3 + 8*sqrt(3)*I*x**2/9 + 16*sqrt(3)*I*x**3/9 + O(x**4) + # testing nseries for acsc at branch points + assert acsc(1 + x)._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(x) + \ + 5*sqrt(2)*x**(S(3)/2)/12 - 43*sqrt(2)*x**(S(5)/2)/160 + O(x**3) + assert acsc(-1 + x)._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(-x) - \ + 5*sqrt(2)*(-x)**(S(3)/2)/12 + 43*sqrt(2)*(-x)**(S(5)/2)/160 + O(x**3) + assert acsc(exp(x))._eval_nseries(x, 3, None) == pi/2 - sqrt(2)*sqrt(x) + \ + sqrt(2)*x**(S(3)/2)/6 - sqrt(2)*x**(S(5)/2)/120 + O(x**3) + assert acsc(-exp(x))._eval_nseries(x, 3, None) == -pi/2 + sqrt(2)*sqrt(x) - \ + sqrt(2)*x**(S(3)/2)/6 + sqrt(2)*x**(S(5)/2)/120 + O(x**3) + + +def test_issue_8653(): + n = Symbol('n', integer=True) + assert sin(n).is_irrational is None + assert cos(n).is_irrational is None + assert tan(n).is_irrational is None + + +def test_issue_9157(): + n = Symbol('n', integer=True, positive=True) + assert atan(n - 1).is_nonnegative is True + + +def test_trig_period(): + x, y = symbols('x, y') + + assert sin(x).period() == 2*pi + assert cos(x).period() == 2*pi + assert tan(x).period() == pi + assert cot(x).period() == pi + assert sec(x).period() == 2*pi + assert csc(x).period() == 2*pi + assert sin(2*x).period() == pi + assert cot(4*x - 6).period() == pi/4 + assert cos((-3)*x).period() == pi*Rational(2, 3) + assert cos(x*y).period(x) == 2*pi/abs(y) + assert sin(3*x*y + 2*pi).period(y) == 2*pi/abs(3*x) + assert tan(3*x).period(y) is S.Zero + raises(NotImplementedError, lambda: sin(x**2).period(x)) + + +def test_issue_7171(): + assert sin(x).rewrite(sqrt) == sin(x) + assert sin(x).rewrite(pow) == sin(x) + + +def test_issue_11864(): + w, k = symbols('w, k', real=True) + F = Piecewise((1, Eq(2*pi*k, 0)), (sin(pi*k)/(pi*k), True)) + soln = Piecewise((1, Eq(2*pi*k, 0)), (sinc(pi*k), True)) + assert F.rewrite(sinc) == soln + +def test_real_assumptions(): + z = Symbol('z', real=False, finite=True) + assert sin(z).is_real is None + assert cos(z).is_real is None + assert tan(z).is_real is False + assert sec(z).is_real is None + assert csc(z).is_real is None + assert cot(z).is_real is False + assert asin(p).is_real is None + assert asin(n).is_real is None + assert asec(p).is_real is None + assert asec(n).is_real is None + assert acos(p).is_real is None + assert acos(n).is_real is None + assert acsc(p).is_real is None + assert acsc(n).is_real is None + assert atan(p).is_positive is True + assert atan(n).is_negative is True + assert acot(p).is_positive is True + assert acot(n).is_negative is True + +def test_issue_14320(): + assert asin(sin(2)) == -2 + pi and (-pi/2 <= -2 + pi <= pi/2) and sin(2) == sin(-2 + pi) + assert asin(cos(2)) == -2 + pi/2 and (-pi/2 <= -2 + pi/2 <= pi/2) and cos(2) == sin(-2 + pi/2) + assert acos(sin(2)) == -pi/2 + 2 and (0 <= -pi/2 + 2 <= pi) and sin(2) == cos(-pi/2 + 2) + assert acos(cos(20)) == -6*pi + 20 and (0 <= -6*pi + 20 <= pi) and cos(20) == cos(-6*pi + 20) + assert acos(cos(30)) == -30 + 10*pi and (0 <= -30 + 10*pi <= pi) and cos(30) == cos(-30 + 10*pi) + + assert atan(tan(17)) == -5*pi + 17 and (-pi/2 < -5*pi + 17 < pi/2) and tan(17) == tan(-5*pi + 17) + assert atan(tan(15)) == -5*pi + 15 and (-pi/2 < -5*pi + 15 < pi/2) and tan(15) == tan(-5*pi + 15) + assert atan(cot(12)) == -12 + pi*Rational(7, 2) and (-pi/2 < -12 + pi*Rational(7, 2) < pi/2) and cot(12) == tan(-12 + pi*Rational(7, 2)) + assert acot(cot(15)) == -5*pi + 15 and (-pi/2 < -5*pi + 15 <= pi/2) and cot(15) == cot(-5*pi + 15) + assert acot(tan(19)) == -19 + pi*Rational(13, 2) and (-pi/2 < -19 + pi*Rational(13, 2) <= pi/2) and tan(19) == cot(-19 + pi*Rational(13, 2)) + + assert asec(sec(11)) == -11 + 4*pi and (0 <= -11 + 4*pi <= pi) and cos(11) == cos(-11 + 4*pi) + assert asec(csc(13)) == -13 + pi*Rational(9, 2) and (0 <= -13 + pi*Rational(9, 2) <= pi) and sin(13) == cos(-13 + pi*Rational(9, 2)) + assert acsc(csc(14)) == -4*pi + 14 and (-pi/2 <= -4*pi + 14 <= pi/2) and sin(14) == sin(-4*pi + 14) + assert acsc(sec(10)) == pi*Rational(-7, 2) + 10 and (-pi/2 <= pi*Rational(-7, 2) + 10 <= pi/2) and cos(10) == sin(pi*Rational(-7, 2) + 10) + +def test_issue_14543(): + assert sec(2*pi + 11) == sec(11) + assert sec(2*pi - 11) == sec(11) + assert sec(pi + 11) == -sec(11) + assert sec(pi - 11) == -sec(11) + + assert csc(2*pi + 17) == csc(17) + assert csc(2*pi - 17) == -csc(17) + assert csc(pi + 17) == -csc(17) + assert csc(pi - 17) == csc(17) + + x = Symbol('x') + assert csc(pi/2 + x) == sec(x) + assert csc(pi/2 - x) == sec(x) + assert csc(pi*Rational(3, 2) + x) == -sec(x) + assert csc(pi*Rational(3, 2) - x) == -sec(x) + + assert sec(pi/2 - x) == csc(x) + assert sec(pi/2 + x) == -csc(x) + assert sec(pi*Rational(3, 2) + x) == csc(x) + assert sec(pi*Rational(3, 2) - x) == -csc(x) + + +def test_as_real_imag(): + # This is for https://github.com/sympy/sympy/issues/17142 + # If it start failing again in irrelevant builds or in the master + # please open up the issue again. + expr = atan(I/(I + I*tan(1))) + assert expr.as_real_imag() == (expr, 0) + + +def test_issue_18746(): + e3 = cos(S.Pi*(x/4 + 1/4)) + assert e3.period() == 8 + + +def test_issue_25833(): + assert limit(atan(x**2), x, oo) == pi/2 + assert limit(atan(x**2 - 1), x, oo) == pi/2 + assert limit(atan(log(2**x)/log(2*x)), x, oo) == pi/2 + + +def test_issue_25847(): + #atan + assert atan(sin(x)/x).as_leading_term(x) == pi/4 + raises(PoleError, lambda: atan(exp(1/x)).as_leading_term(x)) + + #asin + assert asin(sin(x)/x).as_leading_term(x) == pi/2 + raises(PoleError, lambda: asin(exp(1/x)).as_leading_term(x)) + + #acos + assert acos(sin(x)/x).as_leading_term(x) == 0 + raises(PoleError, lambda: acos(exp(1/x)).as_leading_term(x)) + + #acot + assert acot(sin(x)/x).as_leading_term(x) == pi/4 + raises(PoleError, lambda: acot(exp(1/x)).as_leading_term(x)) + + #asec + assert asec(sin(x)/x).as_leading_term(x) == 0 + raises(PoleError, lambda: asec(exp(1/x)).as_leading_term(x)) + + #acsc + assert acsc(sin(x)/x).as_leading_term(x) == pi/2 + raises(PoleError, lambda: acsc(exp(1/x)).as_leading_term(x)) + +def test_issue_23843(): + #atan + assert atan(x + I).series(x, oo) == -16/(5*x**5) - 2*I/x**4 + 4/(3*x**3) + I/x**2 - 1/x + pi/2 + O(x**(-6), (x, oo)) + assert atan(x + I).series(x, -oo) == -16/(5*x**5) - 2*I/x**4 + 4/(3*x**3) + I/x**2 - 1/x - pi/2 + O(x**(-6), (x, -oo)) + assert atan(x - I).series(x, oo) == -16/(5*x**5) + 2*I/x**4 + 4/(3*x**3) - I/x**2 - 1/x + pi/2 + O(x**(-6), (x, oo)) + assert atan(x - I).series(x, -oo) == -16/(5*x**5) + 2*I/x**4 + 4/(3*x**3) - I/x**2 - 1/x - pi/2 + O(x**(-6), (x, -oo)) + + #acot + assert acot(x + I).series(x, oo) == 16/(5*x**5) + 2*I/x**4 - 4/(3*x**3) - I/x**2 + 1/x + O(x**(-6), (x, oo)) + assert acot(x + I).series(x, -oo) == 16/(5*x**5) + 2*I/x**4 - 4/(3*x**3) - I/x**2 + 1/x + O(x**(-6), (x, -oo)) + assert acot(x - I).series(x, oo) == 16/(5*x**5) - 2*I/x**4 - 4/(3*x**3) + I/x**2 + 1/x + O(x**(-6), (x, oo)) + assert acot(x - I).series(x, -oo) == 16/(5*x**5) - 2*I/x**4 - 4/(3*x**3) + I/x**2 + 1/x + O(x**(-6), (x, -oo)) diff --git a/lib/python3.11/site-packages/sympy/functions/elementary/trigonometric.py b/lib/python3.11/site-packages/sympy/functions/elementary/trigonometric.py new file mode 100644 index 0000000000000000000000000000000000000000..2608dc492af3c2e480ca103fd900b0dedb45bf09 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/elementary/trigonometric.py @@ -0,0 +1,3605 @@ +from typing import Tuple as tTuple, Union as tUnion +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.expr import Expr +from sympy.core.function import Function, ArgumentIndexError, PoleError, expand_mul +from sympy.core.logic import fuzzy_not, fuzzy_or, FuzzyBool, fuzzy_and +from sympy.core.mod import Mod +from sympy.core.numbers import Rational, pi, Integer, Float, equal_valued +from sympy.core.relational import Ne, Eq +from sympy.core.singleton import S +from sympy.core.symbol import Symbol, Dummy +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial, RisingFactorial +from sympy.functions.combinatorial.numbers import bernoulli, euler +from sympy.functions.elementary.complexes import arg as arg_f, im, re +from sympy.functions.elementary.exponential import log, exp +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt, Min, Max +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary._trigonometric_special import ( + cos_table, ipartfrac, fermat_coords) +from sympy.logic.boolalg import And +from sympy.ntheory import factorint +from sympy.polys.specialpolys import symmetric_poly +from sympy.utilities.iterables import numbered_symbols + + +############################################################################### +########################## UTILITIES ########################################## +############################################################################### + + +def _imaginary_unit_as_coefficient(arg): + """ Helper to extract symbolic coefficient for imaginary unit """ + if isinstance(arg, Float): + return None + else: + return arg.as_coefficient(S.ImaginaryUnit) + +############################################################################### +########################## TRIGONOMETRIC FUNCTIONS ############################ +############################################################################### + + +class TrigonometricFunction(Function): + """Base class for trigonometric functions. """ + + unbranched = True + _singularities = (S.ComplexInfinity,) + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if s.args[0].is_rational and fuzzy_not(s.args[0].is_zero): + return False + else: + return s.is_rational + + def _eval_is_algebraic(self): + s = self.func(*self.args) + if s.func == self.func: + if fuzzy_not(self.args[0].is_zero) and self.args[0].is_algebraic: + return False + pi_coeff = _pi_coeff(self.args[0]) + if pi_coeff is not None and pi_coeff.is_rational: + return True + else: + return s.is_algebraic + + def _eval_expand_complex(self, deep=True, **hints): + re_part, im_part = self.as_real_imag(deep=deep, **hints) + return re_part + im_part*S.ImaginaryUnit + + def _as_real_imag(self, deep=True, **hints): + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.args[0].expand(deep, **hints), S.Zero) + else: + return (self.args[0], S.Zero) + if deep: + re, im = self.args[0].expand(deep, **hints).as_real_imag() + else: + re, im = self.args[0].as_real_imag() + return (re, im) + + def _period(self, general_period, symbol=None): + f = expand_mul(self.args[0]) + if symbol is None: + symbol = tuple(f.free_symbols)[0] + + if not f.has(symbol): + return S.Zero + + if f == symbol: + return general_period + + if symbol in f.free_symbols: + if f.is_Mul: + g, h = f.as_independent(symbol) + if h == symbol: + return general_period/abs(g) + + if f.is_Add: + a, h = f.as_independent(symbol) + g, h = h.as_independent(symbol, as_Add=False) + if h == symbol: + return general_period/abs(g) + + raise NotImplementedError("Use the periodicity function instead.") + + +@cacheit +def _table2(): + # If nested sqrt's are worse than un-evaluation + # you can require q to be in (1, 2, 3, 4, 6, 12) + # q <= 12, q=15, q=20, q=24, q=30, q=40, q=60, q=120 return + # expressions with 2 or fewer sqrt nestings. + return { + 12: (3, 4), + 20: (4, 5), + 30: (5, 6), + 15: (6, 10), + 24: (6, 8), + 40: (8, 10), + 60: (20, 30), + 120: (40, 60) + } + + +def _peeloff_pi(arg): + r""" + Split ARG into two parts, a "rest" and a multiple of $\pi$. + This assumes ARG to be an Add. + The multiple of $\pi$ returned in the second position is always a Rational. + + Examples + ======== + + >>> from sympy.functions.elementary.trigonometric import _peeloff_pi + >>> from sympy import pi + >>> from sympy.abc import x, y + >>> _peeloff_pi(x + pi/2) + (x, 1/2) + >>> _peeloff_pi(x + 2*pi/3 + pi*y) + (x + pi*y + pi/6, 1/2) + + """ + pi_coeff = S.Zero + rest_terms = [] + for a in Add.make_args(arg): + K = a.coeff(pi) + if K and K.is_rational: + pi_coeff += K + else: + rest_terms.append(a) + + if pi_coeff is S.Zero: + return arg, S.Zero + + m1 = (pi_coeff % S.Half) + m2 = pi_coeff - m1 + if m2.is_integer or ((2*m2).is_integer and m2.is_even is False): + return Add(*(rest_terms + [m1*pi])), m2 + return arg, S.Zero + + +def _pi_coeff(arg: Expr, cycles: int = 1) -> tUnion[Expr, None]: + r""" + When arg is a Number times $\pi$ (e.g. $3\pi/2$) then return the Number + normalized to be in the range $[0, 2]$, else `None`. + + When an even multiple of $\pi$ is encountered, if it is multiplying + something with known parity then the multiple is returned as 0 otherwise + as 2. + + Examples + ======== + + >>> from sympy.functions.elementary.trigonometric import _pi_coeff + >>> from sympy import pi, Dummy + >>> from sympy.abc import x + >>> _pi_coeff(3*x*pi) + 3*x + >>> _pi_coeff(11*pi/7) + 11/7 + >>> _pi_coeff(-11*pi/7) + 3/7 + >>> _pi_coeff(4*pi) + 0 + >>> _pi_coeff(5*pi) + 1 + >>> _pi_coeff(5.0*pi) + 1 + >>> _pi_coeff(5.5*pi) + 3/2 + >>> _pi_coeff(2 + pi) + + >>> _pi_coeff(2*Dummy(integer=True)*pi) + 2 + >>> _pi_coeff(2*Dummy(even=True)*pi) + 0 + + """ + if arg is pi: + return S.One + elif not arg: + return S.Zero + elif arg.is_Mul: + cx = arg.coeff(pi) + if cx: + c, x = cx.as_coeff_Mul() # pi is not included as coeff + if c.is_Float: + # recast exact binary fractions to Rationals + f = abs(c) % 1 + if f != 0: + p = -int(round(log(f, 2).evalf())) + m = 2**p + cm = c*m + i = int(cm) + if equal_valued(i, cm): + c = Rational(i, m) + cx = c*x + else: + c = Rational(int(c)) + cx = c*x + if x.is_integer: + c2 = c % 2 + if c2 == 1: + return x + elif not c2: + if x.is_even is not None: # known parity + return S.Zero + return Integer(2) + else: + return c2*x + return cx + elif arg.is_zero: + return S.Zero + return None + + +class sin(TrigonometricFunction): + r""" + The sine function. + + Returns the sine of x (measured in radians). + + Explanation + =========== + + This function will evaluate automatically in the + case $x/\pi$ is some rational number [4]_. For example, + if $x$ is a multiple of $\pi$, $\pi/2$, $\pi/3$, $\pi/4$, and $\pi/6$. + + Examples + ======== + + >>> from sympy import sin, pi + >>> from sympy.abc import x + >>> sin(x**2).diff(x) + 2*x*cos(x**2) + >>> sin(1).diff(x) + 0 + >>> sin(pi) + 0 + >>> sin(pi/2) + 1 + >>> sin(pi/6) + 1/2 + >>> sin(pi/12) + -sqrt(2)/4 + sqrt(6)/4 + + + See Also + ======== + + csc, cos, sec, tan, cot + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Sin + .. [4] https://mathworld.wolfram.com/TrigonometryAngles.html + + """ + + def period(self, symbol=None): + return self._period(2*pi, symbol) + + def fdiff(self, argindex=1): + if argindex == 1: + return cos(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.sets.setexpr import SetExpr + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg.is_zero: + return S.Zero + elif arg in (S.Infinity, S.NegativeInfinity): + return AccumBounds(-1, 1) + + if arg is S.ComplexInfinity: + return S.NaN + + if isinstance(arg, AccumBounds): + from sympy.sets.sets import FiniteSet + min, max = arg.min, arg.max + d = floor(min/(2*pi)) + if min is not S.NegativeInfinity: + min = min - d*2*pi + if max is not S.Infinity: + max = max - d*2*pi + if AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(5, 2))) \ + is not S.EmptySet and \ + AccumBounds(min, max).intersection(FiniteSet(pi*Rational(3, 2), + pi*Rational(7, 2))) is not S.EmptySet: + return AccumBounds(-1, 1) + elif AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(5, 2))) \ + is not S.EmptySet: + return AccumBounds(Min(sin(min), sin(max)), 1) + elif AccumBounds(min, max).intersection(FiniteSet(pi*Rational(3, 2), pi*Rational(8, 2))) \ + is not S.EmptySet: + return AccumBounds(-1, Max(sin(min), sin(max))) + else: + return AccumBounds(Min(sin(min), sin(max)), + Max(sin(min), sin(max))) + elif isinstance(arg, SetExpr): + return arg._eval_func(cls) + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import sinh + return S.ImaginaryUnit*sinh(i_coeff) + + pi_coeff = _pi_coeff(arg) + if pi_coeff is not None: + if pi_coeff.is_integer: + return S.Zero + + if (2*pi_coeff).is_integer: + # is_even-case handled above as then pi_coeff.is_integer, + # so check if known to be not even + if pi_coeff.is_even is False: + return S.NegativeOne**(pi_coeff - S.Half) + + if not pi_coeff.is_Rational: + narg = pi_coeff*pi + if narg != arg: + return cls(narg) + return None + + # https://github.com/sympy/sympy/issues/6048 + # transform a sine to a cosine, to avoid redundant code + if pi_coeff.is_Rational: + x = pi_coeff % 2 + if x > 1: + return -cls((x % 1)*pi) + if 2*x > 1: + return cls((1 - x)*pi) + narg = ((pi_coeff + Rational(3, 2)) % 2)*pi + result = cos(narg) + if not isinstance(result, cos): + return result + if pi_coeff*pi != arg: + return cls(pi_coeff*pi) + return None + + if arg.is_Add: + x, m = _peeloff_pi(arg) + if m: + m = m*pi + return sin(m)*cos(x) + cos(m)*sin(x) + + if arg.is_zero: + return S.Zero + + if isinstance(arg, asin): + return arg.args[0] + + if isinstance(arg, atan): + x = arg.args[0] + return x/sqrt(1 + x**2) + + if isinstance(arg, atan2): + y, x = arg.args + return y/sqrt(x**2 + y**2) + + if isinstance(arg, acos): + x = arg.args[0] + return sqrt(1 - x**2) + + if isinstance(arg, acot): + x = arg.args[0] + return 1/(sqrt(1 + 1/x**2)*x) + + if isinstance(arg, acsc): + x = arg.args[0] + return 1/x + + if isinstance(arg, asec): + x = arg.args[0] + return sqrt(1 - 1/x**2) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + if len(previous_terms) > 2: + p = previous_terms[-2] + return -p*x**2/(n*(n - 1)) + else: + return S.NegativeOne**(n//2)*x**n/factorial(n) + + def _eval_nseries(self, x, n, logx, cdir=0): + arg = self.args[0] + if logx is not None: + arg = arg.subs(log(x), logx) + if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity): + raise PoleError("Cannot expand %s around 0" % (self)) + return Function._eval_nseries(self, x, n=n, logx=logx, cdir=cdir) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + from sympy.functions.elementary.hyperbolic import HyperbolicFunction + I = S.ImaginaryUnit + if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)): + arg = arg.func(arg.args[0]).rewrite(exp) + return (exp(arg*I) - exp(-arg*I))/(2*I) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + if isinstance(arg, log): + I = S.ImaginaryUnit + x = arg.args[0] + return I*x**-I/2 - I*x**I /2 + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return cos(arg - pi/2, evaluate=False) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + tan_half = tan(S.Half*arg) + return 2*tan_half/(1 + tan_half**2) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return sin(arg)*cos(arg)/cos(arg) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + cot_half = cot(S.Half*arg) + return Piecewise((0, And(Eq(im(arg), 0), Eq(Mod(arg, pi), 0))), + (2*cot_half/(1 + cot_half**2), True)) + + def _eval_rewrite_as_pow(self, arg, **kwargs): + return self.rewrite(cos, **kwargs).rewrite(pow, **kwargs) + + def _eval_rewrite_as_sqrt(self, arg, **kwargs): + return self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs) + + def _eval_rewrite_as_csc(self, arg, **kwargs): + return 1/csc(arg) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + return 1/sec(arg - pi/2, evaluate=False) + + def _eval_rewrite_as_sinc(self, arg, **kwargs): + return arg*sinc(arg) + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return sqrt(pi*arg/2)*besselj(S.Half, arg) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + from sympy.functions.elementary.hyperbolic import cosh, sinh + re, im = self._as_real_imag(deep=deep, **hints) + return (sin(re)*cosh(im), cos(re)*sinh(im)) + + def _eval_expand_trig(self, **hints): + from sympy.functions.special.polynomials import chebyshevt, chebyshevu + arg = self.args[0] + x = None + if arg.is_Add: # TODO, implement more if deep stuff here + # TODO: Do this more efficiently for more than two terms + x, y = arg.as_two_terms() + sx = sin(x, evaluate=False)._eval_expand_trig() + sy = sin(y, evaluate=False)._eval_expand_trig() + cx = cos(x, evaluate=False)._eval_expand_trig() + cy = cos(y, evaluate=False)._eval_expand_trig() + return sx*cy + sy*cx + elif arg.is_Mul: + n, x = arg.as_coeff_Mul(rational=True) + if n.is_Integer: # n will be positive because of .eval + # canonicalization + + # See https://mathworld.wolfram.com/Multiple-AngleFormulas.html + if n.is_odd: + return S.NegativeOne**((n - 1)/2)*chebyshevt(n, sin(x)) + else: + return expand_mul(S.NegativeOne**(n/2 - 1)*cos(x)* + chebyshevu(n - 1, sin(x)), deep=False) + return sin(arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = x0/pi + if n.is_integer: + lt = (arg - n*pi).as_leading_term(x) + return (S.NegativeOne**n)*lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in [S.Infinity, S.NegativeInfinity]: + return AccumBounds(-1, 1) + return self.func(x0) if x0.is_finite else self + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + + def _eval_is_finite(self): + arg = self.args[0] + if arg.is_extended_real: + return True + + def _eval_is_zero(self): + rest, pi_mult = _peeloff_pi(self.args[0]) + if rest.is_zero: + return pi_mult.is_integer + + def _eval_is_complex(self): + if self.args[0].is_extended_real \ + or self.args[0].is_complex: + return True + + +class cos(TrigonometricFunction): + """ + The cosine function. + + Returns the cosine of x (measured in radians). + + Explanation + =========== + + See :func:`sin` for notes about automatic evaluation. + + Examples + ======== + + >>> from sympy import cos, pi + >>> from sympy.abc import x + >>> cos(x**2).diff(x) + -2*x*sin(x**2) + >>> cos(1).diff(x) + 0 + >>> cos(pi) + -1 + >>> cos(pi/2) + 0 + >>> cos(2*pi/3) + -1/2 + >>> cos(pi/12) + sqrt(2)/4 + sqrt(6)/4 + + See Also + ======== + + sin, csc, sec, tan, cot + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Cos + + """ + + def period(self, symbol=None): + return self._period(2*pi, symbol) + + def fdiff(self, argindex=1): + if argindex == 1: + return -sin(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + from sympy.functions.special.polynomials import chebyshevt + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.sets.setexpr import SetExpr + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg.is_zero: + return S.One + elif arg in (S.Infinity, S.NegativeInfinity): + # In this case it is better to return AccumBounds(-1, 1) + # rather than returning S.NaN, since AccumBounds(-1, 1) + # preserves the information that sin(oo) is between + # -1 and 1, where S.NaN does not do that. + return AccumBounds(-1, 1) + + if arg is S.ComplexInfinity: + return S.NaN + + if isinstance(arg, AccumBounds): + return sin(arg + pi/2) + elif isinstance(arg, SetExpr): + return arg._eval_func(cls) + + if arg.is_extended_real and arg.is_finite is False: + return AccumBounds(-1, 1) + + if arg.could_extract_minus_sign(): + return cls(-arg) + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import cosh + return cosh(i_coeff) + + pi_coeff = _pi_coeff(arg) + if pi_coeff is not None: + if pi_coeff.is_integer: + return (S.NegativeOne)**pi_coeff + + if (2*pi_coeff).is_integer: + # is_even-case handled above as then pi_coeff.is_integer, + # so check if known to be not even + if pi_coeff.is_even is False: + return S.Zero + + if not pi_coeff.is_Rational: + narg = pi_coeff*pi + if narg != arg: + return cls(narg) + return None + + # cosine formula ##################### + # https://github.com/sympy/sympy/issues/6048 + # explicit calculations are performed for + # cos(k pi/n) for n = 8,10,12,15,20,24,30,40,60,120 + # Some other exact values like cos(k pi/240) can be + # calculated using a partial-fraction decomposition + # by calling cos( X ).rewrite(sqrt) + if pi_coeff.is_Rational: + q = pi_coeff.q + p = pi_coeff.p % (2*q) + if p > q: + narg = (pi_coeff - 1)*pi + return -cls(narg) + if 2*p > q: + narg = (1 - pi_coeff)*pi + return -cls(narg) + + # If nested sqrt's are worse than un-evaluation + # you can require q to be in (1, 2, 3, 4, 6, 12) + # q <= 12, q=15, q=20, q=24, q=30, q=40, q=60, q=120 return + # expressions with 2 or fewer sqrt nestings. + table2 = _table2() + if q in table2: + a, b = table2[q] + a, b = p*pi/a, p*pi/b + nvala, nvalb = cls(a), cls(b) + if None in (nvala, nvalb): + return None + return nvala*nvalb + cls(pi/2 - a)*cls(pi/2 - b) + + if q > 12: + return None + + cst_table_some = { + 3: S.Half, + 5: (sqrt(5) + 1) / 4, + } + if q in cst_table_some: + cts = cst_table_some[pi_coeff.q] + return chebyshevt(pi_coeff.p, cts).expand() + + if 0 == q % 2: + narg = (pi_coeff*2)*pi + nval = cls(narg) + if None == nval: + return None + x = (2*pi_coeff + 1)/2 + sign_cos = (-1)**((-1 if x < 0 else 1)*int(abs(x))) + return sign_cos*sqrt( (1 + nval)/2 ) + return None + + if arg.is_Add: + x, m = _peeloff_pi(arg) + if m: + m = m*pi + return cos(m)*cos(x) - sin(m)*sin(x) + + if arg.is_zero: + return S.One + + if isinstance(arg, acos): + return arg.args[0] + + if isinstance(arg, atan): + x = arg.args[0] + return 1/sqrt(1 + x**2) + + if isinstance(arg, atan2): + y, x = arg.args + return x/sqrt(x**2 + y**2) + + if isinstance(arg, asin): + x = arg.args[0] + return sqrt(1 - x ** 2) + + if isinstance(arg, acot): + x = arg.args[0] + return 1/sqrt(1 + 1/x**2) + + if isinstance(arg, acsc): + x = arg.args[0] + return sqrt(1 - 1/x**2) + + if isinstance(arg, asec): + x = arg.args[0] + return 1/x + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + + if len(previous_terms) > 2: + p = previous_terms[-2] + return -p*x**2/(n*(n - 1)) + else: + return S.NegativeOne**(n//2)*x**n/factorial(n) + + def _eval_nseries(self, x, n, logx, cdir=0): + arg = self.args[0] + if logx is not None: + arg = arg.subs(log(x), logx) + if arg.subs(x, 0).has(S.NaN, S.ComplexInfinity): + raise PoleError("Cannot expand %s around 0" % (self)) + return Function._eval_nseries(self, x, n=n, logx=logx, cdir=cdir) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + I = S.ImaginaryUnit + from sympy.functions.elementary.hyperbolic import HyperbolicFunction + if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)): + arg = arg.func(arg.args[0]).rewrite(exp, **kwargs) + return (exp(arg*I) + exp(-arg*I))/2 + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + if isinstance(arg, log): + I = S.ImaginaryUnit + x = arg.args[0] + return x**I/2 + x**-I/2 + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return sin(arg + pi/2, evaluate=False) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + tan_half = tan(S.Half*arg)**2 + return (1 - tan_half)/(1 + tan_half) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return sin(arg)*cos(arg)/sin(arg) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + cot_half = cot(S.Half*arg)**2 + return Piecewise((1, And(Eq(im(arg), 0), Eq(Mod(arg, 2*pi), 0))), + ((cot_half - 1)/(cot_half + 1), True)) + + def _eval_rewrite_as_pow(self, arg, **kwargs): + return self._eval_rewrite_as_sqrt(arg, **kwargs) + + def _eval_rewrite_as_sqrt(self, arg: Expr, **kwargs): + from sympy.functions.special.polynomials import chebyshevt + + pi_coeff = _pi_coeff(arg) + if pi_coeff is None: + return None + + if isinstance(pi_coeff, Integer): + return None + + if not isinstance(pi_coeff, Rational): + return None + + cst_table_some = cos_table() + + if pi_coeff.q in cst_table_some: + rv = chebyshevt(pi_coeff.p, cst_table_some[pi_coeff.q]()) + if pi_coeff.q < 257: + rv = rv.expand() + return rv + + if not pi_coeff.q % 2: # recursively remove factors of 2 + pico2 = pi_coeff * 2 + nval = cos(pico2 * pi).rewrite(sqrt, **kwargs) + x = (pico2 + 1) / 2 + sign_cos = -1 if int(x) % 2 else 1 + return sign_cos * sqrt((1 + nval) / 2) + + FC = fermat_coords(pi_coeff.q) + if FC: + denoms = FC + else: + denoms = [b**e for b, e in factorint(pi_coeff.q).items()] + + apart = ipartfrac(*denoms) + decomp = (pi_coeff.p * Rational(n, d) for n, d in zip(apart, denoms)) + X = [(x[1], x[0]*pi) for x in zip(decomp, numbered_symbols('z'))] + pcls = cos(sum(x[0] for x in X))._eval_expand_trig().subs(X) + + if not FC or len(FC) == 1: + return pcls + return pcls.rewrite(sqrt, **kwargs) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + return 1/sec(arg) + + def _eval_rewrite_as_csc(self, arg, **kwargs): + return 1/sec(arg).rewrite(csc, **kwargs) + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return Piecewise( + (sqrt(pi*arg/2)*besselj(-S.Half, arg), Ne(arg, 0)), + (1, True) + ) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + from sympy.functions.elementary.hyperbolic import cosh, sinh + re, im = self._as_real_imag(deep=deep, **hints) + return (cos(re)*cosh(im), -sin(re)*sinh(im)) + + def _eval_expand_trig(self, **hints): + from sympy.functions.special.polynomials import chebyshevt + arg = self.args[0] + x = None + if arg.is_Add: # TODO: Do this more efficiently for more than two terms + x, y = arg.as_two_terms() + sx = sin(x, evaluate=False)._eval_expand_trig() + sy = sin(y, evaluate=False)._eval_expand_trig() + cx = cos(x, evaluate=False)._eval_expand_trig() + cy = cos(y, evaluate=False)._eval_expand_trig() + return cx*cy - sx*sy + elif arg.is_Mul: + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff.is_Integer: + return chebyshevt(coeff, cos(terms)) + return cos(arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = (x0 + pi/2)/pi + if n.is_integer: + lt = (arg - n*pi + pi/2).as_leading_term(x) + return (S.NegativeOne**n)*lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in [S.Infinity, S.NegativeInfinity]: + return AccumBounds(-1, 1) + return self.func(x0) if x0.is_finite else self + + def _eval_is_extended_real(self): + if self.args[0].is_extended_real: + return True + + def _eval_is_finite(self): + arg = self.args[0] + + if arg.is_extended_real: + return True + + def _eval_is_complex(self): + if self.args[0].is_extended_real \ + or self.args[0].is_complex: + return True + + def _eval_is_zero(self): + rest, pi_mult = _peeloff_pi(self.args[0]) + if rest.is_zero and pi_mult: + return (pi_mult - S.Half).is_integer + + +class tan(TrigonometricFunction): + """ + The tangent function. + + Returns the tangent of x (measured in radians). + + Explanation + =========== + + See :class:`sin` for notes about automatic evaluation. + + Examples + ======== + + >>> from sympy import tan, pi + >>> from sympy.abc import x + >>> tan(x**2).diff(x) + 2*x*(tan(x**2)**2 + 1) + >>> tan(1).diff(x) + 0 + >>> tan(pi/8).expand() + -1 + sqrt(2) + + See Also + ======== + + sin, csc, cos, sec, cot + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Tan + + """ + + def period(self, symbol=None): + return self._period(pi, symbol) + + def fdiff(self, argindex=1): + if argindex == 1: + return S.One + self**2 + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return atan + + @classmethod + def eval(cls, arg): + from sympy.calculus.accumulationbounds import AccumBounds + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg.is_zero: + return S.Zero + elif arg in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + + if arg is S.ComplexInfinity: + return S.NaN + + if isinstance(arg, AccumBounds): + min, max = arg.min, arg.max + d = floor(min/pi) + if min is not S.NegativeInfinity: + min = min - d*pi + if max is not S.Infinity: + max = max - d*pi + from sympy.sets.sets import FiniteSet + if AccumBounds(min, max).intersection(FiniteSet(pi/2, pi*Rational(3, 2))): + return AccumBounds(S.NegativeInfinity, S.Infinity) + else: + return AccumBounds(tan(min), tan(max)) + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import tanh + return S.ImaginaryUnit*tanh(i_coeff) + + pi_coeff = _pi_coeff(arg, 2) + if pi_coeff is not None: + if pi_coeff.is_integer: + return S.Zero + + if not pi_coeff.is_Rational: + narg = pi_coeff*pi + if narg != arg: + return cls(narg) + return None + + if pi_coeff.is_Rational: + q = pi_coeff.q + p = pi_coeff.p % q + # ensure simplified results are returned for n*pi/5, n*pi/10 + table10 = { + 1: sqrt(1 - 2*sqrt(5)/5), + 2: sqrt(5 - 2*sqrt(5)), + 3: sqrt(1 + 2*sqrt(5)/5), + 4: sqrt(5 + 2*sqrt(5)) + } + if q in (5, 10): + n = 10*p/q + if n > 5: + n = 10 - n + return -table10[n] + else: + return table10[n] + if not pi_coeff.q % 2: + narg = pi_coeff*pi*2 + cresult, sresult = cos(narg), cos(narg - pi/2) + if not isinstance(cresult, cos) \ + and not isinstance(sresult, cos): + if sresult == 0: + return S.ComplexInfinity + return 1/sresult - cresult/sresult + + table2 = _table2() + if q in table2: + a, b = table2[q] + nvala, nvalb = cls(p*pi/a), cls(p*pi/b) + if None in (nvala, nvalb): + return None + return (nvala - nvalb)/(1 + nvala*nvalb) + narg = ((pi_coeff + S.Half) % 1 - S.Half)*pi + # see cos() to specify which expressions should be + # expanded automatically in terms of radicals + cresult, sresult = cos(narg), cos(narg - pi/2) + if not isinstance(cresult, cos) \ + and not isinstance(sresult, cos): + if cresult == 0: + return S.ComplexInfinity + return (sresult/cresult) + if narg != arg: + return cls(narg) + + if arg.is_Add: + x, m = _peeloff_pi(arg) + if m: + tanm = tan(m*pi) + if tanm is S.ComplexInfinity: + return -cot(x) + else: # tanm == 0 + return tan(x) + + if arg.is_zero: + return S.Zero + + if isinstance(arg, atan): + return arg.args[0] + + if isinstance(arg, atan2): + y, x = arg.args + return y/x + + if isinstance(arg, asin): + x = arg.args[0] + return x/sqrt(1 - x**2) + + if isinstance(arg, acos): + x = arg.args[0] + return sqrt(1 - x**2)/x + + if isinstance(arg, acot): + x = arg.args[0] + return 1/x + + if isinstance(arg, acsc): + x = arg.args[0] + return 1/(sqrt(1 - 1/x**2)*x) + + if isinstance(arg, asec): + x = arg.args[0] + return sqrt(1 - 1/x**2)*x + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + a, b = ((n - 1)//2), 2**(n + 1) + + B = bernoulli(n + 1) + F = factorial(n + 1) + + return S.NegativeOne**a*b*(b - 1)*B/F*x**n + + def _eval_nseries(self, x, n, logx, cdir=0): + i = self.args[0].limit(x, 0)*2/pi + if i and i.is_Integer: + return self.rewrite(cos)._eval_nseries(x, n=n, logx=logx) + return Function._eval_nseries(self, x, n=n, logx=logx) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + if isinstance(arg, log): + I = S.ImaginaryUnit + x = arg.args[0] + return I*(x**-I - x**I)/(x**-I + x**I) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + re, im = self._as_real_imag(deep=deep, **hints) + if im: + from sympy.functions.elementary.hyperbolic import cosh, sinh + denom = cos(2*re) + cosh(2*im) + return (sin(2*re)/denom, sinh(2*im)/denom) + else: + return (self.func(re), S.Zero) + + def _eval_expand_trig(self, **hints): + arg = self.args[0] + x = None + if arg.is_Add: + n = len(arg.args) + TX = [] + for x in arg.args: + tx = tan(x, evaluate=False)._eval_expand_trig() + TX.append(tx) + + Yg = numbered_symbols('Y') + Y = [ next(Yg) for i in range(n) ] + + p = [0, 0] + for i in range(n + 1): + p[1 - i % 2] += symmetric_poly(i, Y)*(-1)**((i % 4)//2) + return (p[0]/p[1]).subs(list(zip(Y, TX))) + + elif arg.is_Mul: + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff.is_Integer and coeff > 1: + I = S.ImaginaryUnit + z = Symbol('dummy', real=True) + P = ((1 + I*z)**coeff).expand() + return (im(P)/re(P)).subs([(z, tan(terms))]) + return tan(arg) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + I = S.ImaginaryUnit + from sympy.functions.elementary.hyperbolic import HyperbolicFunction + if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)): + arg = arg.func(arg.args[0]).rewrite(exp) + neg_exp, pos_exp = exp(-arg*I), exp(arg*I) + return I*(neg_exp - pos_exp)/(neg_exp + pos_exp) + + def _eval_rewrite_as_sin(self, x, **kwargs): + return 2*sin(x)**2/sin(2*x) + + def _eval_rewrite_as_cos(self, x, **kwargs): + return cos(x - pi/2, evaluate=False)/cos(x) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return sin(arg)/cos(arg) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + return 1/cot(arg) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + sin_in_sec_form = sin(arg).rewrite(sec, **kwargs) + cos_in_sec_form = cos(arg).rewrite(sec, **kwargs) + return sin_in_sec_form/cos_in_sec_form + + def _eval_rewrite_as_csc(self, arg, **kwargs): + sin_in_csc_form = sin(arg).rewrite(csc, **kwargs) + cos_in_csc_form = cos(arg).rewrite(csc, **kwargs) + return sin_in_csc_form/cos_in_csc_form + + def _eval_rewrite_as_pow(self, arg, **kwargs): + y = self.rewrite(cos, **kwargs).rewrite(pow, **kwargs) + if y.has(cos): + return None + return y + + def _eval_rewrite_as_sqrt(self, arg, **kwargs): + y = self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs) + if y.has(cos): + return None + return y + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return besselj(S.Half, arg)/besselj(-S.Half, arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.functions.elementary.complexes import re + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = 2*x0/pi + if n.is_integer: + lt = (arg - n*pi/2).as_leading_term(x) + return lt if n.is_even else -1/lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + return self.func(x0) if x0.is_finite else self + + def _eval_is_extended_real(self): + # FIXME: currently tan(pi/2) return zoo + return self.args[0].is_extended_real + + def _eval_is_real(self): + arg = self.args[0] + if arg.is_real and (arg/pi - S.Half).is_integer is False: + return True + + def _eval_is_finite(self): + arg = self.args[0] + + if arg.is_real and (arg/pi - S.Half).is_integer is False: + return True + + if arg.is_imaginary: + return True + + def _eval_is_zero(self): + rest, pi_mult = _peeloff_pi(self.args[0]) + if rest.is_zero: + return pi_mult.is_integer + + def _eval_is_complex(self): + arg = self.args[0] + + if arg.is_real and (arg/pi - S.Half).is_integer is False: + return True + + +class cot(TrigonometricFunction): + """ + The cotangent function. + + Returns the cotangent of x (measured in radians). + + Explanation + =========== + + See :class:`sin` for notes about automatic evaluation. + + Examples + ======== + + >>> from sympy import cot, pi + >>> from sympy.abc import x + >>> cot(x**2).diff(x) + 2*x*(-cot(x**2)**2 - 1) + >>> cot(1).diff(x) + 0 + >>> cot(pi/12) + sqrt(3) + 2 + + See Also + ======== + + sin, csc, cos, sec, tan + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Cot + + """ + + def period(self, symbol=None): + return self._period(pi, symbol) + + def fdiff(self, argindex=1): + if argindex == 1: + return S.NegativeOne - self**2 + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return acot + + @classmethod + def eval(cls, arg): + from sympy.calculus.accumulationbounds import AccumBounds + if arg.is_Number: + if arg is S.NaN: + return S.NaN + if arg.is_zero: + return S.ComplexInfinity + elif arg in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + + if arg is S.ComplexInfinity: + return S.NaN + + if isinstance(arg, AccumBounds): + return -tan(arg + pi/2) + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import coth + return -S.ImaginaryUnit*coth(i_coeff) + + pi_coeff = _pi_coeff(arg, 2) + if pi_coeff is not None: + if pi_coeff.is_integer: + return S.ComplexInfinity + + if not pi_coeff.is_Rational: + narg = pi_coeff*pi + if narg != arg: + return cls(narg) + return None + + if pi_coeff.is_Rational: + if pi_coeff.q in (5, 10): + return tan(pi/2 - arg) + if pi_coeff.q > 2 and not pi_coeff.q % 2: + narg = pi_coeff*pi*2 + cresult, sresult = cos(narg), cos(narg - pi/2) + if not isinstance(cresult, cos) \ + and not isinstance(sresult, cos): + return 1/sresult + cresult/sresult + q = pi_coeff.q + p = pi_coeff.p % q + table2 = _table2() + if q in table2: + a, b = table2[q] + nvala, nvalb = cls(p*pi/a), cls(p*pi/b) + if None in (nvala, nvalb): + return None + return (1 + nvala*nvalb)/(nvalb - nvala) + narg = (((pi_coeff + S.Half) % 1) - S.Half)*pi + # see cos() to specify which expressions should be + # expanded automatically in terms of radicals + cresult, sresult = cos(narg), cos(narg - pi/2) + if not isinstance(cresult, cos) \ + and not isinstance(sresult, cos): + if sresult == 0: + return S.ComplexInfinity + return cresult/sresult + if narg != arg: + return cls(narg) + + if arg.is_Add: + x, m = _peeloff_pi(arg) + if m: + cotm = cot(m*pi) + if cotm is S.ComplexInfinity: + return cot(x) + else: # cotm == 0 + return -tan(x) + + if arg.is_zero: + return S.ComplexInfinity + + if isinstance(arg, acot): + return arg.args[0] + + if isinstance(arg, atan): + x = arg.args[0] + return 1/x + + if isinstance(arg, atan2): + y, x = arg.args + return x/y + + if isinstance(arg, asin): + x = arg.args[0] + return sqrt(1 - x**2)/x + + if isinstance(arg, acos): + x = arg.args[0] + return x/sqrt(1 - x**2) + + if isinstance(arg, acsc): + x = arg.args[0] + return sqrt(1 - 1/x**2)*x + + if isinstance(arg, asec): + x = arg.args[0] + return 1/(sqrt(1 - 1/x**2)*x) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return 1/sympify(x) + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + + B = bernoulli(n + 1) + F = factorial(n + 1) + + return S.NegativeOne**((n + 1)//2)*2**(n + 1)*B/F*x**n + + def _eval_nseries(self, x, n, logx, cdir=0): + i = self.args[0].limit(x, 0)/pi + if i and i.is_Integer: + return self.rewrite(cos)._eval_nseries(x, n=n, logx=logx) + return self.rewrite(tan)._eval_nseries(x, n=n, logx=logx) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + re, im = self._as_real_imag(deep=deep, **hints) + if im: + from sympy.functions.elementary.hyperbolic import cosh, sinh + denom = cos(2*re) - cosh(2*im) + return (-sin(2*re)/denom, sinh(2*im)/denom) + else: + return (self.func(re), S.Zero) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + from sympy.functions.elementary.hyperbolic import HyperbolicFunction + I = S.ImaginaryUnit + if isinstance(arg, (TrigonometricFunction, HyperbolicFunction)): + arg = arg.func(arg.args[0]).rewrite(exp, **kwargs) + neg_exp, pos_exp = exp(-arg*I), exp(arg*I) + return I*(pos_exp + neg_exp)/(pos_exp - neg_exp) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + if isinstance(arg, log): + I = S.ImaginaryUnit + x = arg.args[0] + return -I*(x**-I + x**I)/(x**-I - x**I) + + def _eval_rewrite_as_sin(self, x, **kwargs): + return sin(2*x)/(2*(sin(x)**2)) + + def _eval_rewrite_as_cos(self, x, **kwargs): + return cos(x)/cos(x - pi/2, evaluate=False) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return cos(arg)/sin(arg) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + return 1/tan(arg) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + cos_in_sec_form = cos(arg).rewrite(sec, **kwargs) + sin_in_sec_form = sin(arg).rewrite(sec, **kwargs) + return cos_in_sec_form/sin_in_sec_form + + def _eval_rewrite_as_csc(self, arg, **kwargs): + cos_in_csc_form = cos(arg).rewrite(csc, **kwargs) + sin_in_csc_form = sin(arg).rewrite(csc, **kwargs) + return cos_in_csc_form/sin_in_csc_form + + def _eval_rewrite_as_pow(self, arg, **kwargs): + y = self.rewrite(cos, **kwargs).rewrite(pow, **kwargs) + if y.has(cos): + return None + return y + + def _eval_rewrite_as_sqrt(self, arg, **kwargs): + y = self.rewrite(cos, **kwargs).rewrite(sqrt, **kwargs) + if y.has(cos): + return None + return y + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return besselj(-S.Half, arg)/besselj(S.Half, arg) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.functions.elementary.complexes import re + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = 2*x0/pi + if n.is_integer: + lt = (arg - n*pi/2).as_leading_term(x) + return 1/lt if n.is_even else -lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + return self.func(x0) if x0.is_finite else self + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + def _eval_expand_trig(self, **hints): + arg = self.args[0] + x = None + if arg.is_Add: + n = len(arg.args) + CX = [] + for x in arg.args: + cx = cot(x, evaluate=False)._eval_expand_trig() + CX.append(cx) + + Yg = numbered_symbols('Y') + Y = [ next(Yg) for i in range(n) ] + + p = [0, 0] + for i in range(n, -1, -1): + p[(n - i) % 2] += symmetric_poly(i, Y)*(-1)**(((n - i) % 4)//2) + return (p[0]/p[1]).subs(list(zip(Y, CX))) + elif arg.is_Mul: + coeff, terms = arg.as_coeff_Mul(rational=True) + if coeff.is_Integer and coeff > 1: + I = S.ImaginaryUnit + z = Symbol('dummy', real=True) + P = ((z + I)**coeff).expand() + return (re(P)/im(P)).subs([(z, cot(terms))]) + return cot(arg) # XXX sec and csc return 1/cos and 1/sin + + def _eval_is_finite(self): + arg = self.args[0] + if arg.is_real and (arg/pi).is_integer is False: + return True + if arg.is_imaginary: + return True + + def _eval_is_real(self): + arg = self.args[0] + if arg.is_real and (arg/pi).is_integer is False: + return True + + def _eval_is_complex(self): + arg = self.args[0] + if arg.is_real and (arg/pi).is_integer is False: + return True + + def _eval_is_zero(self): + rest, pimult = _peeloff_pi(self.args[0]) + if pimult and rest.is_zero: + return (pimult - S.Half).is_integer + + def _eval_subs(self, old, new): + arg = self.args[0] + argnew = arg.subs(old, new) + if arg != argnew and (argnew/pi).is_integer: + return S.ComplexInfinity + return cot(argnew) + + +class ReciprocalTrigonometricFunction(TrigonometricFunction): + """Base class for reciprocal functions of trigonometric functions. """ + + _reciprocal_of = None # mandatory, to be defined in subclass + _singularities = (S.ComplexInfinity,) + + # _is_even and _is_odd are used for correct evaluation of csc(-x), sec(-x) + # TODO refactor into TrigonometricFunction common parts of + # trigonometric functions eval() like even/odd, func(x+2*k*pi), etc. + + # optional, to be defined in subclasses: + _is_even: FuzzyBool = None + _is_odd: FuzzyBool = None + + @classmethod + def eval(cls, arg): + if arg.could_extract_minus_sign(): + if cls._is_even: + return cls(-arg) + if cls._is_odd: + return -cls(-arg) + + pi_coeff = _pi_coeff(arg) + if (pi_coeff is not None + and not (2*pi_coeff).is_integer + and pi_coeff.is_Rational): + q = pi_coeff.q + p = pi_coeff.p % (2*q) + if p > q: + narg = (pi_coeff - 1)*pi + return -cls(narg) + if 2*p > q: + narg = (1 - pi_coeff)*pi + if cls._is_odd: + return cls(narg) + elif cls._is_even: + return -cls(narg) + + if hasattr(arg, 'inverse') and arg.inverse() == cls: + return arg.args[0] + + t = cls._reciprocal_of.eval(arg) + if t is None: + return t + elif any(isinstance(i, cos) for i in (t, -t)): + return (1/t).rewrite(sec) + elif any(isinstance(i, sin) for i in (t, -t)): + return (1/t).rewrite(csc) + else: + return 1/t + + def _call_reciprocal(self, method_name, *args, **kwargs): + # Calls method_name on _reciprocal_of + o = self._reciprocal_of(self.args[0]) + return getattr(o, method_name)(*args, **kwargs) + + def _calculate_reciprocal(self, method_name, *args, **kwargs): + # If calling method_name on _reciprocal_of returns a value != None + # then return the reciprocal of that value + t = self._call_reciprocal(method_name, *args, **kwargs) + return 1/t if t is not None else t + + def _rewrite_reciprocal(self, method_name, arg): + # Special handling for rewrite functions. If reciprocal rewrite returns + # unmodified expression, then return None + t = self._call_reciprocal(method_name, arg) + if t is not None and t != self._reciprocal_of(arg): + return 1/t + + def _period(self, symbol): + f = expand_mul(self.args[0]) + return self._reciprocal_of(f).period(symbol) + + def fdiff(self, argindex=1): + return -self._calculate_reciprocal("fdiff", argindex)/self**2 + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_exp", arg) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_Pow", arg) + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_sin", arg) + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_cos", arg) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_tan", arg) + + def _eval_rewrite_as_pow(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_pow", arg) + + def _eval_rewrite_as_sqrt(self, arg, **kwargs): + return self._rewrite_reciprocal("_eval_rewrite_as_sqrt", arg) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def as_real_imag(self, deep=True, **hints): + return (1/self._reciprocal_of(self.args[0])).as_real_imag(deep, + **hints) + + def _eval_expand_trig(self, **hints): + return self._calculate_reciprocal("_eval_expand_trig", **hints) + + def _eval_is_extended_real(self): + return self._reciprocal_of(self.args[0])._eval_is_extended_real() + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + return (1/self._reciprocal_of(self.args[0]))._eval_as_leading_term(x) + + def _eval_is_finite(self): + return (1/self._reciprocal_of(self.args[0])).is_finite + + def _eval_nseries(self, x, n, logx, cdir=0): + return (1/self._reciprocal_of(self.args[0]))._eval_nseries(x, n, logx) + + +class sec(ReciprocalTrigonometricFunction): + """ + The secant function. + + Returns the secant of x (measured in radians). + + Explanation + =========== + + See :class:`sin` for notes about automatic evaluation. + + Examples + ======== + + >>> from sympy import sec + >>> from sympy.abc import x + >>> sec(x**2).diff(x) + 2*x*tan(x**2)*sec(x**2) + >>> sec(1).diff(x) + 0 + + See Also + ======== + + sin, csc, cos, tan, cot + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Sec + + """ + + _reciprocal_of = cos + _is_even = True + + def period(self, symbol=None): + return self._period(symbol) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + cot_half_sq = cot(arg/2)**2 + return (cot_half_sq + 1)/(cot_half_sq - 1) + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return (1/cos(arg)) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return sin(arg)/(cos(arg)*sin(arg)) + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return (1/cos(arg).rewrite(sin, **kwargs)) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + return (1/cos(arg).rewrite(tan, **kwargs)) + + def _eval_rewrite_as_csc(self, arg, **kwargs): + return csc(pi/2 - arg, evaluate=False) + + def fdiff(self, argindex=1): + if argindex == 1: + return tan(self.args[0])*sec(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return Piecewise( + (1/(sqrt(pi*arg)/(sqrt(2))*besselj(-S.Half, arg)), Ne(arg, 0)), + (1, True) + ) + + def _eval_is_complex(self): + arg = self.args[0] + + if arg.is_complex and (arg/pi - S.Half).is_integer is False: + return True + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + # Reference Formula: + # https://functions.wolfram.com/ElementaryFunctions/Sec/06/01/02/01/ + if n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + k = n//2 + return S.NegativeOne**k*euler(2*k)/factorial(2*k)*x**(2*k) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.functions.elementary.complexes import re + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = (x0 + pi/2)/pi + if n.is_integer: + lt = (arg - n*pi + pi/2).as_leading_term(x) + return (S.NegativeOne**n)/lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + return self.func(x0) if x0.is_finite else self + + +class csc(ReciprocalTrigonometricFunction): + """ + The cosecant function. + + Returns the cosecant of x (measured in radians). + + Explanation + =========== + + See :func:`sin` for notes about automatic evaluation. + + Examples + ======== + + >>> from sympy import csc + >>> from sympy.abc import x + >>> csc(x**2).diff(x) + -2*x*cot(x**2)*csc(x**2) + >>> csc(1).diff(x) + 0 + + See Also + ======== + + sin, cos, sec, tan, cot + asin, acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_functions + .. [2] https://dlmf.nist.gov/4.14 + .. [3] https://functions.wolfram.com/ElementaryFunctions/Csc + + """ + + _reciprocal_of = sin + _is_odd = True + + def period(self, symbol=None): + return self._period(symbol) + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return (1/sin(arg)) + + def _eval_rewrite_as_sincos(self, arg, **kwargs): + return cos(arg)/(sin(arg)*cos(arg)) + + def _eval_rewrite_as_cot(self, arg, **kwargs): + cot_half = cot(arg/2) + return (1 + cot_half**2)/(2*cot_half) + + def _eval_rewrite_as_cos(self, arg, **kwargs): + return 1/sin(arg).rewrite(cos, **kwargs) + + def _eval_rewrite_as_sec(self, arg, **kwargs): + return sec(pi/2 - arg, evaluate=False) + + def _eval_rewrite_as_tan(self, arg, **kwargs): + return (1/sin(arg).rewrite(tan, **kwargs)) + + def _eval_rewrite_as_besselj(self, arg, **kwargs): + from sympy.functions.special.bessel import besselj + return sqrt(2/pi)*(1/(sqrt(arg)*besselj(S.Half, arg))) + + def fdiff(self, argindex=1): + if argindex == 1: + return -cot(self.args[0])*csc(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_complex(self): + arg = self.args[0] + if arg.is_real and (arg/pi).is_integer is False: + return True + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return 1/sympify(x) + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + k = n//2 + 1 + return (S.NegativeOne**(k - 1)*2*(2**(2*k - 1) - 1)* + bernoulli(2*k)*x**(2*k - 1)/factorial(2*k)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.calculus.accumulationbounds import AccumBounds + from sympy.functions.elementary.complexes import re + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + n = x0/pi + if n.is_integer: + lt = (arg - n*pi).as_leading_term(x) + return (S.NegativeOne**n)/lt + if x0 is S.ComplexInfinity: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if x0 in (S.Infinity, S.NegativeInfinity): + return AccumBounds(S.NegativeInfinity, S.Infinity) + return self.func(x0) if x0.is_finite else self + + +class sinc(Function): + r""" + Represents an unnormalized sinc function: + + .. math:: + + \operatorname{sinc}(x) = + \begin{cases} + \frac{\sin x}{x} & \qquad x \neq 0 \\ + 1 & \qquad x = 0 + \end{cases} + + Examples + ======== + + >>> from sympy import sinc, oo, jn + >>> from sympy.abc import x + >>> sinc(x) + sinc(x) + + * Automated Evaluation + + >>> sinc(0) + 1 + >>> sinc(oo) + 0 + + * Differentiation + + >>> sinc(x).diff() + cos(x)/x - sin(x)/x**2 + + * Series Expansion + + >>> sinc(x).series() + 1 - x**2/6 + x**4/120 + O(x**6) + + * As zero'th order spherical Bessel Function + + >>> sinc(x).rewrite(jn) + jn(0, x) + + See also + ======== + + sin + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Sinc_function + + """ + _singularities = (S.ComplexInfinity,) + + def fdiff(self, argindex=1): + x = self.args[0] + if argindex == 1: + # We would like to return the Piecewise here, but Piecewise.diff + # currently can't handle removable singularities, meaning things + # like sinc(x).diff(x, 2) give the wrong answer at x = 0. See + # https://github.com/sympy/sympy/issues/11402. + # + # return Piecewise(((x*cos(x) - sin(x))/x**2, Ne(x, S.Zero)), (S.Zero, S.true)) + return cos(x)/x - sin(x)/x**2 + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_zero: + return S.One + if arg.is_Number: + if arg in [S.Infinity, S.NegativeInfinity]: + return S.Zero + elif arg is S.NaN: + return S.NaN + + if arg is S.ComplexInfinity: + return S.NaN + + if arg.could_extract_minus_sign(): + return cls(-arg) + + pi_coeff = _pi_coeff(arg) + if pi_coeff is not None: + if pi_coeff.is_integer: + if fuzzy_not(arg.is_zero): + return S.Zero + elif (2*pi_coeff).is_integer: + return S.NegativeOne**(pi_coeff - S.Half)/arg + + def _eval_nseries(self, x, n, logx, cdir=0): + x = self.args[0] + return (sin(x)/x)._eval_nseries(x, n, logx) + + def _eval_rewrite_as_jn(self, arg, **kwargs): + from sympy.functions.special.bessel import jn + return jn(0, arg) + + def _eval_rewrite_as_sin(self, arg, **kwargs): + return Piecewise((sin(arg)/arg, Ne(arg, S.Zero)), (S.One, S.true)) + + def _eval_is_zero(self): + if self.args[0].is_infinite: + return True + rest, pi_mult = _peeloff_pi(self.args[0]) + if rest.is_zero: + return fuzzy_and([pi_mult.is_integer, pi_mult.is_nonzero]) + if rest.is_Number and pi_mult.is_integer: + return False + + def _eval_is_real(self): + if self.args[0].is_extended_real or self.args[0].is_imaginary: + return True + + _eval_is_finite = _eval_is_real + + +############################################################################### +########################### TRIGONOMETRIC INVERSES ############################ +############################################################################### + + +class InverseTrigonometricFunction(Function): + """Base class for inverse trigonometric functions.""" + _singularities = (S.One, S.NegativeOne, S.Zero, S.ComplexInfinity) # type: tTuple[Expr, ...] + + @staticmethod + @cacheit + def _asin_table(): + # Only keys with could_extract_minus_sign() == False + # are actually needed. + return { + sqrt(3)/2: pi/3, + sqrt(2)/2: pi/4, + 1/sqrt(2): pi/4, + sqrt((5 - sqrt(5))/8): pi/5, + sqrt(2)*sqrt(5 - sqrt(5))/4: pi/5, + sqrt((5 + sqrt(5))/8): pi*Rational(2, 5), + sqrt(2)*sqrt(5 + sqrt(5))/4: pi*Rational(2, 5), + S.Half: pi/6, + sqrt(2 - sqrt(2))/2: pi/8, + sqrt(S.Half - sqrt(2)/4): pi/8, + sqrt(2 + sqrt(2))/2: pi*Rational(3, 8), + sqrt(S.Half + sqrt(2)/4): pi*Rational(3, 8), + (sqrt(5) - 1)/4: pi/10, + (1 - sqrt(5))/4: -pi/10, + (sqrt(5) + 1)/4: pi*Rational(3, 10), + sqrt(6)/4 - sqrt(2)/4: pi/12, + -sqrt(6)/4 + sqrt(2)/4: -pi/12, + (sqrt(3) - 1)/sqrt(8): pi/12, + (1 - sqrt(3))/sqrt(8): -pi/12, + sqrt(6)/4 + sqrt(2)/4: pi*Rational(5, 12), + (1 + sqrt(3))/sqrt(8): pi*Rational(5, 12) + } + + + @staticmethod + @cacheit + def _atan_table(): + # Only keys with could_extract_minus_sign() == False + # are actually needed. + return { + sqrt(3)/3: pi/6, + 1/sqrt(3): pi/6, + sqrt(3): pi/3, + sqrt(2) - 1: pi/8, + 1 - sqrt(2): -pi/8, + 1 + sqrt(2): pi*Rational(3, 8), + sqrt(5 - 2*sqrt(5)): pi/5, + sqrt(5 + 2*sqrt(5)): pi*Rational(2, 5), + sqrt(1 - 2*sqrt(5)/5): pi/10, + sqrt(1 + 2*sqrt(5)/5): pi*Rational(3, 10), + 2 - sqrt(3): pi/12, + -2 + sqrt(3): -pi/12, + 2 + sqrt(3): pi*Rational(5, 12) + } + + @staticmethod + @cacheit + def _acsc_table(): + # Keys for which could_extract_minus_sign() + # will obviously return True are omitted. + return { + 2*sqrt(3)/3: pi/3, + sqrt(2): pi/4, + sqrt(2 + 2*sqrt(5)/5): pi/5, + 1/sqrt(Rational(5, 8) - sqrt(5)/8): pi/5, + sqrt(2 - 2*sqrt(5)/5): pi*Rational(2, 5), + 1/sqrt(Rational(5, 8) + sqrt(5)/8): pi*Rational(2, 5), + 2: pi/6, + sqrt(4 + 2*sqrt(2)): pi/8, + 2/sqrt(2 - sqrt(2)): pi/8, + sqrt(4 - 2*sqrt(2)): pi*Rational(3, 8), + 2/sqrt(2 + sqrt(2)): pi*Rational(3, 8), + 1 + sqrt(5): pi/10, + sqrt(5) - 1: pi*Rational(3, 10), + -(sqrt(5) - 1): pi*Rational(-3, 10), + sqrt(6) + sqrt(2): pi/12, + sqrt(6) - sqrt(2): pi*Rational(5, 12), + -(sqrt(6) - sqrt(2)): pi*Rational(-5, 12) + } + + +class asin(InverseTrigonometricFunction): + r""" + The inverse sine function. + + Returns the arcsine of x in radians. + + Explanation + =========== + + ``asin(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the + result is a rational multiple of $\pi$ (see the ``eval`` class method). + + A purely imaginary argument will lead to an asinh expression. + + Examples + ======== + + >>> from sympy import asin, oo + >>> asin(1) + pi/2 + >>> asin(-1) + -pi/2 + >>> asin(-oo) + oo*I + >>> asin(oo) + -oo*I + + See Also + ======== + + sin, csc, cos, sec, tan, cot + acsc, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://dlmf.nist.gov/4.23 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSin + + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/sqrt(1 - self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if s.args[0].is_rational: + return False + else: + return s.is_rational + + def _eval_is_positive(self): + return self._eval_is_extended_real() and self.args[0].is_positive + + def _eval_is_negative(self): + return self._eval_is_extended_real() and self.args[0].is_negative + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.NegativeInfinity*S.ImaginaryUnit + elif arg is S.NegativeInfinity: + return S.Infinity*S.ImaginaryUnit + elif arg.is_zero: + return S.Zero + elif arg is S.One: + return pi/2 + elif arg is S.NegativeOne: + return -pi/2 + + if arg is S.ComplexInfinity: + return S.ComplexInfinity + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_number: + asin_table = cls._asin_table() + if arg in asin_table: + return asin_table[arg] + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import asinh + return S.ImaginaryUnit*asinh(i_coeff) + + if arg.is_zero: + return S.Zero + + if isinstance(arg, sin): + ang = arg.args[0] + if ang.is_comparable: + ang %= 2*pi # restrict to [0,2*pi) + if ang > pi: # restrict to (-pi,pi] + ang = pi - ang + + # restrict to [-pi/2,pi/2] + if ang > pi/2: + ang = pi - ang + if ang < -pi/2: + ang = -pi - ang + + return ang + + if isinstance(arg, cos): # acos(x) + asin(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + return pi/2 - acos(arg) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) >= 2 and n > 2: + p = previous_terms[-2] + return p*(n - 2)**2/(n*(n - 1))*x**2 + else: + k = (n - 1) // 2 + R = RisingFactorial(S.Half, k) + F = factorial(k) + return R/F*x**n/n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # asin + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + if x0.is_zero: + return arg.as_leading_term(x) + + # Handling branch points + if x0 in (-S.One, S.One, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + # Handling points lying on branch cuts (-oo, -1) U (1, oo) + if (1 - x0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_negative: + return -pi - self.func(x0) + elif im(ndir).is_positive: + if x0.is_positive: + return pi - self.func(x0) + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # asin + from sympy.series.order import O + arg0 = self.args[0].subs(x, 0) + # Handling branch points + if arg0 is S.One: + t = Dummy('t', positive=True) + ser = asin(S.One - t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One - self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else pi/2 + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + if arg0 is S.NegativeOne: + t = Dummy('t', positive=True) + ser = asin(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else -pi/2 + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + # Handling points lying on branch cuts (-oo, -1) U (1, oo) + if (1 - arg0**2).is_negative: + ndir = self.args[0].dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_negative: + return -pi - res + elif im(ndir).is_positive: + if arg0.is_positive: + return pi - res + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_acos(self, x, **kwargs): + return pi/2 - acos(x) + + def _eval_rewrite_as_atan(self, x, **kwargs): + return 2*atan(x/(1 + sqrt(1 - x**2))) + + def _eval_rewrite_as_log(self, x, **kwargs): + return -S.ImaginaryUnit*log(S.ImaginaryUnit*x + sqrt(1 - x**2)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_acot(self, arg, **kwargs): + return 2*acot((1 + sqrt(1 - arg**2))/arg) + + def _eval_rewrite_as_asec(self, arg, **kwargs): + return pi/2 - asec(1/arg) + + def _eval_rewrite_as_acsc(self, arg, **kwargs): + return acsc(1/arg) + + def _eval_is_extended_real(self): + x = self.args[0] + return x.is_extended_real and (1 - abs(x)).is_nonnegative + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return sin + + +class acos(InverseTrigonometricFunction): + r""" + The inverse cosine function. + + Explanation + =========== + + Returns the arc cosine of x (measured in radians). + + ``acos(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when + the result is a rational multiple of $\pi$ (see the eval class method). + + ``acos(zoo)`` evaluates to ``zoo`` + (see note in :class:`sympy.functions.elementary.trigonometric.asec`) + + A purely imaginary argument will be rewritten to asinh. + + Examples + ======== + + >>> from sympy import acos, oo + >>> acos(1) + 0 + >>> acos(0) + pi/2 + >>> acos(oo) + oo*I + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acsc, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://dlmf.nist.gov/4.23 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCos + + """ + + def fdiff(self, argindex=1): + if argindex == 1: + return -1/sqrt(1 - self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if s.args[0].is_rational: + return False + else: + return s.is_rational + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity*S.ImaginaryUnit + elif arg is S.NegativeInfinity: + return S.NegativeInfinity*S.ImaginaryUnit + elif arg.is_zero: + return pi/2 + elif arg is S.One: + return S.Zero + elif arg is S.NegativeOne: + return pi + + if arg is S.ComplexInfinity: + return S.ComplexInfinity + + if arg.is_number: + asin_table = cls._asin_table() + if arg in asin_table: + return pi/2 - asin_table[arg] + elif -arg in asin_table: + return pi/2 + asin_table[-arg] + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + return pi/2 - asin(arg) + + if isinstance(arg, cos): + ang = arg.args[0] + if ang.is_comparable: + ang %= 2*pi # restrict to [0,2*pi) + if ang > pi: # restrict to [0,pi] + ang = 2*pi - ang + + return ang + + if isinstance(arg, sin): # acos(x) + asin(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + return pi/2 - asin(arg) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return pi/2 + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) >= 2 and n > 2: + p = previous_terms[-2] + return p*(n - 2)**2/(n*(n - 1))*x**2 + else: + k = (n - 1) // 2 + R = RisingFactorial(S.Half, k) + F = factorial(k) + return -R/F*x**n/n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acos + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + # Handling branch points + if x0 == 1: + return sqrt(2)*sqrt((S.One - arg).as_leading_term(x)) + if x0 in (-S.One, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + # Handling points lying on branch cuts (-oo, -1) U (1, oo) + if (1 - x0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_negative: + return 2*pi - self.func(x0) + elif im(ndir).is_positive: + if x0.is_positive: + return -self.func(x0) + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_is_extended_real(self): + x = self.args[0] + return x.is_extended_real and (1 - abs(x)).is_nonnegative + + def _eval_is_nonnegative(self): + return self._eval_is_extended_real() + + def _eval_nseries(self, x, n, logx, cdir=0): # acos + from sympy.series.order import O + arg0 = self.args[0].subs(x, 0) + # Handling branch points + if arg0 is S.One: + t = Dummy('t', positive=True) + ser = acos(S.One - t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One - self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + if arg0 is S.NegativeOne: + t = Dummy('t', positive=True) + ser = acos(S.NegativeOne + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.One + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + if not g.is_meromorphic(x, 0): # cannot be expanded + return O(1) if n == 0 else pi + O(sqrt(x)) + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + # Handling points lying on branch cuts (-oo, -1) U (1, oo) + if (1 - arg0**2).is_negative: + ndir = self.args[0].dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_negative: + return 2*pi - res + elif im(ndir).is_positive: + if arg0.is_positive: + return -res + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return pi/2 + S.ImaginaryUnit*\ + log(S.ImaginaryUnit*x + sqrt(1 - x**2)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_asin(self, x, **kwargs): + return pi/2 - asin(x) + + def _eval_rewrite_as_atan(self, x, **kwargs): + return atan(sqrt(1 - x**2)/x) + (pi/2)*(1 - x*sqrt(1/x**2)) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return cos + + def _eval_rewrite_as_acot(self, arg, **kwargs): + return pi/2 - 2*acot((1 + sqrt(1 - arg**2))/arg) + + def _eval_rewrite_as_asec(self, arg, **kwargs): + return asec(1/arg) + + def _eval_rewrite_as_acsc(self, arg, **kwargs): + return pi/2 - acsc(1/arg) + + def _eval_conjugate(self): + z = self.args[0] + r = self.func(self.args[0].conjugate()) + if z.is_extended_real is False: + return r + elif z.is_extended_real and (z + 1).is_nonnegative and (z - 1).is_nonpositive: + return r + + +class atan(InverseTrigonometricFunction): + r""" + The inverse tangent function. + + Returns the arc tangent of x (measured in radians). + + Explanation + =========== + + ``atan(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the + result is a rational multiple of $\pi$ (see the eval class method). + + Examples + ======== + + >>> from sympy import atan, oo + >>> atan(0) + 0 + >>> atan(1) + pi/4 + >>> atan(oo) + pi/2 + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acsc, acos, asec, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://dlmf.nist.gov/4.23 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcTan + + """ + + args: tTuple[Expr] + + _singularities = (S.ImaginaryUnit, -S.ImaginaryUnit) + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/(1 + self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if s.args[0].is_rational: + return False + else: + return s.is_rational + + def _eval_is_positive(self): + return self.args[0].is_extended_positive + + def _eval_is_nonnegative(self): + return self.args[0].is_extended_nonnegative + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_is_real(self): + return self.args[0].is_extended_real + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return pi/2 + elif arg is S.NegativeInfinity: + return -pi/2 + elif arg.is_zero: + return S.Zero + elif arg is S.One: + return pi/4 + elif arg is S.NegativeOne: + return -pi/4 + + if arg is S.ComplexInfinity: + from sympy.calculus.accumulationbounds import AccumBounds + return AccumBounds(-pi/2, pi/2) + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_number: + atan_table = cls._atan_table() + if arg in atan_table: + return atan_table[arg] + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import atanh + return S.ImaginaryUnit*atanh(i_coeff) + + if arg.is_zero: + return S.Zero + + if isinstance(arg, tan): + ang = arg.args[0] + if ang.is_comparable: + ang %= pi # restrict to [0,pi) + if ang > pi/2: # restrict to [-pi/2,pi/2] + ang -= pi + + return ang + + if isinstance(arg, cot): # atan(x) + acot(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + ang = pi/2 - acot(arg) + if ang > pi/2: # restrict to [-pi/2,pi/2] + ang -= pi + return ang + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + return S.NegativeOne**((n - 1)//2)*x**n/n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # atan + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + if x0.is_zero: + return arg.as_leading_term(x) + # Handling branch points + if x0 in (-S.ImaginaryUnit, S.ImaginaryUnit, S.ComplexInfinity): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo) + if (1 + x0**2).is_negative: + ndir = arg.dir(x, cdir if cdir else 1) + if re(ndir).is_negative: + if im(x0).is_positive: + return self.func(x0) - pi + elif re(ndir).is_positive: + if im(x0).is_negative: + return self.func(x0) + pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # atan + arg0 = self.args[0].subs(x, 0) + + # Handling branch points + if arg0 in (S.ImaginaryUnit, S.NegativeOne*S.ImaginaryUnit): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + ndir = self.args[0].dir(x, cdir if cdir else 1) + if arg0 is S.ComplexInfinity: + if re(ndir) > 0: + return res - pi + return res + # Handling points lying on branch cuts (-I*oo, -I) U (I, I*oo) + if (1 + arg0**2).is_negative: + if re(ndir).is_negative: + if im(arg0).is_positive: + return res - pi + elif re(ndir).is_positive: + if im(arg0).is_negative: + return res + pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, x, **kwargs): + return S.ImaginaryUnit/2*(log(S.One - S.ImaginaryUnit*x) + - log(S.One + S.ImaginaryUnit*x)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_aseries(self, n, args0, x, logx): + if args0[0] in [S.Infinity, S.NegativeInfinity]: + return (pi/2 - atan(1/self.args[0]))._eval_nseries(x, n, logx) + else: + return super()._eval_aseries(n, args0, x, logx) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return tan + + def _eval_rewrite_as_asin(self, arg, **kwargs): + return sqrt(arg**2)/arg*(pi/2 - asin(1/sqrt(1 + arg**2))) + + def _eval_rewrite_as_acos(self, arg, **kwargs): + return sqrt(arg**2)/arg*acos(1/sqrt(1 + arg**2)) + + def _eval_rewrite_as_acot(self, arg, **kwargs): + return acot(1/arg) + + def _eval_rewrite_as_asec(self, arg, **kwargs): + return sqrt(arg**2)/arg*asec(sqrt(1 + arg**2)) + + def _eval_rewrite_as_acsc(self, arg, **kwargs): + return sqrt(arg**2)/arg*(pi/2 - acsc(sqrt(1 + arg**2))) + + +class acot(InverseTrigonometricFunction): + r""" + The inverse cotangent function. + + Returns the arc cotangent of x (measured in radians). + + Explanation + =========== + + ``acot(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, \tilde{\infty}, 0, 1, -1\}$ + and for some instances when the result is a rational multiple of $\pi$ + (see the eval class method). + + A purely imaginary argument will lead to an ``acoth`` expression. + + ``acot(x)`` has a branch cut along $(-i, i)$, hence it is discontinuous + at 0. Its range for real $x$ is $(-\frac{\pi}{2}, \frac{\pi}{2}]$. + + Examples + ======== + + >>> from sympy import acot, sqrt + >>> acot(0) + pi/2 + >>> acot(1) + pi/4 + >>> acot(sqrt(3) - 2) + -5*pi/12 + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acsc, acos, asec, atan, atan2 + + References + ========== + + .. [1] https://dlmf.nist.gov/4.23 + .. [2] https://functions.wolfram.com/ElementaryFunctions/ArcCot + + """ + _singularities = (S.ImaginaryUnit, -S.ImaginaryUnit) + + def fdiff(self, argindex=1): + if argindex == 1: + return -1/(1 + self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_rational(self): + s = self.func(*self.args) + if s.func == self.func: + if s.args[0].is_rational: + return False + else: + return s.is_rational + + def _eval_is_positive(self): + return self.args[0].is_nonnegative + + def _eval_is_negative(self): + return self.args[0].is_negative + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return pi/ 2 + elif arg is S.One: + return pi/4 + elif arg is S.NegativeOne: + return -pi/4 + + if arg is S.ComplexInfinity: + return S.Zero + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_number: + atan_table = cls._atan_table() + if arg in atan_table: + ang = pi/2 - atan_table[arg] + if ang > pi/2: # restrict to (-pi/2,pi/2] + ang -= pi + return ang + + i_coeff = _imaginary_unit_as_coefficient(arg) + if i_coeff is not None: + from sympy.functions.elementary.hyperbolic import acoth + return -S.ImaginaryUnit*acoth(i_coeff) + + if arg.is_zero: + return pi*S.Half + + if isinstance(arg, cot): + ang = arg.args[0] + if ang.is_comparable: + ang %= pi # restrict to [0,pi) + if ang > pi/2: # restrict to (-pi/2,pi/2] + ang -= pi; + return ang + + if isinstance(arg, tan): # atan(x) + acot(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + ang = pi/2 - atan(arg) + if ang > pi/2: # restrict to (-pi/2,pi/2] + ang -= pi + return ang + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return pi/2 # FIX THIS + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + return S.NegativeOne**((n + 1)//2)*x**n/n + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acot + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + if x0 is S.ComplexInfinity: + return (1/arg).as_leading_term(x) + # Handling branch points + if x0 in (-S.ImaginaryUnit, S.ImaginaryUnit, S.Zero): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + # Handling points lying on branch cuts [-I, I] + if x0.is_imaginary and (1 + x0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if re(ndir).is_positive: + if im(x0).is_positive: + return self.func(x0) + pi + elif re(ndir).is_negative: + if im(x0).is_negative: + return self.func(x0) - pi + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # acot + arg0 = self.args[0].subs(x, 0) + + # Handling branch points + if arg0 in (S.ImaginaryUnit, S.NegativeOne*S.ImaginaryUnit): + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + ndir = self.args[0].dir(x, cdir if cdir else 1) + if arg0.is_zero: + if re(ndir) < 0: + return res - pi + return res + # Handling points lying on branch cuts [-I, I] + if arg0.is_imaginary and (1 + arg0**2).is_positive: + if re(ndir).is_positive: + if im(arg0).is_positive: + return res + pi + elif re(ndir).is_negative: + if im(arg0).is_negative: + return res - pi + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_aseries(self, n, args0, x, logx): + if args0[0] in [S.Infinity, S.NegativeInfinity]: + return atan(1/self.args[0])._eval_nseries(x, n, logx) + else: + return super()._eval_aseries(n, args0, x, logx) + + def _eval_rewrite_as_log(self, x, **kwargs): + return S.ImaginaryUnit/2*(log(1 - S.ImaginaryUnit/x) + - log(1 + S.ImaginaryUnit/x)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return cot + + def _eval_rewrite_as_asin(self, arg, **kwargs): + return (arg*sqrt(1/arg**2)* + (pi/2 - asin(sqrt(-arg**2)/sqrt(-arg**2 - 1)))) + + def _eval_rewrite_as_acos(self, arg, **kwargs): + return arg*sqrt(1/arg**2)*acos(sqrt(-arg**2)/sqrt(-arg**2 - 1)) + + def _eval_rewrite_as_atan(self, arg, **kwargs): + return atan(1/arg) + + def _eval_rewrite_as_asec(self, arg, **kwargs): + return arg*sqrt(1/arg**2)*asec(sqrt((1 + arg**2)/arg**2)) + + def _eval_rewrite_as_acsc(self, arg, **kwargs): + return arg*sqrt(1/arg**2)*(pi/2 - acsc(sqrt((1 + arg**2)/arg**2))) + + +class asec(InverseTrigonometricFunction): + r""" + The inverse secant function. + + Returns the arc secant of x (measured in radians). + + Explanation + =========== + + ``asec(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, 0, 1, -1\}$ and for some instances when the + result is a rational multiple of $\pi$ (see the eval class method). + + ``asec(x)`` has branch cut in the interval $[-1, 1]$. For complex arguments, + it can be defined [4]_ as + + .. math:: + \operatorname{sec^{-1}}(z) = -i\frac{\log\left(\sqrt{1 - z^2} + 1\right)}{z} + + At ``x = 0``, for positive branch cut, the limit evaluates to ``zoo``. For + negative branch cut, the limit + + .. math:: + \lim_{z \to 0}-i\frac{\log\left(-\sqrt{1 - z^2} + 1\right)}{z} + + simplifies to :math:`-i\log\left(z/2 + O\left(z^3\right)\right)` which + ultimately evaluates to ``zoo``. + + As ``acos(x) = asec(1/x)``, a similar argument can be given for + ``acos(x)``. + + Examples + ======== + + >>> from sympy import asec, oo + >>> asec(1) + 0 + >>> asec(-1) + pi + >>> asec(0) + zoo + >>> asec(-oo) + pi/2 + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acsc, acos, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://dlmf.nist.gov/4.23 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcSec + .. [4] https://reference.wolfram.com/language/ref/ArcSec.html + + """ + + @classmethod + def eval(cls, arg): + if arg.is_zero: + return S.ComplexInfinity + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.One: + return S.Zero + elif arg is S.NegativeOne: + return pi + if arg in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]: + return pi/2 + + if arg.is_number: + acsc_table = cls._acsc_table() + if arg in acsc_table: + return pi/2 - acsc_table[arg] + elif -arg in acsc_table: + return pi/2 + acsc_table[-arg] + + if arg.is_infinite: + return pi/2 + + if isinstance(arg, sec): + ang = arg.args[0] + if ang.is_comparable: + ang %= 2*pi # restrict to [0,2*pi) + if ang > pi: # restrict to [0,pi] + ang = 2*pi - ang + + return ang + + if isinstance(arg, csc): # asec(x) + acsc(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + return pi/2 - acsc(arg) + + def fdiff(self, argindex=1): + if argindex == 1: + return 1/(self.args[0]**2*sqrt(1 - 1/self.args[0]**2)) + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return sec + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return S.ImaginaryUnit*log(2 / x) + elif n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 2 and n > 2: + p = previous_terms[-2] + return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2) + else: + k = n // 2 + R = RisingFactorial(S.Half, k) * n + F = factorial(k) * n // 2 * n // 2 + return -S.ImaginaryUnit * R / F * x**n / 4 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # asec + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + # Handling branch points + if x0 == 1: + return sqrt(2)*sqrt((arg - S.One).as_leading_term(x)) + if x0 in (-S.One, S.Zero): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir) + # Handling points lying on branch cuts (-1, 1) + if x0.is_real and (1 - x0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_positive: + return -self.func(x0) + elif im(ndir).is_positive: + if x0.is_negative: + return 2*pi - self.func(x0) + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # asec + from sympy.series.order import O + arg0 = self.args[0].subs(x, 0) + # Handling branch points + if arg0 is S.One: + t = Dummy('t', positive=True) + ser = asec(S.One + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.NegativeOne + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + if arg0 is S.NegativeOne: + t = Dummy('t', positive=True) + ser = asec(S.NegativeOne - t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.NegativeOne - self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + # Handling points lying on branch cuts (-1, 1) + if arg0.is_real and (1 - arg0**2).is_positive: + ndir = self.args[0].dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_positive: + return -res + elif im(ndir).is_positive: + if arg0.is_negative: + return 2*pi - res + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_is_extended_real(self): + x = self.args[0] + if x.is_extended_real is False: + return False + return fuzzy_or(((x - 1).is_nonnegative, (-x - 1).is_nonnegative)) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return pi/2 + S.ImaginaryUnit*log(S.ImaginaryUnit/arg + sqrt(1 - 1/arg**2)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_asin(self, arg, **kwargs): + return pi/2 - asin(1/arg) + + def _eval_rewrite_as_acos(self, arg, **kwargs): + return acos(1/arg) + + def _eval_rewrite_as_atan(self, x, **kwargs): + sx2x = sqrt(x**2)/x + return pi/2*(1 - sx2x) + sx2x*atan(sqrt(x**2 - 1)) + + def _eval_rewrite_as_acot(self, x, **kwargs): + sx2x = sqrt(x**2)/x + return pi/2*(1 - sx2x) + sx2x*acot(1/sqrt(x**2 - 1)) + + def _eval_rewrite_as_acsc(self, arg, **kwargs): + return pi/2 - acsc(arg) + + +class acsc(InverseTrigonometricFunction): + r""" + The inverse cosecant function. + + Returns the arc cosecant of x (measured in radians). + + Explanation + =========== + + ``acsc(x)`` will evaluate automatically in the cases + $x \in \{\infty, -\infty, 0, 1, -1\}$` and for some instances when the + result is a rational multiple of $\pi$ (see the ``eval`` class method). + + Examples + ======== + + >>> from sympy import acsc, oo + >>> acsc(1) + pi/2 + >>> acsc(-1) + -pi/2 + >>> acsc(oo) + 0 + >>> acsc(-oo) == acsc(oo) + True + >>> acsc(0) + zoo + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acos, asec, atan, acot, atan2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://dlmf.nist.gov/4.23 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcCsc + + """ + + @classmethod + def eval(cls, arg): + if arg.is_zero: + return S.ComplexInfinity + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.One: + return pi/2 + elif arg is S.NegativeOne: + return -pi/2 + if arg in [S.Infinity, S.NegativeInfinity, S.ComplexInfinity]: + return S.Zero + + if arg.could_extract_minus_sign(): + return -cls(-arg) + + if arg.is_infinite: + return S.Zero + + if arg.is_number: + acsc_table = cls._acsc_table() + if arg in acsc_table: + return acsc_table[arg] + + if isinstance(arg, csc): + ang = arg.args[0] + if ang.is_comparable: + ang %= 2*pi # restrict to [0,2*pi) + if ang > pi: # restrict to (-pi,pi] + ang = pi - ang + + # restrict to [-pi/2,pi/2] + if ang > pi/2: + ang = pi - ang + if ang < -pi/2: + ang = -pi - ang + + return ang + + if isinstance(arg, sec): # asec(x) + acsc(x) = pi/2 + ang = arg.args[0] + if ang.is_comparable: + return pi/2 - asec(arg) + + def fdiff(self, argindex=1): + if argindex == 1: + return -1/(self.args[0]**2*sqrt(1 - 1/self.args[0]**2)) + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + """ + return csc + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return pi/2 - S.ImaginaryUnit*log(2) + S.ImaginaryUnit*log(x) + elif n < 0 or n % 2 == 1: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 2 and n > 2: + p = previous_terms[-2] + return p * ((n - 1)*(n-2)) * x**2/(4 * (n//2)**2) + else: + k = n // 2 + R = RisingFactorial(S.Half, k) * n + F = factorial(k) * n // 2 * n // 2 + return S.ImaginaryUnit * R / F * x**n / 4 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): # acsc + arg = self.args[0] + x0 = arg.subs(x, 0).cancel() + if x0 is S.NaN: + return self.func(arg.as_leading_term(x)) + # Handling branch points + if x0 in (-S.One, S.One, S.Zero): + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + if x0 is S.ComplexInfinity: + return (1/arg).as_leading_term(x) + # Handling points lying on branch cuts (-1, 1) + if x0.is_real and (1 - x0**2).is_positive: + ndir = arg.dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if x0.is_positive: + return pi - self.func(x0) + elif im(ndir).is_positive: + if x0.is_negative: + return -pi - self.func(x0) + else: + return self.rewrite(log)._eval_as_leading_term(x, logx=logx, cdir=cdir).expand() + return self.func(x0) + + def _eval_nseries(self, x, n, logx, cdir=0): # acsc + from sympy.series.order import O + arg0 = self.args[0].subs(x, 0) + # Handling branch points + if arg0 is S.One: + t = Dummy('t', positive=True) + ser = acsc(S.One + t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.NegativeOne + self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + if arg0 is S.NegativeOne: + t = Dummy('t', positive=True) + ser = acsc(S.NegativeOne - t**2).rewrite(log).nseries(t, 0, 2*n) + arg1 = S.NegativeOne - self.args[0] + f = arg1.as_leading_term(x) + g = (arg1 - f)/ f + res1 = sqrt(S.One + g)._eval_nseries(x, n=n, logx=logx) + res = (res1.removeO()*sqrt(f)).expand() + return ser.removeO().subs(t, res).expand().powsimp() + O(x**n, x) + + res = Function._eval_nseries(self, x, n=n, logx=logx) + if arg0 is S.ComplexInfinity: + return res + # Handling points lying on branch cuts (-1, 1) + if arg0.is_real and (1 - arg0**2).is_positive: + ndir = self.args[0].dir(x, cdir if cdir else 1) + if im(ndir).is_negative: + if arg0.is_positive: + return pi - res + elif im(ndir).is_positive: + if arg0.is_negative: + return -pi - res + else: + return self.rewrite(log)._eval_nseries(x, n, logx=logx, cdir=cdir) + return res + + def _eval_rewrite_as_log(self, arg, **kwargs): + return -S.ImaginaryUnit*log(S.ImaginaryUnit/arg + sqrt(1 - 1/arg**2)) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + def _eval_rewrite_as_asin(self, arg, **kwargs): + return asin(1/arg) + + def _eval_rewrite_as_acos(self, arg, **kwargs): + return pi/2 - acos(1/arg) + + def _eval_rewrite_as_atan(self, x, **kwargs): + return sqrt(x**2)/x*(pi/2 - atan(sqrt(x**2 - 1))) + + def _eval_rewrite_as_acot(self, arg, **kwargs): + return sqrt(arg**2)/arg*(pi/2 - acot(1/sqrt(arg**2 - 1))) + + def _eval_rewrite_as_asec(self, arg, **kwargs): + return pi/2 - asec(arg) + + +class atan2(InverseTrigonometricFunction): + r""" + The function ``atan2(y, x)`` computes `\operatorname{atan}(y/x)` taking + two arguments `y` and `x`. Signs of both `y` and `x` are considered to + determine the appropriate quadrant of `\operatorname{atan}(y/x)`. + The range is `(-\pi, \pi]`. The complete definition reads as follows: + + .. math:: + + \operatorname{atan2}(y, x) = + \begin{cases} + \arctan\left(\frac y x\right) & \qquad x > 0 \\ + \arctan\left(\frac y x\right) + \pi& \qquad y \ge 0, x < 0 \\ + \arctan\left(\frac y x\right) - \pi& \qquad y < 0, x < 0 \\ + +\frac{\pi}{2} & \qquad y > 0, x = 0 \\ + -\frac{\pi}{2} & \qquad y < 0, x = 0 \\ + \text{undefined} & \qquad y = 0, x = 0 + \end{cases} + + Attention: Note the role reversal of both arguments. The `y`-coordinate + is the first argument and the `x`-coordinate the second. + + If either `x` or `y` is complex: + + .. math:: + + \operatorname{atan2}(y, x) = + -i\log\left(\frac{x + iy}{\sqrt{x^2 + y^2}}\right) + + Examples + ======== + + Going counter-clock wise around the origin we find the + following angles: + + >>> from sympy import atan2 + >>> atan2(0, 1) + 0 + >>> atan2(1, 1) + pi/4 + >>> atan2(1, 0) + pi/2 + >>> atan2(1, -1) + 3*pi/4 + >>> atan2(0, -1) + pi + >>> atan2(-1, -1) + -3*pi/4 + >>> atan2(-1, 0) + -pi/2 + >>> atan2(-1, 1) + -pi/4 + + which are all correct. Compare this to the results of the ordinary + `\operatorname{atan}` function for the point `(x, y) = (-1, 1)` + + >>> from sympy import atan, S + >>> atan(S(1)/-1) + -pi/4 + >>> atan2(1, -1) + 3*pi/4 + + where only the `\operatorname{atan2}` function reurns what we expect. + We can differentiate the function with respect to both arguments: + + >>> from sympy import diff + >>> from sympy.abc import x, y + >>> diff(atan2(y, x), x) + -y/(x**2 + y**2) + + >>> diff(atan2(y, x), y) + x/(x**2 + y**2) + + We can express the `\operatorname{atan2}` function in terms of + complex logarithms: + + >>> from sympy import log + >>> atan2(y, x).rewrite(log) + -I*log((x + I*y)/sqrt(x**2 + y**2)) + + and in terms of `\operatorname(atan)`: + + >>> from sympy import atan + >>> atan2(y, x).rewrite(atan) + Piecewise((2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)), (pi, re(x) < 0), (0, Ne(x, 0)), (nan, True)) + + but note that this form is undefined on the negative real axis. + + See Also + ======== + + sin, csc, cos, sec, tan, cot + asin, acsc, acos, asec, atan, acot + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions + .. [2] https://en.wikipedia.org/wiki/Atan2 + .. [3] https://functions.wolfram.com/ElementaryFunctions/ArcTan2 + + """ + + @classmethod + def eval(cls, y, x): + from sympy.functions.special.delta_functions import Heaviside + if x is S.NegativeInfinity: + if y.is_zero: + # Special case y = 0 because we define Heaviside(0) = 1/2 + return pi + return 2*pi*(Heaviside(re(y))) - pi + elif x is S.Infinity: + return S.Zero + elif x.is_imaginary and y.is_imaginary and x.is_number and y.is_number: + x = im(x) + y = im(y) + + if x.is_extended_real and y.is_extended_real: + if x.is_positive: + return atan(y/x) + elif x.is_negative: + if y.is_negative: + return atan(y/x) - pi + elif y.is_nonnegative: + return atan(y/x) + pi + elif x.is_zero: + if y.is_positive: + return pi/2 + elif y.is_negative: + return -pi/2 + elif y.is_zero: + return S.NaN + if y.is_zero: + if x.is_extended_nonzero: + return pi*(S.One - Heaviside(x)) + if x.is_number: + return Piecewise((pi, re(x) < 0), + (0, Ne(x, 0)), + (S.NaN, True)) + if x.is_number and y.is_number: + return -S.ImaginaryUnit*log( + (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2)) + + def _eval_rewrite_as_log(self, y, x, **kwargs): + return -S.ImaginaryUnit*log((x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2)) + + def _eval_rewrite_as_atan(self, y, x, **kwargs): + return Piecewise((2*atan(y/(x + sqrt(x**2 + y**2))), Ne(y, 0)), + (pi, re(x) < 0), + (0, Ne(x, 0)), + (S.NaN, True)) + + def _eval_rewrite_as_arg(self, y, x, **kwargs): + if x.is_extended_real and y.is_extended_real: + return arg_f(x + y*S.ImaginaryUnit) + n = x + S.ImaginaryUnit*y + d = x**2 + y**2 + return arg_f(n/sqrt(d)) - S.ImaginaryUnit*log(abs(n)/sqrt(abs(d))) + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real and self.args[1].is_extended_real + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate(), self.args[1].conjugate()) + + def fdiff(self, argindex): + y, x = self.args + if argindex == 1: + # Diff wrt y + return x/(x**2 + y**2) + elif argindex == 2: + # Diff wrt x + return -y/(x**2 + y**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + y, x = self.args + if x.is_extended_real and y.is_extended_real: + return super()._eval_evalf(prec) diff --git a/lib/python3.11/site-packages/sympy/functions/special/__init__.py b/lib/python3.11/site-packages/sympy/functions/special/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..ab52ace36a8dfbe73179dbf4419a54f7fa1af5fa --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/__init__.py @@ -0,0 +1 @@ +# Stub __init__.py for the sympy.functions.special package diff --git a/lib/python3.11/site-packages/sympy/functions/special/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/functions/special/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ccbcfe90387e52be9acca3eecb9219a9945de427 Binary files /dev/null and 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b/lib/python3.11/site-packages/sympy/functions/special/bessel.py @@ -0,0 +1,2089 @@ +from functools import wraps + +from sympy.core import S +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.expr import Expr +from sympy.core.function import Function, ArgumentIndexError, _mexpand +from sympy.core.logic import fuzzy_or, fuzzy_not +from sympy.core.numbers import Rational, pi, I +from sympy.core.power import Pow +from sympy.core.symbol import Dummy, uniquely_named_symbol, Wild +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.trigonometric import sin, cos, csc, cot +from sympy.functions.elementary.integers import ceiling +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.miscellaneous import cbrt, sqrt, root +from sympy.functions.elementary.complexes import (Abs, re, im, polar_lift, unpolarify) +from sympy.functions.special.gamma_functions import gamma, digamma, uppergamma +from sympy.functions.special.hyper import hyper +from sympy.polys.orthopolys import spherical_bessel_fn + +from mpmath import mp, workprec + +# TODO +# o Scorer functions G1 and G2 +# o Asymptotic expansions +# These are possible, e.g. for fixed order, but since the bessel type +# functions are oscillatory they are not actually tractable at +# infinity, so this is not particularly useful right now. +# o Nicer series expansions. +# o More rewriting. +# o Add solvers to ode.py (or rather add solvers for the hypergeometric equation). + + +class BesselBase(Function): + """ + Abstract base class for Bessel-type functions. + + This class is meant to reduce code duplication. + All Bessel-type functions can 1) be differentiated, with the derivatives + expressed in terms of similar functions, and 2) be rewritten in terms + of other Bessel-type functions. + + Here, Bessel-type functions are assumed to have one complex parameter. + + To use this base class, define class attributes ``_a`` and ``_b`` such that + ``2*F_n' = -_a*F_{n+1} + b*F_{n-1}``. + + """ + + @property + def order(self): + """ The order of the Bessel-type function. """ + return self.args[0] + + @property + def argument(self): + """ The argument of the Bessel-type function. """ + return self.args[1] + + @classmethod + def eval(cls, nu, z): + return + + def fdiff(self, argindex=2): + if argindex != 2: + raise ArgumentIndexError(self, argindex) + return (self._b/2 * self.__class__(self.order - 1, self.argument) - + self._a/2 * self.__class__(self.order + 1, self.argument)) + + def _eval_conjugate(self): + z = self.argument + if z.is_extended_negative is False: + return self.__class__(self.order.conjugate(), z.conjugate()) + + def _eval_is_meromorphic(self, x, a): + nu, z = self.order, self.argument + + if nu.has(x): + return False + if not z._eval_is_meromorphic(x, a): + return None + z0 = z.subs(x, a) + if nu.is_integer: + if isinstance(self, (besselj, besseli, hn1, hn2, jn, yn)) or not nu.is_zero: + return fuzzy_not(z0.is_infinite) + return fuzzy_not(fuzzy_or([z0.is_zero, z0.is_infinite])) + + def _eval_expand_func(self, **hints): + nu, z, f = self.order, self.argument, self.__class__ + if nu.is_real: + if (nu - 1).is_positive: + return (-self._a*self._b*f(nu - 2, z)._eval_expand_func() + + 2*self._a*(nu - 1)*f(nu - 1, z)._eval_expand_func()/z) + elif (nu + 1).is_negative: + return (2*self._b*(nu + 1)*f(nu + 1, z)._eval_expand_func()/z - + self._a*self._b*f(nu + 2, z)._eval_expand_func()) + return self + + def _eval_simplify(self, **kwargs): + from sympy.simplify.simplify import besselsimp + return besselsimp(self) + + +class besselj(BesselBase): + r""" + Bessel function of the first kind. + + Explanation + =========== + + The Bessel $J$ function of order $\nu$ is defined to be the function + satisfying Bessel's differential equation + + .. math :: + z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2} + + z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 - \nu^2) w = 0, + + with Laurent expansion + + .. math :: + J_\nu(z) = z^\nu \left(\frac{1}{\Gamma(\nu + 1) 2^\nu} + O(z^2) \right), + + if $\nu$ is not a negative integer. If $\nu=-n \in \mathbb{Z}_{<0}$ + *is* a negative integer, then the definition is + + .. math :: + J_{-n}(z) = (-1)^n J_n(z). + + Examples + ======== + + Create a Bessel function object: + + >>> from sympy import besselj, jn + >>> from sympy.abc import z, n + >>> b = besselj(n, z) + + Differentiate it: + + >>> b.diff(z) + besselj(n - 1, z)/2 - besselj(n + 1, z)/2 + + Rewrite in terms of spherical Bessel functions: + + >>> b.rewrite(jn) + sqrt(2)*sqrt(z)*jn(n - 1/2, z)/sqrt(pi) + + Access the parameter and argument: + + >>> b.order + n + >>> b.argument + z + + See Also + ======== + + bessely, besseli, besselk + + References + ========== + + .. [1] Abramowitz, Milton; Stegun, Irene A., eds. (1965), "Chapter 9", + Handbook of Mathematical Functions with Formulas, Graphs, and + Mathematical Tables + .. [2] Luke, Y. L. (1969), The Special Functions and Their + Approximations, Volume 1 + .. [3] https://en.wikipedia.org/wiki/Bessel_function + .. [4] https://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/ + + """ + + _a = S.One + _b = S.One + + @classmethod + def eval(cls, nu, z): + if z.is_zero: + if nu.is_zero: + return S.One + elif (nu.is_integer and nu.is_zero is False) or re(nu).is_positive: + return S.Zero + elif re(nu).is_negative and not (nu.is_integer is True): + return S.ComplexInfinity + elif nu.is_imaginary: + return S.NaN + if z in (S.Infinity, S.NegativeInfinity): + return S.Zero + + if z.could_extract_minus_sign(): + return (z)**nu*(-z)**(-nu)*besselj(nu, -z) + if nu.is_integer: + if nu.could_extract_minus_sign(): + return S.NegativeOne**(-nu)*besselj(-nu, z) + newz = z.extract_multiplicatively(I) + if newz: # NOTE we don't want to change the function if z==0 + return I**(nu)*besseli(nu, newz) + + # branch handling: + if nu.is_integer: + newz = unpolarify(z) + if newz != z: + return besselj(nu, newz) + else: + newz, n = z.extract_branch_factor() + if n != 0: + return exp(2*n*pi*nu*I)*besselj(nu, newz) + nnu = unpolarify(nu) + if nu != nnu: + return besselj(nnu, z) + + def _eval_rewrite_as_besseli(self, nu, z, **kwargs): + return exp(I*pi*nu/2)*besseli(nu, polar_lift(-I)*z) + + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + if nu.is_integer is False: + return csc(pi*nu)*bessely(-nu, z) - cot(pi*nu)*bessely(nu, z) + + def _eval_rewrite_as_jn(self, nu, z, **kwargs): + return sqrt(2*z/pi)*jn(nu - S.Half, self.argument) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + nu, z = self.args + try: + arg = z.as_leading_term(x) + except NotImplementedError: + return self + c, e = arg.as_coeff_exponent(x) + + if e.is_positive: + return arg**nu/(2**nu*gamma(nu + 1)) + elif e.is_negative: + cdir = 1 if cdir == 0 else cdir + sign = c*cdir**e + if not sign.is_negative: + # Refer Abramowitz and Stegun 1965, p. 364 for more information on + # asymptotic approximation of besselj function. + return sqrt(2)*cos(z - pi*(2*nu + 1)/4)/sqrt(pi*z) + return self + + return super(besselj, self)._eval_as_leading_term(x, logx, cdir) + + def _eval_is_extended_real(self): + nu, z = self.args + if nu.is_integer and z.is_extended_real: + return True + + def _eval_nseries(self, x, n, logx, cdir=0): + # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/06/01/04/01/01/0003/ + # for more information on nseries expansion of besselj function. + from sympy.series.order import Order + nu, z = self.args + + # In case of powers less than 1, number of terms need to be computed + # separately to avoid repeated callings of _eval_nseries with wrong n + try: + _, exp = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + if exp.is_positive: + newn = ceiling(n/exp) + o = Order(x**n, x) + r = (z/2)._eval_nseries(x, n, logx, cdir).removeO() + if r is S.Zero: + return o + t = (_mexpand(r**2) + o).removeO() + + term = r**nu/gamma(nu + 1) + s = [term] + for k in range(1, (newn + 1)//2): + term *= -t/(k*(nu + k)) + term = (_mexpand(term) + o).removeO() + s.append(term) + return Add(*s) + o + + return super(besselj, self)._eval_nseries(x, n, logx, cdir) + + +class bessely(BesselBase): + r""" + Bessel function of the second kind. + + Explanation + =========== + + The Bessel $Y$ function of order $\nu$ is defined as + + .. math :: + Y_\nu(z) = \lim_{\mu \to \nu} \frac{J_\mu(z) \cos(\pi \mu) + - J_{-\mu}(z)}{\sin(\pi \mu)}, + + where $J_\mu(z)$ is the Bessel function of the first kind. + + It is a solution to Bessel's equation, and linearly independent from + $J_\nu$. + + Examples + ======== + + >>> from sympy import bessely, yn + >>> from sympy.abc import z, n + >>> b = bessely(n, z) + >>> b.diff(z) + bessely(n - 1, z)/2 - bessely(n + 1, z)/2 + >>> b.rewrite(yn) + sqrt(2)*sqrt(z)*yn(n - 1/2, z)/sqrt(pi) + + See Also + ======== + + besselj, besseli, besselk + + References + ========== + + .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselY/ + + """ + + _a = S.One + _b = S.One + + @classmethod + def eval(cls, nu, z): + if z.is_zero: + if nu.is_zero: + return S.NegativeInfinity + elif re(nu).is_zero is False: + return S.ComplexInfinity + elif re(nu).is_zero: + return S.NaN + if z in (S.Infinity, S.NegativeInfinity): + return S.Zero + if z == I*S.Infinity: + return exp(I*pi*(nu + 1)/2) * S.Infinity + if z == I*S.NegativeInfinity: + return exp(-I*pi*(nu + 1)/2) * S.Infinity + + if nu.is_integer: + if nu.could_extract_minus_sign(): + return S.NegativeOne**(-nu)*bessely(-nu, z) + + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + if nu.is_integer is False: + return csc(pi*nu)*(cos(pi*nu)*besselj(nu, z) - besselj(-nu, z)) + + def _eval_rewrite_as_besseli(self, nu, z, **kwargs): + aj = self._eval_rewrite_as_besselj(*self.args) + if aj: + return aj.rewrite(besseli) + + def _eval_rewrite_as_yn(self, nu, z, **kwargs): + return sqrt(2*z/pi) * yn(nu - S.Half, self.argument) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + nu, z = self.args + try: + arg = z.as_leading_term(x) + except NotImplementedError: + return self + c, e = arg.as_coeff_exponent(x) + + if e.is_positive: + term_one = ((2/pi)*log(z/2)*besselj(nu, z)) + term_two = -(z/2)**(-nu)*factorial(nu - 1)/pi if (nu).is_positive else S.Zero + term_three = -(z/2)**nu/(pi*factorial(nu))*(digamma(nu + 1) - S.EulerGamma) + arg = Add(*[term_one, term_two, term_three]).as_leading_term(x, logx=logx) + return arg + elif e.is_negative: + cdir = 1 if cdir == 0 else cdir + sign = c*cdir**e + if not sign.is_negative: + # Refer Abramowitz and Stegun 1965, p. 364 for more information on + # asymptotic approximation of bessely function. + return sqrt(2)*(-sin(pi*nu/2 - z + pi/4) + 3*cos(pi*nu/2 - z + pi/4)/(8*z))*sqrt(1/z)/sqrt(pi) + return self + + return super(bessely, self)._eval_as_leading_term(x, logx, cdir) + + def _eval_is_extended_real(self): + nu, z = self.args + if nu.is_integer and z.is_positive: + return True + + def _eval_nseries(self, x, n, logx, cdir=0): + # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselY/06/01/04/01/02/0008/ + # for more information on nseries expansion of bessely function. + from sympy.series.order import Order + nu, z = self.args + + # In case of powers less than 1, number of terms need to be computed + # separately to avoid repeated callings of _eval_nseries with wrong n + try: + _, exp = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + if exp.is_positive and nu.is_integer: + newn = ceiling(n/exp) + bn = besselj(nu, z) + a = ((2/pi)*log(z/2)*bn)._eval_nseries(x, n, logx, cdir) + + b, c = [], [] + o = Order(x**n, x) + r = (z/2)._eval_nseries(x, n, logx, cdir).removeO() + if r is S.Zero: + return o + t = (_mexpand(r**2) + o).removeO() + + if nu > S.Zero: + term = r**(-nu)*factorial(nu - 1)/pi + b.append(term) + for k in range(1, nu): + denom = (nu - k)*k + if denom == S.Zero: + term *= t/k + else: + term *= t/denom + term = (_mexpand(term) + o).removeO() + b.append(term) + + p = r**nu/(pi*factorial(nu)) + term = p*(digamma(nu + 1) - S.EulerGamma) + c.append(term) + for k in range(1, (newn + 1)//2): + p *= -t/(k*(k + nu)) + p = (_mexpand(p) + o).removeO() + term = p*(digamma(k + nu + 1) + digamma(k + 1)) + c.append(term) + return a - Add(*b) - Add(*c) # Order term comes from a + + return super(bessely, self)._eval_nseries(x, n, logx, cdir) + + +class besseli(BesselBase): + r""" + Modified Bessel function of the first kind. + + Explanation + =========== + + The Bessel $I$ function is a solution to the modified Bessel equation + + .. math :: + z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2} + + z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 + \nu^2)^2 w = 0. + + It can be defined as + + .. math :: + I_\nu(z) = i^{-\nu} J_\nu(iz), + + where $J_\nu(z)$ is the Bessel function of the first kind. + + Examples + ======== + + >>> from sympy import besseli + >>> from sympy.abc import z, n + >>> besseli(n, z).diff(z) + besseli(n - 1, z)/2 + besseli(n + 1, z)/2 + + See Also + ======== + + besselj, bessely, besselk + + References + ========== + + .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselI/ + + """ + + _a = -S.One + _b = S.One + + @classmethod + def eval(cls, nu, z): + if z.is_zero: + if nu.is_zero: + return S.One + elif (nu.is_integer and nu.is_zero is False) or re(nu).is_positive: + return S.Zero + elif re(nu).is_negative and not (nu.is_integer is True): + return S.ComplexInfinity + elif nu.is_imaginary: + return S.NaN + if im(z) in (S.Infinity, S.NegativeInfinity): + return S.Zero + if z is S.Infinity: + return S.Infinity + if z is S.NegativeInfinity: + return (-1)**nu*S.Infinity + + if z.could_extract_minus_sign(): + return (z)**nu*(-z)**(-nu)*besseli(nu, -z) + if nu.is_integer: + if nu.could_extract_minus_sign(): + return besseli(-nu, z) + newz = z.extract_multiplicatively(I) + if newz: # NOTE we don't want to change the function if z==0 + return I**(-nu)*besselj(nu, -newz) + + # branch handling: + if nu.is_integer: + newz = unpolarify(z) + if newz != z: + return besseli(nu, newz) + else: + newz, n = z.extract_branch_factor() + if n != 0: + return exp(2*n*pi*nu*I)*besseli(nu, newz) + nnu = unpolarify(nu) + if nu != nnu: + return besseli(nnu, z) + + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + return exp(-I*pi*nu/2)*besselj(nu, polar_lift(I)*z) + + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + aj = self._eval_rewrite_as_besselj(*self.args) + if aj: + return aj.rewrite(bessely) + + def _eval_rewrite_as_jn(self, nu, z, **kwargs): + return self._eval_rewrite_as_besselj(*self.args).rewrite(jn) + + def _eval_is_extended_real(self): + nu, z = self.args + if nu.is_integer and z.is_extended_real: + return True + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + nu, z = self.args + try: + arg = z.as_leading_term(x) + except NotImplementedError: + return self + c, e = arg.as_coeff_exponent(x) + + if e.is_positive: + return arg**nu/(2**nu*gamma(nu + 1)) + elif e.is_negative: + cdir = 1 if cdir == 0 else cdir + sign = c*cdir**e + if not sign.is_negative: + # Refer Abramowitz and Stegun 1965, p. 377 for more information on + # asymptotic approximation of besseli function. + return exp(z)/sqrt(2*pi*z) + return self + + return super(besseli, self)._eval_as_leading_term(x, logx, cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselI/06/01/04/01/01/0003/ + # for more information on nseries expansion of besseli function. + from sympy.series.order import Order + nu, z = self.args + + # In case of powers less than 1, number of terms need to be computed + # separately to avoid repeated callings of _eval_nseries with wrong n + try: + _, exp = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + if exp.is_positive: + newn = ceiling(n/exp) + o = Order(x**n, x) + r = (z/2)._eval_nseries(x, n, logx, cdir).removeO() + if r is S.Zero: + return o + t = (_mexpand(r**2) + o).removeO() + + term = r**nu/gamma(nu + 1) + s = [term] + for k in range(1, (newn + 1)//2): + term *= t/(k*(nu + k)) + term = (_mexpand(term) + o).removeO() + s.append(term) + return Add(*s) + o + + return super(besseli, self)._eval_nseries(x, n, logx, cdir) + + +class besselk(BesselBase): + r""" + Modified Bessel function of the second kind. + + Explanation + =========== + + The Bessel $K$ function of order $\nu$ is defined as + + .. math :: + K_\nu(z) = \lim_{\mu \to \nu} \frac{\pi}{2} + \frac{I_{-\mu}(z) -I_\mu(z)}{\sin(\pi \mu)}, + + where $I_\mu(z)$ is the modified Bessel function of the first kind. + + It is a solution of the modified Bessel equation, and linearly independent + from $Y_\nu$. + + Examples + ======== + + >>> from sympy import besselk + >>> from sympy.abc import z, n + >>> besselk(n, z).diff(z) + -besselk(n - 1, z)/2 - besselk(n + 1, z)/2 + + See Also + ======== + + besselj, besseli, bessely + + References + ========== + + .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/BesselK/ + + """ + + _a = S.One + _b = -S.One + + @classmethod + def eval(cls, nu, z): + if z.is_zero: + if nu.is_zero: + return S.Infinity + elif re(nu).is_zero is False: + return S.ComplexInfinity + elif re(nu).is_zero: + return S.NaN + if z in (S.Infinity, I*S.Infinity, I*S.NegativeInfinity): + return S.Zero + + if nu.is_integer: + if nu.could_extract_minus_sign(): + return besselk(-nu, z) + + def _eval_rewrite_as_besseli(self, nu, z, **kwargs): + if nu.is_integer is False: + return pi*csc(pi*nu)*(besseli(-nu, z) - besseli(nu, z))/2 + + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + ai = self._eval_rewrite_as_besseli(*self.args) + if ai: + return ai.rewrite(besselj) + + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + aj = self._eval_rewrite_as_besselj(*self.args) + if aj: + return aj.rewrite(bessely) + + def _eval_rewrite_as_yn(self, nu, z, **kwargs): + ay = self._eval_rewrite_as_bessely(*self.args) + if ay: + return ay.rewrite(yn) + + def _eval_is_extended_real(self): + nu, z = self.args + if nu.is_integer and z.is_positive: + return True + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + nu, z = self.args + try: + arg = z.as_leading_term(x) + except NotImplementedError: + return self + _, e = arg.as_coeff_exponent(x) + + if e.is_positive: + term_one = ((-1)**(nu -1)*log(z/2)*besseli(nu, z)) + term_two = (z/2)**(-nu)*factorial(nu - 1)/2 if (nu).is_positive else S.Zero + term_three = (-1)**nu*(z/2)**nu/(2*factorial(nu))*(digamma(nu + 1) - S.EulerGamma) + arg = Add(*[term_one, term_two, term_three]).as_leading_term(x, logx=logx) + return arg + elif e.is_negative: + # Refer Abramowitz and Stegun 1965, p. 378 for more information on + # asymptotic approximation of besselk function. + return sqrt(pi)*exp(-z)/sqrt(2*z) + + return super(besselk, self)._eval_as_leading_term(x, logx, cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + # Refer https://functions.wolfram.com/Bessel-TypeFunctions/BesselK/06/01/04/01/02/0008/ + # for more information on nseries expansion of besselk function. + from sympy.series.order import Order + nu, z = self.args + + # In case of powers less than 1, number of terms need to be computed + # separately to avoid repeated callings of _eval_nseries with wrong n + try: + _, exp = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + if exp.is_positive and nu.is_integer: + newn = ceiling(n/exp) + bn = besseli(nu, z) + a = ((-1)**(nu - 1)*log(z/2)*bn)._eval_nseries(x, n, logx, cdir) + + b, c = [], [] + o = Order(x**n, x) + r = (z/2)._eval_nseries(x, n, logx, cdir).removeO() + if r is S.Zero: + return o + t = (_mexpand(r**2) + o).removeO() + + if nu > S.Zero: + term = r**(-nu)*factorial(nu - 1)/2 + b.append(term) + for k in range(1, nu): + denom = (k - nu)*k + if denom == S.Zero: + term *= t/k + else: + term *= t/denom + term = (_mexpand(term) + o).removeO() + b.append(term) + + p = r**nu*(-1)**nu/(2*factorial(nu)) + term = p*(digamma(nu + 1) - S.EulerGamma) + c.append(term) + for k in range(1, (newn + 1)//2): + p *= t/(k*(k + nu)) + p = (_mexpand(p) + o).removeO() + term = p*(digamma(k + nu + 1) + digamma(k + 1)) + c.append(term) + return a + Add(*b) + Add(*c) # Order term comes from a + + return super(besselk, self)._eval_nseries(x, n, logx, cdir) + + +class hankel1(BesselBase): + r""" + Hankel function of the first kind. + + Explanation + =========== + + This function is defined as + + .. math :: + H_\nu^{(1)} = J_\nu(z) + iY_\nu(z), + + where $J_\nu(z)$ is the Bessel function of the first kind, and + $Y_\nu(z)$ is the Bessel function of the second kind. + + It is a solution to Bessel's equation. + + Examples + ======== + + >>> from sympy import hankel1 + >>> from sympy.abc import z, n + >>> hankel1(n, z).diff(z) + hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2 + + See Also + ======== + + hankel2, besselj, bessely + + References + ========== + + .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/HankelH1/ + + """ + + _a = S.One + _b = S.One + + def _eval_conjugate(self): + z = self.argument + if z.is_extended_negative is False: + return hankel2(self.order.conjugate(), z.conjugate()) + + +class hankel2(BesselBase): + r""" + Hankel function of the second kind. + + Explanation + =========== + + This function is defined as + + .. math :: + H_\nu^{(2)} = J_\nu(z) - iY_\nu(z), + + where $J_\nu(z)$ is the Bessel function of the first kind, and + $Y_\nu(z)$ is the Bessel function of the second kind. + + It is a solution to Bessel's equation, and linearly independent from + $H_\nu^{(1)}$. + + Examples + ======== + + >>> from sympy import hankel2 + >>> from sympy.abc import z, n + >>> hankel2(n, z).diff(z) + hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2 + + See Also + ======== + + hankel1, besselj, bessely + + References + ========== + + .. [1] https://functions.wolfram.com/Bessel-TypeFunctions/HankelH2/ + + """ + + _a = S.One + _b = S.One + + def _eval_conjugate(self): + z = self.argument + if z.is_extended_negative is False: + return hankel1(self.order.conjugate(), z.conjugate()) + + +def assume_integer_order(fn): + @wraps(fn) + def g(self, nu, z): + if nu.is_integer: + return fn(self, nu, z) + return g + + +class SphericalBesselBase(BesselBase): + """ + Base class for spherical Bessel functions. + + These are thin wrappers around ordinary Bessel functions, + since spherical Bessel functions differ from the ordinary + ones just by a slight change in order. + + To use this class, define the ``_eval_evalf()`` and ``_expand()`` methods. + + """ + + def _expand(self, **hints): + """ Expand self into a polynomial. Nu is guaranteed to be Integer. """ + raise NotImplementedError('expansion') + + def _eval_expand_func(self, **hints): + if self.order.is_Integer: + return self._expand(**hints) + return self + + def fdiff(self, argindex=2): + if argindex != 2: + raise ArgumentIndexError(self, argindex) + return self.__class__(self.order - 1, self.argument) - \ + self * (self.order + 1)/self.argument + + +def _jn(n, z): + return (spherical_bessel_fn(n, z)*sin(z) + + S.NegativeOne**(n + 1)*spherical_bessel_fn(-n - 1, z)*cos(z)) + + +def _yn(n, z): + # (-1)**(n + 1) * _jn(-n - 1, z) + return (S.NegativeOne**(n + 1) * spherical_bessel_fn(-n - 1, z)*sin(z) - + spherical_bessel_fn(n, z)*cos(z)) + + +class jn(SphericalBesselBase): + r""" + Spherical Bessel function of the first kind. + + Explanation + =========== + + This function is a solution to the spherical Bessel equation + + .. math :: + z^2 \frac{\mathrm{d}^2 w}{\mathrm{d}z^2} + + 2z \frac{\mathrm{d}w}{\mathrm{d}z} + (z^2 - \nu(\nu + 1)) w = 0. + + It can be defined as + + .. math :: + j_\nu(z) = \sqrt{\frac{\pi}{2z}} J_{\nu + \frac{1}{2}}(z), + + where $J_\nu(z)$ is the Bessel function of the first kind. + + The spherical Bessel functions of integral order are + calculated using the formula: + + .. math:: j_n(z) = f_n(z) \sin{z} + (-1)^{n+1} f_{-n-1}(z) \cos{z}, + + where the coefficients $f_n(z)$ are available as + :func:`sympy.polys.orthopolys.spherical_bessel_fn`. + + Examples + ======== + + >>> from sympy import Symbol, jn, sin, cos, expand_func, besselj, bessely + >>> z = Symbol("z") + >>> nu = Symbol("nu", integer=True) + >>> print(expand_func(jn(0, z))) + sin(z)/z + >>> expand_func(jn(1, z)) == sin(z)/z**2 - cos(z)/z + True + >>> expand_func(jn(3, z)) + (-6/z**2 + 15/z**4)*sin(z) + (1/z - 15/z**3)*cos(z) + >>> jn(nu, z).rewrite(besselj) + sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(nu + 1/2, z)/2 + >>> jn(nu, z).rewrite(bessely) + (-1)**nu*sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(-nu - 1/2, z)/2 + >>> jn(2, 5.2+0.3j).evalf(20) + 0.099419756723640344491 - 0.054525080242173562897*I + + See Also + ======== + + besselj, bessely, besselk, yn + + References + ========== + + .. [1] https://dlmf.nist.gov/10.47 + + """ + @classmethod + def eval(cls, nu, z): + if z.is_zero: + if nu.is_zero: + return S.One + elif nu.is_integer: + if nu.is_positive: + return S.Zero + else: + return S.ComplexInfinity + if z in (S.NegativeInfinity, S.Infinity): + return S.Zero + + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + return sqrt(pi/(2*z)) * besselj(nu + S.Half, z) + + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + return S.NegativeOne**nu * sqrt(pi/(2*z)) * bessely(-nu - S.Half, z) + + def _eval_rewrite_as_yn(self, nu, z, **kwargs): + return S.NegativeOne**(nu) * yn(-nu - 1, z) + + def _expand(self, **hints): + return _jn(self.order, self.argument) + + def _eval_evalf(self, prec): + if self.order.is_Integer: + return self.rewrite(besselj)._eval_evalf(prec) + + +class yn(SphericalBesselBase): + r""" + Spherical Bessel function of the second kind. + + Explanation + =========== + + This function is another solution to the spherical Bessel equation, and + linearly independent from $j_n$. It can be defined as + + .. math :: + y_\nu(z) = \sqrt{\frac{\pi}{2z}} Y_{\nu + \frac{1}{2}}(z), + + where $Y_\nu(z)$ is the Bessel function of the second kind. + + For integral orders $n$, $y_n$ is calculated using the formula: + + .. math:: y_n(z) = (-1)^{n+1} j_{-n-1}(z) + + Examples + ======== + + >>> from sympy import Symbol, yn, sin, cos, expand_func, besselj, bessely + >>> z = Symbol("z") + >>> nu = Symbol("nu", integer=True) + >>> print(expand_func(yn(0, z))) + -cos(z)/z + >>> expand_func(yn(1, z)) == -cos(z)/z**2-sin(z)/z + True + >>> yn(nu, z).rewrite(besselj) + (-1)**(nu + 1)*sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(-nu - 1/2, z)/2 + >>> yn(nu, z).rewrite(bessely) + sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(nu + 1/2, z)/2 + >>> yn(2, 5.2+0.3j).evalf(20) + 0.18525034196069722536 + 0.014895573969924817587*I + + See Also + ======== + + besselj, bessely, besselk, jn + + References + ========== + + .. [1] https://dlmf.nist.gov/10.47 + + """ + @assume_integer_order + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + return S.NegativeOne**(nu+1) * sqrt(pi/(2*z)) * besselj(-nu - S.Half, z) + + @assume_integer_order + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + return sqrt(pi/(2*z)) * bessely(nu + S.Half, z) + + def _eval_rewrite_as_jn(self, nu, z, **kwargs): + return S.NegativeOne**(nu + 1) * jn(-nu - 1, z) + + def _expand(self, **hints): + return _yn(self.order, self.argument) + + def _eval_evalf(self, prec): + if self.order.is_Integer: + return self.rewrite(bessely)._eval_evalf(prec) + + +class SphericalHankelBase(SphericalBesselBase): + + @assume_integer_order + def _eval_rewrite_as_besselj(self, nu, z, **kwargs): + # jn +- I*yn + # jn as beeselj: sqrt(pi/(2*z)) * besselj(nu + S.Half, z) + # yn as besselj: (-1)**(nu+1) * sqrt(pi/(2*z)) * besselj(-nu - S.Half, z) + hks = self._hankel_kind_sign + return sqrt(pi/(2*z))*(besselj(nu + S.Half, z) + + hks*I*S.NegativeOne**(nu+1)*besselj(-nu - S.Half, z)) + + @assume_integer_order + def _eval_rewrite_as_bessely(self, nu, z, **kwargs): + # jn +- I*yn + # jn as bessely: (-1)**nu * sqrt(pi/(2*z)) * bessely(-nu - S.Half, z) + # yn as bessely: sqrt(pi/(2*z)) * bessely(nu + S.Half, z) + hks = self._hankel_kind_sign + return sqrt(pi/(2*z))*(S.NegativeOne**nu*bessely(-nu - S.Half, z) + + hks*I*bessely(nu + S.Half, z)) + + def _eval_rewrite_as_yn(self, nu, z, **kwargs): + hks = self._hankel_kind_sign + return jn(nu, z).rewrite(yn) + hks*I*yn(nu, z) + + def _eval_rewrite_as_jn(self, nu, z, **kwargs): + hks = self._hankel_kind_sign + return jn(nu, z) + hks*I*yn(nu, z).rewrite(jn) + + def _eval_expand_func(self, **hints): + if self.order.is_Integer: + return self._expand(**hints) + else: + nu = self.order + z = self.argument + hks = self._hankel_kind_sign + return jn(nu, z) + hks*I*yn(nu, z) + + def _expand(self, **hints): + n = self.order + z = self.argument + hks = self._hankel_kind_sign + + # fully expanded version + # return ((fn(n, z) * sin(z) + + # (-1)**(n + 1) * fn(-n - 1, z) * cos(z)) + # jn + # (hks * I * (-1)**(n + 1) * + # (fn(-n - 1, z) * hk * I * sin(z) + + # (-1)**(-n) * fn(n, z) * I * cos(z))) # +-I*yn + # ) + + return (_jn(n, z) + hks*I*_yn(n, z)).expand() + + def _eval_evalf(self, prec): + if self.order.is_Integer: + return self.rewrite(besselj)._eval_evalf(prec) + + +class hn1(SphericalHankelBase): + r""" + Spherical Hankel function of the first kind. + + Explanation + =========== + + This function is defined as + + .. math:: h_\nu^(1)(z) = j_\nu(z) + i y_\nu(z), + + where $j_\nu(z)$ and $y_\nu(z)$ are the spherical + Bessel function of the first and second kinds. + + For integral orders $n$, $h_n^(1)$ is calculated using the formula: + + .. math:: h_n^(1)(z) = j_{n}(z) + i (-1)^{n+1} j_{-n-1}(z) + + Examples + ======== + + >>> from sympy import Symbol, hn1, hankel1, expand_func, yn, jn + >>> z = Symbol("z") + >>> nu = Symbol("nu", integer=True) + >>> print(expand_func(hn1(nu, z))) + jn(nu, z) + I*yn(nu, z) + >>> print(expand_func(hn1(0, z))) + sin(z)/z - I*cos(z)/z + >>> print(expand_func(hn1(1, z))) + -I*sin(z)/z - cos(z)/z + sin(z)/z**2 - I*cos(z)/z**2 + >>> hn1(nu, z).rewrite(jn) + (-1)**(nu + 1)*I*jn(-nu - 1, z) + jn(nu, z) + >>> hn1(nu, z).rewrite(yn) + (-1)**nu*yn(-nu - 1, z) + I*yn(nu, z) + >>> hn1(nu, z).rewrite(hankel1) + sqrt(2)*sqrt(pi)*sqrt(1/z)*hankel1(nu, z)/2 + + See Also + ======== + + hn2, jn, yn, hankel1, hankel2 + + References + ========== + + .. [1] https://dlmf.nist.gov/10.47 + + """ + + _hankel_kind_sign = S.One + + @assume_integer_order + def _eval_rewrite_as_hankel1(self, nu, z, **kwargs): + return sqrt(pi/(2*z))*hankel1(nu, z) + + +class hn2(SphericalHankelBase): + r""" + Spherical Hankel function of the second kind. + + Explanation + =========== + + This function is defined as + + .. math:: h_\nu^(2)(z) = j_\nu(z) - i y_\nu(z), + + where $j_\nu(z)$ and $y_\nu(z)$ are the spherical + Bessel function of the first and second kinds. + + For integral orders $n$, $h_n^(2)$ is calculated using the formula: + + .. math:: h_n^(2)(z) = j_{n} - i (-1)^{n+1} j_{-n-1}(z) + + Examples + ======== + + >>> from sympy import Symbol, hn2, hankel2, expand_func, jn, yn + >>> z = Symbol("z") + >>> nu = Symbol("nu", integer=True) + >>> print(expand_func(hn2(nu, z))) + jn(nu, z) - I*yn(nu, z) + >>> print(expand_func(hn2(0, z))) + sin(z)/z + I*cos(z)/z + >>> print(expand_func(hn2(1, z))) + I*sin(z)/z - cos(z)/z + sin(z)/z**2 + I*cos(z)/z**2 + >>> hn2(nu, z).rewrite(hankel2) + sqrt(2)*sqrt(pi)*sqrt(1/z)*hankel2(nu, z)/2 + >>> hn2(nu, z).rewrite(jn) + -(-1)**(nu + 1)*I*jn(-nu - 1, z) + jn(nu, z) + >>> hn2(nu, z).rewrite(yn) + (-1)**nu*yn(-nu - 1, z) - I*yn(nu, z) + + See Also + ======== + + hn1, jn, yn, hankel1, hankel2 + + References + ========== + + .. [1] https://dlmf.nist.gov/10.47 + + """ + + _hankel_kind_sign = -S.One + + @assume_integer_order + def _eval_rewrite_as_hankel2(self, nu, z, **kwargs): + return sqrt(pi/(2*z))*hankel2(nu, z) + + +def jn_zeros(n, k, method="sympy", dps=15): + """ + Zeros of the spherical Bessel function of the first kind. + + Explanation + =========== + + This returns an array of zeros of $jn$ up to the $k$-th zero. + + * method = "sympy": uses `mpmath.besseljzero + `_ + * method = "scipy": uses the + `SciPy's sph_jn `_ + and + `newton `_ + to find all + roots, which is faster than computing the zeros using a general + numerical solver, but it requires SciPy and only works with low + precision floating point numbers. (The function used with + method="sympy" is a recent addition to mpmath; before that a general + solver was used.) + + Examples + ======== + + >>> from sympy import jn_zeros + >>> jn_zeros(2, 4, dps=5) + [5.7635, 9.095, 12.323, 15.515] + + See Also + ======== + + jn, yn, besselj, besselk, bessely + + Parameters + ========== + + n : integer + order of Bessel function + + k : integer + number of zeros to return + + + """ + from math import pi as math_pi + + if method == "sympy": + from mpmath import besseljzero + from mpmath.libmp.libmpf import dps_to_prec + prec = dps_to_prec(dps) + return [Expr._from_mpmath(besseljzero(S(n + 0.5)._to_mpmath(prec), + int(l)), prec) + for l in range(1, k + 1)] + elif method == "scipy": + from scipy.optimize import newton + try: + from scipy.special import spherical_jn + f = lambda x: spherical_jn(n, x) + except ImportError: + from scipy.special import sph_jn + f = lambda x: sph_jn(n, x)[0][-1] + else: + raise NotImplementedError("Unknown method.") + + def solver(f, x): + if method == "scipy": + root = newton(f, x) + else: + raise NotImplementedError("Unknown method.") + return root + + # we need to approximate the position of the first root: + root = n + math_pi + # determine the first root exactly: + root = solver(f, root) + roots = [root] + for i in range(k - 1): + # estimate the position of the next root using the last root + pi: + root = solver(f, root + math_pi) + roots.append(root) + return roots + + +class AiryBase(Function): + """ + Abstract base class for Airy functions. + + This class is meant to reduce code duplication. + + """ + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + def as_real_imag(self, deep=True, **hints): + z = self.args[0] + zc = z.conjugate() + f = self.func + u = (f(z)+f(zc))/2 + v = I*(f(zc)-f(z))/2 + return u, v + + def _eval_expand_complex(self, deep=True, **hints): + re_part, im_part = self.as_real_imag(deep=deep, **hints) + return re_part + im_part*I + + +class airyai(AiryBase): + r""" + The Airy function $\operatorname{Ai}$ of the first kind. + + Explanation + =========== + + The Airy function $\operatorname{Ai}(z)$ is defined to be the function + satisfying Airy's differential equation + + .. math:: + \frac{\mathrm{d}^2 w(z)}{\mathrm{d}z^2} - z w(z) = 0. + + Equivalently, for real $z$ + + .. math:: + \operatorname{Ai}(z) := \frac{1}{\pi} + \int_0^\infty \cos\left(\frac{t^3}{3} + z t\right) \mathrm{d}t. + + Examples + ======== + + Create an Airy function object: + + >>> from sympy import airyai + >>> from sympy.abc import z + + >>> airyai(z) + airyai(z) + + Several special values are known: + + >>> airyai(0) + 3**(1/3)/(3*gamma(2/3)) + >>> from sympy import oo + >>> airyai(oo) + 0 + >>> airyai(-oo) + 0 + + The Airy function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(airyai(z)) + airyai(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(airyai(z), z) + airyaiprime(z) + >>> diff(airyai(z), z, 2) + z*airyai(z) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(airyai(z), z, 0, 3) + 3**(5/6)*gamma(1/3)/(6*pi) - 3**(1/6)*z*gamma(2/3)/(2*pi) + O(z**3) + + We can numerically evaluate the Airy function to arbitrary precision + on the whole complex plane: + + >>> airyai(-2).evalf(50) + 0.22740742820168557599192443603787379946077222541710 + + Rewrite $\operatorname{Ai}(z)$ in terms of hypergeometric functions: + + >>> from sympy import hyper + >>> airyai(z).rewrite(hyper) + -3**(2/3)*z*hyper((), (4/3,), z**3/9)/(3*gamma(1/3)) + 3**(1/3)*hyper((), (2/3,), z**3/9)/(3*gamma(2/3)) + + See Also + ======== + + airybi: Airy function of the second kind. + airyaiprime: Derivative of the Airy function of the first kind. + airybiprime: Derivative of the Airy function of the second kind. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Airy_function + .. [2] https://dlmf.nist.gov/9 + .. [3] https://encyclopediaofmath.org/wiki/Airy_functions + .. [4] https://mathworld.wolfram.com/AiryFunctions.html + + """ + + nargs = 1 + unbranched = True + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return S.One / (3**Rational(2, 3) * gamma(Rational(2, 3))) + if arg.is_zero: + return S.One / (3**Rational(2, 3) * gamma(Rational(2, 3))) + + def fdiff(self, argindex=1): + if argindex == 1: + return airyaiprime(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 1: + p = previous_terms[-1] + return ((cbrt(3)*x)**(-n)*(cbrt(3)*x)**(n + 1)*sin(pi*(n*Rational(2, 3) + Rational(4, 3)))*factorial(n) * + gamma(n/3 + Rational(2, 3))/(sin(pi*(n*Rational(2, 3) + Rational(2, 3)))*factorial(n + 1)*gamma(n/3 + Rational(1, 3))) * p) + else: + return (S.One/(3**Rational(2, 3)*pi) * gamma((n+S.One)/S(3)) * sin(Rational(2, 3)*pi*(n+S.One)) / + factorial(n) * (cbrt(3)*x)**n) + + def _eval_rewrite_as_besselj(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = Pow(-z, Rational(3, 2)) + if re(z).is_negative: + return ot*sqrt(-z) * (besselj(-ot, tt*a) + besselj(ot, tt*a)) + + def _eval_rewrite_as_besseli(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = Pow(z, Rational(3, 2)) + if re(z).is_positive: + return ot*sqrt(z) * (besseli(-ot, tt*a) - besseli(ot, tt*a)) + else: + return ot*(Pow(a, ot)*besseli(-ot, tt*a) - z*Pow(a, -ot)*besseli(ot, tt*a)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + pf1 = S.One / (3**Rational(2, 3)*gamma(Rational(2, 3))) + pf2 = z / (root(3, 3)*gamma(Rational(1, 3))) + return pf1 * hyper([], [Rational(2, 3)], z**3/9) - pf2 * hyper([], [Rational(4, 3)], z**3/9) + + def _eval_expand_func(self, **hints): + arg = self.args[0] + symbs = arg.free_symbols + + if len(symbs) == 1: + z = symbs.pop() + c = Wild("c", exclude=[z]) + d = Wild("d", exclude=[z]) + m = Wild("m", exclude=[z]) + n = Wild("n", exclude=[z]) + M = arg.match(c*(d*z**n)**m) + if M is not None: + m = M[m] + # The transformation is given by 03.05.16.0001.01 + # https://functions.wolfram.com/Bessel-TypeFunctions/AiryAi/16/01/01/0001/ + if (3*m).is_integer: + c = M[c] + d = M[d] + n = M[n] + pf = (d * z**n)**m / (d**m * z**(m*n)) + newarg = c * d**m * z**(m*n) + return S.Half * ((pf + S.One)*airyai(newarg) - (pf - S.One)/sqrt(3)*airybi(newarg)) + + +class airybi(AiryBase): + r""" + The Airy function $\operatorname{Bi}$ of the second kind. + + Explanation + =========== + + The Airy function $\operatorname{Bi}(z)$ is defined to be the function + satisfying Airy's differential equation + + .. math:: + \frac{\mathrm{d}^2 w(z)}{\mathrm{d}z^2} - z w(z) = 0. + + Equivalently, for real $z$ + + .. math:: + \operatorname{Bi}(z) := \frac{1}{\pi} + \int_0^\infty + \exp\left(-\frac{t^3}{3} + z t\right) + + \sin\left(\frac{t^3}{3} + z t\right) \mathrm{d}t. + + Examples + ======== + + Create an Airy function object: + + >>> from sympy import airybi + >>> from sympy.abc import z + + >>> airybi(z) + airybi(z) + + Several special values are known: + + >>> airybi(0) + 3**(5/6)/(3*gamma(2/3)) + >>> from sympy import oo + >>> airybi(oo) + oo + >>> airybi(-oo) + 0 + + The Airy function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(airybi(z)) + airybi(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(airybi(z), z) + airybiprime(z) + >>> diff(airybi(z), z, 2) + z*airybi(z) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(airybi(z), z, 0, 3) + 3**(1/3)*gamma(1/3)/(2*pi) + 3**(2/3)*z*gamma(2/3)/(2*pi) + O(z**3) + + We can numerically evaluate the Airy function to arbitrary precision + on the whole complex plane: + + >>> airybi(-2).evalf(50) + -0.41230258795639848808323405461146104203453483447240 + + Rewrite $\operatorname{Bi}(z)$ in terms of hypergeometric functions: + + >>> from sympy import hyper + >>> airybi(z).rewrite(hyper) + 3**(1/6)*z*hyper((), (4/3,), z**3/9)/gamma(1/3) + 3**(5/6)*hyper((), (2/3,), z**3/9)/(3*gamma(2/3)) + + See Also + ======== + + airyai: Airy function of the first kind. + airyaiprime: Derivative of the Airy function of the first kind. + airybiprime: Derivative of the Airy function of the second kind. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Airy_function + .. [2] https://dlmf.nist.gov/9 + .. [3] https://encyclopediaofmath.org/wiki/Airy_functions + .. [4] https://mathworld.wolfram.com/AiryFunctions.html + + """ + + nargs = 1 + unbranched = True + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return S.One / (3**Rational(1, 6) * gamma(Rational(2, 3))) + + if arg.is_zero: + return S.One / (3**Rational(1, 6) * gamma(Rational(2, 3))) + + def fdiff(self, argindex=1): + if argindex == 1: + return airybiprime(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 1: + p = previous_terms[-1] + return (cbrt(3)*x * Abs(sin(Rational(2, 3)*pi*(n + S.One))) * factorial((n - S.One)/S(3)) / + ((n + S.One) * Abs(cos(Rational(2, 3)*pi*(n + S.Half))) * factorial((n - 2)/S(3))) * p) + else: + return (S.One/(root(3, 6)*pi) * gamma((n + S.One)/S(3)) * Abs(sin(Rational(2, 3)*pi*(n + S.One))) / + factorial(n) * (cbrt(3)*x)**n) + + def _eval_rewrite_as_besselj(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = Pow(-z, Rational(3, 2)) + if re(z).is_negative: + return sqrt(-z/3) * (besselj(-ot, tt*a) - besselj(ot, tt*a)) + + def _eval_rewrite_as_besseli(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = Pow(z, Rational(3, 2)) + if re(z).is_positive: + return sqrt(z)/sqrt(3) * (besseli(-ot, tt*a) + besseli(ot, tt*a)) + else: + b = Pow(a, ot) + c = Pow(a, -ot) + return sqrt(ot)*(b*besseli(-ot, tt*a) + z*c*besseli(ot, tt*a)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + pf1 = S.One / (root(3, 6)*gamma(Rational(2, 3))) + pf2 = z*root(3, 6) / gamma(Rational(1, 3)) + return pf1 * hyper([], [Rational(2, 3)], z**3/9) + pf2 * hyper([], [Rational(4, 3)], z**3/9) + + def _eval_expand_func(self, **hints): + arg = self.args[0] + symbs = arg.free_symbols + + if len(symbs) == 1: + z = symbs.pop() + c = Wild("c", exclude=[z]) + d = Wild("d", exclude=[z]) + m = Wild("m", exclude=[z]) + n = Wild("n", exclude=[z]) + M = arg.match(c*(d*z**n)**m) + if M is not None: + m = M[m] + # The transformation is given by 03.06.16.0001.01 + # https://functions.wolfram.com/Bessel-TypeFunctions/AiryBi/16/01/01/0001/ + if (3*m).is_integer: + c = M[c] + d = M[d] + n = M[n] + pf = (d * z**n)**m / (d**m * z**(m*n)) + newarg = c * d**m * z**(m*n) + return S.Half * (sqrt(3)*(S.One - pf)*airyai(newarg) + (S.One + pf)*airybi(newarg)) + + +class airyaiprime(AiryBase): + r""" + The derivative $\operatorname{Ai}^\prime$ of the Airy function of the first + kind. + + Explanation + =========== + + The Airy function $\operatorname{Ai}^\prime(z)$ is defined to be the + function + + .. math:: + \operatorname{Ai}^\prime(z) := \frac{\mathrm{d} \operatorname{Ai}(z)}{\mathrm{d} z}. + + Examples + ======== + + Create an Airy function object: + + >>> from sympy import airyaiprime + >>> from sympy.abc import z + + >>> airyaiprime(z) + airyaiprime(z) + + Several special values are known: + + >>> airyaiprime(0) + -3**(2/3)/(3*gamma(1/3)) + >>> from sympy import oo + >>> airyaiprime(oo) + 0 + + The Airy function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(airyaiprime(z)) + airyaiprime(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(airyaiprime(z), z) + z*airyai(z) + >>> diff(airyaiprime(z), z, 2) + z*airyaiprime(z) + airyai(z) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(airyaiprime(z), z, 0, 3) + -3**(2/3)/(3*gamma(1/3)) + 3**(1/3)*z**2/(6*gamma(2/3)) + O(z**3) + + We can numerically evaluate the Airy function to arbitrary precision + on the whole complex plane: + + >>> airyaiprime(-2).evalf(50) + 0.61825902074169104140626429133247528291577794512415 + + Rewrite $\operatorname{Ai}^\prime(z)$ in terms of hypergeometric functions: + + >>> from sympy import hyper + >>> airyaiprime(z).rewrite(hyper) + 3**(1/3)*z**2*hyper((), (5/3,), z**3/9)/(6*gamma(2/3)) - 3**(2/3)*hyper((), (1/3,), z**3/9)/(3*gamma(1/3)) + + See Also + ======== + + airyai: Airy function of the first kind. + airybi: Airy function of the second kind. + airybiprime: Derivative of the Airy function of the second kind. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Airy_function + .. [2] https://dlmf.nist.gov/9 + .. [3] https://encyclopediaofmath.org/wiki/Airy_functions + .. [4] https://mathworld.wolfram.com/AiryFunctions.html + + """ + + nargs = 1 + unbranched = True + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + + if arg.is_zero: + return S.NegativeOne / (3**Rational(1, 3) * gamma(Rational(1, 3))) + + def fdiff(self, argindex=1): + if argindex == 1: + return self.args[0]*airyai(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + z = self.args[0]._to_mpmath(prec) + with workprec(prec): + res = mp.airyai(z, derivative=1) + return Expr._from_mpmath(res, prec) + + def _eval_rewrite_as_besselj(self, z, **kwargs): + tt = Rational(2, 3) + a = Pow(-z, Rational(3, 2)) + if re(z).is_negative: + return z/3 * (besselj(-tt, tt*a) - besselj(tt, tt*a)) + + def _eval_rewrite_as_besseli(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = tt * Pow(z, Rational(3, 2)) + if re(z).is_positive: + return z/3 * (besseli(tt, a) - besseli(-tt, a)) + else: + a = Pow(z, Rational(3, 2)) + b = Pow(a, tt) + c = Pow(a, -tt) + return ot * (z**2*c*besseli(tt, tt*a) - b*besseli(-ot, tt*a)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + pf1 = z**2 / (2*3**Rational(2, 3)*gamma(Rational(2, 3))) + pf2 = 1 / (root(3, 3)*gamma(Rational(1, 3))) + return pf1 * hyper([], [Rational(5, 3)], z**3/9) - pf2 * hyper([], [Rational(1, 3)], z**3/9) + + def _eval_expand_func(self, **hints): + arg = self.args[0] + symbs = arg.free_symbols + + if len(symbs) == 1: + z = symbs.pop() + c = Wild("c", exclude=[z]) + d = Wild("d", exclude=[z]) + m = Wild("m", exclude=[z]) + n = Wild("n", exclude=[z]) + M = arg.match(c*(d*z**n)**m) + if M is not None: + m = M[m] + # The transformation is in principle + # given by 03.07.16.0001.01 but note + # that there is an error in this formula. + # https://functions.wolfram.com/Bessel-TypeFunctions/AiryAiPrime/16/01/01/0001/ + if (3*m).is_integer: + c = M[c] + d = M[d] + n = M[n] + pf = (d**m * z**(n*m)) / (d * z**n)**m + newarg = c * d**m * z**(n*m) + return S.Half * ((pf + S.One)*airyaiprime(newarg) + (pf - S.One)/sqrt(3)*airybiprime(newarg)) + + +class airybiprime(AiryBase): + r""" + The derivative $\operatorname{Bi}^\prime$ of the Airy function of the first + kind. + + Explanation + =========== + + The Airy function $\operatorname{Bi}^\prime(z)$ is defined to be the + function + + .. math:: + \operatorname{Bi}^\prime(z) := \frac{\mathrm{d} \operatorname{Bi}(z)}{\mathrm{d} z}. + + Examples + ======== + + Create an Airy function object: + + >>> from sympy import airybiprime + >>> from sympy.abc import z + + >>> airybiprime(z) + airybiprime(z) + + Several special values are known: + + >>> airybiprime(0) + 3**(1/6)/gamma(1/3) + >>> from sympy import oo + >>> airybiprime(oo) + oo + >>> airybiprime(-oo) + 0 + + The Airy function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(airybiprime(z)) + airybiprime(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(airybiprime(z), z) + z*airybi(z) + >>> diff(airybiprime(z), z, 2) + z*airybiprime(z) + airybi(z) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(airybiprime(z), z, 0, 3) + 3**(1/6)/gamma(1/3) + 3**(5/6)*z**2/(6*gamma(2/3)) + O(z**3) + + We can numerically evaluate the Airy function to arbitrary precision + on the whole complex plane: + + >>> airybiprime(-2).evalf(50) + 0.27879516692116952268509756941098324140300059345163 + + Rewrite $\operatorname{Bi}^\prime(z)$ in terms of hypergeometric functions: + + >>> from sympy import hyper + >>> airybiprime(z).rewrite(hyper) + 3**(5/6)*z**2*hyper((), (5/3,), z**3/9)/(6*gamma(2/3)) + 3**(1/6)*hyper((), (1/3,), z**3/9)/gamma(1/3) + + See Also + ======== + + airyai: Airy function of the first kind. + airybi: Airy function of the second kind. + airyaiprime: Derivative of the Airy function of the first kind. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Airy_function + .. [2] https://dlmf.nist.gov/9 + .. [3] https://encyclopediaofmath.org/wiki/Airy_functions + .. [4] https://mathworld.wolfram.com/AiryFunctions.html + + """ + + nargs = 1 + unbranched = True + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Infinity + elif arg is S.NegativeInfinity: + return S.Zero + elif arg.is_zero: + return 3**Rational(1, 6) / gamma(Rational(1, 3)) + + if arg.is_zero: + return 3**Rational(1, 6) / gamma(Rational(1, 3)) + + + def fdiff(self, argindex=1): + if argindex == 1: + return self.args[0]*airybi(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + z = self.args[0]._to_mpmath(prec) + with workprec(prec): + res = mp.airybi(z, derivative=1) + return Expr._from_mpmath(res, prec) + + def _eval_rewrite_as_besselj(self, z, **kwargs): + tt = Rational(2, 3) + a = tt * Pow(-z, Rational(3, 2)) + if re(z).is_negative: + return -z/sqrt(3) * (besselj(-tt, a) + besselj(tt, a)) + + def _eval_rewrite_as_besseli(self, z, **kwargs): + ot = Rational(1, 3) + tt = Rational(2, 3) + a = tt * Pow(z, Rational(3, 2)) + if re(z).is_positive: + return z/sqrt(3) * (besseli(-tt, a) + besseli(tt, a)) + else: + a = Pow(z, Rational(3, 2)) + b = Pow(a, tt) + c = Pow(a, -tt) + return sqrt(ot) * (b*besseli(-tt, tt*a) + z**2*c*besseli(tt, tt*a)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + pf1 = z**2 / (2*root(3, 6)*gamma(Rational(2, 3))) + pf2 = root(3, 6) / gamma(Rational(1, 3)) + return pf1 * hyper([], [Rational(5, 3)], z**3/9) + pf2 * hyper([], [Rational(1, 3)], z**3/9) + + def _eval_expand_func(self, **hints): + arg = self.args[0] + symbs = arg.free_symbols + + if len(symbs) == 1: + z = symbs.pop() + c = Wild("c", exclude=[z]) + d = Wild("d", exclude=[z]) + m = Wild("m", exclude=[z]) + n = Wild("n", exclude=[z]) + M = arg.match(c*(d*z**n)**m) + if M is not None: + m = M[m] + # The transformation is in principle + # given by 03.08.16.0001.01 but note + # that there is an error in this formula. + # https://functions.wolfram.com/Bessel-TypeFunctions/AiryBiPrime/16/01/01/0001/ + if (3*m).is_integer: + c = M[c] + d = M[d] + n = M[n] + pf = (d**m * z**(n*m)) / (d * z**n)**m + newarg = c * d**m * z**(n*m) + return S.Half * (sqrt(3)*(pf - S.One)*airyaiprime(newarg) + (pf + S.One)*airybiprime(newarg)) + + +class marcumq(Function): + r""" + The Marcum Q-function. + + Explanation + =========== + + The Marcum Q-function is defined by the meromorphic continuation of + + .. math:: + Q_m(a, b) = a^{- m + 1} \int_{b}^{\infty} x^{m} e^{- \frac{a^{2}}{2} - \frac{x^{2}}{2}} I_{m - 1}\left(a x\right)\, dx + + Examples + ======== + + >>> from sympy import marcumq + >>> from sympy.abc import m, a, b + >>> marcumq(m, a, b) + marcumq(m, a, b) + + Special values: + + >>> marcumq(m, 0, b) + uppergamma(m, b**2/2)/gamma(m) + >>> marcumq(0, 0, 0) + 0 + >>> marcumq(0, a, 0) + 1 - exp(-a**2/2) + >>> marcumq(1, a, a) + 1/2 + exp(-a**2)*besseli(0, a**2)/2 + >>> marcumq(2, a, a) + 1/2 + exp(-a**2)*besseli(0, a**2)/2 + exp(-a**2)*besseli(1, a**2) + + Differentiation with respect to $a$ and $b$ is supported: + + >>> from sympy import diff + >>> diff(marcumq(m, a, b), a) + a*(-marcumq(m, a, b) + marcumq(m + 1, a, b)) + >>> diff(marcumq(m, a, b), b) + -a**(1 - m)*b**m*exp(-a**2/2 - b**2/2)*besseli(m - 1, a*b) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Marcum_Q-function + .. [2] https://mathworld.wolfram.com/MarcumQ-Function.html + + """ + + @classmethod + def eval(cls, m, a, b): + if a is S.Zero: + if m is S.Zero and b is S.Zero: + return S.Zero + return uppergamma(m, b**2 * S.Half) / gamma(m) + + if m is S.Zero and b is S.Zero: + return 1 - 1 / exp(a**2 * S.Half) + + if a == b: + if m is S.One: + return (1 + exp(-a**2) * besseli(0, a**2))*S.Half + if m == 2: + return S.Half + S.Half * exp(-a**2) * besseli(0, a**2) + exp(-a**2) * besseli(1, a**2) + + if a.is_zero: + if m.is_zero and b.is_zero: + return S.Zero + return uppergamma(m, b**2*S.Half) / gamma(m) + + if m.is_zero and b.is_zero: + return 1 - 1 / exp(a**2*S.Half) + + def fdiff(self, argindex=2): + m, a, b = self.args + if argindex == 2: + return a * (-marcumq(m, a, b) + marcumq(1+m, a, b)) + elif argindex == 3: + return (-b**m / a**(m-1)) * exp(-(a**2 + b**2)/2) * besseli(m-1, a*b) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Integral(self, m, a, b, **kwargs): + from sympy.integrals.integrals import Integral + x = kwargs.get('x', Dummy(uniquely_named_symbol('x').name)) + return a ** (1 - m) * \ + Integral(x**m * exp(-(x**2 + a**2)/2) * besseli(m-1, a*x), [x, b, S.Infinity]) + + def _eval_rewrite_as_Sum(self, m, a, b, **kwargs): + from sympy.concrete.summations import Sum + k = kwargs.get('k', Dummy('k')) + return exp(-(a**2 + b**2) / 2) * Sum((a/b)**k * besseli(k, a*b), [k, 1-m, S.Infinity]) + + def _eval_rewrite_as_besseli(self, m, a, b, **kwargs): + if a == b: + if m == 1: + return (1 + exp(-a**2) * besseli(0, a**2)) / 2 + if m.is_Integer and m >= 2: + s = sum(besseli(i, a**2) for i in range(1, m)) + return S.Half + exp(-a**2) * besseli(0, a**2) / 2 + exp(-a**2) * s + + def _eval_is_zero(self): + if all(arg.is_zero for arg in self.args): + return True diff --git a/lib/python3.11/site-packages/sympy/functions/special/beta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/beta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..fc86fbbf7418aa04637512df91a4fd41778d494f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/beta_functions.py @@ -0,0 +1,389 @@ +from sympy.core import S +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.symbol import Dummy, uniquely_named_symbol +from sympy.functions.special.gamma_functions import gamma, digamma +from sympy.functions.combinatorial.numbers import catalan +from sympy.functions.elementary.complexes import conjugate + +# See mpmath #569 and SymPy #20569 +def betainc_mpmath_fix(a, b, x1, x2, reg=0): + from mpmath import betainc, mpf + if x1 == x2: + return mpf(0) + else: + return betainc(a, b, x1, x2, reg) + +############################################################################### +############################ COMPLETE BETA FUNCTION ########################## +############################################################################### + +class beta(Function): + r""" + The beta integral is called the Eulerian integral of the first kind by + Legendre: + + .. math:: + \mathrm{B}(x,y) \int^{1}_{0} t^{x-1} (1-t)^{y-1} \mathrm{d}t. + + Explanation + =========== + + The Beta function or Euler's first integral is closely associated + with the gamma function. The Beta function is often used in probability + theory and mathematical statistics. It satisfies properties like: + + .. math:: + \mathrm{B}(a,1) = \frac{1}{a} \\ + \mathrm{B}(a,b) = \mathrm{B}(b,a) \\ + \mathrm{B}(a,b) = \frac{\Gamma(a) \Gamma(b)}{\Gamma(a+b)} + + Therefore for integral values of $a$ and $b$: + + .. math:: + \mathrm{B} = \frac{(a-1)! (b-1)!}{(a+b-1)!} + + A special case of the Beta function when `x = y` is the + Central Beta function. It satisfies properties like: + + .. math:: + \mathrm{B}(x) = 2^{1 - 2x}\mathrm{B}(x, \frac{1}{2}) + \mathrm{B}(x) = 2^{1 - 2x} cos(\pi x) \mathrm{B}(\frac{1}{2} - x, x) + \mathrm{B}(x) = \int_{0}^{1} \frac{t^x}{(1 + t)^{2x}} dt + \mathrm{B}(x) = \frac{2}{x} \prod_{n = 1}^{\infty} \frac{n(n + 2x)}{(n + x)^2} + + Examples + ======== + + >>> from sympy import I, pi + >>> from sympy.abc import x, y + + The Beta function obeys the mirror symmetry: + + >>> from sympy import beta, conjugate + >>> conjugate(beta(x, y)) + beta(conjugate(x), conjugate(y)) + + Differentiation with respect to both $x$ and $y$ is supported: + + >>> from sympy import beta, diff + >>> diff(beta(x, y), x) + (polygamma(0, x) - polygamma(0, x + y))*beta(x, y) + + >>> diff(beta(x, y), y) + (polygamma(0, y) - polygamma(0, x + y))*beta(x, y) + + >>> diff(beta(x), x) + 2*(polygamma(0, x) - polygamma(0, 2*x))*beta(x, x) + + We can numerically evaluate the Beta function to + arbitrary precision for any complex numbers x and y: + + >>> from sympy import beta + >>> beta(pi).evalf(40) + 0.02671848900111377452242355235388489324562 + + >>> beta(1 + I).evalf(20) + -0.2112723729365330143 - 0.7655283165378005676*I + + See Also + ======== + + gamma: Gamma function. + uppergamma: Upper incomplete gamma function. + lowergamma: Lower incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + trigamma: Trigamma function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Beta_function + .. [2] https://mathworld.wolfram.com/BetaFunction.html + .. [3] https://dlmf.nist.gov/5.12 + + """ + unbranched = True + + def fdiff(self, argindex): + x, y = self.args + if argindex == 1: + # Diff wrt x + return beta(x, y)*(digamma(x) - digamma(x + y)) + elif argindex == 2: + # Diff wrt y + return beta(x, y)*(digamma(y) - digamma(x + y)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, x, y=None): + if y is None: + return beta(x, x) + if x.is_Number and y.is_Number: + return beta(x, y, evaluate=False).doit() + + def doit(self, **hints): + x = xold = self.args[0] + # Deal with unevaluated single argument beta + single_argument = len(self.args) == 1 + y = yold = self.args[0] if single_argument else self.args[1] + if hints.get('deep', True): + x = x.doit(**hints) + y = y.doit(**hints) + if y.is_zero or x.is_zero: + return S.ComplexInfinity + if y is S.One: + return 1/x + if x is S.One: + return 1/y + if y == x + 1: + return 1/(x*y*catalan(x)) + s = x + y + if (s.is_integer and s.is_negative and x.is_integer is False and + y.is_integer is False): + return S.Zero + if x == xold and y == yold and not single_argument: + return self + return beta(x, y) + + def _eval_expand_func(self, **hints): + x, y = self.args + return gamma(x)*gamma(y) / gamma(x + y) + + def _eval_is_real(self): + return self.args[0].is_real and self.args[1].is_real + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate(), self.args[1].conjugate()) + + def _eval_rewrite_as_gamma(self, x, y, piecewise=True, **kwargs): + return self._eval_expand_func(**kwargs) + + def _eval_rewrite_as_Integral(self, x, y, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [x, y]).name) + return Integral(t**(x - 1)*(1 - t)**(y - 1), (t, 0, 1)) + +############################################################################### +########################## INCOMPLETE BETA FUNCTION ########################### +############################################################################### + +class betainc(Function): + r""" + The Generalized Incomplete Beta function is defined as + + .. math:: + \mathrm{B}_{(x_1, x_2)}(a, b) = \int_{x_1}^{x_2} t^{a - 1} (1 - t)^{b - 1} dt + + The Incomplete Beta function is a special case + of the Generalized Incomplete Beta function : + + .. math:: \mathrm{B}_z (a, b) = \mathrm{B}_{(0, z)}(a, b) + + The Incomplete Beta function satisfies : + + .. math:: \mathrm{B}_z (a, b) = (-1)^a \mathrm{B}_{\frac{z}{z - 1}} (a, 1 - a - b) + + The Beta function is a special case of the Incomplete Beta function : + + .. math:: \mathrm{B}(a, b) = \mathrm{B}_{1}(a, b) + + Examples + ======== + + >>> from sympy import betainc, symbols, conjugate + >>> a, b, x, x1, x2 = symbols('a b x x1 x2') + + The Generalized Incomplete Beta function is given by: + + >>> betainc(a, b, x1, x2) + betainc(a, b, x1, x2) + + The Incomplete Beta function can be obtained as follows: + + >>> betainc(a, b, 0, x) + betainc(a, b, 0, x) + + The Incomplete Beta function obeys the mirror symmetry: + + >>> conjugate(betainc(a, b, x1, x2)) + betainc(conjugate(a), conjugate(b), conjugate(x1), conjugate(x2)) + + We can numerically evaluate the Incomplete Beta function to + arbitrary precision for any complex numbers a, b, x1 and x2: + + >>> from sympy import betainc, I + >>> betainc(2, 3, 4, 5).evalf(10) + 56.08333333 + >>> betainc(0.75, 1 - 4*I, 0, 2 + 3*I).evalf(25) + 0.2241657956955709603655887 + 0.3619619242700451992411724*I + + The Generalized Incomplete Beta function can be expressed + in terms of the Generalized Hypergeometric function. + + >>> from sympy import hyper + >>> betainc(a, b, x1, x2).rewrite(hyper) + (-x1**a*hyper((a, 1 - b), (a + 1,), x1) + x2**a*hyper((a, 1 - b), (a + 1,), x2))/a + + See Also + ======== + + beta: Beta function + hyper: Generalized Hypergeometric function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function + .. [2] https://dlmf.nist.gov/8.17 + .. [3] https://functions.wolfram.com/GammaBetaErf/Beta4/ + .. [4] https://functions.wolfram.com/GammaBetaErf/BetaRegularized4/02/ + + """ + nargs = 4 + unbranched = True + + def fdiff(self, argindex): + a, b, x1, x2 = self.args + if argindex == 3: + # Diff wrt x1 + return -(1 - x1)**(b - 1)*x1**(a - 1) + elif argindex == 4: + # Diff wrt x2 + return (1 - x2)**(b - 1)*x2**(a - 1) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_mpmath(self): + return betainc_mpmath_fix, self.args + + def _eval_is_real(self): + if all(arg.is_real for arg in self.args): + return True + + def _eval_conjugate(self): + return self.func(*map(conjugate, self.args)) + + def _eval_rewrite_as_Integral(self, a, b, x1, x2, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [a, b, x1, x2]).name) + return Integral(t**(a - 1)*(1 - t)**(b - 1), (t, x1, x2)) + + def _eval_rewrite_as_hyper(self, a, b, x1, x2, **kwargs): + from sympy.functions.special.hyper import hyper + return (x2**a * hyper((a, 1 - b), (a + 1,), x2) - x1**a * hyper((a, 1 - b), (a + 1,), x1)) / a + +############################################################################### +#################### REGULARIZED INCOMPLETE BETA FUNCTION ##################### +############################################################################### + +class betainc_regularized(Function): + r""" + The Generalized Regularized Incomplete Beta function is given by + + .. math:: + \mathrm{I}_{(x_1, x_2)}(a, b) = \frac{\mathrm{B}_{(x_1, x_2)}(a, b)}{\mathrm{B}(a, b)} + + The Regularized Incomplete Beta function is a special case + of the Generalized Regularized Incomplete Beta function : + + .. math:: \mathrm{I}_z (a, b) = \mathrm{I}_{(0, z)}(a, b) + + The Regularized Incomplete Beta function is the cumulative distribution + function of the beta distribution. + + Examples + ======== + + >>> from sympy import betainc_regularized, symbols, conjugate + >>> a, b, x, x1, x2 = symbols('a b x x1 x2') + + The Generalized Regularized Incomplete Beta + function is given by: + + >>> betainc_regularized(a, b, x1, x2) + betainc_regularized(a, b, x1, x2) + + The Regularized Incomplete Beta function + can be obtained as follows: + + >>> betainc_regularized(a, b, 0, x) + betainc_regularized(a, b, 0, x) + + The Regularized Incomplete Beta function + obeys the mirror symmetry: + + >>> conjugate(betainc_regularized(a, b, x1, x2)) + betainc_regularized(conjugate(a), conjugate(b), conjugate(x1), conjugate(x2)) + + We can numerically evaluate the Regularized Incomplete Beta function + to arbitrary precision for any complex numbers a, b, x1 and x2: + + >>> from sympy import betainc_regularized, pi, E + >>> betainc_regularized(1, 2, 0, 0.25).evalf(10) + 0.4375000000 + >>> betainc_regularized(pi, E, 0, 1).evalf(5) + 1.00000 + + The Generalized Regularized Incomplete Beta function can be + expressed in terms of the Generalized Hypergeometric function. + + >>> from sympy import hyper + >>> betainc_regularized(a, b, x1, x2).rewrite(hyper) + (-x1**a*hyper((a, 1 - b), (a + 1,), x1) + x2**a*hyper((a, 1 - b), (a + 1,), x2))/(a*beta(a, b)) + + See Also + ======== + + beta: Beta function + hyper: Generalized Hypergeometric function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function + .. [2] https://dlmf.nist.gov/8.17 + .. [3] https://functions.wolfram.com/GammaBetaErf/Beta4/ + .. [4] https://functions.wolfram.com/GammaBetaErf/BetaRegularized4/02/ + + """ + nargs = 4 + unbranched = True + + def __new__(cls, a, b, x1, x2): + return Function.__new__(cls, a, b, x1, x2) + + def _eval_mpmath(self): + return betainc_mpmath_fix, (*self.args, S(1)) + + def fdiff(self, argindex): + a, b, x1, x2 = self.args + if argindex == 3: + # Diff wrt x1 + return -(1 - x1)**(b - 1)*x1**(a - 1) / beta(a, b) + elif argindex == 4: + # Diff wrt x2 + return (1 - x2)**(b - 1)*x2**(a - 1) / beta(a, b) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_real(self): + if all(arg.is_real for arg in self.args): + return True + + def _eval_conjugate(self): + return self.func(*map(conjugate, self.args)) + + def _eval_rewrite_as_Integral(self, a, b, x1, x2, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [a, b, x1, x2]).name) + integrand = t**(a - 1)*(1 - t)**(b - 1) + expr = Integral(integrand, (t, x1, x2)) + return expr / Integral(integrand, (t, 0, 1)) + + def _eval_rewrite_as_hyper(self, a, b, x1, x2, **kwargs): + from sympy.functions.special.hyper import hyper + expr = (x2**a * hyper((a, 1 - b), (a + 1,), x2) - x1**a * hyper((a, 1 - b), (a + 1,), x1)) / a + return expr / beta(a, b) diff --git a/lib/python3.11/site-packages/sympy/functions/special/bsplines.py b/lib/python3.11/site-packages/sympy/functions/special/bsplines.py new file mode 100644 index 0000000000000000000000000000000000000000..6adabb32711447cbba60bbd963104e444599773e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/bsplines.py @@ -0,0 +1,351 @@ +from sympy.core import S, sympify +from sympy.core.symbol import (Dummy, symbols) +from sympy.functions import Piecewise, piecewise_fold +from sympy.logic.boolalg import And +from sympy.sets.sets import Interval + +from functools import lru_cache + + +def _ivl(cond, x): + """return the interval corresponding to the condition + + Conditions in spline's Piecewise give the range over + which an expression is valid like (lo <= x) & (x <= hi). + This function returns (lo, hi). + """ + if isinstance(cond, And) and len(cond.args) == 2: + a, b = cond.args + if a.lts == x: + a, b = b, a + return a.lts, b.gts + raise TypeError('unexpected cond type: %s' % cond) + + +def _add_splines(c, b1, d, b2, x): + """Construct c*b1 + d*b2.""" + + if S.Zero in (b1, c): + rv = piecewise_fold(d * b2) + elif S.Zero in (b2, d): + rv = piecewise_fold(c * b1) + else: + new_args = [] + # Just combining the Piecewise without any fancy optimization + p1 = piecewise_fold(c * b1) + p2 = piecewise_fold(d * b2) + + # Search all Piecewise arguments except (0, True) + p2args = list(p2.args[:-1]) + + # This merging algorithm assumes the conditions in + # p1 and p2 are sorted + for arg in p1.args[:-1]: + expr = arg.expr + cond = arg.cond + + lower = _ivl(cond, x)[0] + + # Check p2 for matching conditions that can be merged + for i, arg2 in enumerate(p2args): + expr2 = arg2.expr + cond2 = arg2.cond + + lower_2, upper_2 = _ivl(cond2, x) + if cond2 == cond: + # Conditions match, join expressions + expr += expr2 + # Remove matching element + del p2args[i] + # No need to check the rest + break + elif lower_2 < lower and upper_2 <= lower: + # Check if arg2 condition smaller than arg1, + # add to new_args by itself (no match expected + # in p1) + new_args.append(arg2) + del p2args[i] + break + + # Checked all, add expr and cond + new_args.append((expr, cond)) + + # Add remaining items from p2args + new_args.extend(p2args) + + # Add final (0, True) + new_args.append((0, True)) + + rv = Piecewise(*new_args, evaluate=False) + + return rv.expand() + + +@lru_cache(maxsize=128) +def bspline_basis(d, knots, n, x): + """ + The $n$-th B-spline at $x$ of degree $d$ with knots. + + Explanation + =========== + + B-Splines are piecewise polynomials of degree $d$. They are defined on a + set of knots, which is a sequence of integers or floats. + + Examples + ======== + + The 0th degree splines have a value of 1 on a single interval: + + >>> from sympy import bspline_basis + >>> from sympy.abc import x + >>> d = 0 + >>> knots = tuple(range(5)) + >>> bspline_basis(d, knots, 0, x) + Piecewise((1, (x >= 0) & (x <= 1)), (0, True)) + + For a given ``(d, knots)`` there are ``len(knots)-d-1`` B-splines + defined, that are indexed by ``n`` (starting at 0). + + Here is an example of a cubic B-spline: + + >>> bspline_basis(3, tuple(range(5)), 0, x) + Piecewise((x**3/6, (x >= 0) & (x <= 1)), + (-x**3/2 + 2*x**2 - 2*x + 2/3, + (x >= 1) & (x <= 2)), + (x**3/2 - 4*x**2 + 10*x - 22/3, + (x >= 2) & (x <= 3)), + (-x**3/6 + 2*x**2 - 8*x + 32/3, + (x >= 3) & (x <= 4)), + (0, True)) + + By repeating knot points, you can introduce discontinuities in the + B-splines and their derivatives: + + >>> d = 1 + >>> knots = (0, 0, 2, 3, 4) + >>> bspline_basis(d, knots, 0, x) + Piecewise((1 - x/2, (x >= 0) & (x <= 2)), (0, True)) + + It is quite time consuming to construct and evaluate B-splines. If + you need to evaluate a B-spline many times, it is best to lambdify them + first: + + >>> from sympy import lambdify + >>> d = 3 + >>> knots = tuple(range(10)) + >>> b0 = bspline_basis(d, knots, 0, x) + >>> f = lambdify(x, b0) + >>> y = f(0.5) + + Parameters + ========== + + d : integer + degree of bspline + + knots : list of integer values + list of knots points of bspline + + n : integer + $n$-th B-spline + + x : symbol + + See Also + ======== + + bspline_basis_set + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/B-spline + + """ + # make sure x has no assumptions so conditions don't evaluate + xvar = x + x = Dummy() + + knots = tuple(sympify(k) for k in knots) + d = int(d) + n = int(n) + n_knots = len(knots) + n_intervals = n_knots - 1 + if n + d + 1 > n_intervals: + raise ValueError("n + d + 1 must not exceed len(knots) - 1") + if d == 0: + result = Piecewise( + (S.One, Interval(knots[n], knots[n + 1]).contains(x)), (0, True) + ) + elif d > 0: + denom = knots[n + d + 1] - knots[n + 1] + if denom != S.Zero: + B = (knots[n + d + 1] - x) / denom + b2 = bspline_basis(d - 1, knots, n + 1, x) + else: + b2 = B = S.Zero + + denom = knots[n + d] - knots[n] + if denom != S.Zero: + A = (x - knots[n]) / denom + b1 = bspline_basis(d - 1, knots, n, x) + else: + b1 = A = S.Zero + + result = _add_splines(A, b1, B, b2, x) + else: + raise ValueError("degree must be non-negative: %r" % n) + + # return result with user-given x + return result.xreplace({x: xvar}) + + +def bspline_basis_set(d, knots, x): + """ + Return the ``len(knots)-d-1`` B-splines at *x* of degree *d* + with *knots*. + + Explanation + =========== + + This function returns a list of piecewise polynomials that are the + ``len(knots)-d-1`` B-splines of degree *d* for the given knots. + This function calls ``bspline_basis(d, knots, n, x)`` for different + values of *n*. + + Examples + ======== + + >>> from sympy import bspline_basis_set + >>> from sympy.abc import x + >>> d = 2 + >>> knots = range(5) + >>> splines = bspline_basis_set(d, knots, x) + >>> splines + [Piecewise((x**2/2, (x >= 0) & (x <= 1)), + (-x**2 + 3*x - 3/2, (x >= 1) & (x <= 2)), + (x**2/2 - 3*x + 9/2, (x >= 2) & (x <= 3)), + (0, True)), + Piecewise((x**2/2 - x + 1/2, (x >= 1) & (x <= 2)), + (-x**2 + 5*x - 11/2, (x >= 2) & (x <= 3)), + (x**2/2 - 4*x + 8, (x >= 3) & (x <= 4)), + (0, True))] + + Parameters + ========== + + d : integer + degree of bspline + + knots : list of integers + list of knots points of bspline + + x : symbol + + See Also + ======== + + bspline_basis + + """ + n_splines = len(knots) - d - 1 + return [bspline_basis(d, tuple(knots), i, x) for i in range(n_splines)] + + +def interpolating_spline(d, x, X, Y): + """ + Return spline of degree *d*, passing through the given *X* + and *Y* values. + + Explanation + =========== + + This function returns a piecewise function such that each part is + a polynomial of degree not greater than *d*. The value of *d* + must be 1 or greater and the values of *X* must be strictly + increasing. + + Examples + ======== + + >>> from sympy import interpolating_spline + >>> from sympy.abc import x + >>> interpolating_spline(1, x, [1, 2, 4, 7], [3, 6, 5, 7]) + Piecewise((3*x, (x >= 1) & (x <= 2)), + (7 - x/2, (x >= 2) & (x <= 4)), + (2*x/3 + 7/3, (x >= 4) & (x <= 7))) + >>> interpolating_spline(3, x, [-2, 0, 1, 3, 4], [4, 2, 1, 1, 3]) + Piecewise((7*x**3/117 + 7*x**2/117 - 131*x/117 + 2, (x >= -2) & (x <= 1)), + (10*x**3/117 - 2*x**2/117 - 122*x/117 + 77/39, (x >= 1) & (x <= 4))) + + Parameters + ========== + + d : integer + Degree of Bspline strictly greater than equal to one + + x : symbol + + X : list of strictly increasing real values + list of X coordinates through which the spline passes + + Y : list of real values + list of corresponding Y coordinates through which the spline passes + + See Also + ======== + + bspline_basis_set, interpolating_poly + + """ + from sympy.solvers.solveset import linsolve + from sympy.matrices.dense import Matrix + + # Input sanitization + d = sympify(d) + if not (d.is_Integer and d.is_positive): + raise ValueError("Spline degree must be a positive integer, not %s." % d) + if len(X) != len(Y): + raise ValueError("Number of X and Y coordinates must be the same.") + if len(X) < d + 1: + raise ValueError("Degree must be less than the number of control points.") + if not all(a < b for a, b in zip(X, X[1:])): + raise ValueError("The x-coordinates must be strictly increasing.") + X = [sympify(i) for i in X] + + # Evaluating knots value + if d.is_odd: + j = (d + 1) // 2 + interior_knots = X[j:-j] + else: + j = d // 2 + interior_knots = [ + (a + b)/2 for a, b in zip(X[j : -j - 1], X[j + 1 : -j]) + ] + + knots = [X[0]] * (d + 1) + list(interior_knots) + [X[-1]] * (d + 1) + + basis = bspline_basis_set(d, knots, x) + + A = [[b.subs(x, v) for b in basis] for v in X] + + coeff = linsolve((Matrix(A), Matrix(Y)), symbols("c0:{}".format(len(X)), cls=Dummy)) + coeff = list(coeff)[0] + intervals = {c for b in basis for (e, c) in b.args if c != True} + + # Sorting the intervals + # ival contains the end-points of each interval + ival = [_ivl(c, x) for c in intervals] + com = zip(ival, intervals) + com = sorted(com, key=lambda x: x[0]) + intervals = [y for x, y in com] + + basis_dicts = [{c: e for (e, c) in b.args} for b in basis] + spline = [] + for i in intervals: + piece = sum( + [c * d.get(i, S.Zero) for (c, d) in zip(coeff, basis_dicts)], S.Zero + ) + spline.append((piece, i)) + return Piecewise(*spline) diff --git a/lib/python3.11/site-packages/sympy/functions/special/delta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/delta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..fd3333d31da2ac2bc645cd0fa0ecdb7e1d45d381 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/delta_functions.py @@ -0,0 +1,664 @@ +from sympy.core import S, diff +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.logic import fuzzy_not +from sympy.core.relational import Eq, Ne +from sympy.functions.elementary.complexes import im, sign +from sympy.functions.elementary.piecewise import Piecewise +from sympy.polys.polyerrors import PolynomialError +from sympy.polys.polyroots import roots +from sympy.utilities.misc import filldedent + + +############################################################################### +################################ DELTA FUNCTION ############################### +############################################################################### + + +class DiracDelta(Function): + r""" + The DiracDelta function and its derivatives. + + Explanation + =========== + + DiracDelta is not an ordinary function. It can be rigorously defined either + as a distribution or as a measure. + + DiracDelta only makes sense in definite integrals, and in particular, + integrals of the form ``Integral(f(x)*DiracDelta(x - x0), (x, a, b))``, + where it equals ``f(x0)`` if ``a <= x0 <= b`` and ``0`` otherwise. Formally, + DiracDelta acts in some ways like a function that is ``0`` everywhere except + at ``0``, but in many ways it also does not. It can often be useful to treat + DiracDelta in formal ways, building up and manipulating expressions with + delta functions (which may eventually be integrated), but care must be taken + to not treat it as a real function. SymPy's ``oo`` is similar. It only + truly makes sense formally in certain contexts (such as integration limits), + but SymPy allows its use everywhere, and it tries to be consistent with + operations on it (like ``1/oo``), but it is easy to get into trouble and get + wrong results if ``oo`` is treated too much like a number. Similarly, if + DiracDelta is treated too much like a function, it is easy to get wrong or + nonsensical results. + + DiracDelta function has the following properties: + + 1) $\frac{d}{d x} \theta(x) = \delta(x)$ + 2) $\int_{-\infty}^\infty \delta(x - a)f(x)\, dx = f(a)$ and $\int_{a- + \epsilon}^{a+\epsilon} \delta(x - a)f(x)\, dx = f(a)$ + 3) $\delta(x) = 0$ for all $x \neq 0$ + 4) $\delta(g(x)) = \sum_i \frac{\delta(x - x_i)}{\|g'(x_i)\|}$ where $x_i$ + are the roots of $g$ + 5) $\delta(-x) = \delta(x)$ + + Derivatives of ``k``-th order of DiracDelta have the following properties: + + 6) $\delta(x, k) = 0$ for all $x \neq 0$ + 7) $\delta(-x, k) = -\delta(x, k)$ for odd $k$ + 8) $\delta(-x, k) = \delta(x, k)$ for even $k$ + + Examples + ======== + + >>> from sympy import DiracDelta, diff, pi + >>> from sympy.abc import x, y + + >>> DiracDelta(x) + DiracDelta(x) + >>> DiracDelta(1) + 0 + >>> DiracDelta(-1) + 0 + >>> DiracDelta(pi) + 0 + >>> DiracDelta(x - 4).subs(x, 4) + DiracDelta(0) + >>> diff(DiracDelta(x)) + DiracDelta(x, 1) + >>> diff(DiracDelta(x - 1), x, 2) + DiracDelta(x - 1, 2) + >>> diff(DiracDelta(x**2 - 1), x, 2) + 2*(2*x**2*DiracDelta(x**2 - 1, 2) + DiracDelta(x**2 - 1, 1)) + >>> DiracDelta(3*x).is_simple(x) + True + >>> DiracDelta(x**2).is_simple(x) + False + >>> DiracDelta((x**2 - 1)*y).expand(diracdelta=True, wrt=x) + DiracDelta(x - 1)/(2*Abs(y)) + DiracDelta(x + 1)/(2*Abs(y)) + + See Also + ======== + + Heaviside + sympy.simplify.simplify.simplify, is_simple + sympy.functions.special.tensor_functions.KroneckerDelta + + References + ========== + + .. [1] https://mathworld.wolfram.com/DeltaFunction.html + + """ + + is_real = True + + def fdiff(self, argindex=1): + """ + Returns the first derivative of a DiracDelta Function. + + Explanation + =========== + + The difference between ``diff()`` and ``fdiff()`` is: ``diff()`` is the + user-level function and ``fdiff()`` is an object method. ``fdiff()`` is + a convenience method available in the ``Function`` class. It returns + the derivative of the function without considering the chain rule. + ``diff(function, x)`` calls ``Function._eval_derivative`` which in turn + calls ``fdiff()`` internally to compute the derivative of the function. + + Examples + ======== + + >>> from sympy import DiracDelta, diff + >>> from sympy.abc import x + + >>> DiracDelta(x).fdiff() + DiracDelta(x, 1) + + >>> DiracDelta(x, 1).fdiff() + DiracDelta(x, 2) + + >>> DiracDelta(x**2 - 1).fdiff() + DiracDelta(x**2 - 1, 1) + + >>> diff(DiracDelta(x, 1)).fdiff() + DiracDelta(x, 3) + + Parameters + ========== + + argindex : integer + degree of derivative + + """ + if argindex == 1: + #I didn't know if there is a better way to handle default arguments + k = 0 + if len(self.args) > 1: + k = self.args[1] + return self.func(self.args[0], k + 1) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg, k=S.Zero): + """ + Returns a simplified form or a value of DiracDelta depending on the + argument passed by the DiracDelta object. + + Explanation + =========== + + The ``eval()`` method is automatically called when the ``DiracDelta`` + class is about to be instantiated and it returns either some simplified + instance or the unevaluated instance depending on the argument passed. + In other words, ``eval()`` method is not needed to be called explicitly, + it is being called and evaluated once the object is called. + + Examples + ======== + + >>> from sympy import DiracDelta, S + >>> from sympy.abc import x + + >>> DiracDelta(x) + DiracDelta(x) + + >>> DiracDelta(-x, 1) + -DiracDelta(x, 1) + + >>> DiracDelta(1) + 0 + + >>> DiracDelta(5, 1) + 0 + + >>> DiracDelta(0) + DiracDelta(0) + + >>> DiracDelta(-1) + 0 + + >>> DiracDelta(S.NaN) + nan + + >>> DiracDelta(x - 100).subs(x, 5) + 0 + + >>> DiracDelta(x - 100).subs(x, 100) + DiracDelta(0) + + Parameters + ========== + + k : integer + order of derivative + + arg : argument passed to DiracDelta + + """ + if not k.is_Integer or k.is_negative: + raise ValueError("Error: the second argument of DiracDelta must be \ + a non-negative integer, %s given instead." % (k,)) + if arg is S.NaN: + return S.NaN + if arg.is_nonzero: + return S.Zero + if fuzzy_not(im(arg).is_zero): + raise ValueError(filldedent(''' + Function defined only for Real Values. + Complex part: %s found in %s .''' % ( + repr(im(arg)), repr(arg)))) + c, nc = arg.args_cnc() + if c and c[0] is S.NegativeOne: + # keep this fast and simple instead of using + # could_extract_minus_sign + if k.is_odd: + return -cls(-arg, k) + elif k.is_even: + return cls(-arg, k) if k else cls(-arg) + elif k.is_zero: + return cls(arg, evaluate=False) + + def _eval_expand_diracdelta(self, **hints): + """ + Compute a simplified representation of the function using + property number 4. Pass ``wrt`` as a hint to expand the expression + with respect to a particular variable. + + Explanation + =========== + + ``wrt`` is: + + - a variable with respect to which a DiracDelta expression will + get expanded. + + Examples + ======== + + >>> from sympy import DiracDelta + >>> from sympy.abc import x, y + + >>> DiracDelta(x*y).expand(diracdelta=True, wrt=x) + DiracDelta(x)/Abs(y) + >>> DiracDelta(x*y).expand(diracdelta=True, wrt=y) + DiracDelta(y)/Abs(x) + + >>> DiracDelta(x**2 + x - 2).expand(diracdelta=True, wrt=x) + DiracDelta(x - 1)/3 + DiracDelta(x + 2)/3 + + See Also + ======== + + is_simple, Diracdelta + + """ + wrt = hints.get('wrt', None) + if wrt is None: + free = self.free_symbols + if len(free) == 1: + wrt = free.pop() + else: + raise TypeError(filldedent(''' + When there is more than 1 free symbol or variable in the expression, + the 'wrt' keyword is required as a hint to expand when using the + DiracDelta hint.''')) + + if not self.args[0].has(wrt) or (len(self.args) > 1 and self.args[1] != 0 ): + return self + try: + argroots = roots(self.args[0], wrt) + result = 0 + valid = True + darg = abs(diff(self.args[0], wrt)) + for r, m in argroots.items(): + if r.is_real is not False and m == 1: + result += self.func(wrt - r)/darg.subs(wrt, r) + else: + # don't handle non-real and if m != 1 then + # a polynomial will have a zero in the derivative (darg) + # at r + valid = False + break + if valid: + return result + except PolynomialError: + pass + return self + + def is_simple(self, x): + """ + Tells whether the argument(args[0]) of DiracDelta is a linear + expression in *x*. + + Examples + ======== + + >>> from sympy import DiracDelta, cos + >>> from sympy.abc import x, y + + >>> DiracDelta(x*y).is_simple(x) + True + >>> DiracDelta(x*y).is_simple(y) + True + + >>> DiracDelta(x**2 + x - 2).is_simple(x) + False + + >>> DiracDelta(cos(x)).is_simple(x) + False + + Parameters + ========== + + x : can be a symbol + + See Also + ======== + + sympy.simplify.simplify.simplify, DiracDelta + + """ + p = self.args[0].as_poly(x) + if p: + return p.degree() == 1 + return False + + def _eval_rewrite_as_Piecewise(self, *args, **kwargs): + """ + Represents DiracDelta in a piecewise form. + + Examples + ======== + + >>> from sympy import DiracDelta, Piecewise, Symbol + >>> x = Symbol('x') + + >>> DiracDelta(x).rewrite(Piecewise) + Piecewise((DiracDelta(0), Eq(x, 0)), (0, True)) + + >>> DiracDelta(x - 5).rewrite(Piecewise) + Piecewise((DiracDelta(0), Eq(x, 5)), (0, True)) + + >>> DiracDelta(x**2 - 5).rewrite(Piecewise) + Piecewise((DiracDelta(0), Eq(x**2, 5)), (0, True)) + + >>> DiracDelta(x - 5, 4).rewrite(Piecewise) + DiracDelta(x - 5, 4) + + """ + if len(args) == 1: + return Piecewise((DiracDelta(0), Eq(args[0], 0)), (0, True)) + + def _eval_rewrite_as_SingularityFunction(self, *args, **kwargs): + """ + Returns the DiracDelta expression written in the form of Singularity + Functions. + + """ + from sympy.solvers import solve + from sympy.functions.special.singularity_functions import SingularityFunction + if self == DiracDelta(0): + return SingularityFunction(0, 0, -1) + if self == DiracDelta(0, 1): + return SingularityFunction(0, 0, -2) + free = self.free_symbols + if len(free) == 1: + x = (free.pop()) + if len(args) == 1: + return SingularityFunction(x, solve(args[0], x)[0], -1) + return SingularityFunction(x, solve(args[0], x)[0], -args[1] - 1) + else: + # I don't know how to handle the case for DiracDelta expressions + # having arguments with more than one variable. + raise TypeError(filldedent(''' + rewrite(SingularityFunction) does not support + arguments with more that one variable.''')) + + +############################################################################### +############################## HEAVISIDE FUNCTION ############################# +############################################################################### + + +class Heaviside(Function): + r""" + Heaviside step function. + + Explanation + =========== + + The Heaviside step function has the following properties: + + 1) $\frac{d}{d x} \theta(x) = \delta(x)$ + 2) $\theta(x) = \begin{cases} 0 & \text{for}\: x < 0 \\ \frac{1}{2} & + \text{for}\: x = 0 \\1 & \text{for}\: x > 0 \end{cases}$ + 3) $\frac{d}{d x} \max(x, 0) = \theta(x)$ + + Heaviside(x) is printed as $\theta(x)$ with the SymPy LaTeX printer. + + The value at 0 is set differently in different fields. SymPy uses 1/2, + which is a convention from electronics and signal processing, and is + consistent with solving improper integrals by Fourier transform and + convolution. + + To specify a different value of Heaviside at ``x=0``, a second argument + can be given. Using ``Heaviside(x, nan)`` gives an expression that will + evaluate to nan for x=0. + + .. versionchanged:: 1.9 ``Heaviside(0)`` now returns 1/2 (before: undefined) + + Examples + ======== + + >>> from sympy import Heaviside, nan + >>> from sympy.abc import x + >>> Heaviside(9) + 1 + >>> Heaviside(-9) + 0 + >>> Heaviside(0) + 1/2 + >>> Heaviside(0, nan) + nan + >>> (Heaviside(x) + 1).replace(Heaviside(x), Heaviside(x, 1)) + Heaviside(x, 1) + 1 + + See Also + ======== + + DiracDelta + + References + ========== + + .. [1] https://mathworld.wolfram.com/HeavisideStepFunction.html + .. [2] https://dlmf.nist.gov/1.16#iv + + """ + + is_real = True + + def fdiff(self, argindex=1): + """ + Returns the first derivative of a Heaviside Function. + + Examples + ======== + + >>> from sympy import Heaviside, diff + >>> from sympy.abc import x + + >>> Heaviside(x).fdiff() + DiracDelta(x) + + >>> Heaviside(x**2 - 1).fdiff() + DiracDelta(x**2 - 1) + + >>> diff(Heaviside(x)).fdiff() + DiracDelta(x, 1) + + Parameters + ========== + + argindex : integer + order of derivative + + """ + if argindex == 1: + return DiracDelta(self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + def __new__(cls, arg, H0=S.Half, **options): + if isinstance(H0, Heaviside) and len(H0.args) == 1: + H0 = S.Half + return super(cls, cls).__new__(cls, arg, H0, **options) + + @property + def pargs(self): + """Args without default S.Half""" + args = self.args + if args[1] is S.Half: + args = args[:1] + return args + + @classmethod + def eval(cls, arg, H0=S.Half): + """ + Returns a simplified form or a value of Heaviside depending on the + argument passed by the Heaviside object. + + Explanation + =========== + + The ``eval()`` method is automatically called when the ``Heaviside`` + class is about to be instantiated and it returns either some simplified + instance or the unevaluated instance depending on the argument passed. + In other words, ``eval()`` method is not needed to be called explicitly, + it is being called and evaluated once the object is called. + + Examples + ======== + + >>> from sympy import Heaviside, S + >>> from sympy.abc import x + + >>> Heaviside(x) + Heaviside(x) + + >>> Heaviside(19) + 1 + + >>> Heaviside(0) + 1/2 + + >>> Heaviside(0, 1) + 1 + + >>> Heaviside(-5) + 0 + + >>> Heaviside(S.NaN) + nan + + >>> Heaviside(x - 100).subs(x, 5) + 0 + + >>> Heaviside(x - 100).subs(x, 105) + 1 + + Parameters + ========== + + arg : argument passed by Heaviside object + + H0 : value of Heaviside(0) + + """ + if arg.is_extended_negative: + return S.Zero + elif arg.is_extended_positive: + return S.One + elif arg.is_zero: + return H0 + elif arg is S.NaN: + return S.NaN + elif fuzzy_not(im(arg).is_zero): + raise ValueError("Function defined only for Real Values. Complex part: %s found in %s ." % (repr(im(arg)), repr(arg)) ) + + def _eval_rewrite_as_Piecewise(self, arg, H0=None, **kwargs): + """ + Represents Heaviside in a Piecewise form. + + Examples + ======== + + >>> from sympy import Heaviside, Piecewise, Symbol, nan + >>> x = Symbol('x') + + >>> Heaviside(x).rewrite(Piecewise) + Piecewise((0, x < 0), (1/2, Eq(x, 0)), (1, True)) + + >>> Heaviside(x,nan).rewrite(Piecewise) + Piecewise((0, x < 0), (nan, Eq(x, 0)), (1, True)) + + >>> Heaviside(x - 5).rewrite(Piecewise) + Piecewise((0, x < 5), (1/2, Eq(x, 5)), (1, True)) + + >>> Heaviside(x**2 - 1).rewrite(Piecewise) + Piecewise((0, x**2 < 1), (1/2, Eq(x**2, 1)), (1, True)) + + """ + if H0 == 0: + return Piecewise((0, arg <= 0), (1, True)) + if H0 == 1: + return Piecewise((0, arg < 0), (1, True)) + return Piecewise((0, arg < 0), (H0, Eq(arg, 0)), (1, True)) + + def _eval_rewrite_as_sign(self, arg, H0=S.Half, **kwargs): + """ + Represents the Heaviside function in the form of sign function. + + Explanation + =========== + + The value of Heaviside(0) must be 1/2 for rewriting as sign to be + strictly equivalent. For easier usage, we also allow this rewriting + when Heaviside(0) is undefined. + + Examples + ======== + + >>> from sympy import Heaviside, Symbol, sign, nan + >>> x = Symbol('x', real=True) + >>> y = Symbol('y') + + >>> Heaviside(x).rewrite(sign) + sign(x)/2 + 1/2 + + >>> Heaviside(x, 0).rewrite(sign) + Piecewise((sign(x)/2 + 1/2, Ne(x, 0)), (0, True)) + + >>> Heaviside(x, nan).rewrite(sign) + Piecewise((sign(x)/2 + 1/2, Ne(x, 0)), (nan, True)) + + >>> Heaviside(x - 2).rewrite(sign) + sign(x - 2)/2 + 1/2 + + >>> Heaviside(x**2 - 2*x + 1).rewrite(sign) + sign(x**2 - 2*x + 1)/2 + 1/2 + + >>> Heaviside(y).rewrite(sign) + Heaviside(y) + + >>> Heaviside(y**2 - 2*y + 1).rewrite(sign) + Heaviside(y**2 - 2*y + 1) + + See Also + ======== + + sign + + """ + if arg.is_extended_real: + pw1 = Piecewise( + ((sign(arg) + 1)/2, Ne(arg, 0)), + (Heaviside(0, H0=H0), True)) + pw2 = Piecewise( + ((sign(arg) + 1)/2, Eq(Heaviside(0, H0=H0), S.Half)), + (pw1, True)) + return pw2 + + def _eval_rewrite_as_SingularityFunction(self, args, H0=S.Half, **kwargs): + """ + Returns the Heaviside expression written in the form of Singularity + Functions. + + """ + from sympy.solvers import solve + from sympy.functions.special.singularity_functions import SingularityFunction + if self == Heaviside(0): + return SingularityFunction(0, 0, 0) + free = self.free_symbols + if len(free) == 1: + x = (free.pop()) + return SingularityFunction(x, solve(args, x)[0], 0) + # TODO + # ((x - 5)**3*Heaviside(x - 5)).rewrite(SingularityFunction) should output + # SingularityFunction(x, 5, 0) instead of (x - 5)**3*SingularityFunction(x, 5, 0) + else: + # I don't know how to handle the case for Heaviside expressions + # having arguments with more than one variable. + raise TypeError(filldedent(''' + rewrite(SingularityFunction) does not + support arguments with more that one variable.''')) diff --git a/lib/python3.11/site-packages/sympy/functions/special/elliptic_integrals.py b/lib/python3.11/site-packages/sympy/functions/special/elliptic_integrals.py new file mode 100644 index 0000000000000000000000000000000000000000..78fbba95b1f47d2e8fdedc62fbc5c2c011ff5e08 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/elliptic_integrals.py @@ -0,0 +1,445 @@ +""" Elliptic Integrals. """ + +from sympy.core import S, pi, I, Rational +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.symbol import Dummy,uniquely_named_symbol +from sympy.functions.elementary.complexes import sign +from sympy.functions.elementary.hyperbolic import atanh +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin, tan +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import hyper, meijerg + +class elliptic_k(Function): + r""" + The complete elliptic integral of the first kind, defined by + + .. math:: K(m) = F\left(\tfrac{\pi}{2}\middle| m\right) + + where $F\left(z\middle| m\right)$ is the Legendre incomplete + elliptic integral of the first kind. + + Explanation + =========== + + The function $K(m)$ is a single-valued function on the complex + plane with branch cut along the interval $(1, \infty)$. + + Note that our notation defines the incomplete elliptic integral + in terms of the parameter $m$ instead of the elliptic modulus + (eccentricity) $k$. + In this case, the parameter $m$ is defined as $m=k^2$. + + Examples + ======== + + >>> from sympy import elliptic_k, I + >>> from sympy.abc import m + >>> elliptic_k(0) + pi/2 + >>> elliptic_k(1.0 + I) + 1.50923695405127 + 0.625146415202697*I + >>> elliptic_k(m).series(n=3) + pi/2 + pi*m/8 + 9*pi*m**2/128 + O(m**3) + + See Also + ======== + + elliptic_f + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals + .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticK + + """ + + @classmethod + def eval(cls, m): + if m.is_zero: + return pi*S.Half + elif m is S.Half: + return 8*pi**Rational(3, 2)/gamma(Rational(-1, 4))**2 + elif m is S.One: + return S.ComplexInfinity + elif m is S.NegativeOne: + return gamma(Rational(1, 4))**2/(4*sqrt(2*pi)) + elif m in (S.Infinity, S.NegativeInfinity, I*S.Infinity, + I*S.NegativeInfinity, S.ComplexInfinity): + return S.Zero + + def fdiff(self, argindex=1): + m = self.args[0] + return (elliptic_e(m) - (1 - m)*elliptic_k(m))/(2*m*(1 - m)) + + def _eval_conjugate(self): + m = self.args[0] + if (m.is_real and (m - 1).is_positive) is False: + return self.func(m.conjugate()) + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.simplify import hyperexpand + return hyperexpand(self.rewrite(hyper)._eval_nseries(x, n=n, logx=logx)) + + def _eval_rewrite_as_hyper(self, m, **kwargs): + return pi*S.Half*hyper((S.Half, S.Half), (S.One,), m) + + def _eval_rewrite_as_meijerg(self, m, **kwargs): + return meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -m)/2 + + def _eval_is_zero(self): + m = self.args[0] + if m.is_infinite: + return True + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', args).name) + m = self.args[0] + return Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, pi/2)) + + +class elliptic_f(Function): + r""" + The Legendre incomplete elliptic integral of the first + kind, defined by + + .. math:: F\left(z\middle| m\right) = + \int_0^z \frac{dt}{\sqrt{1 - m \sin^2 t}} + + Explanation + =========== + + This function reduces to a complete elliptic integral of + the first kind, $K(m)$, when $z = \pi/2$. + + Note that our notation defines the incomplete elliptic integral + in terms of the parameter $m$ instead of the elliptic modulus + (eccentricity) $k$. + In this case, the parameter $m$ is defined as $m=k^2$. + + Examples + ======== + + >>> from sympy import elliptic_f, I + >>> from sympy.abc import z, m + >>> elliptic_f(z, m).series(z) + z + z**5*(3*m**2/40 - m/30) + m*z**3/6 + O(z**6) + >>> elliptic_f(3.0 + I/2, 1.0 + I) + 2.909449841483 + 1.74720545502474*I + + See Also + ======== + + elliptic_k + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals + .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticF + + """ + + @classmethod + def eval(cls, z, m): + if z.is_zero: + return S.Zero + if m.is_zero: + return z + k = 2*z/pi + if k.is_integer: + return k*elliptic_k(m) + elif m in (S.Infinity, S.NegativeInfinity): + return S.Zero + elif z.could_extract_minus_sign(): + return -elliptic_f(-z, m) + + def fdiff(self, argindex=1): + z, m = self.args + fm = sqrt(1 - m*sin(z)**2) + if argindex == 1: + return 1/fm + elif argindex == 2: + return (elliptic_e(z, m)/(2*m*(1 - m)) - elliptic_f(z, m)/(2*m) - + sin(2*z)/(4*(1 - m)*fm)) + raise ArgumentIndexError(self, argindex) + + def _eval_conjugate(self): + z, m = self.args + if (m.is_real and (m - 1).is_positive) is False: + return self.func(z.conjugate(), m.conjugate()) + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', args).name) + z, m = self.args[0], self.args[1] + return Integral(1/(sqrt(1 - m*sin(t)**2)), (t, 0, z)) + + def _eval_is_zero(self): + z, m = self.args + if z.is_zero: + return True + if m.is_extended_real and m.is_infinite: + return True + + +class elliptic_e(Function): + r""" + Called with two arguments $z$ and $m$, evaluates the + incomplete elliptic integral of the second kind, defined by + + .. math:: E\left(z\middle| m\right) = \int_0^z \sqrt{1 - m \sin^2 t} dt + + Called with a single argument $m$, evaluates the Legendre complete + elliptic integral of the second kind + + .. math:: E(m) = E\left(\tfrac{\pi}{2}\middle| m\right) + + Explanation + =========== + + The function $E(m)$ is a single-valued function on the complex + plane with branch cut along the interval $(1, \infty)$. + + Note that our notation defines the incomplete elliptic integral + in terms of the parameter $m$ instead of the elliptic modulus + (eccentricity) $k$. + In this case, the parameter $m$ is defined as $m=k^2$. + + Examples + ======== + + >>> from sympy import elliptic_e, I + >>> from sympy.abc import z, m + >>> elliptic_e(z, m).series(z) + z + z**5*(-m**2/40 + m/30) - m*z**3/6 + O(z**6) + >>> elliptic_e(m).series(n=4) + pi/2 - pi*m/8 - 3*pi*m**2/128 - 5*pi*m**3/512 + O(m**4) + >>> elliptic_e(1 + I, 2 - I/2).n() + 1.55203744279187 + 0.290764986058437*I + >>> elliptic_e(0) + pi/2 + >>> elliptic_e(2.0 - I) + 0.991052601328069 + 0.81879421395609*I + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals + .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticE2 + .. [3] https://functions.wolfram.com/EllipticIntegrals/EllipticE + + """ + + @classmethod + def eval(cls, m, z=None): + if z is not None: + z, m = m, z + k = 2*z/pi + if m.is_zero: + return z + if z.is_zero: + return S.Zero + elif k.is_integer: + return k*elliptic_e(m) + elif m in (S.Infinity, S.NegativeInfinity): + return S.ComplexInfinity + elif z.could_extract_minus_sign(): + return -elliptic_e(-z, m) + else: + if m.is_zero: + return pi/2 + elif m is S.One: + return S.One + elif m is S.Infinity: + return I*S.Infinity + elif m is S.NegativeInfinity: + return S.Infinity + elif m is S.ComplexInfinity: + return S.ComplexInfinity + + def fdiff(self, argindex=1): + if len(self.args) == 2: + z, m = self.args + if argindex == 1: + return sqrt(1 - m*sin(z)**2) + elif argindex == 2: + return (elliptic_e(z, m) - elliptic_f(z, m))/(2*m) + else: + m = self.args[0] + if argindex == 1: + return (elliptic_e(m) - elliptic_k(m))/(2*m) + raise ArgumentIndexError(self, argindex) + + def _eval_conjugate(self): + if len(self.args) == 2: + z, m = self.args + if (m.is_real and (m - 1).is_positive) is False: + return self.func(z.conjugate(), m.conjugate()) + else: + m = self.args[0] + if (m.is_real and (m - 1).is_positive) is False: + return self.func(m.conjugate()) + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.simplify import hyperexpand + if len(self.args) == 1: + return hyperexpand(self.rewrite(hyper)._eval_nseries(x, n=n, logx=logx)) + return super()._eval_nseries(x, n=n, logx=logx) + + def _eval_rewrite_as_hyper(self, *args, **kwargs): + if len(args) == 1: + m = args[0] + return (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), m) + + def _eval_rewrite_as_meijerg(self, *args, **kwargs): + if len(args) == 1: + m = args[0] + return -meijerg(((S.Half, Rational(3, 2)), []), \ + ((S.Zero,), (S.Zero,)), -m)/4 + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + from sympy.integrals.integrals import Integral + z, m = (pi/2, self.args[0]) if len(self.args) == 1 else self.args + t = Dummy(uniquely_named_symbol('t', args).name) + return Integral(sqrt(1 - m*sin(t)**2), (t, 0, z)) + + +class elliptic_pi(Function): + r""" + Called with three arguments $n$, $z$ and $m$, evaluates the + Legendre incomplete elliptic integral of the third kind, defined by + + .. math:: \Pi\left(n; z\middle| m\right) = \int_0^z \frac{dt} + {\left(1 - n \sin^2 t\right) \sqrt{1 - m \sin^2 t}} + + Called with two arguments $n$ and $m$, evaluates the complete + elliptic integral of the third kind: + + .. math:: \Pi\left(n\middle| m\right) = + \Pi\left(n; \tfrac{\pi}{2}\middle| m\right) + + Explanation + =========== + + Note that our notation defines the incomplete elliptic integral + in terms of the parameter $m$ instead of the elliptic modulus + (eccentricity) $k$. + In this case, the parameter $m$ is defined as $m=k^2$. + + Examples + ======== + + >>> from sympy import elliptic_pi, I + >>> from sympy.abc import z, n, m + >>> elliptic_pi(n, z, m).series(z, n=4) + z + z**3*(m/6 + n/3) + O(z**4) + >>> elliptic_pi(0.5 + I, 1.0 - I, 1.2) + 2.50232379629182 - 0.760939574180767*I + >>> elliptic_pi(0, 0) + pi/2 + >>> elliptic_pi(1.0 - I/3, 2.0 + I) + 3.29136443417283 + 0.32555634906645*I + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Elliptic_integrals + .. [2] https://functions.wolfram.com/EllipticIntegrals/EllipticPi3 + .. [3] https://functions.wolfram.com/EllipticIntegrals/EllipticPi + + """ + + @classmethod + def eval(cls, n, m, z=None): + if z is not None: + n, z, m = n, m, z + if n.is_zero: + return elliptic_f(z, m) + elif n is S.One: + return (elliptic_f(z, m) + + (sqrt(1 - m*sin(z)**2)*tan(z) - + elliptic_e(z, m))/(1 - m)) + k = 2*z/pi + if k.is_integer: + return k*elliptic_pi(n, m) + elif m.is_zero: + return atanh(sqrt(n - 1)*tan(z))/sqrt(n - 1) + elif n == m: + return (elliptic_f(z, n) - elliptic_pi(1, z, n) + + tan(z)/sqrt(1 - n*sin(z)**2)) + elif n in (S.Infinity, S.NegativeInfinity): + return S.Zero + elif m in (S.Infinity, S.NegativeInfinity): + return S.Zero + elif z.could_extract_minus_sign(): + return -elliptic_pi(n, -z, m) + if n.is_zero: + return elliptic_f(z, m) + if m.is_extended_real and m.is_infinite or \ + n.is_extended_real and n.is_infinite: + return S.Zero + else: + if n.is_zero: + return elliptic_k(m) + elif n is S.One: + return S.ComplexInfinity + elif m.is_zero: + return pi/(2*sqrt(1 - n)) + elif m == S.One: + return S.NegativeInfinity/sign(n - 1) + elif n == m: + return elliptic_e(n)/(1 - n) + elif n in (S.Infinity, S.NegativeInfinity): + return S.Zero + elif m in (S.Infinity, S.NegativeInfinity): + return S.Zero + if n.is_zero: + return elliptic_k(m) + if m.is_extended_real and m.is_infinite or \ + n.is_extended_real and n.is_infinite: + return S.Zero + + def _eval_conjugate(self): + if len(self.args) == 3: + n, z, m = self.args + if (n.is_real and (n - 1).is_positive) is False and \ + (m.is_real and (m - 1).is_positive) is False: + return self.func(n.conjugate(), z.conjugate(), m.conjugate()) + else: + n, m = self.args + return self.func(n.conjugate(), m.conjugate()) + + def fdiff(self, argindex=1): + if len(self.args) == 3: + n, z, m = self.args + fm, fn = sqrt(1 - m*sin(z)**2), 1 - n*sin(z)**2 + if argindex == 1: + return (elliptic_e(z, m) + (m - n)*elliptic_f(z, m)/n + + (n**2 - m)*elliptic_pi(n, z, m)/n - + n*fm*sin(2*z)/(2*fn))/(2*(m - n)*(n - 1)) + elif argindex == 2: + return 1/(fm*fn) + elif argindex == 3: + return (elliptic_e(z, m)/(m - 1) + + elliptic_pi(n, z, m) - + m*sin(2*z)/(2*(m - 1)*fm))/(2*(n - m)) + else: + n, m = self.args + if argindex == 1: + return (elliptic_e(m) + (m - n)*elliptic_k(m)/n + + (n**2 - m)*elliptic_pi(n, m)/n)/(2*(m - n)*(n - 1)) + elif argindex == 2: + return (elliptic_e(m)/(m - 1) + elliptic_pi(n, m))/(2*(n - m)) + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + from sympy.integrals.integrals import Integral + if len(self.args) == 2: + n, m, z = self.args[0], self.args[1], pi/2 + else: + n, z, m = self.args + t = Dummy(uniquely_named_symbol('t', args).name) + return Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, z)) diff --git a/lib/python3.11/site-packages/sympy/functions/special/error_functions.py b/lib/python3.11/site-packages/sympy/functions/special/error_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..09279588b6589552e7cc2186a7b384e7dd410975 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/error_functions.py @@ -0,0 +1,2782 @@ +""" This module contains various functions that are special cases + of incomplete gamma functions. It should probably be renamed. """ + +from sympy.core import EulerGamma # Must be imported from core, not core.numbers +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.function import Function, ArgumentIndexError, expand_mul +from sympy.core.numbers import I, pi, Rational +from sympy.core.relational import is_eq +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.core.symbol import Dummy, uniquely_named_symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial, factorial2, RisingFactorial +from sympy.functions.elementary.complexes import polar_lift, re, unpolarify +from sympy.functions.elementary.integers import ceiling, floor +from sympy.functions.elementary.miscellaneous import sqrt, root +from sympy.functions.elementary.exponential import exp, log, exp_polar +from sympy.functions.elementary.hyperbolic import cosh, sinh +from sympy.functions.elementary.trigonometric import cos, sin, sinc +from sympy.functions.special.hyper import hyper, meijerg + +# TODO series expansions +# TODO see the "Note:" in Ei + +# Helper function +def real_to_real_as_real_imag(self, deep=True, **hints): + if self.args[0].is_extended_real: + if deep: + hints['complex'] = False + return (self.expand(deep, **hints), S.Zero) + else: + return (self, S.Zero) + if deep: + x, y = self.args[0].expand(deep, **hints).as_real_imag() + else: + x, y = self.args[0].as_real_imag() + re = (self.func(x + I*y) + self.func(x - I*y))/2 + im = (self.func(x + I*y) - self.func(x - I*y))/(2*I) + return (re, im) + + +############################################################################### +################################ ERROR FUNCTION ############################### +############################################################################### + + +class erf(Function): + r""" + The Gauss error function. + + Explanation + =========== + + This function is defined as: + + .. math :: + \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \mathrm{d}t. + + Examples + ======== + + >>> from sympy import I, oo, erf + >>> from sympy.abc import z + + Several special values are known: + + >>> erf(0) + 0 + >>> erf(oo) + 1 + >>> erf(-oo) + -1 + >>> erf(I*oo) + oo*I + >>> erf(-I*oo) + -oo*I + + In general one can pull out factors of -1 and $I$ from the argument: + + >>> erf(-z) + -erf(z) + + The error function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(erf(z)) + erf(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(erf(z), z) + 2*exp(-z**2)/sqrt(pi) + + We can numerically evaluate the error function to arbitrary precision + on the whole complex plane: + + >>> erf(4).evalf(30) + 0.999999984582742099719981147840 + + >>> erf(-4*I).evalf(30) + -1296959.73071763923152794095062*I + + See Also + ======== + + erfc: Complementary error function. + erfi: Imaginary error function. + erf2: Two-argument error function. + erfinv: Inverse error function. + erfcinv: Inverse Complementary error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Error_function + .. [2] https://dlmf.nist.gov/7 + .. [3] https://mathworld.wolfram.com/Erf.html + .. [4] https://functions.wolfram.com/GammaBetaErf/Erf + + """ + + unbranched = True + + def fdiff(self, argindex=1): + if argindex == 1: + return 2*exp(-self.args[0]**2)/sqrt(pi) + else: + raise ArgumentIndexError(self, argindex) + + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + + """ + return erfinv + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.One + elif arg is S.NegativeInfinity: + return S.NegativeOne + elif arg.is_zero: + return S.Zero + + if isinstance(arg, erfinv): + return arg.args[0] + + if isinstance(arg, erfcinv): + return S.One - arg.args[0] + + if arg.is_zero: + return S.Zero + + # Only happens with unevaluated erf2inv + if isinstance(arg, erf2inv) and arg.args[0].is_zero: + return arg.args[1] + + # Try to pull out factors of I + t = arg.extract_multiplicatively(I) + if t in (S.Infinity, S.NegativeInfinity): + return arg + + # Try to pull out factors of -1 + if arg.could_extract_minus_sign(): + return -cls(-arg) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + k = floor((n - 1)/S(2)) + if len(previous_terms) > 2: + return -previous_terms[-2] * x**2 * (n - 2)/(n*k) + else: + return 2*S.NegativeOne**k * x**n/(n*factorial(k)*sqrt(pi)) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_is_real(self): + return self.args[0].is_extended_real + + def _eval_is_finite(self): + if self.args[0].is_finite: + return True + else: + return self.args[0].is_extended_real + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return sqrt(z**2)/z*(S.One - uppergamma(S.Half, z**2)/sqrt(pi)) + + def _eval_rewrite_as_fresnels(self, z, **kwargs): + arg = (S.One - I)*z/sqrt(pi) + return (S.One + I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_fresnelc(self, z, **kwargs): + arg = (S.One - I)*z/sqrt(pi) + return (S.One + I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], -z**2) + + def _eval_rewrite_as_expint(self, z, **kwargs): + return sqrt(z**2)/z - z*expint(S.Half, z**2)/sqrt(pi) + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + from sympy.series.limits import limit + if limitvar: + lim = limit(z, limitvar, S.Infinity) + if lim is S.NegativeInfinity: + return S.NegativeOne + _erfs(-z)*exp(-z**2) + return S.One - _erfs(z)*exp(-z**2) + + def _eval_rewrite_as_erfc(self, z, **kwargs): + return S.One - erfc(z) + + def _eval_rewrite_as_erfi(self, z, **kwargs): + return -I*erfi(I*z) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.ComplexInfinity: + arg0 = arg.limit(x, 0, dir='-' if cdir == -1 else '+') + if x in arg.free_symbols and arg0.is_zero: + return 2*arg/sqrt(pi) + else: + return self.func(arg0) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + if point in [S.Infinity, S.NegativeInfinity]: + z = self.args[0] + + try: + _, ex = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + ex = -ex # as x->1/x for aseries + if ex.is_positive: + newn = ceiling(n/ex) + s = [S.NegativeOne**k * factorial2(2*k - 1) / (z**(2*k + 1) * 2**k) + for k in range(newn)] + [Order(1/z**newn, x)] + return S.One - (exp(-z**2)/sqrt(pi)) * Add(*s) + + return super(erf, self)._eval_aseries(n, args0, x, logx) + + as_real_imag = real_to_real_as_real_imag + + +class erfc(Function): + r""" + Complementary Error Function. + + Explanation + =========== + + The function is defined as: + + .. math :: + \mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} \mathrm{d}t + + Examples + ======== + + >>> from sympy import I, oo, erfc + >>> from sympy.abc import z + + Several special values are known: + + >>> erfc(0) + 1 + >>> erfc(oo) + 0 + >>> erfc(-oo) + 2 + >>> erfc(I*oo) + -oo*I + >>> erfc(-I*oo) + oo*I + + The error function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(erfc(z)) + erfc(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(erfc(z), z) + -2*exp(-z**2)/sqrt(pi) + + It also follows + + >>> erfc(-z) + 2 - erfc(z) + + We can numerically evaluate the complementary error function to arbitrary + precision on the whole complex plane: + + >>> erfc(4).evalf(30) + 0.0000000154172579002800188521596734869 + + >>> erfc(4*I).evalf(30) + 1.0 - 1296959.73071763923152794095062*I + + See Also + ======== + + erf: Gaussian error function. + erfi: Imaginary error function. + erf2: Two-argument error function. + erfinv: Inverse error function. + erfcinv: Inverse Complementary error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Error_function + .. [2] https://dlmf.nist.gov/7 + .. [3] https://mathworld.wolfram.com/Erfc.html + .. [4] https://functions.wolfram.com/GammaBetaErf/Erfc + + """ + + unbranched = True + + def fdiff(self, argindex=1): + if argindex == 1: + return -2*exp(-self.args[0]**2)/sqrt(pi) + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + + """ + return erfcinv + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is S.Infinity: + return S.Zero + elif arg.is_zero: + return S.One + + if isinstance(arg, erfinv): + return S.One - arg.args[0] + + if isinstance(arg, erfcinv): + return arg.args[0] + + if arg.is_zero: + return S.One + + # Try to pull out factors of I + t = arg.extract_multiplicatively(I) + if t in (S.Infinity, S.NegativeInfinity): + return -arg + + # Try to pull out factors of -1 + if arg.could_extract_minus_sign(): + return 2 - cls(-arg) + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n == 0: + return S.One + elif n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + k = floor((n - 1)/S(2)) + if len(previous_terms) > 2: + return -previous_terms[-2] * x**2 * (n - 2)/(n*k) + else: + return -2*S.NegativeOne**k * x**n/(n*factorial(k)*sqrt(pi)) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_is_real(self): + return self.args[0].is_extended_real + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return self.rewrite(erf).rewrite("tractable", deep=True, limitvar=limitvar) + + def _eval_rewrite_as_erf(self, z, **kwargs): + return S.One - erf(z) + + def _eval_rewrite_as_erfi(self, z, **kwargs): + return S.One + I*erfi(I*z) + + def _eval_rewrite_as_fresnels(self, z, **kwargs): + arg = (S.One - I)*z/sqrt(pi) + return S.One - (S.One + I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_fresnelc(self, z, **kwargs): + arg = (S.One-I)*z/sqrt(pi) + return S.One - (S.One + I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return S.One - z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return S.One - 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], -z**2) + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return S.One - sqrt(z**2)/z*(S.One - uppergamma(S.Half, z**2)/sqrt(pi)) + + def _eval_rewrite_as_expint(self, z, **kwargs): + return S.One - sqrt(z**2)/z + z*expint(S.Half, z**2)/sqrt(pi) + + def _eval_expand_func(self, **hints): + return self.rewrite(erf) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.ComplexInfinity: + arg0 = arg.limit(x, 0, dir='-' if cdir == -1 else '+') + if arg0.is_zero: + return S.One + else: + return self.func(arg0) + + as_real_imag = real_to_real_as_real_imag + + def _eval_aseries(self, n, args0, x, logx): + return S.One - erf(*self.args)._eval_aseries(n, args0, x, logx) + + +class erfi(Function): + r""" + Imaginary error function. + + Explanation + =========== + + The function erfi is defined as: + + .. math :: + \mathrm{erfi}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{t^2} \mathrm{d}t + + Examples + ======== + + >>> from sympy import I, oo, erfi + >>> from sympy.abc import z + + Several special values are known: + + >>> erfi(0) + 0 + >>> erfi(oo) + oo + >>> erfi(-oo) + -oo + >>> erfi(I*oo) + I + >>> erfi(-I*oo) + -I + + In general one can pull out factors of -1 and $I$ from the argument: + + >>> erfi(-z) + -erfi(z) + + >>> from sympy import conjugate + >>> conjugate(erfi(z)) + erfi(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(erfi(z), z) + 2*exp(z**2)/sqrt(pi) + + We can numerically evaluate the imaginary error function to arbitrary + precision on the whole complex plane: + + >>> erfi(2).evalf(30) + 18.5648024145755525987042919132 + + >>> erfi(-2*I).evalf(30) + -0.995322265018952734162069256367*I + + See Also + ======== + + erf: Gaussian error function. + erfc: Complementary error function. + erf2: Two-argument error function. + erfinv: Inverse error function. + erfcinv: Inverse Complementary error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Error_function + .. [2] https://mathworld.wolfram.com/Erfi.html + .. [3] https://functions.wolfram.com/GammaBetaErf/Erfi + + """ + + unbranched = True + + def fdiff(self, argindex=1): + if argindex == 1: + return 2*exp(self.args[0]**2)/sqrt(pi) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, z): + if z.is_Number: + if z is S.NaN: + return S.NaN + elif z.is_zero: + return S.Zero + elif z is S.Infinity: + return S.Infinity + + if z.is_zero: + return S.Zero + + # Try to pull out factors of -1 + if z.could_extract_minus_sign(): + return -cls(-z) + + # Try to pull out factors of I + nz = z.extract_multiplicatively(I) + if nz is not None: + if nz is S.Infinity: + return I + if isinstance(nz, erfinv): + return I*nz.args[0] + if isinstance(nz, erfcinv): + return I*(S.One - nz.args[0]) + # Only happens with unevaluated erf2inv + if isinstance(nz, erf2inv) and nz.args[0].is_zero: + return I*nz.args[1] + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0 or n % 2 == 0: + return S.Zero + else: + x = sympify(x) + k = floor((n - 1)/S(2)) + if len(previous_terms) > 2: + return previous_terms[-2] * x**2 * (n - 2)/(n*k) + else: + return 2 * x**n/(n*factorial(k)*sqrt(pi)) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return self.rewrite(erf).rewrite("tractable", deep=True, limitvar=limitvar) + + def _eval_rewrite_as_erf(self, z, **kwargs): + return -I*erf(I*z) + + def _eval_rewrite_as_erfc(self, z, **kwargs): + return I*erfc(I*z) - I + + def _eval_rewrite_as_fresnels(self, z, **kwargs): + arg = (S.One + I)*z/sqrt(pi) + return (S.One - I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_fresnelc(self, z, **kwargs): + arg = (S.One + I)*z/sqrt(pi) + return (S.One - I)*(fresnelc(arg) - I*fresnels(arg)) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return z/sqrt(pi)*meijerg([S.Half], [], [0], [Rational(-1, 2)], -z**2) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return 2*z/sqrt(pi)*hyper([S.Half], [3*S.Half], z**2) + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return sqrt(-z**2)/z*(uppergamma(S.Half, -z**2)/sqrt(pi) - S.One) + + def _eval_rewrite_as_expint(self, z, **kwargs): + return sqrt(-z**2)/z - z*expint(S.Half, -z**2)/sqrt(pi) + + def _eval_expand_func(self, **hints): + return self.rewrite(erf) + + as_real_imag = real_to_real_as_real_imag + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if x in arg.free_symbols and arg0.is_zero: + return 2*arg/sqrt(pi) + elif arg0.is_finite: + return self.func(arg0) + return self.func(arg) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + if point is S.Infinity: + z = self.args[0] + s = [factorial2(2*k - 1) / (2**k * z**(2*k + 1)) + for k in range(n)] + [Order(1/z**n, x)] + return -I + (exp(z**2)/sqrt(pi)) * Add(*s) + + return super(erfi, self)._eval_aseries(n, args0, x, logx) + + +class erf2(Function): + r""" + Two-argument error function. + + Explanation + =========== + + This function is defined as: + + .. math :: + \mathrm{erf2}(x, y) = \frac{2}{\sqrt{\pi}} \int_x^y e^{-t^2} \mathrm{d}t + + Examples + ======== + + >>> from sympy import oo, erf2 + >>> from sympy.abc import x, y + + Several special values are known: + + >>> erf2(0, 0) + 0 + >>> erf2(x, x) + 0 + >>> erf2(x, oo) + 1 - erf(x) + >>> erf2(x, -oo) + -erf(x) - 1 + >>> erf2(oo, y) + erf(y) - 1 + >>> erf2(-oo, y) + erf(y) + 1 + + In general one can pull out factors of -1: + + >>> erf2(-x, -y) + -erf2(x, y) + + The error function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(erf2(x, y)) + erf2(conjugate(x), conjugate(y)) + + Differentiation with respect to $x$, $y$ is supported: + + >>> from sympy import diff + >>> diff(erf2(x, y), x) + -2*exp(-x**2)/sqrt(pi) + >>> diff(erf2(x, y), y) + 2*exp(-y**2)/sqrt(pi) + + See Also + ======== + + erf: Gaussian error function. + erfc: Complementary error function. + erfi: Imaginary error function. + erfinv: Inverse error function. + erfcinv: Inverse Complementary error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://functions.wolfram.com/GammaBetaErf/Erf2/ + + """ + + + def fdiff(self, argindex): + x, y = self.args + if argindex == 1: + return -2*exp(-x**2)/sqrt(pi) + elif argindex == 2: + return 2*exp(-y**2)/sqrt(pi) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, x, y): + chk = (S.Infinity, S.NegativeInfinity, S.Zero) + if x is S.NaN or y is S.NaN: + return S.NaN + elif x == y: + return S.Zero + elif x in chk or y in chk: + return erf(y) - erf(x) + + if isinstance(y, erf2inv) and y.args[0] == x: + return y.args[1] + + if x.is_zero or y.is_zero or x.is_extended_real and x.is_infinite or \ + y.is_extended_real and y.is_infinite: + return erf(y) - erf(x) + + #Try to pull out -1 factor + sign_x = x.could_extract_minus_sign() + sign_y = y.could_extract_minus_sign() + if (sign_x and sign_y): + return -cls(-x, -y) + elif (sign_x or sign_y): + return erf(y)-erf(x) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate(), self.args[1].conjugate()) + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real and self.args[1].is_extended_real + + def _eval_rewrite_as_erf(self, x, y, **kwargs): + return erf(y) - erf(x) + + def _eval_rewrite_as_erfc(self, x, y, **kwargs): + return erfc(x) - erfc(y) + + def _eval_rewrite_as_erfi(self, x, y, **kwargs): + return I*(erfi(I*x)-erfi(I*y)) + + def _eval_rewrite_as_fresnels(self, x, y, **kwargs): + return erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels) + + def _eval_rewrite_as_fresnelc(self, x, y, **kwargs): + return erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc) + + def _eval_rewrite_as_meijerg(self, x, y, **kwargs): + return erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg) + + def _eval_rewrite_as_hyper(self, x, y, **kwargs): + return erf(y).rewrite(hyper) - erf(x).rewrite(hyper) + + def _eval_rewrite_as_uppergamma(self, x, y, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return (sqrt(y**2)/y*(S.One - uppergamma(S.Half, y**2)/sqrt(pi)) - + sqrt(x**2)/x*(S.One - uppergamma(S.Half, x**2)/sqrt(pi))) + + def _eval_rewrite_as_expint(self, x, y, **kwargs): + return erf(y).rewrite(expint) - erf(x).rewrite(expint) + + def _eval_expand_func(self, **hints): + return self.rewrite(erf) + + def _eval_is_zero(self): + return is_eq(*self.args) + +class erfinv(Function): + r""" + Inverse Error Function. The erfinv function is defined as: + + .. math :: + \mathrm{erf}(x) = y \quad \Rightarrow \quad \mathrm{erfinv}(y) = x + + Examples + ======== + + >>> from sympy import erfinv + >>> from sympy.abc import x + + Several special values are known: + + >>> erfinv(0) + 0 + >>> erfinv(1) + oo + + Differentiation with respect to $x$ is supported: + + >>> from sympy import diff + >>> diff(erfinv(x), x) + sqrt(pi)*exp(erfinv(x)**2)/2 + + We can numerically evaluate the inverse error function to arbitrary + precision on [-1, 1]: + + >>> erfinv(0.2).evalf(30) + 0.179143454621291692285822705344 + + See Also + ======== + + erf: Gaussian error function. + erfc: Complementary error function. + erfi: Imaginary error function. + erf2: Two-argument error function. + erfcinv: Inverse Complementary error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Error_function#Inverse_functions + .. [2] https://functions.wolfram.com/GammaBetaErf/InverseErf/ + + """ + + + def fdiff(self, argindex =1): + if argindex == 1: + return sqrt(pi)*exp(self.func(self.args[0])**2)*S.Half + else : + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + + """ + return erf + + @classmethod + def eval(cls, z): + if z is S.NaN: + return S.NaN + elif z is S.NegativeOne: + return S.NegativeInfinity + elif z.is_zero: + return S.Zero + elif z is S.One: + return S.Infinity + + if isinstance(z, erf) and z.args[0].is_extended_real: + return z.args[0] + + if z.is_zero: + return S.Zero + + # Try to pull out factors of -1 + nz = z.extract_multiplicatively(-1) + if nz is not None and (isinstance(nz, erf) and (nz.args[0]).is_extended_real): + return -nz.args[0] + + def _eval_rewrite_as_erfcinv(self, z, **kwargs): + return erfcinv(1-z) + + def _eval_is_zero(self): + return self.args[0].is_zero + + +class erfcinv (Function): + r""" + Inverse Complementary Error Function. The erfcinv function is defined as: + + .. math :: + \mathrm{erfc}(x) = y \quad \Rightarrow \quad \mathrm{erfcinv}(y) = x + + Examples + ======== + + >>> from sympy import erfcinv + >>> from sympy.abc import x + + Several special values are known: + + >>> erfcinv(1) + 0 + >>> erfcinv(0) + oo + + Differentiation with respect to $x$ is supported: + + >>> from sympy import diff + >>> diff(erfcinv(x), x) + -sqrt(pi)*exp(erfcinv(x)**2)/2 + + See Also + ======== + + erf: Gaussian error function. + erfc: Complementary error function. + erfi: Imaginary error function. + erf2: Two-argument error function. + erfinv: Inverse error function. + erf2inv: Inverse two-argument error function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Error_function#Inverse_functions + .. [2] https://functions.wolfram.com/GammaBetaErf/InverseErfc/ + + """ + + + def fdiff(self, argindex =1): + if argindex == 1: + return -sqrt(pi)*exp(self.func(self.args[0])**2)*S.Half + else: + raise ArgumentIndexError(self, argindex) + + def inverse(self, argindex=1): + """ + Returns the inverse of this function. + + """ + return erfc + + @classmethod + def eval(cls, z): + if z is S.NaN: + return S.NaN + elif z.is_zero: + return S.Infinity + elif z is S.One: + return S.Zero + elif z == 2: + return S.NegativeInfinity + + if z.is_zero: + return S.Infinity + + def _eval_rewrite_as_erfinv(self, z, **kwargs): + return erfinv(1-z) + + def _eval_is_zero(self): + return (self.args[0] - 1).is_zero + + def _eval_is_infinite(self): + return self.args[0].is_zero + + +class erf2inv(Function): + r""" + Two-argument Inverse error function. The erf2inv function is defined as: + + .. math :: + \mathrm{erf2}(x, w) = y \quad \Rightarrow \quad \mathrm{erf2inv}(x, y) = w + + Examples + ======== + + >>> from sympy import erf2inv, oo + >>> from sympy.abc import x, y + + Several special values are known: + + >>> erf2inv(0, 0) + 0 + >>> erf2inv(1, 0) + 1 + >>> erf2inv(0, 1) + oo + >>> erf2inv(0, y) + erfinv(y) + >>> erf2inv(oo, y) + erfcinv(-y) + + Differentiation with respect to $x$ and $y$ is supported: + + >>> from sympy import diff + >>> diff(erf2inv(x, y), x) + exp(-x**2 + erf2inv(x, y)**2) + >>> diff(erf2inv(x, y), y) + sqrt(pi)*exp(erf2inv(x, y)**2)/2 + + See Also + ======== + + erf: Gaussian error function. + erfc: Complementary error function. + erfi: Imaginary error function. + erf2: Two-argument error function. + erfinv: Inverse error function. + erfcinv: Inverse complementary error function. + + References + ========== + + .. [1] https://functions.wolfram.com/GammaBetaErf/InverseErf2/ + + """ + + + def fdiff(self, argindex): + x, y = self.args + if argindex == 1: + return exp(self.func(x,y)**2-x**2) + elif argindex == 2: + return sqrt(pi)*S.Half*exp(self.func(x,y)**2) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, x, y): + if x is S.NaN or y is S.NaN: + return S.NaN + elif x.is_zero and y.is_zero: + return S.Zero + elif x.is_zero and y is S.One: + return S.Infinity + elif x is S.One and y.is_zero: + return S.One + elif x.is_zero: + return erfinv(y) + elif x is S.Infinity: + return erfcinv(-y) + elif y.is_zero: + return x + elif y is S.Infinity: + return erfinv(x) + + if x.is_zero: + if y.is_zero: + return S.Zero + else: + return erfinv(y) + if y.is_zero: + return x + + def _eval_is_zero(self): + x, y = self.args + if x.is_zero and y.is_zero: + return True + +############################################################################### +#################### EXPONENTIAL INTEGRALS #################################### +############################################################################### + +class Ei(Function): + r""" + The classical exponential integral. + + Explanation + =========== + + For use in SymPy, this function is defined as + + .. math:: \operatorname{Ei}(x) = \sum_{n=1}^\infty \frac{x^n}{n\, n!} + + \log(x) + \gamma, + + where $\gamma$ is the Euler-Mascheroni constant. + + If $x$ is a polar number, this defines an analytic function on the + Riemann surface of the logarithm. Otherwise this defines an analytic + function in the cut plane $\mathbb{C} \setminus (-\infty, 0]$. + + **Background** + + The name exponential integral comes from the following statement: + + .. math:: \operatorname{Ei}(x) = \int_{-\infty}^x \frac{e^t}{t} \mathrm{d}t + + If the integral is interpreted as a Cauchy principal value, this statement + holds for $x > 0$ and $\operatorname{Ei}(x)$ as defined above. + + Examples + ======== + + >>> from sympy import Ei, polar_lift, exp_polar, I, pi + >>> from sympy.abc import x + + >>> Ei(-1) + Ei(-1) + + This yields a real value: + + >>> Ei(-1).n(chop=True) + -0.219383934395520 + + On the other hand the analytic continuation is not real: + + >>> Ei(polar_lift(-1)).n(chop=True) + -0.21938393439552 + 3.14159265358979*I + + The exponential integral has a logarithmic branch point at the origin: + + >>> Ei(x*exp_polar(2*I*pi)) + Ei(x) + 2*I*pi + + Differentiation is supported: + + >>> Ei(x).diff(x) + exp(x)/x + + The exponential integral is related to many other special functions. + For example: + + >>> from sympy import expint, Shi + >>> Ei(x).rewrite(expint) + -expint(1, x*exp_polar(I*pi)) - I*pi + >>> Ei(x).rewrite(Shi) + Chi(x) + Shi(x) + + See Also + ======== + + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + uppergamma: Upper incomplete gamma function. + + References + ========== + + .. [1] https://dlmf.nist.gov/6.6 + .. [2] https://en.wikipedia.org/wiki/Exponential_integral + .. [3] Abramowitz & Stegun, section 5: https://web.archive.org/web/20201128173312/http://people.math.sfu.ca/~cbm/aands/page_228.htm + + """ + + + @classmethod + def eval(cls, z): + if z.is_zero: + return S.NegativeInfinity + elif z is S.Infinity: + return S.Infinity + elif z is S.NegativeInfinity: + return S.Zero + + if z.is_zero: + return S.NegativeInfinity + + nz, n = z.extract_branch_factor() + if n: + return Ei(nz) + 2*I*pi*n + + def fdiff(self, argindex=1): + arg = unpolarify(self.args[0]) + if argindex == 1: + return exp(arg)/arg + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + if (self.args[0]/polar_lift(-1)).is_positive: + return Function._eval_evalf(self, prec) + (I*pi)._eval_evalf(prec) + return Function._eval_evalf(self, prec) + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + # XXX this does not currently work usefully because uppergamma + # immediately turns into expint + return -uppergamma(0, polar_lift(-1)*z) - I*pi + + def _eval_rewrite_as_expint(self, z, **kwargs): + return -expint(1, polar_lift(-1)*z) - I*pi + + def _eval_rewrite_as_li(self, z, **kwargs): + if isinstance(z, log): + return li(z.args[0]) + # TODO: + # Actually it only holds that: + # Ei(z) = li(exp(z)) + # for -pi < imag(z) <= pi + return li(exp(z)) + + def _eval_rewrite_as_Si(self, z, **kwargs): + if z.is_negative: + return Shi(z) + Chi(z) - I*pi + else: + return Shi(z) + Chi(z) + _eval_rewrite_as_Ci = _eval_rewrite_as_Si + _eval_rewrite_as_Chi = _eval_rewrite_as_Si + _eval_rewrite_as_Shi = _eval_rewrite_as_Si + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return exp(z) * _eis(z) + + def _eval_rewrite_as_Integral(self, z, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [z]).name) + return Integral(S.Exp1**t/t, (t, S.NegativeInfinity, z)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy import re + x0 = self.args[0].limit(x, 0) + arg = self.args[0].as_leading_term(x, cdir=cdir) + cdir = arg.dir(x, cdir) + if x0.is_zero: + c, e = arg.as_coeff_exponent(x) + logx = log(x) if logx is None else logx + return log(c) + e*logx + EulerGamma - ( + I*pi if re(cdir).is_negative else S.Zero) + return super()._eval_as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + x0 = self.args[0].limit(x, 0) + if x0.is_zero: + f = self._eval_rewrite_as_Si(*self.args) + return f._eval_nseries(x, n, logx) + return super()._eval_nseries(x, n, logx) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + if point is S.Infinity: + z = self.args[0] + s = [factorial(k) / (z)**k for k in range(n)] + \ + [Order(1/z**n, x)] + return (exp(z)/z) * Add(*s) + + return super(Ei, self)._eval_aseries(n, args0, x, logx) + + +class expint(Function): + r""" + Generalized exponential integral. + + Explanation + =========== + + This function is defined as + + .. math:: \operatorname{E}_\nu(z) = z^{\nu - 1} \Gamma(1 - \nu, z), + + where $\Gamma(1 - \nu, z)$ is the upper incomplete gamma function + (``uppergamma``). + + Hence for $z$ with positive real part we have + + .. math:: \operatorname{E}_\nu(z) + = \int_1^\infty \frac{e^{-zt}}{t^\nu} \mathrm{d}t, + + which explains the name. + + The representation as an incomplete gamma function provides an analytic + continuation for $\operatorname{E}_\nu(z)$. If $\nu$ is a + non-positive integer, the exponential integral is thus an unbranched + function of $z$, otherwise there is a branch point at the origin. + Refer to the incomplete gamma function documentation for details of the + branching behavior. + + Examples + ======== + + >>> from sympy import expint, S + >>> from sympy.abc import nu, z + + Differentiation is supported. Differentiation with respect to $z$ further + explains the name: for integral orders, the exponential integral is an + iterated integral of the exponential function. + + >>> expint(nu, z).diff(z) + -expint(nu - 1, z) + + Differentiation with respect to $\nu$ has no classical expression: + + >>> expint(nu, z).diff(nu) + -z**(nu - 1)*meijerg(((), (1, 1)), ((0, 0, 1 - nu), ()), z) + + At non-postive integer orders, the exponential integral reduces to the + exponential function: + + >>> expint(0, z) + exp(-z)/z + >>> expint(-1, z) + exp(-z)/z + exp(-z)/z**2 + + At half-integers it reduces to error functions: + + >>> expint(S(1)/2, z) + sqrt(pi)*erfc(sqrt(z))/sqrt(z) + + At positive integer orders it can be rewritten in terms of exponentials + and ``expint(1, z)``. Use ``expand_func()`` to do this: + + >>> from sympy import expand_func + >>> expand_func(expint(5, z)) + z**4*expint(1, z)/24 + (-z**3 + z**2 - 2*z + 6)*exp(-z)/24 + + The generalised exponential integral is essentially equivalent to the + incomplete gamma function: + + >>> from sympy import uppergamma + >>> expint(nu, z).rewrite(uppergamma) + z**(nu - 1)*uppergamma(1 - nu, z) + + As such it is branched at the origin: + + >>> from sympy import exp_polar, pi, I + >>> expint(4, z*exp_polar(2*pi*I)) + I*pi*z**3/3 + expint(4, z) + >>> expint(nu, z*exp_polar(2*pi*I)) + z**(nu - 1)*(exp(2*I*pi*nu) - 1)*gamma(1 - nu) + expint(nu, z) + + See Also + ======== + + Ei: Another related function called exponential integral. + E1: The classical case, returns expint(1, z). + li: Logarithmic integral. + Li: Offset logarithmic integral. + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + uppergamma + + References + ========== + + .. [1] https://dlmf.nist.gov/8.19 + .. [2] https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/ + .. [3] https://en.wikipedia.org/wiki/Exponential_integral + + """ + + + @classmethod + def eval(cls, nu, z): + from sympy.functions.special.gamma_functions import (gamma, uppergamma) + nu2 = unpolarify(nu) + if nu != nu2: + return expint(nu2, z) + if nu.is_Integer and nu <= 0 or (not nu.is_Integer and (2*nu).is_Integer): + return unpolarify(expand_mul(z**(nu - 1)*uppergamma(1 - nu, z))) + + # Extract branching information. This can be deduced from what is + # explained in lowergamma.eval(). + z, n = z.extract_branch_factor() + if n is S.Zero: + return + if nu.is_integer: + if not nu > 0: + return + return expint(nu, z) \ + - 2*pi*I*n*S.NegativeOne**(nu - 1)/factorial(nu - 1)*unpolarify(z)**(nu - 1) + else: + return (exp(2*I*pi*nu*n) - 1)*z**(nu - 1)*gamma(1 - nu) + expint(nu, z) + + def fdiff(self, argindex): + nu, z = self.args + if argindex == 1: + return -z**(nu - 1)*meijerg([], [1, 1], [0, 0, 1 - nu], [], z) + elif argindex == 2: + return -expint(nu - 1, z) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_uppergamma(self, nu, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return z**(nu - 1)*uppergamma(1 - nu, z) + + def _eval_rewrite_as_Ei(self, nu, z, **kwargs): + if nu == 1: + return -Ei(z*exp_polar(-I*pi)) - I*pi + elif nu.is_Integer and nu > 1: + # DLMF, 8.19.7 + x = -unpolarify(z) + return x**(nu - 1)/factorial(nu - 1)*E1(z).rewrite(Ei) + \ + exp(x)/factorial(nu - 1) * \ + Add(*[factorial(nu - k - 2)*x**k for k in range(nu - 1)]) + else: + return self + + def _eval_expand_func(self, **hints): + return self.rewrite(Ei).rewrite(expint, **hints) + + def _eval_rewrite_as_Si(self, nu, z, **kwargs): + if nu != 1: + return self + return Shi(z) - Chi(z) + _eval_rewrite_as_Ci = _eval_rewrite_as_Si + _eval_rewrite_as_Chi = _eval_rewrite_as_Si + _eval_rewrite_as_Shi = _eval_rewrite_as_Si + + def _eval_nseries(self, x, n, logx, cdir=0): + if not self.args[0].has(x): + nu = self.args[0] + if nu == 1: + f = self._eval_rewrite_as_Si(*self.args) + return f._eval_nseries(x, n, logx) + elif nu.is_Integer and nu > 1: + f = self._eval_rewrite_as_Ei(*self.args) + return f._eval_nseries(x, n, logx) + return super()._eval_nseries(x, n, logx) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[1] + nu = self.args[0] + + if point is S.Infinity: + z = self.args[1] + s = [S.NegativeOne**k * RisingFactorial(nu, k) / z**k for k in range(n)] + [Order(1/z**n, x)] + return (exp(-z)/z) * Add(*s) + + return super(expint, self)._eval_aseries(n, args0, x, logx) + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + from sympy.integrals.integrals import Integral + n, x = self.args + t = Dummy(uniquely_named_symbol('t', args).name) + return Integral(t**-n * exp(-t*x), (t, 1, S.Infinity)) + + +def E1(z): + """ + Classical case of the generalized exponential integral. + + Explanation + =========== + + This is equivalent to ``expint(1, z)``. + + Examples + ======== + + >>> from sympy import E1 + >>> E1(0) + expint(1, 0) + + >>> E1(5) + expint(1, 5) + + See Also + ======== + + Ei: Exponential integral. + expint: Generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + + """ + return expint(1, z) + + +class li(Function): + r""" + The classical logarithmic integral. + + Explanation + =========== + + For use in SymPy, this function is defined as + + .. math:: \operatorname{li}(x) = \int_0^x \frac{1}{\log(t)} \mathrm{d}t \,. + + Examples + ======== + + >>> from sympy import I, oo, li + >>> from sympy.abc import z + + Several special values are known: + + >>> li(0) + 0 + >>> li(1) + -oo + >>> li(oo) + oo + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(li(z), z) + 1/log(z) + + Defining the ``li`` function via an integral: + >>> from sympy import integrate + >>> integrate(li(z)) + z*li(z) - Ei(2*log(z)) + + >>> integrate(li(z),z) + z*li(z) - Ei(2*log(z)) + + + The logarithmic integral can also be defined in terms of ``Ei``: + + >>> from sympy import Ei + >>> li(z).rewrite(Ei) + Ei(log(z)) + >>> diff(li(z).rewrite(Ei), z) + 1/log(z) + + We can numerically evaluate the logarithmic integral to arbitrary precision + on the whole complex plane (except the singular points): + + >>> li(2).evalf(30) + 1.04516378011749278484458888919 + + >>> li(2*I).evalf(30) + 1.0652795784357498247001125598 + 3.08346052231061726610939702133*I + + We can even compute Soldner's constant by the help of mpmath: + + >>> from mpmath import findroot + >>> findroot(li, 2) + 1.45136923488338 + + Further transformations include rewriting ``li`` in terms of + the trigonometric integrals ``Si``, ``Ci``, ``Shi`` and ``Chi``: + + >>> from sympy import Si, Ci, Shi, Chi + >>> li(z).rewrite(Si) + -log(I*log(z)) - log(1/log(z))/2 + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)) + >>> li(z).rewrite(Ci) + -log(I*log(z)) - log(1/log(z))/2 + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)) + >>> li(z).rewrite(Shi) + -log(1/log(z))/2 + log(log(z))/2 + Chi(log(z)) - Shi(log(z)) + >>> li(z).rewrite(Chi) + -log(1/log(z))/2 + log(log(z))/2 + Chi(log(z)) - Shi(log(z)) + + See Also + ======== + + Li: Offset logarithmic integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Logarithmic_integral + .. [2] https://mathworld.wolfram.com/LogarithmicIntegral.html + .. [3] https://dlmf.nist.gov/6 + .. [4] https://mathworld.wolfram.com/SoldnersConstant.html + + """ + + + @classmethod + def eval(cls, z): + if z.is_zero: + return S.Zero + elif z is S.One: + return S.NegativeInfinity + elif z is S.Infinity: + return S.Infinity + if z.is_zero: + return S.Zero + + def fdiff(self, argindex=1): + arg = self.args[0] + if argindex == 1: + return S.One / log(arg) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_conjugate(self): + z = self.args[0] + # Exclude values on the branch cut (-oo, 0) + if not z.is_extended_negative: + return self.func(z.conjugate()) + + def _eval_rewrite_as_Li(self, z, **kwargs): + return Li(z) + li(2) + + def _eval_rewrite_as_Ei(self, z, **kwargs): + return Ei(log(z)) + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return (-uppergamma(0, -log(z)) + + S.Half*(log(log(z)) - log(S.One/log(z))) - log(-log(z))) + + def _eval_rewrite_as_Si(self, z, **kwargs): + return (Ci(I*log(z)) - I*Si(I*log(z)) - + S.Half*(log(S.One/log(z)) - log(log(z))) - log(I*log(z))) + + _eval_rewrite_as_Ci = _eval_rewrite_as_Si + + def _eval_rewrite_as_Shi(self, z, **kwargs): + return (Chi(log(z)) - Shi(log(z)) - S.Half*(log(S.One/log(z)) - log(log(z)))) + + _eval_rewrite_as_Chi = _eval_rewrite_as_Shi + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return (log(z)*hyper((1, 1), (2, 2), log(z)) + + S.Half*(log(log(z)) - log(S.One/log(z))) + EulerGamma) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return (-log(-log(z)) - S.Half*(log(S.One/log(z)) - log(log(z))) + - meijerg(((), (1,)), ((0, 0), ()), -log(z))) + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return z * _eis(log(z)) + + def _eval_nseries(self, x, n, logx, cdir=0): + z = self.args[0] + s = [(log(z))**k / (factorial(k) * k) for k in range(1, n)] + return EulerGamma + log(log(z)) + Add(*s) + + def _eval_is_zero(self): + z = self.args[0] + if z.is_zero: + return True + +class Li(Function): + r""" + The offset logarithmic integral. + + Explanation + =========== + + For use in SymPy, this function is defined as + + .. math:: \operatorname{Li}(x) = \operatorname{li}(x) - \operatorname{li}(2) + + Examples + ======== + + >>> from sympy import Li + >>> from sympy.abc import z + + The following special value is known: + + >>> Li(2) + 0 + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(Li(z), z) + 1/log(z) + + The shifted logarithmic integral can be written in terms of $li(z)$: + + >>> from sympy import li + >>> Li(z).rewrite(li) + li(z) - li(2) + + We can numerically evaluate the logarithmic integral to arbitrary precision + on the whole complex plane (except the singular points): + + >>> Li(2).evalf(30) + 0 + + >>> Li(4).evalf(30) + 1.92242131492155809316615998938 + + See Also + ======== + + li: Logarithmic integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Logarithmic_integral + .. [2] https://mathworld.wolfram.com/LogarithmicIntegral.html + .. [3] https://dlmf.nist.gov/6 + + """ + + + @classmethod + def eval(cls, z): + if z is S.Infinity: + return S.Infinity + elif z == S(2): + return S.Zero + + def fdiff(self, argindex=1): + arg = self.args[0] + if argindex == 1: + return S.One / log(arg) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + return self.rewrite(li).evalf(prec) + + def _eval_rewrite_as_li(self, z, **kwargs): + return li(z) - li(2) + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return self.rewrite(li).rewrite("tractable", deep=True) + + def _eval_nseries(self, x, n, logx, cdir=0): + f = self._eval_rewrite_as_li(*self.args) + return f._eval_nseries(x, n, logx) + +############################################################################### +#################### TRIGONOMETRIC INTEGRALS ################################## +############################################################################### + +class TrigonometricIntegral(Function): + """ Base class for trigonometric integrals. """ + + + @classmethod + def eval(cls, z): + if z is S.Zero: + return cls._atzero + elif z is S.Infinity: + return cls._atinf() + elif z is S.NegativeInfinity: + return cls._atneginf() + + if z.is_zero: + return cls._atzero + + nz = z.extract_multiplicatively(polar_lift(I)) + if nz is None and cls._trigfunc(0) == 0: + nz = z.extract_multiplicatively(I) + if nz is not None: + return cls._Ifactor(nz, 1) + nz = z.extract_multiplicatively(polar_lift(-I)) + if nz is not None: + return cls._Ifactor(nz, -1) + + nz = z.extract_multiplicatively(polar_lift(-1)) + if nz is None and cls._trigfunc(0) == 0: + nz = z.extract_multiplicatively(-1) + if nz is not None: + return cls._minusfactor(nz) + + nz, n = z.extract_branch_factor() + if n == 0 and nz == z: + return + return 2*pi*I*n*cls._trigfunc(0) + cls(nz) + + def fdiff(self, argindex=1): + arg = unpolarify(self.args[0]) + if argindex == 1: + return self._trigfunc(arg)/arg + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Ei(self, z, **kwargs): + return self._eval_rewrite_as_expint(z).rewrite(Ei) + + def _eval_rewrite_as_uppergamma(self, z, **kwargs): + from sympy.functions.special.gamma_functions import uppergamma + return self._eval_rewrite_as_expint(z).rewrite(uppergamma) + + def _eval_nseries(self, x, n, logx, cdir=0): + # NOTE this is fairly inefficient + if self.args[0].subs(x, 0) != 0: + return super()._eval_nseries(x, n, logx) + baseseries = self._trigfunc(x)._eval_nseries(x, n, logx) + if self._trigfunc(0) != 0: + baseseries -= 1 + baseseries = baseseries.replace(Pow, lambda t, n: t**n/n, simultaneous=False) + if self._trigfunc(0) != 0: + baseseries += EulerGamma + log(x) + return baseseries.subs(x, self.args[0])._eval_nseries(x, n, logx) + + +class Si(TrigonometricIntegral): + r""" + Sine integral. + + Explanation + =========== + + This function is defined by + + .. math:: \operatorname{Si}(z) = \int_0^z \frac{\sin{t}}{t} \mathrm{d}t. + + It is an entire function. + + Examples + ======== + + >>> from sympy import Si + >>> from sympy.abc import z + + The sine integral is an antiderivative of $sin(z)/z$: + + >>> Si(z).diff(z) + sin(z)/z + + It is unbranched: + + >>> from sympy import exp_polar, I, pi + >>> Si(z*exp_polar(2*I*pi)) + Si(z) + + Sine integral behaves much like ordinary sine under multiplication by ``I``: + + >>> Si(I*z) + I*Shi(z) + >>> Si(-z) + -Si(z) + + It can also be expressed in terms of exponential integrals, but beware + that the latter is branched: + + >>> from sympy import expint + >>> Si(z).rewrite(expint) + -I*(-expint(1, z*exp_polar(-I*pi/2))/2 + + expint(1, z*exp_polar(I*pi/2))/2) + pi/2 + + It can be rewritten in the form of sinc function (by definition): + + >>> from sympy import sinc + >>> Si(z).rewrite(sinc) + Integral(sinc(_t), (_t, 0, z)) + + See Also + ======== + + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + sinc: unnormalized sinc function + E1: Special case of the generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral + + """ + + _trigfunc = sin + _atzero = S.Zero + + @classmethod + def _atinf(cls): + return pi*S.Half + + @classmethod + def _atneginf(cls): + return -pi*S.Half + + @classmethod + def _minusfactor(cls, z): + return -Si(z) + + @classmethod + def _Ifactor(cls, z, sign): + return I*Shi(z)*sign + + def _eval_rewrite_as_expint(self, z, **kwargs): + # XXX should we polarify z? + return pi/2 + (E1(polar_lift(I)*z) - E1(polar_lift(-I)*z))/2/I + + def _eval_rewrite_as_Integral(self, z, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [z]).name) + return Integral(sinc(t), (t, 0, z)) + + _eval_rewrite_as_sinc = _eval_rewrite_as_Integral + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + return arg + elif not arg0.is_infinite: + return self.func(arg0) + else: + return self + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + # Expansion at oo + if point is S.Infinity: + z = self.args[0] + p = [S.NegativeOne**k * factorial(2*k) / z**(2*k + 1) + for k in range(n//2 + 1)] + [Order(1/z**n, x)] + q = [S.NegativeOne**k * factorial(2*k + 1) / z**(2*(k + 1)) + for k in range(n//2)] + [Order(1/z**n, x)] + return pi/2 - cos(z)*Add(*p) - sin(z)*Add(*q) + + # All other points are not handled + return super(Si, self)._eval_aseries(n, args0, x, logx) + + def _eval_is_zero(self): + z = self.args[0] + if z.is_zero: + return True + + +class Ci(TrigonometricIntegral): + r""" + Cosine integral. + + Explanation + =========== + + This function is defined for positive $x$ by + + .. math:: \operatorname{Ci}(x) = \gamma + \log{x} + + \int_0^x \frac{\cos{t} - 1}{t} \mathrm{d}t + = -\int_x^\infty \frac{\cos{t}}{t} \mathrm{d}t, + + where $\gamma$ is the Euler-Mascheroni constant. + + We have + + .. math:: \operatorname{Ci}(z) = + -\frac{\operatorname{E}_1\left(e^{i\pi/2} z\right) + + \operatorname{E}_1\left(e^{-i \pi/2} z\right)}{2} + + which holds for all polar $z$ and thus provides an analytic + continuation to the Riemann surface of the logarithm. + + The formula also holds as stated + for $z \in \mathbb{C}$ with $\Re(z) > 0$. + By lifting to the principal branch, we obtain an analytic function on the + cut complex plane. + + Examples + ======== + + >>> from sympy import Ci + >>> from sympy.abc import z + + The cosine integral is a primitive of $\cos(z)/z$: + + >>> Ci(z).diff(z) + cos(z)/z + + It has a logarithmic branch point at the origin: + + >>> from sympy import exp_polar, I, pi + >>> Ci(z*exp_polar(2*I*pi)) + Ci(z) + 2*I*pi + + The cosine integral behaves somewhat like ordinary $\cos$ under + multiplication by $i$: + + >>> from sympy import polar_lift + >>> Ci(polar_lift(I)*z) + Chi(z) + I*pi/2 + >>> Ci(polar_lift(-1)*z) + Ci(z) + I*pi + + It can also be expressed in terms of exponential integrals: + + >>> from sympy import expint + >>> Ci(z).rewrite(expint) + -expint(1, z*exp_polar(-I*pi/2))/2 - expint(1, z*exp_polar(I*pi/2))/2 + + See Also + ======== + + Si: Sine integral. + Shi: Hyperbolic sine integral. + Chi: Hyperbolic cosine integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral + + """ + + _trigfunc = cos + _atzero = S.ComplexInfinity + + @classmethod + def _atinf(cls): + return S.Zero + + @classmethod + def _atneginf(cls): + return I*pi + + @classmethod + def _minusfactor(cls, z): + return Ci(z) + I*pi + + @classmethod + def _Ifactor(cls, z, sign): + return Chi(z) + I*pi/2*sign + + def _eval_rewrite_as_expint(self, z, **kwargs): + return -(E1(polar_lift(I)*z) + E1(polar_lift(-I)*z))/2 + + def _eval_rewrite_as_Integral(self, z, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [z]).name) + return S.EulerGamma + log(z) - Integral((1-cos(t))/t, (t, 0, z)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + c, e = arg.as_coeff_exponent(x) + logx = log(x) if logx is None else logx + return log(c) + e*logx + EulerGamma + elif arg0.is_finite: + return self.func(arg0) + else: + return self + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + if point in (S.Infinity, S.NegativeInfinity): + z = self.args[0] + p = [S.NegativeOne**k * factorial(2*k) / z**(2*k + 1) + for k in range(n//2 + 1)] + [Order(1/z**n, x)] + q = [S.NegativeOne**k * factorial(2*k + 1) / z**(2*(k + 1)) + for k in range(n//2)] + [Order(1/z**n, x)] + result = sin(z)*(Add(*p)) - cos(z)*(Add(*q)) + + if point is S.NegativeInfinity: + result += I*pi + return result + + return super(Ci, self)._eval_aseries(n, args0, x, logx) + +class Shi(TrigonometricIntegral): + r""" + Sinh integral. + + Explanation + =========== + + This function is defined by + + .. math:: \operatorname{Shi}(z) = \int_0^z \frac{\sinh{t}}{t} \mathrm{d}t. + + It is an entire function. + + Examples + ======== + + >>> from sympy import Shi + >>> from sympy.abc import z + + The Sinh integral is a primitive of $\sinh(z)/z$: + + >>> Shi(z).diff(z) + sinh(z)/z + + It is unbranched: + + >>> from sympy import exp_polar, I, pi + >>> Shi(z*exp_polar(2*I*pi)) + Shi(z) + + The $\sinh$ integral behaves much like ordinary $\sinh$ under + multiplication by $i$: + + >>> Shi(I*z) + I*Si(z) + >>> Shi(-z) + -Shi(z) + + It can also be expressed in terms of exponential integrals, but beware + that the latter is branched: + + >>> from sympy import expint + >>> Shi(z).rewrite(expint) + expint(1, z)/2 - expint(1, z*exp_polar(I*pi))/2 - I*pi/2 + + See Also + ======== + + Si: Sine integral. + Ci: Cosine integral. + Chi: Hyperbolic cosine integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral + + """ + + _trigfunc = sinh + _atzero = S.Zero + + @classmethod + def _atinf(cls): + return S.Infinity + + @classmethod + def _atneginf(cls): + return S.NegativeInfinity + + @classmethod + def _minusfactor(cls, z): + return -Shi(z) + + @classmethod + def _Ifactor(cls, z, sign): + return I*Si(z)*sign + + def _eval_rewrite_as_expint(self, z, **kwargs): + # XXX should we polarify z? + return (E1(z) - E1(exp_polar(I*pi)*z))/2 - I*pi/2 + + def _eval_is_zero(self): + z = self.args[0] + if z.is_zero: + return True + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + return arg + elif not arg0.is_infinite: + return self.func(arg0) + else: + return self + + +class Chi(TrigonometricIntegral): + r""" + Cosh integral. + + Explanation + =========== + + This function is defined for positive $x$ by + + .. math:: \operatorname{Chi}(x) = \gamma + \log{x} + + \int_0^x \frac{\cosh{t} - 1}{t} \mathrm{d}t, + + where $\gamma$ is the Euler-Mascheroni constant. + + We have + + .. math:: \operatorname{Chi}(z) = \operatorname{Ci}\left(e^{i \pi/2}z\right) + - i\frac{\pi}{2}, + + which holds for all polar $z$ and thus provides an analytic + continuation to the Riemann surface of the logarithm. + By lifting to the principal branch we obtain an analytic function on the + cut complex plane. + + Examples + ======== + + >>> from sympy import Chi + >>> from sympy.abc import z + + The $\cosh$ integral is a primitive of $\cosh(z)/z$: + + >>> Chi(z).diff(z) + cosh(z)/z + + It has a logarithmic branch point at the origin: + + >>> from sympy import exp_polar, I, pi + >>> Chi(z*exp_polar(2*I*pi)) + Chi(z) + 2*I*pi + + The $\cosh$ integral behaves somewhat like ordinary $\cosh$ under + multiplication by $i$: + + >>> from sympy import polar_lift + >>> Chi(polar_lift(I)*z) + Ci(z) + I*pi/2 + >>> Chi(polar_lift(-1)*z) + Chi(z) + I*pi + + It can also be expressed in terms of exponential integrals: + + >>> from sympy import expint + >>> Chi(z).rewrite(expint) + -expint(1, z)/2 - expint(1, z*exp_polar(I*pi))/2 - I*pi/2 + + See Also + ======== + + Si: Sine integral. + Ci: Cosine integral. + Shi: Hyperbolic sine integral. + Ei: Exponential integral. + expint: Generalised exponential integral. + E1: Special case of the generalised exponential integral. + li: Logarithmic integral. + Li: Offset logarithmic integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigonometric_integral + + """ + + _trigfunc = cosh + _atzero = S.ComplexInfinity + + @classmethod + def _atinf(cls): + return S.Infinity + + @classmethod + def _atneginf(cls): + return S.Infinity + + @classmethod + def _minusfactor(cls, z): + return Chi(z) + I*pi + + @classmethod + def _Ifactor(cls, z, sign): + return Ci(z) + I*pi/2*sign + + def _eval_rewrite_as_expint(self, z, **kwargs): + return -I*pi/2 - (E1(z) + E1(exp_polar(I*pi)*z))/2 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.NaN: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + c, e = arg.as_coeff_exponent(x) + logx = log(x) if logx is None else logx + return log(c) + e*logx + EulerGamma + elif arg0.is_finite: + return self.func(arg0) + else: + return self + + +############################################################################### +#################### FRESNEL INTEGRALS ######################################## +############################################################################### + +class FresnelIntegral(Function): + """ Base class for the Fresnel integrals.""" + + unbranched = True + + @classmethod + def eval(cls, z): + # Values at positive infinities signs + # if any were extracted automatically + if z is S.Infinity: + return S.Half + + # Value at zero + if z.is_zero: + return S.Zero + + # Try to pull out factors of -1 and I + prefact = S.One + newarg = z + changed = False + + nz = newarg.extract_multiplicatively(-1) + if nz is not None: + prefact = -prefact + newarg = nz + changed = True + + nz = newarg.extract_multiplicatively(I) + if nz is not None: + prefact = cls._sign*I*prefact + newarg = nz + changed = True + + if changed: + return prefact*cls(newarg) + + def fdiff(self, argindex=1): + if argindex == 1: + return self._trigfunc(S.Half*pi*self.args[0]**2) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_is_extended_real(self): + return self.args[0].is_extended_real + + _eval_is_finite = _eval_is_extended_real + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + as_real_imag = real_to_real_as_real_imag + + +class fresnels(FresnelIntegral): + r""" + Fresnel integral S. + + Explanation + =========== + + This function is defined by + + .. math:: \operatorname{S}(z) = \int_0^z \sin{\frac{\pi}{2} t^2} \mathrm{d}t. + + It is an entire function. + + Examples + ======== + + >>> from sympy import I, oo, fresnels + >>> from sympy.abc import z + + Several special values are known: + + >>> fresnels(0) + 0 + >>> fresnels(oo) + 1/2 + >>> fresnels(-oo) + -1/2 + >>> fresnels(I*oo) + -I/2 + >>> fresnels(-I*oo) + I/2 + + In general one can pull out factors of -1 and $i$ from the argument: + + >>> fresnels(-z) + -fresnels(z) + >>> fresnels(I*z) + -I*fresnels(z) + + The Fresnel S integral obeys the mirror symmetry + $\overline{S(z)} = S(\bar{z})$: + + >>> from sympy import conjugate + >>> conjugate(fresnels(z)) + fresnels(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(fresnels(z), z) + sin(pi*z**2/2) + + Defining the Fresnel functions via an integral: + + >>> from sympy import integrate, pi, sin, expand_func + >>> integrate(sin(pi*z**2/2), z) + 3*fresnels(z)*gamma(3/4)/(4*gamma(7/4)) + >>> expand_func(integrate(sin(pi*z**2/2), z)) + fresnels(z) + + We can numerically evaluate the Fresnel integral to arbitrary precision + on the whole complex plane: + + >>> fresnels(2).evalf(30) + 0.343415678363698242195300815958 + + >>> fresnels(-2*I).evalf(30) + 0.343415678363698242195300815958*I + + See Also + ======== + + fresnelc: Fresnel cosine integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Fresnel_integral + .. [2] https://dlmf.nist.gov/7 + .. [3] https://mathworld.wolfram.com/FresnelIntegrals.html + .. [4] https://functions.wolfram.com/GammaBetaErf/FresnelS + .. [5] The converging factors for the fresnel integrals + by John W. Wrench Jr. and Vicki Alley + + """ + _trigfunc = sin + _sign = -S.One + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 1: + p = previous_terms[-1] + return (-pi**2*x**4*(4*n - 1)/(8*n*(2*n + 1)*(4*n + 3))) * p + else: + return x**3 * (-x**4)**n * (S(2)**(-2*n - 1)*pi**(2*n + 1)) / ((4*n + 3)*factorial(2*n + 1)) + + def _eval_rewrite_as_erf(self, z, **kwargs): + return (S.One + I)/4 * (erf((S.One + I)/2*sqrt(pi)*z) - I*erf((S.One - I)/2*sqrt(pi)*z)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return pi*z**3/6 * hyper([Rational(3, 4)], [Rational(3, 2), Rational(7, 4)], -pi**2*z**4/16) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return (pi*z**Rational(9, 4) / (sqrt(2)*(z**2)**Rational(3, 4)*(-z)**Rational(3, 4)) + * meijerg([], [1], [Rational(3, 4)], [Rational(1, 4), 0], -pi**2*z**4/16)) + + def _eval_rewrite_as_Integral(self, z, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [z]).name) + return Integral(sin(pi*t**2/2), (t, 0, z)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.series.order import Order + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.ComplexInfinity: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + return pi*arg**3/6 + elif arg0 in [S.Infinity, S.NegativeInfinity]: + s = 1 if arg0 is S.Infinity else -1 + return s*S.Half + Order(x, x) + else: + return self.func(arg0) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + # Expansion at oo and -oo + if point in [S.Infinity, -S.Infinity]: + z = self.args[0] + + # expansion of S(x) = S1(x*sqrt(pi/2)), see reference[5] page 1-8 + # as only real infinities are dealt with, sin and cos are O(1) + p = [S.NegativeOne**k * factorial(4*k + 1) / + (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*factorial(2*k)) + for k in range(0, n) if 4*k + 3 < n] + q = [1/(2*z)] + [S.NegativeOne**k * factorial(4*k - 1) / + (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*factorial(2*k - 1)) + for k in range(1, n) if 4*k + 1 < n] + + p = [-sqrt(2/pi)*t for t in p] + q = [-sqrt(2/pi)*t for t in q] + s = 1 if point is S.Infinity else -1 + # The expansion at oo is 1/2 + some odd powers of z + # To get the expansion at -oo, replace z by -z and flip the sign + # The result -1/2 + the same odd powers of z as before. + return s*S.Half + (sin(z**2)*Add(*p) + cos(z**2)*Add(*q) + ).subs(x, sqrt(2/pi)*x) + Order(1/z**n, x) + + # All other points are not handled + return super()._eval_aseries(n, args0, x, logx) + + +class fresnelc(FresnelIntegral): + r""" + Fresnel integral C. + + Explanation + =========== + + This function is defined by + + .. math:: \operatorname{C}(z) = \int_0^z \cos{\frac{\pi}{2} t^2} \mathrm{d}t. + + It is an entire function. + + Examples + ======== + + >>> from sympy import I, oo, fresnelc + >>> from sympy.abc import z + + Several special values are known: + + >>> fresnelc(0) + 0 + >>> fresnelc(oo) + 1/2 + >>> fresnelc(-oo) + -1/2 + >>> fresnelc(I*oo) + I/2 + >>> fresnelc(-I*oo) + -I/2 + + In general one can pull out factors of -1 and $i$ from the argument: + + >>> fresnelc(-z) + -fresnelc(z) + >>> fresnelc(I*z) + I*fresnelc(z) + + The Fresnel C integral obeys the mirror symmetry + $\overline{C(z)} = C(\bar{z})$: + + >>> from sympy import conjugate + >>> conjugate(fresnelc(z)) + fresnelc(conjugate(z)) + + Differentiation with respect to $z$ is supported: + + >>> from sympy import diff + >>> diff(fresnelc(z), z) + cos(pi*z**2/2) + + Defining the Fresnel functions via an integral: + + >>> from sympy import integrate, pi, cos, expand_func + >>> integrate(cos(pi*z**2/2), z) + fresnelc(z)*gamma(1/4)/(4*gamma(5/4)) + >>> expand_func(integrate(cos(pi*z**2/2), z)) + fresnelc(z) + + We can numerically evaluate the Fresnel integral to arbitrary precision + on the whole complex plane: + + >>> fresnelc(2).evalf(30) + 0.488253406075340754500223503357 + + >>> fresnelc(-2*I).evalf(30) + -0.488253406075340754500223503357*I + + See Also + ======== + + fresnels: Fresnel sine integral. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Fresnel_integral + .. [2] https://dlmf.nist.gov/7 + .. [3] https://mathworld.wolfram.com/FresnelIntegrals.html + .. [4] https://functions.wolfram.com/GammaBetaErf/FresnelC + .. [5] The converging factors for the fresnel integrals + by John W. Wrench Jr. and Vicki Alley + + """ + _trigfunc = cos + _sign = S.One + + @staticmethod + @cacheit + def taylor_term(n, x, *previous_terms): + if n < 0: + return S.Zero + else: + x = sympify(x) + if len(previous_terms) > 1: + p = previous_terms[-1] + return (-pi**2*x**4*(4*n - 3)/(8*n*(2*n - 1)*(4*n + 1))) * p + else: + return x * (-x**4)**n * (S(2)**(-2*n)*pi**(2*n)) / ((4*n + 1)*factorial(2*n)) + + def _eval_rewrite_as_erf(self, z, **kwargs): + return (S.One - I)/4 * (erf((S.One + I)/2*sqrt(pi)*z) + I*erf((S.One - I)/2*sqrt(pi)*z)) + + def _eval_rewrite_as_hyper(self, z, **kwargs): + return z * hyper([Rational(1, 4)], [S.Half, Rational(5, 4)], -pi**2*z**4/16) + + def _eval_rewrite_as_meijerg(self, z, **kwargs): + return (pi*z**Rational(3, 4) / (sqrt(2)*root(z**2, 4)*root(-z, 4)) + * meijerg([], [1], [Rational(1, 4)], [Rational(3, 4), 0], -pi**2*z**4/16)) + + def _eval_rewrite_as_Integral(self, z, **kwargs): + from sympy.integrals.integrals import Integral + t = Dummy(uniquely_named_symbol('t', [z]).name) + return Integral(cos(pi*t**2/2), (t, 0, z)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.series.order import Order + arg = self.args[0].as_leading_term(x, logx=logx, cdir=cdir) + arg0 = arg.subs(x, 0) + + if arg0 is S.ComplexInfinity: + arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + if arg0.is_zero: + return arg + elif arg0 in [S.Infinity, S.NegativeInfinity]: + s = 1 if arg0 is S.Infinity else -1 + return s*S.Half + Order(x, x) + else: + return self.func(arg0) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + # Expansion at oo + if point in [S.Infinity, -S.Infinity]: + z = self.args[0] + + # expansion of C(x) = C1(x*sqrt(pi/2)), see reference[5] page 1-8 + # as only real infinities are dealt with, sin and cos are O(1) + p = [S.NegativeOne**k * factorial(4*k + 1) / + (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*factorial(2*k)) + for k in range(n) if 4*k + 3 < n] + q = [1/(2*z)] + [S.NegativeOne**k * factorial(4*k - 1) / + (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*factorial(2*k - 1)) + for k in range(1, n) if 4*k + 1 < n] + + p = [-sqrt(2/pi)*t for t in p] + q = [ sqrt(2/pi)*t for t in q] + s = 1 if point is S.Infinity else -1 + # The expansion at oo is 1/2 + some odd powers of z + # To get the expansion at -oo, replace z by -z and flip the sign + # The result -1/2 + the same odd powers of z as before. + return s*S.Half + (cos(z**2)*Add(*p) + sin(z**2)*Add(*q) + ).subs(x, sqrt(2/pi)*x) + Order(1/z**n, x) + + # All other points are not handled + return super()._eval_aseries(n, args0, x, logx) + + +############################################################################### +#################### HELPER FUNCTIONS ######################################### +############################################################################### + + +class _erfs(Function): + """ + Helper function to make the $\\mathrm{erf}(z)$ function + tractable for the Gruntz algorithm. + + """ + @classmethod + def eval(cls, arg): + if arg.is_zero: + return S.One + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + point = args0[0] + + # Expansion at oo + if point is S.Infinity: + z = self.args[0] + l = [1/sqrt(pi) * factorial(2*k)*(-S( + 4))**(-k)/factorial(k) * (1/z)**(2*k + 1) for k in range(n)] + o = Order(1/z**(2*n + 1), x) + # It is very inefficient to first add the order and then do the nseries + return (Add(*l))._eval_nseries(x, n, logx) + o + + # Expansion at I*oo + t = point.extract_multiplicatively(I) + if t is S.Infinity: + z = self.args[0] + # TODO: is the series really correct? + l = [1/sqrt(pi) * factorial(2*k)*(-S( + 4))**(-k)/factorial(k) * (1/z)**(2*k + 1) for k in range(n)] + o = Order(1/z**(2*n + 1), x) + # It is very inefficient to first add the order and then do the nseries + return (Add(*l))._eval_nseries(x, n, logx) + o + + # All other points are not handled + return super()._eval_aseries(n, args0, x, logx) + + def fdiff(self, argindex=1): + if argindex == 1: + z = self.args[0] + return -2/sqrt(pi) + 2*z*_erfs(z) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_intractable(self, z, **kwargs): + return (S.One - erf(z))*exp(z**2) + + +class _eis(Function): + """ + Helper function to make the $\\mathrm{Ei}(z)$ and $\\mathrm{li}(z)$ + functions tractable for the Gruntz algorithm. + + """ + + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + if args0[0] != S.Infinity: + return super(_erfs, self)._eval_aseries(n, args0, x, logx) + + z = self.args[0] + l = [factorial(k) * (1/z)**(k + 1) for k in range(n)] + o = Order(1/z**(n + 1), x) + # It is very inefficient to first add the order and then do the nseries + return (Add(*l))._eval_nseries(x, n, logx) + o + + + def fdiff(self, argindex=1): + if argindex == 1: + z = self.args[0] + return S.One / z - _eis(z) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_intractable(self, z, **kwargs): + return exp(-z)*Ei(z) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + x0 = self.args[0].limit(x, 0) + if x0.is_zero: + f = self._eval_rewrite_as_intractable(*self.args) + return f._eval_as_leading_term(x, logx=logx, cdir=cdir) + return super()._eval_as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + x0 = self.args[0].limit(x, 0) + if x0.is_zero: + f = self._eval_rewrite_as_intractable(*self.args) + return f._eval_nseries(x, n, logx) + return super()._eval_nseries(x, n, logx) diff --git a/lib/python3.11/site-packages/sympy/functions/special/gamma_functions.py b/lib/python3.11/site-packages/sympy/functions/special/gamma_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..ab47a59116f4272ef140a5951894ca952c5c066e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/gamma_functions.py @@ -0,0 +1,1344 @@ +from math import prod + +from sympy.core import Add, S, Dummy, expand_func +from sympy.core.expr import Expr +from sympy.core.function import Function, ArgumentIndexError, PoleError +from sympy.core.logic import fuzzy_and, fuzzy_not +from sympy.core.numbers import Rational, pi, oo, I +from sympy.core.power import Pow +from sympy.functions.special.zeta_functions import zeta +from sympy.functions.special.error_functions import erf, erfc, Ei +from sympy.functions.elementary.complexes import re, unpolarify +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.integers import ceiling, floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin, cos, cot +from sympy.functions.combinatorial.numbers import bernoulli, harmonic +from sympy.functions.combinatorial.factorials import factorial, rf, RisingFactorial +from sympy.utilities.misc import as_int + +from mpmath import mp, workprec +from mpmath.libmp.libmpf import prec_to_dps + +def intlike(n): + try: + as_int(n, strict=False) + return True + except ValueError: + return False + +############################################################################### +############################ COMPLETE GAMMA FUNCTION ########################## +############################################################################### + +class gamma(Function): + r""" + The gamma function + + .. math:: + \Gamma(x) := \int^{\infty}_{0} t^{x-1} e^{-t} \mathrm{d}t. + + Explanation + =========== + + The ``gamma`` function implements the function which passes through the + values of the factorial function (i.e., $\Gamma(n) = (n - 1)!$ when n is + an integer). More generally, $\Gamma(z)$ is defined in the whole complex + plane except at the negative integers where there are simple poles. + + Examples + ======== + + >>> from sympy import S, I, pi, gamma + >>> from sympy.abc import x + + Several special values are known: + + >>> gamma(1) + 1 + >>> gamma(4) + 6 + >>> gamma(S(3)/2) + sqrt(pi)/2 + + The ``gamma`` function obeys the mirror symmetry: + + >>> from sympy import conjugate + >>> conjugate(gamma(x)) + gamma(conjugate(x)) + + Differentiation with respect to $x$ is supported: + + >>> from sympy import diff + >>> diff(gamma(x), x) + gamma(x)*polygamma(0, x) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(gamma(x), x, 0, 3) + 1/x - EulerGamma + x*(EulerGamma**2/2 + pi**2/12) + x**2*(-EulerGamma*pi**2/12 - zeta(3)/3 - EulerGamma**3/6) + O(x**3) + + We can numerically evaluate the ``gamma`` function to arbitrary precision + on the whole complex plane: + + >>> gamma(pi).evalf(40) + 2.288037795340032417959588909060233922890 + >>> gamma(1+I).evalf(20) + 0.49801566811835604271 - 0.15494982830181068512*I + + See Also + ======== + + lowergamma: Lower incomplete gamma function. + uppergamma: Upper incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gamma_function + .. [2] https://dlmf.nist.gov/5 + .. [3] https://mathworld.wolfram.com/GammaFunction.html + .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma/ + + """ + + unbranched = True + _singularities = (S.ComplexInfinity,) + + def fdiff(self, argindex=1): + if argindex == 1: + return self.func(self.args[0])*polygamma(0, self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, arg): + if arg.is_Number: + if arg is S.NaN: + return S.NaN + elif arg is oo: + return oo + elif intlike(arg): + if arg.is_positive: + return factorial(arg - 1) + else: + return S.ComplexInfinity + elif arg.is_Rational: + if arg.q == 2: + n = abs(arg.p) // arg.q + + if arg.is_positive: + k, coeff = n, S.One + else: + n = k = n + 1 + + if n & 1 == 0: + coeff = S.One + else: + coeff = S.NegativeOne + + coeff *= prod(range(3, 2*k, 2)) + + if arg.is_positive: + return coeff*sqrt(pi) / 2**n + else: + return 2**n*sqrt(pi) / coeff + + def _eval_expand_func(self, **hints): + arg = self.args[0] + if arg.is_Rational: + if abs(arg.p) > arg.q: + x = Dummy('x') + n = arg.p // arg.q + p = arg.p - n*arg.q + return self.func(x + n)._eval_expand_func().subs(x, Rational(p, arg.q)) + + if arg.is_Add: + coeff, tail = arg.as_coeff_add() + if coeff and coeff.q != 1: + intpart = floor(coeff) + tail = (coeff - intpart,) + tail + coeff = intpart + tail = arg._new_rawargs(*tail, reeval=False) + return self.func(tail)*RisingFactorial(tail, coeff) + + return self.func(*self.args) + + def _eval_conjugate(self): + return self.func(self.args[0].conjugate()) + + def _eval_is_real(self): + x = self.args[0] + if x.is_nonpositive and x.is_integer: + return False + if intlike(x) and x <= 0: + return False + if x.is_positive or x.is_noninteger: + return True + + def _eval_is_positive(self): + x = self.args[0] + if x.is_positive: + return True + elif x.is_noninteger: + return floor(x).is_even + + def _eval_rewrite_as_tractable(self, z, limitvar=None, **kwargs): + return exp(loggamma(z)) + + def _eval_rewrite_as_factorial(self, z, **kwargs): + return factorial(z - 1) + + def _eval_nseries(self, x, n, logx, cdir=0): + x0 = self.args[0].limit(x, 0) + if not (x0.is_Integer and x0 <= 0): + return super()._eval_nseries(x, n, logx) + t = self.args[0] - x0 + return (self.func(t + 1)/rf(self.args[0], -x0 + 1))._eval_nseries(x, n, logx) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[0] + x0 = arg.subs(x, 0) + + if x0.is_integer and x0.is_nonpositive: + n = -x0 + res = S.NegativeOne**n/self.func(n + 1) + return res/(arg + n).as_leading_term(x) + elif not x0.is_infinite: + return self.func(x0) + raise PoleError() + + +############################################################################### +################## LOWER and UPPER INCOMPLETE GAMMA FUNCTIONS ################# +############################################################################### + +class lowergamma(Function): + r""" + The lower incomplete gamma function. + + Explanation + =========== + + It can be defined as the meromorphic continuation of + + .. math:: + \gamma(s, x) := \int_0^x t^{s-1} e^{-t} \mathrm{d}t = \Gamma(s) - \Gamma(s, x). + + This can be shown to be the same as + + .. math:: + \gamma(s, x) = \frac{x^s}{s} {}_1F_1\left({s \atop s+1} \middle| -x\right), + + where ${}_1F_1$ is the (confluent) hypergeometric function. + + Examples + ======== + + >>> from sympy import lowergamma, S + >>> from sympy.abc import s, x + >>> lowergamma(s, x) + lowergamma(s, x) + >>> lowergamma(3, x) + -2*(x**2/2 + x + 1)*exp(-x) + 2 + >>> lowergamma(-S(1)/2, x) + -2*sqrt(pi)*erf(sqrt(x)) - 2*exp(-x)/sqrt(x) + + See Also + ======== + + gamma: Gamma function. + uppergamma: Upper incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_gamma_function + .. [2] Abramowitz, Milton; Stegun, Irene A., eds. (1965), Chapter 6, + Section 5, Handbook of Mathematical Functions with Formulas, Graphs, + and Mathematical Tables + .. [3] https://dlmf.nist.gov/8 + .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma2/ + .. [5] https://functions.wolfram.com/GammaBetaErf/Gamma3/ + + """ + + + def fdiff(self, argindex=2): + from sympy.functions.special.hyper import meijerg + if argindex == 2: + a, z = self.args + return exp(-unpolarify(z))*z**(a - 1) + elif argindex == 1: + a, z = self.args + return gamma(a)*digamma(a) - log(z)*uppergamma(a, z) \ + - meijerg([], [1, 1], [0, 0, a], [], z) + + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, a, x): + # For lack of a better place, we use this one to extract branching + # information. The following can be + # found in the literature (c/f references given above), albeit scattered: + # 1) For fixed x != 0, lowergamma(s, x) is an entire function of s + # 2) For fixed positive integers s, lowergamma(s, x) is an entire + # function of x. + # 3) For fixed non-positive integers s, + # lowergamma(s, exp(I*2*pi*n)*x) = + # 2*pi*I*n*(-1)**(-s)/factorial(-s) + lowergamma(s, x) + # (this follows from lowergamma(s, x).diff(x) = x**(s-1)*exp(-x)). + # 4) For fixed non-integral s, + # lowergamma(s, x) = x**s*gamma(s)*lowergamma_unbranched(s, x), + # where lowergamma_unbranched(s, x) is an entire function (in fact + # of both s and x), i.e. + # lowergamma(s, exp(2*I*pi*n)*x) = exp(2*pi*I*n*a)*lowergamma(a, x) + if x is S.Zero: + return S.Zero + nx, n = x.extract_branch_factor() + if a.is_integer and a.is_positive: + nx = unpolarify(x) + if nx != x: + return lowergamma(a, nx) + elif a.is_integer and a.is_nonpositive: + if n != 0: + return 2*pi*I*n*S.NegativeOne**(-a)/factorial(-a) + lowergamma(a, nx) + elif n != 0: + return exp(2*pi*I*n*a)*lowergamma(a, nx) + + # Special values. + if a.is_Number: + if a is S.One: + return S.One - exp(-x) + elif a is S.Half: + return sqrt(pi)*erf(sqrt(x)) + elif a.is_Integer or (2*a).is_Integer: + b = a - 1 + if b.is_positive: + if a.is_integer: + return factorial(b) - exp(-x) * factorial(b) * Add(*[x ** k / factorial(k) for k in range(a)]) + else: + return gamma(a)*(lowergamma(S.Half, x)/sqrt(pi) - exp(-x)*Add(*[x**(k - S.Half)/gamma(S.Half + k) for k in range(1, a + S.Half)])) + + if not a.is_Integer: + return S.NegativeOne**(S.Half - a)*pi*erf(sqrt(x))/gamma(1 - a) + exp(-x)*Add(*[x**(k + a - 1)*gamma(a)/gamma(a + k) for k in range(1, Rational(3, 2) - a)]) + + if x.is_zero: + return S.Zero + + def _eval_evalf(self, prec): + if all(x.is_number for x in self.args): + a = self.args[0]._to_mpmath(prec) + z = self.args[1]._to_mpmath(prec) + with workprec(prec): + res = mp.gammainc(a, 0, z) + return Expr._from_mpmath(res, prec) + else: + return self + + def _eval_conjugate(self): + x = self.args[1] + if x not in (S.Zero, S.NegativeInfinity): + return self.func(self.args[0].conjugate(), x.conjugate()) + + def _eval_is_meromorphic(self, x, a): + # By https://en.wikipedia.org/wiki/Incomplete_gamma_function#Holomorphic_extension, + # lowergamma(s, z) = z**s*gamma(s)*gammastar(s, z), + # where gammastar(s, z) is holomorphic for all s and z. + # Hence the singularities of lowergamma are z = 0 (branch + # point) and nonpositive integer values of s (poles of gamma(s)). + s, z = self.args + args_merom = fuzzy_and([z._eval_is_meromorphic(x, a), + s._eval_is_meromorphic(x, a)]) + if not args_merom: + return args_merom + z0 = z.subs(x, a) + if s.is_integer: + return fuzzy_and([s.is_positive, z0.is_finite]) + s0 = s.subs(x, a) + return fuzzy_and([s0.is_finite, z0.is_finite, fuzzy_not(z0.is_zero)]) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import O + s, z = self.args + if args0[0] is oo and not z.has(x): + coeff = z**s*exp(-z) + sum_expr = sum(z**k/rf(s, k + 1) for k in range(n - 1)) + o = O(z**s*s**(-n)) + return coeff*sum_expr + o + return super()._eval_aseries(n, args0, x, logx) + + def _eval_rewrite_as_uppergamma(self, s, x, **kwargs): + return gamma(s) - uppergamma(s, x) + + def _eval_rewrite_as_expint(self, s, x, **kwargs): + from sympy.functions.special.error_functions import expint + if s.is_integer and s.is_nonpositive: + return self + return self.rewrite(uppergamma).rewrite(expint) + + def _eval_is_zero(self): + x = self.args[1] + if x.is_zero: + return True + + +class uppergamma(Function): + r""" + The upper incomplete gamma function. + + Explanation + =========== + + It can be defined as the meromorphic continuation of + + .. math:: + \Gamma(s, x) := \int_x^\infty t^{s-1} e^{-t} \mathrm{d}t = \Gamma(s) - \gamma(s, x). + + where $\gamma(s, x)$ is the lower incomplete gamma function, + :class:`lowergamma`. This can be shown to be the same as + + .. math:: + \Gamma(s, x) = \Gamma(s) - \frac{x^s}{s} {}_1F_1\left({s \atop s+1} \middle| -x\right), + + where ${}_1F_1$ is the (confluent) hypergeometric function. + + The upper incomplete gamma function is also essentially equivalent to the + generalized exponential integral: + + .. math:: + \operatorname{E}_{n}(x) = \int_{1}^{\infty}{\frac{e^{-xt}}{t^n} \, dt} = x^{n-1}\Gamma(1-n,x). + + Examples + ======== + + >>> from sympy import uppergamma, S + >>> from sympy.abc import s, x + >>> uppergamma(s, x) + uppergamma(s, x) + >>> uppergamma(3, x) + 2*(x**2/2 + x + 1)*exp(-x) + >>> uppergamma(-S(1)/2, x) + -2*sqrt(pi)*erfc(sqrt(x)) + 2*exp(-x)/sqrt(x) + >>> uppergamma(-2, x) + expint(3, x)/x**2 + + See Also + ======== + + gamma: Gamma function. + lowergamma: Lower incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Incomplete_gamma_function#Upper_incomplete_gamma_function + .. [2] Abramowitz, Milton; Stegun, Irene A., eds. (1965), Chapter 6, + Section 5, Handbook of Mathematical Functions with Formulas, Graphs, + and Mathematical Tables + .. [3] https://dlmf.nist.gov/8 + .. [4] https://functions.wolfram.com/GammaBetaErf/Gamma2/ + .. [5] https://functions.wolfram.com/GammaBetaErf/Gamma3/ + .. [6] https://en.wikipedia.org/wiki/Exponential_integral#Relation_with_other_functions + + """ + + + def fdiff(self, argindex=2): + from sympy.functions.special.hyper import meijerg + if argindex == 2: + a, z = self.args + return -exp(-unpolarify(z))*z**(a - 1) + elif argindex == 1: + a, z = self.args + return uppergamma(a, z)*log(z) + meijerg([], [1, 1], [0, 0, a], [], z) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_evalf(self, prec): + if all(x.is_number for x in self.args): + a = self.args[0]._to_mpmath(prec) + z = self.args[1]._to_mpmath(prec) + with workprec(prec): + res = mp.gammainc(a, z, mp.inf) + return Expr._from_mpmath(res, prec) + return self + + @classmethod + def eval(cls, a, z): + from sympy.functions.special.error_functions import expint + if z.is_Number: + if z is S.NaN: + return S.NaN + elif z is oo: + return S.Zero + elif z.is_zero: + if re(a).is_positive: + return gamma(a) + + # We extract branching information here. C/f lowergamma. + nx, n = z.extract_branch_factor() + if a.is_integer and a.is_positive: + nx = unpolarify(z) + if z != nx: + return uppergamma(a, nx) + elif a.is_integer and a.is_nonpositive: + if n != 0: + return -2*pi*I*n*S.NegativeOne**(-a)/factorial(-a) + uppergamma(a, nx) + elif n != 0: + return gamma(a)*(1 - exp(2*pi*I*n*a)) + exp(2*pi*I*n*a)*uppergamma(a, nx) + + # Special values. + if a.is_Number: + if a is S.Zero and z.is_positive: + return -Ei(-z) + elif a is S.One: + return exp(-z) + elif a is S.Half: + return sqrt(pi)*erfc(sqrt(z)) + elif a.is_Integer or (2*a).is_Integer: + b = a - 1 + if b.is_positive: + if a.is_integer: + return exp(-z) * factorial(b) * Add(*[z**k / factorial(k) + for k in range(a)]) + else: + return (gamma(a) * erfc(sqrt(z)) + + S.NegativeOne**(a - S(3)/2) * exp(-z) * sqrt(z) + * Add(*[gamma(-S.Half - k) * (-z)**k / gamma(1-a) + for k in range(a - S.Half)])) + elif b.is_Integer: + return expint(-b, z)*unpolarify(z)**(b + 1) + + if not a.is_Integer: + return (S.NegativeOne**(S.Half - a) * pi*erfc(sqrt(z))/gamma(1-a) + - z**a * exp(-z) * Add(*[z**k * gamma(a) / gamma(a+k+1) + for k in range(S.Half - a)])) + + if a.is_zero and z.is_positive: + return -Ei(-z) + + if z.is_zero and re(a).is_positive: + return gamma(a) + + def _eval_conjugate(self): + z = self.args[1] + if z not in (S.Zero, S.NegativeInfinity): + return self.func(self.args[0].conjugate(), z.conjugate()) + + def _eval_is_meromorphic(self, x, a): + return lowergamma._eval_is_meromorphic(self, x, a) + + def _eval_rewrite_as_lowergamma(self, s, x, **kwargs): + return gamma(s) - lowergamma(s, x) + + def _eval_rewrite_as_tractable(self, s, x, **kwargs): + return exp(loggamma(s)) - lowergamma(s, x) + + def _eval_rewrite_as_expint(self, s, x, **kwargs): + from sympy.functions.special.error_functions import expint + return expint(1 - s, x)*x**s + + +############################################################################### +###################### POLYGAMMA and LOGGAMMA FUNCTIONS ####################### +############################################################################### + +class polygamma(Function): + r""" + The function ``polygamma(n, z)`` returns ``log(gamma(z)).diff(n + 1)``. + + Explanation + =========== + + It is a meromorphic function on $\mathbb{C}$ and defined as the $(n+1)$-th + derivative of the logarithm of the gamma function: + + .. math:: + \psi^{(n)} (z) := \frac{\mathrm{d}^{n+1}}{\mathrm{d} z^{n+1}} \log\Gamma(z). + + For `n` not a nonnegative integer the generalization by Espinosa and Moll [5]_ + is used: + + .. math:: \psi(s,z) = \frac{\zeta'(s+1, z) + (\gamma + \psi(-s)) \zeta(s+1, z)} + {\Gamma(-s)} + + Examples + ======== + + Several special values are known: + + >>> from sympy import S, polygamma + >>> polygamma(0, 1) + -EulerGamma + >>> polygamma(0, 1/S(2)) + -2*log(2) - EulerGamma + >>> polygamma(0, 1/S(3)) + -log(3) - sqrt(3)*pi/6 - EulerGamma - log(sqrt(3)) + >>> polygamma(0, 1/S(4)) + -pi/2 - log(4) - log(2) - EulerGamma + >>> polygamma(0, 2) + 1 - EulerGamma + >>> polygamma(0, 23) + 19093197/5173168 - EulerGamma + + >>> from sympy import oo, I + >>> polygamma(0, oo) + oo + >>> polygamma(0, -oo) + oo + >>> polygamma(0, I*oo) + oo + >>> polygamma(0, -I*oo) + oo + + Differentiation with respect to $x$ is supported: + + >>> from sympy import Symbol, diff + >>> x = Symbol("x") + >>> diff(polygamma(0, x), x) + polygamma(1, x) + >>> diff(polygamma(0, x), x, 2) + polygamma(2, x) + >>> diff(polygamma(0, x), x, 3) + polygamma(3, x) + >>> diff(polygamma(1, x), x) + polygamma(2, x) + >>> diff(polygamma(1, x), x, 2) + polygamma(3, x) + >>> diff(polygamma(2, x), x) + polygamma(3, x) + >>> diff(polygamma(2, x), x, 2) + polygamma(4, x) + + >>> n = Symbol("n") + >>> diff(polygamma(n, x), x) + polygamma(n + 1, x) + >>> diff(polygamma(n, x), x, 2) + polygamma(n + 2, x) + + We can rewrite ``polygamma`` functions in terms of harmonic numbers: + + >>> from sympy import harmonic + >>> polygamma(0, x).rewrite(harmonic) + harmonic(x - 1) - EulerGamma + >>> polygamma(2, x).rewrite(harmonic) + 2*harmonic(x - 1, 3) - 2*zeta(3) + >>> ni = Symbol("n", integer=True) + >>> polygamma(ni, x).rewrite(harmonic) + (-1)**(n + 1)*(-harmonic(x - 1, n + 1) + zeta(n + 1))*factorial(n) + + See Also + ======== + + gamma: Gamma function. + lowergamma: Lower incomplete gamma function. + uppergamma: Upper incomplete gamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Polygamma_function + .. [2] https://mathworld.wolfram.com/PolygammaFunction.html + .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma/ + .. [4] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/ + .. [5] O. Espinosa and V. Moll, "A generalized polygamma function", + *Integral Transforms and Special Functions* (2004), 101-115. + + """ + + @classmethod + def eval(cls, n, z): + if n is S.NaN or z is S.NaN: + return S.NaN + elif z is oo: + return oo if n.is_zero else S.Zero + elif z.is_Integer and z.is_nonpositive: + return S.ComplexInfinity + elif n is S.NegativeOne: + return loggamma(z) - log(2*pi) / 2 + elif n.is_zero: + if z is -oo or z.extract_multiplicatively(I) in (oo, -oo): + return oo + elif z.is_Integer: + return harmonic(z-1) - S.EulerGamma + elif z.is_Rational: + # TODO n == 1 also can do some rational z + p, q = z.as_numer_denom() + # only expand for small denominators to avoid creating long expressions + if q <= 6: + return expand_func(polygamma(S.Zero, z, evaluate=False)) + elif n.is_integer and n.is_nonnegative: + nz = unpolarify(z) + if z != nz: + return polygamma(n, nz) + if z.is_Integer: + return S.NegativeOne**(n+1) * factorial(n) * zeta(n+1, z) + elif z is S.Half: + return S.NegativeOne**(n+1) * factorial(n) * (2**(n+1)-1) * zeta(n+1) + + def _eval_is_real(self): + if self.args[0].is_positive and self.args[1].is_positive: + return True + + def _eval_is_complex(self): + z = self.args[1] + is_negative_integer = fuzzy_and([z.is_negative, z.is_integer]) + return fuzzy_and([z.is_complex, fuzzy_not(is_negative_integer)]) + + def _eval_is_positive(self): + n, z = self.args + if n.is_positive: + if n.is_odd and z.is_real: + return True + if n.is_even and z.is_positive: + return False + + def _eval_is_negative(self): + n, z = self.args + if n.is_positive: + if n.is_even and z.is_positive: + return True + if n.is_odd and z.is_real: + return False + + def _eval_expand_func(self, **hints): + n, z = self.args + + if n.is_Integer and n.is_nonnegative: + if z.is_Add: + coeff = z.args[0] + if coeff.is_Integer: + e = -(n + 1) + if coeff > 0: + tail = Add(*[Pow( + z - i, e) for i in range(1, int(coeff) + 1)]) + else: + tail = -Add(*[Pow( + z + i, e) for i in range(int(-coeff))]) + return polygamma(n, z - coeff) + S.NegativeOne**n*factorial(n)*tail + + elif z.is_Mul: + coeff, z = z.as_two_terms() + if coeff.is_Integer and coeff.is_positive: + tail = [polygamma(n, z + Rational( + i, coeff)) for i in range(int(coeff))] + if n == 0: + return Add(*tail)/coeff + log(coeff) + else: + return Add(*tail)/coeff**(n + 1) + z *= coeff + + if n == 0 and z.is_Rational: + p, q = z.as_numer_denom() + + # Reference: + # Values of the polygamma functions at rational arguments, J. Choi, 2007 + part_1 = -S.EulerGamma - pi * cot(p * pi / q) / 2 - log(q) + Add( + *[cos(2 * k * pi * p / q) * log(2 * sin(k * pi / q)) for k in range(1, q)]) + + if z > 0: + n = floor(z) + z0 = z - n + return part_1 + Add(*[1 / (z0 + k) for k in range(n)]) + elif z < 0: + n = floor(1 - z) + z0 = z + n + return part_1 - Add(*[1 / (z0 - 1 - k) for k in range(n)]) + + if n == -1: + return loggamma(z) - log(2*pi) / 2 + if n.is_integer is False or n.is_nonnegative is False: + s = Dummy("s") + dzt = zeta(s, z).diff(s).subs(s, n+1) + return (dzt + (S.EulerGamma + digamma(-n)) * zeta(n+1, z)) / gamma(-n) + + return polygamma(n, z) + + def _eval_rewrite_as_zeta(self, n, z, **kwargs): + if n.is_integer and n.is_positive: + return S.NegativeOne**(n + 1)*factorial(n)*zeta(n + 1, z) + + def _eval_rewrite_as_harmonic(self, n, z, **kwargs): + if n.is_integer: + if n.is_zero: + return harmonic(z - 1) - S.EulerGamma + else: + return S.NegativeOne**(n+1) * factorial(n) * (zeta(n+1) - harmonic(z-1, n+1)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.series.order import Order + n, z = [a.as_leading_term(x) for a in self.args] + o = Order(z, x) + if n == 0 and o.contains(1/x): + logx = log(x) if logx is None else logx + return o.getn() * logx + else: + return self.func(n, z) + + def fdiff(self, argindex=2): + if argindex == 2: + n, z = self.args[:2] + return polygamma(n + 1, z) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + if args0[1] != oo or not \ + (self.args[0].is_Integer and self.args[0].is_nonnegative): + return super()._eval_aseries(n, args0, x, logx) + z = self.args[1] + N = self.args[0] + + if N == 0: + # digamma function series + # Abramowitz & Stegun, p. 259, 6.3.18 + r = log(z) - 1/(2*z) + o = None + if n < 2: + o = Order(1/z, x) + else: + m = ceiling((n + 1)//2) + l = [bernoulli(2*k) / (2*k*z**(2*k)) for k in range(1, m)] + r -= Add(*l) + o = Order(1/z**n, x) + return r._eval_nseries(x, n, logx) + o + else: + # proper polygamma function + # Abramowitz & Stegun, p. 260, 6.4.10 + # We return terms to order higher than O(x**n) on purpose + # -- otherwise we would not be able to return any terms for + # quite a long time! + fac = gamma(N) + e0 = fac + N*fac/(2*z) + m = ceiling((n + 1)//2) + for k in range(1, m): + fac = fac*(2*k + N - 1)*(2*k + N - 2) / ((2*k)*(2*k - 1)) + e0 += bernoulli(2*k)*fac/z**(2*k) + o = Order(1/z**(2*m), x) + if n == 0: + o = Order(1/z, x) + elif n == 1: + o = Order(1/z**2, x) + r = e0._eval_nseries(z, n, logx) + o + return (-1 * (-1/z)**N * r)._eval_nseries(x, n, logx) + + def _eval_evalf(self, prec): + if not all(i.is_number for i in self.args): + return + s = self.args[0]._to_mpmath(prec+12) + z = self.args[1]._to_mpmath(prec+12) + if mp.isint(z) and z <= 0: + return S.ComplexInfinity + with workprec(prec+12): + if mp.isint(s) and s >= 0: + res = mp.polygamma(s, z) + else: + zt = mp.zeta(s+1, z) + dzt = mp.zeta(s+1, z, 1) + res = (dzt + (mp.euler + mp.digamma(-s)) * zt) * mp.rgamma(-s) + return Expr._from_mpmath(res, prec) + + +class loggamma(Function): + r""" + The ``loggamma`` function implements the logarithm of the + gamma function (i.e., $\log\Gamma(x)$). + + Examples + ======== + + Several special values are known. For numerical integral + arguments we have: + + >>> from sympy import loggamma + >>> loggamma(-2) + oo + >>> loggamma(0) + oo + >>> loggamma(1) + 0 + >>> loggamma(2) + 0 + >>> loggamma(3) + log(2) + + And for symbolic values: + + >>> from sympy import Symbol + >>> n = Symbol("n", integer=True, positive=True) + >>> loggamma(n) + log(gamma(n)) + >>> loggamma(-n) + oo + + For half-integral values: + + >>> from sympy import S + >>> loggamma(S(5)/2) + log(3*sqrt(pi)/4) + >>> loggamma(n/2) + log(2**(1 - n)*sqrt(pi)*gamma(n)/gamma(n/2 + 1/2)) + + And general rational arguments: + + >>> from sympy import expand_func + >>> L = loggamma(S(16)/3) + >>> expand_func(L).doit() + -5*log(3) + loggamma(1/3) + log(4) + log(7) + log(10) + log(13) + >>> L = loggamma(S(19)/4) + >>> expand_func(L).doit() + -4*log(4) + loggamma(3/4) + log(3) + log(7) + log(11) + log(15) + >>> L = loggamma(S(23)/7) + >>> expand_func(L).doit() + -3*log(7) + log(2) + loggamma(2/7) + log(9) + log(16) + + The ``loggamma`` function has the following limits towards infinity: + + >>> from sympy import oo + >>> loggamma(oo) + oo + >>> loggamma(-oo) + zoo + + The ``loggamma`` function obeys the mirror symmetry + if $x \in \mathbb{C} \setminus \{-\infty, 0\}$: + + >>> from sympy.abc import x + >>> from sympy import conjugate + >>> conjugate(loggamma(x)) + loggamma(conjugate(x)) + + Differentiation with respect to $x$ is supported: + + >>> from sympy import diff + >>> diff(loggamma(x), x) + polygamma(0, x) + + Series expansion is also supported: + + >>> from sympy import series + >>> series(loggamma(x), x, 0, 4).cancel() + -log(x) - EulerGamma*x + pi**2*x**2/12 - x**3*zeta(3)/3 + O(x**4) + + We can numerically evaluate the ``loggamma`` function + to arbitrary precision on the whole complex plane: + + >>> from sympy import I + >>> loggamma(5).evalf(30) + 3.17805383034794561964694160130 + >>> loggamma(I).evalf(20) + -0.65092319930185633889 - 1.8724366472624298171*I + + See Also + ======== + + gamma: Gamma function. + lowergamma: Lower incomplete gamma function. + uppergamma: Upper incomplete gamma function. + polygamma: Polygamma function. + digamma: Digamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gamma_function + .. [2] https://dlmf.nist.gov/5 + .. [3] https://mathworld.wolfram.com/LogGammaFunction.html + .. [4] https://functions.wolfram.com/GammaBetaErf/LogGamma/ + + """ + @classmethod + def eval(cls, z): + if z.is_integer: + if z.is_nonpositive: + return oo + elif z.is_positive: + return log(gamma(z)) + elif z.is_rational: + p, q = z.as_numer_denom() + # Half-integral values: + if p.is_positive and q == 2: + return log(sqrt(pi) * 2**(1 - p) * gamma(p) / gamma((p + 1)*S.Half)) + + if z is oo: + return oo + elif abs(z) is oo: + return S.ComplexInfinity + if z is S.NaN: + return S.NaN + + def _eval_expand_func(self, **hints): + from sympy.concrete.summations import Sum + z = self.args[0] + + if z.is_Rational: + p, q = z.as_numer_denom() + # General rational arguments (u + p/q) + # Split z as n + p/q with p < q + n = p // q + p = p - n*q + if p.is_positive and q.is_positive and p < q: + k = Dummy("k") + if n.is_positive: + return loggamma(p / q) - n*log(q) + Sum(log((k - 1)*q + p), (k, 1, n)) + elif n.is_negative: + return loggamma(p / q) - n*log(q) + pi*I*n - Sum(log(k*q - p), (k, 1, -n)) + elif n.is_zero: + return loggamma(p / q) + + return self + + def _eval_nseries(self, x, n, logx=None, cdir=0): + x0 = self.args[0].limit(x, 0) + if x0.is_zero: + f = self._eval_rewrite_as_intractable(*self.args) + return f._eval_nseries(x, n, logx) + return super()._eval_nseries(x, n, logx) + + def _eval_aseries(self, n, args0, x, logx): + from sympy.series.order import Order + if args0[0] != oo: + return super()._eval_aseries(n, args0, x, logx) + z = self.args[0] + r = log(z)*(z - S.Half) - z + log(2*pi)/2 + l = [bernoulli(2*k) / (2*k*(2*k - 1)*z**(2*k - 1)) for k in range(1, n)] + o = None + if n == 0: + o = Order(1, x) + else: + o = Order(1/z**n, x) + # It is very inefficient to first add the order and then do the nseries + return (r + Add(*l))._eval_nseries(x, n, logx) + o + + def _eval_rewrite_as_intractable(self, z, **kwargs): + return log(gamma(z)) + + def _eval_is_real(self): + z = self.args[0] + if z.is_positive: + return True + elif z.is_nonpositive: + return False + + def _eval_conjugate(self): + z = self.args[0] + if z not in (S.Zero, S.NegativeInfinity): + return self.func(z.conjugate()) + + def fdiff(self, argindex=1): + if argindex == 1: + return polygamma(0, self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + +class digamma(Function): + r""" + The ``digamma`` function is the first derivative of the ``loggamma`` + function + + .. math:: + \psi(x) := \frac{\mathrm{d}}{\mathrm{d} z} \log\Gamma(z) + = \frac{\Gamma'(z)}{\Gamma(z) }. + + In this case, ``digamma(z) = polygamma(0, z)``. + + Examples + ======== + + >>> from sympy import digamma + >>> digamma(0) + zoo + >>> from sympy import Symbol + >>> z = Symbol('z') + >>> digamma(z) + polygamma(0, z) + + To retain ``digamma`` as it is: + + >>> digamma(0, evaluate=False) + digamma(0) + >>> digamma(z, evaluate=False) + digamma(z) + + See Also + ======== + + gamma: Gamma function. + lowergamma: Lower incomplete gamma function. + uppergamma: Upper incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + trigamma: Trigamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Digamma_function + .. [2] https://mathworld.wolfram.com/DigammaFunction.html + .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/ + + """ + def _eval_evalf(self, prec): + z = self.args[0] + nprec = prec_to_dps(prec) + return polygamma(0, z).evalf(n=nprec) + + def fdiff(self, argindex=1): + z = self.args[0] + return polygamma(0, z).fdiff() + + def _eval_is_real(self): + z = self.args[0] + return polygamma(0, z).is_real + + def _eval_is_positive(self): + z = self.args[0] + return polygamma(0, z).is_positive + + def _eval_is_negative(self): + z = self.args[0] + return polygamma(0, z).is_negative + + def _eval_aseries(self, n, args0, x, logx): + as_polygamma = self.rewrite(polygamma) + args0 = [S.Zero,] + args0 + return as_polygamma._eval_aseries(n, args0, x, logx) + + @classmethod + def eval(cls, z): + return polygamma(0, z) + + def _eval_expand_func(self, **hints): + z = self.args[0] + return polygamma(0, z).expand(func=True) + + def _eval_rewrite_as_harmonic(self, z, **kwargs): + return harmonic(z - 1) - S.EulerGamma + + def _eval_rewrite_as_polygamma(self, z, **kwargs): + return polygamma(0, z) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + z = self.args[0] + return polygamma(0, z).as_leading_term(x) + + + +class trigamma(Function): + r""" + The ``trigamma`` function is the second derivative of the ``loggamma`` + function + + .. math:: + \psi^{(1)}(z) := \frac{\mathrm{d}^{2}}{\mathrm{d} z^{2}} \log\Gamma(z). + + In this case, ``trigamma(z) = polygamma(1, z)``. + + Examples + ======== + + >>> from sympy import trigamma + >>> trigamma(0) + zoo + >>> from sympy import Symbol + >>> z = Symbol('z') + >>> trigamma(z) + polygamma(1, z) + + To retain ``trigamma`` as it is: + + >>> trigamma(0, evaluate=False) + trigamma(0) + >>> trigamma(z, evaluate=False) + trigamma(z) + + + See Also + ======== + + gamma: Gamma function. + lowergamma: Lower incomplete gamma function. + uppergamma: Upper incomplete gamma function. + polygamma: Polygamma function. + loggamma: Log Gamma function. + digamma: Digamma function. + sympy.functions.special.beta_functions.beta: Euler Beta function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Trigamma_function + .. [2] https://mathworld.wolfram.com/TrigammaFunction.html + .. [3] https://functions.wolfram.com/GammaBetaErf/PolyGamma2/ + + """ + def _eval_evalf(self, prec): + z = self.args[0] + nprec = prec_to_dps(prec) + return polygamma(1, z).evalf(n=nprec) + + def fdiff(self, argindex=1): + z = self.args[0] + return polygamma(1, z).fdiff() + + def _eval_is_real(self): + z = self.args[0] + return polygamma(1, z).is_real + + def _eval_is_positive(self): + z = self.args[0] + return polygamma(1, z).is_positive + + def _eval_is_negative(self): + z = self.args[0] + return polygamma(1, z).is_negative + + def _eval_aseries(self, n, args0, x, logx): + as_polygamma = self.rewrite(polygamma) + args0 = [S.One,] + args0 + return as_polygamma._eval_aseries(n, args0, x, logx) + + @classmethod + def eval(cls, z): + return polygamma(1, z) + + def _eval_expand_func(self, **hints): + z = self.args[0] + return polygamma(1, z).expand(func=True) + + def _eval_rewrite_as_zeta(self, z, **kwargs): + return zeta(2, z) + + def _eval_rewrite_as_polygamma(self, z, **kwargs): + return polygamma(1, z) + + def _eval_rewrite_as_harmonic(self, z, **kwargs): + return -harmonic(z - 1, 2) + pi**2 / 6 + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + z = self.args[0] + return polygamma(1, z).as_leading_term(x) + + +############################################################################### +##################### COMPLETE MULTIVARIATE GAMMA FUNCTION #################### +############################################################################### + + +class multigamma(Function): + r""" + The multivariate gamma function is a generalization of the gamma function + + .. math:: + \Gamma_p(z) = \pi^{p(p-1)/4}\prod_{k=1}^p \Gamma[z + (1 - k)/2]. + + In a special case, ``multigamma(x, 1) = gamma(x)``. + + Examples + ======== + + >>> from sympy import S, multigamma + >>> from sympy import Symbol + >>> x = Symbol('x') + >>> p = Symbol('p', positive=True, integer=True) + + >>> multigamma(x, p) + pi**(p*(p - 1)/4)*Product(gamma(-_k/2 + x + 1/2), (_k, 1, p)) + + Several special values are known: + + >>> multigamma(1, 1) + 1 + >>> multigamma(4, 1) + 6 + >>> multigamma(S(3)/2, 1) + sqrt(pi)/2 + + Writing ``multigamma`` in terms of the ``gamma`` function: + + >>> multigamma(x, 1) + gamma(x) + + >>> multigamma(x, 2) + sqrt(pi)*gamma(x)*gamma(x - 1/2) + + >>> multigamma(x, 3) + pi**(3/2)*gamma(x)*gamma(x - 1)*gamma(x - 1/2) + + Parameters + ========== + + p : order or dimension of the multivariate gamma function + + See Also + ======== + + gamma, lowergamma, uppergamma, polygamma, loggamma, digamma, trigamma, + sympy.functions.special.beta_functions.beta + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Multivariate_gamma_function + + """ + unbranched = True + + def fdiff(self, argindex=2): + from sympy.concrete.summations import Sum + if argindex == 2: + x, p = self.args + k = Dummy("k") + return self.func(x, p)*Sum(polygamma(0, x + (1 - k)/2), (k, 1, p)) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, x, p): + from sympy.concrete.products import Product + if p.is_positive is False or p.is_integer is False: + raise ValueError('Order parameter p must be positive integer.') + k = Dummy("k") + return (pi**(p*(p - 1)/4)*Product(gamma(x + (1 - k)/2), + (k, 1, p))).doit() + + def _eval_conjugate(self): + x, p = self.args + return self.func(x.conjugate(), p) + + def _eval_is_real(self): + x, p = self.args + y = 2*x + if y.is_integer and (y <= (p - 1)) is True: + return False + if intlike(y) and (y <= (p - 1)): + return False + if y > (p - 1) or y.is_noninteger: + return True diff --git a/lib/python3.11/site-packages/sympy/functions/special/hyper.py b/lib/python3.11/site-packages/sympy/functions/special/hyper.py new file mode 100644 index 0000000000000000000000000000000000000000..4b1b3948ae4b74d6e28d54ba47b64533059cb06a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/hyper.py @@ -0,0 +1,1185 @@ +"""Hypergeometric and Meijer G-functions""" +from collections import Counter + +from sympy.core import S, Mod +from sympy.core.add import Add +from sympy.core.expr import Expr +from sympy.core.function import Function, Derivative, ArgumentIndexError + +from sympy.core.containers import Tuple +from sympy.core.mul import Mul +from sympy.core.numbers import I, pi, oo, zoo +from sympy.core.parameters import global_parameters +from sympy.core.relational import Ne +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import Dummy + +from sympy.external.gmpy import lcm +from sympy.functions import (sqrt, exp, log, sin, cos, asin, atan, + sinh, cosh, asinh, acosh, atanh, acoth) +from sympy.functions import factorial, RisingFactorial +from sympy.functions.elementary.complexes import Abs, re, unpolarify +from sympy.functions.elementary.exponential import exp_polar +from sympy.functions.elementary.integers import ceiling +from sympy.functions.elementary.piecewise import Piecewise +from sympy.logic.boolalg import (And, Or) +from sympy import ordered + + +class TupleArg(Tuple): + + # This method is only needed because hyper._eval_as_leading_term falls back + # (via super()) on using Function._eval_as_leading_term, which in turn + # calls as_leading_term on the args of the hyper. Ideally hyper should just + # have an _eval_as_leading_term method that handles all cases and this + # method should be removed because leading terms of tuples don't make + # sense. + def as_leading_term(self, *x, logx=None, cdir=0): + return TupleArg(*[f.as_leading_term(*x, logx=logx, cdir=cdir) for f in self.args]) + + def limit(self, x, xlim, dir='+'): + """ Compute limit x->xlim. + """ + from sympy.series.limits import limit + return TupleArg(*[limit(f, x, xlim, dir) for f in self.args]) + + +# TODO should __new__ accept **options? +# TODO should constructors should check if parameters are sensible? + + +def _prep_tuple(v): + """ + Turn an iterable argument *v* into a tuple and unpolarify, since both + hypergeometric and meijer g-functions are unbranched in their parameters. + + Examples + ======== + + >>> from sympy.functions.special.hyper import _prep_tuple + >>> _prep_tuple([1, 2, 3]) + (1, 2, 3) + >>> _prep_tuple((4, 5)) + (4, 5) + >>> _prep_tuple((7, 8, 9)) + (7, 8, 9) + + """ + return TupleArg(*[unpolarify(x) for x in v]) + + +class TupleParametersBase(Function): + """ Base class that takes care of differentiation, when some of + the arguments are actually tuples. """ + # This is not deduced automatically since there are Tuples as arguments. + is_commutative = True + + def _eval_derivative(self, s): + try: + res = 0 + if self.args[0].has(s) or self.args[1].has(s): + for i, p in enumerate(self._diffargs): + m = self._diffargs[i].diff(s) + if m != 0: + res += self.fdiff((1, i))*m + return res + self.fdiff(3)*self.args[2].diff(s) + except (ArgumentIndexError, NotImplementedError): + return Derivative(self, s) + + +class hyper(TupleParametersBase): + r""" + The generalized hypergeometric function is defined by a series where + the ratios of successive terms are a rational function of the summation + index. When convergent, it is continued analytically to the largest + possible domain. + + Explanation + =========== + + The hypergeometric function depends on two vectors of parameters, called + the numerator parameters $a_p$, and the denominator parameters + $b_q$. It also has an argument $z$. The series definition is + + .. math :: + {}_pF_q\left(\begin{matrix} a_1, \cdots, a_p \\ b_1, \cdots, b_q \end{matrix} + \middle| z \right) + = \sum_{n=0}^\infty \frac{(a_1)_n \cdots (a_p)_n}{(b_1)_n \cdots (b_q)_n} + \frac{z^n}{n!}, + + where $(a)_n = (a)(a+1)\cdots(a+n-1)$ denotes the rising factorial. + + If one of the $b_q$ is a non-positive integer then the series is + undefined unless one of the $a_p$ is a larger (i.e., smaller in + magnitude) non-positive integer. If none of the $b_q$ is a + non-positive integer and one of the $a_p$ is a non-positive + integer, then the series reduces to a polynomial. To simplify the + following discussion, we assume that none of the $a_p$ or + $b_q$ is a non-positive integer. For more details, see the + references. + + The series converges for all $z$ if $p \le q$, and thus + defines an entire single-valued function in this case. If $p = + q+1$ the series converges for $|z| < 1$, and can be continued + analytically into a half-plane. If $p > q+1$ the series is + divergent for all $z$. + + Please note the hypergeometric function constructor currently does *not* + check if the parameters actually yield a well-defined function. + + Examples + ======== + + The parameters $a_p$ and $b_q$ can be passed as arbitrary + iterables, for example: + + >>> from sympy import hyper + >>> from sympy.abc import x, n, a + >>> h = hyper((1, 2, 3), [3, 4], x); h + hyper((1, 2), (4,), x) + >>> hyper((3, 1, 2), [3, 4], x, evaluate=False) # don't remove duplicates + hyper((1, 2, 3), (3, 4), x) + + There is also pretty printing (it looks better using Unicode): + + >>> from sympy import pprint + >>> pprint(h, use_unicode=False) + _ + |_ /1, 2 | \ + | | | x| + 2 1 \ 4 | / + + The parameters must always be iterables, even if they are vectors of + length one or zero: + + >>> hyper((1, ), [], x) + hyper((1,), (), x) + + But of course they may be variables (but if they depend on $x$ then you + should not expect much implemented functionality): + + >>> hyper((n, a), (n**2,), x) + hyper((a, n), (n**2,), x) + + The hypergeometric function generalizes many named special functions. + The function ``hyperexpand()`` tries to express a hypergeometric function + using named special functions. For example: + + >>> from sympy import hyperexpand + >>> hyperexpand(hyper([], [], x)) + exp(x) + + You can also use ``expand_func()``: + + >>> from sympy import expand_func + >>> expand_func(x*hyper([1, 1], [2], -x)) + log(x + 1) + + More examples: + + >>> from sympy import S + >>> hyperexpand(hyper([], [S(1)/2], -x**2/4)) + cos(x) + >>> hyperexpand(x*hyper([S(1)/2, S(1)/2], [S(3)/2], x**2)) + asin(x) + + We can also sometimes ``hyperexpand()`` parametric functions: + + >>> from sympy.abc import a + >>> hyperexpand(hyper([-a], [], x)) + (1 - x)**a + + See Also + ======== + + sympy.simplify.hyperexpand + gamma + meijerg + + References + ========== + + .. [1] Luke, Y. L. (1969), The Special Functions and Their Approximations, + Volume 1 + .. [2] https://en.wikipedia.org/wiki/Generalized_hypergeometric_function + + """ + + + def __new__(cls, ap, bq, z, **kwargs): + # TODO should we check convergence conditions? + if kwargs.pop('evaluate', global_parameters.evaluate): + ca = Counter(Tuple(*ap)) + cb = Counter(Tuple(*bq)) + common = ca & cb + arg = ap, bq = [], [] + for i, c in enumerate((ca, cb)): + c -= common + for k in ordered(c): + arg[i].extend([k]*c[k]) + else: + ap = list(ordered(ap)) + bq = list(ordered(bq)) + return Function.__new__(cls, _prep_tuple(ap), _prep_tuple(bq), z, **kwargs) + + @classmethod + def eval(cls, ap, bq, z): + if len(ap) <= len(bq) or (len(ap) == len(bq) + 1 and (Abs(z) <= 1) == True): + nz = unpolarify(z) + if z != nz: + return hyper(ap, bq, nz) + + def fdiff(self, argindex=3): + if argindex != 3: + raise ArgumentIndexError(self, argindex) + nap = Tuple(*[a + 1 for a in self.ap]) + nbq = Tuple(*[b + 1 for b in self.bq]) + fac = Mul(*self.ap)/Mul(*self.bq) + return fac*hyper(nap, nbq, self.argument) + + def _eval_expand_func(self, **hints): + from sympy.functions.special.gamma_functions import gamma + from sympy.simplify.hyperexpand import hyperexpand + if len(self.ap) == 2 and len(self.bq) == 1 and self.argument == 1: + a, b = self.ap + c = self.bq[0] + return gamma(c)*gamma(c - a - b)/gamma(c - a)/gamma(c - b) + return hyperexpand(self) + + def _eval_rewrite_as_Sum(self, ap, bq, z, **kwargs): + from sympy.concrete.summations import Sum + n = Dummy("n", integer=True) + rfap = [RisingFactorial(a, n) for a in ap] + rfbq = [RisingFactorial(b, n) for b in bq] + coeff = Mul(*rfap) / Mul(*rfbq) + return Piecewise((Sum(coeff * z**n / factorial(n), (n, 0, oo)), + self.convergence_statement), (self, True)) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + arg = self.args[2] + x0 = arg.subs(x, 0) + if x0 is S.NaN: + x0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + + if x0 is S.Zero: + return S.One + return super()._eval_as_leading_term(x, logx=logx, cdir=cdir) + + def _eval_nseries(self, x, n, logx, cdir=0): + + from sympy.series.order import Order + + arg = self.args[2] + x0 = arg.limit(x, 0) + ap = self.args[0] + bq = self.args[1] + + if not (arg == x and x0 == 0): + # It would be better to do something with arg.nseries here, rather + # than falling back on Function._eval_nseries. The code below + # though is not sufficient if arg is something like x/(x+1). + from sympy.simplify.hyperexpand import hyperexpand + return hyperexpand(super()._eval_nseries(x, n, logx)) + + terms = [] + + for i in range(n): + num = Mul(*[RisingFactorial(a, i) for a in ap]) + den = Mul(*[RisingFactorial(b, i) for b in bq]) + terms.append(((num/den) * (arg**i)) / factorial(i)) + + return (Add(*terms) + Order(x**n,x)) + + @property + def argument(self): + """ Argument of the hypergeometric function. """ + return self.args[2] + + @property + def ap(self): + """ Numerator parameters of the hypergeometric function. """ + return Tuple(*self.args[0]) + + @property + def bq(self): + """ Denominator parameters of the hypergeometric function. """ + return Tuple(*self.args[1]) + + @property + def _diffargs(self): + return self.ap + self.bq + + @property + def eta(self): + """ A quantity related to the convergence of the series. """ + return sum(self.ap) - sum(self.bq) + + @property + def radius_of_convergence(self): + """ + Compute the radius of convergence of the defining series. + + Explanation + =========== + + Note that even if this is not ``oo``, the function may still be + evaluated outside of the radius of convergence by analytic + continuation. But if this is zero, then the function is not actually + defined anywhere else. + + Examples + ======== + + >>> from sympy import hyper + >>> from sympy.abc import z + >>> hyper((1, 2), [3], z).radius_of_convergence + 1 + >>> hyper((1, 2, 3), [4], z).radius_of_convergence + 0 + >>> hyper((1, 2), (3, 4), z).radius_of_convergence + oo + + """ + if any(a.is_integer and (a <= 0) == True for a in self.ap + self.bq): + aints = [a for a in self.ap if a.is_Integer and (a <= 0) == True] + bints = [a for a in self.bq if a.is_Integer and (a <= 0) == True] + if len(aints) < len(bints): + return S.Zero + popped = False + for b in bints: + cancelled = False + while aints: + a = aints.pop() + if a >= b: + cancelled = True + break + popped = True + if not cancelled: + return S.Zero + if aints or popped: + # There are still non-positive numerator parameters. + # This is a polynomial. + return oo + if len(self.ap) == len(self.bq) + 1: + return S.One + elif len(self.ap) <= len(self.bq): + return oo + else: + return S.Zero + + @property + def convergence_statement(self): + """ Return a condition on z under which the series converges. """ + R = self.radius_of_convergence + if R == 0: + return False + if R == oo: + return True + # The special functions and their approximations, page 44 + e = self.eta + z = self.argument + c1 = And(re(e) < 0, abs(z) <= 1) + c2 = And(0 <= re(e), re(e) < 1, abs(z) <= 1, Ne(z, 1)) + c3 = And(re(e) >= 1, abs(z) < 1) + return Or(c1, c2, c3) + + def _eval_simplify(self, **kwargs): + from sympy.simplify.hyperexpand import hyperexpand + return hyperexpand(self) + + +class meijerg(TupleParametersBase): + r""" + The Meijer G-function is defined by a Mellin-Barnes type integral that + resembles an inverse Mellin transform. It generalizes the hypergeometric + functions. + + Explanation + =========== + + The Meijer G-function depends on four sets of parameters. There are + "*numerator parameters*" + $a_1, \ldots, a_n$ and $a_{n+1}, \ldots, a_p$, and there are + "*denominator parameters*" + $b_1, \ldots, b_m$ and $b_{m+1}, \ldots, b_q$. + Confusingly, it is traditionally denoted as follows (note the position + of $m$, $n$, $p$, $q$, and how they relate to the lengths of the four + parameter vectors): + + .. math :: + G_{p,q}^{m,n} \left(\begin{matrix}a_1, \cdots, a_n & a_{n+1}, \cdots, a_p \\ + b_1, \cdots, b_m & b_{m+1}, \cdots, b_q + \end{matrix} \middle| z \right). + + However, in SymPy the four parameter vectors are always available + separately (see examples), so that there is no need to keep track of the + decorating sub- and super-scripts on the G symbol. + + The G function is defined as the following integral: + + .. math :: + \frac{1}{2 \pi i} \int_L \frac{\prod_{j=1}^m \Gamma(b_j - s) + \prod_{j=1}^n \Gamma(1 - a_j + s)}{\prod_{j=m+1}^q \Gamma(1- b_j +s) + \prod_{j=n+1}^p \Gamma(a_j - s)} z^s \mathrm{d}s, + + where $\Gamma(z)$ is the gamma function. There are three possible + contours which we will not describe in detail here (see the references). + If the integral converges along more than one of them, the definitions + agree. The contours all separate the poles of $\Gamma(1-a_j+s)$ + from the poles of $\Gamma(b_k-s)$, so in particular the G function + is undefined if $a_j - b_k \in \mathbb{Z}_{>0}$ for some + $j \le n$ and $k \le m$. + + The conditions under which one of the contours yields a convergent integral + are complicated and we do not state them here, see the references. + + Please note currently the Meijer G-function constructor does *not* check any + convergence conditions. + + Examples + ======== + + You can pass the parameters either as four separate vectors: + + >>> from sympy import meijerg, Tuple, pprint + >>> from sympy.abc import x, a + >>> pprint(meijerg((1, 2), (a, 4), (5,), [], x), use_unicode=False) + __1, 2 /1, 2 4, a | \ + /__ | | x| + \_|4, 1 \ 5 | / + + Or as two nested vectors: + + >>> pprint(meijerg([(1, 2), (3, 4)], ([5], Tuple()), x), use_unicode=False) + __1, 2 /1, 2 3, 4 | \ + /__ | | x| + \_|4, 1 \ 5 | / + + As with the hypergeometric function, the parameters may be passed as + arbitrary iterables. Vectors of length zero and one also have to be + passed as iterables. The parameters need not be constants, but if they + depend on the argument then not much implemented functionality should be + expected. + + All the subvectors of parameters are available: + + >>> from sympy import pprint + >>> g = meijerg([1], [2], [3], [4], x) + >>> pprint(g, use_unicode=False) + __1, 1 /1 2 | \ + /__ | | x| + \_|2, 2 \3 4 | / + >>> g.an + (1,) + >>> g.ap + (1, 2) + >>> g.aother + (2,) + >>> g.bm + (3,) + >>> g.bq + (3, 4) + >>> g.bother + (4,) + + The Meijer G-function generalizes the hypergeometric functions. + In some cases it can be expressed in terms of hypergeometric functions, + using Slater's theorem. For example: + + >>> from sympy import hyperexpand + >>> from sympy.abc import a, b, c + >>> hyperexpand(meijerg([a], [], [c], [b], x), allow_hyper=True) + x**c*gamma(-a + c + 1)*hyper((-a + c + 1,), + (-b + c + 1,), -x)/gamma(-b + c + 1) + + Thus the Meijer G-function also subsumes many named functions as special + cases. You can use ``expand_func()`` or ``hyperexpand()`` to (try to) + rewrite a Meijer G-function in terms of named special functions. For + example: + + >>> from sympy import expand_func, S + >>> expand_func(meijerg([[],[]], [[0],[]], -x)) + exp(x) + >>> hyperexpand(meijerg([[],[]], [[S(1)/2],[0]], (x/2)**2)) + sin(x)/sqrt(pi) + + See Also + ======== + + hyper + sympy.simplify.hyperexpand + + References + ========== + + .. [1] Luke, Y. L. (1969), The Special Functions and Their Approximations, + Volume 1 + .. [2] https://en.wikipedia.org/wiki/Meijer_G-function + + """ + + + def __new__(cls, *args, **kwargs): + if len(args) == 5: + args = [(args[0], args[1]), (args[2], args[3]), args[4]] + if len(args) != 3: + raise TypeError("args must be either as, as', bs, bs', z or " + "as, bs, z") + + def tr(p): + if len(p) != 2: + raise TypeError("wrong argument") + p = [list(ordered(i)) for i in p] + return TupleArg(_prep_tuple(p[0]), _prep_tuple(p[1])) + + arg0, arg1 = tr(args[0]), tr(args[1]) + if Tuple(arg0, arg1).has(oo, zoo, -oo): + raise ValueError("G-function parameters must be finite") + if any((a - b).is_Integer and a - b > 0 + for a in arg0[0] for b in arg1[0]): + raise ValueError("no parameter a1, ..., an may differ from " + "any b1, ..., bm by a positive integer") + + # TODO should we check convergence conditions? + return Function.__new__(cls, arg0, arg1, args[2], **kwargs) + + def fdiff(self, argindex=3): + if argindex != 3: + return self._diff_wrt_parameter(argindex[1]) + if len(self.an) >= 1: + a = list(self.an) + a[0] -= 1 + G = meijerg(a, self.aother, self.bm, self.bother, self.argument) + return 1/self.argument * ((self.an[0] - 1)*self + G) + elif len(self.bm) >= 1: + b = list(self.bm) + b[0] += 1 + G = meijerg(self.an, self.aother, b, self.bother, self.argument) + return 1/self.argument * (self.bm[0]*self - G) + else: + return S.Zero + + def _diff_wrt_parameter(self, idx): + # Differentiation wrt a parameter can only be done in very special + # cases. In particular, if we want to differentiate with respect to + # `a`, all other gamma factors have to reduce to rational functions. + # + # Let MT denote mellin transform. Suppose T(-s) is the gamma factor + # appearing in the definition of G. Then + # + # MT(log(z)G(z)) = d/ds T(s) = d/da T(s) + ... + # + # Thus d/da G(z) = log(z)G(z) - ... + # The ... can be evaluated as a G function under the above conditions, + # the formula being most easily derived by using + # + # d Gamma(s + n) Gamma(s + n) / 1 1 1 \ + # -- ------------ = ------------ | - + ---- + ... + --------- | + # ds Gamma(s) Gamma(s) \ s s + 1 s + n - 1 / + # + # which follows from the difference equation of the digamma function. + # (There is a similar equation for -n instead of +n). + + # We first figure out how to pair the parameters. + an = list(self.an) + ap = list(self.aother) + bm = list(self.bm) + bq = list(self.bother) + if idx < len(an): + an.pop(idx) + else: + idx -= len(an) + if idx < len(ap): + ap.pop(idx) + else: + idx -= len(ap) + if idx < len(bm): + bm.pop(idx) + else: + bq.pop(idx - len(bm)) + pairs1 = [] + pairs2 = [] + for l1, l2, pairs in [(an, bq, pairs1), (ap, bm, pairs2)]: + while l1: + x = l1.pop() + found = None + for i, y in enumerate(l2): + if not Mod((x - y).simplify(), 1): + found = i + break + if found is None: + raise NotImplementedError('Derivative not expressible ' + 'as G-function?') + y = l2[i] + l2.pop(i) + pairs.append((x, y)) + + # Now build the result. + res = log(self.argument)*self + + for a, b in pairs1: + sign = 1 + n = a - b + base = b + if n < 0: + sign = -1 + n = b - a + base = a + for k in range(n): + res -= sign*meijerg(self.an + (base + k + 1,), self.aother, + self.bm, self.bother + (base + k + 0,), + self.argument) + + for a, b in pairs2: + sign = 1 + n = b - a + base = a + if n < 0: + sign = -1 + n = a - b + base = b + for k in range(n): + res -= sign*meijerg(self.an, self.aother + (base + k + 1,), + self.bm + (base + k + 0,), self.bother, + self.argument) + + return res + + def get_period(self): + """ + Return a number $P$ such that $G(x*exp(I*P)) == G(x)$. + + Examples + ======== + + >>> from sympy import meijerg, pi, S + >>> from sympy.abc import z + + >>> meijerg([1], [], [], [], z).get_period() + 2*pi + >>> meijerg([pi], [], [], [], z).get_period() + oo + >>> meijerg([1, 2], [], [], [], z).get_period() + oo + >>> meijerg([1,1], [2], [1, S(1)/2, S(1)/3], [1], z).get_period() + 12*pi + + """ + # This follows from slater's theorem. + def compute(l): + # first check that no two differ by an integer + for i, b in enumerate(l): + if not b.is_Rational: + return oo + for j in range(i + 1, len(l)): + if not Mod((b - l[j]).simplify(), 1): + return oo + return lcm(*(x.q for x in l)) + beta = compute(self.bm) + alpha = compute(self.an) + p, q = len(self.ap), len(self.bq) + if p == q: + if oo in (alpha, beta): + return oo + return 2*pi*lcm(alpha, beta) + elif p < q: + return 2*pi*beta + else: + return 2*pi*alpha + + def _eval_expand_func(self, **hints): + from sympy.simplify.hyperexpand import hyperexpand + return hyperexpand(self) + + def _eval_evalf(self, prec): + # The default code is insufficient for polar arguments. + # mpmath provides an optional argument "r", which evaluates + # G(z**(1/r)). I am not sure what its intended use is, but we hijack it + # here in the following way: to evaluate at a number z of |argument| + # less than (say) n*pi, we put r=1/n, compute z' = root(z, n) + # (carefully so as not to loose the branch information), and evaluate + # G(z'**(1/r)) = G(z'**n) = G(z). + import mpmath + znum = self.argument._eval_evalf(prec) + if znum.has(exp_polar): + znum, branch = znum.as_coeff_mul(exp_polar) + if len(branch) != 1: + return + branch = branch[0].args[0]/I + else: + branch = S.Zero + n = ceiling(abs(branch/pi)) + 1 + znum = znum**(S.One/n)*exp(I*branch / n) + + # Convert all args to mpf or mpc + try: + [z, r, ap, bq] = [arg._to_mpmath(prec) + for arg in [znum, 1/n, self.args[0], self.args[1]]] + except ValueError: + return + + with mpmath.workprec(prec): + v = mpmath.meijerg(ap, bq, z, r) + + return Expr._from_mpmath(v, prec) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + from sympy.simplify.hyperexpand import hyperexpand + return hyperexpand(self).as_leading_term(x, logx=logx, cdir=cdir) + + def integrand(self, s): + """ Get the defining integrand D(s). """ + from sympy.functions.special.gamma_functions import gamma + return self.argument**s \ + * Mul(*(gamma(b - s) for b in self.bm)) \ + * Mul(*(gamma(1 - a + s) for a in self.an)) \ + / Mul(*(gamma(1 - b + s) for b in self.bother)) \ + / Mul(*(gamma(a - s) for a in self.aother)) + + @property + def argument(self): + """ Argument of the Meijer G-function. """ + return self.args[2] + + @property + def an(self): + """ First set of numerator parameters. """ + return Tuple(*self.args[0][0]) + + @property + def ap(self): + """ Combined numerator parameters. """ + return Tuple(*(self.args[0][0] + self.args[0][1])) + + @property + def aother(self): + """ Second set of numerator parameters. """ + return Tuple(*self.args[0][1]) + + @property + def bm(self): + """ First set of denominator parameters. """ + return Tuple(*self.args[1][0]) + + @property + def bq(self): + """ Combined denominator parameters. """ + return Tuple(*(self.args[1][0] + self.args[1][1])) + + @property + def bother(self): + """ Second set of denominator parameters. """ + return Tuple(*self.args[1][1]) + + @property + def _diffargs(self): + return self.ap + self.bq + + @property + def nu(self): + """ A quantity related to the convergence region of the integral, + c.f. references. """ + return sum(self.bq) - sum(self.ap) + + @property + def delta(self): + """ A quantity related to the convergence region of the integral, + c.f. references. """ + return len(self.bm) + len(self.an) - S(len(self.ap) + len(self.bq))/2 + + @property + def is_number(self): + """ Returns true if expression has numeric data only. """ + return not self.free_symbols + + +class HyperRep(Function): + """ + A base class for "hyper representation functions". + + This is used exclusively in ``hyperexpand()``, but fits more logically here. + + pFq is branched at 1 if p == q+1. For use with slater-expansion, we want + define an "analytic continuation" to all polar numbers, which is + continuous on circles and on the ray t*exp_polar(I*pi). Moreover, we want + a "nice" expression for the various cases. + + This base class contains the core logic, concrete derived classes only + supply the actual functions. + + """ + + + @classmethod + def eval(cls, *args): + newargs = tuple(map(unpolarify, args[:-1])) + args[-1:] + if args != newargs: + return cls(*newargs) + + @classmethod + def _expr_small(cls, x): + """ An expression for F(x) which holds for |x| < 1. """ + raise NotImplementedError + + @classmethod + def _expr_small_minus(cls, x): + """ An expression for F(-x) which holds for |x| < 1. """ + raise NotImplementedError + + @classmethod + def _expr_big(cls, x, n): + """ An expression for F(exp_polar(2*I*pi*n)*x), |x| > 1. """ + raise NotImplementedError + + @classmethod + def _expr_big_minus(cls, x, n): + """ An expression for F(exp_polar(2*I*pi*n + pi*I)*x), |x| > 1. """ + raise NotImplementedError + + def _eval_rewrite_as_nonrep(self, *args, **kwargs): + x, n = self.args[-1].extract_branch_factor(allow_half=True) + minus = False + newargs = self.args[:-1] + (x,) + if not n.is_Integer: + minus = True + n -= S.Half + newerargs = newargs + (n,) + if minus: + small = self._expr_small_minus(*newargs) + big = self._expr_big_minus(*newerargs) + else: + small = self._expr_small(*newargs) + big = self._expr_big(*newerargs) + + if big == small: + return small + return Piecewise((big, abs(x) > 1), (small, True)) + + def _eval_rewrite_as_nonrepsmall(self, *args, **kwargs): + x, n = self.args[-1].extract_branch_factor(allow_half=True) + args = self.args[:-1] + (x,) + if not n.is_Integer: + return self._expr_small_minus(*args) + return self._expr_small(*args) + + +class HyperRep_power1(HyperRep): + """ Return a representative for hyper([-a], [], z) == (1 - z)**a. """ + + @classmethod + def _expr_small(cls, a, x): + return (1 - x)**a + + @classmethod + def _expr_small_minus(cls, a, x): + return (1 + x)**a + + @classmethod + def _expr_big(cls, a, x, n): + if a.is_integer: + return cls._expr_small(a, x) + return (x - 1)**a*exp((2*n - 1)*pi*I*a) + + @classmethod + def _expr_big_minus(cls, a, x, n): + if a.is_integer: + return cls._expr_small_minus(a, x) + return (1 + x)**a*exp(2*n*pi*I*a) + + +class HyperRep_power2(HyperRep): + """ Return a representative for hyper([a, a - 1/2], [2*a], z). """ + + @classmethod + def _expr_small(cls, a, x): + return 2**(2*a - 1)*(1 + sqrt(1 - x))**(1 - 2*a) + + @classmethod + def _expr_small_minus(cls, a, x): + return 2**(2*a - 1)*(1 + sqrt(1 + x))**(1 - 2*a) + + @classmethod + def _expr_big(cls, a, x, n): + sgn = -1 + if n.is_odd: + sgn = 1 + n -= 1 + return 2**(2*a - 1)*(1 + sgn*I*sqrt(x - 1))**(1 - 2*a) \ + *exp(-2*n*pi*I*a) + + @classmethod + def _expr_big_minus(cls, a, x, n): + sgn = 1 + if n.is_odd: + sgn = -1 + return sgn*2**(2*a - 1)*(sqrt(1 + x) + sgn)**(1 - 2*a)*exp(-2*pi*I*a*n) + + +class HyperRep_log1(HyperRep): + """ Represent -z*hyper([1, 1], [2], z) == log(1 - z). """ + @classmethod + def _expr_small(cls, x): + return log(1 - x) + + @classmethod + def _expr_small_minus(cls, x): + return log(1 + x) + + @classmethod + def _expr_big(cls, x, n): + return log(x - 1) + (2*n - 1)*pi*I + + @classmethod + def _expr_big_minus(cls, x, n): + return log(1 + x) + 2*n*pi*I + + +class HyperRep_atanh(HyperRep): + """ Represent hyper([1/2, 1], [3/2], z) == atanh(sqrt(z))/sqrt(z). """ + @classmethod + def _expr_small(cls, x): + return atanh(sqrt(x))/sqrt(x) + + def _expr_small_minus(cls, x): + return atan(sqrt(x))/sqrt(x) + + def _expr_big(cls, x, n): + if n.is_even: + return (acoth(sqrt(x)) + I*pi/2)/sqrt(x) + else: + return (acoth(sqrt(x)) - I*pi/2)/sqrt(x) + + def _expr_big_minus(cls, x, n): + if n.is_even: + return atan(sqrt(x))/sqrt(x) + else: + return (atan(sqrt(x)) - pi)/sqrt(x) + + +class HyperRep_asin1(HyperRep): + """ Represent hyper([1/2, 1/2], [3/2], z) == asin(sqrt(z))/sqrt(z). """ + @classmethod + def _expr_small(cls, z): + return asin(sqrt(z))/sqrt(z) + + @classmethod + def _expr_small_minus(cls, z): + return asinh(sqrt(z))/sqrt(z) + + @classmethod + def _expr_big(cls, z, n): + return S.NegativeOne**n*((S.Half - n)*pi/sqrt(z) + I*acosh(sqrt(z))/sqrt(z)) + + @classmethod + def _expr_big_minus(cls, z, n): + return S.NegativeOne**n*(asinh(sqrt(z))/sqrt(z) + n*pi*I/sqrt(z)) + + +class HyperRep_asin2(HyperRep): + """ Represent hyper([1, 1], [3/2], z) == asin(sqrt(z))/sqrt(z)/sqrt(1-z). """ + # TODO this can be nicer + @classmethod + def _expr_small(cls, z): + return HyperRep_asin1._expr_small(z) \ + /HyperRep_power1._expr_small(S.Half, z) + + @classmethod + def _expr_small_minus(cls, z): + return HyperRep_asin1._expr_small_minus(z) \ + /HyperRep_power1._expr_small_minus(S.Half, z) + + @classmethod + def _expr_big(cls, z, n): + return HyperRep_asin1._expr_big(z, n) \ + /HyperRep_power1._expr_big(S.Half, z, n) + + @classmethod + def _expr_big_minus(cls, z, n): + return HyperRep_asin1._expr_big_minus(z, n) \ + /HyperRep_power1._expr_big_minus(S.Half, z, n) + + +class HyperRep_sqrts1(HyperRep): + """ Return a representative for hyper([-a, 1/2 - a], [1/2], z). """ + + @classmethod + def _expr_small(cls, a, z): + return ((1 - sqrt(z))**(2*a) + (1 + sqrt(z))**(2*a))/2 + + @classmethod + def _expr_small_minus(cls, a, z): + return (1 + z)**a*cos(2*a*atan(sqrt(z))) + + @classmethod + def _expr_big(cls, a, z, n): + if n.is_even: + return ((sqrt(z) + 1)**(2*a)*exp(2*pi*I*n*a) + + (sqrt(z) - 1)**(2*a)*exp(2*pi*I*(n - 1)*a))/2 + else: + n -= 1 + return ((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n + 1)) + + (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n))/2 + + @classmethod + def _expr_big_minus(cls, a, z, n): + if n.is_even: + return (1 + z)**a*exp(2*pi*I*n*a)*cos(2*a*atan(sqrt(z))) + else: + return (1 + z)**a*exp(2*pi*I*n*a)*cos(2*a*atan(sqrt(z)) - 2*pi*a) + + +class HyperRep_sqrts2(HyperRep): + """ Return a representative for + sqrt(z)/2*[(1-sqrt(z))**2a - (1 + sqrt(z))**2a] + == -2*z/(2*a+1) d/dz hyper([-a - 1/2, -a], [1/2], z)""" + + @classmethod + def _expr_small(cls, a, z): + return sqrt(z)*((1 - sqrt(z))**(2*a) - (1 + sqrt(z))**(2*a))/2 + + @classmethod + def _expr_small_minus(cls, a, z): + return sqrt(z)*(1 + z)**a*sin(2*a*atan(sqrt(z))) + + @classmethod + def _expr_big(cls, a, z, n): + if n.is_even: + return sqrt(z)/2*((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n - 1)) - + (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n)) + else: + n -= 1 + return sqrt(z)/2*((sqrt(z) - 1)**(2*a)*exp(2*pi*I*a*(n + 1)) - + (sqrt(z) + 1)**(2*a)*exp(2*pi*I*a*n)) + + def _expr_big_minus(cls, a, z, n): + if n.is_even: + return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z)*sin(2*a*atan(sqrt(z))) + else: + return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z) \ + *sin(2*a*atan(sqrt(z)) - 2*pi*a) + + +class HyperRep_log2(HyperRep): + """ Represent log(1/2 + sqrt(1 - z)/2) == -z/4*hyper([3/2, 1, 1], [2, 2], z) """ + + @classmethod + def _expr_small(cls, z): + return log(S.Half + sqrt(1 - z)/2) + + @classmethod + def _expr_small_minus(cls, z): + return log(S.Half + sqrt(1 + z)/2) + + @classmethod + def _expr_big(cls, z, n): + if n.is_even: + return (n - S.Half)*pi*I + log(sqrt(z)/2) + I*asin(1/sqrt(z)) + else: + return (n - S.Half)*pi*I + log(sqrt(z)/2) - I*asin(1/sqrt(z)) + + def _expr_big_minus(cls, z, n): + if n.is_even: + return pi*I*n + log(S.Half + sqrt(1 + z)/2) + else: + return pi*I*n + log(sqrt(1 + z)/2 - S.Half) + + +class HyperRep_cosasin(HyperRep): + """ Represent hyper([a, -a], [1/2], z) == cos(2*a*asin(sqrt(z))). """ + # Note there are many alternative expressions, e.g. as powers of a sum of + # square roots. + + @classmethod + def _expr_small(cls, a, z): + return cos(2*a*asin(sqrt(z))) + + @classmethod + def _expr_small_minus(cls, a, z): + return cosh(2*a*asinh(sqrt(z))) + + @classmethod + def _expr_big(cls, a, z, n): + return cosh(2*a*acosh(sqrt(z)) + a*pi*I*(2*n - 1)) + + @classmethod + def _expr_big_minus(cls, a, z, n): + return cosh(2*a*asinh(sqrt(z)) + 2*a*pi*I*n) + + +class HyperRep_sinasin(HyperRep): + """ Represent 2*a*z*hyper([1 - a, 1 + a], [3/2], z) + == sqrt(z)/sqrt(1-z)*sin(2*a*asin(sqrt(z))) """ + + @classmethod + def _expr_small(cls, a, z): + return sqrt(z)/sqrt(1 - z)*sin(2*a*asin(sqrt(z))) + + @classmethod + def _expr_small_minus(cls, a, z): + return -sqrt(z)/sqrt(1 + z)*sinh(2*a*asinh(sqrt(z))) + + @classmethod + def _expr_big(cls, a, z, n): + return -1/sqrt(1 - 1/z)*sinh(2*a*acosh(sqrt(z)) + a*pi*I*(2*n - 1)) + + @classmethod + def _expr_big_minus(cls, a, z, n): + return -1/sqrt(1 + 1/z)*sinh(2*a*asinh(sqrt(z)) + 2*a*pi*I*n) + +class appellf1(Function): + r""" + This is the Appell hypergeometric function of two variables as: + + .. math :: + F_1(a,b_1,b_2,c,x,y) = \sum_{m=0}^{\infty} \sum_{n=0}^{\infty} + \frac{(a)_{m+n} (b_1)_m (b_2)_n}{(c)_{m+n}} + \frac{x^m y^n}{m! n!}. + + Examples + ======== + + >>> from sympy import appellf1, symbols + >>> x, y, a, b1, b2, c = symbols('x y a b1 b2 c') + >>> appellf1(2., 1., 6., 4., 5., 6.) + 0.0063339426292673 + >>> appellf1(12., 12., 6., 4., 0.5, 0.12) + 172870711.659936 + >>> appellf1(40, 2, 6, 4, 15, 60) + appellf1(40, 2, 6, 4, 15, 60) + >>> appellf1(20., 12., 10., 3., 0.5, 0.12) + 15605338197184.4 + >>> appellf1(40, 2, 6, 4, x, y) + appellf1(40, 2, 6, 4, x, y) + >>> appellf1(a, b1, b2, c, x, y) + appellf1(a, b1, b2, c, x, y) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Appell_series + .. [2] https://functions.wolfram.com/HypergeometricFunctions/AppellF1/ + + """ + + @classmethod + def eval(cls, a, b1, b2, c, x, y): + if default_sort_key(b1) > default_sort_key(b2): + b1, b2 = b2, b1 + x, y = y, x + return cls(a, b1, b2, c, x, y) + elif b1 == b2 and default_sort_key(x) > default_sort_key(y): + x, y = y, x + return cls(a, b1, b2, c, x, y) + if x == 0 and y == 0: + return S.One + + def fdiff(self, argindex=5): + a, b1, b2, c, x, y = self.args + if argindex == 5: + return (a*b1/c)*appellf1(a + 1, b1 + 1, b2, c + 1, x, y) + elif argindex == 6: + return (a*b2/c)*appellf1(a + 1, b1, b2 + 1, c + 1, x, y) + elif argindex in (1, 2, 3, 4): + return Derivative(self, self.args[argindex-1]) + else: + raise ArgumentIndexError(self, argindex) diff --git a/lib/python3.11/site-packages/sympy/functions/special/mathieu_functions.py b/lib/python3.11/site-packages/sympy/functions/special/mathieu_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..03a5e278a1d5804c62af4c484db7701ab132e474 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/mathieu_functions.py @@ -0,0 +1,269 @@ +""" This module contains the Mathieu functions. +""" + +from sympy.core.function import Function, ArgumentIndexError +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin, cos + + +class MathieuBase(Function): + """ + Abstract base class for Mathieu functions. + + This class is meant to reduce code duplication. + + """ + + unbranched = True + + def _eval_conjugate(self): + a, q, z = self.args + return self.func(a.conjugate(), q.conjugate(), z.conjugate()) + + +class mathieus(MathieuBase): + r""" + The Mathieu Sine function $S(a,q,z)$. + + Explanation + =========== + + This function is one solution of the Mathieu differential equation: + + .. math :: + y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 + + The other solution is the Mathieu Cosine function. + + Examples + ======== + + >>> from sympy import diff, mathieus + >>> from sympy.abc import a, q, z + + >>> mathieus(a, q, z) + mathieus(a, q, z) + + >>> mathieus(a, 0, z) + sin(sqrt(a)*z) + + >>> diff(mathieus(a, q, z), z) + mathieusprime(a, q, z) + + See Also + ======== + + mathieuc: Mathieu cosine function. + mathieusprime: Derivative of Mathieu sine function. + mathieucprime: Derivative of Mathieu cosine function. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Mathieu_function + .. [2] https://dlmf.nist.gov/28 + .. [3] https://mathworld.wolfram.com/MathieuFunction.html + .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuS/ + + """ + + def fdiff(self, argindex=1): + if argindex == 3: + a, q, z = self.args + return mathieusprime(a, q, z) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, a, q, z): + if q.is_Number and q.is_zero: + return sin(sqrt(a)*z) + # Try to pull out factors of -1 + if z.could_extract_minus_sign(): + return -cls(a, q, -z) + + +class mathieuc(MathieuBase): + r""" + The Mathieu Cosine function $C(a,q,z)$. + + Explanation + =========== + + This function is one solution of the Mathieu differential equation: + + .. math :: + y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 + + The other solution is the Mathieu Sine function. + + Examples + ======== + + >>> from sympy import diff, mathieuc + >>> from sympy.abc import a, q, z + + >>> mathieuc(a, q, z) + mathieuc(a, q, z) + + >>> mathieuc(a, 0, z) + cos(sqrt(a)*z) + + >>> diff(mathieuc(a, q, z), z) + mathieucprime(a, q, z) + + See Also + ======== + + mathieus: Mathieu sine function + mathieusprime: Derivative of Mathieu sine function + mathieucprime: Derivative of Mathieu cosine function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Mathieu_function + .. [2] https://dlmf.nist.gov/28 + .. [3] https://mathworld.wolfram.com/MathieuFunction.html + .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuC/ + + """ + + def fdiff(self, argindex=1): + if argindex == 3: + a, q, z = self.args + return mathieucprime(a, q, z) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, a, q, z): + if q.is_Number and q.is_zero: + return cos(sqrt(a)*z) + # Try to pull out factors of -1 + if z.could_extract_minus_sign(): + return cls(a, q, -z) + + +class mathieusprime(MathieuBase): + r""" + The derivative $S^{\prime}(a,q,z)$ of the Mathieu Sine function. + + Explanation + =========== + + This function is one solution of the Mathieu differential equation: + + .. math :: + y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 + + The other solution is the Mathieu Cosine function. + + Examples + ======== + + >>> from sympy import diff, mathieusprime + >>> from sympy.abc import a, q, z + + >>> mathieusprime(a, q, z) + mathieusprime(a, q, z) + + >>> mathieusprime(a, 0, z) + sqrt(a)*cos(sqrt(a)*z) + + >>> diff(mathieusprime(a, q, z), z) + (-a + 2*q*cos(2*z))*mathieus(a, q, z) + + See Also + ======== + + mathieus: Mathieu sine function + mathieuc: Mathieu cosine function + mathieucprime: Derivative of Mathieu cosine function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Mathieu_function + .. [2] https://dlmf.nist.gov/28 + .. [3] https://mathworld.wolfram.com/MathieuFunction.html + .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuSPrime/ + + """ + + def fdiff(self, argindex=1): + if argindex == 3: + a, q, z = self.args + return (2*q*cos(2*z) - a)*mathieus(a, q, z) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, a, q, z): + if q.is_Number and q.is_zero: + return sqrt(a)*cos(sqrt(a)*z) + # Try to pull out factors of -1 + if z.could_extract_minus_sign(): + return cls(a, q, -z) + + +class mathieucprime(MathieuBase): + r""" + The derivative $C^{\prime}(a,q,z)$ of the Mathieu Cosine function. + + Explanation + =========== + + This function is one solution of the Mathieu differential equation: + + .. math :: + y(x)^{\prime\prime} + (a - 2 q \cos(2 x)) y(x) = 0 + + The other solution is the Mathieu Sine function. + + Examples + ======== + + >>> from sympy import diff, mathieucprime + >>> from sympy.abc import a, q, z + + >>> mathieucprime(a, q, z) + mathieucprime(a, q, z) + + >>> mathieucprime(a, 0, z) + -sqrt(a)*sin(sqrt(a)*z) + + >>> diff(mathieucprime(a, q, z), z) + (-a + 2*q*cos(2*z))*mathieuc(a, q, z) + + See Also + ======== + + mathieus: Mathieu sine function + mathieuc: Mathieu cosine function + mathieusprime: Derivative of Mathieu sine function + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Mathieu_function + .. [2] https://dlmf.nist.gov/28 + .. [3] https://mathworld.wolfram.com/MathieuFunction.html + .. [4] https://functions.wolfram.com/MathieuandSpheroidalFunctions/MathieuCPrime/ + + """ + + def fdiff(self, argindex=1): + if argindex == 3: + a, q, z = self.args + return (2*q*cos(2*z) - a)*mathieuc(a, q, z) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, a, q, z): + if q.is_Number and q.is_zero: + return -sqrt(a)*sin(sqrt(a)*z) + # Try to pull out factors of -1 + if z.could_extract_minus_sign(): + return -cls(a, q, -z) diff --git a/lib/python3.11/site-packages/sympy/functions/special/polynomials.py b/lib/python3.11/site-packages/sympy/functions/special/polynomials.py new file mode 100644 index 0000000000000000000000000000000000000000..cab0413b215d9ea92e236e42b9d942f5661846f7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/polynomials.py @@ -0,0 +1,1447 @@ +""" +This module mainly implements special orthogonal polynomials. + +See also functions.combinatorial.numbers which contains some +combinatorial polynomials. + +""" + +from sympy.core import Rational +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.singleton import S +from sympy.core.symbol import Dummy +from sympy.functions.combinatorial.factorials import binomial, factorial, RisingFactorial +from sympy.functions.elementary.complexes import re +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import cos, sec +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import hyper +from sympy.polys.orthopolys import (chebyshevt_poly, chebyshevu_poly, + gegenbauer_poly, hermite_poly, hermite_prob_poly, + jacobi_poly, laguerre_poly, legendre_poly) + +_x = Dummy('x') + + +class OrthogonalPolynomial(Function): + """Base class for orthogonal polynomials. + """ + + @classmethod + def _eval_at_order(cls, n, x): + if n.is_integer and n >= 0: + return cls._ortho_poly(int(n), _x).subs(_x, x) + + def _eval_conjugate(self): + return self.func(self.args[0], self.args[1].conjugate()) + +#---------------------------------------------------------------------------- +# Jacobi polynomials +# + + +class jacobi(OrthogonalPolynomial): + r""" + Jacobi polynomial $P_n^{\left(\alpha, \beta\right)}(x)$. + + Explanation + =========== + + ``jacobi(n, alpha, beta, x)`` gives the $n$th Jacobi polynomial + in $x$, $P_n^{\left(\alpha, \beta\right)}(x)$. + + The Jacobi polynomials are orthogonal on $[-1, 1]$ with respect + to the weight $\left(1-x\right)^\alpha \left(1+x\right)^\beta$. + + Examples + ======== + + >>> from sympy import jacobi, S, conjugate, diff + >>> from sympy.abc import a, b, n, x + + >>> jacobi(0, a, b, x) + 1 + >>> jacobi(1, a, b, x) + a/2 - b/2 + x*(a/2 + b/2 + 1) + >>> jacobi(2, a, b, x) + a**2/8 - a*b/4 - a/8 + b**2/8 - b/8 + x**2*(a**2/8 + a*b/4 + 7*a/8 + b**2/8 + 7*b/8 + 3/2) + x*(a**2/4 + 3*a/4 - b**2/4 - 3*b/4) - 1/2 + + >>> jacobi(n, a, b, x) + jacobi(n, a, b, x) + + >>> jacobi(n, a, a, x) + RisingFactorial(a + 1, n)*gegenbauer(n, + a + 1/2, x)/RisingFactorial(2*a + 1, n) + + >>> jacobi(n, 0, 0, x) + legendre(n, x) + + >>> jacobi(n, S(1)/2, S(1)/2, x) + RisingFactorial(3/2, n)*chebyshevu(n, x)/factorial(n + 1) + + >>> jacobi(n, -S(1)/2, -S(1)/2, x) + RisingFactorial(1/2, n)*chebyshevt(n, x)/factorial(n) + + >>> jacobi(n, a, b, -x) + (-1)**n*jacobi(n, b, a, x) + + >>> jacobi(n, a, b, 0) + gamma(a + n + 1)*hyper((-n, -b - n), (a + 1,), -1)/(2**n*factorial(n)*gamma(a + 1)) + >>> jacobi(n, a, b, 1) + RisingFactorial(a + 1, n)/factorial(n) + + >>> conjugate(jacobi(n, a, b, x)) + jacobi(n, conjugate(a), conjugate(b), conjugate(x)) + + >>> diff(jacobi(n,a,b,x), x) + (a/2 + b/2 + n/2 + 1/2)*jacobi(n - 1, a + 1, b + 1, x) + + See Also + ======== + + gegenbauer, + chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly, + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Jacobi_polynomials + .. [2] https://mathworld.wolfram.com/JacobiPolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/JacobiP/ + + """ + + @classmethod + def eval(cls, n, a, b, x): + # Simplify to other polynomials + # P^{a, a}_n(x) + if a == b: + if a == Rational(-1, 2): + return RisingFactorial(S.Half, n) / factorial(n) * chebyshevt(n, x) + elif a.is_zero: + return legendre(n, x) + elif a == S.Half: + return RisingFactorial(3*S.Half, n) / factorial(n + 1) * chebyshevu(n, x) + else: + return RisingFactorial(a + 1, n) / RisingFactorial(2*a + 1, n) * gegenbauer(n, a + S.Half, x) + elif b == -a: + # P^{a, -a}_n(x) + return gamma(n + a + 1) / gamma(n + 1) * (1 + x)**(a/2) / (1 - x)**(a/2) * assoc_legendre(n, -a, x) + + if not n.is_Number: + # Symbolic result P^{a,b}_n(x) + # P^{a,b}_n(-x) ---> (-1)**n * P^{b,a}_n(-x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * jacobi(n, b, a, -x) + # We can evaluate for some special values of x + if x.is_zero: + return (2**(-n) * gamma(a + n + 1) / (gamma(a + 1) * factorial(n)) * + hyper([-b - n, -n], [a + 1], -1)) + if x == S.One: + return RisingFactorial(a + 1, n) / factorial(n) + elif x is S.Infinity: + if n.is_positive: + # Make sure a+b+2*n \notin Z + if (a + b + 2*n).is_integer: + raise ValueError("Error. a + b + 2*n should not be an integer.") + return RisingFactorial(a + b + n + 1, n) * S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + return jacobi_poly(n, a, b, x) + + def fdiff(self, argindex=4): + from sympy.concrete.summations import Sum + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt a + n, a, b, x = self.args + k = Dummy("k") + f1 = 1 / (a + b + n + k + 1) + f2 = ((a + b + 2*k + 1) * RisingFactorial(b + k + 1, n - k) / + ((n - k) * RisingFactorial(a + b + k + 1, n - k))) + return Sum(f1 * (jacobi(n, a, b, x) + f2*jacobi(k, a, b, x)), (k, 0, n - 1)) + elif argindex == 3: + # Diff wrt b + n, a, b, x = self.args + k = Dummy("k") + f1 = 1 / (a + b + n + k + 1) + f2 = (-1)**(n - k) * ((a + b + 2*k + 1) * RisingFactorial(a + k + 1, n - k) / + ((n - k) * RisingFactorial(a + b + k + 1, n - k))) + return Sum(f1 * (jacobi(n, a, b, x) + f2*jacobi(k, a, b, x)), (k, 0, n - 1)) + elif argindex == 4: + # Diff wrt x + n, a, b, x = self.args + return S.Half * (a + b + n + 1) * jacobi(n - 1, a + 1, b + 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, a, b, x, **kwargs): + from sympy.concrete.summations import Sum + # Make sure n \in N + if n.is_negative or n.is_integer is False: + raise ValueError("Error: n should be a non-negative integer.") + k = Dummy("k") + kern = (RisingFactorial(-n, k) * RisingFactorial(a + b + n + 1, k) * RisingFactorial(a + k + 1, n - k) / + factorial(k) * ((1 - x)/2)**k) + return 1 / factorial(n) * Sum(kern, (k, 0, n)) + + def _eval_rewrite_as_polynomial(self, n, a, b, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, a, b, x, **kwargs) + + def _eval_conjugate(self): + n, a, b, x = self.args + return self.func(n, a.conjugate(), b.conjugate(), x.conjugate()) + + +def jacobi_normalized(n, a, b, x): + r""" + Jacobi polynomial $P_n^{\left(\alpha, \beta\right)}(x)$. + + Explanation + =========== + + ``jacobi_normalized(n, alpha, beta, x)`` gives the $n$th + Jacobi polynomial in $x$, $P_n^{\left(\alpha, \beta\right)}(x)$. + + The Jacobi polynomials are orthogonal on $[-1, 1]$ with respect + to the weight $\left(1-x\right)^\alpha \left(1+x\right)^\beta$. + + This functions returns the polynomials normilzed: + + .. math:: + + \int_{-1}^{1} + P_m^{\left(\alpha, \beta\right)}(x) + P_n^{\left(\alpha, \beta\right)}(x) + (1-x)^{\alpha} (1+x)^{\beta} \mathrm{d}x + = \delta_{m,n} + + Examples + ======== + + >>> from sympy import jacobi_normalized + >>> from sympy.abc import n,a,b,x + + >>> jacobi_normalized(n, a, b, x) + jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1)/((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1))) + + Parameters + ========== + + n : integer degree of polynomial + + a : alpha value + + b : beta value + + x : symbol + + See Also + ======== + + gegenbauer, + chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly, + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Jacobi_polynomials + .. [2] https://mathworld.wolfram.com/JacobiPolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/JacobiP/ + + """ + nfactor = (S(2)**(a + b + 1) * (gamma(n + a + 1) * gamma(n + b + 1)) + / (2*n + a + b + 1) / (factorial(n) * gamma(n + a + b + 1))) + + return jacobi(n, a, b, x) / sqrt(nfactor) + + +#---------------------------------------------------------------------------- +# Gegenbauer polynomials +# + + +class gegenbauer(OrthogonalPolynomial): + r""" + Gegenbauer polynomial $C_n^{\left(\alpha\right)}(x)$. + + Explanation + =========== + + ``gegenbauer(n, alpha, x)`` gives the $n$th Gegenbauer polynomial + in $x$, $C_n^{\left(\alpha\right)}(x)$. + + The Gegenbauer polynomials are orthogonal on $[-1, 1]$ with + respect to the weight $\left(1-x^2\right)^{\alpha-\frac{1}{2}}$. + + Examples + ======== + + >>> from sympy import gegenbauer, conjugate, diff + >>> from sympy.abc import n,a,x + >>> gegenbauer(0, a, x) + 1 + >>> gegenbauer(1, a, x) + 2*a*x + >>> gegenbauer(2, a, x) + -a + x**2*(2*a**2 + 2*a) + >>> gegenbauer(3, a, x) + x**3*(4*a**3/3 + 4*a**2 + 8*a/3) + x*(-2*a**2 - 2*a) + + >>> gegenbauer(n, a, x) + gegenbauer(n, a, x) + >>> gegenbauer(n, a, -x) + (-1)**n*gegenbauer(n, a, x) + + >>> gegenbauer(n, a, 0) + 2**n*sqrt(pi)*gamma(a + n/2)/(gamma(a)*gamma(1/2 - n/2)*gamma(n + 1)) + >>> gegenbauer(n, a, 1) + gamma(2*a + n)/(gamma(2*a)*gamma(n + 1)) + + >>> conjugate(gegenbauer(n, a, x)) + gegenbauer(n, conjugate(a), conjugate(x)) + + >>> diff(gegenbauer(n, a, x), x) + 2*a*gegenbauer(n - 1, a + 1, x) + + See Also + ======== + + jacobi, + chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gegenbauer_polynomials + .. [2] https://mathworld.wolfram.com/GegenbauerPolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/GegenbauerC3/ + + """ + + @classmethod + def eval(cls, n, a, x): + # For negative n the polynomials vanish + # See https://functions.wolfram.com/Polynomials/GegenbauerC3/03/01/03/0012/ + if n.is_negative: + return S.Zero + + # Some special values for fixed a + if a == S.Half: + return legendre(n, x) + elif a == S.One: + return chebyshevu(n, x) + elif a == S.NegativeOne: + return S.Zero + + if not n.is_Number: + # Handle this before the general sign extraction rule + if x == S.NegativeOne: + if (re(a) > S.Half) == True: + return S.ComplexInfinity + else: + return (cos(S.Pi*(a+n)) * sec(S.Pi*a) * gamma(2*a+n) / + (gamma(2*a) * gamma(n+1))) + + # Symbolic result C^a_n(x) + # C^a_n(-x) ---> (-1)**n * C^a_n(x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * gegenbauer(n, a, -x) + # We can evaluate for some special values of x + if x.is_zero: + return (2**n * sqrt(S.Pi) * gamma(a + S.Half*n) / + (gamma((1 - n)/2) * gamma(n + 1) * gamma(a)) ) + if x == S.One: + return gamma(2*a + n) / (gamma(2*a) * gamma(n + 1)) + elif x is S.Infinity: + if n.is_positive: + return RisingFactorial(a, n) * S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + return gegenbauer_poly(n, a, x) + + def fdiff(self, argindex=3): + from sympy.concrete.summations import Sum + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt a + n, a, x = self.args + k = Dummy("k") + factor1 = 2 * (1 + (-1)**(n - k)) * (k + a) / ((k + + n + 2*a) * (n - k)) + factor2 = 2*(k + 1) / ((k + 2*a) * (2*k + 2*a + 1)) + \ + 2 / (k + n + 2*a) + kern = factor1*gegenbauer(k, a, x) + factor2*gegenbauer(n, a, x) + return Sum(kern, (k, 0, n - 1)) + elif argindex == 3: + # Diff wrt x + n, a, x = self.args + return 2*a*gegenbauer(n - 1, a + 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, a, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = ((-1)**k * RisingFactorial(a, n - k) * (2*x)**(n - 2*k) / + (factorial(k) * factorial(n - 2*k))) + return Sum(kern, (k, 0, floor(n/2))) + + def _eval_rewrite_as_polynomial(self, n, a, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, a, x, **kwargs) + + def _eval_conjugate(self): + n, a, x = self.args + return self.func(n, a.conjugate(), x.conjugate()) + +#---------------------------------------------------------------------------- +# Chebyshev polynomials of first and second kind +# + + +class chebyshevt(OrthogonalPolynomial): + r""" + Chebyshev polynomial of the first kind, $T_n(x)$. + + Explanation + =========== + + ``chebyshevt(n, x)`` gives the $n$th Chebyshev polynomial (of the first + kind) in $x$, $T_n(x)$. + + The Chebyshev polynomials of the first kind are orthogonal on + $[-1, 1]$ with respect to the weight $\frac{1}{\sqrt{1-x^2}}$. + + Examples + ======== + + >>> from sympy import chebyshevt, diff + >>> from sympy.abc import n,x + >>> chebyshevt(0, x) + 1 + >>> chebyshevt(1, x) + x + >>> chebyshevt(2, x) + 2*x**2 - 1 + + >>> chebyshevt(n, x) + chebyshevt(n, x) + >>> chebyshevt(n, -x) + (-1)**n*chebyshevt(n, x) + >>> chebyshevt(-n, x) + chebyshevt(n, x) + + >>> chebyshevt(n, 0) + cos(pi*n/2) + >>> chebyshevt(n, -1) + (-1)**n + + >>> diff(chebyshevt(n, x), x) + n*chebyshevu(n - 1, x) + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Chebyshev_polynomial + .. [2] https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html + .. [3] https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html + .. [4] https://functions.wolfram.com/Polynomials/ChebyshevT/ + .. [5] https://functions.wolfram.com/Polynomials/ChebyshevU/ + + """ + + _ortho_poly = staticmethod(chebyshevt_poly) + + @classmethod + def eval(cls, n, x): + if not n.is_Number: + # Symbolic result T_n(x) + # T_n(-x) ---> (-1)**n * T_n(x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * chebyshevt(n, -x) + # T_{-n}(x) ---> T_n(x) + if n.could_extract_minus_sign(): + return chebyshevt(-n, x) + # We can evaluate for some special values of x + if x.is_zero: + return cos(S.Half * S.Pi * n) + if x == S.One: + return S.One + elif x is S.Infinity: + return S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + if n.is_negative: + # T_{-n}(x) == T_n(x) + return cls._eval_at_order(-n, x) + else: + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt x + n, x = self.args + return n * chebyshevu(n - 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = binomial(n, 2*k) * (x**2 - 1)**k * x**(n - 2*k) + return Sum(kern, (k, 0, floor(n/2))) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + +class chebyshevu(OrthogonalPolynomial): + r""" + Chebyshev polynomial of the second kind, $U_n(x)$. + + Explanation + =========== + + ``chebyshevu(n, x)`` gives the $n$th Chebyshev polynomial of the second + kind in x, $U_n(x)$. + + The Chebyshev polynomials of the second kind are orthogonal on + $[-1, 1]$ with respect to the weight $\sqrt{1-x^2}$. + + Examples + ======== + + >>> from sympy import chebyshevu, diff + >>> from sympy.abc import n,x + >>> chebyshevu(0, x) + 1 + >>> chebyshevu(1, x) + 2*x + >>> chebyshevu(2, x) + 4*x**2 - 1 + + >>> chebyshevu(n, x) + chebyshevu(n, x) + >>> chebyshevu(n, -x) + (-1)**n*chebyshevu(n, x) + >>> chebyshevu(-n, x) + -chebyshevu(n - 2, x) + + >>> chebyshevu(n, 0) + cos(pi*n/2) + >>> chebyshevu(n, 1) + n + 1 + + >>> diff(chebyshevu(n, x), x) + (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1) + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Chebyshev_polynomial + .. [2] https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html + .. [3] https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html + .. [4] https://functions.wolfram.com/Polynomials/ChebyshevT/ + .. [5] https://functions.wolfram.com/Polynomials/ChebyshevU/ + + """ + + _ortho_poly = staticmethod(chebyshevu_poly) + + @classmethod + def eval(cls, n, x): + if not n.is_Number: + # Symbolic result U_n(x) + # U_n(-x) ---> (-1)**n * U_n(x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * chebyshevu(n, -x) + # U_{-n}(x) ---> -U_{n-2}(x) + if n.could_extract_minus_sign(): + if n == S.NegativeOne: + # n can not be -1 here + return S.Zero + elif not (-n - 2).could_extract_minus_sign(): + return -chebyshevu(-n - 2, x) + # We can evaluate for some special values of x + if x.is_zero: + return cos(S.Half * S.Pi * n) + if x == S.One: + return S.One + n + elif x is S.Infinity: + return S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + if n.is_negative: + # U_{-n}(x) ---> -U_{n-2}(x) + if n == S.NegativeOne: + return S.Zero + else: + return -cls._eval_at_order(-n - 2, x) + else: + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt x + n, x = self.args + return ((n + 1) * chebyshevt(n + 1, x) - x * chebyshevu(n, x)) / (x**2 - 1) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = S.NegativeOne**k * factorial( + n - k) * (2*x)**(n - 2*k) / (factorial(k) * factorial(n - 2*k)) + return Sum(kern, (k, 0, floor(n/2))) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + +class chebyshevt_root(Function): + r""" + ``chebyshev_root(n, k)`` returns the $k$th root (indexed from zero) of + the $n$th Chebyshev polynomial of the first kind; that is, if + $0 \le k < n$, ``chebyshevt(n, chebyshevt_root(n, k)) == 0``. + + Examples + ======== + + >>> from sympy import chebyshevt, chebyshevt_root + >>> chebyshevt_root(3, 2) + -sqrt(3)/2 + >>> chebyshevt(3, chebyshevt_root(3, 2)) + 0 + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + """ + + @classmethod + def eval(cls, n, k): + if not ((0 <= k) and (k < n)): + raise ValueError("must have 0 <= k < n, " + "got k = %s and n = %s" % (k, n)) + return cos(S.Pi*(2*k + 1)/(2*n)) + + +class chebyshevu_root(Function): + r""" + ``chebyshevu_root(n, k)`` returns the $k$th root (indexed from zero) of the + $n$th Chebyshev polynomial of the second kind; that is, if $0 \le k < n$, + ``chebyshevu(n, chebyshevu_root(n, k)) == 0``. + + Examples + ======== + + >>> from sympy import chebyshevu, chebyshevu_root + >>> chebyshevu_root(3, 2) + -sqrt(2)/2 + >>> chebyshevu(3, chebyshevu_root(3, 2)) + 0 + + See Also + ======== + + chebyshevt, chebyshevt_root, chebyshevu, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + """ + + + @classmethod + def eval(cls, n, k): + if not ((0 <= k) and (k < n)): + raise ValueError("must have 0 <= k < n, " + "got k = %s and n = %s" % (k, n)) + return cos(S.Pi*(k + 1)/(n + 1)) + +#---------------------------------------------------------------------------- +# Legendre polynomials and Associated Legendre polynomials +# + + +class legendre(OrthogonalPolynomial): + r""" + ``legendre(n, x)`` gives the $n$th Legendre polynomial of $x$, $P_n(x)$ + + Explanation + =========== + + The Legendre polynomials are orthogonal on $[-1, 1]$ with respect to + the constant weight 1. They satisfy $P_n(1) = 1$ for all $n$; further, + $P_n$ is odd for odd $n$ and even for even $n$. + + Examples + ======== + + >>> from sympy import legendre, diff + >>> from sympy.abc import x, n + >>> legendre(0, x) + 1 + >>> legendre(1, x) + x + >>> legendre(2, x) + 3*x**2/2 - 1/2 + >>> legendre(n, x) + legendre(n, x) + >>> diff(legendre(n,x), x) + n*(x*legendre(n, x) - legendre(n - 1, x))/(x**2 - 1) + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + assoc_legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Legendre_polynomial + .. [2] https://mathworld.wolfram.com/LegendrePolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/LegendreP/ + .. [4] https://functions.wolfram.com/Polynomials/LegendreP2/ + + """ + + _ortho_poly = staticmethod(legendre_poly) + + @classmethod + def eval(cls, n, x): + if not n.is_Number: + # Symbolic result L_n(x) + # L_n(-x) ---> (-1)**n * L_n(x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * legendre(n, -x) + # L_{-n}(x) ---> L_{n-1}(x) + if n.could_extract_minus_sign() and not(-n - 1).could_extract_minus_sign(): + return legendre(-n - S.One, x) + # We can evaluate for some special values of x + if x.is_zero: + return sqrt(S.Pi)/(gamma(S.Half - n/2)*gamma(S.One + n/2)) + elif x == S.One: + return S.One + elif x is S.Infinity: + return S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial; + # L_{-n}(x) ---> L_{n-1}(x) + if n.is_negative: + n = -n - S.One + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt x + # Find better formula, this is unsuitable for x = +/-1 + # https://www.autodiff.org/ad16/Oral/Buecker_Legendre.pdf says + # at x = 1: + # n*(n + 1)/2 , m = 0 + # oo , m = 1 + # -(n-1)*n*(n+1)*(n+2)/4 , m = 2 + # 0 , m = 3, 4, ..., n + # + # at x = -1 + # (-1)**(n+1)*n*(n + 1)/2 , m = 0 + # (-1)**n*oo , m = 1 + # (-1)**n*(n-1)*n*(n+1)*(n+2)/4 , m = 2 + # 0 , m = 3, 4, ..., n + n, x = self.args + return n/(x**2 - 1)*(x*legendre(n, x) - legendre(n - 1, x)) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = S.NegativeOne**k*binomial(n, k)**2*((1 + x)/2)**(n - k)*((1 - x)/2)**k + return Sum(kern, (k, 0, n)) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + +class assoc_legendre(Function): + r""" + ``assoc_legendre(n, m, x)`` gives $P_n^m(x)$, where $n$ and $m$ are + the degree and order or an expression which is related to the nth + order Legendre polynomial, $P_n(x)$ in the following manner: + + .. math:: + P_n^m(x) = (-1)^m (1 - x^2)^{\frac{m}{2}} + \frac{\mathrm{d}^m P_n(x)}{\mathrm{d} x^m} + + Explanation + =========== + + Associated Legendre polynomials are orthogonal on $[-1, 1]$ with: + + - weight $= 1$ for the same $m$ and different $n$. + - weight $= \frac{1}{1-x^2}$ for the same $n$ and different $m$. + + Examples + ======== + + >>> from sympy import assoc_legendre + >>> from sympy.abc import x, m, n + >>> assoc_legendre(0,0, x) + 1 + >>> assoc_legendre(1,0, x) + x + >>> assoc_legendre(1,1, x) + -sqrt(1 - x**2) + >>> assoc_legendre(n,m,x) + assoc_legendre(n, m, x) + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, + hermite, hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Associated_Legendre_polynomials + .. [2] https://mathworld.wolfram.com/LegendrePolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/LegendreP/ + .. [4] https://functions.wolfram.com/Polynomials/LegendreP2/ + + """ + + @classmethod + def _eval_at_order(cls, n, m): + P = legendre_poly(n, _x, polys=True).diff((_x, m)) + return S.NegativeOne**m * (1 - _x**2)**Rational(m, 2) * P.as_expr() + + @classmethod + def eval(cls, n, m, x): + if m.could_extract_minus_sign(): + # P^{-m}_n ---> F * P^m_n + return S.NegativeOne**(-m) * (factorial(m + n)/factorial(n - m)) * assoc_legendre(n, -m, x) + if m == 0: + # P^0_n ---> L_n + return legendre(n, x) + if x == 0: + return 2**m*sqrt(S.Pi) / (gamma((1 - m - n)/2)*gamma(1 - (m - n)/2)) + if n.is_Number and m.is_Number and n.is_integer and m.is_integer: + if n.is_negative: + raise ValueError("%s : 1st index must be nonnegative integer (got %r)" % (cls, n)) + if abs(m) > n: + raise ValueError("%s : abs('2nd index') must be <= '1st index' (got %r, %r)" % (cls, n, m)) + return cls._eval_at_order(int(n), abs(int(m))).subs(_x, x) + + def fdiff(self, argindex=3): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt m + raise ArgumentIndexError(self, argindex) + elif argindex == 3: + # Diff wrt x + # Find better formula, this is unsuitable for x = 1 + n, m, x = self.args + return 1/(x**2 - 1)*(x*n*assoc_legendre(n, m, x) - (m + n)*assoc_legendre(n - 1, m, x)) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, m, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = factorial(2*n - 2*k)/(2**n*factorial(n - k)*factorial( + k)*factorial(n - 2*k - m))*S.NegativeOne**k*x**(n - m - 2*k) + return (1 - x**2)**(m/2) * Sum(kern, (k, 0, floor((n - m)*S.Half))) + + def _eval_rewrite_as_polynomial(self, n, m, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, m, x, **kwargs) + + def _eval_conjugate(self): + n, m, x = self.args + return self.func(n, m.conjugate(), x.conjugate()) + +#---------------------------------------------------------------------------- +# Hermite polynomials +# + + +class hermite(OrthogonalPolynomial): + r""" + ``hermite(n, x)`` gives the $n$th Hermite polynomial in $x$, $H_n(x)$. + + Explanation + =========== + + The Hermite polynomials are orthogonal on $(-\infty, \infty)$ + with respect to the weight $\exp\left(-x^2\right)$. + + Examples + ======== + + >>> from sympy import hermite, diff + >>> from sympy.abc import x, n + >>> hermite(0, x) + 1 + >>> hermite(1, x) + 2*x + >>> hermite(2, x) + 4*x**2 - 2 + >>> hermite(n, x) + hermite(n, x) + >>> diff(hermite(n,x), x) + 2*n*hermite(n - 1, x) + >>> hermite(n, -x) + (-1)**n*hermite(n, x) + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite_prob, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hermite_polynomial + .. [2] https://mathworld.wolfram.com/HermitePolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/HermiteH/ + + """ + + _ortho_poly = staticmethod(hermite_poly) + + @classmethod + def eval(cls, n, x): + if not n.is_Number: + # Symbolic result H_n(x) + # H_n(-x) ---> (-1)**n * H_n(x) + if x.could_extract_minus_sign(): + return S.NegativeOne**n * hermite(n, -x) + # We can evaluate for some special values of x + if x.is_zero: + return 2**n * sqrt(S.Pi) / gamma((S.One - n)/2) + elif x is S.Infinity: + return S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + if n.is_negative: + raise ValueError( + "The index n must be nonnegative integer (got %r)" % n) + else: + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt x + n, x = self.args + return 2*n*hermite(n - 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = S.NegativeOne**k / (factorial(k)*factorial(n - 2*k)) * (2*x)**(n - 2*k) + return factorial(n)*Sum(kern, (k, 0, floor(n/2))) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + def _eval_rewrite_as_hermite_prob(self, n, x, **kwargs): + return sqrt(2)**n * hermite_prob(n, x*sqrt(2)) + + +class hermite_prob(OrthogonalPolynomial): + r""" + ``hermite_prob(n, x)`` gives the $n$th probabilist's Hermite polynomial + in $x$, $He_n(x)$. + + Explanation + =========== + + The probabilist's Hermite polynomials are orthogonal on $(-\infty, \infty)$ + with respect to the weight $\exp\left(-\frac{x^2}{2}\right)$. They are monic + polynomials, related to the plain Hermite polynomials (:py:class:`~.hermite`) by + + .. math :: He_n(x) = 2^{-n/2} H_n(x/\sqrt{2}) + + Examples + ======== + + >>> from sympy import hermite_prob, diff, I + >>> from sympy.abc import x, n + >>> hermite_prob(1, x) + x + >>> hermite_prob(5, x) + x**5 - 10*x**3 + 15*x + >>> diff(hermite_prob(n,x), x) + n*hermite_prob(n - 1, x) + >>> hermite_prob(n, -x) + (-1)**n*hermite_prob(n, x) + + The sum of absolute values of coefficients of $He_n(x)$ is the number of + matchings in the complete graph $K_n$ or telephone number, A000085 in the OEIS: + + >>> [hermite_prob(n,I) / I**n for n in range(11)] + [1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496] + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, + laguerre, assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hermite_polynomial + .. [2] https://mathworld.wolfram.com/HermitePolynomial.html + """ + + _ortho_poly = staticmethod(hermite_prob_poly) + + @classmethod + def eval(cls, n, x): + if not n.is_Number: + if x.could_extract_minus_sign(): + return S.NegativeOne**n * hermite_prob(n, -x) + if x.is_zero: + return sqrt(S.Pi) / gamma((S.One-n) / 2) + elif x is S.Infinity: + return S.Infinity + else: + if n.is_negative: + ValueError("n must be a nonnegative integer, not %r" % n) + else: + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 2: + n, x = self.args + return n*hermite_prob(n-1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + k = Dummy("k") + kern = (-S.Half)**k * x**(n-2*k) / (factorial(k) * factorial(n-2*k)) + return factorial(n)*Sum(kern, (k, 0, floor(n/2))) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + def _eval_rewrite_as_hermite(self, n, x, **kwargs): + return sqrt(2)**(-n) * hermite(n, x/sqrt(2)) + + +#---------------------------------------------------------------------------- +# Laguerre polynomials +# + + +class laguerre(OrthogonalPolynomial): + r""" + Returns the $n$th Laguerre polynomial in $x$, $L_n(x)$. + + Examples + ======== + + >>> from sympy import laguerre, diff + >>> from sympy.abc import x, n + >>> laguerre(0, x) + 1 + >>> laguerre(1, x) + 1 - x + >>> laguerre(2, x) + x**2/2 - 2*x + 1 + >>> laguerre(3, x) + -x**3/6 + 3*x**2/2 - 3*x + 1 + + >>> laguerre(n, x) + laguerre(n, x) + + >>> diff(laguerre(n, x), x) + -assoc_laguerre(n - 1, 1, x) + + Parameters + ========== + + n : int + Degree of Laguerre polynomial. Must be `n \ge 0`. + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + assoc_laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Laguerre_polynomial + .. [2] https://mathworld.wolfram.com/LaguerrePolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/LaguerreL/ + .. [4] https://functions.wolfram.com/Polynomials/LaguerreL3/ + + """ + + _ortho_poly = staticmethod(laguerre_poly) + + @classmethod + def eval(cls, n, x): + if n.is_integer is False: + raise ValueError("Error: n should be an integer.") + if not n.is_Number: + # Symbolic result L_n(x) + # L_{n}(-x) ---> exp(-x) * L_{-n-1}(x) + # L_{-n}(x) ---> exp(x) * L_{n-1}(-x) + if n.could_extract_minus_sign() and not(-n - 1).could_extract_minus_sign(): + return exp(x)*laguerre(-n - 1, -x) + # We can evaluate for some special values of x + if x.is_zero: + return S.One + elif x is S.NegativeInfinity: + return S.Infinity + elif x is S.Infinity: + return S.NegativeOne**n * S.Infinity + else: + if n.is_negative: + return exp(x)*laguerre(-n - 1, -x) + else: + return cls._eval_at_order(n, x) + + def fdiff(self, argindex=2): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt x + n, x = self.args + return -assoc_laguerre(n - 1, 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, x, **kwargs): + from sympy.concrete.summations import Sum + # Make sure n \in N_0 + if n.is_negative: + return exp(x) * self._eval_rewrite_as_Sum(-n - 1, -x, **kwargs) + if n.is_integer is False: + raise ValueError("Error: n should be an integer.") + k = Dummy("k") + kern = RisingFactorial(-n, k) / factorial(k)**2 * x**k + return Sum(kern, (k, 0, n)) + + def _eval_rewrite_as_polynomial(self, n, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, x, **kwargs) + + +class assoc_laguerre(OrthogonalPolynomial): + r""" + Returns the $n$th generalized Laguerre polynomial in $x$, $L_n(x)$. + + Examples + ======== + + >>> from sympy import assoc_laguerre, diff + >>> from sympy.abc import x, n, a + >>> assoc_laguerre(0, a, x) + 1 + >>> assoc_laguerre(1, a, x) + a - x + 1 + >>> assoc_laguerre(2, a, x) + a**2/2 + 3*a/2 + x**2/2 + x*(-a - 2) + 1 + >>> assoc_laguerre(3, a, x) + a**3/6 + a**2 + 11*a/6 - x**3/6 + x**2*(a/2 + 3/2) + + x*(-a**2/2 - 5*a/2 - 3) + 1 + + >>> assoc_laguerre(n, a, 0) + binomial(a + n, a) + + >>> assoc_laguerre(n, a, x) + assoc_laguerre(n, a, x) + + >>> assoc_laguerre(n, 0, x) + laguerre(n, x) + + >>> diff(assoc_laguerre(n, a, x), x) + -assoc_laguerre(n - 1, a + 1, x) + + >>> diff(assoc_laguerre(n, a, x), a) + Sum(assoc_laguerre(_k, a, x)/(-a + n), (_k, 0, n - 1)) + + Parameters + ========== + + n : int + Degree of Laguerre polynomial. Must be `n \ge 0`. + + alpha : Expr + Arbitrary expression. For ``alpha=0`` regular Laguerre + polynomials will be generated. + + See Also + ======== + + jacobi, gegenbauer, + chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, + legendre, assoc_legendre, + hermite, hermite_prob, + laguerre, + sympy.polys.orthopolys.jacobi_poly + sympy.polys.orthopolys.gegenbauer_poly + sympy.polys.orthopolys.chebyshevt_poly + sympy.polys.orthopolys.chebyshevu_poly + sympy.polys.orthopolys.hermite_poly + sympy.polys.orthopolys.hermite_prob_poly + sympy.polys.orthopolys.legendre_poly + sympy.polys.orthopolys.laguerre_poly + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Laguerre_polynomial#Generalized_Laguerre_polynomials + .. [2] https://mathworld.wolfram.com/AssociatedLaguerrePolynomial.html + .. [3] https://functions.wolfram.com/Polynomials/LaguerreL/ + .. [4] https://functions.wolfram.com/Polynomials/LaguerreL3/ + + """ + + @classmethod + def eval(cls, n, alpha, x): + # L_{n}^{0}(x) ---> L_{n}(x) + if alpha.is_zero: + return laguerre(n, x) + + if not n.is_Number: + # We can evaluate for some special values of x + if x.is_zero: + return binomial(n + alpha, alpha) + elif x is S.Infinity and n > 0: + return S.NegativeOne**n * S.Infinity + elif x is S.NegativeInfinity and n > 0: + return S.Infinity + else: + # n is a given fixed integer, evaluate into polynomial + if n.is_negative: + raise ValueError( + "The index n must be nonnegative integer (got %r)" % n) + else: + return laguerre_poly(n, x, alpha) + + def fdiff(self, argindex=3): + from sympy.concrete.summations import Sum + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt alpha + n, alpha, x = self.args + k = Dummy("k") + return Sum(assoc_laguerre(k, alpha, x) / (n - alpha), (k, 0, n - 1)) + elif argindex == 3: + # Diff wrt x + n, alpha, x = self.args + return -assoc_laguerre(n - 1, alpha + 1, x) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Sum(self, n, alpha, x, **kwargs): + from sympy.concrete.summations import Sum + # Make sure n \in N_0 + if n.is_negative or n.is_integer is False: + raise ValueError("Error: n should be a non-negative integer.") + k = Dummy("k") + kern = RisingFactorial( + -n, k) / (gamma(k + alpha + 1) * factorial(k)) * x**k + return gamma(n + alpha + 1) / factorial(n) * Sum(kern, (k, 0, n)) + + def _eval_rewrite_as_polynomial(self, n, alpha, x, **kwargs): + # This function is just kept for backwards compatibility + # but should not be used + return self._eval_rewrite_as_Sum(n, alpha, x, **kwargs) + + def _eval_conjugate(self): + n, alpha, x = self.args + return self.func(n, alpha.conjugate(), x.conjugate()) diff --git a/lib/python3.11/site-packages/sympy/functions/special/singularity_functions.py b/lib/python3.11/site-packages/sympy/functions/special/singularity_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..2de3678367b331641dcfd3bbd580b7f9dce1bb8c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/singularity_functions.py @@ -0,0 +1,235 @@ +from sympy.core import S, oo, diff +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.logic import fuzzy_not +from sympy.core.relational import Eq +from sympy.functions.elementary.complexes import im +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.delta_functions import Heaviside + +############################################################################### +############################# SINGULARITY FUNCTION ############################ +############################################################################### + + +class SingularityFunction(Function): + r""" + Singularity functions are a class of discontinuous functions. + + Explanation + =========== + + Singularity functions take a variable, an offset, and an exponent as + arguments. These functions are represented using Macaulay brackets as: + + SingularityFunction(x, a, n) := ^n + + The singularity function will automatically evaluate to + ``Derivative(DiracDelta(x - a), x, -n - 1)`` if ``n < 0`` + and ``(x - a)**n*Heaviside(x - a, 1)`` if ``n >= 0``. + + Examples + ======== + + >>> from sympy import SingularityFunction, diff, Piecewise, DiracDelta, Heaviside, Symbol + >>> from sympy.abc import x, a, n + >>> SingularityFunction(x, a, n) + SingularityFunction(x, a, n) + >>> y = Symbol('y', positive=True) + >>> n = Symbol('n', nonnegative=True) + >>> SingularityFunction(y, -10, n) + (y + 10)**n + >>> y = Symbol('y', negative=True) + >>> SingularityFunction(y, 10, n) + 0 + >>> SingularityFunction(x, 4, -1).subs(x, 4) + oo + >>> SingularityFunction(x, 10, -2).subs(x, 10) + oo + >>> SingularityFunction(4, 1, 5) + 243 + >>> diff(SingularityFunction(x, 1, 5) + SingularityFunction(x, 1, 4), x) + 4*SingularityFunction(x, 1, 3) + 5*SingularityFunction(x, 1, 4) + >>> diff(SingularityFunction(x, 4, 0), x, 2) + SingularityFunction(x, 4, -2) + >>> SingularityFunction(x, 4, 5).rewrite(Piecewise) + Piecewise(((x - 4)**5, x >= 4), (0, True)) + >>> expr = SingularityFunction(x, a, n) + >>> y = Symbol('y', positive=True) + >>> n = Symbol('n', nonnegative=True) + >>> expr.subs({x: y, a: -10, n: n}) + (y + 10)**n + + The methods ``rewrite(DiracDelta)``, ``rewrite(Heaviside)``, and + ``rewrite('HeavisideDiracDelta')`` returns the same output. One can use any + of these methods according to their choice. + + >>> expr = SingularityFunction(x, 4, 5) + SingularityFunction(x, -3, -1) - SingularityFunction(x, 0, -2) + >>> expr.rewrite(Heaviside) + (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1) + >>> expr.rewrite(DiracDelta) + (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1) + >>> expr.rewrite('HeavisideDiracDelta') + (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1) + + See Also + ======== + + DiracDelta, Heaviside + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Singularity_function + + """ + + is_real = True + + def fdiff(self, argindex=1): + """ + Returns the first derivative of a DiracDelta Function. + + Explanation + =========== + + The difference between ``diff()`` and ``fdiff()`` is: ``diff()`` is the + user-level function and ``fdiff()`` is an object method. ``fdiff()`` is + a convenience method available in the ``Function`` class. It returns + the derivative of the function without considering the chain rule. + ``diff(function, x)`` calls ``Function._eval_derivative`` which in turn + calls ``fdiff()`` internally to compute the derivative of the function. + + """ + + if argindex == 1: + x, a, n = self.args + if n in (S.Zero, S.NegativeOne, S(-2), S(-3)): + return self.func(x, a, n-1) + elif n.is_positive: + return n*self.func(x, a, n-1) + else: + raise ArgumentIndexError(self, argindex) + + @classmethod + def eval(cls, variable, offset, exponent): + """ + Returns a simplified form or a value of Singularity Function depending + on the argument passed by the object. + + Explanation + =========== + + The ``eval()`` method is automatically called when the + ``SingularityFunction`` class is about to be instantiated and it + returns either some simplified instance or the unevaluated instance + depending on the argument passed. In other words, ``eval()`` method is + not needed to be called explicitly, it is being called and evaluated + once the object is called. + + Examples + ======== + + >>> from sympy import SingularityFunction, Symbol, nan + >>> from sympy.abc import x, a, n + >>> SingularityFunction(x, a, n) + SingularityFunction(x, a, n) + >>> SingularityFunction(5, 3, 2) + 4 + >>> SingularityFunction(x, a, nan) + nan + >>> SingularityFunction(x, 3, 0).subs(x, 3) + 1 + >>> SingularityFunction(4, 1, 5) + 243 + >>> x = Symbol('x', positive = True) + >>> a = Symbol('a', negative = True) + >>> n = Symbol('n', nonnegative = True) + >>> SingularityFunction(x, a, n) + (-a + x)**n + >>> x = Symbol('x', negative = True) + >>> a = Symbol('a', positive = True) + >>> SingularityFunction(x, a, n) + 0 + + """ + + x = variable + a = offset + n = exponent + shift = (x - a) + + if fuzzy_not(im(shift).is_zero): + raise ValueError("Singularity Functions are defined only for Real Numbers.") + if fuzzy_not(im(n).is_zero): + raise ValueError("Singularity Functions are not defined for imaginary exponents.") + if shift is S.NaN or n is S.NaN: + return S.NaN + if (n + 4).is_negative: + raise ValueError("Singularity Functions are not defined for exponents less than -4.") + if shift.is_extended_negative: + return S.Zero + if n.is_nonnegative: + if shift.is_zero: # use literal 0 in case of Symbol('z', zero=True) + return S.Zero**n + if shift.is_extended_nonnegative: + return shift**n + if n in (S.NegativeOne, -2, -3, -4): + if shift.is_negative or shift.is_extended_positive: + return S.Zero + if shift.is_zero: + return oo + + def _eval_rewrite_as_Piecewise(self, *args, **kwargs): + ''' + Converts a Singularity Function expression into its Piecewise form. + + ''' + x, a, n = self.args + + if n in (S.NegativeOne, S(-2), S(-3), S(-4)): + return Piecewise((oo, Eq(x - a, 0)), (0, True)) + elif n.is_nonnegative: + return Piecewise(((x - a)**n, x - a >= 0), (0, True)) + + def _eval_rewrite_as_Heaviside(self, *args, **kwargs): + ''' + Rewrites a Singularity Function expression using Heavisides and DiracDeltas. + + ''' + x, a, n = self.args + + if n == -4: + return diff(Heaviside(x - a), x.free_symbols.pop(), 4) + if n == -3: + return diff(Heaviside(x - a), x.free_symbols.pop(), 3) + if n == -2: + return diff(Heaviside(x - a), x.free_symbols.pop(), 2) + if n == -1: + return diff(Heaviside(x - a), x.free_symbols.pop(), 1) + if n.is_nonnegative: + return (x - a)**n*Heaviside(x - a, 1) + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + z, a, n = self.args + shift = (z - a).subs(x, 0) + if n < 0: + return S.Zero + elif n.is_zero and shift.is_zero: + return S.Zero if cdir == -1 else S.One + elif shift.is_positive: + return shift**n + return S.Zero + + def _eval_nseries(self, x, n, logx=None, cdir=0): + z, a, n = self.args + shift = (z - a).subs(x, 0) + if n < 0: + return S.Zero + elif n.is_zero and shift.is_zero: + return S.Zero if cdir == -1 else S.One + elif shift.is_positive: + return ((z - a)**n)._eval_nseries(x, n, logx=logx, cdir=cdir) + return S.Zero + + _eval_rewrite_as_DiracDelta = _eval_rewrite_as_Heaviside + _eval_rewrite_as_HeavisideDiracDelta = _eval_rewrite_as_Heaviside diff --git a/lib/python3.11/site-packages/sympy/functions/special/spherical_harmonics.py b/lib/python3.11/site-packages/sympy/functions/special/spherical_harmonics.py new file mode 100644 index 0000000000000000000000000000000000000000..81d4d62da0809498051755220653c1679394ec5b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/spherical_harmonics.py @@ -0,0 +1,334 @@ +from sympy.core.expr import Expr +from sympy.core.function import Function, ArgumentIndexError +from sympy.core.numbers import I, pi +from sympy.core.singleton import S +from sympy.core.symbol import Dummy +from sympy.functions import assoc_legendre +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import Abs, conjugate +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sin, cos, cot + +_x = Dummy("x") + +class Ynm(Function): + r""" + Spherical harmonics defined as + + .. math:: + Y_n^m(\theta, \varphi) := \sqrt{\frac{(2n+1)(n-m)!}{4\pi(n+m)!}} + \exp(i m \varphi) + \mathrm{P}_n^m\left(\cos(\theta)\right) + + Explanation + =========== + + ``Ynm()`` gives the spherical harmonic function of order $n$ and $m$ + in $\theta$ and $\varphi$, $Y_n^m(\theta, \varphi)$. The four + parameters are as follows: $n \geq 0$ an integer and $m$ an integer + such that $-n \leq m \leq n$ holds. The two angles are real-valued + with $\theta \in [0, \pi]$ and $\varphi \in [0, 2\pi]$. + + Examples + ======== + + >>> from sympy import Ynm, Symbol, simplify + >>> from sympy.abc import n,m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + + >>> Ynm(n, m, theta, phi) + Ynm(n, m, theta, phi) + + Several symmetries are known, for the order: + + >>> Ynm(n, -m, theta, phi) + (-1)**m*exp(-2*I*m*phi)*Ynm(n, m, theta, phi) + + As well as for the angles: + + >>> Ynm(n, m, -theta, phi) + Ynm(n, m, theta, phi) + + >>> Ynm(n, m, theta, -phi) + exp(-2*I*m*phi)*Ynm(n, m, theta, phi) + + For specific integers $n$ and $m$ we can evaluate the harmonics + to more useful expressions: + + >>> simplify(Ynm(0, 0, theta, phi).expand(func=True)) + 1/(2*sqrt(pi)) + + >>> simplify(Ynm(1, -1, theta, phi).expand(func=True)) + sqrt(6)*exp(-I*phi)*sin(theta)/(4*sqrt(pi)) + + >>> simplify(Ynm(1, 0, theta, phi).expand(func=True)) + sqrt(3)*cos(theta)/(2*sqrt(pi)) + + >>> simplify(Ynm(1, 1, theta, phi).expand(func=True)) + -sqrt(6)*exp(I*phi)*sin(theta)/(4*sqrt(pi)) + + >>> simplify(Ynm(2, -2, theta, phi).expand(func=True)) + sqrt(30)*exp(-2*I*phi)*sin(theta)**2/(8*sqrt(pi)) + + >>> simplify(Ynm(2, -1, theta, phi).expand(func=True)) + sqrt(30)*exp(-I*phi)*sin(2*theta)/(8*sqrt(pi)) + + >>> simplify(Ynm(2, 0, theta, phi).expand(func=True)) + sqrt(5)*(3*cos(theta)**2 - 1)/(4*sqrt(pi)) + + >>> simplify(Ynm(2, 1, theta, phi).expand(func=True)) + -sqrt(30)*exp(I*phi)*sin(2*theta)/(8*sqrt(pi)) + + >>> simplify(Ynm(2, 2, theta, phi).expand(func=True)) + sqrt(30)*exp(2*I*phi)*sin(theta)**2/(8*sqrt(pi)) + + We can differentiate the functions with respect + to both angles: + + >>> from sympy import Ynm, Symbol, diff + >>> from sympy.abc import n,m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + + >>> diff(Ynm(n, m, theta, phi), theta) + m*cot(theta)*Ynm(n, m, theta, phi) + sqrt((-m + n)*(m + n + 1))*exp(-I*phi)*Ynm(n, m + 1, theta, phi) + + >>> diff(Ynm(n, m, theta, phi), phi) + I*m*Ynm(n, m, theta, phi) + + Further we can compute the complex conjugation: + + >>> from sympy import Ynm, Symbol, conjugate + >>> from sympy.abc import n,m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + + >>> conjugate(Ynm(n, m, theta, phi)) + (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi) + + To get back the well known expressions in spherical + coordinates, we use full expansion: + + >>> from sympy import Ynm, Symbol, expand_func + >>> from sympy.abc import n,m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + + >>> expand_func(Ynm(n, m, theta, phi)) + sqrt((2*n + 1)*factorial(-m + n)/factorial(m + n))*exp(I*m*phi)*assoc_legendre(n, m, cos(theta))/(2*sqrt(pi)) + + See Also + ======== + + Ynm_c, Znm + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics + .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html + .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/ + .. [4] https://dlmf.nist.gov/14.30 + + """ + + @classmethod + def eval(cls, n, m, theta, phi): + # Handle negative index m and arguments theta, phi + if m.could_extract_minus_sign(): + m = -m + return S.NegativeOne**m * exp(-2*I*m*phi) * Ynm(n, m, theta, phi) + if theta.could_extract_minus_sign(): + theta = -theta + return Ynm(n, m, theta, phi) + if phi.could_extract_minus_sign(): + phi = -phi + return exp(-2*I*m*phi) * Ynm(n, m, theta, phi) + + # TODO Add more simplififcation here + + def _eval_expand_func(self, **hints): + n, m, theta, phi = self.args + rv = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) * + exp(I*m*phi) * assoc_legendre(n, m, cos(theta))) + # We can do this because of the range of theta + return rv.subs(sqrt(-cos(theta)**2 + 1), sin(theta)) + + def fdiff(self, argindex=4): + if argindex == 1: + # Diff wrt n + raise ArgumentIndexError(self, argindex) + elif argindex == 2: + # Diff wrt m + raise ArgumentIndexError(self, argindex) + elif argindex == 3: + # Diff wrt theta + n, m, theta, phi = self.args + return (m * cot(theta) * Ynm(n, m, theta, phi) + + sqrt((n - m)*(n + m + 1)) * exp(-I*phi) * Ynm(n, m + 1, theta, phi)) + elif argindex == 4: + # Diff wrt phi + n, m, theta, phi = self.args + return I * m * Ynm(n, m, theta, phi) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_polynomial(self, n, m, theta, phi, **kwargs): + # TODO: Make sure n \in N + # TODO: Assert |m| <= n ortherwise we should return 0 + return self.expand(func=True) + + def _eval_rewrite_as_sin(self, n, m, theta, phi, **kwargs): + return self.rewrite(cos) + + def _eval_rewrite_as_cos(self, n, m, theta, phi, **kwargs): + # This method can be expensive due to extensive use of simplification! + from sympy.simplify import simplify, trigsimp + # TODO: Make sure n \in N + # TODO: Assert |m| <= n ortherwise we should return 0 + term = simplify(self.expand(func=True)) + # We can do this because of the range of theta + term = term.xreplace({Abs(sin(theta)):sin(theta)}) + return simplify(trigsimp(term)) + + def _eval_conjugate(self): + # TODO: Make sure theta \in R and phi \in R + n, m, theta, phi = self.args + return S.NegativeOne**m * self.func(n, -m, theta, phi) + + def as_real_imag(self, deep=True, **hints): + # TODO: Handle deep and hints + n, m, theta, phi = self.args + re = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) * + cos(m*phi) * assoc_legendre(n, m, cos(theta))) + im = (sqrt((2*n + 1)/(4*pi) * factorial(n - m)/factorial(n + m)) * + sin(m*phi) * assoc_legendre(n, m, cos(theta))) + return (re, im) + + def _eval_evalf(self, prec): + # Note: works without this function by just calling + # mpmath for Legendre polynomials. But using + # the dedicated function directly is cleaner. + from mpmath import mp, workprec + n = self.args[0]._to_mpmath(prec) + m = self.args[1]._to_mpmath(prec) + theta = self.args[2]._to_mpmath(prec) + phi = self.args[3]._to_mpmath(prec) + with workprec(prec): + res = mp.spherharm(n, m, theta, phi) + return Expr._from_mpmath(res, prec) + + +def Ynm_c(n, m, theta, phi): + r""" + Conjugate spherical harmonics defined as + + .. math:: + \overline{Y_n^m(\theta, \varphi)} := (-1)^m Y_n^{-m}(\theta, \varphi). + + Examples + ======== + + >>> from sympy import Ynm_c, Symbol, simplify + >>> from sympy.abc import n,m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + >>> Ynm_c(n, m, theta, phi) + (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi) + >>> Ynm_c(n, m, -theta, phi) + (-1)**(2*m)*exp(-2*I*m*phi)*Ynm(n, m, theta, phi) + + For specific integers $n$ and $m$ we can evaluate the harmonics + to more useful expressions: + + >>> simplify(Ynm_c(0, 0, theta, phi).expand(func=True)) + 1/(2*sqrt(pi)) + >>> simplify(Ynm_c(1, -1, theta, phi).expand(func=True)) + sqrt(6)*exp(I*(-phi + 2*conjugate(phi)))*sin(theta)/(4*sqrt(pi)) + + See Also + ======== + + Ynm, Znm + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics + .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html + .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/ + + """ + return conjugate(Ynm(n, m, theta, phi)) + + +class Znm(Function): + r""" + Real spherical harmonics defined as + + .. math:: + + Z_n^m(\theta, \varphi) := + \begin{cases} + \frac{Y_n^m(\theta, \varphi) + \overline{Y_n^m(\theta, \varphi)}}{\sqrt{2}} &\quad m > 0 \\ + Y_n^m(\theta, \varphi) &\quad m = 0 \\ + \frac{Y_n^m(\theta, \varphi) - \overline{Y_n^m(\theta, \varphi)}}{i \sqrt{2}} &\quad m < 0 \\ + \end{cases} + + which gives in simplified form + + .. math:: + + Z_n^m(\theta, \varphi) = + \begin{cases} + \frac{Y_n^m(\theta, \varphi) + (-1)^m Y_n^{-m}(\theta, \varphi)}{\sqrt{2}} &\quad m > 0 \\ + Y_n^m(\theta, \varphi) &\quad m = 0 \\ + \frac{Y_n^m(\theta, \varphi) - (-1)^m Y_n^{-m}(\theta, \varphi)}{i \sqrt{2}} &\quad m < 0 \\ + \end{cases} + + Examples + ======== + + >>> from sympy import Znm, Symbol, simplify + >>> from sympy.abc import n, m + >>> theta = Symbol("theta") + >>> phi = Symbol("phi") + >>> Znm(n, m, theta, phi) + Znm(n, m, theta, phi) + + For specific integers n and m we can evaluate the harmonics + to more useful expressions: + + >>> simplify(Znm(0, 0, theta, phi).expand(func=True)) + 1/(2*sqrt(pi)) + >>> simplify(Znm(1, 1, theta, phi).expand(func=True)) + -sqrt(3)*sin(theta)*cos(phi)/(2*sqrt(pi)) + >>> simplify(Znm(2, 1, theta, phi).expand(func=True)) + -sqrt(15)*sin(2*theta)*cos(phi)/(4*sqrt(pi)) + + See Also + ======== + + Ynm, Ynm_c + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Spherical_harmonics + .. [2] https://mathworld.wolfram.com/SphericalHarmonic.html + .. [3] https://functions.wolfram.com/Polynomials/SphericalHarmonicY/ + + """ + + @classmethod + def eval(cls, n, m, theta, phi): + if m.is_positive: + zz = (Ynm(n, m, theta, phi) + Ynm_c(n, m, theta, phi)) / sqrt(2) + return zz + elif m.is_zero: + return Ynm(n, m, theta, phi) + elif m.is_negative: + zz = (Ynm(n, m, theta, phi) - Ynm_c(n, m, theta, phi)) / (sqrt(2)*I) + return zz diff --git a/lib/python3.11/site-packages/sympy/functions/special/tensor_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tensor_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..ea91dc63d1f8a3d557112de1d1927b167752c48c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tensor_functions.py @@ -0,0 +1,474 @@ +from math import prod + +from sympy.core import S, Integer +from sympy.core.function import Function +from sympy.core.logic import fuzzy_not +from sympy.core.relational import Ne +from sympy.core.sorting import default_sort_key +from sympy.external.gmpy import SYMPY_INTS +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.piecewise import Piecewise +from sympy.utilities.iterables import has_dups + +############################################################################### +###################### Kronecker Delta, Levi-Civita etc. ###################### +############################################################################### + + +def Eijk(*args, **kwargs): + """ + Represent the Levi-Civita symbol. + + This is a compatibility wrapper to ``LeviCivita()``. + + See Also + ======== + + LeviCivita + + """ + return LeviCivita(*args, **kwargs) + + +def eval_levicivita(*args): + """Evaluate Levi-Civita symbol.""" + n = len(args) + return prod( + prod(args[j] - args[i] for j in range(i + 1, n)) + / factorial(i) for i in range(n)) + # converting factorial(i) to int is slightly faster + + +class LeviCivita(Function): + """ + Represent the Levi-Civita symbol. + + Explanation + =========== + + For even permutations of indices it returns 1, for odd permutations -1, and + for everything else (a repeated index) it returns 0. + + Thus it represents an alternating pseudotensor. + + Examples + ======== + + >>> from sympy import LeviCivita + >>> from sympy.abc import i, j, k + >>> LeviCivita(1, 2, 3) + 1 + >>> LeviCivita(1, 3, 2) + -1 + >>> LeviCivita(1, 2, 2) + 0 + >>> LeviCivita(i, j, k) + LeviCivita(i, j, k) + >>> LeviCivita(i, j, i) + 0 + + See Also + ======== + + Eijk + + """ + + is_integer = True + + @classmethod + def eval(cls, *args): + if all(isinstance(a, (SYMPY_INTS, Integer)) for a in args): + return eval_levicivita(*args) + if has_dups(args): + return S.Zero + + def doit(self, **hints): + return eval_levicivita(*self.args) + + +class KroneckerDelta(Function): + """ + The discrete, or Kronecker, delta function. + + Explanation + =========== + + A function that takes in two integers $i$ and $j$. It returns $0$ if $i$ + and $j$ are not equal, or it returns $1$ if $i$ and $j$ are equal. + + Examples + ======== + + An example with integer indices: + + >>> from sympy import KroneckerDelta + >>> KroneckerDelta(1, 2) + 0 + >>> KroneckerDelta(3, 3) + 1 + + Symbolic indices: + + >>> from sympy.abc import i, j, k + >>> KroneckerDelta(i, j) + KroneckerDelta(i, j) + >>> KroneckerDelta(i, i) + 1 + >>> KroneckerDelta(i, i + 1) + 0 + >>> KroneckerDelta(i, i + 1 + k) + KroneckerDelta(i, i + k + 1) + + Parameters + ========== + + i : Number, Symbol + The first index of the delta function. + j : Number, Symbol + The second index of the delta function. + + See Also + ======== + + eval + DiracDelta + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Kronecker_delta + + """ + + is_integer = True + + @classmethod + def eval(cls, i, j, delta_range=None): + """ + Evaluates the discrete delta function. + + Examples + ======== + + >>> from sympy import KroneckerDelta + >>> from sympy.abc import i, j, k + + >>> KroneckerDelta(i, j) + KroneckerDelta(i, j) + >>> KroneckerDelta(i, i) + 1 + >>> KroneckerDelta(i, i + 1) + 0 + >>> KroneckerDelta(i, i + 1 + k) + KroneckerDelta(i, i + k + 1) + + # indirect doctest + + """ + + if delta_range is not None: + dinf, dsup = delta_range + if (dinf - i > 0) == True: + return S.Zero + if (dinf - j > 0) == True: + return S.Zero + if (dsup - i < 0) == True: + return S.Zero + if (dsup - j < 0) == True: + return S.Zero + + diff = i - j + if diff.is_zero: + return S.One + elif fuzzy_not(diff.is_zero): + return S.Zero + + if i.assumptions0.get("below_fermi") and \ + j.assumptions0.get("above_fermi"): + return S.Zero + if j.assumptions0.get("below_fermi") and \ + i.assumptions0.get("above_fermi"): + return S.Zero + # to make KroneckerDelta canonical + # following lines will check if inputs are in order + # if not, will return KroneckerDelta with correct order + if default_sort_key(j) < default_sort_key(i): + if delta_range: + return cls(j, i, delta_range) + else: + return cls(j, i) + + @property + def delta_range(self): + if len(self.args) > 2: + return self.args[2] + + def _eval_power(self, expt): + if expt.is_positive: + return self + if expt.is_negative and expt is not S.NegativeOne: + return 1/self + + @property + def is_above_fermi(self): + """ + True if Delta can be non-zero above fermi. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> p = Symbol('p') + >>> q = Symbol('q') + >>> KroneckerDelta(p, a).is_above_fermi + True + >>> KroneckerDelta(p, i).is_above_fermi + False + >>> KroneckerDelta(p, q).is_above_fermi + True + + See Also + ======== + + is_below_fermi, is_only_below_fermi, is_only_above_fermi + + """ + if self.args[0].assumptions0.get("below_fermi"): + return False + if self.args[1].assumptions0.get("below_fermi"): + return False + return True + + @property + def is_below_fermi(self): + """ + True if Delta can be non-zero below fermi. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> p = Symbol('p') + >>> q = Symbol('q') + >>> KroneckerDelta(p, a).is_below_fermi + False + >>> KroneckerDelta(p, i).is_below_fermi + True + >>> KroneckerDelta(p, q).is_below_fermi + True + + See Also + ======== + + is_above_fermi, is_only_above_fermi, is_only_below_fermi + + """ + if self.args[0].assumptions0.get("above_fermi"): + return False + if self.args[1].assumptions0.get("above_fermi"): + return False + return True + + @property + def is_only_above_fermi(self): + """ + True if Delta is restricted to above fermi. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> p = Symbol('p') + >>> q = Symbol('q') + >>> KroneckerDelta(p, a).is_only_above_fermi + True + >>> KroneckerDelta(p, q).is_only_above_fermi + False + >>> KroneckerDelta(p, i).is_only_above_fermi + False + + See Also + ======== + + is_above_fermi, is_below_fermi, is_only_below_fermi + + """ + return ( self.args[0].assumptions0.get("above_fermi") + or + self.args[1].assumptions0.get("above_fermi") + ) or False + + @property + def is_only_below_fermi(self): + """ + True if Delta is restricted to below fermi. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> p = Symbol('p') + >>> q = Symbol('q') + >>> KroneckerDelta(p, i).is_only_below_fermi + True + >>> KroneckerDelta(p, q).is_only_below_fermi + False + >>> KroneckerDelta(p, a).is_only_below_fermi + False + + See Also + ======== + + is_above_fermi, is_below_fermi, is_only_above_fermi + + """ + return ( self.args[0].assumptions0.get("below_fermi") + or + self.args[1].assumptions0.get("below_fermi") + ) or False + + @property + def indices_contain_equal_information(self): + """ + Returns True if indices are either both above or below fermi. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> p = Symbol('p') + >>> q = Symbol('q') + >>> KroneckerDelta(p, q).indices_contain_equal_information + True + >>> KroneckerDelta(p, q+1).indices_contain_equal_information + True + >>> KroneckerDelta(i, p).indices_contain_equal_information + False + + """ + if (self.args[0].assumptions0.get("below_fermi") and + self.args[1].assumptions0.get("below_fermi")): + return True + if (self.args[0].assumptions0.get("above_fermi") + and self.args[1].assumptions0.get("above_fermi")): + return True + + # if both indices are general we are True, else false + return self.is_below_fermi and self.is_above_fermi + + @property + def preferred_index(self): + """ + Returns the index which is preferred to keep in the final expression. + + Explanation + =========== + + The preferred index is the index with more information regarding fermi + level. If indices contain the same information, 'a' is preferred before + 'b'. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> j = Symbol('j', below_fermi=True) + >>> p = Symbol('p') + >>> KroneckerDelta(p, i).preferred_index + i + >>> KroneckerDelta(p, a).preferred_index + a + >>> KroneckerDelta(i, j).preferred_index + i + + See Also + ======== + + killable_index + + """ + if self._get_preferred_index(): + return self.args[1] + else: + return self.args[0] + + @property + def killable_index(self): + """ + Returns the index which is preferred to substitute in the final + expression. + + Explanation + =========== + + The index to substitute is the index with less information regarding + fermi level. If indices contain the same information, 'a' is preferred + before 'b'. + + Examples + ======== + + >>> from sympy import KroneckerDelta, Symbol + >>> a = Symbol('a', above_fermi=True) + >>> i = Symbol('i', below_fermi=True) + >>> j = Symbol('j', below_fermi=True) + >>> p = Symbol('p') + >>> KroneckerDelta(p, i).killable_index + p + >>> KroneckerDelta(p, a).killable_index + p + >>> KroneckerDelta(i, j).killable_index + j + + See Also + ======== + + preferred_index + + """ + if self._get_preferred_index(): + return self.args[0] + else: + return self.args[1] + + def _get_preferred_index(self): + """ + Returns the index which is preferred to keep in the final expression. + + The preferred index is the index with more information regarding fermi + level. 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0000000000000000000000000000000000000000..345f18ba092324bc2bf161fe7582c0ad3d9b619f Binary files /dev/null and b/lib/python3.11/site-packages/sympy/functions/special/tests/__pycache__/test_zeta_functions.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_bessel.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_bessel.py new file mode 100644 index 0000000000000000000000000000000000000000..aaeb3df5c63776cb11023cfe8011e2b416caf68e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_bessel.py @@ -0,0 +1,765 @@ +from itertools import product + +from sympy.concrete.summations import Sum +from sympy.core.function import (diff, expand_func) +from sympy.core.numbers import (I, Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (conjugate, polar_lift) +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.hyperbolic import (cosh, sinh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.bessel import (besseli, besselj, besselk, bessely, hankel1, hankel2, hn1, hn2, jn, jn_zeros, yn) +from sympy.functions.special.gamma_functions import (gamma, uppergamma) +from sympy.functions.special.hyper import hyper +from sympy.integrals.integrals import Integral +from sympy.series.order import O +from sympy.series.series import series +from sympy.functions.special.bessel import (airyai, airybi, + airyaiprime, airybiprime, marcumq) +from sympy.core.random import (random_complex_number as randcplx, + verify_numerically as tn, + test_derivative_numerically as td, + _randint) +from sympy.simplify import besselsimp +from sympy.testing.pytest import raises, slow + +from sympy.abc import z, n, k, x + +randint = _randint() + + +def test_bessel_rand(): + for f in [besselj, bessely, besseli, besselk, hankel1, hankel2]: + assert td(f(randcplx(), z), z) + + for f in [jn, yn, hn1, hn2]: + assert td(f(randint(-10, 10), z), z) + + +def test_bessel_twoinputs(): + for f in [besselj, bessely, besseli, besselk, hankel1, hankel2, jn, yn]: + raises(TypeError, lambda: f(1)) + raises(TypeError, lambda: f(1, 2, 3)) + + +def test_besselj_leading_term(): + assert besselj(0, x).as_leading_term(x) == 1 + assert besselj(1, sin(x)).as_leading_term(x) == x/2 + assert besselj(1, 2*sqrt(x)).as_leading_term(x) == sqrt(x) + + # https://github.com/sympy/sympy/issues/21701 + assert (besselj(z, x)/x**z).as_leading_term(x) == 1/(2**z*gamma(z + 1)) + + +def test_bessely_leading_term(): + assert bessely(0, x).as_leading_term(x) == (2*log(x) - 2*log(2) + 2*S.EulerGamma)/pi + assert bessely(1, sin(x)).as_leading_term(x) == -2/(pi*x) + assert bessely(1, 2*sqrt(x)).as_leading_term(x) == -1/(pi*sqrt(x)) + + +def test_besseli_leading_term(): + assert besseli(0, x).as_leading_term(x) == 1 + assert besseli(1, sin(x)).as_leading_term(x) == x/2 + assert besseli(1, 2*sqrt(x)).as_leading_term(x) == sqrt(x) + + +def test_besselk_leading_term(): + assert besselk(0, x).as_leading_term(x) == -log(x) - S.EulerGamma + log(2) + assert besselk(1, sin(x)).as_leading_term(x) == 1/x + assert besselk(1, 2*sqrt(x)).as_leading_term(x) == 1/(2*sqrt(x)) + + +def test_besselj_series(): + assert besselj(0, x).series(x) == 1 - x**2/4 + x**4/64 + O(x**6) + assert besselj(0, x**(1.1)).series(x) == 1 + x**4.4/64 - x**2.2/4 + O(x**6) + assert besselj(0, x**2 + x).series(x) == 1 - x**2/4 - x**3/2\ + - 15*x**4/64 + x**5/16 + O(x**6) + assert besselj(0, sqrt(x) + x).series(x, n=4) == 1 - x/4 - 15*x**2/64\ + + 215*x**3/2304 - x**Rational(3, 2)/2 + x**Rational(5, 2)/16\ + + 23*x**Rational(7, 2)/384 + O(x**4) + assert besselj(0, x/(1 - x)).series(x) == 1 - x**2/4 - x**3/2 - 47*x**4/64\ + - 15*x**5/16 + O(x**6) + assert besselj(0, log(1 + x)).series(x) == 1 - x**2/4 + x**3/4\ + - 41*x**4/192 + 17*x**5/96 + O(x**6) + assert besselj(1, sin(x)).series(x) == x/2 - 7*x**3/48 + 73*x**5/1920 + O(x**6) + assert besselj(1, 2*sqrt(x)).series(x) == sqrt(x) - x**Rational(3, 2)/2\ + + x**Rational(5, 2)/12 - x**Rational(7, 2)/144 + x**Rational(9, 2)/2880\ + - x**Rational(11, 2)/86400 + O(x**6) + assert besselj(-2, sin(x)).series(x, n=4) == besselj(2, sin(x)).series(x, n=4) + + +def test_bessely_series(): + const = 2*S.EulerGamma/pi - 2*log(2)/pi + 2*log(x)/pi + assert bessely(0, x).series(x, n=4) == const + x**2*(-log(x)/(2*pi)\ + + (2 - 2*S.EulerGamma)/(4*pi) + log(2)/(2*pi)) + O(x**4*log(x)) + assert bessely(1, x).series(x, n=4) == -2/(pi*x) + x*(log(x)/pi - log(2)/pi - \ + (1 - 2*S.EulerGamma)/(2*pi)) + x**3*(-log(x)/(8*pi) + \ + (S(5)/2 - 2*S.EulerGamma)/(16*pi) + log(2)/(8*pi)) + O(x**4*log(x)) + assert bessely(2, x).series(x, n=4) == -4/(pi*x**2) - 1/pi + x**2*(log(x)/(4*pi) - \ + log(2)/(4*pi) - (S(3)/2 - 2*S.EulerGamma)/(8*pi)) + O(x**4*log(x)) + assert bessely(3, x).series(x, n=4) == -16/(pi*x**3) - 2/(pi*x) - \ + x/(4*pi) + x**3*(log(x)/(24*pi) - log(2)/(24*pi) - \ + (S(11)/6 - 2*S.EulerGamma)/(48*pi)) + O(x**4*log(x)) + assert bessely(0, x**(1.1)).series(x, n=4) == 2*S.EulerGamma/pi\ + - 2*log(2)/pi + 2.2*log(x)/pi + x**2.2*(-0.55*log(x)/pi\ + + (2 - 2*S.EulerGamma)/(4*pi) + log(2)/(2*pi)) + O(x**4*log(x)) + assert bessely(0, x**2 + x).series(x, n=4) == \ + const - (2 - 2*S.EulerGamma)*(-x**3/(2*pi) - x**2/(4*pi)) + 2*x/pi\ + + x**2*(-log(x)/(2*pi) - 1/pi + log(2)/(2*pi))\ + + x**3*(-log(x)/pi + 1/(6*pi) + log(2)/pi) + O(x**4*log(x)) + assert bessely(0, x/(1 - x)).series(x, n=3) == const\ + + 2*x/pi + x**2*(-log(x)/(2*pi) + (2 - 2*S.EulerGamma)/(4*pi)\ + + log(2)/(2*pi) + 1/pi) + O(x**3*log(x)) + assert bessely(0, log(1 + x)).series(x, n=3) == const\ + - x/pi + x**2*(-log(x)/(2*pi) + (2 - 2*S.EulerGamma)/(4*pi)\ + + log(2)/(2*pi) + 5/(12*pi)) + O(x**3*log(x)) + assert bessely(1, sin(x)).series(x, n=4) == -1/(pi*(-x**3/12 + x/2)) - \ + (1 - 2*S.EulerGamma)*(-x**3/12 + x/2)/pi + x*(log(x)/pi - log(2)/pi) + \ + x**3*(-7*log(x)/(24*pi) - 1/(6*pi) + (S(5)/2 - 2*S.EulerGamma)/(16*pi) + + 7*log(2)/(24*pi)) + O(x**4*log(x)) + assert bessely(1, 2*sqrt(x)).series(x, n=3) == -1/(pi*sqrt(x)) + \ + sqrt(x)*(log(x)/pi - (1 - 2*S.EulerGamma)/pi) + x**(S(3)/2)*(-log(x)/(2*pi) + \ + (S(5)/2 - 2*S.EulerGamma)/(2*pi)) + x**(S(5)/2)*(log(x)/(12*pi) - \ + (S(10)/3 - 2*S.EulerGamma)/(12*pi)) + O(x**3*log(x)) + assert bessely(-2, sin(x)).series(x, n=4) == bessely(2, sin(x)).series(x, n=4) + + +def test_besseli_series(): + assert besseli(0, x).series(x) == 1 + x**2/4 + x**4/64 + O(x**6) + assert besseli(0, x**(1.1)).series(x) == 1 + x**4.4/64 + x**2.2/4 + O(x**6) + assert besseli(0, x**2 + x).series(x) == 1 + x**2/4 + x**3/2 + 17*x**4/64 + \ + x**5/16 + O(x**6) + assert besseli(0, sqrt(x) + x).series(x, n=4) == 1 + x/4 + 17*x**2/64 + \ + 217*x**3/2304 + x**(S(3)/2)/2 + x**(S(5)/2)/16 + 25*x**(S(7)/2)/384 + O(x**4) + assert besseli(0, x/(1 - x)).series(x) == 1 + x**2/4 + x**3/2 + 49*x**4/64 + \ + 17*x**5/16 + O(x**6) + assert besseli(0, log(1 + x)).series(x) == 1 + x**2/4 - x**3/4 + 47*x**4/192 - \ + 23*x**5/96 + O(x**6) + assert besseli(1, sin(x)).series(x) == x/2 - x**3/48 - 47*x**5/1920 + O(x**6) + assert besseli(1, 2*sqrt(x)).series(x) == sqrt(x) + x**(S(3)/2)/2 + x**(S(5)/2)/12 + \ + x**(S(7)/2)/144 + x**(S(9)/2)/2880 + x**(S(11)/2)/86400 + O(x**6) + assert besseli(-2, sin(x)).series(x, n=4) == besseli(2, sin(x)).series(x, n=4) + + +def test_besselk_series(): + const = log(2) - S.EulerGamma - log(x) + assert besselk(0, x).series(x, n=4) == const + \ + x**2*(-log(x)/4 - S.EulerGamma/4 + log(2)/4 + S(1)/4) + O(x**4*log(x)) + assert besselk(1, x).series(x, n=4) == 1/x + x*(log(x)/2 - log(2)/2 - \ + S(1)/4 + S.EulerGamma/2) + x**3*(log(x)/16 - S(5)/64 - log(2)/16 + \ + S.EulerGamma/16) + O(x**4*log(x)) + assert besselk(2, x).series(x, n=4) == 2/x**2 - S(1)/2 + x**2*(-log(x)/8 - \ + S.EulerGamma/8 + log(2)/8 + S(3)/32) + O(x**4*log(x)) + assert besselk(0, x**(1.1)).series(x, n=4) == log(2) - S.EulerGamma - \ + 1.1*log(x) + x**2.2*(-0.275*log(x) - S.EulerGamma/4 + \ + log(2)/4 + S(1)/4) + O(x**4*log(x)) + assert besselk(0, x**2 + x).series(x, n=4) == const + \ + (2 - 2*S.EulerGamma)*(x**3/4 + x**2/8) - x + x**2*(-log(x)/4 + \ + log(2)/4 + S(1)/2) + x**3*(-log(x)/2 - S(7)/12 + log(2)/2) + O(x**4*log(x)) + assert besselk(0, x/(1 - x)).series(x, n=3) == const - x + x**2*(-log(x)/4 - \ + S(1)/4 - S.EulerGamma/4 + log(2)/4) + O(x**3*log(x)) + assert besselk(0, log(1 + x)).series(x, n=3) == const + x/2 + \ + x**2*(-log(x)/4 - S.EulerGamma/4 + S(1)/24 + log(2)/4) + O(x**3*log(x)) + assert besselk(1, 2*sqrt(x)).series(x, n=3) == 1/(2*sqrt(x)) + \ + sqrt(x)*(log(x)/2 - S(1)/2 + S.EulerGamma) + x**(S(3)/2)*(log(x)/4 - S(5)/8 + \ + S.EulerGamma/2) + x**(S(5)/2)*(log(x)/24 - S(5)/36 + S.EulerGamma/12) + O(x**3*log(x)) + assert besselk(-2, sin(x)).series(x, n=4) == besselk(2, sin(x)).series(x, n=4) + + +def test_diff(): + assert besselj(n, z).diff(z) == besselj(n - 1, z)/2 - besselj(n + 1, z)/2 + assert bessely(n, z).diff(z) == bessely(n - 1, z)/2 - bessely(n + 1, z)/2 + assert besseli(n, z).diff(z) == besseli(n - 1, z)/2 + besseli(n + 1, z)/2 + assert besselk(n, z).diff(z) == -besselk(n - 1, z)/2 - besselk(n + 1, z)/2 + assert hankel1(n, z).diff(z) == hankel1(n - 1, z)/2 - hankel1(n + 1, z)/2 + assert hankel2(n, z).diff(z) == hankel2(n - 1, z)/2 - hankel2(n + 1, z)/2 + + +def test_rewrite(): + assert besselj(n, z).rewrite(jn) == sqrt(2*z/pi)*jn(n - S.Half, z) + assert bessely(n, z).rewrite(yn) == sqrt(2*z/pi)*yn(n - S.Half, z) + assert besseli(n, z).rewrite(besselj) == \ + exp(-I*n*pi/2)*besselj(n, polar_lift(I)*z) + assert besselj(n, z).rewrite(besseli) == \ + exp(I*n*pi/2)*besseli(n, polar_lift(-I)*z) + + nu = randcplx() + + assert tn(besselj(nu, z), besselj(nu, z).rewrite(besseli), z) + assert tn(besselj(nu, z), besselj(nu, z).rewrite(bessely), z) + + assert tn(besseli(nu, z), besseli(nu, z).rewrite(besselj), z) + assert tn(besseli(nu, z), besseli(nu, z).rewrite(bessely), z) + + assert tn(bessely(nu, z), bessely(nu, z).rewrite(besselj), z) + assert tn(bessely(nu, z), bessely(nu, z).rewrite(besseli), z) + + assert tn(besselk(nu, z), besselk(nu, z).rewrite(besselj), z) + assert tn(besselk(nu, z), besselk(nu, z).rewrite(besseli), z) + assert tn(besselk(nu, z), besselk(nu, z).rewrite(bessely), z) + + # check that a rewrite was triggered, when the order is set to a generic + # symbol 'nu' + assert yn(nu, z) != yn(nu, z).rewrite(jn) + assert hn1(nu, z) != hn1(nu, z).rewrite(jn) + assert hn2(nu, z) != hn2(nu, z).rewrite(jn) + assert jn(nu, z) != jn(nu, z).rewrite(yn) + assert hn1(nu, z) != hn1(nu, z).rewrite(yn) + assert hn2(nu, z) != hn2(nu, z).rewrite(yn) + + # rewriting spherical bessel functions (SBFs) w.r.t. besselj, bessely is + # not allowed if a generic symbol 'nu' is used as the order of the SBFs + # to avoid inconsistencies (the order of bessel[jy] is allowed to be + # complex-valued, whereas SBFs are defined only for integer orders) + order = nu + for f in (besselj, bessely): + assert hn1(order, z) == hn1(order, z).rewrite(f) + assert hn2(order, z) == hn2(order, z).rewrite(f) + + assert jn(order, z).rewrite(besselj) == sqrt(2)*sqrt(pi)*sqrt(1/z)*besselj(order + S.Half, z)/2 + assert jn(order, z).rewrite(bessely) == (-1)**nu*sqrt(2)*sqrt(pi)*sqrt(1/z)*bessely(-order - S.Half, z)/2 + + # for integral orders rewriting SBFs w.r.t bessel[jy] is allowed + N = Symbol('n', integer=True) + ri = randint(-11, 10) + for order in (ri, N): + for f in (besselj, bessely): + assert yn(order, z) != yn(order, z).rewrite(f) + assert jn(order, z) != jn(order, z).rewrite(f) + assert hn1(order, z) != hn1(order, z).rewrite(f) + assert hn2(order, z) != hn2(order, z).rewrite(f) + + for func, refunc in product((yn, jn, hn1, hn2), + (jn, yn, besselj, bessely)): + assert tn(func(ri, z), func(ri, z).rewrite(refunc), z) + + +def test_expand(): + assert expand_func(besselj(S.Half, z).rewrite(jn)) == \ + sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z)) + assert expand_func(bessely(S.Half, z).rewrite(yn)) == \ + -sqrt(2)*cos(z)/(sqrt(pi)*sqrt(z)) + + # XXX: teach sin/cos to work around arguments like + # x*exp_polar(I*pi*n/2). Then change besselsimp -> expand_func + assert besselsimp(besselj(S.Half, z)) == sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z)) + assert besselsimp(besselj(Rational(-1, 2), z)) == sqrt(2)*cos(z)/(sqrt(pi)*sqrt(z)) + assert besselsimp(besselj(Rational(5, 2), z)) == \ + -sqrt(2)*(z**2*sin(z) + 3*z*cos(z) - 3*sin(z))/(sqrt(pi)*z**Rational(5, 2)) + assert besselsimp(besselj(Rational(-5, 2), z)) == \ + -sqrt(2)*(z**2*cos(z) - 3*z*sin(z) - 3*cos(z))/(sqrt(pi)*z**Rational(5, 2)) + + assert besselsimp(bessely(S.Half, z)) == \ + -(sqrt(2)*cos(z))/(sqrt(pi)*sqrt(z)) + assert besselsimp(bessely(Rational(-1, 2), z)) == sqrt(2)*sin(z)/(sqrt(pi)*sqrt(z)) + assert besselsimp(bessely(Rational(5, 2), z)) == \ + sqrt(2)*(z**2*cos(z) - 3*z*sin(z) - 3*cos(z))/(sqrt(pi)*z**Rational(5, 2)) + assert besselsimp(bessely(Rational(-5, 2), z)) == \ + -sqrt(2)*(z**2*sin(z) + 3*z*cos(z) - 3*sin(z))/(sqrt(pi)*z**Rational(5, 2)) + + assert besselsimp(besseli(S.Half, z)) == sqrt(2)*sinh(z)/(sqrt(pi)*sqrt(z)) + assert besselsimp(besseli(Rational(-1, 2), z)) == \ + sqrt(2)*cosh(z)/(sqrt(pi)*sqrt(z)) + assert besselsimp(besseli(Rational(5, 2), z)) == \ + sqrt(2)*(z**2*sinh(z) - 3*z*cosh(z) + 3*sinh(z))/(sqrt(pi)*z**Rational(5, 2)) + assert besselsimp(besseli(Rational(-5, 2), z)) == \ + sqrt(2)*(z**2*cosh(z) - 3*z*sinh(z) + 3*cosh(z))/(sqrt(pi)*z**Rational(5, 2)) + + assert besselsimp(besselk(S.Half, z)) == \ + besselsimp(besselk(Rational(-1, 2), z)) == sqrt(pi)*exp(-z)/(sqrt(2)*sqrt(z)) + assert besselsimp(besselk(Rational(5, 2), z)) == \ + besselsimp(besselk(Rational(-5, 2), z)) == \ + sqrt(2)*sqrt(pi)*(z**2 + 3*z + 3)*exp(-z)/(2*z**Rational(5, 2)) + + n = Symbol('n', integer=True, positive=True) + + assert expand_func(besseli(n + 2, z)) == \ + besseli(n, z) + (-2*n - 2)*(-2*n*besseli(n, z)/z + besseli(n - 1, z))/z + assert expand_func(besselj(n + 2, z)) == \ + -besselj(n, z) + (2*n + 2)*(2*n*besselj(n, z)/z - besselj(n - 1, z))/z + assert expand_func(besselk(n + 2, z)) == \ + besselk(n, z) + (2*n + 2)*(2*n*besselk(n, z)/z + besselk(n - 1, z))/z + assert expand_func(bessely(n + 2, z)) == \ + -bessely(n, z) + (2*n + 2)*(2*n*bessely(n, z)/z - bessely(n - 1, z))/z + + assert expand_func(besseli(n + S.Half, z).rewrite(jn)) == \ + (sqrt(2)*sqrt(z)*exp(-I*pi*(n + S.Half)/2) * + exp_polar(I*pi/4)*jn(n, z*exp_polar(I*pi/2))/sqrt(pi)) + assert expand_func(besselj(n + S.Half, z).rewrite(jn)) == \ + sqrt(2)*sqrt(z)*jn(n, z)/sqrt(pi) + + r = Symbol('r', real=True) + p = Symbol('p', positive=True) + i = Symbol('i', integer=True) + + for besselx in [besselj, bessely, besseli, besselk]: + assert besselx(i, p).is_extended_real is True + assert besselx(i, x).is_extended_real is None + assert besselx(x, z).is_extended_real is None + + for besselx in [besselj, besseli]: + assert besselx(i, r).is_extended_real is True + for besselx in [bessely, besselk]: + assert besselx(i, r).is_extended_real is None + + for besselx in [besselj, bessely, besseli, besselk]: + assert expand_func(besselx(oo, x)) == besselx(oo, x, evaluate=False) + assert expand_func(besselx(-oo, x)) == besselx(-oo, x, evaluate=False) + + +# Quite varying time, but often really slow +@slow +def test_slow_expand(): + def check(eq, ans): + return tn(eq, ans) and eq == ans + + rn = randcplx(a=1, b=0, d=0, c=2) + + for besselx in [besselj, bessely, besseli, besselk]: + ri = S(2*randint(-11, 10) + 1) / 2 # half integer in [-21/2, 21/2] + assert tn(besselsimp(besselx(ri, z)), besselx(ri, z)) + + assert check(expand_func(besseli(rn, x)), + besseli(rn - 2, x) - 2*(rn - 1)*besseli(rn - 1, x)/x) + assert check(expand_func(besseli(-rn, x)), + besseli(-rn + 2, x) + 2*(-rn + 1)*besseli(-rn + 1, x)/x) + + assert check(expand_func(besselj(rn, x)), + -besselj(rn - 2, x) + 2*(rn - 1)*besselj(rn - 1, x)/x) + assert check(expand_func(besselj(-rn, x)), + -besselj(-rn + 2, x) + 2*(-rn + 1)*besselj(-rn + 1, x)/x) + + assert check(expand_func(besselk(rn, x)), + besselk(rn - 2, x) + 2*(rn - 1)*besselk(rn - 1, x)/x) + assert check(expand_func(besselk(-rn, x)), + besselk(-rn + 2, x) - 2*(-rn + 1)*besselk(-rn + 1, x)/x) + + assert check(expand_func(bessely(rn, x)), + -bessely(rn - 2, x) + 2*(rn - 1)*bessely(rn - 1, x)/x) + assert check(expand_func(bessely(-rn, x)), + -bessely(-rn + 2, x) + 2*(-rn + 1)*bessely(-rn + 1, x)/x) + + +def mjn(n, z): + return expand_func(jn(n, z)) + + +def myn(n, z): + return expand_func(yn(n, z)) + + +def test_jn(): + z = symbols("z") + assert jn(0, 0) == 1 + assert jn(1, 0) == 0 + assert jn(-1, 0) == S.ComplexInfinity + assert jn(z, 0) == jn(z, 0, evaluate=False) + assert jn(0, oo) == 0 + assert jn(0, -oo) == 0 + + assert mjn(0, z) == sin(z)/z + assert mjn(1, z) == sin(z)/z**2 - cos(z)/z + assert mjn(2, z) == (3/z**3 - 1/z)*sin(z) - (3/z**2) * cos(z) + assert mjn(3, z) == (15/z**4 - 6/z**2)*sin(z) + (1/z - 15/z**3)*cos(z) + assert mjn(4, z) == (1/z + 105/z**5 - 45/z**3)*sin(z) + \ + (-105/z**4 + 10/z**2)*cos(z) + assert mjn(5, z) == (945/z**6 - 420/z**4 + 15/z**2)*sin(z) + \ + (-1/z - 945/z**5 + 105/z**3)*cos(z) + assert mjn(6, z) == (-1/z + 10395/z**7 - 4725/z**5 + 210/z**3)*sin(z) + \ + (-10395/z**6 + 1260/z**4 - 21/z**2)*cos(z) + + assert expand_func(jn(n, z)) == jn(n, z) + + # SBFs not defined for complex-valued orders + assert jn(2+3j, 5.2+0.3j).evalf() == jn(2+3j, 5.2+0.3j) + + assert eq([jn(2, 5.2+0.3j).evalf(10)], + [0.09941975672 - 0.05452508024*I]) + + +def test_yn(): + z = symbols("z") + assert myn(0, z) == -cos(z)/z + assert myn(1, z) == -cos(z)/z**2 - sin(z)/z + assert myn(2, z) == -((3/z**3 - 1/z)*cos(z) + (3/z**2)*sin(z)) + assert expand_func(yn(n, z)) == yn(n, z) + + # SBFs not defined for complex-valued orders + assert yn(2+3j, 5.2+0.3j).evalf() == yn(2+3j, 5.2+0.3j) + + assert eq([yn(2, 5.2+0.3j).evalf(10)], + [0.185250342 + 0.01489557397*I]) + + +def test_sympify_yn(): + assert S(15) in myn(3, pi).atoms() + assert myn(3, pi) == 15/pi**4 - 6/pi**2 + + +def eq(a, b, tol=1e-6): + for u, v in zip(a, b): + if not (abs(u - v) < tol): + return False + return True + + +def test_jn_zeros(): + assert eq(jn_zeros(0, 4), [3.141592, 6.283185, 9.424777, 12.566370]) + assert eq(jn_zeros(1, 4), [4.493409, 7.725251, 10.904121, 14.066193]) + assert eq(jn_zeros(2, 4), [5.763459, 9.095011, 12.322940, 15.514603]) + assert eq(jn_zeros(3, 4), [6.987932, 10.417118, 13.698023, 16.923621]) + assert eq(jn_zeros(4, 4), [8.182561, 11.704907, 15.039664, 18.301255]) + + +def test_bessel_eval(): + n, m, k = Symbol('n', integer=True), Symbol('m'), Symbol('k', integer=True, zero=False) + + for f in [besselj, besseli]: + assert f(0, 0) is S.One + assert f(2.1, 0) is S.Zero + assert f(-3, 0) is S.Zero + assert f(-10.2, 0) is S.ComplexInfinity + assert f(1 + 3*I, 0) is S.Zero + assert f(-3 + I, 0) is S.ComplexInfinity + assert f(-2*I, 0) is S.NaN + assert f(n, 0) != S.One and f(n, 0) != S.Zero + assert f(m, 0) != S.One and f(m, 0) != S.Zero + assert f(k, 0) is S.Zero + + assert bessely(0, 0) is S.NegativeInfinity + assert besselk(0, 0) is S.Infinity + for f in [bessely, besselk]: + assert f(1 + I, 0) is S.ComplexInfinity + assert f(I, 0) is S.NaN + + for f in [besselj, bessely]: + assert f(m, S.Infinity) is S.Zero + assert f(m, S.NegativeInfinity) is S.Zero + + for f in [besseli, besselk]: + assert f(m, I*S.Infinity) is S.Zero + assert f(m, I*S.NegativeInfinity) is S.Zero + + for f in [besseli, besselk]: + assert f(-4, z) == f(4, z) + assert f(-3, z) == f(3, z) + assert f(-n, z) == f(n, z) + assert f(-m, z) != f(m, z) + + for f in [besselj, bessely]: + assert f(-4, z) == f(4, z) + assert f(-3, z) == -f(3, z) + assert f(-n, z) == (-1)**n*f(n, z) + assert f(-m, z) != (-1)**m*f(m, z) + + for f in [besselj, besseli]: + assert f(m, -z) == (-z)**m*z**(-m)*f(m, z) + + assert besseli(2, -z) == besseli(2, z) + assert besseli(3, -z) == -besseli(3, z) + + assert besselj(0, -z) == besselj(0, z) + assert besselj(1, -z) == -besselj(1, z) + + assert besseli(0, I*z) == besselj(0, z) + assert besseli(1, I*z) == I*besselj(1, z) + assert besselj(3, I*z) == -I*besseli(3, z) + + +def test_bessel_nan(): + # FIXME: could have these return NaN; for now just fix infinite recursion + for f in [besselj, bessely, besseli, besselk, hankel1, hankel2, yn, jn]: + assert f(1, S.NaN) == f(1, S.NaN, evaluate=False) + + +def test_meromorphic(): + assert besselj(2, x).is_meromorphic(x, 1) == True + assert besselj(2, x).is_meromorphic(x, 0) == True + assert besselj(2, x).is_meromorphic(x, oo) == False + assert besselj(S(2)/3, x).is_meromorphic(x, 1) == True + assert besselj(S(2)/3, x).is_meromorphic(x, 0) == False + assert besselj(S(2)/3, x).is_meromorphic(x, oo) == False + assert besselj(x, 2*x).is_meromorphic(x, 2) == False + assert besselk(0, x).is_meromorphic(x, 1) == True + assert besselk(2, x).is_meromorphic(x, 0) == True + assert besseli(0, x).is_meromorphic(x, 1) == True + assert besseli(2, x).is_meromorphic(x, 0) == True + assert bessely(0, x).is_meromorphic(x, 1) == True + assert bessely(0, x).is_meromorphic(x, 0) == False + assert bessely(2, x).is_meromorphic(x, 0) == True + assert hankel1(3, x**2 + 2*x).is_meromorphic(x, 1) == True + assert hankel1(0, x).is_meromorphic(x, 0) == False + assert hankel2(11, 4).is_meromorphic(x, 5) == True + assert hn1(6, 7*x**3 + 4).is_meromorphic(x, 7) == True + assert hn2(3, 2*x).is_meromorphic(x, 9) == True + assert jn(5, 2*x + 7).is_meromorphic(x, 4) == True + assert yn(8, x**2 + 11).is_meromorphic(x, 6) == True + + +def test_conjugate(): + n = Symbol('n') + z = Symbol('z', extended_real=False) + x = Symbol('x', extended_real=True) + y = Symbol('y', positive=True) + t = Symbol('t', negative=True) + + for f in [besseli, besselj, besselk, bessely, hankel1, hankel2]: + assert f(n, -1).conjugate() != f(conjugate(n), -1) + assert f(n, x).conjugate() != f(conjugate(n), x) + assert f(n, t).conjugate() != f(conjugate(n), t) + + rz = randcplx(b=0.5) + + for f in [besseli, besselj, besselk, bessely]: + assert f(n, 1 + I).conjugate() == f(conjugate(n), 1 - I) + assert f(n, 0).conjugate() == f(conjugate(n), 0) + assert f(n, 1).conjugate() == f(conjugate(n), 1) + assert f(n, z).conjugate() == f(conjugate(n), conjugate(z)) + assert f(n, y).conjugate() == f(conjugate(n), y) + assert tn(f(n, rz).conjugate(), f(conjugate(n), conjugate(rz))) + + assert hankel1(n, 1 + I).conjugate() == hankel2(conjugate(n), 1 - I) + assert hankel1(n, 0).conjugate() == hankel2(conjugate(n), 0) + assert hankel1(n, 1).conjugate() == hankel2(conjugate(n), 1) + assert hankel1(n, y).conjugate() == hankel2(conjugate(n), y) + assert hankel1(n, z).conjugate() == hankel2(conjugate(n), conjugate(z)) + assert tn(hankel1(n, rz).conjugate(), hankel2(conjugate(n), conjugate(rz))) + + assert hankel2(n, 1 + I).conjugate() == hankel1(conjugate(n), 1 - I) + assert hankel2(n, 0).conjugate() == hankel1(conjugate(n), 0) + assert hankel2(n, 1).conjugate() == hankel1(conjugate(n), 1) + assert hankel2(n, y).conjugate() == hankel1(conjugate(n), y) + assert hankel2(n, z).conjugate() == hankel1(conjugate(n), conjugate(z)) + assert tn(hankel2(n, rz).conjugate(), hankel1(conjugate(n), conjugate(rz))) + + +def test_branching(): + assert besselj(polar_lift(k), x) == besselj(k, x) + assert besseli(polar_lift(k), x) == besseli(k, x) + + n = Symbol('n', integer=True) + assert besselj(n, exp_polar(2*pi*I)*x) == besselj(n, x) + assert besselj(n, polar_lift(x)) == besselj(n, x) + assert besseli(n, exp_polar(2*pi*I)*x) == besseli(n, x) + assert besseli(n, polar_lift(x)) == besseli(n, x) + + def tn(func, s): + from sympy.core.random import uniform + c = uniform(1, 5) + expr = func(s, c*exp_polar(I*pi)) - func(s, c*exp_polar(-I*pi)) + eps = 1e-15 + expr2 = func(s + eps, -c + eps*I) - func(s + eps, -c - eps*I) + return abs(expr.n() - expr2.n()).n() < 1e-10 + + nu = Symbol('nu') + assert besselj(nu, exp_polar(2*pi*I)*x) == exp(2*pi*I*nu)*besselj(nu, x) + assert besseli(nu, exp_polar(2*pi*I)*x) == exp(2*pi*I*nu)*besseli(nu, x) + assert tn(besselj, 2) + assert tn(besselj, pi) + assert tn(besselj, I) + assert tn(besseli, 2) + assert tn(besseli, pi) + assert tn(besseli, I) + + +def test_airy_base(): + z = Symbol('z') + x = Symbol('x', real=True) + y = Symbol('y', real=True) + + assert conjugate(airyai(z)) == airyai(conjugate(z)) + assert airyai(x).is_extended_real + + assert airyai(x+I*y).as_real_imag() == ( + airyai(x - I*y)/2 + airyai(x + I*y)/2, + I*(airyai(x - I*y) - airyai(x + I*y))/2) + + +def test_airyai(): + z = Symbol('z', real=False) + t = Symbol('t', negative=True) + p = Symbol('p', positive=True) + + assert isinstance(airyai(z), airyai) + + assert airyai(0) == 3**Rational(1, 3)/(3*gamma(Rational(2, 3))) + assert airyai(oo) == 0 + assert airyai(-oo) == 0 + + assert diff(airyai(z), z) == airyaiprime(z) + + assert series(airyai(z), z, 0, 3) == ( + 3**Rational(5, 6)*gamma(Rational(1, 3))/(6*pi) - 3**Rational(1, 6)*z*gamma(Rational(2, 3))/(2*pi) + O(z**3)) + + assert airyai(z).rewrite(hyper) == ( + -3**Rational(2, 3)*z*hyper((), (Rational(4, 3),), z**3/9)/(3*gamma(Rational(1, 3))) + + 3**Rational(1, 3)*hyper((), (Rational(2, 3),), z**3/9)/(3*gamma(Rational(2, 3)))) + + assert isinstance(airyai(z).rewrite(besselj), airyai) + assert airyai(t).rewrite(besselj) == ( + sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) + + besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3) + assert airyai(z).rewrite(besseli) == ( + -z*besseli(Rational(1, 3), 2*z**Rational(3, 2)/3)/(3*(z**Rational(3, 2))**Rational(1, 3)) + + (z**Rational(3, 2))**Rational(1, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3)/3) + assert airyai(p).rewrite(besseli) == ( + sqrt(p)*(besseli(Rational(-1, 3), 2*p**Rational(3, 2)/3) - + besseli(Rational(1, 3), 2*p**Rational(3, 2)/3))/3) + + assert expand_func(airyai(2*(3*z**5)**Rational(1, 3))) == ( + -sqrt(3)*(-1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airybi(2*3**Rational(1, 3)*z**Rational(5, 3))/6 + + (1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airyai(2*3**Rational(1, 3)*z**Rational(5, 3))/2) + + +def test_airybi(): + z = Symbol('z', real=False) + t = Symbol('t', negative=True) + p = Symbol('p', positive=True) + + assert isinstance(airybi(z), airybi) + + assert airybi(0) == 3**Rational(5, 6)/(3*gamma(Rational(2, 3))) + assert airybi(oo) is oo + assert airybi(-oo) == 0 + + assert diff(airybi(z), z) == airybiprime(z) + + assert series(airybi(z), z, 0, 3) == ( + 3**Rational(1, 3)*gamma(Rational(1, 3))/(2*pi) + 3**Rational(2, 3)*z*gamma(Rational(2, 3))/(2*pi) + O(z**3)) + + assert airybi(z).rewrite(hyper) == ( + 3**Rational(1, 6)*z*hyper((), (Rational(4, 3),), z**3/9)/gamma(Rational(1, 3)) + + 3**Rational(5, 6)*hyper((), (Rational(2, 3),), z**3/9)/(3*gamma(Rational(2, 3)))) + + assert isinstance(airybi(z).rewrite(besselj), airybi) + assert airyai(t).rewrite(besselj) == ( + sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) + + besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3) + assert airybi(z).rewrite(besseli) == ( + sqrt(3)*(z*besseli(Rational(1, 3), 2*z**Rational(3, 2)/3)/(z**Rational(3, 2))**Rational(1, 3) + + (z**Rational(3, 2))**Rational(1, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3))/3) + assert airybi(p).rewrite(besseli) == ( + sqrt(3)*sqrt(p)*(besseli(Rational(-1, 3), 2*p**Rational(3, 2)/3) + + besseli(Rational(1, 3), 2*p**Rational(3, 2)/3))/3) + + assert expand_func(airybi(2*(3*z**5)**Rational(1, 3))) == ( + sqrt(3)*(1 - (z**5)**Rational(1, 3)/z**Rational(5, 3))*airyai(2*3**Rational(1, 3)*z**Rational(5, 3))/2 + + (1 + (z**5)**Rational(1, 3)/z**Rational(5, 3))*airybi(2*3**Rational(1, 3)*z**Rational(5, 3))/2) + + +def test_airyaiprime(): + z = Symbol('z', real=False) + t = Symbol('t', negative=True) + p = Symbol('p', positive=True) + + assert isinstance(airyaiprime(z), airyaiprime) + + assert airyaiprime(0) == -3**Rational(2, 3)/(3*gamma(Rational(1, 3))) + assert airyaiprime(oo) == 0 + + assert diff(airyaiprime(z), z) == z*airyai(z) + + assert series(airyaiprime(z), z, 0, 3) == ( + -3**Rational(2, 3)/(3*gamma(Rational(1, 3))) + 3**Rational(1, 3)*z**2/(6*gamma(Rational(2, 3))) + O(z**3)) + + assert airyaiprime(z).rewrite(hyper) == ( + 3**Rational(1, 3)*z**2*hyper((), (Rational(5, 3),), z**3/9)/(6*gamma(Rational(2, 3))) - + 3**Rational(2, 3)*hyper((), (Rational(1, 3),), z**3/9)/(3*gamma(Rational(1, 3)))) + + assert isinstance(airyaiprime(z).rewrite(besselj), airyaiprime) + assert airyai(t).rewrite(besselj) == ( + sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) + + besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3) + assert airyaiprime(z).rewrite(besseli) == ( + z**2*besseli(Rational(2, 3), 2*z**Rational(3, 2)/3)/(3*(z**Rational(3, 2))**Rational(2, 3)) - + (z**Rational(3, 2))**Rational(2, 3)*besseli(Rational(-1, 3), 2*z**Rational(3, 2)/3)/3) + assert airyaiprime(p).rewrite(besseli) == ( + p*(-besseli(Rational(-2, 3), 2*p**Rational(3, 2)/3) + besseli(Rational(2, 3), 2*p**Rational(3, 2)/3))/3) + + assert expand_func(airyaiprime(2*(3*z**5)**Rational(1, 3))) == ( + sqrt(3)*(z**Rational(5, 3)/(z**5)**Rational(1, 3) - 1)*airybiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/6 + + (z**Rational(5, 3)/(z**5)**Rational(1, 3) + 1)*airyaiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2) + + +def test_airybiprime(): + z = Symbol('z', real=False) + t = Symbol('t', negative=True) + p = Symbol('p', positive=True) + + assert isinstance(airybiprime(z), airybiprime) + + assert airybiprime(0) == 3**Rational(1, 6)/gamma(Rational(1, 3)) + assert airybiprime(oo) is oo + assert airybiprime(-oo) == 0 + + assert diff(airybiprime(z), z) == z*airybi(z) + + assert series(airybiprime(z), z, 0, 3) == ( + 3**Rational(1, 6)/gamma(Rational(1, 3)) + 3**Rational(5, 6)*z**2/(6*gamma(Rational(2, 3))) + O(z**3)) + + assert airybiprime(z).rewrite(hyper) == ( + 3**Rational(5, 6)*z**2*hyper((), (Rational(5, 3),), z**3/9)/(6*gamma(Rational(2, 3))) + + 3**Rational(1, 6)*hyper((), (Rational(1, 3),), z**3/9)/gamma(Rational(1, 3))) + + assert isinstance(airybiprime(z).rewrite(besselj), airybiprime) + assert airyai(t).rewrite(besselj) == ( + sqrt(-t)*(besselj(Rational(-1, 3), 2*(-t)**Rational(3, 2)/3) + + besselj(Rational(1, 3), 2*(-t)**Rational(3, 2)/3))/3) + assert airybiprime(z).rewrite(besseli) == ( + sqrt(3)*(z**2*besseli(Rational(2, 3), 2*z**Rational(3, 2)/3)/(z**Rational(3, 2))**Rational(2, 3) + + (z**Rational(3, 2))**Rational(2, 3)*besseli(Rational(-2, 3), 2*z**Rational(3, 2)/3))/3) + assert airybiprime(p).rewrite(besseli) == ( + sqrt(3)*p*(besseli(Rational(-2, 3), 2*p**Rational(3, 2)/3) + besseli(Rational(2, 3), 2*p**Rational(3, 2)/3))/3) + + assert expand_func(airybiprime(2*(3*z**5)**Rational(1, 3))) == ( + sqrt(3)*(z**Rational(5, 3)/(z**5)**Rational(1, 3) - 1)*airyaiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2 + + (z**Rational(5, 3)/(z**5)**Rational(1, 3) + 1)*airybiprime(2*3**Rational(1, 3)*z**Rational(5, 3))/2) + + +def test_marcumq(): + m = Symbol('m') + a = Symbol('a') + b = Symbol('b') + + assert marcumq(0, 0, 0) == 0 + assert marcumq(m, 0, b) == uppergamma(m, b**2/2)/gamma(m) + assert marcumq(2, 0, 5) == 27*exp(Rational(-25, 2))/2 + assert marcumq(0, a, 0) == 1 - exp(-a**2/2) + assert marcumq(0, pi, 0) == 1 - exp(-pi**2/2) + assert marcumq(1, a, a) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + assert marcumq(2, a, a) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + exp(-a**2)*besseli(1, a**2) + + assert diff(marcumq(1, a, 3), a) == a*(-marcumq(1, a, 3) + marcumq(2, a, 3)) + assert diff(marcumq(2, 3, b), b) == -b**2*exp(-b**2/2 - Rational(9, 2))*besseli(1, 3*b)/3 + + x = Symbol('x') + assert marcumq(2, 3, 4).rewrite(Integral, x=x) == \ + Integral(x**2*exp(-x**2/2 - Rational(9, 2))*besseli(1, 3*x), (x, 4, oo))/3 + assert eq([marcumq(5, -2, 3).rewrite(Integral).evalf(10)], + [0.7905769565]) + + k = Symbol('k') + assert marcumq(-3, -5, -7).rewrite(Sum, k=k) == \ + exp(-37)*Sum((Rational(5, 7))**k*besseli(k, 35), (k, 4, oo)) + assert eq([marcumq(1, 3, 1).rewrite(Sum).evalf(10)], + [0.9891705502]) + + assert marcumq(1, a, a, evaluate=False).rewrite(besseli) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + assert marcumq(2, a, a, evaluate=False).rewrite(besseli) == S.Half + exp(-a**2)*besseli(0, a**2)/2 + \ + exp(-a**2)*besseli(1, a**2) + assert marcumq(3, a, a).rewrite(besseli) == (besseli(1, a**2) + besseli(2, a**2))*exp(-a**2) + \ + S.Half + exp(-a**2)*besseli(0, a**2)/2 + assert marcumq(5, 8, 8).rewrite(besseli) == exp(-64)*besseli(0, 64)/2 + \ + (besseli(4, 64) + besseli(3, 64) + besseli(2, 64) + besseli(1, 64))*exp(-64) + S.Half + assert marcumq(m, a, a).rewrite(besseli) == marcumq(m, a, a) + + x = Symbol('x', integer=True) + assert marcumq(x, a, a).rewrite(besseli) == marcumq(x, a, a) + + +def test_issue_26134(): + x = Symbol('x') + assert marcumq(2, 3, 4).rewrite(Integral, x=x).dummy_eq( + Integral(x**2*exp(-x**2/2 - Rational(9, 2))*besseli(1, 3*x), (x, 4, oo))/3) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_beta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_beta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..b34cb2febf9e2746d869cd878525d2794535aea5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_beta_functions.py @@ -0,0 +1,89 @@ +from sympy.core.function import (diff, expand_func) +from sympy.core.numbers import I, Rational, pi +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, symbols) +from sympy.functions.combinatorial.numbers import catalan +from sympy.functions.elementary.complexes import conjugate +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.beta_functions import (beta, betainc, betainc_regularized) +from sympy.functions.special.gamma_functions import gamma, polygamma +from sympy.functions.special.hyper import hyper +from sympy.integrals.integrals import Integral +from sympy.core.function import ArgumentIndexError +from sympy.core.expr import unchanged +from sympy.testing.pytest import raises + + +def test_beta(): + x, y = symbols('x y') + t = Dummy('t') + + assert unchanged(beta, x, y) + assert unchanged(beta, x, x) + + assert beta(5, -3).is_real == True + assert beta(3, y).is_real is None + + assert expand_func(beta(x, y)) == gamma(x)*gamma(y)/gamma(x + y) + assert expand_func(beta(x, y) - beta(y, x)) == 0 # Symmetric + assert expand_func(beta(x, y)) == expand_func(beta(x, y + 1) + beta(x + 1, y)).simplify() + + assert diff(beta(x, y), x) == beta(x, y)*(polygamma(0, x) - polygamma(0, x + y)) + assert diff(beta(x, y), y) == beta(x, y)*(polygamma(0, y) - polygamma(0, x + y)) + + assert conjugate(beta(x, y)) == beta(conjugate(x), conjugate(y)) + + raises(ArgumentIndexError, lambda: beta(x, y).fdiff(3)) + + assert beta(x, y).rewrite(gamma) == gamma(x)*gamma(y)/gamma(x + y) + assert beta(x).rewrite(gamma) == gamma(x)**2/gamma(2*x) + assert beta(x, y).rewrite(Integral).dummy_eq(Integral(t**(x - 1) * (1 - t)**(y - 1), (t, 0, 1))) + assert beta(Rational(-19, 10), Rational(-1, 10)) == S.Zero + assert beta(Rational(-19, 10), Rational(-9, 10)) == \ + 800*2**(S(4)/5)*sqrt(pi)*gamma(S.One/10)/(171*gamma(-S(7)/5)) + assert beta(Rational(19, 10), Rational(29, 10)) == 100/(551*catalan(Rational(19, 10))) + assert beta(1, 0) == S.ComplexInfinity + assert beta(0, 1) == S.ComplexInfinity + assert beta(2, 3) == S.One/12 + assert unchanged(beta, x, x + 1) + assert unchanged(beta, x, 1) + assert unchanged(beta, 1, y) + assert beta(x, x + 1).doit() == 1/(x*(x+1)*catalan(x)) + assert beta(1, y).doit() == 1/y + assert beta(x, 1).doit() == 1/x + assert beta(Rational(-19, 10), Rational(-1, 10), evaluate=False).doit() == S.Zero + assert beta(2) == beta(2, 2) + assert beta(x, evaluate=False) != beta(x, x) + assert beta(x, evaluate=False).doit() == beta(x, x) + + +def test_betainc(): + a, b, x1, x2 = symbols('a b x1 x2') + + assert unchanged(betainc, a, b, x1, x2) + assert unchanged(betainc, a, b, 0, x1) + + assert betainc(1, 2, 0, -5).is_real == True + assert betainc(1, 2, 0, x2).is_real is None + assert conjugate(betainc(I, 2, 3 - I, 1 + 4*I)) == betainc(-I, 2, 3 + I, 1 - 4*I) + + assert betainc(a, b, 0, 1).rewrite(Integral).dummy_eq(beta(a, b).rewrite(Integral)) + assert betainc(1, 2, 0, x2).rewrite(hyper) == x2*hyper((1, -1), (2,), x2) + + assert betainc(1, 2, 3, 3).evalf() == 0 + + +def test_betainc_regularized(): + a, b, x1, x2 = symbols('a b x1 x2') + + assert unchanged(betainc_regularized, a, b, x1, x2) + assert unchanged(betainc_regularized, a, b, 0, x1) + + assert betainc_regularized(3, 5, 0, -1).is_real == True + assert betainc_regularized(3, 5, 0, x2).is_real is None + assert conjugate(betainc_regularized(3*I, 1, 2 + I, 1 + 2*I)) == betainc_regularized(-3*I, 1, 2 - I, 1 - 2*I) + + assert betainc_regularized(a, b, 0, 1).rewrite(Integral) == 1 + assert betainc_regularized(1, 2, x1, x2).rewrite(hyper) == 2*x2*hyper((1, -1), (2,), x2) - 2*x1*hyper((1, -1), (2,), x1) + + assert betainc_regularized(4, 1, 5, 5).evalf() == 0 diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_bsplines.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_bsplines.py new file mode 100644 index 0000000000000000000000000000000000000000..136831b96ba16c95edba12ecd47b6f1566b68427 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_bsplines.py @@ -0,0 +1,167 @@ +from sympy.functions import bspline_basis_set, interpolating_spline +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.piecewise import Piecewise +from sympy.logic.boolalg import And +from sympy.sets.sets import Interval +from sympy.testing.pytest import slow + +x, y = symbols('x,y') + + +def test_basic_degree_0(): + d = 0 + knots = range(5) + splines = bspline_basis_set(d, knots, x) + for i in range(len(splines)): + assert splines[i] == Piecewise((1, Interval(i, i + 1).contains(x)), + (0, True)) + + +def test_basic_degree_1(): + d = 1 + knots = range(5) + splines = bspline_basis_set(d, knots, x) + assert splines[0] == Piecewise((x, Interval(0, 1).contains(x)), + (2 - x, Interval(1, 2).contains(x)), + (0, True)) + assert splines[1] == Piecewise((-1 + x, Interval(1, 2).contains(x)), + (3 - x, Interval(2, 3).contains(x)), + (0, True)) + assert splines[2] == Piecewise((-2 + x, Interval(2, 3).contains(x)), + (4 - x, Interval(3, 4).contains(x)), + (0, True)) + + +def test_basic_degree_2(): + d = 2 + knots = range(5) + splines = bspline_basis_set(d, knots, x) + b0 = Piecewise((x**2/2, Interval(0, 1).contains(x)), + (Rational(-3, 2) + 3*x - x**2, Interval(1, 2).contains(x)), + (Rational(9, 2) - 3*x + x**2/2, Interval(2, 3).contains(x)), + (0, True)) + b1 = Piecewise((S.Half - x + x**2/2, Interval(1, 2).contains(x)), + (Rational(-11, 2) + 5*x - x**2, Interval(2, 3).contains(x)), + (8 - 4*x + x**2/2, Interval(3, 4).contains(x)), + (0, True)) + assert splines[0] == b0 + assert splines[1] == b1 + + +def test_basic_degree_3(): + d = 3 + knots = range(5) + splines = bspline_basis_set(d, knots, x) + b0 = Piecewise( + (x**3/6, Interval(0, 1).contains(x)), + (Rational(2, 3) - 2*x + 2*x**2 - x**3/2, Interval(1, 2).contains(x)), + (Rational(-22, 3) + 10*x - 4*x**2 + x**3/2, Interval(2, 3).contains(x)), + (Rational(32, 3) - 8*x + 2*x**2 - x**3/6, Interval(3, 4).contains(x)), + (0, True) + ) + assert splines[0] == b0 + + +def test_repeated_degree_1(): + d = 1 + knots = [0, 0, 1, 2, 2, 3, 4, 4] + splines = bspline_basis_set(d, knots, x) + assert splines[0] == Piecewise((1 - x, Interval(0, 1).contains(x)), + (0, True)) + assert splines[1] == Piecewise((x, Interval(0, 1).contains(x)), + (2 - x, Interval(1, 2).contains(x)), + (0, True)) + assert splines[2] == Piecewise((-1 + x, Interval(1, 2).contains(x)), + (0, True)) + assert splines[3] == Piecewise((3 - x, Interval(2, 3).contains(x)), + (0, True)) + assert splines[4] == Piecewise((-2 + x, Interval(2, 3).contains(x)), + (4 - x, Interval(3, 4).contains(x)), + (0, True)) + assert splines[5] == Piecewise((-3 + x, Interval(3, 4).contains(x)), + (0, True)) + + +def test_repeated_degree_2(): + d = 2 + knots = [0, 0, 1, 2, 2, 3, 4, 4] + splines = bspline_basis_set(d, knots, x) + + assert splines[0] == Piecewise(((-3*x**2/2 + 2*x), And(x <= 1, x >= 0)), + (x**2/2 - 2*x + 2, And(x <= 2, x >= 1)), + (0, True)) + assert splines[1] == Piecewise((x**2/2, And(x <= 1, x >= 0)), + (-3*x**2/2 + 4*x - 2, And(x <= 2, x >= 1)), + (0, True)) + assert splines[2] == Piecewise((x**2 - 2*x + 1, And(x <= 2, x >= 1)), + (x**2 - 6*x + 9, And(x <= 3, x >= 2)), + (0, True)) + assert splines[3] == Piecewise((-3*x**2/2 + 8*x - 10, And(x <= 3, x >= 2)), + (x**2/2 - 4*x + 8, And(x <= 4, x >= 3)), + (0, True)) + assert splines[4] == Piecewise((x**2/2 - 2*x + 2, And(x <= 3, x >= 2)), + (-3*x**2/2 + 10*x - 16, And(x <= 4, x >= 3)), + (0, True)) + +# Tests for interpolating_spline + + +def test_10_points_degree_1(): + d = 1 + X = [-5, 2, 3, 4, 7, 9, 10, 30, 31, 34] + Y = [-10, -2, 2, 4, 7, 6, 20, 45, 19, 25] + spline = interpolating_spline(d, x, X, Y) + + assert spline == Piecewise((x*Rational(8, 7) - Rational(30, 7), (x >= -5) & (x <= 2)), (4*x - 10, (x >= 2) & (x <= 3)), + (2*x - 4, (x >= 3) & (x <= 4)), (x, (x >= 4) & (x <= 7)), + (-x/2 + Rational(21, 2), (x >= 7) & (x <= 9)), (14*x - 120, (x >= 9) & (x <= 10)), + (x*Rational(5, 4) + Rational(15, 2), (x >= 10) & (x <= 30)), (-26*x + 825, (x >= 30) & (x <= 31)), + (2*x - 43, (x >= 31) & (x <= 34))) + + +def test_3_points_degree_2(): + d = 2 + X = [-3, 10, 19] + Y = [3, -4, 30] + spline = interpolating_spline(d, x, X, Y) + + assert spline == Piecewise((505*x**2/2574 - x*Rational(4921, 2574) - Rational(1931, 429), (x >= -3) & (x <= 19))) + + +def test_5_points_degree_2(): + d = 2 + X = [-3, 2, 4, 5, 10] + Y = [-1, 2, 5, 10, 14] + spline = interpolating_spline(d, x, X, Y) + + assert spline == Piecewise((4*x**2/329 + x*Rational(1007, 1645) + Rational(1196, 1645), (x >= -3) & (x <= 3)), + (2701*x**2/1645 - x*Rational(15079, 1645) + Rational(5065, 329), (x >= 3) & (x <= Rational(9, 2))), + (-1319*x**2/1645 + x*Rational(21101, 1645) - Rational(11216, 329), (x >= Rational(9, 2)) & (x <= 10))) + + +@slow +def test_6_points_degree_3(): + d = 3 + X = [-1, 0, 2, 3, 9, 12] + Y = [-4, 3, 3, 7, 9, 20] + spline = interpolating_spline(d, x, X, Y) + + assert spline == Piecewise((6058*x**3/5301 - 18427*x**2/5301 + x*Rational(12622, 5301) + 3, (x >= -1) & (x <= 2)), + (-8327*x**3/5301 + 67883*x**2/5301 - x*Rational(159998, 5301) + Rational(43661, 1767), (x >= 2) & (x <= 3)), + (5414*x**3/47709 - 1386*x**2/589 + x*Rational(4267, 279) - Rational(12232, 589), (x >= 3) & (x <= 12))) + + +def test_issue_19262(): + Delta = symbols('Delta', positive=True) + knots = [i*Delta for i in range(4)] + basis = bspline_basis_set(1, knots, x) + y = symbols('y', nonnegative=True) + basis2 = bspline_basis_set(1, knots, y) + assert basis[0].subs(x, y) == basis2[0] + assert interpolating_spline(1, x, + [Delta*i for i in [1, 2, 4, 7]], [3, 6, 5, 7] + ) == Piecewise((3*x/Delta, (Delta <= x) & (x <= 2*Delta)), + (7 - x/(2*Delta), (x >= 2*Delta) & (x <= 4*Delta)), + (Rational(7, 3) + 2*x/(3*Delta), (x >= 4*Delta) & (x <= 7*Delta))) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_delta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_delta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..d5a39d9e352143cf878cf69fa42f454f58be65c9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_delta_functions.py @@ -0,0 +1,165 @@ +from sympy.core.numbers import (I, nan, oo, pi) +from sympy.core.relational import (Eq, Ne) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import (adjoint, conjugate, sign, transpose) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.delta_functions import (DiracDelta, Heaviside) +from sympy.functions.special.singularity_functions import SingularityFunction +from sympy.simplify.simplify import signsimp + + +from sympy.testing.pytest import raises + +from sympy.core.expr import unchanged + +from sympy.core.function import ArgumentIndexError + + +x, y = symbols('x y') +i = symbols('t', nonzero=True) +j = symbols('j', positive=True) +k = symbols('k', negative=True) + +def test_DiracDelta(): + assert DiracDelta(1) == 0 + assert DiracDelta(5.1) == 0 + assert DiracDelta(-pi) == 0 + assert DiracDelta(5, 7) == 0 + assert DiracDelta(x, 0) == DiracDelta(x) + assert DiracDelta(i) == 0 + assert DiracDelta(j) == 0 + assert DiracDelta(k) == 0 + assert DiracDelta(nan) is nan + assert DiracDelta(0).func is DiracDelta + assert DiracDelta(x).func is DiracDelta + # FIXME: this is generally undefined @ x=0 + # But then limit(Delta(c)*Heaviside(x),x,-oo) + # need's to be implemented. + # assert 0*DiracDelta(x) == 0 + + assert adjoint(DiracDelta(x)) == DiracDelta(x) + assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y) + assert conjugate(DiracDelta(x)) == DiracDelta(x) + assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y) + assert transpose(DiracDelta(x)) == DiracDelta(x) + assert transpose(DiracDelta(x - y)) == DiracDelta(x - y) + + assert DiracDelta(x).diff(x) == DiracDelta(x, 1) + assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2) + + assert DiracDelta(x).is_simple(x) is True + assert DiracDelta(3*x).is_simple(x) is True + assert DiracDelta(x**2).is_simple(x) is False + assert DiracDelta(sqrt(x)).is_simple(x) is False + assert DiracDelta(x).is_simple(y) is False + + assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y) + assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x) + assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y) + assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y) + assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True, wrt=x) == ( + DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2) + + assert DiracDelta(2*x) != DiracDelta(x) # scaling property + assert DiracDelta(x) == DiracDelta(-x) # even function + assert DiracDelta(-x, 2) == DiracDelta(x, 2) + assert DiracDelta(-x, 1) == -DiracDelta(x, 1) # odd deriv is odd + assert DiracDelta(-oo*x) == DiracDelta(oo*x) + assert DiracDelta(x - y) != DiracDelta(y - x) + assert signsimp(DiracDelta(x - y) - DiracDelta(y - x)) == 0 + + assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y) + assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x) + assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y) + assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y) + assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True) == ( + DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2) + + raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2)) + raises(ValueError, lambda: DiracDelta(x, -1)) + raises(ValueError, lambda: DiracDelta(I)) + raises(ValueError, lambda: DiracDelta(2 + 3*I)) + + +def test_heaviside(): + assert Heaviside(-5) == 0 + assert Heaviside(1) == 1 + assert Heaviside(0) == S.Half + + assert Heaviside(0, x) == x + assert unchanged(Heaviside,x, nan) + assert Heaviside(0, nan) == nan + + h0 = Heaviside(x, 0) + h12 = Heaviside(x, S.Half) + h1 = Heaviside(x, 1) + + assert h0.args == h0.pargs == (x, 0) + assert h1.args == h1.pargs == (x, 1) + assert h12.args == (x, S.Half) + assert h12.pargs == (x,) # default 1/2 suppressed + + assert adjoint(Heaviside(x)) == Heaviside(x) + assert adjoint(Heaviside(x - y)) == Heaviside(x - y) + assert conjugate(Heaviside(x)) == Heaviside(x) + assert conjugate(Heaviside(x - y)) == Heaviside(x - y) + assert transpose(Heaviside(x)) == Heaviside(x) + assert transpose(Heaviside(x - y)) == Heaviside(x - y) + + assert Heaviside(x).diff(x) == DiracDelta(x) + assert Heaviside(x + I).is_Function is True + assert Heaviside(I*x).is_Function is True + + raises(ArgumentIndexError, lambda: Heaviside(x).fdiff(2)) + raises(ValueError, lambda: Heaviside(I)) + raises(ValueError, lambda: Heaviside(2 + 3*I)) + + +def test_rewrite(): + x, y = Symbol('x', real=True), Symbol('y') + assert Heaviside(x).rewrite(Piecewise) == ( + Piecewise((0, x < 0), (Heaviside(0), Eq(x, 0)), (1, True))) + assert Heaviside(y).rewrite(Piecewise) == ( + Piecewise((0, y < 0), (Heaviside(0), Eq(y, 0)), (1, True))) + assert Heaviside(x, y).rewrite(Piecewise) == ( + Piecewise((0, x < 0), (y, Eq(x, 0)), (1, True))) + assert Heaviside(x, 0).rewrite(Piecewise) == ( + Piecewise((0, x <= 0), (1, True))) + assert Heaviside(x, 1).rewrite(Piecewise) == ( + Piecewise((0, x < 0), (1, True))) + assert Heaviside(x, nan).rewrite(Piecewise) == ( + Piecewise((0, x < 0), (nan, Eq(x, 0)), (1, True))) + + assert Heaviside(x).rewrite(sign) == \ + Heaviside(x, H0=Heaviside(0)).rewrite(sign) == \ + Piecewise( + (sign(x)/2 + S(1)/2, Eq(Heaviside(0), S(1)/2)), + (Piecewise( + (sign(x)/2 + S(1)/2, Ne(x, 0)), (Heaviside(0), True)), True) + ) + + assert Heaviside(y).rewrite(sign) == Heaviside(y) + assert Heaviside(x, S.Half).rewrite(sign) == (sign(x)+1)/2 + assert Heaviside(x, y).rewrite(sign) == \ + Piecewise( + (sign(x)/2 + S(1)/2, Eq(y, S(1)/2)), + (Piecewise( + (sign(x)/2 + S(1)/2, Ne(x, 0)), (y, True)), True) + ) + + assert DiracDelta(y).rewrite(Piecewise) == Piecewise((DiracDelta(0), Eq(y, 0)), (0, True)) + assert DiracDelta(y, 1).rewrite(Piecewise) == DiracDelta(y, 1) + assert DiracDelta(x - 5).rewrite(Piecewise) == ( + Piecewise((DiracDelta(0), Eq(x - 5, 0)), (0, True))) + + assert (x*DiracDelta(x - 10)).rewrite(SingularityFunction) == x*SingularityFunction(x, 10, -1) + assert 5*x*y*DiracDelta(y, 1).rewrite(SingularityFunction) == 5*x*y*SingularityFunction(y, 0, -2) + assert DiracDelta(0).rewrite(SingularityFunction) == SingularityFunction(0, 0, -1) + assert DiracDelta(0, 1).rewrite(SingularityFunction) == SingularityFunction(0, 0, -2) + + assert Heaviside(x).rewrite(SingularityFunction) == SingularityFunction(x, 0, 0) + assert 5*x*y*Heaviside(y + 1).rewrite(SingularityFunction) == 5*x*y*SingularityFunction(y, -1, 0) + assert ((x - 3)**3*Heaviside(x - 3)).rewrite(SingularityFunction) == (x - 3)**3*SingularityFunction(x, 3, 0) + assert Heaviside(0).rewrite(SingularityFunction) == S.Half diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py new file mode 100644 index 0000000000000000000000000000000000000000..a11e531af32301a00b6fc864064d02f9318929e1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_elliptic_integrals.py @@ -0,0 +1,181 @@ +from sympy.core.numbers import (I, Rational, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.elementary.hyperbolic import atanh +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (sin, tan) +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import (hyper, meijerg) +from sympy.integrals.integrals import Integral +from sympy.series.order import O +from sympy.functions.special.elliptic_integrals import (elliptic_k as K, + elliptic_f as F, elliptic_e as E, elliptic_pi as P) +from sympy.core.random import (test_derivative_numerically as td, + random_complex_number as randcplx, + verify_numerically as tn) +from sympy.abc import z, m, n + +i = Symbol('i', integer=True) +j = Symbol('k', integer=True, positive=True) +t = Dummy('t') + +def test_K(): + assert K(0) == pi/2 + assert K(S.Half) == 8*pi**Rational(3, 2)/gamma(Rational(-1, 4))**2 + assert K(1) is zoo + assert K(-1) == gamma(Rational(1, 4))**2/(4*sqrt(2*pi)) + assert K(oo) == 0 + assert K(-oo) == 0 + assert K(I*oo) == 0 + assert K(-I*oo) == 0 + assert K(zoo) == 0 + + assert K(z).diff(z) == (E(z) - (1 - z)*K(z))/(2*z*(1 - z)) + assert td(K(z), z) + + zi = Symbol('z', real=False) + assert K(zi).conjugate() == K(zi.conjugate()) + zr = Symbol('z', negative=True) + assert K(zr).conjugate() == K(zr) + + assert K(z).rewrite(hyper) == \ + (pi/2)*hyper((S.Half, S.Half), (S.One,), z) + assert tn(K(z), (pi/2)*hyper((S.Half, S.Half), (S.One,), z)) + assert K(z).rewrite(meijerg) == \ + meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2 + assert tn(K(z), meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2) + + assert K(z).series(z) == pi/2 + pi*z/8 + 9*pi*z**2/128 + \ + 25*pi*z**3/512 + 1225*pi*z**4/32768 + 3969*pi*z**5/131072 + O(z**6) + + assert K(m).rewrite(Integral).dummy_eq( + Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, pi/2))) + +def test_F(): + assert F(z, 0) == z + assert F(0, m) == 0 + assert F(pi*i/2, m) == i*K(m) + assert F(z, oo) == 0 + assert F(z, -oo) == 0 + + assert F(-z, m) == -F(z, m) + + assert F(z, m).diff(z) == 1/sqrt(1 - m*sin(z)**2) + assert F(z, m).diff(m) == E(z, m)/(2*m*(1 - m)) - F(z, m)/(2*m) - \ + sin(2*z)/(4*(1 - m)*sqrt(1 - m*sin(z)**2)) + r = randcplx() + assert td(F(z, r), z) + assert td(F(r, m), m) + + mi = Symbol('m', real=False) + assert F(z, mi).conjugate() == F(z.conjugate(), mi.conjugate()) + mr = Symbol('m', negative=True) + assert F(z, mr).conjugate() == F(z.conjugate(), mr) + + assert F(z, m).series(z) == \ + z + z**5*(3*m**2/40 - m/30) + m*z**3/6 + O(z**6) + + assert F(z, m).rewrite(Integral).dummy_eq( + Integral(1/sqrt(1 - m*sin(t)**2), (t, 0, z))) + +def test_E(): + assert E(z, 0) == z + assert E(0, m) == 0 + assert E(i*pi/2, m) == i*E(m) + assert E(z, oo) is zoo + assert E(z, -oo) is zoo + assert E(0) == pi/2 + assert E(1) == 1 + assert E(oo) == I*oo + assert E(-oo) is oo + assert E(zoo) is zoo + + assert E(-z, m) == -E(z, m) + + assert E(z, m).diff(z) == sqrt(1 - m*sin(z)**2) + assert E(z, m).diff(m) == (E(z, m) - F(z, m))/(2*m) + assert E(z).diff(z) == (E(z) - K(z))/(2*z) + r = randcplx() + assert td(E(r, m), m) + assert td(E(z, r), z) + assert td(E(z), z) + + mi = Symbol('m', real=False) + assert E(z, mi).conjugate() == E(z.conjugate(), mi.conjugate()) + assert E(mi).conjugate() == E(mi.conjugate()) + mr = Symbol('m', negative=True) + assert E(z, mr).conjugate() == E(z.conjugate(), mr) + assert E(mr).conjugate() == E(mr) + + assert E(z).rewrite(hyper) == (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), z) + assert tn(E(z), (pi/2)*hyper((Rational(-1, 2), S.Half), (S.One,), z)) + assert E(z).rewrite(meijerg) == \ + -meijerg(((S.Half, Rational(3, 2)), []), ((S.Zero,), (S.Zero,)), -z)/4 + assert tn(E(z), -meijerg(((S.Half, Rational(3, 2)), []), ((S.Zero,), (S.Zero,)), -z)/4) + + assert E(z, m).series(z) == \ + z + z**5*(-m**2/40 + m/30) - m*z**3/6 + O(z**6) + assert E(z).series(z) == pi/2 - pi*z/8 - 3*pi*z**2/128 - \ + 5*pi*z**3/512 - 175*pi*z**4/32768 - 441*pi*z**5/131072 + O(z**6) + assert E(4*z/(z+1)).series(z) == \ + pi/2 - pi*z/2 + pi*z**2/8 - 3*pi*z**3/8 - 15*pi*z**4/128 - 93*pi*z**5/128 + O(z**6) + + assert E(z, m).rewrite(Integral).dummy_eq( + Integral(sqrt(1 - m*sin(t)**2), (t, 0, z))) + assert E(m).rewrite(Integral).dummy_eq( + Integral(sqrt(1 - m*sin(t)**2), (t, 0, pi/2))) + +def test_P(): + assert P(0, z, m) == F(z, m) + assert P(1, z, m) == F(z, m) + \ + (sqrt(1 - m*sin(z)**2)*tan(z) - E(z, m))/(1 - m) + assert P(n, i*pi/2, m) == i*P(n, m) + assert P(n, z, 0) == atanh(sqrt(n - 1)*tan(z))/sqrt(n - 1) + assert P(n, z, n) == F(z, n) - P(1, z, n) + tan(z)/sqrt(1 - n*sin(z)**2) + assert P(oo, z, m) == 0 + assert P(-oo, z, m) == 0 + assert P(n, z, oo) == 0 + assert P(n, z, -oo) == 0 + assert P(0, m) == K(m) + assert P(1, m) is zoo + assert P(n, 0) == pi/(2*sqrt(1 - n)) + assert P(2, 1) is -oo + assert P(-1, 1) is oo + assert P(n, n) == E(n)/(1 - n) + + assert P(n, -z, m) == -P(n, z, m) + + ni, mi = Symbol('n', real=False), Symbol('m', real=False) + assert P(ni, z, mi).conjugate() == \ + P(ni.conjugate(), z.conjugate(), mi.conjugate()) + nr, mr = Symbol('n', negative=True), \ + Symbol('m', negative=True) + assert P(nr, z, mr).conjugate() == P(nr, z.conjugate(), mr) + assert P(n, m).conjugate() == P(n.conjugate(), m.conjugate()) + + assert P(n, z, m).diff(n) == (E(z, m) + (m - n)*F(z, m)/n + + (n**2 - m)*P(n, z, m)/n - n*sqrt(1 - + m*sin(z)**2)*sin(2*z)/(2*(1 - n*sin(z)**2)))/(2*(m - n)*(n - 1)) + assert P(n, z, m).diff(z) == 1/(sqrt(1 - m*sin(z)**2)*(1 - n*sin(z)**2)) + assert P(n, z, m).diff(m) == (E(z, m)/(m - 1) + P(n, z, m) - + m*sin(2*z)/(2*(m - 1)*sqrt(1 - m*sin(z)**2)))/(2*(n - m)) + assert P(n, m).diff(n) == (E(m) + (m - n)*K(m)/n + + (n**2 - m)*P(n, m)/n)/(2*(m - n)*(n - 1)) + assert P(n, m).diff(m) == (E(m)/(m - 1) + P(n, m))/(2*(n - m)) + + # These tests fail due to + # https://github.com/fredrik-johansson/mpmath/issues/571#issuecomment-777201962 + # https://github.com/sympy/sympy/issues/20933#issuecomment-777080385 + # + # rx, ry = randcplx(), randcplx() + # assert td(P(n, rx, ry), n) + # assert td(P(rx, z, ry), z) + # assert td(P(rx, ry, m), m) + + assert P(n, z, m).series(z) == z + z**3*(m/6 + n/3) + \ + z**5*(3*m**2/40 + m*n/10 - m/30 + n**2/5 - n/15) + O(z**6) + + assert P(n, z, m).rewrite(Integral).dummy_eq( + Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, z))) + assert P(n, m).rewrite(Integral).dummy_eq( + Integral(1/((1 - n*sin(t)**2)*sqrt(1 - m*sin(t)**2)), (t, 0, pi/2))) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_error_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_error_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..fef718517884e3f0bbd31f229283702adab03465 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_error_functions.py @@ -0,0 +1,837 @@ +from sympy.core.function import (diff, expand, expand_func) +from sympy.core import EulerGamma +from sympy.core.numbers import (E, Float, I, Rational, nan, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols, Dummy) +from sympy.functions.elementary.complexes import (conjugate, im, polar_lift, re) +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.hyperbolic import (cosh, sinh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.functions.special.error_functions import (Chi, Ci, E1, Ei, Li, Shi, Si, erf, erf2, erf2inv, erfc, erfcinv, erfi, erfinv, expint, fresnelc, fresnels, li) +from sympy.functions.special.gamma_functions import (gamma, uppergamma) +from sympy.functions.special.hyper import (hyper, meijerg) +from sympy.integrals.integrals import (Integral, integrate) +from sympy.series.gruntz import gruntz +from sympy.series.limits import limit +from sympy.series.order import O +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.functions.special.error_functions import _erfs, _eis +from sympy.testing.pytest import raises + +x, y, z = symbols('x,y,z') +w = Symbol("w", real=True) +n = Symbol("n", integer=True) +t = Dummy('t') + + +def test_erf(): + assert erf(nan) is nan + + assert erf(oo) == 1 + assert erf(-oo) == -1 + + assert erf(0) is S.Zero + + assert erf(I*oo) == oo*I + assert erf(-I*oo) == -oo*I + + assert erf(-2) == -erf(2) + assert erf(-x*y) == -erf(x*y) + assert erf(-x - y) == -erf(x + y) + + assert erf(erfinv(x)) == x + assert erf(erfcinv(x)) == 1 - x + assert erf(erf2inv(0, x)) == x + assert erf(erf2inv(0, x, evaluate=False)) == x # To cover code in erf + assert erf(erf2inv(0, erf(erfcinv(1 - erf(erfinv(x)))))) == x + + assert erf(I).is_real is False + assert erf(0, evaluate=False).is_real + assert erf(0, evaluate=False).is_zero + + assert conjugate(erf(z)) == erf(conjugate(z)) + + assert erf(x).as_leading_term(x) == 2*x/sqrt(pi) + assert erf(x*y).as_leading_term(y) == 2*x*y/sqrt(pi) + assert (erf(x*y)/erf(y)).as_leading_term(y) == x + assert erf(1/x).as_leading_term(x) == S.One + + assert erf(z).rewrite('uppergamma') == sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z + assert erf(z).rewrite('erfc') == S.One - erfc(z) + assert erf(z).rewrite('erfi') == -I*erfi(I*z) + assert erf(z).rewrite('fresnels') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) - + I*fresnels(z*(1 - I)/sqrt(pi))) + assert erf(z).rewrite('fresnelc') == (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) - + I*fresnels(z*(1 - I)/sqrt(pi))) + assert erf(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi) + assert erf(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)/sqrt(pi) + assert erf(z).rewrite('expint') == sqrt(z**2)/z - z*expint(S.Half, z**2)/sqrt(S.Pi) + + assert limit(exp(x)*exp(x**2)*(erf(x + 1/exp(x)) - erf(x)), x, oo) == \ + 2/sqrt(pi) + assert limit((1 - erf(z))*exp(z**2)*z, z, oo) == 1/sqrt(pi) + assert limit((1 - erf(x))*exp(x**2)*sqrt(pi)*x, x, oo) == 1 + assert limit(((1 - erf(x))*exp(x**2)*sqrt(pi)*x - 1)*2*x**2, x, oo) == -1 + assert limit(erf(x)/x, x, 0) == 2/sqrt(pi) + assert limit(x**(-4) - sqrt(pi)*erf(x**2) / (2*x**6), x, 0) == S(1)/3 + + assert erf(x).as_real_imag() == \ + (erf(re(x) - I*im(x))/2 + erf(re(x) + I*im(x))/2, + -I*(-erf(re(x) - I*im(x)) + erf(re(x) + I*im(x)))/2) + + assert erf(x).as_real_imag(deep=False) == \ + (erf(re(x) - I*im(x))/2 + erf(re(x) + I*im(x))/2, + -I*(-erf(re(x) - I*im(x)) + erf(re(x) + I*im(x)))/2) + + assert erf(w).as_real_imag() == (erf(w), 0) + assert erf(w).as_real_imag(deep=False) == (erf(w), 0) + # issue 13575 + assert erf(I).as_real_imag() == (0, -I*erf(I)) + + raises(ArgumentIndexError, lambda: erf(x).fdiff(2)) + + assert erf(x).inverse() == erfinv + + +def test_erf_series(): + assert erf(x).series(x, 0, 7) == 2*x/sqrt(pi) - \ + 2*x**3/3/sqrt(pi) + x**5/5/sqrt(pi) + O(x**7) + + assert erf(x).series(x, oo) == \ + -exp(-x**2)*(3/(4*x**5) - 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))/sqrt(pi) + 1 + assert erf(x**2).series(x, oo, n=8) == \ + (-1/(2*x**6) + x**(-2) + O(x**(-8), (x, oo)))*exp(-x**4)/sqrt(pi)*-1 + 1 + assert erf(sqrt(x)).series(x, oo, n=3) == (sqrt(1/x) - (1/x)**(S(3)/2)/2\ + + 3*(1/x)**(S(5)/2)/4 + O(x**(-3), (x, oo)))*exp(-x)/sqrt(pi)*-1 + 1 + + +def test_erf_evalf(): + assert abs( erf(Float(2.0)) - 0.995322265 ) < 1E-8 # XXX + + +def test__erfs(): + assert _erfs(z).diff(z) == -2/sqrt(S.Pi) + 2*z*_erfs(z) + + assert _erfs(1/z).series(z) == \ + z/sqrt(pi) - z**3/(2*sqrt(pi)) + 3*z**5/(4*sqrt(pi)) + O(z**6) + + assert expand(erf(z).rewrite('tractable').diff(z).rewrite('intractable')) \ + == erf(z).diff(z) + assert _erfs(z).rewrite("intractable") == (-erf(z) + 1)*exp(z**2) + raises(ArgumentIndexError, lambda: _erfs(z).fdiff(2)) + + +def test_erfc(): + assert erfc(nan) is nan + + assert erfc(oo) is S.Zero + assert erfc(-oo) == 2 + + assert erfc(0) == 1 + + assert erfc(I*oo) == -oo*I + assert erfc(-I*oo) == oo*I + + assert erfc(-x) == S(2) - erfc(x) + assert erfc(erfcinv(x)) == x + + assert erfc(I).is_real is False + assert erfc(0, evaluate=False).is_real + assert erfc(0, evaluate=False).is_zero is False + + assert erfc(erfinv(x)) == 1 - x + + assert conjugate(erfc(z)) == erfc(conjugate(z)) + + assert erfc(x).as_leading_term(x) is S.One + assert erfc(1/x).as_leading_term(x) == S.Zero + + assert erfc(z).rewrite('erf') == 1 - erf(z) + assert erfc(z).rewrite('erfi') == 1 + I*erfi(I*z) + assert erfc(z).rewrite('fresnels') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) - + I*fresnels(z*(1 - I)/sqrt(pi))) + assert erfc(z).rewrite('fresnelc') == 1 - (1 + I)*(fresnelc(z*(1 - I)/sqrt(pi)) - + I*fresnels(z*(1 - I)/sqrt(pi))) + assert erfc(z).rewrite('hyper') == 1 - 2*z*hyper([S.Half], [3*S.Half], -z**2)/sqrt(pi) + assert erfc(z).rewrite('meijerg') == 1 - z*meijerg([S.Half], [], [0], [Rational(-1, 2)], z**2)/sqrt(pi) + assert erfc(z).rewrite('uppergamma') == 1 - sqrt(z**2)*(1 - erfc(sqrt(z**2)))/z + assert erfc(z).rewrite('expint') == S.One - sqrt(z**2)/z + z*expint(S.Half, z**2)/sqrt(S.Pi) + assert erfc(z).rewrite('tractable') == _erfs(z)*exp(-z**2) + assert expand_func(erf(x) + erfc(x)) is S.One + + assert erfc(x).as_real_imag() == \ + (erfc(re(x) - I*im(x))/2 + erfc(re(x) + I*im(x))/2, + -I*(-erfc(re(x) - I*im(x)) + erfc(re(x) + I*im(x)))/2) + + assert erfc(x).as_real_imag(deep=False) == \ + (erfc(re(x) - I*im(x))/2 + erfc(re(x) + I*im(x))/2, + -I*(-erfc(re(x) - I*im(x)) + erfc(re(x) + I*im(x)))/2) + + assert erfc(w).as_real_imag() == (erfc(w), 0) + assert erfc(w).as_real_imag(deep=False) == (erfc(w), 0) + raises(ArgumentIndexError, lambda: erfc(x).fdiff(2)) + + assert erfc(x).inverse() == erfcinv + + +def test_erfc_series(): + assert erfc(x).series(x, 0, 7) == 1 - 2*x/sqrt(pi) + \ + 2*x**3/3/sqrt(pi) - x**5/5/sqrt(pi) + O(x**7) + + assert erfc(x).series(x, oo) == \ + (3/(4*x**5) - 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))*exp(-x**2)/sqrt(pi) + + +def test_erfc_evalf(): + assert abs( erfc(Float(2.0)) - 0.00467773 ) < 1E-8 # XXX + + +def test_erfi(): + assert erfi(nan) is nan + + assert erfi(oo) is S.Infinity + assert erfi(-oo) is S.NegativeInfinity + + assert erfi(0) is S.Zero + + assert erfi(I*oo) == I + assert erfi(-I*oo) == -I + + assert erfi(-x) == -erfi(x) + + assert erfi(I*erfinv(x)) == I*x + assert erfi(I*erfcinv(x)) == I*(1 - x) + assert erfi(I*erf2inv(0, x)) == I*x + assert erfi(I*erf2inv(0, x, evaluate=False)) == I*x # To cover code in erfi + + assert erfi(I).is_real is False + assert erfi(0, evaluate=False).is_real + assert erfi(0, evaluate=False).is_zero + + assert conjugate(erfi(z)) == erfi(conjugate(z)) + + assert erfi(x).as_leading_term(x) == 2*x/sqrt(pi) + assert erfi(x*y).as_leading_term(y) == 2*x*y/sqrt(pi) + assert (erfi(x*y)/erfi(y)).as_leading_term(y) == x + assert erfi(1/x).as_leading_term(x) == erfi(1/x) + + assert erfi(z).rewrite('erf') == -I*erf(I*z) + assert erfi(z).rewrite('erfc') == I*erfc(I*z) - I + assert erfi(z).rewrite('fresnels') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) - + I*fresnels(z*(1 + I)/sqrt(pi))) + assert erfi(z).rewrite('fresnelc') == (1 - I)*(fresnelc(z*(1 + I)/sqrt(pi)) - + I*fresnels(z*(1 + I)/sqrt(pi))) + assert erfi(z).rewrite('hyper') == 2*z*hyper([S.Half], [3*S.Half], z**2)/sqrt(pi) + assert erfi(z).rewrite('meijerg') == z*meijerg([S.Half], [], [0], [Rational(-1, 2)], -z**2)/sqrt(pi) + assert erfi(z).rewrite('uppergamma') == (sqrt(-z**2)/z*(uppergamma(S.Half, + -z**2)/sqrt(S.Pi) - S.One)) + assert erfi(z).rewrite('expint') == sqrt(-z**2)/z - z*expint(S.Half, -z**2)/sqrt(S.Pi) + assert erfi(z).rewrite('tractable') == -I*(-_erfs(I*z)*exp(z**2) + 1) + assert expand_func(erfi(I*z)) == I*erf(z) + + assert erfi(x).as_real_imag() == \ + (erfi(re(x) - I*im(x))/2 + erfi(re(x) + I*im(x))/2, + -I*(-erfi(re(x) - I*im(x)) + erfi(re(x) + I*im(x)))/2) + assert erfi(x).as_real_imag(deep=False) == \ + (erfi(re(x) - I*im(x))/2 + erfi(re(x) + I*im(x))/2, + -I*(-erfi(re(x) - I*im(x)) + erfi(re(x) + I*im(x)))/2) + + assert erfi(w).as_real_imag() == (erfi(w), 0) + assert erfi(w).as_real_imag(deep=False) == (erfi(w), 0) + + raises(ArgumentIndexError, lambda: erfi(x).fdiff(2)) + + +def test_erfi_series(): + assert erfi(x).series(x, 0, 7) == 2*x/sqrt(pi) + \ + 2*x**3/3/sqrt(pi) + x**5/5/sqrt(pi) + O(x**7) + + assert erfi(x).series(x, oo) == \ + (3/(4*x**5) + 1/(2*x**3) + 1/x + O(x**(-6), (x, oo)))*exp(x**2)/sqrt(pi) - I + + +def test_erfi_evalf(): + assert abs( erfi(Float(2.0)) - 18.5648024145756 ) < 1E-13 # XXX + + +def test_erf2(): + + assert erf2(0, 0) is S.Zero + assert erf2(x, x) is S.Zero + assert erf2(nan, 0) is nan + + assert erf2(-oo, y) == erf(y) + 1 + assert erf2( oo, y) == erf(y) - 1 + assert erf2( x, oo) == 1 - erf(x) + assert erf2( x,-oo) == -1 - erf(x) + assert erf2(x, erf2inv(x, y)) == y + + assert erf2(-x, -y) == -erf2(x,y) + assert erf2(-x, y) == erf(y) + erf(x) + assert erf2( x, -y) == -erf(y) - erf(x) + assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels) + assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc) + assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper) + assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg) + assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma) + assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint) + + assert erf2(I, 0).is_real is False + assert erf2(0, 0, evaluate=False).is_real + assert erf2(0, 0, evaluate=False).is_zero + assert erf2(x, x, evaluate=False).is_zero + assert erf2(x, y).is_zero is None + + assert expand_func(erf(x) + erf2(x, y)) == erf(y) + + assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y)) + + assert erf2(x, y).rewrite('erf') == erf(y) - erf(x) + assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y) + assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y)) + + assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1) + assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2) + assert erf2(x, y).diff(x) == -2*exp(-x**2)/sqrt(pi) + assert erf2(x, y).diff(y) == 2*exp(-y**2)/sqrt(pi) + raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3)) + + assert erf2(x, y).is_extended_real is None + xr, yr = symbols('xr yr', extended_real=True) + assert erf2(xr, yr).is_extended_real is True + + +def test_erfinv(): + assert erfinv(0) is S.Zero + assert erfinv(1) is S.Infinity + assert erfinv(nan) is S.NaN + assert erfinv(-1) is S.NegativeInfinity + + assert erfinv(erf(w)) == w + assert erfinv(erf(-w)) == -w + + assert erfinv(x).diff() == sqrt(pi)*exp(erfinv(x)**2)/2 + raises(ArgumentIndexError, lambda: erfinv(x).fdiff(2)) + + assert erfinv(z).rewrite('erfcinv') == erfcinv(1-z) + assert erfinv(z).inverse() == erf + + +def test_erfinv_evalf(): + assert abs( erfinv(Float(0.2)) - 0.179143454621292 ) < 1E-13 + + +def test_erfcinv(): + assert erfcinv(1) is S.Zero + assert erfcinv(0) is S.Infinity + assert erfcinv(nan) is S.NaN + + assert erfcinv(x).diff() == -sqrt(pi)*exp(erfcinv(x)**2)/2 + raises(ArgumentIndexError, lambda: erfcinv(x).fdiff(2)) + + assert erfcinv(z).rewrite('erfinv') == erfinv(1-z) + assert erfcinv(z).inverse() == erfc + + +def test_erf2inv(): + assert erf2inv(0, 0) is S.Zero + assert erf2inv(0, 1) is S.Infinity + assert erf2inv(1, 0) is S.One + assert erf2inv(0, y) == erfinv(y) + assert erf2inv(oo, y) == erfcinv(-y) + assert erf2inv(x, 0) == x + assert erf2inv(x, oo) == erfinv(x) + assert erf2inv(nan, 0) is nan + assert erf2inv(0, nan) is nan + + assert erf2inv(x, y).diff(x) == exp(-x**2 + erf2inv(x, y)**2) + assert erf2inv(x, y).diff(y) == sqrt(pi)*exp(erf2inv(x, y)**2)/2 + raises(ArgumentIndexError, lambda: erf2inv(x, y).fdiff(3)) + + +# NOTE we multiply by exp_polar(I*pi) and need this to be on the principal +# branch, hence take x in the lower half plane (d=0). + + +def mytn(expr1, expr2, expr3, x, d=0): + from sympy.core.random import verify_numerically, random_complex_number + subs = {} + for a in expr1.free_symbols: + if a != x: + subs[a] = random_complex_number() + return expr2 == expr3 and verify_numerically(expr1.subs(subs), + expr2.subs(subs), x, d=d) + + +def mytd(expr1, expr2, x): + from sympy.core.random import test_derivative_numerically, \ + random_complex_number + subs = {} + for a in expr1.free_symbols: + if a != x: + subs[a] = random_complex_number() + return expr1.diff(x) == expr2 and test_derivative_numerically(expr1.subs(subs), x) + + +def tn_branch(func, s=None): + from sympy.core.random import uniform + + def fn(x): + if s is None: + return func(x) + return func(s, x) + c = uniform(1, 5) + expr = fn(c*exp_polar(I*pi)) - fn(c*exp_polar(-I*pi)) + eps = 1e-15 + expr2 = fn(-c + eps*I) - fn(-c - eps*I) + return abs(expr.n() - expr2.n()).n() < 1e-10 + + +def test_ei(): + assert Ei(0) is S.NegativeInfinity + assert Ei(oo) is S.Infinity + assert Ei(-oo) is S.Zero + + assert tn_branch(Ei) + assert mytd(Ei(x), exp(x)/x, x) + assert mytn(Ei(x), Ei(x).rewrite(uppergamma), + -uppergamma(0, x*polar_lift(-1)) - I*pi, x) + assert mytn(Ei(x), Ei(x).rewrite(expint), + -expint(1, x*polar_lift(-1)) - I*pi, x) + assert Ei(x).rewrite(expint).rewrite(Ei) == Ei(x) + assert Ei(x*exp_polar(2*I*pi)) == Ei(x) + 2*I*pi + assert Ei(x*exp_polar(-2*I*pi)) == Ei(x) - 2*I*pi + + assert mytn(Ei(x), Ei(x).rewrite(Shi), Chi(x) + Shi(x), x) + assert mytn(Ei(x*polar_lift(I)), Ei(x*polar_lift(I)).rewrite(Si), + Ci(x) + I*Si(x) + I*pi/2, x) + + assert Ei(log(x)).rewrite(li) == li(x) + assert Ei(2*log(x)).rewrite(li) == li(x**2) + + assert gruntz(Ei(x+exp(-x))*exp(-x)*x, x, oo) == 1 + + assert Ei(x).series(x) == EulerGamma + log(x) + x + x**2/4 + \ + x**3/18 + x**4/96 + x**5/600 + O(x**6) + assert Ei(x).series(x, 1, 3) == Ei(1) + E*(x - 1) + O((x - 1)**3, (x, 1)) + assert Ei(x).series(x, oo) == \ + (120/x**5 + 24/x**4 + 6/x**3 + 2/x**2 + 1/x + 1 + O(x**(-6), (x, oo)))*exp(x)/x + + assert str(Ei(cos(2)).evalf(n=10)) == '-0.6760647401' + raises(ArgumentIndexError, lambda: Ei(x).fdiff(2)) + + +def test_expint(): + assert mytn(expint(x, y), expint(x, y).rewrite(uppergamma), + y**(x - 1)*uppergamma(1 - x, y), x) + assert mytd( + expint(x, y), -y**(x - 1)*meijerg([], [1, 1], [0, 0, 1 - x], [], y), x) + assert mytd(expint(x, y), -expint(x - 1, y), y) + assert mytn(expint(1, x), expint(1, x).rewrite(Ei), + -Ei(x*polar_lift(-1)) + I*pi, x) + + assert expint(-4, x) == exp(-x)/x + 4*exp(-x)/x**2 + 12*exp(-x)/x**3 \ + + 24*exp(-x)/x**4 + 24*exp(-x)/x**5 + assert expint(Rational(-3, 2), x) == \ + exp(-x)/x + 3*exp(-x)/(2*x**2) + 3*sqrt(pi)*erfc(sqrt(x))/(4*x**S('5/2')) + + assert tn_branch(expint, 1) + assert tn_branch(expint, 2) + assert tn_branch(expint, 3) + assert tn_branch(expint, 1.7) + assert tn_branch(expint, pi) + + assert expint(y, x*exp_polar(2*I*pi)) == \ + x**(y - 1)*(exp(2*I*pi*y) - 1)*gamma(-y + 1) + expint(y, x) + assert expint(y, x*exp_polar(-2*I*pi)) == \ + x**(y - 1)*(exp(-2*I*pi*y) - 1)*gamma(-y + 1) + expint(y, x) + assert expint(2, x*exp_polar(2*I*pi)) == 2*I*pi*x + expint(2, x) + assert expint(2, x*exp_polar(-2*I*pi)) == -2*I*pi*x + expint(2, x) + assert expint(1, x).rewrite(Ei).rewrite(expint) == expint(1, x) + assert expint(x, y).rewrite(Ei) == expint(x, y) + assert expint(x, y).rewrite(Ci) == expint(x, y) + + assert mytn(E1(x), E1(x).rewrite(Shi), Shi(x) - Chi(x), x) + assert mytn(E1(polar_lift(I)*x), E1(polar_lift(I)*x).rewrite(Si), + -Ci(x) + I*Si(x) - I*pi/2, x) + + assert mytn(expint(2, x), expint(2, x).rewrite(Ei).rewrite(expint), + -x*E1(x) + exp(-x), x) + assert mytn(expint(3, x), expint(3, x).rewrite(Ei).rewrite(expint), + x**2*E1(x)/2 + (1 - x)*exp(-x)/2, x) + + assert expint(Rational(3, 2), z).nseries(z) == \ + 2 + 2*z - z**2/3 + z**3/15 - z**4/84 + z**5/540 - \ + 2*sqrt(pi)*sqrt(z) + O(z**6) + + assert E1(z).series(z) == -EulerGamma - log(z) + z - \ + z**2/4 + z**3/18 - z**4/96 + z**5/600 + O(z**6) + + assert expint(4, z).series(z) == Rational(1, 3) - z/2 + z**2/2 + \ + z**3*(log(z)/6 - Rational(11, 36) + EulerGamma/6 - I*pi/6) - z**4/24 + \ + z**5/240 + O(z**6) + + assert expint(n, x).series(x, oo, n=3) == \ + (n*(n + 1)/x**2 - n/x + 1 + O(x**(-3), (x, oo)))*exp(-x)/x + + assert expint(z, y).series(z, 0, 2) == exp(-y)/y - z*meijerg(((), (1, 1)), + ((0, 0, 1), ()), y)/y + O(z**2) + raises(ArgumentIndexError, lambda: expint(x, y).fdiff(3)) + + neg = Symbol('neg', negative=True) + assert Ei(neg).rewrite(Si) == Shi(neg) + Chi(neg) - I*pi + + +def test__eis(): + assert _eis(z).diff(z) == -_eis(z) + 1/z + + assert _eis(1/z).series(z) == \ + z + z**2 + 2*z**3 + 6*z**4 + 24*z**5 + O(z**6) + + assert Ei(z).rewrite('tractable') == exp(z)*_eis(z) + assert li(z).rewrite('tractable') == z*_eis(log(z)) + + assert _eis(z).rewrite('intractable') == exp(-z)*Ei(z) + + assert expand(li(z).rewrite('tractable').diff(z).rewrite('intractable')) \ + == li(z).diff(z) + + assert expand(Ei(z).rewrite('tractable').diff(z).rewrite('intractable')) \ + == Ei(z).diff(z) + + assert _eis(z).series(z, n=3) == EulerGamma + log(z) + z*(-log(z) - \ + EulerGamma + 1) + z**2*(log(z)/2 - Rational(3, 4) + EulerGamma/2)\ + + O(z**3*log(z)) + raises(ArgumentIndexError, lambda: _eis(z).fdiff(2)) + + +def tn_arg(func): + def test(arg, e1, e2): + from sympy.core.random import uniform + v = uniform(1, 5) + v1 = func(arg*x).subs(x, v).n() + v2 = func(e1*v + e2*1e-15).n() + return abs(v1 - v2).n() < 1e-10 + return test(exp_polar(I*pi/2), I, 1) and \ + test(exp_polar(-I*pi/2), -I, 1) and \ + test(exp_polar(I*pi), -1, I) and \ + test(exp_polar(-I*pi), -1, -I) + + +def test_li(): + z = Symbol("z") + zr = Symbol("z", real=True) + zp = Symbol("z", positive=True) + zn = Symbol("z", negative=True) + + assert li(0) is S.Zero + assert li(1) is -oo + assert li(oo) is oo + + assert isinstance(li(z), li) + assert unchanged(li, -zp) + assert unchanged(li, zn) + + assert diff(li(z), z) == 1/log(z) + + assert conjugate(li(z)) == li(conjugate(z)) + assert conjugate(li(-zr)) == li(-zr) + assert unchanged(conjugate, li(-zp)) + assert unchanged(conjugate, li(zn)) + + assert li(z).rewrite(Li) == Li(z) + li(2) + assert li(z).rewrite(Ei) == Ei(log(z)) + assert li(z).rewrite(uppergamma) == (-log(1/log(z))/2 - log(-log(z)) + + log(log(z))/2 - expint(1, -log(z))) + assert li(z).rewrite(Si) == (-log(I*log(z)) - log(1/log(z))/2 + + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z))) + assert li(z).rewrite(Ci) == (-log(I*log(z)) - log(1/log(z))/2 + + log(log(z))/2 + Ci(I*log(z)) + Shi(log(z))) + assert li(z).rewrite(Shi) == (-log(1/log(z))/2 + log(log(z))/2 + + Chi(log(z)) - Shi(log(z))) + assert li(z).rewrite(Chi) == (-log(1/log(z))/2 + log(log(z))/2 + + Chi(log(z)) - Shi(log(z))) + assert li(z).rewrite(hyper) ==(log(z)*hyper((1, 1), (2, 2), log(z)) - + log(1/log(z))/2 + log(log(z))/2 + EulerGamma) + assert li(z).rewrite(meijerg) == (-log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 - + meijerg(((), (1,)), ((0, 0), ()), -log(z))) + + assert gruntz(1/li(z), z, oo) is S.Zero + assert li(z).series(z) == log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + \ + log(z) + log(log(z)) + EulerGamma + raises(ArgumentIndexError, lambda: li(z).fdiff(2)) + + +def test_Li(): + assert Li(2) is S.Zero + assert Li(oo) is oo + + assert isinstance(Li(z), Li) + + assert diff(Li(z), z) == 1/log(z) + + assert gruntz(1/Li(z), z, oo) is S.Zero + assert Li(z).rewrite(li) == li(z) - li(2) + assert Li(z).series(z) == \ + log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + log(z) + log(log(z)) - li(2) + EulerGamma + raises(ArgumentIndexError, lambda: Li(z).fdiff(2)) + + +def test_si(): + assert Si(I*x) == I*Shi(x) + assert Shi(I*x) == I*Si(x) + assert Si(-I*x) == -I*Shi(x) + assert Shi(-I*x) == -I*Si(x) + assert Si(-x) == -Si(x) + assert Shi(-x) == -Shi(x) + assert Si(exp_polar(2*pi*I)*x) == Si(x) + assert Si(exp_polar(-2*pi*I)*x) == Si(x) + assert Shi(exp_polar(2*pi*I)*x) == Shi(x) + assert Shi(exp_polar(-2*pi*I)*x) == Shi(x) + + assert Si(oo) == pi/2 + assert Si(-oo) == -pi/2 + assert Shi(oo) is oo + assert Shi(-oo) is -oo + + assert mytd(Si(x), sin(x)/x, x) + assert mytd(Shi(x), sinh(x)/x, x) + + assert mytn(Si(x), Si(x).rewrite(Ei), + -I*(-Ei(x*exp_polar(-I*pi/2))/2 + + Ei(x*exp_polar(I*pi/2))/2 - I*pi) + pi/2, x) + assert mytn(Si(x), Si(x).rewrite(expint), + -I*(-expint(1, x*exp_polar(-I*pi/2))/2 + + expint(1, x*exp_polar(I*pi/2))/2) + pi/2, x) + assert mytn(Shi(x), Shi(x).rewrite(Ei), + Ei(x)/2 - Ei(x*exp_polar(I*pi))/2 + I*pi/2, x) + assert mytn(Shi(x), Shi(x).rewrite(expint), + expint(1, x)/2 - expint(1, x*exp_polar(I*pi))/2 - I*pi/2, x) + + assert tn_arg(Si) + assert tn_arg(Shi) + + assert Si(x)._eval_as_leading_term(x) == x + assert Si(2*x)._eval_as_leading_term(x) == 2*x + assert Si(sin(x))._eval_as_leading_term(x) == x + assert Si(x + 1)._eval_as_leading_term(x) == Si(1) + assert Si(1/x)._eval_as_leading_term(x, cdir=1) == \ + Si(1/x)._eval_as_leading_term(x, cdir=-1) == Si(1/x) + + assert Si(x).nseries(x, n=8) == \ + x - x**3/18 + x**5/600 - x**7/35280 + O(x**8) + assert Shi(x).nseries(x, n=8) == \ + x + x**3/18 + x**5/600 + x**7/35280 + O(x**8) + assert Si(sin(x)).nseries(x, n=5) == x - 2*x**3/9 + O(x**5) + assert Si(x).nseries(x, 1, n=3) == \ + Si(1) + (x - 1)*sin(1) + (x - 1)**2*(-sin(1)/2 + cos(1)/2) + O((x - 1)**3, (x, 1)) + + assert Si(x).series(x, oo) == -sin(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, oo))) - \ + cos(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, oo))) + pi/2 + + t = Symbol('t', Dummy=True) + assert Si(x).rewrite(sinc).dummy_eq(Integral(sinc(t), (t, 0, x))) + + assert limit(Shi(x), x, S.Infinity) == S.Infinity + assert limit(Shi(x), x, S.NegativeInfinity) == S.NegativeInfinity + + +def test_ci(): + m1 = exp_polar(I*pi) + m1_ = exp_polar(-I*pi) + pI = exp_polar(I*pi/2) + mI = exp_polar(-I*pi/2) + + assert Ci(m1*x) == Ci(x) + I*pi + assert Ci(m1_*x) == Ci(x) - I*pi + assert Ci(pI*x) == Chi(x) + I*pi/2 + assert Ci(mI*x) == Chi(x) - I*pi/2 + assert Chi(m1*x) == Chi(x) + I*pi + assert Chi(m1_*x) == Chi(x) - I*pi + assert Chi(pI*x) == Ci(x) + I*pi/2 + assert Chi(mI*x) == Ci(x) - I*pi/2 + assert Ci(exp_polar(2*I*pi)*x) == Ci(x) + 2*I*pi + assert Chi(exp_polar(-2*I*pi)*x) == Chi(x) - 2*I*pi + assert Chi(exp_polar(2*I*pi)*x) == Chi(x) + 2*I*pi + assert Ci(exp_polar(-2*I*pi)*x) == Ci(x) - 2*I*pi + + assert Ci(oo) is S.Zero + assert Ci(-oo) == I*pi + assert Chi(oo) is oo + assert Chi(-oo) is oo + + assert mytd(Ci(x), cos(x)/x, x) + assert mytd(Chi(x), cosh(x)/x, x) + + assert mytn(Ci(x), Ci(x).rewrite(Ei), + Ei(x*exp_polar(-I*pi/2))/2 + Ei(x*exp_polar(I*pi/2))/2, x) + assert mytn(Chi(x), Chi(x).rewrite(Ei), + Ei(x)/2 + Ei(x*exp_polar(I*pi))/2 - I*pi/2, x) + + assert tn_arg(Ci) + assert tn_arg(Chi) + + assert Ci(x).nseries(x, n=4) == \ + EulerGamma + log(x) - x**2/4 + O(x**4) + assert Chi(x).nseries(x, n=4) == \ + EulerGamma + log(x) + x**2/4 + O(x**4) + + assert Ci(x).series(x, oo) == -cos(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, oo))) + \ + sin(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, oo))) + + assert Ci(x).series(x, -oo) == -cos(x)*(-6/x**4 + x**(-2) + O(x**(-6), (x, -oo))) + \ + sin(x)*(24/x**5 - 2/x**3 + 1/x + O(x**(-6), (x, -oo))) + I*pi + + assert limit(log(x) - Ci(2*x), x, 0) == -log(2) - EulerGamma + assert Ci(x).rewrite(uppergamma) == -expint(1, x*exp_polar(-I*pi/2))/2 -\ + expint(1, x*exp_polar(I*pi/2))/2 + assert Ci(x).rewrite(expint) == -expint(1, x*exp_polar(-I*pi/2))/2 -\ + expint(1, x*exp_polar(I*pi/2))/2 + raises(ArgumentIndexError, lambda: Ci(x).fdiff(2)) + + +def test_fresnel(): + assert fresnels(0) is S.Zero + assert fresnels(oo) is S.Half + assert fresnels(-oo) == Rational(-1, 2) + assert fresnels(I*oo) == -I*S.Half + + assert unchanged(fresnels, z) + assert fresnels(-z) == -fresnels(z) + assert fresnels(I*z) == -I*fresnels(z) + assert fresnels(-I*z) == I*fresnels(z) + + assert conjugate(fresnels(z)) == fresnels(conjugate(z)) + + assert fresnels(z).diff(z) == sin(pi*z**2/2) + + assert fresnels(z).rewrite(erf) == (S.One + I)/4 * ( + erf((S.One + I)/2*sqrt(pi)*z) - I*erf((S.One - I)/2*sqrt(pi)*z)) + + assert fresnels(z).rewrite(hyper) == \ + pi*z**3/6 * hyper([Rational(3, 4)], [Rational(3, 2), Rational(7, 4)], -pi**2*z**4/16) + + assert fresnels(z).series(z, n=15) == \ + pi*z**3/6 - pi**3*z**7/336 + pi**5*z**11/42240 + O(z**15) + + assert fresnels(w).is_extended_real is True + assert fresnels(w).is_finite is True + + assert fresnels(z).is_extended_real is None + assert fresnels(z).is_finite is None + + assert fresnels(z).as_real_imag() == (fresnels(re(z) - I*im(z))/2 + + fresnels(re(z) + I*im(z))/2, + -I*(-fresnels(re(z) - I*im(z)) + fresnels(re(z) + I*im(z)))/2) + + assert fresnels(z).as_real_imag(deep=False) == (fresnels(re(z) - I*im(z))/2 + + fresnels(re(z) + I*im(z))/2, + -I*(-fresnels(re(z) - I*im(z)) + fresnels(re(z) + I*im(z)))/2) + + assert fresnels(w).as_real_imag() == (fresnels(w), 0) + assert fresnels(w).as_real_imag(deep=True) == (fresnels(w), 0) + + assert fresnels(2 + 3*I).as_real_imag() == ( + fresnels(2 + 3*I)/2 + fresnels(2 - 3*I)/2, + -I*(fresnels(2 + 3*I) - fresnels(2 - 3*I))/2 + ) + + assert expand_func(integrate(fresnels(z), z)) == \ + z*fresnels(z) + cos(pi*z**2/2)/pi + + assert fresnels(z).rewrite(meijerg) == sqrt(2)*pi*z**Rational(9, 4) * \ + meijerg(((), (1,)), ((Rational(3, 4),), + (Rational(1, 4), 0)), -pi**2*z**4/16)/(2*(-z)**Rational(3, 4)*(z**2)**Rational(3, 4)) + + assert fresnelc(0) is S.Zero + assert fresnelc(oo) == S.Half + assert fresnelc(-oo) == Rational(-1, 2) + assert fresnelc(I*oo) == I*S.Half + + assert unchanged(fresnelc, z) + assert fresnelc(-z) == -fresnelc(z) + assert fresnelc(I*z) == I*fresnelc(z) + assert fresnelc(-I*z) == -I*fresnelc(z) + + assert conjugate(fresnelc(z)) == fresnelc(conjugate(z)) + + assert fresnelc(z).diff(z) == cos(pi*z**2/2) + + assert fresnelc(z).rewrite(erf) == (S.One - I)/4 * ( + erf((S.One + I)/2*sqrt(pi)*z) + I*erf((S.One - I)/2*sqrt(pi)*z)) + + assert fresnelc(z).rewrite(hyper) == \ + z * hyper([Rational(1, 4)], [S.Half, Rational(5, 4)], -pi**2*z**4/16) + + assert fresnelc(w).is_extended_real is True + + assert fresnelc(z).as_real_imag() == \ + (fresnelc(re(z) - I*im(z))/2 + fresnelc(re(z) + I*im(z))/2, + -I*(-fresnelc(re(z) - I*im(z)) + fresnelc(re(z) + I*im(z)))/2) + + assert fresnelc(z).as_real_imag(deep=False) == \ + (fresnelc(re(z) - I*im(z))/2 + fresnelc(re(z) + I*im(z))/2, + -I*(-fresnelc(re(z) - I*im(z)) + fresnelc(re(z) + I*im(z)))/2) + + assert fresnelc(2 + 3*I).as_real_imag() == ( + fresnelc(2 - 3*I)/2 + fresnelc(2 + 3*I)/2, + -I*(fresnelc(2 + 3*I) - fresnelc(2 - 3*I))/2 + ) + + assert expand_func(integrate(fresnelc(z), z)) == \ + z*fresnelc(z) - sin(pi*z**2/2)/pi + + assert fresnelc(z).rewrite(meijerg) == sqrt(2)*pi*z**Rational(3, 4) * \ + meijerg(((), (1,)), ((Rational(1, 4),), + (Rational(3, 4), 0)), -pi**2*z**4/16)/(2*(-z)**Rational(1, 4)*(z**2)**Rational(1, 4)) + + from sympy.core.random import verify_numerically + + verify_numerically(re(fresnels(z)), fresnels(z).as_real_imag()[0], z) + verify_numerically(im(fresnels(z)), fresnels(z).as_real_imag()[1], z) + verify_numerically(fresnels(z), fresnels(z).rewrite(hyper), z) + verify_numerically(fresnels(z), fresnels(z).rewrite(meijerg), z) + + verify_numerically(re(fresnelc(z)), fresnelc(z).as_real_imag()[0], z) + verify_numerically(im(fresnelc(z)), fresnelc(z).as_real_imag()[1], z) + verify_numerically(fresnelc(z), fresnelc(z).rewrite(hyper), z) + verify_numerically(fresnelc(z), fresnelc(z).rewrite(meijerg), z) + + raises(ArgumentIndexError, lambda: fresnels(z).fdiff(2)) + raises(ArgumentIndexError, lambda: fresnelc(z).fdiff(2)) + + assert fresnels(x).taylor_term(-1, x) is S.Zero + assert fresnelc(x).taylor_term(-1, x) is S.Zero + assert fresnelc(x).taylor_term(1, x) == -pi**2*x**5/40 + + +def test_fresnel_series(): + assert fresnelc(z).series(z, n=15) == \ + z - pi**2*z**5/40 + pi**4*z**9/3456 - pi**6*z**13/599040 + O(z**15) + + # issues 6510, 10102 + fs = (S.Half - sin(pi*z**2/2)/(pi**2*z**3) + + (-1/(pi*z) + 3/(pi**3*z**5))*cos(pi*z**2/2)) + fc = (S.Half - cos(pi*z**2/2)/(pi**2*z**3) + + (1/(pi*z) - 3/(pi**3*z**5))*sin(pi*z**2/2)) + assert fresnels(z).series(z, oo) == fs + O(z**(-6), (z, oo)) + assert fresnelc(z).series(z, oo) == fc + O(z**(-6), (z, oo)) + assert (fresnels(z).series(z, -oo) + fs.subs(z, -z)).expand().is_Order + assert (fresnelc(z).series(z, -oo) + fc.subs(z, -z)).expand().is_Order + assert (fresnels(1/z).series(z) - fs.subs(z, 1/z)).expand().is_Order + assert (fresnelc(1/z).series(z) - fc.subs(z, 1/z)).expand().is_Order + assert ((2*fresnels(3*z)).series(z, oo) - 2*fs.subs(z, 3*z)).expand().is_Order + assert ((3*fresnelc(2*z)).series(z, oo) - 3*fc.subs(z, 2*z)).expand().is_Order + + +def test_integral_rewrites(): #issues 26134, 26144, 26306 + assert expint(n, x).rewrite(Integral).dummy_eq(Integral(t**-n * exp(-t*x), (t, 1, oo))) + assert Si(x).rewrite(Integral).dummy_eq(Integral(sinc(t), (t, 0, x))) + assert Ci(x).rewrite(Integral).dummy_eq(log(x) - Integral((1 - cos(t))/t, (t, 0, x)) + EulerGamma) + assert fresnels(x).rewrite(Integral).dummy_eq(Integral(sin(pi*t**2/2), (t, 0, x))) + assert fresnelc(x).rewrite(Integral).dummy_eq(Integral(cos(pi*t**2/2), (t, 0, x))) + assert Ei(x).rewrite(Integral).dummy_eq(Integral(exp(t)/t, (t, -oo, x))) + assert fresnels(x).diff(x) == fresnels(x).rewrite(Integral).diff(x) + assert fresnelc(x).diff(x) == fresnelc(x).rewrite(Integral).diff(x) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_gamma_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_gamma_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..03e933e9c10f348c88fc8a93c1170216d74de128 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_gamma_functions.py @@ -0,0 +1,741 @@ +from sympy.core.function import expand_func, Subs +from sympy.core import EulerGamma +from sympy.core.numbers import (I, Rational, nan, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.combinatorial.numbers import harmonic +from sympy.functions.elementary.complexes import (Abs, conjugate, im, re) +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.hyperbolic import tanh +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin, atan) +from sympy.functions.special.error_functions import (Ei, erf, erfc) +from sympy.functions.special.gamma_functions import (digamma, gamma, loggamma, lowergamma, multigamma, polygamma, trigamma, uppergamma) +from sympy.functions.special.zeta_functions import zeta +from sympy.series.order import O + +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.testing.pytest import raises +from sympy.core.random import (test_derivative_numerically as td, + random_complex_number as randcplx, + verify_numerically as tn) + +x = Symbol('x') +y = Symbol('y') +n = Symbol('n', integer=True) +w = Symbol('w', real=True) + +def test_gamma(): + assert gamma(nan) is nan + assert gamma(oo) is oo + + assert gamma(-100) is zoo + assert gamma(0) is zoo + assert gamma(-100.0) is zoo + + assert gamma(1) == 1 + assert gamma(2) == 1 + assert gamma(3) == 2 + + assert gamma(102) == factorial(101) + + assert gamma(S.Half) == sqrt(pi) + + assert gamma(Rational(3, 2)) == sqrt(pi)*S.Half + assert gamma(Rational(5, 2)) == sqrt(pi)*Rational(3, 4) + assert gamma(Rational(7, 2)) == sqrt(pi)*Rational(15, 8) + + assert gamma(Rational(-1, 2)) == -2*sqrt(pi) + assert gamma(Rational(-3, 2)) == sqrt(pi)*Rational(4, 3) + assert gamma(Rational(-5, 2)) == sqrt(pi)*Rational(-8, 15) + + assert gamma(Rational(-15, 2)) == sqrt(pi)*Rational(256, 2027025) + + assert gamma(Rational( + -11, 8)).expand(func=True) == Rational(64, 33)*gamma(Rational(5, 8)) + assert gamma(Rational( + -10, 3)).expand(func=True) == Rational(81, 280)*gamma(Rational(2, 3)) + assert gamma(Rational( + 14, 3)).expand(func=True) == Rational(880, 81)*gamma(Rational(2, 3)) + assert gamma(Rational( + 17, 7)).expand(func=True) == Rational(30, 49)*gamma(Rational(3, 7)) + assert gamma(Rational( + 19, 8)).expand(func=True) == Rational(33, 64)*gamma(Rational(3, 8)) + + assert gamma(x).diff(x) == gamma(x)*polygamma(0, x) + + assert gamma(x - 1).expand(func=True) == gamma(x)/(x - 1) + assert gamma(x + 2).expand(func=True, mul=False) == x*(x + 1)*gamma(x) + + assert conjugate(gamma(x)) == gamma(conjugate(x)) + + assert expand_func(gamma(x + Rational(3, 2))) == \ + (x + S.Half)*gamma(x + S.Half) + + assert expand_func(gamma(x - S.Half)) == \ + gamma(S.Half + x)/(x - S.Half) + + # Test a bug: + assert expand_func(gamma(x + Rational(3, 4))) == gamma(x + Rational(3, 4)) + + # XXX: Not sure about these tests. I can fix them by defining e.g. + # exp_polar.is_integer but I'm not sure if that makes sense. + assert gamma(3*exp_polar(I*pi)/4).is_nonnegative is False + assert gamma(3*exp_polar(I*pi)/4).is_extended_nonpositive is True + + y = Symbol('y', nonpositive=True, integer=True) + assert gamma(y).is_real == False + y = Symbol('y', positive=True, noninteger=True) + assert gamma(y).is_real == True + + assert gamma(-1.0, evaluate=False).is_real == False + assert gamma(0, evaluate=False).is_real == False + assert gamma(-2, evaluate=False).is_real == False + + +def test_gamma_rewrite(): + assert gamma(n).rewrite(factorial) == factorial(n - 1) + + +def test_gamma_series(): + assert gamma(x + 1).series(x, 0, 3) == \ + 1 - EulerGamma*x + x**2*(EulerGamma**2/2 + pi**2/12) + O(x**3) + assert gamma(x).series(x, -1, 3) == \ + -1/(x + 1) + EulerGamma - 1 + (x + 1)*(-1 - pi**2/12 - EulerGamma**2/2 + \ + EulerGamma) + (x + 1)**2*(-1 - pi**2/12 - EulerGamma**2/2 + EulerGamma**3/6 - \ + polygamma(2, 1)/6 + EulerGamma*pi**2/12 + EulerGamma) + O((x + 1)**3, (x, -1)) + + +def tn_branch(s, func): + from sympy.core.random import uniform + c = uniform(1, 5) + expr = func(s, c*exp_polar(I*pi)) - func(s, c*exp_polar(-I*pi)) + eps = 1e-15 + expr2 = func(s + eps, -c + eps*I) - func(s + eps, -c - eps*I) + return abs(expr.n() - expr2.n()).n() < 1e-10 + + +def test_lowergamma(): + from sympy.functions.special.error_functions import expint + from sympy.functions.special.hyper import meijerg + assert lowergamma(x, 0) == 0 + assert lowergamma(x, y).diff(y) == y**(x - 1)*exp(-y) + assert td(lowergamma(randcplx(), y), y) + assert td(lowergamma(x, randcplx()), x) + assert lowergamma(x, y).diff(x) == \ + gamma(x)*digamma(x) - uppergamma(x, y)*log(y) \ + - meijerg([], [1, 1], [0, 0, x], [], y) + + assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x)) + assert not lowergamma(S.Half - 3, x).has(lowergamma) + assert not lowergamma(S.Half + 3, x).has(lowergamma) + assert lowergamma(S.Half, x, evaluate=False).has(lowergamma) + assert tn(lowergamma(S.Half + 3, x, evaluate=False), + lowergamma(S.Half + 3, x), x) + assert tn(lowergamma(S.Half - 3, x, evaluate=False), + lowergamma(S.Half - 3, x), x) + + assert tn_branch(-3, lowergamma) + assert tn_branch(-4, lowergamma) + assert tn_branch(Rational(1, 3), lowergamma) + assert tn_branch(pi, lowergamma) + assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x) + assert lowergamma(y, exp_polar(5*pi*I)*x) == \ + exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I)) + assert lowergamma(-2, exp_polar(5*pi*I)*x) == \ + lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I + + assert conjugate(lowergamma(x, y)) == lowergamma(conjugate(x), conjugate(y)) + assert conjugate(lowergamma(x, 0)) == 0 + assert unchanged(conjugate, lowergamma(x, -oo)) + + assert lowergamma(0, x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(S(1)/3, x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(1, x, evaluate=False)._eval_is_meromorphic(x, 0) == True + assert lowergamma(x, x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(x + 1, x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(1/x, x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(0, x + 1)._eval_is_meromorphic(x, 0) == False + assert lowergamma(S(1)/3, x + 1)._eval_is_meromorphic(x, 0) == True + assert lowergamma(1, x + 1, evaluate=False)._eval_is_meromorphic(x, 0) == True + assert lowergamma(x, x + 1)._eval_is_meromorphic(x, 0) == True + assert lowergamma(x + 1, x + 1)._eval_is_meromorphic(x, 0) == True + assert lowergamma(1/x, x + 1)._eval_is_meromorphic(x, 0) == False + assert lowergamma(0, 1/x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(S(1)/3, 1/x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(1, 1/x, evaluate=False)._eval_is_meromorphic(x, 0) == False + assert lowergamma(x, 1/x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(x + 1, 1/x)._eval_is_meromorphic(x, 0) == False + assert lowergamma(1/x, 1/x)._eval_is_meromorphic(x, 0) == False + + assert lowergamma(x, 2).series(x, oo, 3) == \ + 2**x*(1 + 2/(x + 1))*exp(-2)/x + O(exp(x*log(2))/x**3, (x, oo)) + + assert lowergamma( + x, y).rewrite(expint) == -y**x*expint(-x + 1, y) + gamma(x) + k = Symbol('k', integer=True) + assert lowergamma( + k, y).rewrite(expint) == -y**k*expint(-k + 1, y) + gamma(k) + k = Symbol('k', integer=True, positive=False) + assert lowergamma(k, y).rewrite(expint) == lowergamma(k, y) + assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y) + + assert lowergamma(70, 6) == factorial(69) - 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320 * exp(-6) + assert (lowergamma(S(77) / 2, 6) - lowergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16 + assert (lowergamma(-S(77) / 2, 6) - lowergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16 + + +def test_uppergamma(): + from sympy.functions.special.error_functions import expint + from sympy.functions.special.hyper import meijerg + assert uppergamma(4, 0) == 6 + assert uppergamma(x, y).diff(y) == -y**(x - 1)*exp(-y) + assert td(uppergamma(randcplx(), y), y) + assert uppergamma(x, y).diff(x) == \ + uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y) + assert td(uppergamma(x, randcplx()), x) + + p = Symbol('p', positive=True) + assert uppergamma(0, p) == -Ei(-p) + assert uppergamma(p, 0) == gamma(p) + assert uppergamma(S.Half, x) == sqrt(pi)*erfc(sqrt(x)) + assert not uppergamma(S.Half - 3, x).has(uppergamma) + assert not uppergamma(S.Half + 3, x).has(uppergamma) + assert uppergamma(S.Half, x, evaluate=False).has(uppergamma) + assert tn(uppergamma(S.Half + 3, x, evaluate=False), + uppergamma(S.Half + 3, x), x) + assert tn(uppergamma(S.Half - 3, x, evaluate=False), + uppergamma(S.Half - 3, x), x) + + assert unchanged(uppergamma, x, -oo) + assert unchanged(uppergamma, x, 0) + + assert tn_branch(-3, uppergamma) + assert tn_branch(-4, uppergamma) + assert tn_branch(Rational(1, 3), uppergamma) + assert tn_branch(pi, uppergamma) + assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x) + assert uppergamma(y, exp_polar(5*pi*I)*x) == \ + exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + \ + gamma(y)*(1 - exp(4*pi*I*y)) + assert uppergamma(-2, exp_polar(5*pi*I)*x) == \ + uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I + + assert uppergamma(-2, x) == expint(3, x)/x**2 + + assert conjugate(uppergamma(x, y)) == uppergamma(conjugate(x), conjugate(y)) + assert unchanged(conjugate, uppergamma(x, -oo)) + + assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y) + assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y) + + assert uppergamma(70, 6) == 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320*exp(-6) + assert (uppergamma(S(77) / 2, 6) - uppergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16 + assert (uppergamma(-S(77) / 2, 6) - uppergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16 + + +def test_polygamma(): + assert polygamma(n, nan) is nan + + assert polygamma(0, oo) is oo + assert polygamma(0, -oo) is oo + assert polygamma(0, I*oo) is oo + assert polygamma(0, -I*oo) is oo + assert polygamma(1, oo) == 0 + assert polygamma(5, oo) == 0 + + assert polygamma(0, -9) is zoo + + assert polygamma(0, -9) is zoo + assert polygamma(0, -1) is zoo + assert polygamma(Rational(3, 2), -1) is zoo + + assert polygamma(0, 0) is zoo + + assert polygamma(0, 1) == -EulerGamma + assert polygamma(0, 7) == Rational(49, 20) - EulerGamma + + assert polygamma(1, 1) == pi**2/6 + assert polygamma(1, 2) == pi**2/6 - 1 + assert polygamma(1, 3) == pi**2/6 - Rational(5, 4) + assert polygamma(3, 1) == pi**4 / 15 + assert polygamma(3, 5) == 6*(Rational(-22369, 20736) + pi**4/90) + assert polygamma(5, 1) == 8 * pi**6 / 63 + + assert polygamma(1, S.Half) == pi**2 / 2 + assert polygamma(2, S.Half) == -14*zeta(3) + assert polygamma(11, S.Half) == 176896*pi**12 + + def t(m, n): + x = S(m)/n + r = polygamma(0, x) + if r.has(polygamma): + return False + return abs(polygamma(0, x.n()).n() - r.n()).n() < 1e-10 + assert t(1, 2) + assert t(3, 2) + assert t(-1, 2) + assert t(1, 4) + assert t(-3, 4) + assert t(1, 3) + assert t(4, 3) + assert t(3, 4) + assert t(2, 3) + assert t(123, 5) + + assert polygamma(0, x).rewrite(zeta) == polygamma(0, x) + assert polygamma(1, x).rewrite(zeta) == zeta(2, x) + assert polygamma(2, x).rewrite(zeta) == -2*zeta(3, x) + assert polygamma(I, 2).rewrite(zeta) == polygamma(I, 2) + n1 = Symbol('n1') + n2 = Symbol('n2', real=True) + n3 = Symbol('n3', integer=True) + n4 = Symbol('n4', positive=True) + n5 = Symbol('n5', positive=True, integer=True) + assert polygamma(n1, x).rewrite(zeta) == polygamma(n1, x) + assert polygamma(n2, x).rewrite(zeta) == polygamma(n2, x) + assert polygamma(n3, x).rewrite(zeta) == polygamma(n3, x) + assert polygamma(n4, x).rewrite(zeta) == polygamma(n4, x) + assert polygamma(n5, x).rewrite(zeta) == (-1)**(n5 + 1) * factorial(n5) * zeta(n5 + 1, x) + + assert polygamma(3, 7*x).diff(x) == 7*polygamma(4, 7*x) + + assert polygamma(0, x).rewrite(harmonic) == harmonic(x - 1) - EulerGamma + assert polygamma(2, x).rewrite(harmonic) == 2*harmonic(x - 1, 3) - 2*zeta(3) + ni = Symbol("n", integer=True) + assert polygamma(ni, x).rewrite(harmonic) == (-1)**(ni + 1)*(-harmonic(x - 1, ni + 1) + + zeta(ni + 1))*factorial(ni) + + # Polygamma of non-negative integer order is unbranched: + k = Symbol('n', integer=True, nonnegative=True) + assert polygamma(k, exp_polar(2*I*pi)*x) == polygamma(k, x) + + # but negative integers are branched! + k = Symbol('n', integer=True) + assert polygamma(k, exp_polar(2*I*pi)*x).args == (k, exp_polar(2*I*pi)*x) + + # Polygamma of order -1 is loggamma: + assert polygamma(-1, x) == loggamma(x) - log(2*pi) / 2 + + # But smaller orders are iterated integrals and don't have a special name + assert polygamma(-2, x).func is polygamma + + # Test a bug + assert polygamma(0, -x).expand(func=True) == polygamma(0, -x) + + assert polygamma(2, 2.5).is_positive == False + assert polygamma(2, -2.5).is_positive == False + assert polygamma(3, 2.5).is_positive == True + assert polygamma(3, -2.5).is_positive is True + assert polygamma(-2, -2.5).is_positive is None + assert polygamma(-3, -2.5).is_positive is None + + assert polygamma(2, 2.5).is_negative == True + assert polygamma(3, 2.5).is_negative == False + assert polygamma(3, -2.5).is_negative == False + assert polygamma(2, -2.5).is_negative is True + assert polygamma(-2, -2.5).is_negative is None + assert polygamma(-3, -2.5).is_negative is None + + assert polygamma(I, 2).is_positive is None + assert polygamma(I, 3).is_negative is None + + # issue 17350 + assert (I*polygamma(I, pi)).as_real_imag() == \ + (-im(polygamma(I, pi)), re(polygamma(I, pi))) + assert (tanh(polygamma(I, 1))).rewrite(exp) == \ + (exp(polygamma(I, 1)) - exp(-polygamma(I, 1)))/(exp(polygamma(I, 1)) + exp(-polygamma(I, 1))) + assert (I / polygamma(I, 4)).rewrite(exp) == \ + I*exp(-I*atan(im(polygamma(I, 4))/re(polygamma(I, 4))))/Abs(polygamma(I, 4)) + + # issue 12569 + assert unchanged(im, polygamma(0, I)) + assert polygamma(Symbol('a', positive=True), Symbol('b', positive=True)).is_real is True + assert polygamma(0, I).is_real is None + + assert str(polygamma(pi, 3).evalf(n=10)) == "0.1169314564" + assert str(polygamma(2.3, 1.0).evalf(n=10)) == "-3.003302909" + assert str(polygamma(-1, 1).evalf(n=10)) == "-0.9189385332" # not zero + assert str(polygamma(I, 1).evalf(n=10)) == "-3.109856569 + 1.89089016*I" + assert str(polygamma(1, I).evalf(n=10)) == "-0.5369999034 - 0.7942335428*I" + assert str(polygamma(I, I).evalf(n=10)) == "6.332362889 + 45.92828268*I" + + +def test_polygamma_expand_func(): + assert polygamma(0, x).expand(func=True) == polygamma(0, x) + assert polygamma(0, 2*x).expand(func=True) == \ + polygamma(0, x)/2 + polygamma(0, S.Half + x)/2 + log(2) + assert polygamma(1, 2*x).expand(func=True) == \ + polygamma(1, x)/4 + polygamma(1, S.Half + x)/4 + assert polygamma(2, x).expand(func=True) == \ + polygamma(2, x) + assert polygamma(0, -1 + x).expand(func=True) == \ + polygamma(0, x) - 1/(x - 1) + assert polygamma(0, 1 + x).expand(func=True) == \ + 1/x + polygamma(0, x ) + assert polygamma(0, 2 + x).expand(func=True) == \ + 1/x + 1/(1 + x) + polygamma(0, x) + assert polygamma(0, 3 + x).expand(func=True) == \ + polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + assert polygamma(0, 4 + x).expand(func=True) == \ + polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + 1/(3 + x) + assert polygamma(1, 1 + x).expand(func=True) == \ + polygamma(1, x) - 1/x**2 + assert polygamma(1, 2 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 + assert polygamma(1, 3 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - 1/(2 + x)**2 + assert polygamma(1, 4 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - \ + 1/(2 + x)**2 - 1/(3 + x)**2 + assert polygamma(0, x + y).expand(func=True) == \ + polygamma(0, x + y) + assert polygamma(1, x + y).expand(func=True) == \ + polygamma(1, x + y) + assert polygamma(1, 3 + 4*x + y).expand(func=True, multinomial=False) == \ + polygamma(1, y + 4*x) - 1/(y + 4*x)**2 - \ + 1/(1 + y + 4*x)**2 - 1/(2 + y + 4*x)**2 + assert polygamma(3, 3 + 4*x + y).expand(func=True, multinomial=False) == \ + polygamma(3, y + 4*x) - 6/(y + 4*x)**4 - \ + 6/(1 + y + 4*x)**4 - 6/(2 + y + 4*x)**4 + assert polygamma(3, 4*x + y + 1).expand(func=True, multinomial=False) == \ + polygamma(3, y + 4*x) - 6/(y + 4*x)**4 + e = polygamma(3, 4*x + y + Rational(3, 2)) + assert e.expand(func=True) == e + e = polygamma(3, x + y + Rational(3, 4)) + assert e.expand(func=True, basic=False) == e + + assert polygamma(-1, x, evaluate=False).expand(func=True) == \ + loggamma(x) - log(pi)/2 - log(2)/2 + p2 = polygamma(-2, x).expand(func=True) + x**2/2 - x/2 + S(1)/12 + assert isinstance(p2, Subs) + assert p2.point == (-1,) + + +def test_digamma(): + assert digamma(nan) == nan + + assert digamma(oo) == oo + assert digamma(-oo) == oo + assert digamma(I*oo) == oo + assert digamma(-I*oo) == oo + + assert digamma(-9) == zoo + + assert digamma(-9) == zoo + assert digamma(-1) == zoo + + assert digamma(0) == zoo + + assert digamma(1) == -EulerGamma + assert digamma(7) == Rational(49, 20) - EulerGamma + + def t(m, n): + x = S(m)/n + r = digamma(x) + if r.has(digamma): + return False + return abs(digamma(x.n()).n() - r.n()).n() < 1e-10 + assert t(1, 2) + assert t(3, 2) + assert t(-1, 2) + assert t(1, 4) + assert t(-3, 4) + assert t(1, 3) + assert t(4, 3) + assert t(3, 4) + assert t(2, 3) + assert t(123, 5) + + assert digamma(x).rewrite(zeta) == polygamma(0, x) + + assert digamma(x).rewrite(harmonic) == harmonic(x - 1) - EulerGamma + + assert digamma(I).is_real is None + + assert digamma(x,evaluate=False).fdiff() == polygamma(1, x) + + assert digamma(x,evaluate=False).is_real is None + + assert digamma(x,evaluate=False).is_positive is None + + assert digamma(x,evaluate=False).is_negative is None + + assert digamma(x,evaluate=False).rewrite(polygamma) == polygamma(0, x) + + +def test_digamma_expand_func(): + assert digamma(x).expand(func=True) == polygamma(0, x) + assert digamma(2*x).expand(func=True) == \ + polygamma(0, x)/2 + polygamma(0, Rational(1, 2) + x)/2 + log(2) + assert digamma(-1 + x).expand(func=True) == \ + polygamma(0, x) - 1/(x - 1) + assert digamma(1 + x).expand(func=True) == \ + 1/x + polygamma(0, x ) + assert digamma(2 + x).expand(func=True) == \ + 1/x + 1/(1 + x) + polygamma(0, x) + assert digamma(3 + x).expand(func=True) == \ + polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + assert digamma(4 + x).expand(func=True) == \ + polygamma(0, x) + 1/x + 1/(1 + x) + 1/(2 + x) + 1/(3 + x) + assert digamma(x + y).expand(func=True) == \ + polygamma(0, x + y) + +def test_trigamma(): + assert trigamma(nan) == nan + + assert trigamma(oo) == 0 + + assert trigamma(1) == pi**2/6 + assert trigamma(2) == pi**2/6 - 1 + assert trigamma(3) == pi**2/6 - Rational(5, 4) + + assert trigamma(x, evaluate=False).rewrite(zeta) == zeta(2, x) + assert trigamma(x, evaluate=False).rewrite(harmonic) == \ + trigamma(x).rewrite(polygamma).rewrite(harmonic) + + assert trigamma(x,evaluate=False).fdiff() == polygamma(2, x) + + assert trigamma(x,evaluate=False).is_real is None + + assert trigamma(x,evaluate=False).is_positive is None + + assert trigamma(x,evaluate=False).is_negative is None + + assert trigamma(x,evaluate=False).rewrite(polygamma) == polygamma(1, x) + +def test_trigamma_expand_func(): + assert trigamma(2*x).expand(func=True) == \ + polygamma(1, x)/4 + polygamma(1, Rational(1, 2) + x)/4 + assert trigamma(1 + x).expand(func=True) == \ + polygamma(1, x) - 1/x**2 + assert trigamma(2 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 + assert trigamma(3 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - 1/(2 + x)**2 + assert trigamma(4 + x).expand(func=True, multinomial=False) == \ + polygamma(1, x) - 1/x**2 - 1/(1 + x)**2 - \ + 1/(2 + x)**2 - 1/(3 + x)**2 + assert trigamma(x + y).expand(func=True) == \ + polygamma(1, x + y) + assert trigamma(3 + 4*x + y).expand(func=True, multinomial=False) == \ + polygamma(1, y + 4*x) - 1/(y + 4*x)**2 - \ + 1/(1 + y + 4*x)**2 - 1/(2 + y + 4*x)**2 + +def test_loggamma(): + raises(TypeError, lambda: loggamma(2, 3)) + raises(ArgumentIndexError, lambda: loggamma(x).fdiff(2)) + + assert loggamma(-1) is oo + assert loggamma(-2) is oo + assert loggamma(0) is oo + assert loggamma(1) == 0 + assert loggamma(2) == 0 + assert loggamma(3) == log(2) + assert loggamma(4) == log(6) + + n = Symbol("n", integer=True, positive=True) + assert loggamma(n) == log(gamma(n)) + assert loggamma(-n) is oo + assert loggamma(n/2) == log(2**(-n + 1)*sqrt(pi)*gamma(n)/gamma(n/2 + S.Half)) + + assert loggamma(oo) is oo + assert loggamma(-oo) is zoo + assert loggamma(I*oo) is zoo + assert loggamma(-I*oo) is zoo + assert loggamma(zoo) is zoo + assert loggamma(nan) is nan + + L = loggamma(Rational(16, 3)) + E = -5*log(3) + loggamma(Rational(1, 3)) + log(4) + log(7) + log(10) + log(13) + assert expand_func(L).doit() == E + assert L.n() == E.n() + + L = loggamma(Rational(19, 4)) + E = -4*log(4) + loggamma(Rational(3, 4)) + log(3) + log(7) + log(11) + log(15) + assert expand_func(L).doit() == E + assert L.n() == E.n() + + L = loggamma(Rational(23, 7)) + E = -3*log(7) + log(2) + loggamma(Rational(2, 7)) + log(9) + log(16) + assert expand_func(L).doit() == E + assert L.n() == E.n() + + L = loggamma(Rational(19, 4) - 7) + E = -log(9) - log(5) + loggamma(Rational(3, 4)) + 3*log(4) - 3*I*pi + assert expand_func(L).doit() == E + assert L.n() == E.n() + + L = loggamma(Rational(23, 7) - 6) + E = -log(19) - log(12) - log(5) + loggamma(Rational(2, 7)) + 3*log(7) - 3*I*pi + assert expand_func(L).doit() == E + assert L.n() == E.n() + + assert loggamma(x).diff(x) == polygamma(0, x) + s1 = loggamma(1/(x + sin(x)) + cos(x)).nseries(x, n=4) + s2 = (-log(2*x) - 1)/(2*x) - log(x/pi)/2 + (4 - log(2*x))*x/24 + O(x**2) + \ + log(x)*x**2/2 + assert (s1 - s2).expand(force=True).removeO() == 0 + s1 = loggamma(1/x).series(x) + s2 = (1/x - S.Half)*log(1/x) - 1/x + log(2*pi)/2 + \ + x/12 - x**3/360 + x**5/1260 + O(x**7) + assert ((s1 - s2).expand(force=True)).removeO() == 0 + + assert loggamma(x).rewrite('intractable') == log(gamma(x)) + + s1 = loggamma(x).series(x).cancel() + assert s1 == -log(x) - EulerGamma*x + pi**2*x**2/12 + x**3*polygamma(2, 1)/6 + \ + pi**4*x**4/360 + x**5*polygamma(4, 1)/120 + O(x**6) + assert s1 == loggamma(x).rewrite('intractable').series(x).cancel() + + assert conjugate(loggamma(x)) == loggamma(conjugate(x)) + assert conjugate(loggamma(0)) is oo + assert conjugate(loggamma(1)) == loggamma(conjugate(1)) + assert conjugate(loggamma(-oo)) == conjugate(zoo) + + assert loggamma(Symbol('v', positive=True)).is_real is True + assert loggamma(Symbol('v', zero=True)).is_real is False + assert loggamma(Symbol('v', negative=True)).is_real is False + assert loggamma(Symbol('v', nonpositive=True)).is_real is False + assert loggamma(Symbol('v', nonnegative=True)).is_real is None + assert loggamma(Symbol('v', imaginary=True)).is_real is None + assert loggamma(Symbol('v', real=True)).is_real is None + assert loggamma(Symbol('v')).is_real is None + + assert loggamma(S.Half).is_real is True + assert loggamma(0).is_real is False + assert loggamma(Rational(-1, 2)).is_real is False + assert loggamma(I).is_real is None + assert loggamma(2 + 3*I).is_real is None + + def tN(N, M): + assert loggamma(1/x)._eval_nseries(x, n=N).getn() == M + tN(0, 0) + tN(1, 1) + tN(2, 2) + tN(3, 3) + tN(4, 4) + tN(5, 5) + + +def test_polygamma_expansion(): + # A. & S., pa. 259 and 260 + assert polygamma(0, 1/x).nseries(x, n=3) == \ + -log(x) - x/2 - x**2/12 + O(x**3) + assert polygamma(1, 1/x).series(x, n=5) == \ + x + x**2/2 + x**3/6 + O(x**5) + assert polygamma(3, 1/x).nseries(x, n=11) == \ + 2*x**3 + 3*x**4 + 2*x**5 - x**7 + 4*x**9/3 + O(x**11) + + +def test_polygamma_leading_term(): + expr = -log(1/x) + polygamma(0, 1 + 1/x) + S.EulerGamma + assert expr.as_leading_term(x, logx=-y) == S.EulerGamma + + +def test_issue_8657(): + n = Symbol('n', negative=True, integer=True) + m = Symbol('m', integer=True) + o = Symbol('o', positive=True) + p = Symbol('p', negative=True, integer=False) + assert gamma(n).is_real is False + assert gamma(m).is_real is None + assert gamma(o).is_real is True + assert gamma(p).is_real is True + assert gamma(w).is_real is None + + +def test_issue_8524(): + x = Symbol('x', positive=True) + y = Symbol('y', negative=True) + z = Symbol('z', positive=False) + p = Symbol('p', negative=False) + q = Symbol('q', integer=True) + r = Symbol('r', integer=False) + e = Symbol('e', even=True, negative=True) + assert gamma(x).is_positive is True + assert gamma(y).is_positive is None + assert gamma(z).is_positive is None + assert gamma(p).is_positive is None + assert gamma(q).is_positive is None + assert gamma(r).is_positive is None + assert gamma(e + S.Half).is_positive is True + assert gamma(e - S.Half).is_positive is False + +def test_issue_14450(): + assert uppergamma(Rational(3, 8), x).evalf() == uppergamma(Rational(3, 8), x) + assert lowergamma(x, Rational(3, 8)).evalf() == lowergamma(x, Rational(3, 8)) + # some values from Wolfram Alpha for comparison + assert abs(uppergamma(Rational(3, 8), 2).evalf() - 0.07105675881) < 1e-9 + assert abs(lowergamma(Rational(3, 8), 2).evalf() - 2.2993794256) < 1e-9 + +def test_issue_14528(): + k = Symbol('k', integer=True, nonpositive=True) + assert isinstance(gamma(k), gamma) + +def test_multigamma(): + from sympy.concrete.products import Product + p = Symbol('p') + _k = Dummy('_k') + + assert multigamma(x, p).dummy_eq(pi**(p*(p - 1)/4)*\ + Product(gamma(x + (1 - _k)/2), (_k, 1, p))) + + assert conjugate(multigamma(x, p)).dummy_eq(pi**((conjugate(p) - 1)*\ + conjugate(p)/4)*Product(gamma(conjugate(x) + (1-conjugate(_k))/2), (_k, 1, p))) + assert conjugate(multigamma(x, 1)) == gamma(conjugate(x)) + + p = Symbol('p', positive=True) + assert conjugate(multigamma(x, p)).dummy_eq(pi**((p - 1)*p/4)*\ + Product(gamma(conjugate(x) + (1-conjugate(_k))/2), (_k, 1, p))) + + assert multigamma(nan, 1) is nan + assert multigamma(oo, 1).doit() is oo + + assert multigamma(1, 1) == 1 + assert multigamma(2, 1) == 1 + assert multigamma(3, 1) == 2 + + assert multigamma(102, 1) == factorial(101) + assert multigamma(S.Half, 1) == sqrt(pi) + + assert multigamma(1, 2) == pi + assert multigamma(2, 2) == pi/2 + + assert multigamma(1, 3) is zoo + assert multigamma(2, 3) == pi**2/2 + assert multigamma(3, 3) == 3*pi**2/2 + + assert multigamma(x, 1).diff(x) == gamma(x)*polygamma(0, x) + assert multigamma(x, 2).diff(x) == sqrt(pi)*gamma(x)*gamma(x - S.Half)*\ + polygamma(0, x) + sqrt(pi)*gamma(x)*gamma(x - S.Half)*polygamma(0, x - S.Half) + + assert multigamma(x - 1, 1).expand(func=True) == gamma(x)/(x - 1) + assert multigamma(x + 2, 1).expand(func=True, mul=False) == x*(x + 1)*\ + gamma(x) + assert multigamma(x - 1, 2).expand(func=True) == sqrt(pi)*gamma(x)*\ + gamma(x + S.Half)/(x**3 - 3*x**2 + x*Rational(11, 4) - Rational(3, 4)) + assert multigamma(x - 1, 3).expand(func=True) == pi**Rational(3, 2)*gamma(x)**2*\ + gamma(x + S.Half)/(x**5 - 6*x**4 + 55*x**3/4 - 15*x**2 + x*Rational(31, 4) - Rational(3, 2)) + + assert multigamma(n, 1).rewrite(factorial) == factorial(n - 1) + assert multigamma(n, 2).rewrite(factorial) == sqrt(pi)*\ + factorial(n - Rational(3, 2))*factorial(n - 1) + assert multigamma(n, 3).rewrite(factorial) == pi**Rational(3, 2)*\ + factorial(n - 2)*factorial(n - Rational(3, 2))*factorial(n - 1) + + assert multigamma(Rational(-1, 2), 3, evaluate=False).is_real == False + assert multigamma(S.Half, 3, evaluate=False).is_real == False + assert multigamma(0, 1, evaluate=False).is_real == False + assert multigamma(1, 3, evaluate=False).is_real == False + assert multigamma(-1.0, 3, evaluate=False).is_real == False + assert multigamma(0.7, 3, evaluate=False).is_real == True + assert multigamma(3, 3, evaluate=False).is_real == True + +def test_gamma_as_leading_term(): + assert gamma(x).as_leading_term(x) == 1/x + assert gamma(2 + x).as_leading_term(x) == S(1) + assert gamma(cos(x)).as_leading_term(x) == S(1) + assert gamma(sin(x)).as_leading_term(x) == 1/x diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_hyper.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_hyper.py new file mode 100644 index 0000000000000000000000000000000000000000..f1be5b5f0db158ff76173e180ed8d88bd59461b9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_hyper.py @@ -0,0 +1,403 @@ +from sympy.core.containers import Tuple +from sympy.core.function import Derivative +from sympy.core.numbers import (I, Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import cos +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import (appellf1, hyper, meijerg) +from sympy.series.order import O +from sympy.abc import x, z, k +from sympy.series.limits import limit +from sympy.testing.pytest import raises, slow +from sympy.core.random import ( + random_complex_number as randcplx, + verify_numerically as tn, + test_derivative_numerically as td) + + +def test_TupleParametersBase(): + # test that our implementation of the chain rule works + p = hyper((), (), z**2) + assert p.diff(z) == p*2*z + + +def test_hyper(): + raises(TypeError, lambda: hyper(1, 2, z)) + + assert hyper((2, 1), (1,), z) == hyper(Tuple(1, 2), Tuple(1), z) + assert hyper((2, 1, 2), (1, 2, 1, 3), z) == hyper((2,), (1, 3), z) + u = hyper((2, 1, 2), (1, 2, 1, 3), z, evaluate=False) + assert u.ap == Tuple(1, 2, 2) + assert u.bq == Tuple(1, 1, 2, 3) + + h = hyper((1, 2), (3, 4, 5), z) + assert h.ap == Tuple(1, 2) + assert h.bq == Tuple(3, 4, 5) + assert h.argument == z + assert h.is_commutative is True + h = hyper((2, 1), (4, 3, 5), z) + assert h.ap == Tuple(1, 2) + assert h.bq == Tuple(3, 4, 5) + assert h.argument == z + assert h.is_commutative is True + + # just a few checks to make sure that all arguments go where they should + assert tn(hyper(Tuple(), Tuple(), z), exp(z), z) + assert tn(z*hyper((1, 1), Tuple(2), -z), log(1 + z), z) + + # differentiation + h = hyper( + (randcplx(), randcplx(), randcplx()), (randcplx(), randcplx()), z) + assert td(h, z) + + a1, a2, b1, b2, b3 = symbols('a1:3, b1:4') + assert hyper((a1, a2), (b1, b2, b3), z).diff(z) == \ + a1*a2/(b1*b2*b3) * hyper((a1 + 1, a2 + 1), (b1 + 1, b2 + 1, b3 + 1), z) + + # differentiation wrt parameters is not supported + assert hyper([z], [], z).diff(z) == Derivative(hyper([z], [], z), z) + + # hyper is unbranched wrt parameters + from sympy.functions.elementary.complexes import polar_lift + assert hyper([polar_lift(z)], [polar_lift(k)], polar_lift(x)) == \ + hyper([z], [k], polar_lift(x)) + + # hyper does not automatically evaluate anyway, but the test is to make + # sure that the evaluate keyword is accepted + assert hyper((1, 2), (1,), z, evaluate=False).func is hyper + + +def test_expand_func(): + # evaluation at 1 of Gauss' hypergeometric function: + from sympy.abc import a, b, c + from sympy.core.function import expand_func + a1, b1, c1 = randcplx(), randcplx(), randcplx() + 5 + assert expand_func(hyper([a, b], [c], 1)) == \ + gamma(c)*gamma(-a - b + c)/(gamma(-a + c)*gamma(-b + c)) + assert abs(expand_func(hyper([a1, b1], [c1], 1)).n() + - hyper([a1, b1], [c1], 1).n()) < 1e-10 + + # hyperexpand wrapper for hyper: + assert expand_func(hyper([], [], z)) == exp(z) + assert expand_func(hyper([1, 2, 3], [], z)) == hyper([1, 2, 3], [], z) + assert expand_func(meijerg([[1, 1], []], [[1], [0]], z)) == log(z + 1) + assert expand_func(meijerg([[1, 1], []], [[], []], z)) == \ + meijerg([[1, 1], []], [[], []], z) + + +def replace_dummy(expr, sym): + from sympy.core.symbol import Dummy + dum = expr.atoms(Dummy) + if not dum: + return expr + assert len(dum) == 1 + return expr.xreplace({dum.pop(): sym}) + + +def test_hyper_rewrite_sum(): + from sympy.concrete.summations import Sum + from sympy.core.symbol import Dummy + from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial) + _k = Dummy("k") + assert replace_dummy(hyper((1, 2), (1, 3), x).rewrite(Sum), _k) == \ + Sum(x**_k / factorial(_k) * RisingFactorial(2, _k) / + RisingFactorial(3, _k), (_k, 0, oo)) + + assert hyper((1, 2, 3), (-1, 3), z).rewrite(Sum) == \ + hyper((1, 2, 3), (-1, 3), z) + + +def test_radius_of_convergence(): + assert hyper((1, 2), [3], z).radius_of_convergence == 1 + assert hyper((1, 2), [3, 4], z).radius_of_convergence is oo + assert hyper((1, 2, 3), [4], z).radius_of_convergence == 0 + assert hyper((0, 1, 2), [4], z).radius_of_convergence is oo + assert hyper((-1, 1, 2), [-4], z).radius_of_convergence == 0 + assert hyper((-1, -2, 2), [-1], z).radius_of_convergence is oo + assert hyper((-1, 2), [-1, -2], z).radius_of_convergence == 0 + assert hyper([-1, 1, 3], [-2, 2], z).radius_of_convergence == 1 + assert hyper([-1, 1], [-2, 2], z).radius_of_convergence is oo + assert hyper([-1, 1, 3], [-2], z).radius_of_convergence == 0 + assert hyper((-1, 2, 3, 4), [], z).radius_of_convergence is oo + + assert hyper([1, 1], [3], 1).convergence_statement == True + assert hyper([1, 1], [2], 1).convergence_statement == False + assert hyper([1, 1], [2], -1).convergence_statement == True + assert hyper([1, 1], [1], -1).convergence_statement == False + + +def test_meijer(): + raises(TypeError, lambda: meijerg(1, z)) + raises(TypeError, lambda: meijerg(((1,), (2,)), (3,), (4,), z)) + + assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == \ + meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z) + + g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z) + assert g.an == Tuple(1, 2) + assert g.ap == Tuple(1, 2, 3, 4, 5) + assert g.aother == Tuple(3, 4, 5) + assert g.bm == Tuple(6, 7, 8, 9) + assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14) + assert g.bother == Tuple(10, 11, 12, 13, 14) + assert g.argument == z + assert g.nu == 75 + assert g.delta == -1 + assert g.is_commutative is True + assert g.is_number is False + #issue 13071 + assert meijerg([[],[]], [[S.Half],[0]], 1).is_number is True + + assert meijerg([1, 2], [3], [4], [5], z).delta == S.Half + + # just a few checks to make sure that all arguments go where they should + assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z) + assert tn(sqrt(pi)*meijerg(Tuple(), Tuple(), + Tuple(0), Tuple(S.Half), z**2/4), cos(z), z) + assert tn(meijerg(Tuple(1, 1), Tuple(), Tuple(1), Tuple(0), z), + log(1 + z), z) + + # test exceptions + raises(ValueError, lambda: meijerg(((3, 1), (2,)), ((oo,), (2, 0)), x)) + raises(ValueError, lambda: meijerg(((3, 1), (2,)), ((1,), (2, 0)), x)) + + # differentiation + g = meijerg((randcplx(),), (randcplx() + 2*I,), Tuple(), + (randcplx(), randcplx()), z) + assert td(g, z) + + g = meijerg(Tuple(), (randcplx(),), Tuple(), + (randcplx(), randcplx()), z) + assert td(g, z) + + g = meijerg(Tuple(), Tuple(), Tuple(randcplx()), + Tuple(randcplx(), randcplx()), z) + assert td(g, z) + + a1, a2, b1, b2, c1, c2, d1, d2 = symbols('a1:3, b1:3, c1:3, d1:3') + assert meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == \ + (meijerg((a1 - 1, a2), (b1, b2), (c1, c2), (d1, d2), z) + + (a1 - 1)*meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z))/z + + assert meijerg([z, z], [], [], [], z).diff(z) == \ + Derivative(meijerg([z, z], [], [], [], z), z) + + # meijerg is unbranched wrt parameters + from sympy.functions.elementary.complexes import polar_lift as pl + assert meijerg([pl(a1)], [pl(a2)], [pl(b1)], [pl(b2)], pl(z)) == \ + meijerg([a1], [a2], [b1], [b2], pl(z)) + + # integrand + from sympy.abc import a, b, c, d, s + assert meijerg([a], [b], [c], [d], z).integrand(s) == \ + z**s*gamma(c - s)*gamma(-a + s + 1)/(gamma(b - s)*gamma(-d + s + 1)) + + +def test_meijerg_derivative(): + assert meijerg([], [1, 1], [0, 0, x], [], z).diff(x) == \ + log(z)*meijerg([], [1, 1], [0, 0, x], [], z) \ + + 2*meijerg([], [1, 1, 1], [0, 0, x, 0], [], z) + + y = randcplx() + a = 5 # mpmath chokes with non-real numbers, and Mod1 with floats + assert td(meijerg([x], [], [], [], y), x) + assert td(meijerg([x**2], [], [], [], y), x) + assert td(meijerg([], [x], [], [], y), x) + assert td(meijerg([], [], [x], [], y), x) + assert td(meijerg([], [], [], [x], y), x) + assert td(meijerg([x], [a], [a + 1], [], y), x) + assert td(meijerg([x], [a + 1], [a], [], y), x) + assert td(meijerg([x, a], [], [], [a + 1], y), x) + assert td(meijerg([x, a + 1], [], [], [a], y), x) + b = Rational(3, 2) + assert td(meijerg([a + 2], [b], [b - 3, x], [a], y), x) + + +def test_meijerg_period(): + assert meijerg([], [1], [0], [], x).get_period() == 2*pi + assert meijerg([1], [], [], [0], x).get_period() == 2*pi + assert meijerg([], [], [0], [], x).get_period() == 2*pi # exp(x) + assert meijerg( + [], [], [0], [S.Half], x).get_period() == 2*pi # cos(sqrt(x)) + assert meijerg( + [], [], [S.Half], [0], x).get_period() == 4*pi # sin(sqrt(x)) + assert meijerg([1, 1], [], [1], [0], x).get_period() is oo # log(1 + x) + + +def test_hyper_unpolarify(): + from sympy.functions.elementary.exponential import exp_polar + a = exp_polar(2*pi*I)*x + b = x + assert hyper([], [], a).argument == b + assert hyper([0], [], a).argument == a + assert hyper([0], [0], a).argument == b + assert hyper([0, 1], [0], a).argument == a + assert hyper([0, 1], [0], exp_polar(2*pi*I)).argument == 1 + + +@slow +def test_hyperrep(): + from sympy.functions.special.hyper import (HyperRep, HyperRep_atanh, + HyperRep_power1, HyperRep_power2, HyperRep_log1, HyperRep_asin1, + HyperRep_asin2, HyperRep_sqrts1, HyperRep_sqrts2, HyperRep_log2, + HyperRep_cosasin, HyperRep_sinasin) + # First test the base class works. + from sympy.functions.elementary.exponential import exp_polar + from sympy.functions.elementary.piecewise import Piecewise + a, b, c, d, z = symbols('a b c d z') + + class myrep(HyperRep): + @classmethod + def _expr_small(cls, x): + return a + + @classmethod + def _expr_small_minus(cls, x): + return b + + @classmethod + def _expr_big(cls, x, n): + return c*n + + @classmethod + def _expr_big_minus(cls, x, n): + return d*n + assert myrep(z).rewrite('nonrep') == Piecewise((0, abs(z) > 1), (a, True)) + assert myrep(exp_polar(I*pi)*z).rewrite('nonrep') == \ + Piecewise((0, abs(z) > 1), (b, True)) + assert myrep(exp_polar(2*I*pi)*z).rewrite('nonrep') == \ + Piecewise((c, abs(z) > 1), (a, True)) + assert myrep(exp_polar(3*I*pi)*z).rewrite('nonrep') == \ + Piecewise((d, abs(z) > 1), (b, True)) + assert myrep(exp_polar(4*I*pi)*z).rewrite('nonrep') == \ + Piecewise((2*c, abs(z) > 1), (a, True)) + assert myrep(exp_polar(5*I*pi)*z).rewrite('nonrep') == \ + Piecewise((2*d, abs(z) > 1), (b, True)) + assert myrep(z).rewrite('nonrepsmall') == a + assert myrep(exp_polar(I*pi)*z).rewrite('nonrepsmall') == b + + def t(func, hyp, z): + """ Test that func is a valid representation of hyp. """ + # First test that func agrees with hyp for small z + if not tn(func.rewrite('nonrepsmall'), hyp, z, + a=Rational(-1, 2), b=Rational(-1, 2), c=S.Half, d=S.Half): + return False + # Next check that the two small representations agree. + if not tn( + func.rewrite('nonrepsmall').subs( + z, exp_polar(I*pi)*z).replace(exp_polar, exp), + func.subs(z, exp_polar(I*pi)*z).rewrite('nonrepsmall'), + z, a=Rational(-1, 2), b=Rational(-1, 2), c=S.Half, d=S.Half): + return False + # Next check continuity along exp_polar(I*pi)*t + expr = func.subs(z, exp_polar(I*pi)*z).rewrite('nonrep') + if abs(expr.subs(z, 1 + 1e-15).n() - expr.subs(z, 1 - 1e-15).n()) > 1e-10: + return False + # Finally check continuity of the big reps. + + def dosubs(func, a, b): + rv = func.subs(z, exp_polar(a)*z).rewrite('nonrep') + return rv.subs(z, exp_polar(b)*z).replace(exp_polar, exp) + for n in [0, 1, 2, 3, 4, -1, -2, -3, -4]: + expr1 = dosubs(func, 2*I*pi*n, I*pi/2) + expr2 = dosubs(func, 2*I*pi*n + I*pi, -I*pi/2) + if not tn(expr1, expr2, z): + return False + expr1 = dosubs(func, 2*I*pi*(n + 1), -I*pi/2) + expr2 = dosubs(func, 2*I*pi*n + I*pi, I*pi/2) + if not tn(expr1, expr2, z): + return False + return True + + # Now test the various representatives. + a = Rational(1, 3) + assert t(HyperRep_atanh(z), hyper([S.Half, 1], [Rational(3, 2)], z), z) + assert t(HyperRep_power1(a, z), hyper([-a], [], z), z) + assert t(HyperRep_power2(a, z), hyper([a, a - S.Half], [2*a], z), z) + assert t(HyperRep_log1(z), -z*hyper([1, 1], [2], z), z) + assert t(HyperRep_asin1(z), hyper([S.Half, S.Half], [Rational(3, 2)], z), z) + assert t(HyperRep_asin2(z), hyper([1, 1], [Rational(3, 2)], z), z) + assert t(HyperRep_sqrts1(a, z), hyper([-a, S.Half - a], [S.Half], z), z) + assert t(HyperRep_sqrts2(a, z), + -2*z/(2*a + 1)*hyper([-a - S.Half, -a], [S.Half], z).diff(z), z) + assert t(HyperRep_log2(z), -z/4*hyper([Rational(3, 2), 1, 1], [2, 2], z), z) + assert t(HyperRep_cosasin(a, z), hyper([-a, a], [S.Half], z), z) + assert t(HyperRep_sinasin(a, z), 2*a*z*hyper([1 - a, 1 + a], [Rational(3, 2)], z), z) + + +@slow +def test_meijerg_eval(): + from sympy.functions.elementary.exponential import exp_polar + from sympy.functions.special.bessel import besseli + from sympy.abc import l + a = randcplx() + arg = x*exp_polar(k*pi*I) + expr1 = pi*meijerg([[], [(a + 1)/2]], [[a/2], [-a/2, (a + 1)/2]], arg**2/4) + expr2 = besseli(a, arg) + + # Test that the two expressions agree for all arguments. + for x_ in [0.5, 1.5]: + for k_ in [0.0, 0.1, 0.3, 0.5, 0.8, 1, 5.751, 15.3]: + assert abs((expr1 - expr2).n(subs={x: x_, k: k_})) < 1e-10 + assert abs((expr1 - expr2).n(subs={x: x_, k: -k_})) < 1e-10 + + # Test continuity independently + eps = 1e-13 + expr2 = expr1.subs(k, l) + for x_ in [0.5, 1.5]: + for k_ in [0.5, Rational(1, 3), 0.25, 0.75, Rational(2, 3), 1.0, 1.5]: + assert abs((expr1 - expr2).n( + subs={x: x_, k: k_ + eps, l: k_ - eps})) < 1e-10 + assert abs((expr1 - expr2).n( + subs={x: x_, k: -k_ + eps, l: -k_ - eps})) < 1e-10 + + expr = (meijerg(((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(-I*pi)/4) + + meijerg(((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(I*pi)/4)) \ + /(2*sqrt(pi)) + assert (expr - pi/exp(1)).n(chop=True) == 0 + + +def test_limits(): + k, x = symbols('k, x') + assert hyper((1,), (Rational(4, 3), Rational(5, 3)), k**2).series(k) == \ + 1 + 9*k**2/20 + 81*k**4/1120 + O(k**6) # issue 6350 + + # https://github.com/sympy/sympy/issues/11465 + assert limit(1/hyper((1, ), (1, ), x), x, 0) == 1 + + +def test_appellf1(): + a, b1, b2, c, x, y = symbols('a b1 b2 c x y') + assert appellf1(a, b2, b1, c, y, x) == appellf1(a, b1, b2, c, x, y) + assert appellf1(a, b1, b1, c, y, x) == appellf1(a, b1, b1, c, x, y) + assert appellf1(a, b1, b2, c, S.Zero, S.Zero) is S.One + + f = appellf1(a, b1, b2, c, S.Zero, S.Zero, evaluate=False) + assert f.func is appellf1 + assert f.doit() is S.One + + +def test_derivative_appellf1(): + from sympy.core.function import diff + a, b1, b2, c, x, y, z = symbols('a b1 b2 c x y z') + assert diff(appellf1(a, b1, b2, c, x, y), x) == a*b1*appellf1(a + 1, b2, b1 + 1, c + 1, y, x)/c + assert diff(appellf1(a, b1, b2, c, x, y), y) == a*b2*appellf1(a + 1, b1, b2 + 1, c + 1, x, y)/c + assert diff(appellf1(a, b1, b2, c, x, y), z) == 0 + assert diff(appellf1(a, b1, b2, c, x, y), a) == Derivative(appellf1(a, b1, b2, c, x, y), a) + + +def test_eval_nseries(): + a1, b1, a2, b2 = symbols('a1 b1 a2 b2') + assert hyper((1,2), (1,2,3), x**2)._eval_nseries(x, 7, None) == \ + 1 + x**2/3 + x**4/24 + x**6/360 + O(x**7) + assert exp(x)._eval_nseries(x,7,None) == \ + hyper((a1, b1), (a1, b1), x)._eval_nseries(x, 7, None) + assert hyper((a1, a2), (b1, b2), x)._eval_nseries(z, 7, None) ==\ + hyper((a1, a2), (b1, b2), x) + O(z**7) + assert hyper((-S(1)/2, S(1)/2), (1,), 4*x/(x + 1)).nseries(x) == \ + 1 - x + x**2/4 - 3*x**3/4 - 15*x**4/64 - 93*x**5/64 + O(x**6) + assert (pi/2*hyper((-S(1)/2, S(1)/2), (1,), 4*x/(x + 1))).nseries(x) == \ + pi/2 - pi*x/2 + pi*x**2/8 - 3*pi*x**3/8 - 15*pi*x**4/128 - 93*pi*x**5/128 + O(x**6) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_mathieu.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_mathieu.py new file mode 100644 index 0000000000000000000000000000000000000000..b9296f0657d920c8d297f820fb3ab8b6a53129ab --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_mathieu.py @@ -0,0 +1,29 @@ +from sympy.core.function import diff +from sympy.functions.elementary.complexes import conjugate +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.mathieu_functions import (mathieuc, mathieucprime, mathieus, mathieusprime) + +from sympy.abc import a, q, z + + +def test_mathieus(): + assert isinstance(mathieus(a, q, z), mathieus) + assert mathieus(a, 0, z) == sin(sqrt(a)*z) + assert conjugate(mathieus(a, q, z)) == mathieus(conjugate(a), conjugate(q), conjugate(z)) + assert diff(mathieus(a, q, z), z) == mathieusprime(a, q, z) + +def test_mathieuc(): + assert isinstance(mathieuc(a, q, z), mathieuc) + assert mathieuc(a, 0, z) == cos(sqrt(a)*z) + assert diff(mathieuc(a, q, z), z) == mathieucprime(a, q, z) + +def test_mathieusprime(): + assert isinstance(mathieusprime(a, q, z), mathieusprime) + assert mathieusprime(a, 0, z) == sqrt(a)*cos(sqrt(a)*z) + assert diff(mathieusprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieus(a, q, z) + +def test_mathieucprime(): + assert isinstance(mathieucprime(a, q, z), mathieucprime) + assert mathieucprime(a, 0, z) == -sqrt(a)*sin(sqrt(a)*z) + assert diff(mathieucprime(a, q, z), z) == (-a + 2*q*cos(2*z))*mathieuc(a, q, z) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_singularity_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_singularity_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..dbd85cb0c7e5524d4fe1441615879b9776ad1693 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_singularity_functions.py @@ -0,0 +1,129 @@ +from sympy.core.function import (Derivative, diff) +from sympy.core.numbers import (Float, I, nan, oo, pi) +from sympy.core.relational import Eq +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.delta_functions import (DiracDelta, Heaviside) +from sympy.functions.special.singularity_functions import SingularityFunction +from sympy.series.order import O + + +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.testing.pytest import raises + +x, y, a, n = symbols('x y a n') + + +def test_fdiff(): + assert SingularityFunction(x, 4, 5).fdiff() == 5*SingularityFunction(x, 4, 4) + assert SingularityFunction(x, 4, -1).fdiff() == SingularityFunction(x, 4, -2) + assert SingularityFunction(x, 4, -2).fdiff() == SingularityFunction(x, 4, -3) + assert SingularityFunction(x, 4, -3).fdiff() == SingularityFunction(x, 4, -4) + assert SingularityFunction(x, 4, 0).fdiff() == SingularityFunction(x, 4, -1) + + assert SingularityFunction(y, 6, 2).diff(y) == 2*SingularityFunction(y, 6, 1) + assert SingularityFunction(y, -4, -1).diff(y) == SingularityFunction(y, -4, -2) + assert SingularityFunction(y, 4, 0).diff(y) == SingularityFunction(y, 4, -1) + assert SingularityFunction(y, 4, 0).diff(y, 2) == SingularityFunction(y, 4, -2) + + n = Symbol('n', positive=True) + assert SingularityFunction(x, a, n).fdiff() == n*SingularityFunction(x, a, n - 1) + assert SingularityFunction(y, a, n).diff(y) == n*SingularityFunction(y, a, n - 1) + + expr_in = 4*SingularityFunction(x, a, n) + 3*SingularityFunction(x, a, -1) + -10*SingularityFunction(x, a, 0) + expr_out = n*4*SingularityFunction(x, a, n - 1) + 3*SingularityFunction(x, a, -2) - 10*SingularityFunction(x, a, -1) + assert diff(expr_in, x) == expr_out + + assert SingularityFunction(x, -10, 5).diff(evaluate=False) == ( + Derivative(SingularityFunction(x, -10, 5), x)) + + raises(ArgumentIndexError, lambda: SingularityFunction(x, 4, 5).fdiff(2)) + + +def test_eval(): + assert SingularityFunction(x, a, n).func == SingularityFunction + assert unchanged(SingularityFunction, x, 5, n) + assert SingularityFunction(5, 3, 2) == 4 + assert SingularityFunction(3, 5, 1) == 0 + assert SingularityFunction(3, 3, 0) == 1 + assert SingularityFunction(3, 3, 1) == 0 + assert SingularityFunction(Symbol('z', zero=True), 0, 1) == 0 # like sin(z) == 0 + assert SingularityFunction(4, 4, -1) is oo + assert SingularityFunction(4, 2, -1) == 0 + assert SingularityFunction(4, 7, -1) == 0 + assert SingularityFunction(5, 6, -2) == 0 + assert SingularityFunction(4, 2, -2) == 0 + assert SingularityFunction(4, 4, -2) is oo + assert SingularityFunction(4, 2, -3) == 0 + assert SingularityFunction(8, 8, -3) is oo + assert SingularityFunction(4, 2, -4) == 0 + assert SingularityFunction(8, 8, -4) is oo + assert (SingularityFunction(6.1, 4, 5)).evalf(5) == Float('40.841', '5') + assert SingularityFunction(6.1, pi, 2) == (-pi + 6.1)**2 + assert SingularityFunction(x, a, nan) is nan + assert SingularityFunction(x, nan, 1) is nan + assert SingularityFunction(nan, a, n) is nan + + raises(ValueError, lambda: SingularityFunction(x, a, I)) + raises(ValueError, lambda: SingularityFunction(2*I, I, n)) + raises(ValueError, lambda: SingularityFunction(x, a, -5)) + + +def test_leading_term(): + l = Symbol('l', positive=True) + assert SingularityFunction(x, 3, 2).as_leading_term(x) == 0 + assert SingularityFunction(x, -2, 1).as_leading_term(x) == 2 + assert SingularityFunction(x, 0, 0).as_leading_term(x) == 1 + assert SingularityFunction(x, 0, 0).as_leading_term(x, cdir=-1) == 0 + assert SingularityFunction(x, 0, -1).as_leading_term(x) == 0 + assert SingularityFunction(x, 0, -2).as_leading_term(x) == 0 + assert SingularityFunction(x, 0, -3).as_leading_term(x) == 0 + assert SingularityFunction(x, 0, -4).as_leading_term(x) == 0 + assert (SingularityFunction(x + l, 0, 1)/2\ + - SingularityFunction(x + l, l/2, 1)\ + + SingularityFunction(x + l, l, 1)/2).as_leading_term(x) == -x/2 + + +def test_series(): + l = Symbol('l', positive=True) + assert SingularityFunction(x, -3, 2).series(x) == x**2 + 6*x + 9 + assert SingularityFunction(x, -2, 1).series(x) == x + 2 + assert SingularityFunction(x, 0, 0).series(x) == 1 + assert SingularityFunction(x, 0, 0).series(x, dir='-') == 0 + assert SingularityFunction(x, 0, -1).series(x) == 0 + assert SingularityFunction(x, 0, -2).series(x) == 0 + assert SingularityFunction(x, 0, -3).series(x) == 0 + assert SingularityFunction(x, 0, -4).series(x) == 0 + assert (SingularityFunction(x + l, 0, 1)/2\ + - SingularityFunction(x + l, l/2, 1)\ + + SingularityFunction(x + l, l, 1)/2).nseries(x) == -x/2 + O(x**6) + + +def test_rewrite(): + assert SingularityFunction(x, 4, 5).rewrite(Piecewise) == ( + Piecewise(((x - 4)**5, x - 4 >= 0), (0, True))) + assert SingularityFunction(x, -10, 0).rewrite(Piecewise) == ( + Piecewise((1, x + 10 >= 0), (0, True))) + assert SingularityFunction(x, 2, -1).rewrite(Piecewise) == ( + Piecewise((oo, Eq(x - 2, 0)), (0, True))) + assert SingularityFunction(x, 0, -2).rewrite(Piecewise) == ( + Piecewise((oo, Eq(x, 0)), (0, True))) + + n = Symbol('n', nonnegative=True) + p = SingularityFunction(x, a, n).rewrite(Piecewise) + assert p == ( + Piecewise(((x - a)**n, x - a >= 0), (0, True))) + assert p.subs(x, a).subs(n, 0) == 1 + + expr_in = SingularityFunction(x, 4, 5) + SingularityFunction(x, -3, -1) - SingularityFunction(x, 0, -2) + expr_out = (x - 4)**5*Heaviside(x - 4, 1) + DiracDelta(x + 3) - DiracDelta(x, 1) + assert expr_in.rewrite(Heaviside) == expr_out + assert expr_in.rewrite(DiracDelta) == expr_out + assert expr_in.rewrite('HeavisideDiracDelta') == expr_out + + expr_in = SingularityFunction(x, a, n) + SingularityFunction(x, a, -1) - SingularityFunction(x, a, -2) + expr_out = (x - a)**n*Heaviside(x - a, 1) + DiracDelta(x - a) + DiracDelta(a - x, 1) + assert expr_in.rewrite(Heaviside) == expr_out + assert expr_in.rewrite(DiracDelta) == expr_out + assert expr_in.rewrite('HeavisideDiracDelta') == expr_out diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_spec_polynomials.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_spec_polynomials.py new file mode 100644 index 0000000000000000000000000000000000000000..584ad3cf97df8b9d92da9fc7805ab4296f40671c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_spec_polynomials.py @@ -0,0 +1,475 @@ +from sympy.concrete.summations import Sum +from sympy.core.function import (Derivative, diff) +from sympy.core.numbers import (Rational, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol) +from sympy.functions.combinatorial.factorials import (RisingFactorial, binomial, factorial) +from sympy.functions.elementary.complexes import conjugate +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import cos +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import hyper +from sympy.functions.special.polynomials import (assoc_laguerre, assoc_legendre, chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, gegenbauer, hermite, hermite_prob, jacobi, jacobi_normalized, laguerre, legendre) +from sympy.polys.orthopolys import laguerre_poly +from sympy.polys.polyroots import roots + +from sympy.core.expr import unchanged +from sympy.core.function import ArgumentIndexError +from sympy.testing.pytest import raises + + +x = Symbol('x') + + +def test_jacobi(): + n = Symbol("n") + a = Symbol("a") + b = Symbol("b") + + assert jacobi(0, a, b, x) == 1 + assert jacobi(1, a, b, x) == a/2 - b/2 + x*(a/2 + b/2 + 1) + + assert jacobi(n, a, a, x) == RisingFactorial( + a + 1, n)*gegenbauer(n, a + S.Half, x)/RisingFactorial(2*a + 1, n) + assert jacobi(n, a, -a, x) == ((-1)**a*(-x + 1)**(-a/2)*(x + 1)**(a/2)*assoc_legendre(n, a, x)* + factorial(-a + n)*gamma(a + n + 1)/(factorial(a + n)*gamma(n + 1))) + assert jacobi(n, -b, b, x) == ((-x + 1)**(b/2)*(x + 1)**(-b/2)*assoc_legendre(n, b, x)* + gamma(-b + n + 1)/gamma(n + 1)) + assert jacobi(n, 0, 0, x) == legendre(n, x) + assert jacobi(n, S.Half, S.Half, x) == RisingFactorial( + Rational(3, 2), n)*chebyshevu(n, x)/factorial(n + 1) + assert jacobi(n, Rational(-1, 2), Rational(-1, 2), x) == RisingFactorial( + S.Half, n)*chebyshevt(n, x)/factorial(n) + + X = jacobi(n, a, b, x) + assert isinstance(X, jacobi) + + assert jacobi(n, a, b, -x) == (-1)**n*jacobi(n, b, a, x) + assert jacobi(n, a, b, 0) == 2**(-n)*gamma(a + n + 1)*hyper( + (-b - n, -n), (a + 1,), -1)/(factorial(n)*gamma(a + 1)) + assert jacobi(n, a, b, 1) == RisingFactorial(a + 1, n)/factorial(n) + + m = Symbol("m", positive=True) + assert jacobi(m, a, b, oo) == oo*RisingFactorial(a + b + m + 1, m) + assert unchanged(jacobi, n, a, b, oo) + + assert conjugate(jacobi(m, a, b, x)) == \ + jacobi(m, conjugate(a), conjugate(b), conjugate(x)) + + _k = Dummy('k') + assert diff(jacobi(n, a, b, x), n) == Derivative(jacobi(n, a, b, x), n) + assert diff(jacobi(n, a, b, x), a).dummy_eq(Sum((jacobi(n, a, b, x) + + (2*_k + a + b + 1)*RisingFactorial(_k + b + 1, -_k + n)*jacobi(_k, a, + b, x)/((-_k + n)*RisingFactorial(_k + a + b + 1, -_k + n)))/(_k + a + + b + n + 1), (_k, 0, n - 1))) + assert diff(jacobi(n, a, b, x), b).dummy_eq(Sum(((-1)**(-_k + n)*(2*_k + + a + b + 1)*RisingFactorial(_k + a + 1, -_k + n)*jacobi(_k, a, b, x)/ + ((-_k + n)*RisingFactorial(_k + a + b + 1, -_k + n)) + jacobi(n, a, + b, x))/(_k + a + b + n + 1), (_k, 0, n - 1))) + assert diff(jacobi(n, a, b, x), x) == \ + (a/2 + b/2 + n/2 + S.Half)*jacobi(n - 1, a + 1, b + 1, x) + + assert jacobi_normalized(n, a, b, x) == \ + (jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1) + /((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1)))) + + raises(ValueError, lambda: jacobi(-2.1, a, b, x)) + raises(ValueError, lambda: jacobi(Dummy(positive=True, integer=True), 1, 2, oo)) + + assert jacobi(n, a, b, x).rewrite(Sum).dummy_eq(Sum((S.Half - x/2) + **_k*RisingFactorial(-n, _k)*RisingFactorial(_k + a + 1, -_k + n)* + RisingFactorial(a + b + n + 1, _k)/factorial(_k), (_k, 0, n))/factorial(n)) + assert jacobi(n, a, b, x).rewrite("polynomial").dummy_eq(Sum((S.Half - x/2) + **_k*RisingFactorial(-n, _k)*RisingFactorial(_k + a + 1, -_k + n)* + RisingFactorial(a + b + n + 1, _k)/factorial(_k), (_k, 0, n))/factorial(n)) + raises(ArgumentIndexError, lambda: jacobi(n, a, b, x).fdiff(5)) + + +def test_gegenbauer(): + n = Symbol("n") + a = Symbol("a") + + assert gegenbauer(0, a, x) == 1 + assert gegenbauer(1, a, x) == 2*a*x + assert gegenbauer(2, a, x) == -a + x**2*(2*a**2 + 2*a) + assert gegenbauer(3, a, x) == \ + x**3*(4*a**3/3 + 4*a**2 + a*Rational(8, 3)) + x*(-2*a**2 - 2*a) + + assert gegenbauer(-1, a, x) == 0 + assert gegenbauer(n, S.Half, x) == legendre(n, x) + assert gegenbauer(n, 1, x) == chebyshevu(n, x) + assert gegenbauer(n, -1, x) == 0 + + X = gegenbauer(n, a, x) + assert isinstance(X, gegenbauer) + + assert gegenbauer(n, a, -x) == (-1)**n*gegenbauer(n, a, x) + assert gegenbauer(n, a, 0) == 2**n*sqrt(pi) * \ + gamma(a + n/2)/(gamma(a)*gamma(-n/2 + S.Half)*gamma(n + 1)) + assert gegenbauer(n, a, 1) == gamma(2*a + n)/(gamma(2*a)*gamma(n + 1)) + + assert gegenbauer(n, Rational(3, 4), -1) is zoo + assert gegenbauer(n, Rational(1, 4), -1) == (sqrt(2)*cos(pi*(n + S.One/4))* + gamma(n + S.Half)/(sqrt(pi)*gamma(n + 1))) + + m = Symbol("m", positive=True) + assert gegenbauer(m, a, oo) == oo*RisingFactorial(a, m) + assert unchanged(gegenbauer, n, a, oo) + + assert conjugate(gegenbauer(n, a, x)) == gegenbauer(n, conjugate(a), conjugate(x)) + + _k = Dummy('k') + + assert diff(gegenbauer(n, a, x), n) == Derivative(gegenbauer(n, a, x), n) + assert diff(gegenbauer(n, a, x), a).dummy_eq(Sum((2*(-1)**(-_k + n) + 2)* + (_k + a)*gegenbauer(_k, a, x)/((-_k + n)*(_k + 2*a + n)) + ((2*_k + + 2)/((_k + 2*a)*(2*_k + 2*a + 1)) + 2/(_k + 2*a + n))*gegenbauer(n, a + , x), (_k, 0, n - 1))) + assert diff(gegenbauer(n, a, x), x) == 2*a*gegenbauer(n - 1, a + 1, x) + + assert gegenbauer(n, a, x).rewrite(Sum).dummy_eq( + Sum((-1)**_k*(2*x)**(-2*_k + n)*RisingFactorial(a, -_k + n) + /(factorial(_k)*factorial(-2*_k + n)), (_k, 0, floor(n/2)))) + assert gegenbauer(n, a, x).rewrite("polynomial").dummy_eq( + Sum((-1)**_k*(2*x)**(-2*_k + n)*RisingFactorial(a, -_k + n) + /(factorial(_k)*factorial(-2*_k + n)), (_k, 0, floor(n/2)))) + + raises(ArgumentIndexError, lambda: gegenbauer(n, a, x).fdiff(4)) + + +def test_legendre(): + assert legendre(0, x) == 1 + assert legendre(1, x) == x + assert legendre(2, x) == ((3*x**2 - 1)/2).expand() + assert legendre(3, x) == ((5*x**3 - 3*x)/2).expand() + assert legendre(4, x) == ((35*x**4 - 30*x**2 + 3)/8).expand() + assert legendre(5, x) == ((63*x**5 - 70*x**3 + 15*x)/8).expand() + assert legendre(6, x) == ((231*x**6 - 315*x**4 + 105*x**2 - 5)/16).expand() + + assert legendre(10, -1) == 1 + assert legendre(11, -1) == -1 + assert legendre(10, 1) == 1 + assert legendre(11, 1) == 1 + assert legendre(10, 0) != 0 + assert legendre(11, 0) == 0 + + assert legendre(-1, x) == 1 + k = Symbol('k') + assert legendre(5 - k, x).subs(k, 2) == ((5*x**3 - 3*x)/2).expand() + + assert roots(legendre(4, x), x) == { + sqrt(Rational(3, 7) - Rational(2, 35)*sqrt(30)): 1, + -sqrt(Rational(3, 7) - Rational(2, 35)*sqrt(30)): 1, + sqrt(Rational(3, 7) + Rational(2, 35)*sqrt(30)): 1, + -sqrt(Rational(3, 7) + Rational(2, 35)*sqrt(30)): 1, + } + + n = Symbol("n") + + X = legendre(n, x) + assert isinstance(X, legendre) + assert unchanged(legendre, n, x) + + assert legendre(n, 0) == sqrt(pi)/(gamma(S.Half - n/2)*gamma(n/2 + 1)) + assert legendre(n, 1) == 1 + assert legendre(n, oo) is oo + assert legendre(-n, x) == legendre(n - 1, x) + assert legendre(n, -x) == (-1)**n*legendre(n, x) + assert unchanged(legendre, -n + k, x) + + assert conjugate(legendre(n, x)) == legendre(n, conjugate(x)) + + assert diff(legendre(n, x), x) == \ + n*(x*legendre(n, x) - legendre(n - 1, x))/(x**2 - 1) + assert diff(legendre(n, x), n) == Derivative(legendre(n, x), n) + + _k = Dummy('k') + assert legendre(n, x).rewrite(Sum).dummy_eq(Sum((-1)**_k*(S.Half - + x/2)**_k*(x/2 + S.Half)**(-_k + n)*binomial(n, _k)**2, (_k, 0, n))) + assert legendre(n, x).rewrite("polynomial").dummy_eq(Sum((-1)**_k*(S.Half - + x/2)**_k*(x/2 + S.Half)**(-_k + n)*binomial(n, _k)**2, (_k, 0, n))) + raises(ArgumentIndexError, lambda: legendre(n, x).fdiff(1)) + raises(ArgumentIndexError, lambda: legendre(n, x).fdiff(3)) + + +def test_assoc_legendre(): + Plm = assoc_legendre + Q = sqrt(1 - x**2) + + assert Plm(0, 0, x) == 1 + assert Plm(1, 0, x) == x + assert Plm(1, 1, x) == -Q + assert Plm(2, 0, x) == (3*x**2 - 1)/2 + assert Plm(2, 1, x) == -3*x*Q + assert Plm(2, 2, x) == 3*Q**2 + assert Plm(3, 0, x) == (5*x**3 - 3*x)/2 + assert Plm(3, 1, x).expand() == (( 3*(1 - 5*x**2)/2 ).expand() * Q).expand() + assert Plm(3, 2, x) == 15*x * Q**2 + assert Plm(3, 3, x) == -15 * Q**3 + + # negative m + assert Plm(1, -1, x) == -Plm(1, 1, x)/2 + assert Plm(2, -2, x) == Plm(2, 2, x)/24 + assert Plm(2, -1, x) == -Plm(2, 1, x)/6 + assert Plm(3, -3, x) == -Plm(3, 3, x)/720 + assert Plm(3, -2, x) == Plm(3, 2, x)/120 + assert Plm(3, -1, x) == -Plm(3, 1, x)/12 + + n = Symbol("n") + m = Symbol("m") + X = Plm(n, m, x) + assert isinstance(X, assoc_legendre) + + assert Plm(n, 0, x) == legendre(n, x) + assert Plm(n, m, 0) == 2**m*sqrt(pi)/(gamma(-m/2 - n/2 + + S.Half)*gamma(-m/2 + n/2 + 1)) + + assert diff(Plm(m, n, x), x) == (m*x*assoc_legendre(m, n, x) - + (m + n)*assoc_legendre(m - 1, n, x))/(x**2 - 1) + + _k = Dummy('k') + assert Plm(m, n, x).rewrite(Sum).dummy_eq( + (1 - x**2)**(n/2)*Sum((-1)**_k*2**(-m)*x**(-2*_k + m - n)*factorial + (-2*_k + 2*m)/(factorial(_k)*factorial(-_k + m)*factorial(-2*_k + m + - n)), (_k, 0, floor(m/2 - n/2)))) + assert Plm(m, n, x).rewrite("polynomial").dummy_eq( + (1 - x**2)**(n/2)*Sum((-1)**_k*2**(-m)*x**(-2*_k + m - n)*factorial + (-2*_k + 2*m)/(factorial(_k)*factorial(-_k + m)*factorial(-2*_k + m + - n)), (_k, 0, floor(m/2 - n/2)))) + assert conjugate(assoc_legendre(n, m, x)) == \ + assoc_legendre(n, conjugate(m), conjugate(x)) + raises(ValueError, lambda: Plm(0, 1, x)) + raises(ValueError, lambda: Plm(-1, 1, x)) + raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(1)) + raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(2)) + raises(ArgumentIndexError, lambda: Plm(n, m, x).fdiff(4)) + + +def test_chebyshev(): + assert chebyshevt(0, x) == 1 + assert chebyshevt(1, x) == x + assert chebyshevt(2, x) == 2*x**2 - 1 + assert chebyshevt(3, x) == 4*x**3 - 3*x + + for n in range(1, 4): + for k in range(n): + z = chebyshevt_root(n, k) + assert chebyshevt(n, z) == 0 + raises(ValueError, lambda: chebyshevt_root(n, n)) + + for n in range(1, 4): + for k in range(n): + z = chebyshevu_root(n, k) + assert chebyshevu(n, z) == 0 + raises(ValueError, lambda: chebyshevu_root(n, n)) + + n = Symbol("n") + X = chebyshevt(n, x) + assert isinstance(X, chebyshevt) + assert unchanged(chebyshevt, n, x) + assert chebyshevt(n, -x) == (-1)**n*chebyshevt(n, x) + assert chebyshevt(-n, x) == chebyshevt(n, x) + + assert chebyshevt(n, 0) == cos(pi*n/2) + assert chebyshevt(n, 1) == 1 + assert chebyshevt(n, oo) is oo + + assert conjugate(chebyshevt(n, x)) == chebyshevt(n, conjugate(x)) + + assert diff(chebyshevt(n, x), x) == n*chebyshevu(n - 1, x) + + X = chebyshevu(n, x) + assert isinstance(X, chebyshevu) + + y = Symbol('y') + assert chebyshevu(n, -x) == (-1)**n*chebyshevu(n, x) + assert chebyshevu(-n, x) == -chebyshevu(n - 2, x) + assert unchanged(chebyshevu, -n + y, x) + + assert chebyshevu(n, 0) == cos(pi*n/2) + assert chebyshevu(n, 1) == n + 1 + assert chebyshevu(n, oo) is oo + + assert conjugate(chebyshevu(n, x)) == chebyshevu(n, conjugate(x)) + + assert diff(chebyshevu(n, x), x) == \ + (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1) + + _k = Dummy('k') + assert chebyshevt(n, x).rewrite(Sum).dummy_eq(Sum(x**(-2*_k + n) + *(x**2 - 1)**_k*binomial(n, 2*_k), (_k, 0, floor(n/2)))) + assert chebyshevt(n, x).rewrite("polynomial").dummy_eq(Sum(x**(-2*_k + n) + *(x**2 - 1)**_k*binomial(n, 2*_k), (_k, 0, floor(n/2)))) + assert chebyshevu(n, x).rewrite(Sum).dummy_eq(Sum((-1)**_k*(2*x) + **(-2*_k + n)*factorial(-_k + n)/(factorial(_k)* + factorial(-2*_k + n)), (_k, 0, floor(n/2)))) + assert chebyshevu(n, x).rewrite("polynomial").dummy_eq(Sum((-1)**_k*(2*x) + **(-2*_k + n)*factorial(-_k + n)/(factorial(_k)* + factorial(-2*_k + n)), (_k, 0, floor(n/2)))) + raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(1)) + raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(3)) + raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(1)) + raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(3)) + + +def test_hermite(): + assert hermite(0, x) == 1 + assert hermite(1, x) == 2*x + assert hermite(2, x) == 4*x**2 - 2 + assert hermite(3, x) == 8*x**3 - 12*x + assert hermite(4, x) == 16*x**4 - 48*x**2 + 12 + assert hermite(6, x) == 64*x**6 - 480*x**4 + 720*x**2 - 120 + + n = Symbol("n") + assert unchanged(hermite, n, x) + assert hermite(n, -x) == (-1)**n*hermite(n, x) + assert unchanged(hermite, -n, x) + + assert hermite(n, 0) == 2**n*sqrt(pi)/gamma(S.Half - n/2) + assert hermite(n, oo) is oo + + assert conjugate(hermite(n, x)) == hermite(n, conjugate(x)) + + _k = Dummy('k') + assert hermite(n, x).rewrite(Sum).dummy_eq(factorial(n)*Sum((-1) + **_k*(2*x)**(-2*_k + n)/(factorial(_k)*factorial(-2*_k + n)), (_k, + 0, floor(n/2)))) + assert hermite(n, x).rewrite("polynomial").dummy_eq(factorial(n)*Sum((-1) + **_k*(2*x)**(-2*_k + n)/(factorial(_k)*factorial(-2*_k + n)), (_k, + 0, floor(n/2)))) + + assert diff(hermite(n, x), x) == 2*n*hermite(n - 1, x) + assert diff(hermite(n, x), n) == Derivative(hermite(n, x), n) + raises(ArgumentIndexError, lambda: hermite(n, x).fdiff(3)) + + assert hermite(n, x).rewrite(hermite_prob) == \ + sqrt(2)**n * hermite_prob(n, x*sqrt(2)) + + +def test_hermite_prob(): + assert hermite_prob(0, x) == 1 + assert hermite_prob(1, x) == x + assert hermite_prob(2, x) == x**2 - 1 + assert hermite_prob(3, x) == x**3 - 3*x + assert hermite_prob(4, x) == x**4 - 6*x**2 + 3 + assert hermite_prob(6, x) == x**6 - 15*x**4 + 45*x**2 - 15 + + n = Symbol("n") + assert unchanged(hermite_prob, n, x) + assert hermite_prob(n, -x) == (-1)**n*hermite_prob(n, x) + assert unchanged(hermite_prob, -n, x) + + assert hermite_prob(n, 0) == sqrt(pi)/gamma(S.Half - n/2) + assert hermite_prob(n, oo) is oo + + assert conjugate(hermite_prob(n, x)) == hermite_prob(n, conjugate(x)) + + _k = Dummy('k') + assert hermite_prob(n, x).rewrite(Sum).dummy_eq(factorial(n) * + Sum((-S.Half)**_k * x**(n-2*_k) / (factorial(_k) * factorial(n-2*_k)), + (_k, 0, floor(n/2)))) + assert hermite_prob(n, x).rewrite("polynomial").dummy_eq(factorial(n) * + Sum((-S.Half)**_k * x**(n-2*_k) / (factorial(_k) * factorial(n-2*_k)), + (_k, 0, floor(n/2)))) + + assert diff(hermite_prob(n, x), x) == n*hermite_prob(n-1, x) + assert diff(hermite_prob(n, x), n) == Derivative(hermite_prob(n, x), n) + raises(ArgumentIndexError, lambda: hermite_prob(n, x).fdiff(3)) + + assert hermite_prob(n, x).rewrite(hermite) == \ + sqrt(2)**(-n) * hermite(n, x/sqrt(2)) + + +def test_laguerre(): + n = Symbol("n") + m = Symbol("m", negative=True) + + # Laguerre polynomials: + assert laguerre(0, x) == 1 + assert laguerre(1, x) == -x + 1 + assert laguerre(2, x) == x**2/2 - 2*x + 1 + assert laguerre(3, x) == -x**3/6 + 3*x**2/2 - 3*x + 1 + assert laguerre(-2, x) == (x + 1)*exp(x) + + X = laguerre(n, x) + assert isinstance(X, laguerre) + + assert laguerre(n, 0) == 1 + assert laguerre(n, oo) == (-1)**n*oo + assert laguerre(n, -oo) is oo + + assert conjugate(laguerre(n, x)) == laguerre(n, conjugate(x)) + + _k = Dummy('k') + + assert laguerre(n, x).rewrite(Sum).dummy_eq( + Sum(x**_k*RisingFactorial(-n, _k)/factorial(_k)**2, (_k, 0, n))) + assert laguerre(n, x).rewrite("polynomial").dummy_eq( + Sum(x**_k*RisingFactorial(-n, _k)/factorial(_k)**2, (_k, 0, n))) + assert laguerre(m, x).rewrite(Sum).dummy_eq( + exp(x)*Sum((-x)**_k*RisingFactorial(m + 1, _k)/factorial(_k)**2, + (_k, 0, -m - 1))) + assert laguerre(m, x).rewrite("polynomial").dummy_eq( + exp(x)*Sum((-x)**_k*RisingFactorial(m + 1, _k)/factorial(_k)**2, + (_k, 0, -m - 1))) + + assert diff(laguerre(n, x), x) == -assoc_laguerre(n - 1, 1, x) + + k = Symbol('k') + assert laguerre(-n, x) == exp(x)*laguerre(n - 1, -x) + assert laguerre(-3, x) == exp(x)*laguerre(2, -x) + assert unchanged(laguerre, -n + k, x) + + raises(ValueError, lambda: laguerre(-2.1, x)) + raises(ValueError, lambda: laguerre(Rational(5, 2), x)) + raises(ArgumentIndexError, lambda: laguerre(n, x).fdiff(1)) + raises(ArgumentIndexError, lambda: laguerre(n, x).fdiff(3)) + + +def test_assoc_laguerre(): + n = Symbol("n") + m = Symbol("m") + alpha = Symbol("alpha") + + # generalized Laguerre polynomials: + assert assoc_laguerre(0, alpha, x) == 1 + assert assoc_laguerre(1, alpha, x) == -x + alpha + 1 + assert assoc_laguerre(2, alpha, x).expand() == \ + (x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand() + assert assoc_laguerre(3, alpha, x).expand() == \ + (-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 + + (alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand() + + # Test the lowest 10 polynomials with laguerre_poly, to make sure it works: + for i in range(10): + assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x) + + X = assoc_laguerre(n, m, x) + assert isinstance(X, assoc_laguerre) + + assert assoc_laguerre(n, 0, x) == laguerre(n, x) + assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha) + p = Symbol("p", positive=True) + assert assoc_laguerre(p, alpha, oo) == (-1)**p*oo + assert assoc_laguerre(p, alpha, -oo) is oo + + assert diff(assoc_laguerre(n, alpha, x), x) == \ + -assoc_laguerre(n - 1, alpha + 1, x) + _k = Dummy('k') + assert diff(assoc_laguerre(n, alpha, x), alpha).dummy_eq( + Sum(assoc_laguerre(_k, alpha, x)/(-alpha + n), (_k, 0, n - 1))) + + assert conjugate(assoc_laguerre(n, alpha, x)) == \ + assoc_laguerre(n, conjugate(alpha), conjugate(x)) + + assert assoc_laguerre(n, alpha, x).rewrite(Sum).dummy_eq( + gamma(alpha + n + 1)*Sum(x**_k*RisingFactorial(-n, _k)/ + (factorial(_k)*gamma(_k + alpha + 1)), (_k, 0, n))/factorial(n)) + assert assoc_laguerre(n, alpha, x).rewrite("polynomial").dummy_eq( + gamma(alpha + n + 1)*Sum(x**_k*RisingFactorial(-n, _k)/ + (factorial(_k)*gamma(_k + alpha + 1)), (_k, 0, n))/factorial(n)) + raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x)) + raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(1)) + raises(ArgumentIndexError, lambda: assoc_laguerre(n, alpha, x).fdiff(4)) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py new file mode 100644 index 0000000000000000000000000000000000000000..2e0d4ffebabb62c13d3fc2996e8ba23866467720 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_spherical_harmonics.py @@ -0,0 +1,66 @@ +from sympy.core.function import diff +from sympy.core.numbers import (I, pi) +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import conjugate +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, cot, sin) +from sympy.functions.special.spherical_harmonics import Ynm, Znm, Ynm_c + + +def test_Ynm(): + # https://en.wikipedia.org/wiki/Spherical_harmonics + th, ph = Symbol("theta", real=True), Symbol("phi", real=True) + from sympy.abc import n,m + + assert Ynm(0, 0, th, ph).expand(func=True) == 1/(2*sqrt(pi)) + assert Ynm(1, -1, th, ph) == -exp(-2*I*ph)*Ynm(1, 1, th, ph) + assert Ynm(1, -1, th, ph).expand(func=True) == sqrt(6)*sin(th)*exp(-I*ph)/(4*sqrt(pi)) + assert Ynm(1, 0, th, ph).expand(func=True) == sqrt(3)*cos(th)/(2*sqrt(pi)) + assert Ynm(1, 1, th, ph).expand(func=True) == -sqrt(6)*sin(th)*exp(I*ph)/(4*sqrt(pi)) + assert Ynm(2, 0, th, ph).expand(func=True) == 3*sqrt(5)*cos(th)**2/(4*sqrt(pi)) - sqrt(5)/(4*sqrt(pi)) + assert Ynm(2, 1, th, ph).expand(func=True) == -sqrt(30)*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi)) + assert Ynm(2, -2, th, ph).expand(func=True) == (-sqrt(30)*exp(-2*I*ph)*cos(th)**2/(8*sqrt(pi)) + + sqrt(30)*exp(-2*I*ph)/(8*sqrt(pi))) + assert Ynm(2, 2, th, ph).expand(func=True) == (-sqrt(30)*exp(2*I*ph)*cos(th)**2/(8*sqrt(pi)) + + sqrt(30)*exp(2*I*ph)/(8*sqrt(pi))) + + assert diff(Ynm(n, m, th, ph), th) == (m*cot(th)*Ynm(n, m, th, ph) + + sqrt((-m + n)*(m + n + 1))*exp(-I*ph)*Ynm(n, m + 1, th, ph)) + assert diff(Ynm(n, m, th, ph), ph) == I*m*Ynm(n, m, th, ph) + + assert conjugate(Ynm(n, m, th, ph)) == (-1)**(2*m)*exp(-2*I*m*ph)*Ynm(n, m, th, ph) + + assert Ynm(n, m, -th, ph) == Ynm(n, m, th, ph) + assert Ynm(n, m, th, -ph) == exp(-2*I*m*ph)*Ynm(n, m, th, ph) + assert Ynm(n, -m, th, ph) == (-1)**m*exp(-2*I*m*ph)*Ynm(n, m, th, ph) + + +def test_Ynm_c(): + th, ph = Symbol("theta", real=True), Symbol("phi", real=True) + from sympy.abc import n,m + + assert Ynm_c(n, m, th, ph) == (-1)**(2*m)*exp(-2*I*m*ph)*Ynm(n, m, th, ph) + + +def test_Znm(): + # https://en.wikipedia.org/wiki/Solid_harmonics#List_of_lowest_functions + th, ph = Symbol("theta", real=True), Symbol("phi", real=True) + + assert Znm(0, 0, th, ph) == Ynm(0, 0, th, ph) + assert Znm(1, -1, th, ph) == (-sqrt(2)*I*(Ynm(1, 1, th, ph) + - exp(-2*I*ph)*Ynm(1, 1, th, ph))/2) + assert Znm(1, 0, th, ph) == Ynm(1, 0, th, ph) + assert Znm(1, 1, th, ph) == (sqrt(2)*(Ynm(1, 1, th, ph) + + exp(-2*I*ph)*Ynm(1, 1, th, ph))/2) + assert Znm(0, 0, th, ph).expand(func=True) == 1/(2*sqrt(pi)) + assert Znm(1, -1, th, ph).expand(func=True) == (sqrt(3)*I*sin(th)*exp(I*ph)/(4*sqrt(pi)) + - sqrt(3)*I*sin(th)*exp(-I*ph)/(4*sqrt(pi))) + assert Znm(1, 0, th, ph).expand(func=True) == sqrt(3)*cos(th)/(2*sqrt(pi)) + assert Znm(1, 1, th, ph).expand(func=True) == (-sqrt(3)*sin(th)*exp(I*ph)/(4*sqrt(pi)) + - sqrt(3)*sin(th)*exp(-I*ph)/(4*sqrt(pi))) + assert Znm(2, -1, th, ph).expand(func=True) == (sqrt(15)*I*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi)) + - sqrt(15)*I*sin(th)*exp(-I*ph)*cos(th)/(4*sqrt(pi))) + assert Znm(2, 0, th, ph).expand(func=True) == 3*sqrt(5)*cos(th)**2/(4*sqrt(pi)) - sqrt(5)/(4*sqrt(pi)) + assert Znm(2, 1, th, ph).expand(func=True) == (-sqrt(15)*sin(th)*exp(I*ph)*cos(th)/(4*sqrt(pi)) + - sqrt(15)*sin(th)*exp(-I*ph)*cos(th)/(4*sqrt(pi))) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_tensor_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_tensor_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..7d4f31c45ae0a60a6f72dc5551794b2110f5ab99 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_tensor_functions.py @@ -0,0 +1,145 @@ +from sympy.core.relational import Ne +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.elementary.complexes import (adjoint, conjugate, transpose) +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.tensor_functions import (Eijk, KroneckerDelta, LeviCivita) + +from sympy.physics.secondquant import evaluate_deltas, F + +x, y = symbols('x y') + + +def test_levicivita(): + assert Eijk(1, 2, 3) == LeviCivita(1, 2, 3) + assert LeviCivita(1, 2, 3) == 1 + assert LeviCivita(int(1), int(2), int(3)) == 1 + assert LeviCivita(1, 3, 2) == -1 + assert LeviCivita(1, 2, 2) == 0 + i, j, k = symbols('i j k') + assert LeviCivita(i, j, k) == LeviCivita(i, j, k, evaluate=False) + assert LeviCivita(i, j, i) == 0 + assert LeviCivita(1, i, i) == 0 + assert LeviCivita(i, j, k).doit() == (j - i)*(k - i)*(k - j)/2 + assert LeviCivita(1, 2, 3, 1) == 0 + assert LeviCivita(4, 5, 1, 2, 3) == 1 + assert LeviCivita(4, 5, 2, 1, 3) == -1 + + assert LeviCivita(i, j, k).is_integer is True + + assert adjoint(LeviCivita(i, j, k)) == LeviCivita(i, j, k) + assert conjugate(LeviCivita(i, j, k)) == LeviCivita(i, j, k) + assert transpose(LeviCivita(i, j, k)) == LeviCivita(i, j, k) + + +def test_kronecker_delta(): + i, j = symbols('i j') + k = Symbol('k', nonzero=True) + assert KroneckerDelta(1, 1) == 1 + assert KroneckerDelta(1, 2) == 0 + assert KroneckerDelta(k, 0) == 0 + assert KroneckerDelta(x, x) == 1 + assert KroneckerDelta(x**2 - y**2, x**2 - y**2) == 1 + assert KroneckerDelta(i, i) == 1 + assert KroneckerDelta(i, i + 1) == 0 + assert KroneckerDelta(0, 0) == 1 + assert KroneckerDelta(0, 1) == 0 + assert KroneckerDelta(i + k, i) == 0 + assert KroneckerDelta(i + k, i + k) == 1 + assert KroneckerDelta(i + k, i + 1 + k) == 0 + assert KroneckerDelta(i, j).subs({"i": 1, "j": 0}) == 0 + assert KroneckerDelta(i, j).subs({"i": 3, "j": 3}) == 1 + + assert KroneckerDelta(i, j)**0 == 1 + for n in range(1, 10): + assert KroneckerDelta(i, j)**n == KroneckerDelta(i, j) + assert KroneckerDelta(i, j)**-n == 1/KroneckerDelta(i, j) + + assert KroneckerDelta(i, j).is_integer is True + + assert adjoint(KroneckerDelta(i, j)) == KroneckerDelta(i, j) + assert conjugate(KroneckerDelta(i, j)) == KroneckerDelta(i, j) + assert transpose(KroneckerDelta(i, j)) == KroneckerDelta(i, j) + # to test if canonical + assert (KroneckerDelta(i, j) == KroneckerDelta(j, i)) == True + + assert KroneckerDelta(i, j).rewrite(Piecewise) == Piecewise((0, Ne(i, j)), (1, True)) + + # Tests with range: + assert KroneckerDelta(i, j, (0, i)).args == (i, j, (0, i)) + assert KroneckerDelta(i, j, (-j, i)).delta_range == (-j, i) + + # If index is out of range, return zero: + assert KroneckerDelta(i, j, (0, i-1)) == 0 + assert KroneckerDelta(-1, j, (0, i-1)) == 0 + assert KroneckerDelta(j, -1, (0, i-1)) == 0 + assert KroneckerDelta(j, i, (0, i-1)) == 0 + + +def test_kronecker_delta_secondquant(): + """secondquant-specific methods""" + D = KroneckerDelta + i, j, v, w = symbols('i j v w', below_fermi=True, cls=Dummy) + a, b, t, u = symbols('a b t u', above_fermi=True, cls=Dummy) + p, q, r, s = symbols('p q r s', cls=Dummy) + + assert D(i, a) == 0 + assert D(i, t) == 0 + + assert D(i, j).is_above_fermi is False + assert D(a, b).is_above_fermi is True + assert D(p, q).is_above_fermi is True + assert D(i, q).is_above_fermi is False + assert D(q, i).is_above_fermi is False + assert D(q, v).is_above_fermi is False + assert D(a, q).is_above_fermi is True + + assert D(i, j).is_below_fermi is True + assert D(a, b).is_below_fermi is False + assert D(p, q).is_below_fermi is True + assert D(p, j).is_below_fermi is True + assert D(q, b).is_below_fermi is False + + assert D(i, j).is_only_above_fermi is False + assert D(a, b).is_only_above_fermi is True + assert D(p, q).is_only_above_fermi is False + assert D(i, q).is_only_above_fermi is False + assert D(q, i).is_only_above_fermi is False + assert D(a, q).is_only_above_fermi is True + + assert D(i, j).is_only_below_fermi is True + assert D(a, b).is_only_below_fermi is False + assert D(p, q).is_only_below_fermi is False + assert D(p, j).is_only_below_fermi is True + assert D(q, b).is_only_below_fermi is False + + assert not D(i, q).indices_contain_equal_information + assert not D(a, q).indices_contain_equal_information + assert D(p, q).indices_contain_equal_information + assert D(a, b).indices_contain_equal_information + assert D(i, j).indices_contain_equal_information + + assert D(q, b).preferred_index == b + assert D(q, b).killable_index == q + assert D(q, t).preferred_index == t + assert D(q, t).killable_index == q + assert D(q, i).preferred_index == i + assert D(q, i).killable_index == q + assert D(q, v).preferred_index == v + assert D(q, v).killable_index == q + assert D(q, p).preferred_index == p + assert D(q, p).killable_index == q + + EV = evaluate_deltas + assert EV(D(a, q)*F(q)) == F(a) + assert EV(D(i, q)*F(q)) == F(i) + assert EV(D(a, q)*F(a)) == D(a, q)*F(a) + assert EV(D(i, q)*F(i)) == D(i, q)*F(i) + assert EV(D(a, b)*F(a)) == F(b) + assert EV(D(a, b)*F(b)) == F(a) + assert EV(D(i, j)*F(i)) == F(j) + assert EV(D(i, j)*F(j)) == F(i) + assert EV(D(p, q)*F(q)) == F(p) + assert EV(D(p, q)*F(p)) == F(q) + assert EV(D(p, j)*D(p, i)*F(i)) == F(j) + assert EV(D(p, j)*D(p, i)*F(j)) == F(i) + assert EV(D(p, q)*D(p, i))*F(i) == D(q, i)*F(i) diff --git a/lib/python3.11/site-packages/sympy/functions/special/tests/test_zeta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/tests/test_zeta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..c2083b0b6e8cb38fde17fb1ede2a34be6338b1dc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/tests/test_zeta_functions.py @@ -0,0 +1,286 @@ +from sympy.concrete.summations import Sum +from sympy.core.function import expand_func +from sympy.core.numbers import (Float, I, Rational, nan, oo, pi, zoo) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions.elementary.complexes import (Abs, polar_lift) +from sympy.functions.elementary.exponential import (exp, exp_polar, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.zeta_functions import (dirichlet_eta, lerchphi, polylog, riemann_xi, stieltjes, zeta) +from sympy.series.order import O +from sympy.core.function import ArgumentIndexError +from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic +from sympy.testing.pytest import raises +from sympy.core.random import (test_derivative_numerically as td, + random_complex_number as randcplx, verify_numerically) + +x = Symbol('x') +a = Symbol('a') +b = Symbol('b', negative=True) +z = Symbol('z') +s = Symbol('s') + + +def test_zeta_eval(): + + assert zeta(nan) is nan + assert zeta(x, nan) is nan + + assert zeta(0) == Rational(-1, 2) + assert zeta(0, x) == S.Half - x + assert zeta(0, b) == S.Half - b + + assert zeta(1) is zoo + assert zeta(1, 2) is zoo + assert zeta(1, -7) is zoo + assert zeta(1, x) is zoo + + assert zeta(2, 1) == pi**2/6 + assert zeta(3, 1) == zeta(3) + + assert zeta(2) == pi**2/6 + assert zeta(4) == pi**4/90 + assert zeta(6) == pi**6/945 + + assert zeta(4, 3) == pi**4/90 - Rational(17, 16) + assert zeta(7, 4) == zeta(7) - Rational(282251, 279936) + assert zeta(S.Half, 2).func == zeta + assert expand_func(zeta(S.Half, 2)) == zeta(S.Half) - 1 + assert zeta(x, 3).func == zeta + assert expand_func(zeta(x, 3)) == zeta(x) - 1 - 1/2**x + + assert zeta(2, 0) is nan + assert zeta(3, -1) is nan + assert zeta(4, -2) is nan + + assert zeta(oo) == 1 + + assert zeta(-1) == Rational(-1, 12) + assert zeta(-2) == 0 + assert zeta(-3) == Rational(1, 120) + assert zeta(-4) == 0 + assert zeta(-5) == Rational(-1, 252) + + assert zeta(-1, 3) == Rational(-37, 12) + assert zeta(-1, 7) == Rational(-253, 12) + assert zeta(-1, -4) == Rational(-121, 12) + assert zeta(-1, -9) == Rational(-541, 12) + + assert zeta(-4, 3) == -17 + assert zeta(-4, -8) == 8772 + + assert zeta(0, 1) == Rational(-1, 2) + assert zeta(0, -1) == Rational(3, 2) + + assert zeta(0, 2) == Rational(-3, 2) + assert zeta(0, -2) == Rational(5, 2) + + assert zeta( + 3).evalf(20).epsilon_eq(Float("1.2020569031595942854", 20), 1e-19) + + +def test_zeta_series(): + assert zeta(x, a).series(a, z, 2) == \ + zeta(x, z) - x*(a-z)*zeta(x+1, z) + O((a-z)**2, (a, z)) + + +def test_dirichlet_eta_eval(): + assert dirichlet_eta(0) == S.Half + assert dirichlet_eta(-1) == Rational(1, 4) + assert dirichlet_eta(1) == log(2) + assert dirichlet_eta(1, S.Half).simplify() == pi/2 + assert dirichlet_eta(1, 2) == 1 - log(2) + assert dirichlet_eta(2) == pi**2/12 + assert dirichlet_eta(4) == pi**4*Rational(7, 720) + assert str(dirichlet_eta(I).evalf(n=10)) == '0.5325931818 + 0.2293848577*I' + assert str(dirichlet_eta(I, I).evalf(n=10)) == '3.462349253 + 0.220285771*I' + + +def test_riemann_xi_eval(): + assert riemann_xi(2) == pi/6 + assert riemann_xi(0) == Rational(1, 2) + assert riemann_xi(1) == Rational(1, 2) + assert riemann_xi(3).rewrite(zeta) == 3*zeta(3)/(2*pi) + assert riemann_xi(4) == pi**2/15 + + +def test_rewriting(): + from sympy.functions.elementary.piecewise import Piecewise + assert isinstance(dirichlet_eta(x).rewrite(zeta), Piecewise) + assert isinstance(dirichlet_eta(x).rewrite(genocchi), Piecewise) + assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x)/(1 - 2**(1 - x)) + assert zeta(x).rewrite(dirichlet_eta, a=2) == zeta(x) + assert verify_numerically(dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x) + assert verify_numerically(dirichlet_eta(x), dirichlet_eta(x).rewrite(genocchi), x) + assert verify_numerically(zeta(x), zeta(x).rewrite(dirichlet_eta), x) + + assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a) + assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1)*z + + assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a) + assert z*lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z) + + +def test_derivatives(): + from sympy.core.function import Derivative + assert zeta(x, a).diff(x) == Derivative(zeta(x, a), x) + assert zeta(x, a).diff(a) == -x*zeta(x + 1, a) + assert lerchphi( + z, s, a).diff(z) == (lerchphi(z, s - 1, a) - a*lerchphi(z, s, a))/z + assert lerchphi(z, s, a).diff(a) == -s*lerchphi(z, s + 1, a) + assert polylog(s, z).diff(z) == polylog(s - 1, z)/z + + b = randcplx() + c = randcplx() + assert td(zeta(b, x), x) + assert td(polylog(b, z), z) + assert td(lerchphi(c, b, x), x) + assert td(lerchphi(x, b, c), x) + raises(ArgumentIndexError, lambda: lerchphi(c, b, x).fdiff(2)) + raises(ArgumentIndexError, lambda: lerchphi(c, b, x).fdiff(4)) + raises(ArgumentIndexError, lambda: polylog(b, z).fdiff(1)) + raises(ArgumentIndexError, lambda: polylog(b, z).fdiff(3)) + + +def myexpand(func, target): + expanded = expand_func(func) + if target is not None: + return expanded == target + if expanded == func: # it didn't expand + return False + + # check to see that the expanded and original evaluate to the same value + subs = {} + for a in func.free_symbols: + subs[a] = randcplx() + return abs(func.subs(subs).n() + - expanded.replace(exp_polar, exp).subs(subs).n()) < 1e-10 + + +def test_polylog_expansion(): + assert polylog(s, 0) == 0 + assert polylog(s, 1) == zeta(s) + assert polylog(s, -1) == -dirichlet_eta(s) + assert polylog(s, exp_polar(I*pi*Rational(4, 3))) == polylog(s, exp(I*pi*Rational(4, 3))) + assert polylog(s, exp_polar(I*pi)/3) == polylog(s, exp(I*pi)/3) + + assert myexpand(polylog(1, z), -log(1 - z)) + assert myexpand(polylog(0, z), z/(1 - z)) + assert myexpand(polylog(-1, z), z/(1 - z)**2) + assert ((1-z)**3 * expand_func(polylog(-2, z))).simplify() == z*(1 + z) + assert myexpand(polylog(-5, z), None) + + +def test_polylog_series(): + assert polylog(1, z).series(z, n=5) == z + z**2/2 + z**3/3 + z**4/4 + O(z**5) + assert polylog(1, sqrt(z)).series(z, n=3) == z/2 + z**2/4 + sqrt(z)\ + + z**(S(3)/2)/3 + z**(S(5)/2)/5 + O(z**3) + + # https://github.com/sympy/sympy/issues/9497 + assert polylog(S(3)/2, -z).series(z, 0, 5) == -z + sqrt(2)*z**2/4\ + - sqrt(3)*z**3/9 + z**4/8 + O(z**5) + + +def test_issue_8404(): + i = Symbol('i', integer=True) + assert Abs(Sum(1/(3*i + 1)**2, (i, 0, S.Infinity)).doit().n(4) + - 1.122) < 0.001 + + +def test_polylog_values(): + assert polylog(2, 2) == pi**2/4 - I*pi*log(2) + assert polylog(2, S.Half) == pi**2/12 - log(2)**2/2 + for z in [S.Half, 2, (sqrt(5)-1)/2, -(sqrt(5)-1)/2, -(sqrt(5)+1)/2, (3-sqrt(5))/2]: + assert Abs(polylog(2, z).evalf() - polylog(2, z, evaluate=False).evalf()) < 1e-15 + z = Symbol("z") + for s in [-1, 0]: + for _ in range(10): + assert verify_numerically(polylog(s, z), polylog(s, z, evaluate=False), + z, a=-3, b=-2, c=S.Half, d=2) + assert verify_numerically(polylog(s, z), polylog(s, z, evaluate=False), + z, a=2, b=-2, c=5, d=2) + + from sympy.integrals.integrals import Integral + assert polylog(0, Integral(1, (x, 0, 1))) == -S.Half + + +def test_lerchphi_expansion(): + assert myexpand(lerchphi(1, s, a), zeta(s, a)) + assert myexpand(lerchphi(z, s, 1), polylog(s, z)/z) + + # direct summation + assert myexpand(lerchphi(z, -1, a), a/(1 - z) + z/(1 - z)**2) + assert myexpand(lerchphi(z, -3, a), None) + # polylog reduction + assert myexpand(lerchphi(z, s, S.Half), + 2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z) + - polylog(s, polar_lift(-1)*sqrt(z))/sqrt(z))) + assert myexpand(lerchphi(z, s, 2), -1/z + polylog(s, z)/z**2) + assert myexpand(lerchphi(z, s, Rational(3, 2)), None) + assert myexpand(lerchphi(z, s, Rational(7, 3)), None) + assert myexpand(lerchphi(z, s, Rational(-1, 3)), None) + assert myexpand(lerchphi(z, s, Rational(-5, 2)), None) + + # hurwitz zeta reduction + assert myexpand(lerchphi(-1, s, a), + 2**(-s)*zeta(s, a/2) - 2**(-s)*zeta(s, (a + 1)/2)) + assert myexpand(lerchphi(I, s, a), None) + assert myexpand(lerchphi(-I, s, a), None) + assert myexpand(lerchphi(exp(I*pi*Rational(2, 5)), s, a), None) + + +def test_stieltjes(): + assert isinstance(stieltjes(x), stieltjes) + assert isinstance(stieltjes(x, a), stieltjes) + + # Zero'th constant EulerGamma + assert stieltjes(0) == S.EulerGamma + assert stieltjes(0, 1) == S.EulerGamma + + # Not defined + assert stieltjes(nan) is nan + assert stieltjes(0, nan) is nan + assert stieltjes(-1) is S.ComplexInfinity + assert stieltjes(1.5) is S.ComplexInfinity + assert stieltjes(z, 0) is S.ComplexInfinity + assert stieltjes(z, -1) is S.ComplexInfinity + + +def test_stieltjes_evalf(): + assert abs(stieltjes(0).evalf() - 0.577215664) < 1E-9 + assert abs(stieltjes(0, 0.5).evalf() - 1.963510026) < 1E-9 + assert abs(stieltjes(1, 2).evalf() + 0.072815845) < 1E-9 + + +def test_issue_10475(): + a = Symbol('a', extended_real=True) + b = Symbol('b', extended_positive=True) + s = Symbol('s', zero=False) + + assert zeta(2 + I).is_finite + assert zeta(1).is_finite is False + assert zeta(x).is_finite is None + assert zeta(x + I).is_finite is None + assert zeta(a).is_finite is None + assert zeta(b).is_finite is None + assert zeta(-b).is_finite is True + assert zeta(b**2 - 2*b + 1).is_finite is None + assert zeta(a + I).is_finite is True + assert zeta(b + 1).is_finite is True + assert zeta(s + 1).is_finite is True + + +def test_issue_14177(): + n = Symbol('n', nonnegative=True, integer=True) + + assert zeta(-n).rewrite(bernoulli) == bernoulli(n+1) / (-n-1) + assert zeta(-n, a).rewrite(bernoulli) == bernoulli(n+1, a) / (-n-1) + z2n = -(2*I*pi)**(2*n)*bernoulli(2*n) / (2*factorial(2*n)) + assert zeta(2*n).rewrite(bernoulli) == z2n + assert expand_func(zeta(s, n+1)) == zeta(s) - harmonic(n, s) + assert expand_func(zeta(-b, -n)) is nan + assert expand_func(zeta(-b, n)) == zeta(-b, n) + + n = Symbol('n') + + assert zeta(2*n) == zeta(2*n) # As sign of z (= 2*n) is not determined diff --git a/lib/python3.11/site-packages/sympy/functions/special/zeta_functions.py b/lib/python3.11/site-packages/sympy/functions/special/zeta_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..430cafecde534bddd89c5e71306905654af65cb2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/functions/special/zeta_functions.py @@ -0,0 +1,787 @@ +""" Riemann zeta and related function. """ + +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.function import ArgumentIndexError, expand_mul, Function +from sympy.core.numbers import pi, I, Integer +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import Dummy +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic +from sympy.functions.elementary.complexes import re, unpolarify, Abs, polar_lift +from sympy.functions.elementary.exponential import log, exp_polar, exp +from sympy.functions.elementary.integers import ceiling, floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.polys.polytools import Poly + +############################################################################### +###################### LERCH TRANSCENDENT ##################################### +############################################################################### + + +class lerchphi(Function): + r""" + Lerch transcendent (Lerch phi function). + + Explanation + =========== + + For $\operatorname{Re}(a) > 0$, $|z| < 1$ and $s \in \mathbb{C}$, the + Lerch transcendent is defined as + + .. math :: \Phi(z, s, a) = \sum_{n=0}^\infty \frac{z^n}{(n + a)^s}, + + where the standard branch of the argument is used for $n + a$, + and by analytic continuation for other values of the parameters. + + A commonly used related function is the Lerch zeta function, defined by + + .. math:: L(q, s, a) = \Phi(e^{2\pi i q}, s, a). + + **Analytic Continuation and Branching Behavior** + + It can be shown that + + .. math:: \Phi(z, s, a) = z\Phi(z, s, a+1) + a^{-s}. + + This provides the analytic continuation to $\operatorname{Re}(a) \le 0$. + + Assume now $\operatorname{Re}(a) > 0$. The integral representation + + .. math:: \Phi_0(z, s, a) = \int_0^\infty \frac{t^{s-1} e^{-at}}{1 - ze^{-t}} + \frac{\mathrm{d}t}{\Gamma(s)} + + provides an analytic continuation to $\mathbb{C} - [1, \infty)$. + Finally, for $x \in (1, \infty)$ we find + + .. math:: \lim_{\epsilon \to 0^+} \Phi_0(x + i\epsilon, s, a) + -\lim_{\epsilon \to 0^+} \Phi_0(x - i\epsilon, s, a) + = \frac{2\pi i \log^{s-1}{x}}{x^a \Gamma(s)}, + + using the standard branch for both $\log{x}$ and + $\log{\log{x}}$ (a branch of $\log{\log{x}}$ is needed to + evaluate $\log{x}^{s-1}$). + This concludes the analytic continuation. The Lerch transcendent is thus + branched at $z \in \{0, 1, \infty\}$ and + $a \in \mathbb{Z}_{\le 0}$. For fixed $z, a$ outside these + branch points, it is an entire function of $s$. + + Examples + ======== + + The Lerch transcendent is a fairly general function, for this reason it does + not automatically evaluate to simpler functions. Use ``expand_func()`` to + achieve this. + + If $z=1$, the Lerch transcendent reduces to the Hurwitz zeta function: + + >>> from sympy import lerchphi, expand_func + >>> from sympy.abc import z, s, a + >>> expand_func(lerchphi(1, s, a)) + zeta(s, a) + + More generally, if $z$ is a root of unity, the Lerch transcendent + reduces to a sum of Hurwitz zeta functions: + + >>> expand_func(lerchphi(-1, s, a)) + zeta(s, a/2)/2**s - zeta(s, a/2 + 1/2)/2**s + + If $a=1$, the Lerch transcendent reduces to the polylogarithm: + + >>> expand_func(lerchphi(z, s, 1)) + polylog(s, z)/z + + More generally, if $a$ is rational, the Lerch transcendent reduces + to a sum of polylogarithms: + + >>> from sympy import S + >>> expand_func(lerchphi(z, s, S(1)/2)) + 2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z) - + polylog(s, sqrt(z)*exp_polar(I*pi))/sqrt(z)) + >>> expand_func(lerchphi(z, s, S(3)/2)) + -2**s/z + 2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z) - + polylog(s, sqrt(z)*exp_polar(I*pi))/sqrt(z))/z + + The derivatives with respect to $z$ and $a$ can be computed in + closed form: + + >>> lerchphi(z, s, a).diff(z) + (-a*lerchphi(z, s, a) + lerchphi(z, s - 1, a))/z + >>> lerchphi(z, s, a).diff(a) + -s*lerchphi(z, s + 1, a) + + See Also + ======== + + polylog, zeta + + References + ========== + + .. [1] Bateman, H.; Erdelyi, A. (1953), Higher Transcendental Functions, + Vol. I, New York: McGraw-Hill. Section 1.11. + .. [2] https://dlmf.nist.gov/25.14 + .. [3] https://en.wikipedia.org/wiki/Lerch_transcendent + + """ + + def _eval_expand_func(self, **hints): + z, s, a = self.args + if z == 1: + return zeta(s, a) + if s.is_Integer and s <= 0: + t = Dummy('t') + p = Poly((t + a)**(-s), t) + start = 1/(1 - t) + res = S.Zero + for c in reversed(p.all_coeffs()): + res += c*start + start = t*start.diff(t) + return res.subs(t, z) + + if a.is_Rational: + # See section 18 of + # Kelly B. Roach. Hypergeometric Function Representations. + # In: Proceedings of the 1997 International Symposium on Symbolic and + # Algebraic Computation, pages 205-211, New York, 1997. ACM. + # TODO should something be polarified here? + add = S.Zero + mul = S.One + # First reduce a to the interaval (0, 1] + if a > 1: + n = floor(a) + if n == a: + n -= 1 + a -= n + mul = z**(-n) + add = Add(*[-z**(k - n)/(a + k)**s for k in range(n)]) + elif a <= 0: + n = floor(-a) + 1 + a += n + mul = z**n + add = Add(*[z**(n - 1 - k)/(a - k - 1)**s for k in range(n)]) + + m, n = S([a.p, a.q]) + zet = exp_polar(2*pi*I/n) + root = z**(1/n) + up_zet = unpolarify(zet) + addargs = [] + for k in range(n): + p = polylog(s, zet**k*root) + if isinstance(p, polylog): + p = p._eval_expand_func(**hints) + addargs.append(p/(up_zet**k*root)**m) + return add + mul*n**(s - 1)*Add(*addargs) + + # TODO use minpoly instead of ad-hoc methods when issue 5888 is fixed + if isinstance(z, exp) and (z.args[0]/(pi*I)).is_Rational or z in [-1, I, -I]: + # TODO reference? + if z == -1: + p, q = S([1, 2]) + elif z == I: + p, q = S([1, 4]) + elif z == -I: + p, q = S([-1, 4]) + else: + arg = z.args[0]/(2*pi*I) + p, q = S([arg.p, arg.q]) + return Add(*[exp(2*pi*I*k*p/q)/q**s*zeta(s, (k + a)/q) + for k in range(q)]) + + return lerchphi(z, s, a) + + def fdiff(self, argindex=1): + z, s, a = self.args + if argindex == 3: + return -s*lerchphi(z, s + 1, a) + elif argindex == 1: + return (lerchphi(z, s - 1, a) - a*lerchphi(z, s, a))/z + else: + raise ArgumentIndexError + + def _eval_rewrite_helper(self, target): + res = self._eval_expand_func() + if res.has(target): + return res + else: + return self + + def _eval_rewrite_as_zeta(self, z, s, a, **kwargs): + return self._eval_rewrite_helper(zeta) + + def _eval_rewrite_as_polylog(self, z, s, a, **kwargs): + return self._eval_rewrite_helper(polylog) + +############################################################################### +###################### POLYLOGARITHM ########################################## +############################################################################### + + +class polylog(Function): + r""" + Polylogarithm function. + + Explanation + =========== + + For $|z| < 1$ and $s \in \mathbb{C}$, the polylogarithm is + defined by + + .. math:: \operatorname{Li}_s(z) = \sum_{n=1}^\infty \frac{z^n}{n^s}, + + where the standard branch of the argument is used for $n$. It admits + an analytic continuation which is branched at $z=1$ (notably not on the + sheet of initial definition), $z=0$ and $z=\infty$. + + The name polylogarithm comes from the fact that for $s=1$, the + polylogarithm is related to the ordinary logarithm (see examples), and that + + .. math:: \operatorname{Li}_{s+1}(z) = + \int_0^z \frac{\operatorname{Li}_s(t)}{t} \mathrm{d}t. + + The polylogarithm is a special case of the Lerch transcendent: + + .. math:: \operatorname{Li}_{s}(z) = z \Phi(z, s, 1). + + Examples + ======== + + For $z \in \{0, 1, -1\}$, the polylogarithm is automatically expressed + using other functions: + + >>> from sympy import polylog + >>> from sympy.abc import s + >>> polylog(s, 0) + 0 + >>> polylog(s, 1) + zeta(s) + >>> polylog(s, -1) + -dirichlet_eta(s) + + If $s$ is a negative integer, $0$ or $1$, the polylogarithm can be + expressed using elementary functions. This can be done using + ``expand_func()``: + + >>> from sympy import expand_func + >>> from sympy.abc import z + >>> expand_func(polylog(1, z)) + -log(1 - z) + >>> expand_func(polylog(0, z)) + z/(1 - z) + + The derivative with respect to $z$ can be computed in closed form: + + >>> polylog(s, z).diff(z) + polylog(s - 1, z)/z + + The polylogarithm can be expressed in terms of the lerch transcendent: + + >>> from sympy import lerchphi + >>> polylog(s, z).rewrite(lerchphi) + z*lerchphi(z, s, 1) + + See Also + ======== + + zeta, lerchphi + + """ + + @classmethod + def eval(cls, s, z): + if z.is_number: + if z is S.One: + return zeta(s) + elif z is S.NegativeOne: + return -dirichlet_eta(s) + elif z is S.Zero: + return S.Zero + elif s == 2: + dilogtable = _dilogtable() + if z in dilogtable: + return dilogtable[z] + + if z.is_zero: + return S.Zero + + # Make an effort to determine if z is 1 to avoid replacing into + # expression with singularity + zone = z.equals(S.One) + + if zone: + return zeta(s) + elif zone is False: + # For s = 0 or -1 use explicit formulas to evaluate, but + # automatically expanding polylog(1, z) to -log(1-z) seems + # undesirable for summation methods based on hypergeometric + # functions + if s is S.Zero: + return z/(1 - z) + elif s is S.NegativeOne: + return z/(1 - z)**2 + if s.is_zero: + return z/(1 - z) + + # polylog is branched, but not over the unit disk + if z.has(exp_polar, polar_lift) and (zone or (Abs(z) <= S.One) == True): + return cls(s, unpolarify(z)) + + def fdiff(self, argindex=1): + s, z = self.args + if argindex == 2: + return polylog(s - 1, z)/z + raise ArgumentIndexError + + def _eval_rewrite_as_lerchphi(self, s, z, **kwargs): + return z*lerchphi(z, s, 1) + + def _eval_expand_func(self, **hints): + s, z = self.args + if s == 1: + return -log(1 - z) + if s.is_Integer and s <= 0: + u = Dummy('u') + start = u/(1 - u) + for _ in range(-s): + start = u*start.diff(u) + return expand_mul(start).subs(u, z) + return polylog(s, z) + + def _eval_is_zero(self): + z = self.args[1] + if z.is_zero: + return True + + def _eval_nseries(self, x, n, logx, cdir=0): + from sympy.series.order import Order + nu, z = self.args + + z0 = z.subs(x, 0) + if z0 is S.NaN: + z0 = z.limit(x, 0, dir='-' if re(cdir).is_negative else '+') + + if z0.is_zero: + # In case of powers less than 1, number of terms need to be computed + # separately to avoid repeated callings of _eval_nseries with wrong n + try: + _, exp = z.leadterm(x) + except (ValueError, NotImplementedError): + return self + + if exp.is_positive: + newn = ceiling(n/exp) + o = Order(x**n, x) + r = z._eval_nseries(x, n, logx, cdir).removeO() + if r is S.Zero: + return o + + term = r + s = [term] + for k in range(2, newn): + term *= r + s.append(term/k**nu) + return Add(*s) + o + + return super(polylog, self)._eval_nseries(x, n, logx, cdir) + +############################################################################### +###################### HURWITZ GENERALIZED ZETA FUNCTION ###################### +############################################################################### + + +class zeta(Function): + r""" + Hurwitz zeta function (or Riemann zeta function). + + Explanation + =========== + + For $\operatorname{Re}(a) > 0$ and $\operatorname{Re}(s) > 1$, this + function is defined as + + .. math:: \zeta(s, a) = \sum_{n=0}^\infty \frac{1}{(n + a)^s}, + + where the standard choice of argument for $n + a$ is used. For fixed + $a$ not a nonpositive integer the Hurwitz zeta function admits a + meromorphic continuation to all of $\mathbb{C}$; it is an unbranched + function with a simple pole at $s = 1$. + + The Hurwitz zeta function is a special case of the Lerch transcendent: + + .. math:: \zeta(s, a) = \Phi(1, s, a). + + This formula defines an analytic continuation for all possible values of + $s$ and $a$ (also $\operatorname{Re}(a) < 0$), see the documentation of + :class:`lerchphi` for a description of the branching behavior. + + If no value is passed for $a$ a default value of $a = 1$ is assumed, + yielding the Riemann zeta function. + + Examples + ======== + + For $a = 1$ the Hurwitz zeta function reduces to the famous Riemann + zeta function: + + .. math:: \zeta(s, 1) = \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}. + + >>> from sympy import zeta + >>> from sympy.abc import s + >>> zeta(s, 1) + zeta(s) + >>> zeta(s) + zeta(s) + + The Riemann zeta function can also be expressed using the Dirichlet eta + function: + + >>> from sympy import dirichlet_eta + >>> zeta(s).rewrite(dirichlet_eta) + dirichlet_eta(s)/(1 - 2**(1 - s)) + + The Riemann zeta function at nonnegative even and negative integer + values is related to the Bernoulli numbers and polynomials: + + >>> zeta(2) + pi**2/6 + >>> zeta(4) + pi**4/90 + >>> zeta(0) + -1/2 + >>> zeta(-1) + -1/12 + >>> zeta(-4) + 0 + + The specific formulae are: + + .. math:: \zeta(2n) = -\frac{(2\pi i)^{2n} B_{2n}}{2(2n)!} + .. math:: \zeta(-n,a) = -\frac{B_{n+1}(a)}{n+1} + + No closed-form expressions are known at positive odd integers, but + numerical evaluation is possible: + + >>> zeta(3).n() + 1.20205690315959 + + The derivative of $\zeta(s, a)$ with respect to $a$ can be computed: + + >>> from sympy.abc import a + >>> zeta(s, a).diff(a) + -s*zeta(s + 1, a) + + However the derivative with respect to $s$ has no useful closed form + expression: + + >>> zeta(s, a).diff(s) + Derivative(zeta(s, a), s) + + The Hurwitz zeta function can be expressed in terms of the Lerch + transcendent, :class:`~.lerchphi`: + + >>> from sympy import lerchphi + >>> zeta(s, a).rewrite(lerchphi) + lerchphi(1, s, a) + + See Also + ======== + + dirichlet_eta, lerchphi, polylog + + References + ========== + + .. [1] https://dlmf.nist.gov/25.11 + .. [2] https://en.wikipedia.org/wiki/Hurwitz_zeta_function + + """ + + @classmethod + def eval(cls, s, a=None): + if a is S.One: + return cls(s) + elif s is S.NaN or a is S.NaN: + return S.NaN + elif s is S.One: + return S.ComplexInfinity + elif s is S.Infinity: + return S.One + elif a is S.Infinity: + return S.Zero + + sint = s.is_Integer + if a is None: + a = S.One + if sint and s.is_nonpositive: + return bernoulli(1-s, a) / (s-1) + elif a is S.One: + if sint and s.is_even: + return -(2*pi*I)**s * bernoulli(s) / (2*factorial(s)) + elif sint and a.is_Integer and a.is_positive: + return cls(s) - harmonic(a-1, s) + elif a.is_Integer and a.is_nonpositive and \ + (s.is_integer is False or s.is_nonpositive is False): + return S.NaN + + def _eval_rewrite_as_bernoulli(self, s, a=1, **kwargs): + if a == 1 and s.is_integer and s.is_nonnegative and s.is_even: + return -(2*pi*I)**s * bernoulli(s) / (2*factorial(s)) + return bernoulli(1-s, a) / (s-1) + + def _eval_rewrite_as_dirichlet_eta(self, s, a=1, **kwargs): + if a != 1: + return self + s = self.args[0] + return dirichlet_eta(s)/(1 - 2**(1 - s)) + + def _eval_rewrite_as_lerchphi(self, s, a=1, **kwargs): + return lerchphi(1, s, a) + + def _eval_is_finite(self): + arg_is_one = (self.args[0] - 1).is_zero + if arg_is_one is not None: + return not arg_is_one + + def _eval_expand_func(self, **hints): + s = self.args[0] + a = self.args[1] if len(self.args) > 1 else S.One + if a.is_integer: + if a.is_positive: + return zeta(s) - harmonic(a-1, s) + if a.is_nonpositive and (s.is_integer is False or + s.is_nonpositive is False): + return S.NaN + return self + + def fdiff(self, argindex=1): + if len(self.args) == 2: + s, a = self.args + else: + s, a = self.args + (1,) + if argindex == 2: + return -s*zeta(s + 1, a) + else: + raise ArgumentIndexError + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + if len(self.args) == 2: + s, a = self.args + else: + s, a = self.args + (S.One,) + + try: + c, e = a.leadterm(x) + except NotImplementedError: + return self + + if e.is_negative and not s.is_positive: + raise NotImplementedError + + return super(zeta, self)._eval_as_leading_term(x, logx, cdir) + + +class dirichlet_eta(Function): + r""" + Dirichlet eta function. + + Explanation + =========== + + For $\operatorname{Re}(s) > 0$ and $0 < x \le 1$, this function is defined as + + .. math:: \eta(s, a) = \sum_{n=0}^\infty \frac{(-1)^n}{(n+a)^s}. + + It admits a unique analytic continuation to all of $\mathbb{C}$ for any + fixed $a$ not a nonpositive integer. It is an entire, unbranched function. + + It can be expressed using the Hurwitz zeta function as + + .. math:: \eta(s, a) = \zeta(s,a) - 2^{1-s} \zeta\left(s, \frac{a+1}{2}\right) + + and using the generalized Genocchi function as + + .. math:: \eta(s, a) = \frac{G(1-s, a)}{2(s-1)}. + + In both cases the limiting value of $\log2 - \psi(a) + \psi\left(\frac{a+1}{2}\right)$ + is used when $s = 1$. + + Examples + ======== + + >>> from sympy import dirichlet_eta, zeta + >>> from sympy.abc import s + >>> dirichlet_eta(s).rewrite(zeta) + Piecewise((log(2), Eq(s, 1)), ((1 - 2**(1 - s))*zeta(s), True)) + + See Also + ======== + + zeta + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Dirichlet_eta_function + .. [2] Peter Luschny, "An introduction to the Bernoulli function", + https://arxiv.org/abs/2009.06743 + + """ + + @classmethod + def eval(cls, s, a=None): + if a is S.One: + return cls(s) + if a is None: + if s == 1: + return log(2) + z = zeta(s) + if not z.has(zeta): + return (1 - 2**(1-s)) * z + return + elif s == 1: + from sympy.functions.special.gamma_functions import digamma + return log(2) - digamma(a) + digamma((a+1)/2) + z1 = zeta(s, a) + z2 = zeta(s, (a+1)/2) + if not z1.has(zeta) and not z2.has(zeta): + return z1 - 2**(1-s) * z2 + + def _eval_rewrite_as_zeta(self, s, a=1, **kwargs): + from sympy.functions.special.gamma_functions import digamma + if a == 1: + return Piecewise((log(2), Eq(s, 1)), ((1 - 2**(1-s)) * zeta(s), True)) + return Piecewise((log(2) - digamma(a) + digamma((a+1)/2), Eq(s, 1)), + (zeta(s, a) - 2**(1-s) * zeta(s, (a+1)/2), True)) + + def _eval_rewrite_as_genocchi(self, s, a=S.One, **kwargs): + from sympy.functions.special.gamma_functions import digamma + return Piecewise((log(2) - digamma(a) + digamma((a+1)/2), Eq(s, 1)), + (genocchi(1-s, a) / (2 * (s-1)), True)) + + def _eval_evalf(self, prec): + if all(i.is_number for i in self.args): + return self.rewrite(zeta)._eval_evalf(prec) + + +class riemann_xi(Function): + r""" + Riemann Xi function. + + Examples + ======== + + The Riemann Xi function is closely related to the Riemann zeta function. + The zeros of Riemann Xi function are precisely the non-trivial zeros + of the zeta function. + + >>> from sympy import riemann_xi, zeta + >>> from sympy.abc import s + >>> riemann_xi(s).rewrite(zeta) + s*(s - 1)*gamma(s/2)*zeta(s)/(2*pi**(s/2)) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Riemann_Xi_function + + """ + + + @classmethod + def eval(cls, s): + from sympy.functions.special.gamma_functions import gamma + z = zeta(s) + if s in (S.Zero, S.One): + return S.Half + + if not isinstance(z, zeta): + return s*(s - 1)*gamma(s/2)*z/(2*pi**(s/2)) + + def _eval_rewrite_as_zeta(self, s, **kwargs): + from sympy.functions.special.gamma_functions import gamma + return s*(s - 1)*gamma(s/2)*zeta(s)/(2*pi**(s/2)) + + +class stieltjes(Function): + r""" + Represents Stieltjes constants, $\gamma_{k}$ that occur in + Laurent Series expansion of the Riemann zeta function. + + Examples + ======== + + >>> from sympy import stieltjes + >>> from sympy.abc import n, m + >>> stieltjes(n) + stieltjes(n) + + The zero'th stieltjes constant: + + >>> stieltjes(0) + EulerGamma + >>> stieltjes(0, 1) + EulerGamma + + For generalized stieltjes constants: + + >>> stieltjes(n, m) + stieltjes(n, m) + + Constants are only defined for integers >= 0: + + >>> stieltjes(-1) + zoo + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Stieltjes_constants + + """ + + @classmethod + def eval(cls, n, a=None): + if a is not None: + a = sympify(a) + if a is S.NaN: + return S.NaN + if a.is_Integer and a.is_nonpositive: + return S.ComplexInfinity + + if n.is_Number: + if n is S.NaN: + return S.NaN + elif n < 0: + return S.ComplexInfinity + elif not n.is_Integer: + return S.ComplexInfinity + elif n is S.Zero and a in [None, 1]: + return S.EulerGamma + + if n.is_extended_negative: + return S.ComplexInfinity + + if n.is_zero and a in [None, 1]: + return S.EulerGamma + + if n.is_integer == False: + return S.ComplexInfinity + + +@cacheit +def _dilogtable(): + return { + S.Half: pi**2/12 - log(2)**2/2, + Integer(2) : pi**2/4 - I*pi*log(2), + -(sqrt(5) - 1)/2 : -pi**2/15 + log((sqrt(5)-1)/2)**2/2, + -(sqrt(5) + 1)/2 : -pi**2/10 - log((sqrt(5)+1)/2)**2, + (3 - sqrt(5))/2 : pi**2/15 - log((sqrt(5)-1)/2)**2, + (sqrt(5) - 1)/2 : pi**2/10 - log((sqrt(5)-1)/2)**2, + I : I*S.Catalan - pi**2/48, + -I : -I*S.Catalan - pi**2/48, + 1 - I : pi**2/16 - I*S.Catalan - pi*I/4*log(2), + 1 + I : pi**2/16 + I*S.Catalan + pi*I/4*log(2), + (1 - I)/2 : -log(2)**2/8 + pi*I*log(2)/8 + 5*pi**2/96 - I*S.Catalan + } diff --git a/lib/python3.11/site-packages/sympy/galgebra.py b/lib/python3.11/site-packages/sympy/galgebra.py new file mode 100644 index 0000000000000000000000000000000000000000..be812bfcbcece834c86d7b55eb846286acd0ac08 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/galgebra.py @@ -0,0 +1 @@ +raise ImportError("""As of SymPy 1.0 the galgebra module is maintained separately at https://github.com/pygae/galgebra""") diff --git a/lib/python3.11/site-packages/sympy/geometry/__init__.py b/lib/python3.11/site-packages/sympy/geometry/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..bb85d4ff5d53eb44a039a95cfc2fff687322cc76 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/__init__.py @@ -0,0 +1,45 @@ +""" +A geometry module for the SymPy library. This module contains all of the +entities and functions needed to construct basic geometrical data and to +perform simple informational queries. + +Usage: +====== + +Examples +======== + +""" +from sympy.geometry.point import Point, Point2D, Point3D +from sympy.geometry.line import Line, Ray, Segment, Line2D, Segment2D, Ray2D, \ + Line3D, Segment3D, Ray3D +from sympy.geometry.plane import Plane +from sympy.geometry.ellipse import Ellipse, Circle +from sympy.geometry.polygon import Polygon, RegularPolygon, Triangle, rad, deg +from sympy.geometry.util import are_similar, centroid, convex_hull, idiff, \ + intersection, closest_points, farthest_points +from sympy.geometry.exceptions import GeometryError +from sympy.geometry.curve import Curve +from sympy.geometry.parabola import Parabola + +__all__ = [ + 'Point', 'Point2D', 'Point3D', + + 'Line', 'Ray', 'Segment', 'Line2D', 'Segment2D', 'Ray2D', 'Line3D', + 'Segment3D', 'Ray3D', + + 'Plane', + + 'Ellipse', 'Circle', + + 'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg', + + 'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection', + 'closest_points', 'farthest_points', + + 'GeometryError', + + 'Curve', + + 'Parabola', +] diff --git a/lib/python3.11/site-packages/sympy/geometry/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/geometry/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ca6e996dda6be32cfcfacb4a99a114752cd2e4e9 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/geometry/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/geometry/__pycache__/curve.cpython-311.pyc b/lib/python3.11/site-packages/sympy/geometry/__pycache__/curve.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..13d4e73db2fd2a9397d5f0fdd81c73dcf2c9947a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/geometry/__pycache__/curve.cpython-311.pyc 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import integrate +from sympy.matrices import Matrix, rot_axis3 +from sympy.utilities.iterables import is_sequence + +from mpmath.libmp.libmpf import prec_to_dps + + +class Curve(GeometrySet): + """A curve in space. + + A curve is defined by parametric functions for the coordinates, a + parameter and the lower and upper bounds for the parameter value. + + Parameters + ========== + + function : list of functions + limits : 3-tuple + Function parameter and lower and upper bounds. + + Attributes + ========== + + functions + parameter + limits + + Raises + ====== + + ValueError + When `functions` are specified incorrectly. + When `limits` are specified incorrectly. + + Examples + ======== + + >>> from sympy import Curve, sin, cos, interpolate + >>> from sympy.abc import t, a + >>> C = Curve((sin(t), cos(t)), (t, 0, 2)) + >>> C.functions + (sin(t), cos(t)) + >>> C.limits + (t, 0, 2) + >>> C.parameter + t + >>> C = Curve((t, interpolate([1, 4, 9, 16], t)), (t, 0, 1)); C + Curve((t, t**2), (t, 0, 1)) + >>> C.subs(t, 4) + Point2D(4, 16) + >>> C.arbitrary_point(a) + Point2D(a, a**2) + + See Also + ======== + + sympy.core.function.Function + sympy.polys.polyfuncs.interpolate + + """ + + def __new__(cls, function, limits): + if not is_sequence(function) or len(function) != 2: + raise ValueError("Function argument should be (x(t), y(t)) " + "but got %s" % str(function)) + if not is_sequence(limits) or len(limits) != 3: + raise ValueError("Limit argument should be (t, tmin, tmax) " + "but got %s" % str(limits)) + + return GeometryEntity.__new__(cls, Tuple(*function), Tuple(*limits)) + + def __call__(self, f): + return self.subs(self.parameter, f) + + def _eval_subs(self, old, new): + if old == self.parameter: + return Point(*[f.subs(old, new) for f in self.functions]) + + def _eval_evalf(self, prec=15, **options): + f, (t, a, b) = self.args + dps = prec_to_dps(prec) + f = tuple([i.evalf(n=dps, **options) for i in f]) + a, b = [i.evalf(n=dps, **options) for i in (a, b)] + return self.func(f, (t, a, b)) + + def arbitrary_point(self, parameter='t'): + """A parameterized point on the curve. + + Parameters + ========== + + parameter : str or Symbol, optional + Default value is 't'. + The Curve's parameter is selected with None or self.parameter + otherwise the provided symbol is used. + + Returns + ======= + + Point : + Returns a point in parametric form. + + Raises + ====== + + ValueError + When `parameter` already appears in the functions. + + Examples + ======== + + >>> from sympy import Curve, Symbol + >>> from sympy.abc import s + >>> C = Curve([2*s, s**2], (s, 0, 2)) + >>> C.arbitrary_point() + Point2D(2*t, t**2) + >>> C.arbitrary_point(C.parameter) + Point2D(2*s, s**2) + >>> C.arbitrary_point(None) + Point2D(2*s, s**2) + >>> C.arbitrary_point(Symbol('a')) + Point2D(2*a, a**2) + + See Also + ======== + + sympy.geometry.point.Point + + """ + if parameter is None: + return Point(*self.functions) + + tnew = _symbol(parameter, self.parameter, real=True) + t = self.parameter + if (tnew.name != t.name and + tnew.name in (f.name for f in self.free_symbols)): + raise ValueError('Symbol %s already appears in object ' + 'and cannot be used as a parameter.' % tnew.name) + return Point(*[w.subs(t, tnew) for w in self.functions]) + + @property + def free_symbols(self): + """Return a set of symbols other than the bound symbols used to + parametrically define the Curve. + + Returns + ======= + + set : + Set of all non-parameterized symbols. + + Examples + ======== + + >>> from sympy.abc import t, a + >>> from sympy import Curve + >>> Curve((t, t**2), (t, 0, 2)).free_symbols + set() + >>> Curve((t, t**2), (t, a, 2)).free_symbols + {a} + + """ + free = set() + for a in self.functions + self.limits[1:]: + free |= a.free_symbols + free = free.difference({self.parameter}) + return free + + @property + def ambient_dimension(self): + """The dimension of the curve. + + Returns + ======= + + int : + the dimension of curve. + + Examples + ======== + + >>> from sympy.abc import t + >>> from sympy import Curve + >>> C = Curve((t, t**2), (t, 0, 2)) + >>> C.ambient_dimension + 2 + + """ + + return len(self.args[0]) + + @property + def functions(self): + """The functions specifying the curve. + + Returns + ======= + + functions : + list of parameterized coordinate functions. + + Examples + ======== + + >>> from sympy.abc import t + >>> from sympy import Curve + >>> C = Curve((t, t**2), (t, 0, 2)) + >>> C.functions + (t, t**2) + + See Also + ======== + + parameter + + """ + return self.args[0] + + @property + def limits(self): + """The limits for the curve. + + Returns + ======= + + limits : tuple + Contains parameter and lower and upper limits. + + Examples + ======== + + >>> from sympy.abc import t + >>> from sympy import Curve + >>> C = Curve([t, t**3], (t, -2, 2)) + >>> C.limits + (t, -2, 2) + + See Also + ======== + + plot_interval + + """ + return self.args[1] + + @property + def parameter(self): + """The curve function variable. + + Returns + ======= + + Symbol : + returns a bound symbol. + + Examples + ======== + + >>> from sympy.abc import t + >>> from sympy import Curve + >>> C = Curve([t, t**2], (t, 0, 2)) + >>> C.parameter + t + + See Also + ======== + + functions + + """ + return self.args[1][0] + + @property + def length(self): + """The curve length. + + Examples + ======== + + >>> from sympy import Curve + >>> from sympy.abc import t + >>> Curve((t, t), (t, 0, 1)).length + sqrt(2) + + """ + integrand = sqrt(sum(diff(func, self.limits[0])**2 for func in self.functions)) + return integrate(integrand, self.limits) + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of the curve. + + Parameters + ========== + + parameter : str or Symbol, optional + Default value is 't'; + otherwise the provided symbol is used. + + Returns + ======= + + List : + the plot interval as below: + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Curve, sin + >>> from sympy.abc import x, s + >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval() + [t, 1, 2] + >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval(s) + [s, 1, 2] + + See Also + ======== + + limits : Returns limits of the parameter interval + + """ + t = _symbol(parameter, self.parameter, real=True) + return [t] + list(self.limits[1:]) + + def rotate(self, angle=0, pt=None): + """This function is used to rotate a curve along given point ``pt`` at given angle(in radian). + + Parameters + ========== + + angle : + the angle at which the curve will be rotated(in radian) in counterclockwise direction. + default value of angle is 0. + + pt : Point + the point along which the curve will be rotated. + If no point given, the curve will be rotated around origin. + + Returns + ======= + + Curve : + returns a curve rotated at given angle along given point. + + Examples + ======== + + >>> from sympy import Curve, pi + >>> from sympy.abc import x + >>> Curve((x, x), (x, 0, 1)).rotate(pi/2) + Curve((-x, x), (x, 0, 1)) + + """ + if pt: + pt = -Point(pt, dim=2) + else: + pt = Point(0,0) + rv = self.translate(*pt.args) + f = list(rv.functions) + f.append(0) + f = Matrix(1, 3, f) + f *= rot_axis3(angle) + rv = self.func(f[0, :2].tolist()[0], self.limits) + pt = -pt + return rv.translate(*pt.args) + + def scale(self, x=1, y=1, pt=None): + """Override GeometryEntity.scale since Curve is not made up of Points. + + Returns + ======= + + Curve : + returns scaled curve. + + Examples + ======== + + >>> from sympy import Curve + >>> from sympy.abc import x + >>> Curve((x, x), (x, 0, 1)).scale(2) + Curve((2*x, x), (x, 0, 1)) + + """ + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + fx, fy = self.functions + return self.func((fx*x, fy*y), self.limits) + + def translate(self, x=0, y=0): + """Translate the Curve by (x, y). + + Returns + ======= + + Curve : + returns a translated curve. + + Examples + ======== + + >>> from sympy import Curve + >>> from sympy.abc import x + >>> Curve((x, x), (x, 0, 1)).translate(1, 2) + Curve((x + 1, x + 2), (x, 0, 1)) + + """ + fx, fy = self.functions + return self.func((fx + x, fy + y), self.limits) diff --git a/lib/python3.11/site-packages/sympy/geometry/ellipse.py b/lib/python3.11/site-packages/sympy/geometry/ellipse.py new file mode 100644 index 0000000000000000000000000000000000000000..bd4902e5f55d23c245d816afc98d462ef06630cb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/ellipse.py @@ -0,0 +1,1767 @@ +"""Elliptical geometrical entities. + +Contains +* Ellipse +* Circle + +""" + +from sympy.core.expr import Expr +from sympy.core.relational import Eq +from sympy.core import S, pi, sympify +from sympy.core.evalf import N +from sympy.core.parameters import global_parameters +from sympy.core.logic import fuzzy_bool +from sympy.core.numbers import Rational, oo +from sympy.core.sorting import ordered +from sympy.core.symbol import Dummy, uniquely_named_symbol, _symbol +from sympy.simplify import simplify, trigsimp +from sympy.functions.elementary.miscellaneous import sqrt, Max +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.functions.special.elliptic_integrals import elliptic_e +from .entity import GeometryEntity, GeometrySet +from .exceptions import GeometryError +from .line import Line, Segment, Ray2D, Segment2D, Line2D, LinearEntity3D +from .point import Point, Point2D, Point3D +from .util import idiff, find +from sympy.polys import DomainError, Poly, PolynomialError +from sympy.polys.polyutils import _not_a_coeff, _nsort +from sympy.solvers import solve +from sympy.solvers.solveset import linear_coeffs +from sympy.utilities.misc import filldedent, func_name + +from mpmath.libmp.libmpf import prec_to_dps + +import random + +x, y = [Dummy('ellipse_dummy', real=True) for i in range(2)] + + +class Ellipse(GeometrySet): + """An elliptical GeometryEntity. + + Parameters + ========== + + center : Point, optional + Default value is Point(0, 0) + hradius : number or SymPy expression, optional + vradius : number or SymPy expression, optional + eccentricity : number or SymPy expression, optional + Two of `hradius`, `vradius` and `eccentricity` must be supplied to + create an Ellipse. The third is derived from the two supplied. + + Attributes + ========== + + center + hradius + vradius + area + circumference + eccentricity + periapsis + apoapsis + focus_distance + foci + + Raises + ====== + + GeometryError + When `hradius`, `vradius` and `eccentricity` are incorrectly supplied + as parameters. + TypeError + When `center` is not a Point. + + See Also + ======== + + Circle + + Notes + ----- + Constructed from a center and two radii, the first being the horizontal + radius (along the x-axis) and the second being the vertical radius (along + the y-axis). + + When symbolic value for hradius and vradius are used, any calculation that + refers to the foci or the major or minor axis will assume that the ellipse + has its major radius on the x-axis. If this is not true then a manual + rotation is necessary. + + Examples + ======== + + >>> from sympy import Ellipse, Point, Rational + >>> e1 = Ellipse(Point(0, 0), 5, 1) + >>> e1.hradius, e1.vradius + (5, 1) + >>> e2 = Ellipse(Point(3, 1), hradius=3, eccentricity=Rational(4, 5)) + >>> e2 + Ellipse(Point2D(3, 1), 3, 9/5) + + """ + + def __contains__(self, o): + if isinstance(o, Point): + res = self.equation(x, y).subs({x: o.x, y: o.y}) + return trigsimp(simplify(res)) is S.Zero + elif isinstance(o, Ellipse): + return self == o + return False + + def __eq__(self, o): + """Is the other GeometryEntity the same as this ellipse?""" + return isinstance(o, Ellipse) and (self.center == o.center and + self.hradius == o.hradius and + self.vradius == o.vradius) + + def __hash__(self): + return super().__hash__() + + def __new__( + cls, center=None, hradius=None, vradius=None, eccentricity=None, **kwargs): + + hradius = sympify(hradius) + vradius = sympify(vradius) + + if center is None: + center = Point(0, 0) + else: + if len(center) != 2: + raise ValueError('The center of "{}" must be a two dimensional point'.format(cls)) + center = Point(center, dim=2) + + if len(list(filter(lambda x: x is not None, (hradius, vradius, eccentricity)))) != 2: + raise ValueError(filldedent(''' + Exactly two arguments of "hradius", "vradius", and + "eccentricity" must not be None.''')) + + if eccentricity is not None: + eccentricity = sympify(eccentricity) + if eccentricity.is_negative: + raise GeometryError("Eccentricity of ellipse/circle should lie between [0, 1)") + elif hradius is None: + hradius = vradius / sqrt(1 - eccentricity**2) + elif vradius is None: + vradius = hradius * sqrt(1 - eccentricity**2) + + if hradius == vradius: + return Circle(center, hradius, **kwargs) + + if S.Zero in (hradius, vradius): + return Segment(Point(center[0] - hradius, center[1] - vradius), Point(center[0] + hradius, center[1] + vradius)) + + if hradius.is_real is False or vradius.is_real is False: + raise GeometryError("Invalid value encountered when computing hradius / vradius.") + + return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs) + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG ellipse element for the Ellipse. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + + c = N(self.center) + h, v = N(self.hradius), N(self.vradius) + return ( + '' + ).format(2. * scale_factor, fill_color, c.x, c.y, h, v) + + @property + def ambient_dimension(self): + return 2 + + @property + def apoapsis(self): + """The apoapsis of the ellipse. + + The greatest distance between the focus and the contour. + + Returns + ======= + + apoapsis : number + + See Also + ======== + + periapsis : Returns shortest distance between foci and contour + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.apoapsis + 2*sqrt(2) + 3 + + """ + return self.major * (1 + self.eccentricity) + + def arbitrary_point(self, parameter='t'): + """A parameterized point on the ellipse. + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + arbitrary_point : Point + + Raises + ====== + + ValueError + When `parameter` already appears in the functions. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e1 = Ellipse(Point(0, 0), 3, 2) + >>> e1.arbitrary_point() + Point2D(3*cos(t), 2*sin(t)) + + """ + t = _symbol(parameter, real=True) + if t.name in (f.name for f in self.free_symbols): + raise ValueError(filldedent('Symbol %s already appears in object ' + 'and cannot be used as a parameter.' % t.name)) + return Point(self.center.x + self.hradius*cos(t), + self.center.y + self.vradius*sin(t)) + + @property + def area(self): + """The area of the ellipse. + + Returns + ======= + + area : number + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.area + 3*pi + + """ + return simplify(S.Pi * self.hradius * self.vradius) + + @property + def bounds(self): + """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding + rectangle for the geometric figure. + + """ + + h, v = self.hradius, self.vradius + return (self.center.x - h, self.center.y - v, self.center.x + h, self.center.y + v) + + @property + def center(self): + """The center of the ellipse. + + Returns + ======= + + center : number + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.center + Point2D(0, 0) + + """ + return self.args[0] + + @property + def circumference(self): + """The circumference of the ellipse. + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.circumference + 12*elliptic_e(8/9) + + """ + if self.eccentricity == 1: + # degenerate + return 4*self.major + elif self.eccentricity == 0: + # circle + return 2*pi*self.hradius + else: + return 4*self.major*elliptic_e(self.eccentricity**2) + + @property + def eccentricity(self): + """The eccentricity of the ellipse. + + Returns + ======= + + eccentricity : number + + Examples + ======== + + >>> from sympy import Point, Ellipse, sqrt + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, sqrt(2)) + >>> e1.eccentricity + sqrt(7)/3 + + """ + return self.focus_distance / self.major + + def encloses_point(self, p): + """ + Return True if p is enclosed by (is inside of) self. + + Notes + ----- + Being on the border of self is considered False. + + Parameters + ========== + + p : Point + + Returns + ======= + + encloses_point : True, False or None + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Ellipse, S + >>> from sympy.abc import t + >>> e = Ellipse((0, 0), 3, 2) + >>> e.encloses_point((0, 0)) + True + >>> e.encloses_point(e.arbitrary_point(t).subs(t, S.Half)) + False + >>> e.encloses_point((4, 0)) + False + + """ + p = Point(p, dim=2) + if p in self: + return False + + if len(self.foci) == 2: + # if the combined distance from the foci to p (h1 + h2) is less + # than the combined distance from the foci to the minor axis + # (which is the same as the major axis length) then p is inside + # the ellipse + h1, h2 = [f.distance(p) for f in self.foci] + test = 2*self.major - (h1 + h2) + else: + test = self.radius - self.center.distance(p) + + return fuzzy_bool(test.is_positive) + + def equation(self, x='x', y='y', _slope=None): + """ + Returns the equation of an ellipse aligned with the x and y axes; + when slope is given, the equation returned corresponds to an ellipse + with a major axis having that slope. + + Parameters + ========== + + x : str, optional + Label for the x-axis. Default value is 'x'. + y : str, optional + Label for the y-axis. Default value is 'y'. + _slope : Expr, optional + The slope of the major axis. Ignored when 'None'. + + Returns + ======= + + equation : SymPy expression + + See Also + ======== + + arbitrary_point : Returns parameterized point on ellipse + + Examples + ======== + + >>> from sympy import Point, Ellipse, pi + >>> from sympy.abc import x, y + >>> e1 = Ellipse(Point(1, 0), 3, 2) + >>> eq1 = e1.equation(x, y); eq1 + y**2/4 + (x/3 - 1/3)**2 - 1 + >>> eq2 = e1.equation(x, y, _slope=1); eq2 + (-x + y + 1)**2/8 + (x + y - 1)**2/18 - 1 + + A point on e1 satisfies eq1. Let's use one on the x-axis: + + >>> p1 = e1.center + Point(e1.major, 0) + >>> assert eq1.subs(x, p1.x).subs(y, p1.y) == 0 + + When rotated the same as the rotated ellipse, about the center + point of the ellipse, it will satisfy the rotated ellipse's + equation, too: + + >>> r1 = p1.rotate(pi/4, e1.center) + >>> assert eq2.subs(x, r1.x).subs(y, r1.y) == 0 + + References + ========== + + .. [1] https://math.stackexchange.com/questions/108270/what-is-the-equation-of-an-ellipse-that-is-not-aligned-with-the-axis + .. [2] https://en.wikipedia.org/wiki/Ellipse#Shifted_ellipse + + """ + + x = _symbol(x, real=True) + y = _symbol(y, real=True) + + dx = x - self.center.x + dy = y - self.center.y + + if _slope is not None: + L = (dy - _slope*dx)**2 + l = (_slope*dy + dx)**2 + h = 1 + _slope**2 + b = h*self.major**2 + a = h*self.minor**2 + return l/b + L/a - 1 + + else: + t1 = (dx/self.hradius)**2 + t2 = (dy/self.vradius)**2 + return t1 + t2 - 1 + + def evolute(self, x='x', y='y'): + """The equation of evolute of the ellipse. + + Parameters + ========== + + x : str, optional + Label for the x-axis. Default value is 'x'. + y : str, optional + Label for the y-axis. Default value is 'y'. + + Returns + ======= + + equation : SymPy expression + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e1 = Ellipse(Point(1, 0), 3, 2) + >>> e1.evolute() + 2**(2/3)*y**(2/3) + (3*x - 3)**(2/3) - 5**(2/3) + """ + if len(self.args) != 3: + raise NotImplementedError('Evolute of arbitrary Ellipse is not supported.') + x = _symbol(x, real=True) + y = _symbol(y, real=True) + t1 = (self.hradius*(x - self.center.x))**Rational(2, 3) + t2 = (self.vradius*(y - self.center.y))**Rational(2, 3) + return t1 + t2 - (self.hradius**2 - self.vradius**2)**Rational(2, 3) + + @property + def foci(self): + """The foci of the ellipse. + + Notes + ----- + The foci can only be calculated if the major/minor axes are known. + + Raises + ====== + + ValueError + When the major and minor axis cannot be determined. + + See Also + ======== + + sympy.geometry.point.Point + focus_distance : Returns the distance between focus and center + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.foci + (Point2D(-2*sqrt(2), 0), Point2D(2*sqrt(2), 0)) + + """ + c = self.center + hr, vr = self.hradius, self.vradius + if hr == vr: + return (c, c) + + # calculate focus distance manually, since focus_distance calls this + # routine + fd = sqrt(self.major**2 - self.minor**2) + if hr == self.minor: + # foci on the y-axis + return (c + Point(0, -fd), c + Point(0, fd)) + elif hr == self.major: + # foci on the x-axis + return (c + Point(-fd, 0), c + Point(fd, 0)) + + @property + def focus_distance(self): + """The focal distance of the ellipse. + + The distance between the center and one focus. + + Returns + ======= + + focus_distance : number + + See Also + ======== + + foci + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.focus_distance + 2*sqrt(2) + + """ + return Point.distance(self.center, self.foci[0]) + + @property + def hradius(self): + """The horizontal radius of the ellipse. + + Returns + ======= + + hradius : number + + See Also + ======== + + vradius, major, minor + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.hradius + 3 + + """ + return self.args[1] + + def intersection(self, o): + """The intersection of this ellipse and another geometrical entity + `o`. + + Parameters + ========== + + o : GeometryEntity + + Returns + ======= + + intersection : list of GeometryEntity objects + + Notes + ----- + Currently supports intersections with Point, Line, Segment, Ray, + Circle and Ellipse types. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity + + Examples + ======== + + >>> from sympy import Ellipse, Point, Line + >>> e = Ellipse(Point(0, 0), 5, 7) + >>> e.intersection(Point(0, 0)) + [] + >>> e.intersection(Point(5, 0)) + [Point2D(5, 0)] + >>> e.intersection(Line(Point(0,0), Point(0, 1))) + [Point2D(0, -7), Point2D(0, 7)] + >>> e.intersection(Line(Point(5,0), Point(5, 1))) + [Point2D(5, 0)] + >>> e.intersection(Line(Point(6,0), Point(6, 1))) + [] + >>> e = Ellipse(Point(-1, 0), 4, 3) + >>> e.intersection(Ellipse(Point(1, 0), 4, 3)) + [Point2D(0, -3*sqrt(15)/4), Point2D(0, 3*sqrt(15)/4)] + >>> e.intersection(Ellipse(Point(5, 0), 4, 3)) + [Point2D(2, -3*sqrt(7)/4), Point2D(2, 3*sqrt(7)/4)] + >>> e.intersection(Ellipse(Point(100500, 0), 4, 3)) + [] + >>> e.intersection(Ellipse(Point(0, 0), 3, 4)) + [Point2D(3, 0), Point2D(-363/175, -48*sqrt(111)/175), Point2D(-363/175, 48*sqrt(111)/175)] + >>> e.intersection(Ellipse(Point(-1, 0), 3, 4)) + [Point2D(-17/5, -12/5), Point2D(-17/5, 12/5), Point2D(7/5, -12/5), Point2D(7/5, 12/5)] + """ + # TODO: Replace solve with nonlinsolve, when nonlinsolve will be able to solve in real domain + + if isinstance(o, Point): + if o in self: + return [o] + else: + return [] + + elif isinstance(o, (Segment2D, Ray2D)): + ellipse_equation = self.equation(x, y) + result = solve([ellipse_equation, Line( + o.points[0], o.points[1]).equation(x, y)], [x, y], + set=True)[1] + return list(ordered([Point(i) for i in result if i in o])) + + elif isinstance(o, Polygon): + return o.intersection(self) + + elif isinstance(o, (Ellipse, Line2D)): + if o == self: + return self + else: + ellipse_equation = self.equation(x, y) + return list(ordered([Point(i) for i in solve( + [ellipse_equation, o.equation(x, y)], [x, y], + set=True)[1]])) + elif isinstance(o, LinearEntity3D): + raise TypeError('Entity must be two dimensional, not three dimensional') + else: + raise TypeError('Intersection not handled for %s' % func_name(o)) + + def is_tangent(self, o): + """Is `o` tangent to the ellipse? + + Parameters + ========== + + o : GeometryEntity + An Ellipse, LinearEntity or Polygon + + Raises + ====== + + NotImplementedError + When the wrong type of argument is supplied. + + Returns + ======= + + is_tangent: boolean + True if o is tangent to the ellipse, False otherwise. + + See Also + ======== + + tangent_lines + + Examples + ======== + + >>> from sympy import Point, Ellipse, Line + >>> p0, p1, p2 = Point(0, 0), Point(3, 0), Point(3, 3) + >>> e1 = Ellipse(p0, 3, 2) + >>> l1 = Line(p1, p2) + >>> e1.is_tangent(l1) + True + + """ + if isinstance(o, Point2D): + return False + elif isinstance(o, Ellipse): + intersect = self.intersection(o) + if isinstance(intersect, Ellipse): + return True + elif intersect: + return all((self.tangent_lines(i)[0]).equals(o.tangent_lines(i)[0]) for i in intersect) + else: + return False + elif isinstance(o, Line2D): + hit = self.intersection(o) + if not hit: + return False + if len(hit) == 1: + return True + # might return None if it can't decide + return hit[0].equals(hit[1]) + elif isinstance(o, (Segment2D, Ray2D)): + intersect = self.intersection(o) + if len(intersect) == 1: + return o in self.tangent_lines(intersect[0])[0] + else: + return False + elif isinstance(o, Polygon): + return all(self.is_tangent(s) for s in o.sides) + elif isinstance(o, (LinearEntity3D, Point3D)): + raise TypeError('Entity must be two dimensional, not three dimensional') + else: + raise TypeError('Is_tangent not handled for %s' % func_name(o)) + + @property + def major(self): + """Longer axis of the ellipse (if it can be determined) else hradius. + + Returns + ======= + + major : number or expression + + See Also + ======== + + hradius, vradius, minor + + Examples + ======== + + >>> from sympy import Point, Ellipse, Symbol + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.major + 3 + + >>> a = Symbol('a') + >>> b = Symbol('b') + >>> Ellipse(p1, a, b).major + a + >>> Ellipse(p1, b, a).major + b + + >>> m = Symbol('m') + >>> M = m + 1 + >>> Ellipse(p1, m, M).major + m + 1 + + """ + ab = self.args[1:3] + if len(ab) == 1: + return ab[0] + a, b = ab + o = b - a < 0 + if o == True: + return a + elif o == False: + return b + return self.hradius + + @property + def minor(self): + """Shorter axis of the ellipse (if it can be determined) else vradius. + + Returns + ======= + + minor : number or expression + + See Also + ======== + + hradius, vradius, major + + Examples + ======== + + >>> from sympy import Point, Ellipse, Symbol + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.minor + 1 + + >>> a = Symbol('a') + >>> b = Symbol('b') + >>> Ellipse(p1, a, b).minor + b + >>> Ellipse(p1, b, a).minor + a + + >>> m = Symbol('m') + >>> M = m + 1 + >>> Ellipse(p1, m, M).minor + m + + """ + ab = self.args[1:3] + if len(ab) == 1: + return ab[0] + a, b = ab + o = a - b < 0 + if o == True: + return a + elif o == False: + return b + return self.vradius + + def normal_lines(self, p, prec=None): + """Normal lines between `p` and the ellipse. + + Parameters + ========== + + p : Point + + Returns + ======= + + normal_lines : list with 1, 2 or 4 Lines + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e = Ellipse((0, 0), 2, 3) + >>> c = e.center + >>> e.normal_lines(c + Point(1, 0)) + [Line2D(Point2D(0, 0), Point2D(1, 0))] + >>> e.normal_lines(c) + [Line2D(Point2D(0, 0), Point2D(0, 1)), Line2D(Point2D(0, 0), Point2D(1, 0))] + + Off-axis points require the solution of a quartic equation. This + often leads to very large expressions that may be of little practical + use. An approximate solution of `prec` digits can be obtained by + passing in the desired value: + + >>> e.normal_lines((3, 3), prec=2) + [Line2D(Point2D(-0.81, -2.7), Point2D(0.19, -1.2)), + Line2D(Point2D(1.5, -2.0), Point2D(2.5, -2.7))] + + Whereas the above solution has an operation count of 12, the exact + solution has an operation count of 2020. + """ + p = Point(p, dim=2) + + # XXX change True to something like self.angle == 0 if the arbitrarily + # rotated ellipse is introduced. + # https://github.com/sympy/sympy/issues/2815) + if True: + rv = [] + if p.x == self.center.x: + rv.append(Line(self.center, slope=oo)) + if p.y == self.center.y: + rv.append(Line(self.center, slope=0)) + if rv: + # at these special orientations of p either 1 or 2 normals + # exist and we are done + return rv + + # find the 4 normal points and construct lines through them with + # the corresponding slope + eq = self.equation(x, y) + dydx = idiff(eq, y, x) + norm = -1/dydx + slope = Line(p, (x, y)).slope + seq = slope - norm + + # TODO: Replace solve with solveset, when this line is tested + yis = solve(seq, y)[0] + xeq = eq.subs(y, yis).as_numer_denom()[0].expand() + if len(xeq.free_symbols) == 1: + try: + # this is so much faster, it's worth a try + xsol = Poly(xeq, x).real_roots() + except (DomainError, PolynomialError, NotImplementedError): + # TODO: Replace solve with solveset, when these lines are tested + xsol = _nsort(solve(xeq, x), separated=True)[0] + points = [Point(i, solve(eq.subs(x, i), y)[0]) for i in xsol] + else: + raise NotImplementedError( + 'intersections for the general ellipse are not supported') + slopes = [norm.subs(zip((x, y), pt.args)) for pt in points] + if prec is not None: + points = [pt.n(prec) for pt in points] + slopes = [i if _not_a_coeff(i) else i.n(prec) for i in slopes] + return [Line(pt, slope=s) for pt, s in zip(points, slopes)] + + @property + def periapsis(self): + """The periapsis of the ellipse. + + The shortest distance between the focus and the contour. + + Returns + ======= + + periapsis : number + + See Also + ======== + + apoapsis : Returns greatest distance between focus and contour + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.periapsis + 3 - 2*sqrt(2) + + """ + return self.major * (1 - self.eccentricity) + + @property + def semilatus_rectum(self): + """ + Calculates the semi-latus rectum of the Ellipse. + + Semi-latus rectum is defined as one half of the chord through a + focus parallel to the conic section directrix of a conic section. + + Returns + ======= + + semilatus_rectum : number + + See Also + ======== + + apoapsis : Returns greatest distance between focus and contour + + periapsis : The shortest distance between the focus and the contour + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.semilatus_rectum + 1/3 + + References + ========== + + .. [1] https://mathworld.wolfram.com/SemilatusRectum.html + .. [2] https://en.wikipedia.org/wiki/Ellipse#Semi-latus_rectum + + """ + return self.major * (1 - self.eccentricity ** 2) + + def auxiliary_circle(self): + """Returns a Circle whose diameter is the major axis of the ellipse. + + Examples + ======== + + >>> from sympy import Ellipse, Point, symbols + >>> c = Point(1, 2) + >>> Ellipse(c, 8, 7).auxiliary_circle() + Circle(Point2D(1, 2), 8) + >>> a, b = symbols('a b') + >>> Ellipse(c, a, b).auxiliary_circle() + Circle(Point2D(1, 2), Max(a, b)) + """ + return Circle(self.center, Max(self.hradius, self.vradius)) + + def director_circle(self): + """ + Returns a Circle consisting of all points where two perpendicular + tangent lines to the ellipse cross each other. + + Returns + ======= + + Circle + A director circle returned as a geometric object. + + Examples + ======== + + >>> from sympy import Ellipse, Point, symbols + >>> c = Point(3,8) + >>> Ellipse(c, 7, 9).director_circle() + Circle(Point2D(3, 8), sqrt(130)) + >>> a, b = symbols('a b') + >>> Ellipse(c, a, b).director_circle() + Circle(Point2D(3, 8), sqrt(a**2 + b**2)) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Director_circle + + """ + return Circle(self.center, sqrt(self.hradius**2 + self.vradius**2)) + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of the Ellipse. + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + plot_interval : list + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e1 = Ellipse(Point(0, 0), 3, 2) + >>> e1.plot_interval() + [t, -pi, pi] + + """ + t = _symbol(parameter, real=True) + return [t, -S.Pi, S.Pi] + + def random_point(self, seed=None): + """A random point on the ellipse. + + Returns + ======= + + point : Point + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e1 = Ellipse(Point(0, 0), 3, 2) + >>> e1.random_point() # gives some random point + Point2D(...) + >>> p1 = e1.random_point(seed=0); p1.n(2) + Point2D(2.1, 1.4) + + Notes + ===== + + When creating a random point, one may simply replace the + parameter with a random number. When doing so, however, the + random number should be made a Rational or else the point + may not test as being in the ellipse: + + >>> from sympy.abc import t + >>> from sympy import Rational + >>> arb = e1.arbitrary_point(t); arb + Point2D(3*cos(t), 2*sin(t)) + >>> arb.subs(t, .1) in e1 + False + >>> arb.subs(t, Rational(.1)) in e1 + True + >>> arb.subs(t, Rational('.1')) in e1 + True + + See Also + ======== + sympy.geometry.point.Point + arbitrary_point : Returns parameterized point on ellipse + """ + t = _symbol('t', real=True) + x, y = self.arbitrary_point(t).args + # get a random value in [-1, 1) corresponding to cos(t) + # and confirm that it will test as being in the ellipse + if seed is not None: + rng = random.Random(seed) + else: + rng = random + # simplify this now or else the Float will turn s into a Float + r = Rational(rng.random()) + c = 2*r - 1 + s = sqrt(1 - c**2) + return Point(x.subs(cos(t), c), y.subs(sin(t), s)) + + def reflect(self, line): + """Override GeometryEntity.reflect since the radius + is not a GeometryEntity. + + Examples + ======== + + >>> from sympy import Circle, Line + >>> Circle((0, 1), 1).reflect(Line((0, 0), (1, 1))) + Circle(Point2D(1, 0), -1) + >>> from sympy import Ellipse, Line, Point + >>> Ellipse(Point(3, 4), 1, 3).reflect(Line(Point(0, -4), Point(5, 0))) + Traceback (most recent call last): + ... + NotImplementedError: + General Ellipse is not supported but the equation of the reflected + Ellipse is given by the zeros of: f(x, y) = (9*x/41 + 40*y/41 + + 37/41)**2 + (40*x/123 - 3*y/41 - 364/123)**2 - 1 + + Notes + ===== + + Until the general ellipse (with no axis parallel to the x-axis) is + supported a NotImplemented error is raised and the equation whose + zeros define the rotated ellipse is given. + + """ + + if line.slope in (0, oo): + c = self.center + c = c.reflect(line) + return self.func(c, -self.hradius, self.vradius) + else: + x, y = [uniquely_named_symbol( + name, (self, line), modify=lambda s: '_' + s, real=True) + for name in 'xy'] + expr = self.equation(x, y) + p = Point(x, y).reflect(line) + result = expr.subs(zip((x, y), p.args + ), simultaneous=True) + raise NotImplementedError(filldedent( + 'General Ellipse is not supported but the equation ' + 'of the reflected Ellipse is given by the zeros of: ' + + "f(%s, %s) = %s" % (str(x), str(y), str(result)))) + + def rotate(self, angle=0, pt=None): + """Rotate ``angle`` radians counterclockwise about Point ``pt``. + + Note: since the general ellipse is not supported, only rotations that + are integer multiples of pi/2 are allowed. + + Examples + ======== + + >>> from sympy import Ellipse, pi + >>> Ellipse((1, 0), 2, 1).rotate(pi/2) + Ellipse(Point2D(0, 1), 1, 2) + >>> Ellipse((1, 0), 2, 1).rotate(pi) + Ellipse(Point2D(-1, 0), 2, 1) + """ + if self.hradius == self.vradius: + return self.func(self.center.rotate(angle, pt), self.hradius) + if (angle/S.Pi).is_integer: + return super().rotate(angle, pt) + if (2*angle/S.Pi).is_integer: + return self.func(self.center.rotate(angle, pt), self.vradius, self.hradius) + # XXX see https://github.com/sympy/sympy/issues/2815 for general ellipes + raise NotImplementedError('Only rotations of pi/2 are currently supported for Ellipse.') + + def scale(self, x=1, y=1, pt=None): + """Override GeometryEntity.scale since it is the major and minor + axes which must be scaled and they are not GeometryEntities. + + Examples + ======== + + >>> from sympy import Ellipse + >>> Ellipse((0, 0), 2, 1).scale(2, 4) + Circle(Point2D(0, 0), 4) + >>> Ellipse((0, 0), 2, 1).scale(2) + Ellipse(Point2D(0, 0), 4, 1) + """ + c = self.center + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + h = self.hradius + v = self.vradius + return self.func(c.scale(x, y), hradius=h*x, vradius=v*y) + + def tangent_lines(self, p): + """Tangent lines between `p` and the ellipse. + + If `p` is on the ellipse, returns the tangent line through point `p`. + Otherwise, returns the tangent line(s) from `p` to the ellipse, or + None if no tangent line is possible (e.g., `p` inside ellipse). + + Parameters + ========== + + p : Point + + Returns + ======= + + tangent_lines : list with 1 or 2 Lines + + Raises + ====== + + NotImplementedError + Can only find tangent lines for a point, `p`, on the ellipse. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Line + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> e1 = Ellipse(Point(0, 0), 3, 2) + >>> e1.tangent_lines(Point(3, 0)) + [Line2D(Point2D(3, 0), Point2D(3, -12))] + + """ + p = Point(p, dim=2) + if self.encloses_point(p): + return [] + + if p in self: + delta = self.center - p + rise = (self.vradius**2)*delta.x + run = -(self.hradius**2)*delta.y + p2 = Point(simplify(p.x + run), + simplify(p.y + rise)) + return [Line(p, p2)] + else: + if len(self.foci) == 2: + f1, f2 = self.foci + maj = self.hradius + test = (2*maj - + Point.distance(f1, p) - + Point.distance(f2, p)) + else: + test = self.radius - Point.distance(self.center, p) + if test.is_number and test.is_positive: + return [] + # else p is outside the ellipse or we can't tell. In case of the + # latter, the solutions returned will only be valid if + # the point is not inside the ellipse; if it is, nan will result. + eq = self.equation(x, y) + dydx = idiff(eq, y, x) + slope = Line(p, Point(x, y)).slope + + # TODO: Replace solve with solveset, when this line is tested + tangent_points = solve([slope - dydx, eq], [x, y]) + + # handle horizontal and vertical tangent lines + if len(tangent_points) == 1: + if tangent_points[0][ + 0] == p.x or tangent_points[0][1] == p.y: + return [Line(p, p + Point(1, 0)), Line(p, p + Point(0, 1))] + else: + return [Line(p, p + Point(0, 1)), Line(p, tangent_points[0])] + + # others + return [Line(p, tangent_points[0]), Line(p, tangent_points[1])] + + @property + def vradius(self): + """The vertical radius of the ellipse. + + Returns + ======= + + vradius : number + + See Also + ======== + + hradius, major, minor + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.vradius + 1 + + """ + return self.args[2] + + + def second_moment_of_area(self, point=None): + """Returns the second moment and product moment area of an ellipse. + + Parameters + ========== + + point : Point, two-tuple of sympifiable objects, or None(default=None) + point is the point about which second moment of area is to be found. + If "point=None" it will be calculated about the axis passing through the + centroid of the ellipse. + + Returns + ======= + + I_xx, I_yy, I_xy : number or SymPy expression + I_xx, I_yy are second moment of area of an ellise. + I_xy is product moment of area of an ellipse. + + Examples + ======== + + >>> from sympy import Point, Ellipse + >>> p1 = Point(0, 0) + >>> e1 = Ellipse(p1, 3, 1) + >>> e1.second_moment_of_area() + (3*pi/4, 27*pi/4, 0) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/List_of_second_moments_of_area + + """ + + I_xx = (S.Pi*(self.hradius)*(self.vradius**3))/4 + I_yy = (S.Pi*(self.hradius**3)*(self.vradius))/4 + I_xy = 0 + + if point is None: + return I_xx, I_yy, I_xy + + # parallel axis theorem + I_xx = I_xx + self.area*((point[1] - self.center.y)**2) + I_yy = I_yy + self.area*((point[0] - self.center.x)**2) + I_xy = I_xy + self.area*(point[0] - self.center.x)*(point[1] - self.center.y) + + return I_xx, I_yy, I_xy + + + def polar_second_moment_of_area(self): + """Returns the polar second moment of area of an Ellipse + + It is a constituent of the second moment of area, linked through + the perpendicular axis theorem. While the planar second moment of + area describes an object's resistance to deflection (bending) when + subjected to a force applied to a plane parallel to the central + axis, the polar second moment of area describes an object's + resistance to deflection when subjected to a moment applied in a + plane perpendicular to the object's central axis (i.e. parallel to + the cross-section) + + Examples + ======== + + >>> from sympy import symbols, Circle, Ellipse + >>> c = Circle((5, 5), 4) + >>> c.polar_second_moment_of_area() + 128*pi + >>> a, b = symbols('a, b') + >>> e = Ellipse((0, 0), a, b) + >>> e.polar_second_moment_of_area() + pi*a**3*b/4 + pi*a*b**3/4 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Polar_moment_of_inertia + + """ + second_moment = self.second_moment_of_area() + return second_moment[0] + second_moment[1] + + + def section_modulus(self, point=None): + """Returns a tuple with the section modulus of an ellipse + + Section modulus is a geometric property of an ellipse defined as the + ratio of second moment of area to the distance of the extreme end of + the ellipse from the centroidal axis. + + Parameters + ========== + + point : Point, two-tuple of sympifyable objects, or None(default=None) + point is the point at which section modulus is to be found. + If "point=None" section modulus will be calculated for the + point farthest from the centroidal axis of the ellipse. + + Returns + ======= + + S_x, S_y: numbers or SymPy expressions + S_x is the section modulus with respect to the x-axis + S_y is the section modulus with respect to the y-axis + A negative sign indicates that the section modulus is + determined for a point below the centroidal axis. + + Examples + ======== + + >>> from sympy import Symbol, Ellipse, Circle, Point2D + >>> d = Symbol('d', positive=True) + >>> c = Circle((0, 0), d/2) + >>> c.section_modulus() + (pi*d**3/32, pi*d**3/32) + >>> e = Ellipse(Point2D(0, 0), 2, 4) + >>> e.section_modulus() + (8*pi, 4*pi) + >>> e.section_modulus((2, 2)) + (16*pi, 4*pi) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Section_modulus + + """ + x_c, y_c = self.center + if point is None: + # taking x and y as maximum distances from centroid + x_min, y_min, x_max, y_max = self.bounds + y = max(y_c - y_min, y_max - y_c) + x = max(x_c - x_min, x_max - x_c) + else: + # taking x and y as distances of the given point from the center + point = Point2D(point) + y = point.y - y_c + x = point.x - x_c + + second_moment = self.second_moment_of_area() + S_x = second_moment[0]/y + S_y = second_moment[1]/x + + return S_x, S_y + + +class Circle(Ellipse): + """A circle in space. + + Constructed simply from a center and a radius, from three + non-collinear points, or the equation of a circle. + + Parameters + ========== + + center : Point + radius : number or SymPy expression + points : sequence of three Points + equation : equation of a circle + + Attributes + ========== + + radius (synonymous with hradius, vradius, major and minor) + circumference + equation + + Raises + ====== + + GeometryError + When the given equation is not that of a circle. + When trying to construct circle from incorrect parameters. + + See Also + ======== + + Ellipse, sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Circle, Eq + >>> from sympy.abc import x, y, a, b + + A circle constructed from a center and radius: + + >>> c1 = Circle(Point(0, 0), 5) + >>> c1.hradius, c1.vradius, c1.radius + (5, 5, 5) + + A circle constructed from three points: + + >>> c2 = Circle(Point(0, 0), Point(1, 1), Point(1, 0)) + >>> c2.hradius, c2.vradius, c2.radius, c2.center + (sqrt(2)/2, sqrt(2)/2, sqrt(2)/2, Point2D(1/2, 1/2)) + + A circle can be constructed from an equation in the form + `a*x**2 + by**2 + gx + hy + c = 0`, too: + + >>> Circle(x**2 + y**2 - 25) + Circle(Point2D(0, 0), 5) + + If the variables corresponding to x and y are named something + else, their name or symbol can be supplied: + + >>> Circle(Eq(a**2 + b**2, 25), x='a', y=b) + Circle(Point2D(0, 0), 5) + """ + + def __new__(cls, *args, **kwargs): + evaluate = kwargs.get('evaluate', global_parameters.evaluate) + if len(args) == 1 and isinstance(args[0], (Expr, Eq)): + x = kwargs.get('x', 'x') + y = kwargs.get('y', 'y') + equation = args[0].expand() + if isinstance(equation, Eq): + equation = equation.lhs - equation.rhs + x = find(x, equation) + y = find(y, equation) + + try: + a, b, c, d, e = linear_coeffs(equation, x**2, y**2, x, y) + except ValueError: + raise GeometryError("The given equation is not that of a circle.") + + if S.Zero in (a, b) or a != b: + raise GeometryError("The given equation is not that of a circle.") + + center_x = -c/a/2 + center_y = -d/b/2 + r2 = (center_x**2) + (center_y**2) - e/a + + return Circle((center_x, center_y), sqrt(r2), evaluate=evaluate) + + else: + c, r = None, None + if len(args) == 3: + args = [Point(a, dim=2, evaluate=evaluate) for a in args] + t = Triangle(*args) + if not isinstance(t, Triangle): + return t + c = t.circumcenter + r = t.circumradius + elif len(args) == 2: + # Assume (center, radius) pair + c = Point(args[0], dim=2, evaluate=evaluate) + r = args[1] + # this will prohibit imaginary radius + try: + r = Point(r, 0, evaluate=evaluate).x + except ValueError: + raise GeometryError("Circle with imaginary radius is not permitted") + + if not (c is None or r is None): + if r == 0: + return c + return GeometryEntity.__new__(cls, c, r, **kwargs) + + raise GeometryError("Circle.__new__ received unknown arguments") + + def _eval_evalf(self, prec=15, **options): + pt, r = self.args + dps = prec_to_dps(prec) + pt = pt.evalf(n=dps, **options) + r = r.evalf(n=dps, **options) + return self.func(pt, r, evaluate=False) + + @property + def circumference(self): + """The circumference of the circle. + + Returns + ======= + + circumference : number or SymPy expression + + Examples + ======== + + >>> from sympy import Point, Circle + >>> c1 = Circle(Point(3, 4), 6) + >>> c1.circumference + 12*pi + + """ + return 2 * S.Pi * self.radius + + def equation(self, x='x', y='y'): + """The equation of the circle. + + Parameters + ========== + + x : str or Symbol, optional + Default value is 'x'. + y : str or Symbol, optional + Default value is 'y'. + + Returns + ======= + + equation : SymPy expression + + Examples + ======== + + >>> from sympy import Point, Circle + >>> c1 = Circle(Point(0, 0), 5) + >>> c1.equation() + x**2 + y**2 - 25 + + """ + x = _symbol(x, real=True) + y = _symbol(y, real=True) + t1 = (x - self.center.x)**2 + t2 = (y - self.center.y)**2 + return t1 + t2 - self.major**2 + + def intersection(self, o): + """The intersection of this circle with another geometrical entity. + + Parameters + ========== + + o : GeometryEntity + + Returns + ======= + + intersection : list of GeometryEntities + + Examples + ======== + + >>> from sympy import Point, Circle, Line, Ray + >>> p1, p2, p3 = Point(0, 0), Point(5, 5), Point(6, 0) + >>> p4 = Point(5, 0) + >>> c1 = Circle(p1, 5) + >>> c1.intersection(p2) + [] + >>> c1.intersection(p4) + [Point2D(5, 0)] + >>> c1.intersection(Ray(p1, p2)) + [Point2D(5*sqrt(2)/2, 5*sqrt(2)/2)] + >>> c1.intersection(Line(p2, p3)) + [] + + """ + return Ellipse.intersection(self, o) + + @property + def radius(self): + """The radius of the circle. + + Returns + ======= + + radius : number or SymPy expression + + See Also + ======== + + Ellipse.major, Ellipse.minor, Ellipse.hradius, Ellipse.vradius + + Examples + ======== + + >>> from sympy import Point, Circle + >>> c1 = Circle(Point(3, 4), 6) + >>> c1.radius + 6 + + """ + return self.args[1] + + def reflect(self, line): + """Override GeometryEntity.reflect since the radius + is not a GeometryEntity. + + Examples + ======== + + >>> from sympy import Circle, Line + >>> Circle((0, 1), 1).reflect(Line((0, 0), (1, 1))) + Circle(Point2D(1, 0), -1) + """ + c = self.center + c = c.reflect(line) + return self.func(c, -self.radius) + + def scale(self, x=1, y=1, pt=None): + """Override GeometryEntity.scale since the radius + is not a GeometryEntity. + + Examples + ======== + + >>> from sympy import Circle + >>> Circle((0, 0), 1).scale(2, 2) + Circle(Point2D(0, 0), 2) + >>> Circle((0, 0), 1).scale(2, 4) + Ellipse(Point2D(0, 0), 2, 4) + """ + c = self.center + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + c = c.scale(x, y) + x, y = [abs(i) for i in (x, y)] + if x == y: + return self.func(c, x*self.radius) + h = v = self.radius + return Ellipse(c, hradius=h*x, vradius=v*y) + + @property + def vradius(self): + """ + This Ellipse property is an alias for the Circle's radius. + + Whereas hradius, major and minor can use Ellipse's conventions, + the vradius does not exist for a circle. It is always a positive + value in order that the Circle, like Polygons, will have an + area that can be positive or negative as determined by the sign + of the hradius. + + Examples + ======== + + >>> from sympy import Point, Circle + >>> c1 = Circle(Point(3, 4), 6) + >>> c1.vradius + 6 + """ + return abs(self.radius) + + +from .polygon import Polygon, Triangle diff --git a/lib/python3.11/site-packages/sympy/geometry/entity.py b/lib/python3.11/site-packages/sympy/geometry/entity.py new file mode 100644 index 0000000000000000000000000000000000000000..5ea1e807542c43eb955c2d778cec0f101d78bdce --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/entity.py @@ -0,0 +1,641 @@ +"""The definition of the base geometrical entity with attributes common to +all derived geometrical entities. + +Contains +======== + +GeometryEntity +GeometricSet + +Notes +===== + +A GeometryEntity is any object that has special geometric properties. +A GeometrySet is a superclass of any GeometryEntity that can also +be viewed as a sympy.sets.Set. In particular, points are the only +GeometryEntity not considered a Set. + +Rn is a GeometrySet representing n-dimensional Euclidean space. R2 and +R3 are currently the only ambient spaces implemented. + +""" +from __future__ import annotations + +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.evalf import EvalfMixin, N +from sympy.core.numbers import oo +from sympy.core.symbol import Dummy +from sympy.core.sympify import sympify +from sympy.functions.elementary.trigonometric import cos, sin, atan +from sympy.matrices import eye +from sympy.multipledispatch import dispatch +from sympy.printing import sstr +from sympy.sets import Set, Union, FiniteSet +from sympy.sets.handlers.intersection import intersection_sets +from sympy.sets.handlers.union import union_sets +from sympy.solvers.solvers import solve +from sympy.utilities.misc import func_name +from sympy.utilities.iterables import is_sequence + + +# How entities are ordered; used by __cmp__ in GeometryEntity +ordering_of_classes = [ + "Point2D", + "Point3D", + "Point", + "Segment2D", + "Ray2D", + "Line2D", + "Segment3D", + "Line3D", + "Ray3D", + "Segment", + "Ray", + "Line", + "Plane", + "Triangle", + "RegularPolygon", + "Polygon", + "Circle", + "Ellipse", + "Curve", + "Parabola" +] + + +x, y = [Dummy('entity_dummy') for i in range(2)] +T = Dummy('entity_dummy', real=True) + + +class GeometryEntity(Basic, EvalfMixin): + """The base class for all geometrical entities. + + This class does not represent any particular geometric entity, it only + provides the implementation of some methods common to all subclasses. + + """ + + __slots__: tuple[str, ...] = () + + def __cmp__(self, other): + """Comparison of two GeometryEntities.""" + n1 = self.__class__.__name__ + n2 = other.__class__.__name__ + c = (n1 > n2) - (n1 < n2) + if not c: + return 0 + + i1 = -1 + for cls in self.__class__.__mro__: + try: + i1 = ordering_of_classes.index(cls.__name__) + break + except ValueError: + i1 = -1 + if i1 == -1: + return c + + i2 = -1 + for cls in other.__class__.__mro__: + try: + i2 = ordering_of_classes.index(cls.__name__) + break + except ValueError: + i2 = -1 + if i2 == -1: + return c + + return (i1 > i2) - (i1 < i2) + + def __contains__(self, other): + """Subclasses should implement this method for anything more complex than equality.""" + if type(self) is type(other): + return self == other + raise NotImplementedError() + + def __getnewargs__(self): + """Returns a tuple that will be passed to __new__ on unpickling.""" + return tuple(self.args) + + def __ne__(self, o): + """Test inequality of two geometrical entities.""" + return not self == o + + def __new__(cls, *args, **kwargs): + # Points are sequences, but they should not + # be converted to Tuples, so use this detection function instead. + def is_seq_and_not_point(a): + # we cannot use isinstance(a, Point) since we cannot import Point + if hasattr(a, 'is_Point') and a.is_Point: + return False + return is_sequence(a) + + args = [Tuple(*a) if is_seq_and_not_point(a) else sympify(a) for a in args] + return Basic.__new__(cls, *args) + + def __radd__(self, a): + """Implementation of reverse add method.""" + return a.__add__(self) + + def __rtruediv__(self, a): + """Implementation of reverse division method.""" + return a.__truediv__(self) + + def __repr__(self): + """String representation of a GeometryEntity that can be evaluated + by sympy.""" + return type(self).__name__ + repr(self.args) + + def __rmul__(self, a): + """Implementation of reverse multiplication method.""" + return a.__mul__(self) + + def __rsub__(self, a): + """Implementation of reverse subtraction method.""" + return a.__sub__(self) + + def __str__(self): + """String representation of a GeometryEntity.""" + return type(self).__name__ + sstr(self.args) + + def _eval_subs(self, old, new): + from sympy.geometry.point import Point, Point3D + if is_sequence(old) or is_sequence(new): + if isinstance(self, Point3D): + old = Point3D(old) + new = Point3D(new) + else: + old = Point(old) + new = Point(new) + return self._subs(old, new) + + def _repr_svg_(self): + """SVG representation of a GeometryEntity suitable for IPython""" + + try: + bounds = self.bounds + except (NotImplementedError, TypeError): + # if we have no SVG representation, return None so IPython + # will fall back to the next representation + return None + + if not all(x.is_number and x.is_finite for x in bounds): + return None + + svg_top = ''' + + + + + + + + + + + ''' + + # Establish SVG canvas that will fit all the data + small space + xmin, ymin, xmax, ymax = map(N, bounds) + if xmin == xmax and ymin == ymax: + # This is a point; buffer using an arbitrary size + xmin, ymin, xmax, ymax = xmin - .5, ymin -.5, xmax + .5, ymax + .5 + else: + # Expand bounds by a fraction of the data ranges + expand = 0.1 # or 10%; this keeps arrowheads in view (R plots use 4%) + widest_part = max([xmax - xmin, ymax - ymin]) + expand_amount = widest_part * expand + xmin -= expand_amount + ymin -= expand_amount + xmax += expand_amount + ymax += expand_amount + dx = xmax - xmin + dy = ymax - ymin + width = min([max([100., dx]), 300]) + height = min([max([100., dy]), 300]) + + scale_factor = 1. if max(width, height) == 0 else max(dx, dy) / max(width, height) + try: + svg = self._svg(scale_factor) + except (NotImplementedError, TypeError): + # if we have no SVG representation, return None so IPython + # will fall back to the next representation + return None + + view_box = "{} {} {} {}".format(xmin, ymin, dx, dy) + transform = "matrix(1,0,0,-1,0,{})".format(ymax + ymin) + svg_top = svg_top.format(view_box, width, height) + + return svg_top + ( + '{}' + ).format(transform, svg) + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG path element for the GeometryEntity. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + raise NotImplementedError() + + def _sympy_(self): + return self + + @property + def ambient_dimension(self): + """What is the dimension of the space that the object is contained in?""" + raise NotImplementedError() + + @property + def bounds(self): + """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding + rectangle for the geometric figure. + + """ + + raise NotImplementedError() + + def encloses(self, o): + """ + Return True if o is inside (not on or outside) the boundaries of self. + + The object will be decomposed into Points and individual Entities need + only define an encloses_point method for their class. + + See Also + ======== + + sympy.geometry.ellipse.Ellipse.encloses_point + sympy.geometry.polygon.Polygon.encloses_point + + Examples + ======== + + >>> from sympy import RegularPolygon, Point, Polygon + >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) + >>> t2 = Polygon(*RegularPolygon(Point(0, 0), 2, 3).vertices) + >>> t2.encloses(t) + True + >>> t.encloses(t2) + False + + """ + + from sympy.geometry.point import Point + from sympy.geometry.line import Segment, Ray, Line + from sympy.geometry.ellipse import Ellipse + from sympy.geometry.polygon import Polygon, RegularPolygon + + if isinstance(o, Point): + return self.encloses_point(o) + elif isinstance(o, Segment): + return all(self.encloses_point(x) for x in o.points) + elif isinstance(o, (Ray, Line)): + return False + elif isinstance(o, Ellipse): + return self.encloses_point(o.center) and \ + self.encloses_point( + Point(o.center.x + o.hradius, o.center.y)) and \ + not self.intersection(o) + elif isinstance(o, Polygon): + if isinstance(o, RegularPolygon): + if not self.encloses_point(o.center): + return False + return all(self.encloses_point(v) for v in o.vertices) + raise NotImplementedError() + + def equals(self, o): + return self == o + + def intersection(self, o): + """ + Returns a list of all of the intersections of self with o. + + Notes + ===== + + An entity is not required to implement this method. + + If two different types of entities can intersect, the item with + higher index in ordering_of_classes should implement + intersections with anything having a lower index. + + See Also + ======== + + sympy.geometry.util.intersection + + """ + raise NotImplementedError() + + def is_similar(self, other): + """Is this geometrical entity similar to another geometrical entity? + + Two entities are similar if a uniform scaling (enlarging or + shrinking) of one of the entities will allow one to obtain the other. + + Notes + ===== + + This method is not intended to be used directly but rather + through the `are_similar` function found in util.py. + An entity is not required to implement this method. + If two different types of entities can be similar, it is only + required that one of them be able to determine this. + + See Also + ======== + + scale + + """ + raise NotImplementedError() + + def reflect(self, line): + """ + Reflects an object across a line. + + Parameters + ========== + + line: Line + + Examples + ======== + + >>> from sympy import pi, sqrt, Line, RegularPolygon + >>> l = Line((0, pi), slope=sqrt(2)) + >>> pent = RegularPolygon((1, 2), 1, 5) + >>> rpent = pent.reflect(l) + >>> rpent + RegularPolygon(Point2D(-2*sqrt(2)*pi/3 - 1/3 + 4*sqrt(2)/3, 2/3 + 2*sqrt(2)/3 + 2*pi/3), -1, 5, -atan(2*sqrt(2)) + 3*pi/5) + + >>> from sympy import pi, Line, Circle, Point + >>> l = Line((0, pi), slope=1) + >>> circ = Circle(Point(0, 0), 5) + >>> rcirc = circ.reflect(l) + >>> rcirc + Circle(Point2D(-pi, pi), -5) + + """ + from sympy.geometry.point import Point + + g = self + l = line + o = Point(0, 0) + if l.slope.is_zero: + v = l.args[0].y + if not v: # x-axis + return g.scale(y=-1) + reps = [(p, p.translate(y=2*(v - p.y))) for p in g.atoms(Point)] + elif l.slope is oo: + v = l.args[0].x + if not v: # y-axis + return g.scale(x=-1) + reps = [(p, p.translate(x=2*(v - p.x))) for p in g.atoms(Point)] + else: + if not hasattr(g, 'reflect') and not all( + isinstance(arg, Point) for arg in g.args): + raise NotImplementedError( + 'reflect undefined or non-Point args in %s' % g) + a = atan(l.slope) + c = l.coefficients + d = -c[-1]/c[1] # y-intercept + # apply the transform to a single point + xf = Point(x, y) + xf = xf.translate(y=-d).rotate(-a, o).scale(y=-1 + ).rotate(a, o).translate(y=d) + # replace every point using that transform + reps = [(p, xf.xreplace({x: p.x, y: p.y})) for p in g.atoms(Point)] + return g.xreplace(dict(reps)) + + def rotate(self, angle, pt=None): + """Rotate ``angle`` radians counterclockwise about Point ``pt``. + + The default pt is the origin, Point(0, 0) + + See Also + ======== + + scale, translate + + Examples + ======== + + >>> from sympy import Point, RegularPolygon, Polygon, pi + >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) + >>> t # vertex on x axis + Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) + >>> t.rotate(pi/2) # vertex on y axis now + Triangle(Point2D(0, 1), Point2D(-sqrt(3)/2, -1/2), Point2D(sqrt(3)/2, -1/2)) + + """ + newargs = [] + for a in self.args: + if isinstance(a, GeometryEntity): + newargs.append(a.rotate(angle, pt)) + else: + newargs.append(a) + return type(self)(*newargs) + + def scale(self, x=1, y=1, pt=None): + """Scale the object by multiplying the x,y-coordinates by x and y. + + If pt is given, the scaling is done relative to that point; the + object is shifted by -pt, scaled, and shifted by pt. + + See Also + ======== + + rotate, translate + + Examples + ======== + + >>> from sympy import RegularPolygon, Point, Polygon + >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) + >>> t + Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) + >>> t.scale(2) + Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)/2), Point2D(-1, -sqrt(3)/2)) + >>> t.scale(2, 2) + Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)), Point2D(-1, -sqrt(3))) + + """ + from sympy.geometry.point import Point + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + return type(self)(*[a.scale(x, y) for a in self.args]) # if this fails, override this class + + def translate(self, x=0, y=0): + """Shift the object by adding to the x,y-coordinates the values x and y. + + See Also + ======== + + rotate, scale + + Examples + ======== + + >>> from sympy import RegularPolygon, Point, Polygon + >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) + >>> t + Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) + >>> t.translate(2) + Triangle(Point2D(3, 0), Point2D(3/2, sqrt(3)/2), Point2D(3/2, -sqrt(3)/2)) + >>> t.translate(2, 2) + Triangle(Point2D(3, 2), Point2D(3/2, sqrt(3)/2 + 2), Point2D(3/2, 2 - sqrt(3)/2)) + + """ + newargs = [] + for a in self.args: + if isinstance(a, GeometryEntity): + newargs.append(a.translate(x, y)) + else: + newargs.append(a) + return self.func(*newargs) + + def parameter_value(self, other, t): + """Return the parameter corresponding to the given point. + Evaluating an arbitrary point of the entity at this parameter + value will return the given point. + + Examples + ======== + + >>> from sympy import Line, Point + >>> from sympy.abc import t + >>> a = Point(0, 0) + >>> b = Point(2, 2) + >>> Line(a, b).parameter_value((1, 1), t) + {t: 1/2} + >>> Line(a, b).arbitrary_point(t).subs(_) + Point2D(1, 1) + """ + from sympy.geometry.point import Point + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if not isinstance(other, Point): + raise ValueError("other must be a point") + sol = solve(self.arbitrary_point(T) - other, T, dict=True) + if not sol: + raise ValueError("Given point is not on %s" % func_name(self)) + return {t: sol[0][T]} + + +class GeometrySet(GeometryEntity, Set): + """Parent class of all GeometryEntity that are also Sets + (compatible with sympy.sets) + """ + __slots__ = () + + def _contains(self, other): + """sympy.sets uses the _contains method, so include it for compatibility.""" + + if isinstance(other, Set) and other.is_FiniteSet: + return all(self.__contains__(i) for i in other) + + return self.__contains__(other) + +@dispatch(GeometrySet, Set) # type:ignore # noqa:F811 +def union_sets(self, o): # noqa:F811 + """ Returns the union of self and o + for use with sympy.sets.Set, if possible. """ + + + # if its a FiniteSet, merge any points + # we contain and return a union with the rest + if o.is_FiniteSet: + other_points = [p for p in o if not self._contains(p)] + if len(other_points) == len(o): + return None + return Union(self, FiniteSet(*other_points)) + if self._contains(o): + return self + return None + + +@dispatch(GeometrySet, Set) # type: ignore # noqa:F811 +def intersection_sets(self, o): # noqa:F811 + """ Returns a sympy.sets.Set of intersection objects, + if possible. """ + + from sympy.geometry.point import Point + + try: + # if o is a FiniteSet, find the intersection directly + # to avoid infinite recursion + if o.is_FiniteSet: + inter = FiniteSet(*(p for p in o if self.contains(p))) + else: + inter = self.intersection(o) + except NotImplementedError: + # sympy.sets.Set.reduce expects None if an object + # doesn't know how to simplify + return None + + # put the points in a FiniteSet + points = FiniteSet(*[p for p in inter if isinstance(p, Point)]) + non_points = [p for p in inter if not isinstance(p, Point)] + + return Union(*(non_points + [points])) + +def translate(x, y): + """Return the matrix to translate a 2-D point by x and y.""" + rv = eye(3) + rv[2, 0] = x + rv[2, 1] = y + return rv + + +def scale(x, y, pt=None): + """Return the matrix to multiply a 2-D point's coordinates by x and y. + + If pt is given, the scaling is done relative to that point.""" + rv = eye(3) + rv[0, 0] = x + rv[1, 1] = y + if pt: + from sympy.geometry.point import Point + pt = Point(pt, dim=2) + tr1 = translate(*(-pt).args) + tr2 = translate(*pt.args) + return tr1*rv*tr2 + return rv + + +def rotate(th): + """Return the matrix to rotate a 2-D point about the origin by ``angle``. + + The angle is measured in radians. To Point a point about a point other + then the origin, translate the Point, do the rotation, and + translate it back: + + >>> from sympy.geometry.entity import rotate, translate + >>> from sympy import Point, pi + >>> rot_about_11 = translate(-1, -1)*rotate(pi/2)*translate(1, 1) + >>> Point(1, 1).transform(rot_about_11) + Point2D(1, 1) + >>> Point(0, 0).transform(rot_about_11) + Point2D(2, 0) + """ + s = sin(th) + rv = eye(3)*cos(th) + rv[0, 1] = s + rv[1, 0] = -s + rv[2, 2] = 1 + return rv diff --git a/lib/python3.11/site-packages/sympy/geometry/exceptions.py b/lib/python3.11/site-packages/sympy/geometry/exceptions.py new file mode 100644 index 0000000000000000000000000000000000000000..41d97af718de2cebad3accefcd60e43ccf74a3f6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/exceptions.py @@ -0,0 +1,5 @@ +"""Geometry Errors.""" + +class GeometryError(ValueError): + """An exception raised by classes in the geometry module.""" + pass diff --git a/lib/python3.11/site-packages/sympy/geometry/line.py b/lib/python3.11/site-packages/sympy/geometry/line.py new file mode 100644 index 0000000000000000000000000000000000000000..e9b29b5766bd4157d2cddd6a403c142768224ac8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/line.py @@ -0,0 +1,2877 @@ +"""Line-like geometrical entities. + +Contains +======== +LinearEntity +Line +Ray +Segment +LinearEntity2D +Line2D +Ray2D +Segment2D +LinearEntity3D +Line3D +Ray3D +Segment3D + +""" + +from sympy.core.containers import Tuple +from sympy.core.evalf import N +from sympy.core.expr import Expr +from sympy.core.numbers import Rational, oo, Float +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.sorting import ordered +from sympy.core.symbol import _symbol, Dummy, uniquely_named_symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (_pi_coeff, acos, tan, atan2) +from .entity import GeometryEntity, GeometrySet +from .exceptions import GeometryError +from .point import Point, Point3D +from .util import find, intersection +from sympy.logic.boolalg import And +from sympy.matrices import Matrix +from sympy.sets.sets import Intersection +from sympy.simplify.simplify import simplify +from sympy.solvers.solvers import solve +from sympy.solvers.solveset import linear_coeffs +from sympy.utilities.misc import Undecidable, filldedent + + +import random + + +t, u = [Dummy('line_dummy') for i in range(2)] + + +class LinearEntity(GeometrySet): + """A base class for all linear entities (Line, Ray and Segment) + in n-dimensional Euclidean space. + + Attributes + ========== + + ambient_dimension + direction + length + p1 + p2 + points + + Notes + ===== + + This is an abstract class and is not meant to be instantiated. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity + + """ + def __new__(cls, p1, p2=None, **kwargs): + p1, p2 = Point._normalize_dimension(p1, p2) + if p1 == p2: + # sometimes we return a single point if we are not given two unique + # points. This is done in the specific subclass + raise ValueError( + "%s.__new__ requires two unique Points." % cls.__name__) + if len(p1) != len(p2): + raise ValueError( + "%s.__new__ requires two Points of equal dimension." % cls.__name__) + + return GeometryEntity.__new__(cls, p1, p2, **kwargs) + + def __contains__(self, other): + """Return a definitive answer or else raise an error if it cannot + be determined that other is on the boundaries of self.""" + result = self.contains(other) + + if result is not None: + return result + else: + raise Undecidable( + "Cannot decide whether '%s' contains '%s'" % (self, other)) + + def _span_test(self, other): + """Test whether the point `other` lies in the positive span of `self`. + A point x is 'in front' of a point y if x.dot(y) >= 0. Return + -1 if `other` is behind `self.p1`, 0 if `other` is `self.p1` and + and 1 if `other` is in front of `self.p1`.""" + if self.p1 == other: + return 0 + + rel_pos = other - self.p1 + d = self.direction + if d.dot(rel_pos) > 0: + return 1 + return -1 + + @property + def ambient_dimension(self): + """A property method that returns the dimension of LinearEntity + object. + + Parameters + ========== + + p1 : LinearEntity + + Returns + ======= + + dimension : integer + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(1, 1) + >>> l1 = Line(p1, p2) + >>> l1.ambient_dimension + 2 + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 1) + >>> l1 = Line(p1, p2) + >>> l1.ambient_dimension + 3 + + """ + return len(self.p1) + + def angle_between(l1, l2): + """Return the non-reflex angle formed by rays emanating from + the origin with directions the same as the direction vectors + of the linear entities. + + Parameters + ========== + + l1 : LinearEntity + l2 : LinearEntity + + Returns + ======= + + angle : angle in radians + + Notes + ===== + + From the dot product of vectors v1 and v2 it is known that: + + ``dot(v1, v2) = |v1|*|v2|*cos(A)`` + + where A is the angle formed between the two vectors. We can + get the directional vectors of the two lines and readily + find the angle between the two using the above formula. + + See Also + ======== + + is_perpendicular, Ray2D.closing_angle + + Examples + ======== + + >>> from sympy import Line + >>> e = Line((0, 0), (1, 0)) + >>> ne = Line((0, 0), (1, 1)) + >>> sw = Line((1, 1), (0, 0)) + >>> ne.angle_between(e) + pi/4 + >>> sw.angle_between(e) + 3*pi/4 + + To obtain the non-obtuse angle at the intersection of lines, use + the ``smallest_angle_between`` method: + + >>> sw.smallest_angle_between(e) + pi/4 + + >>> from sympy import Point3D, Line3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0) + >>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3) + >>> l1.angle_between(l2) + acos(-sqrt(2)/3) + >>> l1.smallest_angle_between(l2) + acos(sqrt(2)/3) + """ + if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity): + raise TypeError('Must pass only LinearEntity objects') + + v1, v2 = l1.direction, l2.direction + return acos(v1.dot(v2)/(abs(v1)*abs(v2))) + + def smallest_angle_between(l1, l2): + """Return the smallest angle formed at the intersection of the + lines containing the linear entities. + + Parameters + ========== + + l1 : LinearEntity + l2 : LinearEntity + + Returns + ======= + + angle : angle in radians + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 0), Point(0, 4), Point(2, -2) + >>> l1, l2 = Line(p1, p2), Line(p1, p3) + >>> l1.smallest_angle_between(l2) + pi/4 + + See Also + ======== + + angle_between, is_perpendicular, Ray2D.closing_angle + """ + if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity): + raise TypeError('Must pass only LinearEntity objects') + + v1, v2 = l1.direction, l2.direction + return acos(abs(v1.dot(v2))/(abs(v1)*abs(v2))) + + def arbitrary_point(self, parameter='t'): + """A parameterized point on the Line. + + Parameters + ========== + + parameter : str, optional + The name of the parameter which will be used for the parametric + point. The default value is 't'. When this parameter is 0, the + first point used to define the line will be returned, and when + it is 1 the second point will be returned. + + Returns + ======= + + point : Point + + Raises + ====== + + ValueError + When ``parameter`` already appears in the Line's definition. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(1, 0), Point(5, 3) + >>> l1 = Line(p1, p2) + >>> l1.arbitrary_point() + Point2D(4*t + 1, 3*t) + >>> from sympy import Point3D, Line3D + >>> p1, p2 = Point3D(1, 0, 0), Point3D(5, 3, 1) + >>> l1 = Line3D(p1, p2) + >>> l1.arbitrary_point() + Point3D(4*t + 1, 3*t, t) + + """ + t = _symbol(parameter, real=True) + if t.name in (f.name for f in self.free_symbols): + raise ValueError(filldedent(''' + Symbol %s already appears in object + and cannot be used as a parameter. + ''' % t.name)) + # multiply on the right so the variable gets + # combined with the coordinates of the point + return self.p1 + (self.p2 - self.p1)*t + + @staticmethod + def are_concurrent(*lines): + """Is a sequence of linear entities concurrent? + + Two or more linear entities are concurrent if they all + intersect at a single point. + + Parameters + ========== + + lines + A sequence of linear entities. + + Returns + ======= + + True : if the set of linear entities intersect in one point + False : otherwise. + + See Also + ======== + + sympy.geometry.util.intersection + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(3, 5) + >>> p3, p4 = Point(-2, -2), Point(0, 2) + >>> l1, l2, l3 = Line(p1, p2), Line(p1, p3), Line(p1, p4) + >>> Line.are_concurrent(l1, l2, l3) + True + >>> l4 = Line(p2, p3) + >>> Line.are_concurrent(l2, l3, l4) + False + >>> from sympy import Point3D, Line3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(3, 5, 2) + >>> p3, p4 = Point3D(-2, -2, -2), Point3D(0, 2, 1) + >>> l1, l2, l3 = Line3D(p1, p2), Line3D(p1, p3), Line3D(p1, p4) + >>> Line3D.are_concurrent(l1, l2, l3) + True + >>> l4 = Line3D(p2, p3) + >>> Line3D.are_concurrent(l2, l3, l4) + False + + """ + common_points = Intersection(*lines) + if common_points.is_FiniteSet and len(common_points) == 1: + return True + return False + + def contains(self, other): + """Subclasses should implement this method and should return + True if other is on the boundaries of self; + False if not on the boundaries of self; + None if a determination cannot be made.""" + raise NotImplementedError() + + @property + def direction(self): + """The direction vector of the LinearEntity. + + Returns + ======= + + p : a Point; the ray from the origin to this point is the + direction of `self` + + Examples + ======== + + >>> from sympy import Line + >>> a, b = (1, 1), (1, 3) + >>> Line(a, b).direction + Point2D(0, 2) + >>> Line(b, a).direction + Point2D(0, -2) + + This can be reported so the distance from the origin is 1: + + >>> Line(b, a).direction.unit + Point2D(0, -1) + + See Also + ======== + + sympy.geometry.point.Point.unit + + """ + return self.p2 - self.p1 + + def intersection(self, other): + """The intersection with another geometrical entity. + + Parameters + ========== + + o : Point or LinearEntity + + Returns + ======= + + intersection : list of geometrical entities + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line, Segment + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(7, 7) + >>> l1 = Line(p1, p2) + >>> l1.intersection(p3) + [Point2D(7, 7)] + >>> p4, p5 = Point(5, 0), Point(0, 3) + >>> l2 = Line(p4, p5) + >>> l1.intersection(l2) + [Point2D(15/8, 15/8)] + >>> p6, p7 = Point(0, 5), Point(2, 6) + >>> s1 = Segment(p6, p7) + >>> l1.intersection(s1) + [] + >>> from sympy import Point3D, Line3D, Segment3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(7, 7, 7) + >>> l1 = Line3D(p1, p2) + >>> l1.intersection(p3) + [Point3D(7, 7, 7)] + >>> l1 = Line3D(Point3D(4,19,12), Point3D(5,25,17)) + >>> l2 = Line3D(Point3D(-3, -15, -19), direction_ratio=[2,8,8]) + >>> l1.intersection(l2) + [Point3D(1, 1, -3)] + >>> p6, p7 = Point3D(0, 5, 2), Point3D(2, 6, 3) + >>> s1 = Segment3D(p6, p7) + >>> l1.intersection(s1) + [] + + """ + def intersect_parallel_rays(ray1, ray2): + if ray1.direction.dot(ray2.direction) > 0: + # rays point in the same direction + # so return the one that is "in front" + return [ray2] if ray1._span_test(ray2.p1) >= 0 else [ray1] + else: + # rays point in opposite directions + st = ray1._span_test(ray2.p1) + if st < 0: + return [] + elif st == 0: + return [ray2.p1] + return [Segment(ray1.p1, ray2.p1)] + + def intersect_parallel_ray_and_segment(ray, seg): + st1, st2 = ray._span_test(seg.p1), ray._span_test(seg.p2) + if st1 < 0 and st2 < 0: + return [] + elif st1 >= 0 and st2 >= 0: + return [seg] + elif st1 >= 0: # st2 < 0: + return [Segment(ray.p1, seg.p1)] + else: # st1 < 0 and st2 >= 0: + return [Segment(ray.p1, seg.p2)] + + def intersect_parallel_segments(seg1, seg2): + if seg1.contains(seg2): + return [seg2] + if seg2.contains(seg1): + return [seg1] + + # direct the segments so they're oriented the same way + if seg1.direction.dot(seg2.direction) < 0: + seg2 = Segment(seg2.p2, seg2.p1) + # order the segments so seg1 is "behind" seg2 + if seg1._span_test(seg2.p1) < 0: + seg1, seg2 = seg2, seg1 + if seg2._span_test(seg1.p2) < 0: + return [] + return [Segment(seg2.p1, seg1.p2)] + + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if other.is_Point: + if self.contains(other): + return [other] + else: + return [] + elif isinstance(other, LinearEntity): + # break into cases based on whether + # the lines are parallel, non-parallel intersecting, or skew + pts = Point._normalize_dimension(self.p1, self.p2, other.p1, other.p2) + rank = Point.affine_rank(*pts) + + if rank == 1: + # we're collinear + if isinstance(self, Line): + return [other] + if isinstance(other, Line): + return [self] + + if isinstance(self, Ray) and isinstance(other, Ray): + return intersect_parallel_rays(self, other) + if isinstance(self, Ray) and isinstance(other, Segment): + return intersect_parallel_ray_and_segment(self, other) + if isinstance(self, Segment) and isinstance(other, Ray): + return intersect_parallel_ray_and_segment(other, self) + if isinstance(self, Segment) and isinstance(other, Segment): + return intersect_parallel_segments(self, other) + elif rank == 2: + # we're in the same plane + l1 = Line(*pts[:2]) + l2 = Line(*pts[2:]) + + # check to see if we're parallel. If we are, we can't + # be intersecting, since the collinear case was already + # handled + if l1.direction.is_scalar_multiple(l2.direction): + return [] + + # find the intersection as if everything were lines + # by solving the equation t*d + p1 == s*d' + p1' + m = Matrix([l1.direction, -l2.direction]).transpose() + v = Matrix([l2.p1 - l1.p1]).transpose() + + # we cannot use m.solve(v) because that only works for square matrices + m_rref, pivots = m.col_insert(2, v).rref(simplify=True) + # rank == 2 ensures we have 2 pivots, but let's check anyway + if len(pivots) != 2: + raise GeometryError("Failed when solving Mx=b when M={} and b={}".format(m, v)) + coeff = m_rref[0, 2] + line_intersection = l1.direction*coeff + self.p1 + + # if both are lines, skip a containment check + if isinstance(self, Line) and isinstance(other, Line): + return [line_intersection] + + if ((isinstance(self, Line) or + self.contains(line_intersection)) and + other.contains(line_intersection)): + return [line_intersection] + if not self.atoms(Float) and not other.atoms(Float): + # if it can fail when there are no Floats then + # maybe the following parametric check should be + # done + return [] + # floats may fail exact containment so check that the + # arbitrary points, when equal, both give a + # non-negative parameter when the arbitrary point + # coordinates are equated + tu = solve(self.arbitrary_point(t) - other.arbitrary_point(u), + t, u, dict=True)[0] + def ok(p, l): + if isinstance(l, Line): + # p > -oo + return True + if isinstance(l, Ray): + # p >= 0 + return p.is_nonnegative + if isinstance(l, Segment): + # 0 <= p <= 1 + return p.is_nonnegative and (1 - p).is_nonnegative + raise ValueError("unexpected line type") + if ok(tu[t], self) and ok(tu[u], other): + return [line_intersection] + return [] + else: + # we're skew + return [] + + return other.intersection(self) + + def is_parallel(l1, l2): + """Are two linear entities parallel? + + Parameters + ========== + + l1 : LinearEntity + l2 : LinearEntity + + Returns + ======= + + True : if l1 and l2 are parallel, + False : otherwise. + + See Also + ======== + + coefficients + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(1, 1) + >>> p3, p4 = Point(3, 4), Point(6, 7) + >>> l1, l2 = Line(p1, p2), Line(p3, p4) + >>> Line.is_parallel(l1, l2) + True + >>> p5 = Point(6, 6) + >>> l3 = Line(p3, p5) + >>> Line.is_parallel(l1, l3) + False + >>> from sympy import Point3D, Line3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(3, 4, 5) + >>> p3, p4 = Point3D(2, 1, 1), Point3D(8, 9, 11) + >>> l1, l2 = Line3D(p1, p2), Line3D(p3, p4) + >>> Line3D.is_parallel(l1, l2) + True + >>> p5 = Point3D(6, 6, 6) + >>> l3 = Line3D(p3, p5) + >>> Line3D.is_parallel(l1, l3) + False + + """ + if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity): + raise TypeError('Must pass only LinearEntity objects') + + return l1.direction.is_scalar_multiple(l2.direction) + + def is_perpendicular(l1, l2): + """Are two linear entities perpendicular? + + Parameters + ========== + + l1 : LinearEntity + l2 : LinearEntity + + Returns + ======= + + True : if l1 and l2 are perpendicular, + False : otherwise. + + See Also + ======== + + coefficients + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(-1, 1) + >>> l1, l2 = Line(p1, p2), Line(p1, p3) + >>> l1.is_perpendicular(l2) + True + >>> p4 = Point(5, 3) + >>> l3 = Line(p1, p4) + >>> l1.is_perpendicular(l3) + False + >>> from sympy import Point3D, Line3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0) + >>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3) + >>> l1.is_perpendicular(l2) + False + >>> p4 = Point3D(5, 3, 7) + >>> l3 = Line3D(p1, p4) + >>> l1.is_perpendicular(l3) + False + + """ + if not isinstance(l1, LinearEntity) and not isinstance(l2, LinearEntity): + raise TypeError('Must pass only LinearEntity objects') + + return S.Zero.equals(l1.direction.dot(l2.direction)) + + def is_similar(self, other): + """ + Return True if self and other are contained in the same line. + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 1), Point(3, 4), Point(2, 3) + >>> l1 = Line(p1, p2) + >>> l2 = Line(p1, p3) + >>> l1.is_similar(l2) + True + """ + l = Line(self.p1, self.p2) + return l.contains(other) + + @property + def length(self): + """ + The length of the line. + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(3, 5) + >>> l1 = Line(p1, p2) + >>> l1.length + oo + """ + return S.Infinity + + @property + def p1(self): + """The first defining point of a linear entity. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> l = Line(p1, p2) + >>> l.p1 + Point2D(0, 0) + + """ + return self.args[0] + + @property + def p2(self): + """The second defining point of a linear entity. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> l = Line(p1, p2) + >>> l.p2 + Point2D(5, 3) + + """ + return self.args[1] + + def parallel_line(self, p): + """Create a new Line parallel to this linear entity which passes + through the point `p`. + + Parameters + ========== + + p : Point + + Returns + ======= + + line : Line + + See Also + ======== + + is_parallel + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2) + >>> l1 = Line(p1, p2) + >>> l2 = l1.parallel_line(p3) + >>> p3 in l2 + True + >>> l1.is_parallel(l2) + True + >>> from sympy import Point3D, Line3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(2, 3, 4), Point3D(-2, 2, 0) + >>> l1 = Line3D(p1, p2) + >>> l2 = l1.parallel_line(p3) + >>> p3 in l2 + True + >>> l1.is_parallel(l2) + True + + """ + p = Point(p, dim=self.ambient_dimension) + return Line(p, p + self.direction) + + def perpendicular_line(self, p): + """Create a new Line perpendicular to this linear entity which passes + through the point `p`. + + Parameters + ========== + + p : Point + + Returns + ======= + + line : Line + + See Also + ======== + + sympy.geometry.line.LinearEntity.is_perpendicular, perpendicular_segment + + Examples + ======== + + >>> from sympy import Point3D, Line3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(2, 3, 4), Point3D(-2, 2, 0) + >>> L = Line3D(p1, p2) + >>> P = L.perpendicular_line(p3); P + Line3D(Point3D(-2, 2, 0), Point3D(4/29, 6/29, 8/29)) + >>> L.is_perpendicular(P) + True + + In 3D the, the first point used to define the line is the point + through which the perpendicular was required to pass; the + second point is (arbitrarily) contained in the given line: + + >>> P.p2 in L + True + """ + p = Point(p, dim=self.ambient_dimension) + if p in self: + p = p + self.direction.orthogonal_direction + return Line(p, self.projection(p)) + + def perpendicular_segment(self, p): + """Create a perpendicular line segment from `p` to this line. + + The endpoints of the segment are ``p`` and the closest point in + the line containing self. (If self is not a line, the point might + not be in self.) + + Parameters + ========== + + p : Point + + Returns + ======= + + segment : Segment + + Notes + ===== + + Returns `p` itself if `p` is on this linear entity. + + See Also + ======== + + perpendicular_line + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 2) + >>> l1 = Line(p1, p2) + >>> s1 = l1.perpendicular_segment(p3) + >>> l1.is_perpendicular(s1) + True + >>> p3 in s1 + True + >>> l1.perpendicular_segment(Point(4, 0)) + Segment2D(Point2D(4, 0), Point2D(2, 2)) + >>> from sympy import Point3D, Line3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 2, 0) + >>> l1 = Line3D(p1, p2) + >>> s1 = l1.perpendicular_segment(p3) + >>> l1.is_perpendicular(s1) + True + >>> p3 in s1 + True + >>> l1.perpendicular_segment(Point3D(4, 0, 0)) + Segment3D(Point3D(4, 0, 0), Point3D(4/3, 4/3, 4/3)) + + """ + p = Point(p, dim=self.ambient_dimension) + if p in self: + return p + l = self.perpendicular_line(p) + # The intersection should be unique, so unpack the singleton + p2, = Intersection(Line(self.p1, self.p2), l) + + return Segment(p, p2) + + @property + def points(self): + """The two points used to define this linear entity. + + Returns + ======= + + points : tuple of Points + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(5, 11) + >>> l1 = Line(p1, p2) + >>> l1.points + (Point2D(0, 0), Point2D(5, 11)) + + """ + return (self.p1, self.p2) + + def projection(self, other): + """Project a point, line, ray, or segment onto this linear entity. + + Parameters + ========== + + other : Point or LinearEntity (Line, Ray, Segment) + + Returns + ======= + + projection : Point or LinearEntity (Line, Ray, Segment) + The return type matches the type of the parameter ``other``. + + Raises + ====== + + GeometryError + When method is unable to perform projection. + + Notes + ===== + + A projection involves taking the two points that define + the linear entity and projecting those points onto a + Line and then reforming the linear entity using these + projections. + A point P is projected onto a line L by finding the point + on L that is closest to P. This point is the intersection + of L and the line perpendicular to L that passes through P. + + See Also + ======== + + sympy.geometry.point.Point, perpendicular_line + + Examples + ======== + + >>> from sympy import Point, Line, Segment, Rational + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(Rational(1, 2), 0) + >>> l1 = Line(p1, p2) + >>> l1.projection(p3) + Point2D(1/4, 1/4) + >>> p4, p5 = Point(10, 0), Point(12, 1) + >>> s1 = Segment(p4, p5) + >>> l1.projection(s1) + Segment2D(Point2D(5, 5), Point2D(13/2, 13/2)) + >>> p1, p2, p3 = Point(0, 0, 1), Point(1, 1, 2), Point(2, 0, 1) + >>> l1 = Line(p1, p2) + >>> l1.projection(p3) + Point3D(2/3, 2/3, 5/3) + >>> p4, p5 = Point(10, 0, 1), Point(12, 1, 3) + >>> s1 = Segment(p4, p5) + >>> l1.projection(s1) + Segment3D(Point3D(10/3, 10/3, 13/3), Point3D(5, 5, 6)) + + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + + def proj_point(p): + return Point.project(p - self.p1, self.direction) + self.p1 + + if isinstance(other, Point): + return proj_point(other) + elif isinstance(other, LinearEntity): + p1, p2 = proj_point(other.p1), proj_point(other.p2) + # test to see if we're degenerate + if p1 == p2: + return p1 + projected = other.__class__(p1, p2) + projected = Intersection(self, projected) + if projected.is_empty: + return projected + # if we happen to have intersected in only a point, return that + if projected.is_FiniteSet and len(projected) == 1: + # projected is a set of size 1, so unpack it in `a` + a, = projected + return a + # order args so projection is in the same direction as self + if self.direction.dot(projected.direction) < 0: + p1, p2 = projected.args + projected = projected.func(p2, p1) + return projected + + raise GeometryError( + "Do not know how to project %s onto %s" % (other, self)) + + def random_point(self, seed=None): + """A random point on a LinearEntity. + + Returns + ======= + + point : Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Line, Ray, Segment + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> line = Line(p1, p2) + >>> r = line.random_point(seed=42) # seed value is optional + >>> r.n(3) + Point2D(-0.72, -0.432) + >>> r in line + True + >>> Ray(p1, p2).random_point(seed=42).n(3) + Point2D(0.72, 0.432) + >>> Segment(p1, p2).random_point(seed=42).n(3) + Point2D(3.2, 1.92) + + """ + if seed is not None: + rng = random.Random(seed) + else: + rng = random + pt = self.arbitrary_point(t) + if isinstance(self, Ray): + v = abs(rng.gauss(0, 1)) + elif isinstance(self, Segment): + v = rng.random() + elif isinstance(self, Line): + v = rng.gauss(0, 1) + else: + raise NotImplementedError('unhandled line type') + return pt.subs(t, Rational(v)) + + def bisectors(self, other): + """Returns the perpendicular lines which pass through the intersections + of self and other that are in the same plane. + + Parameters + ========== + + line : Line3D + + Returns + ======= + + list: two Line instances + + Examples + ======== + + >>> from sympy import Point3D, Line3D + >>> r1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)) + >>> r2 = Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0)) + >>> r1.bisectors(r2) + [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 0)), Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))] + + """ + if not isinstance(other, LinearEntity): + raise GeometryError("Expecting LinearEntity, not %s" % other) + + l1, l2 = self, other + + # make sure dimensions match or else a warning will rise from + # intersection calculation + if l1.p1.ambient_dimension != l2.p1.ambient_dimension: + if isinstance(l1, Line2D): + l1, l2 = l2, l1 + _, p1 = Point._normalize_dimension(l1.p1, l2.p1, on_morph='ignore') + _, p2 = Point._normalize_dimension(l1.p2, l2.p2, on_morph='ignore') + l2 = Line(p1, p2) + + point = intersection(l1, l2) + + # Three cases: Lines may intersect in a point, may be equal or may not intersect. + if not point: + raise GeometryError("The lines do not intersect") + else: + pt = point[0] + if isinstance(pt, Line): + # Intersection is a line because both lines are coincident + return [self] + + + d1 = l1.direction.unit + d2 = l2.direction.unit + + bis1 = Line(pt, pt + d1 + d2) + bis2 = Line(pt, pt + d1 - d2) + + return [bis1, bis2] + + +class Line(LinearEntity): + """An infinite line in space. + + A 2D line is declared with two distinct points, point and slope, or + an equation. A 3D line may be defined with a point and a direction ratio. + + Parameters + ========== + + p1 : Point + p2 : Point + slope : SymPy expression + direction_ratio : list + equation : equation of a line + + Notes + ===== + + `Line` will automatically subclass to `Line2D` or `Line3D` based + on the dimension of `p1`. The `slope` argument is only relevant + for `Line2D` and the `direction_ratio` argument is only relevant + for `Line3D`. + + The order of the points will define the direction of the line + which is used when calculating the angle between lines. + + See Also + ======== + + sympy.geometry.point.Point + sympy.geometry.line.Line2D + sympy.geometry.line.Line3D + + Examples + ======== + + >>> from sympy import Line, Segment, Point, Eq + >>> from sympy.abc import x, y, a, b + + >>> L = Line(Point(2,3), Point(3,5)) + >>> L + Line2D(Point2D(2, 3), Point2D(3, 5)) + >>> L.points + (Point2D(2, 3), Point2D(3, 5)) + >>> L.equation() + -2*x + y + 1 + >>> L.coefficients + (-2, 1, 1) + + Instantiate with keyword ``slope``: + + >>> Line(Point(0, 0), slope=0) + Line2D(Point2D(0, 0), Point2D(1, 0)) + + Instantiate with another linear object + + >>> s = Segment((0, 0), (0, 1)) + >>> Line(s).equation() + x + + The line corresponding to an equation in the for `ax + by + c = 0`, + can be entered: + + >>> Line(3*x + y + 18) + Line2D(Point2D(0, -18), Point2D(1, -21)) + + If `x` or `y` has a different name, then they can be specified, too, + as a string (to match the name) or symbol: + + >>> Line(Eq(3*a + b, -18), x='a', y=b) + Line2D(Point2D(0, -18), Point2D(1, -21)) + """ + def __new__(cls, *args, **kwargs): + if len(args) == 1 and isinstance(args[0], (Expr, Eq)): + missing = uniquely_named_symbol('?', args) + if not kwargs: + x = 'x' + y = 'y' + else: + x = kwargs.pop('x', missing) + y = kwargs.pop('y', missing) + if kwargs: + raise ValueError('expecting only x and y as keywords') + + equation = args[0] + if isinstance(equation, Eq): + equation = equation.lhs - equation.rhs + + def find_or_missing(x): + try: + return find(x, equation) + except ValueError: + return missing + x = find_or_missing(x) + y = find_or_missing(y) + + a, b, c = linear_coeffs(equation, x, y) + + if b: + return Line((0, -c/b), slope=-a/b) + if a: + return Line((-c/a, 0), slope=oo) + + raise ValueError('not found in equation: %s' % (set('xy') - {x, y})) + + else: + if len(args) > 0: + p1 = args[0] + if len(args) > 1: + p2 = args[1] + else: + p2 = None + + if isinstance(p1, LinearEntity): + if p2: + raise ValueError('If p1 is a LinearEntity, p2 must be None.') + dim = len(p1.p1) + else: + p1 = Point(p1) + dim = len(p1) + if p2 is not None or isinstance(p2, Point) and p2.ambient_dimension != dim: + p2 = Point(p2) + + if dim == 2: + return Line2D(p1, p2, **kwargs) + elif dim == 3: + return Line3D(p1, p2, **kwargs) + return LinearEntity.__new__(cls, p1, p2, **kwargs) + + def contains(self, other): + """ + Return True if `other` is on this Line, or False otherwise. + + Examples + ======== + + >>> from sympy import Line,Point + >>> p1, p2 = Point(0, 1), Point(3, 4) + >>> l = Line(p1, p2) + >>> l.contains(p1) + True + >>> l.contains((0, 1)) + True + >>> l.contains((0, 0)) + False + >>> a = (0, 0, 0) + >>> b = (1, 1, 1) + >>> c = (2, 2, 2) + >>> l1 = Line(a, b) + >>> l2 = Line(b, a) + >>> l1 == l2 + False + >>> l1 in l2 + True + + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if isinstance(other, Point): + return Point.is_collinear(other, self.p1, self.p2) + if isinstance(other, LinearEntity): + return Point.is_collinear(self.p1, self.p2, other.p1, other.p2) + return False + + def distance(self, other): + """ + Finds the shortest distance between a line and a point. + + Raises + ====== + + NotImplementedError is raised if `other` is not a Point + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(1, 1) + >>> s = Line(p1, p2) + >>> s.distance(Point(-1, 1)) + sqrt(2) + >>> s.distance((-1, 2)) + 3*sqrt(2)/2 + >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 1) + >>> s = Line(p1, p2) + >>> s.distance(Point(-1, 1, 1)) + 2*sqrt(6)/3 + >>> s.distance((-1, 1, 1)) + 2*sqrt(6)/3 + + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if self.contains(other): + return S.Zero + return self.perpendicular_segment(other).length + + def equals(self, other): + """Returns True if self and other are the same mathematical entities""" + if not isinstance(other, Line): + return False + return Point.is_collinear(self.p1, other.p1, self.p2, other.p2) + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of line. Gives + values that will produce a line that is +/- 5 units long (where a + unit is the distance between the two points that define the line). + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + plot_interval : list (plot interval) + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> l1 = Line(p1, p2) + >>> l1.plot_interval() + [t, -5, 5] + + """ + t = _symbol(parameter, real=True) + return [t, -5, 5] + + +class Ray(LinearEntity): + """A Ray is a semi-line in the space with a source point and a direction. + + Parameters + ========== + + p1 : Point + The source of the Ray + p2 : Point or radian value + This point determines the direction in which the Ray propagates. + If given as an angle it is interpreted in radians with the positive + direction being ccw. + + Attributes + ========== + + source + + See Also + ======== + + sympy.geometry.line.Ray2D + sympy.geometry.line.Ray3D + sympy.geometry.point.Point + sympy.geometry.line.Line + + Notes + ===== + + `Ray` will automatically subclass to `Ray2D` or `Ray3D` based on the + dimension of `p1`. + + Examples + ======== + + >>> from sympy import Ray, Point, pi + >>> r = Ray(Point(2, 3), Point(3, 5)) + >>> r + Ray2D(Point2D(2, 3), Point2D(3, 5)) + >>> r.points + (Point2D(2, 3), Point2D(3, 5)) + >>> r.source + Point2D(2, 3) + >>> r.xdirection + oo + >>> r.ydirection + oo + >>> r.slope + 2 + >>> Ray(Point(0, 0), angle=pi/4).slope + 1 + + """ + def __new__(cls, p1, p2=None, **kwargs): + p1 = Point(p1) + if p2 is not None: + p1, p2 = Point._normalize_dimension(p1, Point(p2)) + dim = len(p1) + + if dim == 2: + return Ray2D(p1, p2, **kwargs) + elif dim == 3: + return Ray3D(p1, p2, **kwargs) + return LinearEntity.__new__(cls, p1, p2, **kwargs) + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG path element for the LinearEntity. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + verts = (N(self.p1), N(self.p2)) + coords = ["{},{}".format(p.x, p.y) for p in verts] + path = "M {} L {}".format(coords[0], " L ".join(coords[1:])) + + return ( + '' + ).format(2.*scale_factor, path, fill_color) + + def contains(self, other): + """ + Is other GeometryEntity contained in this Ray? + + Examples + ======== + + >>> from sympy import Ray,Point,Segment + >>> p1, p2 = Point(0, 0), Point(4, 4) + >>> r = Ray(p1, p2) + >>> r.contains(p1) + True + >>> r.contains((1, 1)) + True + >>> r.contains((1, 3)) + False + >>> s = Segment((1, 1), (2, 2)) + >>> r.contains(s) + True + >>> s = Segment((1, 2), (2, 5)) + >>> r.contains(s) + False + >>> r1 = Ray((2, 2), (3, 3)) + >>> r.contains(r1) + True + >>> r1 = Ray((2, 2), (3, 5)) + >>> r.contains(r1) + False + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if isinstance(other, Point): + if Point.is_collinear(self.p1, self.p2, other): + # if we're in the direction of the ray, our + # direction vector dot the ray's direction vector + # should be non-negative + return bool((self.p2 - self.p1).dot(other - self.p1) >= S.Zero) + return False + elif isinstance(other, Ray): + if Point.is_collinear(self.p1, self.p2, other.p1, other.p2): + return bool((self.p2 - self.p1).dot(other.p2 - other.p1) > S.Zero) + return False + elif isinstance(other, Segment): + return other.p1 in self and other.p2 in self + + # No other known entity can be contained in a Ray + return False + + def distance(self, other): + """ + Finds the shortest distance between the ray and a point. + + Raises + ====== + + NotImplementedError is raised if `other` is not a Point + + Examples + ======== + + >>> from sympy import Point, Ray + >>> p1, p2 = Point(0, 0), Point(1, 1) + >>> s = Ray(p1, p2) + >>> s.distance(Point(-1, -1)) + sqrt(2) + >>> s.distance((-1, 2)) + 3*sqrt(2)/2 + >>> p1, p2 = Point(0, 0, 0), Point(1, 1, 2) + >>> s = Ray(p1, p2) + >>> s + Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 2)) + >>> s.distance(Point(-1, -1, 2)) + 4*sqrt(3)/3 + >>> s.distance((-1, -1, 2)) + 4*sqrt(3)/3 + + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if self.contains(other): + return S.Zero + + proj = Line(self.p1, self.p2).projection(other) + if self.contains(proj): + return abs(other - proj) + else: + return abs(other - self.source) + + def equals(self, other): + """Returns True if self and other are the same mathematical entities""" + if not isinstance(other, Ray): + return False + return self.source == other.source and other.p2 in self + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of the Ray. Gives + values that will produce a ray that is 10 units long (where a unit is + the distance between the two points that define the ray). + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + plot_interval : list + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Ray, pi + >>> r = Ray((0, 0), angle=pi/4) + >>> r.plot_interval() + [t, 0, 10] + + """ + t = _symbol(parameter, real=True) + return [t, 0, 10] + + @property + def source(self): + """The point from which the ray emanates. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Ray + >>> p1, p2 = Point(0, 0), Point(4, 1) + >>> r1 = Ray(p1, p2) + >>> r1.source + Point2D(0, 0) + >>> p1, p2 = Point(0, 0, 0), Point(4, 1, 5) + >>> r1 = Ray(p2, p1) + >>> r1.source + Point3D(4, 1, 5) + + """ + return self.p1 + + +class Segment(LinearEntity): + """A line segment in space. + + Parameters + ========== + + p1 : Point + p2 : Point + + Attributes + ========== + + length : number or SymPy expression + midpoint : Point + + See Also + ======== + + sympy.geometry.line.Segment2D + sympy.geometry.line.Segment3D + sympy.geometry.point.Point + sympy.geometry.line.Line + + Notes + ===== + + If 2D or 3D points are used to define `Segment`, it will + be automatically subclassed to `Segment2D` or `Segment3D`. + + Examples + ======== + + >>> from sympy import Point, Segment + >>> Segment((1, 0), (1, 1)) # tuples are interpreted as pts + Segment2D(Point2D(1, 0), Point2D(1, 1)) + >>> s = Segment(Point(4, 3), Point(1, 1)) + >>> s.points + (Point2D(4, 3), Point2D(1, 1)) + >>> s.slope + 2/3 + >>> s.length + sqrt(13) + >>> s.midpoint + Point2D(5/2, 2) + >>> Segment((1, 0, 0), (1, 1, 1)) # tuples are interpreted as pts + Segment3D(Point3D(1, 0, 0), Point3D(1, 1, 1)) + >>> s = Segment(Point(4, 3, 9), Point(1, 1, 7)); s + Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7)) + >>> s.points + (Point3D(4, 3, 9), Point3D(1, 1, 7)) + >>> s.length + sqrt(17) + >>> s.midpoint + Point3D(5/2, 2, 8) + + """ + def __new__(cls, p1, p2, **kwargs): + p1, p2 = Point._normalize_dimension(Point(p1), Point(p2)) + dim = len(p1) + + if dim == 2: + return Segment2D(p1, p2, **kwargs) + elif dim == 3: + return Segment3D(p1, p2, **kwargs) + return LinearEntity.__new__(cls, p1, p2, **kwargs) + + def contains(self, other): + """ + Is the other GeometryEntity contained within this Segment? + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2 = Point(0, 1), Point(3, 4) + >>> s = Segment(p1, p2) + >>> s2 = Segment(p2, p1) + >>> s.contains(s2) + True + >>> from sympy import Point3D, Segment3D + >>> p1, p2 = Point3D(0, 1, 1), Point3D(3, 4, 5) + >>> s = Segment3D(p1, p2) + >>> s2 = Segment3D(p2, p1) + >>> s.contains(s2) + True + >>> s.contains((p1 + p2)/2) + True + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if isinstance(other, Point): + if Point.is_collinear(other, self.p1, self.p2): + if isinstance(self, Segment2D): + # if it is collinear and is in the bounding box of the + # segment then it must be on the segment + vert = (1/self.slope).equals(0) + if vert is False: + isin = (self.p1.x - other.x)*(self.p2.x - other.x) <= 0 + if isin in (True, False): + return isin + if vert is True: + isin = (self.p1.y - other.y)*(self.p2.y - other.y) <= 0 + if isin in (True, False): + return isin + # use the triangle inequality + d1, d2 = other - self.p1, other - self.p2 + d = self.p2 - self.p1 + # without the call to simplify, SymPy cannot tell that an expression + # like (a+b)*(a/2+b/2) is always non-negative. If it cannot be + # determined, raise an Undecidable error + try: + # the triangle inequality says that |d1|+|d2| >= |d| and is strict + # only if other lies in the line segment + return bool(simplify(Eq(abs(d1) + abs(d2) - abs(d), 0))) + except TypeError: + raise Undecidable("Cannot determine if {} is in {}".format(other, self)) + if isinstance(other, Segment): + return other.p1 in self and other.p2 in self + + return False + + def equals(self, other): + """Returns True if self and other are the same mathematical entities""" + return isinstance(other, self.func) and list( + ordered(self.args)) == list(ordered(other.args)) + + def distance(self, other): + """ + Finds the shortest distance between a line segment and a point. + + Raises + ====== + + NotImplementedError is raised if `other` is not a Point + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2 = Point(0, 1), Point(3, 4) + >>> s = Segment(p1, p2) + >>> s.distance(Point(10, 15)) + sqrt(170) + >>> s.distance((0, 12)) + sqrt(73) + >>> from sympy import Point3D, Segment3D + >>> p1, p2 = Point3D(0, 0, 3), Point3D(1, 1, 4) + >>> s = Segment3D(p1, p2) + >>> s.distance(Point3D(10, 15, 12)) + sqrt(341) + >>> s.distance((10, 15, 12)) + sqrt(341) + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if isinstance(other, Point): + vp1 = other - self.p1 + vp2 = other - self.p2 + + dot_prod_sign_1 = self.direction.dot(vp1) >= 0 + dot_prod_sign_2 = self.direction.dot(vp2) <= 0 + if dot_prod_sign_1 and dot_prod_sign_2: + return Line(self.p1, self.p2).distance(other) + if dot_prod_sign_1 and not dot_prod_sign_2: + return abs(vp2) + if not dot_prod_sign_1 and dot_prod_sign_2: + return abs(vp1) + raise NotImplementedError() + + @property + def length(self): + """The length of the line segment. + + See Also + ======== + + sympy.geometry.point.Point.distance + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2 = Point(0, 0), Point(4, 3) + >>> s1 = Segment(p1, p2) + >>> s1.length + 5 + >>> from sympy import Point3D, Segment3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(4, 3, 3) + >>> s1 = Segment3D(p1, p2) + >>> s1.length + sqrt(34) + + """ + return Point.distance(self.p1, self.p2) + + @property + def midpoint(self): + """The midpoint of the line segment. + + See Also + ======== + + sympy.geometry.point.Point.midpoint + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2 = Point(0, 0), Point(4, 3) + >>> s1 = Segment(p1, p2) + >>> s1.midpoint + Point2D(2, 3/2) + >>> from sympy import Point3D, Segment3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(4, 3, 3) + >>> s1 = Segment3D(p1, p2) + >>> s1.midpoint + Point3D(2, 3/2, 3/2) + + """ + return Point.midpoint(self.p1, self.p2) + + def perpendicular_bisector(self, p=None): + """The perpendicular bisector of this segment. + + If no point is specified or the point specified is not on the + bisector then the bisector is returned as a Line. Otherwise a + Segment is returned that joins the point specified and the + intersection of the bisector and the segment. + + Parameters + ========== + + p : Point + + Returns + ======= + + bisector : Line or Segment + + See Also + ======== + + LinearEntity.perpendicular_segment + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2, p3 = Point(0, 0), Point(6, 6), Point(5, 1) + >>> s1 = Segment(p1, p2) + >>> s1.perpendicular_bisector() + Line2D(Point2D(3, 3), Point2D(-3, 9)) + + >>> s1.perpendicular_bisector(p3) + Segment2D(Point2D(5, 1), Point2D(3, 3)) + + """ + l = self.perpendicular_line(self.midpoint) + if p is not None: + p2 = Point(p, dim=self.ambient_dimension) + if p2 in l: + return Segment(p2, self.midpoint) + return l + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of the Segment gives + values that will produce the full segment in a plot. + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + plot_interval : list + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Point, Segment + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> s1 = Segment(p1, p2) + >>> s1.plot_interval() + [t, 0, 1] + + """ + t = _symbol(parameter, real=True) + return [t, 0, 1] + + +class LinearEntity2D(LinearEntity): + """A base class for all linear entities (line, ray and segment) + in a 2-dimensional Euclidean space. + + Attributes + ========== + + p1 + p2 + coefficients + slope + points + + Notes + ===== + + This is an abstract class and is not meant to be instantiated. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity + + """ + @property + def bounds(self): + """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding + rectangle for the geometric figure. + + """ + verts = self.points + xs = [p.x for p in verts] + ys = [p.y for p in verts] + return (min(xs), min(ys), max(xs), max(ys)) + + def perpendicular_line(self, p): + """Create a new Line perpendicular to this linear entity which passes + through the point `p`. + + Parameters + ========== + + p : Point + + Returns + ======= + + line : Line + + See Also + ======== + + sympy.geometry.line.LinearEntity.is_perpendicular, perpendicular_segment + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2) + >>> L = Line(p1, p2) + >>> P = L.perpendicular_line(p3); P + Line2D(Point2D(-2, 2), Point2D(-5, 4)) + >>> L.is_perpendicular(P) + True + + In 2D, the first point of the perpendicular line is the + point through which was required to pass; the second + point is arbitrarily chosen. To get a line that explicitly + uses a point in the line, create a line from the perpendicular + segment from the line to the point: + + >>> Line(L.perpendicular_segment(p3)) + Line2D(Point2D(-2, 2), Point2D(4/13, 6/13)) + """ + p = Point(p, dim=self.ambient_dimension) + # any two lines in R^2 intersect, so blindly making + # a line through p in an orthogonal direction will work + # and is faster than finding the projection point as in 3D + return Line(p, p + self.direction.orthogonal_direction) + + @property + def slope(self): + """The slope of this linear entity, or infinity if vertical. + + Returns + ======= + + slope : number or SymPy expression + + See Also + ======== + + coefficients + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(0, 0), Point(3, 5) + >>> l1 = Line(p1, p2) + >>> l1.slope + 5/3 + + >>> p3 = Point(0, 4) + >>> l2 = Line(p1, p3) + >>> l2.slope + oo + + """ + d1, d2 = (self.p1 - self.p2).args + if d1 == 0: + return S.Infinity + return simplify(d2/d1) + + +class Line2D(LinearEntity2D, Line): + """An infinite line in space 2D. + + A line is declared with two distinct points or a point and slope + as defined using keyword `slope`. + + Parameters + ========== + + p1 : Point + pt : Point + slope : SymPy expression + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Line, Segment, Point + >>> L = Line(Point(2,3), Point(3,5)) + >>> L + Line2D(Point2D(2, 3), Point2D(3, 5)) + >>> L.points + (Point2D(2, 3), Point2D(3, 5)) + >>> L.equation() + -2*x + y + 1 + >>> L.coefficients + (-2, 1, 1) + + Instantiate with keyword ``slope``: + + >>> Line(Point(0, 0), slope=0) + Line2D(Point2D(0, 0), Point2D(1, 0)) + + Instantiate with another linear object + + >>> s = Segment((0, 0), (0, 1)) + >>> Line(s).equation() + x + """ + def __new__(cls, p1, pt=None, slope=None, **kwargs): + if isinstance(p1, LinearEntity): + if pt is not None: + raise ValueError('When p1 is a LinearEntity, pt should be None') + p1, pt = Point._normalize_dimension(*p1.args, dim=2) + else: + p1 = Point(p1, dim=2) + if pt is not None and slope is None: + try: + p2 = Point(pt, dim=2) + except (NotImplementedError, TypeError, ValueError): + raise ValueError(filldedent(''' + The 2nd argument was not a valid Point. + If it was a slope, enter it with keyword "slope". + ''')) + elif slope is not None and pt is None: + slope = sympify(slope) + if slope.is_finite is False: + # when infinite slope, don't change x + dx = 0 + dy = 1 + else: + # go over 1 up slope + dx = 1 + dy = slope + # XXX avoiding simplification by adding to coords directly + p2 = Point(p1.x + dx, p1.y + dy, evaluate=False) + else: + raise ValueError('A 2nd Point or keyword "slope" must be used.') + return LinearEntity2D.__new__(cls, p1, p2, **kwargs) + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG path element for the LinearEntity. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + verts = (N(self.p1), N(self.p2)) + coords = ["{},{}".format(p.x, p.y) for p in verts] + path = "M {} L {}".format(coords[0], " L ".join(coords[1:])) + + return ( + '' + ).format(2.*scale_factor, path, fill_color) + + @property + def coefficients(self): + """The coefficients (`a`, `b`, `c`) for `ax + by + c = 0`. + + See Also + ======== + + sympy.geometry.line.Line2D.equation + + Examples + ======== + + >>> from sympy import Point, Line + >>> from sympy.abc import x, y + >>> p1, p2 = Point(0, 0), Point(5, 3) + >>> l = Line(p1, p2) + >>> l.coefficients + (-3, 5, 0) + + >>> p3 = Point(x, y) + >>> l2 = Line(p1, p3) + >>> l2.coefficients + (-y, x, 0) + + """ + p1, p2 = self.points + if p1.x == p2.x: + return (S.One, S.Zero, -p1.x) + elif p1.y == p2.y: + return (S.Zero, S.One, -p1.y) + return tuple([simplify(i) for i in + (self.p1.y - self.p2.y, + self.p2.x - self.p1.x, + self.p1.x*self.p2.y - self.p1.y*self.p2.x)]) + + def equation(self, x='x', y='y'): + """The equation of the line: ax + by + c. + + Parameters + ========== + + x : str, optional + The name to use for the x-axis, default value is 'x'. + y : str, optional + The name to use for the y-axis, default value is 'y'. + + Returns + ======= + + equation : SymPy expression + + See Also + ======== + + sympy.geometry.line.Line2D.coefficients + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(1, 0), Point(5, 3) + >>> l1 = Line(p1, p2) + >>> l1.equation() + -3*x + 4*y + 3 + + """ + x = _symbol(x, real=True) + y = _symbol(y, real=True) + p1, p2 = self.points + if p1.x == p2.x: + return x - p1.x + elif p1.y == p2.y: + return y - p1.y + + a, b, c = self.coefficients + return a*x + b*y + c + + +class Ray2D(LinearEntity2D, Ray): + """ + A Ray is a semi-line in the space with a source point and a direction. + + Parameters + ========== + + p1 : Point + The source of the Ray + p2 : Point or radian value + This point determines the direction in which the Ray propagates. + If given as an angle it is interpreted in radians with the positive + direction being ccw. + + Attributes + ========== + + source + xdirection + ydirection + + See Also + ======== + + sympy.geometry.point.Point, Line + + Examples + ======== + + >>> from sympy import Point, pi, Ray + >>> r = Ray(Point(2, 3), Point(3, 5)) + >>> r + Ray2D(Point2D(2, 3), Point2D(3, 5)) + >>> r.points + (Point2D(2, 3), Point2D(3, 5)) + >>> r.source + Point2D(2, 3) + >>> r.xdirection + oo + >>> r.ydirection + oo + >>> r.slope + 2 + >>> Ray(Point(0, 0), angle=pi/4).slope + 1 + + """ + def __new__(cls, p1, pt=None, angle=None, **kwargs): + p1 = Point(p1, dim=2) + if pt is not None and angle is None: + try: + p2 = Point(pt, dim=2) + except (NotImplementedError, TypeError, ValueError): + raise ValueError(filldedent(''' + The 2nd argument was not a valid Point; if + it was meant to be an angle it should be + given with keyword "angle".''')) + if p1 == p2: + raise ValueError('A Ray requires two distinct points.') + elif angle is not None and pt is None: + # we need to know if the angle is an odd multiple of pi/2 + angle = sympify(angle) + c = _pi_coeff(angle) + p2 = None + if c is not None: + if c.is_Rational: + if c.q == 2: + if c.p == 1: + p2 = p1 + Point(0, 1) + elif c.p == 3: + p2 = p1 + Point(0, -1) + elif c.q == 1: + if c.p == 0: + p2 = p1 + Point(1, 0) + elif c.p == 1: + p2 = p1 + Point(-1, 0) + if p2 is None: + c *= S.Pi + else: + c = angle % (2*S.Pi) + if not p2: + m = 2*c/S.Pi + left = And(1 < m, m < 3) # is it in quadrant 2 or 3? + x = Piecewise((-1, left), (Piecewise((0, Eq(m % 1, 0)), (1, True)), True)) + y = Piecewise((-tan(c), left), (Piecewise((1, Eq(m, 1)), (-1, Eq(m, 3)), (tan(c), True)), True)) + p2 = p1 + Point(x, y) + else: + raise ValueError('A 2nd point or keyword "angle" must be used.') + + return LinearEntity2D.__new__(cls, p1, p2, **kwargs) + + @property + def xdirection(self): + """The x direction of the ray. + + Positive infinity if the ray points in the positive x direction, + negative infinity if the ray points in the negative x direction, + or 0 if the ray is vertical. + + See Also + ======== + + ydirection + + Examples + ======== + + >>> from sympy import Point, Ray + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, -1) + >>> r1, r2 = Ray(p1, p2), Ray(p1, p3) + >>> r1.xdirection + oo + >>> r2.xdirection + 0 + + """ + if self.p1.x < self.p2.x: + return S.Infinity + elif self.p1.x == self.p2.x: + return S.Zero + else: + return S.NegativeInfinity + + @property + def ydirection(self): + """The y direction of the ray. + + Positive infinity if the ray points in the positive y direction, + negative infinity if the ray points in the negative y direction, + or 0 if the ray is horizontal. + + See Also + ======== + + xdirection + + Examples + ======== + + >>> from sympy import Point, Ray + >>> p1, p2, p3 = Point(0, 0), Point(-1, -1), Point(-1, 0) + >>> r1, r2 = Ray(p1, p2), Ray(p1, p3) + >>> r1.ydirection + -oo + >>> r2.ydirection + 0 + + """ + if self.p1.y < self.p2.y: + return S.Infinity + elif self.p1.y == self.p2.y: + return S.Zero + else: + return S.NegativeInfinity + + def closing_angle(r1, r2): + """Return the angle by which r2 must be rotated so it faces the same + direction as r1. + + Parameters + ========== + + r1 : Ray2D + r2 : Ray2D + + Returns + ======= + + angle : angle in radians (ccw angle is positive) + + See Also + ======== + + LinearEntity.angle_between + + Examples + ======== + + >>> from sympy import Ray, pi + >>> r1 = Ray((0, 0), (1, 0)) + >>> r2 = r1.rotate(-pi/2) + >>> angle = r1.closing_angle(r2); angle + pi/2 + >>> r2.rotate(angle).direction.unit == r1.direction.unit + True + >>> r2.closing_angle(r1) + -pi/2 + """ + if not all(isinstance(r, Ray2D) for r in (r1, r2)): + # although the direction property is defined for + # all linear entities, only the Ray is truly a + # directed object + raise TypeError('Both arguments must be Ray2D objects.') + + a1 = atan2(*list(reversed(r1.direction.args))) + a2 = atan2(*list(reversed(r2.direction.args))) + if a1*a2 < 0: + a1 = 2*S.Pi + a1 if a1 < 0 else a1 + a2 = 2*S.Pi + a2 if a2 < 0 else a2 + return a1 - a2 + + +class Segment2D(LinearEntity2D, Segment): + """A line segment in 2D space. + + Parameters + ========== + + p1 : Point + p2 : Point + + Attributes + ========== + + length : number or SymPy expression + midpoint : Point + + See Also + ======== + + sympy.geometry.point.Point, Line + + Examples + ======== + + >>> from sympy import Point, Segment + >>> Segment((1, 0), (1, 1)) # tuples are interpreted as pts + Segment2D(Point2D(1, 0), Point2D(1, 1)) + >>> s = Segment(Point(4, 3), Point(1, 1)); s + Segment2D(Point2D(4, 3), Point2D(1, 1)) + >>> s.points + (Point2D(4, 3), Point2D(1, 1)) + >>> s.slope + 2/3 + >>> s.length + sqrt(13) + >>> s.midpoint + Point2D(5/2, 2) + + """ + def __new__(cls, p1, p2, **kwargs): + p1 = Point(p1, dim=2) + p2 = Point(p2, dim=2) + + if p1 == p2: + return p1 + + return LinearEntity2D.__new__(cls, p1, p2, **kwargs) + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG path element for the LinearEntity. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + verts = (N(self.p1), N(self.p2)) + coords = ["{},{}".format(p.x, p.y) for p in verts] + path = "M {} L {}".format(coords[0], " L ".join(coords[1:])) + return ( + '' + ).format(2.*scale_factor, path, fill_color) + + +class LinearEntity3D(LinearEntity): + """An base class for all linear entities (line, ray and segment) + in a 3-dimensional Euclidean space. + + Attributes + ========== + + p1 + p2 + direction_ratio + direction_cosine + points + + Notes + ===== + + This is a base class and is not meant to be instantiated. + """ + def __new__(cls, p1, p2, **kwargs): + p1 = Point3D(p1, dim=3) + p2 = Point3D(p2, dim=3) + if p1 == p2: + # if it makes sense to return a Point, handle in subclass + raise ValueError( + "%s.__new__ requires two unique Points." % cls.__name__) + + return GeometryEntity.__new__(cls, p1, p2, **kwargs) + + ambient_dimension = 3 + + @property + def direction_ratio(self): + """The direction ratio of a given line in 3D. + + See Also + ======== + + sympy.geometry.line.Line3D.equation + + Examples + ======== + + >>> from sympy import Point3D, Line3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(5, 3, 1) + >>> l = Line3D(p1, p2) + >>> l.direction_ratio + [5, 3, 1] + """ + p1, p2 = self.points + return p1.direction_ratio(p2) + + @property + def direction_cosine(self): + """The normalized direction ratio of a given line in 3D. + + See Also + ======== + + sympy.geometry.line.Line3D.equation + + Examples + ======== + + >>> from sympy import Point3D, Line3D + >>> p1, p2 = Point3D(0, 0, 0), Point3D(5, 3, 1) + >>> l = Line3D(p1, p2) + >>> l.direction_cosine + [sqrt(35)/7, 3*sqrt(35)/35, sqrt(35)/35] + >>> sum(i**2 for i in _) + 1 + """ + p1, p2 = self.points + return p1.direction_cosine(p2) + + +class Line3D(LinearEntity3D, Line): + """An infinite 3D line in space. + + A line is declared with two distinct points or a point and direction_ratio + as defined using keyword `direction_ratio`. + + Parameters + ========== + + p1 : Point3D + pt : Point3D + direction_ratio : list + + See Also + ======== + + sympy.geometry.point.Point3D + sympy.geometry.line.Line + sympy.geometry.line.Line2D + + Examples + ======== + + >>> from sympy import Line3D, Point3D + >>> L = Line3D(Point3D(2, 3, 4), Point3D(3, 5, 1)) + >>> L + Line3D(Point3D(2, 3, 4), Point3D(3, 5, 1)) + >>> L.points + (Point3D(2, 3, 4), Point3D(3, 5, 1)) + """ + def __new__(cls, p1, pt=None, direction_ratio=(), **kwargs): + if isinstance(p1, LinearEntity3D): + if pt is not None: + raise ValueError('if p1 is a LinearEntity, pt must be None.') + p1, pt = p1.args + else: + p1 = Point(p1, dim=3) + if pt is not None and len(direction_ratio) == 0: + pt = Point(pt, dim=3) + elif len(direction_ratio) == 3 and pt is None: + pt = Point3D(p1.x + direction_ratio[0], p1.y + direction_ratio[1], + p1.z + direction_ratio[2]) + else: + raise ValueError('A 2nd Point or keyword "direction_ratio" must ' + 'be used.') + + return LinearEntity3D.__new__(cls, p1, pt, **kwargs) + + def equation(self, x='x', y='y', z='z'): + """Return the equations that define the line in 3D. + + Parameters + ========== + + x : str, optional + The name to use for the x-axis, default value is 'x'. + y : str, optional + The name to use for the y-axis, default value is 'y'. + z : str, optional + The name to use for the z-axis, default value is 'z'. + + Returns + ======= + + equation : Tuple of simultaneous equations + + Examples + ======== + + >>> from sympy import Point3D, Line3D, solve + >>> from sympy.abc import x, y, z + >>> p1, p2 = Point3D(1, 0, 0), Point3D(5, 3, 0) + >>> l1 = Line3D(p1, p2) + >>> eq = l1.equation(x, y, z); eq + (-3*x + 4*y + 3, z) + >>> solve(eq.subs(z, 0), (x, y, z)) + {x: 4*y/3 + 1} + """ + x, y, z, k = [_symbol(i, real=True) for i in (x, y, z, 'k')] + p1, p2 = self.points + d1, d2, d3 = p1.direction_ratio(p2) + x1, y1, z1 = p1 + eqs = [-d1*k + x - x1, -d2*k + y - y1, -d3*k + z - z1] + # eliminate k from equations by solving first eq with k for k + for i, e in enumerate(eqs): + if e.has(k): + kk = solve(eqs[i], k)[0] + eqs.pop(i) + break + return Tuple(*[i.subs(k, kk).as_numer_denom()[0] for i in eqs]) + + def distance(self, other): + """ + Finds the shortest distance between a line and another object. + + Parameters + ========== + + Point3D, Line3D, Plane, tuple, list + + Returns + ======= + + distance + + Notes + ===== + + This method accepts only 3D entities as it's parameter + + Tuples and lists are converted to Point3D and therefore must be of + length 3, 2 or 1. + + NotImplementedError is raised if `other` is not an instance of one + of the specified classes: Point3D, Line3D, or Plane. + + Examples + ======== + + >>> from sympy.geometry import Line3D + >>> l1 = Line3D((0, 0, 0), (0, 0, 1)) + >>> l2 = Line3D((0, 1, 0), (1, 1, 1)) + >>> l1.distance(l2) + 1 + + The computed distance may be symbolic, too: + + >>> from sympy.abc import x, y + >>> l1 = Line3D((0, 0, 0), (0, 0, 1)) + >>> l2 = Line3D((0, x, 0), (y, x, 1)) + >>> l1.distance(l2) + Abs(x*y)/Abs(sqrt(y**2)) + + """ + + from .plane import Plane # Avoid circular import + + if isinstance(other, (tuple, list)): + try: + other = Point3D(other) + except ValueError: + pass + + if isinstance(other, Point3D): + return super().distance(other) + + if isinstance(other, Line3D): + if self == other: + return S.Zero + if self.is_parallel(other): + return super().distance(other.p1) + + # Skew lines + self_direction = Matrix(self.direction_ratio) + other_direction = Matrix(other.direction_ratio) + normal = self_direction.cross(other_direction) + plane_through_self = Plane(p1=self.p1, normal_vector=normal) + return other.p1.distance(plane_through_self) + + if isinstance(other, Plane): + return other.distance(self) + + msg = f"{other} has type {type(other)}, which is unsupported" + raise NotImplementedError(msg) + + +class Ray3D(LinearEntity3D, Ray): + """ + A Ray is a semi-line in the space with a source point and a direction. + + Parameters + ========== + + p1 : Point3D + The source of the Ray + p2 : Point or a direction vector + direction_ratio: Determines the direction in which the Ray propagates. + + + Attributes + ========== + + source + xdirection + ydirection + zdirection + + See Also + ======== + + sympy.geometry.point.Point3D, Line3D + + + Examples + ======== + + >>> from sympy import Point3D, Ray3D + >>> r = Ray3D(Point3D(2, 3, 4), Point3D(3, 5, 0)) + >>> r + Ray3D(Point3D(2, 3, 4), Point3D(3, 5, 0)) + >>> r.points + (Point3D(2, 3, 4), Point3D(3, 5, 0)) + >>> r.source + Point3D(2, 3, 4) + >>> r.xdirection + oo + >>> r.ydirection + oo + >>> r.direction_ratio + [1, 2, -4] + + """ + def __new__(cls, p1, pt=None, direction_ratio=(), **kwargs): + if isinstance(p1, LinearEntity3D): + if pt is not None: + raise ValueError('If p1 is a LinearEntity, pt must be None') + p1, pt = p1.args + else: + p1 = Point(p1, dim=3) + if pt is not None and len(direction_ratio) == 0: + pt = Point(pt, dim=3) + elif len(direction_ratio) == 3 and pt is None: + pt = Point3D(p1.x + direction_ratio[0], p1.y + direction_ratio[1], + p1.z + direction_ratio[2]) + else: + raise ValueError(filldedent(''' + A 2nd Point or keyword "direction_ratio" must be used. + ''')) + + return LinearEntity3D.__new__(cls, p1, pt, **kwargs) + + @property + def xdirection(self): + """The x direction of the ray. + + Positive infinity if the ray points in the positive x direction, + negative infinity if the ray points in the negative x direction, + or 0 if the ray is vertical. + + See Also + ======== + + ydirection + + Examples + ======== + + >>> from sympy import Point3D, Ray3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, -1, 0) + >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3) + >>> r1.xdirection + oo + >>> r2.xdirection + 0 + + """ + if self.p1.x < self.p2.x: + return S.Infinity + elif self.p1.x == self.p2.x: + return S.Zero + else: + return S.NegativeInfinity + + @property + def ydirection(self): + """The y direction of the ray. + + Positive infinity if the ray points in the positive y direction, + negative infinity if the ray points in the negative y direction, + or 0 if the ray is horizontal. + + See Also + ======== + + xdirection + + Examples + ======== + + >>> from sympy import Point3D, Ray3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(-1, -1, -1), Point3D(-1, 0, 0) + >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3) + >>> r1.ydirection + -oo + >>> r2.ydirection + 0 + + """ + if self.p1.y < self.p2.y: + return S.Infinity + elif self.p1.y == self.p2.y: + return S.Zero + else: + return S.NegativeInfinity + + @property + def zdirection(self): + """The z direction of the ray. + + Positive infinity if the ray points in the positive z direction, + negative infinity if the ray points in the negative z direction, + or 0 if the ray is horizontal. + + See Also + ======== + + xdirection + + Examples + ======== + + >>> from sympy import Point3D, Ray3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(-1, -1, -1), Point3D(-1, 0, 0) + >>> r1, r2 = Ray3D(p1, p2), Ray3D(p1, p3) + >>> r1.ydirection + -oo + >>> r2.ydirection + 0 + >>> r2.zdirection + 0 + + """ + if self.p1.z < self.p2.z: + return S.Infinity + elif self.p1.z == self.p2.z: + return S.Zero + else: + return S.NegativeInfinity + + +class Segment3D(LinearEntity3D, Segment): + """A line segment in a 3D space. + + Parameters + ========== + + p1 : Point3D + p2 : Point3D + + Attributes + ========== + + length : number or SymPy expression + midpoint : Point3D + + See Also + ======== + + sympy.geometry.point.Point3D, Line3D + + Examples + ======== + + >>> from sympy import Point3D, Segment3D + >>> Segment3D((1, 0, 0), (1, 1, 1)) # tuples are interpreted as pts + Segment3D(Point3D(1, 0, 0), Point3D(1, 1, 1)) + >>> s = Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7)); s + Segment3D(Point3D(4, 3, 9), Point3D(1, 1, 7)) + >>> s.points + (Point3D(4, 3, 9), Point3D(1, 1, 7)) + >>> s.length + sqrt(17) + >>> s.midpoint + Point3D(5/2, 2, 8) + + """ + def __new__(cls, p1, p2, **kwargs): + p1 = Point(p1, dim=3) + p2 = Point(p2, dim=3) + + if p1 == p2: + return p1 + + return LinearEntity3D.__new__(cls, p1, p2, **kwargs) diff --git a/lib/python3.11/site-packages/sympy/geometry/parabola.py b/lib/python3.11/site-packages/sympy/geometry/parabola.py new file mode 100644 index 0000000000000000000000000000000000000000..0b5a3c03fbc9f7b3e2e76538f38d1063539130ae --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/parabola.py @@ -0,0 +1,422 @@ +"""Parabolic geometrical entity. + +Contains +* Parabola + +""" + +from sympy.core import S +from sympy.core.sorting import ordered +from sympy.core.symbol import _symbol, symbols +from sympy.geometry.entity import GeometryEntity, GeometrySet +from sympy.geometry.point import Point, Point2D +from sympy.geometry.line import Line, Line2D, Ray2D, Segment2D, LinearEntity3D +from sympy.geometry.ellipse import Ellipse +from sympy.functions import sign +from sympy.simplify import simplify +from sympy.solvers.solvers import solve + + +class Parabola(GeometrySet): + """A parabolic GeometryEntity. + + A parabola is declared with a point, that is called 'focus', and + a line, that is called 'directrix'. + Only vertical or horizontal parabolas are currently supported. + + Parameters + ========== + + focus : Point + Default value is Point(0, 0) + directrix : Line + + Attributes + ========== + + focus + directrix + axis of symmetry + focal length + p parameter + vertex + eccentricity + + Raises + ====== + ValueError + When `focus` is not a two dimensional point. + When `focus` is a point of directrix. + NotImplementedError + When `directrix` is neither horizontal nor vertical. + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8))) + >>> p1.focus + Point2D(0, 0) + >>> p1.directrix + Line2D(Point2D(5, 8), Point2D(7, 8)) + + """ + + def __new__(cls, focus=None, directrix=None, **kwargs): + + if focus: + focus = Point(focus, dim=2) + else: + focus = Point(0, 0) + + directrix = Line(directrix) + + if directrix.contains(focus): + raise ValueError('The focus must not be a point of directrix') + + return GeometryEntity.__new__(cls, focus, directrix, **kwargs) + + @property + def ambient_dimension(self): + """Returns the ambient dimension of parabola. + + Returns + ======= + + ambient_dimension : integer + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> f1 = Point(0, 0) + >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) + >>> p1.ambient_dimension + 2 + + """ + return 2 + + @property + def axis_of_symmetry(self): + """Return the axis of symmetry of the parabola: a line + perpendicular to the directrix passing through the focus. + + Returns + ======= + + axis_of_symmetry : Line + + See Also + ======== + + sympy.geometry.line.Line + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.axis_of_symmetry + Line2D(Point2D(0, 0), Point2D(0, 1)) + + """ + return self.directrix.perpendicular_line(self.focus) + + @property + def directrix(self): + """The directrix of the parabola. + + Returns + ======= + + directrix : Line + + See Also + ======== + + sympy.geometry.line.Line + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> l1 = Line(Point(5, 8), Point(7, 8)) + >>> p1 = Parabola(Point(0, 0), l1) + >>> p1.directrix + Line2D(Point2D(5, 8), Point2D(7, 8)) + + """ + return self.args[1] + + @property + def eccentricity(self): + """The eccentricity of the parabola. + + Returns + ======= + + eccentricity : number + + A parabola may also be characterized as a conic section with an + eccentricity of 1. As a consequence of this, all parabolas are + similar, meaning that while they can be different sizes, + they are all the same shape. + + See Also + ======== + + https://en.wikipedia.org/wiki/Parabola + + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.eccentricity + 1 + + Notes + ----- + The eccentricity for every Parabola is 1 by definition. + + """ + return S.One + + def equation(self, x='x', y='y'): + """The equation of the parabola. + + Parameters + ========== + x : str, optional + Label for the x-axis. Default value is 'x'. + y : str, optional + Label for the y-axis. Default value is 'y'. + + Returns + ======= + equation : SymPy expression + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.equation() + -x**2 - 16*y + 64 + >>> p1.equation('f') + -f**2 - 16*y + 64 + >>> p1.equation(y='z') + -x**2 - 16*z + 64 + + """ + x = _symbol(x, real=True) + y = _symbol(y, real=True) + + m = self.directrix.slope + if m is S.Infinity: + t1 = 4 * (self.p_parameter) * (x - self.vertex.x) + t2 = (y - self.vertex.y)**2 + elif m == 0: + t1 = 4 * (self.p_parameter) * (y - self.vertex.y) + t2 = (x - self.vertex.x)**2 + else: + a, b = self.focus + c, d = self.directrix.coefficients[:2] + t1 = (x - a)**2 + (y - b)**2 + t2 = self.directrix.equation(x, y)**2/(c**2 + d**2) + return t1 - t2 + + @property + def focal_length(self): + """The focal length of the parabola. + + Returns + ======= + + focal_lenght : number or symbolic expression + + Notes + ===== + + The distance between the vertex and the focus + (or the vertex and directrix), measured along the axis + of symmetry, is the "focal length". + + See Also + ======== + + https://en.wikipedia.org/wiki/Parabola + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.focal_length + 4 + + """ + distance = self.directrix.distance(self.focus) + focal_length = distance/2 + + return focal_length + + @property + def focus(self): + """The focus of the parabola. + + Returns + ======= + + focus : Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> f1 = Point(0, 0) + >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) + >>> p1.focus + Point2D(0, 0) + + """ + return self.args[0] + + def intersection(self, o): + """The intersection of the parabola and another geometrical entity `o`. + + Parameters + ========== + + o : GeometryEntity, LinearEntity + + Returns + ======= + + intersection : list of GeometryEntity objects + + Examples + ======== + + >>> from sympy import Parabola, Point, Ellipse, Line, Segment + >>> p1 = Point(0,0) + >>> l1 = Line(Point(1, -2), Point(-1,-2)) + >>> parabola1 = Parabola(p1, l1) + >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5)) + [Point2D(-2, 0), Point2D(2, 0)] + >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3))) + [Point2D(-4, 3), Point2D(4, 3)] + >>> parabola1.intersection(Segment((-12, -65), (14, -68))) + [] + + """ + x, y = symbols('x y', real=True) + parabola_eq = self.equation() + if isinstance(o, Parabola): + if o in self: + return [o] + else: + return list(ordered([Point(i) for i in solve( + [parabola_eq, o.equation()], [x, y], set=True)[1]])) + elif isinstance(o, Point2D): + if simplify(parabola_eq.subs([(x, o._args[0]), (y, o._args[1])])) == 0: + return [o] + else: + return [] + elif isinstance(o, (Segment2D, Ray2D)): + result = solve([parabola_eq, + Line2D(o.points[0], o.points[1]).equation()], + [x, y], set=True)[1] + return list(ordered([Point2D(i) for i in result if i in o])) + elif isinstance(o, (Line2D, Ellipse)): + return list(ordered([Point2D(i) for i in solve( + [parabola_eq, o.equation()], [x, y], set=True)[1]])) + elif isinstance(o, LinearEntity3D): + raise TypeError('Entity must be two dimensional, not three dimensional') + else: + raise TypeError('Wrong type of argument were put') + + @property + def p_parameter(self): + """P is a parameter of parabola. + + Returns + ======= + + p : number or symbolic expression + + Notes + ===== + + The absolute value of p is the focal length. The sign on p tells + which way the parabola faces. Vertical parabolas that open up + and horizontal that open right, give a positive value for p. + Vertical parabolas that open down and horizontal that open left, + give a negative value for p. + + + See Also + ======== + + https://www.sparknotes.com/math/precalc/conicsections/section2/ + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.p_parameter + -4 + + """ + m = self.directrix.slope + if m is S.Infinity: + x = self.directrix.coefficients[2] + p = sign(self.focus.args[0] + x) + elif m == 0: + y = self.directrix.coefficients[2] + p = sign(self.focus.args[1] + y) + else: + d = self.directrix.projection(self.focus) + p = sign(self.focus.x - d.x) + return p * self.focal_length + + @property + def vertex(self): + """The vertex of the parabola. + + Returns + ======= + + vertex : Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Parabola, Point, Line + >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) + >>> p1.vertex + Point2D(0, 4) + + """ + focus = self.focus + m = self.directrix.slope + if m is S.Infinity: + vertex = Point(focus.args[0] - self.p_parameter, focus.args[1]) + elif m == 0: + vertex = Point(focus.args[0], focus.args[1] - self.p_parameter) + else: + vertex = self.axis_of_symmetry.intersection(self)[0] + return vertex diff --git a/lib/python3.11/site-packages/sympy/geometry/plane.py b/lib/python3.11/site-packages/sympy/geometry/plane.py new file mode 100644 index 0000000000000000000000000000000000000000..fe00ade7511f3f0b158b0d759cb3323232bcf478 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/plane.py @@ -0,0 +1,885 @@ +"""Geometrical Planes. + +Contains +======== +Plane + +""" + +from sympy.core import Dummy, Rational, S, Symbol +from sympy.core.symbol import _symbol +from sympy.functions.elementary.trigonometric import cos, sin, acos, asin, sqrt +from .entity import GeometryEntity +from .line import (Line, Ray, Segment, Line3D, LinearEntity, LinearEntity3D, + Ray3D, Segment3D) +from .point import Point, Point3D +from sympy.matrices import Matrix +from sympy.polys.polytools import cancel +from sympy.solvers import solve, linsolve +from sympy.utilities.iterables import uniq, is_sequence +from sympy.utilities.misc import filldedent, func_name, Undecidable + +from mpmath.libmp.libmpf import prec_to_dps + +import random + + +x, y, z, t = [Dummy('plane_dummy') for i in range(4)] + + +class Plane(GeometryEntity): + """ + A plane is a flat, two-dimensional surface. A plane is the two-dimensional + analogue of a point (zero-dimensions), a line (one-dimension) and a solid + (three-dimensions). A plane can generally be constructed by two types of + inputs. They are: + - three non-collinear points + - a point and the plane's normal vector + + Attributes + ========== + + p1 + normal_vector + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2)) + Plane(Point3D(1, 1, 1), (-1, 2, -1)) + >>> Plane((1, 1, 1), (2, 3, 4), (2, 2, 2)) + Plane(Point3D(1, 1, 1), (-1, 2, -1)) + >>> Plane(Point3D(1, 1, 1), normal_vector=(1,4,7)) + Plane(Point3D(1, 1, 1), (1, 4, 7)) + + """ + def __new__(cls, p1, a=None, b=None, **kwargs): + p1 = Point3D(p1, dim=3) + if a and b: + p2 = Point(a, dim=3) + p3 = Point(b, dim=3) + if Point3D.are_collinear(p1, p2, p3): + raise ValueError('Enter three non-collinear points') + a = p1.direction_ratio(p2) + b = p1.direction_ratio(p3) + normal_vector = tuple(Matrix(a).cross(Matrix(b))) + else: + a = kwargs.pop('normal_vector', a) + evaluate = kwargs.get('evaluate', True) + if is_sequence(a) and len(a) == 3: + normal_vector = Point3D(a).args if evaluate else a + else: + raise ValueError(filldedent(''' + Either provide 3 3D points or a point with a + normal vector expressed as a sequence of length 3''')) + if all(coord.is_zero for coord in normal_vector): + raise ValueError('Normal vector cannot be zero vector') + return GeometryEntity.__new__(cls, p1, normal_vector, **kwargs) + + def __contains__(self, o): + k = self.equation(x, y, z) + if isinstance(o, (LinearEntity, LinearEntity3D)): + d = Point3D(o.arbitrary_point(t)) + e = k.subs([(x, d.x), (y, d.y), (z, d.z)]) + return e.equals(0) + try: + o = Point(o, dim=3, strict=True) + d = k.xreplace(dict(zip((x, y, z), o.args))) + return d.equals(0) + except TypeError: + return False + + def _eval_evalf(self, prec=15, **options): + pt, tup = self.args + dps = prec_to_dps(prec) + pt = pt.evalf(n=dps, **options) + tup = tuple([i.evalf(n=dps, **options) for i in tup]) + return self.func(pt, normal_vector=tup, evaluate=False) + + def angle_between(self, o): + """Angle between the plane and other geometric entity. + + Parameters + ========== + + LinearEntity3D, Plane. + + Returns + ======= + + angle : angle in radians + + Notes + ===== + + This method accepts only 3D entities as it's parameter, but if you want + to calculate the angle between a 2D entity and a plane you should + first convert to a 3D entity by projecting onto a desired plane and + then proceed to calculate the angle. + + Examples + ======== + + >>> from sympy import Point3D, Line3D, Plane + >>> a = Plane(Point3D(1, 2, 2), normal_vector=(1, 2, 3)) + >>> b = Line3D(Point3D(1, 3, 4), Point3D(2, 2, 2)) + >>> a.angle_between(b) + -asin(sqrt(21)/6) + + """ + if isinstance(o, LinearEntity3D): + a = Matrix(self.normal_vector) + b = Matrix(o.direction_ratio) + c = a.dot(b) + d = sqrt(sum(i**2 for i in self.normal_vector)) + e = sqrt(sum(i**2 for i in o.direction_ratio)) + return asin(c/(d*e)) + if isinstance(o, Plane): + a = Matrix(self.normal_vector) + b = Matrix(o.normal_vector) + c = a.dot(b) + d = sqrt(sum(i**2 for i in self.normal_vector)) + e = sqrt(sum(i**2 for i in o.normal_vector)) + return acos(c/(d*e)) + + + def arbitrary_point(self, u=None, v=None): + """ Returns an arbitrary point on the Plane. If given two + parameters, the point ranges over the entire plane. If given 1 + or no parameters, returns a point with one parameter which, + when varying from 0 to 2*pi, moves the point in a circle of + radius 1 about p1 of the Plane. + + Examples + ======== + + >>> from sympy import Plane, Ray + >>> from sympy.abc import u, v, t, r + >>> p = Plane((1, 1, 1), normal_vector=(1, 0, 0)) + >>> p.arbitrary_point(u, v) + Point3D(1, u + 1, v + 1) + >>> p.arbitrary_point(t) + Point3D(1, cos(t) + 1, sin(t) + 1) + + While arbitrary values of u and v can move the point anywhere in + the plane, the single-parameter point can be used to construct a + ray whose arbitrary point can be located at angle t and radius + r from p.p1: + + >>> Ray(p.p1, _).arbitrary_point(r) + Point3D(1, r*cos(t) + 1, r*sin(t) + 1) + + Returns + ======= + + Point3D + + """ + circle = v is None + if circle: + u = _symbol(u or 't', real=True) + else: + u = _symbol(u or 'u', real=True) + v = _symbol(v or 'v', real=True) + x, y, z = self.normal_vector + a, b, c = self.p1.args + # x1, y1, z1 is a nonzero vector parallel to the plane + if x.is_zero and y.is_zero: + x1, y1, z1 = S.One, S.Zero, S.Zero + else: + x1, y1, z1 = -y, x, S.Zero + # x2, y2, z2 is also parallel to the plane, and orthogonal to x1, y1, z1 + x2, y2, z2 = tuple(Matrix((x, y, z)).cross(Matrix((x1, y1, z1)))) + if circle: + x1, y1, z1 = (w/sqrt(x1**2 + y1**2 + z1**2) for w in (x1, y1, z1)) + x2, y2, z2 = (w/sqrt(x2**2 + y2**2 + z2**2) for w in (x2, y2, z2)) + p = Point3D(a + x1*cos(u) + x2*sin(u), \ + b + y1*cos(u) + y2*sin(u), \ + c + z1*cos(u) + z2*sin(u)) + else: + p = Point3D(a + x1*u + x2*v, b + y1*u + y2*v, c + z1*u + z2*v) + return p + + + @staticmethod + def are_concurrent(*planes): + """Is a sequence of Planes concurrent? + + Two or more Planes are concurrent if their intersections + are a common line. + + Parameters + ========== + + planes: list + + Returns + ======= + + Boolean + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(5, 0, 0), normal_vector=(1, -1, 1)) + >>> b = Plane(Point3D(0, -2, 0), normal_vector=(3, 1, 1)) + >>> c = Plane(Point3D(0, -1, 0), normal_vector=(5, -1, 9)) + >>> Plane.are_concurrent(a, b) + True + >>> Plane.are_concurrent(a, b, c) + False + + """ + planes = list(uniq(planes)) + for i in planes: + if not isinstance(i, Plane): + raise ValueError('All objects should be Planes but got %s' % i.func) + if len(planes) < 2: + return False + planes = list(planes) + first = planes.pop(0) + sol = first.intersection(planes[0]) + if sol == []: + return False + else: + line = sol[0] + for i in planes[1:]: + l = first.intersection(i) + if not l or l[0] not in line: + return False + return True + + + def distance(self, o): + """Distance between the plane and another geometric entity. + + Parameters + ========== + + Point3D, LinearEntity3D, Plane. + + Returns + ======= + + distance + + Notes + ===== + + This method accepts only 3D entities as it's parameter, but if you want + to calculate the distance between a 2D entity and a plane you should + first convert to a 3D entity by projecting onto a desired plane and + then proceed to calculate the distance. + + Examples + ======== + + >>> from sympy import Point3D, Line3D, Plane + >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1)) + >>> b = Point3D(1, 2, 3) + >>> a.distance(b) + sqrt(3) + >>> c = Line3D(Point3D(2, 3, 1), Point3D(1, 2, 2)) + >>> a.distance(c) + 0 + + """ + if self.intersection(o) != []: + return S.Zero + + if isinstance(o, (Segment3D, Ray3D)): + a, b = o.p1, o.p2 + pi, = self.intersection(Line3D(a, b)) + if pi in o: + return self.distance(pi) + elif a in Segment3D(pi, b): + return self.distance(a) + else: + assert isinstance(o, Segment3D) is True + return self.distance(b) + + # following code handles `Point3D`, `LinearEntity3D`, `Plane` + a = o if isinstance(o, Point3D) else o.p1 + n = Point3D(self.normal_vector).unit + d = (a - self.p1).dot(n) + return abs(d) + + + def equals(self, o): + """ + Returns True if self and o are the same mathematical entities. + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1)) + >>> b = Plane(Point3D(1, 2, 3), normal_vector=(2, 2, 2)) + >>> c = Plane(Point3D(1, 2, 3), normal_vector=(-1, 4, 6)) + >>> a.equals(a) + True + >>> a.equals(b) + True + >>> a.equals(c) + False + """ + if isinstance(o, Plane): + a = self.equation() + b = o.equation() + return cancel(a/b).is_constant() + else: + return False + + + def equation(self, x=None, y=None, z=None): + """The equation of the Plane. + + Examples + ======== + + >>> from sympy import Point3D, Plane + >>> a = Plane(Point3D(1, 1, 2), Point3D(2, 4, 7), Point3D(3, 5, 1)) + >>> a.equation() + -23*x + 11*y - 2*z + 16 + >>> a = Plane(Point3D(1, 4, 2), normal_vector=(6, 6, 6)) + >>> a.equation() + 6*x + 6*y + 6*z - 42 + + """ + x, y, z = [i if i else Symbol(j, real=True) for i, j in zip((x, y, z), 'xyz')] + a = Point3D(x, y, z) + b = self.p1.direction_ratio(a) + c = self.normal_vector + return (sum(i*j for i, j in zip(b, c))) + + + def intersection(self, o): + """ The intersection with other geometrical entity. + + Parameters + ========== + + Point, Point3D, LinearEntity, LinearEntity3D, Plane + + Returns + ======= + + List + + Examples + ======== + + >>> from sympy import Point3D, Line3D, Plane + >>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1)) + >>> b = Point3D(1, 2, 3) + >>> a.intersection(b) + [Point3D(1, 2, 3)] + >>> c = Line3D(Point3D(1, 4, 7), Point3D(2, 2, 2)) + >>> a.intersection(c) + [Point3D(2, 2, 2)] + >>> d = Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3)) + >>> e = Plane(Point3D(2, 0, 0), normal_vector=(3, 4, -3)) + >>> d.intersection(e) + [Line3D(Point3D(78/23, -24/23, 0), Point3D(147/23, 321/23, 23))] + + """ + if not isinstance(o, GeometryEntity): + o = Point(o, dim=3) + if isinstance(o, Point): + if o in self: + return [o] + else: + return [] + if isinstance(o, (LinearEntity, LinearEntity3D)): + # recast to 3D + p1, p2 = o.p1, o.p2 + if isinstance(o, Segment): + o = Segment3D(p1, p2) + elif isinstance(o, Ray): + o = Ray3D(p1, p2) + elif isinstance(o, Line): + o = Line3D(p1, p2) + else: + raise ValueError('unhandled linear entity: %s' % o.func) + if o in self: + return [o] + else: + a = Point3D(o.arbitrary_point(t)) + p1, n = self.p1, Point3D(self.normal_vector) + + # TODO: Replace solve with solveset, when this line is tested + c = solve((a - p1).dot(n), t) + if not c: + return [] + else: + c = [i for i in c if i.is_real is not False] + if len(c) > 1: + c = [i for i in c if i.is_real] + if len(c) != 1: + raise Undecidable("not sure which point is real") + p = a.subs(t, c[0]) + if p not in o: + return [] # e.g. a segment might not intersect a plane + return [p] + if isinstance(o, Plane): + if self.equals(o): + return [self] + if self.is_parallel(o): + return [] + else: + x, y, z = map(Dummy, 'xyz') + a, b = Matrix([self.normal_vector]), Matrix([o.normal_vector]) + c = list(a.cross(b)) + d = self.equation(x, y, z) + e = o.equation(x, y, z) + result = list(linsolve([d, e], x, y, z))[0] + for i in (x, y, z): result = result.subs(i, 0) + return [Line3D(Point3D(result), direction_ratio=c)] + + + def is_coplanar(self, o): + """ Returns True if `o` is coplanar with self, else False. + + Examples + ======== + + >>> from sympy import Plane + >>> o = (0, 0, 0) + >>> p = Plane(o, (1, 1, 1)) + >>> p2 = Plane(o, (2, 2, 2)) + >>> p == p2 + False + >>> p.is_coplanar(p2) + True + """ + if isinstance(o, Plane): + return not cancel(self.equation(x, y, z)/o.equation(x, y, z)).has(x, y, z) + if isinstance(o, Point3D): + return o in self + elif isinstance(o, LinearEntity3D): + return all(i in self for i in self) + elif isinstance(o, GeometryEntity): # XXX should only be handling 2D objects now + return all(i == 0 for i in self.normal_vector[:2]) + + + def is_parallel(self, l): + """Is the given geometric entity parallel to the plane? + + Parameters + ========== + + LinearEntity3D or Plane + + Returns + ======= + + Boolean + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6)) + >>> b = Plane(Point3D(3,1,3), normal_vector=(4, 8, 12)) + >>> a.is_parallel(b) + True + + """ + if isinstance(l, LinearEntity3D): + a = l.direction_ratio + b = self.normal_vector + c = sum(i*j for i, j in zip(a, b)) + if c == 0: + return True + else: + return False + elif isinstance(l, Plane): + a = Matrix(l.normal_vector) + b = Matrix(self.normal_vector) + if a.cross(b).is_zero_matrix: + return True + else: + return False + + + def is_perpendicular(self, l): + """Is the given geometric entity perpendicualar to the given plane? + + Parameters + ========== + + LinearEntity3D or Plane + + Returns + ======= + + Boolean + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6)) + >>> b = Plane(Point3D(2, 2, 2), normal_vector=(-1, 2, -1)) + >>> a.is_perpendicular(b) + True + + """ + if isinstance(l, LinearEntity3D): + a = Matrix(l.direction_ratio) + b = Matrix(self.normal_vector) + if a.cross(b).is_zero_matrix: + return True + else: + return False + elif isinstance(l, Plane): + a = Matrix(l.normal_vector) + b = Matrix(self.normal_vector) + if a.dot(b) == 0: + return True + else: + return False + else: + return False + + @property + def normal_vector(self): + """Normal vector of the given plane. + + Examples + ======== + + >>> from sympy import Point3D, Plane + >>> a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2)) + >>> a.normal_vector + (-1, 2, -1) + >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 4, 7)) + >>> a.normal_vector + (1, 4, 7) + + """ + return self.args[1] + + @property + def p1(self): + """The only defining point of the plane. Others can be obtained from the + arbitrary_point method. + + See Also + ======== + + sympy.geometry.point.Point3D + + Examples + ======== + + >>> from sympy import Point3D, Plane + >>> a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2)) + >>> a.p1 + Point3D(1, 1, 1) + + """ + return self.args[0] + + def parallel_plane(self, pt): + """ + Plane parallel to the given plane and passing through the point pt. + + Parameters + ========== + + pt: Point3D + + Returns + ======= + + Plane + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(1, 4, 6), normal_vector=(2, 4, 6)) + >>> a.parallel_plane(Point3D(2, 3, 5)) + Plane(Point3D(2, 3, 5), (2, 4, 6)) + + """ + a = self.normal_vector + return Plane(pt, normal_vector=a) + + def perpendicular_line(self, pt): + """A line perpendicular to the given plane. + + Parameters + ========== + + pt: Point3D + + Returns + ======= + + Line3D + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6)) + >>> a.perpendicular_line(Point3D(9, 8, 7)) + Line3D(Point3D(9, 8, 7), Point3D(11, 12, 13)) + + """ + a = self.normal_vector + return Line3D(pt, direction_ratio=a) + + def perpendicular_plane(self, *pts): + """ + Return a perpendicular passing through the given points. If the + direction ratio between the points is the same as the Plane's normal + vector then, to select from the infinite number of possible planes, + a third point will be chosen on the z-axis (or the y-axis + if the normal vector is already parallel to the z-axis). If less than + two points are given they will be supplied as follows: if no point is + given then pt1 will be self.p1; if a second point is not given it will + be a point through pt1 on a line parallel to the z-axis (if the normal + is not already the z-axis, otherwise on the line parallel to the + y-axis). + + Parameters + ========== + + pts: 0, 1 or 2 Point3D + + Returns + ======= + + Plane + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> a, b = Point3D(0, 0, 0), Point3D(0, 1, 0) + >>> Z = (0, 0, 1) + >>> p = Plane(a, normal_vector=Z) + >>> p.perpendicular_plane(a, b) + Plane(Point3D(0, 0, 0), (1, 0, 0)) + """ + if len(pts) > 2: + raise ValueError('No more than 2 pts should be provided.') + + pts = list(pts) + if len(pts) == 0: + pts.append(self.p1) + if len(pts) == 1: + x, y, z = self.normal_vector + if x == y == 0: + dir = (0, 1, 0) + else: + dir = (0, 0, 1) + pts.append(pts[0] + Point3D(*dir)) + + p1, p2 = [Point(i, dim=3) for i in pts] + l = Line3D(p1, p2) + n = Line3D(p1, direction_ratio=self.normal_vector) + if l in n: # XXX should an error be raised instead? + # there are infinitely many perpendicular planes; + x, y, z = self.normal_vector + if x == y == 0: + # the z axis is the normal so pick a pt on the y-axis + p3 = Point3D(0, 1, 0) # case 1 + else: + # else pick a pt on the z axis + p3 = Point3D(0, 0, 1) # case 2 + # in case that point is already given, move it a bit + if p3 in l: + p3 *= 2 # case 3 + else: + p3 = p1 + Point3D(*self.normal_vector) # case 4 + return Plane(p1, p2, p3) + + def projection_line(self, line): + """Project the given line onto the plane through the normal plane + containing the line. + + Parameters + ========== + + LinearEntity or LinearEntity3D + + Returns + ======= + + Point3D, Line3D, Ray3D or Segment3D + + Notes + ===== + + For the interaction between 2D and 3D lines(segments, rays), you should + convert the line to 3D by using this method. For example for finding the + intersection between a 2D and a 3D line, convert the 2D line to a 3D line + by projecting it on a required plane and then proceed to find the + intersection between those lines. + + Examples + ======== + + >>> from sympy import Plane, Line, Line3D, Point3D + >>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1)) + >>> b = Line(Point3D(1, 1), Point3D(2, 2)) + >>> a.projection_line(b) + Line3D(Point3D(4/3, 4/3, 1/3), Point3D(5/3, 5/3, -1/3)) + >>> c = Line3D(Point3D(1, 1, 1), Point3D(2, 2, 2)) + >>> a.projection_line(c) + Point3D(1, 1, 1) + + """ + if not isinstance(line, (LinearEntity, LinearEntity3D)): + raise NotImplementedError('Enter a linear entity only') + a, b = self.projection(line.p1), self.projection(line.p2) + if a == b: + # projection does not imply intersection so for + # this case (line parallel to plane's normal) we + # return the projection point + return a + if isinstance(line, (Line, Line3D)): + return Line3D(a, b) + if isinstance(line, (Ray, Ray3D)): + return Ray3D(a, b) + if isinstance(line, (Segment, Segment3D)): + return Segment3D(a, b) + + def projection(self, pt): + """Project the given point onto the plane along the plane normal. + + Parameters + ========== + + Point or Point3D + + Returns + ======= + + Point3D + + Examples + ======== + + >>> from sympy import Plane, Point3D + >>> A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1)) + + The projection is along the normal vector direction, not the z + axis, so (1, 1) does not project to (1, 1, 2) on the plane A: + + >>> b = Point3D(1, 1) + >>> A.projection(b) + Point3D(5/3, 5/3, 2/3) + >>> _ in A + True + + But the point (1, 1, 2) projects to (1, 1) on the XY-plane: + + >>> XY = Plane((0, 0, 0), (0, 0, 1)) + >>> XY.projection((1, 1, 2)) + Point3D(1, 1, 0) + """ + rv = Point(pt, dim=3) + if rv in self: + return rv + return self.intersection(Line3D(rv, rv + Point3D(self.normal_vector)))[0] + + def random_point(self, seed=None): + """ Returns a random point on the Plane. + + Returns + ======= + + Point3D + + Examples + ======== + + >>> from sympy import Plane + >>> p = Plane((1, 0, 0), normal_vector=(0, 1, 0)) + >>> r = p.random_point(seed=42) # seed value is optional + >>> r.n(3) + Point3D(2.29, 0, -1.35) + + The random point can be moved to lie on the circle of radius + 1 centered on p1: + + >>> c = p.p1 + (r - p.p1).unit + >>> c.distance(p.p1).equals(1) + True + """ + if seed is not None: + rng = random.Random(seed) + else: + rng = random + params = { + x: 2*Rational(rng.gauss(0, 1)) - 1, + y: 2*Rational(rng.gauss(0, 1)) - 1} + return self.arbitrary_point(x, y).subs(params) + + def parameter_value(self, other, u, v=None): + """Return the parameter(s) corresponding to the given point. + + Examples + ======== + + >>> from sympy import pi, Plane + >>> from sympy.abc import t, u, v + >>> p = Plane((2, 0, 0), (0, 0, 1), (0, 1, 0)) + + By default, the parameter value returned defines a point + that is a distance of 1 from the Plane's p1 value and + in line with the given point: + + >>> on_circle = p.arbitrary_point(t).subs(t, pi/4) + >>> on_circle.distance(p.p1) + 1 + >>> p.parameter_value(on_circle, t) + {t: pi/4} + + Moving the point twice as far from p1 does not change + the parameter value: + + >>> off_circle = p.p1 + (on_circle - p.p1)*2 + >>> off_circle.distance(p.p1) + 2 + >>> p.parameter_value(off_circle, t) + {t: pi/4} + + If the 2-value parameter is desired, supply the two + parameter symbols and a replacement dictionary will + be returned: + + >>> p.parameter_value(on_circle, u, v) + {u: sqrt(10)/10, v: sqrt(10)/30} + >>> p.parameter_value(off_circle, u, v) + {u: sqrt(10)/5, v: sqrt(10)/15} + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if not isinstance(other, Point): + raise ValueError("other must be a point") + if other == self.p1: + return other + if isinstance(u, Symbol) and v is None: + delta = self.arbitrary_point(u) - self.p1 + eq = delta - (other - self.p1).unit + sol = solve(eq, u, dict=True) + elif isinstance(u, Symbol) and isinstance(v, Symbol): + pt = self.arbitrary_point(u, v) + sol = solve(pt - other, (u, v), dict=True) + else: + raise ValueError('expecting 1 or 2 symbols') + if not sol: + raise ValueError("Given point is not on %s" % func_name(self)) + return sol[0] # {t: tval} or {u: uval, v: vval} + + @property + def ambient_dimension(self): + return self.p1.ambient_dimension diff --git a/lib/python3.11/site-packages/sympy/geometry/point.py b/lib/python3.11/site-packages/sympy/geometry/point.py new file mode 100644 index 0000000000000000000000000000000000000000..81ca7ce61a08d139d2a0d13e545ce008ba9c4298 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/point.py @@ -0,0 +1,1378 @@ +"""Geometrical Points. + +Contains +======== +Point +Point2D +Point3D + +When methods of Point require 1 or more points as arguments, they +can be passed as a sequence of coordinates or Points: + +>>> from sympy import Point +>>> Point(1, 1).is_collinear((2, 2), (3, 4)) +False +>>> Point(1, 1).is_collinear(Point(2, 2), Point(3, 4)) +False + +""" + +import warnings + +from sympy.core import S, sympify, Expr +from sympy.core.add import Add +from sympy.core.containers import Tuple +from sympy.core.numbers import Float +from sympy.core.parameters import global_parameters +from sympy.simplify import nsimplify, simplify +from sympy.geometry.exceptions import GeometryError +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.complexes import im +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.matrices import Matrix +from sympy.matrices.expressions import Transpose +from sympy.utilities.iterables import uniq, is_sequence +from sympy.utilities.misc import filldedent, func_name, Undecidable + +from .entity import GeometryEntity + +from mpmath.libmp.libmpf import prec_to_dps + + +class Point(GeometryEntity): + """A point in a n-dimensional Euclidean space. + + Parameters + ========== + + coords : sequence of n-coordinate values. In the special + case where n=2 or 3, a Point2D or Point3D will be created + as appropriate. + evaluate : if `True` (default), all floats are turn into + exact types. + dim : number of coordinates the point should have. If coordinates + are unspecified, they are padded with zeros. + on_morph : indicates what should happen when the number of + coordinates of a point need to be changed by adding or + removing zeros. Possible values are `'warn'`, `'error'`, or + `ignore` (default). No warning or error is given when `*args` + is empty and `dim` is given. An error is always raised when + trying to remove nonzero coordinates. + + + Attributes + ========== + + length + origin: A `Point` representing the origin of the + appropriately-dimensioned space. + + Raises + ====== + + TypeError : When instantiating with anything but a Point or sequence + ValueError : when instantiating with a sequence with length < 2 or + when trying to reduce dimensions if keyword `on_morph='error'` is + set. + + See Also + ======== + + sympy.geometry.line.Segment : Connects two Points + + Examples + ======== + + >>> from sympy import Point + >>> from sympy.abc import x + >>> Point(1, 2, 3) + Point3D(1, 2, 3) + >>> Point([1, 2]) + Point2D(1, 2) + >>> Point(0, x) + Point2D(0, x) + >>> Point(dim=4) + Point(0, 0, 0, 0) + + Floats are automatically converted to Rational unless the + evaluate flag is False: + + >>> Point(0.5, 0.25) + Point2D(1/2, 1/4) + >>> Point(0.5, 0.25, evaluate=False) + Point2D(0.5, 0.25) + + """ + + is_Point = True + + def __new__(cls, *args, **kwargs): + evaluate = kwargs.get('evaluate', global_parameters.evaluate) + on_morph = kwargs.get('on_morph', 'ignore') + + # unpack into coords + coords = args[0] if len(args) == 1 else args + + # check args and handle quickly handle Point instances + if isinstance(coords, Point): + # even if we're mutating the dimension of a point, we + # don't reevaluate its coordinates + evaluate = False + if len(coords) == kwargs.get('dim', len(coords)): + return coords + + if not is_sequence(coords): + raise TypeError(filldedent(''' + Expecting sequence of coordinates, not `{}`''' + .format(func_name(coords)))) + # A point where only `dim` is specified is initialized + # to zeros. + if len(coords) == 0 and kwargs.get('dim', None): + coords = (S.Zero,)*kwargs.get('dim') + + coords = Tuple(*coords) + dim = kwargs.get('dim', len(coords)) + + if len(coords) < 2: + raise ValueError(filldedent(''' + Point requires 2 or more coordinates or + keyword `dim` > 1.''')) + if len(coords) != dim: + message = ("Dimension of {} needs to be changed " + "from {} to {}.").format(coords, len(coords), dim) + if on_morph == 'ignore': + pass + elif on_morph == "error": + raise ValueError(message) + elif on_morph == 'warn': + warnings.warn(message, stacklevel=2) + else: + raise ValueError(filldedent(''' + on_morph value should be 'error', + 'warn' or 'ignore'.''')) + if any(coords[dim:]): + raise ValueError('Nonzero coordinates cannot be removed.') + if any(a.is_number and im(a).is_zero is False for a in coords): + raise ValueError('Imaginary coordinates are not permitted.') + if not all(isinstance(a, Expr) for a in coords): + raise TypeError('Coordinates must be valid SymPy expressions.') + + # pad with zeros appropriately + coords = coords[:dim] + (S.Zero,)*(dim - len(coords)) + + # Turn any Floats into rationals and simplify + # any expressions before we instantiate + if evaluate: + coords = coords.xreplace({ + f: simplify(nsimplify(f, rational=True)) + for f in coords.atoms(Float)}) + + # return 2D or 3D instances + if len(coords) == 2: + kwargs['_nocheck'] = True + return Point2D(*coords, **kwargs) + elif len(coords) == 3: + kwargs['_nocheck'] = True + return Point3D(*coords, **kwargs) + + # the general Point + return GeometryEntity.__new__(cls, *coords) + + def __abs__(self): + """Returns the distance between this point and the origin.""" + origin = Point([0]*len(self)) + return Point.distance(origin, self) + + def __add__(self, other): + """Add other to self by incrementing self's coordinates by + those of other. + + Notes + ===== + + >>> from sympy import Point + + When sequences of coordinates are passed to Point methods, they + are converted to a Point internally. This __add__ method does + not do that so if floating point values are used, a floating + point result (in terms of SymPy Floats) will be returned. + + >>> Point(1, 2) + (.1, .2) + Point2D(1.1, 2.2) + + If this is not desired, the `translate` method can be used or + another Point can be added: + + >>> Point(1, 2).translate(.1, .2) + Point2D(11/10, 11/5) + >>> Point(1, 2) + Point(.1, .2) + Point2D(11/10, 11/5) + + See Also + ======== + + sympy.geometry.point.Point.translate + + """ + try: + s, o = Point._normalize_dimension(self, Point(other, evaluate=False)) + except TypeError: + raise GeometryError("Don't know how to add {} and a Point object".format(other)) + + coords = [simplify(a + b) for a, b in zip(s, o)] + return Point(coords, evaluate=False) + + def __contains__(self, item): + return item in self.args + + def __truediv__(self, divisor): + """Divide point's coordinates by a factor.""" + divisor = sympify(divisor) + coords = [simplify(x/divisor) for x in self.args] + return Point(coords, evaluate=False) + + def __eq__(self, other): + if not isinstance(other, Point) or len(self.args) != len(other.args): + return False + return self.args == other.args + + def __getitem__(self, key): + return self.args[key] + + def __hash__(self): + return hash(self.args) + + def __iter__(self): + return self.args.__iter__() + + def __len__(self): + return len(self.args) + + def __mul__(self, factor): + """Multiply point's coordinates by a factor. + + Notes + ===== + + >>> from sympy import Point + + When multiplying a Point by a floating point number, + the coordinates of the Point will be changed to Floats: + + >>> Point(1, 2)*0.1 + Point2D(0.1, 0.2) + + If this is not desired, the `scale` method can be used or + else only multiply or divide by integers: + + >>> Point(1, 2).scale(1.1, 1.1) + Point2D(11/10, 11/5) + >>> Point(1, 2)*11/10 + Point2D(11/10, 11/5) + + See Also + ======== + + sympy.geometry.point.Point.scale + """ + factor = sympify(factor) + coords = [simplify(x*factor) for x in self.args] + return Point(coords, evaluate=False) + + def __rmul__(self, factor): + """Multiply a factor by point's coordinates.""" + return self.__mul__(factor) + + def __neg__(self): + """Negate the point.""" + coords = [-x for x in self.args] + return Point(coords, evaluate=False) + + def __sub__(self, other): + """Subtract two points, or subtract a factor from this point's + coordinates.""" + return self + [-x for x in other] + + @classmethod + def _normalize_dimension(cls, *points, **kwargs): + """Ensure that points have the same dimension. + By default `on_morph='warn'` is passed to the + `Point` constructor.""" + # if we have a built-in ambient dimension, use it + dim = getattr(cls, '_ambient_dimension', None) + # override if we specified it + dim = kwargs.get('dim', dim) + # if no dim was given, use the highest dimensional point + if dim is None: + dim = max(i.ambient_dimension for i in points) + if all(i.ambient_dimension == dim for i in points): + return list(points) + kwargs['dim'] = dim + kwargs['on_morph'] = kwargs.get('on_morph', 'warn') + return [Point(i, **kwargs) for i in points] + + @staticmethod + def affine_rank(*args): + """The affine rank of a set of points is the dimension + of the smallest affine space containing all the points. + For example, if the points lie on a line (and are not all + the same) their affine rank is 1. If the points lie on a plane + but not a line, their affine rank is 2. By convention, the empty + set has affine rank -1.""" + + if len(args) == 0: + return -1 + # make sure we're genuinely points + # and translate every point to the origin + points = Point._normalize_dimension(*[Point(i) for i in args]) + origin = points[0] + points = [i - origin for i in points[1:]] + + m = Matrix([i.args for i in points]) + # XXX fragile -- what is a better way? + return m.rank(iszerofunc = lambda x: + abs(x.n(2)) < 1e-12 if x.is_number else x.is_zero) + + @property + def ambient_dimension(self): + """Number of components this point has.""" + return getattr(self, '_ambient_dimension', len(self)) + + @classmethod + def are_coplanar(cls, *points): + """Return True if there exists a plane in which all the points + lie. A trivial True value is returned if `len(points) < 3` or + all Points are 2-dimensional. + + Parameters + ========== + + A set of points + + Raises + ====== + + ValueError : if less than 3 unique points are given + + Returns + ======= + + boolean + + Examples + ======== + + >>> from sympy import Point3D + >>> p1 = Point3D(1, 2, 2) + >>> p2 = Point3D(2, 7, 2) + >>> p3 = Point3D(0, 0, 2) + >>> p4 = Point3D(1, 1, 2) + >>> Point3D.are_coplanar(p1, p2, p3, p4) + True + >>> p5 = Point3D(0, 1, 3) + >>> Point3D.are_coplanar(p1, p2, p3, p5) + False + + """ + if len(points) <= 1: + return True + + points = cls._normalize_dimension(*[Point(i) for i in points]) + # quick exit if we are in 2D + if points[0].ambient_dimension == 2: + return True + points = list(uniq(points)) + return Point.affine_rank(*points) <= 2 + + def distance(self, other): + """The Euclidean distance between self and another GeometricEntity. + + Returns + ======= + + distance : number or symbolic expression. + + Raises + ====== + + TypeError : if other is not recognized as a GeometricEntity or is a + GeometricEntity for which distance is not defined. + + See Also + ======== + + sympy.geometry.line.Segment.length + sympy.geometry.point.Point.taxicab_distance + + Examples + ======== + + >>> from sympy import Point, Line + >>> p1, p2 = Point(1, 1), Point(4, 5) + >>> l = Line((3, 1), (2, 2)) + >>> p1.distance(p2) + 5 + >>> p1.distance(l) + sqrt(2) + + The computed distance may be symbolic, too: + + >>> from sympy.abc import x, y + >>> p3 = Point(x, y) + >>> p3.distance((0, 0)) + sqrt(x**2 + y**2) + + """ + if not isinstance(other, GeometryEntity): + try: + other = Point(other, dim=self.ambient_dimension) + except TypeError: + raise TypeError("not recognized as a GeometricEntity: %s" % type(other)) + if isinstance(other, Point): + s, p = Point._normalize_dimension(self, Point(other)) + return sqrt(Add(*((a - b)**2 for a, b in zip(s, p)))) + distance = getattr(other, 'distance', None) + if distance is None: + raise TypeError("distance between Point and %s is not defined" % type(other)) + return distance(self) + + def dot(self, p): + """Return dot product of self with another Point.""" + if not is_sequence(p): + p = Point(p) # raise the error via Point + return Add(*(a*b for a, b in zip(self, p))) + + def equals(self, other): + """Returns whether the coordinates of self and other agree.""" + # a point is equal to another point if all its components are equal + if not isinstance(other, Point) or len(self) != len(other): + return False + return all(a.equals(b) for a, b in zip(self, other)) + + def _eval_evalf(self, prec=15, **options): + """Evaluate the coordinates of the point. + + This method will, where possible, create and return a new Point + where the coordinates are evaluated as floating point numbers to + the precision indicated (default=15). + + Parameters + ========== + + prec : int + + Returns + ======= + + point : Point + + Examples + ======== + + >>> from sympy import Point, Rational + >>> p1 = Point(Rational(1, 2), Rational(3, 2)) + >>> p1 + Point2D(1/2, 3/2) + >>> p1.evalf() + Point2D(0.5, 1.5) + + """ + dps = prec_to_dps(prec) + coords = [x.evalf(n=dps, **options) for x in self.args] + return Point(*coords, evaluate=False) + + def intersection(self, other): + """The intersection between this point and another GeometryEntity. + + Parameters + ========== + + other : GeometryEntity or sequence of coordinates + + Returns + ======= + + intersection : list of Points + + Notes + ===== + + The return value will either be an empty list if there is no + intersection, otherwise it will contain this point. + + Examples + ======== + + >>> from sympy import Point + >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 0) + >>> p1.intersection(p2) + [] + >>> p1.intersection(p3) + [Point2D(0, 0)] + + """ + if not isinstance(other, GeometryEntity): + other = Point(other) + if isinstance(other, Point): + if self == other: + return [self] + p1, p2 = Point._normalize_dimension(self, other) + if p1 == self and p1 == p2: + return [self] + return [] + return other.intersection(self) + + def is_collinear(self, *args): + """Returns `True` if there exists a line + that contains `self` and `points`. Returns `False` otherwise. + A trivially True value is returned if no points are given. + + Parameters + ========== + + args : sequence of Points + + Returns + ======= + + is_collinear : boolean + + See Also + ======== + + sympy.geometry.line.Line + + Examples + ======== + + >>> from sympy import Point + >>> from sympy.abc import x + >>> p1, p2 = Point(0, 0), Point(1, 1) + >>> p3, p4, p5 = Point(2, 2), Point(x, x), Point(1, 2) + >>> Point.is_collinear(p1, p2, p3, p4) + True + >>> Point.is_collinear(p1, p2, p3, p5) + False + + """ + points = (self,) + args + points = Point._normalize_dimension(*[Point(i) for i in points]) + points = list(uniq(points)) + return Point.affine_rank(*points) <= 1 + + def is_concyclic(self, *args): + """Do `self` and the given sequence of points lie in a circle? + + Returns True if the set of points are concyclic and + False otherwise. A trivial value of True is returned + if there are fewer than 2 other points. + + Parameters + ========== + + args : sequence of Points + + Returns + ======= + + is_concyclic : boolean + + + Examples + ======== + + >>> from sympy import Point + + Define 4 points that are on the unit circle: + + >>> p1, p2, p3, p4 = Point(1, 0), (0, 1), (-1, 0), (0, -1) + + >>> p1.is_concyclic() == p1.is_concyclic(p2, p3, p4) == True + True + + Define a point not on that circle: + + >>> p = Point(1, 1) + + >>> p.is_concyclic(p1, p2, p3) + False + + """ + points = (self,) + args + points = Point._normalize_dimension(*[Point(i) for i in points]) + points = list(uniq(points)) + if not Point.affine_rank(*points) <= 2: + return False + origin = points[0] + points = [p - origin for p in points] + # points are concyclic if they are coplanar and + # there is a point c so that ||p_i-c|| == ||p_j-c|| for all + # i and j. Rearranging this equation gives us the following + # condition: the matrix `mat` must not a pivot in the last + # column. + mat = Matrix([list(i) + [i.dot(i)] for i in points]) + rref, pivots = mat.rref() + if len(origin) not in pivots: + return True + return False + + @property + def is_nonzero(self): + """True if any coordinate is nonzero, False if every coordinate is zero, + and None if it cannot be determined.""" + is_zero = self.is_zero + if is_zero is None: + return None + return not is_zero + + def is_scalar_multiple(self, p): + """Returns whether each coordinate of `self` is a scalar + multiple of the corresponding coordinate in point p. + """ + s, o = Point._normalize_dimension(self, Point(p)) + # 2d points happen a lot, so optimize this function call + if s.ambient_dimension == 2: + (x1, y1), (x2, y2) = s.args, o.args + rv = (x1*y2 - x2*y1).equals(0) + if rv is None: + raise Undecidable(filldedent( + '''Cannot determine if %s is a scalar multiple of + %s''' % (s, o))) + + # if the vectors p1 and p2 are linearly dependent, then they must + # be scalar multiples of each other + m = Matrix([s.args, o.args]) + return m.rank() < 2 + + @property + def is_zero(self): + """True if every coordinate is zero, False if any coordinate is not zero, + and None if it cannot be determined.""" + nonzero = [x.is_nonzero for x in self.args] + if any(nonzero): + return False + if any(x is None for x in nonzero): + return None + return True + + @property + def length(self): + """ + Treating a Point as a Line, this returns 0 for the length of a Point. + + Examples + ======== + + >>> from sympy import Point + >>> p = Point(0, 1) + >>> p.length + 0 + """ + return S.Zero + + def midpoint(self, p): + """The midpoint between self and point p. + + Parameters + ========== + + p : Point + + Returns + ======= + + midpoint : Point + + See Also + ======== + + sympy.geometry.line.Segment.midpoint + + Examples + ======== + + >>> from sympy import Point + >>> p1, p2 = Point(1, 1), Point(13, 5) + >>> p1.midpoint(p2) + Point2D(7, 3) + + """ + s, p = Point._normalize_dimension(self, Point(p)) + return Point([simplify((a + b)*S.Half) for a, b in zip(s, p)]) + + @property + def origin(self): + """A point of all zeros of the same ambient dimension + as the current point""" + return Point([0]*len(self), evaluate=False) + + @property + def orthogonal_direction(self): + """Returns a non-zero point that is orthogonal to the + line containing `self` and the origin. + + Examples + ======== + + >>> from sympy import Line, Point + >>> a = Point(1, 2, 3) + >>> a.orthogonal_direction + Point3D(-2, 1, 0) + >>> b = _ + >>> Line(b, b.origin).is_perpendicular(Line(a, a.origin)) + True + """ + dim = self.ambient_dimension + # if a coordinate is zero, we can put a 1 there and zeros elsewhere + if self[0].is_zero: + return Point([1] + (dim - 1)*[0]) + if self[1].is_zero: + return Point([0,1] + (dim - 2)*[0]) + # if the first two coordinates aren't zero, we can create a non-zero + # orthogonal vector by swapping them, negating one, and padding with zeros + return Point([-self[1], self[0]] + (dim - 2)*[0]) + + @staticmethod + def project(a, b): + """Project the point `a` onto the line between the origin + and point `b` along the normal direction. + + Parameters + ========== + + a : Point + b : Point + + Returns + ======= + + p : Point + + See Also + ======== + + sympy.geometry.line.LinearEntity.projection + + Examples + ======== + + >>> from sympy import Line, Point + >>> a = Point(1, 2) + >>> b = Point(2, 5) + >>> z = a.origin + >>> p = Point.project(a, b) + >>> Line(p, a).is_perpendicular(Line(p, b)) + True + >>> Point.is_collinear(z, p, b) + True + """ + a, b = Point._normalize_dimension(Point(a), Point(b)) + if b.is_zero: + raise ValueError("Cannot project to the zero vector.") + return b*(a.dot(b) / b.dot(b)) + + def taxicab_distance(self, p): + """The Taxicab Distance from self to point p. + + Returns the sum of the horizontal and vertical distances to point p. + + Parameters + ========== + + p : Point + + Returns + ======= + + taxicab_distance : The sum of the horizontal + and vertical distances to point p. + + See Also + ======== + + sympy.geometry.point.Point.distance + + Examples + ======== + + >>> from sympy import Point + >>> p1, p2 = Point(1, 1), Point(4, 5) + >>> p1.taxicab_distance(p2) + 7 + + """ + s, p = Point._normalize_dimension(self, Point(p)) + return Add(*(abs(a - b) for a, b in zip(s, p))) + + def canberra_distance(self, p): + """The Canberra Distance from self to point p. + + Returns the weighted sum of horizontal and vertical distances to + point p. + + Parameters + ========== + + p : Point + + Returns + ======= + + canberra_distance : The weighted sum of horizontal and vertical + distances to point p. The weight used is the sum of absolute values + of the coordinates. + + Examples + ======== + + >>> from sympy import Point + >>> p1, p2 = Point(1, 1), Point(3, 3) + >>> p1.canberra_distance(p2) + 1 + >>> p1, p2 = Point(0, 0), Point(3, 3) + >>> p1.canberra_distance(p2) + 2 + + Raises + ====== + + ValueError when both vectors are zero. + + See Also + ======== + + sympy.geometry.point.Point.distance + + """ + + s, p = Point._normalize_dimension(self, Point(p)) + if self.is_zero and p.is_zero: + raise ValueError("Cannot project to the zero vector.") + return Add(*((abs(a - b)/(abs(a) + abs(b))) for a, b in zip(s, p))) + + @property + def unit(self): + """Return the Point that is in the same direction as `self` + and a distance of 1 from the origin""" + return self / abs(self) + + +class Point2D(Point): + """A point in a 2-dimensional Euclidean space. + + Parameters + ========== + + coords + A sequence of 2 coordinate values. + + Attributes + ========== + + x + y + length + + Raises + ====== + + TypeError + When trying to add or subtract points with different dimensions. + When trying to create a point with more than two dimensions. + When `intersection` is called with object other than a Point. + + See Also + ======== + + sympy.geometry.line.Segment : Connects two Points + + Examples + ======== + + >>> from sympy import Point2D + >>> from sympy.abc import x + >>> Point2D(1, 2) + Point2D(1, 2) + >>> Point2D([1, 2]) + Point2D(1, 2) + >>> Point2D(0, x) + Point2D(0, x) + + Floats are automatically converted to Rational unless the + evaluate flag is False: + + >>> Point2D(0.5, 0.25) + Point2D(1/2, 1/4) + >>> Point2D(0.5, 0.25, evaluate=False) + Point2D(0.5, 0.25) + + """ + + _ambient_dimension = 2 + + def __new__(cls, *args, _nocheck=False, **kwargs): + if not _nocheck: + kwargs['dim'] = 2 + args = Point(*args, **kwargs) + return GeometryEntity.__new__(cls, *args) + + def __contains__(self, item): + return item == self + + @property + def bounds(self): + """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding + rectangle for the geometric figure. + + """ + + return (self.x, self.y, self.x, self.y) + + def rotate(self, angle, pt=None): + """Rotate ``angle`` radians counterclockwise about Point ``pt``. + + See Also + ======== + + translate, scale + + Examples + ======== + + >>> from sympy import Point2D, pi + >>> t = Point2D(1, 0) + >>> t.rotate(pi/2) + Point2D(0, 1) + >>> t.rotate(pi/2, (2, 0)) + Point2D(2, -1) + + """ + c = cos(angle) + s = sin(angle) + + rv = self + if pt is not None: + pt = Point(pt, dim=2) + rv -= pt + x, y = rv.args + rv = Point(c*x - s*y, s*x + c*y) + if pt is not None: + rv += pt + return rv + + def scale(self, x=1, y=1, pt=None): + """Scale the coordinates of the Point by multiplying by + ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) -- + and then adding ``pt`` back again (i.e. ``pt`` is the point of + reference for the scaling). + + See Also + ======== + + rotate, translate + + Examples + ======== + + >>> from sympy import Point2D + >>> t = Point2D(1, 1) + >>> t.scale(2) + Point2D(2, 1) + >>> t.scale(2, 2) + Point2D(2, 2) + + """ + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + return Point(self.x*x, self.y*y) + + def transform(self, matrix): + """Return the point after applying the transformation described + by the 3x3 Matrix, ``matrix``. + + See Also + ======== + sympy.geometry.point.Point2D.rotate + sympy.geometry.point.Point2D.scale + sympy.geometry.point.Point2D.translate + """ + if not (matrix.is_Matrix and matrix.shape == (3, 3)): + raise ValueError("matrix must be a 3x3 matrix") + x, y = self.args + return Point(*(Matrix(1, 3, [x, y, 1])*matrix).tolist()[0][:2]) + + def translate(self, x=0, y=0): + """Shift the Point by adding x and y to the coordinates of the Point. + + See Also + ======== + + sympy.geometry.point.Point2D.rotate, scale + + Examples + ======== + + >>> from sympy import Point2D + >>> t = Point2D(0, 1) + >>> t.translate(2) + Point2D(2, 1) + >>> t.translate(2, 2) + Point2D(2, 3) + >>> t + Point2D(2, 2) + Point2D(2, 3) + + """ + return Point(self.x + x, self.y + y) + + @property + def coordinates(self): + """ + Returns the two coordinates of the Point. + + Examples + ======== + + >>> from sympy import Point2D + >>> p = Point2D(0, 1) + >>> p.coordinates + (0, 1) + """ + return self.args + + @property + def x(self): + """ + Returns the X coordinate of the Point. + + Examples + ======== + + >>> from sympy import Point2D + >>> p = Point2D(0, 1) + >>> p.x + 0 + """ + return self.args[0] + + @property + def y(self): + """ + Returns the Y coordinate of the Point. + + Examples + ======== + + >>> from sympy import Point2D + >>> p = Point2D(0, 1) + >>> p.y + 1 + """ + return self.args[1] + +class Point3D(Point): + """A point in a 3-dimensional Euclidean space. + + Parameters + ========== + + coords + A sequence of 3 coordinate values. + + Attributes + ========== + + x + y + z + length + + Raises + ====== + + TypeError + When trying to add or subtract points with different dimensions. + When `intersection` is called with object other than a Point. + + Examples + ======== + + >>> from sympy import Point3D + >>> from sympy.abc import x + >>> Point3D(1, 2, 3) + Point3D(1, 2, 3) + >>> Point3D([1, 2, 3]) + Point3D(1, 2, 3) + >>> Point3D(0, x, 3) + Point3D(0, x, 3) + + Floats are automatically converted to Rational unless the + evaluate flag is False: + + >>> Point3D(0.5, 0.25, 2) + Point3D(1/2, 1/4, 2) + >>> Point3D(0.5, 0.25, 3, evaluate=False) + Point3D(0.5, 0.25, 3) + + """ + + _ambient_dimension = 3 + + def __new__(cls, *args, _nocheck=False, **kwargs): + if not _nocheck: + kwargs['dim'] = 3 + args = Point(*args, **kwargs) + return GeometryEntity.__new__(cls, *args) + + def __contains__(self, item): + return item == self + + @staticmethod + def are_collinear(*points): + """Is a sequence of points collinear? + + Test whether or not a set of points are collinear. Returns True if + the set of points are collinear, or False otherwise. + + Parameters + ========== + + points : sequence of Point + + Returns + ======= + + are_collinear : boolean + + See Also + ======== + + sympy.geometry.line.Line3D + + Examples + ======== + + >>> from sympy import Point3D + >>> from sympy.abc import x + >>> p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1) + >>> p3, p4, p5 = Point3D(2, 2, 2), Point3D(x, x, x), Point3D(1, 2, 6) + >>> Point3D.are_collinear(p1, p2, p3, p4) + True + >>> Point3D.are_collinear(p1, p2, p3, p5) + False + """ + return Point.is_collinear(*points) + + def direction_cosine(self, point): + """ + Gives the direction cosine between 2 points + + Parameters + ========== + + p : Point3D + + Returns + ======= + + list + + Examples + ======== + + >>> from sympy import Point3D + >>> p1 = Point3D(1, 2, 3) + >>> p1.direction_cosine(Point3D(2, 3, 5)) + [sqrt(6)/6, sqrt(6)/6, sqrt(6)/3] + """ + a = self.direction_ratio(point) + b = sqrt(Add(*(i**2 for i in a))) + return [(point.x - self.x) / b,(point.y - self.y) / b, + (point.z - self.z) / b] + + def direction_ratio(self, point): + """ + Gives the direction ratio between 2 points + + Parameters + ========== + + p : Point3D + + Returns + ======= + + list + + Examples + ======== + + >>> from sympy import Point3D + >>> p1 = Point3D(1, 2, 3) + >>> p1.direction_ratio(Point3D(2, 3, 5)) + [1, 1, 2] + """ + return [(point.x - self.x),(point.y - self.y),(point.z - self.z)] + + def intersection(self, other): + """The intersection between this point and another GeometryEntity. + + Parameters + ========== + + other : GeometryEntity or sequence of coordinates + + Returns + ======= + + intersection : list of Points + + Notes + ===== + + The return value will either be an empty list if there is no + intersection, otherwise it will contain this point. + + Examples + ======== + + >>> from sympy import Point3D + >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 0, 0) + >>> p1.intersection(p2) + [] + >>> p1.intersection(p3) + [Point3D(0, 0, 0)] + + """ + if not isinstance(other, GeometryEntity): + other = Point(other, dim=3) + if isinstance(other, Point3D): + if self == other: + return [self] + return [] + return other.intersection(self) + + def scale(self, x=1, y=1, z=1, pt=None): + """Scale the coordinates of the Point by multiplying by + ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) -- + and then adding ``pt`` back again (i.e. ``pt`` is the point of + reference for the scaling). + + See Also + ======== + + translate + + Examples + ======== + + >>> from sympy import Point3D + >>> t = Point3D(1, 1, 1) + >>> t.scale(2) + Point3D(2, 1, 1) + >>> t.scale(2, 2) + Point3D(2, 2, 1) + + """ + if pt: + pt = Point3D(pt) + return self.translate(*(-pt).args).scale(x, y, z).translate(*pt.args) + return Point3D(self.x*x, self.y*y, self.z*z) + + def transform(self, matrix): + """Return the point after applying the transformation described + by the 4x4 Matrix, ``matrix``. + + See Also + ======== + sympy.geometry.point.Point3D.scale + sympy.geometry.point.Point3D.translate + """ + if not (matrix.is_Matrix and matrix.shape == (4, 4)): + raise ValueError("matrix must be a 4x4 matrix") + x, y, z = self.args + m = Transpose(matrix) + return Point3D(*(Matrix(1, 4, [x, y, z, 1])*m).tolist()[0][:3]) + + def translate(self, x=0, y=0, z=0): + """Shift the Point by adding x and y to the coordinates of the Point. + + See Also + ======== + + scale + + Examples + ======== + + >>> from sympy import Point3D + >>> t = Point3D(0, 1, 1) + >>> t.translate(2) + Point3D(2, 1, 1) + >>> t.translate(2, 2) + Point3D(2, 3, 1) + >>> t + Point3D(2, 2, 2) + Point3D(2, 3, 3) + + """ + return Point3D(self.x + x, self.y + y, self.z + z) + + @property + def coordinates(self): + """ + Returns the three coordinates of the Point. + + Examples + ======== + + >>> from sympy import Point3D + >>> p = Point3D(0, 1, 2) + >>> p.coordinates + (0, 1, 2) + """ + return self.args + + @property + def x(self): + """ + Returns the X coordinate of the Point. + + Examples + ======== + + >>> from sympy import Point3D + >>> p = Point3D(0, 1, 3) + >>> p.x + 0 + """ + return self.args[0] + + @property + def y(self): + """ + Returns the Y coordinate of the Point. + + Examples + ======== + + >>> from sympy import Point3D + >>> p = Point3D(0, 1, 2) + >>> p.y + 1 + """ + return self.args[1] + + @property + def z(self): + """ + Returns the Z coordinate of the Point. + + Examples + ======== + + >>> from sympy import Point3D + >>> p = Point3D(0, 1, 1) + >>> p.z + 1 + """ + return self.args[2] diff --git a/lib/python3.11/site-packages/sympy/geometry/polygon.py b/lib/python3.11/site-packages/sympy/geometry/polygon.py new file mode 100644 index 0000000000000000000000000000000000000000..63031183438e2d228f881fd82e1b0ecca04ec534 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/polygon.py @@ -0,0 +1,2891 @@ +from sympy.core import Expr, S, oo, pi, sympify +from sympy.core.evalf import N +from sympy.core.sorting import default_sort_key, ordered +from sympy.core.symbol import _symbol, Dummy, Symbol +from sympy.functions.elementary.complexes import sign +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import cos, sin, tan +from .ellipse import Circle +from .entity import GeometryEntity, GeometrySet +from .exceptions import GeometryError +from .line import Line, Segment, Ray +from .point import Point +from sympy.logic import And +from sympy.matrices import Matrix +from sympy.simplify.simplify import simplify +from sympy.solvers.solvers import solve +from sympy.utilities.iterables import has_dups, has_variety, uniq, rotate_left, least_rotation +from sympy.utilities.misc import as_int, func_name + +from mpmath.libmp.libmpf import prec_to_dps + +import warnings + + +x, y, T = [Dummy('polygon_dummy', real=True) for i in range(3)] + + +class Polygon(GeometrySet): + """A two-dimensional polygon. + + A simple polygon in space. Can be constructed from a sequence of points + or from a center, radius, number of sides and rotation angle. + + Parameters + ========== + + vertices + A sequence of points. + + n : int, optional + If $> 0$, an n-sided RegularPolygon is created. + Default value is $0$. + + Attributes + ========== + + area + angles + perimeter + vertices + centroid + sides + + Raises + ====== + + GeometryError + If all parameters are not Points. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment, Triangle + + Notes + ===== + + Polygons are treated as closed paths rather than 2D areas so + some calculations can be be negative or positive (e.g., area) + based on the orientation of the points. + + Any consecutive identical points are reduced to a single point + and any points collinear and between two points will be removed + unless they are needed to define an explicit intersection (see examples). + + A Triangle, Segment or Point will be returned when there are 3 or + fewer points provided. + + Examples + ======== + + >>> from sympy import Polygon, pi + >>> p1, p2, p3, p4, p5 = [(0, 0), (1, 0), (5, 1), (0, 1), (3, 0)] + >>> Polygon(p1, p2, p3, p4) + Polygon(Point2D(0, 0), Point2D(1, 0), Point2D(5, 1), Point2D(0, 1)) + >>> Polygon(p1, p2) + Segment2D(Point2D(0, 0), Point2D(1, 0)) + >>> Polygon(p1, p2, p5) + Segment2D(Point2D(0, 0), Point2D(3, 0)) + + The area of a polygon is calculated as positive when vertices are + traversed in a ccw direction. When the sides of a polygon cross the + area will have positive and negative contributions. The following + defines a Z shape where the bottom right connects back to the top + left. + + >>> Polygon((0, 2), (2, 2), (0, 0), (2, 0)).area + 0 + + When the keyword `n` is used to define the number of sides of the + Polygon then a RegularPolygon is created and the other arguments are + interpreted as center, radius and rotation. The unrotated RegularPolygon + will always have a vertex at Point(r, 0) where `r` is the radius of the + circle that circumscribes the RegularPolygon. Its method `spin` can be + used to increment that angle. + + >>> p = Polygon((0,0), 1, n=3) + >>> p + RegularPolygon(Point2D(0, 0), 1, 3, 0) + >>> p.vertices[0] + Point2D(1, 0) + >>> p.args[0] + Point2D(0, 0) + >>> p.spin(pi/2) + >>> p.vertices[0] + Point2D(0, 1) + + """ + + __slots__ = () + + def __new__(cls, *args, n = 0, **kwargs): + if n: + args = list(args) + # return a virtual polygon with n sides + if len(args) == 2: # center, radius + args.append(n) + elif len(args) == 3: # center, radius, rotation + args.insert(2, n) + return RegularPolygon(*args, **kwargs) + + vertices = [Point(a, dim=2, **kwargs) for a in args] + + # remove consecutive duplicates + nodup = [] + for p in vertices: + if nodup and p == nodup[-1]: + continue + nodup.append(p) + if len(nodup) > 1 and nodup[-1] == nodup[0]: + nodup.pop() # last point was same as first + + # remove collinear points + i = -3 + while i < len(nodup) - 3 and len(nodup) > 2: + a, b, c = nodup[i], nodup[i + 1], nodup[i + 2] + if Point.is_collinear(a, b, c): + nodup.pop(i + 1) + if a == c: + nodup.pop(i) + else: + i += 1 + + vertices = list(nodup) + + if len(vertices) > 3: + return GeometryEntity.__new__(cls, *vertices, **kwargs) + elif len(vertices) == 3: + return Triangle(*vertices, **kwargs) + elif len(vertices) == 2: + return Segment(*vertices, **kwargs) + else: + return Point(*vertices, **kwargs) + + @property + def area(self): + """ + The area of the polygon. + + Notes + ===== + + The area calculation can be positive or negative based on the + orientation of the points. If any side of the polygon crosses + any other side, there will be areas having opposite signs. + + See Also + ======== + + sympy.geometry.ellipse.Ellipse.area + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.area + 3 + + In the Z shaped polygon (with the lower right connecting back + to the upper left) the areas cancel out: + + >>> Z = Polygon((0, 1), (1, 1), (0, 0), (1, 0)) + >>> Z.area + 0 + + In the M shaped polygon, areas do not cancel because no side + crosses any other (though there is a point of contact). + + >>> M = Polygon((0, 0), (0, 1), (2, 0), (3, 1), (3, 0)) + >>> M.area + -3/2 + + """ + area = 0 + args = self.args + for i in range(len(args)): + x1, y1 = args[i - 1].args + x2, y2 = args[i].args + area += x1*y2 - x2*y1 + return simplify(area) / 2 + + @staticmethod + def _is_clockwise(a, b, c): + """Return True/False for cw/ccw orientation. + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> a, b, c = [Point(i) for i in [(0, 0), (1, 1), (1, 0)]] + >>> Polygon._is_clockwise(a, b, c) + True + >>> Polygon._is_clockwise(a, c, b) + False + """ + ba = b - a + ca = c - a + t_area = simplify(ba.x*ca.y - ca.x*ba.y) + res = t_area.is_nonpositive + if res is None: + raise ValueError("Can't determine orientation") + return res + + @property + def angles(self): + """The internal angle at each vertex. + + Returns + ======= + + angles : dict + A dictionary where each key is a vertex and each value is the + internal angle at that vertex. The vertices are represented as + Points. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.LinearEntity.angle_between + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.angles[p1] + pi/2 + >>> poly.angles[p2] + acos(-4*sqrt(17)/17) + + """ + + args = self.vertices + n = len(args) + ret = {} + for i in range(n): + a, b, c = args[i - 2], args[i - 1], args[i] + reflex_ang = Ray(b, a).angle_between(Ray(b, c)) + if self._is_clockwise(a, b, c): + ret[b] = 2*S.Pi - reflex_ang + else: + ret[b] = reflex_ang + + # internal sum should be pi*(n - 2), not pi*(n+2) + # so if ratio is (n+2)/(n-2) > 1 it is wrong + wrong = ((sum(ret.values())/S.Pi-1)/(n - 2) - 1).is_positive + if wrong: + two_pi = 2*S.Pi + for b in ret: + ret[b] = two_pi - ret[b] + elif wrong is None: + raise ValueError("could not determine Polygon orientation.") + return ret + + @property + def ambient_dimension(self): + return self.vertices[0].ambient_dimension + + @property + def perimeter(self): + """The perimeter of the polygon. + + Returns + ======= + + perimeter : number or Basic instance + + See Also + ======== + + sympy.geometry.line.Segment.length + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.perimeter + sqrt(17) + 7 + """ + p = 0 + args = self.vertices + for i in range(len(args)): + p += args[i - 1].distance(args[i]) + return simplify(p) + + @property + def vertices(self): + """The vertices of the polygon. + + Returns + ======= + + vertices : list of Points + + Notes + ===== + + When iterating over the vertices, it is more efficient to index self + rather than to request the vertices and index them. Only use the + vertices when you want to process all of them at once. This is even + more important with RegularPolygons that calculate each vertex. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.vertices + [Point2D(0, 0), Point2D(1, 0), Point2D(5, 1), Point2D(0, 1)] + >>> poly.vertices[0] + Point2D(0, 0) + + """ + return list(self.args) + + @property + def centroid(self): + """The centroid of the polygon. + + Returns + ======= + + centroid : Point + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.util.centroid + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.centroid + Point2D(31/18, 11/18) + + """ + A = 1/(6*self.area) + cx, cy = 0, 0 + args = self.args + for i in range(len(args)): + x1, y1 = args[i - 1].args + x2, y2 = args[i].args + v = x1*y2 - x2*y1 + cx += v*(x1 + x2) + cy += v*(y1 + y2) + return Point(simplify(A*cx), simplify(A*cy)) + + + def second_moment_of_area(self, point=None): + """Returns the second moment and product moment of area of a two dimensional polygon. + + Parameters + ========== + + point : Point, two-tuple of sympifyable objects, or None(default=None) + point is the point about which second moment of area is to be found. + If "point=None" it will be calculated about the axis passing through the + centroid of the polygon. + + Returns + ======= + + I_xx, I_yy, I_xy : number or SymPy expression + I_xx, I_yy are second moment of area of a two dimensional polygon. + I_xy is product moment of area of a two dimensional polygon. + + Examples + ======== + + >>> from sympy import Polygon, symbols + >>> a, b = symbols('a, b') + >>> p1, p2, p3, p4, p5 = [(0, 0), (a, 0), (a, b), (0, b), (a/3, b/3)] + >>> rectangle = Polygon(p1, p2, p3, p4) + >>> rectangle.second_moment_of_area() + (a*b**3/12, a**3*b/12, 0) + >>> rectangle.second_moment_of_area(p5) + (a*b**3/9, a**3*b/9, a**2*b**2/36) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Second_moment_of_area + + """ + + I_xx, I_yy, I_xy = 0, 0, 0 + args = self.vertices + for i in range(len(args)): + x1, y1 = args[i-1].args + x2, y2 = args[i].args + v = x1*y2 - x2*y1 + I_xx += (y1**2 + y1*y2 + y2**2)*v + I_yy += (x1**2 + x1*x2 + x2**2)*v + I_xy += (x1*y2 + 2*x1*y1 + 2*x2*y2 + x2*y1)*v + A = self.area + c_x = self.centroid[0] + c_y = self.centroid[1] + # parallel axis theorem + I_xx_c = (I_xx/12) - (A*(c_y**2)) + I_yy_c = (I_yy/12) - (A*(c_x**2)) + I_xy_c = (I_xy/24) - (A*(c_x*c_y)) + if point is None: + return I_xx_c, I_yy_c, I_xy_c + + I_xx = (I_xx_c + A*((point[1]-c_y)**2)) + I_yy = (I_yy_c + A*((point[0]-c_x)**2)) + I_xy = (I_xy_c + A*((point[0]-c_x)*(point[1]-c_y))) + + return I_xx, I_yy, I_xy + + + def first_moment_of_area(self, point=None): + """ + Returns the first moment of area of a two-dimensional polygon with + respect to a certain point of interest. + + First moment of area is a measure of the distribution of the area + of a polygon in relation to an axis. The first moment of area of + the entire polygon about its own centroid is always zero. Therefore, + here it is calculated for an area, above or below a certain point + of interest, that makes up a smaller portion of the polygon. This + area is bounded by the point of interest and the extreme end + (top or bottom) of the polygon. The first moment for this area is + is then determined about the centroidal axis of the initial polygon. + + References + ========== + + .. [1] https://skyciv.com/docs/tutorials/section-tutorials/calculating-the-statical-or-first-moment-of-area-of-beam-sections/?cc=BMD + .. [2] https://mechanicalc.com/reference/cross-sections + + Parameters + ========== + + point: Point, two-tuple of sympifyable objects, or None (default=None) + point is the point above or below which the area of interest lies + If ``point=None`` then the centroid acts as the point of interest. + + Returns + ======= + + Q_x, Q_y: number or SymPy expressions + Q_x is the first moment of area about the x-axis + Q_y is the first moment of area about the y-axis + A negative sign indicates that the section modulus is + determined for a section below (or left of) the centroidal axis + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> a, b = 50, 10 + >>> p1, p2, p3, p4 = [(0, b), (0, 0), (a, 0), (a, b)] + >>> p = Polygon(p1, p2, p3, p4) + >>> p.first_moment_of_area() + (625, 3125) + >>> p.first_moment_of_area(point=Point(30, 7)) + (525, 3000) + """ + if point: + xc, yc = self.centroid + else: + point = self.centroid + xc, yc = point + + h_line = Line(point, slope=0) + v_line = Line(point, slope=S.Infinity) + + h_poly = self.cut_section(h_line) + v_poly = self.cut_section(v_line) + + poly_1 = h_poly[0] if h_poly[0].area <= h_poly[1].area else h_poly[1] + poly_2 = v_poly[0] if v_poly[0].area <= v_poly[1].area else v_poly[1] + + Q_x = (poly_1.centroid.y - yc)*poly_1.area + Q_y = (poly_2.centroid.x - xc)*poly_2.area + + return Q_x, Q_y + + + def polar_second_moment_of_area(self): + """Returns the polar modulus of a two-dimensional polygon + + It is a constituent of the second moment of area, linked through + the perpendicular axis theorem. While the planar second moment of + area describes an object's resistance to deflection (bending) when + subjected to a force applied to a plane parallel to the central + axis, the polar second moment of area describes an object's + resistance to deflection when subjected to a moment applied in a + plane perpendicular to the object's central axis (i.e. parallel to + the cross-section) + + Examples + ======== + + >>> from sympy import Polygon, symbols + >>> a, b = symbols('a, b') + >>> rectangle = Polygon((0, 0), (a, 0), (a, b), (0, b)) + >>> rectangle.polar_second_moment_of_area() + a**3*b/12 + a*b**3/12 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Polar_moment_of_inertia + + """ + second_moment = self.second_moment_of_area() + return second_moment[0] + second_moment[1] + + + def section_modulus(self, point=None): + """Returns a tuple with the section modulus of a two-dimensional + polygon. + + Section modulus is a geometric property of a polygon defined as the + ratio of second moment of area to the distance of the extreme end of + the polygon from the centroidal axis. + + Parameters + ========== + + point : Point, two-tuple of sympifyable objects, or None(default=None) + point is the point at which section modulus is to be found. + If "point=None" it will be calculated for the point farthest from the + centroidal axis of the polygon. + + Returns + ======= + + S_x, S_y: numbers or SymPy expressions + S_x is the section modulus with respect to the x-axis + S_y is the section modulus with respect to the y-axis + A negative sign indicates that the section modulus is + determined for a point below the centroidal axis + + Examples + ======== + + >>> from sympy import symbols, Polygon, Point + >>> a, b = symbols('a, b', positive=True) + >>> rectangle = Polygon((0, 0), (a, 0), (a, b), (0, b)) + >>> rectangle.section_modulus() + (a*b**2/6, a**2*b/6) + >>> rectangle.section_modulus(Point(a/4, b/4)) + (-a*b**2/3, -a**2*b/3) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Section_modulus + + """ + x_c, y_c = self.centroid + if point is None: + # taking x and y as maximum distances from centroid + x_min, y_min, x_max, y_max = self.bounds + y = max(y_c - y_min, y_max - y_c) + x = max(x_c - x_min, x_max - x_c) + else: + # taking x and y as distances of the given point from the centroid + y = point.y - y_c + x = point.x - x_c + + second_moment= self.second_moment_of_area() + S_x = second_moment[0]/y + S_y = second_moment[1]/x + + return S_x, S_y + + + @property + def sides(self): + """The directed line segments that form the sides of the polygon. + + Returns + ======= + + sides : list of sides + Each side is a directed Segment. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.sides + [Segment2D(Point2D(0, 0), Point2D(1, 0)), + Segment2D(Point2D(1, 0), Point2D(5, 1)), + Segment2D(Point2D(5, 1), Point2D(0, 1)), Segment2D(Point2D(0, 1), Point2D(0, 0))] + + """ + res = [] + args = self.vertices + for i in range(-len(args), 0): + res.append(Segment(args[i], args[i + 1])) + return res + + @property + def bounds(self): + """Return a tuple (xmin, ymin, xmax, ymax) representing the bounding + rectangle for the geometric figure. + + """ + + verts = self.vertices + xs = [p.x for p in verts] + ys = [p.y for p in verts] + return (min(xs), min(ys), max(xs), max(ys)) + + def is_convex(self): + """Is the polygon convex? + + A polygon is convex if all its interior angles are less than 180 + degrees and there are no intersections between sides. + + Returns + ======= + + is_convex : boolean + True if this polygon is convex, False otherwise. + + See Also + ======== + + sympy.geometry.util.convex_hull + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly = Polygon(p1, p2, p3, p4) + >>> poly.is_convex() + True + + """ + # Determine orientation of points + args = self.vertices + cw = self._is_clockwise(args[-2], args[-1], args[0]) + for i in range(1, len(args)): + if cw ^ self._is_clockwise(args[i - 2], args[i - 1], args[i]): + return False + # check for intersecting sides + sides = self.sides + for i, si in enumerate(sides): + pts = si.args + # exclude the sides connected to si + for j in range(1 if i == len(sides) - 1 else 0, i - 1): + sj = sides[j] + if sj.p1 not in pts and sj.p2 not in pts: + hit = si.intersection(sj) + if hit: + return False + return True + + def encloses_point(self, p): + """ + Return True if p is enclosed by (is inside of) self. + + Notes + ===== + + Being on the border of self is considered False. + + Parameters + ========== + + p : Point + + Returns + ======= + + encloses_point : True, False or None + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.ellipse.Ellipse.encloses_point + + Examples + ======== + + >>> from sympy import Polygon, Point + >>> p = Polygon((0, 0), (4, 0), (4, 4)) + >>> p.encloses_point(Point(2, 1)) + True + >>> p.encloses_point(Point(2, 2)) + False + >>> p.encloses_point(Point(5, 5)) + False + + References + ========== + + .. [1] https://paulbourke.net/geometry/polygonmesh/#insidepoly + + """ + p = Point(p, dim=2) + if p in self.vertices or any(p in s for s in self.sides): + return False + + # move to p, checking that the result is numeric + lit = [] + for v in self.vertices: + lit.append(v - p) # the difference is simplified + if lit[-1].free_symbols: + return None + + poly = Polygon(*lit) + + # polygon closure is assumed in the following test but Polygon removes duplicate pts so + # the last point has to be added so all sides are computed. Using Polygon.sides is + # not good since Segments are unordered. + args = poly.args + indices = list(range(-len(args), 1)) + + if poly.is_convex(): + orientation = None + for i in indices: + a = args[i] + b = args[i + 1] + test = ((-a.y)*(b.x - a.x) - (-a.x)*(b.y - a.y)).is_negative + if orientation is None: + orientation = test + elif test is not orientation: + return False + return True + + hit_odd = False + p1x, p1y = args[0].args + for i in indices[1:]: + p2x, p2y = args[i].args + if 0 > min(p1y, p2y): + if 0 <= max(p1y, p2y): + if 0 <= max(p1x, p2x): + if p1y != p2y: + xinters = (-p1y)*(p2x - p1x)/(p2y - p1y) + p1x + if p1x == p2x or 0 <= xinters: + hit_odd = not hit_odd + p1x, p1y = p2x, p2y + return hit_odd + + def arbitrary_point(self, parameter='t'): + """A parameterized point on the polygon. + + The parameter, varying from 0 to 1, assigns points to the position on + the perimeter that is that fraction of the total perimeter. So the + point evaluated at t=1/2 would return the point from the first vertex + that is 1/2 way around the polygon. + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + arbitrary_point : Point + + Raises + ====== + + ValueError + When `parameter` already appears in the Polygon's definition. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Polygon, Symbol + >>> t = Symbol('t', real=True) + >>> tri = Polygon((0, 0), (1, 0), (1, 1)) + >>> p = tri.arbitrary_point('t') + >>> perimeter = tri.perimeter + >>> s1, s2 = [s.length for s in tri.sides[:2]] + >>> p.subs(t, (s1 + s2/2)/perimeter) + Point2D(1, 1/2) + + """ + t = _symbol(parameter, real=True) + if t.name in (f.name for f in self.free_symbols): + raise ValueError('Symbol %s already appears in object and cannot be used as a parameter.' % t.name) + sides = [] + perimeter = self.perimeter + perim_fraction_start = 0 + for s in self.sides: + side_perim_fraction = s.length/perimeter + perim_fraction_end = perim_fraction_start + side_perim_fraction + pt = s.arbitrary_point(parameter).subs( + t, (t - perim_fraction_start)/side_perim_fraction) + sides.append( + (pt, (And(perim_fraction_start <= t, t < perim_fraction_end)))) + perim_fraction_start = perim_fraction_end + return Piecewise(*sides) + + def parameter_value(self, other, t): + if not isinstance(other,GeometryEntity): + other = Point(other, dim=self.ambient_dimension) + if not isinstance(other,Point): + raise ValueError("other must be a point") + if other.free_symbols: + raise NotImplementedError('non-numeric coordinates') + unknown = False + p = self.arbitrary_point(T) + for pt, cond in p.args: + sol = solve(pt - other, T, dict=True) + if not sol: + continue + value = sol[0][T] + if simplify(cond.subs(T, value)) == True: + return {t: value} + unknown = True + if unknown: + raise ValueError("Given point may not be on %s" % func_name(self)) + raise ValueError("Given point is not on %s" % func_name(self)) + + def plot_interval(self, parameter='t'): + """The plot interval for the default geometric plot of the polygon. + + Parameters + ========== + + parameter : str, optional + Default value is 't'. + + Returns + ======= + + plot_interval : list (plot interval) + [parameter, lower_bound, upper_bound] + + Examples + ======== + + >>> from sympy import Polygon + >>> p = Polygon((0, 0), (1, 0), (1, 1)) + >>> p.plot_interval() + [t, 0, 1] + + """ + t = Symbol(parameter, real=True) + return [t, 0, 1] + + def intersection(self, o): + """The intersection of polygon and geometry entity. + + The intersection may be empty and can contain individual Points and + complete Line Segments. + + Parameters + ========== + + other: GeometryEntity + + Returns + ======= + + intersection : list + The list of Segments and Points + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment + + Examples + ======== + + >>> from sympy import Point, Polygon, Line + >>> p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + >>> poly1 = Polygon(p1, p2, p3, p4) + >>> p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)]) + >>> poly2 = Polygon(p5, p6, p7) + >>> poly1.intersection(poly2) + [Point2D(1/3, 1), Point2D(2/3, 0), Point2D(9/5, 1/5), Point2D(7/3, 1)] + >>> poly1.intersection(Line(p1, p2)) + [Segment2D(Point2D(0, 0), Point2D(1, 0))] + >>> poly1.intersection(p1) + [Point2D(0, 0)] + """ + intersection_result = [] + k = o.sides if isinstance(o, Polygon) else [o] + for side in self.sides: + for side1 in k: + intersection_result.extend(side.intersection(side1)) + + intersection_result = list(uniq(intersection_result)) + points = [entity for entity in intersection_result if isinstance(entity, Point)] + segments = [entity for entity in intersection_result if isinstance(entity, Segment)] + + if points and segments: + points_in_segments = list(uniq([point for point in points for segment in segments if point in segment])) + if points_in_segments: + for i in points_in_segments: + points.remove(i) + return list(ordered(segments + points)) + else: + return list(ordered(intersection_result)) + + + def cut_section(self, line): + """ + Returns a tuple of two polygon segments that lie above and below + the intersecting line respectively. + + Parameters + ========== + + line: Line object of geometry module + line which cuts the Polygon. The part of the Polygon that lies + above and below this line is returned. + + Returns + ======= + + upper_polygon, lower_polygon: Polygon objects or None + upper_polygon is the polygon that lies above the given line. + lower_polygon is the polygon that lies below the given line. + upper_polygon and lower polygon are ``None`` when no polygon + exists above the line or below the line. + + Raises + ====== + + ValueError: When the line does not intersect the polygon + + Examples + ======== + + >>> from sympy import Polygon, Line + >>> a, b = 20, 10 + >>> p1, p2, p3, p4 = [(0, b), (0, 0), (a, 0), (a, b)] + >>> rectangle = Polygon(p1, p2, p3, p4) + >>> t = rectangle.cut_section(Line((0, 5), slope=0)) + >>> t + (Polygon(Point2D(0, 10), Point2D(0, 5), Point2D(20, 5), Point2D(20, 10)), + Polygon(Point2D(0, 5), Point2D(0, 0), Point2D(20, 0), Point2D(20, 5))) + >>> upper_segment, lower_segment = t + >>> upper_segment.area + 100 + >>> upper_segment.centroid + Point2D(10, 15/2) + >>> lower_segment.centroid + Point2D(10, 5/2) + + References + ========== + + .. [1] https://github.com/sympy/sympy/wiki/A-method-to-return-a-cut-section-of-any-polygon-geometry + + """ + intersection_points = self.intersection(line) + if not intersection_points: + raise ValueError("This line does not intersect the polygon") + + points = list(self.vertices) + points.append(points[0]) + + eq = line.equation(x, y) + + # considering equation of line to be `ax +by + c` + a = eq.coeff(x) + b = eq.coeff(y) + + upper_vertices = [] + lower_vertices = [] + # prev is true when previous point is above the line + prev = True + prev_point = None + for point in points: + # when coefficient of y is 0, right side of the line is + # considered + compare = eq.subs({x: point.x, y: point.y})/b if b \ + else eq.subs(x, point.x)/a + + # if point lies above line + if compare > 0: + if not prev: + # if previous point lies below the line, the intersection + # point of the polygon edge and the line has to be included + edge = Line(point, prev_point) + new_point = edge.intersection(line) + upper_vertices.append(new_point[0]) + lower_vertices.append(new_point[0]) + + upper_vertices.append(point) + prev = True + else: + if prev and prev_point: + edge = Line(point, prev_point) + new_point = edge.intersection(line) + upper_vertices.append(new_point[0]) + lower_vertices.append(new_point[0]) + lower_vertices.append(point) + prev = False + prev_point = point + + upper_polygon, lower_polygon = None, None + if upper_vertices and isinstance(Polygon(*upper_vertices), Polygon): + upper_polygon = Polygon(*upper_vertices) + if lower_vertices and isinstance(Polygon(*lower_vertices), Polygon): + lower_polygon = Polygon(*lower_vertices) + + return upper_polygon, lower_polygon + + + def distance(self, o): + """ + Returns the shortest distance between self and o. + + If o is a point, then self does not need to be convex. + If o is another polygon self and o must be convex. + + Examples + ======== + + >>> from sympy import Point, Polygon, RegularPolygon + >>> p1, p2 = map(Point, [(0, 0), (7, 5)]) + >>> poly = Polygon(*RegularPolygon(p1, 1, 3).vertices) + >>> poly.distance(p2) + sqrt(61) + """ + if isinstance(o, Point): + dist = oo + for side in self.sides: + current = side.distance(o) + if current == 0: + return S.Zero + elif current < dist: + dist = current + return dist + elif isinstance(o, Polygon) and self.is_convex() and o.is_convex(): + return self._do_poly_distance(o) + raise NotImplementedError() + + def _do_poly_distance(self, e2): + """ + Calculates the least distance between the exteriors of two + convex polygons e1 and e2. Does not check for the convexity + of the polygons as this is checked by Polygon.distance. + + Notes + ===== + + - Prints a warning if the two polygons possibly intersect as the return + value will not be valid in such a case. For a more through test of + intersection use intersection(). + + See Also + ======== + + sympy.geometry.point.Point.distance + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> square = Polygon(Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0)) + >>> triangle = Polygon(Point(1, 2), Point(2, 2), Point(2, 1)) + >>> square._do_poly_distance(triangle) + sqrt(2)/2 + + Description of method used + ========================== + + Method: + [1] https://web.archive.org/web/20150509035744/http://cgm.cs.mcgill.ca/~orm/mind2p.html + Uses rotating calipers: + [2] https://en.wikipedia.org/wiki/Rotating_calipers + and antipodal points: + [3] https://en.wikipedia.org/wiki/Antipodal_point + """ + e1 = self + + '''Tests for a possible intersection between the polygons and outputs a warning''' + e1_center = e1.centroid + e2_center = e2.centroid + e1_max_radius = S.Zero + e2_max_radius = S.Zero + for vertex in e1.vertices: + r = Point.distance(e1_center, vertex) + if e1_max_radius < r: + e1_max_radius = r + for vertex in e2.vertices: + r = Point.distance(e2_center, vertex) + if e2_max_radius < r: + e2_max_radius = r + center_dist = Point.distance(e1_center, e2_center) + if center_dist <= e1_max_radius + e2_max_radius: + warnings.warn("Polygons may intersect producing erroneous output", + stacklevel=3) + + ''' + Find the upper rightmost vertex of e1 and the lowest leftmost vertex of e2 + ''' + e1_ymax = Point(0, -oo) + e2_ymin = Point(0, oo) + + for vertex in e1.vertices: + if vertex.y > e1_ymax.y or (vertex.y == e1_ymax.y and vertex.x > e1_ymax.x): + e1_ymax = vertex + for vertex in e2.vertices: + if vertex.y < e2_ymin.y or (vertex.y == e2_ymin.y and vertex.x < e2_ymin.x): + e2_ymin = vertex + min_dist = Point.distance(e1_ymax, e2_ymin) + + ''' + Produce a dictionary with vertices of e1 as the keys and, for each vertex, the points + to which the vertex is connected as its value. The same is then done for e2. + ''' + e1_connections = {} + e2_connections = {} + + for side in e1.sides: + if side.p1 in e1_connections: + e1_connections[side.p1].append(side.p2) + else: + e1_connections[side.p1] = [side.p2] + + if side.p2 in e1_connections: + e1_connections[side.p2].append(side.p1) + else: + e1_connections[side.p2] = [side.p1] + + for side in e2.sides: + if side.p1 in e2_connections: + e2_connections[side.p1].append(side.p2) + else: + e2_connections[side.p1] = [side.p2] + + if side.p2 in e2_connections: + e2_connections[side.p2].append(side.p1) + else: + e2_connections[side.p2] = [side.p1] + + e1_current = e1_ymax + e2_current = e2_ymin + support_line = Line(Point(S.Zero, S.Zero), Point(S.One, S.Zero)) + + ''' + Determine which point in e1 and e2 will be selected after e2_ymin and e1_ymax, + this information combined with the above produced dictionaries determines the + path that will be taken around the polygons + ''' + point1 = e1_connections[e1_ymax][0] + point2 = e1_connections[e1_ymax][1] + angle1 = support_line.angle_between(Line(e1_ymax, point1)) + angle2 = support_line.angle_between(Line(e1_ymax, point2)) + if angle1 < angle2: + e1_next = point1 + elif angle2 < angle1: + e1_next = point2 + elif Point.distance(e1_ymax, point1) > Point.distance(e1_ymax, point2): + e1_next = point2 + else: + e1_next = point1 + + point1 = e2_connections[e2_ymin][0] + point2 = e2_connections[e2_ymin][1] + angle1 = support_line.angle_between(Line(e2_ymin, point1)) + angle2 = support_line.angle_between(Line(e2_ymin, point2)) + if angle1 > angle2: + e2_next = point1 + elif angle2 > angle1: + e2_next = point2 + elif Point.distance(e2_ymin, point1) > Point.distance(e2_ymin, point2): + e2_next = point2 + else: + e2_next = point1 + + ''' + Loop which determines the distance between anti-podal pairs and updates the + minimum distance accordingly. It repeats until it reaches the starting position. + ''' + while True: + e1_angle = support_line.angle_between(Line(e1_current, e1_next)) + e2_angle = pi - support_line.angle_between(Line( + e2_current, e2_next)) + + if (e1_angle < e2_angle) is True: + support_line = Line(e1_current, e1_next) + e1_segment = Segment(e1_current, e1_next) + min_dist_current = e1_segment.distance(e2_current) + + if min_dist_current.evalf() < min_dist.evalf(): + min_dist = min_dist_current + + if e1_connections[e1_next][0] != e1_current: + e1_current = e1_next + e1_next = e1_connections[e1_next][0] + else: + e1_current = e1_next + e1_next = e1_connections[e1_next][1] + elif (e1_angle > e2_angle) is True: + support_line = Line(e2_next, e2_current) + e2_segment = Segment(e2_current, e2_next) + min_dist_current = e2_segment.distance(e1_current) + + if min_dist_current.evalf() < min_dist.evalf(): + min_dist = min_dist_current + + if e2_connections[e2_next][0] != e2_current: + e2_current = e2_next + e2_next = e2_connections[e2_next][0] + else: + e2_current = e2_next + e2_next = e2_connections[e2_next][1] + else: + support_line = Line(e1_current, e1_next) + e1_segment = Segment(e1_current, e1_next) + e2_segment = Segment(e2_current, e2_next) + min1 = e1_segment.distance(e2_next) + min2 = e2_segment.distance(e1_next) + + min_dist_current = min(min1, min2) + if min_dist_current.evalf() < min_dist.evalf(): + min_dist = min_dist_current + + if e1_connections[e1_next][0] != e1_current: + e1_current = e1_next + e1_next = e1_connections[e1_next][0] + else: + e1_current = e1_next + e1_next = e1_connections[e1_next][1] + + if e2_connections[e2_next][0] != e2_current: + e2_current = e2_next + e2_next = e2_connections[e2_next][0] + else: + e2_current = e2_next + e2_next = e2_connections[e2_next][1] + if e1_current == e1_ymax and e2_current == e2_ymin: + break + return min_dist + + def _svg(self, scale_factor=1., fill_color="#66cc99"): + """Returns SVG path element for the Polygon. + + Parameters + ========== + + scale_factor : float + Multiplication factor for the SVG stroke-width. Default is 1. + fill_color : str, optional + Hex string for fill color. Default is "#66cc99". + """ + verts = map(N, self.vertices) + coords = ["{},{}".format(p.x, p.y) for p in verts] + path = "M {} L {} z".format(coords[0], " L ".join(coords[1:])) + return ( + '' + ).format(2. * scale_factor, path, fill_color) + + def _hashable_content(self): + + D = {} + def ref_list(point_list): + kee = {} + for i, p in enumerate(ordered(set(point_list))): + kee[p] = i + D[i] = p + return [kee[p] for p in point_list] + + S1 = ref_list(self.args) + r_nor = rotate_left(S1, least_rotation(S1)) + S2 = ref_list(list(reversed(self.args))) + r_rev = rotate_left(S2, least_rotation(S2)) + if r_nor < r_rev: + r = r_nor + else: + r = r_rev + canonical_args = [ D[order] for order in r ] + return tuple(canonical_args) + + def __contains__(self, o): + """ + Return True if o is contained within the boundary lines of self.altitudes + + Parameters + ========== + + other : GeometryEntity + + Returns + ======= + + contained in : bool + The points (and sides, if applicable) are contained in self. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity.encloses + + Examples + ======== + + >>> from sympy import Line, Segment, Point + >>> p = Point(0, 0) + >>> q = Point(1, 1) + >>> s = Segment(p, q*2) + >>> l = Line(p, q) + >>> p in q + False + >>> p in s + True + >>> q*3 in s + False + >>> s in l + True + + """ + + if isinstance(o, Polygon): + return self == o + elif isinstance(o, Segment): + return any(o in s for s in self.sides) + elif isinstance(o, Point): + if o in self.vertices: + return True + for side in self.sides: + if o in side: + return True + + return False + + def bisectors(p, prec=None): + """Returns angle bisectors of a polygon. If prec is given + then approximate the point defining the ray to that precision. + + The distance between the points defining the bisector ray is 1. + + Examples + ======== + + >>> from sympy import Polygon, Point + >>> p = Polygon(Point(0, 0), Point(2, 0), Point(1, 1), Point(0, 3)) + >>> p.bisectors(2) + {Point2D(0, 0): Ray2D(Point2D(0, 0), Point2D(0.71, 0.71)), + Point2D(0, 3): Ray2D(Point2D(0, 3), Point2D(0.23, 2.0)), + Point2D(1, 1): Ray2D(Point2D(1, 1), Point2D(0.19, 0.42)), + Point2D(2, 0): Ray2D(Point2D(2, 0), Point2D(1.1, 0.38))} + """ + b = {} + pts = list(p.args) + pts.append(pts[0]) # close it + cw = Polygon._is_clockwise(*pts[:3]) + if cw: + pts = list(reversed(pts)) + for v, a in p.angles.items(): + i = pts.index(v) + p1, p2 = Point._normalize_dimension(pts[i], pts[i + 1]) + ray = Ray(p1, p2).rotate(a/2, v) + dir = ray.direction + ray = Ray(ray.p1, ray.p1 + dir/dir.distance((0, 0))) + if prec is not None: + ray = Ray(ray.p1, ray.p2.n(prec)) + b[v] = ray + return b + + +class RegularPolygon(Polygon): + """ + A regular polygon. + + Such a polygon has all internal angles equal and all sides the same length. + + Parameters + ========== + + center : Point + radius : number or Basic instance + The distance from the center to a vertex + n : int + The number of sides + + Attributes + ========== + + vertices + center + radius + rotation + apothem + interior_angle + exterior_angle + circumcircle + incircle + angles + + Raises + ====== + + GeometryError + If the `center` is not a Point, or the `radius` is not a number or Basic + instance, or the number of sides, `n`, is less than three. + + Notes + ===== + + A RegularPolygon can be instantiated with Polygon with the kwarg n. + + Regular polygons are instantiated with a center, radius, number of sides + and a rotation angle. Whereas the arguments of a Polygon are vertices, the + vertices of the RegularPolygon must be obtained with the vertices method. + + See Also + ======== + + sympy.geometry.point.Point, Polygon + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> r = RegularPolygon(Point(0, 0), 5, 3) + >>> r + RegularPolygon(Point2D(0, 0), 5, 3, 0) + >>> r.vertices[0] + Point2D(5, 0) + + """ + + __slots__ = ('_n', '_center', '_radius', '_rot') + + def __new__(self, c, r, n, rot=0, **kwargs): + r, n, rot = map(sympify, (r, n, rot)) + c = Point(c, dim=2, **kwargs) + if not isinstance(r, Expr): + raise GeometryError("r must be an Expr object, not %s" % r) + if n.is_Number: + as_int(n) # let an error raise if necessary + if n < 3: + raise GeometryError("n must be a >= 3, not %s" % n) + + obj = GeometryEntity.__new__(self, c, r, n, **kwargs) + obj._n = n + obj._center = c + obj._radius = r + obj._rot = rot % (2*S.Pi/n) if rot.is_number else rot + return obj + + def _eval_evalf(self, prec=15, **options): + c, r, n, a = self.args + dps = prec_to_dps(prec) + c, r, a = [i.evalf(n=dps, **options) for i in (c, r, a)] + return self.func(c, r, n, a) + + @property + def args(self): + """ + Returns the center point, the radius, + the number of sides, and the orientation angle. + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> r = RegularPolygon(Point(0, 0), 5, 3) + >>> r.args + (Point2D(0, 0), 5, 3, 0) + """ + return self._center, self._radius, self._n, self._rot + + def __str__(self): + return 'RegularPolygon(%s, %s, %s, %s)' % tuple(self.args) + + def __repr__(self): + return 'RegularPolygon(%s, %s, %s, %s)' % tuple(self.args) + + @property + def area(self): + """Returns the area. + + Examples + ======== + + >>> from sympy import RegularPolygon + >>> square = RegularPolygon((0, 0), 1, 4) + >>> square.area + 2 + >>> _ == square.length**2 + True + """ + c, r, n, rot = self.args + return sign(r)*n*self.length**2/(4*tan(pi/n)) + + @property + def length(self): + """Returns the length of the sides. + + The half-length of the side and the apothem form two legs + of a right triangle whose hypotenuse is the radius of the + regular polygon. + + Examples + ======== + + >>> from sympy import RegularPolygon + >>> from sympy import sqrt + >>> s = square_in_unit_circle = RegularPolygon((0, 0), 1, 4) + >>> s.length + sqrt(2) + >>> sqrt((_/2)**2 + s.apothem**2) == s.radius + True + + """ + return self.radius*2*sin(pi/self._n) + + @property + def center(self): + """The center of the RegularPolygon + + This is also the center of the circumscribing circle. + + Returns + ======= + + center : Point + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.ellipse.Ellipse.center + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 5, 4) + >>> rp.center + Point2D(0, 0) + """ + return self._center + + centroid = center + + @property + def circumcenter(self): + """ + Alias for center. + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 5, 4) + >>> rp.circumcenter + Point2D(0, 0) + """ + return self.center + + @property + def radius(self): + """Radius of the RegularPolygon + + This is also the radius of the circumscribing circle. + + Returns + ======= + + radius : number or instance of Basic + + See Also + ======== + + sympy.geometry.line.Segment.length, sympy.geometry.ellipse.Circle.radius + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy import RegularPolygon, Point + >>> radius = Symbol('r') + >>> rp = RegularPolygon(Point(0, 0), radius, 4) + >>> rp.radius + r + + """ + return self._radius + + @property + def circumradius(self): + """ + Alias for radius. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy import RegularPolygon, Point + >>> radius = Symbol('r') + >>> rp = RegularPolygon(Point(0, 0), radius, 4) + >>> rp.circumradius + r + """ + return self.radius + + @property + def rotation(self): + """CCW angle by which the RegularPolygon is rotated + + Returns + ======= + + rotation : number or instance of Basic + + Examples + ======== + + >>> from sympy import pi + >>> from sympy.abc import a + >>> from sympy import RegularPolygon, Point + >>> RegularPolygon(Point(0, 0), 3, 4, pi/4).rotation + pi/4 + + Numerical rotation angles are made canonical: + + >>> RegularPolygon(Point(0, 0), 3, 4, a).rotation + a + >>> RegularPolygon(Point(0, 0), 3, 4, pi).rotation + 0 + + """ + return self._rot + + @property + def apothem(self): + """The inradius of the RegularPolygon. + + The apothem/inradius is the radius of the inscribed circle. + + Returns + ======= + + apothem : number or instance of Basic + + See Also + ======== + + sympy.geometry.line.Segment.length, sympy.geometry.ellipse.Circle.radius + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy import RegularPolygon, Point + >>> radius = Symbol('r') + >>> rp = RegularPolygon(Point(0, 0), radius, 4) + >>> rp.apothem + sqrt(2)*r/2 + + """ + return self.radius * cos(S.Pi/self._n) + + @property + def inradius(self): + """ + Alias for apothem. + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy import RegularPolygon, Point + >>> radius = Symbol('r') + >>> rp = RegularPolygon(Point(0, 0), radius, 4) + >>> rp.inradius + sqrt(2)*r/2 + """ + return self.apothem + + @property + def interior_angle(self): + """Measure of the interior angles. + + Returns + ======= + + interior_angle : number + + See Also + ======== + + sympy.geometry.line.LinearEntity.angle_between + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 4, 8) + >>> rp.interior_angle + 3*pi/4 + + """ + return (self._n - 2)*S.Pi/self._n + + @property + def exterior_angle(self): + """Measure of the exterior angles. + + Returns + ======= + + exterior_angle : number + + See Also + ======== + + sympy.geometry.line.LinearEntity.angle_between + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 4, 8) + >>> rp.exterior_angle + pi/4 + + """ + return 2*S.Pi/self._n + + @property + def circumcircle(self): + """The circumcircle of the RegularPolygon. + + Returns + ======= + + circumcircle : Circle + + See Also + ======== + + circumcenter, sympy.geometry.ellipse.Circle + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 4, 8) + >>> rp.circumcircle + Circle(Point2D(0, 0), 4) + + """ + return Circle(self.center, self.radius) + + @property + def incircle(self): + """The incircle of the RegularPolygon. + + Returns + ======= + + incircle : Circle + + See Also + ======== + + inradius, sympy.geometry.ellipse.Circle + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 4, 7) + >>> rp.incircle + Circle(Point2D(0, 0), 4*cos(pi/7)) + + """ + return Circle(self.center, self.apothem) + + @property + def angles(self): + """ + Returns a dictionary with keys, the vertices of the Polygon, + and values, the interior angle at each vertex. + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> r = RegularPolygon(Point(0, 0), 5, 3) + >>> r.angles + {Point2D(-5/2, -5*sqrt(3)/2): pi/3, + Point2D(-5/2, 5*sqrt(3)/2): pi/3, + Point2D(5, 0): pi/3} + """ + ret = {} + ang = self.interior_angle + for v in self.vertices: + ret[v] = ang + return ret + + def encloses_point(self, p): + """ + Return True if p is enclosed by (is inside of) self. + + Notes + ===== + + Being on the border of self is considered False. + + The general Polygon.encloses_point method is called only if + a point is not within or beyond the incircle or circumcircle, + respectively. + + Parameters + ========== + + p : Point + + Returns + ======= + + encloses_point : True, False or None + + See Also + ======== + + sympy.geometry.ellipse.Ellipse.encloses_point + + Examples + ======== + + >>> from sympy import RegularPolygon, S, Point, Symbol + >>> p = RegularPolygon((0, 0), 3, 4) + >>> p.encloses_point(Point(0, 0)) + True + >>> r, R = p.inradius, p.circumradius + >>> p.encloses_point(Point((r + R)/2, 0)) + True + >>> p.encloses_point(Point(R/2, R/2 + (R - r)/10)) + False + >>> t = Symbol('t', real=True) + >>> p.encloses_point(p.arbitrary_point().subs(t, S.Half)) + False + >>> p.encloses_point(Point(5, 5)) + False + + """ + + c = self.center + d = Segment(c, p).length + if d >= self.radius: + return False + elif d < self.inradius: + return True + else: + # now enumerate the RegularPolygon like a general polygon. + return Polygon.encloses_point(self, p) + + def spin(self, angle): + """Increment *in place* the virtual Polygon's rotation by ccw angle. + + See also: rotate method which moves the center. + + >>> from sympy import Polygon, Point, pi + >>> r = Polygon(Point(0,0), 1, n=3) + >>> r.vertices[0] + Point2D(1, 0) + >>> r.spin(pi/6) + >>> r.vertices[0] + Point2D(sqrt(3)/2, 1/2) + + See Also + ======== + + rotation + rotate : Creates a copy of the RegularPolygon rotated about a Point + + """ + self._rot += angle + + def rotate(self, angle, pt=None): + """Override GeometryEntity.rotate to first rotate the RegularPolygon + about its center. + + >>> from sympy import Point, RegularPolygon, pi + >>> t = RegularPolygon(Point(1, 0), 1, 3) + >>> t.vertices[0] # vertex on x-axis + Point2D(2, 0) + >>> t.rotate(pi/2).vertices[0] # vertex on y axis now + Point2D(0, 2) + + See Also + ======== + + rotation + spin : Rotates a RegularPolygon in place + + """ + + r = type(self)(*self.args) # need a copy or else changes are in-place + r._rot += angle + return GeometryEntity.rotate(r, angle, pt) + + def scale(self, x=1, y=1, pt=None): + """Override GeometryEntity.scale since it is the radius that must be + scaled (if x == y) or else a new Polygon must be returned. + + >>> from sympy import RegularPolygon + + Symmetric scaling returns a RegularPolygon: + + >>> RegularPolygon((0, 0), 1, 4).scale(2, 2) + RegularPolygon(Point2D(0, 0), 2, 4, 0) + + Asymmetric scaling returns a kite as a Polygon: + + >>> RegularPolygon((0, 0), 1, 4).scale(2, 1) + Polygon(Point2D(2, 0), Point2D(0, 1), Point2D(-2, 0), Point2D(0, -1)) + + """ + if pt: + pt = Point(pt, dim=2) + return self.translate(*(-pt).args).scale(x, y).translate(*pt.args) + if x != y: + return Polygon(*self.vertices).scale(x, y) + c, r, n, rot = self.args + r *= x + return self.func(c, r, n, rot) + + def reflect(self, line): + """Override GeometryEntity.reflect since this is not made of only + points. + + Examples + ======== + + >>> from sympy import RegularPolygon, Line + + >>> RegularPolygon((0, 0), 1, 4).reflect(Line((0, 1), slope=-2)) + RegularPolygon(Point2D(4/5, 2/5), -1, 4, atan(4/3)) + + """ + c, r, n, rot = self.args + v = self.vertices[0] + d = v - c + cc = c.reflect(line) + vv = v.reflect(line) + dd = vv - cc + # calculate rotation about the new center + # which will align the vertices + l1 = Ray((0, 0), dd) + l2 = Ray((0, 0), d) + ang = l1.closing_angle(l2) + rot += ang + # change sign of radius as point traversal is reversed + return self.func(cc, -r, n, rot) + + @property + def vertices(self): + """The vertices of the RegularPolygon. + + Returns + ======= + + vertices : list + Each vertex is a Point. + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import RegularPolygon, Point + >>> rp = RegularPolygon(Point(0, 0), 5, 4) + >>> rp.vertices + [Point2D(5, 0), Point2D(0, 5), Point2D(-5, 0), Point2D(0, -5)] + + """ + c = self._center + r = abs(self._radius) + rot = self._rot + v = 2*S.Pi/self._n + + return [Point(c.x + r*cos(k*v + rot), c.y + r*sin(k*v + rot)) + for k in range(self._n)] + + def __eq__(self, o): + if not isinstance(o, Polygon): + return False + elif not isinstance(o, RegularPolygon): + return Polygon.__eq__(o, self) + return self.args == o.args + + def __hash__(self): + return super().__hash__() + + +class Triangle(Polygon): + """ + A polygon with three vertices and three sides. + + Parameters + ========== + + points : sequence of Points + keyword: asa, sas, or sss to specify sides/angles of the triangle + + Attributes + ========== + + vertices + altitudes + orthocenter + circumcenter + circumradius + circumcircle + inradius + incircle + exradii + medians + medial + nine_point_circle + + Raises + ====== + + GeometryError + If the number of vertices is not equal to three, or one of the vertices + is not a Point, or a valid keyword is not given. + + See Also + ======== + + sympy.geometry.point.Point, Polygon + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> Triangle(Point(0, 0), Point(4, 0), Point(4, 3)) + Triangle(Point2D(0, 0), Point2D(4, 0), Point2D(4, 3)) + + Keywords sss, sas, or asa can be used to give the desired + side lengths (in order) and interior angles (in degrees) that + define the triangle: + + >>> Triangle(sss=(3, 4, 5)) + Triangle(Point2D(0, 0), Point2D(3, 0), Point2D(3, 4)) + >>> Triangle(asa=(30, 1, 30)) + Triangle(Point2D(0, 0), Point2D(1, 0), Point2D(1/2, sqrt(3)/6)) + >>> Triangle(sas=(1, 45, 2)) + Triangle(Point2D(0, 0), Point2D(2, 0), Point2D(sqrt(2)/2, sqrt(2)/2)) + + """ + + def __new__(cls, *args, **kwargs): + if len(args) != 3: + if 'sss' in kwargs: + return _sss(*[simplify(a) for a in kwargs['sss']]) + if 'asa' in kwargs: + return _asa(*[simplify(a) for a in kwargs['asa']]) + if 'sas' in kwargs: + return _sas(*[simplify(a) for a in kwargs['sas']]) + msg = "Triangle instantiates with three points or a valid keyword." + raise GeometryError(msg) + + vertices = [Point(a, dim=2, **kwargs) for a in args] + + # remove consecutive duplicates + nodup = [] + for p in vertices: + if nodup and p == nodup[-1]: + continue + nodup.append(p) + if len(nodup) > 1 and nodup[-1] == nodup[0]: + nodup.pop() # last point was same as first + + # remove collinear points + i = -3 + while i < len(nodup) - 3 and len(nodup) > 2: + a, b, c = sorted( + [nodup[i], nodup[i + 1], nodup[i + 2]], key=default_sort_key) + if Point.is_collinear(a, b, c): + nodup[i] = a + nodup[i + 1] = None + nodup.pop(i + 1) + i += 1 + + vertices = list(filter(lambda x: x is not None, nodup)) + + if len(vertices) == 3: + return GeometryEntity.__new__(cls, *vertices, **kwargs) + elif len(vertices) == 2: + return Segment(*vertices, **kwargs) + else: + return Point(*vertices, **kwargs) + + @property + def vertices(self): + """The triangle's vertices + + Returns + ======= + + vertices : tuple + Each element in the tuple is a Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t = Triangle(Point(0, 0), Point(4, 0), Point(4, 3)) + >>> t.vertices + (Point2D(0, 0), Point2D(4, 0), Point2D(4, 3)) + + """ + return self.args + + def is_similar(t1, t2): + """Is another triangle similar to this one. + + Two triangles are similar if one can be uniformly scaled to the other. + + Parameters + ========== + + other: Triangle + + Returns + ======= + + is_similar : boolean + + See Also + ======== + + sympy.geometry.entity.GeometryEntity.is_similar + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3)) + >>> t2 = Triangle(Point(0, 0), Point(-4, 0), Point(-4, -3)) + >>> t1.is_similar(t2) + True + + >>> t2 = Triangle(Point(0, 0), Point(-4, 0), Point(-4, -4)) + >>> t1.is_similar(t2) + False + + """ + if not isinstance(t2, Polygon): + return False + + s1_1, s1_2, s1_3 = [side.length for side in t1.sides] + s2 = [side.length for side in t2.sides] + + def _are_similar(u1, u2, u3, v1, v2, v3): + e1 = simplify(u1/v1) + e2 = simplify(u2/v2) + e3 = simplify(u3/v3) + return bool(e1 == e2) and bool(e2 == e3) + + # There's only 6 permutations, so write them out + return _are_similar(s1_1, s1_2, s1_3, *s2) or \ + _are_similar(s1_1, s1_3, s1_2, *s2) or \ + _are_similar(s1_2, s1_1, s1_3, *s2) or \ + _are_similar(s1_2, s1_3, s1_1, *s2) or \ + _are_similar(s1_3, s1_1, s1_2, *s2) or \ + _are_similar(s1_3, s1_2, s1_1, *s2) + + def is_equilateral(self): + """Are all the sides the same length? + + Returns + ======= + + is_equilateral : boolean + + See Also + ======== + + sympy.geometry.entity.GeometryEntity.is_similar, RegularPolygon + is_isosceles, is_right, is_scalene + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3)) + >>> t1.is_equilateral() + False + + >>> from sympy import sqrt + >>> t2 = Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))) + >>> t2.is_equilateral() + True + + """ + return not has_variety(s.length for s in self.sides) + + def is_isosceles(self): + """Are two or more of the sides the same length? + + Returns + ======= + + is_isosceles : boolean + + See Also + ======== + + is_equilateral, is_right, is_scalene + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(2, 4)) + >>> t1.is_isosceles() + True + + """ + return has_dups(s.length for s in self.sides) + + def is_scalene(self): + """Are all the sides of the triangle of different lengths? + + Returns + ======= + + is_scalene : boolean + + See Also + ======== + + is_equilateral, is_isosceles, is_right + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(1, 4)) + >>> t1.is_scalene() + True + + """ + return not has_dups(s.length for s in self.sides) + + def is_right(self): + """Is the triangle right-angled. + + Returns + ======= + + is_right : boolean + + See Also + ======== + + sympy.geometry.line.LinearEntity.is_perpendicular + is_equilateral, is_isosceles, is_scalene + + Examples + ======== + + >>> from sympy import Triangle, Point + >>> t1 = Triangle(Point(0, 0), Point(4, 0), Point(4, 3)) + >>> t1.is_right() + True + + """ + s = self.sides + return Segment.is_perpendicular(s[0], s[1]) or \ + Segment.is_perpendicular(s[1], s[2]) or \ + Segment.is_perpendicular(s[0], s[2]) + + @property + def altitudes(self): + """The altitudes of the triangle. + + An altitude of a triangle is a segment through a vertex, + perpendicular to the opposite side, with length being the + height of the vertex measured from the line containing the side. + + Returns + ======= + + altitudes : dict + The dictionary consists of keys which are vertices and values + which are Segments. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment.length + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.altitudes[p1] + Segment2D(Point2D(0, 0), Point2D(1/2, 1/2)) + + """ + s = self.sides + v = self.vertices + return {v[0]: s[1].perpendicular_segment(v[0]), + v[1]: s[2].perpendicular_segment(v[1]), + v[2]: s[0].perpendicular_segment(v[2])} + + @property + def orthocenter(self): + """The orthocenter of the triangle. + + The orthocenter is the intersection of the altitudes of a triangle. + It may lie inside, outside or on the triangle. + + Returns + ======= + + orthocenter : Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.orthocenter + Point2D(0, 0) + + """ + a = self.altitudes + v = self.vertices + return Line(a[v[0]]).intersection(Line(a[v[1]]))[0] + + @property + def circumcenter(self): + """The circumcenter of the triangle + + The circumcenter is the center of the circumcircle. + + Returns + ======= + + circumcenter : Point + + See Also + ======== + + sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.circumcenter + Point2D(1/2, 1/2) + """ + a, b, c = [x.perpendicular_bisector() for x in self.sides] + return a.intersection(b)[0] + + @property + def circumradius(self): + """The radius of the circumcircle of the triangle. + + Returns + ======= + + circumradius : number of Basic instance + + See Also + ======== + + sympy.geometry.ellipse.Circle.radius + + Examples + ======== + + >>> from sympy import Symbol + >>> from sympy import Point, Triangle + >>> a = Symbol('a') + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, a) + >>> t = Triangle(p1, p2, p3) + >>> t.circumradius + sqrt(a**2/4 + 1/4) + """ + return Point.distance(self.circumcenter, self.vertices[0]) + + @property + def circumcircle(self): + """The circle which passes through the three vertices of the triangle. + + Returns + ======= + + circumcircle : Circle + + See Also + ======== + + sympy.geometry.ellipse.Circle + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.circumcircle + Circle(Point2D(1/2, 1/2), sqrt(2)/2) + + """ + return Circle(self.circumcenter, self.circumradius) + + def bisectors(self): + """The angle bisectors of the triangle. + + An angle bisector of a triangle is a straight line through a vertex + which cuts the corresponding angle in half. + + Returns + ======= + + bisectors : dict + Each key is a vertex (Point) and each value is the corresponding + bisector (Segment). + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment + + Examples + ======== + + >>> from sympy import Point, Triangle, Segment + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> from sympy import sqrt + >>> t.bisectors()[p2] == Segment(Point(1, 0), Point(0, sqrt(2) - 1)) + True + + """ + # use lines containing sides so containment check during + # intersection calculation can be avoided, thus reducing + # the processing time for calculating the bisectors + s = [Line(l) for l in self.sides] + v = self.vertices + c = self.incenter + l1 = Segment(v[0], Line(v[0], c).intersection(s[1])[0]) + l2 = Segment(v[1], Line(v[1], c).intersection(s[2])[0]) + l3 = Segment(v[2], Line(v[2], c).intersection(s[0])[0]) + return {v[0]: l1, v[1]: l2, v[2]: l3} + + @property + def incenter(self): + """The center of the incircle. + + The incircle is the circle which lies inside the triangle and touches + all three sides. + + Returns + ======= + + incenter : Point + + See Also + ======== + + incircle, sympy.geometry.point.Point + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.incenter + Point2D(1 - sqrt(2)/2, 1 - sqrt(2)/2) + + """ + s = self.sides + l = Matrix([s[i].length for i in [1, 2, 0]]) + p = sum(l) + v = self.vertices + x = simplify(l.dot(Matrix([vi.x for vi in v]))/p) + y = simplify(l.dot(Matrix([vi.y for vi in v]))/p) + return Point(x, y) + + @property + def inradius(self): + """The radius of the incircle. + + Returns + ======= + + inradius : number of Basic instance + + See Also + ======== + + incircle, sympy.geometry.ellipse.Circle.radius + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(4, 0), Point(0, 3) + >>> t = Triangle(p1, p2, p3) + >>> t.inradius + 1 + + """ + return simplify(2 * self.area / self.perimeter) + + @property + def incircle(self): + """The incircle of the triangle. + + The incircle is the circle which lies inside the triangle and touches + all three sides. + + Returns + ======= + + incircle : Circle + + See Also + ======== + + sympy.geometry.ellipse.Circle + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(2, 0), Point(0, 2) + >>> t = Triangle(p1, p2, p3) + >>> t.incircle + Circle(Point2D(2 - sqrt(2), 2 - sqrt(2)), 2 - sqrt(2)) + + """ + return Circle(self.incenter, self.inradius) + + @property + def exradii(self): + """The radius of excircles of a triangle. + + An excircle of the triangle is a circle lying outside the triangle, + tangent to one of its sides and tangent to the extensions of the + other two. + + Returns + ======= + + exradii : dict + + See Also + ======== + + sympy.geometry.polygon.Triangle.inradius + + Examples + ======== + + The exradius touches the side of the triangle to which it is keyed, e.g. + the exradius touching side 2 is: + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(6, 0), Point(0, 2) + >>> t = Triangle(p1, p2, p3) + >>> t.exradii[t.sides[2]] + -2 + sqrt(10) + + References + ========== + + .. [1] https://mathworld.wolfram.com/Exradius.html + .. [2] https://mathworld.wolfram.com/Excircles.html + + """ + + side = self.sides + a = side[0].length + b = side[1].length + c = side[2].length + s = (a+b+c)/2 + area = self.area + exradii = {self.sides[0]: simplify(area/(s-a)), + self.sides[1]: simplify(area/(s-b)), + self.sides[2]: simplify(area/(s-c))} + + return exradii + + @property + def excenters(self): + """Excenters of the triangle. + + An excenter is the center of a circle that is tangent to a side of the + triangle and the extensions of the other two sides. + + Returns + ======= + + excenters : dict + + + Examples + ======== + + The excenters are keyed to the side of the triangle to which their corresponding + excircle is tangent: The center is keyed, e.g. the excenter of a circle touching + side 0 is: + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(6, 0), Point(0, 2) + >>> t = Triangle(p1, p2, p3) + >>> t.excenters[t.sides[0]] + Point2D(12*sqrt(10), 2/3 + sqrt(10)/3) + + See Also + ======== + + sympy.geometry.polygon.Triangle.exradii + + References + ========== + + .. [1] https://mathworld.wolfram.com/Excircles.html + + """ + + s = self.sides + v = self.vertices + a = s[0].length + b = s[1].length + c = s[2].length + x = [v[0].x, v[1].x, v[2].x] + y = [v[0].y, v[1].y, v[2].y] + + exc_coords = { + "x1": simplify(-a*x[0]+b*x[1]+c*x[2]/(-a+b+c)), + "x2": simplify(a*x[0]-b*x[1]+c*x[2]/(a-b+c)), + "x3": simplify(a*x[0]+b*x[1]-c*x[2]/(a+b-c)), + "y1": simplify(-a*y[0]+b*y[1]+c*y[2]/(-a+b+c)), + "y2": simplify(a*y[0]-b*y[1]+c*y[2]/(a-b+c)), + "y3": simplify(a*y[0]+b*y[1]-c*y[2]/(a+b-c)) + } + + excenters = { + s[0]: Point(exc_coords["x1"], exc_coords["y1"]), + s[1]: Point(exc_coords["x2"], exc_coords["y2"]), + s[2]: Point(exc_coords["x3"], exc_coords["y3"]) + } + + return excenters + + @property + def medians(self): + """The medians of the triangle. + + A median of a triangle is a straight line through a vertex and the + midpoint of the opposite side, and divides the triangle into two + equal areas. + + Returns + ======= + + medians : dict + Each key is a vertex (Point) and each value is the median (Segment) + at that point. + + See Also + ======== + + sympy.geometry.point.Point.midpoint, sympy.geometry.line.Segment.midpoint + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.medians[p1] + Segment2D(Point2D(0, 0), Point2D(1/2, 1/2)) + + """ + s = self.sides + v = self.vertices + return {v[0]: Segment(v[0], s[1].midpoint), + v[1]: Segment(v[1], s[2].midpoint), + v[2]: Segment(v[2], s[0].midpoint)} + + @property + def medial(self): + """The medial triangle of the triangle. + + The triangle which is formed from the midpoints of the three sides. + + Returns + ======= + + medial : Triangle + + See Also + ======== + + sympy.geometry.line.Segment.midpoint + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.medial + Triangle(Point2D(1/2, 0), Point2D(1/2, 1/2), Point2D(0, 1/2)) + + """ + s = self.sides + return Triangle(s[0].midpoint, s[1].midpoint, s[2].midpoint) + + @property + def nine_point_circle(self): + """The nine-point circle of the triangle. + + Nine-point circle is the circumcircle of the medial triangle, which + passes through the feet of altitudes and the middle points of segments + connecting the vertices and the orthocenter. + + Returns + ======= + + nine_point_circle : Circle + + See also + ======== + + sympy.geometry.line.Segment.midpoint + sympy.geometry.polygon.Triangle.medial + sympy.geometry.polygon.Triangle.orthocenter + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.nine_point_circle + Circle(Point2D(1/4, 1/4), sqrt(2)/4) + + """ + return Circle(*self.medial.vertices) + + @property + def eulerline(self): + """The Euler line of the triangle. + + The line which passes through circumcenter, centroid and orthocenter. + + Returns + ======= + + eulerline : Line (or Point for equilateral triangles in which case all + centers coincide) + + Examples + ======== + + >>> from sympy import Point, Triangle + >>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + >>> t = Triangle(p1, p2, p3) + >>> t.eulerline + Line2D(Point2D(0, 0), Point2D(1/2, 1/2)) + + """ + if self.is_equilateral(): + return self.orthocenter + return Line(self.orthocenter, self.circumcenter) + +def rad(d): + """Return the radian value for the given degrees (pi = 180 degrees).""" + return d*pi/180 + + +def deg(r): + """Return the degree value for the given radians (pi = 180 degrees).""" + return r/pi*180 + + +def _slope(d): + rv = tan(rad(d)) + return rv + + +def _asa(d1, l, d2): + """Return triangle having side with length l on the x-axis.""" + xy = Line((0, 0), slope=_slope(d1)).intersection( + Line((l, 0), slope=_slope(180 - d2)))[0] + return Triangle((0, 0), (l, 0), xy) + + +def _sss(l1, l2, l3): + """Return triangle having side of length l1 on the x-axis.""" + c1 = Circle((0, 0), l3) + c2 = Circle((l1, 0), l2) + inter = [a for a in c1.intersection(c2) if a.y.is_nonnegative] + if not inter: + return None + pt = inter[0] + return Triangle((0, 0), (l1, 0), pt) + + +def _sas(l1, d, l2): + """Return triangle having side with length l2 on the x-axis.""" + p1 = Point(0, 0) + p2 = Point(l2, 0) + p3 = Point(cos(rad(d))*l1, sin(rad(d))*l1) + return Triangle(p1, p2, p3) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/__init__.py b/lib/python3.11/site-packages/sympy/geometry/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/geometry/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 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sympy.core.containers import Tuple +from sympy.core.numbers import (Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.hyperbolic import asinh +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon +from sympy.testing.pytest import raises, slow + + +def test_curve(): + x = Symbol('x', real=True) + s = Symbol('s') + z = Symbol('z') + + # this curve is independent of the indicated parameter + c = Curve([2*s, s**2], (z, 0, 2)) + + assert c.parameter == z + assert c.functions == (2*s, s**2) + assert c.arbitrary_point() == Point(2*s, s**2) + assert c.arbitrary_point(z) == Point(2*s, s**2) + + # this is how it is normally used + c = Curve([2*s, s**2], (s, 0, 2)) + + assert c.parameter == s + assert c.functions == (2*s, s**2) + t = Symbol('t') + # the t returned as assumptions + assert c.arbitrary_point() != Point(2*t, t**2) + t = Symbol('t', real=True) + # now t has the same assumptions so the test passes + assert c.arbitrary_point() == Point(2*t, t**2) + assert c.arbitrary_point(z) == Point(2*z, z**2) + assert c.arbitrary_point(c.parameter) == Point(2*s, s**2) + assert c.arbitrary_point(None) == Point(2*s, s**2) + assert c.plot_interval() == [t, 0, 2] + assert c.plot_interval(z) == [z, 0, 2] + + assert Curve([x, x], (x, 0, 1)).rotate(pi/2) == Curve([-x, x], (x, 0, 1)) + assert Curve([x, x], (x, 0, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate( + 1, 3).arbitrary_point(s) == \ + Line((0, 0), (1, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate( + 1, 3).arbitrary_point(s) == \ + Point(-2*s + 7, 3*s + 6) + + raises(ValueError, lambda: Curve((s), (s, 1, 2))) + raises(ValueError, lambda: Curve((x, x * 2), (1, x))) + + raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point()) + raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s)) + + +@slow +def test_free_symbols(): + a, b, c, d, e, f, s = symbols('a:f,s') + assert Point(a, b).free_symbols == {a, b} + assert Line((a, b), (c, d)).free_symbols == {a, b, c, d} + assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d} + assert Ray((a, b), angle=c).free_symbols == {a, b, c} + assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d} + assert Line((a, b), slope=c).free_symbols == {a, b, c} + assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d} + assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d} + assert Ellipse((a, b), c, eccentricity=d).free_symbols == \ + {a, b, c, d} + assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \ + {a, b, c, d} + assert Circle((a, b), c).free_symbols == {a, b, c} + assert Circle((a, b), (c, d), (e, f)).free_symbols == \ + {e, d, c, b, f, a} + assert Polygon((a, b), (c, d), (e, f)).free_symbols == \ + {e, b, d, f, a, c} + assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d} + + +def test_transform(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + c = Curve((x, x**2), (x, 0, 1)) + cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1)) + pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)] + pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)] + + assert c.scale(2, 3, (4, 5)) == cout + assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts + assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out + assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \ + Curve((x + S.Half, 3*x), (x, 0, 1)) + assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \ + Curve((x + 4, 3*x + 5), (x, 0, 1)) + + +def test_length(): + t = Symbol('t', real=True) + + c1 = Curve((t, 0), (t, 0, 1)) + assert c1.length == 1 + + c2 = Curve((t, t), (t, 0, 1)) + assert c2.length == sqrt(2) + + c3 = Curve((t ** 2, t), (t, 2, 5)) + assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2 + + +def test_parameter_value(): + t = Symbol('t') + C = Curve([2*t, t**2], (t, 0, 2)) + assert C.parameter_value((2, 1), t) == {t: 1} + raises(ValueError, lambda: C.parameter_value((2, 0), t)) + + +def test_issue_17997(): + t, s = symbols('t s') + c = Curve((t, t**2), (t, 0, 10)) + p = Curve([2*s, s**2], (s, 0, 2)) + assert c(2) == Point(2, 4) + assert p(1) == Point(2, 1) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_ellipse.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_ellipse.py new file mode 100644 index 0000000000000000000000000000000000000000..a79eba8c35771bda9f0980aca68d937f8e625c0a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_ellipse.py @@ -0,0 +1,613 @@ +from sympy.core import expand +from sympy.core.numbers import (Rational, oo, pi) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import sec +from sympy.geometry.line import Segment2D +from sympy.geometry.point import Point2D +from sympy.geometry import (Circle, Ellipse, GeometryError, Line, Point, + Polygon, Ray, RegularPolygon, Segment, + Triangle, intersection) +from sympy.testing.pytest import raises, slow +from sympy.integrals.integrals import integrate +from sympy.functions.special.elliptic_integrals import elliptic_e +from sympy.functions.elementary.miscellaneous import Max + + +def test_ellipse_equation_using_slope(): + from sympy.abc import x, y + + e1 = Ellipse(Point(1, 0), 3, 2) + assert str(e1.equation(_slope=1)) == str((-x + y + 1)**2/8 + (x + y - 1)**2/18 - 1) + + e2 = Ellipse(Point(0, 0), 4, 1) + assert str(e2.equation(_slope=1)) == str((-x + y)**2/2 + (x + y)**2/32 - 1) + + e3 = Ellipse(Point(1, 5), 6, 2) + assert str(e3.equation(_slope=2)) == str((-2*x + y - 3)**2/20 + (x + 2*y - 11)**2/180 - 1) + + +def test_object_from_equation(): + from sympy.abc import x, y, a, b, c, d, e + assert Circle(x**2 + y**2 + 3*x + 4*y - 8) == Circle(Point2D(S(-3) / 2, -2), sqrt(57) / 2) + assert Circle(x**2 + y**2 + 6*x + 8*y + 25) == Circle(Point2D(-3, -4), 0) + assert Circle(a**2 + b**2 + 6*a + 8*b + 25, x='a', y='b') == Circle(Point2D(-3, -4), 0) + assert Circle(x**2 + y**2 - 25) == Circle(Point2D(0, 0), 5) + assert Circle(x**2 + y**2) == Circle(Point2D(0, 0), 0) + assert Circle(a**2 + b**2, x='a', y='b') == Circle(Point2D(0, 0), 0) + assert Circle(x**2 + y**2 + 6*x + 8) == Circle(Point2D(-3, 0), 1) + assert Circle(x**2 + y**2 + 6*y + 8) == Circle(Point2D(0, -3), 1) + assert Circle((x - 1)**2 + y**2 - 9) == Circle(Point2D(1, 0), 3) + assert Circle(6*(x**2) + 6*(y**2) + 6*x + 8*y - 25) == Circle(Point2D(Rational(-1, 2), Rational(-2, 3)), 5*sqrt(7)/6) + assert Circle(Eq(a**2 + b**2, 25), x='a', y=b) == Circle(Point2D(0, 0), 5) + raises(GeometryError, lambda: Circle(x**2 + y**2 + 3*x + 4*y + 26)) + raises(GeometryError, lambda: Circle(x**2 + y**2 + 25)) + raises(GeometryError, lambda: Circle(a**2 + b**2 + 25, x='a', y='b')) + raises(GeometryError, lambda: Circle(x**2 + 6*y + 8)) + raises(GeometryError, lambda: Circle(6*(x ** 2) + 4*(y**2) + 6*x + 8*y + 25)) + raises(ValueError, lambda: Circle(a**2 + b**2 + 3*a + 4*b - 8)) + # .equation() adds 'real=True' assumption; '==' would fail if assumptions differed + x, y = symbols('x y', real=True) + eq = a*x**2 + a*y**2 + c*x + d*y + e + assert expand(Circle(eq).equation()*a) == eq + + +@slow +def test_ellipse_geom(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + t = Symbol('t', real=True) + y1 = Symbol('y1', real=True) + half = S.Half + p1 = Point(0, 0) + p2 = Point(1, 1) + p4 = Point(0, 1) + + e1 = Ellipse(p1, 1, 1) + e2 = Ellipse(p2, half, 1) + e3 = Ellipse(p1, y1, y1) + c1 = Circle(p1, 1) + c2 = Circle(p2, 1) + c3 = Circle(Point(sqrt(2), sqrt(2)), 1) + l1 = Line(p1, p2) + + # Test creation with three points + cen, rad = Point(3*half, 2), 5*half + assert Circle(Point(0, 0), Point(3, 0), Point(0, 4)) == Circle(cen, rad) + assert Circle(Point(0, 0), Point(1, 1), Point(2, 2)) == Segment2D(Point2D(0, 0), Point2D(2, 2)) + + raises(ValueError, lambda: Ellipse(None, None, None, 1)) + raises(ValueError, lambda: Ellipse()) + raises(GeometryError, lambda: Circle(Point(0, 0))) + raises(GeometryError, lambda: Circle(Symbol('x')*Symbol('y'))) + + # Basic Stuff + assert Ellipse(None, 1, 1).center == Point(0, 0) + assert e1 == c1 + assert e1 != e2 + assert e1 != l1 + assert p4 in e1 + assert e1 in e1 + assert e2 in e2 + assert 1 not in e2 + assert p2 not in e2 + assert e1.area == pi + assert e2.area == pi/2 + assert e3.area == pi*y1*abs(y1) + assert c1.area == e1.area + assert c1.circumference == e1.circumference + assert e3.circumference == 2*pi*y1 + assert e1.plot_interval() == e2.plot_interval() == [t, -pi, pi] + assert e1.plot_interval(x) == e2.plot_interval(x) == [x, -pi, pi] + + assert c1.minor == 1 + assert c1.major == 1 + assert c1.hradius == 1 + assert c1.vradius == 1 + + assert Ellipse((1, 1), 0, 0) == Point(1, 1) + assert Ellipse((1, 1), 1, 0) == Segment(Point(0, 1), Point(2, 1)) + assert Ellipse((1, 1), 0, 1) == Segment(Point(1, 0), Point(1, 2)) + + # Private Functions + assert hash(c1) == hash(Circle(Point(1, 0), Point(0, 1), Point(0, -1))) + assert c1 in e1 + assert (Line(p1, p2) in e1) is False + assert e1.__cmp__(e1) == 0 + assert e1.__cmp__(Point(0, 0)) > 0 + + # Encloses + assert e1.encloses(Segment(Point(-0.5, -0.5), Point(0.5, 0.5))) is True + assert e1.encloses(Line(p1, p2)) is False + assert e1.encloses(Ray(p1, p2)) is False + assert e1.encloses(e1) is False + assert e1.encloses( + Polygon(Point(-0.5, -0.5), Point(-0.5, 0.5), Point(0.5, 0.5))) is True + assert e1.encloses(RegularPolygon(p1, 0.5, 3)) is True + assert e1.encloses(RegularPolygon(p1, 5, 3)) is False + assert e1.encloses(RegularPolygon(p2, 5, 3)) is False + + assert e2.arbitrary_point() in e2 + raises(ValueError, lambda: Ellipse(Point(x, y), 1, 1).arbitrary_point(parameter='x')) + + # Foci + f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0) + ef = Ellipse(Point(0, 0), 4, 2) + assert ef.foci in [(f1, f2), (f2, f1)] + + # Tangents + v = sqrt(2) / 2 + p1_1 = Point(v, v) + p1_2 = p2 + Point(half, 0) + p1_3 = p2 + Point(0, 1) + assert e1.tangent_lines(p4) == c1.tangent_lines(p4) + assert e2.tangent_lines(p1_2) == [Line(Point(Rational(3, 2), 1), Point(Rational(3, 2), S.Half))] + assert e2.tangent_lines(p1_3) == [Line(Point(1, 2), Point(Rational(5, 4), 2))] + assert c1.tangent_lines(p1_1) != [Line(p1_1, Point(0, sqrt(2)))] + assert c1.tangent_lines(p1) == [] + assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1))) + assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1))) + assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2)))) + assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) is False + assert c1.is_tangent(e1) is True + assert c1.is_tangent(Ellipse(Point(2, 0), 1, 1)) is True + assert c1.is_tangent( + Polygon(Point(1, 1), Point(1, -1), Point(2, 0))) is False + assert c1.is_tangent( + Polygon(Point(1, 1), Point(1, 0), Point(2, 0))) is False + assert Circle(Point(5, 5), 3).is_tangent(Circle(Point(0, 5), 1)) is False + + assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == \ + [Line(Point(0, 0), Point(Rational(77, 25), Rational(132, 25))), + Line(Point(0, 0), Point(Rational(33, 5), Rational(22, 5)))] + assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(3, 4)) == \ + [Line(Point(3, 4), Point(4, 4)), Line(Point(3, 4), Point(3, 5))] + assert Circle(Point(5, 5), 2).tangent_lines(Point(3, 3)) == \ + [Line(Point(3, 3), Point(4, 3)), Line(Point(3, 3), Point(3, 4))] + assert Circle(Point(5, 5), 2).tangent_lines(Point(5 - 2*sqrt(2), 5)) == \ + [Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 - sqrt(2))), + Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 + sqrt(2))), ] + assert Circle(Point(5, 5), 5).tangent_lines(Point(4, 0)) == \ + [Line(Point(4, 0), Point(Rational(40, 13), Rational(5, 13))), + Line(Point(4, 0), Point(5, 0))] + assert Circle(Point(5, 5), 5).tangent_lines(Point(0, 6)) == \ + [Line(Point(0, 6), Point(0, 7)), + Line(Point(0, 6), Point(Rational(5, 13), Rational(90, 13)))] + + # for numerical calculations, we shouldn't demand exact equality, + # so only test up to the desired precision + def lines_close(l1, l2, prec): + """ tests whether l1 and 12 are within 10**(-prec) + of each other """ + return abs(l1.p1 - l2.p1) < 10**(-prec) and abs(l1.p2 - l2.p2) < 10**(-prec) + def line_list_close(ll1, ll2, prec): + return all(lines_close(l1, l2, prec) for l1, l2 in zip(ll1, ll2)) + + e = Ellipse(Point(0, 0), 2, 1) + assert e.normal_lines(Point(0, 0)) == \ + [Line(Point(0, 0), Point(0, 1)), Line(Point(0, 0), Point(1, 0))] + assert e.normal_lines(Point(1, 0)) == \ + [Line(Point(0, 0), Point(1, 0))] + assert e.normal_lines((0, 1)) == \ + [Line(Point(0, 0), Point(0, 1))] + assert line_list_close(e.normal_lines(Point(1, 1), 2), [ + Line(Point(Rational(-51, 26), Rational(-1, 5)), Point(Rational(-25, 26), Rational(17, 83))), + Line(Point(Rational(28, 29), Rational(-7, 8)), Point(Rational(57, 29), Rational(-9, 2)))], 2) + # test the failure of Poly.intervals and checks a point on the boundary + p = Point(sqrt(3), S.Half) + assert p in e + assert line_list_close(e.normal_lines(p, 2), [ + Line(Point(Rational(-341, 171), Rational(-1, 13)), Point(Rational(-170, 171), Rational(5, 64))), + Line(Point(Rational(26, 15), Rational(-1, 2)), Point(Rational(41, 15), Rational(-43, 26)))], 2) + # be sure to use the slope that isn't undefined on boundary + e = Ellipse((0, 0), 2, 2*sqrt(3)/3) + assert line_list_close(e.normal_lines((1, 1), 2), [ + Line(Point(Rational(-64, 33), Rational(-20, 71)), Point(Rational(-31, 33), Rational(2, 13))), + Line(Point(1, -1), Point(2, -4))], 2) + # general ellipse fails except under certain conditions + e = Ellipse((0, 0), x, 1) + assert e.normal_lines((x + 1, 0)) == [Line(Point(0, 0), Point(1, 0))] + raises(NotImplementedError, lambda: e.normal_lines((x + 1, 1))) + # Properties + major = 3 + minor = 1 + e4 = Ellipse(p2, minor, major) + assert e4.focus_distance == sqrt(major**2 - minor**2) + ecc = e4.focus_distance / major + assert e4.eccentricity == ecc + assert e4.periapsis == major*(1 - ecc) + assert e4.apoapsis == major*(1 + ecc) + assert e4.semilatus_rectum == major*(1 - ecc ** 2) + # independent of orientation + e4 = Ellipse(p2, major, minor) + assert e4.focus_distance == sqrt(major**2 - minor**2) + ecc = e4.focus_distance / major + assert e4.eccentricity == ecc + assert e4.periapsis == major*(1 - ecc) + assert e4.apoapsis == major*(1 + ecc) + + # Intersection + l1 = Line(Point(1, -5), Point(1, 5)) + l2 = Line(Point(-5, -1), Point(5, -1)) + l3 = Line(Point(-1, -1), Point(1, 1)) + l4 = Line(Point(-10, 0), Point(0, 10)) + pts_c1_l3 = [Point(sqrt(2)/2, sqrt(2)/2), Point(-sqrt(2)/2, -sqrt(2)/2)] + + assert intersection(e2, l4) == [] + assert intersection(c1, Point(1, 0)) == [Point(1, 0)] + assert intersection(c1, l1) == [Point(1, 0)] + assert intersection(c1, l2) == [Point(0, -1)] + assert intersection(c1, l3) in [pts_c1_l3, [pts_c1_l3[1], pts_c1_l3[0]]] + assert intersection(c1, c2) == [Point(0, 1), Point(1, 0)] + assert intersection(c1, c3) == [Point(sqrt(2)/2, sqrt(2)/2)] + assert e1.intersection(l1) == [Point(1, 0)] + assert e2.intersection(l4) == [] + assert e1.intersection(Circle(Point(0, 2), 1)) == [Point(0, 1)] + assert e1.intersection(Circle(Point(5, 0), 1)) == [] + assert e1.intersection(Ellipse(Point(2, 0), 1, 1)) == [Point(1, 0)] + assert e1.intersection(Ellipse(Point(5, 0), 1, 1)) == [] + assert e1.intersection(Point(2, 0)) == [] + assert e1.intersection(e1) == e1 + assert intersection(Ellipse(Point(0, 0), 2, 1), Ellipse(Point(3, 0), 1, 2)) == [Point(2, 0)] + assert intersection(Circle(Point(0, 0), 2), Circle(Point(3, 0), 1)) == [Point(2, 0)] + assert intersection(Circle(Point(0, 0), 2), Circle(Point(7, 0), 1)) == [] + assert intersection(Ellipse(Point(0, 0), 5, 17), Ellipse(Point(4, 0), 1, 0.2) + ) == [Point(5.0, 0, evaluate=False)] + assert intersection(Ellipse(Point(0, 0), 5, 17), Ellipse(Point(4, 0), 0.999, 0.2)) == [] + assert Circle((0, 0), S.Half).intersection( + Triangle((-1, 0), (1, 0), (0, 1))) == [ + Point(Rational(-1, 2), 0), Point(S.Half, 0)] + raises(TypeError, lambda: intersection(e2, Line((0, 0, 0), (0, 0, 1)))) + raises(TypeError, lambda: intersection(e2, Rational(12))) + raises(TypeError, lambda: Ellipse.intersection(e2, 1)) + # some special case intersections + csmall = Circle(p1, 3) + cbig = Circle(p1, 5) + cout = Circle(Point(5, 5), 1) + # one circle inside of another + assert csmall.intersection(cbig) == [] + # separate circles + assert csmall.intersection(cout) == [] + # coincident circles + assert csmall.intersection(csmall) == csmall + + v = sqrt(2) + t1 = Triangle(Point(0, v), Point(0, -v), Point(v, 0)) + points = intersection(t1, c1) + assert len(points) == 4 + assert Point(0, 1) in points + assert Point(0, -1) in points + assert Point(v/2, v/2) in points + assert Point(v/2, -v/2) in points + + circ = Circle(Point(0, 0), 5) + elip = Ellipse(Point(0, 0), 5, 20) + assert intersection(circ, elip) in \ + [[Point(5, 0), Point(-5, 0)], [Point(-5, 0), Point(5, 0)]] + assert elip.tangent_lines(Point(0, 0)) == [] + elip = Ellipse(Point(0, 0), 3, 2) + assert elip.tangent_lines(Point(3, 0)) == \ + [Line(Point(3, 0), Point(3, -12))] + + e1 = Ellipse(Point(0, 0), 5, 10) + e2 = Ellipse(Point(2, 1), 4, 8) + a = Rational(53, 17) + c = 2*sqrt(3991)/17 + ans = [Point(a - c/8, a/2 + c), Point(a + c/8, a/2 - c)] + assert e1.intersection(e2) == ans + e2 = Ellipse(Point(x, y), 4, 8) + c = sqrt(3991) + ans = [Point(-c/68 + a, c*Rational(2, 17) + a/2), Point(c/68 + a, c*Rational(-2, 17) + a/2)] + assert [p.subs({x: 2, y:1}) for p in e1.intersection(e2)] == ans + + # Combinations of above + assert e3.is_tangent(e3.tangent_lines(p1 + Point(y1, 0))[0]) + + e = Ellipse((1, 2), 3, 2) + assert e.tangent_lines(Point(10, 0)) == \ + [Line(Point(10, 0), Point(1, 0)), + Line(Point(10, 0), Point(Rational(14, 5), Rational(18, 5)))] + + # encloses_point + e = Ellipse((0, 0), 1, 2) + assert e.encloses_point(e.center) + assert e.encloses_point(e.center + Point(0, e.vradius - Rational(1, 10))) + assert e.encloses_point(e.center + Point(e.hradius - Rational(1, 10), 0)) + assert e.encloses_point(e.center + Point(e.hradius, 0)) is False + assert e.encloses_point( + e.center + Point(e.hradius + Rational(1, 10), 0)) is False + e = Ellipse((0, 0), 2, 1) + assert e.encloses_point(e.center) + assert e.encloses_point(e.center + Point(0, e.vradius - Rational(1, 10))) + assert e.encloses_point(e.center + Point(e.hradius - Rational(1, 10), 0)) + assert e.encloses_point(e.center + Point(e.hradius, 0)) is False + assert e.encloses_point( + e.center + Point(e.hradius + Rational(1, 10), 0)) is False + assert c1.encloses_point(Point(1, 0)) is False + assert c1.encloses_point(Point(0.3, 0.4)) is True + + assert e.scale(2, 3) == Ellipse((0, 0), 4, 3) + assert e.scale(3, 6) == Ellipse((0, 0), 6, 6) + assert e.rotate(pi) == e + assert e.rotate(pi, (1, 2)) == Ellipse(Point(2, 4), 2, 1) + raises(NotImplementedError, lambda: e.rotate(pi/3)) + + # Circle rotation tests (Issue #11743) + # Link - https://github.com/sympy/sympy/issues/11743 + cir = Circle(Point(1, 0), 1) + assert cir.rotate(pi/2) == Circle(Point(0, 1), 1) + assert cir.rotate(pi/3) == Circle(Point(S.Half, sqrt(3)/2), 1) + assert cir.rotate(pi/3, Point(1, 0)) == Circle(Point(1, 0), 1) + assert cir.rotate(pi/3, Point(0, 1)) == Circle(Point(S.Half + sqrt(3)/2, S.Half + sqrt(3)/2), 1) + + +def test_construction(): + e1 = Ellipse(hradius=2, vradius=1, eccentricity=None) + assert e1.eccentricity == sqrt(3)/2 + + e2 = Ellipse(hradius=2, vradius=None, eccentricity=sqrt(3)/2) + assert e2.vradius == 1 + + e3 = Ellipse(hradius=None, vradius=1, eccentricity=sqrt(3)/2) + assert e3.hradius == 2 + + # filter(None, iterator) filters out anything falsey, including 0 + # eccentricity would be filtered out in this case and the constructor would throw an error + e4 = Ellipse(Point(0, 0), hradius=1, eccentricity=0) + assert e4.vradius == 1 + + #tests for eccentricity > 1 + raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = S(3)/2)) + raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity=sec(5))) + raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity=S.Pi-S(2))) + + #tests for eccentricity = 1 + #if vradius is not defined + assert Ellipse(None, 1, None, 1).length == 2 + #if hradius is not defined + raises(GeometryError, lambda: Ellipse(None, None, 1, eccentricity = 1)) + + #tests for eccentricity < 0 + raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = -3)) + raises(GeometryError, lambda: Ellipse(Point(3, 1), hradius=3, eccentricity = -0.5)) + +def test_ellipse_random_point(): + y1 = Symbol('y1', real=True) + e3 = Ellipse(Point(0, 0), y1, y1) + rx, ry = Symbol('rx'), Symbol('ry') + for ind in range(0, 5): + r = e3.random_point() + # substitution should give zero*y1**2 + assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0) + # test for the case with seed + r = e3.random_point(seed=1) + assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0) + + +def test_repr(): + assert repr(Circle((0, 1), 2)) == 'Circle(Point2D(0, 1), 2)' + + +def test_transform(): + c = Circle((1, 1), 2) + assert c.scale(-1) == Circle((-1, 1), 2) + assert c.scale(y=-1) == Circle((1, -1), 2) + assert c.scale(2) == Ellipse((2, 1), 4, 2) + + assert Ellipse((0, 0), 2, 3).scale(2, 3, (4, 5)) == \ + Ellipse(Point(-4, -10), 4, 9) + assert Circle((0, 0), 2).scale(2, 3, (4, 5)) == \ + Ellipse(Point(-4, -10), 4, 6) + assert Ellipse((0, 0), 2, 3).scale(3, 3, (4, 5)) == \ + Ellipse(Point(-8, -10), 6, 9) + assert Circle((0, 0), 2).scale(3, 3, (4, 5)) == \ + Circle(Point(-8, -10), 6) + assert Circle(Point(-8, -10), 6).scale(Rational(1, 3), Rational(1, 3), (4, 5)) == \ + Circle((0, 0), 2) + assert Circle((0, 0), 2).translate(4, 5) == \ + Circle((4, 5), 2) + assert Circle((0, 0), 2).scale(3, 3) == \ + Circle((0, 0), 6) + + +def test_bounds(): + e1 = Ellipse(Point(0, 0), 3, 5) + e2 = Ellipse(Point(2, -2), 7, 7) + c1 = Circle(Point(2, -2), 7) + c2 = Circle(Point(-2, 0), Point(0, 2), Point(2, 0)) + assert e1.bounds == (-3, -5, 3, 5) + assert e2.bounds == (-5, -9, 9, 5) + assert c1.bounds == (-5, -9, 9, 5) + assert c2.bounds == (-2, -2, 2, 2) + + +def test_reflect(): + b = Symbol('b') + m = Symbol('m') + l = Line((0, b), slope=m) + t1 = Triangle((0, 0), (1, 0), (2, 3)) + assert t1.area == -t1.reflect(l).area + e = Ellipse((1, 0), 1, 2) + assert e.area == -e.reflect(Line((1, 0), slope=0)).area + assert e.area == -e.reflect(Line((1, 0), slope=oo)).area + raises(NotImplementedError, lambda: e.reflect(Line((1, 0), slope=m))) + assert Circle((0, 1), 1).reflect(Line((0, 0), (1, 1))) == Circle(Point2D(1, 0), -1) + + +def test_is_tangent(): + e1 = Ellipse(Point(0, 0), 3, 5) + c1 = Circle(Point(2, -2), 7) + assert e1.is_tangent(Point(0, 0)) is False + assert e1.is_tangent(Point(3, 0)) is False + assert e1.is_tangent(e1) is True + assert e1.is_tangent(Ellipse((0, 0), 1, 2)) is False + assert e1.is_tangent(Ellipse((0, 0), 3, 2)) is True + assert c1.is_tangent(Ellipse((2, -2), 7, 1)) is True + assert c1.is_tangent(Circle((11, -2), 2)) is True + assert c1.is_tangent(Circle((7, -2), 2)) is True + assert c1.is_tangent(Ray((-5, -2), (-15, -20))) is False + assert c1.is_tangent(Ray((-3, -2), (-15, -20))) is False + assert c1.is_tangent(Ray((-3, -22), (15, 20))) is False + assert c1.is_tangent(Ray((9, 20), (9, -20))) is True + assert c1.is_tangent(Ray((2, 5), (9, 5))) is True + assert c1.is_tangent(Segment((2, 5), (9, 5))) is True + assert e1.is_tangent(Segment((2, 2), (-7, 7))) is False + assert e1.is_tangent(Segment((0, 0), (1, 2))) is False + assert c1.is_tangent(Segment((0, 0), (-5, -2))) is False + assert e1.is_tangent(Segment((3, 0), (12, 12))) is False + assert e1.is_tangent(Segment((12, 12), (3, 0))) is False + assert e1.is_tangent(Segment((-3, 0), (3, 0))) is False + assert e1.is_tangent(Segment((-3, 5), (3, 5))) is True + assert e1.is_tangent(Line((10, 0), (10, 10))) is False + assert e1.is_tangent(Line((0, 0), (1, 1))) is False + assert e1.is_tangent(Line((-3, 0), (-2.99, -0.001))) is False + assert e1.is_tangent(Line((-3, 0), (-3, 1))) is True + assert e1.is_tangent(Polygon((0, 0), (5, 5), (5, -5))) is False + assert e1.is_tangent(Polygon((-100, -50), (-40, -334), (-70, -52))) is False + assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 1))) is False + assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 5))) is False + assert e1.is_tangent(Polygon((-3, 0), (0, -5), (3, 0), (0, 5))) is False + assert e1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is True + assert c1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is False + assert e1.is_tangent(Polygon((0, 0), (3, 0), (7, 7), (0, 5))) is False + assert e1.is_tangent(Polygon((3, 12), (3, -12), (6, 5))) is False + assert e1.is_tangent(Polygon((3, 12), (3, -12), (0, -5), (0, 5))) is False + assert e1.is_tangent(Polygon((3, 0), (5, 7), (6, -5))) is False + assert c1.is_tangent(Segment((0, 0), (-5, -2))) is False + assert e1.is_tangent(Segment((-3, 0), (3, 0))) is False + assert e1.is_tangent(Segment((-3, 5), (3, 5))) is True + assert e1.is_tangent(Polygon((0, 0), (5, 5), (5, -5))) is False + assert e1.is_tangent(Polygon((-100, -50), (-40, -334), (-70, -52))) is False + assert e1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is True + assert c1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is False + assert e1.is_tangent(Polygon((3, 12), (3, -12), (0, -5), (0, 5))) is False + assert e1.is_tangent(Polygon((3, 0), (5, 7), (6, -5))) is False + raises(TypeError, lambda: e1.is_tangent(Point(0, 0, 0))) + raises(TypeError, lambda: e1.is_tangent(Rational(5))) + + +def test_parameter_value(): + t = Symbol('t') + e = Ellipse(Point(0, 0), 3, 5) + assert e.parameter_value((3, 0), t) == {t: 0} + raises(ValueError, lambda: e.parameter_value((4, 0), t)) + + +@slow +def test_second_moment_of_area(): + x, y = symbols('x, y') + e = Ellipse(Point(0, 0), 5, 4) + I_yy = 2*4*integrate(sqrt(25 - x**2)*x**2, (x, -5, 5))/5 + I_xx = 2*5*integrate(sqrt(16 - y**2)*y**2, (y, -4, 4))/4 + Y = 3*sqrt(1 - x**2/5**2) + I_xy = integrate(integrate(y, (y, -Y, Y))*x, (x, -5, 5)) + assert I_yy == e.second_moment_of_area()[1] + assert I_xx == e.second_moment_of_area()[0] + assert I_xy == e.second_moment_of_area()[2] + #checking for other point + t1 = e.second_moment_of_area(Point(6,5)) + t2 = (580*pi, 845*pi, 600*pi) + assert t1==t2 + + +def test_section_modulus_and_polar_second_moment_of_area(): + d = Symbol('d', positive=True) + c = Circle((3, 7), 8) + assert c.polar_second_moment_of_area() == 2048*pi + assert c.section_modulus() == (128*pi, 128*pi) + c = Circle((2, 9), d/2) + assert c.polar_second_moment_of_area() == pi*d**3*Abs(d)/64 + pi*d*Abs(d)**3/64 + assert c.section_modulus() == (pi*d**3/S(32), pi*d**3/S(32)) + + a, b = symbols('a, b', positive=True) + e = Ellipse((4, 6), a, b) + assert e.section_modulus() == (pi*a*b**2/S(4), pi*a**2*b/S(4)) + assert e.polar_second_moment_of_area() == pi*a**3*b/S(4) + pi*a*b**3/S(4) + e = e.rotate(pi/2) # no change in polar and section modulus + assert e.section_modulus() == (pi*a**2*b/S(4), pi*a*b**2/S(4)) + assert e.polar_second_moment_of_area() == pi*a**3*b/S(4) + pi*a*b**3/S(4) + + e = Ellipse((a, b), 2, 6) + assert e.section_modulus() == (18*pi, 6*pi) + assert e.polar_second_moment_of_area() == 120*pi + + e = Ellipse(Point(0, 0), 2, 2) + assert e.section_modulus() == (2*pi, 2*pi) + assert e.section_modulus(Point(2, 2)) == (2*pi, 2*pi) + assert e.section_modulus((2, 2)) == (2*pi, 2*pi) + + +def test_circumference(): + M = Symbol('M') + m = Symbol('m') + assert Ellipse(Point(0, 0), M, m).circumference == 4 * M * elliptic_e((M ** 2 - m ** 2) / M**2) + + assert Ellipse(Point(0, 0), 5, 4).circumference == 20 * elliptic_e(S(9) / 25) + + # circle + assert Ellipse(None, 1, None, 0).circumference == 2*pi + + # test numerically + assert abs(Ellipse(None, hradius=5, vradius=3).circumference.evalf(16) - 25.52699886339813) < 1e-10 + + +def test_issue_15259(): + assert Circle((1, 2), 0) == Point(1, 2) + + +def test_issue_15797_equals(): + Ri = 0.024127189424130748 + Ci = (0.0864931002830291, 0.0819863295239654) + A = Point(0, 0.0578591400998346) + c = Circle(Ci, Ri) # evaluated + assert c.is_tangent(c.tangent_lines(A)[0]) == True + assert c.center.x.is_Rational + assert c.center.y.is_Rational + assert c.radius.is_Rational + u = Circle(Ci, Ri, evaluate=False) # unevaluated + assert u.center.x.is_Float + assert u.center.y.is_Float + assert u.radius.is_Float + + +def test_auxiliary_circle(): + x, y, a, b = symbols('x y a b') + e = Ellipse((x, y), a, b) + # the general result + assert e.auxiliary_circle() == Circle((x, y), Max(a, b)) + # a special case where Ellipse is a Circle + assert Circle((3, 4), 8).auxiliary_circle() == Circle((3, 4), 8) + + +def test_director_circle(): + x, y, a, b = symbols('x y a b') + e = Ellipse((x, y), a, b) + # the general result + assert e.director_circle() == Circle((x, y), sqrt(a**2 + b**2)) + # a special case where Ellipse is a Circle + assert Circle((3, 4), 8).director_circle() == Circle((3, 4), 8*sqrt(2)) + + +def test_evolute(): + #ellipse centered at h,k + x, y, h, k = symbols('x y h k',real = True) + a, b = symbols('a b') + e = Ellipse(Point(h, k), a, b) + t1 = (e.hradius*(x - e.center.x))**Rational(2, 3) + t2 = (e.vradius*(y - e.center.y))**Rational(2, 3) + E = t1 + t2 - (e.hradius**2 - e.vradius**2)**Rational(2, 3) + assert e.evolute() == E + #Numerical Example + e = Ellipse(Point(1, 1), 6, 3) + t1 = (6*(x - 1))**Rational(2, 3) + t2 = (3*(y - 1))**Rational(2, 3) + E = t1 + t2 - (27)**Rational(2, 3) + assert e.evolute() == E + + +def test_svg(): + e1 = Ellipse(Point(1, 0), 3, 2) + assert e1._svg(2, "#FFAAFF") == '' diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_entity.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_entity.py new file mode 100644 index 0000000000000000000000000000000000000000..cecfdb785506d1b2f4ef496703c430794f09e589 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_entity.py @@ -0,0 +1,120 @@ +from sympy.core.numbers import (Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.geometry import (Circle, Ellipse, Point, Line, Parabola, + Polygon, Ray, RegularPolygon, Segment, Triangle, Plane, Curve) +from sympy.geometry.entity import scale, GeometryEntity +from sympy.testing.pytest import raises + + +def test_entity(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + + assert GeometryEntity(x, y) in GeometryEntity(x, y) + raises(NotImplementedError, lambda: Point(0, 0) in GeometryEntity(x, y)) + + assert GeometryEntity(x, y) == GeometryEntity(x, y) + assert GeometryEntity(x, y).equals(GeometryEntity(x, y)) + + c = Circle((0, 0), 5) + assert GeometryEntity.encloses(c, Point(0, 0)) + assert GeometryEntity.encloses(c, Segment((0, 0), (1, 1))) + assert GeometryEntity.encloses(c, Line((0, 0), (1, 1))) is False + assert GeometryEntity.encloses(c, Circle((0, 0), 4)) + assert GeometryEntity.encloses(c, Polygon(Point(0, 0), Point(1, 0), Point(0, 1))) + assert GeometryEntity.encloses(c, RegularPolygon(Point(8, 8), 1, 3)) is False + + +def test_svg(): + a = Symbol('a') + b = Symbol('b') + d = Symbol('d') + + entity = Circle(Point(a, b), d) + assert entity._repr_svg_() is None + + entity = Circle(Point(0, 0), S.Infinity) + assert entity._repr_svg_() is None + + +def test_subs(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + p = Point(x, 2) + q = Point(1, 1) + r = Point(3, 4) + for o in [p, + Segment(p, q), + Ray(p, q), + Line(p, q), + Triangle(p, q, r), + RegularPolygon(p, 3, 6), + Polygon(p, q, r, Point(5, 4)), + Circle(p, 3), + Ellipse(p, 3, 4)]: + assert 'y' in str(o.subs(x, y)) + assert p.subs({x: 1}) == Point(1, 2) + assert Point(1, 2).subs(Point(1, 2), Point(3, 4)) == Point(3, 4) + assert Point(1, 2).subs((1, 2), Point(3, 4)) == Point(3, 4) + assert Point(1, 2).subs(Point(1, 2), Point(3, 4)) == Point(3, 4) + assert Point(1, 2).subs({(1, 2)}) == Point(2, 2) + raises(ValueError, lambda: Point(1, 2).subs(1)) + raises(ValueError, lambda: Point(1, 1).subs((Point(1, 1), Point(1, + 2)), 1, 2)) + + +def test_transform(): + assert scale(1, 2, (3, 4)).tolist() == \ + [[1, 0, 0], [0, 2, 0], [0, -4, 1]] + + +def test_reflect_entity_overrides(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + b = Symbol('b') + m = Symbol('m') + l = Line((0, b), slope=m) + p = Point(x, y) + r = p.reflect(l) + c = Circle((x, y), 3) + cr = c.reflect(l) + assert cr == Circle(r, -3) + assert c.area == -cr.area + + pent = RegularPolygon((1, 2), 1, 5) + slope = S.ComplexInfinity + while slope is S.ComplexInfinity: + slope = Rational(*(x._random()/2).as_real_imag()) + l = Line(pent.vertices[1], slope=slope) + rpent = pent.reflect(l) + assert rpent.center == pent.center.reflect(l) + rvert = [i.reflect(l) for i in pent.vertices] + for v in rpent.vertices: + for i in range(len(rvert)): + ri = rvert[i] + if ri.equals(v): + rvert.remove(ri) + break + assert not rvert + assert pent.area.equals(-rpent.area) + + +def test_geometry_EvalfMixin(): + x = pi + t = Symbol('t') + for g in [ + Point(x, x), + Plane(Point(0, x, 0), (0, 0, x)), + Curve((x*t, x), (t, 0, x)), + Ellipse((x, x), x, -x), + Circle((x, x), x), + Line((0, x), (x, 0)), + Segment((0, x), (x, 0)), + Ray((0, x), (x, 0)), + Parabola((0, x), Line((-x, 0), (x, 0))), + Polygon((0, 0), (0, x), (x, 0), (x, x)), + RegularPolygon((0, x), x, 4, x), + Triangle((0, 0), (x, 0), (x, x)), + ]: + assert str(g).replace('pi', '3.1') == str(g.n(2)) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_geometrysets.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_geometrysets.py new file mode 100644 index 0000000000000000000000000000000000000000..c52898b3c9ba4e9db80c244db3aebf88db2cc8b4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_geometrysets.py @@ -0,0 +1,38 @@ +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.geometry import Circle, Line, Point, Polygon, Segment +from sympy.sets import FiniteSet, Union, Intersection, EmptySet + + +def test_booleans(): + """ test basic unions and intersections """ + half = S.Half + + p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) + p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)]) + l1 = Line(Point(0,0), Point(1,1)) + l2 = Line(Point(half, half), Point(5,5)) + l3 = Line(p2, p3) + l4 = Line(p3, p4) + poly1 = Polygon(p1, p2, p3, p4) + poly2 = Polygon(p5, p6, p7) + poly3 = Polygon(p1, p2, p5) + assert Union(l1, l2).equals(l1) + assert Intersection(l1, l2).equals(l1) + assert Intersection(l1, l4) == FiniteSet(Point(1,1)) + assert Intersection(Union(l1, l4), l3) == FiniteSet(Point(Rational(-1, 3), Rational(-1, 3)), Point(5, 1)) + assert Intersection(l1, FiniteSet(Point(7,-7))) == EmptySet + assert Intersection(Circle(Point(0,0), 3), Line(p1,p2)) == FiniteSet(Point(-3,0), Point(3,0)) + assert Intersection(l1, FiniteSet(p1)) == FiniteSet(p1) + assert Union(l1, FiniteSet(p1)) == l1 + + fs = FiniteSet(Point(Rational(1, 3), 1), Point(Rational(2, 3), 0), Point(Rational(9, 5), Rational(1, 5)), Point(Rational(7, 3), 1)) + # test the intersection of polygons + assert Intersection(poly1, poly2) == fs + # make sure if we union polygons with subsets, the subsets go away + assert Union(poly1, poly2, fs) == Union(poly1, poly2) + # make sure that if we union with a FiniteSet that isn't a subset, + # that the points in the intersection stop being listed + assert Union(poly1, FiniteSet(Point(0,0), Point(3,5))) == Union(poly1, FiniteSet(Point(3,5))) + # intersect two polygons that share an edge + assert Intersection(poly1, poly3) == Union(FiniteSet(Point(Rational(3, 2), 1), Point(2, 1)), Segment(Point(0, 0), Point(1, 0))) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_line.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_line.py new file mode 100644 index 0000000000000000000000000000000000000000..5158ec05ab414020fbbe2681a2658454dd15b6eb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_line.py @@ -0,0 +1,861 @@ +from sympy.core.numbers import (Float, Rational, oo, pi) +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, cos, sin) +from sympy.sets import EmptySet +from sympy.simplify.simplify import simplify +from sympy.functions.elementary.trigonometric import tan +from sympy.geometry import (Circle, GeometryError, Line, Point, Ray, + Segment, Triangle, intersection, Point3D, Line3D, Ray3D, Segment3D, + Point2D, Line2D, Plane) +from sympy.geometry.line import Undecidable +from sympy.geometry.polygon import _asa as asa +from sympy.utilities.iterables import cartes +from sympy.testing.pytest import raises, warns + + +x = Symbol('x', real=True) +y = Symbol('y', real=True) +z = Symbol('z', real=True) +k = Symbol('k', real=True) +x1 = Symbol('x1', real=True) +y1 = Symbol('y1', real=True) +t = Symbol('t', real=True) +a, b = symbols('a,b', real=True) +m = symbols('m', real=True) + + +def test_object_from_equation(): + from sympy.abc import x, y, a, b + assert Line(3*x + y + 18) == Line2D(Point2D(0, -18), Point2D(1, -21)) + assert Line(3*x + 5 * y + 1) == Line2D( + Point2D(0, Rational(-1, 5)), Point2D(1, Rational(-4, 5))) + assert Line(3*a + b + 18, x="a", y="b") == Line2D( + Point2D(0, -18), Point2D(1, -21)) + assert Line(3*x + y) == Line2D(Point2D(0, 0), Point2D(1, -3)) + assert Line(x + y) == Line2D(Point2D(0, 0), Point2D(1, -1)) + assert Line(Eq(3*a + b, -18), x="a", y=b) == Line2D( + Point2D(0, -18), Point2D(1, -21)) + # issue 22361 + assert Line(x - 1) == Line2D(Point2D(1, 0), Point2D(1, 1)) + assert Line(2*x - 2, y=x) == Line2D(Point2D(0, 1), Point2D(1, 1)) + assert Line(y) == Line2D(Point2D(0, 0), Point2D(1, 0)) + assert Line(2*y, x=y) == Line2D(Point2D(0, 0), Point2D(0, 1)) + assert Line(y, x=y) == Line2D(Point2D(0, 0), Point2D(0, 1)) + raises(ValueError, lambda: Line(x / y)) + raises(ValueError, lambda: Line(a / b, x='a', y='b')) + raises(ValueError, lambda: Line(y / x)) + raises(ValueError, lambda: Line(b / a, x='a', y='b')) + raises(ValueError, lambda: Line((x + 1)**2 + y)) + + +def feq(a, b): + """Test if two floating point values are 'equal'.""" + t_float = Float("1.0E-10") + return -t_float < a - b < t_float + + +def test_angle_between(): + a = Point(1, 2, 3, 4) + b = a.orthogonal_direction + o = a.origin + assert feq(Line.angle_between(Line(Point(0, 0), Point(1, 1)), + Line(Point(0, 0), Point(5, 0))).evalf(), pi.evalf() / 4) + assert Line(a, o).angle_between(Line(b, o)) == pi / 2 + z = Point3D(0, 0, 0) + assert Line3D.angle_between(Line3D(z, Point3D(1, 1, 1)), + Line3D(z, Point3D(5, 0, 0))) == acos(sqrt(3) / 3) + # direction of points is used to determine angle + assert Line3D.angle_between(Line3D(z, Point3D(1, 1, 1)), + Line3D(Point3D(5, 0, 0), z)) == acos(-sqrt(3) / 3) + + +def test_closing_angle(): + a = Ray((0, 0), angle=0) + b = Ray((1, 2), angle=pi/2) + assert a.closing_angle(b) == -pi/2 + assert b.closing_angle(a) == pi/2 + assert a.closing_angle(a) == 0 + + +def test_smallest_angle(): + a = Line(Point(1, 1), Point(1, 2)) + b = Line(Point(1, 1),Point(2, 3)) + assert a.smallest_angle_between(b) == acos(2*sqrt(5)/5) + + +def test_svg(): + a = Line(Point(1, 1),Point(1, 2)) + assert a._svg() == '' + a = Segment(Point(1, 0),Point(1, 1)) + assert a._svg() == '' + a = Ray(Point(2, 3), Point(3, 5)) + assert a._svg() == '' + + +def test_arbitrary_point(): + l1 = Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)) + l2 = Line(Point(x1, x1), Point(y1, y1)) + assert l2.arbitrary_point() in l2 + assert Ray((1, 1), angle=pi / 4).arbitrary_point() == \ + Point(t + 1, t + 1) + assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2 * t) + assert l1.perpendicular_segment(l1.arbitrary_point()) == l1.arbitrary_point() + assert Ray3D((1, 1, 1), direction_ratio=[1, 2, 3]).arbitrary_point() == \ + Point3D(t + 1, 2 * t + 1, 3 * t + 1) + assert Segment3D(Point3D(0, 0, 0), Point3D(1, 1, 1)).midpoint == \ + Point3D(S.Half, S.Half, S.Half) + assert Segment3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1)).length == sqrt(3) * sqrt((x1 - y1) ** 2) + assert Segment3D((1, 1, 1), (2, 3, 4)).arbitrary_point() == \ + Point3D(t + 1, 2 * t + 1, 3 * t + 1) + raises(ValueError, (lambda: Line((x, 1), (2, 3)).arbitrary_point(x))) + + +def test_are_concurrent_2d(): + l1 = Line(Point(0, 0), Point(1, 1)) + l2 = Line(Point(x1, x1), Point(x1, 1 + x1)) + assert Line.are_concurrent(l1) is False + assert Line.are_concurrent(l1, l2) + assert Line.are_concurrent(l1, l1, l1, l2) + assert Line.are_concurrent(l1, l2, Line(Point(5, x1), Point(Rational(-3, 5), x1))) + assert Line.are_concurrent(l1, Line(Point(0, 0), Point(-x1, x1)), l2) is False + + +def test_are_concurrent_3d(): + p1 = Point3D(0, 0, 0) + l1 = Line(p1, Point3D(1, 1, 1)) + parallel_1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)) + parallel_2 = Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0)) + assert Line3D.are_concurrent(l1) is False + assert Line3D.are_concurrent(l1, Line(Point3D(x1, x1, x1), Point3D(y1, y1, y1))) is False + assert Line3D.are_concurrent(l1, Line3D(p1, Point3D(x1, x1, x1)), + Line(Point3D(x1, x1, x1), Point3D(x1, 1 + x1, 1))) is True + assert Line3D.are_concurrent(parallel_1, parallel_2) is False + + +def test_arguments(): + """Functions accepting `Point` objects in `geometry` + should also accept tuples, lists, and generators and + automatically convert them to points.""" + from sympy.utilities.iterables import subsets + + singles2d = ((1, 2), [1, 3], Point(1, 5)) + doubles2d = subsets(singles2d, 2) + l2d = Line(Point2D(1, 2), Point2D(2, 3)) + singles3d = ((1, 2, 3), [1, 2, 4], Point(1, 2, 6)) + doubles3d = subsets(singles3d, 2) + l3d = Line(Point3D(1, 2, 3), Point3D(1, 1, 2)) + singles4d = ((1, 2, 3, 4), [1, 2, 3, 5], Point(1, 2, 3, 7)) + doubles4d = subsets(singles4d, 2) + l4d = Line(Point(1, 2, 3, 4), Point(2, 2, 2, 2)) + # test 2D + test_single = ['contains', 'distance', 'equals', 'parallel_line', 'perpendicular_line', 'perpendicular_segment', + 'projection', 'intersection'] + for p in doubles2d: + Line2D(*p) + for func in test_single: + for p in singles2d: + getattr(l2d, func)(p) + # test 3D + for p in doubles3d: + Line3D(*p) + for func in test_single: + for p in singles3d: + getattr(l3d, func)(p) + # test 4D + for p in doubles4d: + Line(*p) + for func in test_single: + for p in singles4d: + getattr(l4d, func)(p) + + +def test_basic_properties_2d(): + p1 = Point(0, 0) + p2 = Point(1, 1) + p10 = Point(2000, 2000) + p_r3 = Ray(p1, p2).random_point() + p_r4 = Ray(p2, p1).random_point() + + l1 = Line(p1, p2) + l3 = Line(Point(x1, x1), Point(x1, 1 + x1)) + l4 = Line(p1, Point(1, 0)) + + r1 = Ray(p1, Point(0, 1)) + r2 = Ray(Point(0, 1), p1) + + s1 = Segment(p1, p10) + p_s1 = s1.random_point() + + assert Line((1, 1), slope=1) == Line((1, 1), (2, 2)) + assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2)) + assert Line((1, 1), slope=oo).bounds == (1, 1, 1, 2) + assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2)) + assert Line(p1, p2).scale(2, 1) == Line(p1, Point(2, 1)) + assert Line(p1, p2) == Line(p1, p2) + assert Line(p1, p2) != Line(p2, p1) + assert l1 != Line(Point(x1, x1), Point(y1, y1)) + assert l1 != l3 + assert Line(p1, p10) != Line(p10, p1) + assert Line(p1, p10) != p1 + assert p1 in l1 # is p1 on the line l1? + assert p1 not in l3 + assert s1 in Line(p1, p10) + assert Ray(Point(0, 0), Point(0, 1)) in Ray(Point(0, 0), Point(0, 2)) + assert Ray(Point(0, 0), Point(0, 2)) in Ray(Point(0, 0), Point(0, 1)) + assert Ray(Point(0, 0), Point(0, 2)).xdirection == S.Zero + assert Ray(Point(0, 0), Point(1, 2)).xdirection == S.Infinity + assert Ray(Point(0, 0), Point(-1, 2)).xdirection == S.NegativeInfinity + assert Ray(Point(0, 0), Point(2, 0)).ydirection == S.Zero + assert Ray(Point(0, 0), Point(2, 2)).ydirection == S.Infinity + assert Ray(Point(0, 0), Point(2, -2)).ydirection == S.NegativeInfinity + assert (r1 in s1) is False + assert Segment(p1, p2) in s1 + assert Ray(Point(x1, x1), Point(x1, 1 + x1)) != Ray(p1, Point(-1, 5)) + assert Segment(p1, p2).midpoint == Point(S.Half, S.Half) + assert Segment(p1, Point(-x1, x1)).length == sqrt(2 * (x1 ** 2)) + + assert l1.slope == 1 + assert l3.slope is oo + assert l4.slope == 0 + assert Line(p1, Point(0, 1)).slope is oo + assert Line(r1.source, r1.random_point()).slope == r1.slope + assert Line(r2.source, r2.random_point()).slope == r2.slope + assert Segment(Point(0, -1), Segment(p1, Point(0, 1)).random_point()).slope == Segment(p1, Point(0, 1)).slope + + assert l4.coefficients == (0, 1, 0) + assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0) + assert Line(p1, Point(0, 1)).coefficients == (1, 0, 0) + # issue 7963 + r = Ray((0, 0), angle=x) + assert r.subs(x, 3 * pi / 4) == Ray((0, 0), (-1, 1)) + assert r.subs(x, 5 * pi / 4) == Ray((0, 0), (-1, -1)) + assert r.subs(x, -pi / 4) == Ray((0, 0), (1, -1)) + assert r.subs(x, pi / 2) == Ray((0, 0), (0, 1)) + assert r.subs(x, -pi / 2) == Ray((0, 0), (0, -1)) + + for ind in range(0, 5): + assert l3.random_point() in l3 + + assert p_r3.x >= p1.x and p_r3.y >= p1.y + assert p_r4.x <= p2.x and p_r4.y <= p2.y + assert p1.x <= p_s1.x <= p10.x and p1.y <= p_s1.y <= p10.y + assert hash(s1) != hash(Segment(p10, p1)) + + assert s1.plot_interval() == [t, 0, 1] + assert Line(p1, p10).plot_interval() == [t, -5, 5] + assert Ray((0, 0), angle=pi / 4).plot_interval() == [t, 0, 10] + + +def test_basic_properties_3d(): + p1 = Point3D(0, 0, 0) + p2 = Point3D(1, 1, 1) + p3 = Point3D(x1, x1, x1) + p5 = Point3D(x1, 1 + x1, 1) + + l1 = Line3D(p1, p2) + l3 = Line3D(p3, p5) + + r1 = Ray3D(p1, Point3D(-1, 5, 0)) + r3 = Ray3D(p1, p2) + + s1 = Segment3D(p1, p2) + + assert Line3D((1, 1, 1), direction_ratio=[2, 3, 4]) == Line3D(Point3D(1, 1, 1), Point3D(3, 4, 5)) + assert Line3D((1, 1, 1), direction_ratio=[1, 5, 7]) == Line3D(Point3D(1, 1, 1), Point3D(2, 6, 8)) + assert Line3D((1, 1, 1), direction_ratio=[1, 2, 3]) == Line3D(Point3D(1, 1, 1), Point3D(2, 3, 4)) + assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).direction_cosine == [1, 0, 0] + assert Line3D(Line3D(p1, Point3D(0, 1, 0))) == Line3D(p1, Point3D(0, 1, 0)) + assert Ray3D(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))) == Ray3D(p1, Point3D(1, 0, 0)) + assert Line3D(p1, p2) != Line3D(p2, p1) + assert l1 != l3 + assert l1 != Line3D(p3, Point3D(y1, y1, y1)) + assert r3 != r1 + assert Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 1)) in Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)) + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)) in Ray3D(Point3D(0, 0, 0), Point3D(1, 1, 1)) + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).xdirection == S.Infinity + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).ydirection == S.Infinity + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 2)).zdirection == S.Infinity + assert Ray3D(Point3D(0, 0, 0), Point3D(-2, 2, 2)).xdirection == S.NegativeInfinity + assert Ray3D(Point3D(0, 0, 0), Point3D(2, -2, 2)).ydirection == S.NegativeInfinity + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, -2)).zdirection == S.NegativeInfinity + assert Ray3D(Point3D(0, 0, 0), Point3D(0, 2, 2)).xdirection == S.Zero + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 0, 2)).ydirection == S.Zero + assert Ray3D(Point3D(0, 0, 0), Point3D(2, 2, 0)).zdirection == S.Zero + assert p1 in l1 + assert p1 not in l3 + + assert l1.direction_ratio == [1, 1, 1] + + assert s1.midpoint == Point3D(S.Half, S.Half, S.Half) + # Test zdirection + assert Ray3D(p1, Point3D(0, 0, -1)).zdirection is S.NegativeInfinity + + +def test_contains(): + p1 = Point(0, 0) + + r = Ray(p1, Point(4, 4)) + r1 = Ray3D(p1, Point3D(0, 0, -1)) + r2 = Ray3D(p1, Point3D(0, 1, 0)) + r3 = Ray3D(p1, Point3D(0, 0, 1)) + + l = Line(Point(0, 1), Point(3, 4)) + # Segment contains + assert Point(0, (a + b) / 2) in Segment((0, a), (0, b)) + assert Point((a + b) / 2, 0) in Segment((a, 0), (b, 0)) + assert Point3D(0, 1, 0) in Segment3D((0, 1, 0), (0, 1, 0)) + assert Point3D(1, 0, 0) in Segment3D((1, 0, 0), (1, 0, 0)) + assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains([]) is True + assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains( + Segment3D(Point3D(2, 2, 2), Point3D(3, 2, 2))) is False + # Line contains + assert l.contains(Point(0, 1)) is True + assert l.contains((0, 1)) is True + assert l.contains((0, 0)) is False + # Ray contains + assert r.contains(p1) is True + assert r.contains((1, 1)) is True + assert r.contains((1, 3)) is False + assert r.contains(Segment((1, 1), (2, 2))) is True + assert r.contains(Segment((1, 2), (2, 5))) is False + assert r.contains(Ray((2, 2), (3, 3))) is True + assert r.contains(Ray((2, 2), (3, 5))) is False + assert r1.contains(Segment3D(p1, Point3D(0, 0, -10))) is True + assert r1.contains(Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))) is False + assert r2.contains(Point3D(0, 0, 0)) is True + assert r3.contains(Point3D(0, 0, 0)) is True + assert Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)).contains([]) is False + assert Line3D((0, 0, 0), (x, y, z)).contains((2 * x, 2 * y, 2 * z)) + with warns(UserWarning, test_stacklevel=False): + assert Line3D(p1, Point3D(0, 1, 0)).contains(Point(1.0, 1.0)) is False + + with warns(UserWarning, test_stacklevel=False): + assert r3.contains(Point(1.0, 1.0)) is False + + +def test_contains_nonreal_symbols(): + u, v, w, z = symbols('u, v, w, z') + l = Segment(Point(u, w), Point(v, z)) + p = Point(u*Rational(2, 3) + v/3, w*Rational(2, 3) + z/3) + assert l.contains(p) + + +def test_distance_2d(): + p1 = Point(0, 0) + p2 = Point(1, 1) + half = S.Half + + s1 = Segment(Point(0, 0), Point(1, 1)) + s2 = Segment(Point(half, half), Point(1, 0)) + + r = Ray(p1, p2) + + assert s1.distance(Point(0, 0)) == 0 + assert s1.distance((0, 0)) == 0 + assert s2.distance(Point(0, 0)) == 2 ** half / 2 + assert s2.distance(Point(Rational(3) / 2, Rational(3) / 2)) == 2 ** half + assert Line(p1, p2).distance(Point(-1, 1)) == sqrt(2) + assert Line(p1, p2).distance(Point(1, -1)) == sqrt(2) + assert Line(p1, p2).distance(Point(2, 2)) == 0 + assert Line(p1, p2).distance((-1, 1)) == sqrt(2) + assert Line((0, 0), (0, 1)).distance(p1) == 0 + assert Line((0, 0), (0, 1)).distance(p2) == 1 + assert Line((0, 0), (1, 0)).distance(p1) == 0 + assert Line((0, 0), (1, 0)).distance(p2) == 1 + assert r.distance(Point(-1, -1)) == sqrt(2) + assert r.distance(Point(1, 1)) == 0 + assert r.distance(Point(-1, 1)) == sqrt(2) + assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3 * sqrt(2) / 4 + assert r.distance((1, 1)) == 0 + + +def test_dimension_normalization(): + with warns(UserWarning, test_stacklevel=False): + assert Ray((1, 1), (2, 1, 2)) == Ray((1, 1, 0), (2, 1, 2)) + + +def test_distance_3d(): + p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1) + p3 = Point3D(Rational(3) / 2, Rational(3) / 2, Rational(3) / 2) + + s1 = Segment3D(Point3D(0, 0, 0), Point3D(1, 1, 1)) + s2 = Segment3D(Point3D(S.Half, S.Half, S.Half), Point3D(1, 0, 1)) + + r = Ray3D(p1, p2) + + assert s1.distance(p1) == 0 + assert s2.distance(p1) == sqrt(3) / 2 + assert s2.distance(p3) == 2 * sqrt(6) / 3 + assert s1.distance((0, 0, 0)) == 0 + assert s2.distance((0, 0, 0)) == sqrt(3) / 2 + assert s1.distance(p1) == 0 + assert s2.distance(p1) == sqrt(3) / 2 + assert s2.distance(p3) == 2 * sqrt(6) / 3 + assert s1.distance((0, 0, 0)) == 0 + assert s2.distance((0, 0, 0)) == sqrt(3) / 2 + # Line to point + assert Line3D(p1, p2).distance(Point3D(-1, 1, 1)) == 2 * sqrt(6) / 3 + assert Line3D(p1, p2).distance(Point3D(1, -1, 1)) == 2 * sqrt(6) / 3 + assert Line3D(p1, p2).distance(Point3D(2, 2, 2)) == 0 + assert Line3D(p1, p2).distance((2, 2, 2)) == 0 + assert Line3D(p1, p2).distance((1, -1, 1)) == 2 * sqrt(6) / 3 + assert Line3D((0, 0, 0), (0, 1, 0)).distance(p1) == 0 + assert Line3D((0, 0, 0), (0, 1, 0)).distance(p2) == sqrt(2) + assert Line3D((0, 0, 0), (1, 0, 0)).distance(p1) == 0 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(p2) == sqrt(2) + # Line to line + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 0, 0), (0, 1, 2))) == 0 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 0, 0), (1, 0, 0))) == 0 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((10, 0, 0), (10, 1, 2))) == 0 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Line3D((0, 1, 0), (0, 1, 1))) == 1 + # Line to plane + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((2, 0, 0), (0, 0, 1))) == 0 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((0, 1, 0), (0, 1, 0))) == 1 + assert Line3D((0, 0, 0), (1, 0, 0)).distance(Plane((1, 1, 3), (1, 0, 0))) == 0 + # Ray to point + assert r.distance(Point3D(-1, -1, -1)) == sqrt(3) + assert r.distance(Point3D(1, 1, 1)) == 0 + assert r.distance((-1, -1, -1)) == sqrt(3) + assert r.distance((1, 1, 1)) == 0 + assert Ray3D((0, 0, 0), (1, 1, 2)).distance((-1, -1, 2)) == 4 * sqrt(3) / 3 + assert Ray3D((1, 1, 1), (2, 2, 2)).distance(Point3D(1.5, -3, -1)) == Rational(9) / 2 + assert Ray3D((1, 1, 1), (2, 2, 2)).distance(Point3D(1.5, 3, 1)) == sqrt(78) / 6 + + +def test_equals(): + p1 = Point(0, 0) + p2 = Point(1, 1) + + l1 = Line(p1, p2) + l2 = Line((0, 5), slope=m) + l3 = Line(Point(x1, x1), Point(x1, 1 + x1)) + + assert l1.perpendicular_line(p1.args).equals(Line(Point(0, 0), Point(1, -1))) + assert l1.perpendicular_line(p1).equals(Line(Point(0, 0), Point(1, -1))) + assert Line(Point(x1, x1), Point(y1, y1)).parallel_line(Point(-x1, x1)). \ + equals(Line(Point(-x1, x1), Point(-y1, 2 * x1 - y1))) + assert l3.parallel_line(p1.args).equals(Line(Point(0, 0), Point(0, -1))) + assert l3.parallel_line(p1).equals(Line(Point(0, 0), Point(0, -1))) + assert (l2.distance(Point(2, 3)) - 2 * abs(m + 1) / sqrt(m ** 2 + 1)).equals(0) + assert Line3D(p1, Point3D(0, 1, 0)).equals(Point(1.0, 1.0)) is False + assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).equals(Line3D(Point3D(-5, 0, 0), Point3D(-1, 0, 0))) is True + assert Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).equals(Line3D(p1, Point3D(0, 1, 0))) is False + assert Ray3D(p1, Point3D(0, 0, -1)).equals(Point(1.0, 1.0)) is False + assert Ray3D(p1, Point3D(0, 0, -1)).equals(Ray3D(p1, Point3D(0, 0, -1))) is True + assert Line3D((0, 0), (t, t)).perpendicular_line(Point(0, 1, 0)).equals( + Line3D(Point3D(0, 1, 0), Point3D(S.Half, S.Half, 0))) + assert Line3D((0, 0), (t, t)).perpendicular_segment(Point(0, 1, 0)).equals(Segment3D((0, 1), (S.Half, S.Half))) + assert Line3D(p1, Point3D(0, 1, 0)).equals(Point(1.0, 1.0)) is False + + +def test_equation(): + p1 = Point(0, 0) + p2 = Point(1, 1) + l1 = Line(p1, p2) + l3 = Line(Point(x1, x1), Point(x1, 1 + x1)) + + assert simplify(l1.equation()) in (x - y, y - x) + assert simplify(l3.equation()) in (x - x1, x1 - x) + assert simplify(l1.equation()) in (x - y, y - x) + assert simplify(l3.equation()) in (x - x1, x1 - x) + + assert Line(p1, Point(1, 0)).equation(x=x, y=y) == y + assert Line(p1, Point(0, 1)).equation() == x + assert Line(Point(2, 0), Point(2, 1)).equation() == x - 2 + assert Line(p2, Point(2, 1)).equation() == y - 1 + + assert Line3D(Point(x1, x1, x1), Point(y1, y1, y1) + ).equation() == (-x + y, -x + z) + assert Line3D(Point(1, 2, 3), Point(2, 3, 4) + ).equation() == (-x + y - 1, -x + z - 2) + assert Line3D(Point(1, 2, 3), Point(1, 3, 4) + ).equation() == (x - 1, -y + z - 1) + assert Line3D(Point(1, 2, 3), Point(2, 2, 4) + ).equation() == (y - 2, -x + z - 2) + assert Line3D(Point(1, 2, 3), Point(2, 3, 3) + ).equation() == (-x + y - 1, z - 3) + assert Line3D(Point(1, 2, 3), Point(1, 2, 4) + ).equation() == (x - 1, y - 2) + assert Line3D(Point(1, 2, 3), Point(1, 3, 3) + ).equation() == (x - 1, z - 3) + assert Line3D(Point(1, 2, 3), Point(2, 2, 3) + ).equation() == (y - 2, z - 3) + + +def test_intersection_2d(): + p1 = Point(0, 0) + p2 = Point(1, 1) + p3 = Point(x1, x1) + p4 = Point(y1, y1) + + l1 = Line(p1, p2) + l3 = Line(Point(0, 0), Point(3, 4)) + + r1 = Ray(Point(1, 1), Point(2, 2)) + r2 = Ray(Point(0, 0), Point(3, 4)) + r4 = Ray(p1, p2) + r6 = Ray(Point(0, 1), Point(1, 2)) + r7 = Ray(Point(0.5, 0.5), Point(1, 1)) + + s1 = Segment(p1, p2) + s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5)) + s3 = Segment(Point(0, 0), Point(3, 4)) + + assert intersection(l1, p1) == [p1] + assert intersection(l1, Point(x1, 1 + x1)) == [] + assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]] + assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == [] + assert intersection(l3, l3) == [l3] + assert intersection(l3, r2) == [r2] + assert intersection(l3, s3) == [s3] + assert intersection(s3, l3) == [s3] + assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == [] + assert intersection(r2, l3) == [r2] + assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))] + assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)] + assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))] + + assert r4.intersection(s2) == [s2] + assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == [] + assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))] + assert r4.intersection(Ray(p2, p1)) == [s1] + assert Ray(p2, p1).intersection(r6) == [] + assert r4.intersection(r7) == r7.intersection(r4) == [r7] + assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))] + assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))] + assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \ + [Segment(Point(0, 0), Point(0, 1))] + + assert Segment3D((0, 0), (3, 0)).intersection( + Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))] + assert Segment3D((1, 0), (2, 0)).intersection( + Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))] + assert Segment3D((0, 0), (3, 0)).intersection( + Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))] + assert Segment3D((0, 0), (3, 0)).intersection( + Segment3D((2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))] + assert Segment3D((0, 0), (3, 0)).intersection( + Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))] + assert Segment3D((0, 0), (3, 0)).intersection( + Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)] + assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)] + assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [Segment(Point(0.5, 0.5), p2)] + assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == [] + assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1] + assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))] + assert s1.intersection(Line(Point(1, 0), Point(2, 1))) == [] + assert s1.intersection(s2) == [s2] + assert s2.intersection(s1) == [s2] + + assert asa(120, 8, 52) == \ + Triangle( + Point(0, 0), + Point(8, 0), + Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45), + 4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45))) + assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)] + assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)] + assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)] + assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)] + assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True + assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10)) + assert s1.intersection(Ray((1, 1), (4, 4))) == [Point(1, 1)] + + # This test is disabled because it hangs after rref changes which simplify + # intermediate results and return a different representation from when the + # test was written. + # # 16628 - this should be fast + # p0 = Point2D(Rational(249, 5), Rational(497999, 10000)) + # p1 = Point2D((-58977084786*sqrt(405639795226) + 2030690077184193 + + # 20112207807*sqrt(630547164901) + 99600*sqrt(255775022850776494562626)) + # /(2000*sqrt(255775022850776494562626) + 1991998000*sqrt(405639795226) + # + 1991998000*sqrt(630547164901) + 1622561172902000), + # (-498000*sqrt(255775022850776494562626) - 995999*sqrt(630547164901) + + # 90004251917891999 + + # 496005510002*sqrt(405639795226))/(10000*sqrt(255775022850776494562626) + # + 9959990000*sqrt(405639795226) + 9959990000*sqrt(630547164901) + + # 8112805864510000)) + # p2 = Point2D(Rational(497, 10), Rational(-497, 10)) + # p3 = Point2D(Rational(-497, 10), Rational(-497, 10)) + # l = Line(p0, p1) + # s = Segment(p2, p3) + # n = (-52673223862*sqrt(405639795226) - 15764156209307469 - + # 9803028531*sqrt(630547164901) + + # 33200*sqrt(255775022850776494562626)) + # d = sqrt(405639795226) + 315274080450 + 498000*sqrt( + # 630547164901) + sqrt(255775022850776494562626) + # assert intersection(l, s) == [ + # Point2D(n/d*Rational(3, 2000), Rational(-497, 10))] + + +def test_line_intersection(): + # see also test_issue_11238 in test_matrices.py + x0 = tan(pi*Rational(13, 45)) + x1 = sqrt(3) + x2 = x0**2 + x, y = [8*x0/(x0 + x1), (24*x0 - 8*x1*x2)/(x2 - 3)] + assert Line(Point(0, 0), Point(1, -sqrt(3))).contains(Point(x, y)) is True + + +def test_intersection_3d(): + p1 = Point3D(0, 0, 0) + p2 = Point3D(1, 1, 1) + + l1 = Line3D(p1, p2) + l2 = Line3D(Point3D(0, 0, 0), Point3D(3, 4, 0)) + + r1 = Ray3D(Point3D(1, 1, 1), Point3D(2, 2, 2)) + r2 = Ray3D(Point3D(0, 0, 0), Point3D(3, 4, 0)) + + s1 = Segment3D(Point3D(0, 0, 0), Point3D(3, 4, 0)) + + assert intersection(l1, p1) == [p1] + assert intersection(l1, Point3D(x1, 1 + x1, 1)) == [] + assert intersection(l1, l1.parallel_line(p1)) == [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1))] + assert intersection(l2, r2) == [r2] + assert intersection(l2, s1) == [s1] + assert intersection(r2, l2) == [r2] + assert intersection(r1, Ray3D(Point3D(1, 1, 1), Point3D(-1, -1, -1))) == [Point3D(1, 1, 1)] + assert intersection(r1, Segment3D(Point3D(0, 0, 0), Point3D(2, 2, 2))) == [ + Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))] + assert intersection(Ray3D(Point3D(1, 0, 0), Point3D(-1, 0, 0)), Ray3D(Point3D(0, 1, 0), Point3D(0, -1, 0))) \ + == [Point3D(0, 0, 0)] + assert intersection(r1, Ray3D(Point3D(2, 2, 2), Point3D(0, 0, 0))) == \ + [Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))] + assert intersection(s1, r2) == [s1] + + assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).intersection(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) == \ + [Point3D(2, 2, 1)] + assert Line3D((0, 1, 2), (0, 2, 3)).intersection(Line3D((0, 1, 2), (0, 1, 1))) == [Point3D(0, 1, 2)] + assert Line3D((0, 0), (t, t)).intersection(Line3D((0, 1), (t, t))) == \ + [Point3D(t, t)] + + assert Ray3D(Point3D(0, 0, 0), Point3D(0, 4, 0)).intersection(Ray3D(Point3D(0, 1, 1), Point3D(0, -1, 1))) == [] + + +def test_is_parallel(): + p1 = Point3D(0, 0, 0) + p2 = Point3D(1, 1, 1) + p3 = Point3D(x1, x1, x1) + + l2 = Line(Point(x1, x1), Point(y1, y1)) + l2_1 = Line(Point(x1, x1), Point(x1, 1 + x1)) + + assert Line.is_parallel(Line(Point(0, 0), Point(1, 1)), l2) + assert Line.is_parallel(l2, Line(Point(x1, x1), Point(x1, 1 + x1))) is False + assert Line.is_parallel(l2, l2.parallel_line(Point(-x1, x1))) + assert Line.is_parallel(l2_1, l2_1.parallel_line(Point(0, 0))) + assert Line3D(p1, p2).is_parallel(Line3D(p1, p2)) # same as in 2D + assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).is_parallel(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) is False + assert Line3D(p1, p2).parallel_line(p3) == Line3D(Point3D(x1, x1, x1), + Point3D(x1 + 1, x1 + 1, x1 + 1)) + assert Line3D(p1, p2).parallel_line(p3.args) == \ + Line3D(Point3D(x1, x1, x1), Point3D(x1 + 1, x1 + 1, x1 + 1)) + assert Line3D(Point3D(4, 0, 1), Point3D(0, 4, 1)).is_parallel(Line3D(Point3D(0, 0, 1), Point3D(4, 4, 1))) is False + + +def test_is_perpendicular(): + p1 = Point(0, 0) + p2 = Point(1, 1) + + l1 = Line(p1, p2) + l2 = Line(Point(x1, x1), Point(y1, y1)) + l1_1 = Line(p1, Point(-x1, x1)) + # 2D + assert Line.is_perpendicular(l1, l1_1) + assert Line.is_perpendicular(l1, l2) is False + p = l1.random_point() + assert l1.perpendicular_segment(p) == p + # 3D + assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)), + Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))) is True + assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)), + Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))) is False + assert Line3D.is_perpendicular(Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)), + Line3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1))) is False + + +def test_is_similar(): + p1 = Point(2000, 2000) + p2 = p1.scale(2, 2) + + r1 = Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)) + r2 = Ray(Point(0, 0), Point(0, 1)) + + s1 = Segment(Point(0, 0), p1) + + assert s1.is_similar(Segment(p1, p2)) + assert s1.is_similar(r2) is False + assert r1.is_similar(Line3D(Point3D(1, 1, 1), Point3D(1, 0, 0))) is True + assert r1.is_similar(Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))) is False + + +def test_length(): + s2 = Segment3D(Point3D(x1, x1, x1), Point3D(y1, y1, y1)) + assert Line(Point(0, 0), Point(1, 1)).length is oo + assert s2.length == sqrt(3) * sqrt((x1 - y1) ** 2) + assert Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)).length is oo + + +def test_projection(): + p1 = Point(0, 0) + p2 = Point3D(0, 0, 0) + p3 = Point(-x1, x1) + + l1 = Line(p1, Point(1, 1)) + l2 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)) + l3 = Line3D(p2, Point3D(1, 1, 1)) + + r1 = Ray(Point(1, 1), Point(2, 2)) + + s1 = Segment(Point2D(0, 0), Point2D(0, 1)) + s2 = Segment(Point2D(1, 0), Point2D(2, 1/2)) + + assert Line(Point(x1, x1), Point(y1, y1)).projection(Point(y1, y1)) == Point(y1, y1) + assert Line(Point(x1, x1), Point(x1, 1 + x1)).projection(Point(1, 1)) == Point(x1, 1) + assert Segment(Point(-2, 2), Point(0, 4)).projection(r1) == Segment(Point(-1, 3), Point(0, 4)) + assert Segment(Point(0, 4), Point(-2, 2)).projection(r1) == Segment(Point(0, 4), Point(-1, 3)) + assert s2.projection(s1) == EmptySet + assert l1.projection(p3) == p1 + assert l1.projection(Ray(p1, Point(-1, 5))) == Ray(Point(0, 0), Point(2, 2)) + assert l1.projection(Ray(p1, Point(-1, 1))) == p1 + assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1) + assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2)) + assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2)) + assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1) + assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2)) + assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2)) + + assert l3.projection(Ray3D(p2, Point3D(-1, 5, 0))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(4, 3), Rational(4, 3), Rational(4, 3))) + assert l3.projection(Ray3D(p2, Point3D(-1, 1, 1))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(1, 3), Rational(1, 3), Rational(1, 3))) + assert l2.projection(Point3D(5, 5, 0)) == Point3D(5, 0) + assert l2.projection(Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))).equals(l2) + + +def test_perpendicular_line(): + # 3d - requires a particular orthogonal to be selected + p1, p2, p3 = Point(0, 0, 0), Point(2, 3, 4), Point(-2, 2, 0) + l = Line(p1, p2) + p = l.perpendicular_line(p3) + assert p.p1 == p3 + assert p.p2 in l + # 2d - does not require special selection + p1, p2, p3 = Point(0, 0), Point(2, 3), Point(-2, 2) + l = Line(p1, p2) + p = l.perpendicular_line(p3) + assert p.p1 == p3 + # p is directed from l to p3 + assert p.direction.unit == (p3 - l.projection(p3)).unit + + +def test_perpendicular_bisector(): + s1 = Segment(Point(0, 0), Point(1, 1)) + aline = Line(Point(S.Half, S.Half), Point(Rational(3, 2), Rational(-1, 2))) + on_line = Segment(Point(S.Half, S.Half), Point(Rational(3, 2), Rational(-1, 2))).midpoint + + assert s1.perpendicular_bisector().equals(aline) + assert s1.perpendicular_bisector(on_line).equals(Segment(s1.midpoint, on_line)) + assert s1.perpendicular_bisector(on_line + (1, 0)).equals(aline) + + +def test_raises(): + d, e = symbols('a,b', real=True) + s = Segment((d, 0), (e, 0)) + + raises(TypeError, lambda: Line((1, 1), 1)) + raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0))) + raises(Undecidable, lambda: Point(2 * d, 0) in s) + raises(ValueError, lambda: Ray3D(Point(1.0, 1.0))) + raises(ValueError, lambda: Line3D(Point3D(0, 0, 0), Point3D(0, 0, 0))) + raises(TypeError, lambda: Line3D((1, 1), 1)) + raises(ValueError, lambda: Line3D(Point3D(0, 0, 0))) + raises(TypeError, lambda: Ray((1, 1), 1)) + raises(GeometryError, lambda: Line(Point(0, 0), Point(1, 0)) + .projection(Circle(Point(0, 0), 1))) + + +def test_ray_generation(): + assert Ray((1, 1), angle=pi / 4) == Ray((1, 1), (2, 2)) + assert Ray((1, 1), angle=pi / 2) == Ray((1, 1), (1, 2)) + assert Ray((1, 1), angle=-pi / 2) == Ray((1, 1), (1, 0)) + assert Ray((1, 1), angle=-3 * pi / 2) == Ray((1, 1), (1, 2)) + assert Ray((1, 1), angle=5 * pi / 2) == Ray((1, 1), (1, 2)) + assert Ray((1, 1), angle=5.0 * pi / 2) == Ray((1, 1), (1, 2)) + assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1)) + assert Ray((1, 1), angle=3.0 * pi) == Ray((1, 1), (0, 1)) + assert Ray((1, 1), angle=4.0 * pi) == Ray((1, 1), (2, 1)) + assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1)) + assert Ray((1, 1), angle=4.05 * pi) == Ray(Point(1, 1), + Point(2, -sqrt(5) * sqrt(2 * sqrt(5) + 10) / 4 - sqrt( + 2 * sqrt(5) + 10) / 4 + 2 + sqrt(5))) + assert Ray((1, 1), angle=4.02 * pi) == Ray(Point(1, 1), + Point(2, 1 + tan(4.02 * pi))) + assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5))) + + assert Ray3D((1, 1, 1), direction_ratio=[4, 4, 4]) == Ray3D(Point3D(1, 1, 1), Point3D(5, 5, 5)) + assert Ray3D((1, 1, 1), direction_ratio=[1, 2, 3]) == Ray3D(Point3D(1, 1, 1), Point3D(2, 3, 4)) + assert Ray3D((1, 1, 1), direction_ratio=[1, 1, 1]) == Ray3D(Point3D(1, 1, 1), Point3D(2, 2, 2)) + + +def test_issue_7814(): + circle = Circle(Point(x, 0), y) + line = Line(Point(k, z), slope=0) + _s = sqrt((y - z)*(y + z)) + assert line.intersection(circle) == [Point2D(x + _s, z), Point2D(x - _s, z)] + + +def test_issue_2941(): + def _check(): + for f, g in cartes(*[(Line, Ray, Segment)] * 2): + l1 = f(a, b) + l2 = g(c, d) + assert l1.intersection(l2) == l2.intersection(l1) + # intersect at end point + c, d = (-2, -2), (-2, 0) + a, b = (0, 0), (1, 1) + _check() + # midline intersection + c, d = (-2, -3), (-2, 0) + _check() + + +def test_parameter_value(): + t = Symbol('t') + p1, p2 = Point(0, 1), Point(5, 6) + l = Line(p1, p2) + assert l.parameter_value((5, 6), t) == {t: 1} + raises(ValueError, lambda: l.parameter_value((0, 0), t)) + + +def test_bisectors(): + r1 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0)) + r2 = Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0)) + bisections = r1.bisectors(r2) + assert bisections == [Line3D(Point3D(0, 0, 0), Point3D(1, 1, 0)), + Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))] + ans = [Line3D(Point3D(0, 0, 0), Point3D(1, 0, 1)), + Line3D(Point3D(0, 0, 0), Point3D(-1, 0, 1))] + l1 = (0, 0, 0), (0, 0, 1) + l2 = (0, 0), (1, 0) + for a, b in cartes((Line, Segment, Ray), repeat=2): + assert a(*l1).bisectors(b(*l2)) == ans + + +def test_issue_8615(): + a = Line3D(Point3D(6, 5, 0), Point3D(6, -6, 0)) + b = Line3D(Point3D(6, -1, 19/10), Point3D(6, -1, 0)) + assert a.intersection(b) == [Point3D(6, -1, 0)] + + +def test_issue_12598(): + r1 = Ray(Point(0, 1), Point(0.98, 0.79).n(2)) + r2 = Ray(Point(0, 0), Point(0.71, 0.71).n(2)) + assert str(r1.intersection(r2)[0]) == 'Point2D(0.82, 0.82)' + l1 = Line((0, 0), (1, 1)) + l2 = Segment((-1, 1), (0, -1)).n(2) + assert str(l1.intersection(l2)[0]) == 'Point2D(-0.33, -0.33)' + l2 = Segment((-1, 1), (-1/2, 1/2)).n(2) + assert not l1.intersection(l2) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_parabola.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_parabola.py new file mode 100644 index 0000000000000000000000000000000000000000..2a683f26619952d93475aca9ebd3d47cfb3657a6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_parabola.py @@ -0,0 +1,143 @@ +from sympy.core.numbers import (Rational, oo) +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.complexes import sign +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.geometry.ellipse import (Circle, Ellipse) +from sympy.geometry.line import (Line, Ray2D, Segment2D) +from sympy.geometry.parabola import Parabola +from sympy.geometry.point import (Point, Point2D) +from sympy.testing.pytest import raises + +from sympy.abc import x, y + +def test_parabola_geom(): + a, b = symbols('a b') + p1 = Point(0, 0) + p2 = Point(3, 7) + p3 = Point(0, 4) + p4 = Point(6, 0) + p5 = Point(a, a) + d1 = Line(Point(4, 0), Point(4, 9)) + d2 = Line(Point(7, 6), Point(3, 6)) + d3 = Line(Point(4, 0), slope=oo) + d4 = Line(Point(7, 6), slope=0) + d5 = Line(Point(b, a), slope=oo) + d6 = Line(Point(a, b), slope=0) + + half = S.Half + + pa1 = Parabola(None, d2) + pa2 = Parabola(directrix=d1) + pa3 = Parabola(p1, d1) + pa4 = Parabola(p2, d2) + pa5 = Parabola(p2, d4) + pa6 = Parabola(p3, d2) + pa7 = Parabola(p2, d1) + pa8 = Parabola(p4, d1) + pa9 = Parabola(p4, d3) + pa10 = Parabola(p5, d5) + pa11 = Parabola(p5, d6) + d = Line(Point(3, 7), Point(2, 9)) + pa12 = Parabola(Point(7, 8), d) + pa12r = Parabola(Point(7, 8).reflect(d), d) + + raises(ValueError, lambda: + Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7)))) + raises(ValueError, lambda: + Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2)))) + raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8))) + + # Basic Stuff + assert pa1.focus == Point(0, 0) + assert pa1.ambient_dimension == S(2) + assert pa2 == pa3 + assert pa4 != pa7 + assert pa6 != pa7 + assert pa6.focus == Point2D(0, 4) + assert pa6.focal_length == 1 + assert pa6.p_parameter == -1 + assert pa6.vertex == Point2D(0, 5) + assert pa6.eccentricity == 1 + assert pa7.focus == Point2D(3, 7) + assert pa7.focal_length == half + assert pa7.p_parameter == -half + assert pa7.vertex == Point2D(7*half, 7) + assert pa4.focal_length == half + assert pa4.p_parameter == half + assert pa4.vertex == Point2D(3, 13*half) + assert pa8.focal_length == 1 + assert pa8.p_parameter == 1 + assert pa8.vertex == Point2D(5, 0) + assert pa4.focal_length == pa5.focal_length + assert pa4.p_parameter == pa5.p_parameter + assert pa4.vertex == pa5.vertex + assert pa4.equation() == pa5.equation() + assert pa8.focal_length == pa9.focal_length + assert pa8.p_parameter == pa9.p_parameter + assert pa8.vertex == pa9.vertex + assert pa8.equation() == pa9.equation() + assert pa10.focal_length == pa11.focal_length == sqrt((a - b) ** 2) / 2 # if a, b real == abs(a - b)/2 + assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point(a, + a - sqrt((a - b)**2)*sign(a - b)/2) # change axis x->y, y->x on pa10 + aos = pa12.axis_of_symmetry + assert aos == Line(Point(7, 8), Point(5, 7)) + assert pa12.directrix == Line(Point(3, 7), Point(2, 9)) + assert pa12.directrix.angle_between(aos) == S.Pi/2 + assert pa12.eccentricity == 1 + assert pa12.equation(x, y) == (x - 7)**2 + (y - 8)**2 - (-2*x - y + 13)**2/5 + assert pa12.focal_length == 9*sqrt(5)/10 + assert pa12.focus == Point(7, 8) + assert pa12.p_parameter == 9*sqrt(5)/10 + assert pa12.vertex == Point2D(S(26)/5, S(71)/10) + assert pa12r.focal_length == 9*sqrt(5)/10 + assert pa12r.focus == Point(-S(1)/5, S(22)/5) + assert pa12r.p_parameter == -9*sqrt(5)/10 + assert pa12r.vertex == Point(S(8)/5, S(53)/10) + + +def test_parabola_intersection(): + l1 = Line(Point(1, -2), Point(-1,-2)) + l2 = Line(Point(1, 2), Point(-1,2)) + l3 = Line(Point(1, 0), Point(-1,0)) + + p1 = Point(0,0) + p2 = Point(0, -2) + p3 = Point(120, -12) + parabola1 = Parabola(p1, l1) + + # parabola with parabola + assert parabola1.intersection(parabola1) == [parabola1] + assert parabola1.intersection(Parabola(p1, l2)) == [Point2D(-2, 0), Point2D(2, 0)] + assert parabola1.intersection(Parabola(p2, l3)) == [Point2D(0, -1)] + assert parabola1.intersection(Parabola(Point(16, 0), l1)) == [Point2D(8, 15)] + assert parabola1.intersection(Parabola(Point(0, 16), l1)) == [Point2D(-6, 8), Point2D(6, 8)] + assert parabola1.intersection(Parabola(p3, l3)) == [] + # parabola with point + assert parabola1.intersection(p1) == [] + assert parabola1.intersection(Point2D(0, -1)) == [Point2D(0, -1)] + assert parabola1.intersection(Point2D(4, 3)) == [Point2D(4, 3)] + # parabola with line + assert parabola1.intersection(Line(Point2D(-7, 3), Point(12, 3))) == [Point2D(-4, 3), Point2D(4, 3)] + assert parabola1.intersection(Line(Point(-4, -1), Point(4, -1))) == [Point(0, -1)] + assert parabola1.intersection(Line(Point(2, 0), Point(0, -2))) == [Point2D(2, 0)] + raises(TypeError, lambda: parabola1.intersection(Line(Point(0, 0, 0), Point(1, 1, 1)))) + # parabola with segment + assert parabola1.intersection(Segment2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)] + assert parabola1.intersection(Segment2D((0, -5), (0, 6))) == [Point2D(0, -1)] + assert parabola1.intersection(Segment2D((-12, -65), (14, -68))) == [] + # parabola with ray + assert parabola1.intersection(Ray2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)] + assert parabola1.intersection(Ray2D((0, 7), (1, 14))) == [Point2D(14 + 2*sqrt(57), 105 + 14*sqrt(57))] + assert parabola1.intersection(Ray2D((0, 7), (0, 14))) == [] + # parabola with ellipse/circle + assert parabola1.intersection(Circle(p1, 2)) == [Point2D(-2, 0), Point2D(2, 0)] + assert parabola1.intersection(Circle(p2, 1)) == [Point2D(0, -1)] + assert parabola1.intersection(Ellipse(p2, 2, 1)) == [Point2D(0, -1)] + assert parabola1.intersection(Ellipse(Point(0, 19), 5, 7)) == [] + assert parabola1.intersection(Ellipse((0, 3), 12, 4)) == [ + Point2D(0, -1), + Point2D(-4*sqrt(17)/3, Rational(59, 9)), + Point2D(4*sqrt(17)/3, Rational(59, 9))] + # parabola with unsupported type + raises(TypeError, lambda: parabola1.intersection(2)) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_plane.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_plane.py new file mode 100644 index 0000000000000000000000000000000000000000..1010fce5c3bc68348eacee13f29c1d7588f17e39 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_plane.py @@ -0,0 +1,268 @@ +from sympy.core.numbers import (Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, symbols) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (asin, cos, sin) +from sympy.geometry import Line, Point, Ray, Segment, Point3D, Line3D, Ray3D, Segment3D, Plane, Circle +from sympy.geometry.util import are_coplanar +from sympy.testing.pytest import raises + + +def test_plane(): + x, y, z, u, v = symbols('x y z u v', real=True) + p1 = Point3D(0, 0, 0) + p2 = Point3D(1, 1, 1) + p3 = Point3D(1, 2, 3) + pl3 = Plane(p1, p2, p3) + pl4 = Plane(p1, normal_vector=(1, 1, 1)) + pl4b = Plane(p1, p2) + pl5 = Plane(p3, normal_vector=(1, 2, 3)) + pl6 = Plane(Point3D(2, 3, 7), normal_vector=(2, 2, 2)) + pl7 = Plane(Point3D(1, -5, -6), normal_vector=(1, -2, 1)) + pl8 = Plane(p1, normal_vector=(0, 0, 1)) + pl9 = Plane(p1, normal_vector=(0, 12, 0)) + pl10 = Plane(p1, normal_vector=(-2, 0, 0)) + pl11 = Plane(p2, normal_vector=(0, 0, 1)) + l1 = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1)) + l2 = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1)) + l3 = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9)) + + raises(ValueError, lambda: Plane(p1, p1, p1)) + + assert Plane(p1, p2, p3) != Plane(p1, p3, p2) + assert Plane(p1, p2, p3).is_coplanar(Plane(p1, p3, p2)) + assert Plane(p1, p2, p3).is_coplanar(p1) + assert Plane(p1, p2, p3).is_coplanar(Circle(p1, 1)) is False + assert Plane(p1, normal_vector=(0, 0, 1)).is_coplanar(Circle(p1, 1)) + + assert pl3 == Plane(Point3D(0, 0, 0), normal_vector=(1, -2, 1)) + assert pl3 != pl4 + assert pl4 == pl4b + assert pl5 == Plane(Point3D(1, 2, 3), normal_vector=(1, 2, 3)) + + assert pl5.equation(x, y, z) == x + 2*y + 3*z - 14 + assert pl3.equation(x, y, z) == x - 2*y + z + + assert pl3.p1 == p1 + assert pl4.p1 == p1 + assert pl5.p1 == p3 + + assert pl4.normal_vector == (1, 1, 1) + assert pl5.normal_vector == (1, 2, 3) + + assert p1 in pl3 + assert p1 in pl4 + assert p3 in pl5 + + assert pl3.projection(Point(0, 0)) == p1 + p = pl3.projection(Point3D(1, 1, 0)) + assert p == Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)) + assert p in pl3 + + l = pl3.projection_line(Line(Point(0, 0), Point(1, 1))) + assert l == Line3D(Point3D(0, 0, 0), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))) + assert l in pl3 + # get a segment that does not intersect the plane which is also + # parallel to pl3's normal veector + t = Dummy() + r = pl3.random_point() + a = pl3.perpendicular_line(r).arbitrary_point(t) + s = Segment3D(a.subs(t, 1), a.subs(t, 2)) + assert s.p1 not in pl3 and s.p2 not in pl3 + assert pl3.projection_line(s).equals(r) + assert pl3.projection_line(Segment(Point(1, 0), Point(1, 1))) == \ + Segment3D(Point3D(Rational(5, 6), Rational(1, 3), Rational(-1, 6)), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))) + assert pl6.projection_line(Ray(Point(1, 0), Point(1, 1))) == \ + Ray3D(Point3D(Rational(14, 3), Rational(11, 3), Rational(11, 3)), Point3D(Rational(13, 3), Rational(13, 3), Rational(10, 3))) + assert pl3.perpendicular_line(r.args) == pl3.perpendicular_line(r) + + assert pl3.is_parallel(pl6) is False + assert pl4.is_parallel(pl6) + assert pl3.is_parallel(Line(p1, p2)) + assert pl6.is_parallel(l1) is False + + assert pl3.is_perpendicular(pl6) + assert pl4.is_perpendicular(pl7) + assert pl6.is_perpendicular(pl7) + assert pl6.is_perpendicular(pl4) is False + assert pl6.is_perpendicular(l1) is False + assert pl6.is_perpendicular(Line((0, 0, 0), (1, 1, 1))) + assert pl6.is_perpendicular((1, 1)) is False + + assert pl6.distance(pl6.arbitrary_point(u, v)) == 0 + assert pl7.distance(pl7.arbitrary_point(u, v)) == 0 + assert pl6.distance(pl6.arbitrary_point(t)) == 0 + assert pl7.distance(pl7.arbitrary_point(t)) == 0 + assert pl6.p1.distance(pl6.arbitrary_point(t)).simplify() == 1 + assert pl7.p1.distance(pl7.arbitrary_point(t)).simplify() == 1 + assert pl3.arbitrary_point(t) == Point3D(-sqrt(30)*sin(t)/30 + \ + 2*sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/15 + sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/6) + assert pl3.arbitrary_point(u, v) == Point3D(2*u - v, u + 2*v, 5*v) + + assert pl7.distance(Point3D(1, 3, 5)) == 5*sqrt(6)/6 + assert pl6.distance(Point3D(0, 0, 0)) == 4*sqrt(3) + assert pl6.distance(pl6.p1) == 0 + assert pl7.distance(pl6) == 0 + assert pl7.distance(l1) == 0 + assert pl6.distance(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == \ + pl6.distance(Point3D(1, 3, 4)) == 4*sqrt(3)/3 + assert pl6.distance(Segment3D(Point3D(1, 3, 4), Point3D(0, 3, 7))) == \ + pl6.distance(Point3D(0, 3, 7)) == 2*sqrt(3)/3 + assert pl6.distance(Segment3D(Point3D(0, 3, 7), Point3D(-1, 3, 10))) == 0 + assert pl6.distance(Segment3D(Point3D(-1, 3, 10), Point3D(-2, 3, 13))) == 0 + assert pl6.distance(Segment3D(Point3D(-2, 3, 13), Point3D(-3, 3, 16))) == \ + pl6.distance(Point3D(-2, 3, 13)) == 2*sqrt(3)/3 + assert pl6.distance(Plane(Point3D(5, 5, 5), normal_vector=(8, 8, 8))) == sqrt(3) + assert pl6.distance(Ray3D(Point3D(1, 3, 4), direction_ratio=[1, 0, -3])) == 4*sqrt(3)/3 + assert pl6.distance(Ray3D(Point3D(2, 3, 1), direction_ratio=[-1, 0, 3])) == 0 + + + assert pl6.angle_between(pl3) == pi/2 + assert pl6.angle_between(pl6) == 0 + assert pl6.angle_between(pl4) == 0 + assert pl7.angle_between(Line3D(Point3D(2, 3, 5), Point3D(2, 4, 6))) == \ + -asin(sqrt(3)/6) + assert pl6.angle_between(Ray3D(Point3D(2, 4, 1), Point3D(6, 5, 3))) == \ + asin(sqrt(7)/3) + assert pl7.angle_between(Segment3D(Point3D(5, 6, 1), Point3D(1, 2, 4))) == \ + asin(7*sqrt(246)/246) + + assert are_coplanar(l1, l2, l3) is False + assert are_coplanar(l1) is False + assert are_coplanar(Point3D(2, 7, 2), Point3D(0, 0, 2), + Point3D(1, 1, 2), Point3D(1, 2, 2)) + assert are_coplanar(Plane(p1, p2, p3), Plane(p1, p3, p2)) + assert Plane.are_concurrent(pl3, pl4, pl5) is False + assert Plane.are_concurrent(pl6) is False + raises(ValueError, lambda: Plane.are_concurrent(Point3D(0, 0, 0))) + raises(ValueError, lambda: Plane((1, 2, 3), normal_vector=(0, 0, 0))) + + assert pl3.parallel_plane(Point3D(1, 2, 5)) == Plane(Point3D(1, 2, 5), \ + normal_vector=(1, -2, 1)) + + # perpendicular_plane + p = Plane((0, 0, 0), (1, 0, 0)) + # default + assert p.perpendicular_plane() == Plane(Point3D(0, 0, 0), (0, 1, 0)) + # 1 pt + assert p.perpendicular_plane(Point3D(1, 0, 1)) == \ + Plane(Point3D(1, 0, 1), (0, 1, 0)) + # pts as tuples + assert p.perpendicular_plane((1, 0, 1), (1, 1, 1)) == \ + Plane(Point3D(1, 0, 1), (0, 0, -1)) + # more than two planes + raises(ValueError, lambda: p.perpendicular_plane((1, 0, 1), (1, 1, 1), (1, 1, 0))) + + a, b = Point3D(0, 0, 0), Point3D(0, 1, 0) + Z = (0, 0, 1) + p = Plane(a, normal_vector=Z) + # case 4 + assert p.perpendicular_plane(a, b) == Plane(a, (1, 0, 0)) + n = Point3D(*Z) + # case 1 + assert p.perpendicular_plane(a, n) == Plane(a, (-1, 0, 0)) + # case 2 + assert Plane(a, normal_vector=b.args).perpendicular_plane(a, a + b) == \ + Plane(Point3D(0, 0, 0), (1, 0, 0)) + # case 1&3 + assert Plane(b, normal_vector=Z).perpendicular_plane(b, b + n) == \ + Plane(Point3D(0, 1, 0), (-1, 0, 0)) + # case 2&3 + assert Plane(b, normal_vector=b.args).perpendicular_plane(n, n + b) == \ + Plane(Point3D(0, 0, 1), (1, 0, 0)) + + p = Plane(a, normal_vector=(0, 0, 1)) + assert p.perpendicular_plane() == Plane(a, normal_vector=(1, 0, 0)) + + assert pl6.intersection(pl6) == [pl6] + assert pl4.intersection(pl4.p1) == [pl4.p1] + assert pl3.intersection(pl6) == [ + Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))] + assert pl3.intersection(Line3D(Point3D(1,2,4), Point3D(4,4,2))) == [ + Point3D(2, Rational(8, 3), Rational(10, 3))] + assert pl3.intersection(Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3)) + ) == [Line3D(Point3D(-24, -12, 0), Point3D(-25, -13, -1))] + assert pl6.intersection(Ray3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [ + Point3D(-1, 3, 10)] + assert pl6.intersection(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [] + assert pl7.intersection(Line(Point(2, 3), Point(4, 2))) == [ + Point3D(Rational(13, 2), Rational(3, 4), 0)] + r = Ray(Point(2, 3), Point(4, 2)) + assert Plane((1,2,0), normal_vector=(0,0,1)).intersection(r) == [ + Ray3D(Point(2, 3), Point(4, 2))] + assert pl9.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, 0))] + assert pl10.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(0, 2, 1))] + assert pl4.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))] + assert pl11.intersection(pl8) == [] + assert pl9.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(12, 0, 1))] + assert pl9.intersection(pl4) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, -12))] + assert pl3.random_point() in pl3 + assert pl3.random_point(seed=1) in pl3 + + # test geometrical entity using equals + assert pl4.intersection(pl4.p1)[0].equals(pl4.p1) + assert pl3.intersection(pl6)[0].equals(Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))) + pl8 = Plane((1, 2, 0), normal_vector=(0, 0, 1)) + assert pl8.intersection(Line3D(p1, (1, 12, 0)))[0].equals(Line((0, 0, 0), (0.1, 1.2, 0))) + assert pl8.intersection(Ray3D(p1, (1, 12, 0)))[0].equals(Ray((0, 0, 0), (1, 12, 0))) + assert pl8.intersection(Segment3D(p1, (21, 1, 0)))[0].equals(Segment3D(p1, (21, 1, 0))) + assert pl8.intersection(Plane(p1, normal_vector=(0, 0, 112)))[0].equals(pl8) + assert pl8.intersection(Plane(p1, normal_vector=(0, 12, 0)))[0].equals( + Line3D(p1, direction_ratio=(112 * pi, 0, 0))) + assert pl8.intersection(Plane(p1, normal_vector=(11, 0, 1)))[0].equals( + Line3D(p1, direction_ratio=(0, -11, 0))) + assert pl8.intersection(Plane(p1, normal_vector=(1, 0, 11)))[0].equals( + Line3D(p1, direction_ratio=(0, 11, 0))) + assert pl8.intersection(Plane(p1, normal_vector=(-1, -1, -11)))[0].equals( + Line3D(p1, direction_ratio=(1, -1, 0))) + assert pl3.random_point() in pl3 + assert len(pl8.intersection(Ray3D(Point3D(0, 2, 3), Point3D(1, 0, 3)))) == 0 + # check if two plane are equals + assert pl6.intersection(pl6)[0].equals(pl6) + assert pl8.equals(Plane(p1, normal_vector=(0, 12, 0))) is False + assert pl8.equals(pl8) + assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12))) + assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12*sqrt(3)))) + assert pl8.equals(p1) is False + + # issue 8570 + l2 = Line3D(Point3D(Rational(50000004459633, 5000000000000), + Rational(-891926590718643, 1000000000000000), + Rational(231800966893633, 100000000000000)), + Point3D(Rational(50000004459633, 50000000000000), + Rational(-222981647679771, 250000000000000), + Rational(231800966893633, 100000000000000))) + + p2 = Plane(Point3D(Rational(402775636372767, 100000000000000), + Rational(-97224357654973, 100000000000000), + Rational(216793600814789, 100000000000000)), + (-S('9.00000087501922'), -S('4.81170658872543e-13'), + S('0.0'))) + + assert str([i.n(2) for i in p2.intersection(l2)]) == \ + '[Point3D(4.0, -0.89, 2.3)]' + + +def test_dimension_normalization(): + A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1)) + b = Point(1, 1) + assert A.projection(b) == Point(Rational(5, 3), Rational(5, 3), Rational(2, 3)) + + a, b = Point(0, 0), Point3D(0, 1) + Z = (0, 0, 1) + p = Plane(a, normal_vector=Z) + assert p.perpendicular_plane(a, b) == Plane(Point3D(0, 0, 0), (1, 0, 0)) + assert Plane((1, 2, 1), (2, 1, 0), (3, 1, 2) + ).intersection((2, 1)) == [Point(2, 1, 0)] + + +def test_parameter_value(): + t, u, v = symbols("t, u v") + p1, p2, p3 = Point(0, 0, 0), Point(0, 0, 1), Point(0, 1, 0) + p = Plane(p1, p2, p3) + assert p.parameter_value((0, -3, 2), t) == {t: asin(2*sqrt(13)/13)} + assert p.parameter_value((0, -3, 2), u, v) == {u: 3, v: 2} + assert p.parameter_value(p1, t) == p1 + raises(ValueError, lambda: p.parameter_value((1, 0, 0), t)) + raises(ValueError, lambda: p.parameter_value(Line(Point(0, 0), Point(1, 1)), t)) + raises(ValueError, lambda: p.parameter_value((0, -3, 2), t, 1)) diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_point.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_point.py new file mode 100644 index 0000000000000000000000000000000000000000..abe63874a84ea9426c31bdd517b9282b779cc52b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_point.py @@ -0,0 +1,481 @@ +from sympy.core.basic import Basic +from sympy.core.numbers import (I, Rational, pi) +from sympy.core.parameters import evaluate +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.geometry import Line, Point, Point2D, Point3D, Line3D, Plane +from sympy.geometry.entity import rotate, scale, translate, GeometryEntity +from sympy.matrices import Matrix +from sympy.utilities.iterables import subsets, permutations, cartes +from sympy.utilities.misc import Undecidable +from sympy.testing.pytest import raises, warns + + +def test_point(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + x1 = Symbol('x1', real=True) + x2 = Symbol('x2', real=True) + y1 = Symbol('y1', real=True) + y2 = Symbol('y2', real=True) + half = S.Half + p1 = Point(x1, x2) + p2 = Point(y1, y2) + p3 = Point(0, 0) + p4 = Point(1, 1) + p5 = Point(0, 1) + line = Line(Point(1, 0), slope=1) + + assert p1 in p1 + assert p1 not in p2 + assert p2.y == y2 + assert (p3 + p4) == p4 + assert (p2 - p1) == Point(y1 - x1, y2 - x2) + assert -p2 == Point(-y1, -y2) + raises(TypeError, lambda: Point(1)) + raises(ValueError, lambda: Point([1])) + raises(ValueError, lambda: Point(3, I)) + raises(ValueError, lambda: Point(2*I, I)) + raises(ValueError, lambda: Point(3 + I, I)) + + assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3)) + assert Point.midpoint(p3, p4) == Point(half, half) + assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2) + assert Point.midpoint(p2, p2) == p2 + assert p2.midpoint(p2) == p2 + assert p1.origin == Point(0, 0) + + assert Point.distance(p3, p4) == sqrt(2) + assert Point.distance(p1, p1) == 0 + assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2) + raises(TypeError, lambda: Point.distance(p1, 0)) + raises(TypeError, lambda: Point.distance(p1, GeometryEntity())) + + # distance should be symmetric + assert p1.distance(line) == line.distance(p1) + assert p4.distance(line) == line.distance(p4) + + assert Point.taxicab_distance(p4, p3) == 2 + + assert Point.canberra_distance(p4, p5) == 1 + raises(ValueError, lambda: Point.canberra_distance(p3, p3)) + + p1_1 = Point(x1, x1) + p1_2 = Point(y2, y2) + p1_3 = Point(x1 + 1, x1) + assert Point.is_collinear(p3) + + with warns(UserWarning, test_stacklevel=False): + assert Point.is_collinear(p3, Point(p3, dim=4)) + assert p3.is_collinear() + assert Point.is_collinear(p3, p4) + assert Point.is_collinear(p3, p4, p1_1, p1_2) + assert Point.is_collinear(p3, p4, p1_1, p1_3) is False + assert Point.is_collinear(p3, p3, p4, p5) is False + + raises(TypeError, lambda: Point.is_collinear(line)) + raises(TypeError, lambda: p1_1.is_collinear(line)) + + assert p3.intersection(Point(0, 0)) == [p3] + assert p3.intersection(p4) == [] + assert p3.intersection(line) == [] + with warns(UserWarning, test_stacklevel=False): + assert Point.intersection(Point(0, 0, 0), Point(0, 0)) == [Point(0, 0, 0)] + + x_pos = Symbol('x', positive=True) + p2_1 = Point(x_pos, 0) + p2_2 = Point(0, x_pos) + p2_3 = Point(-x_pos, 0) + p2_4 = Point(0, -x_pos) + p2_5 = Point(x_pos, 5) + assert Point.is_concyclic(p2_1) + assert Point.is_concyclic(p2_1, p2_2) + assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4) + for pts in permutations((p2_1, p2_2, p2_3, p2_5)): + assert Point.is_concyclic(*pts) is False + assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False + assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) is False + assert Point.is_concyclic(Point(0, 0, 0, 0), Point(1, 0, 0, 0), Point(1, 1, 0, 0), Point(1, 1, 1, 0)) is False + + assert p1.is_scalar_multiple(p1) + assert p1.is_scalar_multiple(2*p1) + assert not p1.is_scalar_multiple(p2) + assert Point.is_scalar_multiple(Point(1, 1), (-1, -1)) + assert Point.is_scalar_multiple(Point(0, 0), (0, -1)) + # test when is_scalar_multiple can't be determined + raises(Undecidable, lambda: Point.is_scalar_multiple(Point(sympify("x1%y1"), sympify("x2%y2")), Point(0, 1))) + + assert Point(0, 1).orthogonal_direction == Point(1, 0) + assert Point(1, 0).orthogonal_direction == Point(0, 1) + + assert p1.is_zero is None + assert p3.is_zero + assert p4.is_zero is False + assert p1.is_nonzero is None + assert p3.is_nonzero is False + assert p4.is_nonzero + + assert p4.scale(2, 3) == Point(2, 3) + assert p3.scale(2, 3) == p3 + + assert p4.rotate(pi, Point(0.5, 0.5)) == p3 + assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2) + assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2) + + assert p4 * 5 == Point(5, 5) + assert p4 / 5 == Point(0.2, 0.2) + assert 5 * p4 == Point(5, 5) + + raises(ValueError, lambda: Point(0, 0) + 10) + + # Point differences should be simplified + assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1) + + a, b = S.Half, Rational(1, 3) + assert Point(a, b).evalf(2) == \ + Point(a.n(2), b.n(2), evaluate=False) + raises(ValueError, lambda: Point(1, 2) + 1) + + # test project + assert Point.project((0, 1), (1, 0)) == Point(0, 0) + assert Point.project((1, 1), (1, 0)) == Point(1, 0) + raises(ValueError, lambda: Point.project(p1, Point(0, 0))) + + # test transformations + p = Point(1, 0) + assert p.rotate(pi/2) == Point(0, 1) + assert p.rotate(pi/2, p) == p + p = Point(1, 1) + assert p.scale(2, 3) == Point(2, 3) + assert p.translate(1, 2) == Point(2, 3) + assert p.translate(1) == Point(2, 1) + assert p.translate(y=1) == Point(1, 2) + assert p.translate(*p.args) == Point(2, 2) + + # Check invalid input for transform + raises(ValueError, lambda: p3.transform(p3)) + raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]]))) + + # test __contains__ + assert 0 in Point(0, 0, 0, 0) + assert 1 not in Point(0, 0, 0, 0) + + # test affine_rank + assert Point.affine_rank() == -1 + + +def test_point3D(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + x1 = Symbol('x1', real=True) + x2 = Symbol('x2', real=True) + x3 = Symbol('x3', real=True) + y1 = Symbol('y1', real=True) + y2 = Symbol('y2', real=True) + y3 = Symbol('y3', real=True) + half = S.Half + p1 = Point3D(x1, x2, x3) + p2 = Point3D(y1, y2, y3) + p3 = Point3D(0, 0, 0) + p4 = Point3D(1, 1, 1) + p5 = Point3D(0, 1, 2) + + assert p1 in p1 + assert p1 not in p2 + assert p2.y == y2 + assert (p3 + p4) == p4 + assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3) + assert -p2 == Point3D(-y1, -y2, -y3) + + assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3)) + assert Point3D.midpoint(p3, p4) == Point3D(half, half, half) + assert Point3D.midpoint(p1, p4) == Point3D(half + half*x1, half + half*x2, + half + half*x3) + assert Point3D.midpoint(p2, p2) == p2 + assert p2.midpoint(p2) == p2 + + assert Point3D.distance(p3, p4) == sqrt(3) + assert Point3D.distance(p1, p1) == 0 + assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2) + + p1_1 = Point3D(x1, x1, x1) + p1_2 = Point3D(y2, y2, y2) + p1_3 = Point3D(x1 + 1, x1, x1) + Point3D.are_collinear(p3) + assert Point3D.are_collinear(p3, p4) + assert Point3D.are_collinear(p3, p4, p1_1, p1_2) + assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False + assert Point3D.are_collinear(p3, p3, p4, p5) is False + + assert p3.intersection(Point3D(0, 0, 0)) == [p3] + assert p3.intersection(p4) == [] + + + assert p4 * 5 == Point3D(5, 5, 5) + assert p4 / 5 == Point3D(0.2, 0.2, 0.2) + assert 5 * p4 == Point3D(5, 5, 5) + + raises(ValueError, lambda: Point3D(0, 0, 0) + 10) + + # Test coordinate properties + assert p1.coordinates == (x1, x2, x3) + assert p2.coordinates == (y1, y2, y3) + assert p3.coordinates == (0, 0, 0) + assert p4.coordinates == (1, 1, 1) + assert p5.coordinates == (0, 1, 2) + assert p5.x == 0 + assert p5.y == 1 + assert p5.z == 2 + + # Point differences should be simplified + assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \ + Point3D(0, -1, 1) + + a, b, c = S.Half, Rational(1, 3), Rational(1, 4) + assert Point3D(a, b, c).evalf(2) == \ + Point(a.n(2), b.n(2), c.n(2), evaluate=False) + raises(ValueError, lambda: Point3D(1, 2, 3) + 1) + + # test transformations + p = Point3D(1, 1, 1) + assert p.scale(2, 3) == Point3D(2, 3, 1) + assert p.translate(1, 2) == Point3D(2, 3, 1) + assert p.translate(1) == Point3D(2, 1, 1) + assert p.translate(z=1) == Point3D(1, 1, 2) + assert p.translate(*p.args) == Point3D(2, 2, 2) + + # Test __new__ + assert Point3D(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float + + # Test length property returns correctly + assert p.length == 0 + assert p1_1.length == 0 + assert p1_2.length == 0 + + # Test are_colinear type error + raises(TypeError, lambda: Point3D.are_collinear(p, x)) + + # Test are_coplanar + assert Point.are_coplanar() + assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0)) + assert Point.are_coplanar((1, 2, 0), (1, 2, 3)) + with warns(UserWarning, test_stacklevel=False): + raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3))) + assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3)) + assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False + planar2 = Point3D(1, -1, 1) + planar3 = Point3D(-1, 1, 1) + assert Point3D.are_coplanar(p, planar2, planar3) == True + assert Point3D.are_coplanar(p, planar2, planar3, p3) == False + assert Point.are_coplanar(p, planar2) + planar2 = Point3D(1, 1, 2) + planar3 = Point3D(1, 1, 3) + assert Point3D.are_coplanar(p, planar2, planar3) # line, not plane + plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2)) + assert Point.are_coplanar(*[plane.projection(((-1)**i, i)) for i in range(4)]) + + # all 2D points are coplanar + assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(y, x + 2)) is True + + # Test Intersection + assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)] + + # Test Scale + assert planar2.scale(1, 1, 1) == planar2 + assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1) + assert planar2.scale(1, 1, 1, p3) == planar2 + + # Test Transform + identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) + assert p.transform(identity) == p + trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]]) + assert p.transform(trans) == Point3D(2, 2, 2) + raises(ValueError, lambda: p.transform(p)) + raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]]))) + + # Test Equals + assert p.equals(x1) == False + + # Test __sub__ + p_4d = Point(0, 0, 0, 1) + with warns(UserWarning, test_stacklevel=False): + assert p - p_4d == Point(1, 1, 1, -1) + p_4d3d = Point(0, 0, 1, 0) + with warns(UserWarning, test_stacklevel=False): + assert p - p_4d3d == Point(1, 1, 0, 0) + + +def test_Point2D(): + + # Test Distance + p1 = Point2D(1, 5) + p2 = Point2D(4, 2.5) + p3 = (6, 3) + assert p1.distance(p2) == sqrt(61)/2 + assert p2.distance(p3) == sqrt(17)/2 + + # Test coordinates + assert p1.x == 1 + assert p1.y == 5 + assert p2.x == 4 + assert p2.y == S(5)/2 + assert p1.coordinates == (1, 5) + assert p2.coordinates == (4, S(5)/2) + + # test bounds + assert p1.bounds == (1, 5, 1, 5) + +def test_issue_9214(): + p1 = Point3D(4, -2, 6) + p2 = Point3D(1, 2, 3) + p3 = Point3D(7, 2, 3) + + assert Point3D.are_collinear(p1, p2, p3) is False + + +def test_issue_11617(): + p1 = Point3D(1,0,2) + p2 = Point2D(2,0) + + with warns(UserWarning, test_stacklevel=False): + assert p1.distance(p2) == sqrt(5) + + +def test_transform(): + p = Point(1, 1) + assert p.transform(rotate(pi/2)) == Point(-1, 1) + assert p.transform(scale(3, 2)) == Point(3, 2) + assert p.transform(translate(1, 2)) == Point(2, 3) + assert Point(1, 1).scale(2, 3, (4, 5)) == \ + Point(-2, -7) + assert Point(1, 1).translate(4, 5) == \ + Point(5, 6) + + +def test_concyclic_doctest_bug(): + p1, p2 = Point(-1, 0), Point(1, 0) + p3, p4 = Point(0, 1), Point(-1, 2) + assert Point.is_concyclic(p1, p2, p3) + assert not Point.is_concyclic(p1, p2, p3, p4) + + +def test_arguments(): + """Functions accepting `Point` objects in `geometry` + should also accept tuples and lists and + automatically convert them to points.""" + + singles2d = ((1,2), [1,2], Point(1,2)) + singles2d2 = ((1,3), [1,3], Point(1,3)) + doubles2d = cartes(singles2d, singles2d2) + p2d = Point2D(1,2) + singles3d = ((1,2,3), [1,2,3], Point(1,2,3)) + doubles3d = subsets(singles3d, 2) + p3d = Point3D(1,2,3) + singles4d = ((1,2,3,4), [1,2,3,4], Point(1,2,3,4)) + doubles4d = subsets(singles4d, 2) + p4d = Point(1,2,3,4) + + # test 2D + test_single = ['distance', 'is_scalar_multiple', 'taxicab_distance', 'midpoint', 'intersection', 'dot', 'equals', '__add__', '__sub__'] + test_double = ['is_concyclic', 'is_collinear'] + for p in singles2d: + Point2D(p) + for func in test_single: + for p in singles2d: + getattr(p2d, func)(p) + for func in test_double: + for p in doubles2d: + getattr(p2d, func)(*p) + + # test 3D + test_double = ['is_collinear'] + for p in singles3d: + Point3D(p) + for func in test_single: + for p in singles3d: + getattr(p3d, func)(p) + for func in test_double: + for p in doubles3d: + getattr(p3d, func)(*p) + + # test 4D + test_double = ['is_collinear'] + for p in singles4d: + Point(p) + for func in test_single: + for p in singles4d: + getattr(p4d, func)(p) + for func in test_double: + for p in doubles4d: + getattr(p4d, func)(*p) + + # test evaluate=False for ops + x = Symbol('x') + a = Point(0, 1) + assert a + (0.1, x) == Point(0.1, 1 + x, evaluate=False) + a = Point(0, 1) + assert a/10.0 == Point(0, 0.1, evaluate=False) + a = Point(0, 1) + assert a*10.0 == Point(0.0, 10.0, evaluate=False) + + # test evaluate=False when changing dimensions + u = Point(.1, .2, evaluate=False) + u4 = Point(u, dim=4, on_morph='ignore') + assert u4.args == (.1, .2, 0, 0) + assert all(i.is_Float for i in u4.args[:2]) + # and even when *not* changing dimensions + assert all(i.is_Float for i in Point(u).args) + + # never raise error if creating an origin + assert Point(dim=3, on_morph='error') + + # raise error with unmatched dimension + raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='error')) + # test unknown on_morph + raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='unknown')) + # test invalid expressions + raises(TypeError, lambda: Point(Basic(), Basic())) + +def test_unit(): + assert Point(1, 1).unit == Point(sqrt(2)/2, sqrt(2)/2) + + +def test_dot(): + raises(TypeError, lambda: Point(1, 2).dot(Line((0, 0), (1, 1)))) + + +def test__normalize_dimension(): + assert Point._normalize_dimension(Point(1, 2), Point(3, 4)) == [ + Point(1, 2), Point(3, 4)] + assert Point._normalize_dimension( + Point(1, 2), Point(3, 4, 0), on_morph='ignore') == [ + Point(1, 2, 0), Point(3, 4, 0)] + + +def test_issue_22684(): + # Used to give an error + with evaluate(False): + Point(1, 2) + + +def test_direction_cosine(): + p1 = Point3D(0, 0, 0) + p2 = Point3D(1, 1, 1) + + assert p1.direction_cosine(Point3D(1, 0, 0)) == [1, 0, 0] + assert p1.direction_cosine(Point3D(0, 1, 0)) == [0, 1, 0] + assert p1.direction_cosine(Point3D(0, 0, pi)) == [0, 0, 1] + + assert p1.direction_cosine(Point3D(5, 0, 0)) == [1, 0, 0] + assert p1.direction_cosine(Point3D(0, sqrt(3), 0)) == [0, 1, 0] + assert p1.direction_cosine(Point3D(0, 0, 5)) == [0, 0, 1] + + assert p1.direction_cosine(Point3D(2.4, 2.4, 0)) == [sqrt(2)/2, sqrt(2)/2, 0] + assert p1.direction_cosine(Point3D(1, 1, 1)) == [sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3] + assert p1.direction_cosine(Point3D(-12, 0 -15)) == [-4*sqrt(41)/41, -5*sqrt(41)/41, 0] + + assert p2.direction_cosine(Point3D(0, 0, 0)) == [-sqrt(3) / 3, -sqrt(3) / 3, -sqrt(3) / 3] + assert p2.direction_cosine(Point3D(1, 1, 12)) == [0, 0, 1] + assert p2.direction_cosine(Point3D(12, 1, 12)) == [sqrt(2) / 2, 0, sqrt(2) / 2] diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_polygon.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_polygon.py new file mode 100644 index 0000000000000000000000000000000000000000..976d71078a4ef8d535a9508a64f414c80da16847 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_polygon.py @@ -0,0 +1,676 @@ +from sympy.core.numbers import (Float, Rational, oo, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (acos, cos, sin) +from sympy.functions.elementary.trigonometric import tan +from sympy.geometry import (Circle, Ellipse, GeometryError, Point, Point2D, + Polygon, Ray, RegularPolygon, Segment, Triangle, + are_similar, convex_hull, intersection, Line, Ray2D) +from sympy.testing.pytest import raises, slow, warns +from sympy.core.random import verify_numerically +from sympy.geometry.polygon import rad, deg +from sympy.integrals.integrals import integrate +from sympy.utilities.iterables import rotate_left + + +def feq(a, b): + """Test if two floating point values are 'equal'.""" + t_float = Float("1.0E-10") + return -t_float < a - b < t_float + +@slow +def test_polygon(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + q = Symbol('q', real=True) + u = Symbol('u', real=True) + v = Symbol('v', real=True) + w = Symbol('w', real=True) + x1 = Symbol('x1', real=True) + half = S.Half + a, b, c = Point(0, 0), Point(2, 0), Point(3, 3) + t = Triangle(a, b, c) + assert Polygon(Point(0, 0)) == Point(0, 0) + assert Polygon(a, Point(1, 0), b, c) == t + assert Polygon(Point(1, 0), b, c, a) == t + assert Polygon(b, c, a, Point(1, 0)) == t + # 2 "remove folded" tests + assert Polygon(a, Point(3, 0), b, c) == t + assert Polygon(a, b, Point(3, -1), b, c) == t + # remove multiple collinear points + assert Polygon(Point(-4, 15), Point(-11, 15), Point(-15, 15), + Point(-15, 33/5), Point(-15, -87/10), Point(-15, -15), + Point(-42/5, -15), Point(-2, -15), Point(7, -15), Point(15, -15), + Point(15, -3), Point(15, 10), Point(15, 15)) == \ + Polygon(Point(-15, -15), Point(15, -15), Point(15, 15), Point(-15, 15)) + + p1 = Polygon( + Point(0, 0), Point(3, -1), + Point(6, 0), Point(4, 5), + Point(2, 3), Point(0, 3)) + p2 = Polygon( + Point(6, 0), Point(3, -1), + Point(0, 0), Point(0, 3), + Point(2, 3), Point(4, 5)) + p3 = Polygon( + Point(0, 0), Point(3, 0), + Point(5, 2), Point(4, 4)) + p4 = Polygon( + Point(0, 0), Point(4, 4), + Point(5, 2), Point(3, 0)) + p5 = Polygon( + Point(0, 0), Point(4, 4), + Point(0, 4)) + p6 = Polygon( + Point(-11, 1), Point(-9, 6.6), + Point(-4, -3), Point(-8.4, -8.7)) + p7 = Polygon( + Point(x, y), Point(q, u), + Point(v, w)) + p8 = Polygon( + Point(x, y), Point(v, w), + Point(q, u)) + p9 = Polygon( + Point(0, 0), Point(4, 4), + Point(3, 0), Point(5, 2)) + p10 = Polygon( + Point(0, 2), Point(2, 2), + Point(0, 0), Point(2, 0)) + p11 = Polygon(Point(0, 0), 1, n=3) + p12 = Polygon(Point(0, 0), 1, 0, n=3) + p13 = Polygon( + Point(0, 0),Point(8, 8), + Point(23, 20),Point(0, 20)) + p14 = Polygon(*rotate_left(p13.args, 1)) + + + r = Ray(Point(-9, 6.6), Point(-9, 5.5)) + # + # General polygon + # + assert p1 == p2 + assert len(p1.args) == 6 + assert len(p1.sides) == 6 + assert p1.perimeter == 5 + 2*sqrt(10) + sqrt(29) + sqrt(8) + assert p1.area == 22 + assert not p1.is_convex() + assert Polygon((-1, 1), (2, -1), (2, 1), (-1, -1), (3, 0) + ).is_convex() is False + # ensure convex for both CW and CCW point specification + assert p3.is_convex() + assert p4.is_convex() + dict5 = p5.angles + assert dict5[Point(0, 0)] == pi / 4 + assert dict5[Point(0, 4)] == pi / 2 + assert p5.encloses_point(Point(x, y)) is None + assert p5.encloses_point(Point(1, 3)) + assert p5.encloses_point(Point(0, 0)) is False + assert p5.encloses_point(Point(4, 0)) is False + assert p1.encloses(Circle(Point(2.5, 2.5), 5)) is False + assert p1.encloses(Ellipse(Point(2.5, 2), 5, 6)) is False + assert p5.plot_interval('x') == [x, 0, 1] + assert p5.distance( + Polygon(Point(10, 10), Point(14, 14), Point(10, 14))) == 6 * sqrt(2) + assert p5.distance( + Polygon(Point(1, 8), Point(5, 8), Point(8, 12), Point(1, 12))) == 4 + with warns(UserWarning, \ + match="Polygons may intersect producing erroneous output"): + Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance( + Polygon(Point(0, 0), Point(0, 1), Point(1, 1))) + assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4))) + assert hash(p1) == hash(p2) + assert hash(p7) == hash(p8) + assert hash(p3) != hash(p9) + assert p5 == Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) + assert Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) in p5 + assert p5 != Point(0, 4) + assert Point(0, 1) in p5 + assert p5.arbitrary_point('t').subs(Symbol('t', real=True), 0) == \ + Point(0, 0) + raises(ValueError, lambda: Polygon( + Point(x, 0), Point(0, y), Point(x, y)).arbitrary_point('x')) + assert p6.intersection(r) == [Point(-9, Rational(-84, 13)), Point(-9, Rational(33, 5))] + assert p10.area == 0 + assert p11 == RegularPolygon(Point(0, 0), 1, 3, 0) + assert p11 == p12 + assert p11.vertices[0] == Point(1, 0) + assert p11.args[0] == Point(0, 0) + p11.spin(pi/2) + assert p11.vertices[0] == Point(0, 1) + # + # Regular polygon + # + p1 = RegularPolygon(Point(0, 0), 10, 5) + p2 = RegularPolygon(Point(0, 0), 5, 5) + raises(GeometryError, lambda: RegularPolygon(Point(0, 0), Point(0, + 1), Point(1, 1))) + raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2)) + raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5)) + + assert p1 != p2 + assert p1.interior_angle == pi*Rational(3, 5) + assert p1.exterior_angle == pi*Rational(2, 5) + assert p2.apothem == 5*cos(pi/5) + assert p2.circumcenter == p1.circumcenter == Point(0, 0) + assert p1.circumradius == p1.radius == 10 + assert p2.circumcircle == Circle(Point(0, 0), 5) + assert p2.incircle == Circle(Point(0, 0), p2.apothem) + assert p2.inradius == p2.apothem == (5 * (1 + sqrt(5)) / 4) + p2.spin(pi / 10) + dict1 = p2.angles + assert dict1[Point(0, 5)] == 3 * pi / 5 + assert p1.is_convex() + assert p1.rotation == 0 + assert p1.encloses_point(Point(0, 0)) + assert p1.encloses_point(Point(11, 0)) is False + assert p2.encloses_point(Point(0, 4.9)) + p1.spin(pi/3) + assert p1.rotation == pi/3 + assert p1.vertices[0] == Point(5, 5*sqrt(3)) + for var in p1.args: + if isinstance(var, Point): + assert var == Point(0, 0) + else: + assert var in (5, 10, pi / 3) + assert p1 != Point(0, 0) + assert p1 != p5 + + # while spin works in place (notice that rotation is 2pi/3 below) + # rotate returns a new object + p1_old = p1 + assert p1.rotate(pi/3) == RegularPolygon(Point(0, 0), 10, 5, pi*Rational(2, 3)) + assert p1 == p1_old + + assert p1.area == (-250*sqrt(5) + 1250)/(4*tan(pi/5)) + assert p1.length == 20*sqrt(-sqrt(5)/8 + Rational(5, 8)) + assert p1.scale(2, 2) == \ + RegularPolygon(p1.center, p1.radius*2, p1._n, p1.rotation) + assert RegularPolygon((0, 0), 1, 4).scale(2, 3) == \ + Polygon(Point(2, 0), Point(0, 3), Point(-2, 0), Point(0, -3)) + + assert repr(p1) == str(p1) + + # + # Angles + # + angles = p4.angles + assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) + assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) + assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) + assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) + + angles = p3.angles + assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) + assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) + assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) + assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) + + # https://github.com/sympy/sympy/issues/24885 + interior_angles_sum = sum(p13.angles.values()) + assert feq(interior_angles_sum, (len(p13.angles) - 2)*pi ) + interior_angles_sum = sum(p14.angles.values()) + assert feq(interior_angles_sum, (len(p14.angles) - 2)*pi ) + + # + # Triangle + # + p1 = Point(0, 0) + p2 = Point(5, 0) + p3 = Point(0, 5) + t1 = Triangle(p1, p2, p3) + t2 = Triangle(p1, p2, Point(Rational(5, 2), sqrt(Rational(75, 4)))) + t3 = Triangle(p1, Point(x1, 0), Point(0, x1)) + s1 = t1.sides + assert Triangle(p1, p2, p1) == Polygon(p1, p2, p1) == Segment(p1, p2) + raises(GeometryError, lambda: Triangle(Point(0, 0))) + + # Basic stuff + assert Triangle(p1, p1, p1) == p1 + assert Triangle(p2, p2*2, p2*3) == Segment(p2, p2*3) + assert t1.area == Rational(25, 2) + assert t1.is_right() + assert t2.is_right() is False + assert t3.is_right() + assert p1 in t1 + assert t1.sides[0] in t1 + assert Segment((0, 0), (1, 0)) in t1 + assert Point(5, 5) not in t2 + assert t1.is_convex() + assert feq(t1.angles[p1].evalf(), pi.evalf()/2) + + assert t1.is_equilateral() is False + assert t2.is_equilateral() + assert t3.is_equilateral() is False + assert are_similar(t1, t2) is False + assert are_similar(t1, t3) + assert are_similar(t2, t3) is False + assert t1.is_similar(Point(0, 0)) is False + assert t1.is_similar(t2) is False + + # Bisectors + bisectors = t1.bisectors() + assert bisectors[p1] == Segment( + p1, Point(Rational(5, 2), Rational(5, 2))) + assert t2.bisectors()[p2] == Segment( + Point(5, 0), Point(Rational(5, 4), 5*sqrt(3)/4)) + p4 = Point(0, x1) + assert t3.bisectors()[p4] == Segment(p4, Point(x1*(sqrt(2) - 1), 0)) + ic = (250 - 125*sqrt(2))/50 + assert t1.incenter == Point(ic, ic) + + # Inradius + assert t1.inradius == t1.incircle.radius == 5 - 5*sqrt(2)/2 + assert t2.inradius == t2.incircle.radius == 5*sqrt(3)/6 + assert t3.inradius == t3.incircle.radius == x1**2/((2 + sqrt(2))*Abs(x1)) + + # Exradius + assert t1.exradii[t1.sides[2]] == 5*sqrt(2)/2 + + # Excenters + assert t1.excenters[t1.sides[2]] == Point2D(25*sqrt(2), -5*sqrt(2)/2) + + # Circumcircle + assert t1.circumcircle.center == Point(2.5, 2.5) + + # Medians + Centroid + m = t1.medians + assert t1.centroid == Point(Rational(5, 3), Rational(5, 3)) + assert m[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) + assert t3.medians[p1] == Segment(p1, Point(x1/2, x1/2)) + assert intersection(m[p1], m[p2], m[p3]) == [t1.centroid] + assert t1.medial == Triangle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5)) + + # Nine-point circle + assert t1.nine_point_circle == Circle(Point(2.5, 0), + Point(0, 2.5), Point(2.5, 2.5)) + assert t1.nine_point_circle == Circle(Point(0, 0), + Point(0, 2.5), Point(2.5, 2.5)) + + # Perpendicular + altitudes = t1.altitudes + assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) + assert altitudes[p2].equals(s1[0]) + assert altitudes[p3] == s1[2] + assert t1.orthocenter == p1 + t = S('''Triangle( + Point(100080156402737/5000000000000, 79782624633431/500000000000), + Point(39223884078253/2000000000000, 156345163124289/1000000000000), + Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''') + assert t.orthocenter == S('''Point(-780660869050599840216997''' + '''79471538701955848721853/80368430960602242240789074233100000000000000,''' + '''20151573611150265741278060334545897615974257/16073686192120448448157''' + '''8148466200000000000)''') + + # Ensure + assert len(intersection(*bisectors.values())) == 1 + assert len(intersection(*altitudes.values())) == 1 + assert len(intersection(*m.values())) == 1 + + # Distance + p1 = Polygon( + Point(0, 0), Point(1, 0), + Point(1, 1), Point(0, 1)) + p2 = Polygon( + Point(0, Rational(5)/4), Point(1, Rational(5)/4), + Point(1, Rational(9)/4), Point(0, Rational(9)/4)) + p3 = Polygon( + Point(1, 2), Point(2, 2), + Point(2, 1)) + p4 = Polygon( + Point(1, 1), Point(Rational(6)/5, 1), + Point(1, Rational(6)/5)) + pt1 = Point(half, half) + pt2 = Point(1, 1) + + '''Polygon to Point''' + assert p1.distance(pt1) == half + assert p1.distance(pt2) == 0 + assert p2.distance(pt1) == Rational(3)/4 + assert p3.distance(pt2) == sqrt(2)/2 + + '''Polygon to Polygon''' + # p1.distance(p2) emits a warning + with warns(UserWarning, \ + match="Polygons may intersect producing erroneous output"): + assert p1.distance(p2) == half/2 + + assert p1.distance(p3) == sqrt(2)/2 + + # p3.distance(p4) emits a warning + with warns(UserWarning, \ + match="Polygons may intersect producing erroneous output"): + assert p3.distance(p4) == (sqrt(2)/2 - sqrt(Rational(2)/25)/2) + + +def test_convex_hull(): + p = [Point(-5, -1), Point(-2, 1), Point(-2, -1), Point(-1, -3), \ + Point(0, 0), Point(1, 1), Point(2, 2), Point(2, -1), Point(3, 1), \ + Point(4, -1), Point(6, 2)] + ch = Polygon(p[0], p[3], p[9], p[10], p[6], p[1]) + #test handling of duplicate points + p.append(p[3]) + + #more than 3 collinear points + another_p = [Point(-45, -85), Point(-45, 85), Point(-45, 26), \ + Point(-45, -24)] + ch2 = Segment(another_p[0], another_p[1]) + + assert convex_hull(*another_p) == ch2 + assert convex_hull(*p) == ch + assert convex_hull(p[0]) == p[0] + assert convex_hull(p[0], p[1]) == Segment(p[0], p[1]) + + # no unique points + assert convex_hull(*[p[-1]]*3) == p[-1] + + # collection of items + assert convex_hull(*[Point(0, 0), \ + Segment(Point(1, 0), Point(1, 1)), \ + RegularPolygon(Point(2, 0), 2, 4)]) == \ + Polygon(Point(0, 0), Point(2, -2), Point(4, 0), Point(2, 2)) + + +def test_encloses(): + # square with a dimpled left side + s = Polygon(Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1), \ + Point(S.Half, S.Half)) + # the following is True if the polygon isn't treated as closing on itself + assert s.encloses(Point(0, S.Half)) is False + assert s.encloses(Point(S.Half, S.Half)) is False # it's a vertex + assert s.encloses(Point(Rational(3, 4), S.Half)) is True + + +def test_triangle_kwargs(): + assert Triangle(sss=(3, 4, 5)) == \ + Triangle(Point(0, 0), Point(3, 0), Point(3, 4)) + assert Triangle(asa=(30, 2, 30)) == \ + Triangle(Point(0, 0), Point(2, 0), Point(1, sqrt(3)/3)) + assert Triangle(sas=(1, 45, 2)) == \ + Triangle(Point(0, 0), Point(2, 0), Point(sqrt(2)/2, sqrt(2)/2)) + assert Triangle(sss=(1, 2, 5)) is None + assert deg(rad(180)) == 180 + + +def test_transform(): + pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)] + pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)] + assert Triangle(*pts).scale(2, 3, (4, 5)) == Triangle(*pts_out) + assert RegularPolygon((0, 0), 1, 4).scale(2, 3, (4, 5)) == \ + Polygon(Point(-2, -10), Point(-4, -7), Point(-6, -10), Point(-4, -13)) + # Checks for symmetric scaling + assert RegularPolygon((0, 0), 1, 4).scale(2, 2) == \ + RegularPolygon(Point2D(0, 0), 2, 4, 0) + +def test_reflect(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + b = Symbol('b') + m = Symbol('m') + l = Line((0, b), slope=m) + p = Point(x, y) + r = p.reflect(l) + dp = l.perpendicular_segment(p).length + dr = l.perpendicular_segment(r).length + + assert verify_numerically(dp, dr) + + assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=oo)) \ + == Triangle(Point(5, 0), Point(4, 0), Point(4, 2)) + assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=oo)) \ + == Triangle(Point(-1, 0), Point(-2, 0), Point(-2, 2)) + assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=0)) \ + == Triangle(Point(1, 6), Point(2, 6), Point(2, 4)) + assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=0)) \ + == Triangle(Point(1, 0), Point(2, 0), Point(2, -2)) + +def test_bisectors(): + p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1) + p = Polygon(Point(0, 0), Point(2, 0), Point(1, 1), Point(0, 3)) + q = Polygon(Point(1, 0), Point(2, 0), Point(3, 3), Point(-1, 5)) + poly = Polygon(Point(3, 4), Point(0, 0), Point(8, 7), Point(-1, 1), Point(19, -19)) + t = Triangle(p1, p2, p3) + assert t.bisectors()[p2] == Segment(Point(1, 0), Point(0, sqrt(2) - 1)) + assert p.bisectors()[Point2D(0, 3)] == Ray2D(Point2D(0, 3), \ + Point2D(sin(acos(2*sqrt(5)/5)/2), 3 - cos(acos(2*sqrt(5)/5)/2))) + assert q.bisectors()[Point2D(-1, 5)] == \ + Ray2D(Point2D(-1, 5), Point2D(-1 + sqrt(29)*(5*sin(acos(9*sqrt(145)/145)/2) + \ + 2*cos(acos(9*sqrt(145)/145)/2))/29, sqrt(29)*(-5*cos(acos(9*sqrt(145)/145)/2) + \ + 2*sin(acos(9*sqrt(145)/145)/2))/29 + 5)) + assert poly.bisectors()[Point2D(-1, 1)] == Ray2D(Point2D(-1, 1), \ + Point2D(-1 + sin(acos(sqrt(26)/26)/2 + pi/4), 1 - sin(-acos(sqrt(26)/26)/2 + pi/4))) + +def test_incenter(): + assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).incenter \ + == Point(1 - sqrt(2)/2, 1 - sqrt(2)/2) + +def test_inradius(): + assert Triangle(Point(0, 0), Point(4, 0), Point(0, 3)).inradius == 1 + +def test_incircle(): + assert Triangle(Point(0, 0), Point(2, 0), Point(0, 2)).incircle \ + == Circle(Point(2 - sqrt(2), 2 - sqrt(2)), 2 - sqrt(2)) + +def test_exradii(): + t = Triangle(Point(0, 0), Point(6, 0), Point(0, 2)) + assert t.exradii[t.sides[2]] == (-2 + sqrt(10)) + +def test_medians(): + t = Triangle(Point(0, 0), Point(1, 0), Point(0, 1)) + assert t.medians[Point(0, 0)] == Segment(Point(0, 0), Point(S.Half, S.Half)) + +def test_medial(): + assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).medial \ + == Triangle(Point(S.Half, 0), Point(S.Half, S.Half), Point(0, S.Half)) + +def test_nine_point_circle(): + assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).nine_point_circle \ + == Circle(Point2D(Rational(1, 4), Rational(1, 4)), sqrt(2)/4) + +def test_eulerline(): + assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).eulerline \ + == Line(Point2D(0, 0), Point2D(S.Half, S.Half)) + assert Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))).eulerline \ + == Point2D(5, 5*sqrt(3)/3) + assert Triangle(Point(4, -6), Point(4, -1), Point(-3, 3)).eulerline \ + == Line(Point2D(Rational(64, 7), 3), Point2D(Rational(-29, 14), Rational(-7, 2))) + +def test_intersection(): + poly1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1)) + poly2 = Polygon(Point(0, 1), Point(-5, 0), + Point(0, -4), Point(0, Rational(1, 5)), + Point(S.Half, -0.1), Point(1, 0), Point(0, 1)) + + assert poly1.intersection(poly2) == [Point2D(Rational(1, 3), 0), + Segment(Point(0, Rational(1, 5)), Point(0, 0)), + Segment(Point(1, 0), Point(0, 1))] + assert poly2.intersection(poly1) == [Point(Rational(1, 3), 0), + Segment(Point(0, 0), Point(0, Rational(1, 5))), + Segment(Point(1, 0), Point(0, 1))] + assert poly1.intersection(Point(0, 0)) == [Point(0, 0)] + assert poly1.intersection(Point(-12, -43)) == [] + assert poly2.intersection(Line((-12, 0), (12, 0))) == [Point(-5, 0), + Point(0, 0), Point(Rational(1, 3), 0), Point(1, 0)] + assert poly2.intersection(Line((-12, 12), (12, 12))) == [] + assert poly2.intersection(Ray((-3, 4), (1, 0))) == [Segment(Point(1, 0), + Point(0, 1))] + assert poly2.intersection(Circle((0, -1), 1)) == [Point(0, -2), + Point(0, 0)] + assert poly1.intersection(poly1) == [Segment(Point(0, 0), Point(1, 0)), + Segment(Point(0, 1), Point(0, 0)), Segment(Point(1, 0), Point(0, 1))] + assert poly2.intersection(poly2) == [Segment(Point(-5, 0), Point(0, -4)), + Segment(Point(0, -4), Point(0, Rational(1, 5))), + Segment(Point(0, Rational(1, 5)), Point(S.Half, Rational(-1, 10))), + Segment(Point(0, 1), Point(-5, 0)), + Segment(Point(S.Half, Rational(-1, 10)), Point(1, 0)), + Segment(Point(1, 0), Point(0, 1))] + assert poly2.intersection(Triangle(Point(0, 1), Point(1, 0), Point(-1, 1))) \ + == [Point(Rational(-5, 7), Rational(6, 7)), Segment(Point2D(0, 1), Point(1, 0))] + assert poly1.intersection(RegularPolygon((-12, -15), 3, 3)) == [] + + +def test_parameter_value(): + t = Symbol('t') + sq = Polygon((0, 0), (0, 1), (1, 1), (1, 0)) + assert sq.parameter_value((0.5, 1), t) == {t: Rational(3, 8)} + q = Polygon((0, 0), (2, 1), (2, 4), (4, 0)) + assert q.parameter_value((4, 0), t) == {t: -6 + 3*sqrt(5)} # ~= 0.708 + + raises(ValueError, lambda: sq.parameter_value((5, 6), t)) + raises(ValueError, lambda: sq.parameter_value(Circle(Point(0, 0), 1), t)) + + +def test_issue_12966(): + poly = Polygon(Point(0, 0), Point(0, 10), Point(5, 10), Point(5, 5), + Point(10, 5), Point(10, 0)) + t = Symbol('t') + pt = poly.arbitrary_point(t) + DELTA = 5/poly.perimeter + assert [pt.subs(t, DELTA*i) for i in range(int(1/DELTA))] == [ + Point(0, 0), Point(0, 5), Point(0, 10), Point(5, 10), + Point(5, 5), Point(10, 5), Point(10, 0), Point(5, 0)] + + +def test_second_moment_of_area(): + x, y = symbols('x, y') + # triangle + p1, p2, p3 = [(0, 0), (4, 0), (0, 2)] + p = (0, 0) + # equation of hypotenuse + eq_y = (1-x/4)*2 + I_yy = integrate((x**2) * (integrate(1, (y, 0, eq_y))), (x, 0, 4)) + I_xx = integrate(1 * (integrate(y**2, (y, 0, eq_y))), (x, 0, 4)) + I_xy = integrate(x * (integrate(y, (y, 0, eq_y))), (x, 0, 4)) + + triangle = Polygon(p1, p2, p3) + + assert (I_xx - triangle.second_moment_of_area(p)[0]) == 0 + assert (I_yy - triangle.second_moment_of_area(p)[1]) == 0 + assert (I_xy - triangle.second_moment_of_area(p)[2]) == 0 + + # rectangle + p1, p2, p3, p4=[(0, 0), (4, 0), (4, 2), (0, 2)] + I_yy = integrate((x**2) * integrate(1, (y, 0, 2)), (x, 0, 4)) + I_xx = integrate(1 * integrate(y**2, (y, 0, 2)), (x, 0, 4)) + I_xy = integrate(x * integrate(y, (y, 0, 2)), (x, 0, 4)) + + rectangle = Polygon(p1, p2, p3, p4) + + assert (I_xx - rectangle.second_moment_of_area(p)[0]) == 0 + assert (I_yy - rectangle.second_moment_of_area(p)[1]) == 0 + assert (I_xy - rectangle.second_moment_of_area(p)[2]) == 0 + + + r = RegularPolygon(Point(0, 0), 5, 3) + assert r.second_moment_of_area() == (1875*sqrt(3)/S(32), 1875*sqrt(3)/S(32), 0) + + +def test_first_moment(): + a, b = symbols('a, b', positive=True) + # rectangle + p1 = Polygon((0, 0), (a, 0), (a, b), (0, b)) + assert p1.first_moment_of_area() == (a*b**2/8, a**2*b/8) + assert p1.first_moment_of_area((a/3, b/4)) == (-3*a*b**2/32, -a**2*b/9) + + p1 = Polygon((0, 0), (40, 0), (40, 30), (0, 30)) + assert p1.first_moment_of_area() == (4500, 6000) + + # triangle + p2 = Polygon((0, 0), (a, 0), (a/2, b)) + assert p2.first_moment_of_area() == (4*a*b**2/81, a**2*b/24) + assert p2.first_moment_of_area((a/8, b/6)) == (-25*a*b**2/648, -5*a**2*b/768) + + p2 = Polygon((0, 0), (12, 0), (12, 30)) + assert p2.first_moment_of_area() == (S(1600)/3, -S(640)/3) + + +def test_section_modulus_and_polar_second_moment_of_area(): + a, b = symbols('a, b', positive=True) + x, y = symbols('x, y') + rectangle = Polygon((0, b), (0, 0), (a, 0), (a, b)) + assert rectangle.section_modulus(Point(x, y)) == (a*b**3/12/(-b/2 + y), a**3*b/12/(-a/2 + x)) + assert rectangle.polar_second_moment_of_area() == a**3*b/12 + a*b**3/12 + + convex = RegularPolygon((0, 0), 1, 6) + assert convex.section_modulus() == (Rational(5, 8), sqrt(3)*Rational(5, 16)) + assert convex.polar_second_moment_of_area() == 5*sqrt(3)/S(8) + + concave = Polygon((0, 0), (1, 8), (3, 4), (4, 6), (7, 1)) + assert concave.section_modulus() == (Rational(-6371, 429), Rational(-9778, 519)) + assert concave.polar_second_moment_of_area() == Rational(-38669, 252) + + +def test_cut_section(): + # concave polygon + p = Polygon((-1, -1), (1, Rational(5, 2)), (2, 1), (3, Rational(5, 2)), (4, 2), (5, 3), (-1, 3)) + l = Line((0, 0), (Rational(9, 2), 3)) + p1 = p.cut_section(l)[0] + p2 = p.cut_section(l)[1] + assert p1 == Polygon( + Point2D(Rational(-9, 13), Rational(-6, 13)), Point2D(1, Rational(5, 2)), Point2D(Rational(24, 13), Rational(16, 13)), + Point2D(Rational(12, 5), Rational(8, 5)), Point2D(3, Rational(5, 2)), Point2D(Rational(24, 7), Rational(16, 7)), + Point2D(Rational(9, 2), 3), Point2D(-1, 3), Point2D(-1, Rational(-2, 3))) + assert p2 == Polygon(Point2D(-1, -1), Point2D(Rational(-9, 13), Rational(-6, 13)), Point2D(Rational(24, 13), Rational(16, 13)), + Point2D(2, 1), Point2D(Rational(12, 5), Rational(8, 5)), Point2D(Rational(24, 7), Rational(16, 7)), Point2D(4, 2), Point2D(5, 3), + Point2D(Rational(9, 2), 3), Point2D(-1, Rational(-2, 3))) + + # convex polygon + p = RegularPolygon(Point2D(0, 0), 6, 6) + s = p.cut_section(Line((0, 0), slope=1)) + assert s[0] == Polygon(Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9), Point2D(3, 3*sqrt(3)), + Point2D(-3, 3*sqrt(3)), Point2D(-6, 0), Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3))) + assert s[1] == Polygon(Point2D(6, 0), Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9), + Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3)), Point2D(-3, -3*sqrt(3)), Point2D(3, -3*sqrt(3))) + + # case where line does not intersects but coincides with the edge of polygon + a, b = 20, 10 + t1, t2, t3, t4 = [(0, b), (0, 0), (a, 0), (a, b)] + p = Polygon(t1, t2, t3, t4) + p1, p2 = p.cut_section(Line((0, b), slope=0)) + assert p1 == None + assert p2 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10)) + + p3, p4 = p.cut_section(Line((0, 0), slope=0)) + assert p3 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10)) + assert p4 == None + + # case where the line does not intersect with a polygon at all + raises(ValueError, lambda: p.cut_section(Line((0, a), slope=0))) + +def test_type_of_triangle(): + # Isoceles triangle + p1 = Polygon(Point(0, 0), Point(5, 0), Point(2, 4)) + assert p1.is_isosceles() == True + assert p1.is_scalene() == False + assert p1.is_equilateral() == False + + # Scalene triangle + p2 = Polygon (Point(0, 0), Point(0, 2), Point(4, 0)) + assert p2.is_isosceles() == False + assert p2.is_scalene() == True + assert p2.is_equilateral() == False + + # Equilateral triagle + p3 = Polygon(Point(0, 0), Point(6, 0), Point(3, sqrt(27))) + assert p3.is_isosceles() == True + assert p3.is_scalene() == False + assert p3.is_equilateral() == True + +def test_do_poly_distance(): + # Non-intersecting polygons + square1 = Polygon (Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0)) + triangle1 = Polygon(Point(1, 2), Point(2, 2), Point(2, 1)) + assert square1._do_poly_distance(triangle1) == sqrt(2)/2 + + # Polygons which sides intersect + square2 = Polygon(Point(1, 0), Point(2, 0), Point(2, 1), Point(1, 1)) + with warns(UserWarning, \ + match="Polygons may intersect producing erroneous output", test_stacklevel=False): + assert square1._do_poly_distance(square2) == 0 + + # Polygons which bodies intersect + triangle2 = Polygon(Point(0, -1), Point(2, -1), Point(S.Half, S.Half)) + with warns(UserWarning, \ + match="Polygons may intersect producing erroneous output", test_stacklevel=False): + assert triangle2._do_poly_distance(square1) == 0 diff --git a/lib/python3.11/site-packages/sympy/geometry/tests/test_util.py b/lib/python3.11/site-packages/sympy/geometry/tests/test_util.py new file mode 100644 index 0000000000000000000000000000000000000000..da52a795a9383c6438ca06303e8ae6506dccdc65 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/tests/test_util.py @@ -0,0 +1,170 @@ +import pytest +from sympy.core.numbers import Float +from sympy.core.function import (Derivative, Function) +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.functions import exp, cos, sin, tan, cosh, sinh +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.geometry import Point, Point2D, Line, Polygon, Segment, convex_hull,\ + intersection, centroid, Point3D, Line3D, Ray, Ellipse +from sympy.geometry.util import idiff, closest_points, farthest_points, _ordered_points, are_coplanar +from sympy.solvers.solvers import solve +from sympy.testing.pytest import raises + + +def test_idiff(): + x = Symbol('x', real=True) + y = Symbol('y', real=True) + t = Symbol('t', real=True) + f = Function('f') + g = Function('g') + # the use of idiff in ellipse also provides coverage + circ = x**2 + y**2 - 4 + ans = -3*x*(x**2/y**2 + 1)/y**3 + assert ans == idiff(circ, y, x, 3), idiff(circ, y, x, 3) + assert ans == idiff(circ, [y], x, 3) + assert idiff(circ, y, x, 3) == ans + explicit = 12*x/sqrt(-x**2 + 4)**5 + assert ans.subs(y, solve(circ, y)[0]).equals(explicit) + assert True in [sol.diff(x, 3).equals(explicit) for sol in solve(circ, y)] + assert idiff(x + t + y, [y, t], x) == -Derivative(t, x) - 1 + assert idiff(f(x) * exp(f(x)) - x * exp(x), f(x), x) == (x + 1)*exp(x)*exp(-f(x))/(f(x) + 1) + assert idiff(f(x) - y * exp(x), [f(x), y], x) == (y + Derivative(y, x))*exp(x) + assert idiff(f(x) - y * exp(x), [y, f(x)], x) == -y + Derivative(f(x), x)*exp(-x) + assert idiff(f(x) - g(x), [f(x), g(x)], x) == Derivative(g(x), x) + # this should be fast + fxy = y - (-10*(-sin(x) + 1/x)**2 + tan(x)**2 + 2*cosh(x/10)) + assert idiff(fxy, y, x) == -20*sin(x)*cos(x) + 2*tan(x)**3 + \ + 2*tan(x) + sinh(x/10)/5 + 20*cos(x)/x - 20*sin(x)/x**2 + 20/x**3 + + +def test_intersection(): + assert intersection(Point(0, 0)) == [] + raises(TypeError, lambda: intersection(Point(0, 0), 3)) + assert intersection( + Segment((0, 0), (2, 0)), + Segment((-1, 0), (1, 0)), + Line((0, 0), (0, 1)), pairwise=True) == [ + Point(0, 0), Segment((0, 0), (1, 0))] + assert intersection( + Line((0, 0), (0, 1)), + Segment((0, 0), (2, 0)), + Segment((-1, 0), (1, 0)), pairwise=True) == [ + Point(0, 0), Segment((0, 0), (1, 0))] + assert intersection( + Line((0, 0), (0, 1)), + Segment((0, 0), (2, 0)), + Segment((-1, 0), (1, 0)), + Line((0, 0), slope=1), pairwise=True) == [ + Point(0, 0), Segment((0, 0), (1, 0))] + R = 4.0 + c = intersection( + Ray(Point2D(0.001, -1), + Point2D(0.0008, -1.7)), + Ellipse(center=Point2D(0, 0), hradius=R, vradius=2.0), pairwise=True)[0].coordinates + assert c == pytest.approx( + Point2D(0.000714285723396502, -1.99999996811224, evaluate=False).coordinates) + # check this is responds to a lower precision parameter + R = Float(4, 5) + c2 = intersection( + Ray(Point2D(0.001, -1), + Point2D(0.0008, -1.7)), + Ellipse(center=Point2D(0, 0), hradius=R, vradius=2.0), pairwise=True)[0].coordinates + assert c2 == pytest.approx( + Point2D(0.000714285723396502, -1.99999996811224, evaluate=False).coordinates) + assert c[0]._prec == 53 + assert c2[0]._prec == 20 + + +def test_convex_hull(): + raises(TypeError, lambda: convex_hull(Point(0, 0), 3)) + points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)] + assert convex_hull(*points, **{"polygon": False}) == ( + [Point2D(-5, -2), Point2D(1, -1), Point2D(3, -1), Point2D(15, -4)], + [Point2D(-5, -2), Point2D(15, -4)]) + + +def test_centroid(): + p = Polygon((0, 0), (10, 0), (10, 10)) + q = p.translate(0, 20) + assert centroid(p, q) == Point(20, 40)/3 + p = Segment((0, 0), (2, 0)) + q = Segment((0, 0), (2, 2)) + assert centroid(p, q) == Point(1, -sqrt(2) + 2) + assert centroid(Point(0, 0), Point(2, 0)) == Point(2, 0)/2 + assert centroid(Point(0, 0), Point(0, 0), Point(2, 0)) == Point(2, 0)/3 + + +def test_farthest_points_closest_points(): + from sympy.core.random import randint + from sympy.utilities.iterables import subsets + + for how in (min, max): + if how == min: + func = closest_points + else: + func = farthest_points + + raises(ValueError, lambda: func(Point2D(0, 0), Point2D(0, 0))) + + # 3rd pt dx is close and pt is closer to 1st pt + p1 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 1)] + # 3rd pt dx is close and pt is closer to 2nd pt + p2 = [Point2D(0, 0), Point2D(3, 0), Point2D(2, 1)] + # 3rd pt dx is close and but pt is not closer + p3 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 10)] + # 3rd pt dx is not closer and it's closer to 2nd pt + p4 = [Point2D(0, 0), Point2D(3, 0), Point2D(4, 0)] + # 3rd pt dx is not closer and it's closer to 1st pt + p5 = [Point2D(0, 0), Point2D(3, 0), Point2D(-1, 0)] + # duplicate point doesn't affect outcome + dup = [Point2D(0, 0), Point2D(3, 0), Point2D(3, 0), Point2D(-1, 0)] + # symbolic + x = Symbol('x', positive=True) + s = [Point2D(a) for a in ((x, 1), (x + 3, 2), (x + 2, 2))] + + for points in (p1, p2, p3, p4, p5, dup, s): + d = how(i.distance(j) for i, j in subsets(set(points), 2)) + ans = a, b = list(func(*points))[0] + assert a.distance(b) == d + assert ans == _ordered_points(ans) + + # if the following ever fails, the above tests were not sufficient + # and the logical error in the routine should be fixed + points = set() + while len(points) != 7: + points.add(Point2D(randint(1, 100), randint(1, 100))) + points = list(points) + d = how(i.distance(j) for i, j in subsets(points, 2)) + ans = a, b = list(func(*points))[0] + assert a.distance(b) == d + assert ans == _ordered_points(ans) + + # equidistant points + a, b, c = ( + Point2D(0, 0), Point2D(1, 0), Point2D(S.Half, sqrt(3)/2)) + ans = {_ordered_points((i, j)) + for i, j in subsets((a, b, c), 2)} + assert closest_points(b, c, a) == ans + assert farthest_points(b, c, a) == ans + + # unique to farthest + points = [(1, 1), (1, 2), (3, 1), (-5, 2), (15, 4)] + assert farthest_points(*points) == { + (Point2D(-5, 2), Point2D(15, 4))} + points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)] + assert farthest_points(*points) == { + (Point2D(-5, -2), Point2D(15, -4))} + assert farthest_points((1, 1), (0, 0)) == { + (Point2D(0, 0), Point2D(1, 1))} + raises(ValueError, lambda: farthest_points((1, 1))) + + +def test_are_coplanar(): + a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1)) + b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1)) + c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9)) + d = Line(Point2D(0, 3), Point2D(1, 5)) + + assert are_coplanar(a, b, c) == False + assert are_coplanar(a, d) == False diff --git a/lib/python3.11/site-packages/sympy/geometry/util.py b/lib/python3.11/site-packages/sympy/geometry/util.py new file mode 100644 index 0000000000000000000000000000000000000000..edded73c71e21f1f855114ab3777dd67765dd926 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/geometry/util.py @@ -0,0 +1,733 @@ +"""Utility functions for geometrical entities. + +Contains +======== +intersection +convex_hull +closest_points +farthest_points +are_coplanar +are_similar + +""" + +from collections import deque +from math import sqrt as _sqrt + +from sympy import nsimplify +from .entity import GeometryEntity +from .exceptions import GeometryError +from .point import Point, Point2D, Point3D +from sympy.core.containers import OrderedSet +from sympy.core.exprtools import factor_terms +from sympy.core.function import Function, expand_mul +from sympy.core.numbers import Float +from sympy.core.sorting import ordered +from sympy.core.symbol import Symbol +from sympy.core.singleton import S +from sympy.polys.polytools import cancel +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.utilities.iterables import is_sequence + +from mpmath.libmp.libmpf import prec_to_dps + + +def find(x, equation): + """ + Checks whether a Symbol matching ``x`` is present in ``equation`` + or not. If present, the matching symbol is returned, else a + ValueError is raised. If ``x`` is a string the matching symbol + will have the same name; if ``x`` is a Symbol then it will be + returned if found. + + Examples + ======== + + >>> from sympy.geometry.util import find + >>> from sympy import Dummy + >>> from sympy.abc import x + >>> find('x', x) + x + >>> find('x', Dummy('x')) + _x + + The dummy symbol is returned since it has a matching name: + + >>> _.name == 'x' + True + >>> find(x, Dummy('x')) + Traceback (most recent call last): + ... + ValueError: could not find x + """ + + free = equation.free_symbols + xs = [i for i in free if (i.name if isinstance(x, str) else i) == x] + if not xs: + raise ValueError('could not find %s' % x) + if len(xs) != 1: + raise ValueError('ambiguous %s' % x) + return xs[0] + + +def _ordered_points(p): + """Return the tuple of points sorted numerically according to args""" + return tuple(sorted(p, key=lambda x: x.args)) + + +def are_coplanar(*e): + """ Returns True if the given entities are coplanar otherwise False + + Parameters + ========== + + e: entities to be checked for being coplanar + + Returns + ======= + + Boolean + + Examples + ======== + + >>> from sympy import Point3D, Line3D + >>> from sympy.geometry.util import are_coplanar + >>> a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1)) + >>> b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1)) + >>> c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9)) + >>> are_coplanar(a, b, c) + False + + """ + from .line import LinearEntity3D + from .plane import Plane + # XXX update tests for coverage + + e = set(e) + # first work with a Plane if present + for i in list(e): + if isinstance(i, Plane): + e.remove(i) + return all(p.is_coplanar(i) for p in e) + + if all(isinstance(i, Point3D) for i in e): + if len(e) < 3: + return False + + # remove pts that are collinear with 2 pts + a, b = e.pop(), e.pop() + for i in list(e): + if Point3D.are_collinear(a, b, i): + e.remove(i) + + if not e: + return False + else: + # define a plane + p = Plane(a, b, e.pop()) + for i in e: + if i not in p: + return False + return True + else: + pt3d = [] + for i in e: + if isinstance(i, Point3D): + pt3d.append(i) + elif isinstance(i, LinearEntity3D): + pt3d.extend(i.args) + elif isinstance(i, GeometryEntity): # XXX we should have a GeometryEntity3D class so we can tell the difference between 2D and 3D -- here we just want to deal with 2D objects; if new 3D objects are encountered that we didn't handle above, an error should be raised + # all 2D objects have some Point that defines them; so convert those points to 3D pts by making z=0 + for p in i.args: + if isinstance(p, Point): + pt3d.append(Point3D(*(p.args + (0,)))) + return are_coplanar(*pt3d) + + +def are_similar(e1, e2): + """Are two geometrical entities similar. + + Can one geometrical entity be uniformly scaled to the other? + + Parameters + ========== + + e1 : GeometryEntity + e2 : GeometryEntity + + Returns + ======= + + are_similar : boolean + + Raises + ====== + + GeometryError + When `e1` and `e2` cannot be compared. + + Notes + ===== + + If the two objects are equal then they are similar. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity.is_similar + + Examples + ======== + + >>> from sympy import Point, Circle, Triangle, are_similar + >>> c1, c2 = Circle(Point(0, 0), 4), Circle(Point(1, 4), 3) + >>> t1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1)) + >>> t2 = Triangle(Point(0, 0), Point(2, 0), Point(0, 2)) + >>> t3 = Triangle(Point(0, 0), Point(3, 0), Point(0, 1)) + >>> are_similar(t1, t2) + True + >>> are_similar(t1, t3) + False + + """ + if e1 == e2: + return True + is_similar1 = getattr(e1, 'is_similar', None) + if is_similar1: + return is_similar1(e2) + is_similar2 = getattr(e2, 'is_similar', None) + if is_similar2: + return is_similar2(e1) + n1 = e1.__class__.__name__ + n2 = e2.__class__.__name__ + raise GeometryError( + "Cannot test similarity between %s and %s" % (n1, n2)) + + +def centroid(*args): + """Find the centroid (center of mass) of the collection containing only Points, + Segments or Polygons. The centroid is the weighted average of the individual centroid + where the weights are the lengths (of segments) or areas (of polygons). + Overlapping regions will add to the weight of that region. + + If there are no objects (or a mixture of objects) then None is returned. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.line.Segment, + sympy.geometry.polygon.Polygon + + Examples + ======== + + >>> from sympy import Point, Segment, Polygon + >>> from sympy.geometry.util import centroid + >>> p = Polygon((0, 0), (10, 0), (10, 10)) + >>> q = p.translate(0, 20) + >>> p.centroid, q.centroid + (Point2D(20/3, 10/3), Point2D(20/3, 70/3)) + >>> centroid(p, q) + Point2D(20/3, 40/3) + >>> p, q = Segment((0, 0), (2, 0)), Segment((0, 0), (2, 2)) + >>> centroid(p, q) + Point2D(1, 2 - sqrt(2)) + >>> centroid(Point(0, 0), Point(2, 0)) + Point2D(1, 0) + + Stacking 3 polygons on top of each other effectively triples the + weight of that polygon: + + >>> p = Polygon((0, 0), (1, 0), (1, 1), (0, 1)) + >>> q = Polygon((1, 0), (3, 0), (3, 1), (1, 1)) + >>> centroid(p, q) + Point2D(3/2, 1/2) + >>> centroid(p, p, p, q) # centroid x-coord shifts left + Point2D(11/10, 1/2) + + Stacking the squares vertically above and below p has the same + effect: + + >>> centroid(p, p.translate(0, 1), p.translate(0, -1), q) + Point2D(11/10, 1/2) + + """ + from .line import Segment + from .polygon import Polygon + if args: + if all(isinstance(g, Point) for g in args): + c = Point(0, 0) + for g in args: + c += g + den = len(args) + elif all(isinstance(g, Segment) for g in args): + c = Point(0, 0) + L = 0 + for g in args: + l = g.length + c += g.midpoint*l + L += l + den = L + elif all(isinstance(g, Polygon) for g in args): + c = Point(0, 0) + A = 0 + for g in args: + a = g.area + c += g.centroid*a + A += a + den = A + c /= den + return c.func(*[i.simplify() for i in c.args]) + + +def closest_points(*args): + """Return the subset of points from a set of points that were + the closest to each other in the 2D plane. + + Parameters + ========== + + args + A collection of Points on 2D plane. + + Notes + ===== + + This can only be performed on a set of points whose coordinates can + be ordered on the number line. If there are no ties then a single + pair of Points will be in the set. + + Examples + ======== + + >>> from sympy import closest_points, Triangle + >>> Triangle(sss=(3, 4, 5)).args + (Point2D(0, 0), Point2D(3, 0), Point2D(3, 4)) + >>> closest_points(*_) + {(Point2D(0, 0), Point2D(3, 0))} + + References + ========== + + .. [1] https://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairPS.html + + .. [2] Sweep line algorithm + https://en.wikipedia.org/wiki/Sweep_line_algorithm + + """ + p = [Point2D(i) for i in set(args)] + if len(p) < 2: + raise ValueError('At least 2 distinct points must be given.') + + try: + p.sort(key=lambda x: x.args) + except TypeError: + raise ValueError("The points could not be sorted.") + + if not all(i.is_Rational for j in p for i in j.args): + def hypot(x, y): + arg = x*x + y*y + if arg.is_Rational: + return _sqrt(arg) + return sqrt(arg) + else: + from math import hypot + + rv = [(0, 1)] + best_dist = hypot(p[1].x - p[0].x, p[1].y - p[0].y) + i = 2 + left = 0 + box = deque([0, 1]) + while i < len(p): + while left < i and p[i][0] - p[left][0] > best_dist: + box.popleft() + left += 1 + + for j in box: + d = hypot(p[i].x - p[j].x, p[i].y - p[j].y) + if d < best_dist: + rv = [(j, i)] + elif d == best_dist: + rv.append((j, i)) + else: + continue + best_dist = d + box.append(i) + i += 1 + + return {tuple([p[i] for i in pair]) for pair in rv} + + +def convex_hull(*args, polygon=True): + """The convex hull surrounding the Points contained in the list of entities. + + Parameters + ========== + + args : a collection of Points, Segments and/or Polygons + + Optional parameters + =================== + + polygon : Boolean. If True, returns a Polygon, if false a tuple, see below. + Default is True. + + Returns + ======= + + convex_hull : Polygon if ``polygon`` is True else as a tuple `(U, L)` where + ``L`` and ``U`` are the lower and upper hulls, respectively. + + Notes + ===== + + This can only be performed on a set of points whose coordinates can + be ordered on the number line. + + See Also + ======== + + sympy.geometry.point.Point, sympy.geometry.polygon.Polygon + + Examples + ======== + + >>> from sympy import convex_hull + >>> points = [(1, 1), (1, 2), (3, 1), (-5, 2), (15, 4)] + >>> convex_hull(*points) + Polygon(Point2D(-5, 2), Point2D(1, 1), Point2D(3, 1), Point2D(15, 4)) + >>> convex_hull(*points, **dict(polygon=False)) + ([Point2D(-5, 2), Point2D(15, 4)], + [Point2D(-5, 2), Point2D(1, 1), Point2D(3, 1), Point2D(15, 4)]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Graham_scan + + .. [2] Andrew's Monotone Chain Algorithm + (A.M. Andrew, + "Another Efficient Algorithm for Convex Hulls in Two Dimensions", 1979) + https://web.archive.org/web/20210511015444/http://geomalgorithms.com/a10-_hull-1.html + + """ + from .line import Segment + from .polygon import Polygon + p = OrderedSet() + for e in args: + if not isinstance(e, GeometryEntity): + try: + e = Point(e) + except NotImplementedError: + raise ValueError('%s is not a GeometryEntity and cannot be made into Point' % str(e)) + if isinstance(e, Point): + p.add(e) + elif isinstance(e, Segment): + p.update(e.points) + elif isinstance(e, Polygon): + p.update(e.vertices) + else: + raise NotImplementedError( + 'Convex hull for %s not implemented.' % type(e)) + + # make sure all our points are of the same dimension + if any(len(x) != 2 for x in p): + raise ValueError('Can only compute the convex hull in two dimensions') + + p = list(p) + if len(p) == 1: + return p[0] if polygon else (p[0], None) + elif len(p) == 2: + s = Segment(p[0], p[1]) + return s if polygon else (s, None) + + def _orientation(p, q, r): + '''Return positive if p-q-r are clockwise, neg if ccw, zero if + collinear.''' + return (q.y - p.y)*(r.x - p.x) - (q.x - p.x)*(r.y - p.y) + + # scan to find upper and lower convex hulls of a set of 2d points. + U = [] + L = [] + try: + p.sort(key=lambda x: x.args) + except TypeError: + raise ValueError("The points could not be sorted.") + for p_i in p: + while len(U) > 1 and _orientation(U[-2], U[-1], p_i) <= 0: + U.pop() + while len(L) > 1 and _orientation(L[-2], L[-1], p_i) >= 0: + L.pop() + U.append(p_i) + L.append(p_i) + U.reverse() + convexHull = tuple(L + U[1:-1]) + + if len(convexHull) == 2: + s = Segment(convexHull[0], convexHull[1]) + return s if polygon else (s, None) + if polygon: + return Polygon(*convexHull) + else: + U.reverse() + return (U, L) + +def farthest_points(*args): + """Return the subset of points from a set of points that were + the furthest apart from each other in the 2D plane. + + Parameters + ========== + + args + A collection of Points on 2D plane. + + Notes + ===== + + This can only be performed on a set of points whose coordinates can + be ordered on the number line. If there are no ties then a single + pair of Points will be in the set. + + Examples + ======== + + >>> from sympy.geometry import farthest_points, Triangle + >>> Triangle(sss=(3, 4, 5)).args + (Point2D(0, 0), Point2D(3, 0), Point2D(3, 4)) + >>> farthest_points(*_) + {(Point2D(0, 0), Point2D(3, 4))} + + References + ========== + + .. [1] https://code.activestate.com/recipes/117225-convex-hull-and-diameter-of-2d-point-sets/ + + .. [2] Rotating Callipers Technique + https://en.wikipedia.org/wiki/Rotating_calipers + + """ + + def rotatingCalipers(Points): + U, L = convex_hull(*Points, **{"polygon": False}) + + if L is None: + if isinstance(U, Point): + raise ValueError('At least two distinct points must be given.') + yield U.args + else: + i = 0 + j = len(L) - 1 + while i < len(U) - 1 or j > 0: + yield U[i], L[j] + # if all the way through one side of hull, advance the other side + if i == len(U) - 1: + j -= 1 + elif j == 0: + i += 1 + # still points left on both lists, compare slopes of next hull edges + # being careful to avoid divide-by-zero in slope calculation + elif (U[i+1].y - U[i].y) * (L[j].x - L[j-1].x) > \ + (L[j].y - L[j-1].y) * (U[i+1].x - U[i].x): + i += 1 + else: + j -= 1 + + p = [Point2D(i) for i in set(args)] + + if not all(i.is_Rational for j in p for i in j.args): + def hypot(x, y): + arg = x*x + y*y + if arg.is_Rational: + return _sqrt(arg) + return sqrt(arg) + else: + from math import hypot + + rv = [] + diam = 0 + for pair in rotatingCalipers(args): + h, q = _ordered_points(pair) + d = hypot(h.x - q.x, h.y - q.y) + if d > diam: + rv = [(h, q)] + elif d == diam: + rv.append((h, q)) + else: + continue + diam = d + + return set(rv) + + +def idiff(eq, y, x, n=1): + """Return ``dy/dx`` assuming that ``eq == 0``. + + Parameters + ========== + + y : the dependent variable or a list of dependent variables (with y first) + x : the variable that the derivative is being taken with respect to + n : the order of the derivative (default is 1) + + Examples + ======== + + >>> from sympy.abc import x, y, a + >>> from sympy.geometry.util import idiff + + >>> circ = x**2 + y**2 - 4 + >>> idiff(circ, y, x) + -x/y + >>> idiff(circ, y, x, 2).simplify() + (-x**2 - y**2)/y**3 + + Here, ``a`` is assumed to be independent of ``x``: + + >>> idiff(x + a + y, y, x) + -1 + + Now the x-dependence of ``a`` is made explicit by listing ``a`` after + ``y`` in a list. + + >>> idiff(x + a + y, [y, a], x) + -Derivative(a, x) - 1 + + See Also + ======== + + sympy.core.function.Derivative: represents unevaluated derivatives + sympy.core.function.diff: explicitly differentiates wrt symbols + + """ + if is_sequence(y): + dep = set(y) + y = y[0] + elif isinstance(y, Symbol): + dep = {y} + elif isinstance(y, Function): + pass + else: + raise ValueError("expecting x-dependent symbol(s) or function(s) but got: %s" % y) + + f = {s: Function(s.name)(x) for s in eq.free_symbols + if s != x and s in dep} + + if isinstance(y, Symbol): + dydx = Function(y.name)(x).diff(x) + else: + dydx = y.diff(x) + + eq = eq.subs(f) + derivs = {} + for i in range(n): + # equation will be linear in dydx, a*dydx + b, so dydx = -b/a + deq = eq.diff(x) + b = deq.xreplace({dydx: S.Zero}) + a = (deq - b).xreplace({dydx: S.One}) + yp = factor_terms(expand_mul(cancel((-b/a).subs(derivs)), deep=False)) + if i == n - 1: + return yp.subs([(v, k) for k, v in f.items()]) + derivs[dydx] = yp + eq = dydx - yp + dydx = dydx.diff(x) + + +def intersection(*entities, pairwise=False, **kwargs): + """The intersection of a collection of GeometryEntity instances. + + Parameters + ========== + entities : sequence of GeometryEntity + pairwise (keyword argument) : Can be either True or False + + Returns + ======= + intersection : list of GeometryEntity + + Raises + ====== + NotImplementedError + When unable to calculate intersection. + + Notes + ===== + The intersection of any geometrical entity with itself should return + a list with one item: the entity in question. + An intersection requires two or more entities. If only a single + entity is given then the function will return an empty list. + It is possible for `intersection` to miss intersections that one + knows exists because the required quantities were not fully + simplified internally. + Reals should be converted to Rationals, e.g. Rational(str(real_num)) + or else failures due to floating point issues may result. + + Case 1: When the keyword argument 'pairwise' is False (default value): + In this case, the function returns a list of intersections common to + all entities. + + Case 2: When the keyword argument 'pairwise' is True: + In this case, the functions returns a list intersections that occur + between any pair of entities. + + See Also + ======== + + sympy.geometry.entity.GeometryEntity.intersection + + Examples + ======== + + >>> from sympy import Ray, Circle, intersection + >>> c = Circle((0, 1), 1) + >>> intersection(c, c.center) + [] + >>> right = Ray((0, 0), (1, 0)) + >>> up = Ray((0, 0), (0, 1)) + >>> intersection(c, right, up) + [Point2D(0, 0)] + >>> intersection(c, right, up, pairwise=True) + [Point2D(0, 0), Point2D(0, 2)] + >>> left = Ray((1, 0), (0, 0)) + >>> intersection(right, left) + [Segment2D(Point2D(0, 0), Point2D(1, 0))] + + """ + if len(entities) <= 1: + return [] + + entities = list(entities) + prec = None + for i, e in enumerate(entities): + if not isinstance(e, GeometryEntity): + # entities may be an immutable tuple + e = Point(e) + # convert to exact Rationals + d = {} + for f in e.atoms(Float): + prec = f._prec if prec is None else min(f._prec, prec) + d.setdefault(f, nsimplify(f, rational=True)) + entities[i] = e.xreplace(d) + + if not pairwise: + # find the intersection common to all objects + res = entities[0].intersection(entities[1]) + for entity in entities[2:]: + newres = [] + for x in res: + newres.extend(x.intersection(entity)) + res = newres + else: + # find all pairwise intersections + ans = [] + for j in range(len(entities)): + for k in range(j + 1, len(entities)): + ans.extend(intersection(entities[j], entities[k])) + res = list(ordered(set(ans))) + + # convert back to Floats + if prec is not None: + p = prec_to_dps(prec) + res = [i.n(p) for i in res] + return res diff --git a/lib/python3.11/site-packages/sympy/holonomic/__init__.py b/lib/python3.11/site-packages/sympy/holonomic/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..45412acad0ab9e5c7424b1888648a638ef208142 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/holonomic/__init__.py @@ -0,0 +1,18 @@ +r""" +The :py:mod:`~sympy.holonomic` module is intended to deal with holonomic functions along +with various operations on them like addition, multiplication, composition, +integration and differentiation. The module also implements various kinds of +conversions such as converting holonomic functions to a different form and the +other way around. +""" + +from .holonomic import (DifferentialOperator, HolonomicFunction, DifferentialOperators, + from_hyper, from_meijerg, expr_to_holonomic) +from .recurrence import RecurrenceOperators, RecurrenceOperator, HolonomicSequence + +__all__ = [ + 'DifferentialOperator', 'HolonomicFunction', 'DifferentialOperators', + 'from_hyper', 'from_meijerg', 'expr_to_holonomic', + + 'RecurrenceOperators', 'RecurrenceOperator', 'HolonomicSequence', +] diff --git a/lib/python3.11/site-packages/sympy/holonomic/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/holonomic/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..2f4a5bb0124ef8509cf93d8049c6497965ca93c9 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/holonomic/__pycache__/__init__.cpython-311.pyc differ diff --git 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Dummy, Symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import binomial, factorial, rf +from sympy.functions.elementary.exponential import exp_polar, exp, log +from sympy.functions.elementary.hyperbolic import (cosh, sinh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin, sinc) +from sympy.functions.special.error_functions import (Ci, Shi, Si, erf, erfc, erfi) +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import hyper, meijerg +from sympy.integrals import meijerint +from sympy.matrices import Matrix +from sympy.polys.rings import PolyElement +from sympy.polys.fields import FracElement +from sympy.polys.domains import QQ, RR +from sympy.polys.polyclasses import DMF +from sympy.polys.polyroots import roots +from sympy.polys.polytools import Poly +from sympy.polys.matrices import DomainMatrix +from sympy.printing import sstr +from sympy.series.limits import limit +from sympy.series.order import Order +from sympy.simplify.hyperexpand import hyperexpand +from sympy.simplify.simplify import nsimplify +from sympy.solvers.solvers import solve + +from .recurrence import HolonomicSequence, RecurrenceOperator, RecurrenceOperators +from .holonomicerrors import (NotPowerSeriesError, NotHyperSeriesError, + SingularityError, NotHolonomicError) + + +def _find_nonzero_solution(r, homosys): + ones = lambda shape: DomainMatrix.ones(shape, r.domain) + particular, nullspace = r._solve(homosys) + nullity = nullspace.shape[0] + nullpart = ones((1, nullity)) * nullspace + sol = (particular + nullpart).transpose() + return sol + + + +def DifferentialOperators(base, generator): + r""" + This function is used to create annihilators using ``Dx``. + + Explanation + =========== + + Returns an Algebra of Differential Operators also called Weyl Algebra + and the operator for differentiation i.e. the ``Dx`` operator. + + Parameters + ========== + + base: + Base polynomial ring for the algebra. + The base polynomial ring is the ring of polynomials in :math:`x` that + will appear as coefficients in the operators. + generator: + Generator of the algebra which can + be either a noncommutative ``Symbol`` or a string. e.g. "Dx" or "D". + + Examples + ======== + + >>> from sympy import ZZ + >>> from sympy.abc import x + >>> from sympy.holonomic.holonomic import DifferentialOperators + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + >>> R + Univariate Differential Operator Algebra in intermediate Dx over the base ring ZZ[x] + >>> Dx*x + (1) + (x)*Dx + """ + + ring = DifferentialOperatorAlgebra(base, generator) + return (ring, ring.derivative_operator) + + +class DifferentialOperatorAlgebra: + r""" + An Ore Algebra is a set of noncommutative polynomials in the + intermediate ``Dx`` and coefficients in a base polynomial ring :math:`A`. + It follows the commutation rule: + + .. math :: + Dxa = \sigma(a)Dx + \delta(a) + + for :math:`a \subset A`. + + Where :math:`\sigma: A \Rightarrow A` is an endomorphism and :math:`\delta: A \rightarrow A` + is a skew-derivation i.e. :math:`\delta(ab) = \delta(a) b + \sigma(a) \delta(b)`. + + If one takes the sigma as identity map and delta as the standard derivation + then it becomes the algebra of Differential Operators also called + a Weyl Algebra i.e. an algebra whose elements are Differential Operators. + + This class represents a Weyl Algebra and serves as the parent ring for + Differential Operators. + + Examples + ======== + + >>> from sympy import ZZ + >>> from sympy import symbols + >>> from sympy.holonomic.holonomic import DifferentialOperators + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + >>> R + Univariate Differential Operator Algebra in intermediate Dx over the base ring + ZZ[x] + + See Also + ======== + + DifferentialOperator + """ + + def __init__(self, base, generator): + # the base polynomial ring for the algebra + self.base = base + # the operator representing differentiation i.e. `Dx` + self.derivative_operator = DifferentialOperator( + [base.zero, base.one], self) + + if generator is None: + self.gen_symbol = Symbol('Dx', commutative=False) + else: + if isinstance(generator, str): + self.gen_symbol = Symbol(generator, commutative=False) + elif isinstance(generator, Symbol): + self.gen_symbol = generator + + def __str__(self): + string = 'Univariate Differential Operator Algebra in intermediate '\ + + sstr(self.gen_symbol) + ' over the base ring ' + \ + (self.base).__str__() + + return string + + __repr__ = __str__ + + def __eq__(self, other): + return self.base == other.base and \ + self.gen_symbol == other.gen_symbol + + +class DifferentialOperator: + """ + Differential Operators are elements of Weyl Algebra. The Operators + are defined by a list of polynomials in the base ring and the + parent ring of the Operator i.e. the algebra it belongs to. + + Explanation + =========== + + Takes a list of polynomials for each power of ``Dx`` and the + parent ring which must be an instance of DifferentialOperatorAlgebra. + + A Differential Operator can be created easily using + the operator ``Dx``. See examples below. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import DifferentialOperator, DifferentialOperators + >>> from sympy import ZZ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx') + + >>> DifferentialOperator([0, 1, x**2], R) + (1)*Dx + (x**2)*Dx**2 + + >>> (x*Dx*x + 1 - Dx**2)**2 + (2*x**2 + 2*x + 1) + (4*x**3 + 2*x**2 - 4)*Dx + (x**4 - 6*x - 2)*Dx**2 + (-2*x**2)*Dx**3 + (1)*Dx**4 + + See Also + ======== + + DifferentialOperatorAlgebra + """ + + _op_priority = 20 + + def __init__(self, list_of_poly, parent): + """ + Parameters + ========== + + list_of_poly: + List of polynomials belonging to the base ring of the algebra. + parent: + Parent algebra of the operator. + """ + + # the parent ring for this operator + # must be an DifferentialOperatorAlgebra object + self.parent = parent + base = self.parent.base + self.x = base.gens[0] if isinstance(base.gens[0], Symbol) else base.gens[0][0] + # sequence of polynomials in x for each power of Dx + # the list should not have trailing zeroes + # represents the operator + # convert the expressions into ring elements using from_sympy + for i, j in enumerate(list_of_poly): + if not isinstance(j, base.dtype): + list_of_poly[i] = base.from_sympy(sympify(j)) + else: + list_of_poly[i] = base.from_sympy(base.to_sympy(j)) + + self.listofpoly = list_of_poly + # highest power of `Dx` + self.order = len(self.listofpoly) - 1 + + def __mul__(self, other): + """ + Multiplies two DifferentialOperator and returns another + DifferentialOperator instance using the commutation rule + Dx*a = a*Dx + a' + """ + + listofself = self.listofpoly + if isinstance(other, DifferentialOperator): + listofother = other.listofpoly + elif isinstance(other, self.parent.base.dtype): + listofother = [other] + else: + listofother = [self.parent.base.from_sympy(sympify(other))] + + # multiplies a polynomial `b` with a list of polynomials + def _mul_dmp_diffop(b, listofother): + if isinstance(listofother, list): + return [i * b for i in listofother] + return [b * listofother] + + sol = _mul_dmp_diffop(listofself[0], listofother) + + # compute Dx^i * b + def _mul_Dxi_b(b): + sol1 = [self.parent.base.zero] + sol2 = [] + + if isinstance(b, list): + for i in b: + sol1.append(i) + sol2.append(i.diff()) + else: + sol1.append(self.parent.base.from_sympy(b)) + sol2.append(self.parent.base.from_sympy(b).diff()) + + return _add_lists(sol1, sol2) + + for i in range(1, len(listofself)): + # find Dx^i * b in ith iteration + listofother = _mul_Dxi_b(listofother) + # solution = solution + listofself[i] * (Dx^i * b) + sol = _add_lists(sol, _mul_dmp_diffop(listofself[i], listofother)) + + return DifferentialOperator(sol, self.parent) + + def __rmul__(self, other): + if not isinstance(other, DifferentialOperator): + + if not isinstance(other, self.parent.base.dtype): + other = (self.parent.base).from_sympy(sympify(other)) + + sol = [other * j for j in self.listofpoly] + return DifferentialOperator(sol, self.parent) + + def __add__(self, other): + if isinstance(other, DifferentialOperator): + + sol = _add_lists(self.listofpoly, other.listofpoly) + return DifferentialOperator(sol, self.parent) + + list_self = self.listofpoly + if not isinstance(other, self.parent.base.dtype): + list_other = [((self.parent).base).from_sympy(sympify(other))] + else: + list_other = [other] + sol = [list_self[0] + list_other[0]] + list_self[1:] + return DifferentialOperator(sol, self.parent) + + __radd__ = __add__ + + def __sub__(self, other): + return self + (-1) * other + + def __rsub__(self, other): + return (-1) * self + other + + def __neg__(self): + return -1 * self + + def __truediv__(self, other): + return self * (S.One / other) + + def __pow__(self, n): + if n == 1: + return self + result = DifferentialOperator([self.parent.base.one], self.parent) + if n == 0: + return result + # if self is `Dx` + if self.listofpoly == self.parent.derivative_operator.listofpoly: + sol = [self.parent.base.zero]*n + [self.parent.base.one] + return DifferentialOperator(sol, self.parent) + x = self + while True: + if n % 2: + result *= x + n >>= 1 + if not n: + break + x *= x + return result + + def __str__(self): + listofpoly = self.listofpoly + print_str = '' + + for i, j in enumerate(listofpoly): + if j == self.parent.base.zero: + continue + + j = self.parent.base.to_sympy(j) + + if i == 0: + print_str += '(' + sstr(j) + ')' + continue + + if print_str: + print_str += ' + ' + + if i == 1: + print_str += '(' + sstr(j) + ')*%s' %(self.parent.gen_symbol) + continue + + print_str += '(' + sstr(j) + ')' + '*%s**' %(self.parent.gen_symbol) + sstr(i) + + return print_str + + __repr__ = __str__ + + def __eq__(self, other): + if isinstance(other, DifferentialOperator): + return self.listofpoly == other.listofpoly and \ + self.parent == other.parent + return self.listofpoly[0] == other and \ + all(i is self.parent.base.zero for i in self.listofpoly[1:]) + + def is_singular(self, x0): + """ + Checks if the differential equation is singular at x0. + """ + + base = self.parent.base + return x0 in roots(base.to_sympy(self.listofpoly[-1]), self.x) + + +class HolonomicFunction: + r""" + A Holonomic Function is a solution to a linear homogeneous ordinary + differential equation with polynomial coefficients. This differential + equation can also be represented by an annihilator i.e. a Differential + Operator ``L`` such that :math:`L.f = 0`. For uniqueness of these functions, + initial conditions can also be provided along with the annihilator. + + Explanation + =========== + + Holonomic functions have closure properties and thus forms a ring. + Given two Holonomic Functions f and g, their sum, product, + integral and derivative is also a Holonomic Function. + + For ordinary points initial condition should be a vector of values of + the derivatives i.e. :math:`[y(x_0), y'(x_0), y''(x_0) ... ]`. + + For regular singular points initial conditions can also be provided in this + format: + :math:`{s0: [C_0, C_1, ...], s1: [C^1_0, C^1_1, ...], ...}` + where s0, s1, ... are the roots of indicial equation and vectors + :math:`[C_0, C_1, ...], [C^0_0, C^0_1, ...], ...` are the corresponding initial + terms of the associated power series. See Examples below. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols, S + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + + >>> p = HolonomicFunction(Dx - 1, x, 0, [1]) # e^x + >>> q = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]) # sin(x) + + >>> p + q # annihilator of e^x + sin(x) + HolonomicFunction((-1) + (1)*Dx + (-1)*Dx**2 + (1)*Dx**3, x, 0, [1, 2, 1]) + + >>> p * q # annihilator of e^x * sin(x) + HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x, 0, [0, 1]) + + An example of initial conditions for regular singular points, + the indicial equation has only one root `1/2`. + + >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]}) + HolonomicFunction((-1/2) + (x)*Dx, x, 0, {1/2: [1]}) + + >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]}).to_expr() + sqrt(x) + + To plot a Holonomic Function, one can use `.evalf()` for numerical + computation. Here's an example on `sin(x)**2/x` using numpy and matplotlib. + + >>> import sympy.holonomic # doctest: +SKIP + >>> from sympy import var, sin # doctest: +SKIP + >>> import matplotlib.pyplot as plt # doctest: +SKIP + >>> import numpy as np # doctest: +SKIP + >>> var("x") # doctest: +SKIP + >>> r = np.linspace(1, 5, 100) # doctest: +SKIP + >>> y = sympy.holonomic.expr_to_holonomic(sin(x)**2/x, x0=1).evalf(r) # doctest: +SKIP + >>> plt.plot(r, y, label="holonomic function") # doctest: +SKIP + >>> plt.show() # doctest: +SKIP + + """ + + _op_priority = 20 + + def __init__(self, annihilator, x, x0=0, y0=None): + """ + + Parameters + ========== + + annihilator: + Annihilator of the Holonomic Function, represented by a + `DifferentialOperator` object. + x: + Variable of the function. + x0: + The point at which initial conditions are stored. + Generally an integer. + y0: + The initial condition. The proper format for the initial condition + is described in class docstring. To make the function unique, + length of the vector `y0` should be equal to or greater than the + order of differential equation. + """ + + # initial condition + self.y0 = y0 + # the point for initial conditions, default is zero. + self.x0 = x0 + # differential operator L such that L.f = 0 + self.annihilator = annihilator + self.x = x + + def __str__(self): + if self._have_init_cond(): + str_sol = 'HolonomicFunction(%s, %s, %s, %s)' % (str(self.annihilator),\ + sstr(self.x), sstr(self.x0), sstr(self.y0)) + else: + str_sol = 'HolonomicFunction(%s, %s)' % (str(self.annihilator),\ + sstr(self.x)) + + return str_sol + + __repr__ = __str__ + + def unify(self, other): + """ + Unifies the base polynomial ring of a given two Holonomic + Functions. + """ + + R1 = self.annihilator.parent.base + R2 = other.annihilator.parent.base + + dom1 = R1.dom + dom2 = R2.dom + + if R1 == R2: + return (self, other) + + R = (dom1.unify(dom2)).old_poly_ring(self.x) + + newparent, _ = DifferentialOperators(R, str(self.annihilator.parent.gen_symbol)) + + sol1 = [R1.to_sympy(i) for i in self.annihilator.listofpoly] + sol2 = [R2.to_sympy(i) for i in other.annihilator.listofpoly] + + sol1 = DifferentialOperator(sol1, newparent) + sol2 = DifferentialOperator(sol2, newparent) + + sol1 = HolonomicFunction(sol1, self.x, self.x0, self.y0) + sol2 = HolonomicFunction(sol2, other.x, other.x0, other.y0) + + return (sol1, sol2) + + def is_singularics(self): + """ + Returns True if the function have singular initial condition + in the dictionary format. + + Returns False if the function have ordinary initial condition + in the list format. + + Returns None for all other cases. + """ + + if isinstance(self.y0, dict): + return True + elif isinstance(self.y0, list): + return False + + def _have_init_cond(self): + """ + Checks if the function have initial condition. + """ + return bool(self.y0) + + def _singularics_to_ord(self): + """ + Converts a singular initial condition to ordinary if possible. + """ + a = list(self.y0)[0] + b = self.y0[a] + + if len(self.y0) == 1 and a == int(a) and a > 0: + a = int(a) + y0 = [S.Zero] * a + y0 += [j * factorial(a + i) for i, j in enumerate(b)] + + return HolonomicFunction(self.annihilator, self.x, self.x0, y0) + + def __add__(self, other): + # if the ground domains are different + if self.annihilator.parent.base != other.annihilator.parent.base: + a, b = self.unify(other) + return a + b + + deg1 = self.annihilator.order + deg2 = other.annihilator.order + dim = max(deg1, deg2) + R = self.annihilator.parent.base + K = R.get_field() + + rowsself = [self.annihilator] + rowsother = [other.annihilator] + gen = self.annihilator.parent.derivative_operator + + # constructing annihilators up to order dim + for i in range(dim - deg1): + diff1 = (gen * rowsself[-1]) + rowsself.append(diff1) + + for i in range(dim - deg2): + diff2 = (gen * rowsother[-1]) + rowsother.append(diff2) + + row = rowsself + rowsother + + # constructing the matrix of the ansatz + r = [] + + for expr in row: + p = [] + for i in range(dim + 1): + if i >= len(expr.listofpoly): + p.append(K.zero) + else: + p.append(K.new(expr.listofpoly[i].to_list())) + r.append(p) + + # solving the linear system using gauss jordan solver + r = DomainMatrix(r, (len(row), dim+1), K).transpose() + homosys = DomainMatrix.zeros((dim+1, 1), K) + sol = _find_nonzero_solution(r, homosys) + + # if a solution is not obtained then increasing the order by 1 in each + # iteration + while sol.is_zero_matrix: + dim += 1 + + diff1 = (gen * rowsself[-1]) + rowsself.append(diff1) + + diff2 = (gen * rowsother[-1]) + rowsother.append(diff2) + + row = rowsself + rowsother + r = [] + + for expr in row: + p = [] + for i in range(dim + 1): + if i >= len(expr.listofpoly): + p.append(K.zero) + else: + p.append(K.new(expr.listofpoly[i].to_list())) + r.append(p) + + # solving the linear system using gauss jordan solver + r = DomainMatrix(r, (len(row), dim+1), K).transpose() + homosys = DomainMatrix.zeros((dim+1, 1), K) + sol = _find_nonzero_solution(r, homosys) + + # taking only the coefficients needed to multiply with `self` + # can be also be done the other way by taking R.H.S and multiplying with + # `other` + sol = sol.flat()[:dim + 1 - deg1] + sol1 = _normalize(sol, self.annihilator.parent) + # annihilator of the solution + sol = sol1 * (self.annihilator) + sol = _normalize(sol.listofpoly, self.annihilator.parent, negative=False) + + if not (self._have_init_cond() and other._have_init_cond()): + return HolonomicFunction(sol, self.x) + + # both the functions have ordinary initial conditions + if self.is_singularics() == False and other.is_singularics() == False: + + # directly add the corresponding value + if self.x0 == other.x0: + # try to extended the initial conditions + # using the annihilator + y1 = _extend_y0(self, sol.order) + y2 = _extend_y0(other, sol.order) + y0 = [a + b for a, b in zip(y1, y2)] + return HolonomicFunction(sol, self.x, self.x0, y0) + + # change the initial conditions to a same point + selfat0 = self.annihilator.is_singular(0) + otherat0 = other.annihilator.is_singular(0) + if self.x0 == 0 and not selfat0 and not otherat0: + return self + other.change_ics(0) + if other.x0 == 0 and not selfat0 and not otherat0: + return self.change_ics(0) + other + + selfatx0 = self.annihilator.is_singular(self.x0) + otheratx0 = other.annihilator.is_singular(self.x0) + if not selfatx0 and not otheratx0: + return self + other.change_ics(self.x0) + return self.change_ics(other.x0) + other + + if self.x0 != other.x0: + return HolonomicFunction(sol, self.x) + + # if the functions have singular_ics + y1 = None + y2 = None + + if self.is_singularics() == False and other.is_singularics() == True: + # convert the ordinary initial condition to singular. + _y0 = [j / factorial(i) for i, j in enumerate(self.y0)] + y1 = {S.Zero: _y0} + y2 = other.y0 + elif self.is_singularics() == True and other.is_singularics() == False: + _y0 = [j / factorial(i) for i, j in enumerate(other.y0)] + y1 = self.y0 + y2 = {S.Zero: _y0} + elif self.is_singularics() == True and other.is_singularics() == True: + y1 = self.y0 + y2 = other.y0 + + # computing singular initial condition for the result + # taking union of the series terms of both functions + y0 = {} + for i in y1: + # add corresponding initial terms if the power + # on `x` is same + if i in y2: + y0[i] = [a + b for a, b in zip(y1[i], y2[i])] + else: + y0[i] = y1[i] + for i in y2: + if i not in y1: + y0[i] = y2[i] + return HolonomicFunction(sol, self.x, self.x0, y0) + + def integrate(self, limits, initcond=False): + """ + Integrates the given holonomic function. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(Dx - 1, x, 0, [1]).integrate((x, 0, x)) # e^x - 1 + HolonomicFunction((-1)*Dx + (1)*Dx**2, x, 0, [0, 1]) + >>> HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]).integrate((x, 0, x)) + HolonomicFunction((1)*Dx + (1)*Dx**3, x, 0, [0, 1, 0]) + """ + + # to get the annihilator, just multiply by Dx from right + D = self.annihilator.parent.derivative_operator + + # if the function have initial conditions of the series format + if self.is_singularics() == True: + + r = self._singularics_to_ord() + if r: + return r.integrate(limits, initcond=initcond) + + # computing singular initial condition for the function + # produced after integration. + y0 = {} + for i in self.y0: + c = self.y0[i] + c2 = [] + for j, cj in enumerate(c): + if cj == 0: + c2.append(S.Zero) + + # if power on `x` is -1, the integration becomes log(x) + # TODO: Implement this case + elif i + j + 1 == 0: + raise NotImplementedError("logarithmic terms in the series are not supported") + else: + c2.append(cj / S(i + j + 1)) + y0[i + 1] = c2 + + if hasattr(limits, "__iter__"): + raise NotImplementedError("Definite integration for singular initial conditions") + + return HolonomicFunction(self.annihilator * D, self.x, self.x0, y0) + + # if no initial conditions are available for the function + if not self._have_init_cond(): + if initcond: + return HolonomicFunction(self.annihilator * D, self.x, self.x0, [S.Zero]) + return HolonomicFunction(self.annihilator * D, self.x) + + # definite integral + # initial conditions for the answer will be stored at point `a`, + # where `a` is the lower limit of the integrand + if hasattr(limits, "__iter__"): + + if len(limits) == 3 and limits[0] == self.x: + x0 = self.x0 + a = limits[1] + b = limits[2] + definite = True + + else: + definite = False + + y0 = [S.Zero] + y0 += self.y0 + + indefinite_integral = HolonomicFunction(self.annihilator * D, self.x, self.x0, y0) + + if not definite: + return indefinite_integral + + # use evalf to get the values at `a` + if x0 != a: + try: + indefinite_expr = indefinite_integral.to_expr() + except (NotHyperSeriesError, NotPowerSeriesError): + indefinite_expr = None + + if indefinite_expr: + lower = indefinite_expr.subs(self.x, a) + if isinstance(lower, NaN): + lower = indefinite_expr.limit(self.x, a) + else: + lower = indefinite_integral.evalf(a) + + if b == self.x: + y0[0] = y0[0] - lower + return HolonomicFunction(self.annihilator * D, self.x, x0, y0) + + elif S(b).is_Number: + if indefinite_expr: + upper = indefinite_expr.subs(self.x, b) + if isinstance(upper, NaN): + upper = indefinite_expr.limit(self.x, b) + else: + upper = indefinite_integral.evalf(b) + + return upper - lower + + + # if the upper limit is `x`, the answer will be a function + if b == self.x: + return HolonomicFunction(self.annihilator * D, self.x, a, y0) + + # if the upper limits is a Number, a numerical value will be returned + elif S(b).is_Number: + try: + s = HolonomicFunction(self.annihilator * D, self.x, a,\ + y0).to_expr() + indefinite = s.subs(self.x, b) + if not isinstance(indefinite, NaN): + return indefinite + else: + return s.limit(self.x, b) + except (NotHyperSeriesError, NotPowerSeriesError): + return HolonomicFunction(self.annihilator * D, self.x, a, y0).evalf(b) + + return HolonomicFunction(self.annihilator * D, self.x) + + def diff(self, *args, **kwargs): + r""" + Differentiation of the given Holonomic function. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import ZZ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).diff().to_expr() + cos(x) + >>> HolonomicFunction(Dx - 2, x, 0, [1]).diff().to_expr() + 2*exp(2*x) + + See Also + ======== + + integrate + """ + kwargs.setdefault('evaluate', True) + if args: + if args[0] != self.x: + return S.Zero + elif len(args) == 2: + sol = self + for i in range(args[1]): + sol = sol.diff(args[0]) + return sol + + ann = self.annihilator + + # if the function is constant. + if ann.listofpoly[0] == ann.parent.base.zero and ann.order == 1: + return S.Zero + + # if the coefficient of y in the differential equation is zero. + # a shifting is done to compute the answer in this case. + elif ann.listofpoly[0] == ann.parent.base.zero: + + sol = DifferentialOperator(ann.listofpoly[1:], ann.parent) + + if self._have_init_cond(): + # if ordinary initial condition + if self.is_singularics() == False: + return HolonomicFunction(sol, self.x, self.x0, self.y0[1:]) + # TODO: support for singular initial condition + return HolonomicFunction(sol, self.x) + else: + return HolonomicFunction(sol, self.x) + + # the general algorithm + R = ann.parent.base + K = R.get_field() + + seq_dmf = [K.new(i.to_list()) for i in ann.listofpoly] + + # -y = a1*y'/a0 + a2*y''/a0 ... + an*y^n/a0 + rhs = [i / seq_dmf[0] for i in seq_dmf[1:]] + rhs.insert(0, K.zero) + + # differentiate both lhs and rhs + sol = _derivate_diff_eq(rhs, K) + + # add the term y' in lhs to rhs + sol = _add_lists(sol, [K.zero, K.one]) + + sol = _normalize(sol[1:], self.annihilator.parent, negative=False) + + if not self._have_init_cond() or self.is_singularics() == True: + return HolonomicFunction(sol, self.x) + + y0 = _extend_y0(self, sol.order + 1)[1:] + return HolonomicFunction(sol, self.x, self.x0, y0) + + def __eq__(self, other): + if self.annihilator != other.annihilator or self.x != other.x: + return False + if self._have_init_cond() and other._have_init_cond(): + return self.x0 == other.x0 and self.y0 == other.y0 + return True + + def __mul__(self, other): + ann_self = self.annihilator + + if not isinstance(other, HolonomicFunction): + other = sympify(other) + + if other.has(self.x): + raise NotImplementedError(" Can't multiply a HolonomicFunction and expressions/functions.") + + if not self._have_init_cond(): + return self + y0 = _extend_y0(self, ann_self.order) + y1 = [(Poly.new(j, self.x) * other).rep for j in y0] + return HolonomicFunction(ann_self, self.x, self.x0, y1) + + if self.annihilator.parent.base != other.annihilator.parent.base: + a, b = self.unify(other) + return a * b + + ann_other = other.annihilator + + a = ann_self.order + b = ann_other.order + + R = ann_self.parent.base + K = R.get_field() + + list_self = [K.new(j.to_list()) for j in ann_self.listofpoly] + list_other = [K.new(j.to_list()) for j in ann_other.listofpoly] + + # will be used to reduce the degree + self_red = [-list_self[i] / list_self[a] for i in range(a)] + + other_red = [-list_other[i] / list_other[b] for i in range(b)] + + # coeff_mull[i][j] is the coefficient of Dx^i(f).Dx^j(g) + coeff_mul = [[K.zero for i in range(b + 1)] for j in range(a + 1)] + coeff_mul[0][0] = K.one + + # making the ansatz + lin_sys_elements = [[coeff_mul[i][j] for i in range(a) for j in range(b)]] + lin_sys = DomainMatrix(lin_sys_elements, (1, a*b), K).transpose() + + homo_sys = DomainMatrix.zeros((a*b, 1), K) + + sol = _find_nonzero_solution(lin_sys, homo_sys) + + # until a non trivial solution is found + while sol.is_zero_matrix: + + # updating the coefficients Dx^i(f).Dx^j(g) for next degree + for i in range(a - 1, -1, -1): + for j in range(b - 1, -1, -1): + coeff_mul[i][j + 1] += coeff_mul[i][j] + coeff_mul[i + 1][j] += coeff_mul[i][j] + if isinstance(coeff_mul[i][j], K.dtype): + coeff_mul[i][j] = DMFdiff(coeff_mul[i][j], K) + else: + coeff_mul[i][j] = coeff_mul[i][j].diff(self.x) + + # reduce the terms to lower power using annihilators of f, g + for i in range(a + 1): + if coeff_mul[i][b].is_zero: + continue + for j in range(b): + coeff_mul[i][j] += other_red[j] * coeff_mul[i][b] + coeff_mul[i][b] = K.zero + + # not d2 + 1, as that is already covered in previous loop + for j in range(b): + if coeff_mul[a][j] == 0: + continue + for i in range(a): + coeff_mul[i][j] += self_red[i] * coeff_mul[a][j] + coeff_mul[a][j] = K.zero + + lin_sys_elements.append([coeff_mul[i][j] for i in range(a) for j in range(b)]) + lin_sys = DomainMatrix(lin_sys_elements, (len(lin_sys_elements), a*b), K).transpose() + + sol = _find_nonzero_solution(lin_sys, homo_sys) + + sol_ann = _normalize(sol.flat(), self.annihilator.parent, negative=False) + + if not (self._have_init_cond() and other._have_init_cond()): + return HolonomicFunction(sol_ann, self.x) + + if self.is_singularics() == False and other.is_singularics() == False: + + # if both the conditions are at same point + if self.x0 == other.x0: + + # try to find more initial conditions + y0_self = _extend_y0(self, sol_ann.order) + y0_other = _extend_y0(other, sol_ann.order) + # h(x0) = f(x0) * g(x0) + y0 = [y0_self[0] * y0_other[0]] + + # coefficient of Dx^j(f)*Dx^i(g) in Dx^i(fg) + for i in range(1, min(len(y0_self), len(y0_other))): + coeff = [[0 for i in range(i + 1)] for j in range(i + 1)] + for j in range(i + 1): + for k in range(i + 1): + if j + k == i: + coeff[j][k] = binomial(i, j) + + sol = 0 + for j in range(i + 1): + for k in range(i + 1): + sol += coeff[j][k]* y0_self[j] * y0_other[k] + + y0.append(sol) + + return HolonomicFunction(sol_ann, self.x, self.x0, y0) + + # if the points are different, consider one + selfat0 = self.annihilator.is_singular(0) + otherat0 = other.annihilator.is_singular(0) + + if self.x0 == 0 and not selfat0 and not otherat0: + return self * other.change_ics(0) + if other.x0 == 0 and not selfat0 and not otherat0: + return self.change_ics(0) * other + + selfatx0 = self.annihilator.is_singular(self.x0) + otheratx0 = other.annihilator.is_singular(self.x0) + if not selfatx0 and not otheratx0: + return self * other.change_ics(self.x0) + return self.change_ics(other.x0) * other + + if self.x0 != other.x0: + return HolonomicFunction(sol_ann, self.x) + + # if the functions have singular_ics + y1 = None + y2 = None + + if self.is_singularics() == False and other.is_singularics() == True: + _y0 = [j / factorial(i) for i, j in enumerate(self.y0)] + y1 = {S.Zero: _y0} + y2 = other.y0 + elif self.is_singularics() == True and other.is_singularics() == False: + _y0 = [j / factorial(i) for i, j in enumerate(other.y0)] + y1 = self.y0 + y2 = {S.Zero: _y0} + elif self.is_singularics() == True and other.is_singularics() == True: + y1 = self.y0 + y2 = other.y0 + + y0 = {} + # multiply every possible pair of the series terms + for i in y1: + for j in y2: + k = min(len(y1[i]), len(y2[j])) + c = [sum((y1[i][b] * y2[j][a - b] for b in range(a + 1)), + start=S.Zero) for a in range(k)] + if not i + j in y0: + y0[i + j] = c + else: + y0[i + j] = [a + b for a, b in zip(c, y0[i + j])] + return HolonomicFunction(sol_ann, self.x, self.x0, y0) + + __rmul__ = __mul__ + + def __sub__(self, other): + return self + other * -1 + + def __rsub__(self, other): + return self * -1 + other + + def __neg__(self): + return -1 * self + + def __truediv__(self, other): + return self * (S.One / other) + + def __pow__(self, n): + if self.annihilator.order <= 1: + ann = self.annihilator + parent = ann.parent + + if self.y0 is None: + y0 = None + else: + y0 = [list(self.y0)[0] ** n] + + p0 = ann.listofpoly[0] + p1 = ann.listofpoly[1] + + p0 = (Poly.new(p0, self.x) * n).rep + + sol = [parent.base.to_sympy(i) for i in [p0, p1]] + dd = DifferentialOperator(sol, parent) + return HolonomicFunction(dd, self.x, self.x0, y0) + if n < 0: + raise NotHolonomicError("Negative Power on a Holonomic Function") + Dx = self.annihilator.parent.derivative_operator + result = HolonomicFunction(Dx, self.x, S.Zero, [S.One]) + if n == 0: + return result + x = self + while True: + if n % 2: + result *= x + n >>= 1 + if not n: + break + x *= x + return result + + def degree(self): + """ + Returns the highest power of `x` in the annihilator. + """ + return max(i.degree() for i in self.annihilator.listofpoly) + + def composition(self, expr, *args, **kwargs): + """ + Returns function after composition of a holonomic + function with an algebraic function. The method cannot compute + initial conditions for the result by itself, so they can be also be + provided. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(Dx - 1, x).composition(x**2, 0, [1]) # e^(x**2) + HolonomicFunction((-2*x) + (1)*Dx, x, 0, [1]) + >>> HolonomicFunction(Dx**2 + 1, x).composition(x**2 - 1, 1, [1, 0]) + HolonomicFunction((4*x**3) + (-1)*Dx + (x)*Dx**2, x, 1, [1, 0]) + + See Also + ======== + + from_hyper + """ + + R = self.annihilator.parent + a = self.annihilator.order + diff = expr.diff(self.x) + listofpoly = self.annihilator.listofpoly + + for i, j in enumerate(listofpoly): + if isinstance(j, self.annihilator.parent.base.dtype): + listofpoly[i] = self.annihilator.parent.base.to_sympy(j) + + r = listofpoly[a].subs({self.x:expr}) + subs = [-listofpoly[i].subs({self.x:expr}) / r for i in range (a)] + coeffs = [S.Zero for i in range(a)] # coeffs[i] == coeff of (D^i f)(a) in D^k (f(a)) + coeffs[0] = S.One + system = [coeffs] + homogeneous = Matrix([[S.Zero for i in range(a)]]).transpose() + while True: + coeffs_next = [p.diff(self.x) for p in coeffs] + for i in range(a - 1): + coeffs_next[i + 1] += (coeffs[i] * diff) + for i in range(a): + coeffs_next[i] += (coeffs[-1] * subs[i] * diff) + coeffs = coeffs_next + # check for linear relations + system.append(coeffs) + sol, taus = (Matrix(system).transpose() + ).gauss_jordan_solve(homogeneous) + if sol.is_zero_matrix is not True: + break + + tau = list(taus)[0] + sol = sol.subs(tau, 1) + sol = _normalize(sol[0:], R, negative=False) + + # if initial conditions are given for the resulting function + if args: + return HolonomicFunction(sol, self.x, args[0], args[1]) + return HolonomicFunction(sol, self.x) + + def to_sequence(self, lb=True): + r""" + Finds recurrence relation for the coefficients in the series expansion + of the function about :math:`x_0`, where :math:`x_0` is the point at + which the initial condition is stored. + + Explanation + =========== + + If the point :math:`x_0` is ordinary, solution of the form :math:`[(R, n_0)]` + is returned. Where :math:`R` is the recurrence relation and :math:`n_0` is the + smallest ``n`` for which the recurrence holds true. + + If the point :math:`x_0` is regular singular, a list of solutions in + the format :math:`(R, p, n_0)` is returned, i.e. `[(R, p, n_0), ... ]`. + Each tuple in this vector represents a recurrence relation :math:`R` + associated with a root of the indicial equation ``p``. Conditions of + a different format can also be provided in this case, see the + docstring of HolonomicFunction class. + + If it's not possible to numerically compute a initial condition, + it is returned as a symbol :math:`C_j`, denoting the coefficient of + :math:`(x - x_0)^j` in the power series about :math:`x_0`. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols, S + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(Dx - 1, x, 0, [1]).to_sequence() + [(HolonomicSequence((-1) + (n + 1)Sn, n), u(0) = 1, 0)] + >>> HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]).to_sequence() + [(HolonomicSequence((n**2) + (n**2 + n)Sn, n), u(0) = 0, u(1) = 1, u(2) = -1/2, 2)] + >>> HolonomicFunction(-S(1)/2 + x*Dx, x, 0, {S(1)/2: [1]}).to_sequence() + [(HolonomicSequence((n), n), u(0) = 1, 1/2, 1)] + + See Also + ======== + + HolonomicFunction.series + + References + ========== + + .. [1] https://hal.inria.fr/inria-00070025/document + .. [2] https://www3.risc.jku.at/publications/download/risc_2244/DIPLFORM.pdf + + """ + + if self.x0 != 0: + return self.shift_x(self.x0).to_sequence() + + # check whether a power series exists if the point is singular + if self.annihilator.is_singular(self.x0): + return self._frobenius(lb=lb) + + dict1 = {} + n = Symbol('n', integer=True) + dom = self.annihilator.parent.base.dom + R, _ = RecurrenceOperators(dom.old_poly_ring(n), 'Sn') + + # substituting each term of the form `x^k Dx^j` in the + # annihilator, according to the formula below: + # x^k Dx^j = Sum(rf(n + 1 - k, j) * a(n + j - k) * x^n, (n, k, oo)) + # for explanation see [2]. + for i, j in enumerate(self.annihilator.listofpoly): + + listofdmp = j.all_coeffs() + degree = len(listofdmp) - 1 + + for k in range(degree + 1): + coeff = listofdmp[degree - k] + + if coeff == 0: + continue + + if (i - k, k) in dict1: + dict1[(i - k, k)] += (dom.to_sympy(coeff) * rf(n - k + 1, i)) + else: + dict1[(i - k, k)] = (dom.to_sympy(coeff) * rf(n - k + 1, i)) + + + sol = [] + keylist = [i[0] for i in dict1] + lower = min(keylist) + upper = max(keylist) + degree = self.degree() + + # the recurrence relation holds for all values of + # n greater than smallest_n, i.e. n >= smallest_n + smallest_n = lower + degree + dummys = {} + eqs = [] + unknowns = [] + + # an appropriate shift of the recurrence + for j in range(lower, upper + 1): + if j in keylist: + temp = sum((v.subs(n, n - lower) + for k, v in dict1.items() if k[0] == j), + start=S.Zero) + sol.append(temp) + else: + sol.append(S.Zero) + + # the recurrence relation + sol = RecurrenceOperator(sol, R) + + # computing the initial conditions for recurrence + order = sol.order + all_roots = roots(R.base.to_sympy(sol.listofpoly[-1]), n, filter='Z') + all_roots = all_roots.keys() + + if all_roots: + max_root = max(all_roots) + 1 + smallest_n = max(max_root, smallest_n) + order += smallest_n + + y0 = _extend_y0(self, order) + # u(n) = y^n(0)/factorial(n) + u0 = [j / factorial(i) for i, j in enumerate(y0)] + + # if sufficient conditions can't be computed then + # try to use the series method i.e. + # equate the coefficients of x^k in the equation formed by + # substituting the series in differential equation, to zero. + if len(u0) < order: + + for i in range(degree): + eq = S.Zero + + for j in dict1: + + if i + j[0] < 0: + dummys[i + j[0]] = S.Zero + + elif i + j[0] < len(u0): + dummys[i + j[0]] = u0[i + j[0]] + + elif not i + j[0] in dummys: + dummys[i + j[0]] = Symbol('C_%s' %(i + j[0])) + unknowns.append(dummys[i + j[0]]) + + if j[1] <= i: + eq += dict1[j].subs(n, i) * dummys[i + j[0]] + + eqs.append(eq) + + # solve the system of equations formed + soleqs = solve(eqs, *unknowns) + + if isinstance(soleqs, dict): + + for i in range(len(u0), order): + + if i not in dummys: + dummys[i] = Symbol('C_%s' %i) + + if dummys[i] in soleqs: + u0.append(soleqs[dummys[i]]) + + else: + u0.append(dummys[i]) + + if lb: + return [(HolonomicSequence(sol, u0), smallest_n)] + return [HolonomicSequence(sol, u0)] + + for i in range(len(u0), order): + + if i not in dummys: + dummys[i] = Symbol('C_%s' %i) + + s = False + for j in soleqs: + if dummys[i] in j: + u0.append(j[dummys[i]]) + s = True + if not s: + u0.append(dummys[i]) + + if lb: + return [(HolonomicSequence(sol, u0), smallest_n)] + + return [HolonomicSequence(sol, u0)] + + def _frobenius(self, lb=True): + # compute the roots of indicial equation + indicialroots = self._indicial() + + reals = [] + compl = [] + for i in ordered(indicialroots.keys()): + if i.is_real: + reals.extend([i] * indicialroots[i]) + else: + a, b = i.as_real_imag() + compl.extend([(i, a, b)] * indicialroots[i]) + + # sort the roots for a fixed ordering of solution + compl.sort(key=lambda x : x[1]) + compl.sort(key=lambda x : x[2]) + reals.sort() + + # grouping the roots, roots differ by an integer are put in the same group. + grp = [] + + for i in reals: + if len(grp) == 0: + grp.append([i]) + continue + for j in grp: + if int_valued(j[0] - i): + j.append(i) + break + else: + grp.append([i]) + + # True if none of the roots differ by an integer i.e. + # each element in group have only one member + independent = all(len(i) == 1 for i in grp) + + allpos = all(i >= 0 for i in reals) + allint = all(int_valued(i) for i in reals) + + # if initial conditions are provided + # then use them. + if self.is_singularics() == True: + rootstoconsider = [] + for i in ordered(self.y0.keys()): + for j in ordered(indicialroots.keys()): + if equal_valued(j, i): + rootstoconsider.append(i) + + elif allpos and allint: + rootstoconsider = [min(reals)] + + elif independent: + rootstoconsider = [i[0] for i in grp] + [j[0] for j in compl] + + elif not allint: + rootstoconsider = [i for i in reals if not int(i) == i] + + elif not allpos: + + if not self._have_init_cond() or S(self.y0[0]).is_finite == False: + rootstoconsider = [min(reals)] + + else: + posroots = [i for i in reals if i >= 0] + rootstoconsider = [min(posroots)] + + n = Symbol('n', integer=True) + dom = self.annihilator.parent.base.dom + R, _ = RecurrenceOperators(dom.old_poly_ring(n), 'Sn') + + finalsol = [] + char = ord('C') + + for p in rootstoconsider: + dict1 = {} + + for i, j in enumerate(self.annihilator.listofpoly): + + listofdmp = j.all_coeffs() + degree = len(listofdmp) - 1 + + for k in range(degree + 1): + coeff = listofdmp[degree - k] + + if coeff == 0: + continue + + if (i - k, k - i) in dict1: + dict1[(i - k, k - i)] += (dom.to_sympy(coeff) * rf(n - k + 1 + p, i)) + else: + dict1[(i - k, k - i)] = (dom.to_sympy(coeff) * rf(n - k + 1 + p, i)) + + sol = [] + keylist = [i[0] for i in dict1] + lower = min(keylist) + upper = max(keylist) + degree = max(i[1] for i in dict1) + degree2 = min(i[1] for i in dict1) + + smallest_n = lower + degree + dummys = {} + eqs = [] + unknowns = [] + + for j in range(lower, upper + 1): + if j in keylist: + temp = sum((v.subs(n, n - lower) + for k, v in dict1.items() if k[0] == j), + start=S.Zero) + sol.append(temp) + else: + sol.append(S.Zero) + + # the recurrence relation + sol = RecurrenceOperator(sol, R) + + # computing the initial conditions for recurrence + order = sol.order + all_roots = roots(R.base.to_sympy(sol.listofpoly[-1]), n, filter='Z') + all_roots = all_roots.keys() + + if all_roots: + max_root = max(all_roots) + 1 + smallest_n = max(max_root, smallest_n) + order += smallest_n + + u0 = [] + + if self.is_singularics() == True: + u0 = self.y0[p] + + elif self.is_singularics() == False and p >= 0 and int(p) == p and len(rootstoconsider) == 1: + y0 = _extend_y0(self, order + int(p)) + # u(n) = y^n(0)/factorial(n) + if len(y0) > int(p): + u0 = [y0[i] / factorial(i) for i in range(int(p), len(y0))] + + if len(u0) < order: + + for i in range(degree2, degree): + eq = S.Zero + + for j in dict1: + if i + j[0] < 0: + dummys[i + j[0]] = S.Zero + + elif i + j[0] < len(u0): + dummys[i + j[0]] = u0[i + j[0]] + + elif not i + j[0] in dummys: + letter = chr(char) + '_%s' %(i + j[0]) + dummys[i + j[0]] = Symbol(letter) + unknowns.append(dummys[i + j[0]]) + + if j[1] <= i: + eq += dict1[j].subs(n, i) * dummys[i + j[0]] + + eqs.append(eq) + + # solve the system of equations formed + soleqs = solve(eqs, *unknowns) + + if isinstance(soleqs, dict): + + for i in range(len(u0), order): + + if i not in dummys: + letter = chr(char) + '_%s' %i + dummys[i] = Symbol(letter) + + if dummys[i] in soleqs: + u0.append(soleqs[dummys[i]]) + + else: + u0.append(dummys[i]) + + if lb: + finalsol.append((HolonomicSequence(sol, u0), p, smallest_n)) + continue + else: + finalsol.append((HolonomicSequence(sol, u0), p)) + continue + + for i in range(len(u0), order): + + if i not in dummys: + letter = chr(char) + '_%s' %i + dummys[i] = Symbol(letter) + + s = False + for j in soleqs: + if dummys[i] in j: + u0.append(j[dummys[i]]) + s = True + if not s: + u0.append(dummys[i]) + if lb: + finalsol.append((HolonomicSequence(sol, u0), p, smallest_n)) + + else: + finalsol.append((HolonomicSequence(sol, u0), p)) + char += 1 + return finalsol + + def series(self, n=6, coefficient=False, order=True, _recur=None): + r""" + Finds the power series expansion of given holonomic function about :math:`x_0`. + + Explanation + =========== + + A list of series might be returned if :math:`x_0` is a regular point with + multiple roots of the indicial equation. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(Dx - 1, x, 0, [1]).series() # e^x + 1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + O(x**6) + >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).series(n=8) # sin(x) + x - x**3/6 + x**5/120 - x**7/5040 + O(x**8) + + See Also + ======== + + HolonomicFunction.to_sequence + """ + + if _recur is None: + recurrence = self.to_sequence() + else: + recurrence = _recur + + if isinstance(recurrence, tuple) and len(recurrence) == 2: + recurrence = recurrence[0] + constantpower = 0 + elif isinstance(recurrence, tuple) and len(recurrence) == 3: + constantpower = recurrence[1] + recurrence = recurrence[0] + + elif len(recurrence) == 1 and len(recurrence[0]) == 2: + recurrence = recurrence[0][0] + constantpower = 0 + elif len(recurrence) == 1 and len(recurrence[0]) == 3: + constantpower = recurrence[0][1] + recurrence = recurrence[0][0] + else: + return [self.series(_recur=i) for i in recurrence] + + n = n - int(constantpower) + l = len(recurrence.u0) - 1 + k = recurrence.recurrence.order + x = self.x + x0 = self.x0 + seq_dmp = recurrence.recurrence.listofpoly + R = recurrence.recurrence.parent.base + K = R.get_field() + seq = [K.new(j.to_list()) for j in seq_dmp] + sub = [-seq[i] / seq[k] for i in range(k)] + sol = list(recurrence.u0) + + if l + 1 < n: + # use the initial conditions to find the next term + for i in range(l + 1 - k, n - k): + coeff = sum((DMFsubs(sub[j], i) * sol[i + j] + for j in range(k) if i + j >= 0), start=S.Zero) + sol.append(coeff) + + if coefficient: + return sol + + ser = sum((x**(i + constantpower) * j for i, j in enumerate(sol)), + start=S.Zero) + if order: + ser += Order(x**(n + int(constantpower)), x) + if x0 != 0: + return ser.subs(x, x - x0) + return ser + + def _indicial(self): + """ + Computes roots of the Indicial equation. + """ + + if self.x0 != 0: + return self.shift_x(self.x0)._indicial() + + list_coeff = self.annihilator.listofpoly + R = self.annihilator.parent.base + x = self.x + s = R.zero + y = R.one + + def _pole_degree(poly): + root_all = roots(R.to_sympy(poly), x, filter='Z') + if 0 in root_all.keys(): + return root_all[0] + else: + return 0 + + degree = max(j.degree() for j in list_coeff) + inf = 10 * (max(1, degree) + max(1, self.annihilator.order)) + + deg = lambda q: inf if q.is_zero else _pole_degree(q) + b = min(deg(q) - j for j, q in enumerate(list_coeff)) + + for i, j in enumerate(list_coeff): + listofdmp = j.all_coeffs() + degree = len(listofdmp) - 1 + if 0 <= i + b <= degree: + s = s + listofdmp[degree - i - b] * y + y *= R.from_sympy(x - i) + + return roots(R.to_sympy(s), x) + + def evalf(self, points, method='RK4', h=0.05, derivatives=False): + r""" + Finds numerical value of a holonomic function using numerical methods. + (RK4 by default). A set of points (real or complex) must be provided + which will be the path for the numerical integration. + + Explanation + =========== + + The path should be given as a list :math:`[x_1, x_2, \dots x_n]`. The numerical + values will be computed at each point in this order + :math:`x_1 \rightarrow x_2 \rightarrow x_3 \dots \rightarrow x_n`. + + Returns values of the function at :math:`x_1, x_2, \dots x_n` in a list. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import QQ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') + + A straight line on the real axis from (0 to 1) + + >>> r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1] + + Runge-Kutta 4th order on e^x from 0.1 to 1. + Exact solution at 1 is 2.71828182845905 + + >>> HolonomicFunction(Dx - 1, x, 0, [1]).evalf(r) + [1.10517083333333, 1.22140257085069, 1.34985849706254, 1.49182424008069, + 1.64872063859684, 1.82211796209193, 2.01375162659678, 2.22553956329232, + 2.45960141378007, 2.71827974413517] + + Euler's method for the same + + >>> HolonomicFunction(Dx - 1, x, 0, [1]).evalf(r, method='Euler') + [1.1, 1.21, 1.331, 1.4641, 1.61051, 1.771561, 1.9487171, 2.14358881, + 2.357947691, 2.5937424601] + + One can also observe that the value obtained using Runge-Kutta 4th order + is much more accurate than Euler's method. + """ + + from sympy.holonomic.numerical import _evalf + lp = False + + # if a point `b` is given instead of a mesh + if not hasattr(points, "__iter__"): + lp = True + b = S(points) + if self.x0 == b: + return _evalf(self, [b], method=method, derivatives=derivatives)[-1] + + if not b.is_Number: + raise NotImplementedError + + a = self.x0 + if a > b: + h = -h + n = int((b - a) / h) + points = [a + h] + for i in range(n - 1): + points.append(points[-1] + h) + + for i in roots(self.annihilator.parent.base.to_sympy(self.annihilator.listofpoly[-1]), self.x): + if i == self.x0 or i in points: + raise SingularityError(self, i) + + if lp: + return _evalf(self, points, method=method, derivatives=derivatives)[-1] + return _evalf(self, points, method=method, derivatives=derivatives) + + def change_x(self, z): + """ + Changes only the variable of Holonomic Function, for internal + purposes. For composition use HolonomicFunction.composition() + """ + + dom = self.annihilator.parent.base.dom + R = dom.old_poly_ring(z) + parent, _ = DifferentialOperators(R, 'Dx') + sol = [R(j.to_list()) for j in self.annihilator.listofpoly] + sol = DifferentialOperator(sol, parent) + return HolonomicFunction(sol, z, self.x0, self.y0) + + def shift_x(self, a): + """ + Substitute `x + a` for `x`. + """ + + x = self.x + listaftershift = self.annihilator.listofpoly + base = self.annihilator.parent.base + + sol = [base.from_sympy(base.to_sympy(i).subs(x, x + a)) for i in listaftershift] + sol = DifferentialOperator(sol, self.annihilator.parent) + x0 = self.x0 - a + if not self._have_init_cond(): + return HolonomicFunction(sol, x) + return HolonomicFunction(sol, x, x0, self.y0) + + def to_hyper(self, as_list=False, _recur=None): + r""" + Returns a hypergeometric function (or linear combination of them) + representing the given holonomic function. + + Explanation + =========== + + Returns an answer of the form: + `a_1 \cdot x^{b_1} \cdot{hyper()} + a_2 \cdot x^{b_2} \cdot{hyper()} \dots` + + This is very useful as one can now use ``hyperexpand`` to find the + symbolic expressions/functions. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import ZZ + >>> from sympy import symbols + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx') + >>> # sin(x) + >>> HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_hyper() + x*hyper((), (3/2,), -x**2/4) + >>> # exp(x) + >>> HolonomicFunction(Dx - 1, x, 0, [1]).to_hyper() + hyper((), (), x) + + See Also + ======== + + from_hyper, from_meijerg + """ + + if _recur is None: + recurrence = self.to_sequence() + else: + recurrence = _recur + + if isinstance(recurrence, tuple) and len(recurrence) == 2: + smallest_n = recurrence[1] + recurrence = recurrence[0] + constantpower = 0 + elif isinstance(recurrence, tuple) and len(recurrence) == 3: + smallest_n = recurrence[2] + constantpower = recurrence[1] + recurrence = recurrence[0] + elif len(recurrence) == 1 and len(recurrence[0]) == 2: + smallest_n = recurrence[0][1] + recurrence = recurrence[0][0] + constantpower = 0 + elif len(recurrence) == 1 and len(recurrence[0]) == 3: + smallest_n = recurrence[0][2] + constantpower = recurrence[0][1] + recurrence = recurrence[0][0] + else: + sol = self.to_hyper(as_list=as_list, _recur=recurrence[0]) + for i in recurrence[1:]: + sol += self.to_hyper(as_list=as_list, _recur=i) + return sol + + u0 = recurrence.u0 + r = recurrence.recurrence + x = self.x + x0 = self.x0 + + # order of the recurrence relation + m = r.order + + # when no recurrence exists, and the power series have finite terms + if m == 0: + nonzeroterms = roots(r.parent.base.to_sympy(r.listofpoly[0]), recurrence.n, filter='R') + + sol = S.Zero + for j, i in enumerate(nonzeroterms): + + if i < 0 or not int_valued(i): + continue + + i = int(i) + if i < len(u0): + if isinstance(u0[i], (PolyElement, FracElement)): + u0[i] = u0[i].as_expr() + sol += u0[i] * x**i + + else: + sol += Symbol('C_%s' %j) * x**i + + if isinstance(sol, (PolyElement, FracElement)): + sol = sol.as_expr() * x**constantpower + else: + sol = sol * x**constantpower + if as_list: + if x0 != 0: + return [(sol.subs(x, x - x0), )] + return [(sol, )] + if x0 != 0: + return sol.subs(x, x - x0) + return sol + + if smallest_n + m > len(u0): + raise NotImplementedError("Can't compute sufficient Initial Conditions") + + # check if the recurrence represents a hypergeometric series + if any(i != r.parent.base.zero for i in r.listofpoly[1:-1]): + raise NotHyperSeriesError(self, self.x0) + + a = r.listofpoly[0] + b = r.listofpoly[-1] + + # the constant multiple of argument of hypergeometric function + if isinstance(a.LC(), (PolyElement, FracElement)): + c = - (S(a.LC().as_expr()) * m**(a.degree())) / (S(b.LC().as_expr()) * m**(b.degree())) + else: + c = - (S(a.LC()) * m**(a.degree())) / (S(b.LC()) * m**(b.degree())) + + sol = 0 + + arg1 = roots(r.parent.base.to_sympy(a), recurrence.n) + arg2 = roots(r.parent.base.to_sympy(b), recurrence.n) + + # iterate through the initial conditions to find + # the hypergeometric representation of the given + # function. + # The answer will be a linear combination + # of different hypergeometric series which satisfies + # the recurrence. + if as_list: + listofsol = [] + for i in range(smallest_n + m): + + # if the recurrence relation doesn't hold for `n = i`, + # then a Hypergeometric representation doesn't exist. + # add the algebraic term a * x**i to the solution, + # where a is u0[i] + if i < smallest_n: + if as_list: + listofsol.append(((S(u0[i]) * x**(i+constantpower)).subs(x, x-x0), )) + else: + sol += S(u0[i]) * x**i + continue + + # if the coefficient u0[i] is zero, then the + # independent hypergeomtric series starting with + # x**i is not a part of the answer. + if S(u0[i]) == 0: + continue + + ap = [] + bq = [] + + # substitute m * n + i for n + for k in ordered(arg1.keys()): + ap.extend([nsimplify((i - k) / m)] * arg1[k]) + + for k in ordered(arg2.keys()): + bq.extend([nsimplify((i - k) / m)] * arg2[k]) + + # convention of (k + 1) in the denominator + if 1 in bq: + bq.remove(1) + else: + ap.append(1) + if as_list: + listofsol.append(((S(u0[i])*x**(i+constantpower)).subs(x, x-x0), (hyper(ap, bq, c*x**m)).subs(x, x-x0))) + else: + sol += S(u0[i]) * hyper(ap, bq, c * x**m) * x**i + if as_list: + return listofsol + sol = sol * x**constantpower + if x0 != 0: + return sol.subs(x, x - x0) + + return sol + + def to_expr(self): + """ + Converts a Holonomic Function back to elementary functions. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators + >>> from sympy import ZZ + >>> from sympy import symbols, S + >>> x = symbols('x') + >>> R, Dx = DifferentialOperators(ZZ.old_poly_ring(x),'Dx') + >>> HolonomicFunction(x**2*Dx**2 + x*Dx + (x**2 - 1), x, 0, [0, S(1)/2]).to_expr() + besselj(1, x) + >>> HolonomicFunction((1 + x)*Dx**3 + Dx**2, x, 0, [1, 1, 1]).to_expr() + x*log(x + 1) + log(x + 1) + 1 + + """ + + return hyperexpand(self.to_hyper()).simplify() + + def change_ics(self, b, lenics=None): + """ + Changes the point `x0` to ``b`` for initial conditions. + + Examples + ======== + + >>> from sympy.holonomic import expr_to_holonomic + >>> from sympy import symbols, sin, exp + >>> x = symbols('x') + + >>> expr_to_holonomic(sin(x)).change_ics(1) + HolonomicFunction((1) + (1)*Dx**2, x, 1, [sin(1), cos(1)]) + + >>> expr_to_holonomic(exp(x)).change_ics(2) + HolonomicFunction((-1) + (1)*Dx, x, 2, [exp(2)]) + """ + + symbolic = True + + if lenics is None and len(self.y0) > self.annihilator.order: + lenics = len(self.y0) + dom = self.annihilator.parent.base.domain + + try: + sol = expr_to_holonomic(self.to_expr(), x=self.x, x0=b, lenics=lenics, domain=dom) + except (NotPowerSeriesError, NotHyperSeriesError): + symbolic = False + + if symbolic and sol.x0 == b: + return sol + + y0 = self.evalf(b, derivatives=True) + return HolonomicFunction(self.annihilator, self.x, b, y0) + + def to_meijerg(self): + """ + Returns a linear combination of Meijer G-functions. + + Examples + ======== + + >>> from sympy.holonomic import expr_to_holonomic + >>> from sympy import sin, cos, hyperexpand, log, symbols + >>> x = symbols('x') + >>> hyperexpand(expr_to_holonomic(cos(x) + sin(x)).to_meijerg()) + sin(x) + cos(x) + >>> hyperexpand(expr_to_holonomic(log(x)).to_meijerg()).simplify() + log(x) + + See Also + ======== + + to_hyper + """ + + # convert to hypergeometric first + rep = self.to_hyper(as_list=True) + sol = S.Zero + + for i in rep: + if len(i) == 1: + sol += i[0] + + elif len(i) == 2: + sol += i[0] * _hyper_to_meijerg(i[1]) + + return sol + + +def from_hyper(func, x0=0, evalf=False): + r""" + Converts a hypergeometric function to holonomic. + ``func`` is the Hypergeometric Function and ``x0`` is the point at + which initial conditions are required. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import from_hyper + >>> from sympy import symbols, hyper, S + >>> x = symbols('x') + >>> from_hyper(hyper([], [S(3)/2], x**2/4)) + HolonomicFunction((-x) + (2)*Dx + (x)*Dx**2, x, 1, [sinh(1), -sinh(1) + cosh(1)]) + """ + + a = func.ap + b = func.bq + z = func.args[2] + x = z.atoms(Symbol).pop() + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + + # generalized hypergeometric differential equation + xDx = x*Dx + r1 = 1 + for ai in a: # XXX gives sympify error if Mul is used with list of all factors + r1 *= xDx + ai + xDx_1 = xDx - 1 + # r2 = Mul(*([Dx] + [xDx_1 + bi for bi in b])) # XXX gives sympify error + r2 = Dx + for bi in b: + r2 *= xDx_1 + bi + sol = r1 - r2 + + simp = hyperexpand(func) + + if simp in (Infinity, NegativeInfinity): + return HolonomicFunction(sol, x).composition(z) + + def _find_conditions(simp, x, x0, order, evalf=False): + y0 = [] + for i in range(order): + if evalf: + val = simp.subs(x, x0).evalf() + else: + val = simp.subs(x, x0) + # return None if it is Infinite or NaN + if val.is_finite is False or isinstance(val, NaN): + return None + y0.append(val) + simp = simp.diff(x) + return y0 + + # if the function is known symbolically + if not isinstance(simp, hyper): + y0 = _find_conditions(simp, x, x0, sol.order) + while not y0: + # if values don't exist at 0, then try to find initial + # conditions at 1. If it doesn't exist at 1 too then + # try 2 and so on. + x0 += 1 + y0 = _find_conditions(simp, x, x0, sol.order) + + return HolonomicFunction(sol, x).composition(z, x0, y0) + + if isinstance(simp, hyper): + x0 = 1 + # use evalf if the function can't be simplified + y0 = _find_conditions(simp, x, x0, sol.order, evalf) + while not y0: + x0 += 1 + y0 = _find_conditions(simp, x, x0, sol.order, evalf) + return HolonomicFunction(sol, x).composition(z, x0, y0) + + return HolonomicFunction(sol, x).composition(z) + + +def from_meijerg(func, x0=0, evalf=False, initcond=True, domain=QQ): + """ + Converts a Meijer G-function to Holonomic. + ``func`` is the G-Function and ``x0`` is the point at + which initial conditions are required. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import from_meijerg + >>> from sympy import symbols, meijerg, S + >>> x = symbols('x') + >>> from_meijerg(meijerg(([], []), ([S(1)/2], [0]), x**2/4)) + HolonomicFunction((1) + (1)*Dx**2, x, 0, [0, 1/sqrt(pi)]) + """ + + a = func.ap + b = func.bq + n = len(func.an) + m = len(func.bm) + p = len(a) + z = func.args[2] + x = z.atoms(Symbol).pop() + R, Dx = DifferentialOperators(domain.old_poly_ring(x), 'Dx') + + # compute the differential equation satisfied by the + # Meijer G-function. + xDx = x*Dx + xDx1 = xDx + 1 + r1 = x*(-1)**(m + n - p) + for ai in a: # XXX gives sympify error if args given in list + r1 *= xDx1 - ai + # r2 = Mul(*[xDx - bi for bi in b]) # gives sympify error + r2 = 1 + for bi in b: + r2 *= xDx - bi + sol = r1 - r2 + + if not initcond: + return HolonomicFunction(sol, x).composition(z) + + simp = hyperexpand(func) + + if simp in (Infinity, NegativeInfinity): + return HolonomicFunction(sol, x).composition(z) + + def _find_conditions(simp, x, x0, order, evalf=False): + y0 = [] + for i in range(order): + if evalf: + val = simp.subs(x, x0).evalf() + else: + val = simp.subs(x, x0) + if val.is_finite is False or isinstance(val, NaN): + return None + y0.append(val) + simp = simp.diff(x) + return y0 + + # computing initial conditions + if not isinstance(simp, meijerg): + y0 = _find_conditions(simp, x, x0, sol.order) + while not y0: + x0 += 1 + y0 = _find_conditions(simp, x, x0, sol.order) + + return HolonomicFunction(sol, x).composition(z, x0, y0) + + if isinstance(simp, meijerg): + x0 = 1 + y0 = _find_conditions(simp, x, x0, sol.order, evalf) + while not y0: + x0 += 1 + y0 = _find_conditions(simp, x, x0, sol.order, evalf) + + return HolonomicFunction(sol, x).composition(z, x0, y0) + + return HolonomicFunction(sol, x).composition(z) + + +x_1 = Dummy('x_1') +_lookup_table = None +domain_for_table = None +from sympy.integrals.meijerint import _mytype + + +def expr_to_holonomic(func, x=None, x0=0, y0=None, lenics=None, domain=None, initcond=True): + """ + Converts a function or an expression to a holonomic function. + + Parameters + ========== + + func: + The expression to be converted. + x: + variable for the function. + x0: + point at which initial condition must be computed. + y0: + One can optionally provide initial condition if the method + is not able to do it automatically. + lenics: + Number of terms in the initial condition. By default it is + equal to the order of the annihilator. + domain: + Ground domain for the polynomials in ``x`` appearing as coefficients + in the annihilator. + initcond: + Set it false if you do not want the initial conditions to be computed. + + Examples + ======== + + >>> from sympy.holonomic.holonomic import expr_to_holonomic + >>> from sympy import sin, exp, symbols + >>> x = symbols('x') + >>> expr_to_holonomic(sin(x)) + HolonomicFunction((1) + (1)*Dx**2, x, 0, [0, 1]) + >>> expr_to_holonomic(exp(x)) + HolonomicFunction((-1) + (1)*Dx, x, 0, [1]) + + See Also + ======== + + sympy.integrals.meijerint._rewrite1, _convert_poly_rat_alg, _create_table + """ + func = sympify(func) + syms = func.free_symbols + + if not x: + if len(syms) == 1: + x= syms.pop() + else: + raise ValueError("Specify the variable for the function") + elif x in syms: + syms.remove(x) + + extra_syms = list(syms) + + if domain is None: + if func.has(Float): + domain = RR + else: + domain = QQ + if len(extra_syms) != 0: + domain = domain[extra_syms].get_field() + + # try to convert if the function is polynomial or rational + solpoly = _convert_poly_rat_alg(func, x, x0=x0, y0=y0, lenics=lenics, domain=domain, initcond=initcond) + if solpoly: + return solpoly + + # create the lookup table + global _lookup_table, domain_for_table + if not _lookup_table: + domain_for_table = domain + _lookup_table = {} + _create_table(_lookup_table, domain=domain) + elif domain != domain_for_table: + domain_for_table = domain + _lookup_table = {} + _create_table(_lookup_table, domain=domain) + + # use the table directly to convert to Holonomic + if func.is_Function: + f = func.subs(x, x_1) + t = _mytype(f, x_1) + if t in _lookup_table: + l = _lookup_table[t] + sol = l[0][1].change_x(x) + else: + sol = _convert_meijerint(func, x, initcond=False, domain=domain) + if not sol: + raise NotImplementedError + if y0: + sol.y0 = y0 + if y0 or not initcond: + sol.x0 = x0 + return sol + if not lenics: + lenics = sol.annihilator.order + _y0 = _find_conditions(func, x, x0, lenics) + while not _y0: + x0 += 1 + _y0 = _find_conditions(func, x, x0, lenics) + return HolonomicFunction(sol.annihilator, x, x0, _y0) + + if y0 or not initcond: + sol = sol.composition(func.args[0]) + if y0: + sol.y0 = y0 + sol.x0 = x0 + return sol + if not lenics: + lenics = sol.annihilator.order + + _y0 = _find_conditions(func, x, x0, lenics) + while not _y0: + x0 += 1 + _y0 = _find_conditions(func, x, x0, lenics) + return sol.composition(func.args[0], x0, _y0) + + # iterate through the expression recursively + args = func.args + f = func.func + sol = expr_to_holonomic(args[0], x=x, initcond=False, domain=domain) + + if f is Add: + for i in range(1, len(args)): + sol += expr_to_holonomic(args[i], x=x, initcond=False, domain=domain) + + elif f is Mul: + for i in range(1, len(args)): + sol *= expr_to_holonomic(args[i], x=x, initcond=False, domain=domain) + + elif f is Pow: + sol = sol**args[1] + sol.x0 = x0 + if not sol: + raise NotImplementedError + if y0: + sol.y0 = y0 + if y0 or not initcond: + return sol + if sol.y0: + return sol + if not lenics: + lenics = sol.annihilator.order + if sol.annihilator.is_singular(x0): + r = sol._indicial() + l = list(r) + if len(r) == 1 and r[l[0]] == S.One: + r = l[0] + g = func / (x - x0)**r + singular_ics = _find_conditions(g, x, x0, lenics) + singular_ics = [j / factorial(i) for i, j in enumerate(singular_ics)] + y0 = {r:singular_ics} + return HolonomicFunction(sol.annihilator, x, x0, y0) + + _y0 = _find_conditions(func, x, x0, lenics) + while not _y0: + x0 += 1 + _y0 = _find_conditions(func, x, x0, lenics) + + return HolonomicFunction(sol.annihilator, x, x0, _y0) + + +## Some helper functions ## + +def _normalize(list_of, parent, negative=True): + """ + Normalize a given annihilator + """ + + num = [] + denom = [] + base = parent.base + K = base.get_field() + lcm_denom = base.from_sympy(S.One) + list_of_coeff = [] + + # convert polynomials to the elements of associated + # fraction field + for i, j in enumerate(list_of): + if isinstance(j, base.dtype): + list_of_coeff.append(K.new(j.to_list())) + elif not isinstance(j, K.dtype): + list_of_coeff.append(K.from_sympy(sympify(j))) + else: + list_of_coeff.append(j) + + # corresponding numerators of the sequence of polynomials + num.append(list_of_coeff[i].numer()) + + # corresponding denominators + denom.append(list_of_coeff[i].denom()) + + # lcm of denominators in the coefficients + for i in denom: + lcm_denom = i.lcm(lcm_denom) + + if negative: + lcm_denom = -lcm_denom + + lcm_denom = K.new(lcm_denom.to_list()) + + # multiply the coefficients with lcm + for i, j in enumerate(list_of_coeff): + list_of_coeff[i] = j * lcm_denom + + gcd_numer = base((list_of_coeff[-1].numer() / list_of_coeff[-1].denom()).to_list()) + + # gcd of numerators in the coefficients + for i in num: + gcd_numer = i.gcd(gcd_numer) + + gcd_numer = K.new(gcd_numer.to_list()) + + # divide all the coefficients by the gcd + for i, j in enumerate(list_of_coeff): + frac_ans = j / gcd_numer + list_of_coeff[i] = base((frac_ans.numer() / frac_ans.denom()).to_list()) + + return DifferentialOperator(list_of_coeff, parent) + + +def _derivate_diff_eq(listofpoly, K): + """ + Let a differential equation a0(x)y(x) + a1(x)y'(x) + ... = 0 + where a0, a1,... are polynomials or rational functions. The function + returns b0, b1, b2... such that the differential equation + b0(x)y(x) + b1(x)y'(x) +... = 0 is formed after differentiating the + former equation. + """ + + sol = [] + a = len(listofpoly) - 1 + sol.append(DMFdiff(listofpoly[0], K)) + + for i, j in enumerate(listofpoly[1:]): + sol.append(DMFdiff(j, K) + listofpoly[i]) + + sol.append(listofpoly[a]) + return sol + + +def _hyper_to_meijerg(func): + """ + Converts a `hyper` to meijerg. + """ + ap = func.ap + bq = func.bq + + if any(i <= 0 and int(i) == i for i in ap): + return hyperexpand(func) + + z = func.args[2] + + # parameters of the `meijerg` function. + an = (1 - i for i in ap) + anp = () + bm = (S.Zero, ) + bmq = (1 - i for i in bq) + + k = S.One + + for i in bq: + k = k * gamma(i) + + for i in ap: + k = k / gamma(i) + + return k * meijerg(an, anp, bm, bmq, -z) + + +def _add_lists(list1, list2): + """Takes polynomial sequences of two annihilators a and b and returns + the list of polynomials of sum of a and b. + """ + if len(list1) <= len(list2): + sol = [a + b for a, b in zip(list1, list2)] + list2[len(list1):] + else: + sol = [a + b for a, b in zip(list1, list2)] + list1[len(list2):] + return sol + + +def _extend_y0(Holonomic, n): + """ + Tries to find more initial conditions by substituting the initial + value point in the differential equation. + """ + + if Holonomic.annihilator.is_singular(Holonomic.x0) or Holonomic.is_singularics() == True: + return Holonomic.y0 + + annihilator = Holonomic.annihilator + a = annihilator.order + + listofpoly = [] + + y0 = Holonomic.y0 + R = annihilator.parent.base + K = R.get_field() + + for j in annihilator.listofpoly: + if isinstance(j, annihilator.parent.base.dtype): + listofpoly.append(K.new(j.to_list())) + + if len(y0) < a or n <= len(y0): + return y0 + list_red = [-listofpoly[i] / listofpoly[a] + for i in range(a)] + y1 = y0[:min(len(y0), a)] + for _ in range(n - a): + sol = 0 + for a, b in zip(y1, list_red): + r = DMFsubs(b, Holonomic.x0) + if not getattr(r, 'is_finite', True): + return y0 + if isinstance(r, (PolyElement, FracElement)): + r = r.as_expr() + sol += a * r + y1.append(sol) + list_red = _derivate_diff_eq(list_red, K) + return y0 + y1[len(y0):] + + +def DMFdiff(frac, K): + # differentiate a DMF object represented as p/q + if not isinstance(frac, DMF): + return frac.diff() + + p = K.numer(frac) + q = K.denom(frac) + sol_num = - p * q.diff() + q * p.diff() + sol_denom = q**2 + return K((sol_num.to_list(), sol_denom.to_list())) + + +def DMFsubs(frac, x0, mpm=False): + # substitute the point x0 in DMF object of the form p/q + if not isinstance(frac, DMF): + return frac + + p = frac.num + q = frac.den + sol_p = S.Zero + sol_q = S.Zero + + if mpm: + from mpmath import mp + + for i, j in enumerate(reversed(p)): + if mpm: + j = sympify(j)._to_mpmath(mp.prec) + sol_p += j * x0**i + + for i, j in enumerate(reversed(q)): + if mpm: + j = sympify(j)._to_mpmath(mp.prec) + sol_q += j * x0**i + + if isinstance(sol_p, (PolyElement, FracElement)): + sol_p = sol_p.as_expr() + if isinstance(sol_q, (PolyElement, FracElement)): + sol_q = sol_q.as_expr() + + return sol_p / sol_q + + +def _convert_poly_rat_alg(func, x, x0=0, y0=None, lenics=None, domain=QQ, initcond=True): + """ + Converts polynomials, rationals and algebraic functions to holonomic. + """ + + ispoly = func.is_polynomial() + if not ispoly: + israt = func.is_rational_function() + else: + israt = True + + if not (ispoly or israt): + basepoly, ratexp = func.as_base_exp() + if basepoly.is_polynomial() and ratexp.is_Number: + if isinstance(ratexp, Float): + ratexp = nsimplify(ratexp) + m, n = ratexp.p, ratexp.q + is_alg = True + else: + is_alg = False + else: + is_alg = True + + if not (ispoly or israt or is_alg): + return None + + R = domain.old_poly_ring(x) + _, Dx = DifferentialOperators(R, 'Dx') + + # if the function is constant + if not func.has(x): + return HolonomicFunction(Dx, x, 0, [func]) + + if ispoly: + # differential equation satisfied by polynomial + sol = func * Dx - func.diff(x) + sol = _normalize(sol.listofpoly, sol.parent, negative=False) + is_singular = sol.is_singular(x0) + + # try to compute the conditions for singular points + if y0 is None and x0 == 0 and is_singular: + rep = R.from_sympy(func).to_list() + for i, j in enumerate(reversed(rep)): + if j == 0: + continue + coeff = list(reversed(rep))[i:] + indicial = i + break + for i, j in enumerate(coeff): + if isinstance(j, (PolyElement, FracElement)): + coeff[i] = j.as_expr() + y0 = {indicial: S(coeff)} + + elif israt: + p, q = func.as_numer_denom() + # differential equation satisfied by rational + sol = p * q * Dx + p * q.diff(x) - q * p.diff(x) + sol = _normalize(sol.listofpoly, sol.parent, negative=False) + + elif is_alg: + sol = n * (x / m) * Dx - 1 + sol = HolonomicFunction(sol, x).composition(basepoly).annihilator + is_singular = sol.is_singular(x0) + + # try to compute the conditions for singular points + if y0 is None and x0 == 0 and is_singular and \ + (lenics is None or lenics <= 1): + rep = R.from_sympy(basepoly).to_list() + for i, j in enumerate(reversed(rep)): + if j == 0: + continue + if isinstance(j, (PolyElement, FracElement)): + j = j.as_expr() + + coeff = S(j)**ratexp + indicial = S(i) * ratexp + break + if isinstance(coeff, (PolyElement, FracElement)): + coeff = coeff.as_expr() + y0 = {indicial: S([coeff])} + + if y0 or not initcond: + return HolonomicFunction(sol, x, x0, y0) + + if not lenics: + lenics = sol.order + + if sol.is_singular(x0): + r = HolonomicFunction(sol, x, x0)._indicial() + l = list(r) + if len(r) == 1 and r[l[0]] == S.One: + r = l[0] + g = func / (x - x0)**r + singular_ics = _find_conditions(g, x, x0, lenics) + singular_ics = [j / factorial(i) for i, j in enumerate(singular_ics)] + y0 = {r:singular_ics} + return HolonomicFunction(sol, x, x0, y0) + + y0 = _find_conditions(func, x, x0, lenics) + while not y0: + x0 += 1 + y0 = _find_conditions(func, x, x0, lenics) + + return HolonomicFunction(sol, x, x0, y0) + + +def _convert_meijerint(func, x, initcond=True, domain=QQ): + args = meijerint._rewrite1(func, x) + + if args: + fac, po, g, _ = args + else: + return None + + # lists for sum of meijerg functions + fac_list = [fac * i[0] for i in g] + t = po.as_base_exp() + s = t[1] if t[0] == x else S.Zero + po_list = [s + i[1] for i in g] + G_list = [i[2] for i in g] + + # finds meijerg representation of x**s * meijerg(a1 ... ap, b1 ... bq, z) + def _shift(func, s): + z = func.args[-1] + if z.has(I): + z = z.subs(exp_polar, exp) + + d = z.collect(x, evaluate=False) + b = list(d)[0] + a = d[b] + + t = b.as_base_exp() + b = t[1] if t[0] == x else S.Zero + r = s / b + an = (i + r for i in func.args[0][0]) + ap = (i + r for i in func.args[0][1]) + bm = (i + r for i in func.args[1][0]) + bq = (i + r for i in func.args[1][1]) + + return a**-r, meijerg((an, ap), (bm, bq), z) + + coeff, m = _shift(G_list[0], po_list[0]) + sol = fac_list[0] * coeff * from_meijerg(m, initcond=initcond, domain=domain) + + # add all the meijerg functions after converting to holonomic + for i in range(1, len(G_list)): + coeff, m = _shift(G_list[i], po_list[i]) + sol += fac_list[i] * coeff * from_meijerg(m, initcond=initcond, domain=domain) + + return sol + + +def _create_table(table, domain=QQ): + """ + Creates the look-up table. For a similar implementation + see meijerint._create_lookup_table. + """ + + def add(formula, annihilator, arg, x0=0, y0=()): + """ + Adds a formula in the dictionary + """ + table.setdefault(_mytype(formula, x_1), []).append((formula, + HolonomicFunction(annihilator, arg, x0, y0))) + + R = domain.old_poly_ring(x_1) + _, Dx = DifferentialOperators(R, 'Dx') + + # add some basic functions + add(sin(x_1), Dx**2 + 1, x_1, 0, [0, 1]) + add(cos(x_1), Dx**2 + 1, x_1, 0, [1, 0]) + add(exp(x_1), Dx - 1, x_1, 0, 1) + add(log(x_1), Dx + x_1*Dx**2, x_1, 1, [0, 1]) + + add(erf(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)]) + add(erfc(x_1), 2*x_1*Dx + Dx**2, x_1, 0, [1, -2/sqrt(pi)]) + add(erfi(x_1), -2*x_1*Dx + Dx**2, x_1, 0, [0, 2/sqrt(pi)]) + + add(sinh(x_1), Dx**2 - 1, x_1, 0, [0, 1]) + add(cosh(x_1), Dx**2 - 1, x_1, 0, [1, 0]) + + add(sinc(x_1), x_1 + 2*Dx + x_1*Dx**2, x_1) + + add(Si(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1) + add(Ci(x_1), x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1) + + add(Shi(x_1), -x_1*Dx + 2*Dx**2 + x_1*Dx**3, x_1) + + +def _find_conditions(func, x, x0, order): + y0 = [] + for i in range(order): + val = func.subs(x, x0) + if isinstance(val, NaN): + val = limit(func, x, x0) + if val.is_finite is False or isinstance(val, NaN): + return None + y0.append(val) + func = func.diff(x) + return y0 diff --git a/lib/python3.11/site-packages/sympy/holonomic/holonomicerrors.py b/lib/python3.11/site-packages/sympy/holonomic/holonomicerrors.py new file mode 100644 index 0000000000000000000000000000000000000000..459a94eb25b186e30b9577d972ebc62a36801f6f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/holonomic/holonomicerrors.py @@ -0,0 +1,49 @@ +""" Common Exceptions for `holonomic` module. """ + +class BaseHolonomicError(Exception): + + def new(self, *args): + raise NotImplementedError("abstract base class") + +class NotPowerSeriesError(BaseHolonomicError): + + def __init__(self, holonomic, x0): + self.holonomic = holonomic + self.x0 = x0 + + def __str__(self): + s = 'A Power Series does not exists for ' + s += str(self.holonomic) + s += ' about %s.' %self.x0 + return s + +class NotHolonomicError(BaseHolonomicError): + + def __init__(self, m): + self.m = m + + def __str__(self): + return self.m + +class SingularityError(BaseHolonomicError): + + def __init__(self, holonomic, x0): + self.holonomic = holonomic + self.x0 = x0 + + def __str__(self): + s = str(self.holonomic) + s += ' has a singularity at %s.' %self.x0 + return s + +class NotHyperSeriesError(BaseHolonomicError): + + def __init__(self, holonomic, x0): + self.holonomic = holonomic + self.x0 = x0 + + def __str__(self): + s = 'Power series expansion of ' + s += str(self.holonomic) + s += ' about %s is not hypergeometric' %self.x0 + return s diff --git a/lib/python3.11/site-packages/sympy/holonomic/numerical.py b/lib/python3.11/site-packages/sympy/holonomic/numerical.py new file mode 100644 index 0000000000000000000000000000000000000000..05158446104688f6216d93dcee72fc80fbf37ce1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/holonomic/numerical.py @@ -0,0 +1,109 @@ +"""Numerical Methods for Holonomic Functions""" + +from sympy.core.sympify import sympify +from sympy.holonomic.holonomic import DMFsubs + +from mpmath import mp + + +def _evalf(func, points, derivatives=False, method='RK4'): + """ + Numerical methods for numerical integration along a given set of + points in the complex plane. + """ + + ann = func.annihilator + a = ann.order + R = ann.parent.base + K = R.get_field() + + if method == 'Euler': + meth = _euler + else: + meth = _rk4 + + dmf = [] + for j in ann.listofpoly: + dmf.append(K.new(j.to_list())) + + red = [-dmf[i] / dmf[a] for i in range(a)] + + y0 = func.y0 + if len(y0) < a: + raise TypeError("Not Enough Initial Conditions") + x0 = func.x0 + sol = [meth(red, x0, points[0], y0, a)] + + for i, j in enumerate(points[1:]): + sol.append(meth(red, points[i], j, sol[-1], a)) + + if not derivatives: + return [sympify(i[0]) for i in sol] + else: + return sympify(sol) + + +def _euler(red, x0, x1, y0, a): + """ + Euler's method for numerical integration. + From x0 to x1 with initial values given at x0 as vector y0. + """ + + A = sympify(x0)._to_mpmath(mp.prec) + B = sympify(x1)._to_mpmath(mp.prec) + y_0 = [sympify(i)._to_mpmath(mp.prec) for i in y0] + h = B - A + f_0 = y_0[1:] + f_0_n = 0 + + for i in range(a): + f_0_n += sympify(DMFsubs(red[i], A, mpm=True))._to_mpmath(mp.prec) * y_0[i] + f_0.append(f_0_n) + + sol = [] + for i in range(a): + sol.append(y_0[i] + h * f_0[i]) + + return sol + + +def _rk4(red, x0, x1, y0, a): + """ + Runge-Kutta 4th order numerical method. + """ + + A = sympify(x0)._to_mpmath(mp.prec) + B = sympify(x1)._to_mpmath(mp.prec) + y_0 = [sympify(i)._to_mpmath(mp.prec) for i in y0] + h = B - A + + f_0_n = 0 + f_1_n = 0 + f_2_n = 0 + f_3_n = 0 + + f_0 = y_0[1:] + for i in range(a): + f_0_n += sympify(DMFsubs(red[i], A, mpm=True))._to_mpmath(mp.prec) * y_0[i] + f_0.append(f_0_n) + + f_1 = [y_0[i] + f_0[i]*h/2 for i in range(1, a)] + for i in range(a): + f_1_n += sympify(DMFsubs(red[i], A + h/2, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_0[i]*h/2) + f_1.append(f_1_n) + + f_2 = [y_0[i] + f_1[i]*h/2 for i in range(1, a)] + for i in range(a): + f_2_n += sympify(DMFsubs(red[i], A + h/2, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_1[i]*h/2) + f_2.append(f_2_n) + + f_3 = [y_0[i] + f_2[i]*h for i in range(1, a)] + for i in range(a): + f_3_n += sympify(DMFsubs(red[i], A + h, mpm=True))._to_mpmath(mp.prec) * (y_0[i] + f_2[i]*h) + f_3.append(f_3_n) + + sol = [] + for i in range(a): + sol.append(y_0[i] + h * (f_0[i]+2*f_1[i]+2*f_2[i]+f_3[i])/6) + + return sol diff --git a/lib/python3.11/site-packages/sympy/holonomic/recurrence.py b/lib/python3.11/site-packages/sympy/holonomic/recurrence.py new file mode 100644 index 0000000000000000000000000000000000000000..8c7e21402d313a1528bf1d540bd486ee68656d63 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/holonomic/recurrence.py @@ -0,0 +1,365 @@ +"""Recurrence Operators""" + +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.printing import sstr +from sympy.core.sympify import sympify + + +def RecurrenceOperators(base, generator): + """ + Returns an Algebra of Recurrence Operators and the operator for + shifting i.e. the `Sn` operator. + The first argument needs to be the base polynomial ring for the algebra + and the second argument must be a generator which can be either a + noncommutative Symbol or a string. + + Examples + ======== + + >>> from sympy import ZZ + >>> from sympy import symbols + >>> from sympy.holonomic.recurrence import RecurrenceOperators + >>> n = symbols('n', integer=True) + >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn') + """ + + ring = RecurrenceOperatorAlgebra(base, generator) + return (ring, ring.shift_operator) + + +class RecurrenceOperatorAlgebra: + """ + A Recurrence Operator Algebra is a set of noncommutative polynomials + in intermediate `Sn` and coefficients in a base ring A. It follows the + commutation rule: + Sn * a(n) = a(n + 1) * Sn + + This class represents a Recurrence Operator Algebra and serves as the parent ring + for Recurrence Operators. + + Examples + ======== + + >>> from sympy import ZZ + >>> from sympy import symbols + >>> from sympy.holonomic.recurrence import RecurrenceOperators + >>> n = symbols('n', integer=True) + >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn') + >>> R + Univariate Recurrence Operator Algebra in intermediate Sn over the base ring + ZZ[n] + + See Also + ======== + + RecurrenceOperator + """ + + def __init__(self, base, generator): + # the base ring for the algebra + self.base = base + # the operator representing shift i.e. `Sn` + self.shift_operator = RecurrenceOperator( + [base.zero, base.one], self) + + if generator is None: + self.gen_symbol = symbols('Sn', commutative=False) + else: + if isinstance(generator, str): + self.gen_symbol = symbols(generator, commutative=False) + elif isinstance(generator, Symbol): + self.gen_symbol = generator + + def __str__(self): + string = 'Univariate Recurrence Operator Algebra in intermediate '\ + + sstr(self.gen_symbol) + ' over the base ring ' + \ + (self.base).__str__() + + return string + + __repr__ = __str__ + + def __eq__(self, other): + if self.base == other.base and self.gen_symbol == other.gen_symbol: + return True + else: + return False + + +def _add_lists(list1, list2): + if len(list1) <= len(list2): + sol = [a + b for a, b in zip(list1, list2)] + list2[len(list1):] + else: + sol = [a + b for a, b in zip(list1, list2)] + list1[len(list2):] + return sol + + +class RecurrenceOperator: + """ + The Recurrence Operators are defined by a list of polynomials + in the base ring and the parent ring of the Operator. + + Explanation + =========== + + Takes a list of polynomials for each power of Sn and the + parent ring which must be an instance of RecurrenceOperatorAlgebra. + + A Recurrence Operator can be created easily using + the operator `Sn`. See examples below. + + Examples + ======== + + >>> from sympy.holonomic.recurrence import RecurrenceOperator, RecurrenceOperators + >>> from sympy import ZZ + >>> from sympy import symbols + >>> n = symbols('n', integer=True) + >>> R, Sn = RecurrenceOperators(ZZ.old_poly_ring(n),'Sn') + + >>> RecurrenceOperator([0, 1, n**2], R) + (1)Sn + (n**2)Sn**2 + + >>> Sn*n + (n + 1)Sn + + >>> n*Sn*n + 1 - Sn**2*n + (1) + (n**2 + n)Sn + (-n - 2)Sn**2 + + See Also + ======== + + DifferentialOperatorAlgebra + """ + + _op_priority = 20 + + def __init__(self, list_of_poly, parent): + # the parent ring for this operator + # must be an RecurrenceOperatorAlgebra object + self.parent = parent + # sequence of polynomials in n for each power of Sn + # represents the operator + # convert the expressions into ring elements using from_sympy + if isinstance(list_of_poly, list): + for i, j in enumerate(list_of_poly): + if isinstance(j, int): + list_of_poly[i] = self.parent.base.from_sympy(S(j)) + elif not isinstance(j, self.parent.base.dtype): + list_of_poly[i] = self.parent.base.from_sympy(j) + + self.listofpoly = list_of_poly + self.order = len(self.listofpoly) - 1 + + def __mul__(self, other): + """ + Multiplies two Operators and returns another + RecurrenceOperator instance using the commutation rule + Sn * a(n) = a(n + 1) * Sn + """ + + listofself = self.listofpoly + base = self.parent.base + + if not isinstance(other, RecurrenceOperator): + if not isinstance(other, self.parent.base.dtype): + listofother = [self.parent.base.from_sympy(sympify(other))] + + else: + listofother = [other] + else: + listofother = other.listofpoly + # multiply a polynomial `b` with a list of polynomials + + def _mul_dmp_diffop(b, listofother): + if isinstance(listofother, list): + sol = [] + for i in listofother: + sol.append(i * b) + return sol + else: + return [b * listofother] + + sol = _mul_dmp_diffop(listofself[0], listofother) + + # compute Sn^i * b + def _mul_Sni_b(b): + sol = [base.zero] + + if isinstance(b, list): + for i in b: + j = base.to_sympy(i).subs(base.gens[0], base.gens[0] + S.One) + sol.append(base.from_sympy(j)) + + else: + j = b.subs(base.gens[0], base.gens[0] + S.One) + sol.append(base.from_sympy(j)) + + return sol + + for i in range(1, len(listofself)): + # find Sn^i * b in ith iteration + listofother = _mul_Sni_b(listofother) + # solution = solution + listofself[i] * (Sn^i * b) + sol = _add_lists(sol, _mul_dmp_diffop(listofself[i], listofother)) + + return RecurrenceOperator(sol, self.parent) + + def __rmul__(self, other): + if not isinstance(other, RecurrenceOperator): + + if isinstance(other, int): + other = S(other) + + if not isinstance(other, self.parent.base.dtype): + other = (self.parent.base).from_sympy(other) + + sol = [] + for j in self.listofpoly: + sol.append(other * j) + + return RecurrenceOperator(sol, self.parent) + + def __add__(self, other): + if isinstance(other, RecurrenceOperator): + + sol = _add_lists(self.listofpoly, other.listofpoly) + return RecurrenceOperator(sol, self.parent) + + else: + + if isinstance(other, int): + other = S(other) + list_self = self.listofpoly + if not isinstance(other, self.parent.base.dtype): + list_other = [((self.parent).base).from_sympy(other)] + else: + list_other = [other] + sol = [] + sol.append(list_self[0] + list_other[0]) + sol += list_self[1:] + + return RecurrenceOperator(sol, self.parent) + + __radd__ = __add__ + + def __sub__(self, other): + return self + (-1) * other + + def __rsub__(self, other): + return (-1) * self + other + + def __pow__(self, n): + if n == 1: + return self + result = RecurrenceOperator([self.parent.base.one], self.parent) + if n == 0: + return result + # if self is `Sn` + if self.listofpoly == self.parent.shift_operator.listofpoly: + sol = [self.parent.base.zero] * n + [self.parent.base.one] + return RecurrenceOperator(sol, self.parent) + x = self + while True: + if n % 2: + result *= x + n >>= 1 + if not n: + break + x *= x + return result + + def __str__(self): + listofpoly = self.listofpoly + print_str = '' + + for i, j in enumerate(listofpoly): + if j == self.parent.base.zero: + continue + + j = self.parent.base.to_sympy(j) + + if i == 0: + print_str += '(' + sstr(j) + ')' + continue + + if print_str: + print_str += ' + ' + + if i == 1: + print_str += '(' + sstr(j) + ')Sn' + continue + + print_str += '(' + sstr(j) + ')' + 'Sn**' + sstr(i) + + return print_str + + __repr__ = __str__ + + def __eq__(self, other): + if isinstance(other, RecurrenceOperator): + if self.listofpoly == other.listofpoly and self.parent == other.parent: + return True + else: + return False + else: + if self.listofpoly[0] == other: + for i in self.listofpoly[1:]: + if i is not self.parent.base.zero: + return False + return True + else: + return False + + +class HolonomicSequence: + """ + A Holonomic Sequence is a type of sequence satisfying a linear homogeneous + recurrence relation with Polynomial coefficients. Alternatively, A sequence + is Holonomic if and only if its generating function is a Holonomic Function. + """ + + def __init__(self, recurrence, u0=[]): + self.recurrence = recurrence + if not isinstance(u0, list): + self.u0 = [u0] + else: + self.u0 = u0 + + if len(self.u0) == 0: + self._have_init_cond = False + else: + self._have_init_cond = True + self.n = recurrence.parent.base.gens[0] + + def __repr__(self): + str_sol = 'HolonomicSequence(%s, %s)' % ((self.recurrence).__repr__(), sstr(self.n)) + if not self._have_init_cond: + return str_sol + else: + cond_str = '' + seq_str = 0 + for i in self.u0: + cond_str += ', u(%s) = %s' % (sstr(seq_str), sstr(i)) + seq_str += 1 + + sol = str_sol + cond_str + return sol + + __str__ = __repr__ + + def __eq__(self, other): + if self.recurrence == other.recurrence: + if self.n == other.n: + if self._have_init_cond and other._have_init_cond: + if self.u0 == other.u0: + return True + else: + return False + else: + return True + else: + return 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b/lib/python3.11/site-packages/sympy/holonomic/tests/test_holonomic.py @@ -0,0 +1,851 @@ +from sympy.holonomic import (DifferentialOperator, HolonomicFunction, + DifferentialOperators, from_hyper, + from_meijerg, expr_to_holonomic) +from sympy.holonomic.recurrence import RecurrenceOperators, HolonomicSequence +from sympy.core import EulerGamma +from sympy.core.numbers import (I, Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.hyperbolic import (asinh, cosh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin) +from sympy.functions.special.bessel import besselj +from sympy.functions.special.beta_functions import beta +from sympy.functions.special.error_functions import (Ci, Si, erf, erfc) +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import (hyper, meijerg) +from sympy.printing.str import sstr +from sympy.series.order import O +from sympy.simplify.hyperexpand import hyperexpand +from sympy.polys.domains.integerring import ZZ +from sympy.polys.domains.rationalfield import QQ +from sympy.polys.domains.realfield import RR + + +def test_DifferentialOperator(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + assert Dx == R.derivative_operator + assert Dx == DifferentialOperator([R.base.zero, R.base.one], R) + assert x * Dx + x**2 * Dx**2 == DifferentialOperator([0, x, x**2], R) + assert (x**2 + 1) + Dx + x * \ + Dx**5 == DifferentialOperator([x**2 + 1, 1, 0, 0, 0, x], R) + assert (x * Dx + x**2 + 1 - Dx * (x**3 + x))**3 == (-48 * x**6) + \ + (-57 * x**7) * Dx + (-15 * x**8) * Dx**2 + (-x**9) * Dx**3 + p = (x * Dx**2 + (x**2 + 3) * Dx**5) * (Dx + x**2) + q = (2 * x) + (4 * x**2) * Dx + (x**3) * Dx**2 + \ + (20 * x**2 + x + 60) * Dx**3 + (10 * x**3 + 30 * x) * Dx**4 + \ + (x**4 + 3 * x**2) * Dx**5 + (x**2 + 3) * Dx**6 + assert p == q + + +def test_HolonomicFunction_addition(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx**2 * x, x) + q = HolonomicFunction((2) * Dx + (x) * Dx**2, x) + assert p == q + p = HolonomicFunction(x * Dx + 1, x) + q = HolonomicFunction(Dx + 1, x) + r = HolonomicFunction((x - 2) + (x**2 - 2) * Dx + (x**2 - x) * Dx**2, x) + assert p + q == r + p = HolonomicFunction(x * Dx + Dx**2 * (x**2 + 2), x) + q = HolonomicFunction(Dx - 3, x) + r = HolonomicFunction((-54 * x**2 - 126 * x - 150) + (-135 * x**3 - 252 * x**2 - 270 * x + 140) * Dx +\ + (-27 * x**4 - 24 * x**2 + 14 * x - 150) * Dx**2 + \ + (9 * x**4 + 15 * x**3 + 38 * x**2 + 30 * x +40) * Dx**3, x) + assert p + q == r + p = HolonomicFunction(Dx**5 - 1, x) + q = HolonomicFunction(x**3 + Dx, x) + r = HolonomicFunction((-x**18 + 45*x**14 - 525*x**10 + 1575*x**6 - x**3 - 630*x**2) + \ + (-x**15 + 30*x**11 - 195*x**7 + 210*x**3 - 1)*Dx + (x**18 - 45*x**14 + 525*x**10 - \ + 1575*x**6 + x**3 + 630*x**2)*Dx**5 + (x**15 - 30*x**11 + 195*x**7 - 210*x**3 + \ + 1)*Dx**6, x) + assert p+q == r + + p = x**2 + 3*x + 8 + q = x**3 - 7*x + 5 + p = p*Dx - p.diff() + q = q*Dx - q.diff() + r = HolonomicFunction(p, x) + HolonomicFunction(q, x) + s = HolonomicFunction((6*x**2 + 18*x + 14) + (-4*x**3 - 18*x**2 - 62*x + 10)*Dx +\ + (x**4 + 6*x**3 + 31*x**2 - 10*x - 71)*Dx**2, x) + assert r == s + + +def test_HolonomicFunction_multiplication(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx+x+x*Dx**2, x) + q = HolonomicFunction(x*Dx+Dx*x+Dx**2, x) + r = HolonomicFunction((8*x**6 + 4*x**4 + 6*x**2 + 3) + (24*x**5 - 4*x**3 + 24*x)*Dx + \ + (8*x**6 + 20*x**4 + 12*x**2 + 2)*Dx**2 + (8*x**5 + 4*x**3 + 4*x)*Dx**3 + \ + (2*x**4 + x**2)*Dx**4, x) + assert p*q == r + p = HolonomicFunction(Dx**2+1, x) + q = HolonomicFunction(Dx-1, x) + r = HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x) + assert p*q == r + p = HolonomicFunction(Dx**2+1+x+Dx, x) + q = HolonomicFunction((Dx*x-1)**2, x) + r = HolonomicFunction((4*x**7 + 11*x**6 + 16*x**5 + 4*x**4 - 6*x**3 - 7*x**2 - 8*x - 2) + \ + (8*x**6 + 26*x**5 + 24*x**4 - 3*x**3 - 11*x**2 - 6*x - 2)*Dx + \ + (8*x**6 + 18*x**5 + 15*x**4 - 3*x**3 - 6*x**2 - 6*x - 2)*Dx**2 + (8*x**5 + \ + 10*x**4 + 6*x**3 - 2*x**2 - 4*x)*Dx**3 + (4*x**5 + 3*x**4 - x**2)*Dx**4, x) + assert p*q == r + p = HolonomicFunction(x*Dx**2-1, x) + q = HolonomicFunction(Dx*x-x, x) + r = HolonomicFunction((x - 3) + (-2*x + 2)*Dx + (x)*Dx**2, x) + assert p*q == r + + +def test_HolonomicFunction_power(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx+x+x*Dx**2, x) + a = HolonomicFunction(Dx, x) + for n in range(10): + assert a == p**n + a *= p + + +def test_addition_initial_condition(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx-1, x, 0, [3]) + q = HolonomicFunction(Dx**2+1, x, 0, [1, 0]) + r = HolonomicFunction(-1 + Dx - Dx**2 + Dx**3, x, 0, [4, 3, 2]) + assert p + q == r + p = HolonomicFunction(Dx - x + Dx**2, x, 0, [1, 2]) + q = HolonomicFunction(Dx**2 + x, x, 0, [1, 0]) + r = HolonomicFunction((-x**4 - x**3/4 - x**2 + Rational(1, 4)) + (x**3 + x**2/4 + x*Rational(3, 4) + 1)*Dx + \ + (x*Rational(-3, 2) + Rational(7, 4))*Dx**2 + (x**2 - x*Rational(7, 4) + Rational(1, 4))*Dx**3 + (x**2 + x/4 + S.Half)*Dx**4, x, 0, [2, 2, -2, 2]) + assert p + q == r + p = HolonomicFunction(Dx**2 + 4*x*Dx + x**2, x, 0, [3, 4]) + q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 1]) + r = HolonomicFunction((x**6 + 2*x**4 - 5*x**2 - 6) + (4*x**5 + 36*x**3 - 32*x)*Dx + \ + (x**6 + 3*x**4 + 5*x**2 - 9)*Dx**2 + (4*x**5 + 36*x**3 - 32*x)*Dx**3 + (x**4 + \ + 10*x**2 - 3)*Dx**4, x, 0, [4, 5, -1, -17]) + assert p + q == r + q = HolonomicFunction(Dx**3 + x, x, 2, [3, 0, 1]) + p = HolonomicFunction(Dx - 1, x, 2, [1]) + r = HolonomicFunction((-x**2 - x + 1) + (x**2 + x)*Dx + (-x - 2)*Dx**3 + \ + (x + 1)*Dx**4, x, 2, [4, 1, 2, -5 ]) + assert p + q == r + p = expr_to_holonomic(sin(x)) + q = expr_to_holonomic(1/x, x0=1) + r = HolonomicFunction((x**2 + 6) + (x**3 + 2*x)*Dx + (x**2 + 6)*Dx**2 + (x**3 + 2*x)*Dx**3, \ + x, 1, [sin(1) + 1, -1 + cos(1), -sin(1) + 2]) + assert p + q == r + C_1 = symbols('C_1') + p = expr_to_holonomic(sqrt(x)) + q = expr_to_holonomic(sqrt(x**2-x)) + r = (p + q).to_expr().subs(C_1, -I/2).expand() + assert r == I*sqrt(x)*sqrt(-x + 1) + sqrt(x) + + +def test_multiplication_initial_condition(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx**2 + x*Dx - 1, x, 0, [3, 1]) + q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 1]) + r = HolonomicFunction((x**4 + 14*x**2 + 60) + 4*x*Dx + (x**4 + 9*x**2 + 20)*Dx**2 + \ + (2*x**3 + 18*x)*Dx**3 + (x**2 + 10)*Dx**4, x, 0, [3, 4, 2, 3]) + assert p * q == r + p = HolonomicFunction(Dx**2 + x, x, 0, [1, 0]) + q = HolonomicFunction(Dx**3 - x**2, x, 0, [3, 3, 3]) + r = HolonomicFunction((x**8 - 37*x**7/27 - 10*x**6/27 - 164*x**5/9 - 184*x**4/9 + \ + 160*x**3/27 + 404*x**2/9 + 8*x + Rational(40, 3)) + (6*x**7 - 128*x**6/9 - 98*x**5/9 - 28*x**4/9 + \ + 8*x**3/9 + 28*x**2 + x*Rational(40, 9) - 40)*Dx + (3*x**6 - 82*x**5/9 + 76*x**4/9 + 4*x**3/3 + \ + 220*x**2/9 - x*Rational(80, 3))*Dx**2 + (-2*x**6 + 128*x**5/27 - 2*x**4/3 -80*x**2/9 + Rational(200, 9))*Dx**3 + \ + (3*x**5 - 64*x**4/9 - 28*x**3/9 + 6*x**2 - x*Rational(20, 9) - Rational(20, 3))*Dx**4 + (-4*x**3 + 64*x**2/9 + \ + x*Rational(8, 3))*Dx**5 + (x**4 - 64*x**3/27 - 4*x**2/3 + Rational(20, 9))*Dx**6, x, 0, [3, 3, 3, -3, -12, -24]) + assert p * q == r + p = HolonomicFunction(Dx - 1, x, 0, [2]) + q = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]) + r = HolonomicFunction(2 -2*Dx + Dx**2, x, 0, [0, 2]) + assert p * q == r + q = HolonomicFunction(x*Dx**2 + 1 + 2*Dx, x, 0,[0, 1]) + r = HolonomicFunction((x - 1) + (-2*x + 2)*Dx + x*Dx**2, x, 0, [0, 2]) + assert p * q == r + p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 3]) + q = HolonomicFunction(Dx**3 + 1, x, 0, [1, 2, 1]) + r = HolonomicFunction(6*Dx + 3*Dx**2 + 2*Dx**3 - 3*Dx**4 + Dx**6, x, 0, [1, 5, 14, 17, 17, 2]) + assert p * q == r + p = expr_to_holonomic(sin(x)) + q = expr_to_holonomic(1/x, x0=1) + r = HolonomicFunction(x + 2*Dx + x*Dx**2, x, 1, [sin(1), -sin(1) + cos(1)]) + assert p * q == r + p = expr_to_holonomic(sqrt(x)) + q = expr_to_holonomic(sqrt(x**2-x)) + r = (p * q).to_expr() + assert r == I*x*sqrt(-x + 1) + + +def test_HolonomicFunction_composition(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx-1, x).composition(x**2+x) + r = HolonomicFunction((-2*x - 1) + Dx, x) + assert p == r + p = HolonomicFunction(Dx**2+1, x).composition(x**5+x**2+1) + r = HolonomicFunction((125*x**12 + 150*x**9 + 60*x**6 + 8*x**3) + (-20*x**3 - 2)*Dx + \ + (5*x**4 + 2*x)*Dx**2, x) + assert p == r + p = HolonomicFunction(Dx**2*x+x, x).composition(2*x**3+x**2+1) + r = HolonomicFunction((216*x**9 + 324*x**8 + 180*x**7 + 152*x**6 + 112*x**5 + \ + 36*x**4 + 4*x**3) + (24*x**4 + 16*x**3 + 3*x**2 - 6*x - 1)*Dx + (6*x**5 + 5*x**4 + \ + x**3 + 3*x**2 + x)*Dx**2, x) + assert p == r + p = HolonomicFunction(Dx**2+1, x).composition(1-x**2) + r = HolonomicFunction((4*x**3) - Dx + x*Dx**2, x) + assert p == r + p = HolonomicFunction(Dx**2+1, x).composition(x - 2/(x**2 + 1)) + r = HolonomicFunction((x**12 + 6*x**10 + 12*x**9 + 15*x**8 + 48*x**7 + 68*x**6 + \ + 72*x**5 + 111*x**4 + 112*x**3 + 54*x**2 + 12*x + 1) + (12*x**8 + 32*x**6 + \ + 24*x**4 - 4)*Dx + (x**12 + 6*x**10 + 4*x**9 + 15*x**8 + 16*x**7 + 20*x**6 + 24*x**5+ \ + 15*x**4 + 16*x**3 + 6*x**2 + 4*x + 1)*Dx**2, x) + assert p == r + + +def test_from_hyper(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = hyper([1, 1], [Rational(3, 2)], x**2/4) + q = HolonomicFunction((4*x) + (5*x**2 - 8)*Dx + (x**3 - 4*x)*Dx**2, x, 1, [2*sqrt(3)*pi/9, -4*sqrt(3)*pi/27 + Rational(4, 3)]) + r = from_hyper(p) + assert r == q + p = from_hyper(hyper([1], [Rational(3, 2)], x**2/4)) + q = HolonomicFunction(-x + (-x**2/2 + 2)*Dx + x*Dx**2, x) + # x0 = 1 + y0 = '[sqrt(pi)*exp(1/4)*erf(1/2), -sqrt(pi)*exp(1/4)*erf(1/2)/2 + 1]' + assert sstr(p.y0) == y0 + assert q.annihilator == p.annihilator + + +def test_from_meijerg(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = from_meijerg(meijerg(([], [Rational(3, 2)]), ([S.Half], [S.Half, 1]), x)) + q = HolonomicFunction(x/2 - Rational(1, 4) + (-x**2 + x/4)*Dx + x**2*Dx**2 + x**3*Dx**3, x, 1, \ + [1/sqrt(pi), 1/(2*sqrt(pi)), -1/(4*sqrt(pi))]) + assert p == q + p = from_meijerg(meijerg(([], []), ([0], []), x)) + q = HolonomicFunction(1 + Dx, x, 0, [1]) + assert p == q + p = from_meijerg(meijerg(([1], []), ([S.Half], [0]), x)) + q = HolonomicFunction((x + S.Half)*Dx + x*Dx**2, x, 1, [sqrt(pi)*erf(1), exp(-1)]) + assert p == q + p = from_meijerg(meijerg(([0], [1]), ([0], []), 2*x**2)) + q = HolonomicFunction((3*x**2 - 1)*Dx + x**3*Dx**2, x, 1, [-exp(Rational(-1, 2)) + 1, -exp(Rational(-1, 2))]) + assert p == q + + +def test_to_Sequence(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + n = symbols('n', integer=True) + _, Sn = RecurrenceOperators(ZZ.old_poly_ring(n), 'Sn') + p = HolonomicFunction(x**2*Dx**4 + x + Dx, x).to_sequence() + q = [(HolonomicSequence(1 + (n + 2)*Sn**2 + (n**4 + 6*n**3 + 11*n**2 + 6*n)*Sn**3), 0, 1)] + assert p == q + p = HolonomicFunction(x**2*Dx**4 + x**3 + Dx**2, x).to_sequence() + q = [(HolonomicSequence(1 + (n**4 + 14*n**3 + 72*n**2 + 163*n + 140)*Sn**5), 0, 0)] + assert p == q + p = HolonomicFunction(x**3*Dx**4 + 1 + Dx**2, x).to_sequence() + q = [(HolonomicSequence(1 + (n**4 - 2*n**3 - n**2 + 2*n)*Sn + (n**2 + 3*n + 2)*Sn**2), 0, 0)] + assert p == q + p = HolonomicFunction(3*x**3*Dx**4 + 2*x*Dx + x*Dx**3, x).to_sequence() + q = [(HolonomicSequence(2*n + (3*n**4 - 6*n**3 - 3*n**2 + 6*n)*Sn + (n**3 + 3*n**2 + 2*n)*Sn**2), 0, 1)] + assert p == q + + +def test_to_Sequence_Initial_Coniditons(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + n = symbols('n', integer=True) + _, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') + p = HolonomicFunction(Dx - 1, x, 0, [1]).to_sequence() + q = [(HolonomicSequence(-1 + (n + 1)*Sn, 1), 0)] + assert p == q + p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]).to_sequence() + q = [(HolonomicSequence(1 + (n**2 + 3*n + 2)*Sn**2, [0, 1]), 0)] + assert p == q + p = HolonomicFunction(Dx**2 + 1 + x**3*Dx, x, 0, [2, 3]).to_sequence() + q = [(HolonomicSequence(n + Sn**2 + (n**2 + 7*n + 12)*Sn**4, [2, 3, -1, Rational(-1, 2), Rational(1, 12)]), 1)] + assert p == q + p = HolonomicFunction(x**3*Dx**5 + 1 + Dx, x).to_sequence() + q = [(HolonomicSequence(1 + (n + 1)*Sn + (n**5 - 5*n**3 + 4*n)*Sn**2), 0, 3)] + assert p == q + C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3') + p = expr_to_holonomic(log(1+x**2)) + q = [(HolonomicSequence(n**2 + (n**2 + 2*n)*Sn**2, [0, 0, C_2]), 0, 1)] + assert p.to_sequence() == q + p = p.diff() + q = [(HolonomicSequence((n + 2) + (n + 2)*Sn**2, [C_0, 0]), 1, 0)] + assert p.to_sequence() == q + p = expr_to_holonomic(erf(x) + x).to_sequence() + q = [(HolonomicSequence((2*n**2 - 2*n) + (n**3 + 2*n**2 - n - 2)*Sn**2, [0, 1 + 2/sqrt(pi), 0, C_3]), 0, 2)] + assert p == q + +def test_series(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx**2 + 2*x*Dx, x, 0, [0, 1]).series(n=10) + q = x - x**3/3 + x**5/10 - x**7/42 + x**9/216 + O(x**10) + assert p == q + p = HolonomicFunction(Dx - 1, x).composition(x**2, 0, [1]) # e^(x**2) + q = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]) # cos(x) + r = (p * q).series(n=10) # expansion of cos(x) * exp(x**2) + s = 1 + x**2/2 + x**4/24 - 31*x**6/720 - 179*x**8/8064 + O(x**10) + assert r == s + t = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]) # log(1 + x) + r = (p * t + q).series(n=10) + s = 1 + x - x**2 + 4*x**3/3 - 17*x**4/24 + 31*x**5/30 - 481*x**6/720 +\ + 71*x**7/105 - 20159*x**8/40320 + 379*x**9/840 + O(x**10) + assert r == s + p = HolonomicFunction((6+6*x-3*x**2) - (10*x-3*x**2-3*x**3)*Dx + \ + (4-6*x**3+2*x**4)*Dx**2, x, 0, [0, 1]).series(n=7) + q = x + x**3/6 - 3*x**4/16 + x**5/20 - 23*x**6/960 + O(x**7) + assert p == q + p = HolonomicFunction((6+6*x-3*x**2) - (10*x-3*x**2-3*x**3)*Dx + \ + (4-6*x**3+2*x**4)*Dx**2, x, 0, [1, 0]).series(n=7) + q = 1 - 3*x**2/4 - x**3/4 - 5*x**4/32 - 3*x**5/40 - 17*x**6/384 + O(x**7) + assert p == q + p = expr_to_holonomic(erf(x) + x).series(n=10) + C_3 = symbols('C_3') + q = (erf(x) + x).series(n=10) + assert p.subs(C_3, -2/(3*sqrt(pi))) == q + assert expr_to_holonomic(sqrt(x**3 + x)).series(n=10) == sqrt(x**3 + x).series(n=10) + assert expr_to_holonomic((2*x - 3*x**2)**Rational(1, 3)).series() == ((2*x - 3*x**2)**Rational(1, 3)).series() + assert expr_to_holonomic(sqrt(x**2-x)).series() == (sqrt(x**2-x)).series() + assert expr_to_holonomic(cos(x)**2/x**2, y0={-2: [1, 0, -1]}).series(n=10) == (cos(x)**2/x**2).series(n=10) + assert expr_to_holonomic(cos(x)**2/x**2, x0=1).series(n=10).together() == (cos(x)**2/x**2).series(n=10, x0=1).together() + assert expr_to_holonomic(cos(x-1)**2/(x-1)**2, x0=1, y0={-2: [1, 0, -1]}).series(n=10) \ + == (cos(x-1)**2/(x-1)**2).series(x0=1, n=10) + +def test_evalf_euler(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + + # log(1+x) + p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]) + + # path taken is a straight line from 0 to 1, on the real axis + r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1] + s = '0.699525841805253' # approx. equal to log(2) i.e. 0.693147180559945 + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # path taken is a triangle 0-->1+i-->2 + r = [0.1 + 0.1*I] + for i in range(9): + r.append(r[-1]+0.1+0.1*I) + for i in range(10): + r.append(r[-1]+0.1-0.1*I) + + # close to the exact solution 1.09861228866811 + # imaginary part also close to zero + s = '1.07530466271334 - 0.0251200594793912*I' + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # sin(x) + p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]) + s = '0.905546532085401 - 6.93889390390723e-18*I' + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # computing sin(pi/2) using this method + # using a linear path from 0 to pi/2 + r = [0.1] + for i in range(14): + r.append(r[-1] + 0.1) + r.append(pi/2) + s = '1.08016557252834' # close to 1.0 (exact solution) + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2) + # computing the same value sin(pi/2) using different path + r = [0.1*I] + for i in range(9): + r.append(r[-1]+0.1*I) + for i in range(15): + r.append(r[-1]+0.1) + r.append(pi/2+I) + for i in range(10): + r.append(r[-1]-0.1*I) + + # close to 1.0 + s = '0.976882381836257 - 1.65557671738537e-16*I' + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # cos(x) + p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]) + # compute cos(pi) along 0-->pi + r = [0.05] + for i in range(61): + r.append(r[-1]+0.05) + r.append(pi) + # close to -1 (exact answer) + s = '-1.08140824719196' + assert sstr(p.evalf(r, method='Euler')[-1]) == s + + # a rectangular path (0 -> i -> 2+i -> 2) + r = [0.1*I] + for i in range(9): + r.append(r[-1]+0.1*I) + for i in range(20): + r.append(r[-1]+0.1) + for i in range(10): + r.append(r[-1]-0.1*I) + + p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r, method='Euler') + s = '0.501421652861245 - 3.88578058618805e-16*I' + assert sstr(p[-1]) == s + +def test_evalf_rk4(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + + # log(1+x) + p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]) + + # path taken is a straight line from 0 to 1, on the real axis + r = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1] + s = '0.693146363174626' # approx. equal to log(2) i.e. 0.693147180559945 + assert sstr(p.evalf(r)[-1]) == s + + # path taken is a triangle 0-->1+i-->2 + r = [0.1 + 0.1*I] + for i in range(9): + r.append(r[-1]+0.1+0.1*I) + for i in range(10): + r.append(r[-1]+0.1-0.1*I) + + # close to the exact solution 1.09861228866811 + # imaginary part also close to zero + s = '1.098616 + 1.36083e-7*I' + assert sstr(p.evalf(r)[-1].n(7)) == s + + # sin(x) + p = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]) + s = '0.90929463522785 + 1.52655665885959e-16*I' + assert sstr(p.evalf(r)[-1]) == s + + # computing sin(pi/2) using this method + # using a linear path from 0 to pi/2 + r = [0.1] + for i in range(14): + r.append(r[-1] + 0.1) + r.append(pi/2) + s = '0.999999895088917' # close to 1.0 (exact solution) + assert sstr(p.evalf(r)[-1]) == s + + # trying different path, a rectangle (0-->i-->pi/2 + i-->pi/2) + # computing the same value sin(pi/2) using different path + r = [0.1*I] + for i in range(9): + r.append(r[-1]+0.1*I) + for i in range(15): + r.append(r[-1]+0.1) + r.append(pi/2+I) + for i in range(10): + r.append(r[-1]-0.1*I) + + # close to 1.0 + s = '1.00000003415141 + 6.11940487991086e-16*I' + assert sstr(p.evalf(r)[-1]) == s + + # cos(x) + p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]) + # compute cos(pi) along 0-->pi + r = [0.05] + for i in range(61): + r.append(r[-1]+0.05) + r.append(pi) + # close to -1 (exact answer) + s = '-0.999999993238714' + assert sstr(p.evalf(r)[-1]) == s + + # a rectangular path (0 -> i -> 2+i -> 2) + r = [0.1*I] + for i in range(9): + r.append(r[-1]+0.1*I) + for i in range(20): + r.append(r[-1]+0.1) + for i in range(10): + r.append(r[-1]-0.1*I) + + p = HolonomicFunction(Dx**2 + 1, x, 0, [1,1]).evalf(r) + s = '0.493152791638442 - 1.41553435639707e-15*I' + assert sstr(p[-1]) == s + + +def test_expr_to_holonomic(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = expr_to_holonomic((sin(x)/x)**2) + q = HolonomicFunction(8*x + (4*x**2 + 6)*Dx + 6*x*Dx**2 + x**2*Dx**3, x, 0, \ + [1, 0, Rational(-2, 3)]) + assert p == q + p = expr_to_holonomic(1/(1+x**2)**2) + q = HolonomicFunction(4*x + (x**2 + 1)*Dx, x, 0, [1]) + assert p == q + p = expr_to_holonomic(exp(x)*sin(x)+x*log(1+x)) + q = HolonomicFunction((2*x**3 + 10*x**2 + 20*x + 18) + (-2*x**4 - 10*x**3 - 20*x**2 \ + - 18*x)*Dx + (2*x**5 + 6*x**4 + 7*x**3 + 8*x**2 + 10*x - 4)*Dx**2 + \ + (-2*x**5 - 5*x**4 - 2*x**3 + 2*x**2 - x + 4)*Dx**3 + (x**5 + 2*x**4 - x**3 - \ + 7*x**2/2 + x + Rational(5, 2))*Dx**4, x, 0, [0, 1, 4, -1]) + assert p == q + p = expr_to_holonomic(x*exp(x)+cos(x)+1) + q = HolonomicFunction((-x - 3)*Dx + (x + 2)*Dx**2 + (-x - 3)*Dx**3 + (x + 2)*Dx**4, x, \ + 0, [2, 1, 1, 3]) + assert p == q + assert (x*exp(x)+cos(x)+1).series(n=10) == p.series(n=10) + p = expr_to_holonomic(log(1 + x)**2 + 1) + q = HolonomicFunction(Dx + (3*x + 3)*Dx**2 + (x**2 + 2*x + 1)*Dx**3, x, 0, [1, 0, 2]) + assert p == q + p = expr_to_holonomic(erf(x)**2 + x) + q = HolonomicFunction((8*x**4 - 2*x**2 + 2)*Dx**2 + (6*x**3 - x/2)*Dx**3 + \ + (x**2+ Rational(1, 4))*Dx**4, x, 0, [0, 1, 8/pi, 0]) + assert p == q + p = expr_to_holonomic(cosh(x)*x) + q = HolonomicFunction((-x**2 + 2) -2*x*Dx + x**2*Dx**2, x, 0, [0, 1]) + assert p == q + p = expr_to_holonomic(besselj(2, x)) + q = HolonomicFunction((x**2 - 4) + x*Dx + x**2*Dx**2, x, 0, [0, 0]) + assert p == q + p = expr_to_holonomic(besselj(0, x) + exp(x)) + q = HolonomicFunction((-x**2 - x/2 + S.Half) + (x**2 - x/2 - Rational(3, 2))*Dx + (-x**2 + x/2 + 1)*Dx**2 +\ + (x**2 + x/2)*Dx**3, x, 0, [2, 1, S.Half]) + assert p == q + p = expr_to_holonomic(sin(x)**2/x) + q = HolonomicFunction(4 + 4*x*Dx + 3*Dx**2 + x*Dx**3, x, 0, [0, 1, 0]) + assert p == q + p = expr_to_holonomic(sin(x)**2/x, x0=2) + q = HolonomicFunction((4) + (4*x)*Dx + (3)*Dx**2 + (x)*Dx**3, x, 2, [sin(2)**2/2, + sin(2)*cos(2) - sin(2)**2/4, -3*sin(2)**2/4 + cos(2)**2 - sin(2)*cos(2)]) + assert p == q + p = expr_to_holonomic(log(x)/2 - Ci(2*x)/2 + Ci(2)/2) + q = HolonomicFunction(4*Dx + 4*x*Dx**2 + 3*Dx**3 + x*Dx**4, x, 0, \ + [-log(2)/2 - EulerGamma/2 + Ci(2)/2, 0, 1, 0]) + assert p == q + p = p.to_expr() + q = log(x)/2 - Ci(2*x)/2 + Ci(2)/2 + assert p == q + p = expr_to_holonomic(x**S.Half, x0=1) + q = HolonomicFunction(x*Dx - S.Half, x, 1, [1]) + assert p == q + p = expr_to_holonomic(sqrt(1 + x**2)) + q = HolonomicFunction((-x) + (x**2 + 1)*Dx, x, 0, [1]) + assert p == q + assert (expr_to_holonomic(sqrt(x) + sqrt(2*x)).to_expr()-\ + (sqrt(x) + sqrt(2*x))).simplify() == 0 + assert expr_to_holonomic(3*x+2*sqrt(x)).to_expr() == 3*x+2*sqrt(x) + p = expr_to_holonomic((x**4+x**3+5*x**2+3*x+2)/x**2, lenics=3) + q = HolonomicFunction((-2*x**4 - x**3 + 3*x + 4) + (x**5 + x**4 + 5*x**3 + 3*x**2 + \ + 2*x)*Dx, x, 0, {-2: [2, 3, 5]}) + assert p == q + p = expr_to_holonomic(1/(x-1)**2, lenics=3, x0=1) + q = HolonomicFunction((2) + (x - 1)*Dx, x, 1, {-2: [1, 0, 0]}) + assert p == q + a = symbols("a") + p = expr_to_holonomic(sqrt(a*x), x=x) + assert p.to_expr() == sqrt(a)*sqrt(x) + +def test_to_hyper(): + x = symbols('x') + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx - 2, x, 0, [3]).to_hyper() + q = 3 * hyper([], [], 2*x) + assert p == q + p = hyperexpand(HolonomicFunction((1 + x) * Dx - 3, x, 0, [2]).to_hyper()).expand() + q = 2*x**3 + 6*x**2 + 6*x + 2 + assert p == q + p = HolonomicFunction((1 + x)*Dx**2 + Dx, x, 0, [0, 1]).to_hyper() + q = -x**2*hyper((2, 2, 1), (3, 2), -x)/2 + x + assert p == q + p = HolonomicFunction(2*x*Dx + Dx**2, x, 0, [0, 2/sqrt(pi)]).to_hyper() + q = 2*x*hyper((S.Half,), (Rational(3, 2),), -x**2)/sqrt(pi) + assert p == q + p = hyperexpand(HolonomicFunction(2*x*Dx + Dx**2, x, 0, [1, -2/sqrt(pi)]).to_hyper()) + q = erfc(x) + assert p.rewrite(erfc) == q + p = hyperexpand(HolonomicFunction((x**2 - 1) + x*Dx + x**2*Dx**2, + x, 0, [0, S.Half]).to_hyper()) + q = besselj(1, x) + assert p == q + p = hyperexpand(HolonomicFunction(x*Dx**2 + Dx + x, x, 0, [1, 0]).to_hyper()) + q = besselj(0, x) + assert p == q + +def test_to_expr(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(Dx - 1, x, 0, [1]).to_expr() + q = exp(x) + assert p == q + p = HolonomicFunction(Dx**2 + 1, x, 0, [1, 0]).to_expr() + q = cos(x) + assert p == q + p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 0]).to_expr() + q = cosh(x) + assert p == q + p = HolonomicFunction(2 + (4*x - 1)*Dx + \ + (x**2 - x)*Dx**2, x, 0, [1, 2]).to_expr().expand() + q = 1/(x**2 - 2*x + 1) + assert p == q + p = expr_to_holonomic(sin(x)**2/x).integrate((x, 0, x)).to_expr() + q = (sin(x)**2/x).integrate((x, 0, x)) + assert p == q + C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3') + p = expr_to_holonomic(log(1+x**2)).to_expr() + q = C_2*log(x**2 + 1) + assert p == q + p = expr_to_holonomic(log(1+x**2)).diff().to_expr() + q = C_0*x/(x**2 + 1) + assert p == q + p = expr_to_holonomic(erf(x) + x).to_expr() + q = 3*C_3*x - 3*sqrt(pi)*C_3*erf(x)/2 + x + 2*x/sqrt(pi) + assert p == q + p = expr_to_holonomic(sqrt(x), x0=1).to_expr() + assert p == sqrt(x) + assert expr_to_holonomic(sqrt(x)).to_expr() == sqrt(x) + p = expr_to_holonomic(sqrt(1 + x**2)).to_expr() + assert p == sqrt(1+x**2) + p = expr_to_holonomic((2*x**2 + 1)**Rational(2, 3)).to_expr() + assert p == (2*x**2 + 1)**Rational(2, 3) + p = expr_to_holonomic(sqrt(-x**2+2*x)).to_expr() + assert p == sqrt(x)*sqrt(-x + 2) + p = expr_to_holonomic((-2*x**3+7*x)**Rational(2, 3)).to_expr() + q = x**Rational(2, 3)*(-2*x**2 + 7)**Rational(2, 3) + assert p == q + p = from_hyper(hyper((-2, -3), (S.Half, ), x)) + s = hyperexpand(hyper((-2, -3), (S.Half, ), x)) + D_0 = Symbol('D_0') + C_0 = Symbol('C_0') + assert (p.to_expr().subs({C_0:1, D_0:0}) - s).simplify() == 0 + p.y0 = {0: [1], S.Half: [0]} + assert p.to_expr() == s + assert expr_to_holonomic(x**5).to_expr() == x**5 + assert expr_to_holonomic(2*x**3-3*x**2).to_expr().expand() == \ + 2*x**3-3*x**2 + a = symbols("a") + p = (expr_to_holonomic(1.4*x)*expr_to_holonomic(a*x, x)).to_expr() + q = 1.4*a*x**2 + assert p == q + p = (expr_to_holonomic(1.4*x)+expr_to_holonomic(a*x, x)).to_expr() + q = x*(a + 1.4) + assert p == q + p = (expr_to_holonomic(1.4*x)+expr_to_holonomic(x)).to_expr() + assert p == 2.4*x + + +def test_integrate(): + x = symbols('x') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 2, 3)) + q = '0.166270406994788' + assert sstr(p) == q + p = expr_to_holonomic(sin(x)).integrate((x, 0, x)).to_expr() + q = 1 - cos(x) + assert p == q + p = expr_to_holonomic(sin(x)).integrate((x, 0, 3)) + q = 1 - cos(3) + assert p == q + p = expr_to_holonomic(sin(x)/x, x0=1).integrate((x, 1, 2)) + q = '0.659329913368450' + assert sstr(p) == q + p = expr_to_holonomic(sin(x)**2/x, x0=1).integrate((x, 1, 0)) + q = '-0.423690480850035' + assert sstr(p) == q + p = expr_to_holonomic(sin(x)/x) + assert p.integrate(x).to_expr() == Si(x) + assert p.integrate((x, 0, 2)) == Si(2) + p = expr_to_holonomic(sin(x)**2/x) + q = p.to_expr() + assert p.integrate(x).to_expr() == q.integrate((x, 0, x)) + assert p.integrate((x, 0, 1)) == q.integrate((x, 0, 1)) + assert expr_to_holonomic(1/x, x0=1).integrate(x).to_expr() == log(x) + p = expr_to_holonomic((x + 1)**3*exp(-x), x0=-1).integrate(x).to_expr() + q = (-x**3 - 6*x**2 - 15*x + 6*exp(x + 1) - 16)*exp(-x) + assert p == q + p = expr_to_holonomic(cos(x)**2/x**2, y0={-2: [1, 0, -1]}).integrate(x).to_expr() + q = -Si(2*x) - cos(x)**2/x + assert p == q + p = expr_to_holonomic(sqrt(x**2+x)).integrate(x).to_expr() + q = (x**Rational(3, 2)*(2*x**2 + 3*x + 1) - x*sqrt(x + 1)*asinh(sqrt(x)))/(4*x*sqrt(x + 1)) + assert p == q + p = expr_to_holonomic(sqrt(x**2+1)).integrate(x).to_expr() + q = (sqrt(x**2+1)).integrate(x) + assert (p-q).simplify() == 0 + p = expr_to_holonomic(1/x**2, y0={-2:[1, 0, 0]}) + r = expr_to_holonomic(1/x**2, lenics=3) + assert p == r + q = expr_to_holonomic(cos(x)**2) + assert (r*q).integrate(x).to_expr() == -Si(2*x) - cos(x)**2/x + + +def test_diff(): + x, y = symbols('x, y') + R, Dx = DifferentialOperators(ZZ.old_poly_ring(x), 'Dx') + p = HolonomicFunction(x*Dx**2 + 1, x, 0, [0, 1]) + assert p.diff().to_expr() == p.to_expr().diff().simplify() + p = HolonomicFunction(Dx**2 - 1, x, 0, [1, 0]) + assert p.diff(x, 2).to_expr() == p.to_expr() + p = expr_to_holonomic(Si(x)) + assert p.diff().to_expr() == sin(x)/x + assert p.diff(y) == 0 + C_0, C_1, C_2, C_3 = symbols('C_0, C_1, C_2, C_3') + q = Si(x) + assert p.diff(x).to_expr() == q.diff() + assert p.diff(x, 2).to_expr().subs(C_0, Rational(-1, 3)).cancel() == q.diff(x, 2).cancel() + assert p.diff(x, 3).series().subs({C_3: Rational(-1, 3), C_0: 0}) == q.diff(x, 3).series() + + +def test_extended_domain_in_expr_to_holonomic(): + x = symbols('x') + p = expr_to_holonomic(1.2*cos(3.1*x)) + assert p.to_expr() == 1.2*cos(3.1*x) + assert sstr(p.integrate(x).to_expr()) == '0.387096774193548*sin(3.1*x)' + _, Dx = DifferentialOperators(RR.old_poly_ring(x), 'Dx') + p = expr_to_holonomic(1.1329138213*x) + q = HolonomicFunction((-1.1329138213) + (1.1329138213*x)*Dx, x, 0, {1: [1.1329138213]}) + assert p == q + assert p.to_expr() == 1.1329138213*x + assert sstr(p.integrate((x, 1, 2))) == sstr((1.1329138213*x).integrate((x, 1, 2))) + y, z = symbols('y, z') + p = expr_to_holonomic(sin(x*y*z), x=x) + assert p.to_expr() == sin(x*y*z) + assert p.integrate(x).to_expr() == (-cos(x*y*z) + 1)/(y*z) + p = expr_to_holonomic(sin(x*y + z), x=x).integrate(x).to_expr() + q = (cos(z) - cos(x*y + z))/y + assert p == q + a = symbols('a') + p = expr_to_holonomic(a*x, x) + assert p.to_expr() == a*x + assert p.integrate(x).to_expr() == a*x**2/2 + D_2, C_1 = symbols("D_2, C_1") + p = expr_to_holonomic(x) + expr_to_holonomic(1.2*cos(x)) + p = p.to_expr().subs(D_2, 0) + assert p - x - 1.2*cos(1.0*x) == 0 + p = expr_to_holonomic(x) * expr_to_holonomic(1.2*cos(x)) + p = p.to_expr().subs(C_1, 0) + assert p - 1.2*x*cos(1.0*x) == 0 + + +def test_to_meijerg(): + x = symbols('x') + assert hyperexpand(expr_to_holonomic(sin(x)).to_meijerg()) == sin(x) + assert hyperexpand(expr_to_holonomic(cos(x)).to_meijerg()) == cos(x) + assert hyperexpand(expr_to_holonomic(exp(x)).to_meijerg()) == exp(x) + assert hyperexpand(expr_to_holonomic(log(x)).to_meijerg()).simplify() == log(x) + assert expr_to_holonomic(4*x**2/3 + 7).to_meijerg() == 4*x**2/3 + 7 + assert hyperexpand(expr_to_holonomic(besselj(2, x), lenics=3).to_meijerg()) == besselj(2, x) + p = hyper((Rational(-1, 2), -3), (), x) + assert from_hyper(p).to_meijerg() == hyperexpand(p) + p = hyper((S.One, S(3)), (S(2), ), x) + assert (hyperexpand(from_hyper(p).to_meijerg()) - hyperexpand(p)).expand() == 0 + p = from_hyper(hyper((-2, -3), (S.Half, ), x)) + s = hyperexpand(hyper((-2, -3), (S.Half, ), x)) + C_0 = Symbol('C_0') + C_1 = Symbol('C_1') + D_0 = Symbol('D_0') + assert (hyperexpand(p.to_meijerg()).subs({C_0:1, D_0:0}) - s).simplify() == 0 + p.y0 = {0: [1], S.Half: [0]} + assert (hyperexpand(p.to_meijerg()) - s).simplify() == 0 + p = expr_to_holonomic(besselj(S.Half, x), initcond=False) + assert (p.to_expr() - (D_0*sin(x) + C_0*cos(x) + C_1*sin(x))/sqrt(x)).simplify() == 0 + p = expr_to_holonomic(besselj(S.Half, x), y0={Rational(-1, 2): [sqrt(2)/sqrt(pi), sqrt(2)/sqrt(pi)]}) + assert (p.to_expr() - besselj(S.Half, x) - besselj(Rational(-1, 2), x)).simplify() == 0 + + +def test_gaussian(): + mu, x = symbols("mu x") + sd = symbols("sd", positive=True) + Q = QQ[mu, sd].get_field() + e = sqrt(2)*exp(-(-mu + x)**2/(2*sd**2))/(2*sqrt(pi)*sd) + h1 = expr_to_holonomic(e, x, domain=Q) + + _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx') + h2 = HolonomicFunction((-mu/sd**2 + x/sd**2) + (1)*Dx, x) + + assert h1 == h2 + + +def test_beta(): + a, b, x = symbols("a b x", positive=True) + e = x**(a - 1)*(-x + 1)**(b - 1)/beta(a, b) + Q = QQ[a, b].get_field() + h1 = expr_to_holonomic(e, x, domain=Q) + + _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx') + h2 = HolonomicFunction((a + x*(-a - b + 2) - 1) + (x**2 - x)*Dx, x) + + assert h1 == h2 + + +def test_gamma(): + a, b, x = symbols("a b x", positive=True) + e = b**(-a)*x**(a - 1)*exp(-x/b)/gamma(a) + Q = QQ[a, b].get_field() + h1 = expr_to_holonomic(e, x, domain=Q) + + _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx') + h2 = HolonomicFunction((-a + 1 + x/b) + (x)*Dx, x) + + assert h1 == h2 + + +def test_symbolic_power(): + x, n = symbols("x n") + Q = QQ[n].get_field() + _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx') + h1 = HolonomicFunction((-1) + (x)*Dx, x) ** -n + h2 = HolonomicFunction((n) + (x)*Dx, x) + + assert h1 == h2 + + +def test_negative_power(): + x = symbols("x") + _, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + h1 = HolonomicFunction((-1) + (x)*Dx, x) ** -2 + h2 = HolonomicFunction((2) + (x)*Dx, x) + + assert h1 == h2 + + +def test_expr_in_power(): + x, n = symbols("x n") + Q = QQ[n].get_field() + _, Dx = DifferentialOperators(Q.old_poly_ring(x), 'Dx') + h1 = HolonomicFunction((-1) + (x)*Dx, x) ** (n - 3) + h2 = HolonomicFunction((-n + 3) + (x)*Dx, x) + + assert h1 == h2 + + +def test_DifferentialOperatorEqPoly(): + x = symbols('x', integer=True) + R, Dx = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + do = DifferentialOperator([x**2, R.base.zero, R.base.zero], R) + do2 = DifferentialOperator([x**2, 1, x], R) + assert not do == do2 + + # polynomial comparison issue, see https://github.com/sympy/sympy/pull/15799 + # should work once that is solved + # p = do.listofpoly[0] + # assert do == p + + p2 = do2.listofpoly[0] + assert not do2 == p2 + + +def test_DifferentialOperatorPow(): + x = symbols('x', integer=True) + R, _ = DifferentialOperators(QQ.old_poly_ring(x), 'Dx') + do = DifferentialOperator([x**2, R.base.zero, R.base.zero], R) + a = DifferentialOperator([R.base.one], R) + for n in range(10): + assert a == do**n + a *= do diff --git a/lib/python3.11/site-packages/sympy/holonomic/tests/test_recurrence.py b/lib/python3.11/site-packages/sympy/holonomic/tests/test_recurrence.py new file mode 100644 index 0000000000000000000000000000000000000000..526595e91c5fc507877275e3e53e78c6f3716095 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/holonomic/tests/test_recurrence.py @@ -0,0 +1,41 @@ +from sympy.holonomic.recurrence import RecurrenceOperators, RecurrenceOperator +from sympy.core.symbol import symbols +from sympy.polys.domains.rationalfield import QQ + + +def test_RecurrenceOperator(): + n = symbols('n', integer=True) + R, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') + assert Sn*n == (n + 1)*Sn + assert Sn*n**2 == (n**2+1+2*n)*Sn + assert Sn**2*n**2 == (n**2 + 4*n + 4)*Sn**2 + p = (Sn**3*n**2 + Sn*n)**2 + q = (n**2 + 3*n + 2)*Sn**2 + (2*n**3 + 19*n**2 + 57*n + 52)*Sn**4 + (n**4 + 18*n**3 + \ + 117*n**2 + 324*n + 324)*Sn**6 + assert p == q + + +def test_RecurrenceOperatorEqPoly(): + n = symbols('n', integer=True) + R, Sn = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') + rr = RecurrenceOperator([n**2, 0, 0], R) + rr2 = RecurrenceOperator([n**2, 1, n], R) + assert not rr == rr2 + + # polynomial comparison issue, see https://github.com/sympy/sympy/pull/15799 + # should work once that is solved + # d = rr.listofpoly[0] + # assert rr == d + + d2 = rr2.listofpoly[0] + assert not rr2 == d2 + + +def test_RecurrenceOperatorPow(): + n = symbols('n', integer=True) + R, _ = RecurrenceOperators(QQ.old_poly_ring(n), 'Sn') + rr = RecurrenceOperator([n**2, 0, 0], R) + a = RecurrenceOperator([R.base.one], R) + for m in range(10): + assert a == rr**m + a *= rr diff --git a/lib/python3.11/site-packages/sympy/integrals/__init__.py b/lib/python3.11/site-packages/sympy/integrals/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e78fe96f84d68e9b119571eb22dedb7033811b23 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/__init__.py @@ -0,0 +1,45 @@ +"""Integration functions that integrate a SymPy expression. + + Examples + ======== + + >>> from sympy import integrate, sin + >>> from sympy.abc import x + >>> integrate(1/x,x) + log(x) + >>> integrate(sin(x),x) + -cos(x) +""" +from .integrals import integrate, Integral, line_integrate +from .transforms import (mellin_transform, inverse_mellin_transform, + MellinTransform, InverseMellinTransform, + laplace_transform, inverse_laplace_transform, + laplace_correspondence, laplace_initial_conds, + LaplaceTransform, InverseLaplaceTransform, + fourier_transform, inverse_fourier_transform, + FourierTransform, InverseFourierTransform, + sine_transform, inverse_sine_transform, + SineTransform, InverseSineTransform, + cosine_transform, inverse_cosine_transform, + CosineTransform, InverseCosineTransform, + hankel_transform, inverse_hankel_transform, + HankelTransform, InverseHankelTransform) +from .singularityfunctions import singularityintegrate + +__all__ = [ + 'integrate', 'Integral', 'line_integrate', + + 'mellin_transform', 'inverse_mellin_transform', 'MellinTransform', + 'InverseMellinTransform', 'laplace_transform', + 'inverse_laplace_transform', 'LaplaceTransform', + 'laplace_correspondence', 'laplace_initial_conds', + 'InverseLaplaceTransform', 'fourier_transform', + 'inverse_fourier_transform', 'FourierTransform', + 'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform', + 'SineTransform', 'InverseSineTransform', 'cosine_transform', + 'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform', + 'hankel_transform', 'inverse_hankel_transform', 'HankelTransform', + 'InverseHankelTransform', + + 'singularityintegrate', +] diff --git a/lib/python3.11/site-packages/sympy/integrals/benchmarks/__init__.py b/lib/python3.11/site-packages/sympy/integrals/benchmarks/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/integrals/benchmarks/bench_integrate.py b/lib/python3.11/site-packages/sympy/integrals/benchmarks/bench_integrate.py new file mode 100644 index 0000000000000000000000000000000000000000..833bc57403b34df1e75c798084ffc4d8afe9eae6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/benchmarks/bench_integrate.py @@ -0,0 +1,21 @@ +from sympy.core.symbol import Symbol +from sympy.functions.elementary.trigonometric import sin +from sympy.integrals.integrals import integrate + +x = Symbol('x') + + +def bench_integrate_sin(): + integrate(sin(x), x) + + +def bench_integrate_x1sin(): + integrate(x**1*sin(x), x) + + +def bench_integrate_x2sin(): + integrate(x**2*sin(x), x) + + +def bench_integrate_x3sin(): + integrate(x**3*sin(x), x) diff --git a/lib/python3.11/site-packages/sympy/integrals/deltafunctions.py b/lib/python3.11/site-packages/sympy/integrals/deltafunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..ae9fef0b0010a313e0866a54d978024dd475f882 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/deltafunctions.py @@ -0,0 +1,201 @@ +from sympy.core.mul import Mul +from sympy.core.singleton import S +from sympy.core.sorting import default_sort_key +from sympy.functions import DiracDelta, Heaviside +from .integrals import Integral, integrate + + +def change_mul(node, x): + """change_mul(node, x) + + Rearranges the operands of a product, bringing to front any simple + DiracDelta expression. + + Explanation + =========== + + If no simple DiracDelta expression was found, then all the DiracDelta + expressions are simplified (using DiracDelta.expand(diracdelta=True, wrt=x)). + + Return: (dirac, new node) + Where: + o dirac is either a simple DiracDelta expression or None (if no simple + expression was found); + o new node is either a simplified DiracDelta expressions or None (if it + could not be simplified). + + Examples + ======== + + >>> from sympy import DiracDelta, cos + >>> from sympy.integrals.deltafunctions import change_mul + >>> from sympy.abc import x, y + >>> change_mul(x*y*DiracDelta(x)*cos(x), x) + (DiracDelta(x), x*y*cos(x)) + >>> change_mul(x*y*DiracDelta(x**2 - 1)*cos(x), x) + (None, x*y*cos(x)*DiracDelta(x - 1)/2 + x*y*cos(x)*DiracDelta(x + 1)/2) + >>> change_mul(x*y*DiracDelta(cos(x))*cos(x), x) + (None, None) + + See Also + ======== + + sympy.functions.special.delta_functions.DiracDelta + deltaintegrate + """ + + new_args = [] + dirac = None + + #Sorting is needed so that we consistently collapse the same delta; + #However, we must preserve the ordering of non-commutative terms + c, nc = node.args_cnc() + sorted_args = sorted(c, key=default_sort_key) + sorted_args.extend(nc) + + for arg in sorted_args: + if arg.is_Pow and isinstance(arg.base, DiracDelta): + new_args.append(arg.func(arg.base, arg.exp - 1)) + arg = arg.base + if dirac is None and (isinstance(arg, DiracDelta) and arg.is_simple(x)): + dirac = arg + else: + new_args.append(arg) + if not dirac: # there was no simple dirac + new_args = [] + for arg in sorted_args: + if isinstance(arg, DiracDelta): + new_args.append(arg.expand(diracdelta=True, wrt=x)) + elif arg.is_Pow and isinstance(arg.base, DiracDelta): + new_args.append(arg.func(arg.base.expand(diracdelta=True, wrt=x), arg.exp)) + else: + new_args.append(arg) + if new_args != sorted_args: + nnode = Mul(*new_args).expand() + else: # if the node didn't change there is nothing to do + nnode = None + return (None, nnode) + return (dirac, Mul(*new_args)) + + +def deltaintegrate(f, x): + """ + deltaintegrate(f, x) + + Explanation + =========== + + The idea for integration is the following: + + - If we are dealing with a DiracDelta expression, i.e. DiracDelta(g(x)), + we try to simplify it. + + If we could simplify it, then we integrate the resulting expression. + We already know we can integrate a simplified expression, because only + simple DiracDelta expressions are involved. + + If we couldn't simplify it, there are two cases: + + 1) The expression is a simple expression: we return the integral, + taking care if we are dealing with a Derivative or with a proper + DiracDelta. + + 2) The expression is not simple (i.e. DiracDelta(cos(x))): we can do + nothing at all. + + - If the node is a multiplication node having a DiracDelta term: + + First we expand it. + + If the expansion did work, then we try to integrate the expansion. + + If not, we try to extract a simple DiracDelta term, then we have two + cases: + + 1) We have a simple DiracDelta term, so we return the integral. + + 2) We didn't have a simple term, but we do have an expression with + simplified DiracDelta terms, so we integrate this expression. + + Examples + ======== + + >>> from sympy.abc import x, y, z + >>> from sympy.integrals.deltafunctions import deltaintegrate + >>> from sympy import sin, cos, DiracDelta + >>> deltaintegrate(x*sin(x)*cos(x)*DiracDelta(x - 1), x) + sin(1)*cos(1)*Heaviside(x - 1) + >>> deltaintegrate(y**2*DiracDelta(x - z)*DiracDelta(y - z), y) + z**2*DiracDelta(x - z)*Heaviside(y - z) + + See Also + ======== + + sympy.functions.special.delta_functions.DiracDelta + sympy.integrals.integrals.Integral + """ + if not f.has(DiracDelta): + return None + + # g(x) = DiracDelta(h(x)) + if f.func == DiracDelta: + h = f.expand(diracdelta=True, wrt=x) + if h == f: # can't simplify the expression + #FIXME: the second term tells whether is DeltaDirac or Derivative + #For integrating derivatives of DiracDelta we need the chain rule + if f.is_simple(x): + if (len(f.args) <= 1 or f.args[1] == 0): + return Heaviside(f.args[0]) + else: + return (DiracDelta(f.args[0], f.args[1] - 1) / + f.args[0].as_poly().LC()) + else: # let's try to integrate the simplified expression + fh = integrate(h, x) + return fh + elif f.is_Mul or f.is_Pow: # g(x) = a*b*c*f(DiracDelta(h(x)))*d*e + g = f.expand() + if f != g: # the expansion worked + fh = integrate(g, x) + if fh is not None and not isinstance(fh, Integral): + return fh + else: + # no expansion performed, try to extract a simple DiracDelta term + deltaterm, rest_mult = change_mul(f, x) + + if not deltaterm: + if rest_mult: + fh = integrate(rest_mult, x) + return fh + else: + from sympy.solvers import solve + deltaterm = deltaterm.expand(diracdelta=True, wrt=x) + if deltaterm.is_Mul: # Take out any extracted factors + deltaterm, rest_mult_2 = change_mul(deltaterm, x) + rest_mult = rest_mult*rest_mult_2 + point = solve(deltaterm.args[0], x)[0] + + # Return the largest hyperreal term left after + # repeated integration by parts. For example, + # + # integrate(y*DiracDelta(x, 1),x) == y*DiracDelta(x,0), not 0 + # + # This is so Integral(y*DiracDelta(x).diff(x),x).doit() + # will return y*DiracDelta(x) instead of 0 or DiracDelta(x), + # both of which are correct everywhere the value is defined + # but give wrong answers for nested integration. + n = (0 if len(deltaterm.args)==1 else deltaterm.args[1]) + m = 0 + while n >= 0: + r = S.NegativeOne**n*rest_mult.diff(x, n).subs(x, point) + if r.is_zero: + n -= 1 + m += 1 + else: + if m == 0: + return r*Heaviside(x - point) + else: + return r*DiracDelta(x,m-1) + # In some very weak sense, x=0 is still a singularity, + # but we hope will not be of any practical consequence. + return S.Zero + return None diff --git a/lib/python3.11/site-packages/sympy/integrals/heurisch.py b/lib/python3.11/site-packages/sympy/integrals/heurisch.py new file mode 100644 index 0000000000000000000000000000000000000000..5b9ce143bda946fc3db26011f3d3e2ef73c81aa2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/heurisch.py @@ -0,0 +1,780 @@ +from __future__ import annotations + +from collections import defaultdict +from functools import reduce +from itertools import permutations + +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.mul import Mul +from sympy.core.symbol import Wild, Dummy, Symbol +from sympy.core.basic import sympify +from sympy.core.numbers import Rational, pi, I +from sympy.core.relational import Eq, Ne +from sympy.core.singleton import S +from sympy.core.sorting import ordered +from sympy.core.traversal import iterfreeargs + +from sympy.functions import exp, sin, cos, tan, cot, asin, atan +from sympy.functions import log, sinh, cosh, tanh, coth, asinh +from sympy.functions import sqrt, erf, erfi, li, Ei +from sympy.functions import besselj, bessely, besseli, besselk +from sympy.functions import hankel1, hankel2, jn, yn +from sympy.functions.elementary.complexes import Abs, re, im, sign, arg +from sympy.functions.elementary.exponential import LambertW +from sympy.functions.elementary.integers import floor, ceiling +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.delta_functions import Heaviside, DiracDelta + +from sympy.simplify.radsimp import collect + +from sympy.logic.boolalg import And, Or +from sympy.utilities.iterables import uniq + +from sympy.polys import quo, gcd, lcm, factor_list, cancel, PolynomialError +from sympy.polys.monomials import itermonomials +from sympy.polys.polyroots import root_factors + +from sympy.polys.rings import PolyRing +from sympy.polys.solvers import solve_lin_sys +from sympy.polys.constructor import construct_domain + +from sympy.integrals.integrals import integrate + + +def components(f, x): + """ + Returns a set of all functional components of the given expression + which includes symbols, function applications and compositions and + non-integer powers. Fractional powers are collected with + minimal, positive exponents. + + Examples + ======== + + >>> from sympy import cos, sin + >>> from sympy.abc import x + >>> from sympy.integrals.heurisch import components + + >>> components(sin(x)*cos(x)**2, x) + {x, sin(x), cos(x)} + + See Also + ======== + + heurisch + """ + result = set() + + if f.has_free(x): + if f.is_symbol and f.is_commutative: + result.add(f) + elif f.is_Function or f.is_Derivative: + for g in f.args: + result |= components(g, x) + + result.add(f) + elif f.is_Pow: + result |= components(f.base, x) + + if not f.exp.is_Integer: + if f.exp.is_Rational: + result.add(f.base**Rational(1, f.exp.q)) + else: + result |= components(f.exp, x) | {f} + else: + for g in f.args: + result |= components(g, x) + + return result + +# name -> [] of symbols +_symbols_cache: dict[str, list[Dummy]] = {} + + +# NB @cacheit is not convenient here +def _symbols(name, n): + """get vector of symbols local to this module""" + try: + lsyms = _symbols_cache[name] + except KeyError: + lsyms = [] + _symbols_cache[name] = lsyms + + while len(lsyms) < n: + lsyms.append( Dummy('%s%i' % (name, len(lsyms))) ) + + return lsyms[:n] + + +def heurisch_wrapper(f, x, rewrite=False, hints=None, mappings=None, retries=3, + degree_offset=0, unnecessary_permutations=None, + _try_heurisch=None): + """ + A wrapper around the heurisch integration algorithm. + + Explanation + =========== + + This method takes the result from heurisch and checks for poles in the + denominator. For each of these poles, the integral is reevaluated, and + the final integration result is given in terms of a Piecewise. + + Examples + ======== + + >>> from sympy import cos, symbols + >>> from sympy.integrals.heurisch import heurisch, heurisch_wrapper + >>> n, x = symbols('n x') + >>> heurisch(cos(n*x), x) + sin(n*x)/n + >>> heurisch_wrapper(cos(n*x), x) + Piecewise((sin(n*x)/n, Ne(n, 0)), (x, True)) + + See Also + ======== + + heurisch + """ + from sympy.solvers.solvers import solve, denoms + f = sympify(f) + if not f.has_free(x): + return f*x + + res = heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, + unnecessary_permutations, _try_heurisch) + if not isinstance(res, Basic): + return res + + # We consider each denominator in the expression, and try to find + # cases where one or more symbolic denominator might be zero. The + # conditions for these cases are stored in the list slns. + # + # Since denoms returns a set we use ordered. This is important because the + # ordering of slns determines the order of the resulting Piecewise so we + # need a deterministic order here to make the output deterministic. + slns = [] + for d in ordered(denoms(res)): + try: + slns += solve([d], dict=True, exclude=(x,)) + except NotImplementedError: + pass + if not slns: + return res + slns = list(uniq(slns)) + # Remove the solutions corresponding to poles in the original expression. + slns0 = [] + for d in denoms(f): + try: + slns0 += solve([d], dict=True, exclude=(x,)) + except NotImplementedError: + pass + slns = [s for s in slns if s not in slns0] + if not slns: + return res + if len(slns) > 1: + eqs = [] + for sub_dict in slns: + eqs.extend([Eq(key, value) for key, value in sub_dict.items()]) + slns = solve(eqs, dict=True, exclude=(x,)) + slns + # For each case listed in the list slns, we reevaluate the integral. + pairs = [] + for sub_dict in slns: + expr = heurisch(f.subs(sub_dict), x, rewrite, hints, mappings, retries, + degree_offset, unnecessary_permutations, + _try_heurisch) + cond = And(*[Eq(key, value) for key, value in sub_dict.items()]) + generic = Or(*[Ne(key, value) for key, value in sub_dict.items()]) + if expr is None: + expr = integrate(f.subs(sub_dict),x) + pairs.append((expr, cond)) + # If there is one condition, put the generic case first. Otherwise, + # doing so may lead to longer Piecewise formulas + if len(pairs) == 1: + pairs = [(heurisch(f, x, rewrite, hints, mappings, retries, + degree_offset, unnecessary_permutations, + _try_heurisch), + generic), + (pairs[0][0], True)] + else: + pairs.append((heurisch(f, x, rewrite, hints, mappings, retries, + degree_offset, unnecessary_permutations, + _try_heurisch), + True)) + return Piecewise(*pairs) + +class BesselTable: + """ + Derivatives of Bessel functions of orders n and n-1 + in terms of each other. + + See the docstring of DiffCache. + """ + + def __init__(self): + self.table = {} + self.n = Dummy('n') + self.z = Dummy('z') + self._create_table() + + def _create_table(t): + table, n, z = t.table, t.n, t.z + for f in (besselj, bessely, hankel1, hankel2): + table[f] = (f(n-1, z) - n*f(n, z)/z, + (n-1)*f(n-1, z)/z - f(n, z)) + + f = besseli + table[f] = (f(n-1, z) - n*f(n, z)/z, + (n-1)*f(n-1, z)/z + f(n, z)) + f = besselk + table[f] = (-f(n-1, z) - n*f(n, z)/z, + (n-1)*f(n-1, z)/z - f(n, z)) + + for f in (jn, yn): + table[f] = (f(n-1, z) - (n+1)*f(n, z)/z, + (n-1)*f(n-1, z)/z - f(n, z)) + + def diffs(t, f, n, z): + if f in t.table: + diff0, diff1 = t.table[f] + repl = [(t.n, n), (t.z, z)] + return (diff0.subs(repl), diff1.subs(repl)) + + def has(t, f): + return f in t.table + +_bessel_table = None + +class DiffCache: + """ + Store for derivatives of expressions. + + Explanation + =========== + + The standard form of the derivative of a Bessel function of order n + contains two Bessel functions of orders n-1 and n+1, respectively. + Such forms cannot be used in parallel Risch algorithm, because + there is a linear recurrence relation between the three functions + while the algorithm expects that functions and derivatives are + represented in terms of algebraically independent transcendentals. + + The solution is to take two of the functions, e.g., those of orders + n and n-1, and to express the derivatives in terms of the pair. + To guarantee that the proper form is used the two derivatives are + cached as soon as one is encountered. + + Derivatives of other functions are also cached at no extra cost. + All derivatives are with respect to the same variable `x`. + """ + + def __init__(self, x): + self.cache = {} + self.x = x + + global _bessel_table + if not _bessel_table: + _bessel_table = BesselTable() + + def get_diff(self, f): + cache = self.cache + + if f in cache: + pass + elif (not hasattr(f, 'func') or + not _bessel_table.has(f.func)): + cache[f] = cancel(f.diff(self.x)) + else: + n, z = f.args + d0, d1 = _bessel_table.diffs(f.func, n, z) + dz = self.get_diff(z) + cache[f] = d0*dz + cache[f.func(n-1, z)] = d1*dz + + return cache[f] + +def heurisch(f, x, rewrite=False, hints=None, mappings=None, retries=3, + degree_offset=0, unnecessary_permutations=None, + _try_heurisch=None): + """ + Compute indefinite integral using heuristic Risch algorithm. + + Explanation + =========== + + This is a heuristic approach to indefinite integration in finite + terms using the extended heuristic (parallel) Risch algorithm, based + on Manuel Bronstein's "Poor Man's Integrator". + + The algorithm supports various classes of functions including + transcendental elementary or special functions like Airy, + Bessel, Whittaker and Lambert. + + Note that this algorithm is not a decision procedure. If it isn't + able to compute the antiderivative for a given function, then this is + not a proof that such a functions does not exist. One should use + recursive Risch algorithm in such case. It's an open question if + this algorithm can be made a full decision procedure. + + This is an internal integrator procedure. You should use top level + 'integrate' function in most cases, as this procedure needs some + preprocessing steps and otherwise may fail. + + Specification + ============= + + heurisch(f, x, rewrite=False, hints=None) + + where + f : expression + x : symbol + + rewrite -> force rewrite 'f' in terms of 'tan' and 'tanh' + hints -> a list of functions that may appear in anti-derivate + + - hints = None --> no suggestions at all + - hints = [ ] --> try to figure out + - hints = [f1, ..., fn] --> we know better + + Examples + ======== + + >>> from sympy import tan + >>> from sympy.integrals.heurisch import heurisch + >>> from sympy.abc import x, y + + >>> heurisch(y*tan(x), x) + y*log(tan(x)**2 + 1)/2 + + See Manuel Bronstein's "Poor Man's Integrator": + + References + ========== + + .. [1] https://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/index.html + + For more information on the implemented algorithm refer to: + + .. [2] K. Geddes, L. Stefanus, On the Risch-Norman Integration + Method and its Implementation in Maple, Proceedings of + ISSAC'89, ACM Press, 212-217. + + .. [3] J. H. Davenport, On the Parallel Risch Algorithm (I), + Proceedings of EUROCAM'82, LNCS 144, Springer, 144-157. + + .. [4] J. H. Davenport, On the Parallel Risch Algorithm (III): + Use of Tangents, SIGSAM Bulletin 16 (1982), 3-6. + + .. [5] J. H. Davenport, B. M. Trager, On the Parallel Risch + Algorithm (II), ACM Transactions on Mathematical + Software 11 (1985), 356-362. + + See Also + ======== + + sympy.integrals.integrals.Integral.doit + sympy.integrals.integrals.Integral + sympy.integrals.heurisch.components + """ + f = sympify(f) + + # There are some functions that Heurisch cannot currently handle, + # so do not even try. + # Set _try_heurisch=True to skip this check + if _try_heurisch is not True: + if f.has(Abs, re, im, sign, Heaviside, DiracDelta, floor, ceiling, arg): + return + + if not f.has_free(x): + return f*x + + if not f.is_Add: + indep, f = f.as_independent(x) + else: + indep = S.One + + rewritables = { + (sin, cos, cot): tan, + (sinh, cosh, coth): tanh, + } + + if rewrite: + for candidates, rule in rewritables.items(): + f = f.rewrite(candidates, rule) + else: + for candidates in rewritables.keys(): + if f.has(*candidates): + break + else: + rewrite = True + + terms = components(f, x) + dcache = DiffCache(x) + + if hints is not None: + if not hints: + a = Wild('a', exclude=[x]) + b = Wild('b', exclude=[x]) + c = Wild('c', exclude=[x]) + + for g in set(terms): # using copy of terms + if g.is_Function: + if isinstance(g, li): + M = g.args[0].match(a*x**b) + + if M is not None: + terms.add( x*(li(M[a]*x**M[b]) - (M[a]*x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) ) + #terms.add( x*(li(M[a]*x**M[b]) - (x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) ) + #terms.add( x*(li(M[a]*x**M[b]) - x*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) ) + #terms.add( li(M[a]*x**M[b]) - Ei((M[b]+1)*log(M[a]*x**M[b])/M[b]) ) + + elif isinstance(g, exp): + M = g.args[0].match(a*x**2) + + if M is not None: + if M[a].is_positive: + terms.add(erfi(sqrt(M[a])*x)) + else: # M[a].is_negative or unknown + terms.add(erf(sqrt(-M[a])*x)) + + M = g.args[0].match(a*x**2 + b*x + c) + + if M is not None: + if M[a].is_positive: + terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))* + erfi(sqrt(M[a])*x + M[b]/(2*sqrt(M[a])))) + elif M[a].is_negative: + terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))* + erf(sqrt(-M[a])*x - M[b]/(2*sqrt(-M[a])))) + + M = g.args[0].match(a*log(x)**2) + + if M is not None: + if M[a].is_positive: + terms.add(erfi(sqrt(M[a])*log(x) + 1/(2*sqrt(M[a])))) + if M[a].is_negative: + terms.add(erf(sqrt(-M[a])*log(x) - 1/(2*sqrt(-M[a])))) + + elif g.is_Pow: + if g.exp.is_Rational and g.exp.q == 2: + M = g.base.match(a*x**2 + b) + + if M is not None and M[b].is_positive: + if M[a].is_positive: + terms.add(asinh(sqrt(M[a]/M[b])*x)) + elif M[a].is_negative: + terms.add(asin(sqrt(-M[a]/M[b])*x)) + + M = g.base.match(a*x**2 - b) + + if M is not None and M[b].is_positive: + if M[a].is_positive: + dF = 1/sqrt(M[a]*x**2 - M[b]) + F = log(2*sqrt(M[a])*sqrt(M[a]*x**2 - M[b]) + 2*M[a]*x)/sqrt(M[a]) + dcache.cache[F] = dF # hack: F.diff(x) doesn't automatically simplify to f + terms.add(F) + elif M[a].is_negative: + terms.add(-M[b]/2*sqrt(-M[a])* + atan(sqrt(-M[a])*x/sqrt(M[a]*x**2 - M[b]))) + + else: + terms |= set(hints) + + for g in set(terms): # using copy of terms + terms |= components(dcache.get_diff(g), x) + + # XXX: The commented line below makes heurisch more deterministic wrt + # PYTHONHASHSEED and the iteration order of sets. There are other places + # where sets are iterated over but this one is possibly the most important. + # Theoretically the order here should not matter but different orderings + # can expose potential bugs in the different code paths so potentially it + # is better to keep the non-determinism. + # + # terms = list(ordered(terms)) + + # TODO: caching is significant factor for why permutations work at all. Change this. + V = _symbols('x', len(terms)) + + + # sort mapping expressions from largest to smallest (last is always x). + mapping = list(reversed(list(zip(*ordered( # + [(a[0].as_independent(x)[1], a) for a in zip(terms, V)])))[1])) # + rev_mapping = {v: k for k, v in mapping} # + if mappings is None: # + # optimizing the number of permutations of mapping # + assert mapping[-1][0] == x # if not, find it and correct this comment + unnecessary_permutations = [mapping.pop(-1)] + # only permute types of objects and let the ordering + # of types take care of the order of replacement + types = defaultdict(list) + for i in mapping: + types[type(i)].append(i) + mapping = [types[i] for i in types] + def _iter_mappings(): + for i in permutations(mapping): + yield [j for i in i for j in i] + mappings = _iter_mappings() + else: + unnecessary_permutations = unnecessary_permutations or [] + + def _substitute(expr): + return expr.subs(mapping) + + for mapping in mappings: + mapping = list(mapping) + mapping = mapping + unnecessary_permutations + diffs = [ _substitute(dcache.get_diff(g)) for g in terms ] + denoms = [ g.as_numer_denom()[1] for g in diffs ] + if all(h.is_polynomial(*V) for h in denoms) and _substitute(f).is_rational_function(*V): + denom = reduce(lambda p, q: lcm(p, q, *V), denoms) + break + else: + if not rewrite: + result = heurisch(f, x, rewrite=True, hints=hints, + unnecessary_permutations=unnecessary_permutations) + + if result is not None: + return indep*result + return None + + numers = [ cancel(denom*g) for g in diffs ] + def _derivation(h): + return Add(*[ d * h.diff(v) for d, v in zip(numers, V) ]) + + def _deflation(p): + for y in V: + if not p.has(y): + continue + + if _derivation(p) is not S.Zero: + c, q = p.as_poly(y).primitive() + return _deflation(c)*gcd(q, q.diff(y)).as_expr() + + return p + + def _splitter(p): + for y in V: + if not p.has(y): + continue + + if _derivation(y) is not S.Zero: + c, q = p.as_poly(y).primitive() + + q = q.as_expr() + + h = gcd(q, _derivation(q), y) + s = quo(h, gcd(q, q.diff(y), y), y) + + c_split = _splitter(c) + + if s.as_poly(y).degree() == 0: + return (c_split[0], q * c_split[1]) + + q_split = _splitter(cancel(q / s)) + + return (c_split[0]*q_split[0]*s, c_split[1]*q_split[1]) + + return (S.One, p) + + special = {} + + for term in terms: + if term.is_Function: + if isinstance(term, tan): + special[1 + _substitute(term)**2] = False + elif isinstance(term, tanh): + special[1 + _substitute(term)] = False + special[1 - _substitute(term)] = False + elif isinstance(term, LambertW): + special[_substitute(term)] = True + + F = _substitute(f) + + P, Q = F.as_numer_denom() + + u_split = _splitter(denom) + v_split = _splitter(Q) + + polys = set(list(v_split) + [ u_split[0] ] + list(special.keys())) + + s = u_split[0] * Mul(*[ k for k, v in special.items() if v ]) + polified = [ p.as_poly(*V) for p in [s, P, Q] ] + + if None in polified: + return None + + #--- definitions for _integrate + a, b, c = [ p.total_degree() for p in polified ] + + poly_denom = (s * v_split[0] * _deflation(v_split[1])).as_expr() + + def _exponent(g): + if g.is_Pow: + if g.exp.is_Rational and g.exp.q != 1: + if g.exp.p > 0: + return g.exp.p + g.exp.q - 1 + else: + return abs(g.exp.p + g.exp.q) + else: + return 1 + elif not g.is_Atom and g.args: + return max(_exponent(h) for h in g.args) + else: + return 1 + + A, B = _exponent(f), a + max(b, c) + + if A > 1 and B > 1: + monoms = tuple(ordered(itermonomials(V, A + B - 1 + degree_offset))) + else: + monoms = tuple(ordered(itermonomials(V, A + B + degree_offset))) + + poly_coeffs = _symbols('A', len(monoms)) + + poly_part = Add(*[ poly_coeffs[i]*monomial + for i, monomial in enumerate(monoms) ]) + + reducibles = set() + + for poly in ordered(polys): + coeff, factors = factor_list(poly, *V) + reducibles.add(coeff) + reducibles.update(fact for fact, mul in factors) + + def _integrate(field=None): + atans = set() + pairs = set() + + if field == 'Q': + irreducibles = set(reducibles) + else: + setV = set(V) + irreducibles = set() + for poly in ordered(reducibles): + zV = setV & set(iterfreeargs(poly)) + for z in ordered(zV): + s = set(root_factors(poly, z, filter=field)) + irreducibles |= s + break + + log_part, atan_part = [], [] + + for poly in ordered(irreducibles): + m = collect(poly, I, evaluate=False) + y = m.get(I, S.Zero) + if y: + x = m.get(S.One, S.Zero) + if x.has(I) or y.has(I): + continue # nontrivial x + I*y + pairs.add((x, y)) + irreducibles.remove(poly) + + while pairs: + x, y = pairs.pop() + if (x, -y) in pairs: + pairs.remove((x, -y)) + # Choosing b with no minus sign + if y.could_extract_minus_sign(): + y = -y + irreducibles.add(x*x + y*y) + atans.add(atan(x/y)) + else: + irreducibles.add(x + I*y) + + + B = _symbols('B', len(irreducibles)) + C = _symbols('C', len(atans)) + + # Note: the ordering matters here + for poly, b in reversed(list(zip(ordered(irreducibles), B))): + if poly.has(*V): + poly_coeffs.append(b) + log_part.append(b * log(poly)) + + for poly, c in reversed(list(zip(ordered(atans), C))): + if poly.has(*V): + poly_coeffs.append(c) + atan_part.append(c * poly) + + # TODO: Currently it's better to use symbolic expressions here instead + # of rational functions, because it's simpler and FracElement doesn't + # give big speed improvement yet. This is because cancellation is slow + # due to slow polynomial GCD algorithms. If this gets improved then + # revise this code. + candidate = poly_part/poly_denom + Add(*log_part) + Add(*atan_part) + h = F - _derivation(candidate) / denom + raw_numer = h.as_numer_denom()[0] + + # Rewrite raw_numer as a polynomial in K[coeffs][V] where K is a field + # that we have to determine. We can't use simply atoms() because log(3), + # sqrt(y) and similar expressions can appear, leading to non-trivial + # domains. + syms = set(poly_coeffs) | set(V) + non_syms = set() + + def find_non_syms(expr): + if expr.is_Integer or expr.is_Rational: + pass # ignore trivial numbers + elif expr in syms: + pass # ignore variables + elif not expr.has_free(*syms): + non_syms.add(expr) + elif expr.is_Add or expr.is_Mul or expr.is_Pow: + list(map(find_non_syms, expr.args)) + else: + # TODO: Non-polynomial expression. This should have been + # filtered out at an earlier stage. + raise PolynomialError + + try: + find_non_syms(raw_numer) + except PolynomialError: + return None + else: + ground, _ = construct_domain(non_syms, field=True) + + coeff_ring = PolyRing(poly_coeffs, ground) + ring = PolyRing(V, coeff_ring) + try: + numer = ring.from_expr(raw_numer) + except ValueError: + raise PolynomialError + solution = solve_lin_sys(numer.coeffs(), coeff_ring, _raw=False) + + if solution is None: + return None + else: + return candidate.xreplace(solution).xreplace( + dict(zip(poly_coeffs, [S.Zero]*len(poly_coeffs)))) + + if all(isinstance(_, Symbol) for _ in V): + more_free = F.free_symbols - set(V) + else: + Fd = F.as_dummy() + more_free = Fd.xreplace(dict(zip(V, (Dummy() for _ in V))) + ).free_symbols & Fd.free_symbols + if not more_free: + # all free generators are identified in V + solution = _integrate('Q') + + if solution is None: + solution = _integrate() + else: + solution = _integrate() + + if solution is not None: + antideriv = solution.subs(rev_mapping) + antideriv = cancel(antideriv).expand() + + if antideriv.is_Add: + antideriv = antideriv.as_independent(x)[1] + + return indep*antideriv + else: + if retries >= 0: + result = heurisch(f, x, mappings=mappings, rewrite=rewrite, hints=hints, retries=retries - 1, unnecessary_permutations=unnecessary_permutations) + + if result is not None: + return indep*result + + return None diff --git a/lib/python3.11/site-packages/sympy/integrals/integrals.py b/lib/python3.11/site-packages/sympy/integrals/integrals.py new file mode 100644 index 0000000000000000000000000000000000000000..0a54b5712ad65ad1c49a021950689578b6575106 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/integrals.py @@ -0,0 +1,1640 @@ +from typing import Tuple as tTuple + +from sympy.concrete.expr_with_limits import AddWithLimits +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.expr import Expr +from sympy.core.exprtools import factor_terms +from sympy.core.function import diff +from sympy.core.logic import fuzzy_bool +from sympy.core.mul import Mul +from sympy.core.numbers import oo, pi +from sympy.core.relational import Ne +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, Wild) +from sympy.core.sympify import sympify +from sympy.functions import Piecewise, sqrt, piecewise_fold, tan, cot, atan +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.complexes import Abs, sign +from sympy.functions.elementary.miscellaneous import Min, Max +from sympy.functions.special.singularity_functions import Heaviside +from .rationaltools import ratint +from sympy.matrices import MatrixBase +from sympy.polys import Poly, PolynomialError +from sympy.series.formal import FormalPowerSeries +from sympy.series.limits import limit +from sympy.series.order import Order +from sympy.tensor.functions import shape +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import is_sequence +from sympy.utilities.misc import filldedent + + +class Integral(AddWithLimits): + """Represents unevaluated integral.""" + + __slots__ = () + + args: tTuple[Expr, Tuple] + + def __new__(cls, function, *symbols, **assumptions): + """Create an unevaluated integral. + + Explanation + =========== + + Arguments are an integrand followed by one or more limits. + + If no limits are given and there is only one free symbol in the + expression, that symbol will be used, otherwise an error will be + raised. + + >>> from sympy import Integral + >>> from sympy.abc import x, y + >>> Integral(x) + Integral(x, x) + >>> Integral(y) + Integral(y, y) + + When limits are provided, they are interpreted as follows (using + ``x`` as though it were the variable of integration): + + (x,) or x - indefinite integral + (x, a) - "evaluate at" integral is an abstract antiderivative + (x, a, b) - definite integral + + The ``as_dummy`` method can be used to see which symbols cannot be + targeted by subs: those with a prepended underscore cannot be + changed with ``subs``. (Also, the integration variables themselves -- + the first element of a limit -- can never be changed by subs.) + + >>> i = Integral(x, x) + >>> at = Integral(x, (x, x)) + >>> i.as_dummy() + Integral(x, x) + >>> at.as_dummy() + Integral(_0, (_0, x)) + + """ + + #This will help other classes define their own definitions + #of behaviour with Integral. + if hasattr(function, '_eval_Integral'): + return function._eval_Integral(*symbols, **assumptions) + + if isinstance(function, Poly): + sympy_deprecation_warning( + """ + integrate(Poly) and Integral(Poly) are deprecated. Instead, + use the Poly.integrate() method, or convert the Poly to an + Expr first with the Poly.as_expr() method. + """, + deprecated_since_version="1.6", + active_deprecations_target="deprecated-integrate-poly") + + obj = AddWithLimits.__new__(cls, function, *symbols, **assumptions) + return obj + + def __getnewargs__(self): + return (self.function,) + tuple([tuple(xab) for xab in self.limits]) + + @property + def free_symbols(self): + """ + This method returns the symbols that will exist when the + integral is evaluated. This is useful if one is trying to + determine whether an integral depends on a certain + symbol or not. + + Examples + ======== + + >>> from sympy import Integral + >>> from sympy.abc import x, y + >>> Integral(x, (x, y, 1)).free_symbols + {y} + + See Also + ======== + + sympy.concrete.expr_with_limits.ExprWithLimits.function + sympy.concrete.expr_with_limits.ExprWithLimits.limits + sympy.concrete.expr_with_limits.ExprWithLimits.variables + """ + return super().free_symbols + + def _eval_is_zero(self): + # This is a very naive and quick test, not intended to do the integral to + # answer whether it is zero or not, e.g. Integral(sin(x), (x, 0, 2*pi)) + # is zero but this routine should return None for that case. But, like + # Mul, there are trivial situations for which the integral will be + # zero so we check for those. + if self.function.is_zero: + return True + got_none = False + for l in self.limits: + if len(l) == 3: + z = (l[1] == l[2]) or (l[1] - l[2]).is_zero + if z: + return True + elif z is None: + got_none = True + free = self.function.free_symbols + for xab in self.limits: + if len(xab) == 1: + free.add(xab[0]) + continue + if len(xab) == 2 and xab[0] not in free: + if xab[1].is_zero: + return True + elif xab[1].is_zero is None: + got_none = True + # take integration symbol out of free since it will be replaced + # with the free symbols in the limits + free.discard(xab[0]) + # add in the new symbols + for i in xab[1:]: + free.update(i.free_symbols) + if self.function.is_zero is False and got_none is False: + return False + + def transform(self, x, u): + r""" + Performs a change of variables from `x` to `u` using the relationship + given by `x` and `u` which will define the transformations `f` and `F` + (which are inverses of each other) as follows: + + 1) If `x` is a Symbol (which is a variable of integration) then `u` + will be interpreted as some function, f(u), with inverse F(u). + This, in effect, just makes the substitution of x with f(x). + + 2) If `u` is a Symbol then `x` will be interpreted as some function, + F(x), with inverse f(u). This is commonly referred to as + u-substitution. + + Once f and F have been identified, the transformation is made as + follows: + + .. math:: \int_a^b x \mathrm{d}x \rightarrow \int_{F(a)}^{F(b)} f(x) + \frac{\mathrm{d}}{\mathrm{d}x} + + where `F(x)` is the inverse of `f(x)` and the limits and integrand have + been corrected so as to retain the same value after integration. + + Notes + ===== + + The mappings, F(x) or f(u), must lead to a unique integral. Linear + or rational linear expression, ``2*x``, ``1/x`` and ``sqrt(x)``, will + always work; quadratic expressions like ``x**2 - 1`` are acceptable + as long as the resulting integrand does not depend on the sign of + the solutions (see examples). + + The integral will be returned unchanged if ``x`` is not a variable of + integration. + + ``x`` must be (or contain) only one of of the integration variables. If + ``u`` has more than one free symbol then it should be sent as a tuple + (``u``, ``uvar``) where ``uvar`` identifies which variable is replacing + the integration variable. + XXX can it contain another integration variable? + + Examples + ======== + + >>> from sympy.abc import a, x, u + >>> from sympy import Integral, cos, sqrt + + >>> i = Integral(x*cos(x**2 - 1), (x, 0, 1)) + + transform can change the variable of integration + + >>> i.transform(x, u) + Integral(u*cos(u**2 - 1), (u, 0, 1)) + + transform can perform u-substitution as long as a unique + integrand is obtained: + + >>> ui = i.transform(x**2 - 1, u) + >>> ui + Integral(cos(u)/2, (u, -1, 0)) + + This attempt fails because x = +/-sqrt(u + 1) and the + sign does not cancel out of the integrand: + + >>> Integral(cos(x**2 - 1), (x, 0, 1)).transform(x**2 - 1, u) + Traceback (most recent call last): + ... + ValueError: + The mapping between F(x) and f(u) did not give a unique integrand. + + transform can do a substitution. Here, the previous + result is transformed back into the original expression + using "u-substitution": + + >>> ui.transform(sqrt(u + 1), x) == i + True + + We can accomplish the same with a regular substitution: + + >>> ui.transform(u, x**2 - 1) == i + True + + If the `x` does not contain a symbol of integration then + the integral will be returned unchanged. Integral `i` does + not have an integration variable `a` so no change is made: + + >>> i.transform(a, x) == i + True + + When `u` has more than one free symbol the symbol that is + replacing `x` must be identified by passing `u` as a tuple: + + >>> Integral(x, (x, 0, 1)).transform(x, (u + a, u)) + Integral(a + u, (u, -a, 1 - a)) + >>> Integral(x, (x, 0, 1)).transform(x, (u + a, a)) + Integral(a + u, (a, -u, 1 - u)) + + See Also + ======== + + sympy.concrete.expr_with_limits.ExprWithLimits.variables : Lists the integration variables + as_dummy : Replace integration variables with dummy ones + """ + d = Dummy('d') + + xfree = x.free_symbols.intersection(self.variables) + if len(xfree) > 1: + raise ValueError( + 'F(x) can only contain one of: %s' % self.variables) + xvar = xfree.pop() if xfree else d + + if xvar not in self.variables: + return self + + u = sympify(u) + if isinstance(u, Expr): + ufree = u.free_symbols + if len(ufree) == 0: + raise ValueError(filldedent(''' + f(u) cannot be a constant''')) + if len(ufree) > 1: + raise ValueError(filldedent(''' + When f(u) has more than one free symbol, the one replacing x + must be identified: pass f(u) as (f(u), u)''')) + uvar = ufree.pop() + else: + u, uvar = u + if uvar not in u.free_symbols: + raise ValueError(filldedent(''' + Expecting a tuple (expr, symbol) where symbol identified + a free symbol in expr, but symbol is not in expr's free + symbols.''')) + if not isinstance(uvar, Symbol): + # This probably never evaluates to True + raise ValueError(filldedent(''' + Expecting a tuple (expr, symbol) but didn't get + a symbol; got %s''' % uvar)) + + if x.is_Symbol and u.is_Symbol: + return self.xreplace({x: u}) + + if not x.is_Symbol and not u.is_Symbol: + raise ValueError('either x or u must be a symbol') + + if uvar == xvar: + return self.transform(x, (u.subs(uvar, d), d)).xreplace({d: uvar}) + + if uvar in self.limits: + raise ValueError(filldedent(''' + u must contain the same variable as in x + or a variable that is not already an integration variable''')) + + from sympy.solvers.solvers import solve + if not x.is_Symbol: + F = [x.subs(xvar, d)] + soln = solve(u - x, xvar, check=False) + if not soln: + raise ValueError('no solution for solve(F(x) - f(u), x)') + f = [fi.subs(uvar, d) for fi in soln] + else: + f = [u.subs(uvar, d)] + from sympy.simplify.simplify import posify + pdiff, reps = posify(u - x) + puvar = uvar.subs([(v, k) for k, v in reps.items()]) + soln = [s.subs(reps) for s in solve(pdiff, puvar)] + if not soln: + raise ValueError('no solution for solve(F(x) - f(u), u)') + F = [fi.subs(xvar, d) for fi in soln] + + newfuncs = {(self.function.subs(xvar, fi)*fi.diff(d) + ).subs(d, uvar) for fi in f} + if len(newfuncs) > 1: + raise ValueError(filldedent(''' + The mapping between F(x) and f(u) did not give + a unique integrand.''')) + newfunc = newfuncs.pop() + + def _calc_limit_1(F, a, b): + """ + replace d with a, using subs if possible, otherwise limit + where sign of b is considered + """ + wok = F.subs(d, a) + if wok is S.NaN or wok.is_finite is False and a.is_finite: + return limit(sign(b)*F, d, a) + return wok + + def _calc_limit(a, b): + """ + replace d with a, using subs if possible, otherwise limit + where sign of b is considered + """ + avals = list({_calc_limit_1(Fi, a, b) for Fi in F}) + if len(avals) > 1: + raise ValueError(filldedent(''' + The mapping between F(x) and f(u) did not + give a unique limit.''')) + return avals[0] + + newlimits = [] + for xab in self.limits: + sym = xab[0] + if sym == xvar: + if len(xab) == 3: + a, b = xab[1:] + a, b = _calc_limit(a, b), _calc_limit(b, a) + if fuzzy_bool(a - b > 0): + a, b = b, a + newfunc = -newfunc + newlimits.append((uvar, a, b)) + elif len(xab) == 2: + a = _calc_limit(xab[1], 1) + newlimits.append((uvar, a)) + else: + newlimits.append(uvar) + else: + newlimits.append(xab) + + return self.func(newfunc, *newlimits) + + def doit(self, **hints): + """ + Perform the integration using any hints given. + + Examples + ======== + + >>> from sympy import Piecewise, S + >>> from sympy.abc import x, t + >>> p = x**2 + Piecewise((0, x/t < 0), (1, True)) + >>> p.integrate((t, S(4)/5, 1), (x, -1, 1)) + 1/3 + + See Also + ======== + + sympy.integrals.trigonometry.trigintegrate + sympy.integrals.heurisch.heurisch + sympy.integrals.rationaltools.ratint + as_sum : Approximate the integral using a sum + """ + if not hints.get('integrals', True): + return self + + deep = hints.get('deep', True) + meijerg = hints.get('meijerg', None) + conds = hints.get('conds', 'piecewise') + risch = hints.get('risch', None) + heurisch = hints.get('heurisch', None) + manual = hints.get('manual', None) + if len(list(filter(None, (manual, meijerg, risch, heurisch)))) > 1: + raise ValueError("At most one of manual, meijerg, risch, heurisch can be True") + elif manual: + meijerg = risch = heurisch = False + elif meijerg: + manual = risch = heurisch = False + elif risch: + manual = meijerg = heurisch = False + elif heurisch: + manual = meijerg = risch = False + eval_kwargs = {"meijerg": meijerg, "risch": risch, "manual": manual, "heurisch": heurisch, + "conds": conds} + + if conds not in ('separate', 'piecewise', 'none'): + raise ValueError('conds must be one of "separate", "piecewise", ' + '"none", got: %s' % conds) + + if risch and any(len(xab) > 1 for xab in self.limits): + raise ValueError('risch=True is only allowed for indefinite integrals.') + + # check for the trivial zero + if self.is_zero: + return S.Zero + + # hacks to handle integrals of + # nested summations + from sympy.concrete.summations import Sum + if isinstance(self.function, Sum): + if any(v in self.function.limits[0] for v in self.variables): + raise ValueError('Limit of the sum cannot be an integration variable.') + if any(l.is_infinite for l in self.function.limits[0][1:]): + return self + _i = self + _sum = self.function + return _sum.func(_i.func(_sum.function, *_i.limits).doit(), *_sum.limits).doit() + + # now compute and check the function + function = self.function + + # hack to use a consistent Heaviside(x, 1/2) + function = function.replace( + lambda x: isinstance(x, Heaviside) and x.args[1]*2 != 1, + lambda x: Heaviside(x.args[0])) + + if deep: + function = function.doit(**hints) + if function.is_zero: + return S.Zero + + # hacks to handle special cases + if isinstance(function, MatrixBase): + return function.applyfunc( + lambda f: self.func(f, *self.limits).doit(**hints)) + + if isinstance(function, FormalPowerSeries): + if len(self.limits) > 1: + raise NotImplementedError + xab = self.limits[0] + if len(xab) > 1: + return function.integrate(xab, **eval_kwargs) + else: + return function.integrate(xab[0], **eval_kwargs) + + # There is no trivial answer and special handling + # is done so continue + + # first make sure any definite limits have integration + # variables with matching assumptions + reps = {} + for xab in self.limits: + if len(xab) != 3: + # it makes sense to just make + # all x real but in practice with the + # current state of integration...this + # doesn't work out well + # x = xab[0] + # if x not in reps and not x.is_real: + # reps[x] = Dummy(real=True) + continue + x, a, b = xab + l = (a, b) + if all(i.is_nonnegative for i in l) and not x.is_nonnegative: + d = Dummy(positive=True) + elif all(i.is_nonpositive for i in l) and not x.is_nonpositive: + d = Dummy(negative=True) + elif all(i.is_real for i in l) and not x.is_real: + d = Dummy(real=True) + else: + d = None + if d: + reps[x] = d + if reps: + undo = {v: k for k, v in reps.items()} + did = self.xreplace(reps).doit(**hints) + if isinstance(did, tuple): # when separate=True + did = tuple([i.xreplace(undo) for i in did]) + else: + did = did.xreplace(undo) + return did + + # continue with existing assumptions + undone_limits = [] + # ulj = free symbols of any undone limits' upper and lower limits + ulj = set() + for xab in self.limits: + # compute uli, the free symbols in the + # Upper and Lower limits of limit I + if len(xab) == 1: + uli = set(xab[:1]) + elif len(xab) == 2: + uli = xab[1].free_symbols + elif len(xab) == 3: + uli = xab[1].free_symbols.union(xab[2].free_symbols) + # this integral can be done as long as there is no blocking + # limit that has been undone. An undone limit is blocking if + # it contains an integration variable that is in this limit's + # upper or lower free symbols or vice versa + if xab[0] in ulj or any(v[0] in uli for v in undone_limits): + undone_limits.append(xab) + ulj.update(uli) + function = self.func(*([function] + [xab])) + factored_function = function.factor() + if not isinstance(factored_function, Integral): + function = factored_function + continue + + if function.has(Abs, sign) and ( + (len(xab) < 3 and all(x.is_extended_real for x in xab)) or + (len(xab) == 3 and all(x.is_extended_real and not x.is_infinite for + x in xab[1:]))): + # some improper integrals are better off with Abs + xr = Dummy("xr", real=True) + function = (function.xreplace({xab[0]: xr}) + .rewrite(Piecewise).xreplace({xr: xab[0]})) + elif function.has(Min, Max): + function = function.rewrite(Piecewise) + if (function.has(Piecewise) and + not isinstance(function, Piecewise)): + function = piecewise_fold(function) + if isinstance(function, Piecewise): + if len(xab) == 1: + antideriv = function._eval_integral(xab[0], + **eval_kwargs) + else: + antideriv = self._eval_integral( + function, xab[0], **eval_kwargs) + else: + # There are a number of tradeoffs in using the + # Meijer G method. It can sometimes be a lot faster + # than other methods, and sometimes slower. And + # there are certain types of integrals for which it + # is more likely to work than others. These + # heuristics are incorporated in deciding what + # integration methods to try, in what order. See the + # integrate() docstring for details. + def try_meijerg(function, xab): + ret = None + if len(xab) == 3 and meijerg is not False: + x, a, b = xab + try: + res = meijerint_definite(function, x, a, b) + except NotImplementedError: + _debug('NotImplementedError ' + 'from meijerint_definite') + res = None + if res is not None: + f, cond = res + if conds == 'piecewise': + u = self.func(function, (x, a, b)) + # if Piecewise modifies cond too + # much it may not be recognized by + # _condsimp pattern matching so just + # turn off all evaluation + return Piecewise((f, cond), (u, True), + evaluate=False) + elif conds == 'separate': + if len(self.limits) != 1: + raise ValueError(filldedent(''' + conds=separate not supported in + multiple integrals''')) + ret = f, cond + else: + ret = f + return ret + + meijerg1 = meijerg + if (meijerg is not False and + len(xab) == 3 and xab[1].is_extended_real and xab[2].is_extended_real + and not function.is_Poly and + (xab[1].has(oo, -oo) or xab[2].has(oo, -oo))): + ret = try_meijerg(function, xab) + if ret is not None: + function = ret + continue + meijerg1 = False + # If the special meijerg code did not succeed in + # finding a definite integral, then the code using + # meijerint_indefinite will not either (it might + # find an antiderivative, but the answer is likely + # to be nonsensical). Thus if we are requested to + # only use Meijer G-function methods, we give up at + # this stage. Otherwise we just disable G-function + # methods. + if meijerg1 is False and meijerg is True: + antideriv = None + else: + antideriv = self._eval_integral( + function, xab[0], **eval_kwargs) + if antideriv is None and meijerg is True: + ret = try_meijerg(function, xab) + if ret is not None: + function = ret + continue + + final = hints.get('final', True) + # dotit may be iterated but floor terms making atan and acot + # continuous should only be added in the final round + if (final and not isinstance(antideriv, Integral) and + antideriv is not None): + for atan_term in antideriv.atoms(atan): + atan_arg = atan_term.args[0] + # Checking `atan_arg` to be linear combination of `tan` or `cot` + for tan_part in atan_arg.atoms(tan): + x1 = Dummy('x1') + tan_exp1 = atan_arg.subs(tan_part, x1) + # The coefficient of `tan` should be constant + coeff = tan_exp1.diff(x1) + if x1 not in coeff.free_symbols: + a = tan_part.args[0] + antideriv = antideriv.subs(atan_term, Add(atan_term, + sign(coeff)*pi*floor((a-pi/2)/pi))) + for cot_part in atan_arg.atoms(cot): + x1 = Dummy('x1') + cot_exp1 = atan_arg.subs(cot_part, x1) + # The coefficient of `cot` should be constant + coeff = cot_exp1.diff(x1) + if x1 not in coeff.free_symbols: + a = cot_part.args[0] + antideriv = antideriv.subs(atan_term, Add(atan_term, + sign(coeff)*pi*floor((a)/pi))) + + if antideriv is None: + undone_limits.append(xab) + function = self.func(*([function] + [xab])).factor() + factored_function = function.factor() + if not isinstance(factored_function, Integral): + function = factored_function + continue + else: + if len(xab) == 1: + function = antideriv + else: + if len(xab) == 3: + x, a, b = xab + elif len(xab) == 2: + x, b = xab + a = None + else: + raise NotImplementedError + + if deep: + if isinstance(a, Basic): + a = a.doit(**hints) + if isinstance(b, Basic): + b = b.doit(**hints) + + if antideriv.is_Poly: + gens = list(antideriv.gens) + gens.remove(x) + + antideriv = antideriv.as_expr() + + function = antideriv._eval_interval(x, a, b) + function = Poly(function, *gens) + else: + def is_indef_int(g, x): + return (isinstance(g, Integral) and + any(i == (x,) for i in g.limits)) + + def eval_factored(f, x, a, b): + # _eval_interval for integrals with + # (constant) factors + # a single indefinite integral is assumed + args = [] + for g in Mul.make_args(f): + if is_indef_int(g, x): + args.append(g._eval_interval(x, a, b)) + else: + args.append(g) + return Mul(*args) + + integrals, others, piecewises = [], [], [] + for f in Add.make_args(antideriv): + if any(is_indef_int(g, x) + for g in Mul.make_args(f)): + integrals.append(f) + elif any(isinstance(g, Piecewise) + for g in Mul.make_args(f)): + piecewises.append(piecewise_fold(f)) + else: + others.append(f) + uneval = Add(*[eval_factored(f, x, a, b) + for f in integrals]) + try: + evalued = Add(*others)._eval_interval(x, a, b) + evalued_pw = piecewise_fold(Add(*piecewises))._eval_interval(x, a, b) + function = uneval + evalued + evalued_pw + except NotImplementedError: + # This can happen if _eval_interval depends in a + # complicated way on limits that cannot be computed + undone_limits.append(xab) + function = self.func(*([function] + [xab])) + factored_function = function.factor() + if not isinstance(factored_function, Integral): + function = factored_function + return function + + def _eval_derivative(self, sym): + """Evaluate the derivative of the current Integral object by + differentiating under the integral sign [1], using the Fundamental + Theorem of Calculus [2] when possible. + + Explanation + =========== + + Whenever an Integral is encountered that is equivalent to zero or + has an integrand that is independent of the variable of integration + those integrals are performed. All others are returned as Integral + instances which can be resolved with doit() (provided they are integrable). + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign + .. [2] https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus + + Examples + ======== + + >>> from sympy import Integral + >>> from sympy.abc import x, y + >>> i = Integral(x + y, y, (y, 1, x)) + >>> i.diff(x) + Integral(x + y, (y, x)) + Integral(1, y, (y, 1, x)) + >>> i.doit().diff(x) == i.diff(x).doit() + True + >>> i.diff(y) + 0 + + The previous must be true since there is no y in the evaluated integral: + + >>> i.free_symbols + {x} + >>> i.doit() + 2*x**3/3 - x/2 - 1/6 + + """ + + # differentiate under the integral sign; we do not + # check for regularity conditions (TODO), see issue 4215 + + # get limits and the function + f, limits = self.function, list(self.limits) + + # the order matters if variables of integration appear in the limits + # so work our way in from the outside to the inside. + limit = limits.pop(-1) + if len(limit) == 3: + x, a, b = limit + elif len(limit) == 2: + x, b = limit + a = None + else: + a = b = None + x = limit[0] + + if limits: # f is the argument to an integral + f = self.func(f, *tuple(limits)) + + # assemble the pieces + def _do(f, ab): + dab_dsym = diff(ab, sym) + if not dab_dsym: + return S.Zero + if isinstance(f, Integral): + limits = [(x, x) if (len(l) == 1 and l[0] == x) else l + for l in f.limits] + f = self.func(f.function, *limits) + return f.subs(x, ab)*dab_dsym + + rv = S.Zero + if b is not None: + rv += _do(f, b) + if a is not None: + rv -= _do(f, a) + if len(limit) == 1 and sym == x: + # the dummy variable *is* also the real-world variable + arg = f + rv += arg + else: + # the dummy variable might match sym but it's + # only a dummy and the actual variable is determined + # by the limits, so mask off the variable of integration + # while differentiating + u = Dummy('u') + arg = f.subs(x, u).diff(sym).subs(u, x) + if arg: + rv += self.func(arg, (x, a, b)) + return rv + + def _eval_integral(self, f, x, meijerg=None, risch=None, manual=None, + heurisch=None, conds='piecewise',final=None): + """ + Calculate the anti-derivative to the function f(x). + + Explanation + =========== + + The following algorithms are applied (roughly in this order): + + 1. Simple heuristics (based on pattern matching and integral table): + + - most frequently used functions (e.g. polynomials, products of + trig functions) + + 2. Integration of rational functions: + + - A complete algorithm for integrating rational functions is + implemented (the Lazard-Rioboo-Trager algorithm). The algorithm + also uses the partial fraction decomposition algorithm + implemented in apart() as a preprocessor to make this process + faster. Note that the integral of a rational function is always + elementary, but in general, it may include a RootSum. + + 3. Full Risch algorithm: + + - The Risch algorithm is a complete decision + procedure for integrating elementary functions, which means that + given any elementary function, it will either compute an + elementary antiderivative, or else prove that none exists. + Currently, part of transcendental case is implemented, meaning + elementary integrals containing exponentials, logarithms, and + (soon!) trigonometric functions can be computed. The algebraic + case, e.g., functions containing roots, is much more difficult + and is not implemented yet. + + - If the routine fails (because the integrand is not elementary, or + because a case is not implemented yet), it continues on to the + next algorithms below. If the routine proves that the integrals + is nonelementary, it still moves on to the algorithms below, + because we might be able to find a closed-form solution in terms + of special functions. If risch=True, however, it will stop here. + + 4. The Meijer G-Function algorithm: + + - This algorithm works by first rewriting the integrand in terms of + very general Meijer G-Function (meijerg in SymPy), integrating + it, and then rewriting the result back, if possible. This + algorithm is particularly powerful for definite integrals (which + is actually part of a different method of Integral), since it can + compute closed-form solutions of definite integrals even when no + closed-form indefinite integral exists. But it also is capable + of computing many indefinite integrals as well. + + - Another advantage of this method is that it can use some results + about the Meijer G-Function to give a result in terms of a + Piecewise expression, which allows to express conditionally + convergent integrals. + + - Setting meijerg=True will cause integrate() to use only this + method. + + 5. The "manual integration" algorithm: + + - This algorithm tries to mimic how a person would find an + antiderivative by hand, for example by looking for a + substitution or applying integration by parts. This algorithm + does not handle as many integrands but can return results in a + more familiar form. + + - Sometimes this algorithm can evaluate parts of an integral; in + this case integrate() will try to evaluate the rest of the + integrand using the other methods here. + + - Setting manual=True will cause integrate() to use only this + method. + + 6. The Heuristic Risch algorithm: + + - This is a heuristic version of the Risch algorithm, meaning that + it is not deterministic. This is tried as a last resort because + it can be very slow. It is still used because not enough of the + full Risch algorithm is implemented, so that there are still some + integrals that can only be computed using this method. The goal + is to implement enough of the Risch and Meijer G-function methods + so that this can be deleted. + + Setting heurisch=True will cause integrate() to use only this + method. Set heurisch=False to not use it. + + """ + + from sympy.integrals.risch import risch_integrate, NonElementaryIntegral + from sympy.integrals.manualintegrate import manualintegrate + + if risch: + try: + return risch_integrate(f, x, conds=conds) + except NotImplementedError: + return None + + if manual: + try: + result = manualintegrate(f, x) + if result is not None and result.func != Integral: + return result + except (ValueError, PolynomialError): + pass + + eval_kwargs = {"meijerg": meijerg, "risch": risch, "manual": manual, + "heurisch": heurisch, "conds": conds} + + # if it is a poly(x) then let the polynomial integrate itself (fast) + # + # It is important to make this check first, otherwise the other code + # will return a SymPy expression instead of a Polynomial. + # + # see Polynomial for details. + if isinstance(f, Poly) and not (manual or meijerg or risch): + # Note: this is deprecated, but the deprecation warning is already + # issued in the Integral constructor. + return f.integrate(x) + + # Piecewise antiderivatives need to call special integrate. + if isinstance(f, Piecewise): + return f.piecewise_integrate(x, **eval_kwargs) + + # let's cut it short if `f` does not depend on `x`; if + # x is only a dummy, that will be handled below + if not f.has(x): + return f*x + + # try to convert to poly(x) and then integrate if successful (fast) + poly = f.as_poly(x) + if poly is not None and not (manual or meijerg or risch): + return poly.integrate().as_expr() + + if risch is not False: + try: + result, i = risch_integrate(f, x, separate_integral=True, + conds=conds) + except NotImplementedError: + pass + else: + if i: + # There was a nonelementary integral. Try integrating it. + + # if no part of the NonElementaryIntegral is integrated by + # the Risch algorithm, then use the original function to + # integrate, instead of re-written one + if result == 0: + return NonElementaryIntegral(f, x).doit(risch=False) + else: + return result + i.doit(risch=False) + else: + return result + + # since Integral(f=g1+g2+...) == Integral(g1) + Integral(g2) + ... + # we are going to handle Add terms separately, + # if `f` is not Add -- we only have one term + + # Note that in general, this is a bad idea, because Integral(g1) + + # Integral(g2) might not be computable, even if Integral(g1 + g2) is. + # For example, Integral(x**x + x**x*log(x)). But many heuristics only + # work term-wise. So we compute this step last, after trying + # risch_integrate. We also try risch_integrate again in this loop, + # because maybe the integral is a sum of an elementary part and a + # nonelementary part (like erf(x) + exp(x)). risch_integrate() is + # quite fast, so this is acceptable. + from sympy.simplify.fu import sincos_to_sum + parts = [] + args = Add.make_args(f) + for g in args: + coeff, g = g.as_independent(x) + + # g(x) = const + if g is S.One and not meijerg: + parts.append(coeff*x) + continue + + # g(x) = expr + O(x**n) + order_term = g.getO() + + if order_term is not None: + h = self._eval_integral(g.removeO(), x, **eval_kwargs) + + if h is not None: + h_order_expr = self._eval_integral(order_term.expr, x, **eval_kwargs) + + if h_order_expr is not None: + h_order_term = order_term.func( + h_order_expr, *order_term.variables) + parts.append(coeff*(h + h_order_term)) + continue + + # NOTE: if there is O(x**n) and we fail to integrate then + # there is no point in trying other methods because they + # will fail, too. + return None + + # c + # g(x) = (a*x+b) + if g.is_Pow and not g.exp.has(x) and not meijerg: + a = Wild('a', exclude=[x]) + b = Wild('b', exclude=[x]) + + M = g.base.match(a*x + b) + + if M is not None: + if g.exp == -1: + h = log(g.base) + elif conds != 'piecewise': + h = g.base**(g.exp + 1) / (g.exp + 1) + else: + h1 = log(g.base) + h2 = g.base**(g.exp + 1) / (g.exp + 1) + h = Piecewise((h2, Ne(g.exp, -1)), (h1, True)) + + parts.append(coeff * h / M[a]) + continue + + # poly(x) + # g(x) = ------- + # poly(x) + if g.is_rational_function(x) and not (manual or meijerg or risch): + parts.append(coeff * ratint(g, x)) + continue + + if not (manual or meijerg or risch): + # g(x) = Mul(trig) + h = trigintegrate(g, x, conds=conds) + if h is not None: + parts.append(coeff * h) + continue + + # g(x) has at least a DiracDelta term + h = deltaintegrate(g, x) + if h is not None: + parts.append(coeff * h) + continue + + from .singularityfunctions import singularityintegrate + # g(x) has at least a Singularity Function term + h = singularityintegrate(g, x) + if h is not None: + parts.append(coeff * h) + continue + + # Try risch again. + if risch is not False: + try: + h, i = risch_integrate(g, x, + separate_integral=True, conds=conds) + except NotImplementedError: + h = None + else: + if i: + h = h + i.doit(risch=False) + + parts.append(coeff*h) + continue + + # fall back to heurisch + if heurisch is not False: + from sympy.integrals.heurisch import (heurisch as heurisch_, + heurisch_wrapper) + try: + if conds == 'piecewise': + h = heurisch_wrapper(g, x, hints=[]) + else: + h = heurisch_(g, x, hints=[]) + except PolynomialError: + # XXX: this exception means there is a bug in the + # implementation of heuristic Risch integration + # algorithm. + h = None + else: + h = None + + if meijerg is not False and h is None: + # rewrite using G functions + try: + h = meijerint_indefinite(g, x) + except NotImplementedError: + _debug('NotImplementedError from meijerint_definite') + if h is not None: + parts.append(coeff * h) + continue + + if h is None and manual is not False: + try: + result = manualintegrate(g, x) + if result is not None and not isinstance(result, Integral): + if result.has(Integral) and not manual: + # Try to have other algorithms do the integrals + # manualintegrate can't handle, + # unless we were asked to use manual only. + # Keep the rest of eval_kwargs in case another + # method was set to False already + new_eval_kwargs = eval_kwargs + new_eval_kwargs["manual"] = False + new_eval_kwargs["final"] = False + result = result.func(*[ + arg.doit(**new_eval_kwargs) if + arg.has(Integral) else arg + for arg in result.args + ]).expand(multinomial=False, + log=False, + power_exp=False, + power_base=False) + if not result.has(Integral): + parts.append(coeff * result) + continue + except (ValueError, PolynomialError): + # can't handle some SymPy expressions + pass + + # if we failed maybe it was because we had + # a product that could have been expanded, + # so let's try an expansion of the whole + # thing before giving up; we don't try this + # at the outset because there are things + # that cannot be solved unless they are + # NOT expanded e.g., x**x*(1+log(x)). There + # should probably be a checker somewhere in this + # routine to look for such cases and try to do + # collection on the expressions if they are already + # in an expanded form + if not h and len(args) == 1: + f = sincos_to_sum(f).expand(mul=True, deep=False) + if f.is_Add: + # Note: risch will be identical on the expanded + # expression, but maybe it will be able to pick out parts, + # like x*(exp(x) + erf(x)). + return self._eval_integral(f, x, **eval_kwargs) + + if h is not None: + parts.append(coeff * h) + else: + return None + + return Add(*parts) + + def _eval_lseries(self, x, logx=None, cdir=0): + expr = self.as_dummy() + symb = x + for l in expr.limits: + if x in l[1:]: + symb = l[0] + break + for term in expr.function.lseries(symb, logx): + yield integrate(term, *expr.limits) + + def _eval_nseries(self, x, n, logx=None, cdir=0): + symb = x + for l in self.limits: + if x in l[1:]: + symb = l[0] + break + terms, order = self.function.nseries( + x=symb, n=n, logx=logx).as_coeff_add(Order) + order = [o.subs(symb, x) for o in order] + return integrate(terms, *self.limits) + Add(*order)*x + + def _eval_as_leading_term(self, x, logx=None, cdir=0): + series_gen = self.args[0].lseries(x) + for leading_term in series_gen: + if leading_term != 0: + break + return integrate(leading_term, *self.args[1:]) + + def _eval_simplify(self, **kwargs): + expr = factor_terms(self) + if isinstance(expr, Integral): + from sympy.simplify.simplify import simplify + return expr.func(*[simplify(i, **kwargs) for i in expr.args]) + return expr.simplify(**kwargs) + + def as_sum(self, n=None, method="midpoint", evaluate=True): + """ + Approximates a definite integral by a sum. + + Parameters + ========== + + n : + The number of subintervals to use, optional. + method : + One of: 'left', 'right', 'midpoint', 'trapezoid'. + evaluate : bool + If False, returns an unevaluated Sum expression. The default + is True, evaluate the sum. + + Notes + ===== + + These methods of approximate integration are described in [1]. + + Examples + ======== + + >>> from sympy import Integral, sin, sqrt + >>> from sympy.abc import x, n + >>> e = Integral(sin(x), (x, 3, 7)) + >>> e + Integral(sin(x), (x, 3, 7)) + + For demonstration purposes, this interval will only be split into 2 + regions, bounded by [3, 5] and [5, 7]. + + The left-hand rule uses function evaluations at the left of each + interval: + + >>> e.as_sum(2, 'left') + 2*sin(5) + 2*sin(3) + + The midpoint rule uses evaluations at the center of each interval: + + >>> e.as_sum(2, 'midpoint') + 2*sin(4) + 2*sin(6) + + The right-hand rule uses function evaluations at the right of each + interval: + + >>> e.as_sum(2, 'right') + 2*sin(5) + 2*sin(7) + + The trapezoid rule uses function evaluations on both sides of the + intervals. This is equivalent to taking the average of the left and + right hand rule results: + + >>> s = e.as_sum(2, 'trapezoid') + >>> s + 2*sin(5) + sin(3) + sin(7) + >>> (e.as_sum(2, 'left') + e.as_sum(2, 'right'))/2 == s + True + + Here, the discontinuity at x = 0 can be avoided by using the + midpoint or right-hand method: + + >>> e = Integral(1/sqrt(x), (x, 0, 1)) + >>> e.as_sum(5).n(4) + 1.730 + >>> e.as_sum(10).n(4) + 1.809 + >>> e.doit().n(4) # the actual value is 2 + 2.000 + + The left- or trapezoid method will encounter the discontinuity and + return infinity: + + >>> e.as_sum(5, 'left') + zoo + + The number of intervals can be symbolic. If omitted, a dummy symbol + will be used for it. + + >>> e = Integral(x**2, (x, 0, 2)) + >>> e.as_sum(n, 'right').expand() + 8/3 + 4/n + 4/(3*n**2) + + This shows that the midpoint rule is more accurate, as its error + term decays as the square of n: + + >>> e.as_sum(method='midpoint').expand() + 8/3 - 2/(3*_n**2) + + A symbolic sum is returned with evaluate=False: + + >>> e.as_sum(n, 'midpoint', evaluate=False) + 2*Sum((2*_k/n - 1/n)**2, (_k, 1, n))/n + + See Also + ======== + + Integral.doit : Perform the integration using any hints + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Riemann_sum#Riemann_summation_methods + """ + + from sympy.concrete.summations import Sum + limits = self.limits + if len(limits) > 1: + raise NotImplementedError( + "Multidimensional midpoint rule not implemented yet") + else: + limit = limits[0] + if (len(limit) != 3 or limit[1].is_finite is False or + limit[2].is_finite is False): + raise ValueError("Expecting a definite integral over " + "a finite interval.") + if n is None: + n = Dummy('n', integer=True, positive=True) + else: + n = sympify(n) + if (n.is_positive is False or n.is_integer is False or + n.is_finite is False): + raise ValueError("n must be a positive integer, got %s" % n) + x, a, b = limit + dx = (b - a)/n + k = Dummy('k', integer=True, positive=True) + f = self.function + + if method == "left": + result = dx*Sum(f.subs(x, a + (k-1)*dx), (k, 1, n)) + elif method == "right": + result = dx*Sum(f.subs(x, a + k*dx), (k, 1, n)) + elif method == "midpoint": + result = dx*Sum(f.subs(x, a + k*dx - dx/2), (k, 1, n)) + elif method == "trapezoid": + result = dx*((f.subs(x, a) + f.subs(x, b))/2 + + Sum(f.subs(x, a + k*dx), (k, 1, n - 1))) + else: + raise ValueError("Unknown method %s" % method) + return result.doit() if evaluate else result + + def principal_value(self, **kwargs): + """ + Compute the Cauchy Principal Value of the definite integral of a real function in the given interval + on the real axis. + + Explanation + =========== + + In mathematics, the Cauchy principal value, is a method for assigning values to certain improper + integrals which would otherwise be undefined. + + Examples + ======== + + >>> from sympy import Integral, oo + >>> from sympy.abc import x + >>> Integral(x+1, (x, -oo, oo)).principal_value() + oo + >>> f = 1 / (x**3) + >>> Integral(f, (x, -oo, oo)).principal_value() + 0 + >>> Integral(f, (x, -10, 10)).principal_value() + 0 + >>> Integral(f, (x, -10, oo)).principal_value() + Integral(f, (x, -oo, 10)).principal_value() + 0 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Cauchy_principal_value + .. [2] https://mathworld.wolfram.com/CauchyPrincipalValue.html + """ + if len(self.limits) != 1 or len(list(self.limits[0])) != 3: + raise ValueError("You need to insert a variable, lower_limit, and upper_limit correctly to calculate " + "cauchy's principal value") + x, a, b = self.limits[0] + if not (a.is_comparable and b.is_comparable and a <= b): + raise ValueError("The lower_limit must be smaller than or equal to the upper_limit to calculate " + "cauchy's principal value. Also, a and b need to be comparable.") + if a == b: + return S.Zero + + from sympy.calculus.singularities import singularities + + r = Dummy('r') + f = self.function + singularities_list = [s for s in singularities(f, x) if s.is_comparable and a <= s <= b] + for i in singularities_list: + if i in (a, b): + raise ValueError( + 'The principal value is not defined in the given interval due to singularity at %d.' % (i)) + F = integrate(f, x, **kwargs) + if F.has(Integral): + return self + if a is -oo and b is oo: + I = limit(F - F.subs(x, -x), x, oo) + else: + I = limit(F, x, b, '-') - limit(F, x, a, '+') + for s in singularities_list: + I += limit(((F.subs(x, s - r)) - F.subs(x, s + r)), r, 0, '+') + return I + + + +def integrate(*args, meijerg=None, conds='piecewise', risch=None, heurisch=None, manual=None, **kwargs): + """integrate(f, var, ...) + + .. deprecated:: 1.6 + + Using ``integrate()`` with :class:`~.Poly` is deprecated. Use + :meth:`.Poly.integrate` instead. See :ref:`deprecated-integrate-poly`. + + Explanation + =========== + + Compute definite or indefinite integral of one or more variables + using Risch-Norman algorithm and table lookup. This procedure is + able to handle elementary algebraic and transcendental functions + and also a huge class of special functions, including Airy, + Bessel, Whittaker and Lambert. + + var can be: + + - a symbol -- indefinite integration + - a tuple (symbol, a) -- indefinite integration with result + given with ``a`` replacing ``symbol`` + - a tuple (symbol, a, b) -- definite integration + + Several variables can be specified, in which case the result is + multiple integration. (If var is omitted and the integrand is + univariate, the indefinite integral in that variable will be performed.) + + Indefinite integrals are returned without terms that are independent + of the integration variables. (see examples) + + Definite improper integrals often entail delicate convergence + conditions. Pass conds='piecewise', 'separate' or 'none' to have + these returned, respectively, as a Piecewise function, as a separate + result (i.e. result will be a tuple), or not at all (default is + 'piecewise'). + + **Strategy** + + SymPy uses various approaches to definite integration. One method is to + find an antiderivative for the integrand, and then use the fundamental + theorem of calculus. Various functions are implemented to integrate + polynomial, rational and trigonometric functions, and integrands + containing DiracDelta terms. + + SymPy also implements the part of the Risch algorithm, which is a decision + procedure for integrating elementary functions, i.e., the algorithm can + either find an elementary antiderivative, or prove that one does not + exist. There is also a (very successful, albeit somewhat slow) general + implementation of the heuristic Risch algorithm. This algorithm will + eventually be phased out as more of the full Risch algorithm is + implemented. See the docstring of Integral._eval_integral() for more + details on computing the antiderivative using algebraic methods. + + The option risch=True can be used to use only the (full) Risch algorithm. + This is useful if you want to know if an elementary function has an + elementary antiderivative. If the indefinite Integral returned by this + function is an instance of NonElementaryIntegral, that means that the + Risch algorithm has proven that integral to be non-elementary. Note that + by default, additional methods (such as the Meijer G method outlined + below) are tried on these integrals, as they may be expressible in terms + of special functions, so if you only care about elementary answers, use + risch=True. Also note that an unevaluated Integral returned by this + function is not necessarily a NonElementaryIntegral, even with risch=True, + as it may just be an indication that the particular part of the Risch + algorithm needed to integrate that function is not yet implemented. + + Another family of strategies comes from re-writing the integrand in + terms of so-called Meijer G-functions. Indefinite integrals of a + single G-function can always be computed, and the definite integral + of a product of two G-functions can be computed from zero to + infinity. Various strategies are implemented to rewrite integrands + as G-functions, and use this information to compute integrals (see + the ``meijerint`` module). + + The option manual=True can be used to use only an algorithm that tries + to mimic integration by hand. This algorithm does not handle as many + integrands as the other algorithms implemented but may return results in + a more familiar form. The ``manualintegrate`` module has functions that + return the steps used (see the module docstring for more information). + + In general, the algebraic methods work best for computing + antiderivatives of (possibly complicated) combinations of elementary + functions. The G-function methods work best for computing definite + integrals from zero to infinity of moderately complicated + combinations of special functions, or indefinite integrals of very + simple combinations of special functions. + + The strategy employed by the integration code is as follows: + + - If computing a definite integral, and both limits are real, + and at least one limit is +- oo, try the G-function method of + definite integration first. + + - Try to find an antiderivative, using all available methods, ordered + by performance (that is try fastest method first, slowest last; in + particular polynomial integration is tried first, Meijer + G-functions second to last, and heuristic Risch last). + + - If still not successful, try G-functions irrespective of the + limits. + + The option meijerg=True, False, None can be used to, respectively: + always use G-function methods and no others, never use G-function + methods, or use all available methods (in order as described above). + It defaults to None. + + Examples + ======== + + >>> from sympy import integrate, log, exp, oo + >>> from sympy.abc import a, x, y + + >>> integrate(x*y, x) + x**2*y/2 + + >>> integrate(log(x), x) + x*log(x) - x + + >>> integrate(log(x), (x, 1, a)) + a*log(a) - a + 1 + + >>> integrate(x) + x**2/2 + + Terms that are independent of x are dropped by indefinite integration: + + >>> from sympy import sqrt + >>> integrate(sqrt(1 + x), (x, 0, x)) + 2*(x + 1)**(3/2)/3 - 2/3 + >>> integrate(sqrt(1 + x), x) + 2*(x + 1)**(3/2)/3 + + >>> integrate(x*y) + Traceback (most recent call last): + ... + ValueError: specify integration variables to integrate x*y + + Note that ``integrate(x)`` syntax is meant only for convenience + in interactive sessions and should be avoided in library code. + + >>> integrate(x**a*exp(-x), (x, 0, oo)) # same as conds='piecewise' + Piecewise((gamma(a + 1), re(a) > -1), + (Integral(x**a*exp(-x), (x, 0, oo)), True)) + + >>> integrate(x**a*exp(-x), (x, 0, oo), conds='none') + gamma(a + 1) + + >>> integrate(x**a*exp(-x), (x, 0, oo), conds='separate') + (gamma(a + 1), re(a) > -1) + + See Also + ======== + + Integral, Integral.doit + + """ + doit_flags = { + 'deep': False, + 'meijerg': meijerg, + 'conds': conds, + 'risch': risch, + 'heurisch': heurisch, + 'manual': manual + } + integral = Integral(*args, **kwargs) + + if isinstance(integral, Integral): + return integral.doit(**doit_flags) + else: + new_args = [a.doit(**doit_flags) if isinstance(a, Integral) else a + for a in integral.args] + return integral.func(*new_args) + + +def line_integrate(field, curve, vars): + """line_integrate(field, Curve, variables) + + Compute the line integral. + + Examples + ======== + + >>> from sympy import Curve, line_integrate, E, ln + >>> from sympy.abc import x, y, t + >>> C = Curve([E**t + 1, E**t - 1], (t, 0, ln(2))) + >>> line_integrate(x + y, C, [x, y]) + 3*sqrt(2) + + See Also + ======== + + sympy.integrals.integrals.integrate, Integral + """ + from sympy.geometry import Curve + F = sympify(field) + if not F: + raise ValueError( + "Expecting function specifying field as first argument.") + if not isinstance(curve, Curve): + raise ValueError("Expecting Curve entity as second argument.") + if not is_sequence(vars): + raise ValueError("Expecting ordered iterable for variables.") + if len(curve.functions) != len(vars): + raise ValueError("Field variable size does not match curve dimension.") + + if curve.parameter in vars: + raise ValueError("Curve parameter clashes with field parameters.") + + # Calculate derivatives for line parameter functions + # F(r) -> F(r(t)) and finally F(r(t)*r'(t)) + Ft = F + dldt = 0 + for i, var in enumerate(vars): + _f = curve.functions[i] + _dn = diff(_f, curve.parameter) + # ...arc length + dldt = dldt + (_dn * _dn) + Ft = Ft.subs(var, _f) + Ft = Ft * sqrt(dldt) + + integral = Integral(Ft, curve.limits).doit(deep=False) + return integral + + +### Property function dispatching ### + +@shape.register(Integral) +def _(expr): + return shape(expr.function) + +# Delayed imports +from .deltafunctions import deltaintegrate +from .meijerint import meijerint_definite, meijerint_indefinite, _debug +from .trigonometry import trigintegrate diff --git a/lib/python3.11/site-packages/sympy/integrals/intpoly.py b/lib/python3.11/site-packages/sympy/integrals/intpoly.py new file mode 100644 index 0000000000000000000000000000000000000000..38fd071183fb2192f4c1443d04c8f0ecfb6cc4ea --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/intpoly.py @@ -0,0 +1,1302 @@ +""" +Module to implement integration of uni/bivariate polynomials over +2D Polytopes and uni/bi/trivariate polynomials over 3D Polytopes. + +Uses evaluation techniques as described in Chin et al. (2015) [1]. + + +References +=========== + +.. [1] Chin, Eric B., Jean B. Lasserre, and N. Sukumar. "Numerical integration +of homogeneous functions on convex and nonconvex polygons and polyhedra." +Computational Mechanics 56.6 (2015): 967-981 + +PDF link : http://dilbert.engr.ucdavis.edu/~suku/quadrature/cls-integration.pdf +""" + +from functools import cmp_to_key + +from sympy.abc import x, y, z +from sympy.core import S, diff, Expr, Symbol +from sympy.core.sympify import _sympify +from sympy.geometry import Segment2D, Polygon, Point, Point2D +from sympy.polys.polytools import LC, gcd_list, degree_list, Poly +from sympy.simplify.simplify import nsimplify + + +def polytope_integrate(poly, expr=None, *, clockwise=False, max_degree=None): + """Integrates polynomials over 2/3-Polytopes. + + Explanation + =========== + + This function accepts the polytope in ``poly`` and the function in ``expr`` + (uni/bi/trivariate polynomials are implemented) and returns + the exact integral of ``expr`` over ``poly``. + + Parameters + ========== + + poly : The input Polygon. + + expr : The input polynomial. + + clockwise : Binary value to sort input points of 2-Polytope clockwise.(Optional) + + max_degree : The maximum degree of any monomial of the input polynomial.(Optional) + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import Point, Polygon + >>> from sympy.integrals.intpoly import polytope_integrate + >>> polygon = Polygon(Point(0, 0), Point(0, 1), Point(1, 1), Point(1, 0)) + >>> polys = [1, x, y, x*y, x**2*y, x*y**2] + >>> expr = x*y + >>> polytope_integrate(polygon, expr) + 1/4 + >>> polytope_integrate(polygon, polys, max_degree=3) + {1: 1, x: 1/2, y: 1/2, x*y: 1/4, x*y**2: 1/6, x**2*y: 1/6} + """ + if clockwise: + if isinstance(poly, Polygon): + poly = Polygon(*point_sort(poly.vertices), evaluate=False) + else: + raise TypeError("clockwise=True works for only 2-Polytope" + "V-representation input") + + if isinstance(poly, Polygon): + # For Vertex Representation(2D case) + hp_params = hyperplane_parameters(poly) + facets = poly.sides + elif len(poly[0]) == 2: + # For Hyperplane Representation(2D case) + plen = len(poly) + if len(poly[0][0]) == 2: + intersections = [intersection(poly[(i - 1) % plen], poly[i], + "plane2D") + for i in range(0, plen)] + hp_params = poly + lints = len(intersections) + facets = [Segment2D(intersections[i], + intersections[(i + 1) % lints]) + for i in range(lints)] + else: + raise NotImplementedError("Integration for H-representation 3D" + "case not implemented yet.") + else: + # For Vertex Representation(3D case) + vertices = poly[0] + facets = poly[1:] + hp_params = hyperplane_parameters(facets, vertices) + + if max_degree is None: + if expr is None: + raise TypeError('Input expression must be a valid SymPy expression') + return main_integrate3d(expr, facets, vertices, hp_params) + + if max_degree is not None: + result = {} + if expr is not None: + f_expr = [] + for e in expr: + _ = decompose(e) + if len(_) == 1 and not _.popitem()[0]: + f_expr.append(e) + elif Poly(e).total_degree() <= max_degree: + f_expr.append(e) + expr = f_expr + + if not isinstance(expr, list) and expr is not None: + raise TypeError('Input polynomials must be list of expressions') + + if len(hp_params[0][0]) == 3: + result_dict = main_integrate3d(0, facets, vertices, hp_params, + max_degree) + else: + result_dict = main_integrate(0, facets, hp_params, max_degree) + + if expr is None: + return result_dict + + for poly in expr: + poly = _sympify(poly) + if poly not in result: + if poly.is_zero: + result[S.Zero] = S.Zero + continue + integral_value = S.Zero + monoms = decompose(poly, separate=True) + for monom in monoms: + monom = nsimplify(monom) + coeff, m = strip(monom) + integral_value += result_dict[m] * coeff + result[poly] = integral_value + return result + + if expr is None: + raise TypeError('Input expression must be a valid SymPy expression') + + return main_integrate(expr, facets, hp_params) + + +def strip(monom): + if monom.is_zero: + return S.Zero, S.Zero + elif monom.is_number: + return monom, S.One + else: + coeff = LC(monom) + return coeff, monom / coeff + +def _polynomial_integrate(polynomials, facets, hp_params): + dims = (x, y) + dim_length = len(dims) + integral_value = S.Zero + for deg in polynomials: + poly_contribute = S.Zero + facet_count = 0 + for hp in hp_params: + value_over_boundary = integration_reduction(facets, + facet_count, + hp[0], hp[1], + polynomials[deg], + dims, deg) + poly_contribute += value_over_boundary * (hp[1] / norm(hp[0])) + facet_count += 1 + poly_contribute /= (dim_length + deg) + integral_value += poly_contribute + + return integral_value + + +def main_integrate3d(expr, facets, vertices, hp_params, max_degree=None): + """Function to translate the problem of integrating uni/bi/tri-variate + polynomials over a 3-Polytope to integrating over its faces. + This is done using Generalized Stokes' Theorem and Euler's Theorem. + + Parameters + ========== + + expr : + The input polynomial. + facets : + Faces of the 3-Polytope(expressed as indices of `vertices`). + vertices : + Vertices that constitute the Polytope. + hp_params : + Hyperplane Parameters of the facets. + max_degree : optional + Max degree of constituent monomial in given list of polynomial. + + Examples + ======== + + >>> from sympy.integrals.intpoly import main_integrate3d, \ + hyperplane_parameters + >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\ + (5, 0, 5), (5, 5, 0), (5, 5, 5)],\ + [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\ + [3, 1, 0, 2], [0, 4, 6, 2]] + >>> vertices = cube[0] + >>> faces = cube[1:] + >>> hp_params = hyperplane_parameters(faces, vertices) + >>> main_integrate3d(1, faces, vertices, hp_params) + -125 + """ + result = {} + dims = (x, y, z) + dim_length = len(dims) + if max_degree: + grad_terms = gradient_terms(max_degree, 3) + flat_list = [term for z_terms in grad_terms + for x_term in z_terms + for term in x_term] + + for term in flat_list: + result[term[0]] = 0 + + for facet_count, hp in enumerate(hp_params): + a, b = hp[0], hp[1] + x0 = vertices[facets[facet_count][0]] + + for i, monom in enumerate(flat_list): + # Every monomial is a tuple : + # (term, x_degree, y_degree, z_degree, value over boundary) + expr, x_d, y_d, z_d, z_index, y_index, x_index, _ = monom + degree = x_d + y_d + z_d + if b.is_zero: + value_over_face = S.Zero + else: + value_over_face = \ + integration_reduction_dynamic(facets, facet_count, a, + b, expr, degree, dims, + x_index, y_index, + z_index, x0, grad_terms, + i, vertices, hp) + monom[7] = value_over_face + result[expr] += value_over_face * \ + (b / norm(a)) / (dim_length + x_d + y_d + z_d) + return result + else: + integral_value = S.Zero + polynomials = decompose(expr) + for deg in polynomials: + poly_contribute = S.Zero + facet_count = 0 + for i, facet in enumerate(facets): + hp = hp_params[i] + if hp[1].is_zero: + continue + pi = polygon_integrate(facet, hp, i, facets, vertices, expr, deg) + poly_contribute += pi *\ + (hp[1] / norm(tuple(hp[0]))) + facet_count += 1 + poly_contribute /= (dim_length + deg) + integral_value += poly_contribute + return integral_value + + +def main_integrate(expr, facets, hp_params, max_degree=None): + """Function to translate the problem of integrating univariate/bivariate + polynomials over a 2-Polytope to integrating over its boundary facets. + This is done using Generalized Stokes's Theorem and Euler's Theorem. + + Parameters + ========== + + expr : + The input polynomial. + facets : + Facets(Line Segments) of the 2-Polytope. + hp_params : + Hyperplane Parameters of the facets. + max_degree : optional + The maximum degree of any monomial of the input polynomial. + + >>> from sympy.abc import x, y + >>> from sympy.integrals.intpoly import main_integrate,\ + hyperplane_parameters + >>> from sympy import Point, Polygon + >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1)) + >>> facets = triangle.sides + >>> hp_params = hyperplane_parameters(triangle) + >>> main_integrate(x**2 + y**2, facets, hp_params) + 325/6 + """ + dims = (x, y) + dim_length = len(dims) + result = {} + + if max_degree: + grad_terms = [[0, 0, 0, 0]] + gradient_terms(max_degree) + + for facet_count, hp in enumerate(hp_params): + a, b = hp[0], hp[1] + x0 = facets[facet_count].points[0] + + for i, monom in enumerate(grad_terms): + # Every monomial is a tuple : + # (term, x_degree, y_degree, value over boundary) + m, x_d, y_d, _ = monom + value = result.get(m, None) + degree = S.Zero + if b.is_zero: + value_over_boundary = S.Zero + else: + degree = x_d + y_d + value_over_boundary = \ + integration_reduction_dynamic(facets, facet_count, a, + b, m, degree, dims, x_d, + y_d, max_degree, x0, + grad_terms, i) + monom[3] = value_over_boundary + if value is not None: + result[m] += value_over_boundary * \ + (b / norm(a)) / (dim_length + degree) + else: + result[m] = value_over_boundary * \ + (b / norm(a)) / (dim_length + degree) + return result + else: + if not isinstance(expr, list): + polynomials = decompose(expr) + return _polynomial_integrate(polynomials, facets, hp_params) + else: + return {e: _polynomial_integrate(decompose(e), facets, hp_params) for e in expr} + + +def polygon_integrate(facet, hp_param, index, facets, vertices, expr, degree): + """Helper function to integrate the input uni/bi/trivariate polynomial + over a certain face of the 3-Polytope. + + Parameters + ========== + + facet : + Particular face of the 3-Polytope over which ``expr`` is integrated. + index : + The index of ``facet`` in ``facets``. + facets : + Faces of the 3-Polytope(expressed as indices of `vertices`). + vertices : + Vertices that constitute the facet. + expr : + The input polynomial. + degree : + Degree of ``expr``. + + Examples + ======== + + >>> from sympy.integrals.intpoly import polygon_integrate + >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\ + (5, 0, 5), (5, 5, 0), (5, 5, 5)],\ + [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\ + [3, 1, 0, 2], [0, 4, 6, 2]] + >>> facet = cube[1] + >>> facets = cube[1:] + >>> vertices = cube[0] + >>> polygon_integrate(facet, [(0, 1, 0), 5], 0, facets, vertices, 1, 0) + -25 + """ + expr = S(expr) + if expr.is_zero: + return S.Zero + result = S.Zero + x0 = vertices[facet[0]] + facet_len = len(facet) + for i, fac in enumerate(facet): + side = (vertices[fac], vertices[facet[(i + 1) % facet_len]]) + result += distance_to_side(x0, side, hp_param[0]) *\ + lineseg_integrate(facet, i, side, expr, degree) + if not expr.is_number: + expr = diff(expr, x) * x0[0] + diff(expr, y) * x0[1] +\ + diff(expr, z) * x0[2] + result += polygon_integrate(facet, hp_param, index, facets, vertices, + expr, degree - 1) + result /= (degree + 2) + return result + + +def distance_to_side(point, line_seg, A): + """Helper function to compute the signed distance between given 3D point + and a line segment. + + Parameters + ========== + + point : 3D Point + line_seg : Line Segment + + Examples + ======== + + >>> from sympy.integrals.intpoly import distance_to_side + >>> point = (0, 0, 0) + >>> distance_to_side(point, [(0, 0, 1), (0, 1, 0)], (1, 0, 0)) + -sqrt(2)/2 + """ + x1, x2 = line_seg + rev_normal = [-1 * S(i)/norm(A) for i in A] + vector = [x2[i] - x1[i] for i in range(0, 3)] + vector = [vector[i]/norm(vector) for i in range(0, 3)] + + n_side = cross_product((0, 0, 0), rev_normal, vector) + vectorx0 = [line_seg[0][i] - point[i] for i in range(0, 3)] + dot_product = sum(vectorx0[i] * n_side[i] for i in range(0, 3)) + + return dot_product + + +def lineseg_integrate(polygon, index, line_seg, expr, degree): + """Helper function to compute the line integral of ``expr`` over ``line_seg``. + + Parameters + =========== + + polygon : + Face of a 3-Polytope. + index : + Index of line_seg in polygon. + line_seg : + Line Segment. + + Examples + ======== + + >>> from sympy.integrals.intpoly import lineseg_integrate + >>> polygon = [(0, 5, 0), (5, 5, 0), (5, 5, 5), (0, 5, 5)] + >>> line_seg = [(0, 5, 0), (5, 5, 0)] + >>> lineseg_integrate(polygon, 0, line_seg, 1, 0) + 5 + """ + expr = _sympify(expr) + if expr.is_zero: + return S.Zero + result = S.Zero + x0 = line_seg[0] + distance = norm(tuple([line_seg[1][i] - line_seg[0][i] for i in + range(3)])) + if isinstance(expr, Expr): + expr_dict = {x: line_seg[1][0], + y: line_seg[1][1], + z: line_seg[1][2]} + result += distance * expr.subs(expr_dict) + else: + result += distance * expr + + expr = diff(expr, x) * x0[0] + diff(expr, y) * x0[1] +\ + diff(expr, z) * x0[2] + + result += lineseg_integrate(polygon, index, line_seg, expr, degree - 1) + result /= (degree + 1) + return result + + +def integration_reduction(facets, index, a, b, expr, dims, degree): + """Helper method for main_integrate. Returns the value of the input + expression evaluated over the polytope facet referenced by a given index. + + Parameters + =========== + + facets : + List of facets of the polytope. + index : + Index referencing the facet to integrate the expression over. + a : + Hyperplane parameter denoting direction. + b : + Hyperplane parameter denoting distance. + expr : + The expression to integrate over the facet. + dims : + List of symbols denoting axes. + degree : + Degree of the homogeneous polynomial. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.integrals.intpoly import integration_reduction,\ + hyperplane_parameters + >>> from sympy import Point, Polygon + >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1)) + >>> facets = triangle.sides + >>> a, b = hyperplane_parameters(triangle)[0] + >>> integration_reduction(facets, 0, a, b, 1, (x, y), 0) + 5 + """ + expr = _sympify(expr) + if expr.is_zero: + return expr + + value = S.Zero + x0 = facets[index].points[0] + m = len(facets) + gens = (x, y) + + inner_product = diff(expr, gens[0]) * x0[0] + diff(expr, gens[1]) * x0[1] + + if inner_product != 0: + value += integration_reduction(facets, index, a, b, + inner_product, dims, degree - 1) + + value += left_integral2D(m, index, facets, x0, expr, gens) + + return value/(len(dims) + degree - 1) + + +def left_integral2D(m, index, facets, x0, expr, gens): + """Computes the left integral of Eq 10 in Chin et al. + For the 2D case, the integral is just an evaluation of the polynomial + at the intersection of two facets which is multiplied by the distance + between the first point of facet and that intersection. + + Parameters + ========== + + m : + No. of hyperplanes. + index : + Index of facet to find intersections with. + facets : + List of facets(Line Segments in 2D case). + x0 : + First point on facet referenced by index. + expr : + Input polynomial + gens : + Generators which generate the polynomial + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.integrals.intpoly import left_integral2D + >>> from sympy import Point, Polygon + >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1)) + >>> facets = triangle.sides + >>> left_integral2D(3, 0, facets, facets[0].points[0], 1, (x, y)) + 5 + """ + value = S.Zero + for j in range(m): + intersect = () + if j in ((index - 1) % m, (index + 1) % m): + intersect = intersection(facets[index], facets[j], "segment2D") + if intersect: + distance_origin = norm(tuple(map(lambda x, y: x - y, + intersect, x0))) + if is_vertex(intersect): + if isinstance(expr, Expr): + if len(gens) == 3: + expr_dict = {gens[0]: intersect[0], + gens[1]: intersect[1], + gens[2]: intersect[2]} + else: + expr_dict = {gens[0]: intersect[0], + gens[1]: intersect[1]} + value += distance_origin * expr.subs(expr_dict) + else: + value += distance_origin * expr + return value + + +def integration_reduction_dynamic(facets, index, a, b, expr, degree, dims, + x_index, y_index, max_index, x0, + monomial_values, monom_index, vertices=None, + hp_param=None): + """The same integration_reduction function which uses a dynamic + programming approach to compute terms by using the values of the integral + of previously computed terms. + + Parameters + ========== + + facets : + Facets of the Polytope. + index : + Index of facet to find intersections with.(Used in left_integral()). + a, b : + Hyperplane parameters. + expr : + Input monomial. + degree : + Total degree of ``expr``. + dims : + Tuple denoting axes variables. + x_index : + Exponent of 'x' in ``expr``. + y_index : + Exponent of 'y' in ``expr``. + max_index : + Maximum exponent of any monomial in ``monomial_values``. + x0 : + First point on ``facets[index]``. + monomial_values : + List of monomial values constituting the polynomial. + monom_index : + Index of monomial whose integration is being found. + vertices : optional + Coordinates of vertices constituting the 3-Polytope. + hp_param : optional + Hyperplane Parameter of the face of the facets[index]. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.integrals.intpoly import (integration_reduction_dynamic, \ + hyperplane_parameters) + >>> from sympy import Point, Polygon + >>> triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1)) + >>> facets = triangle.sides + >>> a, b = hyperplane_parameters(triangle)[0] + >>> x0 = facets[0].points[0] + >>> monomial_values = [[0, 0, 0, 0], [1, 0, 0, 5],\ + [y, 0, 1, 15], [x, 1, 0, None]] + >>> integration_reduction_dynamic(facets, 0, a, b, x, 1, (x, y), 1, 0, 1,\ + x0, monomial_values, 3) + 25/2 + """ + value = S.Zero + m = len(facets) + + if expr == S.Zero: + return expr + + if len(dims) == 2: + if not expr.is_number: + _, x_degree, y_degree, _ = monomial_values[monom_index] + x_index = monom_index - max_index + \ + x_index - 2 if x_degree > 0 else 0 + y_index = monom_index - 1 if y_degree > 0 else 0 + x_value, y_value =\ + monomial_values[x_index][3], monomial_values[y_index][3] + + value += x_degree * x_value * x0[0] + y_degree * y_value * x0[1] + + value += left_integral2D(m, index, facets, x0, expr, dims) + else: + # For 3D use case the max_index contains the z_degree of the term + z_index = max_index + if not expr.is_number: + x_degree, y_degree, z_degree = y_index,\ + z_index - x_index - y_index, x_index + x_value = monomial_values[z_index - 1][y_index - 1][x_index][7]\ + if x_degree > 0 else 0 + y_value = monomial_values[z_index - 1][y_index][x_index][7]\ + if y_degree > 0 else 0 + z_value = monomial_values[z_index - 1][y_index][x_index - 1][7]\ + if z_degree > 0 else 0 + + value += x_degree * x_value * x0[0] + y_degree * y_value * x0[1] \ + + z_degree * z_value * x0[2] + + value += left_integral3D(facets, index, expr, + vertices, hp_param, degree) + return value / (len(dims) + degree - 1) + + +def left_integral3D(facets, index, expr, vertices, hp_param, degree): + """Computes the left integral of Eq 10 in Chin et al. + + Explanation + =========== + + For the 3D case, this is the sum of the integral values over constituting + line segments of the face (which is accessed by facets[index]) multiplied + by the distance between the first point of facet and that line segment. + + Parameters + ========== + + facets : + List of faces of the 3-Polytope. + index : + Index of face over which integral is to be calculated. + expr : + Input polynomial. + vertices : + List of vertices that constitute the 3-Polytope. + hp_param : + The hyperplane parameters of the face. + degree : + Degree of the ``expr``. + + Examples + ======== + + >>> from sympy.integrals.intpoly import left_integral3D + >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\ + (5, 0, 5), (5, 5, 0), (5, 5, 5)],\ + [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\ + [3, 1, 0, 2], [0, 4, 6, 2]] + >>> facets = cube[1:] + >>> vertices = cube[0] + >>> left_integral3D(facets, 3, 1, vertices, ([0, -1, 0], -5), 0) + -50 + """ + value = S.Zero + facet = facets[index] + x0 = vertices[facet[0]] + facet_len = len(facet) + for i, fac in enumerate(facet): + side = (vertices[fac], vertices[facet[(i + 1) % facet_len]]) + value += distance_to_side(x0, side, hp_param[0]) * \ + lineseg_integrate(facet, i, side, expr, degree) + return value + + +def gradient_terms(binomial_power=0, no_of_gens=2): + """Returns a list of all the possible monomials between + 0 and y**binomial_power for 2D case and z**binomial_power + for 3D case. + + Parameters + ========== + + binomial_power : + Power upto which terms are generated. + no_of_gens : + Denotes whether terms are being generated for 2D or 3D case. + + Examples + ======== + + >>> from sympy.integrals.intpoly import gradient_terms + >>> gradient_terms(2) + [[1, 0, 0, 0], [y, 0, 1, 0], [y**2, 0, 2, 0], [x, 1, 0, 0], + [x*y, 1, 1, 0], [x**2, 2, 0, 0]] + >>> gradient_terms(2, 3) + [[[[1, 0, 0, 0, 0, 0, 0, 0]]], [[[y, 0, 1, 0, 1, 0, 0, 0], + [z, 0, 0, 1, 1, 0, 1, 0]], [[x, 1, 0, 0, 1, 1, 0, 0]]], + [[[y**2, 0, 2, 0, 2, 0, 0, 0], [y*z, 0, 1, 1, 2, 0, 1, 0], + [z**2, 0, 0, 2, 2, 0, 2, 0]], [[x*y, 1, 1, 0, 2, 1, 0, 0], + [x*z, 1, 0, 1, 2, 1, 1, 0]], [[x**2, 2, 0, 0, 2, 2, 0, 0]]]] + """ + if no_of_gens == 2: + count = 0 + terms = [None] * int((binomial_power ** 2 + 3 * binomial_power + 2) / 2) + for x_count in range(0, binomial_power + 1): + for y_count in range(0, binomial_power - x_count + 1): + terms[count] = [x**x_count*y**y_count, + x_count, y_count, 0] + count += 1 + else: + terms = [[[[x ** x_count * y ** y_count * + z ** (z_count - y_count - x_count), + x_count, y_count, z_count - y_count - x_count, + z_count, x_count, z_count - y_count - x_count, 0] + for y_count in range(z_count - x_count, -1, -1)] + for x_count in range(0, z_count + 1)] + for z_count in range(0, binomial_power + 1)] + return terms + + +def hyperplane_parameters(poly, vertices=None): + """A helper function to return the hyperplane parameters + of which the facets of the polytope are a part of. + + Parameters + ========== + + poly : + The input 2/3-Polytope. + vertices : + Vertex indices of 3-Polytope. + + Examples + ======== + + >>> from sympy import Point, Polygon + >>> from sympy.integrals.intpoly import hyperplane_parameters + >>> hyperplane_parameters(Polygon(Point(0, 3), Point(5, 3), Point(1, 1))) + [((0, 1), 3), ((1, -2), -1), ((-2, -1), -3)] + >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\ + (5, 0, 5), (5, 5, 0), (5, 5, 5)],\ + [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\ + [3, 1, 0, 2], [0, 4, 6, 2]] + >>> hyperplane_parameters(cube[1:], cube[0]) + [([0, -1, 0], -5), ([0, 0, -1], -5), ([-1, 0, 0], -5), + ([0, 1, 0], 0), ([1, 0, 0], 0), ([0, 0, 1], 0)] + """ + if isinstance(poly, Polygon): + vertices = list(poly.vertices) + [poly.vertices[0]] # Close the polygon + params = [None] * (len(vertices) - 1) + + for i in range(len(vertices) - 1): + v1 = vertices[i] + v2 = vertices[i + 1] + + a1 = v1[1] - v2[1] + a2 = v2[0] - v1[0] + b = v2[0] * v1[1] - v2[1] * v1[0] + + factor = gcd_list([a1, a2, b]) + + b = S(b) / factor + a = (S(a1) / factor, S(a2) / factor) + params[i] = (a, b) + else: + params = [None] * len(poly) + for i, polygon in enumerate(poly): + v1, v2, v3 = [vertices[vertex] for vertex in polygon[:3]] + normal = cross_product(v1, v2, v3) + b = sum(normal[j] * v1[j] for j in range(0, 3)) + fac = gcd_list(normal) + if fac.is_zero: + fac = 1 + normal = [j / fac for j in normal] + b = b / fac + params[i] = (normal, b) + return params + + +def cross_product(v1, v2, v3): + """Returns the cross-product of vectors (v2 - v1) and (v3 - v1) + That is : (v2 - v1) X (v3 - v1) + """ + v2 = [v2[j] - v1[j] for j in range(0, 3)] + v3 = [v3[j] - v1[j] for j in range(0, 3)] + return [v3[2] * v2[1] - v3[1] * v2[2], + v3[0] * v2[2] - v3[2] * v2[0], + v3[1] * v2[0] - v3[0] * v2[1]] + + +def best_origin(a, b, lineseg, expr): + """Helper method for polytope_integrate. Currently not used in the main + algorithm. + + Explanation + =========== + + Returns a point on the lineseg whose vector inner product with the + divergence of `expr` yields an expression with the least maximum + total power. + + Parameters + ========== + + a : + Hyperplane parameter denoting direction. + b : + Hyperplane parameter denoting distance. + lineseg : + Line segment on which to find the origin. + expr : + The expression which determines the best point. + + Algorithm(currently works only for 2D use case) + =============================================== + + 1 > Firstly, check for edge cases. Here that would refer to vertical + or horizontal lines. + + 2 > If input expression is a polynomial containing more than one generator + then find out the total power of each of the generators. + + x**2 + 3 + x*y + x**4*y**5 ---> {x: 7, y: 6} + + If expression is a constant value then pick the first boundary point + of the line segment. + + 3 > First check if a point exists on the line segment where the value of + the highest power generator becomes 0. If not check if the value of + the next highest becomes 0. If none becomes 0 within line segment + constraints then pick the first boundary point of the line segment. + Actually, any point lying on the segment can be picked as best origin + in the last case. + + Examples + ======== + + >>> from sympy.integrals.intpoly import best_origin + >>> from sympy.abc import x, y + >>> from sympy import Point, Segment2D + >>> l = Segment2D(Point(0, 3), Point(1, 1)) + >>> expr = x**3*y**7 + >>> best_origin((2, 1), 3, l, expr) + (0, 3.0) + """ + a1, b1 = lineseg.points[0] + + def x_axis_cut(ls): + """Returns the point where the input line segment + intersects the x-axis. + + Parameters + ========== + + ls : + Line segment + """ + p, q = ls.points + if p.y.is_zero: + return tuple(p) + elif q.y.is_zero: + return tuple(q) + elif p.y/q.y < S.Zero: + return p.y * (p.x - q.x)/(q.y - p.y) + p.x, S.Zero + else: + return () + + def y_axis_cut(ls): + """Returns the point where the input line segment + intersects the y-axis. + + Parameters + ========== + + ls : + Line segment + """ + p, q = ls.points + if p.x.is_zero: + return tuple(p) + elif q.x.is_zero: + return tuple(q) + elif p.x/q.x < S.Zero: + return S.Zero, p.x * (p.y - q.y)/(q.x - p.x) + p.y + else: + return () + + gens = (x, y) + power_gens = {} + + for i in gens: + power_gens[i] = S.Zero + + if len(gens) > 1: + # Special case for vertical and horizontal lines + if len(gens) == 2: + if a[0] == 0: + if y_axis_cut(lineseg): + return S.Zero, b/a[1] + else: + return a1, b1 + elif a[1] == 0: + if x_axis_cut(lineseg): + return b/a[0], S.Zero + else: + return a1, b1 + + if isinstance(expr, Expr): # Find the sum total of power of each + if expr.is_Add: # generator and store in a dictionary. + for monomial in expr.args: + if monomial.is_Pow: + if monomial.args[0] in gens: + power_gens[monomial.args[0]] += monomial.args[1] + else: + for univariate in monomial.args: + term_type = len(univariate.args) + if term_type == 0 and univariate in gens: + power_gens[univariate] += 1 + elif term_type == 2 and univariate.args[0] in gens: + power_gens[univariate.args[0]] +=\ + univariate.args[1] + elif expr.is_Mul: + for term in expr.args: + term_type = len(term.args) + if term_type == 0 and term in gens: + power_gens[term] += 1 + elif term_type == 2 and term.args[0] in gens: + power_gens[term.args[0]] += term.args[1] + elif expr.is_Pow: + power_gens[expr.args[0]] = expr.args[1] + elif expr.is_Symbol: + power_gens[expr] += 1 + else: # If `expr` is a constant take first vertex of the line segment. + return a1, b1 + + # TODO : This part is quite hacky. Should be made more robust with + # TODO : respect to symbol names and scalable w.r.t higher dimensions. + power_gens = sorted(power_gens.items(), key=lambda k: str(k[0])) + if power_gens[0][1] >= power_gens[1][1]: + if y_axis_cut(lineseg): + x0 = (S.Zero, b / a[1]) + elif x_axis_cut(lineseg): + x0 = (b / a[0], S.Zero) + else: + x0 = (a1, b1) + else: + if x_axis_cut(lineseg): + x0 = (b/a[0], S.Zero) + elif y_axis_cut(lineseg): + x0 = (S.Zero, b/a[1]) + else: + x0 = (a1, b1) + else: + x0 = (b/a[0]) + return x0 + + +def decompose(expr, separate=False): + """Decomposes an input polynomial into homogeneous ones of + smaller or equal degree. + + Explanation + =========== + + Returns a dictionary with keys as the degree of the smaller + constituting polynomials. Values are the constituting polynomials. + + Parameters + ========== + + expr : Expr + Polynomial(SymPy expression). + separate : bool + If True then simply return a list of the constituent monomials + If not then break up the polynomial into constituent homogeneous + polynomials. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.integrals.intpoly import decompose + >>> decompose(x**2 + x*y + x + y + x**3*y**2 + y**5) + {1: x + y, 2: x**2 + x*y, 5: x**3*y**2 + y**5} + >>> decompose(x**2 + x*y + x + y + x**3*y**2 + y**5, True) + {x, x**2, y, y**5, x*y, x**3*y**2} + """ + poly_dict = {} + + if isinstance(expr, Expr) and not expr.is_number: + if expr.is_Symbol: + poly_dict[1] = expr + elif expr.is_Add: + symbols = expr.atoms(Symbol) + degrees = [(sum(degree_list(monom, *symbols)), monom) + for monom in expr.args] + if separate: + return {monom[1] for monom in degrees} + else: + for monom in degrees: + degree, term = monom + if poly_dict.get(degree): + poly_dict[degree] += term + else: + poly_dict[degree] = term + elif expr.is_Pow: + _, degree = expr.args + poly_dict[degree] = expr + else: # Now expr can only be of `Mul` type + degree = 0 + for term in expr.args: + term_type = len(term.args) + if term_type == 0 and term.is_Symbol: + degree += 1 + elif term_type == 2: + degree += term.args[1] + poly_dict[degree] = expr + else: + poly_dict[0] = expr + + if separate: + return set(poly_dict.values()) + return poly_dict + + +def point_sort(poly, normal=None, clockwise=True): + """Returns the same polygon with points sorted in clockwise or + anti-clockwise order. + + Note that it's necessary for input points to be sorted in some order + (clockwise or anti-clockwise) for the integration algorithm to work. + As a convention algorithm has been implemented keeping clockwise + orientation in mind. + + Parameters + ========== + + poly: + 2D or 3D Polygon. + normal : optional + The normal of the plane which the 3-Polytope is a part of. + clockwise : bool, optional + Returns points sorted in clockwise order if True and + anti-clockwise if False. + + Examples + ======== + + >>> from sympy.integrals.intpoly import point_sort + >>> from sympy import Point + >>> point_sort([Point(0, 0), Point(1, 0), Point(1, 1)]) + [Point2D(1, 1), Point2D(1, 0), Point2D(0, 0)] + """ + pts = poly.vertices if isinstance(poly, Polygon) else poly + n = len(pts) + if n < 2: + return list(pts) + + order = S.One if clockwise else S.NegativeOne + dim = len(pts[0]) + if dim == 2: + center = Point(sum((vertex.x for vertex in pts)) / n, + sum((vertex.y for vertex in pts)) / n) + else: + center = Point(sum((vertex.x for vertex in pts)) / n, + sum((vertex.y for vertex in pts)) / n, + sum((vertex.z for vertex in pts)) / n) + + def compare(a, b): + if a.x - center.x >= S.Zero and b.x - center.x < S.Zero: + return -order + elif a.x - center.x < 0 and b.x - center.x >= 0: + return order + elif a.x - center.x == 0 and b.x - center.x == 0: + if a.y - center.y >= 0 or b.y - center.y >= 0: + return -order if a.y > b.y else order + return -order if b.y > a.y else order + + det = (a.x - center.x) * (b.y - center.y) -\ + (b.x - center.x) * (a.y - center.y) + if det < 0: + return -order + elif det > 0: + return order + + first = (a.x - center.x) * (a.x - center.x) +\ + (a.y - center.y) * (a.y - center.y) + second = (b.x - center.x) * (b.x - center.x) +\ + (b.y - center.y) * (b.y - center.y) + return -order if first > second else order + + def compare3d(a, b): + det = cross_product(center, a, b) + dot_product = sum(det[i] * normal[i] for i in range(0, 3)) + if dot_product < 0: + return -order + elif dot_product > 0: + return order + + return sorted(pts, key=cmp_to_key(compare if dim==2 else compare3d)) + + +def norm(point): + """Returns the Euclidean norm of a point from origin. + + Parameters + ========== + + point: + This denotes a point in the dimension_al spac_e. + + Examples + ======== + + >>> from sympy.integrals.intpoly import norm + >>> from sympy import Point + >>> norm(Point(2, 7)) + sqrt(53) + """ + half = S.Half + if isinstance(point, (list, tuple)): + return sum(coord ** 2 for coord in point) ** half + elif isinstance(point, Point): + if isinstance(point, Point2D): + return (point.x ** 2 + point.y ** 2) ** half + else: + return (point.x ** 2 + point.y ** 2 + point.z) ** half + elif isinstance(point, dict): + return sum(i**2 for i in point.values()) ** half + + +def intersection(geom_1, geom_2, intersection_type): + """Returns intersection between geometric objects. + + Explanation + =========== + + Note that this function is meant for use in integration_reduction and + at that point in the calling function the lines denoted by the segments + surely intersect within segment boundaries. Coincident lines are taken + to be non-intersecting. Also, the hyperplane intersection for 2D case is + also implemented. + + Parameters + ========== + + geom_1, geom_2: + The input line segments. + + Examples + ======== + + >>> from sympy.integrals.intpoly import intersection + >>> from sympy import Point, Segment2D + >>> l1 = Segment2D(Point(1, 1), Point(3, 5)) + >>> l2 = Segment2D(Point(2, 0), Point(2, 5)) + >>> intersection(l1, l2, "segment2D") + (2, 3) + >>> p1 = ((-1, 0), 0) + >>> p2 = ((0, 1), 1) + >>> intersection(p1, p2, "plane2D") + (0, 1) + """ + if intersection_type[:-2] == "segment": + if intersection_type == "segment2D": + x1, y1 = geom_1.points[0] + x2, y2 = geom_1.points[1] + x3, y3 = geom_2.points[0] + x4, y4 = geom_2.points[1] + elif intersection_type == "segment3D": + x1, y1, z1 = geom_1.points[0] + x2, y2, z2 = geom_1.points[1] + x3, y3, z3 = geom_2.points[0] + x4, y4, z4 = geom_2.points[1] + + denom = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4) + if denom: + t1 = x1 * y2 - y1 * x2 + t2 = x3 * y4 - x4 * y3 + return (S(t1 * (x3 - x4) - t2 * (x1 - x2)) / denom, + S(t1 * (y3 - y4) - t2 * (y1 - y2)) / denom) + if intersection_type[:-2] == "plane": + if intersection_type == "plane2D": # Intersection of hyperplanes + a1x, a1y = geom_1[0] + a2x, a2y = geom_2[0] + b1, b2 = geom_1[1], geom_2[1] + + denom = a1x * a2y - a2x * a1y + if denom: + return (S(b1 * a2y - b2 * a1y) / denom, + S(b2 * a1x - b1 * a2x) / denom) + + +def is_vertex(ent): + """If the input entity is a vertex return True. + + Parameter + ========= + + ent : + Denotes a geometric entity representing a point. + + Examples + ======== + + >>> from sympy import Point + >>> from sympy.integrals.intpoly import is_vertex + >>> is_vertex((2, 3)) + True + >>> is_vertex((2, 3, 6)) + True + >>> is_vertex(Point(2, 3)) + True + """ + if isinstance(ent, tuple): + if len(ent) in [2, 3]: + return True + elif isinstance(ent, Point): + return True + return False + + +def plot_polytope(poly): + """Plots the 2D polytope using the functions written in plotting + module which in turn uses matplotlib backend. + + Parameter + ========= + + poly: + Denotes a 2-Polytope. + """ + from sympy.plotting.plot import Plot, List2DSeries + + xl = [vertex.x for vertex in poly.vertices] + yl = [vertex.y for vertex in poly.vertices] + + xl.append(poly.vertices[0].x) # Closing the polygon + yl.append(poly.vertices[0].y) + + l2ds = List2DSeries(xl, yl) + p = Plot(l2ds, axes='label_axes=True') + p.show() + + +def plot_polynomial(expr): + """Plots the polynomial using the functions written in + plotting module which in turn uses matplotlib backend. + + Parameter + ========= + + expr: + Denotes a polynomial(SymPy expression). + """ + from sympy.plotting.plot import plot3d, plot + gens = expr.free_symbols + if len(gens) == 2: + plot3d(expr) + else: + plot(expr) diff --git a/lib/python3.11/site-packages/sympy/integrals/laplace.py b/lib/python3.11/site-packages/sympy/integrals/laplace.py new file mode 100644 index 0000000000000000000000000000000000000000..3c3ddfce3367e98a0b5c121dd8a7b1faf662735f --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/laplace.py @@ -0,0 +1,2373 @@ +"""Laplace Transforms""" +import sys +import sympy +from sympy.core import S, pi, I +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.expr import Expr +from sympy.core.function import ( + AppliedUndef, Derivative, expand, expand_complex, expand_mul, expand_trig, + Lambda, WildFunction, diff, Subs) +from sympy.core.mul import Mul, prod +from sympy.core.relational import ( + _canonical, Ge, Gt, Lt, Unequality, Eq, Ne, Relational) +from sympy.core.sorting import ordered +from sympy.core.symbol import Dummy, symbols, Wild +from sympy.functions.elementary.complexes import ( + re, im, arg, Abs, polar_lift, periodic_argument) +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.hyperbolic import cosh, coth, sinh, asinh +from sympy.functions.elementary.miscellaneous import Max, Min, sqrt +from sympy.functions.elementary.piecewise import ( + Piecewise, piecewise_exclusive) +from sympy.functions.elementary.trigonometric import cos, sin, atan, sinc +from sympy.functions.special.bessel import besseli, besselj, besselk, bessely +from sympy.functions.special.delta_functions import DiracDelta, Heaviside +from sympy.functions.special.error_functions import erf, erfc, Ei +from sympy.functions.special.gamma_functions import ( + digamma, gamma, lowergamma, uppergamma) +from sympy.functions.special.singularity_functions import SingularityFunction +from sympy.integrals import integrate, Integral +from sympy.integrals.transforms import ( + _simplify, IntegralTransform, IntegralTransformError) +from sympy.logic.boolalg import to_cnf, conjuncts, disjuncts, Or, And +from sympy.matrices.matrixbase import MatrixBase +from sympy.polys.matrices.linsolve import _lin_eq2dict +from sympy.polys.polyerrors import PolynomialError +from sympy.polys.polyroots import roots +from sympy.polys.polytools import Poly +from sympy.polys.rationaltools import together +from sympy.polys.rootoftools import RootSum +from sympy.utilities.exceptions import ( + sympy_deprecation_warning, SymPyDeprecationWarning, ignore_warnings) +from sympy.utilities.misc import debugf + +_LT_level = 0 + + +def DEBUG_WRAP(func): + def wrap(*args, **kwargs): + from sympy import SYMPY_DEBUG + global _LT_level + + if not SYMPY_DEBUG: + return func(*args, **kwargs) + + if _LT_level == 0: + print('\n' + '-'*78, file=sys.stderr) + print('-LT- %s%s%s' % (' '*_LT_level, func.__name__, args), + file=sys.stderr) + _LT_level += 1 + if ( + func.__name__ == '_laplace_transform_integration' or + func.__name__ == '_inverse_laplace_transform_integration'): + sympy.SYMPY_DEBUG = False + print('**** %sIntegrating ...' % (' '*_LT_level), file=sys.stderr) + result = func(*args, **kwargs) + sympy.SYMPY_DEBUG = True + else: + result = func(*args, **kwargs) + _LT_level -= 1 + print('-LT- %s---> %s' % (' '*_LT_level, result), file=sys.stderr) + if _LT_level == 0: + print('-'*78 + '\n', file=sys.stderr) + return result + return wrap + + +def _debug(text): + from sympy import SYMPY_DEBUG + global _LT_level + + if SYMPY_DEBUG: + print('-LT- %s%s' % (' '*_LT_level, text), file=sys.stderr) + + +def _simplifyconds(expr, s, a): + r""" + Naively simplify some conditions occurring in ``expr``, + given that `\operatorname{Re}(s) > a`. + + Examples + ======== + + >>> from sympy.integrals.laplace import _simplifyconds + >>> from sympy.abc import x + >>> from sympy import sympify as S + >>> _simplifyconds(abs(x**2) < 1, x, 1) + False + >>> _simplifyconds(abs(x**2) < 1, x, 2) + False + >>> _simplifyconds(abs(x**2) < 1, x, 0) + Abs(x**2) < 1 + >>> _simplifyconds(abs(1/x**2) < 1, x, 1) + True + >>> _simplifyconds(S(1) < abs(x), x, 1) + True + >>> _simplifyconds(S(1) < abs(1/x), x, 1) + False + + >>> from sympy import Ne + >>> _simplifyconds(Ne(1, x**3), x, 1) + True + >>> _simplifyconds(Ne(1, x**3), x, 2) + True + >>> _simplifyconds(Ne(1, x**3), x, 0) + Ne(1, x**3) + """ + + def power(ex): + if ex == s: + return 1 + if ex.is_Pow and ex.base == s: + return ex.exp + return None + + def bigger(ex1, ex2): + """ Return True only if |ex1| > |ex2|, False only if |ex1| < |ex2|. + Else return None. """ + if ex1.has(s) and ex2.has(s): + return None + if isinstance(ex1, Abs): + ex1 = ex1.args[0] + if isinstance(ex2, Abs): + ex2 = ex2.args[0] + if ex1.has(s): + return bigger(1/ex2, 1/ex1) + n = power(ex2) + if n is None: + return None + try: + if n > 0 and (Abs(ex1) <= Abs(a)**n) == S.true: + return False + if n < 0 and (Abs(ex1) >= Abs(a)**n) == S.true: + return True + except TypeError: + return None + + def replie(x, y): + """ simplify x < y """ + if (not (x.is_positive or isinstance(x, Abs)) + or not (y.is_positive or isinstance(y, Abs))): + return (x < y) + r = bigger(x, y) + if r is not None: + return not r + return (x < y) + + def replue(x, y): + b = bigger(x, y) + if b in (True, False): + return True + return Unequality(x, y) + + def repl(ex, *args): + if ex in (True, False): + return bool(ex) + return ex.replace(*args) + + from sympy.simplify.radsimp import collect_abs + expr = collect_abs(expr) + expr = repl(expr, Lt, replie) + expr = repl(expr, Gt, lambda x, y: replie(y, x)) + expr = repl(expr, Unequality, replue) + return S(expr) + + +@DEBUG_WRAP +def expand_dirac_delta(expr): + """ + Expand an expression involving DiractDelta to get it as a linear + combination of DiracDelta functions. + """ + return _lin_eq2dict(expr, expr.atoms(DiracDelta)) + + +@DEBUG_WRAP +def _laplace_transform_integration(f, t, s_, *, simplify): + """ The backend function for doing Laplace transforms by integration. + + This backend assumes that the frontend has already split sums + such that `f` is to an addition anymore. + """ + s = Dummy('s') + + if f.has(DiracDelta): + return None + + F = integrate(f*exp(-s*t), (t, S.Zero, S.Infinity)) + + if not F.has(Integral): + return _simplify(F.subs(s, s_), simplify), S.NegativeInfinity, S.true + + if not F.is_Piecewise: + return None + + F, cond = F.args[0] + if F.has(Integral): + return None + + def process_conds(conds): + """ Turn ``conds`` into a strip and auxiliary conditions. """ + from sympy.solvers.inequalities import _solve_inequality + a = S.NegativeInfinity + aux = S.true + conds = conjuncts(to_cnf(conds)) + p, q, w1, w2, w3, w4, w5 = symbols( + 'p q w1 w2 w3 w4 w5', cls=Wild, exclude=[s]) + patterns = ( + p*Abs(arg((s + w3)*q)) < w2, + p*Abs(arg((s + w3)*q)) <= w2, + Abs(periodic_argument((s + w3)**p*q, w1)) < w2, + Abs(periodic_argument((s + w3)**p*q, w1)) <= w2, + Abs(periodic_argument((polar_lift(s + w3))**p*q, w1)) < w2, + Abs(periodic_argument((polar_lift(s + w3))**p*q, w1)) <= w2) + for c in conds: + a_ = S.Infinity + aux_ = [] + for d in disjuncts(c): + if d.is_Relational and s in d.rhs.free_symbols: + d = d.reversed + if d.is_Relational and isinstance(d, (Ge, Gt)): + d = d.reversedsign + for pat in patterns: + m = d.match(pat) + if m: + break + if m and m[q].is_positive and m[w2]/m[p] == pi/2: + d = -re(s + m[w3]) < 0 + m = d.match(p - cos(w1*Abs(arg(s*w5))*w2)*Abs(s**w3)**w4 < 0) + if not m: + m = d.match( + cos(p - Abs(periodic_argument(s**w1*w5, q))*w2) * + Abs(s**w3)**w4 < 0) + if not m: + m = d.match( + p - cos( + Abs(periodic_argument(polar_lift(s)**w1*w5, q))*w2 + )*Abs(s**w3)**w4 < 0) + if m and all(m[wild].is_positive for wild in [ + w1, w2, w3, w4, w5]): + d = re(s) > m[p] + d_ = d.replace( + re, lambda x: x.expand().as_real_imag()[0]).subs(re(s), t) + if ( + not d.is_Relational or d.rel_op in ('==', '!=') + or d_.has(s) or not d_.has(t)): + aux_ += [d] + continue + soln = _solve_inequality(d_, t) + if not soln.is_Relational or soln.rel_op in ('==', '!='): + aux_ += [d] + continue + if soln.lts == t: + return None + else: + a_ = Min(soln.lts, a_) + if a_ is not S.Infinity: + a = Max(a_, a) + else: + aux = And(aux, Or(*aux_)) + return a, aux.canonical if aux.is_Relational else aux + + conds = [process_conds(c) for c in disjuncts(cond)] + conds2 = [x for x in conds if x[1] != + S.false and x[0] is not S.NegativeInfinity] + if not conds2: + conds2 = [x for x in conds if x[1] != S.false] + conds = list(ordered(conds2)) + + def cnt(expr): + if expr in (True, False): + return 0 + return expr.count_ops() + conds.sort(key=lambda x: (-x[0], cnt(x[1]))) + + if not conds: + return None + a, aux = conds[0] # XXX is [0] always the right one? + + def sbs(expr): + return expr.subs(s, s_) + if simplify: + F = _simplifyconds(F, s, a) + aux = _simplifyconds(aux, s, a) + return _simplify(F.subs(s, s_), simplify), sbs(a), _canonical(sbs(aux)) + + +@DEBUG_WRAP +def _laplace_deep_collect(f, t): + """ + This is an internal helper function that traverses through the epression + tree of `f(t)` and collects arguments. The purpose of it is that + anything like `f(w*t-1*t-c)` will be written as `f((w-1)*t-c)` such that + it can match `f(a*t+b)`. + """ + if not isinstance(f, Expr): + return f + if (p := f.as_poly(t)) is not None: + return p.as_expr() + func = f.func + args = [_laplace_deep_collect(arg, t) for arg in f.args] + return func(*args) + + +@cacheit +def _laplace_build_rules(): + """ + This is an internal helper function that returns the table of Laplace + transform rules in terms of the time variable `t` and the frequency + variable `s`. It is used by ``_laplace_apply_rules``. Each entry is a + tuple containing: + + (time domain pattern, + frequency-domain replacement, + condition for the rule to be applied, + convergence plane, + preparation function) + + The preparation function is a function with one argument that is applied + to the expression before matching. For most rules it should be + ``_laplace_deep_collect``. + """ + t = Dummy('t') + s = Dummy('s') + a = Wild('a', exclude=[t]) + b = Wild('b', exclude=[t]) + n = Wild('n', exclude=[t]) + tau = Wild('tau', exclude=[t]) + omega = Wild('omega', exclude=[t]) + def dco(f): return _laplace_deep_collect(f, t) + _debug('_laplace_build_rules is building rules') + + laplace_transform_rules = [ + (a, a/s, + S.true, S.Zero, dco), # 4.2.1 + (DiracDelta(a*t-b), exp(-s*b/a)/Abs(a), + Or(And(a > 0, b >= 0), And(a < 0, b <= 0)), + S.NegativeInfinity, dco), # Not in Bateman54 + (DiracDelta(a*t-b), S(0), + Or(And(a < 0, b >= 0), And(a > 0, b <= 0)), + S.NegativeInfinity, dco), # Not in Bateman54 + (Heaviside(a*t-b), exp(-s*b/a)/s, + And(a > 0, b > 0), S.Zero, dco), # 4.4.1 + (Heaviside(a*t-b), (1-exp(-s*b/a))/s, + And(a < 0, b < 0), S.Zero, dco), # 4.4.1 + (Heaviside(a*t-b), 1/s, + And(a > 0, b <= 0), S.Zero, dco), # 4.4.1 + (Heaviside(a*t-b), 0, + And(a < 0, b > 0), S.Zero, dco), # 4.4.1 + (t, 1/s**2, + S.true, S.Zero, dco), # 4.2.3 + (1/(a*t+b), -exp(-b/a*s)*Ei(-b/a*s)/a, + Abs(arg(b/a)) < pi, S.Zero, dco), # 4.2.6 + (1/sqrt(a*t+b), sqrt(a*pi/s)*exp(b/a*s)*erfc(sqrt(b/a*s))/a, + Abs(arg(b/a)) < pi, S.Zero, dco), # 4.2.18 + ((a*t+b)**(-S(3)/2), + 2*b**(-S(1)/2)-2*(pi*s/a)**(S(1)/2)*exp(b/a*s) * erfc(sqrt(b/a*s))/a, + Abs(arg(b/a)) < pi, S.Zero, dco), # 4.2.20 + (sqrt(t)/(t+b), sqrt(pi/s)-pi*sqrt(b)*exp(b*s)*erfc(sqrt(b*s)), + Abs(arg(b)) < pi, S.Zero, dco), # 4.2.22 + (1/(a*sqrt(t) + t**(3/2)), pi*a**(S(1)/2)*exp(a*s)*erfc(sqrt(a*s)), + S.true, S.Zero, dco), # Not in Bateman54 + (t**n, gamma(n+1)/s**(n+1), + n > -1, S.Zero, dco), # 4.3.1 + ((a*t+b)**n, uppergamma(n+1, b/a*s)*exp(-b/a*s)/s**(n+1)/a, + And(n > -1, Abs(arg(b/a)) < pi), S.Zero, dco), # 4.3.4 + (t**n/(t+a), a**n*gamma(n+1)*uppergamma(-n, a*s), + And(n > -1, Abs(arg(a)) < pi), S.Zero, dco), # 4.3.7 + (exp(a*t-tau), exp(-tau)/(s-a), + S.true, re(a), dco), # 4.5.1 + (t*exp(a*t-tau), exp(-tau)/(s-a)**2, + S.true, re(a), dco), # 4.5.2 + (t**n*exp(a*t), gamma(n+1)/(s-a)**(n+1), + re(n) > -1, re(a), dco), # 4.5.3 + (exp(-a*t**2), sqrt(pi/4/a)*exp(s**2/4/a)*erfc(s/sqrt(4*a)), + re(a) > 0, S.Zero, dco), # 4.5.21 + (t*exp(-a*t**2), + 1/(2*a)-2/sqrt(pi)/(4*a)**(S(3)/2)*s*erfc(s/sqrt(4*a)), + re(a) > 0, S.Zero, dco), # 4.5.22 + (exp(-a/t), 2*sqrt(a/s)*besselk(1, 2*sqrt(a*s)), + re(a) >= 0, S.Zero, dco), # 4.5.25 + (sqrt(t)*exp(-a/t), + S(1)/2*sqrt(pi/s**3)*(1+2*sqrt(a*s))*exp(-2*sqrt(a*s)), + re(a) >= 0, S.Zero, dco), # 4.5.26 + (exp(-a/t)/sqrt(t), sqrt(pi/s)*exp(-2*sqrt(a*s)), + re(a) >= 0, S.Zero, dco), # 4.5.27 + (exp(-a/t)/(t*sqrt(t)), sqrt(pi/a)*exp(-2*sqrt(a*s)), + re(a) > 0, S.Zero, dco), # 4.5.28 + (t**n*exp(-a/t), 2*(a/s)**((n+1)/2)*besselk(n+1, 2*sqrt(a*s)), + re(a) > 0, S.Zero, dco), # 4.5.29 + (exp(-2*sqrt(a*t)), + s**(-1)-sqrt(pi*a)*s**(-S(3)/2)*exp(a/s) * erfc(sqrt(a/s)), + Abs(arg(a)) < pi, S.Zero, dco), # 4.5.31 + (exp(-2*sqrt(a*t))/sqrt(t), (pi/s)**(S(1)/2)*exp(a/s)*erfc(sqrt(a/s)), + Abs(arg(a)) < pi, S.Zero, dco), # 4.5.33 + (exp(-a*exp(-t)), a**(-s)*lowergamma(s, a), + S.true, S.Zero, dco), # 4.5.36 + (exp(-a*exp(t)), a**s*uppergamma(-s, a), + re(a) > 0, S.Zero, dco), # 4.5.37 + (log(a*t), -log(exp(S.EulerGamma)*s/a)/s, + a > 0, S.Zero, dco), # 4.6.1 + (log(1+a*t), -exp(s/a)/s*Ei(-s/a), + Abs(arg(a)) < pi, S.Zero, dco), # 4.6.4 + (log(a*t+b), (log(b)-exp(s/b/a)/s*a*Ei(-s/b))/s*a, + And(a > 0, Abs(arg(b)) < pi), S.Zero, dco), # 4.6.5 + (log(t)/sqrt(t), -sqrt(pi/s)*log(4*s*exp(S.EulerGamma)), + S.true, S.Zero, dco), # 4.6.9 + (t**n*log(t), gamma(n+1)*s**(-n-1)*(digamma(n+1)-log(s)), + re(n) > -1, S.Zero, dco), # 4.6.11 + (log(a*t)**2, (log(exp(S.EulerGamma)*s/a)**2+pi**2/6)/s, + a > 0, S.Zero, dco), # 4.6.13 + (sin(omega*t), omega/(s**2+omega**2), + S.true, Abs(im(omega)), dco), # 4,7,1 + (Abs(sin(omega*t)), omega/(s**2+omega**2)*coth(pi*s/2/omega), + omega > 0, S.Zero, dco), # 4.7.2 + (sin(omega*t)/t, atan(omega/s), + S.true, Abs(im(omega)), dco), # 4.7.16 + (sin(omega*t)**2/t, log(1+4*omega**2/s**2)/4, + S.true, 2*Abs(im(omega)), dco), # 4.7.17 + (sin(omega*t)**2/t**2, + omega*atan(2*omega/s)-s*log(1+4*omega**2/s**2)/4, + S.true, 2*Abs(im(omega)), dco), # 4.7.20 + (sin(2*sqrt(a*t)), sqrt(pi*a)/s/sqrt(s)*exp(-a/s), + S.true, S.Zero, dco), # 4.7.32 + (sin(2*sqrt(a*t))/t, pi*erf(sqrt(a/s)), + S.true, S.Zero, dco), # 4.7.34 + (cos(omega*t), s/(s**2+omega**2), + S.true, Abs(im(omega)), dco), # 4.7.43 + (cos(omega*t)**2, (s**2+2*omega**2)/(s**2+4*omega**2)/s, + S.true, 2*Abs(im(omega)), dco), # 4.7.45 + (sqrt(t)*cos(2*sqrt(a*t)), sqrt(pi)/2*s**(-S(5)/2)*(s-2*a)*exp(-a/s), + S.true, S.Zero, dco), # 4.7.66 + (cos(2*sqrt(a*t))/sqrt(t), sqrt(pi/s)*exp(-a/s), + S.true, S.Zero, dco), # 4.7.67 + (sin(a*t)*sin(b*t), 2*a*b*s/(s**2+(a+b)**2)/(s**2+(a-b)**2), + S.true, Abs(im(a))+Abs(im(b)), dco), # 4.7.78 + (cos(a*t)*sin(b*t), b*(s**2-a**2+b**2)/(s**2+(a+b)**2)/(s**2+(a-b)**2), + S.true, Abs(im(a))+Abs(im(b)), dco), # 4.7.79 + (cos(a*t)*cos(b*t), s*(s**2+a**2+b**2)/(s**2+(a+b)**2)/(s**2+(a-b)**2), + S.true, Abs(im(a))+Abs(im(b)), dco), # 4.7.80 + (sinh(a*t), a/(s**2-a**2), + S.true, Abs(re(a)), dco), # 4.9.1 + (cosh(a*t), s/(s**2-a**2), + S.true, Abs(re(a)), dco), # 4.9.2 + (sinh(a*t)**2, 2*a**2/(s**3-4*a**2*s), + S.true, 2*Abs(re(a)), dco), # 4.9.3 + (cosh(a*t)**2, (s**2-2*a**2)/(s**3-4*a**2*s), + S.true, 2*Abs(re(a)), dco), # 4.9.4 + (sinh(a*t)/t, log((s+a)/(s-a))/2, + S.true, Abs(re(a)), dco), # 4.9.12 + (t**n*sinh(a*t), gamma(n+1)/2*((s-a)**(-n-1)-(s+a)**(-n-1)), + n > -2, Abs(a), dco), # 4.9.18 + (t**n*cosh(a*t), gamma(n+1)/2*((s-a)**(-n-1)+(s+a)**(-n-1)), + n > -1, Abs(a), dco), # 4.9.19 + (sinh(2*sqrt(a*t)), sqrt(pi*a)/s/sqrt(s)*exp(a/s), + S.true, S.Zero, dco), # 4.9.34 + (cosh(2*sqrt(a*t)), 1/s+sqrt(pi*a)/s/sqrt(s)*exp(a/s)*erf(sqrt(a/s)), + S.true, S.Zero, dco), # 4.9.35 + ( + sqrt(t)*sinh(2*sqrt(a*t)), + pi**(S(1)/2)*s**(-S(5)/2)*(s/2+a) * + exp(a/s)*erf(sqrt(a/s))-a**(S(1)/2)*s**(-2), + S.true, S.Zero, dco), # 4.9.36 + (sqrt(t)*cosh(2*sqrt(a*t)), pi**(S(1)/2)*s**(-S(5)/2)*(s/2+a)*exp(a/s), + S.true, S.Zero, dco), # 4.9.37 + (sinh(2*sqrt(a*t))/sqrt(t), + pi**(S(1)/2)*s**(-S(1)/2)*exp(a/s) * erf(sqrt(a/s)), + S.true, S.Zero, dco), # 4.9.38 + (cosh(2*sqrt(a*t))/sqrt(t), pi**(S(1)/2)*s**(-S(1)/2)*exp(a/s), + S.true, S.Zero, dco), # 4.9.39 + (sinh(sqrt(a*t))**2/sqrt(t), pi**(S(1)/2)/2*s**(-S(1)/2)*(exp(a/s)-1), + S.true, S.Zero, dco), # 4.9.40 + (cosh(sqrt(a*t))**2/sqrt(t), pi**(S(1)/2)/2*s**(-S(1)/2)*(exp(a/s)+1), + S.true, S.Zero, dco), # 4.9.41 + (erf(a*t), exp(s**2/(2*a)**2)*erfc(s/(2*a))/s, + 4*Abs(arg(a)) < pi, S.Zero, dco), # 4.12.2 + (erf(sqrt(a*t)), sqrt(a)/sqrt(s+a)/s, + S.true, Max(S.Zero, -re(a)), dco), # 4.12.4 + (exp(a*t)*erf(sqrt(a*t)), sqrt(a)/sqrt(s)/(s-a), + S.true, Max(S.Zero, re(a)), dco), # 4.12.5 + (erf(sqrt(a/t)/2), (1-exp(-sqrt(a*s)))/s, + re(a) > 0, S.Zero, dco), # 4.12.6 + (erfc(sqrt(a*t)), (sqrt(s+a)-sqrt(a))/sqrt(s+a)/s, + S.true, -re(a), dco), # 4.12.9 + (exp(a*t)*erfc(sqrt(a*t)), 1/(s+sqrt(a*s)), + S.true, S.Zero, dco), # 4.12.10 + (erfc(sqrt(a/t)/2), exp(-sqrt(a*s))/s, + re(a) > 0, S.Zero, dco), # 4.2.11 + (besselj(n, a*t), a**n/(sqrt(s**2+a**2)*(s+sqrt(s**2+a**2))**n), + re(n) > -1, Abs(im(a)), dco), # 4.14.1 + (t**b*besselj(n, a*t), + 2**n/sqrt(pi)*gamma(n+S.Half)*a**n*(s**2+a**2)**(-n-S.Half), + And(re(n) > -S.Half, Eq(b, n)), Abs(im(a)), dco), # 4.14.7 + (t**b*besselj(n, a*t), + 2**(n+1)/sqrt(pi)*gamma(n+S(3)/2)*a**n*s*(s**2+a**2)**(-n-S(3)/2), + And(re(n) > -1, Eq(b, n+1)), Abs(im(a)), dco), # 4.14.8 + (besselj(0, 2*sqrt(a*t)), exp(-a/s)/s, + S.true, S.Zero, dco), # 4.14.25 + (t**(b)*besselj(n, 2*sqrt(a*t)), a**(n/2)*s**(-n-1)*exp(-a/s), + And(re(n) > -1, Eq(b, n*S.Half)), S.Zero, dco), # 4.14.30 + (besselj(0, a*sqrt(t**2+b*t)), + exp(b*s-b*sqrt(s**2+a**2))/sqrt(s**2+a**2), + Abs(arg(b)) < pi, Abs(im(a)), dco), # 4.15.19 + (besseli(n, a*t), a**n/(sqrt(s**2-a**2)*(s+sqrt(s**2-a**2))**n), + re(n) > -1, Abs(re(a)), dco), # 4.16.1 + (t**b*besseli(n, a*t), + 2**n/sqrt(pi)*gamma(n+S.Half)*a**n*(s**2-a**2)**(-n-S.Half), + And(re(n) > -S.Half, Eq(b, n)), Abs(re(a)), dco), # 4.16.6 + (t**b*besseli(n, a*t), + 2**(n+1)/sqrt(pi)*gamma(n+S(3)/2)*a**n*s*(s**2-a**2)**(-n-S(3)/2), + And(re(n) > -1, Eq(b, n+1)), Abs(re(a)), dco), # 4.16.7 + (t**(b)*besseli(n, 2*sqrt(a*t)), a**(n/2)*s**(-n-1)*exp(a/s), + And(re(n) > -1, Eq(b, n*S.Half)), S.Zero, dco), # 4.16.18 + (bessely(0, a*t), -2/pi*asinh(s/a)/sqrt(s**2+a**2), + S.true, Abs(im(a)), dco), # 4.15.44 + (besselk(0, a*t), log((s + sqrt(s**2-a**2))/a)/(sqrt(s**2-a**2)), + S.true, -re(a), dco) # 4.16.23 + ] + return laplace_transform_rules, t, s + + +@DEBUG_WRAP +def _laplace_rule_timescale(f, t, s): + """ + This function applies the time-scaling rule of the Laplace transform in + a straight-forward way. For example, if it gets ``(f(a*t), t, s)``, it will + compute ``LaplaceTransform(f(t)/a, t, s/a)`` if ``a>0``. + """ + + a = Wild('a', exclude=[t]) + g = WildFunction('g', nargs=1) + ma1 = f.match(g) + if ma1: + arg = ma1[g].args[0].collect(t) + ma2 = arg.match(a*t) + if ma2 and ma2[a].is_positive and ma2[a] != 1: + _debug(' rule: time scaling (4.1.4)') + r, pr, cr = _laplace_transform( + 1/ma2[a]*ma1[g].func(t), t, s/ma2[a], simplify=False) + return (r, pr, cr) + return None + + +@DEBUG_WRAP +def _laplace_rule_heaviside(f, t, s): + """ + This function deals with time-shifted Heaviside step functions. If the time + shift is positive, it applies the time-shift rule of the Laplace transform. + For example, if it gets ``(Heaviside(t-a)*f(t), t, s)``, it will compute + ``exp(-a*s)*LaplaceTransform(f(t+a), t, s)``. + + If the time shift is negative, the Heaviside function is simply removed + as it means nothing to the Laplace transform. + + The function does not remove a factor ``Heaviside(t)``; this is done by + the simple rules. + """ + + a = Wild('a', exclude=[t]) + y = Wild('y') + g = Wild('g') + if ma1 := f.match(Heaviside(y) * g): + if ma2 := ma1[y].match(t - a): + if ma2[a].is_positive: + _debug(' rule: time shift (4.1.4)') + r, pr, cr = _laplace_transform( + ma1[g].subs(t, t + ma2[a]), t, s, simplify=False) + return (exp(-ma2[a] * s) * r, pr, cr) + if ma2[a].is_negative: + _debug( + ' rule: Heaviside factor; negative time shift (4.1.4)') + r, pr, cr = _laplace_transform(ma1[g], t, s, simplify=False) + return (r, pr, cr) + if ma2 := ma1[y].match(a - t): + if ma2[a].is_positive: + _debug(' rule: Heaviside window open') + r, pr, cr = _laplace_transform( + (1 - Heaviside(t - ma2[a])) * ma1[g], t, s, simplify=False) + return (r, pr, cr) + if ma2[a].is_negative: + _debug(' rule: Heaviside window closed') + return (0, 0, S.true) + return None + + +@DEBUG_WRAP +def _laplace_rule_exp(f, t, s): + """ + If this function finds a factor ``exp(a*t)``, it applies the + frequency-shift rule of the Laplace transform and adjusts the convergence + plane accordingly. For example, if it gets ``(exp(-a*t)*f(t), t, s)``, it + will compute ``LaplaceTransform(f(t), t, s+a)``. + """ + + a = Wild('a', exclude=[t]) + y = Wild('y') + z = Wild('z') + ma1 = f.match(exp(y)*z) + if ma1: + ma2 = ma1[y].collect(t).match(a*t) + if ma2: + _debug(' rule: multiply with exp (4.1.5)') + r, pr, cr = _laplace_transform(ma1[z], t, s-ma2[a], + simplify=False) + return (r, pr+re(ma2[a]), cr) + return None + + +@DEBUG_WRAP +def _laplace_rule_delta(f, t, s): + """ + If this function finds a factor ``DiracDelta(b*t-a)``, it applies the + masking property of the delta distribution. For example, if it gets + ``(DiracDelta(t-a)*f(t), t, s)``, it will return + ``(f(a)*exp(-a*s), -a, True)``. + """ + # This rule is not in Bateman54 + + a = Wild('a', exclude=[t]) + b = Wild('b', exclude=[t]) + + y = Wild('y') + z = Wild('z') + ma1 = f.match(DiracDelta(y)*z) + if ma1 and not ma1[z].has(DiracDelta): + ma2 = ma1[y].collect(t).match(b*t-a) + if ma2: + _debug(' rule: multiply with DiracDelta') + loc = ma2[a]/ma2[b] + if re(loc) >= 0 and im(loc) == 0: + fn = exp(-ma2[a]/ma2[b]*s)*ma1[z] + if fn.has(sin, cos): + # Then it may be possible that a sinc() is present in the + # term; let's try this: + fn = fn.rewrite(sinc).ratsimp() + n, d = [x.subs(t, ma2[a]/ma2[b]) for x in fn.as_numer_denom()] + if d != 0: + return (n/d/ma2[b], S.NegativeInfinity, S.true) + else: + return None + else: + return (0, S.NegativeInfinity, S.true) + if ma1[y].is_polynomial(t): + ro = roots(ma1[y], t) + if ro != {} and set(ro.values()) == {1}: + slope = diff(ma1[y], t) + r = Add( + *[exp(-x*s)*ma1[z].subs(t, s)/slope.subs(t, x) + for x in list(ro.keys()) if im(x) == 0 and re(x) >= 0]) + return (r, S.NegativeInfinity, S.true) + return None + + +@DEBUG_WRAP +def _laplace_trig_split(fn): + """ + Helper function for `_laplace_rule_trig`. This function returns two terms + `f` and `g`. `f` contains all product terms with sin, cos, sinh, cosh in + them; `g` contains everything else. + """ + trigs = [S.One] + other = [S.One] + for term in Mul.make_args(fn): + if term.has(sin, cos, sinh, cosh, exp): + trigs.append(term) + else: + other.append(term) + f = Mul(*trigs) + g = Mul(*other) + return f, g + + +@DEBUG_WRAP +def _laplace_trig_expsum(f, t): + """ + Helper function for `_laplace_rule_trig`. This function expects the `f` + from `_laplace_trig_split`. It returns two lists `xm` and `xn`. `xm` is + a list of dictionaries with keys `k` and `a` representing a function + `k*exp(a*t)`. `xn` is a list of all terms that cannot be brought into + that form, which may happen, e.g., when a trigonometric function has + another function in its argument. + """ + c1 = Wild('c1', exclude=[t]) + c0 = Wild('c0', exclude=[t]) + p = Wild('p', exclude=[t]) + xm = [] + xn = [] + + x1 = f.rewrite(exp).expand() + + for term in Add.make_args(x1): + if not term.has(t): + xm.append({'k': term, 'a': 0, re: 0, im: 0}) + continue + term = _laplace_deep_collect(term.powsimp(combine='exp'), t) + + if (r := term.match(p*exp(c1*t+c0))) is not None: + xm.append({ + 'k': r[p]*exp(r[c0]), 'a': r[c1], + re: re(r[c1]), im: im(r[c1])}) + else: + xn.append(term) + return xm, xn + + +@DEBUG_WRAP +def _laplace_trig_ltex(xm, t, s): + """ + Helper function for `_laplace_rule_trig`. This function takes the list of + exponentials `xm` from `_laplace_trig_expsum` and simplifies complex + conjugate and real symmetric poles. It returns the result as a sum and + the convergence plane. + """ + results = [] + planes = [] + + def _simpc(coeffs): + nc = coeffs.copy() + for k in range(len(nc)): + ri = nc[k].as_real_imag() + if ri[0].has(im): + nc[k] = nc[k].rewrite(cos) + else: + nc[k] = (ri[0] + I*ri[1]).rewrite(cos) + return nc + + def _quadpole(t1, k1, k2, k3, s): + a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im] + nc = [ + k0 + k1 + k2 + k3, + a*(k0 + k1 - k2 - k3) - 2*I*a_i*k1 + 2*I*a_i*k2, + ( + a**2*(-k0 - k1 - k2 - k3) + + a*(4*I*a_i*k0 + 4*I*a_i*k3) + + 4*a_i**2*k0 + 4*a_i**2*k3), + ( + a**3*(-k0 - k1 + k2 + k3) + + a**2*(4*I*a_i*k0 + 2*I*a_i*k1 - 2*I*a_i*k2 - 4*I*a_i*k3) + + a*(4*a_i**2*k0 - 4*a_i**2*k3)) + ] + dc = [ + S.One, S.Zero, 2*a_i**2 - 2*a_r**2, + S.Zero, a_i**4 + 2*a_i**2*a_r**2 + a_r**4] + n = Add( + *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])]) + d = Add( + *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])]) + return n/d + + def _ccpole(t1, k1, s): + a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im] + nc = [k0 + k1, -a*k0 - a*k1 + 2*I*a_i*k0] + dc = [S.One, -2*a_r, a_i**2 + a_r**2] + n = Add( + *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])]) + d = Add( + *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])]) + return n/d + + def _rspole(t1, k2, s): + a, k0, a_r, a_i = t1['a'], t1['k'], t1[re], t1[im] + nc = [k0 + k2, a*k0 - a*k2 - 2*I*a_i*k0] + dc = [S.One, -2*I*a_i, -a_i**2 - a_r**2] + n = Add( + *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])]) + d = Add( + *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])]) + return n/d + + def _sypole(t1, k3, s): + a, k0 = t1['a'], t1['k'] + nc = [k0 + k3, a*(k0 - k3)] + dc = [S.One, S.Zero, -a**2] + n = Add( + *[x*s**y for x, y in zip(_simpc(nc), range(len(nc))[::-1])]) + d = Add( + *[x*s**y for x, y in zip(dc, range(len(dc))[::-1])]) + return n/d + + def _simplepole(t1, s): + a, k0 = t1['a'], t1['k'] + n = k0 + d = s - a + return n/d + + while len(xm) > 0: + t1 = xm.pop() + i_imagsym = None + i_realsym = None + i_pointsym = None + # The following code checks all remaining poles. If t1 is a pole at + # a+b*I, then we check for a-b*I, -a+b*I, and -a-b*I, and + # assign the respective indices to i_imagsym, i_realsym, i_pointsym. + # -a-b*I / i_pointsym only applies if both a and b are != 0. + for i in range(len(xm)): + real_eq = t1[re] == xm[i][re] + realsym = t1[re] == -xm[i][re] + imag_eq = t1[im] == xm[i][im] + imagsym = t1[im] == -xm[i][im] + if realsym and imagsym and t1[re] != 0 and t1[im] != 0: + i_pointsym = i + elif realsym and imag_eq and t1[re] != 0: + i_realsym = i + elif real_eq and imagsym and t1[im] != 0: + i_imagsym = i + + # The next part looks for four possible pole constellations: + # quad: a+b*I, a-b*I, -a+b*I, -a-b*I + # cc: a+b*I, a-b*I (a may be zero) + # quad: a+b*I, -a+b*I (b may be zero) + # point: a+b*I, -a-b*I (a!=0 and b!=0 is needed, but that has been + # asserted when finding i_pointsym above.) + # If none apply, then t1 is a simple pole. + if ( + i_imagsym is not None and i_realsym is not None + and i_pointsym is not None): + results.append( + _quadpole(t1, + xm[i_imagsym]['k'], xm[i_realsym]['k'], + xm[i_pointsym]['k'], s)) + planes.append(Abs(re(t1['a']))) + # The three additional poles have now been used; to pop them + # easily we have to do it from the back. + indices_to_pop = [i_imagsym, i_realsym, i_pointsym] + indices_to_pop.sort(reverse=True) + for i in indices_to_pop: + xm.pop(i) + elif i_imagsym is not None: + results.append(_ccpole(t1, xm[i_imagsym]['k'], s)) + planes.append(t1[re]) + xm.pop(i_imagsym) + elif i_realsym is not None: + results.append(_rspole(t1, xm[i_realsym]['k'], s)) + planes.append(Abs(t1[re])) + xm.pop(i_realsym) + elif i_pointsym is not None: + results.append(_sypole(t1, xm[i_pointsym]['k'], s)) + planes.append(Abs(t1[re])) + xm.pop(i_pointsym) + else: + results.append(_simplepole(t1, s)) + planes.append(t1[re]) + + return Add(*results), Max(*planes) + + +@DEBUG_WRAP +def _laplace_rule_trig(fn, t_, s): + """ + This rule covers trigonometric factors by splitting everything into a + sum of exponential functions and collecting complex conjugate poles and + real symmetric poles. + """ + t = Dummy('t', real=True) + + if not fn.has(sin, cos, sinh, cosh): + return None + + f, g = _laplace_trig_split(fn.subs(t_, t)) + xm, xn = _laplace_trig_expsum(f, t) + + if len(xn) > 0: + # TODO not implemented yet, but also not important + return None + + if not g.has(t): + r, p = _laplace_trig_ltex(xm, t, s) + return g*r, p, S.true + else: + # Just transform `g` and make frequency-shifted copies + planes = [] + results = [] + G, G_plane, G_cond = _laplace_transform(g, t, s, simplify=False) + for x1 in xm: + results.append(x1['k']*G.subs(s, s-x1['a'])) + planes.append(G_plane+re(x1['a'])) + return Add(*results).subs(t, t_), Max(*planes), G_cond + + +@DEBUG_WRAP +def _laplace_rule_diff(f, t, s): + """ + This function looks for derivatives in the time domain and replaces it + by factors of `s` and initial conditions in the frequency domain. For + example, if it gets ``(diff(f(t), t), t, s)``, it will compute + ``s*LaplaceTransform(f(t), t, s) - f(0)``. + """ + + a = Wild('a', exclude=[t]) + n = Wild('n', exclude=[t]) + g = WildFunction('g') + ma1 = f.match(a*Derivative(g, (t, n))) + if ma1 and ma1[n].is_integer: + m = [z.has(t) for z in ma1[g].args] + if sum(m) == 1: + _debug(' rule: time derivative (4.1.8)') + d = [] + for k in range(ma1[n]): + if k == 0: + y = ma1[g].subs(t, 0) + else: + y = Derivative(ma1[g], (t, k)).subs(t, 0) + d.append(s**(ma1[n]-k-1)*y) + r, pr, cr = _laplace_transform(ma1[g], t, s, simplify=False) + return (ma1[a]*(s**ma1[n]*r - Add(*d)), pr, cr) + return None + + +@DEBUG_WRAP +def _laplace_rule_sdiff(f, t, s): + """ + This function looks for multiplications with polynoimials in `t` as they + correspond to differentiation in the frequency domain. For example, if it + gets ``(t*f(t), t, s)``, it will compute + ``-Derivative(LaplaceTransform(f(t), t, s), s)``. + """ + + if f.is_Mul: + pfac = [1] + ofac = [1] + for fac in Mul.make_args(f): + if fac.is_polynomial(t): + pfac.append(fac) + else: + ofac.append(fac) + if len(pfac) > 1: + pex = prod(pfac) + pc = Poly(pex, t).all_coeffs() + N = len(pc) + if N > 1: + oex = prod(ofac) + r_, p_, c_ = _laplace_transform(oex, t, s, simplify=False) + deri = [r_] + d1 = False + try: + d1 = -diff(deri[-1], s) + except ValueError: + d1 = False + if r_.has(LaplaceTransform): + for k in range(N-1): + deri.append((-1)**(k+1)*Derivative(r_, s, k+1)) + elif d1: + deri.append(d1) + for k in range(N-2): + deri.append(-diff(deri[-1], s)) + if d1: + r = Add(*[pc[N-n-1]*deri[n] for n in range(N)]) + return (r, p_, c_) + # We still have to cover the possibility that there is a symbolic positive + # integer exponent. + n = Wild('n', exclude=[t]) + g = Wild('g') + if ma1 := f.match(t**n*g): + if ma1[n].is_integer and ma1[n].is_positive: + r_, p_, c_ = _laplace_transform(ma1[g], t, s, simplify=False) + return (-1)**ma1[n]*diff(r_, (s, ma1[n])), p_, c_ + return None + + +@DEBUG_WRAP +def _laplace_expand(f, t, s): + """ + This function tries to expand its argument with successively stronger + methods: first it will expand on the top level, then it will expand any + multiplications in depth, then it will try all avilable expansion methods, + and finally it will try to expand trigonometric functions. + + If it can expand, it will then compute the Laplace transform of the + expanded term. + """ + + r = expand(f, deep=False) + if r.is_Add: + return _laplace_transform(r, t, s, simplify=False) + r = expand_mul(f) + if r.is_Add: + return _laplace_transform(r, t, s, simplify=False) + r = expand(f) + if r.is_Add: + return _laplace_transform(r, t, s, simplify=False) + if r != f: + return _laplace_transform(r, t, s, simplify=False) + r = expand(expand_trig(f)) + if r.is_Add: + return _laplace_transform(r, t, s, simplify=False) + return None + + +@DEBUG_WRAP +def _laplace_apply_prog_rules(f, t, s): + """ + This function applies all program rules and returns the result if one + of them gives a result. + """ + + prog_rules = [_laplace_rule_heaviside, _laplace_rule_delta, + _laplace_rule_timescale, _laplace_rule_exp, + _laplace_rule_trig, + _laplace_rule_diff, _laplace_rule_sdiff] + + for p_rule in prog_rules: + if (L := p_rule(f, t, s)) is not None: + return L + return None + + +@DEBUG_WRAP +def _laplace_apply_simple_rules(f, t, s): + """ + This function applies all simple rules and returns the result if one + of them gives a result. + """ + simple_rules, t_, s_ = _laplace_build_rules() + prep_old = '' + prep_f = '' + for t_dom, s_dom, check, plane, prep in simple_rules: + if prep_old != prep: + prep_f = prep(f.subs({t: t_})) + prep_old = prep + ma = prep_f.match(t_dom) + if ma: + try: + c = check.xreplace(ma) + except TypeError: + # This may happen if the time function has imaginary + # numbers in it. Then we give up. + continue + if c == S.true: + return (s_dom.xreplace(ma).subs({s_: s}), + plane.xreplace(ma), S.true) + return None + + +@DEBUG_WRAP +def _piecewise_to_heaviside(f, t): + """ + This function converts a Piecewise expression to an expression written + with Heaviside. It is not exact, but valid in the context of the Laplace + transform. + """ + if not t.is_real: + r = Dummy('r', real=True) + return _piecewise_to_heaviside(f.xreplace({t: r}), r).xreplace({r: t}) + x = piecewise_exclusive(f) + r = [] + for fn, cond in x.args: + # Here we do not need to do many checks because piecewise_exclusive + # has a clearly predictable output. However, if any of the conditions + # is not relative to t, this function just returns the input argument. + if isinstance(cond, Relational) and t in cond.args: + if isinstance(cond, (Eq, Ne)): + # We do not cover this case; these would be single-point + # exceptions that do not play a role in Laplace practice, + # except if they contain Dirac impulses, and then we can + # expect users to not try to use Piecewise for writing it. + return f + else: + r.append(Heaviside(cond.gts - cond.lts)*fn) + elif isinstance(cond, Or) and len(cond.args) == 2: + # Or(t<2, t>4), Or(t>4, t<=2), ... in any order with any <= >= + for c2 in cond.args: + if c2.lhs == t: + r.append(Heaviside(c2.gts - c2.lts)*fn) + else: + return f + elif isinstance(cond, And) and len(cond.args) == 2: + # And(t>2, t<4), And(t>4, t<=2), ... in any order with any <= >= + c0, c1 = cond.args + if c0.lhs == t and c1.lhs == t: + if '>' in c0.rel_op: + c0, c1 = c1, c0 + r.append( + (Heaviside(c1.gts - c1.lts) - + Heaviside(c0.lts - c0.gts))*fn) + else: + return f + else: + return f + return Add(*r) + + +def laplace_correspondence(f, fdict, /): + """ + This helper function takes a function `f` that is the result of a + ``laplace_transform`` or an ``inverse_laplace_transform``. It replaces all + unevaluated ``LaplaceTransform(y(t), t, s)`` by `Y(s)` for any `s` and + all ``InverseLaplaceTransform(Y(s), s, t)`` by `y(t)` for any `t` if + ``fdict`` contains a correspondence ``{y: Y}``. + + Parameters + ========== + + f : sympy expression + Expression containing unevaluated ``LaplaceTransform`` or + ``LaplaceTransform`` objects. + fdict : dictionary + Dictionary containing one or more function correspondences, + e.g., ``{x: X, y: Y}`` meaning that ``X`` and ``Y`` are the + Laplace transforms of ``x`` and ``y``, respectively. + + Examples + ======== + + >>> from sympy import laplace_transform, diff, Function + >>> from sympy import laplace_correspondence, inverse_laplace_transform + >>> from sympy.abc import t, s + >>> y = Function("y") + >>> Y = Function("Y") + >>> z = Function("z") + >>> Z = Function("Z") + >>> f = laplace_transform(diff(y(t), t, 1) + z(t), t, s, noconds=True) + >>> laplace_correspondence(f, {y: Y, z: Z}) + s*Y(s) + Z(s) - y(0) + >>> f = inverse_laplace_transform(Y(s), s, t) + >>> laplace_correspondence(f, {y: Y}) + y(t) + """ + p = Wild('p') + s = Wild('s') + t = Wild('t') + a = Wild('a') + if ( + not isinstance(f, Expr) + or (not f.has(LaplaceTransform) + and not f.has(InverseLaplaceTransform))): + return f + for y, Y in fdict.items(): + if ( + (m := f.match(LaplaceTransform(y(a), t, s))) is not None + and m[a] == m[t]): + return Y(m[s]) + if ( + (m := f.match(InverseLaplaceTransform(Y(a), s, t, p))) + is not None + and m[a] == m[s]): + return y(m[t]) + func = f.func + args = [laplace_correspondence(arg, fdict) for arg in f.args] + return func(*args) + + +def laplace_initial_conds(f, t, fdict, /): + """ + This helper function takes a function `f` that is the result of a + ``laplace_transform``. It takes an fdict of the form ``{y: [1, 4, 2]}``, + where the values in the list are the initial value, the initial slope, the + initial second derivative, etc., of the function `y(t)`, and replaces all + unevaluated initial conditions. + + Parameters + ========== + + f : sympy expression + Expression containing initial conditions of unevaluated functions. + t : sympy expression + Variable for which the initial conditions are to be applied. + fdict : dictionary + Dictionary containing a list of initial conditions for every + function, e.g., ``{y: [0, 1, 2], x: [3, 4, 5]}``. The order + of derivatives is ascending, so `0`, `1`, `2` are `y(0)`, `y'(0)`, + and `y''(0)`, respectively. + + Examples + ======== + + >>> from sympy import laplace_transform, diff, Function + >>> from sympy import laplace_correspondence, laplace_initial_conds + >>> from sympy.abc import t, s + >>> y = Function("y") + >>> Y = Function("Y") + >>> f = laplace_transform(diff(y(t), t, 3), t, s, noconds=True) + >>> g = laplace_correspondence(f, {y: Y}) + >>> laplace_initial_conds(g, t, {y: [2, 4, 8, 16, 32]}) + s**3*Y(s) - 2*s**2 - 4*s - 8 + """ + for y, ic in fdict.items(): + for k in range(len(ic)): + if k == 0: + f = f.replace(y(0), ic[0]) + elif k == 1: + f = f.replace(Subs(Derivative(y(t), t), t, 0), ic[1]) + else: + f = f.replace(Subs(Derivative(y(t), (t, k)), t, 0), ic[k]) + return f + + +@DEBUG_WRAP +def _laplace_transform(fn, t_, s_, *, simplify): + """ + Front-end function of the Laplace transform. It tries to apply all known + rules recursively, and if everything else fails, it tries to integrate. + """ + + terms_t = Add.make_args(fn) + terms_s = [] + terms = [] + planes = [] + conditions = [] + + for ff in terms_t: + k, ft = ff.as_independent(t_, as_Add=False) + if ft.has(SingularityFunction): + _terms = Add.make_args(ft.rewrite(Heaviside)) + for _term in _terms: + k1, f1 = _term.as_independent(t_, as_Add=False) + terms.append((k*k1, f1)) + elif ft.func == Piecewise and not ft.has(DiracDelta(t_)): + _terms = Add.make_args(_piecewise_to_heaviside(ft, t_)) + for _term in _terms: + k1, f1 = _term.as_independent(t_, as_Add=False) + terms.append((k*k1, f1)) + else: + terms.append((k, ft)) + + for k, ft in terms: + if ft.has(SingularityFunction): + r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True) + else: + if ft.has(Heaviside(t_)) and not ft.has(DiracDelta(t_)): + # For t>=0, Heaviside(t)=1 can be used, except if there is also + # a DiracDelta(t) present, in which case removing Heaviside(t) + # is unnecessary because _laplace_rule_delta can deal with it. + ft = ft.subs(Heaviside(t_), 1) + if ( + (r := _laplace_apply_simple_rules(ft, t_, s_)) + is not None or + (r := _laplace_apply_prog_rules(ft, t_, s_)) + is not None or + (r := _laplace_expand(ft, t_, s_)) is not None): + pass + elif any(undef.has(t_) for undef in ft.atoms(AppliedUndef)): + # If there are undefined functions f(t) then integration is + # unlikely to do anything useful so we skip it and given an + # unevaluated LaplaceTransform. + r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True) + elif (r := _laplace_transform_integration( + ft, t_, s_, simplify=simplify)) is not None: + pass + else: + r = (LaplaceTransform(ft, t_, s_), S.NegativeInfinity, True) + (ri_, pi_, ci_) = r + terms_s.append(k*ri_) + planes.append(pi_) + conditions.append(ci_) + + result = Add(*terms_s) + if simplify: + result = result.simplify(doit=False) + plane = Max(*planes) + condition = And(*conditions) + + return result, plane, condition + + +class LaplaceTransform(IntegralTransform): + """ + Class representing unevaluated Laplace transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute Laplace transforms, see the :func:`laplace_transform` + docstring. + + If this is called with ``.doit()``, it returns the Laplace transform as an + expression. If it is called with ``.doit(noconds=False)``, it returns a + tuple containing the same expression, a convergence plane, and conditions. + """ + + _name = 'Laplace' + + def _compute_transform(self, f, t, s, **hints): + _simplify = hints.get('simplify', False) + LT = _laplace_transform_integration(f, t, s, simplify=_simplify) + return LT + + def _as_integral(self, f, t, s): + return Integral(f*exp(-s*t), (t, S.Zero, S.Infinity)) + + def doit(self, **hints): + """ + Try to evaluate the transform in closed form. + + Explanation + =========== + + Standard hints are the following: + - ``noconds``: if True, do not return convergence conditions. The + default setting is `True`. + - ``simplify``: if True, it simplifies the final result. The + default setting is `False`. + """ + _noconds = hints.get('noconds', True) + _simplify = hints.get('simplify', False) + + debugf('[LT doit] (%s, %s, %s)', (self.function, + self.function_variable, + self.transform_variable)) + + t_ = self.function_variable + s_ = self.transform_variable + fn = self.function + + r = _laplace_transform(fn, t_, s_, simplify=_simplify) + + if _noconds: + return r[0] + else: + return r + + +def laplace_transform(f, t, s, legacy_matrix=True, **hints): + r""" + Compute the Laplace Transform `F(s)` of `f(t)`, + + .. math :: F(s) = \int_{0^{-}}^\infty e^{-st} f(t) \mathrm{d}t. + + Explanation + =========== + + For all sensible functions, this converges absolutely in a + half-plane + + .. math :: a < \operatorname{Re}(s) + + This function returns ``(F, a, cond)`` where ``F`` is the Laplace + transform of ``f``, `a` is the half-plane of convergence, and `cond` are + auxiliary convergence conditions. + + The implementation is rule-based, and if you are interested in which + rules are applied, and whether integration is attempted, you can switch + debug information on by setting ``sympy.SYMPY_DEBUG=True``. The numbers + of the rules in the debug information (and the code) refer to Bateman's + Tables of Integral Transforms [1]. + + The lower bound is `0-`, meaning that this bound should be approached + from the lower side. This is only necessary if distributions are involved. + At present, it is only done if `f(t)` contains ``DiracDelta``, in which + case the Laplace transform is computed implicitly as + + .. math :: + F(s) = \lim_{\tau\to 0^{-}} \int_{\tau}^\infty e^{-st} + f(t) \mathrm{d}t + + by applying rules. + + If the Laplace transform cannot be fully computed in closed form, this + function returns expressions containing unevaluated + :class:`LaplaceTransform` objects. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. If + ``noconds=True``, only `F` will be returned (i.e. not ``cond``, and also + not the plane ``a``). + + .. deprecated:: 1.9 + Legacy behavior for matrices where ``laplace_transform`` with + ``noconds=False`` (the default) returns a Matrix whose elements are + tuples. The behavior of ``laplace_transform`` for matrices will change + in a future release of SymPy to return a tuple of the transformed + Matrix and the convergence conditions for the matrix as a whole. Use + ``legacy_matrix=False`` to enable the new behavior. + + Examples + ======== + + >>> from sympy import DiracDelta, exp, laplace_transform + >>> from sympy.abc import t, s, a + >>> laplace_transform(t**4, t, s) + (24/s**5, 0, True) + >>> laplace_transform(t**a, t, s) + (gamma(a + 1)/(s*s**a), 0, re(a) > -1) + >>> laplace_transform(DiracDelta(t)-a*exp(-a*t), t, s, simplify=True) + (s/(a + s), -re(a), True) + + There are also helper functions that make it easy to solve differential + equations by Laplace transform. For example, to solve + + .. math :: m x''(t) + d x'(t) + k x(t) = 0 + + with initial value `0` and initial derivative `v`: + + >>> from sympy import Function, laplace_correspondence, diff, solve + >>> from sympy import laplace_initial_conds, inverse_laplace_transform + >>> from sympy.abc import d, k, m, v + >>> x = Function('x') + >>> X = Function('X') + >>> f = m*diff(x(t), t, 2) + d*diff(x(t), t) + k*x(t) + >>> F = laplace_transform(f, t, s, noconds=True) + >>> F = laplace_correspondence(F, {x: X}) + >>> F = laplace_initial_conds(F, t, {x: [0, v]}) + >>> F + d*s*X(s) + k*X(s) + m*(s**2*X(s) - v) + >>> Xs = solve(F, X(s))[0] + >>> Xs + m*v/(d*s + k + m*s**2) + >>> inverse_laplace_transform(Xs, s, t) + 2*v*exp(-d*t/(2*m))*sin(t*sqrt((-d**2 + 4*k*m)/m**2)/2)*Heaviside(t)/sqrt((-d**2 + 4*k*m)/m**2) + + References + ========== + + .. [1] Erdelyi, A. (ed.), Tables of Integral Transforms, Volume 1, + Bateman Manuscript Prooject, McGraw-Hill (1954), available: + https://resolver.caltech.edu/CaltechAUTHORS:20140123-101456353 + + See Also + ======== + + inverse_laplace_transform, mellin_transform, fourier_transform + hankel_transform, inverse_hankel_transform + + """ + + _noconds = hints.get('noconds', False) + _simplify = hints.get('simplify', False) + + if isinstance(f, MatrixBase) and hasattr(f, 'applyfunc'): + + conds = not hints.get('noconds', False) + + if conds and legacy_matrix: + adt = 'deprecated-laplace-transform-matrix' + sympy_deprecation_warning( + """ +Calling laplace_transform() on a Matrix with noconds=False (the default) is +deprecated. Either noconds=True or use legacy_matrix=False to get the new +behavior. + """, + deprecated_since_version='1.9', + active_deprecations_target=adt, + ) + # Temporarily disable the deprecation warning for non-Expr objects + # in Matrix + with ignore_warnings(SymPyDeprecationWarning): + return f.applyfunc( + lambda fij: laplace_transform(fij, t, s, **hints)) + else: + elements_trans = [laplace_transform( + fij, t, s, **hints) for fij in f] + if conds: + elements, avals, conditions = zip(*elements_trans) + f_laplace = type(f)(*f.shape, elements) + return f_laplace, Max(*avals), And(*conditions) + else: + return type(f)(*f.shape, elements_trans) + + LT, p, c = LaplaceTransform(f, t, s).doit(noconds=False, + simplify=_simplify) + + if not _noconds: + return LT, p, c + else: + return LT + + +@DEBUG_WRAP +def _inverse_laplace_transform_integration(F, s, t_, plane, *, simplify): + """ The backend function for inverse Laplace transforms. """ + from sympy.integrals.meijerint import meijerint_inversion, _get_coeff_exp + from sympy.integrals.transforms import inverse_mellin_transform + + # There are two strategies we can try: + # 1) Use inverse mellin transform, related by a simple change of variables. + # 2) Use the inversion integral. + + t = Dummy('t', real=True) + + def pw_simp(*args): + """ Simplify a piecewise expression from hyperexpand. """ + if len(args) != 3: + return Piecewise(*args) + arg = args[2].args[0].argument + coeff, exponent = _get_coeff_exp(arg, t) + e1 = args[0].args[0] + e2 = args[1].args[0] + return ( + Heaviside(1/Abs(coeff) - t**exponent)*e1 + + Heaviside(t**exponent - 1/Abs(coeff))*e2) + + if F.is_rational_function(s): + F = F.apart(s) + + if F.is_Add: + f = Add( + *[_inverse_laplace_transform_integration(X, s, t, plane, simplify) + for X in F.args]) + return _simplify(f.subs(t, t_), simplify), True + + try: + f, cond = inverse_mellin_transform(F, s, exp(-t), (None, S.Infinity), + needeval=True, noconds=False) + except IntegralTransformError: + f = None + + if f is None: + f = meijerint_inversion(F, s, t) + if f is None: + return None + if f.is_Piecewise: + f, cond = f.args[0] + if f.has(Integral): + return None + else: + cond = S.true + f = f.replace(Piecewise, pw_simp) + + if f.is_Piecewise: + # many of the functions called below can't work with piecewise + # (b/c it has a bool in args) + return f.subs(t, t_), cond + + u = Dummy('u') + + def simp_heaviside(arg, H0=S.Half): + a = arg.subs(exp(-t), u) + if a.has(t): + return Heaviside(arg, H0) + from sympy.solvers.inequalities import _solve_inequality + rel = _solve_inequality(a > 0, u) + if rel.lts == u: + k = log(rel.gts) + return Heaviside(t + k, H0) + else: + k = log(rel.lts) + return Heaviside(-(t + k), H0) + + f = f.replace(Heaviside, simp_heaviside) + + def simp_exp(arg): + return expand_complex(exp(arg)) + + f = f.replace(exp, simp_exp) + + return _simplify(f.subs(t, t_), simplify), cond + + +@DEBUG_WRAP +def _complete_the_square_in_denom(f, s): + from sympy.simplify.radsimp import fraction + [n, d] = fraction(f) + if d.is_polynomial(s): + cf = d.as_poly(s).all_coeffs() + if len(cf) == 3: + a, b, c = cf + d = a*((s+b/(2*a))**2+c/a-(b/(2*a))**2) + return n/d + + +@cacheit +def _inverse_laplace_build_rules(): + """ + This is an internal helper function that returns the table of inverse + Laplace transform rules in terms of the time variable `t` and the + frequency variable `s`. It is used by `_inverse_laplace_apply_rules`. + """ + s = Dummy('s') + t = Dummy('t') + a = Wild('a', exclude=[s]) + b = Wild('b', exclude=[s]) + c = Wild('c', exclude=[s]) + + _debug('_inverse_laplace_build_rules is building rules') + + def _frac(f, s): + try: + return f.factor(s) + except PolynomialError: + return f + + def same(f): return f + # This list is sorted according to the prep function needed. + _ILT_rules = [ + (a/s, a, S.true, same, 1), + ( + b*(s+a)**(-c), t**(c-1)*exp(-a*t)/gamma(c), + S.true, same, 1), + (1/(s**2+a**2)**2, (sin(a*t) - a*t*cos(a*t))/(2*a**3), + S.true, same, 1), + # The next two rules must be there in that order. For the second + # one, the condition would be a != 0 or, respectively, to take the + # limit a -> 0 after the transform if a == 0. It is much simpler if + # the case a == 0 has its own rule. + (1/(s**b), t**(b - 1)/gamma(b), S.true, same, 1), + (1/(s*(s+a)**b), lowergamma(b, a*t)/(a**b*gamma(b)), + S.true, same, 1) + ] + return _ILT_rules, s, t + + +@DEBUG_WRAP +def _inverse_laplace_apply_simple_rules(f, s, t): + """ + Helper function for the class InverseLaplaceTransform. + """ + if f == 1: + _debug(' rule: 1 o---o DiracDelta()') + return DiracDelta(t), S.true + + _ILT_rules, s_, t_ = _inverse_laplace_build_rules() + _prep = '' + fsubs = f.subs({s: s_}) + + for s_dom, t_dom, check, prep, fac in _ILT_rules: + if _prep != (prep, fac): + _F = prep(fsubs*fac) + _prep = (prep, fac) + ma = _F.match(s_dom) + if ma: + c = check + if c is not S.true: + args = [x.xreplace(ma) for x in c[0]] + c = c[1](*args) + if c == S.true: + return Heaviside(t)*t_dom.xreplace(ma).subs({t_: t}), S.true + + return None + + +@DEBUG_WRAP +def _inverse_laplace_diff(f, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + a = Wild('a', exclude=[s]) + n = Wild('n', exclude=[s]) + g = Wild('g') + ma = f.match(a*Derivative(g, (s, n))) + if ma and ma[n].is_integer: + _debug(' rule: t**n*f(t) o---o (-1)**n*diff(F(s), s, n)') + r, c = _inverse_laplace_transform( + ma[g], s, t, plane, simplify=False, dorational=False) + return (-t)**ma[n]*r, c + return None + + +@DEBUG_WRAP +def _inverse_laplace_time_shift(F, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + a = Wild('a', exclude=[s]) + g = Wild('g') + + if not F.has(s): + return F*DiracDelta(t), S.true + if not F.has(exp): + return None + + ma1 = F.match(exp(a*s)) + if ma1: + if ma1[a].is_negative: + _debug(' rule: exp(-a*s) o---o DiracDelta(t-a)') + return DiracDelta(t+ma1[a]), S.true + else: + return InverseLaplaceTransform(F, s, t, plane), S.true + + ma1 = F.match(exp(a*s)*g) + if ma1: + if ma1[a].is_negative: + _debug(' rule: exp(-a*s)*F(s) o---o Heaviside(t-a)*f(t-a)') + return _inverse_laplace_transform( + ma1[g], s, t+ma1[a], plane, simplify=False, dorational=True) + else: + return InverseLaplaceTransform(F, s, t, plane), S.true + return None + + +@DEBUG_WRAP +def _inverse_laplace_freq_shift(F, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + if not F.has(s): + return F*DiracDelta(t), S.true + if len(args := F.args) == 1: + a = Wild('a', exclude=[s]) + if (ma := args[0].match(s-a)) and re(ma[a]).is_positive: + _debug(' rule: F(s-a) o---o exp(-a*t)*f(t)') + return ( + exp(-ma[a]*t) * + InverseLaplaceTransform(F.func(s), s, t, plane), S.true) + return None + + +@DEBUG_WRAP +def _inverse_laplace_time_diff(F, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + n = Wild('n', exclude=[s]) + g = Wild('g') + + ma1 = F.match(s**n*g) + if ma1 and ma1[n].is_integer and ma1[n].is_positive: + _debug(' rule: s**n*F(s) o---o diff(f(t), t, n)') + r, c = _inverse_laplace_transform( + ma1[g], s, t, plane, simplify=False, dorational=True) + r = r.replace(Heaviside(t), 1) + if r.has(InverseLaplaceTransform): + return diff(r, t, ma1[n]), c + else: + return Heaviside(t)*diff(r, t, ma1[n]), c + return None + + +@DEBUG_WRAP +def _inverse_laplace_irrational(fn, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + + a = Wild('a', exclude=[s]) + b = Wild('b', exclude=[s]) + m = Wild('m', exclude=[s]) + n = Wild('n', exclude=[s]) + + result = None + condition = S.true + + fa = fn.as_ordered_factors() + + ma = [x.match((a*s**m+b)**n) for x in fa] + + if None in ma: + return None + + constants = S.One + zeros = [] + poles = [] + rest = [] + + for term in ma: + if term[a] == 0: + constants = constants*term + elif term[n].is_positive: + zeros.append(term) + elif term[n].is_negative: + poles.append(term) + else: + rest.append(term) + + # The code below assumes that the poles are sorted in a specific way: + poles = sorted(poles, key=lambda x: (x[n], x[b] != 0, x[b])) + zeros = sorted(zeros, key=lambda x: (x[n], x[b] != 0, x[b])) + + if len(rest) != 0: + return None + + if len(poles) == 1 and len(zeros) == 0: + if poles[0][n] == -1 and poles[0][m] == S.Half: + # 1/(a0*sqrt(s)+b0) == 1/a0 * 1/(sqrt(s)+b0/a0) + a_ = poles[0][b]/poles[0][a] + k_ = 1/poles[0][a]*constants + if a_.is_positive: + result = ( + k_/sqrt(pi)/sqrt(t) - + k_*a_*exp(a_**2*t)*erfc(a_*sqrt(t))) + _debug(' rule 5.3.4') + elif poles[0][n] == -2 and poles[0][m] == S.Half: + # 1/(a0*sqrt(s)+b0)**2 == 1/a0**2 * 1/(sqrt(s)+b0/a0)**2 + a_sq = poles[0][b]/poles[0][a] + a_ = a_sq**2 + k_ = 1/poles[0][a]**2*constants + if a_sq.is_positive: + result = ( + k_*(1 - 2/sqrt(pi)*sqrt(a_)*sqrt(t) + + (1-2*a_*t)*exp(a_*t)*(erf(sqrt(a_)*sqrt(t))-1))) + _debug(' rule 5.3.10') + elif poles[0][n] == -3 and poles[0][m] == S.Half: + # 1/(a0*sqrt(s)+b0)**3 == 1/a0**3 * 1/(sqrt(s)+b0/a0)**3 + a_ = poles[0][b]/poles[0][a] + k_ = 1/poles[0][a]**3*constants + if a_.is_positive: + result = ( + k_*(2/sqrt(pi)*(a_**2*t+1)*sqrt(t) - + a_*t*exp(a_**2*t)*(2*a_**2*t+3)*erfc(a_*sqrt(t)))) + _debug(' rule 5.3.13') + elif poles[0][n] == -4 and poles[0][m] == S.Half: + # 1/(a0*sqrt(s)+b0)**4 == 1/a0**4 * 1/(sqrt(s)+b0/a0)**4 + a_ = poles[0][b]/poles[0][a] + k_ = 1/poles[0][a]**4*constants/3 + if a_.is_positive: + result = ( + k_*(t*(4*a_**4*t**2+12*a_**2*t+3)*exp(a_**2*t) * + erfc(a_*sqrt(t)) - + 2/sqrt(pi)*a_**3*t**(S(5)/2)*(2*a_**2*t+5))) + _debug(' rule 5.3.16') + elif poles[0][n] == -S.Half and poles[0][m] == 2: + # 1/sqrt(a0*s**2+b0) == 1/sqrt(a0) * 1/sqrt(s**2+b0/a0) + a_ = sqrt(poles[0][b]/poles[0][a]) + k_ = 1/sqrt(poles[0][a])*constants + result = (k_*(besselj(0, a_*t))) + _debug(' rule 5.3.35/44') + + elif len(poles) == 1 and len(zeros) == 1: + if ( + poles[0][n] == -3 and poles[0][m] == S.Half and + zeros[0][n] == S.Half and zeros[0][b] == 0): + # sqrt(az*s)/(ap*sqrt(s+bp)**3) + # == sqrt(az)/ap * sqrt(s)/(sqrt(s+bp)**3) + a_ = poles[0][b] + k_ = sqrt(zeros[0][a])/poles[0][a]*constants + result = ( + k_*(2*a_**4*t**2+5*a_**2*t+1)*exp(a_**2*t) * + erfc(a_*sqrt(t)) - 2/sqrt(pi)*a_*(a_**2*t+2)*sqrt(t)) + _debug(' rule 5.3.14') + if ( + poles[0][n] == -1 and poles[0][m] == 1 and + zeros[0][n] == S.Half and zeros[0][m] == 1): + # sqrt(az*s+bz)/(ap*s+bp) + # == sqrt(az)/ap * (sqrt(s+bz/az)/(s+bp/ap)) + a_ = zeros[0][b]/zeros[0][a] + b_ = poles[0][b]/poles[0][a] + k_ = sqrt(zeros[0][a])/poles[0][a]*constants + result = ( + k_*(exp(-a_*t)/sqrt(t)/sqrt(pi)+sqrt(a_-b_) * + exp(-b_*t)*erf(sqrt(a_-b_)*sqrt(t)))) + _debug(' rule 5.3.22') + + elif len(poles) == 2 and len(zeros) == 0: + if ( + poles[0][n] == -1 and poles[0][m] == 1 and + poles[1][n] == -S.Half and poles[1][m] == 1 and + poles[1][b] == 0): + # 1/((a0*s+b0)*sqrt(a1*s)) + # == 1/(a0*sqrt(a1)) * 1/((s+b0/a0)*sqrt(s)) + a_ = -poles[0][b]/poles[0][a] + k_ = 1/sqrt(poles[1][a])/poles[0][a]*constants + if a_.is_positive: + result = (k_/sqrt(a_)*exp(a_*t)*erf(sqrt(a_)*sqrt(t))) + _debug(' rule 5.3.1') + elif ( + poles[0][n] == -1 and poles[0][m] == 1 and poles[0][b] == 0 and + poles[1][n] == -1 and poles[1][m] == S.Half): + # 1/(a0*s*(a1*sqrt(s)+b1)) + # == 1/(a0*a1) * 1/(s*(sqrt(s)+b1/a1)) + a_ = poles[1][b]/poles[1][a] + k_ = 1/poles[0][a]/poles[1][a]/a_*constants + if a_.is_positive: + result = k_*(1-exp(a_**2*t)*erfc(a_*sqrt(t))) + _debug(' rule 5.3.5') + elif ( + poles[0][n] == -1 and poles[0][m] == S.Half and + poles[1][n] == -S.Half and poles[1][m] == 1 and + poles[1][b] == 0): + # 1/((a0*sqrt(s)+b0)*(sqrt(a1*s)) + # == 1/(a0*sqrt(a1)) * 1/((sqrt(s)+b0/a0)"sqrt(s)) + a_ = poles[0][b]/poles[0][a] + k_ = 1/(poles[0][a]*sqrt(poles[1][a]))*constants + if a_.is_positive: + result = k_*exp(a_**2*t)*erfc(a_*sqrt(t)) + _debug(' rule 5.3.7') + elif ( + poles[0][n] == -S(3)/2 and poles[0][m] == 1 and + poles[0][b] == 0 and poles[1][n] == -1 and + poles[1][m] == S.Half): + # 1/((a0**(3/2)*s**(3/2))*(a1*sqrt(s)+b1)) + # == 1/(a0**(3/2)*a1) 1/((s**(3/2))*(sqrt(s)+b1/a1)) + # Note that Bateman54 5.3 (8) is incorrect; there (sqrt(p)+a) + # should be (sqrt(p)+a)**(-1). + a_ = poles[1][b]/poles[1][a] + k_ = 1/(poles[0][a]**(S(3)/2)*poles[1][a])/a_**2*constants + if a_.is_positive: + result = ( + k_*(2/sqrt(pi)*a_*sqrt(t)+exp(a_**2*t)*erfc(a_*sqrt(t))-1)) + _debug(' rule 5.3.8') + elif ( + poles[0][n] == -2 and poles[0][m] == S.Half and + poles[1][n] == -1 and poles[1][m] == 1 and + poles[1][b] == 0): + # 1/((a0*sqrt(s)+b0)**2*a1*s) + # == 1/a0**2/a1 * 1/(sqrt(s)+b0/a0)**2/s + a_sq = poles[0][b]/poles[0][a] + a_ = a_sq**2 + k_ = 1/poles[0][a]**2/poles[1][a]*constants + if a_sq.is_positive: + result = ( + k_*(1/a_ + (2*t-1/a_)*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) - + 2/sqrt(pi)/sqrt(a_)*sqrt(t))) + _debug(' rule 5.3.11') + elif ( + poles[0][n] == -2 and poles[0][m] == S.Half and + poles[1][n] == -S.Half and poles[1][m] == 1 and + poles[1][b] == 0): + # 1/((a0*sqrt(s)+b0)**2*sqrt(a1*s)) + # == 1/a0**2/sqrt(a1) * 1/(sqrt(s)+b0/a0)**2/sqrt(s) + a_ = poles[0][b]/poles[0][a] + k_ = 1/poles[0][a]**2/sqrt(poles[1][a])*constants + if a_.is_positive: + result = ( + k_*(2/sqrt(pi)*sqrt(t) - + 2*a_*t*exp(a_**2*t)*erfc(a_*sqrt(t)))) + _debug(' rule 5.3.12') + elif ( + poles[0][n] == -3 and poles[0][m] == S.Half and + poles[1][n] == -S.Half and poles[1][m] == 1 and + poles[1][b] == 0): + # 1 / (sqrt(a1*s)*(a0*sqrt(s+b0)**3)) + # == 1/(sqrt(a1)*a0) * 1/(sqrt(s)*(sqrt(s+b0)**3)) + a_ = poles[0][b] + k_ = constants/sqrt(poles[1][a])/poles[0][a] + result = k_*( + (2*a_**2*t+1)*t*exp(a_**2*t)*erfc(a_*sqrt(t)) - + 2/sqrt(pi)*a_*t**(S(3)/2)) + _debug(' rule 5.3.15') + elif ( + poles[0][n] == -1 and poles[0][m] == 1 and + poles[1][n] == -S.Half and poles[1][m] == 1): + # 1 / ( (a0*s+b0)* sqrt(a1*s+b1) ) + # == 1/(sqrt(a1)*a0) * 1 / ( (s+b0/a0)* sqrt(s+b1/a1) ) + a_ = poles[0][b]/poles[0][a] + b_ = poles[1][b]/poles[1][a] + k_ = constants/sqrt(poles[1][a])/poles[0][a] + result = k_*( + 1/sqrt(b_-a_)*exp(-a_*t)*erf(sqrt(b_-a_)*sqrt(t))) + _debug(' rule 5.3.23') + + elif len(poles) == 2 and len(zeros) == 1: + if ( + poles[0][n] == -1 and poles[0][m] == 1 and + poles[1][n] == -1 and poles[1][m] == S.Half and + zeros[0][n] == S.Half and zeros[0][m] == 1 and + zeros[0][b] == 0): + # sqrt(za0*s)/((a0*s+b0)*(a1*sqrt(s)+b1)) + # == sqrt(za0)/(a0*a1) * s/((s+b0/a0)*(sqrt(s)+b1/a1)) + a_sq = poles[1][b]/poles[1][a] + a_ = a_sq**2 + b_ = -poles[0][b]/poles[0][a] + k_ = sqrt(zeros[0][a])/poles[0][a]/poles[1][a]/(a_-b_)*constants + if a_sq.is_positive and b_.is_positive: + result = k_*( + a_*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) + + sqrt(a_)*sqrt(b_)*exp(b_*t)*erfc(sqrt(b_)*sqrt(t)) - + b_*exp(b_*t)) + _debug(' rule 5.3.6') + elif ( + poles[0][n] == -1 and poles[0][m] == 1 and + poles[0][b] == 0 and poles[1][n] == -1 and + poles[1][m] == S.Half and zeros[0][n] == 1 and + zeros[0][m] == S.Half): + # (az*sqrt(s)+bz)/(a0*s*(a1*sqrt(s)+b1)) + # == az/a0/a1 * (sqrt(z)+bz/az)/(s*(sqrt(s)+b1/a1)) + a_num = zeros[0][b]/zeros[0][a] + a_ = poles[1][b]/poles[1][a] + if a_+a_num == 0: + k_ = zeros[0][a]/poles[0][a]/poles[1][a]*constants + result = k_*( + 2*exp(a_**2*t)*erfc(a_*sqrt(t))-1) + _debug(' rule 5.3.17') + elif ( + poles[1][n] == -1 and poles[1][m] == 1 and + poles[1][b] == 0 and poles[0][n] == -2 and + poles[0][m] == S.Half and zeros[0][n] == 2 and + zeros[0][m] == S.Half): + # (az*sqrt(s)+bz)**2/(a1*s*(a0*sqrt(s)+b0)**2) + # == az**2/a1/a0**2 * (sqrt(z)+bz/az)**2/(s*(sqrt(s)+b0/a0)**2) + a_num = zeros[0][b]/zeros[0][a] + a_ = poles[0][b]/poles[0][a] + if a_+a_num == 0: + k_ = zeros[0][a]**2/poles[1][a]/poles[0][a]**2*constants + result = k_*( + 1 + 8*a_**2*t*exp(a_**2*t)*erfc(a_*sqrt(t)) - + 8/sqrt(pi)*a_*sqrt(t)) + _debug(' rule 5.3.18') + elif ( + poles[1][n] == -1 and poles[1][m] == 1 and + poles[1][b] == 0 and poles[0][n] == -3 and + poles[0][m] == S.Half and zeros[0][n] == 3 and + zeros[0][m] == S.Half): + # (az*sqrt(s)+bz)**3/(a1*s*(a0*sqrt(s)+b0)**3) + # == az**3/a1/a0**3 * (sqrt(z)+bz/az)**3/(s*(sqrt(s)+b0/a0)**3) + a_num = zeros[0][b]/zeros[0][a] + a_ = poles[0][b]/poles[0][a] + if a_+a_num == 0: + k_ = zeros[0][a]**3/poles[1][a]/poles[0][a]**3*constants + result = k_*( + 2*(8*a_**4*t**2+8*a_**2*t+1)*exp(a_**2*t) * + erfc(a_*sqrt(t))-8/sqrt(pi)*a_*sqrt(t)*(2*a_**2*t+1)-1) + _debug(' rule 5.3.19') + + elif len(poles) == 3 and len(zeros) == 0: + if ( + poles[0][n] == -1 and poles[0][b] == 0 and poles[0][m] == 1 and + poles[1][n] == -1 and poles[1][m] == 1 and + poles[2][n] == -S.Half and poles[2][m] == 1): + # 1/((a0*s)*(a1*s+b1)*sqrt(a2*s)) + # == 1/(a0*a1*sqrt(a2)) * 1/((s)*(s+b1/a1)*sqrt(s)) + a_ = -poles[1][b]/poles[1][a] + k_ = 1/poles[0][a]/poles[1][a]/sqrt(poles[2][a])*constants + if a_.is_positive: + result = k_ * ( + a_**(-S(3)/2) * exp(a_*t) * erf(sqrt(a_)*sqrt(t)) - + 2/a_/sqrt(pi)*sqrt(t)) + _debug(' rule 5.3.2') + elif ( + poles[0][n] == -1 and poles[0][m] == 1 and + poles[1][n] == -1 and poles[1][m] == S.Half and + poles[2][n] == -S.Half and poles[2][m] == 1 and + poles[2][b] == 0): + # 1/((a0*s+b0)*(a1*sqrt(s)+b1)*(sqrt(a2)*sqrt(s))) + # == 1/(a0*a1*sqrt(a2)) * 1/((s+b0/a0)*(sqrt(s)+b1/a1)*sqrt(s)) + a_sq = poles[1][b]/poles[1][a] + a_ = a_sq**2 + b_ = -poles[0][b]/poles[0][a] + k_ = ( + 1/poles[0][a]/poles[1][a]/sqrt(poles[2][a]) / + (sqrt(b_)*(a_-b_))) + if a_sq.is_positive and b_.is_positive: + result = k_ * ( + sqrt(b_)*exp(a_*t)*erfc(sqrt(a_)*sqrt(t)) + + sqrt(a_)*exp(b_*t)*erf(sqrt(b_)*sqrt(t)) - + sqrt(b_)*exp(b_*t)) + _debug(' rule 5.3.9') + + if result is None: + return None + else: + return Heaviside(t)*result, condition + + +@DEBUG_WRAP +def _inverse_laplace_early_prog_rules(F, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + prog_rules = [_inverse_laplace_irrational] + + for p_rule in prog_rules: + if (r := p_rule(F, s, t, plane)) is not None: + return r + return None + + +@DEBUG_WRAP +def _inverse_laplace_apply_prog_rules(F, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + prog_rules = [_inverse_laplace_time_shift, _inverse_laplace_freq_shift, + _inverse_laplace_time_diff, _inverse_laplace_diff, + _inverse_laplace_irrational] + + for p_rule in prog_rules: + if (r := p_rule(F, s, t, plane)) is not None: + return r + return None + + +@DEBUG_WRAP +def _inverse_laplace_expand(fn, s, t, plane): + """ + Helper function for the class InverseLaplaceTransform. + """ + if fn.is_Add: + return None + r = expand(fn, deep=False) + if r.is_Add: + return _inverse_laplace_transform( + r, s, t, plane, simplify=False, dorational=True) + r = expand_mul(fn) + if r.is_Add: + return _inverse_laplace_transform( + r, s, t, plane, simplify=False, dorational=True) + r = expand(fn) + if r.is_Add: + return _inverse_laplace_transform( + r, s, t, plane, simplify=False, dorational=True) + if fn.is_rational_function(s): + r = fn.apart(s).doit() + if r.is_Add: + return _inverse_laplace_transform( + r, s, t, plane, simplify=False, dorational=True) + return None + + +@DEBUG_WRAP +def _inverse_laplace_rational(fn, s, t, plane, *, simplify): + """ + Helper function for the class InverseLaplaceTransform. + """ + x_ = symbols('x_') + f = fn.apart(s) + terms = Add.make_args(f) + terms_t = [] + conditions = [S.true] + for term in terms: + [n, d] = term.as_numer_denom() + dc = d.as_poly(s).all_coeffs() + dc_lead = dc[0] + dc = [x/dc_lead for x in dc] + nc = [x/dc_lead for x in n.as_poly(s).all_coeffs()] + if len(dc) == 1: + r = nc[0]*DiracDelta(t) + terms_t.append(r) + elif len(dc) == 2: + r = nc[0]*exp(-dc[1]*t) + terms_t.append(Heaviside(t)*r) + elif len(dc) == 3: + a = dc[1]/2 + b = (dc[2]-a**2).factor() + if len(nc) == 1: + nc = [S.Zero] + nc + l, m = tuple(nc) + if b == 0: + r = (m*t+l*(1-a*t))*exp(-a*t) + else: + hyp = False + if b.is_negative: + b = -b + hyp = True + b2 = list(roots(x_**2-b, x_).keys())[0] + bs = sqrt(b).simplify() + if hyp: + r = ( + l*exp(-a*t)*cosh(b2*t) + (m-a*l) / + bs*exp(-a*t)*sinh(bs*t)) + else: + r = l*exp(-a*t)*cos(b2*t) + (m-a*l)/bs*exp(-a*t)*sin(bs*t) + terms_t.append(Heaviside(t)*r) + else: + ft, cond = _inverse_laplace_transform( + term, s, t, plane, simplify=simplify, dorational=False) + terms_t.append(ft) + conditions.append(cond) + + result = Add(*terms_t) + if simplify: + result = result.simplify(doit=False) + return result, And(*conditions) + + +@DEBUG_WRAP +def _inverse_laplace_transform(fn, s_, t_, plane, *, simplify, dorational): + """ + Front-end function of the inverse Laplace transform. It tries to apply all + known rules recursively. If everything else fails, it tries to integrate. + """ + terms = Add.make_args(fn) + terms_t = [] + conditions = [] + + for term in terms: + if term.has(exp): + # Simplify expressions with exp() such that time-shifted + # expressions have negative exponents in the numerator instead of + # positive exponents in the numerator and denominator; this is a + # (necessary) trick. It will, for example, convert + # (s**2*exp(2*s) + 4*exp(s) - 4)*exp(-2*s)/(s*(s**2 + 1)) into + # (s**2 + 4*exp(-s) - 4*exp(-2*s))/(s*(s**2 + 1)) + term = term.subs(s_, -s_).together().subs(s_, -s_) + k, f = term.as_independent(s_, as_Add=False) + if ( + dorational and term.is_rational_function(s_) and + (r := _inverse_laplace_rational( + f, s_, t_, plane, simplify=simplify)) + is not None or + (r := _inverse_laplace_apply_simple_rules(f, s_, t_)) + is not None or + (r := _inverse_laplace_early_prog_rules(f, s_, t_, plane)) + is not None or + (r := _inverse_laplace_expand(f, s_, t_, plane)) + is not None or + (r := _inverse_laplace_apply_prog_rules(f, s_, t_, plane)) + is not None): + pass + elif any(undef.has(s_) for undef in f.atoms(AppliedUndef)): + # If there are undefined functions f(t) then integration is + # unlikely to do anything useful so we skip it and given an + # unevaluated LaplaceTransform. + r = (InverseLaplaceTransform(f, s_, t_, plane), S.true) + elif ( + r := _inverse_laplace_transform_integration( + f, s_, t_, plane, simplify=simplify)) is not None: + pass + else: + r = (InverseLaplaceTransform(f, s_, t_, plane), S.true) + (ri_, ci_) = r + terms_t.append(k*ri_) + conditions.append(ci_) + + result = Add(*terms_t) + if simplify: + result = result.simplify(doit=False) + condition = And(*conditions) + + return result, condition + + +class InverseLaplaceTransform(IntegralTransform): + """ + Class representing unevaluated inverse Laplace transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse Laplace transforms, see the + :func:`inverse_laplace_transform` docstring. + """ + + _name = 'Inverse Laplace' + _none_sentinel = Dummy('None') + _c = Dummy('c') + + def __new__(cls, F, s, x, plane, **opts): + if plane is None: + plane = InverseLaplaceTransform._none_sentinel + return IntegralTransform.__new__(cls, F, s, x, plane, **opts) + + @property + def fundamental_plane(self): + plane = self.args[3] + if plane is InverseLaplaceTransform._none_sentinel: + plane = None + return plane + + def _compute_transform(self, F, s, t, **hints): + return _inverse_laplace_transform_integration( + F, s, t, self.fundamental_plane, **hints) + + def _as_integral(self, F, s, t): + c = self.__class__._c + return ( + Integral(exp(s*t)*F, (s, c - S.ImaginaryUnit*S.Infinity, + c + S.ImaginaryUnit*S.Infinity)) / + (2*S.Pi*S.ImaginaryUnit)) + + def doit(self, **hints): + """ + Try to evaluate the transform in closed form. + + Explanation + =========== + + Standard hints are the following: + - ``noconds``: if True, do not return convergence conditions. The + default setting is `True`. + - ``simplify``: if True, it simplifies the final result. The + default setting is `False`. + """ + _noconds = hints.get('noconds', True) + _simplify = hints.get('simplify', False) + + debugf('[ILT doit] (%s, %s, %s)', (self.function, + self.function_variable, + self.transform_variable)) + + s_ = self.function_variable + t_ = self.transform_variable + fn = self.function + plane = self.fundamental_plane + + r = _inverse_laplace_transform( + fn, s_, t_, plane, simplify=_simplify, dorational=True) + + if _noconds: + return r[0] + else: + return r + + +def inverse_laplace_transform(F, s, t, plane=None, **hints): + r""" + Compute the inverse Laplace transform of `F(s)`, defined as + + .. math :: + f(t) = \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} e^{st} + F(s) \mathrm{d}s, + + for `c` so large that `F(s)` has no singularites in the + half-plane `\operatorname{Re}(s) > c-\epsilon`. + + Explanation + =========== + + The plane can be specified by + argument ``plane``, but will be inferred if passed as None. + + Under certain regularity conditions, this recovers `f(t)` from its + Laplace Transform `F(s)`, for non-negative `t`, and vice + versa. + + If the integral cannot be computed in closed form, this function returns + an unevaluated :class:`InverseLaplaceTransform` object. + + Note that this function will always assume `t` to be real, + regardless of the SymPy assumption on `t`. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + + Examples + ======== + + >>> from sympy import inverse_laplace_transform, exp, Symbol + >>> from sympy.abc import s, t + >>> a = Symbol('a', positive=True) + >>> inverse_laplace_transform(exp(-a*s)/s, s, t) + Heaviside(-a + t) + + See Also + ======== + + laplace_transform + hankel_transform, inverse_hankel_transform + """ + _noconds = hints.get('noconds', True) + _simplify = hints.get('simplify', False) + + if isinstance(F, MatrixBase) and hasattr(F, 'applyfunc'): + return F.applyfunc( + lambda Fij: inverse_laplace_transform(Fij, s, t, plane, **hints)) + + r, c = InverseLaplaceTransform(F, s, t, plane).doit( + noconds=False, simplify=_simplify) + + if _noconds: + return r + else: + return r, c + + +def _fast_inverse_laplace(e, s, t): + """Fast inverse Laplace transform of rational function including RootSum""" + a, b, n = symbols('a, b, n', cls=Wild, exclude=[s]) + + def _ilt(e): + if not e.has(s): + return e + elif e.is_Add: + return _ilt_add(e) + elif e.is_Mul: + return _ilt_mul(e) + elif e.is_Pow: + return _ilt_pow(e) + elif isinstance(e, RootSum): + return _ilt_rootsum(e) + else: + raise NotImplementedError + + def _ilt_add(e): + return e.func(*map(_ilt, e.args)) + + def _ilt_mul(e): + coeff, expr = e.as_independent(s) + if expr.is_Mul: + raise NotImplementedError + return coeff * _ilt(expr) + + def _ilt_pow(e): + match = e.match((a*s + b)**n) + if match is not None: + nm, am, bm = match[n], match[a], match[b] + if nm.is_Integer and nm < 0: + return t**(-nm-1)*exp(-(bm/am)*t)/(am**-nm*gamma(-nm)) + if nm == 1: + return exp(-(bm/am)*t) / am + raise NotImplementedError + + def _ilt_rootsum(e): + expr = e.fun.expr + [variable] = e.fun.variables + return RootSum(e.poly, Lambda(variable, together(_ilt(expr)))) + + return _ilt(e) diff --git a/lib/python3.11/site-packages/sympy/integrals/manualintegrate.py b/lib/python3.11/site-packages/sympy/integrals/manualintegrate.py new file mode 100644 index 0000000000000000000000000000000000000000..2e0789349ca84da3ef1f08bf2603cb05868e4473 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/manualintegrate.py @@ -0,0 +1,2174 @@ +"""Integration method that emulates by-hand techniques. + +This module also provides functionality to get the steps used to evaluate a +particular integral, in the ``integral_steps`` function. This will return +nested ``Rule`` s representing the integration rules used. + +Each ``Rule`` class represents a (maybe parametrized) integration rule, e.g. +``SinRule`` for integrating ``sin(x)`` and ``ReciprocalSqrtQuadraticRule`` +for integrating ``1/sqrt(a+b*x+c*x**2)``. The ``eval`` method returns the +integration result. + +The ``manualintegrate`` function computes the integral by calling ``eval`` +on the rule returned by ``integral_steps``. + +The integrator can be extended with new heuristics and evaluation +techniques. To do so, extend the ``Rule`` class, implement ``eval`` method, +then write a function that accepts an ``IntegralInfo`` object and returns +either a ``Rule`` instance or ``None``. If the new technique requires a new +match, add the key and call to the antiderivative function to integral_steps. +To enable simple substitutions, add the match to find_substitutions. + +""" + +from __future__ import annotations +from typing import NamedTuple, Type, Callable, Sequence +from abc import ABC, abstractmethod +from dataclasses import dataclass +from collections import defaultdict +from collections.abc import Mapping + +from sympy.core.add import Add +from sympy.core.cache import cacheit +from sympy.core.containers import Dict +from sympy.core.expr import Expr +from sympy.core.function import Derivative +from sympy.core.logic import fuzzy_not +from sympy.core.mul import Mul +from sympy.core.numbers import Integer, Number, E +from sympy.core.power import Pow +from sympy.core.relational import Eq, Ne, Boolean +from sympy.core.singleton import S +from sympy.core.symbol import Dummy, Symbol, Wild +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.hyperbolic import (HyperbolicFunction, csch, + cosh, coth, sech, sinh, tanh, asinh) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (TrigonometricFunction, + cos, sin, tan, cot, csc, sec, acos, asin, atan, acot, acsc, asec) +from sympy.functions.special.delta_functions import Heaviside, DiracDelta +from sympy.functions.special.error_functions import (erf, erfi, fresnelc, + fresnels, Ci, Chi, Si, Shi, Ei, li) +from sympy.functions.special.gamma_functions import uppergamma +from sympy.functions.special.elliptic_integrals import elliptic_e, elliptic_f +from sympy.functions.special.polynomials import (chebyshevt, chebyshevu, + legendre, hermite, laguerre, assoc_laguerre, gegenbauer, jacobi, + OrthogonalPolynomial) +from sympy.functions.special.zeta_functions import polylog +from .integrals import Integral +from sympy.logic.boolalg import And +from sympy.ntheory.factor_ import primefactors +from sympy.polys.polytools import degree, lcm_list, gcd_list, Poly +from sympy.simplify.radsimp import fraction +from sympy.simplify.simplify import simplify +from sympy.solvers.solvers import solve +from sympy.strategies.core import switch, do_one, null_safe, condition +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import debug + + +@dataclass +class Rule(ABC): + integrand: Expr + variable: Symbol + + @abstractmethod + def eval(self) -> Expr: + pass + + @abstractmethod + def contains_dont_know(self) -> bool: + pass + + +@dataclass +class AtomicRule(Rule, ABC): + """A simple rule that does not depend on other rules""" + def contains_dont_know(self) -> bool: + return False + + +@dataclass +class ConstantRule(AtomicRule): + """integrate(a, x) -> a*x""" + def eval(self) -> Expr: + return self.integrand * self.variable + + +@dataclass +class ConstantTimesRule(Rule): + """integrate(a*f(x), x) -> a*integrate(f(x), x)""" + constant: Expr + other: Expr + substep: Rule + + def eval(self) -> Expr: + return self.constant * self.substep.eval() + + def contains_dont_know(self) -> bool: + return self.substep.contains_dont_know() + + +@dataclass +class PowerRule(AtomicRule): + """integrate(x**a, x)""" + base: Expr + exp: Expr + + def eval(self) -> Expr: + return Piecewise( + ((self.base**(self.exp + 1))/(self.exp + 1), Ne(self.exp, -1)), + (log(self.base), True), + ) + + +@dataclass +class NestedPowRule(AtomicRule): + """integrate((x**a)**b, x)""" + base: Expr + exp: Expr + + def eval(self) -> Expr: + m = self.base * self.integrand + return Piecewise((m / (self.exp + 1), Ne(self.exp, -1)), + (m * log(self.base), True)) + + +@dataclass +class AddRule(Rule): + """integrate(f(x) + g(x), x) -> integrate(f(x), x) + integrate(g(x), x)""" + substeps: list[Rule] + + def eval(self) -> Expr: + return Add(*(substep.eval() for substep in self.substeps)) + + def contains_dont_know(self) -> bool: + return any(substep.contains_dont_know() for substep in self.substeps) + + +@dataclass +class URule(Rule): + """integrate(f(g(x))*g'(x), x) -> integrate(f(u), u), u = g(x)""" + u_var: Symbol + u_func: Expr + substep: Rule + + def eval(self) -> Expr: + result = self.substep.eval() + if self.u_func.is_Pow: + base, exp_ = self.u_func.as_base_exp() + if exp_ == -1: + # avoid needless -log(1/x) from substitution + result = result.subs(log(self.u_var), -log(base)) + return result.subs(self.u_var, self.u_func) + + def contains_dont_know(self) -> bool: + return self.substep.contains_dont_know() + + +@dataclass +class PartsRule(Rule): + """integrate(u(x)*v'(x), x) -> u(x)*v(x) - integrate(u'(x)*v(x), x)""" + u: Symbol + dv: Expr + v_step: Rule + second_step: Rule | None # None when is a substep of CyclicPartsRule + + def eval(self) -> Expr: + assert self.second_step is not None + v = self.v_step.eval() + return self.u * v - self.second_step.eval() + + def contains_dont_know(self) -> bool: + return self.v_step.contains_dont_know() or ( + self.second_step is not None and self.second_step.contains_dont_know()) + + +@dataclass +class CyclicPartsRule(Rule): + """Apply PartsRule multiple times to integrate exp(x)*sin(x)""" + parts_rules: list[PartsRule] + coefficient: Expr + + def eval(self) -> Expr: + result = [] + sign = 1 + for rule in self.parts_rules: + result.append(sign * rule.u * rule.v_step.eval()) + sign *= -1 + return Add(*result) / (1 - self.coefficient) + + def contains_dont_know(self) -> bool: + return any(substep.contains_dont_know() for substep in self.parts_rules) + + +@dataclass +class TrigRule(AtomicRule, ABC): + pass + + +@dataclass +class SinRule(TrigRule): + """integrate(sin(x), x) -> -cos(x)""" + def eval(self) -> Expr: + return -cos(self.variable) + + +@dataclass +class CosRule(TrigRule): + """integrate(cos(x), x) -> sin(x)""" + def eval(self) -> Expr: + return sin(self.variable) + + +@dataclass +class SecTanRule(TrigRule): + """integrate(sec(x)*tan(x), x) -> sec(x)""" + def eval(self) -> Expr: + return sec(self.variable) + + +@dataclass +class CscCotRule(TrigRule): + """integrate(csc(x)*cot(x), x) -> -csc(x)""" + def eval(self) -> Expr: + return -csc(self.variable) + + +@dataclass +class Sec2Rule(TrigRule): + """integrate(sec(x)**2, x) -> tan(x)""" + def eval(self) -> Expr: + return tan(self.variable) + + +@dataclass +class Csc2Rule(TrigRule): + """integrate(csc(x)**2, x) -> -cot(x)""" + def eval(self) -> Expr: + return -cot(self.variable) + + +@dataclass +class HyperbolicRule(AtomicRule, ABC): + pass + + +@dataclass +class SinhRule(HyperbolicRule): + """integrate(sinh(x), x) -> cosh(x)""" + def eval(self) -> Expr: + return cosh(self.variable) + + +@dataclass +class CoshRule(HyperbolicRule): + """integrate(cosh(x), x) -> sinh(x)""" + def eval(self): + return sinh(self.variable) + + +@dataclass +class ExpRule(AtomicRule): + """integrate(a**x, x) -> a**x/ln(a)""" + base: Expr + exp: Expr + + def eval(self) -> Expr: + return self.integrand / log(self.base) + + +@dataclass +class ReciprocalRule(AtomicRule): + """integrate(1/x, x) -> ln(x)""" + base: Expr + + def eval(self) -> Expr: + return log(self.base) + + +@dataclass +class ArcsinRule(AtomicRule): + """integrate(1/sqrt(1-x**2), x) -> asin(x)""" + def eval(self) -> Expr: + return asin(self.variable) + + +@dataclass +class ArcsinhRule(AtomicRule): + """integrate(1/sqrt(1+x**2), x) -> asin(x)""" + def eval(self) -> Expr: + return asinh(self.variable) + + +@dataclass +class ReciprocalSqrtQuadraticRule(AtomicRule): + """integrate(1/sqrt(a+b*x+c*x**2), x) -> log(2*sqrt(c)*sqrt(a+b*x+c*x**2)+b+2*c*x)/sqrt(c)""" + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + a, b, c, x = self.a, self.b, self.c, self.variable + return log(2*sqrt(c)*sqrt(a+b*x+c*x**2)+b+2*c*x)/sqrt(c) + + +@dataclass +class SqrtQuadraticDenomRule(AtomicRule): + """integrate(poly(x)/sqrt(a+b*x+c*x**2), x)""" + a: Expr + b: Expr + c: Expr + coeffs: list[Expr] + + def eval(self) -> Expr: + a, b, c, coeffs, x = self.a, self.b, self.c, self.coeffs.copy(), self.variable + # Integrate poly/sqrt(a+b*x+c*x**2) using recursion. + # coeffs are coefficients of the polynomial. + # Let I_n = x**n/sqrt(a+b*x+c*x**2), then + # I_n = A * x**(n-1)*sqrt(a+b*x+c*x**2) - B * I_{n-1} - C * I_{n-2} + # where A = 1/(n*c), B = (2*n-1)*b/(2*n*c), C = (n-1)*a/(n*c) + # See https://github.com/sympy/sympy/pull/23608 for proof. + result_coeffs = [] + coeffs = coeffs.copy() + for i in range(len(coeffs)-2): + n = len(coeffs)-1-i + coeff = coeffs[i]/(c*n) + result_coeffs.append(coeff) + coeffs[i+1] -= (2*n-1)*b/2*coeff + coeffs[i+2] -= (n-1)*a*coeff + d, e = coeffs[-1], coeffs[-2] + s = sqrt(a+b*x+c*x**2) + constant = d-b*e/(2*c) + if constant == 0: + I0 = 0 + else: + step = inverse_trig_rule(IntegralInfo(1/s, x), degenerate=False) + I0 = constant*step.eval() + return Add(*(result_coeffs[i]*x**(len(coeffs)-2-i) + for i in range(len(result_coeffs))), e/c)*s + I0 + + +@dataclass +class SqrtQuadraticRule(AtomicRule): + """integrate(sqrt(a+b*x+c*x**2), x)""" + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + step = sqrt_quadratic_rule(IntegralInfo(self.integrand, self.variable), degenerate=False) + return step.eval() + + +@dataclass +class AlternativeRule(Rule): + """Multiple ways to do integration.""" + alternatives: list[Rule] + + def eval(self) -> Expr: + return self.alternatives[0].eval() + + def contains_dont_know(self) -> bool: + return any(substep.contains_dont_know() for substep in self.alternatives) + + +@dataclass +class DontKnowRule(Rule): + """Leave the integral as is.""" + def eval(self) -> Expr: + return Integral(self.integrand, self.variable) + + def contains_dont_know(self) -> bool: + return True + + +@dataclass +class DerivativeRule(AtomicRule): + """integrate(f'(x), x) -> f(x)""" + def eval(self) -> Expr: + assert isinstance(self.integrand, Derivative) + variable_count = list(self.integrand.variable_count) + for i, (var, count) in enumerate(variable_count): + if var == self.variable: + variable_count[i] = (var, count - 1) + break + return Derivative(self.integrand.expr, *variable_count) + + +@dataclass +class RewriteRule(Rule): + """Rewrite integrand to another form that is easier to handle.""" + rewritten: Expr + substep: Rule + + def eval(self) -> Expr: + return self.substep.eval() + + def contains_dont_know(self) -> bool: + return self.substep.contains_dont_know() + + +@dataclass +class CompleteSquareRule(RewriteRule): + """Rewrite a+b*x+c*x**2 to a-b**2/(4*c) + c*(x+b/(2*c))**2""" + pass + + +@dataclass +class PiecewiseRule(Rule): + subfunctions: Sequence[tuple[Rule, bool | Boolean]] + + def eval(self) -> Expr: + return Piecewise(*[(substep.eval(), cond) + for substep, cond in self.subfunctions]) + + def contains_dont_know(self) -> bool: + return any(substep.contains_dont_know() for substep, _ in self.subfunctions) + + +@dataclass +class HeavisideRule(Rule): + harg: Expr + ibnd: Expr + substep: Rule + + def eval(self) -> Expr: + # If we are integrating over x and the integrand has the form + # Heaviside(m*x+b)*g(x) == Heaviside(harg)*g(symbol) + # then there needs to be continuity at -b/m == ibnd, + # so we subtract the appropriate term. + result = self.substep.eval() + return Heaviside(self.harg) * (result - result.subs(self.variable, self.ibnd)) + + def contains_dont_know(self) -> bool: + return self.substep.contains_dont_know() + + +@dataclass +class DiracDeltaRule(AtomicRule): + n: Expr + a: Expr + b: Expr + + def eval(self) -> Expr: + n, a, b, x = self.n, self.a, self.b, self.variable + if n == 0: + return Heaviside(a+b*x)/b + return DiracDelta(a+b*x, n-1)/b + + +@dataclass +class TrigSubstitutionRule(Rule): + theta: Expr + func: Expr + rewritten: Expr + substep: Rule + restriction: bool | Boolean + + def eval(self) -> Expr: + theta, func, x = self.theta, self.func, self.variable + func = func.subs(sec(theta), 1/cos(theta)) + func = func.subs(csc(theta), 1/sin(theta)) + func = func.subs(cot(theta), 1/tan(theta)) + + trig_function = list(func.find(TrigonometricFunction)) + assert len(trig_function) == 1 + trig_function = trig_function[0] + relation = solve(x - func, trig_function) + assert len(relation) == 1 + numer, denom = fraction(relation[0]) + + if isinstance(trig_function, sin): + opposite = numer + hypotenuse = denom + adjacent = sqrt(denom**2 - numer**2) + inverse = asin(relation[0]) + elif isinstance(trig_function, cos): + adjacent = numer + hypotenuse = denom + opposite = sqrt(denom**2 - numer**2) + inverse = acos(relation[0]) + else: # tan + opposite = numer + adjacent = denom + hypotenuse = sqrt(denom**2 + numer**2) + inverse = atan(relation[0]) + + substitution = [ + (sin(theta), opposite/hypotenuse), + (cos(theta), adjacent/hypotenuse), + (tan(theta), opposite/adjacent), + (theta, inverse) + ] + return Piecewise( + (self.substep.eval().subs(substitution).trigsimp(), self.restriction) + ) + + def contains_dont_know(self) -> bool: + return self.substep.contains_dont_know() + + +@dataclass +class ArctanRule(AtomicRule): + """integrate(a/(b*x**2+c), x) -> a/b / sqrt(c/b) * atan(x/sqrt(c/b))""" + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + a, b, c, x = self.a, self.b, self.c, self.variable + return a/b / sqrt(c/b) * atan(x/sqrt(c/b)) + + +@dataclass +class OrthogonalPolyRule(AtomicRule, ABC): + n: Expr + + +@dataclass +class JacobiRule(OrthogonalPolyRule): + a: Expr + b: Expr + + def eval(self) -> Expr: + n, a, b, x = self.n, self.a, self.b, self.variable + return Piecewise( + (2*jacobi(n + 1, a - 1, b - 1, x)/(n + a + b), Ne(n + a + b, 0)), + (x, Eq(n, 0)), + ((a + b + 2)*x**2/4 + (a - b)*x/2, Eq(n, 1))) + + +@dataclass +class GegenbauerRule(OrthogonalPolyRule): + a: Expr + + def eval(self) -> Expr: + n, a, x = self.n, self.a, self.variable + return Piecewise( + (gegenbauer(n + 1, a - 1, x)/(2*(a - 1)), Ne(a, 1)), + (chebyshevt(n + 1, x)/(n + 1), Ne(n, -1)), + (S.Zero, True)) + + +@dataclass +class ChebyshevTRule(OrthogonalPolyRule): + def eval(self) -> Expr: + n, x = self.n, self.variable + return Piecewise( + ((chebyshevt(n + 1, x)/(n + 1) - + chebyshevt(n - 1, x)/(n - 1))/2, Ne(Abs(n), 1)), + (x**2/2, True)) + + +@dataclass +class ChebyshevURule(OrthogonalPolyRule): + def eval(self) -> Expr: + n, x = self.n, self.variable + return Piecewise( + (chebyshevt(n + 1, x)/(n + 1), Ne(n, -1)), + (S.Zero, True)) + + +@dataclass +class LegendreRule(OrthogonalPolyRule): + def eval(self) -> Expr: + n, x = self.n, self.variable + return(legendre(n + 1, x) - legendre(n - 1, x))/(2*n + 1) + + +@dataclass +class HermiteRule(OrthogonalPolyRule): + def eval(self) -> Expr: + n, x = self.n, self.variable + return hermite(n + 1, x)/(2*(n + 1)) + + +@dataclass +class LaguerreRule(OrthogonalPolyRule): + def eval(self) -> Expr: + n, x = self.n, self.variable + return laguerre(n, x) - laguerre(n + 1, x) + + +@dataclass +class AssocLaguerreRule(OrthogonalPolyRule): + a: Expr + + def eval(self) -> Expr: + return -assoc_laguerre(self.n + 1, self.a - 1, self.variable) + + +@dataclass +class IRule(AtomicRule, ABC): + a: Expr + b: Expr + + +@dataclass +class CiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return cos(b)*Ci(a*x) - sin(b)*Si(a*x) + + +@dataclass +class ChiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return cosh(b)*Chi(a*x) + sinh(b)*Shi(a*x) + + +@dataclass +class EiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return exp(b)*Ei(a*x) + + +@dataclass +class SiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return sin(b)*Ci(a*x) + cos(b)*Si(a*x) + + +@dataclass +class ShiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return sinh(b)*Chi(a*x) + cosh(b)*Shi(a*x) + + +@dataclass +class LiRule(IRule): + def eval(self) -> Expr: + a, b, x = self.a, self.b, self.variable + return li(a*x + b)/a + + +@dataclass +class ErfRule(AtomicRule): + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + a, b, c, x = self.a, self.b, self.c, self.variable + if a.is_extended_real: + return Piecewise( + (sqrt(S.Pi)/sqrt(-a)/2 * exp(c - b**2/(4*a)) * + erf((-2*a*x - b)/(2*sqrt(-a))), a < 0), + (sqrt(S.Pi)/sqrt(a)/2 * exp(c - b**2/(4*a)) * + erfi((2*a*x + b)/(2*sqrt(a))), True)) + return sqrt(S.Pi)/sqrt(a)/2 * exp(c - b**2/(4*a)) * \ + erfi((2*a*x + b)/(2*sqrt(a))) + + +@dataclass +class FresnelCRule(AtomicRule): + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + a, b, c, x = self.a, self.b, self.c, self.variable + return sqrt(S.Pi)/sqrt(2*a) * ( + cos(b**2/(4*a) - c)*fresnelc((2*a*x + b)/sqrt(2*a*S.Pi)) + + sin(b**2/(4*a) - c)*fresnels((2*a*x + b)/sqrt(2*a*S.Pi))) + + +@dataclass +class FresnelSRule(AtomicRule): + a: Expr + b: Expr + c: Expr + + def eval(self) -> Expr: + a, b, c, x = self.a, self.b, self.c, self.variable + return sqrt(S.Pi)/sqrt(2*a) * ( + cos(b**2/(4*a) - c)*fresnels((2*a*x + b)/sqrt(2*a*S.Pi)) - + sin(b**2/(4*a) - c)*fresnelc((2*a*x + b)/sqrt(2*a*S.Pi))) + + +@dataclass +class PolylogRule(AtomicRule): + a: Expr + b: Expr + + def eval(self) -> Expr: + return polylog(self.b + 1, self.a * self.variable) + + +@dataclass +class UpperGammaRule(AtomicRule): + a: Expr + e: Expr + + def eval(self) -> Expr: + a, e, x = self.a, self.e, self.variable + return x**e * (-a*x)**(-e) * uppergamma(e + 1, -a*x)/a + + +@dataclass +class EllipticFRule(AtomicRule): + a: Expr + d: Expr + + def eval(self) -> Expr: + return elliptic_f(self.variable, self.d/self.a)/sqrt(self.a) + + +@dataclass +class EllipticERule(AtomicRule): + a: Expr + d: Expr + + def eval(self) -> Expr: + return elliptic_e(self.variable, self.d/self.a)*sqrt(self.a) + + +class IntegralInfo(NamedTuple): + integrand: Expr + symbol: Symbol + + +def manual_diff(f, symbol): + """Derivative of f in form expected by find_substitutions + + SymPy's derivatives for some trig functions (like cot) are not in a form + that works well with finding substitutions; this replaces the + derivatives for those particular forms with something that works better. + + """ + if f.args: + arg = f.args[0] + if isinstance(f, tan): + return arg.diff(symbol) * sec(arg)**2 + elif isinstance(f, cot): + return -arg.diff(symbol) * csc(arg)**2 + elif isinstance(f, sec): + return arg.diff(symbol) * sec(arg) * tan(arg) + elif isinstance(f, csc): + return -arg.diff(symbol) * csc(arg) * cot(arg) + elif isinstance(f, Add): + return sum(manual_diff(arg, symbol) for arg in f.args) + elif isinstance(f, Mul): + if len(f.args) == 2 and isinstance(f.args[0], Number): + return f.args[0] * manual_diff(f.args[1], symbol) + return f.diff(symbol) + +def manual_subs(expr, *args): + """ + A wrapper for `expr.subs(*args)` with additional logic for substitution + of invertible functions. + """ + if len(args) == 1: + sequence = args[0] + if isinstance(sequence, (Dict, Mapping)): + sequence = sequence.items() + elif not iterable(sequence): + raise ValueError("Expected an iterable of (old, new) pairs") + elif len(args) == 2: + sequence = [args] + else: + raise ValueError("subs accepts either 1 or 2 arguments") + + new_subs = [] + for old, new in sequence: + if isinstance(old, log): + # If log(x) = y, then exp(a*log(x)) = exp(a*y) + # that is, x**a = exp(a*y). Replace nontrivial powers of x + # before subs turns them into `exp(y)**a`, but + # do not replace x itself yet, to avoid `log(exp(y))`. + x0 = old.args[0] + expr = expr.replace(lambda x: x.is_Pow and x.base == x0, + lambda x: exp(x.exp*new)) + new_subs.append((x0, exp(new))) + + return expr.subs(list(sequence) + new_subs) + +# Method based on that on SIN, described in "Symbolic Integration: The +# Stormy Decade" + +inverse_trig_functions = (atan, asin, acos, acot, acsc, asec) + + +def find_substitutions(integrand, symbol, u_var): + results = [] + + def test_subterm(u, u_diff): + if u_diff == 0: + return False + substituted = integrand / u_diff + debug("substituted: {}, u: {}, u_var: {}".format(substituted, u, u_var)) + substituted = manual_subs(substituted, u, u_var).cancel() + + if substituted.has_free(symbol): + return False + # avoid increasing the degree of a rational function + if integrand.is_rational_function(symbol) and substituted.is_rational_function(u_var): + deg_before = max(degree(t, symbol) for t in integrand.as_numer_denom()) + deg_after = max(degree(t, u_var) for t in substituted.as_numer_denom()) + if deg_after > deg_before: + return False + return substituted.as_independent(u_var, as_Add=False) + + def exp_subterms(term: Expr): + linear_coeffs = [] + terms = [] + n = Wild('n', properties=[lambda n: n.is_Integer]) + for exp_ in term.find(exp): + arg = exp_.args[0] + if symbol not in arg.free_symbols: + continue + match = arg.match(n*symbol) + if match: + linear_coeffs.append(match[n]) + else: + terms.append(exp_) + if linear_coeffs: + terms.append(exp(gcd_list(linear_coeffs)*symbol)) + return terms + + def possible_subterms(term): + if isinstance(term, (TrigonometricFunction, HyperbolicFunction, + *inverse_trig_functions, + exp, log, Heaviside)): + return [term.args[0]] + elif isinstance(term, (chebyshevt, chebyshevu, + legendre, hermite, laguerre)): + return [term.args[1]] + elif isinstance(term, (gegenbauer, assoc_laguerre)): + return [term.args[2]] + elif isinstance(term, jacobi): + return [term.args[3]] + elif isinstance(term, Mul): + r = [] + for u in term.args: + r.append(u) + r.extend(possible_subterms(u)) + return r + elif isinstance(term, Pow): + r = [arg for arg in term.args if arg.has(symbol)] + if term.exp.is_Integer: + r.extend([term.base**d for d in primefactors(term.exp) + if 1 < d < abs(term.args[1])]) + if term.base.is_Add: + r.extend([t for t in possible_subterms(term.base) + if t.is_Pow]) + return r + elif isinstance(term, Add): + r = [] + for arg in term.args: + r.append(arg) + r.extend(possible_subterms(arg)) + return r + return [] + + for u in list(dict.fromkeys(possible_subterms(integrand) + exp_subterms(integrand))): + if u == symbol: + continue + u_diff = manual_diff(u, symbol) + new_integrand = test_subterm(u, u_diff) + if new_integrand is not False: + constant, new_integrand = new_integrand + if new_integrand == integrand.subs(symbol, u_var): + continue + substitution = (u, constant, new_integrand) + if substitution not in results: + results.append(substitution) + + return results + +def rewriter(condition, rewrite): + """Strategy that rewrites an integrand.""" + def _rewriter(integral): + integrand, symbol = integral + debug("Integral: {} is rewritten with {} on symbol: {}".format(integrand, rewrite, symbol)) + if condition(*integral): + rewritten = rewrite(*integral) + if rewritten != integrand: + substep = integral_steps(rewritten, symbol) + if not isinstance(substep, DontKnowRule) and substep: + return RewriteRule(integrand, symbol, rewritten, substep) + return _rewriter + +def proxy_rewriter(condition, rewrite): + """Strategy that rewrites an integrand based on some other criteria.""" + def _proxy_rewriter(criteria): + criteria, integral = criteria + integrand, symbol = integral + debug("Integral: {} is rewritten with {} on symbol: {} and criteria: {}".format(integrand, rewrite, symbol, criteria)) + args = criteria + list(integral) + if condition(*args): + rewritten = rewrite(*args) + if rewritten != integrand: + return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol)) + return _proxy_rewriter + +def multiplexer(conditions): + """Apply the rule that matches the condition, else None""" + def multiplexer_rl(expr): + for key, rule in conditions.items(): + if key(expr): + return rule(expr) + return multiplexer_rl + +def alternatives(*rules): + """Strategy that makes an AlternativeRule out of multiple possible results.""" + def _alternatives(integral): + alts = [] + count = 0 + debug("List of Alternative Rules") + for rule in rules: + count = count + 1 + debug("Rule {}: {}".format(count, rule)) + + result = rule(integral) + if (result and not isinstance(result, DontKnowRule) and + result != integral and result not in alts): + alts.append(result) + if len(alts) == 1: + return alts[0] + elif alts: + doable = [rule for rule in alts if not rule.contains_dont_know()] + if doable: + return AlternativeRule(*integral, doable) + else: + return AlternativeRule(*integral, alts) + return _alternatives + +def constant_rule(integral): + return ConstantRule(*integral) + +def power_rule(integral): + integrand, symbol = integral + base, expt = integrand.as_base_exp() + + if symbol not in expt.free_symbols and isinstance(base, Symbol): + if simplify(expt + 1) == 0: + return ReciprocalRule(integrand, symbol, base) + return PowerRule(integrand, symbol, base, expt) + elif symbol not in base.free_symbols and isinstance(expt, Symbol): + rule = ExpRule(integrand, symbol, base, expt) + + if fuzzy_not(log(base).is_zero): + return rule + elif log(base).is_zero: + return ConstantRule(1, symbol) + + return PiecewiseRule(integrand, symbol, [ + (rule, Ne(log(base), 0)), + (ConstantRule(1, symbol), True) + ]) + +def exp_rule(integral): + integrand, symbol = integral + if isinstance(integrand.args[0], Symbol): + return ExpRule(integrand, symbol, E, integrand.args[0]) + + +def orthogonal_poly_rule(integral): + orthogonal_poly_classes = { + jacobi: JacobiRule, + gegenbauer: GegenbauerRule, + chebyshevt: ChebyshevTRule, + chebyshevu: ChebyshevURule, + legendre: LegendreRule, + hermite: HermiteRule, + laguerre: LaguerreRule, + assoc_laguerre: AssocLaguerreRule + } + orthogonal_poly_var_index = { + jacobi: 3, + gegenbauer: 2, + assoc_laguerre: 2 + } + integrand, symbol = integral + for klass in orthogonal_poly_classes: + if isinstance(integrand, klass): + var_index = orthogonal_poly_var_index.get(klass, 1) + if (integrand.args[var_index] is symbol and not + any(v.has(symbol) for v in integrand.args[:var_index])): + return orthogonal_poly_classes[klass](integrand, symbol, *integrand.args[:var_index]) + + +_special_function_patterns: list[tuple[Type, Expr, Callable | None, tuple]] = [] +_wilds = [] +_symbol = Dummy('x') + + +def special_function_rule(integral): + integrand, symbol = integral + if not _special_function_patterns: + a = Wild('a', exclude=[_symbol], properties=[lambda x: not x.is_zero]) + b = Wild('b', exclude=[_symbol]) + c = Wild('c', exclude=[_symbol]) + d = Wild('d', exclude=[_symbol], properties=[lambda x: not x.is_zero]) + e = Wild('e', exclude=[_symbol], properties=[ + lambda x: not (x.is_nonnegative and x.is_integer)]) + _wilds.extend((a, b, c, d, e)) + # patterns consist of a SymPy class, a wildcard expr, an optional + # condition coded as a lambda (when Wild properties are not enough), + # followed by an applicable rule + linear_pattern = a*_symbol + b + quadratic_pattern = a*_symbol**2 + b*_symbol + c + _special_function_patterns.extend(( + (Mul, exp(linear_pattern, evaluate=False)/_symbol, None, EiRule), + (Mul, cos(linear_pattern, evaluate=False)/_symbol, None, CiRule), + (Mul, cosh(linear_pattern, evaluate=False)/_symbol, None, ChiRule), + (Mul, sin(linear_pattern, evaluate=False)/_symbol, None, SiRule), + (Mul, sinh(linear_pattern, evaluate=False)/_symbol, None, ShiRule), + (Pow, 1/log(linear_pattern, evaluate=False), None, LiRule), + (exp, exp(quadratic_pattern, evaluate=False), None, ErfRule), + (sin, sin(quadratic_pattern, evaluate=False), None, FresnelSRule), + (cos, cos(quadratic_pattern, evaluate=False), None, FresnelCRule), + (Mul, _symbol**e*exp(a*_symbol, evaluate=False), None, UpperGammaRule), + (Mul, polylog(b, a*_symbol, evaluate=False)/_symbol, None, PolylogRule), + (Pow, 1/sqrt(a - d*sin(_symbol, evaluate=False)**2), + lambda a, d: a != d, EllipticFRule), + (Pow, sqrt(a - d*sin(_symbol, evaluate=False)**2), + lambda a, d: a != d, EllipticERule), + )) + _integrand = integrand.subs(symbol, _symbol) + for type_, pattern, constraint, rule in _special_function_patterns: + if isinstance(_integrand, type_): + match = _integrand.match(pattern) + if match: + wild_vals = tuple(match.get(w) for w in _wilds + if match.get(w) is not None) + if constraint is None or constraint(*wild_vals): + return rule(integrand, symbol, *wild_vals) + + +def _add_degenerate_step(generic_cond, generic_step: Rule, degenerate_step: Rule | None) -> Rule: + if degenerate_step is None: + return generic_step + if isinstance(generic_step, PiecewiseRule): + subfunctions = [(substep, (cond & generic_cond).simplify()) + for substep, cond in generic_step.subfunctions] + else: + subfunctions = [(generic_step, generic_cond)] + if isinstance(degenerate_step, PiecewiseRule): + subfunctions += degenerate_step.subfunctions + else: + subfunctions.append((degenerate_step, S.true)) + return PiecewiseRule(generic_step.integrand, generic_step.variable, subfunctions) + + +def nested_pow_rule(integral: IntegralInfo): + # nested (c*(a+b*x)**d)**e + integrand, x = integral + + a_ = Wild('a', exclude=[x]) + b_ = Wild('b', exclude=[x, 0]) + pattern = a_+b_*x + generic_cond = S.true + + class NoMatch(Exception): + pass + + def _get_base_exp(expr: Expr) -> tuple[Expr, Expr]: + if not expr.has_free(x): + return S.One, S.Zero + if expr.is_Mul: + _, terms = expr.as_coeff_mul() + if not terms: + return S.One, S.Zero + results = [_get_base_exp(term) for term in terms] + bases = {b for b, _ in results} + bases.discard(S.One) + if len(bases) == 1: + return bases.pop(), Add(*(e for _, e in results)) + raise NoMatch + if expr.is_Pow: + b, e = expr.base, expr.exp # type: ignore + if e.has_free(x): + raise NoMatch + base_, sub_exp = _get_base_exp(b) + return base_, sub_exp * e + match = expr.match(pattern) + if match: + a, b = match[a_], match[b_] + base_ = x + a/b + nonlocal generic_cond + generic_cond = Ne(b, 0) + return base_, S.One + raise NoMatch + + try: + base, exp_ = _get_base_exp(integrand) + except NoMatch: + return + if generic_cond is S.true: + degenerate_step = None + else: + # equivalent with subs(b, 0) but no need to find b + degenerate_step = ConstantRule(integrand.subs(x, 0), x) + generic_step = NestedPowRule(integrand, x, base, exp_) + return _add_degenerate_step(generic_cond, generic_step, degenerate_step) + + +def inverse_trig_rule(integral: IntegralInfo, degenerate=True): + """ + Set degenerate=False on recursive call where coefficient of quadratic term + is assumed non-zero. + """ + integrand, symbol = integral + base, exp = integrand.as_base_exp() + a = Wild('a', exclude=[symbol]) + b = Wild('b', exclude=[symbol]) + c = Wild('c', exclude=[symbol, 0]) + match = base.match(a + b*symbol + c*symbol**2) + + if not match: + return + + def make_inverse_trig(RuleClass, a, sign_a, c, sign_c, h) -> Rule: + u_var = Dummy("u") + rewritten = 1/sqrt(sign_a*a + sign_c*c*(symbol-h)**2) # a>0, c>0 + quadratic_base = sqrt(c/a)*(symbol-h) + constant = 1/sqrt(c) + u_func = None + if quadratic_base is not symbol: + u_func = quadratic_base + quadratic_base = u_var + standard_form = 1/sqrt(sign_a + sign_c*quadratic_base**2) + substep = RuleClass(standard_form, quadratic_base) + if constant != 1: + substep = ConstantTimesRule(constant*standard_form, symbol, constant, standard_form, substep) + if u_func is not None: + substep = URule(rewritten, symbol, u_var, u_func, substep) + if h != 0: + substep = CompleteSquareRule(integrand, symbol, rewritten, substep) + return substep + + a, b, c = [match.get(i, S.Zero) for i in (a, b, c)] + generic_cond = Ne(c, 0) + if not degenerate or generic_cond is S.true: + degenerate_step = None + elif b.is_zero: + degenerate_step = ConstantRule(a ** exp, symbol) + else: + degenerate_step = sqrt_linear_rule(IntegralInfo((a + b * symbol) ** exp, symbol)) + + if simplify(2*exp + 1) == 0: + h, k = -b/(2*c), a - b**2/(4*c) # rewrite base to k + c*(symbol-h)**2 + non_square_cond = Ne(k, 0) + square_step = None + if non_square_cond is not S.true: + square_step = NestedPowRule(1/sqrt(c*(symbol-h)**2), symbol, symbol-h, S.NegativeOne) + if non_square_cond is S.false: + return square_step + generic_step = ReciprocalSqrtQuadraticRule(integrand, symbol, a, b, c) + step = _add_degenerate_step(non_square_cond, generic_step, square_step) + if k.is_real and c.is_real: + # list of ((rule, base_exp, a, sign_a, b, sign_b), condition) + rules = [] + for args, cond in ( # don't apply ArccoshRule to x**2-1 + ((ArcsinRule, k, 1, -c, -1, h), And(k > 0, c < 0)), # 1-x**2 + ((ArcsinhRule, k, 1, c, 1, h), And(k > 0, c > 0)), # 1+x**2 + ): + if cond is S.true: + return make_inverse_trig(*args) + if cond is not S.false: + rules.append((make_inverse_trig(*args), cond)) + if rules: + if not k.is_positive: # conditions are not thorough, need fall back rule + rules.append((generic_step, S.true)) + step = PiecewiseRule(integrand, symbol, rules) + else: + step = generic_step + return _add_degenerate_step(generic_cond, step, degenerate_step) + if exp == S.Half: + step = SqrtQuadraticRule(integrand, symbol, a, b, c) + return _add_degenerate_step(generic_cond, step, degenerate_step) + + +def add_rule(integral): + integrand, symbol = integral + results = [integral_steps(g, symbol) + for g in integrand.as_ordered_terms()] + return None if None in results else AddRule(integrand, symbol, results) + + +def mul_rule(integral: IntegralInfo): + integrand, symbol = integral + + # Constant times function case + coeff, f = integrand.as_independent(symbol) + if coeff != 1: + next_step = integral_steps(f, symbol) + if next_step is not None: + return ConstantTimesRule(integrand, symbol, coeff, f, next_step) + + +def _parts_rule(integrand, symbol) -> tuple[Expr, Expr, Expr, Expr, Rule] | None: + # LIATE rule: + # log, inverse trig, algebraic, trigonometric, exponential + def pull_out_algebraic(integrand): + integrand = integrand.cancel().together() + # iterating over Piecewise args would not work here + algebraic = ([] if isinstance(integrand, Piecewise) or not integrand.is_Mul + else [arg for arg in integrand.args if arg.is_algebraic_expr(symbol)]) + if algebraic: + u = Mul(*algebraic) + dv = (integrand / u).cancel() + return u, dv + + def pull_out_u(*functions) -> Callable[[Expr], tuple[Expr, Expr] | None]: + def pull_out_u_rl(integrand: Expr) -> tuple[Expr, Expr] | None: + if any(integrand.has(f) for f in functions): + args = [arg for arg in integrand.args + if any(isinstance(arg, cls) for cls in functions)] + if args: + u = Mul(*args) + dv = integrand / u + return u, dv + return None + + return pull_out_u_rl + + liate_rules = [pull_out_u(log), pull_out_u(*inverse_trig_functions), + pull_out_algebraic, pull_out_u(sin, cos), + pull_out_u(exp)] + + + dummy = Dummy("temporary") + # we can integrate log(x) and atan(x) by setting dv = 1 + if isinstance(integrand, (log, *inverse_trig_functions)): + integrand = dummy * integrand + + for index, rule in enumerate(liate_rules): + result = rule(integrand) + + if result: + u, dv = result + + # Don't pick u to be a constant if possible + if symbol not in u.free_symbols and not u.has(dummy): + return None + + u = u.subs(dummy, 1) + dv = dv.subs(dummy, 1) + + # Don't pick a non-polynomial algebraic to be differentiated + if rule == pull_out_algebraic and not u.is_polynomial(symbol): + return None + # Don't trade one logarithm for another + if isinstance(u, log): + rec_dv = 1/dv + if (rec_dv.is_polynomial(symbol) and + degree(rec_dv, symbol) == 1): + return None + + # Can integrate a polynomial times OrthogonalPolynomial + if rule == pull_out_algebraic: + if dv.is_Derivative or dv.has(TrigonometricFunction) or \ + isinstance(dv, OrthogonalPolynomial): + v_step = integral_steps(dv, symbol) + if v_step.contains_dont_know(): + return None + else: + du = u.diff(symbol) + v = v_step.eval() + return u, dv, v, du, v_step + + # make sure dv is amenable to integration + accept = False + if index < 2: # log and inverse trig are usually worth trying + accept = True + elif (rule == pull_out_algebraic and dv.args and + all(isinstance(a, (sin, cos, exp)) + for a in dv.args)): + accept = True + else: + for lrule in liate_rules[index + 1:]: + r = lrule(integrand) + if r and r[0].subs(dummy, 1).equals(dv): + accept = True + break + + if accept: + du = u.diff(symbol) + v_step = integral_steps(simplify(dv), symbol) + if not v_step.contains_dont_know(): + v = v_step.eval() + return u, dv, v, du, v_step + return None + + +def parts_rule(integral): + integrand, symbol = integral + constant, integrand = integrand.as_coeff_Mul() + + result = _parts_rule(integrand, symbol) + + steps = [] + if result: + u, dv, v, du, v_step = result + debug("u : {}, dv : {}, v : {}, du : {}, v_step: {}".format(u, dv, v, du, v_step)) + steps.append(result) + + if isinstance(v, Integral): + return + + # Set a limit on the number of times u can be used + if isinstance(u, (sin, cos, exp, sinh, cosh)): + cachekey = u.xreplace({symbol: _cache_dummy}) + if _parts_u_cache[cachekey] > 2: + return + _parts_u_cache[cachekey] += 1 + + # Try cyclic integration by parts a few times + for _ in range(4): + debug("Cyclic integration {} with v: {}, du: {}, integrand: {}".format(_, v, du, integrand)) + coefficient = ((v * du) / integrand).cancel() + if coefficient == 1: + break + if symbol not in coefficient.free_symbols: + rule = CyclicPartsRule(integrand, symbol, + [PartsRule(None, None, u, dv, v_step, None) + for (u, dv, v, du, v_step) in steps], + (-1) ** len(steps) * coefficient) + if (constant != 1) and rule: + rule = ConstantTimesRule(constant * integrand, symbol, constant, integrand, rule) + return rule + + # _parts_rule is sensitive to constants, factor it out + next_constant, next_integrand = (v * du).as_coeff_Mul() + result = _parts_rule(next_integrand, symbol) + + if result: + u, dv, v, du, v_step = result + u *= next_constant + du *= next_constant + steps.append((u, dv, v, du, v_step)) + else: + break + + def make_second_step(steps, integrand): + if steps: + u, dv, v, du, v_step = steps[0] + return PartsRule(integrand, symbol, u, dv, v_step, make_second_step(steps[1:], v * du)) + return integral_steps(integrand, symbol) + + if steps: + u, dv, v, du, v_step = steps[0] + rule = PartsRule(integrand, symbol, u, dv, v_step, make_second_step(steps[1:], v * du)) + if (constant != 1) and rule: + rule = ConstantTimesRule(constant * integrand, symbol, constant, integrand, rule) + return rule + + +def trig_rule(integral): + integrand, symbol = integral + if integrand == sin(symbol): + return SinRule(integrand, symbol) + if integrand == cos(symbol): + return CosRule(integrand, symbol) + if integrand == sec(symbol)**2: + return Sec2Rule(integrand, symbol) + if integrand == csc(symbol)**2: + return Csc2Rule(integrand, symbol) + + if isinstance(integrand, tan): + rewritten = sin(*integrand.args) / cos(*integrand.args) + elif isinstance(integrand, cot): + rewritten = cos(*integrand.args) / sin(*integrand.args) + elif isinstance(integrand, sec): + arg = integrand.args[0] + rewritten = ((sec(arg)**2 + tan(arg) * sec(arg)) / + (sec(arg) + tan(arg))) + elif isinstance(integrand, csc): + arg = integrand.args[0] + rewritten = ((csc(arg)**2 + cot(arg) * csc(arg)) / + (csc(arg) + cot(arg))) + else: + return + + return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol)) + +def trig_product_rule(integral: IntegralInfo): + integrand, symbol = integral + if integrand == sec(symbol) * tan(symbol): + return SecTanRule(integrand, symbol) + if integrand == csc(symbol) * cot(symbol): + return CscCotRule(integrand, symbol) + + +def quadratic_denom_rule(integral): + integrand, symbol = integral + a = Wild('a', exclude=[symbol]) + b = Wild('b', exclude=[symbol]) + c = Wild('c', exclude=[symbol]) + + match = integrand.match(a / (b * symbol ** 2 + c)) + + if match: + a, b, c = match[a], match[b], match[c] + general_rule = ArctanRule(integrand, symbol, a, b, c) + if b.is_extended_real and c.is_extended_real: + positive_cond = c/b > 0 + if positive_cond is S.true: + return general_rule + coeff = a/(2*sqrt(-c)*sqrt(b)) + constant = sqrt(-c/b) + r1 = 1/(symbol-constant) + r2 = 1/(symbol+constant) + log_steps = [ReciprocalRule(r1, symbol, symbol-constant), + ConstantTimesRule(-r2, symbol, -1, r2, ReciprocalRule(r2, symbol, symbol+constant))] + rewritten = sub = r1 - r2 + negative_step = AddRule(sub, symbol, log_steps) + if coeff != 1: + rewritten = Mul(coeff, sub, evaluate=False) + negative_step = ConstantTimesRule(rewritten, symbol, coeff, sub, negative_step) + negative_step = RewriteRule(integrand, symbol, rewritten, negative_step) + if positive_cond is S.false: + return negative_step + return PiecewiseRule(integrand, symbol, [(general_rule, positive_cond), (negative_step, S.true)]) + + power = PowerRule(integrand, symbol, symbol, -2) + if b != 1: + power = ConstantTimesRule(integrand, symbol, 1/b, symbol**-2, power) + + return PiecewiseRule(integrand, symbol, [(general_rule, Ne(c, 0)), (power, True)]) + + d = Wild('d', exclude=[symbol]) + match2 = integrand.match(a / (b * symbol ** 2 + c * symbol + d)) + if match2: + b, c = match2[b], match2[c] + if b.is_zero: + return + u = Dummy('u') + u_func = symbol + c/(2*b) + integrand2 = integrand.subs(symbol, u - c / (2*b)) + next_step = integral_steps(integrand2, u) + if next_step: + return URule(integrand2, symbol, u, u_func, next_step) + else: + return + e = Wild('e', exclude=[symbol]) + match3 = integrand.match((a* symbol + b) / (c * symbol ** 2 + d * symbol + e)) + if match3: + a, b, c, d, e = match3[a], match3[b], match3[c], match3[d], match3[e] + if c.is_zero: + return + denominator = c * symbol**2 + d * symbol + e + const = a/(2*c) + numer1 = (2*c*symbol+d) + numer2 = - const*d + b + u = Dummy('u') + step1 = URule(integrand, symbol, + u, denominator, integral_steps(u**(-1), u)) + if const != 1: + step1 = ConstantTimesRule(const*numer1/denominator, symbol, + const, numer1/denominator, step1) + if numer2.is_zero: + return step1 + step2 = integral_steps(numer2/denominator, symbol) + substeps = AddRule(integrand, symbol, [step1, step2]) + rewriten = const*numer1/denominator+numer2/denominator + return RewriteRule(integrand, symbol, rewriten, substeps) + + return + + +def sqrt_linear_rule(integral: IntegralInfo): + """ + Substitute common (a+b*x)**(1/n) + """ + integrand, x = integral + a = Wild('a', exclude=[x]) + b = Wild('b', exclude=[x, 0]) + a0 = b0 = 0 + bases, qs, bs = [], [], [] + for pow_ in integrand.find(Pow): # collect all (a+b*x)**(p/q) + base, exp_ = pow_.base, pow_.exp + if exp_.is_Integer or x not in base.free_symbols: # skip 1/x and sqrt(2) + continue + if not exp_.is_Rational: # exclude x**pi + return + match = base.match(a+b*x) + if not match: # skip non-linear + continue # for sqrt(x+sqrt(x)), although base is non-linear, we can still substitute sqrt(x) + a1, b1 = match[a], match[b] + if a0*b1 != a1*b0 or not (b0/b1).is_nonnegative: # cannot transform sqrt(x) to sqrt(x+1) or sqrt(-x) + return + if b0 == 0 or (b0/b1 > 1) is S.true: # choose the latter of sqrt(2*x) and sqrt(x) as representative + a0, b0 = a1, b1 + bases.append(base) + bs.append(b1) + qs.append(exp_.q) + if b0 == 0: # no such pattern found + return + q0: Integer = lcm_list(qs) + u_x = (a0 + b0*x)**(1/q0) + u = Dummy("u") + substituted = integrand.subs({base**(S.One/q): (b/b0)**(S.One/q)*u**(q0/q) + for base, b, q in zip(bases, bs, qs)}).subs(x, (u**q0-a0)/b0) + substep = integral_steps(substituted*u**(q0-1)*q0/b0, u) + if not substep.contains_dont_know(): + step: Rule = URule(integrand, x, u, u_x, substep) + generic_cond = Ne(b0, 0) + if generic_cond is not S.true: # possible degenerate case + simplified = integrand.subs(dict.fromkeys(bs, 0)) + degenerate_step = integral_steps(simplified, x) + step = PiecewiseRule(integrand, x, [(step, generic_cond), (degenerate_step, S.true)]) + return step + + +def sqrt_quadratic_rule(integral: IntegralInfo, degenerate=True): + integrand, x = integral + a = Wild('a', exclude=[x]) + b = Wild('b', exclude=[x]) + c = Wild('c', exclude=[x, 0]) + f = Wild('f') + n = Wild('n', properties=[lambda n: n.is_Integer and n.is_odd]) + match = integrand.match(f*sqrt(a+b*x+c*x**2)**n) + if not match: + return + a, b, c, f, n = match[a], match[b], match[c], match[f], match[n] + f_poly = f.as_poly(x) + if f_poly is None: + return + + generic_cond = Ne(c, 0) + if not degenerate or generic_cond is S.true: + degenerate_step = None + elif b.is_zero: + degenerate_step = integral_steps(f*sqrt(a)**n, x) + else: + degenerate_step = sqrt_linear_rule(IntegralInfo(f*sqrt(a+b*x)**n, x)) + + def sqrt_quadratic_denom_rule(numer_poly: Poly, integrand: Expr): + denom = sqrt(a+b*x+c*x**2) + deg = numer_poly.degree() + if deg <= 1: + # integrand == (d+e*x)/sqrt(a+b*x+c*x**2) + e, d = numer_poly.all_coeffs() if deg == 1 else (S.Zero, numer_poly.as_expr()) + # rewrite numerator to A*(2*c*x+b) + B + A = e/(2*c) + B = d-A*b + pre_substitute = (2*c*x+b)/denom + constant_step: Rule | None = None + linear_step: Rule | None = None + if A != 0: + u = Dummy("u") + pow_rule = PowerRule(1/sqrt(u), u, u, -S.Half) + linear_step = URule(pre_substitute, x, u, a+b*x+c*x**2, pow_rule) + if A != 1: + linear_step = ConstantTimesRule(A*pre_substitute, x, A, pre_substitute, linear_step) + if B != 0: + constant_step = inverse_trig_rule(IntegralInfo(1/denom, x), degenerate=False) + if B != 1: + constant_step = ConstantTimesRule(B/denom, x, B, 1/denom, constant_step) # type: ignore + if linear_step and constant_step: + add = Add(A*pre_substitute, B/denom, evaluate=False) + step: Rule | None = RewriteRule(integrand, x, add, AddRule(add, x, [linear_step, constant_step])) + else: + step = linear_step or constant_step + else: + coeffs = numer_poly.all_coeffs() + step = SqrtQuadraticDenomRule(integrand, x, a, b, c, coeffs) + return step + + if n > 0: # rewrite poly * sqrt(s)**(2*k-1) to poly*s**k / sqrt(s) + numer_poly = f_poly * (a+b*x+c*x**2)**((n+1)/2) + rewritten = numer_poly.as_expr()/sqrt(a+b*x+c*x**2) + substep = sqrt_quadratic_denom_rule(numer_poly, rewritten) + generic_step = RewriteRule(integrand, x, rewritten, substep) + elif n == -1: + generic_step = sqrt_quadratic_denom_rule(f_poly, integrand) + else: + return # todo: handle n < -1 case + return _add_degenerate_step(generic_cond, generic_step, degenerate_step) + + +def hyperbolic_rule(integral: tuple[Expr, Symbol]): + integrand, symbol = integral + if isinstance(integrand, HyperbolicFunction) and integrand.args[0] == symbol: + if integrand.func == sinh: + return SinhRule(integrand, symbol) + if integrand.func == cosh: + return CoshRule(integrand, symbol) + u = Dummy('u') + if integrand.func == tanh: + rewritten = sinh(symbol)/cosh(symbol) + return RewriteRule(integrand, symbol, rewritten, + URule(rewritten, symbol, u, cosh(symbol), ReciprocalRule(1/u, u, u))) + if integrand.func == coth: + rewritten = cosh(symbol)/sinh(symbol) + return RewriteRule(integrand, symbol, rewritten, + URule(rewritten, symbol, u, sinh(symbol), ReciprocalRule(1/u, u, u))) + else: + rewritten = integrand.rewrite(tanh) + if integrand.func == sech: + return RewriteRule(integrand, symbol, rewritten, + URule(rewritten, symbol, u, tanh(symbol/2), + ArctanRule(2/(u**2 + 1), u, S(2), S.One, S.One))) + if integrand.func == csch: + return RewriteRule(integrand, symbol, rewritten, + URule(rewritten, symbol, u, tanh(symbol/2), + ReciprocalRule(1/u, u, u))) + +@cacheit +def make_wilds(symbol): + a = Wild('a', exclude=[symbol]) + b = Wild('b', exclude=[symbol]) + m = Wild('m', exclude=[symbol], properties=[lambda n: isinstance(n, Integer)]) + n = Wild('n', exclude=[symbol], properties=[lambda n: isinstance(n, Integer)]) + + return a, b, m, n + +@cacheit +def sincos_pattern(symbol): + a, b, m, n = make_wilds(symbol) + pattern = sin(a*symbol)**m * cos(b*symbol)**n + + return pattern, a, b, m, n + +@cacheit +def tansec_pattern(symbol): + a, b, m, n = make_wilds(symbol) + pattern = tan(a*symbol)**m * sec(b*symbol)**n + + return pattern, a, b, m, n + +@cacheit +def cotcsc_pattern(symbol): + a, b, m, n = make_wilds(symbol) + pattern = cot(a*symbol)**m * csc(b*symbol)**n + + return pattern, a, b, m, n + +@cacheit +def heaviside_pattern(symbol): + m = Wild('m', exclude=[symbol]) + b = Wild('b', exclude=[symbol]) + g = Wild('g') + pattern = Heaviside(m*symbol + b) * g + + return pattern, m, b, g + +def uncurry(func): + def uncurry_rl(args): + return func(*args) + return uncurry_rl + +def trig_rewriter(rewrite): + def trig_rewriter_rl(args): + a, b, m, n, integrand, symbol = args + rewritten = rewrite(a, b, m, n, integrand, symbol) + if rewritten != integrand: + return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol)) + return trig_rewriter_rl + +sincos_botheven_condition = uncurry( + lambda a, b, m, n, i, s: m.is_even and n.is_even and + m.is_nonnegative and n.is_nonnegative) + +sincos_botheven = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (((1 - cos(2*a*symbol)) / 2) ** (m / 2)) * + (((1 + cos(2*b*symbol)) / 2) ** (n / 2)) )) + +sincos_sinodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd and m >= 3) + +sincos_sinodd = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (1 - cos(a*symbol)**2)**((m - 1) / 2) * + sin(a*symbol) * + cos(b*symbol) ** n)) + +sincos_cosodd_condition = uncurry(lambda a, b, m, n, i, s: n.is_odd and n >= 3) + +sincos_cosodd = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (1 - sin(b*symbol)**2)**((n - 1) / 2) * + cos(b*symbol) * + sin(a*symbol) ** m)) + +tansec_seceven_condition = uncurry(lambda a, b, m, n, i, s: n.is_even and n >= 4) +tansec_seceven = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (1 + tan(b*symbol)**2) ** (n/2 - 1) * + sec(b*symbol)**2 * + tan(a*symbol) ** m )) + +tansec_tanodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd) +tansec_tanodd = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (sec(a*symbol)**2 - 1) ** ((m - 1) / 2) * + tan(a*symbol) * + sec(b*symbol) ** n )) + +tan_tansquared_condition = uncurry(lambda a, b, m, n, i, s: m == 2 and n == 0) +tan_tansquared = trig_rewriter( + lambda a, b, m, n, i, symbol: ( sec(a*symbol)**2 - 1)) + +cotcsc_csceven_condition = uncurry(lambda a, b, m, n, i, s: n.is_even and n >= 4) +cotcsc_csceven = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (1 + cot(b*symbol)**2) ** (n/2 - 1) * + csc(b*symbol)**2 * + cot(a*symbol) ** m )) + +cotcsc_cotodd_condition = uncurry(lambda a, b, m, n, i, s: m.is_odd) +cotcsc_cotodd = trig_rewriter( + lambda a, b, m, n, i, symbol: ( (csc(a*symbol)**2 - 1) ** ((m - 1) / 2) * + cot(a*symbol) * + csc(b*symbol) ** n )) + +def trig_sincos_rule(integral): + integrand, symbol = integral + + if any(integrand.has(f) for f in (sin, cos)): + pattern, a, b, m, n = sincos_pattern(symbol) + match = integrand.match(pattern) + if not match: + return + + return multiplexer({ + sincos_botheven_condition: sincos_botheven, + sincos_sinodd_condition: sincos_sinodd, + sincos_cosodd_condition: sincos_cosodd + })(tuple( + [match.get(i, S.Zero) for i in (a, b, m, n)] + + [integrand, symbol])) + +def trig_tansec_rule(integral): + integrand, symbol = integral + + integrand = integrand.subs({ + 1 / cos(symbol): sec(symbol) + }) + + if any(integrand.has(f) for f in (tan, sec)): + pattern, a, b, m, n = tansec_pattern(symbol) + match = integrand.match(pattern) + if not match: + return + + return multiplexer({ + tansec_tanodd_condition: tansec_tanodd, + tansec_seceven_condition: tansec_seceven, + tan_tansquared_condition: tan_tansquared + })(tuple( + [match.get(i, S.Zero) for i in (a, b, m, n)] + + [integrand, symbol])) + +def trig_cotcsc_rule(integral): + integrand, symbol = integral + integrand = integrand.subs({ + 1 / sin(symbol): csc(symbol), + 1 / tan(symbol): cot(symbol), + cos(symbol) / tan(symbol): cot(symbol) + }) + + if any(integrand.has(f) for f in (cot, csc)): + pattern, a, b, m, n = cotcsc_pattern(symbol) + match = integrand.match(pattern) + if not match: + return + + return multiplexer({ + cotcsc_cotodd_condition: cotcsc_cotodd, + cotcsc_csceven_condition: cotcsc_csceven + })(tuple( + [match.get(i, S.Zero) for i in (a, b, m, n)] + + [integrand, symbol])) + +def trig_sindouble_rule(integral): + integrand, symbol = integral + a = Wild('a', exclude=[sin(2*symbol)]) + match = integrand.match(sin(2*symbol)*a) + if match: + sin_double = 2*sin(symbol)*cos(symbol)/sin(2*symbol) + return integral_steps(integrand * sin_double, symbol) + +def trig_powers_products_rule(integral): + return do_one(null_safe(trig_sincos_rule), + null_safe(trig_tansec_rule), + null_safe(trig_cotcsc_rule), + null_safe(trig_sindouble_rule))(integral) + +def trig_substitution_rule(integral): + integrand, symbol = integral + A = Wild('a', exclude=[0, symbol]) + B = Wild('b', exclude=[0, symbol]) + theta = Dummy("theta") + target_pattern = A + B*symbol**2 + + matches = integrand.find(target_pattern) + for expr in matches: + match = expr.match(target_pattern) + a = match.get(A, S.Zero) + b = match.get(B, S.Zero) + + a_positive = ((a.is_number and a > 0) or a.is_positive) + b_positive = ((b.is_number and b > 0) or b.is_positive) + a_negative = ((a.is_number and a < 0) or a.is_negative) + b_negative = ((b.is_number and b < 0) or b.is_negative) + x_func = None + if a_positive and b_positive: + # a**2 + b*x**2. Assume sec(theta) > 0, -pi/2 < theta < pi/2 + x_func = (sqrt(a)/sqrt(b)) * tan(theta) + # Do not restrict the domain: tan(theta) takes on any real + # value on the interval -pi/2 < theta < pi/2 so x takes on + # any value + restriction = True + elif a_positive and b_negative: + # a**2 - b*x**2. Assume cos(theta) > 0, -pi/2 < theta < pi/2 + constant = sqrt(a)/sqrt(-b) + x_func = constant * sin(theta) + restriction = And(symbol > -constant, symbol < constant) + elif a_negative and b_positive: + # b*x**2 - a**2. Assume sin(theta) > 0, 0 < theta < pi + constant = sqrt(-a)/sqrt(b) + x_func = constant * sec(theta) + restriction = And(symbol > -constant, symbol < constant) + if x_func: + # Manually simplify sqrt(trig(theta)**2) to trig(theta) + # Valid due to assumed domain restriction + substitutions = {} + for f in [sin, cos, tan, + sec, csc, cot]: + substitutions[sqrt(f(theta)**2)] = f(theta) + substitutions[sqrt(f(theta)**(-2))] = 1/f(theta) + + replaced = integrand.subs(symbol, x_func).trigsimp() + replaced = manual_subs(replaced, substitutions) + if not replaced.has(symbol): + replaced *= manual_diff(x_func, theta) + replaced = replaced.trigsimp() + secants = replaced.find(1/cos(theta)) + if secants: + replaced = replaced.xreplace({ + 1/cos(theta): sec(theta) + }) + + substep = integral_steps(replaced, theta) + if not substep.contains_dont_know(): + return TrigSubstitutionRule(integrand, symbol, + theta, x_func, replaced, substep, restriction) + +def heaviside_rule(integral): + integrand, symbol = integral + pattern, m, b, g = heaviside_pattern(symbol) + match = integrand.match(pattern) + if match and 0 != match[g]: + # f = Heaviside(m*x + b)*g + substep = integral_steps(match[g], symbol) + m, b = match[m], match[b] + return HeavisideRule(integrand, symbol, m*symbol + b, -b/m, substep) + + +def dirac_delta_rule(integral: IntegralInfo): + integrand, x = integral + if len(integrand.args) == 1: + n = S.Zero + else: + n = integrand.args[1] + if not n.is_Integer or n < 0: + return + a, b = Wild('a', exclude=[x]), Wild('b', exclude=[x, 0]) + match = integrand.args[0].match(a+b*x) + if not match: + return + a, b = match[a], match[b] + generic_cond = Ne(b, 0) + if generic_cond is S.true: + degenerate_step = None + else: + degenerate_step = ConstantRule(DiracDelta(a, n), x) + generic_step = DiracDeltaRule(integrand, x, n, a, b) + return _add_degenerate_step(generic_cond, generic_step, degenerate_step) + + +def substitution_rule(integral): + integrand, symbol = integral + + u_var = Dummy("u") + substitutions = find_substitutions(integrand, symbol, u_var) + count = 0 + if substitutions: + debug("List of Substitution Rules") + ways = [] + for u_func, c, substituted in substitutions: + subrule = integral_steps(substituted, u_var) + count = count + 1 + debug("Rule {}: {}".format(count, subrule)) + + if subrule.contains_dont_know(): + continue + + if simplify(c - 1) != 0: + _, denom = c.as_numer_denom() + if subrule: + subrule = ConstantTimesRule(c * substituted, u_var, c, substituted, subrule) + + if denom.free_symbols: + piecewise = [] + could_be_zero = [] + + if isinstance(denom, Mul): + could_be_zero = denom.args + else: + could_be_zero.append(denom) + + for expr in could_be_zero: + if not fuzzy_not(expr.is_zero): + substep = integral_steps(manual_subs(integrand, expr, 0), symbol) + + if substep: + piecewise.append(( + substep, + Eq(expr, 0) + )) + piecewise.append((subrule, True)) + subrule = PiecewiseRule(substituted, symbol, piecewise) + + ways.append(URule(integrand, symbol, u_var, u_func, subrule)) + + if len(ways) > 1: + return AlternativeRule(integrand, symbol, ways) + elif ways: + return ways[0] + + +partial_fractions_rule = rewriter( + lambda integrand, symbol: integrand.is_rational_function(), + lambda integrand, symbol: integrand.apart(symbol)) + +cancel_rule = rewriter( + # lambda integrand, symbol: integrand.is_algebraic_expr(), + # lambda integrand, symbol: isinstance(integrand, Mul), + lambda integrand, symbol: True, + lambda integrand, symbol: integrand.cancel()) + +distribute_expand_rule = rewriter( + lambda integrand, symbol: ( + isinstance(integrand, (Pow, Mul)) or all(arg.is_Pow or arg.is_polynomial(symbol) for arg in integrand.args)), + lambda integrand, symbol: integrand.expand()) + +trig_expand_rule = rewriter( + # If there are trig functions with different arguments, expand them + lambda integrand, symbol: ( + len({a.args[0] for a in integrand.atoms(TrigonometricFunction)}) > 1), + lambda integrand, symbol: integrand.expand(trig=True)) + +def derivative_rule(integral): + integrand = integral[0] + diff_variables = integrand.variables + undifferentiated_function = integrand.expr + integrand_variables = undifferentiated_function.free_symbols + + if integral.symbol in integrand_variables: + if integral.symbol in diff_variables: + return DerivativeRule(*integral) + else: + return DontKnowRule(integrand, integral.symbol) + else: + return ConstantRule(*integral) + +def rewrites_rule(integral): + integrand, symbol = integral + + if integrand.match(1/cos(symbol)): + rewritten = integrand.subs(1/cos(symbol), sec(symbol)) + return RewriteRule(integrand, symbol, rewritten, integral_steps(rewritten, symbol)) + +def fallback_rule(integral): + return DontKnowRule(*integral) + +# Cache is used to break cyclic integrals. +# Need to use the same dummy variable in cached expressions for them to match. +# Also record "u" of integration by parts, to avoid infinite repetition. +_integral_cache: dict[Expr, Expr | None] = {} +_parts_u_cache: dict[Expr, int] = defaultdict(int) +_cache_dummy = Dummy("z") + +def integral_steps(integrand, symbol, **options): + """Returns the steps needed to compute an integral. + + Explanation + =========== + + This function attempts to mirror what a student would do by hand as + closely as possible. + + SymPy Gamma uses this to provide a step-by-step explanation of an + integral. The code it uses to format the results of this function can be + found at + https://github.com/sympy/sympy_gamma/blob/master/app/logic/intsteps.py. + + Examples + ======== + + >>> from sympy import exp, sin + >>> from sympy.integrals.manualintegrate import integral_steps + >>> from sympy.abc import x + >>> print(repr(integral_steps(exp(x) / (1 + exp(2 * x)), x))) \ + # doctest: +NORMALIZE_WHITESPACE + URule(integrand=exp(x)/(exp(2*x) + 1), variable=x, u_var=_u, u_func=exp(x), + substep=ArctanRule(integrand=1/(_u**2 + 1), variable=_u, a=1, b=1, c=1)) + >>> print(repr(integral_steps(sin(x), x))) \ + # doctest: +NORMALIZE_WHITESPACE + SinRule(integrand=sin(x), variable=x) + >>> print(repr(integral_steps((x**2 + 3)**2, x))) \ + # doctest: +NORMALIZE_WHITESPACE + RewriteRule(integrand=(x**2 + 3)**2, variable=x, rewritten=x**4 + 6*x**2 + 9, + substep=AddRule(integrand=x**4 + 6*x**2 + 9, variable=x, + substeps=[PowerRule(integrand=x**4, variable=x, base=x, exp=4), + ConstantTimesRule(integrand=6*x**2, variable=x, constant=6, other=x**2, + substep=PowerRule(integrand=x**2, variable=x, base=x, exp=2)), + ConstantRule(integrand=9, variable=x)])) + + Returns + ======= + + rule : Rule + The first step; most rules have substeps that must also be + considered. These substeps can be evaluated using ``manualintegrate`` + to obtain a result. + + """ + cachekey = integrand.xreplace({symbol: _cache_dummy}) + if cachekey in _integral_cache: + if _integral_cache[cachekey] is None: + # Stop this attempt, because it leads around in a loop + return DontKnowRule(integrand, symbol) + else: + # TODO: This is for future development, as currently + # _integral_cache gets no values other than None + return (_integral_cache[cachekey].xreplace(_cache_dummy, symbol), + symbol) + else: + _integral_cache[cachekey] = None + + integral = IntegralInfo(integrand, symbol) + + def key(integral): + integrand = integral.integrand + + if symbol not in integrand.free_symbols: + return Number + for cls in (Symbol, TrigonometricFunction, OrthogonalPolynomial): + if isinstance(integrand, cls): + return cls + return type(integrand) + + def integral_is_subclass(*klasses): + def _integral_is_subclass(integral): + k = key(integral) + return k and issubclass(k, klasses) + return _integral_is_subclass + + result = do_one( + null_safe(special_function_rule), + null_safe(switch(key, { + Pow: do_one(null_safe(power_rule), null_safe(inverse_trig_rule), + null_safe(sqrt_linear_rule), + null_safe(quadratic_denom_rule)), + Symbol: power_rule, + exp: exp_rule, + Add: add_rule, + Mul: do_one(null_safe(mul_rule), null_safe(trig_product_rule), + null_safe(heaviside_rule), null_safe(quadratic_denom_rule), + null_safe(sqrt_linear_rule), + null_safe(sqrt_quadratic_rule)), + Derivative: derivative_rule, + TrigonometricFunction: trig_rule, + Heaviside: heaviside_rule, + DiracDelta: dirac_delta_rule, + OrthogonalPolynomial: orthogonal_poly_rule, + Number: constant_rule + })), + do_one( + null_safe(trig_rule), + null_safe(hyperbolic_rule), + null_safe(alternatives( + rewrites_rule, + substitution_rule, + condition( + integral_is_subclass(Mul, Pow), + partial_fractions_rule), + condition( + integral_is_subclass(Mul, Pow), + cancel_rule), + condition( + integral_is_subclass(Mul, log, + *inverse_trig_functions), + parts_rule), + condition( + integral_is_subclass(Mul, Pow), + distribute_expand_rule), + trig_powers_products_rule, + trig_expand_rule + )), + null_safe(condition(integral_is_subclass(Mul, Pow), nested_pow_rule)), + null_safe(trig_substitution_rule) + ), + fallback_rule)(integral) + del _integral_cache[cachekey] + return result + + +def manualintegrate(f, var): + """manualintegrate(f, var) + + Explanation + =========== + + Compute indefinite integral of a single variable using an algorithm that + resembles what a student would do by hand. + + Unlike :func:`~.integrate`, var can only be a single symbol. + + Examples + ======== + + >>> from sympy import sin, cos, tan, exp, log, integrate + >>> from sympy.integrals.manualintegrate import manualintegrate + >>> from sympy.abc import x + >>> manualintegrate(1 / x, x) + log(x) + >>> integrate(1/x) + log(x) + >>> manualintegrate(log(x), x) + x*log(x) - x + >>> integrate(log(x)) + x*log(x) - x + >>> manualintegrate(exp(x) / (1 + exp(2 * x)), x) + atan(exp(x)) + >>> integrate(exp(x) / (1 + exp(2 * x))) + RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x)))) + >>> manualintegrate(cos(x)**4 * sin(x), x) + -cos(x)**5/5 + >>> integrate(cos(x)**4 * sin(x), x) + -cos(x)**5/5 + >>> manualintegrate(cos(x)**4 * sin(x)**3, x) + cos(x)**7/7 - cos(x)**5/5 + >>> integrate(cos(x)**4 * sin(x)**3, x) + cos(x)**7/7 - cos(x)**5/5 + >>> manualintegrate(tan(x), x) + -log(cos(x)) + >>> integrate(tan(x), x) + -log(cos(x)) + + See Also + ======== + + sympy.integrals.integrals.integrate + sympy.integrals.integrals.Integral.doit + sympy.integrals.integrals.Integral + """ + result = integral_steps(f, var).eval() + # Clear the cache of u-parts + _parts_u_cache.clear() + # If we got Piecewise with two parts, put generic first + if isinstance(result, Piecewise) and len(result.args) == 2: + cond = result.args[0][1] + if isinstance(cond, Eq) and result.args[1][1] == True: + result = result.func( + (result.args[1][0], Ne(*cond.args)), + (result.args[0][0], True)) + return result diff --git a/lib/python3.11/site-packages/sympy/integrals/meijerint.py b/lib/python3.11/site-packages/sympy/integrals/meijerint.py new file mode 100644 index 0000000000000000000000000000000000000000..5b518fdf2a16b5de63e311bf706fd5a4678e6cee --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/meijerint.py @@ -0,0 +1,2191 @@ +""" +Integrate functions by rewriting them as Meijer G-functions. + +There are three user-visible functions that can be used by other parts of the +sympy library to solve various integration problems: + +- meijerint_indefinite +- meijerint_definite +- meijerint_inversion + +They can be used to compute, respectively, indefinite integrals, definite +integrals over intervals of the real line, and inverse laplace-type integrals +(from c-I*oo to c+I*oo). See the respective docstrings for details. + +The main references for this are: + +[L] Luke, Y. L. (1969), The Special Functions and Their Approximations, + Volume 1 + +[R] Kelly B. Roach. Meijer G Function Representations. + In: Proceedings of the 1997 International Symposium on Symbolic and + Algebraic Computation, pages 205-211, New York, 1997. ACM. + +[P] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev (1990). + Integrals and Series: More Special Functions, Vol. 3,. + Gordon and Breach Science Publisher +""" + +from __future__ import annotations +import itertools + +from sympy import SYMPY_DEBUG +from sympy.core import S, Expr +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.cache import cacheit +from sympy.core.containers import Tuple +from sympy.core.exprtools import factor_terms +from sympy.core.function import (expand, expand_mul, expand_power_base, + expand_trig, Function) +from sympy.core.mul import Mul +from sympy.core.intfunc import ilcm +from sympy.core.numbers import Rational, pi +from sympy.core.relational import Eq, Ne, _canonical_coeff +from sympy.core.sorting import default_sort_key, ordered +from sympy.core.symbol import Dummy, symbols, Wild, Symbol +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.complexes import (re, im, arg, Abs, sign, + unpolarify, polarify, polar_lift, principal_branch, unbranched_argument, + periodic_argument) +from sympy.functions.elementary.exponential import exp, exp_polar, log +from sympy.functions.elementary.integers import ceiling +from sympy.functions.elementary.hyperbolic import (cosh, sinh, + _rewrite_hyperbolics_as_exp, HyperbolicFunction) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold +from sympy.functions.elementary.trigonometric import (cos, sin, sinc, + TrigonometricFunction) +from sympy.functions.special.bessel import besselj, bessely, besseli, besselk +from sympy.functions.special.delta_functions import DiracDelta, Heaviside +from sympy.functions.special.elliptic_integrals import elliptic_k, elliptic_e +from sympy.functions.special.error_functions import (erf, erfc, erfi, Ei, + expint, Si, Ci, Shi, Chi, fresnels, fresnelc) +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import hyper, meijerg +from sympy.functions.special.singularity_functions import SingularityFunction +from .integrals import Integral +from sympy.logic.boolalg import And, Or, BooleanAtom, Not, BooleanFunction +from sympy.polys import cancel, factor +from sympy.utilities.iterables import multiset_partitions +from sympy.utilities.misc import debug as _debug +from sympy.utilities.misc import debugf as _debugf + +# keep this at top for easy reference +z = Dummy('z') + + +def _has(res, *f): + # return True if res has f; in the case of Piecewise + # only return True if *all* pieces have f + res = piecewise_fold(res) + if getattr(res, 'is_Piecewise', False): + return all(_has(i, *f) for i in res.args) + return res.has(*f) + + +def _create_lookup_table(table): + """ Add formulae for the function -> meijerg lookup table. """ + def wild(n): + return Wild(n, exclude=[z]) + p, q, a, b, c = list(map(wild, 'pqabc')) + n = Wild('n', properties=[lambda x: x.is_Integer and x > 0]) + t = p*z**q + + def add(formula, an, ap, bm, bq, arg=t, fac=S.One, cond=True, hint=True): + table.setdefault(_mytype(formula, z), []).append((formula, + [(fac, meijerg(an, ap, bm, bq, arg))], cond, hint)) + + def addi(formula, inst, cond, hint=True): + table.setdefault( + _mytype(formula, z), []).append((formula, inst, cond, hint)) + + def constant(a): + return [(a, meijerg([1], [], [], [0], z)), + (a, meijerg([], [1], [0], [], z))] + table[()] = [(a, constant(a), True, True)] + + # [P], Section 8. + class IsNonPositiveInteger(Function): + + @classmethod + def eval(cls, arg): + arg = unpolarify(arg) + if arg.is_Integer is True: + return arg <= 0 + + # Section 8.4.2 + # TODO this needs more polar_lift (c/f entry for exp) + add(Heaviside(t - b)*(t - b)**(a - 1), [a], [], [], [0], t/b, + gamma(a)*b**(a - 1), And(b > 0)) + add(Heaviside(b - t)*(b - t)**(a - 1), [], [a], [0], [], t/b, + gamma(a)*b**(a - 1), And(b > 0)) + add(Heaviside(z - (b/p)**(1/q))*(t - b)**(a - 1), [a], [], [], [0], t/b, + gamma(a)*b**(a - 1), And(b > 0)) + add(Heaviside((b/p)**(1/q) - z)*(b - t)**(a - 1), [], [a], [0], [], t/b, + gamma(a)*b**(a - 1), And(b > 0)) + add((b + t)**(-a), [1 - a], [], [0], [], t/b, b**(-a)/gamma(a), + hint=Not(IsNonPositiveInteger(a))) + add(Abs(b - t)**(-a), [1 - a], [(1 - a)/2], [0], [(1 - a)/2], t/b, + 2*sin(pi*a/2)*gamma(1 - a)*Abs(b)**(-a), re(a) < 1) + add((t**a - b**a)/(t - b), [0, a], [], [0, a], [], t/b, + b**(a - 1)*sin(a*pi)/pi) + + # 12 + def A1(r, sign, nu): + return pi**Rational(-1, 2)*(-sign*nu/2)**(1 - 2*r) + + def tmpadd(r, sgn): + # XXX the a**2 is bad for matching + add((sqrt(a**2 + t) + sgn*a)**b/(a**2 + t)**r, + [(1 + b)/2, 1 - 2*r + b/2], [], + [(b - sgn*b)/2], [(b + sgn*b)/2], t/a**2, + a**(b - 2*r)*A1(r, sgn, b)) + tmpadd(0, 1) + tmpadd(0, -1) + tmpadd(S.Half, 1) + tmpadd(S.Half, -1) + + # 13 + def tmpadd(r, sgn): + add((sqrt(a + p*z**q) + sgn*sqrt(p)*z**(q/2))**b/(a + p*z**q)**r, + [1 - r + sgn*b/2], [1 - r - sgn*b/2], [0, S.Half], [], + p*z**q/a, a**(b/2 - r)*A1(r, sgn, b)) + tmpadd(0, 1) + tmpadd(0, -1) + tmpadd(S.Half, 1) + tmpadd(S.Half, -1) + # (those after look obscure) + + # Section 8.4.3 + add(exp(polar_lift(-1)*t), [], [], [0], []) + + # TODO can do sin^n, sinh^n by expansion ... where? + # 8.4.4 (hyperbolic functions) + add(sinh(t), [], [1], [S.Half], [1, 0], t**2/4, pi**Rational(3, 2)) + add(cosh(t), [], [S.Half], [0], [S.Half, S.Half], t**2/4, pi**Rational(3, 2)) + + # Section 8.4.5 + # TODO can do t + a. but can also do by expansion... (XXX not really) + add(sin(t), [], [], [S.Half], [0], t**2/4, sqrt(pi)) + add(cos(t), [], [], [0], [S.Half], t**2/4, sqrt(pi)) + + # Section 8.4.6 (sinc function) + add(sinc(t), [], [], [0], [Rational(-1, 2)], t**2/4, sqrt(pi)/2) + + # Section 8.5.5 + def make_log1(subs): + N = subs[n] + return [(S.NegativeOne**N*factorial(N), + meijerg([], [1]*(N + 1), [0]*(N + 1), [], t))] + + def make_log2(subs): + N = subs[n] + return [(factorial(N), + meijerg([1]*(N + 1), [], [], [0]*(N + 1), t))] + # TODO these only hold for positive p, and can be made more general + # but who uses log(x)*Heaviside(a-x) anyway ... + # TODO also it would be nice to derive them recursively ... + addi(log(t)**n*Heaviside(1 - t), make_log1, True) + addi(log(t)**n*Heaviside(t - 1), make_log2, True) + + def make_log3(subs): + return make_log1(subs) + make_log2(subs) + addi(log(t)**n, make_log3, True) + addi(log(t + a), + constant(log(a)) + [(S.One, meijerg([1, 1], [], [1], [0], t/a))], + True) + addi(log(Abs(t - a)), constant(log(Abs(a))) + + [(pi, meijerg([1, 1], [S.Half], [1], [0, S.Half], t/a))], + True) + # TODO log(x)/(x+a) and log(x)/(x-1) can also be done. should they + # be derivable? + # TODO further formulae in this section seem obscure + + # Sections 8.4.9-10 + # TODO + + # Section 8.4.11 + addi(Ei(t), + constant(-S.ImaginaryUnit*pi) + [(S.NegativeOne, meijerg([], [1], [0, 0], [], + t*polar_lift(-1)))], + True) + + # Section 8.4.12 + add(Si(t), [1], [], [S.Half], [0, 0], t**2/4, sqrt(pi)/2) + add(Ci(t), [], [1], [0, 0], [S.Half], t**2/4, -sqrt(pi)/2) + + # Section 8.4.13 + add(Shi(t), [S.Half], [], [0], [Rational(-1, 2), Rational(-1, 2)], polar_lift(-1)*t**2/4, + t*sqrt(pi)/4) + add(Chi(t), [], [S.Half, 1], [0, 0], [S.Half, S.Half], t**2/4, - + pi**S('3/2')/2) + + # generalized exponential integral + add(expint(a, t), [], [a], [a - 1, 0], [], t) + + # Section 8.4.14 + add(erf(t), [1], [], [S.Half], [0], t**2, 1/sqrt(pi)) + # TODO exp(-x)*erf(I*x) does not work + add(erfc(t), [], [1], [0, S.Half], [], t**2, 1/sqrt(pi)) + # This formula for erfi(z) yields a wrong(?) minus sign + #add(erfi(t), [1], [], [S.Half], [0], -t**2, I/sqrt(pi)) + add(erfi(t), [S.Half], [], [0], [Rational(-1, 2)], -t**2, t/sqrt(pi)) + + # Fresnel Integrals + add(fresnels(t), [1], [], [Rational(3, 4)], [0, Rational(1, 4)], pi**2*t**4/16, S.Half) + add(fresnelc(t), [1], [], [Rational(1, 4)], [0, Rational(3, 4)], pi**2*t**4/16, S.Half) + + ##### bessel-type functions ##### + # Section 8.4.19 + add(besselj(a, t), [], [], [a/2], [-a/2], t**2/4) + + # all of the following are derivable + #add(sin(t)*besselj(a, t), [Rational(1, 4), Rational(3, 4)], [], [(1+a)/2], + # [-a/2, a/2, (1-a)/2], t**2, 1/sqrt(2)) + #add(cos(t)*besselj(a, t), [Rational(1, 4), Rational(3, 4)], [], [a/2], + # [-a/2, (1+a)/2, (1-a)/2], t**2, 1/sqrt(2)) + #add(besselj(a, t)**2, [S.Half], [], [a], [-a, 0], t**2, 1/sqrt(pi)) + #add(besselj(a, t)*besselj(b, t), [0, S.Half], [], [(a + b)/2], + # [-(a+b)/2, (a - b)/2, (b - a)/2], t**2, 1/sqrt(pi)) + + # Section 8.4.20 + add(bessely(a, t), [], [-(a + 1)/2], [a/2, -a/2], [-(a + 1)/2], t**2/4) + + # TODO all of the following should be derivable + #add(sin(t)*bessely(a, t), [Rational(1, 4), Rational(3, 4)], [(1 - a - 1)/2], + # [(1 + a)/2, (1 - a)/2], [(1 - a - 1)/2, (1 - 1 - a)/2, (1 - 1 + a)/2], + # t**2, 1/sqrt(2)) + #add(cos(t)*bessely(a, t), [Rational(1, 4), Rational(3, 4)], [(0 - a - 1)/2], + # [(0 + a)/2, (0 - a)/2], [(0 - a - 1)/2, (1 - 0 - a)/2, (1 - 0 + a)/2], + # t**2, 1/sqrt(2)) + #add(besselj(a, t)*bessely(b, t), [0, S.Half], [(a - b - 1)/2], + # [(a + b)/2, (a - b)/2], [(a - b - 1)/2, -(a + b)/2, (b - a)/2], + # t**2, 1/sqrt(pi)) + #addi(bessely(a, t)**2, + # [(2/sqrt(pi), meijerg([], [S.Half, S.Half - a], [0, a, -a], + # [S.Half - a], t**2)), + # (1/sqrt(pi), meijerg([S.Half], [], [a], [-a, 0], t**2))], + # True) + #addi(bessely(a, t)*bessely(b, t), + # [(2/sqrt(pi), meijerg([], [0, S.Half, (1 - a - b)/2], + # [(a + b)/2, (a - b)/2, (b - a)/2, -(a + b)/2], + # [(1 - a - b)/2], t**2)), + # (1/sqrt(pi), meijerg([0, S.Half], [], [(a + b)/2], + # [-(a + b)/2, (a - b)/2, (b - a)/2], t**2))], + # True) + + # Section 8.4.21 ? + # Section 8.4.22 + add(besseli(a, t), [], [(1 + a)/2], [a/2], [-a/2, (1 + a)/2], t**2/4, pi) + # TODO many more formulas. should all be derivable + + # Section 8.4.23 + add(besselk(a, t), [], [], [a/2, -a/2], [], t**2/4, S.Half) + # TODO many more formulas. should all be derivable + + # Complete elliptic integrals K(z) and E(z) + add(elliptic_k(t), [S.Half, S.Half], [], [0], [0], -t, S.Half) + add(elliptic_e(t), [S.Half, 3*S.Half], [], [0], [0], -t, Rational(-1, 2)/2) + + +#################################################################### +# First some helper functions. +#################################################################### + +from sympy.utilities.timeutils import timethis +timeit = timethis('meijerg') + + +def _mytype(f: Basic, x: Symbol) -> tuple[type[Basic], ...]: + """ Create a hashable entity describing the type of f. """ + def key(x: type[Basic]) -> tuple[int, int, str]: + return x.class_key() + + if x not in f.free_symbols: + return () + elif f.is_Function: + return type(f), + return tuple(sorted((t for a in f.args for t in _mytype(a, x)), key=key)) + + +class _CoeffExpValueError(ValueError): + """ + Exception raised by _get_coeff_exp, for internal use only. + """ + pass + + +def _get_coeff_exp(expr, x): + """ + When expr is known to be of the form c*x**b, with c and/or b possibly 1, + return c, b. + + Examples + ======== + + >>> from sympy.abc import x, a, b + >>> from sympy.integrals.meijerint import _get_coeff_exp + >>> _get_coeff_exp(a*x**b, x) + (a, b) + >>> _get_coeff_exp(x, x) + (1, 1) + >>> _get_coeff_exp(2*x, x) + (2, 1) + >>> _get_coeff_exp(x**3, x) + (1, 3) + """ + from sympy.simplify import powsimp + (c, m) = expand_power_base(powsimp(expr)).as_coeff_mul(x) + if not m: + return c, S.Zero + [m] = m + if m.is_Pow: + if m.base != x: + raise _CoeffExpValueError('expr not of form a*x**b') + return c, m.exp + elif m == x: + return c, S.One + else: + raise _CoeffExpValueError('expr not of form a*x**b: %s' % expr) + + +def _exponents(expr, x): + """ + Find the exponents of ``x`` (not including zero) in ``expr``. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _exponents + >>> from sympy.abc import x, y + >>> from sympy import sin + >>> _exponents(x, x) + {1} + >>> _exponents(x**2, x) + {2} + >>> _exponents(x**2 + x, x) + {1, 2} + >>> _exponents(x**3*sin(x + x**y) + 1/x, x) + {-1, 1, 3, y} + """ + def _exponents_(expr, x, res): + if expr == x: + res.update([1]) + return + if expr.is_Pow and expr.base == x: + res.update([expr.exp]) + return + for argument in expr.args: + _exponents_(argument, x, res) + res = set() + _exponents_(expr, x, res) + return res + + +def _functions(expr, x): + """ Find the types of functions in expr, to estimate the complexity. """ + return {e.func for e in expr.atoms(Function) if x in e.free_symbols} + + +def _find_splitting_points(expr, x): + """ + Find numbers a such that a linear substitution x -> x + a would + (hopefully) simplify expr. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _find_splitting_points as fsp + >>> from sympy import sin + >>> from sympy.abc import x + >>> fsp(x, x) + {0} + >>> fsp((x-1)**3, x) + {1} + >>> fsp(sin(x+3)*x, x) + {-3, 0} + """ + p, q = [Wild(n, exclude=[x]) for n in 'pq'] + + def compute_innermost(expr, res): + if not isinstance(expr, Expr): + return + m = expr.match(p*x + q) + if m and m[p] != 0: + res.add(-m[q]/m[p]) + return + if expr.is_Atom: + return + for argument in expr.args: + compute_innermost(argument, res) + innermost = set() + compute_innermost(expr, innermost) + return innermost + + +def _split_mul(f, x): + """ + Split expression ``f`` into fac, po, g, where fac is a constant factor, + po = x**s for some s independent of s, and g is "the rest". + + Examples + ======== + + >>> from sympy.integrals.meijerint import _split_mul + >>> from sympy import sin + >>> from sympy.abc import s, x + >>> _split_mul((3*x)**s*sin(x**2)*x, x) + (3**s, x*x**s, sin(x**2)) + """ + fac = S.One + po = S.One + g = S.One + f = expand_power_base(f) + + args = Mul.make_args(f) + for a in args: + if a == x: + po *= x + elif x not in a.free_symbols: + fac *= a + else: + if a.is_Pow and x not in a.exp.free_symbols: + c, t = a.base.as_coeff_mul(x) + if t != (x,): + c, t = expand_mul(a.base).as_coeff_mul(x) + if t == (x,): + po *= x**a.exp + fac *= unpolarify(polarify(c**a.exp, subs=False)) + continue + g *= a + + return fac, po, g + + +def _mul_args(f): + """ + Return a list ``L`` such that ``Mul(*L) == f``. + + If ``f`` is not a ``Mul`` or ``Pow``, ``L=[f]``. + If ``f=g**n`` for an integer ``n``, ``L=[g]*n``. + If ``f`` is a ``Mul``, ``L`` comes from applying ``_mul_args`` to all factors of ``f``. + """ + args = Mul.make_args(f) + gs = [] + for g in args: + if g.is_Pow and g.exp.is_Integer: + n = g.exp + base = g.base + if n < 0: + n = -n + base = 1/base + gs += [base]*n + else: + gs.append(g) + return gs + + +def _mul_as_two_parts(f): + """ + Find all the ways to split ``f`` into a product of two terms. + Return None on failure. + + Explanation + =========== + + Although the order is canonical from multiset_partitions, this is + not necessarily the best order to process the terms. For example, + if the case of len(gs) == 2 is removed and multiset is allowed to + sort the terms, some tests fail. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _mul_as_two_parts + >>> from sympy import sin, exp, ordered + >>> from sympy.abc import x + >>> list(ordered(_mul_as_two_parts(x*sin(x)*exp(x)))) + [(x, exp(x)*sin(x)), (x*exp(x), sin(x)), (x*sin(x), exp(x))] + """ + + gs = _mul_args(f) + if len(gs) < 2: + return None + if len(gs) == 2: + return [tuple(gs)] + return [(Mul(*x), Mul(*y)) for (x, y) in multiset_partitions(gs, 2)] + + +def _inflate_g(g, n): + """ Return C, h such that h is a G function of argument z**n and + g = C*h. """ + # TODO should this be a method of meijerg? + # See: [L, page 150, equation (5)] + def inflate(params, n): + """ (a1, .., ak) -> (a1/n, (a1+1)/n, ..., (ak + n-1)/n) """ + return [(a + i)/n for a, i in itertools.product(params, range(n))] + v = S(len(g.ap) - len(g.bq)) + C = n**(1 + g.nu + v/2) + C /= (2*pi)**((n - 1)*g.delta) + return C, meijerg(inflate(g.an, n), inflate(g.aother, n), + inflate(g.bm, n), inflate(g.bother, n), + g.argument**n * n**(n*v)) + + +def _flip_g(g): + """ Turn the G function into one of inverse argument + (i.e. G(1/x) -> G'(x)) """ + # See [L], section 5.2 + def tr(l): + return [1 - a for a in l] + return meijerg(tr(g.bm), tr(g.bother), tr(g.an), tr(g.aother), 1/g.argument) + + +def _inflate_fox_h(g, a): + r""" + Let d denote the integrand in the definition of the G function ``g``. + Consider the function H which is defined in the same way, but with + integrand d/Gamma(a*s) (contour conventions as usual). + + If ``a`` is rational, the function H can be written as C*G, for a constant C + and a G-function G. + + This function returns C, G. + """ + if a < 0: + return _inflate_fox_h(_flip_g(g), -a) + p = S(a.p) + q = S(a.q) + # We use the substitution s->qs, i.e. inflate g by q. We are left with an + # extra factor of Gamma(p*s), for which we use Gauss' multiplication + # theorem. + D, g = _inflate_g(g, q) + z = g.argument + D /= (2*pi)**((1 - p)/2)*p**Rational(-1, 2) + z /= p**p + bs = [(n + 1)/p for n in range(p)] + return D, meijerg(g.an, g.aother, g.bm, list(g.bother) + bs, z) + +_dummies: dict[tuple[str, str], Dummy] = {} + + +def _dummy(name, token, expr, **kwargs): + """ + Return a dummy. This will return the same dummy if the same token+name is + requested more than once, and it is not already in expr. + This is for being cache-friendly. + """ + d = _dummy_(name, token, **kwargs) + if d in expr.free_symbols: + return Dummy(name, **kwargs) + return d + + +def _dummy_(name, token, **kwargs): + """ + Return a dummy associated to name and token. Same effect as declaring + it globally. + """ + global _dummies + if not (name, token) in _dummies: + _dummies[(name, token)] = Dummy(name, **kwargs) + return _dummies[(name, token)] + + +def _is_analytic(f, x): + """ Check if f(x), when expressed using G functions on the positive reals, + will in fact agree with the G functions almost everywhere """ + return not any(x in expr.free_symbols for expr in f.atoms(Heaviside, Abs)) + + +def _condsimp(cond, first=True): + """ + Do naive simplifications on ``cond``. + + Explanation + =========== + + Note that this routine is completely ad-hoc, simplification rules being + added as need arises rather than following any logical pattern. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _condsimp as simp + >>> from sympy import Or, Eq + >>> from sympy.abc import x, y + >>> simp(Or(x < y, Eq(x, y))) + x <= y + """ + if first: + cond = cond.replace(lambda _: _.is_Relational, _canonical_coeff) + first = False + if not isinstance(cond, BooleanFunction): + return cond + p, q, r = symbols('p q r', cls=Wild) + # transforms tests use 0, 4, 5 and 11-14 + # meijer tests use 0, 2, 11, 14 + # joint_rv uses 6, 7 + rules = [ + (Or(p < q, Eq(p, q)), p <= q), # 0 + # The next two obviously are instances of a general pattern, but it is + # easier to spell out the few cases we care about. + (And(Abs(arg(p)) <= pi, Abs(arg(p) - 2*pi) <= pi), + Eq(arg(p) - pi, 0)), # 1 + (And(Abs(2*arg(p) + pi) <= pi, Abs(2*arg(p) - pi) <= pi), + Eq(arg(p), 0)), # 2 + (And(Abs(2*arg(p) + pi) < pi, Abs(2*arg(p) - pi) <= pi), + S.false), # 3 + (And(Abs(arg(p) - pi/2) <= pi/2, Abs(arg(p) + pi/2) <= pi/2), + Eq(arg(p), 0)), # 4 + (And(Abs(arg(p) - pi/2) <= pi/2, Abs(arg(p) + pi/2) < pi/2), + S.false), # 5 + (And(Abs(arg(p**2/2 + 1)) < pi, Ne(Abs(arg(p**2/2 + 1)), pi)), + S.true), # 6 + (Or(Abs(arg(p**2/2 + 1)) < pi, Ne(1/(p**2/2 + 1), 0)), + S.true), # 7 + (And(Abs(unbranched_argument(p)) <= pi, + Abs(unbranched_argument(exp_polar(-2*pi*S.ImaginaryUnit)*p)) <= pi), + Eq(unbranched_argument(exp_polar(-S.ImaginaryUnit*pi)*p), 0)), # 8 + (And(Abs(unbranched_argument(p)) <= pi/2, + Abs(unbranched_argument(exp_polar(-pi*S.ImaginaryUnit)*p)) <= pi/2), + Eq(unbranched_argument(exp_polar(-S.ImaginaryUnit*pi/2)*p), 0)), # 9 + (Or(p <= q, And(p < q, r)), p <= q), # 10 + (Ne(p**2, 1) & (p**2 > 1), p**2 > 1), # 11 + (Ne(1/p, 1) & (cos(Abs(arg(p)))*Abs(p) > 1), Abs(p) > 1), # 12 + (Ne(p, 2) & (cos(Abs(arg(p)))*Abs(p) > 2), Abs(p) > 2), # 13 + ((Abs(arg(p)) < pi/2) & (cos(Abs(arg(p)))*sqrt(Abs(p**2)) > 1), p**2 > 1), # 14 + ] + cond = cond.func(*[_condsimp(_, first) for _ in cond.args]) + change = True + while change: + change = False + for irule, (fro, to) in enumerate(rules): + if fro.func != cond.func: + continue + for n, arg1 in enumerate(cond.args): + if r in fro.args[0].free_symbols: + m = arg1.match(fro.args[1]) + num = 1 + else: + num = 0 + m = arg1.match(fro.args[0]) + if not m: + continue + otherargs = [x.subs(m) for x in fro.args[:num] + fro.args[num + 1:]] + otherlist = [n] + for arg2 in otherargs: + for k, arg3 in enumerate(cond.args): + if k in otherlist: + continue + if arg2 == arg3: + otherlist += [k] + break + if isinstance(arg3, And) and arg2.args[1] == r and \ + isinstance(arg2, And) and arg2.args[0] in arg3.args: + otherlist += [k] + break + if isinstance(arg3, And) and arg2.args[0] == r and \ + isinstance(arg2, And) and arg2.args[1] in arg3.args: + otherlist += [k] + break + if len(otherlist) != len(otherargs) + 1: + continue + newargs = [arg_ for (k, arg_) in enumerate(cond.args) + if k not in otherlist] + [to.subs(m)] + if SYMPY_DEBUG: + if irule not in (0, 2, 4, 5, 6, 7, 11, 12, 13, 14): + print('used new rule:', irule) + cond = cond.func(*newargs) + change = True + break + + # final tweak + def rel_touchup(rel): + if rel.rel_op != '==' or rel.rhs != 0: + return rel + + # handle Eq(*, 0) + LHS = rel.lhs + m = LHS.match(arg(p)**q) + if not m: + m = LHS.match(unbranched_argument(polar_lift(p)**q)) + if not m: + if isinstance(LHS, periodic_argument) and not LHS.args[0].is_polar \ + and LHS.args[1] is S.Infinity: + return (LHS.args[0] > 0) + return rel + return (m[p] > 0) + cond = cond.replace(lambda _: _.is_Relational, rel_touchup) + if SYMPY_DEBUG: + print('_condsimp: ', cond) + return cond + +def _eval_cond(cond): + """ Re-evaluate the conditions. """ + if isinstance(cond, bool): + return cond + return _condsimp(cond.doit()) + +#################################################################### +# Now the "backbone" functions to do actual integration. +#################################################################### + + +def _my_principal_branch(expr, period, full_pb=False): + """ Bring expr nearer to its principal branch by removing superfluous + factors. + This function does *not* guarantee to yield the principal branch, + to avoid introducing opaque principal_branch() objects, + unless full_pb=True. """ + res = principal_branch(expr, period) + if not full_pb: + res = res.replace(principal_branch, lambda x, y: x) + return res + + +def _rewrite_saxena_1(fac, po, g, x): + """ + Rewrite the integral fac*po*g dx, from zero to infinity, as + integral fac*G, where G has argument a*x. Note po=x**s. + Return fac, G. + """ + _, s = _get_coeff_exp(po, x) + a, b = _get_coeff_exp(g.argument, x) + period = g.get_period() + a = _my_principal_branch(a, period) + + # We substitute t = x**b. + C = fac/(Abs(b)*a**((s + 1)/b - 1)) + # Absorb a factor of (at)**((1 + s)/b - 1). + + def tr(l): + return [a + (1 + s)/b - 1 for a in l] + return C, meijerg(tr(g.an), tr(g.aother), tr(g.bm), tr(g.bother), + a*x) + + +def _check_antecedents_1(g, x, helper=False): + r""" + Return a condition under which the mellin transform of g exists. + Any power of x has already been absorbed into the G function, + so this is just $\int_0^\infty g\, dx$. + + See [L, section 5.6.1]. (Note that s=1.) + + If ``helper`` is True, only check if the MT exists at infinity, i.e. if + $\int_1^\infty g\, dx$ exists. + """ + # NOTE if you update these conditions, please update the documentation as well + delta = g.delta + eta, _ = _get_coeff_exp(g.argument, x) + m, n, p, q = S([len(g.bm), len(g.an), len(g.ap), len(g.bq)]) + + if p > q: + def tr(l): + return [1 - x for x in l] + return _check_antecedents_1(meijerg(tr(g.bm), tr(g.bother), + tr(g.an), tr(g.aother), x/eta), + x) + + tmp = [-re(b) < 1 for b in g.bm] + [1 < 1 - re(a) for a in g.an] + cond_3 = And(*tmp) + + tmp += [-re(b) < 1 for b in g.bother] + tmp += [1 < 1 - re(a) for a in g.aother] + cond_3_star = And(*tmp) + + cond_4 = (-re(g.nu) + (q + 1 - p)/2 > q - p) + + def debug(*msg): + _debug(*msg) + + def debugf(string, arg): + _debugf(string, arg) + + debug('Checking antecedents for 1 function:') + debugf(' delta=%s, eta=%s, m=%s, n=%s, p=%s, q=%s', + (delta, eta, m, n, p, q)) + debugf(' ap = %s, %s', (list(g.an), list(g.aother))) + debugf(' bq = %s, %s', (list(g.bm), list(g.bother))) + debugf(' cond_3=%s, cond_3*=%s, cond_4=%s', (cond_3, cond_3_star, cond_4)) + + conds = [] + + # case 1 + case1 = [] + tmp1 = [1 <= n, p < q, 1 <= m] + tmp2 = [1 <= p, 1 <= m, Eq(q, p + 1), Not(And(Eq(n, 0), Eq(m, p + 1)))] + tmp3 = [1 <= p, Eq(q, p)] + for k in range(ceiling(delta/2) + 1): + tmp3 += [Ne(Abs(unbranched_argument(eta)), (delta - 2*k)*pi)] + tmp = [delta > 0, Abs(unbranched_argument(eta)) < delta*pi] + extra = [Ne(eta, 0), cond_3] + if helper: + extra = [] + for t in [tmp1, tmp2, tmp3]: + case1 += [And(*(t + tmp + extra))] + conds += case1 + debug(' case 1:', case1) + + # case 2 + extra = [cond_3] + if helper: + extra = [] + case2 = [And(Eq(n, 0), p + 1 <= m, m <= q, + Abs(unbranched_argument(eta)) < delta*pi, *extra)] + conds += case2 + debug(' case 2:', case2) + + # case 3 + extra = [cond_3, cond_4] + if helper: + extra = [] + case3 = [And(p < q, 1 <= m, delta > 0, Eq(Abs(unbranched_argument(eta)), delta*pi), + *extra)] + case3 += [And(p <= q - 2, Eq(delta, 0), Eq(Abs(unbranched_argument(eta)), 0), *extra)] + conds += case3 + debug(' case 3:', case3) + + # TODO altered cases 4-7 + + # extra case from wofram functions site: + # (reproduced verbatim from Prudnikov, section 2.24.2) + # https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/01/ + case_extra = [] + case_extra += [Eq(p, q), Eq(delta, 0), Eq(unbranched_argument(eta), 0), Ne(eta, 0)] + if not helper: + case_extra += [cond_3] + s = [] + for a, b in zip(g.ap, g.bq): + s += [b - a] + case_extra += [re(Add(*s)) < 0] + case_extra = And(*case_extra) + conds += [case_extra] + debug(' extra case:', [case_extra]) + + case_extra_2 = [And(delta > 0, Abs(unbranched_argument(eta)) < delta*pi)] + if not helper: + case_extra_2 += [cond_3] + case_extra_2 = And(*case_extra_2) + conds += [case_extra_2] + debug(' second extra case:', [case_extra_2]) + + # TODO This leaves only one case from the three listed by Prudnikov. + # Investigate if these indeed cover everything; if so, remove the rest. + + return Or(*conds) + + +def _int0oo_1(g, x): + r""" + Evaluate $\int_0^\infty g\, dx$ using G functions, + assuming the necessary conditions are fulfilled. + + Examples + ======== + + >>> from sympy.abc import a, b, c, d, x, y + >>> from sympy import meijerg + >>> from sympy.integrals.meijerint import _int0oo_1 + >>> _int0oo_1(meijerg([a], [b], [c], [d], x*y), x) + gamma(-a)*gamma(c + 1)/(y*gamma(-d)*gamma(b + 1)) + """ + from sympy.simplify import gammasimp + # See [L, section 5.6.1]. Note that s=1. + eta, _ = _get_coeff_exp(g.argument, x) + res = 1/eta + # XXX TODO we should reduce order first + for b in g.bm: + res *= gamma(b + 1) + for a in g.an: + res *= gamma(1 - a - 1) + for b in g.bother: + res /= gamma(1 - b - 1) + for a in g.aother: + res /= gamma(a + 1) + return gammasimp(unpolarify(res)) + + +def _rewrite_saxena(fac, po, g1, g2, x, full_pb=False): + """ + Rewrite the integral ``fac*po*g1*g2`` from 0 to oo in terms of G + functions with argument ``c*x``. + + Explanation + =========== + + Return C, f1, f2 such that integral C f1 f2 from 0 to infinity equals + integral fac ``po``, ``g1``, ``g2`` from 0 to infinity. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _rewrite_saxena + >>> from sympy.abc import s, t, m + >>> from sympy import meijerg + >>> g1 = meijerg([], [], [0], [], s*t) + >>> g2 = meijerg([], [], [m/2], [-m/2], t**2/4) + >>> r = _rewrite_saxena(1, t**0, g1, g2, t) + >>> r[0] + s/(4*sqrt(pi)) + >>> r[1] + meijerg(((), ()), ((-1/2, 0), ()), s**2*t/4) + >>> r[2] + meijerg(((), ()), ((m/2,), (-m/2,)), t/4) + """ + def pb(g): + a, b = _get_coeff_exp(g.argument, x) + per = g.get_period() + return meijerg(g.an, g.aother, g.bm, g.bother, + _my_principal_branch(a, per, full_pb)*x**b) + + _, s = _get_coeff_exp(po, x) + _, b1 = _get_coeff_exp(g1.argument, x) + _, b2 = _get_coeff_exp(g2.argument, x) + if (b1 < 0) == True: + b1 = -b1 + g1 = _flip_g(g1) + if (b2 < 0) == True: + b2 = -b2 + g2 = _flip_g(g2) + if not b1.is_Rational or not b2.is_Rational: + return + m1, n1 = b1.p, b1.q + m2, n2 = b2.p, b2.q + tau = ilcm(m1*n2, m2*n1) + r1 = tau//(m1*n2) + r2 = tau//(m2*n1) + + C1, g1 = _inflate_g(g1, r1) + C2, g2 = _inflate_g(g2, r2) + g1 = pb(g1) + g2 = pb(g2) + + fac *= C1*C2 + a1, b = _get_coeff_exp(g1.argument, x) + a2, _ = _get_coeff_exp(g2.argument, x) + + # arbitrarily tack on the x**s part to g1 + # TODO should we try both? + exp = (s + 1)/b - 1 + fac = fac/(Abs(b) * a1**exp) + + def tr(l): + return [a + exp for a in l] + g1 = meijerg(tr(g1.an), tr(g1.aother), tr(g1.bm), tr(g1.bother), a1*x) + g2 = meijerg(g2.an, g2.aother, g2.bm, g2.bother, a2*x) + + from sympy.simplify import powdenest + return powdenest(fac, polar=True), g1, g2 + + +def _check_antecedents(g1, g2, x): + """ Return a condition under which the integral theorem applies. """ + # Yes, this is madness. + # XXX TODO this is a testing *nightmare* + # NOTE if you update these conditions, please update the documentation as well + + # The following conditions are found in + # [P], Section 2.24.1 + # + # They are also reproduced (verbatim!) at + # https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/ + # + # Note: k=l=r=alpha=1 + sigma, _ = _get_coeff_exp(g1.argument, x) + omega, _ = _get_coeff_exp(g2.argument, x) + s, t, u, v = S([len(g1.bm), len(g1.an), len(g1.ap), len(g1.bq)]) + m, n, p, q = S([len(g2.bm), len(g2.an), len(g2.ap), len(g2.bq)]) + bstar = s + t - (u + v)/2 + cstar = m + n - (p + q)/2 + rho = g1.nu + (u - v)/2 + 1 + mu = g2.nu + (p - q)/2 + 1 + phi = q - p - (v - u) + eta = 1 - (v - u) - mu - rho + psi = (pi*(q - m - n) + Abs(unbranched_argument(omega)))/(q - p) + theta = (pi*(v - s - t) + Abs(unbranched_argument(sigma)))/(v - u) + + _debug('Checking antecedents:') + _debugf(' sigma=%s, s=%s, t=%s, u=%s, v=%s, b*=%s, rho=%s', + (sigma, s, t, u, v, bstar, rho)) + _debugf(' omega=%s, m=%s, n=%s, p=%s, q=%s, c*=%s, mu=%s,', + (omega, m, n, p, q, cstar, mu)) + _debugf(' phi=%s, eta=%s, psi=%s, theta=%s', (phi, eta, psi, theta)) + + def _c1(): + for g in [g1, g2]: + for i, j in itertools.product(g.an, g.bm): + diff = i - j + if diff.is_integer and diff.is_positive: + return False + return True + c1 = _c1() + c2 = And(*[re(1 + i + j) > 0 for i in g1.bm for j in g2.bm]) + c3 = And(*[re(1 + i + j) < 1 + 1 for i in g1.an for j in g2.an]) + c4 = And(*[(p - q)*re(1 + i - 1) - re(mu) > Rational(-3, 2) for i in g1.an]) + c5 = And(*[(p - q)*re(1 + i) - re(mu) > Rational(-3, 2) for i in g1.bm]) + c6 = And(*[(u - v)*re(1 + i - 1) - re(rho) > Rational(-3, 2) for i in g2.an]) + c7 = And(*[(u - v)*re(1 + i) - re(rho) > Rational(-3, 2) for i in g2.bm]) + c8 = (Abs(phi) + 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu - + 1)*(v - u)) > 0) + c9 = (Abs(phi) - 2*re((rho - 1)*(q - p) + (v - u)*(q - p) + (mu - + 1)*(v - u)) > 0) + c10 = (Abs(unbranched_argument(sigma)) < bstar*pi) + c11 = Eq(Abs(unbranched_argument(sigma)), bstar*pi) + c12 = (Abs(unbranched_argument(omega)) < cstar*pi) + c13 = Eq(Abs(unbranched_argument(omega)), cstar*pi) + + # The following condition is *not* implemented as stated on the wolfram + # function site. In the book of Prudnikov there is an additional part + # (the And involving re()). However, I only have this book in russian, and + # I don't read any russian. The following condition is what other people + # have told me it means. + # Worryingly, it is different from the condition implemented in REDUCE. + # The REDUCE implementation: + # https://reduce-algebra.svn.sourceforge.net/svnroot/reduce-algebra/trunk/packages/defint/definta.red + # (search for tst14) + # The Wolfram alpha version: + # https://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/03/03/0014/ + z0 = exp(-(bstar + cstar)*pi*S.ImaginaryUnit) + zos = unpolarify(z0*omega/sigma) + zso = unpolarify(z0*sigma/omega) + if zos == 1/zso: + c14 = And(Eq(phi, 0), bstar + cstar <= 1, + Or(Ne(zos, 1), re(mu + rho + v - u) < 1, + re(mu + rho + q - p) < 1)) + else: + def _cond(z): + '''Returns True if abs(arg(1-z)) < pi, avoiding arg(0). + + Explanation + =========== + + If ``z`` is 1 then arg is NaN. This raises a + TypeError on `NaN < pi`. Previously this gave `False` so + this behavior has been hardcoded here but someone should + check if this NaN is more serious! This NaN is triggered by + test_meijerint() in test_meijerint.py: + `meijerint_definite(exp(x), x, 0, I)` + ''' + return z != 1 and Abs(arg(1 - z)) < pi + + c14 = And(Eq(phi, 0), bstar - 1 + cstar <= 0, + Or(And(Ne(zos, 1), _cond(zos)), + And(re(mu + rho + v - u) < 1, Eq(zos, 1)))) + + c14_alt = And(Eq(phi, 0), cstar - 1 + bstar <= 0, + Or(And(Ne(zso, 1), _cond(zso)), + And(re(mu + rho + q - p) < 1, Eq(zso, 1)))) + + # Since r=k=l=1, in our case there is c14_alt which is the same as calling + # us with (g1, g2) = (g2, g1). The conditions below enumerate all cases + # (i.e. we don't have to try arguments reversed by hand), and indeed try + # all symmetric cases. (i.e. whenever there is a condition involving c14, + # there is also a dual condition which is exactly what we would get when g1, + # g2 were interchanged, *but c14 was unaltered*). + # Hence the following seems correct: + c14 = Or(c14, c14_alt) + + ''' + When `c15` is NaN (e.g. from `psi` being NaN as happens during + 'test_issue_4992' and/or `theta` is NaN as in 'test_issue_6253', + both in `test_integrals.py`) the comparison to 0 formerly gave False + whereas now an error is raised. To keep the old behavior, the value + of NaN is replaced with False but perhaps a closer look at this condition + should be made: XXX how should conditions leading to c15=NaN be handled? + ''' + try: + lambda_c = (q - p)*Abs(omega)**(1/(q - p))*cos(psi) \ + + (v - u)*Abs(sigma)**(1/(v - u))*cos(theta) + # the TypeError might be raised here, e.g. if lambda_c is NaN + if _eval_cond(lambda_c > 0) != False: + c15 = (lambda_c > 0) + else: + def lambda_s0(c1, c2): + return c1*(q - p)*Abs(omega)**(1/(q - p))*sin(psi) \ + + c2*(v - u)*Abs(sigma)**(1/(v - u))*sin(theta) + lambda_s = Piecewise( + ((lambda_s0(+1, +1)*lambda_s0(-1, -1)), + And(Eq(unbranched_argument(sigma), 0), Eq(unbranched_argument(omega), 0))), + (lambda_s0(sign(unbranched_argument(omega)), +1)*lambda_s0(sign(unbranched_argument(omega)), -1), + And(Eq(unbranched_argument(sigma), 0), Ne(unbranched_argument(omega), 0))), + (lambda_s0(+1, sign(unbranched_argument(sigma)))*lambda_s0(-1, sign(unbranched_argument(sigma))), + And(Ne(unbranched_argument(sigma), 0), Eq(unbranched_argument(omega), 0))), + (lambda_s0(sign(unbranched_argument(omega)), sign(unbranched_argument(sigma))), True)) + tmp = [lambda_c > 0, + And(Eq(lambda_c, 0), Ne(lambda_s, 0), re(eta) > -1), + And(Eq(lambda_c, 0), Eq(lambda_s, 0), re(eta) > 0)] + c15 = Or(*tmp) + except TypeError: + c15 = False + for cond, i in [(c1, 1), (c2, 2), (c3, 3), (c4, 4), (c5, 5), (c6, 6), + (c7, 7), (c8, 8), (c9, 9), (c10, 10), (c11, 11), + (c12, 12), (c13, 13), (c14, 14), (c15, 15)]: + _debugf(' c%s: %s', (i, cond)) + + # We will return Or(*conds) + conds = [] + + def pr(count): + _debugf(' case %s: %s', (count, conds[-1])) + conds += [And(m*n*s*t != 0, bstar.is_positive is True, cstar.is_positive is True, c1, c2, c3, c10, + c12)] # 1 + pr(1) + conds += [And(Eq(u, v), Eq(bstar, 0), cstar.is_positive is True, sigma.is_positive is True, re(rho) < 1, + c1, c2, c3, c12)] # 2 + pr(2) + conds += [And(Eq(p, q), Eq(cstar, 0), bstar.is_positive is True, omega.is_positive is True, re(mu) < 1, + c1, c2, c3, c10)] # 3 + pr(3) + conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0), + sigma.is_positive is True, omega.is_positive is True, re(mu) < 1, re(rho) < 1, + Ne(sigma, omega), c1, c2, c3)] # 4 + pr(4) + conds += [And(Eq(p, q), Eq(u, v), Eq(bstar, 0), Eq(cstar, 0), + sigma.is_positive is True, omega.is_positive is True, re(mu + rho) < 1, + Ne(omega, sigma), c1, c2, c3)] # 5 + pr(5) + conds += [And(p > q, s.is_positive is True, bstar.is_positive is True, cstar >= 0, + c1, c2, c3, c5, c10, c13)] # 6 + pr(6) + conds += [And(p < q, t.is_positive is True, bstar.is_positive is True, cstar >= 0, + c1, c2, c3, c4, c10, c13)] # 7 + pr(7) + conds += [And(u > v, m.is_positive is True, cstar.is_positive is True, bstar >= 0, + c1, c2, c3, c7, c11, c12)] # 8 + pr(8) + conds += [And(u < v, n.is_positive is True, cstar.is_positive is True, bstar >= 0, + c1, c2, c3, c6, c11, c12)] # 9 + pr(9) + conds += [And(p > q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True, + re(rho) < 1, c1, c2, c3, c5, c13)] # 10 + pr(10) + conds += [And(p < q, Eq(u, v), Eq(bstar, 0), cstar >= 0, sigma.is_positive is True, + re(rho) < 1, c1, c2, c3, c4, c13)] # 11 + pr(11) + conds += [And(Eq(p, q), u > v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True, + re(mu) < 1, c1, c2, c3, c7, c11)] # 12 + pr(12) + conds += [And(Eq(p, q), u < v, bstar >= 0, Eq(cstar, 0), omega.is_positive is True, + re(mu) < 1, c1, c2, c3, c6, c11)] # 13 + pr(13) + conds += [And(p < q, u > v, bstar >= 0, cstar >= 0, + c1, c2, c3, c4, c7, c11, c13)] # 14 + pr(14) + conds += [And(p > q, u < v, bstar >= 0, cstar >= 0, + c1, c2, c3, c5, c6, c11, c13)] # 15 + pr(15) + conds += [And(p > q, u > v, bstar >= 0, cstar >= 0, + c1, c2, c3, c5, c7, c8, c11, c13, c14)] # 16 + pr(16) + conds += [And(p < q, u < v, bstar >= 0, cstar >= 0, + c1, c2, c3, c4, c6, c9, c11, c13, c14)] # 17 + pr(17) + conds += [And(Eq(t, 0), s.is_positive is True, bstar.is_positive is True, phi.is_positive is True, c1, c2, c10)] # 18 + pr(18) + conds += [And(Eq(s, 0), t.is_positive is True, bstar.is_positive is True, phi.is_negative is True, c1, c3, c10)] # 19 + pr(19) + conds += [And(Eq(n, 0), m.is_positive is True, cstar.is_positive is True, phi.is_negative is True, c1, c2, c12)] # 20 + pr(20) + conds += [And(Eq(m, 0), n.is_positive is True, cstar.is_positive is True, phi.is_positive is True, c1, c3, c12)] # 21 + pr(21) + conds += [And(Eq(s*t, 0), bstar.is_positive is True, cstar.is_positive is True, + c1, c2, c3, c10, c12)] # 22 + pr(22) + conds += [And(Eq(m*n, 0), bstar.is_positive is True, cstar.is_positive is True, + c1, c2, c3, c10, c12)] # 23 + pr(23) + + # The following case is from [Luke1969]. As far as I can tell, it is *not* + # covered by Prudnikov's. + # Let G1 and G2 be the two G-functions. Suppose the integral exists from + # 0 to a > 0 (this is easy the easy part), that G1 is exponential decay at + # infinity, and that the mellin transform of G2 exists. + # Then the integral exists. + mt1_exists = _check_antecedents_1(g1, x, helper=True) + mt2_exists = _check_antecedents_1(g2, x, helper=True) + conds += [And(mt2_exists, Eq(t, 0), u < s, bstar.is_positive is True, c10, c1, c2, c3)] + pr('E1') + conds += [And(mt2_exists, Eq(s, 0), v < t, bstar.is_positive is True, c10, c1, c2, c3)] + pr('E2') + conds += [And(mt1_exists, Eq(n, 0), p < m, cstar.is_positive is True, c12, c1, c2, c3)] + pr('E3') + conds += [And(mt1_exists, Eq(m, 0), q < n, cstar.is_positive is True, c12, c1, c2, c3)] + pr('E4') + + # Let's short-circuit if this worked ... + # the rest is corner-cases and terrible to read. + r = Or(*conds) + if _eval_cond(r) != False: + return r + + conds += [And(m + n > p, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True, cstar.is_negative is True, + Abs(unbranched_argument(omega)) < (m + n - p + 1)*pi, + c1, c2, c10, c14, c15)] # 24 + pr(24) + conds += [And(m + n > q, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar.is_negative is True, + Abs(unbranched_argument(omega)) < (m + n - q + 1)*pi, + c1, c3, c10, c14, c15)] # 25 + pr(25) + conds += [And(Eq(p, q - 1), Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True, + cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)), + c1, c2, c10, c14, c15)] # 26 + pr(26) + conds += [And(Eq(p, q + 1), Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, + cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)), + c1, c3, c10, c14, c15)] # 27 + pr(27) + conds += [And(p < q - 1, Eq(t, 0), Eq(phi, 0), s.is_positive is True, bstar.is_positive is True, + cstar >= 0, cstar*pi < Abs(unbranched_argument(omega)), + Abs(unbranched_argument(omega)) < (m + n - p + 1)*pi, + c1, c2, c10, c14, c15)] # 28 + pr(28) + conds += [And( + p > q + 1, Eq(s, 0), Eq(phi, 0), t.is_positive is True, bstar.is_positive is True, cstar >= 0, + cstar*pi < Abs(unbranched_argument(omega)), + Abs(unbranched_argument(omega)) < (m + n - q + 1)*pi, + c1, c3, c10, c14, c15)] # 29 + pr(29) + conds += [And(Eq(n, 0), Eq(phi, 0), s + t > 0, m.is_positive is True, cstar.is_positive is True, bstar.is_negative is True, + Abs(unbranched_argument(sigma)) < (s + t - u + 1)*pi, + c1, c2, c12, c14, c15)] # 30 + pr(30) + conds += [And(Eq(m, 0), Eq(phi, 0), s + t > v, n.is_positive is True, cstar.is_positive is True, bstar.is_negative is True, + Abs(unbranched_argument(sigma)) < (s + t - v + 1)*pi, + c1, c3, c12, c14, c15)] # 31 + pr(31) + conds += [And(Eq(n, 0), Eq(phi, 0), Eq(u, v - 1), m.is_positive is True, cstar.is_positive is True, + bstar >= 0, bstar*pi < Abs(unbranched_argument(sigma)), + Abs(unbranched_argument(sigma)) < (bstar + 1)*pi, + c1, c2, c12, c14, c15)] # 32 + pr(32) + conds += [And(Eq(m, 0), Eq(phi, 0), Eq(u, v + 1), n.is_positive is True, cstar.is_positive is True, + bstar >= 0, bstar*pi < Abs(unbranched_argument(sigma)), + Abs(unbranched_argument(sigma)) < (bstar + 1)*pi, + c1, c3, c12, c14, c15)] # 33 + pr(33) + conds += [And( + Eq(n, 0), Eq(phi, 0), u < v - 1, m.is_positive is True, cstar.is_positive is True, bstar >= 0, + bstar*pi < Abs(unbranched_argument(sigma)), + Abs(unbranched_argument(sigma)) < (s + t - u + 1)*pi, + c1, c2, c12, c14, c15)] # 34 + pr(34) + conds += [And( + Eq(m, 0), Eq(phi, 0), u > v + 1, n.is_positive is True, cstar.is_positive is True, bstar >= 0, + bstar*pi < Abs(unbranched_argument(sigma)), + Abs(unbranched_argument(sigma)) < (s + t - v + 1)*pi, + c1, c3, c12, c14, c15)] # 35 + pr(35) + + return Or(*conds) + + # NOTE An alternative, but as far as I can tell weaker, set of conditions + # can be found in [L, section 5.6.2]. + + +def _int0oo(g1, g2, x): + """ + Express integral from zero to infinity g1*g2 using a G function, + assuming the necessary conditions are fulfilled. + + Examples + ======== + + >>> from sympy.integrals.meijerint import _int0oo + >>> from sympy.abc import s, t, m + >>> from sympy import meijerg, S + >>> g1 = meijerg([], [], [-S(1)/2, 0], [], s**2*t/4) + >>> g2 = meijerg([], [], [m/2], [-m/2], t/4) + >>> _int0oo(g1, g2, t) + 4*meijerg(((0, 1/2), ()), ((m/2,), (-m/2,)), s**(-2))/s**2 + """ + # See: [L, section 5.6.2, equation (1)] + eta, _ = _get_coeff_exp(g1.argument, x) + omega, _ = _get_coeff_exp(g2.argument, x) + + def neg(l): + return [-x for x in l] + a1 = neg(g1.bm) + list(g2.an) + a2 = list(g2.aother) + neg(g1.bother) + b1 = neg(g1.an) + list(g2.bm) + b2 = list(g2.bother) + neg(g1.aother) + return meijerg(a1, a2, b1, b2, omega/eta)/eta + + +def _rewrite_inversion(fac, po, g, x): + """ Absorb ``po`` == x**s into g. """ + _, s = _get_coeff_exp(po, x) + a, b = _get_coeff_exp(g.argument, x) + + def tr(l): + return [t + s/b for t in l] + from sympy.simplify import powdenest + return (powdenest(fac/a**(s/b), polar=True), + meijerg(tr(g.an), tr(g.aother), tr(g.bm), tr(g.bother), g.argument)) + + +def _check_antecedents_inversion(g, x): + """ Check antecedents for the laplace inversion integral. """ + _debug('Checking antecedents for inversion:') + z = g.argument + _, e = _get_coeff_exp(z, x) + if e < 0: + _debug(' Flipping G.') + # We want to assume that argument gets large as |x| -> oo + return _check_antecedents_inversion(_flip_g(g), x) + + def statement_half(a, b, c, z, plus): + coeff, exponent = _get_coeff_exp(z, x) + a *= exponent + b *= coeff**c + c *= exponent + conds = [] + wp = b*exp(S.ImaginaryUnit*re(c)*pi/2) + wm = b*exp(-S.ImaginaryUnit*re(c)*pi/2) + if plus: + w = wp + else: + w = wm + conds += [And(Or(Eq(b, 0), re(c) <= 0), re(a) <= -1)] + conds += [And(Ne(b, 0), Eq(im(c), 0), re(c) > 0, re(w) < 0)] + conds += [And(Ne(b, 0), Eq(im(c), 0), re(c) > 0, re(w) <= 0, + re(a) <= -1)] + return Or(*conds) + + def statement(a, b, c, z): + """ Provide a convergence statement for z**a * exp(b*z**c), + c/f sphinx docs. """ + return And(statement_half(a, b, c, z, True), + statement_half(a, b, c, z, False)) + + # Notations from [L], section 5.7-10 + m, n, p, q = S([len(g.bm), len(g.an), len(g.ap), len(g.bq)]) + tau = m + n - p + nu = q - m - n + rho = (tau - nu)/2 + sigma = q - p + if sigma == 1: + epsilon = S.Half + elif sigma > 1: + epsilon = 1 + else: + epsilon = S.NaN + theta = ((1 - sigma)/2 + Add(*g.bq) - Add(*g.ap))/sigma + delta = g.delta + _debugf(' m=%s, n=%s, p=%s, q=%s, tau=%s, nu=%s, rho=%s, sigma=%s', + (m, n, p, q, tau, nu, rho, sigma)) + _debugf(' epsilon=%s, theta=%s, delta=%s', (epsilon, theta, delta)) + + # First check if the computation is valid. + if not (g.delta >= e/2 or (p >= 1 and p >= q)): + _debug(' Computation not valid for these parameters.') + return False + + # Now check if the inversion integral exists. + + # Test "condition A" + for a, b in itertools.product(g.an, g.bm): + if (a - b).is_integer and a > b: + _debug(' Not a valid G function.') + return False + + # There are two cases. If p >= q, we can directly use a slater expansion + # like [L], 5.2 (11). Note in particular that the asymptotics of such an + # expansion even hold when some of the parameters differ by integers, i.e. + # the formula itself would not be valid! (b/c G functions are cts. in their + # parameters) + # When p < q, we need to use the theorems of [L], 5.10. + + if p >= q: + _debug(' Using asymptotic Slater expansion.') + return And(*[statement(a - 1, 0, 0, z) for a in g.an]) + + def E(z): + return And(*[statement(a - 1, 0, 0, z) for a in g.an]) + + def H(z): + return statement(theta, -sigma, 1/sigma, z) + + def Hp(z): + return statement_half(theta, -sigma, 1/sigma, z, True) + + def Hm(z): + return statement_half(theta, -sigma, 1/sigma, z, False) + + # [L], section 5.10 + conds = [] + # Theorem 1 -- p < q from test above + conds += [And(1 <= n, 1 <= m, rho*pi - delta >= pi/2, delta > 0, + E(z*exp(S.ImaginaryUnit*pi*(nu + 1))))] + # Theorem 2, statements (2) and (3) + conds += [And(p + 1 <= m, m + 1 <= q, delta > 0, delta < pi/2, n == 0, + (m - p + 1)*pi - delta >= pi/2, + Hp(z*exp(S.ImaginaryUnit*pi*(q - m))), + Hm(z*exp(-S.ImaginaryUnit*pi*(q - m))))] + # Theorem 2, statement (5) -- p < q from test above + conds += [And(m == q, n == 0, delta > 0, + (sigma + epsilon)*pi - delta >= pi/2, H(z))] + # Theorem 3, statements (6) and (7) + conds += [And(Or(And(p <= q - 2, 1 <= tau, tau <= sigma/2), + And(p + 1 <= m + n, m + n <= (p + q)/2)), + delta > 0, delta < pi/2, (tau + 1)*pi - delta >= pi/2, + Hp(z*exp(S.ImaginaryUnit*pi*nu)), + Hm(z*exp(-S.ImaginaryUnit*pi*nu)))] + # Theorem 4, statements (10) and (11) -- p < q from test above + conds += [And(1 <= m, rho > 0, delta > 0, delta + rho*pi < pi/2, + (tau + epsilon)*pi - delta >= pi/2, + Hp(z*exp(S.ImaginaryUnit*pi*nu)), + Hm(z*exp(-S.ImaginaryUnit*pi*nu)))] + # Trivial case + conds += [m == 0] + + # TODO + # Theorem 5 is quite general + # Theorem 6 contains special cases for q=p+1 + + return Or(*conds) + + +def _int_inversion(g, x, t): + """ + Compute the laplace inversion integral, assuming the formula applies. + """ + b, a = _get_coeff_exp(g.argument, x) + C, g = _inflate_fox_h(meijerg(g.an, g.aother, g.bm, g.bother, b/t**a), -a) + return C/t*g + + +#################################################################### +# Finally, the real meat. +#################################################################### + +_lookup_table = None + + +@cacheit +@timeit +def _rewrite_single(f, x, recursive=True): + """ + Try to rewrite f as a sum of single G functions of the form + C*x**s*G(a*x**b), where b is a rational number and C is independent of x. + We guarantee that result.argument.as_coeff_mul(x) returns (a, (x**b,)) + or (a, ()). + Returns a list of tuples (C, s, G) and a condition cond. + Returns None on failure. + """ + from .transforms import (mellin_transform, inverse_mellin_transform, + IntegralTransformError, MellinTransformStripError) + + global _lookup_table + if not _lookup_table: + _lookup_table = {} + _create_lookup_table(_lookup_table) + + if isinstance(f, meijerg): + coeff, m = factor(f.argument, x).as_coeff_mul(x) + if len(m) > 1: + return None + m = m[0] + if m.is_Pow: + if m.base != x or not m.exp.is_Rational: + return None + elif m != x: + return None + return [(1, 0, meijerg(f.an, f.aother, f.bm, f.bother, coeff*m))], True + + f_ = f + f = f.subs(x, z) + t = _mytype(f, z) + if t in _lookup_table: + l = _lookup_table[t] + for formula, terms, cond, hint in l: + subs = f.match(formula, old=True) + if subs: + subs_ = {} + for fro, to in subs.items(): + subs_[fro] = unpolarify(polarify(to, lift=True), + exponents_only=True) + subs = subs_ + if not isinstance(hint, bool): + hint = hint.subs(subs) + if hint == False: + continue + if not isinstance(cond, (bool, BooleanAtom)): + cond = unpolarify(cond.subs(subs)) + if _eval_cond(cond) == False: + continue + if not isinstance(terms, list): + terms = terms(subs) + res = [] + for fac, g in terms: + r1 = _get_coeff_exp(unpolarify(fac.subs(subs).subs(z, x), + exponents_only=True), x) + try: + g = g.subs(subs).subs(z, x) + except ValueError: + continue + # NOTE these substitutions can in principle introduce oo, + # zoo and other absurdities. It shouldn't matter, + # but better be safe. + if Tuple(*(r1 + (g,))).has(S.Infinity, S.ComplexInfinity, S.NegativeInfinity): + continue + g = meijerg(g.an, g.aother, g.bm, g.bother, + unpolarify(g.argument, exponents_only=True)) + res.append(r1 + (g,)) + if res: + return res, cond + + # try recursive mellin transform + if not recursive: + return None + _debug('Trying recursive Mellin transform method.') + + def my_imt(F, s, x, strip): + """ Calling simplify() all the time is slow and not helpful, since + most of the time it only factors things in a way that has to be + un-done anyway. But sometimes it can remove apparent poles. """ + # XXX should this be in inverse_mellin_transform? + try: + return inverse_mellin_transform(F, s, x, strip, + as_meijerg=True, needeval=True) + except MellinTransformStripError: + from sympy.simplify import simplify + return inverse_mellin_transform( + simplify(cancel(expand(F))), s, x, strip, + as_meijerg=True, needeval=True) + f = f_ + s = _dummy('s', 'rewrite-single', f) + # to avoid infinite recursion, we have to force the two g functions case + + def my_integrator(f, x): + r = _meijerint_definite_4(f, x, only_double=True) + if r is not None: + from sympy.simplify import hyperexpand + res, cond = r + res = _my_unpolarify(hyperexpand(res, rewrite='nonrepsmall')) + return Piecewise((res, cond), + (Integral(f, (x, S.Zero, S.Infinity)), True)) + return Integral(f, (x, S.Zero, S.Infinity)) + try: + F, strip, _ = mellin_transform(f, x, s, integrator=my_integrator, + simplify=False, needeval=True) + g = my_imt(F, s, x, strip) + except IntegralTransformError: + g = None + if g is None: + # We try to find an expression by analytic continuation. + # (also if the dummy is already in the expression, there is no point in + # putting in another one) + a = _dummy_('a', 'rewrite-single') + if a not in f.free_symbols and _is_analytic(f, x): + try: + F, strip, _ = mellin_transform(f.subs(x, a*x), x, s, + integrator=my_integrator, + needeval=True, simplify=False) + g = my_imt(F, s, x, strip).subs(a, 1) + except IntegralTransformError: + g = None + if g is None or g.has(S.Infinity, S.NaN, S.ComplexInfinity): + _debug('Recursive Mellin transform failed.') + return None + args = Add.make_args(g) + res = [] + for f in args: + c, m = f.as_coeff_mul(x) + if len(m) > 1: + raise NotImplementedError('Unexpected form...') + g = m[0] + a, b = _get_coeff_exp(g.argument, x) + res += [(c, 0, meijerg(g.an, g.aother, g.bm, g.bother, + unpolarify(polarify( + a, lift=True), exponents_only=True) + *x**b))] + _debug('Recursive Mellin transform worked:', g) + return res, True + + +def _rewrite1(f, x, recursive=True): + """ + Try to rewrite ``f`` using a (sum of) single G functions with argument a*x**b. + Return fac, po, g such that f = fac*po*g, fac is independent of ``x``. + and po = x**s. + Here g is a result from _rewrite_single. + Return None on failure. + """ + fac, po, g = _split_mul(f, x) + g = _rewrite_single(g, x, recursive) + if g: + return fac, po, g[0], g[1] + + +def _rewrite2(f, x): + """ + Try to rewrite ``f`` as a product of two G functions of arguments a*x**b. + Return fac, po, g1, g2 such that f = fac*po*g1*g2, where fac is + independent of x and po is x**s. + Here g1 and g2 are results of _rewrite_single. + Returns None on failure. + """ + fac, po, g = _split_mul(f, x) + if any(_rewrite_single(expr, x, False) is None for expr in _mul_args(g)): + return None + l = _mul_as_two_parts(g) + if not l: + return None + l = list(ordered(l, [ + lambda p: max(len(_exponents(p[0], x)), len(_exponents(p[1], x))), + lambda p: max(len(_functions(p[0], x)), len(_functions(p[1], x))), + lambda p: max(len(_find_splitting_points(p[0], x)), + len(_find_splitting_points(p[1], x)))])) + + for recursive, (fac1, fac2) in itertools.product((False, True), l): + g1 = _rewrite_single(fac1, x, recursive) + g2 = _rewrite_single(fac2, x, recursive) + if g1 and g2: + cond = And(g1[1], g2[1]) + if cond != False: + return fac, po, g1[0], g2[0], cond + + +def meijerint_indefinite(f, x): + """ + Compute an indefinite integral of ``f`` by rewriting it as a G function. + + Examples + ======== + + >>> from sympy.integrals.meijerint import meijerint_indefinite + >>> from sympy import sin + >>> from sympy.abc import x + >>> meijerint_indefinite(sin(x), x) + -cos(x) + """ + f = sympify(f) + results = [] + for a in sorted(_find_splitting_points(f, x) | {S.Zero}, key=default_sort_key): + res = _meijerint_indefinite_1(f.subs(x, x + a), x) + if not res: + continue + res = res.subs(x, x - a) + if _has(res, hyper, meijerg): + results.append(res) + else: + return res + if f.has(HyperbolicFunction): + _debug('Try rewriting hyperbolics in terms of exp.') + rv = meijerint_indefinite( + _rewrite_hyperbolics_as_exp(f), x) + if rv: + if not isinstance(rv, list): + from sympy.simplify.radsimp import collect + return collect(factor_terms(rv), rv.atoms(exp)) + results.extend(rv) + if results: + return next(ordered(results)) + + +def _meijerint_indefinite_1(f, x): + """ Helper that does not attempt any substitution. """ + _debug('Trying to compute the indefinite integral of', f, 'wrt', x) + from sympy.simplify import hyperexpand, powdenest + + gs = _rewrite1(f, x) + if gs is None: + # Note: the code that calls us will do expand() and try again + return None + + fac, po, gl, cond = gs + _debug(' could rewrite:', gs) + res = S.Zero + for C, s, g in gl: + a, b = _get_coeff_exp(g.argument, x) + _, c = _get_coeff_exp(po, x) + c += s + + # we do a substitution t=a*x**b, get integrand fac*t**rho*g + fac_ = fac * C * x**(1 + c) / b + rho = (c + 1)/b + + # we now use t**rho*G(params, t) = G(params + rho, t) + # [L, page 150, equation (4)] + # and integral G(params, t) dt = G(1, params+1, 0, t) + # (or a similar expression with 1 and 0 exchanged ... pick the one + # which yields a well-defined function) + # [R, section 5] + # (Note that this dummy will immediately go away again, so we + # can safely pass S.One for ``expr``.) + t = _dummy('t', 'meijerint-indefinite', S.One) + + def tr(p): + return [a + rho for a in p] + if any(b.is_integer and (b <= 0) == True for b in tr(g.bm)): + r = -meijerg( + list(g.an), list(g.aother) + [1-rho], list(g.bm) + [-rho], list(g.bother), t) + else: + r = meijerg( + list(g.an) + [1-rho], list(g.aother), list(g.bm), list(g.bother) + [-rho], t) + # The antiderivative is most often expected to be defined + # in the neighborhood of x = 0. + if b.is_extended_nonnegative and not f.subs(x, 0).has(S.NaN, S.ComplexInfinity): + place = 0 # Assume we can expand at zero + else: + place = None + r = hyperexpand(r.subs(t, a*x**b), place=place) + + # now substitute back + # Note: we really do want the powers of x to combine. + res += powdenest(fac_*r, polar=True) + + def _clean(res): + """This multiplies out superfluous powers of x we created, and chops off + constants: + + >> _clean(x*(exp(x)/x - 1/x) + 3) + exp(x) + + cancel is used before mul_expand since it is possible for an + expression to have an additive constant that does not become isolated + with simple expansion. Such a situation was identified in issue 6369: + + Examples + ======== + + >>> from sympy import sqrt, cancel + >>> from sympy.abc import x + >>> a = sqrt(2*x + 1) + >>> bad = (3*x*a**5 + 2*x - a**5 + 1)/a**2 + >>> bad.expand().as_independent(x)[0] + 0 + >>> cancel(bad).expand().as_independent(x)[0] + 1 + """ + res = expand_mul(cancel(res), deep=False) + return Add._from_args(res.as_coeff_add(x)[1]) + + res = piecewise_fold(res, evaluate=None) + if res.is_Piecewise: + newargs = [] + for e, c in res.args: + e = _my_unpolarify(_clean(e)) + newargs += [(e, c)] + res = Piecewise(*newargs, evaluate=False) + else: + res = _my_unpolarify(_clean(res)) + return Piecewise((res, _my_unpolarify(cond)), (Integral(f, x), True)) + + +@timeit +def meijerint_definite(f, x, a, b): + """ + Integrate ``f`` over the interval [``a``, ``b``], by rewriting it as a product + of two G functions, or as a single G function. + + Return res, cond, where cond are convergence conditions. + + Examples + ======== + + >>> from sympy.integrals.meijerint import meijerint_definite + >>> from sympy import exp, oo + >>> from sympy.abc import x + >>> meijerint_definite(exp(-x**2), x, -oo, oo) + (sqrt(pi), True) + + This function is implemented as a succession of functions + meijerint_definite, _meijerint_definite_2, _meijerint_definite_3, + _meijerint_definite_4. Each function in the list calls the next one + (presumably) several times. This means that calling meijerint_definite + can be very costly. + """ + # This consists of three steps: + # 1) Change the integration limits to 0, oo + # 2) Rewrite in terms of G functions + # 3) Evaluate the integral + # + # There are usually several ways of doing this, and we want to try all. + # This function does (1), calls _meijerint_definite_2 for step (2). + _debugf('Integrating %s wrt %s from %s to %s.', (f, x, a, b)) + f = sympify(f) + if f.has(DiracDelta): + _debug('Integrand has DiracDelta terms - giving up.') + return None + + if f.has(SingularityFunction): + _debug('Integrand has Singularity Function terms - giving up.') + return None + + f_, x_, a_, b_ = f, x, a, b + + # Let's use a dummy in case any of the boundaries has x. + d = Dummy('x') + f = f.subs(x, d) + x = d + + if a == b: + return (S.Zero, True) + + results = [] + if a is S.NegativeInfinity and b is not S.Infinity: + return meijerint_definite(f.subs(x, -x), x, -b, -a) + + elif a is S.NegativeInfinity: + # Integrating -oo to oo. We need to find a place to split the integral. + _debug(' Integrating -oo to +oo.') + innermost = _find_splitting_points(f, x) + _debug(' Sensible splitting points:', innermost) + for c in sorted(innermost, key=default_sort_key, reverse=True) + [S.Zero]: + _debug(' Trying to split at', c) + if not c.is_extended_real: + _debug(' Non-real splitting point.') + continue + res1 = _meijerint_definite_2(f.subs(x, x + c), x) + if res1 is None: + _debug(' But could not compute first integral.') + continue + res2 = _meijerint_definite_2(f.subs(x, c - x), x) + if res2 is None: + _debug(' But could not compute second integral.') + continue + res1, cond1 = res1 + res2, cond2 = res2 + cond = _condsimp(And(cond1, cond2)) + if cond == False: + _debug(' But combined condition is always false.') + continue + res = res1 + res2 + return res, cond + + elif a is S.Infinity: + res = meijerint_definite(f, x, b, S.Infinity) + return -res[0], res[1] + + elif (a, b) == (S.Zero, S.Infinity): + # This is a common case - try it directly first. + res = _meijerint_definite_2(f, x) + if res: + if _has(res[0], meijerg): + results.append(res) + else: + return res + + else: + if b is S.Infinity: + for split in _find_splitting_points(f, x): + if (a - split >= 0) == True: + _debugf('Trying x -> x + %s', split) + res = _meijerint_definite_2(f.subs(x, x + split) + *Heaviside(x + split - a), x) + if res: + if _has(res[0], meijerg): + results.append(res) + else: + return res + + f = f.subs(x, x + a) + b = b - a + a = 0 + if b is not S.Infinity: + phi = exp(S.ImaginaryUnit*arg(b)) + b = Abs(b) + f = f.subs(x, phi*x) + f *= Heaviside(b - x)*phi + b = S.Infinity + + _debug('Changed limits to', a, b) + _debug('Changed function to', f) + res = _meijerint_definite_2(f, x) + if res: + if _has(res[0], meijerg): + results.append(res) + else: + return res + if f_.has(HyperbolicFunction): + _debug('Try rewriting hyperbolics in terms of exp.') + rv = meijerint_definite( + _rewrite_hyperbolics_as_exp(f_), x_, a_, b_) + if rv: + if not isinstance(rv, list): + from sympy.simplify.radsimp import collect + rv = (collect(factor_terms(rv[0]), rv[0].atoms(exp)),) + rv[1:] + return rv + results.extend(rv) + if results: + return next(ordered(results)) + + +def _guess_expansion(f, x): + """ Try to guess sensible rewritings for integrand f(x). """ + res = [(f, 'original integrand')] + + orig = res[-1][0] + saw = {orig} + expanded = expand_mul(orig) + if expanded not in saw: + res += [(expanded, 'expand_mul')] + saw.add(expanded) + + expanded = expand(orig) + if expanded not in saw: + res += [(expanded, 'expand')] + saw.add(expanded) + + if orig.has(TrigonometricFunction, HyperbolicFunction): + expanded = expand_mul(expand_trig(orig)) + if expanded not in saw: + res += [(expanded, 'expand_trig, expand_mul')] + saw.add(expanded) + + if orig.has(cos, sin): + from sympy.simplify.fu import sincos_to_sum + reduced = sincos_to_sum(orig) + if reduced not in saw: + res += [(reduced, 'trig power reduction')] + saw.add(reduced) + + return res + + +def _meijerint_definite_2(f, x): + """ + Try to integrate f dx from zero to infinity. + + The body of this function computes various 'simplifications' + f1, f2, ... of f (e.g. by calling expand_mul(), trigexpand() + - see _guess_expansion) and calls _meijerint_definite_3 with each of + these in succession. + If _meijerint_definite_3 succeeds with any of the simplified functions, + returns this result. + """ + # This function does preparation for (2), calls + # _meijerint_definite_3 for (2) and (3) combined. + + # use a positive dummy - we integrate from 0 to oo + # XXX if a nonnegative symbol is used there will be test failures + dummy = _dummy('x', 'meijerint-definite2', f, positive=True) + f = f.subs(x, dummy) + x = dummy + + if f == 0: + return S.Zero, True + + for g, explanation in _guess_expansion(f, x): + _debug('Trying', explanation) + res = _meijerint_definite_3(g, x) + if res: + return res + + +def _meijerint_definite_3(f, x): + """ + Try to integrate f dx from zero to infinity. + + This function calls _meijerint_definite_4 to try to compute the + integral. If this fails, it tries using linearity. + """ + res = _meijerint_definite_4(f, x) + if res and res[1] != False: + return res + if f.is_Add: + _debug('Expanding and evaluating all terms.') + ress = [_meijerint_definite_4(g, x) for g in f.args] + if all(r is not None for r in ress): + conds = [] + res = S.Zero + for r, c in ress: + res += r + conds += [c] + c = And(*conds) + if c != False: + return res, c + + +def _my_unpolarify(f): + return _eval_cond(unpolarify(f)) + + +@timeit +def _meijerint_definite_4(f, x, only_double=False): + """ + Try to integrate f dx from zero to infinity. + + Explanation + =========== + + This function tries to apply the integration theorems found in literature, + i.e. it tries to rewrite f as either one or a product of two G-functions. + + The parameter ``only_double`` is used internally in the recursive algorithm + to disable trying to rewrite f as a single G-function. + """ + from sympy.simplify import hyperexpand + # This function does (2) and (3) + _debug('Integrating', f) + # Try single G function. + if not only_double: + gs = _rewrite1(f, x, recursive=False) + if gs is not None: + fac, po, g, cond = gs + _debug('Could rewrite as single G function:', fac, po, g) + res = S.Zero + for C, s, f in g: + if C == 0: + continue + C, f = _rewrite_saxena_1(fac*C, po*x**s, f, x) + res += C*_int0oo_1(f, x) + cond = And(cond, _check_antecedents_1(f, x)) + if cond == False: + break + cond = _my_unpolarify(cond) + if cond == False: + _debug('But cond is always False.') + else: + _debug('Result before branch substitutions is:', res) + return _my_unpolarify(hyperexpand(res)), cond + + # Try two G functions. + gs = _rewrite2(f, x) + if gs is not None: + for full_pb in [False, True]: + fac, po, g1, g2, cond = gs + _debug('Could rewrite as two G functions:', fac, po, g1, g2) + res = S.Zero + for C1, s1, f1 in g1: + for C2, s2, f2 in g2: + r = _rewrite_saxena(fac*C1*C2, po*x**(s1 + s2), + f1, f2, x, full_pb) + if r is None: + _debug('Non-rational exponents.') + return + C, f1_, f2_ = r + _debug('Saxena subst for yielded:', C, f1_, f2_) + cond = And(cond, _check_antecedents(f1_, f2_, x)) + if cond == False: + break + res += C*_int0oo(f1_, f2_, x) + else: + continue + break + cond = _my_unpolarify(cond) + if cond == False: + _debugf('But cond is always False (full_pb=%s).', full_pb) + else: + _debugf('Result before branch substitutions is: %s', (res, )) + if only_double: + return res, cond + return _my_unpolarify(hyperexpand(res)), cond + + +def meijerint_inversion(f, x, t): + r""" + Compute the inverse laplace transform + $\int_{c+i\infty}^{c-i\infty} f(x) e^{tx}\, dx$, + for real c larger than the real part of all singularities of ``f``. + + Note that ``t`` is always assumed real and positive. + + Return None if the integral does not exist or could not be evaluated. + + Examples + ======== + + >>> from sympy.abc import x, t + >>> from sympy.integrals.meijerint import meijerint_inversion + >>> meijerint_inversion(1/x, x, t) + Heaviside(t) + """ + f_ = f + t_ = t + t = Dummy('t', polar=True) # We don't want sqrt(t**2) = abs(t) etc + f = f.subs(t_, t) + _debug('Laplace-inverting', f) + if not _is_analytic(f, x): + _debug('But expression is not analytic.') + return None + # Exponentials correspond to shifts; we filter them out and then + # shift the result later. If we are given an Add this will not + # work, but the calling code will take care of that. + shift = S.Zero + + if f.is_Mul: + args = list(f.args) + elif isinstance(f, exp): + args = [f] + else: + args = None + + if args: + newargs = [] + exponentials = [] + while args: + arg = args.pop() + if isinstance(arg, exp): + arg2 = expand(arg) + if arg2.is_Mul: + args += arg2.args + continue + try: + a, b = _get_coeff_exp(arg.args[0], x) + except _CoeffExpValueError: + b = 0 + if b == 1: + exponentials.append(a) + else: + newargs.append(arg) + elif arg.is_Pow: + arg2 = expand(arg) + if arg2.is_Mul: + args += arg2.args + continue + if x not in arg.base.free_symbols: + try: + a, b = _get_coeff_exp(arg.exp, x) + except _CoeffExpValueError: + b = 0 + if b == 1: + exponentials.append(a*log(arg.base)) + newargs.append(arg) + else: + newargs.append(arg) + shift = Add(*exponentials) + f = Mul(*newargs) + + if x not in f.free_symbols: + _debug('Expression consists of constant and exp shift:', f, shift) + cond = Eq(im(shift), 0) + if cond == False: + _debug('but shift is nonreal, cannot be a Laplace transform') + return None + res = f*DiracDelta(t + shift) + _debug('Result is a delta function, possibly conditional:', res, cond) + # cond is True or Eq + return Piecewise((res.subs(t, t_), cond)) + + gs = _rewrite1(f, x) + if gs is not None: + fac, po, g, cond = gs + _debug('Could rewrite as single G function:', fac, po, g) + res = S.Zero + for C, s, f in g: + C, f = _rewrite_inversion(fac*C, po*x**s, f, x) + res += C*_int_inversion(f, x, t) + cond = And(cond, _check_antecedents_inversion(f, x)) + if cond == False: + break + cond = _my_unpolarify(cond) + if cond == False: + _debug('But cond is always False.') + else: + _debug('Result before branch substitution:', res) + from sympy.simplify import hyperexpand + res = _my_unpolarify(hyperexpand(res)) + if not res.has(Heaviside): + res *= Heaviside(t) + res = res.subs(t, t + shift) + if not isinstance(cond, bool): + cond = cond.subs(t, t + shift) + from .transforms import InverseLaplaceTransform + return Piecewise((res.subs(t, t_), cond), + (InverseLaplaceTransform(f_.subs(t, t_), x, t_, None), True)) diff --git a/lib/python3.11/site-packages/sympy/integrals/meijerint_doc.py b/lib/python3.11/site-packages/sympy/integrals/meijerint_doc.py new file mode 100644 index 0000000000000000000000000000000000000000..712a52e183006528b8c50a56207d44742e28f0c0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/meijerint_doc.py @@ -0,0 +1,37 @@ +""" This module cooks up a docstring when imported. Its only purpose is to + be displayed in the sphinx documentation. """ + +from __future__ import annotations +from typing import Any + +from sympy.integrals.meijerint import _create_lookup_table +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.relational import Eq +from sympy.core.symbol import Symbol +from sympy.printing.latex import latex + +t: dict[tuple[type[Basic], ...], list[Any]] = {} +_create_lookup_table(t) + + +doc = "" +for about, category in t.items(): + if about == (): + doc += 'Elementary functions:\n\n' + else: + doc += 'Functions involving ' + ', '.join('`%s`' % latex( + list(category[0][0].atoms(func))[0]) for func in about) + ':\n\n' + for formula, gs, cond, hint in category: + if not isinstance(gs, list): + g = Symbol('\\text{generated}') + else: + g = Add(*[fac*f for (fac, f) in gs]) + obj = Eq(formula, g) + if cond is True: + cond = "" + else: + cond = ',\\text{ if } %s' % latex(cond) + doc += ".. math::\n %s%s\n\n" % (latex(obj), cond) + +__doc__ = doc diff --git a/lib/python3.11/site-packages/sympy/integrals/prde.py b/lib/python3.11/site-packages/sympy/integrals/prde.py new file mode 100644 index 0000000000000000000000000000000000000000..4488cbfc4000a06d47886d026f6807e68d64c8cb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/prde.py @@ -0,0 +1,1333 @@ +""" +Algorithms for solving Parametric Risch Differential Equations. + +The methods used for solving Parametric Risch Differential Equations parallel +those for solving Risch Differential Equations. See the outline in the +docstring of rde.py for more information. + +The Parametric Risch Differential Equation problem is, given f, g1, ..., gm in +K(t), to determine if there exist y in K(t) and c1, ..., cm in Const(K) such +that Dy + f*y == Sum(ci*gi, (i, 1, m)), and to find such y and ci if they exist. + +For the algorithms here G is a list of tuples of factions of the terms on the +right hand side of the equation (i.e., gi in k(t)), and Q is a list of terms on +the right hand side of the equation (i.e., qi in k[t]). See the docstring of +each function for more information. +""" +import itertools +from functools import reduce + +from sympy.core.intfunc import ilcm +from sympy.core import Dummy, Add, Mul, Pow, S +from sympy.integrals.rde import (order_at, order_at_oo, weak_normalizer, + bound_degree) +from sympy.integrals.risch import (gcdex_diophantine, frac_in, derivation, + residue_reduce, splitfactor, residue_reduce_derivation, DecrementLevel, + recognize_log_derivative) +from sympy.polys import Poly, lcm, cancel, sqf_list +from sympy.polys.polymatrix import PolyMatrix as Matrix +from sympy.solvers import solve + +zeros = Matrix.zeros +eye = Matrix.eye + + +def prde_normal_denom(fa, fd, G, DE): + """ + Parametric Risch Differential Equation - Normal part of the denominator. + + Explanation + =========== + + Given a derivation D on k[t] and f, g1, ..., gm in k(t) with f weakly + normalized with respect to t, return the tuple (a, b, G, h) such that + a, h in k[t], b in k, G = [g1, ..., gm] in k(t)^m, and for any solution + c1, ..., cm in Const(k) and y in k(t) of Dy + f*y == Sum(ci*gi, (i, 1, m)), + q == y*h in k satisfies a*Dq + b*q == Sum(ci*Gi, (i, 1, m)). + """ + dn, ds = splitfactor(fd, DE) + Gas, Gds = list(zip(*G)) + gd = reduce(lambda i, j: i.lcm(j), Gds, Poly(1, DE.t)) + en, es = splitfactor(gd, DE) + + p = dn.gcd(en) + h = en.gcd(en.diff(DE.t)).quo(p.gcd(p.diff(DE.t))) + + a = dn*h + c = a*h + + ba = a*fa - dn*derivation(h, DE)*fd + ba, bd = ba.cancel(fd, include=True) + + G = [(c*A).cancel(D, include=True) for A, D in G] + + return (a, (ba, bd), G, h) + +def real_imag(ba, bd, gen): + """ + Helper function, to get the real and imaginary part of a rational function + evaluated at sqrt(-1) without actually evaluating it at sqrt(-1). + + Explanation + =========== + + Separates the even and odd power terms by checking the degree of terms wrt + mod 4. Returns a tuple (ba[0], ba[1], bd) where ba[0] is real part + of the numerator ba[1] is the imaginary part and bd is the denominator + of the rational function. + """ + bd = bd.as_poly(gen).as_dict() + ba = ba.as_poly(gen).as_dict() + denom_real = [value if key[0] % 4 == 0 else -value if key[0] % 4 == 2 else 0 for key, value in bd.items()] + denom_imag = [value if key[0] % 4 == 1 else -value if key[0] % 4 == 3 else 0 for key, value in bd.items()] + bd_real = sum(r for r in denom_real) + bd_imag = sum(r for r in denom_imag) + num_real = [value if key[0] % 4 == 0 else -value if key[0] % 4 == 2 else 0 for key, value in ba.items()] + num_imag = [value if key[0] % 4 == 1 else -value if key[0] % 4 == 3 else 0 for key, value in ba.items()] + ba_real = sum(r for r in num_real) + ba_imag = sum(r for r in num_imag) + ba = ((ba_real*bd_real + ba_imag*bd_imag).as_poly(gen), (ba_imag*bd_real - ba_real*bd_imag).as_poly(gen)) + bd = (bd_real*bd_real + bd_imag*bd_imag).as_poly(gen) + return (ba[0], ba[1], bd) + + +def prde_special_denom(a, ba, bd, G, DE, case='auto'): + """ + Parametric Risch Differential Equation - Special part of the denominator. + + Explanation + =========== + + Case is one of {'exp', 'tan', 'primitive'} for the hyperexponential, + hypertangent, and primitive cases, respectively. For the hyperexponential + (resp. hypertangent) case, given a derivation D on k[t] and a in k[t], + b in k, and g1, ..., gm in k(t) with Dt/t in k (resp. Dt/(t**2 + 1) in + k, sqrt(-1) not in k), a != 0, and gcd(a, t) == 1 (resp. + gcd(a, t**2 + 1) == 1), return the tuple (A, B, GG, h) such that A, B, h in + k[t], GG = [gg1, ..., ggm] in k(t)^m, and for any solution c1, ..., cm in + Const(k) and q in k of a*Dq + b*q == Sum(ci*gi, (i, 1, m)), r == q*h in + k[t] satisfies A*Dr + B*r == Sum(ci*ggi, (i, 1, m)). + + For case == 'primitive', k == k[t], so it returns (a, b, G, 1) in this + case. + """ + # TODO: Merge this with the very similar special_denom() in rde.py + if case == 'auto': + case = DE.case + + if case == 'exp': + p = Poly(DE.t, DE.t) + elif case == 'tan': + p = Poly(DE.t**2 + 1, DE.t) + elif case in ('primitive', 'base'): + B = ba.quo(bd) + return (a, B, G, Poly(1, DE.t)) + else: + raise ValueError("case must be one of {'exp', 'tan', 'primitive', " + "'base'}, not %s." % case) + + nb = order_at(ba, p, DE.t) - order_at(bd, p, DE.t) + nc = min(order_at(Ga, p, DE.t) - order_at(Gd, p, DE.t) for Ga, Gd in G) + n = min(0, nc - min(0, nb)) + if not nb: + # Possible cancellation. + if case == 'exp': + dcoeff = DE.d.quo(Poly(DE.t, DE.t)) + with DecrementLevel(DE): # We are guaranteed to not have problems, + # because case != 'base'. + alphaa, alphad = frac_in(-ba.eval(0)/bd.eval(0)/a.eval(0), DE.t) + etaa, etad = frac_in(dcoeff, DE.t) + A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE) + if A is not None: + Q, m, z = A + if Q == 1: + n = min(n, m) + + elif case == 'tan': + dcoeff = DE.d.quo(Poly(DE.t**2 + 1, DE.t)) + with DecrementLevel(DE): # We are guaranteed to not have problems, + # because case != 'base'. + betaa, alphaa, alphad = real_imag(ba, bd*a, DE.t) + betad = alphad + etaa, etad = frac_in(dcoeff, DE.t) + if recognize_log_derivative(Poly(2, DE.t)*betaa, betad, DE): + A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE) + B = parametric_log_deriv(betaa, betad, etaa, etad, DE) + if A is not None and B is not None: + Q, s, z = A + # TODO: Add test + if Q == 1: + n = min(n, s/2) + + N = max(0, -nb) + pN = p**N + pn = p**-n # This is 1/h + + A = a*pN + B = ba*pN.quo(bd) + Poly(n, DE.t)*a*derivation(p, DE).quo(p)*pN + G = [(Ga*pN*pn).cancel(Gd, include=True) for Ga, Gd in G] + h = pn + + # (a*p**N, (b + n*a*Dp/p)*p**N, g1*p**(N - n), ..., gm*p**(N - n), p**-n) + return (A, B, G, h) + + +def prde_linear_constraints(a, b, G, DE): + """ + Parametric Risch Differential Equation - Generate linear constraints on the constants. + + Explanation + =========== + + Given a derivation D on k[t], a, b, in k[t] with gcd(a, b) == 1, and + G = [g1, ..., gm] in k(t)^m, return Q = [q1, ..., qm] in k[t]^m and a + matrix M with entries in k(t) such that for any solution c1, ..., cm in + Const(k) and p in k[t] of a*Dp + b*p == Sum(ci*gi, (i, 1, m)), + (c1, ..., cm) is a solution of Mx == 0, and p and the ci satisfy + a*Dp + b*p == Sum(ci*qi, (i, 1, m)). + + Because M has entries in k(t), and because Matrix does not play well with + Poly, M will be a Matrix of Basic expressions. + """ + m = len(G) + + Gns, Gds = list(zip(*G)) + d = reduce(lambda i, j: i.lcm(j), Gds) + d = Poly(d, field=True) + Q = [(ga*(d).quo(gd)).div(d) for ga, gd in G] + + if not all(ri.is_zero for _, ri in Q): + N = max(ri.degree(DE.t) for _, ri in Q) + M = Matrix(N + 1, m, lambda i, j: Q[j][1].nth(i), DE.t) + else: + M = Matrix(0, m, [], DE.t) # No constraints, return the empty matrix. + + qs, _ = list(zip(*Q)) + return (qs, M) + +def poly_linear_constraints(p, d): + """ + Given p = [p1, ..., pm] in k[t]^m and d in k[t], return + q = [q1, ..., qm] in k[t]^m and a matrix M with entries in k such + that Sum(ci*pi, (i, 1, m)), for c1, ..., cm in k, is divisible + by d if and only if (c1, ..., cm) is a solution of Mx = 0, in + which case the quotient is Sum(ci*qi, (i, 1, m)). + """ + m = len(p) + q, r = zip(*[pi.div(d) for pi in p]) + + if not all(ri.is_zero for ri in r): + n = max(ri.degree() for ri in r) + M = Matrix(n + 1, m, lambda i, j: r[j].nth(i), d.gens) + else: + M = Matrix(0, m, [], d.gens) # No constraints. + + return q, M + +def constant_system(A, u, DE): + """ + Generate a system for the constant solutions. + + Explanation + =========== + + Given a differential field (K, D) with constant field C = Const(K), a Matrix + A, and a vector (Matrix) u with coefficients in K, returns the tuple + (B, v, s), where B is a Matrix with coefficients in C and v is a vector + (Matrix) such that either v has coefficients in C, in which case s is True + and the solutions in C of Ax == u are exactly all the solutions of Bx == v, + or v has a non-constant coefficient, in which case s is False Ax == u has no + constant solution. + + This algorithm is used both in solving parametric problems and in + determining if an element a of K is a derivative of an element of K or the + logarithmic derivative of a K-radical using the structure theorem approach. + + Because Poly does not play well with Matrix yet, this algorithm assumes that + all matrix entries are Basic expressions. + """ + if not A: + return A, u + Au = A.row_join(u) + Au, _ = Au.rref() + # Warning: This will NOT return correct results if cancel() cannot reduce + # an identically zero expression to 0. The danger is that we might + # incorrectly prove that an integral is nonelementary (such as + # risch_integrate(exp((sin(x)**2 + cos(x)**2 - 1)*x**2), x). + # But this is a limitation in computer algebra in general, and implicit + # in the correctness of the Risch Algorithm is the computability of the + # constant field (actually, this same correctness problem exists in any + # algorithm that uses rref()). + # + # We therefore limit ourselves to constant fields that are computable + # via the cancel() function, in order to prevent a speed bottleneck from + # calling some more complex simplification function (rational function + # coefficients will fall into this class). Furthermore, (I believe) this + # problem will only crop up if the integral explicitly contains an + # expression in the constant field that is identically zero, but cannot + # be reduced to such by cancel(). Therefore, a careful user can avoid this + # problem entirely by being careful with the sorts of expressions that + # appear in his integrand in the variables other than the integration + # variable (the structure theorems should be able to completely decide these + # problems in the integration variable). + + A, u = Au[:, :-1], Au[:, -1] + + D = lambda x: derivation(x, DE, basic=True) + + for j, i in itertools.product(range(A.cols), range(A.rows)): + if A[i, j].expr.has(*DE.T): + # This assumes that const(F(t0, ..., tn) == const(K) == F + Ri = A[i, :] + # Rm+1; m = A.rows + DAij = D(A[i, j]) + Rm1 = Ri.applyfunc(lambda x: D(x) / DAij) + um1 = D(u[i]) / DAij + + Aj = A[:, j] + A = A - Aj * Rm1 + u = u - Aj * um1 + + A = A.col_join(Rm1) + u = u.col_join(Matrix([um1], u.gens)) + + return (A, u) + + +def prde_spde(a, b, Q, n, DE): + """ + Special Polynomial Differential Equation algorithm: Parametric Version. + + Explanation + =========== + + Given a derivation D on k[t], an integer n, and a, b, q1, ..., qm in k[t] + with deg(a) > 0 and gcd(a, b) == 1, return (A, B, Q, R, n1), with + Qq = [q1, ..., qm] and R = [r1, ..., rm], such that for any solution + c1, ..., cm in Const(k) and q in k[t] of degree at most n of + a*Dq + b*q == Sum(ci*gi, (i, 1, m)), p = (q - Sum(ci*ri, (i, 1, m)))/a has + degree at most n1 and satisfies A*Dp + B*p == Sum(ci*qi, (i, 1, m)) + """ + R, Z = list(zip(*[gcdex_diophantine(b, a, qi) for qi in Q])) + + A = a + B = b + derivation(a, DE) + Qq = [zi - derivation(ri, DE) for ri, zi in zip(R, Z)] + R = list(R) + n1 = n - a.degree(DE.t) + + return (A, B, Qq, R, n1) + + +def prde_no_cancel_b_large(b, Q, n, DE): + """ + Parametric Poly Risch Differential Equation - No cancellation: deg(b) large enough. + + Explanation + =========== + + Given a derivation D on k[t], n in ZZ, and b, q1, ..., qm in k[t] with + b != 0 and either D == d/dt or deg(b) > max(0, deg(D) - 1), returns + h1, ..., hr in k[t] and a matrix A with coefficients in Const(k) such that + if c1, ..., cm in Const(k) and q in k[t] satisfy deg(q) <= n and + Dq + b*q == Sum(ci*qi, (i, 1, m)), then q = Sum(dj*hj, (j, 1, r)), where + d1, ..., dr in Const(k) and A*Matrix([[c1, ..., cm, d1, ..., dr]]).T == 0. + """ + db = b.degree(DE.t) + m = len(Q) + H = [Poly(0, DE.t)]*m + + for N, i in itertools.product(range(n, -1, -1), range(m)): # [n, ..., 0] + si = Q[i].nth(N + db)/b.LC() + sitn = Poly(si*DE.t**N, DE.t) + H[i] = H[i] + sitn + Q[i] = Q[i] - derivation(sitn, DE) - b*sitn + + if all(qi.is_zero for qi in Q): + dc = -1 + else: + dc = max(qi.degree(DE.t) for qi in Q) + M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i), DE.t) + A, u = constant_system(M, zeros(dc + 1, 1, DE.t), DE) + c = eye(m, DE.t) + A = A.row_join(zeros(A.rows, m, DE.t)).col_join(c.row_join(-c)) + + return (H, A) + + +def prde_no_cancel_b_small(b, Q, n, DE): + """ + Parametric Poly Risch Differential Equation - No cancellation: deg(b) small enough. + + Explanation + =========== + + Given a derivation D on k[t], n in ZZ, and b, q1, ..., qm in k[t] with + deg(b) < deg(D) - 1 and either D == d/dt or deg(D) >= 2, returns + h1, ..., hr in k[t] and a matrix A with coefficients in Const(k) such that + if c1, ..., cm in Const(k) and q in k[t] satisfy deg(q) <= n and + Dq + b*q == Sum(ci*qi, (i, 1, m)) then q = Sum(dj*hj, (j, 1, r)) where + d1, ..., dr in Const(k) and A*Matrix([[c1, ..., cm, d1, ..., dr]]).T == 0. + """ + m = len(Q) + H = [Poly(0, DE.t)]*m + + for N, i in itertools.product(range(n, 0, -1), range(m)): # [n, ..., 1] + si = Q[i].nth(N + DE.d.degree(DE.t) - 1)/(N*DE.d.LC()) + sitn = Poly(si*DE.t**N, DE.t) + H[i] = H[i] + sitn + Q[i] = Q[i] - derivation(sitn, DE) - b*sitn + + if b.degree(DE.t) > 0: + for i in range(m): + si = Poly(Q[i].nth(b.degree(DE.t))/b.LC(), DE.t) + H[i] = H[i] + si + Q[i] = Q[i] - derivation(si, DE) - b*si + if all(qi.is_zero for qi in Q): + dc = -1 + else: + dc = max(qi.degree(DE.t) for qi in Q) + M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i), DE.t) + A, u = constant_system(M, zeros(dc + 1, 1, DE.t), DE) + c = eye(m, DE.t) + A = A.row_join(zeros(A.rows, m, DE.t)).col_join(c.row_join(-c)) + return (H, A) + + # else: b is in k, deg(qi) < deg(Dt) + + t = DE.t + if DE.case != 'base': + with DecrementLevel(DE): + t0 = DE.t # k = k0(t0) + ba, bd = frac_in(b, t0, field=True) + Q0 = [frac_in(qi.TC(), t0, field=True) for qi in Q] + f, B = param_rischDE(ba, bd, Q0, DE) + + # f = [f1, ..., fr] in k^r and B is a matrix with + # m + r columns and entries in Const(k) = Const(k0) + # such that Dy0 + b*y0 = Sum(ci*qi, (i, 1, m)) has + # a solution y0 in k with c1, ..., cm in Const(k) + # if and only y0 = Sum(dj*fj, (j, 1, r)) where + # d1, ..., dr ar in Const(k) and + # B*Matrix([c1, ..., cm, d1, ..., dr]) == 0. + + # Transform fractions (fa, fd) in f into constant + # polynomials fa/fd in k[t]. + # (Is there a better way?) + f = [Poly(fa.as_expr()/fd.as_expr(), t, field=True) + for fa, fd in f] + B = Matrix.from_Matrix(B.to_Matrix(), t) + else: + # Base case. Dy == 0 for all y in k and b == 0. + # Dy + b*y = Sum(ci*qi) is solvable if and only if + # Sum(ci*qi) == 0 in which case the solutions are + # y = d1*f1 for f1 = 1 and any d1 in Const(k) = k. + + f = [Poly(1, t, field=True)] # r = 1 + B = Matrix([[qi.TC() for qi in Q] + [S.Zero]], DE.t) + # The condition for solvability is + # B*Matrix([c1, ..., cm, d1]) == 0 + # There are no constraints on d1. + + # Coefficients of t^j (j > 0) in Sum(ci*qi) must be zero. + d = max(qi.degree(DE.t) for qi in Q) + if d > 0: + M = Matrix(d, m, lambda i, j: Q[j].nth(i + 1), DE.t) + A, _ = constant_system(M, zeros(d, 1, DE.t), DE) + else: + # No constraints on the hj. + A = Matrix(0, m, [], DE.t) + + # Solutions of the original equation are + # y = Sum(dj*fj, (j, 1, r) + Sum(ei*hi, (i, 1, m)), + # where ei == ci (i = 1, ..., m), when + # A*Matrix([c1, ..., cm]) == 0 and + # B*Matrix([c1, ..., cm, d1, ..., dr]) == 0 + + # Build combined constraint matrix with m + r + m columns. + + r = len(f) + I = eye(m, DE.t) + A = A.row_join(zeros(A.rows, r + m, DE.t)) + B = B.row_join(zeros(B.rows, m, DE.t)) + C = I.row_join(zeros(m, r, DE.t)).row_join(-I) + + return f + H, A.col_join(B).col_join(C) + + +def prde_cancel_liouvillian(b, Q, n, DE): + """ + Pg, 237. + """ + H = [] + + # Why use DecrementLevel? Below line answers that: + # Assuming that we can solve such problems over 'k' (not k[t]) + if DE.case == 'primitive': + with DecrementLevel(DE): + ba, bd = frac_in(b, DE.t, field=True) + + for i in range(n, -1, -1): + if DE.case == 'exp': # this re-checking can be avoided + with DecrementLevel(DE): + ba, bd = frac_in(b + (i*(derivation(DE.t, DE)/DE.t)).as_poly(b.gens), + DE.t, field=True) + with DecrementLevel(DE): + Qy = [frac_in(q.nth(i), DE.t, field=True) for q in Q] + fi, Ai = param_rischDE(ba, bd, Qy, DE) + fi = [Poly(fa.as_expr()/fd.as_expr(), DE.t, field=True) + for fa, fd in fi] + Ai = Ai.set_gens(DE.t) + + ri = len(fi) + + if i == n: + M = Ai + else: + M = Ai.col_join(M.row_join(zeros(M.rows, ri, DE.t))) + + Fi, hi = [None]*ri, [None]*ri + + # from eq. on top of p.238 (unnumbered) + for j in range(ri): + hji = fi[j] * (DE.t**i).as_poly(fi[j].gens) + hi[j] = hji + # building up Sum(djn*(D(fjn*t^n) - b*fjnt^n)) + Fi[j] = -(derivation(hji, DE) - b*hji) + + H += hi + # in the next loop instead of Q it has + # to be Q + Fi taking its place + Q = Q + Fi + + return (H, M) + + +def param_poly_rischDE(a, b, q, n, DE): + """Polynomial solutions of a parametric Risch differential equation. + + Explanation + =========== + + Given a derivation D in k[t], a, b in k[t] relatively prime, and q + = [q1, ..., qm] in k[t]^m, return h = [h1, ..., hr] in k[t]^r and + a matrix A with m + r columns and entries in Const(k) such that + a*Dp + b*p = Sum(ci*qi, (i, 1, m)) has a solution p of degree <= n + in k[t] with c1, ..., cm in Const(k) if and only if p = Sum(dj*hj, + (j, 1, r)) where d1, ..., dr are in Const(k) and (c1, ..., cm, + d1, ..., dr) is a solution of Ax == 0. + """ + m = len(q) + if n < 0: + # Only the trivial zero solution is possible. + # Find relations between the qi. + if all(qi.is_zero for qi in q): + return [], zeros(1, m, DE.t) # No constraints. + + N = max(qi.degree(DE.t) for qi in q) + M = Matrix(N + 1, m, lambda i, j: q[j].nth(i), DE.t) + A, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE) + + return [], A + + if a.is_ground: + # Normalization: a = 1. + a = a.LC() + b, q = b.quo_ground(a), [qi.quo_ground(a) for qi in q] + + if not b.is_zero and (DE.case == 'base' or + b.degree() > max(0, DE.d.degree() - 1)): + return prde_no_cancel_b_large(b, q, n, DE) + + elif ((b.is_zero or b.degree() < DE.d.degree() - 1) + and (DE.case == 'base' or DE.d.degree() >= 2)): + return prde_no_cancel_b_small(b, q, n, DE) + + elif (DE.d.degree() >= 2 and + b.degree() == DE.d.degree() - 1 and + n > -b.as_poly().LC()/DE.d.as_poly().LC()): + raise NotImplementedError("prde_no_cancel_b_equal() is " + "not yet implemented.") + + else: + # Liouvillian cases + if DE.case in ('primitive', 'exp'): + return prde_cancel_liouvillian(b, q, n, DE) + else: + raise NotImplementedError("non-linear and hypertangent " + "cases have not yet been implemented") + + # else: deg(a) > 0 + + # Iterate SPDE as long as possible cumulating coefficient + # and terms for the recovery of original solutions. + alpha, beta = a.one, [a.zero]*m + while n >= 0: # and a, b relatively prime + a, b, q, r, n = prde_spde(a, b, q, n, DE) + beta = [betai + alpha*ri for betai, ri in zip(beta, r)] + alpha *= a + # Solutions p of a*Dp + b*p = Sum(ci*qi) correspond to + # solutions alpha*p + Sum(ci*betai) of the initial equation. + d = a.gcd(b) + if not d.is_ground: + break + + # a*Dp + b*p = Sum(ci*qi) may have a polynomial solution + # only if the sum is divisible by d. + + qq, M = poly_linear_constraints(q, d) + # qq = [qq1, ..., qqm] where qqi = qi.quo(d). + # M is a matrix with m columns an entries in k. + # Sum(fi*qi, (i, 1, m)), where f1, ..., fm are elements of k, is + # divisible by d if and only if M*Matrix([f1, ..., fm]) == 0, + # in which case the quotient is Sum(fi*qqi). + + A, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE) + # A is a matrix with m columns and entries in Const(k). + # Sum(ci*qqi) is Sum(ci*qi).quo(d), and the remainder is zero + # for c1, ..., cm in Const(k) if and only if + # A*Matrix([c1, ...,cm]) == 0. + + V = A.nullspace() + # V = [v1, ..., vu] where each vj is a column matrix with + # entries aj1, ..., ajm in Const(k). + # Sum(aji*qi) is divisible by d with exact quotient Sum(aji*qqi). + # Sum(ci*qi) is divisible by d if and only if ci = Sum(dj*aji) + # (i = 1, ..., m) for some d1, ..., du in Const(k). + # In that case, solutions of + # a*Dp + b*p = Sum(ci*qi) = Sum(dj*Sum(aji*qi)) + # are the same as those of + # (a/d)*Dp + (b/d)*p = Sum(dj*rj) + # where rj = Sum(aji*qqi). + + if not V: # No non-trivial solution. + return [], eye(m, DE.t) # Could return A, but this has + # the minimum number of rows. + + Mqq = Matrix([qq]) # A single row. + r = [(Mqq*vj)[0] for vj in V] # [r1, ..., ru] + + # Solutions of (a/d)*Dp + (b/d)*p = Sum(dj*rj) correspond to + # solutions alpha*p + Sum(Sum(dj*aji)*betai) of the initial + # equation. These are equal to alpha*p + Sum(dj*fj) where + # fj = Sum(aji*betai). + Mbeta = Matrix([beta]) + f = [(Mbeta*vj)[0] for vj in V] # [f1, ..., fu] + + # + # Solve the reduced equation recursively. + # + g, B = param_poly_rischDE(a.quo(d), b.quo(d), r, n, DE) + + # g = [g1, ..., gv] in k[t]^v and and B is a matrix with u + v + # columns and entries in Const(k) such that + # (a/d)*Dp + (b/d)*p = Sum(dj*rj) has a solution p of degree <= n + # in k[t] if and only if p = Sum(ek*gk) where e1, ..., ev are in + # Const(k) and B*Matrix([d1, ..., du, e1, ..., ev]) == 0. + # The solutions of the original equation are then + # Sum(dj*fj, (j, 1, u)) + alpha*Sum(ek*gk, (k, 1, v)). + + # Collect solution components. + h = f + [alpha*gk for gk in g] + + # Build combined relation matrix. + A = -eye(m, DE.t) + for vj in V: + A = A.row_join(vj) + A = A.row_join(zeros(m, len(g), DE.t)) + A = A.col_join(zeros(B.rows, m, DE.t).row_join(B)) + + return h, A + + +def param_rischDE(fa, fd, G, DE): + """ + Solve a Parametric Risch Differential Equation: Dy + f*y == Sum(ci*Gi, (i, 1, m)). + + Explanation + =========== + + Given a derivation D in k(t), f in k(t), and G + = [G1, ..., Gm] in k(t)^m, return h = [h1, ..., hr] in k(t)^r and + a matrix A with m + r columns and entries in Const(k) such that + Dy + f*y = Sum(ci*Gi, (i, 1, m)) has a solution y + in k(t) with c1, ..., cm in Const(k) if and only if y = Sum(dj*hj, + (j, 1, r)) where d1, ..., dr are in Const(k) and (c1, ..., cm, + d1, ..., dr) is a solution of Ax == 0. + + Elements of k(t) are tuples (a, d) with a and d in k[t]. + """ + m = len(G) + q, (fa, fd) = weak_normalizer(fa, fd, DE) + # Solutions of the weakly normalized equation Dz + f*z = q*Sum(ci*Gi) + # correspond to solutions y = z/q of the original equation. + gamma = q + G = [(q*ga).cancel(gd, include=True) for ga, gd in G] + + a, (ba, bd), G, hn = prde_normal_denom(fa, fd, G, DE) + # Solutions q in k of a*Dq + b*q = Sum(ci*Gi) correspond + # to solutions z = q/hn of the weakly normalized equation. + gamma *= hn + + A, B, G, hs = prde_special_denom(a, ba, bd, G, DE) + # Solutions p in k[t] of A*Dp + B*p = Sum(ci*Gi) correspond + # to solutions q = p/hs of the previous equation. + gamma *= hs + + g = A.gcd(B) + a, b, g = A.quo(g), B.quo(g), [gia.cancel(gid*g, include=True) for + gia, gid in G] + + # a*Dp + b*p = Sum(ci*gi) may have a polynomial solution + # only if the sum is in k[t]. + + q, M = prde_linear_constraints(a, b, g, DE) + + # q = [q1, ..., qm] where qi in k[t] is the polynomial component + # of the partial fraction expansion of gi. + # M is a matrix with m columns and entries in k. + # Sum(fi*gi, (i, 1, m)), where f1, ..., fm are elements of k, + # is a polynomial if and only if M*Matrix([f1, ..., fm]) == 0, + # in which case the sum is equal to Sum(fi*qi). + + M, _ = constant_system(M, zeros(M.rows, 1, DE.t), DE) + # M is a matrix with m columns and entries in Const(k). + # Sum(ci*gi) is in k[t] for c1, ..., cm in Const(k) + # if and only if M*Matrix([c1, ..., cm]) == 0, + # in which case the sum is Sum(ci*qi). + + ## Reduce number of constants at this point + + V = M.nullspace() + # V = [v1, ..., vu] where each vj is a column matrix with + # entries aj1, ..., ajm in Const(k). + # Sum(aji*gi) is in k[t] and equal to Sum(aji*qi) (j = 1, ..., u). + # Sum(ci*gi) is in k[t] if and only is ci = Sum(dj*aji) + # (i = 1, ..., m) for some d1, ..., du in Const(k). + # In that case, + # Sum(ci*gi) = Sum(ci*qi) = Sum(dj*Sum(aji*qi)) = Sum(dj*rj) + # where rj = Sum(aji*qi) (j = 1, ..., u) in k[t]. + + if not V: # No non-trivial solution + return [], eye(m, DE.t) + + Mq = Matrix([q]) # A single row. + r = [(Mq*vj)[0] for vj in V] # [r1, ..., ru] + + # Solutions of a*Dp + b*p = Sum(dj*rj) correspond to solutions + # y = p/gamma of the initial equation with ci = Sum(dj*aji). + + try: + # We try n=5. At least for prde_spde, it will always + # terminate no matter what n is. + n = bound_degree(a, b, r, DE, parametric=True) + except NotImplementedError: + # A temporary bound is set. Eventually, it will be removed. + # the currently added test case takes large time + # even with n=5, and much longer with large n's. + n = 5 + + h, B = param_poly_rischDE(a, b, r, n, DE) + + # h = [h1, ..., hv] in k[t]^v and and B is a matrix with u + v + # columns and entries in Const(k) such that + # a*Dp + b*p = Sum(dj*rj) has a solution p of degree <= n + # in k[t] if and only if p = Sum(ek*hk) where e1, ..., ev are in + # Const(k) and B*Matrix([d1, ..., du, e1, ..., ev]) == 0. + # The solutions of the original equation for ci = Sum(dj*aji) + # (i = 1, ..., m) are then y = Sum(ek*hk, (k, 1, v))/gamma. + + ## Build combined relation matrix with m + u + v columns. + + A = -eye(m, DE.t) + for vj in V: + A = A.row_join(vj) + A = A.row_join(zeros(m, len(h), DE.t)) + A = A.col_join(zeros(B.rows, m, DE.t).row_join(B)) + + ## Eliminate d1, ..., du. + + W = A.nullspace() + + # W = [w1, ..., wt] where each wl is a column matrix with + # entries blk (k = 1, ..., m + u + v) in Const(k). + # The vectors (bl1, ..., blm) generate the space of those + # constant families (c1, ..., cm) for which a solution of + # the equation Dy + f*y == Sum(ci*Gi) exists. They generate + # the space and form a basis except possibly when Dy + f*y == 0 + # is solvable in k(t}. The corresponding solutions are + # y = Sum(blk'*hk, (k, 1, v))/gamma, where k' = k + m + u. + + v = len(h) + shape = (len(W), m+v) + elements = [wl[:m] + wl[-v:] for wl in W] # excise dj's. + items = [e for row in elements for e in row] + + # Need to set the shape in case W is empty + M = Matrix(*shape, items, DE.t) + N = M.nullspace() + + # N = [n1, ..., ns] where the ni in Const(k)^(m + v) are column + # vectors generating the space of linear relations between + # c1, ..., cm, e1, ..., ev. + + C = Matrix([ni[:] for ni in N], DE.t) # rows n1, ..., ns. + + return [hk.cancel(gamma, include=True) for hk in h], C + + +def limited_integrate_reduce(fa, fd, G, DE): + """ + Simpler version of step 1 & 2 for the limited integration problem. + + Explanation + =========== + + Given a derivation D on k(t) and f, g1, ..., gn in k(t), return + (a, b, h, N, g, V) such that a, b, h in k[t], N is a non-negative integer, + g in k(t), V == [v1, ..., vm] in k(t)^m, and for any solution v in k(t), + c1, ..., cm in C of f == Dv + Sum(ci*wi, (i, 1, m)), p = v*h is in k, and + p and the ci satisfy a*Dp + b*p == g + Sum(ci*vi, (i, 1, m)). Furthermore, + if S1irr == Sirr, then p is in k[t], and if t is nonlinear or Liouvillian + over k, then deg(p) <= N. + + So that the special part is always computed, this function calls the more + general prde_special_denom() automatically if it cannot determine that + S1irr == Sirr. Furthermore, it will automatically call bound_degree() when + t is linear and non-Liouvillian, which for the transcendental case, implies + that Dt == a*t + b with for some a, b in k*. + """ + dn, ds = splitfactor(fd, DE) + E = [splitfactor(gd, DE) for _, gd in G] + En, Es = list(zip(*E)) + c = reduce(lambda i, j: i.lcm(j), (dn,) + En) # lcm(dn, en1, ..., enm) + hn = c.gcd(c.diff(DE.t)) + a = hn + b = -derivation(hn, DE) + N = 0 + + # These are the cases where we know that S1irr = Sirr, but there could be + # others, and this algorithm will need to be extended to handle them. + if DE.case in ('base', 'primitive', 'exp', 'tan'): + hs = reduce(lambda i, j: i.lcm(j), (ds,) + Es) # lcm(ds, es1, ..., esm) + a = hn*hs + b -= (hn*derivation(hs, DE)).quo(hs) + mu = min(order_at_oo(fa, fd, DE.t), min(order_at_oo(ga, gd, DE.t) for + ga, gd in G)) + # So far, all the above are also nonlinear or Liouvillian, but if this + # changes, then this will need to be updated to call bound_degree() + # as per the docstring of this function (DE.case == 'other_linear'). + N = hn.degree(DE.t) + hs.degree(DE.t) + max(0, 1 - DE.d.degree(DE.t) - mu) + else: + # TODO: implement this + raise NotImplementedError + + V = [(-a*hn*ga).cancel(gd, include=True) for ga, gd in G] + return (a, b, a, N, (a*hn*fa).cancel(fd, include=True), V) + + +def limited_integrate(fa, fd, G, DE): + """ + Solves the limited integration problem: f = Dv + Sum(ci*wi, (i, 1, n)) + """ + fa, fd = fa*Poly(1/fd.LC(), DE.t), fd.monic() + # interpreting limited integration problem as a + # parametric Risch DE problem + Fa = Poly(0, DE.t) + Fd = Poly(1, DE.t) + G = [(fa, fd)] + G + h, A = param_rischDE(Fa, Fd, G, DE) + V = A.nullspace() + V = [v for v in V if v[0] != 0] + if not V: + return None + else: + # we can take any vector from V, we take V[0] + c0 = V[0][0] + # v = [-1, c1, ..., cm, d1, ..., dr] + v = V[0]/(-c0) + r = len(h) + m = len(v) - r - 1 + C = list(v[1: m + 1]) + y = -sum(v[m + 1 + i]*h[i][0].as_expr()/h[i][1].as_expr() \ + for i in range(r)) + y_num, y_den = y.as_numer_denom() + Ya, Yd = Poly(y_num, DE.t), Poly(y_den, DE.t) + Y = Ya*Poly(1/Yd.LC(), DE.t), Yd.monic() + return Y, C + + +def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None): + """ + Parametric logarithmic derivative heuristic. + + Explanation + =========== + + Given a derivation D on k[t], f in k(t), and a hyperexponential monomial + theta over k(t), raises either NotImplementedError, in which case the + heuristic failed, or returns None, in which case it has proven that no + solution exists, or returns a solution (n, m, v) of the equation + n*f == Dv/v + m*Dtheta/theta, with v in k(t)* and n, m in ZZ with n != 0. + + If this heuristic fails, the structure theorem approach will need to be + used. + + The argument w == Dtheta/theta + """ + # TODO: finish writing this and write tests + c1 = c1 or Dummy('c1') + + p, a = fa.div(fd) + q, b = wa.div(wd) + + B = max(0, derivation(DE.t, DE).degree(DE.t) - 1) + C = max(p.degree(DE.t), q.degree(DE.t)) + + if q.degree(DE.t) > B: + eqs = [p.nth(i) - c1*q.nth(i) for i in range(B + 1, C + 1)] + s = solve(eqs, c1) + if not s or not s[c1].is_Rational: + # deg(q) > B, no solution for c. + return None + + M, N = s[c1].as_numer_denom() + M_poly = M.as_poly(q.gens) + N_poly = N.as_poly(q.gens) + + nfmwa = N_poly*fa*wd - M_poly*wa*fd + nfmwd = fd*wd + Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE, 'auto') + if Qv is None: + # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical. + return None + + Q, v = Qv + + if Q.is_zero or v.is_zero: + return None + + return (Q*N, Q*M, v) + + if p.degree(DE.t) > B: + return None + + c = lcm(fd.as_poly(DE.t).LC(), wd.as_poly(DE.t).LC()) + l = fd.monic().lcm(wd.monic())*Poly(c, DE.t) + ln, ls = splitfactor(l, DE) + z = ls*ln.gcd(ln.diff(DE.t)) + + if not z.has(DE.t): + # TODO: We treat this as 'no solution', until the structure + # theorem version of parametric_log_deriv is implemented. + return None + + u1, r1 = (fa*l.quo(fd)).div(z) # (l*f).div(z) + u2, r2 = (wa*l.quo(wd)).div(z) # (l*w).div(z) + + eqs = [r1.nth(i) - c1*r2.nth(i) for i in range(z.degree(DE.t))] + s = solve(eqs, c1) + if not s or not s[c1].is_Rational: + # deg(q) <= B, no solution for c. + return None + + M, N = s[c1].as_numer_denom() + + nfmwa = N.as_poly(DE.t)*fa*wd - M.as_poly(DE.t)*wa*fd + nfmwd = fd*wd + Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE) + if Qv is None: + # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical. + return None + + Q, v = Qv + + if Q.is_zero or v.is_zero: + return None + + return (Q*N, Q*M, v) + + +def parametric_log_deriv(fa, fd, wa, wd, DE): + # TODO: Write the full algorithm using the structure theorems. +# try: + A = parametric_log_deriv_heu(fa, fd, wa, wd, DE) +# except NotImplementedError: + # Heuristic failed, we have to use the full method. + # TODO: This could be implemented more efficiently. + # It isn't too worrisome, because the heuristic handles most difficult + # cases. + return A + + +def is_deriv_k(fa, fd, DE): + r""" + Checks if Df/f is the derivative of an element of k(t). + + Explanation + =========== + + a in k(t) is the derivative of an element of k(t) if there exists b in k(t) + such that a = Db. Either returns (ans, u), such that Df/f == Du, or None, + which means that Df/f is not the derivative of an element of k(t). ans is + a list of tuples such that Add(*[i*j for i, j in ans]) == u. This is useful + for seeing exactly which elements of k(t) produce u. + + This function uses the structure theorem approach, which says that for any + f in K, Df/f is the derivative of a element of K if and only if there are ri + in QQ such that:: + + --- --- Dt + \ r * Dt + \ r * i Df + / i i / i --- = --. + --- --- t f + i in L i in E i + K/C(x) K/C(x) + + + Where C = Const(K), L_K/C(x) = { i in {1, ..., n} such that t_i is + transcendental over C(x)(t_1, ..., t_i-1) and Dt_i = Da_i/a_i, for some a_i + in C(x)(t_1, ..., t_i-1)* } (i.e., the set of all indices of logarithmic + monomials of K over C(x)), and E_K/C(x) = { i in {1, ..., n} such that t_i + is transcendental over C(x)(t_1, ..., t_i-1) and Dt_i/t_i = Da_i, for some + a_i in C(x)(t_1, ..., t_i-1) } (i.e., the set of all indices of + hyperexponential monomials of K over C(x)). If K is an elementary extension + over C(x), then the cardinality of L_K/C(x) U E_K/C(x) is exactly the + transcendence degree of K over C(x). Furthermore, because Const_D(K) == + Const_D(C(x)) == C, deg(Dt_i) == 1 when t_i is in E_K/C(x) and + deg(Dt_i) == 0 when t_i is in L_K/C(x), implying in particular that E_K/C(x) + and L_K/C(x) are disjoint. + + The sets L_K/C(x) and E_K/C(x) must, by their nature, be computed + recursively using this same function. Therefore, it is required to pass + them as indices to D (or T). E_args are the arguments of the + hyperexponentials indexed by E_K (i.e., if i is in E_K, then T[i] == + exp(E_args[i])). This is needed to compute the final answer u such that + Df/f == Du. + + log(f) will be the same as u up to a additive constant. This is because + they will both behave the same as monomials. For example, both log(x) and + log(2*x) == log(x) + log(2) satisfy Dt == 1/x, because log(2) is constant. + Therefore, the term const is returned. const is such that + log(const) + f == u. This is calculated by dividing the arguments of one + logarithm from the other. Therefore, it is necessary to pass the arguments + of the logarithmic terms in L_args. + + To handle the case where we are given Df/f, not f, use is_deriv_k_in_field(). + + See also + ======== + is_log_deriv_k_t_radical_in_field, is_log_deriv_k_t_radical + + """ + # Compute Df/f + dfa, dfd = (fd*derivation(fa, DE) - fa*derivation(fd, DE)), fd*fa + dfa, dfd = dfa.cancel(dfd, include=True) + + # Our assumption here is that each monomial is recursively transcendental + if len(DE.exts) != len(DE.D): + if [i for i in DE.cases if i == 'tan'] or \ + ({i for i in DE.cases if i == 'primitive'} - + set(DE.indices('log'))): + raise NotImplementedError("Real version of the structure " + "theorems with hypertangent support is not yet implemented.") + + # TODO: What should really be done in this case? + raise NotImplementedError("Nonelementary extensions not supported " + "in the structure theorems.") + + E_part = [DE.D[i].quo(Poly(DE.T[i], DE.T[i])).as_expr() for i in DE.indices('exp')] + L_part = [DE.D[i].as_expr() for i in DE.indices('log')] + + # The expression dfa/dfd might not be polynomial in any of its symbols so we + # use a Dummy as the generator for PolyMatrix. + dum = Dummy() + lhs = Matrix([E_part + L_part], dum) + rhs = Matrix([dfa.as_expr()/dfd.as_expr()], dum) + + A, u = constant_system(lhs, rhs, DE) + + u = u.to_Matrix() # Poly to Expr + + if not A or not all(derivation(i, DE, basic=True).is_zero for i in u): + # If the elements of u are not all constant + # Note: See comment in constant_system + + # Also note: derivation(basic=True) calls cancel() + return None + else: + if not all(i.is_Rational for i in u): + raise NotImplementedError("Cannot work with non-rational " + "coefficients in this case.") + else: + terms = ([DE.extargs[i] for i in DE.indices('exp')] + + [DE.T[i] for i in DE.indices('log')]) + ans = list(zip(terms, u)) + result = Add(*[Mul(i, j) for i, j in ans]) + argterms = ([DE.T[i] for i in DE.indices('exp')] + + [DE.extargs[i] for i in DE.indices('log')]) + l = [] + ld = [] + for i, j in zip(argterms, u): + # We need to get around things like sqrt(x**2) != x + # and also sqrt(x**2 + 2*x + 1) != x + 1 + # Issue 10798: i need not be a polynomial + i, d = i.as_numer_denom() + icoeff, iterms = sqf_list(i) + l.append(Mul(*([Pow(icoeff, j)] + [Pow(b, e*j) for b, e in iterms]))) + dcoeff, dterms = sqf_list(d) + ld.append(Mul(*([Pow(dcoeff, j)] + [Pow(b, e*j) for b, e in dterms]))) + const = cancel(fa.as_expr()/fd.as_expr()/Mul(*l)*Mul(*ld)) + + return (ans, result, const) + + +def is_log_deriv_k_t_radical(fa, fd, DE, Df=True): + r""" + Checks if Df is the logarithmic derivative of a k(t)-radical. + + Explanation + =========== + + b in k(t) can be written as the logarithmic derivative of a k(t) radical if + there exist n in ZZ and u in k(t) with n, u != 0 such that n*b == Du/u. + Either returns (ans, u, n, const) or None, which means that Df cannot be + written as the logarithmic derivative of a k(t)-radical. ans is a list of + tuples such that Mul(*[i**j for i, j in ans]) == u. This is useful for + seeing exactly what elements of k(t) produce u. + + This function uses the structure theorem approach, which says that for any + f in K, Df is the logarithmic derivative of a K-radical if and only if there + are ri in QQ such that:: + + --- --- Dt + \ r * Dt + \ r * i + / i i / i --- = Df. + --- --- t + i in L i in E i + K/C(x) K/C(x) + + + Where C = Const(K), L_K/C(x) = { i in {1, ..., n} such that t_i is + transcendental over C(x)(t_1, ..., t_i-1) and Dt_i = Da_i/a_i, for some a_i + in C(x)(t_1, ..., t_i-1)* } (i.e., the set of all indices of logarithmic + monomials of K over C(x)), and E_K/C(x) = { i in {1, ..., n} such that t_i + is transcendental over C(x)(t_1, ..., t_i-1) and Dt_i/t_i = Da_i, for some + a_i in C(x)(t_1, ..., t_i-1) } (i.e., the set of all indices of + hyperexponential monomials of K over C(x)). If K is an elementary extension + over C(x), then the cardinality of L_K/C(x) U E_K/C(x) is exactly the + transcendence degree of K over C(x). Furthermore, because Const_D(K) == + Const_D(C(x)) == C, deg(Dt_i) == 1 when t_i is in E_K/C(x) and + deg(Dt_i) == 0 when t_i is in L_K/C(x), implying in particular that E_K/C(x) + and L_K/C(x) are disjoint. + + The sets L_K/C(x) and E_K/C(x) must, by their nature, be computed + recursively using this same function. Therefore, it is required to pass + them as indices to D (or T). L_args are the arguments of the logarithms + indexed by L_K (i.e., if i is in L_K, then T[i] == log(L_args[i])). This is + needed to compute the final answer u such that n*f == Du/u. + + exp(f) will be the same as u up to a multiplicative constant. This is + because they will both behave the same as monomials. For example, both + exp(x) and exp(x + 1) == E*exp(x) satisfy Dt == t. Therefore, the term const + is returned. const is such that exp(const)*f == u. This is calculated by + subtracting the arguments of one exponential from the other. Therefore, it + is necessary to pass the arguments of the exponential terms in E_args. + + To handle the case where we are given Df, not f, use + is_log_deriv_k_t_radical_in_field(). + + See also + ======== + + is_log_deriv_k_t_radical_in_field, is_deriv_k + + """ + if Df: + dfa, dfd = (fd*derivation(fa, DE) - fa*derivation(fd, DE)).cancel(fd**2, + include=True) + else: + dfa, dfd = fa, fd + + # Our assumption here is that each monomial is recursively transcendental + if len(DE.exts) != len(DE.D): + if [i for i in DE.cases if i == 'tan'] or \ + ({i for i in DE.cases if i == 'primitive'} - + set(DE.indices('log'))): + raise NotImplementedError("Real version of the structure " + "theorems with hypertangent support is not yet implemented.") + + # TODO: What should really be done in this case? + raise NotImplementedError("Nonelementary extensions not supported " + "in the structure theorems.") + + E_part = [DE.D[i].quo(Poly(DE.T[i], DE.T[i])).as_expr() for i in DE.indices('exp')] + L_part = [DE.D[i].as_expr() for i in DE.indices('log')] + + # The expression dfa/dfd might not be polynomial in any of its symbols so we + # use a Dummy as the generator for PolyMatrix. + dum = Dummy() + lhs = Matrix([E_part + L_part], dum) + rhs = Matrix([dfa.as_expr()/dfd.as_expr()], dum) + + A, u = constant_system(lhs, rhs, DE) + + u = u.to_Matrix() # Poly to Expr + + if not A or not all(derivation(i, DE, basic=True).is_zero for i in u): + # If the elements of u are not all constant + # Note: See comment in constant_system + + # Also note: derivation(basic=True) calls cancel() + return None + else: + if not all(i.is_Rational for i in u): + # TODO: But maybe we can tell if they're not rational, like + # log(2)/log(3). Also, there should be an option to continue + # anyway, even if the result might potentially be wrong. + raise NotImplementedError("Cannot work with non-rational " + "coefficients in this case.") + else: + n = S.One*reduce(ilcm, [i.as_numer_denom()[1] for i in u]) + u *= n + terms = ([DE.T[i] for i in DE.indices('exp')] + + [DE.extargs[i] for i in DE.indices('log')]) + ans = list(zip(terms, u)) + result = Mul(*[Pow(i, j) for i, j in ans]) + + # exp(f) will be the same as result up to a multiplicative + # constant. We now find the log of that constant. + argterms = ([DE.extargs[i] for i in DE.indices('exp')] + + [DE.T[i] for i in DE.indices('log')]) + const = cancel(fa.as_expr()/fd.as_expr() - + Add(*[Mul(i, j/n) for i, j in zip(argterms, u)])) + + return (ans, result, n, const) + + +def is_log_deriv_k_t_radical_in_field(fa, fd, DE, case='auto', z=None): + """ + Checks if f can be written as the logarithmic derivative of a k(t)-radical. + + Explanation + =========== + + It differs from is_log_deriv_k_t_radical(fa, fd, DE, Df=False) + for any given fa, fd, DE in that it finds the solution in the + given field not in some (possibly unspecified extension) and + "in_field" with the function name is used to indicate that. + + f in k(t) can be written as the logarithmic derivative of a k(t) radical if + there exist n in ZZ and u in k(t) with n, u != 0 such that n*f == Du/u. + Either returns (n, u) or None, which means that f cannot be written as the + logarithmic derivative of a k(t)-radical. + + case is one of {'primitive', 'exp', 'tan', 'auto'} for the primitive, + hyperexponential, and hypertangent cases, respectively. If case is 'auto', + it will attempt to determine the type of the derivation automatically. + + See also + ======== + is_log_deriv_k_t_radical, is_deriv_k + + """ + fa, fd = fa.cancel(fd, include=True) + + # f must be simple + n, s = splitfactor(fd, DE) + if not s.is_one: + pass + + z = z or Dummy('z') + H, b = residue_reduce(fa, fd, DE, z=z) + if not b: + # I will have to verify, but I believe that the answer should be + # None in this case. This should never happen for the + # functions given when solving the parametric logarithmic + # derivative problem when integration elementary functions (see + # Bronstein's book, page 255), so most likely this indicates a bug. + return None + + roots = [(i, i.real_roots()) for i, _ in H] + if not all(len(j) == i.degree() and all(k.is_Rational for k in j) for + i, j in roots): + # If f is the logarithmic derivative of a k(t)-radical, then all the + # roots of the resultant must be rational numbers. + return None + + # [(a, i), ...], where i*log(a) is a term in the log-part of the integral + # of f + respolys, residues = list(zip(*roots)) or [[], []] + # Note: this might be empty, but everything below should work find in that + # case (it should be the same as if it were [[1, 1]]) + residueterms = [(H[j][1].subs(z, i), i) for j in range(len(H)) for + i in residues[j]] + + # TODO: finish writing this and write tests + + p = cancel(fa.as_expr()/fd.as_expr() - residue_reduce_derivation(H, DE, z)) + + p = p.as_poly(DE.t) + if p is None: + # f - Dg will be in k[t] if f is the logarithmic derivative of a k(t)-radical + return None + + if p.degree(DE.t) >= max(1, DE.d.degree(DE.t)): + return None + + if case == 'auto': + case = DE.case + + if case == 'exp': + wa, wd = derivation(DE.t, DE).cancel(Poly(DE.t, DE.t), include=True) + with DecrementLevel(DE): + pa, pd = frac_in(p, DE.t, cancel=True) + wa, wd = frac_in((wa, wd), DE.t) + A = parametric_log_deriv(pa, pd, wa, wd, DE) + if A is None: + return None + n, e, u = A + u *= DE.t**e + + elif case == 'primitive': + with DecrementLevel(DE): + pa, pd = frac_in(p, DE.t) + A = is_log_deriv_k_t_radical_in_field(pa, pd, DE, case='auto') + if A is None: + return None + n, u = A + + elif case == 'base': + # TODO: we can use more efficient residue reduction from ratint() + if not fd.is_sqf or fa.degree() >= fd.degree(): + # f is the logarithmic derivative in the base case if and only if + # f = fa/fd, fd is square-free, deg(fa) < deg(fd), and + # gcd(fa, fd) == 1. The last condition is handled by cancel() above. + return None + # Note: if residueterms = [], returns (1, 1) + # f had better be 0 in that case. + n = S.One*reduce(ilcm, [i.as_numer_denom()[1] for _, i in residueterms], 1) + u = Mul(*[Pow(i, j*n) for i, j in residueterms]) + return (n, u) + + elif case == 'tan': + raise NotImplementedError("The hypertangent case is " + "not yet implemented for is_log_deriv_k_t_radical_in_field()") + + elif case in ('other_linear', 'other_nonlinear'): + # XXX: If these are supported by the structure theorems, change to NotImplementedError. + raise ValueError("The %s case is not supported in this function." % case) + + else: + raise ValueError("case must be one of {'primitive', 'exp', 'tan', " + "'base', 'auto'}, not %s" % case) + + common_denom = S.One*reduce(ilcm, [i.as_numer_denom()[1] for i in [j for _, j in + residueterms]] + [n], 1) + residueterms = [(i, j*common_denom) for i, j in residueterms] + m = common_denom//n + if common_denom != n*m: # Verify exact division + raise ValueError("Inexact division") + u = cancel(u**m*Mul(*[Pow(i, j) for i, j in residueterms])) + + return (common_denom, u) diff --git a/lib/python3.11/site-packages/sympy/integrals/quadrature.py b/lib/python3.11/site-packages/sympy/integrals/quadrature.py new file mode 100644 index 0000000000000000000000000000000000000000..b518bd427dc9980d6a941d2e1ef4d139c5f0f5f9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/quadrature.py @@ -0,0 +1,617 @@ +from sympy.core import S, Dummy, pi +from sympy.functions.combinatorial.factorials import factorial +from sympy.functions.elementary.trigonometric import sin, cos +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.gamma_functions import gamma +from sympy.polys.orthopolys import (legendre_poly, laguerre_poly, + hermite_poly, jacobi_poly) +from sympy.polys.rootoftools import RootOf + + +def gauss_legendre(n, n_digits): + r""" + Computes the Gauss-Legendre quadrature [1]_ points and weights. + + Explanation + =========== + + The Gauss-Legendre quadrature approximates the integral: + + .. math:: + \int_{-1}^1 f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of `P_n` + and the weights `w_i` are given by: + + .. math:: + w_i = \frac{2}{\left(1-x_i^2\right) \left(P'_n(x_i)\right)^2} + + Parameters + ========== + + n : + The order of quadrature. + n_digits : + Number of significant digits of the points and weights to return. + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_legendre + >>> x, w = gauss_legendre(3, 5) + >>> x + [-0.7746, 0, 0.7746] + >>> w + [0.55556, 0.88889, 0.55556] + >>> x, w = gauss_legendre(4, 5) + >>> x + [-0.86114, -0.33998, 0.33998, 0.86114] + >>> w + [0.34785, 0.65215, 0.65215, 0.34785] + + See Also + ======== + + gauss_laguerre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gaussian_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/legendre_rule/legendre_rule.html + """ + x = Dummy("x") + p = legendre_poly(n, x, polys=True) + pd = p.diff(x) + xi = [] + w = [] + for r in p.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append((2/((1-r**2) * pd.subs(x, r)**2)).n(n_digits)) + return xi, w + + +def gauss_laguerre(n, n_digits): + r""" + Computes the Gauss-Laguerre quadrature [1]_ points and weights. + + Explanation + =========== + + The Gauss-Laguerre quadrature approximates the integral: + + .. math:: + \int_0^{\infty} e^{-x} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i) + + + The nodes `x_i` of an order `n` quadrature rule are the roots of `L_n` + and the weights `w_i` are given by: + + .. math:: + w_i = \frac{x_i}{(n+1)^2 \left(L_{n+1}(x_i)\right)^2} + + Parameters + ========== + + n : + The order of quadrature. + n_digits : + Number of significant digits of the points and weights to return. + + Returns + ======= + + (x, w) : The ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_laguerre + >>> x, w = gauss_laguerre(3, 5) + >>> x + [0.41577, 2.2943, 6.2899] + >>> w + [0.71109, 0.27852, 0.010389] + >>> x, w = gauss_laguerre(6, 5) + >>> x + [0.22285, 1.1889, 2.9927, 5.7751, 9.8375, 15.983] + >>> w + [0.45896, 0.417, 0.11337, 0.010399, 0.00026102, 8.9855e-7] + + See Also + ======== + + gauss_legendre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/laguerre_rule/laguerre_rule.html + """ + x = Dummy("x") + p = laguerre_poly(n, x, polys=True) + p1 = laguerre_poly(n+1, x, polys=True) + xi = [] + w = [] + for r in p.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append((r/((n+1)**2 * p1.subs(x, r)**2)).n(n_digits)) + return xi, w + + +def gauss_hermite(n, n_digits): + r""" + Computes the Gauss-Hermite quadrature [1]_ points and weights. + + Explanation + =========== + + The Gauss-Hermite quadrature approximates the integral: + + .. math:: + \int_{-\infty}^{\infty} e^{-x^2} f(x)\,dx \approx + \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of `H_n` + and the weights `w_i` are given by: + + .. math:: + w_i = \frac{2^{n-1} n! \sqrt{\pi}}{n^2 \left(H_{n-1}(x_i)\right)^2} + + Parameters + ========== + + n : + The order of quadrature. + n_digits : + Number of significant digits of the points and weights to return. + + Returns + ======= + + (x, w) : The ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_hermite + >>> x, w = gauss_hermite(3, 5) + >>> x + [-1.2247, 0, 1.2247] + >>> w + [0.29541, 1.1816, 0.29541] + + >>> x, w = gauss_hermite(6, 5) + >>> x + [-2.3506, -1.3358, -0.43608, 0.43608, 1.3358, 2.3506] + >>> w + [0.00453, 0.15707, 0.72463, 0.72463, 0.15707, 0.00453] + + See Also + ======== + + gauss_legendre, gauss_laguerre, gauss_gen_laguerre, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gauss-Hermite_Quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/hermite_rule/hermite_rule.html + .. [3] https://people.sc.fsu.edu/~jburkardt/cpp_src/gen_hermite_rule/gen_hermite_rule.html + """ + x = Dummy("x") + p = hermite_poly(n, x, polys=True) + p1 = hermite_poly(n-1, x, polys=True) + xi = [] + w = [] + for r in p.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append(((2**(n-1) * factorial(n) * sqrt(pi)) / + (n**2 * p1.subs(x, r)**2)).n(n_digits)) + return xi, w + + +def gauss_gen_laguerre(n, alpha, n_digits): + r""" + Computes the generalized Gauss-Laguerre quadrature [1]_ points and weights. + + Explanation + =========== + + The generalized Gauss-Laguerre quadrature approximates the integral: + + .. math:: + \int_{0}^\infty x^{\alpha} e^{-x} f(x)\,dx \approx + \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of + `L^{\alpha}_n` and the weights `w_i` are given by: + + .. math:: + w_i = \frac{\Gamma(\alpha+n)} + {n \Gamma(n) L^{\alpha}_{n-1}(x_i) L^{\alpha+1}_{n-1}(x_i)} + + Parameters + ========== + + n : + The order of quadrature. + + alpha : + The exponent of the singularity, `\alpha > -1`. + + n_digits : + Number of significant digits of the points and weights to return. + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy import S + >>> from sympy.integrals.quadrature import gauss_gen_laguerre + >>> x, w = gauss_gen_laguerre(3, -S.Half, 5) + >>> x + [0.19016, 1.7845, 5.5253] + >>> w + [1.4493, 0.31413, 0.00906] + + >>> x, w = gauss_gen_laguerre(4, 3*S.Half, 5) + >>> x + [0.97851, 2.9904, 6.3193, 11.712] + >>> w + [0.53087, 0.67721, 0.11895, 0.0023152] + + See Also + ======== + + gauss_legendre, gauss_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/gen_laguerre_rule/gen_laguerre_rule.html + """ + x = Dummy("x") + p = laguerre_poly(n, x, alpha=alpha, polys=True) + p1 = laguerre_poly(n-1, x, alpha=alpha, polys=True) + p2 = laguerre_poly(n-1, x, alpha=alpha+1, polys=True) + xi = [] + w = [] + for r in p.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append((gamma(alpha+n) / + (n*gamma(n)*p1.subs(x, r)*p2.subs(x, r))).n(n_digits)) + return xi, w + + +def gauss_chebyshev_t(n, n_digits): + r""" + Computes the Gauss-Chebyshev quadrature [1]_ points and weights of + the first kind. + + Explanation + =========== + + The Gauss-Chebyshev quadrature of the first kind approximates the integral: + + .. math:: + \int_{-1}^{1} \frac{1}{\sqrt{1-x^2}} f(x)\,dx \approx + \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of `T_n` + and the weights `w_i` are given by: + + .. math:: + w_i = \frac{\pi}{n} + + Parameters + ========== + + n : + The order of quadrature. + + n_digits : + Number of significant digits of the points and weights to return. + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_chebyshev_t + >>> x, w = gauss_chebyshev_t(3, 5) + >>> x + [0.86602, 0, -0.86602] + >>> w + [1.0472, 1.0472, 1.0472] + + >>> x, w = gauss_chebyshev_t(6, 5) + >>> x + [0.96593, 0.70711, 0.25882, -0.25882, -0.70711, -0.96593] + >>> w + [0.5236, 0.5236, 0.5236, 0.5236, 0.5236, 0.5236] + + See Also + ======== + + gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_u, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev1_rule/chebyshev1_rule.html + """ + xi = [] + w = [] + for i in range(1, n+1): + xi.append((cos((2*i-S.One)/(2*n)*S.Pi)).n(n_digits)) + w.append((S.Pi/n).n(n_digits)) + return xi, w + + +def gauss_chebyshev_u(n, n_digits): + r""" + Computes the Gauss-Chebyshev quadrature [1]_ points and weights of + the second kind. + + Explanation + =========== + + The Gauss-Chebyshev quadrature of the second kind approximates the + integral: + + .. math:: + \int_{-1}^{1} \sqrt{1-x^2} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of `U_n` + and the weights `w_i` are given by: + + .. math:: + w_i = \frac{\pi}{n+1} \sin^2 \left(\frac{i}{n+1}\pi\right) + + Parameters + ========== + + n : the order of quadrature + + n_digits : number of significant digits of the points and weights to return + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_chebyshev_u + >>> x, w = gauss_chebyshev_u(3, 5) + >>> x + [0.70711, 0, -0.70711] + >>> w + [0.3927, 0.7854, 0.3927] + + >>> x, w = gauss_chebyshev_u(6, 5) + >>> x + [0.90097, 0.62349, 0.22252, -0.22252, -0.62349, -0.90097] + >>> w + [0.084489, 0.27433, 0.42658, 0.42658, 0.27433, 0.084489] + + See Also + ======== + + gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_t, gauss_jacobi, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev2_rule/chebyshev2_rule.html + """ + xi = [] + w = [] + for i in range(1, n+1): + xi.append((cos(i/(n+S.One)*S.Pi)).n(n_digits)) + w.append((S.Pi/(n+S.One)*sin(i*S.Pi/(n+S.One))**2).n(n_digits)) + return xi, w + + +def gauss_jacobi(n, alpha, beta, n_digits): + r""" + Computes the Gauss-Jacobi quadrature [1]_ points and weights. + + Explanation + =========== + + The Gauss-Jacobi quadrature of the first kind approximates the integral: + + .. math:: + \int_{-1}^1 (1-x)^\alpha (1+x)^\beta f(x)\,dx \approx + \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of + `P^{(\alpha,\beta)}_n` and the weights `w_i` are given by: + + .. math:: + w_i = -\frac{2n+\alpha+\beta+2}{n+\alpha+\beta+1} + \frac{\Gamma(n+\alpha+1)\Gamma(n+\beta+1)} + {\Gamma(n+\alpha+\beta+1)(n+1)!} + \frac{2^{\alpha+\beta}}{P'_n(x_i) + P^{(\alpha,\beta)}_{n+1}(x_i)} + + Parameters + ========== + + n : the order of quadrature + + alpha : the first parameter of the Jacobi Polynomial, `\alpha > -1` + + beta : the second parameter of the Jacobi Polynomial, `\beta > -1` + + n_digits : number of significant digits of the points and weights to return + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy import S + >>> from sympy.integrals.quadrature import gauss_jacobi + >>> x, w = gauss_jacobi(3, S.Half, -S.Half, 5) + >>> x + [-0.90097, -0.22252, 0.62349] + >>> w + [1.7063, 1.0973, 0.33795] + + >>> x, w = gauss_jacobi(6, 1, 1, 5) + >>> x + [-0.87174, -0.5917, -0.2093, 0.2093, 0.5917, 0.87174] + >>> w + [0.050584, 0.22169, 0.39439, 0.39439, 0.22169, 0.050584] + + See Also + ======== + + gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, + gauss_chebyshev_t, gauss_chebyshev_u, gauss_lobatto + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gauss%E2%80%93Jacobi_quadrature + .. [2] https://people.sc.fsu.edu/~jburkardt/cpp_src/jacobi_rule/jacobi_rule.html + .. [3] https://people.sc.fsu.edu/~jburkardt/cpp_src/gegenbauer_rule/gegenbauer_rule.html + """ + x = Dummy("x") + p = jacobi_poly(n, alpha, beta, x, polys=True) + pd = p.diff(x) + pn = jacobi_poly(n+1, alpha, beta, x, polys=True) + xi = [] + w = [] + for r in p.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append(( + - (2*n+alpha+beta+2) / (n+alpha+beta+S.One) * + (gamma(n+alpha+1)*gamma(n+beta+1)) / + (gamma(n+alpha+beta+S.One)*gamma(n+2)) * + 2**(alpha+beta) / (pd.subs(x, r) * pn.subs(x, r))).n(n_digits)) + return xi, w + + +def gauss_lobatto(n, n_digits): + r""" + Computes the Gauss-Lobatto quadrature [1]_ points and weights. + + Explanation + =========== + + The Gauss-Lobatto quadrature approximates the integral: + + .. math:: + \int_{-1}^1 f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i) + + The nodes `x_i` of an order `n` quadrature rule are the roots of `P'_(n-1)` + and the weights `w_i` are given by: + + .. math:: + &w_i = \frac{2}{n(n-1) \left[P_{n-1}(x_i)\right]^2},\quad x\neq\pm 1\\ + &w_i = \frac{2}{n(n-1)},\quad x=\pm 1 + + Parameters + ========== + + n : the order of quadrature + + n_digits : number of significant digits of the points and weights to return + + Returns + ======= + + (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats. + The points `x_i` and weights `w_i` are returned as ``(x, w)`` + tuple of lists. + + Examples + ======== + + >>> from sympy.integrals.quadrature import gauss_lobatto + >>> x, w = gauss_lobatto(3, 5) + >>> x + [-1, 0, 1] + >>> w + [0.33333, 1.3333, 0.33333] + >>> x, w = gauss_lobatto(4, 5) + >>> x + [-1, -0.44721, 0.44721, 1] + >>> w + [0.16667, 0.83333, 0.83333, 0.16667] + + See Also + ======== + + gauss_legendre,gauss_laguerre, gauss_gen_laguerre, gauss_hermite, gauss_chebyshev_t, gauss_chebyshev_u, gauss_jacobi + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Lobatto_rules + .. [2] https://web.archive.org/web/20200118141346/http://people.math.sfu.ca/~cbm/aands/page_888.htm + """ + x = Dummy("x") + p = legendre_poly(n-1, x, polys=True) + pd = p.diff(x) + xi = [] + w = [] + for r in pd.real_roots(): + if isinstance(r, RootOf): + r = r.eval_rational(S.One/10**(n_digits+2)) + xi.append(r.n(n_digits)) + w.append((2/(n*(n-1) * p.subs(x, r)**2)).n(n_digits)) + + xi.insert(0, -1) + xi.append(1) + w.insert(0, (S(2)/(n*(n-1))).n(n_digits)) + w.append((S(2)/(n*(n-1))).n(n_digits)) + return xi, w diff --git a/lib/python3.11/site-packages/sympy/integrals/rationaltools.py b/lib/python3.11/site-packages/sympy/integrals/rationaltools.py new file mode 100644 index 0000000000000000000000000000000000000000..cc6423c1bb40d69067f1b9364b06dba63fef0fd8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/rationaltools.py @@ -0,0 +1,429 @@ +"""This module implements tools for integrating rational functions. """ + +from sympy.core.function import Lambda +from sympy.core.numbers import I +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol, symbols) +from sympy.functions.elementary.exponential import log +from sympy.functions.elementary.trigonometric import atan +from sympy.polys.polyroots import roots +from sympy.polys.polytools import cancel +from sympy.polys.rootoftools import RootSum +from sympy.polys import Poly, resultant, ZZ + + +def ratint(f, x, **flags): + """ + Performs indefinite integration of rational functions. + + Explanation + =========== + + Given a field :math:`K` and a rational function :math:`f = p/q`, + where :math:`p` and :math:`q` are polynomials in :math:`K[x]`, + returns a function :math:`g` such that :math:`f = g'`. + + Examples + ======== + + >>> from sympy.integrals.rationaltools import ratint + >>> from sympy.abc import x + + >>> ratint(36/(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2), x) + (12*x + 6)/(x**2 - 1) + 4*log(x - 2) - 4*log(x + 1) + + References + ========== + + .. [1] M. Bronstein, Symbolic Integration I: Transcendental + Functions, Second Edition, Springer-Verlag, 2005, pp. 35-70 + + See Also + ======== + + sympy.integrals.integrals.Integral.doit + sympy.integrals.rationaltools.ratint_logpart + sympy.integrals.rationaltools.ratint_ratpart + + """ + if isinstance(f, tuple): + p, q = f + else: + p, q = f.as_numer_denom() + + p, q = Poly(p, x, composite=False, field=True), Poly(q, x, composite=False, field=True) + + coeff, p, q = p.cancel(q) + poly, p = p.div(q) + + result = poly.integrate(x).as_expr() + + if p.is_zero: + return coeff*result + + g, h = ratint_ratpart(p, q, x) + + P, Q = h.as_numer_denom() + + P = Poly(P, x) + Q = Poly(Q, x) + + q, r = P.div(Q) + + result += g + q.integrate(x).as_expr() + + if not r.is_zero: + symbol = flags.get('symbol', 't') + + if not isinstance(symbol, Symbol): + t = Dummy(symbol) + else: + t = symbol.as_dummy() + + L = ratint_logpart(r, Q, x, t) + + real = flags.get('real') + + if real is None: + if isinstance(f, tuple): + p, q = f + atoms = p.atoms() | q.atoms() + else: + atoms = f.atoms() + + for elt in atoms - {x}: + if not elt.is_extended_real: + real = False + break + else: + real = True + + eps = S.Zero + + if not real: + for h, q in L: + _, h = h.primitive() + eps += RootSum( + q, Lambda(t, t*log(h.as_expr())), quadratic=True) + else: + for h, q in L: + _, h = h.primitive() + R = log_to_real(h, q, x, t) + + if R is not None: + eps += R + else: + eps += RootSum( + q, Lambda(t, t*log(h.as_expr())), quadratic=True) + + result += eps + + return coeff*result + + +def ratint_ratpart(f, g, x): + """ + Horowitz-Ostrogradsky algorithm. + + Explanation + =========== + + Given a field K and polynomials f and g in K[x], such that f and g + are coprime and deg(f) < deg(g), returns fractions A and B in K(x), + such that f/g = A' + B and B has square-free denominator. + + Examples + ======== + + >>> from sympy.integrals.rationaltools import ratint_ratpart + >>> from sympy.abc import x, y + >>> from sympy import Poly + >>> ratint_ratpart(Poly(1, x, domain='ZZ'), + ... Poly(x + 1, x, domain='ZZ'), x) + (0, 1/(x + 1)) + >>> ratint_ratpart(Poly(1, x, domain='EX'), + ... Poly(x**2 + y**2, x, domain='EX'), x) + (0, 1/(x**2 + y**2)) + >>> ratint_ratpart(Poly(36, x, domain='ZZ'), + ... Poly(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2, x, domain='ZZ'), x) + ((12*x + 6)/(x**2 - 1), 12/(x**2 - x - 2)) + + See Also + ======== + + ratint, ratint_logpart + """ + from sympy.solvers.solvers import solve + + f = Poly(f, x) + g = Poly(g, x) + + u, v, _ = g.cofactors(g.diff()) + + n = u.degree() + m = v.degree() + + A_coeffs = [ Dummy('a' + str(n - i)) for i in range(0, n) ] + B_coeffs = [ Dummy('b' + str(m - i)) for i in range(0, m) ] + + C_coeffs = A_coeffs + B_coeffs + + A = Poly(A_coeffs, x, domain=ZZ[C_coeffs]) + B = Poly(B_coeffs, x, domain=ZZ[C_coeffs]) + + H = f - A.diff()*v + A*(u.diff()*v).quo(u) - B*u + + result = solve(H.coeffs(), C_coeffs) + + A = A.as_expr().subs(result) + B = B.as_expr().subs(result) + + rat_part = cancel(A/u.as_expr(), x) + log_part = cancel(B/v.as_expr(), x) + + return rat_part, log_part + + +def ratint_logpart(f, g, x, t=None): + r""" + Lazard-Rioboo-Trager algorithm. + + Explanation + =========== + + Given a field K and polynomials f and g in K[x], such that f and g + are coprime, deg(f) < deg(g) and g is square-free, returns a list + of tuples (s_i, q_i) of polynomials, for i = 1..n, such that s_i + in K[t, x] and q_i in K[t], and:: + + ___ ___ + d f d \ ` \ ` + -- - = -- ) ) a log(s_i(a, x)) + dx g dx /__, /__, + i=1..n a | q_i(a) = 0 + + Examples + ======== + + >>> from sympy.integrals.rationaltools import ratint_logpart + >>> from sympy.abc import x + >>> from sympy import Poly + >>> ratint_logpart(Poly(1, x, domain='ZZ'), + ... Poly(x**2 + x + 1, x, domain='ZZ'), x) + [(Poly(x + 3*_t/2 + 1/2, x, domain='QQ[_t]'), + ...Poly(3*_t**2 + 1, _t, domain='ZZ'))] + >>> ratint_logpart(Poly(12, x, domain='ZZ'), + ... Poly(x**2 - x - 2, x, domain='ZZ'), x) + [(Poly(x - 3*_t/8 - 1/2, x, domain='QQ[_t]'), + ...Poly(-_t**2 + 16, _t, domain='ZZ'))] + + See Also + ======== + + ratint, ratint_ratpart + """ + f, g = Poly(f, x), Poly(g, x) + + t = t or Dummy('t') + a, b = g, f - g.diff()*Poly(t, x) + + res, R = resultant(a, b, includePRS=True) + res = Poly(res, t, composite=False) + + assert res, "BUG: resultant(%s, %s) cannot be zero" % (a, b) + + R_map, H = {}, [] + + for r in R: + R_map[r.degree()] = r + + def _include_sign(c, sqf): + if c.is_extended_real and (c < 0) == True: + h, k = sqf[0] + c_poly = c.as_poly(h.gens) + sqf[0] = h*c_poly, k + + C, res_sqf = res.sqf_list() + _include_sign(C, res_sqf) + + for q, i in res_sqf: + _, q = q.primitive() + + if g.degree() == i: + H.append((g, q)) + else: + h = R_map[i] + h_lc = Poly(h.LC(), t, field=True) + + c, h_lc_sqf = h_lc.sqf_list(all=True) + _include_sign(c, h_lc_sqf) + + for a, j in h_lc_sqf: + h = h.quo(Poly(a.gcd(q)**j, x)) + + inv, coeffs = h_lc.invert(q), [S.One] + + for coeff in h.coeffs()[1:]: + coeff = coeff.as_poly(inv.gens) + T = (inv*coeff).rem(q) + coeffs.append(T.as_expr()) + + h = Poly(dict(list(zip(h.monoms(), coeffs))), x) + + H.append((h, q)) + + return H + + +def log_to_atan(f, g): + """ + Convert complex logarithms to real arctangents. + + Explanation + =========== + + Given a real field K and polynomials f and g in K[x], with g != 0, + returns a sum h of arctangents of polynomials in K[x], such that: + + dh d f + I g + -- = -- I log( ------- ) + dx dx f - I g + + Examples + ======== + + >>> from sympy.integrals.rationaltools import log_to_atan + >>> from sympy.abc import x + >>> from sympy import Poly, sqrt, S + >>> log_to_atan(Poly(x, x, domain='ZZ'), Poly(1, x, domain='ZZ')) + 2*atan(x) + >>> log_to_atan(Poly(x + S(1)/2, x, domain='QQ'), + ... Poly(sqrt(3)/2, x, domain='EX')) + 2*atan(2*sqrt(3)*x/3 + sqrt(3)/3) + + See Also + ======== + + log_to_real + """ + if f.degree() < g.degree(): + f, g = -g, f + + f = f.to_field() + g = g.to_field() + + p, q = f.div(g) + + if q.is_zero: + return 2*atan(p.as_expr()) + else: + s, t, h = g.gcdex(-f) + u = (f*s + g*t).quo(h) + A = 2*atan(u.as_expr()) + + return A + log_to_atan(s, t) + + +def log_to_real(h, q, x, t): + r""" + Convert complex logarithms to real functions. + + Explanation + =========== + + Given real field K and polynomials h in K[t,x] and q in K[t], + returns real function f such that: + ___ + df d \ ` + -- = -- ) a log(h(a, x)) + dx dx /__, + a | q(a) = 0 + + Examples + ======== + + >>> from sympy.integrals.rationaltools import log_to_real + >>> from sympy.abc import x, y + >>> from sympy import Poly, S + >>> log_to_real(Poly(x + 3*y/2 + S(1)/2, x, domain='QQ[y]'), + ... Poly(3*y**2 + 1, y, domain='ZZ'), x, y) + 2*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3 + >>> log_to_real(Poly(x**2 - 1, x, domain='ZZ'), + ... Poly(-2*y + 1, y, domain='ZZ'), x, y) + log(x**2 - 1)/2 + + See Also + ======== + + log_to_atan + """ + from sympy.simplify.radsimp import collect + u, v = symbols('u,v', cls=Dummy) + + H = h.as_expr().xreplace({t: u + I*v}).expand() + Q = q.as_expr().xreplace({t: u + I*v}).expand() + + H_map = collect(H, I, evaluate=False) + Q_map = collect(Q, I, evaluate=False) + + a, b = H_map.get(S.One, S.Zero), H_map.get(I, S.Zero) + c, d = Q_map.get(S.One, S.Zero), Q_map.get(I, S.Zero) + + R = Poly(resultant(c, d, v), u) + + R_u = roots(R, filter='R') + + if len(R_u) != R.count_roots(): + return None + + result = S.Zero + + for r_u in R_u.keys(): + C = Poly(c.xreplace({u: r_u}), v) + if not C: + # t was split into real and imaginary parts + # and denom Q(u, v) = c + I*d. We just found + # that c(r_u) is 0 so the roots are in d + C = Poly(d.xreplace({u: r_u}), v) + # we were going to reject roots from C that + # did not set d to zero, but since we are now + # using C = d and c is already 0, there is + # nothing to check + d = S.Zero + + R_v = roots(C, filter='R') + + if len(R_v) != C.count_roots(): + return None + + R_v_paired = [] # take one from each pair of conjugate roots + for r_v in R_v: + if r_v not in R_v_paired and -r_v not in R_v_paired: + if r_v.is_negative or r_v.could_extract_minus_sign(): + R_v_paired.append(-r_v) + elif not r_v.is_zero: + R_v_paired.append(r_v) + + for r_v in R_v_paired: + + D = d.xreplace({u: r_u, v: r_v}) + + if D.evalf(chop=True) != 0: + continue + + A = Poly(a.xreplace({u: r_u, v: r_v}), x) + B = Poly(b.xreplace({u: r_u, v: r_v}), x) + + AB = (A**2 + B**2).as_expr() + + result += r_u*log(AB) + r_v*log_to_atan(A, B) + + R_q = roots(q, filter='R') + + if len(R_q) != q.count_roots(): + return None + + for r in R_q.keys(): + result += r*log(h.as_expr().subs(t, r)) + + return result diff --git a/lib/python3.11/site-packages/sympy/integrals/rde.py b/lib/python3.11/site-packages/sympy/integrals/rde.py new file mode 100644 index 0000000000000000000000000000000000000000..142d37595de6d275205d1717a6e0fde7cc9d16b8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/rde.py @@ -0,0 +1,800 @@ +""" +Algorithms for solving the Risch differential equation. + +Given a differential field K of characteristic 0 that is a simple +monomial extension of a base field k and f, g in K, the Risch +Differential Equation problem is to decide if there exist y in K such +that Dy + f*y == g and to find one if there are some. If t is a +monomial over k and the coefficients of f and g are in k(t), then y is +in k(t), and the outline of the algorithm here is given as: + +1. Compute the normal part n of the denominator of y. The problem is +then reduced to finding y' in k, where y == y'/n. +2. Compute the special part s of the denominator of y. The problem is +then reduced to finding y'' in k[t], where y == y''/(n*s) +3. Bound the degree of y''. +4. Reduce the equation Dy + f*y == g to a similar equation with f, g in +k[t]. +5. Find the solutions in k[t] of bounded degree of the reduced equation. + +See Chapter 6 of "Symbolic Integration I: Transcendental Functions" by +Manuel Bronstein. See also the docstring of risch.py. +""" + +from operator import mul +from functools import reduce + +from sympy.core import oo +from sympy.core.symbol import Dummy + +from sympy.polys import Poly, gcd, ZZ, cancel + +from sympy.functions.elementary.complexes import (im, re) +from sympy.functions.elementary.miscellaneous import sqrt + +from sympy.integrals.risch import (gcdex_diophantine, frac_in, derivation, + splitfactor, NonElementaryIntegralException, DecrementLevel, recognize_log_derivative) + +# TODO: Add messages to NonElementaryIntegralException errors + + +def order_at(a, p, t): + """ + Computes the order of a at p, with respect to t. + + Explanation + =========== + + For a, p in k[t], the order of a at p is defined as nu_p(a) = max({n + in Z+ such that p**n|a}), where a != 0. If a == 0, nu_p(a) = +oo. + + To compute the order at a rational function, a/b, use the fact that + nu_p(a/b) == nu_p(a) - nu_p(b). + """ + if a.is_zero: + return oo + if p == Poly(t, t): + return a.as_poly(t).ET()[0][0] + + # Uses binary search for calculating the power. power_list collects the tuples + # (p^k,k) where each k is some power of 2. After deciding the largest k + # such that k is power of 2 and p^k|a the loop iteratively calculates + # the actual power. + power_list = [] + p1 = p + r = a.rem(p1) + tracks_power = 1 + while r.is_zero: + power_list.append((p1,tracks_power)) + p1 = p1*p1 + tracks_power *= 2 + r = a.rem(p1) + n = 0 + product = Poly(1, t) + while len(power_list) != 0: + final = power_list.pop() + productf = product*final[0] + r = a.rem(productf) + if r.is_zero: + n += final[1] + product = productf + return n + + +def order_at_oo(a, d, t): + """ + Computes the order of a/d at oo (infinity), with respect to t. + + For f in k(t), the order or f at oo is defined as deg(d) - deg(a), where + f == a/d. + """ + if a.is_zero: + return oo + return d.degree(t) - a.degree(t) + + +def weak_normalizer(a, d, DE, z=None): + """ + Weak normalization. + + Explanation + =========== + + Given a derivation D on k[t] and f == a/d in k(t), return q in k[t] + such that f - Dq/q is weakly normalized with respect to t. + + f in k(t) is said to be "weakly normalized" with respect to t if + residue_p(f) is not a positive integer for any normal irreducible p + in k[t] such that f is in R_p (Definition 6.1.1). If f has an + elementary integral, this is equivalent to no logarithm of + integral(f) whose argument depends on t has a positive integer + coefficient, where the arguments of the logarithms not in k(t) are + in k[t]. + + Returns (q, f - Dq/q) + """ + z = z or Dummy('z') + dn, ds = splitfactor(d, DE) + + # Compute d1, where dn == d1*d2**2*...*dn**n is a square-free + # factorization of d. + g = gcd(dn, dn.diff(DE.t)) + d_sqf_part = dn.quo(g) + d1 = d_sqf_part.quo(gcd(d_sqf_part, g)) + + a1, b = gcdex_diophantine(d.quo(d1).as_poly(DE.t), d1.as_poly(DE.t), + a.as_poly(DE.t)) + r = (a - Poly(z, DE.t)*derivation(d1, DE)).as_poly(DE.t).resultant( + d1.as_poly(DE.t)) + r = Poly(r, z) + + if not r.expr.has(z): + return (Poly(1, DE.t), (a, d)) + + N = [i for i in r.real_roots() if i in ZZ and i > 0] + + q = reduce(mul, [gcd(a - Poly(n, DE.t)*derivation(d1, DE), d1) for n in N], + Poly(1, DE.t)) + + dq = derivation(q, DE) + sn = q*a - d*dq + sd = q*d + sn, sd = sn.cancel(sd, include=True) + + return (q, (sn, sd)) + + +def normal_denom(fa, fd, ga, gd, DE): + """ + Normal part of the denominator. + + Explanation + =========== + + Given a derivation D on k[t] and f, g in k(t) with f weakly + normalized with respect to t, either raise NonElementaryIntegralException, + in which case the equation Dy + f*y == g has no solution in k(t), or the + quadruplet (a, b, c, h) such that a, h in k[t], b, c in k, and for any + solution y in k(t) of Dy + f*y == g, q = y*h in k satisfies + a*Dq + b*q == c. + + This constitutes step 1 in the outline given in the rde.py docstring. + """ + dn, ds = splitfactor(fd, DE) + en, es = splitfactor(gd, DE) + + p = dn.gcd(en) + h = en.gcd(en.diff(DE.t)).quo(p.gcd(p.diff(DE.t))) + + a = dn*h + c = a*h + if c.div(en)[1]: + # en does not divide dn*h**2 + raise NonElementaryIntegralException + ca = c*ga + ca, cd = ca.cancel(gd, include=True) + + ba = a*fa - dn*derivation(h, DE)*fd + ba, bd = ba.cancel(fd, include=True) + + # (dn*h, dn*h*f - dn*Dh, dn*h**2*g, h) + return (a, (ba, bd), (ca, cd), h) + + +def special_denom(a, ba, bd, ca, cd, DE, case='auto'): + """ + Special part of the denominator. + + Explanation + =========== + + case is one of {'exp', 'tan', 'primitive'} for the hyperexponential, + hypertangent, and primitive cases, respectively. For the + hyperexponential (resp. hypertangent) case, given a derivation D on + k[t] and a in k[t], b, c, in k with Dt/t in k (resp. Dt/(t**2 + 1) in + k, sqrt(-1) not in k), a != 0, and gcd(a, t) == 1 (resp. + gcd(a, t**2 + 1) == 1), return the quadruplet (A, B, C, 1/h) such that + A, B, C, h in k[t] and for any solution q in k of a*Dq + b*q == c, + r = qh in k[t] satisfies A*Dr + B*r == C. + + For ``case == 'primitive'``, k == k[t], so it returns (a, b, c, 1) in + this case. + + This constitutes step 2 of the outline given in the rde.py docstring. + """ + # TODO: finish writing this and write tests + + if case == 'auto': + case = DE.case + + if case == 'exp': + p = Poly(DE.t, DE.t) + elif case == 'tan': + p = Poly(DE.t**2 + 1, DE.t) + elif case in ('primitive', 'base'): + B = ba.to_field().quo(bd) + C = ca.to_field().quo(cd) + return (a, B, C, Poly(1, DE.t)) + else: + raise ValueError("case must be one of {'exp', 'tan', 'primitive', " + "'base'}, not %s." % case) + + nb = order_at(ba, p, DE.t) - order_at(bd, p, DE.t) + nc = order_at(ca, p, DE.t) - order_at(cd, p, DE.t) + + n = min(0, nc - min(0, nb)) + if not nb: + # Possible cancellation. + from .prde import parametric_log_deriv + if case == 'exp': + dcoeff = DE.d.quo(Poly(DE.t, DE.t)) + with DecrementLevel(DE): # We are guaranteed to not have problems, + # because case != 'base'. + alphaa, alphad = frac_in(-ba.eval(0)/bd.eval(0)/a.eval(0), DE.t) + etaa, etad = frac_in(dcoeff, DE.t) + A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE) + if A is not None: + Q, m, z = A + if Q == 1: + n = min(n, m) + + elif case == 'tan': + dcoeff = DE.d.quo(Poly(DE.t**2+1, DE.t)) + with DecrementLevel(DE): # We are guaranteed to not have problems, + # because case != 'base'. + alphaa, alphad = frac_in(im(-ba.eval(sqrt(-1))/bd.eval(sqrt(-1))/a.eval(sqrt(-1))), DE.t) + betaa, betad = frac_in(re(-ba.eval(sqrt(-1))/bd.eval(sqrt(-1))/a.eval(sqrt(-1))), DE.t) + etaa, etad = frac_in(dcoeff, DE.t) + + if recognize_log_derivative(Poly(2, DE.t)*betaa, betad, DE): + A = parametric_log_deriv(alphaa*Poly(sqrt(-1), DE.t)*betad+alphad*betaa, alphad*betad, etaa, etad, DE) + if A is not None: + Q, m, z = A + if Q == 1: + n = min(n, m) + N = max(0, -nb, n - nc) + pN = p**N + pn = p**-n + + A = a*pN + B = ba*pN.quo(bd) + Poly(n, DE.t)*a*derivation(p, DE).quo(p)*pN + C = (ca*pN*pn).quo(cd) + h = pn + + # (a*p**N, (b + n*a*Dp/p)*p**N, c*p**(N - n), p**-n) + return (A, B, C, h) + + +def bound_degree(a, b, cQ, DE, case='auto', parametric=False): + """ + Bound on polynomial solutions. + + Explanation + =========== + + Given a derivation D on k[t] and ``a``, ``b``, ``c`` in k[t] with ``a != 0``, return + n in ZZ such that deg(q) <= n for any solution q in k[t] of + a*Dq + b*q == c, when parametric=False, or deg(q) <= n for any solution + c1, ..., cm in Const(k) and q in k[t] of a*Dq + b*q == Sum(ci*gi, (i, 1, m)) + when parametric=True. + + For ``parametric=False``, ``cQ`` is ``c``, a ``Poly``; for ``parametric=True``, ``cQ`` is Q == + [q1, ..., qm], a list of Polys. + + This constitutes step 3 of the outline given in the rde.py docstring. + """ + # TODO: finish writing this and write tests + + if case == 'auto': + case = DE.case + + da = a.degree(DE.t) + db = b.degree(DE.t) + + # The parametric and regular cases are identical, except for this part + if parametric: + dc = max(i.degree(DE.t) for i in cQ) + else: + dc = cQ.degree(DE.t) + + alpha = cancel(-b.as_poly(DE.t).LC().as_expr()/ + a.as_poly(DE.t).LC().as_expr()) + + if case == 'base': + n = max(0, dc - max(db, da - 1)) + if db == da - 1 and alpha.is_Integer: + n = max(0, alpha, dc - db) + + elif case == 'primitive': + if db > da: + n = max(0, dc - db) + else: + n = max(0, dc - da + 1) + + etaa, etad = frac_in(DE.d, DE.T[DE.level - 1]) + + t1 = DE.t + with DecrementLevel(DE): + alphaa, alphad = frac_in(alpha, DE.t) + if db == da - 1: + from .prde import limited_integrate + # if alpha == m*Dt + Dz for z in k and m in ZZ: + try: + (za, zd), m = limited_integrate(alphaa, alphad, [(etaa, etad)], + DE) + except NonElementaryIntegralException: + pass + else: + if len(m) != 1: + raise ValueError("Length of m should be 1") + n = max(n, m[0]) + + elif db == da: + # if alpha == Dz/z for z in k*: + # beta = -lc(a*Dz + b*z)/(z*lc(a)) + # if beta == m*Dt + Dw for w in k and m in ZZ: + # n = max(n, m) + from .prde import is_log_deriv_k_t_radical_in_field + A = is_log_deriv_k_t_radical_in_field(alphaa, alphad, DE) + if A is not None: + aa, z = A + if aa == 1: + beta = -(a*derivation(z, DE).as_poly(t1) + + b*z.as_poly(t1)).LC()/(z.as_expr()*a.LC()) + betaa, betad = frac_in(beta, DE.t) + from .prde import limited_integrate + try: + (za, zd), m = limited_integrate(betaa, betad, + [(etaa, etad)], DE) + except NonElementaryIntegralException: + pass + else: + if len(m) != 1: + raise ValueError("Length of m should be 1") + n = max(n, m[0].as_expr()) + + elif case == 'exp': + from .prde import parametric_log_deriv + + n = max(0, dc - max(db, da)) + if da == db: + etaa, etad = frac_in(DE.d.quo(Poly(DE.t, DE.t)), DE.T[DE.level - 1]) + with DecrementLevel(DE): + alphaa, alphad = frac_in(alpha, DE.t) + A = parametric_log_deriv(alphaa, alphad, etaa, etad, DE) + if A is not None: + # if alpha == m*Dt/t + Dz/z for z in k* and m in ZZ: + # n = max(n, m) + a, m, z = A + if a == 1: + n = max(n, m) + + elif case in ('tan', 'other_nonlinear'): + delta = DE.d.degree(DE.t) + lam = DE.d.LC() + alpha = cancel(alpha/lam) + n = max(0, dc - max(da + delta - 1, db)) + if db == da + delta - 1 and alpha.is_Integer: + n = max(0, alpha, dc - db) + + else: + raise ValueError("case must be one of {'exp', 'tan', 'primitive', " + "'other_nonlinear', 'base'}, not %s." % case) + + return n + + +def spde(a, b, c, n, DE): + """ + Rothstein's Special Polynomial Differential Equation algorithm. + + Explanation + =========== + + Given a derivation D on k[t], an integer n and ``a``,``b``,``c`` in k[t] with + ``a != 0``, either raise NonElementaryIntegralException, in which case the + equation a*Dq + b*q == c has no solution of degree at most ``n`` in + k[t], or return the tuple (B, C, m, alpha, beta) such that B, C, + alpha, beta in k[t], m in ZZ, and any solution q in k[t] of degree + at most n of a*Dq + b*q == c must be of the form + q == alpha*h + beta, where h in k[t], deg(h) <= m, and Dh + B*h == C. + + This constitutes step 4 of the outline given in the rde.py docstring. + """ + zero = Poly(0, DE.t) + + alpha = Poly(1, DE.t) + beta = Poly(0, DE.t) + + while True: + if c.is_zero: + return (zero, zero, 0, zero, beta) # -1 is more to the point + if (n < 0) is True: + raise NonElementaryIntegralException + + g = a.gcd(b) + if not c.rem(g).is_zero: # g does not divide c + raise NonElementaryIntegralException + + a, b, c = a.quo(g), b.quo(g), c.quo(g) + + if a.degree(DE.t) == 0: + b = b.to_field().quo(a) + c = c.to_field().quo(a) + return (b, c, n, alpha, beta) + + r, z = gcdex_diophantine(b, a, c) + b += derivation(a, DE) + c = z - derivation(r, DE) + n -= a.degree(DE.t) + + beta += alpha * r + alpha *= a + +def no_cancel_b_large(b, c, n, DE): + """ + Poly Risch Differential Equation - No cancellation: deg(b) large enough. + + Explanation + =========== + + Given a derivation D on k[t], ``n`` either an integer or +oo, and ``b``,``c`` + in k[t] with ``b != 0`` and either D == d/dt or + deg(b) > max(0, deg(D) - 1), either raise NonElementaryIntegralException, in + which case the equation ``Dq + b*q == c`` has no solution of degree at + most n in k[t], or a solution q in k[t] of this equation with + ``deg(q) < n``. + """ + q = Poly(0, DE.t) + + while not c.is_zero: + m = c.degree(DE.t) - b.degree(DE.t) + if not 0 <= m <= n: # n < 0 or m < 0 or m > n + raise NonElementaryIntegralException + + p = Poly(c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC()*DE.t**m, DE.t, + expand=False) + q = q + p + n = m - 1 + c = c - derivation(p, DE) - b*p + + return q + + +def no_cancel_b_small(b, c, n, DE): + """ + Poly Risch Differential Equation - No cancellation: deg(b) small enough. + + Explanation + =========== + + Given a derivation D on k[t], ``n`` either an integer or +oo, and ``b``,``c`` + in k[t] with deg(b) < deg(D) - 1 and either D == d/dt or + deg(D) >= 2, either raise NonElementaryIntegralException, in which case the + equation Dq + b*q == c has no solution of degree at most n in k[t], + or a solution q in k[t] of this equation with deg(q) <= n, or the + tuple (h, b0, c0) such that h in k[t], b0, c0, in k, and for any + solution q in k[t] of degree at most n of Dq + bq == c, y == q - h + is a solution in k of Dy + b0*y == c0. + """ + q = Poly(0, DE.t) + + while not c.is_zero: + if n == 0: + m = 0 + else: + m = c.degree(DE.t) - DE.d.degree(DE.t) + 1 + + if not 0 <= m <= n: # n < 0 or m < 0 or m > n + raise NonElementaryIntegralException + + if m > 0: + p = Poly(c.as_poly(DE.t).LC()/(m*DE.d.as_poly(DE.t).LC())*DE.t**m, + DE.t, expand=False) + else: + if b.degree(DE.t) != c.degree(DE.t): + raise NonElementaryIntegralException + if b.degree(DE.t) == 0: + return (q, b.as_poly(DE.T[DE.level - 1]), + c.as_poly(DE.T[DE.level - 1])) + p = Poly(c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC(), DE.t, + expand=False) + + q = q + p + n = m - 1 + c = c - derivation(p, DE) - b*p + + return q + + +# TODO: better name for this function +def no_cancel_equal(b, c, n, DE): + """ + Poly Risch Differential Equation - No cancellation: deg(b) == deg(D) - 1 + + Explanation + =========== + + Given a derivation D on k[t] with deg(D) >= 2, n either an integer + or +oo, and b, c in k[t] with deg(b) == deg(D) - 1, either raise + NonElementaryIntegralException, in which case the equation Dq + b*q == c has + no solution of degree at most n in k[t], or a solution q in k[t] of + this equation with deg(q) <= n, or the tuple (h, m, C) such that h + in k[t], m in ZZ, and C in k[t], and for any solution q in k[t] of + degree at most n of Dq + b*q == c, y == q - h is a solution in k[t] + of degree at most m of Dy + b*y == C. + """ + q = Poly(0, DE.t) + lc = cancel(-b.as_poly(DE.t).LC()/DE.d.as_poly(DE.t).LC()) + if lc.is_Integer and lc.is_positive: + M = lc + else: + M = -1 + + while not c.is_zero: + m = max(M, c.degree(DE.t) - DE.d.degree(DE.t) + 1) + + if not 0 <= m <= n: # n < 0 or m < 0 or m > n + raise NonElementaryIntegralException + + u = cancel(m*DE.d.as_poly(DE.t).LC() + b.as_poly(DE.t).LC()) + if u.is_zero: + return (q, m, c) + if m > 0: + p = Poly(c.as_poly(DE.t).LC()/u*DE.t**m, DE.t, expand=False) + else: + if c.degree(DE.t) != DE.d.degree(DE.t) - 1: + raise NonElementaryIntegralException + else: + p = c.as_poly(DE.t).LC()/b.as_poly(DE.t).LC() + + q = q + p + n = m - 1 + c = c - derivation(p, DE) - b*p + + return q + + +def cancel_primitive(b, c, n, DE): + """ + Poly Risch Differential Equation - Cancellation: Primitive case. + + Explanation + =========== + + Given a derivation D on k[t], n either an integer or +oo, ``b`` in k, and + ``c`` in k[t] with Dt in k and ``b != 0``, either raise + NonElementaryIntegralException, in which case the equation Dq + b*q == c + has no solution of degree at most n in k[t], or a solution q in k[t] of + this equation with deg(q) <= n. + """ + # Delayed imports + from .prde import is_log_deriv_k_t_radical_in_field + with DecrementLevel(DE): + ba, bd = frac_in(b, DE.t) + A = is_log_deriv_k_t_radical_in_field(ba, bd, DE) + if A is not None: + n, z = A + if n == 1: # b == Dz/z + raise NotImplementedError("is_deriv_in_field() is required to " + " solve this problem.") + # if z*c == Dp for p in k[t] and deg(p) <= n: + # return p/z + # else: + # raise NonElementaryIntegralException + + if c.is_zero: + return c # return 0 + + if n < c.degree(DE.t): + raise NonElementaryIntegralException + + q = Poly(0, DE.t) + while not c.is_zero: + m = c.degree(DE.t) + if n < m: + raise NonElementaryIntegralException + with DecrementLevel(DE): + a2a, a2d = frac_in(c.LC(), DE.t) + sa, sd = rischDE(ba, bd, a2a, a2d, DE) + stm = Poly(sa.as_expr()/sd.as_expr()*DE.t**m, DE.t, expand=False) + q += stm + n = m - 1 + c -= b*stm + derivation(stm, DE) + + return q + + +def cancel_exp(b, c, n, DE): + """ + Poly Risch Differential Equation - Cancellation: Hyperexponential case. + + Explanation + =========== + + Given a derivation D on k[t], n either an integer or +oo, ``b`` in k, and + ``c`` in k[t] with Dt/t in k and ``b != 0``, either raise + NonElementaryIntegralException, in which case the equation Dq + b*q == c + has no solution of degree at most n in k[t], or a solution q in k[t] of + this equation with deg(q) <= n. + """ + from .prde import parametric_log_deriv + eta = DE.d.quo(Poly(DE.t, DE.t)).as_expr() + + with DecrementLevel(DE): + etaa, etad = frac_in(eta, DE.t) + ba, bd = frac_in(b, DE.t) + A = parametric_log_deriv(ba, bd, etaa, etad, DE) + if A is not None: + a, m, z = A + if a == 1: + raise NotImplementedError("is_deriv_in_field() is required to " + "solve this problem.") + # if c*z*t**m == Dp for p in k and q = p/(z*t**m) in k[t] and + # deg(q) <= n: + # return q + # else: + # raise NonElementaryIntegralException + + if c.is_zero: + return c # return 0 + + if n < c.degree(DE.t): + raise NonElementaryIntegralException + + q = Poly(0, DE.t) + while not c.is_zero: + m = c.degree(DE.t) + if n < m: + raise NonElementaryIntegralException + # a1 = b + m*Dt/t + a1 = b.as_expr() + with DecrementLevel(DE): + # TODO: Write a dummy function that does this idiom + a1a, a1d = frac_in(a1, DE.t) + a1a = a1a*etad + etaa*a1d*Poly(m, DE.t) + a1d = a1d*etad + + a2a, a2d = frac_in(c.LC(), DE.t) + + sa, sd = rischDE(a1a, a1d, a2a, a2d, DE) + stm = Poly(sa.as_expr()/sd.as_expr()*DE.t**m, DE.t, expand=False) + q += stm + n = m - 1 + c -= b*stm + derivation(stm, DE) # deg(c) becomes smaller + return q + + +def solve_poly_rde(b, cQ, n, DE, parametric=False): + """ + Solve a Polynomial Risch Differential Equation with degree bound ``n``. + + This constitutes step 4 of the outline given in the rde.py docstring. + + For parametric=False, cQ is c, a Poly; for parametric=True, cQ is Q == + [q1, ..., qm], a list of Polys. + """ + # No cancellation + if not b.is_zero and (DE.case == 'base' or + b.degree(DE.t) > max(0, DE.d.degree(DE.t) - 1)): + + if parametric: + # Delayed imports + from .prde import prde_no_cancel_b_large + return prde_no_cancel_b_large(b, cQ, n, DE) + return no_cancel_b_large(b, cQ, n, DE) + + elif (b.is_zero or b.degree(DE.t) < DE.d.degree(DE.t) - 1) and \ + (DE.case == 'base' or DE.d.degree(DE.t) >= 2): + + if parametric: + from .prde import prde_no_cancel_b_small + return prde_no_cancel_b_small(b, cQ, n, DE) + + R = no_cancel_b_small(b, cQ, n, DE) + + if isinstance(R, Poly): + return R + else: + # XXX: Might k be a field? (pg. 209) + h, b0, c0 = R + with DecrementLevel(DE): + b0, c0 = b0.as_poly(DE.t), c0.as_poly(DE.t) + if b0 is None: # See above comment + raise ValueError("b0 should be a non-Null value") + if c0 is None: + raise ValueError("c0 should be a non-Null value") + y = solve_poly_rde(b0, c0, n, DE).as_poly(DE.t) + return h + y + + elif DE.d.degree(DE.t) >= 2 and b.degree(DE.t) == DE.d.degree(DE.t) - 1 and \ + n > -b.as_poly(DE.t).LC()/DE.d.as_poly(DE.t).LC(): + + # TODO: Is this check necessary, and if so, what should it do if it fails? + # b comes from the first element returned from spde() + if not b.as_poly(DE.t).LC().is_number: + raise TypeError("Result should be a number") + + if parametric: + raise NotImplementedError("prde_no_cancel_b_equal() is not yet " + "implemented.") + + R = no_cancel_equal(b, cQ, n, DE) + + if isinstance(R, Poly): + return R + else: + h, m, C = R + # XXX: Or should it be rischDE()? + y = solve_poly_rde(b, C, m, DE) + return h + y + + else: + # Cancellation + if b.is_zero: + raise NotImplementedError("Remaining cases for Poly (P)RDE are " + "not yet implemented (is_deriv_in_field() required).") + else: + if DE.case == 'exp': + if parametric: + raise NotImplementedError("Parametric RDE cancellation " + "hyperexponential case is not yet implemented.") + return cancel_exp(b, cQ, n, DE) + + elif DE.case == 'primitive': + if parametric: + raise NotImplementedError("Parametric RDE cancellation " + "primitive case is not yet implemented.") + return cancel_primitive(b, cQ, n, DE) + + else: + raise NotImplementedError("Other Poly (P)RDE cancellation " + "cases are not yet implemented (%s)." % DE.case) + + if parametric: + raise NotImplementedError("Remaining cases for Poly PRDE not yet " + "implemented.") + raise NotImplementedError("Remaining cases for Poly RDE not yet " + "implemented.") + + +def rischDE(fa, fd, ga, gd, DE): + """ + Solve a Risch Differential Equation: Dy + f*y == g. + + Explanation + =========== + + See the outline in the docstring of rde.py for more information + about the procedure used. Either raise NonElementaryIntegralException, in + which case there is no solution y in the given differential field, + or return y in k(t) satisfying Dy + f*y == g, or raise + NotImplementedError, in which case, the algorithms necessary to + solve the given Risch Differential Equation have not yet been + implemented. + """ + _, (fa, fd) = weak_normalizer(fa, fd, DE) + a, (ba, bd), (ca, cd), hn = normal_denom(fa, fd, ga, gd, DE) + A, B, C, hs = special_denom(a, ba, bd, ca, cd, DE) + try: + # Until this is fully implemented, use oo. Note that this will almost + # certainly cause non-termination in spde() (unless A == 1), and + # *might* lead to non-termination in the next step for a nonelementary + # integral (I don't know for certain yet). Fortunately, spde() is + # currently written recursively, so this will just give + # RuntimeError: maximum recursion depth exceeded. + n = bound_degree(A, B, C, DE) + except NotImplementedError: + # Useful for debugging: + # import warnings + # warnings.warn("rischDE: Proceeding with n = oo; may cause " + # "non-termination.") + n = oo + + B, C, m, alpha, beta = spde(A, B, C, n, DE) + if C.is_zero: + y = C + else: + y = solve_poly_rde(B, C, m, DE) + + return (alpha*y + beta, hn*hs) diff --git a/lib/python3.11/site-packages/sympy/integrals/risch.py b/lib/python3.11/site-packages/sympy/integrals/risch.py new file mode 100644 index 0000000000000000000000000000000000000000..cff9fc4863b29333af727d905fba0e6854013e99 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/risch.py @@ -0,0 +1,1851 @@ +""" +The Risch Algorithm for transcendental function integration. + +The core algorithms for the Risch algorithm are here. The subproblem +algorithms are in the rde.py and prde.py files for the Risch +Differential Equation solver and the parametric problems solvers, +respectively. All important information concerning the differential extension +for an integrand is stored in a DifferentialExtension object, which in the code +is usually called DE. Throughout the code and Inside the DifferentialExtension +object, the conventions/attribute names are that the base domain is QQ and each +differential extension is x, t0, t1, ..., tn-1 = DE.t. DE.x is the variable of +integration (Dx == 1), DE.D is a list of the derivatives of +x, t1, t2, ..., tn-1 = t, DE.T is the list [x, t1, t2, ..., tn-1], DE.t is the +outer-most variable of the differential extension at the given level (the level +can be adjusted using DE.increment_level() and DE.decrement_level()), +k is the field C(x, t0, ..., tn-2), where C is the constant field. The +numerator of a fraction is denoted by a and the denominator by +d. If the fraction is named f, fa == numer(f) and fd == denom(f). +Fractions are returned as tuples (fa, fd). DE.d and DE.t are used to +represent the topmost derivation and extension variable, respectively. +The docstring of a function signifies whether an argument is in k[t], in +which case it will just return a Poly in t, or in k(t), in which case it +will return the fraction (fa, fd). Other variable names probably come +from the names used in Bronstein's book. +""" +from types import GeneratorType +from functools import reduce + +from sympy.core.function import Lambda +from sympy.core.mul import Mul +from sympy.core.intfunc import ilcm +from sympy.core.numbers import I +from sympy.core.power import Pow +from sympy.core.relational import Ne +from sympy.core.singleton import S +from sympy.core.sorting import ordered, default_sort_key +from sympy.core.symbol import Dummy, Symbol +from sympy.functions.elementary.exponential import log, exp +from sympy.functions.elementary.hyperbolic import (cosh, coth, sinh, + tanh) +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.elementary.trigonometric import (atan, sin, cos, + tan, acot, cot, asin, acos) +from .integrals import integrate, Integral +from .heurisch import _symbols +from sympy.polys.polyerrors import PolynomialError +from sympy.polys.polytools import (real_roots, cancel, Poly, gcd, + reduced) +from sympy.polys.rootoftools import RootSum +from sympy.utilities.iterables import numbered_symbols + + +def integer_powers(exprs): + """ + Rewrites a list of expressions as integer multiples of each other. + + Explanation + =========== + + For example, if you have [x, x/2, x**2 + 1, 2*x/3], then you can rewrite + this as [(x/6) * 6, (x/6) * 3, (x**2 + 1) * 1, (x/6) * 4]. This is useful + in the Risch integration algorithm, where we must write exp(x) + exp(x/2) + as (exp(x/2))**2 + exp(x/2), but not as exp(x) + sqrt(exp(x)) (this is + because only the transcendental case is implemented and we therefore cannot + integrate algebraic extensions). The integer multiples returned by this + function for each term are the smallest possible (their content equals 1). + + Returns a list of tuples where the first element is the base term and the + second element is a list of `(item, factor)` terms, where `factor` is the + integer multiplicative factor that must multiply the base term to obtain + the original item. + + The easiest way to understand this is to look at an example: + + >>> from sympy.abc import x + >>> from sympy.integrals.risch import integer_powers + >>> integer_powers([x, x/2, x**2 + 1, 2*x/3]) + [(x/6, [(x, 6), (x/2, 3), (2*x/3, 4)]), (x**2 + 1, [(x**2 + 1, 1)])] + + We can see how this relates to the example at the beginning of the + docstring. It chose x/6 as the first base term. Then, x can be written as + (x/2) * 2, so we get (0, 2), and so on. Now only element (x**2 + 1) + remains, and there are no other terms that can be written as a rational + multiple of that, so we get that it can be written as (x**2 + 1) * 1. + + """ + # Here is the strategy: + + # First, go through each term and determine if it can be rewritten as a + # rational multiple of any of the terms gathered so far. + # cancel(a/b).is_Rational is sufficient for this. If it is a multiple, we + # add its multiple to the dictionary. + + terms = {} + for term in exprs: + for trm, trm_list in terms.items(): + a = cancel(term/trm) + if a.is_Rational: + trm_list.append((term, a)) + break + else: + terms[term] = [(term, S.One)] + + # After we have done this, we have all the like terms together, so we just + # need to find a common denominator so that we can get the base term and + # integer multiples such that each term can be written as an integer + # multiple of the base term, and the content of the integers is 1. + + newterms = {} + for term, term_list in terms.items(): + common_denom = reduce(ilcm, [i.as_numer_denom()[1] for _, i in + term_list]) + newterm = term/common_denom + newmults = [(i, j*common_denom) for i, j in term_list] + newterms[newterm] = newmults + + return sorted(iter(newterms.items()), key=lambda item: item[0].sort_key()) + + +class DifferentialExtension: + """ + A container for all the information relating to a differential extension. + + Explanation + =========== + + The attributes of this object are (see also the docstring of __init__): + + - f: The original (Expr) integrand. + - x: The variable of integration. + - T: List of variables in the extension. + - D: List of derivations in the extension; corresponds to the elements of T. + - fa: Poly of the numerator of the integrand. + - fd: Poly of the denominator of the integrand. + - Tfuncs: Lambda() representations of each element of T (except for x). + For back-substitution after integration. + - backsubs: A (possibly empty) list of further substitutions to be made on + the final integral to make it look more like the integrand. + - exts: + - extargs: + - cases: List of string representations of the cases of T. + - t: The top level extension variable, as defined by the current level + (see level below). + - d: The top level extension derivation, as defined by the current + derivation (see level below). + - case: The string representation of the case of self.d. + (Note that self.T and self.D will always contain the complete extension, + regardless of the level. Therefore, you should ALWAYS use DE.t and DE.d + instead of DE.T[-1] and DE.D[-1]. If you want to have a list of the + derivations or variables only up to the current level, use + DE.D[:len(DE.D) + DE.level + 1] and DE.T[:len(DE.T) + DE.level + 1]. Note + that, in particular, the derivation() function does this.) + + The following are also attributes, but will probably not be useful other + than in internal use: + - newf: Expr form of fa/fd. + - level: The number (between -1 and -len(self.T)) such that + self.T[self.level] == self.t and self.D[self.level] == self.d. + Use the methods self.increment_level() and self.decrement_level() to change + the current level. + """ + # __slots__ is defined mainly so we can iterate over all the attributes + # of the class easily (the memory use doesn't matter too much, since we + # only create one DifferentialExtension per integration). Also, it's nice + # to have a safeguard when debugging. + __slots__ = ('f', 'x', 'T', 'D', 'fa', 'fd', 'Tfuncs', 'backsubs', + 'exts', 'extargs', 'cases', 'case', 't', 'd', 'newf', 'level', + 'ts', 'dummy') + + def __init__(self, f=None, x=None, handle_first='log', dummy=False, extension=None, rewrite_complex=None): + """ + Tries to build a transcendental extension tower from ``f`` with respect to ``x``. + + Explanation + =========== + + If it is successful, creates a DifferentialExtension object with, among + others, the attributes fa, fd, D, T, Tfuncs, and backsubs such that + fa and fd are Polys in T[-1] with rational coefficients in T[:-1], + fa/fd == f, and D[i] is a Poly in T[i] with rational coefficients in + T[:i] representing the derivative of T[i] for each i from 1 to len(T). + Tfuncs is a list of Lambda objects for back replacing the functions + after integrating. Lambda() is only used (instead of lambda) to make + them easier to test and debug. Note that Tfuncs corresponds to the + elements of T, except for T[0] == x, but they should be back-substituted + in reverse order. backsubs is a (possibly empty) back-substitution list + that should be applied on the completed integral to make it look more + like the original integrand. + + If it is unsuccessful, it raises NotImplementedError. + + You can also create an object by manually setting the attributes as a + dictionary to the extension keyword argument. You must include at least + D. Warning, any attribute that is not given will be set to None. The + attributes T, t, d, cases, case, x, and level are set automatically and + do not need to be given. The functions in the Risch Algorithm will NOT + check to see if an attribute is None before using it. This also does not + check to see if the extension is valid (non-algebraic) or even if it is + self-consistent. Therefore, this should only be used for + testing/debugging purposes. + """ + # XXX: If you need to debug this function, set the break point here + + if extension: + if 'D' not in extension: + raise ValueError("At least the key D must be included with " + "the extension flag to DifferentialExtension.") + for attr in extension: + setattr(self, attr, extension[attr]) + + self._auto_attrs() + + return + elif f is None or x is None: + raise ValueError("Either both f and x or a manual extension must " + "be given.") + + if handle_first not in ('log', 'exp'): + raise ValueError("handle_first must be 'log' or 'exp', not %s." % + str(handle_first)) + + # f will be the original function, self.f might change if we reset + # (e.g., we pull out a constant from an exponential) + self.f = f + self.x = x + # setting the default value 'dummy' + self.dummy = dummy + self.reset() + exp_new_extension, log_new_extension = True, True + + # case of 'automatic' choosing + if rewrite_complex is None: + rewrite_complex = I in self.f.atoms() + + if rewrite_complex: + rewritables = { + (sin, cos, cot, tan, sinh, cosh, coth, tanh): exp, + (asin, acos, acot, atan): log, + } + # rewrite the trigonometric components + for candidates, rule in rewritables.items(): + self.newf = self.newf.rewrite(candidates, rule) + self.newf = cancel(self.newf) + else: + if any(i.has(x) for i in self.f.atoms(sin, cos, tan, atan, asin, acos)): + raise NotImplementedError("Trigonometric extensions are not " + "supported (yet!)") + + exps = set() + pows = set() + numpows = set() + sympows = set() + logs = set() + symlogs = set() + + while True: + if self.newf.is_rational_function(*self.T): + break + + if not exp_new_extension and not log_new_extension: + # We couldn't find a new extension on the last pass, so I guess + # we can't do it. + raise NotImplementedError("Couldn't find an elementary " + "transcendental extension for %s. Try using a " % str(f) + + "manual extension with the extension flag.") + + exps, pows, numpows, sympows, log_new_extension = \ + self._rewrite_exps_pows(exps, pows, numpows, sympows, log_new_extension) + + logs, symlogs = self._rewrite_logs(logs, symlogs) + + if handle_first == 'exp' or not log_new_extension: + exp_new_extension = self._exp_part(exps) + if exp_new_extension is None: + # reset and restart + self.f = self.newf + self.reset() + exp_new_extension = True + continue + + if handle_first == 'log' or not exp_new_extension: + log_new_extension = self._log_part(logs) + + self.fa, self.fd = frac_in(self.newf, self.t) + self._auto_attrs() + + return + + def __getattr__(self, attr): + # Avoid AttributeErrors when debugging + if attr not in self.__slots__: + raise AttributeError("%s has no attribute %s" % (repr(self), repr(attr))) + return None + + def _rewrite_exps_pows(self, exps, pows, numpows, + sympows, log_new_extension): + """ + Rewrite exps/pows for better processing. + """ + from .prde import is_deriv_k + + # Pre-preparsing. + ################# + # Get all exp arguments, so we can avoid ahead of time doing + # something like t1 = exp(x), t2 = exp(x/2) == sqrt(t1). + + # Things like sqrt(exp(x)) do not automatically simplify to + # exp(x/2), so they will be viewed as algebraic. The easiest way + # to handle this is to convert all instances of exp(a)**Rational + # to exp(Rational*a) before doing anything else. Note that the + # _exp_part code can generate terms of this form, so we do need to + # do this at each pass (or else modify it to not do that). + + ratpows = [i for i in self.newf.atoms(Pow) + if (isinstance(i.base, exp) and i.exp.is_Rational)] + + ratpows_repl = [ + (i, i.base.base**(i.exp*i.base.exp)) for i in ratpows] + self.backsubs += [(j, i) for i, j in ratpows_repl] + self.newf = self.newf.xreplace(dict(ratpows_repl)) + + # To make the process deterministic, the args are sorted + # so that functions with smaller op-counts are processed first. + # Ties are broken with the default_sort_key. + + # XXX Although the method is deterministic no additional work + # has been done to guarantee that the simplest solution is + # returned and that it would be affected be using different + # variables. Though it is possible that this is the case + # one should know that it has not been done intentionally, so + # further improvements may be possible. + + # TODO: This probably doesn't need to be completely recomputed at + # each pass. + exps = update_sets(exps, self.newf.atoms(exp), + lambda i: i.exp.is_rational_function(*self.T) and + i.exp.has(*self.T)) + pows = update_sets(pows, self.newf.atoms(Pow), + lambda i: i.exp.is_rational_function(*self.T) and + i.exp.has(*self.T)) + numpows = update_sets(numpows, set(pows), + lambda i: not i.base.has(*self.T)) + sympows = update_sets(sympows, set(pows) - set(numpows), + lambda i: i.base.is_rational_function(*self.T) and + not i.exp.is_Integer) + + # The easiest way to deal with non-base E powers is to convert them + # into base E, integrate, and then convert back. + for i in ordered(pows): + old = i + new = exp(i.exp*log(i.base)) + # If exp is ever changed to automatically reduce exp(x*log(2)) + # to 2**x, then this will break. The solution is to not change + # exp to do that :) + if i in sympows: + if i.exp.is_Rational: + raise NotImplementedError("Algebraic extensions are " + "not supported (%s)." % str(i)) + # We can add a**b only if log(a) in the extension, because + # a**b == exp(b*log(a)). + basea, based = frac_in(i.base, self.t) + A = is_deriv_k(basea, based, self) + if A is None: + # Nonelementary monomial (so far) + + # TODO: Would there ever be any benefit from just + # adding log(base) as a new monomial? + # ANSWER: Yes, otherwise we can't integrate x**x (or + # rather prove that it has no elementary integral) + # without first manually rewriting it as exp(x*log(x)) + self.newf = self.newf.xreplace({old: new}) + self.backsubs += [(new, old)] + log_new_extension = self._log_part([log(i.base)]) + exps = update_sets(exps, self.newf.atoms(exp), lambda i: + i.exp.is_rational_function(*self.T) and i.exp.has(*self.T)) + continue + ans, u, const = A + newterm = exp(i.exp*(log(const) + u)) + # Under the current implementation, exp kills terms + # only if they are of the form a*log(x), where a is a + # Number. This case should have already been killed by the + # above tests. Again, if this changes to kill more than + # that, this will break, which maybe is a sign that you + # shouldn't be changing that. Actually, if anything, this + # auto-simplification should be removed. See + # https://groups.google.com/group/sympy/browse_thread/thread/a61d48235f16867f + + self.newf = self.newf.xreplace({i: newterm}) + + elif i not in numpows: + continue + else: + # i in numpows + newterm = new + # TODO: Just put it in self.Tfuncs + self.backsubs.append((new, old)) + self.newf = self.newf.xreplace({old: newterm}) + exps.append(newterm) + + return exps, pows, numpows, sympows, log_new_extension + + def _rewrite_logs(self, logs, symlogs): + """ + Rewrite logs for better processing. + """ + atoms = self.newf.atoms(log) + logs = update_sets(logs, atoms, + lambda i: i.args[0].is_rational_function(*self.T) and + i.args[0].has(*self.T)) + symlogs = update_sets(symlogs, atoms, + lambda i: i.has(*self.T) and i.args[0].is_Pow and + i.args[0].base.is_rational_function(*self.T) and + not i.args[0].exp.is_Integer) + + # We can handle things like log(x**y) by converting it to y*log(x) + # This will fix not only symbolic exponents of the argument, but any + # non-Integer exponent, like log(sqrt(x)). The exponent can also + # depend on x, like log(x**x). + for i in ordered(symlogs): + # Unlike in the exponential case above, we do not ever + # potentially add new monomials (above we had to add log(a)). + # Therefore, there is no need to run any is_deriv functions + # here. Just convert log(a**b) to b*log(a) and let + # log_new_extension() handle it from there. + lbase = log(i.args[0].base) + logs.append(lbase) + new = i.args[0].exp*lbase + self.newf = self.newf.xreplace({i: new}) + self.backsubs.append((new, i)) + + # remove any duplicates + logs = sorted(set(logs), key=default_sort_key) + + return logs, symlogs + + def _auto_attrs(self): + """ + Set attributes that are generated automatically. + """ + if not self.T: + # i.e., when using the extension flag and T isn't given + self.T = [i.gen for i in self.D] + if not self.x: + self.x = self.T[0] + self.cases = [get_case(d, t) for d, t in zip(self.D, self.T)] + self.level = -1 + self.t = self.T[self.level] + self.d = self.D[self.level] + self.case = self.cases[self.level] + + def _exp_part(self, exps): + """ + Try to build an exponential extension. + + Returns + ======= + + Returns True if there was a new extension, False if there was no new + extension but it was able to rewrite the given exponentials in terms + of the existing extension, and None if the entire extension building + process should be restarted. If the process fails because there is no + way around an algebraic extension (e.g., exp(log(x)/2)), it will raise + NotImplementedError. + """ + from .prde import is_log_deriv_k_t_radical + new_extension = False + restart = False + expargs = [i.exp for i in exps] + ip = integer_powers(expargs) + for arg, others in ip: + # Minimize potential problems with algebraic substitution + others.sort(key=lambda i: i[1]) + + arga, argd = frac_in(arg, self.t) + A = is_log_deriv_k_t_radical(arga, argd, self) + + if A is not None: + ans, u, n, const = A + # if n is 1 or -1, it's algebraic, but we can handle it + if n == -1: + # This probably will never happen, because + # Rational.as_numer_denom() returns the negative term in + # the numerator. But in case that changes, reduce it to + # n == 1. + n = 1 + u **= -1 + const *= -1 + ans = [(i, -j) for i, j in ans] + + if n == 1: + # Example: exp(x + x**2) over QQ(x, exp(x), exp(x**2)) + self.newf = self.newf.xreplace({exp(arg): exp(const)*Mul(*[ + u**power for u, power in ans])}) + self.newf = self.newf.xreplace({exp(p*exparg): + exp(const*p) * Mul(*[u**power for u, power in ans]) + for exparg, p in others}) + # TODO: Add something to backsubs to put exp(const*p) + # back together. + + continue + + else: + # Bad news: we have an algebraic radical. But maybe we + # could still avoid it by choosing a different extension. + # For example, integer_powers() won't handle exp(x/2 + 1) + # over QQ(x, exp(x)), but if we pull out the exp(1), it + # will. Or maybe we have exp(x + x**2/2), over + # QQ(x, exp(x), exp(x**2)), which is exp(x)*sqrt(exp(x**2)), + # but if we use QQ(x, exp(x), exp(x**2/2)), then they will + # all work. + # + # So here is what we do: If there is a non-zero const, pull + # it out and retry. Also, if len(ans) > 1, then rewrite + # exp(arg) as the product of exponentials from ans, and + # retry that. If const == 0 and len(ans) == 1, then we + # assume that it would have been handled by either + # integer_powers() or n == 1 above if it could be handled, + # so we give up at that point. For example, you can never + # handle exp(log(x)/2) because it equals sqrt(x). + + if const or len(ans) > 1: + rad = Mul(*[term**(power/n) for term, power in ans]) + self.newf = self.newf.xreplace({exp(p*exparg): + exp(const*p)*rad for exparg, p in others}) + self.newf = self.newf.xreplace(dict(list(zip(reversed(self.T), + reversed([f(self.x) for f in self.Tfuncs]))))) + restart = True + break + else: + # TODO: give algebraic dependence in error string + raise NotImplementedError("Cannot integrate over " + "algebraic extensions.") + + else: + arga, argd = frac_in(arg, self.t) + darga = (argd*derivation(Poly(arga, self.t), self) - + arga*derivation(Poly(argd, self.t), self)) + dargd = argd**2 + darga, dargd = darga.cancel(dargd, include=True) + darg = darga.as_expr()/dargd.as_expr() + self.t = next(self.ts) + self.T.append(self.t) + self.extargs.append(arg) + self.exts.append('exp') + self.D.append(darg.as_poly(self.t, expand=False)*Poly(self.t, + self.t, expand=False)) + if self.dummy: + i = Dummy("i") + else: + i = Symbol('i') + self.Tfuncs += [Lambda(i, exp(arg.subs(self.x, i)))] + self.newf = self.newf.xreplace( + {exp(exparg): self.t**p for exparg, p in others}) + new_extension = True + + if restart: + return None + return new_extension + + def _log_part(self, logs): + """ + Try to build a logarithmic extension. + + Returns + ======= + + Returns True if there was a new extension and False if there was no new + extension but it was able to rewrite the given logarithms in terms + of the existing extension. Unlike with exponential extensions, there + is no way that a logarithm is not transcendental over and cannot be + rewritten in terms of an already existing extension in a non-algebraic + way, so this function does not ever return None or raise + NotImplementedError. + """ + from .prde import is_deriv_k + new_extension = False + logargs = [i.args[0] for i in logs] + for arg in ordered(logargs): + # The log case is easier, because whenever a logarithm is algebraic + # over the base field, it is of the form a1*t1 + ... an*tn + c, + # which is a polynomial, so we can just replace it with that. + # In other words, we don't have to worry about radicals. + arga, argd = frac_in(arg, self.t) + A = is_deriv_k(arga, argd, self) + if A is not None: + ans, u, const = A + newterm = log(const) + u + self.newf = self.newf.xreplace({log(arg): newterm}) + continue + + else: + arga, argd = frac_in(arg, self.t) + darga = (argd*derivation(Poly(arga, self.t), self) - + arga*derivation(Poly(argd, self.t), self)) + dargd = argd**2 + darg = darga.as_expr()/dargd.as_expr() + self.t = next(self.ts) + self.T.append(self.t) + self.extargs.append(arg) + self.exts.append('log') + self.D.append(cancel(darg.as_expr()/arg).as_poly(self.t, + expand=False)) + if self.dummy: + i = Dummy("i") + else: + i = Symbol('i') + self.Tfuncs += [Lambda(i, log(arg.subs(self.x, i)))] + self.newf = self.newf.xreplace({log(arg): self.t}) + new_extension = True + + return new_extension + + @property + def _important_attrs(self): + """ + Returns some of the more important attributes of self. + + Explanation + =========== + + Used for testing and debugging purposes. + + The attributes are (fa, fd, D, T, Tfuncs, backsubs, + exts, extargs). + """ + return (self.fa, self.fd, self.D, self.T, self.Tfuncs, + self.backsubs, self.exts, self.extargs) + + # NOTE: this printing doesn't follow the Python's standard + # eval(repr(DE)) == DE, where DE is the DifferentialExtension object, + # also this printing is supposed to contain all the important + # attributes of a DifferentialExtension object + def __repr__(self): + # no need to have GeneratorType object printed in it + r = [(attr, getattr(self, attr)) for attr in self.__slots__ + if not isinstance(getattr(self, attr), GeneratorType)] + return self.__class__.__name__ + '(dict(%r))' % (r) + + # fancy printing of DifferentialExtension object + def __str__(self): + return (self.__class__.__name__ + '({fa=%s, fd=%s, D=%s})' % + (self.fa, self.fd, self.D)) + + # should only be used for debugging purposes, internally + # f1 = f2 = log(x) at different places in code execution + # may return D1 != D2 as True, since 'level' or other attribute + # may differ + def __eq__(self, other): + for attr in self.__class__.__slots__: + d1, d2 = getattr(self, attr), getattr(other, attr) + if not (isinstance(d1, GeneratorType) or d1 == d2): + return False + return True + + def reset(self): + """ + Reset self to an initial state. Used by __init__. + """ + self.t = self.x + self.T = [self.x] + self.D = [Poly(1, self.x)] + self.level = -1 + self.exts = [None] + self.extargs = [None] + if self.dummy: + self.ts = numbered_symbols('t', cls=Dummy) + else: + # For testing + self.ts = numbered_symbols('t') + # For various things that we change to make things work that we need to + # change back when we are done. + self.backsubs = [] + self.Tfuncs = [] + self.newf = self.f + + def indices(self, extension): + """ + Parameters + ========== + + extension : str + Represents a valid extension type. + + Returns + ======= + + list: A list of indices of 'exts' where extension of + type 'extension' is present. + + Examples + ======== + + >>> from sympy.integrals.risch import DifferentialExtension + >>> from sympy import log, exp + >>> from sympy.abc import x + >>> DE = DifferentialExtension(log(x) + exp(x), x, handle_first='exp') + >>> DE.indices('log') + [2] + >>> DE.indices('exp') + [1] + + """ + return [i for i, ext in enumerate(self.exts) if ext == extension] + + def increment_level(self): + """ + Increment the level of self. + + Explanation + =========== + + This makes the working differential extension larger. self.level is + given relative to the end of the list (-1, -2, etc.), so we do not need + do worry about it when building the extension. + """ + if self.level >= -1: + raise ValueError("The level of the differential extension cannot " + "be incremented any further.") + + self.level += 1 + self.t = self.T[self.level] + self.d = self.D[self.level] + self.case = self.cases[self.level] + return None + + def decrement_level(self): + """ + Decrease the level of self. + + Explanation + =========== + + This makes the working differential extension smaller. self.level is + given relative to the end of the list (-1, -2, etc.), so we do not need + do worry about it when building the extension. + """ + if self.level <= -len(self.T): + raise ValueError("The level of the differential extension cannot " + "be decremented any further.") + + self.level -= 1 + self.t = self.T[self.level] + self.d = self.D[self.level] + self.case = self.cases[self.level] + return None + + +def update_sets(seq, atoms, func): + s = set(seq) + s = atoms.intersection(s) + new = atoms - s + s.update(list(filter(func, new))) + return list(s) + + +class DecrementLevel: + """ + A context manager for decrementing the level of a DifferentialExtension. + """ + __slots__ = ('DE',) + + def __init__(self, DE): + self.DE = DE + return + + def __enter__(self): + self.DE.decrement_level() + + def __exit__(self, exc_type, exc_value, traceback): + self.DE.increment_level() + + +class NonElementaryIntegralException(Exception): + """ + Exception used by subroutines within the Risch algorithm to indicate to one + another that the function being integrated does not have an elementary + integral in the given differential field. + """ + # TODO: Rewrite algorithms below to use this (?) + + # TODO: Pass through information about why the integral was nonelementary, + # and store that in the resulting NonElementaryIntegral somehow. + pass + + +def gcdex_diophantine(a, b, c): + """ + Extended Euclidean Algorithm, Diophantine version. + + Explanation + =========== + + Given ``a``, ``b`` in K[x] and ``c`` in (a, b), the ideal generated by ``a`` and + ``b``, return (s, t) such that s*a + t*b == c and either s == 0 or s.degree() + < b.degree(). + """ + # Extended Euclidean Algorithm (Diophantine Version) pg. 13 + # TODO: This should go in densetools.py. + # XXX: Bettter name? + + s, g = a.half_gcdex(b) + s *= c.exquo(g) # Inexact division means c is not in (a, b) + if s and s.degree() >= b.degree(): + _, s = s.div(b) + t = (c - s*a).exquo(b) + return (s, t) + + +def frac_in(f, t, *, cancel=False, **kwargs): + """ + Returns the tuple (fa, fd), where fa and fd are Polys in t. + + Explanation + =========== + + This is a common idiom in the Risch Algorithm functions, so we abstract + it out here. ``f`` should be a basic expression, a Poly, or a tuple (fa, fd), + where fa and fd are either basic expressions or Polys, and f == fa/fd. + **kwargs are applied to Poly. + """ + if isinstance(f, tuple): + fa, fd = f + f = fa.as_expr()/fd.as_expr() + fa, fd = f.as_expr().as_numer_denom() + fa, fd = fa.as_poly(t, **kwargs), fd.as_poly(t, **kwargs) + if cancel: + fa, fd = fa.cancel(fd, include=True) + if fa is None or fd is None: + raise ValueError("Could not turn %s into a fraction in %s." % (f, t)) + return (fa, fd) + + +def as_poly_1t(p, t, z): + """ + (Hackish) way to convert an element ``p`` of K[t, 1/t] to K[t, z]. + + In other words, ``z == 1/t`` will be a dummy variable that Poly can handle + better. + + See issue 5131. + + Examples + ======== + + >>> from sympy import random_poly + >>> from sympy.integrals.risch import as_poly_1t + >>> from sympy.abc import x, z + + >>> p1 = random_poly(x, 10, -10, 10) + >>> p2 = random_poly(x, 10, -10, 10) + >>> p = p1 + p2.subs(x, 1/x) + >>> as_poly_1t(p, x, z).as_expr().subs(z, 1/x) == p + True + """ + # TODO: Use this on the final result. That way, we can avoid answers like + # (...)*exp(-x). + pa, pd = frac_in(p, t, cancel=True) + if not pd.is_monomial: + # XXX: Is there a better Poly exception that we could raise here? + # Either way, if you see this (from the Risch Algorithm) it indicates + # a bug. + raise PolynomialError("%s is not an element of K[%s, 1/%s]." % (p, t, t)) + + t_part, remainder = pa.div(pd) + + ans = t_part.as_poly(t, z, expand=False) + + if remainder: + one = remainder.one + tp = t*one + r = pd.degree() - remainder.degree() + z_part = remainder.transform(one, tp) * tp**r + z_part = z_part.replace(t, z).to_field().quo_ground(pd.LC()) + ans += z_part.as_poly(t, z, expand=False) + + return ans + + +def derivation(p, DE, coefficientD=False, basic=False): + """ + Computes Dp. + + Explanation + =========== + + Given the derivation D with D = d/dx and p is a polynomial in t over + K(x), return Dp. + + If coefficientD is True, it computes the derivation kD + (kappaD), which is defined as kD(sum(ai*Xi**i, (i, 0, n))) == + sum(Dai*Xi**i, (i, 1, n)) (Definition 3.2.2, page 80). X in this case is + T[-1], so coefficientD computes the derivative just with respect to T[:-1], + with T[-1] treated as a constant. + + If ``basic=True``, the returns a Basic expression. Elements of D can still be + instances of Poly. + """ + if basic: + r = 0 + else: + r = Poly(0, DE.t) + + t = DE.t + if coefficientD: + if DE.level <= -len(DE.T): + # 'base' case, the answer is 0. + return r + DE.decrement_level() + + D = DE.D[:len(DE.D) + DE.level + 1] + T = DE.T[:len(DE.T) + DE.level + 1] + + for d, v in zip(D, T): + pv = p.as_poly(v) + if pv is None or basic: + pv = p.as_expr() + + if basic: + r += d.as_expr()*pv.diff(v) + else: + r += (d.as_expr()*pv.diff(v).as_expr()).as_poly(t) + + if basic: + r = cancel(r) + if coefficientD: + DE.increment_level() + + return r + + +def get_case(d, t): + """ + Returns the type of the derivation d. + + Returns one of {'exp', 'tan', 'base', 'primitive', 'other_linear', + 'other_nonlinear'}. + """ + if not d.expr.has(t): + if d.is_one: + return 'base' + return 'primitive' + if d.rem(Poly(t, t)).is_zero: + return 'exp' + if d.rem(Poly(1 + t**2, t)).is_zero: + return 'tan' + if d.degree(t) > 1: + return 'other_nonlinear' + return 'other_linear' + + +def splitfactor(p, DE, coefficientD=False, z=None): + """ + Splitting factorization. + + Explanation + =========== + + Given a derivation D on k[t] and ``p`` in k[t], return (p_n, p_s) in + k[t] x k[t] such that p = p_n*p_s, p_s is special, and each square + factor of p_n is normal. + + Page. 100 + """ + kinv = [1/x for x in DE.T[:DE.level]] + if z: + kinv.append(z) + + One = Poly(1, DE.t, domain=p.get_domain()) + Dp = derivation(p, DE, coefficientD=coefficientD) + # XXX: Is this right? + if p.is_zero: + return (p, One) + + if not p.expr.has(DE.t): + s = p.as_poly(*kinv).gcd(Dp.as_poly(*kinv)).as_poly(DE.t) + n = p.exquo(s) + return (n, s) + + if not Dp.is_zero: + h = p.gcd(Dp).to_field() + g = p.gcd(p.diff(DE.t)).to_field() + s = h.exquo(g) + + if s.degree(DE.t) == 0: + return (p, One) + + q_split = splitfactor(p.exquo(s), DE, coefficientD=coefficientD) + + return (q_split[0], q_split[1]*s) + else: + return (p, One) + + +def splitfactor_sqf(p, DE, coefficientD=False, z=None, basic=False): + """ + Splitting Square-free Factorization. + + Explanation + =========== + + Given a derivation D on k[t] and ``p`` in k[t], returns (N1, ..., Nm) + and (S1, ..., Sm) in k[t]^m such that p = + (N1*N2**2*...*Nm**m)*(S1*S2**2*...*Sm**m) is a splitting + factorization of ``p`` and the Ni and Si are square-free and coprime. + """ + # TODO: This algorithm appears to be faster in every case + # TODO: Verify this and splitfactor() for multiple extensions + kkinv = [1/x for x in DE.T[:DE.level]] + DE.T[:DE.level] + if z: + kkinv = [z] + + S = [] + N = [] + p_sqf = p.sqf_list_include() + if p.is_zero: + return (((p, 1),), ()) + + for pi, i in p_sqf: + Si = pi.as_poly(*kkinv).gcd(derivation(pi, DE, + coefficientD=coefficientD,basic=basic).as_poly(*kkinv)).as_poly(DE.t) + pi = Poly(pi, DE.t) + Si = Poly(Si, DE.t) + Ni = pi.exquo(Si) + if not Si.is_one: + S.append((Si, i)) + if not Ni.is_one: + N.append((Ni, i)) + + return (tuple(N), tuple(S)) + + +def canonical_representation(a, d, DE): + """ + Canonical Representation. + + Explanation + =========== + + Given a derivation D on k[t] and f = a/d in k(t), return (f_p, f_s, + f_n) in k[t] x k(t) x k(t) such that f = f_p + f_s + f_n is the + canonical representation of f (f_p is a polynomial, f_s is reduced + (has a special denominator), and f_n is simple (has a normal + denominator). + """ + # Make d monic + l = Poly(1/d.LC(), DE.t) + a, d = a.mul(l), d.mul(l) + + q, r = a.div(d) + dn, ds = splitfactor(d, DE) + + b, c = gcdex_diophantine(dn.as_poly(DE.t), ds.as_poly(DE.t), r.as_poly(DE.t)) + b, c = b.as_poly(DE.t), c.as_poly(DE.t) + + return (q, (b, ds), (c, dn)) + + +def hermite_reduce(a, d, DE): + """ + Hermite Reduction - Mack's Linear Version. + + Given a derivation D on k(t) and f = a/d in k(t), returns g, h, r in + k(t) such that f = Dg + h + r, h is simple, and r is reduced. + + """ + # Make d monic + l = Poly(1/d.LC(), DE.t) + a, d = a.mul(l), d.mul(l) + + fp, fs, fn = canonical_representation(a, d, DE) + a, d = fn + l = Poly(1/d.LC(), DE.t) + a, d = a.mul(l), d.mul(l) + + ga = Poly(0, DE.t) + gd = Poly(1, DE.t) + + dd = derivation(d, DE) + dm = gcd(d.to_field(), dd.to_field()).as_poly(DE.t) + ds, _ = d.div(dm) + + while dm.degree(DE.t) > 0: + + ddm = derivation(dm, DE) + dm2 = gcd(dm.to_field(), ddm.to_field()) + dms, _ = dm.div(dm2) + ds_ddm = ds.mul(ddm) + ds_ddm_dm, _ = ds_ddm.div(dm) + + b, c = gcdex_diophantine(-ds_ddm_dm.as_poly(DE.t), + dms.as_poly(DE.t), a.as_poly(DE.t)) + b, c = b.as_poly(DE.t), c.as_poly(DE.t) + + db = derivation(b, DE).as_poly(DE.t) + ds_dms, _ = ds.div(dms) + a = c.as_poly(DE.t) - db.mul(ds_dms).as_poly(DE.t) + + ga = ga*dm + b*gd + gd = gd*dm + ga, gd = ga.cancel(gd, include=True) + dm = dm2 + + q, r = a.div(ds) + ga, gd = ga.cancel(gd, include=True) + + r, d = r.cancel(ds, include=True) + rra = q*fs[1] + fp*fs[1] + fs[0] + rrd = fs[1] + rra, rrd = rra.cancel(rrd, include=True) + + return ((ga, gd), (r, d), (rra, rrd)) + + +def polynomial_reduce(p, DE): + """ + Polynomial Reduction. + + Explanation + =========== + + Given a derivation D on k(t) and p in k[t] where t is a nonlinear + monomial over k, return q, r in k[t] such that p = Dq + r, and + deg(r) < deg_t(Dt). + """ + q = Poly(0, DE.t) + while p.degree(DE.t) >= DE.d.degree(DE.t): + m = p.degree(DE.t) - DE.d.degree(DE.t) + 1 + q0 = Poly(DE.t**m, DE.t).mul(Poly(p.as_poly(DE.t).LC()/ + (m*DE.d.LC()), DE.t)) + q += q0 + p = p - derivation(q0, DE) + + return (q, p) + + +def laurent_series(a, d, F, n, DE): + """ + Contribution of ``F`` to the full partial fraction decomposition of A/D. + + Explanation + =========== + + Given a field K of characteristic 0 and ``A``,``D``,``F`` in K[x] with D monic, + nonzero, coprime with A, and ``F`` the factor of multiplicity n in the square- + free factorization of D, return the principal parts of the Laurent series of + A/D at all the zeros of ``F``. + """ + if F.degree()==0: + return 0 + Z = _symbols('z', n) + z = Symbol('z') + Z.insert(0, z) + delta_a = Poly(0, DE.t) + delta_d = Poly(1, DE.t) + + E = d.quo(F**n) + ha, hd = (a, E*Poly(z**n, DE.t)) + dF = derivation(F,DE) + B, _ = gcdex_diophantine(E, F, Poly(1,DE.t)) + C, _ = gcdex_diophantine(dF, F, Poly(1,DE.t)) + + # initialization + F_store = F + V, DE_D_list, H_list= [], [], [] + + for j in range(0, n): + # jth derivative of z would be substituted with dfnth/(j+1) where dfnth =(d^n)f/(dx)^n + F_store = derivation(F_store, DE) + v = (F_store.as_expr())/(j + 1) + V.append(v) + DE_D_list.append(Poly(Z[j + 1],Z[j])) + + DE_new = DifferentialExtension(extension = {'D': DE_D_list}) #a differential indeterminate + for j in range(0, n): + zEha = Poly(z**(n + j), DE.t)*E**(j + 1)*ha + zEhd = hd + Pa, Pd = cancel((zEha, zEhd))[1], cancel((zEha, zEhd))[2] + Q = Pa.quo(Pd) + for i in range(0, j + 1): + Q = Q.subs(Z[i], V[i]) + Dha = (hd*derivation(ha, DE, basic=True).as_poly(DE.t) + + ha*derivation(hd, DE, basic=True).as_poly(DE.t) + + hd*derivation(ha, DE_new, basic=True).as_poly(DE.t) + + ha*derivation(hd, DE_new, basic=True).as_poly(DE.t)) + Dhd = Poly(j + 1, DE.t)*hd**2 + ha, hd = Dha, Dhd + + Ff, _ = F.div(gcd(F, Q)) + F_stara, F_stard = frac_in(Ff, DE.t) + if F_stara.degree(DE.t) - F_stard.degree(DE.t) > 0: + QBC = Poly(Q, DE.t)*B**(1 + j)*C**(n + j) + H = QBC + H_list.append(H) + H = (QBC*F_stard).rem(F_stara) + alphas = real_roots(F_stara) + for alpha in list(alphas): + delta_a = delta_a*Poly((DE.t - alpha)**(n - j), DE.t) + Poly(H.eval(alpha), DE.t) + delta_d = delta_d*Poly((DE.t - alpha)**(n - j), DE.t) + return (delta_a, delta_d, H_list) + + +def recognize_derivative(a, d, DE, z=None): + """ + Compute the squarefree factorization of the denominator of f + and for each Di the polynomial H in K[x] (see Theorem 2.7.1), using the + LaurentSeries algorithm. Write Di = GiEi where Gj = gcd(Hn, Di) and + gcd(Ei,Hn) = 1. Since the residues of f at the roots of Gj are all 0, and + the residue of f at a root alpha of Ei is Hi(a) != 0, f is the derivative of a + rational function if and only if Ei = 1 for each i, which is equivalent to + Di | H[-1] for each i. + """ + flag =True + a, d = a.cancel(d, include=True) + _, r = a.div(d) + Np, Sp = splitfactor_sqf(d, DE, coefficientD=True, z=z) + + j = 1 + for s, _ in Sp: + delta_a, delta_d, H = laurent_series(r, d, s, j, DE) + g = gcd(d, H[-1]).as_poly() + if g is not d: + flag = False + break + j = j + 1 + return flag + + +def recognize_log_derivative(a, d, DE, z=None): + """ + There exists a v in K(x)* such that f = dv/v + where f a rational function if and only if f can be written as f = A/D + where D is squarefree,deg(A) < deg(D), gcd(A, D) = 1, + and all the roots of the Rothstein-Trager resultant are integers. In that case, + any of the Rothstein-Trager, Lazard-Rioboo-Trager or Czichowski algorithm + produces u in K(x) such that du/dx = uf. + """ + + z = z or Dummy('z') + a, d = a.cancel(d, include=True) + _, a = a.div(d) + + pz = Poly(z, DE.t) + Dd = derivation(d, DE) + q = a - pz*Dd + r, _ = d.resultant(q, includePRS=True) + r = Poly(r, z) + Np, Sp = splitfactor_sqf(r, DE, coefficientD=True, z=z) + + for s, _ in Sp: + # TODO also consider the complex roots which should + # turn the flag false + a = real_roots(s.as_poly(z)) + + if not all(j.is_Integer for j in a): + return False + return True + +def residue_reduce(a, d, DE, z=None, invert=True): + """ + Lazard-Rioboo-Rothstein-Trager resultant reduction. + + Explanation + =========== + + Given a derivation ``D`` on k(t) and f in k(t) simple, return g + elementary over k(t) and a Boolean b in {True, False} such that f - + Dg in k[t] if b == True or f + h and f + h - Dg do not have an + elementary integral over k(t) for any h in k (reduced) if b == + False. + + Returns (G, b), where G is a tuple of tuples of the form (s_i, S_i), + such that g = Add(*[RootSum(s_i, lambda z: z*log(S_i(z, t))) for + S_i, s_i in G]). f - Dg is the remaining integral, which is elementary + only if b == True, and hence the integral of f is elementary only if + b == True. + + f - Dg is not calculated in this function because that would require + explicitly calculating the RootSum. Use residue_reduce_derivation(). + """ + # TODO: Use log_to_atan() from rationaltools.py + # If r = residue_reduce(...), then the logarithmic part is given by: + # sum([RootSum(a[0].as_poly(z), lambda i: i*log(a[1].as_expr()).subs(z, + # i)).subs(t, log(x)) for a in r[0]]) + + z = z or Dummy('z') + a, d = a.cancel(d, include=True) + a, d = a.to_field().mul_ground(1/d.LC()), d.to_field().mul_ground(1/d.LC()) + kkinv = [1/x for x in DE.T[:DE.level]] + DE.T[:DE.level] + + if a.is_zero: + return ([], True) + _, a = a.div(d) + + pz = Poly(z, DE.t) + + Dd = derivation(d, DE) + q = a - pz*Dd + + if Dd.degree(DE.t) <= d.degree(DE.t): + r, R = d.resultant(q, includePRS=True) + else: + r, R = q.resultant(d, includePRS=True) + + R_map, H = {}, [] + for i in R: + R_map[i.degree()] = i + + r = Poly(r, z) + Np, Sp = splitfactor_sqf(r, DE, coefficientD=True, z=z) + + for s, i in Sp: + if i == d.degree(DE.t): + s = Poly(s, z).monic() + H.append((s, d)) + else: + h = R_map.get(i) + if h is None: + continue + h_lc = Poly(h.as_poly(DE.t).LC(), DE.t, field=True) + + h_lc_sqf = h_lc.sqf_list_include(all=True) + + for a, j in h_lc_sqf: + h = Poly(h, DE.t, field=True).exquo(Poly(gcd(a, s**j, *kkinv), + DE.t)) + + s = Poly(s, z).monic() + + if invert: + h_lc = Poly(h.as_poly(DE.t).LC(), DE.t, field=True, expand=False) + inv, coeffs = h_lc.as_poly(z, field=True).invert(s), [S.One] + + for coeff in h.coeffs()[1:]: + L = reduced(inv*coeff.as_poly(inv.gens), [s])[1] + coeffs.append(L.as_expr()) + + h = Poly(dict(list(zip(h.monoms(), coeffs))), DE.t) + + H.append((s, h)) + + b = not any(cancel(i.as_expr()).has(DE.t, z) for i, _ in Np) + + return (H, b) + + +def residue_reduce_to_basic(H, DE, z): + """ + Converts the tuple returned by residue_reduce() into a Basic expression. + """ + # TODO: check what Lambda does with RootOf + i = Dummy('i') + s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs]))) + + return sum(RootSum(a[0].as_poly(z), Lambda(i, i*log(a[1].as_expr()).subs( + {z: i}).subs(s))) for a in H) + + +def residue_reduce_derivation(H, DE, z): + """ + Computes the derivation of an expression returned by residue_reduce(). + + In general, this is a rational function in t, so this returns an + as_expr() result. + """ + # TODO: verify that this is correct for multiple extensions + i = Dummy('i') + return S(sum(RootSum(a[0].as_poly(z), Lambda(i, i*derivation(a[1], + DE).as_expr().subs(z, i)/a[1].as_expr().subs(z, i))) for a in H)) + + +def integrate_primitive_polynomial(p, DE): + """ + Integration of primitive polynomials. + + Explanation + =========== + + Given a primitive monomial t over k, and ``p`` in k[t], return q in k[t], + r in k, and a bool b in {True, False} such that r = p - Dq is in k if b is + True, or r = p - Dq does not have an elementary integral over k(t) if b is + False. + """ + Zero = Poly(0, DE.t) + q = Poly(0, DE.t) + + if not p.expr.has(DE.t): + return (Zero, p, True) + + from .prde import limited_integrate + while True: + if not p.expr.has(DE.t): + return (q, p, True) + + Dta, Dtb = frac_in(DE.d, DE.T[DE.level - 1]) + + with DecrementLevel(DE): # We had better be integrating the lowest extension (x) + # with ratint(). + a = p.LC() + aa, ad = frac_in(a, DE.t) + + try: + rv = limited_integrate(aa, ad, [(Dta, Dtb)], DE) + if rv is None: + raise NonElementaryIntegralException + (ba, bd), c = rv + except NonElementaryIntegralException: + return (q, p, False) + + m = p.degree(DE.t) + q0 = c[0].as_poly(DE.t)*Poly(DE.t**(m + 1)/(m + 1), DE.t) + \ + (ba.as_expr()/bd.as_expr()).as_poly(DE.t)*Poly(DE.t**m, DE.t) + + p = p - derivation(q0, DE) + q = q + q0 + + +def integrate_primitive(a, d, DE, z=None): + """ + Integration of primitive functions. + + Explanation + =========== + + Given a primitive monomial t over k and f in k(t), return g elementary over + k(t), i in k(t), and b in {True, False} such that i = f - Dg is in k if b + is True or i = f - Dg does not have an elementary integral over k(t) if b + is False. + + This function returns a Basic expression for the first argument. If b is + True, the second argument is Basic expression in k to recursively integrate. + If b is False, the second argument is an unevaluated Integral, which has + been proven to be nonelementary. + """ + # XXX: a and d must be canceled, or this might return incorrect results + z = z or Dummy("z") + s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs]))) + + g1, h, r = hermite_reduce(a, d, DE) + g2, b = residue_reduce(h[0], h[1], DE, z=z) + if not b: + i = cancel(a.as_expr()/d.as_expr() - (g1[1]*derivation(g1[0], DE) - + g1[0]*derivation(g1[1], DE)).as_expr()/(g1[1]**2).as_expr() - + residue_reduce_derivation(g2, DE, z)) + i = NonElementaryIntegral(cancel(i).subs(s), DE.x) + return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) + + residue_reduce_to_basic(g2, DE, z), i, b) + + # h - Dg2 + r + p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2, + DE, z) + r[0].as_expr()/r[1].as_expr()) + p = p.as_poly(DE.t) + + q, i, b = integrate_primitive_polynomial(p, DE) + + ret = ((g1[0].as_expr()/g1[1].as_expr() + q.as_expr()).subs(s) + + residue_reduce_to_basic(g2, DE, z)) + if not b: + # TODO: This does not do the right thing when b is False + i = NonElementaryIntegral(cancel(i.as_expr()).subs(s), DE.x) + else: + i = cancel(i.as_expr()) + + return (ret, i, b) + + +def integrate_hyperexponential_polynomial(p, DE, z): + """ + Integration of hyperexponential polynomials. + + Explanation + =========== + + Given a hyperexponential monomial t over k and ``p`` in k[t, 1/t], return q in + k[t, 1/t] and a bool b in {True, False} such that p - Dq in k if b is True, + or p - Dq does not have an elementary integral over k(t) if b is False. + """ + t1 = DE.t + dtt = DE.d.exquo(Poly(DE.t, DE.t)) + qa = Poly(0, DE.t) + qd = Poly(1, DE.t) + b = True + + if p.is_zero: + return(qa, qd, b) + + from sympy.integrals.rde import rischDE + + with DecrementLevel(DE): + for i in range(-p.degree(z), p.degree(t1) + 1): + if not i: + continue + elif i < 0: + # If you get AttributeError: 'NoneType' object has no attribute 'nth' + # then this should really not have expand=False + # But it shouldn't happen because p is already a Poly in t and z + a = p.as_poly(z, expand=False).nth(-i) + else: + # If you get AttributeError: 'NoneType' object has no attribute 'nth' + # then this should really not have expand=False + a = p.as_poly(t1, expand=False).nth(i) + + aa, ad = frac_in(a, DE.t, field=True) + aa, ad = aa.cancel(ad, include=True) + iDt = Poly(i, t1)*dtt + iDta, iDtd = frac_in(iDt, DE.t, field=True) + try: + va, vd = rischDE(iDta, iDtd, Poly(aa, DE.t), Poly(ad, DE.t), DE) + va, vd = frac_in((va, vd), t1, cancel=True) + except NonElementaryIntegralException: + b = False + else: + qa = qa*vd + va*Poly(t1**i)*qd + qd *= vd + + return (qa, qd, b) + + +def integrate_hyperexponential(a, d, DE, z=None, conds='piecewise'): + """ + Integration of hyperexponential functions. + + Explanation + =========== + + Given a hyperexponential monomial t over k and f in k(t), return g + elementary over k(t), i in k(t), and a bool b in {True, False} such that + i = f - Dg is in k if b is True or i = f - Dg does not have an elementary + integral over k(t) if b is False. + + This function returns a Basic expression for the first argument. If b is + True, the second argument is Basic expression in k to recursively integrate. + If b is False, the second argument is an unevaluated Integral, which has + been proven to be nonelementary. + """ + # XXX: a and d must be canceled, or this might return incorrect results + z = z or Dummy("z") + s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs]))) + + g1, h, r = hermite_reduce(a, d, DE) + g2, b = residue_reduce(h[0], h[1], DE, z=z) + if not b: + i = cancel(a.as_expr()/d.as_expr() - (g1[1]*derivation(g1[0], DE) - + g1[0]*derivation(g1[1], DE)).as_expr()/(g1[1]**2).as_expr() - + residue_reduce_derivation(g2, DE, z)) + i = NonElementaryIntegral(cancel(i.subs(s)), DE.x) + return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) + + residue_reduce_to_basic(g2, DE, z), i, b) + + # p should be a polynomial in t and 1/t, because Sirr == k[t, 1/t] + # h - Dg2 + r + p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2, + DE, z) + r[0].as_expr()/r[1].as_expr()) + pp = as_poly_1t(p, DE.t, z) + + qa, qd, b = integrate_hyperexponential_polynomial(pp, DE, z) + + i = pp.nth(0, 0) + + ret = ((g1[0].as_expr()/g1[1].as_expr()).subs(s) \ + + residue_reduce_to_basic(g2, DE, z)) + + qas = qa.as_expr().subs(s) + qds = qd.as_expr().subs(s) + if conds == 'piecewise' and DE.x not in qds.free_symbols: + # We have to be careful if the exponent is S.Zero! + + # XXX: Does qd = 0 always necessarily correspond to the exponential + # equaling 1? + ret += Piecewise( + (qas/qds, Ne(qds, 0)), + (integrate((p - i).subs(DE.t, 1).subs(s), DE.x), True) + ) + else: + ret += qas/qds + + if not b: + i = p - (qd*derivation(qa, DE) - qa*derivation(qd, DE)).as_expr()/\ + (qd**2).as_expr() + i = NonElementaryIntegral(cancel(i).subs(s), DE.x) + return (ret, i, b) + + +def integrate_hypertangent_polynomial(p, DE): + """ + Integration of hypertangent polynomials. + + Explanation + =========== + + Given a differential field k such that sqrt(-1) is not in k, a + hypertangent monomial t over k, and p in k[t], return q in k[t] and + c in k such that p - Dq - c*D(t**2 + 1)/(t**1 + 1) is in k and p - + Dq does not have an elementary integral over k(t) if Dc != 0. + """ + # XXX: Make sure that sqrt(-1) is not in k. + q, r = polynomial_reduce(p, DE) + a = DE.d.exquo(Poly(DE.t**2 + 1, DE.t)) + c = Poly(r.nth(1)/(2*a.as_expr()), DE.t) + return (q, c) + + +def integrate_nonlinear_no_specials(a, d, DE, z=None): + """ + Integration of nonlinear monomials with no specials. + + Explanation + =========== + + Given a nonlinear monomial t over k such that Sirr ({p in k[t] | p is + special, monic, and irreducible}) is empty, and f in k(t), returns g + elementary over k(t) and a Boolean b in {True, False} such that f - Dg is + in k if b == True, or f - Dg does not have an elementary integral over k(t) + if b == False. + + This function is applicable to all nonlinear extensions, but in the case + where it returns b == False, it will only have proven that the integral of + f - Dg is nonelementary if Sirr is empty. + + This function returns a Basic expression. + """ + # TODO: Integral from k? + # TODO: split out nonelementary integral + # XXX: a and d must be canceled, or this might not return correct results + z = z or Dummy("z") + s = list(zip(reversed(DE.T), reversed([f(DE.x) for f in DE.Tfuncs]))) + + g1, h, r = hermite_reduce(a, d, DE) + g2, b = residue_reduce(h[0], h[1], DE, z=z) + if not b: + return ((g1[0].as_expr()/g1[1].as_expr()).subs(s) + + residue_reduce_to_basic(g2, DE, z), b) + + # Because f has no specials, this should be a polynomial in t, or else + # there is a bug. + p = cancel(h[0].as_expr()/h[1].as_expr() - residue_reduce_derivation(g2, + DE, z).as_expr() + r[0].as_expr()/r[1].as_expr()).as_poly(DE.t) + q1, q2 = polynomial_reduce(p, DE) + + if q2.expr.has(DE.t): + b = False + else: + b = True + + ret = (cancel(g1[0].as_expr()/g1[1].as_expr() + q1.as_expr()).subs(s) + + residue_reduce_to_basic(g2, DE, z)) + return (ret, b) + + +class NonElementaryIntegral(Integral): + """ + Represents a nonelementary Integral. + + Explanation + =========== + + If the result of integrate() is an instance of this class, it is + guaranteed to be nonelementary. Note that integrate() by default will try + to find any closed-form solution, even in terms of special functions which + may themselves not be elementary. To make integrate() only give + elementary solutions, or, in the cases where it can prove the integral to + be nonelementary, instances of this class, use integrate(risch=True). + In this case, integrate() may raise NotImplementedError if it cannot make + such a determination. + + integrate() uses the deterministic Risch algorithm to integrate elementary + functions or prove that they have no elementary integral. In some cases, + this algorithm can split an integral into an elementary and nonelementary + part, so that the result of integrate will be the sum of an elementary + expression and a NonElementaryIntegral. + + Examples + ======== + + >>> from sympy import integrate, exp, log, Integral + >>> from sympy.abc import x + + >>> a = integrate(exp(-x**2), x, risch=True) + >>> print(a) + Integral(exp(-x**2), x) + >>> type(a) + + + >>> expr = (2*log(x)**2 - log(x) - x**2)/(log(x)**3 - x**2*log(x)) + >>> b = integrate(expr, x, risch=True) + >>> print(b) + -log(-x + log(x))/2 + log(x + log(x))/2 + Integral(1/log(x), x) + >>> type(b.atoms(Integral).pop()) + + + """ + # TODO: This is useful in and of itself, because isinstance(result, + # NonElementaryIntegral) will tell if the integral has been proven to be + # elementary. But should we do more? Perhaps a no-op .doit() if + # elementary=True? Or maybe some information on why the integral is + # nonelementary. + pass + + +def risch_integrate(f, x, extension=None, handle_first='log', + separate_integral=False, rewrite_complex=None, + conds='piecewise'): + r""" + The Risch Integration Algorithm. + + Explanation + =========== + + Only transcendental functions are supported. Currently, only exponentials + and logarithms are supported, but support for trigonometric functions is + forthcoming. + + If this function returns an unevaluated Integral in the result, it means + that it has proven that integral to be nonelementary. Any errors will + result in raising NotImplementedError. The unevaluated Integral will be + an instance of NonElementaryIntegral, a subclass of Integral. + + handle_first may be either 'exp' or 'log'. This changes the order in + which the extension is built, and may result in a different (but + equivalent) solution (for an example of this, see issue 5109). It is also + possible that the integral may be computed with one but not the other, + because not all cases have been implemented yet. It defaults to 'log' so + that the outer extension is exponential when possible, because more of the + exponential case has been implemented. + + If ``separate_integral`` is ``True``, the result is returned as a tuple (ans, i), + where the integral is ans + i, ans is elementary, and i is either a + NonElementaryIntegral or 0. This useful if you want to try further + integrating the NonElementaryIntegral part using other algorithms to + possibly get a solution in terms of special functions. It is False by + default. + + Examples + ======== + + >>> from sympy.integrals.risch import risch_integrate + >>> from sympy import exp, log, pprint + >>> from sympy.abc import x + + First, we try integrating exp(-x**2). Except for a constant factor of + 2/sqrt(pi), this is the famous error function. + + >>> pprint(risch_integrate(exp(-x**2), x)) + / + | + | 2 + | -x + | e dx + | + / + + The unevaluated Integral in the result means that risch_integrate() has + proven that exp(-x**2) does not have an elementary anti-derivative. + + In many cases, risch_integrate() can split out the elementary + anti-derivative part from the nonelementary anti-derivative part. + For example, + + >>> pprint(risch_integrate((2*log(x)**2 - log(x) - x**2)/(log(x)**3 - + ... x**2*log(x)), x)) + / + | + log(-x + log(x)) log(x + log(x)) | 1 + - ---------------- + --------------- + | ------ dx + 2 2 | log(x) + | + / + + This means that it has proven that the integral of 1/log(x) is + nonelementary. This function is also known as the logarithmic integral, + and is often denoted as Li(x). + + risch_integrate() currently only accepts purely transcendental functions + with exponentials and logarithms, though note that this can include + nested exponentials and logarithms, as well as exponentials with bases + other than E. + + >>> pprint(risch_integrate(exp(x)*exp(exp(x)), x)) + / x\ + \e / + e + >>> pprint(risch_integrate(exp(exp(x)), x)) + / + | + | / x\ + | \e / + | e dx + | + / + + >>> pprint(risch_integrate(x*x**x*log(x) + x**x + x*x**x, x)) + x + x*x + >>> pprint(risch_integrate(x**x, x)) + / + | + | x + | x dx + | + / + + >>> pprint(risch_integrate(-1/(x*log(x)*log(log(x))**2), x)) + 1 + ----------- + log(log(x)) + + """ + f = S(f) + + DE = extension or DifferentialExtension(f, x, handle_first=handle_first, + dummy=True, rewrite_complex=rewrite_complex) + fa, fd = DE.fa, DE.fd + + result = S.Zero + for case in reversed(DE.cases): + if not fa.expr.has(DE.t) and not fd.expr.has(DE.t) and not case == 'base': + DE.decrement_level() + fa, fd = frac_in((fa, fd), DE.t) + continue + + fa, fd = fa.cancel(fd, include=True) + if case == 'exp': + ans, i, b = integrate_hyperexponential(fa, fd, DE, conds=conds) + elif case == 'primitive': + ans, i, b = integrate_primitive(fa, fd, DE) + elif case == 'base': + # XXX: We can't call ratint() directly here because it doesn't + # handle polynomials correctly. + ans = integrate(fa.as_expr()/fd.as_expr(), DE.x, risch=False) + b = False + i = S.Zero + else: + raise NotImplementedError("Only exponential and logarithmic " + "extensions are currently supported.") + + result += ans + if b: + DE.decrement_level() + fa, fd = frac_in(i, DE.t) + else: + result = result.subs(DE.backsubs) + if not i.is_zero: + i = NonElementaryIntegral(i.function.subs(DE.backsubs),i.limits) + if not separate_integral: + result += i + return result + else: + + if isinstance(i, NonElementaryIntegral): + return (result, i) + else: + return (result, 0) diff --git a/lib/python3.11/site-packages/sympy/integrals/singularityfunctions.py b/lib/python3.11/site-packages/sympy/integrals/singularityfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..3e33d0542c45b67b193f17e00c25837f3a82109a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/singularityfunctions.py @@ -0,0 +1,63 @@ +from sympy.functions import SingularityFunction, DiracDelta +from sympy.integrals import integrate + + +def singularityintegrate(f, x): + """ + This function handles the indefinite integrations of Singularity functions. + The ``integrate`` function calls this function internally whenever an + instance of SingularityFunction is passed as argument. + + Explanation + =========== + + The idea for integration is the following: + + - If we are dealing with a SingularityFunction expression, + i.e. ``SingularityFunction(x, a, n)``, we just return + ``SingularityFunction(x, a, n + 1)/(n + 1)`` if ``n >= 0`` and + ``SingularityFunction(x, a, n + 1)`` if ``n < 0``. + + - If the node is a multiplication or power node having a + SingularityFunction term we rewrite the whole expression in terms of + Heaviside and DiracDelta and then integrate the output. Lastly, we + rewrite the output of integration back in terms of SingularityFunction. + + - If none of the above case arises, we return None. + + Examples + ======== + + >>> from sympy.integrals.singularityfunctions import singularityintegrate + >>> from sympy import SingularityFunction, symbols, Function + >>> x, a, n, y = symbols('x a n y') + >>> f = Function('f') + >>> singularityintegrate(SingularityFunction(x, a, 3), x) + SingularityFunction(x, a, 4)/4 + >>> singularityintegrate(5*SingularityFunction(x, 5, -2), x) + 5*SingularityFunction(x, 5, -1) + >>> singularityintegrate(6*SingularityFunction(x, 5, -1), x) + 6*SingularityFunction(x, 5, 0) + >>> singularityintegrate(x*SingularityFunction(x, 0, -1), x) + 0 + >>> singularityintegrate(SingularityFunction(x, 1, -1) * f(x), x) + f(1)*SingularityFunction(x, 1, 0) + + """ + + if not f.has(SingularityFunction): + return None + + if isinstance(f, SingularityFunction): + x, a, n = f.args + if n.is_positive or n.is_zero: + return SingularityFunction(x, a, n + 1)/(n + 1) + elif n in (-1, -2, -3, -4): + return SingularityFunction(x, a, n + 1) + + if f.is_Mul or f.is_Pow: + + expr = f.rewrite(DiracDelta) + expr = integrate(expr, x) + return expr.rewrite(SingularityFunction) + return None diff --git a/lib/python3.11/site-packages/sympy/integrals/transforms.py b/lib/python3.11/site-packages/sympy/integrals/transforms.py new file mode 100644 index 0000000000000000000000000000000000000000..1cd8eefbb3b1fa7749955cf2ad349a35a71debc3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/transforms.py @@ -0,0 +1,1590 @@ +""" Integral Transforms """ +from functools import reduce, wraps +from itertools import repeat +from sympy.core import S, pi +from sympy.core.add import Add +from sympy.core.function import ( + AppliedUndef, count_ops, expand, expand_mul, Function) +from sympy.core.mul import Mul +from sympy.core.intfunc import igcd, ilcm +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import Dummy +from sympy.core.traversal import postorder_traversal +from sympy.functions.combinatorial.factorials import factorial, rf +from sympy.functions.elementary.complexes import re, arg, Abs +from sympy.functions.elementary.exponential import exp, exp_polar +from sympy.functions.elementary.hyperbolic import cosh, coth, sinh, tanh +from sympy.functions.elementary.integers import ceiling +from sympy.functions.elementary.miscellaneous import Max, Min, sqrt +from sympy.functions.elementary.piecewise import piecewise_fold +from sympy.functions.elementary.trigonometric import cos, cot, sin, tan +from sympy.functions.special.bessel import besselj +from sympy.functions.special.delta_functions import Heaviside +from sympy.functions.special.gamma_functions import gamma +from sympy.functions.special.hyper import meijerg +from sympy.integrals import integrate, Integral +from sympy.integrals.meijerint import _dummy +from sympy.logic.boolalg import to_cnf, conjuncts, disjuncts, Or, And +from sympy.polys.polyroots import roots +from sympy.polys.polytools import factor, Poly +from sympy.polys.rootoftools import CRootOf +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import debug + + +########################################################################## +# Helpers / Utilities +########################################################################## + + +class IntegralTransformError(NotImplementedError): + """ + Exception raised in relation to problems computing transforms. + + Explanation + =========== + + This class is mostly used internally; if integrals cannot be computed + objects representing unevaluated transforms are usually returned. + + The hint ``needeval=True`` can be used to disable returning transform + objects, and instead raise this exception if an integral cannot be + computed. + """ + def __init__(self, transform, function, msg): + super().__init__( + "%s Transform could not be computed: %s." % (transform, msg)) + self.function = function + + +class IntegralTransform(Function): + """ + Base class for integral transforms. + + Explanation + =========== + + This class represents unevaluated transforms. + + To implement a concrete transform, derive from this class and implement + the ``_compute_transform(f, x, s, **hints)`` and ``_as_integral(f, x, s)`` + functions. If the transform cannot be computed, raise :obj:`IntegralTransformError`. + + Also set ``cls._name``. For instance, + + >>> from sympy import LaplaceTransform + >>> LaplaceTransform._name + 'Laplace' + + Implement ``self._collapse_extra`` if your function returns more than just a + number and possibly a convergence condition. + """ + + @property + def function(self): + """ The function to be transformed. """ + return self.args[0] + + @property + def function_variable(self): + """ The dependent variable of the function to be transformed. """ + return self.args[1] + + @property + def transform_variable(self): + """ The independent transform variable. """ + return self.args[2] + + @property + def free_symbols(self): + """ + This method returns the symbols that will exist when the transform + is evaluated. + """ + return self.function.free_symbols.union({self.transform_variable}) \ + - {self.function_variable} + + def _compute_transform(self, f, x, s, **hints): + raise NotImplementedError + + def _as_integral(self, f, x, s): + raise NotImplementedError + + def _collapse_extra(self, extra): + cond = And(*extra) + if cond == False: + raise IntegralTransformError(self.__class__.name, None, '') + return cond + + def _try_directly(self, **hints): + T = None + try_directly = not any(func.has(self.function_variable) + for func in self.function.atoms(AppliedUndef)) + if try_directly: + try: + T = self._compute_transform(self.function, + self.function_variable, self.transform_variable, **hints) + except IntegralTransformError: + debug('[IT _try ] Caught IntegralTransformError, returns None') + T = None + + fn = self.function + if not fn.is_Add: + fn = expand_mul(fn) + return fn, T + + def doit(self, **hints): + """ + Try to evaluate the transform in closed form. + + Explanation + =========== + + This general function handles linearity, but apart from that leaves + pretty much everything to _compute_transform. + + Standard hints are the following: + + - ``simplify``: whether or not to simplify the result + - ``noconds``: if True, do not return convergence conditions + - ``needeval``: if True, raise IntegralTransformError instead of + returning IntegralTransform objects + + The default values of these hints depend on the concrete transform, + usually the default is + ``(simplify, noconds, needeval) = (True, False, False)``. + """ + needeval = hints.pop('needeval', False) + simplify = hints.pop('simplify', True) + hints['simplify'] = simplify + + fn, T = self._try_directly(**hints) + + if T is not None: + return T + + if fn.is_Add: + hints['needeval'] = needeval + res = [self.__class__(*([x] + list(self.args[1:]))).doit(**hints) + for x in fn.args] + extra = [] + ress = [] + for x in res: + if not isinstance(x, tuple): + x = [x] + ress.append(x[0]) + if len(x) == 2: + # only a condition + extra.append(x[1]) + elif len(x) > 2: + # some region parameters and a condition (Mellin, Laplace) + extra += [x[1:]] + if simplify==True: + res = Add(*ress).simplify() + else: + res = Add(*ress) + if not extra: + return res + try: + extra = self._collapse_extra(extra) + if iterable(extra): + return (res,) + tuple(extra) + else: + return (res, extra) + except IntegralTransformError: + pass + + if needeval: + raise IntegralTransformError( + self.__class__._name, self.function, 'needeval') + + # TODO handle derivatives etc + + # pull out constant coefficients + coeff, rest = fn.as_coeff_mul(self.function_variable) + return coeff*self.__class__(*([Mul(*rest)] + list(self.args[1:]))) + + @property + def as_integral(self): + return self._as_integral(self.function, self.function_variable, + self.transform_variable) + + def _eval_rewrite_as_Integral(self, *args, **kwargs): + return self.as_integral + + +def _simplify(expr, doit): + if doit: + from sympy.simplify import simplify + from sympy.simplify.powsimp import powdenest + return simplify(powdenest(piecewise_fold(expr), polar=True)) + return expr + + +def _noconds_(default): + """ + This is a decorator generator for dropping convergence conditions. + + Explanation + =========== + + Suppose you define a function ``transform(*args)`` which returns a tuple of + the form ``(result, cond1, cond2, ...)``. + + Decorating it ``@_noconds_(default)`` will add a new keyword argument + ``noconds`` to it. If ``noconds=True``, the return value will be altered to + be only ``result``, whereas if ``noconds=False`` the return value will not + be altered. + + The default value of the ``noconds`` keyword will be ``default`` (i.e. the + argument of this function). + """ + def make_wrapper(func): + @wraps(func) + def wrapper(*args, noconds=default, **kwargs): + res = func(*args, **kwargs) + if noconds: + return res[0] + return res + return wrapper + return make_wrapper +_noconds = _noconds_(False) + + +########################################################################## +# Mellin Transform +########################################################################## + +def _default_integrator(f, x): + return integrate(f, (x, S.Zero, S.Infinity)) + + +@_noconds +def _mellin_transform(f, x, s_, integrator=_default_integrator, simplify=True): + """ Backend function to compute Mellin transforms. """ + # We use a fresh dummy, because assumptions on s might drop conditions on + # convergence of the integral. + s = _dummy('s', 'mellin-transform', f) + F = integrator(x**(s - 1) * f, x) + + if not F.has(Integral): + return _simplify(F.subs(s, s_), simplify), (S.NegativeInfinity, S.Infinity), S.true + + if not F.is_Piecewise: # XXX can this work if integration gives continuous result now? + raise IntegralTransformError('Mellin', f, 'could not compute integral') + + F, cond = F.args[0] + if F.has(Integral): + raise IntegralTransformError( + 'Mellin', f, 'integral in unexpected form') + + def process_conds(cond): + """ + Turn ``cond`` into a strip (a, b), and auxiliary conditions. + """ + from sympy.solvers.inequalities import _solve_inequality + a = S.NegativeInfinity + b = S.Infinity + aux = S.true + conds = conjuncts(to_cnf(cond)) + t = Dummy('t', real=True) + for c in conds: + a_ = S.Infinity + b_ = S.NegativeInfinity + aux_ = [] + for d in disjuncts(c): + d_ = d.replace( + re, lambda x: x.as_real_imag()[0]).subs(re(s), t) + if not d.is_Relational or \ + d.rel_op in ('==', '!=') \ + or d_.has(s) or not d_.has(t): + aux_ += [d] + continue + soln = _solve_inequality(d_, t) + if not soln.is_Relational or \ + soln.rel_op in ('==', '!='): + aux_ += [d] + continue + if soln.lts == t: + b_ = Max(soln.gts, b_) + else: + a_ = Min(soln.lts, a_) + if a_ is not S.Infinity and a_ != b: + a = Max(a_, a) + elif b_ is not S.NegativeInfinity and b_ != a: + b = Min(b_, b) + else: + aux = And(aux, Or(*aux_)) + return a, b, aux + + conds = [process_conds(c) for c in disjuncts(cond)] + conds = [x for x in conds if x[2] != False] + conds.sort(key=lambda x: (x[0] - x[1], count_ops(x[2]))) + + if not conds: + raise IntegralTransformError('Mellin', f, 'no convergence found') + + a, b, aux = conds[0] + return _simplify(F.subs(s, s_), simplify), (a, b), aux + + +class MellinTransform(IntegralTransform): + """ + Class representing unevaluated Mellin transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute Mellin transforms, see the :func:`mellin_transform` + docstring. + """ + + _name = 'Mellin' + + def _compute_transform(self, f, x, s, **hints): + return _mellin_transform(f, x, s, **hints) + + def _as_integral(self, f, x, s): + return Integral(f*x**(s - 1), (x, S.Zero, S.Infinity)) + + def _collapse_extra(self, extra): + a = [] + b = [] + cond = [] + for (sa, sb), c in extra: + a += [sa] + b += [sb] + cond += [c] + res = (Max(*a), Min(*b)), And(*cond) + if (res[0][0] >= res[0][1]) == True or res[1] == False: + raise IntegralTransformError( + 'Mellin', None, 'no combined convergence.') + return res + + +def mellin_transform(f, x, s, **hints): + r""" + Compute the Mellin transform `F(s)` of `f(x)`, + + .. math :: F(s) = \int_0^\infty x^{s-1} f(x) \mathrm{d}x. + + For all "sensible" functions, this converges absolutely in a strip + `a < \operatorname{Re}(s) < b`. + + Explanation + =========== + + The Mellin transform is related via change of variables to the Fourier + transform, and also to the (bilateral) Laplace transform. + + This function returns ``(F, (a, b), cond)`` + where ``F`` is the Mellin transform of ``f``, ``(a, b)`` is the fundamental strip + (as above), and ``cond`` are auxiliary convergence conditions. + + If the integral cannot be computed in closed form, this function returns + an unevaluated :class:`MellinTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. If ``noconds=False``, + then only `F` will be returned (i.e. not ``cond``, and also not the strip + ``(a, b)``). + + Examples + ======== + + >>> from sympy import mellin_transform, exp + >>> from sympy.abc import x, s + >>> mellin_transform(exp(-x), x, s) + (gamma(s), (0, oo), True) + + See Also + ======== + + inverse_mellin_transform, laplace_transform, fourier_transform + hankel_transform, inverse_hankel_transform + """ + return MellinTransform(f, x, s).doit(**hints) + + +def _rewrite_sin(m_n, s, a, b): + """ + Re-write the sine function ``sin(m*s + n)`` as gamma functions, compatible + with the strip (a, b). + + Return ``(gamma1, gamma2, fac)`` so that ``f == fac/(gamma1 * gamma2)``. + + Examples + ======== + + >>> from sympy.integrals.transforms import _rewrite_sin + >>> from sympy import pi, S + >>> from sympy.abc import s + >>> _rewrite_sin((pi, 0), s, 0, 1) + (gamma(s), gamma(1 - s), pi) + >>> _rewrite_sin((pi, 0), s, 1, 0) + (gamma(s - 1), gamma(2 - s), -pi) + >>> _rewrite_sin((pi, 0), s, -1, 0) + (gamma(s + 1), gamma(-s), -pi) + >>> _rewrite_sin((pi, pi/2), s, S(1)/2, S(3)/2) + (gamma(s - 1/2), gamma(3/2 - s), -pi) + >>> _rewrite_sin((pi, pi), s, 0, 1) + (gamma(s), gamma(1 - s), -pi) + >>> _rewrite_sin((2*pi, 0), s, 0, S(1)/2) + (gamma(2*s), gamma(1 - 2*s), pi) + >>> _rewrite_sin((2*pi, 0), s, S(1)/2, 1) + (gamma(2*s - 1), gamma(2 - 2*s), -pi) + """ + # (This is a separate function because it is moderately complicated, + # and I want to doctest it.) + # We want to use pi/sin(pi*x) = gamma(x)*gamma(1-x). + # But there is one comlication: the gamma functions determine the + # inegration contour in the definition of the G-function. Usually + # it would not matter if this is slightly shifted, unless this way + # we create an undefined function! + # So we try to write this in such a way that the gammas are + # eminently on the right side of the strip. + m, n = m_n + + m = expand_mul(m/pi) + n = expand_mul(n/pi) + r = ceiling(-m*a - n.as_real_imag()[0]) # Don't use re(n), does not expand + return gamma(m*s + n + r), gamma(1 - n - r - m*s), (-1)**r*pi + + +class MellinTransformStripError(ValueError): + """ + Exception raised by _rewrite_gamma. Mainly for internal use. + """ + pass + + +def _rewrite_gamma(f, s, a, b): + """ + Try to rewrite the product f(s) as a product of gamma functions, + so that the inverse Mellin transform of f can be expressed as a meijer + G function. + + Explanation + =========== + + Return (an, ap), (bm, bq), arg, exp, fac such that + G((an, ap), (bm, bq), arg/z**exp)*fac is the inverse Mellin transform of f(s). + + Raises IntegralTransformError or MellinTransformStripError on failure. + + It is asserted that f has no poles in the fundamental strip designated by + (a, b). One of a and b is allowed to be None. The fundamental strip is + important, because it determines the inversion contour. + + This function can handle exponentials, linear factors, trigonometric + functions. + + This is a helper function for inverse_mellin_transform that will not + attempt any transformations on f. + + Examples + ======== + + >>> from sympy.integrals.transforms import _rewrite_gamma + >>> from sympy.abc import s + >>> from sympy import oo + >>> _rewrite_gamma(s*(s+3)*(s-1), s, -oo, oo) + (([], [-3, 0, 1]), ([-2, 1, 2], []), 1, 1, -1) + >>> _rewrite_gamma((s-1)**2, s, -oo, oo) + (([], [1, 1]), ([2, 2], []), 1, 1, 1) + + Importance of the fundamental strip: + + >>> _rewrite_gamma(1/s, s, 0, oo) + (([1], []), ([], [0]), 1, 1, 1) + >>> _rewrite_gamma(1/s, s, None, oo) + (([1], []), ([], [0]), 1, 1, 1) + >>> _rewrite_gamma(1/s, s, 0, None) + (([1], []), ([], [0]), 1, 1, 1) + >>> _rewrite_gamma(1/s, s, -oo, 0) + (([], [1]), ([0], []), 1, 1, -1) + >>> _rewrite_gamma(1/s, s, None, 0) + (([], [1]), ([0], []), 1, 1, -1) + >>> _rewrite_gamma(1/s, s, -oo, None) + (([], [1]), ([0], []), 1, 1, -1) + + >>> _rewrite_gamma(2**(-s+3), s, -oo, oo) + (([], []), ([], []), 1/2, 1, 8) + """ + # Our strategy will be as follows: + # 1) Guess a constant c such that the inversion integral should be + # performed wrt s'=c*s (instead of plain s). Write s for s'. + # 2) Process all factors, rewrite them independently as gamma functions in + # argument s, or exponentials of s. + # 3) Try to transform all gamma functions s.t. they have argument + # a+s or a-s. + # 4) Check that the resulting G function parameters are valid. + # 5) Combine all the exponentials. + + a_, b_ = S([a, b]) + + def left(c, is_numer): + """ + Decide whether pole at c lies to the left of the fundamental strip. + """ + # heuristically, this is the best chance for us to solve the inequalities + c = expand(re(c)) + if a_ is None and b_ is S.Infinity: + return True + if a_ is None: + return c < b_ + if b_ is None: + return c <= a_ + if (c >= b_) == True: + return False + if (c <= a_) == True: + return True + if is_numer: + return None + if a_.free_symbols or b_.free_symbols or c.free_symbols: + return None # XXX + #raise IntegralTransformError('Inverse Mellin', f, + # 'Could not determine position of singularity %s' + # ' relative to fundamental strip' % c) + raise MellinTransformStripError('Pole inside critical strip?') + + # 1) + s_multipliers = [] + for g in f.atoms(gamma): + if not g.has(s): + continue + arg = g.args[0] + if arg.is_Add: + arg = arg.as_independent(s)[1] + coeff, _ = arg.as_coeff_mul(s) + s_multipliers += [coeff] + for g in f.atoms(sin, cos, tan, cot): + if not g.has(s): + continue + arg = g.args[0] + if arg.is_Add: + arg = arg.as_independent(s)[1] + coeff, _ = arg.as_coeff_mul(s) + s_multipliers += [coeff/pi] + s_multipliers = [Abs(x) if x.is_extended_real else x for x in s_multipliers] + common_coefficient = S.One + for x in s_multipliers: + if not x.is_Rational: + common_coefficient = x + break + s_multipliers = [x/common_coefficient for x in s_multipliers] + if not (all(x.is_Rational for x in s_multipliers) and + common_coefficient.is_extended_real): + raise IntegralTransformError("Gamma", None, "Nonrational multiplier") + s_multiplier = common_coefficient/reduce(ilcm, [S(x.q) + for x in s_multipliers], S.One) + if s_multiplier == common_coefficient: + if len(s_multipliers) == 0: + s_multiplier = common_coefficient + else: + s_multiplier = common_coefficient \ + *reduce(igcd, [S(x.p) for x in s_multipliers]) + + f = f.subs(s, s/s_multiplier) + fac = S.One/s_multiplier + exponent = S.One/s_multiplier + if a_ is not None: + a_ *= s_multiplier + if b_ is not None: + b_ *= s_multiplier + + # 2) + numer, denom = f.as_numer_denom() + numer = Mul.make_args(numer) + denom = Mul.make_args(denom) + args = list(zip(numer, repeat(True))) + list(zip(denom, repeat(False))) + + facs = [] + dfacs = [] + # *_gammas will contain pairs (a, c) representing Gamma(a*s + c) + numer_gammas = [] + denom_gammas = [] + # exponentials will contain bases for exponentials of s + exponentials = [] + + def exception(fact): + return IntegralTransformError("Inverse Mellin", f, "Unrecognised form '%s'." % fact) + while args: + fact, is_numer = args.pop() + if is_numer: + ugammas, lgammas = numer_gammas, denom_gammas + ufacs = facs + else: + ugammas, lgammas = denom_gammas, numer_gammas + ufacs = dfacs + + def linear_arg(arg): + """ Test if arg is of form a*s+b, raise exception if not. """ + if not arg.is_polynomial(s): + raise exception(fact) + p = Poly(arg, s) + if p.degree() != 1: + raise exception(fact) + return p.all_coeffs() + + # constants + if not fact.has(s): + ufacs += [fact] + # exponentials + elif fact.is_Pow or isinstance(fact, exp): + if fact.is_Pow: + base = fact.base + exp_ = fact.exp + else: + base = exp_polar(1) + exp_ = fact.exp + if exp_.is_Integer: + cond = is_numer + if exp_ < 0: + cond = not cond + args += [(base, cond)]*Abs(exp_) + continue + elif not base.has(s): + a, b = linear_arg(exp_) + if not is_numer: + base = 1/base + exponentials += [base**a] + facs += [base**b] + else: + raise exception(fact) + # linear factors + elif fact.is_polynomial(s): + p = Poly(fact, s) + if p.degree() != 1: + # We completely factor the poly. For this we need the roots. + # Now roots() only works in some cases (low degree), and CRootOf + # only works without parameters. So try both... + coeff = p.LT()[1] + rs = roots(p, s) + if len(rs) != p.degree(): + rs = CRootOf.all_roots(p) + ufacs += [coeff] + args += [(s - c, is_numer) for c in rs] + continue + a, c = p.all_coeffs() + ufacs += [a] + c /= -a + # Now need to convert s - c + if left(c, is_numer): + ugammas += [(S.One, -c + 1)] + lgammas += [(S.One, -c)] + else: + ufacs += [-1] + ugammas += [(S.NegativeOne, c + 1)] + lgammas += [(S.NegativeOne, c)] + elif isinstance(fact, gamma): + a, b = linear_arg(fact.args[0]) + if is_numer: + if (a > 0 and (left(-b/a, is_numer) == False)) or \ + (a < 0 and (left(-b/a, is_numer) == True)): + raise NotImplementedError( + 'Gammas partially over the strip.') + ugammas += [(a, b)] + elif isinstance(fact, sin): + # We try to re-write all trigs as gammas. This is not in + # general the best strategy, since sometimes this is impossible, + # but rewriting as exponentials would work. However trig functions + # in inverse mellin transforms usually all come from simplifying + # gamma terms, so this should work. + a = fact.args[0] + if is_numer: + # No problem with the poles. + gamma1, gamma2, fac_ = gamma(a/pi), gamma(1 - a/pi), pi + else: + gamma1, gamma2, fac_ = _rewrite_sin(linear_arg(a), s, a_, b_) + args += [(gamma1, not is_numer), (gamma2, not is_numer)] + ufacs += [fac_] + elif isinstance(fact, tan): + a = fact.args[0] + args += [(sin(a, evaluate=False), is_numer), + (sin(pi/2 - a, evaluate=False), not is_numer)] + elif isinstance(fact, cos): + a = fact.args[0] + args += [(sin(pi/2 - a, evaluate=False), is_numer)] + elif isinstance(fact, cot): + a = fact.args[0] + args += [(sin(pi/2 - a, evaluate=False), is_numer), + (sin(a, evaluate=False), not is_numer)] + else: + raise exception(fact) + + fac *= Mul(*facs)/Mul(*dfacs) + + # 3) + an, ap, bm, bq = [], [], [], [] + for gammas, plus, minus, is_numer in [(numer_gammas, an, bm, True), + (denom_gammas, bq, ap, False)]: + while gammas: + a, c = gammas.pop() + if a != -1 and a != +1: + # We use the gamma function multiplication theorem. + p = Abs(S(a)) + newa = a/p + newc = c/p + if not a.is_Integer: + raise TypeError("a is not an integer") + for k in range(p): + gammas += [(newa, newc + k/p)] + if is_numer: + fac *= (2*pi)**((1 - p)/2) * p**(c - S.Half) + exponentials += [p**a] + else: + fac /= (2*pi)**((1 - p)/2) * p**(c - S.Half) + exponentials += [p**(-a)] + continue + if a == +1: + plus.append(1 - c) + else: + minus.append(c) + + # 4) + # TODO + + # 5) + arg = Mul(*exponentials) + + # for testability, sort the arguments + an.sort(key=default_sort_key) + ap.sort(key=default_sort_key) + bm.sort(key=default_sort_key) + bq.sort(key=default_sort_key) + + return (an, ap), (bm, bq), arg, exponent, fac + + +@_noconds_(True) +def _inverse_mellin_transform(F, s, x_, strip, as_meijerg=False): + """ A helper for the real inverse_mellin_transform function, this one here + assumes x to be real and positive. """ + x = _dummy('t', 'inverse-mellin-transform', F, positive=True) + # Actually, we won't try integration at all. Instead we use the definition + # of the Meijer G function as a fairly general inverse mellin transform. + F = F.rewrite(gamma) + for g in [factor(F), expand_mul(F), expand(F)]: + if g.is_Add: + # do all terms separately + ress = [_inverse_mellin_transform(G, s, x, strip, as_meijerg, + noconds=False) + for G in g.args] + conds = [p[1] for p in ress] + ress = [p[0] for p in ress] + res = Add(*ress) + if not as_meijerg: + res = factor(res, gens=res.atoms(Heaviside)) + return res.subs(x, x_), And(*conds) + + try: + a, b, C, e, fac = _rewrite_gamma(g, s, strip[0], strip[1]) + except IntegralTransformError: + continue + try: + G = meijerg(a, b, C/x**e) + except ValueError: + continue + if as_meijerg: + h = G + else: + try: + from sympy.simplify import hyperexpand + h = hyperexpand(G) + except NotImplementedError: + raise IntegralTransformError( + 'Inverse Mellin', F, 'Could not calculate integral') + + if h.is_Piecewise and len(h.args) == 3: + # XXX we break modularity here! + h = Heaviside(x - Abs(C))*h.args[0].args[0] \ + + Heaviside(Abs(C) - x)*h.args[1].args[0] + # We must ensure that the integral along the line we want converges, + # and return that value. + # See [L], 5.2 + cond = [Abs(arg(G.argument)) < G.delta*pi] + # Note: we allow ">=" here, this corresponds to convergence if we let + # limits go to oo symmetrically. ">" corresponds to absolute convergence. + cond += [And(Or(len(G.ap) != len(G.bq), 0 >= re(G.nu) + 1), + Abs(arg(G.argument)) == G.delta*pi)] + cond = Or(*cond) + if cond == False: + raise IntegralTransformError( + 'Inverse Mellin', F, 'does not converge') + return (h*fac).subs(x, x_), cond + + raise IntegralTransformError('Inverse Mellin', F, '') + +_allowed = None + + +class InverseMellinTransform(IntegralTransform): + """ + Class representing unevaluated inverse Mellin transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse Mellin transforms, see the + :func:`inverse_mellin_transform` docstring. + """ + + _name = 'Inverse Mellin' + _none_sentinel = Dummy('None') + _c = Dummy('c') + + def __new__(cls, F, s, x, a, b, **opts): + if a is None: + a = InverseMellinTransform._none_sentinel + if b is None: + b = InverseMellinTransform._none_sentinel + return IntegralTransform.__new__(cls, F, s, x, a, b, **opts) + + @property + def fundamental_strip(self): + a, b = self.args[3], self.args[4] + if a is InverseMellinTransform._none_sentinel: + a = None + if b is InverseMellinTransform._none_sentinel: + b = None + return a, b + + def _compute_transform(self, F, s, x, **hints): + # IntegralTransform's doit will cause this hint to exist, but + # InverseMellinTransform should ignore it + hints.pop('simplify', True) + global _allowed + if _allowed is None: + _allowed = { + exp, gamma, sin, cos, tan, cot, cosh, sinh, tanh, coth, + factorial, rf} + for f in postorder_traversal(F): + if f.is_Function and f.has(s) and f.func not in _allowed: + raise IntegralTransformError('Inverse Mellin', F, + 'Component %s not recognised.' % f) + strip = self.fundamental_strip + return _inverse_mellin_transform(F, s, x, strip, **hints) + + def _as_integral(self, F, s, x): + c = self.__class__._c + return Integral(F*x**(-s), (s, c - S.ImaginaryUnit*S.Infinity, c + + S.ImaginaryUnit*S.Infinity))/(2*S.Pi*S.ImaginaryUnit) + + +def inverse_mellin_transform(F, s, x, strip, **hints): + r""" + Compute the inverse Mellin transform of `F(s)` over the fundamental + strip given by ``strip=(a, b)``. + + Explanation + =========== + + This can be defined as + + .. math:: f(x) = \frac{1}{2\pi i} \int_{c - i\infty}^{c + i\infty} x^{-s} F(s) \mathrm{d}s, + + for any `c` in the fundamental strip. Under certain regularity + conditions on `F` and/or `f`, + this recovers `f` from its Mellin transform `F` + (and vice versa), for positive real `x`. + + One of `a` or `b` may be passed as ``None``; a suitable `c` will be + inferred. + + If the integral cannot be computed in closed form, this function returns + an unevaluated :class:`InverseMellinTransform` object. + + Note that this function will assume x to be positive and real, regardless + of the SymPy assumptions! + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + + Examples + ======== + + >>> from sympy import inverse_mellin_transform, oo, gamma + >>> from sympy.abc import x, s + >>> inverse_mellin_transform(gamma(s), s, x, (0, oo)) + exp(-x) + + The fundamental strip matters: + + >>> f = 1/(s**2 - 1) + >>> inverse_mellin_transform(f, s, x, (-oo, -1)) + x*(1 - 1/x**2)*Heaviside(x - 1)/2 + >>> inverse_mellin_transform(f, s, x, (-1, 1)) + -x*Heaviside(1 - x)/2 - Heaviside(x - 1)/(2*x) + >>> inverse_mellin_transform(f, s, x, (1, oo)) + (1/2 - x**2/2)*Heaviside(1 - x)/x + + See Also + ======== + + mellin_transform + hankel_transform, inverse_hankel_transform + """ + return InverseMellinTransform(F, s, x, strip[0], strip[1]).doit(**hints) + + +########################################################################## +# Fourier Transform +########################################################################## + +@_noconds_(True) +def _fourier_transform(f, x, k, a, b, name, simplify=True): + r""" + Compute a general Fourier-type transform + + .. math:: + + F(k) = a \int_{-\infty}^{\infty} e^{bixk} f(x)\, dx. + + For suitable choice of *a* and *b*, this reduces to the standard Fourier + and inverse Fourier transforms. + """ + F = integrate(a*f*exp(b*S.ImaginaryUnit*x*k), (x, S.NegativeInfinity, S.Infinity)) + + if not F.has(Integral): + return _simplify(F, simplify), S.true + + integral_f = integrate(f, (x, S.NegativeInfinity, S.Infinity)) + if integral_f in (S.NegativeInfinity, S.Infinity, S.NaN) or integral_f.has(Integral): + raise IntegralTransformError(name, f, 'function not integrable on real axis') + + if not F.is_Piecewise: + raise IntegralTransformError(name, f, 'could not compute integral') + + F, cond = F.args[0] + if F.has(Integral): + raise IntegralTransformError(name, f, 'integral in unexpected form') + + return _simplify(F, simplify), cond + + +class FourierTypeTransform(IntegralTransform): + """ Base class for Fourier transforms.""" + + def a(self): + raise NotImplementedError( + "Class %s must implement a(self) but does not" % self.__class__) + + def b(self): + raise NotImplementedError( + "Class %s must implement b(self) but does not" % self.__class__) + + def _compute_transform(self, f, x, k, **hints): + return _fourier_transform(f, x, k, + self.a(), self.b(), + self.__class__._name, **hints) + + def _as_integral(self, f, x, k): + a = self.a() + b = self.b() + return Integral(a*f*exp(b*S.ImaginaryUnit*x*k), (x, S.NegativeInfinity, S.Infinity)) + + +class FourierTransform(FourierTypeTransform): + """ + Class representing unevaluated Fourier transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute Fourier transforms, see the :func:`fourier_transform` + docstring. + """ + + _name = 'Fourier' + + def a(self): + return 1 + + def b(self): + return -2*S.Pi + + +def fourier_transform(f, x, k, **hints): + r""" + Compute the unitary, ordinary-frequency Fourier transform of ``f``, defined + as + + .. math:: F(k) = \int_{-\infty}^\infty f(x) e^{-2\pi i x k} \mathrm{d} x. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`FourierTransform` object. + + For other Fourier transform conventions, see the function + :func:`sympy.integrals.transforms._fourier_transform`. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import fourier_transform, exp + >>> from sympy.abc import x, k + >>> fourier_transform(exp(-x**2), x, k) + sqrt(pi)*exp(-pi**2*k**2) + >>> fourier_transform(exp(-x**2), x, k, noconds=False) + (sqrt(pi)*exp(-pi**2*k**2), True) + + See Also + ======== + + inverse_fourier_transform + sine_transform, inverse_sine_transform + cosine_transform, inverse_cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return FourierTransform(f, x, k).doit(**hints) + + +class InverseFourierTransform(FourierTypeTransform): + """ + Class representing unevaluated inverse Fourier transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse Fourier transforms, see the + :func:`inverse_fourier_transform` docstring. + """ + + _name = 'Inverse Fourier' + + def a(self): + return 1 + + def b(self): + return 2*S.Pi + + +def inverse_fourier_transform(F, k, x, **hints): + r""" + Compute the unitary, ordinary-frequency inverse Fourier transform of `F`, + defined as + + .. math:: f(x) = \int_{-\infty}^\infty F(k) e^{2\pi i x k} \mathrm{d} k. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`InverseFourierTransform` object. + + For other Fourier transform conventions, see the function + :func:`sympy.integrals.transforms._fourier_transform`. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import inverse_fourier_transform, exp, sqrt, pi + >>> from sympy.abc import x, k + >>> inverse_fourier_transform(sqrt(pi)*exp(-(pi*k)**2), k, x) + exp(-x**2) + >>> inverse_fourier_transform(sqrt(pi)*exp(-(pi*k)**2), k, x, noconds=False) + (exp(-x**2), True) + + See Also + ======== + + fourier_transform + sine_transform, inverse_sine_transform + cosine_transform, inverse_cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return InverseFourierTransform(F, k, x).doit(**hints) + + +########################################################################## +# Fourier Sine and Cosine Transform +########################################################################## + +@_noconds_(True) +def _sine_cosine_transform(f, x, k, a, b, K, name, simplify=True): + """ + Compute a general sine or cosine-type transform + F(k) = a int_0^oo b*sin(x*k) f(x) dx. + F(k) = a int_0^oo b*cos(x*k) f(x) dx. + + For suitable choice of a and b, this reduces to the standard sine/cosine + and inverse sine/cosine transforms. + """ + F = integrate(a*f*K(b*x*k), (x, S.Zero, S.Infinity)) + + if not F.has(Integral): + return _simplify(F, simplify), S.true + + if not F.is_Piecewise: + raise IntegralTransformError(name, f, 'could not compute integral') + + F, cond = F.args[0] + if F.has(Integral): + raise IntegralTransformError(name, f, 'integral in unexpected form') + + return _simplify(F, simplify), cond + + +class SineCosineTypeTransform(IntegralTransform): + """ + Base class for sine and cosine transforms. + Specify cls._kern. + """ + + def a(self): + raise NotImplementedError( + "Class %s must implement a(self) but does not" % self.__class__) + + def b(self): + raise NotImplementedError( + "Class %s must implement b(self) but does not" % self.__class__) + + + def _compute_transform(self, f, x, k, **hints): + return _sine_cosine_transform(f, x, k, + self.a(), self.b(), + self.__class__._kern, + self.__class__._name, **hints) + + def _as_integral(self, f, x, k): + a = self.a() + b = self.b() + K = self.__class__._kern + return Integral(a*f*K(b*x*k), (x, S.Zero, S.Infinity)) + + +class SineTransform(SineCosineTypeTransform): + """ + Class representing unevaluated sine transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute sine transforms, see the :func:`sine_transform` + docstring. + """ + + _name = 'Sine' + _kern = sin + + def a(self): + return sqrt(2)/sqrt(pi) + + def b(self): + return S.One + + +def sine_transform(f, x, k, **hints): + r""" + Compute the unitary, ordinary-frequency sine transform of `f`, defined + as + + .. math:: F(k) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty f(x) \sin(2\pi x k) \mathrm{d} x. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`SineTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import sine_transform, exp + >>> from sympy.abc import x, k, a + >>> sine_transform(x*exp(-a*x**2), x, k) + sqrt(2)*k*exp(-k**2/(4*a))/(4*a**(3/2)) + >>> sine_transform(x**(-a), x, k) + 2**(1/2 - a)*k**(a - 1)*gamma(1 - a/2)/gamma(a/2 + 1/2) + + See Also + ======== + + fourier_transform, inverse_fourier_transform + inverse_sine_transform + cosine_transform, inverse_cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return SineTransform(f, x, k).doit(**hints) + + +class InverseSineTransform(SineCosineTypeTransform): + """ + Class representing unevaluated inverse sine transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse sine transforms, see the + :func:`inverse_sine_transform` docstring. + """ + + _name = 'Inverse Sine' + _kern = sin + + def a(self): + return sqrt(2)/sqrt(pi) + + def b(self): + return S.One + + +def inverse_sine_transform(F, k, x, **hints): + r""" + Compute the unitary, ordinary-frequency inverse sine transform of `F`, + defined as + + .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \sin(2\pi x k) \mathrm{d} k. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`InverseSineTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import inverse_sine_transform, exp, sqrt, gamma + >>> from sympy.abc import x, k, a + >>> inverse_sine_transform(2**((1-2*a)/2)*k**(a - 1)* + ... gamma(-a/2 + 1)/gamma((a+1)/2), k, x) + x**(-a) + >>> inverse_sine_transform(sqrt(2)*k*exp(-k**2/(4*a))/(4*sqrt(a)**3), k, x) + x*exp(-a*x**2) + + See Also + ======== + + fourier_transform, inverse_fourier_transform + sine_transform + cosine_transform, inverse_cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return InverseSineTransform(F, k, x).doit(**hints) + + +class CosineTransform(SineCosineTypeTransform): + """ + Class representing unevaluated cosine transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute cosine transforms, see the :func:`cosine_transform` + docstring. + """ + + _name = 'Cosine' + _kern = cos + + def a(self): + return sqrt(2)/sqrt(pi) + + def b(self): + return S.One + + +def cosine_transform(f, x, k, **hints): + r""" + Compute the unitary, ordinary-frequency cosine transform of `f`, defined + as + + .. math:: F(k) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty f(x) \cos(2\pi x k) \mathrm{d} x. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`CosineTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import cosine_transform, exp, sqrt, cos + >>> from sympy.abc import x, k, a + >>> cosine_transform(exp(-a*x), x, k) + sqrt(2)*a/(sqrt(pi)*(a**2 + k**2)) + >>> cosine_transform(exp(-a*sqrt(x))*cos(a*sqrt(x)), x, k) + a*exp(-a**2/(2*k))/(2*k**(3/2)) + + See Also + ======== + + fourier_transform, inverse_fourier_transform, + sine_transform, inverse_sine_transform + inverse_cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return CosineTransform(f, x, k).doit(**hints) + + +class InverseCosineTransform(SineCosineTypeTransform): + """ + Class representing unevaluated inverse cosine transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse cosine transforms, see the + :func:`inverse_cosine_transform` docstring. + """ + + _name = 'Inverse Cosine' + _kern = cos + + def a(self): + return sqrt(2)/sqrt(pi) + + def b(self): + return S.One + + +def inverse_cosine_transform(F, k, x, **hints): + r""" + Compute the unitary, ordinary-frequency inverse cosine transform of `F`, + defined as + + .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \cos(2\pi x k) \mathrm{d} k. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`InverseCosineTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import inverse_cosine_transform, sqrt, pi + >>> from sympy.abc import x, k, a + >>> inverse_cosine_transform(sqrt(2)*a/(sqrt(pi)*(a**2 + k**2)), k, x) + exp(-a*x) + >>> inverse_cosine_transform(1/sqrt(k), k, x) + 1/sqrt(x) + + See Also + ======== + + fourier_transform, inverse_fourier_transform, + sine_transform, inverse_sine_transform + cosine_transform + hankel_transform, inverse_hankel_transform + mellin_transform, laplace_transform + """ + return InverseCosineTransform(F, k, x).doit(**hints) + + +########################################################################## +# Hankel Transform +########################################################################## + +@_noconds_(True) +def _hankel_transform(f, r, k, nu, name, simplify=True): + r""" + Compute a general Hankel transform + + .. math:: F_\nu(k) = \int_{0}^\infty f(r) J_\nu(k r) r \mathrm{d} r. + """ + F = integrate(f*besselj(nu, k*r)*r, (r, S.Zero, S.Infinity)) + + if not F.has(Integral): + return _simplify(F, simplify), S.true + + if not F.is_Piecewise: + raise IntegralTransformError(name, f, 'could not compute integral') + + F, cond = F.args[0] + if F.has(Integral): + raise IntegralTransformError(name, f, 'integral in unexpected form') + + return _simplify(F, simplify), cond + + +class HankelTypeTransform(IntegralTransform): + """ + Base class for Hankel transforms. + """ + + def doit(self, **hints): + return self._compute_transform(self.function, + self.function_variable, + self.transform_variable, + self.args[3], + **hints) + + def _compute_transform(self, f, r, k, nu, **hints): + return _hankel_transform(f, r, k, nu, self._name, **hints) + + def _as_integral(self, f, r, k, nu): + return Integral(f*besselj(nu, k*r)*r, (r, S.Zero, S.Infinity)) + + @property + def as_integral(self): + return self._as_integral(self.function, + self.function_variable, + self.transform_variable, + self.args[3]) + + +class HankelTransform(HankelTypeTransform): + """ + Class representing unevaluated Hankel transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute Hankel transforms, see the :func:`hankel_transform` + docstring. + """ + + _name = 'Hankel' + + +def hankel_transform(f, r, k, nu, **hints): + r""" + Compute the Hankel transform of `f`, defined as + + .. math:: F_\nu(k) = \int_{0}^\infty f(r) J_\nu(k r) r \mathrm{d} r. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`HankelTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import hankel_transform, inverse_hankel_transform + >>> from sympy import exp + >>> from sympy.abc import r, k, m, nu, a + + >>> ht = hankel_transform(1/r**m, r, k, nu) + >>> ht + 2*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/(2**m*gamma(m/2 + nu/2)) + + >>> inverse_hankel_transform(ht, k, r, nu) + r**(-m) + + >>> ht = hankel_transform(exp(-a*r), r, k, 0) + >>> ht + a/(k**3*(a**2/k**2 + 1)**(3/2)) + + >>> inverse_hankel_transform(ht, k, r, 0) + exp(-a*r) + + See Also + ======== + + fourier_transform, inverse_fourier_transform + sine_transform, inverse_sine_transform + cosine_transform, inverse_cosine_transform + inverse_hankel_transform + mellin_transform, laplace_transform + """ + return HankelTransform(f, r, k, nu).doit(**hints) + + +class InverseHankelTransform(HankelTypeTransform): + """ + Class representing unevaluated inverse Hankel transforms. + + For usage of this class, see the :class:`IntegralTransform` docstring. + + For how to compute inverse Hankel transforms, see the + :func:`inverse_hankel_transform` docstring. + """ + + _name = 'Inverse Hankel' + + +def inverse_hankel_transform(F, k, r, nu, **hints): + r""" + Compute the inverse Hankel transform of `F` defined as + + .. math:: f(r) = \int_{0}^\infty F_\nu(k) J_\nu(k r) k \mathrm{d} k. + + Explanation + =========== + + If the transform cannot be computed in closed form, this + function returns an unevaluated :class:`InverseHankelTransform` object. + + For a description of possible hints, refer to the docstring of + :func:`sympy.integrals.transforms.IntegralTransform.doit`. + Note that for this transform, by default ``noconds=True``. + + Examples + ======== + + >>> from sympy import hankel_transform, inverse_hankel_transform + >>> from sympy import exp + >>> from sympy.abc import r, k, m, nu, a + + >>> ht = hankel_transform(1/r**m, r, k, nu) + >>> ht + 2*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/(2**m*gamma(m/2 + nu/2)) + + >>> inverse_hankel_transform(ht, k, r, nu) + r**(-m) + + >>> ht = hankel_transform(exp(-a*r), r, k, 0) + >>> ht + a/(k**3*(a**2/k**2 + 1)**(3/2)) + + >>> inverse_hankel_transform(ht, k, r, 0) + exp(-a*r) + + See Also + ======== + + fourier_transform, inverse_fourier_transform + sine_transform, inverse_sine_transform + cosine_transform, inverse_cosine_transform + hankel_transform + mellin_transform, laplace_transform + """ + return InverseHankelTransform(F, k, r, nu).doit(**hints) + + +########################################################################## +# Laplace Transform +########################################################################## + +# Stub classes and functions that used to be here +import sympy.integrals.laplace as _laplace + +LaplaceTransform = _laplace.LaplaceTransform +laplace_transform = _laplace.laplace_transform +laplace_correspondence = _laplace.laplace_correspondence +laplace_initial_conds = _laplace.laplace_initial_conds +InverseLaplaceTransform = _laplace.InverseLaplaceTransform +inverse_laplace_transform = _laplace.inverse_laplace_transform diff --git a/lib/python3.11/site-packages/sympy/integrals/trigonometry.py b/lib/python3.11/site-packages/sympy/integrals/trigonometry.py new file mode 100644 index 0000000000000000000000000000000000000000..dd6389bcc79f28ed6c255546685da1a0e061c327 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/integrals/trigonometry.py @@ -0,0 +1,335 @@ +from sympy.core import cacheit, Dummy, Ne, Integer, Rational, S, Wild +from sympy.functions import binomial, sin, cos, Piecewise, Abs +from .integrals import integrate + +# TODO sin(a*x)*cos(b*x) -> sin((a+b)x) + sin((a-b)x) ? + +# creating, each time, Wild's and sin/cos/Mul is expensive. Also, our match & +# subs are very slow when not cached, and if we create Wild each time, we +# effectively block caching. +# +# so we cache the pattern + +# need to use a function instead of lamda since hash of lambda changes on +# each call to _pat_sincos +def _integer_instance(n): + return isinstance(n, Integer) + +@cacheit +def _pat_sincos(x): + a = Wild('a', exclude=[x]) + n, m = [Wild(s, exclude=[x], properties=[_integer_instance]) + for s in 'nm'] + pat = sin(a*x)**n * cos(a*x)**m + return pat, a, n, m + +_u = Dummy('u') + + +def trigintegrate(f, x, conds='piecewise'): + """ + Integrate f = Mul(trig) over x. + + Examples + ======== + + >>> from sympy import sin, cos, tan, sec + >>> from sympy.integrals.trigonometry import trigintegrate + >>> from sympy.abc import x + + >>> trigintegrate(sin(x)*cos(x), x) + sin(x)**2/2 + + >>> trigintegrate(sin(x)**2, x) + x/2 - sin(x)*cos(x)/2 + + >>> trigintegrate(tan(x)*sec(x), x) + 1/cos(x) + + >>> trigintegrate(sin(x)*tan(x), x) + -log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - sin(x) + + References + ========== + + .. [1] https://en.wikibooks.org/wiki/Calculus/Integration_techniques + + See Also + ======== + + sympy.integrals.integrals.Integral.doit + sympy.integrals.integrals.Integral + """ + pat, a, n, m = _pat_sincos(x) + + f = f.rewrite('sincos') + M = f.match(pat) + + if M is None: + return + + n, m = M[n], M[m] + if n.is_zero and m.is_zero: + return x + zz = x if n.is_zero else S.Zero + + a = M[a] + + if n.is_odd or m.is_odd: + u = _u + n_, m_ = n.is_odd, m.is_odd + + # take smallest n or m -- to choose simplest substitution + if n_ and m_: + + # Make sure to choose the positive one + # otherwise an incorrect integral can occur. + if n < 0 and m > 0: + m_ = True + n_ = False + elif m < 0 and n > 0: + n_ = True + m_ = False + # Both are negative so choose the smallest n or m + # in absolute value for simplest substitution. + elif (n < 0 and m < 0): + n_ = n > m + m_ = not (n > m) + + # Both n and m are odd and positive + else: + n_ = (n < m) # NB: careful here, one of the + m_ = not (n < m) # conditions *must* be true + + # n m u=C (n-1)/2 m + # S(x) * C(x) dx --> -(1-u^2) * u du + if n_: + ff = -(1 - u**2)**((n - 1)/2) * u**m + uu = cos(a*x) + + # n m u=S n (m-1)/2 + # S(x) * C(x) dx --> u * (1-u^2) du + elif m_: + ff = u**n * (1 - u**2)**((m - 1)/2) + uu = sin(a*x) + + fi = integrate(ff, u) # XXX cyclic deps + fx = fi.subs(u, uu) + if conds == 'piecewise': + return Piecewise((fx / a, Ne(a, 0)), (zz, True)) + return fx / a + + # n & m are both even + # + # 2k 2m 2l 2l + # we transform S (x) * C (x) into terms with only S (x) or C (x) + # + # example: + # 100 4 100 2 2 100 4 2 + # S (x) * C (x) = S (x) * (1-S (x)) = S (x) * (1 + S (x) - 2*S (x)) + # + # 104 102 100 + # = S (x) - 2*S (x) + S (x) + # 2k + # then S is integrated with recursive formula + + # take largest n or m -- to choose simplest substitution + n_ = (Abs(n) > Abs(m)) + m_ = (Abs(m) > Abs(n)) + res = S.Zero + + if n_: + # 2k 2 k i 2i + # C = (1 - S ) = sum(i, (-) * B(k, i) * S ) + if m > 0: + for i in range(0, m//2 + 1): + res += (S.NegativeOne**i * binomial(m//2, i) * + _sin_pow_integrate(n + 2*i, x)) + + elif m == 0: + res = _sin_pow_integrate(n, x) + else: + + # m < 0 , |n| > |m| + # / + # | + # | m n + # | cos (x) sin (x) dx = + # | + # | + #/ + # / + # | + # -1 m+1 n-1 n - 1 | m+2 n-2 + # ________ cos (x) sin (x) + _______ | cos (x) sin (x) dx + # | + # m + 1 m + 1 | + # / + + res = (Rational(-1, m + 1) * cos(x)**(m + 1) * sin(x)**(n - 1) + + Rational(n - 1, m + 1) * + trigintegrate(cos(x)**(m + 2)*sin(x)**(n - 2), x)) + + elif m_: + # 2k 2 k i 2i + # S = (1 - C ) = sum(i, (-) * B(k, i) * C ) + if n > 0: + + # / / + # | | + # | m n | -m n + # | cos (x)*sin (x) dx or | cos (x) * sin (x) dx + # | | + # / / + # + # |m| > |n| ; m, n >0 ; m, n belong to Z - {0} + # n 2 + # sin (x) term is expanded here in terms of cos (x), + # and then integrated. + # + + for i in range(0, n//2 + 1): + res += (S.NegativeOne**i * binomial(n//2, i) * + _cos_pow_integrate(m + 2*i, x)) + + elif n == 0: + + # / + # | + # | 1 + # | _ _ _ + # | m + # | cos (x) + # / + # + + res = _cos_pow_integrate(m, x) + else: + + # n < 0 , |m| > |n| + # / + # | + # | m n + # | cos (x) sin (x) dx = + # | + # | + #/ + # / + # | + # 1 m-1 n+1 m - 1 | m-2 n+2 + # _______ cos (x) sin (x) + _______ | cos (x) sin (x) dx + # | + # n + 1 n + 1 | + # / + + res = (Rational(1, n + 1) * cos(x)**(m - 1)*sin(x)**(n + 1) + + Rational(m - 1, n + 1) * + trigintegrate(cos(x)**(m - 2)*sin(x)**(n + 2), x)) + + else: + if m == n: + ##Substitute sin(2x)/2 for sin(x)cos(x) and then Integrate. + res = integrate((sin(2*x)*S.Half)**m, x) + elif (m == -n): + if n < 0: + # Same as the scheme described above. + # the function argument to integrate in the end will + # be 1, this cannot be integrated by trigintegrate. + # Hence use sympy.integrals.integrate. + res = (Rational(1, n + 1) * cos(x)**(m - 1) * sin(x)**(n + 1) + + Rational(m - 1, n + 1) * + integrate(cos(x)**(m - 2) * sin(x)**(n + 2), x)) + else: + res = (Rational(-1, m + 1) * cos(x)**(m + 1) * sin(x)**(n - 1) + + Rational(n - 1, m + 1) * + integrate(cos(x)**(m + 2)*sin(x)**(n - 2), x)) + if conds == 'piecewise': + return Piecewise((res.subs(x, a*x) / a, Ne(a, 0)), (zz, True)) + return res.subs(x, a*x) / a + + +def _sin_pow_integrate(n, x): + if n > 0: + if n == 1: + #Recursion break + return -cos(x) + + # n > 0 + # / / + # | | + # | n -1 n-1 n - 1 | n-2 + # | sin (x) dx = ______ cos (x) sin (x) + _______ | sin (x) dx + # | | + # | n n | + #/ / + # + # + + return (Rational(-1, n) * cos(x) * sin(x)**(n - 1) + + Rational(n - 1, n) * _sin_pow_integrate(n - 2, x)) + + if n < 0: + if n == -1: + ##Make sure this does not come back here again. + ##Recursion breaks here or at n==0. + return trigintegrate(1/sin(x), x) + + # n < 0 + # / / + # | | + # | n 1 n+1 n + 2 | n+2 + # | sin (x) dx = _______ cos (x) sin (x) + _______ | sin (x) dx + # | | + # | n + 1 n + 1 | + #/ / + # + + return (Rational(1, n + 1) * cos(x) * sin(x)**(n + 1) + + Rational(n + 2, n + 1) * _sin_pow_integrate(n + 2, x)) + + else: + #n == 0 + #Recursion break. + return x + + +def _cos_pow_integrate(n, x): + if n > 0: + if n == 1: + #Recursion break. + return sin(x) + + # n > 0 + # / / + # | | + # | n 1 n-1 n - 1 | n-2 + # | sin (x) dx = ______ sin (x) cos (x) + _______ | cos (x) dx + # | | + # | n n | + #/ / + # + + return (Rational(1, n) * sin(x) * cos(x)**(n - 1) + + Rational(n - 1, n) * _cos_pow_integrate(n - 2, x)) + + if n < 0: + if n == -1: + ##Recursion break + return trigintegrate(1/cos(x), x) + + # n < 0 + # / / + # | | + # | n -1 n+1 n + 2 | n+2 + # | cos (x) dx = _______ sin (x) cos (x) + _______ | cos (x) dx + # | | + # | n + 1 n + 1 | + #/ / + # + + return (Rational(-1, n + 1) * sin(x) * cos(x)**(n + 1) + + Rational(n + 2, n + 1) * _cos_pow_integrate(n + 2, x)) + else: + # n == 0 + #Recursion Break. + return x diff --git a/lib/python3.11/site-packages/sympy/liealgebras/__pycache__/__init__.cpython-311.pyc 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simplify_logic, bool_map, true, false, + gateinputcount) +from .inference import satisfiable + +__all__ = [ + 'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor', + 'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic', + 'bool_map', 'true', 'false', 'gateinputcount', + + 'satisfiable', +] diff --git a/lib/python3.11/site-packages/sympy/logic/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..e51a856feccf5d8bd5a498f7bd4e8f7c36ed84f3 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/logic/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/logic/__pycache__/inference.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/__pycache__/inference.cpython-311.pyc new file mode 100644 index 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branching rules, +efficient unit propagation. + +References: + - https://en.wikipedia.org/wiki/DPLL_algorithm + - https://www.researchgate.net/publication/242384772_Implementations_of_the_DPLL_Algorithm +""" + +from sympy.core.sorting import default_sort_key +from sympy.logic.boolalg import Or, Not, conjuncts, disjuncts, to_cnf, \ + to_int_repr, _find_predicates +from sympy.assumptions.cnf import CNF +from sympy.logic.inference import pl_true, literal_symbol + + +def dpll_satisfiable(expr): + """ + Check satisfiability of a propositional sentence. + It returns a model rather than True when it succeeds + + >>> from sympy.abc import A, B + >>> from sympy.logic.algorithms.dpll import dpll_satisfiable + >>> dpll_satisfiable(A & ~B) + {A: True, B: False} + >>> dpll_satisfiable(A & ~A) + False + + """ + if not isinstance(expr, CNF): + clauses = conjuncts(to_cnf(expr)) + else: + clauses = expr.clauses + if False in clauses: + return False + symbols = sorted(_find_predicates(expr), key=default_sort_key) + symbols_int_repr = set(range(1, len(symbols) + 1)) + clauses_int_repr = to_int_repr(clauses, symbols) + result = dpll_int_repr(clauses_int_repr, symbols_int_repr, {}) + if not result: + return result + output = {} + for key in result: + output.update({symbols[key - 1]: result[key]}) + return output + + +def dpll(clauses, symbols, model): + """ + Compute satisfiability in a partial model. + Clauses is an array of conjuncts. + + >>> from sympy.abc import A, B, D + >>> from sympy.logic.algorithms.dpll import dpll + >>> dpll([A, B, D], [A, B], {D: False}) + False + + """ + # compute DP kernel + P, value = find_unit_clause(clauses, model) + while P: + model.update({P: value}) + symbols.remove(P) + if not value: + P = ~P + clauses = unit_propagate(clauses, P) + P, value = find_unit_clause(clauses, model) + P, value = find_pure_symbol(symbols, clauses) + while P: + model.update({P: value}) + symbols.remove(P) + if not value: + P = ~P + clauses = unit_propagate(clauses, P) + P, value = find_pure_symbol(symbols, clauses) + # end DP kernel + unknown_clauses = [] + for c in clauses: + val = pl_true(c, model) + if val is False: + return False + if val is not True: + unknown_clauses.append(c) + if not unknown_clauses: + return model + if not clauses: + return model + P = symbols.pop() + model_copy = model.copy() + model.update({P: True}) + model_copy.update({P: False}) + symbols_copy = symbols[:] + return (dpll(unit_propagate(unknown_clauses, P), symbols, model) or + dpll(unit_propagate(unknown_clauses, Not(P)), symbols_copy, model_copy)) + + +def dpll_int_repr(clauses, symbols, model): + """ + Compute satisfiability in a partial model. + Arguments are expected to be in integer representation + + >>> from sympy.logic.algorithms.dpll import dpll_int_repr + >>> dpll_int_repr([{1}, {2}, {3}], {1, 2}, {3: False}) + False + + """ + # compute DP kernel + P, value = find_unit_clause_int_repr(clauses, model) + while P: + model.update({P: value}) + symbols.remove(P) + if not value: + P = -P + clauses = unit_propagate_int_repr(clauses, P) + P, value = find_unit_clause_int_repr(clauses, model) + P, value = find_pure_symbol_int_repr(symbols, clauses) + while P: + model.update({P: value}) + symbols.remove(P) + if not value: + P = -P + clauses = unit_propagate_int_repr(clauses, P) + P, value = find_pure_symbol_int_repr(symbols, clauses) + # end DP kernel + unknown_clauses = [] + for c in clauses: + val = pl_true_int_repr(c, model) + if val is False: + return False + if val is not True: + unknown_clauses.append(c) + if not unknown_clauses: + return model + P = symbols.pop() + model_copy = model.copy() + model.update({P: True}) + model_copy.update({P: False}) + symbols_copy = symbols.copy() + return (dpll_int_repr(unit_propagate_int_repr(unknown_clauses, P), symbols, model) or + dpll_int_repr(unit_propagate_int_repr(unknown_clauses, -P), symbols_copy, model_copy)) + +### helper methods for DPLL + + +def pl_true_int_repr(clause, model={}): + """ + Lightweight version of pl_true. + Argument clause represents the set of args of an Or clause. This is used + inside dpll_int_repr, it is not meant to be used directly. + + >>> from sympy.logic.algorithms.dpll import pl_true_int_repr + >>> pl_true_int_repr({1, 2}, {1: False}) + >>> pl_true_int_repr({1, 2}, {1: False, 2: False}) + False + + """ + result = False + for lit in clause: + if lit < 0: + p = model.get(-lit) + if p is not None: + p = not p + else: + p = model.get(lit) + if p is True: + return True + elif p is None: + result = None + return result + + +def unit_propagate(clauses, symbol): + """ + Returns an equivalent set of clauses + If a set of clauses contains the unit clause l, the other clauses are + simplified by the application of the two following rules: + + 1. every clause containing l is removed + 2. in every clause that contains ~l this literal is deleted + + Arguments are expected to be in CNF. + + >>> from sympy.abc import A, B, D + >>> from sympy.logic.algorithms.dpll import unit_propagate + >>> unit_propagate([A | B, D | ~B, B], B) + [D, B] + + """ + output = [] + for c in clauses: + if c.func != Or: + output.append(c) + continue + for arg in c.args: + if arg == ~symbol: + output.append(Or(*[x for x in c.args if x != ~symbol])) + break + if arg == symbol: + break + else: + output.append(c) + return output + + +def unit_propagate_int_repr(clauses, s): + """ + Same as unit_propagate, but arguments are expected to be in integer + representation + + >>> from sympy.logic.algorithms.dpll import unit_propagate_int_repr + >>> unit_propagate_int_repr([{1, 2}, {3, -2}, {2}], 2) + [{3}] + + """ + negated = {-s} + return [clause - negated for clause in clauses if s not in clause] + + +def find_pure_symbol(symbols, unknown_clauses): + """ + Find a symbol and its value if it appears only as a positive literal + (or only as a negative) in clauses. + + >>> from sympy.abc import A, B, D + >>> from sympy.logic.algorithms.dpll import find_pure_symbol + >>> find_pure_symbol([A, B, D], [A|~B,~B|~D,D|A]) + (A, True) + + """ + for sym in symbols: + found_pos, found_neg = False, False + for c in unknown_clauses: + if not found_pos and sym in disjuncts(c): + found_pos = True + if not found_neg and Not(sym) in disjuncts(c): + found_neg = True + if found_pos != found_neg: + return sym, found_pos + return None, None + + +def find_pure_symbol_int_repr(symbols, unknown_clauses): + """ + Same as find_pure_symbol, but arguments are expected + to be in integer representation + + >>> from sympy.logic.algorithms.dpll import find_pure_symbol_int_repr + >>> find_pure_symbol_int_repr({1,2,3}, + ... [{1, -2}, {-2, -3}, {3, 1}]) + (1, True) + + """ + all_symbols = set().union(*unknown_clauses) + found_pos = all_symbols.intersection(symbols) + found_neg = all_symbols.intersection([-s for s in symbols]) + for p in found_pos: + if -p not in found_neg: + return p, True + for p in found_neg: + if -p not in found_pos: + return -p, False + return None, None + + +def find_unit_clause(clauses, model): + """ + A unit clause has only 1 variable that is not bound in the model. + + >>> from sympy.abc import A, B, D + >>> from sympy.logic.algorithms.dpll import find_unit_clause + >>> find_unit_clause([A | B | D, B | ~D, A | ~B], {A:True}) + (B, False) + + """ + for clause in clauses: + num_not_in_model = 0 + for literal in disjuncts(clause): + sym = literal_symbol(literal) + if sym not in model: + num_not_in_model += 1 + P, value = sym, not isinstance(literal, Not) + if num_not_in_model == 1: + return P, value + return None, None + + +def find_unit_clause_int_repr(clauses, model): + """ + Same as find_unit_clause, but arguments are expected to be in + integer representation. + + >>> from sympy.logic.algorithms.dpll import find_unit_clause_int_repr + >>> find_unit_clause_int_repr([{1, 2, 3}, + ... {2, -3}, {1, -2}], {1: True}) + (2, False) + + """ + bound = set(model) | {-sym for sym in model} + for clause in clauses: + unbound = clause - bound + if len(unbound) == 1: + p = unbound.pop() + if p < 0: + return -p, False + else: + return p, True + return None, None diff --git a/lib/python3.11/site-packages/sympy/logic/algorithms/dpll2.py b/lib/python3.11/site-packages/sympy/logic/algorithms/dpll2.py new file mode 100644 index 0000000000000000000000000000000000000000..75115e01efb221d765e81b195fcf20293c26abee --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/algorithms/dpll2.py @@ -0,0 +1,684 @@ +"""Implementation of DPLL algorithm + +Features: + - Clause learning + - Watch literal scheme + - VSIDS heuristic + +References: + - https://en.wikipedia.org/wiki/DPLL_algorithm +""" + +from collections import defaultdict +from heapq import heappush, heappop + +from sympy.core.sorting import ordered +from sympy.assumptions.cnf import EncodedCNF + +from sympy.logic.algorithms.lra_theory import LRASolver + + +def dpll_satisfiable(expr, all_models=False, use_lra_theory=False): + """ + Check satisfiability of a propositional sentence. + It returns a model rather than True when it succeeds. + Returns a generator of all models if all_models is True. + + Examples + ======== + + >>> from sympy.abc import A, B + >>> from sympy.logic.algorithms.dpll2 import dpll_satisfiable + >>> dpll_satisfiable(A & ~B) + {A: True, B: False} + >>> dpll_satisfiable(A & ~A) + False + + """ + if not isinstance(expr, EncodedCNF): + exprs = EncodedCNF() + exprs.add_prop(expr) + expr = exprs + + # Return UNSAT when False (encoded as 0) is present in the CNF + if {0} in expr.data: + if all_models: + return (f for f in [False]) + return False + + if use_lra_theory: + lra, immediate_conflicts = LRASolver.from_encoded_cnf(expr) + else: + lra = None + immediate_conflicts = [] + solver = SATSolver(expr.data + immediate_conflicts, expr.variables, set(), expr.symbols, lra_theory=lra) + models = solver._find_model() + + if all_models: + return _all_models(models) + + try: + return next(models) + except StopIteration: + return False + + # Uncomment to confirm the solution is valid (hitting set for the clauses) + #else: + #for cls in clauses_int_repr: + #assert solver.var_settings.intersection(cls) + + +def _all_models(models): + satisfiable = False + try: + while True: + yield next(models) + satisfiable = True + except StopIteration: + if not satisfiable: + yield False + + +class SATSolver: + """ + Class for representing a SAT solver capable of + finding a model to a boolean theory in conjunctive + normal form. + """ + + def __init__(self, clauses, variables, var_settings, symbols=None, + heuristic='vsids', clause_learning='none', INTERVAL=500, + lra_theory = None): + + self.var_settings = var_settings + self.heuristic = heuristic + self.is_unsatisfied = False + self._unit_prop_queue = [] + self.update_functions = [] + self.INTERVAL = INTERVAL + + if symbols is None: + self.symbols = list(ordered(variables)) + else: + self.symbols = symbols + + self._initialize_variables(variables) + self._initialize_clauses(clauses) + + if 'vsids' == heuristic: + self._vsids_init() + self.heur_calculate = self._vsids_calculate + self.heur_lit_assigned = self._vsids_lit_assigned + self.heur_lit_unset = self._vsids_lit_unset + self.heur_clause_added = self._vsids_clause_added + + # Note: Uncomment this if/when clause learning is enabled + #self.update_functions.append(self._vsids_decay) + + else: + raise NotImplementedError + + if 'simple' == clause_learning: + self.add_learned_clause = self._simple_add_learned_clause + self.compute_conflict = self._simple_compute_conflict + self.update_functions.append(self._simple_clean_clauses) + elif 'none' == clause_learning: + self.add_learned_clause = lambda x: None + self.compute_conflict = lambda: None + else: + raise NotImplementedError + + # Create the base level + self.levels = [Level(0)] + self._current_level.varsettings = var_settings + + # Keep stats + self.num_decisions = 0 + self.num_learned_clauses = 0 + self.original_num_clauses = len(self.clauses) + + self.lra = lra_theory + + def _initialize_variables(self, variables): + """Set up the variable data structures needed.""" + self.sentinels = defaultdict(set) + self.occurrence_count = defaultdict(int) + self.variable_set = [False] * (len(variables) + 1) + + def _initialize_clauses(self, clauses): + """Set up the clause data structures needed. + + For each clause, the following changes are made: + - Unit clauses are queued for propagation right away. + - Non-unit clauses have their first and last literals set as sentinels. + - The number of clauses a literal appears in is computed. + """ + self.clauses = [list(clause) for clause in clauses] + + for i, clause in enumerate(self.clauses): + + # Handle the unit clauses + if 1 == len(clause): + self._unit_prop_queue.append(clause[0]) + continue + + self.sentinels[clause[0]].add(i) + self.sentinels[clause[-1]].add(i) + + for lit in clause: + self.occurrence_count[lit] += 1 + + def _find_model(self): + """ + Main DPLL loop. Returns a generator of models. + + Variables are chosen successively, and assigned to be either + True or False. If a solution is not found with this setting, + the opposite is chosen and the search continues. The solver + halts when every variable has a setting. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> list(l._find_model()) + [{1: True, 2: False, 3: False}, {1: True, 2: True, 3: True}] + + >>> from sympy.abc import A, B, C + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set(), [A, B, C]) + >>> list(l._find_model()) + [{A: True, B: False, C: False}, {A: True, B: True, C: True}] + + """ + + # We use this variable to keep track of if we should flip a + # variable setting in successive rounds + flip_var = False + + # Check if unit prop says the theory is unsat right off the bat + self._simplify() + if self.is_unsatisfied: + return + + # While the theory still has clauses remaining + while True: + # Perform cleanup / fixup at regular intervals + if self.num_decisions % self.INTERVAL == 0: + for func in self.update_functions: + func() + + if flip_var: + # We have just backtracked and we are trying to opposite literal + flip_var = False + lit = self._current_level.decision + + else: + # Pick a literal to set + lit = self.heur_calculate() + self.num_decisions += 1 + + # Stopping condition for a satisfying theory + if 0 == lit: + + # check if assignment satisfies lra theory + if self.lra: + for enc_var in self.var_settings: + res = self.lra.assert_lit(enc_var) + if res is not None: + break + res = self.lra.check() + self.lra.reset_bounds() + else: + res = None + if res is None or res[0]: + yield {self.symbols[abs(lit) - 1]: + lit > 0 for lit in self.var_settings} + else: + self._simple_add_learned_clause(res[1]) + + while self._current_level.flipped: + self._undo() + if len(self.levels) == 1: + return + flip_lit = -self._current_level.decision + self._undo() + self.levels.append(Level(flip_lit, flipped=True)) + flip_var = True + continue + + # Start the new decision level + self.levels.append(Level(lit)) + + # Assign the literal, updating the clauses it satisfies + self._assign_literal(lit) + + # _simplify the theory + self._simplify() + + # Check if we've made the theory unsat + if self.is_unsatisfied: + + self.is_unsatisfied = False + + # We unroll all of the decisions until we can flip a literal + while self._current_level.flipped: + self._undo() + + # If we've unrolled all the way, the theory is unsat + if 1 == len(self.levels): + return + + # Detect and add a learned clause + self.add_learned_clause(self.compute_conflict()) + + # Try the opposite setting of the most recent decision + flip_lit = -self._current_level.decision + self._undo() + self.levels.append(Level(flip_lit, flipped=True)) + flip_var = True + + ######################## + # Helper Methods # + ######################## + @property + def _current_level(self): + """The current decision level data structure + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{1}, {2}], {1, 2}, set()) + >>> next(l._find_model()) + {1: True, 2: True} + >>> l._current_level.decision + 0 + >>> l._current_level.flipped + False + >>> l._current_level.var_settings + {1, 2} + + """ + return self.levels[-1] + + def _clause_sat(self, cls): + """Check if a clause is satisfied by the current variable setting. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{1}, {-1}], {1}, set()) + >>> try: + ... next(l._find_model()) + ... except StopIteration: + ... pass + >>> l._clause_sat(0) + False + >>> l._clause_sat(1) + True + + """ + for lit in self.clauses[cls]: + if lit in self.var_settings: + return True + return False + + def _is_sentinel(self, lit, cls): + """Check if a literal is a sentinel of a given clause. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> next(l._find_model()) + {1: True, 2: False, 3: False} + >>> l._is_sentinel(2, 3) + True + >>> l._is_sentinel(-3, 1) + False + + """ + return cls in self.sentinels[lit] + + def _assign_literal(self, lit): + """Make a literal assignment. + + The literal assignment must be recorded as part of the current + decision level. Additionally, if the literal is marked as a + sentinel of any clause, then a new sentinel must be chosen. If + this is not possible, then unit propagation is triggered and + another literal is added to the queue to be set in the future. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> next(l._find_model()) + {1: True, 2: False, 3: False} + >>> l.var_settings + {-3, -2, 1} + + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> l._assign_literal(-1) + >>> try: + ... next(l._find_model()) + ... except StopIteration: + ... pass + >>> l.var_settings + {-1} + + """ + self.var_settings.add(lit) + self._current_level.var_settings.add(lit) + self.variable_set[abs(lit)] = True + self.heur_lit_assigned(lit) + + sentinel_list = list(self.sentinels[-lit]) + + for cls in sentinel_list: + if not self._clause_sat(cls): + other_sentinel = None + for newlit in self.clauses[cls]: + if newlit != -lit: + if self._is_sentinel(newlit, cls): + other_sentinel = newlit + elif not self.variable_set[abs(newlit)]: + self.sentinels[-lit].remove(cls) + self.sentinels[newlit].add(cls) + other_sentinel = None + break + + # Check if no sentinel update exists + if other_sentinel: + self._unit_prop_queue.append(other_sentinel) + + def _undo(self): + """ + _undo the changes of the most recent decision level. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> next(l._find_model()) + {1: True, 2: False, 3: False} + >>> level = l._current_level + >>> level.decision, level.var_settings, level.flipped + (-3, {-3, -2}, False) + >>> l._undo() + >>> level = l._current_level + >>> level.decision, level.var_settings, level.flipped + (0, {1}, False) + + """ + # Undo the variable settings + for lit in self._current_level.var_settings: + self.var_settings.remove(lit) + self.heur_lit_unset(lit) + self.variable_set[abs(lit)] = False + + # Pop the level off the stack + self.levels.pop() + + ######################### + # Propagation # + ######################### + """ + Propagation methods should attempt to soundly simplify the boolean + theory, and return True if any simplification occurred and False + otherwise. + """ + def _simplify(self): + """Iterate over the various forms of propagation to simplify the theory. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> l.variable_set + [False, False, False, False] + >>> l.sentinels + {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}} + + >>> l._simplify() + + >>> l.variable_set + [False, True, False, False] + >>> l.sentinels + {-3: {0, 2}, -2: {3, 4}, -1: set(), 2: {0, 3}, + ...3: {2, 4}} + + """ + changed = True + while changed: + changed = False + changed |= self._unit_prop() + changed |= self._pure_literal() + + def _unit_prop(self): + """Perform unit propagation on the current theory.""" + result = len(self._unit_prop_queue) > 0 + while self._unit_prop_queue: + next_lit = self._unit_prop_queue.pop() + if -next_lit in self.var_settings: + self.is_unsatisfied = True + self._unit_prop_queue = [] + return False + else: + self._assign_literal(next_lit) + + return result + + def _pure_literal(self): + """Look for pure literals and assign them when found.""" + return False + + ######################### + # Heuristics # + ######################### + def _vsids_init(self): + """Initialize the data structures needed for the VSIDS heuristic.""" + self.lit_heap = [] + self.lit_scores = {} + + for var in range(1, len(self.variable_set)): + self.lit_scores[var] = float(-self.occurrence_count[var]) + self.lit_scores[-var] = float(-self.occurrence_count[-var]) + heappush(self.lit_heap, (self.lit_scores[var], var)) + heappush(self.lit_heap, (self.lit_scores[-var], -var)) + + def _vsids_decay(self): + """Decay the VSIDS scores for every literal. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + + >>> l.lit_scores + {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0} + + >>> l._vsids_decay() + + >>> l.lit_scores + {-3: -1.0, -2: -1.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -1.0} + + """ + # We divide every literal score by 2 for a decay factor + # Note: This doesn't change the heap property + for lit in self.lit_scores.keys(): + self.lit_scores[lit] /= 2.0 + + def _vsids_calculate(self): + """ + VSIDS Heuristic Calculation + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + + >>> l.lit_heap + [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)] + + >>> l._vsids_calculate() + -3 + + >>> l.lit_heap + [(-2.0, -2), (-2.0, 2), (0.0, -1), (0.0, 1), (-2.0, 3)] + + """ + if len(self.lit_heap) == 0: + return 0 + + # Clean out the front of the heap as long the variables are set + while self.variable_set[abs(self.lit_heap[0][1])]: + heappop(self.lit_heap) + if len(self.lit_heap) == 0: + return 0 + + return heappop(self.lit_heap)[1] + + def _vsids_lit_assigned(self, lit): + """Handle the assignment of a literal for the VSIDS heuristic.""" + pass + + def _vsids_lit_unset(self, lit): + """Handle the unsetting of a literal for the VSIDS heuristic. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> l.lit_heap + [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)] + + >>> l._vsids_lit_unset(2) + + >>> l.lit_heap + [(-2.0, -3), (-2.0, -2), (-2.0, -2), (-2.0, 2), (-2.0, 3), (0.0, -1), + ...(-2.0, 2), (0.0, 1)] + + """ + var = abs(lit) + heappush(self.lit_heap, (self.lit_scores[var], var)) + heappush(self.lit_heap, (self.lit_scores[-var], -var)) + + def _vsids_clause_added(self, cls): + """Handle the addition of a new clause for the VSIDS heuristic. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + + >>> l.num_learned_clauses + 0 + >>> l.lit_scores + {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0} + + >>> l._vsids_clause_added({2, -3}) + + >>> l.num_learned_clauses + 1 + >>> l.lit_scores + {-3: -1.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -2.0} + + """ + self.num_learned_clauses += 1 + for lit in cls: + self.lit_scores[lit] += 1 + + ######################## + # Clause Learning # + ######################## + def _simple_add_learned_clause(self, cls): + """Add a new clause to the theory. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + + >>> l.num_learned_clauses + 0 + >>> l.clauses + [[2, -3], [1], [3, -3], [2, -2], [3, -2]] + >>> l.sentinels + {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}} + + >>> l._simple_add_learned_clause([3]) + + >>> l.clauses + [[2, -3], [1], [3, -3], [2, -2], [3, -2], [3]] + >>> l.sentinels + {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4, 5}} + + """ + cls_num = len(self.clauses) + self.clauses.append(cls) + + for lit in cls: + self.occurrence_count[lit] += 1 + + self.sentinels[cls[0]].add(cls_num) + self.sentinels[cls[-1]].add(cls_num) + + self.heur_clause_added(cls) + + def _simple_compute_conflict(self): + """ Build a clause representing the fact that at least one decision made + so far is wrong. + + Examples + ======== + + >>> from sympy.logic.algorithms.dpll2 import SATSolver + >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, + ... {3, -2}], {1, 2, 3}, set()) + >>> next(l._find_model()) + {1: True, 2: False, 3: False} + >>> l._simple_compute_conflict() + [3] + + """ + return [-(level.decision) for level in self.levels[1:]] + + def _simple_clean_clauses(self): + """Clean up learned clauses.""" + pass + + +class Level: + """ + Represents a single level in the DPLL algorithm, and contains + enough information for a sound backtracking procedure. + """ + + def __init__(self, decision, flipped=False): + self.decision = decision + self.var_settings = set() + self.flipped = flipped diff --git a/lib/python3.11/site-packages/sympy/logic/algorithms/lra_theory.py b/lib/python3.11/site-packages/sympy/logic/algorithms/lra_theory.py new file mode 100644 index 0000000000000000000000000000000000000000..6ddca1b573746e53ea811af624088c9989f62955 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/algorithms/lra_theory.py @@ -0,0 +1,915 @@ +"""Implements "A Fast Linear-Arithmetic Solver for DPLL(T)" + +The LRASolver class defined in this file can be used +in conjunction with a SAT solver to check the +satisfiability of formulas involving inequalities. + +Here's an example of how that would work: + + Suppose you want to check the satisfiability of + the following formula: + + >>> from sympy.core.relational import Eq + >>> from sympy.abc import x, y + >>> f = ((x > 0) | (x < 0)) & (Eq(x, 0) | Eq(y, 1)) & (~Eq(y, 1) | Eq(1, 2)) + + First a preprocessing step should be done on f. During preprocessing, + f should be checked for any predicates such as `Q.prime` that can't be + handled. Also unequality like `~Eq(y, 1)` should be split. + + I should mention that the paper says to split both equalities and + unequality, but this implementation only requires that unequality + be split. + + >>> f = ((x > 0) | (x < 0)) & (Eq(x, 0) | Eq(y, 1)) & ((y < 1) | (y > 1) | Eq(1, 2)) + + Then an LRASolver instance needs to be initialized with this formula. + + >>> from sympy.assumptions.cnf import CNF, EncodedCNF + >>> from sympy.assumptions.ask import Q + >>> from sympy.logic.algorithms.lra_theory import LRASolver + >>> cnf = CNF.from_prop(f) + >>> enc = EncodedCNF() + >>> enc.add_from_cnf(cnf) + >>> lra, conflicts = LRASolver.from_encoded_cnf(enc) + + Any immediate one-lital conflicts clauses will be detected here. + In this example, `~Eq(1, 2)` is one such conflict clause. We'll + want to add it to `f` so that the SAT solver is forced to + assign Eq(1, 2) to False. + + >>> f = f & ~Eq(1, 2) + + Now that the one-literal conflict clauses have been added + and an lra object has been initialized, we can pass `f` + to a SAT solver. The SAT solver will give us a satisfying + assignment such as: + + (1 = 2): False + (y = 1): True + (y < 1): True + (y > 1): True + (x = 0): True + (x < 0): True + (x > 0): True + + Next you would pass this assignment to the LRASolver + which will be able to determine that this particular + assignment is satisfiable or not. + + Note that since EncodedCNF is inherently non-deterministic, + the int each predicate is encoded as is not consistent. As a + result, the code bellow likely does not reflect the assignment + given above. + + >>> lra.assert_lit(-1) #doctest: +SKIP + >>> lra.assert_lit(2) #doctest: +SKIP + >>> lra.assert_lit(3) #doctest: +SKIP + >>> lra.assert_lit(4) #doctest: +SKIP + >>> lra.assert_lit(5) #doctest: +SKIP + >>> lra.assert_lit(6) #doctest: +SKIP + >>> lra.assert_lit(7) #doctest: +SKIP + >>> is_sat, conflict_or_assignment = lra.check() + + As the particular assignment suggested is not satisfiable, + the LRASolver will return unsat and a conflict clause when + given that assignment. The conflict clause will always be + minimal, but there can be multiple minimal conflict clauses. + One possible conflict clause could be `~(x < 0) | ~(x > 0)`. + + We would then add whatever conflict clause is given to + `f` to prevent the SAT solver from coming up with an + assignment with the same conflicting literals. In this case, + the conflict clause `~(x < 0) | ~(x > 0)` would prevent + any assignment where both (x < 0) and (x > 0) were both + true. + + The SAT solver would then find another assignment + and we would check that assignment with the LRASolver + and so on. Eventually either a satisfying assignment + that the SAT solver and LRASolver agreed on would be found + or enough conflict clauses would be added so that the + boolean formula was unsatisfiable. + + +This implementation is based on [1]_, which includes a +detailed explanation of the algorithm and pseudocode +for the most important functions. + +[1]_ also explains how backtracking and theory propagation +could be implemented to speed up the current implementation, +but these are not currently implemented. + +TODO: + - Handle non-rational real numbers + - Handle positive and negative infinity + - Implement backtracking and theory proposition + - Simplify matrix by removing unused variables using Gaussian elimination + +References +========== + +.. [1] Dutertre, B., de Moura, L.: + A Fast Linear-Arithmetic Solver for DPLL(T) + https://link.springer.com/chapter/10.1007/11817963_11 +""" +from sympy.solvers.solveset import linear_eq_to_matrix +from sympy.matrices.dense import eye +from sympy.assumptions import Predicate +from sympy.assumptions.assume import AppliedPredicate +from sympy.assumptions.ask import Q +from sympy.core import Dummy +from sympy.core.mul import Mul +from sympy.core.add import Add +from sympy.core.relational import Eq, Ne +from sympy.core.sympify import sympify +from sympy.core.singleton import S +from sympy.core.numbers import Rational, oo +from sympy.matrices.dense import Matrix + +class UnhandledInput(Exception): + """ + Raised while creating an LRASolver if non-linearity + or non-rational numbers are present. + """ + +# predicates that LRASolver understands and makes use of +ALLOWED_PRED = {Q.eq, Q.gt, Q.lt, Q.le, Q.ge} + +# if true ~Q.gt(x, y) implies Q.le(x, y) +HANDLE_NEGATION = True + +class LRASolver(): + """ + Linear Arithmetic Solver for DPLL(T) implemented with an algorithm based on + the Dual Simplex method. Uses Bland's pivoting rule to avoid cycling. + + References + ========== + + .. [1] Dutertre, B., de Moura, L.: + A Fast Linear-Arithmetic Solver for DPLL(T) + https://link.springer.com/chapter/10.1007/11817963_11 + """ + + def __init__(self, A, slack_variables, nonslack_variables, enc_to_boundary, s_subs, testing_mode): + """ + Use the "from_encoded_cnf" method to create a new LRASolver. + """ + self.run_checks = testing_mode + self.s_subs = s_subs # used only for test_lra_theory.test_random_problems + + if any(not isinstance(a, Rational) for a in A): + raise UnhandledInput("Non-rational numbers are not handled") + if any(not isinstance(b.bound, Rational) for b in enc_to_boundary.values()): + raise UnhandledInput("Non-rational numbers are not handled") + m, n = len(slack_variables), len(slack_variables)+len(nonslack_variables) + if m != 0: + assert A.shape == (m, n) + if self.run_checks: + assert A[:, n-m:] == -eye(m) + + self.enc_to_boundary = enc_to_boundary # mapping of int to Boundry objects + self.boundary_to_enc = {value: key for key, value in enc_to_boundary.items()} + self.A = A + self.slack = slack_variables + self.nonslack = nonslack_variables + self.all_var = nonslack_variables + slack_variables + + self.slack_set = set(slack_variables) + + self.is_sat = True # While True, all constraints asserted so far are satisfiable + self.result = None # always one of: (True, assignment), (False, conflict clause), None + + @staticmethod + def from_encoded_cnf(encoded_cnf, testing_mode=False): + """ + Creates an LRASolver from an EncodedCNF object + and a list of conflict clauses for propositions + that can be simplified to True or False. + + Parameters + ========== + + encoded_cnf : EncodedCNF + + testing_mode : bool + Setting testing_mode to True enables some slow assert statements + and sorting to reduce nonterministic behavior. + + Returns + ======= + + (lra, conflicts) + + lra : LRASolver + + conflicts : list + Contains a one-literal conflict clause for each proposition + that can be simplified to True or False. + + Example + ======= + + >>> from sympy.core.relational import Eq + >>> from sympy.assumptions.cnf import CNF, EncodedCNF + >>> from sympy.assumptions.ask import Q + >>> from sympy.logic.algorithms.lra_theory import LRASolver + >>> from sympy.abc import x, y, z + >>> phi = (x >= 0) & ((x + y <= 2) | (x + 2 * y - z >= 6)) + >>> phi = phi & (Eq(x + y, 2) | (x + 2 * y - z > 4)) + >>> phi = phi & Q.gt(2, 1) + >>> cnf = CNF.from_prop(phi) + >>> enc = EncodedCNF() + >>> enc.from_cnf(cnf) + >>> lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True) + >>> lra #doctest: +SKIP + + >>> conflicts #doctest: +SKIP + [[4]] + """ + # This function has three main jobs: + # - raise errors if the input formula is not handled + # - preprocesses the formula into a matirx and single variable constraints + # - create one-literal conflict clauses from predicates that are always True + # or always False such as Q.gt(3, 2) + # + # See the preprocessing section of "A Fast Linear-Arithmetic Solver for DPLL(T)" + # for an explanation of how the formula is converted into a matrix + # and a set of single variable constraints. + + encoding = {} # maps int to boundary + A = [] + + basic = [] + s_count = 0 + s_subs = {} + nonbasic = [] + + if testing_mode: + # sort to reduce nondeterminism + encoded_cnf_items = sorted(encoded_cnf.encoding.items(), key=lambda x: str(x)) + else: + encoded_cnf_items = encoded_cnf.encoding.items() + + empty_var = Dummy() + var_to_lra_var = {} + conflicts = [] + + for prop, enc in encoded_cnf_items: + if isinstance(prop, Predicate): + prop = prop(empty_var) + if not isinstance(prop, AppliedPredicate): + if prop == True: + conflicts.append([enc]) + continue + if prop == False: + conflicts.append([-enc]) + continue + + raise ValueError(f"Unhandled Predicate: {prop}") + + assert prop.function in ALLOWED_PRED + if prop.lhs == S.NaN or prop.rhs == S.NaN: + raise ValueError(f"{prop} contains nan") + if prop.lhs.is_imaginary or prop.rhs.is_imaginary: + raise UnhandledInput(f"{prop} contains an imaginary component") + if prop.lhs == oo or prop.rhs == oo: + raise UnhandledInput(f"{prop} contains infinity") + + prop = _eval_binrel(prop) # simplify variable-less quantities to True / False if possible + if prop == True: + conflicts.append([enc]) + continue + elif prop == False: + conflicts.append([-enc]) + continue + elif prop is None: + raise UnhandledInput(f"{prop} could not be simplified") + + expr = prop.lhs - prop.rhs + if prop.function in [Q.ge, Q.gt]: + expr = -expr + + # expr should be less than (or equal to) 0 + # otherwise prop is False + if prop.function in [Q.le, Q.ge]: + bool = (expr <= 0) + elif prop.function in [Q.lt, Q.gt]: + bool = (expr < 0) + else: + assert prop.function == Q.eq + bool = Eq(expr, 0) + + if bool == True: + conflicts.append([enc]) + continue + elif bool == False: + conflicts.append([-enc]) + continue + + + vars, const = _sep_const_terms(expr) # example: (2x + 3y + 2) --> (2x + 3y), (2) + vars, var_coeff = _sep_const_coeff(vars) # examples: (2x) --> (x, 2); (2x + 3y) --> (2x + 3y), (1) + const = const / var_coeff + + terms = _list_terms(vars) # example: (2x + 3y) --> [2x, 3y] + for term in terms: + term, _ = _sep_const_coeff(term) + assert len(term.free_symbols) > 0 + if term not in var_to_lra_var: + var_to_lra_var[term] = LRAVariable(term) + nonbasic.append(term) + + if len(terms) > 1: + if vars not in s_subs: + s_count += 1 + d = Dummy(f"s{s_count}") + var_to_lra_var[d] = LRAVariable(d) + basic.append(d) + s_subs[vars] = d + A.append(vars - d) + var = s_subs[vars] + else: + var = terms[0] + + assert var_coeff != 0 + + equality = prop.function == Q.eq + upper = var_coeff > 0 if not equality else None + strict = prop.function in [Q.gt, Q.lt] + b = Boundary(var_to_lra_var[var], -const, upper, equality, strict) + encoding[enc] = b + + fs = [v.free_symbols for v in nonbasic + basic] + assert all(len(syms) > 0 for syms in fs) + fs_count = sum(len(syms) for syms in fs) + if len(fs) > 0 and len(set.union(*fs)) < fs_count: + raise UnhandledInput("Nonlinearity is not handled") + + A, _ = linear_eq_to_matrix(A, nonbasic + basic) + nonbasic = [var_to_lra_var[nb] for nb in nonbasic] + basic = [var_to_lra_var[b] for b in basic] + for idx, var in enumerate(nonbasic + basic): + var.col_idx = idx + + return LRASolver(A, basic, nonbasic, encoding, s_subs, testing_mode), conflicts + + def reset_bounds(self): + """ + Resets the state of the LRASolver to before + anything was asserted. + """ + self.result = None + for var in self.all_var: + var.lower = LRARational(-float("inf"), 0) + var.lower_from_eq = False + var.lower_from_neg = False + var.upper = LRARational(float("inf"), 0) + var.upper_from_eq= False + var.lower_from_neg = False + var.assign = LRARational(0, 0) + + def assert_lit(self, enc_constraint): + """ + Assert a literal representing a constraint + and update the internal state accordingly. + + Note that due to peculiarities of this implementation + asserting ~(x > 0) will assert (x <= 0) but asserting + ~Eq(x, 0) will not do anything. + + Parameters + ========== + + enc_constraint : int + A mapping of encodings to constraints + can be found in `self.enc_to_boundary`. + + Returns + ======= + + None or (False, explanation) + + explanation : set of ints + A conflict clause that "explains" why + the literals asserted so far are unsatisfiable. + """ + if abs(enc_constraint) not in self.enc_to_boundary: + return None + + if not HANDLE_NEGATION and enc_constraint < 0: + return None + + boundary = self.enc_to_boundary[abs(enc_constraint)] + sym, c, negated = boundary.var, boundary.bound, enc_constraint < 0 + + if boundary.equality and negated: + return None # negated equality is not handled and should only appear in conflict clauses + + upper = boundary.upper != negated + if boundary.strict != negated: + delta = -1 if upper else 1 + c = LRARational(c, delta) + else: + c = LRARational(c, 0) + + if boundary.equality: + res1 = self._assert_lower(sym, c, from_equality=True, from_neg=negated) + if res1 and res1[0] == False: + res = res1 + else: + res2 = self._assert_upper(sym, c, from_equality=True, from_neg=negated) + res = res2 + elif upper: + res = self._assert_upper(sym, c, from_neg=negated) + else: + res = self._assert_lower(sym, c, from_neg=negated) + + if self.is_sat and sym not in self.slack_set: + self.is_sat = res is None + else: + self.is_sat = False + + return res + + def _assert_upper(self, xi, ci, from_equality=False, from_neg=False): + """ + Adjusts the upper bound on variable xi if the new upper bound is + more limiting. The assignment of variable xi is adjusted to be + within the new bound if needed. + + Also calls `self._update` to update the assignment for slack variables + to keep all equalities satisfied. + """ + if self.result: + assert self.result[0] != False + self.result = None + if ci >= xi.upper: + return None + if ci < xi.lower: + assert (xi.lower[1] >= 0) is True + assert (ci[1] <= 0) is True + + lit1, neg1 = Boundary.from_lower(xi) + + lit2 = Boundary(var=xi, const=ci[0], strict=ci[1] != 0, upper=True, equality=from_equality) + if from_neg: + lit2 = lit2.get_negated() + neg2 = -1 if from_neg else 1 + + conflict = [-neg1*self.boundary_to_enc[lit1], -neg2*self.boundary_to_enc[lit2]] + self.result = False, conflict + return self.result + xi.upper = ci + xi.upper_from_eq = from_equality + xi.upper_from_neg = from_neg + if xi in self.nonslack and xi.assign > ci: + self._update(xi, ci) + + if self.run_checks and all(v.assign[0] != float("inf") and v.assign[0] != -float("inf") + for v in self.all_var): + M = self.A + X = Matrix([v.assign[0] for v in self.all_var]) + assert all(abs(val) < 10 ** (-10) for val in M * X) + + return None + + def _assert_lower(self, xi, ci, from_equality=False, from_neg=False): + """ + Adjusts the lower bound on variable xi if the new lower bound is + more limiting. The assignment of variable xi is adjusted to be + within the new bound if needed. + + Also calls `self._update` to update the assignment for slack variables + to keep all equalities satisfied. + """ + if self.result: + assert self.result[0] != False + self.result = None + if ci <= xi.lower: + return None + if ci > xi.upper: + assert (xi.upper[1] <= 0) is True + assert (ci[1] >= 0) is True + + lit1, neg1 = Boundary.from_upper(xi) + + lit2 = Boundary(var=xi, const=ci[0], strict=ci[1] != 0, upper=False, equality=from_equality) + if from_neg: + lit2 = lit2.get_negated() + neg2 = -1 if from_neg else 1 + + conflict = [-neg1*self.boundary_to_enc[lit1],-neg2*self.boundary_to_enc[lit2]] + self.result = False, conflict + return self.result + xi.lower = ci + xi.lower_from_eq = from_equality + xi.lower_from_neg = from_neg + if xi in self.nonslack and xi.assign < ci: + self._update(xi, ci) + + if self.run_checks and all(v.assign[0] != float("inf") and v.assign[0] != -float("inf") + for v in self.all_var): + M = self.A + X = Matrix([v.assign[0] for v in self.all_var]) + assert all(abs(val) < 10 ** (-10) for val in M * X) + + return None + + def _update(self, xi, v): + """ + Updates all slack variables that have equations that contain + variable xi so that they stay satisfied given xi is equal to v. + """ + i = xi.col_idx + for j, b in enumerate(self.slack): + aji = self.A[j, i] + b.assign = b.assign + (v - xi.assign)*aji + xi.assign = v + + def check(self): + """ + Searches for an assignment that satisfies all constraints + or determines that no such assignment exists and gives + a minimal conflict clause that "explains" why the + constraints are unsatisfiable. + + Returns + ======= + + (True, assignment) or (False, explanation) + + assignment : dict of LRAVariables to values + Assigned values are tuples that represent a rational number + plus some infinatesimal delta. + + explanation : set of ints + """ + if self.is_sat: + return True, {var: var.assign for var in self.all_var} + if self.result: + return self.result + + from sympy.matrices.dense import Matrix + M = self.A.copy() + basic = {s: i for i, s in enumerate(self.slack)} # contains the row index associated with each basic variable + nonbasic = set(self.nonslack) + iteration = 0 + while True: + iteration += 1 + + if self.run_checks: + # nonbasic variables must always be within bounds + assert all(((nb.assign >= nb.lower) == True) and ((nb.assign <= nb.upper) == True) for nb in nonbasic) + + # assignments for x must always satisfy Ax = 0 + # probably have to turn this off when dealing with strict ineq + if all(v.assign[0] != float("inf") and v.assign[0] != -float("inf") + for v in self.all_var): + X = Matrix([v.assign[0] for v in self.all_var]) + assert all(abs(val) < 10**(-10) for val in M*X) + + # check upper and lower match this format: + # x <= rat + delta iff x < rat + # x >= rat - delta iff x > rat + # this wouldn't make sense: + # x <= rat - delta + # x >= rat + delta + assert all(x.upper[1] <= 0 for x in self.all_var) + assert all(x.lower[1] >= 0 for x in self.all_var) + + cand = [b for b in basic if b.assign < b.lower or b.assign > b.upper] + + if len(cand) == 0: + return True, {var: var.assign for var in self.all_var} + + xi = min(cand, key=lambda v: v.col_idx) # Bland's rule + i = basic[xi] + + if xi.assign < xi.lower: + cand = [nb for nb in nonbasic + if (M[i, nb.col_idx] > 0 and nb.assign < nb.upper) + or (M[i, nb.col_idx] < 0 and nb.assign > nb.lower)] + if len(cand) == 0: + N_plus = [nb for nb in nonbasic if M[i, nb.col_idx] > 0] + N_minus = [nb for nb in nonbasic if M[i, nb.col_idx] < 0] + + conflict = [] + conflict += [Boundary.from_upper(nb) for nb in N_plus] + conflict += [Boundary.from_lower(nb) for nb in N_minus] + conflict.append(Boundary.from_lower(xi)) + conflict = [-neg*self.boundary_to_enc[c] for c, neg in conflict] + return False, conflict + xj = min(cand, key=str) + M = self._pivot_and_update(M, basic, nonbasic, xi, xj, xi.lower) + + if xi.assign > xi.upper: + cand = [nb for nb in nonbasic + if (M[i, nb.col_idx] < 0 and nb.assign < nb.upper) + or (M[i, nb.col_idx] > 0 and nb.assign > nb.lower)] + + if len(cand) == 0: + N_plus = [nb for nb in nonbasic if M[i, nb.col_idx] > 0] + N_minus = [nb for nb in nonbasic if M[i, nb.col_idx] < 0] + + conflict = [] + conflict += [Boundary.from_upper(nb) for nb in N_minus] + conflict += [Boundary.from_lower(nb) for nb in N_plus] + conflict.append(Boundary.from_upper(xi)) + + conflict = [-neg*self.boundary_to_enc[c] for c, neg in conflict] + return False, conflict + xj = min(cand, key=lambda v: v.col_idx) + M = self._pivot_and_update(M, basic, nonbasic, xi, xj, xi.upper) + + def _pivot_and_update(self, M, basic, nonbasic, xi, xj, v): + """ + Pivots basic variable xi with nonbasic variable xj, + and sets value of xi to v and adjusts the values of all basic variables + to keep equations satisfied. + """ + i, j = basic[xi], xj.col_idx + assert M[i, j] != 0 + theta = (v - xi.assign)*(1/M[i, j]) + xi.assign = v + xj.assign = xj.assign + theta + for xk in basic: + if xk != xi: + k = basic[xk] + akj = M[k, j] + xk.assign = xk.assign + theta*akj + # pivot + basic[xj] = basic[xi] + del basic[xi] + nonbasic.add(xi) + nonbasic.remove(xj) + return self._pivot(M, i, j) + + @staticmethod + def _pivot(M, i, j): + """ + Performs a pivot operation about entry i, j of M by performing + a series of row operations on a copy of M and returing the result. + The original M is left unmodified. + + Conceptually, M represents a system of equations and pivoting + can be thought of as rearranging equation i to be in terms of + variable j and then substituting in the rest of the equations + to get rid of other occurances of variable j. + + Example + ======= + + >>> from sympy.matrices.dense import Matrix + >>> from sympy.logic.algorithms.lra_theory import LRASolver + >>> from sympy import var + >>> Matrix(3, 3, var('a:i')) + Matrix([ + [a, b, c], + [d, e, f], + [g, h, i]]) + + This matrix is equivalent to: + 0 = a*x + b*y + c*z + 0 = d*x + e*y + f*z + 0 = g*x + h*y + i*z + + >>> LRASolver._pivot(_, 1, 0) + Matrix([ + [ 0, -a*e/d + b, -a*f/d + c], + [-1, -e/d, -f/d], + [ 0, h - e*g/d, i - f*g/d]]) + + We rearrange equation 1 in terms of variable 0 (x) + and substitute to remove x from the other equations. + + 0 = 0 + (-a*e/d + b)*y + (-a*f/d + c)*z + 0 = -x + (-e/d)*y + (-f/d)*z + 0 = 0 + (h - e*g/d)*y + (i - f*g/d)*z + """ + _, _, Mij = M[i, :], M[:, j], M[i, j] + if Mij == 0: + raise ZeroDivisionError("Tried to pivot about zero-valued entry.") + A = M.copy() + A[i, :] = -A[i, :]/Mij + for row in range(M.shape[0]): + if row != i: + A[row, :] = A[row, :] + A[row, j] * A[i, :] + + return A + + +def _sep_const_coeff(expr): + """ + Example + ======= + + >>> from sympy.logic.algorithms.lra_theory import _sep_const_coeff + >>> from sympy.abc import x, y + >>> _sep_const_coeff(2*x) + (x, 2) + >>> _sep_const_coeff(2*x + 3*y) + (2*x + 3*y, 1) + """ + if isinstance(expr, Add): + return expr, sympify(1) + + if isinstance(expr, Mul): + coeffs = expr.args + else: + coeffs = [expr] + + var, const = [], [] + for c in coeffs: + c = sympify(c) + if len(c.free_symbols)==0: + const.append(c) + else: + var.append(c) + return Mul(*var), Mul(*const) + + +def _list_terms(expr): + if not isinstance(expr, Add): + return [expr] + + return expr.args + + +def _sep_const_terms(expr): + """ + Example + ======= + + >>> from sympy.logic.algorithms.lra_theory import _sep_const_terms + >>> from sympy.abc import x, y + >>> _sep_const_terms(2*x + 3*y + 2) + (2*x + 3*y, 2) + """ + if isinstance(expr, Add): + terms = expr.args + else: + terms = [expr] + + var, const = [], [] + for t in terms: + if len(t.free_symbols) == 0: + const.append(t) + else: + var.append(t) + return sum(var), sum(const) + + +def _eval_binrel(binrel): + """ + Simplify binary relation to True / False if possible. + """ + if not (len(binrel.lhs.free_symbols) == 0 and len(binrel.rhs.free_symbols) == 0): + return binrel + if binrel.function == Q.lt: + res = binrel.lhs < binrel.rhs + elif binrel.function == Q.gt: + res = binrel.lhs > binrel.rhs + elif binrel.function == Q.le: + res = binrel.lhs <= binrel.rhs + elif binrel.function == Q.ge: + res = binrel.lhs >= binrel.rhs + elif binrel.function == Q.eq: + res = Eq(binrel.lhs, binrel.rhs) + elif binrel.function == Q.ne: + res = Ne(binrel.lhs, binrel.rhs) + + if res == True or res == False: + return res + else: + return None + + +class Boundary: + """ + Represents an upper or lower bound or an equality between a symbol + and some constant. + """ + def __init__(self, var, const, upper, equality, strict=None): + if not equality in [True, False]: + assert equality in [True, False] + + + self.var = var + if isinstance(const, tuple): + s = const[1] != 0 + if strict: + assert s == strict + self.bound = const[0] + self.strict = s + else: + self.bound = const + self.strict = strict + self.upper = upper if not equality else None + self.equality = equality + self.strict = strict + assert self.strict is not None + + @staticmethod + def from_upper(var): + neg = -1 if var.upper_from_neg else 1 + b = Boundary(var, var.upper[0], True, var.upper_from_eq, var.upper[1] != 0) + if neg < 0: + b = b.get_negated() + return b, neg + + @staticmethod + def from_lower(var): + neg = -1 if var.lower_from_neg else 1 + b = Boundary(var, var.lower[0], False, var.lower_from_eq, var.lower[1] != 0) + if neg < 0: + b = b.get_negated() + return b, neg + + def get_negated(self): + return Boundary(self.var, self.bound, not self.upper, self.equality, not self.strict) + + def get_inequality(self): + if self.equality: + return Eq(self.var.var, self.bound) + elif self.upper and self.strict: + return self.var.var < self.bound + elif not self.upper and self.strict: + return self.var.var > self.bound + elif self.upper: + return self.var.var <= self.bound + else: + return self.var.var >= self.bound + + def __repr__(self): + return repr("Boundry(" + repr(self.get_inequality()) + ")") + + def __eq__(self, other): + other = (other.var, other.bound, other.strict, other.upper, other.equality) + return (self.var, self.bound, self.strict, self.upper, self.equality) == other + + def __hash__(self): + return hash((self.var, self.bound, self.strict, self.upper, self.equality)) + + +class LRARational(): + """ + Represents a rational plus or minus some amount + of arbitrary small deltas. + """ + def __init__(self, rational, delta): + self.value = (rational, delta) + + def __lt__(self, other): + return self.value < other.value + + def __le__(self, other): + return self.value <= other.value + + def __eq__(self, other): + return self.value == other.value + + def __add__(self, other): + return LRARational(self.value[0] + other.value[0], self.value[1] + other.value[1]) + + def __sub__(self, other): + return LRARational(self.value[0] - other.value[0], self.value[1] - other.value[1]) + + def __mul__(self, other): + assert not isinstance(other, LRARational) + return LRARational(self.value[0] * other, self.value[1] * other) + + def __getitem__(self, index): + return self.value[index] + + def __repr__(self): + return repr(self.value) + + +class LRAVariable(): + """ + Object to keep track of upper and lower bounds + on `self.var`. + """ + def __init__(self, var): + self.upper = LRARational(float("inf"), 0) + self.upper_from_eq = False + self.upper_from_neg = False + self.lower = LRARational(-float("inf"), 0) + self.lower_from_eq = False + self.lower_from_neg = False + self.assign = LRARational(0,0) + self.var = var + self.col_idx = None + + def __repr__(self): + return repr(self.var) + + def __eq__(self, other): + if not isinstance(other, LRAVariable): + return False + return other.var == self.var + + def __hash__(self): + return hash(self.var) diff --git a/lib/python3.11/site-packages/sympy/logic/algorithms/minisat22_wrapper.py b/lib/python3.11/site-packages/sympy/logic/algorithms/minisat22_wrapper.py new file mode 100644 index 0000000000000000000000000000000000000000..1d5c1f8f14f04309f7cb8197cc05d01a3c108545 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/algorithms/minisat22_wrapper.py @@ -0,0 +1,46 @@ +from sympy.assumptions.cnf import EncodedCNF + +def minisat22_satisfiable(expr, all_models=False, minimal=False): + + if not isinstance(expr, EncodedCNF): + exprs = EncodedCNF() + exprs.add_prop(expr) + expr = exprs + + from pysat.solvers import Minisat22 + + # Return UNSAT when False (encoded as 0) is present in the CNF + if {0} in expr.data: + if all_models: + return (f for f in [False]) + return False + + r = Minisat22(expr.data) + + if minimal: + r.set_phases([-(i+1) for i in range(r.nof_vars())]) + + if not r.solve(): + return False + + if not all_models: + return {expr.symbols[abs(lit) - 1]: lit > 0 for lit in r.get_model()} + + else: + # Make solutions SymPy compatible by creating a generator + def _gen(results): + satisfiable = False + while results.solve(): + sol = results.get_model() + yield {expr.symbols[abs(lit) - 1]: lit > 0 for lit in sol} + if minimal: + results.add_clause([-i for i in sol if i>0]) + else: + results.add_clause([-i for i in sol]) + satisfiable = True + if not satisfiable: + yield False + raise StopIteration + + + return _gen(r) diff --git a/lib/python3.11/site-packages/sympy/logic/algorithms/pycosat_wrapper.py b/lib/python3.11/site-packages/sympy/logic/algorithms/pycosat_wrapper.py new file mode 100644 index 0000000000000000000000000000000000000000..5ff498b7e3f6b73d95e9b949598ef32df4ecf226 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/algorithms/pycosat_wrapper.py @@ -0,0 +1,41 @@ +from sympy.assumptions.cnf import EncodedCNF + + +def pycosat_satisfiable(expr, all_models=False): + import pycosat + if not isinstance(expr, EncodedCNF): + exprs = EncodedCNF() + exprs.add_prop(expr) + expr = exprs + + # Return UNSAT when False (encoded as 0) is present in the CNF + if {0} in expr.data: + if all_models: + return (f for f in [False]) + return False + + if not all_models: + r = pycosat.solve(expr.data) + result = (r != "UNSAT") + if not result: + return result + return {expr.symbols[abs(lit) - 1]: lit > 0 for lit in r} + else: + r = pycosat.itersolve(expr.data) + result = (r != "UNSAT") + if not result: + return result + + # Make solutions SymPy compatible by creating a generator + def _gen(results): + satisfiable = False + try: + while True: + sol = next(results) + yield {expr.symbols[abs(lit) - 1]: lit > 0 for lit in sol} + satisfiable = True + except StopIteration: + if not satisfiable: + yield False + + return _gen(r) diff --git a/lib/python3.11/site-packages/sympy/logic/algorithms/z3_wrapper.py b/lib/python3.11/site-packages/sympy/logic/algorithms/z3_wrapper.py new file mode 100644 index 0000000000000000000000000000000000000000..fe44f713a2edfd5286c0f81b737212146766b11b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/algorithms/z3_wrapper.py @@ -0,0 +1,115 @@ +from sympy.printing.smtlib import smtlib_code +from sympy.assumptions.assume import AppliedPredicate +from sympy.assumptions.cnf import EncodedCNF +from sympy.assumptions.ask import Q + +from sympy.core import Add, Mul +from sympy.core.relational import Equality, LessThan, GreaterThan, StrictLessThan, StrictGreaterThan +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import Pow +from sympy.functions.elementary.miscellaneous import Min, Max +from sympy.logic.boolalg import And, Or, Xor, Implies +from sympy.logic.boolalg import Not, ITE +from sympy.assumptions.relation.equality import StrictGreaterThanPredicate, StrictLessThanPredicate, GreaterThanPredicate, LessThanPredicate, EqualityPredicate +from sympy.external import import_module + +def z3_satisfiable(expr, all_models=False): + if not isinstance(expr, EncodedCNF): + exprs = EncodedCNF() + exprs.add_prop(expr) + expr = exprs + + z3 = import_module("z3") + if z3 is None: + raise ImportError("z3 is not installed") + + s = encoded_cnf_to_z3_solver(expr, z3) + + res = str(s.check()) + if res == "unsat": + return False + elif res == "sat": + return z3_model_to_sympy_model(s.model(), expr) + else: + return None + + +def z3_model_to_sympy_model(z3_model, enc_cnf): + rev_enc = {value : key for key, value in enc_cnf.encoding.items()} + return {rev_enc[int(var.name()[1:])] : bool(z3_model[var]) for var in z3_model} + + +def clause_to_assertion(clause): + clause_strings = [f"d{abs(lit)}" if lit > 0 else f"(not d{abs(lit)})" for lit in clause] + return "(assert (or " + " ".join(clause_strings) + "))" + + +def encoded_cnf_to_z3_solver(enc_cnf, z3): + def dummify_bool(pred): + return False + assert isinstance(pred, AppliedPredicate) + + if pred.function in [Q.positive, Q.negative, Q.zero]: + return pred + else: + return False + + s = z3.Solver() + + declarations = [f"(declare-const d{var} Bool)" for var in enc_cnf.variables] + assertions = [clause_to_assertion(clause) for clause in enc_cnf.data] + + symbols = set() + for pred, enc in enc_cnf.encoding.items(): + if not isinstance(pred, AppliedPredicate): + continue + if pred.function not in (Q.gt, Q.lt, Q.ge, Q.le, Q.ne, Q.eq, Q.positive, Q.negative, Q.extended_negative, Q.extended_positive, Q.zero, Q.nonzero, Q.nonnegative, Q.nonpositive, Q.extended_nonzero, Q.extended_nonnegative, Q.extended_nonpositive): + continue + + pred_str = smtlib_code(pred, auto_declare=False, auto_assert=False, known_functions=known_functions) + + symbols |= pred.free_symbols + pred = pred_str + clause = f"(implies d{enc} {pred})" + assertion = "(assert " + clause + ")" + assertions.append(assertion) + + for sym in symbols: + declarations.append(f"(declare-const {sym} Real)") + + declarations = "\n".join(declarations) + assertions = "\n".join(assertions) + s.from_string(declarations) + s.from_string(assertions) + + return s + + +known_functions = { + Add: '+', + Mul: '*', + + Equality: '=', + LessThan: '<=', + GreaterThan: '>=', + StrictLessThan: '<', + StrictGreaterThan: '>', + + EqualityPredicate(): '=', + LessThanPredicate(): '<=', + GreaterThanPredicate(): '>=', + StrictLessThanPredicate(): '<', + StrictGreaterThanPredicate(): '>', + + Abs: 'abs', + Min: 'min', + Max: 'max', + Pow: '^', + + And: 'and', + Or: 'or', + Xor: 'xor', + Not: 'not', + ITE: 'ite', + Implies: '=>', + } diff --git a/lib/python3.11/site-packages/sympy/logic/boolalg.py b/lib/python3.11/site-packages/sympy/logic/boolalg.py new file mode 100644 index 0000000000000000000000000000000000000000..2c944e1f950d7f9a06c7f80dbce1bbf6c6cbd266 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/boolalg.py @@ -0,0 +1,3541 @@ +""" +Boolean algebra module for SymPy +""" + +from collections import defaultdict +from itertools import chain, combinations, product, permutations +from sympy.core.add import Add +from sympy.core.basic import Basic +from sympy.core.cache import cacheit +from sympy.core.containers import Tuple +from sympy.core.decorators import sympify_method_args, sympify_return +from sympy.core.function import Application, Derivative +from sympy.core.kind import BooleanKind, NumberKind +from sympy.core.numbers import Number +from sympy.core.operations import LatticeOp +from sympy.core.singleton import Singleton, S +from sympy.core.sorting import ordered +from sympy.core.sympify import _sympy_converter, _sympify, sympify +from sympy.utilities.iterables import sift, ibin +from sympy.utilities.misc import filldedent + + +def as_Boolean(e): + """Like ``bool``, return the Boolean value of an expression, e, + which can be any instance of :py:class:`~.Boolean` or ``bool``. + + Examples + ======== + + >>> from sympy import true, false, nan + >>> from sympy.logic.boolalg import as_Boolean + >>> from sympy.abc import x + >>> as_Boolean(0) is false + True + >>> as_Boolean(1) is true + True + >>> as_Boolean(x) + x + >>> as_Boolean(2) + Traceback (most recent call last): + ... + TypeError: expecting bool or Boolean, not `2`. + >>> as_Boolean(nan) + Traceback (most recent call last): + ... + TypeError: expecting bool or Boolean, not `nan`. + + """ + from sympy.core.symbol import Symbol + if e == True: + return true + if e == False: + return false + if isinstance(e, Symbol): + z = e.is_zero + if z is None: + return e + return false if z else true + if isinstance(e, Boolean): + return e + raise TypeError('expecting bool or Boolean, not `%s`.' % e) + + +@sympify_method_args +class Boolean(Basic): + """A Boolean object is an object for which logic operations make sense.""" + + __slots__ = () + + kind = BooleanKind + + @sympify_return([('other', 'Boolean')], NotImplemented) + def __and__(self, other): + return And(self, other) + + __rand__ = __and__ + + @sympify_return([('other', 'Boolean')], NotImplemented) + def __or__(self, other): + return Or(self, other) + + __ror__ = __or__ + + def __invert__(self): + """Overloading for ~""" + return Not(self) + + @sympify_return([('other', 'Boolean')], NotImplemented) + def __rshift__(self, other): + return Implies(self, other) + + @sympify_return([('other', 'Boolean')], NotImplemented) + def __lshift__(self, other): + return Implies(other, self) + + __rrshift__ = __lshift__ + __rlshift__ = __rshift__ + + @sympify_return([('other', 'Boolean')], NotImplemented) + def __xor__(self, other): + return Xor(self, other) + + __rxor__ = __xor__ + + def equals(self, other): + """ + Returns ``True`` if the given formulas have the same truth table. + For two formulas to be equal they must have the same literals. + + Examples + ======== + + >>> from sympy.abc import A, B, C + >>> from sympy import And, Or, Not + >>> (A >> B).equals(~B >> ~A) + True + >>> Not(And(A, B, C)).equals(And(Not(A), Not(B), Not(C))) + False + >>> Not(And(A, Not(A))).equals(Or(B, Not(B))) + False + + """ + from sympy.logic.inference import satisfiable + from sympy.core.relational import Relational + + if self.has(Relational) or other.has(Relational): + raise NotImplementedError('handling of relationals') + return self.atoms() == other.atoms() and \ + not satisfiable(Not(Equivalent(self, other))) + + def to_nnf(self, simplify=True): + # override where necessary + return self + + def as_set(self): + """ + Rewrites Boolean expression in terms of real sets. + + Examples + ======== + + >>> from sympy import Symbol, Eq, Or, And + >>> x = Symbol('x', real=True) + >>> Eq(x, 0).as_set() + {0} + >>> (x > 0).as_set() + Interval.open(0, oo) + >>> And(-2 < x, x < 2).as_set() + Interval.open(-2, 2) + >>> Or(x < -2, 2 < x).as_set() + Union(Interval.open(-oo, -2), Interval.open(2, oo)) + + """ + from sympy.calculus.util import periodicity + from sympy.core.relational import Relational + + free = self.free_symbols + if len(free) == 1: + x = free.pop() + if x.kind is NumberKind: + reps = {} + for r in self.atoms(Relational): + if periodicity(r, x) not in (0, None): + s = r._eval_as_set() + if s in (S.EmptySet, S.UniversalSet, S.Reals): + reps[r] = s.as_relational(x) + continue + raise NotImplementedError(filldedent(''' + as_set is not implemented for relationals + with periodic solutions + ''')) + new = self.subs(reps) + if new.func != self.func: + return new.as_set() # restart with new obj + else: + return new._eval_as_set() + + return self._eval_as_set() + else: + raise NotImplementedError("Sorry, as_set has not yet been" + " implemented for multivariate" + " expressions") + + @property + def binary_symbols(self): + from sympy.core.relational import Eq, Ne + return set().union(*[i.binary_symbols for i in self.args + if i.is_Boolean or i.is_Symbol + or isinstance(i, (Eq, Ne))]) + + def _eval_refine(self, assumptions): + from sympy.assumptions import ask + ret = ask(self, assumptions) + if ret is True: + return true + elif ret is False: + return false + return None + + +class BooleanAtom(Boolean): + """ + Base class of :py:class:`~.BooleanTrue` and :py:class:`~.BooleanFalse`. + """ + is_Boolean = True + is_Atom = True + _op_priority = 11 # higher than Expr + + def simplify(self, *a, **kw): + return self + + def expand(self, *a, **kw): + return self + + @property + def canonical(self): + return self + + def _noop(self, other=None): + raise TypeError('BooleanAtom not allowed in this context.') + + __add__ = _noop + __radd__ = _noop + __sub__ = _noop + __rsub__ = _noop + __mul__ = _noop + __rmul__ = _noop + __pow__ = _noop + __rpow__ = _noop + __truediv__ = _noop + __rtruediv__ = _noop + __mod__ = _noop + __rmod__ = _noop + _eval_power = _noop + + # /// drop when Py2 is no longer supported + def __lt__(self, other): + raise TypeError(filldedent(''' + A Boolean argument can only be used in + Eq and Ne; all other relationals expect + real expressions. + ''')) + + __le__ = __lt__ + __gt__ = __lt__ + __ge__ = __lt__ + # \\\ + + def _eval_simplify(self, **kwargs): + return self + + +class BooleanTrue(BooleanAtom, metaclass=Singleton): + """ + SymPy version of ``True``, a singleton that can be accessed via ``S.true``. + + This is the SymPy version of ``True``, for use in the logic module. The + primary advantage of using ``true`` instead of ``True`` is that shorthand Boolean + operations like ``~`` and ``>>`` will work as expected on this class, whereas with + True they act bitwise on 1. Functions in the logic module will return this + class when they evaluate to true. + + Notes + ===== + + There is liable to be some confusion as to when ``True`` should + be used and when ``S.true`` should be used in various contexts + throughout SymPy. An important thing to remember is that + ``sympify(True)`` returns ``S.true``. This means that for the most + part, you can just use ``True`` and it will automatically be converted + to ``S.true`` when necessary, similar to how you can generally use 1 + instead of ``S.One``. + + The rule of thumb is: + + "If the boolean in question can be replaced by an arbitrary symbolic + ``Boolean``, like ``Or(x, y)`` or ``x > 1``, use ``S.true``. + Otherwise, use ``True``" + + In other words, use ``S.true`` only on those contexts where the + boolean is being used as a symbolic representation of truth. + For example, if the object ends up in the ``.args`` of any expression, + then it must necessarily be ``S.true`` instead of ``True``, as + elements of ``.args`` must be ``Basic``. On the other hand, + ``==`` is not a symbolic operation in SymPy, since it always returns + ``True`` or ``False``, and does so in terms of structural equality + rather than mathematical, so it should return ``True``. The assumptions + system should use ``True`` and ``False``. Aside from not satisfying + the above rule of thumb, the assumptions system uses a three-valued logic + (``True``, ``False``, ``None``), whereas ``S.true`` and ``S.false`` + represent a two-valued logic. When in doubt, use ``True``. + + "``S.true == True is True``." + + While "``S.true is True``" is ``False``, "``S.true == True``" + is ``True``, so if there is any doubt over whether a function or + expression will return ``S.true`` or ``True``, just use ``==`` + instead of ``is`` to do the comparison, and it will work in either + case. Finally, for boolean flags, it's better to just use ``if x`` + instead of ``if x is True``. To quote PEP 8: + + Do not compare boolean values to ``True`` or ``False`` + using ``==``. + + * Yes: ``if greeting:`` + * No: ``if greeting == True:`` + * Worse: ``if greeting is True:`` + + Examples + ======== + + >>> from sympy import sympify, true, false, Or + >>> sympify(True) + True + >>> _ is True, _ is true + (False, True) + + >>> Or(true, false) + True + >>> _ is true + True + + Python operators give a boolean result for true but a + bitwise result for True + + >>> ~true, ~True # doctest: +SKIP + (False, -2) + >>> true >> true, True >> True + (True, 0) + + See Also + ======== + + sympy.logic.boolalg.BooleanFalse + + """ + def __bool__(self): + return True + + def __hash__(self): + return hash(True) + + def __eq__(self, other): + if other is True: + return True + if other is False: + return False + return super().__eq__(other) + + @property + def negated(self): + return false + + def as_set(self): + """ + Rewrite logic operators and relationals in terms of real sets. + + Examples + ======== + + >>> from sympy import true + >>> true.as_set() + UniversalSet + + """ + return S.UniversalSet + + +class BooleanFalse(BooleanAtom, metaclass=Singleton): + """ + SymPy version of ``False``, a singleton that can be accessed via ``S.false``. + + This is the SymPy version of ``False``, for use in the logic module. The + primary advantage of using ``false`` instead of ``False`` is that shorthand + Boolean operations like ``~`` and ``>>`` will work as expected on this class, + whereas with ``False`` they act bitwise on 0. Functions in the logic module + will return this class when they evaluate to false. + + Notes + ====== + + See the notes section in :py:class:`sympy.logic.boolalg.BooleanTrue` + + Examples + ======== + + >>> from sympy import sympify, true, false, Or + >>> sympify(False) + False + >>> _ is False, _ is false + (False, True) + + >>> Or(true, false) + True + >>> _ is true + True + + Python operators give a boolean result for false but a + bitwise result for False + + >>> ~false, ~False # doctest: +SKIP + (True, -1) + >>> false >> false, False >> False + (True, 0) + + See Also + ======== + + sympy.logic.boolalg.BooleanTrue + + """ + def __bool__(self): + return False + + def __hash__(self): + return hash(False) + + def __eq__(self, other): + if other is True: + return False + if other is False: + return True + return super().__eq__(other) + + @property + def negated(self): + return true + + def as_set(self): + """ + Rewrite logic operators and relationals in terms of real sets. + + Examples + ======== + + >>> from sympy import false + >>> false.as_set() + EmptySet + """ + return S.EmptySet + + +true = BooleanTrue() +false = BooleanFalse() +# We want S.true and S.false to work, rather than S.BooleanTrue and +# S.BooleanFalse, but making the class and instance names the same causes some +# major issues (like the inability to import the class directly from this +# file). +S.true = true +S.false = false + +_sympy_converter[bool] = lambda x: true if x else false + + +class BooleanFunction(Application, Boolean): + """Boolean function is a function that lives in a boolean space + It is used as base class for :py:class:`~.And`, :py:class:`~.Or`, + :py:class:`~.Not`, etc. + """ + is_Boolean = True + + def _eval_simplify(self, **kwargs): + rv = simplify_univariate(self) + if not isinstance(rv, BooleanFunction): + return rv.simplify(**kwargs) + rv = rv.func(*[a.simplify(**kwargs) for a in rv.args]) + return simplify_logic(rv) + + def simplify(self, **kwargs): + from sympy.simplify.simplify import simplify + return simplify(self, **kwargs) + + def __lt__(self, other): + raise TypeError(filldedent(''' + A Boolean argument can only be used in + Eq and Ne; all other relationals expect + real expressions. + ''')) + __le__ = __lt__ + __ge__ = __lt__ + __gt__ = __lt__ + + @classmethod + def binary_check_and_simplify(self, *args): + return [as_Boolean(i) for i in args] + + def to_nnf(self, simplify=True): + return self._to_nnf(*self.args, simplify=simplify) + + def to_anf(self, deep=True): + return self._to_anf(*self.args, deep=deep) + + @classmethod + def _to_nnf(cls, *args, **kwargs): + simplify = kwargs.get('simplify', True) + argset = set() + for arg in args: + if not is_literal(arg): + arg = arg.to_nnf(simplify) + if simplify: + if isinstance(arg, cls): + arg = arg.args + else: + arg = (arg,) + for a in arg: + if Not(a) in argset: + return cls.zero + argset.add(a) + else: + argset.add(arg) + return cls(*argset) + + @classmethod + def _to_anf(cls, *args, **kwargs): + deep = kwargs.get('deep', True) + new_args = [] + for arg in args: + if deep: + if not is_literal(arg) or isinstance(arg, Not): + arg = arg.to_anf(deep=deep) + new_args.append(arg) + return cls(*new_args, remove_true=False) + + # the diff method below is copied from Expr class + def diff(self, *symbols, **assumptions): + assumptions.setdefault("evaluate", True) + return Derivative(self, *symbols, **assumptions) + + def _eval_derivative(self, x): + if x in self.binary_symbols: + from sympy.core.relational import Eq + from sympy.functions.elementary.piecewise import Piecewise + return Piecewise( + (0, Eq(self.subs(x, 0), self.subs(x, 1))), + (1, True)) + elif x in self.free_symbols: + # not implemented, see https://www.encyclopediaofmath.org/ + # index.php/Boolean_differential_calculus + pass + else: + return S.Zero + + +class And(LatticeOp, BooleanFunction): + """ + Logical AND function. + + It evaluates its arguments in order, returning false immediately + when an argument is false and true if they are all true. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import And + >>> x & y + x & y + + Notes + ===== + + The ``&`` operator is provided as a convenience, but note that its use + here is different from its normal use in Python, which is bitwise + and. Hence, ``And(a, b)`` and ``a & b`` will produce different results if + ``a`` and ``b`` are integers. + + >>> And(x, y).subs(x, 1) + y + + """ + zero = false + identity = true + + nargs = None + + @classmethod + def _new_args_filter(cls, args): + args = BooleanFunction.binary_check_and_simplify(*args) + args = LatticeOp._new_args_filter(args, And) + newargs = [] + rel = set() + for x in ordered(args): + if x.is_Relational: + c = x.canonical + if c in rel: + continue + elif c.negated.canonical in rel: + return [false] + else: + rel.add(c) + newargs.append(x) + return newargs + + def _eval_subs(self, old, new): + args = [] + bad = None + for i in self.args: + try: + i = i.subs(old, new) + except TypeError: + # store TypeError + if bad is None: + bad = i + continue + if i == False: + return false + elif i != True: + args.append(i) + if bad is not None: + # let it raise + bad.subs(old, new) + # If old is And, replace the parts of the arguments with new if all + # are there + if isinstance(old, And): + old_set = set(old.args) + if old_set.issubset(args): + args = set(args) - old_set + args.add(new) + + return self.func(*args) + + def _eval_simplify(self, **kwargs): + from sympy.core.relational import Equality, Relational + from sympy.solvers.solveset import linear_coeffs + # standard simplify + rv = super()._eval_simplify(**kwargs) + if not isinstance(rv, And): + return rv + + # simplify args that are equalities involving + # symbols so x == 0 & x == y -> x==0 & y == 0 + Rel, nonRel = sift(rv.args, lambda i: isinstance(i, Relational), + binary=True) + if not Rel: + return rv + eqs, other = sift(Rel, lambda i: isinstance(i, Equality), binary=True) + + measure = kwargs['measure'] + if eqs: + ratio = kwargs['ratio'] + reps = {} + sifted = {} + # group by length of free symbols + sifted = sift(ordered([ + (i.free_symbols, i) for i in eqs]), + lambda x: len(x[0])) + eqs = [] + nonlineqs = [] + while 1 in sifted: + for free, e in sifted.pop(1): + x = free.pop() + if (e.lhs != x or x in e.rhs.free_symbols) and x not in reps: + try: + m, b = linear_coeffs( + Add(e.lhs, -e.rhs, evaluate=False), x) + enew = e.func(x, -b/m) + if measure(enew) <= ratio*measure(e): + e = enew + else: + eqs.append(e) + continue + except ValueError: + pass + if x in reps: + eqs.append(e.subs(x, reps[x])) + elif e.lhs == x and x not in e.rhs.free_symbols: + reps[x] = e.rhs + eqs.append(e) + else: + # x is not yet identified, but may be later + nonlineqs.append(e) + resifted = defaultdict(list) + for k in sifted: + for f, e in sifted[k]: + e = e.xreplace(reps) + f = e.free_symbols + resifted[len(f)].append((f, e)) + sifted = resifted + for k in sifted: + eqs.extend([e for f, e in sifted[k]]) + nonlineqs = [ei.subs(reps) for ei in nonlineqs] + other = [ei.subs(reps) for ei in other] + rv = rv.func(*([i.canonical for i in (eqs + nonlineqs + other)] + nonRel)) + patterns = _simplify_patterns_and() + threeterm_patterns = _simplify_patterns_and3() + return _apply_patternbased_simplification(rv, patterns, + measure, false, + threeterm_patterns=threeterm_patterns) + + def _eval_as_set(self): + from sympy.sets.sets import Intersection + return Intersection(*[arg.as_set() for arg in self.args]) + + def _eval_rewrite_as_Nor(self, *args, **kwargs): + return Nor(*[Not(arg) for arg in self.args]) + + def to_anf(self, deep=True): + if deep: + result = And._to_anf(*self.args, deep=deep) + return distribute_xor_over_and(result) + return self + + +class Or(LatticeOp, BooleanFunction): + """ + Logical OR function + + It evaluates its arguments in order, returning true immediately + when an argument is true, and false if they are all false. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import Or + >>> x | y + x | y + + Notes + ===== + + The ``|`` operator is provided as a convenience, but note that its use + here is different from its normal use in Python, which is bitwise + or. Hence, ``Or(a, b)`` and ``a | b`` will return different things if + ``a`` and ``b`` are integers. + + >>> Or(x, y).subs(x, 0) + y + + """ + zero = true + identity = false + + @classmethod + def _new_args_filter(cls, args): + newargs = [] + rel = [] + args = BooleanFunction.binary_check_and_simplify(*args) + for x in args: + if x.is_Relational: + c = x.canonical + if c in rel: + continue + nc = c.negated.canonical + if any(r == nc for r in rel): + return [true] + rel.append(c) + newargs.append(x) + return LatticeOp._new_args_filter(newargs, Or) + + def _eval_subs(self, old, new): + args = [] + bad = None + for i in self.args: + try: + i = i.subs(old, new) + except TypeError: + # store TypeError + if bad is None: + bad = i + continue + if i == True: + return true + elif i != False: + args.append(i) + if bad is not None: + # let it raise + bad.subs(old, new) + # If old is Or, replace the parts of the arguments with new if all + # are there + if isinstance(old, Or): + old_set = set(old.args) + if old_set.issubset(args): + args = set(args) - old_set + args.add(new) + + return self.func(*args) + + def _eval_as_set(self): + from sympy.sets.sets import Union + return Union(*[arg.as_set() for arg in self.args]) + + def _eval_rewrite_as_Nand(self, *args, **kwargs): + return Nand(*[Not(arg) for arg in self.args]) + + def _eval_simplify(self, **kwargs): + from sympy.core.relational import Le, Ge, Eq + lege = self.atoms(Le, Ge) + if lege: + reps = {i: self.func( + Eq(i.lhs, i.rhs), i.strict) for i in lege} + return self.xreplace(reps)._eval_simplify(**kwargs) + # standard simplify + rv = super()._eval_simplify(**kwargs) + if not isinstance(rv, Or): + return rv + patterns = _simplify_patterns_or() + return _apply_patternbased_simplification(rv, patterns, + kwargs['measure'], true) + + def to_anf(self, deep=True): + args = range(1, len(self.args) + 1) + args = (combinations(self.args, j) for j in args) + args = chain.from_iterable(args) # powerset + args = (And(*arg) for arg in args) + args = (to_anf(x, deep=deep) if deep else x for x in args) + return Xor(*list(args), remove_true=False) + + +class Not(BooleanFunction): + """ + Logical Not function (negation) + + + Returns ``true`` if the statement is ``false`` or ``False``. + Returns ``false`` if the statement is ``true`` or ``True``. + + Examples + ======== + + >>> from sympy import Not, And, Or + >>> from sympy.abc import x, A, B + >>> Not(True) + False + >>> Not(False) + True + >>> Not(And(True, False)) + True + >>> Not(Or(True, False)) + False + >>> Not(And(And(True, x), Or(x, False))) + ~x + >>> ~x + ~x + >>> Not(And(Or(A, B), Or(~A, ~B))) + ~((A | B) & (~A | ~B)) + + Notes + ===== + + - The ``~`` operator is provided as a convenience, but note that its use + here is different from its normal use in Python, which is bitwise + not. In particular, ``~a`` and ``Not(a)`` will be different if ``a`` is + an integer. Furthermore, since bools in Python subclass from ``int``, + ``~True`` is the same as ``~1`` which is ``-2``, which has a boolean + value of True. To avoid this issue, use the SymPy boolean types + ``true`` and ``false``. + + - As of Python 3.12, the bitwise not operator ``~`` used on a + Python ``bool`` is deprecated and will emit a warning. + + >>> from sympy import true + >>> ~True # doctest: +SKIP + -2 + >>> ~true + False + + """ + + is_Not = True + + @classmethod + def eval(cls, arg): + if isinstance(arg, Number) or arg in (True, False): + return false if arg else true + if arg.is_Not: + return arg.args[0] + # Simplify Relational objects. + if arg.is_Relational: + return arg.negated + + def _eval_as_set(self): + """ + Rewrite logic operators and relationals in terms of real sets. + + Examples + ======== + + >>> from sympy import Not, Symbol + >>> x = Symbol('x') + >>> Not(x > 0).as_set() + Interval(-oo, 0) + """ + return self.args[0].as_set().complement(S.Reals) + + def to_nnf(self, simplify=True): + if is_literal(self): + return self + + expr = self.args[0] + + func, args = expr.func, expr.args + + if func == And: + return Or._to_nnf(*[Not(arg) for arg in args], simplify=simplify) + + if func == Or: + return And._to_nnf(*[Not(arg) for arg in args], simplify=simplify) + + if func == Implies: + a, b = args + return And._to_nnf(a, Not(b), simplify=simplify) + + if func == Equivalent: + return And._to_nnf(Or(*args), Or(*[Not(arg) for arg in args]), + simplify=simplify) + + if func == Xor: + result = [] + for i in range(1, len(args)+1, 2): + for neg in combinations(args, i): + clause = [Not(s) if s in neg else s for s in args] + result.append(Or(*clause)) + return And._to_nnf(*result, simplify=simplify) + + if func == ITE: + a, b, c = args + return And._to_nnf(Or(a, Not(c)), Or(Not(a), Not(b)), simplify=simplify) + + raise ValueError("Illegal operator %s in expression" % func) + + def to_anf(self, deep=True): + return Xor._to_anf(true, self.args[0], deep=deep) + + +class Xor(BooleanFunction): + """ + Logical XOR (exclusive OR) function. + + + Returns True if an odd number of the arguments are True and the rest are + False. + + Returns False if an even number of the arguments are True and the rest are + False. + + Examples + ======== + + >>> from sympy.logic.boolalg import Xor + >>> from sympy import symbols + >>> x, y = symbols('x y') + >>> Xor(True, False) + True + >>> Xor(True, True) + False + >>> Xor(True, False, True, True, False) + True + >>> Xor(True, False, True, False) + False + >>> x ^ y + x ^ y + + Notes + ===== + + The ``^`` operator is provided as a convenience, but note that its use + here is different from its normal use in Python, which is bitwise xor. In + particular, ``a ^ b`` and ``Xor(a, b)`` will be different if ``a`` and + ``b`` are integers. + + >>> Xor(x, y).subs(y, 0) + x + + """ + def __new__(cls, *args, remove_true=True, **kwargs): + argset = set() + obj = super().__new__(cls, *args, **kwargs) + for arg in obj._args: + if isinstance(arg, Number) or arg in (True, False): + if arg: + arg = true + else: + continue + if isinstance(arg, Xor): + for a in arg.args: + argset.remove(a) if a in argset else argset.add(a) + elif arg in argset: + argset.remove(arg) + else: + argset.add(arg) + rel = [(r, r.canonical, r.negated.canonical) + for r in argset if r.is_Relational] + odd = False # is number of complimentary pairs odd? start 0 -> False + remove = [] + for i, (r, c, nc) in enumerate(rel): + for j in range(i + 1, len(rel)): + rj, cj = rel[j][:2] + if cj == nc: + odd = not odd + break + elif cj == c: + break + else: + continue + remove.append((r, rj)) + if odd: + argset.remove(true) if true in argset else argset.add(true) + for a, b in remove: + argset.remove(a) + argset.remove(b) + if len(argset) == 0: + return false + elif len(argset) == 1: + return argset.pop() + elif True in argset and remove_true: + argset.remove(True) + return Not(Xor(*argset)) + else: + obj._args = tuple(ordered(argset)) + obj._argset = frozenset(argset) + return obj + + # XXX: This should be cached on the object rather than using cacheit + # Maybe it can be computed in __new__? + @property # type: ignore + @cacheit + def args(self): + return tuple(ordered(self._argset)) + + def to_nnf(self, simplify=True): + args = [] + for i in range(0, len(self.args)+1, 2): + for neg in combinations(self.args, i): + clause = [Not(s) if s in neg else s for s in self.args] + args.append(Or(*clause)) + return And._to_nnf(*args, simplify=simplify) + + def _eval_rewrite_as_Or(self, *args, **kwargs): + a = self.args + return Or(*[_convert_to_varsSOP(x, self.args) + for x in _get_odd_parity_terms(len(a))]) + + def _eval_rewrite_as_And(self, *args, **kwargs): + a = self.args + return And(*[_convert_to_varsPOS(x, self.args) + for x in _get_even_parity_terms(len(a))]) + + def _eval_simplify(self, **kwargs): + # as standard simplify uses simplify_logic which writes things as + # And and Or, we only simplify the partial expressions before using + # patterns + rv = self.func(*[a.simplify(**kwargs) for a in self.args]) + rv = rv.to_anf() + if not isinstance(rv, Xor): # This shouldn't really happen here + return rv + patterns = _simplify_patterns_xor() + return _apply_patternbased_simplification(rv, patterns, + kwargs['measure'], None) + + def _eval_subs(self, old, new): + # If old is Xor, replace the parts of the arguments with new if all + # are there + if isinstance(old, Xor): + old_set = set(old.args) + if old_set.issubset(self.args): + args = set(self.args) - old_set + args.add(new) + return self.func(*args) + + +class Nand(BooleanFunction): + """ + Logical NAND function. + + It evaluates its arguments in order, giving True immediately if any + of them are False, and False if they are all True. + + Returns True if any of the arguments are False + Returns False if all arguments are True + + Examples + ======== + + >>> from sympy.logic.boolalg import Nand + >>> from sympy import symbols + >>> x, y = symbols('x y') + >>> Nand(False, True) + True + >>> Nand(True, True) + False + >>> Nand(x, y) + ~(x & y) + + """ + @classmethod + def eval(cls, *args): + return Not(And(*args)) + + +class Nor(BooleanFunction): + """ + Logical NOR function. + + It evaluates its arguments in order, giving False immediately if any + of them are True, and True if they are all False. + + Returns False if any argument is True + Returns True if all arguments are False + + Examples + ======== + + >>> from sympy.logic.boolalg import Nor + >>> from sympy import symbols + >>> x, y = symbols('x y') + + >>> Nor(True, False) + False + >>> Nor(True, True) + False + >>> Nor(False, True) + False + >>> Nor(False, False) + True + >>> Nor(x, y) + ~(x | y) + + """ + @classmethod + def eval(cls, *args): + return Not(Or(*args)) + + +class Xnor(BooleanFunction): + """ + Logical XNOR function. + + Returns False if an odd number of the arguments are True and the rest are + False. + + Returns True if an even number of the arguments are True and the rest are + False. + + Examples + ======== + + >>> from sympy.logic.boolalg import Xnor + >>> from sympy import symbols + >>> x, y = symbols('x y') + >>> Xnor(True, False) + False + >>> Xnor(True, True) + True + >>> Xnor(True, False, True, True, False) + False + >>> Xnor(True, False, True, False) + True + + """ + @classmethod + def eval(cls, *args): + return Not(Xor(*args)) + + +class Implies(BooleanFunction): + r""" + Logical implication. + + A implies B is equivalent to if A then B. Mathematically, it is written + as `A \Rightarrow B` and is equivalent to `\neg A \vee B` or ``~A | B``. + + Accepts two Boolean arguments; A and B. + Returns False if A is True and B is False + Returns True otherwise. + + Examples + ======== + + >>> from sympy.logic.boolalg import Implies + >>> from sympy import symbols + >>> x, y = symbols('x y') + + >>> Implies(True, False) + False + >>> Implies(False, False) + True + >>> Implies(True, True) + True + >>> Implies(False, True) + True + >>> x >> y + Implies(x, y) + >>> y << x + Implies(x, y) + + Notes + ===== + + The ``>>`` and ``<<`` operators are provided as a convenience, but note + that their use here is different from their normal use in Python, which is + bit shifts. Hence, ``Implies(a, b)`` and ``a >> b`` will return different + things if ``a`` and ``b`` are integers. In particular, since Python + considers ``True`` and ``False`` to be integers, ``True >> True`` will be + the same as ``1 >> 1``, i.e., 0, which has a truth value of False. To + avoid this issue, use the SymPy objects ``true`` and ``false``. + + >>> from sympy import true, false + >>> True >> False + 1 + >>> true >> false + False + + """ + @classmethod + def eval(cls, *args): + try: + newargs = [] + for x in args: + if isinstance(x, Number) or x in (0, 1): + newargs.append(bool(x)) + else: + newargs.append(x) + A, B = newargs + except ValueError: + raise ValueError( + "%d operand(s) used for an Implies " + "(pairs are required): %s" % (len(args), str(args))) + if A in (True, False) or B in (True, False): + return Or(Not(A), B) + elif A == B: + return true + elif A.is_Relational and B.is_Relational: + if A.canonical == B.canonical: + return true + if A.negated.canonical == B.canonical: + return B + else: + return Basic.__new__(cls, *args) + + def to_nnf(self, simplify=True): + a, b = self.args + return Or._to_nnf(Not(a), b, simplify=simplify) + + def to_anf(self, deep=True): + a, b = self.args + return Xor._to_anf(true, a, And(a, b), deep=deep) + + +class Equivalent(BooleanFunction): + """ + Equivalence relation. + + ``Equivalent(A, B)`` is True iff A and B are both True or both False. + + Returns True if all of the arguments are logically equivalent. + Returns False otherwise. + + For two arguments, this is equivalent to :py:class:`~.Xnor`. + + Examples + ======== + + >>> from sympy.logic.boolalg import Equivalent, And + >>> from sympy.abc import x + >>> Equivalent(False, False, False) + True + >>> Equivalent(True, False, False) + False + >>> Equivalent(x, And(x, True)) + True + + """ + def __new__(cls, *args, **options): + from sympy.core.relational import Relational + args = [_sympify(arg) for arg in args] + + argset = set(args) + for x in args: + if isinstance(x, Number) or x in [True, False]: # Includes 0, 1 + argset.discard(x) + argset.add(bool(x)) + rel = [] + for r in argset: + if isinstance(r, Relational): + rel.append((r, r.canonical, r.negated.canonical)) + remove = [] + for i, (r, c, nc) in enumerate(rel): + for j in range(i + 1, len(rel)): + rj, cj = rel[j][:2] + if cj == nc: + return false + elif cj == c: + remove.append((r, rj)) + break + for a, b in remove: + argset.remove(a) + argset.remove(b) + argset.add(True) + if len(argset) <= 1: + return true + if True in argset: + argset.discard(True) + return And(*argset) + if False in argset: + argset.discard(False) + return And(*[Not(arg) for arg in argset]) + _args = frozenset(argset) + obj = super().__new__(cls, _args) + obj._argset = _args + return obj + + # XXX: This should be cached on the object rather than using cacheit + # Maybe it can be computed in __new__? + @property # type: ignore + @cacheit + def args(self): + return tuple(ordered(self._argset)) + + def to_nnf(self, simplify=True): + args = [] + for a, b in zip(self.args, self.args[1:]): + args.append(Or(Not(a), b)) + args.append(Or(Not(self.args[-1]), self.args[0])) + return And._to_nnf(*args, simplify=simplify) + + def to_anf(self, deep=True): + a = And(*self.args) + b = And(*[to_anf(Not(arg), deep=False) for arg in self.args]) + b = distribute_xor_over_and(b) + return Xor._to_anf(a, b, deep=deep) + + +class ITE(BooleanFunction): + """ + If-then-else clause. + + ``ITE(A, B, C)`` evaluates and returns the result of B if A is true + else it returns the result of C. All args must be Booleans. + + From a logic gate perspective, ITE corresponds to a 2-to-1 multiplexer, + where A is the select signal. + + Examples + ======== + + >>> from sympy.logic.boolalg import ITE, And, Xor, Or + >>> from sympy.abc import x, y, z + >>> ITE(True, False, True) + False + >>> ITE(Or(True, False), And(True, True), Xor(True, True)) + True + >>> ITE(x, y, z) + ITE(x, y, z) + >>> ITE(True, x, y) + x + >>> ITE(False, x, y) + y + >>> ITE(x, y, y) + y + + Trying to use non-Boolean args will generate a TypeError: + + >>> ITE(True, [], ()) + Traceback (most recent call last): + ... + TypeError: expecting bool, Boolean or ITE, not `[]` + + """ + def __new__(cls, *args, **kwargs): + from sympy.core.relational import Eq, Ne + if len(args) != 3: + raise ValueError('expecting exactly 3 args') + a, b, c = args + # check use of binary symbols + if isinstance(a, (Eq, Ne)): + # in this context, we can evaluate the Eq/Ne + # if one arg is a binary symbol and the other + # is true/false + b, c = map(as_Boolean, (b, c)) + bin_syms = set().union(*[i.binary_symbols for i in (b, c)]) + if len(set(a.args) - bin_syms) == 1: + # one arg is a binary_symbols + _a = a + if a.lhs is true: + a = a.rhs + elif a.rhs is true: + a = a.lhs + elif a.lhs is false: + a = Not(a.rhs) + elif a.rhs is false: + a = Not(a.lhs) + else: + # binary can only equal True or False + a = false + if isinstance(_a, Ne): + a = Not(a) + else: + a, b, c = BooleanFunction.binary_check_and_simplify( + a, b, c) + rv = None + if kwargs.get('evaluate', True): + rv = cls.eval(a, b, c) + if rv is None: + rv = BooleanFunction.__new__(cls, a, b, c, evaluate=False) + return rv + + @classmethod + def eval(cls, *args): + from sympy.core.relational import Eq, Ne + # do the args give a singular result? + a, b, c = args + if isinstance(a, (Ne, Eq)): + _a = a + if true in a.args: + a = a.lhs if a.rhs is true else a.rhs + elif false in a.args: + a = Not(a.lhs) if a.rhs is false else Not(a.rhs) + else: + _a = None + if _a is not None and isinstance(_a, Ne): + a = Not(a) + if a is true: + return b + if a is false: + return c + if b == c: + return b + else: + # or maybe the results allow the answer to be expressed + # in terms of the condition + if b is true and c is false: + return a + if b is false and c is true: + return Not(a) + if [a, b, c] != args: + return cls(a, b, c, evaluate=False) + + def to_nnf(self, simplify=True): + a, b, c = self.args + return And._to_nnf(Or(Not(a), b), Or(a, c), simplify=simplify) + + def _eval_as_set(self): + return self.to_nnf().as_set() + + def _eval_rewrite_as_Piecewise(self, *args, **kwargs): + from sympy.functions.elementary.piecewise import Piecewise + return Piecewise((args[1], args[0]), (args[2], True)) + + +class Exclusive(BooleanFunction): + """ + True if only one or no argument is true. + + ``Exclusive(A, B, C)`` is equivalent to ``~(A & B) & ~(A & C) & ~(B & C)``. + + For two arguments, this is equivalent to :py:class:`~.Xor`. + + Examples + ======== + + >>> from sympy.logic.boolalg import Exclusive + >>> Exclusive(False, False, False) + True + >>> Exclusive(False, True, False) + True + >>> Exclusive(False, True, True) + False + + """ + @classmethod + def eval(cls, *args): + and_args = [] + for a, b in combinations(args, 2): + and_args.append(Not(And(a, b))) + return And(*and_args) + + +# end class definitions. Some useful methods + + +def conjuncts(expr): + """Return a list of the conjuncts in ``expr``. + + Examples + ======== + + >>> from sympy.logic.boolalg import conjuncts + >>> from sympy.abc import A, B + >>> conjuncts(A & B) + frozenset({A, B}) + >>> conjuncts(A | B) + frozenset({A | B}) + + """ + return And.make_args(expr) + + +def disjuncts(expr): + """Return a list of the disjuncts in ``expr``. + + Examples + ======== + + >>> from sympy.logic.boolalg import disjuncts + >>> from sympy.abc import A, B + >>> disjuncts(A | B) + frozenset({A, B}) + >>> disjuncts(A & B) + frozenset({A & B}) + + """ + return Or.make_args(expr) + + +def distribute_and_over_or(expr): + """ + Given a sentence ``expr`` consisting of conjunctions and disjunctions + of literals, return an equivalent sentence in CNF. + + Examples + ======== + + >>> from sympy.logic.boolalg import distribute_and_over_or, And, Or, Not + >>> from sympy.abc import A, B, C + >>> distribute_and_over_or(Or(A, And(Not(B), Not(C)))) + (A | ~B) & (A | ~C) + + """ + return _distribute((expr, And, Or)) + + +def distribute_or_over_and(expr): + """ + Given a sentence ``expr`` consisting of conjunctions and disjunctions + of literals, return an equivalent sentence in DNF. + + Note that the output is NOT simplified. + + Examples + ======== + + >>> from sympy.logic.boolalg import distribute_or_over_and, And, Or, Not + >>> from sympy.abc import A, B, C + >>> distribute_or_over_and(And(Or(Not(A), B), C)) + (B & C) | (C & ~A) + + """ + return _distribute((expr, Or, And)) + + +def distribute_xor_over_and(expr): + """ + Given a sentence ``expr`` consisting of conjunction and + exclusive disjunctions of literals, return an + equivalent exclusive disjunction. + + Note that the output is NOT simplified. + + Examples + ======== + + >>> from sympy.logic.boolalg import distribute_xor_over_and, And, Xor, Not + >>> from sympy.abc import A, B, C + >>> distribute_xor_over_and(And(Xor(Not(A), B), C)) + (B & C) ^ (C & ~A) + """ + return _distribute((expr, Xor, And)) + + +def _distribute(info): + """ + Distributes ``info[1]`` over ``info[2]`` with respect to ``info[0]``. + """ + if isinstance(info[0], info[2]): + for arg in info[0].args: + if isinstance(arg, info[1]): + conj = arg + break + else: + return info[0] + rest = info[2](*[a for a in info[0].args if a is not conj]) + return info[1](*list(map(_distribute, + [(info[2](c, rest), info[1], info[2]) + for c in conj.args])), remove_true=False) + elif isinstance(info[0], info[1]): + return info[1](*list(map(_distribute, + [(x, info[1], info[2]) + for x in info[0].args])), + remove_true=False) + else: + return info[0] + + +def to_anf(expr, deep=True): + r""" + Converts expr to Algebraic Normal Form (ANF). + + ANF is a canonical normal form, which means that two + equivalent formulas will convert to the same ANF. + + A logical expression is in ANF if it has the form + + .. math:: 1 \oplus a \oplus b \oplus ab \oplus abc + + i.e. it can be: + - purely true, + - purely false, + - conjunction of variables, + - exclusive disjunction. + + The exclusive disjunction can only contain true, variables + or conjunction of variables. No negations are permitted. + + If ``deep`` is ``False``, arguments of the boolean + expression are considered variables, i.e. only the + top-level expression is converted to ANF. + + Examples + ======== + >>> from sympy.logic.boolalg import And, Or, Not, Implies, Equivalent + >>> from sympy.logic.boolalg import to_anf + >>> from sympy.abc import A, B, C + >>> to_anf(Not(A)) + A ^ True + >>> to_anf(And(Or(A, B), Not(C))) + A ^ B ^ (A & B) ^ (A & C) ^ (B & C) ^ (A & B & C) + >>> to_anf(Implies(Not(A), Equivalent(B, C)), deep=False) + True ^ ~A ^ (~A & (Equivalent(B, C))) + + """ + expr = sympify(expr) + + if is_anf(expr): + return expr + return expr.to_anf(deep=deep) + + +def to_nnf(expr, simplify=True): + """ + Converts ``expr`` to Negation Normal Form (NNF). + + A logical expression is in NNF if it + contains only :py:class:`~.And`, :py:class:`~.Or` and :py:class:`~.Not`, + and :py:class:`~.Not` is applied only to literals. + If ``simplify`` is ``True``, the result contains no redundant clauses. + + Examples + ======== + + >>> from sympy.abc import A, B, C, D + >>> from sympy.logic.boolalg import Not, Equivalent, to_nnf + >>> to_nnf(Not((~A & ~B) | (C & D))) + (A | B) & (~C | ~D) + >>> to_nnf(Equivalent(A >> B, B >> A)) + (A | ~B | (A & ~B)) & (B | ~A | (B & ~A)) + + """ + if is_nnf(expr, simplify): + return expr + return expr.to_nnf(simplify) + + +def to_cnf(expr, simplify=False, force=False): + """ + Convert a propositional logical sentence ``expr`` to conjunctive normal + form: ``((A | ~B | ...) & (B | C | ...) & ...)``. + If ``simplify`` is ``True``, ``expr`` is evaluated to its simplest CNF + form using the Quine-McCluskey algorithm; this may take a long + time. If there are more than 8 variables the ``force`` flag must be set + to ``True`` to simplify (default is ``False``). + + Examples + ======== + + >>> from sympy.logic.boolalg import to_cnf + >>> from sympy.abc import A, B, D + >>> to_cnf(~(A | B) | D) + (D | ~A) & (D | ~B) + >>> to_cnf((A | B) & (A | ~A), True) + A | B + + """ + expr = sympify(expr) + if not isinstance(expr, BooleanFunction): + return expr + + if simplify: + if not force and len(_find_predicates(expr)) > 8: + raise ValueError(filldedent(''' + To simplify a logical expression with more + than 8 variables may take a long time and requires + the use of `force=True`.''')) + return simplify_logic(expr, 'cnf', True, force=force) + + # Don't convert unless we have to + if is_cnf(expr): + return expr + + expr = eliminate_implications(expr) + res = distribute_and_over_or(expr) + + return res + + +def to_dnf(expr, simplify=False, force=False): + """ + Convert a propositional logical sentence ``expr`` to disjunctive normal + form: ``((A & ~B & ...) | (B & C & ...) | ...)``. + If ``simplify`` is ``True``, ``expr`` is evaluated to its simplest DNF form using + the Quine-McCluskey algorithm; this may take a long + time. If there are more than 8 variables, the ``force`` flag must be set to + ``True`` to simplify (default is ``False``). + + Examples + ======== + + >>> from sympy.logic.boolalg import to_dnf + >>> from sympy.abc import A, B, C + >>> to_dnf(B & (A | C)) + (A & B) | (B & C) + >>> to_dnf((A & B) | (A & ~B) | (B & C) | (~B & C), True) + A | C + + """ + expr = sympify(expr) + if not isinstance(expr, BooleanFunction): + return expr + + if simplify: + if not force and len(_find_predicates(expr)) > 8: + raise ValueError(filldedent(''' + To simplify a logical expression with more + than 8 variables may take a long time and requires + the use of `force=True`.''')) + return simplify_logic(expr, 'dnf', True, force=force) + + # Don't convert unless we have to + if is_dnf(expr): + return expr + + expr = eliminate_implications(expr) + return distribute_or_over_and(expr) + + +def is_anf(expr): + r""" + Checks if ``expr`` is in Algebraic Normal Form (ANF). + + A logical expression is in ANF if it has the form + + .. math:: 1 \oplus a \oplus b \oplus ab \oplus abc + + i.e. it is purely true, purely false, conjunction of + variables or exclusive disjunction. The exclusive + disjunction can only contain true, variables or + conjunction of variables. No negations are permitted. + + Examples + ======== + + >>> from sympy.logic.boolalg import And, Not, Xor, true, is_anf + >>> from sympy.abc import A, B, C + >>> is_anf(true) + True + >>> is_anf(A) + True + >>> is_anf(And(A, B, C)) + True + >>> is_anf(Xor(A, Not(B))) + False + + """ + expr = sympify(expr) + + if is_literal(expr) and not isinstance(expr, Not): + return True + + if isinstance(expr, And): + for arg in expr.args: + if not arg.is_Symbol: + return False + return True + + elif isinstance(expr, Xor): + for arg in expr.args: + if isinstance(arg, And): + for a in arg.args: + if not a.is_Symbol: + return False + elif is_literal(arg): + if isinstance(arg, Not): + return False + else: + return False + return True + + else: + return False + + +def is_nnf(expr, simplified=True): + """ + Checks if ``expr`` is in Negation Normal Form (NNF). + + A logical expression is in NNF if it + contains only :py:class:`~.And`, :py:class:`~.Or` and :py:class:`~.Not`, + and :py:class:`~.Not` is applied only to literals. + If ``simplified`` is ``True``, checks if result contains no redundant clauses. + + Examples + ======== + + >>> from sympy.abc import A, B, C + >>> from sympy.logic.boolalg import Not, is_nnf + >>> is_nnf(A & B | ~C) + True + >>> is_nnf((A | ~A) & (B | C)) + False + >>> is_nnf((A | ~A) & (B | C), False) + True + >>> is_nnf(Not(A & B) | C) + False + >>> is_nnf((A >> B) & (B >> A)) + False + + """ + + expr = sympify(expr) + if is_literal(expr): + return True + + stack = [expr] + + while stack: + expr = stack.pop() + if expr.func in (And, Or): + if simplified: + args = expr.args + for arg in args: + if Not(arg) in args: + return False + stack.extend(expr.args) + + elif not is_literal(expr): + return False + + return True + + +def is_cnf(expr): + """ + Test whether or not an expression is in conjunctive normal form. + + Examples + ======== + + >>> from sympy.logic.boolalg import is_cnf + >>> from sympy.abc import A, B, C + >>> is_cnf(A | B | C) + True + >>> is_cnf(A & B & C) + True + >>> is_cnf((A & B) | C) + False + + """ + return _is_form(expr, And, Or) + + +def is_dnf(expr): + """ + Test whether or not an expression is in disjunctive normal form. + + Examples + ======== + + >>> from sympy.logic.boolalg import is_dnf + >>> from sympy.abc import A, B, C + >>> is_dnf(A | B | C) + True + >>> is_dnf(A & B & C) + True + >>> is_dnf((A & B) | C) + True + >>> is_dnf(A & (B | C)) + False + + """ + return _is_form(expr, Or, And) + + +def _is_form(expr, function1, function2): + """ + Test whether or not an expression is of the required form. + + """ + expr = sympify(expr) + + vals = function1.make_args(expr) if isinstance(expr, function1) else [expr] + for lit in vals: + if isinstance(lit, function2): + vals2 = function2.make_args(lit) if isinstance(lit, function2) else [lit] + for l in vals2: + if is_literal(l) is False: + return False + elif is_literal(lit) is False: + return False + + return True + + +def eliminate_implications(expr): + """ + Change :py:class:`~.Implies` and :py:class:`~.Equivalent` into + :py:class:`~.And`, :py:class:`~.Or`, and :py:class:`~.Not`. + That is, return an expression that is equivalent to ``expr``, but has only + ``&``, ``|``, and ``~`` as logical + operators. + + Examples + ======== + + >>> from sympy.logic.boolalg import Implies, Equivalent, \ + eliminate_implications + >>> from sympy.abc import A, B, C + >>> eliminate_implications(Implies(A, B)) + B | ~A + >>> eliminate_implications(Equivalent(A, B)) + (A | ~B) & (B | ~A) + >>> eliminate_implications(Equivalent(A, B, C)) + (A | ~C) & (B | ~A) & (C | ~B) + + """ + return to_nnf(expr, simplify=False) + + +def is_literal(expr): + """ + Returns True if expr is a literal, else False. + + Examples + ======== + + >>> from sympy import Or, Q + >>> from sympy.abc import A, B + >>> from sympy.logic.boolalg import is_literal + >>> is_literal(A) + True + >>> is_literal(~A) + True + >>> is_literal(Q.zero(A)) + True + >>> is_literal(A + B) + True + >>> is_literal(Or(A, B)) + False + + """ + from sympy.assumptions import AppliedPredicate + + if isinstance(expr, Not): + return is_literal(expr.args[0]) + elif expr in (True, False) or isinstance(expr, AppliedPredicate) or expr.is_Atom: + return True + elif not isinstance(expr, BooleanFunction) and all( + (isinstance(expr, AppliedPredicate) or a.is_Atom) for a in expr.args): + return True + return False + + +def to_int_repr(clauses, symbols): + """ + Takes clauses in CNF format and puts them into an integer representation. + + Examples + ======== + + >>> from sympy.logic.boolalg import to_int_repr + >>> from sympy.abc import x, y + >>> to_int_repr([x | y, y], [x, y]) == [{1, 2}, {2}] + True + + """ + + # Convert the symbol list into a dict + symbols = dict(zip(symbols, range(1, len(symbols) + 1))) + + def append_symbol(arg, symbols): + if isinstance(arg, Not): + return -symbols[arg.args[0]] + else: + return symbols[arg] + + return [{append_symbol(arg, symbols) for arg in Or.make_args(c)} + for c in clauses] + + +def term_to_integer(term): + """ + Return an integer corresponding to the base-2 digits given by *term*. + + Parameters + ========== + + term : a string or list of ones and zeros + + Examples + ======== + + >>> from sympy.logic.boolalg import term_to_integer + >>> term_to_integer([1, 0, 0]) + 4 + >>> term_to_integer('100') + 4 + + """ + + return int(''.join(list(map(str, list(term)))), 2) + + +integer_to_term = ibin # XXX could delete? + + +def truth_table(expr, variables, input=True): + """ + Return a generator of all possible configurations of the input variables, + and the result of the boolean expression for those values. + + Parameters + ========== + + expr : Boolean expression + + variables : list of variables + + input : bool (default ``True``) + Indicates whether to return the input combinations. + + Examples + ======== + + >>> from sympy.logic.boolalg import truth_table + >>> from sympy.abc import x,y + >>> table = truth_table(x >> y, [x, y]) + >>> for t in table: + ... print('{0} -> {1}'.format(*t)) + [0, 0] -> True + [0, 1] -> True + [1, 0] -> False + [1, 1] -> True + + >>> table = truth_table(x | y, [x, y]) + >>> list(table) + [([0, 0], False), ([0, 1], True), ([1, 0], True), ([1, 1], True)] + + If ``input`` is ``False``, ``truth_table`` returns only a list of truth values. + In this case, the corresponding input values of variables can be + deduced from the index of a given output. + + >>> from sympy.utilities.iterables import ibin + >>> vars = [y, x] + >>> values = truth_table(x >> y, vars, input=False) + >>> values = list(values) + >>> values + [True, False, True, True] + + >>> for i, value in enumerate(values): + ... print('{0} -> {1}'.format(list(zip( + ... vars, ibin(i, len(vars)))), value)) + [(y, 0), (x, 0)] -> True + [(y, 0), (x, 1)] -> False + [(y, 1), (x, 0)] -> True + [(y, 1), (x, 1)] -> True + + """ + variables = [sympify(v) for v in variables] + + expr = sympify(expr) + if not isinstance(expr, BooleanFunction) and not is_literal(expr): + return + + table = product((0, 1), repeat=len(variables)) + for term in table: + value = expr.xreplace(dict(zip(variables, term))) + + if input: + yield list(term), value + else: + yield value + + +def _check_pair(minterm1, minterm2): + """ + Checks if a pair of minterms differs by only one bit. If yes, returns + index, else returns `-1`. + """ + # Early termination seems to be faster than list comprehension, + # at least for large examples. + index = -1 + for x, i in enumerate(minterm1): # zip(minterm1, minterm2) is slower + if i != minterm2[x]: + if index == -1: + index = x + else: + return -1 + return index + + +def _convert_to_varsSOP(minterm, variables): + """ + Converts a term in the expansion of a function from binary to its + variable form (for SOP). + """ + temp = [variables[n] if val == 1 else Not(variables[n]) + for n, val in enumerate(minterm) if val != 3] + return And(*temp) + + +def _convert_to_varsPOS(maxterm, variables): + """ + Converts a term in the expansion of a function from binary to its + variable form (for POS). + """ + temp = [variables[n] if val == 0 else Not(variables[n]) + for n, val in enumerate(maxterm) if val != 3] + return Or(*temp) + + +def _convert_to_varsANF(term, variables): + """ + Converts a term in the expansion of a function from binary to its + variable form (for ANF). + + Parameters + ========== + + term : list of 1's and 0's (complementation pattern) + variables : list of variables + + """ + temp = [variables[n] for n, t in enumerate(term) if t == 1] + + if not temp: + return true + + return And(*temp) + + +def _get_odd_parity_terms(n): + """ + Returns a list of lists, with all possible combinations of n zeros and ones + with an odd number of ones. + """ + return [e for e in [ibin(i, n) for i in range(2**n)] if sum(e) % 2 == 1] + + +def _get_even_parity_terms(n): + """ + Returns a list of lists, with all possible combinations of n zeros and ones + with an even number of ones. + """ + return [e for e in [ibin(i, n) for i in range(2**n)] if sum(e) % 2 == 0] + + +def _simplified_pairs(terms): + """ + Reduces a set of minterms, if possible, to a simplified set of minterms + with one less variable in the terms using QM method. + """ + if not terms: + return [] + + simplified_terms = [] + todo = list(range(len(terms))) + + # Count number of ones as _check_pair can only potentially match if there + # is at most a difference of a single one + termdict = defaultdict(list) + for n, term in enumerate(terms): + ones = sum(1 for t in term if t == 1) + termdict[ones].append(n) + + variables = len(terms[0]) + for k in range(variables): + for i in termdict[k]: + for j in termdict[k+1]: + index = _check_pair(terms[i], terms[j]) + if index != -1: + # Mark terms handled + todo[i] = todo[j] = None + # Copy old term + newterm = terms[i][:] + # Set differing position to don't care + newterm[index] = 3 + # Add if not already there + if newterm not in simplified_terms: + simplified_terms.append(newterm) + + if simplified_terms: + # Further simplifications only among the new terms + simplified_terms = _simplified_pairs(simplified_terms) + + # Add remaining, non-simplified, terms + simplified_terms.extend([terms[i] for i in todo if i is not None]) + return simplified_terms + + +def _rem_redundancy(l1, terms): + """ + After the truth table has been sufficiently simplified, use the prime + implicant table method to recognize and eliminate redundant pairs, + and return the essential arguments. + """ + + if not terms: + return [] + + nterms = len(terms) + nl1 = len(l1) + + # Create dominating matrix + dommatrix = [[0]*nl1 for n in range(nterms)] + colcount = [0]*nl1 + rowcount = [0]*nterms + for primei, prime in enumerate(l1): + for termi, term in enumerate(terms): + # Check prime implicant covering term + if all(t == 3 or t == mt for t, mt in zip(prime, term)): + dommatrix[termi][primei] = 1 + colcount[primei] += 1 + rowcount[termi] += 1 + + # Keep track if anything changed + anythingchanged = True + # Then, go again + while anythingchanged: + anythingchanged = False + + for rowi in range(nterms): + # Still non-dominated? + if rowcount[rowi]: + row = dommatrix[rowi] + for row2i in range(nterms): + # Still non-dominated? + if rowi != row2i and rowcount[rowi] and (rowcount[rowi] <= rowcount[row2i]): + row2 = dommatrix[row2i] + if all(row2[n] >= row[n] for n in range(nl1)): + # row2 dominating row, remove row2 + rowcount[row2i] = 0 + anythingchanged = True + for primei, prime in enumerate(row2): + if prime: + # Make corresponding entry 0 + dommatrix[row2i][primei] = 0 + colcount[primei] -= 1 + + colcache = {} + + for coli in range(nl1): + # Still non-dominated? + if colcount[coli]: + if coli in colcache: + col = colcache[coli] + else: + col = [dommatrix[i][coli] for i in range(nterms)] + colcache[coli] = col + for col2i in range(nl1): + # Still non-dominated? + if coli != col2i and colcount[col2i] and (colcount[coli] >= colcount[col2i]): + if col2i in colcache: + col2 = colcache[col2i] + else: + col2 = [dommatrix[i][col2i] for i in range(nterms)] + colcache[col2i] = col2 + if all(col[n] >= col2[n] for n in range(nterms)): + # col dominating col2, remove col2 + colcount[col2i] = 0 + anythingchanged = True + for termi, term in enumerate(col2): + if term and dommatrix[termi][col2i]: + # Make corresponding entry 0 + dommatrix[termi][col2i] = 0 + rowcount[termi] -= 1 + + if not anythingchanged: + # Heuristically select the prime implicant covering most terms + maxterms = 0 + bestcolidx = -1 + for coli in range(nl1): + s = colcount[coli] + if s > maxterms: + bestcolidx = coli + maxterms = s + + # In case we found a prime implicant covering at least two terms + if bestcolidx != -1 and maxterms > 1: + for primei, prime in enumerate(l1): + if primei != bestcolidx: + for termi, term in enumerate(colcache[bestcolidx]): + if term and dommatrix[termi][primei]: + # Make corresponding entry 0 + dommatrix[termi][primei] = 0 + anythingchanged = True + rowcount[termi] -= 1 + colcount[primei] -= 1 + + return [l1[i] for i in range(nl1) if colcount[i]] + + +def _input_to_binlist(inputlist, variables): + binlist = [] + bits = len(variables) + for val in inputlist: + if isinstance(val, int): + binlist.append(ibin(val, bits)) + elif isinstance(val, dict): + nonspecvars = list(variables) + for key in val.keys(): + nonspecvars.remove(key) + for t in product((0, 1), repeat=len(nonspecvars)): + d = dict(zip(nonspecvars, t)) + d.update(val) + binlist.append([d[v] for v in variables]) + elif isinstance(val, (list, tuple)): + if len(val) != bits: + raise ValueError("Each term must contain {bits} bits as there are" + "\n{bits} variables (or be an integer)." + "".format(bits=bits)) + binlist.append(list(val)) + else: + raise TypeError("A term list can only contain lists," + " ints or dicts.") + return binlist + + +def SOPform(variables, minterms, dontcares=None): + """ + The SOPform function uses simplified_pairs and a redundant group- + eliminating algorithm to convert the list of all input combos that + generate '1' (the minterms) into the smallest sum-of-products form. + + The variables must be given as the first argument. + + Return a logical :py:class:`~.Or` function (i.e., the "sum of products" or + "SOP" form) that gives the desired outcome. If there are inputs that can + be ignored, pass them as a list, too. + + The result will be one of the (perhaps many) functions that satisfy + the conditions. + + Examples + ======== + + >>> from sympy.logic import SOPform + >>> from sympy import symbols + >>> w, x, y, z = symbols('w x y z') + >>> minterms = [[0, 0, 0, 1], [0, 0, 1, 1], + ... [0, 1, 1, 1], [1, 0, 1, 1], [1, 1, 1, 1]] + >>> dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]] + >>> SOPform([w, x, y, z], minterms, dontcares) + (y & z) | (~w & ~x) + + The terms can also be represented as integers: + + >>> minterms = [1, 3, 7, 11, 15] + >>> dontcares = [0, 2, 5] + >>> SOPform([w, x, y, z], minterms, dontcares) + (y & z) | (~w & ~x) + + They can also be specified using dicts, which does not have to be fully + specified: + + >>> minterms = [{w: 0, x: 1}, {y: 1, z: 1, x: 0}] + >>> SOPform([w, x, y, z], minterms) + (x & ~w) | (y & z & ~x) + + Or a combination: + + >>> minterms = [4, 7, 11, [1, 1, 1, 1]] + >>> dontcares = [{w : 0, x : 0, y: 0}, 5] + >>> SOPform([w, x, y, z], minterms, dontcares) + (w & y & z) | (~w & ~y) | (x & z & ~w) + + See also + ======== + + POSform + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Quine-McCluskey_algorithm + .. [2] https://en.wikipedia.org/wiki/Don%27t-care_term + + """ + if not minterms: + return false + + variables = tuple(map(sympify, variables)) + + + minterms = _input_to_binlist(minterms, variables) + dontcares = _input_to_binlist((dontcares or []), variables) + for d in dontcares: + if d in minterms: + raise ValueError('%s in minterms is also in dontcares' % d) + + return _sop_form(variables, minterms, dontcares) + + +def _sop_form(variables, minterms, dontcares): + new = _simplified_pairs(minterms + dontcares) + essential = _rem_redundancy(new, minterms) + return Or(*[_convert_to_varsSOP(x, variables) for x in essential]) + + +def POSform(variables, minterms, dontcares=None): + """ + The POSform function uses simplified_pairs and a redundant-group + eliminating algorithm to convert the list of all input combinations + that generate '1' (the minterms) into the smallest product-of-sums form. + + The variables must be given as the first argument. + + Return a logical :py:class:`~.And` function (i.e., the "product of sums" + or "POS" form) that gives the desired outcome. If there are inputs that can + be ignored, pass them as a list, too. + + The result will be one of the (perhaps many) functions that satisfy + the conditions. + + Examples + ======== + + >>> from sympy.logic import POSform + >>> from sympy import symbols + >>> w, x, y, z = symbols('w x y z') + >>> minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], + ... [1, 0, 1, 1], [1, 1, 1, 1]] + >>> dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]] + >>> POSform([w, x, y, z], minterms, dontcares) + z & (y | ~w) + + The terms can also be represented as integers: + + >>> minterms = [1, 3, 7, 11, 15] + >>> dontcares = [0, 2, 5] + >>> POSform([w, x, y, z], minterms, dontcares) + z & (y | ~w) + + They can also be specified using dicts, which does not have to be fully + specified: + + >>> minterms = [{w: 0, x: 1}, {y: 1, z: 1, x: 0}] + >>> POSform([w, x, y, z], minterms) + (x | y) & (x | z) & (~w | ~x) + + Or a combination: + + >>> minterms = [4, 7, 11, [1, 1, 1, 1]] + >>> dontcares = [{w : 0, x : 0, y: 0}, 5] + >>> POSform([w, x, y, z], minterms, dontcares) + (w | x) & (y | ~w) & (z | ~y) + + See also + ======== + + SOPform + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Quine-McCluskey_algorithm + .. [2] https://en.wikipedia.org/wiki/Don%27t-care_term + + """ + if not minterms: + return false + + variables = tuple(map(sympify, variables)) + minterms = _input_to_binlist(minterms, variables) + dontcares = _input_to_binlist((dontcares or []), variables) + for d in dontcares: + if d in minterms: + raise ValueError('%s in minterms is also in dontcares' % d) + + maxterms = [] + for t in product((0, 1), repeat=len(variables)): + t = list(t) + if (t not in minterms) and (t not in dontcares): + maxterms.append(t) + + new = _simplified_pairs(maxterms + dontcares) + essential = _rem_redundancy(new, maxterms) + return And(*[_convert_to_varsPOS(x, variables) for x in essential]) + + +def ANFform(variables, truthvalues): + """ + The ANFform function converts the list of truth values to + Algebraic Normal Form (ANF). + + The variables must be given as the first argument. + + Return True, False, logical :py:class:`~.And` function (i.e., the + "Zhegalkin monomial") or logical :py:class:`~.Xor` function (i.e., + the "Zhegalkin polynomial"). When True and False + are represented by 1 and 0, respectively, then + :py:class:`~.And` is multiplication and :py:class:`~.Xor` is addition. + + Formally a "Zhegalkin monomial" is the product (logical + And) of a finite set of distinct variables, including + the empty set whose product is denoted 1 (True). + A "Zhegalkin polynomial" is the sum (logical Xor) of a + set of Zhegalkin monomials, with the empty set denoted + by 0 (False). + + Parameters + ========== + + variables : list of variables + truthvalues : list of 1's and 0's (result column of truth table) + + Examples + ======== + >>> from sympy.logic.boolalg import ANFform + >>> from sympy.abc import x, y + >>> ANFform([x], [1, 0]) + x ^ True + >>> ANFform([x, y], [0, 1, 1, 1]) + x ^ y ^ (x & y) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Zhegalkin_polynomial + + """ + + n_vars = len(variables) + n_values = len(truthvalues) + + if n_values != 2 ** n_vars: + raise ValueError("The number of truth values must be equal to 2^%d, " + "got %d" % (n_vars, n_values)) + + variables = tuple(map(sympify, variables)) + + coeffs = anf_coeffs(truthvalues) + terms = [] + + for i, t in enumerate(product((0, 1), repeat=n_vars)): + if coeffs[i] == 1: + terms.append(t) + + return Xor(*[_convert_to_varsANF(x, variables) for x in terms], + remove_true=False) + + +def anf_coeffs(truthvalues): + """ + Convert a list of truth values of some boolean expression + to the list of coefficients of the polynomial mod 2 (exclusive + disjunction) representing the boolean expression in ANF + (i.e., the "Zhegalkin polynomial"). + + There are `2^n` possible Zhegalkin monomials in `n` variables, since + each monomial is fully specified by the presence or absence of + each variable. + + We can enumerate all the monomials. For example, boolean + function with four variables ``(a, b, c, d)`` can contain + up to `2^4 = 16` monomials. The 13-th monomial is the + product ``a & b & d``, because 13 in binary is 1, 1, 0, 1. + + A given monomial's presence or absence in a polynomial corresponds + to that monomial's coefficient being 1 or 0 respectively. + + Examples + ======== + >>> from sympy.logic.boolalg import anf_coeffs, bool_monomial, Xor + >>> from sympy.abc import a, b, c + >>> truthvalues = [0, 1, 1, 0, 0, 1, 0, 1] + >>> coeffs = anf_coeffs(truthvalues) + >>> coeffs + [0, 1, 1, 0, 0, 0, 1, 0] + >>> polynomial = Xor(*[ + ... bool_monomial(k, [a, b, c]) + ... for k, coeff in enumerate(coeffs) if coeff == 1 + ... ]) + >>> polynomial + b ^ c ^ (a & b) + + """ + + s = '{:b}'.format(len(truthvalues)) + n = len(s) - 1 + + if len(truthvalues) != 2**n: + raise ValueError("The number of truth values must be a power of two, " + "got %d" % len(truthvalues)) + + coeffs = [[v] for v in truthvalues] + + for i in range(n): + tmp = [] + for j in range(2 ** (n-i-1)): + tmp.append(coeffs[2*j] + + list(map(lambda x, y: x^y, coeffs[2*j], coeffs[2*j+1]))) + coeffs = tmp + + return coeffs[0] + + +def bool_minterm(k, variables): + """ + Return the k-th minterm. + + Minterms are numbered by a binary encoding of the complementation + pattern of the variables. This convention assigns the value 1 to + the direct form and 0 to the complemented form. + + Parameters + ========== + + k : int or list of 1's and 0's (complementation pattern) + variables : list of variables + + Examples + ======== + + >>> from sympy.logic.boolalg import bool_minterm + >>> from sympy.abc import x, y, z + >>> bool_minterm([1, 0, 1], [x, y, z]) + x & z & ~y + >>> bool_minterm(6, [x, y, z]) + x & y & ~z + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Canonical_normal_form#Indexing_minterms + + """ + if isinstance(k, int): + k = ibin(k, len(variables)) + variables = tuple(map(sympify, variables)) + return _convert_to_varsSOP(k, variables) + + +def bool_maxterm(k, variables): + """ + Return the k-th maxterm. + + Each maxterm is assigned an index based on the opposite + conventional binary encoding used for minterms. The maxterm + convention assigns the value 0 to the direct form and 1 to + the complemented form. + + Parameters + ========== + + k : int or list of 1's and 0's (complementation pattern) + variables : list of variables + + Examples + ======== + >>> from sympy.logic.boolalg import bool_maxterm + >>> from sympy.abc import x, y, z + >>> bool_maxterm([1, 0, 1], [x, y, z]) + y | ~x | ~z + >>> bool_maxterm(6, [x, y, z]) + z | ~x | ~y + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Canonical_normal_form#Indexing_maxterms + + """ + if isinstance(k, int): + k = ibin(k, len(variables)) + variables = tuple(map(sympify, variables)) + return _convert_to_varsPOS(k, variables) + + +def bool_monomial(k, variables): + """ + Return the k-th monomial. + + Monomials are numbered by a binary encoding of the presence and + absences of the variables. This convention assigns the value + 1 to the presence of variable and 0 to the absence of variable. + + Each boolean function can be uniquely represented by a + Zhegalkin Polynomial (Algebraic Normal Form). The Zhegalkin + Polynomial of the boolean function with `n` variables can contain + up to `2^n` monomials. We can enumerate all the monomials. + Each monomial is fully specified by the presence or absence + of each variable. + + For example, boolean function with four variables ``(a, b, c, d)`` + can contain up to `2^4 = 16` monomials. The 13-th monomial is the + product ``a & b & d``, because 13 in binary is 1, 1, 0, 1. + + Parameters + ========== + + k : int or list of 1's and 0's + variables : list of variables + + Examples + ======== + >>> from sympy.logic.boolalg import bool_monomial + >>> from sympy.abc import x, y, z + >>> bool_monomial([1, 0, 1], [x, y, z]) + x & z + >>> bool_monomial(6, [x, y, z]) + x & y + + """ + if isinstance(k, int): + k = ibin(k, len(variables)) + variables = tuple(map(sympify, variables)) + return _convert_to_varsANF(k, variables) + + +def _find_predicates(expr): + """Helper to find logical predicates in BooleanFunctions. + + A logical predicate is defined here as anything within a BooleanFunction + that is not a BooleanFunction itself. + + """ + if not isinstance(expr, BooleanFunction): + return {expr} + return set().union(*(map(_find_predicates, expr.args))) + + +def simplify_logic(expr, form=None, deep=True, force=False, dontcare=None): + """ + This function simplifies a boolean function to its simplified version + in SOP or POS form. The return type is an :py:class:`~.Or` or + :py:class:`~.And` object in SymPy. + + Parameters + ========== + + expr : Boolean + + form : string (``'cnf'`` or ``'dnf'``) or ``None`` (default). + If ``'cnf'`` or ``'dnf'``, the simplest expression in the corresponding + normal form is returned; if ``None``, the answer is returned + according to the form with fewest args (in CNF by default). + + deep : bool (default ``True``) + Indicates whether to recursively simplify any + non-boolean functions contained within the input. + + force : bool (default ``False``) + As the simplifications require exponential time in the number + of variables, there is by default a limit on expressions with + 8 variables. When the expression has more than 8 variables + only symbolical simplification (controlled by ``deep``) is + made. By setting ``force`` to ``True``, this limit is removed. Be + aware that this can lead to very long simplification times. + + dontcare : Boolean + Optimize expression under the assumption that inputs where this + expression is true are don't care. This is useful in e.g. Piecewise + conditions, where later conditions do not need to consider inputs that + are converted by previous conditions. For example, if a previous + condition is ``And(A, B)``, the simplification of expr can be made + with don't cares for ``And(A, B)``. + + Examples + ======== + + >>> from sympy.logic import simplify_logic + >>> from sympy.abc import x, y, z + >>> b = (~x & ~y & ~z) | ( ~x & ~y & z) + >>> simplify_logic(b) + ~x & ~y + >>> simplify_logic(x | y, dontcare=y) + x + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Don%27t-care_term + + """ + + if form not in (None, 'cnf', 'dnf'): + raise ValueError("form can be cnf or dnf only") + expr = sympify(expr) + # check for quick exit if form is given: right form and all args are + # literal and do not involve Not + if form: + form_ok = False + if form == 'cnf': + form_ok = is_cnf(expr) + elif form == 'dnf': + form_ok = is_dnf(expr) + + if form_ok and all(is_literal(a) + for a in expr.args): + return expr + from sympy.core.relational import Relational + if deep: + variables = expr.atoms(Relational) + from sympy.simplify.simplify import simplify + s = tuple(map(simplify, variables)) + expr = expr.xreplace(dict(zip(variables, s))) + if not isinstance(expr, BooleanFunction): + return expr + # Replace Relationals with Dummys to possibly + # reduce the number of variables + repl = {} + undo = {} + from sympy.core.symbol import Dummy + variables = expr.atoms(Relational) + if dontcare is not None: + dontcare = sympify(dontcare) + variables.update(dontcare.atoms(Relational)) + while variables: + var = variables.pop() + if var.is_Relational: + d = Dummy() + undo[d] = var + repl[var] = d + nvar = var.negated + if nvar in variables: + repl[nvar] = Not(d) + variables.remove(nvar) + + expr = expr.xreplace(repl) + + if dontcare is not None: + dontcare = dontcare.xreplace(repl) + + # Get new variables after replacing + variables = _find_predicates(expr) + if not force and len(variables) > 8: + return expr.xreplace(undo) + if dontcare is not None: + # Add variables from dontcare + dcvariables = _find_predicates(dontcare) + variables.update(dcvariables) + # if too many restore to variables only + if not force and len(variables) > 8: + variables = _find_predicates(expr) + dontcare = None + # group into constants and variable values + c, v = sift(ordered(variables), lambda x: x in (True, False), binary=True) + variables = c + v + # standardize constants to be 1 or 0 in keeping with truthtable + c = [1 if i == True else 0 for i in c] + truthtable = _get_truthtable(v, expr, c) + if dontcare is not None: + dctruthtable = _get_truthtable(v, dontcare, c) + truthtable = [t for t in truthtable if t not in dctruthtable] + else: + dctruthtable = [] + big = len(truthtable) >= (2 ** (len(variables) - 1)) + if form == 'dnf' or form is None and big: + return _sop_form(variables, truthtable, dctruthtable).xreplace(undo) + return POSform(variables, truthtable, dctruthtable).xreplace(undo) + + +def _get_truthtable(variables, expr, const): + """ Return a list of all combinations leading to a True result for ``expr``. + """ + _variables = variables.copy() + def _get_tt(inputs): + if _variables: + v = _variables.pop() + tab = [[i[0].xreplace({v: false}), [0] + i[1]] for i in inputs if i[0] is not false] + tab.extend([[i[0].xreplace({v: true}), [1] + i[1]] for i in inputs if i[0] is not false]) + return _get_tt(tab) + return inputs + res = [const + k[1] for k in _get_tt([[expr, []]]) if k[0]] + if res == [[]]: + return [] + else: + return res + + +def _finger(eq): + """ + Assign a 5-item fingerprint to each symbol in the equation: + [ + # of times it appeared as a Symbol; + # of times it appeared as a Not(symbol); + # of times it appeared as a Symbol in an And or Or; + # of times it appeared as a Not(Symbol) in an And or Or; + a sorted tuple of tuples, (i, j, k), where i is the number of arguments + in an And or Or with which it appeared as a Symbol, and j is + the number of arguments that were Not(Symbol); k is the number + of times that (i, j) was seen. + ] + + Examples + ======== + + >>> from sympy.logic.boolalg import _finger as finger + >>> from sympy import And, Or, Not, Xor, to_cnf, symbols + >>> from sympy.abc import a, b, x, y + >>> eq = Or(And(Not(y), a), And(Not(y), b), And(x, y)) + >>> dict(finger(eq)) + {(0, 0, 1, 0, ((2, 0, 1),)): [x], + (0, 0, 1, 0, ((2, 1, 1),)): [a, b], + (0, 0, 1, 2, ((2, 0, 1),)): [y]} + >>> dict(finger(x & ~y)) + {(0, 1, 0, 0, ()): [y], (1, 0, 0, 0, ()): [x]} + + In the following, the (5, 2, 6) means that there were 6 Or + functions in which a symbol appeared as itself amongst 5 arguments in + which there were also 2 negated symbols, e.g. ``(a0 | a1 | a2 | ~a3 | ~a4)`` + is counted once for a0, a1 and a2. + + >>> dict(finger(to_cnf(Xor(*symbols('a:5'))))) + {(0, 0, 8, 8, ((5, 0, 1), (5, 2, 6), (5, 4, 1))): [a0, a1, a2, a3, a4]} + + The equation must not have more than one level of nesting: + + >>> dict(finger(And(Or(x, y), y))) + {(0, 0, 1, 0, ((2, 0, 1),)): [x], (1, 0, 1, 0, ((2, 0, 1),)): [y]} + >>> dict(finger(And(Or(x, And(a, x)), y))) + Traceback (most recent call last): + ... + NotImplementedError: unexpected level of nesting + + So y and x have unique fingerprints, but a and b do not. + """ + f = eq.free_symbols + d = dict(list(zip(f, [[0]*4 + [defaultdict(int)] for fi in f]))) + for a in eq.args: + if a.is_Symbol: + d[a][0] += 1 + elif a.is_Not: + d[a.args[0]][1] += 1 + else: + o = len(a.args), sum(isinstance(ai, Not) for ai in a.args) + for ai in a.args: + if ai.is_Symbol: + d[ai][2] += 1 + d[ai][-1][o] += 1 + elif ai.is_Not: + d[ai.args[0]][3] += 1 + else: + raise NotImplementedError('unexpected level of nesting') + inv = defaultdict(list) + for k, v in ordered(iter(d.items())): + v[-1] = tuple(sorted([i + (j,) for i, j in v[-1].items()])) + inv[tuple(v)].append(k) + return inv + + +def bool_map(bool1, bool2): + """ + Return the simplified version of *bool1*, and the mapping of variables + that makes the two expressions *bool1* and *bool2* represent the same + logical behaviour for some correspondence between the variables + of each. + If more than one mappings of this sort exist, one of them + is returned. + + For example, ``And(x, y)`` is logically equivalent to ``And(a, b)`` for + the mapping ``{x: a, y: b}`` or ``{x: b, y: a}``. + If no such mapping exists, return ``False``. + + Examples + ======== + + >>> from sympy import SOPform, bool_map, Or, And, Not, Xor + >>> from sympy.abc import w, x, y, z, a, b, c, d + >>> function1 = SOPform([x, z, y],[[1, 0, 1], [0, 0, 1]]) + >>> function2 = SOPform([a, b, c],[[1, 0, 1], [1, 0, 0]]) + >>> bool_map(function1, function2) + (y & ~z, {y: a, z: b}) + + The results are not necessarily unique, but they are canonical. Here, + ``(w, z)`` could be ``(a, d)`` or ``(d, a)``: + + >>> eq = Or(And(Not(y), w), And(Not(y), z), And(x, y)) + >>> eq2 = Or(And(Not(c), a), And(Not(c), d), And(b, c)) + >>> bool_map(eq, eq2) + ((x & y) | (w & ~y) | (z & ~y), {w: a, x: b, y: c, z: d}) + >>> eq = And(Xor(a, b), c, And(c,d)) + >>> bool_map(eq, eq.subs(c, x)) + (c & d & (a | b) & (~a | ~b), {a: a, b: b, c: d, d: x}) + + """ + + def match(function1, function2): + """Return the mapping that equates variables between two + simplified boolean expressions if possible. + + By "simplified" we mean that a function has been denested + and is either an And (or an Or) whose arguments are either + symbols (x), negated symbols (Not(x)), or Or (or an And) whose + arguments are only symbols or negated symbols. For example, + ``And(x, Not(y), Or(w, Not(z)))``. + + Basic.match is not robust enough (see issue 4835) so this is + a workaround that is valid for simplified boolean expressions + """ + + # do some quick checks + if function1.__class__ != function2.__class__: + return None # maybe simplification makes them the same? + if len(function1.args) != len(function2.args): + return None # maybe simplification makes them the same? + if function1.is_Symbol: + return {function1: function2} + + # get the fingerprint dictionaries + f1 = _finger(function1) + f2 = _finger(function2) + + # more quick checks + if len(f1) != len(f2): + return False + + # assemble the match dictionary if possible + matchdict = {} + for k in f1.keys(): + if k not in f2: + return False + if len(f1[k]) != len(f2[k]): + return False + for i, x in enumerate(f1[k]): + matchdict[x] = f2[k][i] + return matchdict + + a = simplify_logic(bool1) + b = simplify_logic(bool2) + m = match(a, b) + if m: + return a, m + return m + + +def _apply_patternbased_simplification(rv, patterns, measure, + dominatingvalue, + replacementvalue=None, + threeterm_patterns=None): + """ + Replace patterns of Relational + + Parameters + ========== + + rv : Expr + Boolean expression + + patterns : tuple + Tuple of tuples, with (pattern to simplify, simplified pattern) with + two terms. + + measure : function + Simplification measure. + + dominatingvalue : Boolean or ``None`` + The dominating value for the function of consideration. + For example, for :py:class:`~.And` ``S.false`` is dominating. + As soon as one expression is ``S.false`` in :py:class:`~.And`, + the whole expression is ``S.false``. + + replacementvalue : Boolean or ``None``, optional + The resulting value for the whole expression if one argument + evaluates to ``dominatingvalue``. + For example, for :py:class:`~.Nand` ``S.false`` is dominating, but + in this case the resulting value is ``S.true``. Default is ``None``. + If ``replacementvalue`` is ``None`` and ``dominatingvalue`` is not + ``None``, ``replacementvalue = dominatingvalue``. + + threeterm_patterns : tuple, optional + Tuple of tuples, with (pattern to simplify, simplified pattern) with + three terms. + + """ + from sympy.core.relational import Relational, _canonical + + if replacementvalue is None and dominatingvalue is not None: + replacementvalue = dominatingvalue + # Use replacement patterns for Relationals + Rel, nonRel = sift(rv.args, lambda i: isinstance(i, Relational), + binary=True) + if len(Rel) <= 1: + return rv + Rel, nonRealRel = sift(Rel, lambda i: not any(s.is_real is False + for s in i.free_symbols), + binary=True) + Rel = [i.canonical for i in Rel] + + if threeterm_patterns and len(Rel) >= 3: + Rel = _apply_patternbased_threeterm_simplification(Rel, + threeterm_patterns, rv.func, dominatingvalue, + replacementvalue, measure) + + Rel = _apply_patternbased_twoterm_simplification(Rel, patterns, + rv.func, dominatingvalue, replacementvalue, measure) + + rv = rv.func(*([_canonical(i) for i in ordered(Rel)] + + nonRel + nonRealRel)) + return rv + + +def _apply_patternbased_twoterm_simplification(Rel, patterns, func, + dominatingvalue, + replacementvalue, + measure): + """ Apply pattern-based two-term simplification.""" + from sympy.functions.elementary.miscellaneous import Min, Max + from sympy.core.relational import Ge, Gt, _Inequality + changed = True + while changed and len(Rel) >= 2: + changed = False + # Use only < or <= + Rel = [r.reversed if isinstance(r, (Ge, Gt)) else r for r in Rel] + # Sort based on ordered + Rel = list(ordered(Rel)) + # Eq and Ne must be tested reversed as well + rtmp = [(r, ) if isinstance(r, _Inequality) else (r, r.reversed) for r in Rel] + # Create a list of possible replacements + results = [] + # Try all combinations of possibly reversed relational + for ((i, pi), (j, pj)) in combinations(enumerate(rtmp), 2): + for pattern, simp in patterns: + res = [] + for p1, p2 in product(pi, pj): + # use SymPy matching + oldexpr = Tuple(p1, p2) + tmpres = oldexpr.match(pattern) + if tmpres: + res.append((tmpres, oldexpr)) + + if res: + for tmpres, oldexpr in res: + # we have a matching, compute replacement + np = simp.xreplace(tmpres) + if np == dominatingvalue: + # if dominatingvalue, the whole expression + # will be replacementvalue + return [replacementvalue] + # add replacement + if not isinstance(np, ITE) and not np.has(Min, Max): + # We only want to use ITE and Min/Max replacements if + # they simplify to a relational + costsaving = measure(func(*oldexpr.args)) - measure(np) + if costsaving > 0: + results.append((costsaving, ([i, j], np))) + if results: + # Sort results based on complexity + results = sorted(results, + key=lambda pair: pair[0], reverse=True) + # Replace the one providing most simplification + replacement = results[0][1] + idx, newrel = replacement + idx.sort() + # Remove the old relationals + for index in reversed(idx): + del Rel[index] + if dominatingvalue is None or newrel != Not(dominatingvalue): + # Insert the new one (no need to insert a value that will + # not affect the result) + if newrel.func == func: + for a in newrel.args: + Rel.append(a) + else: + Rel.append(newrel) + # We did change something so try again + changed = True + return Rel + + +def _apply_patternbased_threeterm_simplification(Rel, patterns, func, + dominatingvalue, + replacementvalue, + measure): + """ Apply pattern-based three-term simplification.""" + from sympy.functions.elementary.miscellaneous import Min, Max + from sympy.core.relational import Le, Lt, _Inequality + changed = True + while changed and len(Rel) >= 3: + changed = False + # Use only > or >= + Rel = [r.reversed if isinstance(r, (Le, Lt)) else r for r in Rel] + # Sort based on ordered + Rel = list(ordered(Rel)) + # Create a list of possible replacements + results = [] + # Eq and Ne must be tested reversed as well + rtmp = [(r, ) if isinstance(r, _Inequality) else (r, r.reversed) for r in Rel] + # Try all combinations of possibly reversed relational + for ((i, pi), (j, pj), (k, pk)) in permutations(enumerate(rtmp), 3): + for pattern, simp in patterns: + res = [] + for p1, p2, p3 in product(pi, pj, pk): + # use SymPy matching + oldexpr = Tuple(p1, p2, p3) + tmpres = oldexpr.match(pattern) + if tmpres: + res.append((tmpres, oldexpr)) + + if res: + for tmpres, oldexpr in res: + # we have a matching, compute replacement + np = simp.xreplace(tmpres) + if np == dominatingvalue: + # if dominatingvalue, the whole expression + # will be replacementvalue + return [replacementvalue] + # add replacement + if not isinstance(np, ITE) and not np.has(Min, Max): + # We only want to use ITE and Min/Max replacements if + # they simplify to a relational + costsaving = measure(func(*oldexpr.args)) - measure(np) + if costsaving > 0: + results.append((costsaving, ([i, j, k], np))) + if results: + # Sort results based on complexity + results = sorted(results, + key=lambda pair: pair[0], reverse=True) + # Replace the one providing most simplification + replacement = results[0][1] + idx, newrel = replacement + idx.sort() + # Remove the old relationals + for index in reversed(idx): + del Rel[index] + if dominatingvalue is None or newrel != Not(dominatingvalue): + # Insert the new one (no need to insert a value that will + # not affect the result) + if newrel.func == func: + for a in newrel.args: + Rel.append(a) + else: + Rel.append(newrel) + # We did change something so try again + changed = True + return Rel + + +@cacheit +def _simplify_patterns_and(): + """ Two-term patterns for And.""" + + from sympy.core import Wild + from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt + from sympy.functions.elementary.complexes import Abs + from sympy.functions.elementary.miscellaneous import Min, Max + a = Wild('a') + b = Wild('b') + c = Wild('c') + # Relationals patterns should be in alphabetical order + # (pattern1, pattern2, simplified) + # Do not use Ge, Gt + _matchers_and = ((Tuple(Eq(a, b), Lt(a, b)), false), + #(Tuple(Eq(a, b), Lt(b, a)), S.false), + #(Tuple(Le(b, a), Lt(a, b)), S.false), + #(Tuple(Lt(b, a), Le(a, b)), S.false), + (Tuple(Lt(b, a), Lt(a, b)), false), + (Tuple(Eq(a, b), Le(b, a)), Eq(a, b)), + #(Tuple(Eq(a, b), Le(a, b)), Eq(a, b)), + #(Tuple(Le(b, a), Lt(b, a)), Gt(a, b)), + (Tuple(Le(b, a), Le(a, b)), Eq(a, b)), + #(Tuple(Le(b, a), Ne(a, b)), Gt(a, b)), + #(Tuple(Lt(b, a), Ne(a, b)), Gt(a, b)), + (Tuple(Le(a, b), Lt(a, b)), Lt(a, b)), + (Tuple(Le(a, b), Ne(a, b)), Lt(a, b)), + (Tuple(Lt(a, b), Ne(a, b)), Lt(a, b)), + # Sign + (Tuple(Eq(a, b), Eq(a, -b)), And(Eq(a, S.Zero), Eq(b, S.Zero))), + # Min/Max/ITE + (Tuple(Le(b, a), Le(c, a)), Ge(a, Max(b, c))), + (Tuple(Le(b, a), Lt(c, a)), ITE(b > c, Ge(a, b), Gt(a, c))), + (Tuple(Lt(b, a), Lt(c, a)), Gt(a, Max(b, c))), + (Tuple(Le(a, b), Le(a, c)), Le(a, Min(b, c))), + (Tuple(Le(a, b), Lt(a, c)), ITE(b < c, Le(a, b), Lt(a, c))), + (Tuple(Lt(a, b), Lt(a, c)), Lt(a, Min(b, c))), + (Tuple(Le(a, b), Le(c, a)), ITE(Eq(b, c), Eq(a, b), ITE(b < c, false, And(Le(a, b), Ge(a, c))))), + (Tuple(Le(c, a), Le(a, b)), ITE(Eq(b, c), Eq(a, b), ITE(b < c, false, And(Le(a, b), Ge(a, c))))), + (Tuple(Lt(a, b), Lt(c, a)), ITE(b < c, false, And(Lt(a, b), Gt(a, c)))), + (Tuple(Lt(c, a), Lt(a, b)), ITE(b < c, false, And(Lt(a, b), Gt(a, c)))), + (Tuple(Le(a, b), Lt(c, a)), ITE(b <= c, false, And(Le(a, b), Gt(a, c)))), + (Tuple(Le(c, a), Lt(a, b)), ITE(b <= c, false, And(Lt(a, b), Ge(a, c)))), + (Tuple(Eq(a, b), Eq(a, c)), ITE(Eq(b, c), Eq(a, b), false)), + (Tuple(Lt(a, b), Lt(-b, a)), ITE(b > 0, Lt(Abs(a), b), false)), + (Tuple(Le(a, b), Le(-b, a)), ITE(b >= 0, Le(Abs(a), b), false)), + ) + return _matchers_and + + +@cacheit +def _simplify_patterns_and3(): + """ Three-term patterns for And.""" + + from sympy.core import Wild + from sympy.core.relational import Eq, Ge, Gt + + a = Wild('a') + b = Wild('b') + c = Wild('c') + # Relationals patterns should be in alphabetical order + # (pattern1, pattern2, pattern3, simplified) + # Do not use Le, Lt + _matchers_and = ((Tuple(Ge(a, b), Ge(b, c), Gt(c, a)), false), + (Tuple(Ge(a, b), Gt(b, c), Gt(c, a)), false), + (Tuple(Gt(a, b), Gt(b, c), Gt(c, a)), false), + # (Tuple(Ge(c, a), Gt(a, b), Gt(b, c)), S.false), + # Lower bound relations + # Commented out combinations that does not simplify + (Tuple(Ge(a, b), Ge(a, c), Ge(b, c)), And(Ge(a, b), Ge(b, c))), + (Tuple(Ge(a, b), Ge(a, c), Gt(b, c)), And(Ge(a, b), Gt(b, c))), + # (Tuple(Ge(a, b), Gt(a, c), Ge(b, c)), And(Ge(a, b), Ge(b, c))), + (Tuple(Ge(a, b), Gt(a, c), Gt(b, c)), And(Ge(a, b), Gt(b, c))), + # (Tuple(Gt(a, b), Ge(a, c), Ge(b, c)), And(Gt(a, b), Ge(b, c))), + (Tuple(Ge(a, c), Gt(a, b), Gt(b, c)), And(Gt(a, b), Gt(b, c))), + (Tuple(Ge(b, c), Gt(a, b), Gt(a, c)), And(Gt(a, b), Ge(b, c))), + (Tuple(Gt(a, b), Gt(a, c), Gt(b, c)), And(Gt(a, b), Gt(b, c))), + # Upper bound relations + # Commented out combinations that does not simplify + (Tuple(Ge(b, a), Ge(c, a), Ge(b, c)), And(Ge(c, a), Ge(b, c))), + (Tuple(Ge(b, a), Ge(c, a), Gt(b, c)), And(Ge(c, a), Gt(b, c))), + # (Tuple(Ge(b, a), Gt(c, a), Ge(b, c)), And(Gt(c, a), Ge(b, c))), + (Tuple(Ge(b, a), Gt(c, a), Gt(b, c)), And(Gt(c, a), Gt(b, c))), + # (Tuple(Gt(b, a), Ge(c, a), Ge(b, c)), And(Ge(c, a), Ge(b, c))), + (Tuple(Ge(c, a), Gt(b, a), Gt(b, c)), And(Ge(c, a), Gt(b, c))), + (Tuple(Ge(b, c), Gt(b, a), Gt(c, a)), And(Gt(c, a), Ge(b, c))), + (Tuple(Gt(b, a), Gt(c, a), Gt(b, c)), And(Gt(c, a), Gt(b, c))), + # Circular relation + (Tuple(Ge(a, b), Ge(b, c), Ge(c, a)), And(Eq(a, b), Eq(b, c))), + ) + return _matchers_and + + +@cacheit +def _simplify_patterns_or(): + """ Two-term patterns for Or.""" + + from sympy.core import Wild + from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt + from sympy.functions.elementary.complexes import Abs + from sympy.functions.elementary.miscellaneous import Min, Max + a = Wild('a') + b = Wild('b') + c = Wild('c') + # Relationals patterns should be in alphabetical order + # (pattern1, pattern2, simplified) + # Do not use Ge, Gt + _matchers_or = ((Tuple(Le(b, a), Le(a, b)), true), + #(Tuple(Le(b, a), Lt(a, b)), true), + (Tuple(Le(b, a), Ne(a, b)), true), + #(Tuple(Le(a, b), Lt(b, a)), true), + #(Tuple(Le(a, b), Ne(a, b)), true), + #(Tuple(Eq(a, b), Le(b, a)), Ge(a, b)), + #(Tuple(Eq(a, b), Lt(b, a)), Ge(a, b)), + (Tuple(Eq(a, b), Le(a, b)), Le(a, b)), + (Tuple(Eq(a, b), Lt(a, b)), Le(a, b)), + #(Tuple(Le(b, a), Lt(b, a)), Ge(a, b)), + (Tuple(Lt(b, a), Lt(a, b)), Ne(a, b)), + (Tuple(Lt(b, a), Ne(a, b)), Ne(a, b)), + (Tuple(Le(a, b), Lt(a, b)), Le(a, b)), + #(Tuple(Lt(a, b), Ne(a, b)), Ne(a, b)), + (Tuple(Eq(a, b), Ne(a, c)), ITE(Eq(b, c), true, Ne(a, c))), + (Tuple(Ne(a, b), Ne(a, c)), ITE(Eq(b, c), Ne(a, b), true)), + # Min/Max/ITE + (Tuple(Le(b, a), Le(c, a)), Ge(a, Min(b, c))), + #(Tuple(Ge(b, a), Ge(c, a)), Ge(Min(b, c), a)), + (Tuple(Le(b, a), Lt(c, a)), ITE(b > c, Lt(c, a), Le(b, a))), + (Tuple(Lt(b, a), Lt(c, a)), Gt(a, Min(b, c))), + #(Tuple(Gt(b, a), Gt(c, a)), Gt(Min(b, c), a)), + (Tuple(Le(a, b), Le(a, c)), Le(a, Max(b, c))), + #(Tuple(Le(b, a), Le(c, a)), Le(Max(b, c), a)), + (Tuple(Le(a, b), Lt(a, c)), ITE(b >= c, Le(a, b), Lt(a, c))), + (Tuple(Lt(a, b), Lt(a, c)), Lt(a, Max(b, c))), + #(Tuple(Lt(b, a), Lt(c, a)), Lt(Max(b, c), a)), + (Tuple(Le(a, b), Le(c, a)), ITE(b >= c, true, Or(Le(a, b), Ge(a, c)))), + (Tuple(Le(c, a), Le(a, b)), ITE(b >= c, true, Or(Le(a, b), Ge(a, c)))), + (Tuple(Lt(a, b), Lt(c, a)), ITE(b > c, true, Or(Lt(a, b), Gt(a, c)))), + (Tuple(Lt(c, a), Lt(a, b)), ITE(b > c, true, Or(Lt(a, b), Gt(a, c)))), + (Tuple(Le(a, b), Lt(c, a)), ITE(b >= c, true, Or(Le(a, b), Gt(a, c)))), + (Tuple(Le(c, a), Lt(a, b)), ITE(b >= c, true, Or(Lt(a, b), Ge(a, c)))), + (Tuple(Lt(b, a), Lt(a, -b)), ITE(b >= 0, Gt(Abs(a), b), true)), + (Tuple(Le(b, a), Le(a, -b)), ITE(b > 0, Ge(Abs(a), b), true)), + ) + return _matchers_or + + +@cacheit +def _simplify_patterns_xor(): + """ Two-term patterns for Xor.""" + + from sympy.functions.elementary.miscellaneous import Min, Max + from sympy.core import Wild + from sympy.core.relational import Eq, Ne, Ge, Gt, Le, Lt + a = Wild('a') + b = Wild('b') + c = Wild('c') + # Relationals patterns should be in alphabetical order + # (pattern1, pattern2, simplified) + # Do not use Ge, Gt + _matchers_xor = (#(Tuple(Le(b, a), Lt(a, b)), true), + #(Tuple(Lt(b, a), Le(a, b)), true), + #(Tuple(Eq(a, b), Le(b, a)), Gt(a, b)), + #(Tuple(Eq(a, b), Lt(b, a)), Ge(a, b)), + (Tuple(Eq(a, b), Le(a, b)), Lt(a, b)), + (Tuple(Eq(a, b), Lt(a, b)), Le(a, b)), + (Tuple(Le(a, b), Lt(a, b)), Eq(a, b)), + (Tuple(Le(a, b), Le(b, a)), Ne(a, b)), + (Tuple(Le(b, a), Ne(a, b)), Le(a, b)), + # (Tuple(Lt(b, a), Lt(a, b)), Ne(a, b)), + (Tuple(Lt(b, a), Ne(a, b)), Lt(a, b)), + # (Tuple(Le(a, b), Lt(a, b)), Eq(a, b)), + # (Tuple(Le(a, b), Ne(a, b)), Ge(a, b)), + # (Tuple(Lt(a, b), Ne(a, b)), Gt(a, b)), + # Min/Max/ITE + (Tuple(Le(b, a), Le(c, a)), + And(Ge(a, Min(b, c)), Lt(a, Max(b, c)))), + (Tuple(Le(b, a), Lt(c, a)), + ITE(b > c, And(Gt(a, c), Lt(a, b)), + And(Ge(a, b), Le(a, c)))), + (Tuple(Lt(b, a), Lt(c, a)), + And(Gt(a, Min(b, c)), Le(a, Max(b, c)))), + (Tuple(Le(a, b), Le(a, c)), + And(Le(a, Max(b, c)), Gt(a, Min(b, c)))), + (Tuple(Le(a, b), Lt(a, c)), + ITE(b < c, And(Lt(a, c), Gt(a, b)), + And(Le(a, b), Ge(a, c)))), + (Tuple(Lt(a, b), Lt(a, c)), + And(Lt(a, Max(b, c)), Ge(a, Min(b, c)))), + ) + return _matchers_xor + + +def simplify_univariate(expr): + """return a simplified version of univariate boolean expression, else ``expr``""" + from sympy.functions.elementary.piecewise import Piecewise + from sympy.core.relational import Eq, Ne + if not isinstance(expr, BooleanFunction): + return expr + if expr.atoms(Eq, Ne): + return expr + c = expr + free = c.free_symbols + if len(free) != 1: + return c + x = free.pop() + ok, i = Piecewise((0, c), evaluate=False + )._intervals(x, err_on_Eq=True) + if not ok: + return c + if not i: + return false + args = [] + for a, b, _, _ in i: + if a is S.NegativeInfinity: + if b is S.Infinity: + c = true + else: + if c.subs(x, b) == True: + c = (x <= b) + else: + c = (x < b) + else: + incl_a = (c.subs(x, a) == True) + incl_b = (c.subs(x, b) == True) + if incl_a and incl_b: + if b.is_infinite: + c = (x >= a) + else: + c = And(a <= x, x <= b) + elif incl_a: + c = And(a <= x, x < b) + elif incl_b: + if b.is_infinite: + c = (x > a) + else: + c = And(a < x, x <= b) + else: + c = And(a < x, x < b) + args.append(c) + return Or(*args) + + +# Classes corresponding to logic gates +# Used in gateinputcount method +BooleanGates = (And, Or, Xor, Nand, Nor, Not, Xnor, ITE) + +def gateinputcount(expr): + """ + Return the total number of inputs for the logic gates realizing the + Boolean expression. + + Returns + ======= + + int + Number of gate inputs + + Note + ==== + + Not all Boolean functions count as gate here, only those that are + considered to be standard gates. These are: :py:class:`~.And`, + :py:class:`~.Or`, :py:class:`~.Xor`, :py:class:`~.Not`, and + :py:class:`~.ITE` (multiplexer). :py:class:`~.Nand`, :py:class:`~.Nor`, + and :py:class:`~.Xnor` will be evaluated to ``Not(And())`` etc. + + Examples + ======== + + >>> from sympy.logic import And, Or, Nand, Not, gateinputcount + >>> from sympy.abc import x, y, z + >>> expr = And(x, y) + >>> gateinputcount(expr) + 2 + >>> gateinputcount(Or(expr, z)) + 4 + + Note that ``Nand`` is automatically evaluated to ``Not(And())`` so + + >>> gateinputcount(Nand(x, y, z)) + 4 + >>> gateinputcount(Not(And(x, y, z))) + 4 + + Although this can be avoided by using ``evaluate=False`` + + >>> gateinputcount(Nand(x, y, z, evaluate=False)) + 3 + + Also note that a comparison will count as a Boolean variable: + + >>> gateinputcount(And(x > z, y >= 2)) + 2 + + As will a symbol: + >>> gateinputcount(x) + 0 + + """ + if not isinstance(expr, Boolean): + raise TypeError("Expression must be Boolean") + if isinstance(expr, BooleanGates): + return len(expr.args) + sum(gateinputcount(x) for x in expr.args) + return 0 diff --git a/lib/python3.11/site-packages/sympy/logic/inference.py b/lib/python3.11/site-packages/sympy/logic/inference.py new file mode 100644 index 0000000000000000000000000000000000000000..c3798231c09ae351ea7e7026d622b834fea3e3fa --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/inference.py @@ -0,0 +1,340 @@ +"""Inference in propositional logic""" + +from sympy.logic.boolalg import And, Not, conjuncts, to_cnf, BooleanFunction +from sympy.core.sorting import ordered +from sympy.core.sympify import sympify +from sympy.external.importtools import import_module + + +def literal_symbol(literal): + """ + The symbol in this literal (without the negation). + + Examples + ======== + + >>> from sympy.abc import A + >>> from sympy.logic.inference import literal_symbol + >>> literal_symbol(A) + A + >>> literal_symbol(~A) + A + + """ + + if literal is True or literal is False: + return literal + elif literal.is_Symbol: + return literal + elif literal.is_Not: + return literal_symbol(literal.args[0]) + else: + raise ValueError("Argument must be a boolean literal.") + + +def satisfiable(expr, algorithm=None, all_models=False, minimal=False, use_lra_theory=False): + """ + Check satisfiability of a propositional sentence. + Returns a model when it succeeds. + Returns {true: true} for trivially true expressions. + + On setting all_models to True, if given expr is satisfiable then + returns a generator of models. However, if expr is unsatisfiable + then returns a generator containing the single element False. + + Examples + ======== + + >>> from sympy.abc import A, B + >>> from sympy.logic.inference import satisfiable + >>> satisfiable(A & ~B) + {A: True, B: False} + >>> satisfiable(A & ~A) + False + >>> satisfiable(True) + {True: True} + >>> next(satisfiable(A & ~A, all_models=True)) + False + >>> models = satisfiable((A >> B) & B, all_models=True) + >>> next(models) + {A: False, B: True} + >>> next(models) + {A: True, B: True} + >>> def use_models(models): + ... for model in models: + ... if model: + ... # Do something with the model. + ... print(model) + ... else: + ... # Given expr is unsatisfiable. + ... print("UNSAT") + >>> use_models(satisfiable(A >> ~A, all_models=True)) + {A: False} + >>> use_models(satisfiable(A ^ A, all_models=True)) + UNSAT + + """ + if use_lra_theory: + if algorithm is not None and algorithm != "dpll2": + raise ValueError(f"Currently only dpll2 can handle using lra theory. {algorithm} is not handled.") + algorithm = "dpll2" + + if algorithm is None or algorithm == "pycosat": + pycosat = import_module('pycosat') + if pycosat is not None: + algorithm = "pycosat" + else: + if algorithm == "pycosat": + raise ImportError("pycosat module is not present") + # Silently fall back to dpll2 if pycosat + # is not installed + algorithm = "dpll2" + + if algorithm=="minisat22": + pysat = import_module('pysat') + if pysat is None: + algorithm = "dpll2" + + if algorithm=="z3": + z3 = import_module('z3') + if z3 is None: + algorithm = "dpll2" + + if algorithm == "dpll": + from sympy.logic.algorithms.dpll import dpll_satisfiable + return dpll_satisfiable(expr) + elif algorithm == "dpll2": + from sympy.logic.algorithms.dpll2 import dpll_satisfiable + return dpll_satisfiable(expr, all_models, use_lra_theory=use_lra_theory) + elif algorithm == "pycosat": + from sympy.logic.algorithms.pycosat_wrapper import pycosat_satisfiable + return pycosat_satisfiable(expr, all_models) + elif algorithm == "minisat22": + from sympy.logic.algorithms.minisat22_wrapper import minisat22_satisfiable + return minisat22_satisfiable(expr, all_models, minimal) + elif algorithm == "z3": + from sympy.logic.algorithms.z3_wrapper import z3_satisfiable + return z3_satisfiable(expr, all_models) + + raise NotImplementedError + + +def valid(expr): + """ + Check validity of a propositional sentence. + A valid propositional sentence is True under every assignment. + + Examples + ======== + + >>> from sympy.abc import A, B + >>> from sympy.logic.inference import valid + >>> valid(A | ~A) + True + >>> valid(A | B) + False + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Validity + + """ + return not satisfiable(Not(expr)) + + +def pl_true(expr, model=None, deep=False): + """ + Returns whether the given assignment is a model or not. + + If the assignment does not specify the value for every proposition, + this may return None to indicate 'not obvious'. + + Parameters + ========== + + model : dict, optional, default: {} + Mapping of symbols to boolean values to indicate assignment. + deep: boolean, optional, default: False + Gives the value of the expression under partial assignments + correctly. May still return None to indicate 'not obvious'. + + + Examples + ======== + + >>> from sympy.abc import A, B + >>> from sympy.logic.inference import pl_true + >>> pl_true( A & B, {A: True, B: True}) + True + >>> pl_true(A & B, {A: False}) + False + >>> pl_true(A & B, {A: True}) + >>> pl_true(A & B, {A: True}, deep=True) + >>> pl_true(A >> (B >> A)) + >>> pl_true(A >> (B >> A), deep=True) + True + >>> pl_true(A & ~A) + >>> pl_true(A & ~A, deep=True) + False + >>> pl_true(A & B & (~A | ~B), {A: True}) + >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True) + False + + """ + + from sympy.core.symbol import Symbol + + boolean = (True, False) + + def _validate(expr): + if isinstance(expr, Symbol) or expr in boolean: + return True + if not isinstance(expr, BooleanFunction): + return False + return all(_validate(arg) for arg in expr.args) + + if expr in boolean: + return expr + expr = sympify(expr) + if not _validate(expr): + raise ValueError("%s is not a valid boolean expression" % expr) + if not model: + model = {} + model = {k: v for k, v in model.items() if v in boolean} + result = expr.subs(model) + if result in boolean: + return bool(result) + if deep: + model = dict.fromkeys(result.atoms(), True) + if pl_true(result, model): + if valid(result): + return True + else: + if not satisfiable(result): + return False + return None + + +def entails(expr, formula_set=None): + """ + Check whether the given expr_set entail an expr. + If formula_set is empty then it returns the validity of expr. + + Examples + ======== + + >>> from sympy.abc import A, B, C + >>> from sympy.logic.inference import entails + >>> entails(A, [A >> B, B >> C]) + False + >>> entails(C, [A >> B, B >> C, A]) + True + >>> entails(A >> B) + False + >>> entails(A >> (B >> A)) + True + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Logical_consequence + + """ + if formula_set: + formula_set = list(formula_set) + else: + formula_set = [] + formula_set.append(Not(expr)) + return not satisfiable(And(*formula_set)) + + +class KB: + """Base class for all knowledge bases""" + def __init__(self, sentence=None): + self.clauses_ = set() + if sentence: + self.tell(sentence) + + def tell(self, sentence): + raise NotImplementedError + + def ask(self, query): + raise NotImplementedError + + def retract(self, sentence): + raise NotImplementedError + + @property + def clauses(self): + return list(ordered(self.clauses_)) + + +class PropKB(KB): + """A KB for Propositional Logic. Inefficient, with no indexing.""" + + def tell(self, sentence): + """Add the sentence's clauses to the KB + + Examples + ======== + + >>> from sympy.logic.inference import PropKB + >>> from sympy.abc import x, y + >>> l = PropKB() + >>> l.clauses + [] + + >>> l.tell(x | y) + >>> l.clauses + [x | y] + + >>> l.tell(y) + >>> l.clauses + [y, x | y] + + """ + for c in conjuncts(to_cnf(sentence)): + self.clauses_.add(c) + + def ask(self, query): + """Checks if the query is true given the set of clauses. + + Examples + ======== + + >>> from sympy.logic.inference import PropKB + >>> from sympy.abc import x, y + >>> l = PropKB() + >>> l.tell(x & ~y) + >>> l.ask(x) + True + >>> l.ask(y) + False + + """ + return entails(query, self.clauses_) + + def retract(self, sentence): + """Remove the sentence's clauses from the KB + + Examples + ======== + + >>> from sympy.logic.inference import PropKB + >>> from sympy.abc import x, y + >>> l = PropKB() + >>> l.clauses + [] + + >>> l.tell(x | y) + >>> l.clauses + [x | y] + + >>> l.retract(x | y) + >>> l.clauses + [] + + """ + for c in conjuncts(to_cnf(sentence)): + self.clauses_.discard(c) diff --git a/lib/python3.11/site-packages/sympy/logic/tests/__init__.py b/lib/python3.11/site-packages/sympy/logic/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..23e5ab6d3c0c3508eb2e2acaefbe749bf01f128a Binary files /dev/null and b/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/test_dimacs.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/test_dimacs.cpython-311.pyc new file mode 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b/lib/python3.11/site-packages/sympy/logic/tests/__pycache__/test_lra_theory.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/logic/tests/test_boolalg.py b/lib/python3.11/site-packages/sympy/logic/tests/test_boolalg.py new file mode 100644 index 0000000000000000000000000000000000000000..53de73f190caa663d790acc0d9534a2ea2824404 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/tests/test_boolalg.py @@ -0,0 +1,1352 @@ +from sympy.assumptions.ask import Q +from sympy.assumptions.refine import refine +from sympy.core.numbers import oo +from sympy.core.relational import Equality, Eq, Ne +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, symbols) +from sympy.functions import Piecewise +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.sets.sets import Interval, Union +from sympy.sets.contains import Contains +from sympy.simplify.simplify import simplify +from sympy.logic.boolalg import ( + And, Boolean, Equivalent, ITE, Implies, Nand, Nor, Not, Or, + POSform, SOPform, Xor, Xnor, conjuncts, disjuncts, + distribute_or_over_and, distribute_and_over_or, + eliminate_implications, is_nnf, is_cnf, is_dnf, simplify_logic, + to_nnf, to_cnf, to_dnf, to_int_repr, bool_map, true, false, + BooleanAtom, is_literal, term_to_integer, + truth_table, as_Boolean, to_anf, is_anf, distribute_xor_over_and, + anf_coeffs, ANFform, bool_minterm, bool_maxterm, bool_monomial, + _check_pair, _convert_to_varsSOP, _convert_to_varsPOS, Exclusive, + gateinputcount) +from sympy.assumptions.cnf import CNF + +from sympy.testing.pytest import raises, XFAIL, slow + +from itertools import combinations, permutations, product + +A, B, C, D = symbols('A:D') +a, b, c, d, e, w, x, y, z = symbols('a:e w:z') + + +def test_overloading(): + """Test that |, & are overloaded as expected""" + + assert A & B == And(A, B) + assert A | B == Or(A, B) + assert (A & B) | C == Or(And(A, B), C) + assert A >> B == Implies(A, B) + assert A << B == Implies(B, A) + assert ~A == Not(A) + assert A ^ B == Xor(A, B) + + +def test_And(): + assert And() is true + assert And(A) == A + assert And(True) is true + assert And(False) is false + assert And(True, True) is true + assert And(True, False) is false + assert And(False, False) is false + assert And(True, A) == A + assert And(False, A) is false + assert And(True, True, True) is true + assert And(True, True, A) == A + assert And(True, False, A) is false + assert And(1, A) == A + raises(TypeError, lambda: And(2, A)) + assert And(A < 1, A >= 1) is false + e = A > 1 + assert And(e, e.canonical) == e.canonical + g, l, ge, le = A > B, B < A, A >= B, B <= A + assert And(g, l, ge, le) == And(ge, g) + assert {And(*i) for i in permutations((l,g,le,ge))} == {And(ge, g)} + assert And(And(Eq(a, 0), Eq(b, 0)), And(Ne(a, 0), Eq(c, 0))) is false + + +def test_Or(): + assert Or() is false + assert Or(A) == A + assert Or(True) is true + assert Or(False) is false + assert Or(True, True) is true + assert Or(True, False) is true + assert Or(False, False) is false + assert Or(True, A) is true + assert Or(False, A) == A + assert Or(True, False, False) is true + assert Or(True, False, A) is true + assert Or(False, False, A) == A + assert Or(1, A) is true + raises(TypeError, lambda: Or(2, A)) + assert Or(A < 1, A >= 1) is true + e = A > 1 + assert Or(e, e.canonical) == e + g, l, ge, le = A > B, B < A, A >= B, B <= A + assert Or(g, l, ge, le) == Or(g, ge) + + +def test_Xor(): + assert Xor() is false + assert Xor(A) == A + assert Xor(A, A) is false + assert Xor(True, A, A) is true + assert Xor(A, A, A, A, A) == A + assert Xor(True, False, False, A, B) == ~Xor(A, B) + assert Xor(True) is true + assert Xor(False) is false + assert Xor(True, True) is false + assert Xor(True, False) is true + assert Xor(False, False) is false + assert Xor(True, A) == ~A + assert Xor(False, A) == A + assert Xor(True, False, False) is true + assert Xor(True, False, A) == ~A + assert Xor(False, False, A) == A + assert isinstance(Xor(A, B), Xor) + assert Xor(A, B, Xor(C, D)) == Xor(A, B, C, D) + assert Xor(A, B, Xor(B, C)) == Xor(A, C) + assert Xor(A < 1, A >= 1, B) == Xor(0, 1, B) == Xor(1, 0, B) + e = A > 1 + assert Xor(e, e.canonical) == Xor(0, 0) == Xor(1, 1) + + +def test_rewrite_as_And(): + expr = x ^ y + assert expr.rewrite(And) == (x | y) & (~x | ~y) + + +def test_rewrite_as_Or(): + expr = x ^ y + assert expr.rewrite(Or) == (x & ~y) | (y & ~x) + + +def test_rewrite_as_Nand(): + expr = (y & z) | (z & ~w) + assert expr.rewrite(Nand) == ~(~(y & z) & ~(z & ~w)) + + +def test_rewrite_as_Nor(): + expr = z & (y | ~w) + assert expr.rewrite(Nor) == ~(~z | ~(y | ~w)) + + +def test_Not(): + raises(TypeError, lambda: Not(True, False)) + assert Not(True) is false + assert Not(False) is true + assert Not(0) is true + assert Not(1) is false + assert Not(2) is false + + +def test_Nand(): + assert Nand() is false + assert Nand(A) == ~A + assert Nand(True) is false + assert Nand(False) is true + assert Nand(True, True) is false + assert Nand(True, False) is true + assert Nand(False, False) is true + assert Nand(True, A) == ~A + assert Nand(False, A) is true + assert Nand(True, True, True) is false + assert Nand(True, True, A) == ~A + assert Nand(True, False, A) is true + + +def test_Nor(): + assert Nor() is true + assert Nor(A) == ~A + assert Nor(True) is false + assert Nor(False) is true + assert Nor(True, True) is false + assert Nor(True, False) is false + assert Nor(False, False) is true + assert Nor(True, A) is false + assert Nor(False, A) == ~A + assert Nor(True, True, True) is false + assert Nor(True, True, A) is false + assert Nor(True, False, A) is false + + +def test_Xnor(): + assert Xnor() is true + assert Xnor(A) == ~A + assert Xnor(A, A) is true + assert Xnor(True, A, A) is false + assert Xnor(A, A, A, A, A) == ~A + assert Xnor(True) is false + assert Xnor(False) is true + assert Xnor(True, True) is true + assert Xnor(True, False) is false + assert Xnor(False, False) is true + assert Xnor(True, A) == A + assert Xnor(False, A) == ~A + assert Xnor(True, False, False) is false + assert Xnor(True, False, A) == A + assert Xnor(False, False, A) == ~A + + +def test_Implies(): + raises(ValueError, lambda: Implies(A, B, C)) + assert Implies(True, True) is true + assert Implies(True, False) is false + assert Implies(False, True) is true + assert Implies(False, False) is true + assert Implies(0, A) is true + assert Implies(1, 1) is true + assert Implies(1, 0) is false + assert A >> B == B << A + assert (A < 1) >> (A >= 1) == (A >= 1) + assert (A < 1) >> (S.One > A) is true + assert A >> A is true + + +def test_Equivalent(): + assert Equivalent(A, B) == Equivalent(B, A) == Equivalent(A, B, A) + assert Equivalent() is true + assert Equivalent(A, A) == Equivalent(A) is true + assert Equivalent(True, True) == Equivalent(False, False) is true + assert Equivalent(True, False) == Equivalent(False, True) is false + assert Equivalent(A, True) == A + assert Equivalent(A, False) == Not(A) + assert Equivalent(A, B, True) == A & B + assert Equivalent(A, B, False) == ~A & ~B + assert Equivalent(1, A) == A + assert Equivalent(0, A) == Not(A) + assert Equivalent(A, Equivalent(B, C)) != Equivalent(Equivalent(A, B), C) + assert Equivalent(A < 1, A >= 1) is false + assert Equivalent(A < 1, A >= 1, 0) is false + assert Equivalent(A < 1, A >= 1, 1) is false + assert Equivalent(A < 1, S.One > A) == Equivalent(1, 1) == Equivalent(0, 0) + assert Equivalent(Equality(A, B), Equality(B, A)) is true + + +def test_Exclusive(): + assert Exclusive(False, False, False) is true + assert Exclusive(True, False, False) is true + assert Exclusive(True, True, False) is false + assert Exclusive(True, True, True) is false + + +def test_equals(): + assert Not(Or(A, B)).equals(And(Not(A), Not(B))) is True + assert Equivalent(A, B).equals((A >> B) & (B >> A)) is True + assert ((A | ~B) & (~A | B)).equals((~A & ~B) | (A & B)) is True + assert (A >> B).equals(~A >> ~B) is False + assert (A >> (B >> A)).equals(A >> (C >> A)) is False + raises(NotImplementedError, lambda: (A & B).equals(A > B)) + + +def test_simplification_boolalg(): + """ + Test working of simplification methods. + """ + set1 = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]] + set2 = [[0, 0, 0], [0, 1, 0], [1, 0, 1], [1, 1, 1]] + assert SOPform([x, y, z], set1) == Or(And(Not(x), z), And(Not(z), x)) + assert Not(SOPform([x, y, z], set2)) == \ + Not(Or(And(Not(x), Not(z)), And(x, z))) + assert POSform([x, y, z], set1 + set2) is true + assert SOPform([x, y, z], set1 + set2) is true + assert SOPform([Dummy(), Dummy(), Dummy()], set1 + set2) is true + + minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1], + [1, 1, 1, 1]] + dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]] + assert ( + SOPform([w, x, y, z], minterms, dontcares) == + Or(And(y, z), And(Not(w), Not(x)))) + assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z) + + minterms = [1, 3, 7, 11, 15] + dontcares = [0, 2, 5] + assert ( + SOPform([w, x, y, z], minterms, dontcares) == + Or(And(y, z), And(Not(w), Not(x)))) + assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z) + + minterms = [1, [0, 0, 1, 1], 7, [1, 0, 1, 1], + [1, 1, 1, 1]] + dontcares = [0, [0, 0, 1, 0], 5] + assert ( + SOPform([w, x, y, z], minterms, dontcares) == + Or(And(y, z), And(Not(w), Not(x)))) + assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z) + + minterms = [1, {y: 1, z: 1}] + dontcares = [0, [0, 0, 1, 0], 5] + assert ( + SOPform([w, x, y, z], minterms, dontcares) == + Or(And(y, z), And(Not(w), Not(x)))) + assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z) + + + minterms = [{y: 1, z: 1}, 1] + dontcares = [[0, 0, 0, 0]] + + minterms = [[0, 0, 0]] + raises(ValueError, lambda: SOPform([w, x, y, z], minterms)) + raises(ValueError, lambda: POSform([w, x, y, z], minterms)) + + raises(TypeError, lambda: POSform([w, x, y, z], ["abcdefg"])) + + # test simplification + ans = And(A, Or(B, C)) + assert simplify_logic(A & (B | C)) == ans + assert simplify_logic((A & B) | (A & C)) == ans + assert simplify_logic(Implies(A, B)) == Or(Not(A), B) + assert simplify_logic(Equivalent(A, B)) == \ + Or(And(A, B), And(Not(A), Not(B))) + assert simplify_logic(And(Equality(A, 2), C)) == And(Equality(A, 2), C) + assert simplify_logic(And(Equality(A, 2), A)) == And(Equality(A, 2), A) + assert simplify_logic(And(Equality(A, B), C)) == And(Equality(A, B), C) + assert simplify_logic(Or(And(Equality(A, 3), B), And(Equality(A, 3), C))) \ + == And(Equality(A, 3), Or(B, C)) + b = (~x & ~y & ~z) | (~x & ~y & z) + e = And(A, b) + assert simplify_logic(e) == A & ~x & ~y + raises(ValueError, lambda: simplify_logic(A & (B | C), form='blabla')) + assert simplify(Or(x <= y, And(x < y, z))) == (x <= y) + assert simplify(Or(x <= y, And(y > x, z))) == (x <= y) + assert simplify(Or(x >= y, And(y < x, z))) == (x >= y) + + # Check that expressions with nine variables or more are not simplified + # (without the force-flag) + a, b, c, d, e, f, g, h, j = symbols('a b c d e f g h j') + expr = a & b & c & d & e & f & g & h & j | \ + a & b & c & d & e & f & g & h & ~j + # This expression can be simplified to get rid of the j variables + assert simplify_logic(expr) == expr + + # Test dontcare + assert simplify_logic((a & b) | c | d, dontcare=(a & b)) == c | d + + # check input + ans = SOPform([x, y], [[1, 0]]) + assert SOPform([x, y], [[1, 0]]) == ans + assert POSform([x, y], [[1, 0]]) == ans + + raises(ValueError, lambda: SOPform([x], [[1]], [[1]])) + assert SOPform([x], [[1]], [[0]]) is true + assert SOPform([x], [[0]], [[1]]) is true + assert SOPform([x], [], []) is false + + raises(ValueError, lambda: POSform([x], [[1]], [[1]])) + assert POSform([x], [[1]], [[0]]) is true + assert POSform([x], [[0]], [[1]]) is true + assert POSform([x], [], []) is false + + # check working of simplify + assert simplify((A & B) | (A & C)) == And(A, Or(B, C)) + assert simplify(And(x, Not(x))) == False + assert simplify(Or(x, Not(x))) == True + assert simplify(And(Eq(x, 0), Eq(x, y))) == And(Eq(x, 0), Eq(y, 0)) + assert And(Eq(x - 1, 0), Eq(x, y)).simplify() == And(Eq(x, 1), Eq(y, 1)) + assert And(Ne(x - 1, 0), Ne(x, y)).simplify() == And(Ne(x, 1), Ne(x, y)) + assert And(Eq(x - 1, 0), Ne(x, y)).simplify() == And(Eq(x, 1), Ne(y, 1)) + assert And(Eq(x - 1, 0), Eq(x, z + y), Eq(y + x, 0)).simplify( + ) == And(Eq(x, 1), Eq(y, -1), Eq(z, 2)) + assert And(Eq(x - 1, 0), Eq(x + 2, 3)).simplify() == Eq(x, 1) + assert And(Ne(x - 1, 0), Ne(x + 2, 3)).simplify() == Ne(x, 1) + assert And(Eq(x - 1, 0), Eq(x + 2, 2)).simplify() == False + assert And(Ne(x - 1, 0), Ne(x + 2, 2)).simplify( + ) == And(Ne(x, 1), Ne(x, 0)) + assert simplify(Xor(x, ~x)) == True + + +def test_bool_map(): + """ + Test working of bool_map function. + """ + + minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1], + [1, 1, 1, 1]] + assert bool_map(Not(Not(a)), a) == (a, {a: a}) + assert bool_map(SOPform([w, x, y, z], minterms), + POSform([w, x, y, z], minterms)) == \ + (And(Or(Not(w), y), Or(Not(x), y), z), {x: x, w: w, z: z, y: y}) + assert bool_map(SOPform([x, z, y], [[1, 0, 1]]), + SOPform([a, b, c], [[1, 0, 1]])) != False + function1 = SOPform([x, z, y], [[1, 0, 1], [0, 0, 1]]) + function2 = SOPform([a, b, c], [[1, 0, 1], [1, 0, 0]]) + assert bool_map(function1, function2) == \ + (function1, {y: a, z: b}) + assert bool_map(Xor(x, y), ~Xor(x, y)) == False + assert bool_map(And(x, y), Or(x, y)) is None + assert bool_map(And(x, y), And(x, y, z)) is None + # issue 16179 + assert bool_map(Xor(x, y, z), ~Xor(x, y, z)) == False + assert bool_map(Xor(a, x, y, z), ~Xor(a, x, y, z)) == False + + +def test_bool_symbol(): + """Test that mixing symbols with boolean values + works as expected""" + + assert And(A, True) == A + assert And(A, True, True) == A + assert And(A, False) is false + assert And(A, True, False) is false + assert Or(A, True) is true + assert Or(A, False) == A + + +def test_is_boolean(): + assert isinstance(True, Boolean) is False + assert isinstance(true, Boolean) is True + assert 1 == True + assert 1 != true + assert (1 == true) is False + assert 0 == False + assert 0 != false + assert (0 == false) is False + assert true.is_Boolean is True + assert (A & B).is_Boolean + assert (A | B).is_Boolean + assert (~A).is_Boolean + assert (A ^ B).is_Boolean + assert A.is_Boolean != isinstance(A, Boolean) + assert isinstance(A, Boolean) + + +def test_subs(): + assert (A & B).subs(A, True) == B + assert (A & B).subs(A, False) is false + assert (A & B).subs(B, True) == A + assert (A & B).subs(B, False) is false + assert (A & B).subs({A: True, B: True}) is true + assert (A | B).subs(A, True) is true + assert (A | B).subs(A, False) == B + assert (A | B).subs(B, True) is true + assert (A | B).subs(B, False) == A + assert (A | B).subs({A: True, B: True}) is true + + +""" +we test for axioms of boolean algebra +see https://en.wikipedia.org/wiki/Boolean_algebra_(structure) +""" + + +def test_commutative(): + """Test for commutativity of And and Or""" + A, B = map(Boolean, symbols('A,B')) + + assert A & B == B & A + assert A | B == B | A + + +def test_and_associativity(): + """Test for associativity of And""" + + assert (A & B) & C == A & (B & C) + + +def test_or_assicativity(): + assert ((A | B) | C) == (A | (B | C)) + + +def test_double_negation(): + a = Boolean() + assert ~(~a) == a + + +# test methods + +def test_eliminate_implications(): + assert eliminate_implications(Implies(A, B, evaluate=False)) == (~A) | B + assert eliminate_implications( + A >> (C >> Not(B))) == Or(Or(Not(B), Not(C)), Not(A)) + assert eliminate_implications(Equivalent(A, B, C, D)) == \ + (~A | B) & (~B | C) & (~C | D) & (~D | A) + + +def test_conjuncts(): + assert conjuncts(A & B & C) == {A, B, C} + assert conjuncts((A | B) & C) == {A | B, C} + assert conjuncts(A) == {A} + assert conjuncts(True) == {True} + assert conjuncts(False) == {False} + + +def test_disjuncts(): + assert disjuncts(A | B | C) == {A, B, C} + assert disjuncts((A | B) & C) == {(A | B) & C} + assert disjuncts(A) == {A} + assert disjuncts(True) == {True} + assert disjuncts(False) == {False} + + +def test_distribute(): + assert distribute_and_over_or(Or(And(A, B), C)) == And(Or(A, C), Or(B, C)) + assert distribute_or_over_and(And(A, Or(B, C))) == Or(And(A, B), And(A, C)) + assert distribute_xor_over_and(And(A, Xor(B, C))) == Xor(And(A, B), And(A, C)) + + +def test_to_anf(): + x, y, z = symbols('x,y,z') + assert to_anf(And(x, y)) == And(x, y) + assert to_anf(Or(x, y)) == Xor(x, y, And(x, y)) + assert to_anf(Or(Implies(x, y), And(x, y), y)) == \ + Xor(x, True, x & y, remove_true=False) + assert to_anf(Or(Nand(x, y), Nor(x, y), Xnor(x, y), Implies(x, y))) == True + assert to_anf(Or(x, Not(y), Nor(x,z), And(x, y), Nand(y, z))) == \ + Xor(True, And(y, z), And(x, y, z), remove_true=False) + assert to_anf(Xor(x, y)) == Xor(x, y) + assert to_anf(Not(x)) == Xor(x, True, remove_true=False) + assert to_anf(Nand(x, y)) == Xor(True, And(x, y), remove_true=False) + assert to_anf(Nor(x, y)) == Xor(x, y, True, And(x, y), remove_true=False) + assert to_anf(Implies(x, y)) == Xor(x, True, And(x, y), remove_true=False) + assert to_anf(Equivalent(x, y)) == Xor(x, y, True, remove_true=False) + assert to_anf(Nand(x | y, x >> y), deep=False) == \ + Xor(True, And(Or(x, y), Implies(x, y)), remove_true=False) + assert to_anf(Nor(x ^ y, x & y), deep=False) == \ + Xor(True, Or(Xor(x, y), And(x, y)), remove_true=False) + # issue 25218 + assert to_anf(x ^ ~(x ^ y ^ ~y)) == False + + +def test_to_nnf(): + assert to_nnf(true) is true + assert to_nnf(false) is false + assert to_nnf(A) == A + assert to_nnf(A | ~A | B) is true + assert to_nnf(A & ~A & B) is false + assert to_nnf(A >> B) == ~A | B + assert to_nnf(Equivalent(A, B, C)) == (~A | B) & (~B | C) & (~C | A) + assert to_nnf(A ^ B ^ C) == \ + (A | B | C) & (~A | ~B | C) & (A | ~B | ~C) & (~A | B | ~C) + assert to_nnf(ITE(A, B, C)) == (~A | B) & (A | C) + assert to_nnf(Not(A | B | C)) == ~A & ~B & ~C + assert to_nnf(Not(A & B & C)) == ~A | ~B | ~C + assert to_nnf(Not(A >> B)) == A & ~B + assert to_nnf(Not(Equivalent(A, B, C))) == And(Or(A, B, C), Or(~A, ~B, ~C)) + assert to_nnf(Not(A ^ B ^ C)) == \ + (~A | B | C) & (A | ~B | C) & (A | B | ~C) & (~A | ~B | ~C) + assert to_nnf(Not(ITE(A, B, C))) == (~A | ~B) & (A | ~C) + assert to_nnf((A >> B) ^ (B >> A)) == (A & ~B) | (~A & B) + assert to_nnf((A >> B) ^ (B >> A), False) == \ + (~A | ~B | A | B) & ((A & ~B) | (~A & B)) + assert ITE(A, 1, 0).to_nnf() == A + assert ITE(A, 0, 1).to_nnf() == ~A + # although ITE can hold non-Boolean, it will complain if + # an attempt is made to convert the ITE to Boolean nnf + raises(TypeError, lambda: ITE(A < 1, [1], B).to_nnf()) + + +def test_to_cnf(): + assert to_cnf(~(B | C)) == And(Not(B), Not(C)) + assert to_cnf((A & B) | C) == And(Or(A, C), Or(B, C)) + assert to_cnf(A >> B) == (~A) | B + assert to_cnf(A >> (B & C)) == (~A | B) & (~A | C) + assert to_cnf(A & (B | C) | ~A & (B | C), True) == B | C + assert to_cnf(A & B) == And(A, B) + + assert to_cnf(Equivalent(A, B)) == And(Or(A, Not(B)), Or(B, Not(A))) + assert to_cnf(Equivalent(A, B & C)) == \ + (~A | B) & (~A | C) & (~B | ~C | A) + assert to_cnf(Equivalent(A, B | C), True) == \ + And(Or(Not(B), A), Or(Not(C), A), Or(B, C, Not(A))) + assert to_cnf(A + 1) == A + 1 + + +def test_issue_18904(): + x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 = symbols('x1:16') + eq = (( x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & x9 ) | + ( x1 & x2 & x3 & x4 & x5 & x6 & x7 & x10 & x9 ) | + ( x1 & x11 & x3 & x12 & x5 & x13 & x14 & x15 & x9 )) + assert is_cnf(to_cnf(eq)) + raises(ValueError, lambda: to_cnf(eq, simplify=True)) + for f, t in zip((And, Or), (to_cnf, to_dnf)): + eq = f(x1, x2, x3, x4, x5, x6, x7, x8, x9) + raises(ValueError, lambda: to_cnf(eq, simplify=True)) + assert t(eq, simplify=True, force=True) == eq + + +def test_issue_9949(): + assert is_cnf(to_cnf((b > -5) | (a > 2) & (a < 4))) + + +def test_to_CNF(): + assert CNF.CNF_to_cnf(CNF.to_CNF(~(B | C))) == to_cnf(~(B | C)) + assert CNF.CNF_to_cnf(CNF.to_CNF((A & B) | C)) == to_cnf((A & B) | C) + assert CNF.CNF_to_cnf(CNF.to_CNF(A >> B)) == to_cnf(A >> B) + assert CNF.CNF_to_cnf(CNF.to_CNF(A >> (B & C))) == to_cnf(A >> (B & C)) + assert CNF.CNF_to_cnf(CNF.to_CNF(A & (B | C) | ~A & (B | C))) == to_cnf(A & (B | C) | ~A & (B | C)) + assert CNF.CNF_to_cnf(CNF.to_CNF(A & B)) == to_cnf(A & B) + + +def test_to_dnf(): + assert to_dnf(~(B | C)) == And(Not(B), Not(C)) + assert to_dnf(A & (B | C)) == Or(And(A, B), And(A, C)) + assert to_dnf(A >> B) == (~A) | B + assert to_dnf(A >> (B & C)) == (~A) | (B & C) + assert to_dnf(A | B) == A | B + + assert to_dnf(Equivalent(A, B), True) == \ + Or(And(A, B), And(Not(A), Not(B))) + assert to_dnf(Equivalent(A, B & C), True) == \ + Or(And(A, B, C), And(Not(A), Not(B)), And(Not(A), Not(C))) + assert to_dnf(A + 1) == A + 1 + + +def test_to_int_repr(): + x, y, z = map(Boolean, symbols('x,y,z')) + + def sorted_recursive(arg): + try: + return sorted(sorted_recursive(x) for x in arg) + except TypeError: # arg is not a sequence + return arg + + assert sorted_recursive(to_int_repr([x | y, z | x], [x, y, z])) == \ + sorted_recursive([[1, 2], [1, 3]]) + assert sorted_recursive(to_int_repr([x | y, z | ~x], [x, y, z])) == \ + sorted_recursive([[1, 2], [3, -1]]) + + +def test_is_anf(): + x, y = symbols('x,y') + assert is_anf(true) is True + assert is_anf(false) is True + assert is_anf(x) is True + assert is_anf(And(x, y)) is True + assert is_anf(Xor(x, y, And(x, y))) is True + assert is_anf(Xor(x, y, Or(x, y))) is False + assert is_anf(Xor(Not(x), y)) is False + + +def test_is_nnf(): + assert is_nnf(true) is True + assert is_nnf(A) is True + assert is_nnf(~A) is True + assert is_nnf(A & B) is True + assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), False) is True + assert is_nnf((A | B) & (~A | ~B)) is True + assert is_nnf(Not(Or(A, B))) is False + assert is_nnf(A ^ B) is False + assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), True) is False + + +def test_is_cnf(): + assert is_cnf(x) is True + assert is_cnf(x | y | z) is True + assert is_cnf(x & y & z) is True + assert is_cnf((x | y) & z) is True + assert is_cnf((x & y) | z) is False + assert is_cnf(~(x & y) | z) is False + + +def test_is_dnf(): + assert is_dnf(x) is True + assert is_dnf(x | y | z) is True + assert is_dnf(x & y & z) is True + assert is_dnf((x & y) | z) is True + assert is_dnf((x | y) & z) is False + assert is_dnf(~(x | y) & z) is False + + +def test_ITE(): + A, B, C = symbols('A:C') + assert ITE(True, False, True) is false + assert ITE(True, True, False) is true + assert ITE(False, True, False) is false + assert ITE(False, False, True) is true + assert isinstance(ITE(A, B, C), ITE) + + A = True + assert ITE(A, B, C) == B + A = False + assert ITE(A, B, C) == C + B = True + assert ITE(And(A, B), B, C) == C + assert ITE(Or(A, False), And(B, True), False) is false + assert ITE(x, A, B) == Not(x) + assert ITE(x, B, A) == x + assert ITE(1, x, y) == x + assert ITE(0, x, y) == y + raises(TypeError, lambda: ITE(2, x, y)) + raises(TypeError, lambda: ITE(1, [], y)) + raises(TypeError, lambda: ITE(1, (), y)) + raises(TypeError, lambda: ITE(1, y, [])) + assert ITE(1, 1, 1) is S.true + assert isinstance(ITE(1, 1, 1, evaluate=False), ITE) + + assert ITE(Eq(x, True), y, x) == ITE(x, y, x) + assert ITE(Eq(x, False), y, x) == ITE(~x, y, x) + assert ITE(Ne(x, True), y, x) == ITE(~x, y, x) + assert ITE(Ne(x, False), y, x) == ITE(x, y, x) + assert ITE(Eq(S. true, x), y, x) == ITE(x, y, x) + assert ITE(Eq(S.false, x), y, x) == ITE(~x, y, x) + assert ITE(Ne(S.true, x), y, x) == ITE(~x, y, x) + assert ITE(Ne(S.false, x), y, x) == ITE(x, y, x) + # 0 and 1 in the context are not treated as True/False + # so the equality must always be False since dissimilar + # objects cannot be equal + assert ITE(Eq(x, 0), y, x) == x + assert ITE(Eq(x, 1), y, x) == x + assert ITE(Ne(x, 0), y, x) == y + assert ITE(Ne(x, 1), y, x) == y + assert ITE(Eq(x, 0), y, z).subs(x, 0) == y + assert ITE(Eq(x, 0), y, z).subs(x, 1) == z + raises(ValueError, lambda: ITE(x > 1, y, x, z)) + + +def test_is_literal(): + assert is_literal(True) is True + assert is_literal(False) is True + assert is_literal(A) is True + assert is_literal(~A) is True + assert is_literal(Or(A, B)) is False + assert is_literal(Q.zero(A)) is True + assert is_literal(Not(Q.zero(A))) is True + assert is_literal(Or(A, B)) is False + assert is_literal(And(Q.zero(A), Q.zero(B))) is False + assert is_literal(x < 3) + assert not is_literal(x + y < 3) + + +def test_operators(): + # Mostly test __and__, __rand__, and so on + assert True & A == A & True == A + assert False & A == A & False == False + assert A & B == And(A, B) + assert True | A == A | True == True + assert False | A == A | False == A + assert A | B == Or(A, B) + assert ~A == Not(A) + assert True >> A == A << True == A + assert False >> A == A << False == True + assert A >> True == True << A == True + assert A >> False == False << A == ~A + assert A >> B == B << A == Implies(A, B) + assert True ^ A == A ^ True == ~A + assert False ^ A == A ^ False == A + assert A ^ B == Xor(A, B) + + +def test_true_false(): + assert true is S.true + assert false is S.false + assert true is not True + assert false is not False + assert true + assert not false + assert true == True + assert false == False + assert not (true == False) + assert not (false == True) + assert not (true == false) + + assert hash(true) == hash(True) + assert hash(false) == hash(False) + assert len({true, True}) == len({false, False}) == 1 + + assert isinstance(true, BooleanAtom) + assert isinstance(false, BooleanAtom) + # We don't want to subclass from bool, because bool subclasses from + # int. But operators like &, |, ^, <<, >>, and ~ act differently on 0 and + # 1 then we want them to on true and false. See the docstrings of the + # various And, Or, etc. functions for examples. + assert not isinstance(true, bool) + assert not isinstance(false, bool) + + # Note: using 'is' comparison is important here. We want these to return + # true and false, not True and False + + assert Not(true) is false + assert Not(True) is false + assert Not(false) is true + assert Not(False) is true + assert ~true is false + assert ~false is true + + for T, F in product((True, true), (False, false)): + assert And(T, F) is false + assert And(F, T) is false + assert And(F, F) is false + assert And(T, T) is true + assert And(T, x) == x + assert And(F, x) is false + if not (T is True and F is False): + assert T & F is false + assert F & T is false + if F is not False: + assert F & F is false + if T is not True: + assert T & T is true + + assert Or(T, F) is true + assert Or(F, T) is true + assert Or(F, F) is false + assert Or(T, T) is true + assert Or(T, x) is true + assert Or(F, x) == x + if not (T is True and F is False): + assert T | F is true + assert F | T is true + if F is not False: + assert F | F is false + if T is not True: + assert T | T is true + + assert Xor(T, F) is true + assert Xor(F, T) is true + assert Xor(F, F) is false + assert Xor(T, T) is false + assert Xor(T, x) == ~x + assert Xor(F, x) == x + if not (T is True and F is False): + assert T ^ F is true + assert F ^ T is true + if F is not False: + assert F ^ F is false + if T is not True: + assert T ^ T is false + + assert Nand(T, F) is true + assert Nand(F, T) is true + assert Nand(F, F) is true + assert Nand(T, T) is false + assert Nand(T, x) == ~x + assert Nand(F, x) is true + + assert Nor(T, F) is false + assert Nor(F, T) is false + assert Nor(F, F) is true + assert Nor(T, T) is false + assert Nor(T, x) is false + assert Nor(F, x) == ~x + + assert Implies(T, F) is false + assert Implies(F, T) is true + assert Implies(F, F) is true + assert Implies(T, T) is true + assert Implies(T, x) == x + assert Implies(F, x) is true + assert Implies(x, T) is true + assert Implies(x, F) == ~x + if not (T is True and F is False): + assert T >> F is false + assert F << T is false + assert F >> T is true + assert T << F is true + if F is not False: + assert F >> F is true + assert F << F is true + if T is not True: + assert T >> T is true + assert T << T is true + + assert Equivalent(T, F) is false + assert Equivalent(F, T) is false + assert Equivalent(F, F) is true + assert Equivalent(T, T) is true + assert Equivalent(T, x) == x + assert Equivalent(F, x) == ~x + assert Equivalent(x, T) == x + assert Equivalent(x, F) == ~x + + assert ITE(T, T, T) is true + assert ITE(T, T, F) is true + assert ITE(T, F, T) is false + assert ITE(T, F, F) is false + assert ITE(F, T, T) is true + assert ITE(F, T, F) is false + assert ITE(F, F, T) is true + assert ITE(F, F, F) is false + + assert all(i.simplify(1, 2) is i for i in (S.true, S.false)) + + +def test_bool_as_set(): + assert ITE(y <= 0, False, y >= 1).as_set() == Interval(1, oo) + assert And(x <= 2, x >= -2).as_set() == Interval(-2, 2) + assert Or(x >= 2, x <= -2).as_set() == Interval(-oo, -2) + Interval(2, oo) + assert Not(x > 2).as_set() == Interval(-oo, 2) + # issue 10240 + assert Not(And(x > 2, x < 3)).as_set() == \ + Union(Interval(-oo, 2), Interval(3, oo)) + assert true.as_set() == S.UniversalSet + assert false.as_set() is S.EmptySet + assert x.as_set() == S.UniversalSet + assert And(Or(x < 1, x > 3), x < 2).as_set() == Interval.open(-oo, 1) + assert And(x < 1, sin(x) < 3).as_set() == (x < 1).as_set() + raises(NotImplementedError, lambda: (sin(x) < 1).as_set()) + # watch for object morph in as_set + assert Eq(-1, cos(2*x)**2/sin(2*x)**2).as_set() is S.EmptySet + + +@XFAIL +def test_multivariate_bool_as_set(): + x, y = symbols('x,y') + + assert And(x >= 0, y >= 0).as_set() == Interval(0, oo)*Interval(0, oo) + assert Or(x >= 0, y >= 0).as_set() == S.Reals*S.Reals - \ + Interval(-oo, 0, True, True)*Interval(-oo, 0, True, True) + + +def test_all_or_nothing(): + x = symbols('x', extended_real=True) + args = x >= -oo, x <= oo + v = And(*args) + if v.func is And: + assert len(v.args) == len(args) - args.count(S.true) + else: + assert v == True + v = Or(*args) + if v.func is Or: + assert len(v.args) == 2 + else: + assert v == True + + +def test_canonical_atoms(): + assert true.canonical == true + assert false.canonical == false + + +def test_negated_atoms(): + assert true.negated == false + assert false.negated == true + + +def test_issue_8777(): + assert And(x > 2, x < oo).as_set() == Interval(2, oo, left_open=True) + assert And(x >= 1, x < oo).as_set() == Interval(1, oo) + assert (x < oo).as_set() == Interval(-oo, oo) + assert (x > -oo).as_set() == Interval(-oo, oo) + + +def test_issue_8975(): + assert Or(And(-oo < x, x <= -2), And(2 <= x, x < oo)).as_set() == \ + Interval(-oo, -2) + Interval(2, oo) + + +def test_term_to_integer(): + assert term_to_integer([1, 0, 1, 0, 0, 1, 0]) == 82 + assert term_to_integer('0010101000111001') == 10809 + + +def test_issue_21971(): + a, b, c, d = symbols('a b c d') + f = a & b & c | a & c + assert f.subs(a & c, d) == b & d | d + assert f.subs(a & b & c, d) == a & c | d + + f = (a | b | c) & (a | c) + assert f.subs(a | c, d) == (b | d) & d + assert f.subs(a | b | c, d) == (a | c) & d + + f = (a ^ b ^ c) & (a ^ c) + assert f.subs(a ^ c, d) == (b ^ d) & d + assert f.subs(a ^ b ^ c, d) == (a ^ c) & d + + +def test_truth_table(): + assert list(truth_table(And(x, y), [x, y], input=False)) == \ + [False, False, False, True] + assert list(truth_table(x | y, [x, y], input=False)) == \ + [False, True, True, True] + assert list(truth_table(x >> y, [x, y], input=False)) == \ + [True, True, False, True] + assert list(truth_table(And(x, y), [x, y])) == \ + [([0, 0], False), ([0, 1], False), ([1, 0], False), ([1, 1], True)] + + +def test_issue_8571(): + for t in (S.true, S.false): + raises(TypeError, lambda: +t) + raises(TypeError, lambda: -t) + raises(TypeError, lambda: abs(t)) + # use int(bool(t)) to get 0 or 1 + raises(TypeError, lambda: int(t)) + + for o in [S.Zero, S.One, x]: + for _ in range(2): + raises(TypeError, lambda: o + t) + raises(TypeError, lambda: o - t) + raises(TypeError, lambda: o % t) + raises(TypeError, lambda: o*t) + raises(TypeError, lambda: o/t) + raises(TypeError, lambda: o**t) + o, t = t, o # do again in reversed order + + +def test_expand_relational(): + n = symbols('n', negative=True) + p, q = symbols('p q', positive=True) + r = ((n + q*(-n/q + 1))/(q*(-n/q + 1)) < 0) + assert r is not S.false + assert r.expand() is S.false + assert (q > 0).expand() is S.true + + +def test_issue_12717(): + assert S.true.is_Atom == True + assert S.false.is_Atom == True + + +def test_as_Boolean(): + nz = symbols('nz', nonzero=True) + assert all(as_Boolean(i) is S.true for i in (True, S.true, 1, nz)) + z = symbols('z', zero=True) + assert all(as_Boolean(i) is S.false for i in (False, S.false, 0, z)) + assert all(as_Boolean(i) == i for i in (x, x < 0)) + for i in (2, S(2), x + 1, []): + raises(TypeError, lambda: as_Boolean(i)) + + +def test_binary_symbols(): + assert ITE(x < 1, y, z).binary_symbols == {y, z} + for f in (Eq, Ne): + assert f(x, 1).binary_symbols == set() + assert f(x, True).binary_symbols == {x} + assert f(x, False).binary_symbols == {x} + assert S.true.binary_symbols == set() + assert S.false.binary_symbols == set() + assert x.binary_symbols == {x} + assert And(x, Eq(y, False), Eq(z, 1)).binary_symbols == {x, y} + assert Q.prime(x).binary_symbols == set() + assert Q.lt(x, 1).binary_symbols == set() + assert Q.is_true(x).binary_symbols == {x} + assert Q.eq(x, True).binary_symbols == {x} + assert Q.prime(x).binary_symbols == set() + + +def test_BooleanFunction_diff(): + assert And(x, y).diff(x) == Piecewise((0, Eq(y, False)), (1, True)) + + +def test_issue_14700(): + A, B, C, D, E, F, G, H = symbols('A B C D E F G H') + q = ((B & D & H & ~F) | (B & H & ~C & ~D) | (B & H & ~C & ~F) | + (B & H & ~D & ~G) | (B & H & ~F & ~G) | (C & G & ~B & ~D) | + (C & G & ~D & ~H) | (C & G & ~F & ~H) | (D & F & H & ~B) | + (D & F & ~G & ~H) | (B & D & F & ~C & ~H) | (D & E & F & ~B & ~C) | + (D & F & ~A & ~B & ~C) | (D & F & ~A & ~C & ~H) | + (A & B & D & F & ~E & ~H)) + soldnf = ((B & D & H & ~F) | (D & F & H & ~B) | (B & H & ~C & ~D) | + (B & H & ~D & ~G) | (C & G & ~B & ~D) | (C & G & ~D & ~H) | + (C & G & ~F & ~H) | (D & F & ~G & ~H) | (D & E & F & ~C & ~H) | + (D & F & ~A & ~C & ~H) | (A & B & D & F & ~E & ~H)) + solcnf = ((B | C | D) & (B | D | G) & (C | D | H) & (C | F | H) & + (D | G | H) & (F | G | H) & (B | F | ~D | ~H) & + (~B | ~D | ~F | ~H) & (D | ~B | ~C | ~G | ~H) & + (A | H | ~C | ~D | ~F | ~G) & (H | ~C | ~D | ~E | ~F | ~G) & + (B | E | H | ~A | ~D | ~F | ~G)) + assert simplify_logic(q, "dnf") == soldnf + assert simplify_logic(q, "cnf") == solcnf + + minterms = [[0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], + [0, 0, 1, 1], [1, 0, 1, 1]] + dontcares = [[1, 0, 0, 0], [1, 0, 0, 1], [1, 1, 0, 0], [1, 1, 0, 1]] + assert SOPform([w, x, y, z], minterms) == (x & ~w) | (y & z & ~x) + # Should not be more complicated with don't cares + assert SOPform([w, x, y, z], minterms, dontcares) == \ + (x & ~w) | (y & z & ~x) + + +def test_issue_25115(): + cond = Contains(x, S.Integers) + # Previously this raised an exception: + assert simplify_logic(cond) == cond + + +def test_relational_simplification(): + w, x, y, z = symbols('w x y z', real=True) + d, e = symbols('d e', real=False) + # Test all combinations or sign and order + assert Or(x >= y, x < y).simplify() == S.true + assert Or(x >= y, y > x).simplify() == S.true + assert Or(x >= y, -x > -y).simplify() == S.true + assert Or(x >= y, -y < -x).simplify() == S.true + assert Or(-x <= -y, x < y).simplify() == S.true + assert Or(-x <= -y, -x > -y).simplify() == S.true + assert Or(-x <= -y, y > x).simplify() == S.true + assert Or(-x <= -y, -y < -x).simplify() == S.true + assert Or(y <= x, x < y).simplify() == S.true + assert Or(y <= x, y > x).simplify() == S.true + assert Or(y <= x, -x > -y).simplify() == S.true + assert Or(y <= x, -y < -x).simplify() == S.true + assert Or(-y >= -x, x < y).simplify() == S.true + assert Or(-y >= -x, y > x).simplify() == S.true + assert Or(-y >= -x, -x > -y).simplify() == S.true + assert Or(-y >= -x, -y < -x).simplify() == S.true + + assert Or(x < y, x >= y).simplify() == S.true + assert Or(y > x, x >= y).simplify() == S.true + assert Or(-x > -y, x >= y).simplify() == S.true + assert Or(-y < -x, x >= y).simplify() == S.true + assert Or(x < y, -x <= -y).simplify() == S.true + assert Or(-x > -y, -x <= -y).simplify() == S.true + assert Or(y > x, -x <= -y).simplify() == S.true + assert Or(-y < -x, -x <= -y).simplify() == S.true + assert Or(x < y, y <= x).simplify() == S.true + assert Or(y > x, y <= x).simplify() == S.true + assert Or(-x > -y, y <= x).simplify() == S.true + assert Or(-y < -x, y <= x).simplify() == S.true + assert Or(x < y, -y >= -x).simplify() == S.true + assert Or(y > x, -y >= -x).simplify() == S.true + assert Or(-x > -y, -y >= -x).simplify() == S.true + assert Or(-y < -x, -y >= -x).simplify() == S.true + + # Some other tests + assert Or(x >= y, w < z, x <= y).simplify() == S.true + assert And(x >= y, x < y).simplify() == S.false + assert Or(x >= y, Eq(y, x)).simplify() == (x >= y) + assert And(x >= y, Eq(y, x)).simplify() == Eq(x, y) + assert And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify() == \ + (Eq(x, y) & (x >= 1) & (y >= 5) & (y > z)) + assert Or(Eq(x, y), x >= y, w < y, z < y).simplify() == \ + (x >= y) | (y > z) | (w < y) + assert And(Eq(x, y), x >= y, w < y, y >= z, z < y).simplify() == \ + Eq(x, y) & (y > z) & (w < y) + # assert And(Eq(x, y), x >= y, w < y, y >= z, z < y).simplify(relational_minmax=True) == \ + # And(Eq(x, y), y > Max(w, z)) + # assert Or(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify(relational_minmax=True) == \ + # (Eq(x, y) | (x >= 1) | (y > Min(2, z))) + assert And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y).simplify() == \ + (Eq(x, y) & (x >= 1) & (y >= 5) & (y > z)) + assert (Eq(x, y) & Eq(d, e) & (x >= y) & (d >= e)).simplify() == \ + (Eq(x, y) & Eq(d, e) & (d >= e)) + assert And(Eq(x, y), Eq(x, -y)).simplify() == And(Eq(x, 0), Eq(y, 0)) + assert Xor(x >= y, x <= y).simplify() == Ne(x, y) + assert And(x > 1, x < -1, Eq(x, y)).simplify() == S.false + # From #16690 + assert And(x >= y, Eq(y, 0)).simplify() == And(x >= 0, Eq(y, 0)) + assert Or(Ne(x, 1), Ne(x, 2)).simplify() == S.true + assert And(Eq(x, 1), Ne(2, x)).simplify() == Eq(x, 1) + assert Or(Eq(x, 1), Ne(2, x)).simplify() == Ne(x, 2) + +def test_issue_8373(): + x = symbols('x', real=True) + assert Or(x < 1, x > -1).simplify() == S.true + assert Or(x < 1, x >= 1).simplify() == S.true + assert And(x < 1, x >= 1).simplify() == S.false + assert Or(x <= 1, x >= 1).simplify() == S.true + + +def test_issue_7950(): + x = symbols('x', real=True) + assert And(Eq(x, 1), Eq(x, 2)).simplify() == S.false + + +@slow +def test_relational_simplification_numerically(): + def test_simplification_numerically_function(original, simplified): + symb = original.free_symbols + n = len(symb) + valuelist = list(set(combinations(list(range(-(n-1), n))*n, n))) + for values in valuelist: + sublist = dict(zip(symb, values)) + originalvalue = original.subs(sublist) + simplifiedvalue = simplified.subs(sublist) + assert originalvalue == simplifiedvalue, "Original: {}\nand"\ + " simplified: {}\ndo not evaluate to the same value for {}"\ + "".format(original, simplified, sublist) + + w, x, y, z = symbols('w x y z', real=True) + d, e = symbols('d e', real=False) + + expressions = (And(Eq(x, y), x >= y, w < y, y >= z, z < y), + And(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y), + Or(Eq(x, y), x >= 1, 2 < y, y >= 5, z < y), + And(x >= y, Eq(y, x)), + Or(And(Eq(x, y), x >= y, w < y, Or(y >= z, z < y)), + And(Eq(x, y), x >= 1, 2 < y, y >= -1, z < y)), + (Eq(x, y) & Eq(d, e) & (x >= y) & (d >= e)), + ) + + for expression in expressions: + test_simplification_numerically_function(expression, + expression.simplify()) + + +def test_relational_simplification_patterns_numerically(): + from sympy.core import Wild + from sympy.logic.boolalg import _simplify_patterns_and, \ + _simplify_patterns_or, _simplify_patterns_xor + a = Wild('a') + b = Wild('b') + c = Wild('c') + symb = [a, b, c] + patternlists = [[And, _simplify_patterns_and()], + [Or, _simplify_patterns_or()], + [Xor, _simplify_patterns_xor()]] + valuelist = list(set(combinations(list(range(-2, 3))*3, 3))) + # Skip combinations of +/-2 and 0, except for all 0 + valuelist = [v for v in valuelist if any(w % 2 for w in v) or not any(v)] + for func, patternlist in patternlists: + for pattern in patternlist: + original = func(*pattern[0].args) + simplified = pattern[1] + for values in valuelist: + sublist = dict(zip(symb, values)) + originalvalue = original.xreplace(sublist) + simplifiedvalue = simplified.xreplace(sublist) + assert originalvalue == simplifiedvalue, "Original: {}\nand"\ + " simplified: {}\ndo not evaluate to the same value for"\ + "{}".format(pattern[0], simplified, sublist) + + +def test_issue_16803(): + n = symbols('n') + # No simplification done, but should not raise an exception + assert ((n > 3) | (n < 0) | ((n > 0) & (n < 3))).simplify() == \ + (n > 3) | (n < 0) | ((n > 0) & (n < 3)) + + +def test_issue_17530(): + r = {x: oo, y: oo} + assert Or(x + y > 0, x - y < 0).subs(r) + assert not And(x + y < 0, x - y < 0).subs(r) + raises(TypeError, lambda: Or(x + y < 0, x - y < 0).subs(r)) + raises(TypeError, lambda: And(x + y > 0, x - y < 0).subs(r)) + raises(TypeError, lambda: And(x + y > 0, x - y < 0).subs(r)) + + +def test_anf_coeffs(): + assert anf_coeffs([1, 0]) == [1, 1] + assert anf_coeffs([0, 0, 0, 1]) == [0, 0, 0, 1] + assert anf_coeffs([0, 1, 1, 1]) == [0, 1, 1, 1] + assert anf_coeffs([1, 1, 1, 0]) == [1, 0, 0, 1] + assert anf_coeffs([1, 0, 0, 0]) == [1, 1, 1, 1] + assert anf_coeffs([1, 0, 0, 1]) == [1, 1, 1, 0] + assert anf_coeffs([1, 1, 0, 1]) == [1, 0, 1, 1] + + +def test_ANFform(): + x, y = symbols('x,y') + assert ANFform([x], [1, 1]) == True + assert ANFform([x], [0, 0]) == False + assert ANFform([x], [1, 0]) == Xor(x, True, remove_true=False) + assert ANFform([x, y], [1, 1, 1, 0]) == \ + Xor(True, And(x, y), remove_true=False) + + +def test_bool_minterm(): + x, y = symbols('x,y') + assert bool_minterm(3, [x, y]) == And(x, y) + assert bool_minterm([1, 0], [x, y]) == And(Not(y), x) + + +def test_bool_maxterm(): + x, y = symbols('x,y') + assert bool_maxterm(2, [x, y]) == Or(Not(x), y) + assert bool_maxterm([0, 1], [x, y]) == Or(Not(y), x) + + +def test_bool_monomial(): + x, y = symbols('x,y') + assert bool_monomial(1, [x, y]) == y + assert bool_monomial([1, 1], [x, y]) == And(x, y) + + +def test_check_pair(): + assert _check_pair([0, 1, 0], [0, 1, 1]) == 2 + assert _check_pair([0, 1, 0], [1, 1, 1]) == -1 + + +def test_issue_19114(): + expr = (B & C) | (A & ~C) | (~A & ~B) + # Expression is minimal, but there are multiple minimal forms possible + res1 = (A & B) | (C & ~A) | (~B & ~C) + result = to_dnf(expr, simplify=True) + assert result in (expr, res1) + + +def test_issue_20870(): + result = SOPform([a, b, c, d], [1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15]) + expected = ((d & ~b) | (a & b & c) | (a & ~c & ~d) | + (b & ~a & ~c) | (c & ~a & ~d)) + assert result == expected + + +def test_convert_to_varsSOP(): + assert _convert_to_varsSOP([0, 1, 0], [x, y, z]) == And(Not(x), y, Not(z)) + assert _convert_to_varsSOP([3, 1, 0], [x, y, z]) == And(y, Not(z)) + + +def test_convert_to_varsPOS(): + assert _convert_to_varsPOS([0, 1, 0], [x, y, z]) == Or(x, Not(y), z) + assert _convert_to_varsPOS([3, 1, 0], [x, y, z]) == Or(Not(y), z) + + +def test_gateinputcount(): + a, b, c, d, e = symbols('a:e') + assert gateinputcount(And(a, b)) == 2 + assert gateinputcount(a | b & c & d ^ (e | a)) == 9 + assert gateinputcount(And(a, True)) == 0 + raises(TypeError, lambda: gateinputcount(a*b)) + + +def test_refine(): + # relational + assert not refine(x < 0, ~(x < 0)) + assert refine(x < 0, (x < 0)) + assert refine(x < 0, (0 > x)) is S.true + assert refine(x < 0, (y < 0)) == (x < 0) + assert not refine(x <= 0, ~(x <= 0)) + assert refine(x <= 0, (x <= 0)) + assert refine(x <= 0, (0 >= x)) is S.true + assert refine(x <= 0, (y <= 0)) == (x <= 0) + assert not refine(x > 0, ~(x > 0)) + assert refine(x > 0, (x > 0)) + assert refine(x > 0, (0 < x)) is S.true + assert refine(x > 0, (y > 0)) == (x > 0) + assert not refine(x >= 0, ~(x >= 0)) + assert refine(x >= 0, (x >= 0)) + assert refine(x >= 0, (0 <= x)) is S.true + assert refine(x >= 0, (y >= 0)) == (x >= 0) + assert not refine(Eq(x, 0), ~(Eq(x, 0))) + assert refine(Eq(x, 0), (Eq(x, 0))) + assert refine(Eq(x, 0), (Eq(0, x))) is S.true + assert refine(Eq(x, 0), (Eq(y, 0))) == Eq(x, 0) + assert not refine(Ne(x, 0), ~(Ne(x, 0))) + assert refine(Ne(x, 0), (Ne(0, x))) is S.true + assert refine(Ne(x, 0), (Ne(x, 0))) + assert refine(Ne(x, 0), (Ne(y, 0))) == (Ne(x, 0)) + + # boolean functions + assert refine(And(x > 0, y > 0), (x > 0)) == (y > 0) + assert refine(And(x > 0, y > 0), (x > 0) & (y > 0)) is S.true + + # predicates + assert refine(Q.positive(x), Q.positive(x)) is S.true + assert refine(Q.positive(x), Q.negative(x)) is S.false + assert refine(Q.positive(x), Q.real(x)) == Q.positive(x) + + +def test_relational_threeterm_simplification_patterns_numerically(): + from sympy.core import Wild + from sympy.logic.boolalg import _simplify_patterns_and3 + a = Wild('a') + b = Wild('b') + c = Wild('c') + symb = [a, b, c] + patternlists = [[And, _simplify_patterns_and3()]] + valuelist = list(set(combinations(list(range(-2, 3))*3, 3))) + # Skip combinations of +/-2 and 0, except for all 0 + valuelist = [v for v in valuelist if any(w % 2 for w in v) or not any(v)] + for func, patternlist in patternlists: + for pattern in patternlist: + original = func(*pattern[0].args) + simplified = pattern[1] + for values in valuelist: + sublist = dict(zip(symb, values)) + originalvalue = original.xreplace(sublist) + simplifiedvalue = simplified.xreplace(sublist) + assert originalvalue == simplifiedvalue, "Original: {}\nand"\ + " simplified: {}\ndo not evaluate to the same value for"\ + "{}".format(pattern[0], simplified, sublist) + + +def test_issue_25451(): + x = Or(And(a, c), Eq(a, b)) + assert isinstance(x, Or) + assert set(x.args) == {And(a, c), Eq(a, b)} diff --git a/lib/python3.11/site-packages/sympy/logic/tests/test_dimacs.py b/lib/python3.11/site-packages/sympy/logic/tests/test_dimacs.py new file mode 100644 index 0000000000000000000000000000000000000000..3a9a51a39d33fb807688614cb5809b621ce21a2c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/tests/test_dimacs.py @@ -0,0 +1,234 @@ +"""Various tests on satisfiability using dimacs cnf file syntax +You can find lots of cnf files in +ftp://dimacs.rutgers.edu/pub/challenge/satisfiability/benchmarks/cnf/ +""" + +from sympy.logic.utilities.dimacs import load +from sympy.logic.algorithms.dpll import dpll_satisfiable + + +def test_f1(): + assert bool(dpll_satisfiable(load(f1))) + + +def test_f2(): + assert bool(dpll_satisfiable(load(f2))) + + +def test_f3(): + assert bool(dpll_satisfiable(load(f3))) + + +def test_f4(): + assert not bool(dpll_satisfiable(load(f4))) + + +def test_f5(): + assert bool(dpll_satisfiable(load(f5))) + +f1 = """c simple example +c Resolution: SATISFIABLE +c +p cnf 3 2 +1 -3 0 +2 3 -1 0 +""" + + +f2 = """c an example from Quinn's text, 16 variables and 18 clauses. +c Resolution: SATISFIABLE +c +p cnf 16 18 + 1 2 0 + -2 -4 0 + 3 4 0 + -4 -5 0 + 5 -6 0 + 6 -7 0 + 6 7 0 + 7 -16 0 + 8 -9 0 + -8 -14 0 + 9 10 0 + 9 -10 0 +-10 -11 0 + 10 12 0 + 11 12 0 + 13 14 0 + 14 -15 0 + 15 16 0 +""" + +f3 = """c +p cnf 6 9 +-1 0 +-3 0 +2 -1 0 +2 -4 0 +5 -4 0 +-1 -3 0 +-4 -6 0 +1 3 -2 0 +4 6 -2 -5 0 +""" + +f4 = """c +c file: hole6.cnf [http://people.sc.fsu.edu/~jburkardt/data/cnf/hole6.cnf] +c +c SOURCE: John Hooker (jh38+@andrew.cmu.edu) +c +c DESCRIPTION: Pigeon hole problem of placing n (for file 'holen.cnf') pigeons +c in n+1 holes without placing 2 pigeons in the same hole +c +c NOTE: Part of the collection at the Forschungsinstitut fuer +c anwendungsorientierte Wissensverarbeitung in Ulm Germany. +c +c NOTE: Not satisfiable +c +p cnf 42 133 +-1 -7 0 +-1 -13 0 +-1 -19 0 +-1 -25 0 +-1 -31 0 +-1 -37 0 +-7 -13 0 +-7 -19 0 +-7 -25 0 +-7 -31 0 +-7 -37 0 +-13 -19 0 +-13 -25 0 +-13 -31 0 +-13 -37 0 +-19 -25 0 +-19 -31 0 +-19 -37 0 +-25 -31 0 +-25 -37 0 +-31 -37 0 +-2 -8 0 +-2 -14 0 +-2 -20 0 +-2 -26 0 +-2 -32 0 +-2 -38 0 +-8 -14 0 +-8 -20 0 +-8 -26 0 +-8 -32 0 +-8 -38 0 +-14 -20 0 +-14 -26 0 +-14 -32 0 +-14 -38 0 +-20 -26 0 +-20 -32 0 +-20 -38 0 +-26 -32 0 +-26 -38 0 +-32 -38 0 +-3 -9 0 +-3 -15 0 +-3 -21 0 +-3 -27 0 +-3 -33 0 +-3 -39 0 +-9 -15 0 +-9 -21 0 +-9 -27 0 +-9 -33 0 +-9 -39 0 +-15 -21 0 +-15 -27 0 +-15 -33 0 +-15 -39 0 +-21 -27 0 +-21 -33 0 +-21 -39 0 +-27 -33 0 +-27 -39 0 +-33 -39 0 +-4 -10 0 +-4 -16 0 +-4 -22 0 +-4 -28 0 +-4 -34 0 +-4 -40 0 +-10 -16 0 +-10 -22 0 +-10 -28 0 +-10 -34 0 +-10 -40 0 +-16 -22 0 +-16 -28 0 +-16 -34 0 +-16 -40 0 +-22 -28 0 +-22 -34 0 +-22 -40 0 +-28 -34 0 +-28 -40 0 +-34 -40 0 +-5 -11 0 +-5 -17 0 +-5 -23 0 +-5 -29 0 +-5 -35 0 +-5 -41 0 +-11 -17 0 +-11 -23 0 +-11 -29 0 +-11 -35 0 +-11 -41 0 +-17 -23 0 +-17 -29 0 +-17 -35 0 +-17 -41 0 +-23 -29 0 +-23 -35 0 +-23 -41 0 +-29 -35 0 +-29 -41 0 +-35 -41 0 +-6 -12 0 +-6 -18 0 +-6 -24 0 +-6 -30 0 +-6 -36 0 +-6 -42 0 +-12 -18 0 +-12 -24 0 +-12 -30 0 +-12 -36 0 +-12 -42 0 +-18 -24 0 +-18 -30 0 +-18 -36 0 +-18 -42 0 +-24 -30 0 +-24 -36 0 +-24 -42 0 +-30 -36 0 +-30 -42 0 +-36 -42 0 + 6 5 4 3 2 1 0 + 12 11 10 9 8 7 0 + 18 17 16 15 14 13 0 + 24 23 22 21 20 19 0 + 30 29 28 27 26 25 0 + 36 35 34 33 32 31 0 + 42 41 40 39 38 37 0 +""" + +f5 = """c simple example requiring variable selection +c +c NOTE: Satisfiable +c +p cnf 5 5 +1 2 3 0 +1 -2 3 0 +4 5 -3 0 +1 -4 -3 0 +-1 -5 0 +""" diff --git a/lib/python3.11/site-packages/sympy/logic/tests/test_inference.py b/lib/python3.11/site-packages/sympy/logic/tests/test_inference.py new file mode 100644 index 0000000000000000000000000000000000000000..2b6f49224d6485c4e4f753de33aaf0cfe12154d6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/tests/test_inference.py @@ -0,0 +1,381 @@ +"""For more tests on satisfiability, see test_dimacs""" + +from sympy.assumptions.ask import Q +from sympy.core.symbol import symbols +from sympy.core.relational import Unequality +from sympy.logic.boolalg import And, Or, Implies, Equivalent, true, false +from sympy.logic.inference import literal_symbol, \ + pl_true, satisfiable, valid, entails, PropKB +from sympy.logic.algorithms.dpll import dpll, dpll_satisfiable, \ + find_pure_symbol, find_unit_clause, unit_propagate, \ + find_pure_symbol_int_repr, find_unit_clause_int_repr, \ + unit_propagate_int_repr +from sympy.logic.algorithms.dpll2 import dpll_satisfiable as dpll2_satisfiable + +from sympy.logic.algorithms.z3_wrapper import z3_satisfiable +from sympy.assumptions.cnf import CNF, EncodedCNF +from sympy.logic.tests.test_lra_theory import make_random_problem +from sympy.core.random import randint + +from sympy.testing.pytest import raises, skip +from sympy.external import import_module + + +def test_literal(): + A, B = symbols('A,B') + assert literal_symbol(True) is True + assert literal_symbol(False) is False + assert literal_symbol(A) is A + assert literal_symbol(~A) is A + + +def test_find_pure_symbol(): + A, B, C = symbols('A,B,C') + assert find_pure_symbol([A], [A]) == (A, True) + assert find_pure_symbol([A, B], [~A | B, ~B | A]) == (None, None) + assert find_pure_symbol([A, B, C], [ A | ~B, ~B | ~C, C | A]) == (A, True) + assert find_pure_symbol([A, B, C], [~A | B, B | ~C, C | A]) == (B, True) + assert find_pure_symbol([A, B, C], [~A | ~B, ~B | ~C, C | A]) == (B, False) + assert find_pure_symbol( + [A, B, C], [~A | B, ~B | ~C, C | A]) == (None, None) + + +def test_find_pure_symbol_int_repr(): + assert find_pure_symbol_int_repr([1], [{1}]) == (1, True) + assert find_pure_symbol_int_repr([1, 2], + [{-1, 2}, {-2, 1}]) == (None, None) + assert find_pure_symbol_int_repr([1, 2, 3], + [{1, -2}, {-2, -3}, {3, 1}]) == (1, True) + assert find_pure_symbol_int_repr([1, 2, 3], + [{-1, 2}, {2, -3}, {3, 1}]) == (2, True) + assert find_pure_symbol_int_repr([1, 2, 3], + [{-1, -2}, {-2, -3}, {3, 1}]) == (2, False) + assert find_pure_symbol_int_repr([1, 2, 3], + [{-1, 2}, {-2, -3}, {3, 1}]) == (None, None) + + +def test_unit_clause(): + A, B, C = symbols('A,B,C') + assert find_unit_clause([A], {}) == (A, True) + assert find_unit_clause([A, ~A], {}) == (A, True) # Wrong ?? + assert find_unit_clause([A | B], {A: True}) == (B, True) + assert find_unit_clause([A | B], {B: True}) == (A, True) + assert find_unit_clause( + [A | B | C, B | ~C, A | ~B], {A: True}) == (B, False) + assert find_unit_clause([A | B | C, B | ~C, A | B], {A: True}) == (B, True) + assert find_unit_clause([A | B | C, B | ~C, A ], {}) == (A, True) + + +def test_unit_clause_int_repr(): + assert find_unit_clause_int_repr(map(set, [[1]]), {}) == (1, True) + assert find_unit_clause_int_repr(map(set, [[1], [-1]]), {}) == (1, True) + assert find_unit_clause_int_repr([{1, 2}], {1: True}) == (2, True) + assert find_unit_clause_int_repr([{1, 2}], {2: True}) == (1, True) + assert find_unit_clause_int_repr(map(set, + [[1, 2, 3], [2, -3], [1, -2]]), {1: True}) == (2, False) + assert find_unit_clause_int_repr(map(set, + [[1, 2, 3], [3, -3], [1, 2]]), {1: True}) == (2, True) + + A, B, C = symbols('A,B,C') + assert find_unit_clause([A | B | C, B | ~C, A ], {}) == (A, True) + + +def test_unit_propagate(): + A, B, C = symbols('A,B,C') + assert unit_propagate([A | B], A) == [] + assert unit_propagate([A | B, ~A | C, ~C | B, A], A) == [C, ~C | B, A] + + +def test_unit_propagate_int_repr(): + assert unit_propagate_int_repr([{1, 2}], 1) == [] + assert unit_propagate_int_repr(map(set, + [[1, 2], [-1, 3], [-3, 2], [1]]), 1) == [{3}, {-3, 2}] + + +def test_dpll(): + """This is also tested in test_dimacs""" + A, B, C = symbols('A,B,C') + assert dpll([A | B], [A, B], {A: True, B: True}) == {A: True, B: True} + + +def test_dpll_satisfiable(): + A, B, C = symbols('A,B,C') + assert dpll_satisfiable( A & ~A ) is False + assert dpll_satisfiable( A & ~B ) == {A: True, B: False} + assert dpll_satisfiable( + A | B ) in ({A: True}, {B: True}, {A: True, B: True}) + assert dpll_satisfiable( + (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False}) + assert dpll_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False}, + {A: True, C: True}, {B: True, C: True}) + assert dpll_satisfiable( A & B & C ) == {A: True, B: True, C: True} + assert dpll_satisfiable( (A | B) & (A >> B) ) == {B: True} + assert dpll_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True} + assert dpll_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False} + + +def test_dpll2_satisfiable(): + A, B, C = symbols('A,B,C') + assert dpll2_satisfiable( A & ~A ) is False + assert dpll2_satisfiable( A & ~B ) == {A: True, B: False} + assert dpll2_satisfiable( + A | B ) in ({A: True}, {B: True}, {A: True, B: True}) + assert dpll2_satisfiable( + (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False}) + assert dpll2_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True}, + {A: True, B: True, C: True}) + assert dpll2_satisfiable( A & B & C ) == {A: True, B: True, C: True} + assert dpll2_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False}, + {B: True, A: True}) + assert dpll2_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True} + assert dpll2_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False} + + +def test_minisat22_satisfiable(): + A, B, C = symbols('A,B,C') + minisat22_satisfiable = lambda expr: satisfiable(expr, algorithm="minisat22") + assert minisat22_satisfiable( A & ~A ) is False + assert minisat22_satisfiable( A & ~B ) == {A: True, B: False} + assert minisat22_satisfiable( + A | B ) in ({A: True}, {B: False}, {A: False, B: True}, {A: True, B: True}, {A: True, B: False}) + assert minisat22_satisfiable( + (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False}) + assert minisat22_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True}, + {A: True, B: True, C: True}, {A: False, B: True, C: True}, {A: True, B: False, C: False}) + assert minisat22_satisfiable( A & B & C ) == {A: True, B: True, C: True} + assert minisat22_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False}, + {B: True, A: True}) + assert minisat22_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True} + assert minisat22_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False} + +def test_minisat22_minimal_satisfiable(): + A, B, C = symbols('A,B,C') + minisat22_satisfiable = lambda expr, minimal=True: satisfiable(expr, algorithm="minisat22", minimal=True) + assert minisat22_satisfiable( A & ~A ) is False + assert minisat22_satisfiable( A & ~B ) == {A: True, B: False} + assert minisat22_satisfiable( + A | B ) in ({A: True}, {B: False}, {A: False, B: True}, {A: True, B: True}, {A: True, B: False}) + assert minisat22_satisfiable( + (~A | B) & (~B | A) ) in ({A: True, B: True}, {A: False, B: False}) + assert minisat22_satisfiable( (A | B) & (~B | C) ) in ({A: True, B: False, C: True}, + {A: True, B: True, C: True}, {A: False, B: True, C: True}, {A: True, B: False, C: False}) + assert minisat22_satisfiable( A & B & C ) == {A: True, B: True, C: True} + assert minisat22_satisfiable( (A | B) & (A >> B) ) in ({B: True, A: False}, + {B: True, A: True}) + assert minisat22_satisfiable( Equivalent(A, B) & A ) == {A: True, B: True} + assert minisat22_satisfiable( Equivalent(A, B) & ~A ) == {A: False, B: False} + g = satisfiable((A | B | C),algorithm="minisat22",minimal=True,all_models=True) + sol = next(g) + first_solution = {key for key, value in sol.items() if value} + sol=next(g) + second_solution = {key for key, value in sol.items() if value} + sol=next(g) + third_solution = {key for key, value in sol.items() if value} + assert not first_solution <= second_solution + assert not second_solution <= third_solution + assert not first_solution <= third_solution + +def test_satisfiable(): + A, B, C = symbols('A,B,C') + assert satisfiable(A & (A >> B) & ~B) is False + + +def test_valid(): + A, B, C = symbols('A,B,C') + assert valid(A >> (B >> A)) is True + assert valid((A >> (B >> C)) >> ((A >> B) >> (A >> C))) is True + assert valid((~B >> ~A) >> (A >> B)) is True + assert valid(A | B | C) is False + assert valid(A >> B) is False + + +def test_pl_true(): + A, B, C = symbols('A,B,C') + assert pl_true(True) is True + assert pl_true( A & B, {A: True, B: True}) is True + assert pl_true( A | B, {A: True}) is True + assert pl_true( A | B, {B: True}) is True + assert pl_true( A | B, {A: None, B: True}) is True + assert pl_true( A >> B, {A: False}) is True + assert pl_true( A | B | ~C, {A: False, B: True, C: True}) is True + assert pl_true(Equivalent(A, B), {A: False, B: False}) is True + + # test for false + assert pl_true(False) is False + assert pl_true( A & B, {A: False, B: False}) is False + assert pl_true( A & B, {A: False}) is False + assert pl_true( A & B, {B: False}) is False + assert pl_true( A | B, {A: False, B: False}) is False + + #test for None + assert pl_true(B, {B: None}) is None + assert pl_true( A & B, {A: True, B: None}) is None + assert pl_true( A >> B, {A: True, B: None}) is None + assert pl_true(Equivalent(A, B), {A: None}) is None + assert pl_true(Equivalent(A, B), {A: True, B: None}) is None + + # Test for deep + assert pl_true(A | B, {A: False}, deep=True) is None + assert pl_true(~A & ~B, {A: False}, deep=True) is None + assert pl_true(A | B, {A: False, B: False}, deep=True) is False + assert pl_true(A & B & (~A | ~B), {A: True}, deep=True) is False + assert pl_true((C >> A) >> (B >> A), {C: True}, deep=True) is True + + +def test_pl_true_wrong_input(): + from sympy.core.numbers import pi + raises(ValueError, lambda: pl_true('John Cleese')) + raises(ValueError, lambda: pl_true(42 + pi + pi ** 2)) + raises(ValueError, lambda: pl_true(42)) + + +def test_entails(): + A, B, C = symbols('A, B, C') + assert entails(A, [A >> B, ~B]) is False + assert entails(B, [Equivalent(A, B), A]) is True + assert entails((A >> B) >> (~A >> ~B)) is False + assert entails((A >> B) >> (~B >> ~A)) is True + + +def test_PropKB(): + A, B, C = symbols('A,B,C') + kb = PropKB() + assert kb.ask(A >> B) is False + assert kb.ask(A >> (B >> A)) is True + kb.tell(A >> B) + kb.tell(B >> C) + assert kb.ask(A) is False + assert kb.ask(B) is False + assert kb.ask(C) is False + assert kb.ask(~A) is False + assert kb.ask(~B) is False + assert kb.ask(~C) is False + assert kb.ask(A >> C) is True + kb.tell(A) + assert kb.ask(A) is True + assert kb.ask(B) is True + assert kb.ask(C) is True + assert kb.ask(~C) is False + kb.retract(A) + assert kb.ask(C) is False + + +def test_propKB_tolerant(): + """"tolerant to bad input""" + kb = PropKB() + A, B, C = symbols('A,B,C') + assert kb.ask(B) is False + +def test_satisfiable_non_symbols(): + x, y = symbols('x y') + assumptions = Q.zero(x*y) + facts = Implies(Q.zero(x*y), Q.zero(x) | Q.zero(y)) + query = ~Q.zero(x) & ~Q.zero(y) + refutations = [ + {Q.zero(x): True, Q.zero(x*y): True}, + {Q.zero(y): True, Q.zero(x*y): True}, + {Q.zero(x): True, Q.zero(y): True, Q.zero(x*y): True}, + {Q.zero(x): True, Q.zero(y): False, Q.zero(x*y): True}, + {Q.zero(x): False, Q.zero(y): True, Q.zero(x*y): True}] + assert not satisfiable(And(assumptions, facts, query), algorithm='dpll') + assert satisfiable(And(assumptions, facts, ~query), algorithm='dpll') in refutations + assert not satisfiable(And(assumptions, facts, query), algorithm='dpll2') + assert satisfiable(And(assumptions, facts, ~query), algorithm='dpll2') in refutations + +def test_satisfiable_bool(): + from sympy.core.singleton import S + assert satisfiable(true) == {true: true} + assert satisfiable(S.true) == {true: true} + assert satisfiable(false) is False + assert satisfiable(S.false) is False + + +def test_satisfiable_all_models(): + from sympy.abc import A, B + assert next(satisfiable(False, all_models=True)) is False + assert list(satisfiable((A >> ~A) & A, all_models=True)) == [False] + assert list(satisfiable(True, all_models=True)) == [{true: true}] + + models = [{A: True, B: False}, {A: False, B: True}] + result = satisfiable(A ^ B, all_models=True) + models.remove(next(result)) + models.remove(next(result)) + raises(StopIteration, lambda: next(result)) + assert not models + + assert list(satisfiable(Equivalent(A, B), all_models=True)) == \ + [{A: False, B: False}, {A: True, B: True}] + + models = [{A: False, B: False}, {A: False, B: True}, {A: True, B: True}] + for model in satisfiable(A >> B, all_models=True): + models.remove(model) + assert not models + + # This is a santiy test to check that only the required number + # of solutions are generated. The expr below has 2**100 - 1 models + # which would time out the test if all are generated at once. + from sympy.utilities.iterables import numbered_symbols + from sympy.logic.boolalg import Or + sym = numbered_symbols() + X = [next(sym) for i in range(100)] + result = satisfiable(Or(*X), all_models=True) + for i in range(10): + assert next(result) + + +def test_z3(): + z3 = import_module("z3") + + if not z3: + skip("z3 not installed.") + A, B, C = symbols('A,B,C') + x, y, z = symbols('x,y,z') + assert z3_satisfiable((x >= 2) & (x < 1)) is False + assert z3_satisfiable( A & ~A ) is False + + model = z3_satisfiable(A & (~A | B | C)) + assert bool(model) is True + assert model[A] is True + + # test nonlinear function + assert z3_satisfiable((x ** 2 >= 2) & (x < 1) & (x > -1)) is False + + +def test_z3_vs_lra_dpll2(): + z3 = import_module("z3") + if z3 is None: + skip("z3 not installed.") + + def boolean_formula_to_encoded_cnf(bf): + cnf = CNF.from_prop(bf) + enc = EncodedCNF() + enc.from_cnf(cnf) + return enc + + def make_random_cnf(num_clauses=5, num_constraints=10, num_var=2): + assert num_clauses <= num_constraints + constraints = make_random_problem(num_variables=num_var, num_constraints=num_constraints, rational=False) + clauses = [[cons] for cons in constraints[:num_clauses]] + for cons in constraints[num_clauses:]: + if isinstance(cons, Unequality): + cons = ~cons + i = randint(0, num_clauses-1) + clauses[i].append(cons) + + clauses = [Or(*clause) for clause in clauses] + cnf = And(*clauses) + return boolean_formula_to_encoded_cnf(cnf) + + lra_dpll2_satisfiable = lambda x: dpll2_satisfiable(x, use_lra_theory=True) + + for _ in range(50): + cnf = make_random_cnf(num_clauses=10, num_constraints=15, num_var=2) + + try: + z3_sat = z3_satisfiable(cnf) + except z3.z3types.Z3Exception: + continue + + lra_dpll2_sat = lra_dpll2_satisfiable(cnf) is not False + + assert z3_sat == lra_dpll2_sat diff --git a/lib/python3.11/site-packages/sympy/logic/tests/test_lra_theory.py b/lib/python3.11/site-packages/sympy/logic/tests/test_lra_theory.py new file mode 100644 index 0000000000000000000000000000000000000000..207a3c5ba2c1b16ee5323382deee0863a5dfb595 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/tests/test_lra_theory.py @@ -0,0 +1,440 @@ +from sympy.core.numbers import Rational, I, oo +from sympy.core.relational import Eq +from sympy.core.symbol import symbols +from sympy.core.singleton import S +from sympy.matrices.dense import Matrix +from sympy.matrices.dense import randMatrix +from sympy.assumptions.ask import Q +from sympy.logic.boolalg import And +from sympy.abc import x, y, z +from sympy.assumptions.cnf import CNF, EncodedCNF +from sympy.functions.elementary.trigonometric import cos +from sympy.external import import_module + +from sympy.logic.algorithms.lra_theory import LRASolver, UnhandledInput, LRARational, HANDLE_NEGATION +from sympy.core.random import random, choice, randint +from sympy.core.sympify import sympify +from sympy.ntheory.generate import randprime +from sympy.core.relational import StrictLessThan, StrictGreaterThan +import itertools + +from sympy.testing.pytest import raises, XFAIL, skip + +def make_random_problem(num_variables=2, num_constraints=2, sparsity=.1, rational=True, + disable_strict = False, disable_nonstrict=False, disable_equality=False): + def rand(sparsity=sparsity): + if random() < sparsity: + return sympify(0) + if rational: + int1, int2 = [randprime(0, 50) for _ in range(2)] + return Rational(int1, int2) * choice([-1, 1]) + else: + return randint(1, 10) * choice([-1, 1]) + + variables = symbols('x1:%s' % (num_variables + 1)) + constraints = [] + for _ in range(num_constraints): + lhs, rhs = sum(rand() * x for x in variables), rand(sparsity=0) # sparsity=0 bc of bug with smtlib_code + options = [] + if not disable_equality: + options += [Eq(lhs, rhs)] + if not disable_nonstrict: + options += [lhs <= rhs, lhs >= rhs] + if not disable_strict: + options += [lhs < rhs, lhs > rhs] + + constraints.append(choice(options)) + + return constraints + +def check_if_satisfiable_with_z3(constraints): + from sympy.external.importtools import import_module + from sympy.printing.smtlib import smtlib_code + from sympy.logic.boolalg import And + boolean_formula = And(*constraints) + z3 = import_module("z3") + if z3: + smtlib_string = smtlib_code(boolean_formula) + s = z3.Solver() + s.from_string(smtlib_string) + res = str(s.check()) + if res == 'sat': + return True + elif res == 'unsat': + return False + else: + raise ValueError(f"z3 was not able to check the satisfiability of {boolean_formula}") + +def find_rational_assignment(constr, assignment, iter=20): + eps = sympify(1) + + for _ in range(iter): + assign = {key: val[0] + val[1]*eps for key, val in assignment.items()} + try: + for cons in constr: + assert cons.subs(assign) == True + return assign + except AssertionError: + eps = eps/2 + + return None + +def boolean_formula_to_encoded_cnf(bf): + cnf = CNF.from_prop(bf) + enc = EncodedCNF() + enc.from_cnf(cnf) + return enc + + +def test_from_encoded_cnf(): + s1, s2 = symbols("s1 s2") + + # Test preprocessing + # Example is from section 3 of paper. + phi = (x >= 0) & ((x + y <= 2) | (x + 2 * y - z >= 6)) & (Eq(x + y, 2) | (x + 2 * y - z > 4)) + enc = boolean_formula_to_encoded_cnf(phi) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + assert lra.A.shape == (2, 5) + assert str(lra.slack) == '[_s1, _s2]' + assert str(lra.nonslack) == '[x, y, z]' + assert lra.A == Matrix([[ 1, 1, 0, -1, 0], + [-1, -2, 1, 0, -1]]) + assert {(str(b.var), b.bound, b.upper, b.equality, b.strict) for b in lra.enc_to_boundary.values()} == {('_s1', 2, None, True, False), + ('_s1', 2, True, False, False), + ('_s2', -4, True, False, True), + ('_s2', -6, True, False, False), + ('x', 0, False, False, False)} + + +def test_problem(): + from sympy.logic.algorithms.lra_theory import LRASolver + from sympy.assumptions.cnf import CNF, EncodedCNF + cons = [-2 * x - 2 * y >= 7, -9 * y >= 7, -6 * y >= 5] + cnf = CNF().from_prop(And(*cons)) + enc = EncodedCNF() + enc.from_cnf(cnf) + lra, _ = LRASolver.from_encoded_cnf(enc) + lra.assert_lit(1) + lra.assert_lit(2) + lra.assert_lit(3) + is_sat, assignment = lra.check() + assert is_sat is True + + +def test_random_problems(): + z3 = import_module("z3") + if z3 is None: + skip("z3 is not installed") + + special_cases = []; x1, x2, x3 = symbols("x1 x2 x3") + special_cases.append([x1 - 3 * x2 <= -5, 6 * x1 + 4 * x2 <= 0, -7 * x1 + 3 * x2 <= 3]) + special_cases.append([-3 * x1 >= 3, Eq(4 * x1, -1)]) + special_cases.append([-4 * x1 < 4, 6 * x1 <= -6]) + special_cases.append([-3 * x2 >= 7, 6 * x1 <= -5, -3 * x2 <= -4]) + special_cases.append([x + y >= 2, x + y <= 1]) + special_cases.append([x >= 0, x + y <= 2, x + 2 * y - z >= 6]) # from paper example + special_cases.append([-2 * x1 - 2 * x2 >= 7, -9 * x1 >= 7, -6 * x1 >= 5]) + special_cases.append([2 * x1 > -3, -9 * x1 < -6, 9 * x1 <= 6]) + special_cases.append([-2*x1 < -4, 9*x1 > -9]) + special_cases.append([-6*x1 >= -1, -8*x1 + x2 >= 5, -8*x1 + 7*x2 < 4, x1 > 7]) + special_cases.append([Eq(x1, 2), Eq(5*x1, -2), Eq(-7*x2, -6), Eq(9*x1 + 10*x2, 9)]) + special_cases.append([Eq(3*x1, 6), Eq(x1 - 8*x2, -9), Eq(-7*x1 + 5*x2, 3), Eq(3*x2, 7)]) + special_cases.append([-4*x1 < 4, 6*x1 <= -6]) + special_cases.append([-3*x1 + 8*x2 >= -8, -10*x2 > 9, 8*x1 - 4*x2 < 8, 10*x1 - 9*x2 >= -9]) + special_cases.append([x1 + 5*x2 >= -6, 9*x1 - 3*x2 >= -9, 6*x1 + 6*x2 < -10, -3*x1 + 3*x2 < -7]) + special_cases.append([-9*x1 < 7, -5*x1 - 7*x2 < -1, 3*x1 + 7*x2 > 1, -6*x1 - 6*x2 > 9]) + special_cases.append([9*x1 - 6*x2 >= -7, 9*x1 + 4*x2 < -8, -7*x2 <= 1, 10*x2 <= -7]) + + feasible_count = 0 + for i in range(50): + if i % 8 == 0: + constraints = make_random_problem(num_variables=1, num_constraints=2, rational=False) + elif i % 8 == 1: + constraints = make_random_problem(num_variables=2, num_constraints=4, rational=False, disable_equality=True, + disable_nonstrict=True) + elif i % 8 == 2: + constraints = make_random_problem(num_variables=2, num_constraints=4, rational=False, disable_strict=True) + elif i % 8 == 3: + constraints = make_random_problem(num_variables=3, num_constraints=12, rational=False) + else: + constraints = make_random_problem(num_variables=3, num_constraints=6, rational=False) + + if i < len(special_cases): + constraints = special_cases[i] + + if False in constraints or True in constraints: + continue + + phi = And(*constraints) + if phi == False: + continue + cnf = CNF.from_prop(phi); enc = EncodedCNF() + enc.from_cnf(cnf) + assert all(0 not in clause for clause in enc.data) + + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + s_subs = lra.s_subs + + lra.run_checks = True + s_subs_rev = {value: key for key, value in s_subs.items()} + lits = {lit for clause in enc.data for lit in clause} + + bounds = [(lra.enc_to_boundary[l], l) for l in lits if l in lra.enc_to_boundary] + bounds = sorted(bounds, key=lambda x: (str(x[0].var), x[0].bound, str(x[0].upper))) # to remove nondeterminism + + for b, l in bounds: + if lra.result and lra.result[0] == False: + break + lra.assert_lit(l) + + feasible = lra.check() + + if feasible[0] == True: + feasible_count += 1 + assert check_if_satisfiable_with_z3(constraints) is True + cons_funcs = [cons.func for cons in constraints] + assignment = feasible[1] + assignment = {key.var : value for key, value in assignment.items()} + if not (StrictLessThan in cons_funcs or StrictGreaterThan in cons_funcs): + assignment = {key: value[0] for key, value in assignment.items()} + for cons in constraints: + assert cons.subs(assignment) == True + + else: + rat_assignment = find_rational_assignment(constraints, assignment) + assert rat_assignment is not None + else: + assert check_if_satisfiable_with_z3(constraints) is False + + conflict = feasible[1] + assert len(conflict) >= 2 + conflict = {lra.enc_to_boundary[-l].get_inequality() for l in conflict} + conflict = {clause.subs(s_subs_rev) for clause in conflict} + assert check_if_satisfiable_with_z3(conflict) is False + + # check that conflict clause is probably minimal + for subset in itertools.combinations(conflict, len(conflict)-1): + assert check_if_satisfiable_with_z3(subset) is True + + +@XFAIL +def test_pos_neg_zero(): + bf = Q.positive(x) & Q.negative(x) & Q.zero(y) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 3 + assert lra.check()[0] == False + + bf = Q.positive(x) & Q.lt(x, -1) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + bf = Q.positive(x) & Q.zero(x) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + bf = Q.positive(x) & Q.zero(y) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == True + + +@XFAIL +def test_pos_neg_infinite(): + bf = Q.positive_infinite(x) & Q.lt(x, 10000000) & Q.positive_infinite(y) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 3 + assert lra.check()[0] == False + + bf = Q.positive_infinite(x) & Q.gt(x, 10000000) & Q.positive_infinite(y) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 3 + assert lra.check()[0] == True + + bf = Q.positive_infinite(x) & Q.negative_infinite(x) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in enc.encoding.values(): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + +def test_binrel_evaluation(): + bf = Q.gt(3, 2) + enc = boolean_formula_to_encoded_cnf(bf) + lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True) + assert len(lra.enc_to_boundary) == 0 + assert conflicts == [[1]] + + bf = Q.lt(3, 2) + enc = boolean_formula_to_encoded_cnf(bf) + lra, conflicts = LRASolver.from_encoded_cnf(enc, testing_mode=True) + assert len(lra.enc_to_boundary) == 0 + assert conflicts == [[-1]] + + +def test_negation(): + assert HANDLE_NEGATION is True + bf = Q.gt(x, 1) & ~Q.gt(x, 0) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + assert sorted(lra.check()[1]) in [[-1, 2], [-2, 1]] + + bf = ~Q.gt(x, 1) & ~Q.lt(x, 0) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == True + + bf = ~Q.gt(x, 0) & ~Q.lt(x, 1) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + bf = ~Q.gt(x, 0) & ~Q.le(x, 0) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + bf = ~Q.le(x+y, 2) & ~Q.ge(x-y, 2) & ~Q.ge(y, 0) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 3 + assert lra.check()[0] == False + assert len(lra.check()[1]) == 3 + assert all(i > 0 for i in lra.check()[1]) + + +def test_unhandled_input(): + nan = S.NaN + bf = Q.gt(3, nan) & Q.gt(x, nan) + enc = boolean_formula_to_encoded_cnf(bf) + raises(ValueError, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + + bf = Q.gt(3, I) & Q.gt(x, I) + enc = boolean_formula_to_encoded_cnf(bf) + raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + + bf = Q.gt(3, float("inf")) & Q.gt(x, float("inf")) + enc = boolean_formula_to_encoded_cnf(bf) + raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + + bf = Q.gt(3, oo) & Q.gt(x, oo) + enc = boolean_formula_to_encoded_cnf(bf) + raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + + # test non-linearity + bf = Q.gt(x**2 + x, 2) + enc = boolean_formula_to_encoded_cnf(bf) + raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + + bf = Q.gt(cos(x) + x, 2) + enc = boolean_formula_to_encoded_cnf(bf) + raises(UnhandledInput, lambda: LRASolver.from_encoded_cnf(enc, testing_mode=True)) + +@XFAIL +def test_infinite_strict_inequalities(): + # Extensive testing of the interaction between strict inequalities + # and constraints containing infinity is needed because + # the paper's rule for strict inequalities don't work when + # infinite numbers are allowed. Using the paper's rules you + # can end up with situations where oo + delta > oo is considered + # True when oo + delta should be equal to oo. + # See https://math.stackexchange.com/questions/4757069/can-this-method-of-converting-strict-inequalities-to-equisatisfiable-nonstrict-i + bf = (-x - y >= -float("inf")) & (x > 0) & (y >= float("inf")) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for lit in sorted(enc.encoding.values()): + if lra.assert_lit(lit) is not None: + break + assert len(lra.enc_to_boundary) == 3 + assert lra.check()[0] == True + + +def test_pivot(): + for _ in range(10): + m = randMatrix(5) + rref = m.rref() + for _ in range(5): + i, j = randint(0, 4), randint(0, 4) + if m[i, j] != 0: + assert LRASolver._pivot(m, i, j).rref() == rref + + +def test_reset_bounds(): + bf = Q.ge(x, 1) & Q.lt(x, 1) + enc = boolean_formula_to_encoded_cnf(bf) + lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True) + for clause in enc.data: + for lit in clause: + lra.assert_lit(lit) + assert len(lra.enc_to_boundary) == 2 + assert lra.check()[0] == False + + lra.reset_bounds() + assert lra.check()[0] == True + for var in lra.all_var: + assert var.upper == LRARational(float("inf"), 0) + assert var.upper_from_eq == False + assert var.upper_from_neg == False + assert var.lower == LRARational(-float("inf"), 0) + assert var.lower_from_eq == False + assert var.lower_from_neg == False + assert var.assign == LRARational(0, 0) + assert var.var is not None + assert var.col_idx is not None + + +def test_empty_cnf(): + cnf = CNF() + enc = EncodedCNF() + enc.from_cnf(cnf) + lra, conflict = LRASolver.from_encoded_cnf(enc) + assert len(conflict) == 0 + assert lra.check() == (True, {}) diff --git a/lib/python3.11/site-packages/sympy/logic/utilities/__init__.py b/lib/python3.11/site-packages/sympy/logic/utilities/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..3526c3e53d624bc70afe2df05f123c835781364c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/utilities/__init__.py @@ -0,0 +1,3 @@ +from .dimacs import load_file + +__all__ = ['load_file'] diff --git a/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1780ab58a286500431b806bac8bfb8a1f3a6ed1d Binary files /dev/null and b/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/dimacs.cpython-311.pyc b/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/dimacs.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..db72bdebd9a4272ebe6525cdc9f51ee2341a1ee2 Binary files /dev/null and b/lib/python3.11/site-packages/sympy/logic/utilities/__pycache__/dimacs.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/sympy/logic/utilities/dimacs.py b/lib/python3.11/site-packages/sympy/logic/utilities/dimacs.py new file mode 100644 index 0000000000000000000000000000000000000000..56fd9a20eeaae28b678b498ec4a7401481010bc2 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/logic/utilities/dimacs.py @@ -0,0 +1,70 @@ +"""For reading in DIMACS file format + +www.cs.ubc.ca/~hoos/SATLIB/Benchmarks/SAT/satformat.ps + +""" + +from sympy.core import Symbol +from sympy.logic.boolalg import And, Or +import re + + +def load(s): + """Loads a boolean expression from a string. + + Examples + ======== + + >>> from sympy.logic.utilities.dimacs import load + >>> load('1') + cnf_1 + >>> load('1 2') + cnf_1 | cnf_2 + >>> load('1 \\n 2') + cnf_1 & cnf_2 + >>> load('1 2 \\n 3') + cnf_3 & (cnf_1 | cnf_2) + """ + clauses = [] + + lines = s.split('\n') + + pComment = re.compile(r'c.*') + pStats = re.compile(r'p\s*cnf\s*(\d*)\s*(\d*)') + + while len(lines) > 0: + line = lines.pop(0) + + # Only deal with lines that aren't comments + if not pComment.match(line): + m = pStats.match(line) + + if not m: + nums = line.rstrip('\n').split(' ') + list = [] + for lit in nums: + if lit != '': + if int(lit) == 0: + continue + num = abs(int(lit)) + sign = True + if int(lit) < 0: + sign = False + + if sign: + list.append(Symbol("cnf_%s" % num)) + else: + list.append(~Symbol("cnf_%s" % num)) + + if len(list) > 0: + clauses.append(Or(*list)) + + return And(*clauses) + + +def load_file(location): + """Loads a boolean expression from a file.""" + with open(location) as f: + s = f.read() + + return load(s) diff --git a/lib/python3.11/site-packages/sympy/matrices/__init__.py b/lib/python3.11/site-packages/sympy/matrices/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..37b558f3f03f149dae6af20254e9b88192f7f1ed --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/__init__.py @@ -0,0 +1,72 @@ +"""A module that handles matrices. + +Includes functions for fast creating matrices like zero, one/eye, random +matrix, etc. +""" +from .exceptions import ShapeError, NonSquareMatrixError +from .kind import MatrixKind +from .dense import ( + GramSchmidt, casoratian, diag, eye, hessian, jordan_cell, + list2numpy, matrix2numpy, matrix_multiply_elementwise, ones, + randMatrix, rot_axis1, rot_axis2, rot_axis3, rot_ccw_axis1, + rot_ccw_axis2, rot_ccw_axis3, rot_givens, + symarray, wronskian, zeros) +from .dense import MutableDenseMatrix +from .matrixbase import DeferredVector, MatrixBase + +MutableMatrix = MutableDenseMatrix +Matrix = MutableMatrix + +from .sparse import MutableSparseMatrix +from .sparsetools import banded +from .immutable import ImmutableDenseMatrix, ImmutableSparseMatrix + +ImmutableMatrix = ImmutableDenseMatrix +SparseMatrix = MutableSparseMatrix + +from .expressions import ( + MatrixSlice, BlockDiagMatrix, BlockMatrix, FunctionMatrix, Identity, + Inverse, MatAdd, MatMul, MatPow, MatrixExpr, MatrixSymbol, Trace, + Transpose, ZeroMatrix, OneMatrix, blockcut, block_collapse, matrix_symbols, Adjoint, + hadamard_product, HadamardProduct, HadamardPower, Determinant, det, + diagonalize_vector, DiagMatrix, DiagonalMatrix, DiagonalOf, trace, + DotProduct, kronecker_product, KroneckerProduct, + PermutationMatrix, MatrixPermute, MatrixSet, Permanent, per) + +from .utilities import dotprodsimp + +__all__ = [ + 'ShapeError', 'NonSquareMatrixError', 'MatrixKind', + + 'GramSchmidt', 'casoratian', 'diag', 'eye', 'hessian', 'jordan_cell', + 'list2numpy', 'matrix2numpy', 'matrix_multiply_elementwise', 'ones', + 'randMatrix', 'rot_axis1', 'rot_axis2', 'rot_axis3', 'symarray', + 'wronskian', 'zeros', 'rot_ccw_axis1', 'rot_ccw_axis2', 'rot_ccw_axis3', + 'rot_givens', + + 'MutableDenseMatrix', + + 'DeferredVector', 'MatrixBase', + + 'Matrix', 'MutableMatrix', + + 'MutableSparseMatrix', + + 'banded', + + 'ImmutableDenseMatrix', 'ImmutableSparseMatrix', + + 'ImmutableMatrix', 'SparseMatrix', + + 'MatrixSlice', 'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix', + 'Identity', 'Inverse', 'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr', + 'MatrixSymbol', 'Trace', 'Transpose', 'ZeroMatrix', 'OneMatrix', + 'blockcut', 'block_collapse', 'matrix_symbols', 'Adjoint', + 'hadamard_product', 'HadamardProduct', 'HadamardPower', 'Determinant', + 'det', 'diagonalize_vector', 'DiagMatrix', 'DiagonalMatrix', + 'DiagonalOf', 'trace', 'DotProduct', 'kronecker_product', + 'KroneckerProduct', 'PermutationMatrix', 'MatrixPermute', 'MatrixSet', + 'Permanent', 'per', + + 'dotprodsimp', +] diff --git a/lib/python3.11/site-packages/sympy/matrices/benchmarks/__init__.py b/lib/python3.11/site-packages/sympy/matrices/benchmarks/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git 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b/lib/python3.11/site-packages/sympy/matrices/benchmarks/bench_matrix.py new file mode 100644 index 0000000000000000000000000000000000000000..4fb845600533c4c6fef196fe5a45b98890f4ad78 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/benchmarks/bench_matrix.py @@ -0,0 +1,21 @@ +from sympy.core.numbers import Integer +from sympy.matrices.dense import (eye, zeros) + +i3 = Integer(3) +M = eye(100) + + +def timeit_Matrix__getitem_ii(): + M[3, 3] + + +def timeit_Matrix__getitem_II(): + M[i3, i3] + + +def timeit_Matrix__getslice(): + M[:, :] + + +def timeit_Matrix_zeronm(): + zeros(100, 100) diff --git a/lib/python3.11/site-packages/sympy/matrices/common.py b/lib/python3.11/site-packages/sympy/matrices/common.py new file mode 100644 index 0000000000000000000000000000000000000000..7555ce849c5c47322025a64c88989297c6176456 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/common.py @@ -0,0 +1,3263 @@ +""" +A module contining deprecated matrix mixin classes. + +The classes in this module are deprecated and will be removed in a future +release. They are kept here for backwards compatibility in case downstream +code was subclassing them. + +Importing anything else from this module is deprecated so anything here +should either not be used or should be imported from somewhere else. +""" + +from collections import defaultdict +from collections.abc import Iterable +from inspect import isfunction +from functools import reduce + +from sympy.assumptions.refine import refine +from sympy.core import SympifyError, Add +from sympy.core.basic import Atom +from sympy.core.decorators import call_highest_priority +from sympy.core.logic import fuzzy_and, FuzzyBool +from sympy.core.numbers import Integer +from sympy.core.mod import Mod +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.complexes import Abs, re, im +from sympy.utilities.exceptions import sympy_deprecation_warning +from .utilities import _dotprodsimp, _simplify +from sympy.polys.polytools import Poly +from sympy.utilities.iterables import flatten, is_sequence +from sympy.utilities.misc import as_int, filldedent +from sympy.tensor.array import NDimArray + +from .utilities import _get_intermediate_simp_bool + + +# These exception types were previously defined in this module but were moved +# to exceptions.py. We reimport them here for backwards compatibility in case +# downstream code was importing them from here. +from .exceptions import ( # noqa: F401 + MatrixError, ShapeError, NonSquareMatrixError, NonInvertibleMatrixError, + NonPositiveDefiniteMatrixError +) + + +_DEPRECATED_MIXINS = ( + 'MatrixShaping', + 'MatrixSpecial', + 'MatrixProperties', + 'MatrixOperations', + 'MatrixArithmetic', + 'MatrixCommon', + 'MatrixDeterminant', + 'MatrixReductions', + 'MatrixSubspaces', + 'MatrixEigen', + 'MatrixCalculus', + 'MatrixDeprecated', +) + + +class _MatrixDeprecatedMeta(type): + + # + # Override the default __instancecheck__ implementation to ensure that + # e.g. isinstance(M, MatrixCommon) still works when M is one of the + # matrix classes. Matrix no longer inherits from MatrixCommon so + # isinstance(M, MatrixCommon) would now return False by default. + # + # There were lots of places in the codebase where this was being done + # so it seems likely that downstream code may be doing it too. All use + # of these mixins is deprecated though so we give a deprecation warning + # unconditionally if they are being used with isinstance. + # + # Any code seeing this deprecation warning should be changed to use + # isinstance(M, MatrixBase) instead which also works in previous versions + # of SymPy. + # + + def __instancecheck__(cls, instance): + + sympy_deprecation_warning( + f""" + Checking whether an object is an instance of {cls.__name__} is + deprecated. + + Use `isinstance(obj, Matrix)` instead of `isinstance(obj, {cls.__name__})`. + """, + deprecated_since_version="1.13", + active_deprecations_target="deprecated-matrix-mixins", + stacklevel=3, + ) + + from sympy.matrices.matrixbase import MatrixBase + from sympy.matrices.matrices import ( + MatrixDeterminant, + MatrixReductions, + MatrixSubspaces, + MatrixEigen, + MatrixCalculus, + MatrixDeprecated + ) + + all_mixins = ( + MatrixRequired, + MatrixShaping, + MatrixSpecial, + MatrixProperties, + MatrixOperations, + MatrixArithmetic, + MatrixCommon, + MatrixDeterminant, + MatrixReductions, + MatrixSubspaces, + MatrixEigen, + MatrixCalculus, + MatrixDeprecated + ) + + if cls in all_mixins and isinstance(instance, MatrixBase): + return True + else: + return super().__instancecheck__(instance) + + +class MatrixRequired(metaclass=_MatrixDeprecatedMeta): + """Deprecated mixin class for making matrix classes.""" + + rows = None # type: int + cols = None # type: int + _simplify = None + + def __init_subclass__(cls, **kwargs): + + # Warn if any downstream code is subclassing this class or any of the + # deprecated mixin classes that are all ultimately subclasses of this + # class. + # + # We don't want to warn about the deprecated mixins themselves being + # created, but only about them being used as mixins by downstream code. + # Otherwise just importing this module would trigger a warning. + # Ultimately the whole module should be deprecated and removed but for + # SymPy 1.13 it is premature to do that given that this module was the + # main way to import matrix exception types in all previous versions. + + if cls.__name__ not in _DEPRECATED_MIXINS: + sympy_deprecation_warning( + f""" + Inheriting from the Matrix mixin classes is deprecated. + + The class {cls.__name__} is subclassing a deprecated mixin. + """, + deprecated_since_version="1.13", + active_deprecations_target="deprecated-matrix-mixins", + stacklevel=3, + ) + + super().__init_subclass__(**kwargs) + + @classmethod + def _new(cls, *args, **kwargs): + """`_new` must, at minimum, be callable as + `_new(rows, cols, mat) where mat is a flat list of the + elements of the matrix.""" + raise NotImplementedError("Subclasses must implement this.") + + def __eq__(self, other): + raise NotImplementedError("Subclasses must implement this.") + + def __getitem__(self, key): + """Implementations of __getitem__ should accept ints, in which + case the matrix is indexed as a flat list, tuples (i,j) in which + case the (i,j) entry is returned, slices, or mixed tuples (a,b) + where a and b are any combination of slices and integers.""" + raise NotImplementedError("Subclasses must implement this.") + + def __len__(self): + """The total number of entries in the matrix.""" + raise NotImplementedError("Subclasses must implement this.") + + @property + def shape(self): + raise NotImplementedError("Subclasses must implement this.") + + +class MatrixShaping(MatrixRequired): + """Provides basic matrix shaping and extracting of submatrices""" + + def _eval_col_del(self, col): + def entry(i, j): + return self[i, j] if j < col else self[i, j + 1] + return self._new(self.rows, self.cols - 1, entry) + + def _eval_col_insert(self, pos, other): + + def entry(i, j): + if j < pos: + return self[i, j] + elif pos <= j < pos + other.cols: + return other[i, j - pos] + return self[i, j - other.cols] + + return self._new(self.rows, self.cols + other.cols, entry) + + def _eval_col_join(self, other): + rows = self.rows + + def entry(i, j): + if i < rows: + return self[i, j] + return other[i - rows, j] + + return classof(self, other)._new(self.rows + other.rows, self.cols, + entry) + + def _eval_extract(self, rowsList, colsList): + mat = list(self) + cols = self.cols + indices = (i * cols + j for i in rowsList for j in colsList) + return self._new(len(rowsList), len(colsList), + [mat[i] for i in indices]) + + def _eval_get_diag_blocks(self): + sub_blocks = [] + + def recurse_sub_blocks(M): + i = 1 + while i <= M.shape[0]: + if i == 1: + to_the_right = M[0, i:] + to_the_bottom = M[i:, 0] + else: + to_the_right = M[:i, i:] + to_the_bottom = M[i:, :i] + if any(to_the_right) or any(to_the_bottom): + i += 1 + continue + else: + sub_blocks.append(M[:i, :i]) + if M.shape == M[:i, :i].shape: + return + else: + recurse_sub_blocks(M[i:, i:]) + return + + recurse_sub_blocks(self) + return sub_blocks + + def _eval_row_del(self, row): + def entry(i, j): + return self[i, j] if i < row else self[i + 1, j] + return self._new(self.rows - 1, self.cols, entry) + + def _eval_row_insert(self, pos, other): + entries = list(self) + insert_pos = pos * self.cols + entries[insert_pos:insert_pos] = list(other) + return self._new(self.rows + other.rows, self.cols, entries) + + def _eval_row_join(self, other): + cols = self.cols + + def entry(i, j): + if j < cols: + return self[i, j] + return other[i, j - cols] + + return classof(self, other)._new(self.rows, self.cols + other.cols, + entry) + + def _eval_tolist(self): + return [list(self[i,:]) for i in range(self.rows)] + + def _eval_todok(self): + dok = {} + rows, cols = self.shape + for i in range(rows): + for j in range(cols): + val = self[i, j] + if val != self.zero: + dok[i, j] = val + return dok + + def _eval_vec(self): + rows = self.rows + + def entry(n, _): + # we want to read off the columns first + j = n // rows + i = n - j * rows + return self[i, j] + + return self._new(len(self), 1, entry) + + def _eval_vech(self, diagonal): + c = self.cols + v = [] + if diagonal: + for j in range(c): + for i in range(j, c): + v.append(self[i, j]) + else: + for j in range(c): + for i in range(j + 1, c): + v.append(self[i, j]) + return self._new(len(v), 1, v) + + def col_del(self, col): + """Delete the specified column.""" + if col < 0: + col += self.cols + if not 0 <= col < self.cols: + raise IndexError("Column {} is out of range.".format(col)) + return self._eval_col_del(col) + + def col_insert(self, pos, other): + """Insert one or more columns at the given column position. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(3, 1) + >>> M.col_insert(1, V) + Matrix([ + [0, 1, 0, 0], + [0, 1, 0, 0], + [0, 1, 0, 0]]) + + See Also + ======== + + col + row_insert + """ + # Allows you to build a matrix even if it is null matrix + if not self: + return type(self)(other) + + pos = as_int(pos) + + if pos < 0: + pos = self.cols + pos + if pos < 0: + pos = 0 + elif pos > self.cols: + pos = self.cols + + if self.rows != other.rows: + raise ShapeError( + "The matrices have incompatible number of rows ({} and {})" + .format(self.rows, other.rows)) + + return self._eval_col_insert(pos, other) + + def col_join(self, other): + """Concatenates two matrices along self's last and other's first row. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(1, 3) + >>> M.col_join(V) + Matrix([ + [0, 0, 0], + [0, 0, 0], + [0, 0, 0], + [1, 1, 1]]) + + See Also + ======== + + col + row_join + """ + # A null matrix can always be stacked (see #10770) + if self.rows == 0 and self.cols != other.cols: + return self._new(0, other.cols, []).col_join(other) + + if self.cols != other.cols: + raise ShapeError( + "The matrices have incompatible number of columns ({} and {})" + .format(self.cols, other.cols)) + return self._eval_col_join(other) + + def col(self, j): + """Elementary column selector. + + Examples + ======== + + >>> from sympy import eye + >>> eye(2).col(0) + Matrix([ + [1], + [0]]) + + See Also + ======== + + row + col_del + col_join + col_insert + """ + return self[:, j] + + def extract(self, rowsList, colsList): + r"""Return a submatrix by specifying a list of rows and columns. + Negative indices can be given. All indices must be in the range + $-n \le i < n$ where $n$ is the number of rows or columns. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(4, 3, range(12)) + >>> m + Matrix([ + [0, 1, 2], + [3, 4, 5], + [6, 7, 8], + [9, 10, 11]]) + >>> m.extract([0, 1, 3], [0, 1]) + Matrix([ + [0, 1], + [3, 4], + [9, 10]]) + + Rows or columns can be repeated: + + >>> m.extract([0, 0, 1], [-1]) + Matrix([ + [2], + [2], + [5]]) + + Every other row can be taken by using range to provide the indices: + + >>> m.extract(range(0, m.rows, 2), [-1]) + Matrix([ + [2], + [8]]) + + RowsList or colsList can also be a list of booleans, in which case + the rows or columns corresponding to the True values will be selected: + + >>> m.extract([0, 1, 2, 3], [True, False, True]) + Matrix([ + [0, 2], + [3, 5], + [6, 8], + [9, 11]]) + """ + + if not is_sequence(rowsList) or not is_sequence(colsList): + raise TypeError("rowsList and colsList must be iterable") + # ensure rowsList and colsList are lists of integers + if rowsList and all(isinstance(i, bool) for i in rowsList): + rowsList = [index for index, item in enumerate(rowsList) if item] + if colsList and all(isinstance(i, bool) for i in colsList): + colsList = [index for index, item in enumerate(colsList) if item] + + # ensure everything is in range + rowsList = [a2idx(k, self.rows) for k in rowsList] + colsList = [a2idx(k, self.cols) for k in colsList] + + return self._eval_extract(rowsList, colsList) + + def get_diag_blocks(self): + """Obtains the square sub-matrices on the main diagonal of a square matrix. + + Useful for inverting symbolic matrices or solving systems of + linear equations which may be decoupled by having a block diagonal + structure. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y, z + >>> A = Matrix([[1, 3, 0, 0], [y, z*z, 0, 0], [0, 0, x, 0], [0, 0, 0, 0]]) + >>> a1, a2, a3 = A.get_diag_blocks() + >>> a1 + Matrix([ + [1, 3], + [y, z**2]]) + >>> a2 + Matrix([[x]]) + >>> a3 + Matrix([[0]]) + + """ + return self._eval_get_diag_blocks() + + @classmethod + def hstack(cls, *args): + """Return a matrix formed by joining args horizontally (i.e. + by repeated application of row_join). + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> Matrix.hstack(eye(2), 2*eye(2)) + Matrix([ + [1, 0, 2, 0], + [0, 1, 0, 2]]) + """ + if len(args) == 0: + return cls._new() + + kls = type(args[0]) + return reduce(kls.row_join, args) + + def reshape(self, rows, cols): + """Reshape the matrix. Total number of elements must remain the same. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 3, lambda i, j: 1) + >>> m + Matrix([ + [1, 1, 1], + [1, 1, 1]]) + >>> m.reshape(1, 6) + Matrix([[1, 1, 1, 1, 1, 1]]) + >>> m.reshape(3, 2) + Matrix([ + [1, 1], + [1, 1], + [1, 1]]) + + """ + if self.rows * self.cols != rows * cols: + raise ValueError("Invalid reshape parameters %d %d" % (rows, cols)) + return self._new(rows, cols, lambda i, j: self[i * cols + j]) + + def row_del(self, row): + """Delete the specified row.""" + if row < 0: + row += self.rows + if not 0 <= row < self.rows: + raise IndexError("Row {} is out of range.".format(row)) + + return self._eval_row_del(row) + + def row_insert(self, pos, other): + """Insert one or more rows at the given row position. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(1, 3) + >>> M.row_insert(1, V) + Matrix([ + [0, 0, 0], + [1, 1, 1], + [0, 0, 0], + [0, 0, 0]]) + + See Also + ======== + + row + col_insert + """ + # Allows you to build a matrix even if it is null matrix + if not self: + return self._new(other) + + pos = as_int(pos) + + if pos < 0: + pos = self.rows + pos + if pos < 0: + pos = 0 + elif pos > self.rows: + pos = self.rows + + if self.cols != other.cols: + raise ShapeError( + "The matrices have incompatible number of columns ({} and {})" + .format(self.cols, other.cols)) + + return self._eval_row_insert(pos, other) + + def row_join(self, other): + """Concatenates two matrices along self's last and rhs's first column + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(3, 1) + >>> M.row_join(V) + Matrix([ + [0, 0, 0, 1], + [0, 0, 0, 1], + [0, 0, 0, 1]]) + + See Also + ======== + + row + col_join + """ + # A null matrix can always be stacked (see #10770) + if self.cols == 0 and self.rows != other.rows: + return self._new(other.rows, 0, []).row_join(other) + + if self.rows != other.rows: + raise ShapeError( + "The matrices have incompatible number of rows ({} and {})" + .format(self.rows, other.rows)) + return self._eval_row_join(other) + + def diagonal(self, k=0): + """Returns the kth diagonal of self. The main diagonal + corresponds to `k=0`; diagonals above and below correspond to + `k > 0` and `k < 0`, respectively. The values of `self[i, j]` + for which `j - i = k`, are returned in order of increasing + `i + j`, starting with `i + j = |k|`. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(3, 3, lambda i, j: j - i); m + Matrix([ + [ 0, 1, 2], + [-1, 0, 1], + [-2, -1, 0]]) + >>> _.diagonal() + Matrix([[0, 0, 0]]) + >>> m.diagonal(1) + Matrix([[1, 1]]) + >>> m.diagonal(-2) + Matrix([[-2]]) + + Even though the diagonal is returned as a Matrix, the element + retrieval can be done with a single index: + + >>> Matrix.diag(1, 2, 3).diagonal()[1] # instead of [0, 1] + 2 + + See Also + ======== + + diag + """ + rv = [] + k = as_int(k) + r = 0 if k > 0 else -k + c = 0 if r else k + while True: + if r == self.rows or c == self.cols: + break + rv.append(self[r, c]) + r += 1 + c += 1 + if not rv: + raise ValueError(filldedent(''' + The %s diagonal is out of range [%s, %s]''' % ( + k, 1 - self.rows, self.cols - 1))) + return self._new(1, len(rv), rv) + + def row(self, i): + """Elementary row selector. + + Examples + ======== + + >>> from sympy import eye + >>> eye(2).row(0) + Matrix([[1, 0]]) + + See Also + ======== + + col + row_del + row_join + row_insert + """ + return self[i, :] + + @property + def shape(self): + """The shape (dimensions) of the matrix as the 2-tuple (rows, cols). + + Examples + ======== + + >>> from sympy import zeros + >>> M = zeros(2, 3) + >>> M.shape + (2, 3) + >>> M.rows + 2 + >>> M.cols + 3 + """ + return (self.rows, self.cols) + + def todok(self): + """Return the matrix as dictionary of keys. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix.eye(3) + >>> M.todok() + {(0, 0): 1, (1, 1): 1, (2, 2): 1} + """ + return self._eval_todok() + + def tolist(self): + """Return the Matrix as a nested Python list. + + Examples + ======== + + >>> from sympy import Matrix, ones + >>> m = Matrix(3, 3, range(9)) + >>> m + Matrix([ + [0, 1, 2], + [3, 4, 5], + [6, 7, 8]]) + >>> m.tolist() + [[0, 1, 2], [3, 4, 5], [6, 7, 8]] + >>> ones(3, 0).tolist() + [[], [], []] + + When there are no rows then it will not be possible to tell how + many columns were in the original matrix: + + >>> ones(0, 3).tolist() + [] + + """ + if not self.rows: + return [] + if not self.cols: + return [[] for i in range(self.rows)] + return self._eval_tolist() + + def todod(M): + """Returns matrix as dict of dicts containing non-zero elements of the Matrix + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[0, 1],[0, 3]]) + >>> A + Matrix([ + [0, 1], + [0, 3]]) + >>> A.todod() + {0: {1: 1}, 1: {1: 3}} + + + """ + rowsdict = {} + Mlol = M.tolist() + for i, Mi in enumerate(Mlol): + row = {j: Mij for j, Mij in enumerate(Mi) if Mij} + if row: + rowsdict[i] = row + return rowsdict + + def vec(self): + """Return the Matrix converted into a one column matrix by stacking columns + + Examples + ======== + + >>> from sympy import Matrix + >>> m=Matrix([[1, 3], [2, 4]]) + >>> m + Matrix([ + [1, 3], + [2, 4]]) + >>> m.vec() + Matrix([ + [1], + [2], + [3], + [4]]) + + See Also + ======== + + vech + """ + return self._eval_vec() + + def vech(self, diagonal=True, check_symmetry=True): + """Reshapes the matrix into a column vector by stacking the + elements in the lower triangle. + + Parameters + ========== + + diagonal : bool, optional + If ``True``, it includes the diagonal elements. + + check_symmetry : bool, optional + If ``True``, it checks whether the matrix is symmetric. + + Examples + ======== + + >>> from sympy import Matrix + >>> m=Matrix([[1, 2], [2, 3]]) + >>> m + Matrix([ + [1, 2], + [2, 3]]) + >>> m.vech() + Matrix([ + [1], + [2], + [3]]) + >>> m.vech(diagonal=False) + Matrix([[2]]) + + Notes + ===== + + This should work for symmetric matrices and ``vech`` can + represent symmetric matrices in vector form with less size than + ``vec``. + + See Also + ======== + + vec + """ + if not self.is_square: + raise NonSquareMatrixError + + if check_symmetry and not self.is_symmetric(): + raise ValueError("The matrix is not symmetric.") + + return self._eval_vech(diagonal) + + @classmethod + def vstack(cls, *args): + """Return a matrix formed by joining args vertically (i.e. + by repeated application of col_join). + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> Matrix.vstack(eye(2), 2*eye(2)) + Matrix([ + [1, 0], + [0, 1], + [2, 0], + [0, 2]]) + """ + if len(args) == 0: + return cls._new() + + kls = type(args[0]) + return reduce(kls.col_join, args) + + +class MatrixSpecial(MatrixRequired): + """Construction of special matrices""" + + @classmethod + def _eval_diag(cls, rows, cols, diag_dict): + """diag_dict is a defaultdict containing + all the entries of the diagonal matrix.""" + def entry(i, j): + return diag_dict[(i, j)] + return cls._new(rows, cols, entry) + + @classmethod + def _eval_eye(cls, rows, cols): + vals = [cls.zero]*(rows*cols) + vals[::cols+1] = [cls.one]*min(rows, cols) + return cls._new(rows, cols, vals, copy=False) + + @classmethod + def _eval_jordan_block(cls, size: int, eigenvalue, band='upper'): + if band == 'lower': + def entry(i, j): + if i == j: + return eigenvalue + elif j + 1 == i: + return cls.one + return cls.zero + else: + def entry(i, j): + if i == j: + return eigenvalue + elif i + 1 == j: + return cls.one + return cls.zero + return cls._new(size, size, entry) + + @classmethod + def _eval_ones(cls, rows, cols): + def entry(i, j): + return cls.one + return cls._new(rows, cols, entry) + + @classmethod + def _eval_zeros(cls, rows, cols): + return cls._new(rows, cols, [cls.zero]*(rows*cols), copy=False) + + @classmethod + def _eval_wilkinson(cls, n): + def entry(i, j): + return cls.one if i + 1 == j else cls.zero + + D = cls._new(2*n + 1, 2*n + 1, entry) + + wminus = cls.diag(list(range(-n, n + 1)), unpack=True) + D + D.T + wplus = abs(cls.diag(list(range(-n, n + 1)), unpack=True)) + D + D.T + + return wminus, wplus + + @classmethod + def diag(kls, *args, strict=False, unpack=True, rows=None, cols=None, **kwargs): + """Returns a matrix with the specified diagonal. + If matrices are passed, a block-diagonal matrix + is created (i.e. the "direct sum" of the matrices). + + kwargs + ====== + + rows : rows of the resulting matrix; computed if + not given. + + cols : columns of the resulting matrix; computed if + not given. + + cls : class for the resulting matrix + + unpack : bool which, when True (default), unpacks a single + sequence rather than interpreting it as a Matrix. + + strict : bool which, when False (default), allows Matrices to + have variable-length rows. + + Examples + ======== + + >>> from sympy import Matrix + >>> Matrix.diag(1, 2, 3) + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + + The current default is to unpack a single sequence. If this is + not desired, set `unpack=False` and it will be interpreted as + a matrix. + + >>> Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3) + True + + When more than one element is passed, each is interpreted as + something to put on the diagonal. Lists are converted to + matrices. Filling of the diagonal always continues from + the bottom right hand corner of the previous item: this + will create a block-diagonal matrix whether the matrices + are square or not. + + >>> col = [1, 2, 3] + >>> row = [[4, 5]] + >>> Matrix.diag(col, row) + Matrix([ + [1, 0, 0], + [2, 0, 0], + [3, 0, 0], + [0, 4, 5]]) + + When `unpack` is False, elements within a list need not all be + of the same length. Setting `strict` to True would raise a + ValueError for the following: + + >>> Matrix.diag([[1, 2, 3], [4, 5], [6]], unpack=False) + Matrix([ + [1, 2, 3], + [4, 5, 0], + [6, 0, 0]]) + + The type of the returned matrix can be set with the ``cls`` + keyword. + + >>> from sympy import ImmutableMatrix + >>> from sympy.utilities.misc import func_name + >>> func_name(Matrix.diag(1, cls=ImmutableMatrix)) + 'ImmutableDenseMatrix' + + A zero dimension matrix can be used to position the start of + the filling at the start of an arbitrary row or column: + + >>> from sympy import ones + >>> r2 = ones(0, 2) + >>> Matrix.diag(r2, 1, 2) + Matrix([ + [0, 0, 1, 0], + [0, 0, 0, 2]]) + + See Also + ======== + eye + diagonal + .dense.diag + .expressions.blockmatrix.BlockMatrix + .sparsetools.banded + """ + from sympy.matrices.matrixbase import MatrixBase + from sympy.matrices.dense import Matrix + from sympy.matrices import SparseMatrix + klass = kwargs.get('cls', kls) + if unpack and len(args) == 1 and is_sequence(args[0]) and \ + not isinstance(args[0], MatrixBase): + args = args[0] + + # fill a default dict with the diagonal entries + diag_entries = defaultdict(int) + rmax = cmax = 0 # keep track of the biggest index seen + for m in args: + if isinstance(m, list): + if strict: + # if malformed, Matrix will raise an error + _ = Matrix(m) + r, c = _.shape + m = _.tolist() + else: + r, c, smat = SparseMatrix._handle_creation_inputs(m) + for (i, j), _ in smat.items(): + diag_entries[(i + rmax, j + cmax)] = _ + m = [] # to skip process below + elif hasattr(m, 'shape'): # a Matrix + # convert to list of lists + r, c = m.shape + m = m.tolist() + else: # in this case, we're a single value + diag_entries[(rmax, cmax)] = m + rmax += 1 + cmax += 1 + continue + # process list of lists + for i, mi in enumerate(m): + for j, _ in enumerate(mi): + diag_entries[(i + rmax, j + cmax)] = _ + rmax += r + cmax += c + if rows is None: + rows, cols = cols, rows + if rows is None: + rows, cols = rmax, cmax + else: + cols = rows if cols is None else cols + if rows < rmax or cols < cmax: + raise ValueError(filldedent(''' + The constructed matrix is {} x {} but a size of {} x {} + was specified.'''.format(rmax, cmax, rows, cols))) + return klass._eval_diag(rows, cols, diag_entries) + + @classmethod + def eye(kls, rows, cols=None, **kwargs): + """Returns an identity matrix. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + if rows < 0 or cols < 0: + raise ValueError("Cannot create a {} x {} matrix. " + "Both dimensions must be positive".format(rows, cols)) + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_eye(rows, cols) + + @classmethod + def jordan_block(kls, size=None, eigenvalue=None, *, band='upper', **kwargs): + """Returns a Jordan block + + Parameters + ========== + + size : Integer, optional + Specifies the shape of the Jordan block matrix. + + eigenvalue : Number or Symbol + Specifies the value for the main diagonal of the matrix. + + .. note:: + The keyword ``eigenval`` is also specified as an alias + of this keyword, but it is not recommended to use. + + We may deprecate the alias in later release. + + band : 'upper' or 'lower', optional + Specifies the position of the off-diagonal to put `1` s on. + + cls : Matrix, optional + Specifies the matrix class of the output form. + + If it is not specified, the class type where the method is + being executed on will be returned. + + Returns + ======= + + Matrix + A Jordan block matrix. + + Raises + ====== + + ValueError + If insufficient arguments are given for matrix size + specification, or no eigenvalue is given. + + Examples + ======== + + Creating a default Jordan block: + + >>> from sympy import Matrix + >>> from sympy.abc import x + >>> Matrix.jordan_block(4, x) + Matrix([ + [x, 1, 0, 0], + [0, x, 1, 0], + [0, 0, x, 1], + [0, 0, 0, x]]) + + Creating an alternative Jordan block matrix where `1` is on + lower off-diagonal: + + >>> Matrix.jordan_block(4, x, band='lower') + Matrix([ + [x, 0, 0, 0], + [1, x, 0, 0], + [0, 1, x, 0], + [0, 0, 1, x]]) + + Creating a Jordan block with keyword arguments + + >>> Matrix.jordan_block(size=4, eigenvalue=x) + Matrix([ + [x, 1, 0, 0], + [0, x, 1, 0], + [0, 0, x, 1], + [0, 0, 0, x]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Jordan_matrix + """ + klass = kwargs.pop('cls', kls) + + eigenval = kwargs.get('eigenval', None) + if eigenvalue is None and eigenval is None: + raise ValueError("Must supply an eigenvalue") + elif eigenvalue != eigenval and None not in (eigenval, eigenvalue): + raise ValueError( + "Inconsistent values are given: 'eigenval'={}, " + "'eigenvalue'={}".format(eigenval, eigenvalue)) + else: + if eigenval is not None: + eigenvalue = eigenval + + if size is None: + raise ValueError("Must supply a matrix size") + + size = as_int(size) + return klass._eval_jordan_block(size, eigenvalue, band) + + @classmethod + def ones(kls, rows, cols=None, **kwargs): + """Returns a matrix of ones. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_ones(rows, cols) + + @classmethod + def zeros(kls, rows, cols=None, **kwargs): + """Returns a matrix of zeros. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + if rows < 0 or cols < 0: + raise ValueError("Cannot create a {} x {} matrix. " + "Both dimensions must be positive".format(rows, cols)) + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_zeros(rows, cols) + + @classmethod + def companion(kls, poly): + """Returns a companion matrix of a polynomial. + + Examples + ======== + + >>> from sympy import Matrix, Poly, Symbol, symbols + >>> x = Symbol('x') + >>> c0, c1, c2, c3, c4 = symbols('c0:5') + >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x) + >>> Matrix.companion(p) + Matrix([ + [0, 0, 0, 0, -c0], + [1, 0, 0, 0, -c1], + [0, 1, 0, 0, -c2], + [0, 0, 1, 0, -c3], + [0, 0, 0, 1, -c4]]) + """ + poly = kls._sympify(poly) + if not isinstance(poly, Poly): + raise ValueError("{} must be a Poly instance.".format(poly)) + if not poly.is_monic: + raise ValueError("{} must be a monic polynomial.".format(poly)) + if not poly.is_univariate: + raise ValueError( + "{} must be a univariate polynomial.".format(poly)) + + size = poly.degree() + if not size >= 1: + raise ValueError( + "{} must have degree not less than 1.".format(poly)) + + coeffs = poly.all_coeffs() + def entry(i, j): + if j == size - 1: + return -coeffs[-1 - i] + elif i == j + 1: + return kls.one + return kls.zero + return kls._new(size, size, entry) + + + @classmethod + def wilkinson(kls, n, **kwargs): + """Returns two square Wilkinson Matrix of size 2*n + 1 + $W_{2n + 1}^-, W_{2n + 1}^+ =$ Wilkinson(n) + + Examples + ======== + + >>> from sympy import Matrix + >>> wminus, wplus = Matrix.wilkinson(3) + >>> wminus + Matrix([ + [-3, 1, 0, 0, 0, 0, 0], + [ 1, -2, 1, 0, 0, 0, 0], + [ 0, 1, -1, 1, 0, 0, 0], + [ 0, 0, 1, 0, 1, 0, 0], + [ 0, 0, 0, 1, 1, 1, 0], + [ 0, 0, 0, 0, 1, 2, 1], + [ 0, 0, 0, 0, 0, 1, 3]]) + >>> wplus + Matrix([ + [3, 1, 0, 0, 0, 0, 0], + [1, 2, 1, 0, 0, 0, 0], + [0, 1, 1, 1, 0, 0, 0], + [0, 0, 1, 0, 1, 0, 0], + [0, 0, 0, 1, 1, 1, 0], + [0, 0, 0, 0, 1, 2, 1], + [0, 0, 0, 0, 0, 1, 3]]) + + References + ========== + + .. [1] https://blogs.mathworks.com/cleve/2013/04/15/wilkinsons-matrices-2/ + .. [2] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford, 1965, 662 pp. + + """ + klass = kwargs.get('cls', kls) + n = as_int(n) + return klass._eval_wilkinson(n) + +class MatrixProperties(MatrixRequired): + """Provides basic properties of a matrix.""" + + def _eval_atoms(self, *types): + result = set() + for i in self: + result.update(i.atoms(*types)) + return result + + def _eval_free_symbols(self): + return set().union(*(i.free_symbols for i in self if i)) + + def _eval_has(self, *patterns): + return any(a.has(*patterns) for a in self) + + def _eval_is_anti_symmetric(self, simpfunc): + if not all(simpfunc(self[i, j] + self[j, i]).is_zero for i in range(self.rows) for j in range(self.cols)): + return False + return True + + def _eval_is_diagonal(self): + for i in range(self.rows): + for j in range(self.cols): + if i != j and self[i, j]: + return False + return True + + # _eval_is_hermitian is called by some general SymPy + # routines and has a different *args signature. Make + # sure the names don't clash by adding `_matrix_` in name. + def _eval_is_matrix_hermitian(self, simpfunc): + mat = self._new(self.rows, self.cols, lambda i, j: simpfunc(self[i, j] - self[j, i].conjugate())) + return mat.is_zero_matrix + + def _eval_is_Identity(self) -> FuzzyBool: + def dirac(i, j): + if i == j: + return 1 + return 0 + + return all(self[i, j] == dirac(i, j) + for i in range(self.rows) + for j in range(self.cols)) + + def _eval_is_lower_hessenberg(self): + return all(self[i, j].is_zero + for i in range(self.rows) + for j in range(i + 2, self.cols)) + + def _eval_is_lower(self): + return all(self[i, j].is_zero + for i in range(self.rows) + for j in range(i + 1, self.cols)) + + def _eval_is_symbolic(self): + return self.has(Symbol) + + def _eval_is_symmetric(self, simpfunc): + mat = self._new(self.rows, self.cols, lambda i, j: simpfunc(self[i, j] - self[j, i])) + return mat.is_zero_matrix + + def _eval_is_zero_matrix(self): + if any(i.is_zero == False for i in self): + return False + if any(i.is_zero is None for i in self): + return None + return True + + def _eval_is_upper_hessenberg(self): + return all(self[i, j].is_zero + for i in range(2, self.rows) + for j in range(min(self.cols, (i - 1)))) + + def _eval_values(self): + return [i for i in self if not i.is_zero] + + def _has_positive_diagonals(self): + diagonal_entries = (self[i, i] for i in range(self.rows)) + return fuzzy_and(x.is_positive for x in diagonal_entries) + + def _has_nonnegative_diagonals(self): + diagonal_entries = (self[i, i] for i in range(self.rows)) + return fuzzy_and(x.is_nonnegative for x in diagonal_entries) + + def atoms(self, *types): + """Returns the atoms that form the current object. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import Matrix + >>> Matrix([[x]]) + Matrix([[x]]) + >>> _.atoms() + {x} + >>> Matrix([[x, y], [y, x]]) + Matrix([ + [x, y], + [y, x]]) + >>> _.atoms() + {x, y} + """ + + types = tuple(t if isinstance(t, type) else type(t) for t in types) + if not types: + types = (Atom,) + return self._eval_atoms(*types) + + @property + def free_symbols(self): + """Returns the free symbols within the matrix. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy import Matrix + >>> Matrix([[x], [1]]).free_symbols + {x} + """ + return self._eval_free_symbols() + + def has(self, *patterns): + """Test whether any subexpression matches any of the patterns. + + Examples + ======== + + >>> from sympy import Matrix, SparseMatrix, Float + >>> from sympy.abc import x, y + >>> A = Matrix(((1, x), (0.2, 3))) + >>> B = SparseMatrix(((1, x), (0.2, 3))) + >>> A.has(x) + True + >>> A.has(y) + False + >>> A.has(Float) + True + >>> B.has(x) + True + >>> B.has(y) + False + >>> B.has(Float) + True + """ + return self._eval_has(*patterns) + + def is_anti_symmetric(self, simplify=True): + """Check if matrix M is an antisymmetric matrix, + that is, M is a square matrix with all M[i, j] == -M[j, i]. + + When ``simplify=True`` (default), the sum M[i, j] + M[j, i] is + simplified before testing to see if it is zero. By default, + the SymPy simplify function is used. To use a custom function + set simplify to a function that accepts a single argument which + returns a simplified expression. To skip simplification, set + simplify to False but note that although this will be faster, + it may induce false negatives. + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> m = Matrix(2, 2, [0, 1, -1, 0]) + >>> m + Matrix([ + [ 0, 1], + [-1, 0]]) + >>> m.is_anti_symmetric() + True + >>> x, y = symbols('x y') + >>> m = Matrix(2, 3, [0, 0, x, -y, 0, 0]) + >>> m + Matrix([ + [ 0, 0, x], + [-y, 0, 0]]) + >>> m.is_anti_symmetric() + False + + >>> from sympy.abc import x, y + >>> m = Matrix(3, 3, [0, x**2 + 2*x + 1, y, + ... -(x + 1)**2, 0, x*y, + ... -y, -x*y, 0]) + + Simplification of matrix elements is done by default so even + though two elements which should be equal and opposite would not + pass an equality test, the matrix is still reported as + anti-symmetric: + + >>> m[0, 1] == -m[1, 0] + False + >>> m.is_anti_symmetric() + True + + If ``simplify=False`` is used for the case when a Matrix is already + simplified, this will speed things up. Here, we see that without + simplification the matrix does not appear anti-symmetric: + + >>> print(m.is_anti_symmetric(simplify=False)) + None + + But if the matrix were already expanded, then it would appear + anti-symmetric and simplification in the is_anti_symmetric routine + is not needed: + + >>> m = m.expand() + >>> m.is_anti_symmetric(simplify=False) + True + """ + # accept custom simplification + simpfunc = simplify + if not isfunction(simplify): + simpfunc = _simplify if simplify else lambda x: x + + if not self.is_square: + return False + return self._eval_is_anti_symmetric(simpfunc) + + def is_diagonal(self): + """Check if matrix is diagonal, + that is matrix in which the entries outside the main diagonal are all zero. + + Examples + ======== + + >>> from sympy import Matrix, diag + >>> m = Matrix(2, 2, [1, 0, 0, 2]) + >>> m + Matrix([ + [1, 0], + [0, 2]]) + >>> m.is_diagonal() + True + + >>> m = Matrix(2, 2, [1, 1, 0, 2]) + >>> m + Matrix([ + [1, 1], + [0, 2]]) + >>> m.is_diagonal() + False + + >>> m = diag(1, 2, 3) + >>> m + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + >>> m.is_diagonal() + True + + See Also + ======== + + is_lower + is_upper + sympy.matrices.matrixbase.MatrixCommon.is_diagonalizable + diagonalize + """ + return self._eval_is_diagonal() + + @property + def is_weakly_diagonally_dominant(self): + r"""Tests if the matrix is row weakly diagonally dominant. + + Explanation + =========== + + A $n, n$ matrix $A$ is row weakly diagonally dominant if + + .. math:: + \left|A_{i, i}\right| \ge \sum_{j = 0, j \neq i}^{n-1} + \left|A_{i, j}\right| \quad {\text{for all }} + i \in \{ 0, ..., n-1 \} + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]]) + >>> A.is_weakly_diagonally_dominant + True + + >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]]) + >>> A.is_weakly_diagonally_dominant + False + + >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]]) + >>> A.is_weakly_diagonally_dominant + True + + Notes + ===== + + If you want to test whether a matrix is column diagonally + dominant, you can apply the test after transposing the matrix. + """ + if not self.is_square: + return False + + rows, cols = self.shape + + def test_row(i): + summation = self.zero + for j in range(cols): + if i != j: + summation += Abs(self[i, j]) + return (Abs(self[i, i]) - summation).is_nonnegative + + return fuzzy_and(test_row(i) for i in range(rows)) + + @property + def is_strongly_diagonally_dominant(self): + r"""Tests if the matrix is row strongly diagonally dominant. + + Explanation + =========== + + A $n, n$ matrix $A$ is row strongly diagonally dominant if + + .. math:: + \left|A_{i, i}\right| > \sum_{j = 0, j \neq i}^{n-1} + \left|A_{i, j}\right| \quad {\text{for all }} + i \in \{ 0, ..., n-1 \} + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]]) + >>> A.is_strongly_diagonally_dominant + False + + >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]]) + >>> A.is_strongly_diagonally_dominant + False + + >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]]) + >>> A.is_strongly_diagonally_dominant + True + + Notes + ===== + + If you want to test whether a matrix is column diagonally + dominant, you can apply the test after transposing the matrix. + """ + if not self.is_square: + return False + + rows, cols = self.shape + + def test_row(i): + summation = self.zero + for j in range(cols): + if i != j: + summation += Abs(self[i, j]) + return (Abs(self[i, i]) - summation).is_positive + + return fuzzy_and(test_row(i) for i in range(rows)) + + @property + def is_hermitian(self): + """Checks if the matrix is Hermitian. + + In a Hermitian matrix element i,j is the complex conjugate of + element j,i. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy import I + >>> from sympy.abc import x + >>> a = Matrix([[1, I], [-I, 1]]) + >>> a + Matrix([ + [ 1, I], + [-I, 1]]) + >>> a.is_hermitian + True + >>> a[0, 0] = 2*I + >>> a.is_hermitian + False + >>> a[0, 0] = x + >>> a.is_hermitian + >>> a[0, 1] = a[1, 0]*I + >>> a.is_hermitian + False + """ + if not self.is_square: + return False + + return self._eval_is_matrix_hermitian(_simplify) + + @property + def is_Identity(self) -> FuzzyBool: + if not self.is_square: + return False + return self._eval_is_Identity() + + @property + def is_lower_hessenberg(self): + r"""Checks if the matrix is in the lower-Hessenberg form. + + The lower hessenberg matrix has zero entries + above the first superdiagonal. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 2, 0, 0], [5, 2, 3, 0], [3, 4, 3, 7], [5, 6, 1, 1]]) + >>> a + Matrix([ + [1, 2, 0, 0], + [5, 2, 3, 0], + [3, 4, 3, 7], + [5, 6, 1, 1]]) + >>> a.is_lower_hessenberg + True + + See Also + ======== + + is_upper_hessenberg + is_lower + """ + return self._eval_is_lower_hessenberg() + + @property + def is_lower(self): + """Check if matrix is a lower triangular matrix. True can be returned + even if the matrix is not square. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [1, 0, 0, 1]) + >>> m + Matrix([ + [1, 0], + [0, 1]]) + >>> m.is_lower + True + + >>> m = Matrix(4, 3, [0, 0, 0, 2, 0, 0, 1, 4, 0, 6, 6, 5]) + >>> m + Matrix([ + [0, 0, 0], + [2, 0, 0], + [1, 4, 0], + [6, 6, 5]]) + >>> m.is_lower + True + + >>> from sympy.abc import x, y + >>> m = Matrix(2, 2, [x**2 + y, y**2 + x, 0, x + y]) + >>> m + Matrix([ + [x**2 + y, x + y**2], + [ 0, x + y]]) + >>> m.is_lower + False + + See Also + ======== + + is_upper + is_diagonal + is_lower_hessenberg + """ + return self._eval_is_lower() + + @property + def is_square(self): + """Checks if a matrix is square. + + A matrix is square if the number of rows equals the number of columns. + The empty matrix is square by definition, since the number of rows and + the number of columns are both zero. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> b = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> c = Matrix([]) + >>> a.is_square + False + >>> b.is_square + True + >>> c.is_square + True + """ + return self.rows == self.cols + + def is_symbolic(self): + """Checks if any elements contain Symbols. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.is_symbolic() + True + + """ + return self._eval_is_symbolic() + + def is_symmetric(self, simplify=True): + """Check if matrix is symmetric matrix, + that is square matrix and is equal to its transpose. + + By default, simplifications occur before testing symmetry. + They can be skipped using 'simplify=False'; while speeding things a bit, + this may however induce false negatives. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [0, 1, 1, 2]) + >>> m + Matrix([ + [0, 1], + [1, 2]]) + >>> m.is_symmetric() + True + + >>> m = Matrix(2, 2, [0, 1, 2, 0]) + >>> m + Matrix([ + [0, 1], + [2, 0]]) + >>> m.is_symmetric() + False + + >>> m = Matrix(2, 3, [0, 0, 0, 0, 0, 0]) + >>> m + Matrix([ + [0, 0, 0], + [0, 0, 0]]) + >>> m.is_symmetric() + False + + >>> from sympy.abc import x, y + >>> m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3]) + >>> m + Matrix([ + [ 1, x**2 + 2*x + 1, y], + [(x + 1)**2, 2, 0], + [ y, 0, 3]]) + >>> m.is_symmetric() + True + + If the matrix is already simplified, you may speed-up is_symmetric() + test by using 'simplify=False'. + + >>> bool(m.is_symmetric(simplify=False)) + False + >>> m1 = m.expand() + >>> m1.is_symmetric(simplify=False) + True + """ + simpfunc = simplify + if not isfunction(simplify): + simpfunc = _simplify if simplify else lambda x: x + + if not self.is_square: + return False + + return self._eval_is_symmetric(simpfunc) + + @property + def is_upper_hessenberg(self): + """Checks if the matrix is the upper-Hessenberg form. + + The upper hessenberg matrix has zero entries + below the first subdiagonal. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 4, 2, 3], [3, 4, 1, 7], [0, 2, 3, 4], [0, 0, 1, 3]]) + >>> a + Matrix([ + [1, 4, 2, 3], + [3, 4, 1, 7], + [0, 2, 3, 4], + [0, 0, 1, 3]]) + >>> a.is_upper_hessenberg + True + + See Also + ======== + + is_lower_hessenberg + is_upper + """ + return self._eval_is_upper_hessenberg() + + @property + def is_upper(self): + """Check if matrix is an upper triangular matrix. True can be returned + even if the matrix is not square. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [1, 0, 0, 1]) + >>> m + Matrix([ + [1, 0], + [0, 1]]) + >>> m.is_upper + True + + >>> m = Matrix(4, 3, [5, 1, 9, 0, 4, 6, 0, 0, 5, 0, 0, 0]) + >>> m + Matrix([ + [5, 1, 9], + [0, 4, 6], + [0, 0, 5], + [0, 0, 0]]) + >>> m.is_upper + True + + >>> m = Matrix(2, 3, [4, 2, 5, 6, 1, 1]) + >>> m + Matrix([ + [4, 2, 5], + [6, 1, 1]]) + >>> m.is_upper + False + + See Also + ======== + + is_lower + is_diagonal + is_upper_hessenberg + """ + return all(self[i, j].is_zero + for i in range(1, self.rows) + for j in range(min(i, self.cols))) + + @property + def is_zero_matrix(self): + """Checks if a matrix is a zero matrix. + + A matrix is zero if every element is zero. A matrix need not be square + to be considered zero. The empty matrix is zero by the principle of + vacuous truth. For a matrix that may or may not be zero (e.g. + contains a symbol), this will be None + + Examples + ======== + + >>> from sympy import Matrix, zeros + >>> from sympy.abc import x + >>> a = Matrix([[0, 0], [0, 0]]) + >>> b = zeros(3, 4) + >>> c = Matrix([[0, 1], [0, 0]]) + >>> d = Matrix([]) + >>> e = Matrix([[x, 0], [0, 0]]) + >>> a.is_zero_matrix + True + >>> b.is_zero_matrix + True + >>> c.is_zero_matrix + False + >>> d.is_zero_matrix + True + >>> e.is_zero_matrix + """ + return self._eval_is_zero_matrix() + + def values(self): + """Return non-zero values of self.""" + return self._eval_values() + + +class MatrixOperations(MatrixRequired): + """Provides basic matrix shape and elementwise + operations. Should not be instantiated directly.""" + + def _eval_adjoint(self): + return self.transpose().conjugate() + + def _eval_applyfunc(self, f): + out = self._new(self.rows, self.cols, [f(x) for x in self]) + return out + + def _eval_as_real_imag(self): # type: ignore + return (self.applyfunc(re), self.applyfunc(im)) + + def _eval_conjugate(self): + return self.applyfunc(lambda x: x.conjugate()) + + def _eval_permute_cols(self, perm): + # apply the permutation to a list + mapping = list(perm) + + def entry(i, j): + return self[i, mapping[j]] + + return self._new(self.rows, self.cols, entry) + + def _eval_permute_rows(self, perm): + # apply the permutation to a list + mapping = list(perm) + + def entry(i, j): + return self[mapping[i], j] + + return self._new(self.rows, self.cols, entry) + + def _eval_trace(self): + return sum(self[i, i] for i in range(self.rows)) + + def _eval_transpose(self): + return self._new(self.cols, self.rows, lambda i, j: self[j, i]) + + def adjoint(self): + """Conjugate transpose or Hermitian conjugation.""" + return self._eval_adjoint() + + def applyfunc(self, f): + """Apply a function to each element of the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, lambda i, j: i*2+j) + >>> m + Matrix([ + [0, 1], + [2, 3]]) + >>> m.applyfunc(lambda i: 2*i) + Matrix([ + [0, 2], + [4, 6]]) + + """ + if not callable(f): + raise TypeError("`f` must be callable.") + + return self._eval_applyfunc(f) + + def as_real_imag(self, deep=True, **hints): + """Returns a tuple containing the (real, imaginary) part of matrix.""" + # XXX: Ignoring deep and hints... + return self._eval_as_real_imag() + + def conjugate(self): + """Return the by-element conjugation. + + Examples + ======== + + >>> from sympy import SparseMatrix, I + >>> a = SparseMatrix(((1, 2 + I), (3, 4), (I, -I))) + >>> a + Matrix([ + [1, 2 + I], + [3, 4], + [I, -I]]) + >>> a.C + Matrix([ + [ 1, 2 - I], + [ 3, 4], + [-I, I]]) + + See Also + ======== + + transpose: Matrix transposition + H: Hermite conjugation + sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation + """ + return self._eval_conjugate() + + def doit(self, **hints): + return self.applyfunc(lambda x: x.doit(**hints)) + + def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False): + """Apply evalf() to each element of self.""" + options = {'subs':subs, 'maxn':maxn, 'chop':chop, 'strict':strict, + 'quad':quad, 'verbose':verbose} + return self.applyfunc(lambda i: i.evalf(n, **options)) + + def expand(self, deep=True, modulus=None, power_base=True, power_exp=True, + mul=True, log=True, multinomial=True, basic=True, **hints): + """Apply core.function.expand to each entry of the matrix. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy import Matrix + >>> Matrix(1, 1, [x*(x+1)]) + Matrix([[x*(x + 1)]]) + >>> _.expand() + Matrix([[x**2 + x]]) + + """ + return self.applyfunc(lambda x: x.expand( + deep, modulus, power_base, power_exp, mul, log, multinomial, basic, + **hints)) + + @property + def H(self): + """Return Hermite conjugate. + + Examples + ======== + + >>> from sympy import Matrix, I + >>> m = Matrix((0, 1 + I, 2, 3)) + >>> m + Matrix([ + [ 0], + [1 + I], + [ 2], + [ 3]]) + >>> m.H + Matrix([[0, 1 - I, 2, 3]]) + + See Also + ======== + + conjugate: By-element conjugation + sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation + """ + return self.T.C + + def permute(self, perm, orientation='rows', direction='forward'): + r"""Permute the rows or columns of a matrix by the given list of + swaps. + + Parameters + ========== + + perm : Permutation, list, or list of lists + A representation for the permutation. + + If it is ``Permutation``, it is used directly with some + resizing with respect to the matrix size. + + If it is specified as list of lists, + (e.g., ``[[0, 1], [0, 2]]``), then the permutation is formed + from applying the product of cycles. The direction how the + cyclic product is applied is described in below. + + If it is specified as a list, the list should represent + an array form of a permutation. (e.g., ``[1, 2, 0]``) which + would would form the swapping function + `0 \mapsto 1, 1 \mapsto 2, 2\mapsto 0`. + + orientation : 'rows', 'cols' + A flag to control whether to permute the rows or the columns + + direction : 'forward', 'backward' + A flag to control whether to apply the permutations from + the start of the list first, or from the back of the list + first. + + For example, if the permutation specification is + ``[[0, 1], [0, 2]]``, + + If the flag is set to ``'forward'``, the cycle would be + formed as `0 \mapsto 2, 2 \mapsto 1, 1 \mapsto 0`. + + If the flag is set to ``'backward'``, the cycle would be + formed as `0 \mapsto 1, 1 \mapsto 2, 2 \mapsto 0`. + + If the argument ``perm`` is not in a form of list of lists, + this flag takes no effect. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='forward') + Matrix([ + [0, 0, 1], + [1, 0, 0], + [0, 1, 0]]) + + >>> from sympy import eye + >>> M = eye(3) + >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='backward') + Matrix([ + [0, 1, 0], + [0, 0, 1], + [1, 0, 0]]) + + Notes + ===== + + If a bijective function + `\sigma : \mathbb{N}_0 \rightarrow \mathbb{N}_0` denotes the + permutation. + + If the matrix `A` is the matrix to permute, represented as + a horizontal or a vertical stack of vectors: + + .. math:: + A = + \begin{bmatrix} + a_0 \\ a_1 \\ \vdots \\ a_{n-1} + \end{bmatrix} = + \begin{bmatrix} + \alpha_0 & \alpha_1 & \cdots & \alpha_{n-1} + \end{bmatrix} + + If the matrix `B` is the result, the permutation of matrix rows + is defined as: + + .. math:: + B := \begin{bmatrix} + a_{\sigma(0)} \\ a_{\sigma(1)} \\ \vdots \\ a_{\sigma(n-1)} + \end{bmatrix} + + And the permutation of matrix columns is defined as: + + .. math:: + B := \begin{bmatrix} + \alpha_{\sigma(0)} & \alpha_{\sigma(1)} & + \cdots & \alpha_{\sigma(n-1)} + \end{bmatrix} + """ + from sympy.combinatorics import Permutation + + # allow british variants and `columns` + if direction == 'forwards': + direction = 'forward' + if direction == 'backwards': + direction = 'backward' + if orientation == 'columns': + orientation = 'cols' + + if direction not in ('forward', 'backward'): + raise TypeError("direction='{}' is an invalid kwarg. " + "Try 'forward' or 'backward'".format(direction)) + if orientation not in ('rows', 'cols'): + raise TypeError("orientation='{}' is an invalid kwarg. " + "Try 'rows' or 'cols'".format(orientation)) + + if not isinstance(perm, (Permutation, Iterable)): + raise ValueError( + "{} must be a list, a list of lists, " + "or a SymPy permutation object.".format(perm)) + + # ensure all swaps are in range + max_index = self.rows if orientation == 'rows' else self.cols + if not all(0 <= t <= max_index for t in flatten(list(perm))): + raise IndexError("`swap` indices out of range.") + + if perm and not isinstance(perm, Permutation) and \ + isinstance(perm[0], Iterable): + if direction == 'forward': + perm = list(reversed(perm)) + perm = Permutation(perm, size=max_index+1) + else: + perm = Permutation(perm, size=max_index+1) + + if orientation == 'rows': + return self._eval_permute_rows(perm) + if orientation == 'cols': + return self._eval_permute_cols(perm) + + def permute_cols(self, swaps, direction='forward'): + """Alias for + ``self.permute(swaps, orientation='cols', direction=direction)`` + + See Also + ======== + + permute + """ + return self.permute(swaps, orientation='cols', direction=direction) + + def permute_rows(self, swaps, direction='forward'): + """Alias for + ``self.permute(swaps, orientation='rows', direction=direction)`` + + See Also + ======== + + permute + """ + return self.permute(swaps, orientation='rows', direction=direction) + + def refine(self, assumptions=True): + """Apply refine to each element of the matrix. + + Examples + ======== + + >>> from sympy import Symbol, Matrix, Abs, sqrt, Q + >>> x = Symbol('x') + >>> Matrix([[Abs(x)**2, sqrt(x**2)],[sqrt(x**2), Abs(x)**2]]) + Matrix([ + [ Abs(x)**2, sqrt(x**2)], + [sqrt(x**2), Abs(x)**2]]) + >>> _.refine(Q.real(x)) + Matrix([ + [ x**2, Abs(x)], + [Abs(x), x**2]]) + + """ + return self.applyfunc(lambda x: refine(x, assumptions)) + + def replace(self, F, G, map=False, simultaneous=True, exact=None): + """Replaces Function F in Matrix entries with Function G. + + Examples + ======== + + >>> from sympy import symbols, Function, Matrix + >>> F, G = symbols('F, G', cls=Function) + >>> M = Matrix(2, 2, lambda i, j: F(i+j)) ; M + Matrix([ + [F(0), F(1)], + [F(1), F(2)]]) + >>> N = M.replace(F,G) + >>> N + Matrix([ + [G(0), G(1)], + [G(1), G(2)]]) + """ + return self.applyfunc( + lambda x: x.replace(F, G, map=map, simultaneous=simultaneous, exact=exact)) + + def rot90(self, k=1): + """Rotates Matrix by 90 degrees + + Parameters + ========== + + k : int + Specifies how many times the matrix is rotated by 90 degrees + (clockwise when positive, counter-clockwise when negative). + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> A = Matrix(2, 2, symbols('a:d')) + >>> A + Matrix([ + [a, b], + [c, d]]) + + Rotating the matrix clockwise one time: + + >>> A.rot90(1) + Matrix([ + [c, a], + [d, b]]) + + Rotating the matrix anticlockwise two times: + + >>> A.rot90(-2) + Matrix([ + [d, c], + [b, a]]) + """ + + mod = k%4 + if mod == 0: + return self + if mod == 1: + return self[::-1, ::].T + if mod == 2: + return self[::-1, ::-1] + if mod == 3: + return self[::, ::-1].T + + def simplify(self, **kwargs): + """Apply simplify to each element of the matrix. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, sin, cos + >>> SparseMatrix(1, 1, [x*sin(y)**2 + x*cos(y)**2]) + Matrix([[x*sin(y)**2 + x*cos(y)**2]]) + >>> _.simplify() + Matrix([[x]]) + """ + return self.applyfunc(lambda x: x.simplify(**kwargs)) + + def subs(self, *args, **kwargs): # should mirror core.basic.subs + """Return a new matrix with subs applied to each entry. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, Matrix + >>> SparseMatrix(1, 1, [x]) + Matrix([[x]]) + >>> _.subs(x, y) + Matrix([[y]]) + >>> Matrix(_).subs(y, x) + Matrix([[x]]) + """ + + if len(args) == 1 and not isinstance(args[0], (dict, set)) and iter(args[0]) and not is_sequence(args[0]): + args = (list(args[0]),) + + return self.applyfunc(lambda x: x.subs(*args, **kwargs)) + + def trace(self): + """ + Returns the trace of a square matrix i.e. the sum of the + diagonal elements. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.trace() + 5 + + """ + if self.rows != self.cols: + raise NonSquareMatrixError() + return self._eval_trace() + + def transpose(self): + """ + Returns the transpose of the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.transpose() + Matrix([ + [1, 3], + [2, 4]]) + + >>> from sympy import Matrix, I + >>> m=Matrix(((1, 2+I), (3, 4))) + >>> m + Matrix([ + [1, 2 + I], + [3, 4]]) + >>> m.transpose() + Matrix([ + [ 1, 3], + [2 + I, 4]]) + >>> m.T == m.transpose() + True + + See Also + ======== + + conjugate: By-element conjugation + + """ + return self._eval_transpose() + + @property + def T(self): + '''Matrix transposition''' + return self.transpose() + + @property + def C(self): + '''By-element conjugation''' + return self.conjugate() + + def n(self, *args, **kwargs): + """Apply evalf() to each element of self.""" + return self.evalf(*args, **kwargs) + + def xreplace(self, rule): # should mirror core.basic.xreplace + """Return a new matrix with xreplace applied to each entry. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, Matrix + >>> SparseMatrix(1, 1, [x]) + Matrix([[x]]) + >>> _.xreplace({x: y}) + Matrix([[y]]) + >>> Matrix(_).xreplace({y: x}) + Matrix([[x]]) + """ + return self.applyfunc(lambda x: x.xreplace(rule)) + + def _eval_simplify(self, **kwargs): + # XXX: We can't use self.simplify here as mutable subclasses will + # override simplify and have it return None + return MatrixOperations.simplify(self, **kwargs) + + def _eval_trigsimp(self, **opts): + from sympy.simplify.trigsimp import trigsimp + return self.applyfunc(lambda x: trigsimp(x, **opts)) + + def upper_triangular(self, k=0): + """Return the elements on and above the kth diagonal of a matrix. + If k is not specified then simply returns upper-triangular portion + of a matrix + + Examples + ======== + + >>> from sympy import ones + >>> A = ones(4) + >>> A.upper_triangular() + Matrix([ + [1, 1, 1, 1], + [0, 1, 1, 1], + [0, 0, 1, 1], + [0, 0, 0, 1]]) + + >>> A.upper_triangular(2) + Matrix([ + [0, 0, 1, 1], + [0, 0, 0, 1], + [0, 0, 0, 0], + [0, 0, 0, 0]]) + + >>> A.upper_triangular(-1) + Matrix([ + [1, 1, 1, 1], + [1, 1, 1, 1], + [0, 1, 1, 1], + [0, 0, 1, 1]]) + + """ + + def entry(i, j): + return self[i, j] if i + k <= j else self.zero + + return self._new(self.rows, self.cols, entry) + + + def lower_triangular(self, k=0): + """Return the elements on and below the kth diagonal of a matrix. + If k is not specified then simply returns lower-triangular portion + of a matrix + + Examples + ======== + + >>> from sympy import ones + >>> A = ones(4) + >>> A.lower_triangular() + Matrix([ + [1, 0, 0, 0], + [1, 1, 0, 0], + [1, 1, 1, 0], + [1, 1, 1, 1]]) + + >>> A.lower_triangular(-2) + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [1, 0, 0, 0], + [1, 1, 0, 0]]) + + >>> A.lower_triangular(1) + Matrix([ + [1, 1, 0, 0], + [1, 1, 1, 0], + [1, 1, 1, 1], + [1, 1, 1, 1]]) + + """ + + def entry(i, j): + return self[i, j] if i + k >= j else self.zero + + return self._new(self.rows, self.cols, entry) + + + +class MatrixArithmetic(MatrixRequired): + """Provides basic matrix arithmetic operations. + Should not be instantiated directly.""" + + _op_priority = 10.01 + + def _eval_Abs(self): + return self._new(self.rows, self.cols, lambda i, j: Abs(self[i, j])) + + def _eval_add(self, other): + return self._new(self.rows, self.cols, + lambda i, j: self[i, j] + other[i, j]) + + def _eval_matrix_mul(self, other): + def entry(i, j): + vec = [self[i,k]*other[k,j] for k in range(self.cols)] + try: + return Add(*vec) + except (TypeError, SympifyError): + # Some matrices don't work with `sum` or `Add` + # They don't work with `sum` because `sum` tries to add `0` + # Fall back to a safe way to multiply if the `Add` fails. + return reduce(lambda a, b: a + b, vec) + + return self._new(self.rows, other.cols, entry) + + def _eval_matrix_mul_elementwise(self, other): + return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other[i,j]) + + def _eval_matrix_rmul(self, other): + def entry(i, j): + return sum(other[i,k]*self[k,j] for k in range(other.cols)) + return self._new(other.rows, self.cols, entry) + + def _eval_pow_by_recursion(self, num): + if num == 1: + return self + + if num % 2 == 1: + a, b = self, self._eval_pow_by_recursion(num - 1) + else: + a = b = self._eval_pow_by_recursion(num // 2) + + return a.multiply(b) + + def _eval_pow_by_cayley(self, exp): + from sympy.discrete.recurrences import linrec_coeffs + row = self.shape[0] + p = self.charpoly() + + coeffs = (-p).all_coeffs()[1:] + coeffs = linrec_coeffs(coeffs, exp) + new_mat = self.eye(row) + ans = self.zeros(row) + + for i in range(row): + ans += coeffs[i]*new_mat + new_mat *= self + + return ans + + def _eval_pow_by_recursion_dotprodsimp(self, num, prevsimp=None): + if prevsimp is None: + prevsimp = [True]*len(self) + + if num == 1: + return self + + if num % 2 == 1: + a, b = self, self._eval_pow_by_recursion_dotprodsimp(num - 1, + prevsimp=prevsimp) + else: + a = b = self._eval_pow_by_recursion_dotprodsimp(num // 2, + prevsimp=prevsimp) + + m = a.multiply(b, dotprodsimp=False) + lenm = len(m) + elems = [None]*lenm + + for i in range(lenm): + if prevsimp[i]: + elems[i], prevsimp[i] = _dotprodsimp(m[i], withsimp=True) + else: + elems[i] = m[i] + + return m._new(m.rows, m.cols, elems) + + def _eval_scalar_mul(self, other): + return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other) + + def _eval_scalar_rmul(self, other): + return self._new(self.rows, self.cols, lambda i, j: other*self[i,j]) + + def _eval_Mod(self, other): + return self._new(self.rows, self.cols, lambda i, j: Mod(self[i, j], other)) + + # Python arithmetic functions + def __abs__(self): + """Returns a new matrix with entry-wise absolute values.""" + return self._eval_Abs() + + @call_highest_priority('__radd__') + def __add__(self, other): + """Return self + other, raising ShapeError if shapes do not match.""" + if isinstance(other, NDimArray): # Matrix and array addition is currently not implemented + return NotImplemented + other = _matrixify(other) + # matrix-like objects can have shapes. This is + # our first sanity check. + if hasattr(other, 'shape'): + if self.shape != other.shape: + raise ShapeError("Matrix size mismatch: %s + %s" % ( + self.shape, other.shape)) + + # honest SymPy matrices defer to their class's routine + if getattr(other, 'is_Matrix', False): + # call the highest-priority class's _eval_add + a, b = self, other + if a.__class__ != classof(a, b): + b, a = a, b + return a._eval_add(b) + # Matrix-like objects can be passed to CommonMatrix routines directly. + if getattr(other, 'is_MatrixLike', False): + return MatrixArithmetic._eval_add(self, other) + + raise TypeError('cannot add %s and %s' % (type(self), type(other))) + + @call_highest_priority('__rtruediv__') + def __truediv__(self, other): + return self * (self.one / other) + + @call_highest_priority('__rmatmul__') + def __matmul__(self, other): + other = _matrixify(other) + if not getattr(other, 'is_Matrix', False) and not getattr(other, 'is_MatrixLike', False): + return NotImplemented + + return self.__mul__(other) + + def __mod__(self, other): + return self.applyfunc(lambda x: x % other) + + @call_highest_priority('__rmul__') + def __mul__(self, other): + """Return self*other where other is either a scalar or a matrix + of compatible dimensions. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> 2*A == A*2 == Matrix([[2, 4, 6], [8, 10, 12]]) + True + >>> B = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> A*B + Matrix([ + [30, 36, 42], + [66, 81, 96]]) + >>> B*A + Traceback (most recent call last): + ... + ShapeError: Matrices size mismatch. + >>> + + See Also + ======== + + matrix_multiply_elementwise + """ + + return self.multiply(other) + + def multiply(self, other, dotprodsimp=None): + """Same as __mul__() but with optional simplification. + + Parameters + ========== + + dotprodsimp : bool, optional + Specifies whether intermediate term algebraic simplification is used + during matrix multiplications to control expression blowup and thus + speed up calculation. Default is off. + """ + + isimpbool = _get_intermediate_simp_bool(False, dotprodsimp) + other = _matrixify(other) + # matrix-like objects can have shapes. This is + # our first sanity check. Double check other is not explicitly not a Matrix. + if (hasattr(other, 'shape') and len(other.shape) == 2 and + (getattr(other, 'is_Matrix', True) or + getattr(other, 'is_MatrixLike', True))): + if self.shape[1] != other.shape[0]: + raise ShapeError("Matrix size mismatch: %s * %s." % ( + self.shape, other.shape)) + + # honest SymPy matrices defer to their class's routine + if getattr(other, 'is_Matrix', False): + m = self._eval_matrix_mul(other) + if isimpbool: + return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m]) + return m + + # Matrix-like objects can be passed to CommonMatrix routines directly. + if getattr(other, 'is_MatrixLike', False): + return MatrixArithmetic._eval_matrix_mul(self, other) + + # if 'other' is not iterable then scalar multiplication. + if not isinstance(other, Iterable): + try: + return self._eval_scalar_mul(other) + except TypeError: + pass + + return NotImplemented + + def multiply_elementwise(self, other): + """Return the Hadamard product (elementwise product) of A and B + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[0, 1, 2], [3, 4, 5]]) + >>> B = Matrix([[1, 10, 100], [100, 10, 1]]) + >>> A.multiply_elementwise(B) + Matrix([ + [ 0, 10, 200], + [300, 40, 5]]) + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.cross + sympy.matrices.matrixbase.MatrixBase.dot + multiply + """ + if self.shape != other.shape: + raise ShapeError("Matrix shapes must agree {} != {}".format(self.shape, other.shape)) + + return self._eval_matrix_mul_elementwise(other) + + def __neg__(self): + return self._eval_scalar_mul(-1) + + @call_highest_priority('__rpow__') + def __pow__(self, exp): + """Return self**exp a scalar or symbol.""" + + return self.pow(exp) + + + def pow(self, exp, method=None): + r"""Return self**exp a scalar or symbol. + + Parameters + ========== + + method : multiply, mulsimp, jordan, cayley + If multiply then it returns exponentiation using recursion. + If jordan then Jordan form exponentiation will be used. + If cayley then the exponentiation is done using Cayley-Hamilton + theorem. + If mulsimp then the exponentiation is done using recursion + with dotprodsimp. This specifies whether intermediate term + algebraic simplification is used during naive matrix power to + control expression blowup and thus speed up calculation. + If None, then it heuristically decides which method to use. + + """ + + if method is not None and method not in ['multiply', 'mulsimp', 'jordan', 'cayley']: + raise TypeError('No such method') + if self.rows != self.cols: + raise NonSquareMatrixError() + a = self + jordan_pow = getattr(a, '_matrix_pow_by_jordan_blocks', None) + exp = sympify(exp) + + if exp.is_zero: + return a._new(a.rows, a.cols, lambda i, j: int(i == j)) + if exp == 1: + return a + + diagonal = getattr(a, 'is_diagonal', None) + if diagonal is not None and diagonal(): + return a._new(a.rows, a.cols, lambda i, j: a[i,j]**exp if i == j else 0) + + if exp.is_Number and exp % 1 == 0: + if a.rows == 1: + return a._new([[a[0]**exp]]) + if exp < 0: + exp = -exp + a = a.inv() + # When certain conditions are met, + # Jordan block algorithm is faster than + # computation by recursion. + if method == 'jordan': + try: + return jordan_pow(exp) + except MatrixError: + if method == 'jordan': + raise + + elif method == 'cayley': + if not exp.is_Number or exp % 1 != 0: + raise ValueError("cayley method is only valid for integer powers") + return a._eval_pow_by_cayley(exp) + + elif method == "mulsimp": + if not exp.is_Number or exp % 1 != 0: + raise ValueError("mulsimp method is only valid for integer powers") + return a._eval_pow_by_recursion_dotprodsimp(exp) + + elif method == "multiply": + if not exp.is_Number or exp % 1 != 0: + raise ValueError("multiply method is only valid for integer powers") + return a._eval_pow_by_recursion(exp) + + elif method is None and exp.is_Number and exp % 1 == 0: + if exp.is_Float: + exp = Integer(exp) + # Decide heuristically which method to apply + if a.rows == 2 and exp > 100000: + return jordan_pow(exp) + elif _get_intermediate_simp_bool(True, None): + return a._eval_pow_by_recursion_dotprodsimp(exp) + elif exp > 10000: + return a._eval_pow_by_cayley(exp) + else: + return a._eval_pow_by_recursion(exp) + + if jordan_pow: + try: + return jordan_pow(exp) + except NonInvertibleMatrixError: + # Raised by jordan_pow on zero determinant matrix unless exp is + # definitely known to be a non-negative integer. + # Here we raise if n is definitely not a non-negative integer + # but otherwise we can leave this as an unevaluated MatPow. + if exp.is_integer is False or exp.is_nonnegative is False: + raise + + from sympy.matrices.expressions import MatPow + return MatPow(a, exp) + + @call_highest_priority('__add__') + def __radd__(self, other): + return self + other + + @call_highest_priority('__matmul__') + def __rmatmul__(self, other): + other = _matrixify(other) + if not getattr(other, 'is_Matrix', False) and not getattr(other, 'is_MatrixLike', False): + return NotImplemented + + return self.__rmul__(other) + + @call_highest_priority('__mul__') + def __rmul__(self, other): + return self.rmultiply(other) + + def rmultiply(self, other, dotprodsimp=None): + """Same as __rmul__() but with optional simplification. + + Parameters + ========== + + dotprodsimp : bool, optional + Specifies whether intermediate term algebraic simplification is used + during matrix multiplications to control expression blowup and thus + speed up calculation. Default is off. + """ + isimpbool = _get_intermediate_simp_bool(False, dotprodsimp) + other = _matrixify(other) + # matrix-like objects can have shapes. This is + # our first sanity check. Double check other is not explicitly not a Matrix. + if (hasattr(other, 'shape') and len(other.shape) == 2 and + (getattr(other, 'is_Matrix', True) or + getattr(other, 'is_MatrixLike', True))): + if self.shape[0] != other.shape[1]: + raise ShapeError("Matrix size mismatch.") + + # honest SymPy matrices defer to their class's routine + if getattr(other, 'is_Matrix', False): + m = self._eval_matrix_rmul(other) + if isimpbool: + return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m]) + return m + # Matrix-like objects can be passed to CommonMatrix routines directly. + if getattr(other, 'is_MatrixLike', False): + return MatrixArithmetic._eval_matrix_rmul(self, other) + + # if 'other' is not iterable then scalar multiplication. + if not isinstance(other, Iterable): + try: + return self._eval_scalar_rmul(other) + except TypeError: + pass + + return NotImplemented + + @call_highest_priority('__sub__') + def __rsub__(self, a): + return (-self) + a + + @call_highest_priority('__rsub__') + def __sub__(self, a): + return self + (-a) + + +class MatrixCommon(MatrixArithmetic, MatrixOperations, MatrixProperties, + MatrixSpecial, MatrixShaping): + """All common matrix operations including basic arithmetic, shaping, + and special matrices like `zeros`, and `eye`.""" + _diff_wrt = True # type: bool + + +class _MinimalMatrix: + """Class providing the minimum functionality + for a matrix-like object and implementing every method + required for a `MatrixRequired`. This class does not have everything + needed to become a full-fledged SymPy object, but it will satisfy the + requirements of anything inheriting from `MatrixRequired`. If you wish + to make a specialized matrix type, make sure to implement these + methods and properties with the exception of `__init__` and `__repr__` + which are included for convenience.""" + + is_MatrixLike = True + _sympify = staticmethod(sympify) + _class_priority = 3 + zero = S.Zero + one = S.One + + is_Matrix = True + is_MatrixExpr = False + + @classmethod + def _new(cls, *args, **kwargs): + return cls(*args, **kwargs) + + def __init__(self, rows, cols=None, mat=None, copy=False): + if isfunction(mat): + # if we passed in a function, use that to populate the indices + mat = [mat(i, j) for i in range(rows) for j in range(cols)] + if cols is None and mat is None: + mat = rows + rows, cols = getattr(mat, 'shape', (rows, cols)) + try: + # if we passed in a list of lists, flatten it and set the size + if cols is None and mat is None: + mat = rows + cols = len(mat[0]) + rows = len(mat) + mat = [x for l in mat for x in l] + except (IndexError, TypeError): + pass + self.mat = tuple(self._sympify(x) for x in mat) + self.rows, self.cols = rows, cols + if self.rows is None or self.cols is None: + raise NotImplementedError("Cannot initialize matrix with given parameters") + + def __getitem__(self, key): + def _normalize_slices(row_slice, col_slice): + """Ensure that row_slice and col_slice do not have + `None` in their arguments. Any integers are converted + to slices of length 1""" + if not isinstance(row_slice, slice): + row_slice = slice(row_slice, row_slice + 1, None) + row_slice = slice(*row_slice.indices(self.rows)) + + if not isinstance(col_slice, slice): + col_slice = slice(col_slice, col_slice + 1, None) + col_slice = slice(*col_slice.indices(self.cols)) + + return (row_slice, col_slice) + + def _coord_to_index(i, j): + """Return the index in _mat corresponding + to the (i,j) position in the matrix. """ + return i * self.cols + j + + if isinstance(key, tuple): + i, j = key + if isinstance(i, slice) or isinstance(j, slice): + # if the coordinates are not slices, make them so + # and expand the slices so they don't contain `None` + i, j = _normalize_slices(i, j) + + rowsList, colsList = list(range(self.rows))[i], \ + list(range(self.cols))[j] + indices = (i * self.cols + j for i in rowsList for j in + colsList) + return self._new(len(rowsList), len(colsList), + [self.mat[i] for i in indices]) + + # if the key is a tuple of ints, change + # it to an array index + key = _coord_to_index(i, j) + return self.mat[key] + + def __eq__(self, other): + try: + classof(self, other) + except TypeError: + return False + return ( + self.shape == other.shape and list(self) == list(other)) + + def __len__(self): + return self.rows*self.cols + + def __repr__(self): + return "_MinimalMatrix({}, {}, {})".format(self.rows, self.cols, + self.mat) + + @property + def shape(self): + return (self.rows, self.cols) + + +class _CastableMatrix: # this is needed here ONLY FOR TESTS. + def as_mutable(self): + return self + + def as_immutable(self): + return self + + +class _MatrixWrapper: + """Wrapper class providing the minimum functionality for a matrix-like + object: .rows, .cols, .shape, indexability, and iterability. CommonMatrix + math operations should work on matrix-like objects. This one is intended for + matrix-like objects which use the same indexing format as SymPy with respect + to returning matrix elements instead of rows for non-tuple indexes. + """ + + is_Matrix = False # needs to be here because of __getattr__ + is_MatrixLike = True + + def __init__(self, mat, shape): + self.mat = mat + self.shape = shape + self.rows, self.cols = shape + + def __getitem__(self, key): + if isinstance(key, tuple): + return sympify(self.mat.__getitem__(key)) + + return sympify(self.mat.__getitem__((key // self.rows, key % self.cols))) + + def __iter__(self): # supports numpy.matrix and numpy.array + mat = self.mat + cols = self.cols + + return iter(sympify(mat[r, c]) for r in range(self.rows) for c in range(cols)) + + +def _matrixify(mat): + """If `mat` is a Matrix or is matrix-like, + return a Matrix or MatrixWrapper object. Otherwise + `mat` is passed through without modification.""" + + if getattr(mat, 'is_Matrix', False) or getattr(mat, 'is_MatrixLike', False): + return mat + + if not(getattr(mat, 'is_Matrix', True) or getattr(mat, 'is_MatrixLike', True)): + return mat + + shape = None + + if hasattr(mat, 'shape'): # numpy, scipy.sparse + if len(mat.shape) == 2: + shape = mat.shape + elif hasattr(mat, 'rows') and hasattr(mat, 'cols'): # mpmath + shape = (mat.rows, mat.cols) + + if shape: + return _MatrixWrapper(mat, shape) + + return mat + + +def a2idx(j, n=None): + """Return integer after making positive and validating against n.""" + if not isinstance(j, int): + jindex = getattr(j, '__index__', None) + if jindex is not None: + j = jindex() + else: + raise IndexError("Invalid index a[%r]" % (j,)) + if n is not None: + if j < 0: + j += n + if not (j >= 0 and j < n): + raise IndexError("Index out of range: a[%s]" % (j,)) + return int(j) + + +def classof(A, B): + """ + Get the type of the result when combining matrices of different types. + + Currently the strategy is that immutability is contagious. + + Examples + ======== + + >>> from sympy import Matrix, ImmutableMatrix + >>> from sympy.matrices.matrixbase import classof + >>> M = Matrix([[1, 2], [3, 4]]) # a Mutable Matrix + >>> IM = ImmutableMatrix([[1, 2], [3, 4]]) + >>> classof(M, IM) + + """ + priority_A = getattr(A, '_class_priority', None) + priority_B = getattr(B, '_class_priority', None) + if None not in (priority_A, priority_B): + if A._class_priority > B._class_priority: + return A.__class__ + else: + return B.__class__ + + try: + import numpy + except ImportError: + pass + else: + if isinstance(A, numpy.ndarray): + return B.__class__ + if isinstance(B, numpy.ndarray): + return A.__class__ + + raise TypeError("Incompatible classes %s, %s" % (A.__class__, B.__class__)) diff --git a/lib/python3.11/site-packages/sympy/matrices/decompositions.py b/lib/python3.11/site-packages/sympy/matrices/decompositions.py new file mode 100644 index 0000000000000000000000000000000000000000..a8dd466d84c957b870396a050fd25ec21e7113a3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/decompositions.py @@ -0,0 +1,1621 @@ +import copy + +from sympy.core import S +from sympy.core.function import expand_mul +from sympy.functions.elementary.miscellaneous import Min, sqrt +from sympy.functions.elementary.complexes import sign + +from .exceptions import NonSquareMatrixError, NonPositiveDefiniteMatrixError +from .utilities import _get_intermediate_simp, _iszero +from .determinant import _find_reasonable_pivot_naive + + +def _rank_decomposition(M, iszerofunc=_iszero, simplify=False): + r"""Returns a pair of matrices (`C`, `F`) with matching rank + such that `A = C F`. + + Parameters + ========== + + iszerofunc : Function, optional + A function used for detecting whether an element can + act as a pivot. ``lambda x: x.is_zero`` is used by default. + + simplify : Bool or Function, optional + A function used to simplify elements when looking for a + pivot. By default SymPy's ``simplify`` is used. + + Returns + ======= + + (C, F) : Matrices + `C` and `F` are full-rank matrices with rank as same as `A`, + whose product gives `A`. + + See Notes for additional mathematical details. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([ + ... [1, 3, 1, 4], + ... [2, 7, 3, 9], + ... [1, 5, 3, 1], + ... [1, 2, 0, 8] + ... ]) + >>> C, F = A.rank_decomposition() + >>> C + Matrix([ + [1, 3, 4], + [2, 7, 9], + [1, 5, 1], + [1, 2, 8]]) + >>> F + Matrix([ + [1, 0, -2, 0], + [0, 1, 1, 0], + [0, 0, 0, 1]]) + >>> C * F == A + True + + Notes + ===== + + Obtaining `F`, an RREF of `A`, is equivalent to creating a + product + + .. math:: + E_n E_{n-1} ... E_1 A = F + + where `E_n, E_{n-1}, \dots, E_1` are the elimination matrices or + permutation matrices equivalent to each row-reduction step. + + The inverse of the same product of elimination matrices gives + `C`: + + .. math:: + C = \left(E_n E_{n-1} \dots E_1\right)^{-1} + + It is not necessary, however, to actually compute the inverse: + the columns of `C` are those from the original matrix with the + same column indices as the indices of the pivot columns of `F`. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Rank_factorization + + .. [2] Piziak, R.; Odell, P. L. (1 June 1999). + "Full Rank Factorization of Matrices". + Mathematics Magazine. 72 (3): 193. doi:10.2307/2690882 + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.rref + """ + + F, pivot_cols = M.rref(simplify=simplify, iszerofunc=iszerofunc, + pivots=True) + rank = len(pivot_cols) + + C = M.extract(range(M.rows), pivot_cols) + F = F[:rank, :] + + return C, F + + +def _liupc(M): + """Liu's algorithm, for pre-determination of the Elimination Tree of + the given matrix, used in row-based symbolic Cholesky factorization. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> S = SparseMatrix([ + ... [1, 0, 3, 2], + ... [0, 0, 1, 0], + ... [4, 0, 0, 5], + ... [0, 6, 7, 0]]) + >>> S.liupc() + ([[0], [], [0], [1, 2]], [4, 3, 4, 4]) + + References + ========== + + .. [1] Symbolic Sparse Cholesky Factorization using Elimination Trees, + Jeroen Van Grondelle (1999) + https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582 + """ + # Algorithm 2.4, p 17 of reference + + # get the indices of the elements that are non-zero on or below diag + R = [[] for r in range(M.rows)] + + for r, c, _ in M.row_list(): + if c <= r: + R[r].append(c) + + inf = len(R) # nothing will be this large + parent = [inf]*M.rows + virtual = [inf]*M.rows + + for r in range(M.rows): + for c in R[r][:-1]: + while virtual[c] < r: + t = virtual[c] + virtual[c] = r + c = t + + if virtual[c] == inf: + parent[c] = virtual[c] = r + + return R, parent + +def _row_structure_symbolic_cholesky(M): + """Symbolic cholesky factorization, for pre-determination of the + non-zero structure of the Cholesky factororization. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> S = SparseMatrix([ + ... [1, 0, 3, 2], + ... [0, 0, 1, 0], + ... [4, 0, 0, 5], + ... [0, 6, 7, 0]]) + >>> S.row_structure_symbolic_cholesky() + [[0], [], [0], [1, 2]] + + References + ========== + + .. [1] Symbolic Sparse Cholesky Factorization using Elimination Trees, + Jeroen Van Grondelle (1999) + https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582 + """ + + R, parent = M.liupc() + inf = len(R) # this acts as infinity + Lrow = copy.deepcopy(R) + + for k in range(M.rows): + for j in R[k]: + while j != inf and j != k: + Lrow[k].append(j) + j = parent[j] + + Lrow[k] = sorted(set(Lrow[k])) + + return Lrow + + +def _cholesky(M, hermitian=True): + """Returns the Cholesky-type decomposition L of a matrix A + such that L * L.H == A if hermitian flag is True, + or L * L.T == A if hermitian is False. + + A must be a Hermitian positive-definite matrix if hermitian is True, + or a symmetric matrix if it is False. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) + >>> A.cholesky() + Matrix([ + [ 5, 0, 0], + [ 3, 3, 0], + [-1, 1, 3]]) + >>> A.cholesky() * A.cholesky().T + Matrix([ + [25, 15, -5], + [15, 18, 0], + [-5, 0, 11]]) + + The matrix can have complex entries: + + >>> from sympy import I + >>> A = Matrix(((9, 3*I), (-3*I, 5))) + >>> A.cholesky() + Matrix([ + [ 3, 0], + [-I, 2]]) + >>> A.cholesky() * A.cholesky().H + Matrix([ + [ 9, 3*I], + [-3*I, 5]]) + + Non-hermitian Cholesky-type decomposition may be useful when the + matrix is not positive-definite. + + >>> A = Matrix([[1, 2], [2, 1]]) + >>> L = A.cholesky(hermitian=False) + >>> L + Matrix([ + [1, 0], + [2, sqrt(3)*I]]) + >>> L*L.T == A + True + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.LDLdecomposition + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + QRdecomposition + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if hermitian and not M.is_hermitian: + raise ValueError("Matrix must be Hermitian.") + if not hermitian and not M.is_symmetric(): + raise ValueError("Matrix must be symmetric.") + + L = MutableDenseMatrix.zeros(M.rows, M.rows) + + if hermitian: + for i in range(M.rows): + for j in range(i): + L[i, j] = ((1 / L[j, j])*(M[i, j] - + sum(L[i, k]*L[j, k].conjugate() for k in range(j)))) + + Lii2 = (M[i, i] - + sum(L[i, k]*L[i, k].conjugate() for k in range(i))) + + if Lii2.is_positive is False: + raise NonPositiveDefiniteMatrixError( + "Matrix must be positive-definite") + + L[i, i] = sqrt(Lii2) + + else: + for i in range(M.rows): + for j in range(i): + L[i, j] = ((1 / L[j, j])*(M[i, j] - + sum(L[i, k]*L[j, k] for k in range(j)))) + + L[i, i] = sqrt(M[i, i] - + sum(L[i, k]**2 for k in range(i))) + + return M._new(L) + +def _cholesky_sparse(M, hermitian=True): + """ + Returns the Cholesky decomposition L of a matrix A + such that L * L.T = A + + A must be a square, symmetric, positive-definite + and non-singular matrix + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> A = SparseMatrix(((25,15,-5),(15,18,0),(-5,0,11))) + >>> A.cholesky() + Matrix([ + [ 5, 0, 0], + [ 3, 3, 0], + [-1, 1, 3]]) + >>> A.cholesky() * A.cholesky().T == A + True + + The matrix can have complex entries: + + >>> from sympy import I + >>> A = SparseMatrix(((9, 3*I), (-3*I, 5))) + >>> A.cholesky() + Matrix([ + [ 3, 0], + [-I, 2]]) + >>> A.cholesky() * A.cholesky().H + Matrix([ + [ 9, 3*I], + [-3*I, 5]]) + + Non-hermitian Cholesky-type decomposition may be useful when the + matrix is not positive-definite. + + >>> A = SparseMatrix([[1, 2], [2, 1]]) + >>> L = A.cholesky(hermitian=False) + >>> L + Matrix([ + [1, 0], + [2, sqrt(3)*I]]) + >>> L*L.T == A + True + + See Also + ======== + + sympy.matrices.sparse.SparseMatrix.LDLdecomposition + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + QRdecomposition + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if hermitian and not M.is_hermitian: + raise ValueError("Matrix must be Hermitian.") + if not hermitian and not M.is_symmetric(): + raise ValueError("Matrix must be symmetric.") + + dps = _get_intermediate_simp(expand_mul, expand_mul) + Crowstruc = M.row_structure_symbolic_cholesky() + C = MutableDenseMatrix.zeros(M.rows) + + for i in range(len(Crowstruc)): + for j in Crowstruc[i]: + if i != j: + C[i, j] = M[i, j] + summ = 0 + + for p1 in Crowstruc[i]: + if p1 < j: + for p2 in Crowstruc[j]: + if p2 < j: + if p1 == p2: + if hermitian: + summ += C[i, p1]*C[j, p1].conjugate() + else: + summ += C[i, p1]*C[j, p1] + else: + break + else: + break + + C[i, j] = dps((C[i, j] - summ) / C[j, j]) + + else: # i == j + C[j, j] = M[j, j] + summ = 0 + + for k in Crowstruc[j]: + if k < j: + if hermitian: + summ += C[j, k]*C[j, k].conjugate() + else: + summ += C[j, k]**2 + else: + break + + Cjj2 = dps(C[j, j] - summ) + + if hermitian and Cjj2.is_positive is False: + raise NonPositiveDefiniteMatrixError( + "Matrix must be positive-definite") + + C[j, j] = sqrt(Cjj2) + + return M._new(C) + + +def _LDLdecomposition(M, hermitian=True): + """Returns the LDL Decomposition (L, D) of matrix A, + such that L * D * L.H == A if hermitian flag is True, or + L * D * L.T == A if hermitian is False. + This method eliminates the use of square root. + Further this ensures that all the diagonal entries of L are 1. + A must be a Hermitian positive-definite matrix if hermitian is True, + or a symmetric matrix otherwise. + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) + >>> L, D = A.LDLdecomposition() + >>> L + Matrix([ + [ 1, 0, 0], + [ 3/5, 1, 0], + [-1/5, 1/3, 1]]) + >>> D + Matrix([ + [25, 0, 0], + [ 0, 9, 0], + [ 0, 0, 9]]) + >>> L * D * L.T * A.inv() == eye(A.rows) + True + + The matrix can have complex entries: + + >>> from sympy import I + >>> A = Matrix(((9, 3*I), (-3*I, 5))) + >>> L, D = A.LDLdecomposition() + >>> L + Matrix([ + [ 1, 0], + [-I/3, 1]]) + >>> D + Matrix([ + [9, 0], + [0, 4]]) + >>> L*D*L.H == A + True + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.cholesky + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + QRdecomposition + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if hermitian and not M.is_hermitian: + raise ValueError("Matrix must be Hermitian.") + if not hermitian and not M.is_symmetric(): + raise ValueError("Matrix must be symmetric.") + + D = MutableDenseMatrix.zeros(M.rows, M.rows) + L = MutableDenseMatrix.eye(M.rows) + + if hermitian: + for i in range(M.rows): + for j in range(i): + L[i, j] = (1 / D[j, j])*(M[i, j] - sum( + L[i, k]*L[j, k].conjugate()*D[k, k] for k in range(j))) + + D[i, i] = (M[i, i] - + sum(L[i, k]*L[i, k].conjugate()*D[k, k] for k in range(i))) + + if D[i, i].is_positive is False: + raise NonPositiveDefiniteMatrixError( + "Matrix must be positive-definite") + + else: + for i in range(M.rows): + for j in range(i): + L[i, j] = (1 / D[j, j])*(M[i, j] - sum( + L[i, k]*L[j, k]*D[k, k] for k in range(j))) + + D[i, i] = M[i, i] - sum(L[i, k]**2*D[k, k] for k in range(i)) + + return M._new(L), M._new(D) + +def _LDLdecomposition_sparse(M, hermitian=True): + """ + Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix + ``A``, such that ``L * D * L.T == A``. ``A`` must be a square, + symmetric, positive-definite and non-singular. + + This method eliminates the use of square root and ensures that all + the diagonal entries of L are 1. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) + >>> L, D = A.LDLdecomposition() + >>> L + Matrix([ + [ 1, 0, 0], + [ 3/5, 1, 0], + [-1/5, 1/3, 1]]) + >>> D + Matrix([ + [25, 0, 0], + [ 0, 9, 0], + [ 0, 0, 9]]) + >>> L * D * L.T == A + True + + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if hermitian and not M.is_hermitian: + raise ValueError("Matrix must be Hermitian.") + if not hermitian and not M.is_symmetric(): + raise ValueError("Matrix must be symmetric.") + + dps = _get_intermediate_simp(expand_mul, expand_mul) + Lrowstruc = M.row_structure_symbolic_cholesky() + L = MutableDenseMatrix.eye(M.rows) + D = MutableDenseMatrix.zeros(M.rows, M.cols) + + for i in range(len(Lrowstruc)): + for j in Lrowstruc[i]: + if i != j: + L[i, j] = M[i, j] + summ = 0 + + for p1 in Lrowstruc[i]: + if p1 < j: + for p2 in Lrowstruc[j]: + if p2 < j: + if p1 == p2: + if hermitian: + summ += L[i, p1]*L[j, p1].conjugate()*D[p1, p1] + else: + summ += L[i, p1]*L[j, p1]*D[p1, p1] + else: + break + else: + break + + L[i, j] = dps((L[i, j] - summ) / D[j, j]) + + else: # i == j + D[i, i] = M[i, i] + summ = 0 + + for k in Lrowstruc[i]: + if k < i: + if hermitian: + summ += L[i, k]*L[i, k].conjugate()*D[k, k] + else: + summ += L[i, k]**2*D[k, k] + else: + break + + D[i, i] = dps(D[i, i] - summ) + + if hermitian and D[i, i].is_positive is False: + raise NonPositiveDefiniteMatrixError( + "Matrix must be positive-definite") + + return M._new(L), M._new(D) + + +def _LUdecomposition(M, iszerofunc=_iszero, simpfunc=None, rankcheck=False): + """Returns (L, U, perm) where L is a lower triangular matrix with unit + diagonal, U is an upper triangular matrix, and perm is a list of row + swap index pairs. If A is the original matrix, then + ``A = (L*U).permuteBkwd(perm)``, and the row permutation matrix P such + that $P A = L U$ can be computed by ``P = eye(A.rows).permuteFwd(perm)``. + + See documentation for LUCombined for details about the keyword argument + rankcheck, iszerofunc, and simpfunc. + + Parameters + ========== + + rankcheck : bool, optional + Determines if this function should detect the rank + deficiency of the matrixis and should raise a + ``ValueError``. + + iszerofunc : function, optional + A function which determines if a given expression is zero. + + The function should be a callable that takes a single + SymPy expression and returns a 3-valued boolean value + ``True``, ``False``, or ``None``. + + It is internally used by the pivot searching algorithm. + See the notes section for a more information about the + pivot searching algorithm. + + simpfunc : function or None, optional + A function that simplifies the input. + + If this is specified as a function, this function should be + a callable that takes a single SymPy expression and returns + an another SymPy expression that is algebraically + equivalent. + + If ``None``, it indicates that the pivot search algorithm + should not attempt to simplify any candidate pivots. + + It is internally used by the pivot searching algorithm. + See the notes section for a more information about the + pivot searching algorithm. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[4, 3], [6, 3]]) + >>> L, U, _ = a.LUdecomposition() + >>> L + Matrix([ + [ 1, 0], + [3/2, 1]]) + >>> U + Matrix([ + [4, 3], + [0, -3/2]]) + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.cholesky + sympy.matrices.dense.DenseMatrix.LDLdecomposition + QRdecomposition + LUdecomposition_Simple + LUdecompositionFF + LUsolve + """ + + combined, p = M.LUdecomposition_Simple(iszerofunc=iszerofunc, + simpfunc=simpfunc, rankcheck=rankcheck) + + # L is lower triangular ``M.rows x M.rows`` + # U is upper triangular ``M.rows x M.cols`` + # L has unit diagonal. For each column in combined, the subcolumn + # below the diagonal of combined is shared by L. + # If L has more columns than combined, then the remaining subcolumns + # below the diagonal of L are zero. + # The upper triangular portion of L and combined are equal. + def entry_L(i, j): + if i < j: + # Super diagonal entry + return M.zero + elif i == j: + return M.one + elif j < combined.cols: + return combined[i, j] + + # Subdiagonal entry of L with no corresponding + # entry in combined + return M.zero + + def entry_U(i, j): + return M.zero if i > j else combined[i, j] + + L = M._new(combined.rows, combined.rows, entry_L) + U = M._new(combined.rows, combined.cols, entry_U) + + return L, U, p + +def _LUdecomposition_Simple(M, iszerofunc=_iszero, simpfunc=None, + rankcheck=False): + r"""Compute the PLU decomposition of the matrix. + + Parameters + ========== + + rankcheck : bool, optional + Determines if this function should detect the rank + deficiency of the matrixis and should raise a + ``ValueError``. + + iszerofunc : function, optional + A function which determines if a given expression is zero. + + The function should be a callable that takes a single + SymPy expression and returns a 3-valued boolean value + ``True``, ``False``, or ``None``. + + It is internally used by the pivot searching algorithm. + See the notes section for a more information about the + pivot searching algorithm. + + simpfunc : function or None, optional + A function that simplifies the input. + + If this is specified as a function, this function should be + a callable that takes a single SymPy expression and returns + an another SymPy expression that is algebraically + equivalent. + + If ``None``, it indicates that the pivot search algorithm + should not attempt to simplify any candidate pivots. + + It is internally used by the pivot searching algorithm. + See the notes section for a more information about the + pivot searching algorithm. + + Returns + ======= + + (lu, row_swaps) : (Matrix, list) + If the original matrix is a $m, n$ matrix: + + *lu* is a $m, n$ matrix, which contains result of the + decomposition in a compressed form. See the notes section + to see how the matrix is compressed. + + *row_swaps* is a $m$-element list where each element is a + pair of row exchange indices. + + ``A = (L*U).permute_backward(perm)``, and the row + permutation matrix $P$ from the formula $P A = L U$ can be + computed by ``P=eye(A.row).permute_forward(perm)``. + + Raises + ====== + + ValueError + Raised if ``rankcheck=True`` and the matrix is found to + be rank deficient during the computation. + + Notes + ===== + + About the PLU decomposition: + + PLU decomposition is a generalization of a LU decomposition + which can be extended for rank-deficient matrices. + + It can further be generalized for non-square matrices, and this + is the notation that SymPy is using. + + PLU decomposition is a decomposition of a $m, n$ matrix $A$ in + the form of $P A = L U$ where + + * $L$ is a $m, m$ lower triangular matrix with unit diagonal + entries. + * $U$ is a $m, n$ upper triangular matrix. + * $P$ is a $m, m$ permutation matrix. + + So, for a square matrix, the decomposition would look like: + + .. math:: + L = \begin{bmatrix} + 1 & 0 & 0 & \cdots & 0 \\ + L_{1, 0} & 1 & 0 & \cdots & 0 \\ + L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & 1 + \end{bmatrix} + + .. math:: + U = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\ + 0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\ + 0 & 0 & U_{2, 2} & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + 0 & 0 & 0 & \cdots & U_{n-1, n-1} + \end{bmatrix} + + And for a matrix with more rows than the columns, + the decomposition would look like: + + .. math:: + L = \begin{bmatrix} + 1 & 0 & 0 & \cdots & 0 & 0 & \cdots & 0 \\ + L_{1, 0} & 1 & 0 & \cdots & 0 & 0 & \cdots & 0 \\ + L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 & 0 & \cdots & 0 \\ + \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots + & \vdots \\ + L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & 1 & 0 + & \cdots & 0 \\ + L_{n, 0} & L_{n, 1} & L_{n, 2} & \cdots & L_{n, n-1} & 1 + & \cdots & 0 \\ + \vdots & \vdots & \vdots & \ddots & \vdots & \vdots + & \ddots & \vdots \\ + L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & L_{m-1, n-1} + & 0 & \cdots & 1 \\ + \end{bmatrix} + + .. math:: + U = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\ + 0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\ + 0 & 0 & U_{2, 2} & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + 0 & 0 & 0 & \cdots & U_{n-1, n-1} \\ + 0 & 0 & 0 & \cdots & 0 \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + 0 & 0 & 0 & \cdots & 0 + \end{bmatrix} + + Finally, for a matrix with more columns than the rows, the + decomposition would look like: + + .. math:: + L = \begin{bmatrix} + 1 & 0 & 0 & \cdots & 0 \\ + L_{1, 0} & 1 & 0 & \cdots & 0 \\ + L_{2, 0} & L_{2, 1} & 1 & \cdots & 0 \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & 1 + \end{bmatrix} + + .. math:: + U = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, m-1} + & \cdots & U_{0, n-1} \\ + 0 & U_{1, 1} & U_{1, 2} & \cdots & U_{1, m-1} + & \cdots & U_{1, n-1} \\ + 0 & 0 & U_{2, 2} & \cdots & U_{2, m-1} + & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots + & \cdots & \vdots \\ + 0 & 0 & 0 & \cdots & U_{m-1, m-1} + & \cdots & U_{m-1, n-1} \\ + \end{bmatrix} + + About the compressed LU storage: + + The results of the decomposition are often stored in compressed + forms rather than returning $L$ and $U$ matrices individually. + + It may be less intiuitive, but it is commonly used for a lot of + numeric libraries because of the efficiency. + + The storage matrix is defined as following for this specific + method: + + * The subdiagonal elements of $L$ are stored in the subdiagonal + portion of $LU$, that is $LU_{i, j} = L_{i, j}$ whenever + $i > j$. + * The elements on the diagonal of $L$ are all 1, and are not + explicitly stored. + * $U$ is stored in the upper triangular portion of $LU$, that is + $LU_{i, j} = U_{i, j}$ whenever $i <= j$. + * For a case of $m > n$, the right side of the $L$ matrix is + trivial to store. + * For a case of $m < n$, the below side of the $U$ matrix is + trivial to store. + + So, for a square matrix, the compressed output matrix would be: + + .. math:: + LU = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\ + L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\ + L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots & U_{n-1, n-1} + \end{bmatrix} + + For a matrix with more rows than the columns, the compressed + output matrix would be: + + .. math:: + LU = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, n-1} \\ + L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, n-1} \\ + L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + L_{n-1, 0} & L_{n-1, 1} & L_{n-1, 2} & \cdots + & U_{n-1, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots + & L_{m-1, n-1} \\ + \end{bmatrix} + + For a matrix with more columns than the rows, the compressed + output matrix would be: + + .. math:: + LU = \begin{bmatrix} + U_{0, 0} & U_{0, 1} & U_{0, 2} & \cdots & U_{0, m-1} + & \cdots & U_{0, n-1} \\ + L_{1, 0} & U_{1, 1} & U_{1, 2} & \cdots & U_{1, m-1} + & \cdots & U_{1, n-1} \\ + L_{2, 0} & L_{2, 1} & U_{2, 2} & \cdots & U_{2, m-1} + & \cdots & U_{2, n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots + & \cdots & \vdots \\ + L_{m-1, 0} & L_{m-1, 1} & L_{m-1, 2} & \cdots & U_{m-1, m-1} + & \cdots & U_{m-1, n-1} \\ + \end{bmatrix} + + About the pivot searching algorithm: + + When a matrix contains symbolic entries, the pivot search algorithm + differs from the case where every entry can be categorized as zero or + nonzero. + The algorithm searches column by column through the submatrix whose + top left entry coincides with the pivot position. + If it exists, the pivot is the first entry in the current search + column that iszerofunc guarantees is nonzero. + If no such candidate exists, then each candidate pivot is simplified + if simpfunc is not None. + The search is repeated, with the difference that a candidate may be + the pivot if ``iszerofunc()`` cannot guarantee that it is nonzero. + In the second search the pivot is the first candidate that + iszerofunc can guarantee is nonzero. + If no such candidate exists, then the pivot is the first candidate + for which iszerofunc returns None. + If no such candidate exists, then the search is repeated in the next + column to the right. + The pivot search algorithm differs from the one in ``rref()``, which + relies on ``_find_reasonable_pivot()``. + Future versions of ``LUdecomposition_simple()`` may use + ``_find_reasonable_pivot()``. + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + LUdecompositionFF + LUsolve + """ + + if rankcheck: + # https://github.com/sympy/sympy/issues/9796 + pass + + if S.Zero in M.shape: + # Define LU decomposition of a matrix with no entries as a matrix + # of the same dimensions with all zero entries. + return M.zeros(M.rows, M.cols), [] + + dps = _get_intermediate_simp() + lu = M.as_mutable() + row_swaps = [] + + pivot_col = 0 + + for pivot_row in range(0, lu.rows - 1): + # Search for pivot. Prefer entry that iszeropivot determines + # is nonzero, over entry that iszeropivot cannot guarantee + # is zero. + # XXX ``_find_reasonable_pivot`` uses slow zero testing. Blocked by bug #10279 + # Future versions of LUdecomposition_simple can pass iszerofunc and simpfunc + # to _find_reasonable_pivot(). + # In pass 3 of _find_reasonable_pivot(), the predicate in ``if x.equals(S.Zero):`` + # calls sympy.simplify(), and not the simplification function passed in via + # the keyword argument simpfunc. + iszeropivot = True + + while pivot_col != M.cols and iszeropivot: + sub_col = (lu[r, pivot_col] for r in range(pivot_row, M.rows)) + + pivot_row_offset, pivot_value, is_assumed_non_zero, ind_simplified_pairs =\ + _find_reasonable_pivot_naive(sub_col, iszerofunc, simpfunc) + + iszeropivot = pivot_value is None + + if iszeropivot: + # All candidate pivots in this column are zero. + # Proceed to next column. + pivot_col += 1 + + if rankcheck and pivot_col != pivot_row: + # All entries including and below the pivot position are + # zero, which indicates that the rank of the matrix is + # strictly less than min(num rows, num cols) + # Mimic behavior of previous implementation, by throwing a + # ValueError. + raise ValueError("Rank of matrix is strictly less than" + " number of rows or columns." + " Pass keyword argument" + " rankcheck=False to compute" + " the LU decomposition of this matrix.") + + candidate_pivot_row = None if pivot_row_offset is None else pivot_row + pivot_row_offset + + if candidate_pivot_row is None and iszeropivot: + # If candidate_pivot_row is None and iszeropivot is True + # after pivot search has completed, then the submatrix + # below and to the right of (pivot_row, pivot_col) is + # all zeros, indicating that Gaussian elimination is + # complete. + return lu, row_swaps + + # Update entries simplified during pivot search. + for offset, val in ind_simplified_pairs: + lu[pivot_row + offset, pivot_col] = val + + if pivot_row != candidate_pivot_row: + # Row swap book keeping: + # Record which rows were swapped. + # Update stored portion of L factor by multiplying L on the + # left and right with the current permutation. + # Swap rows of U. + row_swaps.append([pivot_row, candidate_pivot_row]) + + # Update L. + lu[pivot_row, 0:pivot_row], lu[candidate_pivot_row, 0:pivot_row] = \ + lu[candidate_pivot_row, 0:pivot_row], lu[pivot_row, 0:pivot_row] + + # Swap pivot row of U with candidate pivot row. + lu[pivot_row, pivot_col:lu.cols], lu[candidate_pivot_row, pivot_col:lu.cols] = \ + lu[candidate_pivot_row, pivot_col:lu.cols], lu[pivot_row, pivot_col:lu.cols] + + # Introduce zeros below the pivot by adding a multiple of the + # pivot row to a row under it, and store the result in the + # row under it. + # Only entries in the target row whose index is greater than + # start_col may be nonzero. + start_col = pivot_col + 1 + + for row in range(pivot_row + 1, lu.rows): + # Store factors of L in the subcolumn below + # (pivot_row, pivot_row). + lu[row, pivot_row] = \ + dps(lu[row, pivot_col]/lu[pivot_row, pivot_col]) + + # Form the linear combination of the pivot row and the current + # row below the pivot row that zeros the entries below the pivot. + # Employing slicing instead of a loop here raises + # NotImplementedError: Cannot add Zero to MutableSparseMatrix + # in sympy/matrices/tests/test_sparse.py. + # c = pivot_row + 1 if pivot_row == pivot_col else pivot_col + for c in range(start_col, lu.cols): + lu[row, c] = dps(lu[row, c] - lu[row, pivot_row]*lu[pivot_row, c]) + + if pivot_row != pivot_col: + # matrix rank < min(num rows, num cols), + # so factors of L are not stored directly below the pivot. + # These entries are zero by construction, so don't bother + # computing them. + for row in range(pivot_row + 1, lu.rows): + lu[row, pivot_col] = M.zero + + pivot_col += 1 + + if pivot_col == lu.cols: + # All candidate pivots are zero implies that Gaussian + # elimination is complete. + return lu, row_swaps + + if rankcheck: + if iszerofunc( + lu[Min(lu.rows, lu.cols) - 1, Min(lu.rows, lu.cols) - 1]): + raise ValueError("Rank of matrix is strictly less than" + " number of rows or columns." + " Pass keyword argument" + " rankcheck=False to compute" + " the LU decomposition of this matrix.") + + return lu, row_swaps + +def _LUdecompositionFF(M): + """Compute a fraction-free LU decomposition. + + Returns 4 matrices P, L, D, U such that PA = L D**-1 U. + If the elements of the matrix belong to some integral domain I, then all + elements of L, D and U are guaranteed to belong to I. + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + LUdecomposition_Simple + LUsolve + + References + ========== + + .. [1] W. Zhou & D.J. Jeffrey, "Fraction-free matrix factors: new forms + for LU and QR factors". Frontiers in Computer Science in China, + Vol 2, no. 1, pp. 67-80, 2008. + """ + + from sympy.matrices import SparseMatrix + + zeros = SparseMatrix.zeros + eye = SparseMatrix.eye + n, m = M.rows, M.cols + U, L, P = M.as_mutable(), eye(n), eye(n) + DD = zeros(n, n) + oldpivot = 1 + + for k in range(n - 1): + if U[k, k] == 0: + for kpivot in range(k + 1, n): + if U[kpivot, k]: + break + else: + raise ValueError("Matrix is not full rank") + + U[k, k:], U[kpivot, k:] = U[kpivot, k:], U[k, k:] + L[k, :k], L[kpivot, :k] = L[kpivot, :k], L[k, :k] + P[k, :], P[kpivot, :] = P[kpivot, :], P[k, :] + + L [k, k] = Ukk = U[k, k] + DD[k, k] = oldpivot * Ukk + + for i in range(k + 1, n): + L[i, k] = Uik = U[i, k] + + for j in range(k + 1, m): + U[i, j] = (Ukk * U[i, j] - U[k, j] * Uik) / oldpivot + + U[i, k] = 0 + + oldpivot = Ukk + + DD[n - 1, n - 1] = oldpivot + + return P, L, DD, U + +def _singular_value_decomposition(A): + r"""Returns a Condensed Singular Value decomposition. + + Explanation + =========== + + A Singular Value decomposition is a decomposition in the form $A = U \Sigma V^H$ + where + + - $U, V$ are column orthogonal matrix. + - $\Sigma$ is a diagonal matrix, where the main diagonal contains singular + values of matrix A. + + A column orthogonal matrix satisfies + $\mathbb{I} = U^H U$ while a full orthogonal matrix satisfies + relation $\mathbb{I} = U U^H = U^H U$ where $\mathbb{I}$ is an identity + matrix with matching dimensions. + + For matrices which are not square or are rank-deficient, it is + sufficient to return a column orthogonal matrix because augmenting + them may introduce redundant computations. + In condensed Singular Value Decomposition we only return column orthogonal + matrices because of this reason + + If you want to augment the results to return a full orthogonal + decomposition, you should use the following procedures. + + - Augment the $U, V$ matrices with columns that are orthogonal to every + other columns and make it square. + - Augment the $\Sigma$ matrix with zero rows to make it have the same + shape as the original matrix. + + The procedure will be illustrated in the examples section. + + Examples + ======== + + we take a full rank matrix first: + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2],[2,1]]) + >>> U, S, V = A.singular_value_decomposition() + >>> U + Matrix([ + [ sqrt(2)/2, sqrt(2)/2], + [-sqrt(2)/2, sqrt(2)/2]]) + >>> S + Matrix([ + [1, 0], + [0, 3]]) + >>> V + Matrix([ + [-sqrt(2)/2, sqrt(2)/2], + [ sqrt(2)/2, sqrt(2)/2]]) + + If a matrix if square and full rank both U, V + are orthogonal in both directions + + >>> U * U.H + Matrix([ + [1, 0], + [0, 1]]) + >>> U.H * U + Matrix([ + [1, 0], + [0, 1]]) + + >>> V * V.H + Matrix([ + [1, 0], + [0, 1]]) + >>> V.H * V + Matrix([ + [1, 0], + [0, 1]]) + >>> A == U * S * V.H + True + + >>> C = Matrix([ + ... [1, 0, 0, 0, 2], + ... [0, 0, 3, 0, 0], + ... [0, 0, 0, 0, 0], + ... [0, 2, 0, 0, 0], + ... ]) + >>> U, S, V = C.singular_value_decomposition() + + >>> V.H * V + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> V * V.H + Matrix([ + [1/5, 0, 0, 0, 2/5], + [ 0, 1, 0, 0, 0], + [ 0, 0, 1, 0, 0], + [ 0, 0, 0, 0, 0], + [2/5, 0, 0, 0, 4/5]]) + + If you want to augment the results to be a full orthogonal + decomposition, you should augment $V$ with an another orthogonal + column. + + You are able to append an arbitrary standard basis that are linearly + independent to every other columns and you can run the Gram-Schmidt + process to make them augmented as orthogonal basis. + + >>> V_aug = V.row_join(Matrix([[0,0,0,0,1], + ... [0,0,0,1,0]]).H) + >>> V_aug = V_aug.QRdecomposition()[0] + >>> V_aug + Matrix([ + [0, sqrt(5)/5, 0, -2*sqrt(5)/5, 0], + [1, 0, 0, 0, 0], + [0, 0, 1, 0, 0], + [0, 0, 0, 0, 1], + [0, 2*sqrt(5)/5, 0, sqrt(5)/5, 0]]) + >>> V_aug.H * V_aug + Matrix([ + [1, 0, 0, 0, 0], + [0, 1, 0, 0, 0], + [0, 0, 1, 0, 0], + [0, 0, 0, 1, 0], + [0, 0, 0, 0, 1]]) + >>> V_aug * V_aug.H + Matrix([ + [1, 0, 0, 0, 0], + [0, 1, 0, 0, 0], + [0, 0, 1, 0, 0], + [0, 0, 0, 1, 0], + [0, 0, 0, 0, 1]]) + + Similarly we augment U + + >>> U_aug = U.row_join(Matrix([0,0,1,0])) + >>> U_aug = U_aug.QRdecomposition()[0] + >>> U_aug + Matrix([ + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1], + [1, 0, 0, 0]]) + + >>> U_aug.H * U_aug + Matrix([ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1]]) + >>> U_aug * U_aug.H + Matrix([ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1]]) + + We add 2 zero columns and one row to S + + >>> S_aug = S.col_join(Matrix([[0,0,0]])) + >>> S_aug = S_aug.row_join(Matrix([[0,0,0,0], + ... [0,0,0,0]]).H) + >>> S_aug + Matrix([ + [2, 0, 0, 0, 0], + [0, sqrt(5), 0, 0, 0], + [0, 0, 3, 0, 0], + [0, 0, 0, 0, 0]]) + + + + >>> U_aug * S_aug * V_aug.H == C + True + + """ + + AH = A.H + m, n = A.shape + if m >= n: + V, S = (AH * A).diagonalize() + + ranked = [] + for i, x in enumerate(S.diagonal()): + if not x.is_zero: + ranked.append(i) + + V = V[:, ranked] + + Singular_vals = [sqrt(S[i, i]) for i in range(S.rows) if i in ranked] + + S = S.diag(*Singular_vals) + V, _ = V.QRdecomposition() + U = A * V * S.inv() + else: + U, S = (A * AH).diagonalize() + + ranked = [] + for i, x in enumerate(S.diagonal()): + if not x.is_zero: + ranked.append(i) + + U = U[:, ranked] + Singular_vals = [sqrt(S[i, i]) for i in range(S.rows) if i in ranked] + + S = S.diag(*Singular_vals) + U, _ = U.QRdecomposition() + V = AH * U * S.inv() + + return U, S, V + +def _QRdecomposition_optional(M, normalize=True): + def dot(u, v): + return u.dot(v, hermitian=True) + + dps = _get_intermediate_simp(expand_mul, expand_mul) + + A = M.as_mutable() + ranked = [] + + Q = A + R = A.zeros(A.cols) + + for j in range(A.cols): + for i in range(j): + if Q[:, i].is_zero_matrix: + continue + + R[i, j] = dot(Q[:, i], Q[:, j]) / dot(Q[:, i], Q[:, i]) + R[i, j] = dps(R[i, j]) + Q[:, j] -= Q[:, i] * R[i, j] + + Q[:, j] = dps(Q[:, j]) + if Q[:, j].is_zero_matrix is not True: + ranked.append(j) + R[j, j] = M.one + + Q = Q.extract(range(Q.rows), ranked) + R = R.extract(ranked, range(R.cols)) + + if normalize: + # Normalization + for i in range(Q.cols): + norm = Q[:, i].norm() + Q[:, i] /= norm + R[i, :] *= norm + + return M.__class__(Q), M.__class__(R) + + +def _QRdecomposition(M): + r"""Returns a QR decomposition. + + Explanation + =========== + + A QR decomposition is a decomposition in the form $A = Q R$ + where + + - $Q$ is a column orthogonal matrix. + - $R$ is a upper triangular (trapezoidal) matrix. + + A column orthogonal matrix satisfies + $\mathbb{I} = Q^H Q$ while a full orthogonal matrix satisfies + relation $\mathbb{I} = Q Q^H = Q^H Q$ where $I$ is an identity + matrix with matching dimensions. + + For matrices which are not square or are rank-deficient, it is + sufficient to return a column orthogonal matrix because augmenting + them may introduce redundant computations. + And an another advantage of this is that you can easily inspect the + matrix rank by counting the number of columns of $Q$. + + If you want to augment the results to return a full orthogonal + decomposition, you should use the following procedures. + + - Augment the $Q$ matrix with columns that are orthogonal to every + other columns and make it square. + - Augment the $R$ matrix with zero rows to make it have the same + shape as the original matrix. + + The procedure will be illustrated in the examples section. + + Examples + ======== + + A full rank matrix example: + + >>> from sympy import Matrix + >>> A = Matrix([[12, -51, 4], [6, 167, -68], [-4, 24, -41]]) + >>> Q, R = A.QRdecomposition() + >>> Q + Matrix([ + [ 6/7, -69/175, -58/175], + [ 3/7, 158/175, 6/175], + [-2/7, 6/35, -33/35]]) + >>> R + Matrix([ + [14, 21, -14], + [ 0, 175, -70], + [ 0, 0, 35]]) + + If the matrix is square and full rank, the $Q$ matrix becomes + orthogonal in both directions, and needs no augmentation. + + >>> Q * Q.H + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> Q.H * Q + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + + >>> A == Q*R + True + + A rank deficient matrix example: + + >>> A = Matrix([[12, -51, 0], [6, 167, 0], [-4, 24, 0]]) + >>> Q, R = A.QRdecomposition() + >>> Q + Matrix([ + [ 6/7, -69/175], + [ 3/7, 158/175], + [-2/7, 6/35]]) + >>> R + Matrix([ + [14, 21, 0], + [ 0, 175, 0]]) + + QRdecomposition might return a matrix Q that is rectangular. + In this case the orthogonality condition might be satisfied as + $\mathbb{I} = Q.H*Q$ but not in the reversed product + $\mathbb{I} = Q * Q.H$. + + >>> Q.H * Q + Matrix([ + [1, 0], + [0, 1]]) + >>> Q * Q.H + Matrix([ + [27261/30625, 348/30625, -1914/6125], + [ 348/30625, 30589/30625, 198/6125], + [ -1914/6125, 198/6125, 136/1225]]) + + If you want to augment the results to be a full orthogonal + decomposition, you should augment $Q$ with an another orthogonal + column. + + You are able to append an identity matrix, + and you can run the Gram-Schmidt + process to make them augmented as orthogonal basis. + + >>> Q_aug = Q.row_join(Matrix.eye(3)) + >>> Q_aug = Q_aug.QRdecomposition()[0] + >>> Q_aug + Matrix([ + [ 6/7, -69/175, 58/175], + [ 3/7, 158/175, -6/175], + [-2/7, 6/35, 33/35]]) + >>> Q_aug.H * Q_aug + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> Q_aug * Q_aug.H + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + + Augmenting the $R$ matrix with zero row is straightforward. + + >>> R_aug = R.col_join(Matrix([[0, 0, 0]])) + >>> R_aug + Matrix([ + [14, 21, 0], + [ 0, 175, 0], + [ 0, 0, 0]]) + >>> Q_aug * R_aug == A + True + + A zero matrix example: + + >>> from sympy import Matrix + >>> A = Matrix.zeros(3, 4) + >>> Q, R = A.QRdecomposition() + + They may return matrices with zero rows and columns. + + >>> Q + Matrix(3, 0, []) + >>> R + Matrix(0, 4, []) + >>> Q*R + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]]) + + As the same augmentation rule described above, $Q$ can be augmented + with columns of an identity matrix and $R$ can be augmented with + rows of a zero matrix. + + >>> Q_aug = Q.row_join(Matrix.eye(3)) + >>> R_aug = R.col_join(Matrix.zeros(3, 4)) + >>> Q_aug * Q_aug.T + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> R_aug + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]]) + >>> Q_aug * R_aug == A + True + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.cholesky + sympy.matrices.dense.DenseMatrix.LDLdecomposition + sympy.matrices.matrixbase.MatrixBase.LUdecomposition + QRsolve + """ + return _QRdecomposition_optional(M, normalize=True) + +def _upper_hessenberg_decomposition(A): + """Converts a matrix into Hessenberg matrix H. + + Returns 2 matrices H, P s.t. + $P H P^{T} = A$, where H is an upper hessenberg matrix + and P is an orthogonal matrix + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([ + ... [1,2,3], + ... [-3,5,6], + ... [4,-8,9], + ... ]) + >>> H, P = A.upper_hessenberg_decomposition() + >>> H + Matrix([ + [1, 6/5, 17/5], + [5, 213/25, -134/25], + [0, 216/25, 137/25]]) + >>> P + Matrix([ + [1, 0, 0], + [0, -3/5, 4/5], + [0, 4/5, 3/5]]) + >>> P * H * P.H == A + True + + + References + ========== + + .. [#] https://mathworld.wolfram.com/HessenbergDecomposition.html + """ + + M = A.as_mutable() + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + + n = M.cols + P = M.eye(n) + H = M + + for j in range(n - 2): + + u = H[j + 1:, j] + + if u[1:, :].is_zero_matrix: + continue + + if sign(u[0]) != 0: + u[0] = u[0] + sign(u[0]) * u.norm() + else: + u[0] = u[0] + u.norm() + + v = u / u.norm() + + H[j + 1:, :] = H[j + 1:, :] - 2 * v * (v.H * H[j + 1:, :]) + H[:, j + 1:] = H[:, j + 1:] - (H[:, j + 1:] * (2 * v)) * v.H + P[:, j + 1:] = P[:, j + 1:] - (P[:, j + 1:] * (2 * v)) * v.H + + return H, P diff --git a/lib/python3.11/site-packages/sympy/matrices/dense.py b/lib/python3.11/site-packages/sympy/matrices/dense.py new file mode 100644 index 0000000000000000000000000000000000000000..8382da5d9b55249d2c6e2aa645743782a5bd7fa3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/dense.py @@ -0,0 +1,1093 @@ +import random + +from sympy.core.basic import Basic +from sympy.core.singleton import S +from sympy.core.symbol import Symbol +from sympy.core.sympify import sympify +from sympy.functions.elementary.trigonometric import cos, sin +from sympy.utilities.decorator import doctest_depends_on +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import is_sequence + +from .exceptions import ShapeError +from .decompositions import _cholesky, _LDLdecomposition +from .matrixbase import MatrixBase +from .repmatrix import MutableRepMatrix, RepMatrix +from .solvers import _lower_triangular_solve, _upper_triangular_solve + + +__doctest_requires__ = {('symarray',): ['numpy']} + + +def _iszero(x): + """Returns True if x is zero.""" + return x.is_zero + + +class DenseMatrix(RepMatrix): + """Matrix implementation based on DomainMatrix as the internal representation""" + + # + # DenseMatrix is a superclass for both MutableDenseMatrix and + # ImmutableDenseMatrix. Methods shared by both classes but not for the + # Sparse classes should be implemented here. + # + + is_MatrixExpr = False # type: bool + + _op_priority = 10.01 + _class_priority = 4 + + @property + def _mat(self): + sympy_deprecation_warning( + """ + The private _mat attribute of Matrix is deprecated. Use the + .flat() method instead. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-private-matrix-attributes" + ) + + return self.flat() + + def _eval_inverse(self, **kwargs): + return self.inv(method=kwargs.get('method', 'GE'), + iszerofunc=kwargs.get('iszerofunc', _iszero), + try_block_diag=kwargs.get('try_block_diag', False)) + + def as_immutable(self): + """Returns an Immutable version of this Matrix + """ + from .immutable import ImmutableDenseMatrix as cls + return cls._fromrep(self._rep.copy()) + + def as_mutable(self): + """Returns a mutable version of this matrix + + Examples + ======== + + >>> from sympy import ImmutableMatrix + >>> X = ImmutableMatrix([[1, 2], [3, 4]]) + >>> Y = X.as_mutable() + >>> Y[1, 1] = 5 # Can set values in Y + >>> Y + Matrix([ + [1, 2], + [3, 5]]) + """ + return Matrix(self) + + def cholesky(self, hermitian=True): + return _cholesky(self, hermitian=hermitian) + + def LDLdecomposition(self, hermitian=True): + return _LDLdecomposition(self, hermitian=hermitian) + + def lower_triangular_solve(self, rhs): + return _lower_triangular_solve(self, rhs) + + def upper_triangular_solve(self, rhs): + return _upper_triangular_solve(self, rhs) + + cholesky.__doc__ = _cholesky.__doc__ + LDLdecomposition.__doc__ = _LDLdecomposition.__doc__ + lower_triangular_solve.__doc__ = _lower_triangular_solve.__doc__ + upper_triangular_solve.__doc__ = _upper_triangular_solve.__doc__ + + +def _force_mutable(x): + """Return a matrix as a Matrix, otherwise return x.""" + if getattr(x, 'is_Matrix', False): + return x.as_mutable() + elif isinstance(x, Basic): + return x + elif hasattr(x, '__array__'): + a = x.__array__() + if len(a.shape) == 0: + return sympify(a) + return Matrix(x) + return x + + +class MutableDenseMatrix(DenseMatrix, MutableRepMatrix): + + def simplify(self, **kwargs): + """Applies simplify to the elements of a matrix in place. + + This is a shortcut for M.applyfunc(lambda x: simplify(x, ratio, measure)) + + See Also + ======== + + sympy.simplify.simplify.simplify + """ + from sympy.simplify.simplify import simplify as _simplify + for (i, j), element in self.todok().items(): + self[i, j] = _simplify(element, **kwargs) + + +MutableMatrix = Matrix = MutableDenseMatrix + +########### +# Numpy Utility Functions: +# list2numpy, matrix2numpy, symmarray +########### + + +def list2numpy(l, dtype=object): # pragma: no cover + """Converts Python list of SymPy expressions to a NumPy array. + + See Also + ======== + + matrix2numpy + """ + from numpy import empty + a = empty(len(l), dtype) + for i, s in enumerate(l): + a[i] = s + return a + + +def matrix2numpy(m, dtype=object): # pragma: no cover + """Converts SymPy's matrix to a NumPy array. + + See Also + ======== + + list2numpy + """ + from numpy import empty + a = empty(m.shape, dtype) + for i in range(m.rows): + for j in range(m.cols): + a[i, j] = m[i, j] + return a + + +########### +# Rotation matrices: +# rot_givens, rot_axis[123], rot_ccw_axis[123] +########### + + +def rot_givens(i, j, theta, dim=3): + r"""Returns a a Givens rotation matrix, a a rotation in the + plane spanned by two coordinates axes. + + Explanation + =========== + + The Givens rotation corresponds to a generalization of rotation + matrices to any number of dimensions, given by: + + .. math:: + G(i, j, \theta) = + \begin{bmatrix} + 1 & \cdots & 0 & \cdots & 0 & \cdots & 0 \\ + \vdots & \ddots & \vdots & & \vdots & & \vdots \\ + 0 & \cdots & c & \cdots & -s & \cdots & 0 \\ + \vdots & & \vdots & \ddots & \vdots & & \vdots \\ + 0 & \cdots & s & \cdots & c & \cdots & 0 \\ + \vdots & & \vdots & & \vdots & \ddots & \vdots \\ + 0 & \cdots & 0 & \cdots & 0 & \cdots & 1 + \end{bmatrix} + + Where $c = \cos(\theta)$ and $s = \sin(\theta)$ appear at the intersections + ``i``\th and ``j``\th rows and columns. + + For fixed ``i > j``\, the non-zero elements of a Givens matrix are + given by: + + - $g_{kk} = 1$ for $k \ne i,\,j$ + - $g_{kk} = c$ for $k = i,\,j$ + - $g_{ji} = -g_{ij} = -s$ + + Parameters + ========== + + i : int between ``0`` and ``dim - 1`` + Represents first axis + j : int between ``0`` and ``dim - 1`` + Represents second axis + dim : int bigger than 1 + Number of dimentions. Defaults to 3. + + Examples + ======== + + >>> from sympy import pi, rot_givens + + A counterclockwise rotation of pi/3 (60 degrees) around + the third axis (z-axis): + + >>> rot_givens(1, 0, pi/3) + Matrix([ + [ 1/2, -sqrt(3)/2, 0], + [sqrt(3)/2, 1/2, 0], + [ 0, 0, 1]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_givens(1, 0, pi/2) + Matrix([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1]]) + + This can be generalized to any number + of dimensions: + + >>> rot_givens(1, 0, pi/2, dim=4) + Matrix([ + [0, -1, 0, 0], + [1, 0, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Givens_rotation + + See Also + ======== + + rot_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (clockwise around the x axis) + rot_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (clockwise around the y axis) + rot_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (clockwise around the z axis) + rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (counterclockwise around the x axis) + rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (counterclockwise around the y axis) + rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (counterclockwise around the z axis) + """ + if not isinstance(dim, int) or dim < 2: + raise ValueError('dim must be an integer biggen than one, ' + 'got {}.'.format(dim)) + + if i == j: + raise ValueError('i and j must be different, ' + 'got ({}, {})'.format(i, j)) + + for ij in [i, j]: + if not isinstance(ij, int) or ij < 0 or ij > dim - 1: + raise ValueError('i and j must be integers between 0 and ' + '{}, got i={} and j={}.'.format(dim-1, i, j)) + + theta = sympify(theta) + c = cos(theta) + s = sin(theta) + M = eye(dim) + M[i, i] = c + M[j, j] = c + M[i, j] = s + M[j, i] = -s + return M + + +def rot_axis3(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + clockwise rotation around the `z`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + \cos(\theta) & \sin(\theta) & 0 \\ + -\sin(\theta) & \cos(\theta) & 0 \\ + 0 & 0 & 1 + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_axis3 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_axis3(theta) + Matrix([ + [ 1/2, sqrt(3)/2, 0], + [-sqrt(3)/2, 1/2, 0], + [ 0, 0, 1]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_axis3(pi/2) + Matrix([ + [ 0, 1, 0], + [-1, 0, 0], + [ 0, 0, 1]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (counterclockwise around the z axis) + rot_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (clockwise around the x axis) + rot_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (clockwise around the y axis) + """ + return rot_givens(0, 1, theta, dim=3) + + +def rot_axis2(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + clockwise rotation around the `y`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + \cos(\theta) & 0 & -\sin(\theta) \\ + 0 & 1 & 0 \\ + \sin(\theta) & 0 & \cos(\theta) + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_axis2 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_axis2(theta) + Matrix([ + [ 1/2, 0, -sqrt(3)/2], + [ 0, 1, 0], + [sqrt(3)/2, 0, 1/2]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_axis2(pi/2) + Matrix([ + [0, 0, -1], + [0, 1, 0], + [1, 0, 0]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (clockwise around the y axis) + rot_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (counterclockwise around the x axis) + rot_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (counterclockwise around the z axis) + """ + return rot_givens(2, 0, theta, dim=3) + + +def rot_axis1(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + clockwise rotation around the `x`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + 1 & 0 & 0 \\ + 0 & \cos(\theta) & \sin(\theta) \\ + 0 & -\sin(\theta) & \cos(\theta) + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_axis1 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_axis1(theta) + Matrix([ + [1, 0, 0], + [0, 1/2, sqrt(3)/2], + [0, -sqrt(3)/2, 1/2]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_axis1(pi/2) + Matrix([ + [1, 0, 0], + [0, 0, 1], + [0, -1, 0]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (counterclockwise around the x axis) + rot_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (clockwise around the y axis) + rot_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (clockwise around the z axis) + """ + return rot_givens(1, 2, theta, dim=3) + + +def rot_ccw_axis3(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + counterclockwise rotation around the `z`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + \cos(\theta) & -\sin(\theta) & 0 \\ + \sin(\theta) & \cos(\theta) & 0 \\ + 0 & 0 & 1 + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_ccw_axis3 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_ccw_axis3(theta) + Matrix([ + [ 1/2, -sqrt(3)/2, 0], + [sqrt(3)/2, 1/2, 0], + [ 0, 0, 1]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_ccw_axis3(pi/2) + Matrix([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (clockwise around the z axis) + rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (counterclockwise around the x axis) + rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (counterclockwise around the y axis) + """ + return rot_givens(1, 0, theta, dim=3) + + +def rot_ccw_axis2(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + counterclockwise rotation around the `y`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + \cos(\theta) & 0 & \sin(\theta) \\ + 0 & 1 & 0 \\ + -\sin(\theta) & 0 & \cos(\theta) + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_ccw_axis2 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_ccw_axis2(theta) + Matrix([ + [ 1/2, 0, sqrt(3)/2], + [ 0, 1, 0], + [-sqrt(3)/2, 0, 1/2]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_ccw_axis2(pi/2) + Matrix([ + [ 0, 0, 1], + [ 0, 1, 0], + [-1, 0, 0]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (clockwise around the y axis) + rot_ccw_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (counterclockwise around the x axis) + rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (counterclockwise around the z axis) + """ + return rot_givens(0, 2, theta, dim=3) + + +def rot_ccw_axis1(theta): + r"""Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis. + + Explanation + =========== + + For a right-handed coordinate system, this corresponds to a + counterclockwise rotation around the `x`-axis, given by: + + .. math:: + + R = \begin{bmatrix} + 1 & 0 & 0 \\ + 0 & \cos(\theta) & -\sin(\theta) \\ + 0 & \sin(\theta) & \cos(\theta) + \end{bmatrix} + + Examples + ======== + + >>> from sympy import pi, rot_ccw_axis1 + + A rotation of pi/3 (60 degrees): + + >>> theta = pi/3 + >>> rot_ccw_axis1(theta) + Matrix([ + [1, 0, 0], + [0, 1/2, -sqrt(3)/2], + [0, sqrt(3)/2, 1/2]]) + + If we rotate by pi/2 (90 degrees): + + >>> rot_ccw_axis1(pi/2) + Matrix([ + [1, 0, 0], + [0, 0, -1], + [0, 1, 0]]) + + See Also + ======== + + rot_givens: Returns a Givens rotation matrix (generalized rotation for + any number of dimensions) + rot_axis1: Returns a rotation matrix for a rotation of theta (in radians) + about the 1-axis (clockwise around the x axis) + rot_ccw_axis2: Returns a rotation matrix for a rotation of theta (in radians) + about the 2-axis (counterclockwise around the y axis) + rot_ccw_axis3: Returns a rotation matrix for a rotation of theta (in radians) + about the 3-axis (counterclockwise around the z axis) + """ + return rot_givens(2, 1, theta, dim=3) + + +@doctest_depends_on(modules=('numpy',)) +def symarray(prefix, shape, **kwargs): # pragma: no cover + r"""Create a numpy ndarray of symbols (as an object array). + + The created symbols are named ``prefix_i1_i2_``... You should thus provide a + non-empty prefix if you want your symbols to be unique for different output + arrays, as SymPy symbols with identical names are the same object. + + Parameters + ---------- + + prefix : string + A prefix prepended to the name of every symbol. + + shape : int or tuple + Shape of the created array. If an int, the array is one-dimensional; for + more than one dimension the shape must be a tuple. + + \*\*kwargs : dict + keyword arguments passed on to Symbol + + Examples + ======== + These doctests require numpy. + + >>> from sympy import symarray + >>> symarray('', 3) + [_0 _1 _2] + + If you want multiple symarrays to contain distinct symbols, you *must* + provide unique prefixes: + + >>> a = symarray('', 3) + >>> b = symarray('', 3) + >>> a[0] == b[0] + True + >>> a = symarray('a', 3) + >>> b = symarray('b', 3) + >>> a[0] == b[0] + False + + Creating symarrays with a prefix: + + >>> symarray('a', 3) + [a_0 a_1 a_2] + + For more than one dimension, the shape must be given as a tuple: + + >>> symarray('a', (2, 3)) + [[a_0_0 a_0_1 a_0_2] + [a_1_0 a_1_1 a_1_2]] + >>> symarray('a', (2, 3, 2)) + [[[a_0_0_0 a_0_0_1] + [a_0_1_0 a_0_1_1] + [a_0_2_0 a_0_2_1]] + + [[a_1_0_0 a_1_0_1] + [a_1_1_0 a_1_1_1] + [a_1_2_0 a_1_2_1]]] + + For setting assumptions of the underlying Symbols: + + >>> [s.is_real for s in symarray('a', 2, real=True)] + [True, True] + """ + from numpy import empty, ndindex + arr = empty(shape, dtype=object) + for index in ndindex(shape): + arr[index] = Symbol('%s_%s' % (prefix, '_'.join(map(str, index))), + **kwargs) + return arr + + +############### +# Functions +############### + +def casoratian(seqs, n, zero=True): + """Given linear difference operator L of order 'k' and homogeneous + equation Ly = 0 we want to compute kernel of L, which is a set + of 'k' sequences: a(n), b(n), ... z(n). + + Solutions of L are linearly independent iff their Casoratian, + denoted as C(a, b, ..., z), do not vanish for n = 0. + + Casoratian is defined by k x k determinant:: + + + a(n) b(n) . . . z(n) + + | a(n+1) b(n+1) . . . z(n+1) | + | . . . . | + | . . . . | + | . . . . | + + a(n+k-1) b(n+k-1) . . . z(n+k-1) + + + It proves very useful in rsolve_hyper() where it is applied + to a generating set of a recurrence to factor out linearly + dependent solutions and return a basis: + + >>> from sympy import Symbol, casoratian, factorial + >>> n = Symbol('n', integer=True) + + Exponential and factorial are linearly independent: + + >>> casoratian([2**n, factorial(n)], n) != 0 + True + + """ + + seqs = list(map(sympify, seqs)) + + if not zero: + f = lambda i, j: seqs[j].subs(n, n + i) + else: + f = lambda i, j: seqs[j].subs(n, i) + + k = len(seqs) + + return Matrix(k, k, f).det() + + +def eye(*args, **kwargs): + """Create square identity matrix n x n + + See Also + ======== + + diag + zeros + ones + """ + + return Matrix.eye(*args, **kwargs) + + +def diag(*values, strict=True, unpack=False, **kwargs): + """Returns a matrix with the provided values placed on the + diagonal. If non-square matrices are included, they will + produce a block-diagonal matrix. + + Examples + ======== + + This version of diag is a thin wrapper to Matrix.diag that differs + in that it treats all lists like matrices -- even when a single list + is given. If this is not desired, either put a `*` before the list or + set `unpack=True`. + + >>> from sympy import diag + + >>> diag([1, 2, 3], unpack=True) # = diag(1,2,3) or diag(*[1,2,3]) + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + + >>> diag([1, 2, 3]) # a column vector + Matrix([ + [1], + [2], + [3]]) + + See Also + ======== + .matrixbase.MatrixBase.eye + .matrixbase.MatrixBase.diagonal + .matrixbase.MatrixBase.diag + .expressions.blockmatrix.BlockMatrix + """ + return Matrix.diag(*values, strict=strict, unpack=unpack, **kwargs) + + +def GramSchmidt(vlist, orthonormal=False): + """Apply the Gram-Schmidt process to a set of vectors. + + Parameters + ========== + + vlist : List of Matrix + Vectors to be orthogonalized for. + + orthonormal : Bool, optional + If true, return an orthonormal basis. + + Returns + ======= + + vlist : List of Matrix + Orthogonalized vectors + + Notes + ===== + + This routine is mostly duplicate from ``Matrix.orthogonalize``, + except for some difference that this always raises error when + linearly dependent vectors are found, and the keyword ``normalize`` + has been named as ``orthonormal`` in this function. + + See Also + ======== + + .matrixbase.MatrixBase.orthogonalize + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process + """ + return MutableDenseMatrix.orthogonalize( + *vlist, normalize=orthonormal, rankcheck=True + ) + + +def hessian(f, varlist, constraints=()): + """Compute Hessian matrix for a function f wrt parameters in varlist + which may be given as a sequence or a row/column vector. A list of + constraints may optionally be given. + + Examples + ======== + + >>> from sympy import Function, hessian, pprint + >>> from sympy.abc import x, y + >>> f = Function('f')(x, y) + >>> g1 = Function('g')(x, y) + >>> g2 = x**2 + 3*y + >>> pprint(hessian(f, (x, y), [g1, g2])) + [ d d ] + [ 0 0 --(g(x, y)) --(g(x, y)) ] + [ dx dy ] + [ ] + [ 0 0 2*x 3 ] + [ ] + [ 2 2 ] + [d d d ] + [--(g(x, y)) 2*x ---(f(x, y)) -----(f(x, y))] + [dx 2 dy dx ] + [ dx ] + [ ] + [ 2 2 ] + [d d d ] + [--(g(x, y)) 3 -----(f(x, y)) ---(f(x, y)) ] + [dy dy dx 2 ] + [ dy ] + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hessian_matrix + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.jacobian + wronskian + """ + # f is the expression representing a function f, return regular matrix + if isinstance(varlist, MatrixBase): + if 1 not in varlist.shape: + raise ShapeError("`varlist` must be a column or row vector.") + if varlist.cols == 1: + varlist = varlist.T + varlist = varlist.tolist()[0] + if is_sequence(varlist): + n = len(varlist) + if not n: + raise ShapeError("`len(varlist)` must not be zero.") + else: + raise ValueError("Improper variable list in hessian function") + if not getattr(f, 'diff'): + # check differentiability + raise ValueError("Function `f` (%s) is not differentiable" % f) + m = len(constraints) + N = m + n + out = zeros(N) + for k, g in enumerate(constraints): + if not getattr(g, 'diff'): + # check differentiability + raise ValueError("Function `f` (%s) is not differentiable" % f) + for i in range(n): + out[k, i + m] = g.diff(varlist[i]) + for i in range(n): + for j in range(i, n): + out[i + m, j + m] = f.diff(varlist[i]).diff(varlist[j]) + for i in range(N): + for j in range(i + 1, N): + out[j, i] = out[i, j] + return out + + +def jordan_cell(eigenval, n): + """ + Create a Jordan block: + + Examples + ======== + + >>> from sympy import jordan_cell + >>> from sympy.abc import x + >>> jordan_cell(x, 4) + Matrix([ + [x, 1, 0, 0], + [0, x, 1, 0], + [0, 0, x, 1], + [0, 0, 0, x]]) + """ + + return Matrix.jordan_block(size=n, eigenvalue=eigenval) + + +def matrix_multiply_elementwise(A, B): + """Return the Hadamard product (elementwise product) of A and B + + >>> from sympy import Matrix, matrix_multiply_elementwise + >>> A = Matrix([[0, 1, 2], [3, 4, 5]]) + >>> B = Matrix([[1, 10, 100], [100, 10, 1]]) + >>> matrix_multiply_elementwise(A, B) + Matrix([ + [ 0, 10, 200], + [300, 40, 5]]) + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.__mul__ + """ + return A.multiply_elementwise(B) + + +def ones(*args, **kwargs): + """Returns a matrix of ones with ``rows`` rows and ``cols`` columns; + if ``cols`` is omitted a square matrix will be returned. + + See Also + ======== + + zeros + eye + diag + """ + + if 'c' in kwargs: + kwargs['cols'] = kwargs.pop('c') + + return Matrix.ones(*args, **kwargs) + + +def randMatrix(r, c=None, min=0, max=99, seed=None, symmetric=False, + percent=100, prng=None): + """Create random matrix with dimensions ``r`` x ``c``. If ``c`` is omitted + the matrix will be square. If ``symmetric`` is True the matrix must be + square. If ``percent`` is less than 100 then only approximately the given + percentage of elements will be non-zero. + + The pseudo-random number generator used to generate matrix is chosen in the + following way. + + * If ``prng`` is supplied, it will be used as random number generator. + It should be an instance of ``random.Random``, or at least have + ``randint`` and ``shuffle`` methods with same signatures. + * if ``prng`` is not supplied but ``seed`` is supplied, then new + ``random.Random`` with given ``seed`` will be created; + * otherwise, a new ``random.Random`` with default seed will be used. + + Examples + ======== + + >>> from sympy import randMatrix + >>> randMatrix(3) # doctest:+SKIP + [25, 45, 27] + [44, 54, 9] + [23, 96, 46] + >>> randMatrix(3, 2) # doctest:+SKIP + [87, 29] + [23, 37] + [90, 26] + >>> randMatrix(3, 3, 0, 2) # doctest:+SKIP + [0, 2, 0] + [2, 0, 1] + [0, 0, 1] + >>> randMatrix(3, symmetric=True) # doctest:+SKIP + [85, 26, 29] + [26, 71, 43] + [29, 43, 57] + >>> A = randMatrix(3, seed=1) + >>> B = randMatrix(3, seed=2) + >>> A == B + False + >>> A == randMatrix(3, seed=1) + True + >>> randMatrix(3, symmetric=True, percent=50) # doctest:+SKIP + [77, 70, 0], + [70, 0, 0], + [ 0, 0, 88] + """ + # Note that ``Random()`` is equivalent to ``Random(None)`` + prng = prng or random.Random(seed) + + if c is None: + c = r + + if symmetric and r != c: + raise ValueError('For symmetric matrices, r must equal c, but %i != %i' % (r, c)) + + ij = range(r * c) + if percent != 100: + ij = prng.sample(ij, int(len(ij)*percent // 100)) + + m = zeros(r, c) + + if not symmetric: + for ijk in ij: + i, j = divmod(ijk, c) + m[i, j] = prng.randint(min, max) + else: + for ijk in ij: + i, j = divmod(ijk, c) + if i <= j: + m[i, j] = m[j, i] = prng.randint(min, max) + + return m + + +def wronskian(functions, var, method='bareiss'): + """ + Compute Wronskian for [] of functions + + :: + + | f1 f2 ... fn | + | f1' f2' ... fn' | + | . . . . | + W(f1, ..., fn) = | . . . . | + | . . . . | + | (n) (n) (n) | + | D (f1) D (f2) ... D (fn) | + + see: https://en.wikipedia.org/wiki/Wronskian + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.jacobian + hessian + """ + + functions = [sympify(f) for f in functions] + n = len(functions) + if n == 0: + return S.One + W = Matrix(n, n, lambda i, j: functions[i].diff(var, j)) + return W.det(method) + + +def zeros(*args, **kwargs): + """Returns a matrix of zeros with ``rows`` rows and ``cols`` columns; + if ``cols`` is omitted a square matrix will be returned. + + See Also + ======== + + ones + eye + diag + """ + + if 'c' in kwargs: + kwargs['cols'] = kwargs.pop('c') + + return Matrix.zeros(*args, **kwargs) diff --git a/lib/python3.11/site-packages/sympy/matrices/determinant.py b/lib/python3.11/site-packages/sympy/matrices/determinant.py new file mode 100644 index 0000000000000000000000000000000000000000..d85f8a5eae66b425d5f77bc7b085e7c86aae7803 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/determinant.py @@ -0,0 +1,1021 @@ +from types import FunctionType + +from sympy.core.cache import cacheit +from sympy.core.numbers import Float, Integer +from sympy.core.singleton import S +from sympy.core.symbol import uniquely_named_symbol +from sympy.core.mul import Mul +from sympy.polys import PurePoly, cancel +from sympy.functions.combinatorial.numbers import nC +from sympy.polys.matrices.domainmatrix import DomainMatrix +from sympy.polys.matrices.ddm import DDM + +from .exceptions import NonSquareMatrixError +from .utilities import ( + _get_intermediate_simp, _get_intermediate_simp_bool, + _iszero, _is_zero_after_expand_mul, _dotprodsimp, _simplify) + + +def _find_reasonable_pivot(col, iszerofunc=_iszero, simpfunc=_simplify): + """ Find the lowest index of an item in ``col`` that is + suitable for a pivot. If ``col`` consists only of + Floats, the pivot with the largest norm is returned. + Otherwise, the first element where ``iszerofunc`` returns + False is used. If ``iszerofunc`` does not return false, + items are simplified and retested until a suitable + pivot is found. + + Returns a 4-tuple + (pivot_offset, pivot_val, assumed_nonzero, newly_determined) + where pivot_offset is the index of the pivot, pivot_val is + the (possibly simplified) value of the pivot, assumed_nonzero + is True if an assumption that the pivot was non-zero + was made without being proved, and newly_determined are + elements that were simplified during the process of pivot + finding.""" + + newly_determined = [] + col = list(col) + # a column that contains a mix of floats and integers + # but at least one float is considered a numerical + # column, and so we do partial pivoting + if all(isinstance(x, (Float, Integer)) for x in col) and any( + isinstance(x, Float) for x in col): + col_abs = [abs(x) for x in col] + max_value = max(col_abs) + if iszerofunc(max_value): + # just because iszerofunc returned True, doesn't + # mean the value is numerically zero. Make sure + # to replace all entries with numerical zeros + if max_value != 0: + newly_determined = [(i, 0) for i, x in enumerate(col) if x != 0] + return (None, None, False, newly_determined) + index = col_abs.index(max_value) + return (index, col[index], False, newly_determined) + + # PASS 1 (iszerofunc directly) + possible_zeros = [] + for i, x in enumerate(col): + is_zero = iszerofunc(x) + # is someone wrote a custom iszerofunc, it may return + # BooleanFalse or BooleanTrue instead of True or False, + # so use == for comparison instead of `is` + if is_zero == False: + # we found something that is definitely not zero + return (i, x, False, newly_determined) + possible_zeros.append(is_zero) + + # by this point, we've found no certain non-zeros + if all(possible_zeros): + # if everything is definitely zero, we have + # no pivot + return (None, None, False, newly_determined) + + # PASS 2 (iszerofunc after simplify) + # we haven't found any for-sure non-zeros, so + # go through the elements iszerofunc couldn't + # make a determination about and opportunistically + # simplify to see if we find something + for i, x in enumerate(col): + if possible_zeros[i] is not None: + continue + simped = simpfunc(x) + is_zero = iszerofunc(simped) + if is_zero in (True, False): + newly_determined.append((i, simped)) + if is_zero == False: + return (i, simped, False, newly_determined) + possible_zeros[i] = is_zero + + # after simplifying, some things that were recognized + # as zeros might be zeros + if all(possible_zeros): + # if everything is definitely zero, we have + # no pivot + return (None, None, False, newly_determined) + + # PASS 3 (.equals(0)) + # some expressions fail to simplify to zero, but + # ``.equals(0)`` evaluates to True. As a last-ditch + # attempt, apply ``.equals`` to these expressions + for i, x in enumerate(col): + if possible_zeros[i] is not None: + continue + if x.equals(S.Zero): + # ``.iszero`` may return False with + # an implicit assumption (e.g., ``x.equals(0)`` + # when ``x`` is a symbol), so only treat it + # as proved when ``.equals(0)`` returns True + possible_zeros[i] = True + newly_determined.append((i, S.Zero)) + + if all(possible_zeros): + return (None, None, False, newly_determined) + + # at this point there is nothing that could definitely + # be a pivot. To maintain compatibility with existing + # behavior, we'll assume that an illdetermined thing is + # non-zero. We should probably raise a warning in this case + i = possible_zeros.index(None) + return (i, col[i], True, newly_determined) + + +def _find_reasonable_pivot_naive(col, iszerofunc=_iszero, simpfunc=None): + """ + Helper that computes the pivot value and location from a + sequence of contiguous matrix column elements. As a side effect + of the pivot search, this function may simplify some of the elements + of the input column. A list of these simplified entries and their + indices are also returned. + This function mimics the behavior of _find_reasonable_pivot(), + but does less work trying to determine if an indeterminate candidate + pivot simplifies to zero. This more naive approach can be much faster, + with the trade-off that it may erroneously return a pivot that is zero. + + ``col`` is a sequence of contiguous column entries to be searched for + a suitable pivot. + ``iszerofunc`` is a callable that returns a Boolean that indicates + if its input is zero, or None if no such determination can be made. + ``simpfunc`` is a callable that simplifies its input. It must return + its input if it does not simplify its input. Passing in + ``simpfunc=None`` indicates that the pivot search should not attempt + to simplify any candidate pivots. + + Returns a 4-tuple: + (pivot_offset, pivot_val, assumed_nonzero, newly_determined) + ``pivot_offset`` is the sequence index of the pivot. + ``pivot_val`` is the value of the pivot. + pivot_val and col[pivot_index] are equivalent, but will be different + when col[pivot_index] was simplified during the pivot search. + ``assumed_nonzero`` is a boolean indicating if the pivot cannot be + guaranteed to be zero. If assumed_nonzero is true, then the pivot + may or may not be non-zero. If assumed_nonzero is false, then + the pivot is non-zero. + ``newly_determined`` is a list of index-value pairs of pivot candidates + that were simplified during the pivot search. + """ + + # indeterminates holds the index-value pairs of each pivot candidate + # that is neither zero or non-zero, as determined by iszerofunc(). + # If iszerofunc() indicates that a candidate pivot is guaranteed + # non-zero, or that every candidate pivot is zero then the contents + # of indeterminates are unused. + # Otherwise, the only viable candidate pivots are symbolic. + # In this case, indeterminates will have at least one entry, + # and all but the first entry are ignored when simpfunc is None. + indeterminates = [] + for i, col_val in enumerate(col): + col_val_is_zero = iszerofunc(col_val) + if col_val_is_zero == False: + # This pivot candidate is non-zero. + return i, col_val, False, [] + elif col_val_is_zero is None: + # The candidate pivot's comparison with zero + # is indeterminate. + indeterminates.append((i, col_val)) + + if len(indeterminates) == 0: + # All candidate pivots are guaranteed to be zero, i.e. there is + # no pivot. + return None, None, False, [] + + if simpfunc is None: + # Caller did not pass in a simplification function that might + # determine if an indeterminate pivot candidate is guaranteed + # to be nonzero, so assume the first indeterminate candidate + # is non-zero. + return indeterminates[0][0], indeterminates[0][1], True, [] + + # newly_determined holds index-value pairs of candidate pivots + # that were simplified during the search for a non-zero pivot. + newly_determined = [] + for i, col_val in indeterminates: + tmp_col_val = simpfunc(col_val) + if id(col_val) != id(tmp_col_val): + # simpfunc() simplified this candidate pivot. + newly_determined.append((i, tmp_col_val)) + if iszerofunc(tmp_col_val) == False: + # Candidate pivot simplified to a guaranteed non-zero value. + return i, tmp_col_val, False, newly_determined + + return indeterminates[0][0], indeterminates[0][1], True, newly_determined + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _berkowitz_toeplitz_matrix(M): + """Return (A,T) where T the Toeplitz matrix used in the Berkowitz algorithm + corresponding to ``M`` and A is the first principal submatrix. + """ + + # the 0 x 0 case is trivial + if M.rows == 0 and M.cols == 0: + return M._new(1,1, [M.one]) + + # + # Partition M = [ a_11 R ] + # [ C A ] + # + + a, R = M[0,0], M[0, 1:] + C, A = M[1:, 0], M[1:,1:] + + # + # The Toeplitz matrix looks like + # + # [ 1 ] + # [ -a 1 ] + # [ -RC -a 1 ] + # [ -RAC -RC -a 1 ] + # [ -RA**2C -RAC -RC -a 1 ] + # etc. + + # Compute the diagonal entries. + # Because multiplying matrix times vector is so much + # more efficient than matrix times matrix, recursively + # compute -R * A**n * C. + diags = [C] + for i in range(M.rows - 2): + diags.append(A.multiply(diags[i], dotprodsimp=None)) + diags = [(-R).multiply(d, dotprodsimp=None)[0, 0] for d in diags] + diags = [M.one, -a] + diags + + def entry(i,j): + if j > i: + return M.zero + return diags[i - j] + + toeplitz = M._new(M.cols + 1, M.rows, entry) + return (A, toeplitz) + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _berkowitz_vector(M): + """ Run the Berkowitz algorithm and return a vector whose entries + are the coefficients of the characteristic polynomial of ``M``. + + Given N x N matrix, efficiently compute + coefficients of characteristic polynomials of ``M`` + without division in the ground domain. + + This method is particularly useful for computing determinant, + principal minors and characteristic polynomial when ``M`` + has complicated coefficients e.g. polynomials. Semi-direct + usage of this algorithm is also important in computing + efficiently sub-resultant PRS. + + Assuming that M is a square matrix of dimension N x N and + I is N x N identity matrix, then the Berkowitz vector is + an N x 1 vector whose entries are coefficients of the + polynomial + + charpoly(M) = det(t*I - M) + + As a consequence, all polynomials generated by Berkowitz + algorithm are monic. + + For more information on the implemented algorithm refer to: + + [1] S.J. Berkowitz, On computing the determinant in small + parallel time using a small number of processors, ACM, + Information Processing Letters 18, 1984, pp. 147-150 + + [2] M. Keber, Division-Free computation of sub-resultants + using Bezout matrices, Tech. Report MPI-I-2006-1-006, + Saarbrucken, 2006 + """ + + # handle the trivial cases + if M.rows == 0 and M.cols == 0: + return M._new(1, 1, [M.one]) + elif M.rows == 1 and M.cols == 1: + return M._new(2, 1, [M.one, -M[0,0]]) + + submat, toeplitz = _berkowitz_toeplitz_matrix(M) + + return toeplitz.multiply(_berkowitz_vector(submat), dotprodsimp=None) + + +def _adjugate(M, method="berkowitz"): + """Returns the adjugate, or classical adjoint, of + a matrix. That is, the transpose of the matrix of cofactors. + + https://en.wikipedia.org/wiki/Adjugate + + Parameters + ========== + + method : string, optional + Method to use to find the cofactors, can be "bareiss", "berkowitz", + "bird", "laplace" or "lu". + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2], [3, 4]]) + >>> M.adjugate() + Matrix([ + [ 4, -2], + [-3, 1]]) + + See Also + ======== + + cofactor_matrix + sympy.matrices.matrixbase.MatrixBase.transpose + """ + + return M.cofactor_matrix(method=method).transpose() + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _charpoly(M, x='lambda', simplify=_simplify): + """Computes characteristic polynomial det(x*I - M) where I is + the identity matrix. + + A PurePoly is returned, so using different variables for ``x`` does + not affect the comparison or the polynomials: + + Parameters + ========== + + x : string, optional + Name for the "lambda" variable, defaults to "lambda". + + simplify : function, optional + Simplification function to use on the characteristic polynomial + calculated. Defaults to ``simplify``. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[1, 3], [2, 0]]) + >>> M.charpoly() + PurePoly(lambda**2 - lambda - 6, lambda, domain='ZZ') + >>> M.charpoly(x) == M.charpoly(y) + True + >>> M.charpoly(x) == M.charpoly(y) + True + + Specifying ``x`` is optional; a symbol named ``lambda`` is used by + default (which looks good when pretty-printed in unicode): + + >>> M.charpoly().as_expr() + lambda**2 - lambda - 6 + + And if ``x`` clashes with an existing symbol, underscores will + be prepended to the name to make it unique: + + >>> M = Matrix([[1, 2], [x, 0]]) + >>> M.charpoly(x).as_expr() + _x**2 - _x - 2*x + + Whether you pass a symbol or not, the generator can be obtained + with the gen attribute since it may not be the same as the symbol + that was passed: + + >>> M.charpoly(x).gen + _x + >>> M.charpoly(x).gen == x + False + + Notes + ===== + + The Samuelson-Berkowitz algorithm is used to compute + the characteristic polynomial efficiently and without any + division operations. Thus the characteristic polynomial over any + commutative ring without zero divisors can be computed. + + If the determinant det(x*I - M) can be found out easily as + in the case of an upper or a lower triangular matrix, then + instead of Samuelson-Berkowitz algorithm, eigenvalues are computed + and the characteristic polynomial with their help. + + See Also + ======== + + det + """ + + if not M.is_square: + raise NonSquareMatrixError() + + # Use DomainMatrix. We are already going to convert this to a Poly so there + # is no need to worry about expanding powers etc. Also since this algorithm + # does not require division or zero detection it is fine to use EX. + # + # M.to_DM() will fall back on EXRAW rather than EX. EXRAW is a lot faster + # for elementary arithmetic because it does not call cancel for each + # operation but it generates large unsimplified results that are slow in + # the subsequent call to simplify. Using EX instead is faster overall + # but at least in some cases EXRAW+simplify gives a simpler result so we + # preserve that existing behaviour of charpoly for now... + dM = M.to_DM() + + K = dM.domain + + cp = dM.charpoly() + + x = uniquely_named_symbol(x, [M], modify=lambda s: '_' + s) + + if K.is_EXRAW or simplify is not _simplify: + # XXX: Converting back to Expr is expensive. We only do it if the + # caller supplied a custom simplify function for backwards + # compatibility or otherwise if the domain was EX. For any other domain + # there should be no benefit in simplifying at this stage because Poly + # will put everything into canonical form anyway. + berk_vector = [K.to_sympy(c) for c in cp] + berk_vector = [simplify(a) for a in berk_vector] + p = PurePoly(berk_vector, x) + + else: + # Convert from the list of domain elements directly to Poly. + p = PurePoly(cp, x, domain=K) + + return p + + +def _cofactor(M, i, j, method="berkowitz"): + """Calculate the cofactor of an element. + + Parameters + ========== + + method : string, optional + Method to use to find the cofactors, can be "bareiss", "berkowitz", + "bird", "laplace" or "lu". + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2], [3, 4]]) + >>> M.cofactor(0, 1) + -3 + + See Also + ======== + + cofactor_matrix + minor + minor_submatrix + """ + + if not M.is_square or M.rows < 1: + raise NonSquareMatrixError() + + return S.NegativeOne**((i + j) % 2) * M.minor(i, j, method) + + +def _cofactor_matrix(M, method="berkowitz"): + """Return a matrix containing the cofactor of each element. + + Parameters + ========== + + method : string, optional + Method to use to find the cofactors, can be "bareiss", "berkowitz", + "bird", "laplace" or "lu". + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2], [3, 4]]) + >>> M.cofactor_matrix() + Matrix([ + [ 4, -3], + [-2, 1]]) + + See Also + ======== + + cofactor + minor + minor_submatrix + """ + + if not M.is_square: + raise NonSquareMatrixError() + + return M._new(M.rows, M.cols, + lambda i, j: M.cofactor(i, j, method)) + +def _per(M): + """Returns the permanent of a matrix. Unlike determinant, + permanent is defined for both square and non-square matrices. + + For an m x n matrix, with m less than or equal to n, + it is given as the sum over the permutations s of size + less than or equal to m on [1, 2, . . . n] of the product + from i = 1 to m of M[i, s[i]]. Taking the transpose will + not affect the value of the permanent. + + In the case of a square matrix, this is the same as the permutation + definition of the determinant, but it does not take the sign of the + permutation into account. Computing the permanent with this definition + is quite inefficient, so here the Ryser formula is used. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> M.per() + 450 + >>> M = Matrix([1, 5, 7]) + >>> M.per() + 13 + + References + ========== + + .. [1] Prof. Frank Ben's notes: https://math.berkeley.edu/~bernd/ban275.pdf + .. [2] Wikipedia article on Permanent: https://en.wikipedia.org/wiki/Permanent_%28mathematics%29 + .. [3] https://reference.wolfram.com/language/ref/Permanent.html + .. [4] Permanent of a rectangular matrix : https://arxiv.org/pdf/0904.3251.pdf + """ + import itertools + + m, n = M.shape + if m > n: + M = M.T + m, n = n, m + s = list(range(n)) + + subsets = [] + for i in range(1, m + 1): + subsets += list(map(list, itertools.combinations(s, i))) + + perm = 0 + for subset in subsets: + prod = 1 + sub_len = len(subset) + for i in range(m): + prod *= sum(M[i, j] for j in subset) + perm += prod * S.NegativeOne**sub_len * nC(n - sub_len, m - sub_len) + perm *= S.NegativeOne**m + return perm.simplify() + +def _det_DOM(M): + DOM = DomainMatrix.from_Matrix(M, field=True, extension=True) + K = DOM.domain + return K.to_sympy(DOM.det()) + +# This functions is a candidate for caching if it gets implemented for matrices. +def _det(M, method="bareiss", iszerofunc=None): + """Computes the determinant of a matrix if ``M`` is a concrete matrix object + otherwise return an expressions ``Determinant(M)`` if ``M`` is a + ``MatrixSymbol`` or other expression. + + Parameters + ========== + + method : string, optional + Specifies the algorithm used for computing the matrix determinant. + + If the matrix is at most 3x3, a hard-coded formula is used and the + specified method is ignored. Otherwise, it defaults to + ``'bareiss'``. + + Also, if the matrix is an upper or a lower triangular matrix, determinant + is computed by simple multiplication of diagonal elements, and the + specified method is ignored. + + If it is set to ``'domain-ge'``, then Gaussian elimination method will + be used via using DomainMatrix. + + If it is set to ``'bareiss'``, Bareiss' fraction-free algorithm will + be used. + + If it is set to ``'berkowitz'``, Berkowitz' algorithm will be used. + + If it is set to ``'bird'``, Bird's algorithm will be used [1]_. + + If it is set to ``'laplace'``, Laplace's algorithm will be used. + + Otherwise, if it is set to ``'lu'``, LU decomposition will be used. + + .. note:: + For backward compatibility, legacy keys like "bareis" and + "det_lu" can still be used to indicate the corresponding + methods. + And the keys are also case-insensitive for now. However, it is + suggested to use the precise keys for specifying the method. + + iszerofunc : FunctionType or None, optional + If it is set to ``None``, it will be defaulted to ``_iszero`` if the + method is set to ``'bareiss'``, and ``_is_zero_after_expand_mul`` if + the method is set to ``'lu'``. + + It can also accept any user-specified zero testing function, if it + is formatted as a function which accepts a single symbolic argument + and returns ``True`` if it is tested as zero and ``False`` if it + tested as non-zero, and also ``None`` if it is undecidable. + + Returns + ======= + + det : Basic + Result of determinant. + + Raises + ====== + + ValueError + If unrecognized keys are given for ``method`` or ``iszerofunc``. + + NonSquareMatrixError + If attempted to calculate determinant from a non-square matrix. + + Examples + ======== + + >>> from sympy import Matrix, eye, det + >>> I3 = eye(3) + >>> det(I3) + 1 + >>> M = Matrix([[1, 2], [3, 4]]) + >>> det(M) + -2 + >>> det(M) == M.det() + True + >>> M.det(method="domain-ge") + -2 + + References + ========== + + .. [1] Bird, R. S. (2011). A simple division-free algorithm for computing + determinants. Inf. Process. Lett., 111(21), 1072-1074. doi: + 10.1016/j.ipl.2011.08.006 + """ + + # sanitize `method` + method = method.lower() + + if method == "bareis": + method = "bareiss" + elif method == "det_lu": + method = "lu" + + if method not in ("bareiss", "berkowitz", "lu", "domain-ge", "bird", + "laplace"): + raise ValueError("Determinant method '%s' unrecognized" % method) + + if iszerofunc is None: + if method == "bareiss": + iszerofunc = _is_zero_after_expand_mul + elif method == "lu": + iszerofunc = _iszero + + elif not isinstance(iszerofunc, FunctionType): + raise ValueError("Zero testing method '%s' unrecognized" % iszerofunc) + + n = M.rows + + if n == M.cols: # square check is done in individual method functions + if n == 0: + return M.one + elif n == 1: + return M[0, 0] + elif n == 2: + m = M[0, 0] * M[1, 1] - M[0, 1] * M[1, 0] + return _get_intermediate_simp(_dotprodsimp)(m) + elif n == 3: + m = (M[0, 0] * M[1, 1] * M[2, 2] + + M[0, 1] * M[1, 2] * M[2, 0] + + M[0, 2] * M[1, 0] * M[2, 1] + - M[0, 2] * M[1, 1] * M[2, 0] + - M[0, 0] * M[1, 2] * M[2, 1] + - M[0, 1] * M[1, 0] * M[2, 2]) + return _get_intermediate_simp(_dotprodsimp)(m) + + dets = [] + for b in M.strongly_connected_components(): + if method == "domain-ge": # uses DomainMatrix to evaluate determinant + det = _det_DOM(M[b, b]) + elif method == "bareiss": + det = M[b, b]._eval_det_bareiss(iszerofunc=iszerofunc) + elif method == "berkowitz": + det = M[b, b]._eval_det_berkowitz() + elif method == "lu": + det = M[b, b]._eval_det_lu(iszerofunc=iszerofunc) + elif method == "bird": + det = M[b, b]._eval_det_bird() + elif method == "laplace": + det = M[b, b]._eval_det_laplace() + dets.append(det) + return Mul(*dets) + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _det_bareiss(M, iszerofunc=_is_zero_after_expand_mul): + """Compute matrix determinant using Bareiss' fraction-free + algorithm which is an extension of the well known Gaussian + elimination method. This approach is best suited for dense + symbolic matrices and will result in a determinant with + minimal number of fractions. It means that less term + rewriting is needed on resulting formulae. + + Parameters + ========== + + iszerofunc : function, optional + The function to use to determine zeros when doing an LU decomposition. + Defaults to ``lambda x: x.is_zero``. + + TODO: Implement algorithm for sparse matrices (SFF), + http://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps. + """ + + # Recursively implemented Bareiss' algorithm as per Deanna Richelle Leggett's + # thesis http://www.math.usm.edu/perry/Research/Thesis_DRL.pdf + def bareiss(mat, cumm=1): + if mat.rows == 0: + return mat.one + elif mat.rows == 1: + return mat[0, 0] + + # find a pivot and extract the remaining matrix + # With the default iszerofunc, _find_reasonable_pivot slows down + # the computation by the factor of 2.5 in one test. + # Relevant issues: #10279 and #13877. + pivot_pos, pivot_val, _, _ = _find_reasonable_pivot(mat[:, 0], iszerofunc=iszerofunc) + if pivot_pos is None: + return mat.zero + + # if we have a valid pivot, we'll do a "row swap", so keep the + # sign of the det + sign = (-1) ** (pivot_pos % 2) + + # we want every row but the pivot row and every column + rows = [i for i in range(mat.rows) if i != pivot_pos] + cols = list(range(mat.cols)) + tmp_mat = mat.extract(rows, cols) + + def entry(i, j): + ret = (pivot_val*tmp_mat[i, j + 1] - mat[pivot_pos, j + 1]*tmp_mat[i, 0]) / cumm + if _get_intermediate_simp_bool(True): + return _dotprodsimp(ret) + elif not ret.is_Atom: + return cancel(ret) + return ret + + return sign*bareiss(M._new(mat.rows - 1, mat.cols - 1, entry), pivot_val) + + if not M.is_square: + raise NonSquareMatrixError() + + if M.rows == 0: + return M.one + # sympy/matrices/tests/test_matrices.py contains a test that + # suggests that the determinant of a 0 x 0 matrix is one, by + # convention. + + return bareiss(M) + + +def _det_berkowitz(M): + """ Use the Berkowitz algorithm to compute the determinant.""" + + if not M.is_square: + raise NonSquareMatrixError() + + if M.rows == 0: + return M.one + # sympy/matrices/tests/test_matrices.py contains a test that + # suggests that the determinant of a 0 x 0 matrix is one, by + # convention. + + berk_vector = _berkowitz_vector(M) + return (-1)**(len(berk_vector) - 1) * berk_vector[-1] + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _det_LU(M, iszerofunc=_iszero, simpfunc=None): + """ Computes the determinant of a matrix from its LU decomposition. + This function uses the LU decomposition computed by + LUDecomposition_Simple(). + + The keyword arguments iszerofunc and simpfunc are passed to + LUDecomposition_Simple(). + iszerofunc is a callable that returns a boolean indicating if its + input is zero, or None if it cannot make the determination. + simpfunc is a callable that simplifies its input. + The default is simpfunc=None, which indicate that the pivot search + algorithm should not attempt to simplify any candidate pivots. + If simpfunc fails to simplify its input, then it must return its input + instead of a copy. + + Parameters + ========== + + iszerofunc : function, optional + The function to use to determine zeros when doing an LU decomposition. + Defaults to ``lambda x: x.is_zero``. + + simpfunc : function, optional + The simplification function to use when looking for zeros for pivots. + """ + + if not M.is_square: + raise NonSquareMatrixError() + + if M.rows == 0: + return M.one + # sympy/matrices/tests/test_matrices.py contains a test that + # suggests that the determinant of a 0 x 0 matrix is one, by + # convention. + + lu, row_swaps = M.LUdecomposition_Simple(iszerofunc=iszerofunc, + simpfunc=simpfunc) + # P*A = L*U => det(A) = det(L)*det(U)/det(P) = det(P)*det(U). + # Lower triangular factor L encoded in lu has unit diagonal => det(L) = 1. + # P is a permutation matrix => det(P) in {-1, 1} => 1/det(P) = det(P). + # LUdecomposition_Simple() returns a list of row exchange index pairs, rather + # than a permutation matrix, but det(P) = (-1)**len(row_swaps). + + # Avoid forming the potentially time consuming product of U's diagonal entries + # if the product is zero. + # Bottom right entry of U is 0 => det(A) = 0. + # It may be impossible to determine if this entry of U is zero when it is symbolic. + if iszerofunc(lu[lu.rows-1, lu.rows-1]): + return M.zero + + # Compute det(P) + det = -M.one if len(row_swaps)%2 else M.one + + # Compute det(U) by calculating the product of U's diagonal entries. + # The upper triangular portion of lu is the upper triangular portion of the + # U factor in the LU decomposition. + for k in range(lu.rows): + det *= lu[k, k] + + # return det(P)*det(U) + return det + + +@cacheit +def __det_laplace(M): + """Compute the determinant of a matrix using Laplace expansion. + + This is a recursive function, and it should not be called directly. + Use _det_laplace() instead. The reason for splitting this function + into two is to allow caching of determinants of submatrices. While + one could also define this function inside _det_laplace(), that + would remove the advantage of using caching in Cramer Solve. + """ + n = M.shape[0] + if n == 1: + return M[0] + elif n == 2: + return M[0, 0] * M[1, 1] - M[0, 1] * M[1, 0] + else: + return sum((-1) ** i * M[0, i] * + __det_laplace(M.minor_submatrix(0, i)) for i in range(n)) + + +def _det_laplace(M): + """Compute the determinant of a matrix using Laplace expansion. + + While Laplace expansion is not the most efficient method of computing + a determinant, it is a simple one, and it has the advantage of + being division free. To improve efficiency, this function uses + caching to avoid recomputing determinants of submatrices. + """ + if not M.is_square: + raise NonSquareMatrixError() + if M.shape[0] == 0: + return M.one + # sympy/matrices/tests/test_matrices.py contains a test that + # suggests that the determinant of a 0 x 0 matrix is one, by + # convention. + return __det_laplace(M.as_immutable()) + + +def _det_bird(M): + r"""Compute the determinant of a matrix using Bird's algorithm. + + Bird's algorithm is a simple division-free algorithm for computing, which + is of lower order than the Laplace's algorithm. It is described in [1]_. + + References + ========== + + .. [1] Bird, R. S. (2011). A simple division-free algorithm for computing + determinants. Inf. Process. Lett., 111(21), 1072-1074. doi: + 10.1016/j.ipl.2011.08.006 + """ + def mu(X): + n = X.shape[0] + zero = X.domain.zero + + total = zero + diag_sums = [zero] + for i in reversed(range(1, n)): + total -= X[i][i] + diag_sums.append(total) + diag_sums = diag_sums[::-1] + + elems = [[zero] * i + [diag_sums[i]] + X_i[i + 1:] for i, X_i in + enumerate(X)] + return DDM(elems, X.shape, X.domain) + + Mddm = M._rep.to_ddm() + n = M.shape[0] + if n == 0: + return M.one + # sympy/matrices/tests/test_matrices.py contains a test that + # suggests that the determinant of a 0 x 0 matrix is one, by + # convention. + Fn1 = Mddm + for _ in range(n - 1): + Fn1 = mu(Fn1).matmul(Mddm) + detA = Fn1[0][0] + if n % 2 == 0: + detA = -detA + + return Mddm.domain.to_sympy(detA) + + +def _minor(M, i, j, method="berkowitz"): + """Return the (i,j) minor of ``M``. That is, + return the determinant of the matrix obtained by deleting + the `i`th row and `j`th column from ``M``. + + Parameters + ========== + + i, j : int + The row and column to exclude to obtain the submatrix. + + method : string, optional + Method to use to find the determinant of the submatrix, can be + "bareiss", "berkowitz", "bird", "laplace" or "lu". + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> M.minor(1, 1) + -12 + + See Also + ======== + + minor_submatrix + cofactor + det + """ + + if not M.is_square: + raise NonSquareMatrixError() + + return M.minor_submatrix(i, j).det(method=method) + + +def _minor_submatrix(M, i, j): + """Return the submatrix obtained by removing the `i`th row + and `j`th column from ``M`` (works with Pythonic negative indices). + + Parameters + ========== + + i, j : int + The row and column to exclude to obtain the submatrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> M.minor_submatrix(1, 1) + Matrix([ + [1, 3], + [7, 9]]) + + See Also + ======== + + minor + cofactor + """ + + if i < 0: + i += M.rows + if j < 0: + j += M.cols + + if not 0 <= i < M.rows or not 0 <= j < M.cols: + raise ValueError("`i` and `j` must satisfy 0 <= i < ``M.rows`` " + "(%d)" % M.rows + "and 0 <= j < ``M.cols`` (%d)." % M.cols) + + rows = [a for a in range(M.rows) if a != i] + cols = [a for a in range(M.cols) if a != j] + + return M.extract(rows, cols) diff --git a/lib/python3.11/site-packages/sympy/matrices/eigen.py b/lib/python3.11/site-packages/sympy/matrices/eigen.py new file mode 100644 index 0000000000000000000000000000000000000000..87b2418efcece1c0b158ec56995bb011286feb3c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/eigen.py @@ -0,0 +1,1346 @@ +from types import FunctionType +from collections import Counter + +from mpmath import mp, workprec +from mpmath.libmp.libmpf import prec_to_dps + +from sympy.core.sorting import default_sort_key +from sympy.core.evalf import DEFAULT_MAXPREC, PrecisionExhausted +from sympy.core.logic import fuzzy_and, fuzzy_or +from sympy.core.numbers import Float +from sympy.core.sympify import _sympify +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.polys import roots, CRootOf, ZZ, QQ, EX +from sympy.polys.matrices import DomainMatrix +from sympy.polys.matrices.eigen import dom_eigenvects, dom_eigenvects_to_sympy +from sympy.polys.polytools import gcd + +from .exceptions import MatrixError, NonSquareMatrixError +from .determinant import _find_reasonable_pivot + +from .utilities import _iszero, _simplify + + +__doctest_requires__ = { + ('_is_indefinite', + '_is_negative_definite', + '_is_negative_semidefinite', + '_is_positive_definite', + '_is_positive_semidefinite'): ['matplotlib'], +} + + +def _eigenvals_eigenvects_mpmath(M): + norm2 = lambda v: mp.sqrt(sum(i**2 for i in v)) + + v1 = None + prec = max(x._prec for x in M.atoms(Float)) + eps = 2**-prec + + while prec < DEFAULT_MAXPREC: + with workprec(prec): + A = mp.matrix(M.evalf(n=prec_to_dps(prec))) + E, ER = mp.eig(A) + v2 = norm2([i for e in E for i in (mp.re(e), mp.im(e))]) + if v1 is not None and mp.fabs(v1 - v2) < eps: + return E, ER + v1 = v2 + prec *= 2 + + # we get here because the next step would have taken us + # past MAXPREC or because we never took a step; in case + # of the latter, we refuse to send back a solution since + # it would not have been verified; we also resist taking + # a small step to arrive exactly at MAXPREC since then + # the two calculations might be artificially close. + raise PrecisionExhausted + + +def _eigenvals_mpmath(M, multiple=False): + """Compute eigenvalues using mpmath""" + E, _ = _eigenvals_eigenvects_mpmath(M) + result = [_sympify(x) for x in E] + if multiple: + return result + return dict(Counter(result)) + + +def _eigenvects_mpmath(M): + E, ER = _eigenvals_eigenvects_mpmath(M) + result = [] + for i in range(M.rows): + eigenval = _sympify(E[i]) + eigenvect = _sympify(ER[:, i]) + result.append((eigenval, 1, [eigenvect])) + + return result + + +# This function is a candidate for caching if it gets implemented for matrices. +def _eigenvals( + M, error_when_incomplete=True, *, simplify=False, multiple=False, + rational=False, **flags): + r"""Compute eigenvalues of the matrix. + + Parameters + ========== + + error_when_incomplete : bool, optional + If it is set to ``True``, it will raise an error if not all + eigenvalues are computed. This is caused by ``roots`` not returning + a full list of eigenvalues. + + simplify : bool or function, optional + If it is set to ``True``, it attempts to return the most + simplified form of expressions returned by applying default + simplification method in every routine. + + If it is set to ``False``, it will skip simplification in this + particular routine to save computation resources. + + If a function is passed to, it will attempt to apply + the particular function as simplification method. + + rational : bool, optional + If it is set to ``True``, every floating point numbers would be + replaced with rationals before computation. It can solve some + issues of ``roots`` routine not working well with floats. + + multiple : bool, optional + If it is set to ``True``, the result will be in the form of a + list. + + If it is set to ``False``, the result will be in the form of a + dictionary. + + Returns + ======= + + eigs : list or dict + Eigenvalues of a matrix. The return format would be specified by + the key ``multiple``. + + Raises + ====== + + MatrixError + If not enough roots had got computed. + + NonSquareMatrixError + If attempted to compute eigenvalues from a non-square matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [0, 1, 1, 1, 0, 0, 1, 1, 1]) + >>> M.eigenvals() + {-1: 1, 0: 1, 2: 1} + + See Also + ======== + + MatrixBase.charpoly + eigenvects + + Notes + ===== + + Eigenvalues of a matrix $A$ can be computed by solving a matrix + equation $\det(A - \lambda I) = 0$ + + It's not always possible to return radical solutions for + eigenvalues for matrices larger than $4, 4$ shape due to + Abel-Ruffini theorem. + + If there is no radical solution is found for the eigenvalue, + it may return eigenvalues in the form of + :class:`sympy.polys.rootoftools.ComplexRootOf`. + """ + if not M: + if multiple: + return [] + return {} + + if not M.is_square: + raise NonSquareMatrixError("{} must be a square matrix.".format(M)) + + if M._rep.domain not in (ZZ, QQ): + # Skip this check for ZZ/QQ because it can be slow + if all(x.is_number for x in M) and M.has(Float): + return _eigenvals_mpmath(M, multiple=multiple) + + if rational: + from sympy.simplify import nsimplify + M = M.applyfunc( + lambda x: nsimplify(x, rational=True) if x.has(Float) else x) + + if multiple: + return _eigenvals_list( + M, error_when_incomplete=error_when_incomplete, simplify=simplify, + **flags) + return _eigenvals_dict( + M, error_when_incomplete=error_when_incomplete, simplify=simplify, + **flags) + + +eigenvals_error_message = \ +"It is not always possible to express the eigenvalues of a matrix " + \ +"of size 5x5 or higher in radicals. " + \ +"We have CRootOf, but domains other than the rationals are not " + \ +"currently supported. " + \ +"If there are no symbols in the matrix, " + \ +"it should still be possible to compute numeric approximations " + \ +"of the eigenvalues using " + \ +"M.evalf().eigenvals() or M.charpoly().nroots()." + + +def _eigenvals_list( + M, error_when_incomplete=True, simplify=False, **flags): + iblocks = M.strongly_connected_components() + all_eigs = [] + is_dom = M._rep.domain in (ZZ, QQ) + for b in iblocks: + + # Fast path for a 1x1 block: + if is_dom and len(b) == 1: + index = b[0] + val = M[index, index] + all_eigs.append(val) + continue + + block = M[b, b] + + if isinstance(simplify, FunctionType): + charpoly = block.charpoly(simplify=simplify) + else: + charpoly = block.charpoly() + + eigs = roots(charpoly, multiple=True, **flags) + + if len(eigs) != block.rows: + try: + eigs = charpoly.all_roots(multiple=True) + except NotImplementedError: + if error_when_incomplete: + raise MatrixError(eigenvals_error_message) + else: + eigs = [] + + all_eigs += eigs + + if not simplify: + return all_eigs + if not isinstance(simplify, FunctionType): + simplify = _simplify + return [simplify(value) for value in all_eigs] + + +def _eigenvals_dict( + M, error_when_incomplete=True, simplify=False, **flags): + iblocks = M.strongly_connected_components() + all_eigs = {} + is_dom = M._rep.domain in (ZZ, QQ) + for b in iblocks: + + # Fast path for a 1x1 block: + if is_dom and len(b) == 1: + index = b[0] + val = M[index, index] + all_eigs[val] = all_eigs.get(val, 0) + 1 + continue + + block = M[b, b] + + if isinstance(simplify, FunctionType): + charpoly = block.charpoly(simplify=simplify) + else: + charpoly = block.charpoly() + + eigs = roots(charpoly, multiple=False, **flags) + + if sum(eigs.values()) != block.rows: + try: + eigs = dict(charpoly.all_roots(multiple=False)) + except NotImplementedError: + if error_when_incomplete: + raise MatrixError(eigenvals_error_message) + else: + eigs = {} + + for k, v in eigs.items(): + if k in all_eigs: + all_eigs[k] += v + else: + all_eigs[k] = v + + if not simplify: + return all_eigs + if not isinstance(simplify, FunctionType): + simplify = _simplify + return {simplify(key): value for key, value in all_eigs.items()} + + +def _eigenspace(M, eigenval, iszerofunc=_iszero, simplify=False): + """Get a basis for the eigenspace for a particular eigenvalue""" + m = M - M.eye(M.rows) * eigenval + ret = m.nullspace(iszerofunc=iszerofunc) + + # The nullspace for a real eigenvalue should be non-trivial. + # If we didn't find an eigenvector, try once more a little harder + if len(ret) == 0 and simplify: + ret = m.nullspace(iszerofunc=iszerofunc, simplify=True) + if len(ret) == 0: + raise NotImplementedError( + "Can't evaluate eigenvector for eigenvalue {}".format(eigenval)) + return ret + + +def _eigenvects_DOM(M, **kwargs): + DOM = DomainMatrix.from_Matrix(M, field=True, extension=True) + DOM = DOM.to_dense() + + if DOM.domain != EX: + rational, algebraic = dom_eigenvects(DOM) + eigenvects = dom_eigenvects_to_sympy( + rational, algebraic, M.__class__, **kwargs) + eigenvects = sorted(eigenvects, key=lambda x: default_sort_key(x[0])) + + return eigenvects + return None + + +def _eigenvects_sympy(M, iszerofunc, simplify=True, **flags): + eigenvals = M.eigenvals(rational=False, **flags) + + # Make sure that we have all roots in radical form + for x in eigenvals: + if x.has(CRootOf): + raise MatrixError( + "Eigenvector computation is not implemented if the matrix have " + "eigenvalues in CRootOf form") + + eigenvals = sorted(eigenvals.items(), key=default_sort_key) + ret = [] + for val, mult in eigenvals: + vects = _eigenspace(M, val, iszerofunc=iszerofunc, simplify=simplify) + ret.append((val, mult, vects)) + return ret + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _eigenvects(M, error_when_incomplete=True, iszerofunc=_iszero, *, chop=False, **flags): + """Compute eigenvectors of the matrix. + + Parameters + ========== + + error_when_incomplete : bool, optional + Raise an error when not all eigenvalues are computed. This is + caused by ``roots`` not returning a full list of eigenvalues. + + iszerofunc : function, optional + Specifies a zero testing function to be used in ``rref``. + + Default value is ``_iszero``, which uses SymPy's naive and fast + default assumption handler. + + It can also accept any user-specified zero testing function, if it + is formatted as a function which accepts a single symbolic argument + and returns ``True`` if it is tested as zero and ``False`` if it + is tested as non-zero, and ``None`` if it is undecidable. + + simplify : bool or function, optional + If ``True``, ``as_content_primitive()`` will be used to tidy up + normalization artifacts. + + It will also be used by the ``nullspace`` routine. + + chop : bool or positive number, optional + If the matrix contains any Floats, they will be changed to Rationals + for computation purposes, but the answers will be returned after + being evaluated with evalf. The ``chop`` flag is passed to ``evalf``. + When ``chop=True`` a default precision will be used; a number will + be interpreted as the desired level of precision. + + Returns + ======= + + ret : [(eigenval, multiplicity, eigenspace), ...] + A ragged list containing tuples of data obtained by ``eigenvals`` + and ``nullspace``. + + ``eigenspace`` is a list containing the ``eigenvector`` for each + eigenvalue. + + ``eigenvector`` is a vector in the form of a ``Matrix``. e.g. + a vector of length 3 is returned as ``Matrix([a_1, a_2, a_3])``. + + Raises + ====== + + NotImplementedError + If failed to compute nullspace. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [0, 1, 1, 1, 0, 0, 1, 1, 1]) + >>> M.eigenvects() + [(-1, 1, [Matrix([ + [-1], + [ 1], + [ 0]])]), (0, 1, [Matrix([ + [ 0], + [-1], + [ 1]])]), (2, 1, [Matrix([ + [2/3], + [1/3], + [ 1]])])] + + See Also + ======== + + eigenvals + MatrixBase.nullspace + """ + simplify = flags.get('simplify', True) + primitive = flags.get('simplify', False) + flags.pop('simplify', None) # remove this if it's there + flags.pop('multiple', None) # remove this if it's there + + if not isinstance(simplify, FunctionType): + simpfunc = _simplify if simplify else lambda x: x + + has_floats = M.has(Float) + if has_floats: + if all(x.is_number for x in M): + return _eigenvects_mpmath(M) + from sympy.simplify import nsimplify + M = M.applyfunc(lambda x: nsimplify(x, rational=True)) + + ret = _eigenvects_DOM(M) + if ret is None: + ret = _eigenvects_sympy(M, iszerofunc, simplify=simplify, **flags) + + if primitive: + # if the primitive flag is set, get rid of any common + # integer denominators + def denom_clean(l): + return [(v / gcd(list(v))).applyfunc(simpfunc) for v in l] + + ret = [(val, mult, denom_clean(es)) for val, mult, es in ret] + + if has_floats: + # if we had floats to start with, turn the eigenvectors to floats + ret = [(val.evalf(chop=chop), mult, [v.evalf(chop=chop) for v in es]) + for val, mult, es in ret] + + return ret + + +def _is_diagonalizable_with_eigen(M, reals_only=False): + """See _is_diagonalizable. This function returns the bool along with the + eigenvectors to avoid calculating them again in functions like + ``diagonalize``.""" + + if not M.is_square: + return False, [] + + eigenvecs = M.eigenvects(simplify=True) + + for val, mult, basis in eigenvecs: + if reals_only and not val.is_real: # if we have a complex eigenvalue + return False, eigenvecs + + if mult != len(basis): # if the geometric multiplicity doesn't equal the algebraic + return False, eigenvecs + + return True, eigenvecs + +def _is_diagonalizable(M, reals_only=False, **kwargs): + """Returns ``True`` if a matrix is diagonalizable. + + Parameters + ========== + + reals_only : bool, optional + If ``True``, it tests whether the matrix can be diagonalized + to contain only real numbers on the diagonal. + + + If ``False``, it tests whether the matrix can be diagonalized + at all, even with numbers that may not be real. + + Examples + ======== + + Example of a diagonalizable matrix: + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2, 0], [0, 3, 0], [2, -4, 2]]) + >>> M.is_diagonalizable() + True + + Example of a non-diagonalizable matrix: + + >>> M = Matrix([[0, 1], [0, 0]]) + >>> M.is_diagonalizable() + False + + Example of a matrix that is diagonalized in terms of non-real entries: + + >>> M = Matrix([[0, 1], [-1, 0]]) + >>> M.is_diagonalizable(reals_only=False) + True + >>> M.is_diagonalizable(reals_only=True) + False + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.is_diagonal + diagonalize + """ + if not M.is_square: + return False + + if all(e.is_real for e in M) and M.is_symmetric(): + return True + + if all(e.is_complex for e in M) and M.is_hermitian: + return True + + return _is_diagonalizable_with_eigen(M, reals_only=reals_only)[0] + + +#G&VL, Matrix Computations, Algo 5.4.2 +def _householder_vector(x): + if not x.cols == 1: + raise ValueError("Input must be a column matrix") + v = x.copy() + v_plus = x.copy() + v_minus = x.copy() + q = x[0, 0] / abs(x[0, 0]) + norm_x = x.norm() + v_plus[0, 0] = x[0, 0] + q * norm_x + v_minus[0, 0] = x[0, 0] - q * norm_x + if x[1:, 0].norm() == 0: + bet = 0 + v[0, 0] = 1 + else: + if v_plus.norm() <= v_minus.norm(): + v = v_plus + else: + v = v_minus + v = v / v[0] + bet = 2 / (v.norm() ** 2) + return v, bet + + +def _bidiagonal_decmp_hholder(M): + m = M.rows + n = M.cols + A = M.as_mutable() + U, V = A.eye(m), A.eye(n) + for i in range(min(m, n)): + v, bet = _householder_vector(A[i:, i]) + hh_mat = A.eye(m - i) - bet * v * v.H + A[i:, i:] = hh_mat * A[i:, i:] + temp = A.eye(m) + temp[i:, i:] = hh_mat + U = U * temp + if i + 1 <= n - 2: + v, bet = _householder_vector(A[i, i+1:].T) + hh_mat = A.eye(n - i - 1) - bet * v * v.H + A[i:, i+1:] = A[i:, i+1:] * hh_mat + temp = A.eye(n) + temp[i+1:, i+1:] = hh_mat + V = temp * V + return U, A, V + + +def _eval_bidiag_hholder(M): + m = M.rows + n = M.cols + A = M.as_mutable() + for i in range(min(m, n)): + v, bet = _householder_vector(A[i:, i]) + hh_mat = A.eye(m-i) - bet * v * v.H + A[i:, i:] = hh_mat * A[i:, i:] + if i + 1 <= n - 2: + v, bet = _householder_vector(A[i, i+1:].T) + hh_mat = A.eye(n - i - 1) - bet * v * v.H + A[i:, i+1:] = A[i:, i+1:] * hh_mat + return A + + +def _bidiagonal_decomposition(M, upper=True): + """ + Returns $(U,B,V.H)$ for + + $$A = UBV^{H}$$ + + where $A$ is the input matrix, and $B$ is its Bidiagonalized form + + Note: Bidiagonal Computation can hang for symbolic matrices. + + Parameters + ========== + + upper : bool. Whether to do upper bidiagnalization or lower. + True for upper and False for lower. + + References + ========== + + .. [1] Algorithm 5.4.2, Matrix computations by Golub and Van Loan, 4th edition + .. [2] Complex Matrix Bidiagonalization, https://github.com/vslobody/Householder-Bidiagonalization + + """ + + if not isinstance(upper, bool): + raise ValueError("upper must be a boolean") + + if upper: + return _bidiagonal_decmp_hholder(M) + + X = _bidiagonal_decmp_hholder(M.H) + return X[2].H, X[1].H, X[0].H + + +def _bidiagonalize(M, upper=True): + """ + Returns $B$, the Bidiagonalized form of the input matrix. + + Note: Bidiagonal Computation can hang for symbolic matrices. + + Parameters + ========== + + upper : bool. Whether to do upper bidiagnalization or lower. + True for upper and False for lower. + + References + ========== + + .. [1] Algorithm 5.4.2, Matrix computations by Golub and Van Loan, 4th edition + .. [2] Complex Matrix Bidiagonalization : https://github.com/vslobody/Householder-Bidiagonalization + + """ + + if not isinstance(upper, bool): + raise ValueError("upper must be a boolean") + + if upper: + return _eval_bidiag_hholder(M) + return _eval_bidiag_hholder(M.H).H + + +def _diagonalize(M, reals_only=False, sort=False, normalize=False): + """ + Return (P, D), where D is diagonal and + + D = P^-1 * M * P + + where M is current matrix. + + Parameters + ========== + + reals_only : bool. Whether to throw an error if complex numbers are need + to diagonalize. (Default: False) + + sort : bool. Sort the eigenvalues along the diagonal. (Default: False) + + normalize : bool. If True, normalize the columns of P. (Default: False) + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2]) + >>> M + Matrix([ + [1, 2, 0], + [0, 3, 0], + [2, -4, 2]]) + >>> (P, D) = M.diagonalize() + >>> D + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + >>> P + Matrix([ + [-1, 0, -1], + [ 0, 0, -1], + [ 2, 1, 2]]) + >>> P.inv() * M * P + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.is_diagonal + is_diagonalizable + """ + + if not M.is_square: + raise NonSquareMatrixError() + + is_diagonalizable, eigenvecs = _is_diagonalizable_with_eigen(M, + reals_only=reals_only) + + if not is_diagonalizable: + raise MatrixError("Matrix is not diagonalizable") + + if sort: + eigenvecs = sorted(eigenvecs, key=default_sort_key) + + p_cols, diag = [], [] + + for val, mult, basis in eigenvecs: + diag += [val] * mult + p_cols += basis + + if normalize: + p_cols = [v / v.norm() for v in p_cols] + + return M.hstack(*p_cols), M.diag(*diag) + + +def _fuzzy_positive_definite(M): + positive_diagonals = M._has_positive_diagonals() + if positive_diagonals is False: + return False + + if positive_diagonals and M.is_strongly_diagonally_dominant: + return True + + return None + + +def _fuzzy_positive_semidefinite(M): + nonnegative_diagonals = M._has_nonnegative_diagonals() + if nonnegative_diagonals is False: + return False + + if nonnegative_diagonals and M.is_weakly_diagonally_dominant: + return True + + return None + + +def _is_positive_definite(M): + if not M.is_hermitian: + if not M.is_square: + return False + M = M + M.H + + fuzzy = _fuzzy_positive_definite(M) + if fuzzy is not None: + return fuzzy + + return _is_positive_definite_GE(M) + + +def _is_positive_semidefinite(M): + if not M.is_hermitian: + if not M.is_square: + return False + M = M + M.H + + fuzzy = _fuzzy_positive_semidefinite(M) + if fuzzy is not None: + return fuzzy + + return _is_positive_semidefinite_cholesky(M) + + +def _is_negative_definite(M): + return _is_positive_definite(-M) + + +def _is_negative_semidefinite(M): + return _is_positive_semidefinite(-M) + + +def _is_indefinite(M): + if M.is_hermitian: + eigen = M.eigenvals() + args1 = [x.is_positive for x in eigen.keys()] + any_positive = fuzzy_or(args1) + args2 = [x.is_negative for x in eigen.keys()] + any_negative = fuzzy_or(args2) + + return fuzzy_and([any_positive, any_negative]) + + elif M.is_square: + return (M + M.H).is_indefinite + + return False + + +def _is_positive_definite_GE(M): + """A division-free gaussian elimination method for testing + positive-definiteness.""" + M = M.as_mutable() + size = M.rows + + for i in range(size): + is_positive = M[i, i].is_positive + if is_positive is not True: + return is_positive + for j in range(i+1, size): + M[j, i+1:] = M[i, i] * M[j, i+1:] - M[j, i] * M[i, i+1:] + return True + + +def _is_positive_semidefinite_cholesky(M): + """Uses Cholesky factorization with complete pivoting + + References + ========== + + .. [1] http://eprints.ma.man.ac.uk/1199/1/covered/MIMS_ep2008_116.pdf + + .. [2] https://www.value-at-risk.net/cholesky-factorization/ + """ + M = M.as_mutable() + for k in range(M.rows): + diags = [M[i, i] for i in range(k, M.rows)] + pivot, pivot_val, nonzero, _ = _find_reasonable_pivot(diags) + + if nonzero: + return None + + if pivot is None: + for i in range(k+1, M.rows): + for j in range(k, M.cols): + iszero = M[i, j].is_zero + if iszero is None: + return None + elif iszero is False: + return False + return True + + if M[k, k].is_negative or pivot_val.is_negative: + return False + elif not (M[k, k].is_nonnegative and pivot_val.is_nonnegative): + return None + + if pivot > 0: + M.col_swap(k, k+pivot) + M.row_swap(k, k+pivot) + + M[k, k] = sqrt(M[k, k]) + M[k, k+1:] /= M[k, k] + M[k+1:, k+1:] -= M[k, k+1:].H * M[k, k+1:] + + return M[-1, -1].is_nonnegative + + +_doc_positive_definite = \ + r"""Finds out the definiteness of a matrix. + + Explanation + =========== + + A square real matrix $A$ is: + + - A positive definite matrix if $x^T A x > 0$ + for all non-zero real vectors $x$. + - A positive semidefinite matrix if $x^T A x \geq 0$ + for all non-zero real vectors $x$. + - A negative definite matrix if $x^T A x < 0$ + for all non-zero real vectors $x$. + - A negative semidefinite matrix if $x^T A x \leq 0$ + for all non-zero real vectors $x$. + - An indefinite matrix if there exists non-zero real vectors + $x, y$ with $x^T A x > 0 > y^T A y$. + + A square complex matrix $A$ is: + + - A positive definite matrix if $\text{re}(x^H A x) > 0$ + for all non-zero complex vectors $x$. + - A positive semidefinite matrix if $\text{re}(x^H A x) \geq 0$ + for all non-zero complex vectors $x$. + - A negative definite matrix if $\text{re}(x^H A x) < 0$ + for all non-zero complex vectors $x$. + - A negative semidefinite matrix if $\text{re}(x^H A x) \leq 0$ + for all non-zero complex vectors $x$. + - An indefinite matrix if there exists non-zero complex vectors + $x, y$ with $\text{re}(x^H A x) > 0 > \text{re}(y^H A y)$. + + A matrix need not be symmetric or hermitian to be positive definite. + + - A real non-symmetric matrix is positive definite if and only if + $\frac{A + A^T}{2}$ is positive definite. + - A complex non-hermitian matrix is positive definite if and only if + $\frac{A + A^H}{2}$ is positive definite. + + And this extension can apply for all the definitions above. + + However, for complex cases, you can restrict the definition of + $\text{re}(x^H A x) > 0$ to $x^H A x > 0$ and require the matrix + to be hermitian. + But we do not present this restriction for computation because you + can check ``M.is_hermitian`` independently with this and use + the same procedure. + + Examples + ======== + + An example of symmetric positive definite matrix: + + .. plot:: + :context: reset + :format: doctest + :include-source: True + + >>> from sympy import Matrix, symbols + >>> from sympy.plotting import plot3d + >>> a, b = symbols('a b') + >>> x = Matrix([a, b]) + + >>> A = Matrix([[1, 0], [0, 1]]) + >>> A.is_positive_definite + True + >>> A.is_positive_semidefinite + True + + >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1)) + + An example of symmetric positive semidefinite matrix: + + .. plot:: + :context: close-figs + :format: doctest + :include-source: True + + >>> A = Matrix([[1, -1], [-1, 1]]) + >>> A.is_positive_definite + False + >>> A.is_positive_semidefinite + True + + >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1)) + + An example of symmetric negative definite matrix: + + .. plot:: + :context: close-figs + :format: doctest + :include-source: True + + >>> A = Matrix([[-1, 0], [0, -1]]) + >>> A.is_negative_definite + True + >>> A.is_negative_semidefinite + True + >>> A.is_indefinite + False + + >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1)) + + An example of symmetric indefinite matrix: + + .. plot:: + :context: close-figs + :format: doctest + :include-source: True + + >>> A = Matrix([[1, 2], [2, -1]]) + >>> A.is_indefinite + True + + >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1)) + + An example of non-symmetric positive definite matrix. + + .. plot:: + :context: close-figs + :format: doctest + :include-source: True + + >>> A = Matrix([[1, 2], [-2, 1]]) + >>> A.is_positive_definite + True + >>> A.is_positive_semidefinite + True + + >>> p = plot3d((x.T*A*x)[0, 0], (a, -1, 1), (b, -1, 1)) + + Notes + ===== + + Although some people trivialize the definition of positive definite + matrices only for symmetric or hermitian matrices, this restriction + is not correct because it does not classify all instances of + positive definite matrices from the definition $x^T A x > 0$ or + $\text{re}(x^H A x) > 0$. + + For instance, ``Matrix([[1, 2], [-2, 1]])`` presented in + the example above is an example of real positive definite matrix + that is not symmetric. + + However, since the following formula holds true; + + .. math:: + \text{re}(x^H A x) > 0 \iff + \text{re}(x^H \frac{A + A^H}{2} x) > 0 + + We can classify all positive definite matrices that may or may not + be symmetric or hermitian by transforming the matrix to + $\frac{A + A^T}{2}$ or $\frac{A + A^H}{2}$ + (which is guaranteed to be always real symmetric or complex + hermitian) and we can defer most of the studies to symmetric or + hermitian positive definite matrices. + + But it is a different problem for the existence of Cholesky + decomposition. Because even though a non symmetric or a non + hermitian matrix can be positive definite, Cholesky or LDL + decomposition does not exist because the decompositions require the + matrix to be symmetric or hermitian. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Definiteness_of_a_matrix#Eigenvalues + + .. [2] https://mathworld.wolfram.com/PositiveDefiniteMatrix.html + + .. [3] Johnson, C. R. "Positive Definite Matrices." Amer. + Math. Monthly 77, 259-264 1970. + """ + +_is_positive_definite.__doc__ = _doc_positive_definite +_is_positive_semidefinite.__doc__ = _doc_positive_definite +_is_negative_definite.__doc__ = _doc_positive_definite +_is_negative_semidefinite.__doc__ = _doc_positive_definite +_is_indefinite.__doc__ = _doc_positive_definite + + +def _jordan_form(M, calc_transform=True, *, chop=False): + """Return $(P, J)$ where $J$ is a Jordan block + matrix and $P$ is a matrix such that $M = P J P^{-1}$ + + Parameters + ========== + + calc_transform : bool + If ``False``, then only $J$ is returned. + + chop : bool + All matrices are converted to exact types when computing + eigenvalues and eigenvectors. As a result, there may be + approximation errors. If ``chop==True``, these errors + will be truncated. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[ 6, 5, -2, -3], [-3, -1, 3, 3], [ 2, 1, -2, -3], [-1, 1, 5, 5]]) + >>> P, J = M.jordan_form() + >>> J + Matrix([ + [2, 1, 0, 0], + [0, 2, 0, 0], + [0, 0, 2, 1], + [0, 0, 0, 2]]) + + See Also + ======== + + jordan_block + """ + + if not M.is_square: + raise NonSquareMatrixError("Only square matrices have Jordan forms") + + mat = M + has_floats = M.has(Float) + + if has_floats: + try: + max_prec = max(term._prec for term in M.values() if isinstance(term, Float)) + except ValueError: + # if no term in the matrix is explicitly a Float calling max() + # will throw a error so setting max_prec to default value of 53 + max_prec = 53 + + # setting minimum max_dps to 15 to prevent loss of precision in + # matrix containing non evaluated expressions + max_dps = max(prec_to_dps(max_prec), 15) + + def restore_floats(*args): + """If ``has_floats`` is `True`, cast all ``args`` as + matrices of floats.""" + + if has_floats: + args = [m.evalf(n=max_dps, chop=chop) for m in args] + if len(args) == 1: + return args[0] + + return args + + # cache calculations for some speedup + mat_cache = {} + + def eig_mat(val, pow): + """Cache computations of ``(M - val*I)**pow`` for quick + retrieval""" + + if (val, pow) in mat_cache: + return mat_cache[(val, pow)] + + if (val, pow - 1) in mat_cache: + mat_cache[(val, pow)] = mat_cache[(val, pow - 1)].multiply( + mat_cache[(val, 1)], dotprodsimp=None) + else: + mat_cache[(val, pow)] = (mat - val*M.eye(M.rows)).pow(pow) + + return mat_cache[(val, pow)] + + # helper functions + def nullity_chain(val, algebraic_multiplicity): + """Calculate the sequence [0, nullity(E), nullity(E**2), ...] + until it is constant where ``E = M - val*I``""" + + # mat.rank() is faster than computing the null space, + # so use the rank-nullity theorem + cols = M.cols + ret = [0] + nullity = cols - eig_mat(val, 1).rank() + i = 2 + + while nullity != ret[-1]: + ret.append(nullity) + + if nullity == algebraic_multiplicity: + break + + nullity = cols - eig_mat(val, i).rank() + i += 1 + + # Due to issues like #7146 and #15872, SymPy sometimes + # gives the wrong rank. In this case, raise an error + # instead of returning an incorrect matrix + if nullity < ret[-1] or nullity > algebraic_multiplicity: + raise MatrixError( + "SymPy had encountered an inconsistent " + "result while computing Jordan block: " + "{}".format(M)) + + return ret + + def blocks_from_nullity_chain(d): + """Return a list of the size of each Jordan block. + If d_n is the nullity of E**n, then the number + of Jordan blocks of size n is + + 2*d_n - d_(n-1) - d_(n+1)""" + + # d[0] is always the number of columns, so skip past it + mid = [2*d[n] - d[n - 1] - d[n + 1] for n in range(1, len(d) - 1)] + # d is assumed to plateau with "d[ len(d) ] == d[-1]", so + # 2*d_n - d_(n-1) - d_(n+1) == d_n - d_(n-1) + end = [d[-1] - d[-2]] if len(d) > 1 else [d[0]] + + return mid + end + + def pick_vec(small_basis, big_basis): + """Picks a vector from big_basis that isn't in + the subspace spanned by small_basis""" + + if len(small_basis) == 0: + return big_basis[0] + + for v in big_basis: + _, pivots = M.hstack(*(small_basis + [v])).echelon_form( + with_pivots=True) + + if pivots[-1] == len(small_basis): + return v + + # roots doesn't like Floats, so replace them with Rationals + if has_floats: + from sympy.simplify import nsimplify + mat = mat.applyfunc(lambda x: nsimplify(x, rational=True)) + + # first calculate the jordan block structure + eigs = mat.eigenvals() + + # Make sure that we have all roots in radical form + for x in eigs: + if x.has(CRootOf): + raise MatrixError( + "Jordan normal form is not implemented if the matrix have " + "eigenvalues in CRootOf form") + + # most matrices have distinct eigenvalues + # and so are diagonalizable. In this case, don't + # do extra work! + if len(eigs.keys()) == mat.cols: + blocks = sorted(eigs.keys(), key=default_sort_key) + jordan_mat = mat.diag(*blocks) + + if not calc_transform: + return restore_floats(jordan_mat) + + jordan_basis = [eig_mat(eig, 1).nullspace()[0] + for eig in blocks] + basis_mat = mat.hstack(*jordan_basis) + + return restore_floats(basis_mat, jordan_mat) + + block_structure = [] + + for eig in sorted(eigs.keys(), key=default_sort_key): + algebraic_multiplicity = eigs[eig] + chain = nullity_chain(eig, algebraic_multiplicity) + block_sizes = blocks_from_nullity_chain(chain) + + # if block_sizes = = [a, b, c, ...], then the number of + # Jordan blocks of size 1 is a, of size 2 is b, etc. + # create an array that has (eig, block_size) with one + # entry for each block + size_nums = [(i+1, num) for i, num in enumerate(block_sizes)] + + # we expect larger Jordan blocks to come earlier + size_nums.reverse() + + block_structure.extend( + [(eig, size) for size, num in size_nums for _ in range(num)]) + + jordan_form_size = sum(size for eig, size in block_structure) + + if jordan_form_size != M.rows: + raise MatrixError( + "SymPy had encountered an inconsistent result while " + "computing Jordan block. : {}".format(M)) + + blocks = (mat.jordan_block(size=size, eigenvalue=eig) for eig, size in block_structure) + jordan_mat = mat.diag(*blocks) + + if not calc_transform: + return restore_floats(jordan_mat) + + # For each generalized eigenspace, calculate a basis. + # We start by looking for a vector in null( (A - eig*I)**n ) + # which isn't in null( (A - eig*I)**(n-1) ) where n is + # the size of the Jordan block + # + # Ideally we'd just loop through block_structure and + # compute each generalized eigenspace. However, this + # causes a lot of unneeded computation. Instead, we + # go through the eigenvalues separately, since we know + # their generalized eigenspaces must have bases that + # are linearly independent. + jordan_basis = [] + + for eig in sorted(eigs.keys(), key=default_sort_key): + eig_basis = [] + + for block_eig, size in block_structure: + if block_eig != eig: + continue + + null_big = (eig_mat(eig, size)).nullspace() + null_small = (eig_mat(eig, size - 1)).nullspace() + + # we want to pick something that is in the big basis + # and not the small, but also something that is independent + # of any other generalized eigenvectors from a different + # generalized eigenspace sharing the same eigenvalue. + vec = pick_vec(null_small + eig_basis, null_big) + new_vecs = [eig_mat(eig, i).multiply(vec, dotprodsimp=None) + for i in range(size)] + + eig_basis.extend(new_vecs) + jordan_basis.extend(reversed(new_vecs)) + + basis_mat = mat.hstack(*jordan_basis) + + return restore_floats(basis_mat, jordan_mat) + + +def _left_eigenvects(M, **flags): + """Returns left eigenvectors and eigenvalues. + + This function returns the list of triples (eigenval, multiplicity, + basis) for the left eigenvectors. Options are the same as for + eigenvects(), i.e. the ``**flags`` arguments gets passed directly to + eigenvects(). + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[0, 1, 1], [1, 0, 0], [1, 1, 1]]) + >>> M.eigenvects() + [(-1, 1, [Matrix([ + [-1], + [ 1], + [ 0]])]), (0, 1, [Matrix([ + [ 0], + [-1], + [ 1]])]), (2, 1, [Matrix([ + [2/3], + [1/3], + [ 1]])])] + >>> M.left_eigenvects() + [(-1, 1, [Matrix([[-2, 1, 1]])]), (0, 1, [Matrix([[-1, -1, 1]])]), (2, + 1, [Matrix([[1, 1, 1]])])] + + """ + + eigs = M.transpose().eigenvects(**flags) + + return [(val, mult, [l.transpose() for l in basis]) for val, mult, basis in eigs] + + +def _singular_values(M): + """Compute the singular values of a Matrix + + Examples + ======== + + >>> from sympy import Matrix, Symbol + >>> x = Symbol('x', real=True) + >>> M = Matrix([[0, 1, 0], [0, x, 0], [-1, 0, 0]]) + >>> M.singular_values() + [sqrt(x**2 + 1), 1, 0] + + See Also + ======== + + condition_number + """ + + if M.rows >= M.cols: + valmultpairs = M.H.multiply(M).eigenvals() + else: + valmultpairs = M.multiply(M.H).eigenvals() + + # Expands result from eigenvals into a simple list + vals = [] + + for k, v in valmultpairs.items(): + vals += [sqrt(k)] * v # dangerous! same k in several spots! + + # Pad with zeros if singular values are computed in reverse way, + # to give consistent format. + if len(vals) < M.cols: + vals += [M.zero] * (M.cols - len(vals)) + + # sort them in descending order + vals.sort(reverse=True, key=default_sort_key) + + return vals diff --git a/lib/python3.11/site-packages/sympy/matrices/exceptions.py b/lib/python3.11/site-packages/sympy/matrices/exceptions.py new file mode 100644 index 0000000000000000000000000000000000000000..bfc7cfa0bdffd59ff2bc5a9cd85cf9b04ed1a63d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/exceptions.py @@ -0,0 +1,26 @@ +""" +Exceptions raised by the matrix module. +""" + + +class MatrixError(Exception): + pass + + +class ShapeError(ValueError, MatrixError): + """Wrong matrix shape""" + pass + + +class NonSquareMatrixError(ShapeError): + pass + + +class NonInvertibleMatrixError(ValueError, MatrixError): + """The matrix in not invertible (division by multidimensional zero error).""" + pass + + +class NonPositiveDefiniteMatrixError(ValueError, MatrixError): + """The matrix is not a positive-definite matrix.""" + pass diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/__init__.py b/lib/python3.11/site-packages/sympy/matrices/expressions/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..5f4ab203ab74165d1003cdedd83945ea3fcf8f47 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/__init__.py @@ -0,0 +1,62 @@ +""" A module which handles Matrix Expressions """ + +from .slice import MatrixSlice +from .blockmatrix import BlockMatrix, BlockDiagMatrix, block_collapse, blockcut +from .companion import CompanionMatrix +from .funcmatrix import FunctionMatrix +from .inverse import Inverse +from .matadd import MatAdd +from .matexpr import MatrixExpr, MatrixSymbol, matrix_symbols +from .matmul import MatMul +from .matpow import MatPow +from .trace import Trace, trace +from .determinant import Determinant, det, Permanent, per +from .transpose import Transpose +from .adjoint import Adjoint +from .hadamard import hadamard_product, HadamardProduct, hadamard_power, HadamardPower +from .diagonal import DiagonalMatrix, DiagonalOf, DiagMatrix, diagonalize_vector +from .dotproduct import DotProduct +from .kronecker import kronecker_product, KroneckerProduct, combine_kronecker +from .permutation import PermutationMatrix, MatrixPermute +from .sets import MatrixSet +from .special import ZeroMatrix, Identity, OneMatrix + +__all__ = [ + 'MatrixSlice', + + 'BlockMatrix', 'BlockDiagMatrix', 'block_collapse', 'blockcut', + 'FunctionMatrix', + + 'CompanionMatrix', + + 'Inverse', + + 'MatAdd', + + 'Identity', 'MatrixExpr', 'MatrixSymbol', 'ZeroMatrix', 'OneMatrix', + 'matrix_symbols', 'MatrixSet', + + 'MatMul', + + 'MatPow', + + 'Trace', 'trace', + + 'Determinant', 'det', + + 'Transpose', + + 'Adjoint', + + 'hadamard_product', 'HadamardProduct', 'hadamard_power', 'HadamardPower', + + 'DiagonalMatrix', 'DiagonalOf', 'DiagMatrix', 'diagonalize_vector', + + 'DotProduct', + + 'kronecker_product', 'KroneckerProduct', 'combine_kronecker', + + 'PermutationMatrix', 'MatrixPermute', + + 'Permanent', 'per' +] diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/_shape.py b/lib/python3.11/site-packages/sympy/matrices/expressions/_shape.py new file mode 100644 index 0000000000000000000000000000000000000000..a95d481bf8e1edf4c62992044cd50563b335caac --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/_shape.py @@ -0,0 +1,102 @@ +from sympy.core.relational import Eq +from sympy.core.expr import Expr +from sympy.core.numbers import Integer +from sympy.logic.boolalg import Boolean, And +from sympy.matrices.expressions.matexpr import MatrixExpr +from sympy.matrices.exceptions import ShapeError +from typing import Union + + +def is_matadd_valid(*args: MatrixExpr) -> Boolean: + """Return the symbolic condition how ``MatAdd``, ``HadamardProduct`` + makes sense. + + Parameters + ========== + + args + The list of arguments of matrices to be tested for. + + Examples + ======== + + >>> from sympy import MatrixSymbol, symbols + >>> from sympy.matrices.expressions._shape import is_matadd_valid + + >>> m, n, p, q = symbols('m n p q') + >>> A = MatrixSymbol('A', m, n) + >>> B = MatrixSymbol('B', p, q) + >>> is_matadd_valid(A, B) + Eq(m, p) & Eq(n, q) + """ + rows, cols = zip(*(arg.shape for arg in args)) + return And( + *(Eq(i, j) for i, j in zip(rows[:-1], rows[1:])), + *(Eq(i, j) for i, j in zip(cols[:-1], cols[1:])), + ) + + +def is_matmul_valid(*args: Union[MatrixExpr, Expr]) -> Boolean: + """Return the symbolic condition how ``MatMul`` makes sense + + Parameters + ========== + + args + The list of arguments of matrices and scalar expressions to be tested + for. + + Examples + ======== + + >>> from sympy import MatrixSymbol, symbols + >>> from sympy.matrices.expressions._shape import is_matmul_valid + + >>> m, n, p, q = symbols('m n p q') + >>> A = MatrixSymbol('A', m, n) + >>> B = MatrixSymbol('B', p, q) + >>> is_matmul_valid(A, B) + Eq(n, p) + """ + rows, cols = zip(*(arg.shape for arg in args if isinstance(arg, MatrixExpr))) + return And(*(Eq(i, j) for i, j in zip(cols[:-1], rows[1:]))) + + +def is_square(arg: MatrixExpr, /) -> Boolean: + """Return the symbolic condition how the matrix is assumed to be square + + Parameters + ========== + + arg + The matrix to be tested for. + + Examples + ======== + + >>> from sympy import MatrixSymbol, symbols + >>> from sympy.matrices.expressions._shape import is_square + + >>> m, n = symbols('m n') + >>> A = MatrixSymbol('A', m, n) + >>> is_square(A) + Eq(m, n) + """ + return Eq(arg.rows, arg.cols) + + +def validate_matadd_integer(*args: MatrixExpr) -> None: + """Validate matrix shape for addition only for integer values""" + rows, cols = zip(*(x.shape for x in args)) + if len(set(filter(lambda x: isinstance(x, (int, Integer)), rows))) > 1: + raise ShapeError(f"Matrices have mismatching shape: {rows}") + if len(set(filter(lambda x: isinstance(x, (int, Integer)), cols))) > 1: + raise ShapeError(f"Matrices have mismatching shape: {cols}") + + +def validate_matmul_integer(*args: MatrixExpr) -> None: + """Validate matrix shape for multiplication only for integer values""" + for A, B in zip(args[:-1], args[1:]): + i, j = A.cols, B.rows + if isinstance(i, (int, Integer)) and isinstance(j, (int, Integer)) and i != j: + raise ShapeError("Matrices are not aligned", i, j) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/adjoint.py b/lib/python3.11/site-packages/sympy/matrices/expressions/adjoint.py new file mode 100644 index 0000000000000000000000000000000000000000..2039a7b2eb8eeacb02435979121c4133a11d8e02 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/adjoint.py @@ -0,0 +1,60 @@ +from sympy.core import Basic +from sympy.functions import adjoint, conjugate +from sympy.matrices.expressions.matexpr import MatrixExpr + + +class Adjoint(MatrixExpr): + """ + The Hermitian adjoint of a matrix expression. + + This is a symbolic object that simply stores its argument without + evaluating it. To actually compute the adjoint, use the ``adjoint()`` + function. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Adjoint, adjoint + >>> A = MatrixSymbol('A', 3, 5) + >>> B = MatrixSymbol('B', 5, 3) + >>> Adjoint(A*B) + Adjoint(A*B) + >>> adjoint(A*B) + Adjoint(B)*Adjoint(A) + >>> adjoint(A*B) == Adjoint(A*B) + False + >>> adjoint(A*B) == Adjoint(A*B).doit() + True + """ + is_Adjoint = True + + def doit(self, **hints): + arg = self.arg + if hints.get('deep', True) and isinstance(arg, Basic): + return adjoint(arg.doit(**hints)) + else: + return adjoint(self.arg) + + @property + def arg(self): + return self.args[0] + + @property + def shape(self): + return self.arg.shape[::-1] + + def _entry(self, i, j, **kwargs): + return conjugate(self.arg._entry(j, i, **kwargs)) + + def _eval_adjoint(self): + return self.arg + + def _eval_transpose(self): + return self.arg.conjugate() + + def _eval_conjugate(self): + return self.arg.transpose() + + def _eval_trace(self): + from sympy.matrices.expressions.trace import Trace + return conjugate(Trace(self.arg)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/applyfunc.py b/lib/python3.11/site-packages/sympy/matrices/expressions/applyfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..c0363658447a8dc37a152b30e45533bac582b10c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/applyfunc.py @@ -0,0 +1,204 @@ +from sympy.core.expr import ExprBuilder +from sympy.core.function import (Function, FunctionClass, Lambda) +from sympy.core.symbol import Dummy +from sympy.core.sympify import sympify, _sympify +from sympy.matrices.expressions import MatrixExpr +from sympy.matrices.matrixbase import MatrixBase + + +class ElementwiseApplyFunction(MatrixExpr): + r""" + Apply function to a matrix elementwise without evaluating. + + Examples + ======== + + It can be created by calling ``.applyfunc()`` on a matrix + expression: + + >>> from sympy import MatrixSymbol + >>> from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction + >>> from sympy import exp + >>> X = MatrixSymbol("X", 3, 3) + >>> X.applyfunc(exp) + Lambda(_d, exp(_d)).(X) + + Otherwise using the class constructor: + + >>> from sympy import eye + >>> expr = ElementwiseApplyFunction(exp, eye(3)) + >>> expr + Lambda(_d, exp(_d)).(Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]])) + >>> expr.doit() + Matrix([ + [E, 1, 1], + [1, E, 1], + [1, 1, E]]) + + Notice the difference with the real mathematical functions: + + >>> exp(eye(3)) + Matrix([ + [E, 0, 0], + [0, E, 0], + [0, 0, E]]) + """ + + def __new__(cls, function, expr): + expr = _sympify(expr) + if not expr.is_Matrix: + raise ValueError("{} must be a matrix instance.".format(expr)) + + if expr.shape == (1, 1): + # Check if the function returns a matrix, in that case, just apply + # the function instead of creating an ElementwiseApplyFunc object: + ret = function(expr) + if isinstance(ret, MatrixExpr): + return ret + + if not isinstance(function, (FunctionClass, Lambda)): + d = Dummy('d') + function = Lambda(d, function(d)) + + function = sympify(function) + if not isinstance(function, (FunctionClass, Lambda)): + raise ValueError( + "{} should be compatible with SymPy function classes." + .format(function)) + + if 1 not in function.nargs: + raise ValueError( + '{} should be able to accept 1 arguments.'.format(function)) + + if not isinstance(function, Lambda): + d = Dummy('d') + function = Lambda(d, function(d)) + + obj = MatrixExpr.__new__(cls, function, expr) + return obj + + @property + def function(self): + return self.args[0] + + @property + def expr(self): + return self.args[1] + + @property + def shape(self): + return self.expr.shape + + def doit(self, **hints): + deep = hints.get("deep", True) + expr = self.expr + if deep: + expr = expr.doit(**hints) + function = self.function + if isinstance(function, Lambda) and function.is_identity: + # This is a Lambda containing the identity function. + return expr + if isinstance(expr, MatrixBase): + return expr.applyfunc(self.function) + elif isinstance(expr, ElementwiseApplyFunction): + return ElementwiseApplyFunction( + lambda x: self.function(expr.function(x)), + expr.expr + ).doit(**hints) + else: + return self + + def _entry(self, i, j, **kwargs): + return self.function(self.expr._entry(i, j, **kwargs)) + + def _get_function_fdiff(self): + d = Dummy("d") + function = self.function(d) + fdiff = function.diff(d) + if isinstance(fdiff, Function): + fdiff = type(fdiff) + else: + fdiff = Lambda(d, fdiff) + return fdiff + + def _eval_derivative(self, x): + from sympy.matrices.expressions.hadamard import hadamard_product + dexpr = self.expr.diff(x) + fdiff = self._get_function_fdiff() + return hadamard_product( + dexpr, + ElementwiseApplyFunction(fdiff, self.expr) + ) + + def _eval_derivative_matrix_lines(self, x): + from sympy.matrices.expressions.special import Identity + from sympy.tensor.array.expressions.array_expressions import ArrayContraction + from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal + from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct + + fdiff = self._get_function_fdiff() + lr = self.expr._eval_derivative_matrix_lines(x) + ewdiff = ElementwiseApplyFunction(fdiff, self.expr) + if 1 in x.shape: + # Vector: + iscolumn = self.shape[1] == 1 + for i in lr: + if iscolumn: + ptr1 = i.first_pointer + ptr2 = Identity(self.shape[1]) + else: + ptr1 = Identity(self.shape[0]) + ptr2 = i.second_pointer + + subexpr = ExprBuilder( + ArrayDiagonal, + [ + ExprBuilder( + ArrayTensorProduct, + [ + ewdiff, + ptr1, + ptr2, + ] + ), + (0, 2) if iscolumn else (1, 4) + ], + validator=ArrayDiagonal._validate + ) + i._lines = [subexpr] + i._first_pointer_parent = subexpr.args[0].args + i._first_pointer_index = 1 + i._second_pointer_parent = subexpr.args[0].args + i._second_pointer_index = 2 + else: + # Matrix case: + for i in lr: + ptr1 = i.first_pointer + ptr2 = i.second_pointer + newptr1 = Identity(ptr1.shape[1]) + newptr2 = Identity(ptr2.shape[1]) + subexpr = ExprBuilder( + ArrayContraction, + [ + ExprBuilder( + ArrayTensorProduct, + [ptr1, newptr1, ewdiff, ptr2, newptr2] + ), + (1, 2, 4), + (5, 7, 8), + ], + validator=ArrayContraction._validate + ) + i._first_pointer_parent = subexpr.args[0].args + i._first_pointer_index = 1 + i._second_pointer_parent = subexpr.args[0].args + i._second_pointer_index = 4 + i._lines = [subexpr] + return lr + + def _eval_transpose(self): + from sympy.matrices.expressions.transpose import Transpose + return self.func(self.function, Transpose(self.expr).doit()) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/blockmatrix.py b/lib/python3.11/site-packages/sympy/matrices/expressions/blockmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..4b5b840010ec5b4afb0580eb3114dbf011b611ee --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/blockmatrix.py @@ -0,0 +1,980 @@ +from sympy.assumptions.ask import (Q, ask) +from sympy.core import Basic, Add, Mul, S +from sympy.core.sympify import _sympify +from sympy.functions import adjoint +from sympy.functions.elementary.complexes import re, im +from sympy.strategies import typed, exhaust, condition, do_one, unpack +from sympy.strategies.traverse import bottom_up +from sympy.utilities.iterables import is_sequence, sift +from sympy.utilities.misc import filldedent + +from sympy.matrices import Matrix, ShapeError +from sympy.matrices.exceptions import NonInvertibleMatrixError +from sympy.matrices.expressions.determinant import det, Determinant +from sympy.matrices.expressions.inverse import Inverse +from sympy.matrices.expressions.matadd import MatAdd +from sympy.matrices.expressions.matexpr import MatrixExpr, MatrixElement +from sympy.matrices.expressions.matmul import MatMul +from sympy.matrices.expressions.matpow import MatPow +from sympy.matrices.expressions.slice import MatrixSlice +from sympy.matrices.expressions.special import ZeroMatrix, Identity +from sympy.matrices.expressions.trace import trace +from sympy.matrices.expressions.transpose import Transpose, transpose + + +class BlockMatrix(MatrixExpr): + """A BlockMatrix is a Matrix comprised of other matrices. + + The submatrices are stored in a SymPy Matrix object but accessed as part of + a Matrix Expression + + >>> from sympy import (MatrixSymbol, BlockMatrix, symbols, + ... Identity, ZeroMatrix, block_collapse) + >>> n,m,l = symbols('n m l') + >>> X = MatrixSymbol('X', n, n) + >>> Y = MatrixSymbol('Y', m, m) + >>> Z = MatrixSymbol('Z', n, m) + >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m,n), Y]]) + >>> print(B) + Matrix([ + [X, Z], + [0, Y]]) + + >>> C = BlockMatrix([[Identity(n), Z]]) + >>> print(C) + Matrix([[I, Z]]) + + >>> print(block_collapse(C*B)) + Matrix([[X, Z + Z*Y]]) + + Some matrices might be comprised of rows of blocks with + the matrices in each row having the same height and the + rows all having the same total number of columns but + not having the same number of columns for each matrix + in each row. In this case, the matrix is not a block + matrix and should be instantiated by Matrix. + + >>> from sympy import ones, Matrix + >>> dat = [ + ... [ones(3,2), ones(3,3)*2], + ... [ones(2,3)*3, ones(2,2)*4]] + ... + >>> BlockMatrix(dat) + Traceback (most recent call last): + ... + ValueError: + Although this matrix is comprised of blocks, the blocks do not fill + the matrix in a size-symmetric fashion. To create a full matrix from + these arguments, pass them directly to Matrix. + >>> Matrix(dat) + Matrix([ + [1, 1, 2, 2, 2], + [1, 1, 2, 2, 2], + [1, 1, 2, 2, 2], + [3, 3, 3, 4, 4], + [3, 3, 3, 4, 4]]) + + See Also + ======== + sympy.matrices.matrixbase.MatrixBase.irregular + """ + def __new__(cls, *args, **kwargs): + from sympy.matrices.immutable import ImmutableDenseMatrix + isMat = lambda i: getattr(i, 'is_Matrix', False) + if len(args) != 1 or \ + not is_sequence(args[0]) or \ + len({isMat(r) for r in args[0]}) != 1: + raise ValueError(filldedent(''' + expecting a sequence of 1 or more rows + containing Matrices.''')) + rows = args[0] if args else [] + if not isMat(rows): + if rows and isMat(rows[0]): + rows = [rows] # rows is not list of lists or [] + # regularity check + # same number of matrices in each row + blocky = ok = len({len(r) for r in rows}) == 1 + if ok: + # same number of rows for each matrix in a row + for r in rows: + ok = len({i.rows for i in r}) == 1 + if not ok: + break + blocky = ok + if ok: + # same number of cols for each matrix in each col + for c in range(len(rows[0])): + ok = len({rows[i][c].cols + for i in range(len(rows))}) == 1 + if not ok: + break + if not ok: + # same total cols in each row + ok = len({ + sum(i.cols for i in r) for r in rows}) == 1 + if blocky and ok: + raise ValueError(filldedent(''' + Although this matrix is comprised of blocks, + the blocks do not fill the matrix in a + size-symmetric fashion. To create a full matrix + from these arguments, pass them directly to + Matrix.''')) + raise ValueError(filldedent(''' + When there are not the same number of rows in each + row's matrices or there are not the same number of + total columns in each row, the matrix is not a + block matrix. If this matrix is known to consist of + blocks fully filling a 2-D space then see + Matrix.irregular.''')) + mat = ImmutableDenseMatrix(rows, evaluate=False) + obj = Basic.__new__(cls, mat) + return obj + + @property + def shape(self): + numrows = numcols = 0 + M = self.blocks + for i in range(M.shape[0]): + numrows += M[i, 0].shape[0] + for i in range(M.shape[1]): + numcols += M[0, i].shape[1] + return (numrows, numcols) + + @property + def blockshape(self): + return self.blocks.shape + + @property + def blocks(self): + return self.args[0] + + @property + def rowblocksizes(self): + return [self.blocks[i, 0].rows for i in range(self.blockshape[0])] + + @property + def colblocksizes(self): + return [self.blocks[0, i].cols for i in range(self.blockshape[1])] + + def structurally_equal(self, other): + return (isinstance(other, BlockMatrix) + and self.shape == other.shape + and self.blockshape == other.blockshape + and self.rowblocksizes == other.rowblocksizes + and self.colblocksizes == other.colblocksizes) + + def _blockmul(self, other): + if (isinstance(other, BlockMatrix) and + self.colblocksizes == other.rowblocksizes): + return BlockMatrix(self.blocks*other.blocks) + + return self * other + + def _blockadd(self, other): + if (isinstance(other, BlockMatrix) + and self.structurally_equal(other)): + return BlockMatrix(self.blocks + other.blocks) + + return self + other + + def _eval_transpose(self): + # Flip all the individual matrices + matrices = [transpose(matrix) for matrix in self.blocks] + # Make a copy + M = Matrix(self.blockshape[0], self.blockshape[1], matrices) + # Transpose the block structure + M = M.transpose() + return BlockMatrix(M) + + def _eval_adjoint(self): + # Adjoint all the individual matrices + matrices = [adjoint(matrix) for matrix in self.blocks] + # Make a copy + M = Matrix(self.blockshape[0], self.blockshape[1], matrices) + # Transpose the block structure + M = M.transpose() + return BlockMatrix(M) + + def _eval_trace(self): + if self.rowblocksizes == self.colblocksizes: + blocks = [self.blocks[i, i] for i in range(self.blockshape[0])] + return Add(*[trace(block) for block in blocks]) + + def _eval_determinant(self): + if self.blockshape == (1, 1): + return det(self.blocks[0, 0]) + if self.blockshape == (2, 2): + [[A, B], + [C, D]] = self.blocks.tolist() + if ask(Q.invertible(A)): + return det(A)*det(D - C*A.I*B) + elif ask(Q.invertible(D)): + return det(D)*det(A - B*D.I*C) + return Determinant(self) + + def _eval_as_real_imag(self): + real_matrices = [re(matrix) for matrix in self.blocks] + real_matrices = Matrix(self.blockshape[0], self.blockshape[1], real_matrices) + + im_matrices = [im(matrix) for matrix in self.blocks] + im_matrices = Matrix(self.blockshape[0], self.blockshape[1], im_matrices) + + return (BlockMatrix(real_matrices), BlockMatrix(im_matrices)) + + def _eval_derivative(self, x): + return BlockMatrix(self.blocks.diff(x)) + + def transpose(self): + """Return transpose of matrix. + + Examples + ======== + + >>> from sympy import MatrixSymbol, BlockMatrix, ZeroMatrix + >>> from sympy.abc import m, n + >>> X = MatrixSymbol('X', n, n) + >>> Y = MatrixSymbol('Y', m, m) + >>> Z = MatrixSymbol('Z', n, m) + >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m,n), Y]]) + >>> B.transpose() + Matrix([ + [X.T, 0], + [Z.T, Y.T]]) + >>> _.transpose() + Matrix([ + [X, Z], + [0, Y]]) + """ + return self._eval_transpose() + + def schur(self, mat = 'A', generalized = False): + """Return the Schur Complement of the 2x2 BlockMatrix + + Parameters + ========== + + mat : String, optional + The matrix with respect to which the + Schur Complement is calculated. 'A' is + used by default + + generalized : bool, optional + If True, returns the generalized Schur + Component which uses Moore-Penrose Inverse + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol, BlockMatrix + >>> m, n = symbols('m n') + >>> A = MatrixSymbol('A', n, n) + >>> B = MatrixSymbol('B', n, m) + >>> C = MatrixSymbol('C', m, n) + >>> D = MatrixSymbol('D', m, m) + >>> X = BlockMatrix([[A, B], [C, D]]) + + The default Schur Complement is evaluated with "A" + + >>> X.schur() + -C*A**(-1)*B + D + >>> X.schur('D') + A - B*D**(-1)*C + + Schur complement with non-invertible matrices is not + defined. Instead, the generalized Schur complement can + be calculated which uses the Moore-Penrose Inverse. To + achieve this, `generalized` must be set to `True` + + >>> X.schur('B', generalized=True) + C - D*(B.T*B)**(-1)*B.T*A + >>> X.schur('C', generalized=True) + -A*(C.T*C)**(-1)*C.T*D + B + + Returns + ======= + + M : Matrix + The Schur Complement Matrix + + Raises + ====== + + ShapeError + If the block matrix is not a 2x2 matrix + + NonInvertibleMatrixError + If given matrix is non-invertible + + References + ========== + + .. [1] Wikipedia Article on Schur Component : https://en.wikipedia.org/wiki/Schur_complement + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.pinv + """ + + if self.blockshape == (2, 2): + [[A, B], + [C, D]] = self.blocks.tolist() + d={'A' : A, 'B' : B, 'C' : C, 'D' : D} + try: + inv = (d[mat].T*d[mat]).inv()*d[mat].T if generalized else d[mat].inv() + if mat == 'A': + return D - C * inv * B + elif mat == 'B': + return C - D * inv * A + elif mat == 'C': + return B - A * inv * D + elif mat == 'D': + return A - B * inv * C + #For matrices where no sub-matrix is square + return self + except NonInvertibleMatrixError: + raise NonInvertibleMatrixError('The given matrix is not invertible. Please set generalized=True \ + to compute the generalized Schur Complement which uses Moore-Penrose Inverse') + else: + raise ShapeError('Schur Complement can only be calculated for 2x2 block matrices') + + def LDUdecomposition(self): + """Returns the Block LDU decomposition of + a 2x2 Block Matrix + + Returns + ======= + + (L, D, U) : Matrices + L : Lower Diagonal Matrix + D : Diagonal Matrix + U : Upper Diagonal Matrix + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse + >>> m, n = symbols('m n') + >>> A = MatrixSymbol('A', n, n) + >>> B = MatrixSymbol('B', n, m) + >>> C = MatrixSymbol('C', m, n) + >>> D = MatrixSymbol('D', m, m) + >>> X = BlockMatrix([[A, B], [C, D]]) + >>> L, D, U = X.LDUdecomposition() + >>> block_collapse(L*D*U) + Matrix([ + [A, B], + [C, D]]) + + Raises + ====== + + ShapeError + If the block matrix is not a 2x2 matrix + + NonInvertibleMatrixError + If the matrix "A" is non-invertible + + See Also + ======== + sympy.matrices.expressions.blockmatrix.BlockMatrix.UDLdecomposition + sympy.matrices.expressions.blockmatrix.BlockMatrix.LUdecomposition + """ + if self.blockshape == (2,2): + [[A, B], + [C, D]] = self.blocks.tolist() + try: + AI = A.I + except NonInvertibleMatrixError: + raise NonInvertibleMatrixError('Block LDU decomposition cannot be calculated when\ + "A" is singular') + Ip = Identity(B.shape[0]) + Iq = Identity(B.shape[1]) + Z = ZeroMatrix(*B.shape) + L = BlockMatrix([[Ip, Z], [C*AI, Iq]]) + D = BlockDiagMatrix(A, self.schur()) + U = BlockMatrix([[Ip, AI*B],[Z.T, Iq]]) + return L, D, U + else: + raise ShapeError("Block LDU decomposition is supported only for 2x2 block matrices") + + def UDLdecomposition(self): + """Returns the Block UDL decomposition of + a 2x2 Block Matrix + + Returns + ======= + + (U, D, L) : Matrices + U : Upper Diagonal Matrix + D : Diagonal Matrix + L : Lower Diagonal Matrix + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse + >>> m, n = symbols('m n') + >>> A = MatrixSymbol('A', n, n) + >>> B = MatrixSymbol('B', n, m) + >>> C = MatrixSymbol('C', m, n) + >>> D = MatrixSymbol('D', m, m) + >>> X = BlockMatrix([[A, B], [C, D]]) + >>> U, D, L = X.UDLdecomposition() + >>> block_collapse(U*D*L) + Matrix([ + [A, B], + [C, D]]) + + Raises + ====== + + ShapeError + If the block matrix is not a 2x2 matrix + + NonInvertibleMatrixError + If the matrix "D" is non-invertible + + See Also + ======== + sympy.matrices.expressions.blockmatrix.BlockMatrix.LDUdecomposition + sympy.matrices.expressions.blockmatrix.BlockMatrix.LUdecomposition + """ + if self.blockshape == (2,2): + [[A, B], + [C, D]] = self.blocks.tolist() + try: + DI = D.I + except NonInvertibleMatrixError: + raise NonInvertibleMatrixError('Block UDL decomposition cannot be calculated when\ + "D" is singular') + Ip = Identity(A.shape[0]) + Iq = Identity(B.shape[1]) + Z = ZeroMatrix(*B.shape) + U = BlockMatrix([[Ip, B*DI], [Z.T, Iq]]) + D = BlockDiagMatrix(self.schur('D'), D) + L = BlockMatrix([[Ip, Z],[DI*C, Iq]]) + return U, D, L + else: + raise ShapeError("Block UDL decomposition is supported only for 2x2 block matrices") + + def LUdecomposition(self): + """Returns the Block LU decomposition of + a 2x2 Block Matrix + + Returns + ======= + + (L, U) : Matrices + L : Lower Diagonal Matrix + U : Upper Diagonal Matrix + + Examples + ======== + + >>> from sympy import symbols, MatrixSymbol, BlockMatrix, block_collapse + >>> m, n = symbols('m n') + >>> A = MatrixSymbol('A', n, n) + >>> B = MatrixSymbol('B', n, m) + >>> C = MatrixSymbol('C', m, n) + >>> D = MatrixSymbol('D', m, m) + >>> X = BlockMatrix([[A, B], [C, D]]) + >>> L, U = X.LUdecomposition() + >>> block_collapse(L*U) + Matrix([ + [A, B], + [C, D]]) + + Raises + ====== + + ShapeError + If the block matrix is not a 2x2 matrix + + NonInvertibleMatrixError + If the matrix "A" is non-invertible + + See Also + ======== + sympy.matrices.expressions.blockmatrix.BlockMatrix.UDLdecomposition + sympy.matrices.expressions.blockmatrix.BlockMatrix.LDUdecomposition + """ + if self.blockshape == (2,2): + [[A, B], + [C, D]] = self.blocks.tolist() + try: + A = A**S.Half + AI = A.I + except NonInvertibleMatrixError: + raise NonInvertibleMatrixError('Block LU decomposition cannot be calculated when\ + "A" is singular') + Z = ZeroMatrix(*B.shape) + Q = self.schur()**S.Half + L = BlockMatrix([[A, Z], [C*AI, Q]]) + U = BlockMatrix([[A, AI*B],[Z.T, Q]]) + return L, U + else: + raise ShapeError("Block LU decomposition is supported only for 2x2 block matrices") + + def _entry(self, i, j, **kwargs): + # Find row entry + orig_i, orig_j = i, j + for row_block, numrows in enumerate(self.rowblocksizes): + cmp = i < numrows + if cmp == True: + break + elif cmp == False: + i -= numrows + elif row_block < self.blockshape[0] - 1: + # Can't tell which block and it's not the last one, return unevaluated + return MatrixElement(self, orig_i, orig_j) + for col_block, numcols in enumerate(self.colblocksizes): + cmp = j < numcols + if cmp == True: + break + elif cmp == False: + j -= numcols + elif col_block < self.blockshape[1] - 1: + return MatrixElement(self, orig_i, orig_j) + return self.blocks[row_block, col_block][i, j] + + @property + def is_Identity(self): + if self.blockshape[0] != self.blockshape[1]: + return False + for i in range(self.blockshape[0]): + for j in range(self.blockshape[1]): + if i==j and not self.blocks[i, j].is_Identity: + return False + if i!=j and not self.blocks[i, j].is_ZeroMatrix: + return False + return True + + @property + def is_structurally_symmetric(self): + return self.rowblocksizes == self.colblocksizes + + def equals(self, other): + if self == other: + return True + if (isinstance(other, BlockMatrix) and self.blocks == other.blocks): + return True + return super().equals(other) + + +class BlockDiagMatrix(BlockMatrix): + """A sparse matrix with block matrices along its diagonals + + Examples + ======== + + >>> from sympy import MatrixSymbol, BlockDiagMatrix, symbols + >>> n, m, l = symbols('n m l') + >>> X = MatrixSymbol('X', n, n) + >>> Y = MatrixSymbol('Y', m, m) + >>> BlockDiagMatrix(X, Y) + Matrix([ + [X, 0], + [0, Y]]) + + Notes + ===== + + If you want to get the individual diagonal blocks, use + :meth:`get_diag_blocks`. + + See Also + ======== + + sympy.matrices.dense.diag + """ + def __new__(cls, *mats): + return Basic.__new__(BlockDiagMatrix, *[_sympify(m) for m in mats]) + + @property + def diag(self): + return self.args + + @property + def blocks(self): + from sympy.matrices.immutable import ImmutableDenseMatrix + mats = self.args + data = [[mats[i] if i == j else ZeroMatrix(mats[i].rows, mats[j].cols) + for j in range(len(mats))] + for i in range(len(mats))] + return ImmutableDenseMatrix(data, evaluate=False) + + @property + def shape(self): + return (sum(block.rows for block in self.args), + sum(block.cols for block in self.args)) + + @property + def blockshape(self): + n = len(self.args) + return (n, n) + + @property + def rowblocksizes(self): + return [block.rows for block in self.args] + + @property + def colblocksizes(self): + return [block.cols for block in self.args] + + def _all_square_blocks(self): + """Returns true if all blocks are square""" + return all(mat.is_square for mat in self.args) + + def _eval_determinant(self): + if self._all_square_blocks(): + return Mul(*[det(mat) for mat in self.args]) + # At least one block is non-square. Since the entire matrix must be square we know there must + # be at least two blocks in this matrix, in which case the entire matrix is necessarily rank-deficient + return S.Zero + + def _eval_inverse(self, expand='ignored'): + if self._all_square_blocks(): + return BlockDiagMatrix(*[mat.inverse() for mat in self.args]) + # See comment in _eval_determinant() + raise NonInvertibleMatrixError('Matrix det == 0; not invertible.') + + def _eval_transpose(self): + return BlockDiagMatrix(*[mat.transpose() for mat in self.args]) + + def _blockmul(self, other): + if (isinstance(other, BlockDiagMatrix) and + self.colblocksizes == other.rowblocksizes): + return BlockDiagMatrix(*[a*b for a, b in zip(self.args, other.args)]) + else: + return BlockMatrix._blockmul(self, other) + + def _blockadd(self, other): + if (isinstance(other, BlockDiagMatrix) and + self.blockshape == other.blockshape and + self.rowblocksizes == other.rowblocksizes and + self.colblocksizes == other.colblocksizes): + return BlockDiagMatrix(*[a + b for a, b in zip(self.args, other.args)]) + else: + return BlockMatrix._blockadd(self, other) + + def get_diag_blocks(self): + """Return the list of diagonal blocks of the matrix. + + Examples + ======== + + >>> from sympy import BlockDiagMatrix, Matrix + + >>> A = Matrix([[1, 2], [3, 4]]) + >>> B = Matrix([[5, 6], [7, 8]]) + >>> M = BlockDiagMatrix(A, B) + + How to get diagonal blocks from the block diagonal matrix: + + >>> diag_blocks = M.get_diag_blocks() + >>> diag_blocks[0] + Matrix([ + [1, 2], + [3, 4]]) + >>> diag_blocks[1] + Matrix([ + [5, 6], + [7, 8]]) + """ + return self.args + + +def block_collapse(expr): + """Evaluates a block matrix expression + + >>> from sympy import MatrixSymbol, BlockMatrix, symbols, Identity, ZeroMatrix, block_collapse + >>> n,m,l = symbols('n m l') + >>> X = MatrixSymbol('X', n, n) + >>> Y = MatrixSymbol('Y', m, m) + >>> Z = MatrixSymbol('Z', n, m) + >>> B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]]) + >>> print(B) + Matrix([ + [X, Z], + [0, Y]]) + + >>> C = BlockMatrix([[Identity(n), Z]]) + >>> print(C) + Matrix([[I, Z]]) + + >>> print(block_collapse(C*B)) + Matrix([[X, Z + Z*Y]]) + """ + from sympy.strategies.util import expr_fns + + hasbm = lambda expr: isinstance(expr, MatrixExpr) and expr.has(BlockMatrix) + + conditioned_rl = condition( + hasbm, + typed( + {MatAdd: do_one(bc_matadd, bc_block_plus_ident), + MatMul: do_one(bc_matmul, bc_dist), + MatPow: bc_matmul, + Transpose: bc_transpose, + Inverse: bc_inverse, + BlockMatrix: do_one(bc_unpack, deblock)} + ) + ) + + rule = exhaust( + bottom_up( + exhaust(conditioned_rl), + fns=expr_fns + ) + ) + + result = rule(expr) + doit = getattr(result, 'doit', None) + if doit is not None: + return doit() + else: + return result + +def bc_unpack(expr): + if expr.blockshape == (1, 1): + return expr.blocks[0, 0] + return expr + +def bc_matadd(expr): + args = sift(expr.args, lambda M: isinstance(M, BlockMatrix)) + blocks = args[True] + if not blocks: + return expr + + nonblocks = args[False] + block = blocks[0] + for b in blocks[1:]: + block = block._blockadd(b) + if nonblocks: + return MatAdd(*nonblocks) + block + else: + return block + +def bc_block_plus_ident(expr): + idents = [arg for arg in expr.args if arg.is_Identity] + if not idents: + return expr + + blocks = [arg for arg in expr.args if isinstance(arg, BlockMatrix)] + if (blocks and all(b.structurally_equal(blocks[0]) for b in blocks) + and blocks[0].is_structurally_symmetric): + block_id = BlockDiagMatrix(*[Identity(k) + for k in blocks[0].rowblocksizes]) + rest = [arg for arg in expr.args if not arg.is_Identity and not isinstance(arg, BlockMatrix)] + return MatAdd(block_id * len(idents), *blocks, *rest).doit() + + return expr + +def bc_dist(expr): + """ Turn a*[X, Y] into [a*X, a*Y] """ + factor, mat = expr.as_coeff_mmul() + if factor == 1: + return expr + + unpacked = unpack(mat) + + if isinstance(unpacked, BlockDiagMatrix): + B = unpacked.diag + new_B = [factor * mat for mat in B] + return BlockDiagMatrix(*new_B) + elif isinstance(unpacked, BlockMatrix): + B = unpacked.blocks + new_B = [ + [factor * B[i, j] for j in range(B.cols)] for i in range(B.rows)] + return BlockMatrix(new_B) + return expr + + +def bc_matmul(expr): + if isinstance(expr, MatPow): + if expr.args[1].is_Integer and expr.args[1] > 0: + factor, matrices = 1, [expr.args[0]]*expr.args[1] + else: + return expr + else: + factor, matrices = expr.as_coeff_matrices() + + i = 0 + while (i+1 < len(matrices)): + A, B = matrices[i:i+2] + if isinstance(A, BlockMatrix) and isinstance(B, BlockMatrix): + matrices[i] = A._blockmul(B) + matrices.pop(i+1) + elif isinstance(A, BlockMatrix): + matrices[i] = A._blockmul(BlockMatrix([[B]])) + matrices.pop(i+1) + elif isinstance(B, BlockMatrix): + matrices[i] = BlockMatrix([[A]])._blockmul(B) + matrices.pop(i+1) + else: + i+=1 + return MatMul(factor, *matrices).doit() + +def bc_transpose(expr): + collapse = block_collapse(expr.arg) + return collapse._eval_transpose() + + +def bc_inverse(expr): + if isinstance(expr.arg, BlockDiagMatrix): + return expr.inverse() + + expr2 = blockinverse_1x1(expr) + if expr != expr2: + return expr2 + return blockinverse_2x2(Inverse(reblock_2x2(expr.arg))) + +def blockinverse_1x1(expr): + if isinstance(expr.arg, BlockMatrix) and expr.arg.blockshape == (1, 1): + mat = Matrix([[expr.arg.blocks[0].inverse()]]) + return BlockMatrix(mat) + return expr + + +def blockinverse_2x2(expr): + if isinstance(expr.arg, BlockMatrix) and expr.arg.blockshape == (2, 2): + # See: Inverses of 2x2 Block Matrices, Tzon-Tzer Lu and Sheng-Hua Shiou + [[A, B], + [C, D]] = expr.arg.blocks.tolist() + + formula = _choose_2x2_inversion_formula(A, B, C, D) + if formula != None: + MI = expr.arg.schur(formula).I + if formula == 'A': + AI = A.I + return BlockMatrix([[AI + AI * B * MI * C * AI, -AI * B * MI], [-MI * C * AI, MI]]) + if formula == 'B': + BI = B.I + return BlockMatrix([[-MI * D * BI, MI], [BI + BI * A * MI * D * BI, -BI * A * MI]]) + if formula == 'C': + CI = C.I + return BlockMatrix([[-CI * D * MI, CI + CI * D * MI * A * CI], [MI, -MI * A * CI]]) + if formula == 'D': + DI = D.I + return BlockMatrix([[MI, -MI * B * DI], [-DI * C * MI, DI + DI * C * MI * B * DI]]) + + return expr + + +def _choose_2x2_inversion_formula(A, B, C, D): + """ + Assuming [[A, B], [C, D]] would form a valid square block matrix, find + which of the classical 2x2 block matrix inversion formulas would be + best suited. + + Returns 'A', 'B', 'C', 'D' to represent the algorithm involving inversion + of the given argument or None if the matrix cannot be inverted using + any of those formulas. + """ + # Try to find a known invertible matrix. Note that the Schur complement + # is currently not being considered for this + A_inv = ask(Q.invertible(A)) + if A_inv == True: + return 'A' + B_inv = ask(Q.invertible(B)) + if B_inv == True: + return 'B' + C_inv = ask(Q.invertible(C)) + if C_inv == True: + return 'C' + D_inv = ask(Q.invertible(D)) + if D_inv == True: + return 'D' + # Otherwise try to find a matrix that isn't known to be non-invertible + if A_inv != False: + return 'A' + if B_inv != False: + return 'B' + if C_inv != False: + return 'C' + if D_inv != False: + return 'D' + return None + + +def deblock(B): + """ Flatten a BlockMatrix of BlockMatrices """ + if not isinstance(B, BlockMatrix) or not B.blocks.has(BlockMatrix): + return B + wrap = lambda x: x if isinstance(x, BlockMatrix) else BlockMatrix([[x]]) + bb = B.blocks.applyfunc(wrap) # everything is a block + + try: + MM = Matrix(0, sum(bb[0, i].blocks.shape[1] for i in range(bb.shape[1])), []) + for row in range(0, bb.shape[0]): + M = Matrix(bb[row, 0].blocks) + for col in range(1, bb.shape[1]): + M = M.row_join(bb[row, col].blocks) + MM = MM.col_join(M) + + return BlockMatrix(MM) + except ShapeError: + return B + + +def reblock_2x2(expr): + """ + Reblock a BlockMatrix so that it has 2x2 blocks of block matrices. If + possible in such a way that the matrix continues to be invertible using the + classical 2x2 block inversion formulas. + """ + if not isinstance(expr, BlockMatrix) or not all(d > 2 for d in expr.blockshape): + return expr + + BM = BlockMatrix # for brevity's sake + rowblocks, colblocks = expr.blockshape + blocks = expr.blocks + for i in range(1, rowblocks): + for j in range(1, colblocks): + # try to split rows at i and cols at j + A = bc_unpack(BM(blocks[:i, :j])) + B = bc_unpack(BM(blocks[:i, j:])) + C = bc_unpack(BM(blocks[i:, :j])) + D = bc_unpack(BM(blocks[i:, j:])) + + formula = _choose_2x2_inversion_formula(A, B, C, D) + if formula is not None: + return BlockMatrix([[A, B], [C, D]]) + + # else: nothing worked, just split upper left corner + return BM([[blocks[0, 0], BM(blocks[0, 1:])], + [BM(blocks[1:, 0]), BM(blocks[1:, 1:])]]) + + +def bounds(sizes): + """ Convert sequence of numbers into pairs of low-high pairs + + >>> from sympy.matrices.expressions.blockmatrix import bounds + >>> bounds((1, 10, 50)) + [(0, 1), (1, 11), (11, 61)] + """ + low = 0 + rv = [] + for size in sizes: + rv.append((low, low + size)) + low += size + return rv + +def blockcut(expr, rowsizes, colsizes): + """ Cut a matrix expression into Blocks + + >>> from sympy import ImmutableMatrix, blockcut + >>> M = ImmutableMatrix(4, 4, range(16)) + >>> B = blockcut(M, (1, 3), (1, 3)) + >>> type(B).__name__ + 'BlockMatrix' + >>> ImmutableMatrix(B.blocks[0, 1]) + Matrix([[1, 2, 3]]) + """ + + rowbounds = bounds(rowsizes) + colbounds = bounds(colsizes) + return BlockMatrix([[MatrixSlice(expr, rowbound, colbound) + for colbound in colbounds] + for rowbound in rowbounds]) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/companion.py b/lib/python3.11/site-packages/sympy/matrices/expressions/companion.py new file mode 100644 index 0000000000000000000000000000000000000000..6969c917f63806cb1f5417804e01ecc1350d1406 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/companion.py @@ -0,0 +1,56 @@ +from sympy.core.singleton import S +from sympy.core.sympify import _sympify +from sympy.polys.polytools import Poly + +from .matexpr import MatrixExpr + + +class CompanionMatrix(MatrixExpr): + """A symbolic companion matrix of a polynomial. + + Examples + ======== + + >>> from sympy import Poly, Symbol, symbols + >>> from sympy.matrices.expressions import CompanionMatrix + >>> x = Symbol('x') + >>> c0, c1, c2, c3, c4 = symbols('c0:5') + >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x) + >>> CompanionMatrix(p) + CompanionMatrix(Poly(x**5 + c4*x**4 + c3*x**3 + c2*x**2 + c1*x + c0, + x, domain='ZZ[c0,c1,c2,c3,c4]')) + """ + def __new__(cls, poly): + poly = _sympify(poly) + if not isinstance(poly, Poly): + raise ValueError("{} must be a Poly instance.".format(poly)) + if not poly.is_monic: + raise ValueError("{} must be a monic polynomial.".format(poly)) + if not poly.is_univariate: + raise ValueError( + "{} must be a univariate polynomial.".format(poly)) + if not poly.degree() >= 1: + raise ValueError( + "{} must have degree not less than 1.".format(poly)) + + return super().__new__(cls, poly) + + + @property + def shape(self): + poly = self.args[0] + size = poly.degree() + return size, size + + + def _entry(self, i, j): + if j == self.cols - 1: + return -self.args[0].all_coeffs()[-1 - i] + elif i == j + 1: + return S.One + return S.Zero + + + def as_explicit(self): + from sympy.matrices.immutable import ImmutableDenseMatrix + return ImmutableDenseMatrix.companion(self.args[0]) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/determinant.py b/lib/python3.11/site-packages/sympy/matrices/expressions/determinant.py new file mode 100644 index 0000000000000000000000000000000000000000..b323b3f93a5a0404bf2205f39d25b931d173b6d9 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/determinant.py @@ -0,0 +1,148 @@ +from sympy.core.basic import Basic +from sympy.core.expr import Expr +from sympy.core.singleton import S +from sympy.core.sympify import sympify +from sympy.matrices.exceptions import NonSquareMatrixError +from sympy.matrices.matrixbase import MatrixBase + + +class Determinant(Expr): + """Matrix Determinant + + Represents the determinant of a matrix expression. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Determinant, eye + >>> A = MatrixSymbol('A', 3, 3) + >>> Determinant(A) + Determinant(A) + >>> Determinant(eye(3)).doit() + 1 + """ + is_commutative = True + + def __new__(cls, mat): + mat = sympify(mat) + if not mat.is_Matrix: + raise TypeError("Input to Determinant, %s, not a matrix" % str(mat)) + + if mat.is_square is False: + raise NonSquareMatrixError("Det of a non-square matrix") + + return Basic.__new__(cls, mat) + + @property + def arg(self): + return self.args[0] + + @property + def kind(self): + return self.arg.kind.element_kind + + def doit(self, **hints): + arg = self.arg + if hints.get('deep', True): + arg = arg.doit(**hints) + + result = arg._eval_determinant() + if result is not None: + return result + + return self + + +def det(matexpr): + """ Matrix Determinant + + Examples + ======== + + >>> from sympy import MatrixSymbol, det, eye + >>> A = MatrixSymbol('A', 3, 3) + >>> det(A) + Determinant(A) + >>> det(eye(3)) + 1 + """ + + return Determinant(matexpr).doit() + +class Permanent(Expr): + """Matrix Permanent + + Represents the permanent of a matrix expression. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Permanent, ones + >>> A = MatrixSymbol('A', 3, 3) + >>> Permanent(A) + Permanent(A) + >>> Permanent(ones(3, 3)).doit() + 6 + """ + + def __new__(cls, mat): + mat = sympify(mat) + if not mat.is_Matrix: + raise TypeError("Input to Permanent, %s, not a matrix" % str(mat)) + + return Basic.__new__(cls, mat) + + @property + def arg(self): + return self.args[0] + + def doit(self, expand=False, **hints): + if isinstance(self.arg, MatrixBase): + return self.arg.per() + else: + return self + +def per(matexpr): + """ Matrix Permanent + + Examples + ======== + + >>> from sympy import MatrixSymbol, Matrix, per, ones + >>> A = MatrixSymbol('A', 3, 3) + >>> per(A) + Permanent(A) + >>> per(ones(5, 5)) + 120 + >>> M = Matrix([1, 2, 5]) + >>> per(M) + 8 + """ + + return Permanent(matexpr).doit() + +from sympy.assumptions.ask import ask, Q +from sympy.assumptions.refine import handlers_dict + + +def refine_Determinant(expr, assumptions): + """ + >>> from sympy import MatrixSymbol, Q, assuming, refine, det + >>> X = MatrixSymbol('X', 2, 2) + >>> det(X) + Determinant(X) + >>> with assuming(Q.orthogonal(X)): + ... print(refine(det(X))) + 1 + """ + if ask(Q.orthogonal(expr.arg), assumptions): + return S.One + elif ask(Q.singular(expr.arg), assumptions): + return S.Zero + elif ask(Q.unit_triangular(expr.arg), assumptions): + return S.One + + return expr + + +handlers_dict['Determinant'] = refine_Determinant diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/diagonal.py b/lib/python3.11/site-packages/sympy/matrices/expressions/diagonal.py new file mode 100644 index 0000000000000000000000000000000000000000..ba8a0216588143e3e251dab84c25f038fad550a4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/diagonal.py @@ -0,0 +1,220 @@ +from sympy.core.sympify import _sympify + +from sympy.matrices.expressions import MatrixExpr +from sympy.core import S, Eq, Ge +from sympy.core.mul import Mul +from sympy.functions.special.tensor_functions import KroneckerDelta + + +class DiagonalMatrix(MatrixExpr): + """DiagonalMatrix(M) will create a matrix expression that + behaves as though all off-diagonal elements, + `M[i, j]` where `i != j`, are zero. + + Examples + ======== + + >>> from sympy import MatrixSymbol, DiagonalMatrix, Symbol + >>> n = Symbol('n', integer=True) + >>> m = Symbol('m', integer=True) + >>> D = DiagonalMatrix(MatrixSymbol('x', 2, 3)) + >>> D[1, 2] + 0 + >>> D[1, 1] + x[1, 1] + + The length of the diagonal -- the lesser of the two dimensions of `M` -- + is accessed through the `diagonal_length` property: + + >>> D.diagonal_length + 2 + >>> DiagonalMatrix(MatrixSymbol('x', n + 1, n)).diagonal_length + n + + When one of the dimensions is symbolic the other will be treated as + though it is smaller: + + >>> tall = DiagonalMatrix(MatrixSymbol('x', n, 3)) + >>> tall.diagonal_length + 3 + >>> tall[10, 1] + 0 + + When the size of the diagonal is not known, a value of None will + be returned: + + >>> DiagonalMatrix(MatrixSymbol('x', n, m)).diagonal_length is None + True + + """ + arg = property(lambda self: self.args[0]) + + shape = property(lambda self: self.arg.shape) # type:ignore + + @property + def diagonal_length(self): + r, c = self.shape + if r.is_Integer and c.is_Integer: + m = min(r, c) + elif r.is_Integer and not c.is_Integer: + m = r + elif c.is_Integer and not r.is_Integer: + m = c + elif r == c: + m = r + else: + try: + m = min(r, c) + except TypeError: + m = None + return m + + def _entry(self, i, j, **kwargs): + if self.diagonal_length is not None: + if Ge(i, self.diagonal_length) is S.true: + return S.Zero + elif Ge(j, self.diagonal_length) is S.true: + return S.Zero + eq = Eq(i, j) + if eq is S.true: + return self.arg[i, i] + elif eq is S.false: + return S.Zero + return self.arg[i, j]*KroneckerDelta(i, j) + + +class DiagonalOf(MatrixExpr): + """DiagonalOf(M) will create a matrix expression that + is equivalent to the diagonal of `M`, represented as + a single column matrix. + + Examples + ======== + + >>> from sympy import MatrixSymbol, DiagonalOf, Symbol + >>> n = Symbol('n', integer=True) + >>> m = Symbol('m', integer=True) + >>> x = MatrixSymbol('x', 2, 3) + >>> diag = DiagonalOf(x) + >>> diag.shape + (2, 1) + + The diagonal can be addressed like a matrix or vector and will + return the corresponding element of the original matrix: + + >>> diag[1, 0] == diag[1] == x[1, 1] + True + + The length of the diagonal -- the lesser of the two dimensions of `M` -- + is accessed through the `diagonal_length` property: + + >>> diag.diagonal_length + 2 + >>> DiagonalOf(MatrixSymbol('x', n + 1, n)).diagonal_length + n + + When only one of the dimensions is symbolic the other will be + treated as though it is smaller: + + >>> dtall = DiagonalOf(MatrixSymbol('x', n, 3)) + >>> dtall.diagonal_length + 3 + + When the size of the diagonal is not known, a value of None will + be returned: + + >>> DiagonalOf(MatrixSymbol('x', n, m)).diagonal_length is None + True + + """ + arg = property(lambda self: self.args[0]) + @property + def shape(self): + r, c = self.arg.shape + if r.is_Integer and c.is_Integer: + m = min(r, c) + elif r.is_Integer and not c.is_Integer: + m = r + elif c.is_Integer and not r.is_Integer: + m = c + elif r == c: + m = r + else: + try: + m = min(r, c) + except TypeError: + m = None + return m, S.One + + @property + def diagonal_length(self): + return self.shape[0] + + def _entry(self, i, j, **kwargs): + return self.arg._entry(i, i, **kwargs) + + +class DiagMatrix(MatrixExpr): + """ + Turn a vector into a diagonal matrix. + """ + def __new__(cls, vector): + vector = _sympify(vector) + obj = MatrixExpr.__new__(cls, vector) + shape = vector.shape + dim = shape[1] if shape[0] == 1 else shape[0] + if vector.shape[0] != 1: + obj._iscolumn = True + else: + obj._iscolumn = False + obj._shape = (dim, dim) + obj._vector = vector + return obj + + @property + def shape(self): + return self._shape + + def _entry(self, i, j, **kwargs): + if self._iscolumn: + result = self._vector._entry(i, 0, **kwargs) + else: + result = self._vector._entry(0, j, **kwargs) + if i != j: + result *= KroneckerDelta(i, j) + return result + + def _eval_transpose(self): + return self + + def as_explicit(self): + from sympy.matrices.dense import diag + return diag(*list(self._vector.as_explicit())) + + def doit(self, **hints): + from sympy.assumptions import ask, Q + from sympy.matrices.expressions.matmul import MatMul + from sympy.matrices.expressions.transpose import Transpose + from sympy.matrices.dense import eye + from sympy.matrices.matrixbase import MatrixBase + vector = self._vector + # This accounts for shape (1, 1) and identity matrices, among others: + if ask(Q.diagonal(vector)): + return vector + if isinstance(vector, MatrixBase): + ret = eye(max(vector.shape)) + for i in range(ret.shape[0]): + ret[i, i] = vector[i] + return type(vector)(ret) + if vector.is_MatMul: + matrices = [arg for arg in vector.args if arg.is_Matrix] + scalars = [arg for arg in vector.args if arg not in matrices] + if scalars: + return Mul.fromiter(scalars)*DiagMatrix(MatMul.fromiter(matrices).doit()).doit() + if isinstance(vector, Transpose): + vector = vector.arg + return DiagMatrix(vector) + + +def diagonalize_vector(vector): + return DiagMatrix(vector).doit() diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/dotproduct.py b/lib/python3.11/site-packages/sympy/matrices/expressions/dotproduct.py new file mode 100644 index 0000000000000000000000000000000000000000..3a413f8c79a221505f0c082d7f19f78597a2befc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/dotproduct.py @@ -0,0 +1,55 @@ +from sympy.core import Basic, Expr +from sympy.core.sympify import _sympify +from sympy.matrices.expressions.transpose import transpose + + +class DotProduct(Expr): + """ + Dot product of vector matrices + + The input should be two 1 x n or n x 1 matrices. The output represents the + scalar dotproduct. + + This is similar to using MatrixElement and MatMul, except DotProduct does + not require that one vector to be a row vector and the other vector to be + a column vector. + + >>> from sympy import MatrixSymbol, DotProduct + >>> A = MatrixSymbol('A', 1, 3) + >>> B = MatrixSymbol('B', 1, 3) + >>> DotProduct(A, B) + DotProduct(A, B) + >>> DotProduct(A, B).doit() + A[0, 0]*B[0, 0] + A[0, 1]*B[0, 1] + A[0, 2]*B[0, 2] + """ + + def __new__(cls, arg1, arg2): + arg1, arg2 = _sympify((arg1, arg2)) + + if not arg1.is_Matrix: + raise TypeError("Argument 1 of DotProduct is not a matrix") + if not arg2.is_Matrix: + raise TypeError("Argument 2 of DotProduct is not a matrix") + if not (1 in arg1.shape): + raise TypeError("Argument 1 of DotProduct is not a vector") + if not (1 in arg2.shape): + raise TypeError("Argument 2 of DotProduct is not a vector") + + if set(arg1.shape) != set(arg2.shape): + raise TypeError("DotProduct arguments are not the same length") + + return Basic.__new__(cls, arg1, arg2) + + def doit(self, expand=False, **hints): + if self.args[0].shape == self.args[1].shape: + if self.args[0].shape[0] == 1: + mul = self.args[0]*transpose(self.args[1]) + else: + mul = transpose(self.args[0])*self.args[1] + else: + if self.args[0].shape[0] == 1: + mul = self.args[0]*self.args[1] + else: + mul = transpose(self.args[0])*transpose(self.args[1]) + + return mul[0] diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/factorizations.py b/lib/python3.11/site-packages/sympy/matrices/expressions/factorizations.py new file mode 100644 index 0000000000000000000000000000000000000000..aff2bb81ecff99d8e733f282ac2dd187d76ce895 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/factorizations.py @@ -0,0 +1,62 @@ +from sympy.matrices.expressions import MatrixExpr +from sympy.assumptions.ask import Q + +class Factorization(MatrixExpr): + arg = property(lambda self: self.args[0]) + shape = property(lambda self: self.arg.shape) # type: ignore + +class LofLU(Factorization): + @property + def predicates(self): + return (Q.lower_triangular,) +class UofLU(Factorization): + @property + def predicates(self): + return (Q.upper_triangular,) + +class LofCholesky(LofLU): pass +class UofCholesky(UofLU): pass + +class QofQR(Factorization): + @property + def predicates(self): + return (Q.orthogonal,) +class RofQR(Factorization): + @property + def predicates(self): + return (Q.upper_triangular,) + +class EigenVectors(Factorization): + @property + def predicates(self): + return (Q.orthogonal,) +class EigenValues(Factorization): + @property + def predicates(self): + return (Q.diagonal,) + +class UofSVD(Factorization): + @property + def predicates(self): + return (Q.orthogonal,) +class SofSVD(Factorization): + @property + def predicates(self): + return (Q.diagonal,) +class VofSVD(Factorization): + @property + def predicates(self): + return (Q.orthogonal,) + + +def lu(expr): + return LofLU(expr), UofLU(expr) + +def qr(expr): + return QofQR(expr), RofQR(expr) + +def eig(expr): + return EigenValues(expr), EigenVectors(expr) + +def svd(expr): + return UofSVD(expr), SofSVD(expr), VofSVD(expr) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/fourier.py b/lib/python3.11/site-packages/sympy/matrices/expressions/fourier.py new file mode 100644 index 0000000000000000000000000000000000000000..5fa9222c2a9b218f42636267235d5dd44c25f8bb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/fourier.py @@ -0,0 +1,91 @@ +from sympy.core.sympify import _sympify +from sympy.matrices.expressions import MatrixExpr +from sympy.core.numbers import I +from sympy.core.singleton import S +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt + + +class DFT(MatrixExpr): + r""" + Returns a discrete Fourier transform matrix. The matrix is scaled + with :math:`\frac{1}{\sqrt{n}}` so that it is unitary. + + Parameters + ========== + + n : integer or Symbol + Size of the transform. + + Examples + ======== + + >>> from sympy.abc import n + >>> from sympy.matrices.expressions.fourier import DFT + >>> DFT(3) + DFT(3) + >>> DFT(3).as_explicit() + Matrix([ + [sqrt(3)/3, sqrt(3)/3, sqrt(3)/3], + [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3, sqrt(3)*exp(2*I*pi/3)/3], + [sqrt(3)/3, sqrt(3)*exp(2*I*pi/3)/3, sqrt(3)*exp(-2*I*pi/3)/3]]) + >>> DFT(n).shape + (n, n) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/DFT_matrix + + """ + + def __new__(cls, n): + n = _sympify(n) + cls._check_dim(n) + + obj = super().__new__(cls, n) + return obj + + n = property(lambda self: self.args[0]) # type: ignore + shape = property(lambda self: (self.n, self.n)) # type: ignore + + def _entry(self, i, j, **kwargs): + w = exp(-2*S.Pi*I/self.n) + return w**(i*j) / sqrt(self.n) + + def _eval_inverse(self): + return IDFT(self.n) + + +class IDFT(DFT): + r""" + Returns an inverse discrete Fourier transform matrix. The matrix is scaled + with :math:`\frac{1}{\sqrt{n}}` so that it is unitary. + + Parameters + ========== + + n : integer or Symbol + Size of the transform + + Examples + ======== + + >>> from sympy.matrices.expressions.fourier import DFT, IDFT + >>> IDFT(3) + IDFT(3) + >>> IDFT(4)*DFT(4) + I + + See Also + ======== + + DFT + + """ + def _entry(self, i, j, **kwargs): + w = exp(-2*S.Pi*I/self.n) + return w**(-i*j) / sqrt(self.n) + + def _eval_inverse(self): + return DFT(self.n) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/funcmatrix.py b/lib/python3.11/site-packages/sympy/matrices/expressions/funcmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..91106edb489b73ac9dd6cb94adc508c0db75d3a5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/funcmatrix.py @@ -0,0 +1,118 @@ +from .matexpr import MatrixExpr +from sympy.core.function import FunctionClass, Lambda +from sympy.core.symbol import Dummy +from sympy.core.sympify import _sympify, sympify +from sympy.matrices import Matrix +from sympy.functions.elementary.complexes import re, im + + +class FunctionMatrix(MatrixExpr): + """Represents a matrix using a function (``Lambda``) which gives + outputs according to the coordinates of each matrix entries. + + Parameters + ========== + + rows : nonnegative integer. Can be symbolic. + + cols : nonnegative integer. Can be symbolic. + + lamda : Function, Lambda or str + If it is a SymPy ``Function`` or ``Lambda`` instance, + it should be able to accept two arguments which represents the + matrix coordinates. + + If it is a pure string containing Python ``lambda`` semantics, + it is interpreted by the SymPy parser and casted into a SymPy + ``Lambda`` instance. + + Examples + ======== + + Creating a ``FunctionMatrix`` from ``Lambda``: + + >>> from sympy import FunctionMatrix, symbols, Lambda, MatPow + >>> i, j, n, m = symbols('i,j,n,m') + >>> FunctionMatrix(n, m, Lambda((i, j), i + j)) + FunctionMatrix(n, m, Lambda((i, j), i + j)) + + Creating a ``FunctionMatrix`` from a SymPy function: + + >>> from sympy import KroneckerDelta + >>> X = FunctionMatrix(3, 3, KroneckerDelta) + >>> X.as_explicit() + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + + Creating a ``FunctionMatrix`` from a SymPy undefined function: + + >>> from sympy import Function + >>> f = Function('f') + >>> X = FunctionMatrix(3, 3, f) + >>> X.as_explicit() + Matrix([ + [f(0, 0), f(0, 1), f(0, 2)], + [f(1, 0), f(1, 1), f(1, 2)], + [f(2, 0), f(2, 1), f(2, 2)]]) + + Creating a ``FunctionMatrix`` from Python ``lambda``: + + >>> FunctionMatrix(n, m, 'lambda i, j: i + j') + FunctionMatrix(n, m, Lambda((i, j), i + j)) + + Example of lazy evaluation of matrix product: + + >>> Y = FunctionMatrix(1000, 1000, Lambda((i, j), i + j)) + >>> isinstance(Y*Y, MatPow) # this is an expression object + True + >>> (Y**2)[10,10] # So this is evaluated lazily + 342923500 + + Notes + ===== + + This class provides an alternative way to represent an extremely + dense matrix with entries in some form of a sequence, in a most + sparse way. + """ + def __new__(cls, rows, cols, lamda): + rows, cols = _sympify(rows), _sympify(cols) + cls._check_dim(rows) + cls._check_dim(cols) + + lamda = sympify(lamda) + if not isinstance(lamda, (FunctionClass, Lambda)): + raise ValueError( + "{} should be compatible with SymPy function classes." + .format(lamda)) + + if 2 not in lamda.nargs: + raise ValueError( + '{} should be able to accept 2 arguments.'.format(lamda)) + + if not isinstance(lamda, Lambda): + i, j = Dummy('i'), Dummy('j') + lamda = Lambda((i, j), lamda(i, j)) + + return super().__new__(cls, rows, cols, lamda) + + @property + def shape(self): + return self.args[0:2] + + @property + def lamda(self): + return self.args[2] + + def _entry(self, i, j, **kwargs): + return self.lamda(i, j) + + def _eval_trace(self): + from sympy.matrices.expressions.trace import Trace + from sympy.concrete.summations import Sum + return Trace(self).rewrite(Sum).doit() + + def _eval_as_real_imag(self): + return (re(Matrix(self)), im(Matrix(self))) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/hadamard.py b/lib/python3.11/site-packages/sympy/matrices/expressions/hadamard.py new file mode 100644 index 0000000000000000000000000000000000000000..38c9033ebea3a7bfc569223978dc6ef3890206cf --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/hadamard.py @@ -0,0 +1,464 @@ +from collections import Counter + +from sympy.core import Mul, sympify +from sympy.core.add import Add +from sympy.core.expr import ExprBuilder +from sympy.core.sorting import default_sort_key +from sympy.functions.elementary.exponential import log +from sympy.matrices.expressions.matexpr import MatrixExpr +from sympy.matrices.expressions._shape import validate_matadd_integer as validate +from sympy.matrices.expressions.special import ZeroMatrix, OneMatrix +from sympy.strategies import ( + unpack, flatten, condition, exhaust, rm_id, sort +) +from sympy.utilities.exceptions import sympy_deprecation_warning + + +def hadamard_product(*matrices): + """ + Return the elementwise (aka Hadamard) product of matrices. + + Examples + ======== + + >>> from sympy import hadamard_product, MatrixSymbol + >>> A = MatrixSymbol('A', 2, 3) + >>> B = MatrixSymbol('B', 2, 3) + >>> hadamard_product(A) + A + >>> hadamard_product(A, B) + HadamardProduct(A, B) + >>> hadamard_product(A, B)[0, 1] + A[0, 1]*B[0, 1] + """ + if not matrices: + raise TypeError("Empty Hadamard product is undefined") + if len(matrices) == 1: + return matrices[0] + return HadamardProduct(*matrices).doit() + + +class HadamardProduct(MatrixExpr): + """ + Elementwise product of matrix expressions + + Examples + ======== + + Hadamard product for matrix symbols: + + >>> from sympy import hadamard_product, HadamardProduct, MatrixSymbol + >>> A = MatrixSymbol('A', 5, 5) + >>> B = MatrixSymbol('B', 5, 5) + >>> isinstance(hadamard_product(A, B), HadamardProduct) + True + + Notes + ===== + + This is a symbolic object that simply stores its argument without + evaluating it. To actually compute the product, use the function + ``hadamard_product()`` or ``HadamardProduct.doit`` + """ + is_HadamardProduct = True + + def __new__(cls, *args, evaluate=False, check=None): + args = list(map(sympify, args)) + if len(args) == 0: + # We currently don't have a way to support one-matrices of generic dimensions: + raise ValueError("HadamardProduct needs at least one argument") + + if not all(isinstance(arg, MatrixExpr) for arg in args): + raise TypeError("Mix of Matrix and Scalar symbols") + + if check is not None: + sympy_deprecation_warning( + "Passing check to HadamardProduct is deprecated and the check argument will be removed in a future version.", + deprecated_since_version="1.11", + active_deprecations_target='remove-check-argument-from-matrix-operations') + + if check is not False: + validate(*args) + + obj = super().__new__(cls, *args) + if evaluate: + obj = obj.doit(deep=False) + return obj + + @property + def shape(self): + return self.args[0].shape + + def _entry(self, i, j, **kwargs): + return Mul(*[arg._entry(i, j, **kwargs) for arg in self.args]) + + def _eval_transpose(self): + from sympy.matrices.expressions.transpose import transpose + return HadamardProduct(*list(map(transpose, self.args))) + + def doit(self, **hints): + expr = self.func(*(i.doit(**hints) for i in self.args)) + # Check for explicit matrices: + from sympy.matrices.matrixbase import MatrixBase + from sympy.matrices.immutable import ImmutableMatrix + + explicit = [i for i in expr.args if isinstance(i, MatrixBase)] + if explicit: + remainder = [i for i in expr.args if i not in explicit] + expl_mat = ImmutableMatrix([ + Mul.fromiter(i) for i in zip(*explicit) + ]).reshape(*self.shape) + expr = HadamardProduct(*([expl_mat] + remainder)) + + return canonicalize(expr) + + def _eval_derivative(self, x): + terms = [] + args = list(self.args) + for i in range(len(args)): + factors = args[:i] + [args[i].diff(x)] + args[i+1:] + terms.append(hadamard_product(*factors)) + return Add.fromiter(terms) + + def _eval_derivative_matrix_lines(self, x): + from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal + from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct + from sympy.matrices.expressions.matexpr import _make_matrix + + with_x_ind = [i for i, arg in enumerate(self.args) if arg.has(x)] + lines = [] + for ind in with_x_ind: + left_args = self.args[:ind] + right_args = self.args[ind+1:] + + d = self.args[ind]._eval_derivative_matrix_lines(x) + hadam = hadamard_product(*(right_args + left_args)) + diagonal = [(0, 2), (3, 4)] + diagonal = [e for j, e in enumerate(diagonal) if self.shape[j] != 1] + for i in d: + l1 = i._lines[i._first_line_index] + l2 = i._lines[i._second_line_index] + subexpr = ExprBuilder( + ArrayDiagonal, + [ + ExprBuilder( + ArrayTensorProduct, + [ + ExprBuilder(_make_matrix, [l1]), + hadam, + ExprBuilder(_make_matrix, [l2]), + ] + ), + *diagonal], + + ) + i._first_pointer_parent = subexpr.args[0].args[0].args + i._first_pointer_index = 0 + i._second_pointer_parent = subexpr.args[0].args[2].args + i._second_pointer_index = 0 + i._lines = [subexpr] + lines.append(i) + + return lines + + +# TODO Implement algorithm for rewriting Hadamard product as diagonal matrix +# if matmul identy matrix is multiplied. +def canonicalize(x): + """Canonicalize the Hadamard product ``x`` with mathematical properties. + + Examples + ======== + + >>> from sympy import MatrixSymbol, HadamardProduct + >>> from sympy import OneMatrix, ZeroMatrix + >>> from sympy.matrices.expressions.hadamard import canonicalize + >>> from sympy import init_printing + >>> init_printing(use_unicode=False) + + >>> A = MatrixSymbol('A', 2, 2) + >>> B = MatrixSymbol('B', 2, 2) + >>> C = MatrixSymbol('C', 2, 2) + + Hadamard product associativity: + + >>> X = HadamardProduct(A, HadamardProduct(B, C)) + >>> X + A.*(B.*C) + >>> canonicalize(X) + A.*B.*C + + Hadamard product commutativity: + + >>> X = HadamardProduct(A, B) + >>> Y = HadamardProduct(B, A) + >>> X + A.*B + >>> Y + B.*A + >>> canonicalize(X) + A.*B + >>> canonicalize(Y) + A.*B + + Hadamard product identity: + + >>> X = HadamardProduct(A, OneMatrix(2, 2)) + >>> X + A.*1 + >>> canonicalize(X) + A + + Absorbing element of Hadamard product: + + >>> X = HadamardProduct(A, ZeroMatrix(2, 2)) + >>> X + A.*0 + >>> canonicalize(X) + 0 + + Rewriting to Hadamard Power + + >>> X = HadamardProduct(A, A, A) + >>> X + A.*A.*A + >>> canonicalize(X) + .3 + A + + Notes + ===== + + As the Hadamard product is associative, nested products can be flattened. + + The Hadamard product is commutative so that factors can be sorted for + canonical form. + + A matrix of only ones is an identity for Hadamard product, + so every matrices of only ones can be removed. + + Any zero matrix will make the whole product a zero matrix. + + Duplicate elements can be collected and rewritten as HadamardPower + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hadamard_product_(matrices) + """ + # Associativity + rule = condition( + lambda x: isinstance(x, HadamardProduct), + flatten + ) + fun = exhaust(rule) + x = fun(x) + + # Identity + fun = condition( + lambda x: isinstance(x, HadamardProduct), + rm_id(lambda x: isinstance(x, OneMatrix)) + ) + x = fun(x) + + # Absorbing by Zero Matrix + def absorb(x): + if any(isinstance(c, ZeroMatrix) for c in x.args): + return ZeroMatrix(*x.shape) + else: + return x + fun = condition( + lambda x: isinstance(x, HadamardProduct), + absorb + ) + x = fun(x) + + # Rewriting with HadamardPower + if isinstance(x, HadamardProduct): + tally = Counter(x.args) + + new_arg = [] + for base, exp in tally.items(): + if exp == 1: + new_arg.append(base) + else: + new_arg.append(HadamardPower(base, exp)) + + x = HadamardProduct(*new_arg) + + # Commutativity + fun = condition( + lambda x: isinstance(x, HadamardProduct), + sort(default_sort_key) + ) + x = fun(x) + + # Unpacking + x = unpack(x) + return x + + +def hadamard_power(base, exp): + base = sympify(base) + exp = sympify(exp) + if exp == 1: + return base + if not base.is_Matrix: + return base**exp + if exp.is_Matrix: + raise ValueError("cannot raise expression to a matrix") + return HadamardPower(base, exp) + + +class HadamardPower(MatrixExpr): + r""" + Elementwise power of matrix expressions + + Parameters + ========== + + base : scalar or matrix + + exp : scalar or matrix + + Notes + ===== + + There are four definitions for the hadamard power which can be used. + Let's consider `A, B` as `(m, n)` matrices, and `a, b` as scalars. + + Matrix raised to a scalar exponent: + + .. math:: + A^{\circ b} = \begin{bmatrix} + A_{0, 0}^b & A_{0, 1}^b & \cdots & A_{0, n-1}^b \\ + A_{1, 0}^b & A_{1, 1}^b & \cdots & A_{1, n-1}^b \\ + \vdots & \vdots & \ddots & \vdots \\ + A_{m-1, 0}^b & A_{m-1, 1}^b & \cdots & A_{m-1, n-1}^b + \end{bmatrix} + + Scalar raised to a matrix exponent: + + .. math:: + a^{\circ B} = \begin{bmatrix} + a^{B_{0, 0}} & a^{B_{0, 1}} & \cdots & a^{B_{0, n-1}} \\ + a^{B_{1, 0}} & a^{B_{1, 1}} & \cdots & a^{B_{1, n-1}} \\ + \vdots & \vdots & \ddots & \vdots \\ + a^{B_{m-1, 0}} & a^{B_{m-1, 1}} & \cdots & a^{B_{m-1, n-1}} + \end{bmatrix} + + Matrix raised to a matrix exponent: + + .. math:: + A^{\circ B} = \begin{bmatrix} + A_{0, 0}^{B_{0, 0}} & A_{0, 1}^{B_{0, 1}} & + \cdots & A_{0, n-1}^{B_{0, n-1}} \\ + A_{1, 0}^{B_{1, 0}} & A_{1, 1}^{B_{1, 1}} & + \cdots & A_{1, n-1}^{B_{1, n-1}} \\ + \vdots & \vdots & + \ddots & \vdots \\ + A_{m-1, 0}^{B_{m-1, 0}} & A_{m-1, 1}^{B_{m-1, 1}} & + \cdots & A_{m-1, n-1}^{B_{m-1, n-1}} + \end{bmatrix} + + Scalar raised to a scalar exponent: + + .. math:: + a^{\circ b} = a^b + """ + + def __new__(cls, base, exp): + base = sympify(base) + exp = sympify(exp) + + if base.is_scalar and exp.is_scalar: + return base ** exp + + if isinstance(base, MatrixExpr) and isinstance(exp, MatrixExpr): + validate(base, exp) + + obj = super().__new__(cls, base, exp) + return obj + + @property + def base(self): + return self._args[0] + + @property + def exp(self): + return self._args[1] + + @property + def shape(self): + if self.base.is_Matrix: + return self.base.shape + return self.exp.shape + + def _entry(self, i, j, **kwargs): + base = self.base + exp = self.exp + + if base.is_Matrix: + a = base._entry(i, j, **kwargs) + elif base.is_scalar: + a = base + else: + raise ValueError( + 'The base {} must be a scalar or a matrix.'.format(base)) + + if exp.is_Matrix: + b = exp._entry(i, j, **kwargs) + elif exp.is_scalar: + b = exp + else: + raise ValueError( + 'The exponent {} must be a scalar or a matrix.'.format(exp)) + + return a ** b + + def _eval_transpose(self): + from sympy.matrices.expressions.transpose import transpose + return HadamardPower(transpose(self.base), self.exp) + + def _eval_derivative(self, x): + dexp = self.exp.diff(x) + logbase = self.base.applyfunc(log) + dlbase = logbase.diff(x) + return hadamard_product( + dexp*logbase + self.exp*dlbase, + self + ) + + def _eval_derivative_matrix_lines(self, x): + from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct + from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal + from sympy.matrices.expressions.matexpr import _make_matrix + + lr = self.base._eval_derivative_matrix_lines(x) + for i in lr: + diagonal = [(1, 2), (3, 4)] + diagonal = [e for j, e in enumerate(diagonal) if self.base.shape[j] != 1] + l1 = i._lines[i._first_line_index] + l2 = i._lines[i._second_line_index] + subexpr = ExprBuilder( + ArrayDiagonal, + [ + ExprBuilder( + ArrayTensorProduct, + [ + ExprBuilder(_make_matrix, [l1]), + self.exp*hadamard_power(self.base, self.exp-1), + ExprBuilder(_make_matrix, [l2]), + ] + ), + *diagonal], + validator=ArrayDiagonal._validate + ) + i._first_pointer_parent = subexpr.args[0].args[0].args + i._first_pointer_index = 0 + i._first_line_index = 0 + i._second_pointer_parent = subexpr.args[0].args[2].args + i._second_pointer_index = 0 + i._second_line_index = 0 + i._lines = [subexpr] + return lr diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/inverse.py b/lib/python3.11/site-packages/sympy/matrices/expressions/inverse.py new file mode 100644 index 0000000000000000000000000000000000000000..cfc3feccd7126a761f18f23599eed9413c86a9e5 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/inverse.py @@ -0,0 +1,112 @@ +from sympy.core.sympify import _sympify +from sympy.core import S, Basic + +from sympy.matrices.exceptions import NonSquareMatrixError +from sympy.matrices.expressions.matpow import MatPow + + +class Inverse(MatPow): + """ + The multiplicative inverse of a matrix expression + + This is a symbolic object that simply stores its argument without + evaluating it. To actually compute the inverse, use the ``.inverse()`` + method of matrices. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Inverse + >>> A = MatrixSymbol('A', 3, 3) + >>> B = MatrixSymbol('B', 3, 3) + >>> Inverse(A) + A**(-1) + >>> A.inverse() == Inverse(A) + True + >>> (A*B).inverse() + B**(-1)*A**(-1) + >>> Inverse(A*B) + (A*B)**(-1) + + """ + is_Inverse = True + exp = S.NegativeOne + + def __new__(cls, mat, exp=S.NegativeOne): + # exp is there to make it consistent with + # inverse.func(*inverse.args) == inverse + mat = _sympify(mat) + exp = _sympify(exp) + if not mat.is_Matrix: + raise TypeError("mat should be a matrix") + if mat.is_square is False: + raise NonSquareMatrixError("Inverse of non-square matrix %s" % mat) + return Basic.__new__(cls, mat, exp) + + @property + def arg(self): + return self.args[0] + + @property + def shape(self): + return self.arg.shape + + def _eval_inverse(self): + return self.arg + + def _eval_transpose(self): + return Inverse(self.arg.transpose()) + + def _eval_adjoint(self): + return Inverse(self.arg.adjoint()) + + def _eval_conjugate(self): + return Inverse(self.arg.conjugate()) + + def _eval_determinant(self): + from sympy.matrices.expressions.determinant import det + return 1/det(self.arg) + + def doit(self, **hints): + if 'inv_expand' in hints and hints['inv_expand'] == False: + return self + + arg = self.arg + if hints.get('deep', True): + arg = arg.doit(**hints) + + return arg.inverse() + + def _eval_derivative_matrix_lines(self, x): + arg = self.args[0] + lines = arg._eval_derivative_matrix_lines(x) + for line in lines: + line.first_pointer *= -self.T + line.second_pointer *= self + return lines + + +from sympy.assumptions.ask import ask, Q +from sympy.assumptions.refine import handlers_dict + + +def refine_Inverse(expr, assumptions): + """ + >>> from sympy import MatrixSymbol, Q, assuming, refine + >>> X = MatrixSymbol('X', 2, 2) + >>> X.I + X**(-1) + >>> with assuming(Q.orthogonal(X)): + ... print(refine(X.I)) + X.T + """ + if ask(Q.orthogonal(expr), assumptions): + return expr.arg.T + elif ask(Q.unitary(expr), assumptions): + return expr.arg.conjugate() + elif ask(Q.singular(expr), assumptions): + raise ValueError("Inverse of singular matrix %s" % expr.arg) + + return expr + +handlers_dict['Inverse'] = refine_Inverse diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/kronecker.py b/lib/python3.11/site-packages/sympy/matrices/expressions/kronecker.py new file mode 100644 index 0000000000000000000000000000000000000000..1dd175cb0d500af3e786e2d0dbf6b010947840b4 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/kronecker.py @@ -0,0 +1,434 @@ +"""Implementation of the Kronecker product""" +from functools import reduce +from math import prod + +from sympy.core import Mul, sympify +from sympy.functions import adjoint +from sympy.matrices.exceptions import ShapeError +from sympy.matrices.expressions.matexpr import MatrixExpr +from sympy.matrices.expressions.transpose import transpose +from sympy.matrices.expressions.special import Identity +from sympy.matrices.matrixbase import MatrixBase +from sympy.strategies import ( + canon, condition, distribute, do_one, exhaust, flatten, typed, unpack) +from sympy.strategies.traverse import bottom_up +from sympy.utilities import sift + +from .matadd import MatAdd +from .matmul import MatMul +from .matpow import MatPow + + +def kronecker_product(*matrices): + """ + The Kronecker product of two or more arguments. + + This computes the explicit Kronecker product for subclasses of + ``MatrixBase`` i.e. explicit matrices. Otherwise, a symbolic + ``KroneckerProduct`` object is returned. + + + Examples + ======== + + For ``MatrixSymbol`` arguments a ``KroneckerProduct`` object is returned. + Elements of this matrix can be obtained by indexing, or for MatrixSymbols + with known dimension the explicit matrix can be obtained with + ``.as_explicit()`` + + >>> from sympy import kronecker_product, MatrixSymbol + >>> A = MatrixSymbol('A', 2, 2) + >>> B = MatrixSymbol('B', 2, 2) + >>> kronecker_product(A) + A + >>> kronecker_product(A, B) + KroneckerProduct(A, B) + >>> kronecker_product(A, B)[0, 1] + A[0, 0]*B[0, 1] + >>> kronecker_product(A, B).as_explicit() + Matrix([ + [A[0, 0]*B[0, 0], A[0, 0]*B[0, 1], A[0, 1]*B[0, 0], A[0, 1]*B[0, 1]], + [A[0, 0]*B[1, 0], A[0, 0]*B[1, 1], A[0, 1]*B[1, 0], A[0, 1]*B[1, 1]], + [A[1, 0]*B[0, 0], A[1, 0]*B[0, 1], A[1, 1]*B[0, 0], A[1, 1]*B[0, 1]], + [A[1, 0]*B[1, 0], A[1, 0]*B[1, 1], A[1, 1]*B[1, 0], A[1, 1]*B[1, 1]]]) + + For explicit matrices the Kronecker product is returned as a Matrix + + >>> from sympy import Matrix, kronecker_product + >>> sigma_x = Matrix([ + ... [0, 1], + ... [1, 0]]) + ... + >>> Isigma_y = Matrix([ + ... [0, 1], + ... [-1, 0]]) + ... + >>> kronecker_product(sigma_x, Isigma_y) + Matrix([ + [ 0, 0, 0, 1], + [ 0, 0, -1, 0], + [ 0, 1, 0, 0], + [-1, 0, 0, 0]]) + + See Also + ======== + KroneckerProduct + + """ + if not matrices: + raise TypeError("Empty Kronecker product is undefined") + if len(matrices) == 1: + return matrices[0] + else: + return KroneckerProduct(*matrices).doit() + + +class KroneckerProduct(MatrixExpr): + """ + The Kronecker product of two or more arguments. + + The Kronecker product is a non-commutative product of matrices. + Given two matrices of dimension (m, n) and (s, t) it produces a matrix + of dimension (m s, n t). + + This is a symbolic object that simply stores its argument without + evaluating it. To actually compute the product, use the function + ``kronecker_product()`` or call the ``.doit()`` or ``.as_explicit()`` + methods. + + >>> from sympy import KroneckerProduct, MatrixSymbol + >>> A = MatrixSymbol('A', 5, 5) + >>> B = MatrixSymbol('B', 5, 5) + >>> isinstance(KroneckerProduct(A, B), KroneckerProduct) + True + """ + is_KroneckerProduct = True + + def __new__(cls, *args, check=True): + args = list(map(sympify, args)) + if all(a.is_Identity for a in args): + ret = Identity(prod(a.rows for a in args)) + if all(isinstance(a, MatrixBase) for a in args): + return ret.as_explicit() + else: + return ret + + if check: + validate(*args) + return super().__new__(cls, *args) + + @property + def shape(self): + rows, cols = self.args[0].shape + for mat in self.args[1:]: + rows *= mat.rows + cols *= mat.cols + return (rows, cols) + + def _entry(self, i, j, **kwargs): + result = 1 + for mat in reversed(self.args): + i, m = divmod(i, mat.rows) + j, n = divmod(j, mat.cols) + result *= mat[m, n] + return result + + def _eval_adjoint(self): + return KroneckerProduct(*list(map(adjoint, self.args))).doit() + + def _eval_conjugate(self): + return KroneckerProduct(*[a.conjugate() for a in self.args]).doit() + + def _eval_transpose(self): + return KroneckerProduct(*list(map(transpose, self.args))).doit() + + def _eval_trace(self): + from .trace import trace + return Mul(*[trace(a) for a in self.args]) + + def _eval_determinant(self): + from .determinant import det, Determinant + if not all(a.is_square for a in self.args): + return Determinant(self) + + m = self.rows + return Mul(*[det(a)**(m/a.rows) for a in self.args]) + + def _eval_inverse(self): + try: + return KroneckerProduct(*[a.inverse() for a in self.args]) + except ShapeError: + from sympy.matrices.expressions.inverse import Inverse + return Inverse(self) + + def structurally_equal(self, other): + '''Determine whether two matrices have the same Kronecker product structure + + Examples + ======== + + >>> from sympy import KroneckerProduct, MatrixSymbol, symbols + >>> m, n = symbols(r'm, n', integer=True) + >>> A = MatrixSymbol('A', m, m) + >>> B = MatrixSymbol('B', n, n) + >>> C = MatrixSymbol('C', m, m) + >>> D = MatrixSymbol('D', n, n) + >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(C, D)) + True + >>> KroneckerProduct(A, B).structurally_equal(KroneckerProduct(D, C)) + False + >>> KroneckerProduct(A, B).structurally_equal(C) + False + ''' + # Inspired by BlockMatrix + return (isinstance(other, KroneckerProduct) + and self.shape == other.shape + and len(self.args) == len(other.args) + and all(a.shape == b.shape for (a, b) in zip(self.args, other.args))) + + def has_matching_shape(self, other): + '''Determine whether two matrices have the appropriate structure to bring matrix + multiplication inside the KroneckerProdut + + Examples + ======== + >>> from sympy import KroneckerProduct, MatrixSymbol, symbols + >>> m, n = symbols(r'm, n', integer=True) + >>> A = MatrixSymbol('A', m, n) + >>> B = MatrixSymbol('B', n, m) + >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(B, A)) + True + >>> KroneckerProduct(A, B).has_matching_shape(KroneckerProduct(A, B)) + False + >>> KroneckerProduct(A, B).has_matching_shape(A) + False + ''' + return (isinstance(other, KroneckerProduct) + and self.cols == other.rows + and len(self.args) == len(other.args) + and all(a.cols == b.rows for (a, b) in zip(self.args, other.args))) + + def _eval_expand_kroneckerproduct(self, **hints): + return flatten(canon(typed({KroneckerProduct: distribute(KroneckerProduct, MatAdd)}))(self)) + + def _kronecker_add(self, other): + if self.structurally_equal(other): + return self.__class__(*[a + b for (a, b) in zip(self.args, other.args)]) + else: + return self + other + + def _kronecker_mul(self, other): + if self.has_matching_shape(other): + return self.__class__(*[a*b for (a, b) in zip(self.args, other.args)]) + else: + return self * other + + def doit(self, **hints): + deep = hints.get('deep', True) + if deep: + args = [arg.doit(**hints) for arg in self.args] + else: + args = self.args + return canonicalize(KroneckerProduct(*args)) + + +def validate(*args): + if not all(arg.is_Matrix for arg in args): + raise TypeError("Mix of Matrix and Scalar symbols") + + +# rules + +def extract_commutative(kron): + c_part = [] + nc_part = [] + for arg in kron.args: + c, nc = arg.args_cnc() + c_part.extend(c) + nc_part.append(Mul._from_args(nc)) + + c_part = Mul(*c_part) + if c_part != 1: + return c_part*KroneckerProduct(*nc_part) + return kron + + +def matrix_kronecker_product(*matrices): + """Compute the Kronecker product of a sequence of SymPy Matrices. + + This is the standard Kronecker product of matrices [1]. + + Parameters + ========== + + matrices : tuple of MatrixBase instances + The matrices to take the Kronecker product of. + + Returns + ======= + + matrix : MatrixBase + The Kronecker product matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.matrices.expressions.kronecker import ( + ... matrix_kronecker_product) + + >>> m1 = Matrix([[1,2],[3,4]]) + >>> m2 = Matrix([[1,0],[0,1]]) + >>> matrix_kronecker_product(m1, m2) + Matrix([ + [1, 0, 2, 0], + [0, 1, 0, 2], + [3, 0, 4, 0], + [0, 3, 0, 4]]) + >>> matrix_kronecker_product(m2, m1) + Matrix([ + [1, 2, 0, 0], + [3, 4, 0, 0], + [0, 0, 1, 2], + [0, 0, 3, 4]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Kronecker_product + """ + # Make sure we have a sequence of Matrices + if not all(isinstance(m, MatrixBase) for m in matrices): + raise TypeError( + 'Sequence of Matrices expected, got: %s' % repr(matrices) + ) + + # Pull out the first element in the product. + matrix_expansion = matrices[-1] + # Do the kronecker product working from right to left. + for mat in reversed(matrices[:-1]): + rows = mat.rows + cols = mat.cols + # Go through each row appending kronecker product to. + # running matrix_expansion. + for i in range(rows): + start = matrix_expansion*mat[i*cols] + # Go through each column joining each item + for j in range(cols - 1): + start = start.row_join( + matrix_expansion*mat[i*cols + j + 1] + ) + # If this is the first element, make it the start of the + # new row. + if i == 0: + next = start + else: + next = next.col_join(start) + matrix_expansion = next + + MatrixClass = max(matrices, key=lambda M: M._class_priority).__class__ + if isinstance(matrix_expansion, MatrixClass): + return matrix_expansion + else: + return MatrixClass(matrix_expansion) + + +def explicit_kronecker_product(kron): + # Make sure we have a sequence of Matrices + if not all(isinstance(m, MatrixBase) for m in kron.args): + return kron + + return matrix_kronecker_product(*kron.args) + + +rules = (unpack, + explicit_kronecker_product, + flatten, + extract_commutative) + +canonicalize = exhaust(condition(lambda x: isinstance(x, KroneckerProduct), + do_one(*rules))) + + +def _kronecker_dims_key(expr): + if isinstance(expr, KroneckerProduct): + return tuple(a.shape for a in expr.args) + else: + return (0,) + + +def kronecker_mat_add(expr): + args = sift(expr.args, _kronecker_dims_key) + nonkrons = args.pop((0,), None) + if not args: + return expr + + krons = [reduce(lambda x, y: x._kronecker_add(y), group) + for group in args.values()] + + if not nonkrons: + return MatAdd(*krons) + else: + return MatAdd(*krons) + nonkrons + + +def kronecker_mat_mul(expr): + # modified from block matrix code + factor, matrices = expr.as_coeff_matrices() + + i = 0 + while i < len(matrices) - 1: + A, B = matrices[i:i+2] + if isinstance(A, KroneckerProduct) and isinstance(B, KroneckerProduct): + matrices[i] = A._kronecker_mul(B) + matrices.pop(i+1) + else: + i += 1 + + return factor*MatMul(*matrices) + + +def kronecker_mat_pow(expr): + if isinstance(expr.base, KroneckerProduct) and all(a.is_square for a in expr.base.args): + return KroneckerProduct(*[MatPow(a, expr.exp) for a in expr.base.args]) + else: + return expr + + +def combine_kronecker(expr): + """Combine KronekeckerProduct with expression. + + If possible write operations on KroneckerProducts of compatible shapes + as a single KroneckerProduct. + + Examples + ======== + + >>> from sympy.matrices.expressions import combine_kronecker + >>> from sympy import MatrixSymbol, KroneckerProduct, symbols + >>> m, n = symbols(r'm, n', integer=True) + >>> A = MatrixSymbol('A', m, n) + >>> B = MatrixSymbol('B', n, m) + >>> combine_kronecker(KroneckerProduct(A, B)*KroneckerProduct(B, A)) + KroneckerProduct(A*B, B*A) + >>> combine_kronecker(KroneckerProduct(A, B)+KroneckerProduct(B.T, A.T)) + KroneckerProduct(A + B.T, B + A.T) + >>> C = MatrixSymbol('C', n, n) + >>> D = MatrixSymbol('D', m, m) + >>> combine_kronecker(KroneckerProduct(C, D)**m) + KroneckerProduct(C**m, D**m) + """ + def haskron(expr): + return isinstance(expr, MatrixExpr) and expr.has(KroneckerProduct) + + rule = exhaust( + bottom_up(exhaust(condition(haskron, typed( + {MatAdd: kronecker_mat_add, + MatMul: kronecker_mat_mul, + MatPow: kronecker_mat_pow}))))) + result = rule(expr) + doit = getattr(result, 'doit', None) + if doit is not None: + return doit() + else: + return result diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/matadd.py b/lib/python3.11/site-packages/sympy/matrices/expressions/matadd.py new file mode 100644 index 0000000000000000000000000000000000000000..cfae1e5010e4077c7210c85c4315ed2404f245d7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/matadd.py @@ -0,0 +1,155 @@ +from functools import reduce +import operator + +from sympy.core import Basic, sympify +from sympy.core.add import add, Add, _could_extract_minus_sign +from sympy.core.sorting import default_sort_key +from sympy.functions import adjoint +from sympy.matrices.matrixbase import MatrixBase +from sympy.matrices.expressions.transpose import transpose +from sympy.strategies import (rm_id, unpack, flatten, sort, condition, + exhaust, do_one, glom) +from sympy.matrices.expressions.matexpr import MatrixExpr +from sympy.matrices.expressions.special import ZeroMatrix, GenericZeroMatrix +from sympy.matrices.expressions._shape import validate_matadd_integer as validate +from sympy.utilities.iterables import sift +from sympy.utilities.exceptions import sympy_deprecation_warning + +# XXX: MatAdd should perhaps not subclass directly from Add +class MatAdd(MatrixExpr, Add): + """A Sum of Matrix Expressions + + MatAdd inherits from and operates like SymPy Add + + Examples + ======== + + >>> from sympy import MatAdd, MatrixSymbol + >>> A = MatrixSymbol('A', 5, 5) + >>> B = MatrixSymbol('B', 5, 5) + >>> C = MatrixSymbol('C', 5, 5) + >>> MatAdd(A, B, C) + A + B + C + """ + is_MatAdd = True + + identity = GenericZeroMatrix() + + def __new__(cls, *args, evaluate=False, check=None, _sympify=True): + if not args: + return cls.identity + + # This must be removed aggressively in the constructor to avoid + # TypeErrors from GenericZeroMatrix().shape + args = list(filter(lambda i: cls.identity != i, args)) + if _sympify: + args = list(map(sympify, args)) + + if not all(isinstance(arg, MatrixExpr) for arg in args): + raise TypeError("Mix of Matrix and Scalar symbols") + + obj = Basic.__new__(cls, *args) + + if check is not None: + sympy_deprecation_warning( + "Passing check to MatAdd is deprecated and the check argument will be removed in a future version.", + deprecated_since_version="1.11", + active_deprecations_target='remove-check-argument-from-matrix-operations') + + if check is not False: + validate(*args) + + if evaluate: + obj = cls._evaluate(obj) + + return obj + + @classmethod + def _evaluate(cls, expr): + return canonicalize(expr) + + @property + def shape(self): + return self.args[0].shape + + def could_extract_minus_sign(self): + return _could_extract_minus_sign(self) + + def expand(self, **kwargs): + expanded = super(MatAdd, self).expand(**kwargs) + return self._evaluate(expanded) + + def _entry(self, i, j, **kwargs): + return Add(*[arg._entry(i, j, **kwargs) for arg in self.args]) + + def _eval_transpose(self): + return MatAdd(*[transpose(arg) for arg in self.args]).doit() + + def _eval_adjoint(self): + return MatAdd(*[adjoint(arg) for arg in self.args]).doit() + + def _eval_trace(self): + from .trace import trace + return Add(*[trace(arg) for arg in self.args]).doit() + + def doit(self, **hints): + deep = hints.get('deep', True) + if deep: + args = [arg.doit(**hints) for arg in self.args] + else: + args = self.args + return canonicalize(MatAdd(*args)) + + def _eval_derivative_matrix_lines(self, x): + add_lines = [arg._eval_derivative_matrix_lines(x) for arg in self.args] + return [j for i in add_lines for j in i] + +add.register_handlerclass((Add, MatAdd), MatAdd) + + +factor_of = lambda arg: arg.as_coeff_mmul()[0] +matrix_of = lambda arg: unpack(arg.as_coeff_mmul()[1]) +def combine(cnt, mat): + if cnt == 1: + return mat + else: + return cnt * mat + + +def merge_explicit(matadd): + """ Merge explicit MatrixBase arguments + + Examples + ======== + + >>> from sympy import MatrixSymbol, eye, Matrix, MatAdd, pprint + >>> from sympy.matrices.expressions.matadd import merge_explicit + >>> A = MatrixSymbol('A', 2, 2) + >>> B = eye(2) + >>> C = Matrix([[1, 2], [3, 4]]) + >>> X = MatAdd(A, B, C) + >>> pprint(X) + [1 0] [1 2] + A + [ ] + [ ] + [0 1] [3 4] + >>> pprint(merge_explicit(X)) + [2 2] + A + [ ] + [3 5] + """ + groups = sift(matadd.args, lambda arg: isinstance(arg, MatrixBase)) + if len(groups[True]) > 1: + return MatAdd(*(groups[False] + [reduce(operator.add, groups[True])])) + else: + return matadd + + +rules = (rm_id(lambda x: x == 0 or isinstance(x, ZeroMatrix)), + unpack, + flatten, + glom(matrix_of, factor_of, combine), + merge_explicit, + sort(default_sort_key)) + +canonicalize = exhaust(condition(lambda x: isinstance(x, MatAdd), + do_one(*rules))) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/matexpr.py b/lib/python3.11/site-packages/sympy/matrices/expressions/matexpr.py new file mode 100644 index 0000000000000000000000000000000000000000..01c61828256bacaea46ffe20b5ba41b41ce85b31 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/matexpr.py @@ -0,0 +1,888 @@ +from __future__ import annotations +from functools import wraps + +from sympy.core import S, Integer, Basic, Mul, Add +from sympy.core.assumptions import check_assumptions +from sympy.core.decorators import call_highest_priority +from sympy.core.expr import Expr, ExprBuilder +from sympy.core.logic import FuzzyBool +from sympy.core.symbol import Str, Dummy, symbols, Symbol +from sympy.core.sympify import SympifyError, _sympify +from sympy.external.gmpy import SYMPY_INTS +from sympy.functions import conjugate, adjoint +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.exceptions import NonSquareMatrixError +from sympy.matrices.kind import MatrixKind +from sympy.matrices.matrixbase import MatrixBase +from sympy.multipledispatch import dispatch +from sympy.utilities.misc import filldedent + + +def _sympifyit(arg, retval=None): + # This version of _sympifyit sympifies MutableMatrix objects + def deco(func): + @wraps(func) + def __sympifyit_wrapper(a, b): + try: + b = _sympify(b) + return func(a, b) + except SympifyError: + return retval + + return __sympifyit_wrapper + + return deco + + +class MatrixExpr(Expr): + """Superclass for Matrix Expressions + + MatrixExprs represent abstract matrices, linear transformations represented + within a particular basis. + + Examples + ======== + + >>> from sympy import MatrixSymbol + >>> A = MatrixSymbol('A', 3, 3) + >>> y = MatrixSymbol('y', 3, 1) + >>> x = (A.T*A).I * A * y + + See Also + ======== + + MatrixSymbol, MatAdd, MatMul, Transpose, Inverse + """ + __slots__: tuple[str, ...] = () + + # Should not be considered iterable by the + # sympy.utilities.iterables.iterable function. Subclass that actually are + # iterable (i.e., explicit matrices) should set this to True. + _iterable = False + + _op_priority = 11.0 + + is_Matrix: bool = True + is_MatrixExpr: bool = True + is_Identity: FuzzyBool = None + is_Inverse = False + is_Transpose = False + is_ZeroMatrix = False + is_MatAdd = False + is_MatMul = False + + is_commutative = False + is_number = False + is_symbol = False + is_scalar = False + + kind: MatrixKind = MatrixKind() + + def __new__(cls, *args, **kwargs): + args = map(_sympify, args) + return Basic.__new__(cls, *args, **kwargs) + + # The following is adapted from the core Expr object + + @property + def shape(self) -> tuple[Expr, Expr]: + raise NotImplementedError + + @property + def _add_handler(self): + return MatAdd + + @property + def _mul_handler(self): + return MatMul + + def __neg__(self): + return MatMul(S.NegativeOne, self).doit() + + def __abs__(self): + raise NotImplementedError + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__radd__') + def __add__(self, other): + return MatAdd(self, other).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__add__') + def __radd__(self, other): + return MatAdd(other, self).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__rsub__') + def __sub__(self, other): + return MatAdd(self, -other).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__sub__') + def __rsub__(self, other): + return MatAdd(other, -self).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__rmul__') + def __mul__(self, other): + return MatMul(self, other).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__rmul__') + def __matmul__(self, other): + return MatMul(self, other).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__mul__') + def __rmul__(self, other): + return MatMul(other, self).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__mul__') + def __rmatmul__(self, other): + return MatMul(other, self).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__rpow__') + def __pow__(self, other): + return MatPow(self, other).doit() + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__pow__') + def __rpow__(self, other): + raise NotImplementedError("Matrix Power not defined") + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__rtruediv__') + def __truediv__(self, other): + return self * other**S.NegativeOne + + @_sympifyit('other', NotImplemented) + @call_highest_priority('__truediv__') + def __rtruediv__(self, other): + raise NotImplementedError() + #return MatMul(other, Pow(self, S.NegativeOne)) + + @property + def rows(self): + return self.shape[0] + + @property + def cols(self): + return self.shape[1] + + @property + def is_square(self) -> bool | None: + rows, cols = self.shape + if isinstance(rows, Integer) and isinstance(cols, Integer): + return rows == cols + if rows == cols: + return True + return None + + def _eval_conjugate(self): + from sympy.matrices.expressions.adjoint import Adjoint + return Adjoint(Transpose(self)) + + def as_real_imag(self, deep=True, **hints): + return self._eval_as_real_imag() + + def _eval_as_real_imag(self): + real = S.Half * (self + self._eval_conjugate()) + im = (self - self._eval_conjugate())/(2*S.ImaginaryUnit) + return (real, im) + + def _eval_inverse(self): + return Inverse(self) + + def _eval_determinant(self): + return Determinant(self) + + def _eval_transpose(self): + return Transpose(self) + + def _eval_trace(self): + return None + + def _eval_power(self, exp): + """ + Override this in sub-classes to implement simplification of powers. The cases where the exponent + is -1, 0, 1 are already covered in MatPow.doit(), so implementations can exclude these cases. + """ + return MatPow(self, exp) + + def _eval_simplify(self, **kwargs): + if self.is_Atom: + return self + else: + from sympy.simplify import simplify + return self.func(*[simplify(x, **kwargs) for x in self.args]) + + def _eval_adjoint(self): + from sympy.matrices.expressions.adjoint import Adjoint + return Adjoint(self) + + def _eval_derivative_n_times(self, x, n): + return Basic._eval_derivative_n_times(self, x, n) + + def _eval_derivative(self, x): + # `x` is a scalar: + if self.has(x): + # See if there are other methods using it: + return super()._eval_derivative(x) + else: + return ZeroMatrix(*self.shape) + + @classmethod + def _check_dim(cls, dim): + """Helper function to check invalid matrix dimensions""" + ok = not dim.is_Float and check_assumptions( + dim, integer=True, nonnegative=True) + if ok is False: + raise ValueError( + "The dimension specification {} should be " + "a nonnegative integer.".format(dim)) + + + def _entry(self, i, j, **kwargs): + raise NotImplementedError( + "Indexing not implemented for %s" % self.__class__.__name__) + + def adjoint(self): + return adjoint(self) + + def as_coeff_Mul(self, rational=False): + """Efficiently extract the coefficient of a product.""" + return S.One, self + + def conjugate(self): + return conjugate(self) + + def transpose(self): + from sympy.matrices.expressions.transpose import transpose + return transpose(self) + + @property + def T(self): + '''Matrix transposition''' + return self.transpose() + + def inverse(self): + if self.is_square is False: + raise NonSquareMatrixError('Inverse of non-square matrix') + return self._eval_inverse() + + def inv(self): + return self.inverse() + + def det(self): + from sympy.matrices.expressions.determinant import det + return det(self) + + @property + def I(self): + return self.inverse() + + def valid_index(self, i, j): + def is_valid(idx): + return isinstance(idx, (int, Integer, Symbol, Expr)) + return (is_valid(i) and is_valid(j) and + (self.rows is None or + (i >= -self.rows) != False and (i < self.rows) != False) and + (j >= -self.cols) != False and (j < self.cols) != False) + + def __getitem__(self, key): + if not isinstance(key, tuple) and isinstance(key, slice): + from sympy.matrices.expressions.slice import MatrixSlice + return MatrixSlice(self, key, (0, None, 1)) + if isinstance(key, tuple) and len(key) == 2: + i, j = key + if isinstance(i, slice) or isinstance(j, slice): + from sympy.matrices.expressions.slice import MatrixSlice + return MatrixSlice(self, i, j) + i, j = _sympify(i), _sympify(j) + if self.valid_index(i, j) != False: + return self._entry(i, j) + else: + raise IndexError("Invalid indices (%s, %s)" % (i, j)) + elif isinstance(key, (SYMPY_INTS, Integer)): + # row-wise decomposition of matrix + rows, cols = self.shape + # allow single indexing if number of columns is known + if not isinstance(cols, Integer): + raise IndexError(filldedent(''' + Single indexing is only supported when the number + of columns is known.''')) + key = _sympify(key) + i = key // cols + j = key % cols + if self.valid_index(i, j) != False: + return self._entry(i, j) + else: + raise IndexError("Invalid index %s" % key) + elif isinstance(key, (Symbol, Expr)): + raise IndexError(filldedent(''' + Only integers may be used when addressing the matrix + with a single index.''')) + raise IndexError("Invalid index, wanted %s[i,j]" % self) + + def _is_shape_symbolic(self) -> bool: + return (not isinstance(self.rows, (SYMPY_INTS, Integer)) + or not isinstance(self.cols, (SYMPY_INTS, Integer))) + + def as_explicit(self): + """ + Returns a dense Matrix with elements represented explicitly + + Returns an object of type ImmutableDenseMatrix. + + Examples + ======== + + >>> from sympy import Identity + >>> I = Identity(3) + >>> I + I + >>> I.as_explicit() + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + + See Also + ======== + as_mutable: returns mutable Matrix type + + """ + if self._is_shape_symbolic(): + raise ValueError( + 'Matrix with symbolic shape ' + 'cannot be represented explicitly.') + from sympy.matrices.immutable import ImmutableDenseMatrix + return ImmutableDenseMatrix([[self[i, j] + for j in range(self.cols)] + for i in range(self.rows)]) + + def as_mutable(self): + """ + Returns a dense, mutable matrix with elements represented explicitly + + Examples + ======== + + >>> from sympy import Identity + >>> I = Identity(3) + >>> I + I + >>> I.shape + (3, 3) + >>> I.as_mutable() + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + + See Also + ======== + as_explicit: returns ImmutableDenseMatrix + """ + return self.as_explicit().as_mutable() + + def __array__(self, dtype=object, copy=None): + if copy is not None and not copy: + raise TypeError("Cannot implement copy=False when converting Matrix to ndarray") + from numpy import empty + a = empty(self.shape, dtype=object) + for i in range(self.rows): + for j in range(self.cols): + a[i, j] = self[i, j] + return a + + def equals(self, other): + """ + Test elementwise equality between matrices, potentially of different + types + + >>> from sympy import Identity, eye + >>> Identity(3).equals(eye(3)) + True + """ + return self.as_explicit().equals(other) + + def canonicalize(self): + return self + + def as_coeff_mmul(self): + return S.One, MatMul(self) + + @staticmethod + def from_index_summation(expr, first_index=None, last_index=None, dimensions=None): + r""" + Parse expression of matrices with explicitly summed indices into a + matrix expression without indices, if possible. + + This transformation expressed in mathematical notation: + + `\sum_{j=0}^{N-1} A_{i,j} B_{j,k} \Longrightarrow \mathbf{A}\cdot \mathbf{B}` + + Optional parameter ``first_index``: specify which free index to use as + the index starting the expression. + + Examples + ======== + + >>> from sympy import MatrixSymbol, MatrixExpr, Sum + >>> from sympy.abc import i, j, k, l, N + >>> A = MatrixSymbol("A", N, N) + >>> B = MatrixSymbol("B", N, N) + >>> expr = Sum(A[i, j]*B[j, k], (j, 0, N-1)) + >>> MatrixExpr.from_index_summation(expr) + A*B + + Transposition is detected: + + >>> expr = Sum(A[j, i]*B[j, k], (j, 0, N-1)) + >>> MatrixExpr.from_index_summation(expr) + A.T*B + + Detect the trace: + + >>> expr = Sum(A[i, i], (i, 0, N-1)) + >>> MatrixExpr.from_index_summation(expr) + Trace(A) + + More complicated expressions: + + >>> expr = Sum(A[i, j]*B[k, j]*A[l, k], (j, 0, N-1), (k, 0, N-1)) + >>> MatrixExpr.from_index_summation(expr) + A*B.T*A.T + """ + from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array + from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix + first_indices = [] + if first_index is not None: + first_indices.append(first_index) + if last_index is not None: + first_indices.append(last_index) + arr = convert_indexed_to_array(expr, first_indices=first_indices) + return convert_array_to_matrix(arr) + + def applyfunc(self, func): + from .applyfunc import ElementwiseApplyFunction + return ElementwiseApplyFunction(func, self) + + +@dispatch(MatrixExpr, Expr) +def _eval_is_eq(lhs, rhs): # noqa:F811 + return False + +@dispatch(MatrixExpr, MatrixExpr) # type: ignore +def _eval_is_eq(lhs, rhs): # noqa:F811 + if lhs.shape != rhs.shape: + return False + if (lhs - rhs).is_ZeroMatrix: + return True + +def get_postprocessor(cls): + def _postprocessor(expr): + # To avoid circular imports, we can't have MatMul/MatAdd on the top level + mat_class = {Mul: MatMul, Add: MatAdd}[cls] + nonmatrices = [] + matrices = [] + for term in expr.args: + if isinstance(term, MatrixExpr): + matrices.append(term) + else: + nonmatrices.append(term) + + if not matrices: + return cls._from_args(nonmatrices) + + if nonmatrices: + if cls == Mul: + for i in range(len(matrices)): + if not matrices[i].is_MatrixExpr: + # If one of the matrices explicit, absorb the scalar into it + # (doit will combine all explicit matrices into one, so it + # doesn't matter which) + matrices[i] = matrices[i].__mul__(cls._from_args(nonmatrices)) + nonmatrices = [] + break + + else: + # Maintain the ability to create Add(scalar, matrix) without + # raising an exception. That way different algorithms can + # replace matrix expressions with non-commutative symbols to + # manipulate them like non-commutative scalars. + return cls._from_args(nonmatrices + [mat_class(*matrices).doit(deep=False)]) + + if mat_class == MatAdd: + return mat_class(*matrices).doit(deep=False) + return mat_class(cls._from_args(nonmatrices), *matrices).doit(deep=False) + return _postprocessor + + +Basic._constructor_postprocessor_mapping[MatrixExpr] = { + "Mul": [get_postprocessor(Mul)], + "Add": [get_postprocessor(Add)], +} + + +def _matrix_derivative(expr, x, old_algorithm=False): + + if isinstance(expr, MatrixBase) or isinstance(x, MatrixBase): + # Do not use array expressions for explicit matrices: + old_algorithm = True + + if old_algorithm: + return _matrix_derivative_old_algorithm(expr, x) + + from sympy.tensor.array.expressions.from_matrix_to_array import convert_matrix_to_array + from sympy.tensor.array.expressions.arrayexpr_derivatives import array_derive + from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix + + array_expr = convert_matrix_to_array(expr) + diff_array_expr = array_derive(array_expr, x) + diff_matrix_expr = convert_array_to_matrix(diff_array_expr) + return diff_matrix_expr + + +def _matrix_derivative_old_algorithm(expr, x): + from sympy.tensor.array.array_derivatives import ArrayDerivative + lines = expr._eval_derivative_matrix_lines(x) + + parts = [i.build() for i in lines] + + from sympy.tensor.array.expressions.from_array_to_matrix import convert_array_to_matrix + + parts = [[convert_array_to_matrix(j) for j in i] for i in parts] + + def _get_shape(elem): + if isinstance(elem, MatrixExpr): + return elem.shape + return 1, 1 + + def get_rank(parts): + return sum(j not in (1, None) for i in parts for j in _get_shape(i)) + + ranks = [get_rank(i) for i in parts] + rank = ranks[0] + + def contract_one_dims(parts): + if len(parts) == 1: + return parts[0] + else: + p1, p2 = parts[:2] + if p2.is_Matrix: + p2 = p2.T + if p1 == Identity(1): + pbase = p2 + elif p2 == Identity(1): + pbase = p1 + else: + pbase = p1*p2 + if len(parts) == 2: + return pbase + else: # len(parts) > 2 + if pbase.is_Matrix: + raise ValueError("") + return pbase*Mul.fromiter(parts[2:]) + + if rank <= 2: + return Add.fromiter([contract_one_dims(i) for i in parts]) + + return ArrayDerivative(expr, x) + + +class MatrixElement(Expr): + parent = property(lambda self: self.args[0]) + i = property(lambda self: self.args[1]) + j = property(lambda self: self.args[2]) + _diff_wrt = True + is_symbol = True + is_commutative = True + + def __new__(cls, name, n, m): + n, m = map(_sympify, (n, m)) + if isinstance(name, str): + name = Symbol(name) + else: + if isinstance(name, MatrixBase): + if n.is_Integer and m.is_Integer: + return name[n, m] + name = _sympify(name) # change mutable into immutable + else: + name = _sympify(name) + if not isinstance(name.kind, MatrixKind): + raise TypeError("First argument of MatrixElement should be a matrix") + if not getattr(name, 'valid_index', lambda n, m: True)(n, m): + raise IndexError('indices out of range') + obj = Expr.__new__(cls, name, n, m) + return obj + + @property + def symbol(self): + return self.args[0] + + def doit(self, **hints): + deep = hints.get('deep', True) + if deep: + args = [arg.doit(**hints) for arg in self.args] + else: + args = self.args + return args[0][args[1], args[2]] + + @property + def indices(self): + return self.args[1:] + + def _eval_derivative(self, v): + + if not isinstance(v, MatrixElement): + return self.parent.diff(v)[self.i, self.j] + + M = self.args[0] + + m, n = self.parent.shape + + if M == v.args[0]: + return KroneckerDelta(self.args[1], v.args[1], (0, m-1)) * \ + KroneckerDelta(self.args[2], v.args[2], (0, n-1)) + + if isinstance(M, Inverse): + from sympy.concrete.summations import Sum + i, j = self.args[1:] + i1, i2 = symbols("z1, z2", cls=Dummy) + Y = M.args[0] + r1, r2 = Y.shape + return -Sum(M[i, i1]*Y[i1, i2].diff(v)*M[i2, j], (i1, 0, r1-1), (i2, 0, r2-1)) + + if self.has(v.args[0]): + return None + + return S.Zero + + +class MatrixSymbol(MatrixExpr): + """Symbolic representation of a Matrix object + + Creates a SymPy Symbol to represent a Matrix. This matrix has a shape and + can be included in Matrix Expressions + + Examples + ======== + + >>> from sympy import MatrixSymbol, Identity + >>> A = MatrixSymbol('A', 3, 4) # A 3 by 4 Matrix + >>> B = MatrixSymbol('B', 4, 3) # A 4 by 3 Matrix + >>> A.shape + (3, 4) + >>> 2*A*B + Identity(3) + I + 2*A*B + """ + is_commutative = False + is_symbol = True + _diff_wrt = True + + def __new__(cls, name, n, m): + n, m = _sympify(n), _sympify(m) + + cls._check_dim(m) + cls._check_dim(n) + + if isinstance(name, str): + name = Str(name) + obj = Basic.__new__(cls, name, n, m) + return obj + + @property + def shape(self): + return self.args[1], self.args[2] + + @property + def name(self): + return self.args[0].name + + def _entry(self, i, j, **kwargs): + return MatrixElement(self, i, j) + + @property + def free_symbols(self): + return {self} + + def _eval_simplify(self, **kwargs): + return self + + def _eval_derivative(self, x): + # x is a scalar: + return ZeroMatrix(self.shape[0], self.shape[1]) + + def _eval_derivative_matrix_lines(self, x): + if self != x: + first = ZeroMatrix(x.shape[0], self.shape[0]) if self.shape[0] != 1 else S.Zero + second = ZeroMatrix(x.shape[1], self.shape[1]) if self.shape[1] != 1 else S.Zero + return [_LeftRightArgs( + [first, second], + )] + else: + first = Identity(self.shape[0]) if self.shape[0] != 1 else S.One + second = Identity(self.shape[1]) if self.shape[1] != 1 else S.One + return [_LeftRightArgs( + [first, second], + )] + + +def matrix_symbols(expr): + return [sym for sym in expr.free_symbols if sym.is_Matrix] + + +class _LeftRightArgs: + r""" + Helper class to compute matrix derivatives. + + The logic: when an expression is derived by a matrix `X_{mn}`, two lines of + matrix multiplications are created: the one contracted to `m` (first line), + and the one contracted to `n` (second line). + + Transposition flips the side by which new matrices are connected to the + lines. + + The trace connects the end of the two lines. + """ + + def __init__(self, lines, higher=S.One): + self._lines = list(lines) + self._first_pointer_parent = self._lines + self._first_pointer_index = 0 + self._first_line_index = 0 + self._second_pointer_parent = self._lines + self._second_pointer_index = 1 + self._second_line_index = 1 + self.higher = higher + + @property + def first_pointer(self): + return self._first_pointer_parent[self._first_pointer_index] + + @first_pointer.setter + def first_pointer(self, value): + self._first_pointer_parent[self._first_pointer_index] = value + + @property + def second_pointer(self): + return self._second_pointer_parent[self._second_pointer_index] + + @second_pointer.setter + def second_pointer(self, value): + self._second_pointer_parent[self._second_pointer_index] = value + + def __repr__(self): + built = [self._build(i) for i in self._lines] + return "_LeftRightArgs(lines=%s, higher=%s)" % ( + built, + self.higher, + ) + + def transpose(self): + self._first_pointer_parent, self._second_pointer_parent = self._second_pointer_parent, self._first_pointer_parent + self._first_pointer_index, self._second_pointer_index = self._second_pointer_index, self._first_pointer_index + self._first_line_index, self._second_line_index = self._second_line_index, self._first_line_index + return self + + @staticmethod + def _build(expr): + if isinstance(expr, ExprBuilder): + return expr.build() + if isinstance(expr, list): + if len(expr) == 1: + return expr[0] + else: + return expr[0](*[_LeftRightArgs._build(i) for i in expr[1]]) + else: + return expr + + def build(self): + data = [self._build(i) for i in self._lines] + if self.higher != 1: + data += [self._build(self.higher)] + data = list(data) + return data + + def matrix_form(self): + if self.first != 1 and self.higher != 1: + raise ValueError("higher dimensional array cannot be represented") + + def _get_shape(elem): + if isinstance(elem, MatrixExpr): + return elem.shape + return (None, None) + + if _get_shape(self.first)[1] != _get_shape(self.second)[1]: + # Remove one-dimensional identity matrices: + # (this is needed by `a.diff(a)` where `a` is a vector) + if _get_shape(self.second) == (1, 1): + return self.first*self.second[0, 0] + if _get_shape(self.first) == (1, 1): + return self.first[1, 1]*self.second.T + raise ValueError("incompatible shapes") + if self.first != 1: + return self.first*self.second.T + else: + return self.higher + + def rank(self): + """ + Number of dimensions different from trivial (warning: not related to + matrix rank). + """ + rank = 0 + if self.first != 1: + rank += sum(i != 1 for i in self.first.shape) + if self.second != 1: + rank += sum(i != 1 for i in self.second.shape) + if self.higher != 1: + rank += 2 + return rank + + def _multiply_pointer(self, pointer, other): + from ...tensor.array.expressions.array_expressions import ArrayTensorProduct + from ...tensor.array.expressions.array_expressions import ArrayContraction + + subexpr = ExprBuilder( + ArrayContraction, + [ + ExprBuilder( + ArrayTensorProduct, + [ + pointer, + other + ] + ), + (1, 2) + ], + validator=ArrayContraction._validate + ) + + return subexpr + + def append_first(self, other): + self.first_pointer *= other + + def append_second(self, other): + self.second_pointer *= other + + +def _make_matrix(x): + from sympy.matrices.immutable import ImmutableDenseMatrix + if isinstance(x, MatrixExpr): + return x + return ImmutableDenseMatrix([[x]]) + + +from .matmul import MatMul +from .matadd import MatAdd +from .matpow import MatPow +from .transpose import Transpose +from .inverse import Inverse +from .special import ZeroMatrix, Identity +from .determinant import Determinant diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/matmul.py b/lib/python3.11/site-packages/sympy/matrices/expressions/matmul.py new file mode 100644 index 0000000000000000000000000000000000000000..a4af9f26c6ae191b22864998685f18f142900ded --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/matmul.py @@ -0,0 +1,496 @@ +from sympy.assumptions.ask import ask, Q +from sympy.assumptions.refine import handlers_dict +from sympy.core import Basic, sympify, S +from sympy.core.mul import mul, Mul +from sympy.core.numbers import Number, Integer +from sympy.core.symbol import Dummy +from sympy.functions import adjoint +from sympy.strategies import (rm_id, unpack, typed, flatten, exhaust, + do_one, new) +from sympy.matrices.exceptions import NonInvertibleMatrixError +from sympy.matrices.matrixbase import MatrixBase +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.matrices.expressions._shape import validate_matmul_integer as validate + +from .inverse import Inverse +from .matexpr import MatrixExpr +from .matpow import MatPow +from .transpose import transpose +from .permutation import PermutationMatrix +from .special import ZeroMatrix, Identity, GenericIdentity, OneMatrix + + +# XXX: MatMul should perhaps not subclass directly from Mul +class MatMul(MatrixExpr, Mul): + """ + A product of matrix expressions + + Examples + ======== + + >>> from sympy import MatMul, MatrixSymbol + >>> A = MatrixSymbol('A', 5, 4) + >>> B = MatrixSymbol('B', 4, 3) + >>> C = MatrixSymbol('C', 3, 6) + >>> MatMul(A, B, C) + A*B*C + """ + is_MatMul = True + + identity = GenericIdentity() + + def __new__(cls, *args, evaluate=False, check=None, _sympify=True): + if not args: + return cls.identity + + # This must be removed aggressively in the constructor to avoid + # TypeErrors from GenericIdentity().shape + args = list(filter(lambda i: cls.identity != i, args)) + if _sympify: + args = list(map(sympify, args)) + obj = Basic.__new__(cls, *args) + factor, matrices = obj.as_coeff_matrices() + + if check is not None: + sympy_deprecation_warning( + "Passing check to MatMul is deprecated and the check argument will be removed in a future version.", + deprecated_since_version="1.11", + active_deprecations_target='remove-check-argument-from-matrix-operations') + + if check is not False: + validate(*matrices) + + if not matrices: + # Should it be + # + # return Basic.__neq__(cls, factor, GenericIdentity()) ? + return factor + + if evaluate: + return cls._evaluate(obj) + + return obj + + @classmethod + def _evaluate(cls, expr): + return canonicalize(expr) + + @property + def shape(self): + matrices = [arg for arg in self.args if arg.is_Matrix] + return (matrices[0].rows, matrices[-1].cols) + + def _entry(self, i, j, expand=True, **kwargs): + # Avoid cyclic imports + from sympy.concrete.summations import Sum + from sympy.matrices.immutable import ImmutableMatrix + + coeff, matrices = self.as_coeff_matrices() + + if len(matrices) == 1: # situation like 2*X, matmul is just X + return coeff * matrices[0][i, j] + + indices = [None]*(len(matrices) + 1) + ind_ranges = [None]*(len(matrices) - 1) + indices[0] = i + indices[-1] = j + + def f(): + counter = 1 + while True: + yield Dummy("i_%i" % counter) + counter += 1 + + dummy_generator = kwargs.get("dummy_generator", f()) + + for i in range(1, len(matrices)): + indices[i] = next(dummy_generator) + + for i, arg in enumerate(matrices[:-1]): + ind_ranges[i] = arg.shape[1] - 1 + matrices = [arg._entry(indices[i], indices[i+1], dummy_generator=dummy_generator) for i, arg in enumerate(matrices)] + expr_in_sum = Mul.fromiter(matrices) + if any(v.has(ImmutableMatrix) for v in matrices): + expand = True + result = coeff*Sum( + expr_in_sum, + *zip(indices[1:-1], [0]*len(ind_ranges), ind_ranges) + ) + + # Don't waste time in result.doit() if the sum bounds are symbolic + if not any(isinstance(v, (Integer, int)) for v in ind_ranges): + expand = False + return result.doit() if expand else result + + def as_coeff_matrices(self): + scalars = [x for x in self.args if not x.is_Matrix] + matrices = [x for x in self.args if x.is_Matrix] + coeff = Mul(*scalars) + if coeff.is_commutative is False: + raise NotImplementedError("noncommutative scalars in MatMul are not supported.") + + return coeff, matrices + + def as_coeff_mmul(self): + coeff, matrices = self.as_coeff_matrices() + return coeff, MatMul(*matrices) + + def expand(self, **kwargs): + expanded = super(MatMul, self).expand(**kwargs) + return self._evaluate(expanded) + + def _eval_transpose(self): + """Transposition of matrix multiplication. + + Notes + ===== + + The following rules are applied. + + Transposition for matrix multiplied with another matrix: + `\\left(A B\\right)^{T} = B^{T} A^{T}` + + Transposition for matrix multiplied with scalar: + `\\left(c A\\right)^{T} = c A^{T}` + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Transpose + """ + coeff, matrices = self.as_coeff_matrices() + return MatMul( + coeff, *[transpose(arg) for arg in matrices[::-1]]).doit() + + def _eval_adjoint(self): + return MatMul(*[adjoint(arg) for arg in self.args[::-1]]).doit() + + def _eval_trace(self): + factor, mmul = self.as_coeff_mmul() + if factor != 1: + from .trace import trace + return factor * trace(mmul.doit()) + + def _eval_determinant(self): + from sympy.matrices.expressions.determinant import Determinant + factor, matrices = self.as_coeff_matrices() + square_matrices = only_squares(*matrices) + return factor**self.rows * Mul(*list(map(Determinant, square_matrices))) + + def _eval_inverse(self): + if all(arg.is_square for arg in self.args if isinstance(arg, MatrixExpr)): + return MatMul(*( + arg.inverse() if isinstance(arg, MatrixExpr) else arg**-1 + for arg in self.args[::-1] + ) + ).doit() + return Inverse(self) + + def doit(self, **hints): + deep = hints.get('deep', True) + if deep: + args = tuple(arg.doit(**hints) for arg in self.args) + else: + args = self.args + + # treat scalar*MatrixSymbol or scalar*MatPow separately + expr = canonicalize(MatMul(*args)) + return expr + + # Needed for partial compatibility with Mul + def args_cnc(self, cset=False, warn=True, **kwargs): + coeff_c = [x for x in self.args if x.is_commutative] + coeff_nc = [x for x in self.args if not x.is_commutative] + if cset: + clen = len(coeff_c) + coeff_c = set(coeff_c) + if clen and warn and len(coeff_c) != clen: + raise ValueError('repeated commutative arguments: %s' % + [ci for ci in coeff_c if list(self.args).count(ci) > 1]) + return [coeff_c, coeff_nc] + + def _eval_derivative_matrix_lines(self, x): + from .transpose import Transpose + with_x_ind = [i for i, arg in enumerate(self.args) if arg.has(x)] + lines = [] + for ind in with_x_ind: + left_args = self.args[:ind] + right_args = self.args[ind+1:] + + if right_args: + right_mat = MatMul.fromiter(right_args) + else: + right_mat = Identity(self.shape[1]) + if left_args: + left_rev = MatMul.fromiter([Transpose(i).doit() if i.is_Matrix else i for i in reversed(left_args)]) + else: + left_rev = Identity(self.shape[0]) + + d = self.args[ind]._eval_derivative_matrix_lines(x) + for i in d: + i.append_first(left_rev) + i.append_second(right_mat) + lines.append(i) + + return lines + +mul.register_handlerclass((Mul, MatMul), MatMul) + + +# Rules +def newmul(*args): + if args[0] == 1: + args = args[1:] + return new(MatMul, *args) + +def any_zeros(mul): + if any(arg.is_zero or (arg.is_Matrix and arg.is_ZeroMatrix) + for arg in mul.args): + matrices = [arg for arg in mul.args if arg.is_Matrix] + return ZeroMatrix(matrices[0].rows, matrices[-1].cols) + return mul + +def merge_explicit(matmul): + """ Merge explicit MatrixBase arguments + + >>> from sympy import MatrixSymbol, Matrix, MatMul, pprint + >>> from sympy.matrices.expressions.matmul import merge_explicit + >>> A = MatrixSymbol('A', 2, 2) + >>> B = Matrix([[1, 1], [1, 1]]) + >>> C = Matrix([[1, 2], [3, 4]]) + >>> X = MatMul(A, B, C) + >>> pprint(X) + [1 1] [1 2] + A*[ ]*[ ] + [1 1] [3 4] + >>> pprint(merge_explicit(X)) + [4 6] + A*[ ] + [4 6] + + >>> X = MatMul(B, A, C) + >>> pprint(X) + [1 1] [1 2] + [ ]*A*[ ] + [1 1] [3 4] + >>> pprint(merge_explicit(X)) + [1 1] [1 2] + [ ]*A*[ ] + [1 1] [3 4] + """ + if not any(isinstance(arg, MatrixBase) for arg in matmul.args): + return matmul + newargs = [] + last = matmul.args[0] + for arg in matmul.args[1:]: + if isinstance(arg, (MatrixBase, Number)) and isinstance(last, (MatrixBase, Number)): + last = last * arg + else: + newargs.append(last) + last = arg + newargs.append(last) + + return MatMul(*newargs) + +def remove_ids(mul): + """ Remove Identities from a MatMul + + This is a modified version of sympy.strategies.rm_id. + This is necesssary because MatMul may contain both MatrixExprs and Exprs + as args. + + See Also + ======== + + sympy.strategies.rm_id + """ + # Separate Exprs from MatrixExprs in args + factor, mmul = mul.as_coeff_mmul() + # Apply standard rm_id for MatMuls + result = rm_id(lambda x: x.is_Identity is True)(mmul) + if result != mmul: + return newmul(factor, *result.args) # Recombine and return + else: + return mul + +def factor_in_front(mul): + factor, matrices = mul.as_coeff_matrices() + if factor != 1: + return newmul(factor, *matrices) + return mul + +def combine_powers(mul): + r"""Combine consecutive powers with the same base into one, e.g. + $$A \times A^2 \Rightarrow A^3$$ + + This also cancels out the possible matrix inverses using the + knowledgebase of :class:`~.Inverse`, e.g., + $$ Y \times X \times X^{-1} \Rightarrow Y $$ + """ + factor, args = mul.as_coeff_matrices() + new_args = [args[0]] + + for i in range(1, len(args)): + A = new_args[-1] + B = args[i] + + if isinstance(B, Inverse) and isinstance(B.arg, MatMul): + Bargs = B.arg.args + l = len(Bargs) + if list(Bargs) == new_args[-l:]: + new_args = new_args[:-l] + [Identity(B.shape[0])] + continue + + if isinstance(A, Inverse) and isinstance(A.arg, MatMul): + Aargs = A.arg.args + l = len(Aargs) + if list(Aargs) == args[i:i+l]: + identity = Identity(A.shape[0]) + new_args[-1] = identity + for j in range(i, i+l): + args[j] = identity + continue + + if A.is_square == False or B.is_square == False: + new_args.append(B) + continue + + if isinstance(A, MatPow): + A_base, A_exp = A.args + else: + A_base, A_exp = A, S.One + + if isinstance(B, MatPow): + B_base, B_exp = B.args + else: + B_base, B_exp = B, S.One + + if A_base == B_base: + new_exp = A_exp + B_exp + new_args[-1] = MatPow(A_base, new_exp).doit(deep=False) + continue + elif not isinstance(B_base, MatrixBase): + try: + B_base_inv = B_base.inverse() + except NonInvertibleMatrixError: + B_base_inv = None + if B_base_inv is not None and A_base == B_base_inv: + new_exp = A_exp - B_exp + new_args[-1] = MatPow(A_base, new_exp).doit(deep=False) + continue + new_args.append(B) + + return newmul(factor, *new_args) + +def combine_permutations(mul): + """Refine products of permutation matrices as the products of cycles. + """ + args = mul.args + l = len(args) + if l < 2: + return mul + + result = [args[0]] + for i in range(1, l): + A = result[-1] + B = args[i] + if isinstance(A, PermutationMatrix) and \ + isinstance(B, PermutationMatrix): + cycle_1 = A.args[0] + cycle_2 = B.args[0] + result[-1] = PermutationMatrix(cycle_1 * cycle_2) + else: + result.append(B) + + return MatMul(*result) + +def combine_one_matrices(mul): + """ + Combine products of OneMatrix + + e.g. OneMatrix(2, 3) * OneMatrix(3, 4) -> 3 * OneMatrix(2, 4) + """ + factor, args = mul.as_coeff_matrices() + new_args = [args[0]] + + for B in args[1:]: + A = new_args[-1] + if not isinstance(A, OneMatrix) or not isinstance(B, OneMatrix): + new_args.append(B) + continue + new_args.pop() + new_args.append(OneMatrix(A.shape[0], B.shape[1])) + factor *= A.shape[1] + + return newmul(factor, *new_args) + +def distribute_monom(mul): + """ + Simplify MatMul expressions but distributing + rational term to MatMul. + + e.g. 2*(A+B) -> 2*A + 2*B + """ + args = mul.args + if len(args) == 2: + from .matadd import MatAdd + if args[0].is_MatAdd and args[1].is_Rational: + return MatAdd(*[MatMul(mat, args[1]).doit() for mat in args[0].args]) + if args[1].is_MatAdd and args[0].is_Rational: + return MatAdd(*[MatMul(args[0], mat).doit() for mat in args[1].args]) + return mul + +rules = ( + distribute_monom, any_zeros, remove_ids, combine_one_matrices, combine_powers, unpack, rm_id(lambda x: x == 1), + merge_explicit, factor_in_front, flatten, combine_permutations) + +canonicalize = exhaust(typed({MatMul: do_one(*rules)})) + +def only_squares(*matrices): + """factor matrices only if they are square""" + if matrices[0].rows != matrices[-1].cols: + raise RuntimeError("Invalid matrices being multiplied") + out = [] + start = 0 + for i, M in enumerate(matrices): + if M.cols == matrices[start].rows: + out.append(MatMul(*matrices[start:i+1]).doit()) + start = i+1 + return out + + +def refine_MatMul(expr, assumptions): + """ + >>> from sympy import MatrixSymbol, Q, assuming, refine + >>> X = MatrixSymbol('X', 2, 2) + >>> expr = X * X.T + >>> print(expr) + X*X.T + >>> with assuming(Q.orthogonal(X)): + ... print(refine(expr)) + I + """ + newargs = [] + exprargs = [] + + for args in expr.args: + if args.is_Matrix: + exprargs.append(args) + else: + newargs.append(args) + + last = exprargs[0] + for arg in exprargs[1:]: + if arg == last.T and ask(Q.orthogonal(arg), assumptions): + last = Identity(arg.shape[0]) + elif arg == last.conjugate() and ask(Q.unitary(arg), assumptions): + last = Identity(arg.shape[0]) + else: + newargs.append(last) + last = arg + newargs.append(last) + + return MatMul(*newargs) + + +handlers_dict['MatMul'] = refine_MatMul diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/matpow.py b/lib/python3.11/site-packages/sympy/matrices/expressions/matpow.py new file mode 100644 index 0000000000000000000000000000000000000000..b6472995e134e9e5ebfd28a901480665d1531275 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/matpow.py @@ -0,0 +1,150 @@ +from .matexpr import MatrixExpr +from .special import Identity +from sympy.core import S +from sympy.core.expr import ExprBuilder +from sympy.core.cache import cacheit +from sympy.core.power import Pow +from sympy.core.sympify import _sympify +from sympy.matrices import MatrixBase +from sympy.matrices.exceptions import NonSquareMatrixError + + +class MatPow(MatrixExpr): + def __new__(cls, base, exp, evaluate=False, **options): + base = _sympify(base) + if not base.is_Matrix: + raise TypeError("MatPow base should be a matrix") + + if base.is_square is False: + raise NonSquareMatrixError("Power of non-square matrix %s" % base) + + exp = _sympify(exp) + obj = super().__new__(cls, base, exp) + + if evaluate: + obj = obj.doit(deep=False) + + return obj + + @property + def base(self): + return self.args[0] + + @property + def exp(self): + return self.args[1] + + @property + def shape(self): + return self.base.shape + + @cacheit + def _get_explicit_matrix(self): + return self.base.as_explicit()**self.exp + + def _entry(self, i, j, **kwargs): + from sympy.matrices.expressions import MatMul + A = self.doit() + if isinstance(A, MatPow): + # We still have a MatPow, make an explicit MatMul out of it. + if A.exp.is_Integer and A.exp.is_positive: + A = MatMul(*[A.base for k in range(A.exp)]) + elif not self._is_shape_symbolic(): + return A._get_explicit_matrix()[i, j] + else: + # Leave the expression unevaluated: + from sympy.matrices.expressions.matexpr import MatrixElement + return MatrixElement(self, i, j) + return A[i, j] + + def doit(self, **hints): + if hints.get('deep', True): + base, exp = (arg.doit(**hints) for arg in self.args) + else: + base, exp = self.args + + # combine all powers, e.g. (A ** 2) ** 3 -> A ** 6 + while isinstance(base, MatPow): + exp *= base.args[1] + base = base.args[0] + + if isinstance(base, MatrixBase): + # Delegate + return base ** exp + + # Handle simple cases so that _eval_power() in MatrixExpr sub-classes can ignore them + if exp == S.One: + return base + if exp == S.Zero: + return Identity(base.rows) + if exp == S.NegativeOne: + from sympy.matrices.expressions import Inverse + return Inverse(base).doit(**hints) + + eval_power = getattr(base, '_eval_power', None) + if eval_power is not None: + return eval_power(exp) + + return MatPow(base, exp) + + def _eval_transpose(self): + base, exp = self.args + return MatPow(base.transpose(), exp) + + def _eval_adjoint(self): + base, exp = self.args + return MatPow(base.adjoint(), exp) + + def _eval_conjugate(self): + base, exp = self.args + return MatPow(base.conjugate(), exp) + + def _eval_derivative(self, x): + return Pow._eval_derivative(self, x) + + def _eval_derivative_matrix_lines(self, x): + from sympy.tensor.array.expressions.array_expressions import ArrayContraction + from ...tensor.array.expressions.array_expressions import ArrayTensorProduct + from .matmul import MatMul + from .inverse import Inverse + exp = self.exp + if self.base.shape == (1, 1) and not exp.has(x): + lr = self.base._eval_derivative_matrix_lines(x) + for i in lr: + subexpr = ExprBuilder( + ArrayContraction, + [ + ExprBuilder( + ArrayTensorProduct, + [ + Identity(1), + i._lines[0], + exp*self.base**(exp-1), + i._lines[1], + Identity(1), + ] + ), + (0, 3, 4), (5, 7, 8) + ], + validator=ArrayContraction._validate + ) + i._first_pointer_parent = subexpr.args[0].args + i._first_pointer_index = 0 + i._second_pointer_parent = subexpr.args[0].args + i._second_pointer_index = 4 + i._lines = [subexpr] + return lr + if (exp > 0) == True: + newexpr = MatMul.fromiter([self.base for i in range(exp)]) + elif (exp == -1) == True: + return Inverse(self.base)._eval_derivative_matrix_lines(x) + elif (exp < 0) == True: + newexpr = MatMul.fromiter([Inverse(self.base) for i in range(-exp)]) + elif (exp == 0) == True: + return self.doit()._eval_derivative_matrix_lines(x) + else: + raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x)) + return newexpr._eval_derivative_matrix_lines(x) + + def _eval_inverse(self): + return MatPow(self.base, -self.exp) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/permutation.py b/lib/python3.11/site-packages/sympy/matrices/expressions/permutation.py new file mode 100644 index 0000000000000000000000000000000000000000..5634fa941a53d8890583fe61bb29bc34f4e6000d --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/permutation.py @@ -0,0 +1,303 @@ +from sympy.core import S +from sympy.core.sympify import _sympify +from sympy.functions import KroneckerDelta + +from .matexpr import MatrixExpr +from .special import ZeroMatrix, Identity, OneMatrix + + +class PermutationMatrix(MatrixExpr): + """A Permutation Matrix + + Parameters + ========== + + perm : Permutation + The permutation the matrix uses. + + The size of the permutation determines the matrix size. + + See the documentation of + :class:`sympy.combinatorics.permutations.Permutation` for + the further information of how to create a permutation object. + + Examples + ======== + + >>> from sympy import Matrix, PermutationMatrix + >>> from sympy.combinatorics import Permutation + + Creating a permutation matrix: + + >>> p = Permutation(1, 2, 0) + >>> P = PermutationMatrix(p) + >>> P = P.as_explicit() + >>> P + Matrix([ + [0, 1, 0], + [0, 0, 1], + [1, 0, 0]]) + + Permuting a matrix row and column: + + >>> M = Matrix([0, 1, 2]) + >>> Matrix(P*M) + Matrix([ + [1], + [2], + [0]]) + + >>> Matrix(M.T*P) + Matrix([[2, 0, 1]]) + + See Also + ======== + + sympy.combinatorics.permutations.Permutation + """ + + def __new__(cls, perm): + from sympy.combinatorics.permutations import Permutation + + perm = _sympify(perm) + if not isinstance(perm, Permutation): + raise ValueError( + "{} must be a SymPy Permutation instance.".format(perm)) + + return super().__new__(cls, perm) + + @property + def shape(self): + size = self.args[0].size + return (size, size) + + @property + def is_Identity(self): + return self.args[0].is_Identity + + def doit(self, **hints): + if self.is_Identity: + return Identity(self.rows) + return self + + def _entry(self, i, j, **kwargs): + perm = self.args[0] + return KroneckerDelta(perm.apply(i), j) + + def _eval_power(self, exp): + return PermutationMatrix(self.args[0] ** exp).doit() + + def _eval_inverse(self): + return PermutationMatrix(self.args[0] ** -1) + + _eval_transpose = _eval_adjoint = _eval_inverse + + def _eval_determinant(self): + sign = self.args[0].signature() + if sign == 1: + return S.One + elif sign == -1: + return S.NegativeOne + raise NotImplementedError + + def _eval_rewrite_as_BlockDiagMatrix(self, *args, **kwargs): + from sympy.combinatorics.permutations import Permutation + from .blockmatrix import BlockDiagMatrix + + perm = self.args[0] + full_cyclic_form = perm.full_cyclic_form + + cycles_picks = [] + + # Stage 1. Decompose the cycles into the blockable form. + a, b, c = 0, 0, 0 + flag = False + for cycle in full_cyclic_form: + l = len(cycle) + m = max(cycle) + + if not flag: + if m + 1 > a + l: + flag = True + temp = [cycle] + b = m + c = l + else: + cycles_picks.append([cycle]) + a += l + + else: + if m > b: + if m + 1 == a + c + l: + temp.append(cycle) + cycles_picks.append(temp) + flag = False + a = m+1 + else: + b = m + temp.append(cycle) + c += l + else: + if b + 1 == a + c + l: + temp.append(cycle) + cycles_picks.append(temp) + flag = False + a = b+1 + else: + temp.append(cycle) + c += l + + # Stage 2. Normalize each decomposed cycles and build matrix. + p = 0 + args = [] + for pick in cycles_picks: + new_cycles = [] + l = 0 + for cycle in pick: + new_cycle = [i - p for i in cycle] + new_cycles.append(new_cycle) + l += len(cycle) + p += l + perm = Permutation(new_cycles) + mat = PermutationMatrix(perm) + args.append(mat) + + return BlockDiagMatrix(*args) + + +class MatrixPermute(MatrixExpr): + r"""Symbolic representation for permuting matrix rows or columns. + + Parameters + ========== + + perm : Permutation, PermutationMatrix + The permutation to use for permuting the matrix. + The permutation can be resized to the suitable one, + + axis : 0 or 1 + The axis to permute alongside. + If `0`, it will permute the matrix rows. + If `1`, it will permute the matrix columns. + + Notes + ===== + + This follows the same notation used in + :meth:`sympy.matrices.matrixbase.MatrixBase.permute`. + + Examples + ======== + + >>> from sympy import Matrix, MatrixPermute + >>> from sympy.combinatorics import Permutation + + Permuting the matrix rows: + + >>> p = Permutation(1, 2, 0) + >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> B = MatrixPermute(A, p, axis=0) + >>> B.as_explicit() + Matrix([ + [4, 5, 6], + [7, 8, 9], + [1, 2, 3]]) + + Permuting the matrix columns: + + >>> B = MatrixPermute(A, p, axis=1) + >>> B.as_explicit() + Matrix([ + [2, 3, 1], + [5, 6, 4], + [8, 9, 7]]) + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.permute + """ + def __new__(cls, mat, perm, axis=S.Zero): + from sympy.combinatorics.permutations import Permutation + + mat = _sympify(mat) + if not mat.is_Matrix: + raise ValueError( + "{} must be a SymPy matrix instance.".format(perm)) + + perm = _sympify(perm) + if isinstance(perm, PermutationMatrix): + perm = perm.args[0] + + if not isinstance(perm, Permutation): + raise ValueError( + "{} must be a SymPy Permutation or a PermutationMatrix " \ + "instance".format(perm)) + + axis = _sympify(axis) + if axis not in (0, 1): + raise ValueError("The axis must be 0 or 1.") + + mat_size = mat.shape[axis] + if mat_size != perm.size: + try: + perm = perm.resize(mat_size) + except ValueError: + raise ValueError( + "Size does not match between the permutation {} " + "and the matrix {} threaded over the axis {} " + "and cannot be converted." + .format(perm, mat, axis)) + + return super().__new__(cls, mat, perm, axis) + + def doit(self, deep=True, **hints): + mat, perm, axis = self.args + + if deep: + mat = mat.doit(deep=deep, **hints) + perm = perm.doit(deep=deep, **hints) + + if perm.is_Identity: + return mat + + if mat.is_Identity: + if axis is S.Zero: + return PermutationMatrix(perm) + elif axis is S.One: + return PermutationMatrix(perm**-1) + + if isinstance(mat, (ZeroMatrix, OneMatrix)): + return mat + + if isinstance(mat, MatrixPermute) and mat.args[2] == axis: + return MatrixPermute(mat.args[0], perm * mat.args[1], axis) + + return self + + @property + def shape(self): + return self.args[0].shape + + def _entry(self, i, j, **kwargs): + mat, perm, axis = self.args + + if axis == 0: + return mat[perm.apply(i), j] + elif axis == 1: + return mat[i, perm.apply(j)] + + def _eval_rewrite_as_MatMul(self, *args, **kwargs): + from .matmul import MatMul + + mat, perm, axis = self.args + + deep = kwargs.get("deep", True) + + if deep: + mat = mat.rewrite(MatMul) + + if axis == 0: + return MatMul(PermutationMatrix(perm), mat) + elif axis == 1: + return MatMul(mat, PermutationMatrix(perm**-1)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/sets.py b/lib/python3.11/site-packages/sympy/matrices/expressions/sets.py new file mode 100644 index 0000000000000000000000000000000000000000..ab4930ea8f1b058977a8dd1abdc62f1f5e2195c1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/sets.py @@ -0,0 +1,68 @@ +from sympy.core.assumptions import check_assumptions +from sympy.core.logic import fuzzy_and +from sympy.core.sympify import _sympify +from sympy.matrices.kind import MatrixKind +from sympy.sets.sets import Set, SetKind +from sympy.core.kind import NumberKind +from .matexpr import MatrixExpr + + +class MatrixSet(Set): + """ + MatrixSet represents the set of matrices with ``shape = (n, m)`` over the + given set. + + Examples + ======== + + >>> from sympy.matrices import MatrixSet + >>> from sympy import S, I, Matrix + >>> M = MatrixSet(2, 2, set=S.Reals) + >>> X = Matrix([[1, 2], [3, 4]]) + >>> X in M + True + >>> X = Matrix([[1, 2], [I, 4]]) + >>> X in M + False + + """ + is_empty = False + + def __new__(cls, n, m, set): + n, m, set = _sympify(n), _sympify(m), _sympify(set) + cls._check_dim(n) + cls._check_dim(m) + if not isinstance(set, Set): + raise TypeError("{} should be an instance of Set.".format(set)) + return Set.__new__(cls, n, m, set) + + @property + def shape(self): + return self.args[:2] + + @property + def set(self): + return self.args[2] + + def _contains(self, other): + if not isinstance(other, MatrixExpr): + raise TypeError("{} should be an instance of MatrixExpr.".format(other)) + if other.shape != self.shape: + are_symbolic = any(_sympify(x).is_Symbol for x in other.shape + self.shape) + if are_symbolic: + return None + return False + return fuzzy_and(self.set.contains(x) for x in other) + + @classmethod + def _check_dim(cls, dim): + """Helper function to check invalid matrix dimensions""" + ok = not dim.is_Float and check_assumptions( + dim, integer=True, nonnegative=True) + if ok is False: + raise ValueError( + "The dimension specification {} should be " + "a nonnegative integer.".format(dim)) + + def _kind(self): + return SetKind(MatrixKind(NumberKind)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/slice.py b/lib/python3.11/site-packages/sympy/matrices/expressions/slice.py new file mode 100644 index 0000000000000000000000000000000000000000..1904b49f29c503fb4c0c909532f8342fb0f4b135 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/slice.py @@ -0,0 +1,114 @@ +from sympy.matrices.expressions.matexpr import MatrixExpr +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.functions.elementary.integers import floor + +def normalize(i, parentsize): + if isinstance(i, slice): + i = (i.start, i.stop, i.step) + if not isinstance(i, (tuple, list, Tuple)): + if (i < 0) == True: + i += parentsize + i = (i, i+1, 1) + i = list(i) + if len(i) == 2: + i.append(1) + start, stop, step = i + start = start or 0 + if stop is None: + stop = parentsize + if (start < 0) == True: + start += parentsize + if (stop < 0) == True: + stop += parentsize + step = step or 1 + + if ((stop - start) * step < 1) == True: + raise IndexError() + + return (start, stop, step) + +class MatrixSlice(MatrixExpr): + """ A MatrixSlice of a Matrix Expression + + Examples + ======== + + >>> from sympy import MatrixSlice, ImmutableMatrix + >>> M = ImmutableMatrix(4, 4, range(16)) + >>> M + Matrix([ + [ 0, 1, 2, 3], + [ 4, 5, 6, 7], + [ 8, 9, 10, 11], + [12, 13, 14, 15]]) + + >>> B = MatrixSlice(M, (0, 2), (2, 4)) + >>> ImmutableMatrix(B) + Matrix([ + [2, 3], + [6, 7]]) + """ + parent = property(lambda self: self.args[0]) + rowslice = property(lambda self: self.args[1]) + colslice = property(lambda self: self.args[2]) + + def __new__(cls, parent, rowslice, colslice): + rowslice = normalize(rowslice, parent.shape[0]) + colslice = normalize(colslice, parent.shape[1]) + if not (len(rowslice) == len(colslice) == 3): + raise IndexError() + if ((0 > rowslice[0]) == True or + (parent.shape[0] < rowslice[1]) == True or + (0 > colslice[0]) == True or + (parent.shape[1] < colslice[1]) == True): + raise IndexError() + if isinstance(parent, MatrixSlice): + return mat_slice_of_slice(parent, rowslice, colslice) + return Basic.__new__(cls, parent, Tuple(*rowslice), Tuple(*colslice)) + + @property + def shape(self): + rows = self.rowslice[1] - self.rowslice[0] + rows = rows if self.rowslice[2] == 1 else floor(rows/self.rowslice[2]) + cols = self.colslice[1] - self.colslice[0] + cols = cols if self.colslice[2] == 1 else floor(cols/self.colslice[2]) + return rows, cols + + def _entry(self, i, j, **kwargs): + return self.parent._entry(i*self.rowslice[2] + self.rowslice[0], + j*self.colslice[2] + self.colslice[0], + **kwargs) + + @property + def on_diag(self): + return self.rowslice == self.colslice + + +def slice_of_slice(s, t): + start1, stop1, step1 = s + start2, stop2, step2 = t + + start = start1 + start2*step1 + step = step1 * step2 + stop = start1 + step1*stop2 + + if stop > stop1: + raise IndexError() + + return start, stop, step + + +def mat_slice_of_slice(parent, rowslice, colslice): + """ Collapse nested matrix slices + + >>> from sympy import MatrixSymbol + >>> X = MatrixSymbol('X', 10, 10) + >>> X[:, 1:5][5:8, :] + X[5:8, 1:5] + >>> X[1:9:2, 2:6][1:3, 2] + X[3:7:2, 4:5] + """ + row = slice_of_slice(parent.rowslice, rowslice) + col = slice_of_slice(parent.colslice, colslice) + return MatrixSlice(parent.parent, row, col) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/special.py b/lib/python3.11/site-packages/sympy/matrices/expressions/special.py new file mode 100644 index 0000000000000000000000000000000000000000..d1e426f16ada0e4245b644867974b41b6f86b5cc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/special.py @@ -0,0 +1,299 @@ +from sympy.assumptions.ask import ask, Q +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.sympify import _sympify +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.exceptions import NonInvertibleMatrixError +from .matexpr import MatrixExpr + + +class ZeroMatrix(MatrixExpr): + """The Matrix Zero 0 - additive identity + + Examples + ======== + + >>> from sympy import MatrixSymbol, ZeroMatrix + >>> A = MatrixSymbol('A', 3, 5) + >>> Z = ZeroMatrix(3, 5) + >>> A + Z + A + >>> Z*A.T + 0 + """ + is_ZeroMatrix = True + + def __new__(cls, m, n): + m, n = _sympify(m), _sympify(n) + cls._check_dim(m) + cls._check_dim(n) + + return super().__new__(cls, m, n) + + @property + def shape(self): + return (self.args[0], self.args[1]) + + def _eval_power(self, exp): + # exp = -1, 0, 1 are already handled at this stage + if (exp < 0) == True: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible") + return self + + def _eval_transpose(self): + return ZeroMatrix(self.cols, self.rows) + + def _eval_adjoint(self): + return ZeroMatrix(self.cols, self.rows) + + def _eval_trace(self): + return S.Zero + + def _eval_determinant(self): + return S.Zero + + def _eval_inverse(self): + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + def _eval_as_real_imag(self): + return (self, self) + + def _eval_conjugate(self): + return self + + def _entry(self, i, j, **kwargs): + return S.Zero + + +class GenericZeroMatrix(ZeroMatrix): + """ + A zero matrix without a specified shape + + This exists primarily so MatAdd() with no arguments can return something + meaningful. + """ + def __new__(cls): + # super(ZeroMatrix, cls) instead of super(GenericZeroMatrix, cls) + # because ZeroMatrix.__new__ doesn't have the same signature + return super(ZeroMatrix, cls).__new__(cls) + + @property + def rows(self): + raise TypeError("GenericZeroMatrix does not have a specified shape") + + @property + def cols(self): + raise TypeError("GenericZeroMatrix does not have a specified shape") + + @property + def shape(self): + raise TypeError("GenericZeroMatrix does not have a specified shape") + + # Avoid Matrix.__eq__ which might call .shape + def __eq__(self, other): + return isinstance(other, GenericZeroMatrix) + + def __ne__(self, other): + return not (self == other) + + def __hash__(self): + return super().__hash__() + + + +class Identity(MatrixExpr): + """The Matrix Identity I - multiplicative identity + + Examples + ======== + + >>> from sympy import Identity, MatrixSymbol + >>> A = MatrixSymbol('A', 3, 5) + >>> I = Identity(3) + >>> I*A + A + """ + + is_Identity = True + + def __new__(cls, n): + n = _sympify(n) + cls._check_dim(n) + + return super().__new__(cls, n) + + @property + def rows(self): + return self.args[0] + + @property + def cols(self): + return self.args[0] + + @property + def shape(self): + return (self.args[0], self.args[0]) + + @property + def is_square(self): + return True + + def _eval_transpose(self): + return self + + def _eval_trace(self): + return self.rows + + def _eval_inverse(self): + return self + + def _eval_as_real_imag(self): + return (self, ZeroMatrix(*self.shape)) + + def _eval_conjugate(self): + return self + + def _eval_adjoint(self): + return self + + def _entry(self, i, j, **kwargs): + eq = Eq(i, j) + if eq is S.true: + return S.One + elif eq is S.false: + return S.Zero + return KroneckerDelta(i, j, (0, self.cols-1)) + + def _eval_determinant(self): + return S.One + + def _eval_power(self, exp): + return self + + +class GenericIdentity(Identity): + """ + An identity matrix without a specified shape + + This exists primarily so MatMul() with no arguments can return something + meaningful. + """ + def __new__(cls): + # super(Identity, cls) instead of super(GenericIdentity, cls) because + # Identity.__new__ doesn't have the same signature + return super(Identity, cls).__new__(cls) + + @property + def rows(self): + raise TypeError("GenericIdentity does not have a specified shape") + + @property + def cols(self): + raise TypeError("GenericIdentity does not have a specified shape") + + @property + def shape(self): + raise TypeError("GenericIdentity does not have a specified shape") + + @property + def is_square(self): + return True + + # Avoid Matrix.__eq__ which might call .shape + def __eq__(self, other): + return isinstance(other, GenericIdentity) + + def __ne__(self, other): + return not (self == other) + + def __hash__(self): + return super().__hash__() + + +class OneMatrix(MatrixExpr): + """ + Matrix whose all entries are ones. + """ + def __new__(cls, m, n, evaluate=False): + m, n = _sympify(m), _sympify(n) + cls._check_dim(m) + cls._check_dim(n) + + if evaluate: + condition = Eq(m, 1) & Eq(n, 1) + if condition == True: + return Identity(1) + + obj = super().__new__(cls, m, n) + return obj + + @property + def shape(self): + return self._args + + @property + def is_Identity(self): + return self._is_1x1() == True + + def as_explicit(self): + from sympy.matrices.immutable import ImmutableDenseMatrix + return ImmutableDenseMatrix.ones(*self.shape) + + def doit(self, **hints): + args = self.args + if hints.get('deep', True): + args = [a.doit(**hints) for a in args] + return self.func(*args, evaluate=True) + + def _eval_power(self, exp): + # exp = -1, 0, 1 are already handled at this stage + if self._is_1x1() == True: + return Identity(1) + if (exp < 0) == True: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible") + if ask(Q.integer(exp)): + return self.shape[0] ** (exp - 1) * OneMatrix(*self.shape) + return super()._eval_power(exp) + + def _eval_transpose(self): + return OneMatrix(self.cols, self.rows) + + def _eval_adjoint(self): + return OneMatrix(self.cols, self.rows) + + def _eval_trace(self): + return S.One*self.rows + + def _is_1x1(self): + """Returns true if the matrix is known to be 1x1""" + shape = self.shape + return Eq(shape[0], 1) & Eq(shape[1], 1) + + def _eval_determinant(self): + condition = self._is_1x1() + if condition == True: + return S.One + elif condition == False: + return S.Zero + else: + from sympy.matrices.expressions.determinant import Determinant + return Determinant(self) + + def _eval_inverse(self): + condition = self._is_1x1() + if condition == True: + return Identity(1) + elif condition == False: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + else: + from .inverse import Inverse + return Inverse(self) + + def _eval_as_real_imag(self): + return (self, ZeroMatrix(*self.shape)) + + def _eval_conjugate(self): + return self + + def _entry(self, i, j, **kwargs): + return S.One diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/__init__.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_adjoint.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_adjoint.py new file mode 100644 index 0000000000000000000000000000000000000000..7106b5740b1dc7c32f2c6f5ecb9d286b5e1dd222 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_adjoint.py @@ -0,0 +1,34 @@ +from sympy.core import symbols, S +from sympy.functions import adjoint, conjugate, transpose +from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose +from sympy.matrices import eye, Matrix + +n, m, l, k, p = symbols('n m l k p', integer=True) +A = MatrixSymbol('A', n, m) +B = MatrixSymbol('B', m, l) +C = MatrixSymbol('C', n, n) + + +def test_adjoint(): + Sq = MatrixSymbol('Sq', n, n) + + assert Adjoint(A).shape == (m, n) + assert Adjoint(A*B).shape == (l, n) + assert adjoint(Adjoint(A)) == A + assert isinstance(Adjoint(Adjoint(A)), Adjoint) + + assert conjugate(Adjoint(A)) == Transpose(A) + assert transpose(Adjoint(A)) == Adjoint(Transpose(A)) + + assert Adjoint(eye(3)).doit() == eye(3) + + assert Adjoint(S(5)).doit() == S(5) + + assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]]) + + assert adjoint(trace(Sq)) == conjugate(trace(Sq)) + assert trace(adjoint(Sq)) == conjugate(trace(Sq)) + + assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0]) + + assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..d98732e2751e53938d96d7ea56c916e6fee4578e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_applyfunc.py @@ -0,0 +1,118 @@ +from sympy.core.symbol import symbols, Dummy +from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction +from sympy.core.function import Lambda +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.trigonometric import sin +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.matrices.expressions.matmul import MatMul +from sympy.simplify.simplify import simplify + + +X = MatrixSymbol("X", 3, 3) +Y = MatrixSymbol("Y", 3, 3) + +k = symbols("k") +Xk = MatrixSymbol("X", k, k) + +Xd = X.as_explicit() + +x, y, z, t = symbols("x y z t") + + +def test_applyfunc_matrix(): + x = Dummy('x') + double = Lambda(x, x**2) + + expr = ElementwiseApplyFunction(double, Xd) + assert isinstance(expr, ElementwiseApplyFunction) + assert expr.doit() == Xd.applyfunc(lambda x: x**2) + assert expr.shape == (3, 3) + assert expr.func(*expr.args) == expr + assert simplify(expr) == expr + assert expr[0, 0] == double(Xd[0, 0]) + + expr = ElementwiseApplyFunction(double, X) + assert isinstance(expr, ElementwiseApplyFunction) + assert isinstance(expr.doit(), ElementwiseApplyFunction) + assert expr == X.applyfunc(double) + assert expr.func(*expr.args) == expr + + expr = ElementwiseApplyFunction(exp, X*Y) + assert expr.expr == X*Y + assert expr.function.dummy_eq(Lambda(x, exp(x))) + assert expr.dummy_eq((X*Y).applyfunc(exp)) + assert expr.func(*expr.args) == expr + + assert isinstance(X*expr, MatMul) + assert (X*expr).shape == (3, 3) + Z = MatrixSymbol("Z", 2, 3) + assert (Z*expr).shape == (2, 3) + + expr = ElementwiseApplyFunction(exp, Z.T)*ElementwiseApplyFunction(exp, Z) + assert expr.shape == (3, 3) + expr = ElementwiseApplyFunction(exp, Z)*ElementwiseApplyFunction(exp, Z.T) + assert expr.shape == (2, 2) + + M = Matrix([[x, y], [z, t]]) + expr = ElementwiseApplyFunction(sin, M) + assert isinstance(expr, ElementwiseApplyFunction) + assert expr.function.dummy_eq(Lambda(x, sin(x))) + assert expr.expr == M + assert expr.doit() == M.applyfunc(sin) + assert expr.doit() == Matrix([[sin(x), sin(y)], [sin(z), sin(t)]]) + assert expr.func(*expr.args) == expr + + expr = ElementwiseApplyFunction(double, Xk) + assert expr.doit() == expr + assert expr.subs(k, 2).shape == (2, 2) + assert (expr*expr).shape == (k, k) + M = MatrixSymbol("M", k, t) + expr2 = M.T*expr*M + assert isinstance(expr2, MatMul) + assert expr2.args[1] == expr + assert expr2.shape == (t, t) + expr3 = expr*M + assert expr3.shape == (k, t) + + expr1 = ElementwiseApplyFunction(lambda x: x+1, Xk) + expr2 = ElementwiseApplyFunction(lambda x: x, Xk) + assert expr1 != expr2 + + +def test_applyfunc_entry(): + + af = X.applyfunc(sin) + assert af[0, 0] == sin(X[0, 0]) + + af = Xd.applyfunc(sin) + assert af[0, 0] == sin(X[0, 0]) + + +def test_applyfunc_as_explicit(): + + af = X.applyfunc(sin) + assert af.as_explicit() == Matrix([ + [sin(X[0, 0]), sin(X[0, 1]), sin(X[0, 2])], + [sin(X[1, 0]), sin(X[1, 1]), sin(X[1, 2])], + [sin(X[2, 0]), sin(X[2, 1]), sin(X[2, 2])], + ]) + + +def test_applyfunc_transpose(): + + af = Xk.applyfunc(sin) + assert af.T.dummy_eq(Xk.T.applyfunc(sin)) + + +def test_applyfunc_shape_11_matrices(): + M = MatrixSymbol("M", 1, 1) + + double = Lambda(x, x*2) + + expr = M.applyfunc(sin) + assert isinstance(expr, ElementwiseApplyFunction) + + expr = M.applyfunc(double) + assert isinstance(expr, MatMul) + assert expr == 2*M diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..1d4893cd9a4b3e47dd8e84db33031f7f6f3201fd --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_blockmatrix.py @@ -0,0 +1,469 @@ +from sympy.matrices.expressions.trace import Trace +from sympy.testing.pytest import raises, slow +from sympy.matrices.expressions.blockmatrix import ( + block_collapse, bc_matmul, bc_block_plus_ident, BlockDiagMatrix, + BlockMatrix, bc_dist, bc_matadd, bc_transpose, bc_inverse, + blockcut, reblock_2x2, deblock) +from sympy.matrices.expressions import ( + MatrixSymbol, Identity, trace, det, ZeroMatrix, OneMatrix) +from sympy.matrices.expressions.inverse import Inverse +from sympy.matrices.expressions.matpow import MatPow +from sympy.matrices.expressions.transpose import Transpose +from sympy.matrices.exceptions import NonInvertibleMatrixError +from sympy.matrices import ( + Matrix, ImmutableMatrix, ImmutableSparseMatrix, zeros) +from sympy.core import Tuple, Expr, S, Function +from sympy.core.symbol import Symbol, symbols +from sympy.functions import transpose, im, re + +i, j, k, l, m, n, p = symbols('i:n, p', integer=True) +A = MatrixSymbol('A', n, n) +B = MatrixSymbol('B', n, n) +C = MatrixSymbol('C', n, n) +D = MatrixSymbol('D', n, n) +G = MatrixSymbol('G', n, n) +H = MatrixSymbol('H', n, n) +b1 = BlockMatrix([[G, H]]) +b2 = BlockMatrix([[G], [H]]) + +def test_bc_matmul(): + assert bc_matmul(H*b1*b2*G) == BlockMatrix([[(H*G*G + H*H*H)*G]]) + +def test_bc_matadd(): + assert bc_matadd(BlockMatrix([[G, H]]) + BlockMatrix([[H, H]])) == \ + BlockMatrix([[G+H, H+H]]) + +def test_bc_transpose(): + assert bc_transpose(Transpose(BlockMatrix([[A, B], [C, D]]))) == \ + BlockMatrix([[A.T, C.T], [B.T, D.T]]) + +def test_bc_dist_diag(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', m, m) + C = MatrixSymbol('C', l, l) + X = BlockDiagMatrix(A, B, C) + + assert bc_dist(X+X).equals(BlockDiagMatrix(2*A, 2*B, 2*C)) + +def test_block_plus_ident(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', n, m) + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', m, m) + X = BlockMatrix([[A, B], [C, D]]) + Z = MatrixSymbol('Z', n + m, n + m) + assert bc_block_plus_ident(X + Identity(m + n) + Z) == \ + BlockDiagMatrix(Identity(n), Identity(m)) + X + Z + +def test_BlockMatrix(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', n, k) + C = MatrixSymbol('C', l, m) + D = MatrixSymbol('D', l, k) + M = MatrixSymbol('M', m + k, p) + N = MatrixSymbol('N', l + n, k + m) + X = BlockMatrix(Matrix([[A, B], [C, D]])) + + assert X.__class__(*X.args) == X + + # block_collapse does nothing on normal inputs + E = MatrixSymbol('E', n, m) + assert block_collapse(A + 2*E) == A + 2*E + F = MatrixSymbol('F', m, m) + assert block_collapse(E.T*A*F) == E.T*A*F + + assert X.shape == (l + n, k + m) + assert X.blockshape == (2, 2) + assert transpose(X) == BlockMatrix(Matrix([[A.T, C.T], [B.T, D.T]])) + assert transpose(X).shape == X.shape[::-1] + + # Test that BlockMatrices and MatrixSymbols can still mix + assert (X*M).is_MatMul + assert X._blockmul(M).is_MatMul + assert (X*M).shape == (n + l, p) + assert (X + N).is_MatAdd + assert X._blockadd(N).is_MatAdd + assert (X + N).shape == X.shape + + E = MatrixSymbol('E', m, 1) + F = MatrixSymbol('F', k, 1) + + Y = BlockMatrix(Matrix([[E], [F]])) + + assert (X*Y).shape == (l + n, 1) + assert block_collapse(X*Y).blocks[0, 0] == A*E + B*F + assert block_collapse(X*Y).blocks[1, 0] == C*E + D*F + + # block_collapse passes down into container objects, transposes, and inverse + assert block_collapse(transpose(X*Y)) == transpose(block_collapse(X*Y)) + assert block_collapse(Tuple(X*Y, 2*X)) == ( + block_collapse(X*Y), block_collapse(2*X)) + + # Make sure that MatrixSymbols will enter 1x1 BlockMatrix if it simplifies + Ab = BlockMatrix([[A]]) + Z = MatrixSymbol('Z', *A.shape) + assert block_collapse(Ab + Z) == A + Z + +def test_block_collapse_explicit_matrices(): + A = Matrix([[1, 2], [3, 4]]) + assert block_collapse(BlockMatrix([[A]])) == A + + A = ImmutableSparseMatrix([[1, 2], [3, 4]]) + assert block_collapse(BlockMatrix([[A]])) == A + +def test_issue_17624(): + a = MatrixSymbol("a", 2, 2) + z = ZeroMatrix(2, 2) + b = BlockMatrix([[a, z], [z, z]]) + assert block_collapse(b * b) == BlockMatrix([[a**2, z], [z, z]]) + assert block_collapse(b * b * b) == BlockMatrix([[a**3, z], [z, z]]) + +def test_issue_18618(): + A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + assert A == Matrix(BlockDiagMatrix(A)) + +def test_BlockMatrix_trace(): + A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD'] + X = BlockMatrix([[A, B], [C, D]]) + assert trace(X) == trace(A) + trace(D) + assert trace(BlockMatrix([ZeroMatrix(n, n)])) == 0 + +def test_BlockMatrix_Determinant(): + A, B, C, D = [MatrixSymbol(s, 3, 3) for s in 'ABCD'] + X = BlockMatrix([[A, B], [C, D]]) + from sympy.assumptions.ask import Q + from sympy.assumptions.assume import assuming + with assuming(Q.invertible(A)): + assert det(X) == det(A) * det(X.schur('A')) + + assert isinstance(det(X), Expr) + assert det(BlockMatrix([A])) == det(A) + assert det(BlockMatrix([ZeroMatrix(n, n)])) == 0 + +def test_squareBlockMatrix(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', n, m) + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', m, m) + X = BlockMatrix([[A, B], [C, D]]) + Y = BlockMatrix([[A]]) + + assert X.is_square + + Q = X + Identity(m + n) + assert (block_collapse(Q) == + BlockMatrix([[A + Identity(n), B], [C, D + Identity(m)]])) + + assert (X + MatrixSymbol('Q', n + m, n + m)).is_MatAdd + assert (X * MatrixSymbol('Q', n + m, n + m)).is_MatMul + + assert block_collapse(Y.I) == A.I + + assert isinstance(X.inverse(), Inverse) + + assert not X.is_Identity + + Z = BlockMatrix([[Identity(n), B], [C, D]]) + assert not Z.is_Identity + + +def test_BlockMatrix_2x2_inverse_symbolic(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', n, k - m) + C = MatrixSymbol('C', k - n, m) + D = MatrixSymbol('D', k - n, k - m) + X = BlockMatrix([[A, B], [C, D]]) + assert X.is_square and X.shape == (k, k) + assert isinstance(block_collapse(X.I), Inverse) # Can't invert when none of the blocks is square + + # test code path where only A is invertible + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', n, m) + C = MatrixSymbol('C', m, n) + D = ZeroMatrix(m, m) + X = BlockMatrix([[A, B], [C, D]]) + assert block_collapse(X.inverse()) == BlockMatrix([ + [A.I + A.I * B * X.schur('A').I * C * A.I, -A.I * B * X.schur('A').I], + [-X.schur('A').I * C * A.I, X.schur('A').I], + ]) + + # test code path where only B is invertible + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', n, n) + C = ZeroMatrix(m, m) + D = MatrixSymbol('D', m, n) + X = BlockMatrix([[A, B], [C, D]]) + assert block_collapse(X.inverse()) == BlockMatrix([ + [-X.schur('B').I * D * B.I, X.schur('B').I], + [B.I + B.I * A * X.schur('B').I * D * B.I, -B.I * A * X.schur('B').I], + ]) + + # test code path where only C is invertible + A = MatrixSymbol('A', n, m) + B = ZeroMatrix(n, n) + C = MatrixSymbol('C', m, m) + D = MatrixSymbol('D', m, n) + X = BlockMatrix([[A, B], [C, D]]) + assert block_collapse(X.inverse()) == BlockMatrix([ + [-C.I * D * X.schur('C').I, C.I + C.I * D * X.schur('C').I * A * C.I], + [X.schur('C').I, -X.schur('C').I * A * C.I], + ]) + + # test code path where only D is invertible + A = ZeroMatrix(n, n) + B = MatrixSymbol('B', n, m) + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', m, m) + X = BlockMatrix([[A, B], [C, D]]) + assert block_collapse(X.inverse()) == BlockMatrix([ + [X.schur('D').I, -X.schur('D').I * B * D.I], + [-D.I * C * X.schur('D').I, D.I + D.I * C * X.schur('D').I * B * D.I], + ]) + + +def test_BlockMatrix_2x2_inverse_numeric(): + """Test 2x2 block matrix inversion numerically for all 4 formulas""" + M = Matrix([[1, 2], [3, 4]]) + # rank deficient matrices that have full rank when two of them combined + D1 = Matrix([[1, 2], [2, 4]]) + D2 = Matrix([[1, 3], [3, 9]]) + D3 = Matrix([[1, 4], [4, 16]]) + assert D1.rank() == D2.rank() == D3.rank() == 1 + assert (D1 + D2).rank() == (D2 + D3).rank() == (D3 + D1).rank() == 2 + + # Only A is invertible + K = BlockMatrix([[M, D1], [D2, D3]]) + assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv() + # Only B is invertible + K = BlockMatrix([[D1, M], [D2, D3]]) + assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv() + # Only C is invertible + K = BlockMatrix([[D1, D2], [M, D3]]) + assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv() + # Only D is invertible + K = BlockMatrix([[D1, D2], [D3, M]]) + assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv() + + +@slow +def test_BlockMatrix_3x3_symbolic(): + # Only test one of these, instead of all permutations, because it's slow + rowblocksizes = (n, m, k) + colblocksizes = (m, k, n) + K = BlockMatrix([ + [MatrixSymbol('M%s%s' % (rows, cols), rows, cols) for cols in colblocksizes] + for rows in rowblocksizes + ]) + collapse = block_collapse(K.I) + assert isinstance(collapse, BlockMatrix) + + +def test_BlockDiagMatrix(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', m, m) + C = MatrixSymbol('C', l, l) + M = MatrixSymbol('M', n + m + l, n + m + l) + + X = BlockDiagMatrix(A, B, C) + Y = BlockDiagMatrix(A, 2*B, 3*C) + + assert X.blocks[1, 1] == B + assert X.shape == (n + m + l, n + m + l) + assert all(X.blocks[i, j].is_ZeroMatrix if i != j else X.blocks[i, j] in [A, B, C] + for i in range(3) for j in range(3)) + assert X.__class__(*X.args) == X + assert X.get_diag_blocks() == (A, B, C) + + assert isinstance(block_collapse(X.I * X), Identity) + + assert bc_matmul(X*X) == BlockDiagMatrix(A*A, B*B, C*C) + assert block_collapse(X*X) == BlockDiagMatrix(A*A, B*B, C*C) + #XXX: should be == ?? + assert block_collapse(X + X).equals(BlockDiagMatrix(2*A, 2*B, 2*C)) + assert block_collapse(X*Y) == BlockDiagMatrix(A*A, 2*B*B, 3*C*C) + assert block_collapse(X + Y) == BlockDiagMatrix(2*A, 3*B, 4*C) + + # Ensure that BlockDiagMatrices can still interact with normal MatrixExprs + assert (X*(2*M)).is_MatMul + assert (X + (2*M)).is_MatAdd + + assert (X._blockmul(M)).is_MatMul + assert (X._blockadd(M)).is_MatAdd + +def test_BlockDiagMatrix_nonsquare(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', k, l) + X = BlockDiagMatrix(A, B) + assert X.shape == (n + k, m + l) + assert X.shape == (n + k, m + l) + assert X.rowblocksizes == [n, k] + assert X.colblocksizes == [m, l] + C = MatrixSymbol('C', n, m) + D = MatrixSymbol('D', k, l) + Y = BlockDiagMatrix(C, D) + assert block_collapse(X + Y) == BlockDiagMatrix(A + C, B + D) + assert block_collapse(X * Y.T) == BlockDiagMatrix(A * C.T, B * D.T) + raises(NonInvertibleMatrixError, lambda: BlockDiagMatrix(A, C.T).inverse()) + +def test_BlockDiagMatrix_determinant(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', m, m) + assert det(BlockDiagMatrix()) == 1 + assert det(BlockDiagMatrix(A)) == det(A) + assert det(BlockDiagMatrix(A, B)) == det(A) * det(B) + + # non-square blocks + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', n, m) + assert det(BlockDiagMatrix(C, D)) == 0 + +def test_BlockDiagMatrix_trace(): + assert trace(BlockDiagMatrix()) == 0 + assert trace(BlockDiagMatrix(ZeroMatrix(n, n))) == 0 + A = MatrixSymbol('A', n, n) + assert trace(BlockDiagMatrix(A)) == trace(A) + B = MatrixSymbol('B', m, m) + assert trace(BlockDiagMatrix(A, B)) == trace(A) + trace(B) + + # non-square blocks + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', n, m) + assert isinstance(trace(BlockDiagMatrix(C, D)), Trace) + +def test_BlockDiagMatrix_transpose(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', k, l) + assert transpose(BlockDiagMatrix()) == BlockDiagMatrix() + assert transpose(BlockDiagMatrix(A)) == BlockDiagMatrix(A.T) + assert transpose(BlockDiagMatrix(A, B)) == BlockDiagMatrix(A.T, B.T) + +def test_issue_2460(): + bdm1 = BlockDiagMatrix(Matrix([i]), Matrix([j])) + bdm2 = BlockDiagMatrix(Matrix([k]), Matrix([l])) + assert block_collapse(bdm1 + bdm2) == BlockDiagMatrix(Matrix([i + k]), Matrix([j + l])) + +def test_blockcut(): + A = MatrixSymbol('A', n, m) + B = blockcut(A, (n/2, n/2), (m/2, m/2)) + assert B == BlockMatrix([[A[:n/2, :m/2], A[:n/2, m/2:]], + [A[n/2:, :m/2], A[n/2:, m/2:]]]) + + M = ImmutableMatrix(4, 4, range(16)) + B = blockcut(M, (2, 2), (2, 2)) + assert M == ImmutableMatrix(B) + + B = blockcut(M, (1, 3), (2, 2)) + assert ImmutableMatrix(B.blocks[0, 1]) == ImmutableMatrix([[2, 3]]) + +def test_reblock_2x2(): + B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), 2, 2) + for j in range(3)] + for i in range(3)]) + assert B.blocks.shape == (3, 3) + + BB = reblock_2x2(B) + assert BB.blocks.shape == (2, 2) + + assert B.shape == BB.shape + assert B.as_explicit() == BB.as_explicit() + +def test_deblock(): + B = BlockMatrix([[MatrixSymbol('A_%d%d'%(i,j), n, n) + for j in range(4)] + for i in range(4)]) + + assert deblock(reblock_2x2(B)) == B + +def test_block_collapse_type(): + bm1 = BlockDiagMatrix(ImmutableMatrix([1]), ImmutableMatrix([2])) + bm2 = BlockDiagMatrix(ImmutableMatrix([3]), ImmutableMatrix([4])) + + assert bm1.T.__class__ == BlockDiagMatrix + assert block_collapse(bm1 - bm2).__class__ == BlockDiagMatrix + assert block_collapse(Inverse(bm1)).__class__ == BlockDiagMatrix + assert block_collapse(Transpose(bm1)).__class__ == BlockDiagMatrix + assert bc_transpose(Transpose(bm1)).__class__ == BlockDiagMatrix + assert bc_inverse(Inverse(bm1)).__class__ == BlockDiagMatrix + +def test_invalid_block_matrix(): + raises(ValueError, lambda: BlockMatrix([ + [Identity(2), Identity(5)], + ])) + raises(ValueError, lambda: BlockMatrix([ + [Identity(n), Identity(m)], + ])) + raises(ValueError, lambda: BlockMatrix([ + [ZeroMatrix(n, n), ZeroMatrix(n, n)], + [ZeroMatrix(n, n - 1), ZeroMatrix(n, n + 1)], + ])) + raises(ValueError, lambda: BlockMatrix([ + [ZeroMatrix(n - 1, n), ZeroMatrix(n, n)], + [ZeroMatrix(n + 1, n), ZeroMatrix(n, n)], + ])) + +def test_block_lu_decomposition(): + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', n, m) + C = MatrixSymbol('C', m, n) + D = MatrixSymbol('D', m, m) + X = BlockMatrix([[A, B], [C, D]]) + + #LDU decomposition + L, D, U = X.LDUdecomposition() + assert block_collapse(L*D*U) == X + + #UDL decomposition + U, D, L = X.UDLdecomposition() + assert block_collapse(U*D*L) == X + + #LU decomposition + L, U = X.LUdecomposition() + assert block_collapse(L*U) == X + +def test_issue_21866(): + n = 10 + I = Identity(n) + O = ZeroMatrix(n, n) + A = BlockMatrix([[ I, O, O, O ], + [ O, I, O, O ], + [ O, O, I, O ], + [ I, O, O, I ]]) + Ainv = block_collapse(A.inv()) + AinvT = BlockMatrix([[ I, O, O, O ], + [ O, I, O, O ], + [ O, O, I, O ], + [ -I, O, O, I ]]) + assert Ainv == AinvT + + +def test_adjoint_and_special_matrices(): + A = Identity(3) + B = OneMatrix(3, 2) + C = ZeroMatrix(2, 3) + D = Identity(2) + X = BlockMatrix([[A, B], [C, D]]) + X2 = BlockMatrix([[A, S.ImaginaryUnit*B], [C, D]]) + assert X.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [OneMatrix(2, 3), D]]) + assert re(X) == X + assert X2.adjoint() == BlockMatrix([[A, ZeroMatrix(3, 2)], [-S.ImaginaryUnit*OneMatrix(2, 3), D]]) + assert im(X2) == BlockMatrix([[ZeroMatrix(3, 3), OneMatrix(3, 2)], [ZeroMatrix(2, 3), ZeroMatrix(2, 2)]]) + + +def test_block_matrix_derivative(): + x = symbols('x') + A = Matrix(3, 3, [Function(f'a{i}')(x) for i in range(9)]) + bc = BlockMatrix([[A[:2, :2], A[:2, 2]], [A[2, :2], A[2:, 2]]]) + assert Matrix(bc.diff(x)) - A.diff(x) == zeros(3, 3) + + +def test_transpose_inverse_commute(): + n = Symbol('n') + I = Identity(n) + Z = ZeroMatrix(n, n) + A = BlockMatrix([[I, Z], [Z, I]]) + + assert block_collapse(A.transpose().inverse()) == A + assert block_collapse(A.inverse().transpose()) == A + + assert block_collapse(MatPow(A.transpose(), -2)) == MatPow(A, -2) + assert block_collapse(MatPow(A, -2).transpose()) == MatPow(A, -2) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_companion.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_companion.py new file mode 100644 index 0000000000000000000000000000000000000000..edc592c29098eddce0c6352806aa73d5d889e999 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_companion.py @@ -0,0 +1,48 @@ +from sympy.core.expr import unchanged +from sympy.core.symbol import Symbol, symbols +from sympy.matrices.immutable import ImmutableDenseMatrix +from sympy.matrices.expressions.companion import CompanionMatrix +from sympy.polys.polytools import Poly +from sympy.testing.pytest import raises + + +def test_creation(): + x = Symbol('x') + y = Symbol('y') + raises(ValueError, lambda: CompanionMatrix(1)) + raises(ValueError, lambda: CompanionMatrix(Poly([1], x))) + raises(ValueError, lambda: CompanionMatrix(Poly([2, 1], x))) + raises(ValueError, lambda: CompanionMatrix(Poly(x*y, [x, y]))) + assert unchanged(CompanionMatrix, Poly([1, 2, 3], x)) + + +def test_shape(): + c0, c1, c2 = symbols('c0:3') + x = Symbol('x') + assert CompanionMatrix(Poly([1, c0], x)).shape == (1, 1) + assert CompanionMatrix(Poly([1, c1, c0], x)).shape == (2, 2) + assert CompanionMatrix(Poly([1, c2, c1, c0], x)).shape == (3, 3) + + +def test_entry(): + c0, c1, c2 = symbols('c0:3') + x = Symbol('x') + A = CompanionMatrix(Poly([1, c2, c1, c0], x)) + assert A[0, 0] == 0 + assert A[1, 0] == 1 + assert A[1, 1] == 0 + assert A[2, 1] == 1 + assert A[0, 2] == -c0 + assert A[1, 2] == -c1 + assert A[2, 2] == -c2 + + +def test_as_explicit(): + c0, c1, c2 = symbols('c0:3') + x = Symbol('x') + assert CompanionMatrix(Poly([1, c0], x)).as_explicit() == \ + ImmutableDenseMatrix([-c0]) + assert CompanionMatrix(Poly([1, c1, c0], x)).as_explicit() == \ + ImmutableDenseMatrix([[0, -c0], [1, -c1]]) + assert CompanionMatrix(Poly([1, c2, c1, c0], x)).as_explicit() == \ + ImmutableDenseMatrix([[0, 0, -c0], [1, 0, -c1], [0, 1, -c2]]) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_derivatives.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_derivatives.py new file mode 100644 index 0000000000000000000000000000000000000000..77484c994dda62eea9771a76afd8b3caeadacb93 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_derivatives.py @@ -0,0 +1,477 @@ +""" +Some examples have been taken from: + +http://www.math.uwaterloo.ca/~hwolkowi//matrixcookbook.pdf +""" +from sympy import KroneckerProduct +from sympy.combinatorics import Permutation +from sympy.concrete.summations import Sum +from sympy.core.numbers import Rational +from sympy.core.singleton import S +from sympy.core.symbol import symbols +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.trigonometric import (cos, sin, tan) +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.expressions.determinant import Determinant +from sympy.matrices.expressions.diagonal import DiagMatrix +from sympy.matrices.expressions.hadamard import (HadamardPower, HadamardProduct, hadamard_product) +from sympy.matrices.expressions.inverse import Inverse +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.matrices.expressions.special import OneMatrix +from sympy.matrices.expressions.trace import Trace +from sympy.matrices.expressions.matadd import MatAdd +from sympy.matrices.expressions.matmul import MatMul +from sympy.matrices.expressions.special import (Identity, ZeroMatrix) +from sympy.tensor.array.array_derivatives import ArrayDerivative +from sympy.matrices.expressions import hadamard_power +from sympy.tensor.array.expressions.array_expressions import ArrayAdd, ArrayTensorProduct, PermuteDims + +i, j, k = symbols("i j k") +m, n = symbols("m n") + +X = MatrixSymbol("X", k, k) +x = MatrixSymbol("x", k, 1) +y = MatrixSymbol("y", k, 1) + +A = MatrixSymbol("A", k, k) +B = MatrixSymbol("B", k, k) +C = MatrixSymbol("C", k, k) +D = MatrixSymbol("D", k, k) + +a = MatrixSymbol("a", k, 1) +b = MatrixSymbol("b", k, 1) +c = MatrixSymbol("c", k, 1) +d = MatrixSymbol("d", k, 1) + + +KDelta = lambda i, j: KroneckerDelta(i, j, (0, k-1)) + + +def _check_derivative_with_explicit_matrix(expr, x, diffexpr, dim=2): + # TODO: this is commented because it slows down the tests. + return + + expr = expr.xreplace({k: dim}) + x = x.xreplace({k: dim}) + diffexpr = diffexpr.xreplace({k: dim}) + + expr = expr.as_explicit() + x = x.as_explicit() + diffexpr = diffexpr.as_explicit() + + assert expr.diff(x).reshape(*diffexpr.shape).tomatrix() == diffexpr + + +def test_matrix_derivative_by_scalar(): + assert A.diff(i) == ZeroMatrix(k, k) + assert (A*(X + B)*c).diff(i) == ZeroMatrix(k, 1) + assert x.diff(i) == ZeroMatrix(k, 1) + assert (x.T*y).diff(i) == ZeroMatrix(1, 1) + assert (x*x.T).diff(i) == ZeroMatrix(k, k) + assert (x + y).diff(i) == ZeroMatrix(k, 1) + assert hadamard_power(x, 2).diff(i) == ZeroMatrix(k, 1) + assert hadamard_power(x, i).diff(i).dummy_eq( + HadamardProduct(x.applyfunc(log), HadamardPower(x, i))) + assert hadamard_product(x, y).diff(i) == ZeroMatrix(k, 1) + assert hadamard_product(i*OneMatrix(k, 1), x, y).diff(i) == hadamard_product(x, y) + assert (i*x).diff(i) == x + assert (sin(i)*A*B*x).diff(i) == cos(i)*A*B*x + assert x.applyfunc(sin).diff(i) == ZeroMatrix(k, 1) + assert Trace(i**2*X).diff(i) == 2*i*Trace(X) + + mu = symbols("mu") + expr = (2*mu*x) + assert expr.diff(x) == 2*mu*Identity(k) + + +def test_one_matrix(): + assert MatMul(x.T, OneMatrix(k, 1)).diff(x) == OneMatrix(k, 1) + + +def test_matrix_derivative_non_matrix_result(): + # This is a 4-dimensional array: + I = Identity(k) + AdA = PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2)) + assert A.diff(A) == AdA + assert A.T.diff(A) == PermuteDims(ArrayTensorProduct(I, I), Permutation(3)(1, 2, 3)) + assert (2*A).diff(A) == PermuteDims(ArrayTensorProduct(2*I, I), Permutation(3)(1, 2)) + assert MatAdd(A, A).diff(A) == ArrayAdd(AdA, AdA) + assert (A + B).diff(A) == AdA + + +def test_matrix_derivative_trivial_cases(): + # Cookbook example 33: + # TODO: find a way to represent a four-dimensional zero-array: + assert X.diff(A) == ArrayDerivative(X, A) + + +def test_matrix_derivative_with_inverse(): + + # Cookbook example 61: + expr = a.T*Inverse(X)*b + assert expr.diff(X) == -Inverse(X).T*a*b.T*Inverse(X).T + + # Cookbook example 62: + expr = Determinant(Inverse(X)) + # Not implemented yet: + # assert expr.diff(X) == -Determinant(X.inv())*(X.inv()).T + + # Cookbook example 63: + expr = Trace(A*Inverse(X)*B) + assert expr.diff(X) == -(X**(-1)*B*A*X**(-1)).T + + # Cookbook example 64: + expr = Trace(Inverse(X + A)) + assert expr.diff(X) == -(Inverse(X + A)).T**2 + + +def test_matrix_derivative_vectors_and_scalars(): + + assert x.diff(x) == Identity(k) + assert x[i, 0].diff(x[m, 0]).doit() == KDelta(m, i) + + assert x.T.diff(x) == Identity(k) + + # Cookbook example 69: + expr = x.T*a + assert expr.diff(x) == a + assert expr[0, 0].diff(x[m, 0]).doit() == a[m, 0] + expr = a.T*x + assert expr.diff(x) == a + + # Cookbook example 70: + expr = a.T*X*b + assert expr.diff(X) == a*b.T + + # Cookbook example 71: + expr = a.T*X.T*b + assert expr.diff(X) == b*a.T + + # Cookbook example 72: + expr = a.T*X*a + assert expr.diff(X) == a*a.T + expr = a.T*X.T*a + assert expr.diff(X) == a*a.T + + # Cookbook example 77: + expr = b.T*X.T*X*c + assert expr.diff(X) == X*b*c.T + X*c*b.T + + # Cookbook example 78: + expr = (B*x + b).T*C*(D*x + d) + assert expr.diff(x) == B.T*C*(D*x + d) + D.T*C.T*(B*x + b) + + # Cookbook example 81: + expr = x.T*B*x + assert expr.diff(x) == B*x + B.T*x + + # Cookbook example 82: + expr = b.T*X.T*D*X*c + assert expr.diff(X) == D.T*X*b*c.T + D*X*c*b.T + + # Cookbook example 83: + expr = (X*b + c).T*D*(X*b + c) + assert expr.diff(X) == D*(X*b + c)*b.T + D.T*(X*b + c)*b.T + assert str(expr[0, 0].diff(X[m, n]).doit()) == \ + 'b[n, 0]*Sum((c[_i_1, 0] + Sum(X[_i_1, _i_3]*b[_i_3, 0], (_i_3, 0, k - 1)))*D[_i_1, m], (_i_1, 0, k - 1)) + Sum((c[_i_2, 0] + Sum(X[_i_2, _i_4]*b[_i_4, 0], (_i_4, 0, k - 1)))*D[m, _i_2]*b[n, 0], (_i_2, 0, k - 1))' + + # See https://github.com/sympy/sympy/issues/16504#issuecomment-1018339957 + expr = x*x.T*x + I = Identity(k) + assert expr.diff(x) == KroneckerProduct(I, x.T*x) + 2*x*x.T + + +def test_matrix_derivatives_of_traces(): + + expr = Trace(A)*A + I = Identity(k) + assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2))) + assert expr[i, j].diff(A[m, n]).doit() == ( + KDelta(i, m)*KDelta(j, n)*Trace(A) + + KDelta(m, n)*A[i, j] + ) + + ## First order: + + # Cookbook example 99: + expr = Trace(X) + assert expr.diff(X) == Identity(k) + assert expr.rewrite(Sum).diff(X[m, n]).doit() == KDelta(m, n) + + # Cookbook example 100: + expr = Trace(X*A) + assert expr.diff(X) == A.T + assert expr.rewrite(Sum).diff(X[m, n]).doit() == A[n, m] + + # Cookbook example 101: + expr = Trace(A*X*B) + assert expr.diff(X) == A.T*B.T + assert expr.rewrite(Sum).diff(X[m, n]).doit().dummy_eq((A.T*B.T)[m, n]) + + # Cookbook example 102: + expr = Trace(A*X.T*B) + assert expr.diff(X) == B*A + + # Cookbook example 103: + expr = Trace(X.T*A) + assert expr.diff(X) == A + + # Cookbook example 104: + expr = Trace(A*X.T) + assert expr.diff(X) == A + + # Cookbook example 105: + # TODO: TensorProduct is not supported + #expr = Trace(TensorProduct(A, X)) + #assert expr.diff(X) == Trace(A)*Identity(k) + + ## Second order: + + # Cookbook example 106: + expr = Trace(X**2) + assert expr.diff(X) == 2*X.T + + # Cookbook example 107: + expr = Trace(X**2*B) + assert expr.diff(X) == (X*B + B*X).T + expr = Trace(MatMul(X, X, B)) + assert expr.diff(X) == (X*B + B*X).T + + # Cookbook example 108: + expr = Trace(X.T*B*X) + assert expr.diff(X) == B*X + B.T*X + + # Cookbook example 109: + expr = Trace(B*X*X.T) + assert expr.diff(X) == B*X + B.T*X + + # Cookbook example 110: + expr = Trace(X*X.T*B) + assert expr.diff(X) == B*X + B.T*X + + # Cookbook example 111: + expr = Trace(X*B*X.T) + assert expr.diff(X) == X*B.T + X*B + + # Cookbook example 112: + expr = Trace(B*X.T*X) + assert expr.diff(X) == X*B.T + X*B + + # Cookbook example 113: + expr = Trace(X.T*X*B) + assert expr.diff(X) == X*B.T + X*B + + # Cookbook example 114: + expr = Trace(A*X*B*X) + assert expr.diff(X) == A.T*X.T*B.T + B.T*X.T*A.T + + # Cookbook example 115: + expr = Trace(X.T*X) + assert expr.diff(X) == 2*X + expr = Trace(X*X.T) + assert expr.diff(X) == 2*X + + # Cookbook example 116: + expr = Trace(B.T*X.T*C*X*B) + assert expr.diff(X) == C.T*X*B*B.T + C*X*B*B.T + + # Cookbook example 117: + expr = Trace(X.T*B*X*C) + assert expr.diff(X) == B*X*C + B.T*X*C.T + + # Cookbook example 118: + expr = Trace(A*X*B*X.T*C) + assert expr.diff(X) == A.T*C.T*X*B.T + C*A*X*B + + # Cookbook example 119: + expr = Trace((A*X*B + C)*(A*X*B + C).T) + assert expr.diff(X) == 2*A.T*(A*X*B + C)*B.T + + # Cookbook example 120: + # TODO: no support for TensorProduct. + # expr = Trace(TensorProduct(X, X)) + # expr = Trace(X)*Trace(X) + # expr.diff(X) == 2*Trace(X)*Identity(k) + + # Higher Order + + # Cookbook example 121: + expr = Trace(X**k) + #assert expr.diff(X) == k*(X**(k-1)).T + + # Cookbook example 122: + expr = Trace(A*X**k) + #assert expr.diff(X) == # Needs indices + + # Cookbook example 123: + expr = Trace(B.T*X.T*C*X*X.T*C*X*B) + assert expr.diff(X) == C*X*X.T*C*X*B*B.T + C.T*X*B*B.T*X.T*C.T*X + C*X*B*B.T*X.T*C*X + C.T*X*X.T*C.T*X*B*B.T + + # Other + + # Cookbook example 124: + expr = Trace(A*X**(-1)*B) + assert expr.diff(X) == -Inverse(X).T*A.T*B.T*Inverse(X).T + + # Cookbook example 125: + expr = Trace(Inverse(X.T*C*X)*A) + # Warning: result in the cookbook is equivalent if B and C are symmetric: + assert expr.diff(X) == - X.inv().T*A.T*X.inv()*C.inv().T*X.inv().T - X.inv().T*A*X.inv()*C.inv()*X.inv().T + + # Cookbook example 126: + expr = Trace((X.T*C*X).inv()*(X.T*B*X)) + assert expr.diff(X) == -2*C*X*(X.T*C*X).inv()*X.T*B*X*(X.T*C*X).inv() + 2*B*X*(X.T*C*X).inv() + + # Cookbook example 127: + expr = Trace((A + X.T*C*X).inv()*(X.T*B*X)) + # Warning: result in the cookbook is equivalent if B and C are symmetric: + assert expr.diff(X) == B*X*Inverse(A + X.T*C*X) - C*X*Inverse(A + X.T*C*X)*X.T*B*X*Inverse(A + X.T*C*X) - C.T*X*Inverse(A.T + (C*X).T*X)*X.T*B.T*X*Inverse(A.T + (C*X).T*X) + B.T*X*Inverse(A.T + (C*X).T*X) + + +def test_derivatives_of_complicated_matrix_expr(): + expr = a.T*(A*X*(X.T*B + X*A) + B.T*X.T*(a*b.T*(X*D*X.T + X*(X.T*B + A*X)*D*B - X.T*C.T*A)*B + B*(X*D.T + B*A*X*A.T - 3*X*D))*B + 42*X*B*X.T*A.T*(X + X.T))*b + result = (B*(B*A*X*A.T - 3*X*D + X*D.T) + a*b.T*(X*(A*X + X.T*B)*D*B + X*D*X.T - X.T*C.T*A)*B)*B*b*a.T*B.T + B**2*b*a.T*B.T*X.T*a*b.T*X*D + 42*A*X*B.T*X.T*a*b.T + B*D*B**3*b*a.T*B.T*X.T*a*b.T*X + B*b*a.T*A*X + a*b.T*(42*X + 42*X.T)*A*X*B.T + b*a.T*X*B*a*b.T*B.T**2*X*D.T + b*a.T*X*B*a*b.T*B.T**3*D.T*(B.T*X + X.T*A.T) + 42*b*a.T*X*B*X.T*A.T + A.T*(42*X + 42*X.T)*b*a.T*X*B + A.T*B.T**2*X*B*a*b.T*B.T*A + A.T*a*b.T*(A.T*X.T + B.T*X) + A.T*X.T*b*a.T*X*B*a*b.T*B.T**3*D.T + B.T*X*B*a*b.T*B.T*D - 3*B.T*X*B*a*b.T*B.T*D.T - C.T*A*B**2*b*a.T*B.T*X.T*a*b.T + X.T*A.T*a*b.T*A.T + assert expr.diff(X) == result + + +def test_mixed_deriv_mixed_expressions(): + + expr = 3*Trace(A) + assert expr.diff(A) == 3*Identity(k) + + expr = k + deriv = expr.diff(A) + assert isinstance(deriv, ZeroMatrix) + assert deriv == ZeroMatrix(k, k) + + expr = Trace(A)**2 + assert expr.diff(A) == (2*Trace(A))*Identity(k) + + expr = Trace(A)*A + I = Identity(k) + assert expr.diff(A) == ArrayAdd(ArrayTensorProduct(I, A), PermuteDims(ArrayTensorProduct(Trace(A)*I, I), Permutation(3)(1, 2))) + + expr = Trace(Trace(A)*A) + assert expr.diff(A) == (2*Trace(A))*Identity(k) + + expr = Trace(Trace(Trace(A)*A)*A) + assert expr.diff(A) == (3*Trace(A)**2)*Identity(k) + + +def test_derivatives_matrix_norms(): + + expr = x.T*y + assert expr.diff(x) == y + assert expr[0, 0].diff(x[m, 0]).doit() == y[m, 0] + + expr = (x.T*y)**S.Half + assert expr.diff(x) == y/(2*sqrt(x.T*y)) + + expr = (x.T*x)**S.Half + assert expr.diff(x) == x*(x.T*x)**Rational(-1, 2) + + expr = (c.T*a*x.T*b)**S.Half + assert expr.diff(x) == b*a.T*c/sqrt(c.T*a*x.T*b)/2 + + expr = (c.T*a*x.T*b)**Rational(1, 3) + assert expr.diff(x) == b*a.T*c*(c.T*a*x.T*b)**Rational(-2, 3)/3 + + expr = (a.T*X*b)**S.Half + assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T + + expr = d.T*x*(a.T*X*b)**S.Half*y.T*c + assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*x.T*d*y.T*c*b.T + + +def test_derivatives_elementwise_applyfunc(): + + expr = x.applyfunc(tan) + assert expr.diff(x).dummy_eq( + DiagMatrix(x.applyfunc(lambda x: tan(x)**2 + 1))) + assert expr[i, 0].diff(x[m, 0]).doit() == (tan(x[i, 0])**2 + 1)*KDelta(i, m) + _check_derivative_with_explicit_matrix(expr, x, expr.diff(x)) + + expr = (i**2*x).applyfunc(sin) + assert expr.diff(i).dummy_eq( + HadamardProduct((2*i)*x, (i**2*x).applyfunc(cos))) + assert expr[i, 0].diff(i).doit() == 2*i*x[i, 0]*cos(i**2*x[i, 0]) + _check_derivative_with_explicit_matrix(expr, i, expr.diff(i)) + + expr = (log(i)*A*B).applyfunc(sin) + assert expr.diff(i).dummy_eq( + HadamardProduct(A*B/i, (log(i)*A*B).applyfunc(cos))) + _check_derivative_with_explicit_matrix(expr, i, expr.diff(i)) + + expr = A*x.applyfunc(exp) + # TODO: restore this result (currently returning the transpose): + # assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(exp))*A.T) + _check_derivative_with_explicit_matrix(expr, x, expr.diff(x)) + + expr = x.T*A*x + k*y.applyfunc(sin).T*x + assert expr.diff(x).dummy_eq(A.T*x + A*x + k*y.applyfunc(sin)) + _check_derivative_with_explicit_matrix(expr, x, expr.diff(x)) + + expr = x.applyfunc(sin).T*y + # TODO: restore (currently returning the transpose): + # assert expr.diff(x).dummy_eq(DiagMatrix(x.applyfunc(cos))*y) + _check_derivative_with_explicit_matrix(expr, x, expr.diff(x)) + + expr = (a.T * X * b).applyfunc(sin) + assert expr.diff(X).dummy_eq(a*(a.T*X*b).applyfunc(cos)*b.T) + _check_derivative_with_explicit_matrix(expr, X, expr.diff(X)) + + expr = a.T * X.applyfunc(sin) * b + assert expr.diff(X).dummy_eq( + DiagMatrix(a)*X.applyfunc(cos)*DiagMatrix(b)) + _check_derivative_with_explicit_matrix(expr, X, expr.diff(X)) + + expr = a.T * (A*X*B).applyfunc(sin) * b + assert expr.diff(X).dummy_eq( + A.T*DiagMatrix(a)*(A*X*B).applyfunc(cos)*DiagMatrix(b)*B.T) + _check_derivative_with_explicit_matrix(expr, X, expr.diff(X)) + + expr = a.T * (A*X*b).applyfunc(sin) * b.T + # TODO: not implemented + #assert expr.diff(X) == ... + #_check_derivative_with_explicit_matrix(expr, X, expr.diff(X)) + + expr = a.T*A*X.applyfunc(sin)*B*b + assert expr.diff(X).dummy_eq( + HadamardProduct(A.T * a * b.T * B.T, X.applyfunc(cos))) + + expr = a.T * (A*X.applyfunc(sin)*B).applyfunc(log) * b + # TODO: wrong + # assert expr.diff(X) == A.T*DiagMatrix(a)*(A*X.applyfunc(sin)*B).applyfunc(Lambda(k, 1/k))*DiagMatrix(b)*B.T + + expr = a.T * (X.applyfunc(sin)).applyfunc(log) * b + # TODO: wrong + # assert expr.diff(X) == DiagMatrix(a)*X.applyfunc(sin).applyfunc(Lambda(k, 1/k))*DiagMatrix(b) + + +def test_derivatives_of_hadamard_expressions(): + + # Hadamard Product + + expr = hadamard_product(a, x, b) + assert expr.diff(x) == DiagMatrix(hadamard_product(b, a)) + + expr = a.T*hadamard_product(A, X, B)*b + assert expr.diff(X) == HadamardProduct(a*b.T, A, B) + + # Hadamard Power + + expr = hadamard_power(x, 2) + assert expr.diff(x).doit() == 2*DiagMatrix(x) + + expr = hadamard_power(x.T, 2) + assert expr.diff(x).doit() == 2*DiagMatrix(x) + + expr = hadamard_power(x, S.Half) + assert expr.diff(x) == S.Half*DiagMatrix(hadamard_power(x, Rational(-1, 2))) + + expr = hadamard_power(a.T*X*b, 2) + assert expr.diff(X) == 2*a*a.T*X*b*b.T + + expr = hadamard_power(a.T*X*b, S.Half) + assert expr.diff(X) == a/(2*sqrt(a.T*X*b))*b.T diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_determinant.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_determinant.py new file mode 100644 index 0000000000000000000000000000000000000000..d1a66c728f076f8c769d2519ee47c8a9cc90a90e --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_determinant.py @@ -0,0 +1,65 @@ +from sympy.core import S, symbols +from sympy.matrices import eye, ones, Matrix, ShapeError +from sympy.matrices.expressions import ( + Identity, MatrixExpr, MatrixSymbol, Determinant, + det, per, ZeroMatrix, Transpose, + Permanent, MatMul +) +from sympy.matrices.expressions.special import OneMatrix +from sympy.testing.pytest import raises +from sympy.assumptions.ask import Q +from sympy.assumptions.refine import refine + +n = symbols('n', integer=True) +A = MatrixSymbol('A', n, n) +B = MatrixSymbol('B', n, n) +C = MatrixSymbol('C', 3, 4) + + +def test_det(): + assert isinstance(Determinant(A), Determinant) + assert not isinstance(Determinant(A), MatrixExpr) + raises(ShapeError, lambda: Determinant(C)) + assert det(eye(3)) == 1 + assert det(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 17 + _ = A / det(A) # Make sure this is possible + + raises(TypeError, lambda: Determinant(S.One)) + + assert Determinant(A).arg is A + + +def test_eval_determinant(): + assert det(Identity(n)) == 1 + assert det(ZeroMatrix(n, n)) == 0 + assert det(OneMatrix(n, n)) == Determinant(OneMatrix(n, n)) + assert det(OneMatrix(1, 1)) == 1 + assert det(OneMatrix(2, 2)) == 0 + assert det(Transpose(A)) == det(A) + assert Determinant(MatMul(eye(2), eye(2))).doit(deep=True) == 1 + + +def test_refine(): + assert refine(det(A), Q.orthogonal(A)) == 1 + assert refine(det(A), Q.singular(A)) == 0 + assert refine(det(A), Q.unit_triangular(A)) == 1 + assert refine(det(A), Q.normal(A)) == det(A) + + +def test_commutative(): + det_a = Determinant(A) + det_b = Determinant(B) + assert det_a.is_commutative + assert det_b.is_commutative + assert det_a * det_b == det_b * det_a + + +def test_permanent(): + assert isinstance(Permanent(A), Permanent) + assert not isinstance(Permanent(A), MatrixExpr) + assert isinstance(Permanent(C), Permanent) + assert Permanent(ones(3, 3)).doit() == 6 + _ = C / per(C) + assert per(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 103 + raises(TypeError, lambda: Permanent(S.One)) + assert Permanent(A).arg is A diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_diagonal.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_diagonal.py new file mode 100644 index 0000000000000000000000000000000000000000..3e4f7ea4c178121c33eeb26c09675403d274c1e8 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_diagonal.py @@ -0,0 +1,156 @@ +from sympy.matrices.expressions import MatrixSymbol +from sympy.matrices.expressions.diagonal import DiagonalMatrix, DiagonalOf, DiagMatrix, diagonalize_vector +from sympy.assumptions.ask import (Q, ask) +from sympy.core.symbol import Symbol +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions.matmul import MatMul +from sympy.matrices.expressions.special import Identity +from sympy.testing.pytest import raises + + +n = Symbol('n') +m = Symbol('m') + + +def test_DiagonalMatrix(): + x = MatrixSymbol('x', n, m) + D = DiagonalMatrix(x) + assert D.diagonal_length is None + assert D.shape == (n, m) + + x = MatrixSymbol('x', n, n) + D = DiagonalMatrix(x) + assert D.diagonal_length == n + assert D.shape == (n, n) + assert D[1, 2] == 0 + assert D[1, 1] == x[1, 1] + i = Symbol('i') + j = Symbol('j') + x = MatrixSymbol('x', 3, 3) + ij = DiagonalMatrix(x)[i, j] + assert ij != 0 + assert ij.subs({i:0, j:0}) == x[0, 0] + assert ij.subs({i:0, j:1}) == 0 + assert ij.subs({i:1, j:1}) == x[1, 1] + assert ask(Q.diagonal(D)) # affirm that D is diagonal + + x = MatrixSymbol('x', n, 3) + D = DiagonalMatrix(x) + assert D.diagonal_length == 3 + assert D.shape == (n, 3) + assert D[2, m] == KroneckerDelta(2, m)*x[2, m] + assert D[3, m] == 0 + raises(IndexError, lambda: D[m, 3]) + + x = MatrixSymbol('x', 3, n) + D = DiagonalMatrix(x) + assert D.diagonal_length == 3 + assert D.shape == (3, n) + assert D[m, 2] == KroneckerDelta(m, 2)*x[m, 2] + assert D[m, 3] == 0 + raises(IndexError, lambda: D[3, m]) + + x = MatrixSymbol('x', n, m) + D = DiagonalMatrix(x) + assert D.diagonal_length is None + assert D.shape == (n, m) + assert D[m, 4] != 0 + + x = MatrixSymbol('x', 3, 4) + assert [DiagonalMatrix(x)[i] for i in range(12)] == [ + x[0, 0], 0, 0, 0, 0, x[1, 1], 0, 0, 0, 0, x[2, 2], 0] + + # shape is retained, issue 12427 + assert ( + DiagonalMatrix(MatrixSymbol('x', 3, 4))* + DiagonalMatrix(MatrixSymbol('x', 4, 2))).shape == (3, 2) + + +def test_DiagonalOf(): + x = MatrixSymbol('x', n, n) + d = DiagonalOf(x) + assert d.shape == (n, 1) + assert d.diagonal_length == n + assert d[2, 0] == d[2] == x[2, 2] + + x = MatrixSymbol('x', n, m) + d = DiagonalOf(x) + assert d.shape == (None, 1) + assert d.diagonal_length is None + assert d[2, 0] == d[2] == x[2, 2] + + d = DiagonalOf(MatrixSymbol('x', 4, 3)) + assert d.shape == (3, 1) + d = DiagonalOf(MatrixSymbol('x', n, 3)) + assert d.shape == (3, 1) + d = DiagonalOf(MatrixSymbol('x', 3, n)) + assert d.shape == (3, 1) + x = MatrixSymbol('x', n, m) + assert [DiagonalOf(x)[i] for i in range(4)] ==[ + x[0, 0], x[1, 1], x[2, 2], x[3, 3]] + + +def test_DiagMatrix(): + x = MatrixSymbol('x', n, 1) + d = DiagMatrix(x) + assert d.shape == (n, n) + assert d[0, 1] == 0 + assert d[0, 0] == x[0, 0] + + a = MatrixSymbol('a', 1, 1) + d = diagonalize_vector(a) + assert isinstance(d, MatrixSymbol) + assert a == d + assert diagonalize_vector(Identity(3)) == Identity(3) + assert DiagMatrix(Identity(3)).doit() == Identity(3) + assert isinstance(DiagMatrix(Identity(3)), DiagMatrix) + + # A diagonal matrix is equal to its transpose: + assert DiagMatrix(x).T == DiagMatrix(x) + assert diagonalize_vector(x.T) == DiagMatrix(x) + + dx = DiagMatrix(x) + assert dx[0, 0] == x[0, 0] + assert dx[1, 1] == x[1, 0] + assert dx[0, 1] == 0 + assert dx[0, m] == x[0, 0]*KroneckerDelta(0, m) + + z = MatrixSymbol('z', 1, n) + dz = DiagMatrix(z) + assert dz[0, 0] == z[0, 0] + assert dz[1, 1] == z[0, 1] + assert dz[0, 1] == 0 + assert dz[0, m] == z[0, m]*KroneckerDelta(0, m) + + v = MatrixSymbol('v', 3, 1) + dv = DiagMatrix(v) + assert dv.as_explicit() == Matrix([ + [v[0, 0], 0, 0], + [0, v[1, 0], 0], + [0, 0, v[2, 0]], + ]) + + v = MatrixSymbol('v', 1, 3) + dv = DiagMatrix(v) + assert dv.as_explicit() == Matrix([ + [v[0, 0], 0, 0], + [0, v[0, 1], 0], + [0, 0, v[0, 2]], + ]) + + dv = DiagMatrix(3*v) + assert dv.args == (3*v,) + assert dv.doit() == 3*DiagMatrix(v) + assert isinstance(dv.doit(), MatMul) + + a = MatrixSymbol("a", 3, 1).as_explicit() + expr = DiagMatrix(a) + result = Matrix([ + [a[0, 0], 0, 0], + [0, a[1, 0], 0], + [0, 0, a[2, 0]], + ]) + assert expr.doit() == result + expr = DiagMatrix(a.T) + assert expr.doit() == result diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py new file mode 100644 index 0000000000000000000000000000000000000000..abf8ab8e935cbd3039f25f83d3603ac444e5a7bb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_dotproduct.py @@ -0,0 +1,35 @@ +from sympy.core.expr import unchanged +from sympy.core.mul import Mul +from sympy.matrices import Matrix +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.matrices.expressions.dotproduct import DotProduct +from sympy.testing.pytest import raises + + +A = Matrix(3, 1, [1, 2, 3]) +B = Matrix(3, 1, [1, 3, 5]) +C = Matrix(4, 1, [1, 2, 4, 5]) +D = Matrix(2, 2, [1, 2, 3, 4]) + +def test_docproduct(): + assert DotProduct(A, B).doit() == 22 + assert DotProduct(A.T, B).doit() == 22 + assert DotProduct(A, B.T).doit() == 22 + assert DotProduct(A.T, B.T).doit() == 22 + + raises(TypeError, lambda: DotProduct(1, A)) + raises(TypeError, lambda: DotProduct(A, 1)) + raises(TypeError, lambda: DotProduct(A, D)) + raises(TypeError, lambda: DotProduct(D, A)) + + raises(TypeError, lambda: DotProduct(B, C).doit()) + +def test_dotproduct_symbolic(): + A = MatrixSymbol('A', 3, 1) + B = MatrixSymbol('B', 3, 1) + + dot = DotProduct(A, B) + assert dot.is_scalar == True + assert unchanged(Mul, 2, dot) + # XXX Fix forced evaluation for arithmetics with matrix expressions + assert dot * A == (A[0, 0]*B[0, 0] + A[1, 0]*B[1, 0] + A[2, 0]*B[2, 0])*A diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_factorizations.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_factorizations.py new file mode 100644 index 0000000000000000000000000000000000000000..a0319acabbb7409dfa5c24ceca39e25ff0240618 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_factorizations.py @@ -0,0 +1,29 @@ +from sympy.matrices.expressions.factorizations import lu, LofCholesky, qr, svd +from sympy.assumptions.ask import (Q, ask) +from sympy.core.symbol import Symbol +from sympy.matrices.expressions.matexpr import MatrixSymbol + +n = Symbol('n') +X = MatrixSymbol('X', n, n) + +def test_LU(): + L, U = lu(X) + assert L.shape == U.shape == X.shape + assert ask(Q.lower_triangular(L)) + assert ask(Q.upper_triangular(U)) + +def test_Cholesky(): + LofCholesky(X) + +def test_QR(): + Q_, R = qr(X) + assert Q_.shape == R.shape == X.shape + assert ask(Q.orthogonal(Q_)) + assert ask(Q.upper_triangular(R)) + +def test_svd(): + U, S, V = svd(X) + assert U.shape == S.shape == V.shape == X.shape + assert ask(Q.orthogonal(U)) + assert ask(Q.orthogonal(V)) + assert ask(Q.diagonal(S)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_fourier.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_fourier.py new file mode 100644 index 0000000000000000000000000000000000000000..0230c8a0957ed28fb0a5cc1e9ee77ecae797265b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_fourier.py @@ -0,0 +1,44 @@ +from sympy.assumptions.ask import (Q, ask) +from sympy.core.numbers import (I, Rational) +from sympy.core.singleton import S +from sympy.functions.elementary.complexes import Abs +from sympy.functions.elementary.exponential import exp +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.simplify.simplify import simplify +from sympy.core.symbol import symbols +from sympy.matrices.expressions.fourier import DFT, IDFT +from sympy.matrices import det, Matrix, Identity +from sympy.testing.pytest import raises + + +def test_dft_creation(): + assert DFT(2) + assert DFT(0) + raises(ValueError, lambda: DFT(-1)) + raises(ValueError, lambda: DFT(2.0)) + raises(ValueError, lambda: DFT(2 + 1j)) + + n = symbols('n') + assert DFT(n) + n = symbols('n', integer=False) + raises(ValueError, lambda: DFT(n)) + n = symbols('n', negative=True) + raises(ValueError, lambda: DFT(n)) + + +def test_dft(): + n, i, j = symbols('n i j') + assert DFT(4).shape == (4, 4) + assert ask(Q.unitary(DFT(4))) + assert Abs(simplify(det(Matrix(DFT(4))))) == 1 + assert DFT(n)*IDFT(n) == Identity(n) + assert DFT(n)[i, j] == exp(-2*S.Pi*I/n)**(i*j) / sqrt(n) + + +def test_dft2(): + assert DFT(1).as_explicit() == Matrix([[1]]) + assert DFT(2).as_explicit() == 1/sqrt(2)*Matrix([[1,1],[1,-1]]) + assert DFT(4).as_explicit() == Matrix([[S.Half, S.Half, S.Half, S.Half], + [S.Half, -I/2, Rational(-1,2), I/2], + [S.Half, Rational(-1,2), S.Half, Rational(-1,2)], + [S.Half, I/2, Rational(-1,2), -I/2]]) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..e4850fe5c739b9390fac6afa10757b5babf821c6 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_funcmatrix.py @@ -0,0 +1,54 @@ +from sympy.core import symbols, Lambda +from sympy.core.sympify import SympifyError +from sympy.functions import KroneckerDelta +from sympy.matrices import Matrix +from sympy.matrices.expressions import FunctionMatrix, MatrixExpr, Identity +from sympy.testing.pytest import raises + + +def test_funcmatrix_creation(): + i, j, k = symbols('i j k') + assert FunctionMatrix(2, 2, Lambda((i, j), 0)) + assert FunctionMatrix(0, 0, Lambda((i, j), 0)) + + raises(ValueError, lambda: FunctionMatrix(-1, 0, Lambda((i, j), 0))) + raises(ValueError, lambda: FunctionMatrix(2.0, 0, Lambda((i, j), 0))) + raises(ValueError, lambda: FunctionMatrix(2j, 0, Lambda((i, j), 0))) + raises(ValueError, lambda: FunctionMatrix(0, -1, Lambda((i, j), 0))) + raises(ValueError, lambda: FunctionMatrix(0, 2.0, Lambda((i, j), 0))) + raises(ValueError, lambda: FunctionMatrix(0, 2j, Lambda((i, j), 0))) + + raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda(i, 0))) + raises(SympifyError, lambda: FunctionMatrix(2, 2, lambda i, j: 0)) + raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i,), 0))) + raises(ValueError, lambda: FunctionMatrix(2, 2, Lambda((i, j, k), 0))) + raises(ValueError, lambda: FunctionMatrix(2, 2, i+j)) + assert FunctionMatrix(2, 2, "lambda i, j: 0") == \ + FunctionMatrix(2, 2, Lambda((i, j), 0)) + + m = FunctionMatrix(2, 2, KroneckerDelta) + assert m.as_explicit() == Identity(2).as_explicit() + assert m.args[2].dummy_eq(Lambda((i, j), KroneckerDelta(i, j))) + + n = symbols('n') + assert FunctionMatrix(n, n, Lambda((i, j), 0)) + n = symbols('n', integer=False) + raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0))) + n = symbols('n', negative=True) + raises(ValueError, lambda: FunctionMatrix(n, n, Lambda((i, j), 0))) + + +def test_funcmatrix(): + i, j = symbols('i,j') + X = FunctionMatrix(3, 3, Lambda((i, j), i - j)) + assert X[1, 1] == 0 + assert X[1, 2] == -1 + assert X.shape == (3, 3) + assert X.rows == X.cols == 3 + assert Matrix(X) == Matrix(3, 3, lambda i, j: i - j) + assert isinstance(X*X + X, MatrixExpr) + + +def test_replace_issue(): + X = FunctionMatrix(3, 3, KroneckerDelta) + assert X.replace(lambda x: True, lambda x: x) == X diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_hadamard.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_hadamard.py new file mode 100644 index 0000000000000000000000000000000000000000..800fa830a9b089103d69b372db93ebcea541d02b --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_hadamard.py @@ -0,0 +1,141 @@ +from sympy.matrices.dense import Matrix, eye +from sympy.matrices.exceptions import ShapeError +from sympy.matrices.expressions.matadd import MatAdd +from sympy.matrices.expressions.special import Identity, OneMatrix, ZeroMatrix +from sympy.core import symbols +from sympy.testing.pytest import raises, warns_deprecated_sympy + +from sympy.matrices import MatrixSymbol +from sympy.matrices.expressions import (HadamardProduct, hadamard_product, HadamardPower, hadamard_power) + +n, m, k = symbols('n,m,k') +Z = MatrixSymbol('Z', n, n) +A = MatrixSymbol('A', n, m) +B = MatrixSymbol('B', n, m) +C = MatrixSymbol('C', m, k) + + +def test_HadamardProduct(): + assert HadamardProduct(A, B, A).shape == A.shape + + raises(TypeError, lambda: HadamardProduct(A, n)) + raises(TypeError, lambda: HadamardProduct(A, 1)) + + assert HadamardProduct(A, 2*B, -A)[1, 1] == \ + -2 * A[1, 1] * B[1, 1] * A[1, 1] + + mix = HadamardProduct(Z*A, B)*C + assert mix.shape == (n, k) + + assert set(HadamardProduct(A, B, A).T.args) == {A.T, A.T, B.T} + + +def test_HadamardProduct_isnt_commutative(): + assert HadamardProduct(A, B) != HadamardProduct(B, A) + + +def test_mixed_indexing(): + X = MatrixSymbol('X', 2, 2) + Y = MatrixSymbol('Y', 2, 2) + Z = MatrixSymbol('Z', 2, 2) + + assert (X*HadamardProduct(Y, Z))[0, 0] == \ + X[0, 0]*Y[0, 0]*Z[0, 0] + X[0, 1]*Y[1, 0]*Z[1, 0] + + +def test_canonicalize(): + X = MatrixSymbol('X', 2, 2) + Y = MatrixSymbol('Y', 2, 2) + with warns_deprecated_sympy(): + expr = HadamardProduct(X, check=False) + assert isinstance(expr, HadamardProduct) + expr2 = expr.doit() # unpack is called + assert isinstance(expr2, MatrixSymbol) + Z = ZeroMatrix(2, 2) + U = OneMatrix(2, 2) + assert HadamardProduct(Z, X).doit() == Z + assert HadamardProduct(U, X, X, U).doit() == HadamardPower(X, 2) + assert HadamardProduct(X, U, Y).doit() == HadamardProduct(X, Y) + assert HadamardProduct(X, Z, U, Y).doit() == Z + + +def test_hadamard(): + m, n, p = symbols('m, n, p', integer=True) + A = MatrixSymbol('A', m, n) + B = MatrixSymbol('B', m, n) + X = MatrixSymbol('X', m, m) + I = Identity(m) + + raises(TypeError, lambda: hadamard_product()) + assert hadamard_product(A) == A + assert isinstance(hadamard_product(A, B), HadamardProduct) + assert hadamard_product(A, B).doit() == hadamard_product(A, B) + assert hadamard_product(X, I) == HadamardProduct(I, X) + assert isinstance(hadamard_product(X, I), HadamardProduct) + + a = MatrixSymbol("a", k, 1) + expr = MatAdd(ZeroMatrix(k, 1), OneMatrix(k, 1)) + expr = HadamardProduct(expr, a) + assert expr.doit() == a + + raises(ValueError, lambda: HadamardProduct()) + + +def test_hadamard_product_with_explicit_mat(): + A = MatrixSymbol("A", 3, 3).as_explicit() + B = MatrixSymbol("B", 3, 3).as_explicit() + X = MatrixSymbol("X", 3, 3) + expr = hadamard_product(A, B) + ret = Matrix([i*j for i, j in zip(A, B)]).reshape(3, 3) + assert expr == ret + expr = hadamard_product(A, X, B) + assert expr == HadamardProduct(ret, X) + expr = hadamard_product(eye(3), A) + assert expr == Matrix([[A[0, 0], 0, 0], [0, A[1, 1], 0], [0, 0, A[2, 2]]]) + expr = hadamard_product(eye(3), eye(3)) + assert expr == eye(3) + + +def test_hadamard_power(): + m, n, p = symbols('m, n, p', integer=True) + A = MatrixSymbol('A', m, n) + + assert hadamard_power(A, 1) == A + assert isinstance(hadamard_power(A, 2), HadamardPower) + assert hadamard_power(A, n).T == hadamard_power(A.T, n) + assert hadamard_power(A, n)[0, 0] == A[0, 0]**n + assert hadamard_power(m, n) == m**n + raises(ValueError, lambda: hadamard_power(A, A)) + + +def test_hadamard_power_explicit(): + A = MatrixSymbol('A', 2, 2) + B = MatrixSymbol('B', 2, 2) + a, b = symbols('a b') + + assert HadamardPower(a, b) == a**b + + assert HadamardPower(a, B).as_explicit() == \ + Matrix([ + [a**B[0, 0], a**B[0, 1]], + [a**B[1, 0], a**B[1, 1]]]) + + assert HadamardPower(A, b).as_explicit() == \ + Matrix([ + [A[0, 0]**b, A[0, 1]**b], + [A[1, 0]**b, A[1, 1]**b]]) + + assert HadamardPower(A, B).as_explicit() == \ + Matrix([ + [A[0, 0]**B[0, 0], A[0, 1]**B[0, 1]], + [A[1, 0]**B[1, 0], A[1, 1]**B[1, 1]]]) + + +def test_shape_error(): + A = MatrixSymbol('A', 2, 3) + B = MatrixSymbol('B', 3, 3) + raises(ShapeError, lambda: HadamardProduct(A, B)) + raises(ShapeError, lambda: HadamardPower(A, B)) + A = MatrixSymbol('A', 3, 2) + raises(ShapeError, lambda: HadamardProduct(A, B)) + raises(ShapeError, lambda: HadamardPower(A, B)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_indexing.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_indexing.py new file mode 100644 index 0000000000000000000000000000000000000000..500761f248eef5f627c2a7344a6817aca0b8a802 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_indexing.py @@ -0,0 +1,299 @@ +from sympy.concrete.summations import Sum +from sympy.core.symbol import symbols, Symbol, Dummy +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.dense import eye +from sympy.matrices.expressions.blockmatrix import BlockMatrix +from sympy.matrices.expressions.hadamard import HadamardPower +from sympy.matrices.expressions.matexpr import (MatrixSymbol, + MatrixExpr, MatrixElement) +from sympy.matrices.expressions.matpow import MatPow +from sympy.matrices.expressions.special import (ZeroMatrix, Identity, + OneMatrix) +from sympy.matrices.expressions.trace import Trace, trace +from sympy.matrices.immutable import ImmutableMatrix +from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct +from sympy.testing.pytest import XFAIL, raises + +k, l, m, n = symbols('k l m n', integer=True) +i, j = symbols('i j', integer=True) + +W = MatrixSymbol('W', k, l) +X = MatrixSymbol('X', l, m) +Y = MatrixSymbol('Y', l, m) +Z = MatrixSymbol('Z', m, n) + +X1 = MatrixSymbol('X1', m, m) +X2 = MatrixSymbol('X2', m, m) +X3 = MatrixSymbol('X3', m, m) +X4 = MatrixSymbol('X4', m, m) + +A = MatrixSymbol('A', 2, 2) +B = MatrixSymbol('B', 2, 2) +x = MatrixSymbol('x', 1, 2) +y = MatrixSymbol('x', 2, 1) + + +def test_symbolic_indexing(): + x12 = X[1, 2] + assert all(s in str(x12) for s in ['1', '2', X.name]) + # We don't care about the exact form of this. We do want to make sure + # that all of these features are present + + +def test_add_index(): + assert (X + Y)[i, j] == X[i, j] + Y[i, j] + + +def test_mul_index(): + assert (A*y)[0, 0] == A[0, 0]*y[0, 0] + A[0, 1]*y[1, 0] + assert (A*B).as_mutable() == (A.as_mutable() * B.as_mutable()) + X = MatrixSymbol('X', n, m) + Y = MatrixSymbol('Y', m, k) + + result = (X*Y)[4,2] + expected = Sum(X[4, i]*Y[i, 2], (i, 0, m - 1)) + assert result.args[0].dummy_eq(expected.args[0], i) + assert result.args[1][1:] == expected.args[1][1:] + + +def test_pow_index(): + Q = MatPow(A, 2) + assert Q[0, 0] == A[0, 0]**2 + A[0, 1]*A[1, 0] + n = symbols("n") + Q2 = A**n + assert Q2[0, 0] == 2*( + -sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] + + 4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2 + )**n * \ + A[0, 1]*A[1, 0]/( + (sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + + A[1, 1]**2) + A[0, 0] - A[1, 1])* + sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2) + ) - 2*( + sqrt((A[0, 0] + A[1, 1])**2 - 4*A[0, 0]*A[1, 1] + + 4*A[0, 1]*A[1, 0])/2 + A[0, 0]/2 + A[1, 1]/2 + )**n * A[0, 1]*A[1, 0]/( + (-sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + + A[1, 1]**2) + A[0, 0] - A[1, 1])* + sqrt(A[0, 0]**2 - 2*A[0, 0]*A[1, 1] + 4*A[0, 1]*A[1, 0] + A[1, 1]**2) + ) + + +def test_transpose_index(): + assert X.T[i, j] == X[j, i] + + +def test_Identity_index(): + I = Identity(3) + assert I[0, 0] == I[1, 1] == I[2, 2] == 1 + assert I[1, 0] == I[0, 1] == I[2, 1] == 0 + assert I[i, 0].delta_range == (0, 2) + raises(IndexError, lambda: I[3, 3]) + + +def test_block_index(): + I = Identity(3) + Z = ZeroMatrix(3, 3) + B = BlockMatrix([[I, I], [I, I]]) + e3 = ImmutableMatrix(eye(3)) + BB = BlockMatrix([[e3, e3], [e3, e3]]) + assert B[0, 0] == B[3, 0] == B[0, 3] == B[3, 3] == 1 + assert B[4, 3] == B[5, 1] == 0 + + BB = BlockMatrix([[e3, e3], [e3, e3]]) + assert B.as_explicit() == BB.as_explicit() + + BI = BlockMatrix([[I, Z], [Z, I]]) + + assert BI.as_explicit().equals(eye(6)) + + +def test_block_index_symbolic(): + # Note that these matrices may be zero-sized and indices may be negative, which causes + # all naive simplifications given in the comments to be invalid + A1 = MatrixSymbol('A1', n, k) + A2 = MatrixSymbol('A2', n, l) + A3 = MatrixSymbol('A3', m, k) + A4 = MatrixSymbol('A4', m, l) + A = BlockMatrix([[A1, A2], [A3, A4]]) + assert A[0, 0] == MatrixElement(A, 0, 0) # Cannot be A1[0, 0] + assert A[n - 1, k - 1] == A1[n - 1, k - 1] + assert A[n, k] == A4[0, 0] + assert A[n + m - 1, 0] == MatrixElement(A, n + m - 1, 0) # Cannot be A3[m - 1, 0] + assert A[0, k + l - 1] == MatrixElement(A, 0, k + l - 1) # Cannot be A2[0, l - 1] + assert A[n + m - 1, k + l - 1] == MatrixElement(A, n + m - 1, k + l - 1) # Cannot be A4[m - 1, l - 1] + assert A[i, j] == MatrixElement(A, i, j) + assert A[n + i, k + j] == MatrixElement(A, n + i, k + j) # Cannot be A4[i, j] + assert A[n - i - 1, k - j - 1] == MatrixElement(A, n - i - 1, k - j - 1) # Cannot be A1[n - i - 1, k - j - 1] + + +def test_block_index_symbolic_nonzero(): + # All invalid simplifications from test_block_index_symbolic() that become valid if all + # matrices have nonzero size and all indices are nonnegative + k, l, m, n = symbols('k l m n', integer=True, positive=True) + i, j = symbols('i j', integer=True, nonnegative=True) + A1 = MatrixSymbol('A1', n, k) + A2 = MatrixSymbol('A2', n, l) + A3 = MatrixSymbol('A3', m, k) + A4 = MatrixSymbol('A4', m, l) + A = BlockMatrix([[A1, A2], [A3, A4]]) + assert A[0, 0] == A1[0, 0] + assert A[n + m - 1, 0] == A3[m - 1, 0] + assert A[0, k + l - 1] == A2[0, l - 1] + assert A[n + m - 1, k + l - 1] == A4[m - 1, l - 1] + assert A[i, j] == MatrixElement(A, i, j) + assert A[n + i, k + j] == A4[i, j] + assert A[n - i - 1, k - j - 1] == A1[n - i - 1, k - j - 1] + assert A[2 * n, 2 * k] == A4[n, k] + + +def test_block_index_large(): + n, m, k = symbols('n m k', integer=True, positive=True) + i = symbols('i', integer=True, nonnegative=True) + A1 = MatrixSymbol('A1', n, n) + A2 = MatrixSymbol('A2', n, m) + A3 = MatrixSymbol('A3', n, k) + A4 = MatrixSymbol('A4', m, n) + A5 = MatrixSymbol('A5', m, m) + A6 = MatrixSymbol('A6', m, k) + A7 = MatrixSymbol('A7', k, n) + A8 = MatrixSymbol('A8', k, m) + A9 = MatrixSymbol('A9', k, k) + A = BlockMatrix([[A1, A2, A3], [A4, A5, A6], [A7, A8, A9]]) + assert A[n + i, n + i] == MatrixElement(A, n + i, n + i) + + +@XFAIL +def test_block_index_symbolic_fail(): + # To make this work, symbolic matrix dimensions would need to be somehow assumed nonnegative + # even if the symbols aren't specified as such. Then 2 * n < n would correctly evaluate to + # False in BlockMatrix._entry() + A1 = MatrixSymbol('A1', n, 1) + A2 = MatrixSymbol('A2', m, 1) + A = BlockMatrix([[A1], [A2]]) + assert A[2 * n, 0] == A2[n, 0] + + +def test_slicing(): + A.as_explicit()[0, :] # does not raise an error + + +def test_errors(): + raises(IndexError, lambda: Identity(2)[1, 2, 3, 4, 5]) + raises(IndexError, lambda: Identity(2)[[1, 2, 3, 4, 5]]) + + +def test_matrix_expression_to_indices(): + i, j = symbols("i, j") + i1, i2, i3 = symbols("i_1:4") + + def replace_dummies(expr): + repl = {i: Symbol(i.name) for i in expr.atoms(Dummy)} + return expr.xreplace(repl) + + expr = W*X*Z + assert replace_dummies(expr._entry(i, j)) == \ + Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) + assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr + + expr = Z.T*X.T*W.T + assert replace_dummies(expr._entry(i, j)) == \ + Sum(W[j, i2]*X[i2, i1]*Z[i1, i], (i1, 0, m-1), (i2, 0, l-1)) + assert MatrixExpr.from_index_summation(expr._entry(i, j), i) == expr + + expr = W*X*Z + W*Y*Z + assert replace_dummies(expr._entry(i, j)) == \ + Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\ + Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) + assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr + + expr = 2*W*X*Z + 3*W*Y*Z + assert replace_dummies(expr._entry(i, j)) == \ + 2*Sum(W[i, i1]*X[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) +\ + 3*Sum(W[i, i1]*Y[i1, i2]*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) + assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr + + expr = W*(X + Y)*Z + assert replace_dummies(expr._entry(i, j)) == \ + Sum(W[i, i1]*(X[i1, i2] + Y[i1, i2])*Z[i2, j], (i1, 0, l-1), (i2, 0, m-1)) + assert MatrixExpr.from_index_summation(expr._entry(i, j)) == expr + + expr = A*B**2*A + #assert replace_dummies(expr._entry(i, j)) == \ + # Sum(A[i, i1]*B[i1, i2]*B[i2, i3]*A[i3, j], (i1, 0, 1), (i2, 0, 1), (i3, 0, 1)) + + # Check that different dummies are used in sub-multiplications: + expr = (X1*X2 + X2*X1)*X3 + assert replace_dummies(expr._entry(i, j)) == \ + Sum((Sum(X1[i, i2] * X2[i2, i1], (i2, 0, m - 1)) + Sum(X1[i3, i1] * X2[i, i3], (i3, 0, m - 1))) * X3[ + i1, j], (i1, 0, m - 1)) + + +def test_matrix_expression_from_index_summation(): + from sympy.abc import a,b,c,d + A = MatrixSymbol("A", k, k) + B = MatrixSymbol("B", k, k) + C = MatrixSymbol("C", k, k) + w1 = MatrixSymbol("w1", k, 1) + + i0, i1, i2, i3, i4 = symbols("i0:5", cls=Dummy) + + expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1)) + assert MatrixExpr.from_index_summation(expr, a) == W*X*Z + expr = Sum(W.T[b,a]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m-1)) + assert MatrixExpr.from_index_summation(expr, a) == W*X*Z + expr = Sum(A[b, a]*B[b, c]*C[c, d], (b, 0, k-1), (c, 0, k-1)) + assert MatrixSymbol.from_index_summation(expr, a) == A.T*B*C + expr = Sum(A[b, a]*B[c, b]*C[c, d], (b, 0, k-1), (c, 0, k-1)) + assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C + expr = Sum(C[c, d]*A[b, a]*B[c, b], (b, 0, k-1), (c, 0, k-1)) + assert MatrixSymbol.from_index_summation(expr, a) == A.T*B.T*C + expr = Sum(A[a, b] + B[a, b], (a, 0, k-1), (b, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == OneMatrix(1, k)*A*OneMatrix(k, 1) + OneMatrix(1, k)*B*OneMatrix(k, 1) + expr = Sum(A[a, b]**2, (a, 0, k - 1), (b, 0, k - 1)) + assert MatrixExpr.from_index_summation(expr, a) == Trace(A * A.T) + expr = Sum(A[a, b]**3, (a, 0, k - 1), (b, 0, k - 1)) + assert MatrixExpr.from_index_summation(expr, a) == Trace(HadamardPower(A.T, 2) * A) + expr = Sum((A[a, b] + B[a, b])*C[b, c], (b, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == (A+B)*C + expr = Sum((A[a, b] + B[b, a])*C[b, c], (b, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == (A+B.T)*C + expr = Sum(A[a, b]*A[b, c]*A[c, d], (b, 0, k-1), (c, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == A**3 + expr = Sum(A[a, b]*A[b, c]*B[c, d], (b, 0, k-1), (c, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == A**2*B + + # Parse the trace of a matrix: + + expr = Sum(A[a, a], (a, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, None) == trace(A) + expr = Sum(A[a, a]*B[b, c]*C[c, d], (a, 0, k-1), (c, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, b) == trace(A)*B*C + + # Check wrong sum ranges (should raise an exception): + + ## Case 1: 0 to m instead of 0 to m-1 + expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 0, m)) + raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a)) + ## Case 2: 1 to m-1 instead of 0 to m-1 + expr = Sum(W[a,b]*X[b,c]*Z[c,d], (b, 0, l-1), (c, 1, m-1)) + raises(ValueError, lambda: MatrixExpr.from_index_summation(expr, a)) + + # Parse nested sums: + expr = Sum(A[a, b]*Sum(B[b, c]*C[c, d], (c, 0, k-1)), (b, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == A*B*C + + # Test Kronecker delta: + expr = Sum(A[a, b]*KroneckerDelta(b, c)*B[c, d], (b, 0, k-1), (c, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, a) == A*B + + expr = Sum(KroneckerDelta(i1, m)*KroneckerDelta(i2, n)*A[i, i1]*A[j, i2], (i1, 0, k-1), (i2, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, m) == ArrayTensorProduct(A.T, A) + + # Test numbered indices: + expr = Sum(A[i1, i2]*w1[i2, 0], (i2, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*w1, i1, 0) + + expr = Sum(A[i1, i2]*B[i2, 0], (i2, 0, k-1)) + assert MatrixExpr.from_index_summation(expr, i1) == MatrixElement(A*B, i1, 0) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_inverse.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_inverse.py new file mode 100644 index 0000000000000000000000000000000000000000..4bcc7d4de2b2bee4c4922bda8bc48a52aa205961 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_inverse.py @@ -0,0 +1,69 @@ +from sympy.core import symbols, S +from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix +from sympy.matrices.exceptions import NonInvertibleMatrixError, NonSquareMatrixError +from sympy.matrices import eye, Identity +from sympy.testing.pytest import raises +from sympy.assumptions.ask import Q +from sympy.assumptions.refine import refine + +n, m, l = symbols('n m l', integer=True) +A = MatrixSymbol('A', n, m) +B = MatrixSymbol('B', m, l) +C = MatrixSymbol('C', n, n) +D = MatrixSymbol('D', n, n) +E = MatrixSymbol('E', m, n) + + +def test_inverse(): + assert Inverse(C).args == (C, S.NegativeOne) + assert Inverse(C).shape == (n, n) + assert Inverse(A*E).shape == (n, n) + assert Inverse(E*A).shape == (m, m) + assert Inverse(C).inverse() == C + assert Inverse(Inverse(C)).doit() == C + assert isinstance(Inverse(Inverse(C)), Inverse) + + assert Inverse(*Inverse(E*A).args) == Inverse(E*A) + + assert C.inverse().inverse() == C + + assert C.inverse()*C == Identity(C.rows) + + assert Identity(n).inverse() == Identity(n) + assert (3*Identity(n)).inverse() == Identity(n)/3 + + # Simplifies Muls if possible (i.e. submatrices are square) + assert (C*D).inverse() == D.I*C.I + # But still works when not possible + assert isinstance((A*E).inverse(), Inverse) + assert Inverse(C*D).doit(inv_expand=False) == Inverse(C*D) + + assert Inverse(eye(3)).doit() == eye(3) + assert Inverse(eye(3)).doit(deep=False) == eye(3) + + assert OneMatrix(1, 1).I == Identity(1) + assert isinstance(OneMatrix(n, n).I, Inverse) + +def test_inverse_non_invertible(): + raises(NonInvertibleMatrixError, lambda: ZeroMatrix(n, n).I) + raises(NonInvertibleMatrixError, lambda: OneMatrix(2, 2).I) + +def test_refine(): + assert refine(C.I, Q.orthogonal(C)) == C.T + + +def test_inverse_matpow_canonicalization(): + A = MatrixSymbol('A', 3, 3) + assert Inverse(MatPow(A, 3)).doit() == MatPow(Inverse(A), 3).doit() + + +def test_nonsquare_error(): + A = MatrixSymbol('A', 3, 4) + raises(NonSquareMatrixError, lambda: Inverse(A)) + + +def test_adjoint_trnaspose_conjugate(): + A = MatrixSymbol('A', n, n) + assert A.transpose().inverse() == A.inverse().transpose() + assert A.conjugate().inverse() == A.inverse().conjugate() + assert A.adjoint().inverse() == A.inverse().adjoint() diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_kronecker.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_kronecker.py new file mode 100644 index 0000000000000000000000000000000000000000..b4444716a76a52e3638dd7a36238a9f459179083 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_kronecker.py @@ -0,0 +1,150 @@ +from sympy.core.mod import Mod +from sympy.core.numbers import I +from sympy.core.symbol import symbols +from sympy.functions.elementary.integers import floor +from sympy.matrices.dense import (Matrix, eye) +from sympy.matrices import MatrixSymbol, Identity +from sympy.matrices.expressions import det, trace + +from sympy.matrices.expressions.kronecker import (KroneckerProduct, + kronecker_product, + combine_kronecker) + + +mat1 = Matrix([[1, 2 * I], [1 + I, 3]]) +mat2 = Matrix([[2 * I, 3], [4 * I, 2]]) + +i, j, k, n, m, o, p, x = symbols('i,j,k,n,m,o,p,x') +Z = MatrixSymbol('Z', n, n) +W = MatrixSymbol('W', m, m) +A = MatrixSymbol('A', n, m) +B = MatrixSymbol('B', n, m) +C = MatrixSymbol('C', m, k) + + +def test_KroneckerProduct(): + assert isinstance(KroneckerProduct(A, B), KroneckerProduct) + assert KroneckerProduct(A, B).subs(A, C) == KroneckerProduct(C, B) + assert KroneckerProduct(A, C).shape == (n*m, m*k) + assert (KroneckerProduct(A, C) + KroneckerProduct(-A, C)).is_ZeroMatrix + assert (KroneckerProduct(W, Z) * KroneckerProduct(W.I, Z.I)).is_Identity + + +def test_KroneckerProduct_identity(): + assert KroneckerProduct(Identity(m), Identity(n)) == Identity(m*n) + assert KroneckerProduct(eye(2), eye(3)) == eye(6) + + +def test_KroneckerProduct_explicit(): + X = MatrixSymbol('X', 2, 2) + Y = MatrixSymbol('Y', 2, 2) + kp = KroneckerProduct(X, Y) + assert kp.shape == (4, 4) + assert kp.as_explicit() == Matrix( + [ + [X[0, 0]*Y[0, 0], X[0, 0]*Y[0, 1], X[0, 1]*Y[0, 0], X[0, 1]*Y[0, 1]], + [X[0, 0]*Y[1, 0], X[0, 0]*Y[1, 1], X[0, 1]*Y[1, 0], X[0, 1]*Y[1, 1]], + [X[1, 0]*Y[0, 0], X[1, 0]*Y[0, 1], X[1, 1]*Y[0, 0], X[1, 1]*Y[0, 1]], + [X[1, 0]*Y[1, 0], X[1, 0]*Y[1, 1], X[1, 1]*Y[1, 0], X[1, 1]*Y[1, 1]] + ] + ) + + +def test_tensor_product_adjoint(): + assert KroneckerProduct(I*A, B).adjoint() == \ + -I*KroneckerProduct(A.adjoint(), B.adjoint()) + assert KroneckerProduct(mat1, mat2).adjoint() == \ + kronecker_product(mat1.adjoint(), mat2.adjoint()) + + +def test_tensor_product_conjugate(): + assert KroneckerProduct(I*A, B).conjugate() == \ + -I*KroneckerProduct(A.conjugate(), B.conjugate()) + assert KroneckerProduct(mat1, mat2).conjugate() == \ + kronecker_product(mat1.conjugate(), mat2.conjugate()) + + +def test_tensor_product_transpose(): + assert KroneckerProduct(I*A, B).transpose() == \ + I*KroneckerProduct(A.transpose(), B.transpose()) + assert KroneckerProduct(mat1, mat2).transpose() == \ + kronecker_product(mat1.transpose(), mat2.transpose()) + + +def test_KroneckerProduct_is_associative(): + assert kronecker_product(A, kronecker_product( + B, C)) == kronecker_product(kronecker_product(A, B), C) + assert kronecker_product(A, kronecker_product( + B, C)) == KroneckerProduct(A, B, C) + + +def test_KroneckerProduct_is_bilinear(): + assert kronecker_product(x*A, B) == x*kronecker_product(A, B) + assert kronecker_product(A, x*B) == x*kronecker_product(A, B) + + +def test_KroneckerProduct_determinant(): + kp = kronecker_product(W, Z) + assert det(kp) == det(W)**n * det(Z)**m + + +def test_KroneckerProduct_trace(): + kp = kronecker_product(W, Z) + assert trace(kp) == trace(W)*trace(Z) + + +def test_KroneckerProduct_isnt_commutative(): + assert KroneckerProduct(A, B) != KroneckerProduct(B, A) + assert KroneckerProduct(A, B).is_commutative is False + + +def test_KroneckerProduct_extracts_commutative_part(): + assert kronecker_product(x * A, 2 * B) == x * \ + 2 * KroneckerProduct(A, B) + + +def test_KroneckerProduct_inverse(): + kp = kronecker_product(W, Z) + assert kp.inverse() == kronecker_product(W.inverse(), Z.inverse()) + + +def test_KroneckerProduct_combine_add(): + kp1 = kronecker_product(A, B) + kp2 = kronecker_product(C, W) + assert combine_kronecker(kp1*kp2) == kronecker_product(A*C, B*W) + + +def test_KroneckerProduct_combine_mul(): + X = MatrixSymbol('X', m, n) + Y = MatrixSymbol('Y', m, n) + kp1 = kronecker_product(A, X) + kp2 = kronecker_product(B, Y) + assert combine_kronecker(kp1+kp2) == kronecker_product(A+B, X+Y) + + +def test_KroneckerProduct_combine_pow(): + X = MatrixSymbol('X', n, n) + Y = MatrixSymbol('Y', n, n) + assert combine_kronecker(KroneckerProduct( + X, Y)**x) == KroneckerProduct(X**x, Y**x) + assert combine_kronecker(x * KroneckerProduct(X, Y) + ** 2) == x * KroneckerProduct(X**2, Y**2) + assert combine_kronecker( + x * (KroneckerProduct(X, Y)**2) * KroneckerProduct(A, B)) == x * KroneckerProduct(X**2 * A, Y**2 * B) + # cannot simplify because of non-square arguments to kronecker product: + assert combine_kronecker(KroneckerProduct(A, B.T) ** m) == KroneckerProduct(A, B.T) ** m + + +def test_KroneckerProduct_expand(): + X = MatrixSymbol('X', n, n) + Y = MatrixSymbol('Y', n, n) + + assert KroneckerProduct(X + Y, Y + Z).expand(kroneckerproduct=True) == \ + KroneckerProduct(X, Y) + KroneckerProduct(X, Z) + \ + KroneckerProduct(Y, Y) + KroneckerProduct(Y, Z) + +def test_KroneckerProduct_entry(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', o, p) + + assert KroneckerProduct(A, B)._entry(i, j) == A[Mod(floor(i/o), n), Mod(floor(j/p), m)]*B[Mod(i, o), Mod(j, p)] diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matadd.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matadd.py new file mode 100644 index 0000000000000000000000000000000000000000..43229ae8c2e42f0253a5f3eceefa5fffe7a99f29 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matadd.py @@ -0,0 +1,58 @@ +from sympy.matrices.expressions import MatrixSymbol, MatAdd, MatPow, MatMul +from sympy.matrices.expressions.special import GenericZeroMatrix, ZeroMatrix +from sympy.matrices.exceptions import ShapeError +from sympy.matrices import eye, ImmutableMatrix +from sympy.core import Add, Basic, S +from sympy.core.add import add +from sympy.testing.pytest import XFAIL, raises + +X = MatrixSymbol('X', 2, 2) +Y = MatrixSymbol('Y', 2, 2) + +def test_evaluate(): + assert MatAdd(X, X, evaluate=True) == add(X, X, evaluate=True) == MatAdd(X, X).doit() + +def test_sort_key(): + assert MatAdd(Y, X).doit().args == add(Y, X).doit().args == (X, Y) + + +def test_matadd_sympify(): + assert isinstance(MatAdd(eye(1), eye(1)).args[0], Basic) + assert isinstance(add(eye(1), eye(1)).args[0], Basic) + + +def test_matadd_of_matrices(): + assert MatAdd(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2)) + assert add(eye(2), 4*eye(2), eye(2)).doit() == ImmutableMatrix(6*eye(2)) + + +def test_doit_args(): + A = ImmutableMatrix([[1, 2], [3, 4]]) + B = ImmutableMatrix([[2, 3], [4, 5]]) + assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2 + assert MatAdd(A, MatMul(A, B)).doit() == A + A*B + assert (MatAdd(A, X, MatMul(A, B), Y, MatAdd(2*A, B)).doit() == + add(A, X, MatMul(A, B), Y, add(2*A, B)).doit() == + MatAdd(3*A + A*B + B, X, Y)) + + +def test_generic_identity(): + assert MatAdd.identity == GenericZeroMatrix() + assert MatAdd.identity != S.Zero + + +def test_zero_matrix_add(): + assert Add(ZeroMatrix(2, 2), ZeroMatrix(2, 2)) == ZeroMatrix(2, 2) + +@XFAIL +def test_matrix_Add_with_scalar(): + raises(TypeError, lambda: Add(0, ZeroMatrix(2, 2))) + + +def test_shape_error(): + A = MatrixSymbol('A', 2, 3) + B = MatrixSymbol('B', 3, 3) + raises(ShapeError, lambda: MatAdd(A, B)) + + A = MatrixSymbol('A', 3, 2) + raises(ShapeError, lambda: MatAdd(A, B)) diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matexpr.py b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matexpr.py new file mode 100644 index 0000000000000000000000000000000000000000..f2319e8d8097c2ad3519eab783c4665623c55b80 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/tests/test_matexpr.py @@ -0,0 +1,592 @@ +from sympy.concrete.summations import Sum +from sympy.core.exprtools import gcd_terms +from sympy.core.function import (diff, expand) +from sympy.core.relational import Eq +from sympy.core.symbol import (Dummy, Symbol, Str) +from sympy.functions.special.tensor_functions import KroneckerDelta +from sympy.matrices.dense import zeros +from sympy.polys.polytools import factor + +from sympy.core import (S, symbols, Add, Mul, SympifyError, Rational, + Function) +from sympy.functions import sin, cos, tan, sqrt, cbrt, exp +from sympy.simplify import simplify +from sympy.matrices import (ImmutableMatrix, Inverse, MatAdd, MatMul, + MatPow, Matrix, MatrixExpr, MatrixSymbol, + SparseMatrix, Transpose, Adjoint, MatrixSet) +from sympy.matrices.exceptions import NonSquareMatrixError +from sympy.matrices.expressions.determinant import Determinant, det +from sympy.matrices.expressions.matexpr import MatrixElement +from sympy.matrices.expressions.special import ZeroMatrix, Identity +from sympy.testing.pytest import raises, XFAIL, skip +from importlib.metadata import version + +n, m, l, k, p = symbols('n m l k p', integer=True) +x = symbols('x') +A = MatrixSymbol('A', n, m) +B = MatrixSymbol('B', m, l) +C = MatrixSymbol('C', n, n) +D = MatrixSymbol('D', n, n) +E = MatrixSymbol('E', m, n) +w = MatrixSymbol('w', n, 1) + + +def test_matrix_symbol_creation(): + assert MatrixSymbol('A', 2, 2) + assert MatrixSymbol('A', 0, 0) + raises(ValueError, lambda: MatrixSymbol('A', -1, 2)) + raises(ValueError, lambda: MatrixSymbol('A', 2.0, 2)) + raises(ValueError, lambda: MatrixSymbol('A', 2j, 2)) + raises(ValueError, lambda: MatrixSymbol('A', 2, -1)) + raises(ValueError, lambda: MatrixSymbol('A', 2, 2.0)) + raises(ValueError, lambda: MatrixSymbol('A', 2, 2j)) + + n = symbols('n') + assert MatrixSymbol('A', n, n) + n = symbols('n', integer=False) + raises(ValueError, lambda: MatrixSymbol('A', n, n)) + n = symbols('n', negative=True) + raises(ValueError, lambda: MatrixSymbol('A', n, n)) + + +def test_matexpr_properties(): + assert A.shape == (n, m) + assert (A * B).shape == (n, l) + assert A[0, 1].indices == (0, 1) + assert A[0, 0].symbol == A + assert A[0, 0].symbol.name == 'A' + + +def test_matexpr(): + assert (x*A).shape == A.shape + assert (x*A).__class__ == MatMul + assert 2*A - A - A == ZeroMatrix(*A.shape) + assert (A*B).shape == (n, l) + + +def test_matexpr_subs(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', m, l) + C = MatrixSymbol('C', m, l) + + assert A.subs(n, m).shape == (m, m) + assert (A*B).subs(B, C) == A*C + assert (A*B).subs(l, n).is_square + + W = MatrixSymbol("W", 3, 3) + X = MatrixSymbol("X", 2, 2) + Y = MatrixSymbol("Y", 1, 2) + Z = MatrixSymbol("Z", n, 2) + # no restrictions on Symbol replacement + assert X.subs(X, Y) == Y + # it might be better to just change the name + y = Str('y') + assert X.subs(Str("X"), y).args == (y, 2, 2) + # it's ok to introduce a wider matrix + assert X[1, 1].subs(X, W) == W[1, 1] + # but for a given MatrixExpression, only change + # name if indexing on the new shape is valid. + # Here, X is 2,2; Y is 1,2 and Y[1, 1] is out + # of range so an error is raised + raises(IndexError, lambda: X[1, 1].subs(X, Y)) + # here, [0, 1] is in range so the subs succeeds + assert X[0, 1].subs(X, Y) == Y[0, 1] + # and here the size of n will accept any index + # in the first position + assert W[2, 1].subs(W, Z) == Z[2, 1] + # but not in the second position + raises(IndexError, lambda: W[2, 2].subs(W, Z)) + # any matrix should raise if invalid + raises(IndexError, lambda: W[2, 2].subs(W, zeros(2))) + + A = SparseMatrix([[1, 2], [3, 4]]) + B = Matrix([[1, 2], [3, 4]]) + C, D = MatrixSymbol('C', 2, 2), MatrixSymbol('D', 2, 2) + + assert (C*D).subs({C: A, D: B}) == MatMul(A, B) + + +def test_addition(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', n, m) + + assert isinstance(A + B, MatAdd) + assert (A + B).shape == A.shape + assert isinstance(A - A + 2*B, MatMul) + + raises(TypeError, lambda: A + 1) + raises(TypeError, lambda: 5 + A) + raises(TypeError, lambda: 5 - A) + + assert A + ZeroMatrix(n, m) - A == ZeroMatrix(n, m) + raises(TypeError, lambda: ZeroMatrix(n, m) + S.Zero) + + +def test_multiplication(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', m, l) + C = MatrixSymbol('C', n, n) + + assert (2*A*B).shape == (n, l) + assert (A*0*B) == ZeroMatrix(n, l) + assert (2*A).shape == A.shape + + assert A * ZeroMatrix(m, m) * B == ZeroMatrix(n, l) + + assert C * Identity(n) * C.I == Identity(n) + + assert B/2 == S.Half*B + raises(NotImplementedError, lambda: 2/B) + + A = MatrixSymbol('A', n, n) + B = MatrixSymbol('B', n, n) + assert Identity(n) * (A + B) == A + B + + assert A**2*A == A**3 + assert A**2*(A.I)**3 == A.I + assert A**3*(A.I)**2 == A + + +def test_MatPow(): + A = MatrixSymbol('A', n, n) + + AA = MatPow(A, 2) + assert AA.exp == 2 + assert AA.base == A + assert (A**n).exp == n + + assert A**0 == Identity(n) + assert A**1 == A + assert A**2 == AA + assert A**-1 == Inverse(A) + assert (A**-1)**-1 == A + assert (A**2)**3 == A**6 + assert A**S.Half == sqrt(A) + assert A**Rational(1, 3) == cbrt(A) + raises(NonSquareMatrixError, lambda: MatrixSymbol('B', 3, 2)**2) + + +def test_MatrixSymbol(): + n, m, t = symbols('n,m,t') + X = MatrixSymbol('X', n, m) + assert X.shape == (n, m) + raises(TypeError, lambda: MatrixSymbol('X', n, m)(t)) # issue 5855 + assert X.doit() == X + + +def test_dense_conversion(): + X = MatrixSymbol('X', 2, 2) + assert ImmutableMatrix(X) == ImmutableMatrix(2, 2, lambda i, j: X[i, j]) + assert Matrix(X) == Matrix(2, 2, lambda i, j: X[i, j]) + + +def test_free_symbols(): + assert (C*D).free_symbols == {C, D} + + +def test_zero_matmul(): + assert isinstance(S.Zero * MatrixSymbol('X', 2, 2), MatrixExpr) + + +def test_matadd_simplify(): + A = MatrixSymbol('A', 1, 1) + assert simplify(MatAdd(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \ + MatAdd(A, Matrix([[1]])) + + +def test_matmul_simplify(): + A = MatrixSymbol('A', 1, 1) + assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \ + MatMul(A, Matrix([[1]])) + + +def test_invariants(): + A = MatrixSymbol('A', n, m) + B = MatrixSymbol('B', m, l) + X = MatrixSymbol('X', n, n) + objs = [Identity(n), ZeroMatrix(m, n), A, MatMul(A, B), MatAdd(A, A), + Transpose(A), Adjoint(A), Inverse(X), MatPow(X, 2), MatPow(X, -1), + MatPow(X, 0)] + for obj in objs: + assert obj == obj.__class__(*obj.args) + + +def test_matexpr_indexing(): + A = MatrixSymbol('A', n, m) + A[1, 2] + A[l, k] + A[l + 1, k + 1] + A = MatrixSymbol('A', 2, 1) + for i in range(-2, 2): + for j in range(-1, 1): + A[i, j] + + +def test_single_indexing(): + A = MatrixSymbol('A', 2, 3) + assert A[1] == A[0, 1] + assert A[int(1)] == A[0, 1] + assert A[3] == A[1, 0] + assert list(A[:2, :2]) == [A[0, 0], A[0, 1], A[1, 0], A[1, 1]] + raises(IndexError, lambda: A[6]) + raises(IndexError, lambda: A[n]) + B = MatrixSymbol('B', n, m) + raises(IndexError, lambda: B[1]) + B = MatrixSymbol('B', n, 3) + assert B[3] == B[1, 0] + + +def test_MatrixElement_commutative(): + assert A[0, 1]*A[1, 0] == A[1, 0]*A[0, 1] + + +def test_MatrixSymbol_determinant(): + A = MatrixSymbol('A', 4, 4) + assert A.as_explicit().det() == A[0, 0]*A[1, 1]*A[2, 2]*A[3, 3] - \ + A[0, 0]*A[1, 1]*A[2, 3]*A[3, 2] - A[0, 0]*A[1, 2]*A[2, 1]*A[3, 3] + \ + A[0, 0]*A[1, 2]*A[2, 3]*A[3, 1] + A[0, 0]*A[1, 3]*A[2, 1]*A[3, 2] - \ + A[0, 0]*A[1, 3]*A[2, 2]*A[3, 1] - A[0, 1]*A[1, 0]*A[2, 2]*A[3, 3] + \ + A[0, 1]*A[1, 0]*A[2, 3]*A[3, 2] + A[0, 1]*A[1, 2]*A[2, 0]*A[3, 3] - \ + A[0, 1]*A[1, 2]*A[2, 3]*A[3, 0] - A[0, 1]*A[1, 3]*A[2, 0]*A[3, 2] + \ + A[0, 1]*A[1, 3]*A[2, 2]*A[3, 0] + A[0, 2]*A[1, 0]*A[2, 1]*A[3, 3] - \ + A[0, 2]*A[1, 0]*A[2, 3]*A[3, 1] - A[0, 2]*A[1, 1]*A[2, 0]*A[3, 3] + \ + A[0, 2]*A[1, 1]*A[2, 3]*A[3, 0] + A[0, 2]*A[1, 3]*A[2, 0]*A[3, 1] - \ + A[0, 2]*A[1, 3]*A[2, 1]*A[3, 0] - A[0, 3]*A[1, 0]*A[2, 1]*A[3, 2] + \ + A[0, 3]*A[1, 0]*A[2, 2]*A[3, 1] + A[0, 3]*A[1, 1]*A[2, 0]*A[3, 2] - \ + A[0, 3]*A[1, 1]*A[2, 2]*A[3, 0] - A[0, 3]*A[1, 2]*A[2, 0]*A[3, 1] + \ + A[0, 3]*A[1, 2]*A[2, 1]*A[3, 0] + + B = MatrixSymbol('B', 4, 4) + assert Determinant(A + B).doit() == det(A + B) == (A + B).det() + + +def test_MatrixElement_diff(): + assert (A[3, 0]*A[0, 0]).diff(A[0, 0]) == A[3, 0] + + +def test_MatrixElement_doit(): + u = MatrixSymbol('u', 2, 1) + v = ImmutableMatrix([3, 5]) + assert u[0, 0].subs(u, v).doit() == v[0, 0] + + +def test_identity_powers(): + M = Identity(n) + assert MatPow(M, 3).doit() == M**3 + assert M**n == M + assert MatPow(M, 0).doit() == M**2 + assert M**-2 == M + assert MatPow(M, -2).doit() == M**0 + N = Identity(3) + assert MatPow(N, 2).doit() == N**n + assert MatPow(N, 3).doit() == N + assert MatPow(N, -2).doit() == N**4 + assert MatPow(N, 2).doit() == N**0 + + +def test_Zero_power(): + z1 = ZeroMatrix(n, n) + assert z1**4 == z1 + raises(ValueError, lambda:z1**-2) + assert z1**0 == Identity(n) + assert MatPow(z1, 2).doit() == z1**2 + raises(ValueError, lambda:MatPow(z1, -2).doit()) + z2 = ZeroMatrix(3, 3) + assert MatPow(z2, 4).doit() == z2**4 + raises(ValueError, lambda:z2**-3) + assert z2**3 == MatPow(z2, 3).doit() + assert z2**0 == Identity(3) + raises(ValueError, lambda:MatPow(z2, -1).doit()) + + +def test_matrixelement_diff(): + dexpr = diff((D*w)[k,0], w[p,0]) + + assert w[k, p].diff(w[k, p]) == 1 + assert w[k, p].diff(w[0, 0]) == KroneckerDelta(0, k, (0, n-1))*KroneckerDelta(0, p, (0, 0)) + _i_1 = Dummy("_i_1") + assert dexpr.dummy_eq(Sum(KroneckerDelta(_i_1, p, (0, n-1))*D[k, _i_1], (_i_1, 0, n - 1))) + assert dexpr.doit() == D[k, p] + + +def test_MatrixElement_with_values(): + x, y, z, w = symbols("x y z w") + M = Matrix([[x, y], [z, w]]) + i, j = symbols("i, j") + Mij = M[i, j] + assert isinstance(Mij, MatrixElement) + Ms = SparseMatrix([[2, 3], [4, 5]]) + msij = Ms[i, j] + assert isinstance(msij, MatrixElement) + for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]: + assert Mij.subs({i: oi, j: oj}) == M[oi, oj] + assert msij.subs({i: oi, j: oj}) == Ms[oi, oj] + A = MatrixSymbol("A", 2, 2) + assert A[0, 0].subs(A, M) == x + assert A[i, j].subs(A, M) == M[i, j] + assert M[i, j].subs(M, A) == A[i, j] + + assert isinstance(M[3*i - 2, j], MatrixElement) + assert M[3*i - 2, j].subs({i: 1, j: 0}) == M[1, 0] + assert isinstance(M[i, 0], MatrixElement) + assert M[i, 0].subs(i, 0) == M[0, 0] + assert M[0, i].subs(i, 1) == M[0, 1] + + assert M[i, j].diff(x) == Matrix([[1, 0], [0, 0]])[i, j] + + raises(ValueError, lambda: M[i, 2]) + raises(ValueError, lambda: M[i, -1]) + raises(ValueError, lambda: M[2, i]) + raises(ValueError, lambda: M[-1, i]) + + +def test_inv(): + B = MatrixSymbol('B', 3, 3) + assert B.inv() == B**-1 + + # https://github.com/sympy/sympy/issues/19162 + X = MatrixSymbol('X', 1, 1).as_explicit() + assert X.inv() == Matrix([[1/X[0, 0]]]) + + X = MatrixSymbol('X', 2, 2).as_explicit() + detX = X[0, 0]*X[1, 1] - X[0, 1]*X[1, 0] + invX = Matrix([[ X[1, 1], -X[0, 1]], + [-X[1, 0], X[0, 0]]]) / detX + assert X.inv() == invX + + +@XFAIL +def test_factor_expand(): + A = MatrixSymbol("A", n, n) + B = MatrixSymbol("B", n, n) + expr1 = (A + B)*(C + D) + expr2 = A*C + B*C + A*D + B*D + assert expr1 != expr2 + assert expand(expr1) == expr2 + assert factor(expr2) == expr1 + + expr = B**(-1)*(A**(-1)*B**(-1) - A**(-1)*C*B**(-1))**(-1)*A**(-1) + I = Identity(n) + # Ideally we get the first, but we at least don't want a wrong answer + assert factor(expr) in [I - C, B**-1*(A**-1*(I - C)*B**-1)**-1*A**-1] + +def test_numpy_conversion(): + try: + from numpy import array, array_equal + except ImportError: + skip('NumPy must be available to test creating matrices from ndarrays') + A = MatrixSymbol('A', 2, 2) + np_array = array([[MatrixElement(A, 0, 0), MatrixElement(A, 0, 1)], + [MatrixElement(A, 1, 0), MatrixElement(A, 1, 1)]]) + assert array_equal(array(A), np_array) + assert array_equal(array(A, copy=True), np_array) + if(int(version('numpy').split('.')[0]) >= 2): #run this test only if numpy is new enough that copy variable is passed properly. + raises(TypeError, lambda: array(A, copy=False)) + +def test_issue_2749(): + A = MatrixSymbol("A", 5, 2) + assert (A.T * A).I.as_explicit() == Matrix([[(A.T * A).I[0, 0], (A.T * A).I[0, 1]], \ + [(A.T * A).I[1, 0], (A.T * A).I[1, 1]]]) + + +def test_issue_2750(): + x = MatrixSymbol('x', 1, 1) + assert (x.T*x).as_explicit()**-1 == Matrix([[x[0, 0]**(-2)]]) + + +def test_issue_7842(): + A = MatrixSymbol('A', 3, 1) + B = MatrixSymbol('B', 2, 1) + assert Eq(A, B) == False + assert Eq(A[1,0], B[1, 0]).func is Eq + A = ZeroMatrix(2, 3) + B = ZeroMatrix(2, 3) + assert Eq(A, B) == True + + +def test_issue_21195(): + t = symbols('t') + x = Function('x')(t) + dx = x.diff(t) + exp1 = cos(x) + cos(x)*dx + exp2 = sin(x) + tan(x)*(dx.diff(t)) + exp3 = sin(x)*sin(t)*(dx.diff(t)).diff(t) + A = Matrix([[exp1], [exp2], [exp3]]) + B = Matrix([[exp1.diff(x)], [exp2.diff(x)], [exp3.diff(x)]]) + assert A.diff(x) == B + + +def test_issue_24859(): + A = MatrixSymbol('A', 2, 3) + B = MatrixSymbol('B', 3, 2) + J = A*B + Jinv = Matrix(J).adjugate() + u = MatrixSymbol('u', 2, 3) + Jk = Jinv.subs(A, A + x*u) + + expected = B[0, 1]*u[1, 0] + B[1, 1]*u[1, 1] + B[2, 1]*u[1, 2] + assert Jk[0, 0].diff(x) == expected + assert diff(Jk[0, 0], x).doit() == expected + + +def test_MatMul_postprocessor(): + z = zeros(2) + z1 = ZeroMatrix(2, 2) + assert Mul(0, z) == Mul(z, 0) in [z, z1] + + M = Matrix([[1, 2], [3, 4]]) + Mx = Matrix([[x, 2*x], [3*x, 4*x]]) + assert Mul(x, M) == Mul(M, x) == Mx + + A = MatrixSymbol("A", 2, 2) + assert Mul(A, M) == MatMul(A, M) + assert Mul(M, A) == MatMul(M, A) + # Scalars should be absorbed into constant matrices + a = Mul(x, M, A) + b = Mul(M, x, A) + c = Mul(M, A, x) + assert a == b == c == MatMul(Mx, A) + a = Mul(x, A, M) + b = Mul(A, x, M) + c = Mul(A, M, x) + assert a == b == c == MatMul(A, Mx) + assert Mul(M, M) == M**2 + assert Mul(A, M, M) == MatMul(A, M**2) + assert Mul(M, M, A) == MatMul(M**2, A) + assert Mul(M, A, M) == MatMul(M, A, M) + + assert Mul(A, x, M, M, x) == MatMul(A, Mx**2) + + +@XFAIL +def test_MatAdd_postprocessor_xfail(): + # This is difficult to get working because of the way that Add processes + # its args. + z = zeros(2) + assert Add(z, S.NaN) == Add(S.NaN, z) + + +def test_MatAdd_postprocessor(): + # Some of these are nonsensical, but we do not raise errors for Add + # because that breaks algorithms that want to replace matrices with dummy + # symbols. + + z = zeros(2) + + assert Add(0, z) == Add(z, 0) == z + + a = Add(S.Infinity, z) + assert a == Add(z, S.Infinity) + assert isinstance(a, Add) + assert a.args == (S.Infinity, z) + + a = Add(S.ComplexInfinity, z) + assert a == Add(z, S.ComplexInfinity) + assert isinstance(a, Add) + assert a.args == (S.ComplexInfinity, z) + + a = Add(z, S.NaN) + # assert a == Add(S.NaN, z) # See the XFAIL above + assert isinstance(a, Add) + assert a.args == (S.NaN, z) + + M = Matrix([[1, 2], [3, 4]]) + a = Add(x, M) + assert a == Add(M, x) + assert isinstance(a, Add) + assert a.args == (x, M) + + A = MatrixSymbol("A", 2, 2) + assert Add(A, M) == Add(M, A) == A + M + + # Scalars should be absorbed into constant matrices (producing an error) + a = Add(x, M, A) + assert a == Add(M, x, A) == Add(M, A, x) == Add(x, A, M) == Add(A, x, M) == Add(A, M, x) + assert isinstance(a, Add) + assert a.args == (x, A + M) + + assert Add(M, M) == 2*M + assert Add(M, A, M) == Add(M, M, A) == Add(A, M, M) == A + 2*M + + a = Add(A, x, M, M, x) + assert isinstance(a, Add) + assert a.args == (2*x, A + 2*M) + + +def test_simplify_matrix_expressions(): + # Various simplification functions + assert type(gcd_terms(C*D + D*C)) == MatAdd + a = gcd_terms(2*C*D + 4*D*C) + assert type(a) == MatAdd + assert a.args == (2*C*D, 4*D*C) + + +def test_exp(): + A = MatrixSymbol('A', 2, 2) + B = MatrixSymbol('B', 2, 2) + expr1 = exp(A)*exp(B) + expr2 = exp(B)*exp(A) + assert expr1 != expr2 + assert expr1 - expr2 != 0 + assert not isinstance(expr1, exp) + assert not isinstance(expr2, exp) + + +def test_invalid_args(): + raises(SympifyError, lambda: MatrixSymbol(1, 2, 'A')) + + +def test_matrixsymbol_from_symbol(): + # The label should be preserved during doit and subs + A_label = Symbol('A', complex=True) + A = MatrixSymbol(A_label, 2, 2) + + A_1 = A.doit() + A_2 = A.subs(2, 3) + assert A_1.args == A.args + assert A_2.args[0] == A.args[0] + + +def test_as_explicit(): + Z = MatrixSymbol('Z', 2, 3) + assert Z.as_explicit() == ImmutableMatrix([ + [Z[0, 0], Z[0, 1], Z[0, 2]], + [Z[1, 0], Z[1, 1], Z[1, 2]], + ]) + raises(ValueError, lambda: A.as_explicit()) + + +def test_MatrixSet(): + M = MatrixSet(2, 2, set=S.Reals) + assert M.shape == (2, 2) + assert M.set == S.Reals + X = Matrix([[1, 2], [3, 4]]) + assert X in M + X = ZeroMatrix(2, 2) + assert X in M + raises(TypeError, lambda: A in M) + raises(TypeError, lambda: 1 in M) + M = MatrixSet(n, m, set=S.Reals) + assert A in M + raises(TypeError, lambda: C in M) + raises(TypeError, lambda: X in M) + M = MatrixSet(2, 2, set={1, 2, 3}) + X = Matrix([[1, 2], [3, 4]]) + Y = Matrix([[1, 2]]) + assert (X in M) == S.false + assert (Y in M) == S.false + raises(ValueError, lambda: MatrixSet(2, -2, S.Reals)) + raises(ValueError, lambda: MatrixSet(2.4, -1, S.Reals)) + raises(TypeError, lambda: MatrixSet(2, 2, (1, 2, 3))) + + +def test_matrixsymbol_solving(): + A = MatrixSymbol('A', 2, 2) + B = MatrixSymbol('B', 2, 2) + Z = ZeroMatrix(2, 2) + assert -(-A + B) - A + B == Z + assert (-(-A + B) - A + B).simplify() == Z + assert (-(-A + B) - A + B).expand() == Z + assert (-(-A + B) - A + B - Z).simplify() == Z + assert (-(-A + B) - A + B - Z).expand() == Z + assert (A*(A + B) + B*(A.T + B.T)).expand() == A**2 + A*B + B*A.T + B*B.T diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/trace.py b/lib/python3.11/site-packages/sympy/matrices/expressions/trace.py new file mode 100644 index 0000000000000000000000000000000000000000..b5f9f94ea7486dc21b47c2e2e783a93280b180e0 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/trace.py @@ -0,0 +1,167 @@ +from sympy.core.basic import Basic +from sympy.core.expr import Expr, ExprBuilder +from sympy.core.singleton import S +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import uniquely_named_symbol +from sympy.core.sympify import sympify +from sympy.matrices.matrixbase import MatrixBase +from sympy.matrices.exceptions import NonSquareMatrixError + + +class Trace(Expr): + """Matrix Trace + + Represents the trace of a matrix expression. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Trace, eye + >>> A = MatrixSymbol('A', 3, 3) + >>> Trace(A) + Trace(A) + >>> Trace(eye(3)) + Trace(Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]])) + >>> Trace(eye(3)).simplify() + 3 + """ + is_Trace = True + is_commutative = True + + def __new__(cls, mat): + mat = sympify(mat) + + if not mat.is_Matrix: + raise TypeError("input to Trace, %s, is not a matrix" % str(mat)) + + if mat.is_square is False: + raise NonSquareMatrixError("Trace of a non-square matrix") + + return Basic.__new__(cls, mat) + + def _eval_transpose(self): + return self + + def _eval_derivative(self, v): + from sympy.concrete.summations import Sum + from .matexpr import MatrixElement + if isinstance(v, MatrixElement): + return self.rewrite(Sum).diff(v) + expr = self.doit() + if isinstance(expr, Trace): + # Avoid looping infinitely: + raise NotImplementedError + return expr._eval_derivative(v) + + def _eval_derivative_matrix_lines(self, x): + from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct, ArrayContraction + r = self.args[0]._eval_derivative_matrix_lines(x) + for lr in r: + if lr.higher == 1: + lr.higher = ExprBuilder( + ArrayContraction, + [ + ExprBuilder( + ArrayTensorProduct, + [ + lr._lines[0], + lr._lines[1], + ] + ), + (1, 3), + ], + validator=ArrayContraction._validate + ) + else: + # This is not a matrix line: + lr.higher = ExprBuilder( + ArrayContraction, + [ + ExprBuilder( + ArrayTensorProduct, + [ + lr._lines[0], + lr._lines[1], + lr.higher, + ] + ), + (1, 3), (0, 2) + ] + ) + lr._lines = [S.One, S.One] + lr._first_pointer_parent = lr._lines + lr._second_pointer_parent = lr._lines + lr._first_pointer_index = 0 + lr._second_pointer_index = 1 + return r + + @property + def arg(self): + return self.args[0] + + def doit(self, **hints): + if hints.get('deep', True): + arg = self.arg.doit(**hints) + result = arg._eval_trace() + if result is not None: + return result + else: + return Trace(arg) + else: + # _eval_trace would go too deep here + if isinstance(self.arg, MatrixBase): + return trace(self.arg) + else: + return Trace(self.arg) + + def as_explicit(self): + return Trace(self.arg.as_explicit()).doit() + + def _normalize(self): + # Normalization of trace of matrix products. Use transposition and + # cyclic properties of traces to make sure the arguments of the matrix + # product are sorted and the first argument is not a transposition. + from sympy.matrices.expressions.matmul import MatMul + from sympy.matrices.expressions.transpose import Transpose + trace_arg = self.arg + if isinstance(trace_arg, MatMul): + + def get_arg_key(x): + a = trace_arg.args[x] + if isinstance(a, Transpose): + a = a.arg + return default_sort_key(a) + + indmin = min(range(len(trace_arg.args)), key=get_arg_key) + if isinstance(trace_arg.args[indmin], Transpose): + trace_arg = Transpose(trace_arg).doit() + indmin = min(range(len(trace_arg.args)), key=lambda x: default_sort_key(trace_arg.args[x])) + trace_arg = MatMul.fromiter(trace_arg.args[indmin:] + trace_arg.args[:indmin]) + return Trace(trace_arg) + return self + + def _eval_rewrite_as_Sum(self, expr, **kwargs): + from sympy.concrete.summations import Sum + i = uniquely_named_symbol('i', [expr]) + s = Sum(self.arg[i, i], (i, 0, self.arg.rows - 1)) + return s.doit() + + +def trace(expr): + """Trace of a Matrix. Sum of the diagonal elements. + + Examples + ======== + + >>> from sympy import trace, Symbol, MatrixSymbol, eye + >>> n = Symbol('n') + >>> X = MatrixSymbol('X', n, n) # A square matrix + >>> trace(2*X) + 2*Trace(X) + >>> trace(eye(3)) + 3 + """ + return Trace(expr).doit() diff --git a/lib/python3.11/site-packages/sympy/matrices/expressions/transpose.py b/lib/python3.11/site-packages/sympy/matrices/expressions/transpose.py new file mode 100644 index 0000000000000000000000000000000000000000..b11f7fc21490aab219420610ca529d81d6995d40 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/expressions/transpose.py @@ -0,0 +1,103 @@ +from sympy.core.basic import Basic +from sympy.matrices.expressions.matexpr import MatrixExpr + + +class Transpose(MatrixExpr): + """ + The transpose of a matrix expression. + + This is a symbolic object that simply stores its argument without + evaluating it. To actually compute the transpose, use the ``transpose()`` + function, or the ``.T`` attribute of matrices. + + Examples + ======== + + >>> from sympy import MatrixSymbol, Transpose, transpose + >>> A = MatrixSymbol('A', 3, 5) + >>> B = MatrixSymbol('B', 5, 3) + >>> Transpose(A) + A.T + >>> A.T == transpose(A) == Transpose(A) + True + >>> Transpose(A*B) + (A*B).T + >>> transpose(A*B) + B.T*A.T + + """ + is_Transpose = True + + def doit(self, **hints): + arg = self.arg + if hints.get('deep', True) and isinstance(arg, Basic): + arg = arg.doit(**hints) + _eval_transpose = getattr(arg, '_eval_transpose', None) + if _eval_transpose is not None: + result = _eval_transpose() + return result if result is not None else Transpose(arg) + else: + return Transpose(arg) + + @property + def arg(self): + return self.args[0] + + @property + def shape(self): + return self.arg.shape[::-1] + + def _entry(self, i, j, expand=False, **kwargs): + return self.arg._entry(j, i, expand=expand, **kwargs) + + def _eval_adjoint(self): + return self.arg.conjugate() + + def _eval_conjugate(self): + return self.arg.adjoint() + + def _eval_transpose(self): + return self.arg + + def _eval_trace(self): + from .trace import Trace + return Trace(self.arg) # Trace(X.T) => Trace(X) + + def _eval_determinant(self): + from sympy.matrices.expressions.determinant import det + return det(self.arg) + + def _eval_derivative(self, x): + # x is a scalar: + return self.arg._eval_derivative(x) + + def _eval_derivative_matrix_lines(self, x): + lines = self.args[0]._eval_derivative_matrix_lines(x) + return [i.transpose() for i in lines] + + +def transpose(expr): + """Matrix transpose""" + return Transpose(expr).doit(deep=False) + + +from sympy.assumptions.ask import ask, Q +from sympy.assumptions.refine import handlers_dict + + +def refine_Transpose(expr, assumptions): + """ + >>> from sympy import MatrixSymbol, Q, assuming, refine + >>> X = MatrixSymbol('X', 2, 2) + >>> X.T + X.T + >>> with assuming(Q.symmetric(X)): + ... print(refine(X.T)) + X + """ + if ask(Q.symmetric(expr), assumptions): + return expr.arg + + return expr + +handlers_dict['Transpose'] = refine_Transpose diff --git a/lib/python3.11/site-packages/sympy/matrices/graph.py b/lib/python3.11/site-packages/sympy/matrices/graph.py new file mode 100644 index 0000000000000000000000000000000000000000..4c6356db884cfcd3c759ada07ac559f43dbcbbcb --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/graph.py @@ -0,0 +1,279 @@ +from sympy.utilities.iterables import \ + flatten, connected_components, strongly_connected_components +from .exceptions import NonSquareMatrixError + + +def _connected_components(M): + """Returns the list of connected vertices of the graph when + a square matrix is viewed as a weighted graph. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([ + ... [66, 0, 0, 68, 0, 0, 0, 0, 67], + ... [0, 55, 0, 0, 0, 0, 54, 53, 0], + ... [0, 0, 0, 0, 1, 2, 0, 0, 0], + ... [86, 0, 0, 88, 0, 0, 0, 0, 87], + ... [0, 0, 10, 0, 11, 12, 0, 0, 0], + ... [0, 0, 20, 0, 21, 22, 0, 0, 0], + ... [0, 45, 0, 0, 0, 0, 44, 43, 0], + ... [0, 35, 0, 0, 0, 0, 34, 33, 0], + ... [76, 0, 0, 78, 0, 0, 0, 0, 77]]) + >>> A.connected_components() + [[0, 3, 8], [1, 6, 7], [2, 4, 5]] + + Notes + ===== + + Even if any symbolic elements of the matrix can be indeterminate + to be zero mathematically, this only takes the account of the + structural aspect of the matrix, so they will considered to be + nonzero. + """ + if not M.is_square: + raise NonSquareMatrixError + + V = range(M.rows) + E = sorted(M.todok().keys()) + return connected_components((V, E)) + + +def _strongly_connected_components(M): + """Returns the list of strongly connected vertices of the graph when + a square matrix is viewed as a weighted graph. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([ + ... [44, 0, 0, 0, 43, 0, 45, 0, 0], + ... [0, 66, 62, 61, 0, 68, 0, 60, 67], + ... [0, 0, 22, 21, 0, 0, 0, 20, 0], + ... [0, 0, 12, 11, 0, 0, 0, 10, 0], + ... [34, 0, 0, 0, 33, 0, 35, 0, 0], + ... [0, 86, 82, 81, 0, 88, 0, 80, 87], + ... [54, 0, 0, 0, 53, 0, 55, 0, 0], + ... [0, 0, 2, 1, 0, 0, 0, 0, 0], + ... [0, 76, 72, 71, 0, 78, 0, 70, 77]]) + >>> A.strongly_connected_components() + [[0, 4, 6], [2, 3, 7], [1, 5, 8]] + """ + if not M.is_square: + raise NonSquareMatrixError + + # RepMatrix uses the more efficient DomainMatrix.scc() method + rep = getattr(M, '_rep', None) + if rep is not None: + return rep.scc() + + V = range(M.rows) + E = sorted(M.todok().keys()) + return strongly_connected_components((V, E)) + + +def _connected_components_decomposition(M): + """Decomposes a square matrix into block diagonal form only + using the permutations. + + Explanation + =========== + + The decomposition is in a form of $A = P^{-1} B P$ where $P$ is a + permutation matrix and $B$ is a block diagonal matrix. + + Returns + ======= + + P, B : PermutationMatrix, BlockDiagMatrix + *P* is a permutation matrix for the similarity transform + as in the explanation. And *B* is the block diagonal matrix of + the result of the permutation. + + If you would like to get the diagonal blocks from the + BlockDiagMatrix, see + :meth:`~sympy.matrices.expressions.blockmatrix.BlockDiagMatrix.get_diag_blocks`. + + Examples + ======== + + >>> from sympy import Matrix, pprint + >>> A = Matrix([ + ... [66, 0, 0, 68, 0, 0, 0, 0, 67], + ... [0, 55, 0, 0, 0, 0, 54, 53, 0], + ... [0, 0, 0, 0, 1, 2, 0, 0, 0], + ... [86, 0, 0, 88, 0, 0, 0, 0, 87], + ... [0, 0, 10, 0, 11, 12, 0, 0, 0], + ... [0, 0, 20, 0, 21, 22, 0, 0, 0], + ... [0, 45, 0, 0, 0, 0, 44, 43, 0], + ... [0, 35, 0, 0, 0, 0, 34, 33, 0], + ... [76, 0, 0, 78, 0, 0, 0, 0, 77]]) + + >>> P, B = A.connected_components_decomposition() + >>> pprint(P) + PermutationMatrix((1 3)(2 8 5 7 4 6)) + >>> pprint(B) + [[66 68 67] ] + [[ ] ] + [[86 88 87] 0 0 ] + [[ ] ] + [[76 78 77] ] + [ ] + [ [55 54 53] ] + [ [ ] ] + [ 0 [45 44 43] 0 ] + [ [ ] ] + [ [35 34 33] ] + [ ] + [ [0 1 2 ]] + [ [ ]] + [ 0 0 [10 11 12]] + [ [ ]] + [ [20 21 22]] + + >>> P = P.as_explicit() + >>> B = B.as_explicit() + >>> P.T*B*P == A + True + + Notes + ===== + + This problem corresponds to the finding of the connected components + of a graph, when a matrix is viewed as a weighted graph. + """ + from sympy.combinatorics.permutations import Permutation + from sympy.matrices.expressions.blockmatrix import BlockDiagMatrix + from sympy.matrices.expressions.permutation import PermutationMatrix + + iblocks = M.connected_components() + + p = Permutation(flatten(iblocks)) + P = PermutationMatrix(p) + + blocks = [] + for b in iblocks: + blocks.append(M[b, b]) + B = BlockDiagMatrix(*blocks) + return P, B + + +def _strongly_connected_components_decomposition(M, lower=True): + """Decomposes a square matrix into block triangular form only + using the permutations. + + Explanation + =========== + + The decomposition is in a form of $A = P^{-1} B P$ where $P$ is a + permutation matrix and $B$ is a block diagonal matrix. + + Parameters + ========== + + lower : bool + Makes $B$ lower block triangular when ``True``. + Otherwise, makes $B$ upper block triangular. + + Returns + ======= + + P, B : PermutationMatrix, BlockMatrix + *P* is a permutation matrix for the similarity transform + as in the explanation. And *B* is the block triangular matrix of + the result of the permutation. + + Examples + ======== + + >>> from sympy import Matrix, pprint + >>> A = Matrix([ + ... [44, 0, 0, 0, 43, 0, 45, 0, 0], + ... [0, 66, 62, 61, 0, 68, 0, 60, 67], + ... [0, 0, 22, 21, 0, 0, 0, 20, 0], + ... [0, 0, 12, 11, 0, 0, 0, 10, 0], + ... [34, 0, 0, 0, 33, 0, 35, 0, 0], + ... [0, 86, 82, 81, 0, 88, 0, 80, 87], + ... [54, 0, 0, 0, 53, 0, 55, 0, 0], + ... [0, 0, 2, 1, 0, 0, 0, 0, 0], + ... [0, 76, 72, 71, 0, 78, 0, 70, 77]]) + + A lower block triangular decomposition: + + >>> P, B = A.strongly_connected_components_decomposition() + >>> pprint(P) + PermutationMatrix((8)(1 4 3 2 6)(5 7)) + >>> pprint(B) + [[44 43 45] [0 0 0] [0 0 0] ] + [[ ] [ ] [ ] ] + [[34 33 35] [0 0 0] [0 0 0] ] + [[ ] [ ] [ ] ] + [[54 53 55] [0 0 0] [0 0 0] ] + [ ] + [ [0 0 0] [22 21 20] [0 0 0] ] + [ [ ] [ ] [ ] ] + [ [0 0 0] [12 11 10] [0 0 0] ] + [ [ ] [ ] [ ] ] + [ [0 0 0] [2 1 0 ] [0 0 0] ] + [ ] + [ [0 0 0] [62 61 60] [66 68 67]] + [ [ ] [ ] [ ]] + [ [0 0 0] [82 81 80] [86 88 87]] + [ [ ] [ ] [ ]] + [ [0 0 0] [72 71 70] [76 78 77]] + + >>> P = P.as_explicit() + >>> B = B.as_explicit() + >>> P.T * B * P == A + True + + An upper block triangular decomposition: + + >>> P, B = A.strongly_connected_components_decomposition(lower=False) + >>> pprint(P) + PermutationMatrix((0 1 5 7 4 3 2 8 6)) + >>> pprint(B) + [[66 68 67] [62 61 60] [0 0 0] ] + [[ ] [ ] [ ] ] + [[86 88 87] [82 81 80] [0 0 0] ] + [[ ] [ ] [ ] ] + [[76 78 77] [72 71 70] [0 0 0] ] + [ ] + [ [0 0 0] [22 21 20] [0 0 0] ] + [ [ ] [ ] [ ] ] + [ [0 0 0] [12 11 10] [0 0 0] ] + [ [ ] [ ] [ ] ] + [ [0 0 0] [2 1 0 ] [0 0 0] ] + [ ] + [ [0 0 0] [0 0 0] [44 43 45]] + [ [ ] [ ] [ ]] + [ [0 0 0] [0 0 0] [34 33 35]] + [ [ ] [ ] [ ]] + [ [0 0 0] [0 0 0] [54 53 55]] + + >>> P = P.as_explicit() + >>> B = B.as_explicit() + >>> P.T * B * P == A + True + """ + from sympy.combinatorics.permutations import Permutation + from sympy.matrices.expressions.blockmatrix import BlockMatrix + from sympy.matrices.expressions.permutation import PermutationMatrix + + iblocks = M.strongly_connected_components() + if not lower: + iblocks = list(reversed(iblocks)) + + p = Permutation(flatten(iblocks)) + P = PermutationMatrix(p) + + rows = [] + for a in iblocks: + cols = [] + for b in iblocks: + cols.append(M[a, b]) + rows.append(cols) + B = BlockMatrix(rows) + return P, B diff --git a/lib/python3.11/site-packages/sympy/matrices/immutable.py b/lib/python3.11/site-packages/sympy/matrices/immutable.py new file mode 100644 index 0000000000000000000000000000000000000000..7ec2174bf1c785e1a4698e1b55078d300e62dafe --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/immutable.py @@ -0,0 +1,196 @@ +from mpmath.matrices.matrices import _matrix + +from sympy.core import Basic, Dict, Tuple +from sympy.core.numbers import Integer +from sympy.core.cache import cacheit +from sympy.core.sympify import _sympy_converter as sympify_converter, _sympify +from sympy.matrices.dense import DenseMatrix +from sympy.matrices.expressions import MatrixExpr +from sympy.matrices.matrixbase import MatrixBase +from sympy.matrices.repmatrix import RepMatrix +from sympy.matrices.sparse import SparseRepMatrix +from sympy.multipledispatch import dispatch + + +def sympify_matrix(arg): + return arg.as_immutable() + + +sympify_converter[MatrixBase] = sympify_matrix + + +def sympify_mpmath_matrix(arg): + mat = [_sympify(x) for x in arg] + return ImmutableDenseMatrix(arg.rows, arg.cols, mat) + + +sympify_converter[_matrix] = sympify_mpmath_matrix + + +class ImmutableRepMatrix(RepMatrix, MatrixExpr): # type: ignore + """Immutable matrix based on RepMatrix + + Uses DomainMAtrix as the internal representation. + """ + + # + # This is a subclass of RepMatrix that adds/overrides some methods to make + # the instances Basic and immutable. ImmutableRepMatrix is a superclass for + # both ImmutableDenseMatrix and ImmutableSparseMatrix. + # + + def __new__(cls, *args, **kwargs): + return cls._new(*args, **kwargs) + + __hash__ = MatrixExpr.__hash__ + + def copy(self): + return self + + @property + def cols(self): + return self._cols + + @property + def rows(self): + return self._rows + + @property + def shape(self): + return self._rows, self._cols + + def as_immutable(self): + return self + + def _entry(self, i, j, **kwargs): + return self[i, j] + + def __setitem__(self, *args): + raise TypeError("Cannot set values of {}".format(self.__class__)) + + def is_diagonalizable(self, reals_only=False, **kwargs): + return super().is_diagonalizable( + reals_only=reals_only, **kwargs) + + is_diagonalizable.__doc__ = SparseRepMatrix.is_diagonalizable.__doc__ + is_diagonalizable = cacheit(is_diagonalizable) + + def analytic_func(self, f, x): + return self.as_mutable().analytic_func(f, x).as_immutable() + + +class ImmutableDenseMatrix(DenseMatrix, ImmutableRepMatrix): # type: ignore + """Create an immutable version of a matrix. + + Examples + ======== + + >>> from sympy import eye, ImmutableMatrix + >>> ImmutableMatrix(eye(3)) + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> _[0, 0] = 42 + Traceback (most recent call last): + ... + TypeError: Cannot set values of ImmutableDenseMatrix + """ + + # MatrixExpr is set as NotIterable, but we want explicit matrices to be + # iterable + _iterable = True + _class_priority = 8 + _op_priority = 10.001 + + @classmethod + def _new(cls, *args, **kwargs): + if len(args) == 1 and isinstance(args[0], ImmutableDenseMatrix): + return args[0] + if kwargs.get('copy', True) is False: + if len(args) != 3: + raise TypeError("'copy=False' requires a matrix be initialized as rows,cols,[list]") + rows, cols, flat_list = args + else: + rows, cols, flat_list = cls._handle_creation_inputs(*args, **kwargs) + flat_list = list(flat_list) # create a shallow copy + + rep = cls._flat_list_to_DomainMatrix(rows, cols, flat_list) + + return cls._fromrep(rep) + + @classmethod + def _fromrep(cls, rep): + rows, cols = rep.shape + flat_list = rep.to_sympy().to_list_flat() + obj = Basic.__new__(cls, + Integer(rows), + Integer(cols), + Tuple(*flat_list, sympify=False)) + obj._rows = rows + obj._cols = cols + obj._rep = rep + return obj + + +# make sure ImmutableDenseMatrix is aliased as ImmutableMatrix +ImmutableMatrix = ImmutableDenseMatrix + + +class ImmutableSparseMatrix(SparseRepMatrix, ImmutableRepMatrix): # type:ignore + """Create an immutable version of a sparse matrix. + + Examples + ======== + + >>> from sympy import eye, ImmutableSparseMatrix + >>> ImmutableSparseMatrix(1, 1, {}) + Matrix([[0]]) + >>> ImmutableSparseMatrix(eye(3)) + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> _[0, 0] = 42 + Traceback (most recent call last): + ... + TypeError: Cannot set values of ImmutableSparseMatrix + >>> _.shape + (3, 3) + """ + is_Matrix = True + _class_priority = 9 + + @classmethod + def _new(cls, *args, **kwargs): + rows, cols, smat = cls._handle_creation_inputs(*args, **kwargs) + + rep = cls._smat_to_DomainMatrix(rows, cols, smat) + + return cls._fromrep(rep) + + @classmethod + def _fromrep(cls, rep): + rows, cols = rep.shape + smat = rep.to_sympy().to_dok() + obj = Basic.__new__(cls, Integer(rows), Integer(cols), Dict(smat)) + obj._rows = rows + obj._cols = cols + obj._rep = rep + return obj + + +@dispatch(ImmutableDenseMatrix, ImmutableDenseMatrix) +def _eval_is_eq(lhs, rhs): # noqa:F811 + """Helper method for Equality with matrices.sympy. + + Relational automatically converts matrices to ImmutableDenseMatrix + instances, so this method only applies here. Returns True if the + matrices are definitively the same, False if they are definitively + different, and None if undetermined (e.g. if they contain Symbols). + Returning None triggers default handling of Equalities. + + """ + if lhs.shape != rhs.shape: + return False + return (lhs - rhs).is_zero_matrix diff --git a/lib/python3.11/site-packages/sympy/matrices/inverse.py b/lib/python3.11/site-packages/sympy/matrices/inverse.py new file mode 100644 index 0000000000000000000000000000000000000000..61d9e12edf013d2f5555d61786343aa3840edfd3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/inverse.py @@ -0,0 +1,524 @@ +from sympy.polys.matrices.exceptions import DMNonInvertibleMatrixError +from sympy.polys.domains import EX + +from .exceptions import MatrixError, NonSquareMatrixError, NonInvertibleMatrixError +from .utilities import _iszero + + +def _pinv_full_rank(M): + """Subroutine for full row or column rank matrices. + + For full row rank matrices, inverse of ``A * A.H`` Exists. + For full column rank matrices, inverse of ``A.H * A`` Exists. + + This routine can apply for both cases by checking the shape + and have small decision. + """ + + if M.is_zero_matrix: + return M.H + + if M.rows >= M.cols: + return M.H.multiply(M).inv().multiply(M.H) + else: + return M.H.multiply(M.multiply(M.H).inv()) + +def _pinv_rank_decomposition(M): + """Subroutine for rank decomposition + + With rank decompositions, `A` can be decomposed into two full- + rank matrices, and each matrix can take pseudoinverse + individually. + """ + + if M.is_zero_matrix: + return M.H + + B, C = M.rank_decomposition() + + Bp = _pinv_full_rank(B) + Cp = _pinv_full_rank(C) + + return Cp.multiply(Bp) + +def _pinv_diagonalization(M): + """Subroutine using diagonalization + + This routine can sometimes fail if SymPy's eigenvalue + computation is not reliable. + """ + + if M.is_zero_matrix: + return M.H + + A = M + AH = M.H + + try: + if M.rows >= M.cols: + P, D = AH.multiply(A).diagonalize(normalize=True) + D_pinv = D.applyfunc(lambda x: 0 if _iszero(x) else 1 / x) + + return P.multiply(D_pinv).multiply(P.H).multiply(AH) + + else: + P, D = A.multiply(AH).diagonalize( + normalize=True) + D_pinv = D.applyfunc(lambda x: 0 if _iszero(x) else 1 / x) + + return AH.multiply(P).multiply(D_pinv).multiply(P.H) + + except MatrixError: + raise NotImplementedError( + 'pinv for rank-deficient matrices where ' + 'diagonalization of A.H*A fails is not supported yet.') + +def _pinv(M, method='RD'): + """Calculate the Moore-Penrose pseudoinverse of the matrix. + + The Moore-Penrose pseudoinverse exists and is unique for any matrix. + If the matrix is invertible, the pseudoinverse is the same as the + inverse. + + Parameters + ========== + + method : String, optional + Specifies the method for computing the pseudoinverse. + + If ``'RD'``, Rank-Decomposition will be used. + + If ``'ED'``, Diagonalization will be used. + + Examples + ======== + + Computing pseudoinverse by rank decomposition : + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> A.pinv() + Matrix([ + [-17/18, 4/9], + [ -1/9, 1/9], + [ 13/18, -2/9]]) + + Computing pseudoinverse by diagonalization : + + >>> B = A.pinv(method='ED') + >>> B.simplify() + >>> B + Matrix([ + [-17/18, 4/9], + [ -1/9, 1/9], + [ 13/18, -2/9]]) + + See Also + ======== + + inv + pinv_solve + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse + + """ + + # Trivial case: pseudoinverse of all-zero matrix is its transpose. + if M.is_zero_matrix: + return M.H + + if method == 'RD': + return _pinv_rank_decomposition(M) + elif method == 'ED': + return _pinv_diagonalization(M) + else: + raise ValueError('invalid pinv method %s' % repr(method)) + + +def _verify_invertible(M, iszerofunc=_iszero): + """Initial check to see if a matrix is invertible. Raises or returns + determinant for use in _inv_ADJ.""" + + if not M.is_square: + raise NonSquareMatrixError("A Matrix must be square to invert.") + + d = M.det(method='berkowitz') + zero = d.equals(0) + + if zero is None: # if equals() can't decide, will rref be able to? + ok = M.rref(simplify=True)[0] + zero = any(iszerofunc(ok[j, j]) for j in range(ok.rows)) + + if zero: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + return d + +def _inv_ADJ(M, iszerofunc=_iszero): + """Calculates the inverse using the adjugate matrix and a determinant. + + See Also + ======== + + inv + inverse_GE + inverse_LU + inverse_CH + inverse_LDL + """ + + d = _verify_invertible(M, iszerofunc=iszerofunc) + + return M.adjugate() / d + +def _inv_GE(M, iszerofunc=_iszero): + """Calculates the inverse using Gaussian elimination. + + See Also + ======== + + inv + inverse_ADJ + inverse_LU + inverse_CH + inverse_LDL + """ + + from .dense import Matrix + + if not M.is_square: + raise NonSquareMatrixError("A Matrix must be square to invert.") + + big = Matrix.hstack(M.as_mutable(), Matrix.eye(M.rows)) + red = big.rref(iszerofunc=iszerofunc, simplify=True)[0] + + if any(iszerofunc(red[j, j]) for j in range(red.rows)): + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + return M._new(red[:, big.rows:]) + +def _inv_LU(M, iszerofunc=_iszero): + """Calculates the inverse using LU decomposition. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_CH + inverse_LDL + """ + + if not M.is_square: + raise NonSquareMatrixError("A Matrix must be square to invert.") + if M.free_symbols: + _verify_invertible(M, iszerofunc=iszerofunc) + + return M.LUsolve(M.eye(M.rows), iszerofunc=_iszero) + +def _inv_CH(M, iszerofunc=_iszero): + """Calculates the inverse using cholesky decomposition. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_LU + inverse_LDL + """ + + _verify_invertible(M, iszerofunc=iszerofunc) + + return M.cholesky_solve(M.eye(M.rows)) + +def _inv_LDL(M, iszerofunc=_iszero): + """Calculates the inverse using LDL decomposition. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_LU + inverse_CH + """ + + _verify_invertible(M, iszerofunc=iszerofunc) + + return M.LDLsolve(M.eye(M.rows)) + +def _inv_QR(M, iszerofunc=_iszero): + """Calculates the inverse using QR decomposition. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_CH + inverse_LDL + """ + + _verify_invertible(M, iszerofunc=iszerofunc) + + return M.QRsolve(M.eye(M.rows)) + +def _try_DM(M, use_EX=False): + """Try to convert a matrix to a ``DomainMatrix``.""" + dM = M.to_DM() + K = dM.domain + + # Return DomainMatrix if a domain is found. Only use EX if use_EX=True. + if not use_EX and K.is_EXRAW: + return None + elif K.is_EXRAW: + return dM.convert_to(EX) + else: + return dM + + +def _use_exact_domain(dom): + """Check whether to convert to an exact domain.""" + # DomainMatrix can handle RR and CC with partial pivoting. Other inexact + # domains like RR[a,b,...] can only be handled by converting to an exact + # domain like QQ[a,b,...] + if dom.is_RR or dom.is_CC: + return False + else: + return not dom.is_Exact + + +def _inv_DM(dM, cancel=True): + """Calculates the inverse using ``DomainMatrix``. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_CH + inverse_LDL + sympy.polys.matrices.domainmatrix.DomainMatrix.inv + """ + m, n = dM.shape + dom = dM.domain + + if m != n: + raise NonSquareMatrixError("A Matrix must be square to invert.") + + # Convert RR[a,b,...] to QQ[a,b,...] + use_exact = _use_exact_domain(dom) + + if use_exact: + dom_exact = dom.get_exact() + dM = dM.convert_to(dom_exact) + + try: + dMi, den = dM.inv_den() + except DMNonInvertibleMatrixError: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + if use_exact: + dMi = dMi.convert_to(dom) + den = dom.convert_from(den, dom_exact) + + if cancel: + # Convert to field and cancel with the denominator. + if not dMi.domain.is_Field: + dMi = dMi.to_field() + Mi = (dMi / den).to_Matrix() + else: + # Convert to Matrix and divide without cancelling + Mi = dMi.to_Matrix() / dMi.domain.to_sympy(den) + + return Mi + +def _inv_block(M, iszerofunc=_iszero): + """Calculates the inverse using BLOCKWISE inversion. + + See Also + ======== + + inv + inverse_ADJ + inverse_GE + inverse_CH + inverse_LDL + """ + from sympy.matrices.expressions.blockmatrix import BlockMatrix + i = M.shape[0] + if i <= 20 : + return M.inv(method="LU", iszerofunc=_iszero) + A = M[:i // 2, :i //2] + B = M[:i // 2, i // 2:] + C = M[i // 2:, :i // 2] + D = M[i // 2:, i // 2:] + try: + D_inv = _inv_block(D) + except NonInvertibleMatrixError: + return M.inv(method="LU", iszerofunc=_iszero) + B_D_i = B*D_inv + BDC = B_D_i*C + A_n = A - BDC + try: + A_n = _inv_block(A_n) + except NonInvertibleMatrixError: + return M.inv(method="LU", iszerofunc=_iszero) + B_n = -A_n*B_D_i + dc = D_inv*C + C_n = -dc*A_n + D_n = D_inv + dc*-B_n + nn = BlockMatrix([[A_n, B_n], [C_n, D_n]]).as_explicit() + return nn + +def _inv(M, method=None, iszerofunc=_iszero, try_block_diag=False): + """ + Return the inverse of a matrix using the method indicated. The default + is DM if a suitable domain is found or otherwise GE for dense matrices + LDL for sparse matrices. + + Parameters + ========== + + method : ('DM', 'DMNC', 'GE', 'LU', 'ADJ', 'CH', 'LDL', 'QR') + + iszerofunc : function, optional + Zero-testing function to use. + + try_block_diag : bool, optional + If True then will try to form block diagonal matrices using the + method get_diag_blocks(), invert these individually, and then + reconstruct the full inverse matrix. + + Examples + ======== + + >>> from sympy import SparseMatrix, Matrix + >>> A = SparseMatrix([ + ... [ 2, -1, 0], + ... [-1, 2, -1], + ... [ 0, 0, 2]]) + >>> A.inv('CH') + Matrix([ + [2/3, 1/3, 1/6], + [1/3, 2/3, 1/3], + [ 0, 0, 1/2]]) + >>> A.inv(method='LDL') # use of 'method=' is optional + Matrix([ + [2/3, 1/3, 1/6], + [1/3, 2/3, 1/3], + [ 0, 0, 1/2]]) + >>> A * _ + Matrix([ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + >>> A = Matrix(A) + >>> A.inv('CH') + Matrix([ + [2/3, 1/3, 1/6], + [1/3, 2/3, 1/3], + [ 0, 0, 1/2]]) + >>> A.inv('ADJ') == A.inv('GE') == A.inv('LU') == A.inv('CH') == A.inv('LDL') == A.inv('QR') + True + + Notes + ===== + + According to the ``method`` keyword, it calls the appropriate method: + + DM .... Use DomainMatrix ``inv_den`` method + DMNC .... Use DomainMatrix ``inv_den`` method without cancellation + GE .... inverse_GE(); default for dense matrices + LU .... inverse_LU() + ADJ ... inverse_ADJ() + CH ... inverse_CH() + LDL ... inverse_LDL(); default for sparse matrices + QR ... inverse_QR() + + Note, the GE and LU methods may require the matrix to be simplified + before it is inverted in order to properly detect zeros during + pivoting. In difficult cases a custom zero detection function can + be provided by setting the ``iszerofunc`` argument to a function that + should return True if its argument is zero. The ADJ routine computes + the determinant and uses that to detect singular matrices in addition + to testing for zeros on the diagonal. + + See Also + ======== + + inverse_ADJ + inverse_GE + inverse_LU + inverse_CH + inverse_LDL + + Raises + ====== + + ValueError + If the determinant of the matrix is zero. + """ + + from sympy.matrices import diag, SparseMatrix + + if not M.is_square: + raise NonSquareMatrixError("A Matrix must be square to invert.") + + if try_block_diag: + blocks = M.get_diag_blocks() + r = [] + + for block in blocks: + r.append(block.inv(method=method, iszerofunc=iszerofunc)) + + return diag(*r) + + # Default: Use DomainMatrix if the domain is not EX. + # If DM is requested explicitly then use it even if the domain is EX. + if method is None and iszerofunc is _iszero: + dM = _try_DM(M, use_EX=False) + if dM is not None: + method = 'DM' + elif method in ("DM", "DMNC"): + dM = _try_DM(M, use_EX=True) + + # A suitable domain was not found, fall back to GE for dense matrices + # and LDL for sparse matrices. + if method is None: + if isinstance(M, SparseMatrix): + method = 'LDL' + else: + method = 'GE' + + if method == "DM": + rv = _inv_DM(dM) + elif method == "DMNC": + rv = _inv_DM(dM, cancel=False) + elif method == "GE": + rv = M.inverse_GE(iszerofunc=iszerofunc) + elif method == "LU": + rv = M.inverse_LU(iszerofunc=iszerofunc) + elif method == "ADJ": + rv = M.inverse_ADJ(iszerofunc=iszerofunc) + elif method == "CH": + rv = M.inverse_CH(iszerofunc=iszerofunc) + elif method == "LDL": + rv = M.inverse_LDL(iszerofunc=iszerofunc) + elif method == "QR": + rv = M.inverse_QR(iszerofunc=iszerofunc) + elif method == "BLOCK": + rv = M.inverse_BLOCK(iszerofunc=iszerofunc) + else: + raise ValueError("Inversion method unrecognized") + + return M._new(rv) diff --git a/lib/python3.11/site-packages/sympy/matrices/kind.py b/lib/python3.11/site-packages/sympy/matrices/kind.py new file mode 100644 index 0000000000000000000000000000000000000000..f9f53ffe16f7cbde60213e49071a2a74e80e5c6c --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/kind.py @@ -0,0 +1,97 @@ +# sympy.matrices.kind + +from sympy.core.kind import Kind, _NumberKind, NumberKind +from sympy.core.mul import Mul + + +class MatrixKind(Kind): + """ + Kind for all matrices in SymPy. + + Basic class for this kind is ``MatrixBase`` and ``MatrixExpr``, + but any expression representing the matrix can have this. + + Parameters + ========== + + element_kind : Kind + Kind of the element. Default is + :class:`sympy.core.kind.NumberKind`, + which means that the matrix contains only numbers. + + Examples + ======== + + Any instance of matrix class has kind ``MatrixKind``: + + >>> from sympy import MatrixSymbol + >>> A = MatrixSymbol('A', 2, 2) + >>> A.kind + MatrixKind(NumberKind) + + An expression representing a matrix may not be an instance of + the Matrix class, but it will have kind ``MatrixKind``: + + >>> from sympy import MatrixExpr, Integral + >>> from sympy.abc import x + >>> intM = Integral(A, x) + >>> isinstance(intM, MatrixExpr) + False + >>> intM.kind + MatrixKind(NumberKind) + + Use ``isinstance()`` to check for ``MatrixKind`` without specifying the + element kind. Use ``is`` to check the kind including the element kind: + + >>> from sympy import Matrix + >>> from sympy.core import NumberKind + >>> from sympy.matrices import MatrixKind + >>> M = Matrix([1, 2]) + >>> isinstance(M.kind, MatrixKind) + True + >>> M.kind is MatrixKind(NumberKind) + True + + See Also + ======== + + sympy.core.kind.NumberKind + sympy.core.kind.UndefinedKind + sympy.core.containers.TupleKind + sympy.sets.sets.SetKind + + """ + def __new__(cls, element_kind=NumberKind): + obj = super().__new__(cls, element_kind) + obj.element_kind = element_kind + return obj + + def __repr__(self): + return "MatrixKind(%s)" % self.element_kind + + +@Mul._kind_dispatcher.register(_NumberKind, MatrixKind) +def num_mat_mul(k1, k2): + """ + Return MatrixKind. The element kind is selected by recursive dispatching. + Do not need to dispatch in reversed order because KindDispatcher + searches for this automatically. + """ + # Deal with Mul._kind_dispatcher's commutativity + # XXX: this function is called with either k1 or k2 as MatrixKind because + # the Mul kind dispatcher is commutative. Maybe it shouldn't be. Need to + # swap the args here because NumberKind does not have an element_kind + # attribute. + if not isinstance(k2, MatrixKind): + k1, k2 = k2, k1 + elemk = Mul._kind_dispatcher(k1, k2.element_kind) + return MatrixKind(elemk) + + +@Mul._kind_dispatcher.register(MatrixKind, MatrixKind) +def mat_mat_mul(k1, k2): + """ + Return MatrixKind. The element kind is selected by recursive dispatching. + """ + elemk = Mul._kind_dispatcher(k1.element_kind, k2.element_kind) + return MatrixKind(elemk) diff --git a/lib/python3.11/site-packages/sympy/matrices/matrices.py b/lib/python3.11/site-packages/sympy/matrices/matrices.py new file mode 100644 index 0000000000000000000000000000000000000000..fed41a626cb395ac0529071317630d853e0d3a96 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/matrices.py @@ -0,0 +1,687 @@ +# +# A module consisting of deprecated matrix classes. New code should not be +# added here. +# +from sympy.core.basic import Basic +from sympy.core.symbol import Dummy + +from .common import MatrixCommon + +from .exceptions import NonSquareMatrixError + +from .utilities import _iszero, _is_zero_after_expand_mul, _simplify + +from .determinant import ( + _find_reasonable_pivot, _find_reasonable_pivot_naive, + _adjugate, _charpoly, _cofactor, _cofactor_matrix, _per, + _det, _det_bareiss, _det_berkowitz, _det_bird, _det_laplace, _det_LU, + _minor, _minor_submatrix) + +from .reductions import _is_echelon, _echelon_form, _rank, _rref +from .subspaces import _columnspace, _nullspace, _rowspace, _orthogonalize + +from .eigen import ( + _eigenvals, _eigenvects, + _bidiagonalize, _bidiagonal_decomposition, + _is_diagonalizable, _diagonalize, + _is_positive_definite, _is_positive_semidefinite, + _is_negative_definite, _is_negative_semidefinite, _is_indefinite, + _jordan_form, _left_eigenvects, _singular_values) + + +# This class was previously defined in this module, but was moved to +# sympy.matrices.matrixbase. We import it here for backwards compatibility in +# case someone was importing it from here. +from .matrixbase import MatrixBase + + +__doctest_requires__ = { + ('MatrixEigen.is_indefinite', + 'MatrixEigen.is_negative_definite', + 'MatrixEigen.is_negative_semidefinite', + 'MatrixEigen.is_positive_definite', + 'MatrixEigen.is_positive_semidefinite'): ['matplotlib'], +} + + +class MatrixDeterminant(MatrixCommon): + """Provides basic matrix determinant operations. Should not be instantiated + directly. See ``determinant.py`` for their implementations.""" + + def _eval_det_bareiss(self, iszerofunc=_is_zero_after_expand_mul): + return _det_bareiss(self, iszerofunc=iszerofunc) + + def _eval_det_berkowitz(self): + return _det_berkowitz(self) + + def _eval_det_lu(self, iszerofunc=_iszero, simpfunc=None): + return _det_LU(self, iszerofunc=iszerofunc, simpfunc=simpfunc) + + def _eval_det_bird(self): + return _det_bird(self) + + def _eval_det_laplace(self): + return _det_laplace(self) + + def _eval_determinant(self): # for expressions.determinant.Determinant + return _det(self) + + def adjugate(self, method="berkowitz"): + return _adjugate(self, method=method) + + def charpoly(self, x='lambda', simplify=_simplify): + return _charpoly(self, x=x, simplify=simplify) + + def cofactor(self, i, j, method="berkowitz"): + return _cofactor(self, i, j, method=method) + + def cofactor_matrix(self, method="berkowitz"): + return _cofactor_matrix(self, method=method) + + def det(self, method="bareiss", iszerofunc=None): + return _det(self, method=method, iszerofunc=iszerofunc) + + def per(self): + return _per(self) + + def minor(self, i, j, method="berkowitz"): + return _minor(self, i, j, method=method) + + def minor_submatrix(self, i, j): + return _minor_submatrix(self, i, j) + + _find_reasonable_pivot.__doc__ = _find_reasonable_pivot.__doc__ + _find_reasonable_pivot_naive.__doc__ = _find_reasonable_pivot_naive.__doc__ + _eval_det_bareiss.__doc__ = _det_bareiss.__doc__ + _eval_det_berkowitz.__doc__ = _det_berkowitz.__doc__ + _eval_det_bird.__doc__ = _det_bird.__doc__ + _eval_det_laplace.__doc__ = _det_laplace.__doc__ + _eval_det_lu.__doc__ = _det_LU.__doc__ + _eval_determinant.__doc__ = _det.__doc__ + adjugate.__doc__ = _adjugate.__doc__ + charpoly.__doc__ = _charpoly.__doc__ + cofactor.__doc__ = _cofactor.__doc__ + cofactor_matrix.__doc__ = _cofactor_matrix.__doc__ + det.__doc__ = _det.__doc__ + per.__doc__ = _per.__doc__ + minor.__doc__ = _minor.__doc__ + minor_submatrix.__doc__ = _minor_submatrix.__doc__ + + +class MatrixReductions(MatrixDeterminant): + """Provides basic matrix row/column operations. Should not be instantiated + directly. See ``reductions.py`` for some of their implementations.""" + + def echelon_form(self, iszerofunc=_iszero, simplify=False, with_pivots=False): + return _echelon_form(self, iszerofunc=iszerofunc, simplify=simplify, + with_pivots=with_pivots) + + @property + def is_echelon(self): + return _is_echelon(self) + + def rank(self, iszerofunc=_iszero, simplify=False): + return _rank(self, iszerofunc=iszerofunc, simplify=simplify) + + def rref_rhs(self, rhs): + """Return reduced row-echelon form of matrix, matrix showing + rhs after reduction steps. ``rhs`` must have the same number + of rows as ``self``. + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> r1, r2 = symbols('r1 r2') + >>> Matrix([[1, 1], [2, 1]]).rref_rhs(Matrix([r1, r2])) + (Matrix([ + [1, 0], + [0, 1]]), Matrix([ + [ -r1 + r2], + [2*r1 - r2]])) + """ + r, _ = _rref(self.hstack(self, self.eye(self.rows), rhs)) + return r[:, :self.cols], r[:, -rhs.cols:] + + def rref(self, iszerofunc=_iszero, simplify=False, pivots=True, + normalize_last=True): + return _rref(self, iszerofunc=iszerofunc, simplify=simplify, + pivots=pivots, normalize_last=normalize_last) + + echelon_form.__doc__ = _echelon_form.__doc__ + is_echelon.__doc__ = _is_echelon.__doc__ + rank.__doc__ = _rank.__doc__ + rref.__doc__ = _rref.__doc__ + + def _normalize_op_args(self, op, col, k, col1, col2, error_str="col"): + """Validate the arguments for a row/column operation. ``error_str`` + can be one of "row" or "col" depending on the arguments being parsed.""" + if op not in ["n->kn", "n<->m", "n->n+km"]: + raise ValueError("Unknown {} operation '{}'. Valid col operations " + "are 'n->kn', 'n<->m', 'n->n+km'".format(error_str, op)) + + # define self_col according to error_str + self_cols = self.cols if error_str == 'col' else self.rows + + # normalize and validate the arguments + if op == "n->kn": + col = col if col is not None else col1 + if col is None or k is None: + raise ValueError("For a {0} operation 'n->kn' you must provide the " + "kwargs `{0}` and `k`".format(error_str)) + if not 0 <= col < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col)) + + elif op == "n<->m": + # we need two cols to swap. It does not matter + # how they were specified, so gather them together and + # remove `None` + cols = {col, k, col1, col2}.difference([None]) + if len(cols) > 2: + # maybe the user left `k` by mistake? + cols = {col, col1, col2}.difference([None]) + if len(cols) != 2: + raise ValueError("For a {0} operation 'n<->m' you must provide the " + "kwargs `{0}1` and `{0}2`".format(error_str)) + col1, col2 = cols + if not 0 <= col1 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col1)) + if not 0 <= col2 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2)) + + elif op == "n->n+km": + col = col1 if col is None else col + col2 = col1 if col2 is None else col2 + if col is None or col2 is None or k is None: + raise ValueError("For a {0} operation 'n->n+km' you must provide the " + "kwargs `{0}`, `k`, and `{0}2`".format(error_str)) + if col == col2: + raise ValueError("For a {0} operation 'n->n+km' `{0}` and `{0}2` must " + "be different.".format(error_str)) + if not 0 <= col < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col)) + if not 0 <= col2 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2)) + + else: + raise ValueError('invalid operation %s' % repr(op)) + + return op, col, k, col1, col2 + + def _eval_col_op_multiply_col_by_const(self, col, k): + def entry(i, j): + if j == col: + return k * self[i, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_col_op_swap(self, col1, col2): + def entry(i, j): + if j == col1: + return self[i, col2] + elif j == col2: + return self[i, col1] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_col_op_add_multiple_to_other_col(self, col, k, col2): + def entry(i, j): + if j == col: + return self[i, j] + k * self[i, col2] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_swap(self, row1, row2): + def entry(i, j): + if i == row1: + return self[row2, j] + elif i == row2: + return self[row1, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_multiply_row_by_const(self, row, k): + def entry(i, j): + if i == row: + return k * self[i, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_add_multiple_to_other_row(self, row, k, row2): + def entry(i, j): + if i == row: + return self[i, j] + k * self[row2, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def elementary_col_op(self, op="n->kn", col=None, k=None, col1=None, col2=None): + """Performs the elementary column operation `op`. + + `op` may be one of + + * ``"n->kn"`` (column n goes to k*n) + * ``"n<->m"`` (swap column n and column m) + * ``"n->n+km"`` (column n goes to column n + k*column m) + + Parameters + ========== + + op : string; the elementary row operation + col : the column to apply the column operation + k : the multiple to apply in the column operation + col1 : one column of a column swap + col2 : second column of a column swap or column "m" in the column operation + "n->n+km" + """ + + op, col, k, col1, col2 = self._normalize_op_args(op, col, k, col1, col2, "col") + + # now that we've validated, we're all good to dispatch + if op == "n->kn": + return self._eval_col_op_multiply_col_by_const(col, k) + if op == "n<->m": + return self._eval_col_op_swap(col1, col2) + if op == "n->n+km": + return self._eval_col_op_add_multiple_to_other_col(col, k, col2) + + def elementary_row_op(self, op="n->kn", row=None, k=None, row1=None, row2=None): + """Performs the elementary row operation `op`. + + `op` may be one of + + * ``"n->kn"`` (row n goes to k*n) + * ``"n<->m"`` (swap row n and row m) + * ``"n->n+km"`` (row n goes to row n + k*row m) + + Parameters + ========== + + op : string; the elementary row operation + row : the row to apply the row operation + k : the multiple to apply in the row operation + row1 : one row of a row swap + row2 : second row of a row swap or row "m" in the row operation + "n->n+km" + """ + + op, row, k, row1, row2 = self._normalize_op_args(op, row, k, row1, row2, "row") + + # now that we've validated, we're all good to dispatch + if op == "n->kn": + return self._eval_row_op_multiply_row_by_const(row, k) + if op == "n<->m": + return self._eval_row_op_swap(row1, row2) + if op == "n->n+km": + return self._eval_row_op_add_multiple_to_other_row(row, k, row2) + + +class MatrixSubspaces(MatrixReductions): + """Provides methods relating to the fundamental subspaces of a matrix. + Should not be instantiated directly. See ``subspaces.py`` for their + implementations.""" + + def columnspace(self, simplify=False): + return _columnspace(self, simplify=simplify) + + def nullspace(self, simplify=False, iszerofunc=_iszero): + return _nullspace(self, simplify=simplify, iszerofunc=iszerofunc) + + def rowspace(self, simplify=False): + return _rowspace(self, simplify=simplify) + + # This is a classmethod but is converted to such later in order to allow + # assignment of __doc__ since that does not work for already wrapped + # classmethods in Python 3.6. + def orthogonalize(cls, *vecs, **kwargs): + return _orthogonalize(cls, *vecs, **kwargs) + + columnspace.__doc__ = _columnspace.__doc__ + nullspace.__doc__ = _nullspace.__doc__ + rowspace.__doc__ = _rowspace.__doc__ + orthogonalize.__doc__ = _orthogonalize.__doc__ + + orthogonalize = classmethod(orthogonalize) # type:ignore + + +class MatrixEigen(MatrixSubspaces): + """Provides basic matrix eigenvalue/vector operations. + Should not be instantiated directly. See ``eigen.py`` for their + implementations.""" + + def eigenvals(self, error_when_incomplete=True, **flags): + return _eigenvals(self, error_when_incomplete=error_when_incomplete, **flags) + + def eigenvects(self, error_when_incomplete=True, iszerofunc=_iszero, **flags): + return _eigenvects(self, error_when_incomplete=error_when_incomplete, + iszerofunc=iszerofunc, **flags) + + def is_diagonalizable(self, reals_only=False, **kwargs): + return _is_diagonalizable(self, reals_only=reals_only, **kwargs) + + def diagonalize(self, reals_only=False, sort=False, normalize=False): + return _diagonalize(self, reals_only=reals_only, sort=sort, + normalize=normalize) + + def bidiagonalize(self, upper=True): + return _bidiagonalize(self, upper=upper) + + def bidiagonal_decomposition(self, upper=True): + return _bidiagonal_decomposition(self, upper=upper) + + @property + def is_positive_definite(self): + return _is_positive_definite(self) + + @property + def is_positive_semidefinite(self): + return _is_positive_semidefinite(self) + + @property + def is_negative_definite(self): + return _is_negative_definite(self) + + @property + def is_negative_semidefinite(self): + return _is_negative_semidefinite(self) + + @property + def is_indefinite(self): + return _is_indefinite(self) + + def jordan_form(self, calc_transform=True, **kwargs): + return _jordan_form(self, calc_transform=calc_transform, **kwargs) + + def left_eigenvects(self, **flags): + return _left_eigenvects(self, **flags) + + def singular_values(self): + return _singular_values(self) + + eigenvals.__doc__ = _eigenvals.__doc__ + eigenvects.__doc__ = _eigenvects.__doc__ + is_diagonalizable.__doc__ = _is_diagonalizable.__doc__ + diagonalize.__doc__ = _diagonalize.__doc__ + is_positive_definite.__doc__ = _is_positive_definite.__doc__ + is_positive_semidefinite.__doc__ = _is_positive_semidefinite.__doc__ + is_negative_definite.__doc__ = _is_negative_definite.__doc__ + is_negative_semidefinite.__doc__ = _is_negative_semidefinite.__doc__ + is_indefinite.__doc__ = _is_indefinite.__doc__ + jordan_form.__doc__ = _jordan_form.__doc__ + left_eigenvects.__doc__ = _left_eigenvects.__doc__ + singular_values.__doc__ = _singular_values.__doc__ + bidiagonalize.__doc__ = _bidiagonalize.__doc__ + bidiagonal_decomposition.__doc__ = _bidiagonal_decomposition.__doc__ + + +class MatrixCalculus(MatrixCommon): + """Provides calculus-related matrix operations.""" + + def diff(self, *args, evaluate=True, **kwargs): + """Calculate the derivative of each element in the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.diff(x) + Matrix([ + [1, 0], + [0, 0]]) + + See Also + ======== + + integrate + limit + """ + # XXX this should be handled here rather than in Derivative + from sympy.tensor.array.array_derivatives import ArrayDerivative + deriv = ArrayDerivative(self, *args, evaluate=evaluate) + # XXX This can rather changed to always return immutable matrix + if not isinstance(self, Basic) and evaluate: + return deriv.as_mutable() + return deriv + + def _eval_derivative(self, arg): + return self.applyfunc(lambda x: x.diff(arg)) + + def integrate(self, *args, **kwargs): + """Integrate each element of the matrix. ``args`` will + be passed to the ``integrate`` function. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.integrate((x, )) + Matrix([ + [x**2/2, x*y], + [ x, 0]]) + >>> M.integrate((x, 0, 2)) + Matrix([ + [2, 2*y], + [2, 0]]) + + See Also + ======== + + limit + diff + """ + return self.applyfunc(lambda x: x.integrate(*args, **kwargs)) + + def jacobian(self, X): + """Calculates the Jacobian matrix (derivative of a vector-valued function). + + Parameters + ========== + + ``self`` : vector of expressions representing functions f_i(x_1, ..., x_n). + X : set of x_i's in order, it can be a list or a Matrix + + Both ``self`` and X can be a row or a column matrix in any order + (i.e., jacobian() should always work). + + Examples + ======== + + >>> from sympy import sin, cos, Matrix + >>> from sympy.abc import rho, phi + >>> X = Matrix([rho*cos(phi), rho*sin(phi), rho**2]) + >>> Y = Matrix([rho, phi]) + >>> X.jacobian(Y) + Matrix([ + [cos(phi), -rho*sin(phi)], + [sin(phi), rho*cos(phi)], + [ 2*rho, 0]]) + >>> X = Matrix([rho*cos(phi), rho*sin(phi)]) + >>> X.jacobian(Y) + Matrix([ + [cos(phi), -rho*sin(phi)], + [sin(phi), rho*cos(phi)]]) + + See Also + ======== + + hessian + wronskian + """ + if not isinstance(X, MatrixBase): + X = self._new(X) + # Both X and ``self`` can be a row or a column matrix, so we need to make + # sure all valid combinations work, but everything else fails: + if self.shape[0] == 1: + m = self.shape[1] + elif self.shape[1] == 1: + m = self.shape[0] + else: + raise TypeError("``self`` must be a row or a column matrix") + if X.shape[0] == 1: + n = X.shape[1] + elif X.shape[1] == 1: + n = X.shape[0] + else: + raise TypeError("X must be a row or a column matrix") + + # m is the number of functions and n is the number of variables + # computing the Jacobian is now easy: + return self._new(m, n, lambda j, i: self[j].diff(X[i])) + + def limit(self, *args): + """Calculate the limit of each element in the matrix. + ``args`` will be passed to the ``limit`` function. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.limit(x, 2) + Matrix([ + [2, y], + [1, 0]]) + + See Also + ======== + + integrate + diff + """ + return self.applyfunc(lambda x: x.limit(*args)) + + +# https://github.com/sympy/sympy/pull/12854 +class MatrixDeprecated(MatrixCommon): + """A class to house deprecated matrix methods.""" + def berkowitz_charpoly(self, x=Dummy('lambda'), simplify=_simplify): + return self.charpoly(x=x) + + def berkowitz_det(self): + """Computes determinant using Berkowitz method. + + See Also + ======== + + det + berkowitz + """ + return self.det(method='berkowitz') + + def berkowitz_eigenvals(self, **flags): + """Computes eigenvalues of a Matrix using Berkowitz method. + + See Also + ======== + + berkowitz + """ + return self.eigenvals(**flags) + + def berkowitz_minors(self): + """Computes principal minors using Berkowitz method. + + See Also + ======== + + berkowitz + """ + sign, minors = self.one, [] + + for poly in self.berkowitz(): + minors.append(sign * poly[-1]) + sign = -sign + + return tuple(minors) + + def berkowitz(self): + from sympy.matrices import zeros + berk = ((1,),) + if not self: + return berk + + if not self.is_square: + raise NonSquareMatrixError() + + A, N = self, self.rows + transforms = [0] * (N - 1) + + for n in range(N, 1, -1): + T, k = zeros(n + 1, n), n - 1 + + R, C = -A[k, :k], A[:k, k] + A, a = A[:k, :k], -A[k, k] + + items = [C] + + for i in range(0, n - 2): + items.append(A * items[i]) + + for i, B in enumerate(items): + items[i] = (R * B)[0, 0] + + items = [self.one, a] + items + + for i in range(n): + T[i:, i] = items[:n - i + 1] + + transforms[k - 1] = T + + polys = [self._new([self.one, -A[0, 0]])] + + for i, T in enumerate(transforms): + polys.append(T * polys[i]) + + return berk + tuple(map(tuple, polys)) + + def cofactorMatrix(self, method="berkowitz"): + return self.cofactor_matrix(method=method) + + def det_bareis(self): + return _det_bareiss(self) + + def det_LU_decomposition(self): + """Compute matrix determinant using LU decomposition. + + + Note that this method fails if the LU decomposition itself + fails. In particular, if the matrix has no inverse this method + will fail. + + TODO: Implement algorithm for sparse matrices (SFF), + https://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps + + See Also + ======== + + + det + det_bareiss + berkowitz_det + """ + return self.det(method='lu') + + def jordan_cell(self, eigenval, n): + return self.jordan_block(size=n, eigenvalue=eigenval) + + def jordan_cells(self, calc_transformation=True): + P, J = self.jordan_form() + return P, J.get_diag_blocks() + + def minorEntry(self, i, j, method="berkowitz"): + return self.minor(i, j, method=method) + + def minorMatrix(self, i, j): + return self.minor_submatrix(i, j) + + def permuteBkwd(self, perm): + """Permute the rows of the matrix with the given permutation in reverse.""" + return self.permute_rows(perm, direction='backward') + + def permuteFwd(self, perm): + """Permute the rows of the matrix with the given permutation.""" + return self.permute_rows(perm, direction='forward') diff --git a/lib/python3.11/site-packages/sympy/matrices/matrixbase.py b/lib/python3.11/site-packages/sympy/matrices/matrixbase.py new file mode 100644 index 0000000000000000000000000000000000000000..5b548a71edae6dfe5cf9e0612393beb9796c1b6a --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/matrixbase.py @@ -0,0 +1,5424 @@ +from collections import defaultdict +from collections.abc import Iterable +from inspect import isfunction +from functools import reduce + +from sympy.assumptions.refine import refine +from sympy.core import SympifyError, Add +from sympy.core.basic import Atom, Basic +from sympy.core.kind import UndefinedKind +from sympy.core.numbers import Integer +from sympy.core.mod import Mod +from sympy.core.symbol import Symbol, Dummy +from sympy.core.sympify import sympify, _sympify +from sympy.core.function import diff +from sympy.polys import cancel +from sympy.functions.elementary.complexes import Abs, re, im +from sympy.printing import sstr +from sympy.functions.elementary.miscellaneous import Max, Min, sqrt +from sympy.functions.special.tensor_functions import KroneckerDelta, LeviCivita +from sympy.core.singleton import S +from sympy.printing.defaults import Printable +from sympy.printing.str import StrPrinter +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.combinatorial.factorials import binomial, factorial + +import mpmath as mp +from collections.abc import Callable +from sympy.utilities.iterables import reshape +from sympy.core.expr import Expr +from sympy.core.power import Pow +from sympy.core.symbol import uniquely_named_symbol + +from .utilities import _dotprodsimp, _simplify as _utilities_simplify +from sympy.polys.polytools import Poly +from sympy.utilities.iterables import flatten, is_sequence +from sympy.utilities.misc import as_int, filldedent +from sympy.core.decorators import call_highest_priority +from sympy.core.logic import fuzzy_and, FuzzyBool +from sympy.tensor.array import NDimArray +from sympy.utilities.iterables import NotIterable + +from .utilities import _get_intermediate_simp_bool + +from .kind import MatrixKind + +from .exceptions import ( + MatrixError, ShapeError, NonSquareMatrixError, NonInvertibleMatrixError, +) + +from .utilities import _iszero, _is_zero_after_expand_mul + +from .determinant import ( + _find_reasonable_pivot, _find_reasonable_pivot_naive, + _adjugate, _charpoly, _cofactor, _cofactor_matrix, _per, + _det, _det_bareiss, _det_berkowitz, _det_bird, _det_laplace, _det_LU, + _minor, _minor_submatrix) + +from .reductions import _is_echelon, _echelon_form, _rank, _rref + +from .solvers import ( + _diagonal_solve, _lower_triangular_solve, _upper_triangular_solve, + _cholesky_solve, _LDLsolve, _LUsolve, _QRsolve, _gauss_jordan_solve, + _pinv_solve, _cramer_solve, _solve, _solve_least_squares) + +from .inverse import ( + _pinv, _inv_ADJ, _inv_GE, _inv_LU, _inv_CH, _inv_LDL, _inv_QR, + _inv, _inv_block) + +from .subspaces import _columnspace, _nullspace, _rowspace, _orthogonalize + +from .eigen import ( + _eigenvals, _eigenvects, + _bidiagonalize, _bidiagonal_decomposition, + _is_diagonalizable, _diagonalize, + _is_positive_definite, _is_positive_semidefinite, + _is_negative_definite, _is_negative_semidefinite, _is_indefinite, + _jordan_form, _left_eigenvects, _singular_values) + +from .decompositions import ( + _rank_decomposition, _cholesky, _LDLdecomposition, + _LUdecomposition, _LUdecomposition_Simple, _LUdecompositionFF, + _singular_value_decomposition, _QRdecomposition, _upper_hessenberg_decomposition) + +from .graph import ( + _connected_components, _connected_components_decomposition, + _strongly_connected_components, _strongly_connected_components_decomposition) + + +__doctest_requires__ = { + ('MatrixBase.is_indefinite', + 'MatrixBase.is_positive_definite', + 'MatrixBase.is_positive_semidefinite', + 'MatrixBase.is_negative_definite', + 'MatrixBase.is_negative_semidefinite'): ['matplotlib'], +} + + +class MatrixBase(Printable): + """All common matrix operations including basic arithmetic, shaping, + and special matrices like `zeros`, and `eye`.""" + + _op_priority = 10.01 + + # Added just for numpy compatibility + __array_priority__ = 11 + + is_Matrix = True + _class_priority = 3 + _sympify = staticmethod(sympify) + zero = S.Zero + one = S.One + + _diff_wrt = True # type: bool + rows = None # type: int + cols = None # type: int + _simplify = None + + @classmethod + def _new(cls, *args, **kwargs): + """`_new` must, at minimum, be callable as + `_new(rows, cols, mat) where mat is a flat list of the + elements of the matrix.""" + raise NotImplementedError("Subclasses must implement this.") + + def __eq__(self, other): + raise NotImplementedError("Subclasses must implement this.") + + def __getitem__(self, key): + """Implementations of __getitem__ should accept ints, in which + case the matrix is indexed as a flat list, tuples (i,j) in which + case the (i,j) entry is returned, slices, or mixed tuples (a,b) + where a and b are any combination of slices and integers.""" + raise NotImplementedError("Subclasses must implement this.") + + @property + def shape(self): + """The shape (dimensions) of the matrix as the 2-tuple (rows, cols). + + Examples + ======== + + >>> from sympy import zeros + >>> M = zeros(2, 3) + >>> M.shape + (2, 3) + >>> M.rows + 2 + >>> M.cols + 3 + """ + return (self.rows, self.cols) + + def _eval_col_del(self, col): + def entry(i, j): + return self[i, j] if j < col else self[i, j + 1] + return self._new(self.rows, self.cols - 1, entry) + + def _eval_col_insert(self, pos, other): + + def entry(i, j): + if j < pos: + return self[i, j] + elif pos <= j < pos + other.cols: + return other[i, j - pos] + return self[i, j - other.cols] + + return self._new(self.rows, self.cols + other.cols, entry) + + def _eval_col_join(self, other): + rows = self.rows + + def entry(i, j): + if i < rows: + return self[i, j] + return other[i - rows, j] + + return classof(self, other)._new(self.rows + other.rows, self.cols, + entry) + + def _eval_extract(self, rowsList, colsList): + mat = list(self) + cols = self.cols + indices = (i * cols + j for i in rowsList for j in colsList) + return self._new(len(rowsList), len(colsList), + [mat[i] for i in indices]) + + def _eval_get_diag_blocks(self): + sub_blocks = [] + + def recurse_sub_blocks(M): + i = 1 + while i <= M.shape[0]: + if i == 1: + to_the_right = M[0, i:] + to_the_bottom = M[i:, 0] + else: + to_the_right = M[:i, i:] + to_the_bottom = M[i:, :i] + if any(to_the_right) or any(to_the_bottom): + i += 1 + continue + else: + sub_blocks.append(M[:i, :i]) + if M.shape == M[:i, :i].shape: + return + else: + recurse_sub_blocks(M[i:, i:]) + return + + recurse_sub_blocks(self) + return sub_blocks + + def _eval_row_del(self, row): + def entry(i, j): + return self[i, j] if i < row else self[i + 1, j] + return self._new(self.rows - 1, self.cols, entry) + + def _eval_row_insert(self, pos, other): + entries = list(self) + insert_pos = pos * self.cols + entries[insert_pos:insert_pos] = list(other) + return self._new(self.rows + other.rows, self.cols, entries) + + def _eval_row_join(self, other): + cols = self.cols + + def entry(i, j): + if j < cols: + return self[i, j] + return other[i, j - cols] + + return classof(self, other)._new(self.rows, self.cols + other.cols, + entry) + + def _eval_tolist(self): + return [list(self[i,:]) for i in range(self.rows)] + + def _eval_todok(self): + dok = {} + rows, cols = self.shape + for i in range(rows): + for j in range(cols): + val = self[i, j] + if val != self.zero: + dok[i, j] = val + return dok + + @classmethod + def _eval_from_dok(cls, rows, cols, dok): + out_flat = [cls.zero] * (rows * cols) + for (i, j), val in dok.items(): + out_flat[i * cols + j] = val + return cls._new(rows, cols, out_flat) + + def _eval_vec(self): + rows = self.rows + + def entry(n, _): + # we want to read off the columns first + j = n // rows + i = n - j * rows + return self[i, j] + + return self._new(len(self), 1, entry) + + def _eval_vech(self, diagonal): + c = self.cols + v = [] + if diagonal: + for j in range(c): + for i in range(j, c): + v.append(self[i, j]) + else: + for j in range(c): + for i in range(j + 1, c): + v.append(self[i, j]) + return self._new(len(v), 1, v) + + def col_del(self, col): + """Delete the specified column.""" + if col < 0: + col += self.cols + if not 0 <= col < self.cols: + raise IndexError("Column {} is out of range.".format(col)) + return self._eval_col_del(col) + + def col_insert(self, pos, other): + """Insert one or more columns at the given column position. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(3, 1) + >>> M.col_insert(1, V) + Matrix([ + [0, 1, 0, 0], + [0, 1, 0, 0], + [0, 1, 0, 0]]) + + See Also + ======== + + col + row_insert + """ + # Allows you to build a matrix even if it is null matrix + if not self: + return type(self)(other) + + pos = as_int(pos) + + if pos < 0: + pos = self.cols + pos + if pos < 0: + pos = 0 + elif pos > self.cols: + pos = self.cols + + if self.rows != other.rows: + raise ShapeError( + "The matrices have incompatible number of rows ({} and {})" + .format(self.rows, other.rows)) + + return self._eval_col_insert(pos, other) + + def col_join(self, other): + """Concatenates two matrices along self's last and other's first row. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(1, 3) + >>> M.col_join(V) + Matrix([ + [0, 0, 0], + [0, 0, 0], + [0, 0, 0], + [1, 1, 1]]) + + See Also + ======== + + col + row_join + """ + # A null matrix can always be stacked (see #10770) + if self.rows == 0 and self.cols != other.cols: + return self._new(0, other.cols, []).col_join(other) + + if self.cols != other.cols: + raise ShapeError( + "The matrices have incompatible number of columns ({} and {})" + .format(self.cols, other.cols)) + return self._eval_col_join(other) + + def col(self, j): + """Elementary column selector. + + Examples + ======== + + >>> from sympy import eye + >>> eye(2).col(0) + Matrix([ + [1], + [0]]) + + See Also + ======== + + row + col_del + col_join + col_insert + """ + return self[:, j] + + def extract(self, rowsList, colsList): + r"""Return a submatrix by specifying a list of rows and columns. + Negative indices can be given. All indices must be in the range + $-n \le i < n$ where $n$ is the number of rows or columns. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(4, 3, range(12)) + >>> m + Matrix([ + [0, 1, 2], + [3, 4, 5], + [6, 7, 8], + [9, 10, 11]]) + >>> m.extract([0, 1, 3], [0, 1]) + Matrix([ + [0, 1], + [3, 4], + [9, 10]]) + + Rows or columns can be repeated: + + >>> m.extract([0, 0, 1], [-1]) + Matrix([ + [2], + [2], + [5]]) + + Every other row can be taken by using range to provide the indices: + + >>> m.extract(range(0, m.rows, 2), [-1]) + Matrix([ + [2], + [8]]) + + RowsList or colsList can also be a list of booleans, in which case + the rows or columns corresponding to the True values will be selected: + + >>> m.extract([0, 1, 2, 3], [True, False, True]) + Matrix([ + [0, 2], + [3, 5], + [6, 8], + [9, 11]]) + """ + + if not is_sequence(rowsList) or not is_sequence(colsList): + raise TypeError("rowsList and colsList must be iterable") + # ensure rowsList and colsList are lists of integers + if rowsList and all(isinstance(i, bool) for i in rowsList): + rowsList = [index for index, item in enumerate(rowsList) if item] + if colsList and all(isinstance(i, bool) for i in colsList): + colsList = [index for index, item in enumerate(colsList) if item] + + # ensure everything is in range + rowsList = [a2idx(k, self.rows) for k in rowsList] + colsList = [a2idx(k, self.cols) for k in colsList] + + return self._eval_extract(rowsList, colsList) + + def get_diag_blocks(self): + """Obtains the square sub-matrices on the main diagonal of a square matrix. + + Useful for inverting symbolic matrices or solving systems of + linear equations which may be decoupled by having a block diagonal + structure. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y, z + >>> A = Matrix([[1, 3, 0, 0], [y, z*z, 0, 0], [0, 0, x, 0], [0, 0, 0, 0]]) + >>> a1, a2, a3 = A.get_diag_blocks() + >>> a1 + Matrix([ + [1, 3], + [y, z**2]]) + >>> a2 + Matrix([[x]]) + >>> a3 + Matrix([[0]]) + + """ + return self._eval_get_diag_blocks() + + @classmethod + def hstack(cls, *args): + """Return a matrix formed by joining args horizontally (i.e. + by repeated application of row_join). + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> Matrix.hstack(eye(2), 2*eye(2)) + Matrix([ + [1, 0, 2, 0], + [0, 1, 0, 2]]) + """ + if len(args) == 0: + return cls._new() + + kls = type(args[0]) + return reduce(kls.row_join, args) + + def reshape(self, rows, cols): + """Reshape the matrix. Total number of elements must remain the same. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 3, lambda i, j: 1) + >>> m + Matrix([ + [1, 1, 1], + [1, 1, 1]]) + >>> m.reshape(1, 6) + Matrix([[1, 1, 1, 1, 1, 1]]) + >>> m.reshape(3, 2) + Matrix([ + [1, 1], + [1, 1], + [1, 1]]) + + """ + if self.rows * self.cols != rows * cols: + raise ValueError("Invalid reshape parameters %d %d" % (rows, cols)) + return self._new(rows, cols, lambda i, j: self[i * cols + j]) + + def row_del(self, row): + """Delete the specified row.""" + if row < 0: + row += self.rows + if not 0 <= row < self.rows: + raise IndexError("Row {} is out of range.".format(row)) + + return self._eval_row_del(row) + + def row_insert(self, pos, other): + """Insert one or more rows at the given row position. + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(1, 3) + >>> M.row_insert(1, V) + Matrix([ + [0, 0, 0], + [1, 1, 1], + [0, 0, 0], + [0, 0, 0]]) + + See Also + ======== + + row + col_insert + """ + # Allows you to build a matrix even if it is null matrix + if not self: + return self._new(other) + + pos = as_int(pos) + + if pos < 0: + pos = self.rows + pos + if pos < 0: + pos = 0 + elif pos > self.rows: + pos = self.rows + + if self.cols != other.cols: + raise ShapeError( + "The matrices have incompatible number of columns ({} and {})" + .format(self.cols, other.cols)) + + return self._eval_row_insert(pos, other) + + def row_join(self, other): + """Concatenates two matrices along self's last and rhs's first column + + Examples + ======== + + >>> from sympy import zeros, ones + >>> M = zeros(3) + >>> V = ones(3, 1) + >>> M.row_join(V) + Matrix([ + [0, 0, 0, 1], + [0, 0, 0, 1], + [0, 0, 0, 1]]) + + See Also + ======== + + row + col_join + """ + # A null matrix can always be stacked (see #10770) + if self.cols == 0 and self.rows != other.rows: + return self._new(other.rows, 0, []).row_join(other) + + if self.rows != other.rows: + raise ShapeError( + "The matrices have incompatible number of rows ({} and {})" + .format(self.rows, other.rows)) + return self._eval_row_join(other) + + def diagonal(self, k=0): + """Returns the kth diagonal of self. The main diagonal + corresponds to `k=0`; diagonals above and below correspond to + `k > 0` and `k < 0`, respectively. The values of `self[i, j]` + for which `j - i = k`, are returned in order of increasing + `i + j`, starting with `i + j = |k|`. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(3, 3, lambda i, j: j - i); m + Matrix([ + [ 0, 1, 2], + [-1, 0, 1], + [-2, -1, 0]]) + >>> _.diagonal() + Matrix([[0, 0, 0]]) + >>> m.diagonal(1) + Matrix([[1, 1]]) + >>> m.diagonal(-2) + Matrix([[-2]]) + + Even though the diagonal is returned as a Matrix, the element + retrieval can be done with a single index: + + >>> Matrix.diag(1, 2, 3).diagonal()[1] # instead of [0, 1] + 2 + + See Also + ======== + + diag + """ + rv = [] + k = as_int(k) + r = 0 if k > 0 else -k + c = 0 if r else k + while True: + if r == self.rows or c == self.cols: + break + rv.append(self[r, c]) + r += 1 + c += 1 + if not rv: + raise ValueError(filldedent(''' + The %s diagonal is out of range [%s, %s]''' % ( + k, 1 - self.rows, self.cols - 1))) + return self._new(1, len(rv), rv) + + def row(self, i): + """Elementary row selector. + + Examples + ======== + + >>> from sympy import eye + >>> eye(2).row(0) + Matrix([[1, 0]]) + + See Also + ======== + + col + row_del + row_join + row_insert + """ + return self[i, :] + + def todok(self): + """Return the matrix as dictionary of keys. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix.eye(3) + >>> M.todok() + {(0, 0): 1, (1, 1): 1, (2, 2): 1} + """ + return self._eval_todok() + + @classmethod + def from_dok(cls, rows, cols, dok): + """Create a matrix from a dictionary of keys. + + Examples + ======== + + >>> from sympy import Matrix + >>> d = {(0, 0): 1, (1, 2): 3, (2, 1): 4} + >>> Matrix.from_dok(3, 3, d) + Matrix([ + [1, 0, 0], + [0, 0, 3], + [0, 4, 0]]) + """ + dok = {ij: cls._sympify(val) for ij, val in dok.items()} + return cls._eval_from_dok(rows, cols, dok) + + def tolist(self): + """Return the Matrix as a nested Python list. + + Examples + ======== + + >>> from sympy import Matrix, ones + >>> m = Matrix(3, 3, range(9)) + >>> m + Matrix([ + [0, 1, 2], + [3, 4, 5], + [6, 7, 8]]) + >>> m.tolist() + [[0, 1, 2], [3, 4, 5], [6, 7, 8]] + >>> ones(3, 0).tolist() + [[], [], []] + + When there are no rows then it will not be possible to tell how + many columns were in the original matrix: + + >>> ones(0, 3).tolist() + [] + + """ + if not self.rows: + return [] + if not self.cols: + return [[] for i in range(self.rows)] + return self._eval_tolist() + + def todod(M): + """Returns matrix as dict of dicts containing non-zero elements of the Matrix + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[0, 1],[0, 3]]) + >>> A + Matrix([ + [0, 1], + [0, 3]]) + >>> A.todod() + {0: {1: 1}, 1: {1: 3}} + + + """ + rowsdict = {} + Mlol = M.tolist() + for i, Mi in enumerate(Mlol): + row = {j: Mij for j, Mij in enumerate(Mi) if Mij} + if row: + rowsdict[i] = row + return rowsdict + + def vec(self): + """Return the Matrix converted into a one column matrix by stacking columns + + Examples + ======== + + >>> from sympy import Matrix + >>> m=Matrix([[1, 3], [2, 4]]) + >>> m + Matrix([ + [1, 3], + [2, 4]]) + >>> m.vec() + Matrix([ + [1], + [2], + [3], + [4]]) + + See Also + ======== + + vech + """ + return self._eval_vec() + + def vech(self, diagonal=True, check_symmetry=True): + """Reshapes the matrix into a column vector by stacking the + elements in the lower triangle. + + Parameters + ========== + + diagonal : bool, optional + If ``True``, it includes the diagonal elements. + + check_symmetry : bool, optional + If ``True``, it checks whether the matrix is symmetric. + + Examples + ======== + + >>> from sympy import Matrix + >>> m=Matrix([[1, 2], [2, 3]]) + >>> m + Matrix([ + [1, 2], + [2, 3]]) + >>> m.vech() + Matrix([ + [1], + [2], + [3]]) + >>> m.vech(diagonal=False) + Matrix([[2]]) + + Notes + ===== + + This should work for symmetric matrices and ``vech`` can + represent symmetric matrices in vector form with less size than + ``vec``. + + See Also + ======== + + vec + """ + if not self.is_square: + raise NonSquareMatrixError + + if check_symmetry and not self.is_symmetric(): + raise ValueError("The matrix is not symmetric.") + + return self._eval_vech(diagonal) + + @classmethod + def vstack(cls, *args): + """Return a matrix formed by joining args vertically (i.e. + by repeated application of col_join). + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> Matrix.vstack(eye(2), 2*eye(2)) + Matrix([ + [1, 0], + [0, 1], + [2, 0], + [0, 2]]) + """ + if len(args) == 0: + return cls._new() + + kls = type(args[0]) + return reduce(kls.col_join, args) + + @classmethod + def _eval_diag(cls, rows, cols, diag_dict): + """diag_dict is a defaultdict containing + all the entries of the diagonal matrix.""" + def entry(i, j): + return diag_dict[(i, j)] + return cls._new(rows, cols, entry) + + @classmethod + def _eval_eye(cls, rows, cols): + vals = [cls.zero]*(rows*cols) + vals[::cols+1] = [cls.one]*min(rows, cols) + return cls._new(rows, cols, vals, copy=False) + + @classmethod + def _eval_jordan_block(cls, size: int, eigenvalue, band='upper'): + if band == 'lower': + def entry(i, j): + if i == j: + return eigenvalue + elif j + 1 == i: + return cls.one + return cls.zero + else: + def entry(i, j): + if i == j: + return eigenvalue + elif i + 1 == j: + return cls.one + return cls.zero + return cls._new(size, size, entry) + + @classmethod + def _eval_ones(cls, rows, cols): + def entry(i, j): + return cls.one + return cls._new(rows, cols, entry) + + @classmethod + def _eval_zeros(cls, rows, cols): + return cls._new(rows, cols, [cls.zero]*(rows*cols), copy=False) + + @classmethod + def _eval_wilkinson(cls, n): + def entry(i, j): + return cls.one if i + 1 == j else cls.zero + + D = cls._new(2*n + 1, 2*n + 1, entry) + + wminus = cls.diag(list(range(-n, n + 1)), unpack=True) + D + D.T + wplus = abs(cls.diag(list(range(-n, n + 1)), unpack=True)) + D + D.T + + return wminus, wplus + + @classmethod + def diag(kls, *args, strict=False, unpack=True, rows=None, cols=None, **kwargs): + """Returns a matrix with the specified diagonal. + If matrices are passed, a block-diagonal matrix + is created (i.e. the "direct sum" of the matrices). + + kwargs + ====== + + rows : rows of the resulting matrix; computed if + not given. + + cols : columns of the resulting matrix; computed if + not given. + + cls : class for the resulting matrix + + unpack : bool which, when True (default), unpacks a single + sequence rather than interpreting it as a Matrix. + + strict : bool which, when False (default), allows Matrices to + have variable-length rows. + + Examples + ======== + + >>> from sympy import Matrix + >>> Matrix.diag(1, 2, 3) + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + + The current default is to unpack a single sequence. If this is + not desired, set `unpack=False` and it will be interpreted as + a matrix. + + >>> Matrix.diag([1, 2, 3]) == Matrix.diag(1, 2, 3) + True + + When more than one element is passed, each is interpreted as + something to put on the diagonal. Lists are converted to + matrices. Filling of the diagonal always continues from + the bottom right hand corner of the previous item: this + will create a block-diagonal matrix whether the matrices + are square or not. + + >>> col = [1, 2, 3] + >>> row = [[4, 5]] + >>> Matrix.diag(col, row) + Matrix([ + [1, 0, 0], + [2, 0, 0], + [3, 0, 0], + [0, 4, 5]]) + + When `unpack` is False, elements within a list need not all be + of the same length. Setting `strict` to True would raise a + ValueError for the following: + + >>> Matrix.diag([[1, 2, 3], [4, 5], [6]], unpack=False) + Matrix([ + [1, 2, 3], + [4, 5, 0], + [6, 0, 0]]) + + The type of the returned matrix can be set with the ``cls`` + keyword. + + >>> from sympy import ImmutableMatrix + >>> from sympy.utilities.misc import func_name + >>> func_name(Matrix.diag(1, cls=ImmutableMatrix)) + 'ImmutableDenseMatrix' + + A zero dimension matrix can be used to position the start of + the filling at the start of an arbitrary row or column: + + >>> from sympy import ones + >>> r2 = ones(0, 2) + >>> Matrix.diag(r2, 1, 2) + Matrix([ + [0, 0, 1, 0], + [0, 0, 0, 2]]) + + See Also + ======== + eye + diagonal + .dense.diag + .expressions.blockmatrix.BlockMatrix + .sparsetools.banded + """ + from sympy.matrices.matrixbase import MatrixBase + from sympy.matrices.dense import Matrix + from sympy.matrices import SparseMatrix + klass = kwargs.get('cls', kls) + if unpack and len(args) == 1 and is_sequence(args[0]) and \ + not isinstance(args[0], MatrixBase): + args = args[0] + + # fill a default dict with the diagonal entries + diag_entries = defaultdict(int) + rmax = cmax = 0 # keep track of the biggest index seen + for m in args: + if isinstance(m, list): + if strict: + # if malformed, Matrix will raise an error + _ = Matrix(m) + r, c = _.shape + m = _.tolist() + else: + r, c, smat = SparseMatrix._handle_creation_inputs(m) + for (i, j), _ in smat.items(): + diag_entries[(i + rmax, j + cmax)] = _ + m = [] # to skip process below + elif hasattr(m, 'shape'): # a Matrix + # convert to list of lists + r, c = m.shape + m = m.tolist() + else: # in this case, we're a single value + diag_entries[(rmax, cmax)] = m + rmax += 1 + cmax += 1 + continue + # process list of lists + for i, mi in enumerate(m): + for j, _ in enumerate(mi): + diag_entries[(i + rmax, j + cmax)] = _ + rmax += r + cmax += c + if rows is None: + rows, cols = cols, rows + if rows is None: + rows, cols = rmax, cmax + else: + cols = rows if cols is None else cols + if rows < rmax or cols < cmax: + raise ValueError(filldedent(''' + The constructed matrix is {} x {} but a size of {} x {} + was specified.'''.format(rmax, cmax, rows, cols))) + return klass._eval_diag(rows, cols, diag_entries) + + @classmethod + def eye(kls, rows, cols=None, **kwargs): + """Returns an identity matrix. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + if rows < 0 or cols < 0: + raise ValueError("Cannot create a {} x {} matrix. " + "Both dimensions must be positive".format(rows, cols)) + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_eye(rows, cols) + + @classmethod + def jordan_block(kls, size=None, eigenvalue=None, *, band='upper', **kwargs): + """Returns a Jordan block + + Parameters + ========== + + size : Integer, optional + Specifies the shape of the Jordan block matrix. + + eigenvalue : Number or Symbol + Specifies the value for the main diagonal of the matrix. + + .. note:: + The keyword ``eigenval`` is also specified as an alias + of this keyword, but it is not recommended to use. + + We may deprecate the alias in later release. + + band : 'upper' or 'lower', optional + Specifies the position of the off-diagonal to put `1` s on. + + cls : Matrix, optional + Specifies the matrix class of the output form. + + If it is not specified, the class type where the method is + being executed on will be returned. + + Returns + ======= + + Matrix + A Jordan block matrix. + + Raises + ====== + + ValueError + If insufficient arguments are given for matrix size + specification, or no eigenvalue is given. + + Examples + ======== + + Creating a default Jordan block: + + >>> from sympy import Matrix + >>> from sympy.abc import x + >>> Matrix.jordan_block(4, x) + Matrix([ + [x, 1, 0, 0], + [0, x, 1, 0], + [0, 0, x, 1], + [0, 0, 0, x]]) + + Creating an alternative Jordan block matrix where `1` is on + lower off-diagonal: + + >>> Matrix.jordan_block(4, x, band='lower') + Matrix([ + [x, 0, 0, 0], + [1, x, 0, 0], + [0, 1, x, 0], + [0, 0, 1, x]]) + + Creating a Jordan block with keyword arguments + + >>> Matrix.jordan_block(size=4, eigenvalue=x) + Matrix([ + [x, 1, 0, 0], + [0, x, 1, 0], + [0, 0, x, 1], + [0, 0, 0, x]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Jordan_matrix + """ + klass = kwargs.pop('cls', kls) + + eigenval = kwargs.get('eigenval', None) + if eigenvalue is None and eigenval is None: + raise ValueError("Must supply an eigenvalue") + elif eigenvalue != eigenval and None not in (eigenval, eigenvalue): + raise ValueError( + "Inconsistent values are given: 'eigenval'={}, " + "'eigenvalue'={}".format(eigenval, eigenvalue)) + else: + if eigenval is not None: + eigenvalue = eigenval + + if size is None: + raise ValueError("Must supply a matrix size") + + size = as_int(size) + return klass._eval_jordan_block(size, eigenvalue, band) + + @classmethod + def ones(kls, rows, cols=None, **kwargs): + """Returns a matrix of ones. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_ones(rows, cols) + + @classmethod + def zeros(kls, rows, cols=None, **kwargs): + """Returns a matrix of zeros. + + Parameters + ========== + + rows : rows of the matrix + cols : cols of the matrix (if None, cols=rows) + + kwargs + ====== + cls : class of the returned matrix + """ + if cols is None: + cols = rows + if rows < 0 or cols < 0: + raise ValueError("Cannot create a {} x {} matrix. " + "Both dimensions must be positive".format(rows, cols)) + klass = kwargs.get('cls', kls) + rows, cols = as_int(rows), as_int(cols) + + return klass._eval_zeros(rows, cols) + + @classmethod + def companion(kls, poly): + """Returns a companion matrix of a polynomial. + + Examples + ======== + + >>> from sympy import Matrix, Poly, Symbol, symbols + >>> x = Symbol('x') + >>> c0, c1, c2, c3, c4 = symbols('c0:5') + >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x) + >>> Matrix.companion(p) + Matrix([ + [0, 0, 0, 0, -c0], + [1, 0, 0, 0, -c1], + [0, 1, 0, 0, -c2], + [0, 0, 1, 0, -c3], + [0, 0, 0, 1, -c4]]) + """ + poly = kls._sympify(poly) + if not isinstance(poly, Poly): + raise ValueError("{} must be a Poly instance.".format(poly)) + if not poly.is_monic: + raise ValueError("{} must be a monic polynomial.".format(poly)) + if not poly.is_univariate: + raise ValueError( + "{} must be a univariate polynomial.".format(poly)) + + size = poly.degree() + if not size >= 1: + raise ValueError( + "{} must have degree not less than 1.".format(poly)) + + coeffs = poly.all_coeffs() + def entry(i, j): + if j == size - 1: + return -coeffs[-1 - i] + elif i == j + 1: + return kls.one + return kls.zero + return kls._new(size, size, entry) + + + @classmethod + def wilkinson(kls, n, **kwargs): + """Returns two square Wilkinson Matrix of size 2*n + 1 + $W_{2n + 1}^-, W_{2n + 1}^+ =$ Wilkinson(n) + + Examples + ======== + + >>> from sympy import Matrix + >>> wminus, wplus = Matrix.wilkinson(3) + >>> wminus + Matrix([ + [-3, 1, 0, 0, 0, 0, 0], + [ 1, -2, 1, 0, 0, 0, 0], + [ 0, 1, -1, 1, 0, 0, 0], + [ 0, 0, 1, 0, 1, 0, 0], + [ 0, 0, 0, 1, 1, 1, 0], + [ 0, 0, 0, 0, 1, 2, 1], + [ 0, 0, 0, 0, 0, 1, 3]]) + >>> wplus + Matrix([ + [3, 1, 0, 0, 0, 0, 0], + [1, 2, 1, 0, 0, 0, 0], + [0, 1, 1, 1, 0, 0, 0], + [0, 0, 1, 0, 1, 0, 0], + [0, 0, 0, 1, 1, 1, 0], + [0, 0, 0, 0, 1, 2, 1], + [0, 0, 0, 0, 0, 1, 3]]) + + References + ========== + + .. [1] https://blogs.mathworks.com/cleve/2013/04/15/wilkinsons-matrices-2/ + .. [2] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford, 1965, 662 pp. + + """ + klass = kwargs.get('cls', kls) + n = as_int(n) + return klass._eval_wilkinson(n) + + # The RepMatrix subclass uses more efficient sparse implementations of + # _eval_iter_values and other things. + + def _eval_iter_values(self): + return (i for i in self if i is not S.Zero) + + def _eval_values(self): + return list(self.iter_values()) + + def _eval_iter_items(self): + for i in range(self.rows): + for j in range(self.cols): + if self[i, j]: + yield (i, j), self[i, j] + + def _eval_atoms(self, *types): + values = self.values() + if len(values) < self.rows * self.cols and isinstance(S.Zero, types): + s = {S.Zero} + else: + s = set() + return s.union(*[v.atoms(*types) for v in values]) + + def _eval_free_symbols(self): + return set().union(*(i.free_symbols for i in set(self.values()))) + + def _eval_has(self, *patterns): + return any(a.has(*patterns) for a in self.iter_values()) + + def _eval_is_symbolic(self): + return self.has(Symbol) + + # _eval_is_hermitian is called by some general SymPy + # routines and has a different *args signature. Make + # sure the names don't clash by adding `_matrix_` in name. + def _eval_is_matrix_hermitian(self, simpfunc): + herm = lambda i, j: simpfunc(self[i, j] - self[j, i].conjugate()).is_zero + return fuzzy_and(herm(i, j) for (i, j), v in self.iter_items()) + + def _eval_is_zero_matrix(self): + return fuzzy_and(v.is_zero for v in self.iter_values()) + + def _eval_is_Identity(self) -> FuzzyBool: + one = self.one + zero = self.zero + ident = lambda i, j, v: v is one if i == j else v is zero + return all(ident(i, j, v) for (i, j), v in self.iter_items()) + + def _eval_is_diagonal(self): + return fuzzy_and(v.is_zero for (i, j), v in self.iter_items() if i != j) + + def _eval_is_lower(self): + return all(v.is_zero for (i, j), v in self.iter_items() if i < j) + + def _eval_is_upper(self): + return all(v.is_zero for (i, j), v in self.iter_items() if i > j) + + def _eval_is_lower_hessenberg(self): + return all(v.is_zero for (i, j), v in self.iter_items() if i + 1 < j) + + def _eval_is_upper_hessenberg(self): + return all(v.is_zero for (i, j), v in self.iter_items() if i > j + 1) + + def _eval_is_symmetric(self, simpfunc): + sym = lambda i, j: simpfunc(self[i, j] - self[j, i]).is_zero + return fuzzy_and(sym(i, j) for (i, j), v in self.iter_items()) + + def _eval_is_anti_symmetric(self, simpfunc): + anti = lambda i, j: simpfunc(self[i, j] + self[j, i]).is_zero + return fuzzy_and(anti(i, j) for (i, j), v in self.iter_items()) + + def _has_positive_diagonals(self): + diagonal_entries = (self[i, i] for i in range(self.rows)) + return fuzzy_and(x.is_positive for x in diagonal_entries) + + def _has_nonnegative_diagonals(self): + diagonal_entries = (self[i, i] for i in range(self.rows)) + return fuzzy_and(x.is_nonnegative for x in diagonal_entries) + + def atoms(self, *types): + """Returns the atoms that form the current object. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import Matrix + >>> Matrix([[x]]) + Matrix([[x]]) + >>> _.atoms() + {x} + >>> Matrix([[x, y], [y, x]]) + Matrix([ + [x, y], + [y, x]]) + >>> _.atoms() + {x, y} + """ + + types = tuple(t if isinstance(t, type) else type(t) for t in types) + if not types: + types = (Atom,) + return self._eval_atoms(*types) + + @property + def free_symbols(self): + """Returns the free symbols within the matrix. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy import Matrix + >>> Matrix([[x], [1]]).free_symbols + {x} + """ + return self._eval_free_symbols() + + def has(self, *patterns): + """Test whether any subexpression matches any of the patterns. + + Examples + ======== + + >>> from sympy import Matrix, SparseMatrix, Float + >>> from sympy.abc import x, y + >>> A = Matrix(((1, x), (0.2, 3))) + >>> B = SparseMatrix(((1, x), (0.2, 3))) + >>> A.has(x) + True + >>> A.has(y) + False + >>> A.has(Float) + True + >>> B.has(x) + True + >>> B.has(y) + False + >>> B.has(Float) + True + """ + return self._eval_has(*patterns) + + def is_anti_symmetric(self, simplify=True): + """Check if matrix M is an antisymmetric matrix, + that is, M is a square matrix with all M[i, j] == -M[j, i]. + + When ``simplify=True`` (default), the sum M[i, j] + M[j, i] is + simplified before testing to see if it is zero. By default, + the SymPy simplify function is used. To use a custom function + set simplify to a function that accepts a single argument which + returns a simplified expression. To skip simplification, set + simplify to False but note that although this will be faster, + it may induce false negatives. + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> m = Matrix(2, 2, [0, 1, -1, 0]) + >>> m + Matrix([ + [ 0, 1], + [-1, 0]]) + >>> m.is_anti_symmetric() + True + >>> x, y = symbols('x y') + >>> m = Matrix(2, 3, [0, 0, x, -y, 0, 0]) + >>> m + Matrix([ + [ 0, 0, x], + [-y, 0, 0]]) + >>> m.is_anti_symmetric() + False + + >>> from sympy.abc import x, y + >>> m = Matrix(3, 3, [0, x**2 + 2*x + 1, y, + ... -(x + 1)**2, 0, x*y, + ... -y, -x*y, 0]) + + Simplification of matrix elements is done by default so even + though two elements which should be equal and opposite would not + pass an equality test, the matrix is still reported as + anti-symmetric: + + >>> m[0, 1] == -m[1, 0] + False + >>> m.is_anti_symmetric() + True + + If ``simplify=False`` is used for the case when a Matrix is already + simplified, this will speed things up. Here, we see that without + simplification the matrix does not appear anti-symmetric: + + >>> print(m.is_anti_symmetric(simplify=False)) + None + + But if the matrix were already expanded, then it would appear + anti-symmetric and simplification in the is_anti_symmetric routine + is not needed: + + >>> m = m.expand() + >>> m.is_anti_symmetric(simplify=False) + True + """ + # accept custom simplification + simpfunc = simplify + if not isfunction(simplify): + simpfunc = _utilities_simplify if simplify else lambda x: x + + if not self.is_square: + return False + return self._eval_is_anti_symmetric(simpfunc) + + def is_diagonal(self): + """Check if matrix is diagonal, + that is matrix in which the entries outside the main diagonal are all zero. + + Examples + ======== + + >>> from sympy import Matrix, diag + >>> m = Matrix(2, 2, [1, 0, 0, 2]) + >>> m + Matrix([ + [1, 0], + [0, 2]]) + >>> m.is_diagonal() + True + + >>> m = Matrix(2, 2, [1, 1, 0, 2]) + >>> m + Matrix([ + [1, 1], + [0, 2]]) + >>> m.is_diagonal() + False + + >>> m = diag(1, 2, 3) + >>> m + Matrix([ + [1, 0, 0], + [0, 2, 0], + [0, 0, 3]]) + >>> m.is_diagonal() + True + + See Also + ======== + + is_lower + is_upper + sympy.matrices.matrixbase.MatrixBase.is_diagonalizable + diagonalize + """ + return self._eval_is_diagonal() + + @property + def is_weakly_diagonally_dominant(self): + r"""Tests if the matrix is row weakly diagonally dominant. + + Explanation + =========== + + A $n, n$ matrix $A$ is row weakly diagonally dominant if + + .. math:: + \left|A_{i, i}\right| \ge \sum_{j = 0, j \neq i}^{n-1} + \left|A_{i, j}\right| \quad {\text{for all }} + i \in \{ 0, ..., n-1 \} + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]]) + >>> A.is_weakly_diagonally_dominant + True + + >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]]) + >>> A.is_weakly_diagonally_dominant + False + + >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]]) + >>> A.is_weakly_diagonally_dominant + True + + Notes + ===== + + If you want to test whether a matrix is column diagonally + dominant, you can apply the test after transposing the matrix. + """ + if not self.is_square: + return False + + rows, cols = self.shape + + def test_row(i): + summation = self.zero + for j in range(cols): + if i != j: + summation += Abs(self[i, j]) + return (Abs(self[i, i]) - summation).is_nonnegative + + return fuzzy_and(test_row(i) for i in range(rows)) + + @property + def is_strongly_diagonally_dominant(self): + r"""Tests if the matrix is row strongly diagonally dominant. + + Explanation + =========== + + A $n, n$ matrix $A$ is row strongly diagonally dominant if + + .. math:: + \left|A_{i, i}\right| > \sum_{j = 0, j \neq i}^{n-1} + \left|A_{i, j}\right| \quad {\text{for all }} + i \in \{ 0, ..., n-1 \} + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[3, -2, 1], [1, -3, 2], [-1, 2, 4]]) + >>> A.is_strongly_diagonally_dominant + False + + >>> A = Matrix([[-2, 2, 1], [1, 3, 2], [1, -2, 0]]) + >>> A.is_strongly_diagonally_dominant + False + + >>> A = Matrix([[-4, 2, 1], [1, 6, 2], [1, -2, 5]]) + >>> A.is_strongly_diagonally_dominant + True + + Notes + ===== + + If you want to test whether a matrix is column diagonally + dominant, you can apply the test after transposing the matrix. + """ + if not self.is_square: + return False + + rows, cols = self.shape + + def test_row(i): + summation = self.zero + for j in range(cols): + if i != j: + summation += Abs(self[i, j]) + return (Abs(self[i, i]) - summation).is_positive + + return fuzzy_and(test_row(i) for i in range(rows)) + + @property + def is_hermitian(self): + """Checks if the matrix is Hermitian. + + In a Hermitian matrix element i,j is the complex conjugate of + element j,i. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy import I + >>> from sympy.abc import x + >>> a = Matrix([[1, I], [-I, 1]]) + >>> a + Matrix([ + [ 1, I], + [-I, 1]]) + >>> a.is_hermitian + True + >>> a[0, 0] = 2*I + >>> a.is_hermitian + False + >>> a[0, 0] = x + >>> a.is_hermitian + >>> a[0, 1] = a[1, 0]*I + >>> a.is_hermitian + False + """ + if not self.is_square: + return False + + return self._eval_is_matrix_hermitian(_utilities_simplify) + + @property + def is_Identity(self) -> FuzzyBool: + if not self.is_square: + return False + return self._eval_is_Identity() + + @property + def is_lower_hessenberg(self): + r"""Checks if the matrix is in the lower-Hessenberg form. + + The lower hessenberg matrix has zero entries + above the first superdiagonal. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 2, 0, 0], [5, 2, 3, 0], [3, 4, 3, 7], [5, 6, 1, 1]]) + >>> a + Matrix([ + [1, 2, 0, 0], + [5, 2, 3, 0], + [3, 4, 3, 7], + [5, 6, 1, 1]]) + >>> a.is_lower_hessenberg + True + + See Also + ======== + + is_upper_hessenberg + is_lower + """ + return self._eval_is_lower_hessenberg() + + @property + def is_lower(self): + """Check if matrix is a lower triangular matrix. True can be returned + even if the matrix is not square. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [1, 0, 0, 1]) + >>> m + Matrix([ + [1, 0], + [0, 1]]) + >>> m.is_lower + True + + >>> m = Matrix(4, 3, [0, 0, 0, 2, 0, 0, 1, 4, 0, 6, 6, 5]) + >>> m + Matrix([ + [0, 0, 0], + [2, 0, 0], + [1, 4, 0], + [6, 6, 5]]) + >>> m.is_lower + True + + >>> from sympy.abc import x, y + >>> m = Matrix(2, 2, [x**2 + y, y**2 + x, 0, x + y]) + >>> m + Matrix([ + [x**2 + y, x + y**2], + [ 0, x + y]]) + >>> m.is_lower + False + + See Also + ======== + + is_upper + is_diagonal + is_lower_hessenberg + """ + return self._eval_is_lower() + + @property + def is_square(self): + """Checks if a matrix is square. + + A matrix is square if the number of rows equals the number of columns. + The empty matrix is square by definition, since the number of rows and + the number of columns are both zero. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> b = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> c = Matrix([]) + >>> a.is_square + False + >>> b.is_square + True + >>> c.is_square + True + """ + return self.rows == self.cols + + def is_symbolic(self): + """Checks if any elements contain Symbols. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.is_symbolic() + True + + """ + return self._eval_is_symbolic() + + def is_symmetric(self, simplify=True): + """Check if matrix is symmetric matrix, + that is square matrix and is equal to its transpose. + + By default, simplifications occur before testing symmetry. + They can be skipped using 'simplify=False'; while speeding things a bit, + this may however induce false negatives. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [0, 1, 1, 2]) + >>> m + Matrix([ + [0, 1], + [1, 2]]) + >>> m.is_symmetric() + True + + >>> m = Matrix(2, 2, [0, 1, 2, 0]) + >>> m + Matrix([ + [0, 1], + [2, 0]]) + >>> m.is_symmetric() + False + + >>> m = Matrix(2, 3, [0, 0, 0, 0, 0, 0]) + >>> m + Matrix([ + [0, 0, 0], + [0, 0, 0]]) + >>> m.is_symmetric() + False + + >>> from sympy.abc import x, y + >>> m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3]) + >>> m + Matrix([ + [ 1, x**2 + 2*x + 1, y], + [(x + 1)**2, 2, 0], + [ y, 0, 3]]) + >>> m.is_symmetric() + True + + If the matrix is already simplified, you may speed-up is_symmetric() + test by using 'simplify=False'. + + >>> bool(m.is_symmetric(simplify=False)) + False + >>> m1 = m.expand() + >>> m1.is_symmetric(simplify=False) + True + """ + simpfunc = simplify + if not isfunction(simplify): + simpfunc = _utilities_simplify if simplify else lambda x: x + + if not self.is_square: + return False + + return self._eval_is_symmetric(simpfunc) + + @property + def is_upper_hessenberg(self): + """Checks if the matrix is the upper-Hessenberg form. + + The upper hessenberg matrix has zero entries + below the first subdiagonal. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[1, 4, 2, 3], [3, 4, 1, 7], [0, 2, 3, 4], [0, 0, 1, 3]]) + >>> a + Matrix([ + [1, 4, 2, 3], + [3, 4, 1, 7], + [0, 2, 3, 4], + [0, 0, 1, 3]]) + >>> a.is_upper_hessenberg + True + + See Also + ======== + + is_lower_hessenberg + is_upper + """ + return self._eval_is_upper_hessenberg() + + @property + def is_upper(self): + """Check if matrix is an upper triangular matrix. True can be returned + even if the matrix is not square. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, [1, 0, 0, 1]) + >>> m + Matrix([ + [1, 0], + [0, 1]]) + >>> m.is_upper + True + + >>> m = Matrix(4, 3, [5, 1, 9, 0, 4, 6, 0, 0, 5, 0, 0, 0]) + >>> m + Matrix([ + [5, 1, 9], + [0, 4, 6], + [0, 0, 5], + [0, 0, 0]]) + >>> m.is_upper + True + + >>> m = Matrix(2, 3, [4, 2, 5, 6, 1, 1]) + >>> m + Matrix([ + [4, 2, 5], + [6, 1, 1]]) + >>> m.is_upper + False + + See Also + ======== + + is_lower + is_diagonal + is_upper_hessenberg + """ + return self._eval_is_upper() + + @property + def is_zero_matrix(self): + """Checks if a matrix is a zero matrix. + + A matrix is zero if every element is zero. A matrix need not be square + to be considered zero. The empty matrix is zero by the principle of + vacuous truth. For a matrix that may or may not be zero (e.g. + contains a symbol), this will be None + + Examples + ======== + + >>> from sympy import Matrix, zeros + >>> from sympy.abc import x + >>> a = Matrix([[0, 0], [0, 0]]) + >>> b = zeros(3, 4) + >>> c = Matrix([[0, 1], [0, 0]]) + >>> d = Matrix([]) + >>> e = Matrix([[x, 0], [0, 0]]) + >>> a.is_zero_matrix + True + >>> b.is_zero_matrix + True + >>> c.is_zero_matrix + False + >>> d.is_zero_matrix + True + >>> e.is_zero_matrix + """ + return self._eval_is_zero_matrix() + + def values(self): + """Return non-zero values of self. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix([[0, 1], [2, 3]]) + >>> m.values() + [1, 2, 3] + + See Also + ======== + + iter_values + tolist + flat + """ + return self._eval_values() + + def iter_values(self): + """ + Iterate over non-zero values of self. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix([[0, 1], [2, 3]]) + >>> list(m.iter_values()) + [1, 2, 3] + + See Also + ======== + + values + """ + return self._eval_iter_values() + + def iter_items(self): + """Iterate over indices and values of nonzero items. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix([[0, 1], [2, 3]]) + >>> list(m.iter_items()) + [((0, 1), 1), ((1, 0), 2), ((1, 1), 3)] + + See Also + ======== + + iter_values + todok + """ + return self._eval_iter_items() + + def _eval_adjoint(self): + return self.transpose().conjugate() + + def _eval_applyfunc(self, f): + cols = self.cols + size = self.rows*self.cols + + dok = self.todok() + valmap = {v: f(v) for v in dok.values()} + + if len(dok) < size and ((fzero := f(S.Zero)) is not S.Zero): + out_flat = [fzero]*size + for (i, j), v in dok.items(): + out_flat[i*cols + j] = valmap[v] + out = self._new(self.rows, self.cols, out_flat) + else: + fdok = {ij: valmap[v] for ij, v in dok.items()} + out = self.from_dok(self.rows, self.cols, fdok) + + return out + + def _eval_as_real_imag(self): # type: ignore + return (self.applyfunc(re), self.applyfunc(im)) + + def _eval_conjugate(self): + return self.applyfunc(lambda x: x.conjugate()) + + def _eval_permute_cols(self, perm): + # apply the permutation to a list + mapping = list(perm) + + def entry(i, j): + return self[i, mapping[j]] + + return self._new(self.rows, self.cols, entry) + + def _eval_permute_rows(self, perm): + # apply the permutation to a list + mapping = list(perm) + + def entry(i, j): + return self[mapping[i], j] + + return self._new(self.rows, self.cols, entry) + + def _eval_trace(self): + return sum(self[i, i] for i in range(self.rows)) + + def _eval_transpose(self): + return self._new(self.cols, self.rows, lambda i, j: self[j, i]) + + def adjoint(self): + """Conjugate transpose or Hermitian conjugation.""" + return self._eval_adjoint() + + def applyfunc(self, f): + """Apply a function to each element of the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix(2, 2, lambda i, j: i*2+j) + >>> m + Matrix([ + [0, 1], + [2, 3]]) + >>> m.applyfunc(lambda i: 2*i) + Matrix([ + [0, 2], + [4, 6]]) + + """ + if not callable(f): + raise TypeError("`f` must be callable.") + + return self._eval_applyfunc(f) + + def as_real_imag(self, deep=True, **hints): + """Returns a tuple containing the (real, imaginary) part of matrix.""" + # XXX: Ignoring deep and hints... + return self._eval_as_real_imag() + + def conjugate(self): + """Return the by-element conjugation. + + Examples + ======== + + >>> from sympy import SparseMatrix, I + >>> a = SparseMatrix(((1, 2 + I), (3, 4), (I, -I))) + >>> a + Matrix([ + [1, 2 + I], + [3, 4], + [I, -I]]) + >>> a.C + Matrix([ + [ 1, 2 - I], + [ 3, 4], + [-I, I]]) + + See Also + ======== + + transpose: Matrix transposition + H: Hermite conjugation + sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation + """ + return self._eval_conjugate() + + def doit(self, **hints): + return self.applyfunc(lambda x: x.doit(**hints)) + + def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False): + """Apply evalf() to each element of self.""" + options = {'subs':subs, 'maxn':maxn, 'chop':chop, 'strict':strict, + 'quad':quad, 'verbose':verbose} + return self.applyfunc(lambda i: i.evalf(n, **options)) + + def expand(self, deep=True, modulus=None, power_base=True, power_exp=True, + mul=True, log=True, multinomial=True, basic=True, **hints): + """Apply core.function.expand to each entry of the matrix. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy import Matrix + >>> Matrix(1, 1, [x*(x+1)]) + Matrix([[x*(x + 1)]]) + >>> _.expand() + Matrix([[x**2 + x]]) + + """ + return self.applyfunc(lambda x: x.expand( + deep, modulus, power_base, power_exp, mul, log, multinomial, basic, + **hints)) + + @property + def H(self): + """Return Hermite conjugate. + + Examples + ======== + + >>> from sympy import Matrix, I + >>> m = Matrix((0, 1 + I, 2, 3)) + >>> m + Matrix([ + [ 0], + [1 + I], + [ 2], + [ 3]]) + >>> m.H + Matrix([[0, 1 - I, 2, 3]]) + + See Also + ======== + + conjugate: By-element conjugation + sympy.matrices.matrixbase.MatrixBase.D: Dirac conjugation + """ + return self.T.C + + def permute(self, perm, orientation='rows', direction='forward'): + r"""Permute the rows or columns of a matrix by the given list of + swaps. + + Parameters + ========== + + perm : Permutation, list, or list of lists + A representation for the permutation. + + If it is ``Permutation``, it is used directly with some + resizing with respect to the matrix size. + + If it is specified as list of lists, + (e.g., ``[[0, 1], [0, 2]]``), then the permutation is formed + from applying the product of cycles. The direction how the + cyclic product is applied is described in below. + + If it is specified as a list, the list should represent + an array form of a permutation. (e.g., ``[1, 2, 0]``) which + would would form the swapping function + `0 \mapsto 1, 1 \mapsto 2, 2\mapsto 0`. + + orientation : 'rows', 'cols' + A flag to control whether to permute the rows or the columns + + direction : 'forward', 'backward' + A flag to control whether to apply the permutations from + the start of the list first, or from the back of the list + first. + + For example, if the permutation specification is + ``[[0, 1], [0, 2]]``, + + If the flag is set to ``'forward'``, the cycle would be + formed as `0 \mapsto 2, 2 \mapsto 1, 1 \mapsto 0`. + + If the flag is set to ``'backward'``, the cycle would be + formed as `0 \mapsto 1, 1 \mapsto 2, 2 \mapsto 0`. + + If the argument ``perm`` is not in a form of list of lists, + this flag takes no effect. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='forward') + Matrix([ + [0, 0, 1], + [1, 0, 0], + [0, 1, 0]]) + + >>> from sympy import eye + >>> M = eye(3) + >>> M.permute([[0, 1], [0, 2]], orientation='rows', direction='backward') + Matrix([ + [0, 1, 0], + [0, 0, 1], + [1, 0, 0]]) + + Notes + ===== + + If a bijective function + `\sigma : \mathbb{N}_0 \rightarrow \mathbb{N}_0` denotes the + permutation. + + If the matrix `A` is the matrix to permute, represented as + a horizontal or a vertical stack of vectors: + + .. math:: + A = + \begin{bmatrix} + a_0 \\ a_1 \\ \vdots \\ a_{n-1} + \end{bmatrix} = + \begin{bmatrix} + \alpha_0 & \alpha_1 & \cdots & \alpha_{n-1} + \end{bmatrix} + + If the matrix `B` is the result, the permutation of matrix rows + is defined as: + + .. math:: + B := \begin{bmatrix} + a_{\sigma(0)} \\ a_{\sigma(1)} \\ \vdots \\ a_{\sigma(n-1)} + \end{bmatrix} + + And the permutation of matrix columns is defined as: + + .. math:: + B := \begin{bmatrix} + \alpha_{\sigma(0)} & \alpha_{\sigma(1)} & + \cdots & \alpha_{\sigma(n-1)} + \end{bmatrix} + """ + from sympy.combinatorics import Permutation + + # allow british variants and `columns` + if direction == 'forwards': + direction = 'forward' + if direction == 'backwards': + direction = 'backward' + if orientation == 'columns': + orientation = 'cols' + + if direction not in ('forward', 'backward'): + raise TypeError("direction='{}' is an invalid kwarg. " + "Try 'forward' or 'backward'".format(direction)) + if orientation not in ('rows', 'cols'): + raise TypeError("orientation='{}' is an invalid kwarg. " + "Try 'rows' or 'cols'".format(orientation)) + + if not isinstance(perm, (Permutation, Iterable)): + raise ValueError( + "{} must be a list, a list of lists, " + "or a SymPy permutation object.".format(perm)) + + # ensure all swaps are in range + max_index = self.rows if orientation == 'rows' else self.cols + if not all(0 <= t <= max_index for t in flatten(list(perm))): + raise IndexError("`swap` indices out of range.") + + if perm and not isinstance(perm, Permutation) and \ + isinstance(perm[0], Iterable): + if direction == 'forward': + perm = list(reversed(perm)) + perm = Permutation(perm, size=max_index+1) + else: + perm = Permutation(perm, size=max_index+1) + + if orientation == 'rows': + return self._eval_permute_rows(perm) + if orientation == 'cols': + return self._eval_permute_cols(perm) + + def permute_cols(self, swaps, direction='forward'): + """Alias for + ``self.permute(swaps, orientation='cols', direction=direction)`` + + See Also + ======== + + permute + """ + return self.permute(swaps, orientation='cols', direction=direction) + + def permute_rows(self, swaps, direction='forward'): + """Alias for + ``self.permute(swaps, orientation='rows', direction=direction)`` + + See Also + ======== + + permute + """ + return self.permute(swaps, orientation='rows', direction=direction) + + def refine(self, assumptions=True): + """Apply refine to each element of the matrix. + + Examples + ======== + + >>> from sympy import Symbol, Matrix, Abs, sqrt, Q + >>> x = Symbol('x') + >>> Matrix([[Abs(x)**2, sqrt(x**2)],[sqrt(x**2), Abs(x)**2]]) + Matrix([ + [ Abs(x)**2, sqrt(x**2)], + [sqrt(x**2), Abs(x)**2]]) + >>> _.refine(Q.real(x)) + Matrix([ + [ x**2, Abs(x)], + [Abs(x), x**2]]) + + """ + return self.applyfunc(lambda x: refine(x, assumptions)) + + def replace(self, F, G, map=False, simultaneous=True, exact=None): + """Replaces Function F in Matrix entries with Function G. + + Examples + ======== + + >>> from sympy import symbols, Function, Matrix + >>> F, G = symbols('F, G', cls=Function) + >>> M = Matrix(2, 2, lambda i, j: F(i+j)) ; M + Matrix([ + [F(0), F(1)], + [F(1), F(2)]]) + >>> N = M.replace(F,G) + >>> N + Matrix([ + [G(0), G(1)], + [G(1), G(2)]]) + """ + kwargs = {'map': map, 'simultaneous': simultaneous, 'exact': exact} + + if map: + + d = {} + def func(eij): + eij, dij = eij.replace(F, G, **kwargs) + d.update(dij) + return eij + + M = self.applyfunc(func) + return M, d + + else: + return self.applyfunc(lambda i: i.replace(F, G, **kwargs)) + + def rot90(self, k=1): + """Rotates Matrix by 90 degrees + + Parameters + ========== + + k : int + Specifies how many times the matrix is rotated by 90 degrees + (clockwise when positive, counter-clockwise when negative). + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> A = Matrix(2, 2, symbols('a:d')) + >>> A + Matrix([ + [a, b], + [c, d]]) + + Rotating the matrix clockwise one time: + + >>> A.rot90(1) + Matrix([ + [c, a], + [d, b]]) + + Rotating the matrix anticlockwise two times: + + >>> A.rot90(-2) + Matrix([ + [d, c], + [b, a]]) + """ + + mod = k%4 + if mod == 0: + return self + if mod == 1: + return self[::-1, ::].T + if mod == 2: + return self[::-1, ::-1] + if mod == 3: + return self[::, ::-1].T + + def simplify(self, **kwargs): + """Apply simplify to each element of the matrix. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, sin, cos + >>> SparseMatrix(1, 1, [x*sin(y)**2 + x*cos(y)**2]) + Matrix([[x*sin(y)**2 + x*cos(y)**2]]) + >>> _.simplify() + Matrix([[x]]) + """ + return self.applyfunc(lambda x: x.simplify(**kwargs)) + + def subs(self, *args, **kwargs): # should mirror core.basic.subs + """Return a new matrix with subs applied to each entry. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, Matrix + >>> SparseMatrix(1, 1, [x]) + Matrix([[x]]) + >>> _.subs(x, y) + Matrix([[y]]) + >>> Matrix(_).subs(y, x) + Matrix([[x]]) + """ + + if len(args) == 1 and not isinstance(args[0], (dict, set)) and iter(args[0]) and not is_sequence(args[0]): + args = (list(args[0]),) + + return self.applyfunc(lambda x: x.subs(*args, **kwargs)) + + def trace(self): + """ + Returns the trace of a square matrix i.e. the sum of the + diagonal elements. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.trace() + 5 + + """ + if self.rows != self.cols: + raise NonSquareMatrixError() + return self._eval_trace() + + def transpose(self): + """ + Returns the transpose of the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.transpose() + Matrix([ + [1, 3], + [2, 4]]) + + >>> from sympy import Matrix, I + >>> m=Matrix(((1, 2+I), (3, 4))) + >>> m + Matrix([ + [1, 2 + I], + [3, 4]]) + >>> m.transpose() + Matrix([ + [ 1, 3], + [2 + I, 4]]) + >>> m.T == m.transpose() + True + + See Also + ======== + + conjugate: By-element conjugation + + """ + return self._eval_transpose() + + @property + def T(self): + '''Matrix transposition''' + return self.transpose() + + @property + def C(self): + '''By-element conjugation''' + return self.conjugate() + + def n(self, *args, **kwargs): + """Apply evalf() to each element of self.""" + return self.evalf(*args, **kwargs) + + def xreplace(self, rule): # should mirror core.basic.xreplace + """Return a new matrix with xreplace applied to each entry. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy import SparseMatrix, Matrix + >>> SparseMatrix(1, 1, [x]) + Matrix([[x]]) + >>> _.xreplace({x: y}) + Matrix([[y]]) + >>> Matrix(_).xreplace({y: x}) + Matrix([[x]]) + """ + return self.applyfunc(lambda x: x.xreplace(rule)) + + def _eval_simplify(self, **kwargs): + # XXX: We can't use self.simplify here as mutable subclasses will + # override simplify and have it return None + return self.applyfunc(lambda x: x.simplify(**kwargs)) + + def _eval_trigsimp(self, **opts): + from sympy.simplify.trigsimp import trigsimp + return self.applyfunc(lambda x: trigsimp(x, **opts)) + + def upper_triangular(self, k=0): + """Return the elements on and above the kth diagonal of a matrix. + If k is not specified then simply returns upper-triangular portion + of a matrix + + Examples + ======== + + >>> from sympy import ones + >>> A = ones(4) + >>> A.upper_triangular() + Matrix([ + [1, 1, 1, 1], + [0, 1, 1, 1], + [0, 0, 1, 1], + [0, 0, 0, 1]]) + + >>> A.upper_triangular(2) + Matrix([ + [0, 0, 1, 1], + [0, 0, 0, 1], + [0, 0, 0, 0], + [0, 0, 0, 0]]) + + >>> A.upper_triangular(-1) + Matrix([ + [1, 1, 1, 1], + [1, 1, 1, 1], + [0, 1, 1, 1], + [0, 0, 1, 1]]) + + """ + + def entry(i, j): + return self[i, j] if i + k <= j else self.zero + + return self._new(self.rows, self.cols, entry) + + def lower_triangular(self, k=0): + """Return the elements on and below the kth diagonal of a matrix. + If k is not specified then simply returns lower-triangular portion + of a matrix + + Examples + ======== + + >>> from sympy import ones + >>> A = ones(4) + >>> A.lower_triangular() + Matrix([ + [1, 0, 0, 0], + [1, 1, 0, 0], + [1, 1, 1, 0], + [1, 1, 1, 1]]) + + >>> A.lower_triangular(-2) + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [1, 0, 0, 0], + [1, 1, 0, 0]]) + + >>> A.lower_triangular(1) + Matrix([ + [1, 1, 0, 0], + [1, 1, 1, 0], + [1, 1, 1, 1], + [1, 1, 1, 1]]) + + """ + + def entry(i, j): + return self[i, j] if i + k >= j else self.zero + + return self._new(self.rows, self.cols, entry) + + def _eval_Abs(self): + return self._new(self.rows, self.cols, lambda i, j: Abs(self[i, j])) + + def _eval_add(self, other): + return self._new(self.rows, self.cols, + lambda i, j: self[i, j] + other[i, j]) + + def _eval_matrix_mul(self, other): + def entry(i, j): + vec = [self[i,k]*other[k,j] for k in range(self.cols)] + try: + return Add(*vec) + except (TypeError, SympifyError): + # Some matrices don't work with `sum` or `Add` + # They don't work with `sum` because `sum` tries to add `0` + # Fall back to a safe way to multiply if the `Add` fails. + return reduce(lambda a, b: a + b, vec) + + return self._new(self.rows, other.cols, entry) + + def _eval_matrix_mul_elementwise(self, other): + return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other[i,j]) + + def _eval_matrix_rmul(self, other): + def entry(i, j): + return sum(other[i,k]*self[k,j] for k in range(other.cols)) + return self._new(other.rows, self.cols, entry) + + def _eval_pow_by_recursion(self, num): + if num == 1: + return self + + if num % 2 == 1: + a, b = self, self._eval_pow_by_recursion(num - 1) + else: + a = b = self._eval_pow_by_recursion(num // 2) + + return a.multiply(b) + + def _eval_pow_by_cayley(self, exp): + from sympy.discrete.recurrences import linrec_coeffs + row = self.shape[0] + p = self.charpoly() + + coeffs = (-p).all_coeffs()[1:] + coeffs = linrec_coeffs(coeffs, exp) + new_mat = self.eye(row) + ans = self.zeros(row) + + for i in range(row): + ans += coeffs[i]*new_mat + new_mat *= self + + return ans + + def _eval_pow_by_recursion_dotprodsimp(self, num, prevsimp=None): + if prevsimp is None: + prevsimp = [True]*len(self) + + if num == 1: + return self + + if num % 2 == 1: + a, b = self, self._eval_pow_by_recursion_dotprodsimp(num - 1, + prevsimp=prevsimp) + else: + a = b = self._eval_pow_by_recursion_dotprodsimp(num // 2, + prevsimp=prevsimp) + + m = a.multiply(b, dotprodsimp=False) + lenm = len(m) + elems = [None]*lenm + + for i in range(lenm): + if prevsimp[i]: + elems[i], prevsimp[i] = _dotprodsimp(m[i], withsimp=True) + else: + elems[i] = m[i] + + return m._new(m.rows, m.cols, elems) + + def _eval_scalar_mul(self, other): + return self._new(self.rows, self.cols, lambda i, j: self[i,j]*other) + + def _eval_scalar_rmul(self, other): + return self._new(self.rows, self.cols, lambda i, j: other*self[i,j]) + + def _eval_Mod(self, other): + return self._new(self.rows, self.cols, lambda i, j: Mod(self[i, j], other)) + + # Python arithmetic functions + def __abs__(self): + """Returns a new matrix with entry-wise absolute values.""" + return self._eval_Abs() + + @call_highest_priority('__radd__') + def __add__(self, other): + """Return self + other, raising ShapeError if shapes do not match.""" + + other, T = _coerce_operand(self, other) + + if T != "is_matrix": + return NotImplemented + + if self.shape != other.shape: + raise ShapeError(f"Matrix size mismatch: {self.shape} + {other.shape}.") + + # Unify matrix types + a, b = self, other + if a.__class__ != classof(a, b): + b, a = a, b + + return a._eval_add(b) + + @call_highest_priority('__rtruediv__') + def __truediv__(self, other): + return self * (self.one / other) + + @call_highest_priority('__rmatmul__') + def __matmul__(self, other): + self, other, T = _unify_with_other(self, other) + + if T != "is_matrix": + return NotImplemented + + return self.__mul__(other) + + def __mod__(self, other): + return self.applyfunc(lambda x: x % other) + + @call_highest_priority('__rmul__') + def __mul__(self, other): + """Return self*other where other is either a scalar or a matrix + of compatible dimensions. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> 2*A == A*2 == Matrix([[2, 4, 6], [8, 10, 12]]) + True + >>> B = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> A*B + Matrix([ + [30, 36, 42], + [66, 81, 96]]) + >>> B*A + Traceback (most recent call last): + ... + ShapeError: Matrices size mismatch. + >>> + + See Also + ======== + + matrix_multiply_elementwise + """ + + return self.multiply(other) + + def multiply(self, other, dotprodsimp=None): + """Same as __mul__() but with optional simplification. + + Parameters + ========== + + dotprodsimp : bool, optional + Specifies whether intermediate term algebraic simplification is used + during matrix multiplications to control expression blowup and thus + speed up calculation. Default is off. + """ + + isimpbool = _get_intermediate_simp_bool(False, dotprodsimp) + + self, other, T = _unify_with_other(self, other) + + if T == "possible_scalar": + try: + return self._eval_scalar_mul(other) + except TypeError: + return NotImplemented + + elif T == "is_matrix": + + if self.shape[1] != other.shape[0]: + raise ShapeError(f"Matrix size mismatch: {self.shape} * {other.shape}.") + + m = self._eval_matrix_mul(other) + + if isimpbool: + m = m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m]) + + return m + + else: + return NotImplemented + + def multiply_elementwise(self, other): + """Return the Hadamard product (elementwise product) of A and B + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[0, 1, 2], [3, 4, 5]]) + >>> B = Matrix([[1, 10, 100], [100, 10, 1]]) + >>> A.multiply_elementwise(B) + Matrix([ + [ 0, 10, 200], + [300, 40, 5]]) + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.cross + sympy.matrices.matrixbase.MatrixBase.dot + multiply + """ + if self.shape != other.shape: + raise ShapeError("Matrix shapes must agree {} != {}".format(self.shape, other.shape)) + + return self._eval_matrix_mul_elementwise(other) + + def __neg__(self): + return self._eval_scalar_mul(-1) + + @call_highest_priority('__rpow__') + def __pow__(self, exp): + """Return self**exp a scalar or symbol.""" + + return self.pow(exp) + + + def pow(self, exp, method=None): + r"""Return self**exp a scalar or symbol. + + Parameters + ========== + + method : multiply, mulsimp, jordan, cayley + If multiply then it returns exponentiation using recursion. + If jordan then Jordan form exponentiation will be used. + If cayley then the exponentiation is done using Cayley-Hamilton + theorem. + If mulsimp then the exponentiation is done using recursion + with dotprodsimp. This specifies whether intermediate term + algebraic simplification is used during naive matrix power to + control expression blowup and thus speed up calculation. + If None, then it heuristically decides which method to use. + + """ + + if method is not None and method not in ['multiply', 'mulsimp', 'jordan', 'cayley']: + raise TypeError('No such method') + if self.rows != self.cols: + raise NonSquareMatrixError() + a = self + jordan_pow = getattr(a, '_matrix_pow_by_jordan_blocks', None) + exp = sympify(exp) + + if exp.is_zero: + return a._new(a.rows, a.cols, lambda i, j: int(i == j)) + if exp == 1: + return a + + diagonal = getattr(a, 'is_diagonal', None) + if diagonal is not None and diagonal(): + return a._new(a.rows, a.cols, lambda i, j: a[i,j]**exp if i == j else 0) + + if exp.is_Number and exp % 1 == 0: + if a.rows == 1: + return a._new([[a[0]**exp]]) + if exp < 0: + exp = -exp + a = a.inv() + # When certain conditions are met, + # Jordan block algorithm is faster than + # computation by recursion. + if method == 'jordan': + try: + return jordan_pow(exp) + except MatrixError: + if method == 'jordan': + raise + + elif method == 'cayley': + if not exp.is_Number or exp % 1 != 0: + raise ValueError("cayley method is only valid for integer powers") + return a._eval_pow_by_cayley(exp) + + elif method == "mulsimp": + if not exp.is_Number or exp % 1 != 0: + raise ValueError("mulsimp method is only valid for integer powers") + return a._eval_pow_by_recursion_dotprodsimp(exp) + + elif method == "multiply": + if not exp.is_Number or exp % 1 != 0: + raise ValueError("multiply method is only valid for integer powers") + return a._eval_pow_by_recursion(exp) + + elif method is None and exp.is_Number and exp % 1 == 0: + if exp.is_Float: + exp = Integer(exp) + # Decide heuristically which method to apply + if a.rows == 2 and exp > 100000: + return jordan_pow(exp) + elif _get_intermediate_simp_bool(True, None): + return a._eval_pow_by_recursion_dotprodsimp(exp) + elif exp > 10000: + return a._eval_pow_by_cayley(exp) + else: + return a._eval_pow_by_recursion(exp) + + if jordan_pow: + try: + return jordan_pow(exp) + except NonInvertibleMatrixError: + # Raised by jordan_pow on zero determinant matrix unless exp is + # definitely known to be a non-negative integer. + # Here we raise if n is definitely not a non-negative integer + # but otherwise we can leave this as an unevaluated MatPow. + if exp.is_integer is False or exp.is_nonnegative is False: + raise + + from sympy.matrices.expressions import MatPow + return MatPow(a, exp) + + @call_highest_priority('__add__') + def __radd__(self, other): + return self + other + + @call_highest_priority('__matmul__') + def __rmatmul__(self, other): + self, other, T = _unify_with_other(self, other) + + if T != "is_matrix": + return NotImplemented + + return self.__rmul__(other) + + @call_highest_priority('__mul__') + def __rmul__(self, other): + return self.rmultiply(other) + + def rmultiply(self, other, dotprodsimp=None): + """Same as __rmul__() but with optional simplification. + + Parameters + ========== + + dotprodsimp : bool, optional + Specifies whether intermediate term algebraic simplification is used + during matrix multiplications to control expression blowup and thus + speed up calculation. Default is off. + """ + isimpbool = _get_intermediate_simp_bool(False, dotprodsimp) + self, other, T = _unify_with_other(self, other) + + if T == "possible_scalar": + try: + return self._eval_scalar_rmul(other) + except TypeError: + return NotImplemented + + elif T == "is_matrix": + if self.shape[0] != other.shape[1]: + raise ShapeError("Matrix size mismatch.") + + m = self._eval_matrix_rmul(other) + + if isimpbool: + return m._new(m.rows, m.cols, [_dotprodsimp(e) for e in m]) + + return m + + else: + return NotImplemented + + @call_highest_priority('__sub__') + def __rsub__(self, a): + return (-self) + a + + @call_highest_priority('__rsub__') + def __sub__(self, a): + return self + (-a) + + def _eval_det_bareiss(self, iszerofunc=_is_zero_after_expand_mul): + return _det_bareiss(self, iszerofunc=iszerofunc) + + def _eval_det_berkowitz(self): + return _det_berkowitz(self) + + def _eval_det_lu(self, iszerofunc=_iszero, simpfunc=None): + return _det_LU(self, iszerofunc=iszerofunc, simpfunc=simpfunc) + + def _eval_det_bird(self): + return _det_bird(self) + + def _eval_det_laplace(self): + return _det_laplace(self) + + def _eval_determinant(self): # for expressions.determinant.Determinant + return _det(self) + + def adjugate(self, method="berkowitz"): + return _adjugate(self, method=method) + + def charpoly(self, x='lambda', simplify=_utilities_simplify): + return _charpoly(self, x=x, simplify=simplify) + + def cofactor(self, i, j, method="berkowitz"): + return _cofactor(self, i, j, method=method) + + def cofactor_matrix(self, method="berkowitz"): + return _cofactor_matrix(self, method=method) + + def det(self, method="bareiss", iszerofunc=None): + return _det(self, method=method, iszerofunc=iszerofunc) + + def per(self): + return _per(self) + + def minor(self, i, j, method="berkowitz"): + return _minor(self, i, j, method=method) + + def minor_submatrix(self, i, j): + return _minor_submatrix(self, i, j) + + _find_reasonable_pivot.__doc__ = _find_reasonable_pivot.__doc__ + _find_reasonable_pivot_naive.__doc__ = _find_reasonable_pivot_naive.__doc__ + _eval_det_bareiss.__doc__ = _det_bareiss.__doc__ + _eval_det_berkowitz.__doc__ = _det_berkowitz.__doc__ + _eval_det_bird.__doc__ = _det_bird.__doc__ + _eval_det_laplace.__doc__ = _det_laplace.__doc__ + _eval_det_lu.__doc__ = _det_LU.__doc__ + _eval_determinant.__doc__ = _det.__doc__ + adjugate.__doc__ = _adjugate.__doc__ + charpoly.__doc__ = _charpoly.__doc__ + cofactor.__doc__ = _cofactor.__doc__ + cofactor_matrix.__doc__ = _cofactor_matrix.__doc__ + det.__doc__ = _det.__doc__ + per.__doc__ = _per.__doc__ + minor.__doc__ = _minor.__doc__ + minor_submatrix.__doc__ = _minor_submatrix.__doc__ + + def echelon_form(self, iszerofunc=_iszero, simplify=False, with_pivots=False): + return _echelon_form(self, iszerofunc=iszerofunc, simplify=simplify, + with_pivots=with_pivots) + + @property + def is_echelon(self): + return _is_echelon(self) + + def rank(self, iszerofunc=_iszero, simplify=False): + return _rank(self, iszerofunc=iszerofunc, simplify=simplify) + + def rref_rhs(self, rhs): + """Return reduced row-echelon form of matrix, matrix showing + rhs after reduction steps. ``rhs`` must have the same number + of rows as ``self``. + + Examples + ======== + + >>> from sympy import Matrix, symbols + >>> r1, r2 = symbols('r1 r2') + >>> Matrix([[1, 1], [2, 1]]).rref_rhs(Matrix([r1, r2])) + (Matrix([ + [1, 0], + [0, 1]]), Matrix([ + [ -r1 + r2], + [2*r1 - r2]])) + """ + r, _ = _rref(self.hstack(self, self.eye(self.rows), rhs)) + return r[:, :self.cols], r[:, -rhs.cols:] + + def rref(self, iszerofunc=_iszero, simplify=False, pivots=True, + normalize_last=True): + return _rref(self, iszerofunc=iszerofunc, simplify=simplify, + pivots=pivots, normalize_last=normalize_last) + + echelon_form.__doc__ = _echelon_form.__doc__ + is_echelon.__doc__ = _is_echelon.__doc__ + rank.__doc__ = _rank.__doc__ + rref.__doc__ = _rref.__doc__ + + def _normalize_op_args(self, op, col, k, col1, col2, error_str="col"): + """Validate the arguments for a row/column operation. ``error_str`` + can be one of "row" or "col" depending on the arguments being parsed.""" + if op not in ["n->kn", "n<->m", "n->n+km"]: + raise ValueError("Unknown {} operation '{}'. Valid col operations " + "are 'n->kn', 'n<->m', 'n->n+km'".format(error_str, op)) + + # define self_col according to error_str + self_cols = self.cols if error_str == 'col' else self.rows + + # normalize and validate the arguments + if op == "n->kn": + col = col if col is not None else col1 + if col is None or k is None: + raise ValueError("For a {0} operation 'n->kn' you must provide the " + "kwargs `{0}` and `k`".format(error_str)) + if not 0 <= col < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col)) + + elif op == "n<->m": + # we need two cols to swap. It does not matter + # how they were specified, so gather them together and + # remove `None` + cols = {col, k, col1, col2}.difference([None]) + if len(cols) > 2: + # maybe the user left `k` by mistake? + cols = {col, col1, col2}.difference([None]) + if len(cols) != 2: + raise ValueError("For a {0} operation 'n<->m' you must provide the " + "kwargs `{0}1` and `{0}2`".format(error_str)) + col1, col2 = cols + if not 0 <= col1 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col1)) + if not 0 <= col2 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2)) + + elif op == "n->n+km": + col = col1 if col is None else col + col2 = col1 if col2 is None else col2 + if col is None or col2 is None or k is None: + raise ValueError("For a {0} operation 'n->n+km' you must provide the " + "kwargs `{0}`, `k`, and `{0}2`".format(error_str)) + if col == col2: + raise ValueError("For a {0} operation 'n->n+km' `{0}` and `{0}2` must " + "be different.".format(error_str)) + if not 0 <= col < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col)) + if not 0 <= col2 < self_cols: + raise ValueError("This matrix does not have a {} '{}'".format(error_str, col2)) + + else: + raise ValueError('invalid operation %s' % repr(op)) + + return op, col, k, col1, col2 + + def _eval_col_op_multiply_col_by_const(self, col, k): + def entry(i, j): + if j == col: + return k * self[i, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_col_op_swap(self, col1, col2): + def entry(i, j): + if j == col1: + return self[i, col2] + elif j == col2: + return self[i, col1] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_col_op_add_multiple_to_other_col(self, col, k, col2): + def entry(i, j): + if j == col: + return self[i, j] + k * self[i, col2] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_swap(self, row1, row2): + def entry(i, j): + if i == row1: + return self[row2, j] + elif i == row2: + return self[row1, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_multiply_row_by_const(self, row, k): + def entry(i, j): + if i == row: + return k * self[i, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def _eval_row_op_add_multiple_to_other_row(self, row, k, row2): + def entry(i, j): + if i == row: + return self[i, j] + k * self[row2, j] + return self[i, j] + return self._new(self.rows, self.cols, entry) + + def elementary_col_op(self, op="n->kn", col=None, k=None, col1=None, col2=None): + """Performs the elementary column operation `op`. + + `op` may be one of + + * ``"n->kn"`` (column n goes to k*n) + * ``"n<->m"`` (swap column n and column m) + * ``"n->n+km"`` (column n goes to column n + k*column m) + + Parameters + ========== + + op : string; the elementary row operation + col : the column to apply the column operation + k : the multiple to apply in the column operation + col1 : one column of a column swap + col2 : second column of a column swap or column "m" in the column operation + "n->n+km" + """ + + op, col, k, col1, col2 = self._normalize_op_args(op, col, k, col1, col2, "col") + + # now that we've validated, we're all good to dispatch + if op == "n->kn": + return self._eval_col_op_multiply_col_by_const(col, k) + if op == "n<->m": + return self._eval_col_op_swap(col1, col2) + if op == "n->n+km": + return self._eval_col_op_add_multiple_to_other_col(col, k, col2) + + def elementary_row_op(self, op="n->kn", row=None, k=None, row1=None, row2=None): + """Performs the elementary row operation `op`. + + `op` may be one of + + * ``"n->kn"`` (row n goes to k*n) + * ``"n<->m"`` (swap row n and row m) + * ``"n->n+km"`` (row n goes to row n + k*row m) + + Parameters + ========== + + op : string; the elementary row operation + row : the row to apply the row operation + k : the multiple to apply in the row operation + row1 : one row of a row swap + row2 : second row of a row swap or row "m" in the row operation + "n->n+km" + """ + + op, row, k, row1, row2 = self._normalize_op_args(op, row, k, row1, row2, "row") + + # now that we've validated, we're all good to dispatch + if op == "n->kn": + return self._eval_row_op_multiply_row_by_const(row, k) + if op == "n<->m": + return self._eval_row_op_swap(row1, row2) + if op == "n->n+km": + return self._eval_row_op_add_multiple_to_other_row(row, k, row2) + + def columnspace(self, simplify=False): + return _columnspace(self, simplify=simplify) + + def nullspace(self, simplify=False, iszerofunc=_iszero): + return _nullspace(self, simplify=simplify, iszerofunc=iszerofunc) + + def rowspace(self, simplify=False): + return _rowspace(self, simplify=simplify) + + # This is a classmethod but is converted to such later in order to allow + # assignment of __doc__ since that does not work for already wrapped + # classmethods in Python 3.6. + def orthogonalize(cls, *vecs, **kwargs): + return _orthogonalize(cls, *vecs, **kwargs) + + columnspace.__doc__ = _columnspace.__doc__ + nullspace.__doc__ = _nullspace.__doc__ + rowspace.__doc__ = _rowspace.__doc__ + orthogonalize.__doc__ = _orthogonalize.__doc__ + + orthogonalize = classmethod(orthogonalize) # type:ignore + + def eigenvals(self, error_when_incomplete=True, **flags): + return _eigenvals(self, error_when_incomplete=error_when_incomplete, **flags) + + def eigenvects(self, error_when_incomplete=True, iszerofunc=_iszero, **flags): + return _eigenvects(self, error_when_incomplete=error_when_incomplete, + iszerofunc=iszerofunc, **flags) + + def is_diagonalizable(self, reals_only=False, **kwargs): + return _is_diagonalizable(self, reals_only=reals_only, **kwargs) + + def diagonalize(self, reals_only=False, sort=False, normalize=False): + return _diagonalize(self, reals_only=reals_only, sort=sort, + normalize=normalize) + + def bidiagonalize(self, upper=True): + return _bidiagonalize(self, upper=upper) + + def bidiagonal_decomposition(self, upper=True): + return _bidiagonal_decomposition(self, upper=upper) + + @property + def is_positive_definite(self): + return _is_positive_definite(self) + + @property + def is_positive_semidefinite(self): + return _is_positive_semidefinite(self) + + @property + def is_negative_definite(self): + return _is_negative_definite(self) + + @property + def is_negative_semidefinite(self): + return _is_negative_semidefinite(self) + + @property + def is_indefinite(self): + return _is_indefinite(self) + + def jordan_form(self, calc_transform=True, **kwargs): + return _jordan_form(self, calc_transform=calc_transform, **kwargs) + + def left_eigenvects(self, **flags): + return _left_eigenvects(self, **flags) + + def singular_values(self): + return _singular_values(self) + + eigenvals.__doc__ = _eigenvals.__doc__ + eigenvects.__doc__ = _eigenvects.__doc__ + is_diagonalizable.__doc__ = _is_diagonalizable.__doc__ + diagonalize.__doc__ = _diagonalize.__doc__ + is_positive_definite.__doc__ = _is_positive_definite.__doc__ + is_positive_semidefinite.__doc__ = _is_positive_semidefinite.__doc__ + is_negative_definite.__doc__ = _is_negative_definite.__doc__ + is_negative_semidefinite.__doc__ = _is_negative_semidefinite.__doc__ + is_indefinite.__doc__ = _is_indefinite.__doc__ + jordan_form.__doc__ = _jordan_form.__doc__ + left_eigenvects.__doc__ = _left_eigenvects.__doc__ + singular_values.__doc__ = _singular_values.__doc__ + bidiagonalize.__doc__ = _bidiagonalize.__doc__ + bidiagonal_decomposition.__doc__ = _bidiagonal_decomposition.__doc__ + + def diff(self, *args, evaluate=True, **kwargs): + """Calculate the derivative of each element in the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.diff(x) + Matrix([ + [1, 0], + [0, 0]]) + + See Also + ======== + + integrate + limit + """ + # XXX this should be handled here rather than in Derivative + from sympy.tensor.array.array_derivatives import ArrayDerivative + deriv = ArrayDerivative(self, *args, evaluate=evaluate) + # XXX This can rather changed to always return immutable matrix + if not isinstance(self, Basic) and evaluate: + return deriv.as_mutable() + return deriv + + def _eval_derivative(self, arg): + return self.applyfunc(lambda x: x.diff(arg)) + + def integrate(self, *args, **kwargs): + """Integrate each element of the matrix. ``args`` will + be passed to the ``integrate`` function. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.integrate((x, )) + Matrix([ + [x**2/2, x*y], + [ x, 0]]) + >>> M.integrate((x, 0, 2)) + Matrix([ + [2, 2*y], + [2, 0]]) + + See Also + ======== + + limit + diff + """ + return self.applyfunc(lambda x: x.integrate(*args, **kwargs)) + + def jacobian(self, X): + """Calculates the Jacobian matrix (derivative of a vector-valued function). + + Parameters + ========== + + ``self`` : vector of expressions representing functions f_i(x_1, ..., x_n). + X : set of x_i's in order, it can be a list or a Matrix + + Both ``self`` and X can be a row or a column matrix in any order + (i.e., jacobian() should always work). + + Examples + ======== + + >>> from sympy import sin, cos, Matrix + >>> from sympy.abc import rho, phi + >>> X = Matrix([rho*cos(phi), rho*sin(phi), rho**2]) + >>> Y = Matrix([rho, phi]) + >>> X.jacobian(Y) + Matrix([ + [cos(phi), -rho*sin(phi)], + [sin(phi), rho*cos(phi)], + [ 2*rho, 0]]) + >>> X = Matrix([rho*cos(phi), rho*sin(phi)]) + >>> X.jacobian(Y) + Matrix([ + [cos(phi), -rho*sin(phi)], + [sin(phi), rho*cos(phi)]]) + + See Also + ======== + + hessian + wronskian + """ + from sympy.matrices.matrixbase import MatrixBase + if not isinstance(X, MatrixBase): + X = self._new(X) + # Both X and ``self`` can be a row or a column matrix, so we need to make + # sure all valid combinations work, but everything else fails: + if self.shape[0] == 1: + m = self.shape[1] + elif self.shape[1] == 1: + m = self.shape[0] + else: + raise TypeError("``self`` must be a row or a column matrix") + if X.shape[0] == 1: + n = X.shape[1] + elif X.shape[1] == 1: + n = X.shape[0] + else: + raise TypeError("X must be a row or a column matrix") + + # m is the number of functions and n is the number of variables + # computing the Jacobian is now easy: + return self._new(m, n, lambda j, i: self[j].diff(X[i])) + + def limit(self, *args): + """Calculate the limit of each element in the matrix. + ``args`` will be passed to the ``limit`` function. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x, y + >>> M = Matrix([[x, y], [1, 0]]) + >>> M.limit(x, 2) + Matrix([ + [2, y], + [1, 0]]) + + See Also + ======== + + integrate + diff + """ + return self.applyfunc(lambda x: x.limit(*args)) + + def berkowitz_charpoly(self, x=Dummy('lambda'), simplify=_utilities_simplify): + return self.charpoly(x=x) + + def berkowitz_det(self): + """Computes determinant using Berkowitz method. + + See Also + ======== + + det + """ + return self.det(method='berkowitz') + + def berkowitz_eigenvals(self, **flags): + """Computes eigenvalues of a Matrix using Berkowitz method.""" + return self.eigenvals(**flags) + + def berkowitz_minors(self): + """Computes principal minors using Berkowitz method.""" + sign, minors = self.one, [] + + for poly in self.berkowitz(): + minors.append(sign * poly[-1]) + sign = -sign + + return tuple(minors) + + def berkowitz(self): + from sympy.matrices import zeros + berk = ((1,),) + if not self: + return berk + + if not self.is_square: + raise NonSquareMatrixError() + + A, N = self, self.rows + transforms = [0] * (N - 1) + + for n in range(N, 1, -1): + T, k = zeros(n + 1, n), n - 1 + + R, C = -A[k, :k], A[:k, k] + A, a = A[:k, :k], -A[k, k] + + items = [C] + + for i in range(0, n - 2): + items.append(A * items[i]) + + for i, B in enumerate(items): + items[i] = (R * B)[0, 0] + + items = [self.one, a] + items + + for i in range(n): + T[i:, i] = items[:n - i + 1] + + transforms[k - 1] = T + + polys = [self._new([self.one, -A[0, 0]])] + + for i, T in enumerate(transforms): + polys.append(T * polys[i]) + + return berk + tuple(map(tuple, polys)) + + def cofactorMatrix(self, method="berkowitz"): + return self.cofactor_matrix(method=method) + + def det_bareis(self): + return _det_bareiss(self) + + def det_LU_decomposition(self): + """Compute matrix determinant using LU decomposition. + + + Note that this method fails if the LU decomposition itself + fails. In particular, if the matrix has no inverse this method + will fail. + + TODO: Implement algorithm for sparse matrices (SFF), + http://www.eecis.udel.edu/~saunders/papers/sffge/it5.ps. + + See Also + ======== + + + det + berkowitz_det + """ + return self.det(method='lu') + + def jordan_cell(self, eigenval, n): + return self.jordan_block(size=n, eigenvalue=eigenval) + + def jordan_cells(self, calc_transformation=True): + P, J = self.jordan_form() + return P, J.get_diag_blocks() + + def minorEntry(self, i, j, method="berkowitz"): + return self.minor(i, j, method=method) + + def minorMatrix(self, i, j): + return self.minor_submatrix(i, j) + + def permuteBkwd(self, perm): + """Permute the rows of the matrix with the given permutation in reverse.""" + return self.permute_rows(perm, direction='backward') + + def permuteFwd(self, perm): + """Permute the rows of the matrix with the given permutation.""" + return self.permute_rows(perm, direction='forward') + + @property + def kind(self) -> MatrixKind: + elem_kinds = {e.kind for e in self.flat()} + if len(elem_kinds) == 1: + elemkind, = elem_kinds + else: + elemkind = UndefinedKind + return MatrixKind(elemkind) + + def flat(self): + """ + Returns a flat list of all elements in the matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> m = Matrix([[0, 2], [3, 4]]) + >>> m.flat() + [0, 2, 3, 4] + + See Also + ======== + + tolist + values + """ + return [self[i, j] for i in range(self.rows) for j in range(self.cols)] + + def __array__(self, dtype=object, copy=None): + if copy is not None and not copy: + raise TypeError("Cannot implement copy=False when converting Matrix to ndarray") + from .dense import matrix2numpy + return matrix2numpy(self, dtype=dtype) + + def __len__(self): + """Return the number of elements of ``self``. + + Implemented mainly so bool(Matrix()) == False. + """ + return self.rows * self.cols + + def _matrix_pow_by_jordan_blocks(self, num): + from sympy.matrices import diag, MutableMatrix + + def jordan_cell_power(jc, n): + N = jc.shape[0] + l = jc[0,0] + if l.is_zero: + if N == 1 and n.is_nonnegative: + jc[0,0] = l**n + elif not (n.is_integer and n.is_nonnegative): + raise NonInvertibleMatrixError("Non-invertible matrix can only be raised to a nonnegative integer") + else: + for i in range(N): + jc[0,i] = KroneckerDelta(i, n) + else: + for i in range(N): + bn = binomial(n, i) + if isinstance(bn, binomial): + bn = bn._eval_expand_func() + jc[0,i] = l**(n-i)*bn + for i in range(N): + for j in range(1, N-i): + jc[j,i+j] = jc [j-1,i+j-1] + + P, J = self.jordan_form() + jordan_cells = J.get_diag_blocks() + # Make sure jordan_cells matrices are mutable: + jordan_cells = [MutableMatrix(j) for j in jordan_cells] + for j in jordan_cells: + jordan_cell_power(j, num) + return self._new(P.multiply(diag(*jordan_cells)) + .multiply(P.inv())) + + def __str__(self): + if S.Zero in self.shape: + return 'Matrix(%s, %s, [])' % (self.rows, self.cols) + return "Matrix(%s)" % str(self.tolist()) + + def _format_str(self, printer=None): + if not printer: + printer = StrPrinter() + # Handle zero dimensions: + if S.Zero in self.shape: + return 'Matrix(%s, %s, [])' % (self.rows, self.cols) + if self.rows == 1: + return "Matrix([%s])" % self.table(printer, rowsep=',\n') + return "Matrix([\n%s])" % self.table(printer, rowsep=',\n') + + @classmethod + def irregular(cls, ntop, *matrices, **kwargs): + """Return a matrix filled by the given matrices which + are listed in order of appearance from left to right, top to + bottom as they first appear in the matrix. They must fill the + matrix completely. + + Examples + ======== + + >>> from sympy import ones, Matrix + >>> Matrix.irregular(3, ones(2,1), ones(3,3)*2, ones(2,2)*3, + ... ones(1,1)*4, ones(2,2)*5, ones(1,2)*6, ones(1,2)*7) + Matrix([ + [1, 2, 2, 2, 3, 3], + [1, 2, 2, 2, 3, 3], + [4, 2, 2, 2, 5, 5], + [6, 6, 7, 7, 5, 5]]) + """ + ntop = as_int(ntop) + # make sure we are working with explicit matrices + b = [i.as_explicit() if hasattr(i, 'as_explicit') else i + for i in matrices] + q = list(range(len(b))) + dat = [i.rows for i in b] + active = [q.pop(0) for _ in range(ntop)] + cols = sum(b[i].cols for i in active) + rows = [] + while any(dat): + r = [] + for a, j in enumerate(active): + r.extend(b[j][-dat[j], :]) + dat[j] -= 1 + if dat[j] == 0 and q: + active[a] = q.pop(0) + if len(r) != cols: + raise ValueError(filldedent(''' + Matrices provided do not appear to fill + the space completely.''')) + rows.append(r) + return cls._new(rows) + + @classmethod + def _handle_ndarray(cls, arg): + # NumPy array or matrix or some other object that implements + # __array__. So let's first use this method to get a + # numpy.array() and then make a Python list out of it. + arr = arg.__array__() + if len(arr.shape) == 2: + rows, cols = arr.shape[0], arr.shape[1] + flat_list = [cls._sympify(i) for i in arr.ravel()] + return rows, cols, flat_list + elif len(arr.shape) == 1: + flat_list = [cls._sympify(i) for i in arr] + return arr.shape[0], 1, flat_list + else: + raise NotImplementedError( + "SymPy supports just 1D and 2D matrices") + + @classmethod + def _handle_creation_inputs(cls, *args, **kwargs): + """Return the number of rows, cols and flat matrix elements. + + Examples + ======== + + >>> from sympy import Matrix, I + + Matrix can be constructed as follows: + + * from a nested list of iterables + + >>> Matrix( ((1, 2+I), (3, 4)) ) + Matrix([ + [1, 2 + I], + [3, 4]]) + + * from un-nested iterable (interpreted as a column) + + >>> Matrix( [1, 2] ) + Matrix([ + [1], + [2]]) + + * from un-nested iterable with dimensions + + >>> Matrix(1, 2, [1, 2] ) + Matrix([[1, 2]]) + + * from no arguments (a 0 x 0 matrix) + + >>> Matrix() + Matrix(0, 0, []) + + * from a rule + + >>> Matrix(2, 2, lambda i, j: i/(j + 1) ) + Matrix([ + [0, 0], + [1, 1/2]]) + + See Also + ======== + irregular - filling a matrix with irregular blocks + """ + from sympy.matrices import SparseMatrix + from sympy.matrices.expressions.matexpr import MatrixSymbol + from sympy.matrices.expressions.blockmatrix import BlockMatrix + + flat_list = None + + if len(args) == 1: + # Matrix(SparseMatrix(...)) + if isinstance(args[0], SparseMatrix): + return args[0].rows, args[0].cols, flatten(args[0].tolist()) + + # Matrix(Matrix(...)) + elif isinstance(args[0], MatrixBase): + return args[0].rows, args[0].cols, args[0].flat() + + # Matrix(MatrixSymbol('X', 2, 2)) + elif isinstance(args[0], Basic) and args[0].is_Matrix: + return args[0].rows, args[0].cols, args[0].as_explicit().flat() + + elif isinstance(args[0], mp.matrix): + M = args[0] + flat_list = [cls._sympify(x) for x in M] + return M.rows, M.cols, flat_list + + # Matrix(numpy.ones((2, 2))) + elif hasattr(args[0], "__array__"): + return cls._handle_ndarray(args[0]) + + # Matrix([1, 2, 3]) or Matrix([[1, 2], [3, 4]]) + elif is_sequence(args[0]) \ + and not isinstance(args[0], DeferredVector): + dat = list(args[0]) + ismat = lambda i: isinstance(i, MatrixBase) and ( + evaluate or isinstance(i, (BlockMatrix, MatrixSymbol))) + raw = lambda i: is_sequence(i) and not ismat(i) + evaluate = kwargs.get('evaluate', True) + + + if evaluate: + + def make_explicit(x): + """make Block and Symbol explicit""" + if isinstance(x, BlockMatrix): + return x.as_explicit() + elif isinstance(x, MatrixSymbol) and all(_.is_Integer for _ in x.shape): + return x.as_explicit() + else: + return x + + def make_explicit_row(row): + # Could be list or could be list of lists + if isinstance(row, (list, tuple)): + return [make_explicit(x) for x in row] + else: + return make_explicit(row) + + if isinstance(dat, (list, tuple)): + dat = [make_explicit_row(row) for row in dat] + + if dat in ([], [[]]): + rows = cols = 0 + flat_list = [] + elif not any(raw(i) or ismat(i) for i in dat): + # a column as a list of values + flat_list = [cls._sympify(i) for i in dat] + rows = len(flat_list) + cols = 1 if rows else 0 + elif evaluate and all(ismat(i) for i in dat): + # a column as a list of matrices + ncol = {i.cols for i in dat if any(i.shape)} + if ncol: + if len(ncol) != 1: + raise ValueError('mismatched dimensions') + flat_list = [_ for i in dat for r in i.tolist() for _ in r] + cols = ncol.pop() + rows = len(flat_list)//cols + else: + rows = cols = 0 + flat_list = [] + elif evaluate and any(ismat(i) for i in dat): + ncol = set() + flat_list = [] + for i in dat: + if ismat(i): + flat_list.extend( + [k for j in i.tolist() for k in j]) + if any(i.shape): + ncol.add(i.cols) + elif raw(i): + if i: + ncol.add(len(i)) + flat_list.extend([cls._sympify(ij) for ij in i]) + else: + ncol.add(1) + flat_list.append(i) + if len(ncol) > 1: + raise ValueError('mismatched dimensions') + cols = ncol.pop() + rows = len(flat_list)//cols + else: + # list of lists; each sublist is a logical row + # which might consist of many rows if the values in + # the row are matrices + flat_list = [] + ncol = set() + rows = cols = 0 + for row in dat: + if not is_sequence(row) and \ + not getattr(row, 'is_Matrix', False): + raise ValueError('expecting list of lists') + + if hasattr(row, '__array__'): + if 0 in row.shape: + continue + + if evaluate and all(ismat(i) for i in row): + r, c, flatT = cls._handle_creation_inputs( + [i.T for i in row]) + T = reshape(flatT, [c]) + flat = \ + [T[i][j] for j in range(c) for i in range(r)] + r, c = c, r + else: + r = 1 + if getattr(row, 'is_Matrix', False): + c = 1 + flat = [row] + else: + c = len(row) + flat = [cls._sympify(i) for i in row] + ncol.add(c) + if len(ncol) > 1: + raise ValueError('mismatched dimensions') + flat_list.extend(flat) + rows += r + cols = ncol.pop() if ncol else 0 + + elif len(args) == 3: + rows = as_int(args[0]) + cols = as_int(args[1]) + + if rows < 0 or cols < 0: + raise ValueError("Cannot create a {} x {} matrix. " + "Both dimensions must be positive".format(rows, cols)) + + # Matrix(2, 2, lambda i, j: i+j) + if len(args) == 3 and isinstance(args[2], Callable): + op = args[2] + flat_list = [] + for i in range(rows): + flat_list.extend( + [cls._sympify(op(cls._sympify(i), cls._sympify(j))) + for j in range(cols)]) + + # Matrix(2, 2, [1, 2, 3, 4]) + elif len(args) == 3 and is_sequence(args[2]): + flat_list = args[2] + if len(flat_list) != rows * cols: + raise ValueError( + 'List length should be equal to rows*columns') + flat_list = [cls._sympify(i) for i in flat_list] + + + # Matrix() + elif len(args) == 0: + # Empty Matrix + rows = cols = 0 + flat_list = [] + + if flat_list is None: + raise TypeError(filldedent(''' + Data type not understood; expecting list of lists + or lists of values.''')) + + return rows, cols, flat_list + + def _setitem(self, key, value): + """Helper to set value at location given by key. + + Examples + ======== + + >>> from sympy import Matrix, I, zeros, ones + >>> m = Matrix(((1, 2+I), (3, 4))) + >>> m + Matrix([ + [1, 2 + I], + [3, 4]]) + >>> m[1, 0] = 9 + >>> m + Matrix([ + [1, 2 + I], + [9, 4]]) + >>> m[1, 0] = [[0, 1]] + + To replace row r you assign to position r*m where m + is the number of columns: + + >>> M = zeros(4) + >>> m = M.cols + >>> M[3*m] = ones(1, m)*2; M + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [2, 2, 2, 2]]) + + And to replace column c you can assign to position c: + + >>> M[2] = ones(m, 1)*4; M + Matrix([ + [0, 0, 4, 0], + [0, 0, 4, 0], + [0, 0, 4, 0], + [2, 2, 4, 2]]) + """ + from .dense import Matrix + + is_slice = isinstance(key, slice) + i, j = key = self.key2ij(key) + is_mat = isinstance(value, MatrixBase) + if isinstance(i, slice) or isinstance(j, slice): + if is_mat: + self.copyin_matrix(key, value) + return + if not isinstance(value, Expr) and is_sequence(value): + self.copyin_list(key, value) + return + raise ValueError('unexpected value: %s' % value) + else: + if (not is_mat and + not isinstance(value, Basic) and is_sequence(value)): + value = Matrix(value) + is_mat = True + if is_mat: + if is_slice: + key = (slice(*divmod(i, self.cols)), + slice(*divmod(j, self.cols))) + else: + key = (slice(i, i + value.rows), + slice(j, j + value.cols)) + self.copyin_matrix(key, value) + else: + return i, j, self._sympify(value) + return + + def add(self, b): + """Return self + b.""" + return self + b + + def condition_number(self): + """Returns the condition number of a matrix. + + This is the maximum singular value divided by the minimum singular value + + Examples + ======== + + >>> from sympy import Matrix, S + >>> A = Matrix([[1, 0, 0], [0, 10, 0], [0, 0, S.One/10]]) + >>> A.condition_number() + 100 + + See Also + ======== + + singular_values + """ + + if not self: + return self.zero + singularvalues = self.singular_values() + return Max(*singularvalues) / Min(*singularvalues) + + def copy(self): + """ + Returns the copy of a matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.copy() + Matrix([ + [1, 2], + [3, 4]]) + + """ + return self._new(self.rows, self.cols, self.flat()) + + def cross(self, b): + r""" + Return the cross product of ``self`` and ``b`` relaxing the condition + of compatible dimensions: if each has 3 elements, a matrix of the + same type and shape as ``self`` will be returned. If ``b`` has the same + shape as ``self`` then common identities for the cross product (like + `a \times b = - b \times a`) will hold. + + Parameters + ========== + b : 3x1 or 1x3 Matrix + + See Also + ======== + + dot + hat + vee + multiply + multiply_elementwise + """ + from sympy.matrices.expressions.matexpr import MatrixExpr + + if not isinstance(b, (MatrixBase, MatrixExpr)): + raise TypeError( + "{} must be a Matrix, not {}.".format(b, type(b))) + + if not (self.rows * self.cols == b.rows * b.cols == 3): + raise ShapeError("Dimensions incorrect for cross product: %s x %s" % + ((self.rows, self.cols), (b.rows, b.cols))) + else: + return self._new(self.rows, self.cols, ( + (self[1] * b[2] - self[2] * b[1]), + (self[2] * b[0] - self[0] * b[2]), + (self[0] * b[1] - self[1] * b[0]))) + + def hat(self): + r""" + Return the skew-symmetric matrix representing the cross product, + so that ``self.hat() * b`` is equivalent to ``self.cross(b)``. + + Examples + ======== + + Calling ``hat`` creates a skew-symmetric 3x3 Matrix from a 3x1 Matrix: + + >>> from sympy import Matrix + >>> a = Matrix([1, 2, 3]) + >>> a.hat() + Matrix([ + [ 0, -3, 2], + [ 3, 0, -1], + [-2, 1, 0]]) + + Multiplying it with another 3x1 Matrix calculates the cross product: + + >>> b = Matrix([3, 2, 1]) + >>> a.hat() * b + Matrix([ + [-4], + [ 8], + [-4]]) + + Which is equivalent to calling the ``cross`` method: + + >>> a.cross(b) + Matrix([ + [-4], + [ 8], + [-4]]) + + See Also + ======== + + dot + cross + vee + multiply + multiply_elementwise + """ + + if self.shape != (3, 1): + raise ShapeError("Dimensions incorrect, expected (3, 1), got " + + str(self.shape)) + else: + x, y, z = self + return self._new(3, 3, ( + 0, -z, y, + z, 0, -x, + -y, x, 0)) + + def vee(self): + r""" + Return a 3x1 vector from a skew-symmetric matrix representing the cross product, + so that ``self * b`` is equivalent to ``self.vee().cross(b)``. + + Examples + ======== + + Calling ``vee`` creates a vector from a skew-symmetric Matrix: + + >>> from sympy import Matrix + >>> A = Matrix([[0, -3, 2], [3, 0, -1], [-2, 1, 0]]) + >>> a = A.vee() + >>> a + Matrix([ + [1], + [2], + [3]]) + + Calculating the matrix product of the original matrix with a vector + is equivalent to a cross product: + + >>> b = Matrix([3, 2, 1]) + >>> A * b + Matrix([ + [-4], + [ 8], + [-4]]) + + >>> a.cross(b) + Matrix([ + [-4], + [ 8], + [-4]]) + + ``vee`` can also be used to retrieve angular velocity expressions. + Defining a rotation matrix: + + >>> from sympy import rot_ccw_axis3, trigsimp + >>> from sympy.physics.mechanics import dynamicsymbols + >>> theta = dynamicsymbols('theta') + >>> R = rot_ccw_axis3(theta) + >>> R + Matrix([ + [cos(theta(t)), -sin(theta(t)), 0], + [sin(theta(t)), cos(theta(t)), 0], + [ 0, 0, 1]]) + + We can retrive the angular velocity: + + >>> Omega = R.T * R.diff() + >>> Omega = trigsimp(Omega) + >>> Omega.vee() + Matrix([ + [ 0], + [ 0], + [Derivative(theta(t), t)]]) + + See Also + ======== + + dot + cross + hat + multiply + multiply_elementwise + """ + + if self.shape != (3, 3): + raise ShapeError("Dimensions incorrect, expected (3, 3), got " + + str(self.shape)) + elif not self.is_anti_symmetric(): + raise ValueError("Matrix is not skew-symmetric") + else: + return self._new(3, 1, ( + self[2, 1], + self[0, 2], + self[1, 0])) + + @property + def D(self): + """Return Dirac conjugate (if ``self.rows == 4``). + + Examples + ======== + + >>> from sympy import Matrix, I, eye + >>> m = Matrix((0, 1 + I, 2, 3)) + >>> m.D + Matrix([[0, 1 - I, -2, -3]]) + >>> m = (eye(4) + I*eye(4)) + >>> m[0, 3] = 2 + >>> m.D + Matrix([ + [1 - I, 0, 0, 0], + [ 0, 1 - I, 0, 0], + [ 0, 0, -1 + I, 0], + [ 2, 0, 0, -1 + I]]) + + If the matrix does not have 4 rows an AttributeError will be raised + because this property is only defined for matrices with 4 rows. + + >>> Matrix(eye(2)).D + Traceback (most recent call last): + ... + AttributeError: Matrix has no attribute D. + + See Also + ======== + + sympy.matrices.matrixbase.MatrixBase.conjugate: By-element conjugation + sympy.matrices.matrixbase.MatrixBase.H: Hermite conjugation + """ + from sympy.physics.matrices import mgamma + if self.rows != 4: + # In Python 3.2, properties can only return an AttributeError + # so we can't raise a ShapeError -- see commit which added the + # first line of this inline comment. Also, there is no need + # for a message since MatrixBase will raise the AttributeError + raise AttributeError + return self.H * mgamma(0) + + def dot(self, b, hermitian=None, conjugate_convention=None): + """Return the dot or inner product of two vectors of equal length. + Here ``self`` must be a ``Matrix`` of size 1 x n or n x 1, and ``b`` + must be either a matrix of size 1 x n, n x 1, or a list/tuple of length n. + A scalar is returned. + + By default, ``dot`` does not conjugate ``self`` or ``b``, even if there are + complex entries. Set ``hermitian=True`` (and optionally a ``conjugate_convention``) + to compute the hermitian inner product. + + Possible kwargs are ``hermitian`` and ``conjugate_convention``. + + If ``conjugate_convention`` is ``"left"``, ``"math"`` or ``"maths"``, + the conjugate of the first vector (``self``) is used. If ``"right"`` + or ``"physics"`` is specified, the conjugate of the second vector ``b`` is used. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> v = Matrix([1, 1, 1]) + >>> M.row(0).dot(v) + 6 + >>> M.col(0).dot(v) + 12 + >>> v = [3, 2, 1] + >>> M.row(0).dot(v) + 10 + + >>> from sympy import I + >>> q = Matrix([1*I, 1*I, 1*I]) + >>> q.dot(q, hermitian=False) + -3 + + >>> q.dot(q, hermitian=True) + 3 + + >>> q1 = Matrix([1, 1, 1*I]) + >>> q.dot(q1, hermitian=True, conjugate_convention="maths") + 1 - 2*I + >>> q.dot(q1, hermitian=True, conjugate_convention="physics") + 1 + 2*I + + + See Also + ======== + + cross + multiply + multiply_elementwise + """ + from .dense import Matrix + + if not isinstance(b, MatrixBase): + if is_sequence(b): + if len(b) != self.cols and len(b) != self.rows: + raise ShapeError( + "Dimensions incorrect for dot product: %s, %s" % ( + self.shape, len(b))) + return self.dot(Matrix(b)) + else: + raise TypeError( + "`b` must be an ordered iterable or Matrix, not %s." % + type(b)) + + if (1 not in self.shape) or (1 not in b.shape): + raise ShapeError + if len(self) != len(b): + raise ShapeError( + "Dimensions incorrect for dot product: %s, %s" % (self.shape, b.shape)) + + mat = self + n = len(mat) + if mat.shape != (1, n): + mat = mat.reshape(1, n) + if b.shape != (n, 1): + b = b.reshape(n, 1) + + # Now ``mat`` is a row vector and ``b`` is a column vector. + + # If it so happens that only conjugate_convention is passed + # then automatically set hermitian to True. If only hermitian + # is true but no conjugate_convention is not passed then + # automatically set it to ``"maths"`` + + if conjugate_convention is not None and hermitian is None: + hermitian = True + if hermitian and conjugate_convention is None: + conjugate_convention = "maths" + + if hermitian == True: + if conjugate_convention in ("maths", "left", "math"): + mat = mat.conjugate() + elif conjugate_convention in ("physics", "right"): + b = b.conjugate() + else: + raise ValueError("Unknown conjugate_convention was entered." + " conjugate_convention must be one of the" + " following: math, maths, left, physics or right.") + return (mat * b)[0] + + def dual(self): + """Returns the dual of a matrix. + + A dual of a matrix is: + + ``(1/2)*levicivita(i, j, k, l)*M(k, l)`` summed over indices `k` and `l` + + Since the levicivita method is anti_symmetric for any pairwise + exchange of indices, the dual of a symmetric matrix is the zero + matrix. Strictly speaking the dual defined here assumes that the + 'matrix' `M` is a contravariant anti_symmetric second rank tensor, + so that the dual is a covariant second rank tensor. + + """ + from sympy.matrices import zeros + + M, n = self[:, :], self.rows + work = zeros(n) + if self.is_symmetric(): + return work + + for i in range(1, n): + for j in range(1, n): + acum = 0 + for k in range(1, n): + acum += LeviCivita(i, j, 0, k) * M[0, k] + work[i, j] = acum + work[j, i] = -acum + + for l in range(1, n): + acum = 0 + for a in range(1, n): + for b in range(1, n): + acum += LeviCivita(0, l, a, b) * M[a, b] + acum /= 2 + work[0, l] = -acum + work[l, 0] = acum + + return work + + def _eval_matrix_exp_jblock(self): + """A helper function to compute an exponential of a Jordan block + matrix + + Examples + ======== + + >>> from sympy import Symbol, Matrix + >>> l = Symbol('lamda') + + A trivial example of 1*1 Jordan block: + + >>> m = Matrix.jordan_block(1, l) + >>> m._eval_matrix_exp_jblock() + Matrix([[exp(lamda)]]) + + An example of 3*3 Jordan block: + + >>> m = Matrix.jordan_block(3, l) + >>> m._eval_matrix_exp_jblock() + Matrix([ + [exp(lamda), exp(lamda), exp(lamda)/2], + [ 0, exp(lamda), exp(lamda)], + [ 0, 0, exp(lamda)]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Matrix_function#Jordan_decomposition + """ + size = self.rows + l = self[0, 0] + exp_l = exp(l) + + bands = {i: exp_l / factorial(i) for i in range(size)} + + from .sparsetools import banded + return self.__class__(banded(size, bands)) + + + def analytic_func(self, f, x): + """ + Computes f(A) where A is a Square Matrix + and f is an analytic function. + + Examples + ======== + + >>> from sympy import Symbol, Matrix, S, log + + >>> x = Symbol('x') + >>> m = Matrix([[S(5)/4, S(3)/4], [S(3)/4, S(5)/4]]) + >>> f = log(x) + >>> m.analytic_func(f, x) + Matrix([ + [ 0, log(2)], + [log(2), 0]]) + + Parameters + ========== + + f : Expr + Analytic Function + x : Symbol + parameter of f + + """ + + f, x = _sympify(f), _sympify(x) + if not self.is_square: + raise NonSquareMatrixError + if not x.is_symbol: + raise ValueError("{} must be a symbol.".format(x)) + if x not in f.free_symbols: + raise ValueError( + "{} must be a parameter of {}.".format(x, f)) + if x in self.free_symbols: + raise ValueError( + "{} must not be a parameter of {}.".format(x, self)) + + eigen = self.eigenvals() + max_mul = max(eigen.values()) + derivative = {} + dd = f + for i in range(max_mul - 1): + dd = diff(dd, x) + derivative[i + 1] = dd + n = self.shape[0] + r = self.zeros(n) + f_val = self.zeros(n, 1) + row = 0 + + for i in eigen: + mul = eigen[i] + f_val[row] = f.subs(x, i) + if f_val[row].is_number and not f_val[row].is_complex: + raise ValueError( + "Cannot evaluate the function because the " + "function {} is not analytic at the given " + "eigenvalue {}".format(f, f_val[row])) + val = 1 + for a in range(n): + r[row, a] = val + val *= i + if mul > 1: + coe = [1 for ii in range(n)] + deri = 1 + while mul > 1: + row = row + 1 + mul -= 1 + d_i = derivative[deri].subs(x, i) + if d_i.is_number and not d_i.is_complex: + raise ValueError( + "Cannot evaluate the function because the " + "derivative {} is not analytic at the given " + "eigenvalue {}".format(derivative[deri], d_i)) + f_val[row] = d_i + for a in range(n): + if a - deri + 1 <= 0: + r[row, a] = 0 + coe[a] = 0 + continue + coe[a] = coe[a]*(a - deri + 1) + r[row, a] = coe[a]*pow(i, a - deri) + deri += 1 + row += 1 + c = r.solve(f_val) + ans = self.zeros(n) + pre = self.eye(n) + for i in range(n): + ans = ans + c[i]*pre + pre *= self + return ans + + + def exp(self): + """Return the exponential of a square matrix. + + Examples + ======== + + >>> from sympy import Symbol, Matrix + + >>> t = Symbol('t') + >>> m = Matrix([[0, 1], [-1, 0]]) * t + >>> m.exp() + Matrix([ + [ exp(I*t)/2 + exp(-I*t)/2, -I*exp(I*t)/2 + I*exp(-I*t)/2], + [I*exp(I*t)/2 - I*exp(-I*t)/2, exp(I*t)/2 + exp(-I*t)/2]]) + """ + if not self.is_square: + raise NonSquareMatrixError( + "Exponentiation is valid only for square matrices") + try: + P, J = self.jordan_form() + cells = J.get_diag_blocks() + except MatrixError: + raise NotImplementedError( + "Exponentiation is implemented only for matrices for which the Jordan normal form can be computed") + + blocks = [cell._eval_matrix_exp_jblock() for cell in cells] + from sympy.matrices import diag + eJ = diag(*blocks) + # n = self.rows + ret = P.multiply(eJ, dotprodsimp=None).multiply(P.inv(), dotprodsimp=None) + if all(value.is_real for value in self.values()): + return type(self)(re(ret)) + else: + return type(self)(ret) + + def _eval_matrix_log_jblock(self): + """Helper function to compute logarithm of a jordan block. + + Examples + ======== + + >>> from sympy import Symbol, Matrix + >>> l = Symbol('lamda') + + A trivial example of 1*1 Jordan block: + + >>> m = Matrix.jordan_block(1, l) + >>> m._eval_matrix_log_jblock() + Matrix([[log(lamda)]]) + + An example of 3*3 Jordan block: + + >>> m = Matrix.jordan_block(3, l) + >>> m._eval_matrix_log_jblock() + Matrix([ + [log(lamda), 1/lamda, -1/(2*lamda**2)], + [ 0, log(lamda), 1/lamda], + [ 0, 0, log(lamda)]]) + """ + size = self.rows + l = self[0, 0] + + if l.is_zero: + raise MatrixError( + 'Could not take logarithm or reciprocal for the given ' + 'eigenvalue {}'.format(l)) + + bands = {0: log(l)} + for i in range(1, size): + bands[i] = -((-l) ** -i) / i + + from .sparsetools import banded + return self.__class__(banded(size, bands)) + + def log(self, simplify=cancel): + """Return the logarithm of a square matrix. + + Parameters + ========== + + simplify : function, bool + The function to simplify the result with. + + Default is ``cancel``, which is effective to reduce the + expression growing for taking reciprocals and inverses for + symbolic matrices. + + Examples + ======== + + >>> from sympy import S, Matrix + + Examples for positive-definite matrices: + + >>> m = Matrix([[1, 1], [0, 1]]) + >>> m.log() + Matrix([ + [0, 1], + [0, 0]]) + + >>> m = Matrix([[S(5)/4, S(3)/4], [S(3)/4, S(5)/4]]) + >>> m.log() + Matrix([ + [ 0, log(2)], + [log(2), 0]]) + + Examples for non positive-definite matrices: + + >>> m = Matrix([[S(3)/4, S(5)/4], [S(5)/4, S(3)/4]]) + >>> m.log() + Matrix([ + [ I*pi/2, log(2) - I*pi/2], + [log(2) - I*pi/2, I*pi/2]]) + + >>> m = Matrix( + ... [[0, 0, 0, 1], + ... [0, 0, 1, 0], + ... [0, 1, 0, 0], + ... [1, 0, 0, 0]]) + >>> m.log() + Matrix([ + [ I*pi/2, 0, 0, -I*pi/2], + [ 0, I*pi/2, -I*pi/2, 0], + [ 0, -I*pi/2, I*pi/2, 0], + [-I*pi/2, 0, 0, I*pi/2]]) + """ + if not self.is_square: + raise NonSquareMatrixError( + "Logarithm is valid only for square matrices") + + try: + if simplify: + P, J = simplify(self).jordan_form() + else: + P, J = self.jordan_form() + + cells = J.get_diag_blocks() + except MatrixError: + raise NotImplementedError( + "Logarithm is implemented only for matrices for which " + "the Jordan normal form can be computed") + + blocks = [ + cell._eval_matrix_log_jblock() + for cell in cells] + from sympy.matrices import diag + eJ = diag(*blocks) + + if simplify: + ret = simplify(P * eJ * simplify(P.inv())) + ret = self.__class__(ret) + else: + ret = P * eJ * P.inv() + + return ret + + def is_nilpotent(self): + """Checks if a matrix is nilpotent. + + A matrix B is nilpotent if for some integer k, B**k is + a zero matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> a = Matrix([[0, 0, 0], [1, 0, 0], [1, 1, 0]]) + >>> a.is_nilpotent() + True + + >>> a = Matrix([[1, 0, 1], [1, 0, 0], [1, 1, 0]]) + >>> a.is_nilpotent() + False + """ + if not self: + return True + if not self.is_square: + raise NonSquareMatrixError( + "Nilpotency is valid only for square matrices") + x = uniquely_named_symbol('x', self, modify=lambda s: '_' + s) + p = self.charpoly(x) + if p.args[0] == x ** self.rows: + return True + return False + + def key2bounds(self, keys): + """Converts a key with potentially mixed types of keys (integer and slice) + into a tuple of ranges and raises an error if any index is out of ``self``'s + range. + + See Also + ======== + + key2ij + """ + islice, jslice = [isinstance(k, slice) for k in keys] + if islice: + if not self.rows: + rlo = rhi = 0 + else: + rlo, rhi = keys[0].indices(self.rows)[:2] + else: + rlo = a2idx(keys[0], self.rows) + rhi = rlo + 1 + if jslice: + if not self.cols: + clo = chi = 0 + else: + clo, chi = keys[1].indices(self.cols)[:2] + else: + clo = a2idx(keys[1], self.cols) + chi = clo + 1 + return rlo, rhi, clo, chi + + def key2ij(self, key): + """Converts key into canonical form, converting integers or indexable + items into valid integers for ``self``'s range or returning slices + unchanged. + + See Also + ======== + + key2bounds + """ + if is_sequence(key): + if not len(key) == 2: + raise TypeError('key must be a sequence of length 2') + return [a2idx(i, n) if not isinstance(i, slice) else i + for i, n in zip(key, self.shape)] + elif isinstance(key, slice): + return key.indices(len(self))[:2] + else: + return divmod(a2idx(key, len(self)), self.cols) + + def normalized(self, iszerofunc=_iszero): + """Return the normalized version of ``self``. + + Parameters + ========== + + iszerofunc : Function, optional + A function to determine whether ``self`` is a zero vector. + The default ``_iszero`` tests to see if each element is + exactly zero. + + Returns + ======= + + Matrix + Normalized vector form of ``self``. + It has the same length as a unit vector. However, a zero vector + will be returned for a vector with norm 0. + + Raises + ====== + + ShapeError + If the matrix is not in a vector form. + + See Also + ======== + + norm + """ + if self.rows != 1 and self.cols != 1: + raise ShapeError("A Matrix must be a vector to normalize.") + norm = self.norm() + if iszerofunc(norm): + out = self.zeros(self.rows, self.cols) + else: + out = self.applyfunc(lambda i: i / norm) + return out + + def norm(self, ord=None): + """Return the Norm of a Matrix or Vector. + + In the simplest case this is the geometric size of the vector + Other norms can be specified by the ord parameter + + + ===== ============================ ========================== + ord norm for matrices norm for vectors + ===== ============================ ========================== + None Frobenius norm 2-norm + 'fro' Frobenius norm - does not exist + inf maximum row sum max(abs(x)) + -inf -- min(abs(x)) + 1 maximum column sum as below + -1 -- as below + 2 2-norm (largest sing. value) as below + -2 smallest singular value as below + other - does not exist sum(abs(x)**ord)**(1./ord) + ===== ============================ ========================== + + Examples + ======== + + >>> from sympy import Matrix, Symbol, trigsimp, cos, sin, oo + >>> x = Symbol('x', real=True) + >>> v = Matrix([cos(x), sin(x)]) + >>> trigsimp( v.norm() ) + 1 + >>> v.norm(10) + (sin(x)**10 + cos(x)**10)**(1/10) + >>> A = Matrix([[1, 1], [1, 1]]) + >>> A.norm(1) # maximum sum of absolute values of A is 2 + 2 + >>> A.norm(2) # Spectral norm (max of |Ax|/|x| under 2-vector-norm) + 2 + >>> A.norm(-2) # Inverse spectral norm (smallest singular value) + 0 + >>> A.norm() # Frobenius Norm + 2 + >>> A.norm(oo) # Infinity Norm + 2 + >>> Matrix([1, -2]).norm(oo) + 2 + >>> Matrix([-1, 2]).norm(-oo) + 1 + + See Also + ======== + + normalized + """ + # Row or Column Vector Norms + vals = list(self.values()) or [0] + if S.One in self.shape: + if ord in (2, None): # Common case sqrt() + return sqrt(Add(*(abs(i) ** 2 for i in vals))) + + elif ord == 1: # sum(abs(x)) + return Add(*(abs(i) for i in vals)) + + elif ord is S.Infinity: # max(abs(x)) + return Max(*[abs(i) for i in vals]) + + elif ord is S.NegativeInfinity: # min(abs(x)) + return Min(*[abs(i) for i in vals]) + + # Otherwise generalize the 2-norm, Sum(x_i**ord)**(1/ord) + # Note that while useful this is not mathematically a norm + try: + return Pow(Add(*(abs(i) ** ord for i in vals)), S.One / ord) + except (NotImplementedError, TypeError): + raise ValueError("Expected order to be Number, Symbol, oo") + + # Matrix Norms + else: + if ord == 1: # Maximum column sum + m = self.applyfunc(abs) + return Max(*[sum(m.col(i)) for i in range(m.cols)]) + + elif ord == 2: # Spectral Norm + # Maximum singular value + return Max(*self.singular_values()) + + elif ord == -2: + # Minimum singular value + return Min(*self.singular_values()) + + elif ord is S.Infinity: # Infinity Norm - Maximum row sum + m = self.applyfunc(abs) + return Max(*[sum(m.row(i)) for i in range(m.rows)]) + + elif (ord is None or isinstance(ord, + str) and ord.lower() in + ['f', 'fro', 'frobenius', 'vector']): + # Reshape as vector and send back to norm function + return self.vec().norm(ord=2) + + else: + raise NotImplementedError("Matrix Norms under development") + + def print_nonzero(self, symb="X"): + """Shows location of non-zero entries for fast shape lookup. + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> m = Matrix(2, 3, lambda i, j: i*3+j) + >>> m + Matrix([ + [0, 1, 2], + [3, 4, 5]]) + >>> m.print_nonzero() + [ XX] + [XXX] + >>> m = eye(4) + >>> m.print_nonzero("x") + [x ] + [ x ] + [ x ] + [ x] + + """ + s = [] + for i in range(self.rows): + line = [] + for j in range(self.cols): + if self[i, j] == 0: + line.append(" ") + else: + line.append(str(symb)) + s.append("[%s]" % ''.join(line)) + print('\n'.join(s)) + + def project(self, v): + """Return the projection of ``self`` onto the line containing ``v``. + + Examples + ======== + + >>> from sympy import Matrix, S, sqrt + >>> V = Matrix([sqrt(3)/2, S.Half]) + >>> x = Matrix([[1, 0]]) + >>> V.project(x) + Matrix([[sqrt(3)/2, 0]]) + >>> V.project(-x) + Matrix([[sqrt(3)/2, 0]]) + """ + return v * (self.dot(v) / v.dot(v)) + + def table(self, printer, rowstart='[', rowend=']', rowsep='\n', + colsep=', ', align='right'): + r""" + String form of Matrix as a table. + + ``printer`` is the printer to use for on the elements (generally + something like StrPrinter()) + + ``rowstart`` is the string used to start each row (by default '['). + + ``rowend`` is the string used to end each row (by default ']'). + + ``rowsep`` is the string used to separate rows (by default a newline). + + ``colsep`` is the string used to separate columns (by default ', '). + + ``align`` defines how the elements are aligned. Must be one of 'left', + 'right', or 'center'. You can also use '<', '>', and '^' to mean the + same thing, respectively. + + This is used by the string printer for Matrix. + + Examples + ======== + + >>> from sympy import Matrix, StrPrinter + >>> M = Matrix([[1, 2], [-33, 4]]) + >>> printer = StrPrinter() + >>> M.table(printer) + '[ 1, 2]\n[-33, 4]' + >>> print(M.table(printer)) + [ 1, 2] + [-33, 4] + >>> print(M.table(printer, rowsep=',\n')) + [ 1, 2], + [-33, 4] + >>> print('[%s]' % M.table(printer, rowsep=',\n')) + [[ 1, 2], + [-33, 4]] + >>> print(M.table(printer, colsep=' ')) + [ 1 2] + [-33 4] + >>> print(M.table(printer, align='center')) + [ 1 , 2] + [-33, 4] + >>> print(M.table(printer, rowstart='{', rowend='}')) + { 1, 2} + {-33, 4} + """ + # Handle zero dimensions: + if S.Zero in self.shape: + return '[]' + # Build table of string representations of the elements + res = [] + # Track per-column max lengths for pretty alignment + maxlen = [0] * self.cols + for i in range(self.rows): + res.append([]) + for j in range(self.cols): + s = printer._print(self[i, j]) + res[-1].append(s) + maxlen[j] = max(len(s), maxlen[j]) + # Patch strings together + align = { + 'left': 'ljust', + 'right': 'rjust', + 'center': 'center', + '<': 'ljust', + '>': 'rjust', + '^': 'center', + }[align] + for i, row in enumerate(res): + for j, elem in enumerate(row): + row[j] = getattr(elem, align)(maxlen[j]) + res[i] = rowstart + colsep.join(row) + rowend + return rowsep.join(res) + + def rank_decomposition(self, iszerofunc=_iszero, simplify=False): + return _rank_decomposition(self, iszerofunc=iszerofunc, + simplify=simplify) + + def cholesky(self, hermitian=True): + raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix') + + def LDLdecomposition(self, hermitian=True): + raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix') + + def LUdecomposition(self, iszerofunc=_iszero, simpfunc=None, + rankcheck=False): + return _LUdecomposition(self, iszerofunc=iszerofunc, simpfunc=simpfunc, + rankcheck=rankcheck) + + def LUdecomposition_Simple(self, iszerofunc=_iszero, simpfunc=None, + rankcheck=False): + return _LUdecomposition_Simple(self, iszerofunc=iszerofunc, + simpfunc=simpfunc, rankcheck=rankcheck) + + def LUdecompositionFF(self): + return _LUdecompositionFF(self) + + def singular_value_decomposition(self): + return _singular_value_decomposition(self) + + def QRdecomposition(self): + return _QRdecomposition(self) + + def upper_hessenberg_decomposition(self): + return _upper_hessenberg_decomposition(self) + + def diagonal_solve(self, rhs): + return _diagonal_solve(self, rhs) + + def lower_triangular_solve(self, rhs): + raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix') + + def upper_triangular_solve(self, rhs): + raise NotImplementedError('This function is implemented in DenseMatrix or SparseMatrix') + + def cholesky_solve(self, rhs): + return _cholesky_solve(self, rhs) + + def LDLsolve(self, rhs): + return _LDLsolve(self, rhs) + + def LUsolve(self, rhs, iszerofunc=_iszero): + return _LUsolve(self, rhs, iszerofunc=iszerofunc) + + def QRsolve(self, b): + return _QRsolve(self, b) + + def gauss_jordan_solve(self, B, freevar=False): + return _gauss_jordan_solve(self, B, freevar=freevar) + + def pinv_solve(self, B, arbitrary_matrix=None): + return _pinv_solve(self, B, arbitrary_matrix=arbitrary_matrix) + + def cramer_solve(self, rhs, det_method="laplace"): + return _cramer_solve(self, rhs, det_method=det_method) + + def solve(self, rhs, method='GJ'): + return _solve(self, rhs, method=method) + + def solve_least_squares(self, rhs, method='CH'): + return _solve_least_squares(self, rhs, method=method) + + def pinv(self, method='RD'): + return _pinv(self, method=method) + + def inverse_ADJ(self, iszerofunc=_iszero): + return _inv_ADJ(self, iszerofunc=iszerofunc) + + def inverse_BLOCK(self, iszerofunc=_iszero): + return _inv_block(self, iszerofunc=iszerofunc) + + def inverse_GE(self, iszerofunc=_iszero): + return _inv_GE(self, iszerofunc=iszerofunc) + + def inverse_LU(self, iszerofunc=_iszero): + return _inv_LU(self, iszerofunc=iszerofunc) + + def inverse_CH(self, iszerofunc=_iszero): + return _inv_CH(self, iszerofunc=iszerofunc) + + def inverse_LDL(self, iszerofunc=_iszero): + return _inv_LDL(self, iszerofunc=iszerofunc) + + def inverse_QR(self, iszerofunc=_iszero): + return _inv_QR(self, iszerofunc=iszerofunc) + + def inv(self, method=None, iszerofunc=_iszero, try_block_diag=False): + return _inv(self, method=method, iszerofunc=iszerofunc, + try_block_diag=try_block_diag) + + def connected_components(self): + return _connected_components(self) + + def connected_components_decomposition(self): + return _connected_components_decomposition(self) + + def strongly_connected_components(self): + return _strongly_connected_components(self) + + def strongly_connected_components_decomposition(self, lower=True): + return _strongly_connected_components_decomposition(self, lower=lower) + + _sage_ = Basic._sage_ + + rank_decomposition.__doc__ = _rank_decomposition.__doc__ + cholesky.__doc__ = _cholesky.__doc__ + LDLdecomposition.__doc__ = _LDLdecomposition.__doc__ + LUdecomposition.__doc__ = _LUdecomposition.__doc__ + LUdecomposition_Simple.__doc__ = _LUdecomposition_Simple.__doc__ + LUdecompositionFF.__doc__ = _LUdecompositionFF.__doc__ + singular_value_decomposition.__doc__ = _singular_value_decomposition.__doc__ + QRdecomposition.__doc__ = _QRdecomposition.__doc__ + upper_hessenberg_decomposition.__doc__ = _upper_hessenberg_decomposition.__doc__ + + diagonal_solve.__doc__ = _diagonal_solve.__doc__ + lower_triangular_solve.__doc__ = _lower_triangular_solve.__doc__ + upper_triangular_solve.__doc__ = _upper_triangular_solve.__doc__ + cholesky_solve.__doc__ = _cholesky_solve.__doc__ + LDLsolve.__doc__ = _LDLsolve.__doc__ + LUsolve.__doc__ = _LUsolve.__doc__ + QRsolve.__doc__ = _QRsolve.__doc__ + gauss_jordan_solve.__doc__ = _gauss_jordan_solve.__doc__ + pinv_solve.__doc__ = _pinv_solve.__doc__ + cramer_solve.__doc__ = _cramer_solve.__doc__ + solve.__doc__ = _solve.__doc__ + solve_least_squares.__doc__ = _solve_least_squares.__doc__ + + pinv.__doc__ = _pinv.__doc__ + inverse_ADJ.__doc__ = _inv_ADJ.__doc__ + inverse_GE.__doc__ = _inv_GE.__doc__ + inverse_LU.__doc__ = _inv_LU.__doc__ + inverse_CH.__doc__ = _inv_CH.__doc__ + inverse_LDL.__doc__ = _inv_LDL.__doc__ + inverse_QR.__doc__ = _inv_QR.__doc__ + inverse_BLOCK.__doc__ = _inv_block.__doc__ + inv.__doc__ = _inv.__doc__ + + connected_components.__doc__ = _connected_components.__doc__ + connected_components_decomposition.__doc__ = \ + _connected_components_decomposition.__doc__ + strongly_connected_components.__doc__ = \ + _strongly_connected_components.__doc__ + strongly_connected_components_decomposition.__doc__ = \ + _strongly_connected_components_decomposition.__doc__ + + +def _convert_matrix(typ, mat): + """Convert mat to a Matrix of type typ.""" + from sympy.matrices.matrixbase import MatrixBase + if getattr(mat, "is_Matrix", False) and not isinstance(mat, MatrixBase): + # This is needed for interop between Matrix and the redundant matrix + # mixin types like _MinimalMatrix etc. If anyone should happen to be + # using those then this keeps them working. Really _MinimalMatrix etc + # should be deprecated and removed though. + return typ(*mat.shape, list(mat)) + else: + return typ(mat) + + +def _has_matrix_shape(other): + shape = getattr(other, 'shape', None) + if shape is None: + return False + return isinstance(shape, tuple) and len(shape) == 2 + + +def _has_rows_cols(other): + return hasattr(other, 'rows') and hasattr(other, 'cols') + + +def _coerce_operand(self, other): + """Convert other to a Matrix, or check for possible scalar.""" + + INVALID = None, 'invalid_type' + + # Disallow mixing Matrix and Array + if isinstance(other, NDimArray): + return INVALID + + is_Matrix = getattr(other, 'is_Matrix', None) + + # Return a Matrix as-is + if is_Matrix: + return other, 'is_matrix' + + # Try to convert numpy array, mpmath matrix etc. + if is_Matrix is None: + if _has_matrix_shape(other) or _has_rows_cols(other): + return _convert_matrix(type(self), other), 'is_matrix' + + # Could be a scalar but only if not iterable... + if not isinstance(other, Iterable): + return other, 'possible_scalar' + + return INVALID + + +def classof(A, B): + """ + Get the type of the result when combining matrices of different types. + + Currently the strategy is that immutability is contagious. + + Examples + ======== + + >>> from sympy import Matrix, ImmutableMatrix + >>> from sympy.matrices.matrixbase import classof + >>> M = Matrix([[1, 2], [3, 4]]) # a Mutable Matrix + >>> IM = ImmutableMatrix([[1, 2], [3, 4]]) + >>> classof(M, IM) + + """ + priority_A = getattr(A, '_class_priority', None) + priority_B = getattr(B, '_class_priority', None) + if None not in (priority_A, priority_B): + if A._class_priority > B._class_priority: + return A.__class__ + else: + return B.__class__ + + try: + import numpy + except ImportError: + pass + else: + if isinstance(A, numpy.ndarray): + return B.__class__ + if isinstance(B, numpy.ndarray): + return A.__class__ + + raise TypeError("Incompatible classes %s, %s" % (A.__class__, B.__class__)) + + +def _unify_with_other(self, other): + """Unify self and other into a single matrix type, or check for scalar.""" + other, T = _coerce_operand(self, other) + + if T == "is_matrix": + typ = classof(self, other) + if typ != self.__class__: + self = _convert_matrix(typ, self) + if typ != other.__class__: + other = _convert_matrix(typ, other) + + return self, other, T + + +def a2idx(j, n=None): + """Return integer after making positive and validating against n.""" + if not isinstance(j, int): + jindex = getattr(j, '__index__', None) + if jindex is not None: + j = jindex() + else: + raise IndexError("Invalid index a[%r]" % (j,)) + if n is not None: + if j < 0: + j += n + if not (j >= 0 and j < n): + raise IndexError("Index out of range: a[%s]" % (j,)) + return int(j) + + +class DeferredVector(Symbol, NotIterable): + """A vector whose components are deferred (e.g. for use with lambdify). + + Examples + ======== + + >>> from sympy import DeferredVector, lambdify + >>> X = DeferredVector( 'X' ) + >>> X + X + >>> expr = (X[0] + 2, X[2] + 3) + >>> func = lambdify( X, expr) + >>> func( [1, 2, 3] ) + (3, 6) + """ + + def __getitem__(self, i): + if i == -0: + i = 0 + if i < 0: + raise IndexError('DeferredVector index out of range') + component_name = '%s[%d]' % (self.name, i) + return Symbol(component_name) + + def __str__(self): + return sstr(self) + + def __repr__(self): + return "DeferredVector('%s')" % self.name diff --git a/lib/python3.11/site-packages/sympy/matrices/normalforms.py b/lib/python3.11/site-packages/sympy/matrices/normalforms.py new file mode 100644 index 0000000000000000000000000000000000000000..293692ecf2bb08678d47851c814d645406d0c935 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/normalforms.py @@ -0,0 +1,127 @@ +'''Functions returning normal forms of matrices''' + +from sympy.polys.domains.integerring import ZZ +from sympy.polys.polytools import Poly +from sympy.polys.matrices import DomainMatrix +from sympy.polys.matrices.normalforms import ( + smith_normal_form as _snf, + invariant_factors as _invf, + hermite_normal_form as _hnf, + ) + + +def _to_domain(m, domain=None): + """Convert Matrix to DomainMatrix""" + # XXX: deprecated support for RawMatrix: + ring = getattr(m, "ring", None) + m = m.applyfunc(lambda e: e.as_expr() if isinstance(e, Poly) else e) + + dM = DomainMatrix.from_Matrix(m) + + domain = domain or ring + if domain is not None: + dM = dM.convert_to(domain) + return dM + + +def smith_normal_form(m, domain=None): + ''' + Return the Smith Normal Form of a matrix `m` over the ring `domain`. + This will only work if the ring is a principal ideal domain. + + Examples + ======== + + >>> from sympy import Matrix, ZZ + >>> from sympy.matrices.normalforms import smith_normal_form + >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]]) + >>> print(smith_normal_form(m, domain=ZZ)) + Matrix([[1, 0, 0], [0, 10, 0], [0, 0, -30]]) + + ''' + dM = _to_domain(m, domain) + return _snf(dM).to_Matrix() + + +def invariant_factors(m, domain=None): + ''' + Return the tuple of abelian invariants for a matrix `m` + (as in the Smith-Normal form) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Smith_normal_form#Algorithm + .. [2] https://web.archive.org/web/20200331143852/https://sierra.nmsu.edu/morandi/notes/SmithNormalForm.pdf + + ''' + dM = _to_domain(m, domain) + factors = _invf(dM) + factors = tuple(dM.domain.to_sympy(f) for f in factors) + # XXX: deprecated. + if hasattr(m, "ring"): + if m.ring.is_PolynomialRing: + K = m.ring + to_poly = lambda f: Poly(f, K.symbols, domain=K.domain) + factors = tuple(to_poly(f) for f in factors) + return factors + + +def hermite_normal_form(A, *, D=None, check_rank=False): + r""" + Compute the Hermite Normal Form of a Matrix *A* of integers. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.matrices.normalforms import hermite_normal_form + >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]]) + >>> print(hermite_normal_form(m)) + Matrix([[10, 0, 2], [0, 15, 3], [0, 0, 2]]) + + Parameters + ========== + + A : $m \times n$ ``Matrix`` of integers. + + D : int, optional + Let $W$ be the HNF of *A*. If known in advance, a positive integer *D* + being any multiple of $\det(W)$ may be provided. In this case, if *A* + also has rank $m$, then we may use an alternative algorithm that works + mod *D* in order to prevent coefficient explosion. + + check_rank : boolean, optional (default=False) + The basic assumption is that, if you pass a value for *D*, then + you already believe that *A* has rank $m$, so we do not waste time + checking it for you. If you do want this to be checked (and the + ordinary, non-modulo *D* algorithm to be used if the check fails), then + set *check_rank* to ``True``. + + Returns + ======= + + ``Matrix`` + The HNF of matrix *A*. + + Raises + ====== + + DMDomainError + If the domain of the matrix is not :ref:`ZZ`. + + DMShapeError + If the mod *D* algorithm is used but the matrix has more rows than + columns. + + References + ========== + + .. [1] Cohen, H. *A Course in Computational Algebraic Number Theory.* + (See Algorithms 2.4.5 and 2.4.8.) + + """ + # Accept any of Python int, SymPy Integer, and ZZ itself: + if D is not None and not ZZ.of_type(D): + D = ZZ(int(D)) + return _hnf(A._rep, D=D, check_rank=check_rank).to_Matrix() diff --git a/lib/python3.11/site-packages/sympy/matrices/reductions.py b/lib/python3.11/site-packages/sympy/matrices/reductions.py new file mode 100644 index 0000000000000000000000000000000000000000..aace8c0336358e1869a34d99f79390cc0c0163fe --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/reductions.py @@ -0,0 +1,387 @@ +from types import FunctionType + +from sympy.polys.polyerrors import CoercionFailed +from sympy.polys.domains import ZZ, QQ + +from .utilities import _get_intermediate_simp, _iszero, _dotprodsimp, _simplify +from .determinant import _find_reasonable_pivot + + +def _row_reduce_list(mat, rows, cols, one, iszerofunc, simpfunc, + normalize_last=True, normalize=True, zero_above=True): + """Row reduce a flat list representation of a matrix and return a tuple + (rref_matrix, pivot_cols, swaps) where ``rref_matrix`` is a flat list, + ``pivot_cols`` are the pivot columns and ``swaps`` are any row swaps that + were used in the process of row reduction. + + Parameters + ========== + + mat : list + list of matrix elements, must be ``rows`` * ``cols`` in length + + rows, cols : integer + number of rows and columns in flat list representation + + one : SymPy object + represents the value one, from ``Matrix.one`` + + iszerofunc : determines if an entry can be used as a pivot + + simpfunc : used to simplify elements and test if they are + zero if ``iszerofunc`` returns `None` + + normalize_last : indicates where all row reduction should + happen in a fraction-free manner and then the rows are + normalized (so that the pivots are 1), or whether + rows should be normalized along the way (like the naive + row reduction algorithm) + + normalize : whether pivot rows should be normalized so that + the pivot value is 1 + + zero_above : whether entries above the pivot should be zeroed. + If ``zero_above=False``, an echelon matrix will be returned. + """ + + def get_col(i): + return mat[i::cols] + + def row_swap(i, j): + mat[i*cols:(i + 1)*cols], mat[j*cols:(j + 1)*cols] = \ + mat[j*cols:(j + 1)*cols], mat[i*cols:(i + 1)*cols] + + def cross_cancel(a, i, b, j): + """Does the row op row[i] = a*row[i] - b*row[j]""" + q = (j - i)*cols + for p in range(i*cols, (i + 1)*cols): + mat[p] = isimp(a*mat[p] - b*mat[p + q]) + + isimp = _get_intermediate_simp(_dotprodsimp) + piv_row, piv_col = 0, 0 + pivot_cols = [] + swaps = [] + + # use a fraction free method to zero above and below each pivot + while piv_col < cols and piv_row < rows: + pivot_offset, pivot_val, \ + assumed_nonzero, newly_determined = _find_reasonable_pivot( + get_col(piv_col)[piv_row:], iszerofunc, simpfunc) + + # _find_reasonable_pivot may have simplified some things + # in the process. Let's not let them go to waste + for (offset, val) in newly_determined: + offset += piv_row + mat[offset*cols + piv_col] = val + + if pivot_offset is None: + piv_col += 1 + continue + + pivot_cols.append(piv_col) + if pivot_offset != 0: + row_swap(piv_row, pivot_offset + piv_row) + swaps.append((piv_row, pivot_offset + piv_row)) + + # if we aren't normalizing last, we normalize + # before we zero the other rows + if normalize_last is False: + i, j = piv_row, piv_col + mat[i*cols + j] = one + for p in range(i*cols + j + 1, (i + 1)*cols): + mat[p] = isimp(mat[p] / pivot_val) + # after normalizing, the pivot value is 1 + pivot_val = one + + # zero above and below the pivot + for row in range(rows): + # don't zero our current row + if row == piv_row: + continue + # don't zero above the pivot unless we're told. + if zero_above is False and row < piv_row: + continue + # if we're already a zero, don't do anything + val = mat[row*cols + piv_col] + if iszerofunc(val): + continue + + cross_cancel(pivot_val, row, val, piv_row) + piv_row += 1 + + # normalize each row + if normalize_last is True and normalize is True: + for piv_i, piv_j in enumerate(pivot_cols): + pivot_val = mat[piv_i*cols + piv_j] + mat[piv_i*cols + piv_j] = one + for p in range(piv_i*cols + piv_j + 1, (piv_i + 1)*cols): + mat[p] = isimp(mat[p] / pivot_val) + + return mat, tuple(pivot_cols), tuple(swaps) + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _row_reduce(M, iszerofunc, simpfunc, normalize_last=True, + normalize=True, zero_above=True): + + mat, pivot_cols, swaps = _row_reduce_list(list(M), M.rows, M.cols, M.one, + iszerofunc, simpfunc, normalize_last=normalize_last, + normalize=normalize, zero_above=zero_above) + + return M._new(M.rows, M.cols, mat), pivot_cols, swaps + + +def _is_echelon(M, iszerofunc=_iszero): + """Returns `True` if the matrix is in echelon form. That is, all rows of + zeros are at the bottom, and below each leading non-zero in a row are + exclusively zeros.""" + + if M.rows <= 0 or M.cols <= 0: + return True + + zeros_below = all(iszerofunc(t) for t in M[1:, 0]) + + if iszerofunc(M[0, 0]): + return zeros_below and _is_echelon(M[:, 1:], iszerofunc) + + return zeros_below and _is_echelon(M[1:, 1:], iszerofunc) + + +def _echelon_form(M, iszerofunc=_iszero, simplify=False, with_pivots=False): + """Returns a matrix row-equivalent to ``M`` that is in echelon form. Note + that echelon form of a matrix is *not* unique, however, properties like the + row space and the null space are preserved. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2], [3, 4]]) + >>> M.echelon_form() + Matrix([ + [1, 2], + [0, -2]]) + """ + + simpfunc = simplify if isinstance(simplify, FunctionType) else _simplify + + mat, pivots, _ = _row_reduce(M, iszerofunc, simpfunc, + normalize_last=True, normalize=False, zero_above=False) + + if with_pivots: + return mat, pivots + + return mat + + +# This functions is a candidate for caching if it gets implemented for matrices. +def _rank(M, iszerofunc=_iszero, simplify=False): + """Returns the rank of a matrix. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x + >>> m = Matrix([[1, 2], [x, 1 - 1/x]]) + >>> m.rank() + 2 + >>> n = Matrix(3, 3, range(1, 10)) + >>> n.rank() + 2 + """ + + def _permute_complexity_right(M, iszerofunc): + """Permute columns with complicated elements as + far right as they can go. Since the ``sympy`` row reduction + algorithms start on the left, having complexity right-shifted + speeds things up. + + Returns a tuple (mat, perm) where perm is a permutation + of the columns to perform to shift the complex columns right, and mat + is the permuted matrix.""" + + def complexity(i): + # the complexity of a column will be judged by how many + # element's zero-ness cannot be determined + return sum(1 if iszerofunc(e) is None else 0 for e in M[:, i]) + + complex = [(complexity(i), i) for i in range(M.cols)] + perm = [j for (i, j) in sorted(complex)] + + return (M.permute(perm, orientation='cols'), perm) + + simpfunc = simplify if isinstance(simplify, FunctionType) else _simplify + + # for small matrices, we compute the rank explicitly + # if is_zero on elements doesn't answer the question + # for small matrices, we fall back to the full routine. + if M.rows <= 0 or M.cols <= 0: + return 0 + + if M.rows <= 1 or M.cols <= 1: + zeros = [iszerofunc(x) for x in M] + + if False in zeros: + return 1 + + if M.rows == 2 and M.cols == 2: + zeros = [iszerofunc(x) for x in M] + + if False not in zeros and None not in zeros: + return 0 + + d = M.det() + + if iszerofunc(d) and False in zeros: + return 1 + if iszerofunc(d) is False: + return 2 + + mat, _ = _permute_complexity_right(M, iszerofunc=iszerofunc) + _, pivots, _ = _row_reduce(mat, iszerofunc, simpfunc, normalize_last=True, + normalize=False, zero_above=False) + + return len(pivots) + + +def _to_DM_ZZ_QQ(M): + # We have to test for _rep here because there are tests that otherwise fail + # with e.g. "AttributeError: 'SubspaceOnlyMatrix' object has no attribute + # '_rep'." There is almost certainly no value in such tests. The + # presumption seems to be that someone could create a new class by + # inheriting some of the Matrix classes and not the full set that is used + # by the standard Matrix class but if anyone tried that it would fail in + # many ways. + if not hasattr(M, '_rep'): + return None + + rep = M._rep + K = rep.domain + + if K.is_ZZ: + return rep + elif K.is_QQ: + try: + return rep.convert_to(ZZ) + except CoercionFailed: + return rep + else: + if not all(e.is_Rational for e in M): + return None + try: + return rep.convert_to(ZZ) + except CoercionFailed: + return rep.convert_to(QQ) + + +def _rref_dm(dM): + """Compute the reduced row echelon form of a DomainMatrix.""" + K = dM.domain + + if K.is_ZZ: + dM_rref, den, pivots = dM.rref_den(keep_domain=False) + dM_rref = dM_rref.to_field() / den + elif K.is_QQ: + dM_rref, pivots = dM.rref() + else: + assert False # pragma: no cover + + M_rref = dM_rref.to_Matrix() + + return M_rref, pivots + + +def _rref(M, iszerofunc=_iszero, simplify=False, pivots=True, + normalize_last=True): + """Return reduced row-echelon form of matrix and indices + of pivot vars. + + Parameters + ========== + + iszerofunc : Function + A function used for detecting whether an element can + act as a pivot. ``lambda x: x.is_zero`` is used by default. + + simplify : Function + A function used to simplify elements when looking for a pivot. + By default SymPy's ``simplify`` is used. + + pivots : True or False + If ``True``, a tuple containing the row-reduced matrix and a tuple + of pivot columns is returned. If ``False`` just the row-reduced + matrix is returned. + + normalize_last : True or False + If ``True``, no pivots are normalized to `1` until after all + entries above and below each pivot are zeroed. This means the row + reduction algorithm is fraction free until the very last step. + If ``False``, the naive row reduction procedure is used where + each pivot is normalized to be `1` before row operations are + used to zero above and below the pivot. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x + >>> m = Matrix([[1, 2], [x, 1 - 1/x]]) + >>> m.rref() + (Matrix([ + [1, 0], + [0, 1]]), (0, 1)) + >>> rref_matrix, rref_pivots = m.rref() + >>> rref_matrix + Matrix([ + [1, 0], + [0, 1]]) + >>> rref_pivots + (0, 1) + + ``iszerofunc`` can correct rounding errors in matrices with float + values. In the following example, calling ``rref()`` leads to + floating point errors, incorrectly row reducing the matrix. + ``iszerofunc= lambda x: abs(x) < 1e-9`` sets sufficiently small numbers + to zero, avoiding this error. + + >>> m = Matrix([[0.9, -0.1, -0.2, 0], [-0.8, 0.9, -0.4, 0], [-0.1, -0.8, 0.6, 0]]) + >>> m.rref() + (Matrix([ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0]]), (0, 1, 2)) + >>> m.rref(iszerofunc=lambda x:abs(x)<1e-9) + (Matrix([ + [1, 0, -0.301369863013699, 0], + [0, 1, -0.712328767123288, 0], + [0, 0, 0, 0]]), (0, 1)) + + Notes + ===== + + The default value of ``normalize_last=True`` can provide significant + speedup to row reduction, especially on matrices with symbols. However, + if you depend on the form row reduction algorithm leaves entries + of the matrix, set ``normalize_last=False`` + """ + # Try to use DomainMatrix for ZZ or QQ + dM = _to_DM_ZZ_QQ(M) + + if dM is not None: + # Use DomainMatrix for ZZ or QQ + mat, pivot_cols = _rref_dm(dM) + else: + # Use the generic Matrix routine. + if isinstance(simplify, FunctionType): + simpfunc = simplify + else: + simpfunc = _simplify + + mat, pivot_cols, _ = _row_reduce(M, iszerofunc, simpfunc, + normalize_last, normalize=True, zero_above=True) + + if pivots: + return mat, pivot_cols + else: + return mat diff --git a/lib/python3.11/site-packages/sympy/matrices/repmatrix.py b/lib/python3.11/site-packages/sympy/matrices/repmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..e20781eefc600c7ea8b08f4051b76aef451b88a3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/repmatrix.py @@ -0,0 +1,1025 @@ +from collections import defaultdict + +from operator import index as index_ + +from sympy.core.expr import Expr +from sympy.core.kind import Kind, NumberKind, UndefinedKind +from sympy.core.numbers import Integer, Rational +from sympy.core.sympify import _sympify, SympifyError +from sympy.core.singleton import S +from sympy.polys.domains import ZZ, QQ, GF, EXRAW +from sympy.polys.matrices import DomainMatrix +from sympy.polys.matrices.exceptions import DMNonInvertibleMatrixError +from sympy.polys.polyerrors import CoercionFailed +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import is_sequence +from sympy.utilities.misc import filldedent, as_int + +from .exceptions import ShapeError, NonSquareMatrixError, NonInvertibleMatrixError +from .matrixbase import classof, MatrixBase +from .kind import MatrixKind + + +class RepMatrix(MatrixBase): + """Matrix implementation based on DomainMatrix as an internal representation. + + The RepMatrix class is a superclass for Matrix, ImmutableMatrix, + SparseMatrix and ImmutableSparseMatrix which are the main usable matrix + classes in SymPy. Most methods on this class are simply forwarded to + DomainMatrix. + """ + + # + # MatrixBase is the common superclass for all of the usable explicit matrix + # classes in SymPy. The idea is that MatrixBase is an abstract class though + # and that subclasses will implement the lower-level methods. + # + # RepMatrix is a subclass of MatrixBase that uses DomainMatrix as an + # internal representation and delegates lower-level methods to + # DomainMatrix. All of SymPy's standard explicit matrix classes subclass + # RepMatrix and so use DomainMatrix internally. + # + # A RepMatrix uses an internal DomainMatrix with the domain set to ZZ, QQ + # or EXRAW. The EXRAW domain is equivalent to the previous implementation + # of Matrix that used Expr for the elements. The ZZ and QQ domains are used + # when applicable just because they are compatible with the previous + # implementation but are much more efficient. Other domains such as QQ[x] + # are not used because they differ from Expr in some way (e.g. automatic + # expansion of powers and products). + # + + _rep: DomainMatrix + + def __eq__(self, other): + # Skip sympify for mutable matrices... + if not isinstance(other, RepMatrix): + try: + other = _sympify(other) + except SympifyError: + return NotImplemented + if not isinstance(other, RepMatrix): + return NotImplemented + + return self._rep.unify_eq(other._rep) + + def to_DM(self, domain=None, **kwargs): + """Convert to a :class:`~.DomainMatrix`. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 2], [3, 4]]) + >>> M.to_DM() + DomainMatrix({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ) + + The :meth:`DomainMatrix.to_Matrix` method can be used to convert back: + + >>> M.to_DM().to_Matrix() == M + True + + The domain can be given explicitly or otherwise it will be chosen by + :func:`construct_domain`. Any keyword arguments (besides ``domain``) + are passed to :func:`construct_domain`: + + >>> from sympy import QQ, symbols + >>> x = symbols('x') + >>> M = Matrix([[x, 1], [1, x]]) + >>> M + Matrix([ + [x, 1], + [1, x]]) + >>> M.to_DM().domain + ZZ[x] + >>> M.to_DM(field=True).domain + ZZ(x) + >>> M.to_DM(domain=QQ[x]).domain + QQ[x] + + See Also + ======== + + DomainMatrix + DomainMatrix.to_Matrix + DomainMatrix.convert_to + DomainMatrix.choose_domain + construct_domain + """ + if domain is not None: + if kwargs: + raise TypeError("Options cannot be used with domain parameter") + return self._rep.convert_to(domain) + + rep = self._rep + dom = rep.domain + + # If the internal DomainMatrix is already ZZ or QQ then we can maybe + # bypass calling construct_domain or performing any conversions. Some + # kwargs might affect this though e.g. field=True (not sure if there + # are others). + if not kwargs: + if dom.is_ZZ: + return rep.copy() + elif dom.is_QQ: + # All elements might be integers + try: + return rep.convert_to(ZZ) + except CoercionFailed: + pass + return rep.copy() + + # Let construct_domain choose a domain + rep_dom = rep.choose_domain(**kwargs) + + # XXX: There should be an option to construct_domain to choose EXRAW + # instead of EX. At least converting to EX does not initially trigger + # EX.simplify which is what we want here but should probably be + # considered a bug in EX. Perhaps also this could be handled in + # DomainMatrix.choose_domain rather than here... + if rep_dom.domain.is_EX: + rep_dom = rep_dom.convert_to(EXRAW) + + return rep_dom + + @classmethod + def _unify_element_sympy(cls, rep, element): + domain = rep.domain + element = _sympify(element) + + if domain != EXRAW: + # The domain can only be ZZ, QQ or EXRAW + if element.is_Integer: + new_domain = domain + elif element.is_Rational: + new_domain = QQ + else: + new_domain = EXRAW + + # XXX: This converts the domain for all elements in the matrix + # which can be slow. This happens e.g. if __setitem__ changes one + # element to something that does not fit in the domain + if new_domain != domain: + rep = rep.convert_to(new_domain) + domain = new_domain + + if domain != EXRAW: + element = new_domain.from_sympy(element) + + if domain == EXRAW and not isinstance(element, Expr): + sympy_deprecation_warning( + """ + non-Expr objects in a Matrix is deprecated. Matrix represents + a mathematical matrix. To represent a container of non-numeric + entities, Use a list of lists, TableForm, NumPy array, or some + other data structure instead. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-non-expr-in-matrix", + stacklevel=4, + ) + + return rep, element + + @classmethod + def _dod_to_DomainMatrix(cls, rows, cols, dod, types): + + if not all(issubclass(typ, Expr) for typ in types): + sympy_deprecation_warning( + """ + non-Expr objects in a Matrix is deprecated. Matrix represents + a mathematical matrix. To represent a container of non-numeric + entities, Use a list of lists, TableForm, NumPy array, or some + other data structure instead. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-non-expr-in-matrix", + stacklevel=6, + ) + + rep = DomainMatrix(dod, (rows, cols), EXRAW) + + if all(issubclass(typ, Rational) for typ in types): + if all(issubclass(typ, Integer) for typ in types): + rep = rep.convert_to(ZZ) + else: + rep = rep.convert_to(QQ) + + return rep + + @classmethod + def _flat_list_to_DomainMatrix(cls, rows, cols, flat_list): + + elements_dod = defaultdict(dict) + for n, element in enumerate(flat_list): + if element != 0: + i, j = divmod(n, cols) + elements_dod[i][j] = element + + types = set(map(type, flat_list)) + + rep = cls._dod_to_DomainMatrix(rows, cols, elements_dod, types) + return rep + + @classmethod + def _smat_to_DomainMatrix(cls, rows, cols, smat): + + elements_dod = defaultdict(dict) + for (i, j), element in smat.items(): + if element != 0: + elements_dod[i][j] = element + + types = set(map(type, smat.values())) + + rep = cls._dod_to_DomainMatrix(rows, cols, elements_dod, types) + return rep + + def flat(self): + return self._rep.to_sympy().to_list_flat() + + def _eval_tolist(self): + return self._rep.to_sympy().to_list() + + def _eval_todok(self): + return self._rep.to_sympy().to_dok() + + @classmethod + def _eval_from_dok(cls, rows, cols, dok): + return cls._fromrep(cls._smat_to_DomainMatrix(rows, cols, dok)) + + def _eval_values(self): + return list(self._eval_iter_values()) + + def _eval_iter_values(self): + rep = self._rep + K = rep.domain + values = rep.iter_values() + if not K.is_EXRAW: + values = map(K.to_sympy, values) + return values + + def _eval_iter_items(self): + rep = self._rep + K = rep.domain + to_sympy = K.to_sympy + items = rep.iter_items() + if not K.is_EXRAW: + items = ((i, to_sympy(v)) for i, v in items) + return items + + def copy(self): + return self._fromrep(self._rep.copy()) + + @property + def kind(self) -> MatrixKind: + domain = self._rep.domain + element_kind: Kind + if domain in (ZZ, QQ): + element_kind = NumberKind + elif domain == EXRAW: + kinds = {e.kind for e in self.values()} + if len(kinds) == 1: + [element_kind] = kinds + else: + element_kind = UndefinedKind + else: # pragma: no cover + raise RuntimeError("Domain should only be ZZ, QQ or EXRAW") + return MatrixKind(element_kind) + + def _eval_has(self, *patterns): + # if the matrix has any zeros, see if S.Zero + # has the pattern. If _smat is full length, + # the matrix has no zeros. + zhas = False + dok = self.todok() + if len(dok) != self.rows*self.cols: + zhas = S.Zero.has(*patterns) + return zhas or any(value.has(*patterns) for value in dok.values()) + + def _eval_is_Identity(self): + if not all(self[i, i] == 1 for i in range(self.rows)): + return False + return len(self.todok()) == self.rows + + def _eval_is_symmetric(self, simpfunc): + diff = (self - self.T).applyfunc(simpfunc) + return len(diff.values()) == 0 + + def _eval_transpose(self): + """Returns the transposed SparseMatrix of this SparseMatrix. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> a = SparseMatrix(((1, 2), (3, 4))) + >>> a + Matrix([ + [1, 2], + [3, 4]]) + >>> a.T + Matrix([ + [1, 3], + [2, 4]]) + """ + return self._fromrep(self._rep.transpose()) + + def _eval_col_join(self, other): + return self._fromrep(self._rep.vstack(other._rep)) + + def _eval_row_join(self, other): + return self._fromrep(self._rep.hstack(other._rep)) + + def _eval_extract(self, rowsList, colsList): + return self._fromrep(self._rep.extract(rowsList, colsList)) + + def __getitem__(self, key): + return _getitem_RepMatrix(self, key) + + @classmethod + def _eval_zeros(cls, rows, cols): + rep = DomainMatrix.zeros((rows, cols), ZZ) + return cls._fromrep(rep) + + @classmethod + def _eval_eye(cls, rows, cols): + rep = DomainMatrix.eye((rows, cols), ZZ) + return cls._fromrep(rep) + + def _eval_add(self, other): + return classof(self, other)._fromrep(self._rep + other._rep) + + def _eval_matrix_mul(self, other): + return classof(self, other)._fromrep(self._rep * other._rep) + + def _eval_matrix_mul_elementwise(self, other): + selfrep, otherrep = self._rep.unify(other._rep) + newrep = selfrep.mul_elementwise(otherrep) + return classof(self, other)._fromrep(newrep) + + def _eval_scalar_mul(self, other): + rep, other = self._unify_element_sympy(self._rep, other) + return self._fromrep(rep.scalarmul(other)) + + def _eval_scalar_rmul(self, other): + rep, other = self._unify_element_sympy(self._rep, other) + return self._fromrep(rep.rscalarmul(other)) + + def _eval_Abs(self): + return self._fromrep(self._rep.applyfunc(abs)) + + def _eval_conjugate(self): + rep = self._rep + domain = rep.domain + if domain in (ZZ, QQ): + return self.copy() + else: + return self._fromrep(rep.applyfunc(lambda e: e.conjugate())) + + def equals(self, other, failing_expression=False): + """Applies ``equals`` to corresponding elements of the matrices, + trying to prove that the elements are equivalent, returning True + if they are, False if any pair is not, and None (or the first + failing expression if failing_expression is True) if it cannot + be decided if the expressions are equivalent or not. This is, in + general, an expensive operation. + + Examples + ======== + + >>> from sympy import Matrix + >>> from sympy.abc import x + >>> A = Matrix([x*(x - 1), 0]) + >>> B = Matrix([x**2 - x, 0]) + >>> A == B + False + >>> A.simplify() == B.simplify() + True + >>> A.equals(B) + True + >>> A.equals(2) + False + + See Also + ======== + sympy.core.expr.Expr.equals + """ + if self.shape != getattr(other, 'shape', None): + return False + + rv = True + for i in range(self.rows): + for j in range(self.cols): + ans = self[i, j].equals(other[i, j], failing_expression) + if ans is False: + return False + elif ans is not True and rv is True: + rv = ans + return rv + + def inv_mod(M, m): + r""" + Returns the inverse of the integer matrix ``M`` modulo ``m``. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix(2, 2, [1, 2, 3, 4]) + >>> A.inv_mod(5) + Matrix([ + [3, 1], + [4, 2]]) + >>> A.inv_mod(3) + Matrix([ + [1, 1], + [0, 1]]) + + """ + + if not M.is_square: + raise NonSquareMatrixError() + + try: + m = as_int(m) + except ValueError: + raise TypeError("inv_mod: modulus m must be an integer") + + K = GF(m, symmetric=False) + + try: + dM = M.to_DM(K) + except CoercionFailed: + raise ValueError("inv_mod: matrix entries must be integers") + + try: + dMi = dM.inv() + except DMNonInvertibleMatrixError as exc: + msg = f'Matrix is not invertible (mod {m})' + raise NonInvertibleMatrixError(msg) from exc + + return dMi.to_Matrix() + + def lll(self, delta=0.75): + """LLL-reduced basis for the rowspace of a matrix of integers. + + Performs the Lenstra–Lenstra–Lovász (LLL) basis reduction algorithm. + + The implementation is provided by :class:`~DomainMatrix`. See + :meth:`~DomainMatrix.lll` for more details. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 0, 0, 0, -20160], + ... [0, 1, 0, 0, 33768], + ... [0, 0, 1, 0, 39578], + ... [0, 0, 0, 1, 47757]]) + >>> M.lll() + Matrix([ + [ 10, -3, -2, 8, -4], + [ 3, -9, 8, 1, -11], + [ -3, 13, -9, -3, -9], + [-12, -7, -11, 9, -1]]) + + See Also + ======== + + lll_transform + sympy.polys.matrices.domainmatrix.DomainMatrix.lll + """ + delta = QQ.from_sympy(_sympify(delta)) + dM = self._rep.convert_to(ZZ) + basis = dM.lll(delta=delta) + return self._fromrep(basis) + + def lll_transform(self, delta=0.75): + """LLL-reduced basis and transformation matrix. + + Performs the Lenstra–Lenstra–Lovász (LLL) basis reduction algorithm. + + The implementation is provided by :class:`~DomainMatrix`. See + :meth:`~DomainMatrix.lll_transform` for more details. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 0, 0, 0, -20160], + ... [0, 1, 0, 0, 33768], + ... [0, 0, 1, 0, 39578], + ... [0, 0, 0, 1, 47757]]) + >>> B, T = M.lll_transform() + >>> B + Matrix([ + [ 10, -3, -2, 8, -4], + [ 3, -9, 8, 1, -11], + [ -3, 13, -9, -3, -9], + [-12, -7, -11, 9, -1]]) + >>> T + Matrix([ + [ 10, -3, -2, 8], + [ 3, -9, 8, 1], + [ -3, 13, -9, -3], + [-12, -7, -11, 9]]) + + The transformation matrix maps the original basis to the LLL-reduced + basis: + + >>> T * M == B + True + + See Also + ======== + + lll + sympy.polys.matrices.domainmatrix.DomainMatrix.lll_transform + """ + delta = QQ.from_sympy(_sympify(delta)) + dM = self._rep.convert_to(ZZ) + basis, transform = dM.lll_transform(delta=delta) + B = self._fromrep(basis) + T = self._fromrep(transform) + return B, T + + +class MutableRepMatrix(RepMatrix): + """Mutable matrix based on DomainMatrix as the internal representation""" + + # + # MutableRepMatrix is a subclass of RepMatrix that adds/overrides methods + # to make the instances mutable. MutableRepMatrix is a superclass for both + # MutableDenseMatrix and MutableSparseMatrix. + # + + is_zero = False + + def __new__(cls, *args, **kwargs): + return cls._new(*args, **kwargs) + + @classmethod + def _new(cls, *args, copy=True, **kwargs): + if copy is False: + # The input was rows, cols, [list]. + # It should be used directly without creating a copy. + if len(args) != 3: + raise TypeError("'copy=False' requires a matrix be initialized as rows,cols,[list]") + rows, cols, flat_list = args + else: + rows, cols, flat_list = cls._handle_creation_inputs(*args, **kwargs) + flat_list = list(flat_list) # create a shallow copy + + rep = cls._flat_list_to_DomainMatrix(rows, cols, flat_list) + + return cls._fromrep(rep) + + @classmethod + def _fromrep(cls, rep): + obj = super().__new__(cls) + obj.rows, obj.cols = rep.shape + obj._rep = rep + return obj + + def copy(self): + return self._fromrep(self._rep.copy()) + + def as_mutable(self): + return self.copy() + + def __setitem__(self, key, value): + """ + + Examples + ======== + + >>> from sympy import Matrix, I, zeros, ones + >>> m = Matrix(((1, 2+I), (3, 4))) + >>> m + Matrix([ + [1, 2 + I], + [3, 4]]) + >>> m[1, 0] = 9 + >>> m + Matrix([ + [1, 2 + I], + [9, 4]]) + >>> m[1, 0] = [[0, 1]] + + To replace row r you assign to position r*m where m + is the number of columns: + + >>> M = zeros(4) + >>> m = M.cols + >>> M[3*m] = ones(1, m)*2; M + Matrix([ + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [2, 2, 2, 2]]) + + And to replace column c you can assign to position c: + + >>> M[2] = ones(m, 1)*4; M + Matrix([ + [0, 0, 4, 0], + [0, 0, 4, 0], + [0, 0, 4, 0], + [2, 2, 4, 2]]) + """ + rv = self._setitem(key, value) + if rv is not None: + i, j, value = rv + self._rep, value = self._unify_element_sympy(self._rep, value) + self._rep.rep.setitem(i, j, value) + + def _eval_col_del(self, col): + self._rep = DomainMatrix.hstack(self._rep[:,:col], self._rep[:,col+1:]) + self.cols -= 1 + + def _eval_row_del(self, row): + self._rep = DomainMatrix.vstack(self._rep[:row,:], self._rep[row+1:, :]) + self.rows -= 1 + + def _eval_col_insert(self, col, other): + other = self._new(other) + return self.hstack(self[:,:col], other, self[:,col:]) + + def _eval_row_insert(self, row, other): + other = self._new(other) + return self.vstack(self[:row,:], other, self[row:,:]) + + def col_op(self, j, f): + """In-place operation on col j using two-arg functor whose args are + interpreted as (self[i, j], i). + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M + Matrix([ + [1, 2, 0], + [0, 1, 0], + [0, 0, 1]]) + + See Also + ======== + col + row_op + """ + for i in range(self.rows): + self[i, j] = f(self[i, j], i) + + def col_swap(self, i, j): + """Swap the two given columns of the matrix in-place. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[1, 0], [1, 0]]) + >>> M + Matrix([ + [1, 0], + [1, 0]]) + >>> M.col_swap(0, 1) + >>> M + Matrix([ + [0, 1], + [0, 1]]) + + See Also + ======== + + col + row_swap + """ + for k in range(0, self.rows): + self[k, i], self[k, j] = self[k, j], self[k, i] + + def row_op(self, i, f): + """In-place operation on row ``i`` using two-arg functor whose args are + interpreted as ``(self[i, j], j)``. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M + Matrix([ + [1, 0, 0], + [2, 1, 0], + [0, 0, 1]]) + + See Also + ======== + row + zip_row_op + col_op + + """ + for j in range(self.cols): + self[i, j] = f(self[i, j], j) + + #The next three methods give direct support for the most common row operations inplace. + def row_mult(self,i,factor): + """Multiply the given row by the given factor in-place. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.row_mult(1,7); M + Matrix([ + [1, 0, 0], + [0, 7, 0], + [0, 0, 1]]) + + """ + for j in range(self.cols): + self[i,j] *= factor + + def row_add(self,s,t,k): + """Add k times row s (source) to row t (target) in place. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.row_add(0, 2,3); M + Matrix([ + [1, 0, 0], + [0, 1, 0], + [3, 0, 1]]) + """ + + for j in range(self.cols): + self[t,j] += k*self[s,j] + + def row_swap(self, i, j): + """Swap the two given rows of the matrix in-place. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix([[0, 1], [1, 0]]) + >>> M + Matrix([ + [0, 1], + [1, 0]]) + >>> M.row_swap(0, 1) + >>> M + Matrix([ + [1, 0], + [0, 1]]) + + See Also + ======== + + row + col_swap + """ + for k in range(0, self.cols): + self[i, k], self[j, k] = self[j, k], self[i, k] + + def zip_row_op(self, i, k, f): + """In-place operation on row ``i`` using two-arg functor whose args are + interpreted as ``(self[i, j], self[k, j])``. + + Examples + ======== + + >>> from sympy import eye + >>> M = eye(3) + >>> M.zip_row_op(1, 0, lambda v, u: v + 2*u); M + Matrix([ + [1, 0, 0], + [2, 1, 0], + [0, 0, 1]]) + + See Also + ======== + row + row_op + col_op + + """ + for j in range(self.cols): + self[i, j] = f(self[i, j], self[k, j]) + + def copyin_list(self, key, value): + """Copy in elements from a list. + + Parameters + ========== + + key : slice + The section of this matrix to replace. + value : iterable + The iterable to copy values from. + + Examples + ======== + + >>> from sympy import eye + >>> I = eye(3) + >>> I[:2, 0] = [1, 2] # col + >>> I + Matrix([ + [1, 0, 0], + [2, 1, 0], + [0, 0, 1]]) + >>> I[1, :2] = [[3, 4]] + >>> I + Matrix([ + [1, 0, 0], + [3, 4, 0], + [0, 0, 1]]) + + See Also + ======== + + copyin_matrix + """ + if not is_sequence(value): + raise TypeError("`value` must be an ordered iterable, not %s." % type(value)) + return self.copyin_matrix(key, type(self)(value)) + + def copyin_matrix(self, key, value): + """Copy in values from a matrix into the given bounds. + + Parameters + ========== + + key : slice + The section of this matrix to replace. + value : Matrix + The matrix to copy values from. + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> M = Matrix([[0, 1], [2, 3], [4, 5]]) + >>> I = eye(3) + >>> I[:3, :2] = M + >>> I + Matrix([ + [0, 1, 0], + [2, 3, 0], + [4, 5, 1]]) + >>> I[0, 1] = M + >>> I + Matrix([ + [0, 0, 1], + [2, 2, 3], + [4, 4, 5]]) + + See Also + ======== + + copyin_list + """ + rlo, rhi, clo, chi = self.key2bounds(key) + shape = value.shape + dr, dc = rhi - rlo, chi - clo + if shape != (dr, dc): + raise ShapeError(filldedent("The Matrix `value` doesn't have the " + "same dimensions " + "as the in sub-Matrix given by `key`.")) + + for i in range(value.rows): + for j in range(value.cols): + self[i + rlo, j + clo] = value[i, j] + + def fill(self, value): + """Fill self with the given value. + + Notes + ===== + + Unless many values are going to be deleted (i.e. set to zero) + this will create a matrix that is slower than a dense matrix in + operations. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> M = SparseMatrix.zeros(3); M + Matrix([ + [0, 0, 0], + [0, 0, 0], + [0, 0, 0]]) + >>> M.fill(1); M + Matrix([ + [1, 1, 1], + [1, 1, 1], + [1, 1, 1]]) + + See Also + ======== + + zeros + ones + """ + value = _sympify(value) + if not value: + self._rep = DomainMatrix.zeros(self.shape, EXRAW) + else: + elements_dod = {i: dict.fromkeys(range(self.cols), value) for i in range(self.rows)} + self._rep = DomainMatrix(elements_dod, self.shape, EXRAW) + + +def _getitem_RepMatrix(self, key): + """Return portion of self defined by key. If the key involves a slice + then a list will be returned (if key is a single slice) or a matrix + (if key was a tuple involving a slice). + + Examples + ======== + + >>> from sympy import Matrix, I + >>> m = Matrix([ + ... [1, 2 + I], + ... [3, 4 ]]) + + If the key is a tuple that does not involve a slice then that element + is returned: + + >>> m[1, 0] + 3 + + When a tuple key involves a slice, a matrix is returned. Here, the + first column is selected (all rows, column 0): + + >>> m[:, 0] + Matrix([ + [1], + [3]]) + + If the slice is not a tuple then it selects from the underlying + list of elements that are arranged in row order and a list is + returned if a slice is involved: + + >>> m[0] + 1 + >>> m[::2] + [1, 3] + """ + if isinstance(key, tuple): + i, j = key + try: + return self._rep.getitem_sympy(index_(i), index_(j)) + except (TypeError, IndexError): + if (isinstance(i, Expr) and not i.is_number) or (isinstance(j, Expr) and not j.is_number): + if ((j < 0) is True) or ((j >= self.shape[1]) is True) or\ + ((i < 0) is True) or ((i >= self.shape[0]) is True): + raise ValueError("index out of boundary") + from sympy.matrices.expressions.matexpr import MatrixElement + return MatrixElement(self, i, j) + + if isinstance(i, slice): + i = range(self.rows)[i] + elif is_sequence(i): + pass + else: + i = [i] + if isinstance(j, slice): + j = range(self.cols)[j] + elif is_sequence(j): + pass + else: + j = [j] + return self.extract(i, j) + + else: + # Index/slice like a flattened list + rows, cols = self.shape + + # Raise the appropriate exception: + if not rows * cols: + return [][key] + + rep = self._rep.rep + domain = rep.domain + is_slice = isinstance(key, slice) + + if is_slice: + values = [rep.getitem(*divmod(n, cols)) for n in range(rows * cols)[key]] + else: + values = [rep.getitem(*divmod(index_(key), cols))] + + if domain != EXRAW: + to_sympy = domain.to_sympy + values = [to_sympy(val) for val in values] + + if is_slice: + return values + else: + return values[0] diff --git a/lib/python3.11/site-packages/sympy/matrices/solvers.py b/lib/python3.11/site-packages/sympy/matrices/solvers.py new file mode 100644 index 0000000000000000000000000000000000000000..01a85b29bec04981854233fb6ad393685bf793e1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/solvers.py @@ -0,0 +1,942 @@ +from sympy.core.function import expand_mul +from sympy.core.symbol import Dummy, uniquely_named_symbol, symbols +from sympy.utilities.iterables import numbered_symbols + +from .exceptions import ShapeError, NonSquareMatrixError, NonInvertibleMatrixError +from .eigen import _fuzzy_positive_definite +from .utilities import _get_intermediate_simp, _iszero + + +def _diagonal_solve(M, rhs): + """Solves ``Ax = B`` efficiently, where A is a diagonal Matrix, + with non-zero diagonal entries. + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> A = eye(2)*2 + >>> B = Matrix([[1, 2], [3, 4]]) + >>> A.diagonal_solve(B) == B/2 + True + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + cholesky_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + if not M.is_diagonal(): + raise TypeError("Matrix should be diagonal") + if rhs.rows != M.rows: + raise TypeError("Size mismatch") + + return M._new( + rhs.rows, rhs.cols, lambda i, j: rhs[i, j] / M[i, i]) + + +def _lower_triangular_solve(M, rhs): + """Solves ``Ax = B``, where A is a lower triangular matrix. + + See Also + ======== + + upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if rhs.rows != M.rows: + raise ShapeError("Matrices size mismatch.") + if not M.is_lower: + raise ValueError("Matrix must be lower triangular.") + + dps = _get_intermediate_simp() + X = MutableDenseMatrix.zeros(M.rows, rhs.cols) + + for j in range(rhs.cols): + for i in range(M.rows): + if M[i, i] == 0: + raise TypeError("Matrix must be non-singular.") + + X[i, j] = dps((rhs[i, j] - sum(M[i, k]*X[k, j] + for k in range(i))) / M[i, i]) + + return M._new(X) + +def _lower_triangular_solve_sparse(M, rhs): + """Solves ``Ax = B``, where A is a lower triangular matrix. + + See Also + ======== + + upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if rhs.rows != M.rows: + raise ShapeError("Matrices size mismatch.") + if not M.is_lower: + raise ValueError("Matrix must be lower triangular.") + + dps = _get_intermediate_simp() + rows = [[] for i in range(M.rows)] + + for i, j, v in M.row_list(): + if i > j: + rows[i].append((j, v)) + + X = rhs.as_mutable() + + for j in range(rhs.cols): + for i in range(rhs.rows): + for u, v in rows[i]: + X[i, j] -= v*X[u, j] + + X[i, j] = dps(X[i, j] / M[i, i]) + + return M._new(X) + + +def _upper_triangular_solve(M, rhs): + """Solves ``Ax = B``, where A is an upper triangular matrix. + + See Also + ======== + + lower_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + from .dense import MutableDenseMatrix + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if rhs.rows != M.rows: + raise ShapeError("Matrix size mismatch.") + if not M.is_upper: + raise TypeError("Matrix is not upper triangular.") + + dps = _get_intermediate_simp() + X = MutableDenseMatrix.zeros(M.rows, rhs.cols) + + for j in range(rhs.cols): + for i in reversed(range(M.rows)): + if M[i, i] == 0: + raise ValueError("Matrix must be non-singular.") + + X[i, j] = dps((rhs[i, j] - sum(M[i, k]*X[k, j] + for k in range(i + 1, M.rows))) / M[i, i]) + + return M._new(X) + +def _upper_triangular_solve_sparse(M, rhs): + """Solves ``Ax = B``, where A is an upper triangular matrix. + + See Also + ======== + + lower_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + if not M.is_square: + raise NonSquareMatrixError("Matrix must be square.") + if rhs.rows != M.rows: + raise ShapeError("Matrix size mismatch.") + if not M.is_upper: + raise TypeError("Matrix is not upper triangular.") + + dps = _get_intermediate_simp() + rows = [[] for i in range(M.rows)] + + for i, j, v in M.row_list(): + if i < j: + rows[i].append((j, v)) + + X = rhs.as_mutable() + + for j in range(rhs.cols): + for i in reversed(range(rhs.rows)): + for u, v in reversed(rows[i]): + X[i, j] -= v*X[u, j] + + X[i, j] = dps(X[i, j] / M[i, i]) + + return M._new(X) + + +def _cholesky_solve(M, rhs): + """Solves ``Ax = B`` using Cholesky decomposition, + for a general square non-singular matrix. + For a non-square matrix with rows > cols, + the least squares solution is returned. + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + if M.rows < M.cols: + raise NotImplementedError( + 'Under-determined System. Try M.gauss_jordan_solve(rhs)') + + hermitian = True + reform = False + + if M.is_symmetric(): + hermitian = False + elif not M.is_hermitian: + reform = True + + if reform or _fuzzy_positive_definite(M) is False: + H = M.H + M = H.multiply(M) + rhs = H.multiply(rhs) + hermitian = not M.is_symmetric() + + L = M.cholesky(hermitian=hermitian) + Y = L.lower_triangular_solve(rhs) + + if hermitian: + return (L.H).upper_triangular_solve(Y) + else: + return (L.T).upper_triangular_solve(Y) + + +def _LDLsolve(M, rhs): + """Solves ``Ax = B`` using LDL decomposition, + for a general square and non-singular matrix. + + For a non-square matrix with rows > cols, + the least squares solution is returned. + + Examples + ======== + + >>> from sympy import Matrix, eye + >>> A = eye(2)*2 + >>> B = Matrix([[1, 2], [3, 4]]) + >>> A.LDLsolve(B) == B/2 + True + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.LDLdecomposition + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LUsolve + QRsolve + pinv_solve + cramer_solve + """ + + if M.rows < M.cols: + raise NotImplementedError( + 'Under-determined System. Try M.gauss_jordan_solve(rhs)') + + hermitian = True + reform = False + + if M.is_symmetric(): + hermitian = False + elif not M.is_hermitian: + reform = True + + if reform or _fuzzy_positive_definite(M) is False: + H = M.H + M = H.multiply(M) + rhs = H.multiply(rhs) + hermitian = not M.is_symmetric() + + L, D = M.LDLdecomposition(hermitian=hermitian) + Y = L.lower_triangular_solve(rhs) + Z = D.diagonal_solve(Y) + + if hermitian: + return (L.H).upper_triangular_solve(Z) + else: + return (L.T).upper_triangular_solve(Z) + + +def _LUsolve(M, rhs, iszerofunc=_iszero): + """Solve the linear system ``Ax = rhs`` for ``x`` where ``A = M``. + + This is for symbolic matrices, for real or complex ones use + mpmath.lu_solve or mpmath.qr_solve. + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + QRsolve + pinv_solve + LUdecomposition + cramer_solve + """ + + if rhs.rows != M.rows: + raise ShapeError( + "``M`` and ``rhs`` must have the same number of rows.") + + m = M.rows + n = M.cols + + if m < n: + raise NotImplementedError("Underdetermined systems not supported.") + + try: + A, perm = M.LUdecomposition_Simple( + iszerofunc=iszerofunc, rankcheck=True) + except ValueError: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + dps = _get_intermediate_simp() + b = rhs.permute_rows(perm).as_mutable() + + # forward substitution, all diag entries are scaled to 1 + for i in range(m): + for j in range(min(i, n)): + scale = A[i, j] + b.zip_row_op(i, j, lambda x, y: dps(x - y * scale)) + + # consistency check for overdetermined systems + if m > n: + for i in range(n, m): + for j in range(b.cols): + if not iszerofunc(b[i, j]): + raise ValueError("The system is inconsistent.") + + b = b[0:n, :] # truncate zero rows if consistent + + # backward substitution + for i in range(n - 1, -1, -1): + for j in range(i + 1, n): + scale = A[i, j] + b.zip_row_op(i, j, lambda x, y: dps(x - y * scale)) + + scale = A[i, i] + b.row_op(i, lambda x, _: dps(x / scale)) + + return rhs.__class__(b) + + +def _QRsolve(M, b): + """Solve the linear system ``Ax = b``. + + ``M`` is the matrix ``A``, the method argument is the vector + ``b``. The method returns the solution vector ``x``. If ``b`` is a + matrix, the system is solved for each column of ``b`` and the + return value is a matrix of the same shape as ``b``. + + This method is slower (approximately by a factor of 2) but + more stable for floating-point arithmetic than the LUsolve method. + However, LUsolve usually uses an exact arithmetic, so you do not need + to use QRsolve. + + This is mainly for educational purposes and symbolic matrices, for real + (or complex) matrices use mpmath.qr_solve. + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + pinv_solve + QRdecomposition + cramer_solve + """ + + dps = _get_intermediate_simp(expand_mul, expand_mul) + Q, R = M.QRdecomposition() + y = Q.T * b + + # back substitution to solve R*x = y: + # We build up the result "backwards" in the vector 'x' and reverse it + # only in the end. + x = [] + n = R.rows + + for j in range(n - 1, -1, -1): + tmp = y[j, :] + + for k in range(j + 1, n): + tmp -= R[j, k] * x[n - 1 - k] + + tmp = dps(tmp) + + x.append(tmp / R[j, j]) + + return M.vstack(*x[::-1]) + + +def _gauss_jordan_solve(M, B, freevar=False): + """ + Solves ``Ax = B`` using Gauss Jordan elimination. + + There may be zero, one, or infinite solutions. If one solution + exists, it will be returned. If infinite solutions exist, it will + be returned parametrically. If no solutions exist, It will throw + ValueError. + + Parameters + ========== + + B : Matrix + The right hand side of the equation to be solved for. Must have + the same number of rows as matrix A. + + freevar : boolean, optional + Flag, when set to `True` will return the indices of the free + variables in the solutions (column Matrix), for a system that is + undetermined (e.g. A has more columns than rows), for which + infinite solutions are possible, in terms of arbitrary + values of free variables. Default `False`. + + Returns + ======= + + x : Matrix + The matrix that will satisfy ``Ax = B``. Will have as many rows as + matrix A has columns, and as many columns as matrix B. + + params : Matrix + If the system is underdetermined (e.g. A has more columns than + rows), infinite solutions are possible, in terms of arbitrary + parameters. These arbitrary parameters are returned as params + Matrix. + + free_var_index : List, optional + If the system is underdetermined (e.g. A has more columns than + rows), infinite solutions are possible, in terms of arbitrary + values of free variables. Then the indices of the free variables + in the solutions (column Matrix) are returned by free_var_index, + if the flag `freevar` is set to `True`. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 1, 1], [1, 2, 2, -1], [2, 4, 0, 6]]) + >>> B = Matrix([7, 12, 4]) + >>> sol, params = A.gauss_jordan_solve(B) + >>> sol + Matrix([ + [-2*tau0 - 3*tau1 + 2], + [ tau0], + [ 2*tau1 + 5], + [ tau1]]) + >>> params + Matrix([ + [tau0], + [tau1]]) + >>> taus_zeroes = { tau:0 for tau in params } + >>> sol_unique = sol.xreplace(taus_zeroes) + >>> sol_unique + Matrix([ + [2], + [0], + [5], + [0]]) + + + >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 10]]) + >>> B = Matrix([3, 6, 9]) + >>> sol, params = A.gauss_jordan_solve(B) + >>> sol + Matrix([ + [-1], + [ 2], + [ 0]]) + >>> params + Matrix(0, 1, []) + + >>> A = Matrix([[2, -7], [-1, 4]]) + >>> B = Matrix([[-21, 3], [12, -2]]) + >>> sol, params = A.gauss_jordan_solve(B) + >>> sol + Matrix([ + [0, -2], + [3, -1]]) + >>> params + Matrix(0, 2, []) + + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 1, 1], [1, 2, 2, -1], [2, 4, 0, 6]]) + >>> B = Matrix([7, 12, 4]) + >>> sol, params, freevars = A.gauss_jordan_solve(B, freevar=True) + >>> sol + Matrix([ + [-2*tau0 - 3*tau1 + 2], + [ tau0], + [ 2*tau1 + 5], + [ tau1]]) + >>> params + Matrix([ + [tau0], + [tau1]]) + >>> freevars + [1, 3] + + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gaussian_elimination + + """ + + from sympy.matrices import Matrix, zeros + + cls = M.__class__ + aug = M.hstack(M.copy(), B.copy()) + B_cols = B.cols + row, col = aug[:, :-B_cols].shape + + # solve by reduced row echelon form + A, pivots = aug.rref(simplify=True) + A, v = A[:, :-B_cols], A[:, -B_cols:] + pivots = list(filter(lambda p: p < col, pivots)) + rank = len(pivots) + + # Get index of free symbols (free parameters) + # non-pivots columns are free variables + free_var_index = [c for c in range(A.cols) if c not in pivots] + + # Bring to block form + permutation = Matrix(pivots + free_var_index).T + + # check for existence of solutions + # rank of aug Matrix should be equal to rank of coefficient matrix + if not v[rank:, :].is_zero_matrix: + raise ValueError("Linear system has no solution") + + # Free parameters + # what are current unnumbered free symbol names? + name = uniquely_named_symbol('tau', [aug], + compare=lambda i: str(i).rstrip('1234567890'), + modify=lambda s: '_' + s).name + gen = numbered_symbols(name) + tau = Matrix([next(gen) for k in range((col - rank)*B_cols)]).reshape( + col - rank, B_cols) + + # Full parametric solution + V = A[:rank, free_var_index] + vt = v[:rank, :] + free_sol = tau.vstack(vt - V * tau, tau) + + # Undo permutation + sol = zeros(col, B_cols) + + for k in range(col): + sol[permutation[k], :] = free_sol[k,:] + + sol, tau = cls(sol), cls(tau) + + if freevar: + return sol, tau, free_var_index + else: + return sol, tau + + +def _pinv_solve(M, B, arbitrary_matrix=None): + """Solve ``Ax = B`` using the Moore-Penrose pseudoinverse. + + There may be zero, one, or infinite solutions. If one solution + exists, it will be returned. If infinite solutions exist, one will + be returned based on the value of arbitrary_matrix. If no solutions + exist, the least-squares solution is returned. + + Parameters + ========== + + B : Matrix + The right hand side of the equation to be solved for. Must have + the same number of rows as matrix A. + arbitrary_matrix : Matrix + If the system is underdetermined (e.g. A has more columns than + rows), infinite solutions are possible, in terms of an arbitrary + matrix. This parameter may be set to a specific matrix to use + for that purpose; if so, it must be the same shape as x, with as + many rows as matrix A has columns, and as many columns as matrix + B. If left as None, an appropriate matrix containing dummy + symbols in the form of ``wn_m`` will be used, with n and m being + row and column position of each symbol. + + Returns + ======= + + x : Matrix + The matrix that will satisfy ``Ax = B``. Will have as many rows as + matrix A has columns, and as many columns as matrix B. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[1, 2, 3], [4, 5, 6]]) + >>> B = Matrix([7, 8]) + >>> A.pinv_solve(B) + Matrix([ + [ _w0_0/6 - _w1_0/3 + _w2_0/6 - 55/18], + [-_w0_0/3 + 2*_w1_0/3 - _w2_0/3 + 1/9], + [ _w0_0/6 - _w1_0/3 + _w2_0/6 + 59/18]]) + >>> A.pinv_solve(B, arbitrary_matrix=Matrix([0, 0, 0])) + Matrix([ + [-55/18], + [ 1/9], + [ 59/18]]) + + See Also + ======== + + sympy.matrices.dense.DenseMatrix.lower_triangular_solve + sympy.matrices.dense.DenseMatrix.upper_triangular_solve + gauss_jordan_solve + cholesky_solve + diagonal_solve + LDLsolve + LUsolve + QRsolve + pinv + + Notes + ===== + + This may return either exact solutions or least squares solutions. + To determine which, check ``A * A.pinv() * B == B``. It will be + True if exact solutions exist, and False if only a least-squares + solution exists. Be aware that the left hand side of that equation + may need to be simplified to correctly compare to the right hand + side. + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#Obtaining_all_solutions_of_a_linear_system + + """ + + from sympy.matrices import eye + + A = M + A_pinv = M.pinv() + + if arbitrary_matrix is None: + rows, cols = A.cols, B.cols + w = symbols('w:{}_:{}'.format(rows, cols), cls=Dummy) + arbitrary_matrix = M.__class__(cols, rows, w).T + + return A_pinv.multiply(B) + (eye(A.cols) - + A_pinv.multiply(A)).multiply(arbitrary_matrix) + + +def _cramer_solve(M, rhs, det_method="laplace"): + """Solves system of linear equations using Cramer's rule. + + This method is relatively inefficient compared to other methods. + However it only uses a single division, assuming a division-free determinant + method is provided. This is helpful to minimize the chance of divide-by-zero + cases in symbolic solutions to linear systems. + + Parameters + ========== + M : Matrix + The matrix representing the left hand side of the equation. + rhs : Matrix + The matrix representing the right hand side of the equation. + det_method : str or callable + The method to use to calculate the determinant of the matrix. + The default is ``'laplace'``. If a callable is passed, it should take a + single argument, the matrix, and return the determinant of the matrix. + + Returns + ======= + x : Matrix + The matrix that will satisfy ``Ax = B``. Will have as many rows as + matrix A has columns, and as many columns as matrix B. + + Examples + ======== + + >>> from sympy import Matrix + >>> A = Matrix([[0, -6, 1], [0, -6, -1], [-5, -2, 3]]) + >>> B = Matrix([[-30, -9], [-18, -27], [-26, 46]]) + >>> x = A.cramer_solve(B) + >>> x + Matrix([ + [ 0, -5], + [ 4, 3], + [-6, 9]]) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Cramer%27s_rule#Explicit_formulas_for_small_systems + + """ + from .dense import zeros + + def entry(i, j): + return rhs[i, sol] if j == col else M[i, j] + + if det_method == "bird": + from .determinant import _det_bird + det = _det_bird + elif det_method == "laplace": + from .determinant import _det_laplace + det = _det_laplace + elif isinstance(det_method, str): + det = lambda matrix: matrix.det(method=det_method) + else: + det = det_method + det_M = det(M) + x = zeros(*rhs.shape) + for sol in range(rhs.shape[1]): + for col in range(rhs.shape[0]): + x[col, sol] = det(M.__class__(*M.shape, entry)) / det_M + return M.__class__(x) + + +def _solve(M, rhs, method='GJ'): + """Solves linear equation where the unique solution exists. + + Parameters + ========== + + rhs : Matrix + Vector representing the right hand side of the linear equation. + + method : string, optional + If set to ``'GJ'`` or ``'GE'``, the Gauss-Jordan elimination will be + used, which is implemented in the routine ``gauss_jordan_solve``. + + If set to ``'LU'``, ``LUsolve`` routine will be used. + + If set to ``'QR'``, ``QRsolve`` routine will be used. + + If set to ``'PINV'``, ``pinv_solve`` routine will be used. + + If set to ``'CRAMER'``, ``cramer_solve`` routine will be used. + + It also supports the methods available for special linear systems + + For positive definite systems: + + If set to ``'CH'``, ``cholesky_solve`` routine will be used. + + If set to ``'LDL'``, ``LDLsolve`` routine will be used. + + To use a different method and to compute the solution via the + inverse, use a method defined in the .inv() docstring. + + Returns + ======= + + solutions : Matrix + Vector representing the solution. + + Raises + ====== + + ValueError + If there is not a unique solution then a ``ValueError`` will be + raised. + + If ``M`` is not square, a ``ValueError`` and a different routine + for solving the system will be suggested. + """ + + if method in ('GJ', 'GE'): + try: + soln, param = M.gauss_jordan_solve(rhs) + + if param: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible. " + "Try ``M.gauss_jordan_solve(rhs)`` to obtain a parametric solution.") + + except ValueError: + raise NonInvertibleMatrixError("Matrix det == 0; not invertible.") + + return soln + + elif method == 'LU': + return M.LUsolve(rhs) + elif method == 'CH': + return M.cholesky_solve(rhs) + elif method == 'QR': + return M.QRsolve(rhs) + elif method == 'LDL': + return M.LDLsolve(rhs) + elif method == 'PINV': + return M.pinv_solve(rhs) + elif method == 'CRAMER': + return M.cramer_solve(rhs) + else: + return M.inv(method=method).multiply(rhs) + + +def _solve_least_squares(M, rhs, method='CH'): + """Return the least-square fit to the data. + + Parameters + ========== + + rhs : Matrix + Vector representing the right hand side of the linear equation. + + method : string or boolean, optional + If set to ``'CH'``, ``cholesky_solve`` routine will be used. + + If set to ``'LDL'``, ``LDLsolve`` routine will be used. + + If set to ``'QR'``, ``QRsolve`` routine will be used. + + If set to ``'PINV'``, ``pinv_solve`` routine will be used. + + Otherwise, the conjugate of ``M`` will be used to create a system + of equations that is passed to ``solve`` along with the hint + defined by ``method``. + + Returns + ======= + + solutions : Matrix + Vector representing the solution. + + Examples + ======== + + >>> from sympy import Matrix, ones + >>> A = Matrix([1, 2, 3]) + >>> B = Matrix([2, 3, 4]) + >>> S = Matrix(A.row_join(B)) + >>> S + Matrix([ + [1, 2], + [2, 3], + [3, 4]]) + + If each line of S represent coefficients of Ax + By + and x and y are [2, 3] then S*xy is: + + >>> r = S*Matrix([2, 3]); r + Matrix([ + [ 8], + [13], + [18]]) + + But let's add 1 to the middle value and then solve for the + least-squares value of xy: + + >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy + Matrix([ + [ 5/3], + [10/3]]) + + The error is given by S*xy - r: + + >>> S*xy - r + Matrix([ + [1/3], + [1/3], + [1/3]]) + >>> _.norm().n(2) + 0.58 + + If a different xy is used, the norm will be higher: + + >>> xy += ones(2, 1)/10 + >>> (S*xy - r).norm().n(2) + 1.5 + + """ + + if method == 'CH': + return M.cholesky_solve(rhs) + elif method == 'QR': + return M.QRsolve(rhs) + elif method == 'LDL': + return M.LDLsolve(rhs) + elif method == 'PINV': + return M.pinv_solve(rhs) + else: + t = M.H + return (t * M).solve(t * rhs, method=method) diff --git a/lib/python3.11/site-packages/sympy/matrices/sparse.py b/lib/python3.11/site-packages/sympy/matrices/sparse.py new file mode 100644 index 0000000000000000000000000000000000000000..95a7b3ca0ac29cf4409ec1eeecd059f9643e9bbc --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/sparse.py @@ -0,0 +1,473 @@ +from collections.abc import Callable + +from sympy.core.containers import Dict +from sympy.utilities.exceptions import sympy_deprecation_warning +from sympy.utilities.iterables import is_sequence +from sympy.utilities.misc import as_int + +from .matrixbase import MatrixBase +from .repmatrix import MutableRepMatrix, RepMatrix + +from .utilities import _iszero + +from .decompositions import ( + _liupc, _row_structure_symbolic_cholesky, _cholesky_sparse, + _LDLdecomposition_sparse) + +from .solvers import ( + _lower_triangular_solve_sparse, _upper_triangular_solve_sparse) + + +class SparseRepMatrix(RepMatrix): + """ + A sparse matrix (a matrix with a large number of zero elements). + + Examples + ======== + + >>> from sympy import SparseMatrix, ones + >>> SparseMatrix(2, 2, range(4)) + Matrix([ + [0, 1], + [2, 3]]) + >>> SparseMatrix(2, 2, {(1, 1): 2}) + Matrix([ + [0, 0], + [0, 2]]) + + A SparseMatrix can be instantiated from a ragged list of lists: + + >>> SparseMatrix([[1, 2, 3], [1, 2], [1]]) + Matrix([ + [1, 2, 3], + [1, 2, 0], + [1, 0, 0]]) + + For safety, one may include the expected size and then an error + will be raised if the indices of any element are out of range or + (for a flat list) if the total number of elements does not match + the expected shape: + + >>> SparseMatrix(2, 2, [1, 2]) + Traceback (most recent call last): + ... + ValueError: List length (2) != rows*columns (4) + + Here, an error is not raised because the list is not flat and no + element is out of range: + + >>> SparseMatrix(2, 2, [[1, 2]]) + Matrix([ + [1, 2], + [0, 0]]) + + But adding another element to the first (and only) row will cause + an error to be raised: + + >>> SparseMatrix(2, 2, [[1, 2, 3]]) + Traceback (most recent call last): + ... + ValueError: The location (0, 2) is out of designated range: (1, 1) + + To autosize the matrix, pass None for rows: + + >>> SparseMatrix(None, [[1, 2, 3]]) + Matrix([[1, 2, 3]]) + >>> SparseMatrix(None, {(1, 1): 1, (3, 3): 3}) + Matrix([ + [0, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 3]]) + + Values that are themselves a Matrix are automatically expanded: + + >>> SparseMatrix(4, 4, {(1, 1): ones(2)}) + Matrix([ + [0, 0, 0, 0], + [0, 1, 1, 0], + [0, 1, 1, 0], + [0, 0, 0, 0]]) + + A ValueError is raised if the expanding matrix tries to overwrite + a different element already present: + + >>> SparseMatrix(3, 3, {(0, 0): ones(2), (1, 1): 2}) + Traceback (most recent call last): + ... + ValueError: collision at (1, 1) + + See Also + ======== + DenseMatrix + MutableSparseMatrix + ImmutableSparseMatrix + """ + + @classmethod + def _handle_creation_inputs(cls, *args, **kwargs): + if len(args) == 1 and isinstance(args[0], MatrixBase): + rows = args[0].rows + cols = args[0].cols + smat = args[0].todok() + return rows, cols, smat + + smat = {} + # autosizing + if len(args) == 2 and args[0] is None: + args = [None, None, args[1]] + + if len(args) == 3: + r, c = args[:2] + if r is c is None: + rows = cols = None + elif None in (r, c): + raise ValueError( + 'Pass rows=None and no cols for autosizing.') + else: + rows, cols = as_int(args[0]), as_int(args[1]) + + if isinstance(args[2], Callable): + op = args[2] + + if None in (rows, cols): + raise ValueError( + "{} and {} must be integers for this " + "specification.".format(rows, cols)) + + row_indices = [cls._sympify(i) for i in range(rows)] + col_indices = [cls._sympify(j) for j in range(cols)] + + for i in row_indices: + for j in col_indices: + value = cls._sympify(op(i, j)) + if value != cls.zero: + smat[i, j] = value + + return rows, cols, smat + + elif isinstance(args[2], (dict, Dict)): + def update(i, j, v): + # update smat and make sure there are no collisions + if v: + if (i, j) in smat and v != smat[i, j]: + raise ValueError( + "There is a collision at {} for {} and {}." + .format((i, j), v, smat[i, j]) + ) + smat[i, j] = v + + # manual copy, copy.deepcopy() doesn't work + for (r, c), v in args[2].items(): + if isinstance(v, MatrixBase): + for (i, j), vv in v.todok().items(): + update(r + i, c + j, vv) + elif isinstance(v, (list, tuple)): + _, _, smat = cls._handle_creation_inputs(v, **kwargs) + for i, j in smat: + update(r + i, c + j, smat[i, j]) + else: + v = cls._sympify(v) + update(r, c, cls._sympify(v)) + + elif is_sequence(args[2]): + flat = not any(is_sequence(i) for i in args[2]) + if not flat: + _, _, smat = \ + cls._handle_creation_inputs(args[2], **kwargs) + else: + flat_list = args[2] + if len(flat_list) != rows * cols: + raise ValueError( + "The length of the flat list ({}) does not " + "match the specified size ({} * {})." + .format(len(flat_list), rows, cols) + ) + + for i in range(rows): + for j in range(cols): + value = flat_list[i*cols + j] + value = cls._sympify(value) + if value != cls.zero: + smat[i, j] = value + + if rows is None: # autosizing + keys = smat.keys() + rows = max(r for r, _ in keys) + 1 if keys else 0 + cols = max(c for _, c in keys) + 1 if keys else 0 + + else: + for i, j in smat.keys(): + if i and i >= rows or j and j >= cols: + raise ValueError( + "The location {} is out of the designated range" + "[{}, {}]x[{}, {}]" + .format((i, j), 0, rows - 1, 0, cols - 1) + ) + + return rows, cols, smat + + elif len(args) == 1 and isinstance(args[0], (list, tuple)): + # list of values or lists + v = args[0] + c = 0 + for i, row in enumerate(v): + if not isinstance(row, (list, tuple)): + row = [row] + for j, vv in enumerate(row): + if vv != cls.zero: + smat[i, j] = cls._sympify(vv) + c = max(c, len(row)) + rows = len(v) if c else 0 + cols = c + return rows, cols, smat + + else: + # handle full matrix forms with _handle_creation_inputs + rows, cols, mat = super()._handle_creation_inputs(*args) + for i in range(rows): + for j in range(cols): + value = mat[cols*i + j] + if value != cls.zero: + smat[i, j] = value + + return rows, cols, smat + + @property + def _smat(self): + + sympy_deprecation_warning( + """ + The private _smat attribute of SparseMatrix is deprecated. Use the + .todok() method instead. + """, + deprecated_since_version="1.9", + active_deprecations_target="deprecated-private-matrix-attributes" + ) + + return self.todok() + + def _eval_inverse(self, **kwargs): + return self.inv(method=kwargs.get('method', 'LDL'), + iszerofunc=kwargs.get('iszerofunc', _iszero), + try_block_diag=kwargs.get('try_block_diag', False)) + + def applyfunc(self, f): + """Apply a function to each element of the matrix. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j) + >>> m + Matrix([ + [0, 1], + [2, 3]]) + >>> m.applyfunc(lambda i: 2*i) + Matrix([ + [0, 2], + [4, 6]]) + + """ + if not callable(f): + raise TypeError("`f` must be callable.") + + # XXX: This only applies the function to the nonzero elements of the + # matrix so is inconsistent with DenseMatrix.applyfunc e.g. + # zeros(2, 2).applyfunc(lambda x: x + 1) + dok = {} + for k, v in self.todok().items(): + fv = f(v) + if fv != 0: + dok[k] = fv + + return self._new(self.rows, self.cols, dok) + + def as_immutable(self): + """Returns an Immutable version of this Matrix.""" + from .immutable import ImmutableSparseMatrix + return ImmutableSparseMatrix(self) + + def as_mutable(self): + """Returns a mutable version of this matrix. + + Examples + ======== + + >>> from sympy import ImmutableMatrix + >>> X = ImmutableMatrix([[1, 2], [3, 4]]) + >>> Y = X.as_mutable() + >>> Y[1, 1] = 5 # Can set values in Y + >>> Y + Matrix([ + [1, 2], + [3, 5]]) + """ + return MutableSparseMatrix(self) + + def col_list(self): + """Returns a column-sorted list of non-zero elements of the matrix. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> a=SparseMatrix(((1, 2), (3, 4))) + >>> a + Matrix([ + [1, 2], + [3, 4]]) + >>> a.CL + [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)] + + See Also + ======== + + sympy.matrices.sparse.SparseMatrix.row_list + """ + return [tuple(k + (self[k],)) for k in sorted(self.todok().keys(), key=lambda k: list(reversed(k)))] + + def nnz(self): + """Returns the number of non-zero elements in Matrix.""" + return len(self.todok()) + + def row_list(self): + """Returns a row-sorted list of non-zero elements of the matrix. + + Examples + ======== + + >>> from sympy import SparseMatrix + >>> a = SparseMatrix(((1, 2), (3, 4))) + >>> a + Matrix([ + [1, 2], + [3, 4]]) + >>> a.RL + [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)] + + See Also + ======== + + sympy.matrices.sparse.SparseMatrix.col_list + """ + return [tuple(k + (self[k],)) for k in + sorted(self.todok().keys(), key=list)] + + def scalar_multiply(self, scalar): + "Scalar element-wise multiplication" + return scalar * self + + def solve_least_squares(self, rhs, method='LDL'): + """Return the least-square fit to the data. + + By default the cholesky_solve routine is used (method='CH'); other + methods of matrix inversion can be used. To find out which are + available, see the docstring of the .inv() method. + + Examples + ======== + + >>> from sympy import SparseMatrix, Matrix, ones + >>> A = Matrix([1, 2, 3]) + >>> B = Matrix([2, 3, 4]) + >>> S = SparseMatrix(A.row_join(B)) + >>> S + Matrix([ + [1, 2], + [2, 3], + [3, 4]]) + + If each line of S represent coefficients of Ax + By + and x and y are [2, 3] then S*xy is: + + >>> r = S*Matrix([2, 3]); r + Matrix([ + [ 8], + [13], + [18]]) + + But let's add 1 to the middle value and then solve for the + least-squares value of xy: + + >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy + Matrix([ + [ 5/3], + [10/3]]) + + The error is given by S*xy - r: + + >>> S*xy - r + Matrix([ + [1/3], + [1/3], + [1/3]]) + >>> _.norm().n(2) + 0.58 + + If a different xy is used, the norm will be higher: + + >>> xy += ones(2, 1)/10 + >>> (S*xy - r).norm().n(2) + 1.5 + + """ + t = self.T + return (t*self).inv(method=method)*t*rhs + + def solve(self, rhs, method='LDL'): + """Return solution to self*soln = rhs using given inversion method. + + For a list of possible inversion methods, see the .inv() docstring. + """ + if not self.is_square: + if self.rows < self.cols: + raise ValueError('Under-determined system.') + elif self.rows > self.cols: + raise ValueError('For over-determined system, M, having ' + 'more rows than columns, try M.solve_least_squares(rhs).') + else: + return self.inv(method=method).multiply(rhs) + + RL = property(row_list, None, None, "Alternate faster representation") + CL = property(col_list, None, None, "Alternate faster representation") + + def liupc(self): + return _liupc(self) + + def row_structure_symbolic_cholesky(self): + return _row_structure_symbolic_cholesky(self) + + def cholesky(self, hermitian=True): + return _cholesky_sparse(self, hermitian=hermitian) + + def LDLdecomposition(self, hermitian=True): + return _LDLdecomposition_sparse(self, hermitian=hermitian) + + def lower_triangular_solve(self, rhs): + return _lower_triangular_solve_sparse(self, rhs) + + def upper_triangular_solve(self, rhs): + return _upper_triangular_solve_sparse(self, rhs) + + liupc.__doc__ = _liupc.__doc__ + row_structure_symbolic_cholesky.__doc__ = _row_structure_symbolic_cholesky.__doc__ + cholesky.__doc__ = _cholesky_sparse.__doc__ + LDLdecomposition.__doc__ = _LDLdecomposition_sparse.__doc__ + lower_triangular_solve.__doc__ = lower_triangular_solve.__doc__ + upper_triangular_solve.__doc__ = upper_triangular_solve.__doc__ + + +class MutableSparseMatrix(SparseRepMatrix, MutableRepMatrix): + + @classmethod + def _new(cls, *args, **kwargs): + rows, cols, smat = cls._handle_creation_inputs(*args, **kwargs) + + rep = cls._smat_to_DomainMatrix(rows, cols, smat) + + return cls._fromrep(rep) + + +SparseMatrix = MutableSparseMatrix diff --git a/lib/python3.11/site-packages/sympy/matrices/sparsetools.py b/lib/python3.11/site-packages/sympy/matrices/sparsetools.py new file mode 100644 index 0000000000000000000000000000000000000000..50048f6dc7e5cf160366963d16427987616ddce7 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/sparsetools.py @@ -0,0 +1,300 @@ +from sympy.core.containers import Dict +from sympy.core.symbol import Dummy +from sympy.utilities.iterables import is_sequence +from sympy.utilities.misc import as_int, filldedent + +from .sparse import MutableSparseMatrix as SparseMatrix + + +def _doktocsr(dok): + """Converts a sparse matrix to Compressed Sparse Row (CSR) format. + + Parameters + ========== + + A : contains non-zero elements sorted by key (row, column) + JA : JA[i] is the column corresponding to A[i] + IA : IA[i] contains the index in A for the first non-zero element + of row[i]. Thus IA[i+1] - IA[i] gives number of non-zero + elements row[i]. The length of IA is always 1 more than the + number of rows in the matrix. + + Examples + ======== + + >>> from sympy.matrices.sparsetools import _doktocsr + >>> from sympy import SparseMatrix, diag + >>> m = SparseMatrix(diag(1, 2, 3)) + >>> m[2, 0] = -1 + >>> _doktocsr(m) + [[1, 2, -1, 3], [0, 1, 0, 2], [0, 1, 2, 4], [3, 3]] + + """ + row, JA, A = [list(i) for i in zip(*dok.row_list())] + IA = [0]*((row[0] if row else 0) + 1) + for i, r in enumerate(row): + IA.extend([i]*(r - row[i - 1])) # if i = 0 nothing is extended + IA.extend([len(A)]*(dok.rows - len(IA) + 1)) + shape = [dok.rows, dok.cols] + return [A, JA, IA, shape] + + +def _csrtodok(csr): + """Converts a CSR representation to DOK representation. + + Examples + ======== + + >>> from sympy.matrices.sparsetools import _csrtodok + >>> _csrtodok([[5, 8, 3, 6], [0, 1, 2, 1], [0, 0, 2, 3, 4], [4, 3]]) + Matrix([ + [0, 0, 0], + [5, 8, 0], + [0, 0, 3], + [0, 6, 0]]) + + """ + smat = {} + A, JA, IA, shape = csr + for i in range(len(IA) - 1): + indices = slice(IA[i], IA[i + 1]) + for l, m in zip(A[indices], JA[indices]): + smat[i, m] = l + return SparseMatrix(*shape, smat) + + +def banded(*args, **kwargs): + """Returns a SparseMatrix from the given dictionary describing + the diagonals of the matrix. The keys are positive for upper + diagonals and negative for those below the main diagonal. The + values may be: + + * expressions or single-argument functions, + + * lists or tuples of values, + + * matrices + + Unless dimensions are given, the size of the returned matrix will + be large enough to contain the largest non-zero value provided. + + kwargs + ====== + + rows : rows of the resulting matrix; computed if + not given. + + cols : columns of the resulting matrix; computed if + not given. + + Examples + ======== + + >>> from sympy import banded, ones, Matrix + >>> from sympy.abc import x + + If explicit values are given in tuples, + the matrix will autosize to contain all values, otherwise + a single value is filled onto the entire diagonal: + + >>> banded({1: (1, 2, 3), -1: (4, 5, 6), 0: x}) + Matrix([ + [x, 1, 0, 0], + [4, x, 2, 0], + [0, 5, x, 3], + [0, 0, 6, x]]) + + A function accepting a single argument can be used to fill the + diagonal as a function of diagonal index (which starts at 0). + The size (or shape) of the matrix must be given to obtain more + than a 1x1 matrix: + + >>> s = lambda d: (1 + d)**2 + >>> banded(5, {0: s, 2: s, -2: 2}) + Matrix([ + [1, 0, 1, 0, 0], + [0, 4, 0, 4, 0], + [2, 0, 9, 0, 9], + [0, 2, 0, 16, 0], + [0, 0, 2, 0, 25]]) + + The diagonal of matrices placed on a diagonal will coincide + with the indicated diagonal: + + >>> vert = Matrix([1, 2, 3]) + >>> banded({0: vert}, cols=3) + Matrix([ + [1, 0, 0], + [2, 1, 0], + [3, 2, 1], + [0, 3, 2], + [0, 0, 3]]) + + >>> banded(4, {0: ones(2)}) + Matrix([ + [1, 1, 0, 0], + [1, 1, 0, 0], + [0, 0, 1, 1], + [0, 0, 1, 1]]) + + Errors are raised if the designated size will not hold + all values an integral number of times. Here, the rows + are designated as odd (but an even number is required to + hold the off-diagonal 2x2 ones): + + >>> banded({0: 2, 1: ones(2)}, rows=5) + Traceback (most recent call last): + ... + ValueError: + sequence does not fit an integral number of times in the matrix + + And here, an even number of rows is given...but the square + matrix has an even number of columns, too. As we saw + in the previous example, an odd number is required: + + >>> banded(4, {0: 2, 1: ones(2)}) # trying to make 4x4 and cols must be odd + Traceback (most recent call last): + ... + ValueError: + sequence does not fit an integral number of times in the matrix + + A way around having to count rows is to enclosing matrix elements + in a tuple and indicate the desired number of them to the right: + + >>> banded({0: 2, 2: (ones(2),)*3}) + Matrix([ + [2, 0, 1, 1, 0, 0, 0, 0], + [0, 2, 1, 1, 0, 0, 0, 0], + [0, 0, 2, 0, 1, 1, 0, 0], + [0, 0, 0, 2, 1, 1, 0, 0], + [0, 0, 0, 0, 2, 0, 1, 1], + [0, 0, 0, 0, 0, 2, 1, 1]]) + + An error will be raised if more than one value + is written to a given entry. Here, the ones overlap + with the main diagonal if they are placed on the + first diagonal: + + >>> banded({0: (2,)*5, 1: (ones(2),)*3}) + Traceback (most recent call last): + ... + ValueError: collision at (1, 1) + + By placing a 0 at the bottom left of the 2x2 matrix of + ones, the collision is avoided: + + >>> u2 = Matrix([ + ... [1, 1], + ... [0, 1]]) + >>> banded({0: [2]*5, 1: [u2]*3}) + Matrix([ + [2, 1, 1, 0, 0, 0, 0], + [0, 2, 1, 0, 0, 0, 0], + [0, 0, 2, 1, 1, 0, 0], + [0, 0, 0, 2, 1, 0, 0], + [0, 0, 0, 0, 2, 1, 1], + [0, 0, 0, 0, 0, 0, 1]]) + """ + try: + if len(args) not in (1, 2, 3): + raise TypeError + if not isinstance(args[-1], (dict, Dict)): + raise TypeError + if len(args) == 1: + rows = kwargs.get('rows', None) + cols = kwargs.get('cols', None) + if rows is not None: + rows = as_int(rows) + if cols is not None: + cols = as_int(cols) + elif len(args) == 2: + rows = cols = as_int(args[0]) + else: + rows, cols = map(as_int, args[:2]) + # fails with ValueError if any keys are not ints + _ = all(as_int(k) for k in args[-1]) + except (ValueError, TypeError): + raise TypeError(filldedent( + '''unrecognized input to banded: + expecting [[row,] col,] {int: value}''')) + def rc(d): + # return row,col coord of diagonal start + r = -d if d < 0 else 0 + c = 0 if r else d + return r, c + smat = {} + undone = [] + tba = Dummy() + # first handle objects with size + for d, v in args[-1].items(): + r, c = rc(d) + # note: only list and tuple are recognized since this + # will allow other Basic objects like Tuple + # into the matrix if so desired + if isinstance(v, (list, tuple)): + extra = 0 + for i, vi in enumerate(v): + i += extra + if is_sequence(vi): + vi = SparseMatrix(vi) + smat[r + i, c + i] = vi + extra += min(vi.shape) - 1 + else: + smat[r + i, c + i] = vi + elif is_sequence(v): + v = SparseMatrix(v) + rv, cv = v.shape + if rows and cols: + nr, xr = divmod(rows - r, rv) + nc, xc = divmod(cols - c, cv) + x = xr or xc + do = min(nr, nc) + elif rows: + do, x = divmod(rows - r, rv) + elif cols: + do, x = divmod(cols - c, cv) + else: + do = 1 + x = 0 + if x: + raise ValueError(filldedent(''' + sequence does not fit an integral number of times + in the matrix''')) + j = min(v.shape) + for i in range(do): + smat[r, c] = v + r += j + c += j + elif v: + smat[r, c] = tba + undone.append((d, v)) + s = SparseMatrix(None, smat) # to expand matrices + smat = s.todok() + # check for dim errors here + if rows is not None and rows < s.rows: + raise ValueError('Designated rows %s < needed %s' % (rows, s.rows)) + if cols is not None and cols < s.cols: + raise ValueError('Designated cols %s < needed %s' % (cols, s.cols)) + if rows is cols is None: + rows = s.rows + cols = s.cols + elif rows is not None and cols is None: + cols = max(rows, s.cols) + elif cols is not None and rows is None: + rows = max(cols, s.rows) + def update(i, j, v): + # update smat and make sure there are + # no collisions + if v: + if (i, j) in smat and smat[i, j] not in (tba, v): + raise ValueError('collision at %s' % ((i, j),)) + smat[i, j] = v + if undone: + for d, vi in undone: + r, c = rc(d) + v = vi if callable(vi) else lambda _: vi + i = 0 + while r + i < rows and c + i < cols: + update(r + i, c + i, v(i)) + i += 1 + return SparseMatrix(rows, cols, smat) diff --git a/lib/python3.11/site-packages/sympy/matrices/subspaces.py b/lib/python3.11/site-packages/sympy/matrices/subspaces.py new file mode 100644 index 0000000000000000000000000000000000000000..1ab0b71b4289ebaeb6394059c6a7cd49d3a148a1 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/subspaces.py @@ -0,0 +1,174 @@ +from .utilities import _iszero + + +def _columnspace(M, simplify=False): + """Returns a list of vectors (Matrix objects) that span columnspace of ``M`` + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6]) + >>> M + Matrix([ + [ 1, 3, 0], + [-2, -6, 0], + [ 3, 9, 6]]) + >>> M.columnspace() + [Matrix([ + [ 1], + [-2], + [ 3]]), Matrix([ + [0], + [0], + [6]])] + + See Also + ======== + + nullspace + rowspace + """ + + reduced, pivots = M.echelon_form(simplify=simplify, with_pivots=True) + + return [M.col(i) for i in pivots] + + +def _nullspace(M, simplify=False, iszerofunc=_iszero): + """Returns list of vectors (Matrix objects) that span nullspace of ``M`` + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6]) + >>> M + Matrix([ + [ 1, 3, 0], + [-2, -6, 0], + [ 3, 9, 6]]) + >>> M.nullspace() + [Matrix([ + [-3], + [ 1], + [ 0]])] + + See Also + ======== + + columnspace + rowspace + """ + + reduced, pivots = M.rref(iszerofunc=iszerofunc, simplify=simplify) + + free_vars = [i for i in range(M.cols) if i not in pivots] + basis = [] + + for free_var in free_vars: + # for each free variable, we will set it to 1 and all others + # to 0. Then, we will use back substitution to solve the system + vec = [M.zero] * M.cols + vec[free_var] = M.one + + for piv_row, piv_col in enumerate(pivots): + vec[piv_col] -= reduced[piv_row, free_var] + + basis.append(vec) + + return [M._new(M.cols, 1, b) for b in basis] + + +def _rowspace(M, simplify=False): + """Returns a list of vectors that span the row space of ``M``. + + Examples + ======== + + >>> from sympy import Matrix + >>> M = Matrix(3, 3, [1, 3, 0, -2, -6, 0, 3, 9, 6]) + >>> M + Matrix([ + [ 1, 3, 0], + [-2, -6, 0], + [ 3, 9, 6]]) + >>> M.rowspace() + [Matrix([[1, 3, 0]]), Matrix([[0, 0, 6]])] + """ + + reduced, pivots = M.echelon_form(simplify=simplify, with_pivots=True) + + return [reduced.row(i) for i in range(len(pivots))] + + +def _orthogonalize(cls, *vecs, normalize=False, rankcheck=False): + """Apply the Gram-Schmidt orthogonalization procedure + to vectors supplied in ``vecs``. + + Parameters + ========== + + vecs + vectors to be made orthogonal + + normalize : bool + If ``True``, return an orthonormal basis. + + rankcheck : bool + If ``True``, the computation does not stop when encountering + linearly dependent vectors. + + If ``False``, it will raise ``ValueError`` when any zero + or linearly dependent vectors are found. + + Returns + ======= + + list + List of orthogonal (or orthonormal) basis vectors. + + Examples + ======== + + >>> from sympy import I, Matrix + >>> v = [Matrix([1, I]), Matrix([1, -I])] + >>> Matrix.orthogonalize(*v) + [Matrix([ + [1], + [I]]), Matrix([ + [ 1], + [-I]])] + + See Also + ======== + + MatrixBase.QRdecomposition + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process + """ + from .decompositions import _QRdecomposition_optional + + if not vecs: + return [] + + all_row_vecs = (vecs[0].rows == 1) + + vecs = [x.vec() for x in vecs] + M = cls.hstack(*vecs) + Q, R = _QRdecomposition_optional(M, normalize=normalize) + + if rankcheck and Q.cols < len(vecs): + raise ValueError("GramSchmidt: vector set not linearly independent") + + ret = [] + for i in range(Q.cols): + if all_row_vecs: + col = cls(Q[:, i].T) + else: + col = cls(Q[:, i]) + ret.append(col) + return ret diff --git a/lib/python3.11/site-packages/sympy/matrices/utilities.py b/lib/python3.11/site-packages/sympy/matrices/utilities.py new file mode 100644 index 0000000000000000000000000000000000000000..b8a680b47e63615e210e561639a192ba47c642d3 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/matrices/utilities.py @@ -0,0 +1,72 @@ +from contextlib import contextmanager +from threading import local + +from sympy.core.function import expand_mul + + +class DotProdSimpState(local): + def __init__(self): + self.state = None + +_dotprodsimp_state = DotProdSimpState() + +@contextmanager +def dotprodsimp(x): + old = _dotprodsimp_state.state + + try: + _dotprodsimp_state.state = x + yield + finally: + _dotprodsimp_state.state = old + + +def _dotprodsimp(expr, withsimp=False): + """Wrapper for simplify.dotprodsimp to avoid circular imports.""" + from sympy.simplify.simplify import dotprodsimp as dps + return dps(expr, withsimp=withsimp) + + +def _get_intermediate_simp(deffunc=lambda x: x, offfunc=lambda x: x, + onfunc=_dotprodsimp, dotprodsimp=None): + """Support function for controlling intermediate simplification. Returns a + simplification function according to the global setting of dotprodsimp + operation. + + ``deffunc`` - Function to be used by default. + ``offfunc`` - Function to be used if dotprodsimp has been turned off. + ``onfunc`` - Function to be used if dotprodsimp has been turned on. + ``dotprodsimp`` - True, False or None. Will be overridden by global + _dotprodsimp_state.state if that is not None. + """ + + if dotprodsimp is False or _dotprodsimp_state.state is False: + return offfunc + if dotprodsimp is True or _dotprodsimp_state.state is True: + return onfunc + + return deffunc # None, None + + +def _get_intermediate_simp_bool(default=False, dotprodsimp=None): + """Same as ``_get_intermediate_simp`` but returns bools instead of functions + by default.""" + + return _get_intermediate_simp(default, False, True, dotprodsimp) + + +def _iszero(x): + """Returns True if x is zero.""" + return getattr(x, 'is_zero', None) + + +def _is_zero_after_expand_mul(x): + """Tests by expand_mul only, suitable for polynomials and rational + functions.""" + return expand_mul(x) == 0 + + +def _simplify(expr): + """ Wrapper to avoid circular imports. """ + from sympy.simplify.simplify import simplify + return simplify(expr) diff --git a/lib/python3.11/site-packages/sympy/release.py b/lib/python3.11/site-packages/sympy/release.py new file mode 100644 index 0000000000000000000000000000000000000000..4b67c39d7e3b39d3ea20d65b8a3c081a50320293 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/release.py @@ -0,0 +1 @@ +__version__ = "1.13.1" diff --git a/lib/python3.11/site-packages/sympy/this.py b/lib/python3.11/site-packages/sympy/this.py new file mode 100644 index 0000000000000000000000000000000000000000..c2a5504ac42c7d57790d65524b066a6df86ab539 --- /dev/null +++ b/lib/python3.11/site-packages/sympy/this.py @@ -0,0 +1,21 @@ +""" +The Zen of SymPy. +""" + +s = """The Zen of SymPy + +Unevaluated is better than evaluated. +The user interface matters. +Printing matters. +Pure Python can be fast enough. +If it's too slow, it's (probably) your fault. +Documentation matters. +Correctness is more important than speed. +Push it in now and improve upon it later. +Coverage by testing matters. +Smart tests are better than random tests. +But random tests sometimes find what your smartest test missed. +The Python way is probably the right way. +Community is more important than code.""" + +print(s) diff --git a/lib/python3.11/site-packages/torchvision.libs/libsharpyuv.5c41a003.so.0 b/lib/python3.11/site-packages/torchvision.libs/libsharpyuv.5c41a003.so.0 new file mode 100644 index 0000000000000000000000000000000000000000..f77d830efb43c49a8e614599b30b3a90cbd08bab Binary files /dev/null and b/lib/python3.11/site-packages/torchvision.libs/libsharpyuv.5c41a003.so.0 differ diff --git a/lib/python3.11/site-packages/triton-3.2.0.dist-info/INSTALLER b/lib/python3.11/site-packages/triton-3.2.0.dist-info/INSTALLER new file mode 100644 index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68 --- /dev/null +++ b/lib/python3.11/site-packages/triton-3.2.0.dist-info/INSTALLER @@ -0,0 +1 @@ +pip diff --git a/lib/python3.11/site-packages/triton-3.2.0.dist-info/METADATA b/lib/python3.11/site-packages/triton-3.2.0.dist-info/METADATA new file mode 100644 index 0000000000000000000000000000000000000000..3c296c8d892606cf442f810a616e3051849f9d7d --- /dev/null +++ b/lib/python3.11/site-packages/triton-3.2.0.dist-info/METADATA @@ -0,0 +1,39 @@ +Metadata-Version: 2.2 +Name: triton +Version: 3.2.0 +Summary: A language and compiler for custom Deep Learning operations +Home-page: https://github.com/triton-lang/triton/ +Author: Philippe Tillet +Author-email: phil@openai.com +Keywords: Compiler,Deep Learning +Classifier: Development Status :: 4 - Beta +Classifier: Intended Audience :: Developers +Classifier: Topic :: Software Development :: Build Tools +Classifier: License :: OSI Approved :: MIT License +Classifier: Programming Language :: Python :: 3.9 +Classifier: Programming Language :: Python :: 3.10 +Classifier: Programming Language :: Python :: 3.11 +Classifier: Programming Language :: Python :: 3.12 +Classifier: Programming Language :: Python :: 3.13 +Provides-Extra: build +Requires-Dist: cmake>=3.20; extra == "build" +Requires-Dist: lit; extra == "build" +Provides-Extra: tests +Requires-Dist: autopep8; extra == "tests" +Requires-Dist: flake8; extra == "tests" +Requires-Dist: isort; extra == "tests" +Requires-Dist: numpy; extra == "tests" +Requires-Dist: pytest; extra == "tests" +Requires-Dist: scipy>=1.7.1; extra == "tests" +Requires-Dist: llnl-hatchet; extra == "tests" +Provides-Extra: tutorials +Requires-Dist: matplotlib; extra == "tutorials" +Requires-Dist: pandas; extra == "tutorials" +Requires-Dist: tabulate; extra == "tutorials" +Dynamic: author +Dynamic: author-email +Dynamic: classifier +Dynamic: home-page +Dynamic: keywords +Dynamic: provides-extra +Dynamic: summary diff --git a/lib/python3.11/site-packages/triton-3.2.0.dist-info/RECORD b/lib/python3.11/site-packages/triton-3.2.0.dist-info/RECORD new file mode 100644 index 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a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/device_library_decls.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/device_library_decls.h new file mode 100644 index 0000000000000000000000000000000000000000..edc4692c838ee37ced0c35fe1561c73cd73a49a9 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/device_library_decls.h @@ -0,0 +1,133 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +/** + * @file amd_detail/device_library_decls.h + * @brief Contains declarations for types and functions in device library. + * Uses int64_t and uint64_t instead of long, long long, unsigned + * long and unsigned long long types for device library API + * declarations. + */ + +#ifndef HIP_INCLUDE_HIP_AMD_DETAIL_DEVICE_LIBRARY_DECLS_H +#define HIP_INCLUDE_HIP_AMD_DETAIL_DEVICE_LIBRARY_DECLS_H + +#if !defined(__HIPCC_RTC__) +#include "hip/amd_detail/host_defines.h" +#endif + +typedef unsigned char uchar; +typedef unsigned short ushort; +typedef unsigned int uint; +typedef unsigned long ulong; +typedef unsigned long long ullong; + +extern "C" __device__ __attribute__((const)) bool __ockl_wfany_i32(int); +extern "C" __device__ __attribute__((const)) bool __ockl_wfall_i32(int); +extern "C" __device__ uint __ockl_activelane_u32(void); + +extern "C" __device__ __attribute__((const)) uint __ockl_mul24_u32(uint, uint); +extern "C" __device__ __attribute__((const)) int __ockl_mul24_i32(int, int); +extern "C" __device__ __attribute__((const)) uint __ockl_mul_hi_u32(uint, uint); +extern "C" __device__ __attribute__((const)) int __ockl_mul_hi_i32(int, int); +extern "C" __device__ __attribute__((const)) uint __ockl_sadd_u32(uint, uint, uint); + +extern "C" __device__ __attribute__((const)) uchar __ockl_clz_u8(uchar); +extern "C" __device__ __attribute__((const)) ushort __ockl_clz_u16(ushort); +extern "C" __device__ __attribute__((const)) uint __ockl_clz_u32(uint); +extern "C" __device__ __attribute__((const)) uint64_t __ockl_clz_u64(uint64_t); + +extern "C" __device__ __attribute__((const)) float __ocml_floor_f32(float); +extern "C" __device__ __attribute__((const)) float __ocml_rint_f32(float); +extern "C" __device__ __attribute__((const)) float __ocml_ceil_f32(float); +extern "C" __device__ __attribute__((const)) float __ocml_trunc_f32(float); + +extern "C" __device__ __attribute__((const)) float __ocml_fmin_f32(float, float); +extern "C" __device__ __attribute__((const)) float __ocml_fmax_f32(float, float); + +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtn_f32_f64(double); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtp_f32_f64(double); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtz_f32_f64(double); + +extern "C" __device__ __attribute__((const)) _Float16 __ocml_cvtrtn_f16_f32(float); +extern "C" __device__ __attribute__((const)) _Float16 __ocml_cvtrtp_f16_f32(float); +extern "C" __device__ __attribute__((const)) _Float16 __ocml_cvtrtz_f16_f32(float); + +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtn_f32_s32(int); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtp_f32_s32(int); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtz_f32_s32(int); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtn_f32_u32(uint32_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtp_f32_u32(uint32_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtz_f32_u32(uint32_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtn_f32_s64(int64_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtp_f32_s64(int64_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtz_f32_s64(int64_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtn_f32_u64(uint64_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtp_f32_u64(uint64_t); +extern "C" __device__ __attribute__((const)) float __ocml_cvtrtz_f32_u64(uint64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtn_f64_s64(int64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtp_f64_s64(int64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtz_f64_s64(int64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtn_f64_u64(uint64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtp_f64_u64(uint64_t); +extern "C" __device__ __attribute__((const)) double __ocml_cvtrtz_f64_u64(uint64_t); + +extern "C" __device__ __attribute__((convergent)) void __ockl_gws_init(uint nwm1, uint rid); +extern "C" __device__ __attribute__((convergent)) void __ockl_gws_barrier(uint nwm1, uint rid); + +extern "C" __device__ __attribute__((const)) uint32_t __ockl_lane_u32(); +extern "C" __device__ __attribute__((const)) int __ockl_grid_is_valid(void); +extern "C" __device__ __attribute__((convergent)) void __ockl_grid_sync(void); +extern "C" __device__ __attribute__((const)) uint __ockl_multi_grid_num_grids(void); +extern "C" __device__ __attribute__((const)) uint __ockl_multi_grid_grid_rank(void); +extern "C" __device__ __attribute__((const)) uint __ockl_multi_grid_size(void); +extern "C" __device__ __attribute__((const)) uint __ockl_multi_grid_thread_rank(void); +extern "C" __device__ __attribute__((const)) int __ockl_multi_grid_is_valid(void); +extern "C" __device__ __attribute__((convergent)) void __ockl_multi_grid_sync(void); + +extern "C" __device__ void __ockl_atomic_add_noret_f32(float*, float); + +extern "C" __device__ __attribute__((convergent)) int __ockl_wgred_add_i32(int a); +extern "C" __device__ __attribute__((convergent)) int __ockl_wgred_and_i32(int a); +extern "C" __device__ __attribute__((convergent)) int __ockl_wgred_or_i32(int a); + +extern "C" __device__ uint64_t __ockl_fprintf_stderr_begin(); +extern "C" __device__ uint64_t __ockl_fprintf_append_args(uint64_t msg_desc, uint32_t num_args, + uint64_t value0, uint64_t value1, + uint64_t value2, uint64_t value3, + uint64_t value4, uint64_t value5, + uint64_t value6, uint32_t is_last); +extern "C" __device__ uint64_t __ockl_fprintf_append_string_n(uint64_t msg_desc, const char* data, + uint64_t length, uint32_t is_last); + +// Introduce local address space +#define __local __attribute__((address_space(3))) + +#ifdef __HIP_DEVICE_COMPILE__ +__device__ inline static __local void* __to_local(unsigned x) { return (__local void*)x; } +#endif //__HIP_DEVICE_COMPILE__ + +// Using hip.amdgcn.bc - sync threads +#define __CLK_LOCAL_MEM_FENCE 0x01 +typedef unsigned __cl_mem_fence_flags; + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/functional_grid_launch.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/functional_grid_launch.hpp new file mode 100644 index 0000000000000000000000000000000000000000..6f2857de46d8d9ffc4f92aa9375234a8aadf6294 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/functional_grid_launch.hpp @@ -0,0 +1,218 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#include "concepts.hpp" +#include "helpers.hpp" +#include "program_state.hpp" +#include "hip_runtime_api.h" + +#include +#include +#include +#include +#include +#include + +hipError_t ihipExtLaunchMultiKernelMultiDevice(hipLaunchParams* launchParamsList, int numDevices, + unsigned int flags, hip_impl::program_state& ps); + +hipError_t hipLaunchCooperativeKernel(const void* f, dim3 gridDim, + dim3 blockDim, void** args, + size_t sharedMem, hipStream_t stream, + hip_impl::program_state& ps); + +hipError_t hipLaunchCooperativeKernelMultiDevice(hipLaunchParams* launchParamsList, + int numDevices, + unsigned int flags, + hip_impl::program_state& ps); + +#pragma GCC visibility push(hidden) + +namespace hip_impl { +template {}>::type* = nullptr> +inline T round_up_to_next_multiple_nonnegative(T x, T y) { + T tmp = x + y - 1; + return tmp - tmp % y; +} + +template < + std::size_t n, + typename... Ts, + typename std::enable_if::type* = nullptr> +inline hip_impl::kernarg make_kernarg( + const std::tuple&, + const kernargs_size_align&, + hip_impl::kernarg kernarg) { + return kernarg; +} + +template < + std::size_t n, + typename... Ts, + typename std::enable_if::type* = nullptr> +inline hip_impl::kernarg make_kernarg( + const std::tuple& formals, + const kernargs_size_align& size_align, + hip_impl::kernarg kernarg) { + using T = typename std::tuple_element>::type; + + static_assert( + !std::is_reference{}, + "A __global__ function cannot have a reference as one of its " + "arguments."); + #if defined(HIP_STRICT) + static_assert( + std::is_trivially_copyable{}, + "Only TriviallyCopyable types can be arguments to a __global__ " + "function"); + #endif + + kernarg.resize(round_up_to_next_multiple_nonnegative( + kernarg.size(), size_align.alignment(n)) + size_align.size(n)); + + std::memcpy( + kernarg.data() + kernarg.size() - size_align.size(n), + &std::get(formals), + size_align.size(n)); + return make_kernarg(formals, size_align, std::move(kernarg)); +} + +template +inline hip_impl::kernarg make_kernarg( + void (*kernel)(Formals...), std::tuple actuals) { + static_assert(sizeof...(Formals) == sizeof...(Actuals), + "The count of formal arguments must match the count of actuals."); + + if (sizeof...(Formals) == 0) return {}; + + std::tuple to_formals{std::move(actuals)}; + hip_impl::kernarg kernarg; + kernarg.reserve(sizeof(to_formals)); + + auto& ps = hip_impl::get_program_state(); + return make_kernarg<0>(to_formals, + ps.get_kernargs_size_align( + reinterpret_cast(kernel)), + std::move(kernarg)); +} + + +HIP_INTERNAL_EXPORTED_API hsa_agent_t target_agent(hipStream_t stream); + +inline +__attribute__((visibility("hidden"))) +void hipLaunchKernelGGLImpl( + std::uintptr_t function_address, + const dim3& numBlocks, + const dim3& dimBlocks, + std::uint32_t sharedMemBytes, + hipStream_t stream, + void** kernarg) { + + const auto& kd = hip_impl::get_program_state().kernel_descriptor(function_address, + target_agent(stream)); + + hipModuleLaunchKernel(kd, numBlocks.x, numBlocks.y, numBlocks.z, + dimBlocks.x, dimBlocks.y, dimBlocks.z, sharedMemBytes, + stream, nullptr, kernarg); +} +} // Namespace hip_impl. + + +template +inline +hipError_t hipOccupancyMaxPotentialBlockSize(int* gridSize, int* blockSize, + T kernel, size_t dynSharedMemPerBlk = 0, int blockSizeLimit = 0) { + + using namespace hip_impl; + + hip_impl::hip_init(); + auto f = get_program_state().kernel_descriptor(reinterpret_cast(kernel), + target_agent(0)); + + return hipModuleOccupancyMaxPotentialBlockSize(gridSize, blockSize, f, + dynSharedMemPerBlk, blockSizeLimit); +} + +template +inline +hipError_t hipOccupancyMaxPotentialBlockSizeWithFlags(int* gridSize, int* blockSize, + T kernel, size_t dynSharedMemPerBlk = 0, int blockSizeLimit = 0, unsigned int flags = 0 ) { + + using namespace hip_impl; + + hip_impl::hip_init(); + if(flags != hipOccupancyDefault) return hipErrorNotSupported; + auto f = get_program_state().kernel_descriptor(reinterpret_cast(kernel), + target_agent(0)); + + return hipModuleOccupancyMaxPotentialBlockSize(gridSize, blockSize, f, + dynSharedMemPerBlk, blockSizeLimit); +} + +template +inline +void hipLaunchKernelGGL(F kernel, const dim3& numBlocks, const dim3& dimBlocks, + std::uint32_t sharedMemBytes, hipStream_t stream, + Args... args) { + hip_impl::hip_init(); + auto kernarg = hip_impl::make_kernarg(kernel, std::tuple{std::move(args)...}); + std::size_t kernarg_size = kernarg.size(); + + void* config[]{ + HIP_LAUNCH_PARAM_BUFFER_POINTER, + kernarg.data(), + HIP_LAUNCH_PARAM_BUFFER_SIZE, + &kernarg_size, + HIP_LAUNCH_PARAM_END}; + + hip_impl::hipLaunchKernelGGLImpl(reinterpret_cast(kernel), + numBlocks, dimBlocks, sharedMemBytes, + stream, &config[0]); +} + +template +inline +__attribute__((visibility("hidden"))) +hipError_t hipLaunchCooperativeKernel(F f, dim3 gridDim, dim3 blockDim, + void** args, size_t sharedMem, + hipStream_t stream) { + hip_impl::hip_init(); + auto& ps = hip_impl::get_program_state(); + return hipLaunchCooperativeKernel(reinterpret_cast(f), gridDim, + blockDim, args, sharedMem, stream, ps); +} + +inline +__attribute__((visibility("hidden"))) +hipError_t hipLaunchCooperativeKernelMultiDevice(hipLaunchParams* launchParamsList, + int numDevices, + unsigned int flags) { + + hip_impl::hip_init(); + auto& ps = hip_impl::get_program_state(); + return hipLaunchCooperativeKernelMultiDevice(launchParamsList, numDevices, flags, ps); +} + +#pragma GCC visibility pop diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.h new file mode 100644 index 0000000000000000000000000000000000000000..22841a5657083dbef747f4b008c9e3ee197dd2c1 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.h @@ -0,0 +1,67 @@ +#pragma once + +#include + +#include + +#define GRID_LAUNCH_VERSION 20 + +// Extern definitions +namespace hc{ +class completion_future; +class accelerator_view; +} + + +// 3 dim structure for groups and grids. +typedef struct gl_dim3 +{ + int x,y,z; + gl_dim3(uint32_t _x=1, uint32_t _y=1, uint32_t _z=1) : x(_x), y(_y), z(_z) {}; +} gl_dim3; + +typedef enum gl_barrier_bit { + barrier_bit_queue_default, + barrier_bit_none, + barrier_bit_wait, +} gl_barrier_bit; + + +// grid_launch_parm contains information used to launch the kernel. +typedef struct grid_launch_parm +{ + //! Grid dimensions + gl_dim3 grid_dim; + + //! Group dimensions + gl_dim3 group_dim; + + //! Amount of dynamic group memory to use with the kernel launch. + //! This memory is in addition to the amount used statically in the kernel. + unsigned int dynamic_group_mem_bytes; + + //! Control setting of barrier bit on per-packet basis: + //! See gl_barrier_bit description. + //! Placeholder, is not used to control packet dispatch yet + enum gl_barrier_bit barrier_bit; + + //! Value of packet fences to apply to launch. + //! The correspond to the value of bits 9:14 in the AQL packet, + //! see HSA_PACKET_HEADER_ACQUIRE_FENCE_SCOPE and hsa_fence_scope_t. + unsigned int launch_fence; + + //! Pointer to the accelerator_view where the kernel should execute. + //! If NULL, the default view on the default accelerator is used. + hc::accelerator_view *av; + + //! Pointer to the completion_future used to track the status of the command. + //! If NULL, the command does not write status. In this case, + //! synchronization can be enforced with queue-level waits or + //! waiting on younger commands. + hc::completion_future *cf; + + grid_launch_parm() = default; +} grid_launch_parm; + + +extern void init_grid_launch(grid_launch_parm *gl); diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.hpp new file mode 100644 index 0000000000000000000000000000000000000000..04ce7e03664bce142fe3f081d44f8d677ebce5a5 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch.hpp @@ -0,0 +1,50 @@ +#pragma once + +#include "grid_launch.h" +#include "hc.hpp" + +class grid_launch_parm_cxx : public grid_launch_parm +{ +public: + grid_launch_parm_cxx() = default; + + // customized serialization: don't need av and cf in kernel + __attribute__((annotate("serialize"))) + void __cxxamp_serialize(Kalmar::Serialize& s) const { + s.Append(sizeof(int), &grid_dim.x); + s.Append(sizeof(int), &grid_dim.y); + s.Append(sizeof(int), &grid_dim.z); + s.Append(sizeof(int), &group_dim.x); + s.Append(sizeof(int), &group_dim.y); + s.Append(sizeof(int), &group_dim.z); + } + + __attribute__((annotate("user_deserialize"))) + grid_launch_parm_cxx(int grid_dim_x, int grid_dim_y, int grid_dim_z, + int group_dim_x, int group_dim_y, int group_dim_z) { + grid_dim.x = grid_dim_x; + grid_dim.y = grid_dim_y; + grid_dim.z = grid_dim_z; + group_dim.x = group_dim_x; + group_dim.y = group_dim_y; + group_dim.z = group_dim_z; + } +}; + + +extern inline void grid_launch_init(grid_launch_parm *lp) { + lp->grid_dim.x = lp->grid_dim.y = lp->grid_dim.z = 1; + + lp->group_dim.x = lp->group_dim.y = lp->group_dim.z = 1; + + lp->dynamic_group_mem_bytes = 0; + + lp->barrier_bit = barrier_bit_queue_default; + lp->launch_fence = -1; + + // TODO - set to NULL? + static hc::accelerator_view av = hc::accelerator().get_default_view(); + lp->av = &av; + lp->cf = NULL; +} + diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch_GGL.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch_GGL.hpp new file mode 100644 index 0000000000000000000000000000000000000000..df5949d7d00b135f6b4f2be7af45653568b388c7 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/grid_launch_GGL.hpp @@ -0,0 +1,26 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ +#pragma once + +#if GENERIC_GRID_LAUNCH == 1 +#include "macro_based_grid_launch.hpp" +#endif // GENERIC_GRID_LAUNCH \ No newline at end of file diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/helpers.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/helpers.hpp new file mode 100644 index 0000000000000000000000000000000000000000..5f7935c1ec83b092ad595b3c3b5456a5d7e89f21 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/helpers.hpp @@ -0,0 +1,137 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once +#include "concepts.hpp" + +#include // For std::conditional, std::decay, std::enable_if, + // std::false_type, std result_of and std::true_type. +#include // For std::declval. + +#ifdef __has_include // Check if __has_include is present +# if __has_include() // Check for version header +# include +# if defined(__cpp_lib_is_invocable) && !defined(HIP_HAS_INVOCABLE) +# define HIP_HAS_INVOCABLE __cpp_lib_is_invocable +# endif +# if defined(__cpp_lib_result_of_sfinae) && !defined(HIP_HAS_RESULT_OF_SFINAE) +# define HIP_HAS_RESULT_OF_SFINAE __cpp_lib_result_of_sfinae +# endif +# endif +#endif + +#ifndef HIP_HAS_INVOCABLE +#define HIP_HAS_INVOCABLE 0 +#endif + +#ifndef HIP_HAS_RESULT_OF_SFINAE +#define HIP_HAS_RESULT_OF_SFINAE 0 +#endif + +namespace std { // TODO: these should be removed as soon as possible. +#if (__cplusplus < 201406L) +#if (__cplusplus < 201402L) +template +using enable_if_t = typename enable_if::type; +template +using conditional_t = typename conditional::type; +template +using decay_t = typename decay::type; +template +using result_of_t = typename result_of::type; +template +using remove_reference_t = typename remove_reference::type; +#endif +#endif +} // namespace std + +namespace hip_impl { +template +using void_t_ = void; + +#if HIP_HAS_INVOCABLE +template +struct is_callable_impl; + +template +struct is_callable_impl : std::is_invocable {}; +#elif HIP_HAS_RESULT_OF_SFINAE +template +struct is_callable_impl : std::false_type {}; + +template +struct is_callable_impl::type > > : std::true_type {}; +#else +template +auto simple_invoke(T Base::*pmd, Derived&& ref) +-> decltype(static_cast(ref).*pmd); + +template +auto simple_invoke(PMD&& pmd, Pointer&& ptr) +-> decltype((*static_cast(ptr)).*static_cast(pmd)); + +template +auto simple_invoke(T Base::*pmd, const std::reference_wrapper& ref) +-> decltype(ref.get().*pmd); + +template +auto simple_invoke(T Base::*pmf, Derived&& ref, Args&&... args) +-> decltype((static_cast(ref).*pmf)(static_cast(args)...)); + +template +auto simple_invoke(PMF&& pmf, Pointer&& ptr, Args&&... args) +-> decltype(((*static_cast(ptr)).*static_cast(pmf))(static_cast(args)...)); + +template +auto simple_invoke(T Base::*pmf, const std::reference_wrapper& ref, Args&&... args) +-> decltype((ref.get().*pmf)(static_cast(args)...)); + +template +auto simple_invoke(F&& f, Ts&&... xs) +-> decltype(f(static_cast(xs)...)); + +template +struct is_callable_impl : std::false_type {}; + +template +struct is_callable_impl(), std::declval()...))> > + : std::true_type {}; + +#endif + +template +struct is_callable : is_callable_impl {}; + +#define count_macro_args_impl_hip_(_0, _1, _2, _3, _4, _5, _6, _7, _8, _9, _10, _11, _12, _13, \ + _14, _15, _16, _17, _18, _19, _20, _21, _22, _23, _24, _25, \ + _26, _27, _28, _29, _30, _31, _n, ...) \ + _n +#define count_macro_args_hip_(...) \ + count_macro_args_impl_hip_(, ##__VA_ARGS__, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, \ + 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, \ + 0) + +#define overloaded_macro_expand_hip_(macro, arg_cnt) macro##arg_cnt +#define overload_macro_impl_hip_(macro, arg_cnt) overloaded_macro_expand_hip_(macro, arg_cnt) +#define overload_macro_hip_(macro, ...) \ + overload_macro_impl_hip_(macro, count_macro_args_hip_(__VA_ARGS__))(__VA_ARGS__) +} // namespace hip_impl diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_api_trace.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_api_trace.hpp new file mode 100644 index 0000000000000000000000000000000000000000..2152d519ebe1b808328f9f8f3cbd1d13e67aec0f --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_api_trace.hpp @@ -0,0 +1,1350 @@ +/* + Copyright (c) 2023 Advanced Micro Devices, Inc. All rights reserved. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. + */ +#pragma once + +#include + +// HIP API interface +typedef hipError_t (*t___hipPopCallConfiguration)(dim3* gridDim, dim3* blockDim, size_t* sharedMem, + hipStream_t* stream); +typedef hipError_t (*t___hipPushCallConfiguration)(dim3 gridDim, dim3 blockDim, size_t sharedMem, + hipStream_t stream); +typedef void** (*t___hipRegisterFatBinary)(const void* data); +typedef void (*t___hipRegisterFunction)(void** modules, const void* hostFunction, + char* deviceFunction, const char* deviceName, + unsigned int threadLimit, uint3* tid, uint3* bid, + dim3* blockDim, dim3* gridDim, int* wSize); +typedef void (*t___hipRegisterManagedVar)(void* hipModule, void** pointer, void* init_value, + const char* name, size_t size, unsigned align); +typedef void (*t___hipRegisterSurface)(void** modules, void* var, char* hostVar, + char* deviceVar, int type, int ext); +typedef void (*t___hipRegisterTexture)(void** modules, void* var, char* hostVar, + char* deviceVar, int type, int norm, int ext); +typedef void (*t___hipRegisterVar)(void** modules, void* var, char* hostVar, + char* deviceVar, int ext, size_t size, int constant, int global); +typedef void (*t___hipUnregisterFatBinary)(void** modules); + +typedef const char* (*t_hipApiName)(uint32_t id); +typedef hipError_t (*t_hipArray3DCreate)(hipArray_t* array, + const HIP_ARRAY3D_DESCRIPTOR* pAllocateArray); +typedef hipError_t (*t_hipArray3DGetDescriptor)(HIP_ARRAY3D_DESCRIPTOR* pArrayDescriptor, + hipArray_t array); +typedef hipError_t (*t_hipArrayCreate)(hipArray_t* pHandle, + const HIP_ARRAY_DESCRIPTOR* pAllocateArray); +typedef hipError_t (*t_hipArrayDestroy)(hipArray_t array); +typedef hipError_t (*t_hipArrayGetDescriptor)(HIP_ARRAY_DESCRIPTOR* pArrayDescriptor, + hipArray_t array); +typedef hipError_t (*t_hipArrayGetInfo)(hipChannelFormatDesc* desc, hipExtent* extent, + unsigned int* flags, hipArray_t array); +typedef hipError_t (*t_hipBindTexture)(size_t* offset, const textureReference* tex, + const void* devPtr, const hipChannelFormatDesc* desc, + size_t size); +typedef hipError_t (*t_hipBindTexture2D)(size_t* offset, const textureReference* tex, + const void* devPtr, const hipChannelFormatDesc* desc, + size_t width, size_t height, size_t pitch); +typedef hipError_t (*t_hipBindTextureToArray)(const textureReference* tex, hipArray_const_t array, + const hipChannelFormatDesc* desc); +typedef hipError_t (*t_hipBindTextureToMipmappedArray)(const textureReference* tex, + hipMipmappedArray_const_t mipmappedArray, + const hipChannelFormatDesc* desc); +typedef hipError_t (*t_hipChooseDevice)(int* device, const hipDeviceProp_t* prop); +typedef hipError_t (*t_hipChooseDeviceR0000)(int* device, const hipDeviceProp_tR0000* properties); +typedef hipError_t (*t_hipConfigureCall)(dim3 gridDim, dim3 blockDim, size_t sharedMem, + hipStream_t stream); +typedef hipError_t (*t_hipCreateSurfaceObject)(hipSurfaceObject_t* pSurfObject, + const hipResourceDesc* pResDesc); +typedef hipError_t (*t_hipCreateTextureObject)(hipTextureObject_t* pTexObject, + const hipResourceDesc* pResDesc, + const hipTextureDesc* pTexDesc, + const struct hipResourceViewDesc* pResViewDesc); +typedef hipError_t (*t_hipCtxCreate)(hipCtx_t* ctx, unsigned int flags, hipDevice_t device); +typedef hipError_t (*t_hipCtxDestroy)(hipCtx_t ctx); +typedef hipError_t (*t_hipCtxDisablePeerAccess)(hipCtx_t peerCtx); +typedef hipError_t (*t_hipCtxEnablePeerAccess)(hipCtx_t peerCtx, unsigned int flags); +typedef hipError_t (*t_hipCtxGetApiVersion)(hipCtx_t ctx, int* apiVersion); +typedef hipError_t (*t_hipCtxGetCacheConfig)(hipFuncCache_t* cacheConfig); +typedef hipError_t (*t_hipCtxGetCurrent)(hipCtx_t* ctx); +typedef hipError_t (*t_hipCtxGetDevice)(hipDevice_t* device); +typedef hipError_t (*t_hipCtxGetFlags)(unsigned int* flags); +typedef hipError_t (*t_hipCtxGetSharedMemConfig)(hipSharedMemConfig* pConfig); +typedef hipError_t (*t_hipCtxPopCurrent)(hipCtx_t* ctx); +typedef hipError_t (*t_hipCtxPushCurrent)(hipCtx_t ctx); +typedef hipError_t (*t_hipCtxSetCacheConfig)(hipFuncCache_t cacheConfig); +typedef hipError_t (*t_hipCtxSetCurrent)(hipCtx_t ctx); +typedef hipError_t (*t_hipCtxSetSharedMemConfig)(hipSharedMemConfig config); +typedef hipError_t (*t_hipCtxSynchronize)(void); +typedef hipError_t (*t_hipDestroyExternalMemory)(hipExternalMemory_t extMem); +typedef hipError_t (*t_hipDestroyExternalSemaphore)(hipExternalSemaphore_t extSem); +typedef hipError_t (*t_hipDestroySurfaceObject)(hipSurfaceObject_t surfaceObject); +typedef hipError_t (*t_hipDestroyTextureObject)(hipTextureObject_t textureObject); +typedef hipError_t (*t_hipDeviceCanAccessPeer)(int* canAccessPeer, int deviceId, int peerDeviceId); +typedef hipError_t (*t_hipDeviceComputeCapability)(int* major, int* minor, hipDevice_t device); +typedef hipError_t (*t_hipDeviceDisablePeerAccess)(int peerDeviceId); +typedef hipError_t (*t_hipDeviceEnablePeerAccess)(int peerDeviceId, unsigned int flags); +typedef hipError_t (*t_hipDeviceGet)(hipDevice_t* device, int ordinal); +typedef hipError_t (*t_hipDeviceGetAttribute)(int* pi, hipDeviceAttribute_t attr, int deviceId); +typedef hipError_t (*t_hipDeviceGetByPCIBusId)(int* device, const char* pciBusId); +typedef hipError_t (*t_hipDeviceGetCacheConfig)(hipFuncCache_t* cacheConfig); +typedef hipError_t (*t_hipDeviceGetDefaultMemPool)(hipMemPool_t* mem_pool, int device); +typedef hipError_t (*t_hipDeviceGetGraphMemAttribute)(int device, hipGraphMemAttributeType attr, + void* value); +typedef hipError_t (*t_hipDeviceGetLimit)(size_t* pValue, enum hipLimit_t limit); +typedef hipError_t (*t_hipDeviceGetMemPool)(hipMemPool_t* mem_pool, int device); +typedef hipError_t (*t_hipDeviceGetName)(char* name, int len, hipDevice_t device); +typedef hipError_t (*t_hipDeviceGetP2PAttribute)(int* value, hipDeviceP2PAttr attr, int srcDevice, + int dstDevice); +typedef hipError_t (*t_hipDeviceGetPCIBusId)(char* pciBusId, int len, int device); +typedef hipError_t (*t_hipDeviceGetSharedMemConfig)(hipSharedMemConfig* pConfig); +typedef hipError_t (*t_hipDeviceGetStreamPriorityRange)(int* leastPriority, int* greatestPriority); +typedef hipError_t (*t_hipDeviceGetUuid)(hipUUID* uuid, hipDevice_t device); +typedef hipError_t (*t_hipDeviceGraphMemTrim)(int device); +typedef hipError_t (*t_hipDevicePrimaryCtxGetState)(hipDevice_t dev, unsigned int* flags, + int* active); +typedef hipError_t (*t_hipDevicePrimaryCtxRelease)(hipDevice_t dev); +typedef hipError_t (*t_hipDevicePrimaryCtxReset)(hipDevice_t dev); +typedef hipError_t (*t_hipDevicePrimaryCtxRetain)(hipCtx_t* pctx, hipDevice_t dev); +typedef hipError_t (*t_hipDevicePrimaryCtxSetFlags)(hipDevice_t dev, unsigned int flags); +typedef hipError_t (*t_hipDeviceReset)(void); +typedef hipError_t (*t_hipDeviceSetCacheConfig)(hipFuncCache_t cacheConfig); +typedef hipError_t (*t_hipDeviceSetGraphMemAttribute)(int device, hipGraphMemAttributeType attr, + void* value); +typedef hipError_t (*t_hipDeviceSetLimit)(enum hipLimit_t limit, size_t value); +typedef hipError_t (*t_hipDeviceSetMemPool)(int device, hipMemPool_t mem_pool); +typedef hipError_t (*t_hipDeviceSetSharedMemConfig)(hipSharedMemConfig config); +typedef hipError_t (*t_hipDeviceSynchronize)(void); +typedef hipError_t (*t_hipDeviceTotalMem)(size_t* bytes, hipDevice_t device); +typedef hipError_t (*t_hipDriverGetVersion)(int* driverVersion); +typedef hipError_t (*t_hipDrvGetErrorName)(hipError_t hipError, const char** errorString); +typedef hipError_t (*t_hipDrvGetErrorString)(hipError_t hipError, const char** errorString); +typedef hipError_t (*t_hipDrvGraphAddMemcpyNode)(hipGraphNode_t* phGraphNode, hipGraph_t hGraph, + const hipGraphNode_t* dependencies, + size_t numDependencies, + const HIP_MEMCPY3D* copyParams, hipCtx_t ctx); +typedef hipError_t (*t_hipDrvMemcpy2DUnaligned)(const hip_Memcpy2D* pCopy); +typedef hipError_t (*t_hipDrvMemcpy3D)(const HIP_MEMCPY3D* pCopy); +typedef hipError_t (*t_hipDrvMemcpy3DAsync)(const HIP_MEMCPY3D* pCopy, hipStream_t stream); +typedef hipError_t (*t_hipDrvPointerGetAttributes)(unsigned int numAttributes, + hipPointer_attribute* attributes, void** data, + hipDeviceptr_t ptr); +typedef hipError_t (*t_hipEventCreate)(hipEvent_t* event); +typedef hipError_t (*t_hipEventCreateWithFlags)(hipEvent_t* event, unsigned flags); +typedef hipError_t (*t_hipEventDestroy)(hipEvent_t event); +typedef hipError_t (*t_hipEventElapsedTime)(float* ms, hipEvent_t start, hipEvent_t stop); +typedef hipError_t (*t_hipEventQuery)(hipEvent_t event); +typedef hipError_t (*t_hipEventRecord)(hipEvent_t event, hipStream_t stream); +typedef hipError_t (*t_hipEventSynchronize)(hipEvent_t event); +typedef hipError_t (*t_hipExtGetLinkTypeAndHopCount)(int device1, int device2, uint32_t* linktype, + uint32_t* hopcount); +typedef hipError_t (*t_hipExtLaunchKernel)(const void* function_address, dim3 numBlocks, + dim3 dimBlocks, void** args, size_t sharedMemBytes, + hipStream_t stream, hipEvent_t startEvent, + hipEvent_t stopEvent, int flags); +typedef hipError_t (*t_hipExtLaunchMultiKernelMultiDevice)(hipLaunchParams* launchParamsList, + int numDevices, unsigned int flags); +typedef hipError_t (*t_hipExtMallocWithFlags)(void** ptr, size_t sizeBytes, unsigned int flags); +typedef hipError_t (*t_hipExtStreamCreateWithCUMask)(hipStream_t* stream, uint32_t cuMaskSize, + const uint32_t* cuMask); +typedef hipError_t (*t_hipExtStreamGetCUMask)(hipStream_t stream, uint32_t cuMaskSize, + uint32_t* cuMask); +typedef hipError_t (*t_hipExternalMemoryGetMappedBuffer)( + void** devPtr, hipExternalMemory_t extMem, const hipExternalMemoryBufferDesc* bufferDesc); +typedef hipError_t (*t_hipFree)(void* ptr); +typedef hipError_t (*t_hipFreeArray)(hipArray_t array); +typedef hipError_t (*t_hipFreeAsync)(void* dev_ptr, hipStream_t stream); +typedef hipError_t (*t_hipFreeHost)(void* ptr); +typedef hipError_t (*t_hipFreeMipmappedArray)(hipMipmappedArray_t mipmappedArray); +typedef hipError_t (*t_hipFuncGetAttribute)(int* value, hipFunction_attribute attrib, + hipFunction_t hfunc); +typedef hipError_t (*t_hipFuncGetAttributes)(struct hipFuncAttributes* attr, const void* func); +typedef hipError_t (*t_hipFuncSetAttribute)(const void* func, hipFuncAttribute attr, int value); +typedef hipError_t (*t_hipFuncSetCacheConfig)(const void* func, hipFuncCache_t config); +typedef hipError_t (*t_hipFuncSetSharedMemConfig)(const void* func, hipSharedMemConfig config); +typedef hipError_t (*t_hipGLGetDevices)(unsigned int* pHipDeviceCount, int* pHipDevices, + unsigned int hipDeviceCount, hipGLDeviceList deviceList); +typedef hipError_t (*t_hipGetChannelDesc)(hipChannelFormatDesc* desc, hipArray_const_t array); +typedef hipError_t (*t_hipGetDevice)(int* deviceId); +typedef hipError_t (*t_hipGetDeviceCount)(int* count); +typedef hipError_t (*t_hipGetDeviceFlags)(unsigned int* flags); +typedef hipError_t (*t_hipGetDevicePropertiesR0600)(hipDeviceProp_tR0600* prop, int device); +typedef hipError_t (*t_hipGetDevicePropertiesR0000)(hipDeviceProp_tR0000* prop, int device); +typedef const char* (*t_hipGetErrorName)(hipError_t hip_error); +typedef const char* (*t_hipGetErrorString)(hipError_t hipError); +typedef hipError_t (*t_hipGetLastError)(void); +typedef hipError_t (*t_hipGetMipmappedArrayLevel)(hipArray_t* levelArray, + hipMipmappedArray_const_t mipmappedArray, + unsigned int level); +typedef hipError_t (*t_hipGetSymbolAddress)(void** devPtr, const void* symbol); +typedef hipError_t (*t_hipGetSymbolSize)(size_t* size, const void* symbol); +typedef hipError_t (*t_hipGetTextureAlignmentOffset)(size_t* offset, + const textureReference* texref); +typedef hipError_t (*t_hipGetTextureObjectResourceDesc)(hipResourceDesc* pResDesc, + hipTextureObject_t textureObject); +typedef hipError_t (*t_hipGetTextureObjectResourceViewDesc)( + struct hipResourceViewDesc* pResViewDesc, hipTextureObject_t textureObject); +typedef hipError_t (*t_hipGetTextureObjectTextureDesc)(hipTextureDesc* pTexDesc, + hipTextureObject_t textureObject); +typedef hipError_t (*t_hipGetTextureReference)(const textureReference** texref, const void* symbol); +typedef hipError_t (*t_hipGraphAddChildGraphNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, hipGraph_t childGraph); +typedef hipError_t (*t_hipGraphAddDependencies)(hipGraph_t graph, const hipGraphNode_t* from, + const hipGraphNode_t* to, size_t numDependencies); +typedef hipError_t (*t_hipGraphAddEmptyNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies); +typedef hipError_t (*t_hipGraphAddEventRecordNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, hipEvent_t event); +typedef hipError_t (*t_hipGraphAddEventWaitNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, hipEvent_t event); +typedef hipError_t (*t_hipGraphAddHostNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, + const hipHostNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphAddKernelNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, + const hipKernelNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphAddMemAllocNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, + hipMemAllocNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphAddMemFreeNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, void* dev_ptr); +typedef hipError_t (*t_hipGraphAddMemcpyNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, + const hipMemcpy3DParms* pCopyParams); +typedef hipError_t (*t_hipGraphAddMemcpyNode1D)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, void* dst, const void* src, + size_t count, hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphAddMemcpyNodeFromSymbol)(hipGraphNode_t* pGraphNode, + hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, void* dst, + const void* symbol, size_t count, + size_t offset, hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphAddMemcpyNodeToSymbol)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, const void* symbol, + const void* src, size_t count, size_t offset, + hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphAddMemsetNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, + size_t numDependencies, + const hipMemsetParams* pMemsetParams); +typedef hipError_t (*t_hipGraphChildGraphNodeGetGraph)(hipGraphNode_t node, hipGraph_t* pGraph); +typedef hipError_t (*t_hipGraphClone)(hipGraph_t* pGraphClone, hipGraph_t originalGraph); +typedef hipError_t (*t_hipGraphCreate)(hipGraph_t* pGraph, unsigned int flags); +typedef hipError_t (*t_hipGraphDebugDotPrint)(hipGraph_t graph, const char* path, + unsigned int flags); +typedef hipError_t (*t_hipGraphDestroy)(hipGraph_t graph); +typedef hipError_t (*t_hipGraphDestroyNode)(hipGraphNode_t node); +typedef hipError_t (*t_hipGraphEventRecordNodeGetEvent)(hipGraphNode_t node, hipEvent_t* event_out); +typedef hipError_t (*t_hipGraphEventRecordNodeSetEvent)(hipGraphNode_t node, hipEvent_t event); +typedef hipError_t (*t_hipGraphEventWaitNodeGetEvent)(hipGraphNode_t node, hipEvent_t* event_out); +typedef hipError_t (*t_hipGraphEventWaitNodeSetEvent)(hipGraphNode_t node, hipEvent_t event); +typedef hipError_t (*t_hipGraphExecChildGraphNodeSetParams)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + hipGraph_t childGraph); +typedef hipError_t (*t_hipGraphExecDestroy)(hipGraphExec_t graphExec); +typedef hipError_t (*t_hipGraphExecEventRecordNodeSetEvent)(hipGraphExec_t hGraphExec, + hipGraphNode_t hNode, hipEvent_t event); +typedef hipError_t (*t_hipGraphExecEventWaitNodeSetEvent)(hipGraphExec_t hGraphExec, + hipGraphNode_t hNode, hipEvent_t event); +typedef hipError_t (*t_hipGraphExecHostNodeSetParams)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + const hipHostNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphExecKernelNodeSetParams)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + const hipKernelNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphExecMemcpyNodeSetParams)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + hipMemcpy3DParms* pNodeParams); +typedef hipError_t (*t_hipGraphExecMemcpyNodeSetParams1D)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, void* dst, + const void* src, size_t count, + hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphExecMemcpyNodeSetParamsFromSymbol)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, void* dst, + const void* symbol, size_t count, + size_t offset, + hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphExecMemcpyNodeSetParamsToSymbol)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + const void* symbol, const void* src, + size_t count, size_t offset, + hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphExecMemsetNodeSetParams)(hipGraphExec_t hGraphExec, + hipGraphNode_t node, + const hipMemsetParams* pNodeParams); +typedef hipError_t (*t_hipGraphExecUpdate)(hipGraphExec_t hGraphExec, hipGraph_t hGraph, + hipGraphNode_t* hErrorNode_out, + hipGraphExecUpdateResult* updateResult_out); +typedef hipError_t (*t_hipGraphGetEdges)(hipGraph_t graph, hipGraphNode_t* from, hipGraphNode_t* to, + size_t* numEdges); +typedef hipError_t (*t_hipGraphGetNodes)(hipGraph_t graph, hipGraphNode_t* nodes, size_t* numNodes); +typedef hipError_t (*t_hipGraphGetRootNodes)(hipGraph_t graph, hipGraphNode_t* pRootNodes, + size_t* pNumRootNodes); +typedef hipError_t (*t_hipGraphHostNodeGetParams)(hipGraphNode_t node, + hipHostNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphHostNodeSetParams)(hipGraphNode_t node, + const hipHostNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphInstantiate)(hipGraphExec_t* pGraphExec, hipGraph_t graph, + hipGraphNode_t* pErrorNode, char* pLogBuffer, + size_t bufferSize); +typedef hipError_t (*t_hipGraphInstantiateWithFlags)(hipGraphExec_t* pGraphExec, hipGraph_t graph, + unsigned long long flags); +typedef hipError_t (*t_hipGraphKernelNodeCopyAttributes)(hipGraphNode_t hSrc, hipGraphNode_t hDst); +typedef hipError_t (*t_hipGraphKernelNodeGetAttribute)(hipGraphNode_t hNode, + hipKernelNodeAttrID attr, + hipKernelNodeAttrValue* value); +typedef hipError_t (*t_hipGraphKernelNodeGetParams)(hipGraphNode_t node, + hipKernelNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphKernelNodeSetAttribute)(hipGraphNode_t hNode, + hipKernelNodeAttrID attr, + const hipKernelNodeAttrValue* value); +typedef hipError_t (*t_hipGraphKernelNodeSetParams)(hipGraphNode_t node, + const hipKernelNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphLaunch)(hipGraphExec_t graphExec, hipStream_t stream); +typedef hipError_t (*t_hipGraphMemAllocNodeGetParams)(hipGraphNode_t node, + hipMemAllocNodeParams* pNodeParams); +typedef hipError_t (*t_hipGraphMemFreeNodeGetParams)(hipGraphNode_t node, void* dev_ptr); +typedef hipError_t (*t_hipGraphMemcpyNodeGetParams)(hipGraphNode_t node, + hipMemcpy3DParms* pNodeParams); +typedef hipError_t (*t_hipGraphMemcpyNodeSetParams)(hipGraphNode_t node, + const hipMemcpy3DParms* pNodeParams); +typedef hipError_t (*t_hipGraphMemcpyNodeSetParams1D)(hipGraphNode_t node, void* dst, + const void* src, size_t count, + hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphMemcpyNodeSetParamsFromSymbol)(hipGraphNode_t node, void* dst, + const void* symbol, size_t count, + size_t offset, hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphMemcpyNodeSetParamsToSymbol)(hipGraphNode_t node, const void* symbol, + const void* src, size_t count, + size_t offset, hipMemcpyKind kind); +typedef hipError_t (*t_hipGraphMemsetNodeGetParams)(hipGraphNode_t node, + hipMemsetParams* pNodeParams); +typedef hipError_t (*t_hipGraphMemsetNodeSetParams)(hipGraphNode_t node, + const hipMemsetParams* pNodeParams); +typedef hipError_t (*t_hipGraphNodeFindInClone)(hipGraphNode_t* pNode, hipGraphNode_t originalNode, + hipGraph_t clonedGraph); +typedef hipError_t (*t_hipGraphNodeGetDependencies)(hipGraphNode_t node, + hipGraphNode_t* pDependencies, + size_t* pNumDependencies); +typedef hipError_t (*t_hipGraphNodeGetDependentNodes)(hipGraphNode_t node, + hipGraphNode_t* pDependentNodes, + size_t* pNumDependentNodes); +typedef hipError_t (*t_hipGraphNodeGetEnabled)(hipGraphExec_t hGraphExec, hipGraphNode_t hNode, + unsigned int* isEnabled); +typedef hipError_t (*t_hipGraphNodeGetType)(hipGraphNode_t node, hipGraphNodeType* pType); +typedef hipError_t (*t_hipGraphNodeSetEnabled)(hipGraphExec_t hGraphExec, hipGraphNode_t hNode, + unsigned int isEnabled); +typedef hipError_t (*t_hipGraphReleaseUserObject)(hipGraph_t graph, hipUserObject_t object, + unsigned int count); +typedef hipError_t (*t_hipGraphRemoveDependencies)(hipGraph_t graph, const hipGraphNode_t* from, + const hipGraphNode_t* to, + size_t numDependencies); +typedef hipError_t (*t_hipGraphRetainUserObject)(hipGraph_t graph, hipUserObject_t object, + unsigned int count, unsigned int flags); +typedef hipError_t (*t_hipGraphUpload)(hipGraphExec_t graphExec, hipStream_t stream); +typedef hipError_t (*t_hipGraphicsGLRegisterBuffer)(hipGraphicsResource** resource, GLuint buffer, + unsigned int flags); +typedef hipError_t (*t_hipGraphicsGLRegisterImage)(hipGraphicsResource** resource, GLuint image, + GLenum target, unsigned int flags); +typedef hipError_t (*t_hipGraphicsMapResources)(int count, hipGraphicsResource_t* resources, + hipStream_t stream); +typedef hipError_t (*t_hipGraphicsResourceGetMappedPointer)(void** devPtr, size_t* size, + hipGraphicsResource_t resource); +typedef hipError_t (*t_hipGraphicsSubResourceGetMappedArray)(hipArray_t* array, + hipGraphicsResource_t resource, + unsigned int arrayIndex, + unsigned int mipLevel); +typedef hipError_t (*t_hipGraphicsUnmapResources)(int count, hipGraphicsResource_t* resources, + hipStream_t stream); +typedef hipError_t (*t_hipGraphicsUnregisterResource)(hipGraphicsResource_t resource); +typedef hipError_t (*t_hipHostAlloc)(void** ptr, size_t size, unsigned int flags); +typedef hipError_t (*t_hipHostFree)(void* ptr); +typedef hipError_t (*t_hipHostGetDevicePointer)(void** devPtr, void* hstPtr, unsigned int flags); +typedef hipError_t (*t_hipHostGetFlags)(unsigned int* flagsPtr, void* hostPtr); +typedef hipError_t (*t_hipHostMalloc)(void** ptr, size_t size, unsigned int flags); +typedef hipError_t (*t_hipHostRegister)(void* hostPtr, size_t sizeBytes, unsigned int flags); +typedef hipError_t (*t_hipHostUnregister)(void* hostPtr); +typedef hipError_t (*t_hipImportExternalMemory)(hipExternalMemory_t* extMem_out, + const hipExternalMemoryHandleDesc* memHandleDesc); +typedef hipError_t (*t_hipImportExternalSemaphore)( + hipExternalSemaphore_t* extSem_out, const hipExternalSemaphoreHandleDesc* semHandleDesc); +typedef hipError_t (*t_hipInit)(unsigned int flags); +typedef hipError_t (*t_hipIpcCloseMemHandle)(void* devPtr); +typedef hipError_t (*t_hipIpcGetEventHandle)(hipIpcEventHandle_t* handle, hipEvent_t event); +typedef hipError_t (*t_hipIpcGetMemHandle)(hipIpcMemHandle_t* handle, void* devPtr); +typedef hipError_t (*t_hipIpcOpenEventHandle)(hipEvent_t* event, hipIpcEventHandle_t handle); +typedef hipError_t (*t_hipIpcOpenMemHandle)(void** devPtr, hipIpcMemHandle_t handle, + unsigned int flags); +typedef const char* (*t_hipKernelNameRef)(const hipFunction_t f); +typedef const char* (*t_hipKernelNameRefByPtr)(const void* hostFunction, hipStream_t stream); +typedef hipError_t (*t_hipLaunchByPtr)(const void* func); +typedef hipError_t (*t_hipLaunchCooperativeKernel)(const void* f, dim3 gridDim, dim3 blockDimX, + void** kernelParams, unsigned int sharedMemBytes, + hipStream_t stream); +typedef hipError_t (*t_hipLaunchCooperativeKernelMultiDevice)(hipLaunchParams* launchParamsList, + int numDevices, unsigned int flags); +typedef hipError_t (*t_hipLaunchHostFunc)(hipStream_t stream, hipHostFn_t fn, void* userData); +typedef hipError_t (*t_hipLaunchKernel)(const void* function_address, dim3 numBlocks, + dim3 dimBlocks, void** args, size_t sharedMemBytes, + hipStream_t stream); +typedef hipError_t (*t_hipMalloc)(void** ptr, size_t size); +typedef hipError_t (*t_hipMalloc3D)(hipPitchedPtr* pitchedDevPtr, hipExtent extent); +typedef hipError_t (*t_hipMalloc3DArray)(hipArray_t* array, const struct hipChannelFormatDesc* desc, + struct hipExtent extent, unsigned int flags); +typedef hipError_t (*t_hipMallocArray)(hipArray_t* array, const hipChannelFormatDesc* desc, + size_t width, size_t height, unsigned int flags); +typedef hipError_t (*t_hipMallocAsync)(void** dev_ptr, size_t size, hipStream_t stream); +typedef hipError_t (*t_hipMallocFromPoolAsync)(void** dev_ptr, size_t size, hipMemPool_t mem_pool, + hipStream_t stream); +typedef hipError_t (*t_hipMallocHost)(void** ptr, size_t size); +typedef hipError_t (*t_hipMallocManaged)(void** dev_ptr, size_t size, unsigned int flags); +typedef hipError_t (*t_hipMallocMipmappedArray)(hipMipmappedArray_t* mipmappedArray, + const struct hipChannelFormatDesc* desc, + struct hipExtent extent, unsigned int numLevels, + unsigned int flags); +typedef hipError_t (*t_hipMallocPitch)(void** ptr, size_t* pitch, size_t width, size_t height); +typedef hipError_t (*t_hipMemAddressFree)(void* devPtr, size_t size); +typedef hipError_t (*t_hipMemAddressReserve)(void** ptr, size_t size, size_t alignment, void* addr, + unsigned long long flags); +typedef hipError_t (*t_hipMemAdvise)(const void* dev_ptr, size_t count, hipMemoryAdvise advice, + int device); +typedef hipError_t (*t_hipMemAllocHost)(void** ptr, size_t size); +typedef hipError_t (*t_hipMemAllocPitch)(hipDeviceptr_t* dptr, size_t* pitch, size_t widthInBytes, + size_t height, unsigned int elementSizeBytes); +typedef hipError_t (*t_hipMemCreate)(hipMemGenericAllocationHandle_t* handle, size_t size, + const hipMemAllocationProp* prop, unsigned long long flags); +typedef hipError_t (*t_hipMemExportToShareableHandle)(void* shareableHandle, + hipMemGenericAllocationHandle_t handle, + hipMemAllocationHandleType handleType, + unsigned long long flags); +typedef hipError_t (*t_hipMemGetAccess)(unsigned long long* flags, const hipMemLocation* location, + void* ptr); +typedef hipError_t (*t_hipMemGetAddressRange)(hipDeviceptr_t* pbase, size_t* psize, + hipDeviceptr_t dptr); +typedef hipError_t (*t_hipMemGetAllocationGranularity)(size_t* granularity, + const hipMemAllocationProp* prop, + hipMemAllocationGranularity_flags option); +typedef hipError_t (*t_hipMemGetAllocationPropertiesFromHandle)( + hipMemAllocationProp* prop, hipMemGenericAllocationHandle_t handle); +typedef hipError_t (*t_hipMemGetInfo)(size_t* free, size_t* total); +typedef hipError_t (*t_hipMemImportFromShareableHandle)(hipMemGenericAllocationHandle_t* handle, + void* osHandle, + hipMemAllocationHandleType shHandleType); +typedef hipError_t (*t_hipMemMap)(void* ptr, size_t size, size_t offset, + hipMemGenericAllocationHandle_t handle, unsigned long long flags); +typedef hipError_t (*t_hipMemMapArrayAsync)(hipArrayMapInfo* mapInfoList, unsigned int count, + hipStream_t stream); +typedef hipError_t (*t_hipMemPoolCreate)(hipMemPool_t* mem_pool, const hipMemPoolProps* pool_props); +typedef hipError_t (*t_hipMemPoolDestroy)(hipMemPool_t mem_pool); +typedef hipError_t (*t_hipMemPoolExportPointer)(hipMemPoolPtrExportData* export_data, + void* dev_ptr); +typedef hipError_t (*t_hipMemPoolExportToShareableHandle)(void* shared_handle, + hipMemPool_t mem_pool, + hipMemAllocationHandleType handle_type, + unsigned int flags); +typedef hipError_t (*t_hipMemPoolGetAccess)(hipMemAccessFlags* flags, hipMemPool_t mem_pool, + hipMemLocation* location); +typedef hipError_t (*t_hipMemPoolGetAttribute)(hipMemPool_t mem_pool, hipMemPoolAttr attr, + void* value); +typedef hipError_t (*t_hipMemPoolImportFromShareableHandle)(hipMemPool_t* mem_pool, + void* shared_handle, + hipMemAllocationHandleType handle_type, + unsigned int flags); +typedef hipError_t (*t_hipMemPoolImportPointer)(void** dev_ptr, hipMemPool_t mem_pool, + hipMemPoolPtrExportData* export_data); +typedef hipError_t (*t_hipMemPoolSetAccess)(hipMemPool_t mem_pool, + const hipMemAccessDesc* desc_list, size_t count); +typedef hipError_t (*t_hipMemPoolSetAttribute)(hipMemPool_t mem_pool, hipMemPoolAttr attr, + void* value); +typedef hipError_t (*t_hipMemPoolTrimTo)(hipMemPool_t mem_pool, size_t min_bytes_to_hold); +typedef hipError_t (*t_hipMemPrefetchAsync)(const void* dev_ptr, size_t count, int device, + hipStream_t stream); +typedef hipError_t (*t_hipMemPtrGetInfo)(void* ptr, size_t* size); +typedef hipError_t (*t_hipMemRangeGetAttribute)(void* data, size_t data_size, + hipMemRangeAttribute attribute, const void* dev_ptr, + size_t count); +typedef hipError_t (*t_hipMemRangeGetAttributes)(void** data, size_t* data_sizes, + hipMemRangeAttribute* attributes, + size_t num_attributes, const void* dev_ptr, + size_t count); +typedef hipError_t (*t_hipMemRelease)(hipMemGenericAllocationHandle_t handle); +typedef hipError_t (*t_hipMemRetainAllocationHandle)(hipMemGenericAllocationHandle_t* handle, + void* addr); +typedef hipError_t (*t_hipMemSetAccess)(void* ptr, size_t size, const hipMemAccessDesc* desc, + size_t count); +typedef hipError_t (*t_hipMemUnmap)(void* ptr, size_t size); +typedef hipError_t (*t_hipMemcpy)(void* dst, const void* src, size_t sizeBytes, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpy2D)(void* dst, size_t dpitch, const void* src, size_t spitch, + size_t width, size_t height, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpy2DAsync)(void* dst, size_t dpitch, const void* src, size_t spitch, + size_t width, size_t height, hipMemcpyKind kind, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpy2DFromArray)(void* dst, size_t dpitch, hipArray_const_t src, + size_t wOffset, size_t hOffset, size_t width, + size_t height, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpy2DFromArrayAsync)(void* dst, size_t dpitch, hipArray_const_t src, + size_t wOffset, size_t hOffset, size_t width, + size_t height, hipMemcpyKind kind, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpy2DToArray)(hipArray_t dst, size_t wOffset, size_t hOffset, + const void* src, size_t spitch, size_t width, + size_t height, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpy2DToArrayAsync)(hipArray_t dst, size_t wOffset, size_t hOffset, + const void* src, size_t spitch, size_t width, + size_t height, hipMemcpyKind kind, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpy3D)(const struct hipMemcpy3DParms* p); +typedef hipError_t (*t_hipMemcpy3DAsync)(const struct hipMemcpy3DParms* p, hipStream_t stream); +typedef hipError_t (*t_hipMemcpyAsync)(void* dst, const void* src, size_t sizeBytes, + hipMemcpyKind kind, hipStream_t stream); +typedef hipError_t (*t_hipMemcpyAtoH)(void* dst, hipArray_t srcArray, size_t srcOffset, + size_t count); +typedef hipError_t (*t_hipMemcpyDtoD)(hipDeviceptr_t dst, hipDeviceptr_t src, size_t sizeBytes); +typedef hipError_t (*t_hipMemcpyDtoDAsync)(hipDeviceptr_t dst, hipDeviceptr_t src, size_t sizeBytes, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpyDtoH)(void* dst, hipDeviceptr_t src, size_t sizeBytes); +typedef hipError_t (*t_hipMemcpyDtoHAsync)(void* dst, hipDeviceptr_t src, size_t sizeBytes, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpyFromArray)(void* dst, hipArray_const_t srcArray, size_t wOffset, + size_t hOffset, size_t count, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpyFromSymbol)(void* dst, const void* symbol, size_t sizeBytes, + size_t offset, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpyFromSymbolAsync)(void* dst, const void* symbol, size_t sizeBytes, + size_t offset, hipMemcpyKind kind, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpyHtoA)(hipArray_t dstArray, size_t dstOffset, const void* srcHost, + size_t count); +typedef hipError_t (*t_hipMemcpyHtoD)(hipDeviceptr_t dst, void* src, size_t sizeBytes); +typedef hipError_t (*t_hipMemcpyHtoDAsync)(hipDeviceptr_t dst, void* src, size_t sizeBytes, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpyParam2D)(const hip_Memcpy2D* pCopy); +typedef hipError_t (*t_hipMemcpyParam2DAsync)(const hip_Memcpy2D* pCopy, hipStream_t stream); +typedef hipError_t (*t_hipMemcpyPeer)(void* dst, int dstDeviceId, const void* src, int srcDeviceId, + size_t sizeBytes); +typedef hipError_t (*t_hipMemcpyPeerAsync)(void* dst, int dstDeviceId, const void* src, + int srcDevice, size_t sizeBytes, hipStream_t stream); +typedef hipError_t (*t_hipMemcpyToArray)(hipArray_t dst, size_t wOffset, size_t hOffset, + const void* src, size_t count, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpyToSymbol)(const void* symbol, const void* src, size_t sizeBytes, + size_t offset, hipMemcpyKind kind); +typedef hipError_t (*t_hipMemcpyToSymbolAsync)(const void* symbol, const void* src, + size_t sizeBytes, size_t offset, hipMemcpyKind kind, + hipStream_t stream); +typedef hipError_t (*t_hipMemcpyWithStream)(void* dst, const void* src, size_t sizeBytes, + hipMemcpyKind kind, hipStream_t stream); +typedef hipError_t (*t_hipMemset)(void* dst, int value, size_t sizeBytes); +typedef hipError_t (*t_hipMemset2D)(void* dst, size_t pitch, int value, size_t width, + size_t height); +typedef hipError_t (*t_hipMemset2DAsync)(void* dst, size_t pitch, int value, size_t width, + size_t height, hipStream_t stream); +typedef hipError_t (*t_hipMemset3D)(hipPitchedPtr pitchedDevPtr, int value, hipExtent extent); +typedef hipError_t (*t_hipMemset3DAsync)(hipPitchedPtr pitchedDevPtr, int value, hipExtent extent, + hipStream_t stream); +typedef hipError_t (*t_hipMemsetAsync)(void* dst, int value, size_t sizeBytes, hipStream_t stream); +typedef hipError_t (*t_hipMemsetD16)(hipDeviceptr_t dest, unsigned short value, size_t count); +typedef hipError_t (*t_hipMemsetD16Async)(hipDeviceptr_t dest, unsigned short value, size_t count, + hipStream_t stream); +typedef hipError_t (*t_hipMemsetD32)(hipDeviceptr_t dest, int value, size_t count); +typedef hipError_t (*t_hipMemsetD32Async)(hipDeviceptr_t dst, int value, size_t count, + hipStream_t stream); +typedef hipError_t (*t_hipMemsetD8)(hipDeviceptr_t dest, unsigned char value, size_t count); +typedef hipError_t (*t_hipMemsetD8Async)(hipDeviceptr_t dest, unsigned char value, size_t count, + hipStream_t stream); +typedef hipError_t (*t_hipMipmappedArrayCreate)(hipMipmappedArray_t* pHandle, + HIP_ARRAY3D_DESCRIPTOR* pMipmappedArrayDesc, + unsigned int numMipmapLevels); +typedef hipError_t (*t_hipMipmappedArrayDestroy)(hipMipmappedArray_t hMipmappedArray); +typedef hipError_t (*t_hipMipmappedArrayGetLevel)(hipArray_t* pLevelArray, + hipMipmappedArray_t hMipMappedArray, + unsigned int level); +typedef hipError_t (*t_hipModuleGetFunction)(hipFunction_t* function, hipModule_t module, + const char* kname); +typedef hipError_t (*t_hipModuleGetGlobal)(hipDeviceptr_t* dptr, size_t* bytes, hipModule_t hmod, + const char* name); +typedef hipError_t (*t_hipModuleGetTexRef)(textureReference** texRef, hipModule_t hmod, + const char* name); +typedef hipError_t (*t_hipModuleLaunchCooperativeKernel)( + hipFunction_t f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, + unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, + unsigned int sharedMemBytes, hipStream_t stream, void** kernelParams); +typedef hipError_t (*t_hipModuleLaunchCooperativeKernelMultiDevice)( + hipFunctionLaunchParams* launchParamsList, unsigned int numDevices, unsigned int flags); +typedef hipError_t (*t_hipModuleLaunchKernel)(hipFunction_t f, unsigned int gridDimX, + unsigned int gridDimY, unsigned int gridDimZ, + unsigned int blockDimX, unsigned int blockDimY, + unsigned int blockDimZ, unsigned int sharedMemBytes, + hipStream_t stream, void** kernelParams, + void** extra); +typedef hipError_t (*t_hipModuleLoad)(hipModule_t* module, const char* fname); +typedef hipError_t (*t_hipModuleLoadData)(hipModule_t* module, const void* image); +typedef hipError_t (*t_hipModuleLoadDataEx)(hipModule_t* module, const void* image, + unsigned int numOptions, hipJitOption* options, + void** optionValues); +typedef hipError_t (*t_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor)( + int* numBlocks, hipFunction_t f, int blockSize, size_t dynSharedMemPerBlk); +typedef hipError_t (*t_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags)( + int* numBlocks, hipFunction_t f, int blockSize, size_t dynSharedMemPerBlk, unsigned int flags); +typedef hipError_t (*t_hipModuleOccupancyMaxPotentialBlockSize)(int* gridSize, int* blockSize, + hipFunction_t f, + size_t dynSharedMemPerBlk, + int blockSizeLimit); +typedef hipError_t (*t_hipModuleOccupancyMaxPotentialBlockSizeWithFlags)( + int* gridSize, int* blockSize, hipFunction_t f, size_t dynSharedMemPerBlk, int blockSizeLimit, + unsigned int flags); +typedef hipError_t (*t_hipModuleUnload)(hipModule_t module); +typedef hipError_t (*t_hipOccupancyMaxActiveBlocksPerMultiprocessor)(int* numBlocks, const void* f, + int blockSize, + size_t dynSharedMemPerBlk); +typedef hipError_t (*t_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags)( + int* numBlocks, const void* f, int blockSize, size_t dynSharedMemPerBlk, unsigned int flags); +typedef hipError_t (*t_hipOccupancyMaxPotentialBlockSize)(int* gridSize, int* blockSize, + const void* f, size_t dynSharedMemPerBlk, + int blockSizeLimit); +typedef hipError_t (*t_hipPeekAtLastError)(void); +typedef hipError_t (*t_hipPointerGetAttribute)(void* data, hipPointer_attribute attribute, + hipDeviceptr_t ptr); +typedef hipError_t (*t_hipPointerGetAttributes)(hipPointerAttribute_t* attributes, const void* ptr); +typedef hipError_t (*t_hipPointerSetAttribute)(const void* value, hipPointer_attribute attribute, + hipDeviceptr_t ptr); +typedef hipError_t (*t_hipProfilerStart)(); +typedef hipError_t (*t_hipProfilerStop)(); +typedef hipError_t (*t_hipRuntimeGetVersion)(int* runtimeVersion); +typedef hipError_t (*t_hipSetDevice)(int deviceId); +typedef hipError_t (*t_hipSetDeviceFlags)(unsigned flags); +typedef hipError_t (*t_hipSetupArgument)(const void* arg, size_t size, size_t offset); +typedef hipError_t (*t_hipSignalExternalSemaphoresAsync)( + const hipExternalSemaphore_t* extSemArray, const hipExternalSemaphoreSignalParams* paramsArray, + unsigned int numExtSems, hipStream_t stream); +typedef hipError_t (*t_hipStreamAddCallback)(hipStream_t stream, hipStreamCallback_t callback, + void* userData, unsigned int flags); +typedef hipError_t (*t_hipStreamAttachMemAsync)(hipStream_t stream, void* dev_ptr, size_t length, + unsigned int flags); +typedef hipError_t (*t_hipStreamBeginCapture)(hipStream_t stream, hipStreamCaptureMode mode); +typedef hipError_t (*t_hipStreamCreate)(hipStream_t* stream); +typedef hipError_t (*t_hipStreamCreateWithFlags)(hipStream_t* stream, unsigned int flags); +typedef hipError_t (*t_hipStreamCreateWithPriority)(hipStream_t* stream, unsigned int flags, + int priority); +typedef hipError_t (*t_hipStreamDestroy)(hipStream_t stream); +typedef hipError_t (*t_hipStreamEndCapture)(hipStream_t stream, hipGraph_t* pGraph); +typedef hipError_t (*t_hipStreamGetCaptureInfo)(hipStream_t stream, + hipStreamCaptureStatus* pCaptureStatus, + unsigned long long* pId); +typedef hipError_t (*t_hipStreamGetCaptureInfo_v2)( + hipStream_t stream, hipStreamCaptureStatus* captureStatus_out, unsigned long long* id_out, + hipGraph_t* graph_out, const hipGraphNode_t** dependencies_out, size_t* numDependencies_out); +typedef hipError_t (*t_hipStreamGetDevice)(hipStream_t stream, hipDevice_t* device); +typedef hipError_t (*t_hipStreamGetFlags)(hipStream_t stream, unsigned int* flags); +typedef hipError_t (*t_hipStreamGetPriority)(hipStream_t stream, int* priority); +typedef hipError_t (*t_hipStreamIsCapturing)(hipStream_t stream, + hipStreamCaptureStatus* pCaptureStatus); +typedef hipError_t (*t_hipStreamQuery)(hipStream_t stream); +typedef hipError_t (*t_hipStreamSynchronize)(hipStream_t stream); +typedef hipError_t (*t_hipStreamUpdateCaptureDependencies)(hipStream_t stream, + hipGraphNode_t* dependencies, + size_t numDependencies, + unsigned int flags); +typedef hipError_t (*t_hipStreamWaitEvent)(hipStream_t stream, hipEvent_t event, + unsigned int flags); +typedef hipError_t (*t_hipStreamWaitValue32)(hipStream_t stream, void* ptr, uint32_t value, + unsigned int flags, uint32_t mask); +typedef hipError_t (*t_hipStreamWaitValue64)(hipStream_t stream, void* ptr, uint64_t value, + unsigned int flags, uint64_t mask); +typedef hipError_t (*t_hipStreamWriteValue32)(hipStream_t stream, void* ptr, uint32_t value, + unsigned int flags); +typedef hipError_t (*t_hipStreamWriteValue64)(hipStream_t stream, void* ptr, uint64_t value, + unsigned int flags); +typedef hipError_t (*t_hipTexObjectCreate)(hipTextureObject_t* pTexObject, + const HIP_RESOURCE_DESC* pResDesc, + const HIP_TEXTURE_DESC* pTexDesc, + const HIP_RESOURCE_VIEW_DESC* pResViewDesc); +typedef hipError_t (*t_hipTexObjectDestroy)(hipTextureObject_t texObject); +typedef hipError_t (*t_hipTexObjectGetResourceDesc)(HIP_RESOURCE_DESC* pResDesc, + hipTextureObject_t texObject); +typedef hipError_t (*t_hipTexObjectGetResourceViewDesc)(HIP_RESOURCE_VIEW_DESC* pResViewDesc, + hipTextureObject_t texObject); +typedef hipError_t (*t_hipTexObjectGetTextureDesc)(HIP_TEXTURE_DESC* pTexDesc, + hipTextureObject_t texObject); +typedef hipError_t (*t_hipTexRefGetAddress)(hipDeviceptr_t* dev_ptr, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetAddressMode)(enum hipTextureAddressMode* pam, + const textureReference* texRef, int dim); +typedef hipError_t (*t_hipTexRefGetFilterMode)(enum hipTextureFilterMode* pfm, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetFlags)(unsigned int* pFlags, const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetFormat)(hipArray_Format* pFormat, int* pNumChannels, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetMaxAnisotropy)(int* pmaxAnsio, const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetMipMappedArray)(hipMipmappedArray_t* pArray, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetMipmapFilterMode)(enum hipTextureFilterMode* pfm, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetMipmapLevelBias)(float* pbias, const textureReference* texRef); +typedef hipError_t (*t_hipTexRefGetMipmapLevelClamp)(float* pminMipmapLevelClamp, + float* pmaxMipmapLevelClamp, + const textureReference* texRef); +typedef hipError_t (*t_hipTexRefSetAddress)(size_t* ByteOffset, textureReference* texRef, + hipDeviceptr_t dptr, size_t bytes); +typedef hipError_t (*t_hipTexRefSetAddress2D)(textureReference* texRef, + const HIP_ARRAY_DESCRIPTOR* desc, hipDeviceptr_t dptr, + size_t Pitch); +typedef hipError_t (*t_hipTexRefSetAddressMode)(textureReference* texRef, int dim, + enum hipTextureAddressMode am); +typedef hipError_t (*t_hipTexRefSetArray)(textureReference* tex, hipArray_const_t array, + unsigned int flags); +typedef hipError_t (*t_hipTexRefSetBorderColor)(textureReference* texRef, float* pBorderColor); +typedef hipError_t (*t_hipTexRefSetFilterMode)(textureReference* texRef, + enum hipTextureFilterMode fm); +typedef hipError_t (*t_hipTexRefSetFlags)(textureReference* texRef, unsigned int Flags); +typedef hipError_t (*t_hipTexRefSetFormat)(textureReference* texRef, hipArray_Format fmt, + int NumPackedComponents); +typedef hipError_t (*t_hipTexRefSetMaxAnisotropy)(textureReference* texRef, unsigned int maxAniso); +typedef hipError_t (*t_hipTexRefSetMipmapFilterMode)(textureReference* texRef, + enum hipTextureFilterMode fm); +typedef hipError_t (*t_hipTexRefSetMipmapLevelBias)(textureReference* texRef, float bias); +typedef hipError_t (*t_hipTexRefSetMipmapLevelClamp)(textureReference* texRef, + float minMipMapLevelClamp, + float maxMipMapLevelClamp); +typedef hipError_t (*t_hipTexRefSetMipmappedArray)(textureReference* texRef, + struct hipMipmappedArray* mipmappedArray, + unsigned int Flags); +typedef hipError_t (*t_hipThreadExchangeStreamCaptureMode)(hipStreamCaptureMode* mode); +typedef hipError_t (*t_hipUnbindTexture)(const textureReference* tex); +typedef hipError_t (*t_hipUserObjectCreate)(hipUserObject_t* object_out, void* ptr, + hipHostFn_t destroy, unsigned int initialRefcount, + unsigned int flags); +typedef hipError_t (*t_hipUserObjectRelease)(hipUserObject_t object, unsigned int count); +typedef hipError_t (*t_hipUserObjectRetain)(hipUserObject_t object, unsigned int count); +typedef hipError_t (*t_hipWaitExternalSemaphoresAsync)( + const hipExternalSemaphore_t* extSemArray, const hipExternalSemaphoreWaitParams* paramsArray, + unsigned int numExtSems, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpy_spt)(void* dst, const void* src, size_t sizeBytes, + hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpyToSymbol_spt)(const void* symbol, const void* src, size_t sizeBytes, + size_t offset, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpyFromSymbol_spt)(void* dst, const void* symbol, size_t sizeBytes, + size_t offset, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpy2D_spt)(void* dst, size_t dpitch, const void* src, size_t spitch, + size_t width, size_t height, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpy2DFromArray_spt)(void* dst, size_t dpitch, hipArray_const_t src, + size_t wOffset, size_t hOffset, size_t width, + size_t height, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpy3D_spt)(const struct hipMemcpy3DParms* p); + +typedef hipError_t (*t_hipMemset_spt)(void* dst, int value, size_t sizeBytes); + +typedef hipError_t (*t_hipMemsetAsync_spt)(void* dst, int value, size_t sizeBytes, + hipStream_t stream); + +typedef hipError_t (*t_hipMemset2D_spt)(void* dst, size_t pitch, int value, size_t width, + size_t height); + +typedef hipError_t (*t_hipMemset2DAsync_spt)(void* dst, size_t pitch, int value, size_t width, + size_t height, hipStream_t stream); + +typedef hipError_t (*t_hipMemset3DAsync_spt)(hipPitchedPtr pitchedDevPtr, int value, + hipExtent extent, hipStream_t stream); + +typedef hipError_t (*t_hipMemset3D_spt)(hipPitchedPtr pitchedDevPtr, int value, hipExtent extent); + +typedef hipError_t (*t_hipMemcpyAsync_spt)(void* dst, const void* src, size_t sizeBytes, + hipMemcpyKind kind, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpy3DAsync_spt)(const hipMemcpy3DParms* p, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpy2DAsync_spt)(void* dst, size_t dpitch, const void* src, + size_t spitch, size_t width, size_t height, + hipMemcpyKind kind, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpyFromSymbolAsync_spt)(void* dst, const void* symbol, + size_t sizeBytes, size_t offset, + hipMemcpyKind kind, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpyToSymbolAsync_spt)(const void* symbol, const void* src, + size_t sizeBytes, size_t offset, + hipMemcpyKind kind, hipStream_t stream); + +typedef hipError_t (*t_hipMemcpyFromArray_spt)(void* dst, hipArray_const_t src, size_t wOffsetSrc, + size_t hOffset, size_t count, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpy2DToArray_spt)(hipArray_t dst, size_t wOffset, size_t hOffset, + const void* src, size_t spitch, size_t width, + size_t height, hipMemcpyKind kind); + +typedef hipError_t (*t_hipMemcpy2DFromArrayAsync_spt)(void* dst, size_t dpitch, + hipArray_const_t src, size_t wOffsetSrc, + size_t hOffsetSrc, size_t width, + size_t height, hipMemcpyKind kind, + hipStream_t stream); + +typedef hipError_t (*t_hipMemcpy2DToArrayAsync_spt)(hipArray_t dst, size_t wOffset, size_t hOffset, + const void* src, size_t spitch, size_t width, + size_t height, hipMemcpyKind kind, + hipStream_t stream); + +typedef hipError_t (*t_hipStreamQuery_spt)(hipStream_t stream); + +typedef hipError_t (*t_hipStreamSynchronize_spt)(hipStream_t stream); + +typedef hipError_t (*t_hipStreamGetPriority_spt)(hipStream_t stream, int* priority); + +typedef hipError_t (*t_hipStreamWaitEvent_spt)(hipStream_t stream, hipEvent_t event, + unsigned int flags); + +typedef hipError_t (*t_hipStreamGetFlags_spt)(hipStream_t stream, unsigned int* flags); + +typedef hipError_t (*t_hipStreamAddCallback_spt)(hipStream_t stream, hipStreamCallback_t callback, + void* userData, unsigned int flags); +typedef hipError_t (*t_hipEventRecord_spt)(hipEvent_t event, hipStream_t stream); +typedef hipError_t (*t_hipLaunchCooperativeKernel_spt)(const void* f, dim3 gridDim, dim3 blockDim, + void** kernelParams, uint32_t sharedMemBytes, + hipStream_t hStream); + +typedef hipError_t (*t_hipLaunchKernel_spt)(const void* function_address, dim3 numBlocks, + dim3 dimBlocks, void** args, size_t sharedMemBytes, + hipStream_t stream); + +typedef hipError_t (*t_hipGraphLaunch_spt)(hipGraphExec_t graphExec, hipStream_t stream); +typedef hipError_t (*t_hipStreamBeginCapture_spt)(hipStream_t stream, hipStreamCaptureMode mode); +typedef hipError_t (*t_hipStreamEndCapture_spt)(hipStream_t stream, hipGraph_t* pGraph); +typedef hipError_t (*t_hipStreamIsCapturing_spt)(hipStream_t stream, + hipStreamCaptureStatus* pCaptureStatus); +typedef hipError_t (*t_hipStreamGetCaptureInfo_spt)(hipStream_t stream, + hipStreamCaptureStatus* pCaptureStatus, + unsigned long long* pId); +typedef hipError_t (*t_hipStreamGetCaptureInfo_v2_spt)( + hipStream_t stream, hipStreamCaptureStatus* captureStatus_out, unsigned long long* id_out, + hipGraph_t* graph_out, const hipGraphNode_t** dependencies_out, size_t* numDependencies_out); +typedef hipError_t (*t_hipLaunchHostFunc_spt)(hipStream_t stream, hipHostFn_t fn, void* userData); +typedef hipChannelFormatDesc (*t_hipCreateChannelDesc)(int x, int y, int z, int w, + hipChannelFormatKind f); +typedef hipError_t (*t_hipExtModuleLaunchKernel)(hipFunction_t f, uint32_t globalWorkSizeX, + uint32_t globalWorkSizeY, uint32_t globalWorkSizeZ, + uint32_t localWorkSizeX, uint32_t localWorkSizeY, + uint32_t localWorkSizeZ, size_t sharedMemBytes, + hipStream_t hStream, void** kernelParams, + void** extra, hipEvent_t startEvent, + hipEvent_t stopEvent, uint32_t flags); +typedef hipError_t (*t_hipHccModuleLaunchKernel)(hipFunction_t f, uint32_t globalWorkSizeX, + uint32_t globalWorkSizeY, uint32_t globalWorkSizeZ, + uint32_t localWorkSizeX, uint32_t localWorkSizeY, + uint32_t localWorkSizeZ, size_t sharedMemBytes, + hipStream_t hStream, void** kernelParams, + void** extra, hipEvent_t startEvent, + hipEvent_t stopEvent); +typedef int (*t_hipGetStreamDeviceId)(hipStream_t stream); + +typedef hipError_t (*t_hipDrvGraphAddMemsetNode)(hipGraphNode_t* phGraphNode, hipGraph_t hGraph, + const hipGraphNode_t* dependencies, size_t numDependencies, + const HIP_MEMSET_NODE_PARAMS* memsetParams, hipCtx_t ctx); +typedef hipError_t (*t_hipGraphAddExternalSemaphoresWaitNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, size_t numDependencies, + const hipExternalSemaphoreWaitNodeParams* nodeParams); +typedef hipError_t (*t_hipGraphAddExternalSemaphoresSignalNode)(hipGraphNode_t* pGraphNode, hipGraph_t graph, + const hipGraphNode_t* pDependencies, size_t numDependencies, + const hipExternalSemaphoreSignalNodeParams* nodeParams); +typedef hipError_t (*t_hipGraphExternalSemaphoresSignalNodeSetParams)(hipGraphNode_t hNode, + const hipExternalSemaphoreSignalNodeParams* nodeParams); +typedef hipError_t (*t_hipGraphExternalSemaphoresWaitNodeSetParams)(hipGraphNode_t hNode, + const hipExternalSemaphoreWaitNodeParams* nodeParams); +typedef hipError_t (*t_hipGraphExternalSemaphoresSignalNodeGetParams)(hipGraphNode_t hNode, + hipExternalSemaphoreSignalNodeParams* params_out); +typedef hipError_t (*t_hipGraphExternalSemaphoresWaitNodeGetParams)(hipGraphNode_t hNode, + hipExternalSemaphoreWaitNodeParams* params_out); +typedef hipError_t (*t_hipGraphExecExternalSemaphoresSignalNodeSetParams)(hipGraphExec_t hGraphExec, hipGraphNode_t hNode, + const hipExternalSemaphoreSignalNodeParams* nodeParams); +typedef hipError_t (*t_hipGraphExecExternalSemaphoresWaitNodeSetParams)(hipGraphExec_t hGraphExec, hipGraphNode_t hNode, + const hipExternalSemaphoreWaitNodeParams* nodeParams); + +// HIP Compiler dispatch table +struct HipCompilerDispatchTable { + size_t size; + t___hipPopCallConfiguration __hipPopCallConfiguration_fn; + t___hipPushCallConfiguration __hipPushCallConfiguration_fn; + t___hipRegisterFatBinary __hipRegisterFatBinary_fn; + t___hipRegisterFunction __hipRegisterFunction_fn; + t___hipRegisterManagedVar __hipRegisterManagedVar_fn; + t___hipRegisterSurface __hipRegisterSurface_fn; + t___hipRegisterTexture __hipRegisterTexture_fn; + t___hipRegisterVar __hipRegisterVar_fn; + t___hipUnregisterFatBinary __hipUnregisterFatBinary_fn; +}; + +// HIP API dispatch table +struct HipDispatchTable { + size_t size; + t_hipApiName hipApiName_fn; + t_hipArray3DCreate hipArray3DCreate_fn; + t_hipArray3DGetDescriptor hipArray3DGetDescriptor_fn; + t_hipArrayCreate hipArrayCreate_fn; + t_hipArrayDestroy hipArrayDestroy_fn; + t_hipArrayGetDescriptor hipArrayGetDescriptor_fn; + t_hipArrayGetInfo hipArrayGetInfo_fn; + t_hipBindTexture hipBindTexture_fn; + t_hipBindTexture2D hipBindTexture2D_fn; + t_hipBindTextureToArray hipBindTextureToArray_fn; + t_hipBindTextureToMipmappedArray hipBindTextureToMipmappedArray_fn; + t_hipChooseDevice hipChooseDevice_fn; + t_hipChooseDeviceR0000 hipChooseDeviceR0000_fn; + t_hipConfigureCall hipConfigureCall_fn; + t_hipCreateSurfaceObject hipCreateSurfaceObject_fn; + t_hipCreateTextureObject hipCreateTextureObject_fn; + t_hipCtxCreate hipCtxCreate_fn; + t_hipCtxDestroy hipCtxDestroy_fn; + t_hipCtxDisablePeerAccess hipCtxDisablePeerAccess_fn; + t_hipCtxEnablePeerAccess hipCtxEnablePeerAccess_fn; + t_hipCtxGetApiVersion hipCtxGetApiVersion_fn; + t_hipCtxGetCacheConfig hipCtxGetCacheConfig_fn; + t_hipCtxGetCurrent hipCtxGetCurrent_fn; + t_hipCtxGetDevice hipCtxGetDevice_fn; + t_hipCtxGetFlags hipCtxGetFlags_fn; + t_hipCtxGetSharedMemConfig hipCtxGetSharedMemConfig_fn; + t_hipCtxPopCurrent hipCtxPopCurrent_fn; + t_hipCtxPushCurrent hipCtxPushCurrent_fn; + t_hipCtxSetCacheConfig hipCtxSetCacheConfig_fn; + t_hipCtxSetCurrent hipCtxSetCurrent_fn; + t_hipCtxSetSharedMemConfig hipCtxSetSharedMemConfig_fn; + t_hipCtxSynchronize hipCtxSynchronize_fn; + t_hipDestroyExternalMemory hipDestroyExternalMemory_fn; + t_hipDestroyExternalSemaphore hipDestroyExternalSemaphore_fn; + t_hipDestroySurfaceObject hipDestroySurfaceObject_fn; + t_hipDestroyTextureObject hipDestroyTextureObject_fn; + t_hipDeviceCanAccessPeer hipDeviceCanAccessPeer_fn; + t_hipDeviceComputeCapability hipDeviceComputeCapability_fn; + t_hipDeviceDisablePeerAccess hipDeviceDisablePeerAccess_fn; + t_hipDeviceEnablePeerAccess hipDeviceEnablePeerAccess_fn; + t_hipDeviceGet hipDeviceGet_fn; + t_hipDeviceGetAttribute hipDeviceGetAttribute_fn; + t_hipDeviceGetByPCIBusId hipDeviceGetByPCIBusId_fn; + t_hipDeviceGetCacheConfig hipDeviceGetCacheConfig_fn; + t_hipDeviceGetDefaultMemPool hipDeviceGetDefaultMemPool_fn; + t_hipDeviceGetGraphMemAttribute hipDeviceGetGraphMemAttribute_fn; + t_hipDeviceGetLimit hipDeviceGetLimit_fn; + t_hipDeviceGetMemPool hipDeviceGetMemPool_fn; + t_hipDeviceGetName hipDeviceGetName_fn; + t_hipDeviceGetP2PAttribute hipDeviceGetP2PAttribute_fn; + t_hipDeviceGetPCIBusId hipDeviceGetPCIBusId_fn; + t_hipDeviceGetSharedMemConfig hipDeviceGetSharedMemConfig_fn; + t_hipDeviceGetStreamPriorityRange hipDeviceGetStreamPriorityRange_fn; + t_hipDeviceGetUuid hipDeviceGetUuid_fn; + t_hipDeviceGraphMemTrim hipDeviceGraphMemTrim_fn; + t_hipDevicePrimaryCtxGetState hipDevicePrimaryCtxGetState_fn; + t_hipDevicePrimaryCtxRelease hipDevicePrimaryCtxRelease_fn; + t_hipDevicePrimaryCtxReset hipDevicePrimaryCtxReset_fn; + t_hipDevicePrimaryCtxRetain hipDevicePrimaryCtxRetain_fn; + t_hipDevicePrimaryCtxSetFlags hipDevicePrimaryCtxSetFlags_fn; + t_hipDeviceReset hipDeviceReset_fn; + t_hipDeviceSetCacheConfig hipDeviceSetCacheConfig_fn; + t_hipDeviceSetGraphMemAttribute hipDeviceSetGraphMemAttribute_fn; + t_hipDeviceSetLimit hipDeviceSetLimit_fn; + t_hipDeviceSetMemPool hipDeviceSetMemPool_fn; + t_hipDeviceSetSharedMemConfig hipDeviceSetSharedMemConfig_fn; + t_hipDeviceSynchronize hipDeviceSynchronize_fn; + t_hipDeviceTotalMem hipDeviceTotalMem_fn; + t_hipDriverGetVersion hipDriverGetVersion_fn; + t_hipDrvGetErrorName hipDrvGetErrorName_fn; + t_hipDrvGetErrorString hipDrvGetErrorString_fn; + t_hipDrvGraphAddMemcpyNode hipDrvGraphAddMemcpyNode_fn; + t_hipDrvMemcpy2DUnaligned hipDrvMemcpy2DUnaligned_fn; + t_hipDrvMemcpy3D hipDrvMemcpy3D_fn; + t_hipDrvMemcpy3DAsync hipDrvMemcpy3DAsync_fn; + t_hipDrvPointerGetAttributes hipDrvPointerGetAttributes_fn; + t_hipEventCreate hipEventCreate_fn; + t_hipEventCreateWithFlags hipEventCreateWithFlags_fn; + t_hipEventDestroy hipEventDestroy_fn; + t_hipEventElapsedTime hipEventElapsedTime_fn; + t_hipEventQuery hipEventQuery_fn; + t_hipEventRecord hipEventRecord_fn; + t_hipEventSynchronize hipEventSynchronize_fn; + t_hipExtGetLinkTypeAndHopCount hipExtGetLinkTypeAndHopCount_fn; + t_hipExtLaunchKernel hipExtLaunchKernel_fn; + t_hipExtLaunchMultiKernelMultiDevice hipExtLaunchMultiKernelMultiDevice_fn; + t_hipExtMallocWithFlags hipExtMallocWithFlags_fn; + t_hipExtStreamCreateWithCUMask hipExtStreamCreateWithCUMask_fn; + t_hipExtStreamGetCUMask hipExtStreamGetCUMask_fn; + t_hipExternalMemoryGetMappedBuffer hipExternalMemoryGetMappedBuffer_fn; + t_hipFree hipFree_fn; + t_hipFreeArray hipFreeArray_fn; + t_hipFreeAsync hipFreeAsync_fn; + t_hipFreeHost hipFreeHost_fn; + t_hipFreeMipmappedArray hipFreeMipmappedArray_fn; + t_hipFuncGetAttribute hipFuncGetAttribute_fn; + t_hipFuncGetAttributes hipFuncGetAttributes_fn; + t_hipFuncSetAttribute hipFuncSetAttribute_fn; + t_hipFuncSetCacheConfig hipFuncSetCacheConfig_fn; + t_hipFuncSetSharedMemConfig hipFuncSetSharedMemConfig_fn; + t_hipGLGetDevices hipGLGetDevices_fn; + t_hipGetChannelDesc hipGetChannelDesc_fn; + t_hipGetDevice hipGetDevice_fn; + t_hipGetDeviceCount hipGetDeviceCount_fn; + t_hipGetDeviceFlags hipGetDeviceFlags_fn; + t_hipGetDevicePropertiesR0600 hipGetDevicePropertiesR0600_fn; + t_hipGetDevicePropertiesR0000 hipGetDevicePropertiesR0000_fn; + t_hipGetErrorName hipGetErrorName_fn; + t_hipGetErrorString hipGetErrorString_fn; + t_hipGetLastError hipGetLastError_fn; + t_hipGetMipmappedArrayLevel hipGetMipmappedArrayLevel_fn; + t_hipGetSymbolAddress hipGetSymbolAddress_fn; + t_hipGetSymbolSize hipGetSymbolSize_fn; + t_hipGetTextureAlignmentOffset hipGetTextureAlignmentOffset_fn; + t_hipGetTextureObjectResourceDesc hipGetTextureObjectResourceDesc_fn; + t_hipGetTextureObjectResourceViewDesc hipGetTextureObjectResourceViewDesc_fn; + t_hipGetTextureObjectTextureDesc hipGetTextureObjectTextureDesc_fn; + t_hipGetTextureReference hipGetTextureReference_fn; + t_hipGraphAddChildGraphNode hipGraphAddChildGraphNode_fn; + t_hipGraphAddDependencies hipGraphAddDependencies_fn; + t_hipGraphAddEmptyNode hipGraphAddEmptyNode_fn; + t_hipGraphAddEventRecordNode hipGraphAddEventRecordNode_fn; + t_hipGraphAddEventWaitNode hipGraphAddEventWaitNode_fn; + t_hipGraphAddHostNode hipGraphAddHostNode_fn; + t_hipGraphAddKernelNode hipGraphAddKernelNode_fn; + t_hipGraphAddMemAllocNode hipGraphAddMemAllocNode_fn; + t_hipGraphAddMemFreeNode hipGraphAddMemFreeNode_fn; + t_hipGraphAddMemcpyNode hipGraphAddMemcpyNode_fn; + t_hipGraphAddMemcpyNode1D hipGraphAddMemcpyNode1D_fn; + t_hipGraphAddMemcpyNodeFromSymbol hipGraphAddMemcpyNodeFromSymbol_fn; + t_hipGraphAddMemcpyNodeToSymbol hipGraphAddMemcpyNodeToSymbol_fn; + t_hipGraphAddMemsetNode hipGraphAddMemsetNode_fn; + t_hipGraphChildGraphNodeGetGraph hipGraphChildGraphNodeGetGraph_fn; + t_hipGraphClone hipGraphClone_fn; + t_hipGraphCreate hipGraphCreate_fn; + t_hipGraphDebugDotPrint hipGraphDebugDotPrint_fn; + t_hipGraphDestroy hipGraphDestroy_fn; + t_hipGraphDestroyNode hipGraphDestroyNode_fn; + t_hipGraphEventRecordNodeGetEvent hipGraphEventRecordNodeGetEvent_fn; + t_hipGraphEventRecordNodeSetEvent hipGraphEventRecordNodeSetEvent_fn; + t_hipGraphEventWaitNodeGetEvent hipGraphEventWaitNodeGetEvent_fn; + t_hipGraphEventWaitNodeSetEvent hipGraphEventWaitNodeSetEvent_fn; + t_hipGraphExecChildGraphNodeSetParams hipGraphExecChildGraphNodeSetParams_fn; + t_hipGraphExecDestroy hipGraphExecDestroy_fn; + t_hipGraphExecEventRecordNodeSetEvent hipGraphExecEventRecordNodeSetEvent_fn; + t_hipGraphExecEventWaitNodeSetEvent hipGraphExecEventWaitNodeSetEvent_fn; + t_hipGraphExecHostNodeSetParams hipGraphExecHostNodeSetParams_fn; + t_hipGraphExecKernelNodeSetParams hipGraphExecKernelNodeSetParams_fn; + t_hipGraphExecMemcpyNodeSetParams hipGraphExecMemcpyNodeSetParams_fn; + t_hipGraphExecMemcpyNodeSetParams1D hipGraphExecMemcpyNodeSetParams1D_fn; + t_hipGraphExecMemcpyNodeSetParamsFromSymbol hipGraphExecMemcpyNodeSetParamsFromSymbol_fn; + t_hipGraphExecMemcpyNodeSetParamsToSymbol hipGraphExecMemcpyNodeSetParamsToSymbol_fn; + t_hipGraphExecMemsetNodeSetParams hipGraphExecMemsetNodeSetParams_fn; + t_hipGraphExecUpdate hipGraphExecUpdate_fn; + t_hipGraphGetEdges hipGraphGetEdges_fn; + t_hipGraphGetNodes hipGraphGetNodes_fn; + t_hipGraphGetRootNodes hipGraphGetRootNodes_fn; + t_hipGraphHostNodeGetParams hipGraphHostNodeGetParams_fn; + t_hipGraphHostNodeSetParams hipGraphHostNodeSetParams_fn; + t_hipGraphInstantiate hipGraphInstantiate_fn; + t_hipGraphInstantiateWithFlags hipGraphInstantiateWithFlags_fn; + t_hipGraphKernelNodeCopyAttributes hipGraphKernelNodeCopyAttributes_fn; + t_hipGraphKernelNodeGetAttribute hipGraphKernelNodeGetAttribute_fn; + t_hipGraphKernelNodeGetParams hipGraphKernelNodeGetParams_fn; + t_hipGraphKernelNodeSetAttribute hipGraphKernelNodeSetAttribute_fn; + t_hipGraphKernelNodeSetParams hipGraphKernelNodeSetParams_fn; + t_hipGraphLaunch hipGraphLaunch_fn; + t_hipGraphMemAllocNodeGetParams hipGraphMemAllocNodeGetParams_fn; + t_hipGraphMemFreeNodeGetParams hipGraphMemFreeNodeGetParams_fn; + t_hipGraphMemcpyNodeGetParams hipGraphMemcpyNodeGetParams_fn; + t_hipGraphMemcpyNodeSetParams hipGraphMemcpyNodeSetParams_fn; + t_hipGraphMemcpyNodeSetParams1D hipGraphMemcpyNodeSetParams1D_fn; + t_hipGraphMemcpyNodeSetParamsFromSymbol hipGraphMemcpyNodeSetParamsFromSymbol_fn; + t_hipGraphMemcpyNodeSetParamsToSymbol hipGraphMemcpyNodeSetParamsToSymbol_fn; + t_hipGraphMemsetNodeGetParams hipGraphMemsetNodeGetParams_fn; + t_hipGraphMemsetNodeSetParams hipGraphMemsetNodeSetParams_fn; + t_hipGraphNodeFindInClone hipGraphNodeFindInClone_fn; + t_hipGraphNodeGetDependencies hipGraphNodeGetDependencies_fn; + t_hipGraphNodeGetDependentNodes hipGraphNodeGetDependentNodes_fn; + t_hipGraphNodeGetEnabled hipGraphNodeGetEnabled_fn; + t_hipGraphNodeGetType hipGraphNodeGetType_fn; + t_hipGraphNodeSetEnabled hipGraphNodeSetEnabled_fn; + t_hipGraphReleaseUserObject hipGraphReleaseUserObject_fn; + t_hipGraphRemoveDependencies hipGraphRemoveDependencies_fn; + t_hipGraphRetainUserObject hipGraphRetainUserObject_fn; + t_hipGraphUpload hipGraphUpload_fn; + t_hipGraphicsGLRegisterBuffer hipGraphicsGLRegisterBuffer_fn; + t_hipGraphicsGLRegisterImage hipGraphicsGLRegisterImage_fn; + t_hipGraphicsMapResources hipGraphicsMapResources_fn; + t_hipGraphicsResourceGetMappedPointer hipGraphicsResourceGetMappedPointer_fn; + t_hipGraphicsSubResourceGetMappedArray hipGraphicsSubResourceGetMappedArray_fn; + t_hipGraphicsUnmapResources hipGraphicsUnmapResources_fn; + t_hipGraphicsUnregisterResource hipGraphicsUnregisterResource_fn; + t_hipHostAlloc hipHostAlloc_fn; + t_hipHostFree hipHostFree_fn; + t_hipHostGetDevicePointer hipHostGetDevicePointer_fn; + t_hipHostGetFlags hipHostGetFlags_fn; + t_hipHostMalloc hipHostMalloc_fn; + t_hipHostRegister hipHostRegister_fn; + t_hipHostUnregister hipHostUnregister_fn; + t_hipImportExternalMemory hipImportExternalMemory_fn; + t_hipImportExternalSemaphore hipImportExternalSemaphore_fn; + t_hipInit hipInit_fn; + t_hipIpcCloseMemHandle hipIpcCloseMemHandle_fn; + t_hipIpcGetEventHandle hipIpcGetEventHandle_fn; + t_hipIpcGetMemHandle hipIpcGetMemHandle_fn; + t_hipIpcOpenEventHandle hipIpcOpenEventHandle_fn; + t_hipIpcOpenMemHandle hipIpcOpenMemHandle_fn; + t_hipKernelNameRef hipKernelNameRef_fn; + t_hipKernelNameRefByPtr hipKernelNameRefByPtr_fn; + t_hipLaunchByPtr hipLaunchByPtr_fn; + t_hipLaunchCooperativeKernel hipLaunchCooperativeKernel_fn; + t_hipLaunchCooperativeKernelMultiDevice hipLaunchCooperativeKernelMultiDevice_fn; + t_hipLaunchHostFunc hipLaunchHostFunc_fn; + t_hipLaunchKernel hipLaunchKernel_fn; + t_hipMalloc hipMalloc_fn; + t_hipMalloc3D hipMalloc3D_fn; + t_hipMalloc3DArray hipMalloc3DArray_fn; + t_hipMallocArray hipMallocArray_fn; + t_hipMallocAsync hipMallocAsync_fn; + t_hipMallocFromPoolAsync hipMallocFromPoolAsync_fn; + t_hipMallocHost hipMallocHost_fn; + t_hipMallocManaged hipMallocManaged_fn; + t_hipMallocMipmappedArray hipMallocMipmappedArray_fn; + t_hipMallocPitch hipMallocPitch_fn; + t_hipMemAddressFree hipMemAddressFree_fn; + t_hipMemAddressReserve hipMemAddressReserve_fn; + t_hipMemAdvise hipMemAdvise_fn; + t_hipMemAllocHost hipMemAllocHost_fn; + t_hipMemAllocPitch hipMemAllocPitch_fn; + t_hipMemCreate hipMemCreate_fn; + t_hipMemExportToShareableHandle hipMemExportToShareableHandle_fn; + t_hipMemGetAccess hipMemGetAccess_fn; + t_hipMemGetAddressRange hipMemGetAddressRange_fn; + t_hipMemGetAllocationGranularity hipMemGetAllocationGranularity_fn; + t_hipMemGetAllocationPropertiesFromHandle hipMemGetAllocationPropertiesFromHandle_fn; + t_hipMemGetInfo hipMemGetInfo_fn; + t_hipMemImportFromShareableHandle hipMemImportFromShareableHandle_fn; + t_hipMemMap hipMemMap_fn; + t_hipMemMapArrayAsync hipMemMapArrayAsync_fn; + t_hipMemPoolCreate hipMemPoolCreate_fn; + t_hipMemPoolDestroy hipMemPoolDestroy_fn; + t_hipMemPoolExportPointer hipMemPoolExportPointer_fn; + t_hipMemPoolExportToShareableHandle hipMemPoolExportToShareableHandle_fn; + t_hipMemPoolGetAccess hipMemPoolGetAccess_fn; + t_hipMemPoolGetAttribute hipMemPoolGetAttribute_fn; + t_hipMemPoolImportFromShareableHandle hipMemPoolImportFromShareableHandle_fn; + t_hipMemPoolImportPointer hipMemPoolImportPointer_fn; + t_hipMemPoolSetAccess hipMemPoolSetAccess_fn; + t_hipMemPoolSetAttribute hipMemPoolSetAttribute_fn; + t_hipMemPoolTrimTo hipMemPoolTrimTo_fn; + t_hipMemPrefetchAsync hipMemPrefetchAsync_fn; + t_hipMemPtrGetInfo hipMemPtrGetInfo_fn; + t_hipMemRangeGetAttribute hipMemRangeGetAttribute_fn; + t_hipMemRangeGetAttributes hipMemRangeGetAttributes_fn; + t_hipMemRelease hipMemRelease_fn; + t_hipMemRetainAllocationHandle hipMemRetainAllocationHandle_fn; + t_hipMemSetAccess hipMemSetAccess_fn; + t_hipMemUnmap hipMemUnmap_fn; + t_hipMemcpy hipMemcpy_fn; + t_hipMemcpy2D hipMemcpy2D_fn; + t_hipMemcpy2DAsync hipMemcpy2DAsync_fn; + t_hipMemcpy2DFromArray hipMemcpy2DFromArray_fn; + t_hipMemcpy2DFromArrayAsync hipMemcpy2DFromArrayAsync_fn; + t_hipMemcpy2DToArray hipMemcpy2DToArray_fn; + t_hipMemcpy2DToArrayAsync hipMemcpy2DToArrayAsync_fn; + t_hipMemcpy3D hipMemcpy3D_fn; + t_hipMemcpy3DAsync hipMemcpy3DAsync_fn; + t_hipMemcpyAsync hipMemcpyAsync_fn; + t_hipMemcpyAtoH hipMemcpyAtoH_fn; + t_hipMemcpyDtoD hipMemcpyDtoD_fn; + t_hipMemcpyDtoDAsync hipMemcpyDtoDAsync_fn; + t_hipMemcpyDtoH hipMemcpyDtoH_fn; + t_hipMemcpyDtoHAsync hipMemcpyDtoHAsync_fn; + t_hipMemcpyFromArray hipMemcpyFromArray_fn; + t_hipMemcpyFromSymbol hipMemcpyFromSymbol_fn; + t_hipMemcpyFromSymbolAsync hipMemcpyFromSymbolAsync_fn; + t_hipMemcpyHtoA hipMemcpyHtoA_fn; + t_hipMemcpyHtoD hipMemcpyHtoD_fn; + t_hipMemcpyHtoDAsync hipMemcpyHtoDAsync_fn; + t_hipMemcpyParam2D hipMemcpyParam2D_fn; + t_hipMemcpyParam2DAsync hipMemcpyParam2DAsync_fn; + t_hipMemcpyPeer hipMemcpyPeer_fn; + t_hipMemcpyPeerAsync hipMemcpyPeerAsync_fn; + t_hipMemcpyToArray hipMemcpyToArray_fn; + t_hipMemcpyToSymbol hipMemcpyToSymbol_fn; + t_hipMemcpyToSymbolAsync hipMemcpyToSymbolAsync_fn; + t_hipMemcpyWithStream hipMemcpyWithStream_fn; + t_hipMemset hipMemset_fn; + t_hipMemset2D hipMemset2D_fn; + t_hipMemset2DAsync hipMemset2DAsync_fn; + t_hipMemset3D hipMemset3D_fn; + t_hipMemset3DAsync hipMemset3DAsync_fn; + t_hipMemsetAsync hipMemsetAsync_fn; + t_hipMemsetD16 hipMemsetD16_fn; + t_hipMemsetD16Async hipMemsetD16Async_fn; + t_hipMemsetD32 hipMemsetD32_fn; + t_hipMemsetD32Async hipMemsetD32Async_fn; + t_hipMemsetD8 hipMemsetD8_fn; + t_hipMemsetD8Async hipMemsetD8Async_fn; + t_hipMipmappedArrayCreate hipMipmappedArrayCreate_fn; + t_hipMipmappedArrayDestroy hipMipmappedArrayDestroy_fn; + t_hipMipmappedArrayGetLevel hipMipmappedArrayGetLevel_fn; + t_hipModuleGetFunction hipModuleGetFunction_fn; + t_hipModuleGetGlobal hipModuleGetGlobal_fn; + t_hipModuleGetTexRef hipModuleGetTexRef_fn; + t_hipModuleLaunchCooperativeKernel hipModuleLaunchCooperativeKernel_fn; + t_hipModuleLaunchCooperativeKernelMultiDevice hipModuleLaunchCooperativeKernelMultiDevice_fn; + t_hipModuleLaunchKernel hipModuleLaunchKernel_fn; + t_hipModuleLoad hipModuleLoad_fn; + t_hipModuleLoadData hipModuleLoadData_fn; + t_hipModuleLoadDataEx hipModuleLoadDataEx_fn; + t_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor + hipModuleOccupancyMaxActiveBlocksPerMultiprocessor_fn; + t_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_fn; + t_hipModuleOccupancyMaxPotentialBlockSize hipModuleOccupancyMaxPotentialBlockSize_fn; + t_hipModuleOccupancyMaxPotentialBlockSizeWithFlags + hipModuleOccupancyMaxPotentialBlockSizeWithFlags_fn; + t_hipModuleUnload hipModuleUnload_fn; + t_hipOccupancyMaxActiveBlocksPerMultiprocessor hipOccupancyMaxActiveBlocksPerMultiprocessor_fn; + t_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_fn; + t_hipOccupancyMaxPotentialBlockSize hipOccupancyMaxPotentialBlockSize_fn; + t_hipPeekAtLastError hipPeekAtLastError_fn; + t_hipPointerGetAttribute hipPointerGetAttribute_fn; + t_hipPointerGetAttributes hipPointerGetAttributes_fn; + t_hipPointerSetAttribute hipPointerSetAttribute_fn; + t_hipProfilerStart hipProfilerStart_fn; + t_hipProfilerStop hipProfilerStop_fn; + t_hipRuntimeGetVersion hipRuntimeGetVersion_fn; + t_hipSetDevice hipSetDevice_fn; + t_hipSetDeviceFlags hipSetDeviceFlags_fn; + t_hipSetupArgument hipSetupArgument_fn; + t_hipSignalExternalSemaphoresAsync hipSignalExternalSemaphoresAsync_fn; + t_hipStreamAddCallback hipStreamAddCallback_fn; + t_hipStreamAttachMemAsync hipStreamAttachMemAsync_fn; + t_hipStreamBeginCapture hipStreamBeginCapture_fn; + t_hipStreamCreate hipStreamCreate_fn; + t_hipStreamCreateWithFlags hipStreamCreateWithFlags_fn; + t_hipStreamCreateWithPriority hipStreamCreateWithPriority_fn; + t_hipStreamDestroy hipStreamDestroy_fn; + t_hipStreamEndCapture hipStreamEndCapture_fn; + t_hipStreamGetCaptureInfo hipStreamGetCaptureInfo_fn; + t_hipStreamGetCaptureInfo_v2 hipStreamGetCaptureInfo_v2_fn; + t_hipStreamGetDevice hipStreamGetDevice_fn; + t_hipStreamGetFlags hipStreamGetFlags_fn; + t_hipStreamGetPriority hipStreamGetPriority_fn; + t_hipStreamIsCapturing hipStreamIsCapturing_fn; + t_hipStreamQuery hipStreamQuery_fn; + t_hipStreamSynchronize hipStreamSynchronize_fn; + t_hipStreamUpdateCaptureDependencies hipStreamUpdateCaptureDependencies_fn; + t_hipStreamWaitEvent hipStreamWaitEvent_fn; + t_hipStreamWaitValue32 hipStreamWaitValue32_fn; + t_hipStreamWaitValue64 hipStreamWaitValue64_fn; + t_hipStreamWriteValue32 hipStreamWriteValue32_fn; + t_hipStreamWriteValue64 hipStreamWriteValue64_fn; + t_hipTexObjectCreate hipTexObjectCreate_fn; + t_hipTexObjectDestroy hipTexObjectDestroy_fn; + t_hipTexObjectGetResourceDesc hipTexObjectGetResourceDesc_fn; + t_hipTexObjectGetResourceViewDesc hipTexObjectGetResourceViewDesc_fn; + t_hipTexObjectGetTextureDesc hipTexObjectGetTextureDesc_fn; + t_hipTexRefGetAddress hipTexRefGetAddress_fn; + t_hipTexRefGetAddressMode hipTexRefGetAddressMode_fn; + t_hipTexRefGetFilterMode hipTexRefGetFilterMode_fn; + t_hipTexRefGetFlags hipTexRefGetFlags_fn; + t_hipTexRefGetFormat hipTexRefGetFormat_fn; + t_hipTexRefGetMaxAnisotropy hipTexRefGetMaxAnisotropy_fn; + t_hipTexRefGetMipMappedArray hipTexRefGetMipMappedArray_fn; + t_hipTexRefGetMipmapFilterMode hipTexRefGetMipmapFilterMode_fn; + t_hipTexRefGetMipmapLevelBias hipTexRefGetMipmapLevelBias_fn; + t_hipTexRefGetMipmapLevelClamp hipTexRefGetMipmapLevelClamp_fn; + t_hipTexRefSetAddress hipTexRefSetAddress_fn; + t_hipTexRefSetAddress2D hipTexRefSetAddress2D_fn; + t_hipTexRefSetAddressMode hipTexRefSetAddressMode_fn; + t_hipTexRefSetArray hipTexRefSetArray_fn; + t_hipTexRefSetBorderColor hipTexRefSetBorderColor_fn; + t_hipTexRefSetFilterMode hipTexRefSetFilterMode_fn; + t_hipTexRefSetFlags hipTexRefSetFlags_fn; + t_hipTexRefSetFormat hipTexRefSetFormat_fn; + t_hipTexRefSetMaxAnisotropy hipTexRefSetMaxAnisotropy_fn; + t_hipTexRefSetMipmapFilterMode hipTexRefSetMipmapFilterMode_fn; + t_hipTexRefSetMipmapLevelBias hipTexRefSetMipmapLevelBias_fn; + t_hipTexRefSetMipmapLevelClamp hipTexRefSetMipmapLevelClamp_fn; + t_hipTexRefSetMipmappedArray hipTexRefSetMipmappedArray_fn; + t_hipThreadExchangeStreamCaptureMode hipThreadExchangeStreamCaptureMode_fn; + t_hipUnbindTexture hipUnbindTexture_fn; + t_hipUserObjectCreate hipUserObjectCreate_fn; + t_hipUserObjectRelease hipUserObjectRelease_fn; + t_hipUserObjectRetain hipUserObjectRetain_fn; + t_hipWaitExternalSemaphoresAsync hipWaitExternalSemaphoresAsync_fn; + t_hipCreateChannelDesc hipCreateChannelDesc_fn; + t_hipExtModuleLaunchKernel hipExtModuleLaunchKernel_fn; + t_hipHccModuleLaunchKernel hipHccModuleLaunchKernel_fn; + t_hipMemcpy_spt hipMemcpy_spt_fn; + t_hipMemcpyToSymbol_spt hipMemcpyToSymbol_spt_fn; + t_hipMemcpyFromSymbol_spt hipMemcpyFromSymbol_spt_fn; + t_hipMemcpy2D_spt hipMemcpy2D_spt_fn; + t_hipMemcpy2DFromArray_spt hipMemcpy2DFromArray_spt_fn; + t_hipMemcpy3D_spt hipMemcpy3D_spt_fn; + t_hipMemset_spt hipMemset_spt_fn; + t_hipMemsetAsync_spt hipMemsetAsync_spt_fn; + t_hipMemset2D_spt hipMemset2D_spt_fn; + t_hipMemset2DAsync_spt hipMemset2DAsync_spt_fn; + t_hipMemset3DAsync_spt hipMemset3DAsync_spt_fn; + t_hipMemset3D_spt hipMemset3D_spt_fn; + t_hipMemcpyAsync_spt hipMemcpyAsync_spt_fn; + t_hipMemcpy3DAsync_spt hipMemcpy3DAsync_spt_fn; + t_hipMemcpy2DAsync_spt hipMemcpy2DAsync_spt_fn; + t_hipMemcpyFromSymbolAsync_spt hipMemcpyFromSymbolAsync_spt_fn; + t_hipMemcpyToSymbolAsync_spt hipMemcpyToSymbolAsync_spt_fn; + t_hipMemcpyFromArray_spt hipMemcpyFromArray_spt_fn; + t_hipMemcpy2DToArray_spt hipMemcpy2DToArray_spt_fn; + t_hipMemcpy2DFromArrayAsync_spt hipMemcpy2DFromArrayAsync_spt_fn; + t_hipMemcpy2DToArrayAsync_spt hipMemcpy2DToArrayAsync_spt_fn; + t_hipStreamQuery_spt hipStreamQuery_spt_fn; + t_hipStreamSynchronize_spt hipStreamSynchronize_spt_fn; + t_hipStreamGetPriority_spt hipStreamGetPriority_spt_fn; + t_hipStreamWaitEvent_spt hipStreamWaitEvent_spt_fn; + t_hipStreamGetFlags_spt hipStreamGetFlags_spt_fn; + t_hipStreamAddCallback_spt hipStreamAddCallback_spt_fn; + t_hipEventRecord_spt hipEventRecord_spt_fn; + t_hipLaunchCooperativeKernel_spt hipLaunchCooperativeKernel_spt_fn; + t_hipLaunchKernel_spt hipLaunchKernel_spt_fn; + t_hipGraphLaunch_spt hipGraphLaunch_spt_fn; + t_hipStreamBeginCapture_spt hipStreamBeginCapture_spt_fn; + t_hipStreamEndCapture_spt hipStreamEndCapture_spt_fn; + t_hipStreamIsCapturing_spt hipStreamIsCapturing_spt_fn; + t_hipStreamGetCaptureInfo_spt hipStreamGetCaptureInfo_spt_fn; + t_hipStreamGetCaptureInfo_v2_spt hipStreamGetCaptureInfo_v2_spt_fn; + t_hipLaunchHostFunc_spt hipLaunchHostFunc_spt_fn; + t_hipGetStreamDeviceId hipGetStreamDeviceId_fn; + t_hipDrvGraphAddMemsetNode hipDrvGraphAddMemsetNode_fn; + t_hipGraphAddExternalSemaphoresWaitNode hipGraphAddExternalSemaphoresWaitNode_fn; + t_hipGraphAddExternalSemaphoresSignalNode hipGraphAddExternalSemaphoresSignalNode_fn; + t_hipGraphExternalSemaphoresSignalNodeSetParams hipGraphExternalSemaphoresSignalNodeSetParams_fn; + t_hipGraphExternalSemaphoresWaitNodeSetParams hipGraphExternalSemaphoresWaitNodeSetParams_fn; + t_hipGraphExternalSemaphoresSignalNodeGetParams hipGraphExternalSemaphoresSignalNodeGetParams_fn; + t_hipGraphExternalSemaphoresWaitNodeGetParams hipGraphExternalSemaphoresWaitNodeGetParams_fn; + t_hipGraphExecExternalSemaphoresSignalNodeSetParams hipGraphExecExternalSemaphoresSignalNodeSetParams_fn; + t_hipGraphExecExternalSemaphoresWaitNodeSetParams hipGraphExecExternalSemaphoresWaitNodeSetParams_fn; +}; diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_assert.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_assert.h new file mode 100644 index 0000000000000000000000000000000000000000..7d634eae0df3a94002d697d641f367ebb5226a2a --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_assert.h @@ -0,0 +1,101 @@ +/* +Copyright (c) 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +// abort +extern "C" __device__ inline __attribute__((weak)) +void abort() { + __builtin_trap(); +} + +// The noinline attribute helps encapsulate the printf expansion, +// which otherwise has a performance impact just by increasing the +// size of the calling function. Additionally, the weak attribute +// allows the function to exist as a global although its definition is +// included in every compilation unit. +#if defined(_WIN32) || defined(_WIN64) +extern "C" __device__ __attribute__((noinline)) __attribute__((weak)) +void _wassert(const wchar_t *_msg, const wchar_t *_file, unsigned _line) { + // FIXME: Need `wchar_t` support to generate assertion message. + __builtin_trap(); +} +#else /* defined(_WIN32) || defined(_WIN64) */ +extern "C" __device__ __attribute__((noinline)) __attribute__((weak)) +void __assert_fail(const char *assertion, + const char *file, + unsigned int line, + const char *function) +{ + const char fmt[] = "%s:%u: %s: Device-side assertion `%s' failed.\n"; + + // strlen is not available as a built-in yet, so we create our own + // loop in a macro. With a string literal argument, the compiler + // usually manages to replace the loop with a constant. + // + // The macro does not check for null pointer, since all the string + // arguments are defined to be constant literals when called from + // the assert() macro. + // + // NOTE: The loop below includes the null terminator in the length + // as required by append_string_n(). +#define __hip_get_string_length(LEN, STR) \ + do { \ + const char *tmp = STR; \ + while (*tmp++); \ + LEN = tmp - STR; \ + } while (0) + + auto msg = __ockl_fprintf_stderr_begin(); + int len = 0; + __hip_get_string_length(len, fmt); + msg = __ockl_fprintf_append_string_n(msg, fmt, len, 0); + __hip_get_string_length(len, file); + msg = __ockl_fprintf_append_string_n(msg, file, len, 0); + msg = __ockl_fprintf_append_args(msg, 1, line, 0, 0, 0, 0, 0, 0, 0); + __hip_get_string_length(len, function); + msg = __ockl_fprintf_append_string_n(msg, function, len, 0); + __hip_get_string_length(len, assertion); + __ockl_fprintf_append_string_n(msg, assertion, len, /* is_last = */ 1); + +#undef __hip_get_string_length + + __builtin_trap(); +} + +extern "C" __device__ __attribute__((noinline)) __attribute__((weak)) +void __assertfail() +{ + // ignore all the args for now. + __builtin_trap(); +} +#endif /* defined(_WIN32) || defined(_WIN64) */ + +#if defined(NDEBUG) +#define __hip_assert(COND) +#else +#define __hip_assert(COND) \ + do { \ + if (!(COND)) \ + __builtin_trap(); \ + } while (0) +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_cooperative_groups_helper.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_cooperative_groups_helper.h new file mode 100644 index 0000000000000000000000000000000000000000..f62246a031a5b17ce4c3cf1596e44c97127fe2d3 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_cooperative_groups_helper.h @@ -0,0 +1,242 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +/** + * @file amd_detail/hip_cooperative_groups_helper.h + * + * @brief Device side implementation of cooperative group feature. + * + * Defines helper constructs and APIs which aid the types and device API + * wrappers defined within `amd_detail/hip_cooperative_groups.h`. + */ +#ifndef HIP_INCLUDE_HIP_AMD_DETAIL_HIP_COOPERATIVE_GROUPS_HELPER_H +#define HIP_INCLUDE_HIP_AMD_DETAIL_HIP_COOPERATIVE_GROUPS_HELPER_H + +#if __cplusplus +#if !defined(__HIPCC_RTC__) +#include // threadId, blockId +#include +#endif +#if !defined(__align__) +#define __align__(x) __attribute__((aligned(x))) +#endif + +#if !defined(__CG_QUALIFIER__) +#define __CG_QUALIFIER__ __device__ __forceinline__ +#endif + +#if !defined(__CG_STATIC_QUALIFIER__) +#define __CG_STATIC_QUALIFIER__ __device__ static __forceinline__ +#endif + +#if !defined(_CG_STATIC_CONST_DECL_) +#define _CG_STATIC_CONST_DECL_ static constexpr +#endif + +#if __AMDGCN_WAVEFRONT_SIZE == 32 +using lane_mask = unsigned int; +#else +using lane_mask = unsigned long long int; +#endif + +namespace cooperative_groups { + +/* Global scope */ +template +using is_power_of_2 = std::integral_constant; + +template +using is_valid_wavefront = std::integral_constant; + +template +using is_valid_tile_size = + std::integral_constant::value && is_valid_wavefront::value>; + +template +using is_valid_type = + std::integral_constant::value || std::is_floating_point::value>; + +namespace internal { + +/** +* @brief Enums representing different cooperative group types +* @note This enum is only applicable on Linux. +* + */ +typedef enum { + cg_invalid, + cg_multi_grid, + cg_grid, + cg_workgroup, + cg_tiled_group, + cg_coalesced_group +} group_type; +/** + * @ingroup CooperativeG + * @{ + * This section describes the cooperative groups functions of HIP runtime API. + * + * The cooperative groups provides flexible thread parallel programming algorithms, threads + * cooperate and share data to perform collective computations. + * + * @note Cooperative groups feature is implemented on Linux, under developement + * on Windows. + * + */ +/** + * + * @brief Functionalities related to multi-grid cooperative group type + * @note The following cooperative groups functions are only applicable on Linux. + * + */ +namespace multi_grid { + +__CG_STATIC_QUALIFIER__ uint32_t num_grids() { + return static_cast(__ockl_multi_grid_num_grids()); } + +__CG_STATIC_QUALIFIER__ uint32_t grid_rank() { + return static_cast(__ockl_multi_grid_grid_rank()); } + +__CG_STATIC_QUALIFIER__ uint32_t size() { return static_cast(__ockl_multi_grid_size()); } + +__CG_STATIC_QUALIFIER__ uint32_t thread_rank() { + return static_cast(__ockl_multi_grid_thread_rank()); } + +__CG_STATIC_QUALIFIER__ bool is_valid() { return static_cast(__ockl_multi_grid_is_valid()); } + +__CG_STATIC_QUALIFIER__ void sync() { __ockl_multi_grid_sync(); } + +} // namespace multi_grid + +/** + * @brief Functionalities related to grid cooperative group type + * @note The following cooperative groups functions are only applicable on Linux. + */ +namespace grid { + +__CG_STATIC_QUALIFIER__ uint32_t size() { + return static_cast((blockDim.z * gridDim.z) * (blockDim.y * gridDim.y) * + (blockDim.x * gridDim.x)); +} + +__CG_STATIC_QUALIFIER__ uint32_t thread_rank() { + // Compute global id of the workgroup to which the current thread belongs to + uint32_t blkIdx = static_cast((blockIdx.z * gridDim.y * gridDim.x) + + (blockIdx.y * gridDim.x) + (blockIdx.x)); + + // Compute total number of threads being passed to reach current workgroup + // within grid + uint32_t num_threads_till_current_workgroup = + static_cast(blkIdx * (blockDim.x * blockDim.y * blockDim.z)); + + // Compute thread local rank within current workgroup + uint32_t local_thread_rank = static_cast((threadIdx.z * blockDim.y * blockDim.x) + + (threadIdx.y * blockDim.x) + (threadIdx.x)); + + return (num_threads_till_current_workgroup + local_thread_rank); +} + +__CG_STATIC_QUALIFIER__ bool is_valid() { return static_cast(__ockl_grid_is_valid()); } + +__CG_STATIC_QUALIFIER__ void sync() { __ockl_grid_sync(); } + +} // namespace grid + +/** + * @brief Functionalities related to `workgroup` (thread_block in CUDA terminology) + * cooperative group type + * @note The following cooperative groups functions are only applicable on Linux. + */ +namespace workgroup { + +__CG_STATIC_QUALIFIER__ dim3 group_index() { + return (dim3(static_cast(blockIdx.x), static_cast(blockIdx.y), + static_cast(blockIdx.z))); +} + +__CG_STATIC_QUALIFIER__ dim3 thread_index() { + return (dim3(static_cast(threadIdx.x), static_cast(threadIdx.y), + static_cast(threadIdx.z))); +} + +__CG_STATIC_QUALIFIER__ uint32_t size() { + return (static_cast(blockDim.x * blockDim.y * blockDim.z)); +} + +__CG_STATIC_QUALIFIER__ uint32_t thread_rank() { + return (static_cast((threadIdx.z * blockDim.y * blockDim.x) + + (threadIdx.y * blockDim.x) + (threadIdx.x))); +} + +__CG_STATIC_QUALIFIER__ bool is_valid() { + return true; +} + +__CG_STATIC_QUALIFIER__ void sync() { __syncthreads(); } + +__CG_STATIC_QUALIFIER__ dim3 block_dim() { + return (dim3(static_cast(blockDim.x), static_cast(blockDim.y), + static_cast(blockDim.z))); +} + +} // namespace workgroup + +namespace tiled_group { + +// enforce ordering for memory intructions +__CG_STATIC_QUALIFIER__ void sync() { __builtin_amdgcn_fence(__ATOMIC_ACQ_REL, "agent"); } + +} // namespace tiled_group + +namespace coalesced_group { + +// enforce ordering for memory intructions +__CG_STATIC_QUALIFIER__ void sync() { __builtin_amdgcn_fence(__ATOMIC_ACQ_REL, "agent"); } + +// Masked bit count +// +// For each thread, this function returns the number of active threads which +// have i-th bit of x set and come before the current thread. +__CG_STATIC_QUALIFIER__ unsigned int masked_bit_count(lane_mask x, unsigned int add = 0) { + unsigned int counter=0; + #if __AMDGCN_WAVEFRONT_SIZE == 32 + counter = __builtin_amdgcn_mbcnt_lo(x, add); + #else + counter = __builtin_amdgcn_mbcnt_lo(static_cast(x), add); + counter = __builtin_amdgcn_mbcnt_hi(static_cast(x >> 32), counter); + #endif + + return counter; +} + +} // namespace coalesced_group + + +} // namespace internal + +} // namespace cooperative_groups +/** +* @} +*/ + +#endif // __cplusplus +#endif // HIP_INCLUDE_HIP_AMD_DETAIL_HIP_COOPERATIVE_GROUPS_HELPER_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_gcc.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_gcc.h new file mode 100644 index 0000000000000000000000000000000000000000..e76a7fff3a7bdc0061cc81b3aa77f6f9fa1fec88 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_gcc.h @@ -0,0 +1,254 @@ +#pragma once + +#if defined(__cplusplus) + #include +#endif + +struct __half_raw { + unsigned short x; +}; + +struct __half2_raw { + unsigned short x; + unsigned short y; +}; + +#if defined(__cplusplus) + struct __half; + + __half __float2half(float); + float __half2float(__half); + + // BEGIN STRUCT __HALF + struct __half { + protected: + unsigned short __x; + public: + // CREATORS + __half() = default; + __half(const __half_raw& x) : __x{x.x} {} + #if !defined(__HIP_NO_HALF_CONVERSIONS__) + __half(float x) : __x{__float2half(x).__x} {} + __half(double x) : __x{__float2half(x).__x} {} + #endif + __half(const __half&) = default; + __half(__half&&) = default; + ~__half() = default; + + // MANIPULATORS + __half& operator=(const __half&) = default; + __half& operator=(__half&&) = default; + __half& operator=(const __half_raw& x) { __x = x.x; return *this; } + #if !defined(__HIP_NO_HALF_CONVERSIONS__) + __half& operator=(float x) + { + __x = __float2half(x).__x; + return *this; + } + __half& operator=(double x) + { + return *this = static_cast(x); + } + #endif + + // ACCESSORS + operator float() const { return __half2float(*this); } + operator __half_raw() const { return __half_raw{__x}; } + }; + // END STRUCT __HALF + + // BEGIN STRUCT __HALF2 + struct __half2 { + public: + __half x; + __half y; + + // CREATORS + __half2() = default; + __half2(const __half2_raw& ix) + : + x{reinterpret_cast(ix.x)}, + y{reinterpret_cast(ix.y)} + {} + __half2(const __half& ix, const __half& iy) : x{ix}, y{iy} {} + __half2(const __half2&) = default; + __half2(__half2&&) = default; + ~__half2() = default; + + // MANIPULATORS + __half2& operator=(const __half2&) = default; + __half2& operator=(__half2&&) = default; + __half2& operator=(const __half2_raw& ix) + { + x = reinterpret_cast(ix.x); + y = reinterpret_cast(ix.y); + return *this; + } + + // ACCESSORS + operator __half2_raw() const + { + return __half2_raw{ + reinterpret_cast(x), + reinterpret_cast(y)}; + } + }; + // END STRUCT __HALF2 + + inline + unsigned short __internal_float2half( + float flt, unsigned int& sgn, unsigned int& rem) + { + unsigned int x{}; + std::memcpy(&x, &flt, sizeof(flt)); + + unsigned int u = (x & 0x7fffffffU); + sgn = ((x >> 16) & 0x8000U); + + // NaN/+Inf/-Inf + if (u >= 0x7f800000U) { + rem = 0; + return static_cast( + (u == 0x7f800000U) ? (sgn | 0x7c00U) : 0x7fffU); + } + // Overflows + if (u > 0x477fefffU) { + rem = 0x80000000U; + return static_cast(sgn | 0x7bffU); + } + // Normal numbers + if (u >= 0x38800000U) { + rem = u << 19; + u -= 0x38000000U; + return static_cast(sgn | (u >> 13)); + } + // +0/-0 + if (u < 0x33000001U) { + rem = u; + return static_cast(sgn); + } + // Denormal numbers + unsigned int exponent = u >> 23; + unsigned int mantissa = (u & 0x7fffffU); + unsigned int shift = 0x7eU - exponent; + mantissa |= 0x800000U; + rem = mantissa << (32 - shift); + return static_cast(sgn | (mantissa >> shift)); + } + + inline + __half __float2half(float x) + { + __half_raw r; + unsigned int sgn{}; + unsigned int rem{}; + r.x = __internal_float2half(x, sgn, rem); + if (rem > 0x80000000U || (rem == 0x80000000U && (r.x & 0x1))) ++r.x; + + return r; + } + + inline + __half __float2half_rn(float x) { return __float2half(x); } + + inline + __half __float2half_rz(float x) + { + __half_raw r; + unsigned int sgn{}; + unsigned int rem{}; + r.x = __internal_float2half(x, sgn, rem); + + return r; + } + + inline + __half __float2half_rd(float x) + { + __half_raw r; + unsigned int sgn{}; + unsigned int rem{}; + r.x = __internal_float2half(x, sgn, rem); + if (rem && sgn) ++r.x; + + return r; + } + + inline + __half __float2half_ru(float x) + { + __half_raw r; + unsigned int sgn{}; + unsigned int rem{}; + r.x = __internal_float2half(x, sgn, rem); + if (rem && !sgn) ++r.x; + + return r; + } + + inline + __half2 __float2half2_rn(float x) + { + return __half2{__float2half_rn(x), __float2half_rn(x)}; + } + + inline + __half2 __floats2half2_rn(float x, float y) + { + return __half2{__float2half_rn(x), __float2half_rn(y)}; + } + + inline + float __internal_half2float(unsigned short x) + { + unsigned int sign = ((x >> 15) & 1); + unsigned int exponent = ((x >> 10) & 0x1f); + unsigned int mantissa = ((x & 0x3ff) << 13); + + if (exponent == 0x1fU) { /* NaN or Inf */ + mantissa = (mantissa ? (sign = 0, 0x7fffffU) : 0); + exponent = 0xffU; + } else if (!exponent) { /* Denorm or Zero */ + if (mantissa) { + unsigned int msb; + exponent = 0x71U; + do { + msb = (mantissa & 0x400000U); + mantissa <<= 1; /* normalize */ + --exponent; + } while (!msb); + mantissa &= 0x7fffffU; /* 1.mantissa is implicit */ + } + } else { + exponent += 0x70U; + } + unsigned int u = ((sign << 31) | (exponent << 23) | mantissa); + float f; + memcpy(&f, &u, sizeof(u)); + + return f; + } + + inline + float __half2float(__half x) + { + return __internal_half2float(static_cast<__half_raw>(x).x); + } + + inline + float __low2float(__half2 x) + { + return __internal_half2float(static_cast<__half2_raw>(x).x); + } + + inline + float __high2float(__half2 x) + { + return __internal_half2float(static_cast<__half2_raw>(x).y); + } + + #if !defined(HIP_NO_HALF) + using half = __half; + using half2 = __half2; + #endif +#endif // defined(__cplusplus) diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_math_fwd.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_math_fwd.h new file mode 100644 index 0000000000000000000000000000000000000000..9b2efefe6bd000c46ce6e24b85b9033cc6329826 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_fp16_math_fwd.h @@ -0,0 +1,96 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +// /* +// Half Math Functions +// */ +#if !defined(__HIPCC_RTC__) +#include "host_defines.h" +#endif +#ifndef __CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ +extern "C" +{ + __device__ __attribute__((const)) _Float16 __ocml_ceil_f16(_Float16); + __device__ _Float16 __ocml_cos_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_exp_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_exp10_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_exp2_f16(_Float16); + __device__ __attribute__((const)) _Float16 __ocml_floor_f16(_Float16); + __device__ __attribute__((const)) + _Float16 __ocml_fma_f16(_Float16, _Float16, _Float16); + __device__ __attribute__((const)) _Float16 __ocml_fabs_f16(_Float16); + __device__ __attribute__((const)) int __ocml_isinf_f16(_Float16); + __device__ __attribute__((const)) int __ocml_isnan_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_log_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_log10_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_log2_f16(_Float16); + __device__ __attribute__((pure)) _Float16 __ocml_pown_f16(_Float16, int); + __device__ __attribute__((const)) _Float16 __ocml_rint_f16(_Float16); + __device__ __attribute__((const)) _Float16 __ocml_rsqrt_f16(_Float16); + __device__ _Float16 __ocml_sin_f16(_Float16); + __device__ __attribute__((const)) _Float16 __ocml_sqrt_f16(_Float16); + __device__ __attribute__((const)) _Float16 __ocml_trunc_f16(_Float16); + __device__ __attribute__((const)) _Float16 __ocml_fmax_f16(_Float16, _Float16); + __device__ __attribute__((const)) _Float16 __ocml_fmin_f16(_Float16, _Float16); + + typedef _Float16 __2f16 __attribute__((ext_vector_type(2))); + typedef short __2i16 __attribute__((ext_vector_type(2))); + + #if defined(__clang__) && defined(__HIP__) + __device__ __attribute__((const)) float __ockl_fdot2(__2f16 a, __2f16 b, float c, bool s); + #endif + + __device__ __attribute__((const)) __2f16 __ocml_ceil_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_fabs_2f16(__2f16); + __device__ __2f16 __ocml_cos_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_exp_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_exp10_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_exp2_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_floor_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_fma_2f16(__2f16, __2f16, __2f16); + __device__ __attribute__((const)) __2i16 __ocml_isinf_2f16(__2f16); + __device__ __attribute__((const)) __2i16 __ocml_isnan_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_log_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_log10_2f16(__2f16); + __device__ __attribute__((pure)) __2f16 __ocml_log2_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_rint_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_rsqrt_2f16(__2f16); + __device__ __2f16 __ocml_sin_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_sqrt_2f16(__2f16); + __device__ __attribute__((const)) __2f16 __ocml_trunc_2f16(__2f16); + + __device__ __attribute__((const)) _Float16 __ocml_cvtrtn_f16_f32(float); + __device__ __attribute__((const)) _Float16 __ocml_cvtrtp_f16_f32(float); + __device__ __attribute__((const)) _Float16 __ocml_cvtrtz_f16_f32(float); + +} +#endif // !__CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ +//TODO: remove these after they get into clang header __clang_hip_libdevice_declares.h' +extern "C" { + __device__ __attribute__((const)) _Float16 __ocml_fmax_f16(_Float16, _Float16); + __device__ __attribute__((const)) _Float16 __ocml_fmin_f16(_Float16, _Float16); + __device__ __attribute__((const)) _Float16 __ocml_cvtrtn_f16_f32(float); + __device__ __attribute__((const)) _Float16 __ocml_cvtrtp_f16_f32(float); + __device__ __attribute__((const)) _Float16 __ocml_cvtrtz_f16_f32(float); +} diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_ldg.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_ldg.h new file mode 100644 index 0000000000000000000000000000000000000000..ce1fb51f464c4d8c9be1baa52512e356ba01a216 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_ldg.h @@ -0,0 +1,100 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#ifndef HIP_INCLUDE_HIP_AMD_DETAIL_HIP_LDG_H +#define HIP_INCLUDE_HIP_AMD_DETAIL_HIP_LDG_H + +#if __HIP_CLANG_ONLY__ +#include "amd_hip_vector_types.h" +#include "host_defines.h" + +__device__ inline static char __ldg(const char* ptr) { return *ptr; } + +__device__ inline static char2 __ldg(const char2* ptr) { return *ptr; } + +__device__ inline static char4 __ldg(const char4* ptr) { return *ptr; } + +__device__ inline static signed char __ldg(const signed char* ptr) { return ptr[0]; } + +__device__ inline static unsigned char __ldg(const unsigned char* ptr) { return ptr[0]; } + + +__device__ inline static short __ldg(const short* ptr) { return ptr[0]; } + +__device__ inline static short2 __ldg(const short2* ptr) { return ptr[0]; } + +__device__ inline static short4 __ldg(const short4* ptr) { return ptr[0]; } + +__device__ inline static unsigned short __ldg(const unsigned short* ptr) { return ptr[0]; } + + +__device__ inline static int __ldg(const int* ptr) { return ptr[0]; } + +__device__ inline static int2 __ldg(const int2* ptr) { return ptr[0]; } + +__device__ inline static int4 __ldg(const int4* ptr) { return ptr[0]; } + +__device__ inline static unsigned int __ldg(const unsigned int* ptr) { return ptr[0]; } + + +__device__ inline static long __ldg(const long* ptr) { return ptr[0]; } + +__device__ inline static unsigned long __ldg(const unsigned long* ptr) { return ptr[0]; } + + +__device__ inline static long long __ldg(const long long* ptr) { return ptr[0]; } + +__device__ inline static longlong2 __ldg(const longlong2* ptr) { return ptr[0]; } + +__device__ inline static unsigned long long __ldg(const unsigned long long* ptr) { return ptr[0]; } + + +__device__ inline static uchar2 __ldg(const uchar2* ptr) { return ptr[0]; } + +__device__ inline static uchar4 __ldg(const uchar4* ptr) { return ptr[0]; } + + +__device__ inline static ushort2 __ldg(const ushort2* ptr) { return ptr[0]; } + + +__device__ inline static uint2 __ldg(const uint2* ptr) { return ptr[0]; } + +__device__ inline static uint4 __ldg(const uint4* ptr) { return ptr[0]; } + + +__device__ inline static ulonglong2 __ldg(const ulonglong2* ptr) { return ptr[0]; } + + +__device__ inline static float __ldg(const float* ptr) { return ptr[0]; } + +__device__ inline static float2 __ldg(const float2* ptr) { return ptr[0]; } + +__device__ inline static float4 __ldg(const float4* ptr) { return ptr[0]; } + + +__device__ inline static double __ldg(const double* ptr) { return ptr[0]; } + +__device__ inline static double2 __ldg(const double2* ptr) { return ptr[0]; } + +#endif // __HIP_CLANG_ONLY__ + +#endif // HIP_LDG_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_prof_str.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_prof_str.h new file mode 100644 index 0000000000000000000000000000000000000000..3c9c09f2cee89f727642eca39f9c353546ea6ff1 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_prof_str.h @@ -0,0 +1,10169 @@ +// Generated file. DO NOT EDIT. +// +// This file is automatically generated by the hip_prof_gen.py script. +// If changes are required, run the script and commit the updated file. + +#ifndef _HIP_PROF_STR_H +#define _HIP_PROF_STR_H +#define HIP_PROF_VER 1 + +#include +#include +#include "amd_hip_gl_interop.h" + +#define HIP_API_ID_CONCAT_HELPER(a,b) a##b +#define HIP_API_ID_CONCAT(a,b) HIP_API_ID_CONCAT_HELPER(a,b) + +// HIP API callbacks ID enumeration +enum hip_api_id_t { + HIP_API_ID_NONE = 0, + HIP_API_ID_FIRST = 1, + HIP_API_ID___hipPopCallConfiguration = 1, + HIP_API_ID___hipPushCallConfiguration = 2, + HIP_API_ID_hipArray3DCreate = 3, + HIP_API_ID_hipArrayCreate = 4, + HIP_API_ID_hipArrayDestroy = 5, + HIP_API_ID_hipChooseDeviceR0000 = 6, + HIP_API_ID_hipConfigureCall = 7, + HIP_API_ID_hipCtxCreate = 8, + HIP_API_ID_hipCtxDestroy = 9, + HIP_API_ID_hipCtxDisablePeerAccess = 10, + HIP_API_ID_hipCtxEnablePeerAccess = 11, + HIP_API_ID_hipCtxGetApiVersion = 12, + HIP_API_ID_hipCtxGetCacheConfig = 13, + HIP_API_ID_hipCtxGetCurrent = 14, + HIP_API_ID_hipCtxGetDevice = 15, + HIP_API_ID_hipCtxGetFlags = 16, + HIP_API_ID_hipCtxGetSharedMemConfig = 17, + HIP_API_ID_hipCtxPopCurrent = 18, + HIP_API_ID_hipCtxPushCurrent = 19, + HIP_API_ID_hipCtxSetCacheConfig = 20, + HIP_API_ID_hipCtxSetCurrent = 21, + HIP_API_ID_hipCtxSetSharedMemConfig = 22, + HIP_API_ID_hipCtxSynchronize = 23, + HIP_API_ID_hipDestroyExternalMemory = 24, + HIP_API_ID_hipDestroyExternalSemaphore = 25, + HIP_API_ID_hipDeviceCanAccessPeer = 26, + HIP_API_ID_hipDeviceComputeCapability = 27, + HIP_API_ID_hipDeviceDisablePeerAccess = 28, + HIP_API_ID_hipDeviceEnablePeerAccess = 29, + HIP_API_ID_hipDeviceGet = 30, + HIP_API_ID_hipDeviceGetAttribute = 31, + HIP_API_ID_hipDeviceGetByPCIBusId = 32, + HIP_API_ID_hipDeviceGetCacheConfig = 33, + HIP_API_ID_hipDeviceGetLimit = 34, + HIP_API_ID_hipDeviceGetName = 35, + HIP_API_ID_hipDeviceGetP2PAttribute = 36, + HIP_API_ID_hipDeviceGetPCIBusId = 37, + HIP_API_ID_hipDeviceGetSharedMemConfig = 38, + HIP_API_ID_hipDeviceGetStreamPriorityRange = 39, + HIP_API_ID_hipDevicePrimaryCtxGetState = 40, + HIP_API_ID_hipDevicePrimaryCtxRelease = 41, + HIP_API_ID_hipDevicePrimaryCtxReset = 42, + HIP_API_ID_hipDevicePrimaryCtxRetain = 43, + HIP_API_ID_hipDevicePrimaryCtxSetFlags = 44, + HIP_API_ID_hipDeviceReset = 45, + HIP_API_ID_hipDeviceSetCacheConfig = 46, + HIP_API_ID_hipDeviceSetSharedMemConfig = 47, + HIP_API_ID_hipDeviceSynchronize = 48, + HIP_API_ID_hipDeviceTotalMem = 49, + HIP_API_ID_RESERVED_50 = 50, + HIP_API_ID_hipDrvMemcpy2DUnaligned = 51, + HIP_API_ID_hipDrvMemcpy3D = 52, + HIP_API_ID_hipDrvMemcpy3DAsync = 53, + HIP_API_ID_hipEventCreate = 54, + HIP_API_ID_hipEventCreateWithFlags = 55, + HIP_API_ID_hipEventDestroy = 56, + HIP_API_ID_hipEventElapsedTime = 57, + HIP_API_ID_hipEventQuery = 58, + HIP_API_ID_hipEventRecord = 59, + HIP_API_ID_hipEventSynchronize = 60, + HIP_API_ID_hipExtGetLinkTypeAndHopCount = 61, + HIP_API_ID_hipExtLaunchKernel = 62, + HIP_API_ID_hipExtLaunchMultiKernelMultiDevice = 63, + HIP_API_ID_hipExtMallocWithFlags = 64, + HIP_API_ID_hipExtModuleLaunchKernel = 65, + HIP_API_ID_hipExtStreamCreateWithCUMask = 66, + HIP_API_ID_hipExtStreamGetCUMask = 67, + HIP_API_ID_hipExternalMemoryGetMappedBuffer = 68, + HIP_API_ID_hipFree = 69, + HIP_API_ID_hipFreeArray = 70, + HIP_API_ID_hipFreeHost = 71, + HIP_API_ID_hipFreeMipmappedArray = 72, + HIP_API_ID_hipFuncGetAttribute = 73, + HIP_API_ID_hipFuncGetAttributes = 74, + HIP_API_ID_hipFuncSetAttribute = 75, + HIP_API_ID_hipFuncSetCacheConfig = 76, + HIP_API_ID_hipFuncSetSharedMemConfig = 77, + HIP_API_ID_hipGetDevice = 78, + HIP_API_ID_hipGetDeviceCount = 79, + HIP_API_ID_hipGetDeviceFlags = 80, + HIP_API_ID_hipGetDevicePropertiesR0000 = 81, + HIP_API_ID_RESERVED_82 = 82, + HIP_API_ID_hipGetErrorString = 83, + HIP_API_ID_hipGetLastError = 84, + HIP_API_ID_hipGetMipmappedArrayLevel = 85, + HIP_API_ID_hipGetSymbolAddress = 86, + HIP_API_ID_hipGetSymbolSize = 87, + HIP_API_ID_hipHccModuleLaunchKernel = 88, + HIP_API_ID_hipHostAlloc = 89, + HIP_API_ID_hipHostFree = 90, + HIP_API_ID_hipHostGetDevicePointer = 91, + HIP_API_ID_hipHostGetFlags = 92, + HIP_API_ID_hipHostMalloc = 93, + HIP_API_ID_hipHostRegister = 94, + HIP_API_ID_hipHostUnregister = 95, + HIP_API_ID_hipImportExternalMemory = 96, + HIP_API_ID_hipImportExternalSemaphore = 97, + HIP_API_ID_hipInit = 98, + HIP_API_ID_hipIpcCloseMemHandle = 99, + HIP_API_ID_hipIpcGetEventHandle = 100, + HIP_API_ID_hipIpcGetMemHandle = 101, + HIP_API_ID_hipIpcOpenEventHandle = 102, + HIP_API_ID_hipIpcOpenMemHandle = 103, + HIP_API_ID_hipLaunchByPtr = 104, + HIP_API_ID_hipLaunchCooperativeKernel = 105, + HIP_API_ID_hipLaunchCooperativeKernelMultiDevice = 106, + HIP_API_ID_hipLaunchKernel = 107, + HIP_API_ID_hipMalloc = 108, + HIP_API_ID_hipMalloc3D = 109, + HIP_API_ID_hipMalloc3DArray = 110, + HIP_API_ID_hipMallocArray = 111, + HIP_API_ID_hipMallocHost = 112, + HIP_API_ID_hipMallocManaged = 113, + HIP_API_ID_hipMallocMipmappedArray = 114, + HIP_API_ID_hipMallocPitch = 115, + HIP_API_ID_hipMemAdvise = 116, + HIP_API_ID_hipMemAllocHost = 117, + HIP_API_ID_hipMemAllocPitch = 118, + HIP_API_ID_hipMemGetAddressRange = 119, + HIP_API_ID_hipMemGetInfo = 120, + HIP_API_ID_hipMemPrefetchAsync = 121, + HIP_API_ID_hipMemPtrGetInfo = 122, + HIP_API_ID_hipMemRangeGetAttribute = 123, + HIP_API_ID_hipMemRangeGetAttributes = 124, + HIP_API_ID_hipMemcpy = 125, + HIP_API_ID_hipMemcpy2D = 126, + HIP_API_ID_hipMemcpy2DAsync = 127, + HIP_API_ID_hipMemcpy2DFromArray = 128, + HIP_API_ID_hipMemcpy2DFromArrayAsync = 129, + HIP_API_ID_hipMemcpy2DToArray = 130, + HIP_API_ID_hipMemcpy2DToArrayAsync = 131, + HIP_API_ID_hipMemcpy3D = 132, + HIP_API_ID_hipMemcpy3DAsync = 133, + HIP_API_ID_hipMemcpyAsync = 134, + HIP_API_ID_hipMemcpyAtoH = 135, + HIP_API_ID_hipMemcpyDtoD = 136, + HIP_API_ID_hipMemcpyDtoDAsync = 137, + HIP_API_ID_hipMemcpyDtoH = 138, + HIP_API_ID_hipMemcpyDtoHAsync = 139, + HIP_API_ID_hipMemcpyFromArray = 140, + HIP_API_ID_hipMemcpyFromSymbol = 141, + HIP_API_ID_hipMemcpyFromSymbolAsync = 142, + HIP_API_ID_hipMemcpyHtoA = 143, + HIP_API_ID_hipMemcpyHtoD = 144, + HIP_API_ID_hipMemcpyHtoDAsync = 145, + HIP_API_ID_hipMemcpyParam2D = 146, + HIP_API_ID_hipMemcpyParam2DAsync = 147, + HIP_API_ID_hipMemcpyPeer = 148, + HIP_API_ID_hipMemcpyPeerAsync = 149, + HIP_API_ID_hipMemcpyToArray = 150, + HIP_API_ID_hipMemcpyToSymbol = 151, + HIP_API_ID_hipMemcpyToSymbolAsync = 152, + HIP_API_ID_hipMemcpyWithStream = 153, + HIP_API_ID_hipMemset = 154, + HIP_API_ID_hipMemset2D = 155, + HIP_API_ID_hipMemset2DAsync = 156, + HIP_API_ID_hipMemset3D = 157, + HIP_API_ID_hipMemset3DAsync = 158, + HIP_API_ID_hipMemsetAsync = 159, + HIP_API_ID_hipMemsetD16 = 160, + HIP_API_ID_hipMemsetD16Async = 161, + HIP_API_ID_hipMemsetD32 = 162, + HIP_API_ID_hipMemsetD32Async = 163, + HIP_API_ID_hipMemsetD8 = 164, + HIP_API_ID_hipMemsetD8Async = 165, + HIP_API_ID_hipModuleGetFunction = 166, + HIP_API_ID_hipModuleGetGlobal = 167, + HIP_API_ID_hipModuleGetTexRef = 168, + HIP_API_ID_hipModuleLaunchKernel = 169, + HIP_API_ID_hipModuleLoad = 170, + HIP_API_ID_hipModuleLoadData = 171, + HIP_API_ID_hipModuleLoadDataEx = 172, + HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor = 173, + HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags = 174, + HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSize = 175, + HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSizeWithFlags = 176, + HIP_API_ID_hipModuleUnload = 177, + HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessor = 178, + HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags = 179, + HIP_API_ID_hipOccupancyMaxPotentialBlockSize = 180, + HIP_API_ID_hipPeekAtLastError = 181, + HIP_API_ID_hipPointerGetAttributes = 182, + HIP_API_ID_hipProfilerStart = 183, + HIP_API_ID_hipProfilerStop = 184, + HIP_API_ID_RESERVED_185 = 185, + HIP_API_ID_hipSetDevice = 186, + HIP_API_ID_hipSetDeviceFlags = 187, + HIP_API_ID_hipSetupArgument = 188, + HIP_API_ID_hipSignalExternalSemaphoresAsync = 189, + HIP_API_ID_hipStreamAddCallback = 190, + HIP_API_ID_hipStreamAttachMemAsync = 191, + HIP_API_ID_hipStreamCreate = 192, + HIP_API_ID_hipStreamCreateWithFlags = 193, + HIP_API_ID_hipStreamCreateWithPriority = 194, + HIP_API_ID_hipStreamDestroy = 195, + HIP_API_ID_hipStreamGetFlags = 196, + HIP_API_ID_hipStreamGetPriority = 197, + HIP_API_ID_hipStreamQuery = 198, + HIP_API_ID_hipStreamSynchronize = 199, + HIP_API_ID_hipStreamWaitEvent = 200, + HIP_API_ID_hipStreamWaitValue32 = 201, + HIP_API_ID_hipStreamWaitValue64 = 202, + HIP_API_ID_hipStreamWriteValue32 = 203, + HIP_API_ID_hipStreamWriteValue64 = 204, + HIP_API_ID_hipWaitExternalSemaphoresAsync = 205, + HIP_API_ID_hipCreateSurfaceObject = 206, + HIP_API_ID_hipDestroySurfaceObject = 207, + HIP_API_ID_hipGraphAddKernelNode = 208, + HIP_API_ID_hipGraphAddMemcpyNode = 209, + HIP_API_ID_hipGraphAddMemsetNode = 210, + HIP_API_ID_hipGraphCreate = 211, + HIP_API_ID_hipGraphDestroy = 212, + HIP_API_ID_hipGraphExecDestroy = 213, + HIP_API_ID_hipGraphInstantiate = 214, + HIP_API_ID_hipGraphLaunch = 215, + HIP_API_ID_hipMipmappedArrayCreate = 216, + HIP_API_ID_hipMipmappedArrayDestroy = 217, + HIP_API_ID_hipMipmappedArrayGetLevel = 218, + HIP_API_ID_hipStreamBeginCapture = 219, + HIP_API_ID_hipStreamEndCapture = 220, + HIP_API_ID_hipTexRefGetAddress = 221, + HIP_API_ID_hipTexRefGetFlags = 222, + HIP_API_ID_hipTexRefGetFormat = 223, + HIP_API_ID_hipTexRefGetMaxAnisotropy = 224, + HIP_API_ID_hipTexRefGetMipMappedArray = 225, + HIP_API_ID_hipTexRefGetMipmapLevelBias = 226, + HIP_API_ID_hipTexRefGetMipmapLevelClamp = 227, + HIP_API_ID_hipTexRefSetAddress = 228, + HIP_API_ID_hipTexRefSetAddress2D = 229, + HIP_API_ID_hipTexRefSetBorderColor = 230, + HIP_API_ID_hipTexRefSetFormat = 231, + HIP_API_ID_hipTexRefSetMaxAnisotropy = 232, + HIP_API_ID_hipTexRefSetMipmapLevelClamp = 233, + HIP_API_ID_hipTexRefSetMipmappedArray = 234, + HIP_API_ID_hipGLGetDevices = 235, + HIP_API_ID_hipGraphAddDependencies = 236, + HIP_API_ID_hipGraphAddEmptyNode = 237, + HIP_API_ID_hipGraphExecKernelNodeSetParams = 238, + HIP_API_ID_hipGraphGetNodes = 239, + HIP_API_ID_hipGraphGetRootNodes = 240, + HIP_API_ID_hipGraphKernelNodeGetParams = 241, + HIP_API_ID_hipGraphKernelNodeSetParams = 242, + HIP_API_ID_hipGraphMemcpyNodeGetParams = 243, + HIP_API_ID_hipGraphMemcpyNodeSetParams = 244, + HIP_API_ID_hipGraphMemsetNodeGetParams = 245, + HIP_API_ID_hipGraphMemsetNodeSetParams = 246, + HIP_API_ID_hipGraphicsGLRegisterBuffer = 247, + HIP_API_ID_hipGraphicsMapResources = 248, + HIP_API_ID_hipGraphicsResourceGetMappedPointer = 249, + HIP_API_ID_hipGraphicsUnmapResources = 250, + HIP_API_ID_hipGraphicsUnregisterResource = 251, + HIP_API_ID_hipGraphAddChildGraphNode = 252, + HIP_API_ID_hipGraphAddEventRecordNode = 253, + HIP_API_ID_hipGraphAddEventWaitNode = 254, + HIP_API_ID_hipGraphAddHostNode = 255, + HIP_API_ID_hipGraphAddMemcpyNode1D = 256, + HIP_API_ID_hipGraphAddMemcpyNodeFromSymbol = 257, + HIP_API_ID_hipGraphAddMemcpyNodeToSymbol = 258, + HIP_API_ID_hipGraphChildGraphNodeGetGraph = 259, + HIP_API_ID_hipGraphClone = 260, + HIP_API_ID_hipGraphDestroyNode = 261, + HIP_API_ID_hipGraphEventRecordNodeGetEvent = 262, + HIP_API_ID_hipGraphEventRecordNodeSetEvent = 263, + HIP_API_ID_hipGraphEventWaitNodeGetEvent = 264, + HIP_API_ID_hipGraphEventWaitNodeSetEvent = 265, + HIP_API_ID_hipGraphExecChildGraphNodeSetParams = 266, + HIP_API_ID_hipGraphExecEventRecordNodeSetEvent = 267, + HIP_API_ID_hipGraphExecEventWaitNodeSetEvent = 268, + HIP_API_ID_hipGraphExecHostNodeSetParams = 269, + HIP_API_ID_hipGraphExecMemcpyNodeSetParams = 270, + HIP_API_ID_hipGraphExecMemcpyNodeSetParams1D = 271, + HIP_API_ID_hipGraphExecMemcpyNodeSetParamsFromSymbol = 272, + HIP_API_ID_hipGraphExecMemcpyNodeSetParamsToSymbol = 273, + HIP_API_ID_hipGraphExecMemsetNodeSetParams = 274, + HIP_API_ID_hipGraphExecUpdate = 275, + HIP_API_ID_hipGraphGetEdges = 276, + HIP_API_ID_hipGraphHostNodeGetParams = 277, + HIP_API_ID_hipGraphHostNodeSetParams = 278, + HIP_API_ID_hipGraphInstantiateWithFlags = 279, + HIP_API_ID_hipGraphMemcpyNodeSetParams1D = 280, + HIP_API_ID_hipGraphMemcpyNodeSetParamsFromSymbol = 281, + HIP_API_ID_hipGraphMemcpyNodeSetParamsToSymbol = 282, + HIP_API_ID_hipGraphNodeFindInClone = 283, + HIP_API_ID_hipGraphNodeGetDependencies = 284, + HIP_API_ID_hipGraphNodeGetDependentNodes = 285, + HIP_API_ID_hipGraphNodeGetType = 286, + HIP_API_ID_hipGraphRemoveDependencies = 287, + HIP_API_ID_hipStreamGetCaptureInfo = 288, + HIP_API_ID_hipStreamGetCaptureInfo_v2 = 289, + HIP_API_ID_hipStreamIsCapturing = 290, + HIP_API_ID_hipStreamUpdateCaptureDependencies = 291, + HIP_API_ID_hipDrvPointerGetAttributes = 292, + HIP_API_ID_hipGraphicsGLRegisterImage = 293, + HIP_API_ID_hipGraphicsSubResourceGetMappedArray = 294, + HIP_API_ID_hipPointerGetAttribute = 295, + HIP_API_ID_RESERVED_296 = 296, + HIP_API_ID_hipThreadExchangeStreamCaptureMode = 297, + HIP_API_ID_hipDeviceGetUuid = 298, + HIP_API_ID_hipGetChannelDesc = 299, + HIP_API_ID_hipGraphKernelNodeGetAttribute = 300, + HIP_API_ID_hipGraphKernelNodeSetAttribute = 301, + HIP_API_ID_hipLaunchHostFunc = 302, + HIP_API_ID_hipDeviceGetDefaultMemPool = 303, + HIP_API_ID_hipDeviceGetMemPool = 304, + HIP_API_ID_hipDeviceSetMemPool = 305, + HIP_API_ID_hipFreeAsync = 306, + HIP_API_ID_hipMallocAsync = 307, + HIP_API_ID_hipMallocFromPoolAsync = 308, + HIP_API_ID_hipMemPoolCreate = 309, + HIP_API_ID_hipMemPoolDestroy = 310, + HIP_API_ID_hipMemPoolExportPointer = 311, + HIP_API_ID_hipMemPoolExportToShareableHandle = 312, + HIP_API_ID_hipMemPoolGetAccess = 313, + HIP_API_ID_hipMemPoolGetAttribute = 314, + HIP_API_ID_hipMemPoolImportFromShareableHandle = 315, + HIP_API_ID_hipMemPoolImportPointer = 316, + HIP_API_ID_hipMemPoolSetAccess = 317, + HIP_API_ID_hipMemPoolSetAttribute = 318, + HIP_API_ID_hipMemPoolTrimTo = 319, + HIP_API_ID_hipMemAddressFree = 320, + HIP_API_ID_hipMemAddressReserve = 321, + HIP_API_ID_hipMemCreate = 322, + HIP_API_ID_hipMemExportToShareableHandle = 323, + HIP_API_ID_hipMemGetAccess = 324, + HIP_API_ID_hipMemGetAllocationGranularity = 325, + HIP_API_ID_hipMemGetAllocationPropertiesFromHandle = 326, + HIP_API_ID_hipMemImportFromShareableHandle = 327, + HIP_API_ID_hipMemMap = 328, + HIP_API_ID_hipMemMapArrayAsync = 329, + HIP_API_ID_hipMemRelease = 330, + HIP_API_ID_hipMemRetainAllocationHandle = 331, + HIP_API_ID_hipMemSetAccess = 332, + HIP_API_ID_hipMemUnmap = 333, + HIP_API_ID_hipDeviceSetGraphMemAttribute = 334, + HIP_API_ID_hipDeviceGetGraphMemAttribute = 335, + HIP_API_ID_hipDeviceGraphMemTrim = 336, + HIP_API_ID_hipDeviceSetLimit = 337, + HIP_API_ID_hipTexRefSetArray = 338, + HIP_API_ID_hipTexRefSetFlags = 339, + HIP_API_ID_hipTexRefSetMipmapLevelBias = 340, + HIP_API_ID_hipDriverGetVersion = 341, + HIP_API_ID_hipGraphUpload = 342, + HIP_API_ID_hipRuntimeGetVersion = 343, + HIP_API_ID_hipUserObjectCreate = 344, + HIP_API_ID_hipUserObjectRelease = 345, + HIP_API_ID_hipUserObjectRetain = 346, + HIP_API_ID_hipGraphRetainUserObject = 347, + HIP_API_ID_hipGraphReleaseUserObject = 348, + HIP_API_ID_hipGraphDebugDotPrint = 349, + HIP_API_ID_hipGraphKernelNodeCopyAttributes = 350, + HIP_API_ID_hipGraphNodeGetEnabled = 351, + HIP_API_ID_hipGraphNodeSetEnabled = 352, + HIP_API_ID_hipPointerSetAttribute = 353, + HIP_API_ID_hipGraphAddMemAllocNode = 354, + HIP_API_ID_hipGraphAddMemFreeNode = 355, + HIP_API_ID_hipGraphMemAllocNodeGetParams = 356, + HIP_API_ID_hipGraphMemFreeNodeGetParams = 357, + HIP_API_ID_hipModuleLaunchCooperativeKernel = 358, + HIP_API_ID_hipModuleLaunchCooperativeKernelMultiDevice = 359, + HIP_API_ID_hipArray3DGetDescriptor = 360, + HIP_API_ID_hipArrayGetDescriptor = 361, + HIP_API_ID_hipArrayGetInfo = 362, + HIP_API_ID_hipStreamGetDevice = 363, + HIP_API_ID_hipExternalMemoryGetMappedMipmappedArray = 364, + HIP_API_ID_hipChooseDeviceR0600 = 365, + HIP_API_ID_hipDrvGraphAddMemcpyNode = 366, + HIP_API_ID_hipDrvGraphAddMemsetNode = 367, + HIP_API_ID_hipDrvGraphMemcpyNodeGetParams = 368, + HIP_API_ID_hipDrvGraphMemcpyNodeSetParams = 369, + HIP_API_ID_hipGetDevicePropertiesR0600 = 370, + HIP_API_ID_hipGraphAddExternalSemaphoresSignalNode = 371, + HIP_API_ID_hipGraphAddExternalSemaphoresWaitNode = 372, + HIP_API_ID_hipGraphExecExternalSemaphoresSignalNodeSetParams = 373, + HIP_API_ID_hipGraphExecExternalSemaphoresWaitNodeSetParams = 374, + HIP_API_ID_hipGraphExternalSemaphoresSignalNodeGetParams = 375, + HIP_API_ID_hipGraphExternalSemaphoresSignalNodeSetParams = 376, + HIP_API_ID_hipGraphExternalSemaphoresWaitNodeGetParams = 377, + HIP_API_ID_hipGraphExternalSemaphoresWaitNodeSetParams = 378, + HIP_API_ID_hipExtGetLastError = 379, + HIP_API_ID_LAST = 379, + + HIP_API_ID_hipChooseDevice = HIP_API_ID_CONCAT(HIP_API_ID_,hipChooseDevice), + HIP_API_ID_hipGetDeviceProperties = HIP_API_ID_CONCAT(HIP_API_ID_,hipGetDeviceProperties), + + HIP_API_ID_hipBindTexture = HIP_API_ID_NONE, + HIP_API_ID_hipBindTexture2D = HIP_API_ID_NONE, + HIP_API_ID_hipBindTextureToArray = HIP_API_ID_NONE, + HIP_API_ID_hipBindTextureToMipmappedArray = HIP_API_ID_NONE, + HIP_API_ID_hipCreateTextureObject = HIP_API_ID_NONE, + HIP_API_ID_hipDestroyTextureObject = HIP_API_ID_NONE, + HIP_API_ID_hipDeviceGetCount = HIP_API_ID_NONE, + HIP_API_ID_hipGetTextureAlignmentOffset = HIP_API_ID_NONE, + HIP_API_ID_hipGetTextureObjectResourceDesc = HIP_API_ID_NONE, + HIP_API_ID_hipGetTextureObjectResourceViewDesc = HIP_API_ID_NONE, + HIP_API_ID_hipGetTextureObjectTextureDesc = HIP_API_ID_NONE, + HIP_API_ID_hipGetTextureReference = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpy2DArrayToArray = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpyAtoA = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpyAtoD = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpyAtoHAsync = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpyDtoA = HIP_API_ID_NONE, + HIP_API_ID_hipMemcpyHtoAAsync = HIP_API_ID_NONE, + HIP_API_ID_hipSetValidDevices = HIP_API_ID_NONE, + HIP_API_ID_hipTexObjectCreate = HIP_API_ID_NONE, + HIP_API_ID_hipTexObjectDestroy = HIP_API_ID_NONE, + HIP_API_ID_hipTexObjectGetResourceDesc = HIP_API_ID_NONE, + HIP_API_ID_hipTexObjectGetResourceViewDesc = HIP_API_ID_NONE, + HIP_API_ID_hipTexObjectGetTextureDesc = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetAddressMode = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetArray = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetBorderColor = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetFilterMode = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetMipmapFilterMode = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefGetMipmappedArray = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefSetAddressMode = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefSetFilterMode = HIP_API_ID_NONE, + HIP_API_ID_hipTexRefSetMipmapFilterMode = HIP_API_ID_NONE, + HIP_API_ID_hipUnbindTexture = HIP_API_ID_NONE, +}; + +#undef HIP_API_ID_CONCAT_HELPER +#undef HIP_API_ID_CONCAT + +// Return the HIP API string for a given callback ID +static inline const char* hip_api_name(const uint32_t id) { + switch(id) { + case HIP_API_ID___hipPopCallConfiguration: return "__hipPopCallConfiguration"; + case HIP_API_ID___hipPushCallConfiguration: return "__hipPushCallConfiguration"; + case HIP_API_ID_hipArray3DCreate: return "hipArray3DCreate"; + case HIP_API_ID_hipArray3DGetDescriptor: return "hipArray3DGetDescriptor"; + case HIP_API_ID_hipArrayCreate: return "hipArrayCreate"; + case HIP_API_ID_hipArrayDestroy: return "hipArrayDestroy"; + case HIP_API_ID_hipArrayGetDescriptor: return "hipArrayGetDescriptor"; + case HIP_API_ID_hipArrayGetInfo: return "hipArrayGetInfo"; + case HIP_API_ID_hipChooseDeviceR0000: return "hipChooseDeviceR0000"; + case HIP_API_ID_hipChooseDeviceR0600: return "hipChooseDeviceR0600"; + case HIP_API_ID_hipConfigureCall: return "hipConfigureCall"; + case HIP_API_ID_hipCreateSurfaceObject: return "hipCreateSurfaceObject"; + case HIP_API_ID_hipCtxCreate: return "hipCtxCreate"; + case HIP_API_ID_hipCtxDestroy: return "hipCtxDestroy"; + case HIP_API_ID_hipCtxDisablePeerAccess: return "hipCtxDisablePeerAccess"; + case HIP_API_ID_hipCtxEnablePeerAccess: return "hipCtxEnablePeerAccess"; + case HIP_API_ID_hipCtxGetApiVersion: return "hipCtxGetApiVersion"; + case HIP_API_ID_hipCtxGetCacheConfig: return "hipCtxGetCacheConfig"; + case HIP_API_ID_hipCtxGetCurrent: return "hipCtxGetCurrent"; + case HIP_API_ID_hipCtxGetDevice: return "hipCtxGetDevice"; + case HIP_API_ID_hipCtxGetFlags: return "hipCtxGetFlags"; + case HIP_API_ID_hipCtxGetSharedMemConfig: return "hipCtxGetSharedMemConfig"; + case HIP_API_ID_hipCtxPopCurrent: return "hipCtxPopCurrent"; + case HIP_API_ID_hipCtxPushCurrent: return "hipCtxPushCurrent"; + case HIP_API_ID_hipCtxSetCacheConfig: return "hipCtxSetCacheConfig"; + case HIP_API_ID_hipCtxSetCurrent: return "hipCtxSetCurrent"; + case HIP_API_ID_hipCtxSetSharedMemConfig: return "hipCtxSetSharedMemConfig"; + case HIP_API_ID_hipCtxSynchronize: return "hipCtxSynchronize"; + case HIP_API_ID_hipDestroyExternalMemory: return "hipDestroyExternalMemory"; + case HIP_API_ID_hipDestroyExternalSemaphore: return "hipDestroyExternalSemaphore"; + case HIP_API_ID_hipDestroySurfaceObject: return "hipDestroySurfaceObject"; + case HIP_API_ID_hipDeviceCanAccessPeer: return "hipDeviceCanAccessPeer"; + case HIP_API_ID_hipDeviceComputeCapability: return "hipDeviceComputeCapability"; + case HIP_API_ID_hipDeviceDisablePeerAccess: return "hipDeviceDisablePeerAccess"; + case HIP_API_ID_hipDeviceEnablePeerAccess: return "hipDeviceEnablePeerAccess"; + case HIP_API_ID_hipDeviceGet: return "hipDeviceGet"; + case HIP_API_ID_hipDeviceGetAttribute: return "hipDeviceGetAttribute"; + case HIP_API_ID_hipDeviceGetByPCIBusId: return "hipDeviceGetByPCIBusId"; + case HIP_API_ID_hipDeviceGetCacheConfig: return "hipDeviceGetCacheConfig"; + case HIP_API_ID_hipDeviceGetDefaultMemPool: return "hipDeviceGetDefaultMemPool"; + case HIP_API_ID_hipDeviceGetGraphMemAttribute: return "hipDeviceGetGraphMemAttribute"; + case HIP_API_ID_hipDeviceGetLimit: return "hipDeviceGetLimit"; + case HIP_API_ID_hipDeviceGetMemPool: return "hipDeviceGetMemPool"; + case HIP_API_ID_hipDeviceGetName: return "hipDeviceGetName"; + case HIP_API_ID_hipDeviceGetP2PAttribute: return "hipDeviceGetP2PAttribute"; + case HIP_API_ID_hipDeviceGetPCIBusId: return "hipDeviceGetPCIBusId"; + case HIP_API_ID_hipDeviceGetSharedMemConfig: return "hipDeviceGetSharedMemConfig"; + case HIP_API_ID_hipDeviceGetStreamPriorityRange: return "hipDeviceGetStreamPriorityRange"; + case HIP_API_ID_hipDeviceGetUuid: return "hipDeviceGetUuid"; + case HIP_API_ID_hipDeviceGraphMemTrim: return "hipDeviceGraphMemTrim"; + case HIP_API_ID_hipDevicePrimaryCtxGetState: return "hipDevicePrimaryCtxGetState"; + case HIP_API_ID_hipDevicePrimaryCtxRelease: return "hipDevicePrimaryCtxRelease"; + case HIP_API_ID_hipDevicePrimaryCtxReset: return "hipDevicePrimaryCtxReset"; + case HIP_API_ID_hipDevicePrimaryCtxRetain: return "hipDevicePrimaryCtxRetain"; + case HIP_API_ID_hipDevicePrimaryCtxSetFlags: return "hipDevicePrimaryCtxSetFlags"; + case HIP_API_ID_hipDeviceReset: return "hipDeviceReset"; + case HIP_API_ID_hipDeviceSetCacheConfig: return "hipDeviceSetCacheConfig"; + case HIP_API_ID_hipDeviceSetGraphMemAttribute: return "hipDeviceSetGraphMemAttribute"; + case HIP_API_ID_hipDeviceSetLimit: return "hipDeviceSetLimit"; + case HIP_API_ID_hipDeviceSetMemPool: return "hipDeviceSetMemPool"; + case HIP_API_ID_hipDeviceSetSharedMemConfig: return "hipDeviceSetSharedMemConfig"; + case HIP_API_ID_hipDeviceSynchronize: return "hipDeviceSynchronize"; + case HIP_API_ID_hipDeviceTotalMem: return "hipDeviceTotalMem"; + case HIP_API_ID_hipDriverGetVersion: return "hipDriverGetVersion"; + case HIP_API_ID_hipDrvGraphAddMemcpyNode: return "hipDrvGraphAddMemcpyNode"; + case HIP_API_ID_hipDrvGraphAddMemsetNode: return "hipDrvGraphAddMemsetNode"; + case HIP_API_ID_hipDrvGraphMemcpyNodeGetParams: return "hipDrvGraphMemcpyNodeGetParams"; + case HIP_API_ID_hipDrvGraphMemcpyNodeSetParams: return "hipDrvGraphMemcpyNodeSetParams"; + case HIP_API_ID_hipDrvMemcpy2DUnaligned: return "hipDrvMemcpy2DUnaligned"; + case HIP_API_ID_hipDrvMemcpy3D: return "hipDrvMemcpy3D"; + case HIP_API_ID_hipDrvMemcpy3DAsync: return "hipDrvMemcpy3DAsync"; + case HIP_API_ID_hipDrvPointerGetAttributes: return "hipDrvPointerGetAttributes"; + case HIP_API_ID_hipEventCreate: return "hipEventCreate"; + case HIP_API_ID_hipEventCreateWithFlags: return "hipEventCreateWithFlags"; + case HIP_API_ID_hipEventDestroy: return "hipEventDestroy"; + case HIP_API_ID_hipEventElapsedTime: return "hipEventElapsedTime"; + case HIP_API_ID_hipEventQuery: return "hipEventQuery"; + case HIP_API_ID_hipEventRecord: return "hipEventRecord"; + case HIP_API_ID_hipEventSynchronize: return "hipEventSynchronize"; + case HIP_API_ID_hipExtGetLinkTypeAndHopCount: return "hipExtGetLinkTypeAndHopCount"; + case HIP_API_ID_hipExtLaunchKernel: return "hipExtLaunchKernel"; + case HIP_API_ID_hipExtLaunchMultiKernelMultiDevice: return "hipExtLaunchMultiKernelMultiDevice"; + case HIP_API_ID_hipExtMallocWithFlags: return "hipExtMallocWithFlags"; + case HIP_API_ID_hipExtModuleLaunchKernel: return "hipExtModuleLaunchKernel"; + case HIP_API_ID_hipExtStreamCreateWithCUMask: return "hipExtStreamCreateWithCUMask"; + case HIP_API_ID_hipExtStreamGetCUMask: return "hipExtStreamGetCUMask"; + case HIP_API_ID_hipExternalMemoryGetMappedBuffer: return "hipExternalMemoryGetMappedBuffer"; + case HIP_API_ID_hipExternalMemoryGetMappedMipmappedArray: return "hipExternalMemoryGetMappedMipmappedArray"; + case HIP_API_ID_hipFree: return "hipFree"; + case HIP_API_ID_hipFreeArray: return "hipFreeArray"; + case HIP_API_ID_hipFreeAsync: return "hipFreeAsync"; + case HIP_API_ID_hipFreeHost: return "hipFreeHost"; + case HIP_API_ID_hipFreeMipmappedArray: return "hipFreeMipmappedArray"; + case HIP_API_ID_hipFuncGetAttribute: return "hipFuncGetAttribute"; + case HIP_API_ID_hipFuncGetAttributes: return "hipFuncGetAttributes"; + case HIP_API_ID_hipFuncSetAttribute: return "hipFuncSetAttribute"; + case HIP_API_ID_hipFuncSetCacheConfig: return "hipFuncSetCacheConfig"; + case HIP_API_ID_hipFuncSetSharedMemConfig: return "hipFuncSetSharedMemConfig"; + case HIP_API_ID_hipGLGetDevices: return "hipGLGetDevices"; + case HIP_API_ID_hipGetChannelDesc: return "hipGetChannelDesc"; + case HIP_API_ID_hipGetDevice: return "hipGetDevice"; + case HIP_API_ID_hipGetDeviceCount: return "hipGetDeviceCount"; + case HIP_API_ID_hipGetDeviceFlags: return "hipGetDeviceFlags"; + case HIP_API_ID_hipGetDevicePropertiesR0000: return "hipGetDevicePropertiesR0000"; + case HIP_API_ID_hipGetDevicePropertiesR0600: return "hipGetDevicePropertiesR0600"; + case HIP_API_ID_hipGetErrorString: return "hipGetErrorString"; + case HIP_API_ID_hipGetLastError: return "hipGetLastError"; + case HIP_API_ID_hipGetMipmappedArrayLevel: return "hipGetMipmappedArrayLevel"; + case HIP_API_ID_hipGetSymbolAddress: return "hipGetSymbolAddress"; + case HIP_API_ID_hipGetSymbolSize: return "hipGetSymbolSize"; + case HIP_API_ID_hipGraphAddChildGraphNode: return "hipGraphAddChildGraphNode"; + case HIP_API_ID_hipGraphAddDependencies: return "hipGraphAddDependencies"; + case HIP_API_ID_hipGraphAddEmptyNode: return "hipGraphAddEmptyNode"; + case HIP_API_ID_hipGraphAddEventRecordNode: return "hipGraphAddEventRecordNode"; + case HIP_API_ID_hipGraphAddEventWaitNode: return "hipGraphAddEventWaitNode"; + case HIP_API_ID_hipGraphAddExternalSemaphoresSignalNode: return "hipGraphAddExternalSemaphoresSignalNode"; + case HIP_API_ID_hipGraphAddExternalSemaphoresWaitNode: return "hipGraphAddExternalSemaphoresWaitNode"; + case HIP_API_ID_hipGraphAddHostNode: return "hipGraphAddHostNode"; + case HIP_API_ID_hipGraphAddKernelNode: return "hipGraphAddKernelNode"; + case HIP_API_ID_hipGraphAddMemAllocNode: return "hipGraphAddMemAllocNode"; + case HIP_API_ID_hipGraphAddMemFreeNode: return "hipGraphAddMemFreeNode"; + case HIP_API_ID_hipGraphAddMemcpyNode: return "hipGraphAddMemcpyNode"; + case HIP_API_ID_hipGraphAddMemcpyNode1D: return "hipGraphAddMemcpyNode1D"; + case HIP_API_ID_hipGraphAddMemcpyNodeFromSymbol: return "hipGraphAddMemcpyNodeFromSymbol"; + case HIP_API_ID_hipGraphAddMemcpyNodeToSymbol: return "hipGraphAddMemcpyNodeToSymbol"; + case HIP_API_ID_hipGraphAddMemsetNode: return "hipGraphAddMemsetNode"; + case HIP_API_ID_hipGraphChildGraphNodeGetGraph: return "hipGraphChildGraphNodeGetGraph"; + case HIP_API_ID_hipGraphClone: return "hipGraphClone"; + case HIP_API_ID_hipGraphCreate: return "hipGraphCreate"; + case HIP_API_ID_hipGraphDebugDotPrint: return "hipGraphDebugDotPrint"; + case HIP_API_ID_hipGraphDestroy: return "hipGraphDestroy"; + case HIP_API_ID_hipGraphDestroyNode: return "hipGraphDestroyNode"; + case HIP_API_ID_hipGraphEventRecordNodeGetEvent: return "hipGraphEventRecordNodeGetEvent"; + case HIP_API_ID_hipGraphEventRecordNodeSetEvent: return "hipGraphEventRecordNodeSetEvent"; + case HIP_API_ID_hipGraphEventWaitNodeGetEvent: return "hipGraphEventWaitNodeGetEvent"; + case HIP_API_ID_hipGraphEventWaitNodeSetEvent: return "hipGraphEventWaitNodeSetEvent"; + case HIP_API_ID_hipGraphExecChildGraphNodeSetParams: return "hipGraphExecChildGraphNodeSetParams"; + case HIP_API_ID_hipGraphExecDestroy: return "hipGraphExecDestroy"; + case HIP_API_ID_hipGraphExecEventRecordNodeSetEvent: return "hipGraphExecEventRecordNodeSetEvent"; + case HIP_API_ID_hipGraphExecEventWaitNodeSetEvent: return "hipGraphExecEventWaitNodeSetEvent"; + case HIP_API_ID_hipGraphExecExternalSemaphoresSignalNodeSetParams: return "hipGraphExecExternalSemaphoresSignalNodeSetParams"; + case HIP_API_ID_hipGraphExecExternalSemaphoresWaitNodeSetParams: return "hipGraphExecExternalSemaphoresWaitNodeSetParams"; + case HIP_API_ID_hipGraphExecHostNodeSetParams: return "hipGraphExecHostNodeSetParams"; + case HIP_API_ID_hipGraphExecKernelNodeSetParams: return "hipGraphExecKernelNodeSetParams"; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams: return "hipGraphExecMemcpyNodeSetParams"; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams1D: return "hipGraphExecMemcpyNodeSetParams1D"; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsFromSymbol: return "hipGraphExecMemcpyNodeSetParamsFromSymbol"; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsToSymbol: return "hipGraphExecMemcpyNodeSetParamsToSymbol"; + case HIP_API_ID_hipGraphExecMemsetNodeSetParams: return "hipGraphExecMemsetNodeSetParams"; + case HIP_API_ID_hipGraphExecUpdate: return "hipGraphExecUpdate"; + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeGetParams: return "hipGraphExternalSemaphoresSignalNodeGetParams"; + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeSetParams: return "hipGraphExternalSemaphoresSignalNodeSetParams"; + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeGetParams: return "hipGraphExternalSemaphoresWaitNodeGetParams"; + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeSetParams: return "hipGraphExternalSemaphoresWaitNodeSetParams"; + case HIP_API_ID_hipGraphGetEdges: return "hipGraphGetEdges"; + case HIP_API_ID_hipGraphGetNodes: return "hipGraphGetNodes"; + case HIP_API_ID_hipGraphGetRootNodes: return "hipGraphGetRootNodes"; + case HIP_API_ID_hipGraphHostNodeGetParams: return "hipGraphHostNodeGetParams"; + case HIP_API_ID_hipGraphHostNodeSetParams: return "hipGraphHostNodeSetParams"; + case HIP_API_ID_hipGraphInstantiate: return "hipGraphInstantiate"; + case HIP_API_ID_hipGraphInstantiateWithFlags: return "hipGraphInstantiateWithFlags"; + case HIP_API_ID_hipGraphKernelNodeCopyAttributes: return "hipGraphKernelNodeCopyAttributes"; + case HIP_API_ID_hipGraphKernelNodeGetAttribute: return "hipGraphKernelNodeGetAttribute"; + case HIP_API_ID_hipGraphKernelNodeGetParams: return "hipGraphKernelNodeGetParams"; + case HIP_API_ID_hipGraphKernelNodeSetAttribute: return "hipGraphKernelNodeSetAttribute"; + case HIP_API_ID_hipGraphKernelNodeSetParams: return "hipGraphKernelNodeSetParams"; + case HIP_API_ID_hipGraphLaunch: return "hipGraphLaunch"; + case HIP_API_ID_hipGraphMemAllocNodeGetParams: return "hipGraphMemAllocNodeGetParams"; + case HIP_API_ID_hipGraphMemFreeNodeGetParams: return "hipGraphMemFreeNodeGetParams"; + case HIP_API_ID_hipGraphMemcpyNodeGetParams: return "hipGraphMemcpyNodeGetParams"; + case HIP_API_ID_hipGraphMemcpyNodeSetParams: return "hipGraphMemcpyNodeSetParams"; + case HIP_API_ID_hipGraphMemcpyNodeSetParams1D: return "hipGraphMemcpyNodeSetParams1D"; + case HIP_API_ID_hipGraphMemcpyNodeSetParamsFromSymbol: return "hipGraphMemcpyNodeSetParamsFromSymbol"; + case HIP_API_ID_hipGraphMemcpyNodeSetParamsToSymbol: return "hipGraphMemcpyNodeSetParamsToSymbol"; + case HIP_API_ID_hipGraphMemsetNodeGetParams: return "hipGraphMemsetNodeGetParams"; + case HIP_API_ID_hipGraphMemsetNodeSetParams: return "hipGraphMemsetNodeSetParams"; + case HIP_API_ID_hipGraphNodeFindInClone: return "hipGraphNodeFindInClone"; + case HIP_API_ID_hipGraphNodeGetDependencies: return "hipGraphNodeGetDependencies"; + case HIP_API_ID_hipGraphNodeGetDependentNodes: return "hipGraphNodeGetDependentNodes"; + case HIP_API_ID_hipGraphNodeGetEnabled: return "hipGraphNodeGetEnabled"; + case HIP_API_ID_hipGraphNodeGetType: return "hipGraphNodeGetType"; + case HIP_API_ID_hipGraphNodeSetEnabled: return "hipGraphNodeSetEnabled"; + case HIP_API_ID_hipGraphReleaseUserObject: return "hipGraphReleaseUserObject"; + case HIP_API_ID_hipGraphRemoveDependencies: return "hipGraphRemoveDependencies"; + case HIP_API_ID_hipGraphRetainUserObject: return "hipGraphRetainUserObject"; + case HIP_API_ID_hipGraphUpload: return "hipGraphUpload"; + case HIP_API_ID_hipGraphicsGLRegisterBuffer: return "hipGraphicsGLRegisterBuffer"; + case HIP_API_ID_hipGraphicsGLRegisterImage: return "hipGraphicsGLRegisterImage"; + case HIP_API_ID_hipGraphicsMapResources: return "hipGraphicsMapResources"; + case HIP_API_ID_hipGraphicsResourceGetMappedPointer: return "hipGraphicsResourceGetMappedPointer"; + case HIP_API_ID_hipGraphicsSubResourceGetMappedArray: return "hipGraphicsSubResourceGetMappedArray"; + case HIP_API_ID_hipGraphicsUnmapResources: return "hipGraphicsUnmapResources"; + case HIP_API_ID_hipGraphicsUnregisterResource: return "hipGraphicsUnregisterResource"; + case HIP_API_ID_hipHccModuleLaunchKernel: return "hipHccModuleLaunchKernel"; + case HIP_API_ID_hipHostAlloc: return "hipHostAlloc"; + case HIP_API_ID_hipHostFree: return "hipHostFree"; + case HIP_API_ID_hipHostGetDevicePointer: return "hipHostGetDevicePointer"; + case HIP_API_ID_hipHostGetFlags: return "hipHostGetFlags"; + case HIP_API_ID_hipHostMalloc: return "hipHostMalloc"; + case HIP_API_ID_hipHostRegister: return "hipHostRegister"; + case HIP_API_ID_hipHostUnregister: return "hipHostUnregister"; + case HIP_API_ID_hipImportExternalMemory: return "hipImportExternalMemory"; + case HIP_API_ID_hipImportExternalSemaphore: return "hipImportExternalSemaphore"; + case HIP_API_ID_hipInit: return "hipInit"; + case HIP_API_ID_hipIpcCloseMemHandle: return "hipIpcCloseMemHandle"; + case HIP_API_ID_hipIpcGetEventHandle: return "hipIpcGetEventHandle"; + case HIP_API_ID_hipIpcGetMemHandle: return "hipIpcGetMemHandle"; + case HIP_API_ID_hipIpcOpenEventHandle: return "hipIpcOpenEventHandle"; + case HIP_API_ID_hipIpcOpenMemHandle: return "hipIpcOpenMemHandle"; + case HIP_API_ID_hipLaunchByPtr: return "hipLaunchByPtr"; + case HIP_API_ID_hipLaunchCooperativeKernel: return "hipLaunchCooperativeKernel"; + case HIP_API_ID_hipLaunchCooperativeKernelMultiDevice: return "hipLaunchCooperativeKernelMultiDevice"; + case HIP_API_ID_hipLaunchHostFunc: return "hipLaunchHostFunc"; + case HIP_API_ID_hipLaunchKernel: return "hipLaunchKernel"; + case HIP_API_ID_hipMalloc: return "hipMalloc"; + case HIP_API_ID_hipMalloc3D: return "hipMalloc3D"; + case HIP_API_ID_hipMalloc3DArray: return "hipMalloc3DArray"; + case HIP_API_ID_hipMallocArray: return "hipMallocArray"; + case HIP_API_ID_hipMallocAsync: return "hipMallocAsync"; + case HIP_API_ID_hipMallocFromPoolAsync: return "hipMallocFromPoolAsync"; + case HIP_API_ID_hipMallocHost: return "hipMallocHost"; + case HIP_API_ID_hipMallocManaged: return "hipMallocManaged"; + case HIP_API_ID_hipMallocMipmappedArray: return "hipMallocMipmappedArray"; + case HIP_API_ID_hipMallocPitch: return "hipMallocPitch"; + case HIP_API_ID_hipMemAddressFree: return "hipMemAddressFree"; + case HIP_API_ID_hipMemAddressReserve: return "hipMemAddressReserve"; + case HIP_API_ID_hipMemAdvise: return "hipMemAdvise"; + case HIP_API_ID_hipMemAllocHost: return "hipMemAllocHost"; + case HIP_API_ID_hipMemAllocPitch: return "hipMemAllocPitch"; + case HIP_API_ID_hipMemCreate: return "hipMemCreate"; + case HIP_API_ID_hipMemExportToShareableHandle: return "hipMemExportToShareableHandle"; + case HIP_API_ID_hipMemGetAccess: return "hipMemGetAccess"; + case HIP_API_ID_hipMemGetAddressRange: return "hipMemGetAddressRange"; + case HIP_API_ID_hipMemGetAllocationGranularity: return "hipMemGetAllocationGranularity"; + case HIP_API_ID_hipMemGetAllocationPropertiesFromHandle: return "hipMemGetAllocationPropertiesFromHandle"; + case HIP_API_ID_hipMemGetInfo: return "hipMemGetInfo"; + case HIP_API_ID_hipMemImportFromShareableHandle: return "hipMemImportFromShareableHandle"; + case HIP_API_ID_hipMemMap: return "hipMemMap"; + case HIP_API_ID_hipMemMapArrayAsync: return "hipMemMapArrayAsync"; + case HIP_API_ID_hipMemPoolCreate: return "hipMemPoolCreate"; + case HIP_API_ID_hipMemPoolDestroy: return "hipMemPoolDestroy"; + case HIP_API_ID_hipMemPoolExportPointer: return "hipMemPoolExportPointer"; + case HIP_API_ID_hipMemPoolExportToShareableHandle: return "hipMemPoolExportToShareableHandle"; + case HIP_API_ID_hipMemPoolGetAccess: return "hipMemPoolGetAccess"; + case HIP_API_ID_hipMemPoolGetAttribute: return "hipMemPoolGetAttribute"; + case HIP_API_ID_hipMemPoolImportFromShareableHandle: return "hipMemPoolImportFromShareableHandle"; + case HIP_API_ID_hipMemPoolImportPointer: return "hipMemPoolImportPointer"; + case HIP_API_ID_hipMemPoolSetAccess: return "hipMemPoolSetAccess"; + case HIP_API_ID_hipMemPoolSetAttribute: return "hipMemPoolSetAttribute"; + case HIP_API_ID_hipMemPoolTrimTo: return "hipMemPoolTrimTo"; + case HIP_API_ID_hipMemPrefetchAsync: return "hipMemPrefetchAsync"; + case HIP_API_ID_hipMemPtrGetInfo: return "hipMemPtrGetInfo"; + case HIP_API_ID_hipMemRangeGetAttribute: return "hipMemRangeGetAttribute"; + case HIP_API_ID_hipMemRangeGetAttributes: return "hipMemRangeGetAttributes"; + case HIP_API_ID_hipMemRelease: return "hipMemRelease"; + case HIP_API_ID_hipMemRetainAllocationHandle: return "hipMemRetainAllocationHandle"; + case HIP_API_ID_hipMemSetAccess: return "hipMemSetAccess"; + case HIP_API_ID_hipMemUnmap: return "hipMemUnmap"; + case HIP_API_ID_hipMemcpy: return "hipMemcpy"; + case HIP_API_ID_hipMemcpy2D: return "hipMemcpy2D"; + case HIP_API_ID_hipMemcpy2DAsync: return "hipMemcpy2DAsync"; + case HIP_API_ID_hipMemcpy2DFromArray: return "hipMemcpy2DFromArray"; + case HIP_API_ID_hipMemcpy2DFromArrayAsync: return "hipMemcpy2DFromArrayAsync"; + case HIP_API_ID_hipMemcpy2DToArray: return "hipMemcpy2DToArray"; + case HIP_API_ID_hipMemcpy2DToArrayAsync: return "hipMemcpy2DToArrayAsync"; + case HIP_API_ID_hipMemcpy3D: return "hipMemcpy3D"; + case HIP_API_ID_hipMemcpy3DAsync: return "hipMemcpy3DAsync"; + case HIP_API_ID_hipMemcpyAsync: return "hipMemcpyAsync"; + case HIP_API_ID_hipMemcpyAtoH: return "hipMemcpyAtoH"; + case HIP_API_ID_hipMemcpyDtoD: return "hipMemcpyDtoD"; + case HIP_API_ID_hipMemcpyDtoDAsync: return "hipMemcpyDtoDAsync"; + case HIP_API_ID_hipMemcpyDtoH: return "hipMemcpyDtoH"; + case HIP_API_ID_hipMemcpyDtoHAsync: return "hipMemcpyDtoHAsync"; + case HIP_API_ID_hipMemcpyFromArray: return "hipMemcpyFromArray"; + case HIP_API_ID_hipMemcpyFromSymbol: return "hipMemcpyFromSymbol"; + case HIP_API_ID_hipMemcpyFromSymbolAsync: return "hipMemcpyFromSymbolAsync"; + case HIP_API_ID_hipMemcpyHtoA: return "hipMemcpyHtoA"; + case HIP_API_ID_hipMemcpyHtoD: return "hipMemcpyHtoD"; + case HIP_API_ID_hipMemcpyHtoDAsync: return "hipMemcpyHtoDAsync"; + case HIP_API_ID_hipMemcpyParam2D: return "hipMemcpyParam2D"; + case HIP_API_ID_hipMemcpyParam2DAsync: return "hipMemcpyParam2DAsync"; + case HIP_API_ID_hipMemcpyPeer: return "hipMemcpyPeer"; + case HIP_API_ID_hipMemcpyPeerAsync: return "hipMemcpyPeerAsync"; + case HIP_API_ID_hipMemcpyToArray: return "hipMemcpyToArray"; + case HIP_API_ID_hipMemcpyToSymbol: return "hipMemcpyToSymbol"; + case HIP_API_ID_hipMemcpyToSymbolAsync: return "hipMemcpyToSymbolAsync"; + case HIP_API_ID_hipMemcpyWithStream: return "hipMemcpyWithStream"; + case HIP_API_ID_hipMemset: return "hipMemset"; + case HIP_API_ID_hipMemset2D: return "hipMemset2D"; + case HIP_API_ID_hipMemset2DAsync: return "hipMemset2DAsync"; + case HIP_API_ID_hipMemset3D: return "hipMemset3D"; + case HIP_API_ID_hipMemset3DAsync: return "hipMemset3DAsync"; + case HIP_API_ID_hipMemsetAsync: return "hipMemsetAsync"; + case HIP_API_ID_hipMemsetD16: return "hipMemsetD16"; + case HIP_API_ID_hipMemsetD16Async: return "hipMemsetD16Async"; + case HIP_API_ID_hipMemsetD32: return "hipMemsetD32"; + case HIP_API_ID_hipMemsetD32Async: return "hipMemsetD32Async"; + case HIP_API_ID_hipMemsetD8: return "hipMemsetD8"; + case HIP_API_ID_hipMemsetD8Async: return "hipMemsetD8Async"; + case HIP_API_ID_hipMipmappedArrayCreate: return "hipMipmappedArrayCreate"; + case HIP_API_ID_hipMipmappedArrayDestroy: return "hipMipmappedArrayDestroy"; + case HIP_API_ID_hipMipmappedArrayGetLevel: return "hipMipmappedArrayGetLevel"; + case HIP_API_ID_hipModuleGetFunction: return "hipModuleGetFunction"; + case HIP_API_ID_hipModuleGetGlobal: return "hipModuleGetGlobal"; + case HIP_API_ID_hipModuleGetTexRef: return "hipModuleGetTexRef"; + case HIP_API_ID_hipModuleLaunchCooperativeKernel: return "hipModuleLaunchCooperativeKernel"; + case HIP_API_ID_hipModuleLaunchCooperativeKernelMultiDevice: return "hipModuleLaunchCooperativeKernelMultiDevice"; + case HIP_API_ID_hipModuleLaunchKernel: return "hipModuleLaunchKernel"; + case HIP_API_ID_hipModuleLoad: return "hipModuleLoad"; + case HIP_API_ID_hipModuleLoadData: return "hipModuleLoadData"; + case HIP_API_ID_hipModuleLoadDataEx: return "hipModuleLoadDataEx"; + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor: return "hipModuleOccupancyMaxActiveBlocksPerMultiprocessor"; + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: return "hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags"; + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSize: return "hipModuleOccupancyMaxPotentialBlockSize"; + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSizeWithFlags: return "hipModuleOccupancyMaxPotentialBlockSizeWithFlags"; + case HIP_API_ID_hipModuleUnload: return "hipModuleUnload"; + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessor: return "hipOccupancyMaxActiveBlocksPerMultiprocessor"; + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: return "hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags"; + case HIP_API_ID_hipOccupancyMaxPotentialBlockSize: return "hipOccupancyMaxPotentialBlockSize"; + case HIP_API_ID_hipPeekAtLastError: return "hipPeekAtLastError"; + case HIP_API_ID_hipPointerGetAttribute: return "hipPointerGetAttribute"; + case HIP_API_ID_hipPointerGetAttributes: return "hipPointerGetAttributes"; + case HIP_API_ID_hipPointerSetAttribute: return "hipPointerSetAttribute"; + case HIP_API_ID_hipProfilerStart: return "hipProfilerStart"; + case HIP_API_ID_hipProfilerStop: return "hipProfilerStop"; + case HIP_API_ID_hipRuntimeGetVersion: return "hipRuntimeGetVersion"; + case HIP_API_ID_hipSetDevice: return "hipSetDevice"; + case HIP_API_ID_hipSetDeviceFlags: return "hipSetDeviceFlags"; + case HIP_API_ID_hipSetupArgument: return "hipSetupArgument"; + case HIP_API_ID_hipSignalExternalSemaphoresAsync: return "hipSignalExternalSemaphoresAsync"; + case HIP_API_ID_hipStreamAddCallback: return "hipStreamAddCallback"; + case HIP_API_ID_hipStreamAttachMemAsync: return "hipStreamAttachMemAsync"; + case HIP_API_ID_hipStreamBeginCapture: return "hipStreamBeginCapture"; + case HIP_API_ID_hipStreamCreate: return "hipStreamCreate"; + case HIP_API_ID_hipStreamCreateWithFlags: return "hipStreamCreateWithFlags"; + case HIP_API_ID_hipStreamCreateWithPriority: return "hipStreamCreateWithPriority"; + case HIP_API_ID_hipStreamDestroy: return "hipStreamDestroy"; + case HIP_API_ID_hipStreamEndCapture: return "hipStreamEndCapture"; + case HIP_API_ID_hipStreamGetCaptureInfo: return "hipStreamGetCaptureInfo"; + case HIP_API_ID_hipStreamGetCaptureInfo_v2: return "hipStreamGetCaptureInfo_v2"; + case HIP_API_ID_hipStreamGetDevice: return "hipStreamGetDevice"; + case HIP_API_ID_hipStreamGetFlags: return "hipStreamGetFlags"; + case HIP_API_ID_hipStreamGetPriority: return "hipStreamGetPriority"; + case HIP_API_ID_hipStreamIsCapturing: return "hipStreamIsCapturing"; + case HIP_API_ID_hipStreamQuery: return "hipStreamQuery"; + case HIP_API_ID_hipStreamSynchronize: return "hipStreamSynchronize"; + case HIP_API_ID_hipStreamUpdateCaptureDependencies: return "hipStreamUpdateCaptureDependencies"; + case HIP_API_ID_hipStreamWaitEvent: return "hipStreamWaitEvent"; + case HIP_API_ID_hipStreamWaitValue32: return "hipStreamWaitValue32"; + case HIP_API_ID_hipStreamWaitValue64: return "hipStreamWaitValue64"; + case HIP_API_ID_hipStreamWriteValue32: return "hipStreamWriteValue32"; + case HIP_API_ID_hipStreamWriteValue64: return "hipStreamWriteValue64"; + case HIP_API_ID_hipTexRefGetAddress: return "hipTexRefGetAddress"; + case HIP_API_ID_hipTexRefGetFlags: return "hipTexRefGetFlags"; + case HIP_API_ID_hipTexRefGetFormat: return "hipTexRefGetFormat"; + case HIP_API_ID_hipTexRefGetMaxAnisotropy: return "hipTexRefGetMaxAnisotropy"; + case HIP_API_ID_hipTexRefGetMipMappedArray: return "hipTexRefGetMipMappedArray"; + case HIP_API_ID_hipTexRefGetMipmapLevelBias: return "hipTexRefGetMipmapLevelBias"; + case HIP_API_ID_hipTexRefGetMipmapLevelClamp: return "hipTexRefGetMipmapLevelClamp"; + case HIP_API_ID_hipTexRefSetAddress: return "hipTexRefSetAddress"; + case HIP_API_ID_hipTexRefSetAddress2D: return "hipTexRefSetAddress2D"; + case HIP_API_ID_hipTexRefSetArray: return "hipTexRefSetArray"; + case HIP_API_ID_hipTexRefSetBorderColor: return "hipTexRefSetBorderColor"; + case HIP_API_ID_hipTexRefSetFlags: return "hipTexRefSetFlags"; + case HIP_API_ID_hipTexRefSetFormat: return "hipTexRefSetFormat"; + case HIP_API_ID_hipTexRefSetMaxAnisotropy: return "hipTexRefSetMaxAnisotropy"; + case HIP_API_ID_hipTexRefSetMipmapLevelBias: return "hipTexRefSetMipmapLevelBias"; + case HIP_API_ID_hipTexRefSetMipmapLevelClamp: return "hipTexRefSetMipmapLevelClamp"; + case HIP_API_ID_hipTexRefSetMipmappedArray: return "hipTexRefSetMipmappedArray"; + case HIP_API_ID_hipThreadExchangeStreamCaptureMode: return "hipThreadExchangeStreamCaptureMode"; + case HIP_API_ID_hipUserObjectCreate: return "hipUserObjectCreate"; + case HIP_API_ID_hipUserObjectRelease: return "hipUserObjectRelease"; + case HIP_API_ID_hipUserObjectRetain: return "hipUserObjectRetain"; + case HIP_API_ID_hipWaitExternalSemaphoresAsync: return "hipWaitExternalSemaphoresAsync"; + case HIP_API_ID_hipExtGetLastError: return "hipExtGetLastError"; + }; + return "unknown"; +}; + +#include +// Return the HIP API callback ID for a given name +static inline uint32_t hipApiIdByName(const char* name) { + if (strcmp("__hipPopCallConfiguration", name) == 0) return HIP_API_ID___hipPopCallConfiguration; + if (strcmp("__hipPushCallConfiguration", name) == 0) return HIP_API_ID___hipPushCallConfiguration; + if (strcmp("hipArray3DCreate", name) == 0) return HIP_API_ID_hipArray3DCreate; + if (strcmp("hipArray3DGetDescriptor", name) == 0) return HIP_API_ID_hipArray3DGetDescriptor; + if (strcmp("hipArrayCreate", name) == 0) return HIP_API_ID_hipArrayCreate; + if (strcmp("hipArrayDestroy", name) == 0) return HIP_API_ID_hipArrayDestroy; + if (strcmp("hipArrayGetDescriptor", name) == 0) return HIP_API_ID_hipArrayGetDescriptor; + if (strcmp("hipArrayGetInfo", name) == 0) return HIP_API_ID_hipArrayGetInfo; + if (strcmp("hipChooseDeviceR0000", name) == 0) return HIP_API_ID_hipChooseDeviceR0000; + if (strcmp("hipChooseDeviceR0600", name) == 0) return HIP_API_ID_hipChooseDeviceR0600; + if (strcmp("hipConfigureCall", name) == 0) return HIP_API_ID_hipConfigureCall; + if (strcmp("hipCreateSurfaceObject", name) == 0) return HIP_API_ID_hipCreateSurfaceObject; + if (strcmp("hipCtxCreate", name) == 0) return HIP_API_ID_hipCtxCreate; + if (strcmp("hipCtxDestroy", name) == 0) return HIP_API_ID_hipCtxDestroy; + if (strcmp("hipCtxDisablePeerAccess", name) == 0) return HIP_API_ID_hipCtxDisablePeerAccess; + if (strcmp("hipCtxEnablePeerAccess", name) == 0) return HIP_API_ID_hipCtxEnablePeerAccess; + if (strcmp("hipCtxGetApiVersion", name) == 0) return HIP_API_ID_hipCtxGetApiVersion; + if (strcmp("hipCtxGetCacheConfig", name) == 0) return HIP_API_ID_hipCtxGetCacheConfig; + if (strcmp("hipCtxGetCurrent", name) == 0) return HIP_API_ID_hipCtxGetCurrent; + if (strcmp("hipCtxGetDevice", name) == 0) return HIP_API_ID_hipCtxGetDevice; + if (strcmp("hipCtxGetFlags", name) == 0) return HIP_API_ID_hipCtxGetFlags; + if (strcmp("hipCtxGetSharedMemConfig", name) == 0) return HIP_API_ID_hipCtxGetSharedMemConfig; + if (strcmp("hipCtxPopCurrent", name) == 0) return HIP_API_ID_hipCtxPopCurrent; + if (strcmp("hipCtxPushCurrent", name) == 0) return HIP_API_ID_hipCtxPushCurrent; + if (strcmp("hipCtxSetCacheConfig", name) == 0) return HIP_API_ID_hipCtxSetCacheConfig; + if (strcmp("hipCtxSetCurrent", name) == 0) return HIP_API_ID_hipCtxSetCurrent; + if (strcmp("hipCtxSetSharedMemConfig", name) == 0) return HIP_API_ID_hipCtxSetSharedMemConfig; + if (strcmp("hipCtxSynchronize", name) == 0) return HIP_API_ID_hipCtxSynchronize; + if (strcmp("hipDestroyExternalMemory", name) == 0) return HIP_API_ID_hipDestroyExternalMemory; + if (strcmp("hipDestroyExternalSemaphore", name) == 0) return HIP_API_ID_hipDestroyExternalSemaphore; + if (strcmp("hipDestroySurfaceObject", name) == 0) return HIP_API_ID_hipDestroySurfaceObject; + if (strcmp("hipDeviceCanAccessPeer", name) == 0) return HIP_API_ID_hipDeviceCanAccessPeer; + if (strcmp("hipDeviceComputeCapability", name) == 0) return HIP_API_ID_hipDeviceComputeCapability; + if (strcmp("hipDeviceDisablePeerAccess", name) == 0) return HIP_API_ID_hipDeviceDisablePeerAccess; + if (strcmp("hipDeviceEnablePeerAccess", name) == 0) return HIP_API_ID_hipDeviceEnablePeerAccess; + if (strcmp("hipDeviceGet", name) == 0) return HIP_API_ID_hipDeviceGet; + if (strcmp("hipDeviceGetAttribute", name) == 0) return HIP_API_ID_hipDeviceGetAttribute; + if (strcmp("hipDeviceGetByPCIBusId", name) == 0) return HIP_API_ID_hipDeviceGetByPCIBusId; + if (strcmp("hipDeviceGetCacheConfig", name) == 0) return HIP_API_ID_hipDeviceGetCacheConfig; + if (strcmp("hipDeviceGetDefaultMemPool", name) == 0) return HIP_API_ID_hipDeviceGetDefaultMemPool; + if (strcmp("hipDeviceGetGraphMemAttribute", name) == 0) return HIP_API_ID_hipDeviceGetGraphMemAttribute; + if (strcmp("hipDeviceGetLimit", name) == 0) return HIP_API_ID_hipDeviceGetLimit; + if (strcmp("hipDeviceGetMemPool", name) == 0) return HIP_API_ID_hipDeviceGetMemPool; + if (strcmp("hipDeviceGetName", name) == 0) return HIP_API_ID_hipDeviceGetName; + if (strcmp("hipDeviceGetP2PAttribute", name) == 0) return HIP_API_ID_hipDeviceGetP2PAttribute; + if (strcmp("hipDeviceGetPCIBusId", name) == 0) return HIP_API_ID_hipDeviceGetPCIBusId; + if (strcmp("hipDeviceGetSharedMemConfig", name) == 0) return HIP_API_ID_hipDeviceGetSharedMemConfig; + if (strcmp("hipDeviceGetStreamPriorityRange", name) == 0) return HIP_API_ID_hipDeviceGetStreamPriorityRange; + if (strcmp("hipDeviceGetUuid", name) == 0) return HIP_API_ID_hipDeviceGetUuid; + if (strcmp("hipDeviceGraphMemTrim", name) == 0) return HIP_API_ID_hipDeviceGraphMemTrim; + if (strcmp("hipDevicePrimaryCtxGetState", name) == 0) return HIP_API_ID_hipDevicePrimaryCtxGetState; + if (strcmp("hipDevicePrimaryCtxRelease", name) == 0) return HIP_API_ID_hipDevicePrimaryCtxRelease; + if (strcmp("hipDevicePrimaryCtxReset", name) == 0) return HIP_API_ID_hipDevicePrimaryCtxReset; + if (strcmp("hipDevicePrimaryCtxRetain", name) == 0) return HIP_API_ID_hipDevicePrimaryCtxRetain; + if (strcmp("hipDevicePrimaryCtxSetFlags", name) == 0) return HIP_API_ID_hipDevicePrimaryCtxSetFlags; + if (strcmp("hipDeviceReset", name) == 0) return HIP_API_ID_hipDeviceReset; + if (strcmp("hipDeviceSetCacheConfig", name) == 0) return HIP_API_ID_hipDeviceSetCacheConfig; + if (strcmp("hipDeviceSetGraphMemAttribute", name) == 0) return HIP_API_ID_hipDeviceSetGraphMemAttribute; + if (strcmp("hipDeviceSetLimit", name) == 0) return HIP_API_ID_hipDeviceSetLimit; + if (strcmp("hipDeviceSetMemPool", name) == 0) return HIP_API_ID_hipDeviceSetMemPool; + if (strcmp("hipDeviceSetSharedMemConfig", name) == 0) return HIP_API_ID_hipDeviceSetSharedMemConfig; + if (strcmp("hipDeviceSynchronize", name) == 0) return HIP_API_ID_hipDeviceSynchronize; + if (strcmp("hipDeviceTotalMem", name) == 0) return HIP_API_ID_hipDeviceTotalMem; + if (strcmp("hipDriverGetVersion", name) == 0) return HIP_API_ID_hipDriverGetVersion; + if (strcmp("hipDrvGraphAddMemcpyNode", name) == 0) return HIP_API_ID_hipDrvGraphAddMemcpyNode; + if (strcmp("hipDrvGraphAddMemsetNode", name) == 0) return HIP_API_ID_hipDrvGraphAddMemsetNode; + if (strcmp("hipDrvGraphMemcpyNodeGetParams", name) == 0) return HIP_API_ID_hipDrvGraphMemcpyNodeGetParams; + if (strcmp("hipDrvGraphMemcpyNodeSetParams", name) == 0) return HIP_API_ID_hipDrvGraphMemcpyNodeSetParams; + if (strcmp("hipDrvMemcpy2DUnaligned", name) == 0) return HIP_API_ID_hipDrvMemcpy2DUnaligned; + if (strcmp("hipDrvMemcpy3D", name) == 0) return HIP_API_ID_hipDrvMemcpy3D; + if (strcmp("hipDrvMemcpy3DAsync", name) == 0) return HIP_API_ID_hipDrvMemcpy3DAsync; + if (strcmp("hipDrvPointerGetAttributes", name) == 0) return HIP_API_ID_hipDrvPointerGetAttributes; + if (strcmp("hipEventCreate", name) == 0) return HIP_API_ID_hipEventCreate; + if (strcmp("hipEventCreateWithFlags", name) == 0) return HIP_API_ID_hipEventCreateWithFlags; + if (strcmp("hipEventDestroy", name) == 0) return HIP_API_ID_hipEventDestroy; + if (strcmp("hipEventElapsedTime", name) == 0) return HIP_API_ID_hipEventElapsedTime; + if (strcmp("hipEventQuery", name) == 0) return HIP_API_ID_hipEventQuery; + if (strcmp("hipEventRecord", name) == 0) return HIP_API_ID_hipEventRecord; + if (strcmp("hipEventSynchronize", name) == 0) return HIP_API_ID_hipEventSynchronize; + if (strcmp("hipExtGetLinkTypeAndHopCount", name) == 0) return HIP_API_ID_hipExtGetLinkTypeAndHopCount; + if (strcmp("hipExtLaunchKernel", name) == 0) return HIP_API_ID_hipExtLaunchKernel; + if (strcmp("hipExtLaunchMultiKernelMultiDevice", name) == 0) return HIP_API_ID_hipExtLaunchMultiKernelMultiDevice; + if (strcmp("hipExtMallocWithFlags", name) == 0) return HIP_API_ID_hipExtMallocWithFlags; + if (strcmp("hipExtModuleLaunchKernel", name) == 0) return HIP_API_ID_hipExtModuleLaunchKernel; + if (strcmp("hipExtStreamCreateWithCUMask", name) == 0) return HIP_API_ID_hipExtStreamCreateWithCUMask; + if (strcmp("hipExtStreamGetCUMask", name) == 0) return HIP_API_ID_hipExtStreamGetCUMask; + if (strcmp("hipExternalMemoryGetMappedBuffer", name) == 0) return HIP_API_ID_hipExternalMemoryGetMappedBuffer; + if (strcmp("hipExternalMemoryGetMappedMipmappedArray", name) == 0) return HIP_API_ID_hipExternalMemoryGetMappedMipmappedArray; + if (strcmp("hipFree", name) == 0) return HIP_API_ID_hipFree; + if (strcmp("hipFreeArray", name) == 0) return HIP_API_ID_hipFreeArray; + if (strcmp("hipFreeAsync", name) == 0) return HIP_API_ID_hipFreeAsync; + if (strcmp("hipFreeHost", name) == 0) return HIP_API_ID_hipFreeHost; + if (strcmp("hipFreeMipmappedArray", name) == 0) return HIP_API_ID_hipFreeMipmappedArray; + if (strcmp("hipFuncGetAttribute", name) == 0) return HIP_API_ID_hipFuncGetAttribute; + if (strcmp("hipFuncGetAttributes", name) == 0) return HIP_API_ID_hipFuncGetAttributes; + if (strcmp("hipFuncSetAttribute", name) == 0) return HIP_API_ID_hipFuncSetAttribute; + if (strcmp("hipFuncSetCacheConfig", name) == 0) return HIP_API_ID_hipFuncSetCacheConfig; + if (strcmp("hipFuncSetSharedMemConfig", name) == 0) return HIP_API_ID_hipFuncSetSharedMemConfig; + if (strcmp("hipGLGetDevices", name) == 0) return HIP_API_ID_hipGLGetDevices; + if (strcmp("hipGetChannelDesc", name) == 0) return HIP_API_ID_hipGetChannelDesc; + if (strcmp("hipGetDevice", name) == 0) return HIP_API_ID_hipGetDevice; + if (strcmp("hipGetDeviceCount", name) == 0) return HIP_API_ID_hipGetDeviceCount; + if (strcmp("hipGetDeviceFlags", name) == 0) return HIP_API_ID_hipGetDeviceFlags; + if (strcmp("hipGetDevicePropertiesR0000", name) == 0) return HIP_API_ID_hipGetDevicePropertiesR0000; + if (strcmp("hipGetDevicePropertiesR0600", name) == 0) return HIP_API_ID_hipGetDevicePropertiesR0600; + if (strcmp("hipGetErrorString", name) == 0) return HIP_API_ID_hipGetErrorString; + if (strcmp("hipGetLastError", name) == 0) return HIP_API_ID_hipGetLastError; + if (strcmp("hipGetMipmappedArrayLevel", name) == 0) return HIP_API_ID_hipGetMipmappedArrayLevel; + if (strcmp("hipGetSymbolAddress", name) == 0) return HIP_API_ID_hipGetSymbolAddress; + if (strcmp("hipGetSymbolSize", name) == 0) return HIP_API_ID_hipGetSymbolSize; + if (strcmp("hipGraphAddChildGraphNode", name) == 0) return HIP_API_ID_hipGraphAddChildGraphNode; + if (strcmp("hipGraphAddDependencies", name) == 0) return HIP_API_ID_hipGraphAddDependencies; + if (strcmp("hipGraphAddEmptyNode", name) == 0) return HIP_API_ID_hipGraphAddEmptyNode; + if (strcmp("hipGraphAddEventRecordNode", name) == 0) return HIP_API_ID_hipGraphAddEventRecordNode; + if (strcmp("hipGraphAddEventWaitNode", name) == 0) return HIP_API_ID_hipGraphAddEventWaitNode; + if (strcmp("hipGraphAddExternalSemaphoresSignalNode", name) == 0) return HIP_API_ID_hipGraphAddExternalSemaphoresSignalNode; + if (strcmp("hipGraphAddExternalSemaphoresWaitNode", name) == 0) return HIP_API_ID_hipGraphAddExternalSemaphoresWaitNode; + if (strcmp("hipGraphAddHostNode", name) == 0) return HIP_API_ID_hipGraphAddHostNode; + if (strcmp("hipGraphAddKernelNode", name) == 0) return HIP_API_ID_hipGraphAddKernelNode; + if (strcmp("hipGraphAddMemAllocNode", name) == 0) return HIP_API_ID_hipGraphAddMemAllocNode; + if (strcmp("hipGraphAddMemFreeNode", name) == 0) return HIP_API_ID_hipGraphAddMemFreeNode; + if (strcmp("hipGraphAddMemcpyNode", name) == 0) return HIP_API_ID_hipGraphAddMemcpyNode; + if (strcmp("hipGraphAddMemcpyNode1D", name) == 0) return HIP_API_ID_hipGraphAddMemcpyNode1D; + if (strcmp("hipGraphAddMemcpyNodeFromSymbol", name) == 0) return HIP_API_ID_hipGraphAddMemcpyNodeFromSymbol; + if (strcmp("hipGraphAddMemcpyNodeToSymbol", name) == 0) return HIP_API_ID_hipGraphAddMemcpyNodeToSymbol; + if (strcmp("hipGraphAddMemsetNode", name) == 0) return HIP_API_ID_hipGraphAddMemsetNode; + if (strcmp("hipGraphChildGraphNodeGetGraph", name) == 0) return HIP_API_ID_hipGraphChildGraphNodeGetGraph; + if (strcmp("hipGraphClone", name) == 0) return HIP_API_ID_hipGraphClone; + if (strcmp("hipGraphCreate", name) == 0) return HIP_API_ID_hipGraphCreate; + if (strcmp("hipGraphDebugDotPrint", name) == 0) return HIP_API_ID_hipGraphDebugDotPrint; + if (strcmp("hipGraphDestroy", name) == 0) return HIP_API_ID_hipGraphDestroy; + if (strcmp("hipGraphDestroyNode", name) == 0) return HIP_API_ID_hipGraphDestroyNode; + if (strcmp("hipGraphEventRecordNodeGetEvent", name) == 0) return HIP_API_ID_hipGraphEventRecordNodeGetEvent; + if (strcmp("hipGraphEventRecordNodeSetEvent", name) == 0) return HIP_API_ID_hipGraphEventRecordNodeSetEvent; + if (strcmp("hipGraphEventWaitNodeGetEvent", name) == 0) return HIP_API_ID_hipGraphEventWaitNodeGetEvent; + if (strcmp("hipGraphEventWaitNodeSetEvent", name) == 0) return HIP_API_ID_hipGraphEventWaitNodeSetEvent; + if (strcmp("hipGraphExecChildGraphNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecChildGraphNodeSetParams; + if (strcmp("hipGraphExecDestroy", name) == 0) return HIP_API_ID_hipGraphExecDestroy; + if (strcmp("hipGraphExecEventRecordNodeSetEvent", name) == 0) return HIP_API_ID_hipGraphExecEventRecordNodeSetEvent; + if (strcmp("hipGraphExecEventWaitNodeSetEvent", name) == 0) return HIP_API_ID_hipGraphExecEventWaitNodeSetEvent; + if (strcmp("hipGraphExecExternalSemaphoresSignalNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecExternalSemaphoresSignalNodeSetParams; + if (strcmp("hipGraphExecExternalSemaphoresWaitNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecExternalSemaphoresWaitNodeSetParams; + if (strcmp("hipGraphExecHostNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecHostNodeSetParams; + if (strcmp("hipGraphExecKernelNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecKernelNodeSetParams; + if (strcmp("hipGraphExecMemcpyNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecMemcpyNodeSetParams; + if (strcmp("hipGraphExecMemcpyNodeSetParams1D", name) == 0) return HIP_API_ID_hipGraphExecMemcpyNodeSetParams1D; + if (strcmp("hipGraphExecMemcpyNodeSetParamsFromSymbol", name) == 0) return HIP_API_ID_hipGraphExecMemcpyNodeSetParamsFromSymbol; + if (strcmp("hipGraphExecMemcpyNodeSetParamsToSymbol", name) == 0) return HIP_API_ID_hipGraphExecMemcpyNodeSetParamsToSymbol; + if (strcmp("hipGraphExecMemsetNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExecMemsetNodeSetParams; + if (strcmp("hipGraphExecUpdate", name) == 0) return HIP_API_ID_hipGraphExecUpdate; + if (strcmp("hipGraphExternalSemaphoresSignalNodeGetParams", name) == 0) return HIP_API_ID_hipGraphExternalSemaphoresSignalNodeGetParams; + if (strcmp("hipGraphExternalSemaphoresSignalNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExternalSemaphoresSignalNodeSetParams; + if (strcmp("hipGraphExternalSemaphoresWaitNodeGetParams", name) == 0) return HIP_API_ID_hipGraphExternalSemaphoresWaitNodeGetParams; + if (strcmp("hipGraphExternalSemaphoresWaitNodeSetParams", name) == 0) return HIP_API_ID_hipGraphExternalSemaphoresWaitNodeSetParams; + if (strcmp("hipGraphGetEdges", name) == 0) return HIP_API_ID_hipGraphGetEdges; + if (strcmp("hipGraphGetNodes", name) == 0) return HIP_API_ID_hipGraphGetNodes; + if (strcmp("hipGraphGetRootNodes", name) == 0) return HIP_API_ID_hipGraphGetRootNodes; + if (strcmp("hipGraphHostNodeGetParams", name) == 0) return HIP_API_ID_hipGraphHostNodeGetParams; + if (strcmp("hipGraphHostNodeSetParams", name) == 0) return HIP_API_ID_hipGraphHostNodeSetParams; + if (strcmp("hipGraphInstantiate", name) == 0) return HIP_API_ID_hipGraphInstantiate; + if (strcmp("hipGraphInstantiateWithFlags", name) == 0) return HIP_API_ID_hipGraphInstantiateWithFlags; + if (strcmp("hipGraphKernelNodeCopyAttributes", name) == 0) return HIP_API_ID_hipGraphKernelNodeCopyAttributes; + if (strcmp("hipGraphKernelNodeGetAttribute", name) == 0) return HIP_API_ID_hipGraphKernelNodeGetAttribute; + if (strcmp("hipGraphKernelNodeGetParams", name) == 0) return HIP_API_ID_hipGraphKernelNodeGetParams; + if (strcmp("hipGraphKernelNodeSetAttribute", name) == 0) return HIP_API_ID_hipGraphKernelNodeSetAttribute; + if (strcmp("hipGraphKernelNodeSetParams", name) == 0) return HIP_API_ID_hipGraphKernelNodeSetParams; + if (strcmp("hipGraphLaunch", name) == 0) return HIP_API_ID_hipGraphLaunch; + if (strcmp("hipGraphMemAllocNodeGetParams", name) == 0) return HIP_API_ID_hipGraphMemAllocNodeGetParams; + if (strcmp("hipGraphMemFreeNodeGetParams", name) == 0) return HIP_API_ID_hipGraphMemFreeNodeGetParams; + if (strcmp("hipGraphMemcpyNodeGetParams", name) == 0) return HIP_API_ID_hipGraphMemcpyNodeGetParams; + if (strcmp("hipGraphMemcpyNodeSetParams", name) == 0) return HIP_API_ID_hipGraphMemcpyNodeSetParams; + if (strcmp("hipGraphMemcpyNodeSetParams1D", name) == 0) return HIP_API_ID_hipGraphMemcpyNodeSetParams1D; + if (strcmp("hipGraphMemcpyNodeSetParamsFromSymbol", name) == 0) return HIP_API_ID_hipGraphMemcpyNodeSetParamsFromSymbol; + if (strcmp("hipGraphMemcpyNodeSetParamsToSymbol", name) == 0) return HIP_API_ID_hipGraphMemcpyNodeSetParamsToSymbol; + if (strcmp("hipGraphMemsetNodeGetParams", name) == 0) return HIP_API_ID_hipGraphMemsetNodeGetParams; + if (strcmp("hipGraphMemsetNodeSetParams", name) == 0) return HIP_API_ID_hipGraphMemsetNodeSetParams; + if (strcmp("hipGraphNodeFindInClone", name) == 0) return HIP_API_ID_hipGraphNodeFindInClone; + if (strcmp("hipGraphNodeGetDependencies", name) == 0) return HIP_API_ID_hipGraphNodeGetDependencies; + if (strcmp("hipGraphNodeGetDependentNodes", name) == 0) return HIP_API_ID_hipGraphNodeGetDependentNodes; + if (strcmp("hipGraphNodeGetEnabled", name) == 0) return HIP_API_ID_hipGraphNodeGetEnabled; + if (strcmp("hipGraphNodeGetType", name) == 0) return HIP_API_ID_hipGraphNodeGetType; + if (strcmp("hipGraphNodeSetEnabled", name) == 0) return HIP_API_ID_hipGraphNodeSetEnabled; + if (strcmp("hipGraphReleaseUserObject", name) == 0) return HIP_API_ID_hipGraphReleaseUserObject; + if (strcmp("hipGraphRemoveDependencies", name) == 0) return HIP_API_ID_hipGraphRemoveDependencies; + if (strcmp("hipGraphRetainUserObject", name) == 0) return HIP_API_ID_hipGraphRetainUserObject; + if (strcmp("hipGraphUpload", name) == 0) return HIP_API_ID_hipGraphUpload; + if (strcmp("hipGraphicsGLRegisterBuffer", name) == 0) return HIP_API_ID_hipGraphicsGLRegisterBuffer; + if (strcmp("hipGraphicsGLRegisterImage", name) == 0) return HIP_API_ID_hipGraphicsGLRegisterImage; + if (strcmp("hipGraphicsMapResources", name) == 0) return HIP_API_ID_hipGraphicsMapResources; + if (strcmp("hipGraphicsResourceGetMappedPointer", name) == 0) return HIP_API_ID_hipGraphicsResourceGetMappedPointer; + if (strcmp("hipGraphicsSubResourceGetMappedArray", name) == 0) return HIP_API_ID_hipGraphicsSubResourceGetMappedArray; + if (strcmp("hipGraphicsUnmapResources", name) == 0) return HIP_API_ID_hipGraphicsUnmapResources; + if (strcmp("hipGraphicsUnregisterResource", name) == 0) return HIP_API_ID_hipGraphicsUnregisterResource; + if (strcmp("hipHccModuleLaunchKernel", name) == 0) return HIP_API_ID_hipHccModuleLaunchKernel; + if (strcmp("hipHostAlloc", name) == 0) return HIP_API_ID_hipHostAlloc; + if (strcmp("hipHostFree", name) == 0) return HIP_API_ID_hipHostFree; + if (strcmp("hipHostGetDevicePointer", name) == 0) return HIP_API_ID_hipHostGetDevicePointer; + if (strcmp("hipHostGetFlags", name) == 0) return HIP_API_ID_hipHostGetFlags; + if (strcmp("hipHostMalloc", name) == 0) return HIP_API_ID_hipHostMalloc; + if (strcmp("hipHostRegister", name) == 0) return HIP_API_ID_hipHostRegister; + if (strcmp("hipHostUnregister", name) == 0) return HIP_API_ID_hipHostUnregister; + if (strcmp("hipImportExternalMemory", name) == 0) return HIP_API_ID_hipImportExternalMemory; + if (strcmp("hipImportExternalSemaphore", name) == 0) return HIP_API_ID_hipImportExternalSemaphore; + if (strcmp("hipInit", name) == 0) return HIP_API_ID_hipInit; + if (strcmp("hipIpcCloseMemHandle", name) == 0) return HIP_API_ID_hipIpcCloseMemHandle; + if (strcmp("hipIpcGetEventHandle", name) == 0) return HIP_API_ID_hipIpcGetEventHandle; + if (strcmp("hipIpcGetMemHandle", name) == 0) return HIP_API_ID_hipIpcGetMemHandle; + if (strcmp("hipIpcOpenEventHandle", name) == 0) return HIP_API_ID_hipIpcOpenEventHandle; + if (strcmp("hipIpcOpenMemHandle", name) == 0) return HIP_API_ID_hipIpcOpenMemHandle; + if (strcmp("hipLaunchByPtr", name) == 0) return HIP_API_ID_hipLaunchByPtr; + if (strcmp("hipLaunchCooperativeKernel", name) == 0) return HIP_API_ID_hipLaunchCooperativeKernel; + if (strcmp("hipLaunchCooperativeKernelMultiDevice", name) == 0) return HIP_API_ID_hipLaunchCooperativeKernelMultiDevice; + if (strcmp("hipLaunchHostFunc", name) == 0) return HIP_API_ID_hipLaunchHostFunc; + if (strcmp("hipLaunchKernel", name) == 0) return HIP_API_ID_hipLaunchKernel; + if (strcmp("hipMalloc", name) == 0) return HIP_API_ID_hipMalloc; + if (strcmp("hipMalloc3D", name) == 0) return HIP_API_ID_hipMalloc3D; + if (strcmp("hipMalloc3DArray", name) == 0) return HIP_API_ID_hipMalloc3DArray; + if (strcmp("hipMallocArray", name) == 0) return HIP_API_ID_hipMallocArray; + if (strcmp("hipMallocAsync", name) == 0) return HIP_API_ID_hipMallocAsync; + if (strcmp("hipMallocFromPoolAsync", name) == 0) return HIP_API_ID_hipMallocFromPoolAsync; + if (strcmp("hipMallocHost", name) == 0) return HIP_API_ID_hipMallocHost; + if (strcmp("hipMallocManaged", name) == 0) return HIP_API_ID_hipMallocManaged; + if (strcmp("hipMallocMipmappedArray", name) == 0) return HIP_API_ID_hipMallocMipmappedArray; + if (strcmp("hipMallocPitch", name) == 0) return HIP_API_ID_hipMallocPitch; + if (strcmp("hipMemAddressFree", name) == 0) return HIP_API_ID_hipMemAddressFree; + if (strcmp("hipMemAddressReserve", name) == 0) return HIP_API_ID_hipMemAddressReserve; + if (strcmp("hipMemAdvise", name) == 0) return HIP_API_ID_hipMemAdvise; + if (strcmp("hipMemAllocHost", name) == 0) return HIP_API_ID_hipMemAllocHost; + if (strcmp("hipMemAllocPitch", name) == 0) return HIP_API_ID_hipMemAllocPitch; + if (strcmp("hipMemCreate", name) == 0) return HIP_API_ID_hipMemCreate; + if (strcmp("hipMemExportToShareableHandle", name) == 0) return HIP_API_ID_hipMemExportToShareableHandle; + if (strcmp("hipMemGetAccess", name) == 0) return HIP_API_ID_hipMemGetAccess; + if (strcmp("hipMemGetAddressRange", name) == 0) return HIP_API_ID_hipMemGetAddressRange; + if (strcmp("hipMemGetAllocationGranularity", name) == 0) return HIP_API_ID_hipMemGetAllocationGranularity; + if (strcmp("hipMemGetAllocationPropertiesFromHandle", name) == 0) return HIP_API_ID_hipMemGetAllocationPropertiesFromHandle; + if (strcmp("hipMemGetInfo", name) == 0) return HIP_API_ID_hipMemGetInfo; + if (strcmp("hipMemImportFromShareableHandle", name) == 0) return HIP_API_ID_hipMemImportFromShareableHandle; + if (strcmp("hipMemMap", name) == 0) return HIP_API_ID_hipMemMap; + if (strcmp("hipMemMapArrayAsync", name) == 0) return HIP_API_ID_hipMemMapArrayAsync; + if (strcmp("hipMemPoolCreate", name) == 0) return HIP_API_ID_hipMemPoolCreate; + if (strcmp("hipMemPoolDestroy", name) == 0) return HIP_API_ID_hipMemPoolDestroy; + if (strcmp("hipMemPoolExportPointer", name) == 0) return HIP_API_ID_hipMemPoolExportPointer; + if (strcmp("hipMemPoolExportToShareableHandle", name) == 0) return HIP_API_ID_hipMemPoolExportToShareableHandle; + if (strcmp("hipMemPoolGetAccess", name) == 0) return HIP_API_ID_hipMemPoolGetAccess; + if (strcmp("hipMemPoolGetAttribute", name) == 0) return HIP_API_ID_hipMemPoolGetAttribute; + if (strcmp("hipMemPoolImportFromShareableHandle", name) == 0) return HIP_API_ID_hipMemPoolImportFromShareableHandle; + if (strcmp("hipMemPoolImportPointer", name) == 0) return HIP_API_ID_hipMemPoolImportPointer; + if (strcmp("hipMemPoolSetAccess", name) == 0) return HIP_API_ID_hipMemPoolSetAccess; + if (strcmp("hipMemPoolSetAttribute", name) == 0) return HIP_API_ID_hipMemPoolSetAttribute; + if (strcmp("hipMemPoolTrimTo", name) == 0) return HIP_API_ID_hipMemPoolTrimTo; + if (strcmp("hipMemPrefetchAsync", name) == 0) return HIP_API_ID_hipMemPrefetchAsync; + if (strcmp("hipMemPtrGetInfo", name) == 0) return HIP_API_ID_hipMemPtrGetInfo; + if (strcmp("hipMemRangeGetAttribute", name) == 0) return HIP_API_ID_hipMemRangeGetAttribute; + if (strcmp("hipMemRangeGetAttributes", name) == 0) return HIP_API_ID_hipMemRangeGetAttributes; + if (strcmp("hipMemRelease", name) == 0) return HIP_API_ID_hipMemRelease; + if (strcmp("hipMemRetainAllocationHandle", name) == 0) return HIP_API_ID_hipMemRetainAllocationHandle; + if (strcmp("hipMemSetAccess", name) == 0) return HIP_API_ID_hipMemSetAccess; + if (strcmp("hipMemUnmap", name) == 0) return HIP_API_ID_hipMemUnmap; + if (strcmp("hipMemcpy", name) == 0) return HIP_API_ID_hipMemcpy; + if (strcmp("hipMemcpy2D", name) == 0) return HIP_API_ID_hipMemcpy2D; + if (strcmp("hipMemcpy2DAsync", name) == 0) return HIP_API_ID_hipMemcpy2DAsync; + if (strcmp("hipMemcpy2DFromArray", name) == 0) return HIP_API_ID_hipMemcpy2DFromArray; + if (strcmp("hipMemcpy2DFromArrayAsync", name) == 0) return HIP_API_ID_hipMemcpy2DFromArrayAsync; + if (strcmp("hipMemcpy2DToArray", name) == 0) return HIP_API_ID_hipMemcpy2DToArray; + if (strcmp("hipMemcpy2DToArrayAsync", name) == 0) return HIP_API_ID_hipMemcpy2DToArrayAsync; + if (strcmp("hipMemcpy3D", name) == 0) return HIP_API_ID_hipMemcpy3D; + if (strcmp("hipMemcpy3DAsync", name) == 0) return HIP_API_ID_hipMemcpy3DAsync; + if (strcmp("hipMemcpyAsync", name) == 0) return HIP_API_ID_hipMemcpyAsync; + if (strcmp("hipMemcpyAtoH", name) == 0) return HIP_API_ID_hipMemcpyAtoH; + if (strcmp("hipMemcpyDtoD", name) == 0) return HIP_API_ID_hipMemcpyDtoD; + if (strcmp("hipMemcpyDtoDAsync", name) == 0) return HIP_API_ID_hipMemcpyDtoDAsync; + if (strcmp("hipMemcpyDtoH", name) == 0) return HIP_API_ID_hipMemcpyDtoH; + if (strcmp("hipMemcpyDtoHAsync", name) == 0) return HIP_API_ID_hipMemcpyDtoHAsync; + if (strcmp("hipMemcpyFromArray", name) == 0) return HIP_API_ID_hipMemcpyFromArray; + if (strcmp("hipMemcpyFromSymbol", name) == 0) return HIP_API_ID_hipMemcpyFromSymbol; + if (strcmp("hipMemcpyFromSymbolAsync", name) == 0) return HIP_API_ID_hipMemcpyFromSymbolAsync; + if (strcmp("hipMemcpyHtoA", name) == 0) return HIP_API_ID_hipMemcpyHtoA; + if (strcmp("hipMemcpyHtoD", name) == 0) return HIP_API_ID_hipMemcpyHtoD; + if (strcmp("hipMemcpyHtoDAsync", name) == 0) return HIP_API_ID_hipMemcpyHtoDAsync; + if (strcmp("hipMemcpyParam2D", name) == 0) return HIP_API_ID_hipMemcpyParam2D; + if (strcmp("hipMemcpyParam2DAsync", name) == 0) return HIP_API_ID_hipMemcpyParam2DAsync; + if (strcmp("hipMemcpyPeer", name) == 0) return HIP_API_ID_hipMemcpyPeer; + if (strcmp("hipMemcpyPeerAsync", name) == 0) return HIP_API_ID_hipMemcpyPeerAsync; + if (strcmp("hipMemcpyToArray", name) == 0) return HIP_API_ID_hipMemcpyToArray; + if (strcmp("hipMemcpyToSymbol", name) == 0) return HIP_API_ID_hipMemcpyToSymbol; + if (strcmp("hipMemcpyToSymbolAsync", name) == 0) return HIP_API_ID_hipMemcpyToSymbolAsync; + if (strcmp("hipMemcpyWithStream", name) == 0) return HIP_API_ID_hipMemcpyWithStream; + if (strcmp("hipMemset", name) == 0) return HIP_API_ID_hipMemset; + if (strcmp("hipMemset2D", name) == 0) return HIP_API_ID_hipMemset2D; + if (strcmp("hipMemset2DAsync", name) == 0) return HIP_API_ID_hipMemset2DAsync; + if (strcmp("hipMemset3D", name) == 0) return HIP_API_ID_hipMemset3D; + if (strcmp("hipMemset3DAsync", name) == 0) return HIP_API_ID_hipMemset3DAsync; + if (strcmp("hipMemsetAsync", name) == 0) return HIP_API_ID_hipMemsetAsync; + if (strcmp("hipMemsetD16", name) == 0) return HIP_API_ID_hipMemsetD16; + if (strcmp("hipMemsetD16Async", name) == 0) return HIP_API_ID_hipMemsetD16Async; + if (strcmp("hipMemsetD32", name) == 0) return HIP_API_ID_hipMemsetD32; + if (strcmp("hipMemsetD32Async", name) == 0) return HIP_API_ID_hipMemsetD32Async; + if (strcmp("hipMemsetD8", name) == 0) return HIP_API_ID_hipMemsetD8; + if (strcmp("hipMemsetD8Async", name) == 0) return HIP_API_ID_hipMemsetD8Async; + if (strcmp("hipMipmappedArrayCreate", name) == 0) return HIP_API_ID_hipMipmappedArrayCreate; + if (strcmp("hipMipmappedArrayDestroy", name) == 0) return HIP_API_ID_hipMipmappedArrayDestroy; + if (strcmp("hipMipmappedArrayGetLevel", name) == 0) return HIP_API_ID_hipMipmappedArrayGetLevel; + if (strcmp("hipModuleGetFunction", name) == 0) return HIP_API_ID_hipModuleGetFunction; + if (strcmp("hipModuleGetGlobal", name) == 0) return HIP_API_ID_hipModuleGetGlobal; + if (strcmp("hipModuleGetTexRef", name) == 0) return HIP_API_ID_hipModuleGetTexRef; + if (strcmp("hipModuleLaunchCooperativeKernel", name) == 0) return HIP_API_ID_hipModuleLaunchCooperativeKernel; + if (strcmp("hipModuleLaunchCooperativeKernelMultiDevice", name) == 0) return HIP_API_ID_hipModuleLaunchCooperativeKernelMultiDevice; + if (strcmp("hipModuleLaunchKernel", name) == 0) return HIP_API_ID_hipModuleLaunchKernel; + if (strcmp("hipModuleLoad", name) == 0) return HIP_API_ID_hipModuleLoad; + if (strcmp("hipModuleLoadData", name) == 0) return HIP_API_ID_hipModuleLoadData; + if (strcmp("hipModuleLoadDataEx", name) == 0) return HIP_API_ID_hipModuleLoadDataEx; + if (strcmp("hipModuleOccupancyMaxActiveBlocksPerMultiprocessor", name) == 0) return HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor; + if (strcmp("hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags", name) == 0) return HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags; + if (strcmp("hipModuleOccupancyMaxPotentialBlockSize", name) == 0) return HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSize; + if (strcmp("hipModuleOccupancyMaxPotentialBlockSizeWithFlags", name) == 0) return HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSizeWithFlags; + if (strcmp("hipModuleUnload", name) == 0) return HIP_API_ID_hipModuleUnload; + if (strcmp("hipOccupancyMaxActiveBlocksPerMultiprocessor", name) == 0) return HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessor; + if (strcmp("hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags", name) == 0) return HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags; + if (strcmp("hipOccupancyMaxPotentialBlockSize", name) == 0) return HIP_API_ID_hipOccupancyMaxPotentialBlockSize; + if (strcmp("hipPeekAtLastError", name) == 0) return HIP_API_ID_hipPeekAtLastError; + if (strcmp("hipPointerGetAttribute", name) == 0) return HIP_API_ID_hipPointerGetAttribute; + if (strcmp("hipPointerGetAttributes", name) == 0) return HIP_API_ID_hipPointerGetAttributes; + if (strcmp("hipPointerSetAttribute", name) == 0) return HIP_API_ID_hipPointerSetAttribute; + if (strcmp("hipProfilerStart", name) == 0) return HIP_API_ID_hipProfilerStart; + if (strcmp("hipProfilerStop", name) == 0) return HIP_API_ID_hipProfilerStop; + if (strcmp("hipRuntimeGetVersion", name) == 0) return HIP_API_ID_hipRuntimeGetVersion; + if (strcmp("hipSetDevice", name) == 0) return HIP_API_ID_hipSetDevice; + if (strcmp("hipSetDeviceFlags", name) == 0) return HIP_API_ID_hipSetDeviceFlags; + if (strcmp("hipSetupArgument", name) == 0) return HIP_API_ID_hipSetupArgument; + if (strcmp("hipSignalExternalSemaphoresAsync", name) == 0) return HIP_API_ID_hipSignalExternalSemaphoresAsync; + if (strcmp("hipStreamAddCallback", name) == 0) return HIP_API_ID_hipStreamAddCallback; + if (strcmp("hipStreamAttachMemAsync", name) == 0) return HIP_API_ID_hipStreamAttachMemAsync; + if (strcmp("hipStreamBeginCapture", name) == 0) return HIP_API_ID_hipStreamBeginCapture; + if (strcmp("hipStreamCreate", name) == 0) return HIP_API_ID_hipStreamCreate; + if (strcmp("hipStreamCreateWithFlags", name) == 0) return HIP_API_ID_hipStreamCreateWithFlags; + if (strcmp("hipStreamCreateWithPriority", name) == 0) return HIP_API_ID_hipStreamCreateWithPriority; + if (strcmp("hipStreamDestroy", name) == 0) return HIP_API_ID_hipStreamDestroy; + if (strcmp("hipStreamEndCapture", name) == 0) return HIP_API_ID_hipStreamEndCapture; + if (strcmp("hipStreamGetCaptureInfo", name) == 0) return HIP_API_ID_hipStreamGetCaptureInfo; + if (strcmp("hipStreamGetCaptureInfo_v2", name) == 0) return HIP_API_ID_hipStreamGetCaptureInfo_v2; + if (strcmp("hipStreamGetDevice", name) == 0) return HIP_API_ID_hipStreamGetDevice; + if (strcmp("hipStreamGetFlags", name) == 0) return HIP_API_ID_hipStreamGetFlags; + if (strcmp("hipStreamGetPriority", name) == 0) return HIP_API_ID_hipStreamGetPriority; + if (strcmp("hipStreamIsCapturing", name) == 0) return HIP_API_ID_hipStreamIsCapturing; + if (strcmp("hipStreamQuery", name) == 0) return HIP_API_ID_hipStreamQuery; + if (strcmp("hipStreamSynchronize", name) == 0) return HIP_API_ID_hipStreamSynchronize; + if (strcmp("hipStreamUpdateCaptureDependencies", name) == 0) return HIP_API_ID_hipStreamUpdateCaptureDependencies; + if (strcmp("hipStreamWaitEvent", name) == 0) return HIP_API_ID_hipStreamWaitEvent; + if (strcmp("hipStreamWaitValue32", name) == 0) return HIP_API_ID_hipStreamWaitValue32; + if (strcmp("hipStreamWaitValue64", name) == 0) return HIP_API_ID_hipStreamWaitValue64; + if (strcmp("hipStreamWriteValue32", name) == 0) return HIP_API_ID_hipStreamWriteValue32; + if (strcmp("hipStreamWriteValue64", name) == 0) return HIP_API_ID_hipStreamWriteValue64; + if (strcmp("hipTexRefGetAddress", name) == 0) return HIP_API_ID_hipTexRefGetAddress; + if (strcmp("hipTexRefGetFlags", name) == 0) return HIP_API_ID_hipTexRefGetFlags; + if (strcmp("hipTexRefGetFormat", name) == 0) return HIP_API_ID_hipTexRefGetFormat; + if (strcmp("hipTexRefGetMaxAnisotropy", name) == 0) return HIP_API_ID_hipTexRefGetMaxAnisotropy; + if (strcmp("hipTexRefGetMipMappedArray", name) == 0) return HIP_API_ID_hipTexRefGetMipMappedArray; + if (strcmp("hipTexRefGetMipmapLevelBias", name) == 0) return HIP_API_ID_hipTexRefGetMipmapLevelBias; + if (strcmp("hipTexRefGetMipmapLevelClamp", name) == 0) return HIP_API_ID_hipTexRefGetMipmapLevelClamp; + if (strcmp("hipTexRefSetAddress", name) == 0) return HIP_API_ID_hipTexRefSetAddress; + if (strcmp("hipTexRefSetAddress2D", name) == 0) return HIP_API_ID_hipTexRefSetAddress2D; + if (strcmp("hipTexRefSetArray", name) == 0) return HIP_API_ID_hipTexRefSetArray; + if (strcmp("hipTexRefSetBorderColor", name) == 0) return HIP_API_ID_hipTexRefSetBorderColor; + if (strcmp("hipTexRefSetFlags", name) == 0) return HIP_API_ID_hipTexRefSetFlags; + if (strcmp("hipTexRefSetFormat", name) == 0) return HIP_API_ID_hipTexRefSetFormat; + if (strcmp("hipTexRefSetMaxAnisotropy", name) == 0) return HIP_API_ID_hipTexRefSetMaxAnisotropy; + if (strcmp("hipTexRefSetMipmapLevelBias", name) == 0) return HIP_API_ID_hipTexRefSetMipmapLevelBias; + if (strcmp("hipTexRefSetMipmapLevelClamp", name) == 0) return HIP_API_ID_hipTexRefSetMipmapLevelClamp; + if (strcmp("hipTexRefSetMipmappedArray", name) == 0) return HIP_API_ID_hipTexRefSetMipmappedArray; + if (strcmp("hipThreadExchangeStreamCaptureMode", name) == 0) return HIP_API_ID_hipThreadExchangeStreamCaptureMode; + if (strcmp("hipUserObjectCreate", name) == 0) return HIP_API_ID_hipUserObjectCreate; + if (strcmp("hipUserObjectRelease", name) == 0) return HIP_API_ID_hipUserObjectRelease; + if (strcmp("hipUserObjectRetain", name) == 0) return HIP_API_ID_hipUserObjectRetain; + if (strcmp("hipWaitExternalSemaphoresAsync", name) == 0) return HIP_API_ID_hipWaitExternalSemaphoresAsync; + if (strcmp("hipExtGetLastError", name) == 0) return HIP_API_ID_hipExtGetLastError; + return HIP_API_ID_NONE; +} + +// HIP API callbacks data structures +typedef struct hip_api_data_s { + uint64_t correlation_id; + uint32_t phase; + union { + struct { + dim3* gridDim; + dim3 gridDim__val; + dim3* blockDim; + dim3 blockDim__val; + size_t* sharedMem; + size_t sharedMem__val; + hipStream_t* stream; + hipStream_t stream__val; + } __hipPopCallConfiguration; + struct { + dim3 gridDim; + dim3 blockDim; + size_t sharedMem; + hipStream_t stream; + } __hipPushCallConfiguration; + struct { + hipArray_t* array; + hipArray_t array__val; + const HIP_ARRAY3D_DESCRIPTOR* pAllocateArray; + HIP_ARRAY3D_DESCRIPTOR pAllocateArray__val; + } hipArray3DCreate; + struct { + HIP_ARRAY3D_DESCRIPTOR* pArrayDescriptor; + HIP_ARRAY3D_DESCRIPTOR pArrayDescriptor__val; + hipArray_t array; + } hipArray3DGetDescriptor; + struct { + hipArray_t* pHandle; + hipArray_t pHandle__val; + const HIP_ARRAY_DESCRIPTOR* pAllocateArray; + HIP_ARRAY_DESCRIPTOR pAllocateArray__val; + } hipArrayCreate; + struct { + hipArray_t array; + } hipArrayDestroy; + struct { + HIP_ARRAY_DESCRIPTOR* pArrayDescriptor; + HIP_ARRAY_DESCRIPTOR pArrayDescriptor__val; + hipArray_t array; + } hipArrayGetDescriptor; + struct { + hipChannelFormatDesc* desc; + hipChannelFormatDesc desc__val; + hipExtent* extent; + hipExtent extent__val; + unsigned int* flags; + unsigned int flags__val; + hipArray_t array; + } hipArrayGetInfo; + struct { + int* device; + int device__val; + const hipDeviceProp_tR0000* prop; + hipDeviceProp_tR0000 prop__val; + } hipChooseDeviceR0000; + struct { + int* device; + int device__val; + const hipDeviceProp_tR0600* prop; + hipDeviceProp_tR0600 prop__val; + } hipChooseDeviceR0600; + struct { + dim3 gridDim; + dim3 blockDim; + size_t sharedMem; + hipStream_t stream; + } hipConfigureCall; + struct { + hipSurfaceObject_t* pSurfObject; + hipSurfaceObject_t pSurfObject__val; + const hipResourceDesc* pResDesc; + hipResourceDesc pResDesc__val; + } hipCreateSurfaceObject; + struct { + hipCtx_t* ctx; + hipCtx_t ctx__val; + unsigned int flags; + hipDevice_t device; + } hipCtxCreate; + struct { + hipCtx_t ctx; + } hipCtxDestroy; + struct { + hipCtx_t peerCtx; + } hipCtxDisablePeerAccess; + struct { + hipCtx_t peerCtx; + unsigned int flags; + } hipCtxEnablePeerAccess; + struct { + hipCtx_t ctx; + int* apiVersion; + int apiVersion__val; + } hipCtxGetApiVersion; + struct { + hipFuncCache_t* cacheConfig; + hipFuncCache_t cacheConfig__val; + } hipCtxGetCacheConfig; + struct { + hipCtx_t* ctx; + hipCtx_t ctx__val; + } hipCtxGetCurrent; + struct { + hipDevice_t* device; + hipDevice_t device__val; + } hipCtxGetDevice; + struct { + unsigned int* flags; + unsigned int flags__val; + } hipCtxGetFlags; + struct { + hipSharedMemConfig* pConfig; + hipSharedMemConfig pConfig__val; + } hipCtxGetSharedMemConfig; + struct { + hipCtx_t* ctx; + hipCtx_t ctx__val; + } hipCtxPopCurrent; + struct { + hipCtx_t ctx; + } hipCtxPushCurrent; + struct { + hipFuncCache_t cacheConfig; + } hipCtxSetCacheConfig; + struct { + hipCtx_t ctx; + } hipCtxSetCurrent; + struct { + hipSharedMemConfig config; + } hipCtxSetSharedMemConfig; + struct { + hipExternalMemory_t extMem; + } hipDestroyExternalMemory; + struct { + hipExternalSemaphore_t extSem; + } hipDestroyExternalSemaphore; + struct { + hipSurfaceObject_t surfaceObject; + } hipDestroySurfaceObject; + struct { + int* canAccessPeer; + int canAccessPeer__val; + int deviceId; + int peerDeviceId; + } hipDeviceCanAccessPeer; + struct { + int* major; + int major__val; + int* minor; + int minor__val; + hipDevice_t device; + } hipDeviceComputeCapability; + struct { + int peerDeviceId; + } hipDeviceDisablePeerAccess; + struct { + int peerDeviceId; + unsigned int flags; + } hipDeviceEnablePeerAccess; + struct { + hipDevice_t* device; + hipDevice_t device__val; + int ordinal; + } hipDeviceGet; + struct { + int* pi; + int pi__val; + hipDeviceAttribute_t attr; + int deviceId; + } hipDeviceGetAttribute; + struct { + int* device; + int device__val; + const char* pciBusId; + char pciBusId__val; + } hipDeviceGetByPCIBusId; + struct { + hipFuncCache_t* cacheConfig; + hipFuncCache_t cacheConfig__val; + } hipDeviceGetCacheConfig; + struct { + hipMemPool_t* mem_pool; + hipMemPool_t mem_pool__val; + int device; + } hipDeviceGetDefaultMemPool; + struct { + int device; + hipGraphMemAttributeType attr; + void* value; + } hipDeviceGetGraphMemAttribute; + struct { + size_t* pValue; + size_t pValue__val; + enum hipLimit_t limit; + } hipDeviceGetLimit; + struct { + hipMemPool_t* mem_pool; + hipMemPool_t mem_pool__val; + int device; + } hipDeviceGetMemPool; + struct { + char* name; + char name__val; + int len; + hipDevice_t device; + } hipDeviceGetName; + struct { + int* value; + int value__val; + hipDeviceP2PAttr attr; + int srcDevice; + int dstDevice; + } hipDeviceGetP2PAttribute; + struct { + char* pciBusId; + char pciBusId__val; + int len; + int device; + } hipDeviceGetPCIBusId; + struct { + hipSharedMemConfig* pConfig; + hipSharedMemConfig pConfig__val; + } hipDeviceGetSharedMemConfig; + struct { + int* leastPriority; + int leastPriority__val; + int* greatestPriority; + int greatestPriority__val; + } hipDeviceGetStreamPriorityRange; + struct { + hipUUID* uuid; + hipUUID uuid__val; + hipDevice_t device; + } hipDeviceGetUuid; + struct { + int device; + } hipDeviceGraphMemTrim; + struct { + hipDevice_t dev; + unsigned int* flags; + unsigned int flags__val; + int* active; + int active__val; + } hipDevicePrimaryCtxGetState; + struct { + hipDevice_t dev; + } hipDevicePrimaryCtxRelease; + struct { + hipDevice_t dev; + } hipDevicePrimaryCtxReset; + struct { + hipCtx_t* pctx; + hipCtx_t pctx__val; + hipDevice_t dev; + } hipDevicePrimaryCtxRetain; + struct { + hipDevice_t dev; + unsigned int flags; + } hipDevicePrimaryCtxSetFlags; + struct { + hipFuncCache_t cacheConfig; + } hipDeviceSetCacheConfig; + struct { + int device; + hipGraphMemAttributeType attr; + void* value; + } hipDeviceSetGraphMemAttribute; + struct { + enum hipLimit_t limit; + size_t value; + } hipDeviceSetLimit; + struct { + int device; + hipMemPool_t mem_pool; + } hipDeviceSetMemPool; + struct { + hipSharedMemConfig config; + } hipDeviceSetSharedMemConfig; + struct { + size_t* bytes; + size_t bytes__val; + hipDevice_t device; + } hipDeviceTotalMem; + struct { + int* driverVersion; + int driverVersion__val; + } hipDriverGetVersion; + struct { + hipGraphNode_t* phGraphNode; + hipGraphNode_t phGraphNode__val; + hipGraph_t hGraph; + const hipGraphNode_t* dependencies; + hipGraphNode_t dependencies__val; + size_t numDependencies; + const HIP_MEMCPY3D* copyParams; + HIP_MEMCPY3D copyParams__val; + hipCtx_t ctx; + } hipDrvGraphAddMemcpyNode; + struct { + hipGraphNode_t* phGraphNode; + hipGraphNode_t phGraphNode__val; + hipGraph_t hGraph; + const hipGraphNode_t* dependencies; + hipGraphNode_t dependencies__val; + size_t numDependencies; + const HIP_MEMSET_NODE_PARAMS* memsetParams; + HIP_MEMSET_NODE_PARAMS memsetParams__val; + hipCtx_t ctx; + } hipDrvGraphAddMemsetNode; + struct { + hipGraphNode_t hNode; + HIP_MEMCPY3D* nodeParams; + HIP_MEMCPY3D nodeParams__val; + } hipDrvGraphMemcpyNodeGetParams; + struct { + hipGraphNode_t hNode; + const HIP_MEMCPY3D* nodeParams; + HIP_MEMCPY3D nodeParams__val; + } hipDrvGraphMemcpyNodeSetParams; + struct { + const hip_Memcpy2D* pCopy; + hip_Memcpy2D pCopy__val; + } hipDrvMemcpy2DUnaligned; + struct { + const HIP_MEMCPY3D* pCopy; + HIP_MEMCPY3D pCopy__val; + } hipDrvMemcpy3D; + struct { + const HIP_MEMCPY3D* pCopy; + HIP_MEMCPY3D pCopy__val; + hipStream_t stream; + } hipDrvMemcpy3DAsync; + struct { + unsigned int numAttributes; + hipPointer_attribute* attributes; + hipPointer_attribute attributes__val; + void** data; + void* data__val; + hipDeviceptr_t ptr; + } hipDrvPointerGetAttributes; + struct { + hipEvent_t* event; + hipEvent_t event__val; + } hipEventCreate; + struct { + hipEvent_t* event; + hipEvent_t event__val; + unsigned int flags; + } hipEventCreateWithFlags; + struct { + hipEvent_t event; + } hipEventDestroy; + struct { + float* ms; + float ms__val; + hipEvent_t start; + hipEvent_t stop; + } hipEventElapsedTime; + struct { + hipEvent_t event; + } hipEventQuery; + struct { + hipEvent_t event; + hipStream_t stream; + } hipEventRecord; + struct { + hipEvent_t event; + } hipEventSynchronize; + struct { + int device1; + int device2; + unsigned int* linktype; + unsigned int linktype__val; + unsigned int* hopcount; + unsigned int hopcount__val; + } hipExtGetLinkTypeAndHopCount; + struct { + const void* function_address; + dim3 numBlocks; + dim3 dimBlocks; + void** args; + void* args__val; + size_t sharedMemBytes; + hipStream_t stream; + hipEvent_t startEvent; + hipEvent_t stopEvent; + int flags; + } hipExtLaunchKernel; + struct { + hipLaunchParams* launchParamsList; + hipLaunchParams launchParamsList__val; + int numDevices; + unsigned int flags; + } hipExtLaunchMultiKernelMultiDevice; + struct { + void** ptr; + void* ptr__val; + size_t sizeBytes; + unsigned int flags; + } hipExtMallocWithFlags; + struct { + hipFunction_t f; + unsigned int globalWorkSizeX; + unsigned int globalWorkSizeY; + unsigned int globalWorkSizeZ; + unsigned int localWorkSizeX; + unsigned int localWorkSizeY; + unsigned int localWorkSizeZ; + size_t sharedMemBytes; + hipStream_t hStream; + void** kernelParams; + void* kernelParams__val; + void** extra; + void* extra__val; + hipEvent_t startEvent; + hipEvent_t stopEvent; + unsigned int flags; + } hipExtModuleLaunchKernel; + struct { + hipStream_t* stream; + hipStream_t stream__val; + unsigned int cuMaskSize; + const unsigned int* cuMask; + unsigned int cuMask__val; + } hipExtStreamCreateWithCUMask; + struct { + hipStream_t stream; + unsigned int cuMaskSize; + unsigned int* cuMask; + unsigned int cuMask__val; + } hipExtStreamGetCUMask; + struct { + void** devPtr; + void* devPtr__val; + hipExternalMemory_t extMem; + const hipExternalMemoryBufferDesc* bufferDesc; + hipExternalMemoryBufferDesc bufferDesc__val; + } hipExternalMemoryGetMappedBuffer; + struct { + hipMipmappedArray_t* mipmap; + hipMipmappedArray_t mipmap__val; + hipExternalMemory_t extMem; + const hipExternalMemoryMipmappedArrayDesc* mipmapDesc; + hipExternalMemoryMipmappedArrayDesc mipmapDesc__val; + } hipExternalMemoryGetMappedMipmappedArray; + struct { + void* ptr; + } hipFree; + struct { + hipArray_t array; + } hipFreeArray; + struct { + void* dev_ptr; + hipStream_t stream; + } hipFreeAsync; + struct { + void* ptr; + } hipFreeHost; + struct { + hipMipmappedArray_t mipmappedArray; + } hipFreeMipmappedArray; + struct { + int* value; + int value__val; + hipFunction_attribute attrib; + hipFunction_t hfunc; + } hipFuncGetAttribute; + struct { + hipFuncAttributes* attr; + hipFuncAttributes attr__val; + const void* func; + } hipFuncGetAttributes; + struct { + const void* func; + hipFuncAttribute attr; + int value; + } hipFuncSetAttribute; + struct { + const void* func; + hipFuncCache_t config; + } hipFuncSetCacheConfig; + struct { + const void* func; + hipSharedMemConfig config; + } hipFuncSetSharedMemConfig; + struct { + unsigned int* pHipDeviceCount; + unsigned int pHipDeviceCount__val; + int* pHipDevices; + int pHipDevices__val; + unsigned int hipDeviceCount; + hipGLDeviceList deviceList; + } hipGLGetDevices; + struct { + hipChannelFormatDesc* desc; + hipChannelFormatDesc desc__val; + hipArray_const_t array; + } hipGetChannelDesc; + struct { + int* deviceId; + int deviceId__val; + } hipGetDevice; + struct { + int* count; + int count__val; + } hipGetDeviceCount; + struct { + unsigned int* flags; + unsigned int flags__val; + } hipGetDeviceFlags; + struct { + hipDeviceProp_tR0000* prop; + hipDeviceProp_tR0000 prop__val; + int device; + } hipGetDevicePropertiesR0000; + struct { + hipDeviceProp_tR0600* prop; + hipDeviceProp_tR0600 prop__val; + int deviceId; + } hipGetDevicePropertiesR0600; + struct { + hipArray_t* levelArray; + hipArray_t levelArray__val; + hipMipmappedArray_const_t mipmappedArray; + unsigned int level; + } hipGetMipmappedArrayLevel; + struct { + void** devPtr; + void* devPtr__val; + const void* symbol; + } hipGetSymbolAddress; + struct { + size_t* size; + size_t size__val; + const void* symbol; + } hipGetSymbolSize; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + hipGraph_t childGraph; + } hipGraphAddChildGraphNode; + struct { + hipGraph_t graph; + const hipGraphNode_t* from; + hipGraphNode_t from__val; + const hipGraphNode_t* to; + hipGraphNode_t to__val; + size_t numDependencies; + } hipGraphAddDependencies; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + } hipGraphAddEmptyNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + hipEvent_t event; + } hipGraphAddEventRecordNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + hipEvent_t event; + } hipGraphAddEventWaitNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipExternalSemaphoreSignalNodeParams* nodeParams; + hipExternalSemaphoreSignalNodeParams nodeParams__val; + } hipGraphAddExternalSemaphoresSignalNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipExternalSemaphoreWaitNodeParams* nodeParams; + hipExternalSemaphoreWaitNodeParams nodeParams__val; + } hipGraphAddExternalSemaphoresWaitNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipHostNodeParams* pNodeParams; + hipHostNodeParams pNodeParams__val; + } hipGraphAddHostNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipKernelNodeParams* pNodeParams; + hipKernelNodeParams pNodeParams__val; + } hipGraphAddKernelNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + hipMemAllocNodeParams* pNodeParams; + hipMemAllocNodeParams pNodeParams__val; + } hipGraphAddMemAllocNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + void* dev_ptr; + } hipGraphAddMemFreeNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipMemcpy3DParms* pCopyParams; + hipMemcpy3DParms pCopyParams__val; + } hipGraphAddMemcpyNode; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + void* dst; + const void* src; + size_t count; + hipMemcpyKind kind; + } hipGraphAddMemcpyNode1D; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + void* dst; + const void* symbol; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphAddMemcpyNodeFromSymbol; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const void* symbol; + const void* src; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphAddMemcpyNodeToSymbol; + struct { + hipGraphNode_t* pGraphNode; + hipGraphNode_t pGraphNode__val; + hipGraph_t graph; + const hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t numDependencies; + const hipMemsetParams* pMemsetParams; + hipMemsetParams pMemsetParams__val; + } hipGraphAddMemsetNode; + struct { + hipGraphNode_t node; + hipGraph_t* pGraph; + hipGraph_t pGraph__val; + } hipGraphChildGraphNodeGetGraph; + struct { + hipGraph_t* pGraphClone; + hipGraph_t pGraphClone__val; + hipGraph_t originalGraph; + } hipGraphClone; + struct { + hipGraph_t* pGraph; + hipGraph_t pGraph__val; + unsigned int flags; + } hipGraphCreate; + struct { + hipGraph_t graph; + const char* path; + char path__val; + unsigned int flags; + } hipGraphDebugDotPrint; + struct { + hipGraph_t graph; + } hipGraphDestroy; + struct { + hipGraphNode_t node; + } hipGraphDestroyNode; + struct { + hipGraphNode_t node; + hipEvent_t* event_out; + hipEvent_t event_out__val; + } hipGraphEventRecordNodeGetEvent; + struct { + hipGraphNode_t node; + hipEvent_t event; + } hipGraphEventRecordNodeSetEvent; + struct { + hipGraphNode_t node; + hipEvent_t* event_out; + hipEvent_t event_out__val; + } hipGraphEventWaitNodeGetEvent; + struct { + hipGraphNode_t node; + hipEvent_t event; + } hipGraphEventWaitNodeSetEvent; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + hipGraph_t childGraph; + } hipGraphExecChildGraphNodeSetParams; + struct { + hipGraphExec_t graphExec; + } hipGraphExecDestroy; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + hipEvent_t event; + } hipGraphExecEventRecordNodeSetEvent; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + hipEvent_t event; + } hipGraphExecEventWaitNodeSetEvent; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + const hipExternalSemaphoreSignalNodeParams* nodeParams; + hipExternalSemaphoreSignalNodeParams nodeParams__val; + } hipGraphExecExternalSemaphoresSignalNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + const hipExternalSemaphoreWaitNodeParams* nodeParams; + hipExternalSemaphoreWaitNodeParams nodeParams__val; + } hipGraphExecExternalSemaphoresWaitNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + const hipHostNodeParams* pNodeParams; + hipHostNodeParams pNodeParams__val; + } hipGraphExecHostNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + const hipKernelNodeParams* pNodeParams; + hipKernelNodeParams pNodeParams__val; + } hipGraphExecKernelNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + hipMemcpy3DParms* pNodeParams; + hipMemcpy3DParms pNodeParams__val; + } hipGraphExecMemcpyNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + void* dst; + const void* src; + size_t count; + hipMemcpyKind kind; + } hipGraphExecMemcpyNodeSetParams1D; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + void* dst; + const void* symbol; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphExecMemcpyNodeSetParamsFromSymbol; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + const void* symbol; + const void* src; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphExecMemcpyNodeSetParamsToSymbol; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t node; + const hipMemsetParams* pNodeParams; + hipMemsetParams pNodeParams__val; + } hipGraphExecMemsetNodeSetParams; + struct { + hipGraphExec_t hGraphExec; + hipGraph_t hGraph; + hipGraphNode_t* hErrorNode_out; + hipGraphNode_t hErrorNode_out__val; + hipGraphExecUpdateResult* updateResult_out; + hipGraphExecUpdateResult updateResult_out__val; + } hipGraphExecUpdate; + struct { + hipGraphNode_t hNode; + hipExternalSemaphoreSignalNodeParams* params_out; + hipExternalSemaphoreSignalNodeParams params_out__val; + } hipGraphExternalSemaphoresSignalNodeGetParams; + struct { + hipGraphNode_t hNode; + const hipExternalSemaphoreSignalNodeParams* nodeParams; + hipExternalSemaphoreSignalNodeParams nodeParams__val; + } hipGraphExternalSemaphoresSignalNodeSetParams; + struct { + hipGraphNode_t hNode; + hipExternalSemaphoreWaitNodeParams* params_out; + hipExternalSemaphoreWaitNodeParams params_out__val; + } hipGraphExternalSemaphoresWaitNodeGetParams; + struct { + hipGraphNode_t hNode; + const hipExternalSemaphoreWaitNodeParams* nodeParams; + hipExternalSemaphoreWaitNodeParams nodeParams__val; + } hipGraphExternalSemaphoresWaitNodeSetParams; + struct { + hipGraph_t graph; + hipGraphNode_t* from; + hipGraphNode_t from__val; + hipGraphNode_t* to; + hipGraphNode_t to__val; + size_t* numEdges; + size_t numEdges__val; + } hipGraphGetEdges; + struct { + hipGraph_t graph; + hipGraphNode_t* nodes; + hipGraphNode_t nodes__val; + size_t* numNodes; + size_t numNodes__val; + } hipGraphGetNodes; + struct { + hipGraph_t graph; + hipGraphNode_t* pRootNodes; + hipGraphNode_t pRootNodes__val; + size_t* pNumRootNodes; + size_t pNumRootNodes__val; + } hipGraphGetRootNodes; + struct { + hipGraphNode_t node; + hipHostNodeParams* pNodeParams; + hipHostNodeParams pNodeParams__val; + } hipGraphHostNodeGetParams; + struct { + hipGraphNode_t node; + const hipHostNodeParams* pNodeParams; + hipHostNodeParams pNodeParams__val; + } hipGraphHostNodeSetParams; + struct { + hipGraphExec_t* pGraphExec; + hipGraphExec_t pGraphExec__val; + hipGraph_t graph; + hipGraphNode_t* pErrorNode; + hipGraphNode_t pErrorNode__val; + char* pLogBuffer; + char pLogBuffer__val; + size_t bufferSize; + } hipGraphInstantiate; + struct { + hipGraphExec_t* pGraphExec; + hipGraphExec_t pGraphExec__val; + hipGraph_t graph; + unsigned long long flags; + } hipGraphInstantiateWithFlags; + struct { + hipGraphNode_t hSrc; + hipGraphNode_t hDst; + } hipGraphKernelNodeCopyAttributes; + struct { + hipGraphNode_t hNode; + hipKernelNodeAttrID attr; + hipKernelNodeAttrValue* value; + hipKernelNodeAttrValue value__val; + } hipGraphKernelNodeGetAttribute; + struct { + hipGraphNode_t node; + hipKernelNodeParams* pNodeParams; + hipKernelNodeParams pNodeParams__val; + } hipGraphKernelNodeGetParams; + struct { + hipGraphNode_t hNode; + hipKernelNodeAttrID attr; + const hipKernelNodeAttrValue* value; + hipKernelNodeAttrValue value__val; + } hipGraphKernelNodeSetAttribute; + struct { + hipGraphNode_t node; + const hipKernelNodeParams* pNodeParams; + hipKernelNodeParams pNodeParams__val; + } hipGraphKernelNodeSetParams; + struct { + hipGraphExec_t graphExec; + hipStream_t stream; + } hipGraphLaunch; + struct { + hipGraphNode_t node; + hipMemAllocNodeParams* pNodeParams; + hipMemAllocNodeParams pNodeParams__val; + } hipGraphMemAllocNodeGetParams; + struct { + hipGraphNode_t node; + void* dev_ptr; + } hipGraphMemFreeNodeGetParams; + struct { + hipGraphNode_t node; + hipMemcpy3DParms* pNodeParams; + hipMemcpy3DParms pNodeParams__val; + } hipGraphMemcpyNodeGetParams; + struct { + hipGraphNode_t node; + const hipMemcpy3DParms* pNodeParams; + hipMemcpy3DParms pNodeParams__val; + } hipGraphMemcpyNodeSetParams; + struct { + hipGraphNode_t node; + void* dst; + const void* src; + size_t count; + hipMemcpyKind kind; + } hipGraphMemcpyNodeSetParams1D; + struct { + hipGraphNode_t node; + void* dst; + const void* symbol; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphMemcpyNodeSetParamsFromSymbol; + struct { + hipGraphNode_t node; + const void* symbol; + const void* src; + size_t count; + size_t offset; + hipMemcpyKind kind; + } hipGraphMemcpyNodeSetParamsToSymbol; + struct { + hipGraphNode_t node; + hipMemsetParams* pNodeParams; + hipMemsetParams pNodeParams__val; + } hipGraphMemsetNodeGetParams; + struct { + hipGraphNode_t node; + const hipMemsetParams* pNodeParams; + hipMemsetParams pNodeParams__val; + } hipGraphMemsetNodeSetParams; + struct { + hipGraphNode_t* pNode; + hipGraphNode_t pNode__val; + hipGraphNode_t originalNode; + hipGraph_t clonedGraph; + } hipGraphNodeFindInClone; + struct { + hipGraphNode_t node; + hipGraphNode_t* pDependencies; + hipGraphNode_t pDependencies__val; + size_t* pNumDependencies; + size_t pNumDependencies__val; + } hipGraphNodeGetDependencies; + struct { + hipGraphNode_t node; + hipGraphNode_t* pDependentNodes; + hipGraphNode_t pDependentNodes__val; + size_t* pNumDependentNodes; + size_t pNumDependentNodes__val; + } hipGraphNodeGetDependentNodes; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + unsigned int* isEnabled; + unsigned int isEnabled__val; + } hipGraphNodeGetEnabled; + struct { + hipGraphNode_t node; + hipGraphNodeType* pType; + hipGraphNodeType pType__val; + } hipGraphNodeGetType; + struct { + hipGraphExec_t hGraphExec; + hipGraphNode_t hNode; + unsigned int isEnabled; + } hipGraphNodeSetEnabled; + struct { + hipGraph_t graph; + hipUserObject_t object; + unsigned int count; + } hipGraphReleaseUserObject; + struct { + hipGraph_t graph; + const hipGraphNode_t* from; + hipGraphNode_t from__val; + const hipGraphNode_t* to; + hipGraphNode_t to__val; + size_t numDependencies; + } hipGraphRemoveDependencies; + struct { + hipGraph_t graph; + hipUserObject_t object; + unsigned int count; + unsigned int flags; + } hipGraphRetainUserObject; + struct { + hipGraphExec_t graphExec; + hipStream_t stream; + } hipGraphUpload; + struct { + hipGraphicsResource** resource; + hipGraphicsResource* resource__val; + GLuint buffer; + unsigned int flags; + } hipGraphicsGLRegisterBuffer; + struct { + hipGraphicsResource** resource; + hipGraphicsResource* resource__val; + GLuint image; + GLenum target; + unsigned int flags; + } hipGraphicsGLRegisterImage; + struct { + int count; + hipGraphicsResource_t* resources; + hipGraphicsResource_t resources__val; + hipStream_t stream; + } hipGraphicsMapResources; + struct { + void** devPtr; + void* devPtr__val; + size_t* size; + size_t size__val; + hipGraphicsResource_t resource; + } hipGraphicsResourceGetMappedPointer; + struct { + hipArray_t* array; + hipArray_t array__val; + hipGraphicsResource_t resource; + unsigned int arrayIndex; + unsigned int mipLevel; + } hipGraphicsSubResourceGetMappedArray; + struct { + int count; + hipGraphicsResource_t* resources; + hipGraphicsResource_t resources__val; + hipStream_t stream; + } hipGraphicsUnmapResources; + struct { + hipGraphicsResource_t resource; + } hipGraphicsUnregisterResource; + struct { + hipFunction_t f; + unsigned int globalWorkSizeX; + unsigned int globalWorkSizeY; + unsigned int globalWorkSizeZ; + unsigned int blockDimX; + unsigned int blockDimY; + unsigned int blockDimZ; + size_t sharedMemBytes; + hipStream_t hStream; + void** kernelParams; + void* kernelParams__val; + void** extra; + void* extra__val; + hipEvent_t startEvent; + hipEvent_t stopEvent; + } hipHccModuleLaunchKernel; + struct { + void** ptr; + void* ptr__val; + size_t size; + unsigned int flags; + } hipHostAlloc; + struct { + void* ptr; + } hipHostFree; + struct { + void** devPtr; + void* devPtr__val; + void* hstPtr; + unsigned int flags; + } hipHostGetDevicePointer; + struct { + unsigned int* flagsPtr; + unsigned int flagsPtr__val; + void* hostPtr; + } hipHostGetFlags; + struct { + void** ptr; + void* ptr__val; + size_t size; + unsigned int flags; + } hipHostMalloc; + struct { + void* hostPtr; + size_t sizeBytes; + unsigned int flags; + } hipHostRegister; + struct { + void* hostPtr; + } hipHostUnregister; + struct { + hipExternalMemory_t* extMem_out; + hipExternalMemory_t extMem_out__val; + const hipExternalMemoryHandleDesc* memHandleDesc; + hipExternalMemoryHandleDesc memHandleDesc__val; + } hipImportExternalMemory; + struct { + hipExternalSemaphore_t* extSem_out; + hipExternalSemaphore_t extSem_out__val; + const hipExternalSemaphoreHandleDesc* semHandleDesc; + hipExternalSemaphoreHandleDesc semHandleDesc__val; + } hipImportExternalSemaphore; + struct { + unsigned int flags; + } hipInit; + struct { + void* devPtr; + } hipIpcCloseMemHandle; + struct { + hipIpcEventHandle_t* handle; + hipIpcEventHandle_t handle__val; + hipEvent_t event; + } hipIpcGetEventHandle; + struct { + hipIpcMemHandle_t* handle; + hipIpcMemHandle_t handle__val; + void* devPtr; + } hipIpcGetMemHandle; + struct { + hipEvent_t* event; + hipEvent_t event__val; + hipIpcEventHandle_t handle; + } hipIpcOpenEventHandle; + struct { + void** devPtr; + void* devPtr__val; + hipIpcMemHandle_t handle; + unsigned int flags; + } hipIpcOpenMemHandle; + struct { + const void* hostFunction; + } hipLaunchByPtr; + struct { + const void* f; + dim3 gridDim; + dim3 blockDimX; + void** kernelParams; + void* kernelParams__val; + unsigned int sharedMemBytes; + hipStream_t stream; + } hipLaunchCooperativeKernel; + struct { + hipLaunchParams* launchParamsList; + hipLaunchParams launchParamsList__val; + int numDevices; + unsigned int flags; + } hipLaunchCooperativeKernelMultiDevice; + struct { + hipStream_t stream; + hipHostFn_t fn; + void* userData; + } hipLaunchHostFunc; + struct { + const void* function_address; + dim3 numBlocks; + dim3 dimBlocks; + void** args; + void* args__val; + size_t sharedMemBytes; + hipStream_t stream; + } hipLaunchKernel; + struct { + void** ptr; + void* ptr__val; + size_t size; + } hipMalloc; + struct { + hipPitchedPtr* pitchedDevPtr; + hipPitchedPtr pitchedDevPtr__val; + hipExtent extent; + } hipMalloc3D; + struct { + hipArray_t* array; + hipArray_t array__val; + const hipChannelFormatDesc* desc; + hipChannelFormatDesc desc__val; + hipExtent extent; + unsigned int flags; + } hipMalloc3DArray; + struct { + hipArray_t* array; + hipArray_t array__val; + const hipChannelFormatDesc* desc; + hipChannelFormatDesc desc__val; + size_t width; + size_t height; + unsigned int flags; + } hipMallocArray; + struct { + void** dev_ptr; + void* dev_ptr__val; + size_t size; + hipStream_t stream; + } hipMallocAsync; + struct { + void** dev_ptr; + void* dev_ptr__val; + size_t size; + hipMemPool_t mem_pool; + hipStream_t stream; + } hipMallocFromPoolAsync; + struct { + void** ptr; + void* ptr__val; + size_t size; + } hipMallocHost; + struct { + void** dev_ptr; + void* dev_ptr__val; + size_t size; + unsigned int flags; + } hipMallocManaged; + struct { + hipMipmappedArray_t* mipmappedArray; + hipMipmappedArray_t mipmappedArray__val; + const hipChannelFormatDesc* desc; + hipChannelFormatDesc desc__val; + hipExtent extent; + unsigned int numLevels; + unsigned int flags; + } hipMallocMipmappedArray; + struct { + void** ptr; + void* ptr__val; + size_t* pitch; + size_t pitch__val; + size_t width; + size_t height; + } hipMallocPitch; + struct { + void* devPtr; + size_t size; + } hipMemAddressFree; + struct { + void** ptr; + void* ptr__val; + size_t size; + size_t alignment; + void* addr; + unsigned long long flags; + } hipMemAddressReserve; + struct { + const void* dev_ptr; + size_t count; + hipMemoryAdvise advice; + int device; + } hipMemAdvise; + struct { + void** ptr; + void* ptr__val; + size_t size; + } hipMemAllocHost; + struct { + hipDeviceptr_t* dptr; + hipDeviceptr_t dptr__val; + size_t* pitch; + size_t pitch__val; + size_t widthInBytes; + size_t height; + unsigned int elementSizeBytes; + } hipMemAllocPitch; + struct { + hipMemGenericAllocationHandle_t* handle; + hipMemGenericAllocationHandle_t handle__val; + size_t size; + const hipMemAllocationProp* prop; + hipMemAllocationProp prop__val; + unsigned long long flags; + } hipMemCreate; + struct { + void* shareableHandle; + hipMemGenericAllocationHandle_t handle; + hipMemAllocationHandleType handleType; + unsigned long long flags; + } hipMemExportToShareableHandle; + struct { + unsigned long long* flags; + unsigned long long flags__val; + const hipMemLocation* location; + hipMemLocation location__val; + void* ptr; + } hipMemGetAccess; + struct { + hipDeviceptr_t* pbase; + hipDeviceptr_t pbase__val; + size_t* psize; + size_t psize__val; + hipDeviceptr_t dptr; + } hipMemGetAddressRange; + struct { + size_t* granularity; + size_t granularity__val; + const hipMemAllocationProp* prop; + hipMemAllocationProp prop__val; + hipMemAllocationGranularity_flags option; + } hipMemGetAllocationGranularity; + struct { + hipMemAllocationProp* prop; + hipMemAllocationProp prop__val; + hipMemGenericAllocationHandle_t handle; + } hipMemGetAllocationPropertiesFromHandle; + struct { + size_t* free; + size_t free__val; + size_t* total; + size_t total__val; + } hipMemGetInfo; + struct { + hipMemGenericAllocationHandle_t* handle; + hipMemGenericAllocationHandle_t handle__val; + void* osHandle; + hipMemAllocationHandleType shHandleType; + } hipMemImportFromShareableHandle; + struct { + void* ptr; + size_t size; + size_t offset; + hipMemGenericAllocationHandle_t handle; + unsigned long long flags; + } hipMemMap; + struct { + hipArrayMapInfo* mapInfoList; + hipArrayMapInfo mapInfoList__val; + unsigned int count; + hipStream_t stream; + } hipMemMapArrayAsync; + struct { + hipMemPool_t* mem_pool; + hipMemPool_t mem_pool__val; + const hipMemPoolProps* pool_props; + hipMemPoolProps pool_props__val; + } hipMemPoolCreate; + struct { + hipMemPool_t mem_pool; + } hipMemPoolDestroy; + struct { + hipMemPoolPtrExportData* export_data; + hipMemPoolPtrExportData export_data__val; + void* dev_ptr; + } hipMemPoolExportPointer; + struct { + void* shared_handle; + hipMemPool_t mem_pool; + hipMemAllocationHandleType handle_type; + unsigned int flags; + } hipMemPoolExportToShareableHandle; + struct { + hipMemAccessFlags* flags; + hipMemAccessFlags flags__val; + hipMemPool_t mem_pool; + hipMemLocation* location; + hipMemLocation location__val; + } hipMemPoolGetAccess; + struct { + hipMemPool_t mem_pool; + hipMemPoolAttr attr; + void* value; + } hipMemPoolGetAttribute; + struct { + hipMemPool_t* mem_pool; + hipMemPool_t mem_pool__val; + void* shared_handle; + hipMemAllocationHandleType handle_type; + unsigned int flags; + } hipMemPoolImportFromShareableHandle; + struct { + void** dev_ptr; + void* dev_ptr__val; + hipMemPool_t mem_pool; + hipMemPoolPtrExportData* export_data; + hipMemPoolPtrExportData export_data__val; + } hipMemPoolImportPointer; + struct { + hipMemPool_t mem_pool; + const hipMemAccessDesc* desc_list; + hipMemAccessDesc desc_list__val; + size_t count; + } hipMemPoolSetAccess; + struct { + hipMemPool_t mem_pool; + hipMemPoolAttr attr; + void* value; + } hipMemPoolSetAttribute; + struct { + hipMemPool_t mem_pool; + size_t min_bytes_to_hold; + } hipMemPoolTrimTo; + struct { + const void* dev_ptr; + size_t count; + int device; + hipStream_t stream; + } hipMemPrefetchAsync; + struct { + void* ptr; + size_t* size; + size_t size__val; + } hipMemPtrGetInfo; + struct { + void* data; + size_t data_size; + hipMemRangeAttribute attribute; + const void* dev_ptr; + size_t count; + } hipMemRangeGetAttribute; + struct { + void** data; + void* data__val; + size_t* data_sizes; + size_t data_sizes__val; + hipMemRangeAttribute* attributes; + hipMemRangeAttribute attributes__val; + size_t num_attributes; + const void* dev_ptr; + size_t count; + } hipMemRangeGetAttributes; + struct { + hipMemGenericAllocationHandle_t handle; + } hipMemRelease; + struct { + hipMemGenericAllocationHandle_t* handle; + hipMemGenericAllocationHandle_t handle__val; + void* addr; + } hipMemRetainAllocationHandle; + struct { + void* ptr; + size_t size; + const hipMemAccessDesc* desc; + hipMemAccessDesc desc__val; + size_t count; + } hipMemSetAccess; + struct { + void* ptr; + size_t size; + } hipMemUnmap; + struct { + void* dst; + const void* src; + size_t sizeBytes; + hipMemcpyKind kind; + } hipMemcpy; + struct { + void* dst; + size_t dpitch; + const void* src; + size_t spitch; + size_t width; + size_t height; + hipMemcpyKind kind; + } hipMemcpy2D; + struct { + void* dst; + size_t dpitch; + const void* src; + size_t spitch; + size_t width; + size_t height; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpy2DAsync; + struct { + void* dst; + size_t dpitch; + hipArray_const_t src; + size_t wOffset; + size_t hOffset; + size_t width; + size_t height; + hipMemcpyKind kind; + } hipMemcpy2DFromArray; + struct { + void* dst; + size_t dpitch; + hipArray_const_t src; + size_t wOffset; + size_t hOffset; + size_t width; + size_t height; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpy2DFromArrayAsync; + struct { + hipArray_t dst; + size_t wOffset; + size_t hOffset; + const void* src; + size_t spitch; + size_t width; + size_t height; + hipMemcpyKind kind; + } hipMemcpy2DToArray; + struct { + hipArray_t dst; + size_t wOffset; + size_t hOffset; + const void* src; + size_t spitch; + size_t width; + size_t height; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpy2DToArrayAsync; + struct { + const hipMemcpy3DParms* p; + hipMemcpy3DParms p__val; + } hipMemcpy3D; + struct { + const hipMemcpy3DParms* p; + hipMemcpy3DParms p__val; + hipStream_t stream; + } hipMemcpy3DAsync; + struct { + void* dst; + const void* src; + size_t sizeBytes; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpyAsync; + struct { + void* dst; + hipArray_t srcArray; + size_t srcOffset; + size_t count; + } hipMemcpyAtoH; + struct { + hipDeviceptr_t dst; + hipDeviceptr_t src; + size_t sizeBytes; + } hipMemcpyDtoD; + struct { + hipDeviceptr_t dst; + hipDeviceptr_t src; + size_t sizeBytes; + hipStream_t stream; + } hipMemcpyDtoDAsync; + struct { + void* dst; + hipDeviceptr_t src; + size_t sizeBytes; + } hipMemcpyDtoH; + struct { + void* dst; + hipDeviceptr_t src; + size_t sizeBytes; + hipStream_t stream; + } hipMemcpyDtoHAsync; + struct { + void* dst; + hipArray_const_t srcArray; + size_t wOffset; + size_t hOffset; + size_t count; + hipMemcpyKind kind; + } hipMemcpyFromArray; + struct { + void* dst; + const void* symbol; + size_t sizeBytes; + size_t offset; + hipMemcpyKind kind; + } hipMemcpyFromSymbol; + struct { + void* dst; + const void* symbol; + size_t sizeBytes; + size_t offset; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpyFromSymbolAsync; + struct { + hipArray_t dstArray; + size_t dstOffset; + const void* srcHost; + size_t count; + } hipMemcpyHtoA; + struct { + hipDeviceptr_t dst; + void* src; + size_t sizeBytes; + } hipMemcpyHtoD; + struct { + hipDeviceptr_t dst; + void* src; + size_t sizeBytes; + hipStream_t stream; + } hipMemcpyHtoDAsync; + struct { + const hip_Memcpy2D* pCopy; + hip_Memcpy2D pCopy__val; + } hipMemcpyParam2D; + struct { + const hip_Memcpy2D* pCopy; + hip_Memcpy2D pCopy__val; + hipStream_t stream; + } hipMemcpyParam2DAsync; + struct { + void* dst; + int dstDeviceId; + const void* src; + int srcDeviceId; + size_t sizeBytes; + } hipMemcpyPeer; + struct { + void* dst; + int dstDeviceId; + const void* src; + int srcDevice; + size_t sizeBytes; + hipStream_t stream; + } hipMemcpyPeerAsync; + struct { + hipArray_t dst; + size_t wOffset; + size_t hOffset; + const void* src; + size_t count; + hipMemcpyKind kind; + } hipMemcpyToArray; + struct { + const void* symbol; + const void* src; + size_t sizeBytes; + size_t offset; + hipMemcpyKind kind; + } hipMemcpyToSymbol; + struct { + const void* symbol; + const void* src; + size_t sizeBytes; + size_t offset; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpyToSymbolAsync; + struct { + void* dst; + const void* src; + size_t sizeBytes; + hipMemcpyKind kind; + hipStream_t stream; + } hipMemcpyWithStream; + struct { + void* dst; + int value; + size_t sizeBytes; + } hipMemset; + struct { + void* dst; + size_t pitch; + int value; + size_t width; + size_t height; + } hipMemset2D; + struct { + void* dst; + size_t pitch; + int value; + size_t width; + size_t height; + hipStream_t stream; + } hipMemset2DAsync; + struct { + hipPitchedPtr pitchedDevPtr; + int value; + hipExtent extent; + } hipMemset3D; + struct { + hipPitchedPtr pitchedDevPtr; + int value; + hipExtent extent; + hipStream_t stream; + } hipMemset3DAsync; + struct { + void* dst; + int value; + size_t sizeBytes; + hipStream_t stream; + } hipMemsetAsync; + struct { + hipDeviceptr_t dest; + unsigned short value; + size_t count; + } hipMemsetD16; + struct { + hipDeviceptr_t dest; + unsigned short value; + size_t count; + hipStream_t stream; + } hipMemsetD16Async; + struct { + hipDeviceptr_t dest; + int value; + size_t count; + } hipMemsetD32; + struct { + hipDeviceptr_t dst; + int value; + size_t count; + hipStream_t stream; + } hipMemsetD32Async; + struct { + hipDeviceptr_t dest; + unsigned char value; + size_t count; + } hipMemsetD8; + struct { + hipDeviceptr_t dest; + unsigned char value; + size_t count; + hipStream_t stream; + } hipMemsetD8Async; + struct { + hipMipmappedArray_t* pHandle; + hipMipmappedArray_t pHandle__val; + HIP_ARRAY3D_DESCRIPTOR* pMipmappedArrayDesc; + HIP_ARRAY3D_DESCRIPTOR pMipmappedArrayDesc__val; + unsigned int numMipmapLevels; + } hipMipmappedArrayCreate; + struct { + hipMipmappedArray_t hMipmappedArray; + } hipMipmappedArrayDestroy; + struct { + hipArray_t* pLevelArray; + hipArray_t pLevelArray__val; + hipMipmappedArray_t hMipMappedArray; + unsigned int level; + } hipMipmappedArrayGetLevel; + struct { + hipFunction_t* function; + hipFunction_t function__val; + hipModule_t module; + const char* kname; + char kname__val; + } hipModuleGetFunction; + struct { + hipDeviceptr_t* dptr; + hipDeviceptr_t dptr__val; + size_t* bytes; + size_t bytes__val; + hipModule_t hmod; + const char* name; + char name__val; + } hipModuleGetGlobal; + struct { + textureReference** texRef; + textureReference* texRef__val; + hipModule_t hmod; + const char* name; + char name__val; + } hipModuleGetTexRef; + struct { + hipFunction_t f; + unsigned int gridDimX; + unsigned int gridDimY; + unsigned int gridDimZ; + unsigned int blockDimX; + unsigned int blockDimY; + unsigned int blockDimZ; + unsigned int sharedMemBytes; + hipStream_t stream; + void** kernelParams; + void* kernelParams__val; + } hipModuleLaunchCooperativeKernel; + struct { + hipFunctionLaunchParams* launchParamsList; + hipFunctionLaunchParams launchParamsList__val; + unsigned int numDevices; + unsigned int flags; + } hipModuleLaunchCooperativeKernelMultiDevice; + struct { + hipFunction_t f; + unsigned int gridDimX; + unsigned int gridDimY; + unsigned int gridDimZ; + unsigned int blockDimX; + unsigned int blockDimY; + unsigned int blockDimZ; + unsigned int sharedMemBytes; + hipStream_t stream; + void** kernelParams; + void* kernelParams__val; + void** extra; + void* extra__val; + } hipModuleLaunchKernel; + struct { + hipModule_t* module; + hipModule_t module__val; + const char* fname; + char fname__val; + } hipModuleLoad; + struct { + hipModule_t* module; + hipModule_t module__val; + const void* image; + } hipModuleLoadData; + struct { + hipModule_t* module; + hipModule_t module__val; + const void* image; + unsigned int numOptions; + hipJitOption* options; + hipJitOption options__val; + void** optionsValues; + void* optionsValues__val; + } hipModuleLoadDataEx; + struct { + int* numBlocks; + int numBlocks__val; + hipFunction_t f; + int blockSize; + size_t dynSharedMemPerBlk; + } hipModuleOccupancyMaxActiveBlocksPerMultiprocessor; + struct { + int* numBlocks; + int numBlocks__val; + hipFunction_t f; + int blockSize; + size_t dynSharedMemPerBlk; + unsigned int flags; + } hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags; + struct { + int* gridSize; + int gridSize__val; + int* blockSize; + int blockSize__val; + hipFunction_t f; + size_t dynSharedMemPerBlk; + int blockSizeLimit; + } hipModuleOccupancyMaxPotentialBlockSize; + struct { + int* gridSize; + int gridSize__val; + int* blockSize; + int blockSize__val; + hipFunction_t f; + size_t dynSharedMemPerBlk; + int blockSizeLimit; + unsigned int flags; + } hipModuleOccupancyMaxPotentialBlockSizeWithFlags; + struct { + hipModule_t module; + } hipModuleUnload; + struct { + int* numBlocks; + int numBlocks__val; + const void* f; + int blockSize; + size_t dynamicSMemSize; + } hipOccupancyMaxActiveBlocksPerMultiprocessor; + struct { + int* numBlocks; + int numBlocks__val; + const void* f; + int blockSize; + size_t dynamicSMemSize; + unsigned int flags; + } hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags; + struct { + int* gridSize; + int gridSize__val; + int* blockSize; + int blockSize__val; + const void* f; + size_t dynSharedMemPerBlk; + int blockSizeLimit; + } hipOccupancyMaxPotentialBlockSize; + struct { + void* data; + hipPointer_attribute attribute; + hipDeviceptr_t ptr; + } hipPointerGetAttribute; + struct { + hipPointerAttribute_t* attributes; + hipPointerAttribute_t attributes__val; + const void* ptr; + } hipPointerGetAttributes; + struct { + const void* value; + hipPointer_attribute attribute; + hipDeviceptr_t ptr; + } hipPointerSetAttribute; + struct { + int* runtimeVersion; + int runtimeVersion__val; + } hipRuntimeGetVersion; + struct { + int deviceId; + } hipSetDevice; + struct { + unsigned int flags; + } hipSetDeviceFlags; + struct { + const void* arg; + size_t size; + size_t offset; + } hipSetupArgument; + struct { + const hipExternalSemaphore_t* extSemArray; + hipExternalSemaphore_t extSemArray__val; + const hipExternalSemaphoreSignalParams* paramsArray; + hipExternalSemaphoreSignalParams paramsArray__val; + unsigned int numExtSems; + hipStream_t stream; + } hipSignalExternalSemaphoresAsync; + struct { + hipStream_t stream; + hipStreamCallback_t callback; + void* userData; + unsigned int flags; + } hipStreamAddCallback; + struct { + hipStream_t stream; + void* dev_ptr; + size_t length; + unsigned int flags; + } hipStreamAttachMemAsync; + struct { + hipStream_t stream; + hipStreamCaptureMode mode; + } hipStreamBeginCapture; + struct { + hipStream_t* stream; + hipStream_t stream__val; + } hipStreamCreate; + struct { + hipStream_t* stream; + hipStream_t stream__val; + unsigned int flags; + } hipStreamCreateWithFlags; + struct { + hipStream_t* stream; + hipStream_t stream__val; + unsigned int flags; + int priority; + } hipStreamCreateWithPriority; + struct { + hipStream_t stream; + } hipStreamDestroy; + struct { + hipStream_t stream; + hipGraph_t* pGraph; + hipGraph_t pGraph__val; + } hipStreamEndCapture; + struct { + hipStream_t stream; + hipStreamCaptureStatus* pCaptureStatus; + hipStreamCaptureStatus pCaptureStatus__val; + unsigned long long* pId; + unsigned long long pId__val; + } hipStreamGetCaptureInfo; + struct { + hipStream_t stream; + hipStreamCaptureStatus* captureStatus_out; + hipStreamCaptureStatus captureStatus_out__val; + unsigned long long* id_out; + unsigned long long id_out__val; + hipGraph_t* graph_out; + hipGraph_t graph_out__val; + const hipGraphNode_t** dependencies_out; + const hipGraphNode_t* dependencies_out__val; + size_t* numDependencies_out; + size_t numDependencies_out__val; + } hipStreamGetCaptureInfo_v2; + struct { + hipStream_t stream; + hipDevice_t* device; + hipDevice_t device__val; + } hipStreamGetDevice; + struct { + hipStream_t stream; + unsigned int* flags; + unsigned int flags__val; + } hipStreamGetFlags; + struct { + hipStream_t stream; + int* priority; + int priority__val; + } hipStreamGetPriority; + struct { + hipStream_t stream; + hipStreamCaptureStatus* pCaptureStatus; + hipStreamCaptureStatus pCaptureStatus__val; + } hipStreamIsCapturing; + struct { + hipStream_t stream; + } hipStreamQuery; + struct { + hipStream_t stream; + } hipStreamSynchronize; + struct { + hipStream_t stream; + hipGraphNode_t* dependencies; + hipGraphNode_t dependencies__val; + size_t numDependencies; + unsigned int flags; + } hipStreamUpdateCaptureDependencies; + struct { + hipStream_t stream; + hipEvent_t event; + unsigned int flags; + } hipStreamWaitEvent; + struct { + hipStream_t stream; + void* ptr; + unsigned int value; + unsigned int flags; + unsigned int mask; + } hipStreamWaitValue32; + struct { + hipStream_t stream; + void* ptr; + uint64_t value; + unsigned int flags; + uint64_t mask; + } hipStreamWaitValue64; + struct { + hipStream_t stream; + void* ptr; + unsigned int value; + unsigned int flags; + } hipStreamWriteValue32; + struct { + hipStream_t stream; + void* ptr; + uint64_t value; + unsigned int flags; + } hipStreamWriteValue64; + struct { + hipDeviceptr_t* dev_ptr; + hipDeviceptr_t dev_ptr__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetAddress; + struct { + unsigned int* pFlags; + unsigned int pFlags__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetFlags; + struct { + hipArray_Format* pFormat; + hipArray_Format pFormat__val; + int* pNumChannels; + int pNumChannels__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetFormat; + struct { + int* pmaxAnsio; + int pmaxAnsio__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetMaxAnisotropy; + struct { + hipMipmappedArray_t* pArray; + hipMipmappedArray_t pArray__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetMipMappedArray; + struct { + float* pbias; + float pbias__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetMipmapLevelBias; + struct { + float* pminMipmapLevelClamp; + float pminMipmapLevelClamp__val; + float* pmaxMipmapLevelClamp; + float pmaxMipmapLevelClamp__val; + const textureReference* texRef; + textureReference texRef__val; + } hipTexRefGetMipmapLevelClamp; + struct { + size_t* ByteOffset; + size_t ByteOffset__val; + textureReference* texRef; + textureReference texRef__val; + hipDeviceptr_t dptr; + size_t bytes; + } hipTexRefSetAddress; + struct { + textureReference* texRef; + textureReference texRef__val; + const HIP_ARRAY_DESCRIPTOR* desc; + HIP_ARRAY_DESCRIPTOR desc__val; + hipDeviceptr_t dptr; + size_t Pitch; + } hipTexRefSetAddress2D; + struct { + textureReference* tex; + textureReference tex__val; + hipArray_const_t array; + unsigned int flags; + } hipTexRefSetArray; + struct { + textureReference* texRef; + textureReference texRef__val; + float* pBorderColor; + float pBorderColor__val; + } hipTexRefSetBorderColor; + struct { + textureReference* texRef; + textureReference texRef__val; + unsigned int Flags; + } hipTexRefSetFlags; + struct { + textureReference* texRef; + textureReference texRef__val; + hipArray_Format fmt; + int NumPackedComponents; + } hipTexRefSetFormat; + struct { + textureReference* texRef; + textureReference texRef__val; + unsigned int maxAniso; + } hipTexRefSetMaxAnisotropy; + struct { + textureReference* texRef; + textureReference texRef__val; + float bias; + } hipTexRefSetMipmapLevelBias; + struct { + textureReference* texRef; + textureReference texRef__val; + float minMipMapLevelClamp; + float maxMipMapLevelClamp; + } hipTexRefSetMipmapLevelClamp; + struct { + textureReference* texRef; + textureReference texRef__val; + hipMipmappedArray* mipmappedArray; + hipMipmappedArray mipmappedArray__val; + unsigned int Flags; + } hipTexRefSetMipmappedArray; + struct { + hipStreamCaptureMode* mode; + hipStreamCaptureMode mode__val; + } hipThreadExchangeStreamCaptureMode; + struct { + hipUserObject_t* object_out; + hipUserObject_t object_out__val; + void* ptr; + hipHostFn_t destroy; + unsigned int initialRefcount; + unsigned int flags; + } hipUserObjectCreate; + struct { + hipUserObject_t object; + unsigned int count; + } hipUserObjectRelease; + struct { + hipUserObject_t object; + unsigned int count; + } hipUserObjectRetain; + struct { + const hipExternalSemaphore_t* extSemArray; + hipExternalSemaphore_t extSemArray__val; + const hipExternalSemaphoreWaitParams* paramsArray; + hipExternalSemaphoreWaitParams paramsArray__val; + unsigned int numExtSems; + hipStream_t stream; + } hipWaitExternalSemaphoresAsync; + } args; + uint64_t *phase_data; +} hip_api_data_t; + +// HIP API callbacks args data filling macros +// __hipPopCallConfiguration[('dim3*', 'gridDim'), ('dim3*', 'blockDim'), ('size_t*', 'sharedMem'), ('hipStream_t*', 'stream')] +#define INIT___hipPopCallConfiguration_CB_ARGS_DATA(cb_data) { \ + cb_data.args.__hipPopCallConfiguration.gridDim = (dim3*)gridDim; \ + cb_data.args.__hipPopCallConfiguration.blockDim = (dim3*)blockDim; \ + cb_data.args.__hipPopCallConfiguration.sharedMem = (size_t*)sharedMem; \ + cb_data.args.__hipPopCallConfiguration.stream = (hipStream_t*)stream; \ +}; +// __hipPushCallConfiguration[('dim3', 'gridDim'), ('dim3', 'blockDim'), ('size_t', 'sharedMem'), ('hipStream_t', 'stream')] +#define INIT___hipPushCallConfiguration_CB_ARGS_DATA(cb_data) { \ + cb_data.args.__hipPushCallConfiguration.gridDim = (dim3)gridDim; \ + cb_data.args.__hipPushCallConfiguration.blockDim = (dim3)blockDim; \ + cb_data.args.__hipPushCallConfiguration.sharedMem = (size_t)sharedMem; \ + cb_data.args.__hipPushCallConfiguration.stream = (hipStream_t)stream; \ +}; +// hipArray3DCreate[('hipArray_t*', 'array'), ('const HIP_ARRAY3D_DESCRIPTOR*', 'pAllocateArray')] +#define INIT_hipArray3DCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArray3DCreate.array = (hipArray_t*)array; \ + cb_data.args.hipArray3DCreate.pAllocateArray = (const HIP_ARRAY3D_DESCRIPTOR*)pAllocateArray; \ +}; +// hipArray3DGetDescriptor[('HIP_ARRAY3D_DESCRIPTOR*', 'pArrayDescriptor'), ('hipArray_t', 'array')] +#define INIT_hipArray3DGetDescriptor_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArray3DGetDescriptor.pArrayDescriptor = (HIP_ARRAY3D_DESCRIPTOR*)pArrayDescriptor; \ + cb_data.args.hipArray3DGetDescriptor.array = (hipArray_t)array; \ +}; +// hipArrayCreate[('hipArray_t*', 'pHandle'), ('const HIP_ARRAY_DESCRIPTOR*', 'pAllocateArray')] +#define INIT_hipArrayCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArrayCreate.pHandle = (hipArray_t*)array; \ + cb_data.args.hipArrayCreate.pAllocateArray = (const HIP_ARRAY_DESCRIPTOR*)pAllocateArray; \ +}; +// hipArrayDestroy[('hipArray_t', 'array')] +#define INIT_hipArrayDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArrayDestroy.array = (hipArray_t)array; \ +}; +// hipArrayGetDescriptor[('HIP_ARRAY_DESCRIPTOR*', 'pArrayDescriptor'), ('hipArray_t', 'array')] +#define INIT_hipArrayGetDescriptor_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArrayGetDescriptor.pArrayDescriptor = (HIP_ARRAY_DESCRIPTOR*)pArrayDescriptor; \ + cb_data.args.hipArrayGetDescriptor.array = (hipArray_t)array; \ +}; +// hipArrayGetInfo[('hipChannelFormatDesc*', 'desc'), ('hipExtent*', 'extent'), ('unsigned int*', 'flags'), ('hipArray_t', 'array')] +#define INIT_hipArrayGetInfo_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipArrayGetInfo.desc = (hipChannelFormatDesc*)desc; \ + cb_data.args.hipArrayGetInfo.extent = (hipExtent*)extent; \ + cb_data.args.hipArrayGetInfo.flags = (unsigned int*)flags; \ + cb_data.args.hipArrayGetInfo.array = (hipArray_t)array; \ +}; +// hipChooseDeviceR0000[('int*', 'device'), ('const hipDeviceProp_tR0000*', 'prop')] +#define INIT_hipChooseDeviceR0000_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipChooseDeviceR0000.device = (int*)device; \ + cb_data.args.hipChooseDeviceR0000.prop = (const hipDeviceProp_tR0000*)properties; \ +}; +// hipChooseDeviceR0600[('int*', 'device'), ('const hipDeviceProp_tR0600*', 'prop')] +#define INIT_hipChooseDeviceR0600_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipChooseDeviceR0600.device = (int*)device; \ + cb_data.args.hipChooseDeviceR0600.prop = (const hipDeviceProp_tR0600*)properties; \ +}; +// hipConfigureCall[('dim3', 'gridDim'), ('dim3', 'blockDim'), ('size_t', 'sharedMem'), ('hipStream_t', 'stream')] +#define INIT_hipConfigureCall_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipConfigureCall.gridDim = (dim3)gridDim; \ + cb_data.args.hipConfigureCall.blockDim = (dim3)blockDim; \ + cb_data.args.hipConfigureCall.sharedMem = (size_t)sharedMem; \ + cb_data.args.hipConfigureCall.stream = (hipStream_t)stream; \ +}; +// hipCreateSurfaceObject[('hipSurfaceObject_t*', 'pSurfObject'), ('const hipResourceDesc*', 'pResDesc')] +#define INIT_hipCreateSurfaceObject_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCreateSurfaceObject.pSurfObject = (hipSurfaceObject_t*)pSurfObject; \ + cb_data.args.hipCreateSurfaceObject.pResDesc = (const hipResourceDesc*)pResDesc; \ +}; +// hipCtxCreate[('hipCtx_t*', 'ctx'), ('unsigned int', 'flags'), ('hipDevice_t', 'device')] +#define INIT_hipCtxCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxCreate.ctx = (hipCtx_t*)ctx; \ + cb_data.args.hipCtxCreate.flags = (unsigned int)flags; \ + cb_data.args.hipCtxCreate.device = (hipDevice_t)device; \ +}; +// hipCtxDestroy[('hipCtx_t', 'ctx')] +#define INIT_hipCtxDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxDestroy.ctx = (hipCtx_t)ctx; \ +}; +// hipCtxDisablePeerAccess[('hipCtx_t', 'peerCtx')] +#define INIT_hipCtxDisablePeerAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxDisablePeerAccess.peerCtx = (hipCtx_t)peerCtx; \ +}; +// hipCtxEnablePeerAccess[('hipCtx_t', 'peerCtx'), ('unsigned int', 'flags')] +#define INIT_hipCtxEnablePeerAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxEnablePeerAccess.peerCtx = (hipCtx_t)peerCtx; \ + cb_data.args.hipCtxEnablePeerAccess.flags = (unsigned int)flags; \ +}; +// hipCtxGetApiVersion[('hipCtx_t', 'ctx'), ('int*', 'apiVersion')] +#define INIT_hipCtxGetApiVersion_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetApiVersion.ctx = (hipCtx_t)ctx; \ + cb_data.args.hipCtxGetApiVersion.apiVersion = (int*)apiVersion; \ +}; +// hipCtxGetCacheConfig[('hipFuncCache_t*', 'cacheConfig')] +#define INIT_hipCtxGetCacheConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetCacheConfig.cacheConfig = (hipFuncCache_t*)cacheConfig; \ +}; +// hipCtxGetCurrent[('hipCtx_t*', 'ctx')] +#define INIT_hipCtxGetCurrent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetCurrent.ctx = (hipCtx_t*)ctx; \ +}; +// hipCtxGetDevice[('hipDevice_t*', 'device')] +#define INIT_hipCtxGetDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetDevice.device = (hipDevice_t*)device; \ +}; +// hipCtxGetFlags[('unsigned int*', 'flags')] +#define INIT_hipCtxGetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetFlags.flags = (unsigned int*)flags; \ +}; +// hipCtxGetSharedMemConfig[('hipSharedMemConfig*', 'pConfig')] +#define INIT_hipCtxGetSharedMemConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxGetSharedMemConfig.pConfig = (hipSharedMemConfig*)pConfig; \ +}; +// hipCtxPopCurrent[('hipCtx_t*', 'ctx')] +#define INIT_hipCtxPopCurrent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxPopCurrent.ctx = (hipCtx_t*)ctx; \ +}; +// hipCtxPushCurrent[('hipCtx_t', 'ctx')] +#define INIT_hipCtxPushCurrent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxPushCurrent.ctx = (hipCtx_t)ctx; \ +}; +// hipCtxSetCacheConfig[('hipFuncCache_t', 'cacheConfig')] +#define INIT_hipCtxSetCacheConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxSetCacheConfig.cacheConfig = (hipFuncCache_t)cacheConfig; \ +}; +// hipCtxSetCurrent[('hipCtx_t', 'ctx')] +#define INIT_hipCtxSetCurrent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxSetCurrent.ctx = (hipCtx_t)ctx; \ +}; +// hipCtxSetSharedMemConfig[('hipSharedMemConfig', 'config')] +#define INIT_hipCtxSetSharedMemConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipCtxSetSharedMemConfig.config = (hipSharedMemConfig)config; \ +}; +// hipCtxSynchronize[] +#define INIT_hipCtxSynchronize_CB_ARGS_DATA(cb_data) { \ +}; +// hipDestroyExternalMemory[('hipExternalMemory_t', 'extMem')] +#define INIT_hipDestroyExternalMemory_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDestroyExternalMemory.extMem = (hipExternalMemory_t)extMem; \ +}; +// hipDestroyExternalSemaphore[('hipExternalSemaphore_t', 'extSem')] +#define INIT_hipDestroyExternalSemaphore_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDestroyExternalSemaphore.extSem = (hipExternalSemaphore_t)extSem; \ +}; +// hipDestroySurfaceObject[('hipSurfaceObject_t', 'surfaceObject')] +#define INIT_hipDestroySurfaceObject_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDestroySurfaceObject.surfaceObject = (hipSurfaceObject_t)surfaceObject; \ +}; +// hipDeviceCanAccessPeer[('int*', 'canAccessPeer'), ('int', 'deviceId'), ('int', 'peerDeviceId')] +#define INIT_hipDeviceCanAccessPeer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceCanAccessPeer.canAccessPeer = (int*)canAccess; \ + cb_data.args.hipDeviceCanAccessPeer.deviceId = (int)deviceId; \ + cb_data.args.hipDeviceCanAccessPeer.peerDeviceId = (int)peerDeviceId; \ +}; +// hipDeviceComputeCapability[('int*', 'major'), ('int*', 'minor'), ('hipDevice_t', 'device')] +#define INIT_hipDeviceComputeCapability_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceComputeCapability.major = (int*)major; \ + cb_data.args.hipDeviceComputeCapability.minor = (int*)minor; \ + cb_data.args.hipDeviceComputeCapability.device = (hipDevice_t)device; \ +}; +// hipDeviceDisablePeerAccess[('int', 'peerDeviceId')] +#define INIT_hipDeviceDisablePeerAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceDisablePeerAccess.peerDeviceId = (int)peerDeviceId; \ +}; +// hipDeviceEnablePeerAccess[('int', 'peerDeviceId'), ('unsigned int', 'flags')] +#define INIT_hipDeviceEnablePeerAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceEnablePeerAccess.peerDeviceId = (int)peerDeviceId; \ + cb_data.args.hipDeviceEnablePeerAccess.flags = (unsigned int)flags; \ +}; +// hipDeviceGet[('hipDevice_t*', 'device'), ('int', 'ordinal')] +#define INIT_hipDeviceGet_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGet.device = (hipDevice_t*)device; \ + cb_data.args.hipDeviceGet.ordinal = (int)deviceId; \ +}; +// hipDeviceGetAttribute[('int*', 'pi'), ('hipDeviceAttribute_t', 'attr'), ('int', 'deviceId')] +#define INIT_hipDeviceGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetAttribute.pi = (int*)pi; \ + cb_data.args.hipDeviceGetAttribute.attr = (hipDeviceAttribute_t)attr; \ + cb_data.args.hipDeviceGetAttribute.deviceId = (int)device; \ +}; +// hipDeviceGetByPCIBusId[('int*', 'device'), ('const char*', 'pciBusId')] +#define INIT_hipDeviceGetByPCIBusId_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetByPCIBusId.device = (int*)device; \ + cb_data.args.hipDeviceGetByPCIBusId.pciBusId = (pciBusIdstr) ? strdup(pciBusIdstr) : NULL; \ +}; +// hipDeviceGetCacheConfig[('hipFuncCache_t*', 'cacheConfig')] +#define INIT_hipDeviceGetCacheConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetCacheConfig.cacheConfig = (hipFuncCache_t*)cacheConfig; \ +}; +// hipDeviceGetDefaultMemPool[('hipMemPool_t*', 'mem_pool'), ('int', 'device')] +#define INIT_hipDeviceGetDefaultMemPool_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetDefaultMemPool.mem_pool = (hipMemPool_t*)mem_pool; \ + cb_data.args.hipDeviceGetDefaultMemPool.device = (int)device; \ +}; +// hipDeviceGetGraphMemAttribute[('int', 'device'), ('hipGraphMemAttributeType', 'attr'), ('void*', 'value')] +#define INIT_hipDeviceGetGraphMemAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetGraphMemAttribute.device = (int)device; \ + cb_data.args.hipDeviceGetGraphMemAttribute.attr = (hipGraphMemAttributeType)attr; \ + cb_data.args.hipDeviceGetGraphMemAttribute.value = (void*)value; \ +}; +// hipDeviceGetLimit[('size_t*', 'pValue'), ('hipLimit_t', 'limit')] +#define INIT_hipDeviceGetLimit_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetLimit.pValue = (size_t*)pValue; \ + cb_data.args.hipDeviceGetLimit.limit = (hipLimit_t)limit; \ +}; +// hipDeviceGetMemPool[('hipMemPool_t*', 'mem_pool'), ('int', 'device')] +#define INIT_hipDeviceGetMemPool_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetMemPool.mem_pool = (hipMemPool_t*)mem_pool; \ + cb_data.args.hipDeviceGetMemPool.device = (int)device; \ +}; +// hipDeviceGetName[('char*', 'name'), ('int', 'len'), ('hipDevice_t', 'device')] +#define INIT_hipDeviceGetName_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetName.name = (char*)name; \ + cb_data.args.hipDeviceGetName.len = (int)len; \ + cb_data.args.hipDeviceGetName.device = (hipDevice_t)device; \ +}; +// hipDeviceGetP2PAttribute[('int*', 'value'), ('hipDeviceP2PAttr', 'attr'), ('int', 'srcDevice'), ('int', 'dstDevice')] +#define INIT_hipDeviceGetP2PAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetP2PAttribute.value = (int*)value; \ + cb_data.args.hipDeviceGetP2PAttribute.attr = (hipDeviceP2PAttr)attr; \ + cb_data.args.hipDeviceGetP2PAttribute.srcDevice = (int)srcDevice; \ + cb_data.args.hipDeviceGetP2PAttribute.dstDevice = (int)dstDevice; \ +}; +// hipDeviceGetPCIBusId[('char*', 'pciBusId'), ('int', 'len'), ('int', 'device')] +#define INIT_hipDeviceGetPCIBusId_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetPCIBusId.pciBusId = (char*)pciBusId; \ + cb_data.args.hipDeviceGetPCIBusId.len = (int)len; \ + cb_data.args.hipDeviceGetPCIBusId.device = (int)device; \ +}; +// hipDeviceGetSharedMemConfig[('hipSharedMemConfig*', 'pConfig')] +#define INIT_hipDeviceGetSharedMemConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetSharedMemConfig.pConfig = (hipSharedMemConfig*)pConfig; \ +}; +// hipDeviceGetStreamPriorityRange[('int*', 'leastPriority'), ('int*', 'greatestPriority')] +#define INIT_hipDeviceGetStreamPriorityRange_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetStreamPriorityRange.leastPriority = (int*)leastPriority; \ + cb_data.args.hipDeviceGetStreamPriorityRange.greatestPriority = (int*)greatestPriority; \ +}; +// hipDeviceGetUuid[('hipUUID*', 'uuid'), ('hipDevice_t', 'device')] +#define INIT_hipDeviceGetUuid_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGetUuid.uuid = (hipUUID*)uuid; \ + cb_data.args.hipDeviceGetUuid.device = (hipDevice_t)device; \ +}; +// hipDeviceGraphMemTrim[('int', 'device')] +#define INIT_hipDeviceGraphMemTrim_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceGraphMemTrim.device = (int)device; \ +}; +// hipDevicePrimaryCtxGetState[('hipDevice_t', 'dev'), ('unsigned int*', 'flags'), ('int*', 'active')] +#define INIT_hipDevicePrimaryCtxGetState_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDevicePrimaryCtxGetState.dev = (hipDevice_t)dev; \ + cb_data.args.hipDevicePrimaryCtxGetState.flags = (unsigned int*)flags; \ + cb_data.args.hipDevicePrimaryCtxGetState.active = (int*)active; \ +}; +// hipDevicePrimaryCtxRelease[('hipDevice_t', 'dev')] +#define INIT_hipDevicePrimaryCtxRelease_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDevicePrimaryCtxRelease.dev = (hipDevice_t)dev; \ +}; +// hipDevicePrimaryCtxReset[('hipDevice_t', 'dev')] +#define INIT_hipDevicePrimaryCtxReset_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDevicePrimaryCtxReset.dev = (hipDevice_t)dev; \ +}; +// hipDevicePrimaryCtxRetain[('hipCtx_t*', 'pctx'), ('hipDevice_t', 'dev')] +#define INIT_hipDevicePrimaryCtxRetain_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDevicePrimaryCtxRetain.pctx = (hipCtx_t*)pctx; \ + cb_data.args.hipDevicePrimaryCtxRetain.dev = (hipDevice_t)dev; \ +}; +// hipDevicePrimaryCtxSetFlags[('hipDevice_t', 'dev'), ('unsigned int', 'flags')] +#define INIT_hipDevicePrimaryCtxSetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDevicePrimaryCtxSetFlags.dev = (hipDevice_t)dev; \ + cb_data.args.hipDevicePrimaryCtxSetFlags.flags = (unsigned int)flags; \ +}; +// hipDeviceReset[] +#define INIT_hipDeviceReset_CB_ARGS_DATA(cb_data) { \ +}; +// hipDeviceSetCacheConfig[('hipFuncCache_t', 'cacheConfig')] +#define INIT_hipDeviceSetCacheConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceSetCacheConfig.cacheConfig = (hipFuncCache_t)cacheConfig; \ +}; +// hipDeviceSetGraphMemAttribute[('int', 'device'), ('hipGraphMemAttributeType', 'attr'), ('void*', 'value')] +#define INIT_hipDeviceSetGraphMemAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceSetGraphMemAttribute.device = (int)device; \ + cb_data.args.hipDeviceSetGraphMemAttribute.attr = (hipGraphMemAttributeType)attr; \ + cb_data.args.hipDeviceSetGraphMemAttribute.value = (void*)value; \ +}; +// hipDeviceSetLimit[('hipLimit_t', 'limit'), ('size_t', 'value')] +#define INIT_hipDeviceSetLimit_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceSetLimit.limit = (hipLimit_t)limit; \ + cb_data.args.hipDeviceSetLimit.value = (size_t)value; \ +}; +// hipDeviceSetMemPool[('int', 'device'), ('hipMemPool_t', 'mem_pool')] +#define INIT_hipDeviceSetMemPool_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceSetMemPool.device = (int)device; \ + cb_data.args.hipDeviceSetMemPool.mem_pool = (hipMemPool_t)mem_pool; \ +}; +// hipDeviceSetSharedMemConfig[('hipSharedMemConfig', 'config')] +#define INIT_hipDeviceSetSharedMemConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceSetSharedMemConfig.config = (hipSharedMemConfig)config; \ +}; +// hipDeviceSynchronize[] +#define INIT_hipDeviceSynchronize_CB_ARGS_DATA(cb_data) { \ +}; +// hipDeviceTotalMem[('size_t*', 'bytes'), ('hipDevice_t', 'device')] +#define INIT_hipDeviceTotalMem_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDeviceTotalMem.bytes = (size_t*)bytes; \ + cb_data.args.hipDeviceTotalMem.device = (hipDevice_t)device; \ +}; +// hipDriverGetVersion[('int*', 'driverVersion')] +#define INIT_hipDriverGetVersion_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDriverGetVersion.driverVersion = (int*)driverVersion; \ +}; +// hipDrvGraphAddMemcpyNode[('hipGraphNode_t*', 'phGraphNode'), ('hipGraph_t', 'hGraph'), ('const hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('const HIP_MEMCPY3D*', 'copyParams'), ('hipCtx_t', 'ctx')] +#define INIT_hipDrvGraphAddMemcpyNode_CB_ARGS_DATA(cb_data) { \ +}; +// hipDrvGraphAddMemsetNode[('hipGraphNode_t*', 'phGraphNode'), ('hipGraph_t', 'hGraph'), ('const hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('const HIP_MEMSET_NODE_PARAMS*', 'memsetParams'), ('hipCtx_t', 'ctx')] +#define INIT_hipDrvGraphAddMemsetNode_CB_ARGS_DATA(cb_data) { \ +}; +// hipDrvGraphMemcpyNodeGetParams[('hipGraphNode_t', 'hNode'), ('HIP_MEMCPY3D*', 'nodeParams')] +#define INIT_hipDrvGraphMemcpyNodeGetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipDrvGraphMemcpyNodeSetParams[('hipGraphNode_t', 'hNode'), ('const HIP_MEMCPY3D*', 'nodeParams')] +#define INIT_hipDrvGraphMemcpyNodeSetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipDrvMemcpy2DUnaligned[('const hip_Memcpy2D*', 'pCopy')] +#define INIT_hipDrvMemcpy2DUnaligned_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDrvMemcpy2DUnaligned.pCopy = (const hip_Memcpy2D*)pCopy; \ +}; +// hipDrvMemcpy3D[('const HIP_MEMCPY3D*', 'pCopy')] +#define INIT_hipDrvMemcpy3D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDrvMemcpy3D.pCopy = (const HIP_MEMCPY3D*)pCopy; \ +}; +// hipDrvMemcpy3DAsync[('const HIP_MEMCPY3D*', 'pCopy'), ('hipStream_t', 'stream')] +#define INIT_hipDrvMemcpy3DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDrvMemcpy3DAsync.pCopy = (const HIP_MEMCPY3D*)pCopy; \ + cb_data.args.hipDrvMemcpy3DAsync.stream = (hipStream_t)stream; \ +}; +// hipDrvPointerGetAttributes[('unsigned int', 'numAttributes'), ('hipPointer_attribute*', 'attributes'), ('void**', 'data'), ('hipDeviceptr_t', 'ptr')] +#define INIT_hipDrvPointerGetAttributes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipDrvPointerGetAttributes.numAttributes = (unsigned int)numAttributes; \ + cb_data.args.hipDrvPointerGetAttributes.attributes = (hipPointer_attribute*)attributes; \ + cb_data.args.hipDrvPointerGetAttributes.data = (void**)data; \ + cb_data.args.hipDrvPointerGetAttributes.ptr = (hipDeviceptr_t)ptr; \ +}; +// hipEventCreate[('hipEvent_t*', 'event')] +#define INIT_hipEventCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventCreate.event = (hipEvent_t*)event; \ +}; +// hipEventCreateWithFlags[('hipEvent_t*', 'event'), ('unsigned int', 'flags')] +#define INIT_hipEventCreateWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventCreateWithFlags.event = (hipEvent_t*)event; \ + cb_data.args.hipEventCreateWithFlags.flags = (unsigned int)flags; \ +}; +// hipEventDestroy[('hipEvent_t', 'event')] +#define INIT_hipEventDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventDestroy.event = (hipEvent_t)event; \ +}; +// hipEventElapsedTime[('float*', 'ms'), ('hipEvent_t', 'start'), ('hipEvent_t', 'stop')] +#define INIT_hipEventElapsedTime_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventElapsedTime.ms = (float*)ms; \ + cb_data.args.hipEventElapsedTime.start = (hipEvent_t)start; \ + cb_data.args.hipEventElapsedTime.stop = (hipEvent_t)stop; \ +}; +// hipEventQuery[('hipEvent_t', 'event')] +#define INIT_hipEventQuery_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventQuery.event = (hipEvent_t)event; \ +}; +// hipEventRecord[('hipEvent_t', 'event'), ('hipStream_t', 'stream')] +#define INIT_hipEventRecord_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventRecord.event = (hipEvent_t)event; \ + cb_data.args.hipEventRecord.stream = (hipStream_t)stream; \ +}; +// hipEventSynchronize[('hipEvent_t', 'event')] +#define INIT_hipEventSynchronize_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipEventSynchronize.event = (hipEvent_t)event; \ +}; +// hipExtGetLinkTypeAndHopCount[('int', 'device1'), ('int', 'device2'), ('unsigned int*', 'linktype'), ('unsigned int*', 'hopcount')] +#define INIT_hipExtGetLinkTypeAndHopCount_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtGetLinkTypeAndHopCount.device1 = (int)device1; \ + cb_data.args.hipExtGetLinkTypeAndHopCount.device2 = (int)device2; \ + cb_data.args.hipExtGetLinkTypeAndHopCount.linktype = (unsigned int*)linktype; \ + cb_data.args.hipExtGetLinkTypeAndHopCount.hopcount = (unsigned int*)hopcount; \ +}; +// hipExtLaunchKernel[('const void*', 'function_address'), ('dim3', 'numBlocks'), ('dim3', 'dimBlocks'), ('void**', 'args'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent'), ('int', 'flags')] +#define INIT_hipExtLaunchKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtLaunchKernel.function_address = (const void*)hostFunction; \ + cb_data.args.hipExtLaunchKernel.numBlocks = (dim3)gridDim; \ + cb_data.args.hipExtLaunchKernel.dimBlocks = (dim3)blockDim; \ + cb_data.args.hipExtLaunchKernel.args = (void**)args; \ + cb_data.args.hipExtLaunchKernel.sharedMemBytes = (size_t)sharedMemBytes; \ + cb_data.args.hipExtLaunchKernel.stream = (hipStream_t)stream; \ + cb_data.args.hipExtLaunchKernel.startEvent = (hipEvent_t)startEvent; \ + cb_data.args.hipExtLaunchKernel.stopEvent = (hipEvent_t)stopEvent; \ + cb_data.args.hipExtLaunchKernel.flags = (int)flags; \ +}; +// hipExtLaunchMultiKernelMultiDevice[('hipLaunchParams*', 'launchParamsList'), ('int', 'numDevices'), ('unsigned int', 'flags')] +#define INIT_hipExtLaunchMultiKernelMultiDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtLaunchMultiKernelMultiDevice.launchParamsList = (hipLaunchParams*)launchParamsList; \ + cb_data.args.hipExtLaunchMultiKernelMultiDevice.numDevices = (int)numDevices; \ + cb_data.args.hipExtLaunchMultiKernelMultiDevice.flags = (unsigned int)flags; \ +}; +// hipExtMallocWithFlags[('void**', 'ptr'), ('size_t', 'sizeBytes'), ('unsigned int', 'flags')] +#define INIT_hipExtMallocWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtMallocWithFlags.ptr = (void**)ptr; \ + cb_data.args.hipExtMallocWithFlags.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipExtMallocWithFlags.flags = (unsigned int)flags; \ +}; +// hipExtModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'globalWorkSizeX'), ('unsigned int', 'globalWorkSizeY'), ('unsigned int', 'globalWorkSizeZ'), ('unsigned int', 'localWorkSizeX'), ('unsigned int', 'localWorkSizeY'), ('unsigned int', 'localWorkSizeZ'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'hStream'), ('void**', 'kernelParams'), ('void**', 'extra'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent'), ('unsigned int', 'flags')] +#define INIT_hipExtModuleLaunchKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtModuleLaunchKernel.f = (hipFunction_t)f; \ + cb_data.args.hipExtModuleLaunchKernel.globalWorkSizeX = (unsigned int)globalWorkSizeX; \ + cb_data.args.hipExtModuleLaunchKernel.globalWorkSizeY = (unsigned int)globalWorkSizeY; \ + cb_data.args.hipExtModuleLaunchKernel.globalWorkSizeZ = (unsigned int)globalWorkSizeZ; \ + cb_data.args.hipExtModuleLaunchKernel.localWorkSizeX = (unsigned int)localWorkSizeX; \ + cb_data.args.hipExtModuleLaunchKernel.localWorkSizeY = (unsigned int)localWorkSizeY; \ + cb_data.args.hipExtModuleLaunchKernel.localWorkSizeZ = (unsigned int)localWorkSizeZ; \ + cb_data.args.hipExtModuleLaunchKernel.sharedMemBytes = (size_t)sharedMemBytes; \ + cb_data.args.hipExtModuleLaunchKernel.hStream = (hipStream_t)hStream; \ + cb_data.args.hipExtModuleLaunchKernel.kernelParams = (void**)kernelParams; \ + cb_data.args.hipExtModuleLaunchKernel.extra = (void**)extra; \ + cb_data.args.hipExtModuleLaunchKernel.startEvent = (hipEvent_t)startEvent; \ + cb_data.args.hipExtModuleLaunchKernel.stopEvent = (hipEvent_t)stopEvent; \ + cb_data.args.hipExtModuleLaunchKernel.flags = (unsigned int)flags; \ +}; +// hipExtStreamCreateWithCUMask[('hipStream_t*', 'stream'), ('unsigned int', 'cuMaskSize'), ('const unsigned int*', 'cuMask')] +#define INIT_hipExtStreamCreateWithCUMask_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtStreamCreateWithCUMask.stream = (hipStream_t*)stream; \ + cb_data.args.hipExtStreamCreateWithCUMask.cuMaskSize = (unsigned int)cuMaskSize; \ + cb_data.args.hipExtStreamCreateWithCUMask.cuMask = (const unsigned int*)cuMask; \ +}; +// hipExtStreamGetCUMask[('hipStream_t', 'stream'), ('unsigned int', 'cuMaskSize'), ('unsigned int*', 'cuMask')] +#define INIT_hipExtStreamGetCUMask_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExtStreamGetCUMask.stream = (hipStream_t)stream; \ + cb_data.args.hipExtStreamGetCUMask.cuMaskSize = (unsigned int)cuMaskSize; \ + cb_data.args.hipExtStreamGetCUMask.cuMask = (unsigned int*)cuMask; \ +}; +// hipExternalMemoryGetMappedBuffer[('void**', 'devPtr'), ('hipExternalMemory_t', 'extMem'), ('const hipExternalMemoryBufferDesc*', 'bufferDesc')] +#define INIT_hipExternalMemoryGetMappedBuffer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExternalMemoryGetMappedBuffer.devPtr = (void**)devPtr; \ + cb_data.args.hipExternalMemoryGetMappedBuffer.extMem = (hipExternalMemory_t)extMem; \ + cb_data.args.hipExternalMemoryGetMappedBuffer.bufferDesc = (const hipExternalMemoryBufferDesc*)bufferDesc; \ +}; +// hipExternalMemoryGetMappedMipmappedArray[('hipMipmappedArray_t*', 'mipmap'), ('hipExternalMemory_t', 'extMem'), ('const hipExternalMemoryMipmappedArrayDesc*', 'mipmapDesc')] +#define INIT_hipExternalMemoryGetMappedMipmappedArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipExternalMemoryGetMappedMipmappedArray.mipmap = (hipMipmappedArray_t*)mipmap; \ + cb_data.args.hipExternalMemoryGetMappedMipmappedArray.extMem = (hipExternalMemory_t)extMem; \ + cb_data.args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc = (const hipExternalMemoryMipmappedArrayDesc*)mipmapDesc; \ +}; +// hipFree[('void*', 'ptr')] +#define INIT_hipFree_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFree.ptr = (void*)ptr; \ +}; +// hipFreeArray[('hipArray_t', 'array')] +#define INIT_hipFreeArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFreeArray.array = (hipArray_t)array; \ +}; +// hipFreeAsync[('void*', 'dev_ptr'), ('hipStream_t', 'stream')] +#define INIT_hipFreeAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFreeAsync.dev_ptr = (void*)dev_ptr; \ + cb_data.args.hipFreeAsync.stream = (hipStream_t)stream; \ +}; +// hipFreeHost[('void*', 'ptr')] +#define INIT_hipFreeHost_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFreeHost.ptr = (void*)ptr; \ +}; +// hipFreeMipmappedArray[('hipMipmappedArray_t', 'mipmappedArray')] +#define INIT_hipFreeMipmappedArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFreeMipmappedArray.mipmappedArray = (hipMipmappedArray_t)mipmappedArray; \ +}; +// hipFuncGetAttribute[('int*', 'value'), ('hipFunction_attribute', 'attrib'), ('hipFunction_t', 'hfunc')] +#define INIT_hipFuncGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFuncGetAttribute.value = (int*)value; \ + cb_data.args.hipFuncGetAttribute.attrib = (hipFunction_attribute)attrib; \ + cb_data.args.hipFuncGetAttribute.hfunc = (hipFunction_t)hfunc; \ +}; +// hipFuncGetAttributes[('hipFuncAttributes*', 'attr'), ('const void*', 'func')] +#define INIT_hipFuncGetAttributes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFuncGetAttributes.attr = (hipFuncAttributes*)attr; \ + cb_data.args.hipFuncGetAttributes.func = (const void*)func; \ +}; +// hipFuncSetAttribute[('const void*', 'func'), ('hipFuncAttribute', 'attr'), ('int', 'value')] +#define INIT_hipFuncSetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFuncSetAttribute.func = (const void*)func; \ + cb_data.args.hipFuncSetAttribute.attr = (hipFuncAttribute)attr; \ + cb_data.args.hipFuncSetAttribute.value = (int)value; \ +}; +// hipFuncSetCacheConfig[('const void*', 'func'), ('hipFuncCache_t', 'config')] +#define INIT_hipFuncSetCacheConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFuncSetCacheConfig.func = (const void*)func; \ + cb_data.args.hipFuncSetCacheConfig.config = (hipFuncCache_t)cacheConfig; \ +}; +// hipFuncSetSharedMemConfig[('const void*', 'func'), ('hipSharedMemConfig', 'config')] +#define INIT_hipFuncSetSharedMemConfig_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipFuncSetSharedMemConfig.func = (const void*)func; \ + cb_data.args.hipFuncSetSharedMemConfig.config = (hipSharedMemConfig)config; \ +}; +// hipGLGetDevices[('unsigned int*', 'pHipDeviceCount'), ('int*', 'pHipDevices'), ('unsigned int', 'hipDeviceCount'), ('hipGLDeviceList', 'deviceList')] +#define INIT_hipGLGetDevices_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGLGetDevices.pHipDeviceCount = (unsigned int*)pHipDeviceCount; \ + cb_data.args.hipGLGetDevices.pHipDevices = (int*)pHipDevices; \ + cb_data.args.hipGLGetDevices.hipDeviceCount = (unsigned int)hipDeviceCount; \ + cb_data.args.hipGLGetDevices.deviceList = (hipGLDeviceList)deviceList; \ +}; +// hipGetChannelDesc[('hipChannelFormatDesc*', 'desc'), ('hipArray_const_t', 'array')] +#define INIT_hipGetChannelDesc_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetChannelDesc.desc = (hipChannelFormatDesc*)desc; \ + cb_data.args.hipGetChannelDesc.array = (hipArray_const_t)array; \ +}; +// hipGetDevice[('int*', 'deviceId')] +#define INIT_hipGetDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetDevice.deviceId = (int*)deviceId; \ +}; +// hipGetDeviceCount[('int*', 'count')] +#define INIT_hipGetDeviceCount_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetDeviceCount.count = (int*)count; \ +}; +// hipGetDeviceFlags[('unsigned int*', 'flags')] +#define INIT_hipGetDeviceFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetDeviceFlags.flags = (unsigned int*)flags; \ +}; +// hipGetDevicePropertiesR0000[('hipDeviceProp_tR0000*', 'prop'), ('int', 'device')] +#define INIT_hipGetDevicePropertiesR0000_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetDevicePropertiesR0000.prop = (hipDeviceProp_tR0000*)prop; \ + cb_data.args.hipGetDevicePropertiesR0000.device = (int)device; \ +}; +// hipGetDevicePropertiesR0600[('hipDeviceProp_tR0600*', 'prop'), ('int', 'deviceId')] +#define INIT_hipGetDevicePropertiesR0600_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetDevicePropertiesR0600.prop = (hipDeviceProp_tR0600*)prop; \ + cb_data.args.hipGetDevicePropertiesR0600.deviceId = (int)device; \ +}; +// hipGetErrorString[] +#define INIT_hipGetErrorString_CB_ARGS_DATA(cb_data) { \ +}; +// hipGetLastError[] +#define INIT_hipGetLastError_CB_ARGS_DATA(cb_data) { \ +}; +// hipGetMipmappedArrayLevel[('hipArray_t*', 'levelArray'), ('hipMipmappedArray_const_t', 'mipmappedArray'), ('unsigned int', 'level')] +#define INIT_hipGetMipmappedArrayLevel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetMipmappedArrayLevel.levelArray = (hipArray_t*)levelArray; \ + cb_data.args.hipGetMipmappedArrayLevel.mipmappedArray = (hipMipmappedArray_const_t)mipmappedArray; \ + cb_data.args.hipGetMipmappedArrayLevel.level = (unsigned int)level; \ +}; +// hipGetSymbolAddress[('void**', 'devPtr'), ('const void*', 'symbol')] +#define INIT_hipGetSymbolAddress_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetSymbolAddress.devPtr = (void**)devPtr; \ + cb_data.args.hipGetSymbolAddress.symbol = (const void*)symbol; \ +}; +// hipGetSymbolSize[('size_t*', 'size'), ('const void*', 'symbol')] +#define INIT_hipGetSymbolSize_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGetSymbolSize.size = (size_t*)sizePtr; \ + cb_data.args.hipGetSymbolSize.symbol = (const void*)symbol; \ +}; +// hipGraphAddChildGraphNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipGraph_t', 'childGraph')] +#define INIT_hipGraphAddChildGraphNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddChildGraphNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddChildGraphNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddChildGraphNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddChildGraphNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddChildGraphNode.childGraph = (hipGraph_t)childGraph; \ +}; +// hipGraphAddDependencies[('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'from'), ('const hipGraphNode_t*', 'to'), ('size_t', 'numDependencies')] +#define INIT_hipGraphAddDependencies_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddDependencies.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddDependencies.from = (const hipGraphNode_t*)from; \ + cb_data.args.hipGraphAddDependencies.to = (const hipGraphNode_t*)to; \ + cb_data.args.hipGraphAddDependencies.numDependencies = (size_t)numDependencies; \ +}; +// hipGraphAddEmptyNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies')] +#define INIT_hipGraphAddEmptyNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddEmptyNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddEmptyNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddEmptyNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddEmptyNode.numDependencies = (size_t)numDependencies; \ +}; +// hipGraphAddEventRecordNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipEvent_t', 'event')] +#define INIT_hipGraphAddEventRecordNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddEventRecordNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddEventRecordNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddEventRecordNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddEventRecordNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddEventRecordNode.event = (hipEvent_t)event; \ +}; +// hipGraphAddEventWaitNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipEvent_t', 'event')] +#define INIT_hipGraphAddEventWaitNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddEventWaitNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddEventWaitNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddEventWaitNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddEventWaitNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddEventWaitNode.event = (hipEvent_t)event; \ +}; +// hipGraphAddExternalSemaphoresSignalNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] +#define INIT_hipGraphAddExternalSemaphoresSignalNode_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphAddExternalSemaphoresWaitNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] +#define INIT_hipGraphAddExternalSemaphoresWaitNode_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphAddHostNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipHostNodeParams*', 'pNodeParams')] +#define INIT_hipGraphAddHostNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddHostNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddHostNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddHostNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddHostNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddHostNode.pNodeParams = (const hipHostNodeParams*)pNodeParams; \ +}; +// hipGraphAddKernelNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipKernelNodeParams*', 'pNodeParams')] +#define INIT_hipGraphAddKernelNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddKernelNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddKernelNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddKernelNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddKernelNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddKernelNode.pNodeParams = (const hipKernelNodeParams*)pNodeParams; \ +}; +// hipGraphAddMemAllocNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipMemAllocNodeParams*', 'pNodeParams')] +#define INIT_hipGraphAddMemAllocNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemAllocNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemAllocNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemAllocNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemAllocNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemAllocNode.pNodeParams = (hipMemAllocNodeParams*)pNodeParams; \ +}; +// hipGraphAddMemFreeNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dev_ptr')] +#define INIT_hipGraphAddMemFreeNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemFreeNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemFreeNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemFreeNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemFreeNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemFreeNode.dev_ptr = (void*)dev_ptr; \ +}; +// hipGraphAddMemcpyNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipMemcpy3DParms*', 'pCopyParams')] +#define INIT_hipGraphAddMemcpyNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemcpyNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemcpyNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemcpyNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemcpyNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemcpyNode.pCopyParams = (const hipMemcpy3DParms*)pCopyParams; \ +}; +// hipGraphAddMemcpyNode1D[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphAddMemcpyNode1D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemcpyNode1D.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemcpyNode1D.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemcpyNode1D.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemcpyNode1D.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemcpyNode1D.dst = (void*)dst; \ + cb_data.args.hipGraphAddMemcpyNode1D.src = (const void*)src; \ + cb_data.args.hipGraphAddMemcpyNode1D.count = (size_t)count; \ + cb_data.args.hipGraphAddMemcpyNode1D.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphAddMemcpyNodeFromSymbol[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphAddMemcpyNodeFromSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.dst = (void*)dst; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.count = (size_t)count; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphAddMemcpyNodeFromSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphAddMemcpyNodeToSymbol[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphAddMemcpyNodeToSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.src = (const void*)src; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.count = (size_t)count; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphAddMemcpyNodeToSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphAddMemsetNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipMemsetParams*', 'pMemsetParams')] +#define INIT_hipGraphAddMemsetNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphAddMemsetNode.pGraphNode = (hipGraphNode_t*)pGraphNode; \ + cb_data.args.hipGraphAddMemsetNode.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphAddMemsetNode.pDependencies = (const hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphAddMemsetNode.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipGraphAddMemsetNode.pMemsetParams = (const hipMemsetParams*)pMemsetParams; \ +}; +// hipGraphChildGraphNodeGetGraph[('hipGraphNode_t', 'node'), ('hipGraph_t*', 'pGraph')] +#define INIT_hipGraphChildGraphNodeGetGraph_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphChildGraphNodeGetGraph.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphChildGraphNodeGetGraph.pGraph = (hipGraph_t*)pGraph; \ +}; +// hipGraphClone[('hipGraph_t*', 'pGraphClone'), ('hipGraph_t', 'originalGraph')] +#define INIT_hipGraphClone_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphClone.pGraphClone = (hipGraph_t*)pGraphClone; \ + cb_data.args.hipGraphClone.originalGraph = (hipGraph_t)originalGraph; \ +}; +// hipGraphCreate[('hipGraph_t*', 'pGraph'), ('unsigned int', 'flags')] +#define INIT_hipGraphCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphCreate.pGraph = (hipGraph_t*)pGraph; \ + cb_data.args.hipGraphCreate.flags = (unsigned int)flags; \ +}; +// hipGraphDebugDotPrint[('hipGraph_t', 'graph'), ('const char*', 'path'), ('unsigned int', 'flags')] +#define INIT_hipGraphDebugDotPrint_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphDebugDotPrint.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphDebugDotPrint.path = (path) ? strdup(path) : NULL; \ + cb_data.args.hipGraphDebugDotPrint.flags = (unsigned int)flags; \ +}; +// hipGraphDestroy[('hipGraph_t', 'graph')] +#define INIT_hipGraphDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphDestroy.graph = (hipGraph_t)graph; \ +}; +// hipGraphDestroyNode[('hipGraphNode_t', 'node')] +#define INIT_hipGraphDestroyNode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphDestroyNode.node = (hipGraphNode_t)node; \ +}; +// hipGraphEventRecordNodeGetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t*', 'event_out')] +#define INIT_hipGraphEventRecordNodeGetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphEventRecordNodeGetEvent.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphEventRecordNodeGetEvent.event_out = (hipEvent_t*)event_out; \ +}; +// hipGraphEventRecordNodeSetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t', 'event')] +#define INIT_hipGraphEventRecordNodeSetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphEventRecordNodeSetEvent.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphEventRecordNodeSetEvent.event = (hipEvent_t)event; \ +}; +// hipGraphEventWaitNodeGetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t*', 'event_out')] +#define INIT_hipGraphEventWaitNodeGetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphEventWaitNodeGetEvent.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphEventWaitNodeGetEvent.event_out = (hipEvent_t*)event_out; \ +}; +// hipGraphEventWaitNodeSetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t', 'event')] +#define INIT_hipGraphEventWaitNodeSetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphEventWaitNodeSetEvent.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphEventWaitNodeSetEvent.event = (hipEvent_t)event; \ +}; +// hipGraphExecChildGraphNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('hipGraph_t', 'childGraph')] +#define INIT_hipGraphExecChildGraphNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecChildGraphNodeSetParams.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecChildGraphNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecChildGraphNodeSetParams.childGraph = (hipGraph_t)childGraph; \ +}; +// hipGraphExecDestroy[('hipGraphExec_t', 'graphExec')] +#define INIT_hipGraphExecDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecDestroy.graphExec = (hipGraphExec_t)pGraphExec; \ +}; +// hipGraphExecEventRecordNodeSetEvent[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('hipEvent_t', 'event')] +#define INIT_hipGraphExecEventRecordNodeSetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecEventRecordNodeSetEvent.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecEventRecordNodeSetEvent.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphExecEventRecordNodeSetEvent.event = (hipEvent_t)event; \ +}; +// hipGraphExecEventWaitNodeSetEvent[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('hipEvent_t', 'event')] +#define INIT_hipGraphExecEventWaitNodeSetEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecEventWaitNodeSetEvent.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecEventWaitNodeSetEvent.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphExecEventWaitNodeSetEvent.event = (hipEvent_t)event; \ +}; +// hipGraphExecExternalSemaphoresSignalNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] +#define INIT_hipGraphExecExternalSemaphoresSignalNodeSetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphExecExternalSemaphoresWaitNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] +#define INIT_hipGraphExecExternalSemaphoresWaitNodeSetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphExecHostNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipHostNodeParams*', 'pNodeParams')] +#define INIT_hipGraphExecHostNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecHostNodeSetParams.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecHostNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecHostNodeSetParams.pNodeParams = (const hipHostNodeParams*)pNodeParams; \ +}; +// hipGraphExecKernelNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipKernelNodeParams*', 'pNodeParams')] +#define INIT_hipGraphExecKernelNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecKernelNodeSetParams.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecKernelNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecKernelNodeSetParams.pNodeParams = (const hipKernelNodeParams*)pNodeParams; \ +}; +// hipGraphExecMemcpyNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('hipMemcpy3DParms*', 'pNodeParams')] +#define INIT_hipGraphExecMemcpyNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecMemcpyNodeSetParams.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams.pNodeParams = (hipMemcpy3DParms*)pNodeParams; \ +}; +// hipGraphExecMemcpyNodeSetParams1D[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphExecMemcpyNodeSetParams1D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.dst = (void*)dst; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.src = (const void*)src; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.count = (size_t)count; \ + cb_data.args.hipGraphExecMemcpyNodeSetParams1D.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphExecMemcpyNodeSetParamsFromSymbol[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphExecMemcpyNodeSetParamsFromSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.dst = (void*)dst; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.count = (size_t)count; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsFromSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphExecMemcpyNodeSetParamsToSymbol[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphExecMemcpyNodeSetParamsToSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.src = (const void*)src; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.count = (size_t)count; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphExecMemcpyNodeSetParamsToSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphExecMemsetNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipMemsetParams*', 'pNodeParams')] +#define INIT_hipGraphExecMemsetNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecMemsetNodeSetParams.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecMemsetNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphExecMemsetNodeSetParams.pNodeParams = (const hipMemsetParams*)pNodeParams; \ +}; +// hipGraphExecUpdate[('hipGraphExec_t', 'hGraphExec'), ('hipGraph_t', 'hGraph'), ('hipGraphNode_t*', 'hErrorNode_out'), ('hipGraphExecUpdateResult*', 'updateResult_out')] +#define INIT_hipGraphExecUpdate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphExecUpdate.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphExecUpdate.hGraph = (hipGraph_t)hGraph; \ + cb_data.args.hipGraphExecUpdate.hErrorNode_out = (hipGraphNode_t*)hErrorNode_out; \ + cb_data.args.hipGraphExecUpdate.updateResult_out = (hipGraphExecUpdateResult*)updateResult_out; \ +}; +// hipGraphExternalSemaphoresSignalNodeGetParams[('hipGraphNode_t', 'hNode'), ('hipExternalSemaphoreSignalNodeParams*', 'params_out')] +#define INIT_hipGraphExternalSemaphoresSignalNodeGetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphExternalSemaphoresSignalNodeSetParams[('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] +#define INIT_hipGraphExternalSemaphoresSignalNodeSetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphExternalSemaphoresWaitNodeGetParams[('hipGraphNode_t', 'hNode'), ('hipExternalSemaphoreWaitNodeParams*', 'params_out')] +#define INIT_hipGraphExternalSemaphoresWaitNodeGetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphExternalSemaphoresWaitNodeSetParams[('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] +#define INIT_hipGraphExternalSemaphoresWaitNodeSetParams_CB_ARGS_DATA(cb_data) { \ +}; +// hipGraphGetEdges[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'from'), ('hipGraphNode_t*', 'to'), ('size_t*', 'numEdges')] +#define INIT_hipGraphGetEdges_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphGetEdges.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphGetEdges.from = (hipGraphNode_t*)from; \ + cb_data.args.hipGraphGetEdges.to = (hipGraphNode_t*)to; \ + cb_data.args.hipGraphGetEdges.numEdges = (size_t*)numEdges; \ +}; +// hipGraphGetNodes[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'nodes'), ('size_t*', 'numNodes')] +#define INIT_hipGraphGetNodes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphGetNodes.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphGetNodes.nodes = (hipGraphNode_t*)nodes; \ + cb_data.args.hipGraphGetNodes.numNodes = (size_t*)numNodes; \ +}; +// hipGraphGetRootNodes[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'pRootNodes'), ('size_t*', 'pNumRootNodes')] +#define INIT_hipGraphGetRootNodes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphGetRootNodes.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphGetRootNodes.pRootNodes = (hipGraphNode_t*)pRootNodes; \ + cb_data.args.hipGraphGetRootNodes.pNumRootNodes = (size_t*)pNumRootNodes; \ +}; +// hipGraphHostNodeGetParams[('hipGraphNode_t', 'node'), ('hipHostNodeParams*', 'pNodeParams')] +#define INIT_hipGraphHostNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphHostNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphHostNodeGetParams.pNodeParams = (hipHostNodeParams*)pNodeParams; \ +}; +// hipGraphHostNodeSetParams[('hipGraphNode_t', 'node'), ('const hipHostNodeParams*', 'pNodeParams')] +#define INIT_hipGraphHostNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphHostNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphHostNodeSetParams.pNodeParams = (const hipHostNodeParams*)pNodeParams; \ +}; +// hipGraphInstantiate[('hipGraphExec_t*', 'pGraphExec'), ('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'pErrorNode'), ('char*', 'pLogBuffer'), ('size_t', 'bufferSize')] +#define INIT_hipGraphInstantiate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphInstantiate.pGraphExec = (hipGraphExec_t*)pGraphExec; \ + cb_data.args.hipGraphInstantiate.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphInstantiate.pErrorNode = (hipGraphNode_t*)pErrorNode; \ + cb_data.args.hipGraphInstantiate.pLogBuffer = (char*)pLogBuffer; \ + cb_data.args.hipGraphInstantiate.bufferSize = (size_t)bufferSize; \ +}; +// hipGraphInstantiateWithFlags[('hipGraphExec_t*', 'pGraphExec'), ('hipGraph_t', 'graph'), ('unsigned long long', 'flags')] +#define INIT_hipGraphInstantiateWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphInstantiateWithFlags.pGraphExec = (hipGraphExec_t*)pGraphExec; \ + cb_data.args.hipGraphInstantiateWithFlags.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphInstantiateWithFlags.flags = (unsigned long long)flags; \ +}; +// hipGraphKernelNodeCopyAttributes[('hipGraphNode_t', 'hSrc'), ('hipGraphNode_t', 'hDst')] +#define INIT_hipGraphKernelNodeCopyAttributes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphKernelNodeCopyAttributes.hSrc = (hipGraphNode_t)hSrc; \ + cb_data.args.hipGraphKernelNodeCopyAttributes.hDst = (hipGraphNode_t)hDst; \ +}; +// hipGraphKernelNodeGetAttribute[('hipGraphNode_t', 'hNode'), ('hipKernelNodeAttrID', 'attr'), ('hipKernelNodeAttrValue*', 'value')] +#define INIT_hipGraphKernelNodeGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphKernelNodeGetAttribute.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphKernelNodeGetAttribute.attr = (hipKernelNodeAttrID)attr; \ + cb_data.args.hipGraphKernelNodeGetAttribute.value = (hipKernelNodeAttrValue*)value; \ +}; +// hipGraphKernelNodeGetParams[('hipGraphNode_t', 'node'), ('hipKernelNodeParams*', 'pNodeParams')] +#define INIT_hipGraphKernelNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphKernelNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphKernelNodeGetParams.pNodeParams = (hipKernelNodeParams*)pNodeParams; \ +}; +// hipGraphKernelNodeSetAttribute[('hipGraphNode_t', 'hNode'), ('hipKernelNodeAttrID', 'attr'), ('const hipKernelNodeAttrValue*', 'value')] +#define INIT_hipGraphKernelNodeSetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphKernelNodeSetAttribute.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphKernelNodeSetAttribute.attr = (hipKernelNodeAttrID)attr; \ + cb_data.args.hipGraphKernelNodeSetAttribute.value = (const hipKernelNodeAttrValue*)value; \ +}; +// hipGraphKernelNodeSetParams[('hipGraphNode_t', 'node'), ('const hipKernelNodeParams*', 'pNodeParams')] +#define INIT_hipGraphKernelNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphKernelNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphKernelNodeSetParams.pNodeParams = (const hipKernelNodeParams*)pNodeParams; \ +}; +// hipGraphLaunch[('hipGraphExec_t', 'graphExec'), ('hipStream_t', 'stream')] +#define INIT_hipGraphLaunch_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphLaunch.graphExec = (hipGraphExec_t)graphExec; \ + cb_data.args.hipGraphLaunch.stream = (hipStream_t)stream; \ +}; +// hipGraphMemAllocNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemAllocNodeParams*', 'pNodeParams')] +#define INIT_hipGraphMemAllocNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemAllocNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemAllocNodeGetParams.pNodeParams = (hipMemAllocNodeParams*)pNodeParams; \ +}; +// hipGraphMemFreeNodeGetParams[('hipGraphNode_t', 'node'), ('void*', 'dev_ptr')] +#define INIT_hipGraphMemFreeNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemFreeNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemFreeNodeGetParams.dev_ptr = (void*)dev_ptr; \ +}; +// hipGraphMemcpyNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemcpy3DParms*', 'pNodeParams')] +#define INIT_hipGraphMemcpyNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemcpyNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemcpyNodeGetParams.pNodeParams = (hipMemcpy3DParms*)pNodeParams; \ +}; +// hipGraphMemcpyNodeSetParams[('hipGraphNode_t', 'node'), ('const hipMemcpy3DParms*', 'pNodeParams')] +#define INIT_hipGraphMemcpyNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemcpyNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemcpyNodeSetParams.pNodeParams = (const hipMemcpy3DParms*)pNodeParams; \ +}; +// hipGraphMemcpyNodeSetParams1D[('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphMemcpyNodeSetParams1D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemcpyNodeSetParams1D.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemcpyNodeSetParams1D.dst = (void*)dst; \ + cb_data.args.hipGraphMemcpyNodeSetParams1D.src = (const void*)src; \ + cb_data.args.hipGraphMemcpyNodeSetParams1D.count = (size_t)count; \ + cb_data.args.hipGraphMemcpyNodeSetParams1D.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphMemcpyNodeSetParamsFromSymbol[('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphMemcpyNodeSetParamsFromSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.dst = (void*)dst; \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.count = (size_t)count; \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphMemcpyNodeSetParamsFromSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphMemcpyNodeSetParamsToSymbol[('hipGraphNode_t', 'node'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipGraphMemcpyNodeSetParamsToSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.src = (const void*)src; \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.count = (size_t)count; \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.offset = (size_t)offset; \ + cb_data.args.hipGraphMemcpyNodeSetParamsToSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipGraphMemsetNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemsetParams*', 'pNodeParams')] +#define INIT_hipGraphMemsetNodeGetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemsetNodeGetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemsetNodeGetParams.pNodeParams = (hipMemsetParams*)pNodeParams; \ +}; +// hipGraphMemsetNodeSetParams[('hipGraphNode_t', 'node'), ('const hipMemsetParams*', 'pNodeParams')] +#define INIT_hipGraphMemsetNodeSetParams_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphMemsetNodeSetParams.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphMemsetNodeSetParams.pNodeParams = (const hipMemsetParams*)pNodeParams; \ +}; +// hipGraphNodeFindInClone[('hipGraphNode_t*', 'pNode'), ('hipGraphNode_t', 'originalNode'), ('hipGraph_t', 'clonedGraph')] +#define INIT_hipGraphNodeFindInClone_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeFindInClone.pNode = (hipGraphNode_t*)pNode; \ + cb_data.args.hipGraphNodeFindInClone.originalNode = (hipGraphNode_t)originalNode; \ + cb_data.args.hipGraphNodeFindInClone.clonedGraph = (hipGraph_t)clonedGraph; \ +}; +// hipGraphNodeGetDependencies[('hipGraphNode_t', 'node'), ('hipGraphNode_t*', 'pDependencies'), ('size_t*', 'pNumDependencies')] +#define INIT_hipGraphNodeGetDependencies_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeGetDependencies.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphNodeGetDependencies.pDependencies = (hipGraphNode_t*)pDependencies; \ + cb_data.args.hipGraphNodeGetDependencies.pNumDependencies = (size_t*)pNumDependencies; \ +}; +// hipGraphNodeGetDependentNodes[('hipGraphNode_t', 'node'), ('hipGraphNode_t*', 'pDependentNodes'), ('size_t*', 'pNumDependentNodes')] +#define INIT_hipGraphNodeGetDependentNodes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeGetDependentNodes.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphNodeGetDependentNodes.pDependentNodes = (hipGraphNode_t*)pDependentNodes; \ + cb_data.args.hipGraphNodeGetDependentNodes.pNumDependentNodes = (size_t*)pNumDependentNodes; \ +}; +// hipGraphNodeGetEnabled[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('unsigned int*', 'isEnabled')] +#define INIT_hipGraphNodeGetEnabled_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeGetEnabled.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphNodeGetEnabled.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphNodeGetEnabled.isEnabled = (unsigned int*)isEnabled; \ +}; +// hipGraphNodeGetType[('hipGraphNode_t', 'node'), ('hipGraphNodeType*', 'pType')] +#define INIT_hipGraphNodeGetType_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeGetType.node = (hipGraphNode_t)node; \ + cb_data.args.hipGraphNodeGetType.pType = (hipGraphNodeType*)pType; \ +}; +// hipGraphNodeSetEnabled[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('unsigned int', 'isEnabled')] +#define INIT_hipGraphNodeSetEnabled_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphNodeSetEnabled.hGraphExec = (hipGraphExec_t)hGraphExec; \ + cb_data.args.hipGraphNodeSetEnabled.hNode = (hipGraphNode_t)hNode; \ + cb_data.args.hipGraphNodeSetEnabled.isEnabled = (unsigned int)isEnabled; \ +}; +// hipGraphReleaseUserObject[('hipGraph_t', 'graph'), ('hipUserObject_t', 'object'), ('unsigned int', 'count')] +#define INIT_hipGraphReleaseUserObject_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphReleaseUserObject.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphReleaseUserObject.object = (hipUserObject_t)object; \ + cb_data.args.hipGraphReleaseUserObject.count = (unsigned int)count; \ +}; +// hipGraphRemoveDependencies[('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'from'), ('const hipGraphNode_t*', 'to'), ('size_t', 'numDependencies')] +#define INIT_hipGraphRemoveDependencies_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphRemoveDependencies.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphRemoveDependencies.from = (const hipGraphNode_t*)from; \ + cb_data.args.hipGraphRemoveDependencies.to = (const hipGraphNode_t*)to; \ + cb_data.args.hipGraphRemoveDependencies.numDependencies = (size_t)numDependencies; \ +}; +// hipGraphRetainUserObject[('hipGraph_t', 'graph'), ('hipUserObject_t', 'object'), ('unsigned int', 'count'), ('unsigned int', 'flags')] +#define INIT_hipGraphRetainUserObject_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphRetainUserObject.graph = (hipGraph_t)graph; \ + cb_data.args.hipGraphRetainUserObject.object = (hipUserObject_t)object; \ + cb_data.args.hipGraphRetainUserObject.count = (unsigned int)count; \ + cb_data.args.hipGraphRetainUserObject.flags = (unsigned int)flags; \ +}; +// hipGraphUpload[('hipGraphExec_t', 'graphExec'), ('hipStream_t', 'stream')] +#define INIT_hipGraphUpload_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphUpload.graphExec = (hipGraphExec_t)graphExec; \ + cb_data.args.hipGraphUpload.stream = (hipStream_t)stream; \ +}; +// hipGraphicsGLRegisterBuffer[('hipGraphicsResource**', 'resource'), ('GLuint', 'buffer'), ('unsigned int', 'flags')] +#define INIT_hipGraphicsGLRegisterBuffer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsGLRegisterBuffer.resource = (hipGraphicsResource**)resource; \ + cb_data.args.hipGraphicsGLRegisterBuffer.buffer = (GLuint)buffer; \ + cb_data.args.hipGraphicsGLRegisterBuffer.flags = (unsigned int)flags; \ +}; +// hipGraphicsGLRegisterImage[('hipGraphicsResource**', 'resource'), ('GLuint', 'image'), ('GLenum', 'target'), ('unsigned int', 'flags')] +#define INIT_hipGraphicsGLRegisterImage_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsGLRegisterImage.resource = (hipGraphicsResource**)resource; \ + cb_data.args.hipGraphicsGLRegisterImage.image = (GLuint)image; \ + cb_data.args.hipGraphicsGLRegisterImage.target = (GLenum)target; \ + cb_data.args.hipGraphicsGLRegisterImage.flags = (unsigned int)flags; \ +}; +// hipGraphicsMapResources[('int', 'count'), ('hipGraphicsResource_t*', 'resources'), ('hipStream_t', 'stream')] +#define INIT_hipGraphicsMapResources_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsMapResources.count = (int)count; \ + cb_data.args.hipGraphicsMapResources.resources = (hipGraphicsResource_t*)resources; \ + cb_data.args.hipGraphicsMapResources.stream = (hipStream_t)stream; \ +}; +// hipGraphicsResourceGetMappedPointer[('void**', 'devPtr'), ('size_t*', 'size'), ('hipGraphicsResource_t', 'resource')] +#define INIT_hipGraphicsResourceGetMappedPointer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsResourceGetMappedPointer.devPtr = (void**)devPtr; \ + cb_data.args.hipGraphicsResourceGetMappedPointer.size = (size_t*)size; \ + cb_data.args.hipGraphicsResourceGetMappedPointer.resource = (hipGraphicsResource_t)resource; \ +}; +// hipGraphicsSubResourceGetMappedArray[('hipArray_t*', 'array'), ('hipGraphicsResource_t', 'resource'), ('unsigned int', 'arrayIndex'), ('unsigned int', 'mipLevel')] +#define INIT_hipGraphicsSubResourceGetMappedArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsSubResourceGetMappedArray.array = (hipArray_t*)array; \ + cb_data.args.hipGraphicsSubResourceGetMappedArray.resource = (hipGraphicsResource_t)resource; \ + cb_data.args.hipGraphicsSubResourceGetMappedArray.arrayIndex = (unsigned int)arrayIndex; \ + cb_data.args.hipGraphicsSubResourceGetMappedArray.mipLevel = (unsigned int)mipLevel; \ +}; +// hipGraphicsUnmapResources[('int', 'count'), ('hipGraphicsResource_t*', 'resources'), ('hipStream_t', 'stream')] +#define INIT_hipGraphicsUnmapResources_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsUnmapResources.count = (int)count; \ + cb_data.args.hipGraphicsUnmapResources.resources = (hipGraphicsResource_t*)resources; \ + cb_data.args.hipGraphicsUnmapResources.stream = (hipStream_t)stream; \ +}; +// hipGraphicsUnregisterResource[('hipGraphicsResource_t', 'resource')] +#define INIT_hipGraphicsUnregisterResource_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipGraphicsUnregisterResource.resource = (hipGraphicsResource_t)resource; \ +}; +// hipHccModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'globalWorkSizeX'), ('unsigned int', 'globalWorkSizeY'), ('unsigned int', 'globalWorkSizeZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'hStream'), ('void**', 'kernelParams'), ('void**', 'extra'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent')] +#define INIT_hipHccModuleLaunchKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHccModuleLaunchKernel.f = (hipFunction_t)f; \ + cb_data.args.hipHccModuleLaunchKernel.globalWorkSizeX = (unsigned int)globalWorkSizeX; \ + cb_data.args.hipHccModuleLaunchKernel.globalWorkSizeY = (unsigned int)globalWorkSizeY; \ + cb_data.args.hipHccModuleLaunchKernel.globalWorkSizeZ = (unsigned int)globalWorkSizeZ; \ + cb_data.args.hipHccModuleLaunchKernel.blockDimX = (unsigned int)blockDimX; \ + cb_data.args.hipHccModuleLaunchKernel.blockDimY = (unsigned int)blockDimY; \ + cb_data.args.hipHccModuleLaunchKernel.blockDimZ = (unsigned int)blockDimZ; \ + cb_data.args.hipHccModuleLaunchKernel.sharedMemBytes = (size_t)sharedMemBytes; \ + cb_data.args.hipHccModuleLaunchKernel.hStream = (hipStream_t)hStream; \ + cb_data.args.hipHccModuleLaunchKernel.kernelParams = (void**)kernelParams; \ + cb_data.args.hipHccModuleLaunchKernel.extra = (void**)extra; \ + cb_data.args.hipHccModuleLaunchKernel.startEvent = (hipEvent_t)startEvent; \ + cb_data.args.hipHccModuleLaunchKernel.stopEvent = (hipEvent_t)stopEvent; \ +}; +// hipHostAlloc[('void**', 'ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] +#define INIT_hipHostAlloc_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostAlloc.ptr = (void**)ptr; \ + cb_data.args.hipHostAlloc.size = (size_t)sizeBytes; \ + cb_data.args.hipHostAlloc.flags = (unsigned int)flags; \ +}; +// hipHostFree[('void*', 'ptr')] +#define INIT_hipHostFree_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostFree.ptr = (void*)ptr; \ +}; +// hipHostGetDevicePointer[('void**', 'devPtr'), ('void*', 'hstPtr'), ('unsigned int', 'flags')] +#define INIT_hipHostGetDevicePointer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostGetDevicePointer.devPtr = (void**)devicePointer; \ + cb_data.args.hipHostGetDevicePointer.hstPtr = (void*)hostPointer; \ + cb_data.args.hipHostGetDevicePointer.flags = (unsigned int)flags; \ +}; +// hipHostGetFlags[('unsigned int*', 'flagsPtr'), ('void*', 'hostPtr')] +#define INIT_hipHostGetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostGetFlags.flagsPtr = (unsigned int*)flagsPtr; \ + cb_data.args.hipHostGetFlags.hostPtr = (void*)hostPtr; \ +}; +// hipHostMalloc[('void**', 'ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] +#define INIT_hipHostMalloc_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostMalloc.ptr = (void**)ptr; \ + cb_data.args.hipHostMalloc.size = (size_t)sizeBytes; \ + cb_data.args.hipHostMalloc.flags = (unsigned int)flags; \ +}; +// hipHostRegister[('void*', 'hostPtr'), ('size_t', 'sizeBytes'), ('unsigned int', 'flags')] +#define INIT_hipHostRegister_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostRegister.hostPtr = (void*)hostPtr; \ + cb_data.args.hipHostRegister.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipHostRegister.flags = (unsigned int)flags; \ +}; +// hipHostUnregister[('void*', 'hostPtr')] +#define INIT_hipHostUnregister_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipHostUnregister.hostPtr = (void*)hostPtr; \ +}; +// hipImportExternalMemory[('hipExternalMemory_t*', 'extMem_out'), ('const hipExternalMemoryHandleDesc*', 'memHandleDesc')] +#define INIT_hipImportExternalMemory_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipImportExternalMemory.extMem_out = (hipExternalMemory_t*)extMem_out; \ + cb_data.args.hipImportExternalMemory.memHandleDesc = (const hipExternalMemoryHandleDesc*)memHandleDesc; \ +}; +// hipImportExternalSemaphore[('hipExternalSemaphore_t*', 'extSem_out'), ('const hipExternalSemaphoreHandleDesc*', 'semHandleDesc')] +#define INIT_hipImportExternalSemaphore_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipImportExternalSemaphore.extSem_out = (hipExternalSemaphore_t*)extSem_out; \ + cb_data.args.hipImportExternalSemaphore.semHandleDesc = (const hipExternalSemaphoreHandleDesc*)semHandleDesc; \ +}; +// hipInit[('unsigned int', 'flags')] +#define INIT_hipInit_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipInit.flags = (unsigned int)flags; \ +}; +// hipIpcCloseMemHandle[('void*', 'devPtr')] +#define INIT_hipIpcCloseMemHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipIpcCloseMemHandle.devPtr = (void*)dev_ptr; \ +}; +// hipIpcGetEventHandle[('hipIpcEventHandle_t*', 'handle'), ('hipEvent_t', 'event')] +#define INIT_hipIpcGetEventHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipIpcGetEventHandle.handle = (hipIpcEventHandle_t*)handle; \ + cb_data.args.hipIpcGetEventHandle.event = (hipEvent_t)event; \ +}; +// hipIpcGetMemHandle[('hipIpcMemHandle_t*', 'handle'), ('void*', 'devPtr')] +#define INIT_hipIpcGetMemHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipIpcGetMemHandle.handle = (hipIpcMemHandle_t*)handle; \ + cb_data.args.hipIpcGetMemHandle.devPtr = (void*)dev_ptr; \ +}; +// hipIpcOpenEventHandle[('hipEvent_t*', 'event'), ('hipIpcEventHandle_t', 'handle')] +#define INIT_hipIpcOpenEventHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipIpcOpenEventHandle.event = (hipEvent_t*)event; \ + cb_data.args.hipIpcOpenEventHandle.handle = (hipIpcEventHandle_t)handle; \ +}; +// hipIpcOpenMemHandle[('void**', 'devPtr'), ('hipIpcMemHandle_t', 'handle'), ('unsigned int', 'flags')] +#define INIT_hipIpcOpenMemHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipIpcOpenMemHandle.devPtr = (void**)dev_ptr; \ + cb_data.args.hipIpcOpenMemHandle.handle = (hipIpcMemHandle_t)handle; \ + cb_data.args.hipIpcOpenMemHandle.flags = (unsigned int)flags; \ +}; +// hipLaunchByPtr[('const void*', 'hostFunction')] +#define INIT_hipLaunchByPtr_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipLaunchByPtr.hostFunction = (const void*)hostFunction; \ +}; +// hipLaunchCooperativeKernel[('const void*', 'f'), ('dim3', 'gridDim'), ('dim3', 'blockDimX'), ('void**', 'kernelParams'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream')] +#define INIT_hipLaunchCooperativeKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipLaunchCooperativeKernel.f = (const void*)f; \ + cb_data.args.hipLaunchCooperativeKernel.gridDim = (dim3)gridDim; \ + cb_data.args.hipLaunchCooperativeKernel.blockDimX = (dim3)blockDim; \ + cb_data.args.hipLaunchCooperativeKernel.kernelParams = (void**)kernelParams; \ + cb_data.args.hipLaunchCooperativeKernel.sharedMemBytes = (unsigned int)sharedMemBytes; \ + cb_data.args.hipLaunchCooperativeKernel.stream = (hipStream_t)hStream; \ +}; +// hipLaunchCooperativeKernelMultiDevice[('hipLaunchParams*', 'launchParamsList'), ('int', 'numDevices'), ('unsigned int', 'flags')] +#define INIT_hipLaunchCooperativeKernelMultiDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipLaunchCooperativeKernelMultiDevice.launchParamsList = (hipLaunchParams*)launchParamsList; \ + cb_data.args.hipLaunchCooperativeKernelMultiDevice.numDevices = (int)numDevices; \ + cb_data.args.hipLaunchCooperativeKernelMultiDevice.flags = (unsigned int)flags; \ +}; +// hipLaunchHostFunc[('hipStream_t', 'stream'), ('hipHostFn_t', 'fn'), ('void*', 'userData')] +#define INIT_hipLaunchHostFunc_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipLaunchHostFunc.stream = (hipStream_t)stream; \ + cb_data.args.hipLaunchHostFunc.fn = (hipHostFn_t)fn; \ + cb_data.args.hipLaunchHostFunc.userData = (void*)userData; \ +}; +// hipLaunchKernel[('const void*', 'function_address'), ('dim3', 'numBlocks'), ('dim3', 'dimBlocks'), ('void**', 'args'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'stream')] +#define INIT_hipLaunchKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipLaunchKernel.function_address = (const void*)hostFunction; \ + cb_data.args.hipLaunchKernel.numBlocks = (dim3)gridDim; \ + cb_data.args.hipLaunchKernel.dimBlocks = (dim3)blockDim; \ + cb_data.args.hipLaunchKernel.args = (void**)args; \ + cb_data.args.hipLaunchKernel.sharedMemBytes = (size_t)sharedMemBytes; \ + cb_data.args.hipLaunchKernel.stream = (hipStream_t)stream; \ +}; +// hipMalloc[('void**', 'ptr'), ('size_t', 'size')] +#define INIT_hipMalloc_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMalloc.ptr = (void**)ptr; \ + cb_data.args.hipMalloc.size = (size_t)sizeBytes; \ +}; +// hipMalloc3D[('hipPitchedPtr*', 'pitchedDevPtr'), ('hipExtent', 'extent')] +#define INIT_hipMalloc3D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMalloc3D.pitchedDevPtr = (hipPitchedPtr*)pitchedDevPtr; \ + cb_data.args.hipMalloc3D.extent = (hipExtent)extent; \ +}; +// hipMalloc3DArray[('hipArray_t*', 'array'), ('const hipChannelFormatDesc*', 'desc'), ('hipExtent', 'extent'), ('unsigned int', 'flags')] +#define INIT_hipMalloc3DArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMalloc3DArray.array = (hipArray_t*)array; \ + cb_data.args.hipMalloc3DArray.desc = (const hipChannelFormatDesc*)desc; \ + cb_data.args.hipMalloc3DArray.extent = (hipExtent)extent; \ + cb_data.args.hipMalloc3DArray.flags = (unsigned int)flags; \ +}; +// hipMallocArray[('hipArray_t*', 'array'), ('const hipChannelFormatDesc*', 'desc'), ('size_t', 'width'), ('size_t', 'height'), ('unsigned int', 'flags')] +#define INIT_hipMallocArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocArray.array = (hipArray_t*)array; \ + cb_data.args.hipMallocArray.desc = (const hipChannelFormatDesc*)desc; \ + cb_data.args.hipMallocArray.width = (size_t)width; \ + cb_data.args.hipMallocArray.height = (size_t)height; \ + cb_data.args.hipMallocArray.flags = (unsigned int)flags; \ +}; +// hipMallocAsync[('void**', 'dev_ptr'), ('size_t', 'size'), ('hipStream_t', 'stream')] +#define INIT_hipMallocAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocAsync.dev_ptr = (void**)dev_ptr; \ + cb_data.args.hipMallocAsync.size = (size_t)size; \ + cb_data.args.hipMallocAsync.stream = (hipStream_t)stream; \ +}; +// hipMallocFromPoolAsync[('void**', 'dev_ptr'), ('size_t', 'size'), ('hipMemPool_t', 'mem_pool'), ('hipStream_t', 'stream')] +#define INIT_hipMallocFromPoolAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocFromPoolAsync.dev_ptr = (void**)dev_ptr; \ + cb_data.args.hipMallocFromPoolAsync.size = (size_t)size; \ + cb_data.args.hipMallocFromPoolAsync.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMallocFromPoolAsync.stream = (hipStream_t)stream; \ +}; +// hipMallocHost[('void**', 'ptr'), ('size_t', 'size')] +#define INIT_hipMallocHost_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocHost.ptr = (void**)ptr; \ + cb_data.args.hipMallocHost.size = (size_t)size; \ +}; +// hipMallocManaged[('void**', 'dev_ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] +#define INIT_hipMallocManaged_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocManaged.dev_ptr = (void**)dev_ptr; \ + cb_data.args.hipMallocManaged.size = (size_t)size; \ + cb_data.args.hipMallocManaged.flags = (unsigned int)flags; \ +}; +// hipMallocMipmappedArray[('hipMipmappedArray_t*', 'mipmappedArray'), ('const hipChannelFormatDesc*', 'desc'), ('hipExtent', 'extent'), ('unsigned int', 'numLevels'), ('unsigned int', 'flags')] +#define INIT_hipMallocMipmappedArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocMipmappedArray.mipmappedArray = (hipMipmappedArray_t*)mipmappedArray; \ + cb_data.args.hipMallocMipmappedArray.desc = (const hipChannelFormatDesc*)desc; \ + cb_data.args.hipMallocMipmappedArray.extent = (hipExtent)extent; \ + cb_data.args.hipMallocMipmappedArray.numLevels = (unsigned int)numLevels; \ + cb_data.args.hipMallocMipmappedArray.flags = (unsigned int)flags; \ +}; +// hipMallocPitch[('void**', 'ptr'), ('size_t*', 'pitch'), ('size_t', 'width'), ('size_t', 'height')] +#define INIT_hipMallocPitch_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMallocPitch.ptr = (void**)ptr; \ + cb_data.args.hipMallocPitch.pitch = (size_t*)pitch; \ + cb_data.args.hipMallocPitch.width = (size_t)width; \ + cb_data.args.hipMallocPitch.height = (size_t)height; \ +}; +// hipMemAddressFree[('void*', 'devPtr'), ('size_t', 'size')] +#define INIT_hipMemAddressFree_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemAddressFree.devPtr = (void*)devPtr; \ + cb_data.args.hipMemAddressFree.size = (size_t)size; \ +}; +// hipMemAddressReserve[('void**', 'ptr'), ('size_t', 'size'), ('size_t', 'alignment'), ('void*', 'addr'), ('unsigned long long', 'flags')] +#define INIT_hipMemAddressReserve_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemAddressReserve.ptr = (void**)ptr; \ + cb_data.args.hipMemAddressReserve.size = (size_t)size; \ + cb_data.args.hipMemAddressReserve.alignment = (size_t)alignment; \ + cb_data.args.hipMemAddressReserve.addr = (void*)addr; \ + cb_data.args.hipMemAddressReserve.flags = (unsigned long long)flags; \ +}; +// hipMemAdvise[('const void*', 'dev_ptr'), ('size_t', 'count'), ('hipMemoryAdvise', 'advice'), ('int', 'device')] +#define INIT_hipMemAdvise_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemAdvise.dev_ptr = (const void*)dev_ptr; \ + cb_data.args.hipMemAdvise.count = (size_t)count; \ + cb_data.args.hipMemAdvise.advice = (hipMemoryAdvise)advice; \ + cb_data.args.hipMemAdvise.device = (int)device; \ +}; +// hipMemAllocHost[('void**', 'ptr'), ('size_t', 'size')] +#define INIT_hipMemAllocHost_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemAllocHost.ptr = (void**)ptr; \ + cb_data.args.hipMemAllocHost.size = (size_t)size; \ +}; +// hipMemAllocPitch[('hipDeviceptr_t*', 'dptr'), ('size_t*', 'pitch'), ('size_t', 'widthInBytes'), ('size_t', 'height'), ('unsigned int', 'elementSizeBytes')] +#define INIT_hipMemAllocPitch_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemAllocPitch.dptr = (hipDeviceptr_t*)dptr; \ + cb_data.args.hipMemAllocPitch.pitch = (size_t*)pitch; \ + cb_data.args.hipMemAllocPitch.widthInBytes = (size_t)widthInBytes; \ + cb_data.args.hipMemAllocPitch.height = (size_t)height; \ + cb_data.args.hipMemAllocPitch.elementSizeBytes = (unsigned int)elementSizeBytes; \ +}; +// hipMemCreate[('hipMemGenericAllocationHandle_t*', 'handle'), ('size_t', 'size'), ('const hipMemAllocationProp*', 'prop'), ('unsigned long long', 'flags')] +#define INIT_hipMemCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemCreate.handle = (hipMemGenericAllocationHandle_t*)handle; \ + cb_data.args.hipMemCreate.size = (size_t)size; \ + cb_data.args.hipMemCreate.prop = (const hipMemAllocationProp*)prop; \ + cb_data.args.hipMemCreate.flags = (unsigned long long)flags; \ +}; +// hipMemExportToShareableHandle[('void*', 'shareableHandle'), ('hipMemGenericAllocationHandle_t', 'handle'), ('hipMemAllocationHandleType', 'handleType'), ('unsigned long long', 'flags')] +#define INIT_hipMemExportToShareableHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemExportToShareableHandle.shareableHandle = (void*)shareableHandle; \ + cb_data.args.hipMemExportToShareableHandle.handle = (hipMemGenericAllocationHandle_t)handle; \ + cb_data.args.hipMemExportToShareableHandle.handleType = (hipMemAllocationHandleType)handleType; \ + cb_data.args.hipMemExportToShareableHandle.flags = (unsigned long long)flags; \ +}; +// hipMemGetAccess[('unsigned long long*', 'flags'), ('const hipMemLocation*', 'location'), ('void*', 'ptr')] +#define INIT_hipMemGetAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemGetAccess.flags = (unsigned long long*)flags; \ + cb_data.args.hipMemGetAccess.location = (const hipMemLocation*)location; \ + cb_data.args.hipMemGetAccess.ptr = (void*)ptr; \ +}; +// hipMemGetAddressRange[('hipDeviceptr_t*', 'pbase'), ('size_t*', 'psize'), ('hipDeviceptr_t', 'dptr')] +#define INIT_hipMemGetAddressRange_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemGetAddressRange.pbase = (hipDeviceptr_t*)pbase; \ + cb_data.args.hipMemGetAddressRange.psize = (size_t*)psize; \ + cb_data.args.hipMemGetAddressRange.dptr = (hipDeviceptr_t)dptr; \ +}; +// hipMemGetAllocationGranularity[('size_t*', 'granularity'), ('const hipMemAllocationProp*', 'prop'), ('hipMemAllocationGranularity_flags', 'option')] +#define INIT_hipMemGetAllocationGranularity_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemGetAllocationGranularity.granularity = (size_t*)granularity; \ + cb_data.args.hipMemGetAllocationGranularity.prop = (const hipMemAllocationProp*)prop; \ + cb_data.args.hipMemGetAllocationGranularity.option = (hipMemAllocationGranularity_flags)option; \ +}; +// hipMemGetAllocationPropertiesFromHandle[('hipMemAllocationProp*', 'prop'), ('hipMemGenericAllocationHandle_t', 'handle')] +#define INIT_hipMemGetAllocationPropertiesFromHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemGetAllocationPropertiesFromHandle.prop = (hipMemAllocationProp*)prop; \ + cb_data.args.hipMemGetAllocationPropertiesFromHandle.handle = (hipMemGenericAllocationHandle_t)handle; \ +}; +// hipMemGetInfo[('size_t*', 'free'), ('size_t*', 'total')] +#define INIT_hipMemGetInfo_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemGetInfo.free = (size_t*)free; \ + cb_data.args.hipMemGetInfo.total = (size_t*)total; \ +}; +// hipMemImportFromShareableHandle[('hipMemGenericAllocationHandle_t*', 'handle'), ('void*', 'osHandle'), ('hipMemAllocationHandleType', 'shHandleType')] +#define INIT_hipMemImportFromShareableHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemImportFromShareableHandle.handle = (hipMemGenericAllocationHandle_t*)handle; \ + cb_data.args.hipMemImportFromShareableHandle.osHandle = (void*)osHandle; \ + cb_data.args.hipMemImportFromShareableHandle.shHandleType = (hipMemAllocationHandleType)shHandleType; \ +}; +// hipMemMap[('void*', 'ptr'), ('size_t', 'size'), ('size_t', 'offset'), ('hipMemGenericAllocationHandle_t', 'handle'), ('unsigned long long', 'flags')] +#define INIT_hipMemMap_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemMap.ptr = (void*)ptr; \ + cb_data.args.hipMemMap.size = (size_t)size; \ + cb_data.args.hipMemMap.offset = (size_t)offset; \ + cb_data.args.hipMemMap.handle = (hipMemGenericAllocationHandle_t)handle; \ + cb_data.args.hipMemMap.flags = (unsigned long long)flags; \ +}; +// hipMemMapArrayAsync[('hipArrayMapInfo*', 'mapInfoList'), ('unsigned int', 'count'), ('hipStream_t', 'stream')] +#define INIT_hipMemMapArrayAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemMapArrayAsync.mapInfoList = (hipArrayMapInfo*)mapInfoList; \ + cb_data.args.hipMemMapArrayAsync.count = (unsigned int)count; \ + cb_data.args.hipMemMapArrayAsync.stream = (hipStream_t)stream; \ +}; +// hipMemPoolCreate[('hipMemPool_t*', 'mem_pool'), ('const hipMemPoolProps*', 'pool_props')] +#define INIT_hipMemPoolCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolCreate.mem_pool = (hipMemPool_t*)mem_pool; \ + cb_data.args.hipMemPoolCreate.pool_props = (const hipMemPoolProps*)pool_props; \ +}; +// hipMemPoolDestroy[('hipMemPool_t', 'mem_pool')] +#define INIT_hipMemPoolDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolDestroy.mem_pool = (hipMemPool_t)mem_pool; \ +}; +// hipMemPoolExportPointer[('hipMemPoolPtrExportData*', 'export_data'), ('void*', 'dev_ptr')] +#define INIT_hipMemPoolExportPointer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolExportPointer.export_data = (hipMemPoolPtrExportData*)export_data; \ + cb_data.args.hipMemPoolExportPointer.dev_ptr = (void*)ptr; \ +}; +// hipMemPoolExportToShareableHandle[('void*', 'shared_handle'), ('hipMemPool_t', 'mem_pool'), ('hipMemAllocationHandleType', 'handle_type'), ('unsigned int', 'flags')] +#define INIT_hipMemPoolExportToShareableHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolExportToShareableHandle.shared_handle = (void*)shared_handle; \ + cb_data.args.hipMemPoolExportToShareableHandle.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolExportToShareableHandle.handle_type = (hipMemAllocationHandleType)handle_type; \ + cb_data.args.hipMemPoolExportToShareableHandle.flags = (unsigned int)flags; \ +}; +// hipMemPoolGetAccess[('hipMemAccessFlags*', 'flags'), ('hipMemPool_t', 'mem_pool'), ('hipMemLocation*', 'location')] +#define INIT_hipMemPoolGetAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolGetAccess.flags = (hipMemAccessFlags*)flags; \ + cb_data.args.hipMemPoolGetAccess.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolGetAccess.location = (hipMemLocation*)location; \ +}; +// hipMemPoolGetAttribute[('hipMemPool_t', 'mem_pool'), ('hipMemPoolAttr', 'attr'), ('void*', 'value')] +#define INIT_hipMemPoolGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolGetAttribute.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolGetAttribute.attr = (hipMemPoolAttr)attr; \ + cb_data.args.hipMemPoolGetAttribute.value = (void*)value; \ +}; +// hipMemPoolImportFromShareableHandle[('hipMemPool_t*', 'mem_pool'), ('void*', 'shared_handle'), ('hipMemAllocationHandleType', 'handle_type'), ('unsigned int', 'flags')] +#define INIT_hipMemPoolImportFromShareableHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolImportFromShareableHandle.mem_pool = (hipMemPool_t*)mem_pool; \ + cb_data.args.hipMemPoolImportFromShareableHandle.shared_handle = (void*)shared_handle; \ + cb_data.args.hipMemPoolImportFromShareableHandle.handle_type = (hipMemAllocationHandleType)handle_type; \ + cb_data.args.hipMemPoolImportFromShareableHandle.flags = (unsigned int)flags; \ +}; +// hipMemPoolImportPointer[('void**', 'dev_ptr'), ('hipMemPool_t', 'mem_pool'), ('hipMemPoolPtrExportData*', 'export_data')] +#define INIT_hipMemPoolImportPointer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolImportPointer.dev_ptr = (void**)ptr; \ + cb_data.args.hipMemPoolImportPointer.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolImportPointer.export_data = (hipMemPoolPtrExportData*)export_data; \ +}; +// hipMemPoolSetAccess[('hipMemPool_t', 'mem_pool'), ('const hipMemAccessDesc*', 'desc_list'), ('size_t', 'count')] +#define INIT_hipMemPoolSetAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolSetAccess.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolSetAccess.desc_list = (const hipMemAccessDesc*)desc_list; \ + cb_data.args.hipMemPoolSetAccess.count = (size_t)count; \ +}; +// hipMemPoolSetAttribute[('hipMemPool_t', 'mem_pool'), ('hipMemPoolAttr', 'attr'), ('void*', 'value')] +#define INIT_hipMemPoolSetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolSetAttribute.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolSetAttribute.attr = (hipMemPoolAttr)attr; \ + cb_data.args.hipMemPoolSetAttribute.value = (void*)value; \ +}; +// hipMemPoolTrimTo[('hipMemPool_t', 'mem_pool'), ('size_t', 'min_bytes_to_hold')] +#define INIT_hipMemPoolTrimTo_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPoolTrimTo.mem_pool = (hipMemPool_t)mem_pool; \ + cb_data.args.hipMemPoolTrimTo.min_bytes_to_hold = (size_t)min_bytes_to_hold; \ +}; +// hipMemPrefetchAsync[('const void*', 'dev_ptr'), ('size_t', 'count'), ('int', 'device'), ('hipStream_t', 'stream')] +#define INIT_hipMemPrefetchAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPrefetchAsync.dev_ptr = (const void*)dev_ptr; \ + cb_data.args.hipMemPrefetchAsync.count = (size_t)count; \ + cb_data.args.hipMemPrefetchAsync.device = (int)device; \ + cb_data.args.hipMemPrefetchAsync.stream = (hipStream_t)stream; \ +}; +// hipMemPtrGetInfo[('void*', 'ptr'), ('size_t*', 'size')] +#define INIT_hipMemPtrGetInfo_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemPtrGetInfo.ptr = (void*)ptr; \ + cb_data.args.hipMemPtrGetInfo.size = (size_t*)size; \ +}; +// hipMemRangeGetAttribute[('void*', 'data'), ('size_t', 'data_size'), ('hipMemRangeAttribute', 'attribute'), ('const void*', 'dev_ptr'), ('size_t', 'count')] +#define INIT_hipMemRangeGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemRangeGetAttribute.data = (void*)data; \ + cb_data.args.hipMemRangeGetAttribute.data_size = (size_t)data_size; \ + cb_data.args.hipMemRangeGetAttribute.attribute = (hipMemRangeAttribute)attribute; \ + cb_data.args.hipMemRangeGetAttribute.dev_ptr = (const void*)dev_ptr; \ + cb_data.args.hipMemRangeGetAttribute.count = (size_t)count; \ +}; +// hipMemRangeGetAttributes[('void**', 'data'), ('size_t*', 'data_sizes'), ('hipMemRangeAttribute*', 'attributes'), ('size_t', 'num_attributes'), ('const void*', 'dev_ptr'), ('size_t', 'count')] +#define INIT_hipMemRangeGetAttributes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemRangeGetAttributes.data = (void**)data; \ + cb_data.args.hipMemRangeGetAttributes.data_sizes = (size_t*)data_sizes; \ + cb_data.args.hipMemRangeGetAttributes.attributes = (hipMemRangeAttribute*)attributes; \ + cb_data.args.hipMemRangeGetAttributes.num_attributes = (size_t)num_attributes; \ + cb_data.args.hipMemRangeGetAttributes.dev_ptr = (const void*)dev_ptr; \ + cb_data.args.hipMemRangeGetAttributes.count = (size_t)count; \ +}; +// hipMemRelease[('hipMemGenericAllocationHandle_t', 'handle')] +#define INIT_hipMemRelease_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemRelease.handle = (hipMemGenericAllocationHandle_t)handle; \ +}; +// hipMemRetainAllocationHandle[('hipMemGenericAllocationHandle_t*', 'handle'), ('void*', 'addr')] +#define INIT_hipMemRetainAllocationHandle_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemRetainAllocationHandle.handle = (hipMemGenericAllocationHandle_t*)handle; \ + cb_data.args.hipMemRetainAllocationHandle.addr = (void*)addr; \ +}; +// hipMemSetAccess[('void*', 'ptr'), ('size_t', 'size'), ('const hipMemAccessDesc*', 'desc'), ('size_t', 'count')] +#define INIT_hipMemSetAccess_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemSetAccess.ptr = (void*)ptr; \ + cb_data.args.hipMemSetAccess.size = (size_t)size; \ + cb_data.args.hipMemSetAccess.desc = (const hipMemAccessDesc*)desc; \ + cb_data.args.hipMemSetAccess.count = (size_t)count; \ +}; +// hipMemUnmap[('void*', 'ptr'), ('size_t', 'size')] +#define INIT_hipMemUnmap_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemUnmap.ptr = (void*)ptr; \ + cb_data.args.hipMemUnmap.size = (size_t)size; \ +}; +// hipMemcpy[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy.dst = (void*)dst; \ + cb_data.args.hipMemcpy.src = (const void*)src; \ + cb_data.args.hipMemcpy.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpy.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpy2D[('void*', 'dst'), ('size_t', 'dpitch'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpy2D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2D.dst = (void*)dst; \ + cb_data.args.hipMemcpy2D.dpitch = (size_t)dpitch; \ + cb_data.args.hipMemcpy2D.src = (const void*)src; \ + cb_data.args.hipMemcpy2D.spitch = (size_t)spitch; \ + cb_data.args.hipMemcpy2D.width = (size_t)width; \ + cb_data.args.hipMemcpy2D.height = (size_t)height; \ + cb_data.args.hipMemcpy2D.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpy2DAsync[('void*', 'dst'), ('size_t', 'dpitch'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpy2DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2DAsync.dst = (void*)dst; \ + cb_data.args.hipMemcpy2DAsync.dpitch = (size_t)dpitch; \ + cb_data.args.hipMemcpy2DAsync.src = (const void*)src; \ + cb_data.args.hipMemcpy2DAsync.spitch = (size_t)spitch; \ + cb_data.args.hipMemcpy2DAsync.width = (size_t)width; \ + cb_data.args.hipMemcpy2DAsync.height = (size_t)height; \ + cb_data.args.hipMemcpy2DAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpy2DAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpy2DFromArray[('void*', 'dst'), ('size_t', 'dpitch'), ('hipArray_const_t', 'src'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpy2DFromArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2DFromArray.dst = (void*)dst; \ + cb_data.args.hipMemcpy2DFromArray.dpitch = (size_t)dpitch; \ + cb_data.args.hipMemcpy2DFromArray.src = (hipArray_const_t)src; \ + cb_data.args.hipMemcpy2DFromArray.wOffset = (size_t)wOffsetSrc; \ + cb_data.args.hipMemcpy2DFromArray.hOffset = (size_t)hOffset; \ + cb_data.args.hipMemcpy2DFromArray.width = (size_t)width; \ + cb_data.args.hipMemcpy2DFromArray.height = (size_t)height; \ + cb_data.args.hipMemcpy2DFromArray.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpy2DFromArrayAsync[('void*', 'dst'), ('size_t', 'dpitch'), ('hipArray_const_t', 'src'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpy2DFromArrayAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2DFromArrayAsync.dst = (void*)dst; \ + cb_data.args.hipMemcpy2DFromArrayAsync.dpitch = (size_t)dpitch; \ + cb_data.args.hipMemcpy2DFromArrayAsync.src = (hipArray_const_t)src; \ + cb_data.args.hipMemcpy2DFromArrayAsync.wOffset = (size_t)wOffsetSrc; \ + cb_data.args.hipMemcpy2DFromArrayAsync.hOffset = (size_t)hOffsetSrc; \ + cb_data.args.hipMemcpy2DFromArrayAsync.width = (size_t)width; \ + cb_data.args.hipMemcpy2DFromArrayAsync.height = (size_t)height; \ + cb_data.args.hipMemcpy2DFromArrayAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpy2DFromArrayAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpy2DToArray[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpy2DToArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2DToArray.dst = (hipArray_t)dst; \ + cb_data.args.hipMemcpy2DToArray.wOffset = (size_t)wOffset; \ + cb_data.args.hipMemcpy2DToArray.hOffset = (size_t)hOffset; \ + cb_data.args.hipMemcpy2DToArray.src = (const void*)src; \ + cb_data.args.hipMemcpy2DToArray.spitch = (size_t)spitch; \ + cb_data.args.hipMemcpy2DToArray.width = (size_t)width; \ + cb_data.args.hipMemcpy2DToArray.height = (size_t)height; \ + cb_data.args.hipMemcpy2DToArray.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpy2DToArrayAsync[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpy2DToArrayAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy2DToArrayAsync.dst = (hipArray_t)dst; \ + cb_data.args.hipMemcpy2DToArrayAsync.wOffset = (size_t)wOffset; \ + cb_data.args.hipMemcpy2DToArrayAsync.hOffset = (size_t)hOffset; \ + cb_data.args.hipMemcpy2DToArrayAsync.src = (const void*)src; \ + cb_data.args.hipMemcpy2DToArrayAsync.spitch = (size_t)spitch; \ + cb_data.args.hipMemcpy2DToArrayAsync.width = (size_t)width; \ + cb_data.args.hipMemcpy2DToArrayAsync.height = (size_t)height; \ + cb_data.args.hipMemcpy2DToArrayAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpy2DToArrayAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpy3D[('const hipMemcpy3DParms*', 'p')] +#define INIT_hipMemcpy3D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy3D.p = (const hipMemcpy3DParms*)p; \ +}; +// hipMemcpy3DAsync[('const hipMemcpy3DParms*', 'p'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpy3DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpy3DAsync.p = (const hipMemcpy3DParms*)p; \ + cb_data.args.hipMemcpy3DAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyAsync[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyAsync.dst = (void*)dst; \ + cb_data.args.hipMemcpyAsync.src = (const void*)src; \ + cb_data.args.hipMemcpyAsync.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpyAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyAtoH[('void*', 'dst'), ('hipArray_t', 'srcArray'), ('size_t', 'srcOffset'), ('size_t', 'count')] +#define INIT_hipMemcpyAtoH_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyAtoH.dst = (void*)dstHost; \ + cb_data.args.hipMemcpyAtoH.srcArray = (hipArray_t)srcArray; \ + cb_data.args.hipMemcpyAtoH.srcOffset = (size_t)srcOffset; \ + cb_data.args.hipMemcpyAtoH.count = (size_t)ByteCount; \ +}; +// hipMemcpyDtoD[('hipDeviceptr_t', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes')] +#define INIT_hipMemcpyDtoD_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyDtoD.dst = (hipDeviceptr_t)dstDevice; \ + cb_data.args.hipMemcpyDtoD.src = (hipDeviceptr_t)srcDevice; \ + cb_data.args.hipMemcpyDtoD.sizeBytes = (size_t)ByteCount; \ +}; +// hipMemcpyDtoDAsync[('hipDeviceptr_t', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyDtoDAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyDtoDAsync.dst = (hipDeviceptr_t)dstDevice; \ + cb_data.args.hipMemcpyDtoDAsync.src = (hipDeviceptr_t)srcDevice; \ + cb_data.args.hipMemcpyDtoDAsync.sizeBytes = (size_t)ByteCount; \ + cb_data.args.hipMemcpyDtoDAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyDtoH[('void*', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes')] +#define INIT_hipMemcpyDtoH_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyDtoH.dst = (void*)dstHost; \ + cb_data.args.hipMemcpyDtoH.src = (hipDeviceptr_t)srcDevice; \ + cb_data.args.hipMemcpyDtoH.sizeBytes = (size_t)ByteCount; \ +}; +// hipMemcpyDtoHAsync[('void*', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyDtoHAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyDtoHAsync.dst = (void*)dstHost; \ + cb_data.args.hipMemcpyDtoHAsync.src = (hipDeviceptr_t)srcDevice; \ + cb_data.args.hipMemcpyDtoHAsync.sizeBytes = (size_t)ByteCount; \ + cb_data.args.hipMemcpyDtoHAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyFromArray[('void*', 'dst'), ('hipArray_const_t', 'srcArray'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpyFromArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyFromArray.dst = (void*)dst; \ + cb_data.args.hipMemcpyFromArray.srcArray = (hipArray_const_t)src; \ + cb_data.args.hipMemcpyFromArray.wOffset = (size_t)wOffsetSrc; \ + cb_data.args.hipMemcpyFromArray.hOffset = (size_t)hOffset; \ + cb_data.args.hipMemcpyFromArray.count = (size_t)count; \ + cb_data.args.hipMemcpyFromArray.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpyFromSymbol[('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpyFromSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyFromSymbol.dst = (void*)dst; \ + cb_data.args.hipMemcpyFromSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipMemcpyFromSymbol.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyFromSymbol.offset = (size_t)offset; \ + cb_data.args.hipMemcpyFromSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpyFromSymbolAsync[('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyFromSymbolAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyFromSymbolAsync.dst = (void*)dst; \ + cb_data.args.hipMemcpyFromSymbolAsync.symbol = (const void*)symbol; \ + cb_data.args.hipMemcpyFromSymbolAsync.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyFromSymbolAsync.offset = (size_t)offset; \ + cb_data.args.hipMemcpyFromSymbolAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpyFromSymbolAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyHtoA[('hipArray_t', 'dstArray'), ('size_t', 'dstOffset'), ('const void*', 'srcHost'), ('size_t', 'count')] +#define INIT_hipMemcpyHtoA_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyHtoA.dstArray = (hipArray_t)dstArray; \ + cb_data.args.hipMemcpyHtoA.dstOffset = (size_t)dstOffset; \ + cb_data.args.hipMemcpyHtoA.srcHost = (const void*)srcHost; \ + cb_data.args.hipMemcpyHtoA.count = (size_t)ByteCount; \ +}; +// hipMemcpyHtoD[('hipDeviceptr_t', 'dst'), ('void*', 'src'), ('size_t', 'sizeBytes')] +#define INIT_hipMemcpyHtoD_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyHtoD.dst = (hipDeviceptr_t)dstDevice; \ + cb_data.args.hipMemcpyHtoD.src = (void*)srcHost; \ + cb_data.args.hipMemcpyHtoD.sizeBytes = (size_t)ByteCount; \ +}; +// hipMemcpyHtoDAsync[('hipDeviceptr_t', 'dst'), ('void*', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyHtoDAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyHtoDAsync.dst = (hipDeviceptr_t)dstDevice; \ + cb_data.args.hipMemcpyHtoDAsync.src = (void*)srcHost; \ + cb_data.args.hipMemcpyHtoDAsync.sizeBytes = (size_t)ByteCount; \ + cb_data.args.hipMemcpyHtoDAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyParam2D[('const hip_Memcpy2D*', 'pCopy')] +#define INIT_hipMemcpyParam2D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyParam2D.pCopy = (const hip_Memcpy2D*)pCopy; \ +}; +// hipMemcpyParam2DAsync[('const hip_Memcpy2D*', 'pCopy'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyParam2DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyParam2DAsync.pCopy = (const hip_Memcpy2D*)pCopy; \ + cb_data.args.hipMemcpyParam2DAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyPeer[('void*', 'dst'), ('int', 'dstDeviceId'), ('const void*', 'src'), ('int', 'srcDeviceId'), ('size_t', 'sizeBytes')] +#define INIT_hipMemcpyPeer_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyPeer.dst = (void*)dst; \ + cb_data.args.hipMemcpyPeer.dstDeviceId = (int)dstDevice; \ + cb_data.args.hipMemcpyPeer.src = (const void*)src; \ + cb_data.args.hipMemcpyPeer.srcDeviceId = (int)srcDevice; \ + cb_data.args.hipMemcpyPeer.sizeBytes = (size_t)sizeBytes; \ +}; +// hipMemcpyPeerAsync[('void*', 'dst'), ('int', 'dstDeviceId'), ('const void*', 'src'), ('int', 'srcDevice'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyPeerAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyPeerAsync.dst = (void*)dst; \ + cb_data.args.hipMemcpyPeerAsync.dstDeviceId = (int)dstDevice; \ + cb_data.args.hipMemcpyPeerAsync.src = (const void*)src; \ + cb_data.args.hipMemcpyPeerAsync.srcDevice = (int)srcDevice; \ + cb_data.args.hipMemcpyPeerAsync.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyPeerAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyToArray[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpyToArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyToArray.dst = (hipArray_t)dst; \ + cb_data.args.hipMemcpyToArray.wOffset = (size_t)wOffset; \ + cb_data.args.hipMemcpyToArray.hOffset = (size_t)hOffset; \ + cb_data.args.hipMemcpyToArray.src = (const void*)src; \ + cb_data.args.hipMemcpyToArray.count = (size_t)count; \ + cb_data.args.hipMemcpyToArray.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpyToSymbol[('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] +#define INIT_hipMemcpyToSymbol_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyToSymbol.symbol = (const void*)symbol; \ + cb_data.args.hipMemcpyToSymbol.src = (const void*)src; \ + cb_data.args.hipMemcpyToSymbol.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyToSymbol.offset = (size_t)offset; \ + cb_data.args.hipMemcpyToSymbol.kind = (hipMemcpyKind)kind; \ +}; +// hipMemcpyToSymbolAsync[('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyToSymbolAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyToSymbolAsync.symbol = (const void*)symbol; \ + cb_data.args.hipMemcpyToSymbolAsync.src = (const void*)src; \ + cb_data.args.hipMemcpyToSymbolAsync.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyToSymbolAsync.offset = (size_t)offset; \ + cb_data.args.hipMemcpyToSymbolAsync.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpyToSymbolAsync.stream = (hipStream_t)stream; \ +}; +// hipMemcpyWithStream[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] +#define INIT_hipMemcpyWithStream_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemcpyWithStream.dst = (void*)dst; \ + cb_data.args.hipMemcpyWithStream.src = (const void*)src; \ + cb_data.args.hipMemcpyWithStream.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemcpyWithStream.kind = (hipMemcpyKind)kind; \ + cb_data.args.hipMemcpyWithStream.stream = (hipStream_t)stream; \ +}; +// hipMemset[('void*', 'dst'), ('int', 'value'), ('size_t', 'sizeBytes')] +#define INIT_hipMemset_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemset.dst = (void*)dst; \ + cb_data.args.hipMemset.value = (int)value; \ + cb_data.args.hipMemset.sizeBytes = (size_t)sizeBytes; \ +}; +// hipMemset2D[('void*', 'dst'), ('size_t', 'pitch'), ('int', 'value'), ('size_t', 'width'), ('size_t', 'height')] +#define INIT_hipMemset2D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemset2D.dst = (void*)dst; \ + cb_data.args.hipMemset2D.pitch = (size_t)pitch; \ + cb_data.args.hipMemset2D.value = (int)value; \ + cb_data.args.hipMemset2D.width = (size_t)width; \ + cb_data.args.hipMemset2D.height = (size_t)height; \ +}; +// hipMemset2DAsync[('void*', 'dst'), ('size_t', 'pitch'), ('int', 'value'), ('size_t', 'width'), ('size_t', 'height'), ('hipStream_t', 'stream')] +#define INIT_hipMemset2DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemset2DAsync.dst = (void*)dst; \ + cb_data.args.hipMemset2DAsync.pitch = (size_t)pitch; \ + cb_data.args.hipMemset2DAsync.value = (int)value; \ + cb_data.args.hipMemset2DAsync.width = (size_t)width; \ + cb_data.args.hipMemset2DAsync.height = (size_t)height; \ + cb_data.args.hipMemset2DAsync.stream = (hipStream_t)stream; \ +}; +// hipMemset3D[('hipPitchedPtr', 'pitchedDevPtr'), ('int', 'value'), ('hipExtent', 'extent')] +#define INIT_hipMemset3D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemset3D.pitchedDevPtr = (hipPitchedPtr)pitchedDevPtr; \ + cb_data.args.hipMemset3D.value = (int)value; \ + cb_data.args.hipMemset3D.extent = (hipExtent)extent; \ +}; +// hipMemset3DAsync[('hipPitchedPtr', 'pitchedDevPtr'), ('int', 'value'), ('hipExtent', 'extent'), ('hipStream_t', 'stream')] +#define INIT_hipMemset3DAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemset3DAsync.pitchedDevPtr = (hipPitchedPtr)pitchedDevPtr; \ + cb_data.args.hipMemset3DAsync.value = (int)value; \ + cb_data.args.hipMemset3DAsync.extent = (hipExtent)extent; \ + cb_data.args.hipMemset3DAsync.stream = (hipStream_t)stream; \ +}; +// hipMemsetAsync[('void*', 'dst'), ('int', 'value'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] +#define INIT_hipMemsetAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetAsync.dst = (void*)dst; \ + cb_data.args.hipMemsetAsync.value = (int)value; \ + cb_data.args.hipMemsetAsync.sizeBytes = (size_t)sizeBytes; \ + cb_data.args.hipMemsetAsync.stream = (hipStream_t)stream; \ +}; +// hipMemsetD16[('hipDeviceptr_t', 'dest'), ('unsigned short', 'value'), ('size_t', 'count')] +#define INIT_hipMemsetD16_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD16.dest = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD16.value = (unsigned short)value; \ + cb_data.args.hipMemsetD16.count = (size_t)count; \ +}; +// hipMemsetD16Async[('hipDeviceptr_t', 'dest'), ('unsigned short', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] +#define INIT_hipMemsetD16Async_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD16Async.dest = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD16Async.value = (unsigned short)value; \ + cb_data.args.hipMemsetD16Async.count = (size_t)count; \ + cb_data.args.hipMemsetD16Async.stream = (hipStream_t)stream; \ +}; +// hipMemsetD32[('hipDeviceptr_t', 'dest'), ('int', 'value'), ('size_t', 'count')] +#define INIT_hipMemsetD32_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD32.dest = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD32.value = (int)value; \ + cb_data.args.hipMemsetD32.count = (size_t)count; \ +}; +// hipMemsetD32Async[('hipDeviceptr_t', 'dst'), ('int', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] +#define INIT_hipMemsetD32Async_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD32Async.dst = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD32Async.value = (int)value; \ + cb_data.args.hipMemsetD32Async.count = (size_t)count; \ + cb_data.args.hipMemsetD32Async.stream = (hipStream_t)stream; \ +}; +// hipMemsetD8[('hipDeviceptr_t', 'dest'), ('unsigned char', 'value'), ('size_t', 'count')] +#define INIT_hipMemsetD8_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD8.dest = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD8.value = (unsigned char)value; \ + cb_data.args.hipMemsetD8.count = (size_t)count; \ +}; +// hipMemsetD8Async[('hipDeviceptr_t', 'dest'), ('unsigned char', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] +#define INIT_hipMemsetD8Async_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMemsetD8Async.dest = (hipDeviceptr_t)dst; \ + cb_data.args.hipMemsetD8Async.value = (unsigned char)value; \ + cb_data.args.hipMemsetD8Async.count = (size_t)count; \ + cb_data.args.hipMemsetD8Async.stream = (hipStream_t)stream; \ +}; +// hipMipmappedArrayCreate[('hipMipmappedArray_t*', 'pHandle'), ('HIP_ARRAY3D_DESCRIPTOR*', 'pMipmappedArrayDesc'), ('unsigned int', 'numMipmapLevels')] +#define INIT_hipMipmappedArrayCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMipmappedArrayCreate.pHandle = (hipMipmappedArray_t*)mipmapped_array_pptr; \ + cb_data.args.hipMipmappedArrayCreate.pMipmappedArrayDesc = (HIP_ARRAY3D_DESCRIPTOR*)mipmapped_array_desc_ptr; \ + cb_data.args.hipMipmappedArrayCreate.numMipmapLevels = (unsigned int)num_mipmap_levels; \ +}; +// hipMipmappedArrayDestroy[('hipMipmappedArray_t', 'hMipmappedArray')] +#define INIT_hipMipmappedArrayDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMipmappedArrayDestroy.hMipmappedArray = (hipMipmappedArray_t)mipmapped_array_ptr; \ +}; +// hipMipmappedArrayGetLevel[('hipArray_t*', 'pLevelArray'), ('hipMipmappedArray_t', 'hMipMappedArray'), ('unsigned int', 'level')] +#define INIT_hipMipmappedArrayGetLevel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipMipmappedArrayGetLevel.pLevelArray = (hipArray_t*)level_array_pptr; \ + cb_data.args.hipMipmappedArrayGetLevel.hMipMappedArray = (hipMipmappedArray_t)mipmapped_array_ptr; \ + cb_data.args.hipMipmappedArrayGetLevel.level = (unsigned int)mip_level; \ +}; +// hipModuleGetFunction[('hipFunction_t*', 'function'), ('hipModule_t', 'module'), ('const char*', 'kname')] +#define INIT_hipModuleGetFunction_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleGetFunction.function = (hipFunction_t*)hfunc; \ + cb_data.args.hipModuleGetFunction.module = (hipModule_t)hmod; \ + cb_data.args.hipModuleGetFunction.kname = (name) ? strdup(name) : NULL; \ +}; +// hipModuleGetGlobal[('hipDeviceptr_t*', 'dptr'), ('size_t*', 'bytes'), ('hipModule_t', 'hmod'), ('const char*', 'name')] +#define INIT_hipModuleGetGlobal_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleGetGlobal.dptr = (hipDeviceptr_t*)dptr; \ + cb_data.args.hipModuleGetGlobal.bytes = (size_t*)bytes; \ + cb_data.args.hipModuleGetGlobal.hmod = (hipModule_t)hmod; \ + cb_data.args.hipModuleGetGlobal.name = (name) ? strdup(name) : NULL; \ +}; +// hipModuleGetTexRef[('textureReference**', 'texRef'), ('hipModule_t', 'hmod'), ('const char*', 'name')] +#define INIT_hipModuleGetTexRef_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleGetTexRef.texRef = (textureReference**)texRef; \ + cb_data.args.hipModuleGetTexRef.hmod = (hipModule_t)hmod; \ + cb_data.args.hipModuleGetTexRef.name = (name) ? strdup(name) : NULL; \ +}; +// hipModuleLaunchCooperativeKernel[('hipFunction_t', 'f'), ('unsigned int', 'gridDimX'), ('unsigned int', 'gridDimY'), ('unsigned int', 'gridDimZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('void**', 'kernelParams')] +#define INIT_hipModuleLaunchCooperativeKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLaunchCooperativeKernel.f = (hipFunction_t)f; \ + cb_data.args.hipModuleLaunchCooperativeKernel.gridDimX = (unsigned int)gridDimX; \ + cb_data.args.hipModuleLaunchCooperativeKernel.gridDimY = (unsigned int)gridDimY; \ + cb_data.args.hipModuleLaunchCooperativeKernel.gridDimZ = (unsigned int)gridDimZ; \ + cb_data.args.hipModuleLaunchCooperativeKernel.blockDimX = (unsigned int)blockDimX; \ + cb_data.args.hipModuleLaunchCooperativeKernel.blockDimY = (unsigned int)blockDimY; \ + cb_data.args.hipModuleLaunchCooperativeKernel.blockDimZ = (unsigned int)blockDimZ; \ + cb_data.args.hipModuleLaunchCooperativeKernel.sharedMemBytes = (unsigned int)sharedMemBytes; \ + cb_data.args.hipModuleLaunchCooperativeKernel.stream = (hipStream_t)stream; \ + cb_data.args.hipModuleLaunchCooperativeKernel.kernelParams = (void**)kernelParams; \ +}; +// hipModuleLaunchCooperativeKernelMultiDevice[('hipFunctionLaunchParams*', 'launchParamsList'), ('unsigned int', 'numDevices'), ('unsigned int', 'flags')] +#define INIT_hipModuleLaunchCooperativeKernelMultiDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList = (hipFunctionLaunchParams*)launchParamsList; \ + cb_data.args.hipModuleLaunchCooperativeKernelMultiDevice.numDevices = (unsigned int)numDevices; \ + cb_data.args.hipModuleLaunchCooperativeKernelMultiDevice.flags = (unsigned int)flags; \ +}; +// hipModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'gridDimX'), ('unsigned int', 'gridDimY'), ('unsigned int', 'gridDimZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('void**', 'kernelParams'), ('void**', 'extra')] +#define INIT_hipModuleLaunchKernel_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLaunchKernel.f = (hipFunction_t)f; \ + cb_data.args.hipModuleLaunchKernel.gridDimX = (unsigned int)gridDimX; \ + cb_data.args.hipModuleLaunchKernel.gridDimY = (unsigned int)gridDimY; \ + cb_data.args.hipModuleLaunchKernel.gridDimZ = (unsigned int)gridDimZ; \ + cb_data.args.hipModuleLaunchKernel.blockDimX = (unsigned int)blockDimX; \ + cb_data.args.hipModuleLaunchKernel.blockDimY = (unsigned int)blockDimY; \ + cb_data.args.hipModuleLaunchKernel.blockDimZ = (unsigned int)blockDimZ; \ + cb_data.args.hipModuleLaunchKernel.sharedMemBytes = (unsigned int)sharedMemBytes; \ + cb_data.args.hipModuleLaunchKernel.stream = (hipStream_t)hStream; \ + cb_data.args.hipModuleLaunchKernel.kernelParams = (void**)kernelParams; \ + cb_data.args.hipModuleLaunchKernel.extra = (void**)extra; \ +}; +// hipModuleLoad[('hipModule_t*', 'module'), ('const char*', 'fname')] +#define INIT_hipModuleLoad_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLoad.module = (hipModule_t*)module; \ + cb_data.args.hipModuleLoad.fname = (fname) ? strdup(fname) : NULL; \ +}; +// hipModuleLoadData[('hipModule_t*', 'module'), ('const void*', 'image')] +#define INIT_hipModuleLoadData_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLoadData.module = (hipModule_t*)module; \ + cb_data.args.hipModuleLoadData.image = (const void*)image; \ +}; +// hipModuleLoadDataEx[('hipModule_t*', 'module'), ('const void*', 'image'), ('unsigned int', 'numOptions'), ('hipJitOption*', 'options'), ('void**', 'optionsValues')] +#define INIT_hipModuleLoadDataEx_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleLoadDataEx.module = (hipModule_t*)module; \ + cb_data.args.hipModuleLoadDataEx.image = (const void*)image; \ + cb_data.args.hipModuleLoadDataEx.numOptions = (unsigned int)numOptions; \ + cb_data.args.hipModuleLoadDataEx.options = (hipJitOption*)options; \ + cb_data.args.hipModuleLoadDataEx.optionsValues = (void**)optionsValues; \ +}; +// hipModuleOccupancyMaxActiveBlocksPerMultiprocessor[('int*', 'numBlocks'), ('hipFunction_t', 'f'), ('int', 'blockSize'), ('size_t', 'dynSharedMemPerBlk')] +#define INIT_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks = (int*)numBlocks; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.f = (hipFunction_t)f; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.blockSize = (int)blockSize; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.dynSharedMemPerBlk = (size_t)dynSharedMemPerBlk; \ +}; +// hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags[('int*', 'numBlocks'), ('hipFunction_t', 'f'), ('int', 'blockSize'), ('size_t', 'dynSharedMemPerBlk'), ('unsigned int', 'flags')] +#define INIT_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks = (int*)numBlocks; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.f = (hipFunction_t)f; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.blockSize = (int)blockSize; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.dynSharedMemPerBlk = (size_t)dynSharedMemPerBlk; \ + cb_data.args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.flags = (unsigned int)flags; \ +}; +// hipModuleOccupancyMaxPotentialBlockSize[('int*', 'gridSize'), ('int*', 'blockSize'), ('hipFunction_t', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit')] +#define INIT_hipModuleOccupancyMaxPotentialBlockSize_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSize.gridSize = (int*)gridSize; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSize.blockSize = (int*)blockSize; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSize.f = (hipFunction_t)f; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSize.dynSharedMemPerBlk = (size_t)dynSharedMemPerBlk; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSize.blockSizeLimit = (int)blockSizeLimit; \ +}; +// hipModuleOccupancyMaxPotentialBlockSizeWithFlags[('int*', 'gridSize'), ('int*', 'blockSize'), ('hipFunction_t', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit'), ('unsigned int', 'flags')] +#define INIT_hipModuleOccupancyMaxPotentialBlockSizeWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize = (int*)gridSize; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize = (int*)blockSize; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.f = (hipFunction_t)f; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.dynSharedMemPerBlk = (size_t)dynSharedMemPerBlk; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSizeLimit = (int)blockSizeLimit; \ + cb_data.args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.flags = (unsigned int)flags; \ +}; +// hipModuleUnload[('hipModule_t', 'module')] +#define INIT_hipModuleUnload_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipModuleUnload.module = (hipModule_t)hmod; \ +}; +// hipOccupancyMaxActiveBlocksPerMultiprocessor[('int*', 'numBlocks'), ('const void*', 'f'), ('int', 'blockSize'), ('size_t', 'dynamicSMemSize')] +#define INIT_hipOccupancyMaxActiveBlocksPerMultiprocessor_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks = (int*)numBlocks; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessor.f = (const void*)f; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessor.blockSize = (int)blockSize; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessor.dynamicSMemSize = (size_t)dynamicSMemSize; \ +}; +// hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags[('int*', 'numBlocks'), ('const void*', 'f'), ('int', 'blockSize'), ('size_t', 'dynamicSMemSize'), ('unsigned int', 'flags')] +#define INIT_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks = (int*)numBlocks; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.f = (const void*)f; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.blockSize = (int)blockSize; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.dynamicSMemSize = (size_t)dynamicSMemSize; \ + cb_data.args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.flags = (unsigned int)flags; \ +}; +// hipOccupancyMaxPotentialBlockSize[('int*', 'gridSize'), ('int*', 'blockSize'), ('const void*', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit')] +#define INIT_hipOccupancyMaxPotentialBlockSize_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipOccupancyMaxPotentialBlockSize.gridSize = (int*)gridSize; \ + cb_data.args.hipOccupancyMaxPotentialBlockSize.blockSize = (int*)blockSize; \ + cb_data.args.hipOccupancyMaxPotentialBlockSize.f = (const void*)f; \ + cb_data.args.hipOccupancyMaxPotentialBlockSize.dynSharedMemPerBlk = (size_t)dynSharedMemPerBlk; \ + cb_data.args.hipOccupancyMaxPotentialBlockSize.blockSizeLimit = (int)blockSizeLimit; \ +}; +// hipPeekAtLastError[] +#define INIT_hipPeekAtLastError_CB_ARGS_DATA(cb_data) { \ +}; +// hipPointerGetAttribute[('void*', 'data'), ('hipPointer_attribute', 'attribute'), ('hipDeviceptr_t', 'ptr')] +#define INIT_hipPointerGetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipPointerGetAttribute.data = (void*)data; \ + cb_data.args.hipPointerGetAttribute.attribute = (hipPointer_attribute)attribute; \ + cb_data.args.hipPointerGetAttribute.ptr = (hipDeviceptr_t)ptr; \ +}; +// hipPointerGetAttributes[('hipPointerAttribute_t*', 'attributes'), ('const void*', 'ptr')] +#define INIT_hipPointerGetAttributes_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipPointerGetAttributes.attributes = (hipPointerAttribute_t*)attributes; \ + cb_data.args.hipPointerGetAttributes.ptr = (const void*)ptr; \ +}; +// hipPointerSetAttribute[('const void*', 'value'), ('hipPointer_attribute', 'attribute'), ('hipDeviceptr_t', 'ptr')] +#define INIT_hipPointerSetAttribute_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipPointerSetAttribute.value = (const void*)value; \ + cb_data.args.hipPointerSetAttribute.attribute = (hipPointer_attribute)attribute; \ + cb_data.args.hipPointerSetAttribute.ptr = (hipDeviceptr_t)ptr; \ +}; +// hipProfilerStart[] +#define INIT_hipProfilerStart_CB_ARGS_DATA(cb_data) { \ +}; +// hipProfilerStop[] +#define INIT_hipProfilerStop_CB_ARGS_DATA(cb_data) { \ +}; +// hipRuntimeGetVersion[('int*', 'runtimeVersion')] +#define INIT_hipRuntimeGetVersion_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipRuntimeGetVersion.runtimeVersion = (int*)runtimeVersion; \ +}; +// hipSetDevice[('int', 'deviceId')] +#define INIT_hipSetDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipSetDevice.deviceId = (int)device; \ +}; +// hipSetDeviceFlags[('unsigned int', 'flags')] +#define INIT_hipSetDeviceFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipSetDeviceFlags.flags = (unsigned int)flags; \ +}; +// hipSetupArgument[('const void*', 'arg'), ('size_t', 'size'), ('size_t', 'offset')] +#define INIT_hipSetupArgument_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipSetupArgument.arg = (const void*)arg; \ + cb_data.args.hipSetupArgument.size = (size_t)size; \ + cb_data.args.hipSetupArgument.offset = (size_t)offset; \ +}; +// hipSignalExternalSemaphoresAsync[('const hipExternalSemaphore_t*', 'extSemArray'), ('const hipExternalSemaphoreSignalParams*', 'paramsArray'), ('unsigned int', 'numExtSems'), ('hipStream_t', 'stream')] +#define INIT_hipSignalExternalSemaphoresAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipSignalExternalSemaphoresAsync.extSemArray = (const hipExternalSemaphore_t*)extSemArray; \ + cb_data.args.hipSignalExternalSemaphoresAsync.paramsArray = (const hipExternalSemaphoreSignalParams*)paramsArray; \ + cb_data.args.hipSignalExternalSemaphoresAsync.numExtSems = (unsigned int)numExtSems; \ + cb_data.args.hipSignalExternalSemaphoresAsync.stream = (hipStream_t)stream; \ +}; +// hipStreamAddCallback[('hipStream_t', 'stream'), ('hipStreamCallback_t', 'callback'), ('void*', 'userData'), ('unsigned int', 'flags')] +#define INIT_hipStreamAddCallback_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamAddCallback.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamAddCallback.callback = (hipStreamCallback_t)callback; \ + cb_data.args.hipStreamAddCallback.userData = (void*)userData; \ + cb_data.args.hipStreamAddCallback.flags = (unsigned int)flags; \ +}; +// hipStreamAttachMemAsync[('hipStream_t', 'stream'), ('void*', 'dev_ptr'), ('size_t', 'length'), ('unsigned int', 'flags')] +#define INIT_hipStreamAttachMemAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamAttachMemAsync.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamAttachMemAsync.dev_ptr = (void*)dev_ptr; \ + cb_data.args.hipStreamAttachMemAsync.length = (size_t)length; \ + cb_data.args.hipStreamAttachMemAsync.flags = (unsigned int)flags; \ +}; +// hipStreamBeginCapture[('hipStream_t', 'stream'), ('hipStreamCaptureMode', 'mode')] +#define INIT_hipStreamBeginCapture_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamBeginCapture.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamBeginCapture.mode = (hipStreamCaptureMode)mode; \ +}; +// hipStreamCreate[('hipStream_t*', 'stream')] +#define INIT_hipStreamCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamCreate.stream = (hipStream_t*)stream; \ +}; +// hipStreamCreateWithFlags[('hipStream_t*', 'stream'), ('unsigned int', 'flags')] +#define INIT_hipStreamCreateWithFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamCreateWithFlags.stream = (hipStream_t*)stream; \ + cb_data.args.hipStreamCreateWithFlags.flags = (unsigned int)flags; \ +}; +// hipStreamCreateWithPriority[('hipStream_t*', 'stream'), ('unsigned int', 'flags'), ('int', 'priority')] +#define INIT_hipStreamCreateWithPriority_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamCreateWithPriority.stream = (hipStream_t*)stream; \ + cb_data.args.hipStreamCreateWithPriority.flags = (unsigned int)flags; \ + cb_data.args.hipStreamCreateWithPriority.priority = (int)priority; \ +}; +// hipStreamDestroy[('hipStream_t', 'stream')] +#define INIT_hipStreamDestroy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamDestroy.stream = (hipStream_t)stream; \ +}; +// hipStreamEndCapture[('hipStream_t', 'stream'), ('hipGraph_t*', 'pGraph')] +#define INIT_hipStreamEndCapture_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamEndCapture.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamEndCapture.pGraph = (hipGraph_t*)pGraph; \ +}; +// hipStreamGetCaptureInfo[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'pCaptureStatus'), ('unsigned long long*', 'pId')] +#define INIT_hipStreamGetCaptureInfo_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamGetCaptureInfo.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamGetCaptureInfo.pCaptureStatus = (hipStreamCaptureStatus*)pCaptureStatus; \ + cb_data.args.hipStreamGetCaptureInfo.pId = (unsigned long long*)pId; \ +}; +// hipStreamGetCaptureInfo_v2[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'captureStatus_out'), ('unsigned long long*', 'id_out'), ('hipGraph_t*', 'graph_out'), ('const hipGraphNode_t**', 'dependencies_out'), ('size_t*', 'numDependencies_out')] +#define INIT_hipStreamGetCaptureInfo_v2_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamGetCaptureInfo_v2.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamGetCaptureInfo_v2.captureStatus_out = (hipStreamCaptureStatus*)captureStatus_out; \ + cb_data.args.hipStreamGetCaptureInfo_v2.id_out = (unsigned long long*)id_out; \ + cb_data.args.hipStreamGetCaptureInfo_v2.graph_out = (hipGraph_t*)graph_out; \ + cb_data.args.hipStreamGetCaptureInfo_v2.dependencies_out = (const hipGraphNode_t**)dependencies_out; \ + cb_data.args.hipStreamGetCaptureInfo_v2.numDependencies_out = (size_t*)numDependencies_out; \ +}; +// hipStreamGetDevice[('hipStream_t', 'stream'), ('hipDevice_t*', 'device')] +#define INIT_hipStreamGetDevice_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamGetDevice.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamGetDevice.device = (hipDevice_t*)device; \ +}; +// hipStreamGetFlags[('hipStream_t', 'stream'), ('unsigned int*', 'flags')] +#define INIT_hipStreamGetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamGetFlags.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamGetFlags.flags = (unsigned int*)flags; \ +}; +// hipStreamGetPriority[('hipStream_t', 'stream'), ('int*', 'priority')] +#define INIT_hipStreamGetPriority_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamGetPriority.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamGetPriority.priority = (int*)priority; \ +}; +// hipStreamIsCapturing[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'pCaptureStatus')] +#define INIT_hipStreamIsCapturing_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamIsCapturing.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamIsCapturing.pCaptureStatus = (hipStreamCaptureStatus*)pCaptureStatus; \ +}; +// hipStreamQuery[('hipStream_t', 'stream')] +#define INIT_hipStreamQuery_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamQuery.stream = (hipStream_t)stream; \ +}; +// hipStreamSynchronize[('hipStream_t', 'stream')] +#define INIT_hipStreamSynchronize_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamSynchronize.stream = (hipStream_t)stream; \ +}; +// hipStreamUpdateCaptureDependencies[('hipStream_t', 'stream'), ('hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('unsigned int', 'flags')] +#define INIT_hipStreamUpdateCaptureDependencies_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamUpdateCaptureDependencies.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamUpdateCaptureDependencies.dependencies = (hipGraphNode_t*)dependencies; \ + cb_data.args.hipStreamUpdateCaptureDependencies.numDependencies = (size_t)numDependencies; \ + cb_data.args.hipStreamUpdateCaptureDependencies.flags = (unsigned int)flags; \ +}; +// hipStreamWaitEvent[('hipStream_t', 'stream'), ('hipEvent_t', 'event'), ('unsigned int', 'flags')] +#define INIT_hipStreamWaitEvent_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamWaitEvent.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamWaitEvent.event = (hipEvent_t)event; \ + cb_data.args.hipStreamWaitEvent.flags = (unsigned int)flags; \ +}; +// hipStreamWaitValue32[('hipStream_t', 'stream'), ('void*', 'ptr'), ('unsigned int', 'value'), ('unsigned int', 'flags'), ('unsigned int', 'mask')] +#define INIT_hipStreamWaitValue32_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamWaitValue32.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamWaitValue32.ptr = (void*)ptr; \ + cb_data.args.hipStreamWaitValue32.value = (unsigned int)value; \ + cb_data.args.hipStreamWaitValue32.flags = (unsigned int)flags; \ + cb_data.args.hipStreamWaitValue32.mask = (unsigned int)mask; \ +}; +// hipStreamWaitValue64[('hipStream_t', 'stream'), ('void*', 'ptr'), ('uint64_t', 'value'), ('unsigned int', 'flags'), ('uint64_t', 'mask')] +#define INIT_hipStreamWaitValue64_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamWaitValue64.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamWaitValue64.ptr = (void*)ptr; \ + cb_data.args.hipStreamWaitValue64.value = (uint64_t)value; \ + cb_data.args.hipStreamWaitValue64.flags = (unsigned int)flags; \ + cb_data.args.hipStreamWaitValue64.mask = (uint64_t)mask; \ +}; +// hipStreamWriteValue32[('hipStream_t', 'stream'), ('void*', 'ptr'), ('unsigned int', 'value'), ('unsigned int', 'flags')] +#define INIT_hipStreamWriteValue32_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamWriteValue32.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamWriteValue32.ptr = (void*)ptr; \ + cb_data.args.hipStreamWriteValue32.value = (unsigned int)value; \ + cb_data.args.hipStreamWriteValue32.flags = (unsigned int)flags; \ +}; +// hipStreamWriteValue64[('hipStream_t', 'stream'), ('void*', 'ptr'), ('uint64_t', 'value'), ('unsigned int', 'flags')] +#define INIT_hipStreamWriteValue64_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipStreamWriteValue64.stream = (hipStream_t)stream; \ + cb_data.args.hipStreamWriteValue64.ptr = (void*)ptr; \ + cb_data.args.hipStreamWriteValue64.value = (uint64_t)value; \ + cb_data.args.hipStreamWriteValue64.flags = (unsigned int)flags; \ +}; +// hipTexRefGetAddress[('hipDeviceptr_t*', 'dev_ptr'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetAddress_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetAddress.dev_ptr = (hipDeviceptr_t*)dptr; \ + cb_data.args.hipTexRefGetAddress.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefGetFlags[('unsigned int*', 'pFlags'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetFlags.pFlags = (unsigned int*)pFlags; \ + cb_data.args.hipTexRefGetFlags.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefGetFormat[('hipArray_Format*', 'pFormat'), ('int*', 'pNumChannels'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetFormat_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetFormat.pFormat = (hipArray_Format*)pFormat; \ + cb_data.args.hipTexRefGetFormat.pNumChannels = (int*)pNumChannels; \ + cb_data.args.hipTexRefGetFormat.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefGetMaxAnisotropy[('int*', 'pmaxAnsio'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetMaxAnisotropy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetMaxAnisotropy.pmaxAnsio = (int*)pmaxAnsio; \ + cb_data.args.hipTexRefGetMaxAnisotropy.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefGetMipMappedArray[('hipMipmappedArray_t*', 'pArray'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetMipMappedArray_CB_ARGS_DATA(cb_data) { \ +}; +// hipTexRefGetMipmapLevelBias[('float*', 'pbias'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetMipmapLevelBias_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetMipmapLevelBias.pbias = (float*)pbias; \ + cb_data.args.hipTexRefGetMipmapLevelBias.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefGetMipmapLevelClamp[('float*', 'pminMipmapLevelClamp'), ('float*', 'pmaxMipmapLevelClamp'), ('const textureReference*', 'texRef')] +#define INIT_hipTexRefGetMipmapLevelClamp_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp = (float*)pminMipmapLevelClamp; \ + cb_data.args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp = (float*)pmaxMipmapLevelClamp; \ + cb_data.args.hipTexRefGetMipmapLevelClamp.texRef = (const textureReference*)texRef; \ +}; +// hipTexRefSetAddress[('size_t*', 'ByteOffset'), ('textureReference*', 'texRef'), ('hipDeviceptr_t', 'dptr'), ('size_t', 'bytes')] +#define INIT_hipTexRefSetAddress_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetAddress.ByteOffset = (size_t*)ByteOffset; \ + cb_data.args.hipTexRefSetAddress.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetAddress.dptr = (hipDeviceptr_t)dptr; \ + cb_data.args.hipTexRefSetAddress.bytes = (size_t)bytes; \ +}; +// hipTexRefSetAddress2D[('textureReference*', 'texRef'), ('const HIP_ARRAY_DESCRIPTOR*', 'desc'), ('hipDeviceptr_t', 'dptr'), ('size_t', 'Pitch')] +#define INIT_hipTexRefSetAddress2D_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetAddress2D.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetAddress2D.desc = (const HIP_ARRAY_DESCRIPTOR*)desc; \ + cb_data.args.hipTexRefSetAddress2D.dptr = (hipDeviceptr_t)dptr; \ + cb_data.args.hipTexRefSetAddress2D.Pitch = (size_t)Pitch; \ +}; +// hipTexRefSetArray[('textureReference*', 'tex'), ('hipArray_const_t', 'array'), ('unsigned int', 'flags')] +#define INIT_hipTexRefSetArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetArray.tex = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetArray.array = (hipArray_const_t)array; \ + cb_data.args.hipTexRefSetArray.flags = (unsigned int)flags; \ +}; +// hipTexRefSetBorderColor[('textureReference*', 'texRef'), ('float*', 'pBorderColor')] +#define INIT_hipTexRefSetBorderColor_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetBorderColor.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetBorderColor.pBorderColor = (float*)pBorderColor; \ +}; +// hipTexRefSetFlags[('textureReference*', 'texRef'), ('unsigned int', 'Flags')] +#define INIT_hipTexRefSetFlags_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetFlags.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetFlags.Flags = (unsigned int)Flags; \ +}; +// hipTexRefSetFormat[('textureReference*', 'texRef'), ('hipArray_Format', 'fmt'), ('int', 'NumPackedComponents')] +#define INIT_hipTexRefSetFormat_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetFormat.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetFormat.fmt = (hipArray_Format)fmt; \ + cb_data.args.hipTexRefSetFormat.NumPackedComponents = (int)NumPackedComponents; \ +}; +// hipTexRefSetMaxAnisotropy[('textureReference*', 'texRef'), ('unsigned int', 'maxAniso')] +#define INIT_hipTexRefSetMaxAnisotropy_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetMaxAnisotropy.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetMaxAnisotropy.maxAniso = (unsigned int)maxAniso; \ +}; +// hipTexRefSetMipmapLevelBias[('textureReference*', 'texRef'), ('float', 'bias')] +#define INIT_hipTexRefSetMipmapLevelBias_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetMipmapLevelBias.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetMipmapLevelBias.bias = (float)bias; \ +}; +// hipTexRefSetMipmapLevelClamp[('textureReference*', 'texRef'), ('float', 'minMipMapLevelClamp'), ('float', 'maxMipMapLevelClamp')] +#define INIT_hipTexRefSetMipmapLevelClamp_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetMipmapLevelClamp.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetMipmapLevelClamp.minMipMapLevelClamp = (float)minMipMapLevelClamp; \ + cb_data.args.hipTexRefSetMipmapLevelClamp.maxMipMapLevelClamp = (float)maxMipMapLevelClamp; \ +}; +// hipTexRefSetMipmappedArray[('textureReference*', 'texRef'), ('hipMipmappedArray*', 'mipmappedArray'), ('unsigned int', 'Flags')] +#define INIT_hipTexRefSetMipmappedArray_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipTexRefSetMipmappedArray.texRef = (textureReference*)texRef; \ + cb_data.args.hipTexRefSetMipmappedArray.mipmappedArray = (hipMipmappedArray*)mipmappedArray; \ + cb_data.args.hipTexRefSetMipmappedArray.Flags = (unsigned int)Flags; \ +}; +// hipThreadExchangeStreamCaptureMode[('hipStreamCaptureMode*', 'mode')] +#define INIT_hipThreadExchangeStreamCaptureMode_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipThreadExchangeStreamCaptureMode.mode = (hipStreamCaptureMode*)mode; \ +}; +// hipUserObjectCreate[('hipUserObject_t*', 'object_out'), ('void*', 'ptr'), ('hipHostFn_t', 'destroy'), ('unsigned int', 'initialRefcount'), ('unsigned int', 'flags')] +#define INIT_hipUserObjectCreate_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipUserObjectCreate.object_out = (hipUserObject_t*)object_out; \ + cb_data.args.hipUserObjectCreate.ptr = (void*)ptr; \ + cb_data.args.hipUserObjectCreate.destroy = (hipHostFn_t)destroy; \ + cb_data.args.hipUserObjectCreate.initialRefcount = (unsigned int)initialRefcount; \ + cb_data.args.hipUserObjectCreate.flags = (unsigned int)flags; \ +}; +// hipUserObjectRelease[('hipUserObject_t', 'object'), ('unsigned int', 'count')] +#define INIT_hipUserObjectRelease_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipUserObjectRelease.object = (hipUserObject_t)object; \ + cb_data.args.hipUserObjectRelease.count = (unsigned int)count; \ +}; +// hipUserObjectRetain[('hipUserObject_t', 'object'), ('unsigned int', 'count')] +#define INIT_hipUserObjectRetain_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipUserObjectRetain.object = (hipUserObject_t)object; \ + cb_data.args.hipUserObjectRetain.count = (unsigned int)count; \ +}; +// hipWaitExternalSemaphoresAsync[('const hipExternalSemaphore_t*', 'extSemArray'), ('const hipExternalSemaphoreWaitParams*', 'paramsArray'), ('unsigned int', 'numExtSems'), ('hipStream_t', 'stream')] +#define INIT_hipWaitExternalSemaphoresAsync_CB_ARGS_DATA(cb_data) { \ + cb_data.args.hipWaitExternalSemaphoresAsync.extSemArray = (const hipExternalSemaphore_t*)extSemArray; \ + cb_data.args.hipWaitExternalSemaphoresAsync.paramsArray = (const hipExternalSemaphoreWaitParams*)paramsArray; \ + cb_data.args.hipWaitExternalSemaphoresAsync.numExtSems = (unsigned int)numExtSems; \ + cb_data.args.hipWaitExternalSemaphoresAsync.stream = (hipStream_t)stream; \ +}; +// hipExtGetLastError[] +#define INIT_hipExtGetLastError_CB_ARGS_DATA(cb_data) { \ +}; +#define INIT_CB_ARGS_DATA(cb_id, cb_data) INIT_##cb_id##_CB_ARGS_DATA(cb_data) + +// Macros for non-public API primitives +// hipBindTexture() +#define INIT_hipBindTexture_CB_ARGS_DATA(cb_data) {}; +// hipBindTexture2D() +#define INIT_hipBindTexture2D_CB_ARGS_DATA(cb_data) {}; +// hipBindTextureToArray() +#define INIT_hipBindTextureToArray_CB_ARGS_DATA(cb_data) {}; +// hipBindTextureToMipmappedArray() +#define INIT_hipBindTextureToMipmappedArray_CB_ARGS_DATA(cb_data) {}; +// hipCreateTextureObject() +#define INIT_hipCreateTextureObject_CB_ARGS_DATA(cb_data) {}; +// hipDestroyTextureObject() +#define INIT_hipDestroyTextureObject_CB_ARGS_DATA(cb_data) {}; +// hipDeviceGetCount() +#define INIT_hipDeviceGetCount_CB_ARGS_DATA(cb_data) {}; +// hipGetTextureAlignmentOffset() +#define INIT_hipGetTextureAlignmentOffset_CB_ARGS_DATA(cb_data) {}; +// hipGetTextureObjectResourceDesc() +#define INIT_hipGetTextureObjectResourceDesc_CB_ARGS_DATA(cb_data) {}; +// hipGetTextureObjectResourceViewDesc() +#define INIT_hipGetTextureObjectResourceViewDesc_CB_ARGS_DATA(cb_data) {}; +// hipGetTextureObjectTextureDesc() +#define INIT_hipGetTextureObjectTextureDesc_CB_ARGS_DATA(cb_data) {}; +// hipGetTextureReference() +#define INIT_hipGetTextureReference_CB_ARGS_DATA(cb_data) {}; +// hipMemcpy2DArrayToArray() +#define INIT_hipMemcpy2DArrayToArray_CB_ARGS_DATA(cb_data) {}; +// hipMemcpyAtoA() +#define INIT_hipMemcpyAtoA_CB_ARGS_DATA(cb_data) {}; +// hipMemcpyAtoD() +#define INIT_hipMemcpyAtoD_CB_ARGS_DATA(cb_data) {}; +// hipMemcpyAtoHAsync() +#define INIT_hipMemcpyAtoHAsync_CB_ARGS_DATA(cb_data) {}; +// hipMemcpyDtoA() +#define INIT_hipMemcpyDtoA_CB_ARGS_DATA(cb_data) {}; +// hipMemcpyHtoAAsync() +#define INIT_hipMemcpyHtoAAsync_CB_ARGS_DATA(cb_data) {}; +// hipSetValidDevices() +#define INIT_hipSetValidDevices_CB_ARGS_DATA(cb_data) {}; +// hipTexObjectCreate() +#define INIT_hipTexObjectCreate_CB_ARGS_DATA(cb_data) {}; +// hipTexObjectDestroy() +#define INIT_hipTexObjectDestroy_CB_ARGS_DATA(cb_data) {}; +// hipTexObjectGetResourceDesc() +#define INIT_hipTexObjectGetResourceDesc_CB_ARGS_DATA(cb_data) {}; +// hipTexObjectGetResourceViewDesc() +#define INIT_hipTexObjectGetResourceViewDesc_CB_ARGS_DATA(cb_data) {}; +// hipTexObjectGetTextureDesc() +#define INIT_hipTexObjectGetTextureDesc_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetAddressMode() +#define INIT_hipTexRefGetAddressMode_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetArray() +#define INIT_hipTexRefGetArray_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetBorderColor() +#define INIT_hipTexRefGetBorderColor_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetFilterMode() +#define INIT_hipTexRefGetFilterMode_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetMipmapFilterMode() +#define INIT_hipTexRefGetMipmapFilterMode_CB_ARGS_DATA(cb_data) {}; +// hipTexRefGetMipmappedArray() +#define INIT_hipTexRefGetMipmappedArray_CB_ARGS_DATA(cb_data) {}; +// hipTexRefSetAddressMode() +#define INIT_hipTexRefSetAddressMode_CB_ARGS_DATA(cb_data) {}; +// hipTexRefSetFilterMode() +#define INIT_hipTexRefSetFilterMode_CB_ARGS_DATA(cb_data) {}; +// hipTexRefSetMipmapFilterMode() +#define INIT_hipTexRefSetMipmapFilterMode_CB_ARGS_DATA(cb_data) {}; +// hipUnbindTexture() +#define INIT_hipUnbindTexture_CB_ARGS_DATA(cb_data) {}; + +#define INIT_NONE_CB_ARGS_DATA(cb_data) {}; + +#if HIP_PROF_HIP_API_STRING +// HIP API args filling helper +static inline void hipApiArgsInit(hip_api_id_t id, hip_api_data_t* data) { + switch (id) { +// __hipPopCallConfiguration[('dim3*', 'gridDim'), ('dim3*', 'blockDim'), ('size_t*', 'sharedMem'), ('hipStream_t*', 'stream')] + case HIP_API_ID___hipPopCallConfiguration: + if (data->args.__hipPopCallConfiguration.gridDim) data->args.__hipPopCallConfiguration.gridDim__val = *(data->args.__hipPopCallConfiguration.gridDim); + if (data->args.__hipPopCallConfiguration.blockDim) data->args.__hipPopCallConfiguration.blockDim__val = *(data->args.__hipPopCallConfiguration.blockDim); + if (data->args.__hipPopCallConfiguration.sharedMem) data->args.__hipPopCallConfiguration.sharedMem__val = *(data->args.__hipPopCallConfiguration.sharedMem); + if (data->args.__hipPopCallConfiguration.stream) data->args.__hipPopCallConfiguration.stream__val = *(data->args.__hipPopCallConfiguration.stream); + break; +// __hipPushCallConfiguration[('dim3', 'gridDim'), ('dim3', 'blockDim'), ('size_t', 'sharedMem'), ('hipStream_t', 'stream')] + case HIP_API_ID___hipPushCallConfiguration: + break; +// hipArray3DCreate[('hipArray_t*', 'array'), ('const HIP_ARRAY3D_DESCRIPTOR*', 'pAllocateArray')] + case HIP_API_ID_hipArray3DCreate: + if (data->args.hipArray3DCreate.array) data->args.hipArray3DCreate.array__val = *(data->args.hipArray3DCreate.array); + if (data->args.hipArray3DCreate.pAllocateArray) data->args.hipArray3DCreate.pAllocateArray__val = *(data->args.hipArray3DCreate.pAllocateArray); + break; +// hipArray3DGetDescriptor[('HIP_ARRAY3D_DESCRIPTOR*', 'pArrayDescriptor'), ('hipArray_t', 'array')] + case HIP_API_ID_hipArray3DGetDescriptor: + if (data->args.hipArray3DGetDescriptor.pArrayDescriptor) data->args.hipArray3DGetDescriptor.pArrayDescriptor__val = *(data->args.hipArray3DGetDescriptor.pArrayDescriptor); + break; +// hipArrayCreate[('hipArray_t*', 'pHandle'), ('const HIP_ARRAY_DESCRIPTOR*', 'pAllocateArray')] + case HIP_API_ID_hipArrayCreate: + if (data->args.hipArrayCreate.pHandle) data->args.hipArrayCreate.pHandle__val = *(data->args.hipArrayCreate.pHandle); + if (data->args.hipArrayCreate.pAllocateArray) data->args.hipArrayCreate.pAllocateArray__val = *(data->args.hipArrayCreate.pAllocateArray); + break; +// hipArrayDestroy[('hipArray_t', 'array')] + case HIP_API_ID_hipArrayDestroy: + break; +// hipArrayGetDescriptor[('HIP_ARRAY_DESCRIPTOR*', 'pArrayDescriptor'), ('hipArray_t', 'array')] + case HIP_API_ID_hipArrayGetDescriptor: + if (data->args.hipArrayGetDescriptor.pArrayDescriptor) data->args.hipArrayGetDescriptor.pArrayDescriptor__val = *(data->args.hipArrayGetDescriptor.pArrayDescriptor); + break; +// hipArrayGetInfo[('hipChannelFormatDesc*', 'desc'), ('hipExtent*', 'extent'), ('unsigned int*', 'flags'), ('hipArray_t', 'array')] + case HIP_API_ID_hipArrayGetInfo: + if (data->args.hipArrayGetInfo.desc) data->args.hipArrayGetInfo.desc__val = *(data->args.hipArrayGetInfo.desc); + if (data->args.hipArrayGetInfo.extent) data->args.hipArrayGetInfo.extent__val = *(data->args.hipArrayGetInfo.extent); + if (data->args.hipArrayGetInfo.flags) data->args.hipArrayGetInfo.flags__val = *(data->args.hipArrayGetInfo.flags); + break; +// hipChooseDeviceR0000[('int*', 'device'), ('const hipDeviceProp_tR0000*', 'prop')] + case HIP_API_ID_hipChooseDeviceR0000: + if (data->args.hipChooseDeviceR0000.device) data->args.hipChooseDeviceR0000.device__val = *(data->args.hipChooseDeviceR0000.device); + if (data->args.hipChooseDeviceR0000.prop) data->args.hipChooseDeviceR0000.prop__val = *(data->args.hipChooseDeviceR0000.prop); + break; +// hipChooseDeviceR0600[('int*', 'device'), ('const hipDeviceProp_tR0600*', 'prop')] + case HIP_API_ID_hipChooseDeviceR0600: + if (data->args.hipChooseDeviceR0600.device) data->args.hipChooseDeviceR0600.device__val = *(data->args.hipChooseDeviceR0600.device); + if (data->args.hipChooseDeviceR0600.prop) data->args.hipChooseDeviceR0600.prop__val = *(data->args.hipChooseDeviceR0600.prop); + break; +// hipConfigureCall[('dim3', 'gridDim'), ('dim3', 'blockDim'), ('size_t', 'sharedMem'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipConfigureCall: + break; +// hipCreateSurfaceObject[('hipSurfaceObject_t*', 'pSurfObject'), ('const hipResourceDesc*', 'pResDesc')] + case HIP_API_ID_hipCreateSurfaceObject: + if (data->args.hipCreateSurfaceObject.pSurfObject) data->args.hipCreateSurfaceObject.pSurfObject__val = *(data->args.hipCreateSurfaceObject.pSurfObject); + if (data->args.hipCreateSurfaceObject.pResDesc) data->args.hipCreateSurfaceObject.pResDesc__val = *(data->args.hipCreateSurfaceObject.pResDesc); + break; +// hipCtxCreate[('hipCtx_t*', 'ctx'), ('unsigned int', 'flags'), ('hipDevice_t', 'device')] + case HIP_API_ID_hipCtxCreate: + if (data->args.hipCtxCreate.ctx) data->args.hipCtxCreate.ctx__val = *(data->args.hipCtxCreate.ctx); + break; +// hipCtxDestroy[('hipCtx_t', 'ctx')] + case HIP_API_ID_hipCtxDestroy: + break; +// hipCtxDisablePeerAccess[('hipCtx_t', 'peerCtx')] + case HIP_API_ID_hipCtxDisablePeerAccess: + break; +// hipCtxEnablePeerAccess[('hipCtx_t', 'peerCtx'), ('unsigned int', 'flags')] + case HIP_API_ID_hipCtxEnablePeerAccess: + break; +// hipCtxGetApiVersion[('hipCtx_t', 'ctx'), ('int*', 'apiVersion')] + case HIP_API_ID_hipCtxGetApiVersion: + if (data->args.hipCtxGetApiVersion.apiVersion) data->args.hipCtxGetApiVersion.apiVersion__val = *(data->args.hipCtxGetApiVersion.apiVersion); + break; +// hipCtxGetCacheConfig[('hipFuncCache_t*', 'cacheConfig')] + case HIP_API_ID_hipCtxGetCacheConfig: + if (data->args.hipCtxGetCacheConfig.cacheConfig) data->args.hipCtxGetCacheConfig.cacheConfig__val = *(data->args.hipCtxGetCacheConfig.cacheConfig); + break; +// hipCtxGetCurrent[('hipCtx_t*', 'ctx')] + case HIP_API_ID_hipCtxGetCurrent: + if (data->args.hipCtxGetCurrent.ctx) data->args.hipCtxGetCurrent.ctx__val = *(data->args.hipCtxGetCurrent.ctx); + break; +// hipCtxGetDevice[('hipDevice_t*', 'device')] + case HIP_API_ID_hipCtxGetDevice: + if (data->args.hipCtxGetDevice.device) data->args.hipCtxGetDevice.device__val = *(data->args.hipCtxGetDevice.device); + break; +// hipCtxGetFlags[('unsigned int*', 'flags')] + case HIP_API_ID_hipCtxGetFlags: + if (data->args.hipCtxGetFlags.flags) data->args.hipCtxGetFlags.flags__val = *(data->args.hipCtxGetFlags.flags); + break; +// hipCtxGetSharedMemConfig[('hipSharedMemConfig*', 'pConfig')] + case HIP_API_ID_hipCtxGetSharedMemConfig: + if (data->args.hipCtxGetSharedMemConfig.pConfig) data->args.hipCtxGetSharedMemConfig.pConfig__val = *(data->args.hipCtxGetSharedMemConfig.pConfig); + break; +// hipCtxPopCurrent[('hipCtx_t*', 'ctx')] + case HIP_API_ID_hipCtxPopCurrent: + if (data->args.hipCtxPopCurrent.ctx) data->args.hipCtxPopCurrent.ctx__val = *(data->args.hipCtxPopCurrent.ctx); + break; +// hipCtxPushCurrent[('hipCtx_t', 'ctx')] + case HIP_API_ID_hipCtxPushCurrent: + break; +// hipCtxSetCacheConfig[('hipFuncCache_t', 'cacheConfig')] + case HIP_API_ID_hipCtxSetCacheConfig: + break; +// hipCtxSetCurrent[('hipCtx_t', 'ctx')] + case HIP_API_ID_hipCtxSetCurrent: + break; +// hipCtxSetSharedMemConfig[('hipSharedMemConfig', 'config')] + case HIP_API_ID_hipCtxSetSharedMemConfig: + break; +// hipCtxSynchronize[] + case HIP_API_ID_hipCtxSynchronize: + break; +// hipDestroyExternalMemory[('hipExternalMemory_t', 'extMem')] + case HIP_API_ID_hipDestroyExternalMemory: + break; +// hipDestroyExternalSemaphore[('hipExternalSemaphore_t', 'extSem')] + case HIP_API_ID_hipDestroyExternalSemaphore: + break; +// hipDestroySurfaceObject[('hipSurfaceObject_t', 'surfaceObject')] + case HIP_API_ID_hipDestroySurfaceObject: + break; +// hipDeviceCanAccessPeer[('int*', 'canAccessPeer'), ('int', 'deviceId'), ('int', 'peerDeviceId')] + case HIP_API_ID_hipDeviceCanAccessPeer: + if (data->args.hipDeviceCanAccessPeer.canAccessPeer) data->args.hipDeviceCanAccessPeer.canAccessPeer__val = *(data->args.hipDeviceCanAccessPeer.canAccessPeer); + break; +// hipDeviceComputeCapability[('int*', 'major'), ('int*', 'minor'), ('hipDevice_t', 'device')] + case HIP_API_ID_hipDeviceComputeCapability: + if (data->args.hipDeviceComputeCapability.major) data->args.hipDeviceComputeCapability.major__val = *(data->args.hipDeviceComputeCapability.major); + if (data->args.hipDeviceComputeCapability.minor) data->args.hipDeviceComputeCapability.minor__val = *(data->args.hipDeviceComputeCapability.minor); + break; +// hipDeviceDisablePeerAccess[('int', 'peerDeviceId')] + case HIP_API_ID_hipDeviceDisablePeerAccess: + break; +// hipDeviceEnablePeerAccess[('int', 'peerDeviceId'), ('unsigned int', 'flags')] + case HIP_API_ID_hipDeviceEnablePeerAccess: + break; +// hipDeviceGet[('hipDevice_t*', 'device'), ('int', 'ordinal')] + case HIP_API_ID_hipDeviceGet: + if (data->args.hipDeviceGet.device) data->args.hipDeviceGet.device__val = *(data->args.hipDeviceGet.device); + break; +// hipDeviceGetAttribute[('int*', 'pi'), ('hipDeviceAttribute_t', 'attr'), ('int', 'deviceId')] + case HIP_API_ID_hipDeviceGetAttribute: + if (data->args.hipDeviceGetAttribute.pi) data->args.hipDeviceGetAttribute.pi__val = *(data->args.hipDeviceGetAttribute.pi); + break; +// hipDeviceGetByPCIBusId[('int*', 'device'), ('const char*', 'pciBusId')] + case HIP_API_ID_hipDeviceGetByPCIBusId: + if (data->args.hipDeviceGetByPCIBusId.device) data->args.hipDeviceGetByPCIBusId.device__val = *(data->args.hipDeviceGetByPCIBusId.device); + if (data->args.hipDeviceGetByPCIBusId.pciBusId) data->args.hipDeviceGetByPCIBusId.pciBusId__val = *(data->args.hipDeviceGetByPCIBusId.pciBusId); + break; +// hipDeviceGetCacheConfig[('hipFuncCache_t*', 'cacheConfig')] + case HIP_API_ID_hipDeviceGetCacheConfig: + if (data->args.hipDeviceGetCacheConfig.cacheConfig) data->args.hipDeviceGetCacheConfig.cacheConfig__val = *(data->args.hipDeviceGetCacheConfig.cacheConfig); + break; +// hipDeviceGetDefaultMemPool[('hipMemPool_t*', 'mem_pool'), ('int', 'device')] + case HIP_API_ID_hipDeviceGetDefaultMemPool: + if (data->args.hipDeviceGetDefaultMemPool.mem_pool) data->args.hipDeviceGetDefaultMemPool.mem_pool__val = *(data->args.hipDeviceGetDefaultMemPool.mem_pool); + break; +// hipDeviceGetGraphMemAttribute[('int', 'device'), ('hipGraphMemAttributeType', 'attr'), ('void*', 'value')] + case HIP_API_ID_hipDeviceGetGraphMemAttribute: + break; +// hipDeviceGetLimit[('size_t*', 'pValue'), ('hipLimit_t', 'limit')] + case HIP_API_ID_hipDeviceGetLimit: + if (data->args.hipDeviceGetLimit.pValue) data->args.hipDeviceGetLimit.pValue__val = *(data->args.hipDeviceGetLimit.pValue); + break; +// hipDeviceGetMemPool[('hipMemPool_t*', 'mem_pool'), ('int', 'device')] + case HIP_API_ID_hipDeviceGetMemPool: + if (data->args.hipDeviceGetMemPool.mem_pool) data->args.hipDeviceGetMemPool.mem_pool__val = *(data->args.hipDeviceGetMemPool.mem_pool); + break; +// hipDeviceGetName[('char*', 'name'), ('int', 'len'), ('hipDevice_t', 'device')] + case HIP_API_ID_hipDeviceGetName: + data->args.hipDeviceGetName.name = (data->args.hipDeviceGetName.name) ? strdup(data->args.hipDeviceGetName.name) : NULL; + break; +// hipDeviceGetP2PAttribute[('int*', 'value'), ('hipDeviceP2PAttr', 'attr'), ('int', 'srcDevice'), ('int', 'dstDevice')] + case HIP_API_ID_hipDeviceGetP2PAttribute: + if (data->args.hipDeviceGetP2PAttribute.value) data->args.hipDeviceGetP2PAttribute.value__val = *(data->args.hipDeviceGetP2PAttribute.value); + break; +// hipDeviceGetPCIBusId[('char*', 'pciBusId'), ('int', 'len'), ('int', 'device')] + case HIP_API_ID_hipDeviceGetPCIBusId: + data->args.hipDeviceGetPCIBusId.pciBusId = (data->args.hipDeviceGetPCIBusId.pciBusId) ? strdup(data->args.hipDeviceGetPCIBusId.pciBusId) : NULL; + break; +// hipDeviceGetSharedMemConfig[('hipSharedMemConfig*', 'pConfig')] + case HIP_API_ID_hipDeviceGetSharedMemConfig: + if (data->args.hipDeviceGetSharedMemConfig.pConfig) data->args.hipDeviceGetSharedMemConfig.pConfig__val = *(data->args.hipDeviceGetSharedMemConfig.pConfig); + break; +// hipDeviceGetStreamPriorityRange[('int*', 'leastPriority'), ('int*', 'greatestPriority')] + case HIP_API_ID_hipDeviceGetStreamPriorityRange: + if (data->args.hipDeviceGetStreamPriorityRange.leastPriority) data->args.hipDeviceGetStreamPriorityRange.leastPriority__val = *(data->args.hipDeviceGetStreamPriorityRange.leastPriority); + if (data->args.hipDeviceGetStreamPriorityRange.greatestPriority) data->args.hipDeviceGetStreamPriorityRange.greatestPriority__val = *(data->args.hipDeviceGetStreamPriorityRange.greatestPriority); + break; +// hipDeviceGetUuid[('hipUUID*', 'uuid'), ('hipDevice_t', 'device')] + case HIP_API_ID_hipDeviceGetUuid: + if (data->args.hipDeviceGetUuid.uuid) data->args.hipDeviceGetUuid.uuid__val = *(data->args.hipDeviceGetUuid.uuid); + break; +// hipDeviceGraphMemTrim[('int', 'device')] + case HIP_API_ID_hipDeviceGraphMemTrim: + break; +// hipDevicePrimaryCtxGetState[('hipDevice_t', 'dev'), ('unsigned int*', 'flags'), ('int*', 'active')] + case HIP_API_ID_hipDevicePrimaryCtxGetState: + if (data->args.hipDevicePrimaryCtxGetState.flags) data->args.hipDevicePrimaryCtxGetState.flags__val = *(data->args.hipDevicePrimaryCtxGetState.flags); + if (data->args.hipDevicePrimaryCtxGetState.active) data->args.hipDevicePrimaryCtxGetState.active__val = *(data->args.hipDevicePrimaryCtxGetState.active); + break; +// hipDevicePrimaryCtxRelease[('hipDevice_t', 'dev')] + case HIP_API_ID_hipDevicePrimaryCtxRelease: + break; +// hipDevicePrimaryCtxReset[('hipDevice_t', 'dev')] + case HIP_API_ID_hipDevicePrimaryCtxReset: + break; +// hipDevicePrimaryCtxRetain[('hipCtx_t*', 'pctx'), ('hipDevice_t', 'dev')] + case HIP_API_ID_hipDevicePrimaryCtxRetain: + if (data->args.hipDevicePrimaryCtxRetain.pctx) data->args.hipDevicePrimaryCtxRetain.pctx__val = *(data->args.hipDevicePrimaryCtxRetain.pctx); + break; +// hipDevicePrimaryCtxSetFlags[('hipDevice_t', 'dev'), ('unsigned int', 'flags')] + case HIP_API_ID_hipDevicePrimaryCtxSetFlags: + break; +// hipDeviceReset[] + case HIP_API_ID_hipDeviceReset: + break; +// hipDeviceSetCacheConfig[('hipFuncCache_t', 'cacheConfig')] + case HIP_API_ID_hipDeviceSetCacheConfig: + break; +// hipDeviceSetGraphMemAttribute[('int', 'device'), ('hipGraphMemAttributeType', 'attr'), ('void*', 'value')] + case HIP_API_ID_hipDeviceSetGraphMemAttribute: + break; +// hipDeviceSetLimit[('hipLimit_t', 'limit'), ('size_t', 'value')] + case HIP_API_ID_hipDeviceSetLimit: + break; +// hipDeviceSetMemPool[('int', 'device'), ('hipMemPool_t', 'mem_pool')] + case HIP_API_ID_hipDeviceSetMemPool: + break; +// hipDeviceSetSharedMemConfig[('hipSharedMemConfig', 'config')] + case HIP_API_ID_hipDeviceSetSharedMemConfig: + break; +// hipDeviceSynchronize[] + case HIP_API_ID_hipDeviceSynchronize: + break; +// hipDeviceTotalMem[('size_t*', 'bytes'), ('hipDevice_t', 'device')] + case HIP_API_ID_hipDeviceTotalMem: + if (data->args.hipDeviceTotalMem.bytes) data->args.hipDeviceTotalMem.bytes__val = *(data->args.hipDeviceTotalMem.bytes); + break; +// hipDriverGetVersion[('int*', 'driverVersion')] + case HIP_API_ID_hipDriverGetVersion: + if (data->args.hipDriverGetVersion.driverVersion) data->args.hipDriverGetVersion.driverVersion__val = *(data->args.hipDriverGetVersion.driverVersion); + break; +// hipDrvGraphAddMemcpyNode[('hipGraphNode_t*', 'phGraphNode'), ('hipGraph_t', 'hGraph'), ('const hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('const HIP_MEMCPY3D*', 'copyParams'), ('hipCtx_t', 'ctx')] + case HIP_API_ID_hipDrvGraphAddMemcpyNode: + if (data->args.hipDrvGraphAddMemcpyNode.phGraphNode) data->args.hipDrvGraphAddMemcpyNode.phGraphNode__val = *(data->args.hipDrvGraphAddMemcpyNode.phGraphNode); + if (data->args.hipDrvGraphAddMemcpyNode.dependencies) data->args.hipDrvGraphAddMemcpyNode.dependencies__val = *(data->args.hipDrvGraphAddMemcpyNode.dependencies); + if (data->args.hipDrvGraphAddMemcpyNode.copyParams) data->args.hipDrvGraphAddMemcpyNode.copyParams__val = *(data->args.hipDrvGraphAddMemcpyNode.copyParams); + break; +// hipDrvGraphAddMemsetNode[('hipGraphNode_t*', 'phGraphNode'), ('hipGraph_t', 'hGraph'), ('const hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('const HIP_MEMSET_NODE_PARAMS*', 'memsetParams'), ('hipCtx_t', 'ctx')] + case HIP_API_ID_hipDrvGraphAddMemsetNode: + if (data->args.hipDrvGraphAddMemsetNode.phGraphNode) data->args.hipDrvGraphAddMemsetNode.phGraphNode__val = *(data->args.hipDrvGraphAddMemsetNode.phGraphNode); + if (data->args.hipDrvGraphAddMemsetNode.dependencies) data->args.hipDrvGraphAddMemsetNode.dependencies__val = *(data->args.hipDrvGraphAddMemsetNode.dependencies); + if (data->args.hipDrvGraphAddMemsetNode.memsetParams) data->args.hipDrvGraphAddMemsetNode.memsetParams__val = *(data->args.hipDrvGraphAddMemsetNode.memsetParams); + break; +// hipDrvGraphMemcpyNodeGetParams[('hipGraphNode_t', 'hNode'), ('HIP_MEMCPY3D*', 'nodeParams')] + case HIP_API_ID_hipDrvGraphMemcpyNodeGetParams: + if (data->args.hipDrvGraphMemcpyNodeGetParams.nodeParams) data->args.hipDrvGraphMemcpyNodeGetParams.nodeParams__val = *(data->args.hipDrvGraphMemcpyNodeGetParams.nodeParams); + break; +// hipDrvGraphMemcpyNodeSetParams[('hipGraphNode_t', 'hNode'), ('const HIP_MEMCPY3D*', 'nodeParams')] + case HIP_API_ID_hipDrvGraphMemcpyNodeSetParams: + if (data->args.hipDrvGraphMemcpyNodeSetParams.nodeParams) data->args.hipDrvGraphMemcpyNodeSetParams.nodeParams__val = *(data->args.hipDrvGraphMemcpyNodeSetParams.nodeParams); + break; +// hipDrvMemcpy2DUnaligned[('const hip_Memcpy2D*', 'pCopy')] + case HIP_API_ID_hipDrvMemcpy2DUnaligned: + if (data->args.hipDrvMemcpy2DUnaligned.pCopy) data->args.hipDrvMemcpy2DUnaligned.pCopy__val = *(data->args.hipDrvMemcpy2DUnaligned.pCopy); + break; +// hipDrvMemcpy3D[('const HIP_MEMCPY3D*', 'pCopy')] + case HIP_API_ID_hipDrvMemcpy3D: + if (data->args.hipDrvMemcpy3D.pCopy) data->args.hipDrvMemcpy3D.pCopy__val = *(data->args.hipDrvMemcpy3D.pCopy); + break; +// hipDrvMemcpy3DAsync[('const HIP_MEMCPY3D*', 'pCopy'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipDrvMemcpy3DAsync: + if (data->args.hipDrvMemcpy3DAsync.pCopy) data->args.hipDrvMemcpy3DAsync.pCopy__val = *(data->args.hipDrvMemcpy3DAsync.pCopy); + break; +// hipDrvPointerGetAttributes[('unsigned int', 'numAttributes'), ('hipPointer_attribute*', 'attributes'), ('void**', 'data'), ('hipDeviceptr_t', 'ptr')] + case HIP_API_ID_hipDrvPointerGetAttributes: + if (data->args.hipDrvPointerGetAttributes.attributes) data->args.hipDrvPointerGetAttributes.attributes__val = *(data->args.hipDrvPointerGetAttributes.attributes); + if (data->args.hipDrvPointerGetAttributes.data) data->args.hipDrvPointerGetAttributes.data__val = *(data->args.hipDrvPointerGetAttributes.data); + break; +// hipEventCreate[('hipEvent_t*', 'event')] + case HIP_API_ID_hipEventCreate: + if (data->args.hipEventCreate.event) data->args.hipEventCreate.event__val = *(data->args.hipEventCreate.event); + break; +// hipEventCreateWithFlags[('hipEvent_t*', 'event'), ('unsigned int', 'flags')] + case HIP_API_ID_hipEventCreateWithFlags: + if (data->args.hipEventCreateWithFlags.event) data->args.hipEventCreateWithFlags.event__val = *(data->args.hipEventCreateWithFlags.event); + break; +// hipEventDestroy[('hipEvent_t', 'event')] + case HIP_API_ID_hipEventDestroy: + break; +// hipEventElapsedTime[('float*', 'ms'), ('hipEvent_t', 'start'), ('hipEvent_t', 'stop')] + case HIP_API_ID_hipEventElapsedTime: + if (data->args.hipEventElapsedTime.ms) data->args.hipEventElapsedTime.ms__val = *(data->args.hipEventElapsedTime.ms); + break; +// hipEventQuery[('hipEvent_t', 'event')] + case HIP_API_ID_hipEventQuery: + break; +// hipEventRecord[('hipEvent_t', 'event'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipEventRecord: + break; +// hipEventSynchronize[('hipEvent_t', 'event')] + case HIP_API_ID_hipEventSynchronize: + break; +// hipExtGetLinkTypeAndHopCount[('int', 'device1'), ('int', 'device2'), ('unsigned int*', 'linktype'), ('unsigned int*', 'hopcount')] + case HIP_API_ID_hipExtGetLinkTypeAndHopCount: + if (data->args.hipExtGetLinkTypeAndHopCount.linktype) data->args.hipExtGetLinkTypeAndHopCount.linktype__val = *(data->args.hipExtGetLinkTypeAndHopCount.linktype); + if (data->args.hipExtGetLinkTypeAndHopCount.hopcount) data->args.hipExtGetLinkTypeAndHopCount.hopcount__val = *(data->args.hipExtGetLinkTypeAndHopCount.hopcount); + break; +// hipExtLaunchKernel[('const void*', 'function_address'), ('dim3', 'numBlocks'), ('dim3', 'dimBlocks'), ('void**', 'args'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent'), ('int', 'flags')] + case HIP_API_ID_hipExtLaunchKernel: + if (data->args.hipExtLaunchKernel.args) data->args.hipExtLaunchKernel.args__val = *(data->args.hipExtLaunchKernel.args); + break; +// hipExtLaunchMultiKernelMultiDevice[('hipLaunchParams*', 'launchParamsList'), ('int', 'numDevices'), ('unsigned int', 'flags')] + case HIP_API_ID_hipExtLaunchMultiKernelMultiDevice: + if (data->args.hipExtLaunchMultiKernelMultiDevice.launchParamsList) data->args.hipExtLaunchMultiKernelMultiDevice.launchParamsList__val = *(data->args.hipExtLaunchMultiKernelMultiDevice.launchParamsList); + break; +// hipExtMallocWithFlags[('void**', 'ptr'), ('size_t', 'sizeBytes'), ('unsigned int', 'flags')] + case HIP_API_ID_hipExtMallocWithFlags: + if (data->args.hipExtMallocWithFlags.ptr) data->args.hipExtMallocWithFlags.ptr__val = *(data->args.hipExtMallocWithFlags.ptr); + break; +// hipExtModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'globalWorkSizeX'), ('unsigned int', 'globalWorkSizeY'), ('unsigned int', 'globalWorkSizeZ'), ('unsigned int', 'localWorkSizeX'), ('unsigned int', 'localWorkSizeY'), ('unsigned int', 'localWorkSizeZ'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'hStream'), ('void**', 'kernelParams'), ('void**', 'extra'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent'), ('unsigned int', 'flags')] + case HIP_API_ID_hipExtModuleLaunchKernel: + if (data->args.hipExtModuleLaunchKernel.kernelParams) data->args.hipExtModuleLaunchKernel.kernelParams__val = *(data->args.hipExtModuleLaunchKernel.kernelParams); + if (data->args.hipExtModuleLaunchKernel.extra) data->args.hipExtModuleLaunchKernel.extra__val = *(data->args.hipExtModuleLaunchKernel.extra); + break; +// hipExtStreamCreateWithCUMask[('hipStream_t*', 'stream'), ('unsigned int', 'cuMaskSize'), ('const unsigned int*', 'cuMask')] + case HIP_API_ID_hipExtStreamCreateWithCUMask: + if (data->args.hipExtStreamCreateWithCUMask.stream) data->args.hipExtStreamCreateWithCUMask.stream__val = *(data->args.hipExtStreamCreateWithCUMask.stream); + if (data->args.hipExtStreamCreateWithCUMask.cuMask) data->args.hipExtStreamCreateWithCUMask.cuMask__val = *(data->args.hipExtStreamCreateWithCUMask.cuMask); + break; +// hipExtStreamGetCUMask[('hipStream_t', 'stream'), ('unsigned int', 'cuMaskSize'), ('unsigned int*', 'cuMask')] + case HIP_API_ID_hipExtStreamGetCUMask: + if (data->args.hipExtStreamGetCUMask.cuMask) data->args.hipExtStreamGetCUMask.cuMask__val = *(data->args.hipExtStreamGetCUMask.cuMask); + break; +// hipExternalMemoryGetMappedBuffer[('void**', 'devPtr'), ('hipExternalMemory_t', 'extMem'), ('const hipExternalMemoryBufferDesc*', 'bufferDesc')] + case HIP_API_ID_hipExternalMemoryGetMappedBuffer: + if (data->args.hipExternalMemoryGetMappedBuffer.devPtr) data->args.hipExternalMemoryGetMappedBuffer.devPtr__val = *(data->args.hipExternalMemoryGetMappedBuffer.devPtr); + if (data->args.hipExternalMemoryGetMappedBuffer.bufferDesc) data->args.hipExternalMemoryGetMappedBuffer.bufferDesc__val = *(data->args.hipExternalMemoryGetMappedBuffer.bufferDesc); + break; +// hipExternalMemoryGetMappedMipmappedArray[('hipMipmappedArray_t*', 'mipmap'), ('hipExternalMemory_t', 'extMem'), ('const hipExternalMemoryMipmappedArrayDesc*', 'mipmapDesc')] + case HIP_API_ID_hipExternalMemoryGetMappedMipmappedArray: + if (data->args.hipExternalMemoryGetMappedMipmappedArray.mipmap) data->args.hipExternalMemoryGetMappedMipmappedArray.mipmap__val = *(data->args.hipExternalMemoryGetMappedMipmappedArray.mipmap); + if (data->args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc) data->args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc__val = *(data->args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc); + break; +// hipFree[('void*', 'ptr')] + case HIP_API_ID_hipFree: + break; +// hipFreeArray[('hipArray_t', 'array')] + case HIP_API_ID_hipFreeArray: + break; +// hipFreeAsync[('void*', 'dev_ptr'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipFreeAsync: + break; +// hipFreeHost[('void*', 'ptr')] + case HIP_API_ID_hipFreeHost: + break; +// hipFreeMipmappedArray[('hipMipmappedArray_t', 'mipmappedArray')] + case HIP_API_ID_hipFreeMipmappedArray: + break; +// hipFuncGetAttribute[('int*', 'value'), ('hipFunction_attribute', 'attrib'), ('hipFunction_t', 'hfunc')] + case HIP_API_ID_hipFuncGetAttribute: + if (data->args.hipFuncGetAttribute.value) data->args.hipFuncGetAttribute.value__val = *(data->args.hipFuncGetAttribute.value); + break; +// hipFuncGetAttributes[('hipFuncAttributes*', 'attr'), ('const void*', 'func')] + case HIP_API_ID_hipFuncGetAttributes: + if (data->args.hipFuncGetAttributes.attr) data->args.hipFuncGetAttributes.attr__val = *(data->args.hipFuncGetAttributes.attr); + break; +// hipFuncSetAttribute[('const void*', 'func'), ('hipFuncAttribute', 'attr'), ('int', 'value')] + case HIP_API_ID_hipFuncSetAttribute: + break; +// hipFuncSetCacheConfig[('const void*', 'func'), ('hipFuncCache_t', 'config')] + case HIP_API_ID_hipFuncSetCacheConfig: + break; +// hipFuncSetSharedMemConfig[('const void*', 'func'), ('hipSharedMemConfig', 'config')] + case HIP_API_ID_hipFuncSetSharedMemConfig: + break; +// hipGLGetDevices[('unsigned int*', 'pHipDeviceCount'), ('int*', 'pHipDevices'), ('unsigned int', 'hipDeviceCount'), ('hipGLDeviceList', 'deviceList')] + case HIP_API_ID_hipGLGetDevices: + if (data->args.hipGLGetDevices.pHipDeviceCount) data->args.hipGLGetDevices.pHipDeviceCount__val = *(data->args.hipGLGetDevices.pHipDeviceCount); + if (data->args.hipGLGetDevices.pHipDevices) data->args.hipGLGetDevices.pHipDevices__val = *(data->args.hipGLGetDevices.pHipDevices); + break; +// hipGetChannelDesc[('hipChannelFormatDesc*', 'desc'), ('hipArray_const_t', 'array')] + case HIP_API_ID_hipGetChannelDesc: + if (data->args.hipGetChannelDesc.desc) data->args.hipGetChannelDesc.desc__val = *(data->args.hipGetChannelDesc.desc); + break; +// hipGetDevice[('int*', 'deviceId')] + case HIP_API_ID_hipGetDevice: + if (data->args.hipGetDevice.deviceId) data->args.hipGetDevice.deviceId__val = *(data->args.hipGetDevice.deviceId); + break; +// hipGetDeviceCount[('int*', 'count')] + case HIP_API_ID_hipGetDeviceCount: + if (data->args.hipGetDeviceCount.count) data->args.hipGetDeviceCount.count__val = *(data->args.hipGetDeviceCount.count); + break; +// hipGetDeviceFlags[('unsigned int*', 'flags')] + case HIP_API_ID_hipGetDeviceFlags: + if (data->args.hipGetDeviceFlags.flags) data->args.hipGetDeviceFlags.flags__val = *(data->args.hipGetDeviceFlags.flags); + break; +// hipGetDevicePropertiesR0000[('hipDeviceProp_tR0000*', 'prop'), ('int', 'device')] + case HIP_API_ID_hipGetDevicePropertiesR0000: + if (data->args.hipGetDevicePropertiesR0000.prop) data->args.hipGetDevicePropertiesR0000.prop__val = *(data->args.hipGetDevicePropertiesR0000.prop); + break; +// hipGetDevicePropertiesR0600[('hipDeviceProp_tR0600*', 'prop'), ('int', 'deviceId')] + case HIP_API_ID_hipGetDevicePropertiesR0600: + if (data->args.hipGetDevicePropertiesR0600.prop) data->args.hipGetDevicePropertiesR0600.prop__val = *(data->args.hipGetDevicePropertiesR0600.prop); + break; +// hipGetErrorString[] + case HIP_API_ID_hipGetErrorString: + break; +// hipGetLastError[] + case HIP_API_ID_hipGetLastError: + break; +// hipExtGetLastError[] + case HIP_API_ID_hipExtGetLastError: + break; +// hipGetMipmappedArrayLevel[('hipArray_t*', 'levelArray'), ('hipMipmappedArray_const_t', 'mipmappedArray'), ('unsigned int', 'level')] + case HIP_API_ID_hipGetMipmappedArrayLevel: + if (data->args.hipGetMipmappedArrayLevel.levelArray) data->args.hipGetMipmappedArrayLevel.levelArray__val = *(data->args.hipGetMipmappedArrayLevel.levelArray); + break; +// hipGetSymbolAddress[('void**', 'devPtr'), ('const void*', 'symbol')] + case HIP_API_ID_hipGetSymbolAddress: + if (data->args.hipGetSymbolAddress.devPtr) data->args.hipGetSymbolAddress.devPtr__val = *(data->args.hipGetSymbolAddress.devPtr); + break; +// hipGetSymbolSize[('size_t*', 'size'), ('const void*', 'symbol')] + case HIP_API_ID_hipGetSymbolSize: + if (data->args.hipGetSymbolSize.size) data->args.hipGetSymbolSize.size__val = *(data->args.hipGetSymbolSize.size); + break; +// hipGraphAddChildGraphNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipGraph_t', 'childGraph')] + case HIP_API_ID_hipGraphAddChildGraphNode: + if (data->args.hipGraphAddChildGraphNode.pGraphNode) data->args.hipGraphAddChildGraphNode.pGraphNode__val = *(data->args.hipGraphAddChildGraphNode.pGraphNode); + if (data->args.hipGraphAddChildGraphNode.pDependencies) data->args.hipGraphAddChildGraphNode.pDependencies__val = *(data->args.hipGraphAddChildGraphNode.pDependencies); + break; +// hipGraphAddDependencies[('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'from'), ('const hipGraphNode_t*', 'to'), ('size_t', 'numDependencies')] + case HIP_API_ID_hipGraphAddDependencies: + if (data->args.hipGraphAddDependencies.from) data->args.hipGraphAddDependencies.from__val = *(data->args.hipGraphAddDependencies.from); + if (data->args.hipGraphAddDependencies.to) data->args.hipGraphAddDependencies.to__val = *(data->args.hipGraphAddDependencies.to); + break; +// hipGraphAddEmptyNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies')] + case HIP_API_ID_hipGraphAddEmptyNode: + if (data->args.hipGraphAddEmptyNode.pGraphNode) data->args.hipGraphAddEmptyNode.pGraphNode__val = *(data->args.hipGraphAddEmptyNode.pGraphNode); + if (data->args.hipGraphAddEmptyNode.pDependencies) data->args.hipGraphAddEmptyNode.pDependencies__val = *(data->args.hipGraphAddEmptyNode.pDependencies); + break; +// hipGraphAddEventRecordNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphAddEventRecordNode: + if (data->args.hipGraphAddEventRecordNode.pGraphNode) data->args.hipGraphAddEventRecordNode.pGraphNode__val = *(data->args.hipGraphAddEventRecordNode.pGraphNode); + if (data->args.hipGraphAddEventRecordNode.pDependencies) data->args.hipGraphAddEventRecordNode.pDependencies__val = *(data->args.hipGraphAddEventRecordNode.pDependencies); + break; +// hipGraphAddEventWaitNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphAddEventWaitNode: + if (data->args.hipGraphAddEventWaitNode.pGraphNode) data->args.hipGraphAddEventWaitNode.pGraphNode__val = *(data->args.hipGraphAddEventWaitNode.pGraphNode); + if (data->args.hipGraphAddEventWaitNode.pDependencies) data->args.hipGraphAddEventWaitNode.pDependencies__val = *(data->args.hipGraphAddEventWaitNode.pDependencies); + break; +// hipGraphAddExternalSemaphoresSignalNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphAddExternalSemaphoresSignalNode: + if (data->args.hipGraphAddExternalSemaphoresSignalNode.pGraphNode) data->args.hipGraphAddExternalSemaphoresSignalNode.pGraphNode__val = *(data->args.hipGraphAddExternalSemaphoresSignalNode.pGraphNode); + if (data->args.hipGraphAddExternalSemaphoresSignalNode.pDependencies) data->args.hipGraphAddExternalSemaphoresSignalNode.pDependencies__val = *(data->args.hipGraphAddExternalSemaphoresSignalNode.pDependencies); + if (data->args.hipGraphAddExternalSemaphoresSignalNode.nodeParams) data->args.hipGraphAddExternalSemaphoresSignalNode.nodeParams__val = *(data->args.hipGraphAddExternalSemaphoresSignalNode.nodeParams); + break; +// hipGraphAddExternalSemaphoresWaitNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphAddExternalSemaphoresWaitNode: + if (data->args.hipGraphAddExternalSemaphoresWaitNode.pGraphNode) data->args.hipGraphAddExternalSemaphoresWaitNode.pGraphNode__val = *(data->args.hipGraphAddExternalSemaphoresWaitNode.pGraphNode); + if (data->args.hipGraphAddExternalSemaphoresWaitNode.pDependencies) data->args.hipGraphAddExternalSemaphoresWaitNode.pDependencies__val = *(data->args.hipGraphAddExternalSemaphoresWaitNode.pDependencies); + if (data->args.hipGraphAddExternalSemaphoresWaitNode.nodeParams) data->args.hipGraphAddExternalSemaphoresWaitNode.nodeParams__val = *(data->args.hipGraphAddExternalSemaphoresWaitNode.nodeParams); + break; +// hipGraphAddHostNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipHostNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphAddHostNode: + if (data->args.hipGraphAddHostNode.pGraphNode) data->args.hipGraphAddHostNode.pGraphNode__val = *(data->args.hipGraphAddHostNode.pGraphNode); + if (data->args.hipGraphAddHostNode.pDependencies) data->args.hipGraphAddHostNode.pDependencies__val = *(data->args.hipGraphAddHostNode.pDependencies); + if (data->args.hipGraphAddHostNode.pNodeParams) data->args.hipGraphAddHostNode.pNodeParams__val = *(data->args.hipGraphAddHostNode.pNodeParams); + break; +// hipGraphAddKernelNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipKernelNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphAddKernelNode: + if (data->args.hipGraphAddKernelNode.pGraphNode) data->args.hipGraphAddKernelNode.pGraphNode__val = *(data->args.hipGraphAddKernelNode.pGraphNode); + if (data->args.hipGraphAddKernelNode.pDependencies) data->args.hipGraphAddKernelNode.pDependencies__val = *(data->args.hipGraphAddKernelNode.pDependencies); + if (data->args.hipGraphAddKernelNode.pNodeParams) data->args.hipGraphAddKernelNode.pNodeParams__val = *(data->args.hipGraphAddKernelNode.pNodeParams); + break; +// hipGraphAddMemAllocNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('hipMemAllocNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphAddMemAllocNode: + if (data->args.hipGraphAddMemAllocNode.pGraphNode) data->args.hipGraphAddMemAllocNode.pGraphNode__val = *(data->args.hipGraphAddMemAllocNode.pGraphNode); + if (data->args.hipGraphAddMemAllocNode.pDependencies) data->args.hipGraphAddMemAllocNode.pDependencies__val = *(data->args.hipGraphAddMemAllocNode.pDependencies); + if (data->args.hipGraphAddMemAllocNode.pNodeParams) data->args.hipGraphAddMemAllocNode.pNodeParams__val = *(data->args.hipGraphAddMemAllocNode.pNodeParams); + break; +// hipGraphAddMemFreeNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dev_ptr')] + case HIP_API_ID_hipGraphAddMemFreeNode: + if (data->args.hipGraphAddMemFreeNode.pGraphNode) data->args.hipGraphAddMemFreeNode.pGraphNode__val = *(data->args.hipGraphAddMemFreeNode.pGraphNode); + if (data->args.hipGraphAddMemFreeNode.pDependencies) data->args.hipGraphAddMemFreeNode.pDependencies__val = *(data->args.hipGraphAddMemFreeNode.pDependencies); + break; +// hipGraphAddMemcpyNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipMemcpy3DParms*', 'pCopyParams')] + case HIP_API_ID_hipGraphAddMemcpyNode: + if (data->args.hipGraphAddMemcpyNode.pGraphNode) data->args.hipGraphAddMemcpyNode.pGraphNode__val = *(data->args.hipGraphAddMemcpyNode.pGraphNode); + if (data->args.hipGraphAddMemcpyNode.pDependencies) data->args.hipGraphAddMemcpyNode.pDependencies__val = *(data->args.hipGraphAddMemcpyNode.pDependencies); + if (data->args.hipGraphAddMemcpyNode.pCopyParams) data->args.hipGraphAddMemcpyNode.pCopyParams__val = *(data->args.hipGraphAddMemcpyNode.pCopyParams); + break; +// hipGraphAddMemcpyNode1D[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphAddMemcpyNode1D: + if (data->args.hipGraphAddMemcpyNode1D.pGraphNode) data->args.hipGraphAddMemcpyNode1D.pGraphNode__val = *(data->args.hipGraphAddMemcpyNode1D.pGraphNode); + if (data->args.hipGraphAddMemcpyNode1D.pDependencies) data->args.hipGraphAddMemcpyNode1D.pDependencies__val = *(data->args.hipGraphAddMemcpyNode1D.pDependencies); + break; +// hipGraphAddMemcpyNodeFromSymbol[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphAddMemcpyNodeFromSymbol: + if (data->args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode) data->args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode__val = *(data->args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode); + if (data->args.hipGraphAddMemcpyNodeFromSymbol.pDependencies) data->args.hipGraphAddMemcpyNodeFromSymbol.pDependencies__val = *(data->args.hipGraphAddMemcpyNodeFromSymbol.pDependencies); + break; +// hipGraphAddMemcpyNodeToSymbol[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphAddMemcpyNodeToSymbol: + if (data->args.hipGraphAddMemcpyNodeToSymbol.pGraphNode) data->args.hipGraphAddMemcpyNodeToSymbol.pGraphNode__val = *(data->args.hipGraphAddMemcpyNodeToSymbol.pGraphNode); + if (data->args.hipGraphAddMemcpyNodeToSymbol.pDependencies) data->args.hipGraphAddMemcpyNodeToSymbol.pDependencies__val = *(data->args.hipGraphAddMemcpyNodeToSymbol.pDependencies); + break; +// hipGraphAddMemsetNode[('hipGraphNode_t*', 'pGraphNode'), ('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'pDependencies'), ('size_t', 'numDependencies'), ('const hipMemsetParams*', 'pMemsetParams')] + case HIP_API_ID_hipGraphAddMemsetNode: + if (data->args.hipGraphAddMemsetNode.pGraphNode) data->args.hipGraphAddMemsetNode.pGraphNode__val = *(data->args.hipGraphAddMemsetNode.pGraphNode); + if (data->args.hipGraphAddMemsetNode.pDependencies) data->args.hipGraphAddMemsetNode.pDependencies__val = *(data->args.hipGraphAddMemsetNode.pDependencies); + if (data->args.hipGraphAddMemsetNode.pMemsetParams) data->args.hipGraphAddMemsetNode.pMemsetParams__val = *(data->args.hipGraphAddMemsetNode.pMemsetParams); + break; +// hipGraphChildGraphNodeGetGraph[('hipGraphNode_t', 'node'), ('hipGraph_t*', 'pGraph')] + case HIP_API_ID_hipGraphChildGraphNodeGetGraph: + if (data->args.hipGraphChildGraphNodeGetGraph.pGraph) data->args.hipGraphChildGraphNodeGetGraph.pGraph__val = *(data->args.hipGraphChildGraphNodeGetGraph.pGraph); + break; +// hipGraphClone[('hipGraph_t*', 'pGraphClone'), ('hipGraph_t', 'originalGraph')] + case HIP_API_ID_hipGraphClone: + if (data->args.hipGraphClone.pGraphClone) data->args.hipGraphClone.pGraphClone__val = *(data->args.hipGraphClone.pGraphClone); + break; +// hipGraphCreate[('hipGraph_t*', 'pGraph'), ('unsigned int', 'flags')] + case HIP_API_ID_hipGraphCreate: + if (data->args.hipGraphCreate.pGraph) data->args.hipGraphCreate.pGraph__val = *(data->args.hipGraphCreate.pGraph); + break; +// hipGraphDebugDotPrint[('hipGraph_t', 'graph'), ('const char*', 'path'), ('unsigned int', 'flags')] + case HIP_API_ID_hipGraphDebugDotPrint: + if (data->args.hipGraphDebugDotPrint.path) data->args.hipGraphDebugDotPrint.path__val = *(data->args.hipGraphDebugDotPrint.path); + break; +// hipGraphDestroy[('hipGraph_t', 'graph')] + case HIP_API_ID_hipGraphDestroy: + break; +// hipGraphDestroyNode[('hipGraphNode_t', 'node')] + case HIP_API_ID_hipGraphDestroyNode: + break; +// hipGraphEventRecordNodeGetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t*', 'event_out')] + case HIP_API_ID_hipGraphEventRecordNodeGetEvent: + if (data->args.hipGraphEventRecordNodeGetEvent.event_out) data->args.hipGraphEventRecordNodeGetEvent.event_out__val = *(data->args.hipGraphEventRecordNodeGetEvent.event_out); + break; +// hipGraphEventRecordNodeSetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphEventRecordNodeSetEvent: + break; +// hipGraphEventWaitNodeGetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t*', 'event_out')] + case HIP_API_ID_hipGraphEventWaitNodeGetEvent: + if (data->args.hipGraphEventWaitNodeGetEvent.event_out) data->args.hipGraphEventWaitNodeGetEvent.event_out__val = *(data->args.hipGraphEventWaitNodeGetEvent.event_out); + break; +// hipGraphEventWaitNodeSetEvent[('hipGraphNode_t', 'node'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphEventWaitNodeSetEvent: + break; +// hipGraphExecChildGraphNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('hipGraph_t', 'childGraph')] + case HIP_API_ID_hipGraphExecChildGraphNodeSetParams: + break; +// hipGraphExecDestroy[('hipGraphExec_t', 'graphExec')] + case HIP_API_ID_hipGraphExecDestroy: + break; +// hipGraphExecEventRecordNodeSetEvent[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphExecEventRecordNodeSetEvent: + break; +// hipGraphExecEventWaitNodeSetEvent[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipGraphExecEventWaitNodeSetEvent: + break; +// hipGraphExecExternalSemaphoresSignalNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphExecExternalSemaphoresSignalNodeSetParams: + if (data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.nodeParams) data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.nodeParams__val = *(data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.nodeParams); + break; +// hipGraphExecExternalSemaphoresWaitNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphExecExternalSemaphoresWaitNodeSetParams: + if (data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.nodeParams) data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.nodeParams__val = *(data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.nodeParams); + break; +// hipGraphExecHostNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipHostNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphExecHostNodeSetParams: + if (data->args.hipGraphExecHostNodeSetParams.pNodeParams) data->args.hipGraphExecHostNodeSetParams.pNodeParams__val = *(data->args.hipGraphExecHostNodeSetParams.pNodeParams); + break; +// hipGraphExecKernelNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipKernelNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphExecKernelNodeSetParams: + if (data->args.hipGraphExecKernelNodeSetParams.pNodeParams) data->args.hipGraphExecKernelNodeSetParams.pNodeParams__val = *(data->args.hipGraphExecKernelNodeSetParams.pNodeParams); + break; +// hipGraphExecMemcpyNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('hipMemcpy3DParms*', 'pNodeParams')] + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams: + if (data->args.hipGraphExecMemcpyNodeSetParams.pNodeParams) data->args.hipGraphExecMemcpyNodeSetParams.pNodeParams__val = *(data->args.hipGraphExecMemcpyNodeSetParams.pNodeParams); + break; +// hipGraphExecMemcpyNodeSetParams1D[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams1D: + break; +// hipGraphExecMemcpyNodeSetParamsFromSymbol[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsFromSymbol: + break; +// hipGraphExecMemcpyNodeSetParamsToSymbol[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsToSymbol: + break; +// hipGraphExecMemsetNodeSetParams[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'node'), ('const hipMemsetParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphExecMemsetNodeSetParams: + if (data->args.hipGraphExecMemsetNodeSetParams.pNodeParams) data->args.hipGraphExecMemsetNodeSetParams.pNodeParams__val = *(data->args.hipGraphExecMemsetNodeSetParams.pNodeParams); + break; +// hipGraphExecUpdate[('hipGraphExec_t', 'hGraphExec'), ('hipGraph_t', 'hGraph'), ('hipGraphNode_t*', 'hErrorNode_out'), ('hipGraphExecUpdateResult*', 'updateResult_out')] + case HIP_API_ID_hipGraphExecUpdate: + if (data->args.hipGraphExecUpdate.hErrorNode_out) data->args.hipGraphExecUpdate.hErrorNode_out__val = *(data->args.hipGraphExecUpdate.hErrorNode_out); + if (data->args.hipGraphExecUpdate.updateResult_out) data->args.hipGraphExecUpdate.updateResult_out__val = *(data->args.hipGraphExecUpdate.updateResult_out); + break; +// hipGraphExternalSemaphoresSignalNodeGetParams[('hipGraphNode_t', 'hNode'), ('hipExternalSemaphoreSignalNodeParams*', 'params_out')] + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeGetParams: + if (data->args.hipGraphExternalSemaphoresSignalNodeGetParams.params_out) data->args.hipGraphExternalSemaphoresSignalNodeGetParams.params_out__val = *(data->args.hipGraphExternalSemaphoresSignalNodeGetParams.params_out); + break; +// hipGraphExternalSemaphoresSignalNodeSetParams[('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreSignalNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeSetParams: + if (data->args.hipGraphExternalSemaphoresSignalNodeSetParams.nodeParams) data->args.hipGraphExternalSemaphoresSignalNodeSetParams.nodeParams__val = *(data->args.hipGraphExternalSemaphoresSignalNodeSetParams.nodeParams); + break; +// hipGraphExternalSemaphoresWaitNodeGetParams[('hipGraphNode_t', 'hNode'), ('hipExternalSemaphoreWaitNodeParams*', 'params_out')] + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeGetParams: + if (data->args.hipGraphExternalSemaphoresWaitNodeGetParams.params_out) data->args.hipGraphExternalSemaphoresWaitNodeGetParams.params_out__val = *(data->args.hipGraphExternalSemaphoresWaitNodeGetParams.params_out); + break; +// hipGraphExternalSemaphoresWaitNodeSetParams[('hipGraphNode_t', 'hNode'), ('const hipExternalSemaphoreWaitNodeParams*', 'nodeParams')] + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeSetParams: + if (data->args.hipGraphExternalSemaphoresWaitNodeSetParams.nodeParams) data->args.hipGraphExternalSemaphoresWaitNodeSetParams.nodeParams__val = *(data->args.hipGraphExternalSemaphoresWaitNodeSetParams.nodeParams); + break; +// hipGraphGetEdges[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'from'), ('hipGraphNode_t*', 'to'), ('size_t*', 'numEdges')] + case HIP_API_ID_hipGraphGetEdges: + if (data->args.hipGraphGetEdges.from) data->args.hipGraphGetEdges.from__val = *(data->args.hipGraphGetEdges.from); + if (data->args.hipGraphGetEdges.to) data->args.hipGraphGetEdges.to__val = *(data->args.hipGraphGetEdges.to); + if (data->args.hipGraphGetEdges.numEdges) data->args.hipGraphGetEdges.numEdges__val = *(data->args.hipGraphGetEdges.numEdges); + break; +// hipGraphGetNodes[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'nodes'), ('size_t*', 'numNodes')] + case HIP_API_ID_hipGraphGetNodes: + if (data->args.hipGraphGetNodes.nodes) data->args.hipGraphGetNodes.nodes__val = *(data->args.hipGraphGetNodes.nodes); + if (data->args.hipGraphGetNodes.numNodes) data->args.hipGraphGetNodes.numNodes__val = *(data->args.hipGraphGetNodes.numNodes); + break; +// hipGraphGetRootNodes[('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'pRootNodes'), ('size_t*', 'pNumRootNodes')] + case HIP_API_ID_hipGraphGetRootNodes: + if (data->args.hipGraphGetRootNodes.pRootNodes) data->args.hipGraphGetRootNodes.pRootNodes__val = *(data->args.hipGraphGetRootNodes.pRootNodes); + if (data->args.hipGraphGetRootNodes.pNumRootNodes) data->args.hipGraphGetRootNodes.pNumRootNodes__val = *(data->args.hipGraphGetRootNodes.pNumRootNodes); + break; +// hipGraphHostNodeGetParams[('hipGraphNode_t', 'node'), ('hipHostNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphHostNodeGetParams: + if (data->args.hipGraphHostNodeGetParams.pNodeParams) data->args.hipGraphHostNodeGetParams.pNodeParams__val = *(data->args.hipGraphHostNodeGetParams.pNodeParams); + break; +// hipGraphHostNodeSetParams[('hipGraphNode_t', 'node'), ('const hipHostNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphHostNodeSetParams: + if (data->args.hipGraphHostNodeSetParams.pNodeParams) data->args.hipGraphHostNodeSetParams.pNodeParams__val = *(data->args.hipGraphHostNodeSetParams.pNodeParams); + break; +// hipGraphInstantiate[('hipGraphExec_t*', 'pGraphExec'), ('hipGraph_t', 'graph'), ('hipGraphNode_t*', 'pErrorNode'), ('char*', 'pLogBuffer'), ('size_t', 'bufferSize')] + case HIP_API_ID_hipGraphInstantiate: + if (data->args.hipGraphInstantiate.pGraphExec) data->args.hipGraphInstantiate.pGraphExec__val = *(data->args.hipGraphInstantiate.pGraphExec); + if (data->args.hipGraphInstantiate.pErrorNode) data->args.hipGraphInstantiate.pErrorNode__val = *(data->args.hipGraphInstantiate.pErrorNode); + data->args.hipGraphInstantiate.pLogBuffer = (data->args.hipGraphInstantiate.pLogBuffer) ? strdup(data->args.hipGraphInstantiate.pLogBuffer) : NULL; + break; +// hipGraphInstantiateWithFlags[('hipGraphExec_t*', 'pGraphExec'), ('hipGraph_t', 'graph'), ('unsigned long long', 'flags')] + case HIP_API_ID_hipGraphInstantiateWithFlags: + if (data->args.hipGraphInstantiateWithFlags.pGraphExec) data->args.hipGraphInstantiateWithFlags.pGraphExec__val = *(data->args.hipGraphInstantiateWithFlags.pGraphExec); + break; +// hipGraphKernelNodeCopyAttributes[('hipGraphNode_t', 'hSrc'), ('hipGraphNode_t', 'hDst')] + case HIP_API_ID_hipGraphKernelNodeCopyAttributes: + break; +// hipGraphKernelNodeGetAttribute[('hipGraphNode_t', 'hNode'), ('hipKernelNodeAttrID', 'attr'), ('hipKernelNodeAttrValue*', 'value')] + case HIP_API_ID_hipGraphKernelNodeGetAttribute: + if (data->args.hipGraphKernelNodeGetAttribute.value) data->args.hipGraphKernelNodeGetAttribute.value__val = *(data->args.hipGraphKernelNodeGetAttribute.value); + break; +// hipGraphKernelNodeGetParams[('hipGraphNode_t', 'node'), ('hipKernelNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphKernelNodeGetParams: + if (data->args.hipGraphKernelNodeGetParams.pNodeParams) data->args.hipGraphKernelNodeGetParams.pNodeParams__val = *(data->args.hipGraphKernelNodeGetParams.pNodeParams); + break; +// hipGraphKernelNodeSetAttribute[('hipGraphNode_t', 'hNode'), ('hipKernelNodeAttrID', 'attr'), ('const hipKernelNodeAttrValue*', 'value')] + case HIP_API_ID_hipGraphKernelNodeSetAttribute: + if (data->args.hipGraphKernelNodeSetAttribute.value) data->args.hipGraphKernelNodeSetAttribute.value__val = *(data->args.hipGraphKernelNodeSetAttribute.value); + break; +// hipGraphKernelNodeSetParams[('hipGraphNode_t', 'node'), ('const hipKernelNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphKernelNodeSetParams: + if (data->args.hipGraphKernelNodeSetParams.pNodeParams) data->args.hipGraphKernelNodeSetParams.pNodeParams__val = *(data->args.hipGraphKernelNodeSetParams.pNodeParams); + break; +// hipGraphLaunch[('hipGraphExec_t', 'graphExec'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipGraphLaunch: + break; +// hipGraphMemAllocNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemAllocNodeParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphMemAllocNodeGetParams: + if (data->args.hipGraphMemAllocNodeGetParams.pNodeParams) data->args.hipGraphMemAllocNodeGetParams.pNodeParams__val = *(data->args.hipGraphMemAllocNodeGetParams.pNodeParams); + break; +// hipGraphMemFreeNodeGetParams[('hipGraphNode_t', 'node'), ('void*', 'dev_ptr')] + case HIP_API_ID_hipGraphMemFreeNodeGetParams: + break; +// hipGraphMemcpyNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemcpy3DParms*', 'pNodeParams')] + case HIP_API_ID_hipGraphMemcpyNodeGetParams: + if (data->args.hipGraphMemcpyNodeGetParams.pNodeParams) data->args.hipGraphMemcpyNodeGetParams.pNodeParams__val = *(data->args.hipGraphMemcpyNodeGetParams.pNodeParams); + break; +// hipGraphMemcpyNodeSetParams[('hipGraphNode_t', 'node'), ('const hipMemcpy3DParms*', 'pNodeParams')] + case HIP_API_ID_hipGraphMemcpyNodeSetParams: + if (data->args.hipGraphMemcpyNodeSetParams.pNodeParams) data->args.hipGraphMemcpyNodeSetParams.pNodeParams__val = *(data->args.hipGraphMemcpyNodeSetParams.pNodeParams); + break; +// hipGraphMemcpyNodeSetParams1D[('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphMemcpyNodeSetParams1D: + break; +// hipGraphMemcpyNodeSetParamsFromSymbol[('hipGraphNode_t', 'node'), ('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphMemcpyNodeSetParamsFromSymbol: + break; +// hipGraphMemcpyNodeSetParamsToSymbol[('hipGraphNode_t', 'node'), ('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'count'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipGraphMemcpyNodeSetParamsToSymbol: + break; +// hipGraphMemsetNodeGetParams[('hipGraphNode_t', 'node'), ('hipMemsetParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphMemsetNodeGetParams: + if (data->args.hipGraphMemsetNodeGetParams.pNodeParams) data->args.hipGraphMemsetNodeGetParams.pNodeParams__val = *(data->args.hipGraphMemsetNodeGetParams.pNodeParams); + break; +// hipGraphMemsetNodeSetParams[('hipGraphNode_t', 'node'), ('const hipMemsetParams*', 'pNodeParams')] + case HIP_API_ID_hipGraphMemsetNodeSetParams: + if (data->args.hipGraphMemsetNodeSetParams.pNodeParams) data->args.hipGraphMemsetNodeSetParams.pNodeParams__val = *(data->args.hipGraphMemsetNodeSetParams.pNodeParams); + break; +// hipGraphNodeFindInClone[('hipGraphNode_t*', 'pNode'), ('hipGraphNode_t', 'originalNode'), ('hipGraph_t', 'clonedGraph')] + case HIP_API_ID_hipGraphNodeFindInClone: + if (data->args.hipGraphNodeFindInClone.pNode) data->args.hipGraphNodeFindInClone.pNode__val = *(data->args.hipGraphNodeFindInClone.pNode); + break; +// hipGraphNodeGetDependencies[('hipGraphNode_t', 'node'), ('hipGraphNode_t*', 'pDependencies'), ('size_t*', 'pNumDependencies')] + case HIP_API_ID_hipGraphNodeGetDependencies: + if (data->args.hipGraphNodeGetDependencies.pDependencies) data->args.hipGraphNodeGetDependencies.pDependencies__val = *(data->args.hipGraphNodeGetDependencies.pDependencies); + if (data->args.hipGraphNodeGetDependencies.pNumDependencies) data->args.hipGraphNodeGetDependencies.pNumDependencies__val = *(data->args.hipGraphNodeGetDependencies.pNumDependencies); + break; +// hipGraphNodeGetDependentNodes[('hipGraphNode_t', 'node'), ('hipGraphNode_t*', 'pDependentNodes'), ('size_t*', 'pNumDependentNodes')] + case HIP_API_ID_hipGraphNodeGetDependentNodes: + if (data->args.hipGraphNodeGetDependentNodes.pDependentNodes) data->args.hipGraphNodeGetDependentNodes.pDependentNodes__val = *(data->args.hipGraphNodeGetDependentNodes.pDependentNodes); + if (data->args.hipGraphNodeGetDependentNodes.pNumDependentNodes) data->args.hipGraphNodeGetDependentNodes.pNumDependentNodes__val = *(data->args.hipGraphNodeGetDependentNodes.pNumDependentNodes); + break; +// hipGraphNodeGetEnabled[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('unsigned int*', 'isEnabled')] + case HIP_API_ID_hipGraphNodeGetEnabled: + if (data->args.hipGraphNodeGetEnabled.isEnabled) data->args.hipGraphNodeGetEnabled.isEnabled__val = *(data->args.hipGraphNodeGetEnabled.isEnabled); + break; +// hipGraphNodeGetType[('hipGraphNode_t', 'node'), ('hipGraphNodeType*', 'pType')] + case HIP_API_ID_hipGraphNodeGetType: + if (data->args.hipGraphNodeGetType.pType) data->args.hipGraphNodeGetType.pType__val = *(data->args.hipGraphNodeGetType.pType); + break; +// hipGraphNodeSetEnabled[('hipGraphExec_t', 'hGraphExec'), ('hipGraphNode_t', 'hNode'), ('unsigned int', 'isEnabled')] + case HIP_API_ID_hipGraphNodeSetEnabled: + break; +// hipGraphReleaseUserObject[('hipGraph_t', 'graph'), ('hipUserObject_t', 'object'), ('unsigned int', 'count')] + case HIP_API_ID_hipGraphReleaseUserObject: + break; +// hipGraphRemoveDependencies[('hipGraph_t', 'graph'), ('const hipGraphNode_t*', 'from'), ('const hipGraphNode_t*', 'to'), ('size_t', 'numDependencies')] + case HIP_API_ID_hipGraphRemoveDependencies: + if (data->args.hipGraphRemoveDependencies.from) data->args.hipGraphRemoveDependencies.from__val = *(data->args.hipGraphRemoveDependencies.from); + if (data->args.hipGraphRemoveDependencies.to) data->args.hipGraphRemoveDependencies.to__val = *(data->args.hipGraphRemoveDependencies.to); + break; +// hipGraphRetainUserObject[('hipGraph_t', 'graph'), ('hipUserObject_t', 'object'), ('unsigned int', 'count'), ('unsigned int', 'flags')] + case HIP_API_ID_hipGraphRetainUserObject: + break; +// hipGraphUpload[('hipGraphExec_t', 'graphExec'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipGraphUpload: + break; +// hipGraphicsGLRegisterBuffer[('hipGraphicsResource**', 'resource'), ('GLuint', 'buffer'), ('unsigned int', 'flags')] + case HIP_API_ID_hipGraphicsGLRegisterBuffer: + if (data->args.hipGraphicsGLRegisterBuffer.resource) data->args.hipGraphicsGLRegisterBuffer.resource__val = *(data->args.hipGraphicsGLRegisterBuffer.resource); + break; +// hipGraphicsGLRegisterImage[('hipGraphicsResource**', 'resource'), ('GLuint', 'image'), ('GLenum', 'target'), ('unsigned int', 'flags')] + case HIP_API_ID_hipGraphicsGLRegisterImage: + if (data->args.hipGraphicsGLRegisterImage.resource) data->args.hipGraphicsGLRegisterImage.resource__val = *(data->args.hipGraphicsGLRegisterImage.resource); + break; +// hipGraphicsMapResources[('int', 'count'), ('hipGraphicsResource_t*', 'resources'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipGraphicsMapResources: + if (data->args.hipGraphicsMapResources.resources) data->args.hipGraphicsMapResources.resources__val = *(data->args.hipGraphicsMapResources.resources); + break; +// hipGraphicsResourceGetMappedPointer[('void**', 'devPtr'), ('size_t*', 'size'), ('hipGraphicsResource_t', 'resource')] + case HIP_API_ID_hipGraphicsResourceGetMappedPointer: + if (data->args.hipGraphicsResourceGetMappedPointer.devPtr) data->args.hipGraphicsResourceGetMappedPointer.devPtr__val = *(data->args.hipGraphicsResourceGetMappedPointer.devPtr); + if (data->args.hipGraphicsResourceGetMappedPointer.size) data->args.hipGraphicsResourceGetMappedPointer.size__val = *(data->args.hipGraphicsResourceGetMappedPointer.size); + break; +// hipGraphicsSubResourceGetMappedArray[('hipArray_t*', 'array'), ('hipGraphicsResource_t', 'resource'), ('unsigned int', 'arrayIndex'), ('unsigned int', 'mipLevel')] + case HIP_API_ID_hipGraphicsSubResourceGetMappedArray: + if (data->args.hipGraphicsSubResourceGetMappedArray.array) data->args.hipGraphicsSubResourceGetMappedArray.array__val = *(data->args.hipGraphicsSubResourceGetMappedArray.array); + break; +// hipGraphicsUnmapResources[('int', 'count'), ('hipGraphicsResource_t*', 'resources'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipGraphicsUnmapResources: + if (data->args.hipGraphicsUnmapResources.resources) data->args.hipGraphicsUnmapResources.resources__val = *(data->args.hipGraphicsUnmapResources.resources); + break; +// hipGraphicsUnregisterResource[('hipGraphicsResource_t', 'resource')] + case HIP_API_ID_hipGraphicsUnregisterResource: + break; +// hipHccModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'globalWorkSizeX'), ('unsigned int', 'globalWorkSizeY'), ('unsigned int', 'globalWorkSizeZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'hStream'), ('void**', 'kernelParams'), ('void**', 'extra'), ('hipEvent_t', 'startEvent'), ('hipEvent_t', 'stopEvent')] + case HIP_API_ID_hipHccModuleLaunchKernel: + if (data->args.hipHccModuleLaunchKernel.kernelParams) data->args.hipHccModuleLaunchKernel.kernelParams__val = *(data->args.hipHccModuleLaunchKernel.kernelParams); + if (data->args.hipHccModuleLaunchKernel.extra) data->args.hipHccModuleLaunchKernel.extra__val = *(data->args.hipHccModuleLaunchKernel.extra); + break; +// hipHostAlloc[('void**', 'ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] + case HIP_API_ID_hipHostAlloc: + if (data->args.hipHostAlloc.ptr) data->args.hipHostAlloc.ptr__val = *(data->args.hipHostAlloc.ptr); + break; +// hipHostFree[('void*', 'ptr')] + case HIP_API_ID_hipHostFree: + break; +// hipHostGetDevicePointer[('void**', 'devPtr'), ('void*', 'hstPtr'), ('unsigned int', 'flags')] + case HIP_API_ID_hipHostGetDevicePointer: + if (data->args.hipHostGetDevicePointer.devPtr) data->args.hipHostGetDevicePointer.devPtr__val = *(data->args.hipHostGetDevicePointer.devPtr); + break; +// hipHostGetFlags[('unsigned int*', 'flagsPtr'), ('void*', 'hostPtr')] + case HIP_API_ID_hipHostGetFlags: + if (data->args.hipHostGetFlags.flagsPtr) data->args.hipHostGetFlags.flagsPtr__val = *(data->args.hipHostGetFlags.flagsPtr); + break; +// hipHostMalloc[('void**', 'ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] + case HIP_API_ID_hipHostMalloc: + if (data->args.hipHostMalloc.ptr) data->args.hipHostMalloc.ptr__val = *(data->args.hipHostMalloc.ptr); + break; +// hipHostRegister[('void*', 'hostPtr'), ('size_t', 'sizeBytes'), ('unsigned int', 'flags')] + case HIP_API_ID_hipHostRegister: + break; +// hipHostUnregister[('void*', 'hostPtr')] + case HIP_API_ID_hipHostUnregister: + break; +// hipImportExternalMemory[('hipExternalMemory_t*', 'extMem_out'), ('const hipExternalMemoryHandleDesc*', 'memHandleDesc')] + case HIP_API_ID_hipImportExternalMemory: + if (data->args.hipImportExternalMemory.extMem_out) data->args.hipImportExternalMemory.extMem_out__val = *(data->args.hipImportExternalMemory.extMem_out); + if (data->args.hipImportExternalMemory.memHandleDesc) data->args.hipImportExternalMemory.memHandleDesc__val = *(data->args.hipImportExternalMemory.memHandleDesc); + break; +// hipImportExternalSemaphore[('hipExternalSemaphore_t*', 'extSem_out'), ('const hipExternalSemaphoreHandleDesc*', 'semHandleDesc')] + case HIP_API_ID_hipImportExternalSemaphore: + if (data->args.hipImportExternalSemaphore.extSem_out) data->args.hipImportExternalSemaphore.extSem_out__val = *(data->args.hipImportExternalSemaphore.extSem_out); + if (data->args.hipImportExternalSemaphore.semHandleDesc) data->args.hipImportExternalSemaphore.semHandleDesc__val = *(data->args.hipImportExternalSemaphore.semHandleDesc); + break; +// hipInit[('unsigned int', 'flags')] + case HIP_API_ID_hipInit: + break; +// hipIpcCloseMemHandle[('void*', 'devPtr')] + case HIP_API_ID_hipIpcCloseMemHandle: + break; +// hipIpcGetEventHandle[('hipIpcEventHandle_t*', 'handle'), ('hipEvent_t', 'event')] + case HIP_API_ID_hipIpcGetEventHandle: + if (data->args.hipIpcGetEventHandle.handle) data->args.hipIpcGetEventHandle.handle__val = *(data->args.hipIpcGetEventHandle.handle); + break; +// hipIpcGetMemHandle[('hipIpcMemHandle_t*', 'handle'), ('void*', 'devPtr')] + case HIP_API_ID_hipIpcGetMemHandle: + if (data->args.hipIpcGetMemHandle.handle) data->args.hipIpcGetMemHandle.handle__val = *(data->args.hipIpcGetMemHandle.handle); + break; +// hipIpcOpenEventHandle[('hipEvent_t*', 'event'), ('hipIpcEventHandle_t', 'handle')] + case HIP_API_ID_hipIpcOpenEventHandle: + if (data->args.hipIpcOpenEventHandle.event) data->args.hipIpcOpenEventHandle.event__val = *(data->args.hipIpcOpenEventHandle.event); + break; +// hipIpcOpenMemHandle[('void**', 'devPtr'), ('hipIpcMemHandle_t', 'handle'), ('unsigned int', 'flags')] + case HIP_API_ID_hipIpcOpenMemHandle: + if (data->args.hipIpcOpenMemHandle.devPtr) data->args.hipIpcOpenMemHandle.devPtr__val = *(data->args.hipIpcOpenMemHandle.devPtr); + break; +// hipLaunchByPtr[('const void*', 'hostFunction')] + case HIP_API_ID_hipLaunchByPtr: + break; +// hipLaunchCooperativeKernel[('const void*', 'f'), ('dim3', 'gridDim'), ('dim3', 'blockDimX'), ('void**', 'kernelParams'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipLaunchCooperativeKernel: + if (data->args.hipLaunchCooperativeKernel.kernelParams) data->args.hipLaunchCooperativeKernel.kernelParams__val = *(data->args.hipLaunchCooperativeKernel.kernelParams); + break; +// hipLaunchCooperativeKernelMultiDevice[('hipLaunchParams*', 'launchParamsList'), ('int', 'numDevices'), ('unsigned int', 'flags')] + case HIP_API_ID_hipLaunchCooperativeKernelMultiDevice: + if (data->args.hipLaunchCooperativeKernelMultiDevice.launchParamsList) data->args.hipLaunchCooperativeKernelMultiDevice.launchParamsList__val = *(data->args.hipLaunchCooperativeKernelMultiDevice.launchParamsList); + break; +// hipLaunchHostFunc[('hipStream_t', 'stream'), ('hipHostFn_t', 'fn'), ('void*', 'userData')] + case HIP_API_ID_hipLaunchHostFunc: + break; +// hipLaunchKernel[('const void*', 'function_address'), ('dim3', 'numBlocks'), ('dim3', 'dimBlocks'), ('void**', 'args'), ('size_t', 'sharedMemBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipLaunchKernel: + if (data->args.hipLaunchKernel.args) data->args.hipLaunchKernel.args__val = *(data->args.hipLaunchKernel.args); + break; +// hipMalloc[('void**', 'ptr'), ('size_t', 'size')] + case HIP_API_ID_hipMalloc: + if (data->args.hipMalloc.ptr) data->args.hipMalloc.ptr__val = *(data->args.hipMalloc.ptr); + break; +// hipMalloc3D[('hipPitchedPtr*', 'pitchedDevPtr'), ('hipExtent', 'extent')] + case HIP_API_ID_hipMalloc3D: + if (data->args.hipMalloc3D.pitchedDevPtr) data->args.hipMalloc3D.pitchedDevPtr__val = *(data->args.hipMalloc3D.pitchedDevPtr); + break; +// hipMalloc3DArray[('hipArray_t*', 'array'), ('const hipChannelFormatDesc*', 'desc'), ('hipExtent', 'extent'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMalloc3DArray: + if (data->args.hipMalloc3DArray.array) data->args.hipMalloc3DArray.array__val = *(data->args.hipMalloc3DArray.array); + if (data->args.hipMalloc3DArray.desc) data->args.hipMalloc3DArray.desc__val = *(data->args.hipMalloc3DArray.desc); + break; +// hipMallocArray[('hipArray_t*', 'array'), ('const hipChannelFormatDesc*', 'desc'), ('size_t', 'width'), ('size_t', 'height'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMallocArray: + if (data->args.hipMallocArray.array) data->args.hipMallocArray.array__val = *(data->args.hipMallocArray.array); + if (data->args.hipMallocArray.desc) data->args.hipMallocArray.desc__val = *(data->args.hipMallocArray.desc); + break; +// hipMallocAsync[('void**', 'dev_ptr'), ('size_t', 'size'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMallocAsync: + if (data->args.hipMallocAsync.dev_ptr) data->args.hipMallocAsync.dev_ptr__val = *(data->args.hipMallocAsync.dev_ptr); + break; +// hipMallocFromPoolAsync[('void**', 'dev_ptr'), ('size_t', 'size'), ('hipMemPool_t', 'mem_pool'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMallocFromPoolAsync: + if (data->args.hipMallocFromPoolAsync.dev_ptr) data->args.hipMallocFromPoolAsync.dev_ptr__val = *(data->args.hipMallocFromPoolAsync.dev_ptr); + break; +// hipMallocHost[('void**', 'ptr'), ('size_t', 'size')] + case HIP_API_ID_hipMallocHost: + if (data->args.hipMallocHost.ptr) data->args.hipMallocHost.ptr__val = *(data->args.hipMallocHost.ptr); + break; +// hipMallocManaged[('void**', 'dev_ptr'), ('size_t', 'size'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMallocManaged: + if (data->args.hipMallocManaged.dev_ptr) data->args.hipMallocManaged.dev_ptr__val = *(data->args.hipMallocManaged.dev_ptr); + break; +// hipMallocMipmappedArray[('hipMipmappedArray_t*', 'mipmappedArray'), ('const hipChannelFormatDesc*', 'desc'), ('hipExtent', 'extent'), ('unsigned int', 'numLevels'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMallocMipmappedArray: + if (data->args.hipMallocMipmappedArray.mipmappedArray) data->args.hipMallocMipmappedArray.mipmappedArray__val = *(data->args.hipMallocMipmappedArray.mipmappedArray); + if (data->args.hipMallocMipmappedArray.desc) data->args.hipMallocMipmappedArray.desc__val = *(data->args.hipMallocMipmappedArray.desc); + break; +// hipMallocPitch[('void**', 'ptr'), ('size_t*', 'pitch'), ('size_t', 'width'), ('size_t', 'height')] + case HIP_API_ID_hipMallocPitch: + if (data->args.hipMallocPitch.ptr) data->args.hipMallocPitch.ptr__val = *(data->args.hipMallocPitch.ptr); + if (data->args.hipMallocPitch.pitch) data->args.hipMallocPitch.pitch__val = *(data->args.hipMallocPitch.pitch); + break; +// hipMemAddressFree[('void*', 'devPtr'), ('size_t', 'size')] + case HIP_API_ID_hipMemAddressFree: + break; +// hipMemAddressReserve[('void**', 'ptr'), ('size_t', 'size'), ('size_t', 'alignment'), ('void*', 'addr'), ('unsigned long long', 'flags')] + case HIP_API_ID_hipMemAddressReserve: + if (data->args.hipMemAddressReserve.ptr) data->args.hipMemAddressReserve.ptr__val = *(data->args.hipMemAddressReserve.ptr); + break; +// hipMemAdvise[('const void*', 'dev_ptr'), ('size_t', 'count'), ('hipMemoryAdvise', 'advice'), ('int', 'device')] + case HIP_API_ID_hipMemAdvise: + break; +// hipMemAllocHost[('void**', 'ptr'), ('size_t', 'size')] + case HIP_API_ID_hipMemAllocHost: + if (data->args.hipMemAllocHost.ptr) data->args.hipMemAllocHost.ptr__val = *(data->args.hipMemAllocHost.ptr); + break; +// hipMemAllocPitch[('hipDeviceptr_t*', 'dptr'), ('size_t*', 'pitch'), ('size_t', 'widthInBytes'), ('size_t', 'height'), ('unsigned int', 'elementSizeBytes')] + case HIP_API_ID_hipMemAllocPitch: + if (data->args.hipMemAllocPitch.dptr) data->args.hipMemAllocPitch.dptr__val = *(data->args.hipMemAllocPitch.dptr); + if (data->args.hipMemAllocPitch.pitch) data->args.hipMemAllocPitch.pitch__val = *(data->args.hipMemAllocPitch.pitch); + break; +// hipMemCreate[('hipMemGenericAllocationHandle_t*', 'handle'), ('size_t', 'size'), ('const hipMemAllocationProp*', 'prop'), ('unsigned long long', 'flags')] + case HIP_API_ID_hipMemCreate: + if (data->args.hipMemCreate.handle) data->args.hipMemCreate.handle__val = *(data->args.hipMemCreate.handle); + if (data->args.hipMemCreate.prop) data->args.hipMemCreate.prop__val = *(data->args.hipMemCreate.prop); + break; +// hipMemExportToShareableHandle[('void*', 'shareableHandle'), ('hipMemGenericAllocationHandle_t', 'handle'), ('hipMemAllocationHandleType', 'handleType'), ('unsigned long long', 'flags')] + case HIP_API_ID_hipMemExportToShareableHandle: + break; +// hipMemGetAccess[('unsigned long long*', 'flags'), ('const hipMemLocation*', 'location'), ('void*', 'ptr')] + case HIP_API_ID_hipMemGetAccess: + if (data->args.hipMemGetAccess.flags) data->args.hipMemGetAccess.flags__val = *(data->args.hipMemGetAccess.flags); + if (data->args.hipMemGetAccess.location) data->args.hipMemGetAccess.location__val = *(data->args.hipMemGetAccess.location); + break; +// hipMemGetAddressRange[('hipDeviceptr_t*', 'pbase'), ('size_t*', 'psize'), ('hipDeviceptr_t', 'dptr')] + case HIP_API_ID_hipMemGetAddressRange: + if (data->args.hipMemGetAddressRange.pbase) data->args.hipMemGetAddressRange.pbase__val = *(data->args.hipMemGetAddressRange.pbase); + if (data->args.hipMemGetAddressRange.psize) data->args.hipMemGetAddressRange.psize__val = *(data->args.hipMemGetAddressRange.psize); + break; +// hipMemGetAllocationGranularity[('size_t*', 'granularity'), ('const hipMemAllocationProp*', 'prop'), ('hipMemAllocationGranularity_flags', 'option')] + case HIP_API_ID_hipMemGetAllocationGranularity: + if (data->args.hipMemGetAllocationGranularity.granularity) data->args.hipMemGetAllocationGranularity.granularity__val = *(data->args.hipMemGetAllocationGranularity.granularity); + if (data->args.hipMemGetAllocationGranularity.prop) data->args.hipMemGetAllocationGranularity.prop__val = *(data->args.hipMemGetAllocationGranularity.prop); + break; +// hipMemGetAllocationPropertiesFromHandle[('hipMemAllocationProp*', 'prop'), ('hipMemGenericAllocationHandle_t', 'handle')] + case HIP_API_ID_hipMemGetAllocationPropertiesFromHandle: + if (data->args.hipMemGetAllocationPropertiesFromHandle.prop) data->args.hipMemGetAllocationPropertiesFromHandle.prop__val = *(data->args.hipMemGetAllocationPropertiesFromHandle.prop); + break; +// hipMemGetInfo[('size_t*', 'free'), ('size_t*', 'total')] + case HIP_API_ID_hipMemGetInfo: + if (data->args.hipMemGetInfo.free) data->args.hipMemGetInfo.free__val = *(data->args.hipMemGetInfo.free); + if (data->args.hipMemGetInfo.total) data->args.hipMemGetInfo.total__val = *(data->args.hipMemGetInfo.total); + break; +// hipMemImportFromShareableHandle[('hipMemGenericAllocationHandle_t*', 'handle'), ('void*', 'osHandle'), ('hipMemAllocationHandleType', 'shHandleType')] + case HIP_API_ID_hipMemImportFromShareableHandle: + if (data->args.hipMemImportFromShareableHandle.handle) data->args.hipMemImportFromShareableHandle.handle__val = *(data->args.hipMemImportFromShareableHandle.handle); + break; +// hipMemMap[('void*', 'ptr'), ('size_t', 'size'), ('size_t', 'offset'), ('hipMemGenericAllocationHandle_t', 'handle'), ('unsigned long long', 'flags')] + case HIP_API_ID_hipMemMap: + break; +// hipMemMapArrayAsync[('hipArrayMapInfo*', 'mapInfoList'), ('unsigned int', 'count'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemMapArrayAsync: + if (data->args.hipMemMapArrayAsync.mapInfoList) data->args.hipMemMapArrayAsync.mapInfoList__val = *(data->args.hipMemMapArrayAsync.mapInfoList); + break; +// hipMemPoolCreate[('hipMemPool_t*', 'mem_pool'), ('const hipMemPoolProps*', 'pool_props')] + case HIP_API_ID_hipMemPoolCreate: + if (data->args.hipMemPoolCreate.mem_pool) data->args.hipMemPoolCreate.mem_pool__val = *(data->args.hipMemPoolCreate.mem_pool); + if (data->args.hipMemPoolCreate.pool_props) data->args.hipMemPoolCreate.pool_props__val = *(data->args.hipMemPoolCreate.pool_props); + break; +// hipMemPoolDestroy[('hipMemPool_t', 'mem_pool')] + case HIP_API_ID_hipMemPoolDestroy: + break; +// hipMemPoolExportPointer[('hipMemPoolPtrExportData*', 'export_data'), ('void*', 'dev_ptr')] + case HIP_API_ID_hipMemPoolExportPointer: + if (data->args.hipMemPoolExportPointer.export_data) data->args.hipMemPoolExportPointer.export_data__val = *(data->args.hipMemPoolExportPointer.export_data); + break; +// hipMemPoolExportToShareableHandle[('void*', 'shared_handle'), ('hipMemPool_t', 'mem_pool'), ('hipMemAllocationHandleType', 'handle_type'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMemPoolExportToShareableHandle: + break; +// hipMemPoolGetAccess[('hipMemAccessFlags*', 'flags'), ('hipMemPool_t', 'mem_pool'), ('hipMemLocation*', 'location')] + case HIP_API_ID_hipMemPoolGetAccess: + if (data->args.hipMemPoolGetAccess.flags) data->args.hipMemPoolGetAccess.flags__val = *(data->args.hipMemPoolGetAccess.flags); + if (data->args.hipMemPoolGetAccess.location) data->args.hipMemPoolGetAccess.location__val = *(data->args.hipMemPoolGetAccess.location); + break; +// hipMemPoolGetAttribute[('hipMemPool_t', 'mem_pool'), ('hipMemPoolAttr', 'attr'), ('void*', 'value')] + case HIP_API_ID_hipMemPoolGetAttribute: + break; +// hipMemPoolImportFromShareableHandle[('hipMemPool_t*', 'mem_pool'), ('void*', 'shared_handle'), ('hipMemAllocationHandleType', 'handle_type'), ('unsigned int', 'flags')] + case HIP_API_ID_hipMemPoolImportFromShareableHandle: + if (data->args.hipMemPoolImportFromShareableHandle.mem_pool) data->args.hipMemPoolImportFromShareableHandle.mem_pool__val = *(data->args.hipMemPoolImportFromShareableHandle.mem_pool); + break; +// hipMemPoolImportPointer[('void**', 'dev_ptr'), ('hipMemPool_t', 'mem_pool'), ('hipMemPoolPtrExportData*', 'export_data')] + case HIP_API_ID_hipMemPoolImportPointer: + if (data->args.hipMemPoolImportPointer.dev_ptr) data->args.hipMemPoolImportPointer.dev_ptr__val = *(data->args.hipMemPoolImportPointer.dev_ptr); + if (data->args.hipMemPoolImportPointer.export_data) data->args.hipMemPoolImportPointer.export_data__val = *(data->args.hipMemPoolImportPointer.export_data); + break; +// hipMemPoolSetAccess[('hipMemPool_t', 'mem_pool'), ('const hipMemAccessDesc*', 'desc_list'), ('size_t', 'count')] + case HIP_API_ID_hipMemPoolSetAccess: + if (data->args.hipMemPoolSetAccess.desc_list) data->args.hipMemPoolSetAccess.desc_list__val = *(data->args.hipMemPoolSetAccess.desc_list); + break; +// hipMemPoolSetAttribute[('hipMemPool_t', 'mem_pool'), ('hipMemPoolAttr', 'attr'), ('void*', 'value')] + case HIP_API_ID_hipMemPoolSetAttribute: + break; +// hipMemPoolTrimTo[('hipMemPool_t', 'mem_pool'), ('size_t', 'min_bytes_to_hold')] + case HIP_API_ID_hipMemPoolTrimTo: + break; +// hipMemPrefetchAsync[('const void*', 'dev_ptr'), ('size_t', 'count'), ('int', 'device'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemPrefetchAsync: + break; +// hipMemPtrGetInfo[('void*', 'ptr'), ('size_t*', 'size')] + case HIP_API_ID_hipMemPtrGetInfo: + if (data->args.hipMemPtrGetInfo.size) data->args.hipMemPtrGetInfo.size__val = *(data->args.hipMemPtrGetInfo.size); + break; +// hipMemRangeGetAttribute[('void*', 'data'), ('size_t', 'data_size'), ('hipMemRangeAttribute', 'attribute'), ('const void*', 'dev_ptr'), ('size_t', 'count')] + case HIP_API_ID_hipMemRangeGetAttribute: + break; +// hipMemRangeGetAttributes[('void**', 'data'), ('size_t*', 'data_sizes'), ('hipMemRangeAttribute*', 'attributes'), ('size_t', 'num_attributes'), ('const void*', 'dev_ptr'), ('size_t', 'count')] + case HIP_API_ID_hipMemRangeGetAttributes: + if (data->args.hipMemRangeGetAttributes.data) data->args.hipMemRangeGetAttributes.data__val = *(data->args.hipMemRangeGetAttributes.data); + if (data->args.hipMemRangeGetAttributes.data_sizes) data->args.hipMemRangeGetAttributes.data_sizes__val = *(data->args.hipMemRangeGetAttributes.data_sizes); + if (data->args.hipMemRangeGetAttributes.attributes) data->args.hipMemRangeGetAttributes.attributes__val = *(data->args.hipMemRangeGetAttributes.attributes); + break; +// hipMemRelease[('hipMemGenericAllocationHandle_t', 'handle')] + case HIP_API_ID_hipMemRelease: + break; +// hipMemRetainAllocationHandle[('hipMemGenericAllocationHandle_t*', 'handle'), ('void*', 'addr')] + case HIP_API_ID_hipMemRetainAllocationHandle: + if (data->args.hipMemRetainAllocationHandle.handle) data->args.hipMemRetainAllocationHandle.handle__val = *(data->args.hipMemRetainAllocationHandle.handle); + break; +// hipMemSetAccess[('void*', 'ptr'), ('size_t', 'size'), ('const hipMemAccessDesc*', 'desc'), ('size_t', 'count')] + case HIP_API_ID_hipMemSetAccess: + if (data->args.hipMemSetAccess.desc) data->args.hipMemSetAccess.desc__val = *(data->args.hipMemSetAccess.desc); + break; +// hipMemUnmap[('void*', 'ptr'), ('size_t', 'size')] + case HIP_API_ID_hipMemUnmap: + break; +// hipMemcpy[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpy: + break; +// hipMemcpy2D[('void*', 'dst'), ('size_t', 'dpitch'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpy2D: + break; +// hipMemcpy2DAsync[('void*', 'dst'), ('size_t', 'dpitch'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpy2DAsync: + break; +// hipMemcpy2DFromArray[('void*', 'dst'), ('size_t', 'dpitch'), ('hipArray_const_t', 'src'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpy2DFromArray: + break; +// hipMemcpy2DFromArrayAsync[('void*', 'dst'), ('size_t', 'dpitch'), ('hipArray_const_t', 'src'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpy2DFromArrayAsync: + break; +// hipMemcpy2DToArray[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpy2DToArray: + break; +// hipMemcpy2DToArrayAsync[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'spitch'), ('size_t', 'width'), ('size_t', 'height'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpy2DToArrayAsync: + break; +// hipMemcpy3D[('const hipMemcpy3DParms*', 'p')] + case HIP_API_ID_hipMemcpy3D: + if (data->args.hipMemcpy3D.p) data->args.hipMemcpy3D.p__val = *(data->args.hipMemcpy3D.p); + break; +// hipMemcpy3DAsync[('const hipMemcpy3DParms*', 'p'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpy3DAsync: + if (data->args.hipMemcpy3DAsync.p) data->args.hipMemcpy3DAsync.p__val = *(data->args.hipMemcpy3DAsync.p); + break; +// hipMemcpyAsync[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyAsync: + break; +// hipMemcpyAtoH[('void*', 'dst'), ('hipArray_t', 'srcArray'), ('size_t', 'srcOffset'), ('size_t', 'count')] + case HIP_API_ID_hipMemcpyAtoH: + break; +// hipMemcpyDtoD[('hipDeviceptr_t', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes')] + case HIP_API_ID_hipMemcpyDtoD: + break; +// hipMemcpyDtoDAsync[('hipDeviceptr_t', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyDtoDAsync: + break; +// hipMemcpyDtoH[('void*', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes')] + case HIP_API_ID_hipMemcpyDtoH: + break; +// hipMemcpyDtoHAsync[('void*', 'dst'), ('hipDeviceptr_t', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyDtoHAsync: + break; +// hipMemcpyFromArray[('void*', 'dst'), ('hipArray_const_t', 'srcArray'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpyFromArray: + break; +// hipMemcpyFromSymbol[('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpyFromSymbol: + break; +// hipMemcpyFromSymbolAsync[('void*', 'dst'), ('const void*', 'symbol'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyFromSymbolAsync: + break; +// hipMemcpyHtoA[('hipArray_t', 'dstArray'), ('size_t', 'dstOffset'), ('const void*', 'srcHost'), ('size_t', 'count')] + case HIP_API_ID_hipMemcpyHtoA: + break; +// hipMemcpyHtoD[('hipDeviceptr_t', 'dst'), ('void*', 'src'), ('size_t', 'sizeBytes')] + case HIP_API_ID_hipMemcpyHtoD: + break; +// hipMemcpyHtoDAsync[('hipDeviceptr_t', 'dst'), ('void*', 'src'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyHtoDAsync: + break; +// hipMemcpyParam2D[('const hip_Memcpy2D*', 'pCopy')] + case HIP_API_ID_hipMemcpyParam2D: + if (data->args.hipMemcpyParam2D.pCopy) data->args.hipMemcpyParam2D.pCopy__val = *(data->args.hipMemcpyParam2D.pCopy); + break; +// hipMemcpyParam2DAsync[('const hip_Memcpy2D*', 'pCopy'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyParam2DAsync: + if (data->args.hipMemcpyParam2DAsync.pCopy) data->args.hipMemcpyParam2DAsync.pCopy__val = *(data->args.hipMemcpyParam2DAsync.pCopy); + break; +// hipMemcpyPeer[('void*', 'dst'), ('int', 'dstDeviceId'), ('const void*', 'src'), ('int', 'srcDeviceId'), ('size_t', 'sizeBytes')] + case HIP_API_ID_hipMemcpyPeer: + break; +// hipMemcpyPeerAsync[('void*', 'dst'), ('int', 'dstDeviceId'), ('const void*', 'src'), ('int', 'srcDevice'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyPeerAsync: + break; +// hipMemcpyToArray[('hipArray_t', 'dst'), ('size_t', 'wOffset'), ('size_t', 'hOffset'), ('const void*', 'src'), ('size_t', 'count'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpyToArray: + break; +// hipMemcpyToSymbol[('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind')] + case HIP_API_ID_hipMemcpyToSymbol: + break; +// hipMemcpyToSymbolAsync[('const void*', 'symbol'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('size_t', 'offset'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyToSymbolAsync: + break; +// hipMemcpyWithStream[('void*', 'dst'), ('const void*', 'src'), ('size_t', 'sizeBytes'), ('hipMemcpyKind', 'kind'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemcpyWithStream: + break; +// hipMemset[('void*', 'dst'), ('int', 'value'), ('size_t', 'sizeBytes')] + case HIP_API_ID_hipMemset: + break; +// hipMemset2D[('void*', 'dst'), ('size_t', 'pitch'), ('int', 'value'), ('size_t', 'width'), ('size_t', 'height')] + case HIP_API_ID_hipMemset2D: + break; +// hipMemset2DAsync[('void*', 'dst'), ('size_t', 'pitch'), ('int', 'value'), ('size_t', 'width'), ('size_t', 'height'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemset2DAsync: + break; +// hipMemset3D[('hipPitchedPtr', 'pitchedDevPtr'), ('int', 'value'), ('hipExtent', 'extent')] + case HIP_API_ID_hipMemset3D: + break; +// hipMemset3DAsync[('hipPitchedPtr', 'pitchedDevPtr'), ('int', 'value'), ('hipExtent', 'extent'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemset3DAsync: + break; +// hipMemsetAsync[('void*', 'dst'), ('int', 'value'), ('size_t', 'sizeBytes'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemsetAsync: + break; +// hipMemsetD16[('hipDeviceptr_t', 'dest'), ('unsigned short', 'value'), ('size_t', 'count')] + case HIP_API_ID_hipMemsetD16: + break; +// hipMemsetD16Async[('hipDeviceptr_t', 'dest'), ('unsigned short', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemsetD16Async: + break; +// hipMemsetD32[('hipDeviceptr_t', 'dest'), ('int', 'value'), ('size_t', 'count')] + case HIP_API_ID_hipMemsetD32: + break; +// hipMemsetD32Async[('hipDeviceptr_t', 'dst'), ('int', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemsetD32Async: + break; +// hipMemsetD8[('hipDeviceptr_t', 'dest'), ('unsigned char', 'value'), ('size_t', 'count')] + case HIP_API_ID_hipMemsetD8: + break; +// hipMemsetD8Async[('hipDeviceptr_t', 'dest'), ('unsigned char', 'value'), ('size_t', 'count'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipMemsetD8Async: + break; +// hipMipmappedArrayCreate[('hipMipmappedArray_t*', 'pHandle'), ('HIP_ARRAY3D_DESCRIPTOR*', 'pMipmappedArrayDesc'), ('unsigned int', 'numMipmapLevels')] + case HIP_API_ID_hipMipmappedArrayCreate: + if (data->args.hipMipmappedArrayCreate.pHandle) data->args.hipMipmappedArrayCreate.pHandle__val = *(data->args.hipMipmappedArrayCreate.pHandle); + if (data->args.hipMipmappedArrayCreate.pMipmappedArrayDesc) data->args.hipMipmappedArrayCreate.pMipmappedArrayDesc__val = *(data->args.hipMipmappedArrayCreate.pMipmappedArrayDesc); + break; +// hipMipmappedArrayDestroy[('hipMipmappedArray_t', 'hMipmappedArray')] + case HIP_API_ID_hipMipmappedArrayDestroy: + break; +// hipMipmappedArrayGetLevel[('hipArray_t*', 'pLevelArray'), ('hipMipmappedArray_t', 'hMipMappedArray'), ('unsigned int', 'level')] + case HIP_API_ID_hipMipmappedArrayGetLevel: + if (data->args.hipMipmappedArrayGetLevel.pLevelArray) data->args.hipMipmappedArrayGetLevel.pLevelArray__val = *(data->args.hipMipmappedArrayGetLevel.pLevelArray); + break; +// hipModuleGetFunction[('hipFunction_t*', 'function'), ('hipModule_t', 'module'), ('const char*', 'kname')] + case HIP_API_ID_hipModuleGetFunction: + if (data->args.hipModuleGetFunction.function) data->args.hipModuleGetFunction.function__val = *(data->args.hipModuleGetFunction.function); + if (data->args.hipModuleGetFunction.kname) data->args.hipModuleGetFunction.kname__val = *(data->args.hipModuleGetFunction.kname); + break; +// hipModuleGetGlobal[('hipDeviceptr_t*', 'dptr'), ('size_t*', 'bytes'), ('hipModule_t', 'hmod'), ('const char*', 'name')] + case HIP_API_ID_hipModuleGetGlobal: + if (data->args.hipModuleGetGlobal.dptr) data->args.hipModuleGetGlobal.dptr__val = *(data->args.hipModuleGetGlobal.dptr); + if (data->args.hipModuleGetGlobal.bytes) data->args.hipModuleGetGlobal.bytes__val = *(data->args.hipModuleGetGlobal.bytes); + if (data->args.hipModuleGetGlobal.name) data->args.hipModuleGetGlobal.name__val = *(data->args.hipModuleGetGlobal.name); + break; +// hipModuleGetTexRef[('textureReference**', 'texRef'), ('hipModule_t', 'hmod'), ('const char*', 'name')] + case HIP_API_ID_hipModuleGetTexRef: + if (data->args.hipModuleGetTexRef.texRef) data->args.hipModuleGetTexRef.texRef__val = *(data->args.hipModuleGetTexRef.texRef); + if (data->args.hipModuleGetTexRef.name) data->args.hipModuleGetTexRef.name__val = *(data->args.hipModuleGetTexRef.name); + break; +// hipModuleLaunchCooperativeKernel[('hipFunction_t', 'f'), ('unsigned int', 'gridDimX'), ('unsigned int', 'gridDimY'), ('unsigned int', 'gridDimZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('void**', 'kernelParams')] + case HIP_API_ID_hipModuleLaunchCooperativeKernel: + if (data->args.hipModuleLaunchCooperativeKernel.kernelParams) data->args.hipModuleLaunchCooperativeKernel.kernelParams__val = *(data->args.hipModuleLaunchCooperativeKernel.kernelParams); + break; +// hipModuleLaunchCooperativeKernelMultiDevice[('hipFunctionLaunchParams*', 'launchParamsList'), ('unsigned int', 'numDevices'), ('unsigned int', 'flags')] + case HIP_API_ID_hipModuleLaunchCooperativeKernelMultiDevice: + if (data->args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList) data->args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList__val = *(data->args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList); + break; +// hipModuleLaunchKernel[('hipFunction_t', 'f'), ('unsigned int', 'gridDimX'), ('unsigned int', 'gridDimY'), ('unsigned int', 'gridDimZ'), ('unsigned int', 'blockDimX'), ('unsigned int', 'blockDimY'), ('unsigned int', 'blockDimZ'), ('unsigned int', 'sharedMemBytes'), ('hipStream_t', 'stream'), ('void**', 'kernelParams'), ('void**', 'extra')] + case HIP_API_ID_hipModuleLaunchKernel: + if (data->args.hipModuleLaunchKernel.kernelParams) data->args.hipModuleLaunchKernel.kernelParams__val = *(data->args.hipModuleLaunchKernel.kernelParams); + if (data->args.hipModuleLaunchKernel.extra) data->args.hipModuleLaunchKernel.extra__val = *(data->args.hipModuleLaunchKernel.extra); + break; +// hipModuleLoad[('hipModule_t*', 'module'), ('const char*', 'fname')] + case HIP_API_ID_hipModuleLoad: + if (data->args.hipModuleLoad.module) data->args.hipModuleLoad.module__val = *(data->args.hipModuleLoad.module); + if (data->args.hipModuleLoad.fname) data->args.hipModuleLoad.fname__val = *(data->args.hipModuleLoad.fname); + break; +// hipModuleLoadData[('hipModule_t*', 'module'), ('const void*', 'image')] + case HIP_API_ID_hipModuleLoadData: + if (data->args.hipModuleLoadData.module) data->args.hipModuleLoadData.module__val = *(data->args.hipModuleLoadData.module); + break; +// hipModuleLoadDataEx[('hipModule_t*', 'module'), ('const void*', 'image'), ('unsigned int', 'numOptions'), ('hipJitOption*', 'options'), ('void**', 'optionsValues')] + case HIP_API_ID_hipModuleLoadDataEx: + if (data->args.hipModuleLoadDataEx.module) data->args.hipModuleLoadDataEx.module__val = *(data->args.hipModuleLoadDataEx.module); + if (data->args.hipModuleLoadDataEx.options) data->args.hipModuleLoadDataEx.options__val = *(data->args.hipModuleLoadDataEx.options); + if (data->args.hipModuleLoadDataEx.optionsValues) data->args.hipModuleLoadDataEx.optionsValues__val = *(data->args.hipModuleLoadDataEx.optionsValues); + break; +// hipModuleOccupancyMaxActiveBlocksPerMultiprocessor[('int*', 'numBlocks'), ('hipFunction_t', 'f'), ('int', 'blockSize'), ('size_t', 'dynSharedMemPerBlk')] + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor: + if (data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks) data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks__val = *(data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks); + break; +// hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags[('int*', 'numBlocks'), ('hipFunction_t', 'f'), ('int', 'blockSize'), ('size_t', 'dynSharedMemPerBlk'), ('unsigned int', 'flags')] + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: + if (data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks) data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks__val = *(data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks); + break; +// hipModuleOccupancyMaxPotentialBlockSize[('int*', 'gridSize'), ('int*', 'blockSize'), ('hipFunction_t', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit')] + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSize: + if (data->args.hipModuleOccupancyMaxPotentialBlockSize.gridSize) data->args.hipModuleOccupancyMaxPotentialBlockSize.gridSize__val = *(data->args.hipModuleOccupancyMaxPotentialBlockSize.gridSize); + if (data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSize) data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSize__val = *(data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSize); + break; +// hipModuleOccupancyMaxPotentialBlockSizeWithFlags[('int*', 'gridSize'), ('int*', 'blockSize'), ('hipFunction_t', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit'), ('unsigned int', 'flags')] + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSizeWithFlags: + if (data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize) data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize__val = *(data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize); + if (data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize) data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize__val = *(data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize); + break; +// hipModuleUnload[('hipModule_t', 'module')] + case HIP_API_ID_hipModuleUnload: + break; +// hipOccupancyMaxActiveBlocksPerMultiprocessor[('int*', 'numBlocks'), ('const void*', 'f'), ('int', 'blockSize'), ('size_t', 'dynamicSMemSize')] + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessor: + if (data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks) data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks__val = *(data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks); + break; +// hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags[('int*', 'numBlocks'), ('const void*', 'f'), ('int', 'blockSize'), ('size_t', 'dynamicSMemSize'), ('unsigned int', 'flags')] + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: + if (data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks) data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks__val = *(data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks); + break; +// hipOccupancyMaxPotentialBlockSize[('int*', 'gridSize'), ('int*', 'blockSize'), ('const void*', 'f'), ('size_t', 'dynSharedMemPerBlk'), ('int', 'blockSizeLimit')] + case HIP_API_ID_hipOccupancyMaxPotentialBlockSize: + if (data->args.hipOccupancyMaxPotentialBlockSize.gridSize) data->args.hipOccupancyMaxPotentialBlockSize.gridSize__val = *(data->args.hipOccupancyMaxPotentialBlockSize.gridSize); + if (data->args.hipOccupancyMaxPotentialBlockSize.blockSize) data->args.hipOccupancyMaxPotentialBlockSize.blockSize__val = *(data->args.hipOccupancyMaxPotentialBlockSize.blockSize); + break; +// hipPeekAtLastError[] + case HIP_API_ID_hipPeekAtLastError: + break; +// hipPointerGetAttribute[('void*', 'data'), ('hipPointer_attribute', 'attribute'), ('hipDeviceptr_t', 'ptr')] + case HIP_API_ID_hipPointerGetAttribute: + break; +// hipPointerGetAttributes[('hipPointerAttribute_t*', 'attributes'), ('const void*', 'ptr')] + case HIP_API_ID_hipPointerGetAttributes: + if (data->args.hipPointerGetAttributes.attributes) data->args.hipPointerGetAttributes.attributes__val = *(data->args.hipPointerGetAttributes.attributes); + break; +// hipPointerSetAttribute[('const void*', 'value'), ('hipPointer_attribute', 'attribute'), ('hipDeviceptr_t', 'ptr')] + case HIP_API_ID_hipPointerSetAttribute: + break; +// hipProfilerStart[] + case HIP_API_ID_hipProfilerStart: + break; +// hipProfilerStop[] + case HIP_API_ID_hipProfilerStop: + break; +// hipRuntimeGetVersion[('int*', 'runtimeVersion')] + case HIP_API_ID_hipRuntimeGetVersion: + if (data->args.hipRuntimeGetVersion.runtimeVersion) data->args.hipRuntimeGetVersion.runtimeVersion__val = *(data->args.hipRuntimeGetVersion.runtimeVersion); + break; +// hipSetDevice[('int', 'deviceId')] + case HIP_API_ID_hipSetDevice: + break; +// hipSetDeviceFlags[('unsigned int', 'flags')] + case HIP_API_ID_hipSetDeviceFlags: + break; +// hipSetupArgument[('const void*', 'arg'), ('size_t', 'size'), ('size_t', 'offset')] + case HIP_API_ID_hipSetupArgument: + break; +// hipSignalExternalSemaphoresAsync[('const hipExternalSemaphore_t*', 'extSemArray'), ('const hipExternalSemaphoreSignalParams*', 'paramsArray'), ('unsigned int', 'numExtSems'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipSignalExternalSemaphoresAsync: + if (data->args.hipSignalExternalSemaphoresAsync.extSemArray) data->args.hipSignalExternalSemaphoresAsync.extSemArray__val = *(data->args.hipSignalExternalSemaphoresAsync.extSemArray); + if (data->args.hipSignalExternalSemaphoresAsync.paramsArray) data->args.hipSignalExternalSemaphoresAsync.paramsArray__val = *(data->args.hipSignalExternalSemaphoresAsync.paramsArray); + break; +// hipStreamAddCallback[('hipStream_t', 'stream'), ('hipStreamCallback_t', 'callback'), ('void*', 'userData'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamAddCallback: + break; +// hipStreamAttachMemAsync[('hipStream_t', 'stream'), ('void*', 'dev_ptr'), ('size_t', 'length'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamAttachMemAsync: + break; +// hipStreamBeginCapture[('hipStream_t', 'stream'), ('hipStreamCaptureMode', 'mode')] + case HIP_API_ID_hipStreamBeginCapture: + break; +// hipStreamCreate[('hipStream_t*', 'stream')] + case HIP_API_ID_hipStreamCreate: + if (data->args.hipStreamCreate.stream) data->args.hipStreamCreate.stream__val = *(data->args.hipStreamCreate.stream); + break; +// hipStreamCreateWithFlags[('hipStream_t*', 'stream'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamCreateWithFlags: + if (data->args.hipStreamCreateWithFlags.stream) data->args.hipStreamCreateWithFlags.stream__val = *(data->args.hipStreamCreateWithFlags.stream); + break; +// hipStreamCreateWithPriority[('hipStream_t*', 'stream'), ('unsigned int', 'flags'), ('int', 'priority')] + case HIP_API_ID_hipStreamCreateWithPriority: + if (data->args.hipStreamCreateWithPriority.stream) data->args.hipStreamCreateWithPriority.stream__val = *(data->args.hipStreamCreateWithPriority.stream); + break; +// hipStreamDestroy[('hipStream_t', 'stream')] + case HIP_API_ID_hipStreamDestroy: + break; +// hipStreamEndCapture[('hipStream_t', 'stream'), ('hipGraph_t*', 'pGraph')] + case HIP_API_ID_hipStreamEndCapture: + if (data->args.hipStreamEndCapture.pGraph) data->args.hipStreamEndCapture.pGraph__val = *(data->args.hipStreamEndCapture.pGraph); + break; +// hipStreamGetCaptureInfo[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'pCaptureStatus'), ('unsigned long long*', 'pId')] + case HIP_API_ID_hipStreamGetCaptureInfo: + if (data->args.hipStreamGetCaptureInfo.pCaptureStatus) data->args.hipStreamGetCaptureInfo.pCaptureStatus__val = *(data->args.hipStreamGetCaptureInfo.pCaptureStatus); + if (data->args.hipStreamGetCaptureInfo.pId) data->args.hipStreamGetCaptureInfo.pId__val = *(data->args.hipStreamGetCaptureInfo.pId); + break; +// hipStreamGetCaptureInfo_v2[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'captureStatus_out'), ('unsigned long long*', 'id_out'), ('hipGraph_t*', 'graph_out'), ('const hipGraphNode_t**', 'dependencies_out'), ('size_t*', 'numDependencies_out')] + case HIP_API_ID_hipStreamGetCaptureInfo_v2: + if (data->args.hipStreamGetCaptureInfo_v2.captureStatus_out) data->args.hipStreamGetCaptureInfo_v2.captureStatus_out__val = *(data->args.hipStreamGetCaptureInfo_v2.captureStatus_out); + if (data->args.hipStreamGetCaptureInfo_v2.id_out) data->args.hipStreamGetCaptureInfo_v2.id_out__val = *(data->args.hipStreamGetCaptureInfo_v2.id_out); + if (data->args.hipStreamGetCaptureInfo_v2.graph_out) data->args.hipStreamGetCaptureInfo_v2.graph_out__val = *(data->args.hipStreamGetCaptureInfo_v2.graph_out); + if (data->args.hipStreamGetCaptureInfo_v2.dependencies_out) data->args.hipStreamGetCaptureInfo_v2.dependencies_out__val = *(data->args.hipStreamGetCaptureInfo_v2.dependencies_out); + if (data->args.hipStreamGetCaptureInfo_v2.numDependencies_out) data->args.hipStreamGetCaptureInfo_v2.numDependencies_out__val = *(data->args.hipStreamGetCaptureInfo_v2.numDependencies_out); + break; +// hipStreamGetDevice[('hipStream_t', 'stream'), ('hipDevice_t*', 'device')] + case HIP_API_ID_hipStreamGetDevice: + if (data->args.hipStreamGetDevice.device) data->args.hipStreamGetDevice.device__val = *(data->args.hipStreamGetDevice.device); + break; +// hipStreamGetFlags[('hipStream_t', 'stream'), ('unsigned int*', 'flags')] + case HIP_API_ID_hipStreamGetFlags: + if (data->args.hipStreamGetFlags.flags) data->args.hipStreamGetFlags.flags__val = *(data->args.hipStreamGetFlags.flags); + break; +// hipStreamGetPriority[('hipStream_t', 'stream'), ('int*', 'priority')] + case HIP_API_ID_hipStreamGetPriority: + if (data->args.hipStreamGetPriority.priority) data->args.hipStreamGetPriority.priority__val = *(data->args.hipStreamGetPriority.priority); + break; +// hipStreamIsCapturing[('hipStream_t', 'stream'), ('hipStreamCaptureStatus*', 'pCaptureStatus')] + case HIP_API_ID_hipStreamIsCapturing: + if (data->args.hipStreamIsCapturing.pCaptureStatus) data->args.hipStreamIsCapturing.pCaptureStatus__val = *(data->args.hipStreamIsCapturing.pCaptureStatus); + break; +// hipStreamQuery[('hipStream_t', 'stream')] + case HIP_API_ID_hipStreamQuery: + break; +// hipStreamSynchronize[('hipStream_t', 'stream')] + case HIP_API_ID_hipStreamSynchronize: + break; +// hipStreamUpdateCaptureDependencies[('hipStream_t', 'stream'), ('hipGraphNode_t*', 'dependencies'), ('size_t', 'numDependencies'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamUpdateCaptureDependencies: + if (data->args.hipStreamUpdateCaptureDependencies.dependencies) data->args.hipStreamUpdateCaptureDependencies.dependencies__val = *(data->args.hipStreamUpdateCaptureDependencies.dependencies); + break; +// hipStreamWaitEvent[('hipStream_t', 'stream'), ('hipEvent_t', 'event'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamWaitEvent: + break; +// hipStreamWaitValue32[('hipStream_t', 'stream'), ('void*', 'ptr'), ('unsigned int', 'value'), ('unsigned int', 'flags'), ('unsigned int', 'mask')] + case HIP_API_ID_hipStreamWaitValue32: + break; +// hipStreamWaitValue64[('hipStream_t', 'stream'), ('void*', 'ptr'), ('uint64_t', 'value'), ('unsigned int', 'flags'), ('uint64_t', 'mask')] + case HIP_API_ID_hipStreamWaitValue64: + break; +// hipStreamWriteValue32[('hipStream_t', 'stream'), ('void*', 'ptr'), ('unsigned int', 'value'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamWriteValue32: + break; +// hipStreamWriteValue64[('hipStream_t', 'stream'), ('void*', 'ptr'), ('uint64_t', 'value'), ('unsigned int', 'flags')] + case HIP_API_ID_hipStreamWriteValue64: + break; +// hipTexRefGetAddress[('hipDeviceptr_t*', 'dev_ptr'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetAddress: + if (data->args.hipTexRefGetAddress.dev_ptr) data->args.hipTexRefGetAddress.dev_ptr__val = *(data->args.hipTexRefGetAddress.dev_ptr); + if (data->args.hipTexRefGetAddress.texRef) data->args.hipTexRefGetAddress.texRef__val = *(data->args.hipTexRefGetAddress.texRef); + break; +// hipTexRefGetFlags[('unsigned int*', 'pFlags'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetFlags: + if (data->args.hipTexRefGetFlags.pFlags) data->args.hipTexRefGetFlags.pFlags__val = *(data->args.hipTexRefGetFlags.pFlags); + if (data->args.hipTexRefGetFlags.texRef) data->args.hipTexRefGetFlags.texRef__val = *(data->args.hipTexRefGetFlags.texRef); + break; +// hipTexRefGetFormat[('hipArray_Format*', 'pFormat'), ('int*', 'pNumChannels'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetFormat: + if (data->args.hipTexRefGetFormat.pFormat) data->args.hipTexRefGetFormat.pFormat__val = *(data->args.hipTexRefGetFormat.pFormat); + if (data->args.hipTexRefGetFormat.pNumChannels) data->args.hipTexRefGetFormat.pNumChannels__val = *(data->args.hipTexRefGetFormat.pNumChannels); + if (data->args.hipTexRefGetFormat.texRef) data->args.hipTexRefGetFormat.texRef__val = *(data->args.hipTexRefGetFormat.texRef); + break; +// hipTexRefGetMaxAnisotropy[('int*', 'pmaxAnsio'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetMaxAnisotropy: + if (data->args.hipTexRefGetMaxAnisotropy.pmaxAnsio) data->args.hipTexRefGetMaxAnisotropy.pmaxAnsio__val = *(data->args.hipTexRefGetMaxAnisotropy.pmaxAnsio); + if (data->args.hipTexRefGetMaxAnisotropy.texRef) data->args.hipTexRefGetMaxAnisotropy.texRef__val = *(data->args.hipTexRefGetMaxAnisotropy.texRef); + break; +// hipTexRefGetMipMappedArray[('hipMipmappedArray_t*', 'pArray'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetMipMappedArray: + if (data->args.hipTexRefGetMipMappedArray.pArray) data->args.hipTexRefGetMipMappedArray.pArray__val = *(data->args.hipTexRefGetMipMappedArray.pArray); + if (data->args.hipTexRefGetMipMappedArray.texRef) data->args.hipTexRefGetMipMappedArray.texRef__val = *(data->args.hipTexRefGetMipMappedArray.texRef); + break; +// hipTexRefGetMipmapLevelBias[('float*', 'pbias'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetMipmapLevelBias: + if (data->args.hipTexRefGetMipmapLevelBias.pbias) data->args.hipTexRefGetMipmapLevelBias.pbias__val = *(data->args.hipTexRefGetMipmapLevelBias.pbias); + if (data->args.hipTexRefGetMipmapLevelBias.texRef) data->args.hipTexRefGetMipmapLevelBias.texRef__val = *(data->args.hipTexRefGetMipmapLevelBias.texRef); + break; +// hipTexRefGetMipmapLevelClamp[('float*', 'pminMipmapLevelClamp'), ('float*', 'pmaxMipmapLevelClamp'), ('const textureReference*', 'texRef')] + case HIP_API_ID_hipTexRefGetMipmapLevelClamp: + if (data->args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp) data->args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp__val = *(data->args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp); + if (data->args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp) data->args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp__val = *(data->args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp); + if (data->args.hipTexRefGetMipmapLevelClamp.texRef) data->args.hipTexRefGetMipmapLevelClamp.texRef__val = *(data->args.hipTexRefGetMipmapLevelClamp.texRef); + break; +// hipTexRefSetAddress[('size_t*', 'ByteOffset'), ('textureReference*', 'texRef'), ('hipDeviceptr_t', 'dptr'), ('size_t', 'bytes')] + case HIP_API_ID_hipTexRefSetAddress: + if (data->args.hipTexRefSetAddress.ByteOffset) data->args.hipTexRefSetAddress.ByteOffset__val = *(data->args.hipTexRefSetAddress.ByteOffset); + if (data->args.hipTexRefSetAddress.texRef) data->args.hipTexRefSetAddress.texRef__val = *(data->args.hipTexRefSetAddress.texRef); + break; +// hipTexRefSetAddress2D[('textureReference*', 'texRef'), ('const HIP_ARRAY_DESCRIPTOR*', 'desc'), ('hipDeviceptr_t', 'dptr'), ('size_t', 'Pitch')] + case HIP_API_ID_hipTexRefSetAddress2D: + if (data->args.hipTexRefSetAddress2D.texRef) data->args.hipTexRefSetAddress2D.texRef__val = *(data->args.hipTexRefSetAddress2D.texRef); + if (data->args.hipTexRefSetAddress2D.desc) data->args.hipTexRefSetAddress2D.desc__val = *(data->args.hipTexRefSetAddress2D.desc); + break; +// hipTexRefSetArray[('textureReference*', 'tex'), ('hipArray_const_t', 'array'), ('unsigned int', 'flags')] + case HIP_API_ID_hipTexRefSetArray: + if (data->args.hipTexRefSetArray.tex) data->args.hipTexRefSetArray.tex__val = *(data->args.hipTexRefSetArray.tex); + break; +// hipTexRefSetBorderColor[('textureReference*', 'texRef'), ('float*', 'pBorderColor')] + case HIP_API_ID_hipTexRefSetBorderColor: + if (data->args.hipTexRefSetBorderColor.texRef) data->args.hipTexRefSetBorderColor.texRef__val = *(data->args.hipTexRefSetBorderColor.texRef); + if (data->args.hipTexRefSetBorderColor.pBorderColor) data->args.hipTexRefSetBorderColor.pBorderColor__val = *(data->args.hipTexRefSetBorderColor.pBorderColor); + break; +// hipTexRefSetFlags[('textureReference*', 'texRef'), ('unsigned int', 'Flags')] + case HIP_API_ID_hipTexRefSetFlags: + if (data->args.hipTexRefSetFlags.texRef) data->args.hipTexRefSetFlags.texRef__val = *(data->args.hipTexRefSetFlags.texRef); + break; +// hipTexRefSetFormat[('textureReference*', 'texRef'), ('hipArray_Format', 'fmt'), ('int', 'NumPackedComponents')] + case HIP_API_ID_hipTexRefSetFormat: + if (data->args.hipTexRefSetFormat.texRef) data->args.hipTexRefSetFormat.texRef__val = *(data->args.hipTexRefSetFormat.texRef); + break; +// hipTexRefSetMaxAnisotropy[('textureReference*', 'texRef'), ('unsigned int', 'maxAniso')] + case HIP_API_ID_hipTexRefSetMaxAnisotropy: + if (data->args.hipTexRefSetMaxAnisotropy.texRef) data->args.hipTexRefSetMaxAnisotropy.texRef__val = *(data->args.hipTexRefSetMaxAnisotropy.texRef); + break; +// hipTexRefSetMipmapLevelBias[('textureReference*', 'texRef'), ('float', 'bias')] + case HIP_API_ID_hipTexRefSetMipmapLevelBias: + if (data->args.hipTexRefSetMipmapLevelBias.texRef) data->args.hipTexRefSetMipmapLevelBias.texRef__val = *(data->args.hipTexRefSetMipmapLevelBias.texRef); + break; +// hipTexRefSetMipmapLevelClamp[('textureReference*', 'texRef'), ('float', 'minMipMapLevelClamp'), ('float', 'maxMipMapLevelClamp')] + case HIP_API_ID_hipTexRefSetMipmapLevelClamp: + if (data->args.hipTexRefSetMipmapLevelClamp.texRef) data->args.hipTexRefSetMipmapLevelClamp.texRef__val = *(data->args.hipTexRefSetMipmapLevelClamp.texRef); + break; +// hipTexRefSetMipmappedArray[('textureReference*', 'texRef'), ('hipMipmappedArray*', 'mipmappedArray'), ('unsigned int', 'Flags')] + case HIP_API_ID_hipTexRefSetMipmappedArray: + if (data->args.hipTexRefSetMipmappedArray.texRef) data->args.hipTexRefSetMipmappedArray.texRef__val = *(data->args.hipTexRefSetMipmappedArray.texRef); + if (data->args.hipTexRefSetMipmappedArray.mipmappedArray) data->args.hipTexRefSetMipmappedArray.mipmappedArray__val = *(data->args.hipTexRefSetMipmappedArray.mipmappedArray); + break; +// hipThreadExchangeStreamCaptureMode[('hipStreamCaptureMode*', 'mode')] + case HIP_API_ID_hipThreadExchangeStreamCaptureMode: + if (data->args.hipThreadExchangeStreamCaptureMode.mode) data->args.hipThreadExchangeStreamCaptureMode.mode__val = *(data->args.hipThreadExchangeStreamCaptureMode.mode); + break; +// hipUserObjectCreate[('hipUserObject_t*', 'object_out'), ('void*', 'ptr'), ('hipHostFn_t', 'destroy'), ('unsigned int', 'initialRefcount'), ('unsigned int', 'flags')] + case HIP_API_ID_hipUserObjectCreate: + if (data->args.hipUserObjectCreate.object_out) data->args.hipUserObjectCreate.object_out__val = *(data->args.hipUserObjectCreate.object_out); + break; +// hipUserObjectRelease[('hipUserObject_t', 'object'), ('unsigned int', 'count')] + case HIP_API_ID_hipUserObjectRelease: + break; +// hipUserObjectRetain[('hipUserObject_t', 'object'), ('unsigned int', 'count')] + case HIP_API_ID_hipUserObjectRetain: + break; +// hipWaitExternalSemaphoresAsync[('const hipExternalSemaphore_t*', 'extSemArray'), ('const hipExternalSemaphoreWaitParams*', 'paramsArray'), ('unsigned int', 'numExtSems'), ('hipStream_t', 'stream')] + case HIP_API_ID_hipWaitExternalSemaphoresAsync: + if (data->args.hipWaitExternalSemaphoresAsync.extSemArray) data->args.hipWaitExternalSemaphoresAsync.extSemArray__val = *(data->args.hipWaitExternalSemaphoresAsync.extSemArray); + if (data->args.hipWaitExternalSemaphoresAsync.paramsArray) data->args.hipWaitExternalSemaphoresAsync.paramsArray__val = *(data->args.hipWaitExternalSemaphoresAsync.paramsArray); + break; + default: break; + }; +} + +#include +#include +// HIP API string method, method name and parameters +static inline const char* hipApiString(hip_api_id_t id, const hip_api_data_t* data) { + std::ostringstream oss; + switch (id) { + case HIP_API_ID___hipPopCallConfiguration: + oss << "__hipPopCallConfiguration("; + if (data->args.__hipPopCallConfiguration.gridDim == NULL) oss << "gridDim=NULL"; + else { oss << "gridDim="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPopCallConfiguration.gridDim__val); } + if (data->args.__hipPopCallConfiguration.blockDim == NULL) oss << ", blockDim=NULL"; + else { oss << ", blockDim="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPopCallConfiguration.blockDim__val); } + if (data->args.__hipPopCallConfiguration.sharedMem == NULL) oss << ", sharedMem=NULL"; + else { oss << ", sharedMem="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPopCallConfiguration.sharedMem__val); } + if (data->args.__hipPopCallConfiguration.stream == NULL) oss << ", stream=NULL"; + else { oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPopCallConfiguration.stream__val); } + oss << ")"; + break; + case HIP_API_ID___hipPushCallConfiguration: + oss << "__hipPushCallConfiguration("; + oss << "gridDim="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPushCallConfiguration.gridDim); + oss << ", blockDim="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPushCallConfiguration.blockDim); + oss << ", sharedMem="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPushCallConfiguration.sharedMem); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.__hipPushCallConfiguration.stream); + oss << ")"; + break; + case HIP_API_ID_hipArray3DCreate: + oss << "hipArray3DCreate("; + if (data->args.hipArray3DCreate.array == NULL) oss << "array=NULL"; + else { oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArray3DCreate.array__val); } + if (data->args.hipArray3DCreate.pAllocateArray == NULL) oss << ", pAllocateArray=NULL"; + else { oss << ", pAllocateArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArray3DCreate.pAllocateArray__val); } + oss << ")"; + break; + case HIP_API_ID_hipArray3DGetDescriptor: + oss << "hipArray3DGetDescriptor("; + if (data->args.hipArray3DGetDescriptor.pArrayDescriptor == NULL) oss << "pArrayDescriptor=NULL"; + else { oss << "pArrayDescriptor="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArray3DGetDescriptor.pArrayDescriptor__val); } + oss << ", array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArray3DGetDescriptor.array); + oss << ")"; + break; + case HIP_API_ID_hipArrayCreate: + oss << "hipArrayCreate("; + if (data->args.hipArrayCreate.pHandle == NULL) oss << "pHandle=NULL"; + else { oss << "pHandle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayCreate.pHandle__val); } + if (data->args.hipArrayCreate.pAllocateArray == NULL) oss << ", pAllocateArray=NULL"; + else { oss << ", pAllocateArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayCreate.pAllocateArray__val); } + oss << ")"; + break; + case HIP_API_ID_hipArrayDestroy: + oss << "hipArrayDestroy("; + oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayDestroy.array); + oss << ")"; + break; + case HIP_API_ID_hipArrayGetDescriptor: + oss << "hipArrayGetDescriptor("; + if (data->args.hipArrayGetDescriptor.pArrayDescriptor == NULL) oss << "pArrayDescriptor=NULL"; + else { oss << "pArrayDescriptor="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetDescriptor.pArrayDescriptor__val); } + oss << ", array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetDescriptor.array); + oss << ")"; + break; + case HIP_API_ID_hipArrayGetInfo: + oss << "hipArrayGetInfo("; + if (data->args.hipArrayGetInfo.desc == NULL) oss << "desc=NULL"; + else { oss << "desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetInfo.desc__val); } + if (data->args.hipArrayGetInfo.extent == NULL) oss << ", extent=NULL"; + else { oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetInfo.extent__val); } + if (data->args.hipArrayGetInfo.flags == NULL) oss << ", flags=NULL"; + else { oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetInfo.flags__val); } + oss << ", array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipArrayGetInfo.array); + oss << ")"; + break; + case HIP_API_ID_hipChooseDeviceR0000: + oss << "hipChooseDeviceR0000("; + if (data->args.hipChooseDeviceR0000.device == NULL) oss << "device=NULL"; + else { oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipChooseDeviceR0000.device__val); } + if (data->args.hipChooseDeviceR0000.prop == NULL) oss << ", prop=NULL"; + else { oss << ", prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipChooseDeviceR0000.prop__val); } + oss << ")"; + break; + case HIP_API_ID_hipChooseDeviceR0600: + oss << "hipChooseDeviceR0600("; + if (data->args.hipChooseDeviceR0600.device == NULL) oss << "device=NULL"; + else { oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipChooseDeviceR0600.device__val); } + if (data->args.hipChooseDeviceR0600.prop == NULL) oss << ", prop=NULL"; + else { oss << ", prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipChooseDeviceR0600.prop__val); } + oss << ")"; + break; + case HIP_API_ID_hipConfigureCall: + oss << "hipConfigureCall("; + oss << "gridDim="; roctracer::hip_support::detail::operator<<(oss, data->args.hipConfigureCall.gridDim); + oss << ", blockDim="; roctracer::hip_support::detail::operator<<(oss, data->args.hipConfigureCall.blockDim); + oss << ", sharedMem="; roctracer::hip_support::detail::operator<<(oss, data->args.hipConfigureCall.sharedMem); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipConfigureCall.stream); + oss << ")"; + break; + case HIP_API_ID_hipCreateSurfaceObject: + oss << "hipCreateSurfaceObject("; + if (data->args.hipCreateSurfaceObject.pSurfObject == NULL) oss << "pSurfObject=NULL"; + else { oss << "pSurfObject="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCreateSurfaceObject.pSurfObject__val); } + if (data->args.hipCreateSurfaceObject.pResDesc == NULL) oss << ", pResDesc=NULL"; + else { oss << ", pResDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCreateSurfaceObject.pResDesc__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxCreate: + oss << "hipCtxCreate("; + if (data->args.hipCtxCreate.ctx == NULL) oss << "ctx=NULL"; + else { oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxCreate.ctx__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxCreate.flags); + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxCreate.device); + oss << ")"; + break; + case HIP_API_ID_hipCtxDestroy: + oss << "hipCtxDestroy("; + oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxDestroy.ctx); + oss << ")"; + break; + case HIP_API_ID_hipCtxDisablePeerAccess: + oss << "hipCtxDisablePeerAccess("; + oss << "peerCtx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxDisablePeerAccess.peerCtx); + oss << ")"; + break; + case HIP_API_ID_hipCtxEnablePeerAccess: + oss << "hipCtxEnablePeerAccess("; + oss << "peerCtx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxEnablePeerAccess.peerCtx); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxEnablePeerAccess.flags); + oss << ")"; + break; + case HIP_API_ID_hipCtxGetApiVersion: + oss << "hipCtxGetApiVersion("; + oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetApiVersion.ctx); + if (data->args.hipCtxGetApiVersion.apiVersion == NULL) oss << ", apiVersion=NULL"; + else { oss << ", apiVersion="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetApiVersion.apiVersion__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxGetCacheConfig: + oss << "hipCtxGetCacheConfig("; + if (data->args.hipCtxGetCacheConfig.cacheConfig == NULL) oss << "cacheConfig=NULL"; + else { oss << "cacheConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetCacheConfig.cacheConfig__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxGetCurrent: + oss << "hipCtxGetCurrent("; + if (data->args.hipCtxGetCurrent.ctx == NULL) oss << "ctx=NULL"; + else { oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetCurrent.ctx__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxGetDevice: + oss << "hipCtxGetDevice("; + if (data->args.hipCtxGetDevice.device == NULL) oss << "device=NULL"; + else { oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetDevice.device__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxGetFlags: + oss << "hipCtxGetFlags("; + if (data->args.hipCtxGetFlags.flags == NULL) oss << "flags=NULL"; + else { oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetFlags.flags__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxGetSharedMemConfig: + oss << "hipCtxGetSharedMemConfig("; + if (data->args.hipCtxGetSharedMemConfig.pConfig == NULL) oss << "pConfig=NULL"; + else { oss << "pConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxGetSharedMemConfig.pConfig__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxPopCurrent: + oss << "hipCtxPopCurrent("; + if (data->args.hipCtxPopCurrent.ctx == NULL) oss << "ctx=NULL"; + else { oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxPopCurrent.ctx__val); } + oss << ")"; + break; + case HIP_API_ID_hipCtxPushCurrent: + oss << "hipCtxPushCurrent("; + oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxPushCurrent.ctx); + oss << ")"; + break; + case HIP_API_ID_hipCtxSetCacheConfig: + oss << "hipCtxSetCacheConfig("; + oss << "cacheConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxSetCacheConfig.cacheConfig); + oss << ")"; + break; + case HIP_API_ID_hipCtxSetCurrent: + oss << "hipCtxSetCurrent("; + oss << "ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxSetCurrent.ctx); + oss << ")"; + break; + case HIP_API_ID_hipCtxSetSharedMemConfig: + oss << "hipCtxSetSharedMemConfig("; + oss << "config="; roctracer::hip_support::detail::operator<<(oss, data->args.hipCtxSetSharedMemConfig.config); + oss << ")"; + break; + case HIP_API_ID_hipCtxSynchronize: + oss << "hipCtxSynchronize("; + oss << ")"; + break; + case HIP_API_ID_hipDestroyExternalMemory: + oss << "hipDestroyExternalMemory("; + oss << "extMem="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDestroyExternalMemory.extMem); + oss << ")"; + break; + case HIP_API_ID_hipDestroyExternalSemaphore: + oss << "hipDestroyExternalSemaphore("; + oss << "extSem="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDestroyExternalSemaphore.extSem); + oss << ")"; + break; + case HIP_API_ID_hipDestroySurfaceObject: + oss << "hipDestroySurfaceObject("; + oss << "surfaceObject="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDestroySurfaceObject.surfaceObject); + oss << ")"; + break; + case HIP_API_ID_hipDeviceCanAccessPeer: + oss << "hipDeviceCanAccessPeer("; + if (data->args.hipDeviceCanAccessPeer.canAccessPeer == NULL) oss << "canAccessPeer=NULL"; + else { oss << "canAccessPeer="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceCanAccessPeer.canAccessPeer__val); } + oss << ", deviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceCanAccessPeer.deviceId); + oss << ", peerDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceCanAccessPeer.peerDeviceId); + oss << ")"; + break; + case HIP_API_ID_hipDeviceComputeCapability: + oss << "hipDeviceComputeCapability("; + if (data->args.hipDeviceComputeCapability.major == NULL) oss << "major=NULL"; + else { oss << "major="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceComputeCapability.major__val); } + if (data->args.hipDeviceComputeCapability.minor == NULL) oss << ", minor=NULL"; + else { oss << ", minor="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceComputeCapability.minor__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceComputeCapability.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceDisablePeerAccess: + oss << "hipDeviceDisablePeerAccess("; + oss << "peerDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceDisablePeerAccess.peerDeviceId); + oss << ")"; + break; + case HIP_API_ID_hipDeviceEnablePeerAccess: + oss << "hipDeviceEnablePeerAccess("; + oss << "peerDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceEnablePeerAccess.peerDeviceId); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceEnablePeerAccess.flags); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGet: + oss << "hipDeviceGet("; + if (data->args.hipDeviceGet.device == NULL) oss << "device=NULL"; + else { oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGet.device__val); } + oss << ", ordinal="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGet.ordinal); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetAttribute: + oss << "hipDeviceGetAttribute("; + if (data->args.hipDeviceGetAttribute.pi == NULL) oss << "pi=NULL"; + else { oss << "pi="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetAttribute.pi__val); } + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetAttribute.attr); + oss << ", deviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetAttribute.deviceId); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetByPCIBusId: + oss << "hipDeviceGetByPCIBusId("; + if (data->args.hipDeviceGetByPCIBusId.device == NULL) oss << "device=NULL"; + else { oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetByPCIBusId.device__val); } + if (data->args.hipDeviceGetByPCIBusId.pciBusId == NULL) oss << ", pciBusId=NULL"; + else { oss << ", pciBusId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetByPCIBusId.pciBusId__val); } + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetCacheConfig: + oss << "hipDeviceGetCacheConfig("; + if (data->args.hipDeviceGetCacheConfig.cacheConfig == NULL) oss << "cacheConfig=NULL"; + else { oss << "cacheConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetCacheConfig.cacheConfig__val); } + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetDefaultMemPool: + oss << "hipDeviceGetDefaultMemPool("; + if (data->args.hipDeviceGetDefaultMemPool.mem_pool == NULL) oss << "mem_pool=NULL"; + else { oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetDefaultMemPool.mem_pool__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetDefaultMemPool.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetGraphMemAttribute: + oss << "hipDeviceGetGraphMemAttribute("; + oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetGraphMemAttribute.device); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetGraphMemAttribute.attr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetGraphMemAttribute.value); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetLimit: + oss << "hipDeviceGetLimit("; + if (data->args.hipDeviceGetLimit.pValue == NULL) oss << "pValue=NULL"; + else { oss << "pValue="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetLimit.pValue__val); } + oss << ", limit="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetLimit.limit); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetMemPool: + oss << "hipDeviceGetMemPool("; + if (data->args.hipDeviceGetMemPool.mem_pool == NULL) oss << "mem_pool=NULL"; + else { oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetMemPool.mem_pool__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetMemPool.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetName: + oss << "hipDeviceGetName("; + if (data->args.hipDeviceGetName.name == NULL) oss << "name=NULL"; + else { oss << "name="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetName.name__val); } + oss << ", len="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetName.len); + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetName.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetP2PAttribute: + oss << "hipDeviceGetP2PAttribute("; + if (data->args.hipDeviceGetP2PAttribute.value == NULL) oss << "value=NULL"; + else { oss << "value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetP2PAttribute.value__val); } + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetP2PAttribute.attr); + oss << ", srcDevice="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetP2PAttribute.srcDevice); + oss << ", dstDevice="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetP2PAttribute.dstDevice); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetPCIBusId: + oss << "hipDeviceGetPCIBusId("; + if (data->args.hipDeviceGetPCIBusId.pciBusId == NULL) oss << "pciBusId=NULL"; + else { oss << "pciBusId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetPCIBusId.pciBusId__val); } + oss << ", len="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetPCIBusId.len); + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetPCIBusId.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetSharedMemConfig: + oss << "hipDeviceGetSharedMemConfig("; + if (data->args.hipDeviceGetSharedMemConfig.pConfig == NULL) oss << "pConfig=NULL"; + else { oss << "pConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetSharedMemConfig.pConfig__val); } + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetStreamPriorityRange: + oss << "hipDeviceGetStreamPriorityRange("; + if (data->args.hipDeviceGetStreamPriorityRange.leastPriority == NULL) oss << "leastPriority=NULL"; + else { oss << "leastPriority="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetStreamPriorityRange.leastPriority__val); } + if (data->args.hipDeviceGetStreamPriorityRange.greatestPriority == NULL) oss << ", greatestPriority=NULL"; + else { oss << ", greatestPriority="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetStreamPriorityRange.greatestPriority__val); } + oss << ")"; + break; + case HIP_API_ID_hipDeviceGetUuid: + oss << "hipDeviceGetUuid("; + if (data->args.hipDeviceGetUuid.uuid == NULL) oss << "uuid=NULL"; + else { oss << "uuid="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetUuid.uuid__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGetUuid.device); + oss << ")"; + break; + case HIP_API_ID_hipDeviceGraphMemTrim: + oss << "hipDeviceGraphMemTrim("; + oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceGraphMemTrim.device); + oss << ")"; + break; + case HIP_API_ID_hipDevicePrimaryCtxGetState: + oss << "hipDevicePrimaryCtxGetState("; + oss << "dev="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxGetState.dev); + if (data->args.hipDevicePrimaryCtxGetState.flags == NULL) oss << ", flags=NULL"; + else { oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxGetState.flags__val); } + if (data->args.hipDevicePrimaryCtxGetState.active == NULL) oss << ", active=NULL"; + else { oss << ", active="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxGetState.active__val); } + oss << ")"; + break; + case HIP_API_ID_hipDevicePrimaryCtxRelease: + oss << "hipDevicePrimaryCtxRelease("; + oss << "dev="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxRelease.dev); + oss << ")"; + break; + case HIP_API_ID_hipDevicePrimaryCtxReset: + oss << "hipDevicePrimaryCtxReset("; + oss << "dev="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxReset.dev); + oss << ")"; + break; + case HIP_API_ID_hipDevicePrimaryCtxRetain: + oss << "hipDevicePrimaryCtxRetain("; + if (data->args.hipDevicePrimaryCtxRetain.pctx == NULL) oss << "pctx=NULL"; + else { oss << "pctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxRetain.pctx__val); } + oss << ", dev="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxRetain.dev); + oss << ")"; + break; + case HIP_API_ID_hipDevicePrimaryCtxSetFlags: + oss << "hipDevicePrimaryCtxSetFlags("; + oss << "dev="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxSetFlags.dev); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDevicePrimaryCtxSetFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipDeviceReset: + oss << "hipDeviceReset("; + oss << ")"; + break; + case HIP_API_ID_hipDeviceSetCacheConfig: + oss << "hipDeviceSetCacheConfig("; + oss << "cacheConfig="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetCacheConfig.cacheConfig); + oss << ")"; + break; + case HIP_API_ID_hipDeviceSetGraphMemAttribute: + oss << "hipDeviceSetGraphMemAttribute("; + oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetGraphMemAttribute.device); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetGraphMemAttribute.attr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetGraphMemAttribute.value); + oss << ")"; + break; + case HIP_API_ID_hipDeviceSetLimit: + oss << "hipDeviceSetLimit("; + oss << "limit="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetLimit.limit); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetLimit.value); + oss << ")"; + break; + case HIP_API_ID_hipDeviceSetMemPool: + oss << "hipDeviceSetMemPool("; + oss << "device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetMemPool.device); + oss << ", mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetMemPool.mem_pool); + oss << ")"; + break; + case HIP_API_ID_hipDeviceSetSharedMemConfig: + oss << "hipDeviceSetSharedMemConfig("; + oss << "config="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceSetSharedMemConfig.config); + oss << ")"; + break; + case HIP_API_ID_hipDeviceSynchronize: + oss << "hipDeviceSynchronize("; + oss << ")"; + break; + case HIP_API_ID_hipDeviceTotalMem: + oss << "hipDeviceTotalMem("; + if (data->args.hipDeviceTotalMem.bytes == NULL) oss << "bytes=NULL"; + else { oss << "bytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceTotalMem.bytes__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDeviceTotalMem.device); + oss << ")"; + break; + case HIP_API_ID_hipDriverGetVersion: + oss << "hipDriverGetVersion("; + if (data->args.hipDriverGetVersion.driverVersion == NULL) oss << "driverVersion=NULL"; + else { oss << "driverVersion="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDriverGetVersion.driverVersion__val); } + oss << ")"; + break; + case HIP_API_ID_hipDrvGraphAddMemcpyNode: + oss << "hipDrvGraphAddMemcpyNode("; + if (data->args.hipDrvGraphAddMemcpyNode.phGraphNode == NULL) oss << "phGraphNode=NULL"; + else { oss << "phGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.phGraphNode__val); } + oss << ", hGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.hGraph); + if (data->args.hipDrvGraphAddMemcpyNode.dependencies == NULL) oss << ", dependencies=NULL"; + else { oss << ", dependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.dependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.numDependencies); + if (data->args.hipDrvGraphAddMemcpyNode.copyParams == NULL) oss << ", copyParams=NULL"; + else { oss << ", copyParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.copyParams__val); } + oss << ", ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemcpyNode.ctx); + oss << ")"; + break; + case HIP_API_ID_hipDrvGraphAddMemsetNode: + oss << "hipDrvGraphAddMemsetNode("; + if (data->args.hipDrvGraphAddMemsetNode.phGraphNode == NULL) oss << "phGraphNode=NULL"; + else { oss << "phGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.phGraphNode__val); } + oss << ", hGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.hGraph); + if (data->args.hipDrvGraphAddMemsetNode.dependencies == NULL) oss << ", dependencies=NULL"; + else { oss << ", dependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.dependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.numDependencies); + if (data->args.hipDrvGraphAddMemsetNode.memsetParams == NULL) oss << ", memsetParams=NULL"; + else { oss << ", memsetParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.memsetParams__val); } + oss << ", ctx="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphAddMemsetNode.ctx); + oss << ")"; + break; + case HIP_API_ID_hipDrvGraphMemcpyNodeGetParams: + oss << "hipDrvGraphMemcpyNodeGetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphMemcpyNodeGetParams.hNode); + if (data->args.hipDrvGraphMemcpyNodeGetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphMemcpyNodeGetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipDrvGraphMemcpyNodeSetParams: + oss << "hipDrvGraphMemcpyNodeSetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphMemcpyNodeSetParams.hNode); + if (data->args.hipDrvGraphMemcpyNodeSetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvGraphMemcpyNodeSetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipDrvMemcpy2DUnaligned: + oss << "hipDrvMemcpy2DUnaligned("; + if (data->args.hipDrvMemcpy2DUnaligned.pCopy == NULL) oss << "pCopy=NULL"; + else { oss << "pCopy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvMemcpy2DUnaligned.pCopy__val); } + oss << ")"; + break; + case HIP_API_ID_hipDrvMemcpy3D: + oss << "hipDrvMemcpy3D("; + if (data->args.hipDrvMemcpy3D.pCopy == NULL) oss << "pCopy=NULL"; + else { oss << "pCopy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvMemcpy3D.pCopy__val); } + oss << ")"; + break; + case HIP_API_ID_hipDrvMemcpy3DAsync: + oss << "hipDrvMemcpy3DAsync("; + if (data->args.hipDrvMemcpy3DAsync.pCopy == NULL) oss << "pCopy=NULL"; + else { oss << "pCopy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvMemcpy3DAsync.pCopy__val); } + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvMemcpy3DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipDrvPointerGetAttributes: + oss << "hipDrvPointerGetAttributes("; + oss << "numAttributes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvPointerGetAttributes.numAttributes); + if (data->args.hipDrvPointerGetAttributes.attributes == NULL) oss << ", attributes=NULL"; + else { oss << ", attributes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvPointerGetAttributes.attributes__val); } + if (data->args.hipDrvPointerGetAttributes.data == NULL) oss << ", data=NULL"; + else { oss << ", data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvPointerGetAttributes.data__val); } + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipDrvPointerGetAttributes.ptr); + oss << ")"; + break; + case HIP_API_ID_hipEventCreate: + oss << "hipEventCreate("; + if (data->args.hipEventCreate.event == NULL) oss << "event=NULL"; + else { oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventCreate.event__val); } + oss << ")"; + break; + case HIP_API_ID_hipEventCreateWithFlags: + oss << "hipEventCreateWithFlags("; + if (data->args.hipEventCreateWithFlags.event == NULL) oss << "event=NULL"; + else { oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventCreateWithFlags.event__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventCreateWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipEventDestroy: + oss << "hipEventDestroy("; + oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventDestroy.event); + oss << ")"; + break; + case HIP_API_ID_hipEventElapsedTime: + oss << "hipEventElapsedTime("; + if (data->args.hipEventElapsedTime.ms == NULL) oss << "ms=NULL"; + else { oss << "ms="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventElapsedTime.ms__val); } + oss << ", start="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventElapsedTime.start); + oss << ", stop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventElapsedTime.stop); + oss << ")"; + break; + case HIP_API_ID_hipEventQuery: + oss << "hipEventQuery("; + oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventQuery.event); + oss << ")"; + break; + case HIP_API_ID_hipEventRecord: + oss << "hipEventRecord("; + oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventRecord.event); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventRecord.stream); + oss << ")"; + break; + case HIP_API_ID_hipEventSynchronize: + oss << "hipEventSynchronize("; + oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipEventSynchronize.event); + oss << ")"; + break; + case HIP_API_ID_hipExtGetLinkTypeAndHopCount: + oss << "hipExtGetLinkTypeAndHopCount("; + oss << "device1="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtGetLinkTypeAndHopCount.device1); + oss << ", device2="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtGetLinkTypeAndHopCount.device2); + if (data->args.hipExtGetLinkTypeAndHopCount.linktype == NULL) oss << ", linktype=NULL"; + else { oss << ", linktype="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtGetLinkTypeAndHopCount.linktype__val); } + if (data->args.hipExtGetLinkTypeAndHopCount.hopcount == NULL) oss << ", hopcount=NULL"; + else { oss << ", hopcount="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtGetLinkTypeAndHopCount.hopcount__val); } + oss << ")"; + break; + case HIP_API_ID_hipExtLaunchKernel: + oss << "hipExtLaunchKernel("; + oss << "function_address="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.function_address); + oss << ", numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.numBlocks); + oss << ", dimBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.dimBlocks); + if (data->args.hipExtLaunchKernel.args == NULL) oss << ", args=NULL"; + else { oss << ", args="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.args__val); } + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.sharedMemBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.stream); + oss << ", startEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.startEvent); + oss << ", stopEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.stopEvent); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchKernel.flags); + oss << ")"; + break; + case HIP_API_ID_hipExtLaunchMultiKernelMultiDevice: + oss << "hipExtLaunchMultiKernelMultiDevice("; + if (data->args.hipExtLaunchMultiKernelMultiDevice.launchParamsList == NULL) oss << "launchParamsList=NULL"; + else { oss << "launchParamsList="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchMultiKernelMultiDevice.launchParamsList__val); } + oss << ", numDevices="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchMultiKernelMultiDevice.numDevices); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtLaunchMultiKernelMultiDevice.flags); + oss << ")"; + break; + case HIP_API_ID_hipExtMallocWithFlags: + oss << "hipExtMallocWithFlags("; + if (data->args.hipExtMallocWithFlags.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtMallocWithFlags.ptr__val); } + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtMallocWithFlags.sizeBytes); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtMallocWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipExtModuleLaunchKernel: + oss << "hipExtModuleLaunchKernel("; + oss << "f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.f); + oss << ", globalWorkSizeX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.globalWorkSizeX); + oss << ", globalWorkSizeY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.globalWorkSizeY); + oss << ", globalWorkSizeZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.globalWorkSizeZ); + oss << ", localWorkSizeX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.localWorkSizeX); + oss << ", localWorkSizeY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.localWorkSizeY); + oss << ", localWorkSizeZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.localWorkSizeZ); + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.sharedMemBytes); + oss << ", hStream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.hStream); + if (data->args.hipExtModuleLaunchKernel.kernelParams == NULL) oss << ", kernelParams=NULL"; + else { oss << ", kernelParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.kernelParams__val); } + if (data->args.hipExtModuleLaunchKernel.extra == NULL) oss << ", extra=NULL"; + else { oss << ", extra="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.extra__val); } + oss << ", startEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.startEvent); + oss << ", stopEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.stopEvent); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtModuleLaunchKernel.flags); + oss << ")"; + break; + case HIP_API_ID_hipExtStreamCreateWithCUMask: + oss << "hipExtStreamCreateWithCUMask("; + if (data->args.hipExtStreamCreateWithCUMask.stream == NULL) oss << "stream=NULL"; + else { oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamCreateWithCUMask.stream__val); } + oss << ", cuMaskSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamCreateWithCUMask.cuMaskSize); + if (data->args.hipExtStreamCreateWithCUMask.cuMask == NULL) oss << ", cuMask=NULL"; + else { oss << ", cuMask="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamCreateWithCUMask.cuMask__val); } + oss << ")"; + break; + case HIP_API_ID_hipExtStreamGetCUMask: + oss << "hipExtStreamGetCUMask("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamGetCUMask.stream); + oss << ", cuMaskSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamGetCUMask.cuMaskSize); + if (data->args.hipExtStreamGetCUMask.cuMask == NULL) oss << ", cuMask=NULL"; + else { oss << ", cuMask="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExtStreamGetCUMask.cuMask__val); } + oss << ")"; + break; + case HIP_API_ID_hipExternalMemoryGetMappedBuffer: + oss << "hipExternalMemoryGetMappedBuffer("; + if (data->args.hipExternalMemoryGetMappedBuffer.devPtr == NULL) oss << "devPtr=NULL"; + else { oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedBuffer.devPtr__val); } + oss << ", extMem="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedBuffer.extMem); + if (data->args.hipExternalMemoryGetMappedBuffer.bufferDesc == NULL) oss << ", bufferDesc=NULL"; + else { oss << ", bufferDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedBuffer.bufferDesc__val); } + oss << ")"; + break; + case HIP_API_ID_hipExternalMemoryGetMappedMipmappedArray: + oss << "hipExternalMemoryGetMappedMipmappedArray("; + if (data->args.hipExternalMemoryGetMappedMipmappedArray.mipmap == NULL) oss << "mipmap=NULL"; + else { oss << "mipmap="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedMipmappedArray.mipmap__val); } + oss << ", extMem="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedMipmappedArray.extMem); + if (data->args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc == NULL) oss << ", mipmapDesc=NULL"; + else { oss << ", mipmapDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipExternalMemoryGetMappedMipmappedArray.mipmapDesc__val); } + oss << ")"; + break; + case HIP_API_ID_hipFree: + oss << "hipFree("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFree.ptr); + oss << ")"; + break; + case HIP_API_ID_hipFreeArray: + oss << "hipFreeArray("; + oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFreeArray.array); + oss << ")"; + break; + case HIP_API_ID_hipFreeAsync: + oss << "hipFreeAsync("; + oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFreeAsync.dev_ptr); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFreeAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipFreeHost: + oss << "hipFreeHost("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFreeHost.ptr); + oss << ")"; + break; + case HIP_API_ID_hipFreeMipmappedArray: + oss << "hipFreeMipmappedArray("; + oss << "mipmappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFreeMipmappedArray.mipmappedArray); + oss << ")"; + break; + case HIP_API_ID_hipFuncGetAttribute: + oss << "hipFuncGetAttribute("; + if (data->args.hipFuncGetAttribute.value == NULL) oss << "value=NULL"; + else { oss << "value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncGetAttribute.value__val); } + oss << ", attrib="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncGetAttribute.attrib); + oss << ", hfunc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncGetAttribute.hfunc); + oss << ")"; + break; + case HIP_API_ID_hipFuncGetAttributes: + oss << "hipFuncGetAttributes("; + if (data->args.hipFuncGetAttributes.attr == NULL) oss << "attr=NULL"; + else { oss << "attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncGetAttributes.attr__val); } + oss << ", func="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncGetAttributes.func); + oss << ")"; + break; + case HIP_API_ID_hipFuncSetAttribute: + oss << "hipFuncSetAttribute("; + oss << "func="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetAttribute.func); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetAttribute.attr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetAttribute.value); + oss << ")"; + break; + case HIP_API_ID_hipFuncSetCacheConfig: + oss << "hipFuncSetCacheConfig("; + oss << "func="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetCacheConfig.func); + oss << ", config="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetCacheConfig.config); + oss << ")"; + break; + case HIP_API_ID_hipFuncSetSharedMemConfig: + oss << "hipFuncSetSharedMemConfig("; + oss << "func="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetSharedMemConfig.func); + oss << ", config="; roctracer::hip_support::detail::operator<<(oss, data->args.hipFuncSetSharedMemConfig.config); + oss << ")"; + break; + case HIP_API_ID_hipGLGetDevices: + oss << "hipGLGetDevices("; + if (data->args.hipGLGetDevices.pHipDeviceCount == NULL) oss << "pHipDeviceCount=NULL"; + else { oss << "pHipDeviceCount="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGLGetDevices.pHipDeviceCount__val); } + if (data->args.hipGLGetDevices.pHipDevices == NULL) oss << ", pHipDevices=NULL"; + else { oss << ", pHipDevices="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGLGetDevices.pHipDevices__val); } + oss << ", hipDeviceCount="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGLGetDevices.hipDeviceCount); + oss << ", deviceList="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGLGetDevices.deviceList); + oss << ")"; + break; + case HIP_API_ID_hipGetChannelDesc: + oss << "hipGetChannelDesc("; + if (data->args.hipGetChannelDesc.desc == NULL) oss << "desc=NULL"; + else { oss << "desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetChannelDesc.desc__val); } + oss << ", array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetChannelDesc.array); + oss << ")"; + break; + case HIP_API_ID_hipGetDevice: + oss << "hipGetDevice("; + if (data->args.hipGetDevice.deviceId == NULL) oss << "deviceId=NULL"; + else { oss << "deviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDevice.deviceId__val); } + oss << ")"; + break; + case HIP_API_ID_hipGetDeviceCount: + oss << "hipGetDeviceCount("; + if (data->args.hipGetDeviceCount.count == NULL) oss << "count=NULL"; + else { oss << "count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDeviceCount.count__val); } + oss << ")"; + break; + case HIP_API_ID_hipGetDeviceFlags: + oss << "hipGetDeviceFlags("; + if (data->args.hipGetDeviceFlags.flags == NULL) oss << "flags=NULL"; + else { oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDeviceFlags.flags__val); } + oss << ")"; + break; + case HIP_API_ID_hipGetDevicePropertiesR0000: + oss << "hipGetDevicePropertiesR0000("; + if (data->args.hipGetDevicePropertiesR0000.prop == NULL) oss << "prop=NULL"; + else { oss << "prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDevicePropertiesR0000.prop__val); } + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDevicePropertiesR0000.device); + oss << ")"; + break; + case HIP_API_ID_hipGetDevicePropertiesR0600: + oss << "hipGetDevicePropertiesR0600("; + if (data->args.hipGetDevicePropertiesR0600.prop == NULL) oss << "prop=NULL"; + else { oss << "prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDevicePropertiesR0600.prop__val); } + oss << ", deviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetDevicePropertiesR0600.deviceId); + oss << ")"; + break; + case HIP_API_ID_hipGetErrorString: + oss << "hipGetErrorString("; + oss << ")"; + break; + case HIP_API_ID_hipGetLastError: + oss << "hipGetLastError("; + oss << ")"; + break; + case HIP_API_ID_hipExtGetLastError: + oss << "hipExtGetLastError("; + oss << ")"; + break; + case HIP_API_ID_hipGetMipmappedArrayLevel: + oss << "hipGetMipmappedArrayLevel("; + if (data->args.hipGetMipmappedArrayLevel.levelArray == NULL) oss << "levelArray=NULL"; + else { oss << "levelArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetMipmappedArrayLevel.levelArray__val); } + oss << ", mipmappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetMipmappedArrayLevel.mipmappedArray); + oss << ", level="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetMipmappedArrayLevel.level); + oss << ")"; + break; + case HIP_API_ID_hipGetSymbolAddress: + oss << "hipGetSymbolAddress("; + if (data->args.hipGetSymbolAddress.devPtr == NULL) oss << "devPtr=NULL"; + else { oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetSymbolAddress.devPtr__val); } + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetSymbolAddress.symbol); + oss << ")"; + break; + case HIP_API_ID_hipGetSymbolSize: + oss << "hipGetSymbolSize("; + if (data->args.hipGetSymbolSize.size == NULL) oss << "size=NULL"; + else { oss << "size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetSymbolSize.size__val); } + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGetSymbolSize.symbol); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddChildGraphNode: + oss << "hipGraphAddChildGraphNode("; + if (data->args.hipGraphAddChildGraphNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddChildGraphNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddChildGraphNode.graph); + if (data->args.hipGraphAddChildGraphNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddChildGraphNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddChildGraphNode.numDependencies); + oss << ", childGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddChildGraphNode.childGraph); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddDependencies: + oss << "hipGraphAddDependencies("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddDependencies.graph); + if (data->args.hipGraphAddDependencies.from == NULL) oss << ", from=NULL"; + else { oss << ", from="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddDependencies.from__val); } + if (data->args.hipGraphAddDependencies.to == NULL) oss << ", to=NULL"; + else { oss << ", to="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddDependencies.to__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddDependencies.numDependencies); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddEmptyNode: + oss << "hipGraphAddEmptyNode("; + if (data->args.hipGraphAddEmptyNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEmptyNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEmptyNode.graph); + if (data->args.hipGraphAddEmptyNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEmptyNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEmptyNode.numDependencies); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddEventRecordNode: + oss << "hipGraphAddEventRecordNode("; + if (data->args.hipGraphAddEventRecordNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventRecordNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventRecordNode.graph); + if (data->args.hipGraphAddEventRecordNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventRecordNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventRecordNode.numDependencies); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventRecordNode.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddEventWaitNode: + oss << "hipGraphAddEventWaitNode("; + if (data->args.hipGraphAddEventWaitNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventWaitNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventWaitNode.graph); + if (data->args.hipGraphAddEventWaitNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventWaitNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventWaitNode.numDependencies); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddEventWaitNode.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddExternalSemaphoresSignalNode: + oss << "hipGraphAddExternalSemaphoresSignalNode("; + if (data->args.hipGraphAddExternalSemaphoresSignalNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresSignalNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresSignalNode.graph); + if (data->args.hipGraphAddExternalSemaphoresSignalNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresSignalNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresSignalNode.numDependencies); + if (data->args.hipGraphAddExternalSemaphoresSignalNode.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresSignalNode.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddExternalSemaphoresWaitNode: + oss << "hipGraphAddExternalSemaphoresWaitNode("; + if (data->args.hipGraphAddExternalSemaphoresWaitNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresWaitNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresWaitNode.graph); + if (data->args.hipGraphAddExternalSemaphoresWaitNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresWaitNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresWaitNode.numDependencies); + if (data->args.hipGraphAddExternalSemaphoresWaitNode.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddExternalSemaphoresWaitNode.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddHostNode: + oss << "hipGraphAddHostNode("; + if (data->args.hipGraphAddHostNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddHostNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddHostNode.graph); + if (data->args.hipGraphAddHostNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddHostNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddHostNode.numDependencies); + if (data->args.hipGraphAddHostNode.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddHostNode.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddKernelNode: + oss << "hipGraphAddKernelNode("; + if (data->args.hipGraphAddKernelNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddKernelNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddKernelNode.graph); + if (data->args.hipGraphAddKernelNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddKernelNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddKernelNode.numDependencies); + if (data->args.hipGraphAddKernelNode.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddKernelNode.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemAllocNode: + oss << "hipGraphAddMemAllocNode("; + if (data->args.hipGraphAddMemAllocNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemAllocNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemAllocNode.graph); + if (data->args.hipGraphAddMemAllocNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemAllocNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemAllocNode.numDependencies); + if (data->args.hipGraphAddMemAllocNode.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemAllocNode.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemFreeNode: + oss << "hipGraphAddMemFreeNode("; + if (data->args.hipGraphAddMemFreeNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemFreeNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemFreeNode.graph); + if (data->args.hipGraphAddMemFreeNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemFreeNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemFreeNode.numDependencies); + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemFreeNode.dev_ptr); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemcpyNode: + oss << "hipGraphAddMemcpyNode("; + if (data->args.hipGraphAddMemcpyNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode.graph); + if (data->args.hipGraphAddMemcpyNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode.numDependencies); + if (data->args.hipGraphAddMemcpyNode.pCopyParams == NULL) oss << ", pCopyParams=NULL"; + else { oss << ", pCopyParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode.pCopyParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemcpyNode1D: + oss << "hipGraphAddMemcpyNode1D("; + if (data->args.hipGraphAddMemcpyNode1D.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.graph); + if (data->args.hipGraphAddMemcpyNode1D.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.numDependencies); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.count); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNode1D.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemcpyNodeFromSymbol: + oss << "hipGraphAddMemcpyNodeFromSymbol("; + if (data->args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.graph); + if (data->args.hipGraphAddMemcpyNodeFromSymbol.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.numDependencies); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.dst); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.symbol); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeFromSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemcpyNodeToSymbol: + oss << "hipGraphAddMemcpyNodeToSymbol("; + if (data->args.hipGraphAddMemcpyNodeToSymbol.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.graph); + if (data->args.hipGraphAddMemcpyNodeToSymbol.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.numDependencies); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.symbol); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemcpyNodeToSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphAddMemsetNode: + oss << "hipGraphAddMemsetNode("; + if (data->args.hipGraphAddMemsetNode.pGraphNode == NULL) oss << "pGraphNode=NULL"; + else { oss << "pGraphNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemsetNode.pGraphNode__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemsetNode.graph); + if (data->args.hipGraphAddMemsetNode.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemsetNode.pDependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemsetNode.numDependencies); + if (data->args.hipGraphAddMemsetNode.pMemsetParams == NULL) oss << ", pMemsetParams=NULL"; + else { oss << ", pMemsetParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphAddMemsetNode.pMemsetParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphChildGraphNodeGetGraph: + oss << "hipGraphChildGraphNodeGetGraph("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphChildGraphNodeGetGraph.node); + if (data->args.hipGraphChildGraphNodeGetGraph.pGraph == NULL) oss << ", pGraph=NULL"; + else { oss << ", pGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphChildGraphNodeGetGraph.pGraph__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphClone: + oss << "hipGraphClone("; + if (data->args.hipGraphClone.pGraphClone == NULL) oss << "pGraphClone=NULL"; + else { oss << "pGraphClone="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphClone.pGraphClone__val); } + oss << ", originalGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphClone.originalGraph); + oss << ")"; + break; + case HIP_API_ID_hipGraphCreate: + oss << "hipGraphCreate("; + if (data->args.hipGraphCreate.pGraph == NULL) oss << "pGraph=NULL"; + else { oss << "pGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphCreate.pGraph__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphCreate.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphDebugDotPrint: + oss << "hipGraphDebugDotPrint("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphDebugDotPrint.graph); + if (data->args.hipGraphDebugDotPrint.path == NULL) oss << ", path=NULL"; + else { oss << ", path="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphDebugDotPrint.path__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphDebugDotPrint.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphDestroy: + oss << "hipGraphDestroy("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphDestroy.graph); + oss << ")"; + break; + case HIP_API_ID_hipGraphDestroyNode: + oss << "hipGraphDestroyNode("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphDestroyNode.node); + oss << ")"; + break; + case HIP_API_ID_hipGraphEventRecordNodeGetEvent: + oss << "hipGraphEventRecordNodeGetEvent("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventRecordNodeGetEvent.node); + if (data->args.hipGraphEventRecordNodeGetEvent.event_out == NULL) oss << ", event_out=NULL"; + else { oss << ", event_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventRecordNodeGetEvent.event_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphEventRecordNodeSetEvent: + oss << "hipGraphEventRecordNodeSetEvent("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventRecordNodeSetEvent.node); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventRecordNodeSetEvent.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphEventWaitNodeGetEvent: + oss << "hipGraphEventWaitNodeGetEvent("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventWaitNodeGetEvent.node); + if (data->args.hipGraphEventWaitNodeGetEvent.event_out == NULL) oss << ", event_out=NULL"; + else { oss << ", event_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventWaitNodeGetEvent.event_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphEventWaitNodeSetEvent: + oss << "hipGraphEventWaitNodeSetEvent("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventWaitNodeSetEvent.node); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphEventWaitNodeSetEvent.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecChildGraphNodeSetParams: + oss << "hipGraphExecChildGraphNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecChildGraphNodeSetParams.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecChildGraphNodeSetParams.node); + oss << ", childGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecChildGraphNodeSetParams.childGraph); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecDestroy: + oss << "hipGraphExecDestroy("; + oss << "graphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecDestroy.graphExec); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecEventRecordNodeSetEvent: + oss << "hipGraphExecEventRecordNodeSetEvent("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventRecordNodeSetEvent.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventRecordNodeSetEvent.hNode); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventRecordNodeSetEvent.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecEventWaitNodeSetEvent: + oss << "hipGraphExecEventWaitNodeSetEvent("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventWaitNodeSetEvent.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventWaitNodeSetEvent.hNode); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecEventWaitNodeSetEvent.event); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecExternalSemaphoresSignalNodeSetParams: + oss << "hipGraphExecExternalSemaphoresSignalNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.hNode); + if (data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresSignalNodeSetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecExternalSemaphoresWaitNodeSetParams: + oss << "hipGraphExecExternalSemaphoresWaitNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.hNode); + if (data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecExternalSemaphoresWaitNodeSetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecHostNodeSetParams: + oss << "hipGraphExecHostNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecHostNodeSetParams.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecHostNodeSetParams.node); + if (data->args.hipGraphExecHostNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecHostNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecKernelNodeSetParams: + oss << "hipGraphExecKernelNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecKernelNodeSetParams.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecKernelNodeSetParams.node); + if (data->args.hipGraphExecKernelNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecKernelNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams: + oss << "hipGraphExecMemcpyNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams.node); + if (data->args.hipGraphExecMemcpyNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParams1D: + oss << "hipGraphExecMemcpyNodeSetParams1D("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.node); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.count); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParams1D.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsFromSymbol: + oss << "hipGraphExecMemcpyNodeSetParamsFromSymbol("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.node); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.dst); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.symbol); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsFromSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecMemcpyNodeSetParamsToSymbol: + oss << "hipGraphExecMemcpyNodeSetParamsToSymbol("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.node); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.symbol); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemcpyNodeSetParamsToSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphExecMemsetNodeSetParams: + oss << "hipGraphExecMemsetNodeSetParams("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemsetNodeSetParams.hGraphExec); + oss << ", node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemsetNodeSetParams.node); + if (data->args.hipGraphExecMemsetNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecMemsetNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExecUpdate: + oss << "hipGraphExecUpdate("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecUpdate.hGraphExec); + oss << ", hGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecUpdate.hGraph); + if (data->args.hipGraphExecUpdate.hErrorNode_out == NULL) oss << ", hErrorNode_out=NULL"; + else { oss << ", hErrorNode_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecUpdate.hErrorNode_out__val); } + if (data->args.hipGraphExecUpdate.updateResult_out == NULL) oss << ", updateResult_out=NULL"; + else { oss << ", updateResult_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExecUpdate.updateResult_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeGetParams: + oss << "hipGraphExternalSemaphoresSignalNodeGetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresSignalNodeGetParams.hNode); + if (data->args.hipGraphExternalSemaphoresSignalNodeGetParams.params_out == NULL) oss << ", params_out=NULL"; + else { oss << ", params_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresSignalNodeGetParams.params_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExternalSemaphoresSignalNodeSetParams: + oss << "hipGraphExternalSemaphoresSignalNodeSetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresSignalNodeSetParams.hNode); + if (data->args.hipGraphExternalSemaphoresSignalNodeSetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresSignalNodeSetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeGetParams: + oss << "hipGraphExternalSemaphoresWaitNodeGetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresWaitNodeGetParams.hNode); + if (data->args.hipGraphExternalSemaphoresWaitNodeGetParams.params_out == NULL) oss << ", params_out=NULL"; + else { oss << ", params_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresWaitNodeGetParams.params_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphExternalSemaphoresWaitNodeSetParams: + oss << "hipGraphExternalSemaphoresWaitNodeSetParams("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresWaitNodeSetParams.hNode); + if (data->args.hipGraphExternalSemaphoresWaitNodeSetParams.nodeParams == NULL) oss << ", nodeParams=NULL"; + else { oss << ", nodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphExternalSemaphoresWaitNodeSetParams.nodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphGetEdges: + oss << "hipGraphGetEdges("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetEdges.graph); + if (data->args.hipGraphGetEdges.from == NULL) oss << ", from=NULL"; + else { oss << ", from="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetEdges.from__val); } + if (data->args.hipGraphGetEdges.to == NULL) oss << ", to=NULL"; + else { oss << ", to="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetEdges.to__val); } + if (data->args.hipGraphGetEdges.numEdges == NULL) oss << ", numEdges=NULL"; + else { oss << ", numEdges="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetEdges.numEdges__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphGetNodes: + oss << "hipGraphGetNodes("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetNodes.graph); + if (data->args.hipGraphGetNodes.nodes == NULL) oss << ", nodes=NULL"; + else { oss << ", nodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetNodes.nodes__val); } + if (data->args.hipGraphGetNodes.numNodes == NULL) oss << ", numNodes=NULL"; + else { oss << ", numNodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetNodes.numNodes__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphGetRootNodes: + oss << "hipGraphGetRootNodes("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetRootNodes.graph); + if (data->args.hipGraphGetRootNodes.pRootNodes == NULL) oss << ", pRootNodes=NULL"; + else { oss << ", pRootNodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetRootNodes.pRootNodes__val); } + if (data->args.hipGraphGetRootNodes.pNumRootNodes == NULL) oss << ", pNumRootNodes=NULL"; + else { oss << ", pNumRootNodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphGetRootNodes.pNumRootNodes__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphHostNodeGetParams: + oss << "hipGraphHostNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphHostNodeGetParams.node); + if (data->args.hipGraphHostNodeGetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphHostNodeGetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphHostNodeSetParams: + oss << "hipGraphHostNodeSetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphHostNodeSetParams.node); + if (data->args.hipGraphHostNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphHostNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphInstantiate: + oss << "hipGraphInstantiate("; + if (data->args.hipGraphInstantiate.pGraphExec == NULL) oss << "pGraphExec=NULL"; + else { oss << "pGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiate.pGraphExec__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiate.graph); + if (data->args.hipGraphInstantiate.pErrorNode == NULL) oss << ", pErrorNode=NULL"; + else { oss << ", pErrorNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiate.pErrorNode__val); } + if (data->args.hipGraphInstantiate.pLogBuffer == NULL) oss << ", pLogBuffer=NULL"; + else { oss << ", pLogBuffer="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiate.pLogBuffer__val); } + oss << ", bufferSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiate.bufferSize); + oss << ")"; + break; + case HIP_API_ID_hipGraphInstantiateWithFlags: + oss << "hipGraphInstantiateWithFlags("; + if (data->args.hipGraphInstantiateWithFlags.pGraphExec == NULL) oss << "pGraphExec=NULL"; + else { oss << "pGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiateWithFlags.pGraphExec__val); } + oss << ", graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiateWithFlags.graph); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphInstantiateWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphKernelNodeCopyAttributes: + oss << "hipGraphKernelNodeCopyAttributes("; + oss << "hSrc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeCopyAttributes.hSrc); + oss << ", hDst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeCopyAttributes.hDst); + oss << ")"; + break; + case HIP_API_ID_hipGraphKernelNodeGetAttribute: + oss << "hipGraphKernelNodeGetAttribute("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeGetAttribute.hNode); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeGetAttribute.attr); + if (data->args.hipGraphKernelNodeGetAttribute.value == NULL) oss << ", value=NULL"; + else { oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeGetAttribute.value__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphKernelNodeGetParams: + oss << "hipGraphKernelNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeGetParams.node); + if (data->args.hipGraphKernelNodeGetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeGetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphKernelNodeSetAttribute: + oss << "hipGraphKernelNodeSetAttribute("; + oss << "hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeSetAttribute.hNode); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeSetAttribute.attr); + if (data->args.hipGraphKernelNodeSetAttribute.value == NULL) oss << ", value=NULL"; + else { oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeSetAttribute.value__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphKernelNodeSetParams: + oss << "hipGraphKernelNodeSetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeSetParams.node); + if (data->args.hipGraphKernelNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphKernelNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphLaunch: + oss << "hipGraphLaunch("; + oss << "graphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphLaunch.graphExec); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphLaunch.stream); + oss << ")"; + break; + case HIP_API_ID_hipGraphMemAllocNodeGetParams: + oss << "hipGraphMemAllocNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemAllocNodeGetParams.node); + if (data->args.hipGraphMemAllocNodeGetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemAllocNodeGetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphMemFreeNodeGetParams: + oss << "hipGraphMemFreeNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemFreeNodeGetParams.node); + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemFreeNodeGetParams.dev_ptr); + oss << ")"; + break; + case HIP_API_ID_hipGraphMemcpyNodeGetParams: + oss << "hipGraphMemcpyNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeGetParams.node); + if (data->args.hipGraphMemcpyNodeGetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeGetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphMemcpyNodeSetParams: + oss << "hipGraphMemcpyNodeSetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams.node); + if (data->args.hipGraphMemcpyNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphMemcpyNodeSetParams1D: + oss << "hipGraphMemcpyNodeSetParams1D("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams1D.node); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams1D.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams1D.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams1D.count); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParams1D.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphMemcpyNodeSetParamsFromSymbol: + oss << "hipGraphMemcpyNodeSetParamsFromSymbol("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.node); + oss << ", dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.dst); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.symbol); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsFromSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphMemcpyNodeSetParamsToSymbol: + oss << "hipGraphMemcpyNodeSetParamsToSymbol("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.node); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.symbol); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.count); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemcpyNodeSetParamsToSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipGraphMemsetNodeGetParams: + oss << "hipGraphMemsetNodeGetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemsetNodeGetParams.node); + if (data->args.hipGraphMemsetNodeGetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemsetNodeGetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphMemsetNodeSetParams: + oss << "hipGraphMemsetNodeSetParams("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemsetNodeSetParams.node); + if (data->args.hipGraphMemsetNodeSetParams.pNodeParams == NULL) oss << ", pNodeParams=NULL"; + else { oss << ", pNodeParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphMemsetNodeSetParams.pNodeParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeFindInClone: + oss << "hipGraphNodeFindInClone("; + if (data->args.hipGraphNodeFindInClone.pNode == NULL) oss << "pNode=NULL"; + else { oss << "pNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeFindInClone.pNode__val); } + oss << ", originalNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeFindInClone.originalNode); + oss << ", clonedGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeFindInClone.clonedGraph); + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeGetDependencies: + oss << "hipGraphNodeGetDependencies("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependencies.node); + if (data->args.hipGraphNodeGetDependencies.pDependencies == NULL) oss << ", pDependencies=NULL"; + else { oss << ", pDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependencies.pDependencies__val); } + if (data->args.hipGraphNodeGetDependencies.pNumDependencies == NULL) oss << ", pNumDependencies=NULL"; + else { oss << ", pNumDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependencies.pNumDependencies__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeGetDependentNodes: + oss << "hipGraphNodeGetDependentNodes("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependentNodes.node); + if (data->args.hipGraphNodeGetDependentNodes.pDependentNodes == NULL) oss << ", pDependentNodes=NULL"; + else { oss << ", pDependentNodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependentNodes.pDependentNodes__val); } + if (data->args.hipGraphNodeGetDependentNodes.pNumDependentNodes == NULL) oss << ", pNumDependentNodes=NULL"; + else { oss << ", pNumDependentNodes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetDependentNodes.pNumDependentNodes__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeGetEnabled: + oss << "hipGraphNodeGetEnabled("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetEnabled.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetEnabled.hNode); + if (data->args.hipGraphNodeGetEnabled.isEnabled == NULL) oss << ", isEnabled=NULL"; + else { oss << ", isEnabled="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetEnabled.isEnabled__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeGetType: + oss << "hipGraphNodeGetType("; + oss << "node="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetType.node); + if (data->args.hipGraphNodeGetType.pType == NULL) oss << ", pType=NULL"; + else { oss << ", pType="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeGetType.pType__val); } + oss << ")"; + break; + case HIP_API_ID_hipGraphNodeSetEnabled: + oss << "hipGraphNodeSetEnabled("; + oss << "hGraphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeSetEnabled.hGraphExec); + oss << ", hNode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeSetEnabled.hNode); + oss << ", isEnabled="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphNodeSetEnabled.isEnabled); + oss << ")"; + break; + case HIP_API_ID_hipGraphReleaseUserObject: + oss << "hipGraphReleaseUserObject("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphReleaseUserObject.graph); + oss << ", object="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphReleaseUserObject.object); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphReleaseUserObject.count); + oss << ")"; + break; + case HIP_API_ID_hipGraphRemoveDependencies: + oss << "hipGraphRemoveDependencies("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRemoveDependencies.graph); + if (data->args.hipGraphRemoveDependencies.from == NULL) oss << ", from=NULL"; + else { oss << ", from="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRemoveDependencies.from__val); } + if (data->args.hipGraphRemoveDependencies.to == NULL) oss << ", to=NULL"; + else { oss << ", to="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRemoveDependencies.to__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRemoveDependencies.numDependencies); + oss << ")"; + break; + case HIP_API_ID_hipGraphRetainUserObject: + oss << "hipGraphRetainUserObject("; + oss << "graph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRetainUserObject.graph); + oss << ", object="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRetainUserObject.object); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRetainUserObject.count); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphRetainUserObject.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphUpload: + oss << "hipGraphUpload("; + oss << "graphExec="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphUpload.graphExec); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphUpload.stream); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsGLRegisterBuffer: + oss << "hipGraphicsGLRegisterBuffer("; + if (data->args.hipGraphicsGLRegisterBuffer.resource == NULL) oss << "resource=NULL"; + else { oss << "resource="; roctracer::hip_support::detail::operator<<(oss, (void*)data->args.hipGraphicsGLRegisterBuffer.resource__val); } + oss << ", buffer="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsGLRegisterBuffer.buffer); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsGLRegisterBuffer.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsGLRegisterImage: + oss << "hipGraphicsGLRegisterImage("; + if (data->args.hipGraphicsGLRegisterImage.resource == NULL) oss << "resource=NULL"; + else { oss << "resource="; roctracer::hip_support::detail::operator<<(oss, (void*)data->args.hipGraphicsGLRegisterImage.resource__val); } + oss << ", image="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsGLRegisterImage.image); + oss << ", target="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsGLRegisterImage.target); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsGLRegisterImage.flags); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsMapResources: + oss << "hipGraphicsMapResources("; + oss << "count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsMapResources.count); + if (data->args.hipGraphicsMapResources.resources == NULL) oss << ", resources=NULL"; + else { oss << ", resources="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsMapResources.resources__val); } + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsMapResources.stream); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsResourceGetMappedPointer: + oss << "hipGraphicsResourceGetMappedPointer("; + if (data->args.hipGraphicsResourceGetMappedPointer.devPtr == NULL) oss << "devPtr=NULL"; + else { oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsResourceGetMappedPointer.devPtr__val); } + if (data->args.hipGraphicsResourceGetMappedPointer.size == NULL) oss << ", size=NULL"; + else { oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsResourceGetMappedPointer.size__val); } + oss << ", resource="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsResourceGetMappedPointer.resource); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsSubResourceGetMappedArray: + oss << "hipGraphicsSubResourceGetMappedArray("; + if (data->args.hipGraphicsSubResourceGetMappedArray.array == NULL) oss << "array=NULL"; + else { oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsSubResourceGetMappedArray.array__val); } + oss << ", resource="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsSubResourceGetMappedArray.resource); + oss << ", arrayIndex="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsSubResourceGetMappedArray.arrayIndex); + oss << ", mipLevel="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsSubResourceGetMappedArray.mipLevel); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsUnmapResources: + oss << "hipGraphicsUnmapResources("; + oss << "count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsUnmapResources.count); + if (data->args.hipGraphicsUnmapResources.resources == NULL) oss << ", resources=NULL"; + else { oss << ", resources="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsUnmapResources.resources__val); } + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsUnmapResources.stream); + oss << ")"; + break; + case HIP_API_ID_hipGraphicsUnregisterResource: + oss << "hipGraphicsUnregisterResource("; + oss << "resource="; roctracer::hip_support::detail::operator<<(oss, data->args.hipGraphicsUnregisterResource.resource); + oss << ")"; + break; + case HIP_API_ID_hipHccModuleLaunchKernel: + oss << "hipHccModuleLaunchKernel("; + oss << "f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.f); + oss << ", globalWorkSizeX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.globalWorkSizeX); + oss << ", globalWorkSizeY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.globalWorkSizeY); + oss << ", globalWorkSizeZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.globalWorkSizeZ); + oss << ", blockDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.blockDimX); + oss << ", blockDimY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.blockDimY); + oss << ", blockDimZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.blockDimZ); + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.sharedMemBytes); + oss << ", hStream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.hStream); + if (data->args.hipHccModuleLaunchKernel.kernelParams == NULL) oss << ", kernelParams=NULL"; + else { oss << ", kernelParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.kernelParams__val); } + if (data->args.hipHccModuleLaunchKernel.extra == NULL) oss << ", extra=NULL"; + else { oss << ", extra="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.extra__val); } + oss << ", startEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.startEvent); + oss << ", stopEvent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHccModuleLaunchKernel.stopEvent); + oss << ")"; + break; + case HIP_API_ID_hipHostAlloc: + oss << "hipHostAlloc("; + if (data->args.hipHostAlloc.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostAlloc.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostAlloc.size); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostAlloc.flags); + oss << ")"; + break; + case HIP_API_ID_hipHostFree: + oss << "hipHostFree("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostFree.ptr); + oss << ")"; + break; + case HIP_API_ID_hipHostGetDevicePointer: + oss << "hipHostGetDevicePointer("; + if (data->args.hipHostGetDevicePointer.devPtr == NULL) oss << "devPtr=NULL"; + else { oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostGetDevicePointer.devPtr__val); } + oss << ", hstPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostGetDevicePointer.hstPtr); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostGetDevicePointer.flags); + oss << ")"; + break; + case HIP_API_ID_hipHostGetFlags: + oss << "hipHostGetFlags("; + if (data->args.hipHostGetFlags.flagsPtr == NULL) oss << "flagsPtr=NULL"; + else { oss << "flagsPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostGetFlags.flagsPtr__val); } + oss << ", hostPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostGetFlags.hostPtr); + oss << ")"; + break; + case HIP_API_ID_hipHostMalloc: + oss << "hipHostMalloc("; + if (data->args.hipHostMalloc.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostMalloc.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostMalloc.size); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostMalloc.flags); + oss << ")"; + break; + case HIP_API_ID_hipHostRegister: + oss << "hipHostRegister("; + oss << "hostPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostRegister.hostPtr); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostRegister.sizeBytes); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostRegister.flags); + oss << ")"; + break; + case HIP_API_ID_hipHostUnregister: + oss << "hipHostUnregister("; + oss << "hostPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipHostUnregister.hostPtr); + oss << ")"; + break; + case HIP_API_ID_hipImportExternalMemory: + oss << "hipImportExternalMemory("; + if (data->args.hipImportExternalMemory.extMem_out == NULL) oss << "extMem_out=NULL"; + else { oss << "extMem_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipImportExternalMemory.extMem_out__val); } + if (data->args.hipImportExternalMemory.memHandleDesc == NULL) oss << ", memHandleDesc=NULL"; + else { oss << ", memHandleDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipImportExternalMemory.memHandleDesc__val); } + oss << ")"; + break; + case HIP_API_ID_hipImportExternalSemaphore: + oss << "hipImportExternalSemaphore("; + if (data->args.hipImportExternalSemaphore.extSem_out == NULL) oss << "extSem_out=NULL"; + else { oss << "extSem_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipImportExternalSemaphore.extSem_out__val); } + if (data->args.hipImportExternalSemaphore.semHandleDesc == NULL) oss << ", semHandleDesc=NULL"; + else { oss << ", semHandleDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipImportExternalSemaphore.semHandleDesc__val); } + oss << ")"; + break; + case HIP_API_ID_hipInit: + oss << "hipInit("; + oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipInit.flags); + oss << ")"; + break; + case HIP_API_ID_hipIpcCloseMemHandle: + oss << "hipIpcCloseMemHandle("; + oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcCloseMemHandle.devPtr); + oss << ")"; + break; + case HIP_API_ID_hipIpcGetEventHandle: + oss << "hipIpcGetEventHandle("; + if (data->args.hipIpcGetEventHandle.handle == NULL) oss << "handle=NULL"; + else { oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcGetEventHandle.handle__val); } + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcGetEventHandle.event); + oss << ")"; + break; + case HIP_API_ID_hipIpcGetMemHandle: + oss << "hipIpcGetMemHandle("; + if (data->args.hipIpcGetMemHandle.handle == NULL) oss << "handle=NULL"; + else { oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcGetMemHandle.handle__val); } + oss << ", devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcGetMemHandle.devPtr); + oss << ")"; + break; + case HIP_API_ID_hipIpcOpenEventHandle: + oss << "hipIpcOpenEventHandle("; + if (data->args.hipIpcOpenEventHandle.event == NULL) oss << "event=NULL"; + else { oss << "event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcOpenEventHandle.event__val); } + oss << ", handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcOpenEventHandle.handle); + oss << ")"; + break; + case HIP_API_ID_hipIpcOpenMemHandle: + oss << "hipIpcOpenMemHandle("; + if (data->args.hipIpcOpenMemHandle.devPtr == NULL) oss << "devPtr=NULL"; + else { oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcOpenMemHandle.devPtr__val); } + oss << ", handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcOpenMemHandle.handle); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipIpcOpenMemHandle.flags); + oss << ")"; + break; + case HIP_API_ID_hipLaunchByPtr: + oss << "hipLaunchByPtr("; + oss << "hostFunction="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchByPtr.hostFunction); + oss << ")"; + break; + case HIP_API_ID_hipLaunchCooperativeKernel: + oss << "hipLaunchCooperativeKernel("; + oss << "f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.f); + oss << ", gridDim="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.gridDim); + oss << ", blockDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.blockDimX); + if (data->args.hipLaunchCooperativeKernel.kernelParams == NULL) oss << ", kernelParams=NULL"; + else { oss << ", kernelParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.kernelParams__val); } + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.sharedMemBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernel.stream); + oss << ")"; + break; + case HIP_API_ID_hipLaunchCooperativeKernelMultiDevice: + oss << "hipLaunchCooperativeKernelMultiDevice("; + if (data->args.hipLaunchCooperativeKernelMultiDevice.launchParamsList == NULL) oss << "launchParamsList=NULL"; + else { oss << "launchParamsList="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernelMultiDevice.launchParamsList__val); } + oss << ", numDevices="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernelMultiDevice.numDevices); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchCooperativeKernelMultiDevice.flags); + oss << ")"; + break; + case HIP_API_ID_hipLaunchHostFunc: + oss << "hipLaunchHostFunc("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchHostFunc.stream); + oss << ", fn="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchHostFunc.fn); + oss << ", userData="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchHostFunc.userData); + oss << ")"; + break; + case HIP_API_ID_hipLaunchKernel: + oss << "hipLaunchKernel("; + oss << "function_address="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.function_address); + oss << ", numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.numBlocks); + oss << ", dimBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.dimBlocks); + if (data->args.hipLaunchKernel.args == NULL) oss << ", args=NULL"; + else { oss << ", args="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.args__val); } + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.sharedMemBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipLaunchKernel.stream); + oss << ")"; + break; + case HIP_API_ID_hipMalloc: + oss << "hipMalloc("; + if (data->args.hipMalloc.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc.size); + oss << ")"; + break; + case HIP_API_ID_hipMalloc3D: + oss << "hipMalloc3D("; + if (data->args.hipMalloc3D.pitchedDevPtr == NULL) oss << "pitchedDevPtr=NULL"; + else { oss << "pitchedDevPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3D.pitchedDevPtr__val); } + oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3D.extent); + oss << ")"; + break; + case HIP_API_ID_hipMalloc3DArray: + oss << "hipMalloc3DArray("; + if (data->args.hipMalloc3DArray.array == NULL) oss << "array=NULL"; + else { oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3DArray.array__val); } + if (data->args.hipMalloc3DArray.desc == NULL) oss << ", desc=NULL"; + else { oss << ", desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3DArray.desc__val); } + oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3DArray.extent); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMalloc3DArray.flags); + oss << ")"; + break; + case HIP_API_ID_hipMallocArray: + oss << "hipMallocArray("; + if (data->args.hipMallocArray.array == NULL) oss << "array=NULL"; + else { oss << "array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocArray.array__val); } + if (data->args.hipMallocArray.desc == NULL) oss << ", desc=NULL"; + else { oss << ", desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocArray.desc__val); } + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocArray.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocArray.height); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocArray.flags); + oss << ")"; + break; + case HIP_API_ID_hipMallocAsync: + oss << "hipMallocAsync("; + if (data->args.hipMallocAsync.dev_ptr == NULL) oss << "dev_ptr=NULL"; + else { oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocAsync.dev_ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocAsync.size); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMallocFromPoolAsync: + oss << "hipMallocFromPoolAsync("; + if (data->args.hipMallocFromPoolAsync.dev_ptr == NULL) oss << "dev_ptr=NULL"; + else { oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocFromPoolAsync.dev_ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocFromPoolAsync.size); + oss << ", mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocFromPoolAsync.mem_pool); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocFromPoolAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMallocHost: + oss << "hipMallocHost("; + if (data->args.hipMallocHost.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocHost.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocHost.size); + oss << ")"; + break; + case HIP_API_ID_hipMallocManaged: + oss << "hipMallocManaged("; + if (data->args.hipMallocManaged.dev_ptr == NULL) oss << "dev_ptr=NULL"; + else { oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocManaged.dev_ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocManaged.size); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocManaged.flags); + oss << ")"; + break; + case HIP_API_ID_hipMallocMipmappedArray: + oss << "hipMallocMipmappedArray("; + if (data->args.hipMallocMipmappedArray.mipmappedArray == NULL) oss << "mipmappedArray=NULL"; + else { oss << "mipmappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocMipmappedArray.mipmappedArray__val); } + if (data->args.hipMallocMipmappedArray.desc == NULL) oss << ", desc=NULL"; + else { oss << ", desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocMipmappedArray.desc__val); } + oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocMipmappedArray.extent); + oss << ", numLevels="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocMipmappedArray.numLevels); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocMipmappedArray.flags); + oss << ")"; + break; + case HIP_API_ID_hipMallocPitch: + oss << "hipMallocPitch("; + if (data->args.hipMallocPitch.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocPitch.ptr__val); } + if (data->args.hipMallocPitch.pitch == NULL) oss << ", pitch=NULL"; + else { oss << ", pitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocPitch.pitch__val); } + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocPitch.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMallocPitch.height); + oss << ")"; + break; + case HIP_API_ID_hipMemAddressFree: + oss << "hipMemAddressFree("; + oss << "devPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressFree.devPtr); + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressFree.size); + oss << ")"; + break; + case HIP_API_ID_hipMemAddressReserve: + oss << "hipMemAddressReserve("; + if (data->args.hipMemAddressReserve.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressReserve.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressReserve.size); + oss << ", alignment="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressReserve.alignment); + oss << ", addr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressReserve.addr); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAddressReserve.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemAdvise: + oss << "hipMemAdvise("; + oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAdvise.dev_ptr); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAdvise.count); + oss << ", advice="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAdvise.advice); + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAdvise.device); + oss << ")"; + break; + case HIP_API_ID_hipMemAllocHost: + oss << "hipMemAllocHost("; + if (data->args.hipMemAllocHost.ptr == NULL) oss << "ptr=NULL"; + else { oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocHost.ptr__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocHost.size); + oss << ")"; + break; + case HIP_API_ID_hipMemAllocPitch: + oss << "hipMemAllocPitch("; + if (data->args.hipMemAllocPitch.dptr == NULL) oss << "dptr=NULL"; + else { oss << "dptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocPitch.dptr__val); } + if (data->args.hipMemAllocPitch.pitch == NULL) oss << ", pitch=NULL"; + else { oss << ", pitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocPitch.pitch__val); } + oss << ", widthInBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocPitch.widthInBytes); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocPitch.height); + oss << ", elementSizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemAllocPitch.elementSizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemCreate: + oss << "hipMemCreate("; + if (data->args.hipMemCreate.handle == NULL) oss << "handle=NULL"; + else { oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemCreate.handle__val); } + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemCreate.size); + if (data->args.hipMemCreate.prop == NULL) oss << ", prop=NULL"; + else { oss << ", prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemCreate.prop__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemCreate.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemExportToShareableHandle: + oss << "hipMemExportToShareableHandle("; + oss << "shareableHandle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemExportToShareableHandle.shareableHandle); + oss << ", handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemExportToShareableHandle.handle); + oss << ", handleType="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemExportToShareableHandle.handleType); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemExportToShareableHandle.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemGetAccess: + oss << "hipMemGetAccess("; + if (data->args.hipMemGetAccess.flags == NULL) oss << "flags=NULL"; + else { oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAccess.flags__val); } + if (data->args.hipMemGetAccess.location == NULL) oss << ", location=NULL"; + else { oss << ", location="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAccess.location__val); } + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAccess.ptr); + oss << ")"; + break; + case HIP_API_ID_hipMemGetAddressRange: + oss << "hipMemGetAddressRange("; + if (data->args.hipMemGetAddressRange.pbase == NULL) oss << "pbase=NULL"; + else { oss << "pbase="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAddressRange.pbase__val); } + if (data->args.hipMemGetAddressRange.psize == NULL) oss << ", psize=NULL"; + else { oss << ", psize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAddressRange.psize__val); } + oss << ", dptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAddressRange.dptr); + oss << ")"; + break; + case HIP_API_ID_hipMemGetAllocationGranularity: + oss << "hipMemGetAllocationGranularity("; + if (data->args.hipMemGetAllocationGranularity.granularity == NULL) oss << "granularity=NULL"; + else { oss << "granularity="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAllocationGranularity.granularity__val); } + if (data->args.hipMemGetAllocationGranularity.prop == NULL) oss << ", prop=NULL"; + else { oss << ", prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAllocationGranularity.prop__val); } + oss << ", option="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAllocationGranularity.option); + oss << ")"; + break; + case HIP_API_ID_hipMemGetAllocationPropertiesFromHandle: + oss << "hipMemGetAllocationPropertiesFromHandle("; + if (data->args.hipMemGetAllocationPropertiesFromHandle.prop == NULL) oss << "prop=NULL"; + else { oss << "prop="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAllocationPropertiesFromHandle.prop__val); } + oss << ", handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetAllocationPropertiesFromHandle.handle); + oss << ")"; + break; + case HIP_API_ID_hipMemGetInfo: + oss << "hipMemGetInfo("; + if (data->args.hipMemGetInfo.free == NULL) oss << "free=NULL"; + else { oss << "free="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetInfo.free__val); } + if (data->args.hipMemGetInfo.total == NULL) oss << ", total=NULL"; + else { oss << ", total="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemGetInfo.total__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemImportFromShareableHandle: + oss << "hipMemImportFromShareableHandle("; + if (data->args.hipMemImportFromShareableHandle.handle == NULL) oss << "handle=NULL"; + else { oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemImportFromShareableHandle.handle__val); } + oss << ", osHandle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemImportFromShareableHandle.osHandle); + oss << ", shHandleType="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemImportFromShareableHandle.shHandleType); + oss << ")"; + break; + case HIP_API_ID_hipMemMap: + oss << "hipMemMap("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMap.ptr); + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMap.size); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMap.offset); + oss << ", handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMap.handle); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMap.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemMapArrayAsync: + oss << "hipMemMapArrayAsync("; + if (data->args.hipMemMapArrayAsync.mapInfoList == NULL) oss << "mapInfoList=NULL"; + else { oss << "mapInfoList="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMapArrayAsync.mapInfoList__val); } + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMapArrayAsync.count); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemMapArrayAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolCreate: + oss << "hipMemPoolCreate("; + if (data->args.hipMemPoolCreate.mem_pool == NULL) oss << "mem_pool=NULL"; + else { oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolCreate.mem_pool__val); } + if (data->args.hipMemPoolCreate.pool_props == NULL) oss << ", pool_props=NULL"; + else { oss << ", pool_props="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolCreate.pool_props__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemPoolDestroy: + oss << "hipMemPoolDestroy("; + oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolDestroy.mem_pool); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolExportPointer: + oss << "hipMemPoolExportPointer("; + if (data->args.hipMemPoolExportPointer.export_data == NULL) oss << "export_data=NULL"; + else { oss << "export_data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportPointer.export_data__val); } + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportPointer.dev_ptr); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolExportToShareableHandle: + oss << "hipMemPoolExportToShareableHandle("; + oss << "shared_handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportToShareableHandle.shared_handle); + oss << ", mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportToShareableHandle.mem_pool); + oss << ", handle_type="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportToShareableHandle.handle_type); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolExportToShareableHandle.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolGetAccess: + oss << "hipMemPoolGetAccess("; + if (data->args.hipMemPoolGetAccess.flags == NULL) oss << "flags=NULL"; + else { oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAccess.flags__val); } + oss << ", mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAccess.mem_pool); + if (data->args.hipMemPoolGetAccess.location == NULL) oss << ", location=NULL"; + else { oss << ", location="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAccess.location__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemPoolGetAttribute: + oss << "hipMemPoolGetAttribute("; + oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAttribute.mem_pool); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAttribute.attr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolGetAttribute.value); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolImportFromShareableHandle: + oss << "hipMemPoolImportFromShareableHandle("; + if (data->args.hipMemPoolImportFromShareableHandle.mem_pool == NULL) oss << "mem_pool=NULL"; + else { oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportFromShareableHandle.mem_pool__val); } + oss << ", shared_handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportFromShareableHandle.shared_handle); + oss << ", handle_type="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportFromShareableHandle.handle_type); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportFromShareableHandle.flags); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolImportPointer: + oss << "hipMemPoolImportPointer("; + if (data->args.hipMemPoolImportPointer.dev_ptr == NULL) oss << "dev_ptr=NULL"; + else { oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportPointer.dev_ptr__val); } + oss << ", mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportPointer.mem_pool); + if (data->args.hipMemPoolImportPointer.export_data == NULL) oss << ", export_data=NULL"; + else { oss << ", export_data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolImportPointer.export_data__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemPoolSetAccess: + oss << "hipMemPoolSetAccess("; + oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAccess.mem_pool); + if (data->args.hipMemPoolSetAccess.desc_list == NULL) oss << ", desc_list=NULL"; + else { oss << ", desc_list="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAccess.desc_list__val); } + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAccess.count); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolSetAttribute: + oss << "hipMemPoolSetAttribute("; + oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAttribute.mem_pool); + oss << ", attr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAttribute.attr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolSetAttribute.value); + oss << ")"; + break; + case HIP_API_ID_hipMemPoolTrimTo: + oss << "hipMemPoolTrimTo("; + oss << "mem_pool="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolTrimTo.mem_pool); + oss << ", min_bytes_to_hold="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPoolTrimTo.min_bytes_to_hold); + oss << ")"; + break; + case HIP_API_ID_hipMemPrefetchAsync: + oss << "hipMemPrefetchAsync("; + oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPrefetchAsync.dev_ptr); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPrefetchAsync.count); + oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPrefetchAsync.device); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPrefetchAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemPtrGetInfo: + oss << "hipMemPtrGetInfo("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPtrGetInfo.ptr); + if (data->args.hipMemPtrGetInfo.size == NULL) oss << ", size=NULL"; + else { oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemPtrGetInfo.size__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemRangeGetAttribute: + oss << "hipMemRangeGetAttribute("; + oss << "data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttribute.data); + oss << ", data_size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttribute.data_size); + oss << ", attribute="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttribute.attribute); + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttribute.dev_ptr); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttribute.count); + oss << ")"; + break; + case HIP_API_ID_hipMemRangeGetAttributes: + oss << "hipMemRangeGetAttributes("; + if (data->args.hipMemRangeGetAttributes.data == NULL) oss << "data=NULL"; + else { oss << "data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.data__val); } + if (data->args.hipMemRangeGetAttributes.data_sizes == NULL) oss << ", data_sizes=NULL"; + else { oss << ", data_sizes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.data_sizes__val); } + if (data->args.hipMemRangeGetAttributes.attributes == NULL) oss << ", attributes=NULL"; + else { oss << ", attributes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.attributes__val); } + oss << ", num_attributes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.num_attributes); + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.dev_ptr); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRangeGetAttributes.count); + oss << ")"; + break; + case HIP_API_ID_hipMemRelease: + oss << "hipMemRelease("; + oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRelease.handle); + oss << ")"; + break; + case HIP_API_ID_hipMemRetainAllocationHandle: + oss << "hipMemRetainAllocationHandle("; + if (data->args.hipMemRetainAllocationHandle.handle == NULL) oss << "handle=NULL"; + else { oss << "handle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRetainAllocationHandle.handle__val); } + oss << ", addr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemRetainAllocationHandle.addr); + oss << ")"; + break; + case HIP_API_ID_hipMemSetAccess: + oss << "hipMemSetAccess("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemSetAccess.ptr); + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemSetAccess.size); + if (data->args.hipMemSetAccess.desc == NULL) oss << ", desc=NULL"; + else { oss << ", desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemSetAccess.desc__val); } + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemSetAccess.count); + oss << ")"; + break; + case HIP_API_ID_hipMemUnmap: + oss << "hipMemUnmap("; + oss << "ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemUnmap.ptr); + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemUnmap.size); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy: + oss << "hipMemcpy("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy.sizeBytes); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2D: + oss << "hipMemcpy2D("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.dst); + oss << ", dpitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.dpitch); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.src); + oss << ", spitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.spitch); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2D.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2DAsync: + oss << "hipMemcpy2DAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.dst); + oss << ", dpitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.dpitch); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.src); + oss << ", spitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.spitch); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2DFromArray: + oss << "hipMemcpy2DFromArray("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.dst); + oss << ", dpitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.dpitch); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.src); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.hOffset); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArray.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2DFromArrayAsync: + oss << "hipMemcpy2DFromArrayAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.dst); + oss << ", dpitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.dpitch); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.src); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.hOffset); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DFromArrayAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2DToArray: + oss << "hipMemcpy2DToArray("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.dst); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.hOffset); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.src); + oss << ", spitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.spitch); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArray.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy2DToArrayAsync: + oss << "hipMemcpy2DToArrayAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.dst); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.hOffset); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.src); + oss << ", spitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.spitch); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.height); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy2DToArrayAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpy3D: + oss << "hipMemcpy3D("; + if (data->args.hipMemcpy3D.p == NULL) oss << "p=NULL"; + else { oss << "p="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy3D.p__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemcpy3DAsync: + oss << "hipMemcpy3DAsync("; + if (data->args.hipMemcpy3DAsync.p == NULL) oss << "p=NULL"; + else { oss << "p="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy3DAsync.p__val); } + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpy3DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyAsync: + oss << "hipMemcpyAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAsync.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAsync.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAsync.sizeBytes); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyAtoH: + oss << "hipMemcpyAtoH("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAtoH.dst); + oss << ", srcArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAtoH.srcArray); + oss << ", srcOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAtoH.srcOffset); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyAtoH.count); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyDtoD: + oss << "hipMemcpyDtoD("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoD.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoD.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoD.sizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyDtoDAsync: + oss << "hipMemcpyDtoDAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoDAsync.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoDAsync.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoDAsync.sizeBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoDAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyDtoH: + oss << "hipMemcpyDtoH("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoH.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoH.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoH.sizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyDtoHAsync: + oss << "hipMemcpyDtoHAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoHAsync.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoHAsync.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoHAsync.sizeBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyDtoHAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyFromArray: + oss << "hipMemcpyFromArray("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.dst); + oss << ", srcArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.srcArray); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.hOffset); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.count); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromArray.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyFromSymbol: + oss << "hipMemcpyFromSymbol("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbol.dst); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbol.symbol); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbol.sizeBytes); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyFromSymbolAsync: + oss << "hipMemcpyFromSymbolAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.dst); + oss << ", symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.symbol); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.sizeBytes); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyFromSymbolAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyHtoA: + oss << "hipMemcpyHtoA("; + oss << "dstArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoA.dstArray); + oss << ", dstOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoA.dstOffset); + oss << ", srcHost="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoA.srcHost); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoA.count); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyHtoD: + oss << "hipMemcpyHtoD("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoD.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoD.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoD.sizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyHtoDAsync: + oss << "hipMemcpyHtoDAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoDAsync.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoDAsync.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoDAsync.sizeBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyHtoDAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyParam2D: + oss << "hipMemcpyParam2D("; + if (data->args.hipMemcpyParam2D.pCopy == NULL) oss << "pCopy=NULL"; + else { oss << "pCopy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyParam2D.pCopy__val); } + oss << ")"; + break; + case HIP_API_ID_hipMemcpyParam2DAsync: + oss << "hipMemcpyParam2DAsync("; + if (data->args.hipMemcpyParam2DAsync.pCopy == NULL) oss << "pCopy=NULL"; + else { oss << "pCopy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyParam2DAsync.pCopy__val); } + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyParam2DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyPeer: + oss << "hipMemcpyPeer("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeer.dst); + oss << ", dstDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeer.dstDeviceId); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeer.src); + oss << ", srcDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeer.srcDeviceId); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeer.sizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyPeerAsync: + oss << "hipMemcpyPeerAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.dst); + oss << ", dstDeviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.dstDeviceId); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.src); + oss << ", srcDevice="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.srcDevice); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.sizeBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyPeerAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyToArray: + oss << "hipMemcpyToArray("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.dst); + oss << ", wOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.wOffset); + oss << ", hOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.hOffset); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.src); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.count); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToArray.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyToSymbol: + oss << "hipMemcpyToSymbol("; + oss << "symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbol.symbol); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbol.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbol.sizeBytes); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbol.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbol.kind); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyToSymbolAsync: + oss << "hipMemcpyToSymbolAsync("; + oss << "symbol="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.symbol); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.sizeBytes); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.offset); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyToSymbolAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemcpyWithStream: + oss << "hipMemcpyWithStream("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyWithStream.dst); + oss << ", src="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyWithStream.src); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyWithStream.sizeBytes); + oss << ", kind="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyWithStream.kind); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemcpyWithStream.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemset: + oss << "hipMemset("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset.dst); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset.value); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset.sizeBytes); + oss << ")"; + break; + case HIP_API_ID_hipMemset2D: + oss << "hipMemset2D("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2D.dst); + oss << ", pitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2D.pitch); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2D.value); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2D.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2D.height); + oss << ")"; + break; + case HIP_API_ID_hipMemset2DAsync: + oss << "hipMemset2DAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.dst); + oss << ", pitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.pitch); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.value); + oss << ", width="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.width); + oss << ", height="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.height); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset2DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemset3D: + oss << "hipMemset3D("; + oss << "pitchedDevPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3D.pitchedDevPtr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3D.value); + oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3D.extent); + oss << ")"; + break; + case HIP_API_ID_hipMemset3DAsync: + oss << "hipMemset3DAsync("; + oss << "pitchedDevPtr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3DAsync.pitchedDevPtr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3DAsync.value); + oss << ", extent="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3DAsync.extent); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemset3DAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemsetAsync: + oss << "hipMemsetAsync("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetAsync.dst); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetAsync.value); + oss << ", sizeBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetAsync.sizeBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD16: + oss << "hipMemsetD16("; + oss << "dest="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16.dest); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16.count); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD16Async: + oss << "hipMemsetD16Async("; + oss << "dest="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16Async.dest); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16Async.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16Async.count); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD16Async.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD32: + oss << "hipMemsetD32("; + oss << "dest="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32.dest); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32.count); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD32Async: + oss << "hipMemsetD32Async("; + oss << "dst="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32Async.dst); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32Async.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32Async.count); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD32Async.stream); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD8: + oss << "hipMemsetD8("; + oss << "dest="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8.dest); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8.count); + oss << ")"; + break; + case HIP_API_ID_hipMemsetD8Async: + oss << "hipMemsetD8Async("; + oss << "dest="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8Async.dest); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8Async.value); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8Async.count); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMemsetD8Async.stream); + oss << ")"; + break; + case HIP_API_ID_hipMipmappedArrayCreate: + oss << "hipMipmappedArrayCreate("; + if (data->args.hipMipmappedArrayCreate.pHandle == NULL) oss << "pHandle=NULL"; + else { oss << "pHandle="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayCreate.pHandle__val); } + if (data->args.hipMipmappedArrayCreate.pMipmappedArrayDesc == NULL) oss << ", pMipmappedArrayDesc=NULL"; + else { oss << ", pMipmappedArrayDesc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayCreate.pMipmappedArrayDesc__val); } + oss << ", numMipmapLevels="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayCreate.numMipmapLevels); + oss << ")"; + break; + case HIP_API_ID_hipMipmappedArrayDestroy: + oss << "hipMipmappedArrayDestroy("; + oss << "hMipmappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayDestroy.hMipmappedArray); + oss << ")"; + break; + case HIP_API_ID_hipMipmappedArrayGetLevel: + oss << "hipMipmappedArrayGetLevel("; + if (data->args.hipMipmappedArrayGetLevel.pLevelArray == NULL) oss << "pLevelArray=NULL"; + else { oss << "pLevelArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayGetLevel.pLevelArray__val); } + oss << ", hMipMappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayGetLevel.hMipMappedArray); + oss << ", level="; roctracer::hip_support::detail::operator<<(oss, data->args.hipMipmappedArrayGetLevel.level); + oss << ")"; + break; + case HIP_API_ID_hipModuleGetFunction: + oss << "hipModuleGetFunction("; + if (data->args.hipModuleGetFunction.function == NULL) oss << "function=NULL"; + else { oss << "function="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetFunction.function__val); } + oss << ", module="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetFunction.module); + if (data->args.hipModuleGetFunction.kname == NULL) oss << ", kname=NULL"; + else { oss << ", kname="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetFunction.kname__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleGetGlobal: + oss << "hipModuleGetGlobal("; + if (data->args.hipModuleGetGlobal.dptr == NULL) oss << "dptr=NULL"; + else { oss << "dptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetGlobal.dptr__val); } + if (data->args.hipModuleGetGlobal.bytes == NULL) oss << ", bytes=NULL"; + else { oss << ", bytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetGlobal.bytes__val); } + oss << ", hmod="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetGlobal.hmod); + if (data->args.hipModuleGetGlobal.name == NULL) oss << ", name=NULL"; + else { oss << ", name="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetGlobal.name__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleGetTexRef: + oss << "hipModuleGetTexRef("; + if (data->args.hipModuleGetTexRef.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, (void*)data->args.hipModuleGetTexRef.texRef__val); } + oss << ", hmod="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetTexRef.hmod); + if (data->args.hipModuleGetTexRef.name == NULL) oss << ", name=NULL"; + else { oss << ", name="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleGetTexRef.name__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleLaunchCooperativeKernel: + oss << "hipModuleLaunchCooperativeKernel("; + oss << "f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.f); + oss << ", gridDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.gridDimX); + oss << ", gridDimY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.gridDimY); + oss << ", gridDimZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.gridDimZ); + oss << ", blockDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.blockDimX); + oss << ", blockDimY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.blockDimY); + oss << ", blockDimZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.blockDimZ); + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.sharedMemBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.stream); + if (data->args.hipModuleLaunchCooperativeKernel.kernelParams == NULL) oss << ", kernelParams=NULL"; + else { oss << ", kernelParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernel.kernelParams__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleLaunchCooperativeKernelMultiDevice: + oss << "hipModuleLaunchCooperativeKernelMultiDevice("; + if (data->args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList == NULL) oss << "launchParamsList=NULL"; + else { oss << "launchParamsList="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernelMultiDevice.launchParamsList__val); } + oss << ", numDevices="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernelMultiDevice.numDevices); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchCooperativeKernelMultiDevice.flags); + oss << ")"; + break; + case HIP_API_ID_hipModuleLaunchKernel: + oss << "hipModuleLaunchKernel("; + oss << "f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.f); + oss << ", gridDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.gridDimX); + oss << ", gridDimY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.gridDimY); + oss << ", gridDimZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.gridDimZ); + oss << ", blockDimX="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.blockDimX); + oss << ", blockDimY="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.blockDimY); + oss << ", blockDimZ="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.blockDimZ); + oss << ", sharedMemBytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.sharedMemBytes); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.stream); + if (data->args.hipModuleLaunchKernel.kernelParams == NULL) oss << ", kernelParams=NULL"; + else { oss << ", kernelParams="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.kernelParams__val); } + if (data->args.hipModuleLaunchKernel.extra == NULL) oss << ", extra=NULL"; + else { oss << ", extra="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLaunchKernel.extra__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleLoad: + oss << "hipModuleLoad("; + if (data->args.hipModuleLoad.module == NULL) oss << "module=NULL"; + else { oss << "module="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoad.module__val); } + if (data->args.hipModuleLoad.fname == NULL) oss << ", fname=NULL"; + else { oss << ", fname="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoad.fname__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleLoadData: + oss << "hipModuleLoadData("; + if (data->args.hipModuleLoadData.module == NULL) oss << "module=NULL"; + else { oss << "module="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadData.module__val); } + oss << ", image="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadData.image); + oss << ")"; + break; + case HIP_API_ID_hipModuleLoadDataEx: + oss << "hipModuleLoadDataEx("; + if (data->args.hipModuleLoadDataEx.module == NULL) oss << "module=NULL"; + else { oss << "module="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadDataEx.module__val); } + oss << ", image="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadDataEx.image); + oss << ", numOptions="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadDataEx.numOptions); + if (data->args.hipModuleLoadDataEx.options == NULL) oss << ", options=NULL"; + else { oss << ", options="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadDataEx.options__val); } + if (data->args.hipModuleLoadDataEx.optionsValues == NULL) oss << ", optionsValues=NULL"; + else { oss << ", optionsValues="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleLoadDataEx.optionsValues__val); } + oss << ")"; + break; + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessor: + oss << "hipModuleOccupancyMaxActiveBlocksPerMultiprocessor("; + if (data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks == NULL) oss << "numBlocks=NULL"; + else { oss << "numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.f); + oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.blockSize); + oss << ", dynSharedMemPerBlk="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessor.dynSharedMemPerBlk); + oss << ")"; + break; + case HIP_API_ID_hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: + oss << "hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags("; + if (data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks == NULL) oss << "numBlocks=NULL"; + else { oss << "numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.f); + oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.blockSize); + oss << ", dynSharedMemPerBlk="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.dynSharedMemPerBlk); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSize: + oss << "hipModuleOccupancyMaxPotentialBlockSize("; + if (data->args.hipModuleOccupancyMaxPotentialBlockSize.gridSize == NULL) oss << "gridSize=NULL"; + else { oss << "gridSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSize.gridSize__val); } + if (data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSize == NULL) oss << ", blockSize=NULL"; + else { oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSize__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSize.f); + oss << ", dynSharedMemPerBlk="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSize.dynSharedMemPerBlk); + oss << ", blockSizeLimit="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSize.blockSizeLimit); + oss << ")"; + break; + case HIP_API_ID_hipModuleOccupancyMaxPotentialBlockSizeWithFlags: + oss << "hipModuleOccupancyMaxPotentialBlockSizeWithFlags("; + if (data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize == NULL) oss << "gridSize=NULL"; + else { oss << "gridSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.gridSize__val); } + if (data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize == NULL) oss << ", blockSize=NULL"; + else { oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSize__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.f); + oss << ", dynSharedMemPerBlk="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.dynSharedMemPerBlk); + oss << ", blockSizeLimit="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.blockSizeLimit); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleOccupancyMaxPotentialBlockSizeWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipModuleUnload: + oss << "hipModuleUnload("; + oss << "module="; roctracer::hip_support::detail::operator<<(oss, data->args.hipModuleUnload.module); + oss << ")"; + break; + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessor: + oss << "hipOccupancyMaxActiveBlocksPerMultiprocessor("; + if (data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks == NULL) oss << "numBlocks=NULL"; + else { oss << "numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.numBlocks__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.f); + oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.blockSize); + oss << ", dynamicSMemSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessor.dynamicSMemSize); + oss << ")"; + break; + case HIP_API_ID_hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags: + oss << "hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags("; + if (data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks == NULL) oss << "numBlocks=NULL"; + else { oss << "numBlocks="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.numBlocks__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.f); + oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.blockSize); + oss << ", dynamicSMemSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.dynamicSMemSize); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxActiveBlocksPerMultiprocessorWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipOccupancyMaxPotentialBlockSize: + oss << "hipOccupancyMaxPotentialBlockSize("; + if (data->args.hipOccupancyMaxPotentialBlockSize.gridSize == NULL) oss << "gridSize=NULL"; + else { oss << "gridSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxPotentialBlockSize.gridSize__val); } + if (data->args.hipOccupancyMaxPotentialBlockSize.blockSize == NULL) oss << ", blockSize=NULL"; + else { oss << ", blockSize="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxPotentialBlockSize.blockSize__val); } + oss << ", f="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxPotentialBlockSize.f); + oss << ", dynSharedMemPerBlk="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxPotentialBlockSize.dynSharedMemPerBlk); + oss << ", blockSizeLimit="; roctracer::hip_support::detail::operator<<(oss, data->args.hipOccupancyMaxPotentialBlockSize.blockSizeLimit); + oss << ")"; + break; + case HIP_API_ID_hipPeekAtLastError: + oss << "hipPeekAtLastError("; + oss << ")"; + break; + case HIP_API_ID_hipPointerGetAttribute: + oss << "hipPointerGetAttribute("; + oss << "data="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerGetAttribute.data); + oss << ", attribute="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerGetAttribute.attribute); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerGetAttribute.ptr); + oss << ")"; + break; + case HIP_API_ID_hipPointerGetAttributes: + oss << "hipPointerGetAttributes("; + if (data->args.hipPointerGetAttributes.attributes == NULL) oss << "attributes=NULL"; + else { oss << "attributes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerGetAttributes.attributes__val); } + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerGetAttributes.ptr); + oss << ")"; + break; + case HIP_API_ID_hipPointerSetAttribute: + oss << "hipPointerSetAttribute("; + oss << "value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerSetAttribute.value); + oss << ", attribute="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerSetAttribute.attribute); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipPointerSetAttribute.ptr); + oss << ")"; + break; + case HIP_API_ID_hipProfilerStart: + oss << "hipProfilerStart("; + oss << ")"; + break; + case HIP_API_ID_hipProfilerStop: + oss << "hipProfilerStop("; + oss << ")"; + break; + case HIP_API_ID_hipRuntimeGetVersion: + oss << "hipRuntimeGetVersion("; + if (data->args.hipRuntimeGetVersion.runtimeVersion == NULL) oss << "runtimeVersion=NULL"; + else { oss << "runtimeVersion="; roctracer::hip_support::detail::operator<<(oss, data->args.hipRuntimeGetVersion.runtimeVersion__val); } + oss << ")"; + break; + case HIP_API_ID_hipSetDevice: + oss << "hipSetDevice("; + oss << "deviceId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSetDevice.deviceId); + oss << ")"; + break; + case HIP_API_ID_hipSetDeviceFlags: + oss << "hipSetDeviceFlags("; + oss << "flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSetDeviceFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipSetupArgument: + oss << "hipSetupArgument("; + oss << "arg="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSetupArgument.arg); + oss << ", size="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSetupArgument.size); + oss << ", offset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSetupArgument.offset); + oss << ")"; + break; + case HIP_API_ID_hipSignalExternalSemaphoresAsync: + oss << "hipSignalExternalSemaphoresAsync("; + if (data->args.hipSignalExternalSemaphoresAsync.extSemArray == NULL) oss << "extSemArray=NULL"; + else { oss << "extSemArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSignalExternalSemaphoresAsync.extSemArray__val); } + if (data->args.hipSignalExternalSemaphoresAsync.paramsArray == NULL) oss << ", paramsArray=NULL"; + else { oss << ", paramsArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSignalExternalSemaphoresAsync.paramsArray__val); } + oss << ", numExtSems="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSignalExternalSemaphoresAsync.numExtSems); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipSignalExternalSemaphoresAsync.stream); + oss << ")"; + break; + case HIP_API_ID_hipStreamAddCallback: + oss << "hipStreamAddCallback("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAddCallback.stream); + oss << ", callback="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAddCallback.callback); + oss << ", userData="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAddCallback.userData); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAddCallback.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamAttachMemAsync: + oss << "hipStreamAttachMemAsync("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAttachMemAsync.stream); + oss << ", dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAttachMemAsync.dev_ptr); + oss << ", length="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAttachMemAsync.length); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamAttachMemAsync.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamBeginCapture: + oss << "hipStreamBeginCapture("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamBeginCapture.stream); + oss << ", mode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamBeginCapture.mode); + oss << ")"; + break; + case HIP_API_ID_hipStreamCreate: + oss << "hipStreamCreate("; + if (data->args.hipStreamCreate.stream == NULL) oss << "stream=NULL"; + else { oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreate.stream__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamCreateWithFlags: + oss << "hipStreamCreateWithFlags("; + if (data->args.hipStreamCreateWithFlags.stream == NULL) oss << "stream=NULL"; + else { oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreateWithFlags.stream__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreateWithFlags.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamCreateWithPriority: + oss << "hipStreamCreateWithPriority("; + if (data->args.hipStreamCreateWithPriority.stream == NULL) oss << "stream=NULL"; + else { oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreateWithPriority.stream__val); } + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreateWithPriority.flags); + oss << ", priority="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamCreateWithPriority.priority); + oss << ")"; + break; + case HIP_API_ID_hipStreamDestroy: + oss << "hipStreamDestroy("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamDestroy.stream); + oss << ")"; + break; + case HIP_API_ID_hipStreamEndCapture: + oss << "hipStreamEndCapture("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamEndCapture.stream); + if (data->args.hipStreamEndCapture.pGraph == NULL) oss << ", pGraph=NULL"; + else { oss << ", pGraph="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamEndCapture.pGraph__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamGetCaptureInfo: + oss << "hipStreamGetCaptureInfo("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo.stream); + if (data->args.hipStreamGetCaptureInfo.pCaptureStatus == NULL) oss << ", pCaptureStatus=NULL"; + else { oss << ", pCaptureStatus="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo.pCaptureStatus__val); } + if (data->args.hipStreamGetCaptureInfo.pId == NULL) oss << ", pId=NULL"; + else { oss << ", pId="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo.pId__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamGetCaptureInfo_v2: + oss << "hipStreamGetCaptureInfo_v2("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo_v2.stream); + if (data->args.hipStreamGetCaptureInfo_v2.captureStatus_out == NULL) oss << ", captureStatus_out=NULL"; + else { oss << ", captureStatus_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo_v2.captureStatus_out__val); } + if (data->args.hipStreamGetCaptureInfo_v2.id_out == NULL) oss << ", id_out=NULL"; + else { oss << ", id_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo_v2.id_out__val); } + if (data->args.hipStreamGetCaptureInfo_v2.graph_out == NULL) oss << ", graph_out=NULL"; + else { oss << ", graph_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo_v2.graph_out__val); } + if (data->args.hipStreamGetCaptureInfo_v2.dependencies_out == NULL) oss << ", dependencies_out=NULL"; + else { oss << ", dependencies_out="; roctracer::hip_support::detail::operator<<(oss, (void*)data->args.hipStreamGetCaptureInfo_v2.dependencies_out__val); } + if (data->args.hipStreamGetCaptureInfo_v2.numDependencies_out == NULL) oss << ", numDependencies_out=NULL"; + else { oss << ", numDependencies_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetCaptureInfo_v2.numDependencies_out__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamGetDevice: + oss << "hipStreamGetDevice("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetDevice.stream); + if (data->args.hipStreamGetDevice.device == NULL) oss << ", device=NULL"; + else { oss << ", device="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetDevice.device__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamGetFlags: + oss << "hipStreamGetFlags("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetFlags.stream); + if (data->args.hipStreamGetFlags.flags == NULL) oss << ", flags=NULL"; + else { oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetFlags.flags__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamGetPriority: + oss << "hipStreamGetPriority("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetPriority.stream); + if (data->args.hipStreamGetPriority.priority == NULL) oss << ", priority=NULL"; + else { oss << ", priority="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamGetPriority.priority__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamIsCapturing: + oss << "hipStreamIsCapturing("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamIsCapturing.stream); + if (data->args.hipStreamIsCapturing.pCaptureStatus == NULL) oss << ", pCaptureStatus=NULL"; + else { oss << ", pCaptureStatus="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamIsCapturing.pCaptureStatus__val); } + oss << ")"; + break; + case HIP_API_ID_hipStreamQuery: + oss << "hipStreamQuery("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamQuery.stream); + oss << ")"; + break; + case HIP_API_ID_hipStreamSynchronize: + oss << "hipStreamSynchronize("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamSynchronize.stream); + oss << ")"; + break; + case HIP_API_ID_hipStreamUpdateCaptureDependencies: + oss << "hipStreamUpdateCaptureDependencies("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamUpdateCaptureDependencies.stream); + if (data->args.hipStreamUpdateCaptureDependencies.dependencies == NULL) oss << ", dependencies=NULL"; + else { oss << ", dependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamUpdateCaptureDependencies.dependencies__val); } + oss << ", numDependencies="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamUpdateCaptureDependencies.numDependencies); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamUpdateCaptureDependencies.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamWaitEvent: + oss << "hipStreamWaitEvent("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitEvent.stream); + oss << ", event="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitEvent.event); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitEvent.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamWaitValue32: + oss << "hipStreamWaitValue32("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue32.stream); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue32.ptr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue32.value); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue32.flags); + oss << ", mask="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue32.mask); + oss << ")"; + break; + case HIP_API_ID_hipStreamWaitValue64: + oss << "hipStreamWaitValue64("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue64.stream); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue64.ptr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue64.value); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue64.flags); + oss << ", mask="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWaitValue64.mask); + oss << ")"; + break; + case HIP_API_ID_hipStreamWriteValue32: + oss << "hipStreamWriteValue32("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue32.stream); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue32.ptr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue32.value); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue32.flags); + oss << ")"; + break; + case HIP_API_ID_hipStreamWriteValue64: + oss << "hipStreamWriteValue64("; + oss << "stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue64.stream); + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue64.ptr); + oss << ", value="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue64.value); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipStreamWriteValue64.flags); + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetAddress: + oss << "hipTexRefGetAddress("; + if (data->args.hipTexRefGetAddress.dev_ptr == NULL) oss << "dev_ptr=NULL"; + else { oss << "dev_ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetAddress.dev_ptr__val); } + if (data->args.hipTexRefGetAddress.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetAddress.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetFlags: + oss << "hipTexRefGetFlags("; + if (data->args.hipTexRefGetFlags.pFlags == NULL) oss << "pFlags=NULL"; + else { oss << "pFlags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetFlags.pFlags__val); } + if (data->args.hipTexRefGetFlags.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetFlags.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetFormat: + oss << "hipTexRefGetFormat("; + if (data->args.hipTexRefGetFormat.pFormat == NULL) oss << "pFormat=NULL"; + else { oss << "pFormat="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetFormat.pFormat__val); } + if (data->args.hipTexRefGetFormat.pNumChannels == NULL) oss << ", pNumChannels=NULL"; + else { oss << ", pNumChannels="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetFormat.pNumChannels__val); } + if (data->args.hipTexRefGetFormat.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetFormat.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetMaxAnisotropy: + oss << "hipTexRefGetMaxAnisotropy("; + if (data->args.hipTexRefGetMaxAnisotropy.pmaxAnsio == NULL) oss << "pmaxAnsio=NULL"; + else { oss << "pmaxAnsio="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMaxAnisotropy.pmaxAnsio__val); } + if (data->args.hipTexRefGetMaxAnisotropy.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMaxAnisotropy.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetMipMappedArray: + oss << "hipTexRefGetMipMappedArray("; + if (data->args.hipTexRefGetMipMappedArray.pArray == NULL) oss << "pArray=NULL"; + else { oss << "pArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipMappedArray.pArray__val); } + if (data->args.hipTexRefGetMipMappedArray.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipMappedArray.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetMipmapLevelBias: + oss << "hipTexRefGetMipmapLevelBias("; + if (data->args.hipTexRefGetMipmapLevelBias.pbias == NULL) oss << "pbias=NULL"; + else { oss << "pbias="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipmapLevelBias.pbias__val); } + if (data->args.hipTexRefGetMipmapLevelBias.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipmapLevelBias.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefGetMipmapLevelClamp: + oss << "hipTexRefGetMipmapLevelClamp("; + if (data->args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp == NULL) oss << "pminMipmapLevelClamp=NULL"; + else { oss << "pminMipmapLevelClamp="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipmapLevelClamp.pminMipmapLevelClamp__val); } + if (data->args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp == NULL) oss << ", pmaxMipmapLevelClamp=NULL"; + else { oss << ", pmaxMipmapLevelClamp="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipmapLevelClamp.pmaxMipmapLevelClamp__val); } + if (data->args.hipTexRefGetMipmapLevelClamp.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefGetMipmapLevelClamp.texRef__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetAddress: + oss << "hipTexRefSetAddress("; + if (data->args.hipTexRefSetAddress.ByteOffset == NULL) oss << "ByteOffset=NULL"; + else { oss << "ByteOffset="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress.ByteOffset__val); } + if (data->args.hipTexRefSetAddress.texRef == NULL) oss << ", texRef=NULL"; + else { oss << ", texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress.texRef__val); } + oss << ", dptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress.dptr); + oss << ", bytes="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress.bytes); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetAddress2D: + oss << "hipTexRefSetAddress2D("; + if (data->args.hipTexRefSetAddress2D.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress2D.texRef__val); } + if (data->args.hipTexRefSetAddress2D.desc == NULL) oss << ", desc=NULL"; + else { oss << ", desc="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress2D.desc__val); } + oss << ", dptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress2D.dptr); + oss << ", Pitch="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetAddress2D.Pitch); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetArray: + oss << "hipTexRefSetArray("; + if (data->args.hipTexRefSetArray.tex == NULL) oss << "tex=NULL"; + else { oss << "tex="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetArray.tex__val); } + oss << ", array="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetArray.array); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetArray.flags); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetBorderColor: + oss << "hipTexRefSetBorderColor("; + if (data->args.hipTexRefSetBorderColor.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetBorderColor.texRef__val); } + if (data->args.hipTexRefSetBorderColor.pBorderColor == NULL) oss << ", pBorderColor=NULL"; + else { oss << ", pBorderColor="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetBorderColor.pBorderColor__val); } + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetFlags: + oss << "hipTexRefSetFlags("; + if (data->args.hipTexRefSetFlags.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetFlags.texRef__val); } + oss << ", Flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetFlags.Flags); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetFormat: + oss << "hipTexRefSetFormat("; + if (data->args.hipTexRefSetFormat.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetFormat.texRef__val); } + oss << ", fmt="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetFormat.fmt); + oss << ", NumPackedComponents="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetFormat.NumPackedComponents); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetMaxAnisotropy: + oss << "hipTexRefSetMaxAnisotropy("; + if (data->args.hipTexRefSetMaxAnisotropy.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMaxAnisotropy.texRef__val); } + oss << ", maxAniso="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMaxAnisotropy.maxAniso); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetMipmapLevelBias: + oss << "hipTexRefSetMipmapLevelBias("; + if (data->args.hipTexRefSetMipmapLevelBias.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmapLevelBias.texRef__val); } + oss << ", bias="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmapLevelBias.bias); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetMipmapLevelClamp: + oss << "hipTexRefSetMipmapLevelClamp("; + if (data->args.hipTexRefSetMipmapLevelClamp.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmapLevelClamp.texRef__val); } + oss << ", minMipMapLevelClamp="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmapLevelClamp.minMipMapLevelClamp); + oss << ", maxMipMapLevelClamp="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmapLevelClamp.maxMipMapLevelClamp); + oss << ")"; + break; + case HIP_API_ID_hipTexRefSetMipmappedArray: + oss << "hipTexRefSetMipmappedArray("; + if (data->args.hipTexRefSetMipmappedArray.texRef == NULL) oss << "texRef=NULL"; + else { oss << "texRef="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmappedArray.texRef__val); } + if (data->args.hipTexRefSetMipmappedArray.mipmappedArray == NULL) oss << ", mipmappedArray=NULL"; + else { oss << ", mipmappedArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmappedArray.mipmappedArray__val); } + oss << ", Flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipTexRefSetMipmappedArray.Flags); + oss << ")"; + break; + case HIP_API_ID_hipThreadExchangeStreamCaptureMode: + oss << "hipThreadExchangeStreamCaptureMode("; + if (data->args.hipThreadExchangeStreamCaptureMode.mode == NULL) oss << "mode=NULL"; + else { oss << "mode="; roctracer::hip_support::detail::operator<<(oss, data->args.hipThreadExchangeStreamCaptureMode.mode__val); } + oss << ")"; + break; + case HIP_API_ID_hipUserObjectCreate: + oss << "hipUserObjectCreate("; + if (data->args.hipUserObjectCreate.object_out == NULL) oss << "object_out=NULL"; + else { oss << "object_out="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectCreate.object_out__val); } + oss << ", ptr="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectCreate.ptr); + oss << ", destroy="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectCreate.destroy); + oss << ", initialRefcount="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectCreate.initialRefcount); + oss << ", flags="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectCreate.flags); + oss << ")"; + break; + case HIP_API_ID_hipUserObjectRelease: + oss << "hipUserObjectRelease("; + oss << "object="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectRelease.object); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectRelease.count); + oss << ")"; + break; + case HIP_API_ID_hipUserObjectRetain: + oss << "hipUserObjectRetain("; + oss << "object="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectRetain.object); + oss << ", count="; roctracer::hip_support::detail::operator<<(oss, data->args.hipUserObjectRetain.count); + oss << ")"; + break; + case HIP_API_ID_hipWaitExternalSemaphoresAsync: + oss << "hipWaitExternalSemaphoresAsync("; + if (data->args.hipWaitExternalSemaphoresAsync.extSemArray == NULL) oss << "extSemArray=NULL"; + else { oss << "extSemArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipWaitExternalSemaphoresAsync.extSemArray__val); } + if (data->args.hipWaitExternalSemaphoresAsync.paramsArray == NULL) oss << ", paramsArray=NULL"; + else { oss << ", paramsArray="; roctracer::hip_support::detail::operator<<(oss, data->args.hipWaitExternalSemaphoresAsync.paramsArray__val); } + oss << ", numExtSems="; roctracer::hip_support::detail::operator<<(oss, data->args.hipWaitExternalSemaphoresAsync.numExtSems); + oss << ", stream="; roctracer::hip_support::detail::operator<<(oss, data->args.hipWaitExternalSemaphoresAsync.stream); + oss << ")"; + break; + default: oss << "unknown"; + }; + return strdup(oss.str().c_str()); +} +#endif // HIP_PROF_HIP_API_STRING +#endif // _HIP_PROF_STR_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_runtime_prof.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_runtime_prof.h new file mode 100644 index 0000000000000000000000000000000000000000..d201ab517c9b9192116fb82c5bbd4e46a8799576 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hip_runtime_prof.h @@ -0,0 +1,77 @@ +/* +Copyright (c) 2019 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#ifndef HIP_INCLUDE_HIP_AMD_DETAIL_HIP_RUNTIME_PROF_H +#define HIP_INCLUDE_HIP_AMD_DETAIL_HIP_RUNTIME_PROF_H + +// HIP ROCclr Op IDs enumeration +enum HipVdiOpId { + kHipVdiOpIdDispatch = 0, + kHipVdiOpIdCopy = 1, + kHipVdiOpIdBarrier = 2, + kHipVdiOpIdNumber = 3 +}; + +// Types of ROCclr commands +enum HipVdiCommandKind { + kHipVdiCommandKernel = 0x11F0, + kHipVdiMemcpyDeviceToHost = 0x11F3, + kHipHipVdiMemcpyHostToDevice = 0x11F4, + kHipVdiMemcpyDeviceToDevice = 0x11F5, + kHipVidMemcpyDeviceToHostRect = 0x1201, + kHipVdiMemcpyHostToDeviceRect = 0x1202, + kHipVdiMemcpyDeviceToDeviceRect = 0x1203, + kHipVdiFillMemory = 0x1207, +}; + +/** + * @brief Initializes activity callback + * + * @param [input] id_callback Event ID callback function + * @param [input] op_callback Event operation callback function + * @param [input] arg Arguments passed into callback + * + * @returns None + */ +void hipInitActivityCallback(void* id_callback, void* op_callback, void* arg); + +/** + * @brief Enables activity callback + * + * @param [input] op Operation, which will trigger a callback (@see HipVdiOpId) + * @param [input] enable Enable state for the callback + * + * @returns True if successful + */ +bool hipEnableActivityCallback(uint32_t op, bool enable); + +/** + * @brief Returns the description string for the operation kind + * + * @param [input] id Command kind id (@see HipVdiCommandKind) + * + * @returns A pointer to a const string with the command description + */ +const char* hipGetCmdName(uint32_t id); + +#endif // HIP_INCLUDE_HIP_AMD_DETAIL_HIP_RUNTIME_PROF_H + diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/host_defines.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/host_defines.h new file mode 100644 index 0000000000000000000000000000000000000000..0fad2b47042b24b62556762070e8bd107f21eb84 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/host_defines.h @@ -0,0 +1,180 @@ +/* +Copyright (c) 2015 - 2022 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +/** + * @file amd_detail/host_defines.h + * @brief TODO-doc + */ + +#ifndef HIP_INCLUDE_HIP_AMD_DETAIL_HOST_DEFINES_H +#define HIP_INCLUDE_HIP_AMD_DETAIL_HOST_DEFINES_H + +// Add guard to Generic Grid Launch method +#ifndef GENERIC_GRID_LAUNCH +#define GENERIC_GRID_LAUNCH 1 +#endif + +#if defined(__clang__) && defined(__HIP__) + +namespace __hip_internal { +typedef unsigned char uint8_t; +typedef unsigned short uint16_t; +typedef unsigned int uint32_t; +typedef unsigned long long uint64_t; +typedef signed char int8_t; +typedef signed short int16_t; +typedef signed int int32_t; +typedef signed long long int64_t; + +template struct integral_constant { + static constexpr const _Tp value = __v; + typedef _Tp value_type; + typedef integral_constant type; + constexpr operator value_type() const { return value; } + constexpr value_type operator()() const { return value; } +}; +template constexpr const _Tp integral_constant<_Tp, __v>::value; + +typedef integral_constant true_type; +typedef integral_constant false_type; + +template using bool_constant = integral_constant; +typedef bool_constant true_type; +typedef bool_constant false_type; + +template struct enable_if {}; +template struct enable_if { typedef __T type; }; + +template struct true_or_false_type : public false_type {}; +template<> struct true_or_false_type : public true_type {}; + +template struct is_integral : public false_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; +template <> struct is_integral : public true_type {}; + +template struct is_arithmetic : public false_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; +template <> struct is_arithmetic : public true_type {}; + +template struct is_floating_point : public false_type {}; +template<> struct is_floating_point : public true_type {}; +template<> struct is_floating_point : public true_type {}; +template<> struct is_floating_point : public true_type {}; + +template struct is_same : public false_type {}; +template struct is_same<__T, __T> : public true_type {}; + +template::value> + struct is_signed : public false_type {}; +template + struct is_signed<_Tp, true> : public true_or_false_type<_Tp(-1) < _Tp(0)> {}; + +template struct char_traits; +template> class basic_istream; +template> class basic_ostream; +typedef basic_istream istream; +typedef basic_ostream ostream; + +template + struct is_standard_layout + : public integral_constant + { }; + +template + struct is_trivial + : public integral_constant + { }; +} +typedef __hip_internal::uint8_t __hip_uint8_t; +typedef __hip_internal::uint16_t __hip_uint16_t; +typedef __hip_internal::uint32_t __hip_uint32_t; +typedef __hip_internal::uint64_t __hip_uint64_t; +typedef __hip_internal::int8_t __hip_int8_t; +typedef __hip_internal::int16_t __hip_int16_t; +typedef __hip_internal::int32_t __hip_int32_t; +typedef __hip_internal::int64_t __hip_int64_t; + +#if !__CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ +#define __host__ __attribute__((host)) +#define __device__ __attribute__((device)) +#define __global__ __attribute__((global)) +#define __shared__ __attribute__((shared)) +#define __constant__ __attribute__((constant)) +#endif // !__CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ + +#if !defined(__has_feature) || !__has_feature(cuda_noinline_keyword) +#define __noinline__ __attribute__((noinline)) +#endif + +#define __forceinline__ inline __attribute__((always_inline)) + +#if __HIP_NO_IMAGE_SUPPORT +#define __hip_img_chk__ __attribute__((unavailable("The image/texture API not supported on the device"))) +#else +#define __hip_img_chk__ +#endif + +#else + +// Non-HCC compiler +/** + * Function and kernel markers + */ +#define __host__ +#define __device__ + +#define __global__ + +#define __noinline__ +#define __forceinline__ inline + +#define __shared__ +#define __constant__ + +#define __hip_img_chk__ +#endif + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hsa_helpers.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hsa_helpers.hpp new file mode 100644 index 0000000000000000000000000000000000000000..0c1708502219abcafef174f434c3be20d61f6e96 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/hsa_helpers.hpp @@ -0,0 +1,102 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ +#pragma once + +#include + +#include +#include +#include + +namespace hip_impl { +inline void* address(hsa_executable_symbol_t x) { + void* r = nullptr; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_ADDRESS, &r); + + return r; +} + +inline hsa_agent_t agent(hsa_executable_symbol_t x) { + hsa_agent_t r = {}; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_AGENT, &r); + + return r; +} + +inline std::uint32_t group_size(hsa_executable_symbol_t x) { + std::uint32_t r = 0u; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_GROUP_SEGMENT_SIZE, &r); + + return r; +} + +inline hsa_isa_t isa(hsa_agent_t x) { + hsa_isa_t r = {}; + hsa_agent_iterate_isas(x, + [](hsa_isa_t i, void* o) { + *static_cast(o) = i; // Pick the first. + + return HSA_STATUS_INFO_BREAK; + }, + &r); + + return r; +} + +inline std::uint64_t kernel_object(hsa_executable_symbol_t x) { + std::uint64_t r = 0u; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_OBJECT, &r); + + return r; +} + +inline std::string name(hsa_executable_symbol_t x) { + std::uint32_t sz = 0u; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_NAME_LENGTH, &sz); + + std::string r(sz, '\0'); + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_NAME, &r.front()); + + return r; +} + +inline std::uint32_t private_size(hsa_executable_symbol_t x) { + std::uint32_t r = 0u; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_PRIVATE_SEGMENT_SIZE, &r); + + return r; +} + +inline std::uint32_t size(hsa_executable_symbol_t x) { + std::uint32_t r = 0; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_SIZE, &r); + + return r; +} + +inline hsa_symbol_kind_t type(hsa_executable_symbol_t x) { + hsa_symbol_kind_t r = {}; + hsa_executable_symbol_get_info(x, HSA_EXECUTABLE_SYMBOL_INFO_TYPE, &r); + + return r; +} +} // namespace hip_impl \ No newline at end of file diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/macro_based_grid_launch.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/macro_based_grid_launch.hpp new file mode 100644 index 0000000000000000000000000000000000000000..d631e4d5cff57a650efa242829b82edb601f9b5e --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/macro_based_grid_launch.hpp @@ -0,0 +1,798 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#include "concepts.hpp" +#include "helpers.hpp" + +#include "hc.hpp" +#include "hip/hip_ext.h" +#include "hip_runtime.h" + +#include +#include +#include +#include +#include + +namespace hip_impl { +namespace { +struct New_grid_launch_tag {}; +struct Old_grid_launch_tag {}; + +template +class RAII_guard { + D dtor_; + + public: + RAII_guard() = default; + + RAII_guard(const C& ctor, D dtor) : dtor_{std::move(dtor)} { ctor(); } + + RAII_guard(const RAII_guard&) = default; + RAII_guard(RAII_guard&&) = default; + + RAII_guard& operator=(const RAII_guard&) = default; + RAII_guard& operator=(RAII_guard&&) = default; + + ~RAII_guard() { dtor_(); } +}; + +template +RAII_guard make_RAII_guard(const C& ctor, D dtor) { + return RAII_guard{ctor, std::move(dtor)}; +} + +template +using is_new_grid_launch_t = typename std::conditional{}, New_grid_launch_tag, + Old_grid_launch_tag>::type; +} // namespace + +// TODO: - dispatch rank should be derived from the domain dimensions passed +// in, and not always assumed to be 3; + +template +requires(Domain == + {Ts...}) inline void grid_launch_hip_impl_(New_grid_launch_tag, dim3 num_blocks, + dim3 dim_blocks, int group_mem_bytes, + const hc::accelerator_view& acc_v, K k) { + const auto d = + hc::extent<3>{num_blocks.z * dim_blocks.z, num_blocks.y * dim_blocks.y, + num_blocks.x * dim_blocks.x} + .tile_with_dynamic(dim_blocks.z, dim_blocks.y, dim_blocks.x, group_mem_bytes); + + try { + hc::parallel_for_each(acc_v, d, k); + } catch (std::exception& ex) { + std::cerr << "Failed in " << __func__ << ", with exception: " << ex.what() << std::endl; + hip_throw(ex); + } +} + +// TODO: these are workarounds, they should be removed. + +hc::accelerator_view lock_stream_hip_(hipStream_t&, void*&); +void print_prelaunch_trace_(const char*, dim3, dim3, int, hipStream_t); +void unlock_stream_hip_(hipStream_t, void*, const char*, hc::accelerator_view*); + +template +requires(Domain == {Ts...}) inline void grid_launch_hip_impl_(New_grid_launch_tag, + dim3 num_blocks, dim3 dim_blocks, + int group_mem_bytes, + hipStream_t stream, + const char* kernel_name, K k) { + void* lck_stream = nullptr; + auto acc_v = lock_stream_hip_(stream, lck_stream); + auto stream_guard = + make_RAII_guard(std::bind(print_prelaunch_trace_, kernel_name, num_blocks, dim_blocks, + group_mem_bytes, stream), + std::bind(unlock_stream_hip_, stream, lck_stream, kernel_name, &acc_v)); + + try { + grid_launch_hip_impl_(New_grid_launch_tag{}, std::move(num_blocks), std::move(dim_blocks), + group_mem_bytes, acc_v, std::move(k)); + } catch (std::exception& ex) { + std::cerr << "Failed in " << __func__ << ", with exception: " << ex.what() << std::endl; + hip_throw(ex); + } +} + +template +requires(Domain == + {hipLaunchParm, Ts...}) inline void grid_launch_hip_impl_(Old_grid_launch_tag, + dim3 num_blocks, dim3 dim_blocks, + int group_mem_bytes, + hipStream_t stream, K k) { + grid_launch_hip_impl_(New_grid_launch_tag{}, std::move(num_blocks), std::move(dim_blocks), + group_mem_bytes, std::move(stream), std::move(k)); +} + +template +requires(Domain == {hipLaunchParm, Ts...}) inline void grid_launch_hip_impl_( + Old_grid_launch_tag, dim3 num_blocks, dim3 dim_blocks, int group_mem_bytes, hipStream_t stream, + const char* kernel_name, K k) { + grid_launch_hip_impl_(New_grid_launch_tag{}, std::move(num_blocks), std::move(dim_blocks), + group_mem_bytes, std::move(stream), kernel_name, std::move(k)); +} + +template +requires(Domain == {Ts...}) inline std::enable_if_t< + !std::is_function::value> grid_launch_hip_(dim3 num_blocks, dim3 dim_blocks, + int group_mem_bytes, hipStream_t stream, + const char* kernel_name, K k) { + grid_launch_hip_impl_(is_new_grid_launch_t{}, std::move(num_blocks), + std::move(dim_blocks), group_mem_bytes, std::move(stream), kernel_name, + std::move(k)); +} + +template +requires(Domain == {Ts...}) inline std::enable_if_t< + !std::is_function::value> grid_launch_hip_(dim3 num_blocks, dim3 dim_blocks, + int group_mem_bytes, hipStream_t stream, K k) { + grid_launch_hip_impl_(is_new_grid_launch_t{}, std::move(num_blocks), + std::move(dim_blocks), group_mem_bytes, std::move(stream), std::move(k)); +} + +// TODO: these are temporary and purposefully noisy and disruptive. +#define make_kernel_name_hip(k, n) \ + HIP_kernel_functor_name_begin##_##k##_##HIP_kernel_functor_name_end##_##n + +#define make_kernel_functor_hip_30(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22, p23, p24, p25, p26, p27) \ + struct make_kernel_name_hip(function_name, 28) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + std::decay_t _p23_; \ + std::decay_t _p24_; \ + std::decay_t _p25_; \ + std::decay_t _p26_; \ + std::decay_t _p27_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_, _p23_, _p24_, _p25_, _p26_, _p27_); \ + } \ + } +#define make_kernel_functor_hip_29(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22, p23, p24, p25, p26) \ + struct make_kernel_name_hip(function_name, 27) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + std::decay_t _p23_; \ + std::decay_t _p24_; \ + std::decay_t _p25_; \ + std::decay_t _p26_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_, _p23_, _p24_, _p25_, _p26_); \ + } \ + } +#define make_kernel_functor_hip_28(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22, p23, p24, p25) \ + struct make_kernel_name_hip(function_name, 26) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + std::decay_t _p23_; \ + std::decay_t _p24_; \ + std::decay_t _p25_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_, _p23_, _p24_, _p25_); \ + } \ + } +#define make_kernel_functor_hip_27(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22, p23, p24) \ + struct make_kernel_name_hip(function_name, 25) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + std::decay_t _p23_; \ + std::decay_t _p24_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_, _p23_, _p24_); \ + } \ + } +#define make_kernel_functor_hip_26(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22, p23) \ + struct make_kernel_name_hip(function_name, 24) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + std::decay_t _p23_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_, _p23_); \ + } \ + } +#define make_kernel_functor_hip_25(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, \ + p22) \ + struct make_kernel_name_hip(function_name, 23) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + std::decay_t _p22_; \ + __attribute__((used, flatten)) void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_, \ + _p22_); \ + } \ + } +#define make_kernel_functor_hip_24(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21) \ + struct make_kernel_name_hip(function_name, 22) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + std::decay_t _p21_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_, _p21_); \ + } \ + } +#define make_kernel_functor_hip_23(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20) \ + struct make_kernel_name_hip(function_name, 21) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + std::decay_t _p20_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_, _p20_); \ + } \ + } +#define make_kernel_functor_hip_22(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19) \ + struct make_kernel_name_hip(function_name, 20) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + std::decay_t _p19_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_, _p19_); \ + } \ + } +#define make_kernel_functor_hip_21(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17, p18) \ + struct make_kernel_name_hip(function_name, 19) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + std::decay_t _p18_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_, _p18_); \ + } \ + } +#define make_kernel_functor_hip_20(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16, p17) \ + struct make_kernel_name_hip(function_name, 18) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + std::decay_t _p17_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_, _p17_); \ + } \ + } +#define make_kernel_functor_hip_19(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15, p16) \ + struct make_kernel_name_hip(function_name, 17) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + std::decay_t _p16_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_, _p16_); \ + } \ + } +#define make_kernel_functor_hip_18(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14, p15) \ + struct make_kernel_name_hip(function_name, 16) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + std::decay_t _p15_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_, _p15_); \ + } \ + } +#define make_kernel_functor_hip_17(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13, p14) \ + struct make_kernel_name_hip(function_name, 15) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + std::decay_t _p14_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_, _p14_); \ + } \ + } +#define make_kernel_functor_hip_16(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12, p13) \ + struct make_kernel_name_hip(function_name, 14) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + std::decay_t _p13_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_, _p13_); \ + } \ + } +#define make_kernel_functor_hip_15(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11, p12) \ + struct make_kernel_name_hip(function_name, 13) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + std::decay_t _p12_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_, \ + _p12_); \ + } \ + } +#define make_kernel_functor_hip_14(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10, p11) \ + struct make_kernel_name_hip(function_name, 12) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + std::decay_t _p11_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_, _p11_); \ + } \ + } +#define make_kernel_functor_hip_13(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9, p10) \ + struct make_kernel_name_hip(function_name, 11) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + std::decay_t _p10_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { \ + kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_, _p10_); \ + } \ + } +#define make_kernel_functor_hip_12(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8, \ + p9) \ + struct make_kernel_name_hip(function_name, 10) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + std::decay_t _p9_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_, _p9_); } \ + } +#define make_kernel_functor_hip_11(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7, p8) \ + struct make_kernel_name_hip(function_name, 9) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + std::decay_t _p8_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_, _p8_); } \ + } +#define make_kernel_functor_hip_10(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6, p7) \ + struct make_kernel_name_hip(function_name, 8) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + std::decay_t _p7_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_, _p7_); } \ + } +#define make_kernel_functor_hip_9(function_name, kernel_name, p0, p1, p2, p3, p4, p5, p6) \ + struct make_kernel_name_hip(function_name, 7) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + std::decay_t _p6_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_, _p6_); } \ + } +#define make_kernel_functor_hip_8(function_name, kernel_name, p0, p1, p2, p3, p4, p5) \ + struct make_kernel_name_hip(function_name, 6) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + std::decay_t _p5_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_, _p5_); } \ + } +#define make_kernel_functor_hip_7(function_name, kernel_name, p0, p1, p2, p3, p4) \ + struct make_kernel_name_hip(function_name, 5) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + std::decay_t _p4_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_, _p4_); } \ + } +#define make_kernel_functor_hip_6(function_name, kernel_name, p0, p1, p2, p3) \ + struct make_kernel_name_hip(function_name, 4) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + std::decay_t _p3_; \ + void operator()(const hc::tiled_index<3>&) const \ + [[hc]] { kernel_name(_p0_, _p1_, _p2_, _p3_); } \ + } +#define make_kernel_functor_hip_5(function_name, kernel_name, p0, p1, p2) \ + struct make_kernel_name_hip(function_name, 3) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + std::decay_t _p2_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { kernel_name(_p0_, _p1_, _p2_); } \ + } +#define make_kernel_functor_hip_4(function_name, kernel_name, p0, p1) \ + struct make_kernel_name_hip(function_name, 2) { \ + std::decay_t _p0_; \ + std::decay_t _p1_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { kernel_name(_p0_, _p1_); } \ + } +#define fofo(f, n) kernel_prefix_hip##f##kernel_suffix_hip##n +#define make_kernel_functor_hip_3(function_name, kernel_name, p0) \ + struct make_kernel_name_hip(function_name, 1) { \ + std::decay_t _p0_; \ + void operator()(const hc::tiled_index<3>&) const [[hc]] { kernel_name(_p0_); } \ + } +#define make_kernel_functor_hip_2(function_name, kernel_name) \ + struct make_kernel_name_hip(function_name, 0) { \ + void operator()(const hc::tiled_index<3>&)[[hc]] { return kernel_name(hipLaunchParm{}); } \ + } +#define make_kernel_functor_hip_1(...) +#define make_kernel_functor_hip_0(...) +#define make_kernel_functor_hip_(...) overload_macro_hip_(make_kernel_functor_hip_, __VA_ARGS__) + + +#define hipLaunchNamedKernelGGL(function_name, kernel_name, num_blocks, dim_blocks, \ + group_mem_bytes, stream, ...) \ + do { \ + make_kernel_functor_hip_(function_name, kernel_name, __VA_ARGS__) \ + hip_kernel_functor_impl_{__VA_ARGS__}; \ + hip_impl::grid_launch_hip_(num_blocks, dim_blocks, group_mem_bytes, stream, #kernel_name, \ + hip_kernel_functor_impl_); \ + } while (0) + +#define hipLaunchKernelGGL(kernel_name, num_blocks, dim_blocks, group_mem_bytes, stream, ...) \ + do { \ + hipLaunchNamedKernelGGL(unnamed, kernel_name, num_blocks, dim_blocks, group_mem_bytes, \ + stream, ##__VA_ARGS__); \ + } while (0) + +#define hipLaunchKernel(kernel_name, num_blocks, dim_blocks, group_mem_bytes, stream, ...) \ + do { \ + hipLaunchKernelGGL(kernel_name, num_blocks, dim_blocks, group_mem_bytes, stream, \ + hipLaunchParm{}, ##__VA_ARGS__); \ + } while (0) +} // namespace hip_impl diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/math_fwd.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/math_fwd.h new file mode 100644 index 0000000000000000000000000000000000000000..9951f8fc34d041a2b6873e1f9453483f1bd5e206 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/math_fwd.h @@ -0,0 +1,698 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#if !defined(__HIPCC_RTC__) +#include "host_defines.h" +#include "amd_hip_vector_types.h" // For Native_vec_ +#endif + +#if defined(__cplusplus) + extern "C" { +#endif + +// DOT FUNCTIONS +#if defined(__clang__) && defined(__HIP__) +__device__ +__attribute__((const)) +int __ockl_sdot2( + HIP_vector_base::Native_vec_, + HIP_vector_base::Native_vec_, + int, bool); + +__device__ +__attribute__((const)) +unsigned int __ockl_udot2( + HIP_vector_base::Native_vec_, + HIP_vector_base::Native_vec_, + unsigned int, bool); + +__device__ +__attribute__((const)) +int __ockl_sdot4( + HIP_vector_base::Native_vec_, + HIP_vector_base::Native_vec_, + int, bool); + +__device__ +__attribute__((const)) +unsigned int __ockl_udot4( + HIP_vector_base::Native_vec_, + HIP_vector_base::Native_vec_, + unsigned int, bool); + +__device__ +__attribute__((const)) +int __ockl_sdot8(int, int, int, bool); + +__device__ +__attribute__((const)) +unsigned int __ockl_udot8(unsigned int, unsigned int, unsigned int, bool); +#endif + +#if !__CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ +// BEGIN FLOAT +__device__ +__attribute__((const)) +float __ocml_acos_f32(float); +__device__ +__attribute__((pure)) +float __ocml_acosh_f32(float); +__device__ +__attribute__((const)) +float __ocml_asin_f32(float); +__device__ +__attribute__((pure)) +float __ocml_asinh_f32(float); +__device__ +__attribute__((const)) +float __ocml_atan2_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_atan_f32(float); +__device__ +__attribute__((pure)) +float __ocml_atanh_f32(float); +__device__ +__attribute__((pure)) +float __ocml_cbrt_f32(float); +__device__ +__attribute__((const)) +float __ocml_ceil_f32(float); +__device__ +__attribute__((const)) +__device__ +float __ocml_copysign_f32(float, float); +__device__ +float __ocml_cos_f32(float); +__device__ +float __ocml_native_cos_f32(float); +__device__ +__attribute__((pure)) +__device__ +float __ocml_cosh_f32(float); +__device__ +float __ocml_cospi_f32(float); +__device__ +float __ocml_i0_f32(float); +__device__ +float __ocml_i1_f32(float); +__device__ +__attribute__((pure)) +float __ocml_erfc_f32(float); +__device__ +__attribute__((pure)) +float __ocml_erfcinv_f32(float); +__device__ +__attribute__((pure)) +float __ocml_erfcx_f32(float); +__device__ +__attribute__((pure)) +float __ocml_erf_f32(float); +__device__ +__attribute__((pure)) +float __ocml_erfinv_f32(float); +__device__ +__attribute__((pure)) +float __ocml_exp10_f32(float); +__device__ +__attribute__((pure)) +float __ocml_native_exp10_f32(float); +__device__ +__attribute__((pure)) +float __ocml_exp2_f32(float); +__device__ +__attribute__((pure)) +float __ocml_exp_f32(float); +__device__ +__attribute__((pure)) +float __ocml_native_exp_f32(float); +__device__ +__attribute__((pure)) +float __ocml_expm1_f32(float); +__device__ +__attribute__((const)) +float __ocml_fabs_f32(float); +__device__ +__attribute__((const)) +float __ocml_fdim_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_floor_f32(float); +__device__ +__attribute__((const)) +float __ocml_fma_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_fmax_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_fmin_f32(float, float); +__device__ +__attribute__((const)) +__device__ +float __ocml_fmod_f32(float, float); +__device__ +float __ocml_frexp_f32(float, __attribute__((address_space(5))) int*); +__device__ +__attribute__((const)) +float __ocml_hypot_f32(float, float); +__device__ +__attribute__((const)) +int __ocml_ilogb_f32(float); +__device__ +__attribute__((const)) +int __ocml_isfinite_f32(float); +__device__ +__attribute__((const)) +int __ocml_isinf_f32(float); +__device__ +__attribute__((const)) +int __ocml_isnan_f32(float); +__device__ +float __ocml_j0_f32(float); +__device__ +float __ocml_j1_f32(float); +__device__ +__attribute__((const)) +float __ocml_ldexp_f32(float, int); +__device__ +float __ocml_lgamma_f32(float); +__device__ +__attribute__((pure)) +float __ocml_log10_f32(float); +__device__ +__attribute__((pure)) +float __ocml_native_log10_f32(float); +__device__ +__attribute__((pure)) +float __ocml_log1p_f32(float); +__device__ +__attribute__((pure)) +float __ocml_log2_f32(float); +__device__ +__attribute__((pure)) +float __ocml_native_log2_f32(float); +__device__ +__attribute__((const)) +float __ocml_logb_f32(float); +__device__ +__attribute__((pure)) +float __ocml_log_f32(float); +__device__ +__attribute__((pure)) +float __ocml_native_log_f32(float); +__device__ +float __ocml_modf_f32(float, __attribute__((address_space(5))) float*); +__device__ +__attribute__((const)) +float __ocml_nearbyint_f32(float); +__device__ +__attribute__((const)) +float __ocml_nextafter_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_len3_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_len4_f32(float, float, float, float); +__device__ +__attribute__((pure)) +float __ocml_ncdf_f32(float); +__device__ +__attribute__((pure)) +float __ocml_ncdfinv_f32(float); +__device__ +__attribute__((pure)) +float __ocml_pow_f32(float, float); +__device__ +__attribute__((pure)) +float __ocml_pown_f32(float, int); +__device__ +__attribute__((pure)) +float __ocml_rcbrt_f32(float); +__device__ +__attribute__((const)) +float __ocml_remainder_f32(float, float); +__device__ +float __ocml_remquo_f32(float, float, __attribute__((address_space(5))) int*); +__device__ +__attribute__((const)) +float __ocml_rhypot_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_rint_f32(float); +__device__ +__attribute__((const)) +float __ocml_rlen3_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_rlen4_f32(float, float, float, float); +__device__ +__attribute__((const)) +float __ocml_round_f32(float); +__device__ +__attribute__((pure)) +float __ocml_rsqrt_f32(float); +__device__ +__attribute__((const)) +float __ocml_scalb_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_scalbn_f32(float, int); +__device__ +__attribute__((const)) +int __ocml_signbit_f32(float); +__device__ +float __ocml_sincos_f32(float, __attribute__((address_space(5))) float*); +__device__ +float __ocml_sincospi_f32(float, __attribute__((address_space(5))) float*); +__device__ +float __ocml_sin_f32(float); +__device__ +float __ocml_native_sin_f32(float); +__device__ +__attribute__((pure)) +float __ocml_sinh_f32(float); +__device__ +float __ocml_sinpi_f32(float); +__device__ +__attribute__((const)) +float __ocml_sqrt_f32(float); +__device__ +__attribute__((const)) +float __ocml_native_sqrt_f32(float); +__device__ +float __ocml_tan_f32(float); +__device__ +__attribute__((pure)) +float __ocml_tanh_f32(float); +__device__ +float __ocml_tgamma_f32(float); +__device__ +__attribute__((const)) +float __ocml_trunc_f32(float); +__device__ +float __ocml_y0_f32(float); +__device__ +float __ocml_y1_f32(float); + +// BEGIN INTRINSICS +__device__ +__attribute__((const)) +float __ocml_add_rte_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_add_rtn_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_add_rtp_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_add_rtz_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_sub_rte_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_sub_rtn_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_sub_rtp_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_sub_rtz_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_mul_rte_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_mul_rtn_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_mul_rtp_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_mul_rtz_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_div_rte_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_div_rtn_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_div_rtp_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_div_rtz_f32(float, float); +__device__ +__attribute__((const)) +float __ocml_sqrt_rte_f32(float); +__device__ +__attribute__((const)) +float __ocml_sqrt_rtn_f32(float); +__device__ +__attribute__((const)) +float __ocml_sqrt_rtp_f32(float); +__device__ +__attribute__((const)) +float __ocml_sqrt_rtz_f32(float); +__device__ +__attribute__((const)) +float __ocml_fma_rte_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_fma_rtn_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_fma_rtp_f32(float, float, float); +__device__ +__attribute__((const)) +float __ocml_fma_rtz_f32(float, float, float); +// END INTRINSICS +// END FLOAT + +// BEGIN DOUBLE +__device__ +__attribute__((const)) +double __ocml_acos_f64(double); +__device__ +__attribute__((pure)) +double __ocml_acosh_f64(double); +__device__ +__attribute__((const)) +double __ocml_asin_f64(double); +__device__ +__attribute__((pure)) +double __ocml_asinh_f64(double); +__device__ +__attribute__((const)) +double __ocml_atan2_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_atan_f64(double); +__device__ +__attribute__((pure)) +double __ocml_atanh_f64(double); +__device__ +__attribute__((pure)) +double __ocml_cbrt_f64(double); +__device__ +__attribute__((const)) +double __ocml_ceil_f64(double); +__device__ +__attribute__((const)) +double __ocml_copysign_f64(double, double); +__device__ +double __ocml_cos_f64(double); +__device__ +__attribute__((pure)) +double __ocml_cosh_f64(double); +__device__ +double __ocml_cospi_f64(double); +__device__ +double __ocml_i0_f64(double); +__device__ +double __ocml_i1_f64(double); +__device__ +__attribute__((pure)) +double __ocml_erfc_f64(double); +__device__ +__attribute__((pure)) +double __ocml_erfcinv_f64(double); +__device__ +__attribute__((pure)) +double __ocml_erfcx_f64(double); +__device__ +__attribute__((pure)) +double __ocml_erf_f64(double); +__device__ +__attribute__((pure)) +double __ocml_erfinv_f64(double); +__device__ +__attribute__((pure)) +double __ocml_exp10_f64(double); +__device__ +__attribute__((pure)) +double __ocml_exp2_f64(double); +__device__ +__attribute__((pure)) +double __ocml_exp_f64(double); +__device__ +__attribute__((pure)) +double __ocml_expm1_f64(double); +__device__ +__attribute__((const)) +double __ocml_fabs_f64(double); +__device__ +__attribute__((const)) +double __ocml_fdim_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_floor_f64(double); +__device__ +__attribute__((const)) +double __ocml_fma_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_fmax_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_fmin_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_fmod_f64(double, double); +__device__ +double __ocml_frexp_f64(double, __attribute__((address_space(5))) int*); +__device__ +__attribute__((const)) +double __ocml_hypot_f64(double, double); +__device__ +__attribute__((const)) +int __ocml_ilogb_f64(double); +__device__ +__attribute__((const)) +int __ocml_isfinite_f64(double); +__device__ +__attribute__((const)) +int __ocml_isinf_f64(double); +__device__ +__attribute__((const)) +int __ocml_isnan_f64(double); +__device__ +double __ocml_j0_f64(double); +__device__ +double __ocml_j1_f64(double); +__device__ +__attribute__((const)) +double __ocml_ldexp_f64(double, int); +__device__ +double __ocml_lgamma_f64(double); +__device__ +__attribute__((pure)) +double __ocml_log10_f64(double); +__device__ +__attribute__((pure)) +double __ocml_log1p_f64(double); +__device__ +__attribute__((pure)) +double __ocml_log2_f64(double); +__device__ +__attribute__((const)) +double __ocml_logb_f64(double); +__device__ +__attribute__((pure)) +double __ocml_log_f64(double); +__device__ +double __ocml_modf_f64(double, __attribute__((address_space(5))) double*); +__device__ +__attribute__((const)) +double __ocml_nearbyint_f64(double); +__device__ +__attribute__((const)) +double __ocml_nextafter_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_len3_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_len4_f64(double, double, double, double); +__device__ +__attribute__((pure)) +double __ocml_ncdf_f64(double); +__device__ +__attribute__((pure)) +double __ocml_ncdfinv_f64(double); +__device__ +__attribute__((pure)) +double __ocml_pow_f64(double, double); +__device__ +__attribute__((pure)) +double __ocml_pown_f64(double, int); +__device__ +__attribute__((pure)) +double __ocml_rcbrt_f64(double); +__device__ +__attribute__((const)) +double __ocml_remainder_f64(double, double); +__device__ +double __ocml_remquo_f64( + double, double, __attribute__((address_space(5))) int*); +__device__ +__attribute__((const)) +double __ocml_rhypot_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_rint_f64(double); +__device__ +__attribute__((const)) +double __ocml_rlen3_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_rlen4_f64(double, double, double, double); +__device__ +__attribute__((const)) +double __ocml_round_f64(double); +__device__ +__attribute__((pure)) +double __ocml_rsqrt_f64(double); +__device__ +__attribute__((const)) +double __ocml_scalb_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_scalbn_f64(double, int); +__device__ +__attribute__((const)) +int __ocml_signbit_f64(double); +__device__ +double __ocml_sincos_f64(double, __attribute__((address_space(5))) double*); +__device__ +double __ocml_sincospi_f64(double, __attribute__((address_space(5))) double*); +__device__ +double __ocml_sin_f64(double); +__device__ +__attribute__((pure)) +double __ocml_sinh_f64(double); +__device__ +double __ocml_sinpi_f64(double); +__device__ +__attribute__((const)) +double __ocml_sqrt_f64(double); +__device__ +double __ocml_tan_f64(double); +__device__ +__attribute__((pure)) +double __ocml_tanh_f64(double); +__device__ +double __ocml_tgamma_f64(double); +__device__ +__attribute__((const)) +double __ocml_trunc_f64(double); +__device__ +double __ocml_y0_f64(double); +__device__ +double __ocml_y1_f64(double); + +// BEGIN INTRINSICS +__device__ +__attribute__((const)) +double __ocml_add_rte_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_add_rtn_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_add_rtp_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_add_rtz_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_sub_rte_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_sub_rtn_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_sub_rtp_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_sub_rtz_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_mul_rte_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_mul_rtn_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_mul_rtp_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_mul_rtz_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_div_rte_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_div_rtn_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_div_rtp_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_div_rtz_f64(double, double); +__device__ +__attribute__((const)) +double __ocml_sqrt_rte_f64(double); +__device__ +__attribute__((const)) +double __ocml_sqrt_rtn_f64(double); +__device__ +__attribute__((const)) +double __ocml_sqrt_rtp_f64(double); +__device__ +__attribute__((const)) +double __ocml_sqrt_rtz_f64(double); +__device__ +__attribute__((const)) +double __ocml_fma_rte_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_fma_rtn_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_fma_rtp_f64(double, double, double); +__device__ +__attribute__((const)) +double __ocml_fma_rtz_f64(double, double, double); +// END INTRINSICS +// END DOUBLE + +#endif // !__CLANG_HIP_RUNTIME_WRAPPER_INCLUDED__ + +#if defined(__cplusplus) + } // extern "C" +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/ockl_image.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/ockl_image.h new file mode 100644 index 0000000000000000000000000000000000000000..50223add4ffc30f6cad200f9e3cd134e11996825 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/ockl_image.h @@ -0,0 +1,177 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#if !defined(__HIPCC_RTC__) +#include +#endif + +extern "C" { + +#define ADDRESS_SPACE_CONSTANT __attribute__((address_space(4))) + +__device__ float4::Native_vec_ __ockl_image_load_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, int c); + +__device__ float4::Native_vec_ __ockl_image_load_1Db(unsigned int ADDRESS_SPACE_CONSTANT*i, int c); + +__device__ float4::Native_vec_ __ockl_image_load_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_load_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_load_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_load_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_load_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int f); + +__device__ float4::Native_vec_ __ockl_image_load_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int f); + +__device__ float4::Native_vec_ __ockl_image_load_lod_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, int c, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int f, int l); + +__device__ float4::Native_vec_ __ockl_image_load_lod_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int f, int l); + +__device__ void __ockl_image_store_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, int c, float4::Native_vec_ p); + +__device__ void __ockl_image_store_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, float4::Native_vec_ p); + +__device__ void __ockl_image_store_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, float4::Native_vec_ p); + +__device__ void __ockl_image_store_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, float4::Native_vec_ p); + +__device__ void __ockl_image_store_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, float4::Native_vec_ p); + +__device__ void __ockl_image_store_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int f, float4::Native_vec_ p); + +__device__ void __ockl_image_store_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int f, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, int c, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, int2::Native_vec_ c, int f, int l, float4::Native_vec_ p); + +__device__ void __ockl_image_store_lod_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, int4::Native_vec_ c, int f, int l, float4::Native_vec_ p); + +__device__ float4::Native_vec_ __ockl_image_sample_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float c); + +__device__ float4::Native_vec_ __ockl_image_sample_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_sample_grad_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float c, float dx, float dy); + +__device__ float4::Native_vec_ __ockl_image_sample_grad_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c, float dx, float dy); + +__device__ float4::Native_vec_ __ockl_image_sample_grad_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c, float2::Native_vec_ dx, float2::Native_vec_ dy); + +__device__ float4::Native_vec_ __ockl_image_sample_grad_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float2::Native_vec_ dx, float2::Native_vec_ dy); + +__device__ float4::Native_vec_ __ockl_image_sample_grad_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float4::Native_vec_ dx, float4::Native_vec_ dy); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_1D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_1Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_2Da(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_3D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_CM(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_sample_lod_CMa(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float4::Native_vec_ c, float l); + +__device__ float4::Native_vec_ __ockl_image_gather4r_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_gather4g_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_gather4b_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ float4::Native_vec_ __ockl_image_gather4a_2D(unsigned int ADDRESS_SPACE_CONSTANT*i, unsigned int ADDRESS_SPACE_CONSTANT*s, float2::Native_vec_ c); + +__device__ int __ockl_image_channel_data_type_1D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_1Da(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_1Db(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_2D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_2Da(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_2Dad(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_2Dd(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_3D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_CM(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_data_type_CMa(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_1D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_1Da(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_1Db(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_2D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_2Da(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_2Dad(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_2Dd(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_3D(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_CM(unsigned int ADDRESS_SPACE_CONSTANT* i); + +__device__ int __ockl_image_channel_order_CMa(unsigned int ADDRESS_SPACE_CONSTANT* i); + +} diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/program_state.hpp b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/program_state.hpp new file mode 100644 index 0000000000000000000000000000000000000000..e06504f71174002e571e5e0e8ee7f815553b04be --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/program_state.hpp @@ -0,0 +1,107 @@ +/* +Copyright (c) 2015 - 2021 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#include +#include +#include +#include + +#include +#include +#include + +#include + +struct ihipModuleSymbol_t; +using hipFunction_t = ihipModuleSymbol_t*; + +namespace hip_impl { + +// This section contains internal APIs that +// needs to be exported +#ifdef __GNUC__ +#pragma GCC visibility push (default) +#endif + +struct kernarg_impl; +class kernarg { +public: + kernarg(); + kernarg(kernarg&&); + ~kernarg(); + std::uint8_t* data(); + std::size_t size(); + void reserve(std::size_t); + void resize(std::size_t); +private: + kernarg_impl* impl; +}; + +class kernargs_size_align; +class program_state_impl; +class program_state { +public: + program_state(); + ~program_state(); + program_state(const program_state&) = delete; + + hipFunction_t kernel_descriptor(std::uintptr_t, + hsa_agent_t); + + kernargs_size_align get_kernargs_size_align(std::uintptr_t); + hsa_executable_t load_executable(const char*, const size_t, + hsa_executable_t, + hsa_agent_t); + hsa_executable_t load_executable_no_copy(const char*, const size_t, + hsa_executable_t, + hsa_agent_t); + + void* global_addr_by_name(const char* name); + +private: + friend class agent_globals_impl; + program_state_impl* impl; +}; + +class kernargs_size_align { +public: + std::size_t size(std::size_t n) const; + std::size_t alignment(std::size_t n) const; + const void* getHandle() const {return handle;}; +private: + const void* handle; + friend kernargs_size_align program_state::get_kernargs_size_align(std::uintptr_t); +}; + +#ifdef __GNUC__ +#pragma GCC visibility pop +#endif + +inline +__attribute__((visibility("hidden"))) +program_state& get_program_state() { + static program_state ps; + return ps; +} +} // Namespace hip_impl. diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_fetch_functions.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_fetch_functions.h new file mode 100644 index 0000000000000000000000000000000000000000..c4dcbe78d82d533427d5b10e8c864710ddb10ede --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_fetch_functions.h @@ -0,0 +1,491 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#if defined(__cplusplus) + +#if !defined(__HIPCC_RTC__) +#include +#include +#include +#include +#endif // !defined(__HIPCC_RTC__) + +#define TEXTURE_PARAMETERS_INIT \ + unsigned int ADDRESS_SPACE_CONSTANT* i = (unsigned int ADDRESS_SPACE_CONSTANT*)t.textureObject; \ + unsigned int ADDRESS_SPACE_CONSTANT* s = i + HIP_SAMPLER_OBJECT_OFFSET_DWORD; + +template +struct __hip_is_tex_surf_scalar_channel_type +{ + static constexpr bool value = + std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value; +}; + +template +struct __hip_is_tex_surf_channel_type +{ + static constexpr bool value = + __hip_is_tex_surf_scalar_channel_type::value; +}; + +template< + typename T, + unsigned int rank> +struct __hip_is_tex_surf_channel_type> +{ + static constexpr bool value = + __hip_is_tex_surf_scalar_channel_type::value && + ((rank == 1) || + (rank == 2) || + (rank == 4)); +}; + +template +struct __hip_is_tex_normalized_channel_type +{ + static constexpr bool value = + std::is_same::value || + std::is_same::value || + std::is_same::value || + std::is_same::value; +}; + +template< + typename T, + unsigned int rank> +struct __hip_is_tex_normalized_channel_type> +{ + static constexpr bool value = + __hip_is_tex_normalized_channel_type::value && + ((rank == 1) || + (rank == 2) || + (rank == 4)); +}; + +template < + typename T, + hipTextureReadMode readMode, + typename Enable = void> +struct __hip_tex_ret +{ + static_assert(std::is_same::value, "Invalid channel type!"); +}; + +/* + * Map from device function return U to scalar texture type T + */ +template +__forceinline__ __device__ +typename std::enable_if< + __hip_is_tex_surf_scalar_channel_type::value, const T>::type +__hipMapFrom(const U &u) { + if constexpr (sizeof(T) < sizeof(float)) { + union { + U u; + int i; + } d = { u }; + return static_cast(d.i); + } else { // sizeof(T) == sizeof(float) + union { + U u; + T t; + } d = { u }; + return d.t; + } +} + +/* + * Map from device function return U to vector texture type T + */ +template +__forceinline__ __device__ +typename std::enable_if< + __hip_is_tex_surf_scalar_channel_type::value, const T>::type +__hipMapFrom(const U &u) { + if constexpr (sizeof(typename T::value_type) < sizeof(float)) { + union { + U u; + int4 i4; + } d = { u }; + return __hipMapVector(d.i4); + } else { // sizeof(typename T::value_type) == sizeof(float) + union { + U u; + T t; + } d = { u }; + return d.t; + } +} + +/* + * Map from scalar texture type T to device function input U + */ +template +__forceinline__ __device__ +typename std::enable_if< +__hip_is_tex_surf_scalar_channel_type::value, const U>::type +__hipMapTo(const T &t) { + if constexpr (sizeof(T) < sizeof(float)) { + union { + U u; + int i; + } d = { 0 }; + d.i = static_cast(t); + return d.u; + } else { // sizeof(T) == sizeof(float) + union { + U u; + T t; + } d = { 0 }; + d.t = t; + return d.u; + } +} + +/* + * Map from vector texture type T to device function input U + */ +template +__forceinline__ __device__ +typename std::enable_if< + __hip_is_tex_surf_scalar_channel_type::value, const U>::type +__hipMapTo(const T &t) { + if constexpr (sizeof(typename T::value_type) < sizeof(float)) { + union { + U u; + int4 i4; + } d = { 0 }; + d.i4 = __hipMapVector(t); + return d.u; + } else { // sizeof(typename T::value_type) == sizeof(float) + union { + U u; + T t; + } d = { 0 }; + d.t = t; + return d.u; + } +} + +template < + typename T, + hipTextureReadMode readMode> +using __hip_tex_ret_t = typename __hip_tex_ret::type; + +template +struct __hip_tex_ret< + T, + hipReadModeElementType, + typename std::enable_if<__hip_is_tex_surf_channel_type::value, bool>::type> +{ + using type = T; +}; + +template< + typename T, + unsigned int rank> +struct __hip_tex_ret< + HIP_vector_type, + hipReadModeElementType, + typename std::enable_if<__hip_is_tex_surf_channel_type>::value, bool>::type> +{ + using type = HIP_vector_type<__hip_tex_ret_t, rank>; +}; + +template +struct __hip_tex_ret< + T, + hipReadModeNormalizedFloat, + typename std::enable_if<__hip_is_tex_normalized_channel_type::value, bool>::type> +{ + using type = float; +}; + +template< + typename T, + unsigned int rank> +struct __hip_tex_ret< + HIP_vector_type, + hipReadModeNormalizedFloat, + typename std::enable_if<__hip_is_tex_normalized_channel_type>::value, bool>::type> +{ + using type = HIP_vector_type<__hip_tex_ret_t, rank>; +}; + + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1Dfetch(texture t, int x) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_load_1Db(i, x); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1D(texture t, float x) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_1D(i, s, x); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2D(texture t, float x, float y) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_2D(i, s, float2(x, y).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1DLayered(texture t, float x, int layer) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_1Da(i, s, float2(x, layer).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2DLayered(texture t, float x, float y, int layer) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_2Da(i, s, float4(x, y, layer, 0.0f).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex3D(texture t, float x, float y, float z) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_3D(i, s, float4(x, y, z, 0.0f).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemap(texture t, float x, float y, float z) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_CM(i, s, float4(x, y, z, 0.0f).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1DLod(texture t, float x, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_1D(i, s, x, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2DLod(texture t, float x, float y, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_2D(i, s, float2(x, y).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1DLayeredLod(texture t, float x, int layer, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_1Da(i, s, float2(x, layer).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2DLayeredLod(texture t, float x, float y, int layer, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_2Da(i, s, float4(x, y, layer, 0.0f).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex3DLod(texture t, float x, float y, float z, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_3D(i, s, float4(x, y, z, 0.0f).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemapLod(texture t, float x, float y, float z, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_CM(i, s, float4(x, y, z, 0.0f).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemapLayered(texture t, float x, float y, float z, int layer) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_CMa(i, s, float4(x, y, z, layer).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemapLayeredLod(texture t, float x, float y, float z, int layer, float level) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_lod_CMa(i, s, float4(x, y, z, layer).data, level); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemapGrad(texture t, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + TEXTURE_PARAMETERS_INIT; + // TODO missing in device libs. + // auto tmp = __ockl_image_sample_grad_CM(i, s, float4(x, y, z, 0.0f).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + // return __hipMapFrom<__hip_tex_ret_t>(tmp); + return {}; +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t texCubemapLayeredGrad(texture t, float x, float y, float z, int layer, float4 dPdx, float4 dPdy) +{ + TEXTURE_PARAMETERS_INIT; + // TODO missing in device libs. + // auto tmp = __ockl_image_sample_grad_CMa(i, s, float4(x, y, z, layer).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + // return __hipMapFrom<__hip_tex_ret_t>(tmp); + return {}; +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1DGrad(texture t, float x, float dPdx, float dPdy) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_grad_1D(i, s, x, dPdx, dPdy); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2DGrad(texture t, float x, float y, float2 dPdx, float2 dPdy) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_grad_2D(i, s, float2(x, y).data, float2(dPdx.x, dPdx.y).data, float2(dPdy.x, dPdy.y).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex1DLayeredGrad(texture t, float x, int layer, float dPdx, float dPdy) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_grad_1Da(i, s, float2(x, layer).data, dPdx, dPdy); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex2DLayeredGrad(texture t, float x, float y, int layer, float2 dPdx, float2 dPdy) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_grad_2Da(i, s, float4(x, y, layer, 0.0f).data, float2(dPdx.x, dPdx.y).data, float2(dPdy.x, dPdy.y).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex_ret_t tex3DGrad(texture t, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + TEXTURE_PARAMETERS_INIT; + auto tmp = __ockl_image_sample_grad_3D(i, s, float4(x, y, z, 0.0f).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + return __hipMapFrom<__hip_tex_ret_t>(tmp); +} + +template < + typename T, + hipTextureReadMode readMode, + typename Enable = void> +struct __hip_tex2dgather_ret +{ + static_assert(std::is_same::value, "Invalid channel type!"); +}; + +template < + typename T, + hipTextureReadMode readMode> +using __hip_tex2dgather_ret_t = typename __hip_tex2dgather_ret::type; + +template +struct __hip_tex2dgather_ret< + T, + hipReadModeElementType, + typename std::enable_if<__hip_is_tex_surf_channel_type::value, bool>::type> +{ + using type = HIP_vector_type; +}; + +template< + typename T, + unsigned int rank> +struct __hip_tex2dgather_ret< + HIP_vector_type, + hipReadModeElementType, + typename std::enable_if<__hip_is_tex_surf_channel_type>::value, bool>::type> +{ + using type = HIP_vector_type; +}; + +template +struct __hip_tex2dgather_ret< + T, + hipReadModeNormalizedFloat, + typename std::enable_if<__hip_is_tex_normalized_channel_type::value, bool>::type> +{ + using type = float4; +}; + +template +static __forceinline__ __device__ __hip_img_chk__ __hip_tex2dgather_ret_t tex2Dgather(texture t, float x, float y, int comp=0) +{ + TEXTURE_PARAMETERS_INIT; + switch (comp) { + case 1: { + auto tmp = __ockl_image_gather4g_2D(i, s, float2(x, y).data); + return __hipMapFrom<__hip_tex2dgather_ret_t>(tmp); + } + case 2: { + auto tmp = __ockl_image_gather4b_2D(i, s, float2(x, y).data); + return __hipMapFrom<__hip_tex2dgather_ret_t>(tmp); + } + case 3: { + auto tmp = __ockl_image_gather4a_2D(i, s, float2(x, y).data); + return __hipMapFrom<__hip_tex2dgather_ret_t>(tmp); + } + default: { + auto tmp = __ockl_image_gather4r_2D(i, s, float2(x, y).data); + return __hipMapFrom<__hip_tex2dgather_ret_t>(tmp); + } + } + return {}; +} + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_indirect_functions.h b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_indirect_functions.h new file mode 100644 index 0000000000000000000000000000000000000000..1e435018dfae6c23e6026ae90a18842f65a48261 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hip/amd_detail/texture_indirect_functions.h @@ -0,0 +1,478 @@ +/* +Copyright (c) 2015 - 2023 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#pragma once + +#if defined(__cplusplus) + +#if !defined(__HIPCC_RTC__) +#include +#include +#include +#include +#include +#endif // !defined(__HIPCC_RTC__) + +#define TEXTURE_OBJECT_PARAMETERS_INIT \ + unsigned int ADDRESS_SPACE_CONSTANT* i = (unsigned int ADDRESS_SPACE_CONSTANT*)textureObject; \ + unsigned int ADDRESS_SPACE_CONSTANT* s = i + HIP_SAMPLER_OBJECT_OFFSET_DWORD; + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1Dfetch(hipTextureObject_t textureObject, int x) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_load_1Db(i, x); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1Dfetch(T *ptr, hipTextureObject_t textureObject, int x) +{ + *ptr = tex1Dfetch(textureObject, x); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1D(hipTextureObject_t textureObject, float x) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_1D(i, s, x); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1D(T *ptr, hipTextureObject_t textureObject, float x) +{ + *ptr = tex1D(textureObject, x); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2D(hipTextureObject_t textureObject, float x, float y) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_2D(i, s, float2(x, y).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2D(T *ptr, hipTextureObject_t textureObject, float x, float y) +{ + *ptr = tex2D(textureObject, x, y); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex3D(hipTextureObject_t textureObject, float x, float y, float z) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_3D(i, s, float4(x, y, z, 0.0f).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex3D(T *ptr, hipTextureObject_t textureObject, float x, float y, float z) +{ + *ptr = tex3D(textureObject, x, y, z); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1DLayered(hipTextureObject_t textureObject, float x, int layer) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_1Da(i, s, float2(x, layer).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1DLayered(T *ptr, hipTextureObject_t textureObject, float x, int layer) +{ + *ptr = tex1DLayered(textureObject, x, layer); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2DLayered(hipTextureObject_t textureObject, float x, float y, int layer) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_2Da(i, s, float4(x, y, layer, 0.0f).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2DLayered(T *ptr, hipTextureObject_t textureObject, float x, float y, int layer) +{ + *ptr = tex1DLayered(textureObject, x, y, layer); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemap(hipTextureObject_t textureObject, float x, float y, float z) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_CM(i, s, float4(x, y, z, 0.0f).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemap(T *ptr, hipTextureObject_t textureObject, float x, float y, float z) +{ + *ptr = texCubemap(textureObject, x, y, z); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemapLayered(hipTextureObject_t textureObject, float x, float y, float z, int layer) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_CMa(i, s, float4(x, y, z, layer).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemapLayered(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, int layer) +{ + *ptr = texCubemapLayered(textureObject, x, y, z, layer); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2Dgather(hipTextureObject_t textureObject, float x, float y, int comp = 0) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + switch (comp) { + case 1: { + auto tmp = __ockl_image_gather4r_2D(i, s, float2(x, y).data); + return __hipMapFrom(tmp); + break; + } + case 2: { + auto tmp = __ockl_image_gather4g_2D(i, s, float2(x, y).data); + return __hipMapFrom(tmp); + break; + } + case 3: { + auto tmp = __ockl_image_gather4b_2D(i, s, float2(x, y).data); + return __hipMapFrom(tmp); + break; + } + default: { + auto tmp = __ockl_image_gather4a_2D(i, s, float2(x, y).data); + return __hipMapFrom(tmp); + break; + } + } + return {}; +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2Dgather(T *ptr, hipTextureObject_t textureObject, float x, float y, int comp = 0) +{ + *ptr = texCubemapLayered(textureObject, x, y, comp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1DLod(hipTextureObject_t textureObject, float x, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_lod_1D(i, s, x, level); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1DLod(T *ptr, hipTextureObject_t textureObject, float x, float level) +{ + *ptr = tex1DLod(textureObject, x, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2DLod(hipTextureObject_t textureObject, float x, float y, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_lod_2D(i, s, float2(x, y).data, level); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2DLod(T *ptr, hipTextureObject_t textureObject, float x, float y, float level) +{ + *ptr = tex2DLod(textureObject, x, y, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex3DLod(hipTextureObject_t textureObject, float x, float y, float z, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_lod_3D(i, s, float4(x, y, z, 0.0f).data, level); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex3DLod(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, float level) +{ + *ptr = tex3DLod(textureObject, x, y, z, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1DLayeredLod(hipTextureObject_t textureObject, float x, int layer, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_1Da(i, s, float2(x, layer).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1DLayeredLod(T *ptr, hipTextureObject_t textureObject, float x, int layer, float level) +{ + *ptr = tex1DLayeredLod(textureObject, x, layer, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2DLayeredLod(hipTextureObject_t textureObject, float x, float y, int layer, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_2Da(i, s, float4(x, y, layer, 0.0f).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2DLayeredLod(T *ptr, hipTextureObject_t textureObject, float x, float y, int layer, float level) +{ + *ptr = tex2DLayeredLod(textureObject, x, y, layer, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemapLod(hipTextureObject_t textureObject, float x, float y, float z, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_lod_CM(i, s, float4(x, y, z, 0.0f).data, level); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemapLod(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, float level) +{ + *ptr = texCubemapLod(textureObject, x, y, z, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemapGrad(hipTextureObject_t textureObject, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + // TODO missing in device libs. + // auto tmp = __ockl_image_sample_grad_CM(i, s, float4(x, y, z, 0.0f).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + // return __hipMapFrom(tmp); + return {}; +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemapGrad(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + *ptr = texCubemapGrad(textureObject, x, y, z, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemapLayeredLod(hipTextureObject_t textureObject, float x, float y, float z, int layer, float level) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_lod_CMa(i, s, float4(x, y, z, layer).data, level); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemapLayeredLod(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, int layer, float level) +{ + *ptr = texCubemapLayeredLod(textureObject, x, y, z, layer, level); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1DGrad(hipTextureObject_t textureObject, float x, float dPdx, float dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_grad_1D(i, s, x, dPdx, dPdy); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1DGrad(T *ptr, hipTextureObject_t textureObject, float x, float dPdx, float dPdy) +{ + *ptr = tex1DGrad(textureObject, x, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2DGrad(hipTextureObject_t textureObject, float x, float y, float2 dPdx, float2 dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_grad_2D(i, s, float2(x, y).data, float2(dPdx.x, dPdx.y).data, float2(dPdy.x, dPdy.y).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2DGrad(T *ptr, hipTextureObject_t textureObject, float x, float y, float2 dPdx, float2 dPdy) +{ + *ptr = tex2DGrad(textureObject, x, y, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex3DGrad(hipTextureObject_t textureObject, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_grad_3D(i, s, float4(x, y, z, 0.0f).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex3DGrad(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, float4 dPdx, float4 dPdy) +{ + *ptr = tex3DGrad(textureObject, x, y, z, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex1DLayeredGrad(hipTextureObject_t textureObject, float x, int layer, float dPdx, float dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_grad_1Da(i, s, float2(x, layer).data, dPdx, dPdy); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex1DLayeredGrad(T *ptr, hipTextureObject_t textureObject, float x, int layer, float dPdx, float dPdy) +{ + *ptr = tex1DLayeredGrad(textureObject, x, layer, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T tex2DLayeredGrad(hipTextureObject_t textureObject, float x, float y, int layer, float2 dPdx, float2 dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + auto tmp = __ockl_image_sample_grad_2Da(i, s, float4(x, y, layer, 0.0f).data, float2(dPdx.x, dPdx.y).data, float2(dPdy.x, dPdy.y).data); + return __hipMapFrom(tmp); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void tex2DLayeredGrad(T *ptr, hipTextureObject_t textureObject, float x, float y, int layer, float2 dPdx, float2 dPdy) +{ + *ptr = tex2DLayeredGrad(textureObject, x, y, layer, dPdx, dPdy); +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ T texCubemapLayeredGrad(hipTextureObject_t textureObject, float x, float y, float z, int layer, float4 dPdx, float4 dPdy) +{ + TEXTURE_OBJECT_PARAMETERS_INIT + // TODO missing in device libs. + // auto tmp = __ockl_image_sample_grad_CMa(i, s, float4(x, y, z, layer).data, float4(dPdx.x, dPdx.y, dPdx.z, 0.0f).data, float4(dPdy.x, dPdy.y, dPdy.z, 0.0f).data); + // return __hipMapFrom(tmp); + return {}; +} + +template < + typename T, + typename std::enable_if<__hip_is_tex_surf_channel_type::value>::type* = nullptr> +static __device__ __hip_img_chk__ void texCubemapLayeredGrad(T *ptr, hipTextureObject_t textureObject, float x, float y, float z, int layer, float4 dPdx, float4 dPdy) +{ + *ptr = texCubemapLayeredGrad(textureObject, x, y, z, layer, dPdx, dPdy); +} + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/Brig.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/Brig.h new file mode 100644 index 0000000000000000000000000000000000000000..4f34bd1d5012c1fca9a01417be4e4d025fa1ff15 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/Brig.h @@ -0,0 +1,1131 @@ +// University of Illinois/NCSA +// Open Source License +// +// Copyright (c) 2013-2015, Advanced Micro Devices, Inc. +// All rights reserved. +// +// Developed by: +// +// HSA Team +// +// Advanced Micro Devices, Inc +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy of +// this software and associated documentation files (the "Software"), to deal with +// the Software without restriction, including without limitation the rights to +// use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies +// of the Software, and to permit persons to whom the Software is furnished to do +// so, subject to the following conditions: +// +// * Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// +// * Redistributions in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimers in the +// documentation and/or other materials provided with the distribution. +// +// * Neither the names of the LLVM Team, University of Illinois at +// Urbana-Champaign, nor the names of its contributors may be used to +// endorse or promote products derived from this Software without specific +// prior written permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS +// FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE +// SOFTWARE. + +#ifndef INCLUDED_BRIG_H +#define INCLUDED_BRIG_H + +#include /* size_t */ +#include /* uintXX_t */ + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +/*========================================================================================*/ +/* =======================================================================================*/ +/* =======================================================================================*/ +/* =======================================================================================*/ + +typedef uint32_t BrigCodeOffset32_t; +typedef uint32_t BrigOperandOffset32_t; +typedef uint32_t BrigDataOffset32_t; + +typedef BrigDataOffset32_t BrigDataOffsetCodeList32_t; +typedef BrigDataOffset32_t BrigDataOffsetOperandList32_t; +typedef BrigDataOffset32_t BrigDataOffsetString32_t; + +typedef uint32_t BrigVersion32_t; +enum BrigVersion { + BRIG_VERSION_HSAIL_MAJOR = 1, + BRIG_VERSION_HSAIL_MINOR = 0, + BRIG_VERSION_BRIG_MAJOR = 1, + BRIG_VERSION_BRIG_MINOR = 0 +}; + +typedef uint16_t BrigKind16_t; +enum BrigKind { + BRIG_KIND_NONE = 0x0000, + + BRIG_KIND_DIRECTIVE_BEGIN = 0x1000, + BRIG_KIND_DIRECTIVE_ARG_BLOCK_END = 0x1000, + BRIG_KIND_DIRECTIVE_ARG_BLOCK_START = 0x1001, + BRIG_KIND_DIRECTIVE_COMMENT = 0x1002, + BRIG_KIND_DIRECTIVE_CONTROL = 0x1003, + BRIG_KIND_DIRECTIVE_EXTENSION = 0x1004, + BRIG_KIND_DIRECTIVE_FBARRIER = 0x1005, + BRIG_KIND_DIRECTIVE_FUNCTION = 0x1006, + BRIG_KIND_DIRECTIVE_INDIRECT_FUNCTION = 0x1007, + BRIG_KIND_DIRECTIVE_KERNEL = 0x1008, + BRIG_KIND_DIRECTIVE_LABEL = 0x1009, + BRIG_KIND_DIRECTIVE_LOC = 0x100a, + BRIG_KIND_DIRECTIVE_MODULE = 0x100b, + BRIG_KIND_DIRECTIVE_PRAGMA = 0x100c, + BRIG_KIND_DIRECTIVE_SIGNATURE = 0x100d, + BRIG_KIND_DIRECTIVE_VARIABLE = 0x100e, + BRIG_KIND_DIRECTIVE_END = 0x100f, + + BRIG_KIND_INST_BEGIN = 0x2000, + BRIG_KIND_INST_ADDR = 0x2000, + BRIG_KIND_INST_ATOMIC = 0x2001, + BRIG_KIND_INST_BASIC = 0x2002, + BRIG_KIND_INST_BR = 0x2003, + BRIG_KIND_INST_CMP = 0x2004, + BRIG_KIND_INST_CVT = 0x2005, + BRIG_KIND_INST_IMAGE = 0x2006, + BRIG_KIND_INST_LANE = 0x2007, + BRIG_KIND_INST_MEM = 0x2008, + BRIG_KIND_INST_MEM_FENCE = 0x2009, + BRIG_KIND_INST_MOD = 0x200a, + BRIG_KIND_INST_QUERY_IMAGE = 0x200b, + BRIG_KIND_INST_QUERY_SAMPLER = 0x200c, + BRIG_KIND_INST_QUEUE = 0x200d, + BRIG_KIND_INST_SEG = 0x200e, + BRIG_KIND_INST_SEG_CVT = 0x200f, + BRIG_KIND_INST_SIGNAL = 0x2010, + BRIG_KIND_INST_SOURCE_TYPE = 0x2011, + BRIG_KIND_INST_END = 0x2012, + + BRIG_KIND_OPERAND_BEGIN = 0x3000, + BRIG_KIND_OPERAND_ADDRESS = 0x3000, + BRIG_KIND_OPERAND_ALIGN = 0x3001, + BRIG_KIND_OPERAND_CODE_LIST = 0x3002, + BRIG_KIND_OPERAND_CODE_REF = 0x3003, + BRIG_KIND_OPERAND_CONSTANT_BYTES = 0x3004, + BRIG_KIND_OPERAND_RESERVED = 0x3005, + BRIG_KIND_OPERAND_CONSTANT_IMAGE = 0x3006, + BRIG_KIND_OPERAND_CONSTANT_OPERAND_LIST = 0x3007, + BRIG_KIND_OPERAND_CONSTANT_SAMPLER = 0x3008, + BRIG_KIND_OPERAND_OPERAND_LIST = 0x3009, + BRIG_KIND_OPERAND_REGISTER = 0x300a, + BRIG_KIND_OPERAND_STRING = 0x300b, + BRIG_KIND_OPERAND_WAVESIZE = 0x300c, + BRIG_KIND_OPERAND_END = 0x300d +}; + +typedef uint8_t BrigAlignment8_t; +enum BrigAlignment { + BRIG_ALIGNMENT_NONE = 0, + BRIG_ALIGNMENT_1 = 1, + BRIG_ALIGNMENT_2 = 2, + BRIG_ALIGNMENT_4 = 3, + BRIG_ALIGNMENT_8 = 4, + BRIG_ALIGNMENT_16 = 5, + BRIG_ALIGNMENT_32 = 6, + BRIG_ALIGNMENT_64 = 7, + BRIG_ALIGNMENT_128 = 8, + BRIG_ALIGNMENT_256 = 9, + BRIG_ALIGNMENT_MAX = BRIG_ALIGNMENT_256 +}; + +typedef uint8_t BrigAllocation8_t; +enum BrigAllocation { + BRIG_ALLOCATION_NONE = 0, + BRIG_ALLOCATION_PROGRAM = 1, + BRIG_ALLOCATION_AGENT = 2, + BRIG_ALLOCATION_AUTOMATIC = 3 +}; + +typedef uint8_t BrigAluModifier8_t; +enum BrigAluModifierMask { + BRIG_ALU_FTZ = 1 +}; + +typedef uint8_t BrigAtomicOperation8_t; +enum BrigAtomicOperation { + BRIG_ATOMIC_ADD = 0, + BRIG_ATOMIC_AND = 1, + BRIG_ATOMIC_CAS = 2, + BRIG_ATOMIC_EXCH = 3, + BRIG_ATOMIC_LD = 4, + BRIG_ATOMIC_MAX = 5, + BRIG_ATOMIC_MIN = 6, + BRIG_ATOMIC_OR = 7, + BRIG_ATOMIC_ST = 8, + BRIG_ATOMIC_SUB = 9, + BRIG_ATOMIC_WRAPDEC = 10, + BRIG_ATOMIC_WRAPINC = 11, + BRIG_ATOMIC_XOR = 12, + BRIG_ATOMIC_WAIT_EQ = 13, + BRIG_ATOMIC_WAIT_NE = 14, + BRIG_ATOMIC_WAIT_LT = 15, + BRIG_ATOMIC_WAIT_GTE = 16, + BRIG_ATOMIC_WAITTIMEOUT_EQ = 17, + BRIG_ATOMIC_WAITTIMEOUT_NE = 18, + BRIG_ATOMIC_WAITTIMEOUT_LT = 19, + BRIG_ATOMIC_WAITTIMEOUT_GTE = 20 +}; + +typedef uint8_t BrigCompareOperation8_t; +enum BrigCompareOperation { + BRIG_COMPARE_EQ = 0, + BRIG_COMPARE_NE = 1, + BRIG_COMPARE_LT = 2, + BRIG_COMPARE_LE = 3, + BRIG_COMPARE_GT = 4, + BRIG_COMPARE_GE = 5, + BRIG_COMPARE_EQU = 6, + BRIG_COMPARE_NEU = 7, + BRIG_COMPARE_LTU = 8, + BRIG_COMPARE_LEU = 9, + BRIG_COMPARE_GTU = 10, + BRIG_COMPARE_GEU = 11, + BRIG_COMPARE_NUM = 12, + BRIG_COMPARE_NAN = 13, + BRIG_COMPARE_SEQ = 14, + BRIG_COMPARE_SNE = 15, + BRIG_COMPARE_SLT = 16, + BRIG_COMPARE_SLE = 17, + BRIG_COMPARE_SGT = 18, + BRIG_COMPARE_SGE = 19, + BRIG_COMPARE_SGEU = 20, + BRIG_COMPARE_SEQU = 21, + BRIG_COMPARE_SNEU = 22, + BRIG_COMPARE_SLTU = 23, + BRIG_COMPARE_SLEU = 24, + BRIG_COMPARE_SNUM = 25, + BRIG_COMPARE_SNAN = 26, + BRIG_COMPARE_SGTU = 27 +}; + +typedef uint16_t BrigControlDirective16_t; +enum BrigControlDirective { + BRIG_CONTROL_NONE = 0, + BRIG_CONTROL_ENABLEBREAKEXCEPTIONS = 1, + BRIG_CONTROL_ENABLEDETECTEXCEPTIONS = 2, + BRIG_CONTROL_MAXDYNAMICGROUPSIZE = 3, + BRIG_CONTROL_MAXFLATGRIDSIZE = 4, + BRIG_CONTROL_MAXFLATWORKGROUPSIZE = 5, + BRIG_CONTROL_REQUIREDDIM = 6, + BRIG_CONTROL_REQUIREDGRIDSIZE = 7, + BRIG_CONTROL_REQUIREDWORKGROUPSIZE = 8, + BRIG_CONTROL_REQUIRENOPARTIALWORKGROUPS = 9 +}; + +typedef uint8_t BrigExecutableModifier8_t; +enum BrigExecutableModifierMask { + BRIG_EXECUTABLE_DEFINITION = 1 +}; + +typedef uint8_t BrigImageChannelOrder8_t; +enum BrigImageChannelOrder { + BRIG_CHANNEL_ORDER_A = 0, + BRIG_CHANNEL_ORDER_R = 1, + BRIG_CHANNEL_ORDER_RX = 2, + BRIG_CHANNEL_ORDER_RG = 3, + BRIG_CHANNEL_ORDER_RGX = 4, + BRIG_CHANNEL_ORDER_RA = 5, + BRIG_CHANNEL_ORDER_RGB = 6, + BRIG_CHANNEL_ORDER_RGBX = 7, + BRIG_CHANNEL_ORDER_RGBA = 8, + BRIG_CHANNEL_ORDER_BGRA = 9, + BRIG_CHANNEL_ORDER_ARGB = 10, + BRIG_CHANNEL_ORDER_ABGR = 11, + BRIG_CHANNEL_ORDER_SRGB = 12, + BRIG_CHANNEL_ORDER_SRGBX = 13, + BRIG_CHANNEL_ORDER_SRGBA = 14, + BRIG_CHANNEL_ORDER_SBGRA = 15, + BRIG_CHANNEL_ORDER_INTENSITY = 16, + BRIG_CHANNEL_ORDER_LUMINANCE = 17, + BRIG_CHANNEL_ORDER_DEPTH = 18, + BRIG_CHANNEL_ORDER_DEPTH_STENCIL = 19, + + BRIG_CHANNEL_ORDER_FIRST_USER_DEFINED = 128 +}; + +typedef uint8_t BrigImageChannelType8_t; +enum BrigImageChannelType { + BRIG_CHANNEL_TYPE_SNORM_INT8 = 0, + BRIG_CHANNEL_TYPE_SNORM_INT16 = 1, + BRIG_CHANNEL_TYPE_UNORM_INT8 = 2, + BRIG_CHANNEL_TYPE_UNORM_INT16 = 3, + BRIG_CHANNEL_TYPE_UNORM_INT24 = 4, + BRIG_CHANNEL_TYPE_UNORM_SHORT_555 = 5, + BRIG_CHANNEL_TYPE_UNORM_SHORT_565 = 6, + BRIG_CHANNEL_TYPE_UNORM_INT_101010 = 7, + BRIG_CHANNEL_TYPE_SIGNED_INT8 = 8, + BRIG_CHANNEL_TYPE_SIGNED_INT16 = 9, + BRIG_CHANNEL_TYPE_SIGNED_INT32 = 10, + BRIG_CHANNEL_TYPE_UNSIGNED_INT8 = 11, + BRIG_CHANNEL_TYPE_UNSIGNED_INT16 = 12, + BRIG_CHANNEL_TYPE_UNSIGNED_INT32 = 13, + BRIG_CHANNEL_TYPE_HALF_FLOAT = 14, + BRIG_CHANNEL_TYPE_FLOAT = 15, + + BRIG_CHANNEL_TYPE_FIRST_USER_DEFINED = 128 +}; + +typedef uint8_t BrigImageGeometry8_t; +enum BrigImageGeometry { + BRIG_GEOMETRY_1D = 0, + BRIG_GEOMETRY_2D = 1, + BRIG_GEOMETRY_3D = 2, + BRIG_GEOMETRY_1DA = 3, + BRIG_GEOMETRY_2DA = 4, + BRIG_GEOMETRY_1DB = 5, + BRIG_GEOMETRY_2DDEPTH = 6, + BRIG_GEOMETRY_2DADEPTH = 7, + + BRIG_GEOMETRY_FIRST_USER_DEFINED = 128 +}; + +typedef uint8_t BrigImageQuery8_t; +enum BrigImageQuery { + BRIG_IMAGE_QUERY_WIDTH = 0, + BRIG_IMAGE_QUERY_HEIGHT = 1, + BRIG_IMAGE_QUERY_DEPTH = 2, + BRIG_IMAGE_QUERY_ARRAY = 3, + BRIG_IMAGE_QUERY_CHANNELORDER = 4, + BRIG_IMAGE_QUERY_CHANNELTYPE = 5, + + BRIG_IMAGE_QUERY_FIRST_USER_DEFINED = 6 +}; + +typedef uint8_t BrigLinkage8_t; +enum BrigLinkage { + BRIG_LINKAGE_NONE = 0, + BRIG_LINKAGE_PROGRAM = 1, + BRIG_LINKAGE_MODULE = 2, + BRIG_LINKAGE_FUNCTION = 3, + BRIG_LINKAGE_ARG = 4 +}; + +typedef uint8_t BrigMachineModel8_t; +enum BrigMachineModel { + BRIG_MACHINE_SMALL = 0, + BRIG_MACHINE_LARGE = 1, +}; + +typedef uint8_t BrigMemoryModifier8_t; +enum BrigMemoryModifierMask { + BRIG_MEMORY_CONST = 1 +}; + +typedef uint8_t BrigMemoryOrder8_t; +enum BrigMemoryOrder { + BRIG_MEMORY_ORDER_NONE = 0, + BRIG_MEMORY_ORDER_RELAXED = 1, + BRIG_MEMORY_ORDER_SC_ACQUIRE = 2, + BRIG_MEMORY_ORDER_SC_RELEASE = 3, + BRIG_MEMORY_ORDER_SC_ACQUIRE_RELEASE = 4, +}; + +typedef uint8_t BrigMemoryScope8_t; +enum BrigMemoryScope { + BRIG_MEMORY_SCOPE_NONE = 0, + BRIG_MEMORY_SCOPE_WORKITEM = 1, + BRIG_MEMORY_SCOPE_WAVEFRONT = 2, + BRIG_MEMORY_SCOPE_WORKGROUP = 3, + BRIG_MEMORY_SCOPE_AGENT = 4, + BRIG_MEMORY_SCOPE_SYSTEM = 5, +}; + +typedef uint16_t BrigOpcode16_t; +enum BrigOpcode { + BRIG_OPCODE_NOP = 0, + BRIG_OPCODE_ABS = 1, + BRIG_OPCODE_ADD = 2, + BRIG_OPCODE_BORROW = 3, + BRIG_OPCODE_CARRY = 4, + BRIG_OPCODE_CEIL = 5, + BRIG_OPCODE_COPYSIGN = 6, + BRIG_OPCODE_DIV = 7, + BRIG_OPCODE_FLOOR = 8, + BRIG_OPCODE_FMA = 9, + BRIG_OPCODE_FRACT = 10, + BRIG_OPCODE_MAD = 11, + BRIG_OPCODE_MAX = 12, + BRIG_OPCODE_MIN = 13, + BRIG_OPCODE_MUL = 14, + BRIG_OPCODE_MULHI = 15, + BRIG_OPCODE_NEG = 16, + BRIG_OPCODE_REM = 17, + BRIG_OPCODE_RINT = 18, + BRIG_OPCODE_SQRT = 19, + BRIG_OPCODE_SUB = 20, + BRIG_OPCODE_TRUNC = 21, + BRIG_OPCODE_MAD24 = 22, + BRIG_OPCODE_MAD24HI = 23, + BRIG_OPCODE_MUL24 = 24, + BRIG_OPCODE_MUL24HI = 25, + BRIG_OPCODE_SHL = 26, + BRIG_OPCODE_SHR = 27, + BRIG_OPCODE_AND = 28, + BRIG_OPCODE_NOT = 29, + BRIG_OPCODE_OR = 30, + BRIG_OPCODE_POPCOUNT = 31, + BRIG_OPCODE_XOR = 32, + BRIG_OPCODE_BITEXTRACT = 33, + BRIG_OPCODE_BITINSERT = 34, + BRIG_OPCODE_BITMASK = 35, + BRIG_OPCODE_BITREV = 36, + BRIG_OPCODE_BITSELECT = 37, + BRIG_OPCODE_FIRSTBIT = 38, + BRIG_OPCODE_LASTBIT = 39, + BRIG_OPCODE_COMBINE = 40, + BRIG_OPCODE_EXPAND = 41, + BRIG_OPCODE_LDA = 42, + BRIG_OPCODE_MOV = 43, + BRIG_OPCODE_SHUFFLE = 44, + BRIG_OPCODE_UNPACKHI = 45, + BRIG_OPCODE_UNPACKLO = 46, + BRIG_OPCODE_PACK = 47, + BRIG_OPCODE_UNPACK = 48, + BRIG_OPCODE_CMOV = 49, + BRIG_OPCODE_CLASS = 50, + BRIG_OPCODE_NCOS = 51, + BRIG_OPCODE_NEXP2 = 52, + BRIG_OPCODE_NFMA = 53, + BRIG_OPCODE_NLOG2 = 54, + BRIG_OPCODE_NRCP = 55, + BRIG_OPCODE_NRSQRT = 56, + BRIG_OPCODE_NSIN = 57, + BRIG_OPCODE_NSQRT = 58, + BRIG_OPCODE_BITALIGN = 59, + BRIG_OPCODE_BYTEALIGN = 60, + BRIG_OPCODE_PACKCVT = 61, + BRIG_OPCODE_UNPACKCVT = 62, + BRIG_OPCODE_LERP = 63, + BRIG_OPCODE_SAD = 64, + BRIG_OPCODE_SADHI = 65, + BRIG_OPCODE_SEGMENTP = 66, + BRIG_OPCODE_FTOS = 67, + BRIG_OPCODE_STOF = 68, + BRIG_OPCODE_CMP = 69, + BRIG_OPCODE_CVT = 70, + BRIG_OPCODE_LD = 71, + BRIG_OPCODE_ST = 72, + BRIG_OPCODE_ATOMIC = 73, + BRIG_OPCODE_ATOMICNORET = 74, + BRIG_OPCODE_SIGNAL = 75, + BRIG_OPCODE_SIGNALNORET = 76, + BRIG_OPCODE_MEMFENCE = 77, + BRIG_OPCODE_RDIMAGE = 78, + BRIG_OPCODE_LDIMAGE = 79, + BRIG_OPCODE_STIMAGE = 80, + BRIG_OPCODE_IMAGEFENCE = 81, + BRIG_OPCODE_QUERYIMAGE = 82, + BRIG_OPCODE_QUERYSAMPLER = 83, + BRIG_OPCODE_CBR = 84, + BRIG_OPCODE_BR = 85, + BRIG_OPCODE_SBR = 86, + BRIG_OPCODE_BARRIER = 87, + BRIG_OPCODE_WAVEBARRIER = 88, + BRIG_OPCODE_ARRIVEFBAR = 89, + BRIG_OPCODE_INITFBAR = 90, + BRIG_OPCODE_JOINFBAR = 91, + BRIG_OPCODE_LEAVEFBAR = 92, + BRIG_OPCODE_RELEASEFBAR = 93, + BRIG_OPCODE_WAITFBAR = 94, + BRIG_OPCODE_LDF = 95, + BRIG_OPCODE_ACTIVELANECOUNT = 96, + BRIG_OPCODE_ACTIVELANEID = 97, + BRIG_OPCODE_ACTIVELANEMASK = 98, + BRIG_OPCODE_ACTIVELANEPERMUTE = 99, + BRIG_OPCODE_CALL = 100, + BRIG_OPCODE_SCALL = 101, + BRIG_OPCODE_ICALL = 102, + BRIG_OPCODE_RET = 103, + BRIG_OPCODE_ALLOCA = 104, + BRIG_OPCODE_CURRENTWORKGROUPSIZE = 105, + BRIG_OPCODE_CURRENTWORKITEMFLATID = 106, + BRIG_OPCODE_DIM = 107, + BRIG_OPCODE_GRIDGROUPS = 108, + BRIG_OPCODE_GRIDSIZE = 109, + BRIG_OPCODE_PACKETCOMPLETIONSIG = 110, + BRIG_OPCODE_PACKETID = 111, + BRIG_OPCODE_WORKGROUPID = 112, + BRIG_OPCODE_WORKGROUPSIZE = 113, + BRIG_OPCODE_WORKITEMABSID = 114, + BRIG_OPCODE_WORKITEMFLATABSID = 115, + BRIG_OPCODE_WORKITEMFLATID = 116, + BRIG_OPCODE_WORKITEMID = 117, + BRIG_OPCODE_CLEARDETECTEXCEPT = 118, + BRIG_OPCODE_GETDETECTEXCEPT = 119, + BRIG_OPCODE_SETDETECTEXCEPT = 120, + BRIG_OPCODE_ADDQUEUEWRITEINDEX = 121, + BRIG_OPCODE_CASQUEUEWRITEINDEX = 122, + BRIG_OPCODE_LDQUEUEREADINDEX = 123, + BRIG_OPCODE_LDQUEUEWRITEINDEX = 124, + BRIG_OPCODE_STQUEUEREADINDEX = 125, + BRIG_OPCODE_STQUEUEWRITEINDEX = 126, + BRIG_OPCODE_CLOCK = 127, + BRIG_OPCODE_CUID = 128, + BRIG_OPCODE_DEBUGTRAP = 129, + BRIG_OPCODE_GROUPBASEPTR = 130, + BRIG_OPCODE_KERNARGBASEPTR = 131, + BRIG_OPCODE_LANEID = 132, + BRIG_OPCODE_MAXCUID = 133, + BRIG_OPCODE_MAXWAVEID = 134, + BRIG_OPCODE_NULLPTR = 135, + BRIG_OPCODE_WAVEID = 136, + + BRIG_OPCODE_FIRST_USER_DEFINED = 32768, +}; + +typedef uint8_t BrigPack8_t; +enum BrigPack { + BRIG_PACK_NONE = 0, + BRIG_PACK_PP = 1, + BRIG_PACK_PS = 2, + BRIG_PACK_SP = 3, + BRIG_PACK_SS = 4, + BRIG_PACK_S = 5, + BRIG_PACK_P = 6, + BRIG_PACK_PPSAT = 7, + BRIG_PACK_PSSAT = 8, + BRIG_PACK_SPSAT = 9, + BRIG_PACK_SSSAT = 10, + BRIG_PACK_SSAT = 11, + BRIG_PACK_PSAT = 12 +}; + +typedef uint8_t BrigProfile8_t; +enum BrigProfile { + BRIG_PROFILE_BASE = 0, + BRIG_PROFILE_FULL = 1, +}; + +typedef uint16_t BrigRegisterKind16_t; +enum BrigRegisterKind { + BRIG_REGISTER_KIND_CONTROL = 0, + BRIG_REGISTER_KIND_SINGLE = 1, + BRIG_REGISTER_KIND_DOUBLE = 2, + BRIG_REGISTER_KIND_QUAD = 3 +}; + +typedef uint8_t BrigRound8_t; +enum BrigRound { + BRIG_ROUND_NONE = 0, + BRIG_ROUND_FLOAT_DEFAULT = 1, + BRIG_ROUND_FLOAT_NEAR_EVEN = 2, + BRIG_ROUND_FLOAT_ZERO = 3, + BRIG_ROUND_FLOAT_PLUS_INFINITY = 4, + BRIG_ROUND_FLOAT_MINUS_INFINITY = 5, + BRIG_ROUND_INTEGER_NEAR_EVEN = 6, + BRIG_ROUND_INTEGER_ZERO = 7, + BRIG_ROUND_INTEGER_PLUS_INFINITY = 8, + BRIG_ROUND_INTEGER_MINUS_INFINITY = 9, + BRIG_ROUND_INTEGER_NEAR_EVEN_SAT = 10, + BRIG_ROUND_INTEGER_ZERO_SAT = 11, + BRIG_ROUND_INTEGER_PLUS_INFINITY_SAT = 12, + BRIG_ROUND_INTEGER_MINUS_INFINITY_SAT = 13, + BRIG_ROUND_INTEGER_SIGNALING_NEAR_EVEN = 14, + BRIG_ROUND_INTEGER_SIGNALING_ZERO = 15, + BRIG_ROUND_INTEGER_SIGNALING_PLUS_INFINITY = 16, + BRIG_ROUND_INTEGER_SIGNALING_MINUS_INFINITY = 17, + BRIG_ROUND_INTEGER_SIGNALING_NEAR_EVEN_SAT = 18, + BRIG_ROUND_INTEGER_SIGNALING_ZERO_SAT = 19, + BRIG_ROUND_INTEGER_SIGNALING_PLUS_INFINITY_SAT = 20, + BRIG_ROUND_INTEGER_SIGNALING_MINUS_INFINITY_SAT = 21 +}; + +typedef uint8_t BrigSamplerAddressing8_t; +enum BrigSamplerAddressing { + BRIG_ADDRESSING_UNDEFINED = 0, + BRIG_ADDRESSING_CLAMP_TO_EDGE = 1, + BRIG_ADDRESSING_CLAMP_TO_BORDER = 2, + BRIG_ADDRESSING_REPEAT = 3, + BRIG_ADDRESSING_MIRRORED_REPEAT = 4, + + BRIG_ADDRESSING_FIRST_USER_DEFINED = 128 +}; + +typedef uint8_t BrigSamplerCoordNormalization8_t; +enum BrigSamplerCoordNormalization { + BRIG_COORD_UNNORMALIZED = 0, + BRIG_COORD_NORMALIZED = 1 +}; + +typedef uint8_t BrigSamplerFilter8_t; +enum BrigSamplerFilter { + BRIG_FILTER_NEAREST = 0, + BRIG_FILTER_LINEAR = 1, + + BRIG_FILTER_FIRST_USER_DEFINED = 128 +}; + +typedef uint8_t BrigSamplerQuery8_t; +enum BrigSamplerQuery { + BRIG_SAMPLER_QUERY_ADDRESSING = 0, + BRIG_SAMPLER_QUERY_COORD = 1, + BRIG_SAMPLER_QUERY_FILTER = 2 +}; + +typedef uint32_t BrigSectionIndex32_t; +enum BrigSectionIndex { + BRIG_SECTION_INDEX_DATA = 0, + BRIG_SECTION_INDEX_CODE = 1, + BRIG_SECTION_INDEX_OPERAND = 2, + + BRIG_SECTION_INDEX_BEGIN_IMPLEMENTATION_DEFINED = 3, +}; + +typedef uint8_t BrigSegCvtModifier8_t; +enum BrigSegCvtModifierMask { + BRIG_SEG_CVT_NONULL = 1 +}; + +typedef uint8_t BrigSegment8_t; +enum BrigSegment { + BRIG_SEGMENT_NONE = 0, + BRIG_SEGMENT_FLAT = 1, + BRIG_SEGMENT_GLOBAL = 2, + BRIG_SEGMENT_READONLY = 3, + BRIG_SEGMENT_KERNARG = 4, + BRIG_SEGMENT_GROUP = 5, + BRIG_SEGMENT_PRIVATE = 6, + BRIG_SEGMENT_SPILL = 7, + BRIG_SEGMENT_ARG = 8, + + BRIG_SEGMENT_FIRST_USER_DEFINED = 128 +}; + +enum { + BRIG_TYPE_BASE_SIZE = 5, + BRIG_TYPE_PACK_SIZE = 2, + BRIG_TYPE_ARRAY_SIZE = 1, + + BRIG_TYPE_BASE_SHIFT = 0, + BRIG_TYPE_PACK_SHIFT = BRIG_TYPE_BASE_SHIFT + BRIG_TYPE_BASE_SIZE, + BRIG_TYPE_ARRAY_SHIFT = BRIG_TYPE_PACK_SHIFT + BRIG_TYPE_PACK_SIZE, + + BRIG_TYPE_BASE_MASK = ((1 << BRIG_TYPE_BASE_SIZE) - 1) << BRIG_TYPE_BASE_SHIFT, + BRIG_TYPE_PACK_MASK = ((1 << BRIG_TYPE_PACK_SIZE) - 1) << BRIG_TYPE_PACK_SHIFT, + BRIG_TYPE_ARRAY_MASK = ((1 << BRIG_TYPE_ARRAY_SIZE) - 1) << BRIG_TYPE_ARRAY_SHIFT, + + BRIG_TYPE_PACK_NONE = 0 << BRIG_TYPE_PACK_SHIFT, + BRIG_TYPE_PACK_32 = 1 << BRIG_TYPE_PACK_SHIFT, + BRIG_TYPE_PACK_64 = 2 << BRIG_TYPE_PACK_SHIFT, + BRIG_TYPE_PACK_128 = 3 << BRIG_TYPE_PACK_SHIFT, + + BRIG_TYPE_ARRAY = 1 << BRIG_TYPE_ARRAY_SHIFT +}; + +typedef uint16_t BrigType16_t; +enum BrigType { + BRIG_TYPE_NONE = 0, + BRIG_TYPE_U8 = 1, + BRIG_TYPE_U16 = 2, + BRIG_TYPE_U32 = 3, + BRIG_TYPE_U64 = 4, + BRIG_TYPE_S8 = 5, + BRIG_TYPE_S16 = 6, + BRIG_TYPE_S32 = 7, + BRIG_TYPE_S64 = 8, + BRIG_TYPE_F16 = 9, + BRIG_TYPE_F32 = 10, + BRIG_TYPE_F64 = 11, + BRIG_TYPE_B1 = 12, + BRIG_TYPE_B8 = 13, + BRIG_TYPE_B16 = 14, + BRIG_TYPE_B32 = 15, + BRIG_TYPE_B64 = 16, + BRIG_TYPE_B128 = 17, + BRIG_TYPE_SAMP = 18, + BRIG_TYPE_ROIMG = 19, + BRIG_TYPE_WOIMG = 20, + BRIG_TYPE_RWIMG = 21, + BRIG_TYPE_SIG32 = 22, + BRIG_TYPE_SIG64 = 23, + + BRIG_TYPE_U8X4 = BRIG_TYPE_U8 | BRIG_TYPE_PACK_32, + BRIG_TYPE_U8X8 = BRIG_TYPE_U8 | BRIG_TYPE_PACK_64, + BRIG_TYPE_U8X16 = BRIG_TYPE_U8 | BRIG_TYPE_PACK_128, + BRIG_TYPE_U16X2 = BRIG_TYPE_U16 | BRIG_TYPE_PACK_32, + BRIG_TYPE_U16X4 = BRIG_TYPE_U16 | BRIG_TYPE_PACK_64, + BRIG_TYPE_U16X8 = BRIG_TYPE_U16 | BRIG_TYPE_PACK_128, + BRIG_TYPE_U32X2 = BRIG_TYPE_U32 | BRIG_TYPE_PACK_64, + BRIG_TYPE_U32X4 = BRIG_TYPE_U32 | BRIG_TYPE_PACK_128, + BRIG_TYPE_U64X2 = BRIG_TYPE_U64 | BRIG_TYPE_PACK_128, + BRIG_TYPE_S8X4 = BRIG_TYPE_S8 | BRIG_TYPE_PACK_32, + BRIG_TYPE_S8X8 = BRIG_TYPE_S8 | BRIG_TYPE_PACK_64, + BRIG_TYPE_S8X16 = BRIG_TYPE_S8 | BRIG_TYPE_PACK_128, + BRIG_TYPE_S16X2 = BRIG_TYPE_S16 | BRIG_TYPE_PACK_32, + BRIG_TYPE_S16X4 = BRIG_TYPE_S16 | BRIG_TYPE_PACK_64, + BRIG_TYPE_S16X8 = BRIG_TYPE_S16 | BRIG_TYPE_PACK_128, + BRIG_TYPE_S32X2 = BRIG_TYPE_S32 | BRIG_TYPE_PACK_64, + BRIG_TYPE_S32X4 = BRIG_TYPE_S32 | BRIG_TYPE_PACK_128, + BRIG_TYPE_S64X2 = BRIG_TYPE_S64 | BRIG_TYPE_PACK_128, + BRIG_TYPE_F16X2 = BRIG_TYPE_F16 | BRIG_TYPE_PACK_32, + BRIG_TYPE_F16X4 = BRIG_TYPE_F16 | BRIG_TYPE_PACK_64, + BRIG_TYPE_F16X8 = BRIG_TYPE_F16 | BRIG_TYPE_PACK_128, + BRIG_TYPE_F32X2 = BRIG_TYPE_F32 | BRIG_TYPE_PACK_64, + BRIG_TYPE_F32X4 = BRIG_TYPE_F32 | BRIG_TYPE_PACK_128, + BRIG_TYPE_F64X2 = BRIG_TYPE_F64 | BRIG_TYPE_PACK_128, + + BRIG_TYPE_U8_ARRAY = BRIG_TYPE_U8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U16_ARRAY = BRIG_TYPE_U16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U32_ARRAY = BRIG_TYPE_U32 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U64_ARRAY = BRIG_TYPE_U64 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S8_ARRAY = BRIG_TYPE_S8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S16_ARRAY = BRIG_TYPE_S16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S32_ARRAY = BRIG_TYPE_S32 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S64_ARRAY = BRIG_TYPE_S64 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F16_ARRAY = BRIG_TYPE_F16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F32_ARRAY = BRIG_TYPE_F32 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F64_ARRAY = BRIG_TYPE_F64 | BRIG_TYPE_ARRAY, + BRIG_TYPE_B8_ARRAY = BRIG_TYPE_B8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_B16_ARRAY = BRIG_TYPE_B16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_B32_ARRAY = BRIG_TYPE_B32 | BRIG_TYPE_ARRAY, + BRIG_TYPE_B64_ARRAY = BRIG_TYPE_B64 | BRIG_TYPE_ARRAY, + BRIG_TYPE_B128_ARRAY = BRIG_TYPE_B128 | BRIG_TYPE_ARRAY, + BRIG_TYPE_SAMP_ARRAY = BRIG_TYPE_SAMP | BRIG_TYPE_ARRAY, + BRIG_TYPE_ROIMG_ARRAY = BRIG_TYPE_ROIMG | BRIG_TYPE_ARRAY, + BRIG_TYPE_WOIMG_ARRAY = BRIG_TYPE_WOIMG | BRIG_TYPE_ARRAY, + BRIG_TYPE_RWIMG_ARRAY = BRIG_TYPE_RWIMG | BRIG_TYPE_ARRAY, + BRIG_TYPE_SIG32_ARRAY = BRIG_TYPE_SIG32 | BRIG_TYPE_ARRAY, + BRIG_TYPE_SIG64_ARRAY = BRIG_TYPE_SIG64 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U8X4_ARRAY = BRIG_TYPE_U8X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U8X8_ARRAY = BRIG_TYPE_U8X8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U8X16_ARRAY = BRIG_TYPE_U8X16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U16X2_ARRAY = BRIG_TYPE_U16X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U16X4_ARRAY = BRIG_TYPE_U16X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U16X8_ARRAY = BRIG_TYPE_U16X8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U32X2_ARRAY = BRIG_TYPE_U32X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U32X4_ARRAY = BRIG_TYPE_U32X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_U64X2_ARRAY = BRIG_TYPE_U64X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S8X4_ARRAY = BRIG_TYPE_S8X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S8X8_ARRAY = BRIG_TYPE_S8X8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S8X16_ARRAY = BRIG_TYPE_S8X16 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S16X2_ARRAY = BRIG_TYPE_S16X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S16X4_ARRAY = BRIG_TYPE_S16X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S16X8_ARRAY = BRIG_TYPE_S16X8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S32X2_ARRAY = BRIG_TYPE_S32X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S32X4_ARRAY = BRIG_TYPE_S32X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_S64X2_ARRAY = BRIG_TYPE_S64X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F16X2_ARRAY = BRIG_TYPE_F16X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F16X4_ARRAY = BRIG_TYPE_F16X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F16X8_ARRAY = BRIG_TYPE_F16X8 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F32X2_ARRAY = BRIG_TYPE_F32X2 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F32X4_ARRAY = BRIG_TYPE_F32X4 | BRIG_TYPE_ARRAY, + BRIG_TYPE_F64X2_ARRAY = BRIG_TYPE_F64X2 | BRIG_TYPE_ARRAY, +}; + +typedef uint8_t BrigVariableModifier8_t; +enum BrigVariableModifierMask { + BRIG_VARIABLE_DEFINITION = 1, + BRIG_VARIABLE_CONST = 2 +}; + +typedef uint8_t BrigWidth8_t; +enum BrigWidth { + BRIG_WIDTH_NONE = 0, + BRIG_WIDTH_1 = 1, + BRIG_WIDTH_2 = 2, + BRIG_WIDTH_4 = 3, + BRIG_WIDTH_8 = 4, + BRIG_WIDTH_16 = 5, + BRIG_WIDTH_32 = 6, + BRIG_WIDTH_64 = 7, + BRIG_WIDTH_128 = 8, + BRIG_WIDTH_256 = 9, + BRIG_WIDTH_512 = 10, + BRIG_WIDTH_1024 = 11, + BRIG_WIDTH_2048 = 12, + BRIG_WIDTH_4096 = 13, + BRIG_WIDTH_8192 = 14, + BRIG_WIDTH_16384 = 15, + BRIG_WIDTH_32768 = 16, + BRIG_WIDTH_65536 = 17, + BRIG_WIDTH_131072 = 18, + BRIG_WIDTH_262144 = 19, + BRIG_WIDTH_524288 = 20, + BRIG_WIDTH_1048576 = 21, + BRIG_WIDTH_2097152 = 22, + BRIG_WIDTH_4194304 = 23, + BRIG_WIDTH_8388608 = 24, + BRIG_WIDTH_16777216 = 25, + BRIG_WIDTH_33554432 = 26, + BRIG_WIDTH_67108864 = 27, + BRIG_WIDTH_134217728 = 28, + BRIG_WIDTH_268435456 = 29, + BRIG_WIDTH_536870912 = 30, + BRIG_WIDTH_1073741824 = 31, + BRIG_WIDTH_2147483648 = 32, + BRIG_WIDTH_WAVESIZE = 33, + BRIG_WIDTH_ALL = 34, +}; + +struct BrigUInt64 { + uint32_t lo; + uint32_t hi; +}; + +struct BrigBase { + uint16_t byteCount; + BrigKind16_t kind; +}; + +struct BrigData { + uint32_t byteCount; + uint8_t bytes[1]; +}; + +struct BrigDirectiveArgBlock { + BrigBase base; +}; + +struct BrigDirectiveComment { + BrigBase base; + BrigDataOffsetString32_t name; +}; + +struct BrigDirectiveControl { + BrigBase base; + BrigControlDirective16_t control; + uint16_t reserved; + BrigDataOffsetOperandList32_t operands; +}; + +struct BrigDirectiveExecutable { + BrigBase base; + BrigDataOffsetString32_t name; + uint16_t outArgCount; + uint16_t inArgCount; + BrigCodeOffset32_t firstInArg; + BrigCodeOffset32_t firstCodeBlockEntry; + BrigCodeOffset32_t nextModuleEntry; + BrigExecutableModifier8_t modifier; + BrigLinkage8_t linkage; + uint16_t reserved; +}; + +struct BrigDirectiveExtension { + BrigBase base; + BrigDataOffsetString32_t name; +}; + +struct BrigDirectiveFbarrier { + BrigBase base; + BrigDataOffsetString32_t name; + BrigVariableModifier8_t modifier; + BrigLinkage8_t linkage; + uint16_t reserved; +}; + +struct BrigDirectiveLabel { + BrigBase base; + BrigDataOffsetString32_t name; +}; + +struct BrigDirectiveLoc { + BrigBase base; + BrigDataOffsetString32_t filename; + uint32_t line; + uint32_t column; +}; + +struct BrigDirectiveNone { + BrigBase base; +}; + +struct BrigDirectivePragma { + BrigBase base; + BrigDataOffsetOperandList32_t operands; +}; + +struct BrigDirectiveVariable { + BrigBase base; + BrigDataOffsetString32_t name; + BrigOperandOffset32_t init; + BrigType16_t type; + BrigSegment8_t segment; + BrigAlignment8_t align; + BrigUInt64 dim; + BrigVariableModifier8_t modifier; + BrigLinkage8_t linkage; + BrigAllocation8_t allocation; + uint8_t reserved; +}; + +struct BrigDirectiveModule { + BrigBase base; + BrigDataOffsetString32_t name; + BrigVersion32_t hsailMajor; + BrigVersion32_t hsailMinor; + BrigProfile8_t profile; + BrigMachineModel8_t machineModel; + BrigRound8_t defaultFloatRound; + uint8_t reserved; +}; + +struct BrigInstBase { + BrigBase base; + BrigOpcode16_t opcode; + BrigType16_t type; + BrigDataOffsetOperandList32_t operands; +}; + +struct BrigInstAddr { + BrigInstBase base; + BrigSegment8_t segment; + uint8_t reserved[3]; +}; + +struct BrigInstAtomic { + BrigInstBase base; + BrigSegment8_t segment; + BrigMemoryOrder8_t memoryOrder; + BrigMemoryScope8_t memoryScope; + BrigAtomicOperation8_t atomicOperation; + uint8_t equivClass; + uint8_t reserved[3]; +}; + +struct BrigInstBasic { + BrigInstBase base; +}; + +struct BrigInstBr { + BrigInstBase base; + BrigWidth8_t width; + uint8_t reserved[3]; +}; + +struct BrigInstCmp { + BrigInstBase base; + BrigType16_t sourceType; + BrigAluModifier8_t modifier; + BrigCompareOperation8_t compare; + BrigPack8_t pack; + uint8_t reserved[3]; +}; + +struct BrigInstCvt { + BrigInstBase base; + BrigType16_t sourceType; + BrigAluModifier8_t modifier; + BrigRound8_t round; +}; + +struct BrigInstImage { + BrigInstBase base; + BrigType16_t imageType; + BrigType16_t coordType; + BrigImageGeometry8_t geometry; + uint8_t equivClass; + uint16_t reserved; +}; + +struct BrigInstLane { + BrigInstBase base; + BrigType16_t sourceType; + BrigWidth8_t width; + uint8_t reserved; +}; + +struct BrigInstMem { + BrigInstBase base; + BrigSegment8_t segment; + BrigAlignment8_t align; + uint8_t equivClass; + BrigWidth8_t width; + BrigMemoryModifier8_t modifier; + uint8_t reserved[3]; +}; + +struct BrigInstMemFence { + BrigInstBase base; + BrigMemoryOrder8_t memoryOrder; + BrigMemoryScope8_t globalSegmentMemoryScope; + BrigMemoryScope8_t groupSegmentMemoryScope; + BrigMemoryScope8_t imageSegmentMemoryScope; +}; + +struct BrigInstMod { + BrigInstBase base; + BrigAluModifier8_t modifier; + BrigRound8_t round; + BrigPack8_t pack; + uint8_t reserved; +}; + +struct BrigInstQueryImage { + BrigInstBase base; + BrigType16_t imageType; + BrigImageGeometry8_t geometry; + BrigImageQuery8_t query; +}; + +struct BrigInstQuerySampler { + BrigInstBase base; + BrigSamplerQuery8_t query; + uint8_t reserved[3]; +}; + +struct BrigInstQueue { + BrigInstBase base; + BrigSegment8_t segment; + BrigMemoryOrder8_t memoryOrder; + uint16_t reserved; +}; + +struct BrigInstSeg { + BrigInstBase base; + BrigSegment8_t segment; + uint8_t reserved[3]; +}; + +struct BrigInstSegCvt { + BrigInstBase base; + BrigType16_t sourceType; + BrigSegment8_t segment; + BrigSegCvtModifier8_t modifier; +}; + +struct BrigInstSignal { + BrigInstBase base; + BrigType16_t signalType; + BrigMemoryOrder8_t memoryOrder; + BrigAtomicOperation8_t signalOperation; +}; + +struct BrigInstSourceType { + BrigInstBase base; + BrigType16_t sourceType; + uint16_t reserved; +}; + +struct BrigOperandAddress { + BrigBase base; + BrigCodeOffset32_t symbol; + BrigOperandOffset32_t reg; + BrigUInt64 offset; +}; + +struct BrigOperandAlign { + BrigBase base; + BrigAlignment8_t align; + uint8_t reserved[3]; +}; + +struct BrigOperandCodeList { + BrigBase base; + BrigDataOffsetCodeList32_t elements; +}; + +struct BrigOperandCodeRef { + BrigBase base; + BrigCodeOffset32_t ref; +}; + +struct BrigOperandConstantBytes { + BrigBase base; + BrigType16_t type; + uint16_t reserved; + BrigDataOffsetString32_t bytes; +}; + +struct BrigOperandConstantOperandList { + BrigBase base; + BrigType16_t type; + uint16_t reserved; + BrigDataOffsetOperandList32_t elements; +}; + +struct BrigOperandConstantImage { + BrigBase base; + BrigType16_t type; + BrigImageGeometry8_t geometry; + BrigImageChannelOrder8_t channelOrder; + BrigImageChannelType8_t channelType; + uint8_t reserved[3]; + BrigUInt64 width; + BrigUInt64 height; + BrigUInt64 depth; + BrigUInt64 array; +}; + +struct BrigOperandOperandList { + BrigBase base; + BrigDataOffsetOperandList32_t elements; +}; + +struct BrigOperandRegister { + BrigBase base; + BrigRegisterKind16_t regKind; + uint16_t regNum; +}; + +struct BrigOperandConstantSampler { + BrigBase base; + BrigType16_t type; + BrigSamplerCoordNormalization8_t coord; + BrigSamplerFilter8_t filter; + BrigSamplerAddressing8_t addressing; + uint8_t reserved[3]; +}; + +struct BrigOperandString { + BrigBase base; + BrigDataOffsetString32_t string; +}; + +struct BrigOperandWavesize { + BrigBase base; +}; + +typedef uint32_t BrigExceptions32_t; +enum BrigExceptionsMask { + BRIG_EXCEPTIONS_INVALID_OPERATION = 1 << 0, + BRIG_EXCEPTIONS_DIVIDE_BY_ZERO = 1 << 1, + BRIG_EXCEPTIONS_OVERFLOW = 1 << 2, + BRIG_EXCEPTIONS_UNDERFLOW = 1 << 3, + BRIG_EXCEPTIONS_INEXACT = 1 << 4, + + BRIG_EXCEPTIONS_FIRST_USER_DEFINED = 1 << 16 +}; + +struct BrigSectionHeader { + uint64_t byteCount; + uint32_t headerByteCount; + uint32_t nameLength; + uint8_t name[1]; +}; + +struct BrigModuleHeader { + char identification[8]; + BrigVersion32_t brigMajor; + BrigVersion32_t brigMinor; + uint64_t byteCount; + uint8_t hash[64]; + uint32_t reserved; + uint32_t sectionCount; + uint64_t sectionIndex; +}; + +typedef BrigModuleHeader* BrigModule_t; + +#ifdef __cplusplus +} +#endif /*__cplusplus*/ + +#endif // defined(INCLUDED_BRIG_H) diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_common.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_common.h new file mode 100644 index 0000000000000000000000000000000000000000..7c4ed3eea47298374b78d1f770aeb0ed8aba9936 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_common.h @@ -0,0 +1,91 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +// The following set of header files provides definitions for AMD GPU +// Architecture: +// - amd_hsa_common.h +// - amd_hsa_elf.h +// - amd_hsa_kernel_code.h +// - amd_hsa_queue.h +// - amd_hsa_signal.h +// +// Refer to "HSA Application Binary Interface: AMD GPU Architecture" for more +// information. + +#ifndef AMD_HSA_COMMON_H +#define AMD_HSA_COMMON_H + +#include +#include + +// Descriptive version of the HSA Application Binary Interface. +#define AMD_HSA_ABI_VERSION "AMD GPU Architecture v0.35 (June 25, 2015)" + +// Alignment attribute that specifies a minimum alignment (in bytes) for +// variables of the specified type. +#if defined(__GNUC__) +# define __ALIGNED__(x) __attribute__((aligned(x))) +#elif defined(_MSC_VER) +# define __ALIGNED__(x) __declspec(align(x)) +#elif defined(RC_INVOKED) +# define __ALIGNED__(x) +#else +# error +#endif + +// Creates enumeration entries for packed types. Enumeration entries include +// bit shift amount, bit width, and bit mask. +#define AMD_HSA_BITS_CREATE_ENUM_ENTRIES(name, shift, width) \ + name##_SHIFT = (shift), \ + name##_WIDTH = (width), \ + name = (((1 << (width)) - 1) << (shift)) \ + +// Gets bits for specified mask from specified src packed instance. +#define AMD_HSA_BITS_GET(src, mask) \ + ((src & mask) >> mask ## _SHIFT) \ + +// Sets val bits for specified mask in specified dst packed instance. +#define AMD_HSA_BITS_SET(dst, mask, val) \ + dst &= (~(1 << mask##_SHIFT) & ~mask); \ + dst |= (((val) << mask##_SHIFT) & mask) \ + +#endif // AMD_HSA_COMMON_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_elf.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_elf.h new file mode 100644 index 0000000000000000000000000000000000000000..0656c9d99419bf78210c7349bfeb25bcbc574b01 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_elf.h @@ -0,0 +1,436 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +// Undefine the macro in case it is defined in the system elf.h. +#undef EM_AMDGPU + +#ifndef AMD_HSA_ELF_H +#define AMD_HSA_ELF_H + +// AMD GPU Specific ELF Header Enumeration Values. +// +// Values are copied from LLVM BinaryFormat/ELF.h . This file also contains +// code object V1 defintions which are not part of the LLVM header. Code object +// V1 was only supported by the Finalizer which is now deprecated and removed. +// +// TODO: Deprecate and remove V1 support and replace this header with using the +// LLVM header. +namespace ELF { + +// Machine architectures +// See current registered ELF machine architectures at: +// http://www.uxsglobal.com/developers/gabi/latest/ch4.eheader.html +enum { + EM_AMDGPU = 224, // AMD GPU architecture +}; + +// OS ABI identification. +enum { + ELFOSABI_AMDGPU_HSA = 64, // AMD HSA runtime +}; + +// AMDGPU OS ABI Version identification. +enum { + // ELFABIVERSION_AMDGPU_HSA_V1 does not exist because OS ABI identification + // was never defined for V1. + ELFABIVERSION_AMDGPU_HSA_V2 = 0, + ELFABIVERSION_AMDGPU_HSA_V3 = 1, + ELFABIVERSION_AMDGPU_HSA_V4 = 2, + ELFABIVERSION_AMDGPU_HSA_V5 = 3 +}; + +// AMDGPU specific e_flags. +enum : unsigned { + // Processor selection mask for EF_AMDGPU_MACH_* values. + EF_AMDGPU_MACH = 0x0ff, + + // Not specified processor. + EF_AMDGPU_MACH_NONE = 0x000, + + // AMDGCN-based processors. + EF_AMDGPU_MACH_AMDGCN_GFX600 = 0x020, + EF_AMDGPU_MACH_AMDGCN_GFX601 = 0x021, + EF_AMDGPU_MACH_AMDGCN_GFX700 = 0x022, + EF_AMDGPU_MACH_AMDGCN_GFX701 = 0x023, + EF_AMDGPU_MACH_AMDGCN_GFX702 = 0x024, + EF_AMDGPU_MACH_AMDGCN_GFX703 = 0x025, + EF_AMDGPU_MACH_AMDGCN_GFX704 = 0x026, + EF_AMDGPU_MACH_AMDGCN_RESERVED_0X27 = 0x027, + EF_AMDGPU_MACH_AMDGCN_GFX801 = 0x028, + EF_AMDGPU_MACH_AMDGCN_GFX802 = 0x029, + EF_AMDGPU_MACH_AMDGCN_GFX803 = 0x02a, + EF_AMDGPU_MACH_AMDGCN_GFX810 = 0x02b, + EF_AMDGPU_MACH_AMDGCN_GFX900 = 0x02c, + EF_AMDGPU_MACH_AMDGCN_GFX902 = 0x02d, + EF_AMDGPU_MACH_AMDGCN_GFX904 = 0x02e, + EF_AMDGPU_MACH_AMDGCN_GFX906 = 0x02f, + EF_AMDGPU_MACH_AMDGCN_GFX908 = 0x030, + EF_AMDGPU_MACH_AMDGCN_GFX909 = 0x031, + EF_AMDGPU_MACH_AMDGCN_GFX90C = 0x032, + EF_AMDGPU_MACH_AMDGCN_GFX1010 = 0x033, + EF_AMDGPU_MACH_AMDGCN_GFX1011 = 0x034, + EF_AMDGPU_MACH_AMDGCN_GFX1012 = 0x035, + EF_AMDGPU_MACH_AMDGCN_GFX1030 = 0x036, + EF_AMDGPU_MACH_AMDGCN_GFX1031 = 0x037, + EF_AMDGPU_MACH_AMDGCN_GFX1032 = 0x038, + EF_AMDGPU_MACH_AMDGCN_GFX1033 = 0x039, + EF_AMDGPU_MACH_AMDGCN_GFX602 = 0x03a, + EF_AMDGPU_MACH_AMDGCN_GFX705 = 0x03b, + EF_AMDGPU_MACH_AMDGCN_GFX805 = 0x03c, + EF_AMDGPU_MACH_AMDGCN_GFX1035 = 0x03d, + EF_AMDGPU_MACH_AMDGCN_GFX1034 = 0x03e, + EF_AMDGPU_MACH_AMDGCN_GFX90A = 0x03f, + EF_AMDGPU_MACH_AMDGCN_GFX940 = 0x040, + EF_AMDGPU_MACH_AMDGCN_GFX1100 = 0x041, + EF_AMDGPU_MACH_AMDGCN_GFX1013 = 0x042, + EF_AMDGPU_MACH_AMDGCN_GFX1150 = 0x043, + EF_AMDGPU_MACH_AMDGCN_GFX1103 = 0x044, + EF_AMDGPU_MACH_AMDGCN_GFX1036 = 0x045, + EF_AMDGPU_MACH_AMDGCN_GFX1101 = 0x046, + EF_AMDGPU_MACH_AMDGCN_GFX1102 = 0x047, + EF_AMDGPU_MACH_AMDGCN_GFX1151 = 0x04a, + EF_AMDGPU_MACH_AMDGCN_GFX941 = 0x04b, + EF_AMDGPU_MACH_AMDGCN_GFX942 = 0x04c, + EF_AMDGPU_MACH_AMDGCN_GFX950 = 0x04f, + + // First/last AMDGCN-based processors. + EF_AMDGPU_MACH_AMDGCN_FIRST = EF_AMDGPU_MACH_AMDGCN_GFX600, + EF_AMDGPU_MACH_AMDGCN_LAST = EF_AMDGPU_MACH_AMDGCN_GFX942, + + // Indicates if the "xnack" target feature is enabled for all code contained + // in the object. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V2. + EF_AMDGPU_FEATURE_XNACK_V2 = 0x01, + // Indicates if the trap handler is enabled for all code contained + // in the object. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V2. + EF_AMDGPU_FEATURE_TRAP_HANDLER_V2 = 0x02, + + // Indicates if the "xnack" target feature is enabled for all code contained + // in the object. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V3. + EF_AMDGPU_FEATURE_XNACK_V3 = 0x100, + // Indicates if the "sramecc" target feature is enabled for all code + // contained in the object. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V3. + EF_AMDGPU_FEATURE_SRAMECC_V3 = 0x200, + + // XNACK selection mask for EF_AMDGPU_FEATURE_XNACK_* values. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V4, + // ELFABIVERSION_AMDGPU_HSA_V5. + EF_AMDGPU_FEATURE_XNACK_V4 = 0x300, + // XNACK is not supported. + EF_AMDGPU_FEATURE_XNACK_UNSUPPORTED_V4 = 0x000, + // XNACK is any/default/unspecified. + EF_AMDGPU_FEATURE_XNACK_ANY_V4 = 0x100, + // XNACK is off. + EF_AMDGPU_FEATURE_XNACK_OFF_V4 = 0x200, + // XNACK is on. + EF_AMDGPU_FEATURE_XNACK_ON_V4 = 0x300, + + // SRAMECC selection mask for EF_AMDGPU_FEATURE_SRAMECC_* values. + // + // Only valid for ELFOSABI_AMDGPU_HSA and ELFABIVERSION_AMDGPU_HSA_V4, + // ELFABIVERSION_AMDGPU_HSA_V5. + EF_AMDGPU_FEATURE_SRAMECC_V4 = 0xc00, + // SRAMECC is not supported. + EF_AMDGPU_FEATURE_SRAMECC_UNSUPPORTED_V4 = 0x000, + // SRAMECC is any/default/unspecified. + EF_AMDGPU_FEATURE_SRAMECC_ANY_V4 = 0x400, + // SRAMECC is off. + EF_AMDGPU_FEATURE_SRAMECC_OFF_V4 = 0x800, + // SRAMECC is on. + EF_AMDGPU_FEATURE_SRAMECC_ON_V4 = 0xc00, +}; + +} // end namespace ELF + +// ELF Section Header Flag Enumeration Values. +#define SHF_AMDGPU_HSA_GLOBAL (0x00100000 & SHF_MASKOS) +#define SHF_AMDGPU_HSA_READONLY (0x00200000 & SHF_MASKOS) +#define SHF_AMDGPU_HSA_CODE (0x00400000 & SHF_MASKOS) +#define SHF_AMDGPU_HSA_AGENT (0x00800000 & SHF_MASKOS) + +// +typedef enum { + AMDGPU_HSA_SEGMENT_GLOBAL_PROGRAM = 0, + AMDGPU_HSA_SEGMENT_GLOBAL_AGENT = 1, + AMDGPU_HSA_SEGMENT_READONLY_AGENT = 2, + AMDGPU_HSA_SEGMENT_CODE_AGENT = 3, + AMDGPU_HSA_SEGMENT_LAST, +} amdgpu_hsa_elf_segment_t; + +// ELF Program Header Type Enumeration Values. +#define PT_AMDGPU_HSA_LOAD_GLOBAL_PROGRAM (PT_LOOS + AMDGPU_HSA_SEGMENT_GLOBAL_PROGRAM) +#define PT_AMDGPU_HSA_LOAD_GLOBAL_AGENT (PT_LOOS + AMDGPU_HSA_SEGMENT_GLOBAL_AGENT) +#define PT_AMDGPU_HSA_LOAD_READONLY_AGENT (PT_LOOS + AMDGPU_HSA_SEGMENT_READONLY_AGENT) +#define PT_AMDGPU_HSA_LOAD_CODE_AGENT (PT_LOOS + AMDGPU_HSA_SEGMENT_CODE_AGENT) + +// ELF Symbol Type Enumeration Values. +#define STT_AMDGPU_HSA_KERNEL (STT_LOOS + 0) +#define STT_AMDGPU_HSA_INDIRECT_FUNCTION (STT_LOOS + 1) +#define STT_AMDGPU_HSA_METADATA (STT_LOOS + 2) + +// ELF Symbol Binding Enumeration Values. +#define STB_AMDGPU_HSA_EXTERNAL (STB_LOOS + 0) + +// ELF Symbol Other Information Creation/Retrieval. +#define ELF64_ST_AMDGPU_ALLOCATION(o) (((o) >> 2) & 0x3) +#define ELF64_ST_AMDGPU_FLAGS(o) ((o) >> 4) +#define ELF64_ST_AMDGPU_OTHER(f, a, v) (((f) << 4) + (((a) & 0x3) << 2) + ((v) & 0x3)) + +typedef enum { + AMDGPU_HSA_SYMBOL_ALLOCATION_DEFAULT = 0, + AMDGPU_HSA_SYMBOL_ALLOCATION_GLOBAL_PROGRAM = 1, + AMDGPU_HSA_SYMBOL_ALLOCATION_GLOBAL_AGENT = 2, + AMDGPU_HSA_SYMBOL_ALLOCATION_READONLY_AGENT = 3, + AMDGPU_HSA_SYMBOL_ALLOCATION_LAST, +} amdgpu_hsa_symbol_allocation_t; + +// ELF Symbol Allocation Enumeration Values. +#define STA_AMDGPU_HSA_DEFAULT AMDGPU_HSA_SYMBOL_ALLOCATION_DEFAULT +#define STA_AMDGPU_HSA_GLOBAL_PROGRAM AMDGPU_HSA_SYMBOL_ALLOCATION_GLOBAL_PROGRAM +#define STA_AMDGPU_HSA_GLOBAL_AGENT AMDGPU_HSA_SYMBOL_ALLOCATION_GLOBAL_AGENT +#define STA_AMDGPU_HSA_READONLY_AGENT AMDGPU_HSA_SYMBOL_ALLOCATION_READONLY_AGENT + +typedef enum { + AMDGPU_HSA_SYMBOL_FLAG_DEFAULT = 0, + AMDGPU_HSA_SYMBOL_FLAG_CONST = 1, + AMDGPU_HSA_SYMBOL_FLAG_LAST, +} amdgpu_hsa_symbol_flag_t; + +// ELF Symbol Flag Enumeration Values. +#define STF_AMDGPU_HSA_CONST AMDGPU_HSA_SYMBOL_FLAG_CONST + +// AMD GPU Relocation Type Enumeration Values. +#define R_AMDGPU_NONE 0 +#define R_AMDGPU_32_LOW 1 +#define R_AMDGPU_32_HIGH 2 +#define R_AMDGPU_64 3 +#define R_AMDGPU_INIT_SAMPLER 4 +#define R_AMDGPU_INIT_IMAGE 5 +#define R_AMDGPU_RELATIVE64 13 + +// AMD GPU Note Type Enumeration Values. +#define NT_AMD_HSA_CODE_OBJECT_VERSION 1 +#define NT_AMD_HSA_HSAIL 2 +#define NT_AMD_HSA_ISA_VERSION 3 +#define NT_AMD_HSA_PRODUCER 4 +#define NT_AMD_HSA_PRODUCER_OPTIONS 5 +#define NT_AMD_HSA_EXTENSION 6 +#define NT_AMD_HSA_ISA_NAME 11 +/* AMDGPU snapshots of runtime, agent and queues state for use in core dump */ +#define NT_AMDGPU_CORE_STATE 33 +#define NT_AMD_HSA_HLDEBUG_DEBUG 101 +#define NT_AMD_HSA_HLDEBUG_TARGET 102 + +// AMD GPU Metadata Kind Enumeration Values. +typedef uint16_t amdgpu_hsa_metadata_kind16_t; +typedef enum { + AMDGPU_HSA_METADATA_KIND_NONE = 0, + AMDGPU_HSA_METADATA_KIND_INIT_SAMP = 1, + AMDGPU_HSA_METADATA_KIND_INIT_ROIMG = 2, + AMDGPU_HSA_METADATA_KIND_INIT_WOIMG = 3, + AMDGPU_HSA_METADATA_KIND_INIT_RWIMG = 4 +} amdgpu_hsa_metadata_kind_t; + +// AMD GPU Sampler Coordinate Normalization Enumeration Values. +typedef uint8_t amdgpu_hsa_sampler_coord8_t; +typedef enum { + AMDGPU_HSA_SAMPLER_COORD_UNNORMALIZED = 0, + AMDGPU_HSA_SAMPLER_COORD_NORMALIZED = 1 +} amdgpu_hsa_sampler_coord_t; + +// AMD GPU Sampler Filter Enumeration Values. +typedef uint8_t amdgpu_hsa_sampler_filter8_t; +typedef enum { + AMDGPU_HSA_SAMPLER_FILTER_NEAREST = 0, + AMDGPU_HSA_SAMPLER_FILTER_LINEAR = 1 +} amdgpu_hsa_sampler_filter_t; + +// AMD GPU Sampler Addressing Enumeration Values. +typedef uint8_t amdgpu_hsa_sampler_addressing8_t; +typedef enum { + AMDGPU_HSA_SAMPLER_ADDRESSING_UNDEFINED = 0, + AMDGPU_HSA_SAMPLER_ADDRESSING_CLAMP_TO_EDGE = 1, + AMDGPU_HSA_SAMPLER_ADDRESSING_CLAMP_TO_BORDER = 2, + AMDGPU_HSA_SAMPLER_ADDRESSING_REPEAT = 3, + AMDGPU_HSA_SAMPLER_ADDRESSING_MIRRORED_REPEAT = 4 +} amdgpu_hsa_sampler_addressing_t; + +// AMD GPU Sampler Descriptor. +typedef struct amdgpu_hsa_sampler_descriptor_s { + uint16_t size; + amdgpu_hsa_metadata_kind16_t kind; + amdgpu_hsa_sampler_coord8_t coord; + amdgpu_hsa_sampler_filter8_t filter; + amdgpu_hsa_sampler_addressing8_t addressing; + uint8_t reserved1; +} amdgpu_hsa_sampler_descriptor_t; + +// AMD GPU Image Geometry Enumeration Values. +typedef uint8_t amdgpu_hsa_image_geometry8_t; +typedef enum { + AMDGPU_HSA_IMAGE_GEOMETRY_1D = 0, + AMDGPU_HSA_IMAGE_GEOMETRY_2D = 1, + AMDGPU_HSA_IMAGE_GEOMETRY_3D = 2, + AMDGPU_HSA_IMAGE_GEOMETRY_1DA = 3, + AMDGPU_HSA_IMAGE_GEOMETRY_2DA = 4, + AMDGPU_HSA_IMAGE_GEOMETRY_1DB = 5, + AMDGPU_HSA_IMAGE_GEOMETRY_2DDEPTH = 6, + AMDGPU_HSA_IMAGE_GEOMETRY_2DADEPTH = 7 +} amdgpu_hsa_image_geometry_t; + +// AMD GPU Image Channel Order Enumeration Values. +typedef uint8_t amdgpu_hsa_image_channel_order8_t; +typedef enum { + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_A = 0, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_R = 1, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RX = 2, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RG = 3, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RGX = 4, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RA = 5, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RGB = 6, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RGBX = 7, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_RGBA = 8, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_BGRA = 9, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_ARGB = 10, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_ABGR = 11, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_SRGB = 12, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_SRGBX = 13, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_SRGBA = 14, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_SBGRA = 15, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_INTENSITY = 16, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_LUMINANCE = 17, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_DEPTH = 18, + AMDGPU_HSA_IMAGE_CHANNEL_ORDER_DEPTH_STENCIL = 19 +} amdgpu_hsa_image_channel_order_t; + +// AMD GPU Image Channel Type Enumeration Values. +typedef uint8_t amdgpu_hsa_image_channel_type8_t; +typedef enum { + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SNORM_INT8 = 0, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SNORM_INT16 = 1, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNORM_INT8 = 2, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNORM_INT16 = 3, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNORM_INT24 = 4, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SHORT_555 = 5, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SHORT_565 = 6, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_INT_101010 = 7, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SIGNED_INT8 = 8, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SIGNED_INT16 = 9, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_SIGNED_INT32 = 10, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNSIGNED_INT8 = 11, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNSIGNED_INT16 = 12, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_UNSIGNED_INT32 = 13, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_HALF_FLOAT = 14, + AMDGPU_HSA_IMAGE_CHANNEL_TYPE_FLOAT = 15 +} amdgpu_hsa_image_channel_type_t; + +// AMD GPU Image Descriptor. +typedef struct amdgpu_hsa_image_descriptor_s { + uint16_t size; + amdgpu_hsa_metadata_kind16_t kind; + amdgpu_hsa_image_geometry8_t geometry; + amdgpu_hsa_image_channel_order8_t channel_order; + amdgpu_hsa_image_channel_type8_t channel_type; + uint8_t reserved1; + uint64_t width; + uint64_t height; + uint64_t depth; + uint64_t array; +} amdgpu_hsa_image_descriptor_t; + +typedef struct amdgpu_hsa_note_code_object_version_s { + uint32_t major_version; + uint32_t minor_version; +} amdgpu_hsa_note_code_object_version_t; + +typedef struct amdgpu_hsa_note_hsail_s { + uint32_t hsail_major_version; + uint32_t hsail_minor_version; + uint8_t profile; + uint8_t machine_model; + uint8_t default_float_round; +} amdgpu_hsa_note_hsail_t; + +typedef struct amdgpu_hsa_note_isa_s { + uint16_t vendor_name_size; + uint16_t architecture_name_size; + uint32_t major; + uint32_t minor; + uint32_t stepping; + char vendor_and_architecture_name[1]; +} amdgpu_hsa_note_isa_t; + +typedef struct amdgpu_hsa_note_producer_s { + uint16_t producer_name_size; + uint16_t reserved; + uint32_t producer_major_version; + uint32_t producer_minor_version; + char producer_name[1]; +} amdgpu_hsa_note_producer_t; + +typedef struct amdgpu_hsa_note_producer_options_s { + uint16_t producer_options_size; + char producer_options[1]; +} amdgpu_hsa_note_producer_options_t; + +typedef enum { + AMDGPU_HSA_RODATA_GLOBAL_PROGRAM = 0, + AMDGPU_HSA_RODATA_GLOBAL_AGENT, + AMDGPU_HSA_RODATA_READONLY_AGENT, + AMDGPU_HSA_DATA_GLOBAL_PROGRAM, + AMDGPU_HSA_DATA_GLOBAL_AGENT, + AMDGPU_HSA_DATA_READONLY_AGENT, + AMDGPU_HSA_BSS_GLOBAL_PROGRAM, + AMDGPU_HSA_BSS_GLOBAL_AGENT, + AMDGPU_HSA_BSS_READONLY_AGENT, + AMDGPU_HSA_SECTION_LAST, +} amdgpu_hsa_elf_section_t; + +#endif // AMD_HSA_ELF_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_kernel_code.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_kernel_code.h new file mode 100644 index 0000000000000000000000000000000000000000..901e49c8dd1d9d5624fb95ada6d695cf9b64e17d --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_kernel_code.h @@ -0,0 +1,269 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef AMD_HSA_KERNEL_CODE_H +#define AMD_HSA_KERNEL_CODE_H + +#include "amd_hsa_common.h" +#include "hsa.h" + +// AMD Kernel Code Version Enumeration Values. +typedef uint32_t amd_kernel_code_version32_t; +enum amd_kernel_code_version_t { + AMD_KERNEL_CODE_VERSION_MAJOR = 1, + AMD_KERNEL_CODE_VERSION_MINOR = 1 +}; + +// AMD Machine Kind Enumeration Values. +typedef uint16_t amd_machine_kind16_t; +enum amd_machine_kind_t { + AMD_MACHINE_KIND_UNDEFINED = 0, + AMD_MACHINE_KIND_AMDGPU = 1 +}; + +// AMD Machine Version. +typedef uint16_t amd_machine_version16_t; + +// AMD Float Round Mode Enumeration Values. +enum amd_float_round_mode_t { + AMD_FLOAT_ROUND_MODE_NEAREST_EVEN = 0, + AMD_FLOAT_ROUND_MODE_PLUS_INFINITY = 1, + AMD_FLOAT_ROUND_MODE_MINUS_INFINITY = 2, + AMD_FLOAT_ROUND_MODE_ZERO = 3 +}; + +// AMD Float Denorm Mode Enumeration Values. +enum amd_float_denorm_mode_t { + AMD_FLOAT_DENORM_MODE_FLUSH_SOURCE_OUTPUT = 0, + AMD_FLOAT_DENORM_MODE_FLUSH_OUTPUT = 1, + AMD_FLOAT_DENORM_MODE_FLUSH_SOURCE = 2, + AMD_FLOAT_DENORM_MODE_NO_FLUSH = 3 +}; + +// AMD Compute Program Resource Register One. +typedef uint32_t amd_compute_pgm_rsrc_one32_t; +enum amd_compute_pgm_rsrc_one_t { + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_GRANULATED_WORKITEM_VGPR_COUNT, 0, 6), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_GRANULATED_WAVEFRONT_SGPR_COUNT, 6, 4), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_PRIORITY, 10, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_FLOAT_ROUND_MODE_32, 12, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_FLOAT_ROUND_MODE_16_64, 14, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_FLOAT_DENORM_MODE_32, 16, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_FLOAT_DENORM_MODE_16_64, 18, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_PRIV, 20, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_ENABLE_DX10_CLAMP, 21, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_DEBUG_MODE, 22, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_ENABLE_IEEE_MODE, 23, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_BULKY, 24, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_CDBG_USER, 25, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_ONE_RESERVED1, 26, 6) +}; + +// AMD System VGPR Workitem ID Enumeration Values. +enum amd_system_vgpr_workitem_id_t { + AMD_SYSTEM_VGPR_WORKITEM_ID_X = 0, + AMD_SYSTEM_VGPR_WORKITEM_ID_X_Y = 1, + AMD_SYSTEM_VGPR_WORKITEM_ID_X_Y_Z = 2, + AMD_SYSTEM_VGPR_WORKITEM_ID_UNDEFINED = 3 +}; + +// AMD Compute Program Resource Register Two. +typedef uint32_t amd_compute_pgm_rsrc_two32_t; +enum amd_compute_pgm_rsrc_two_t { + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_SGPR_PRIVATE_SEGMENT_WAVE_BYTE_OFFSET, 0, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_USER_SGPR_COUNT, 1, 5), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_TRAP_HANDLER, 6, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_SGPR_WORKGROUP_ID_X, 7, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_SGPR_WORKGROUP_ID_Y, 8, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_SGPR_WORKGROUP_ID_Z, 9, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_SGPR_WORKGROUP_INFO, 10, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_VGPR_WORKITEM_ID, 11, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_ADDRESS_WATCH, 13, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_MEMORY_VIOLATION, 14, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_GRANULATED_LDS_SIZE, 15, 9), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_IEEE_754_FP_INVALID_OPERATION, 24, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_FP_DENORMAL_SOURCE, 25, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_IEEE_754_FP_DIVISION_BY_ZERO, 26, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_IEEE_754_FP_OVERFLOW, 27, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_IEEE_754_FP_UNDERFLOW, 28, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_IEEE_754_FP_INEXACT, 29, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_ENABLE_EXCEPTION_INT_DIVISION_BY_ZERO, 30, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_COMPUTE_PGM_RSRC_TWO_RESERVED1, 31, 1) +}; + +// AMD Element Byte Size Enumeration Values. +enum amd_element_byte_size_t { + AMD_ELEMENT_BYTE_SIZE_2 = 0, + AMD_ELEMENT_BYTE_SIZE_4 = 1, + AMD_ELEMENT_BYTE_SIZE_8 = 2, + AMD_ELEMENT_BYTE_SIZE_16 = 3 +}; + +// AMD Kernel Code Properties. +typedef uint32_t amd_kernel_code_properties32_t; +enum amd_kernel_code_properties_t { + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_PRIVATE_SEGMENT_BUFFER, 0, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_DISPATCH_PTR, 1, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_QUEUE_PTR, 2, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_KERNARG_SEGMENT_PTR, 3, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_DISPATCH_ID, 4, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_FLAT_SCRATCH_INIT, 5, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_PRIVATE_SEGMENT_SIZE, 6, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_GRID_WORKGROUP_COUNT_X, 7, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_GRID_WORKGROUP_COUNT_Y, 8, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_SGPR_GRID_WORKGROUP_COUNT_Z, 9, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_RESERVED1, 10, 6), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_ENABLE_ORDERED_APPEND_GDS, 16, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_PRIVATE_ELEMENT_SIZE, 17, 2), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_IS_PTR64, 19, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_IS_DYNAMIC_CALLSTACK, 20, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_IS_DEBUG_ENABLED, 21, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_IS_XNACK_ENABLED, 22, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_KERNEL_CODE_PROPERTIES_RESERVED2, 23, 9) +}; + +// AMD Power Of Two Enumeration Values. +typedef uint8_t amd_powertwo8_t; +enum amd_powertwo_t { + AMD_POWERTWO_1 = 0, + AMD_POWERTWO_2 = 1, + AMD_POWERTWO_4 = 2, + AMD_POWERTWO_8 = 3, + AMD_POWERTWO_16 = 4, + AMD_POWERTWO_32 = 5, + AMD_POWERTWO_64 = 6, + AMD_POWERTWO_128 = 7, + AMD_POWERTWO_256 = 8 +}; + +// AMD Enabled Control Directive Enumeration Values. +typedef uint64_t amd_enabled_control_directive64_t; +enum amd_enabled_control_directive_t { + AMD_ENABLED_CONTROL_DIRECTIVE_ENABLE_BREAK_EXCEPTIONS = 1, + AMD_ENABLED_CONTROL_DIRECTIVE_ENABLE_DETECT_EXCEPTIONS = 2, + AMD_ENABLED_CONTROL_DIRECTIVE_MAX_DYNAMIC_GROUP_SIZE = 4, + AMD_ENABLED_CONTROL_DIRECTIVE_MAX_FLAT_GRID_SIZE = 8, + AMD_ENABLED_CONTROL_DIRECTIVE_MAX_FLAT_WORKGROUP_SIZE = 16, + AMD_ENABLED_CONTROL_DIRECTIVE_REQUIRED_DIM = 32, + AMD_ENABLED_CONTROL_DIRECTIVE_REQUIRED_GRID_SIZE = 64, + AMD_ENABLED_CONTROL_DIRECTIVE_REQUIRED_WORKGROUP_SIZE = 128, + AMD_ENABLED_CONTROL_DIRECTIVE_REQUIRE_NO_PARTIAL_WORKGROUPS = 256 +}; + +// AMD Exception Kind Enumeration Values. +typedef uint16_t amd_exception_kind16_t; +enum amd_exception_kind_t { + AMD_EXCEPTION_KIND_INVALID_OPERATION = 1, + AMD_EXCEPTION_KIND_DIVISION_BY_ZERO = 2, + AMD_EXCEPTION_KIND_OVERFLOW = 4, + AMD_EXCEPTION_KIND_UNDERFLOW = 8, + AMD_EXCEPTION_KIND_INEXACT = 16 +}; + +// AMD Control Directives. +#define AMD_CONTROL_DIRECTIVES_ALIGN_BYTES 64 +#define AMD_CONTROL_DIRECTIVES_ALIGN __ALIGNED__(AMD_CONTROL_DIRECTIVES_ALIGN_BYTES) +typedef AMD_CONTROL_DIRECTIVES_ALIGN struct amd_control_directives_s { + amd_enabled_control_directive64_t enabled_control_directives; + uint16_t enable_break_exceptions; + uint16_t enable_detect_exceptions; + uint32_t max_dynamic_group_size; + uint64_t max_flat_grid_size; + uint32_t max_flat_workgroup_size; + uint8_t required_dim; + uint8_t reserved1[3]; + uint64_t required_grid_size[3]; + uint32_t required_workgroup_size[3]; + uint8_t reserved2[60]; +} amd_control_directives_t; + +// AMD Kernel Code. +#define AMD_ISA_ALIGN_BYTES 256 +#define AMD_KERNEL_CODE_ALIGN_BYTES 64 +#define AMD_KERNEL_CODE_ALIGN __ALIGNED__(AMD_KERNEL_CODE_ALIGN_BYTES) +typedef AMD_KERNEL_CODE_ALIGN struct amd_kernel_code_s { + amd_kernel_code_version32_t amd_kernel_code_version_major; + amd_kernel_code_version32_t amd_kernel_code_version_minor; + amd_machine_kind16_t amd_machine_kind; + amd_machine_version16_t amd_machine_version_major; + amd_machine_version16_t amd_machine_version_minor; + amd_machine_version16_t amd_machine_version_stepping; + int64_t kernel_code_entry_byte_offset; + int64_t kernel_code_prefetch_byte_offset; + uint64_t kernel_code_prefetch_byte_size; + uint64_t max_scratch_backing_memory_byte_size; + amd_compute_pgm_rsrc_one32_t compute_pgm_rsrc1; + amd_compute_pgm_rsrc_two32_t compute_pgm_rsrc2; + amd_kernel_code_properties32_t kernel_code_properties; + uint32_t workitem_private_segment_byte_size; + uint32_t workgroup_group_segment_byte_size; + uint32_t gds_segment_byte_size; + uint64_t kernarg_segment_byte_size; + uint32_t workgroup_fbarrier_count; + uint16_t wavefront_sgpr_count; + uint16_t workitem_vgpr_count; + uint16_t reserved_vgpr_first; + uint16_t reserved_vgpr_count; + uint16_t reserved_sgpr_first; + uint16_t reserved_sgpr_count; + uint16_t debug_wavefront_private_segment_offset_sgpr; + uint16_t debug_private_segment_buffer_sgpr; + amd_powertwo8_t kernarg_segment_alignment; + amd_powertwo8_t group_segment_alignment; + amd_powertwo8_t private_segment_alignment; + amd_powertwo8_t wavefront_size; + int32_t call_convention; + uint8_t reserved1[12]; + uint64_t runtime_loader_kernel_symbol; + amd_control_directives_t control_directives; +} amd_kernel_code_t; + +// TODO: this struct should be completely gone once debugger designs/implements +// Debugger APIs. +typedef struct amd_runtime_loader_debug_info_s { + const void* elf_raw; + size_t elf_size; + const char *kernel_name; + const void *owning_segment; +} amd_runtime_loader_debug_info_t; + +#endif // AMD_HSA_KERNEL_CODE_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_queue.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_queue.h new file mode 100644 index 0000000000000000000000000000000000000000..98c6c31423fb76ca5f1335e3723aafeef6871f37 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_queue.h @@ -0,0 +1,109 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef AMD_HSA_QUEUE_H +#define AMD_HSA_QUEUE_H + +#include "amd_hsa_common.h" +#include "hsa.h" + +// AMD Queue Properties. +typedef uint32_t amd_queue_properties32_t; +enum amd_queue_properties_t { + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_ENABLE_TRAP_HANDLER, 0, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_IS_PTR64, 1, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_ENABLE_TRAP_HANDLER_DEBUG_SGPRS, 2, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_ENABLE_PROFILING, 3, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_USE_SCRATCH_ONCE, 4, 1), + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_PROPERTIES_RESERVED1, 5, 27) +}; + +// AMD Queue. +#define AMD_QUEUE_ALIGN_BYTES 64 +#define AMD_QUEUE_ALIGN __ALIGNED__(AMD_QUEUE_ALIGN_BYTES) + +// AMD Queue Capabilities. +typedef uint32_t amd_queue_capabilities32_t; +enum amd_queue_capabilities_t { + /* Whether this CP queue supports dual-scratch and async-reclaim */ + AMD_HSA_BITS_CREATE_ENUM_ENTRIES(AMD_QUEUE_CAPS_ASYNC_RECLAIM, 0, 1), +}; + +// Members tagged with "async-reclaim" are ignored by CP FW's that do not support +// AMD_QUEUE_CAPS_ASYNC_RECLAIM. CP FW's that support async-reclaim also support +// dual-scratch (alternate scratch). + +typedef struct AMD_QUEUE_ALIGN amd_queue_s { + hsa_queue_t hsa_queue; + uint32_t caps; + uint32_t reserved1[3]; + volatile uint64_t write_dispatch_id; + uint32_t group_segment_aperture_base_hi; + uint32_t private_segment_aperture_base_hi; + uint32_t max_cu_id; + uint32_t max_wave_id; + volatile uint64_t max_legacy_doorbell_dispatch_id_plus_1; + volatile uint32_t legacy_doorbell_lock; + uint32_t reserved2[9]; + volatile uint64_t read_dispatch_id; + uint32_t read_dispatch_id_field_base_byte_offset; + uint32_t compute_tmpring_size; + uint32_t scratch_resource_descriptor[4]; + uint64_t scratch_backing_memory_location; + uint64_t scratch_backing_memory_byte_size; + uint32_t scratch_wave64_lane_byte_size; + amd_queue_properties32_t queue_properties; + volatile uint64_t scratch_last_used_index; /* async-reclaim */ + hsa_signal_t queue_inactive_signal; + uint32_t reserved4[2]; + volatile uint64_t alt_scratch_last_used_index; /* async-reclaim */ + uint64_t alt_scratch_backing_memory_location; /* async-reclaim */ + uint64_t alt_scratch_backing_memory_byte_size; /* async-reclaim */ + uint32_t alt_scratch_dispatch_limit_x; /* async-reclaim */ + uint32_t alt_scratch_dispatch_limit_y; /* async-reclaim */ + uint32_t alt_scratch_dispatch_limit_z; /* async-reclaim */ + uint32_t alt_scratch_wave64_lane_byte_size; /* async-reclaim */ + uint32_t alt_compute_tmpring_size; /* async-reclaim */ + uint32_t reserved5; +} amd_queue_t; + +#endif // AMD_HSA_QUEUE_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_signal.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_signal.h new file mode 100644 index 0000000000000000000000000000000000000000..f9d721f73dd6178b0296abf91f1820502b218b4b --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/amd_hsa_signal.h @@ -0,0 +1,80 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef AMD_HSA_SIGNAL_H +#define AMD_HSA_SIGNAL_H + +#include "amd_hsa_common.h" +#include "amd_hsa_queue.h" + +// AMD Signal Kind Enumeration Values. +typedef int64_t amd_signal_kind64_t; +enum amd_signal_kind_t { + AMD_SIGNAL_KIND_INVALID = 0, + AMD_SIGNAL_KIND_USER = 1, + AMD_SIGNAL_KIND_DOORBELL = -1, + AMD_SIGNAL_KIND_LEGACY_DOORBELL = -2 +}; + +// AMD Signal. +#define AMD_SIGNAL_ALIGN_BYTES 64 +#define AMD_SIGNAL_ALIGN __ALIGNED__(AMD_SIGNAL_ALIGN_BYTES) +typedef struct AMD_SIGNAL_ALIGN amd_signal_s { + amd_signal_kind64_t kind; + union { + volatile int64_t value; + volatile uint32_t* legacy_hardware_doorbell_ptr; + volatile uint64_t* hardware_doorbell_ptr; + }; + uint64_t event_mailbox_ptr; + uint32_t event_id; + uint32_t reserved1; + uint64_t start_ts; + uint64_t end_ts; + union { + amd_queue_t* queue_ptr; + uint64_t reserved2; + }; + uint32_t reserved3[2]; +} amd_signal_t; + +#endif // AMD_HSA_SIGNAL_H diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa.h new file mode 100644 index 0000000000000000000000000000000000000000..9520bd870c9c323b92b8adc780a354c9d368521e --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa.h @@ -0,0 +1,5729 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef HSA_RUNTIME_INC_HSA_H_ +#define HSA_RUNTIME_INC_HSA_H_ + +#include /* size_t */ +#include /* uintXX_t */ + +#ifndef __cplusplus +#include /* bool */ +#endif /* __cplusplus */ + +// Placeholder for calling convention and import/export macros +#ifndef HSA_CALL +#define HSA_CALL +#endif + +#ifndef HSA_EXPORT_DECORATOR +#ifdef __GNUC__ +#define HSA_EXPORT_DECORATOR __attribute__ ((visibility ("default"))) +#else +#define HSA_EXPORT_DECORATOR +#endif +#endif +#define HSA_API_EXPORT HSA_EXPORT_DECORATOR HSA_CALL +#define HSA_API_IMPORT HSA_CALL + +#if !defined(HSA_API) && defined(HSA_EXPORT) +#define HSA_API HSA_API_EXPORT +#else +#define HSA_API HSA_API_IMPORT +#endif + +// Detect and set large model builds. +#undef HSA_LARGE_MODEL +#if defined(__LP64__) || defined(_M_X64) +#define HSA_LARGE_MODEL +#endif + +// Try to detect CPU endianness +#if !defined(LITTLEENDIAN_CPU) && !defined(BIGENDIAN_CPU) +#if defined(__BYTE_ORDER__) && (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__) +#define LITTLEENDIAN_CPU +#elif defined(__BYTE_ORDER__) && (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__) +#define BIGENDIAN_CPU +#elif defined(__i386__) || defined(__x86_64__) || defined(_M_IX86) || \ + defined(_M_X64) || defined(__loongarch64) || defined(__riscv) +#define LITTLEENDIAN_CPU +#endif +#endif + +#undef HSA_LITTLE_ENDIAN +#if defined(LITTLEENDIAN_CPU) +#define HSA_LITTLE_ENDIAN +#elif defined(BIGENDIAN_CPU) +#else +#error "BIGENDIAN_CPU or LITTLEENDIAN_CPU must be defined" +#endif + +#ifndef HSA_DEPRECATED +#define HSA_DEPRECATED +//#ifdef __GNUC__ +//#define HSA_DEPRECATED __attribute__((deprecated)) +//#else +//#define HSA_DEPRECATED __declspec(deprecated) +//#endif +#endif + +#define HSA_VERSION_1_0 1 + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +/** \defgroup status Runtime Notifications + * @{ + */ + +/** + * @brief Status codes. + */ +typedef enum { + /** + * The function has been executed successfully. + */ + HSA_STATUS_SUCCESS = 0x0, + /** + * A traversal over a list of elements has been interrupted by the + * application before completing. + */ + HSA_STATUS_INFO_BREAK = 0x1, + /** + * A generic error has occurred. + */ + HSA_STATUS_ERROR = 0x1000, + /** + * One of the actual arguments does not meet a precondition stated in the + * documentation of the corresponding formal argument. + */ + HSA_STATUS_ERROR_INVALID_ARGUMENT = 0x1001, + /** + * The requested queue creation is not valid. + */ + HSA_STATUS_ERROR_INVALID_QUEUE_CREATION = 0x1002, + /** + * The requested allocation is not valid. + */ + HSA_STATUS_ERROR_INVALID_ALLOCATION = 0x1003, + /** + * The agent is invalid. + */ + HSA_STATUS_ERROR_INVALID_AGENT = 0x1004, + /** + * The memory region is invalid. + */ + HSA_STATUS_ERROR_INVALID_REGION = 0x1005, + /** + * The signal is invalid. + */ + HSA_STATUS_ERROR_INVALID_SIGNAL = 0x1006, + /** + * The queue is invalid. + */ + HSA_STATUS_ERROR_INVALID_QUEUE = 0x1007, + /** + * The HSA runtime failed to allocate the necessary resources. This error + * may also occur when the HSA runtime needs to spawn threads or create + * internal OS-specific events. + */ + HSA_STATUS_ERROR_OUT_OF_RESOURCES = 0x1008, + /** + * The AQL packet is malformed. + */ + HSA_STATUS_ERROR_INVALID_PACKET_FORMAT = 0x1009, + /** + * An error has been detected while releasing a resource. + */ + HSA_STATUS_ERROR_RESOURCE_FREE = 0x100A, + /** + * An API other than ::hsa_init has been invoked while the reference count + * of the HSA runtime is 0. + */ + HSA_STATUS_ERROR_NOT_INITIALIZED = 0x100B, + /** + * The maximum reference count for the object has been reached. + */ + HSA_STATUS_ERROR_REFCOUNT_OVERFLOW = 0x100C, + /** + * The arguments passed to a functions are not compatible. + */ + HSA_STATUS_ERROR_INCOMPATIBLE_ARGUMENTS = 0x100D, + /** + * The index is invalid. + */ + HSA_STATUS_ERROR_INVALID_INDEX = 0x100E, + /** + * The instruction set architecture is invalid. + */ + HSA_STATUS_ERROR_INVALID_ISA = 0x100F, + /** + * The instruction set architecture name is invalid. + */ + HSA_STATUS_ERROR_INVALID_ISA_NAME = 0x1017, + /** + * The code object is invalid. + */ + HSA_STATUS_ERROR_INVALID_CODE_OBJECT = 0x1010, + /** + * The executable is invalid. + */ + HSA_STATUS_ERROR_INVALID_EXECUTABLE = 0x1011, + /** + * The executable is frozen. + */ + HSA_STATUS_ERROR_FROZEN_EXECUTABLE = 0x1012, + /** + * There is no symbol with the given name. + */ + HSA_STATUS_ERROR_INVALID_SYMBOL_NAME = 0x1013, + /** + * The variable is already defined. + */ + HSA_STATUS_ERROR_VARIABLE_ALREADY_DEFINED = 0x1014, + /** + * The variable is undefined. + */ + HSA_STATUS_ERROR_VARIABLE_UNDEFINED = 0x1015, + /** + * An HSAIL operation resulted in a hardware exception. + */ + HSA_STATUS_ERROR_EXCEPTION = 0x1016, + /** + * The code object symbol is invalid. + */ + HSA_STATUS_ERROR_INVALID_CODE_SYMBOL = 0x1018, + /** + * The executable symbol is invalid. + */ + HSA_STATUS_ERROR_INVALID_EXECUTABLE_SYMBOL = 0x1019, + /** + * The file descriptor is invalid. + */ + HSA_STATUS_ERROR_INVALID_FILE = 0x1020, + /** + * The code object reader is invalid. + */ + HSA_STATUS_ERROR_INVALID_CODE_OBJECT_READER = 0x1021, + /** + * The cache is invalid. + */ + HSA_STATUS_ERROR_INVALID_CACHE = 0x1022, + /** + * The wavefront is invalid. + */ + HSA_STATUS_ERROR_INVALID_WAVEFRONT = 0x1023, + /** + * The signal group is invalid. + */ + HSA_STATUS_ERROR_INVALID_SIGNAL_GROUP = 0x1024, + /** + * The HSA runtime is not in the configuration state. + */ + HSA_STATUS_ERROR_INVALID_RUNTIME_STATE = 0x1025, + /** + * The queue received an error that may require process termination. + */ + HSA_STATUS_ERROR_FATAL = 0x1026 +} hsa_status_t; + +/** + * @brief Query additional information about a status code. + * + * @param[in] status Status code. + * + * @param[out] status_string A NUL-terminated string that describes the error + * status. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p status is an invalid + * status code, or @p status_string is NULL. + */ +hsa_status_t HSA_API hsa_status_string( + hsa_status_t status, + const char ** status_string); + +/** @} */ + +/** \defgroup common Common Definitions + * @{ + */ + +/** + * @brief Three-dimensional coordinate. + */ +typedef struct hsa_dim3_s { + /** + * X dimension. + */ + uint32_t x; + + /** + * Y dimension. + */ + uint32_t y; + + /** + * Z dimension. + */ + uint32_t z; +} hsa_dim3_t; + +/** + * @brief Access permissions. + */ +typedef enum { + /** + * Used to remove existing access + */ + HSA_ACCESS_PERMISSION_NONE = 0, + /** + * Read-only access. + */ + HSA_ACCESS_PERMISSION_RO = 1, + /** + * Write-only access. + */ + HSA_ACCESS_PERMISSION_WO = 2, + /** + * Read and write access. + */ + HSA_ACCESS_PERMISSION_RW = 3 +} hsa_access_permission_t; + +/** + * @brief POSIX file descriptor. + */ +typedef int hsa_file_t; + +/** @} **/ + + +/** \defgroup initshutdown Initialization and Shut Down + * @{ + */ + +/** + * @brief Initialize the HSA runtime. + * + * @details Initializes the HSA runtime if it is not already initialized, and + * increases the reference counter associated with the HSA runtime for the + * current process. Invocation of any HSA function other than ::hsa_init results + * in undefined behavior if the current HSA runtime reference counter is less + * than one. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_REFCOUNT_OVERFLOW The HSA runtime reference + * count reaches INT32_MAX. + */ +hsa_status_t HSA_API hsa_init(); + +/** + * @brief Shut down the HSA runtime. + * + * @details Decreases the reference count of the HSA runtime instance. When the + * reference count reaches 0, the HSA runtime is no longer considered valid + * but the application might call ::hsa_init to initialize the HSA runtime + * again. + * + * Once the reference count of the HSA runtime reaches 0, all the resources + * associated with it (queues, signals, agent information, etc.) are + * considered invalid and any attempt to reference them in subsequent API calls + * results in undefined behavior. When the reference count reaches 0, the HSA + * runtime may release resources associated with it. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + */ +hsa_status_t HSA_API hsa_shut_down(); + +/** @} **/ + +/** \defgroup agentinfo System and Agent Information + * @{ + */ + +/** + * @brief Endianness. A convention used to interpret the bytes making up a data + * word. + */ +typedef enum { + /** + * The least significant byte is stored in the smallest address. + */ + HSA_ENDIANNESS_LITTLE = 0, + /** + * The most significant byte is stored in the smallest address. + */ + HSA_ENDIANNESS_BIG = 1 +} hsa_endianness_t; + +/** + * @brief Machine model. A machine model determines the size of certain data + * types in HSA runtime and an agent. + */ +typedef enum { + /** + * Small machine model. Addresses use 32 bits. + */ + HSA_MACHINE_MODEL_SMALL = 0, + /** + * Large machine model. Addresses use 64 bits. + */ + HSA_MACHINE_MODEL_LARGE = 1 +} hsa_machine_model_t; + +/** + * @brief Profile. A profile indicates a particular level of feature + * support. For example, in the base profile the application must use the HSA + * runtime allocator to reserve shared virtual memory, while in the full profile + * any host pointer can be shared across all the agents. + */ +typedef enum { + /** + * Base profile. + */ + HSA_PROFILE_BASE = 0, + /** + * Full profile. + */ + HSA_PROFILE_FULL = 1 +} hsa_profile_t; + +/** + * @brief System attributes. + */ +typedef enum { + /** + * Major version of the HSA runtime specification supported by the + * implementation. The type of this attribute is uint16_t. + */ + HSA_SYSTEM_INFO_VERSION_MAJOR = 0, + /** + * Minor version of the HSA runtime specification supported by the + * implementation. The type of this attribute is uint16_t. + */ + HSA_SYSTEM_INFO_VERSION_MINOR = 1, + /** + * Current timestamp. The value of this attribute monotonically increases at a + * constant rate. The type of this attribute is uint64_t. + */ + HSA_SYSTEM_INFO_TIMESTAMP = 2, + /** + * Timestamp value increase rate, in Hz. The timestamp (clock) frequency is + * in the range 1-400MHz. The type of this attribute is uint64_t. + */ + HSA_SYSTEM_INFO_TIMESTAMP_FREQUENCY = 3, + /** + * Maximum duration of a signal wait operation. Expressed as a count based on + * the timestamp frequency. The type of this attribute is uint64_t. + */ + HSA_SYSTEM_INFO_SIGNAL_MAX_WAIT = 4, + /** + * Endianness of the system. The type of this attribute is ::hsa_endianness_t. + */ + HSA_SYSTEM_INFO_ENDIANNESS = 5, + /** + * Machine model supported by the HSA runtime. The type of this attribute is + * ::hsa_machine_model_t. + */ + HSA_SYSTEM_INFO_MACHINE_MODEL = 6, + /** + * Bit-mask indicating which extensions are supported by the + * implementation. An extension with an ID of @p i is supported if the bit at + * position @p i is set. The type of this attribute is uint8_t[128]. + */ + HSA_SYSTEM_INFO_EXTENSIONS = 7, + /** + * String containing the ROCr build identifier. + */ + HSA_AMD_SYSTEM_INFO_BUILD_VERSION = 0x200, + /** + * Returns true if hsa_amd_svm_* APIs are supported by the driver. The type of + * this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_SVM_SUPPORTED = 0x201, + // TODO: Should this be per Agent? + /** + * Returns true if all Agents have access to system allocated memory (such as + * that allocated by mmap, malloc, or new) by default. + * If false then system allocated memory may only be made SVM accessible to + * an Agent by declaration of accessibility with hsa_amd_svm_set_attributes. + * The type of this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_SVM_ACCESSIBLE_BY_DEFAULT = 0x202, + /** + * Returns true if mwaitx is enabled on this system + * The type of this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_MWAITX_ENABLED = 0x203, + /** + * Returns true if DMABUF APIs are supported by the driver. The type of + * this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_DMABUF_SUPPORTED = 0x204, + /** + * Returns true if Virtual Memory APIs are supported by the driver. The type of + * this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_VIRTUAL_MEM_API_SUPPORTED = 0x205, + /** + * Returns true if XNACK is enabled on this system. The type of + * this attribute is bool. + */ + HSA_AMD_SYSTEM_INFO_XNACK_ENABLED = 0x206, + /** + * Major version of the HSA runtime extension specification supported by the + * implementation. The type of this attribute is uint16_t. + */ + HSA_AMD_SYSTEM_INFO_EXT_VERSION_MAJOR = 0x207, + /** + * Minor version of the HSA runtime extension specification supported by the + * implementation. The type of this attribute is uint16_t. + */ + HSA_AMD_SYSTEM_INFO_EXT_VERSION_MINOR = 0x208, +} hsa_system_info_t; + +/** + * @brief Get the current value of a system attribute. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * system attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_system_get_info( + hsa_system_info_t attribute, + void* value); + +/** + * @brief HSA extensions. + */ +typedef enum { + /** + * Finalizer extension. + */ + HSA_EXTENSION_FINALIZER = 0, + /** + * Images extension. + */ + HSA_EXTENSION_IMAGES = 1, + + /** + * Performance counter extension. + */ + HSA_EXTENSION_PERFORMANCE_COUNTERS = 2, + + /** + * Profiling events extension. + */ + HSA_EXTENSION_PROFILING_EVENTS = 3, + /** + * Extension count. + */ + HSA_EXTENSION_STD_LAST = 3, + /** + * First AMD extension number. + */ + HSA_AMD_FIRST_EXTENSION = 0x200, + /** + * Profiler extension. + */ + HSA_EXTENSION_AMD_PROFILER = 0x200, + /** + * Loader extension. + */ + HSA_EXTENSION_AMD_LOADER = 0x201, + /** + * AqlProfile extension. + */ + HSA_EXTENSION_AMD_AQLPROFILE = 0x202, + /** + * Last AMD extension. + */ + HSA_AMD_LAST_EXTENSION = 0x202 +} hsa_extension_t; + +/** + * @brief Query the name of a given extension. + * + * @param[in] extension Extension identifier. If the extension is not supported + * by the implementation (see ::HSA_SYSTEM_INFO_EXTENSIONS), the behavior + * is undefined. + * + * @param[out] name Pointer to a memory location where the HSA runtime stores + * the extension name. The extension name is a NUL-terminated string. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p name is NULL. + */ +hsa_status_t HSA_API hsa_extension_get_name( + uint16_t extension, + const char **name); + +/** + * @deprecated + * + * @brief Query if a given version of an extension is supported by the HSA + * implementation. + * + * @param[in] extension Extension identifier. + * + * @param[in] version_major Major version number. + * + * @param[in] version_minor Minor version number. + * + * @param[out] result Pointer to a memory location where the HSA runtime stores + * the result of the check. The result is true if the specified version of the + * extension is supported, and false otherwise. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p result is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_system_extension_supported( + uint16_t extension, + uint16_t version_major, + uint16_t version_minor, + bool* result); + +/** + * @brief Query if a given version of an extension is supported by the HSA + * implementation. All minor versions from 0 up to the returned @p version_minor + * must be supported by the implementation. + * + * @param[in] extension Extension identifier. + * + * @param[in] version_major Major version number. + * + * @param[out] version_minor Minor version number. + * + * @param[out] result Pointer to a memory location where the HSA runtime stores + * the result of the check. The result is true if the specified version of the + * extension is supported, and false otherwise. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p version_minor is NULL, or @p result is NULL. + */ +hsa_status_t HSA_API hsa_system_major_extension_supported( + uint16_t extension, + uint16_t version_major, + uint16_t *version_minor, + bool* result); + + +/** + * @deprecated + * + * @brief Retrieve the function pointers corresponding to a given version of an + * extension. Portable applications are expected to invoke the extension API + * using the returned function pointers + * + * @details The application is responsible for verifying that the given version + * of the extension is supported by the HSA implementation (see + * ::hsa_system_extension_supported). If the given combination of extension, + * major version, and minor version is not supported by the implementation, the + * behavior is undefined. + * + * @param[in] extension Extension identifier. + * + * @param[in] version_major Major version number for which to retrieve the + * function pointer table. + * + * @param[in] version_minor Minor version number for which to retrieve the + * function pointer table. + * + * @param[out] table Pointer to an application-allocated function pointer table + * that is populated by the HSA runtime. Must not be NULL. The memory associated + * with table can be reused or freed after the function returns. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p table is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_system_get_extension_table( + uint16_t extension, + uint16_t version_major, + uint16_t version_minor, + void *table); + +/** + * @brief Retrieve the function pointers corresponding to a given major version + * of an extension. Portable applications are expected to invoke the extension + * API using the returned function pointers. + * + * @details The application is responsible for verifying that the given major + * version of the extension is supported by the HSA implementation (see + * ::hsa_system_major_extension_supported). If the given combination of extension + * and major version is not supported by the implementation, the behavior is + * undefined. Additionally if the length doesn't allow space for a full minor + * version, it is implementation defined if only some of the function pointers for + * that minor version get written. + * + * @param[in] extension Extension identifier. + * + * @param[in] version_major Major version number for which to retrieve the + * function pointer table. + * + * @param[in] table_length Size in bytes of the function pointer table to be + * populated. The implementation will not write more than this many bytes to the + * table. + * + * @param[out] table Pointer to an application-allocated function pointer table + * that is populated by the HSA runtime. Must not be NULL. The memory associated + * with table can be reused or freed after the function returns. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p table is NULL. + */ +hsa_status_t HSA_API hsa_system_get_major_extension_table( + uint16_t extension, + uint16_t version_major, + size_t table_length, + void *table); + +/** + * @brief Struct containing an opaque handle to an agent, a device that participates in + * the HSA memory model. An agent can submit AQL packets for execution, and + * may also accept AQL packets for execution (agent dispatch packets or kernel + * dispatch packets launching HSAIL-derived binaries). + */ +typedef struct hsa_agent_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_agent_t; + +/** + * @brief Agent features. + */ +typedef enum { + /** + * The agent supports AQL packets of kernel dispatch type. If this + * feature is enabled, the agent is also a kernel agent. + */ + HSA_AGENT_FEATURE_KERNEL_DISPATCH = 1, + /** + * The agent supports AQL packets of agent dispatch type. + */ + HSA_AGENT_FEATURE_AGENT_DISPATCH = 2 +} hsa_agent_feature_t; + +/** + * @brief Hardware device type. + */ +typedef enum { + /** + * CPU device. + */ + HSA_DEVICE_TYPE_CPU = 0, + /** + * GPU device. + */ + HSA_DEVICE_TYPE_GPU = 1, + /** + * DSP device. + */ + HSA_DEVICE_TYPE_DSP = 2 +} hsa_device_type_t; + +/** + * @brief Default floating-point rounding mode. + */ +typedef enum { + /** + * Use a default floating-point rounding mode specified elsewhere. + */ + HSA_DEFAULT_FLOAT_ROUNDING_MODE_DEFAULT = 0, + /** + * Operations that specify the default floating-point mode are rounded to zero + * by default. + */ + HSA_DEFAULT_FLOAT_ROUNDING_MODE_ZERO = 1, + /** + * Operations that specify the default floating-point mode are rounded to the + * nearest representable number and that ties should be broken by selecting + * the value with an even least significant bit. + */ + HSA_DEFAULT_FLOAT_ROUNDING_MODE_NEAR = 2 +} hsa_default_float_rounding_mode_t; + +/** + * @brief Agent attributes. + */ +typedef enum { + /** + * Agent name. The type of this attribute is a NUL-terminated char[64]. The + * name must be at most 63 characters long (not including the NUL terminator) + * and all array elements not used for the name must be NUL. + */ + HSA_AGENT_INFO_NAME = 0, + /** + * Name of vendor. The type of this attribute is a NUL-terminated char[64]. + * The name must be at most 63 characters long (not including the NUL + * terminator) and all array elements not used for the name must be NUL. + */ + HSA_AGENT_INFO_VENDOR_NAME = 1, + /** + * Agent capability. The type of this attribute is ::hsa_agent_feature_t. + */ + HSA_AGENT_INFO_FEATURE = 2, + /** + * @deprecated Query ::HSA_ISA_INFO_MACHINE_MODELS for a given intruction set + * architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Machine model supported by the agent. The type of this attribute is + * ::hsa_machine_model_t. + */ + HSA_AGENT_INFO_MACHINE_MODEL = 3, + /** + * @deprecated Query ::HSA_ISA_INFO_PROFILES for a given intruction set + * architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Profile supported by the agent. The type of this attribute is + * ::hsa_profile_t. + */ + HSA_AGENT_INFO_PROFILE = 4, + /** + * @deprecated Query ::HSA_ISA_INFO_DEFAULT_FLOAT_ROUNDING_MODES for a given + * intruction set architecture supported by the agent instead. If more than + * one ISA is supported by the agent, the returned value corresponds to the + * first ISA enumerated by ::hsa_agent_iterate_isas. + * + * Default floating-point rounding mode. The type of this attribute is + * ::hsa_default_float_rounding_mode_t, but the value + * ::HSA_DEFAULT_FLOAT_ROUNDING_MODE_DEFAULT is not allowed. + */ + HSA_AGENT_INFO_DEFAULT_FLOAT_ROUNDING_MODE = 5, + /** + * @deprecated Query ::HSA_ISA_INFO_BASE_PROFILE_DEFAULT_FLOAT_ROUNDING_MODES + * for a given intruction set architecture supported by the agent instead. If + * more than one ISA is supported by the agent, the returned value corresponds + * to the first ISA enumerated by ::hsa_agent_iterate_isas. + * + * A bit-mask of ::hsa_default_float_rounding_mode_t values, representing the + * default floating-point rounding modes supported by the agent in the Base + * profile. The type of this attribute is uint32_t. The default floating-point + * rounding mode (::HSA_AGENT_INFO_DEFAULT_FLOAT_ROUNDING_MODE) bit must not + * be set. + */ + HSA_AGENT_INFO_BASE_PROFILE_DEFAULT_FLOAT_ROUNDING_MODES = 23, + /** + * @deprecated Query ::HSA_ISA_INFO_FAST_F16_OPERATION for a given intruction + * set architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Flag indicating that the f16 HSAIL operation is at least as fast as the + * f32 operation in the current agent. The value of this attribute is + * undefined if the agent is not a kernel agent. The type of this + * attribute is bool. + */ + HSA_AGENT_INFO_FAST_F16_OPERATION = 24, + /** + * @deprecated Query ::HSA_WAVEFRONT_INFO_SIZE for a given wavefront and + * intruction set architecture supported by the agent instead. If more than + * one ISA is supported by the agent, the returned value corresponds to the + * first ISA enumerated by ::hsa_agent_iterate_isas and the first wavefront + * enumerated by ::hsa_isa_iterate_wavefronts for that ISA. + * + * Number of work-items in a wavefront. Must be a power of 2 in the range + * [1,256]. The value of this attribute is undefined if the agent is not + * a kernel agent. The type of this attribute is uint32_t. + */ + HSA_AGENT_INFO_WAVEFRONT_SIZE = 6, + /** + * @deprecated Query ::HSA_ISA_INFO_WORKGROUP_MAX_DIM for a given intruction + * set architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Maximum number of work-items of each dimension of a work-group. Each + * maximum must be greater than 0. No maximum can exceed the value of + * ::HSA_AGENT_INFO_WORKGROUP_MAX_SIZE. The value of this attribute is + * undefined if the agent is not a kernel agent. The type of this + * attribute is uint16_t[3]. + */ + HSA_AGENT_INFO_WORKGROUP_MAX_DIM = 7, + /** + * @deprecated Query ::HSA_ISA_INFO_WORKGROUP_MAX_SIZE for a given intruction + * set architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Maximum total number of work-items in a work-group. The value of this + * attribute is undefined if the agent is not a kernel agent. The type + * of this attribute is uint32_t. + */ + HSA_AGENT_INFO_WORKGROUP_MAX_SIZE = 8, + /** + * @deprecated Query ::HSA_ISA_INFO_GRID_MAX_DIM for a given intruction set + * architecture supported by the agent instead. + * + * Maximum number of work-items of each dimension of a grid. Each maximum must + * be greater than 0, and must not be smaller than the corresponding value in + * ::HSA_AGENT_INFO_WORKGROUP_MAX_DIM. No maximum can exceed the value of + * ::HSA_AGENT_INFO_GRID_MAX_SIZE. The value of this attribute is undefined + * if the agent is not a kernel agent. The type of this attribute is + * ::hsa_dim3_t. + */ + HSA_AGENT_INFO_GRID_MAX_DIM = 9, + /** + * @deprecated Query ::HSA_ISA_INFO_GRID_MAX_SIZE for a given intruction set + * architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Maximum total number of work-items in a grid. The value of this attribute + * is undefined if the agent is not a kernel agent. The type of this + * attribute is uint32_t. + */ + HSA_AGENT_INFO_GRID_MAX_SIZE = 10, + /** + * @deprecated Query ::HSA_ISA_INFO_FBARRIER_MAX_SIZE for a given intruction + * set architecture supported by the agent instead. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Maximum number of fbarriers per work-group. Must be at least 32. The value + * of this attribute is undefined if the agent is not a kernel agent. The + * type of this attribute is uint32_t. + */ + HSA_AGENT_INFO_FBARRIER_MAX_SIZE = 11, + /** + * @deprecated The maximum number of queues is not statically determined. + * + * Maximum number of queues that can be active (created but not destroyed) at + * one time in the agent. The type of this attribute is uint32_t. + */ + HSA_AGENT_INFO_QUEUES_MAX = 12, + /** + * Minimum number of packets that a queue created in the agent + * can hold. Must be a power of 2 greater than 0. Must not exceed + * the value of ::HSA_AGENT_INFO_QUEUE_MAX_SIZE. The type of this + * attribute is uint32_t. + */ + HSA_AGENT_INFO_QUEUE_MIN_SIZE = 13, + /** + * Maximum number of packets that a queue created in the agent can + * hold. Must be a power of 2 greater than 0. The type of this attribute + * is uint32_t. + */ + HSA_AGENT_INFO_QUEUE_MAX_SIZE = 14, + /** + * Type of a queue created in the agent. The type of this attribute is + * ::hsa_queue_type32_t. + */ + HSA_AGENT_INFO_QUEUE_TYPE = 15, + /** + * @deprecated NUMA information is not exposed anywhere else in the API. + * + * Identifier of the NUMA node associated with the agent. The type of this + * attribute is uint32_t. + */ + HSA_AGENT_INFO_NODE = 16, + /** + * Type of hardware device associated with the agent. The type of this + * attribute is ::hsa_device_type_t. + */ + HSA_AGENT_INFO_DEVICE = 17, + /** + * @deprecated Query ::hsa_agent_iterate_caches to retrieve information about + * the caches present in a given agent. + * + * Array of data cache sizes (L1..L4). Each size is expressed in bytes. A size + * of 0 for a particular level indicates that there is no cache information + * for that level. The type of this attribute is uint32_t[4]. + */ + HSA_AGENT_INFO_CACHE_SIZE = 18, + /** + * @deprecated An agent may support multiple instruction set + * architectures. See ::hsa_agent_iterate_isas. If more than one ISA is + * supported by the agent, the returned value corresponds to the first ISA + * enumerated by ::hsa_agent_iterate_isas. + * + * Instruction set architecture of the agent. The type of this attribute + * is ::hsa_isa_t. + */ + HSA_AGENT_INFO_ISA = 19, + /** + * Bit-mask indicating which extensions are supported by the agent. An + * extension with an ID of @p i is supported if the bit at position @p i is + * set. The type of this attribute is uint8_t[128]. + */ + HSA_AGENT_INFO_EXTENSIONS = 20, + /** + * Major version of the HSA runtime specification supported by the + * agent. The type of this attribute is uint16_t. + */ + HSA_AGENT_INFO_VERSION_MAJOR = 21, + /** + * Minor version of the HSA runtime specification supported by the + * agent. The type of this attribute is uint16_t. + */ + HSA_AGENT_INFO_VERSION_MINOR = 22, + /** + * This enum does not have a fixed underlying type, thus in C++ post D2338: + * If the enumeration type does not have a fixed underlying type, the value is + * unchanged if the original value is within the range of the enumeration + * values (9.7.1 [dcl.enum]), and otherwise, the behavior is + * undefined. + * Thus increase the range of this enum to encompass vendor extensions. + */ + HSA_AGENT_INFO_LAST = INT32_MAX +} hsa_agent_info_t; + +/** + * @brief Get the current value of an attribute for a given agent. + * + * @param[in] agent A valid agent. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * agent attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_agent_get_info( + hsa_agent_t agent, + hsa_agent_info_t attribute, + void* value); + +/** + * @brief Iterate over the available agents, and invoke an + * application-defined callback on every iteration. + * + * @param[in] callback Callback to be invoked once per agent. The HSA + * runtime passes two arguments to the callback: the agent and the + * application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_iterate_agents returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. +*/ +hsa_status_t HSA_API hsa_iterate_agents( + hsa_status_t (*callback)(hsa_agent_t agent, void* data), + void* data); + +/* + +// If we do not know the size of an attribute, we need to query it first +// Note: this API will not be in the spec unless needed +hsa_status_t HSA_API hsa_agent_get_info_size( + hsa_agent_t agent, + hsa_agent_info_t attribute, + size_t* size); + +// Set the value of an agents attribute +// Note: this API will not be in the spec unless needed +hsa_status_t HSA_API hsa_agent_set_info( + hsa_agent_t agent, + hsa_agent_info_t attribute, + void* value); + +*/ + +/** + * @brief Exception policies applied in the presence of hardware exceptions. + */ +typedef enum { + /** + * If a hardware exception is detected, a work-item signals an exception. + */ + HSA_EXCEPTION_POLICY_BREAK = 1, + /** + * If a hardware exception is detected, a hardware status bit is set. + */ + HSA_EXCEPTION_POLICY_DETECT = 2 +} hsa_exception_policy_t; + +/** + * @deprecated Use ::hsa_isa_get_exception_policies for a given intruction set + * architecture supported by the agent instead. If more than one ISA is + * supported by the agent, this function uses the first value returned by + * ::hsa_agent_iterate_isas. + * + * @brief Retrieve the exception policy support for a given combination of + * agent and profile + * + * @param[in] agent Agent. + * + * @param[in] profile Profile. + * + * @param[out] mask Pointer to a memory location where the HSA runtime stores a + * mask of ::hsa_exception_policy_t values. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p profile is not a valid + * profile, or @p mask is NULL. + * + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_agent_get_exception_policies( + hsa_agent_t agent, + hsa_profile_t profile, + uint16_t *mask); + +/** + * @brief Cache handle. + */ +typedef struct hsa_cache_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_cache_t; + +/** + * @brief Cache attributes. + */ +typedef enum { + /** + * The length of the cache name in bytes, not including the NUL terminator. + * The type of this attribute is uint32_t. + */ + HSA_CACHE_INFO_NAME_LENGTH = 0, + /** + * Human-readable description. The type of this attribute is a NUL-terminated + * character array with the length equal to the value of + * ::HSA_CACHE_INFO_NAME_LENGTH attribute. + */ + HSA_CACHE_INFO_NAME = 1, + /** + * Cache level. A L1 cache must return a value of 1, a L2 must return a value + * of 2, and so on. The type of this attribute is uint8_t. + */ + HSA_CACHE_INFO_LEVEL = 2, + /** + * Cache size, in bytes. A value of 0 indicates that there is no size + * information available. The type of this attribute is uint32_t. + */ + HSA_CACHE_INFO_SIZE = 3 +} hsa_cache_info_t; + +/** + * @brief Get the current value of an attribute for a given cache object. + * + * @param[in] cache Cache. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CACHE The cache is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * instruction set architecture attribute, or @p value is + * NULL. + */ +hsa_status_t HSA_API hsa_cache_get_info( + hsa_cache_t cache, + hsa_cache_info_t attribute, + void* value); + +/** + * @brief Iterate over the memory caches of a given agent, and + * invoke an application-defined callback on every iteration. + * + * @details Caches are visited in ascending order according to the value of the + * ::HSA_CACHE_INFO_LEVEL attribute. + * + * @param[in] agent A valid agent. + * + * @param[in] callback Callback to be invoked once per cache that is present in + * the agent. The HSA runtime passes two arguments to the callback: the cache + * and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * that value is returned. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_agent_iterate_caches( + hsa_agent_t agent, + hsa_status_t (*callback)(hsa_cache_t cache, void* data), + void* data); + +/** + * @deprecated + * + * @brief Query if a given version of an extension is supported by an agent + * + * @param[in] extension Extension identifier. + * + * @param[in] agent Agent. + * + * @param[in] version_major Major version number. + * + * @param[in] version_minor Minor version number. + * + * @param[out] result Pointer to a memory location where the HSA runtime stores + * the result of the check. The result is true if the specified version of the + * extension is supported, and false otherwise. The result must be false if + * ::hsa_system_extension_supported returns false for the same extension + * version. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p result is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_agent_extension_supported( + uint16_t extension, + hsa_agent_t agent, + uint16_t version_major, + uint16_t version_minor, + bool* result); + +/** + * @brief Query if a given version of an extension is supported by an agent. All + * minor versions from 0 up to the returned @p version_minor must be supported. + * + * @param[in] extension Extension identifier. + * + * @param[in] agent Agent. + * + * @param[in] version_major Major version number. + * + * @param[out] version_minor Minor version number. + * + * @param[out] result Pointer to a memory location where the HSA runtime stores + * the result of the check. The result is true if the specified version of the + * extension is supported, and false otherwise. The result must be false if + * ::hsa_system_extension_supported returns false for the same extension + * version. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p extension is not a valid + * extension, or @p version_minor is NULL, or @p result is NULL. + */ +hsa_status_t HSA_API hsa_agent_major_extension_supported( + uint16_t extension, + hsa_agent_t agent, + uint16_t version_major, + uint16_t *version_minor, + bool* result); + + +/** @} */ + + +/** \defgroup signals Signals + * @{ + */ + +/** + * @brief Signal handle. + */ +typedef struct hsa_signal_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. The value 0 is reserved. + */ + uint64_t handle; +} hsa_signal_t; + +/** + * @brief Signal value. The value occupies 32 bits in small machine mode, and 64 + * bits in large machine mode. + */ +#ifdef HSA_LARGE_MODEL + typedef int64_t hsa_signal_value_t; +#else + typedef int32_t hsa_signal_value_t; +#endif + +/** + * @brief Create a signal. + * + * @param[in] initial_value Initial value of the signal. + * + * @param[in] num_consumers Size of @p consumers. A value of 0 indicates that + * any agent might wait on the signal. + * + * @param[in] consumers List of agents that might consume (wait on) the + * signal. If @p num_consumers is 0, this argument is ignored; otherwise, the + * HSA runtime might use the list to optimize the handling of the signal + * object. If an agent not listed in @p consumers waits on the returned + * signal, the behavior is undefined. The memory associated with @p consumers + * can be reused or freed after the function returns. + * + * @param[out] signal Pointer to a memory location where the HSA runtime will + * store the newly created signal handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p signal is NULL, @p + * num_consumers is greater than 0 but @p consumers is NULL, or @p consumers + * contains duplicates. + */ +hsa_status_t HSA_API hsa_signal_create( + hsa_signal_value_t initial_value, + uint32_t num_consumers, + const hsa_agent_t *consumers, + hsa_signal_t *signal); + +/** + * @brief Destroy a signal previous created by ::hsa_signal_create. + * + * @param[in] signal Signal. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL @p signal is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT The handle in @p signal is 0. + */ +hsa_status_t HSA_API hsa_signal_destroy( + hsa_signal_t signal); + +/** + * @brief Atomically read the current value of a signal. + * + * @param[in] signal Signal. + * + * @return Value of the signal. +*/ +hsa_signal_value_t HSA_API hsa_signal_load_scacquire( + hsa_signal_t signal); + +/** + * @copydoc hsa_signal_load_scacquire + */ +hsa_signal_value_t HSA_API hsa_signal_load_relaxed( + hsa_signal_t signal); + +/** + * @deprecated Renamed as ::hsa_signal_load_scacquire. + * + * @copydoc hsa_signal_load_scacquire +*/ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_load_acquire( + hsa_signal_t signal); + +/** + * @brief Atomically set the value of a signal. + * + * @details If the value of the signal is changed, all the agents waiting + * on @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. + * + * @param[in] value New signal value. + */ +void HSA_API hsa_signal_store_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_store_relaxed + */ +void HSA_API hsa_signal_store_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_store_screlease. + * + * @copydoc hsa_signal_store_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_store_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically set the value of a signal without necessarily notifying the + * the agents waiting on it. + * + * @details The agents waiting on @p signal may not wake up even when the new + * value satisfies their wait condition. If the application wants to update the + * signal and there is no need to notify any agent, invoking this function can + * be more efficient than calling the non-silent counterpart. + * + * @param[in] signal Signal. + * + * @param[in] value New signal value. + */ +void HSA_API hsa_signal_silent_store_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_silent_store_relaxed + */ +void HSA_API hsa_signal_silent_store_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically set the value of a signal and return its previous value. + * + * @details If the value of the signal is changed, all the agents waiting + * on @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value New value. + * + * @return Value of the signal prior to the exchange. + * + */ +hsa_signal_value_t HSA_API hsa_signal_exchange_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_exchange_scacq_screl. + * + * @copydoc hsa_signal_exchange_scacq_screl + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_exchange_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_exchange_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_exchange_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_exchange_scacquire. + * + * @copydoc hsa_signal_exchange_scacquire + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_exchange_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_exchange_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_exchange_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); +/** + * @copydoc hsa_signal_exchange_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_exchange_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_exchange_screlease. + * + * @copydoc hsa_signal_exchange_screlease + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_exchange_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically set the value of a signal if the observed value is equal to + * the expected value. The observed value is returned regardless of whether the + * replacement was done. + * + * @details If the value of the signal is changed, all the agents waiting + * on @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue + * doorbell signal, the behavior is undefined. + * + * @param[in] expected Value to compare with. + * + * @param[in] value New value. + * + * @return Observed value of the signal. + * + */ +hsa_signal_value_t HSA_API hsa_signal_cas_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_cas_scacq_screl. + * + * @copydoc hsa_signal_cas_scacq_screl + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_cas_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_cas_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_cas_scacquire( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_cas_scacquire. + * + * @copydoc hsa_signal_cas_scacquire + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_cas_acquire( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_cas_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_cas_relaxed( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_cas_scacq_screl + */ +hsa_signal_value_t HSA_API hsa_signal_cas_screlease( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_cas_screlease. + * + * @copydoc hsa_signal_cas_screlease + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_cas_release( + hsa_signal_t signal, + hsa_signal_value_t expected, + hsa_signal_value_t value); + +/** + * @brief Atomically increment the value of a signal by a given amount. + * + * @details If the value of the signal is changed, all the agents waiting on + * @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value Value to add to the value of the signal. + * + */ +void HSA_API hsa_signal_add_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_add_scacq_screl. + * + * @copydoc hsa_signal_add_scacq_screl + */ +void HSA_API HSA_DEPRECATED hsa_signal_add_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_add_scacq_screl + */ +void HSA_API hsa_signal_add_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_add_scacquire. + * + * @copydoc hsa_signal_add_scacquire + */ +void HSA_API HSA_DEPRECATED hsa_signal_add_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_add_scacq_screl + */ +void HSA_API hsa_signal_add_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_add_scacq_screl + */ +void HSA_API hsa_signal_add_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_add_screlease. + * + * @copydoc hsa_signal_add_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_add_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically decrement the value of a signal by a given amount. + * + * @details If the value of the signal is changed, all the agents waiting on + * @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value Value to subtract from the value of the signal. + * + */ +void HSA_API hsa_signal_subtract_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_subtract_scacq_screl. + * + * @copydoc hsa_signal_subtract_scacq_screl + */ +void HSA_API HSA_DEPRECATED hsa_signal_subtract_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_subtract_scacq_screl + */ +void HSA_API hsa_signal_subtract_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_subtract_scacquire. + * + * @copydoc hsa_signal_subtract_scacquire + */ +void HSA_API HSA_DEPRECATED hsa_signal_subtract_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_subtract_scacq_screl + */ +void HSA_API hsa_signal_subtract_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_subtract_scacq_screl + */ +void HSA_API hsa_signal_subtract_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_subtract_screlease. + * + * @copydoc hsa_signal_subtract_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_subtract_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically perform a bitwise AND operation between the value of a + * signal and a given value. + * + * @details If the value of the signal is changed, all the agents waiting on + * @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value Value to AND with the value of the signal. + * + */ +void HSA_API hsa_signal_and_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_and_scacq_screl. + * + * @copydoc hsa_signal_and_scacq_screl + */ +void HSA_API HSA_DEPRECATED hsa_signal_and_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_and_scacq_screl + */ +void HSA_API hsa_signal_and_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_and_scacquire. + * + * @copydoc hsa_signal_and_scacquire + */ +void HSA_API HSA_DEPRECATED hsa_signal_and_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_and_scacq_screl + */ +void HSA_API hsa_signal_and_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_and_scacq_screl + */ +void HSA_API hsa_signal_and_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_and_screlease. + * + * @copydoc hsa_signal_and_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_and_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically perform a bitwise OR operation between the value of a + * signal and a given value. + * + * @details If the value of the signal is changed, all the agents waiting on + * @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value Value to OR with the value of the signal. + */ +void HSA_API hsa_signal_or_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_or_scacq_screl. + * + * @copydoc hsa_signal_or_scacq_screl + */ +void HSA_API HSA_DEPRECATED hsa_signal_or_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_or_scacq_screl + */ +void HSA_API hsa_signal_or_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_or_scacquire. + * + * @copydoc hsa_signal_or_scacquire + */ +void HSA_API HSA_DEPRECATED hsa_signal_or_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_or_scacq_screl + */ +void HSA_API hsa_signal_or_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_or_scacq_screl + */ +void HSA_API hsa_signal_or_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_or_screlease. + * + * @copydoc hsa_signal_or_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_or_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Atomically perform a bitwise XOR operation between the value of a + * signal and a given value. + * + * @details If the value of the signal is changed, all the agents waiting on + * @p signal for which @p value satisfies their wait condition are awakened. + * + * @param[in] signal Signal. If @p signal is a queue doorbell signal, the + * behavior is undefined. + * + * @param[in] value Value to XOR with the value of the signal. + * + */ +void HSA_API hsa_signal_xor_scacq_screl( + hsa_signal_t signal, + hsa_signal_value_t value); + + +/** + * @deprecated Renamed as ::hsa_signal_xor_scacq_screl. + * + * @copydoc hsa_signal_xor_scacq_screl + */ +void HSA_API HSA_DEPRECATED hsa_signal_xor_acq_rel( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_xor_scacq_screl + */ +void HSA_API hsa_signal_xor_scacquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_xor_scacquire. + * + * @copydoc hsa_signal_xor_scacquire + */ +void HSA_API HSA_DEPRECATED hsa_signal_xor_acquire( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_xor_scacq_screl + */ +void HSA_API hsa_signal_xor_relaxed( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @copydoc hsa_signal_xor_scacq_screl + */ +void HSA_API hsa_signal_xor_screlease( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @deprecated Renamed as ::hsa_signal_xor_screlease. + * + * @copydoc hsa_signal_xor_screlease + */ +void HSA_API HSA_DEPRECATED hsa_signal_xor_release( + hsa_signal_t signal, + hsa_signal_value_t value); + +/** + * @brief Wait condition operator. + */ +typedef enum { + /** + * The two operands are equal. + */ + HSA_SIGNAL_CONDITION_EQ = 0, + /** + * The two operands are not equal. + */ + HSA_SIGNAL_CONDITION_NE = 1, + /** + * The first operand is less than the second operand. + */ + HSA_SIGNAL_CONDITION_LT = 2, + /** + * The first operand is greater than or equal to the second operand. + */ + HSA_SIGNAL_CONDITION_GTE = 3 +} hsa_signal_condition_t; + +/** + * @brief State of the application thread during a signal wait. + */ +typedef enum { + /** + * The application thread may be rescheduled while waiting on the signal. + */ + HSA_WAIT_STATE_BLOCKED = 0, + /** + * The application thread stays active while waiting on a signal. + */ + HSA_WAIT_STATE_ACTIVE = 1 +} hsa_wait_state_t; + + +/** + * @brief Wait until a signal value satisfies a specified condition, or a + * certain amount of time has elapsed. + * + * @details A wait operation can spuriously resume at any time sooner than the + * timeout (for example, due to system or other external factors) even when the + * condition has not been met. + * + * The function is guaranteed to return if the signal value satisfies the + * condition at some point in time during the wait, but the value returned to + * the application might not satisfy the condition. The application must ensure + * that signals are used in such way that wait wakeup conditions are not + * invalidated before dependent threads have woken up. + * + * When the wait operation internally loads the value of the passed signal, it + * uses the memory order indicated in the function name. + * + * @param[in] signal Signal. + * + * @param[in] condition Condition used to compare the signal value with @p + * compare_value. + * + * @param[in] compare_value Value to compare with. + * + * @param[in] timeout_hint Maximum duration of the wait. Specified in the same + * unit as the system timestamp. The operation might block for a shorter or + * longer time even if the condition is not met. A value of UINT64_MAX indicates + * no maximum. + * + * @param[in] wait_state_hint Hint used by the application to indicate the + * preferred waiting state. The actual waiting state is ultimately decided by + * HSA runtime and may not match the provided hint. A value of + * ::HSA_WAIT_STATE_ACTIVE may improve the latency of response to a signal + * update by avoiding rescheduling overhead. + * + * @return Observed value of the signal, which might not satisfy the specified + * condition. + * +*/ +hsa_signal_value_t HSA_API hsa_signal_wait_scacquire( + hsa_signal_t signal, + hsa_signal_condition_t condition, + hsa_signal_value_t compare_value, + uint64_t timeout_hint, + hsa_wait_state_t wait_state_hint); + +/** + * @copydoc hsa_signal_wait_scacquire + */ +hsa_signal_value_t HSA_API hsa_signal_wait_relaxed( + hsa_signal_t signal, + hsa_signal_condition_t condition, + hsa_signal_value_t compare_value, + uint64_t timeout_hint, + hsa_wait_state_t wait_state_hint); + +/** + * @deprecated Renamed as ::hsa_signal_wait_scacquire. + * + * @copydoc hsa_signal_wait_scacquire + */ +hsa_signal_value_t HSA_API HSA_DEPRECATED hsa_signal_wait_acquire( + hsa_signal_t signal, + hsa_signal_condition_t condition, + hsa_signal_value_t compare_value, + uint64_t timeout_hint, + hsa_wait_state_t wait_state_hint); + +/** + * @brief Group of signals. + */ +typedef struct hsa_signal_group_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_signal_group_t; + +/** + * @brief Create a signal group. + * + * @param[in] num_signals Number of elements in @p signals. Must not be 0. + * + * @param[in] signals List of signals in the group. The list must not contain + * any repeated elements. Must not be NULL. + * + * @param[in] num_consumers Number of elements in @p consumers. Must not be 0. + * + * @param[in] consumers List of agents that might consume (wait on) the signal + * group. The list must not contain repeated elements, and must be a subset of + * the set of agents that are allowed to wait on all the signals in the + * group. If an agent not listed in @p consumers waits on the returned group, + * the behavior is undefined. The memory associated with @p consumers can be + * reused or freed after the function returns. Must not be NULL. + * + * @param[out] signal_group Pointer to newly created signal group. Must not be + * NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p num_signals is 0, @p signals + * is NULL, @p num_consumers is 0, @p consumers is NULL, or @p signal_group is + * NULL. + */ +hsa_status_t HSA_API hsa_signal_group_create( + uint32_t num_signals, + const hsa_signal_t *signals, + uint32_t num_consumers, + const hsa_agent_t *consumers, + hsa_signal_group_t *signal_group); + +/** + * @brief Destroy a signal group previous created by ::hsa_signal_group_create. + * + * @param[in] signal_group Signal group. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL_GROUP @p signal_group is invalid. + */ +hsa_status_t HSA_API hsa_signal_group_destroy( + hsa_signal_group_t signal_group); + +/** + * @brief Wait until the value of at least one of the signals in a signal group + * satisfies its associated condition. + * + * @details The function is guaranteed to return if the value of at least one of + * the signals in the group satisfies its associated condition at some point in + * time during the wait, but the signal value returned to the application may no + * longer satisfy the condition. The application must ensure that signals in the + * group are used in such way that wait wakeup conditions are not invalidated + * before dependent threads have woken up. + * + * When this operation internally loads the value of the passed signal, it uses + * the memory order indicated in the function name. + * + * @param[in] signal_group Signal group. + * + * @param[in] conditions List of conditions. Each condition, and the value at + * the same index in @p compare_values, is used to compare the value of the + * signal at that index in @p signal_group (the signal passed by the application + * to ::hsa_signal_group_create at that particular index). The size of @p + * conditions must not be smaller than the number of signals in @p signal_group; + * any extra elements are ignored. Must not be NULL. + * + * @param[in] compare_values List of comparison values. The size of @p + * compare_values must not be smaller than the number of signals in @p + * signal_group; any extra elements are ignored. Must not be NULL. + * + * @param[in] wait_state_hint Hint used by the application to indicate the + * preferred waiting state. The actual waiting state is decided by the HSA runtime + * and may not match the provided hint. A value of ::HSA_WAIT_STATE_ACTIVE may + * improve the latency of response to a signal update by avoiding rescheduling + * overhead. + * + * @param[out] signal Signal in the group that satisfied the associated + * condition. If several signals satisfied their condition, the function can + * return any of those signals. Must not be NULL. + * + * @param[out] value Observed value for @p signal, which might no longer satisfy + * the specified condition. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL_GROUP @p signal_group is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p conditions is NULL, @p + * compare_values is NULL, @p signal is NULL, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_signal_group_wait_any_scacquire( + hsa_signal_group_t signal_group, + const hsa_signal_condition_t *conditions, + const hsa_signal_value_t *compare_values, + hsa_wait_state_t wait_state_hint, + hsa_signal_t *signal, + hsa_signal_value_t *value); + +/** + * @copydoc hsa_signal_group_wait_any_scacquire + */ +hsa_status_t HSA_API hsa_signal_group_wait_any_relaxed( + hsa_signal_group_t signal_group, + const hsa_signal_condition_t *conditions, + const hsa_signal_value_t *compare_values, + hsa_wait_state_t wait_state_hint, + hsa_signal_t *signal, + hsa_signal_value_t *value); + +/** @} */ + +/** \defgroup memory Memory + * @{ + */ + +/** + * @brief A memory region represents a block of virtual memory with certain + * properties. For example, the HSA runtime represents fine-grained memory in + * the global segment using a region. A region might be associated with more + * than one agent. + */ +typedef struct hsa_region_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_region_t; + +/** @} */ + + +/** \defgroup queue Queues + * @{ + */ + +/** + * @brief Queue type. Intended to be used for dynamic queue protocol + * determination. + */ +typedef enum { + /** + * Queue supports multiple producers. Use of multiproducer queue mechanics is + * required. + */ + HSA_QUEUE_TYPE_MULTI = 0, + /** + * Queue only supports a single producer. In some scenarios, the application + * may want to limit the submission of AQL packets to a single agent. Queues + * that support a single producer may be more efficient than queues supporting + * multiple producers. Use of multiproducer queue mechanics is not supported. + */ + HSA_QUEUE_TYPE_SINGLE = 1, + /** + * Queue supports multiple producers and cooperative dispatches. Cooperative + * dispatches are able to use GWS synchronization. Queues of this type may be + * limited in number. The runtime may return the same queue to serve multiple + * ::hsa_queue_create calls when this type is given. Callers must inspect the + * returned queue to discover queue size. Queues of this type are reference + * counted and require a matching number of ::hsa_queue_destroy calls to + * release. Use of multiproducer queue mechanics is required. See + * ::HSA_AMD_AGENT_INFO_COOPERATIVE_QUEUES to query agent support for this + * type. + */ + HSA_QUEUE_TYPE_COOPERATIVE = 2 +} hsa_queue_type_t; + +/** + * @brief A fixed-size type used to represent ::hsa_queue_type_t constants. + */ +typedef uint32_t hsa_queue_type32_t; + +/** + * @brief Queue features. + */ +typedef enum { + /** + * Queue supports kernel dispatch packets. + */ + HSA_QUEUE_FEATURE_KERNEL_DISPATCH = 1, + + /** + * Queue supports agent dispatch packets. + */ + HSA_QUEUE_FEATURE_AGENT_DISPATCH = 2 +} hsa_queue_feature_t; + +/** + * @brief User mode queue. + * + * @details The queue structure is read-only and allocated by the HSA runtime, + * but agents can directly modify the contents of the buffer pointed by @a + * base_address, or use HSA runtime APIs to access the doorbell signal. + * + */ +typedef struct hsa_queue_s { + /** + * Queue type. + */ + hsa_queue_type32_t type; + + /** + * Queue features mask. This is a bit-field of ::hsa_queue_feature_t + * values. Applications should ignore any unknown set bits. + */ + uint32_t features; + +#ifdef HSA_LARGE_MODEL + void* base_address; +#elif defined HSA_LITTLE_ENDIAN + /** + * Starting address of the HSA runtime-allocated buffer used to store the AQL + * packets. Must be aligned to the size of an AQL packet. + */ + void* base_address; + /** + * Reserved. Must be 0. + */ + uint32_t reserved0; +#else + uint32_t reserved0; + void* base_address; +#endif + + /** + * Signal object used by the application to indicate the ID of a packet that + * is ready to be processed. The HSA runtime manages the doorbell signal. If + * the application tries to replace or destroy this signal, the behavior is + * undefined. + * + * If @a type is ::HSA_QUEUE_TYPE_SINGLE, the doorbell signal value must be + * updated in a monotonically increasing fashion. If @a type is + * ::HSA_QUEUE_TYPE_MULTI, the doorbell signal value can be updated with any + * value. + */ + hsa_signal_t doorbell_signal; + + /** + * Maximum number of packets the queue can hold. Must be a power of 2. + */ + uint32_t size; + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; + /** + * Queue identifier, which is unique over the lifetime of the application. + */ + uint64_t id; + +} hsa_queue_t; + +/** + * @brief Create a user mode queue. + * + * @details The HSA runtime creates the queue structure, the underlying packet + * buffer, the completion signal, and the write and read indexes. The initial + * value of the write and read indexes is 0. The type of every packet in the + * buffer is initialized to ::HSA_PACKET_TYPE_INVALID. + * + * The application should only rely on the error code returned to determine if + * the queue is valid. + * + * @param[in] agent Agent where to create the queue. + * + * @param[in] size Number of packets the queue is expected to + * hold. Must be a power of 2 between 1 and the value of + * ::HSA_AGENT_INFO_QUEUE_MAX_SIZE in @p agent. The size of the newly + * created queue is the maximum of @p size and the value of + * ::HSA_AGENT_INFO_QUEUE_MIN_SIZE in @p agent. + * + * @param[in] type Type of the queue, a bitwise OR of hsa_queue_type_t values. + * If the value of ::HSA_AGENT_INFO_QUEUE_TYPE in @p agent is ::HSA_QUEUE_TYPE_SINGLE, + * then @p type must also be ::HSA_QUEUE_TYPE_SINGLE. + * + * @param[in] callback Callback invoked by the HSA runtime for every + * asynchronous event related to the newly created queue. May be NULL. The HSA + * runtime passes three arguments to the callback: a code identifying the event + * that triggered the invocation, a pointer to the queue where the event + * originated, and the application data. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @param[in] private_segment_size Hint indicating the maximum + * expected private segment usage per work-item, in bytes. There may + * be performance degradation if the application places a kernel + * dispatch packet in the queue and the corresponding private segment + * usage exceeds @p private_segment_size. If the application does not + * want to specify any particular value for this argument, @p + * private_segment_size must be UINT32_MAX. If the queue does not + * support kernel dispatch packets, this argument is ignored. + * + * @param[in] group_segment_size Hint indicating the maximum expected + * group segment usage per work-group, in bytes. There may be + * performance degradation if the application places a kernel dispatch + * packet in the queue and the corresponding group segment usage + * exceeds @p group_segment_size. If the application does not want to + * specify any particular value for this argument, @p + * group_segment_size must be UINT32_MAX. If the queue does not + * support kernel dispatch packets, this argument is ignored. + * + * @param[out] queue Memory location where the HSA runtime stores a pointer to + * the newly created queue. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE_CREATION @p agent does not + * support queues of the given type. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p size is not a power of two, + * @p size is 0, @p type is an invalid queue type, or @p queue is NULL. + * + */ +hsa_status_t HSA_API hsa_queue_create( + hsa_agent_t agent, + uint32_t size, + hsa_queue_type32_t type, + void (*callback)(hsa_status_t status, hsa_queue_t *source, void *data), + void *data, + uint32_t private_segment_size, + uint32_t group_segment_size, + hsa_queue_t **queue); + +/** + * @brief Create a queue for which the application or a kernel is responsible + * for processing the AQL packets. + * + * @details The application can use this function to create queues where AQL + * packets are not parsed by the packet processor associated with an agent, + * but rather by a unit of execution running on that agent (for example, a + * thread in the host application). + * + * The application is responsible for ensuring that all the producers and + * consumers of the resulting queue can access the provided doorbell signal + * and memory region. The application is also responsible for ensuring that the + * unit of execution processing the queue packets supports the indicated + * features (AQL packet types). + * + * When the queue is created, the HSA runtime allocates the packet buffer using + * @p region, and the write and read indexes. The initial value of the write and + * read indexes is 0, and the type of every packet in the buffer is initialized + * to ::HSA_PACKET_TYPE_INVALID. The value of the @e size, @e type, @e features, + * and @e doorbell_signal fields in the returned queue match the values passed + * by the application. + * + * @param[in] region Memory region that the HSA runtime should use to allocate + * the AQL packet buffer and any other queue metadata. + * + * @param[in] size Number of packets the queue is expected to hold. Must be a + * power of 2 greater than 0. + * + * @param[in] type Queue type. + * + * @param[in] features Supported queue features. This is a bit-field of + * ::hsa_queue_feature_t values. + * + * @param[in] doorbell_signal Doorbell signal that the HSA runtime must + * associate with the returned queue. The signal handle must not be 0. + * + * @param[out] queue Memory location where the HSA runtime stores a pointer to + * the newly created queue. The application should not rely on the value + * returned for this argument but only in the status code to determine if the + * queue is valid. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p size is not a power of two, @p + * size is 0, @p type is an invalid queue type, the doorbell signal handle is + * 0, or @p queue is NULL. + * + */ +hsa_status_t HSA_API hsa_soft_queue_create( + hsa_region_t region, + uint32_t size, + hsa_queue_type32_t type, + uint32_t features, + hsa_signal_t doorbell_signal, + hsa_queue_t **queue); + +/** + * @brief Destroy a user mode queue. + * + * @details When a queue is destroyed, the state of the AQL packets that have + * not been yet fully processed (their completion phase has not finished) + * becomes undefined. It is the responsibility of the application to ensure that + * all pending queue operations are finished if their results are required. + * + * The resources allocated by the HSA runtime during queue creation (queue + * structure, ring buffer, doorbell signal) are released. The queue should not + * be accessed after being destroyed. + * + * @param[in] queue Pointer to a queue created using ::hsa_queue_create. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE The queue is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p queue is NULL. + */ +hsa_status_t HSA_API hsa_queue_destroy( + hsa_queue_t *queue); + +/** + * @brief Inactivate a queue. + * + * @details Inactivating the queue aborts any pending executions and prevent any + * new packets from being processed. Any more packets written to the queue once + * it is inactivated will be ignored by the packet processor. + * + * @param[in] queue Pointer to a queue. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE The queue is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p queue is NULL. + */ +hsa_status_t HSA_API hsa_queue_inactivate( + hsa_queue_t *queue); + +/** + * @deprecated Renamed as ::hsa_queue_load_read_index_scacquire. + * + * @copydoc hsa_queue_load_read_index_scacquire + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_load_read_index_acquire( + const hsa_queue_t *queue); + +/** + * @brief Atomically load the read index of a queue. + * + * @param[in] queue Pointer to a queue. + * + * @return Read index of the queue pointed by @p queue. + */ +uint64_t HSA_API hsa_queue_load_read_index_scacquire( + const hsa_queue_t *queue); + +/** + * @copydoc hsa_queue_load_read_index_scacquire + */ +uint64_t HSA_API hsa_queue_load_read_index_relaxed( + const hsa_queue_t *queue); + +/** + * @deprecated Renamed as ::hsa_queue_load_write_index_scacquire. + * + * @copydoc hsa_queue_load_write_index_scacquire + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_load_write_index_acquire( + const hsa_queue_t *queue); + +/** + * @brief Atomically load the write index of a queue. + * + * @param[in] queue Pointer to a queue. + * + * @return Write index of the queue pointed by @p queue. + */ +uint64_t HSA_API hsa_queue_load_write_index_scacquire( + const hsa_queue_t *queue); + +/** + * @copydoc hsa_queue_load_write_index_scacquire + */ +uint64_t HSA_API hsa_queue_load_write_index_relaxed( + const hsa_queue_t *queue); + +/** + * @brief Atomically set the write index of a queue. + * + * @details It is recommended that the application uses this function to update + * the write index when there is a single agent submitting work to the queue + * (the queue type is ::HSA_QUEUE_TYPE_SINGLE). + * + * @param[in] queue Pointer to a queue. + * + * @param[in] value Value to assign to the write index. + * + */ +void HSA_API hsa_queue_store_write_index_relaxed( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_store_write_index_screlease. + * + * @copydoc hsa_queue_store_write_index_screlease + */ +void HSA_API HSA_DEPRECATED hsa_queue_store_write_index_release( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @copydoc hsa_queue_store_write_index_relaxed + */ +void HSA_API hsa_queue_store_write_index_screlease( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_cas_write_index_scacq_screl. + * + * @copydoc hsa_queue_cas_write_index_scacq_screl + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_cas_write_index_acq_rel( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @brief Atomically set the write index of a queue if the observed value is + * equal to the expected value. The application can inspect the returned value + * to determine if the replacement was done. + * + * @param[in] queue Pointer to a queue. + * + * @param[in] expected Expected value. + * + * @param[in] value Value to assign to the write index if @p expected matches + * the observed write index. Must be greater than @p expected. + * + * @return Previous value of the write index. + */ +uint64_t HSA_API hsa_queue_cas_write_index_scacq_screl( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_cas_write_index_scacquire. + * + * @copydoc hsa_queue_cas_write_index_scacquire + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_cas_write_index_acquire( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @copydoc hsa_queue_cas_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_cas_write_index_scacquire( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @copydoc hsa_queue_cas_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_cas_write_index_relaxed( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_cas_write_index_screlease. + * + * @copydoc hsa_queue_cas_write_index_screlease + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_cas_write_index_release( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @copydoc hsa_queue_cas_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_cas_write_index_screlease( + const hsa_queue_t *queue, + uint64_t expected, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_add_write_index_scacq_screl. + * + * @copydoc hsa_queue_add_write_index_scacq_screl + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_add_write_index_acq_rel( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @brief Atomically increment the write index of a queue by an offset. + * + * @param[in] queue Pointer to a queue. + * + * @param[in] value Value to add to the write index. + * + * @return Previous value of the write index. + */ +uint64_t HSA_API hsa_queue_add_write_index_scacq_screl( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_add_write_index_scacquire. + * + * @copydoc hsa_queue_add_write_index_scacquire + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_add_write_index_acquire( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @copydoc hsa_queue_add_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_add_write_index_scacquire( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @copydoc hsa_queue_add_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_add_write_index_relaxed( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_add_write_index_screlease. + * + * @copydoc hsa_queue_add_write_index_screlease + */ +uint64_t HSA_API HSA_DEPRECATED hsa_queue_add_write_index_release( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @copydoc hsa_queue_add_write_index_scacq_screl + */ +uint64_t HSA_API hsa_queue_add_write_index_screlease( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @brief Atomically set the read index of a queue. + * + * @details Modifications of the read index are not allowed and result in + * undefined behavior if the queue is associated with an agent for which + * only the corresponding packet processor is permitted to update the read + * index. + * + * @param[in] queue Pointer to a queue. + * + * @param[in] value Value to assign to the read index. + * + */ +void HSA_API hsa_queue_store_read_index_relaxed( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @deprecated Renamed as ::hsa_queue_store_read_index_screlease. + * + * @copydoc hsa_queue_store_read_index_screlease + */ +void HSA_API HSA_DEPRECATED hsa_queue_store_read_index_release( + const hsa_queue_t *queue, + uint64_t value); + +/** + * @copydoc hsa_queue_store_read_index_relaxed + */ +void HSA_API hsa_queue_store_read_index_screlease( + const hsa_queue_t *queue, + uint64_t value); +/** @} */ + + +/** \defgroup aql Architected Queuing Language + * @{ + */ + +/** + * @brief Packet type. + */ +typedef enum { + /** + * Vendor-specific packet. + */ + HSA_PACKET_TYPE_VENDOR_SPECIFIC = 0, + /** + * The packet has been processed in the past, but has not been reassigned to + * the packet processor. A packet processor must not process a packet of this + * type. All queues support this packet type. + */ + HSA_PACKET_TYPE_INVALID = 1, + /** + * Packet used by agents for dispatching jobs to kernel agents. Not all + * queues support packets of this type (see ::hsa_queue_feature_t). + */ + HSA_PACKET_TYPE_KERNEL_DISPATCH = 2, + /** + * Packet used by agents to delay processing of subsequent packets, and to + * express complex dependencies between multiple packets. All queues support + * this packet type. + */ + HSA_PACKET_TYPE_BARRIER_AND = 3, + /** + * Packet used by agents for dispatching jobs to agents. Not all + * queues support packets of this type (see ::hsa_queue_feature_t). + */ + HSA_PACKET_TYPE_AGENT_DISPATCH = 4, + /** + * Packet used by agents to delay processing of subsequent packets, and to + * express complex dependencies between multiple packets. All queues support + * this packet type. + */ + HSA_PACKET_TYPE_BARRIER_OR = 5 +} hsa_packet_type_t; + +/** + * @brief Scope of the memory fence operation associated with a packet. + */ +typedef enum { + /** + * No scope (no fence is applied). The packet relies on external fences to + * ensure visibility of memory updates. + */ + HSA_FENCE_SCOPE_NONE = 0, + /** + * The fence is applied with agent scope for the global segment. + */ + HSA_FENCE_SCOPE_AGENT = 1, + /** + * The fence is applied across both agent and system scope for the global + * segment. + */ + HSA_FENCE_SCOPE_SYSTEM = 2 +} hsa_fence_scope_t; + +/** + * @brief Sub-fields of the @a header field that is present in any AQL + * packet. The offset (with respect to the address of @a header) of a sub-field + * is identical to its enumeration constant. The width of each sub-field is + * determined by the corresponding value in ::hsa_packet_header_width_t. The + * offset and the width are expressed in bits. + */ + typedef enum { + /** + * Packet type. The value of this sub-field must be one of + * ::hsa_packet_type_t. If the type is ::HSA_PACKET_TYPE_VENDOR_SPECIFIC, the + * packet layout is vendor-specific. + */ + HSA_PACKET_HEADER_TYPE = 0, + /** + * Barrier bit. If the barrier bit is set, the processing of the current + * packet only launches when all preceding packets (within the same queue) are + * complete. + */ + HSA_PACKET_HEADER_BARRIER = 8, + /** + * Acquire fence scope. The value of this sub-field determines the scope and + * type of the memory fence operation applied before the packet enters the + * active phase. An acquire fence ensures that any subsequent global segment + * or image loads by any unit of execution that belongs to a dispatch that has + * not yet entered the active phase on any queue of the same kernel agent, + * sees any data previously released at the scopes specified by the acquire + * fence. The value of this sub-field must be one of ::hsa_fence_scope_t. + */ + HSA_PACKET_HEADER_SCACQUIRE_FENCE_SCOPE = 9, + /** + * @deprecated Renamed as ::HSA_PACKET_HEADER_SCACQUIRE_FENCE_SCOPE. + */ + HSA_PACKET_HEADER_ACQUIRE_FENCE_SCOPE = 9, + /** + * Release fence scope, The value of this sub-field determines the scope and + * type of the memory fence operation applied after kernel completion but + * before the packet is completed. A release fence makes any global segment or + * image data that was stored by any unit of execution that belonged to a + * dispatch that has completed the active phase on any queue of the same + * kernel agent visible in all the scopes specified by the release fence. The + * value of this sub-field must be one of ::hsa_fence_scope_t. + */ + HSA_PACKET_HEADER_SCRELEASE_FENCE_SCOPE = 11, + /** + * @deprecated Renamed as ::HSA_PACKET_HEADER_SCRELEASE_FENCE_SCOPE. + */ + HSA_PACKET_HEADER_RELEASE_FENCE_SCOPE = 11 + } hsa_packet_header_t; + +/** + * @brief Width (in bits) of the sub-fields in ::hsa_packet_header_t. + */ + typedef enum { + HSA_PACKET_HEADER_WIDTH_TYPE = 8, + HSA_PACKET_HEADER_WIDTH_BARRIER = 1, + HSA_PACKET_HEADER_WIDTH_SCACQUIRE_FENCE_SCOPE = 2, + /** + * @deprecated Use HSA_PACKET_HEADER_WIDTH_SCACQUIRE_FENCE_SCOPE. + */ + HSA_PACKET_HEADER_WIDTH_ACQUIRE_FENCE_SCOPE = 2, + HSA_PACKET_HEADER_WIDTH_SCRELEASE_FENCE_SCOPE = 2, + /** + * @deprecated Use HSA_PACKET_HEADER_WIDTH_SCRELEASE_FENCE_SCOPE. + */ + HSA_PACKET_HEADER_WIDTH_RELEASE_FENCE_SCOPE = 2 + } hsa_packet_header_width_t; + +/** + * @brief Sub-fields of the kernel dispatch packet @a setup field. The offset + * (with respect to the address of @a setup) of a sub-field is identical to its + * enumeration constant. The width of each sub-field is determined by the + * corresponding value in ::hsa_kernel_dispatch_packet_setup_width_t. The + * offset and the width are expressed in bits. + */ + typedef enum { + /** + * Number of dimensions of the grid. Valid values are 1, 2, or 3. + * + */ + HSA_KERNEL_DISPATCH_PACKET_SETUP_DIMENSIONS = 0 + } hsa_kernel_dispatch_packet_setup_t; + +/** + * @brief Width (in bits) of the sub-fields in + * ::hsa_kernel_dispatch_packet_setup_t. + */ + typedef enum { + HSA_KERNEL_DISPATCH_PACKET_SETUP_WIDTH_DIMENSIONS = 2 + } hsa_kernel_dispatch_packet_setup_width_t; + +/** + * @brief AQL kernel dispatch packet + */ +typedef struct hsa_kernel_dispatch_packet_s { + /** + * Packet header. Used to configure multiple packet parameters such as the + * packet type. The parameters are described by ::hsa_packet_header_t. + */ + uint16_t header; + + /** + * Dispatch setup parameters. Used to configure kernel dispatch parameters + * such as the number of dimensions in the grid. The parameters are described + * by ::hsa_kernel_dispatch_packet_setup_t. + */ + uint16_t setup; + + /** + * X dimension of work-group, in work-items. Must be greater than 0. + */ + uint16_t workgroup_size_x; + + /** + * Y dimension of work-group, in work-items. Must be greater than + * 0. If the grid has 1 dimension, the only valid value is 1. + */ + uint16_t workgroup_size_y; + + /** + * Z dimension of work-group, in work-items. Must be greater than + * 0. If the grid has 1 or 2 dimensions, the only valid value is 1. + */ + uint16_t workgroup_size_z; + + /** + * Reserved. Must be 0. + */ + uint16_t reserved0; + + /** + * X dimension of grid, in work-items. Must be greater than 0. Must + * not be smaller than @a workgroup_size_x. + */ + uint32_t grid_size_x; + + /** + * Y dimension of grid, in work-items. Must be greater than 0. If the grid has + * 1 dimension, the only valid value is 1. Must not be smaller than @a + * workgroup_size_y. + */ + uint32_t grid_size_y; + + /** + * Z dimension of grid, in work-items. Must be greater than 0. If the grid has + * 1 or 2 dimensions, the only valid value is 1. Must not be smaller than @a + * workgroup_size_z. + */ + uint32_t grid_size_z; + + /** + * Size in bytes of private memory allocation request (per work-item). + */ + uint32_t private_segment_size; + + /** + * Size in bytes of group memory allocation request (per work-group). Must not + * be less than the sum of the group memory used by the kernel (and the + * functions it calls directly or indirectly) and the dynamically allocated + * group segment variables. + */ + uint32_t group_segment_size; + + /** + * Opaque handle to a code object that includes an implementation-defined + * executable code for the kernel. + */ + uint64_t kernel_object; + +#ifdef HSA_LARGE_MODEL + void* kernarg_address; +#elif defined HSA_LITTLE_ENDIAN + /** + * Pointer to a buffer containing the kernel arguments. May be NULL. + * + * The buffer must be allocated using ::hsa_memory_allocate, and must not be + * modified once the kernel dispatch packet is enqueued until the dispatch has + * completed execution. + */ + void* kernarg_address; + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; +#else + uint32_t reserved1; + void* kernarg_address; +#endif + + /** + * Reserved. Must be 0. + */ + uint64_t reserved2; + + /** + * Signal used to indicate completion of the job. The application can use the + * special signal handle 0 to indicate that no signal is used. + */ + hsa_signal_t completion_signal; + +} hsa_kernel_dispatch_packet_t; + +/** + * @brief Agent dispatch packet. + */ +typedef struct hsa_agent_dispatch_packet_s { + /** + * Packet header. Used to configure multiple packet parameters such as the + * packet type. The parameters are described by ::hsa_packet_header_t. + */ + uint16_t header; + + /** + * Application-defined function to be performed by the destination agent. + */ + uint16_t type; + + /** + * Reserved. Must be 0. + */ + uint32_t reserved0; + +#ifdef HSA_LARGE_MODEL + void* return_address; +#elif defined HSA_LITTLE_ENDIAN + /** + * Address where to store the function return values, if any. + */ + void* return_address; + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; +#else + uint32_t reserved1; + void* return_address; +#endif + + /** + * Function arguments. + */ + uint64_t arg[4]; + + /** + * Reserved. Must be 0. + */ + uint64_t reserved2; + + /** + * Signal used to indicate completion of the job. The application can use the + * special signal handle 0 to indicate that no signal is used. + */ + hsa_signal_t completion_signal; + +} hsa_agent_dispatch_packet_t; + +/** + * @brief Barrier-AND packet. + */ +typedef struct hsa_barrier_and_packet_s { + /** + * Packet header. Used to configure multiple packet parameters such as the + * packet type. The parameters are described by ::hsa_packet_header_t. + */ + uint16_t header; + + /** + * Reserved. Must be 0. + */ + uint16_t reserved0; + + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; + + /** + * Array of dependent signal objects. Signals with a handle value of 0 are + * allowed and are interpreted by the packet processor as satisfied + * dependencies. + */ + hsa_signal_t dep_signal[5]; + + /** + * Reserved. Must be 0. + */ + uint64_t reserved2; + + /** + * Signal used to indicate completion of the job. The application can use the + * special signal handle 0 to indicate that no signal is used. + */ + hsa_signal_t completion_signal; + +} hsa_barrier_and_packet_t; + +/** + * @brief Barrier-OR packet. + */ +typedef struct hsa_barrier_or_packet_s { + /** + * Packet header. Used to configure multiple packet parameters such as the + * packet type. The parameters are described by ::hsa_packet_header_t. + */ + uint16_t header; + + /** + * Reserved. Must be 0. + */ + uint16_t reserved0; + + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; + + /** + * Array of dependent signal objects. Signals with a handle value of 0 are + * allowed and are interpreted by the packet processor as dependencies not + * satisfied. + */ + hsa_signal_t dep_signal[5]; + + /** + * Reserved. Must be 0. + */ + uint64_t reserved2; + + /** + * Signal used to indicate completion of the job. The application can use the + * special signal handle 0 to indicate that no signal is used. + */ + hsa_signal_t completion_signal; + +} hsa_barrier_or_packet_t; + +/** @} */ + +/** \addtogroup memory Memory + * @{ + */ + +/** + * @brief Memory segments associated with a region. + */ +typedef enum { + /** + * Global segment. Used to hold data that is shared by all agents. + */ + HSA_REGION_SEGMENT_GLOBAL = 0, + /** + * Read-only segment. Used to hold data that remains constant during the + * execution of a kernel. + */ + HSA_REGION_SEGMENT_READONLY = 1, + /** + * Private segment. Used to hold data that is local to a single work-item. + */ + HSA_REGION_SEGMENT_PRIVATE = 2, + /** + * Group segment. Used to hold data that is shared by the work-items of a + * work-group. + */ + HSA_REGION_SEGMENT_GROUP = 3, + /** + * Kernarg segment. Used to store kernel arguments. + */ + HSA_REGION_SEGMENT_KERNARG = 4 +} hsa_region_segment_t; + +/** + * @brief Global region flags. + */ +typedef enum { + /** + * The application can use memory in the region to store kernel arguments, and + * provide the values for the kernarg segment of a kernel dispatch. If this + * flag is set, then ::HSA_REGION_GLOBAL_FLAG_FINE_GRAINED must be set. + */ + HSA_REGION_GLOBAL_FLAG_KERNARG = 1, + /** + * Updates to memory in this region are immediately visible to all the + * agents under the terms of the HSA memory model. If this + * flag is set, then ::HSA_REGION_GLOBAL_FLAG_COARSE_GRAINED must not be set. + */ + HSA_REGION_GLOBAL_FLAG_FINE_GRAINED = 2, + /** + * Updates to memory in this region can be performed by a single agent at + * a time. If a different agent in the system is allowed to access the + * region, the application must explicitely invoke ::hsa_memory_assign_agent + * in order to transfer ownership to that agent for a particular buffer. + */ + HSA_REGION_GLOBAL_FLAG_COARSE_GRAINED = 4, + + /** + * Updates to memory in this region have extended scope, where the device-scope atomics + * to this memory type act as system-scope with respect to all variables located in + * memory regions of this type. + * Note: On non-compliant systems, the application may still be responsible for performing + * device-specific actions necessary to achieve system-scope coherence. + */ + HSA_REGION_GLOBAL_FLAG_EXTENDED_SCOPE_FINE_GRAINED = 8 +} hsa_region_global_flag_t; + +/** + * @brief Attributes of a memory region. + */ +typedef enum { + /** + * Segment where memory in the region can be used. The type of this + * attribute is ::hsa_region_segment_t. + */ + HSA_REGION_INFO_SEGMENT = 0, + /** + * Flag mask. The value of this attribute is undefined if the value of + * ::HSA_REGION_INFO_SEGMENT is not ::HSA_REGION_SEGMENT_GLOBAL. The type of + * this attribute is uint32_t, a bit-field of ::hsa_region_global_flag_t + * values. + */ + HSA_REGION_INFO_GLOBAL_FLAGS = 1, + /** + * Size of this region, in bytes. The type of this attribute is size_t. + */ + HSA_REGION_INFO_SIZE = 2, + /** + * Maximum allocation size in this region, in bytes. Must not exceed the value + * of ::HSA_REGION_INFO_SIZE. The type of this attribute is size_t. + * + * If the region is in the global or readonly segments, this is the maximum + * size that the application can pass to ::hsa_memory_allocate. + * + * If the region is in the group segment, this is the maximum size (per + * work-group) that can be requested for a given kernel dispatch. If the + * region is in the private segment, this is the maximum size (per work-item) + * that can be requested for a specific kernel dispatch, and must be at least + * 256 bytes. + */ + HSA_REGION_INFO_ALLOC_MAX_SIZE = 4, + /** + * Maximum size (per work-group) of private memory that can be requested for a + * specific kernel dispatch. Must be at least 65536 bytes. The type of this + * attribute is uint32_t. The value of this attribute is undefined if the + * region is not in the private segment. + */ + HSA_REGION_INFO_ALLOC_MAX_PRIVATE_WORKGROUP_SIZE = 8, + /** + * Indicates whether memory in this region can be allocated using + * ::hsa_memory_allocate. The type of this attribute is bool. + * + * The value of this flag is always false for regions in the group and private + * segments. + */ + HSA_REGION_INFO_RUNTIME_ALLOC_ALLOWED = 5, + /** + * Allocation granularity of buffers allocated by ::hsa_memory_allocate in + * this region. The size of a buffer allocated in this region is a multiple of + * the value of this attribute. The value of this attribute is only defined if + * ::HSA_REGION_INFO_RUNTIME_ALLOC_ALLOWED is true for this region. The type + * of this attribute is size_t. + */ + HSA_REGION_INFO_RUNTIME_ALLOC_GRANULE = 6, + /** + * Alignment of buffers allocated by ::hsa_memory_allocate in this region. The + * value of this attribute is only defined if + * ::HSA_REGION_INFO_RUNTIME_ALLOC_ALLOWED is true for this region, and must be + * a power of 2. The type of this attribute is size_t. + */ + HSA_REGION_INFO_RUNTIME_ALLOC_ALIGNMENT = 7 +} hsa_region_info_t; + +/** + * @brief Get the current value of an attribute of a region. + * + * @param[in] region A valid region. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to a application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_REGION The region is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * region attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_region_get_info( + hsa_region_t region, + hsa_region_info_t attribute, + void* value); + +/** + * @brief Iterate over the memory regions associated with a given agent, and + * invoke an application-defined callback on every iteration. + * + * @param[in] agent A valid agent. + * + * @param[in] callback Callback to be invoked once per region that is + * accessible from the agent. The HSA runtime passes two arguments to the + * callback, the region and the application data. If @p callback returns a + * status other than ::HSA_STATUS_SUCCESS for a particular iteration, the + * traversal stops and ::hsa_agent_iterate_regions returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_agent_iterate_regions( + hsa_agent_t agent, + hsa_status_t (*callback)(hsa_region_t region, void* data), + void* data); + +/** + * @brief Allocate a block of memory in a given region. + * + * @param[in] region Region where to allocate memory from. The region must have + * the ::HSA_REGION_INFO_RUNTIME_ALLOC_ALLOWED flag set. + * + * @param[in] size Allocation size, in bytes. Must not be zero. This value is + * rounded up to the nearest multiple of ::HSA_REGION_INFO_RUNTIME_ALLOC_GRANULE + * in @p region. + * + * @param[out] ptr Pointer to the location where to store the base address of + * the allocated block. The returned base address is aligned to the value of + * ::HSA_REGION_INFO_RUNTIME_ALLOC_ALIGNMENT in @p region. If the allocation + * fails, the returned value is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_REGION The region is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION The host is not allowed to + * allocate memory in @p region, or @p size is greater than the value of + * HSA_REGION_INFO_ALLOC_MAX_SIZE in @p region. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr is NULL, or @p size is 0. + */ +hsa_status_t HSA_API hsa_memory_allocate(hsa_region_t region, + size_t size, + void** ptr); + +/** + * @brief Deallocate a block of memory previously allocated using + * ::hsa_memory_allocate. + * + * @param[in] ptr Pointer to a memory block. If @p ptr does not match a value + * previously returned by ::hsa_memory_allocate, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + */ +hsa_status_t HSA_API hsa_memory_free(void* ptr); + +/** + * @brief Copy a block of memory from the location pointed to by @p src to the + * memory block pointed to by @p dst. + * + * @param[out] dst Buffer where the content is to be copied. If @p dst is in + * coarse-grained memory, the copied data is only visible to the agent currently + * assigned (::hsa_memory_assign_agent) to @p dst. + * + * @param[in] src A valid pointer to the source of data to be copied. The source + * buffer must not overlap with the destination buffer. If the source buffer is + * in coarse-grained memory then it must be assigned to an agent, from which the + * data will be retrieved. + * + * @param[in] size Number of bytes to copy. If @p size is 0, no copy is + * performed and the function returns success. Copying a number of bytes larger + * than the size of the buffers pointed by @p dst or @p src results in undefined + * behavior. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT The source or destination + * pointers are NULL. + */ +hsa_status_t HSA_API hsa_memory_copy( + void *dst, + const void *src, + size_t size); + +/** + * @brief Change the ownership of a global, coarse-grained buffer. + * + * @details The contents of a coarse-grained buffer are visible to an agent + * only after ownership has been explicitely transferred to that agent. Once the + * operation completes, the previous owner cannot longer access the data in the + * buffer. + * + * An implementation of the HSA runtime is allowed, but not required, to change + * the physical location of the buffer when ownership is transferred to a + * different agent. In general the application must not assume this + * behavior. The virtual location (address) of the passed buffer is never + * modified. + * + * @param[in] ptr Base address of a global buffer. The pointer must match an + * address previously returned by ::hsa_memory_allocate. The size of the buffer + * affected by the ownership change is identical to the size of that previous + * allocation. If @p ptr points to a fine-grained global buffer, no operation is + * performed and the function returns success. If @p ptr does not point to + * global memory, the behavior is undefined. + * + * @param[in] agent Agent that becomes the owner of the buffer. The + * application is responsible for ensuring that @p agent has access to the + * region that contains the buffer. It is allowed to change ownership to an + * agent that is already the owner of the buffer, with the same or different + * access permissions. + * + * @param[in] access Access permissions requested for the new owner. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr is NULL, or @p access is + * not a valid access value. + */ +hsa_status_t HSA_API hsa_memory_assign_agent( + void *ptr, + hsa_agent_t agent, + hsa_access_permission_t access); + +/** + * + * @brief Register a global, fine-grained buffer. + * + * @details Registering a buffer serves as an indication to the HSA runtime that + * the memory might be accessed from a kernel agent other than the + * host. Registration is a performance hint that allows the HSA runtime + * implementation to know which buffers will be accessed by some of the kernel + * agents ahead of time. + * + * Registration is only recommended for buffers in the global segment that have + * not been allocated using the HSA allocator (::hsa_memory_allocate), but an OS + * allocator instead. Registering an OS-allocated buffer in the base profile is + * equivalent to a no-op. + * + * Registrations should not overlap. + * + * @param[in] ptr A buffer in global, fine-grained memory. If a NULL pointer is + * passed, no operation is performed. If the buffer has been allocated using + * ::hsa_memory_allocate, or has already been registered, no operation is + * performed. + * + * @param[in] size Requested registration size in bytes. A size of 0 is + * only allowed if @p ptr is NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p size is 0 but @p ptr + * is not NULL. + */ +hsa_status_t HSA_API hsa_memory_register( + void *ptr, + size_t size); + +/** + * + * @brief Deregister memory previously registered using ::hsa_memory_register. + * + * @details If the memory interval being deregistered does not match a previous + * registration (start and end addresses), the behavior is undefined. + * + * @param[in] ptr A pointer to the base of the buffer to be deregistered. If + * a NULL pointer is passed, no operation is performed. + * + * @param[in] size Size of the buffer to be deregistered. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + */ +hsa_status_t HSA_API hsa_memory_deregister( + void *ptr, + size_t size); + +/** @} */ + + +/** \defgroup instruction-set-architecture Instruction Set Architecture. + * @{ + */ + +/** + * @brief Instruction set architecture. + */ +typedef struct hsa_isa_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_isa_t; + +/** + * @brief Retrieve a reference to an instruction set architecture handle out of + * a symbolic name. + * + * @param[in] name Vendor-specific name associated with a a particular + * instruction set architecture. @p name must start with the vendor name and a + * colon (for example, "AMD:"). The rest of the name is vendor-specific. Must be + * a NUL-terminated string. + * + * @param[out] isa Memory location where the HSA runtime stores the ISA handle + * corresponding to the given name. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA_NAME The given name does not + * correspond to any instruction set architecture. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p name is NULL, or @p isa is + * NULL. + */ +hsa_status_t HSA_API hsa_isa_from_name( + const char *name, + hsa_isa_t *isa); + +/** + * @brief Iterate over the instruction sets supported by the given agent, and + * invoke an application-defined callback on every iteration. The iterator is + * deterministic: if an agent supports several instruction set architectures, + * they are traversed in the same order in every invocation of this function. + * + * @param[in] agent A valid agent. + * + * @param[in] callback Callback to be invoked once per instruction set + * architecture. The HSA runtime passes two arguments to the callback: the + * ISA and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * that status value is returned. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_agent_iterate_isas( + hsa_agent_t agent, + hsa_status_t (*callback)(hsa_isa_t isa, void *data), + void *data); + +/** + * @brief Instruction set architecture attributes. + */ +typedef enum { + /** + * The length of the ISA name in bytes, not including the NUL terminator. The + * type of this attribute is uint32_t. + */ + HSA_ISA_INFO_NAME_LENGTH = 0, + /** + * Human-readable description. The type of this attribute is character array + * with the length equal to the value of ::HSA_ISA_INFO_NAME_LENGTH attribute. + */ + HSA_ISA_INFO_NAME = 1, + /** + * @deprecated + * + * Number of call conventions supported by the instruction set architecture. + * Must be greater than zero. The type of this attribute is uint32_t. + */ + HSA_ISA_INFO_CALL_CONVENTION_COUNT = 2, + /** + * @deprecated + * + * Number of work-items in a wavefront for a given call convention. Must be a + * power of 2 in the range [1,256]. The type of this attribute is uint32_t. + */ + HSA_ISA_INFO_CALL_CONVENTION_INFO_WAVEFRONT_SIZE = 3, + /** + * @deprecated + * + * Number of wavefronts per compute unit for a given call convention. In + * practice, other factors (for example, the amount of group memory used by a + * work-group) may further limit the number of wavefronts per compute + * unit. The type of this attribute is uint32_t. + */ + HSA_ISA_INFO_CALL_CONVENTION_INFO_WAVEFRONTS_PER_COMPUTE_UNIT = 4, + /** + * Machine models supported by the instruction set architecture. The type of + * this attribute is a bool[2]. If the ISA supports the small machine model, + * the element at index ::HSA_MACHINE_MODEL_SMALL is true. If the ISA supports + * the large model, the element at index ::HSA_MACHINE_MODEL_LARGE is true. + */ + HSA_ISA_INFO_MACHINE_MODELS = 5, + /** + * Profiles supported by the instruction set architecture. The type of this + * attribute is a bool[2]. If the ISA supports the base profile, the element + * at index ::HSA_PROFILE_BASE is true. If the ISA supports the full profile, + * the element at index ::HSA_PROFILE_FULL is true. + */ + HSA_ISA_INFO_PROFILES = 6, + /** + * Default floating-point rounding modes supported by the instruction set + * architecture. The type of this attribute is a bool[3]. The value at a given + * index is true if the corresponding rounding mode in + * ::hsa_default_float_rounding_mode_t is supported. At least one default mode + * has to be supported. + * + * If the default mode is supported, then + * ::HSA_ISA_INFO_BASE_PROFILE_DEFAULT_FLOAT_ROUNDING_MODES must report that + * both the zero and the near roundings modes are supported. + */ + HSA_ISA_INFO_DEFAULT_FLOAT_ROUNDING_MODES = 7, + /** + * Default floating-point rounding modes supported by the instruction set + * architecture in the Base profile. The type of this attribute is a + * bool[3]. The value at a given index is true if the corresponding rounding + * mode in ::hsa_default_float_rounding_mode_t is supported. The value at + * index HSA_DEFAULT_FLOAT_ROUNDING_MODE_DEFAULT must be false. At least one + * of the values at indexes ::HSA_DEFAULT_FLOAT_ROUNDING_MODE_ZERO or + * HSA_DEFAULT_FLOAT_ROUNDING_MODE_NEAR must be true. + */ + HSA_ISA_INFO_BASE_PROFILE_DEFAULT_FLOAT_ROUNDING_MODES = 8, + /** + * Flag indicating that the f16 HSAIL operation is at least as fast as the + * f32 operation in the instruction set architecture. The type of this + * attribute is bool. + */ + HSA_ISA_INFO_FAST_F16_OPERATION = 9, + /** + * Maximum number of work-items of each dimension of a work-group. Each + * maximum must be greater than 0. No maximum can exceed the value of + * ::HSA_ISA_INFO_WORKGROUP_MAX_SIZE. The type of this attribute is + * uint16_t[3]. + */ + HSA_ISA_INFO_WORKGROUP_MAX_DIM = 12, + /** + * Maximum total number of work-items in a work-group. The type + * of this attribute is uint32_t. + */ + HSA_ISA_INFO_WORKGROUP_MAX_SIZE = 13, + /** + * Maximum number of work-items of each dimension of a grid. Each maximum must + * be greater than 0, and must not be smaller than the corresponding value in + * ::HSA_ISA_INFO_WORKGROUP_MAX_DIM. No maximum can exceed the value of + * ::HSA_ISA_INFO_GRID_MAX_SIZE. The type of this attribute is + * ::hsa_dim3_t. + */ + HSA_ISA_INFO_GRID_MAX_DIM = 14, + /** + * Maximum total number of work-items in a grid. The type of this + * attribute is uint64_t. + */ + HSA_ISA_INFO_GRID_MAX_SIZE = 16, + /** + * Maximum number of fbarriers per work-group. Must be at least 32. The + * type of this attribute is uint32_t. + */ + HSA_ISA_INFO_FBARRIER_MAX_SIZE = 17 +} hsa_isa_info_t; + +/** + * @deprecated The concept of call convention has been deprecated. If the + * application wants to query the value of an attribute for a given instruction + * set architecture, use ::hsa_isa_get_info_alt instead. If the application + * wants to query an attribute that is specific to a given combination of ISA + * and wavefront, use ::hsa_wavefront_get_info. + * + * @brief Get the current value of an attribute for a given instruction set + * architecture (ISA). + * + * @param[in] isa A valid instruction set architecture. + * + * @param[in] attribute Attribute to query. + * + * @param[in] index Call convention index. Used only for call convention + * attributes, otherwise ignored. Must have a value between 0 (inclusive) and + * the value of the attribute ::HSA_ISA_INFO_CALL_CONVENTION_COUNT (not + * inclusive) in @p isa. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA The instruction set architecture is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_INDEX The index is out of range. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * instruction set architecture attribute, or @p value is + * NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_isa_get_info( + hsa_isa_t isa, + hsa_isa_info_t attribute, + uint32_t index, + void *value); + +/** + * @brief Get the current value of an attribute for a given instruction set + * architecture (ISA). + * + * @param[in] isa A valid instruction set architecture. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA The instruction set architecture is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * instruction set architecture attribute, or @p value is + * NULL. + */ +hsa_status_t HSA_API hsa_isa_get_info_alt( + hsa_isa_t isa, + hsa_isa_info_t attribute, + void *value); + +/** + * @brief Retrieve the exception policy support for a given combination of + * instruction set architecture and profile. + * + * @param[in] isa A valid instruction set architecture. + * + * @param[in] profile Profile. + * + * @param[out] mask Pointer to a memory location where the HSA runtime stores a + * mask of ::hsa_exception_policy_t values. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA The instruction set architecture is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p profile is not a valid + * profile, or @p mask is NULL. + */ +hsa_status_t HSA_API hsa_isa_get_exception_policies( + hsa_isa_t isa, + hsa_profile_t profile, + uint16_t *mask); + +/** + * @brief Floating-point types. + */ +typedef enum { + /** + * 16-bit floating-point type. + */ + HSA_FP_TYPE_16 = 1, + /** + * 32-bit floating-point type. + */ + HSA_FP_TYPE_32 = 2, + /** + * 64-bit floating-point type. + */ + HSA_FP_TYPE_64 = 4 +} hsa_fp_type_t; + +/** + * @brief Flush to zero modes. + */ +typedef enum { + /** + * Flush to zero. + */ + HSA_FLUSH_MODE_FTZ = 1, + /** + * Do not flush to zero. + */ + HSA_FLUSH_MODE_NON_FTZ = 2 +} hsa_flush_mode_t; + +/** + * @brief Round methods. + */ +typedef enum { + /** + * Single round method. + */ + HSA_ROUND_METHOD_SINGLE = 1, + /** + * Double round method. + */ + HSA_ROUND_METHOD_DOUBLE = 2 +} hsa_round_method_t; + +/** + * @brief Retrieve the round method (single or double) used to implement the + * floating-point multiply add instruction (mad) for a given combination of + * instruction set architecture, floating-point type, and flush to zero + * modifier. + * + * @param[in] isa Instruction set architecture. + * + * @param[in] fp_type Floating-point type. + * + * @param[in] flush_mode Flush to zero modifier. + * + * @param[out] round_method Pointer to a memory location where the HSA + * runtime stores the round method used by the implementation. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA The instruction set architecture is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p fp_type is not a valid + * floating-point type, or @p flush_mode is not a valid flush to zero modifier, + * or @p round_method is NULL. + */ +hsa_status_t HSA_API hsa_isa_get_round_method( + hsa_isa_t isa, + hsa_fp_type_t fp_type, + hsa_flush_mode_t flush_mode, + hsa_round_method_t *round_method); + +/** + * @brief Wavefront handle + */ +typedef struct hsa_wavefront_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_wavefront_t; + +/** + * @brief Wavefront attributes. + */ +typedef enum { + /** + * Number of work-items in the wavefront. Must be a power of 2 in the range + * [1,256]. The type of this attribute is uint32_t. + */ + HSA_WAVEFRONT_INFO_SIZE = 0 +} hsa_wavefront_info_t; + +/** + * @brief Get the current value of a wavefront attribute. + * + * @param[in] wavefront A wavefront. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_WAVEFRONT The wavefront is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * wavefront attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_wavefront_get_info( + hsa_wavefront_t wavefront, + hsa_wavefront_info_t attribute, + void *value); + +/** + * @brief Iterate over the different wavefronts supported by an instruction set + * architecture, and invoke an application-defined callback on every iteration. + * + * @param[in] isa Instruction set architecture. + * + * @param[in] callback Callback to be invoked once per wavefront that is + * supported by the agent. The HSA runtime passes two arguments to the callback: + * the wavefront handle and the application data. If @p callback returns a + * status other than ::HSA_STATUS_SUCCESS for a particular iteration, the + * traversal stops and that value is returned. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA The instruction set architecture is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_isa_iterate_wavefronts( + hsa_isa_t isa, + hsa_status_t (*callback)(hsa_wavefront_t wavefront, void *data), + void *data); + +/** + * @deprecated Use ::hsa_agent_iterate_isas to query which instructions set + * architectures are supported by a given agent. + * + * @brief Check if the instruction set architecture of a code object can be + * executed on an agent associated with another architecture. + * + * @param[in] code_object_isa Instruction set architecture associated with a + * code object. + * + * @param[in] agent_isa Instruction set architecture associated with an agent. + * + * @param[out] result Pointer to a memory location where the HSA runtime stores + * the result of the check. If the two architectures are compatible, the result + * is true; if they are incompatible, the result is false. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA @p code_object_isa or @p agent_isa are + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p result is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_isa_compatible( + hsa_isa_t code_object_isa, + hsa_isa_t agent_isa, + bool *result); + +/** @} */ + + +/** \defgroup executable Executable + * @{ + */ + +/** + * @brief Code object reader handle. A code object reader is used to + * load a code object from file (when created using + * ::hsa_code_object_reader_create_from_file), or from memory (if created using + * ::hsa_code_object_reader_create_from_memory). + */ +typedef struct hsa_code_object_reader_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_code_object_reader_t; + +/** + * @brief Create a code object reader to operate on a file. + * + * @param[in] file File descriptor. The file must have been opened by + * application with at least read permissions prior calling this function. The + * file must contain a vendor-specific code object. + * + * The file is owned and managed by the application; the lifetime of the file + * descriptor must exceed that of any associated code object reader. + * + * @param[out] code_object_reader Memory location to store the newly created + * code object reader handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_FILE @p file is invalid. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p code_object_reader is NULL. + */ +hsa_status_t HSA_API hsa_code_object_reader_create_from_file( + hsa_file_t file, + hsa_code_object_reader_t *code_object_reader); + +/** + * @brief Create a code object reader to operate on memory. + * + * @param[in] code_object Memory buffer that contains a vendor-specific code + * object. The buffer is owned and managed by the application; the lifetime of + * the buffer must exceed that of any associated code object reader. + * + * @param[in] size Size of the buffer pointed to by @p code_object. Must not be + * 0. + * + * @param[out] code_object_reader Memory location to store newly created code + * object reader handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p code_object is NULL, @p size + * is zero, or @p code_object_reader is NULL. + */ +hsa_status_t HSA_API hsa_code_object_reader_create_from_memory( + const void *code_object, + size_t size, + hsa_code_object_reader_t *code_object_reader); + +/** + * @brief Destroy a code object reader. + * + * @details The code object reader handle becomes invalid after completion of + * this function. Any file or memory used to create the code object read is not + * closed, removed, or deallocated by this function. + * + * @param[in] code_object_reader Code object reader to destroy. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT_READER @p code_object_reader + * is invalid. + */ +hsa_status_t HSA_API hsa_code_object_reader_destroy( + hsa_code_object_reader_t code_object_reader); + +/** + * @brief Struct containing an opaque handle to an executable, which contains + * ISA for finalized kernels and indirect functions together with the allocated + * global or readonly segment variables they reference. + */ +typedef struct hsa_executable_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_executable_t; + +/** + * @brief Executable state. + */ +typedef enum { + /** + * Executable state, which allows the user to load code objects and define + * external variables. Variable addresses, kernel code handles, and + * indirect function code handles are not available in query operations until + * the executable is frozen (zero always returned). + */ + HSA_EXECUTABLE_STATE_UNFROZEN = 0, + /** + * Executable state, which allows the user to query variable addresses, + * kernel code handles, and indirect function code handles using query + * operations. Loading new code objects, as well as defining external + * variables, is not allowed in this state. + */ + HSA_EXECUTABLE_STATE_FROZEN = 1 +} hsa_executable_state_t; + +/** + * @deprecated Use ::hsa_executable_create_alt instead, which allows the + * application to specify the default floating-point rounding mode of the + * executable and assumes an unfrozen initial state. + * + * @brief Create an empty executable. + * + * @param[in] profile Profile used in the executable. + * + * @param[in] executable_state Executable state. If the state is + * ::HSA_EXECUTABLE_STATE_FROZEN, the resulting executable is useless because no + * code objects can be loaded, and no variables can be defined. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] executable Memory location where the HSA runtime stores the newly + * created executable handle. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p profile is invalid, or + * @p executable is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_executable_create( + hsa_profile_t profile, + hsa_executable_state_t executable_state, + const char *options, + hsa_executable_t *executable); + +/** + * @brief Create an empty executable. + * + * @param[in] profile Profile used in the executable. + * + * @param[in] default_float_rounding_mode Default floating-point rounding mode + * used in the executable. Allowed rounding modes are near and zero (default is + * not allowed). + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] executable Memory location where the HSA runtime stores newly + * created executable handle. The initial state of the executable is + * ::HSA_EXECUTABLE_STATE_UNFROZEN. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p profile is invalid, or + * @p executable is NULL. + */ +hsa_status_t HSA_API hsa_executable_create_alt( + hsa_profile_t profile, + hsa_default_float_rounding_mode_t default_float_rounding_mode, + const char *options, + hsa_executable_t *executable); + +/** + * @brief Destroy an executable. + * + * @details An executable handle becomes invalid after the executable has been + * destroyed. Code object handles that were loaded into this executable are + * still valid after the executable has been destroyed, and can be used as + * intended. Resources allocated outside and associated with this executable + * (such as external global or readonly variables) can be released after the + * executable has been destroyed. + * + * Executable should not be destroyed while kernels are in flight. + * + * @param[in] executable Executable. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + */ +hsa_status_t HSA_API hsa_executable_destroy( + hsa_executable_t executable); + +/** + * @brief Loaded code object handle. + */ +typedef struct hsa_loaded_code_object_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_loaded_code_object_t; + +/** + * @brief Load a program code object into an executable. + * + * @details A program code object contains information about resources that are + * accessible by all kernel agents that run the executable, and can be loaded + * at most once into an executable. + * + * If the program code object uses extensions, the implementation must support + * them for this operation to return successfully. + * + * @param[in] executable Executable. + * + * @param[in] code_object_reader A code object reader that holds the program + * code object to load. If a code object reader is destroyed before all the + * associated executables are destroyed, the behavior is undefined. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] loaded_code_object Pointer to a memory location where the HSA + * runtime stores the loaded code object handle. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE The executable is frozen. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT_READER @p code_object_reader + * is invalid. + * + * @retval ::HSA_STATUS_ERROR_INCOMPATIBLE_ARGUMENTS The program code object is + * not compatible with the executable or the implementation (for example, the + * code object uses an extension that is not supported by the implementation). + */ +hsa_status_t HSA_API hsa_executable_load_program_code_object( + hsa_executable_t executable, + hsa_code_object_reader_t code_object_reader, + const char *options, + hsa_loaded_code_object_t *loaded_code_object); + +/** + * @brief Load an agent code object into an executable. + * + * @details The agent code object contains all defined agent + * allocation variables, functions, indirect functions, and kernels in a given + * program for a given instruction set architecture. + * + * Any module linkage declaration must have been defined either by a define + * variable or by loading a code object that has a symbol with module linkage + * definition. + * + * The default floating-point rounding mode of the code object associated with + * @p code_object_reader must match that of the executable + * (::HSA_EXECUTABLE_INFO_DEFAULT_FLOAT_ROUNDING_MODE), or be default (in which + * case the value of ::HSA_EXECUTABLE_INFO_DEFAULT_FLOAT_ROUNDING_MODE is used). + * If the agent code object uses extensions, the implementation and the agent + * must support them for this operation to return successfully. + * + * @param[in] executable Executable. + * + * @param[in] agent Agent to load code object for. A code object can be loaded + * into an executable at most once for a given agent. The instruction set + * architecture of the code object must be supported by the agent. + * + * @param[in] code_object_reader A code object reader that holds the code object + * to load. If a code object reader is destroyed before all the associated + * executables are destroyed, the behavior is undefined. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] loaded_code_object Pointer to a memory location where the HSA + * runtime stores the loaded code object handle. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE The executable is frozen. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT_READER @p code_object_reader + * is invalid. + * + * @retval ::HSA_STATUS_ERROR_INCOMPATIBLE_ARGUMENTS The code object read by @p + * code_object_reader is not compatible with the agent (for example, the agent + * does not support the instruction set architecture of the code object), the + * executable (for example, there is a default floating-point mode mismatch + * between the two), or the implementation. + */ +hsa_status_t HSA_API hsa_executable_load_agent_code_object( + hsa_executable_t executable, + hsa_agent_t agent, + hsa_code_object_reader_t code_object_reader, + const char *options, + hsa_loaded_code_object_t *loaded_code_object); + +/** + * @brief Freeze the executable. + * + * @details No modifications to executable can be made after freezing: no code + * objects can be loaded to the executable, and no external variables can be + * defined. Freezing the executable does not prevent querying the executable's + * attributes. The application must define all the external variables in an + * executable before freezing it. + * + * @param[in] executable Executable. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_VARIABLE_UNDEFINED One or more variables are + * undefined in the executable. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE @p executable is already frozen. + */ +hsa_status_t HSA_API hsa_executable_freeze( + hsa_executable_t executable, + const char *options); + +/** + * @brief Executable attributes. + */ +typedef enum { + /** + * Profile this executable is created for. The type of this attribute is + * ::hsa_profile_t. + */ + HSA_EXECUTABLE_INFO_PROFILE = 1, + /** + * Executable state. The type of this attribute is ::hsa_executable_state_t. + */ + HSA_EXECUTABLE_INFO_STATE = 2, + /** + * Default floating-point rounding mode specified when executable was created. + * The type of this attribute is ::hsa_default_float_rounding_mode_t. + */ + HSA_EXECUTABLE_INFO_DEFAULT_FLOAT_ROUNDING_MODE = 3 +} hsa_executable_info_t; + +/** + * @brief Get the current value of an attribute for a given executable. + * + * @param[in] executable Executable. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * executable attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_executable_get_info( + hsa_executable_t executable, + hsa_executable_info_t attribute, + void *value); + +/** + * @brief Define an external global variable with program allocation. + * + * @details This function allows the application to provide the definition + * of a variable in the global segment memory with program allocation. The + * variable must be defined before loading a code object into an executable. + * In addition, code objects loaded must not define the variable. + * + * @param[in] executable Executable. Must not be in frozen state. + * + * @param[in] variable_name Name of the variable. The Programmer's Reference + * Manual describes the standard name mangling scheme. + * + * @param[in] address Address where the variable is defined. This address must + * be in global memory and can be read and written by any agent in the + * system. The application cannot deallocate the buffer pointed by @p address + * before @p executable is destroyed. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_VARIABLE_ALREADY_DEFINED The variable is + * already defined. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no variable with the + * @p variable_name. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE @p executable is frozen. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p variable_name is NULL. + */ +hsa_status_t HSA_API hsa_executable_global_variable_define( + hsa_executable_t executable, + const char *variable_name, + void *address); + +/** + * @brief Define an external global variable with agent allocation. + * + * @details This function allows the application to provide the definition + * of a variable in the global segment memory with agent allocation. The + * variable must be defined before loading a code object into an executable. + * In addition, code objects loaded must not define the variable. + * + * @param[in] executable Executable. Must not be in frozen state. + * + * @param[in] agent Agent for which the variable is being defined. + * + * @param[in] variable_name Name of the variable. The Programmer's Reference + * Manual describes the standard name mangling scheme. + * + * @param[in] address Address where the variable is defined. This address must + * have been previously allocated using ::hsa_memory_allocate in a global region + * that is only visible to @p agent. The application cannot deallocate the + * buffer pointed by @p address before @p executable is destroyed. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT @p agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_VARIABLE_ALREADY_DEFINED The variable is + * already defined. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no variable with the + * @p variable_name. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE @p executable is frozen. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p variable_name is NULL. + */ +hsa_status_t HSA_API hsa_executable_agent_global_variable_define( + hsa_executable_t executable, + hsa_agent_t agent, + const char *variable_name, + void *address); + +/** + * @brief Define an external readonly variable. + * + * @details This function allows the application to provide the definition + * of a variable in the readonly segment memory. The variable must be defined + * before loading a code object into an executable. In addition, code objects + * loaded must not define the variable. + * + * @param[in] executable Executable. Must not be in frozen state. + * + * @param[in] agent Agent for which the variable is being defined. + * + * @param[in] variable_name Name of the variable. The Programmer's Reference + * Manual describes the standard name mangling scheme. + * + * @param[in] address Address where the variable is defined. This address must + * have been previously allocated using ::hsa_memory_allocate in a readonly + * region associated with @p agent. The application cannot deallocate the buffer + * pointed by @p address before @p executable is destroyed. + * + * @param[in] address Address where the variable is defined. The buffer pointed + * by @p address is owned by the application, and cannot be deallocated before + * @p executable is destroyed. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE Executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT @p agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_VARIABLE_ALREADY_DEFINED The variable is + * already defined. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no variable with the + * @p variable_name. + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE @p executable is frozen. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p variable_name is NULL. + */ +hsa_status_t HSA_API hsa_executable_readonly_variable_define( + hsa_executable_t executable, + hsa_agent_t agent, + const char *variable_name, + void *address); + +/** + * @brief Validate an executable. Checks that all code objects have matching + * machine model, profile, and default floating-point rounding mode. Checks that + * all declarations have definitions. Checks declaration-definition + * compatibility (see the HSA Programming Reference Manual for compatibility + * rules). Invoking this function is equivalent to invoking + * ::hsa_executable_validate_alt with no options. + * + * @param[in] executable Executable. Must be in frozen state. + * + * @param[out] result Memory location where the HSA runtime stores the + * validation result. If the executable passes validation, the result is 0. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE @p executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p result is NULL. + */ +hsa_status_t HSA_API hsa_executable_validate( + hsa_executable_t executable, + uint32_t *result); + +/** + * @brief Validate an executable. Checks that all code objects have matching + * machine model, profile, and default floating-point rounding mode. Checks that + * all declarations have definitions. Checks declaration-definition + * compatibility (see the HSA Programming Reference Manual for compatibility + * rules). + * + * @param[in] executable Executable. Must be in frozen state. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] result Memory location where the HSA runtime stores the + * validation result. If the executable passes validation, the result is 0. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE @p executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p result is NULL. + */ +hsa_status_t HSA_API hsa_executable_validate_alt( + hsa_executable_t executable, + const char *options, + uint32_t *result); + +/** + * @brief Executable symbol handle. + * + * The lifetime of an executable object symbol matches that of the executable + * associated with it. An operation on a symbol whose associated executable has + * been destroyed results in undefined behavior. + */ +typedef struct hsa_executable_symbol_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_executable_symbol_t; + +/** + * @deprecated Use ::hsa_executable_get_symbol_by_name instead. + * + * @brief Get the symbol handle for a given a symbol name. + * + * @param[in] executable Executable. + * + * @param[in] module_name Module name. Must be NULL if the symbol has + * program linkage. + * + * @param[in] symbol_name Symbol name. + * + * @param[in] agent Agent associated with the symbol. If the symbol is + * independent of any agent (for example, a variable with program + * allocation), this argument is ignored. + * + * @param[in] call_convention Call convention associated with the symbol. If the + * symbol does not correspond to an indirect function, this argument is ignored. + * + * @param[out] symbol Memory location where the HSA runtime stores the symbol + * handle. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no symbol with a name + * that matches @p symbol_name. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p symbol_name is NULL, or + * @p symbol is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_executable_get_symbol( + hsa_executable_t executable, + const char *module_name, + const char *symbol_name, + hsa_agent_t agent, + int32_t call_convention, + hsa_executable_symbol_t *symbol); + +/** + * @brief Retrieve the symbol handle corresponding to a given a symbol name. + * + * @param[in] executable Executable. + * + * @param[in] symbol_name Symbol name. Must be a NUL-terminated character + * array. The Programmer's Reference Manual describes the standard name mangling + * scheme. + * + * @param[in] agent Pointer to the agent for which the symbol with the given + * name is defined. If the symbol corresponding to the given name has program + * allocation, @p agent must be NULL. + * + * @param[out] symbol Memory location where the HSA runtime stores the symbol + * handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no symbol with a name + * that matches @p symbol_name. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p symbol_name is NULL, or @p + * symbol is NULL. + */ +hsa_status_t HSA_API hsa_executable_get_symbol_by_name( + hsa_executable_t executable, + const char *symbol_name, + const hsa_agent_t *agent, + hsa_executable_symbol_t *symbol); + +/** + * @brief Symbol type. + */ +typedef enum { + /** + * Variable. + */ + HSA_SYMBOL_KIND_VARIABLE = 0, + /** + * Kernel. + */ + HSA_SYMBOL_KIND_KERNEL = 1, + /** + * Indirect function. + */ + HSA_SYMBOL_KIND_INDIRECT_FUNCTION = 2 +} hsa_symbol_kind_t; + +/** + * @brief Linkage type of a symbol. + */ +typedef enum { + /** + * Module linkage. + */ + HSA_SYMBOL_LINKAGE_MODULE = 0, + /** + * Program linkage. + */ + HSA_SYMBOL_LINKAGE_PROGRAM = 1 +} hsa_symbol_linkage_t; + +/** + * @brief Allocation type of a variable. + */ +typedef enum { + /** + * Agent allocation. + */ + HSA_VARIABLE_ALLOCATION_AGENT = 0, + /** + * Program allocation. + */ + HSA_VARIABLE_ALLOCATION_PROGRAM = 1 +} hsa_variable_allocation_t; + +/** + * @brief Memory segment associated with a variable. + */ +typedef enum { + /** + * Global memory segment. + */ + HSA_VARIABLE_SEGMENT_GLOBAL = 0, + /** + * Readonly memory segment. + */ + HSA_VARIABLE_SEGMENT_READONLY = 1 +} hsa_variable_segment_t; + +/** + * @brief Executable symbol attributes. + */ +typedef enum { + /** + * The kind of the symbol. The type of this attribute is ::hsa_symbol_kind_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_TYPE = 0, + /** + * The length of the symbol name in bytes, not including the NUL terminator. + * The type of this attribute is uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_NAME_LENGTH = 1, + /** + * The name of the symbol. The type of this attribute is character array with + * the length equal to the value of ::HSA_EXECUTABLE_SYMBOL_INFO_NAME_LENGTH + * attribute. + */ + HSA_EXECUTABLE_SYMBOL_INFO_NAME = 2, + /** + * @deprecated + * + * The length of the module name in bytes (not including the NUL terminator) + * to which this symbol belongs if this symbol has module linkage, otherwise 0 + * is returned. The type of this attribute is uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_MODULE_NAME_LENGTH = 3, + /** + * @deprecated + * + * The module name to which this symbol belongs if this symbol has module + * linkage, otherwise an empty string is returned. The type of this attribute + * is character array with the length equal to the value of + * ::HSA_EXECUTABLE_SYMBOL_INFO_MODULE_NAME_LENGTH attribute. + */ + HSA_EXECUTABLE_SYMBOL_INFO_MODULE_NAME = 4, + /** + * @deprecated + * + * Agent associated with this symbol. If the symbol is a variable, the + * value of this attribute is only defined if + * ::HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_ALLOCATION is + * ::HSA_VARIABLE_ALLOCATION_AGENT. The type of this attribute is hsa_agent_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_AGENT = 20, + /** + * The address of the variable. The value of this attribute is undefined if + * the symbol is not a variable. The type of this attribute is uint64_t. + * + * If executable's state is ::HSA_EXECUTABLE_STATE_UNFROZEN, then 0 is + * returned. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_ADDRESS = 21, + /** + * The linkage kind of the symbol. The type of this attribute is + * ::hsa_symbol_linkage_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_LINKAGE = 5, + /** + * Indicates whether the symbol corresponds to a definition. The type of this + * attribute is bool. + */ + HSA_EXECUTABLE_SYMBOL_INFO_IS_DEFINITION = 17, + /** + * @deprecated + * + * The allocation kind of the variable. The value of this attribute is + * undefined if the symbol is not a variable. The type of this attribute is + * ::hsa_variable_allocation_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_ALLOCATION = 6, + /** + * @deprecated + * + * The segment kind of the variable. The value of this attribute is undefined + * if the symbol is not a variable. The type of this attribute is + * ::hsa_variable_segment_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_SEGMENT = 7, + /** + * @deprecated + * + * Alignment of the symbol in memory. The value of this attribute is undefined + * if the symbol is not a variable. The type of this attribute is uint32_t. + * + * The current alignment of the variable in memory may be greater than the + * value specified in the source program variable declaration. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_ALIGNMENT = 8, + /** + * @deprecated + * + * Size of the variable. The value of this attribute is undefined if + * the symbol is not a variable. The type of this attribute is uint32_t. + * + * A value of 0 is returned if the variable is an external variable and has an + * unknown dimension. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_SIZE = 9, + /** + * @deprecated + * + * Indicates whether the variable is constant. The value of this attribute is + * undefined if the symbol is not a variable. The type of this attribute is + * bool. + */ + HSA_EXECUTABLE_SYMBOL_INFO_VARIABLE_IS_CONST = 10, + /** + * Kernel object handle, used in the kernel dispatch packet. The value of this + * attribute is undefined if the symbol is not a kernel. The type of this + * attribute is uint64_t. + * + * If the state of the executable is ::HSA_EXECUTABLE_STATE_UNFROZEN, then 0 + * is returned. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_OBJECT = 22, + /** + * Size of kernarg segment memory that is required to hold the values of the + * kernel arguments, in bytes. Must be a multiple of 16. The value of this + * attribute is undefined if the symbol is not a kernel. The type of this + * attribute is uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_KERNARG_SEGMENT_SIZE = 11, + /** + * Alignment (in bytes) of the buffer used to pass arguments to the kernel, + * which is the maximum of 16 and the maximum alignment of any of the kernel + * arguments. The value of this attribute is undefined if the symbol is not a + * kernel. The type of this attribute is uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_KERNARG_SEGMENT_ALIGNMENT = 12, + /** + * Size of static group segment memory required by the kernel (per + * work-group), in bytes. The value of this attribute is undefined + * if the symbol is not a kernel. The type of this attribute is uint32_t. + * + * The reported amount does not include any dynamically allocated group + * segment memory that may be requested by the application when a kernel is + * dispatched. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_GROUP_SEGMENT_SIZE = 13, + /** + * Size of static private, spill, and arg segment memory required by + * this kernel (per work-item), in bytes. The value of this attribute is + * undefined if the symbol is not a kernel. The type of this attribute is + * uint32_t. + * + * If the value of ::HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_DYNAMIC_CALLSTACK is + * true, the kernel may use more private memory than the reported value, and + * the application must add the dynamic call stack usage to @a + * private_segment_size when populating a kernel dispatch packet. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_PRIVATE_SEGMENT_SIZE = 14, + /** + * Dynamic callstack flag. The value of this attribute is undefined if the + * symbol is not a kernel. The type of this attribute is bool. + * + * If this flag is set (the value is true), the kernel uses a dynamically + * sized call stack. This can happen if recursive calls, calls to indirect + * functions, or the HSAIL alloca instruction are present in the kernel. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_DYNAMIC_CALLSTACK = 15, + /** + * @deprecated + * + * Call convention of the kernel. The value of this attribute is undefined if + * the symbol is not a kernel. The type of this attribute is uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_KERNEL_CALL_CONVENTION = 18, + /** + * Indirect function object handle. The value of this attribute is undefined + * if the symbol is not an indirect function, or the associated agent does + * not support the Full Profile. The type of this attribute depends on the + * machine model: the type is uint32_t for small machine model, and uint64_t + * for large model. + * + * If the state of the executable is ::HSA_EXECUTABLE_STATE_UNFROZEN, then 0 + * is returned. + */ + HSA_EXECUTABLE_SYMBOL_INFO_INDIRECT_FUNCTION_OBJECT = 23, + /** + * @deprecated + * + * Call convention of the indirect function. The value of this attribute is + * undefined if the symbol is not an indirect function, or the associated + * agent does not support the Full Profile. The type of this attribute is + * uint32_t. + */ + HSA_EXECUTABLE_SYMBOL_INFO_INDIRECT_FUNCTION_CALL_CONVENTION = 16 +} hsa_executable_symbol_info_t; + +/** + * @brief Get the current value of an attribute for a given executable symbol. + * + * @param[in] executable_symbol Executable symbol. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE_SYMBOL The executable symbol is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * executable symbol attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_executable_symbol_get_info( + hsa_executable_symbol_t executable_symbol, + hsa_executable_symbol_info_t attribute, + void *value); + +/** + * @deprecated + * + * @brief Iterate over the symbols in a executable, and invoke an + * application-defined callback on every iteration. + * + * @param[in] executable Executable. + * + * @param[in] callback Callback to be invoked once per executable symbol. The + * HSA runtime passes three arguments to the callback: the executable, a symbol, + * and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_executable_iterate_symbols returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_executable_iterate_symbols( + hsa_executable_t executable, + hsa_status_t (*callback)(hsa_executable_t exec, + hsa_executable_symbol_t symbol, + void *data), + void *data); + +/** + * @brief Iterate over the kernels, indirect functions, and agent allocation + * variables in an executable for a given agent, and invoke an application- + * defined callback on every iteration. + * + * @param[in] executable Executable. + * + * @param[in] agent Agent. + * + * @param[in] callback Callback to be invoked once per executable symbol. The + * HSA runtime passes three arguments to the callback: the executable, a symbol, + * and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_executable_iterate_symbols returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_executable_iterate_agent_symbols( + hsa_executable_t executable, + hsa_agent_t agent, + hsa_status_t (*callback)(hsa_executable_t exec, + hsa_agent_t agent, + hsa_executable_symbol_t symbol, + void *data), + void *data); + +/** + * @brief Iterate over the program allocation variables in an executable, and + * invoke an application-defined callback on every iteration. + * + * @param[in] executable Executable. + * + * @param[in] callback Callback to be invoked once per executable symbol. The + * HSA runtime passes three arguments to the callback: the executable, a symbol, + * and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_executable_iterate_symbols returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_executable_iterate_program_symbols( + hsa_executable_t executable, + hsa_status_t (*callback)(hsa_executable_t exec, + hsa_executable_symbol_t symbol, + void *data), + void *data); + +/** @} */ + + +/** \defgroup code-object Code Objects (deprecated). + * @{ + */ + +/** + * @deprecated + * + * @brief Struct containing an opaque handle to a code object, which contains + * ISA for finalized kernels and indirect functions together with information + * about the global or readonly segment variables they reference. + */ +typedef struct hsa_code_object_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_code_object_t; + +/** + * @deprecated + * + * @brief Application data handle that is passed to the serialization + * and deserialization functions. + */ +typedef struct hsa_callback_data_s { + /** + * Opaque handle. + */ + uint64_t handle; +} hsa_callback_data_t; + +/** + * @deprecated + * + * @brief Serialize a code object. Can be used for offline finalization, + * install-time finalization, disk code caching, etc. + * + * @param[in] code_object Code object. + * + * @param[in] alloc_callback Callback function for memory allocation. Must not + * be NULL. The HSA runtime passes three arguments to the callback: the + * allocation size, the application data, and a pointer to a memory location + * where the application stores the allocation result. The HSA runtime invokes + * @p alloc_callback once to allocate a buffer that contains the serialized + * version of @p code_object. If the callback returns a status code other than + * ::HSA_STATUS_SUCCESS, this function returns the same code. + * + * @param[in] callback_data Application data that is passed to @p + * alloc_callback. May be NULL. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] serialized_code_object Memory location where the HSA runtime + * stores a pointer to the serialized code object. Must not be NULL. + * + * @param[out] serialized_code_object_size Memory location where the HSA runtime + * stores the size (in bytes) of @p serialized_code_object. The returned value + * matches the allocation size passed by the HSA runtime to @p + * alloc_callback. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p alloc_callback, @p + * serialized_code_object, or @p serialized_code_object_size are NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_serialize( + hsa_code_object_t code_object, + hsa_status_t (*alloc_callback)(size_t size, + hsa_callback_data_t data, + void **address), + hsa_callback_data_t callback_data, + const char *options, + void **serialized_code_object, + size_t *serialized_code_object_size); + +/** + * @deprecated + * + * @brief Deserialize a code object. + * + * @param[in] serialized_code_object A serialized code object. Must not be NULL. + * + * @param[in] serialized_code_object_size The size (in bytes) of @p + * serialized_code_object. Must not be 0. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @param[out] code_object Memory location where the HSA runtime stores the + * deserialized code object. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p serialized_code_object, or @p + * code_object are NULL, or @p serialized_code_object_size is 0. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_deserialize( + void *serialized_code_object, + size_t serialized_code_object_size, + const char *options, + hsa_code_object_t *code_object); + +/** + * @deprecated + * + * @brief Destroy a code object. + * + * @details The lifetime of a code object must exceed that of any executable + * where it has been loaded. If an executable that loaded @p code_object has not + * been destroyed, the behavior is undefined. + * + * @param[in] code_object Code object. The handle becomes invalid after it has + * been destroyed. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_destroy( + hsa_code_object_t code_object); + +/** + * @deprecated + * + * @brief Code object type. + */ +typedef enum { + /** + * Produces code object that contains ISA for all kernels and indirect + * functions in HSA source. + */ + HSA_CODE_OBJECT_TYPE_PROGRAM = 0 +} hsa_code_object_type_t; + +/** + * @deprecated + * + * @brief Code object attributes. + */ +typedef enum { + /** + * The version of the code object. The type of this attribute is a + * NUL-terminated char[64]. The name must be at most 63 characters long (not + * including the NUL terminator) and all array elements not used for the name + * must be NUL. + */ + HSA_CODE_OBJECT_INFO_VERSION = 0, + /** + * Type of code object. The type of this attribute is + * ::hsa_code_object_type_t. + */ + HSA_CODE_OBJECT_INFO_TYPE = 1, + /** + * Instruction set architecture this code object is produced for. The type of + * this attribute is ::hsa_isa_t. + */ + HSA_CODE_OBJECT_INFO_ISA = 2, + /** + * Machine model this code object is produced for. The type of this attribute + * is ::hsa_machine_model_t. + */ + HSA_CODE_OBJECT_INFO_MACHINE_MODEL = 3, + /** + * Profile this code object is produced for. The type of this attribute is + * ::hsa_profile_t. + */ + HSA_CODE_OBJECT_INFO_PROFILE = 4, + /** + * Default floating-point rounding mode used when the code object is + * produced. The type of this attribute is + * ::hsa_default_float_rounding_mode_t. + */ + HSA_CODE_OBJECT_INFO_DEFAULT_FLOAT_ROUNDING_MODE = 5 +} hsa_code_object_info_t; + +/** + * @deprecated + * + * @brief Get the current value of an attribute for a given code object. + * + * @param[in] code_object Code object. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * code object attribute, or @p value is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_get_info( + hsa_code_object_t code_object, + hsa_code_object_info_t attribute, + void *value); + +/** + * @deprecated + * + * @brief Load code object into the executable. + * + * @details Every global or readonly variable that is external must be defined + * before loading the code object. An internal global or readonly variable is + * allocated once the code object, that is being loaded, references this + * variable and this variable is not allocated. + * + * Any module linkage declaration must have been defined either by a define + * variable or by loading a code object that has a symbol with module linkage + * definition. + * + * @param[in] executable Executable. + * + * @param[in] agent Agent to load code object for. The agent must support the + * default floating-point rounding mode used by @p code_object. + * + * @param[in] code_object Code object to load. The lifetime of the code object + * must exceed that of the executable: if @p code_object is destroyed before @p + * executable, the behavior is undefined. + * + * @param[in] options Standard and vendor-specific options. Unknown options are + * ignored. A standard option begins with the "-hsa_" prefix. Options beginning + * with the "-hsa_ext__" prefix are reserved for extensions. A + * vendor-specific option begins with the "-_" prefix. Must be a + * NUL-terminated string. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INCOMPATIBLE_ARGUMENTS @p agent is not compatible + * with @p code_object (for example, @p agent does not support the default + * floating-point rounding mode specified by @p code_object), or @p code_object + * is not compatible with @p executable (for example, @p code_object and @p + * executable have different machine models or profiles). + * + * @retval ::HSA_STATUS_ERROR_FROZEN_EXECUTABLE @p executable is frozen. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_executable_load_code_object( + hsa_executable_t executable, + hsa_agent_t agent, + hsa_code_object_t code_object, + const char *options); + +/** + * @deprecated + * + * @brief Code object symbol handle. + * + * The lifetime of a code object symbol matches that of the code object + * associated with it. An operation on a symbol whose associated code object has + * been destroyed results in undefined behavior. + */ +typedef struct hsa_code_symbol_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_code_symbol_t; + +/** + * @deprecated + * + * @brief Get the symbol handle within a code object for a given a symbol name. + * + * @param[in] code_object Code object. + * + * @param[in] symbol_name Symbol name. + * + * @param[out] symbol Memory location where the HSA runtime stores the symbol + * handle. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no symbol with a name + * that matches @p symbol_name. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p symbol_name is NULL, or + * @p symbol is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_get_symbol( + hsa_code_object_t code_object, + const char *symbol_name, + hsa_code_symbol_t *symbol); + +/** + * @deprecated + * + * @brief Get the symbol handle within a code object for a given a symbol name. + * + * @param[in] code_object Code object. + * + * @param[in] module_name Module name. Must be NULL if the symbol has + * program linkage. + * + * @param[in] symbol_name Symbol name. + * + * @param[out] symbol Memory location where the HSA runtime stores the symbol + * handle. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SYMBOL_NAME There is no symbol with a name + * that matches @p symbol_name. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p symbol_name is NULL, or + * @p symbol is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_get_symbol_from_name( + hsa_code_object_t code_object, + const char *module_name, + const char *symbol_name, + hsa_code_symbol_t *symbol); + +/** + * @deprecated + * + * @brief Code object symbol attributes. + */ +typedef enum { + /** + * The type of the symbol. The type of this attribute is ::hsa_symbol_kind_t. + */ + HSA_CODE_SYMBOL_INFO_TYPE = 0, + /** + * The length of the symbol name in bytes, not including the NUL terminator. + * The type of this attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_NAME_LENGTH = 1, + /** + * The name of the symbol. The type of this attribute is character array with + * the length equal to the value of ::HSA_CODE_SYMBOL_INFO_NAME_LENGTH + * attribute. + */ + HSA_CODE_SYMBOL_INFO_NAME = 2, + /** + * The length of the module name in bytes (not including the NUL terminator) + * to which this symbol belongs if this symbol has module linkage, otherwise 0 + * is returned. The type of this attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_MODULE_NAME_LENGTH = 3, + /** + * The module name to which this symbol belongs if this symbol has module + * linkage, otherwise an empty string is returned. The type of this attribute + * is character array with the length equal to the value of + * ::HSA_CODE_SYMBOL_INFO_MODULE_NAME_LENGTH attribute. + */ + HSA_CODE_SYMBOL_INFO_MODULE_NAME = 4, + /** + * The linkage kind of the symbol. The type of this attribute is + * ::hsa_symbol_linkage_t. + */ + HSA_CODE_SYMBOL_INFO_LINKAGE = 5, + /** + * Indicates whether the symbol corresponds to a definition. The type of this + * attribute is bool. + */ + HSA_CODE_SYMBOL_INFO_IS_DEFINITION = 17, + /** + * The allocation kind of the variable. The value of this attribute is + * undefined if the symbol is not a variable. The type of this attribute is + * ::hsa_variable_allocation_t. + */ + HSA_CODE_SYMBOL_INFO_VARIABLE_ALLOCATION = 6, + /** + * The segment kind of the variable. The value of this attribute is + * undefined if the symbol is not a variable. The type of this attribute is + * ::hsa_variable_segment_t. + */ + HSA_CODE_SYMBOL_INFO_VARIABLE_SEGMENT = 7, + /** + * Alignment of the symbol in memory. The value of this attribute is undefined + * if the symbol is not a variable. The type of this attribute is uint32_t. + * + * The current alignment of the variable in memory may be greater than the + * value specified in the source program variable declaration. + */ + HSA_CODE_SYMBOL_INFO_VARIABLE_ALIGNMENT = 8, + /** + * Size of the variable. The value of this attribute is undefined if the + * symbol is not a variable. The type of this attribute is uint32_t. + * + * A size of 0 is returned if the variable is an external variable and has an + * unknown dimension. + */ + HSA_CODE_SYMBOL_INFO_VARIABLE_SIZE = 9, + /** + * Indicates whether the variable is constant. The value of this attribute is + * undefined if the symbol is not a variable. The type of this attribute is + * bool. + */ + HSA_CODE_SYMBOL_INFO_VARIABLE_IS_CONST = 10, + /** + * Size of kernarg segment memory that is required to hold the values of the + * kernel arguments, in bytes. Must be a multiple of 16. The value of this + * attribute is undefined if the symbol is not a kernel. The type of this + * attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_KERNARG_SEGMENT_SIZE = 11, + /** + * Alignment (in bytes) of the buffer used to pass arguments to the kernel, + * which is the maximum of 16 and the maximum alignment of any of the kernel + * arguments. The value of this attribute is undefined if the symbol is not a + * kernel. The type of this attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_KERNARG_SEGMENT_ALIGNMENT = 12, + /** + * Size of static group segment memory required by the kernel (per + * work-group), in bytes. The value of this attribute is undefined + * if the symbol is not a kernel. The type of this attribute is uint32_t. + * + * The reported amount does not include any dynamically allocated group + * segment memory that may be requested by the application when a kernel is + * dispatched. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_GROUP_SEGMENT_SIZE = 13, + /** + * Size of static private, spill, and arg segment memory required by + * this kernel (per work-item), in bytes. The value of this attribute is + * undefined if the symbol is not a kernel. The type of this attribute is + * uint32_t. + * + * If the value of ::HSA_CODE_SYMBOL_INFO_KERNEL_DYNAMIC_CALLSTACK is true, + * the kernel may use more private memory than the reported value, and the + * application must add the dynamic call stack usage to @a + * private_segment_size when populating a kernel dispatch packet. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_PRIVATE_SEGMENT_SIZE = 14, + /** + * Dynamic callstack flag. The value of this attribute is undefined if the + * symbol is not a kernel. The type of this attribute is bool. + * + * If this flag is set (the value is true), the kernel uses a dynamically + * sized call stack. This can happen if recursive calls, calls to indirect + * functions, or the HSAIL alloca instruction are present in the kernel. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_DYNAMIC_CALLSTACK = 15, + /** + * Call convention of the kernel. The value of this attribute is undefined if + * the symbol is not a kernel. The type of this attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_KERNEL_CALL_CONVENTION = 18, + /** + * Call convention of the indirect function. The value of this attribute is + * undefined if the symbol is not an indirect function. The type of this + * attribute is uint32_t. + */ + HSA_CODE_SYMBOL_INFO_INDIRECT_FUNCTION_CALL_CONVENTION = 16 +} hsa_code_symbol_info_t; + +/** + * @deprecated + * + * @brief Get the current value of an attribute for a given code symbol. + * + * @param[in] code_symbol Code symbol. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_SYMBOL The code symbol is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * code symbol attribute, or @p value is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_symbol_get_info( + hsa_code_symbol_t code_symbol, + hsa_code_symbol_info_t attribute, + void *value); + +/** + * @deprecated + * + * @brief Iterate over the symbols in a code object, and invoke an + * application-defined callback on every iteration. + * + * @param[in] code_object Code object. + * + * @param[in] callback Callback to be invoked once per code object symbol. The + * HSA runtime passes three arguments to the callback: the code object, a + * symbol, and the application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_code_object_iterate_symbols returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT @p code_object is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API HSA_DEPRECATED hsa_code_object_iterate_symbols( + hsa_code_object_t code_object, + hsa_status_t (*callback)(hsa_code_object_t code_object, + hsa_code_symbol_t symbol, + void *data), + void *data); + +/** @} */ + +#ifdef __cplusplus +} // end extern "C" block +#endif + +#endif // header guard diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_amd_tool.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_amd_tool.h new file mode 100644 index 0000000000000000000000000000000000000000..fa9cac804a49b40be34bccc966be547d56fb94fb --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_amd_tool.h @@ -0,0 +1,91 @@ +#ifndef HSA_RUNTIME_AMD_TOOL_EVENTS_H_ +#define HSA_RUNTIME_AMD_TOOL_EVENTS_H_ + +// Insert license header + +#include +#include +#include "hsa.h" + + +typedef enum { + HSA_AMD_EVENT_SCRATCH_ALLOC_FLAG_NONE = 0, + HSA_AMD_EVENT_SCRATCH_ALLOC_FLAG_USE_ONCE = + (1 << 0), // This scratch allocation is only valid for 1 dispatch. + HSA_AMD_EVENT_SCRATCH_ALLOC_FLAG_ALT = + (1 << 1), // Used alternate scratch instead of main scratch +} hsa_amd_event_scratch_alloc_flag_t; + +typedef enum { + HSA_AMD_TOOL_EVENT_MIN = 0, + + // Scratch memory tracking + HSA_AMD_TOOL_EVENT_SCRATCH_ALLOC_START, + HSA_AMD_TOOL_EVENT_SCRATCH_ALLOC_END, + HSA_AMD_TOOL_EVENT_SCRATCH_FREE_START, + HSA_AMD_TOOL_EVENT_SCRATCH_FREE_END, + HSA_AMD_TOOL_EVENT_SCRATCH_ASYNC_RECLAIM_START, + HSA_AMD_TOOL_EVENT_SCRATCH_ASYNC_RECLAIM_END, + + // Add new events above ^ + HSA_AMD_TOOL_EVENT_MAX +} hsa_amd_tool_event_kind_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; +} hsa_amd_tool_event_none_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; + uint64_t dispatch_id; // Dispatch ID of the AQL packet that needs more scratch memory +} hsa_amd_event_scratch_alloc_start_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; + uint64_t dispatch_id; // Dispatch ID of the AQL packet that needs more scratch memory + size_t size; // Amount of scratch allocated - in bytes + size_t num_slots; // limit of number of waves +} hsa_amd_event_scratch_alloc_end_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; +} hsa_amd_event_scratch_free_start_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; +} hsa_amd_event_scratch_free_end_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; +} hsa_amd_event_scratch_async_reclaim_start_t; + +typedef struct { + hsa_amd_tool_event_kind_t kind; + const hsa_queue_t* queue; + hsa_amd_event_scratch_alloc_flag_t flags; +} hsa_amd_event_scratch_async_reclaim_end_t; + +typedef union { + const hsa_amd_tool_event_none_t* none; + const hsa_amd_event_scratch_alloc_start_t* scratch_alloc_start; + const hsa_amd_event_scratch_alloc_end_t* scratch_alloc_end; + const hsa_amd_event_scratch_free_start_t* scratch_free_start; + const hsa_amd_event_scratch_free_end_t* scratch_free_end; + const hsa_amd_event_scratch_async_reclaim_start_t* scratch_async_reclaim_start; + const hsa_amd_event_scratch_async_reclaim_end_t* scratch_async_reclaim_end; +} hsa_amd_tool_event_t; + +typedef hsa_status_t (*hsa_amd_tool_event)(hsa_amd_tool_event_t); + + +#endif \ No newline at end of file diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_api_trace.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_api_trace.h new file mode 100644 index 0000000000000000000000000000000000000000..e46c777af13ffa29401f28674c45284825c581c5 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_api_trace.h @@ -0,0 +1,566 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef HSA_RUNTIME_INC_HSA_API_TRACE_H +#define HSA_RUNTIME_INC_HSA_API_TRACE_H + +#include "hsa.h" +#ifdef AMD_INTERNAL_BUILD +#include "hsa_ext_image.h" +#include "hsa_ext_amd.h" +#include "hsa_ext_finalize.h" +#include "hsa_amd_tool.h" +#else +#include "inc/hsa_ext_image.h" +#include "inc/hsa_ext_amd.h" +#include "inc/hsa_ext_finalize.h" +#include "inc/hsa_amd_tool.h" +#endif + +#include +#include +#include + +// Major Ids of the Api tables exported by Hsa Core Runtime +#define HSA_API_TABLE_MAJOR_VERSION 0x03 +#define HSA_CORE_API_TABLE_MAJOR_VERSION 0x02 +#define HSA_AMD_EXT_API_TABLE_MAJOR_VERSION 0x02 +#define HSA_FINALIZER_API_TABLE_MAJOR_VERSION 0x02 +#define HSA_IMAGE_API_TABLE_MAJOR_VERSION 0x02 +#define HSA_AQLPROFILE_API_TABLE_MAJOR_VERSION 0x01 +#define HSA_TOOLS_API_TABLE_MAJOR_VERSION 0x01 + +// Step Ids of the Api tables exported by Hsa Core Runtime +#define HSA_API_TABLE_STEP_VERSION 0x00 +#define HSA_CORE_API_TABLE_STEP_VERSION 0x00 +#define HSA_AMD_EXT_API_TABLE_STEP_VERSION 0x01 +#define HSA_FINALIZER_API_TABLE_STEP_VERSION 0x00 +#define HSA_IMAGE_API_TABLE_STEP_VERSION 0x00 +#define HSA_AQLPROFILE_API_TABLE_STEP_VERSION 0x00 +#define HSA_TOOLS_API_TABLE_STEP_VERSION 0x00 + +// Min function used to copy Api Tables +static inline uint32_t Min(const uint32_t a, const uint32_t b) { + return (a > b) ? b : a; +} + +// Declarations of APIs intended for use only by tools. + +// An AQL packet that can be put in an intercept queue to cause a callback to +// be invoked when the packet is about to be submitted to the underlying +// hardware queue. These packets are not copied to the underlying hardware +// queue. These packets should come immediately before the regular AQL packet +// they relate to. This implies that packet rewriters should always keep these +// packets adjacent to the regular AQL packet that follows them. +const uint32_t AMD_AQL_FORMAT_INTERCEPT_MARKER = 0xFE; + +struct amd_aql_intercept_marker_s; + +// When an intercept queue is processing rewritten packets to put them on the +// underlying hardware queue, if it encounters a +// AMD_AQL_FORMAT_INTERCEPT_MARKER vendor AQL packet it will call the following +// handler. packet points to the packet, queue is the underlying hardware +// queue, and packet_id is the packet id of the next packet to be put on the +// underlying hardware queue. The intercept queue does not put these packets +// onto the underlying hardware queue. +typedef void (*amd_intercept_marker_handler)(const struct amd_aql_intercept_marker_s* packet, + hsa_queue_t* queue, uint64_t packet_id); +// An AQL vendor packet used by the intercept queue to mark the following +// packet. The callback will be invoked to allow a tool to know where in the +// underlying hardware queue the following packet will be placed. user_data can +// be used to hold any data useful to the tool. +typedef struct amd_aql_intercept_marker_s { + uint16_t header; // Must have a packet type of HSA_PACKET_TYPE_VENDOR_SPECIFIC. + uint8_t format; // Must be AMD_AQL_FORMAT_INTERCEPT_MARKER. + uint8_t reserved[5]; // Must be 0. +#ifdef HSA_LARGE_MODEL + amd_intercept_marker_handler callback; +#elif defined HSA_LITTLE_ENDIAN + amd_intercept_marker_handler callback; + uint32_t reserved1; // Must be 0. +#else + uint32_t reserved1; // Must be 0. + amd_intercept_marker_handler callback; +#endif + uint64_t user_data[6]; +} amd_aql_intercept_marker_t; + +typedef void (*hsa_amd_queue_intercept_packet_writer)(const void* pkts, uint64_t pkt_count); +typedef void (*hsa_amd_queue_intercept_handler)(const void* pkts, uint64_t pkt_count, + uint64_t user_pkt_index, void* data, + hsa_amd_queue_intercept_packet_writer writer); +hsa_status_t hsa_amd_queue_intercept_register(hsa_queue_t* queue, + hsa_amd_queue_intercept_handler callback, + void* user_data); +hsa_status_t hsa_amd_queue_intercept_create( + hsa_agent_t agent_handle, uint32_t size, hsa_queue_type32_t type, + void (*callback)(hsa_status_t status, hsa_queue_t* source, void* data), void* data, + uint32_t private_segment_size, uint32_t group_segment_size, hsa_queue_t** queue); + +typedef void (*hsa_amd_runtime_queue_notifier)(const hsa_queue_t* queue, hsa_agent_t agent, + void* data); +hsa_status_t hsa_amd_runtime_queue_create_register(hsa_amd_runtime_queue_notifier callback, + void* user_data); + +// Structure of Version used to identify an instance of Api table +// Must be the first member (offsetof == 0) of all API tables. +// This is the root of the table passing ABI. +struct ApiTableVersion { + uint32_t major_id; + uint32_t minor_id; + uint32_t step_id; + uint32_t reserved; +}; + +struct ToolsApiTable { + ApiTableVersion version; + + hsa_amd_tool_event hsa_amd_tool_scratch_event_alloc_start_fn; + hsa_amd_tool_event hsa_amd_tool_scratch_event_alloc_end_fn; + hsa_amd_tool_event hsa_amd_tool_scratch_event_free_start_fn; + hsa_amd_tool_event hsa_amd_tool_scratch_event_free_end_fn; + hsa_amd_tool_event hsa_amd_tool_scratch_event_async_reclaim_start_fn; + hsa_amd_tool_event hsa_amd_tool_scratch_event_async_reclaim_end_fn; +}; + +// Table to export HSA Finalizer Extension Apis +struct FinalizerExtTable { + ApiTableVersion version; + decltype(hsa_ext_program_create)* hsa_ext_program_create_fn; + decltype(hsa_ext_program_destroy)* hsa_ext_program_destroy_fn; + decltype(hsa_ext_program_add_module)* hsa_ext_program_add_module_fn; + decltype(hsa_ext_program_iterate_modules)* hsa_ext_program_iterate_modules_fn; + decltype(hsa_ext_program_get_info)* hsa_ext_program_get_info_fn; + decltype(hsa_ext_program_finalize)* hsa_ext_program_finalize_fn; +}; + +// Table to export HSA Image Extension Apis +struct ImageExtTable { + ApiTableVersion version; + decltype(hsa_ext_image_get_capability)* hsa_ext_image_get_capability_fn; + decltype(hsa_ext_image_data_get_info)* hsa_ext_image_data_get_info_fn; + decltype(hsa_ext_image_create)* hsa_ext_image_create_fn; + decltype(hsa_ext_image_import)* hsa_ext_image_import_fn; + decltype(hsa_ext_image_export)* hsa_ext_image_export_fn; + decltype(hsa_ext_image_copy)* hsa_ext_image_copy_fn; + decltype(hsa_ext_image_clear)* hsa_ext_image_clear_fn; + decltype(hsa_ext_image_destroy)* hsa_ext_image_destroy_fn; + decltype(hsa_ext_sampler_create)* hsa_ext_sampler_create_fn; + decltype(hsa_ext_sampler_destroy)* hsa_ext_sampler_destroy_fn; + decltype(hsa_ext_image_get_capability_with_layout)* hsa_ext_image_get_capability_with_layout_fn; + decltype(hsa_ext_image_data_get_info_with_layout)* hsa_ext_image_data_get_info_with_layout_fn; + decltype(hsa_ext_image_create_with_layout)* hsa_ext_image_create_with_layout_fn; +}; + +// Table to export AMD Extension Apis +struct AmdExtTable { + ApiTableVersion version; + decltype(hsa_amd_coherency_get_type)* hsa_amd_coherency_get_type_fn; + decltype(hsa_amd_coherency_set_type)* hsa_amd_coherency_set_type_fn; + decltype(hsa_amd_profiling_set_profiler_enabled)* hsa_amd_profiling_set_profiler_enabled_fn; + decltype(hsa_amd_profiling_async_copy_enable) *hsa_amd_profiling_async_copy_enable_fn; + decltype(hsa_amd_profiling_get_dispatch_time)* hsa_amd_profiling_get_dispatch_time_fn; + decltype(hsa_amd_profiling_get_async_copy_time) *hsa_amd_profiling_get_async_copy_time_fn; + decltype(hsa_amd_profiling_convert_tick_to_system_domain)* hsa_amd_profiling_convert_tick_to_system_domain_fn; + decltype(hsa_amd_signal_async_handler)* hsa_amd_signal_async_handler_fn; + decltype(hsa_amd_async_function)* hsa_amd_async_function_fn; + decltype(hsa_amd_signal_wait_any)* hsa_amd_signal_wait_any_fn; + decltype(hsa_amd_queue_cu_set_mask)* hsa_amd_queue_cu_set_mask_fn; + decltype(hsa_amd_memory_pool_get_info)* hsa_amd_memory_pool_get_info_fn; + decltype(hsa_amd_agent_iterate_memory_pools)* hsa_amd_agent_iterate_memory_pools_fn; + decltype(hsa_amd_memory_pool_allocate)* hsa_amd_memory_pool_allocate_fn; + decltype(hsa_amd_memory_pool_free)* hsa_amd_memory_pool_free_fn; + decltype(hsa_amd_memory_async_copy)* hsa_amd_memory_async_copy_fn; + decltype(hsa_amd_memory_async_copy_on_engine)* hsa_amd_memory_async_copy_on_engine_fn; + decltype(hsa_amd_memory_copy_engine_status)* hsa_amd_memory_copy_engine_status_fn; + decltype(hsa_amd_agent_memory_pool_get_info)* hsa_amd_agent_memory_pool_get_info_fn; + decltype(hsa_amd_agents_allow_access)* hsa_amd_agents_allow_access_fn; + decltype(hsa_amd_memory_pool_can_migrate)* hsa_amd_memory_pool_can_migrate_fn; + decltype(hsa_amd_memory_migrate)* hsa_amd_memory_migrate_fn; + decltype(hsa_amd_memory_lock)* hsa_amd_memory_lock_fn; + decltype(hsa_amd_memory_unlock)* hsa_amd_memory_unlock_fn; + decltype(hsa_amd_memory_fill)* hsa_amd_memory_fill_fn; + decltype(hsa_amd_interop_map_buffer)* hsa_amd_interop_map_buffer_fn; + decltype(hsa_amd_interop_unmap_buffer)* hsa_amd_interop_unmap_buffer_fn; + decltype(hsa_amd_image_create)* hsa_amd_image_create_fn; + decltype(hsa_amd_pointer_info)* hsa_amd_pointer_info_fn; + decltype(hsa_amd_pointer_info_set_userdata)* hsa_amd_pointer_info_set_userdata_fn; + decltype(hsa_amd_ipc_memory_create)* hsa_amd_ipc_memory_create_fn; + decltype(hsa_amd_ipc_memory_attach)* hsa_amd_ipc_memory_attach_fn; + decltype(hsa_amd_ipc_memory_detach)* hsa_amd_ipc_memory_detach_fn; + decltype(hsa_amd_signal_create)* hsa_amd_signal_create_fn; + decltype(hsa_amd_ipc_signal_create)* hsa_amd_ipc_signal_create_fn; + decltype(hsa_amd_ipc_signal_attach)* hsa_amd_ipc_signal_attach_fn; + decltype(hsa_amd_register_system_event_handler)* hsa_amd_register_system_event_handler_fn; + decltype(hsa_amd_queue_intercept_create)* hsa_amd_queue_intercept_create_fn; + decltype(hsa_amd_queue_intercept_register)* hsa_amd_queue_intercept_register_fn; + decltype(hsa_amd_queue_set_priority)* hsa_amd_queue_set_priority_fn; + decltype(hsa_amd_memory_async_copy_rect)* hsa_amd_memory_async_copy_rect_fn; + decltype(hsa_amd_runtime_queue_create_register)* hsa_amd_runtime_queue_create_register_fn; + decltype(hsa_amd_memory_lock_to_pool)* hsa_amd_memory_lock_to_pool_fn; + decltype(hsa_amd_register_deallocation_callback)* hsa_amd_register_deallocation_callback_fn; + decltype(hsa_amd_deregister_deallocation_callback)* hsa_amd_deregister_deallocation_callback_fn; + decltype(hsa_amd_signal_value_pointer)* hsa_amd_signal_value_pointer_fn; + decltype(hsa_amd_svm_attributes_set)* hsa_amd_svm_attributes_set_fn; + decltype(hsa_amd_svm_attributes_get)* hsa_amd_svm_attributes_get_fn; + decltype(hsa_amd_svm_prefetch_async)* hsa_amd_svm_prefetch_async_fn; + decltype(hsa_amd_spm_acquire)* hsa_amd_spm_acquire_fn; + decltype(hsa_amd_spm_release)* hsa_amd_spm_release_fn; + decltype(hsa_amd_spm_set_dest_buffer)* hsa_amd_spm_set_dest_buffer_fn; + decltype(hsa_amd_queue_cu_get_mask)* hsa_amd_queue_cu_get_mask_fn; + decltype(hsa_amd_portable_export_dmabuf)* hsa_amd_portable_export_dmabuf_fn; + decltype(hsa_amd_portable_close_dmabuf)* hsa_amd_portable_close_dmabuf_fn; + decltype(hsa_amd_vmem_address_reserve)* hsa_amd_vmem_address_reserve_fn; + decltype(hsa_amd_vmem_address_free)* hsa_amd_vmem_address_free_fn; + decltype(hsa_amd_vmem_handle_create)* hsa_amd_vmem_handle_create_fn; + decltype(hsa_amd_vmem_handle_release)* hsa_amd_vmem_handle_release_fn; + decltype(hsa_amd_vmem_map)* hsa_amd_vmem_map_fn; + decltype(hsa_amd_vmem_unmap)* hsa_amd_vmem_unmap_fn; + decltype(hsa_amd_vmem_set_access)* hsa_amd_vmem_set_access_fn; + decltype(hsa_amd_vmem_get_access)* hsa_amd_vmem_get_access_fn; + decltype(hsa_amd_vmem_export_shareable_handle)* hsa_amd_vmem_export_shareable_handle_fn; + decltype(hsa_amd_vmem_import_shareable_handle)* hsa_amd_vmem_import_shareable_handle_fn; + decltype(hsa_amd_vmem_retain_alloc_handle)* hsa_amd_vmem_retain_alloc_handle_fn; + decltype(hsa_amd_vmem_get_alloc_properties_from_handle)* + hsa_amd_vmem_get_alloc_properties_from_handle_fn; + decltype(hsa_amd_agent_set_async_scratch_limit)* hsa_amd_agent_set_async_scratch_limit_fn; +}; + +// Table to export HSA Core Runtime Apis +struct CoreApiTable { + ApiTableVersion version; + decltype(hsa_init)* hsa_init_fn; + decltype(hsa_shut_down)* hsa_shut_down_fn; + decltype(hsa_system_get_info)* hsa_system_get_info_fn; + decltype(hsa_system_extension_supported)* hsa_system_extension_supported_fn; + decltype(hsa_system_get_extension_table)* hsa_system_get_extension_table_fn; + decltype(hsa_iterate_agents)* hsa_iterate_agents_fn; + decltype(hsa_agent_get_info)* hsa_agent_get_info_fn; + decltype(hsa_queue_create)* hsa_queue_create_fn; + decltype(hsa_soft_queue_create)* hsa_soft_queue_create_fn; + decltype(hsa_queue_destroy)* hsa_queue_destroy_fn; + decltype(hsa_queue_inactivate)* hsa_queue_inactivate_fn; + decltype(hsa_queue_load_read_index_scacquire)* hsa_queue_load_read_index_scacquire_fn; + decltype(hsa_queue_load_read_index_relaxed)* hsa_queue_load_read_index_relaxed_fn; + decltype(hsa_queue_load_write_index_scacquire)* hsa_queue_load_write_index_scacquire_fn; + decltype(hsa_queue_load_write_index_relaxed)* hsa_queue_load_write_index_relaxed_fn; + decltype(hsa_queue_store_write_index_relaxed)* hsa_queue_store_write_index_relaxed_fn; + decltype(hsa_queue_store_write_index_screlease)* hsa_queue_store_write_index_screlease_fn; + decltype(hsa_queue_cas_write_index_scacq_screl)* hsa_queue_cas_write_index_scacq_screl_fn; + decltype(hsa_queue_cas_write_index_scacquire)* hsa_queue_cas_write_index_scacquire_fn; + decltype(hsa_queue_cas_write_index_relaxed)* hsa_queue_cas_write_index_relaxed_fn; + decltype(hsa_queue_cas_write_index_screlease)* hsa_queue_cas_write_index_screlease_fn; + decltype(hsa_queue_add_write_index_scacq_screl)* hsa_queue_add_write_index_scacq_screl_fn; + decltype(hsa_queue_add_write_index_scacquire)* hsa_queue_add_write_index_scacquire_fn; + decltype(hsa_queue_add_write_index_relaxed)* hsa_queue_add_write_index_relaxed_fn; + decltype(hsa_queue_add_write_index_screlease)* hsa_queue_add_write_index_screlease_fn; + decltype(hsa_queue_store_read_index_relaxed)* hsa_queue_store_read_index_relaxed_fn; + decltype(hsa_queue_store_read_index_screlease)* hsa_queue_store_read_index_screlease_fn; + decltype(hsa_agent_iterate_regions)* hsa_agent_iterate_regions_fn; + decltype(hsa_region_get_info)* hsa_region_get_info_fn; + decltype(hsa_agent_get_exception_policies)* hsa_agent_get_exception_policies_fn; + decltype(hsa_agent_extension_supported)* hsa_agent_extension_supported_fn; + decltype(hsa_memory_register)* hsa_memory_register_fn; + decltype(hsa_memory_deregister)* hsa_memory_deregister_fn; + decltype(hsa_memory_allocate)* hsa_memory_allocate_fn; + decltype(hsa_memory_free)* hsa_memory_free_fn; + decltype(hsa_memory_copy)* hsa_memory_copy_fn; + decltype(hsa_memory_assign_agent)* hsa_memory_assign_agent_fn; + decltype(hsa_signal_create)* hsa_signal_create_fn; + decltype(hsa_signal_destroy)* hsa_signal_destroy_fn; + decltype(hsa_signal_load_relaxed)* hsa_signal_load_relaxed_fn; + decltype(hsa_signal_load_scacquire)* hsa_signal_load_scacquire_fn; + decltype(hsa_signal_store_relaxed)* hsa_signal_store_relaxed_fn; + decltype(hsa_signal_store_screlease)* hsa_signal_store_screlease_fn; + decltype(hsa_signal_wait_relaxed)* hsa_signal_wait_relaxed_fn; + decltype(hsa_signal_wait_scacquire)* hsa_signal_wait_scacquire_fn; + decltype(hsa_signal_and_relaxed)* hsa_signal_and_relaxed_fn; + decltype(hsa_signal_and_scacquire)* hsa_signal_and_scacquire_fn; + decltype(hsa_signal_and_screlease)* hsa_signal_and_screlease_fn; + decltype(hsa_signal_and_scacq_screl)* hsa_signal_and_scacq_screl_fn; + decltype(hsa_signal_or_relaxed)* hsa_signal_or_relaxed_fn; + decltype(hsa_signal_or_scacquire)* hsa_signal_or_scacquire_fn; + decltype(hsa_signal_or_screlease)* hsa_signal_or_screlease_fn; + decltype(hsa_signal_or_scacq_screl)* hsa_signal_or_scacq_screl_fn; + decltype(hsa_signal_xor_relaxed)* hsa_signal_xor_relaxed_fn; + decltype(hsa_signal_xor_scacquire)* hsa_signal_xor_scacquire_fn; + decltype(hsa_signal_xor_screlease)* hsa_signal_xor_screlease_fn; + decltype(hsa_signal_xor_scacq_screl)* hsa_signal_xor_scacq_screl_fn; + decltype(hsa_signal_exchange_relaxed)* hsa_signal_exchange_relaxed_fn; + decltype(hsa_signal_exchange_scacquire)* hsa_signal_exchange_scacquire_fn; + decltype(hsa_signal_exchange_screlease)* hsa_signal_exchange_screlease_fn; + decltype(hsa_signal_exchange_scacq_screl)* hsa_signal_exchange_scacq_screl_fn; + decltype(hsa_signal_add_relaxed)* hsa_signal_add_relaxed_fn; + decltype(hsa_signal_add_scacquire)* hsa_signal_add_scacquire_fn; + decltype(hsa_signal_add_screlease)* hsa_signal_add_screlease_fn; + decltype(hsa_signal_add_scacq_screl)* hsa_signal_add_scacq_screl_fn; + decltype(hsa_signal_subtract_relaxed)* hsa_signal_subtract_relaxed_fn; + decltype(hsa_signal_subtract_scacquire)* hsa_signal_subtract_scacquire_fn; + decltype(hsa_signal_subtract_screlease)* hsa_signal_subtract_screlease_fn; + decltype(hsa_signal_subtract_scacq_screl)* hsa_signal_subtract_scacq_screl_fn; + decltype(hsa_signal_cas_relaxed)* hsa_signal_cas_relaxed_fn; + decltype(hsa_signal_cas_scacquire)* hsa_signal_cas_scacquire_fn; + decltype(hsa_signal_cas_screlease)* hsa_signal_cas_screlease_fn; + decltype(hsa_signal_cas_scacq_screl)* hsa_signal_cas_scacq_screl_fn; + + //===--- Instruction Set Architecture -----------------------------------===// + + decltype(hsa_isa_from_name)* hsa_isa_from_name_fn; + // Deprecated since v1.1. + decltype(hsa_isa_get_info)* hsa_isa_get_info_fn; + // Deprecated since v1.1. + decltype(hsa_isa_compatible)* hsa_isa_compatible_fn; + + //===--- Code Objects (deprecated) --------------------------------------===// + + // Deprecated since v1.1. + decltype(hsa_code_object_serialize)* hsa_code_object_serialize_fn; + // Deprecated since v1.1. + decltype(hsa_code_object_deserialize)* hsa_code_object_deserialize_fn; + // Deprecated since v1.1. + decltype(hsa_code_object_destroy)* hsa_code_object_destroy_fn; + // Deprecated since v1.1. + decltype(hsa_code_object_get_info)* hsa_code_object_get_info_fn; + // Deprecated since v1.1. + decltype(hsa_code_object_get_symbol)* hsa_code_object_get_symbol_fn; + // Deprecated since v1.1. + decltype(hsa_code_symbol_get_info)* hsa_code_symbol_get_info_fn; + // Deprecated since v1.1. + decltype(hsa_code_object_iterate_symbols)* hsa_code_object_iterate_symbols_fn; + + //===--- Executable -----------------------------------------------------===// + + // Deprecated since v1.1. + decltype(hsa_executable_create)* hsa_executable_create_fn; + decltype(hsa_executable_destroy)* hsa_executable_destroy_fn; + // Deprecated since v1.1. + decltype(hsa_executable_load_code_object)* hsa_executable_load_code_object_fn; + decltype(hsa_executable_freeze)* hsa_executable_freeze_fn; + decltype(hsa_executable_get_info)* hsa_executable_get_info_fn; + decltype(hsa_executable_global_variable_define)* + hsa_executable_global_variable_define_fn; + decltype(hsa_executable_agent_global_variable_define)* + hsa_executable_agent_global_variable_define_fn; + decltype(hsa_executable_readonly_variable_define)* + hsa_executable_readonly_variable_define_fn; + decltype(hsa_executable_validate)* hsa_executable_validate_fn; + // Deprecated since v1.1. + decltype(hsa_executable_get_symbol)* hsa_executable_get_symbol_fn; + decltype(hsa_executable_symbol_get_info)* hsa_executable_symbol_get_info_fn; + // Deprecated since v1.1. + decltype(hsa_executable_iterate_symbols)* hsa_executable_iterate_symbols_fn; + + //===--- Runtime Notifications ------------------------------------------===// + + decltype(hsa_status_string)* hsa_status_string_fn; + + // Start HSA v1.1 additions + decltype(hsa_extension_get_name)* hsa_extension_get_name_fn; + decltype(hsa_system_major_extension_supported)* hsa_system_major_extension_supported_fn; + decltype(hsa_system_get_major_extension_table)* hsa_system_get_major_extension_table_fn; + decltype(hsa_agent_major_extension_supported)* hsa_agent_major_extension_supported_fn; + decltype(hsa_cache_get_info)* hsa_cache_get_info_fn; + decltype(hsa_agent_iterate_caches)* hsa_agent_iterate_caches_fn; + decltype(hsa_signal_silent_store_relaxed)* hsa_signal_silent_store_relaxed_fn; + decltype(hsa_signal_silent_store_screlease)* hsa_signal_silent_store_screlease_fn; + decltype(hsa_signal_group_create)* hsa_signal_group_create_fn; + decltype(hsa_signal_group_destroy)* hsa_signal_group_destroy_fn; + decltype(hsa_signal_group_wait_any_scacquire)* hsa_signal_group_wait_any_scacquire_fn; + decltype(hsa_signal_group_wait_any_relaxed)* hsa_signal_group_wait_any_relaxed_fn; + + //===--- Instruction Set Architecture - HSA v1.1 additions --------------===// + + decltype(hsa_agent_iterate_isas)* hsa_agent_iterate_isas_fn; + decltype(hsa_isa_get_info_alt)* hsa_isa_get_info_alt_fn; + decltype(hsa_isa_get_exception_policies)* hsa_isa_get_exception_policies_fn; + decltype(hsa_isa_get_round_method)* hsa_isa_get_round_method_fn; + decltype(hsa_wavefront_get_info)* hsa_wavefront_get_info_fn; + decltype(hsa_isa_iterate_wavefronts)* hsa_isa_iterate_wavefronts_fn; + + //===--- Code Objects (deprecated) - HSA v1.1 additions -----------------===// + + // Deprecated since v1.1. + decltype(hsa_code_object_get_symbol_from_name)* + hsa_code_object_get_symbol_from_name_fn; + + //===--- Executable - HSA v1.1 additions --------------------------------===// + + decltype(hsa_code_object_reader_create_from_file)* + hsa_code_object_reader_create_from_file_fn; + decltype(hsa_code_object_reader_create_from_memory)* + hsa_code_object_reader_create_from_memory_fn; + decltype(hsa_code_object_reader_destroy)* hsa_code_object_reader_destroy_fn; + decltype(hsa_executable_create_alt)* hsa_executable_create_alt_fn; + decltype(hsa_executable_load_program_code_object)* + hsa_executable_load_program_code_object_fn; + decltype(hsa_executable_load_agent_code_object)* + hsa_executable_load_agent_code_object_fn; + decltype(hsa_executable_validate_alt)* hsa_executable_validate_alt_fn; + decltype(hsa_executable_get_symbol_by_name)* + hsa_executable_get_symbol_by_name_fn; + decltype(hsa_executable_iterate_agent_symbols)* + hsa_executable_iterate_agent_symbols_fn; + decltype(hsa_executable_iterate_program_symbols)* + hsa_executable_iterate_program_symbols_fn; +}; + +// Table to export HSA Apis from Core Runtime, Amd Extensions +// Finalizer and Images +struct HsaApiTable { + + // Version of Hsa Api Table + ApiTableVersion version; + + // Table of function pointers to HSA Core Runtime + CoreApiTable* core_; + + // Table of function pointers to AMD extensions + AmdExtTable* amd_ext_; + + // Table of function pointers to HSA Finalizer Extension + FinalizerExtTable* finalizer_ext_; + + // Table of function pointers to HSA Image Extension + ImageExtTable* image_ext_; + + // Table of function pointers for tools to use + ToolsApiTable* tools_; +}; + +// Structure containing instances of different api tables +struct HsaApiTableContainer { + HsaApiTable root; + CoreApiTable core; + AmdExtTable amd_ext; + FinalizerExtTable finalizer_ext; + ImageExtTable image_ext; + ToolsApiTable tools; + + // Default initialization of a container instance + HsaApiTableContainer() { + root.version.major_id = HSA_API_TABLE_MAJOR_VERSION; + root.version.minor_id = sizeof(HsaApiTable); + root.version.step_id = HSA_API_TABLE_STEP_VERSION; + + core.version.major_id = HSA_CORE_API_TABLE_MAJOR_VERSION; + core.version.minor_id = sizeof(CoreApiTable); + core.version.step_id = HSA_CORE_API_TABLE_STEP_VERSION; + root.core_ = &core; + + amd_ext.version.major_id = HSA_AMD_EXT_API_TABLE_MAJOR_VERSION; + amd_ext.version.minor_id = sizeof(AmdExtTable); + amd_ext.version.step_id = HSA_AMD_EXT_API_TABLE_STEP_VERSION; + root.amd_ext_ = &amd_ext; + + finalizer_ext.version.major_id = HSA_FINALIZER_API_TABLE_MAJOR_VERSION; + finalizer_ext.version.minor_id = sizeof(FinalizerExtTable); + finalizer_ext.version.step_id = HSA_FINALIZER_API_TABLE_STEP_VERSION; + root.finalizer_ext_ = &finalizer_ext; + + image_ext.version.major_id = HSA_IMAGE_API_TABLE_MAJOR_VERSION; + image_ext.version.minor_id = sizeof(ImageExtTable); + image_ext.version.step_id = HSA_IMAGE_API_TABLE_STEP_VERSION; + root.image_ext_ = &image_ext; + + tools.version.major_id = HSA_TOOLS_API_TABLE_MAJOR_VERSION; + tools.version.minor_id = sizeof(ToolsApiTable); + tools.version.step_id = HSA_TOOLS_API_TABLE_STEP_VERSION; + root.tools_ = &tools; + } +}; + +// Api to copy function pointers of a table +static +void inline copyApi(void* src, void* dest, size_t size) { + assert(size >= sizeof(ApiTableVersion)); + memcpy((char*)src + sizeof(ApiTableVersion), + (char*)dest + sizeof(ApiTableVersion), + (size - sizeof(ApiTableVersion))); +} + +// Copy Api child tables if valid. +static void inline copyElement(ApiTableVersion* dest, ApiTableVersion* src) { + if (src->major_id && (dest->major_id == src->major_id)) { + dest->step_id = src->step_id; + dest->minor_id = Min(dest->minor_id, src->minor_id); + copyApi(dest, src, dest->minor_id); + } else { + dest->major_id = 0; + dest->minor_id = 0; + dest->step_id = 0; + } +} + +// Copy constructor for all Api tables. The function assumes the +// user has initialized an instance of tables container correctly +// for the Major, Minor and Stepping Ids of Root and Child Api tables. +// The function will overwrite the value of Minor Id by taking the +// minimum of source and destination parameters. It will also overwrite +// the stepping Id with value from source parameter. +static void inline copyTables(const HsaApiTable* src, HsaApiTable* dest) { + // Verify Major Id of source and destination tables match + if (dest->version.major_id != src->version.major_id) { + dest->version.major_id = 0; + dest->version.minor_id = 0; + dest->version.step_id = 0; + return; + } + + // Initialize the stepping id and minor id of root table. For the + // minor id which encodes struct size, take the minimum of source + // and destination parameters + dest->version.step_id = src->version.step_id; + dest->version.minor_id = Min(dest->version.minor_id, src->version.minor_id); + + // Copy child tables if present + if ((offsetof(HsaApiTable, core_) < dest->version.minor_id)) + copyElement(&dest->core_->version, &src->core_->version); + if ((offsetof(HsaApiTable, amd_ext_) < dest->version.minor_id)) + copyElement(&dest->amd_ext_->version, &src->amd_ext_->version); + if ((offsetof(HsaApiTable, finalizer_ext_) < dest->version.minor_id)) + copyElement(&dest->finalizer_ext_->version, &src->finalizer_ext_->version); + if ((offsetof(HsaApiTable, image_ext_) < dest->version.minor_id)) + copyElement(&dest->image_ext_->version, &src->image_ext_->version); + if ((offsetof(HsaApiTable, tools_) < dest->version.minor_id)) + copyElement(&dest->tools_->version, &src->tools_->version); +} +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_amd.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_amd.h new file mode 100644 index 0000000000000000000000000000000000000000..187bcd958707e3434db4b144ebf1662504dff3cb --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_amd.h @@ -0,0 +1,3091 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +// HSA AMD extension. + +#ifndef HSA_RUNTIME_EXT_AMD_H_ +#define HSA_RUNTIME_EXT_AMD_H_ + +#include "hsa.h" +#include "hsa_ext_image.h" + +/* + * - 1.0 - initial version + * - 1.1 - dmabuf export + * - 1.2 - hsa_amd_memory_async_copy_on_engine + * - 1.3 - HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_EXTENDED_SCOPE_FINE_GRAINED pool + * - 1.4 - Virtual Memory API + */ +#define HSA_AMD_INTERFACE_VERSION_MAJOR 1 +#define HSA_AMD_INTERFACE_VERSION_MINOR 4 + +#ifdef __cplusplus +extern "C" { +#endif + +/** \addtogroup aql Architected Queuing Language + * @{ + */ + +/** + * @brief Macro to use to determine that a flag is set when querying flags within uint8_t[8] + * types + */ +static __inline__ __attribute__((always_inline)) bool hsa_flag_isset64(uint8_t* value, + uint32_t bit) { + unsigned int index = bit / 8; + unsigned int subBit = bit % 8; + return ((uint8_t*)value)[index] & (1 << subBit); +} + +/** + * @brief A fixed-size type used to represent ::hsa_signal_condition_t constants. + */ +typedef uint32_t hsa_signal_condition32_t; + +/** + * @brief AMD vendor specific packet type. + */ +typedef enum { + /** + * Packet used by agents to delay processing of subsequent packets until a + * configurable condition is satisfied by an HSA signal. Only kernel dispatch + * queues created from AMD GPU Agents support this packet. + */ + HSA_AMD_PACKET_TYPE_BARRIER_VALUE = 2, +} hsa_amd_packet_type_t; + +/** + * @brief A fixed-size type used to represent ::hsa_amd_packet_type_t constants. + */ +typedef uint8_t hsa_amd_packet_type8_t; + +/** + * @brief AMD vendor specific AQL packet header + */ +typedef struct hsa_amd_packet_header_s { + /** + * Packet header. Used to configure multiple packet parameters such as the + * packet type. The parameters are described by ::hsa_packet_header_t. + */ + uint16_t header; + + /** + *Format of the vendor specific packet. + */ + hsa_amd_packet_type8_t AmdFormat; + + /** + * Reserved. Must be 0. + */ + uint8_t reserved; +} hsa_amd_vendor_packet_header_t; + +/** + * @brief AMD barrier value packet. Halts packet processing and waits for + * (signal_value & ::mask) ::cond ::value to be satisfied, where signal_value + * is the value of the signal ::signal. + */ +typedef struct hsa_amd_barrier_value_packet_s { + /** + * AMD vendor specific packet header. + */ + hsa_amd_vendor_packet_header_t header; + + /** + * Reserved. Must be 0. + */ + uint32_t reserved0; + + /** + * Dependent signal object. A signal with a handle value of 0 is + * allowed and is interpreted by the packet processor a satisfied + * dependency. + */ + hsa_signal_t signal; + + /** + * Value to compare against. + */ + hsa_signal_value_t value; + + /** + * Bit mask to be combined by bitwise AND with ::signal's value. + */ + hsa_signal_value_t mask; + + /** + * Comparison operation. See ::hsa_signal_condition_t. + */ + hsa_signal_condition32_t cond; + + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; + + /** + * Reserved. Must be 0. + */ + uint64_t reserved2; + + /** + * Reserved. Must be 0. + */ + uint64_t reserved3; + + /** + * Signal used to indicate completion of the job. The application can use the + * special signal handle 0 to indicate that no signal is used. + */ + hsa_signal_t completion_signal; +} hsa_amd_barrier_value_packet_t; + +/** @} */ + +/** + * @brief Enumeration constants added to ::hsa_status_t. + * + * @remark Additions to hsa_status_t + */ +enum { + /** + * The memory pool is invalid. + */ + HSA_STATUS_ERROR_INVALID_MEMORY_POOL = 40, + + /** + * Agent accessed memory beyond the maximum legal address. + */ + HSA_STATUS_ERROR_MEMORY_APERTURE_VIOLATION = 41, + + /** + * Agent executed an invalid shader instruction. + */ + HSA_STATUS_ERROR_ILLEGAL_INSTRUCTION = 42, + + /** + * Agent attempted to access an inaccessible address. + * See hsa_amd_register_system_event_handler and + * HSA_AMD_GPU_MEMORY_FAULT_EVENT for more information on illegal accesses. + */ + HSA_STATUS_ERROR_MEMORY_FAULT = 43, + + /** + * The CU mask was successfully set but the mask attempted to enable a CU + * which was disabled for the process. CUs disabled for the process remain + * disabled. + */ + HSA_STATUS_CU_MASK_REDUCED = 44, + + /** + * Exceeded number of VGPRs available on this agent + */ + HSA_STATUS_ERROR_OUT_OF_REGISTERS = 45, +}; + +/** + * @brief IOMMU version supported + */ +typedef enum { + /** + * IOMMU not supported + */ + HSA_IOMMU_SUPPORT_NONE = 0, + /* IOMMU V1 support is not relevant to user applications, so not reporting it */ + /** + * IOMMU V2 supported + */ + HSA_IOMMU_SUPPORT_V2 = 1, +} hsa_amd_iommu_version_t; + +/** + * @brief Agent attributes. + */ +typedef enum hsa_amd_agent_info_s { + /** + * Chip identifier. The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_CHIP_ID = 0xA000, + /** + * Size of a cacheline in bytes. The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_CACHELINE_SIZE = 0xA001, + /** + * The number of compute unit available in the agent. The type of this + * attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_COMPUTE_UNIT_COUNT = 0xA002, + /** + * The maximum clock frequency of the agent in MHz. The type of this + * attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_MAX_CLOCK_FREQUENCY = 0xA003, + /** + * Internal driver node identifier. The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_DRIVER_NODE_ID = 0xA004, + /** + * Max number of watch points on memory address ranges to generate exception + * events when the watched addresses are accessed. The type of this + * attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_MAX_ADDRESS_WATCH_POINTS = 0xA005, + /** + * Agent BDF_ID, named LocationID in thunk. The type of this attribute is + * uint32_t. + */ + HSA_AMD_AGENT_INFO_BDFID = 0xA006, + /** + * Memory Interface width, the return value type is uint32_t. + * This attribute is deprecated. + */ + HSA_AMD_AGENT_INFO_MEMORY_WIDTH = 0xA007, + /** + * Max Memory Clock, the return value type is uint32_t. + */ + HSA_AMD_AGENT_INFO_MEMORY_MAX_FREQUENCY = 0xA008, + /** + * Board name of Agent - populated from MarketingName of Kfd Node + * The value is an Ascii string of 64 chars. + */ + HSA_AMD_AGENT_INFO_PRODUCT_NAME = 0xA009, + /** + * Maximum number of waves possible in a Compute Unit. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_MAX_WAVES_PER_CU = 0xA00A, + /** + * Number of SIMD's per compute unit CU + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_SIMDS_PER_CU = 0xA00B, + /** + * Number of Shader Engines (SE) in Gpu + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_SHADER_ENGINES = 0xA00C, + /** + * Number of Shader Arrays Per Shader Engines in Gpu + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_SHADER_ARRAYS_PER_SE = 0xA00D, + /** + * Address of the HDP flush registers. Use of these registers does not conform to the HSA memory + * model and should be treated with caution. + * The type of this attribute is hsa_amd_hdp_flush_t. + */ + HSA_AMD_AGENT_INFO_HDP_FLUSH = 0xA00E, + /** + * PCIe domain for the agent. Pairs with HSA_AMD_AGENT_INFO_BDFID + * to give the full physical location of the Agent. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_DOMAIN = 0xA00F, + /** + * Queries for support of cooperative queues. See ::HSA_QUEUE_TYPE_COOPERATIVE. + * The type of this attribute is bool. + */ + HSA_AMD_AGENT_INFO_COOPERATIVE_QUEUES = 0xA010, + /** + * Queries UUID of an agent. The value is an Ascii string with a maximum + * of 21 chars including NUL. The string value consists of two parts: header + * and body. The header identifies device type (GPU, CPU, DSP) while body + * encodes UUID as a 16 digit hex string + * + * Agents that do not support UUID will return the string "GPU-XX" or + * "CPU-XX" or "DSP-XX" depending upon their device type ::hsa_device_type_t + */ + HSA_AMD_AGENT_INFO_UUID = 0xA011, + /** + * Queries for the ASIC revision of an agent. The value is an integer that + * increments for each revision. This can be used by user-level software to + * change how it operates, depending on the hardware version. This allows + * selective workarounds for hardware errata. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_ASIC_REVISION = 0xA012, + /** + * Queries whether or not the host can directly access SVM memory that is + * physically resident in the agent's local memory. + * The type of this attribute is bool. + */ + HSA_AMD_AGENT_INFO_SVM_DIRECT_HOST_ACCESS = 0xA013, + /** + * Some processors support more CUs than can reliably be used in a cooperative + * dispatch. This queries the count of CUs which are fully enabled for + * cooperative dispatch. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_COOPERATIVE_COMPUTE_UNIT_COUNT = 0xA014, + /** + * Queries the amount of memory available in bytes accross all global pools + * owned by the agent. + * The type of this attribute is uint64_t. + */ + HSA_AMD_AGENT_INFO_MEMORY_AVAIL = 0xA015, + /** + * Timestamp value increase rate, in Hz. The timestamp (clock) frequency is + * in the range 1-400MHz. + * The type of this attribute is uint64_t. + */ + HSA_AMD_AGENT_INFO_TIMESTAMP_FREQUENCY = 0xA016, + /** + * Queries for the ASIC family ID of an agent. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_ASIC_FAMILY_ID = 0xA107, + /** + * Queries for the Packet Processor(CP Firmware) ucode version of an agent. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_UCODE_VERSION = 0xA108, + /** + * Queries for the SDMA engine ucode of an agent. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_SDMA_UCODE_VERSION = 0xA109, + /** + * Queries the number of SDMA engines. + * If HSA_AMD_AGENT_INFO_NUM_SDMA_XGMI_ENG query returns non-zero, + * this query returns the the number of SDMA engines optimized for + * host to device bidirectional traffic. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_SDMA_ENG = 0xA10A, + /** + * Queries the number of additional SDMA engines optimized for D2D xGMI copies. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_SDMA_XGMI_ENG = 0xA10B, + /** + * Queries for version of IOMMU supported by agent. + * The type of this attribute is hsa_amd_iommu_version_t. + */ + HSA_AMD_AGENT_INFO_IOMMU_SUPPORT = 0xA110, + /** + * Queries for number of XCCs within the agent. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_NUM_XCC = 0xA111, + /** + * Queries for driver unique identifier. + * The type of this attribute is uint32_t. + */ + HSA_AMD_AGENT_INFO_DRIVER_UID = 0xA112, + /** + * Returns the hsa_agent_t of the nearest CPU agent + * The type of this attribute is hsa_agent_t. + */ + HSA_AMD_AGENT_INFO_NEAREST_CPU = 0xA113, + /** + * Bit-mask indicating memory properties of this agent. A memory property is set if the flag bit + * is set at that position. User may use the hsa_flag_isset64 macro to verify whether a flag + * is set. The type of this attribute is uint8_t[8]. + */ + HSA_AMD_AGENT_INFO_MEMORY_PROPERTIES = 0xA114, + /** + * Bit-mask indicating AQL Extensions supported by this agent. An AQL extension is set if the flag + * bit is set at that position. User may use the hsa_flag_isset64 macro to verify whether a flag + * is set. The type of this attribute is uint8_t[8]. + */ + HSA_AMD_AGENT_INFO_AQL_EXTENSIONS = 0xA115 /* Not implemented yet */ +} hsa_amd_agent_info_t; + +/** + * @brief Agent memory properties attributes + */ +typedef enum hsa_amd_agent_memory_properties_s { + HSA_AMD_MEMORY_PROPERTY_AGENT_IS_APU = (1 << 0), +} hsa_amd_agent_memory_properties_t; + +/** + * @brief SDMA engine IDs unique by single set bit position. + */ +typedef enum hsa_amd_sdma_engine_id { + HSA_AMD_SDMA_ENGINE_0 = 0x1, + HSA_AMD_SDMA_ENGINE_1 = 0x2, + HSA_AMD_SDMA_ENGINE_2 = 0x4, + HSA_AMD_SDMA_ENGINE_3 = 0x8, + HSA_AMD_SDMA_ENGINE_4 = 0x10, + HSA_AMD_SDMA_ENGINE_5 = 0x20, + HSA_AMD_SDMA_ENGINE_6 = 0x40, + HSA_AMD_SDMA_ENGINE_7 = 0x80, + HSA_AMD_SDMA_ENGINE_8 = 0x100, + HSA_AMD_SDMA_ENGINE_9 = 0x200, + HSA_AMD_SDMA_ENGINE_10 = 0x400, + HSA_AMD_SDMA_ENGINE_11 = 0x800, + HSA_AMD_SDMA_ENGINE_12 = 0x1000, + HSA_AMD_SDMA_ENGINE_13 = 0x2000, + HSA_AMD_SDMA_ENGINE_14 = 0x4000, + HSA_AMD_SDMA_ENGINE_15 = 0x8000 +} hsa_amd_sdma_engine_id_t; + +typedef struct hsa_amd_hdp_flush_s { + uint32_t* HDP_MEM_FLUSH_CNTL; + uint32_t* HDP_REG_FLUSH_CNTL; +} hsa_amd_hdp_flush_t; + +/** + * @brief Region attributes. + */ +typedef enum hsa_amd_region_info_s { + /** + * Determine if host can access the region. The type of this attribute + * is bool. + */ + HSA_AMD_REGION_INFO_HOST_ACCESSIBLE = 0xA000, + /** + * Base address of the region in flat address space. + */ + HSA_AMD_REGION_INFO_BASE = 0xA001, + /** + * Memory Interface width, the return value type is uint32_t. + * This attribute is deprecated. Use HSA_AMD_AGENT_INFO_MEMORY_WIDTH. + */ + HSA_AMD_REGION_INFO_BUS_WIDTH = 0xA002, + /** + * Max Memory Clock, the return value type is uint32_t. + * This attribute is deprecated. Use HSA_AMD_AGENT_INFO_MEMORY_MAX_FREQUENCY. + */ + HSA_AMD_REGION_INFO_MAX_CLOCK_FREQUENCY = 0xA003, +} hsa_amd_region_info_t; + +/** + * @brief Coherency attributes of fine grain region. + */ +typedef enum hsa_amd_coherency_type_s { + /** + * Coherent region. + */ + HSA_AMD_COHERENCY_TYPE_COHERENT = 0, + /** + * Non coherent region. + */ + HSA_AMD_COHERENCY_TYPE_NONCOHERENT = 1 +} hsa_amd_coherency_type_t; + +/** + * @brief Get the coherency type of the fine grain region of an agent. + * + * @param[in] agent A valid agent. + * + * @param[out] type Pointer to a memory location where the HSA runtime will + * store the coherency type of the fine grain region. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p type is NULL. + */ +hsa_status_t HSA_API hsa_amd_coherency_get_type(hsa_agent_t agent, + hsa_amd_coherency_type_t* type); + +/** + * @brief Set the coherency type of the fine grain region of an agent. + * Deprecated. This is supported on KV platforms. For backward compatibility + * other platforms will spuriously succeed. + * + * @param[in] agent A valid agent. + * + * @param[in] type The coherency type to be set. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p type is invalid. + */ +hsa_status_t HSA_API hsa_amd_coherency_set_type(hsa_agent_t agent, + hsa_amd_coherency_type_t type); + +/** + * @brief Structure containing profiling dispatch time information. + * + * Times are reported as ticks in the domain of the HSA system clock. + * The HSA system clock tick and frequency is obtained via hsa_system_get_info. + */ +typedef struct hsa_amd_profiling_dispatch_time_s { + /** + * Dispatch packet processing start time. + */ + uint64_t start; + /** + * Dispatch packet completion time. + */ + uint64_t end; +} hsa_amd_profiling_dispatch_time_t; + +/** + * @brief Structure containing profiling async copy time information. + * + * Times are reported as ticks in the domain of the HSA system clock. + * The HSA system clock tick and frequency is obtained via hsa_system_get_info. + */ +typedef struct hsa_amd_profiling_async_copy_time_s { + /** + * Async copy processing start time. + */ + uint64_t start; + /** + * Async copy completion time. + */ + uint64_t end; +} hsa_amd_profiling_async_copy_time_t; + +/** + * @brief Enable or disable profiling capability of a queue. + * + * @param[in] queue A valid queue. + * + * @param[in] enable 1 to enable profiling. 0 to disable profiling. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE The queue is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p queue is NULL. + */ +hsa_status_t HSA_API + hsa_amd_profiling_set_profiler_enabled(hsa_queue_t* queue, int enable); + +/** + * @brief Enable or disable asynchronous memory copy profiling. + * + * @details The runtime will provide the copy processing start timestamp and + * completion timestamp of each call to hsa_amd_memory_async_copy if the + * async copy profiling is enabled prior to the call to + * hsa_amd_memory_async_copy. The completion signal object is used to + * hold the last async copy start and end timestamp. The client can retrieve + * these timestamps via call to hsa_amd_profiling_get_async_copy_time. + * + * @param[in] enable True to enable profiling. False to disable profiling. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Failed on allocating resources + * needed to profile the asynchronous copy. + */ +hsa_status_t HSA_API + hsa_amd_profiling_async_copy_enable(bool enable); + +/** + * @brief Retrieve packet processing time stamps. + * + * @param[in] agent The agent with which the signal was last used. For + * instance, if the profiled dispatch packet is dispatched onto queue Q, + * which was created on agent A, then this parameter must be A. + * + * @param[in] signal A signal used as the completion signal of the dispatch + * packet to retrieve time stamps from. This dispatch packet must have been + * issued to a queue with profiling enabled and have already completed. Also + * the signal must not have yet been used in any other packet following the + * completion of the profiled dispatch packet. + * + * @param[out] time Packet processing timestamps in the HSA system clock + * domain. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL The signal is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p time is NULL. + */ +hsa_status_t HSA_API hsa_amd_profiling_get_dispatch_time( + hsa_agent_t agent, hsa_signal_t signal, + hsa_amd_profiling_dispatch_time_t* time); + +/** + * @brief Retrieve asynchronous copy timestamps. + * + * @details Async copy profiling is enabled via call to + * hsa_amd_profiling_async_copy_enable. + * + * @param[in] signal A signal used as the completion signal of the call to + * hsa_amd_memory_async_copy. + * + * @param[out] time Async copy processing timestamps in the HSA system clock + * domain. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL The signal is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p time is NULL. + */ +hsa_status_t HSA_API hsa_amd_profiling_get_async_copy_time( + hsa_signal_t signal, hsa_amd_profiling_async_copy_time_t* time); + +/** + * @brief Computes the frequency ratio and offset between the agent clock and + * HSA system clock and converts the agent's tick to HSA system domain tick. + * + * @param[in] agent The agent used to retrieve the agent_tick. It is user's + * responsibility to make sure the tick number is from this agent, otherwise, + * the behavior is undefined. + * + * @param[in] agent_tick The tick count retrieved from the specified @p agent. + * + * @param[out] system_tick The translated HSA system domain clock counter tick. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p system_tick is NULL; + */ +hsa_status_t HSA_API + hsa_amd_profiling_convert_tick_to_system_domain(hsa_agent_t agent, + uint64_t agent_tick, + uint64_t* system_tick); + +/** + * @brief Signal attribute flags. + */ +typedef enum { + /** + * Signal will only be consumed by AMD GPUs. Limits signal consumption to + * AMD GPU agents only. Ignored if @p num_consumers is not zero (all agents). + */ + HSA_AMD_SIGNAL_AMD_GPU_ONLY = 1, + /** + * Signal may be used for interprocess communication. + * IPC signals can be read, written, and waited on from any process. + * Profiling using an IPC enabled signal is only supported in a single process + * at a time. Producing profiling data in one process and consuming it in + * another process is undefined. + */ + HSA_AMD_SIGNAL_IPC = 2, +} hsa_amd_signal_attribute_t; + +/** + * @brief Create a signal with specific attributes. + * + * @param[in] initial_value Initial value of the signal. + * + * @param[in] num_consumers Size of @p consumers. A value of 0 indicates that + * any agent might wait on the signal. + * + * @param[in] consumers List of agents that might consume (wait on) the + * signal. If @p num_consumers is 0, this argument is ignored; otherwise, the + * HSA runtime might use the list to optimize the handling of the signal + * object. If an agent not listed in @p consumers waits on the returned + * signal, the behavior is undefined. The memory associated with @p consumers + * can be reused or freed after the function returns. + * + * @param[in] attributes Requested signal attributes. Multiple signal attributes + * may be requested by combining them with bitwise OR. Requesting no attributes + * (@p attributes == 0) results in the same signal as would have been obtained + * via hsa_signal_create. + * + * @param[out] signal Pointer to a memory location where the HSA runtime will + * store the newly created signal handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p signal is NULL, @p + * num_consumers is greater than 0 but @p consumers is NULL, or @p consumers + * contains duplicates. + */ +hsa_status_t HSA_API hsa_amd_signal_create(hsa_signal_value_t initial_value, uint32_t num_consumers, + const hsa_agent_t* consumers, uint64_t attributes, + hsa_signal_t* signal); + +/** + * @brief Returns a pointer to the value of a signal. + * + * Use of this API does not modify the lifetime of ::signal and any + * hsa_signal_value_t retrieved by this API has lifetime equal to that of + * ::signal. + * + * This API is intended for partial interoperability with non-HSA compatible + * devices and should not be used where HSA interfaces are available. + * + * Use of the signal value must comply with use restritions of ::signal. + * Use may result in data races if the operations performed are not platform + * atomic. Use with HSA_AMD_SIGNAL_AMD_GPU_ONLY or HSA_AMD_SIGNAL_IPC + * attributed signals is required. + * + * @param[in] Signal handle to extract the signal value pointer from. + * + * @param[out] Location where the extracted signal value pointer will be placed. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL signal is not a valid hsa_signal_t + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT value_ptr is NULL. + */ +hsa_status_t hsa_amd_signal_value_pointer(hsa_signal_t signal, + volatile hsa_signal_value_t** value_ptr); + +/** + * @brief Asyncronous signal handler function type. + * + * @details Type definition of callback function to be used with + * hsa_amd_signal_async_handler. This callback is invoked if the associated + * signal and condition are met. The callback receives the value of the signal + * which satisfied the associated wait condition and a user provided value. If + * the callback returns true then the callback will be called again if the + * associated signal and condition are satisfied again. If the callback returns + * false then it will not be called again. + * + * @param[in] value Contains the value of the signal observed by + * hsa_amd_signal_async_handler which caused the signal handler to be invoked. + * + * @param[in] arg Contains the user provided value given when the signal handler + * was registered with hsa_amd_signal_async_handler + * + * @retval true resumes monitoring the signal with this handler (as if calling + * hsa_amd_signal_async_handler again with identical parameters) + * + * @retval false stops monitoring the signal with this handler (handler will + * not be called again for this signal) + * + */ +typedef bool (*hsa_amd_signal_handler)(hsa_signal_value_t value, void* arg); + +/** + * @brief Register asynchronous signal handler function. + * + * @details Allows registering a callback function and user provided value with + * a signal and wait condition. The callback will be invoked if the associated + * signal and wait condition are satisfied. Callbacks will be invoked serially + * but in an arbitrary order so callbacks should be independent of each other. + * After being invoked a callback may continue to wait for its associated signal + * and condition and, possibly, be invoked again. Or the callback may stop + * waiting. If the callback returns true then it will continue waiting and may + * be called again. If false then the callback will not wait again and will not + * be called again for the associated signal and condition. It is possible to + * register the same callback multiple times with the same or different signals + * and/or conditions. Each registration of the callback will be treated entirely + * independently. + * + * @param[in] signal hsa signal to be asynchronously monitored + * + * @param[in] cond condition value to monitor for + * + * @param[in] value signal value used in condition expression + * + * @param[in] handler asynchronous signal handler invoked when signal's + * condition is met + * + * @param[in] arg user provided value which is provided to handler when handler + * is invoked + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL signal is not a valid hsa_signal_t + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT handler is invalid (NULL) + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime is out of + * resources or blocking signals are not supported by the HSA driver component. + * + */ +hsa_status_t HSA_API + hsa_amd_signal_async_handler(hsa_signal_t signal, + hsa_signal_condition_t cond, + hsa_signal_value_t value, + hsa_amd_signal_handler handler, void* arg); + +/** + * @brief Call a function asynchronously + * + * @details Provides access to the runtime's asynchronous event handling thread + * for general asynchronous functions. Functions queued this way are executed + * in the same manner as if they were a signal handler who's signal is + * satisfied. + * + * @param[in] callback asynchronous function to be invoked + * + * @param[in] arg user provided value which is provided to handler when handler + * is invoked + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT handler is invalid (NULL) + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime is out of + * resources or blocking signals are not supported by the HSA driver component. + * + */ +hsa_status_t HSA_API + hsa_amd_async_function(void (*callback)(void* arg), void* arg); + +/** + * @brief Wait for any signal-condition pair to be satisfied. + * + * @details Allows waiting for any of several signal and conditions pairs to be + * satisfied. The function returns the index into the list of signals of the + * first satisfying signal-condition pair. The value of the satisfying signal's + * value is returned in satisfying_value unless satisfying_value is NULL. This + * function provides only relaxed memory semantics. + */ +uint32_t HSA_API + hsa_amd_signal_wait_any(uint32_t signal_count, hsa_signal_t* signals, + hsa_signal_condition_t* conds, + hsa_signal_value_t* values, uint64_t timeout_hint, + hsa_wait_state_t wait_hint, + hsa_signal_value_t* satisfying_value); + +/** + * @brief Query image limits. + * + * @param[in] agent A valid agent. + * + * @param[in] attribute HSA image info attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE @p value is NULL or @p attribute < + * HSA_EXT_AGENT_INFO_IMAGE_1D_MAX_ELEMENTS or @p attribute > + * HSA_EXT_AGENT_INFO_IMAGE_ARRAY_MAX_LAYERS. + * + */ +hsa_status_t HSA_API hsa_amd_image_get_info_max_dim(hsa_agent_t agent, + hsa_agent_info_t attribute, + void* value); + +/** + * @brief Set a queue's CU affinity mask. + * + * @details Enables the queue to run on only selected CUs. The given mask is + * combined by bitwise AND with any device wide mask in HSA_CU_MASK before + * being applied. + * If num_cu_mask_count is 0 then the request is interpreted as a request to + * enable all CUs and no cu_mask array need be given. + * + * @param[in] queue A pointer to HSA queue. + * + * @param[in] num_cu_mask_count Size of CUMask bit array passed in, in bits. + * + * @param[in] cu_mask Bit-vector representing the CU mask. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_CU_MASK_REDUCED The function was successfully executed + * but the given mask attempted to enable a CU which was disabled by + * HSA_CU_MASK. CUs disabled by HSA_CU_MASK remain disabled. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE @p queue is NULL or invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p num_cu_mask_count is not + * a multiple of 32 or @p num_cu_mask_count is not 0 and cu_mask is NULL. + * Devices with work group processors must even-index contiguous pairwise + * CU enable e.g. 0x33(b'110011) is valid while 0x5(0x101) and 0x6(b'0110) + * are invalid. + * + */ +hsa_status_t HSA_API hsa_amd_queue_cu_set_mask(const hsa_queue_t* queue, + uint32_t num_cu_mask_count, + const uint32_t* cu_mask); + +/** + * @brief Retrieve a queue's CU affinity mask. + * + * @details Returns the first num_cu_mask_count bits of a queue's CU mask. + * Ensure that num_cu_mask_count is at least as large as + * HSA_AMD_AGENT_INFO_COMPUTE_UNIT_COUNT to retrieve the entire mask. + * + * @param[in] queue A pointer to HSA queue. + * + * @param[in] num_cu_mask_count Size of CUMask bit array passed in, in bits. + * + * @param[out] cu_mask Bit-vector representing the CU mask. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_QUEUE @p queue is NULL or invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p num_cu_mask_count is 0, not + * a multiple of 32 or @p cu_mask is NULL. + * + */ +hsa_status_t HSA_API hsa_amd_queue_cu_get_mask(const hsa_queue_t* queue, uint32_t num_cu_mask_count, + uint32_t* cu_mask); + +/** + * @brief Memory segments associated with a memory pool. + */ +typedef enum { + /** + * Global segment. Used to hold data that is shared by all agents. + */ + HSA_AMD_SEGMENT_GLOBAL = 0, + /** + * Read-only segment. Used to hold data that remains constant during the + * execution of a kernel. + */ + HSA_AMD_SEGMENT_READONLY = 1, + /** + * Private segment. Used to hold data that is local to a single work-item. + */ + HSA_AMD_SEGMENT_PRIVATE = 2, + /** + * Group segment. Used to hold data that is shared by the work-items of a + * work-group. + */ + HSA_AMD_SEGMENT_GROUP = 3, +} hsa_amd_segment_t; + +/** + * @brief A memory pool encapsulates physical storage on an agent + * along with a memory access model. + * + * @details A memory pool encapsulates a physical partition of an agent's + * memory system along with a memory access model. Division of a single + * memory system into separate pools allows querying each partition's access + * path properties (see ::hsa_amd_agent_memory_pool_get_info). Allocations + * from a pool are preferentially bound to that pool's physical partition. + * Binding to the pool's preferential physical partition may not be + * possible or persistent depending on the system's memory policy + * and/or state which is beyond the scope of HSA APIs. + * + * For example, a multi-node NUMA memory system may be represented by multiple + * pool's with each pool providing size and access path information for the + * partition it represents. Allocations from a pool are preferentially bound + * to the pool's partition (which in this example is a NUMA node) while + * following its memory access model. The actual placement may vary or migrate + * due to the system's NUMA policy and state, which is beyond the scope of + * HSA APIs. + */ +typedef struct hsa_amd_memory_pool_s { + /** + * Opaque handle. + */ + uint64_t handle; +} hsa_amd_memory_pool_t; + +typedef enum hsa_amd_memory_pool_global_flag_s { + /** + * The application can use allocations in the memory pool to store kernel + * arguments, and provide the values for the kernarg segment of + * a kernel dispatch. + */ + HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_KERNARG_INIT = 1, + /** + * Updates to memory in this pool conform to HSA memory consistency model. + * If this flag is set, then ::HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_COARSE_GRAINED + * must not be set. + */ + HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_FINE_GRAINED = 2, + /** + * Writes to memory in this pool can be performed by a single agent at a time. + */ + HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_COARSE_GRAINED = 4, + + /** Updates to memory in this memory pool have extended scope, acting as + * system-scope atomics for variables in memory regions of this type. + * Note: On non-compliant systems, device-specific actions may be required + * for system-scope coherence. */ + HSA_AMD_MEMORY_POOL_GLOBAL_FLAG_EXTENDED_SCOPE_FINE_GRAINED = 8, + +} hsa_amd_memory_pool_global_flag_t; + +typedef enum hsa_amd_memory_pool_location_s { + /** + * This memory pool resides on the host (CPU) + */ + HSA_AMD_MEMORY_POOL_LOCATION_CPU = 0, + /** + * This memory pool resides on a GPU + */ + HSA_AMD_MEMORY_POOL_LOCATION_GPU = 1 +} hsa_amd_memory_pool_location_t; + +/** + * @brief Memory pool features. + */ +typedef enum { + /** + * Segment where the memory pool resides. The type of this attribute is + * ::hsa_amd_segment_t. + */ + HSA_AMD_MEMORY_POOL_INFO_SEGMENT = 0, + /** + * Flag mask. The value of this attribute is undefined if the value of + * ::HSA_AMD_MEMORY_POOL_INFO_SEGMENT is not ::HSA_AMD_SEGMENT_GLOBAL. The type + * of + * this attribute is uint32_t, a bit-field of + * ::hsa_amd_memory_pool_global_flag_t + * values. + */ + HSA_AMD_MEMORY_POOL_INFO_GLOBAL_FLAGS = 1, + /** + * Size of this pool, in bytes. The type of this attribute is size_t. + */ + HSA_AMD_MEMORY_POOL_INFO_SIZE = 2, + /** + * Indicates whether memory in this pool can be allocated using + * ::hsa_amd_memory_pool_allocate. The type of this attribute is bool. + * + * The value of this flag is always false for memory pools in the group and + * private segments. + */ + HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALLOWED = 5, + /** + * Allocation granularity of buffers allocated by + * ::hsa_amd_memory_pool_allocate + * in this memory pool. The size of a buffer allocated in this pool is a + * multiple of the value of this attribute. While this is the minimum size of + * allocation allowed, it is recommened to use + * HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_REC_GRANULE to obtain the recommended + * allocation granularity size for this pool. + * The value of this attribute is only defined if + * ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALLOWED is true for + * this pool. The type of this attribute is size_t. + */ + HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_GRANULE = 6, + /** + * Alignment of buffers allocated by ::hsa_amd_memory_pool_allocate in this + * pool. The value of this attribute is only defined if + * ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALLOWED is true for this pool, and + * must be a power of 2. The type of this attribute is size_t. + */ + HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALIGNMENT = 7, + /** + * This memory_pool can be made directly accessible by all the agents in the + * system (::hsa_amd_agent_memory_pool_get_info does not return + * ::HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED for any agent). The type of this + * attribute is bool. + */ + HSA_AMD_MEMORY_POOL_INFO_ACCESSIBLE_BY_ALL = 15, + /** + * Maximum aggregate allocation size in bytes. The type of this attribute + * is size_t. + */ + HSA_AMD_MEMORY_POOL_INFO_ALLOC_MAX_SIZE = 16, + /** + * Location of this memory pool. The type of this attribute + * is hsa_amd_memory_pool_location_t. + */ + HSA_AMD_MEMORY_POOL_INFO_LOCATION = 17, + /** + * Internal block size for allocations. This would also be the recommended + * granularity size for allocations as this prevents internal fragmentation. + * The value of this attribute is only defined if + * ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALLOWED is true for this pool. + * The size of this attribute is size_t. + */ + HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_REC_GRANULE = 18, +} hsa_amd_memory_pool_info_t; + +/** + * @brief Memory pool flag used to specify allocation directives + * + */ +typedef enum hsa_amd_memory_pool_flag_s { + /** + * Allocates memory that conforms to standard HSA memory consistency model + */ + HSA_AMD_MEMORY_POOL_STANDARD_FLAG = 0, + /** + * Allocates fine grain memory type where memory ordering is per point to point + * connection. Atomic memory operations on these memory buffers are not + * guaranteed to be visible at system scope. + */ + HSA_AMD_MEMORY_POOL_PCIE_FLAG = 1, + +} hsa_amd_memory_pool_flag_t; + +/** + * @brief Get the current value of an attribute of a memory pool. + * + * @param[in] memory_pool A valid memory pool. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to a application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + */ +hsa_status_t HSA_API + hsa_amd_memory_pool_get_info(hsa_amd_memory_pool_t memory_pool, + hsa_amd_memory_pool_info_t attribute, + void* value); + +/** + * @brief Iterate over the memory pools associated with a given agent, and + * invoke an application-defined callback on every iteration. + * + * @details An agent can directly access buffers located in some memory pool, or + * be enabled to access them by the application (see ::hsa_amd_agents_allow_access), + * yet that memory pool may not be returned by this function for that given + * agent. + * + * A memory pool of fine-grained type must be associated only with the host. + * + * @param[in] agent A valid agent. + * + * @param[in] callback Callback to be invoked on the same thread that called + * ::hsa_amd_agent_iterate_memory_pools, serially, once per memory pool that is + * associated with the agent. The HSA runtime passes two arguments to the + * callback: the memory pool, and the application data. If @p callback + * returns a status other than ::HSA_STATUS_SUCCESS for a particular iteration, + * the traversal stops and ::hsa_amd_agent_iterate_memory_pools returns that status + * value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_amd_agent_iterate_memory_pools( + hsa_agent_t agent, + hsa_status_t (*callback)(hsa_amd_memory_pool_t memory_pool, void* data), + void* data); + +/** + * @brief Allocate a block of memory (or buffer) in the specified pool. + * + * @param[in] memory_pool Memory pool where to allocate memory from. The memory + * pool must have the ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALLOWED flag set. + * + * @param[in] size Allocation size, in bytes. Must not be zero. This value is + * rounded up to the nearest multiple of + * ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_GRANULE in @p memory_pool. + * + * @param[in] flags A bit-field that is used to specify allocation + * directives. + * + * @param[out] ptr Pointer to the location where to store the base virtual + * address of + * the allocated block. The returned base address is aligned to the value of + * ::HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_ALIGNMENT in @p memory_pool. If the + * allocation fails, the returned value is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES No memory is available. + * + * @retval ::HSA_STATUS_ERROR_INVALID_MEMORY_POOL The memory pool is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION The host is not allowed to + * allocate memory in @p memory_pool, or @p size is greater than + * the value of HSA_AMD_MEMORY_POOL_INFO_ALLOC_MAX_SIZE in @p memory_pool. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr is NULL, or @p size is 0, + * or flags is not 0. + * + */ +hsa_status_t HSA_API + hsa_amd_memory_pool_allocate(hsa_amd_memory_pool_t memory_pool, size_t size, + uint32_t flags, void** ptr); + +/** + * @brief Deallocate a block of memory previously allocated using + * ::hsa_amd_memory_pool_allocate. + * + * @param[in] ptr Pointer to a memory block. If @p ptr does not match a value + * previously returned by ::hsa_amd_memory_pool_allocate, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + */ +hsa_status_t HSA_API hsa_amd_memory_pool_free(void* ptr); + +/** + * @brief Asynchronously copy a block of memory from the location pointed to by + * @p src on the @p src_agent to the memory block pointed to by @p dst on the @p + * dst_agent. + * Because the DMA engines used may not be in the same coherency domain, the caller must ensure + * that buffers are system-level coherent. In general this requires the sending device to have + * released the buffer to system scope prior to executing the copy API and the receiving device + * must execute a system scope acquire fence prior to use of the destination buffer. + * + * @param[out] dst Buffer where the content is to be copied. + * + * @param[in] dst_agent Agent associated with the @p dst. The agent must be able to directly + * access both the source and destination buffers in their current locations. + * May be zero in which case the runtime will attempt to discover the destination agent. + * Discovery may have variable and/or high latency. + * + * @param[in] src A valid pointer to the source of data to be copied. The source + * buffer must not overlap with the destination buffer, otherwise the copy will succeed + * but contents of @p dst is undefined. + * + * @param[in] src_agent Agent associated with the @p src. The agent must be able to directly + * access both the source and destination buffers in their current locations. + * May be zero in which case the runtime will attempt to discover the destination agent. + * Discovery may have variable and/or high latency. + * + * @param[in] size Number of bytes to copy. If @p size is 0, no copy is + * performed and the function returns success. Copying a number of bytes larger + * than the size of the buffers pointed by @p dst or @p src results in undefined + * behavior. + * + * @param[in] num_dep_signals Number of dependent signals. Can be 0. + * + * @param[in] dep_signals List of signals that must be waited on before the copy + * operation starts. The copy will start after every signal has been observed with + * the value 0. The dependent signal should not include completion signal from + * hsa_amd_memory_async_copy operation to be issued in future as that can result + * in a deadlock. If @p num_dep_signals is 0, this argument is ignored. + * + * @param[in] completion_signal Signal used to indicate completion of the copy + * operation. When the copy operation is finished, the value of the signal is + * decremented. The runtime indicates that an error has occurred during the copy + * operation by setting the value of the completion signal to a negative + * number. The signal handle must not be 0. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. The + * application is responsible for checking for asynchronous error conditions + * (see the description of @p completion_signal). + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT An agent is invalid or no discovered agent has access. + * + * @retval ::HSA_STATUS_ERROR_INVALID_SIGNAL @p completion_signal is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT The source or destination + * pointers are NULL, or the completion signal is 0. + */ +hsa_status_t HSA_API + hsa_amd_memory_async_copy(void* dst, hsa_agent_t dst_agent, const void* src, + hsa_agent_t src_agent, size_t size, + uint32_t num_dep_signals, + const hsa_signal_t* dep_signals, + hsa_signal_t completion_signal); + +/** + * @brief Asynchronously copy a block of memory from the location pointed to by + * @p src on the @p src_agent to the memory block pointed to by @p dst on the @p + * dst_agent on engine_id. + * + * WARNING: Concurrent use of this call with hsa_amd_memory_async_copy can result + * in resource conflicts as HSA runtime will auto assign engines with the latter + * call. Approach using both calls concurrently with caution. + * + * All param definitions are identical to hsa_amd_memory_async_copy with the + * exception of engine_id and force_copy_on_sdma. + * + * @param[in] - engine_id Target engine defined by hsa_amd_sdma_engine_id_t. + * Client should use hsa_amd_memory_copy_engine_status first to get the ID + * availability. + * + * @param[in] - force_copy_on_sdma By default, blit kernel copies are used when + * dst_agent == src_agent. Setting this to true will force the copy over SDMA1. + * + * All return definitions are identical to hsa_amd_memory_async_copy with the + * following ammendments: + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT The source or destination + * pointers are NULL, or the completion signal is 0 or engine_id is improperly + * bounded. + */ +hsa_status_t HSA_API + hsa_amd_memory_async_copy_on_engine(void* dst, hsa_agent_t dst_agent, const void* src, + hsa_agent_t src_agent, size_t size, + uint32_t num_dep_signals, + const hsa_signal_t* dep_signals, + hsa_signal_t completion_signal, + hsa_amd_sdma_engine_id_t engine_id, + bool force_copy_on_sdma); +/** + * @brief Reports the availability of SDMA copy engines. + * + * @param[in] dst_agent Destination agent of copy status direction. + * + * @param[in] src_agent Source agent of copy status direction. + * + * @param[out] engine_ids_mask returns available SDMA engine IDs that can be masked + * with hsa_amd_sdma_engine_id_t. + * + * @retval ::HSA_STATUS_SUCCESS Agent has available SDMA engines. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Agent does not have available SDMA engines. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT dst_agent and src_agent are the same as + * dst_agent == src_agent is generally used for shader copies. + */ +hsa_status_t HSA_API + hsa_amd_memory_copy_engine_status(hsa_agent_t dst_agent, hsa_agent_t src_agent, + uint32_t *engine_ids_mask); + +/* +[Provisional API] +Pitched memory descriptor. +All elements must be 4 byte aligned. Pitch and slice are in bytes. +*/ +typedef struct hsa_pitched_ptr_s { + void* base; + size_t pitch; + size_t slice; +} hsa_pitched_ptr_t; + +/* +[Provisional API] +Copy direction flag. +*/ +typedef enum { + hsaHostToHost = 0, + hsaHostToDevice = 1, + hsaDeviceToHost = 2, + hsaDeviceToDevice = 3 +} hsa_amd_copy_direction_t; + +/* +[Provisional API] +SDMA 3D memory copy API. The same requirements must be met by src and dst as in +hsa_amd_memory_async_copy. +Both src and dst must be directly accessible to the copy_agent during the copy, src and dst rects +must not overlap. +CPU agents are not supported. API requires SDMA and will return an error if SDMA is not available. +Offsets and range carry x in bytes, y and z in rows and layers. +*/ +hsa_status_t HSA_API hsa_amd_memory_async_copy_rect( + const hsa_pitched_ptr_t* dst, const hsa_dim3_t* dst_offset, const hsa_pitched_ptr_t* src, + const hsa_dim3_t* src_offset, const hsa_dim3_t* range, hsa_agent_t copy_agent, + hsa_amd_copy_direction_t dir, uint32_t num_dep_signals, const hsa_signal_t* dep_signals, + hsa_signal_t completion_signal); + +/** + * @brief Type of accesses to a memory pool from a given agent. + */ +typedef enum { + /** + * The agent cannot directly access any buffer in the memory pool. + */ + HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED = 0, + /** + * The agent can directly access a buffer located in the pool; the application + * does not need to invoke ::hsa_amd_agents_allow_access. + */ + HSA_AMD_MEMORY_POOL_ACCESS_ALLOWED_BY_DEFAULT = 1, + /** + * The agent can directly access a buffer located in the pool, but only if the + * application has previously requested access to that buffer using + * ::hsa_amd_agents_allow_access. + */ + HSA_AMD_MEMORY_POOL_ACCESS_DISALLOWED_BY_DEFAULT = 2 +} hsa_amd_memory_pool_access_t; + +/** + * @brief Properties of the relationship between an agent a memory pool. + */ +typedef enum { + /** + * Hyper-transport bus type. + */ + HSA_AMD_LINK_INFO_TYPE_HYPERTRANSPORT = 0, + + /** + * QPI bus type. + */ + HSA_AMD_LINK_INFO_TYPE_QPI = 1, + + /** + * PCIe bus type. + */ + HSA_AMD_LINK_INFO_TYPE_PCIE = 2, + + /** + * Infiniband bus type. + */ + HSA_AMD_LINK_INFO_TYPE_INFINBAND = 3, + + /** + * xGMI link type. + */ + HSA_AMD_LINK_INFO_TYPE_XGMI = 4 + +} hsa_amd_link_info_type_t; + +/** + * @brief Link properties when accessing the memory pool from the specified + * agent. + */ +typedef struct hsa_amd_memory_pool_link_info_s { + /** + * Minimum transfer latency (rounded to ns). + */ + uint32_t min_latency; + + /** + * Maximum transfer latency (rounded to ns). + */ + uint32_t max_latency; + + /** + * Minimum link interface bandwidth in MB/s. + */ + uint32_t min_bandwidth; + + /** + * Maximum link interface bandwidth in MB/s. + */ + uint32_t max_bandwidth; + + /** + * Support for 32-bit atomic transactions. + */ + bool atomic_support_32bit; + + /** + * Support for 64-bit atomic transactions. + */ + bool atomic_support_64bit; + + /** + * Support for cache coherent transactions. + */ + bool coherent_support; + + /** + * The type of bus/link. + */ + hsa_amd_link_info_type_t link_type; + + /** + * NUMA distance of memory pool relative to querying agent + */ + uint32_t numa_distance; +} hsa_amd_memory_pool_link_info_t; + +/** + * @brief Properties of the relationship between an agent a memory pool. + */ +typedef enum { + /** + * Access to buffers located in the memory pool. The type of this attribute + * is ::hsa_amd_memory_pool_access_t. + * + * An agent can always directly access buffers currently located in a memory + * pool that is associated (the memory_pool is one of the values returned by + * ::hsa_amd_agent_iterate_memory_pools on the agent) with that agent. If the + * buffer is currently located in a memory pool that is not associated with + * the agent, and the value returned by this function for the given + * combination of agent and memory pool is not + * HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED, the application still needs to invoke + * ::hsa_amd_agents_allow_access in order to gain direct access to the buffer. + * + * If the given agent can directly access buffers the pool, the result is not + * HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED. If the memory pool is associated with + * the agent, or it is of fined-grained type, the result must not be + * HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED. If the memory pool is not associated + * with the agent, and does not reside in the global segment, the result must + * be HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED. + */ + HSA_AMD_AGENT_MEMORY_POOL_INFO_ACCESS = 0, + + /** + * Number of links to hop when accessing the memory pool from the specified + * agent. The value of this attribute is zero if the memory pool is associated + * with the agent, or if the access type is + * HSA_AMD_MEMORY_POOL_ACCESS_NEVER_ALLOWED. The type of this attribute is + * uint32_t. + */ + HSA_AMD_AGENT_MEMORY_POOL_INFO_NUM_LINK_HOPS = 1, + + /** + * Details of each link hop when accessing the memory pool starting from the + * specified agent. The type of this attribute is an array size of + * HSA_AMD_AGENT_MEMORY_POOL_INFO_NUM_LINK_HOPS with each element containing + * ::hsa_amd_memory_pool_link_info_t. + */ + HSA_AMD_AGENT_MEMORY_POOL_INFO_LINK_INFO = 2 + +} hsa_amd_agent_memory_pool_info_t; + +/** + * @brief Get the current value of an attribute of the relationship between an + * agent and a memory pool. + * + * @param[in] agent Agent. + * + * @param[in] memory_pool Memory pool. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to a application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + */ +hsa_status_t HSA_API hsa_amd_agent_memory_pool_get_info( + hsa_agent_t agent, hsa_amd_memory_pool_t memory_pool, + hsa_amd_agent_memory_pool_info_t attribute, void* value); + +/** + * @brief Enable direct access to a buffer from a given set of agents. + * + * @details + * + * Upon return, only the listed agents and the agent associated with the + * buffer's memory pool have direct access to the @p ptr. + * + * Any agent that has access to the buffer before and after the call to + * ::hsa_amd_agents_allow_access will also have access while + * ::hsa_amd_agents_allow_access is in progress. + * + * The caller is responsible for ensuring that each agent in the list + * must be able to access the memory pool containing @p ptr + * (using ::hsa_amd_agent_memory_pool_get_info with ::HSA_AMD_AGENT_MEMORY_POOL_INFO_ACCESS attribute), + * otherwise error code is returned. + * + * @param[in] num_agents Size of @p agents. + * + * @param[in] agents List of agents. If @p num_agents is 0, this argument is + * ignored. + * + * @param[in] flags A list of bit-field that is used to specify access + * information in a per-agent basis. This is currently reserved and must be NULL. + * + * @param[in] ptr A buffer previously allocated using ::hsa_amd_memory_pool_allocate. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p num_agents is 0, or @p agents + * is NULL, @p flags is not NULL, or attempting to enable access to agent(s) + * because @p ptr is allocated from an inaccessible pool. + * + */ +hsa_status_t HSA_API + hsa_amd_agents_allow_access(uint32_t num_agents, const hsa_agent_t* agents, + const uint32_t* flags, const void* ptr); + +/** + * @brief Query if buffers currently located in some memory pool can be + * relocated to a destination memory pool. + * + * @details If the returned value is non-zero, a migration of a buffer to @p + * dst_memory_pool using ::hsa_amd_memory_migrate may nevertheless fail due to + * resource limitations. + * + * @param[in] src_memory_pool Source memory pool. + * + * @param[in] dst_memory_pool Destination memory pool. + * + * @param[out] result Pointer to a memory location where the result of the query + * is stored. Must not be NULL. If buffers currently located in @p + * src_memory_pool can be relocated to @p dst_memory_pool, the result is + * true. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_MEMORY_POOL One of the memory pools is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p result is NULL. + */ +hsa_status_t HSA_API + hsa_amd_memory_pool_can_migrate(hsa_amd_memory_pool_t src_memory_pool, + hsa_amd_memory_pool_t dst_memory_pool, + bool* result); + +/** + * @brief Relocate a buffer to a new memory pool. + * + * @details When a buffer is migrated, its virtual address remains the same but + * its physical contents are moved to the indicated memory pool. + * + * After migration, only the agent associated with the destination pool will have access. + * + * The caller is also responsible for ensuring that the allocation in the + * source memory pool where the buffer is currently located can be migrated to the + * specified destination memory pool (using ::hsa_amd_memory_pool_can_migrate returns a value of true + * for the source and destination memory pools), otherwise behavior is undefined. + * + * The caller must ensure that the buffer is not accessed while it is migrated. + * + * @param[in] ptr Buffer to be relocated. The buffer must have been released to system + * prior to call this API. The buffer will be released to system upon completion. + * + * @param[in] memory_pool Memory pool where to place the buffer. + * + * @param[in] flags A bit-field that is used to specify migration + * information. Must be zero. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_MEMORY_POOL The destination memory pool is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure in + * allocating the necessary resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p flags is not 0. + */ +hsa_status_t HSA_API hsa_amd_memory_migrate(const void* ptr, + hsa_amd_memory_pool_t memory_pool, + uint32_t flags); + +/** + * + * @brief Pin a host pointer allocated by C/C++ or OS allocator (i.e. ordinary system DRAM) and + * return a new pointer accessible by the @p agents. If the @p host_ptr overlaps with previously + * locked memory, then the overlap area is kept locked (i.e multiple mappings are permitted). In + * this case, the same input @p host_ptr may give different locked @p agent_ptr and when it does, + * they are not necessarily coherent (i.e. accessing either @p agent_ptr is not equivalent). + * Accesses to @p agent_ptr are coarse grained. + * + * @param[in] host_ptr A buffer allocated by C/C++ or OS allocator. + * + * @param[in] size The size to be locked. + * + * @param[in] agents Array of agent handle to gain access to the @p host_ptr. + * If this parameter is NULL and the @p num_agent is 0, all agents + * in the platform will gain access to the @p host_ptr. + * + * @param[out] agent_ptr Pointer to the location where to store the new address. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure in + * allocating the necessary resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT One or more agent in @p agents is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p size is 0 or @p host_ptr or + * @p agent_ptr is NULL or @p agents not NULL but @p num_agent is 0 or @p agents + * is NULL but @p num_agent is not 0. + */ +hsa_status_t HSA_API hsa_amd_memory_lock(void* host_ptr, size_t size, + hsa_agent_t* agents, int num_agent, + void** agent_ptr); + +/** + * + * @brief Pin a host pointer allocated by C/C++ or OS allocator (i.e. ordinary system DRAM) and + * return a new pointer accessible by the @p agents. If the @p host_ptr overlaps with previously + * locked memory, then the overlap area is kept locked (i.e. multiple mappings are permitted). + * In this case, the same input @p host_ptr may give different locked @p agent_ptr and when it + * does, they are not necessarily coherent (i.e. accessing either @p agent_ptr is not equivalent). + * Acesses to the memory via @p agent_ptr have the same access properties as memory allocated from + * @p pool as determined by ::hsa_amd_memory_pool_get_info and ::hsa_amd_agent_memory_pool_get_info + * (ex. coarse/fine grain, platform atomic support, link info). Physical composition and placement + * of the memory (ex. page size, NUMA binding) is not changed. + * + * @param[in] host_ptr A buffer allocated by C/C++ or OS allocator. + * + * @param[in] size The size to be locked. + * + * @param[in] agents Array of agent handle to gain access to the @p host_ptr. + * If this parameter is NULL and the @p num_agent is 0, all agents + * in the platform will gain access to the @p host_ptr. + * + * @param[in] pool Global memory pool owned by a CPU agent. + * + * @param[in] flags A bit-field that is used to specify allocation + * directives. Reserved parameter, must be 0. + * + * @param[out] agent_ptr Pointer to the location where to store the new address. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure in + * allocating the necessary resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT One or more agent in @p agents is + * invalid or can not access @p pool. + * + * @retval ::HSA_STATUS_ERROR_INVALID_MEMORY_POOL @p pool is invalid or not owned + * by a CPU agent. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p size is 0 or @p host_ptr or + * @p agent_ptr is NULL or @p agents not NULL but @p num_agent is 0 or @p agents + * is NULL but @p num_agent is not 0 or flags is not 0. + */ +hsa_status_t HSA_API hsa_amd_memory_lock_to_pool(void* host_ptr, size_t size, hsa_agent_t* agents, + int num_agent, hsa_amd_memory_pool_t pool, + uint32_t flags, void** agent_ptr); + +/** + * + * @brief Unpin the host pointer previously pinned via ::hsa_amd_memory_lock or + * ::hsa_amd_memory_lock_to_pool. + * + * @details The behavior is undefined if the host pointer being unpinned does not + * match previous pinned address or if the host pointer was already deallocated. + * + * @param[in] host_ptr A buffer allocated by C/C++ or OS allocator that was + * pinned previously via ::hsa_amd_memory_lock or ::hsa_amd_memory_lock_to_pool. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + */ +hsa_status_t HSA_API hsa_amd_memory_unlock(void* host_ptr); + +/** + * @brief Sets the first @p count of uint32_t of the block of memory pointed by + * @p ptr to the specified @p value. + * + * @param[in] ptr Pointer to the block of memory to fill. + * + * @param[in] value Value to be set. + * + * @param[in] count Number of uint32_t element to be set to the value. + * + * @retval HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr is NULL or + * not 4 bytes aligned + * + * @retval HSA_STATUS_ERROR_INVALID_ALLOCATION if the given memory + * region was not allocated with HSA runtime APIs. + * + */ +hsa_status_t HSA_API + hsa_amd_memory_fill(void* ptr, uint32_t value, size_t count); + +/** + * @brief Maps an interop object into the HSA flat address space and establishes + * memory residency. The metadata pointer is valid during the lifetime of the + * map (until hsa_amd_interop_unmap_buffer is called). + * Multiple calls to hsa_amd_interop_map_buffer with the same interop_handle + * result in multiple mappings with potentially different addresses and + * different metadata pointers. Concurrent operations on these addresses are + * not coherent. Memory must be fenced to system scope to ensure consistency, + * between mappings and with any views of this buffer in the originating + * software stack. + * + * @param[in] num_agents Number of agents which require access to the memory + * + * @param[in] agents List of accessing agents. + * + * @param[in] interop_handle Handle of interop buffer (dmabuf handle in Linux) + * + * @param [in] flags Reserved, must be 0 + * + * @param[out] size Size in bytes of the mapped object + * + * @param[out] ptr Base address of the mapped object + * + * @param[out] metadata_size Size of metadata in bytes, may be NULL + * + * @param[out] metadata Pointer to metadata, may be NULL + * + * @retval HSA_STATUS_SUCCESS if successfully mapped + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT all other errors + */ +hsa_status_t HSA_API hsa_amd_interop_map_buffer(uint32_t num_agents, + hsa_agent_t* agents, + int interop_handle, + uint32_t flags, + size_t* size, + void** ptr, + size_t* metadata_size, + const void** metadata); + +/** + * @brief Removes a previously mapped interop object from HSA's flat address space. + * Ends lifetime for the mapping's associated metadata pointer. + */ +hsa_status_t HSA_API hsa_amd_interop_unmap_buffer(void* ptr); + +/** + * @brief Encodes an opaque vendor specific image format. The length of data + * depends on the underlying format. This structure must not be copied as its + * true length can not be determined. + */ +typedef struct hsa_amd_image_descriptor_s { + /* + Version number of the descriptor + */ + uint32_t version; + + /* + Vendor and device PCI IDs for the format as VENDOR_ID<<16|DEVICE_ID. + */ + uint32_t deviceID; + + /* + Start of vendor specific data. + */ + uint32_t data[1]; +} hsa_amd_image_descriptor_t; + +/** + * @brief Creates an image from an opaque vendor specific image format. + * Does not modify data at image_data. Intended initially for + * accessing interop images. + * + * @param agent[in] Agent on which to create the image + * + * @param[in] image_descriptor[in] Vendor specific image format + * + * @param[in] image_data Pointer to image backing store + * + * @param[in] access_permission Access permissions for the image object + * + * @param[out] image Created image object. + * + * @retval HSA_STATUS_SUCCESS Image created successfully + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT Bad or mismatched descriptor, + * null image_data, or mismatched access_permission. + */ +hsa_status_t HSA_API hsa_amd_image_create( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const hsa_amd_image_descriptor_t *image_layout, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_t *image +); + +/** + * @brief Denotes the type of memory in a pointer info query. + */ +typedef enum { + /* + Memory is not known to the HSA driver. Unallocated or unlocked system memory. + */ + HSA_EXT_POINTER_TYPE_UNKNOWN = 0, + /* + Memory was allocated with an HSA memory allocator. + */ + HSA_EXT_POINTER_TYPE_HSA = 1, + /* + System memory which has been locked for use with an HSA agent. + + Memory of this type is normal malloc'd memory and is always accessible to + the CPU. Pointer info queries may not include CPU agents in the accessible + agents list as the CPU has implicit access. + */ + HSA_EXT_POINTER_TYPE_LOCKED = 2, + /* + Memory originated in a graphics component and is shared with ROCr. + */ + HSA_EXT_POINTER_TYPE_GRAPHICS = 3, + /* + Memory has been shared with the local process via ROCr IPC APIs. + */ + HSA_EXT_POINTER_TYPE_IPC = 4 +} hsa_amd_pointer_type_t; + +/** + * @brief Describes a memory allocation known to ROCr. + * Within a ROCr major version this structure can only grow. + */ +typedef struct hsa_amd_pointer_info_s { + /* + Size in bytes of this structure. Used for version control within a major ROCr + revision. Set to sizeof(hsa_amd_pointer_t) prior to calling + hsa_amd_pointer_info. If the runtime supports an older version of pointer + info then size will be smaller on return. Members starting after the return + value of size will not be updated by hsa_amd_pointer_info. + */ + uint32_t size; + /* + The type of allocation referenced. + */ + hsa_amd_pointer_type_t type; + /* + Base address at which non-host agents may access the allocation. This field is + not meaningful if the type of the allocation is HSA_EXT_POINTER_TYPE_UNKNOWN. + */ + void* agentBaseAddress; + /* + Base address at which the host agent may access the allocation. This field is + not meaningful if the type of the allocation is HSA_EXT_POINTER_TYPE_UNKNOWN. + */ + void* hostBaseAddress; + /* + Size of the allocation. This field is not meaningful if the type of the allocation + is HSA_EXT_POINTER_TYPE_UNKNOWN. + */ + size_t sizeInBytes; + /* + Application provided value. This field is not meaningful if the type of the + allocation is HSA_EXT_POINTER_TYPE_UNKNOWN. + */ + void* userData; + /* + Reports an agent which "owns" (ie has preferred access to) the pool in which the + allocation was + made. When multiple agents share equal access to a pool (ex: multiple CPU agents, or multi-die + GPU boards) any such agent may be returned. This field is not meaningful if + the type of the allocation is HSA_EXT_POINTER_TYPE_UNKNOWN or if this agent is not available in + this process, for e.g if this agent is masked using ROCR_VISIBLE_DEVICES. + */ + hsa_agent_t agentOwner; + /* + Contains a bitfield of hsa_amd_memory_pool_global_flag_t values. + Reports the effective global flags bitmask for the allocation. This field is not + meaningful if the type of the allocation is HSA_EXT_POINTER_TYPE_UNKNOWN. + */ + uint32_t global_flags; +} hsa_amd_pointer_info_t; + +/** + * @brief Retrieves information about the allocation referenced by the given + * pointer. Optionally returns the number and list of agents which can + * directly access the allocation. In case this virtual address is unknown, the + * pointer type returned will be HSA_EXT_POINTER_TYPE_UNKNOWN and the only fields + * that are valid after hsa_amd_pointer_info returns are size and type. + * + * @param[in] ptr Pointer which references the allocation to retrieve info for. + * + * @param[in, out] info Pointer to structure to be filled with allocation info. + * Data member size must be set to the size of the structure prior to calling + * hsa_amd_pointer_info. On return size will be set to the size of the + * pointer info structure supported by the runtime, if smaller. Members + * beyond the returned value of size will not be updated by the API. + * Must not be NULL. + * + * @param[in] alloc Function pointer to an allocator used to allocate the + * @p accessible array. If NULL @p accessible will not be returned. + * + * @param[out] num_agents_accessible Recieves the count of agents in + * @p accessible. If NULL @p accessible will not be returned. + * + * @param[out] accessible Recieves a pointer to the array, allocated by @p alloc, + * holding the list of agents which may directly access the allocation. + * May be NULL. + * + * @retval HSA_STATUS_SUCCESS Info retrieved successfully + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT NULL in @p ptr or @p info. + */ +hsa_status_t HSA_API hsa_amd_pointer_info(const void* ptr, + hsa_amd_pointer_info_t* info, + void* (*alloc)(size_t), + uint32_t* num_agents_accessible, + hsa_agent_t** accessible); + +/** + * @brief Associates an arbitrary pointer with an allocation known to ROCr. + * The pointer can be fetched by hsa_amd_pointer_info in the userData field. + * + * @param[in] ptr Pointer to the first byte of an allocation known to ROCr + * with which to associate @p userdata. + * + * @param[in] userdata Abitrary pointer to associate with the allocation. + * + * @retval HSA_STATUS_SUCCESS @p userdata successfully stored. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr is not known to ROCr. + */ +hsa_status_t HSA_API hsa_amd_pointer_info_set_userdata(const void* ptr, + void* userdata); + +/** + * @brief 256-bit process independent identifier for a ROCr shared memory + * allocation. + */ +typedef struct hsa_amd_ipc_memory_s { + uint32_t handle[8]; +} hsa_amd_ipc_memory_t; + +/** + * @brief Prepares an allocation for interprocess sharing and creates a + * handle of type hsa_amd_ipc_memory_t uniquely identifying the allocation. A + * handle is valid while the allocation it references remains accessible in + * any process. In general applications should confirm that a shared memory + * region has been attached (via hsa_amd_ipc_memory_attach) in the remote + * process prior to releasing that memory in the local process. + * Repeated calls for the same allocation may, but are not required to, return + * unique handles. The allocation needs to be on memory on an agent of type + * HSA_DEVICE_TYPE_GPU. + * + * @param[in] ptr Pointer to device memory allocated via ROCr APIs to prepare for + * sharing. + * + * @param[in] len Length in bytes of the allocation to share. + * + * @param[out] handle Process independent identifier referencing the shared + * allocation. + * + * @retval HSA_STATUS_SUCCESS allocation is prepared for interprocess sharing. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p ptr does not point to the + * first byte of an allocation made through ROCr, or len is not the full length + * of the allocation or handle is NULL. + */ +hsa_status_t HSA_API hsa_amd_ipc_memory_create(void* ptr, size_t len, + hsa_amd_ipc_memory_t* handle); + +/** + * @brief Imports shared memory into the local process and makes it accessible + * by the given agents. If a shared memory handle is attached multiple times + * in a process each attach may return a different address. Each returned + * address is refcounted and requires a matching number of calls to + * hsa_amd_ipc_memory_detach to release the shared memory mapping. + * + * @param[in] handle Pointer to the identifier for the shared memory. + * + * @param[in] len Length of the shared memory to import. + * Reserved. Must be the full length of the shared allocation in this version. + * + * @param[in] num_agents Count of agents in @p mapping_agents. + * May be zero if all agents are to be allowed access. + * + * @param[in] mapping_agents List of agents to access the shared memory. + * Ignored if @p num_agents is zero. + * + * @param[out] mapped_ptr Recieves a process local pointer to the shared memory. + * + * @retval HSA_STATUS_SUCCESS if memory is successfully imported. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p handle is not valid, @p len is + * incorrect, @p mapped_ptr is NULL, or some agent for which access was + * requested can not access the shared memory. + */ +hsa_status_t HSA_API hsa_amd_ipc_memory_attach( + const hsa_amd_ipc_memory_t* handle, size_t len, + uint32_t num_agents, + const hsa_agent_t* mapping_agents, + void** mapped_ptr); + +/** + * @brief Decrements the reference count for the shared memory mapping and + * releases access to shared memory imported with hsa_amd_ipc_memory_attach. + * + * @param[in] mapped_ptr Pointer to the first byte of a shared allocation + * imported with hsa_amd_ipc_memory_attach. + * + * @retval HSA_STATUS_SUCCESS if @p mapped_ptr was imported with + * hsa_amd_ipc_memory_attach. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p mapped_ptr was not imported + * with hsa_amd_ipc_memory_attach. + */ +hsa_status_t HSA_API hsa_amd_ipc_memory_detach(void* mapped_ptr); + +/** + * @brief 256-bit process independent identifier for a ROCr IPC signal. + */ +typedef hsa_amd_ipc_memory_t hsa_amd_ipc_signal_t; + +/** + * @brief Obtains an interprocess sharing handle for a signal. The handle is + * valid while the signal it references remains valid in any process. In + * general applications should confirm that the signal has been attached (via + * hsa_amd_ipc_signal_attach) in the remote process prior to destroying that + * signal in the local process. + * Repeated calls for the same signal may, but are not required to, return + * unique handles. + * + * @param[in] signal Signal created with attribute HSA_AMD_SIGNAL_IPC. + * + * @param[out] handle Process independent identifier referencing the shared + * signal. + * + * @retval HSA_STATUS_SUCCESS @p handle is ready to use for interprocess sharing. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p signal is not a valid signal + * created with attribute HSA_AMD_SIGNAL_IPC or handle is NULL. + */ +hsa_status_t HSA_API hsa_amd_ipc_signal_create(hsa_signal_t signal, hsa_amd_ipc_signal_t* handle); + +/** + * @brief Imports an IPC capable signal into the local process. If an IPC + * signal handle is attached multiple times in a process each attach may return + * a different signal handle. Each returned signal handle is refcounted and + * requires a matching number of calls to hsa_signal_destroy to release the + * shared signal. + * + * @param[in] handle Pointer to the identifier for the shared signal. + * + * @param[out] signal Recieves a process local signal handle to the shared signal. + * + * @retval HSA_STATUS_SUCCESS if the signal is successfully imported. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED if HSA is not initialized + * + * @retval HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p handle is not valid. + */ +hsa_status_t HSA_API hsa_amd_ipc_signal_attach(const hsa_amd_ipc_signal_t* handle, + hsa_signal_t* signal); + +/** + * @brief GPU system event type. + */ +typedef enum hsa_amd_event_type_s { + /* + AMD GPU memory fault. + */ + HSA_AMD_GPU_MEMORY_FAULT_EVENT = 0, + /* + AMD GPU HW Exception. + */ + HSA_AMD_GPU_HW_EXCEPTION_EVENT, +} hsa_amd_event_type_t; + +/** + * @brief Flags denoting the cause of a memory fault. + */ +typedef enum { + // Page not present or supervisor privilege. + HSA_AMD_MEMORY_FAULT_PAGE_NOT_PRESENT = 1 << 0, + // Write access to a read-only page. + HSA_AMD_MEMORY_FAULT_READ_ONLY = 1 << 1, + // Execute access to a page marked NX. + HSA_AMD_MEMORY_FAULT_NX = 1 << 2, + // GPU attempted access to a host only page. + HSA_AMD_MEMORY_FAULT_HOST_ONLY = 1 << 3, + // DRAM ECC failure. + HSA_AMD_MEMORY_FAULT_DRAMECC = 1 << 4, + // Can't determine the exact fault address. + HSA_AMD_MEMORY_FAULT_IMPRECISE = 1 << 5, + // SRAM ECC failure (ie registers, no fault address). + HSA_AMD_MEMORY_FAULT_SRAMECC = 1 << 6, + // GPU reset following unspecified hang. + HSA_AMD_MEMORY_FAULT_HANG = 1U << 31 +} hsa_amd_memory_fault_reason_t; + +/** + * @brief AMD GPU memory fault event data. + */ +typedef struct hsa_amd_gpu_memory_fault_info_s { + /* + The agent where the memory fault occurred. + */ + hsa_agent_t agent; + /* + Virtual address accessed. + */ + uint64_t virtual_address; + /* + Bit field encoding the memory access failure reasons. There could be multiple bits set + for one fault. Bits are defined in hsa_amd_memory_fault_reason_t. + */ + uint32_t fault_reason_mask; +} hsa_amd_gpu_memory_fault_info_t; + +/** + * @brief Flags denoting the type of a HW exception + */ +typedef enum { + // Unused for now + HSA_AMD_HW_EXCEPTION_RESET_TYPE_OTHER = 1 << 0, +} hsa_amd_hw_exception_reset_type_t; + +/** + * @brief Flags denoting the cause of a HW exception + */ +typedef enum { + // GPU Hang + HSA_AMD_HW_EXCEPTION_CAUSE_GPU_HANG = 1 << 0, + // SRAM ECC + HSA_AMD_HW_EXCEPTION_CAUSE_ECC = 1 << 1, +} hsa_amd_hw_exception_reset_cause_t; + +/** + * @brief AMD GPU HW Exception event data. + */ +typedef struct hsa_amd_gpu_hw_exception_info_s { + /* + The agent where the HW exception occurred. + */ + hsa_agent_t agent; + hsa_amd_hw_exception_reset_type_t reset_type; + hsa_amd_hw_exception_reset_cause_t reset_cause; +} hsa_amd_gpu_hw_exception_info_t; + +/** + * @brief AMD GPU event data passed to event handler. + */ +typedef struct hsa_amd_event_s { + /* + The event type. + */ + hsa_amd_event_type_t event_type; + union { + /* + The memory fault info, only valid when @p event_type is HSA_AMD_GPU_MEMORY_FAULT_EVENT. + */ + hsa_amd_gpu_memory_fault_info_t memory_fault; + /* + The memory fault info, only valid when @p event_type is HSA_AMD_GPU_HW_EXCEPTION_EVENT. + */ + hsa_amd_gpu_hw_exception_info_t hw_exception; + }; +} hsa_amd_event_t; + +typedef hsa_status_t (*hsa_amd_system_event_callback_t)(const hsa_amd_event_t* event, void* data); + +/** + * @brief Register AMD GPU event handler. + * + * @param[in] callback Callback to be invoked when an event is triggered. + * The HSA runtime passes two arguments to the callback: @p event + * is defined per event by the HSA runtime, and @p data is the user data. + * + * @param[in] data User data that is passed to @p callback. May be NULL. + * + * @retval HSA_STATUS_SUCCESS The handler has been registered successfully. + * + * @retval HSA_STATUS_ERROR An event handler has already been registered. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p event is invalid. + */ +hsa_status_t HSA_API hsa_amd_register_system_event_handler(hsa_amd_system_event_callback_t callback, + void* data); + +/** + * @brief Per-queue dispatch and wavefront scheduling priority. + */ +typedef enum hsa_amd_queue_priority_s { + /* + Below normal/high priority compute and all graphics + */ + HSA_AMD_QUEUE_PRIORITY_LOW = 0, + /* + Above low priority compute, below high priority compute and all graphics + */ + HSA_AMD_QUEUE_PRIORITY_NORMAL = 1, + /* + Above low/normal priority compute and all graphics + */ + HSA_AMD_QUEUE_PRIORITY_HIGH = 2, +} hsa_amd_queue_priority_t; + +/** + * @brief Modifies the dispatch and wavefront scheduling prioirty for a + * given compute queue. The default is HSA_AMD_QUEUE_PRIORITY_NORMAL. + * + * @param[in] queue Compute queue to apply new priority to. + * + * @param[in] priority Priority to associate with queue. + * + * @retval HSA_STATUS_SUCCESS if priority was changed successfully. + * + * @retval HSA_STATUS_ERROR_INVALID_QUEUE if queue is not a valid + * compute queue handle. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT if priority is not a valid + * value from hsa_amd_queue_priority_t. + */ +hsa_status_t HSA_API hsa_amd_queue_set_priority(hsa_queue_t* queue, + hsa_amd_queue_priority_t priority); + +/** + * @brief Deallocation notifier function type. + */ +typedef void (*hsa_amd_deallocation_callback_t)(void* ptr, void* user_data); + +/** + * @brief Registers a deallocation notifier monitoring for release of agent + * accessible address @p ptr. If successful, @p callback will be invoked when + * @p ptr is removed from accessibility from all agents. + * + * Notification callbacks are automatically deregistered when they are invoked. + * + * Note: The current version supports notifications of address release + * originating from ::hsa_amd_memory_pool_free. Support for other address + * release APIs will follow. + * + * @param[in] ptr Agent accessible address to monitor for deallocation. Passed + * to @p callback. + * + * @param[in] callback Notifier to be invoked when @p ptr is released from + * agent accessibility. + * + * @param[in] user_data User provided value passed to @p callback. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The notifier registered successfully + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION @p ptr does not refer to a valid agent accessible + * address. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL or @p ptr is NULL. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES if there is a failure in allocating + * necessary resources + */ +hsa_status_t HSA_API hsa_amd_register_deallocation_callback(void* ptr, + hsa_amd_deallocation_callback_t callback, + void* user_data); + +/** + * @brief Removes a deallocation notifier previously registered with + * ::hsa_amd_register_deallocation_callback. Arguments must be identical to + * those given in ::hsa_amd_register_deallocation_callback. + * + * @param[in] ptr Agent accessible address which was monitored for deallocation. + * + * @param[in] callback Notifier to be removed. + * + * @retval ::HSA_STATUS_SUCCESS The notifier has been removed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT The given notifier was not registered. + */ +hsa_status_t HSA_API hsa_amd_deregister_deallocation_callback(void* ptr, + hsa_amd_deallocation_callback_t callback); + +typedef enum hsa_amd_svm_model_s { + /** + * Updates to memory with this attribute conform to HSA memory consistency + * model. + */ + HSA_AMD_SVM_GLOBAL_FLAG_FINE_GRAINED = 0, + /** + * Writes to memory with this attribute can be performed by a single agent + * at a time. + */ + HSA_AMD_SVM_GLOBAL_FLAG_COARSE_GRAINED = 1, + /** + * Memory region queried contains subregions with both + * HSA_AMD_SVM_GLOBAL_FLAG_COARSE_GRAINED and + * HSA_AMD_SVM_GLOBAL_FLAG_FINE_GRAINED attributes. + * + * This attribute can not be used in hsa_amd_svm_attributes_set. It is a + * possible return from hsa_amd_svm_attributes_get indicating that the query + * region contains both coarse and fine grained memory. + */ + HSA_AMD_SVM_GLOBAL_FLAG_INDETERMINATE = 2 +} hsa_amd_svm_model_t; + +typedef enum hsa_amd_svm_attribute_s { + // Memory model attribute. + // Type of this attribute is hsa_amd_svm_model_t. + HSA_AMD_SVM_ATTRIB_GLOBAL_FLAG = 0, + // Marks the range read only. This allows multiple physical copies to be + // placed local to each accessing device. + // Type of this attribute is bool. + HSA_AMD_SVM_ATTRIB_READ_ONLY = 1, + // Automatic migrations should attempt to keep the memory within the xgmi hive + // containing accessible agents. + // Type of this attribute is bool. + HSA_AMD_SVM_ATTRIB_HIVE_LOCAL = 2, + // Page granularity to migrate at once. Page granularity is specified as + // log2(page_count). + // Type of this attribute is uint64_t. + HSA_AMD_SVM_ATTRIB_MIGRATION_GRANULARITY = 3, + // Physical location to prefer when automatic migration occurs. + // Set to the null agent handle (handle == 0) to indicate there + // is no preferred location. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_PREFERRED_LOCATION = 4, + // This attribute can not be used in ::hsa_amd_svm_attributes_set (see + // ::hsa_amd_svm_prefetch_async). + // Queries the physical location of most recent prefetch command. + // If the prefetch location has not been set or is not uniform across the + // address range then returned hsa_agent_t::handle will be 0. + // Querying this attribute will return the destination agent of the most + // recent ::hsa_amd_svm_prefetch_async targeting the address range. If + // multiple async prefetches have been issued targeting the region and the + // most recently issued prefetch has completed then the query will return + // the location of the most recently completed prefetch. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_PREFETCH_LOCATION = 5, + // Optimizes with the anticipation that the majority of operations to the + // range will be read operations. + // Type of this attribute is bool. + HSA_AMD_SVM_ATTRIB_READ_MOSTLY = 6, + // Allows the execution on GPU. + // Type of this attribute is bool. + HSA_AMD_SVM_ATTRIB_GPU_EXEC = 7, + // This attribute can not be used in ::hsa_amd_svm_attributes_get. + // Enables an agent for access to the range. Access may incur a page fault + // and associated memory migration. Either this or + // HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE_IN_PLACE is required prior to SVM + // access if HSA_AMD_SYSTEM_INFO_SVM_ACCESSIBLE_BY_DEFAULT is false. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE = 0x200, + // This attribute can not be used in ::hsa_amd_svm_attributes_get. + // Enables an agent for access to the range without page faults. Access + // will not incur a page fault and will not cause access based migration. + // and associated memory migration. Either this or + // HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE is required prior to SVM access if + // HSA_AMD_SYSTEM_INFO_SVM_ACCESSIBLE_BY_DEFAULT is false. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE_IN_PLACE = 0x201, + // This attribute can not be used in ::hsa_amd_svm_attributes_get. + // Denies an agent access to the memory range. Access will cause a terminal + // segfault. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_AGENT_NO_ACCESS = 0x202, + // This attribute can not be used in ::hsa_amd_svm_attributes_set. + // Returns the access attribute associated with the agent. + // The agent to query must be set in the attribute value field. + // The attribute enum will be replaced with the agent's current access + // attribute for the address range. + // TODO: Clarify KFD return value for non-uniform access attribute. + // Type of this attribute is hsa_agent_t. + HSA_AMD_SVM_ATTRIB_ACCESS_QUERY = 0x203, +} hsa_amd_svm_attribute_t; + +// List type for hsa_amd_svm_attributes_set/get. +typedef struct hsa_amd_svm_attribute_pair_s { + // hsa_amd_svm_attribute_t value. + uint64_t attribute; + // Attribute value. Bit values should be interpreted according to the type + // given in the associated attribute description. + uint64_t value; +} hsa_amd_svm_attribute_pair_t; + +/** + * @brief Sets SVM memory attributes. + * + * If HSA_AMD_SYSTEM_INFO_SVM_ACCESSIBLE_BY_DEFAULT returns false then enabling + * access to an Agent via this API (setting HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE + * or HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE_IN_PLACE) is required prior to SVM + * memory access by that Agent. + * + * Attributes HSA_AMD_SVM_ATTRIB_ACCESS_QUERY and HSA_AMD_SVM_ATTRIB_PREFETCH_LOCATION + * may not be used with this API. + * + * @param[in] ptr Will be aligned down to nearest page boundary. + * + * @param[in] size Will be aligned up to nearest page boundary. + * + * @param[in] attribute_list List of attributes to set for the address range. + * + * @param[in] attribute_count Length of @p attribute_list. + */ +hsa_status_t hsa_amd_svm_attributes_set(void* ptr, size_t size, + hsa_amd_svm_attribute_pair_t* attribute_list, + size_t attribute_count); + +/** + * @brief Gets SVM memory attributes. + * + * Attributes HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE, + * HSA_AMD_SVM_ATTRIB_AGENT_ACCESSIBLE_IN_PLACE and + * HSA_AMD_SVM_ATTRIB_PREFETCH_LOCATION may not be used with this API. + * + * Note that attribute HSA_AMD_SVM_ATTRIB_ACCESS_QUERY takes as input an + * hsa_agent_t and returns the current access type through its attribute field. + * + * @param[in] ptr Will be aligned down to nearest page boundary. + * + * @param[in] size Will be aligned up to nearest page boundary. + * + * @param[in] attribute_list List of attributes to set for the address range. + * + * @param[in] attribute_count Length of @p attribute_list. + */ +hsa_status_t hsa_amd_svm_attributes_get(void* ptr, size_t size, + hsa_amd_svm_attribute_pair_t* attribute_list, + size_t attribute_count); + +/** + * @brief Asynchronously migrates memory to an agent. + * + * Schedules memory migration to @p agent when @p dep_signals have been observed equal to zero. + * @p completion_signal will decrement when the migration is complete. + * + * @param[in] ptr Will be aligned down to nearest page boundary. + * + * @param[in] size Will be aligned up to nearest page boundary. + * + * @param[in] agent Agent to migrate to. + * + * @param[in] num_dep_signals Number of dependent signals. Can be 0. + * + * @param[in] dep_signals List of signals that must be waited on before the migration + * operation starts. The migration will start after every signal has been observed with + * the value 0. If @p num_dep_signals is 0, this argument is ignored. + * + * @param[in] completion_signal Signal used to indicate completion of the migration + * operation. When the migration operation is finished, the value of the signal is + * decremented. The runtime indicates that an error has occurred during the copy + * operation by setting the value of the completion signal to a negative + * number. If no completion signal is required this handle may be null. + */ +hsa_status_t hsa_amd_svm_prefetch_async(void* ptr, size_t size, hsa_agent_t agent, + uint32_t num_dep_signals, const hsa_signal_t* dep_signals, + hsa_signal_t completion_signal); + +/** + * @brief Acquire Stream Performance Monitor on an agent + * + * Acquire exclusive use of SPM on @p preferred_agent. + * See hsa_amd_spm_set_dest_buffer to provide a destination buffer to KFD to start recording and + * retrieve this data. + * @param[in] preferred_agent Agent on which to acquire SPM + */ +hsa_status_t hsa_amd_spm_acquire(hsa_agent_t preferred_agent); + +/** + * @brief Release Stream Performance Monitor on an agent + * + * Release exclusive use of SPM on @p preferred_agent. This will stop KFD writing SPM data. + * If a destination buffer is set, then data in the destination buffer is available to user + * when this function returns. + * + * @param[in] preferred_agent Agent on which to release SPM + */ +hsa_status_t hsa_amd_spm_release(hsa_agent_t preferred_agent); + +/** + * @brief Set up the current destination user mode buffer for stream performance + * counter data. KFD will start writing SPM data into the destination buffer. KFD will continue + * to copy data into the current destination buffer until any of the following functions are called + * - hsa_amd_spm_release + * - hsa_amd_spm_set_dest_buffer with dest set to NULL + * - hsa_amd_spm_set_dest_buffer with dest set to a new buffer + * + * if @p timeout is non-0, the call will wait for up to @p timeout ms for the previous + * buffer to be filled. If previous buffer to be filled before timeout, the @p timeout + * will be updated value with the time remaining. If the timeout is exceeded, the function + * copies any partial data available into the previous user buffer and returns success. + * User should not access destination data while KFD is copying data. + * If the previous destination buffer was full, then @p is_data_loss flag is set. + * @p dest is CPU accessible memory. It could be malloc'ed memory or host allocated memory + * + * @param[in] preferred_agent Agent on which to set the dest buffer + * + * @param[in] size_in_bytes size of the buffer + * + * @param[in/out] timeout timeout in milliseconds + * + * @param[out] size_copied number of bytes copied + * + * @param[in] dest destination address. Set to NULL to stop copy on previous buffer + * + * @param[out] is_data_loss true is data was lost + */ +hsa_status_t hsa_amd_spm_set_dest_buffer(hsa_agent_t preferred_agent, size_t size_in_bytes, + uint32_t* timeout, uint32_t* size_copied, void* dest, + bool* is_data_loss); +/** + * @brief Obtains an OS specific, vendor neutral, handle to a memory allocation. + * + * Obtains an OS specific handle to GPU agent memory. The memory must be part + * of a single allocation from an hsa_amd_memory_pool_t exposed by a GPU Agent. + * The handle may be used with other APIs (e.g. Vulkan) to obtain shared access + * to the allocation. + * + * Shared access to the memory is not guaranteed to be fine grain coherent even + * if the allocation exported is from a fine grain pool. The shared memory + * consistency model will be no stronger than the model exported from, consult + * the importing API to determine the final consistency model. + * + * The allocation's memory remains valid as long as the handle and any mapping + * of the handle remains valid. When the handle and all mappings are closed + * the backing memory will be released for reuse. + * + * @param[in] ptr Pointer to the allocation being exported. + * + * @param[in] size Size in bytes to export following @p ptr. The entire range + * being exported must be contained within a single allocation. + * + * @param[out] dmabuf Pointer to a dma-buf file descriptor holding a reference to the + * allocation. Contents will not be altered in the event of failure. + * + * @param[out] offset Offset in bytes into the memory referenced by the dma-buf + * object at which @p ptr resides. Contents will not be altered in the event + * of failure. + * + * @retval ::HSA_STATUS_SUCCESS Export completed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT One or more arguments is NULL. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION The address range described by + * @p ptr and @p size are not contained within a single allocation. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The allocation described by @p ptr + * and @p size was allocated on a device which can not export memory. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The return file descriptor, + * @p dmabuf, could not be created. + */ +hsa_status_t hsa_amd_portable_export_dmabuf(const void* ptr, size_t size, int* dmabuf, + uint64_t* offset); + +/** + * @brief Closes an OS specific, vendor neutral, handle to a memory allocation. + * + * Closes an OS specific handle to GPU agent memory. + * + * Applications should close a handle after imports are complete. The handle + * is not required to remain open for the lifetime of imported mappings. The + * referenced allocation will remain valid until all handles and mappings + * are closed. + * + * @param[in] dmabuf Handle to be closed. + * + * @retval ::HSA_STATUS_SUCCESS Handle closed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_RESOURCE_FREE A generic error was encountered + * when closing the handle. The handle may have been closed already or an + * async IO error may have occured. + */ +hsa_status_t hsa_amd_portable_close_dmabuf(int dmabuf); + +/* + * @brief Allocate a reserved address range + * + * Reserve a virtual address range. The size must be a multiple of the system page size. + * If it is not possible to allocate the address specified by @p address, then @p va will be + * a different address range. + * Address range should be released by calling hsa_amd_vmem_address_free. + * + * @param[out] va virtual address allocated + * @param[in] size of address range requested + * @param[in] address requested + * @param[in] flags currently unsupported + * + * @retval ::HSA_STATUS_SUCCESS Address range allocated successfully + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Insufficient resources to allocate an address + * range of this size. + */ +hsa_status_t hsa_amd_vmem_address_reserve(void** va, size_t size, uint64_t address, + uint64_t flags); + +/* + * @brief Free a reserved address range + * + * Free a previously allocated address range. The size must match the size of a previously + * allocated address range. + * + * @param[out] va virtual address to be freed + * @param[in] size of address range + * + * @retval ::HSA_STATUS_SUCCESS Address range released successfully + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid va specified + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT Invalid size specified + * @retval ::HSA_STATUS_ERROR_RESOURCE_FREE Address range is still in use + * @retval ::HSA_STATUS_ERROR Internal unexpected error + */ +hsa_status_t hsa_amd_vmem_address_free(void* va, size_t size); + +/** + * @brief Struct containing an opaque handle to a memory allocation handle + */ +typedef struct hsa_amd_vmem_alloc_handle_s { + /** + * Opaque handle. Two handles reference the same object of the enclosing type + * if and only if they are equal. + */ + uint64_t handle; +} hsa_amd_vmem_alloc_handle_t; + +typedef enum { + MEMORY_TYPE_NONE, + MEMORY_TYPE_PINNED, +} hsa_amd_memory_type_t; + +/* + * @brief Create a virtual memory handle + * + * Create a virtual memory handle within this pool + * @p size must be a aligned to allocation granule size for this memory pool, see + * HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_GRANULE + * To minimize internal memory fragmentation, align the size to the recommended allocation granule + * size, see HSA_AMD_MEMORY_POOL_INFO_RUNTIME_ALLOC_REC_GRANULE + * + * @param[in] pool memory to use + * @param[in] size of the memory allocation + * @param[in] type of memory + * @param[in] flags - currently unsupported + * @param[out] memory_handle - handle for the allocation + * + * @retval ::HSA_STATUS_SUCCESS memory allocated successfully + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT Invalid arguments + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION This memory pool does not support allocations + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Insufficient resources to allocate this memory + */ +hsa_status_t hsa_amd_vmem_handle_create(hsa_amd_memory_pool_t pool, size_t size, + hsa_amd_memory_type_t type, uint64_t flags, + hsa_amd_vmem_alloc_handle_t* memory_handle); + +/* + * @brief Release a virtual memory handle + * + * @param[in] memory handle that was previously allocated + * + * @retval ::HSA_STATUS_SUCCESS Address range allocated successfully + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid memory handle + */ +hsa_status_t hsa_amd_vmem_handle_release(hsa_amd_vmem_alloc_handle_t memory_handle); + +/* + * @brief Map a virtual memory handle + * + * Map a virtual memory handle to a reserved address range. The virtual address requested must be + * within a previously reserved address range. @p va and (@p va + size) must be must be within + * (va + size) of the previous allocated address range. + * @p size must be equal to size of the @p memory_handle + * hsa_amd_vmem_set_access needs to be called to make the memory accessible to specific agents + * + * @param[in] va virtual address range where memory will be mapped + * @param[in] size of memory mapping + * @param[in] in_offset offset into memory. Currently unsupported + * @param[in] memory_handle virtual memory handle to be mapped + * @param[in] flags. Currently unsupported + * + * @retval ::HSA_STATUS_SUCCESS Memory mapped successfully + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT va, size or memory_handle are invalid + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Insufficient resources + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_map(void* va, size_t size, size_t in_offset, + hsa_amd_vmem_alloc_handle_t memory_handle, uint64_t flags); + +/* + * @brief Unmap a virtual memory handle + * + * Unmap previously mapped virtual address range + * + * @param[in] va virtual address range where memory will be mapped + * @param[in] size of memory mapping + * + * @retval ::HSA_STATUS_SUCCESS Memory backing unmapped successfully + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION memory_handle is invalid + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT size is invalid + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_unmap(void* va, size_t size); + +typedef struct hsa_amd_memory_access_desc_s { + hsa_access_permission_t permissions; + hsa_agent_t agent_handle; +} hsa_amd_memory_access_desc_t; + +/* + * @brief Make a memory mapping accessible + * + * Make previously mapped virtual address accessible to specific agents. @p size must be equal to + * size of previously mapped virtual memory handle. + * Calling hsa_amd_vmem_set_access multiple times on the same @p va will overwrite previous + * permissions for all agents + * + * @param[in] va previously mapped virtual address + * @param[in] size of memory mapping + * @param[in] desc list of access permissions for each agent + * @param[in] desc_cnt number of elements in desc + * + * @retval ::HSA_STATUS_SUCCESS + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT va, size or memory_handle are invalid + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION memory_handle is invalid + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Insufficient resources + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT Invalid agent in desc + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_set_access(void* va, size_t size, + const hsa_amd_memory_access_desc_t* desc, + size_t desc_cnt); + +/* + * @brief Get current access permissions for memory mapping + * + * Get access permissions for memory mapping for specific agent. + * + * @param[in] va previously mapped virtual address + * @param[in] perms current permissions + * @param[in] agent_handle agent + * + * @retval ::HSA_STATUS_SUCCESS + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT Invalid agent + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION va is not mapped or permissions never set for this + * agent + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_get_access(void* va, hsa_access_permission_t* perms, + hsa_agent_t agent_handle); + +/* + * @brief Get an exportable shareable handle + * + * Get an exportable shareable handle for a memory_handle. This shareabl handle can then be used to + * re-create a virtual memory handle using hsa_amd_vmem_import_shareable_handle. The shareable + * handle can be transferred using mechanisms that support posix file descriptors Once all shareable + * handles are closed, the memory_handle is released. + * + * @param[out] dmabuf_fd shareable handle + * @param[in] handle previously allocated virtual memory handle + * @param[in] flags Currently unsupported + * + * @retval ::HSA_STATUS_SUCCESS + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid memory handle + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Out of resources + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_export_shareable_handle(int* dmabuf_fd, + hsa_amd_vmem_alloc_handle_t handle, + uint64_t flags); +/* + * @brief Import a shareable handle + * + * Import a shareable handle for a memory handle. Importing a shareable handle that has been closed + * and released results in undefined behavior. + * + * @param[in] dmabuf_fd shareable handle exported with hsa_amd_vmem_export_shareable_handle + * @param[out] handle virtual memory handle + * + * @retval ::HSA_STATUS_SUCCESS + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid memory handle + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES Out of resources + * + * @retval ::HSA_STATUS_ERROR Unexpected internal error + */ +hsa_status_t hsa_amd_vmem_import_shareable_handle(int dmabuf_fd, + hsa_amd_vmem_alloc_handle_t* handle); + +/* + * @brief Returns memory handle for mapped memory + * + * Return a memory handle for previously mapped memory. The handle will be the same value of handle + * used to map the memory. The returned handle must be released with corresponding number of calls + * to hsa_amd_vmem_handle_release. + * + * @param[out] memory_handle memory handle for this mapped address + * @param[in] mapped address + * + * @retval ::HSA_STATUS_SUCCESS + * + * @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid address + */ +hsa_status_t hsa_amd_vmem_retain_alloc_handle(hsa_amd_vmem_alloc_handle_t* memory_handle, + void* addr); + +/* +* @brief Returns the current allocation properties of a handle +* +* Returns the allocation properties of an existing handle +* +* @param[in] memory_handle memory handle to be queried +* @param[out] pool memory pool that owns this handle +* @param[out] memory type + +* @retval ::HSA_STATUS_SUCCESS +* +* @retval ::HSA_STATUS_ERROR_INVALID_ALLOCATION Invalid memory_handle +*/ +hsa_status_t hsa_amd_vmem_get_alloc_properties_from_handle( + hsa_amd_vmem_alloc_handle_t memory_handle, hsa_amd_memory_pool_t* pool, + hsa_amd_memory_type_t* type); + +/** + * @brief Set the asynchronous scratch limit threshold on all the queues for this agent. + * Dispatches that are enqueued on HW queues on this agent that are smaller than threshold will not + * result in a scratch use-once method. + * + * Increasing this threshold will only increase the internal limit and not cause immediate allocation + * of additional scratch memory. Decreasing this threshold will result in a release in scratch memory + * on queues where the current amount of allocated scratch exceeds the new limit. + * + * This API is only supported on devices that support asynchronous scratch reclaim. + * + * @param[in] agent A valid agent. + * + * @param[in] threshold Threshold size in bytes + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT This agent does not support asynchronous scratch + * reclaim + */ +hsa_status_t HSA_API hsa_amd_agent_set_async_scratch_limit(hsa_agent_t agent, size_t threshold); + +#ifdef __cplusplus +} // end extern "C" block +#endif + +#endif // header guard diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_finalize.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_finalize.h new file mode 100644 index 0000000000000000000000000000000000000000..94c45820551f5e0823c5107e0e590e296bc62bf8 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_finalize.h @@ -0,0 +1,531 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef HSA_RUNTIME_INC_HSA_EXT_FINALIZE_H_ +#define HSA_RUNTIME_INC_HSA_EXT_FINALIZE_H_ + +#include "hsa.h" + +#undef HSA_API +#ifdef HSA_EXPORT_FINALIZER +#define HSA_API HSA_API_EXPORT +#else +#define HSA_API HSA_API_IMPORT +#endif + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +struct BrigModuleHeader; +typedef struct BrigModuleHeader* BrigModule_t; + +/** \defgroup ext-alt-finalizer-extensions Finalization Extensions + * @{ + */ + +/** + * @brief Enumeration constants added to ::hsa_status_t by this extension. + */ +enum { + /** + * The HSAIL program is invalid. + */ + HSA_EXT_STATUS_ERROR_INVALID_PROGRAM = 0x2000, + /** + * The HSAIL module is invalid. + */ + HSA_EXT_STATUS_ERROR_INVALID_MODULE = 0x2001, + /** + * Machine model or profile of the HSAIL module do not match the machine model + * or profile of the HSAIL program. + */ + HSA_EXT_STATUS_ERROR_INCOMPATIBLE_MODULE = 0x2002, + /** + * The HSAIL module is already a part of the HSAIL program. + */ + HSA_EXT_STATUS_ERROR_MODULE_ALREADY_INCLUDED = 0x2003, + /** + * Compatibility mismatch between symbol declaration and symbol definition. + */ + HSA_EXT_STATUS_ERROR_SYMBOL_MISMATCH = 0x2004, + /** + * The finalization encountered an error while finalizing a kernel or + * indirect function. + */ + HSA_EXT_STATUS_ERROR_FINALIZATION_FAILED = 0x2005, + /** + * Mismatch between a directive in the control directive structure and in + * the HSAIL kernel. + */ + HSA_EXT_STATUS_ERROR_DIRECTIVE_MISMATCH = 0x2006 +}; + +/** @} */ + +/** \defgroup ext-alt-finalizer-program Finalization Program + * @{ + */ + +/** + * @brief HSAIL (BRIG) module. The HSA Programmer's Reference Manual contains + * the definition of the BrigModule_t type. + */ +typedef BrigModule_t hsa_ext_module_t; + +/** + * @brief An opaque handle to a HSAIL program, which groups a set of HSAIL + * modules that collectively define functions and variables used by kernels and + * indirect functions. + */ +typedef struct hsa_ext_program_s { + /** + * Opaque handle. + */ + uint64_t handle; +} hsa_ext_program_t; + +/** + * @brief Create an empty HSAIL program. + * + * @param[in] machine_model Machine model used in the HSAIL program. + * + * @param[in] profile Profile used in the HSAIL program. + * + * @param[in] default_float_rounding_mode Default float rounding mode used in + * the HSAIL program. + * + * @param[in] options Vendor-specific options. May be NULL. + * + * @param[out] program Memory location where the HSA runtime stores the newly + * created HSAIL program handle. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure to allocate + * resources required for the operation. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p machine_model is invalid, + * @p profile is invalid, @p default_float_rounding_mode is invalid, or + * @p program is NULL. + */ +hsa_status_t HSA_API hsa_ext_program_create( + hsa_machine_model_t machine_model, + hsa_profile_t profile, + hsa_default_float_rounding_mode_t default_float_rounding_mode, + const char *options, + hsa_ext_program_t *program); + +/** + * @brief Destroy a HSAIL program. + * + * @details The HSAIL program handle becomes invalid after it has been + * destroyed. Code object handles produced by ::hsa_ext_program_finalize are + * still valid after the HSAIL program has been destroyed, and can be used as + * intended. Resources allocated outside and associated with the HSAIL program + * (such as HSAIL modules that are added to the HSAIL program) can be released + * after the finalization program has been destroyed. + * + * @param[in] program HSAIL program. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_PROGRAM The HSAIL program is + * invalid. + */ +hsa_status_t HSA_API hsa_ext_program_destroy( + hsa_ext_program_t program); + +/** + * @brief Add a HSAIL module to an existing HSAIL program. + * + * @details The HSA runtime does not perform a deep copy of the HSAIL module + * upon addition. Instead, it stores a pointer to the HSAIL module. The + * ownership of the HSAIL module belongs to the application, which must ensure + * that @p module is not released before destroying the HSAIL program. + * + * The HSAIL module is successfully added to the HSAIL program if @p module is + * valid, if all the declarations and definitions for the same symbol are + * compatible, and if @p module specify machine model and profile that matches + * the HSAIL program. + * + * @param[in] program HSAIL program. + * + * @param[in] module HSAIL module. The application can add the same HSAIL module + * to @p program at most once. The HSAIL module must specify the same machine + * model and profile as @p program. If the floating-mode rounding mode of @p + * module is not default, then it should match that of @p program. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure to allocate + * resources required for the operation. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_PROGRAM The HSAIL program is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_MODULE The HSAIL module is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_INCOMPATIBLE_MODULE The machine model of @p + * module does not match machine model of @p program, or the profile of @p + * module does not match profile of @p program. + * + * @retval ::HSA_EXT_STATUS_ERROR_MODULE_ALREADY_INCLUDED The HSAIL module is + * already a part of the HSAIL program. + * + * @retval ::HSA_EXT_STATUS_ERROR_SYMBOL_MISMATCH Symbol declaration and symbol + * definition compatibility mismatch. See the symbol compatibility rules in the + * HSA Programming Reference Manual. + */ +hsa_status_t HSA_API hsa_ext_program_add_module( + hsa_ext_program_t program, + hsa_ext_module_t module); + +/** + * @brief Iterate over the HSAIL modules in a program, and invoke an + * application-defined callback on every iteration. + * + * @param[in] program HSAIL program. + * + * @param[in] callback Callback to be invoked once per HSAIL module in the + * program. The HSA runtime passes three arguments to the callback: the program, + * a HSAIL module, and the application data. If @p callback returns a status + * other than ::HSA_STATUS_SUCCESS for a particular iteration, the traversal + * stops and ::hsa_ext_program_iterate_modules returns that status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_PROGRAM The program is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t HSA_API hsa_ext_program_iterate_modules( + hsa_ext_program_t program, + hsa_status_t (*callback)(hsa_ext_program_t program, hsa_ext_module_t module, + void* data), + void* data); + +/** + * @brief HSAIL program attributes. + */ +typedef enum { + /** + * Machine model specified when the HSAIL program was created. The type + * of this attribute is ::hsa_machine_model_t. + */ + HSA_EXT_PROGRAM_INFO_MACHINE_MODEL = 0, + /** + * Profile specified when the HSAIL program was created. The type of + * this attribute is ::hsa_profile_t. + */ + HSA_EXT_PROGRAM_INFO_PROFILE = 1, + /** + * Default float rounding mode specified when the HSAIL program was + * created. The type of this attribute is ::hsa_default_float_rounding_mode_t. + */ + HSA_EXT_PROGRAM_INFO_DEFAULT_FLOAT_ROUNDING_MODE = 2 +} hsa_ext_program_info_t; + +/** + * @brief Get the current value of an attribute for a given HSAIL program. + * + * @param[in] program HSAIL program. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behaviour is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_PROGRAM The HSAIL program is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * HSAIL program attribute, or @p value is NULL. + */ +hsa_status_t HSA_API hsa_ext_program_get_info( + hsa_ext_program_t program, + hsa_ext_program_info_t attribute, + void *value); + +/** + * @brief Finalizer-determined call convention. + */ +typedef enum { + /** + * Finalizer-determined call convention. + */ + HSA_EXT_FINALIZER_CALL_CONVENTION_AUTO = -1 +} hsa_ext_finalizer_call_convention_t; + +/** + * @brief Control directives specify low-level information about the + * finalization process. + */ +typedef struct hsa_ext_control_directives_s { + /** + * Bitset indicating which control directives are enabled. The bit assigned to + * a control directive is determined by the corresponding value in + * BrigControlDirective. + * + * If a control directive is disabled, its corresponding field value (if any) + * must be 0. Control directives that are only present or absent (such as + * partial workgroups) have no corresponding field as the presence of the bit + * in this mask is sufficient. + */ + uint64_t control_directives_mask; + /** + * Bitset of HSAIL exceptions that must have the BREAK policy enabled. The bit + * assigned to an HSAIL exception is determined by the corresponding value + * in BrigExceptionsMask. If the kernel contains a enablebreakexceptions + * control directive, the finalizer uses the union of the two masks. + */ + uint16_t break_exceptions_mask; + /** + * Bitset of HSAIL exceptions that must have the DETECT policy enabled. The + * bit assigned to an HSAIL exception is determined by the corresponding value + * in BrigExceptionsMask. If the kernel contains a enabledetectexceptions + * control directive, the finalizer uses the union of the two masks. + */ + uint16_t detect_exceptions_mask; + /** + * Maximum size (in bytes) of dynamic group memory that will be allocated by + * the application for any dispatch of the kernel. If the kernel contains a + * maxdynamicsize control directive, the two values should match. + */ + uint32_t max_dynamic_group_size; + /** + * Maximum number of grid work-items that will be used by the application to + * launch the kernel. If the kernel contains a maxflatgridsize control + * directive, the value of @a max_flat_grid_size must not be greater than the + * value of the directive, and takes precedence. + * + * The value specified for maximum absolute grid size must be greater than or + * equal to the product of the values specified by @a required_grid_size. + * + * If the bit at position BRIG_CONTROL_MAXFLATGRIDSIZE is set in @a + * control_directives_mask, this field must be greater than 0. + */ + uint64_t max_flat_grid_size; + /** + * Maximum number of work-group work-items that will be used by the + * application to launch the kernel. If the kernel contains a + * maxflatworkgroupsize control directive, the value of @a + * max_flat_workgroup_size must not be greater than the value of the + * directive, and takes precedence. + * + * The value specified for maximum absolute grid size must be greater than or + * equal to the product of the values specified by @a required_workgroup_size. + * + * If the bit at position BRIG_CONTROL_MAXFLATWORKGROUPSIZE is set in @a + * control_directives_mask, this field must be greater than 0. + */ + uint32_t max_flat_workgroup_size; + /** + * Reserved. Must be 0. + */ + uint32_t reserved1; + /** + * Grid size that will be used by the application in any dispatch of the + * kernel. If the kernel contains a requiredgridsize control directive, the + * dimensions should match. + * + * The specified grid size must be consistent with @a required_workgroup_size + * and @a required_dim. Also, the product of the three dimensions must not + * exceed @a max_flat_grid_size. Note that the listed invariants must hold + * only if all the corresponding control directives are enabled. + * + * If the bit at position BRIG_CONTROL_REQUIREDGRIDSIZE is set in @a + * control_directives_mask, the three dimension values must be greater than 0. + */ + uint64_t required_grid_size[3]; + /** + * Work-group size that will be used by the application in any dispatch of the + * kernel. If the kernel contains a requiredworkgroupsize control directive, + * the dimensions should match. + * + * The specified work-group size must be consistent with @a required_grid_size + * and @a required_dim. Also, the product of the three dimensions must not + * exceed @a max_flat_workgroup_size. Note that the listed invariants must + * hold only if all the corresponding control directives are enabled. + * + * If the bit at position BRIG_CONTROL_REQUIREDWORKGROUPSIZE is set in @a + * control_directives_mask, the three dimension values must be greater than 0. + */ + hsa_dim3_t required_workgroup_size; + /** + * Number of dimensions that will be used by the application to launch the + * kernel. If the kernel contains a requireddim control directive, the two + * values should match. + * + * The specified dimensions must be consistent with @a required_grid_size and + * @a required_workgroup_size. This invariant must hold only if all the + * corresponding control directives are enabled. + * + * If the bit at position BRIG_CONTROL_REQUIREDDIM is set in @a + * control_directives_mask, this field must be 1, 2, or 3. + */ + uint8_t required_dim; + /** + * Reserved. Must be 0. + */ + uint8_t reserved2[75]; +} hsa_ext_control_directives_t; + +/** + * @brief Finalize an HSAIL program for a given instruction set architecture. + * + * @details Finalize all of the kernels and indirect functions that belong to + * the same HSAIL program for a specific instruction set architecture (ISA). The + * transitive closure of all functions specified by call or scall must be + * defined. Kernels and indirect functions that are being finalized must be + * defined. Kernels and indirect functions that are referenced in kernels and + * indirect functions being finalized may or may not be defined, but must be + * declared. All the global/readonly segment variables that are referenced in + * kernels and indirect functions being finalized may or may not be defined, but + * must be declared. + * + * @param[in] program HSAIL program. + * + * @param[in] isa Instruction set architecture to finalize for. + * + * @param[in] call_convention A call convention used in a finalization. Must + * have a value between ::HSA_EXT_FINALIZER_CALL_CONVENTION_AUTO (inclusive) + * and the value of the attribute ::HSA_ISA_INFO_CALL_CONVENTION_COUNT in @p + * isa (not inclusive). + * + * @param[in] control_directives Low-level control directives that influence + * the finalization process. + * + * @param[in] options Vendor-specific options. May be NULL. + * + * @param[in] code_object_type Type of code object to produce. + * + * @param[out] code_object Code object generated by the Finalizer, which + * contains the machine code for the kernels and indirect functions in the HSAIL + * program. The code object is independent of the HSAIL module that was used to + * generate it. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES There is a failure to allocate + * resources required for the operation. + * + * @retval ::HSA_EXT_STATUS_ERROR_INVALID_PROGRAM The HSAIL program is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ISA @p isa is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_DIRECTIVE_MISMATCH The directive in + * the control directive structure and in the HSAIL kernel mismatch, or if the + * same directive is used with a different value in one of the functions used by + * this kernel. + * + * @retval ::HSA_EXT_STATUS_ERROR_FINALIZATION_FAILED The Finalizer + * encountered an error while compiling a kernel or an indirect function. + */ +hsa_status_t HSA_API hsa_ext_program_finalize( + hsa_ext_program_t program, + hsa_isa_t isa, + int32_t call_convention, + hsa_ext_control_directives_t control_directives, + const char *options, + hsa_code_object_type_t code_object_type, + hsa_code_object_t *code_object); + +/** @} */ + +#define hsa_ext_finalizer_1_00 + +typedef struct hsa_ext_finalizer_1_00_pfn_s { + hsa_status_t (*hsa_ext_program_create)( + hsa_machine_model_t machine_model, hsa_profile_t profile, + hsa_default_float_rounding_mode_t default_float_rounding_mode, + const char *options, hsa_ext_program_t *program); + + hsa_status_t (*hsa_ext_program_destroy)(hsa_ext_program_t program); + + hsa_status_t (*hsa_ext_program_add_module)(hsa_ext_program_t program, + hsa_ext_module_t module); + + hsa_status_t (*hsa_ext_program_iterate_modules)( + hsa_ext_program_t program, + hsa_status_t (*callback)(hsa_ext_program_t program, + hsa_ext_module_t module, void *data), + void *data); + + hsa_status_t (*hsa_ext_program_get_info)( + hsa_ext_program_t program, hsa_ext_program_info_t attribute, + void *value); + + hsa_status_t (*hsa_ext_program_finalize)( + hsa_ext_program_t program, hsa_isa_t isa, int32_t call_convention, + hsa_ext_control_directives_t control_directives, const char *options, + hsa_code_object_type_t code_object_type, hsa_code_object_t *code_object); +} hsa_ext_finalizer_1_00_pfn_t; + +#ifdef __cplusplus +} // extern "C" block +#endif // __cplusplus + +#endif // HSA_RUNTIME_INC_HSA_EXT_FINALIZE_H_ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_image.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_image.h new file mode 100644 index 0000000000000000000000000000000000000000..b25f168395ccfca22ad2f22797572a1d72904d71 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ext_image.h @@ -0,0 +1,1454 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef HSA_EXT_IMAGE_H +#define HSA_EXT_IMAGE_H + +#include "hsa.h" + +#undef HSA_API +#ifdef HSA_EXPORT_IMAGES +#define HSA_API HSA_API_EXPORT +#else +#define HSA_API HSA_API_IMPORT +#endif + +#ifdef __cplusplus +extern "C" { +#endif /*__cplusplus*/ + +/** \defgroup ext-images Images and Samplers + * @{ + */ + +/** + * @brief Enumeration constants added to ::hsa_status_t by this extension. + * + * @remark Additions to hsa_status_t + */ +enum { + /** + * Image format is not supported. + */ + HSA_EXT_STATUS_ERROR_IMAGE_FORMAT_UNSUPPORTED = 0x3000, + /** + * Image size is not supported. + */ + HSA_EXT_STATUS_ERROR_IMAGE_SIZE_UNSUPPORTED = 0x3001, + /** + * Image pitch is not supported or invalid. + */ + HSA_EXT_STATUS_ERROR_IMAGE_PITCH_UNSUPPORTED = 0x3002, + /** + * Sampler descriptor is not supported or invalid. + */ + HSA_EXT_STATUS_ERROR_SAMPLER_DESCRIPTOR_UNSUPPORTED = 0x3003 +}; + +/** + * @brief Enumeration constants added to ::hsa_agent_info_t by this + * extension. + * + * @remark Additions to hsa_agent_info_t + */ +enum { + /** + * Maximum number of elements in 1D images. Must be at least 16384. The type + * of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_IMAGE_1D_MAX_ELEMENTS = 0x3000, + /** + * Maximum number of elements in 1DA images. Must be at least 16384. The type + * of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_IMAGE_1DA_MAX_ELEMENTS = 0x3001, + /** + * Maximum number of elements in 1DB images. Must be at least 65536. The type + * of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_IMAGE_1DB_MAX_ELEMENTS = 0x3002, + /** + * Maximum dimensions (width, height) of 2D images, in image elements. The X + * and Y maximums must be at least 16384. The type of this attribute is + * size_t[2]. + */ + HSA_EXT_AGENT_INFO_IMAGE_2D_MAX_ELEMENTS = 0x3003, + /** + * Maximum dimensions (width, height) of 2DA images, in image elements. The X + * and Y maximums must be at least 16384. The type of this attribute is + * size_t[2]. + */ + HSA_EXT_AGENT_INFO_IMAGE_2DA_MAX_ELEMENTS = 0x3004, + /** + * Maximum dimensions (width, height) of 2DDEPTH images, in image + * elements. The X and Y maximums must be at least 16384. The type of this + * attribute is size_t[2]. + */ + HSA_EXT_AGENT_INFO_IMAGE_2DDEPTH_MAX_ELEMENTS = 0x3005, + /** + * Maximum dimensions (width, height) of 2DADEPTH images, in image + * elements. The X and Y maximums must be at least 16384. The type of this + * attribute is size_t[2]. + */ + HSA_EXT_AGENT_INFO_IMAGE_2DADEPTH_MAX_ELEMENTS = 0x3006, + /** + * Maximum dimensions (width, height, depth) of 3D images, in image + * elements. The maximum along any dimension must be at least 2048. The type + * of this attribute is size_t[3]. + */ + HSA_EXT_AGENT_INFO_IMAGE_3D_MAX_ELEMENTS = 0x3007, + /** + * Maximum number of image layers in a image array. Must be at least 2048. The + * type of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_IMAGE_ARRAY_MAX_LAYERS = 0x3008, + /** + * Maximum number of read-only image handles that can be created for an agent at any one + * time. Must be at least 128. The type of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_MAX_IMAGE_RD_HANDLES = 0x3009, + /** + * Maximum number of write-only and read-write image handles (combined) that + * can be created for an agent at any one time. Must be at least 64. The type of this + * attribute is size_t. + */ + HSA_EXT_AGENT_INFO_MAX_IMAGE_RORW_HANDLES = 0x300A, + /** + * Maximum number of sampler handlers that can be created for an agent at any one + * time. Must be at least 16. The type of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_MAX_SAMPLER_HANDLERS = 0x300B, + /** + * Image pitch alignment. The agent only supports linear image data + * layouts with a row pitch that is a multiple of this value. Must be + * a power of 2. The type of this attribute is size_t. + */ + HSA_EXT_AGENT_INFO_IMAGE_LINEAR_ROW_PITCH_ALIGNMENT = 0x300C +}; + +/** + * @brief Image handle, populated by ::hsa_ext_image_create or + * ::hsa_ext_image_create_with_layout. Image + * handles are only unique within an agent, not across agents. + * + */ +typedef struct hsa_ext_image_s { + /** + * Opaque handle. For a given agent, two handles reference the same object of + * the enclosing type if and only if they are equal. + */ + uint64_t handle; + +} hsa_ext_image_t; + +/** + * @brief Geometry associated with the image. This specifies the + * number of image dimensions and whether the image is an image + * array. See the Image Geometry section in the HSA + * Programming Reference Manual for definitions on each + * geometry. The enumeration values match the BRIG type @p + * hsa_ext_brig_image_geometry_t. + */ +typedef enum { +/** + * One-dimensional image addressed by width coordinate. + */ + HSA_EXT_IMAGE_GEOMETRY_1D = 0, + + /** + * Two-dimensional image addressed by width and height coordinates. + */ + HSA_EXT_IMAGE_GEOMETRY_2D = 1, + + /** + * Three-dimensional image addressed by width, height, and depth coordinates. + */ + HSA_EXT_IMAGE_GEOMETRY_3D = 2, + + /** + * Array of one-dimensional images with the same size and format. 1D arrays + * are addressed by width and index coordinate. + */ + HSA_EXT_IMAGE_GEOMETRY_1DA = 3, + + /** + * Array of two-dimensional images with the same size and format. 2D arrays + * are addressed by width, height, and index coordinates. + */ + HSA_EXT_IMAGE_GEOMETRY_2DA = 4, + + /** + * One-dimensional image addressed by width coordinate. It has + * specific restrictions compared to ::HSA_EXT_IMAGE_GEOMETRY_1D. An + * image with an opaque image data layout will always use a linear + * image data layout, and one with an explicit image data layout + * must specify ::HSA_EXT_IMAGE_DATA_LAYOUT_LINEAR. + */ + HSA_EXT_IMAGE_GEOMETRY_1DB = 5, + + /** + * Two-dimensional depth image addressed by width and height coordinates. + */ + HSA_EXT_IMAGE_GEOMETRY_2DDEPTH = 6, + + /** + * Array of two-dimensional depth images with the same size and format. 2D + * arrays are addressed by width, height, and index coordinates. + */ + HSA_EXT_IMAGE_GEOMETRY_2DADEPTH = 7 +} hsa_ext_image_geometry_t; + +/** + * @brief Channel type associated with the elements of an image. See + * the Channel Type section in the HSA Programming Reference + * Manual for definitions on each channel type. The + * enumeration values and definition match the BRIG type @p + * hsa_ext_brig_image_channel_type_t. + */ +typedef enum { + HSA_EXT_IMAGE_CHANNEL_TYPE_SNORM_INT8 = 0, + HSA_EXT_IMAGE_CHANNEL_TYPE_SNORM_INT16 = 1, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_INT8 = 2, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_INT16 = 3, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_INT24 = 4, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_SHORT_555 = 5, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_SHORT_565 = 6, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNORM_SHORT_101010 = 7, + HSA_EXT_IMAGE_CHANNEL_TYPE_SIGNED_INT8 = 8, + HSA_EXT_IMAGE_CHANNEL_TYPE_SIGNED_INT16 = 9, + HSA_EXT_IMAGE_CHANNEL_TYPE_SIGNED_INT32 = 10, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNSIGNED_INT8 = 11, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNSIGNED_INT16 = 12, + HSA_EXT_IMAGE_CHANNEL_TYPE_UNSIGNED_INT32 = 13, + HSA_EXT_IMAGE_CHANNEL_TYPE_HALF_FLOAT = 14, + HSA_EXT_IMAGE_CHANNEL_TYPE_FLOAT = 15 +} hsa_ext_image_channel_type_t; + +/** + * @brief A fixed-size type used to represent ::hsa_ext_image_channel_type_t constants. + */ +typedef uint32_t hsa_ext_image_channel_type32_t; + +/** + * + * @brief Channel order associated with the elements of an image. See + * the Channel Order section in the HSA Programming Reference + * Manual for definitions on each channel order. The + * enumeration values match the BRIG type @p + * hsa_ext_brig_image_channel_order_t. + */ +typedef enum { + HSA_EXT_IMAGE_CHANNEL_ORDER_A = 0, + HSA_EXT_IMAGE_CHANNEL_ORDER_R = 1, + HSA_EXT_IMAGE_CHANNEL_ORDER_RX = 2, + HSA_EXT_IMAGE_CHANNEL_ORDER_RG = 3, + HSA_EXT_IMAGE_CHANNEL_ORDER_RGX = 4, + HSA_EXT_IMAGE_CHANNEL_ORDER_RA = 5, + HSA_EXT_IMAGE_CHANNEL_ORDER_RGB = 6, + HSA_EXT_IMAGE_CHANNEL_ORDER_RGBX = 7, + HSA_EXT_IMAGE_CHANNEL_ORDER_RGBA = 8, + HSA_EXT_IMAGE_CHANNEL_ORDER_BGRA = 9, + HSA_EXT_IMAGE_CHANNEL_ORDER_ARGB = 10, + HSA_EXT_IMAGE_CHANNEL_ORDER_ABGR = 11, + HSA_EXT_IMAGE_CHANNEL_ORDER_SRGB = 12, + HSA_EXT_IMAGE_CHANNEL_ORDER_SRGBX = 13, + HSA_EXT_IMAGE_CHANNEL_ORDER_SRGBA = 14, + HSA_EXT_IMAGE_CHANNEL_ORDER_SBGRA = 15, + HSA_EXT_IMAGE_CHANNEL_ORDER_INTENSITY = 16, + HSA_EXT_IMAGE_CHANNEL_ORDER_LUMINANCE = 17, + HSA_EXT_IMAGE_CHANNEL_ORDER_DEPTH = 18, + HSA_EXT_IMAGE_CHANNEL_ORDER_DEPTH_STENCIL = 19 +} hsa_ext_image_channel_order_t; + +/** + * @brief A fixed-size type used to represent ::hsa_ext_image_channel_order_t constants. + */ +typedef uint32_t hsa_ext_image_channel_order32_t; + + +/** + * @brief Image format. + */ +typedef struct hsa_ext_image_format_s { + /** + * Channel type. + */ + hsa_ext_image_channel_type32_t channel_type; + + /** + * Channel order. + */ + hsa_ext_image_channel_order32_t channel_order; +} hsa_ext_image_format_t; + +/** + * @brief Implementation independent image descriptor. + */ +typedef struct hsa_ext_image_descriptor_s { + /** + * Image geometry. + */ + hsa_ext_image_geometry_t geometry; + /** + * Width of the image, in components. + */ + size_t width; + /** + * Height of the image, in components. Only used if the geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_2D, ::HSA_EXT_IMAGE_GEOMETRY_3D, + * HSA_EXT_IMAGE_GEOMETRY_2DA, HSA_EXT_IMAGE_GEOMETRY_2DDEPTH, or + * HSA_EXT_IMAGE_GEOMETRY_2DADEPTH, otherwise must be 0. + */ + size_t height; + /** + * Depth of the image, in components. Only used if the geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_3D, otherwise must be 0. + */ + size_t depth; + /** + * Number of image layers in the image array. Only used if the geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_1DA, ::HSA_EXT_IMAGE_GEOMETRY_2DA, or + * HSA_EXT_IMAGE_GEOMETRY_2DADEPTH, otherwise must be 0. + */ + size_t array_size; + /** + * Image format. + */ + hsa_ext_image_format_t format; +} hsa_ext_image_descriptor_t; + +/** + * @brief Image capability. + */ +typedef enum { + /** + * Images of this geometry, format, and layout are not supported by + * the agent. + */ + HSA_EXT_IMAGE_CAPABILITY_NOT_SUPPORTED = 0x0, + /** + * Read-only images of this geometry, format, and layout are + * supported by the agent. + */ + HSA_EXT_IMAGE_CAPABILITY_READ_ONLY = 0x1, + /** + * Write-only images of this geometry, format, and layout are + * supported by the agent. + */ + HSA_EXT_IMAGE_CAPABILITY_WRITE_ONLY = 0x2, + /** + * Read-write images of this geometry, format, and layout are + * supported by the agent. + */ + HSA_EXT_IMAGE_CAPABILITY_READ_WRITE = 0x4, + /** + * @deprecated Images of this geometry, format, and layout can be accessed from + * read-modify-write atomic operations in the agent. + */ + HSA_EXT_IMAGE_CAPABILITY_READ_MODIFY_WRITE = 0x8, + /** + * Images of this geometry, format, and layout are guaranteed to + * have a consistent data layout regardless of how they are + * accessed by the associated agent. + */ + HSA_EXT_IMAGE_CAPABILITY_ACCESS_INVARIANT_DATA_LAYOUT = 0x10 +} hsa_ext_image_capability_t; + +/** + * @brief Image data layout. + * + * @details An image data layout denotes such aspects of image data + * layout as tiling and organization of channels in memory. Some image + * data layouts may only apply to specific image geometries, formats, + * and access permissions. Different agents may support different + * image layout identifiers, including vendor specific layouts. Note + * that an agent may not support the same image data layout for + * different access permissions to images with the same image + * geometry, size, and format. If multiple agents support the same + * image data layout then it is possible to use separate image handles + * for each agent that references the same image data. + */ + +typedef enum { + /** + * An implementation specific opaque image data layout which can + * vary depending on the agent, geometry, image format, image size, + * and access permissions. + */ + HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE = 0x0, + /** + * The image data layout is specified by the following rules in + * ascending byte address order. For a 3D image, 2DA image array, + * or 1DA image array, the image data is stored as a linear sequence + * of adjacent 2D image slices, 2D images, or 1D images + * respectively, spaced according to the slice pitch. Each 2D image + * is stored as a linear sequence of adjacent image rows, spaced + * according to the row pitch. Each 1D or 1DB image is stored as a + * single image row. Each image row is stored as a linear sequence + * of image elements. Each image element is stored as a linear + * sequence of image components specified by the left to right + * channel order definition. Each image component is stored using + * the memory type specified by the channel type. + * + * The 1DB image geometry always uses the linear image data layout. + */ + HSA_EXT_IMAGE_DATA_LAYOUT_LINEAR = 0x1 +} hsa_ext_image_data_layout_t; + +/** + * @brief Retrieve the supported image capabilities for a given combination of + * agent, geometry, and image format for an image created with an opaque image + * data layout. + * + * @param[in] agent Agent to be associated with the image handle. + * + * @param[in] geometry Geometry. + * + * @param[in] image_format Pointer to an image format. Must not be NULL. + * + * @param[out] capability_mask Pointer to a memory location where the HSA + * runtime stores a bit-mask of supported image capability + * (::hsa_ext_image_capability_t) values. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_format is + * NULL, or @p capability_mask is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_get_capability( + hsa_agent_t agent, + hsa_ext_image_geometry_t geometry, + const hsa_ext_image_format_t *image_format, + uint32_t *capability_mask); + +/** + * @brief Retrieve the supported image capabilities for a given combination of + * agent, geometry, image format, and image layout for an image created with + * an explicit image data layout. + * + * @param[in] agent Agent to be associated with the image handle. + * + * @param[in] geometry Geometry. + * + * @param[in] image_format Pointer to an image format. Must not be NULL. + * + * @param[in] image_data_layout The image data layout. + * It is invalid to use ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE; use + * ::hsa_ext_image_get_capability instead. + * + * @param[out] capability_mask Pointer to a memory location where the HSA + * runtime stores a bit-mask of supported image capability + * (::hsa_ext_image_capability_t) values. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_format is + * NULL, @p image_data_layout is ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE, + * or @p capability_mask is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_get_capability_with_layout( + hsa_agent_t agent, + hsa_ext_image_geometry_t geometry, + const hsa_ext_image_format_t *image_format, + hsa_ext_image_data_layout_t image_data_layout, + uint32_t *capability_mask); + +/** + * @brief Agent specific image size and alignment requirements, populated by + * ::hsa_ext_image_data_get_info and ::hsa_ext_image_data_get_info_with_layout. + */ +typedef struct hsa_ext_image_data_info_s { + /** + * Image data size, in bytes. + */ + size_t size; + + /** + * Image data alignment, in bytes. Must always be a power of 2. + */ + size_t alignment; + +} hsa_ext_image_data_info_t; + +/** + * @brief Retrieve the image data requirements for a given combination of agent, image + * descriptor, and access permission for an image created with an opaque image + * data layout. + * + * @details The optimal image data size and alignment requirements may + * vary depending on the image attributes specified in @p + * image_descriptor, the @p access_permission, and the @p agent. Also, + * different implementations of the HSA runtime may return different + * requirements for the same input values. + * + * The implementation must return the same image data requirements for + * different access permissions with matching image descriptors as long + * as ::hsa_ext_image_get_capability reports + * ::HSA_EXT_IMAGE_CAPABILITY_ACCESS_INVARIANT_DATA_LAYOUT. Image + * descriptors match if they have the same values, with the exception + * that s-form channel orders match the corresponding non-s-form + * channel order and vice versa. + * + * @param[in] agent Agent to be associated with the image handle. + * + * @param[in] image_descriptor Pointer to an image descriptor. Must not be NULL. + * + * @param[in] access_permission Access permission of the image when + * accessed by @p agent. The access permission defines how the agent + * is allowed to access the image and must match the corresponding + * HSAIL image handle type. The @p agent must support the image format + * specified in @p image_descriptor for the given @p + * access_permission. + * + * @param[out] image_data_info Memory location where the runtime stores the + * size and alignment requirements. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_FORMAT_UNSUPPORTED The @p + * agent does not support the image format specified by @p + * image_descriptor with the specified @p access_permission. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_SIZE_UNSUPPORTED The agent + * does not support the image dimensions specified by @p + * image_descriptor with the specified @p access_permission. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_descriptor is NULL, @p + * access_permission is not a valid access permission value, or @p + * image_data_info is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_data_get_info( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + hsa_access_permission_t access_permission, + hsa_ext_image_data_info_t *image_data_info); + +/** + * @brief Retrieve the image data requirements for a given combination of + * image descriptor, access permission, image data layout, image data row pitch, + * and image data slice pitch for an image created with an explicit image + * data layout. + * + * @details The image data size and alignment requirements may vary + * depending on the image attributes specified in @p image_descriptor, + * the @p access_permission, and the image layout. However, different + * implementations of the HSA runtime will return the same + * requirements for the same input values. + * + * The implementation must return the same image data requirements for + * different access permissions with matching image descriptors and + * matching image layouts as long as ::hsa_ext_image_get_capability + * reports + * ::HSA_EXT_IMAGE_CAPABILITY_ACCESS_INVARIANT_DATA_LAYOUT. Image + * descriptors match if they have the same values, with the exception + * that s-form channel orders match the corresponding non-s-form + * channel order and vice versa. Image layouts match if they are the + * same image data layout and use the same image row and slice pitch + * values. + * + * @param[in] image_descriptor Pointer to an image descriptor. Must not be NULL. + * + * @param[in] access_permission Access permission of the image when + * accessed by an agent. The access permission defines how the agent + * is allowed to access the image and must match the corresponding + * HSAIL image handle type. + * + * @param[in] image_data_layout The image data layout to use. + * It is invalid to use ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE; use + * ::hsa_ext_image_data_get_info instead. + * + * @param[in] image_data_row_pitch The size in bytes for a single row + * of the image in the image data. If 0 is specified then the default + * row pitch value is used: image width * image element byte size. + * The value used must be greater than or equal to the default row + * pitch, and be a multiple of the image element byte size. For the + * linear image layout it must also be a multiple of the image linear + * row pitch alignment for the agents that will access the image data + * using image instructions. + * + * @param[in] image_data_slice_pitch The size in bytes of a single + * slice of a 3D image, or the size in bytes of each image layer in an + * image array in the image data. If 0 is specified then the default + * slice pitch value is used: row pitch * height if geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_3D, ::HSA_EXT_IMAGE_GEOMETRY_2DA, or + * ::HSA_EXT_IMAGE_GEOMETRY_2DADEPTH; row pitch if geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_1DA; and 0 otherwise. The value used must + * be 0 if the default slice pitch is 0, be greater than or equal to + * the default slice pitch, and be a multiple of the row pitch. + * + * @param[out] image_data_info Memory location where the runtime stores the + * size and alignment requirements. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_FORMAT_UNSUPPORTED The image + * format specified by @p image_descriptor is not supported for the + * @p access_permission and @p image_data_layout specified. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_SIZE_UNSUPPORTED The image + * dimensions specified by @p image_descriptor are not supported for + * the @p access_permission and @p image_data_layout specified. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_PITCH_UNSUPPORTED The row and + * slice pitch specified by @p image_data_row_pitch and @p + * image_data_slice_pitch are invalid or not supported. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_descriptor is + * NULL, @p image_data_layout is ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE, + * or @p image_data_info is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_data_get_info_with_layout( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + hsa_access_permission_t access_permission, + hsa_ext_image_data_layout_t image_data_layout, + size_t image_data_row_pitch, + size_t image_data_slice_pitch, + hsa_ext_image_data_info_t *image_data_info); + +/** + * @brief Creates an agent specific image handle to an image with an + * opaque image data layout. + * + * @details Images with an opaque image data layout created with + * different access permissions but matching image descriptors and + * same agent can share the same image data if + * ::HSA_EXT_IMAGE_CAPABILITY_ACCESS_INVARIANT_DATA_LAYOUT is reported + * by ::hsa_ext_image_get_capability for the image format specified in + * the image descriptor. Image descriptors match if they have the same + * values, with the exception that s-form channel orders match the + * corresponding non-s-form channel order and vice versa. + * + * If necessary, an application can use image operations (import, + * export, copy, clear) to prepare the image for the intended use + * regardless of the access permissions. + * + * @param[in] agent agent to be associated with the image handle created. + * + * @param[in] image_descriptor Pointer to an image descriptor. Must not be NULL. + * + * @param[in] image_data Image data buffer that must have been allocated + * according to the size and alignment requirements dictated by + * ::hsa_ext_image_data_get_info. Must not be NULL. + * + * Any previous memory contents are preserved upon creation. The application is + * responsible for ensuring that the lifetime of the image data exceeds that of + * all the associated images. + * + * @param[in] access_permission Access permission of the image when + * accessed by agent. The access permission defines how the agent + * is allowed to access the image using the image handle created and + * must match the corresponding HSAIL image handle type. The agent + * must support the image format specified in @p image_descriptor for + * the given @p access_permission. + * + * @param[out] image Pointer to a memory location where the HSA runtime stores + * the newly created image handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_FORMAT_UNSUPPORTED The agent + * does not have the capability to support the image format contained + * in @p image_descriptor using the specified @p access_permission. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_SIZE_UNSUPPORTED The agent + * does not support the image dimensions specified by @p + * image_descriptor using the specified @p access_permission. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * support the creation of more image handles with the given @p access_permission). + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_descriptor is NULL, @p + * image_data is NULL, @p image_data does not have a valid alignment, + * @p access_permission is not a valid access permission + * value, or @p image is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_create( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_t *image); + +/** + * @brief Creates an agent specific image handle to an image with an explicit + * image data layout. + * + * @details Images with an explicit image data layout created with + * different access permissions but matching image descriptors and + * matching image layout can share the same image data if + * ::HSA_EXT_IMAGE_CAPABILITY_ACCESS_INVARIANT_DATA_LAYOUT is reported + * by ::hsa_ext_image_get_capability_with_layout for the image format + * specified in the image descriptor and specified image data + * layout. Image descriptors match if they have the same values, with + * the exception that s-form channel orders match the corresponding + * non-s-form channel order and vice versa. Image layouts match if + * they are the same image data layout and use the same image row and + * slice values. + * + * If necessary, an application can use image operations (import, export, copy, + * clear) to prepare the image for the intended use regardless of the access + * permissions. + * + * @param[in] agent agent to be associated with the image handle created. + * + * @param[in] image_descriptor Pointer to an image descriptor. Must not be NULL. + * + * @param[in] image_data Image data buffer that must have been allocated + * according to the size and alignment requirements dictated by + * ::hsa_ext_image_data_get_info_with_layout. Must not be NULL. + * + * Any previous memory contents are preserved upon creation. The application is + * responsible for ensuring that the lifetime of the image data exceeds that of + * all the associated images. + * + * @param[in] access_permission Access permission of the image when + * accessed by the agent. The access permission defines how the agent + * is allowed to access the image and must match the corresponding + * HSAIL image handle type. The agent must support the image format + * specified in @p image_descriptor for the given @p access_permission + * and @p image_data_layout. + * + * @param[in] image_data_layout The image data layout to use for the + * @p image_data. It is invalid to use + * ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE; use ::hsa_ext_image_create + * instead. + * + * @param[in] image_data_row_pitch The size in bytes for a single row + * of the image in the image data. If 0 is specified then the default + * row pitch value is used: image width * image element byte size. + * The value used must be greater than or equal to the default row + * pitch, and be a multiple of the image element byte size. For the + * linear image layout it must also be a multiple of the image linear + * row pitch alignment for the agents that will access the image data + * using image instructions. + * + * @param[in] image_data_slice_pitch The size in bytes of a single + * slice of a 3D image, or the size in bytes of each image layer in an + * image array in the image data. If 0 is specified then the default + * slice pitch value is used: row pitch * height if geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_3D, ::HSA_EXT_IMAGE_GEOMETRY_2DA, or + * ::HSA_EXT_IMAGE_GEOMETRY_2DADEPTH; row pitch if geometry is + * ::HSA_EXT_IMAGE_GEOMETRY_1DA; and 0 otherwise. The value used must + * be 0 if the default slice pitch is 0, be greater than or equal to + * the default slice pitch, and be a multiple of the row pitch. + * + * @param[out] image Pointer to a memory location where the HSA runtime stores + * the newly created image handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_FORMAT_UNSUPPORTED The agent does + * not have the capability to support the image format contained in the image + * descriptor using the specified @p access_permission and @p image_data_layout. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_SIZE_UNSUPPORTED The agent + * does not support the image dimensions specified by @p + * image_descriptor using the specified @p access_permission and @p + * image_data_layout. + * + * @retval ::HSA_EXT_STATUS_ERROR_IMAGE_PITCH_UNSUPPORTED The agent does + * not support the row and slice pitch specified by @p image_data_row_pitch + * and @p image_data_slice_pitch, or the values are invalid. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * support the creation of more image handles with the given @p access_permission). + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p image_descriptor is NULL, @p + * image_data is NULL, @p image_data does not have a valid alignment, + * @p image_data_layout is ::HSA_EXT_IMAGE_DATA_LAYOUT_OPAQUE, + * or @p image is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_create_with_layout( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_data_layout_t image_data_layout, + size_t image_data_row_pitch, + size_t image_data_slice_pitch, + hsa_ext_image_t *image); + +/** + * @brief Destroy an image handle previously created using ::hsa_ext_image_create or + * ::hsa_ext_image_create_with_layout. + * + * @details Destroying the image handle does not free the associated image data, + * or modify its contents. The application should not destroy an image handle while + * there are references to it queued for execution or currently being used in a + * kernel dispatch. + * + * @param[in] agent Agent associated with the image handle. + * + * @param[in] image Image handle to destroy. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + */ +hsa_status_t HSA_API hsa_ext_image_destroy( + hsa_agent_t agent, + hsa_ext_image_t image); + +/** + * @brief Copies a portion of one image (the source) to another image (the + * destination). + * + * @details The source and destination image formats should be the + * same, with the exception that s-form channel orders match the + * corresponding non-s-form channel order and vice versa. For example, + * it is allowed to copy a source image with a channel order of + * HSA_EXT_IMAGE_CHANNEL_ORDER_SRGB to a destination image with a + * channel order of HSA_EXT_IMAGE_CHANNEL_ORDER_RGB. + * + * The source and destination images do not have to be of the same geometry and + * appropriate scaling is performed by the HSA runtime. It is possible to copy + * subregions between any combinations of source and destination geometries, provided + * that the dimensions of the subregions are the same. For example, it is + * allowed to copy a rectangular region from a 2D image to a slice of a 3D + * image. + * + * If the source and destination image data overlap, or the combination of + * offset and range references an out-out-bounds element in any of the images, + * the behavior is undefined. + * + * @param[in] agent Agent associated with both the source and destination image handles. + * + * @param[in] src_image Image handle of source image. The agent associated with the source + * image handle must be identical to that of the destination image. + * + * @param[in] src_offset Pointer to the offset within the source image where to + * copy the data from. Must not be NULL. + * + * @param[in] dst_image Image handle of destination image. + * + * @param[in] dst_offset Pointer to the offset within the destination + * image where to copy the data. Must not be NULL. + * + * @param[in] range Dimensions of the image portion to be copied. The HSA + * runtime computes the size of the image data to be copied using this + * argument. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p src_offset is + * NULL, @p dst_offset is NULL, or @p range is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_copy( + hsa_agent_t agent, + hsa_ext_image_t src_image, + const hsa_dim3_t* src_offset, + hsa_ext_image_t dst_image, + const hsa_dim3_t* dst_offset, + const hsa_dim3_t* range); + +/** + * @brief Image region. + */ +typedef struct hsa_ext_image_region_s { + /** + * Offset within an image (in coordinates). + */ + hsa_dim3_t offset; + + /** + * Dimension size of the image range (in coordinates). The x, y, and z dimensions + * correspond to width, height, and depth or index respectively. + */ + hsa_dim3_t range; +} hsa_ext_image_region_t; + +/** + * @brief Import a linearly organized image data from memory directly to an + * image handle. + * + * @details This operation updates the image data referenced by the image handle + * from the source memory. The size of the data imported from memory is + * implicitly derived from the image region. + * + * It is the application's responsibility to avoid out of bounds memory access. + * + * None of the source memory or destination image data memory can + * overlap. Overlapping of any of the source and destination image + * data memory within the import operation produces undefined results. + * + * @param[in] agent Agent associated with the image handle. + * + * @param[in] src_memory Source memory. Must not be NULL. + * + * @param[in] src_row_pitch The size in bytes of a single row of the image in the + * source memory. If the value is smaller than the destination image region + * width * image element byte size, then region width * image element byte + * size is used. + * + * @param[in] src_slice_pitch The size in bytes of a single 2D slice of a 3D image, + * or the size in bytes of each image layer in an image array in the source memory. + * If the geometry is ::HSA_EXT_IMAGE_GEOMETRY_1DA and the value is smaller than the + * value used for @p src_row_pitch, then the value used for @p src_row_pitch is used. + * If the geometry is ::HSA_EXT_IMAGE_GEOMETRY_3D, ::HSA_EXT_IMAGE_GEOMETRY_2DA, or + * HSA_EXT_IMAGE_GEOMETRY_2DADEPTH and the value is smaller than the value used for + * @p src_row_pitch * destination image region height, then the value used for + * @p src_row_pitch * destination image region height is used. + * Otherwise, the value is not used. + * + * @param[in] dst_image Image handle of destination image. + * + * @param[in] image_region Pointer to the image region to be updated. Must not + * be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p src_memory is NULL, or @p + * image_region is NULL. + * + */ +hsa_status_t HSA_API hsa_ext_image_import( + hsa_agent_t agent, + const void *src_memory, + size_t src_row_pitch, + size_t src_slice_pitch, + hsa_ext_image_t dst_image, + const hsa_ext_image_region_t *image_region); + +/** + * @brief Export the image data to linearly organized memory. + * + * @details The operation updates the destination memory with the image data of + * @p src_image. The size of the data exported to memory is implicitly derived + * from the image region. + * + * It is the application's responsibility to avoid out of bounds memory access. + * + * None of the destination memory or source image data memory can + * overlap. Overlapping of any of the source and destination image + * data memory within the export operation produces undefined results. + * + * @param[in] agent Agent associated with the image handle. + * + * @param[in] src_image Image handle of source image. + * + * @param[in] dst_memory Destination memory. Must not be NULL. + * + * @param[in] dst_row_pitch The size in bytes of a single row of the image in the + * destination memory. If the value is smaller than the source image region + * width * image element byte size, then region width * image element byte + * size is used. + * + * @param[in] dst_slice_pitch The size in bytes of a single 2D slice of a 3D image, + * or the size in bytes of each image in an image array in the destination memory. + * If the geometry is ::HSA_EXT_IMAGE_GEOMETRY_1DA and the value is smaller than the + * value used for @p dst_row_pitch, then the value used for @p dst_row_pitch is used. + * If the geometry is ::HSA_EXT_IMAGE_GEOMETRY_3D, ::HSA_EXT_IMAGE_GEOMETRY_2DA, or + * HSA_EXT_IMAGE_GEOMETRY_2DADEPTH and the value is smaller than the value used for + * @p dst_row_pitch * source image region height, then the value used for + * @p dst_row_pitch * source image region height is used. + * Otherwise, the value is not used. + * + * @param[in] image_region Pointer to the image region to be exported. Must not + * be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p dst_memory is NULL, or @p + * image_region is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_export( + hsa_agent_t agent, + hsa_ext_image_t src_image, + void *dst_memory, + size_t dst_row_pitch, + size_t dst_slice_pitch, + const hsa_ext_image_region_t *image_region); + +/** + * @brief Clear a region of an image so that every image element has + * the specified value. + * + * @param[in] agent Agent associated with the image handle. + * + * @param[in] image Image handle for image to be cleared. + * + * @param[in] data The value to which to set each image element being + * cleared. It is specified as an array of image component values. The + * number of array elements must match the number of access components + * for the image channel order. The type of each array element must + * match the image access type of the image channel type. When the + * value is used to set the value of an image element, the conversion + * method corresponding to the image channel type is used. See the + * Channel Order section and Channel Type section in + * the HSA Programming Reference Manual for more + * information. Must not be NULL. + * + * @param[in] image_region Pointer to the image region to clear. Must not be + * NULL. If the region references an out-out-bounds element, the behavior is + * undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p data is NULL, or @p + * image_region is NULL. + */ +hsa_status_t HSA_API hsa_ext_image_clear( + hsa_agent_t agent, + hsa_ext_image_t image, + const void* data, + const hsa_ext_image_region_t *image_region); + +/** + * @brief Sampler handle. Samplers are populated by + * ::hsa_ext_sampler_create. Sampler handles are only unique within an + * agent, not across agents. + */ +typedef struct hsa_ext_sampler_s { + /** + * Opaque handle. For a given agent, two handles reference the same object of + * the enclosing type if and only if they are equal. + */ + uint64_t handle; +} hsa_ext_sampler_t; + +/** + * @brief Sampler address modes. The sampler address mode describes + * the processing of out-of-range image coordinates. See the + * Addressing Mode section in the HSA Programming Reference + * Manual for definitions on each address mode. The values + * match the BRIG type @p hsa_ext_brig_sampler_addressing_t. + */ +typedef enum { + /** + * Out-of-range coordinates are not handled. + */ + HSA_EXT_SAMPLER_ADDRESSING_MODE_UNDEFINED = 0, + + /** + * Clamp out-of-range coordinates to the image edge. + */ + HSA_EXT_SAMPLER_ADDRESSING_MODE_CLAMP_TO_EDGE = 1, + + /** + * Clamp out-of-range coordinates to the image border color. + */ + HSA_EXT_SAMPLER_ADDRESSING_MODE_CLAMP_TO_BORDER = 2, + + /** + * Wrap out-of-range coordinates back into the valid coordinate + * range so the image appears as repeated tiles. + */ + HSA_EXT_SAMPLER_ADDRESSING_MODE_REPEAT = 3, + + /** + * Mirror out-of-range coordinates back into the valid coordinate + * range so the image appears as repeated tiles with every other + * tile a reflection. + */ + HSA_EXT_SAMPLER_ADDRESSING_MODE_MIRRORED_REPEAT = 4 + +} hsa_ext_sampler_addressing_mode_t; + +/** + * @brief A fixed-size type used to represent ::hsa_ext_sampler_addressing_mode_t constants. + */ +typedef uint32_t hsa_ext_sampler_addressing_mode32_t; + +/** + * @brief Sampler coordinate normalization modes. See the + * Coordinate Normalization Mode section in the HSA + * Programming Reference Manual for definitions on each + * coordinate normalization mode. The values match the BRIG type @p + * hsa_ext_brig_sampler_coord_normalization_t. + */ +typedef enum { + + /** + * Coordinates are used to directly address an image element. + */ + HSA_EXT_SAMPLER_COORDINATE_MODE_UNNORMALIZED = 0, + + /** + * Coordinates are scaled by the image dimension size before being + * used to address an image element. + */ + HSA_EXT_SAMPLER_COORDINATE_MODE_NORMALIZED = 1 + +} hsa_ext_sampler_coordinate_mode_t; + +/** + * @brief A fixed-size type used to represent ::hsa_ext_sampler_coordinate_mode_t constants. + */ +typedef uint32_t hsa_ext_sampler_coordinate_mode32_t; + + +/** + * @brief Sampler filter modes. See the Filter Mode section + * in the HSA Programming Reference Manual for definitions + * on each address mode. The enumeration values match the BRIG type @p + * hsa_ext_brig_sampler_filter_t. + */ +typedef enum { + /** + * Filter to the image element nearest (in Manhattan distance) to the + * specified coordinate. + */ + HSA_EXT_SAMPLER_FILTER_MODE_NEAREST = 0, + + /** + * Filter to the image element calculated by combining the elements in a 2x2 + * square block or 2x2x2 cube block around the specified coordinate. The + * elements are combined using linear interpolation. + */ + HSA_EXT_SAMPLER_FILTER_MODE_LINEAR = 1 + +} hsa_ext_sampler_filter_mode_t; + +/** + * @brief A fixed-size type used to represent ::hsa_ext_sampler_filter_mode_t constants. + */ +typedef uint32_t hsa_ext_sampler_filter_mode32_t; + +/** + * @brief Implementation independent sampler descriptor. + */ +typedef struct hsa_ext_sampler_descriptor_s { + /** + * Sampler coordinate mode describes the normalization of image coordinates. + */ + hsa_ext_sampler_coordinate_mode32_t coordinate_mode; + + /** + * Sampler filter type describes the type of sampling performed. + */ + hsa_ext_sampler_filter_mode32_t filter_mode; + + /** + * Sampler address mode describes the processing of out-of-range image + * coordinates. + */ + hsa_ext_sampler_addressing_mode32_t address_mode; + +} hsa_ext_sampler_descriptor_t; + +/** + * @brief Create an agent specific sampler handle for a given agent + * independent sampler descriptor and agent. + * + * @param[in] agent Agent to be associated with the sampler handle created. + * + * @param[in] sampler_descriptor Pointer to a sampler descriptor. Must not be + * NULL. + * + * @param[out] sampler Memory location where the HSA runtime stores the newly + * created sampler handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + * + * @retval ::HSA_EXT_STATUS_ERROR_SAMPLER_DESCRIPTOR_UNSUPPORTED The + * @p agent does not have the capability to support the properties + * specified by @p sampler_descriptor or it is invalid. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to allocate + * the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p sampler_descriptor is NULL, or + * @p sampler is NULL. + */ +hsa_status_t HSA_API hsa_ext_sampler_create( + hsa_agent_t agent, + const hsa_ext_sampler_descriptor_t *sampler_descriptor, + hsa_ext_sampler_t *sampler); + +/** + * @brief Destroy a sampler handle previously created using ::hsa_ext_sampler_create. + * + * @details The sampler handle should not be destroyed while there are + * references to it queued for execution or currently being used in a + * kernel dispatch. + * + * @param[in] agent Agent associated with the sampler handle. + * + * @param[in] sampler Sampler handle to destroy. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_AGENT The agent is invalid. + */ +hsa_status_t HSA_API hsa_ext_sampler_destroy( + hsa_agent_t agent, + hsa_ext_sampler_t sampler); + + +#define hsa_ext_images_1_00 + +/** + * @brief The function pointer table for the images v1.00 extension. Can be returned by ::hsa_system_get_extension_table or ::hsa_system_get_major_extension_table. + */ +typedef struct hsa_ext_images_1_00_pfn_s { + + hsa_status_t (*hsa_ext_image_get_capability)( + hsa_agent_t agent, + hsa_ext_image_geometry_t geometry, + const hsa_ext_image_format_t *image_format, + uint32_t *capability_mask); + + hsa_status_t (*hsa_ext_image_data_get_info)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + hsa_access_permission_t access_permission, + hsa_ext_image_data_info_t *image_data_info); + + hsa_status_t (*hsa_ext_image_create)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_t *image); + + hsa_status_t (*hsa_ext_image_destroy)( + hsa_agent_t agent, + hsa_ext_image_t image); + + hsa_status_t (*hsa_ext_image_copy)( + hsa_agent_t agent, + hsa_ext_image_t src_image, + const hsa_dim3_t* src_offset, + hsa_ext_image_t dst_image, + const hsa_dim3_t* dst_offset, + const hsa_dim3_t* range); + + hsa_status_t (*hsa_ext_image_import)( + hsa_agent_t agent, + const void *src_memory, + size_t src_row_pitch, + size_t src_slice_pitch, + hsa_ext_image_t dst_image, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_image_export)( + hsa_agent_t agent, + hsa_ext_image_t src_image, + void *dst_memory, + size_t dst_row_pitch, + size_t dst_slice_pitch, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_image_clear)( + hsa_agent_t agent, + hsa_ext_image_t image, + const void* data, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_sampler_create)( + hsa_agent_t agent, + const hsa_ext_sampler_descriptor_t *sampler_descriptor, + hsa_ext_sampler_t *sampler); + + hsa_status_t (*hsa_ext_sampler_destroy)( + hsa_agent_t agent, + hsa_ext_sampler_t sampler); + +} hsa_ext_images_1_00_pfn_t; + +#define hsa_ext_images_1 + +/** + * @brief The function pointer table for the images v1 extension. Can be returned by ::hsa_system_get_extension_table or ::hsa_system_get_major_extension_table. + */ +typedef struct hsa_ext_images_1_pfn_s { + + hsa_status_t (*hsa_ext_image_get_capability)( + hsa_agent_t agent, + hsa_ext_image_geometry_t geometry, + const hsa_ext_image_format_t *image_format, + uint32_t *capability_mask); + + hsa_status_t (*hsa_ext_image_data_get_info)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + hsa_access_permission_t access_permission, + hsa_ext_image_data_info_t *image_data_info); + + hsa_status_t (*hsa_ext_image_create)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_t *image); + + hsa_status_t (*hsa_ext_image_destroy)( + hsa_agent_t agent, + hsa_ext_image_t image); + + hsa_status_t (*hsa_ext_image_copy)( + hsa_agent_t agent, + hsa_ext_image_t src_image, + const hsa_dim3_t* src_offset, + hsa_ext_image_t dst_image, + const hsa_dim3_t* dst_offset, + const hsa_dim3_t* range); + + hsa_status_t (*hsa_ext_image_import)( + hsa_agent_t agent, + const void *src_memory, + size_t src_row_pitch, + size_t src_slice_pitch, + hsa_ext_image_t dst_image, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_image_export)( + hsa_agent_t agent, + hsa_ext_image_t src_image, + void *dst_memory, + size_t dst_row_pitch, + size_t dst_slice_pitch, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_image_clear)( + hsa_agent_t agent, + hsa_ext_image_t image, + const void* data, + const hsa_ext_image_region_t *image_region); + + hsa_status_t (*hsa_ext_sampler_create)( + hsa_agent_t agent, + const hsa_ext_sampler_descriptor_t *sampler_descriptor, + hsa_ext_sampler_t *sampler); + + hsa_status_t (*hsa_ext_sampler_destroy)( + hsa_agent_t agent, + hsa_ext_sampler_t sampler); + + hsa_status_t (*hsa_ext_image_get_capability_with_layout)( + hsa_agent_t agent, + hsa_ext_image_geometry_t geometry, + const hsa_ext_image_format_t *image_format, + hsa_ext_image_data_layout_t image_data_layout, + uint32_t *capability_mask); + + hsa_status_t (*hsa_ext_image_data_get_info_with_layout)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + hsa_access_permission_t access_permission, + hsa_ext_image_data_layout_t image_data_layout, + size_t image_data_row_pitch, + size_t image_data_slice_pitch, + hsa_ext_image_data_info_t *image_data_info); + + hsa_status_t (*hsa_ext_image_create_with_layout)( + hsa_agent_t agent, + const hsa_ext_image_descriptor_t *image_descriptor, + const void *image_data, + hsa_access_permission_t access_permission, + hsa_ext_image_data_layout_t image_data_layout, + size_t image_data_row_pitch, + size_t image_data_slice_pitch, + hsa_ext_image_t *image); + +} hsa_ext_images_1_pfn_t; +/** @} */ + +#ifdef __cplusplus +} // end extern "C" block +#endif /*__cplusplus*/ + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_aqlprofile.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_aqlprofile.h new file mode 100644 index 0000000000000000000000000000000000000000..32ca6b7320bb1490af90a573c696413ca1792053 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_aqlprofile.h @@ -0,0 +1,488 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2017-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef OPENSRC_HSA_RUNTIME_INC_HSA_VEN_AMD_AQLPROFILE_H_ +#define OPENSRC_HSA_RUNTIME_INC_HSA_VEN_AMD_AQLPROFILE_H_ + +#include +#include "hsa.h" + +#define HSA_AQLPROFILE_VERSION_MAJOR 2 +#define HSA_AQLPROFILE_VERSION_MINOR 0 + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +//////////////////////////////////////////////////////////////////////////////// +// Library version +uint32_t hsa_ven_amd_aqlprofile_version_major(); +uint32_t hsa_ven_amd_aqlprofile_version_minor(); + +/////////////////////////////////////////////////////////////////////// +// Library API: +// The library provides helper methods for instantiation of +// the profile context object and for populating of the start +// and stop AQL packets. The profile object contains a profiling +// events list and needed for profiling buffers descriptors, +// a command buffer and an output data buffer. To check if there +// was an error the library methods return a status code. Also +// the library provides methods for querying required buffers +// attributes, to validate the event attributes and to get profiling +// output data. +// +// Returned status: +// hsa_status_t – HSA status codes are used from hsa.h header +// +// Supported profiling features: +// +// Supported profiling events +typedef enum { + HSA_VEN_AMD_AQLPROFILE_EVENT_TYPE_PMC = 0, + HSA_VEN_AMD_AQLPROFILE_EVENT_TYPE_TRACE = 1, +} hsa_ven_amd_aqlprofile_event_type_t; + +// Supported performance counters (PMC) blocks +// The block ID is the same for a block instances set, for example +// each block instance from the TCC block set, TCC0, TCC1, …, TCCN +// will have the same block ID HSA_VEN_AMD_AQLPROFILE_BLOCKS_TCC. +typedef enum { + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_CPC = 0, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_CPF = 1, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GDS = 2, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GRBM = 3, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GRBMSE = 4, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SPI = 5, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SQ = 6, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SQCS = 7, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SRBM = 8, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SX = 9, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_TA = 10, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_TCA = 11, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_TCC = 12, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_TCP = 13, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_TD = 14, + // Memory related blocks + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCARB = 15, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCHUB = 16, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCMCBVM = 17, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCSEQ = 18, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCVML2 = 19, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MCXBAR = 20, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_ATC = 21, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_ATCL2 = 22, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GCEA = 23, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_RPB = 24, + // System blocks + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_SDMA = 25, + // GFX10 added blocks + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GL1A = 26, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GL1C = 27, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GL2A = 28, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GL2C = 29, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GCR = 30, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_GUS = 31, + + // UMC & MMEA System Blocks + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_UMC = 32, + HSA_VEN_AMD_AQLPROFILE_BLOCK_NAME_MMEA = 33, + + HSA_VEN_AMD_AQLPROFILE_BLOCKS_NUMBER +} hsa_ven_amd_aqlprofile_block_name_t; + +// PMC event object structure +// ‘counter_id’ value is specified in GFXIPs perfcounter user guides +// which is the counters select value, “Performance Counters Selection” +// chapter. +typedef struct { + hsa_ven_amd_aqlprofile_block_name_t block_name; + uint32_t block_index; + uint32_t counter_id; +} hsa_ven_amd_aqlprofile_event_t; + +// Check if event is valid for the specific GPU +hsa_status_t hsa_ven_amd_aqlprofile_validate_event( + hsa_agent_t agent, // HSA handle for the profiling GPU + const hsa_ven_amd_aqlprofile_event_t* event, // [in] Pointer on validated event + bool* result); // [out] True if the event valid, False otherwise + +// Profiling parameters +// All parameters are generic and if not applicable for a specific +// profile configuration then error status will be returned. +typedef enum { + /* + * Select the target compute unit (wgp) for profiling. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_COMPUTE_UNIT_TARGET = 0, + /* + * VMID Mask + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_VM_ID_MASK = 1, + /* + * Legacy. Deprecated. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_MASK = 2, + /* + * Legacy. Deprecated. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_TOKEN_MASK = 3, + /* + * Legacy. Deprecated. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_TOKEN_MASK2 = 4, + /* + * Shader engine mask for selection. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_SE_MASK = 5, + /* + * Legacy. Deprecated. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_SAMPLE_RATE = 6, + /* + * Legacy. Deprecated. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_K_CONCURRENT = 7, + /* + * Set SIMD Mask (GFX9) or SIMD ID for collection (Navi) + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_SIMD_SELECTION = 8, + /* + * Set true for occupancy collection only. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_OCCUPANCY_MODE = 9, + /* + * ATT collection max data size, in MB. Shared among shader engines. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_ATT_BUFFER_SIZE = 10, + /* + * Mask of which compute units to generate perfcounters. GFX9 only. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_PERFCOUNTER_MASK = 240, + /* + * Select collection period for perfcounters. GFX9 only. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_PERFCOUNTER_CTRL = 241, + /* + * Select perfcounter ID (SQ block) for collection. GFX9 only. + */ + HSA_VEN_AMD_AQLPROFILE_PARAMETER_NAME_PERFCOUNTER_NAME = 242, +} hsa_ven_amd_aqlprofile_parameter_name_t; + +// Profile parameter object +typedef struct { + hsa_ven_amd_aqlprofile_parameter_name_t parameter_name; + uint32_t value; +} hsa_ven_amd_aqlprofile_parameter_t; + +typedef enum { + HSA_VEN_AMD_AQLPROFILE_ATT_CHANNEL_0 = 0, + HSA_VEN_AMD_AQLPROFILE_ATT_CHANNEL_1, + HSA_VEN_AMD_AQLPROFILE_ATT_CHANNEL_2, + HSA_VEN_AMD_AQLPROFILE_ATT_CHANNEL_3 +} hsa_ven_amd_aqlprofile_att_marker_channel_t; + +// +// Profile context object: +// The library provides a profile object structure which contains +// the events array, a buffer for the profiling start/stop commands +// and a buffer for the output data. +// The buffers are specified by the buffer descriptors and allocated +// by the application. The buffers allocation attributes, the command +// buffer size, the PMC output buffer size as well as profiling output +// data can be get using the generic get profile info helper _get_info. +// +// Buffer descriptor +typedef struct { + void* ptr; + uint32_t size; +} hsa_ven_amd_aqlprofile_descriptor_t; + +// Profile context object structure, contains profiling events list and +// needed for profiling buffers descriptors, a command buffer and +// an output data buffer +typedef struct { + hsa_agent_t agent; // GFXIP handle + hsa_ven_amd_aqlprofile_event_type_t type; // Events type + const hsa_ven_amd_aqlprofile_event_t* events; // Events array + uint32_t event_count; // Events count + const hsa_ven_amd_aqlprofile_parameter_t* parameters; // Parameters array + uint32_t parameter_count; // Parameters count + hsa_ven_amd_aqlprofile_descriptor_t output_buffer; // Output buffer + hsa_ven_amd_aqlprofile_descriptor_t command_buffer; // PM4 commands +} hsa_ven_amd_aqlprofile_profile_t; + +// +// AQL packets populating methods: +// The helper methods to populate provided by the application START and +// STOP AQL packets which the application is required to submit before and +// after profiled GPU task packets respectively. +// +// AQL Vendor Specific packet which carries a PM4 command +typedef struct { + uint16_t header; + uint16_t pm4_command[27]; + hsa_signal_t completion_signal; +} hsa_ext_amd_aql_pm4_packet_t; + +// Method to populate the provided AQL packet with profiling start commands +// Only 'pm4_command' fields of the packet are set and the application +// is responsible to set Vendor Specific header type a completion signal +hsa_status_t hsa_ven_amd_aqlprofile_start( + hsa_ven_amd_aqlprofile_profile_t* profile, // [in/out] profile contex object + hsa_ext_amd_aql_pm4_packet_t* aql_start_packet); // [out] profile start AQL packet + +// Method to populate the provided AQL packet with profiling stop commands +// Only 'pm4_command' fields of the packet are set and the application +// is responsible to set Vendor Specific header type and a completion signal +hsa_status_t hsa_ven_amd_aqlprofile_stop( + const hsa_ven_amd_aqlprofile_profile_t* profile, // [in] profile contex object + hsa_ext_amd_aql_pm4_packet_t* aql_stop_packet); // [out] profile stop AQL packet + +// Method to populate the provided AQL packet with profiling read commands +// Only 'pm4_command' fields of the packet are set and the application +// is responsible to set Vendor Specific header type and a completion signal +hsa_status_t hsa_ven_amd_aqlprofile_read( + const hsa_ven_amd_aqlprofile_profile_t* profile, // [in] profile contex object + hsa_ext_amd_aql_pm4_packet_t* aql_read_packet); // [out] profile stop AQL packet + +// Legacy devices, PM4 profiling packet size +const unsigned HSA_VEN_AMD_AQLPROFILE_LEGACY_PM4_PACKET_SIZE = 192; +// Legacy devices, converting the profiling AQL packet to PM4 packet blob +hsa_status_t hsa_ven_amd_aqlprofile_legacy_get_pm4( + const hsa_ext_amd_aql_pm4_packet_t* aql_packet, // [in] AQL packet + void* data); // [out] PM4 packet blob + +// Method to add a marker (correlation ID) into the ATT buffer. +hsa_status_t hsa_ven_amd_aqlprofile_att_marker( + hsa_ven_amd_aqlprofile_profile_t* profile, // [in/out] profile contex object + hsa_ext_amd_aql_pm4_packet_t* aql_marker_packet, // [out] profile marker AQL packet + uint32_t data, // [in] Data to be inserted + hsa_ven_amd_aqlprofile_att_marker_channel_t channel); // [in] Comm channel + +// +// Get profile info: +// Generic method for getting various profile info including profile buffers +// attributes like the command buffer size and the profiling PMC results. +// It’s implied that all counters are 64bit values. +// +// Profile generic output data: +typedef struct { + uint32_t sample_id; // PMC sample or trace buffer index + union { + struct { + hsa_ven_amd_aqlprofile_event_t event; // PMC event + uint64_t result; // PMC result + } pmc_data; + hsa_ven_amd_aqlprofile_descriptor_t trace_data; // Trace output data descriptor + }; +} hsa_ven_amd_aqlprofile_info_data_t; + +// ID query type +typedef struct { + const char* name; + uint32_t id; + uint32_t instance_count; +} hsa_ven_amd_aqlprofile_id_query_t; + +// Profile attributes +typedef enum { + HSA_VEN_AMD_AQLPROFILE_INFO_COMMAND_BUFFER_SIZE = 0, // get_info returns uint32_t value + HSA_VEN_AMD_AQLPROFILE_INFO_PMC_DATA_SIZE = 1, // get_info returns uint32_t value + HSA_VEN_AMD_AQLPROFILE_INFO_PMC_DATA = 2, // get_info returns PMC uint64_t value + // in info_data object + HSA_VEN_AMD_AQLPROFILE_INFO_TRACE_DATA = 3, // get_info returns trace buffer ptr/size + // in info_data object + HSA_VEN_AMD_AQLPROFILE_INFO_BLOCK_COUNTERS = 4, // get_info returns number of block counter + HSA_VEN_AMD_AQLPROFILE_INFO_BLOCK_ID = 5, // get_info returns block id, instances + // by name string using _id_query_t + HSA_VEN_AMD_AQLPROFILE_INFO_ENABLE_CMD = 6, // get_info returns size/pointer for + // counters enable command buffer + HSA_VEN_AMD_AQLPROFILE_INFO_DISABLE_CMD = 7, // get_info returns size/pointer for + // counters disable command buffer +} hsa_ven_amd_aqlprofile_info_type_t; + + +// Definition of output data iterator callback +typedef hsa_status_t (*hsa_ven_amd_aqlprofile_data_callback_t)( + hsa_ven_amd_aqlprofile_info_type_t info_type, // [in] data type, PMC or trace data + hsa_ven_amd_aqlprofile_info_data_t* info_data, // [in] info_data object + void* callback_data); // [in/out] data passed to the callback + +// Method for getting the profile info +hsa_status_t hsa_ven_amd_aqlprofile_get_info( + const hsa_ven_amd_aqlprofile_profile_t* profile, // [in] profile context object + hsa_ven_amd_aqlprofile_info_type_t attribute, // [in] requested profile attribute + void* value); // [in/out] returned value + +// Method for iterating the events output data +hsa_status_t hsa_ven_amd_aqlprofile_iterate_data( + const hsa_ven_amd_aqlprofile_profile_t* profile, // [in] profile context object + hsa_ven_amd_aqlprofile_data_callback_t callback, // [in] callback to iterate the output data + void* data); // [in/out] data passed to the callback + +// Return error string +hsa_status_t hsa_ven_amd_aqlprofile_error_string( + const char** str); // [out] pointer on the error string + +/** + * @brief Callback for iteration of all possible event coordinate IDs and coordinate names. +*/ +typedef hsa_status_t(*hsa_ven_amd_aqlprofile_eventname_callback_t)(int id, const char* name); +/** + * @brief Iterate over all possible event coordinate IDs and their names. +*/ +hsa_status_t hsa_ven_amd_aqlprofile_iterate_event_ids(hsa_ven_amd_aqlprofile_eventname_callback_t); + +/** + * @brief Iterate over all event coordinates for a given agent_t and event_t. + * @param position A counting sequence indicating callback number. + * @param id Coordinate ID as in _iterate_event_ids. + * @param extent Coordinate extent indicating maximum allowed instances. + * @param coordinate The coordinate, in the range [0,extent-1]. + * @param name Coordinate name as in _iterate_event_ids. + * @param userdata Userdata returned from _iterate_event_coord function. +*/ +typedef hsa_status_t(*hsa_ven_amd_aqlprofile_coordinate_callback_t)( + int position, + int id, + int extent, + int coordinate, + const char* name, + void* userdata +); + +/** + * @brief Iterate over all event coordinates for a given agent_t and event_t. + * @param[in] agent HSA agent. + * @param[in] event The event ID and block ID to iterate for. + * @param[in] sample_id aqlprofile_info_data_t.sample_id returned from _aqlprofile_iterate_data. + * @param[in] callback Callback function to return the coordinates. + * @param[in] userdata Arbitrary data pointer to be sent back to the user via callback. +*/ +hsa_status_t hsa_ven_amd_aqlprofile_iterate_event_coord( + hsa_agent_t agent, + hsa_ven_amd_aqlprofile_event_t event, + uint32_t sample_id, + hsa_ven_amd_aqlprofile_coordinate_callback_t callback, + void* userdata +); + +/** + * @brief Extension version. + */ +#define hsa_ven_amd_aqlprofile_VERSION_MAJOR 1 +#define hsa_ven_amd_aqlprofile_LIB(suff) "libhsa-amd-aqlprofile" suff ".so" + +#ifdef HSA_LARGE_MODEL +static const char kAqlProfileLib[] = hsa_ven_amd_aqlprofile_LIB("64"); +#else +static const char kAqlProfileLib[] = hsa_ven_amd_aqlprofile_LIB(""); +#endif + +/** + * @brief Extension function table. + */ +typedef struct hsa_ven_amd_aqlprofile_1_00_pfn_s { + uint32_t (*hsa_ven_amd_aqlprofile_version_major)(); + uint32_t (*hsa_ven_amd_aqlprofile_version_minor)(); + + hsa_status_t (*hsa_ven_amd_aqlprofile_error_string)( + const char** str); + + hsa_status_t (*hsa_ven_amd_aqlprofile_validate_event)( + hsa_agent_t agent, + const hsa_ven_amd_aqlprofile_event_t* event, + bool* result); + + hsa_status_t (*hsa_ven_amd_aqlprofile_start)( + hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ext_amd_aql_pm4_packet_t* aql_start_packet); + + hsa_status_t (*hsa_ven_amd_aqlprofile_stop)( + const hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ext_amd_aql_pm4_packet_t* aql_stop_packet); + + hsa_status_t (*hsa_ven_amd_aqlprofile_read)( + const hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ext_amd_aql_pm4_packet_t* aql_read_packet); + + hsa_status_t (*hsa_ven_amd_aqlprofile_legacy_get_pm4)( + const hsa_ext_amd_aql_pm4_packet_t* aql_packet, + void* data); + + hsa_status_t (*hsa_ven_amd_aqlprofile_get_info)( + const hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ven_amd_aqlprofile_info_type_t attribute, + void* value); + + hsa_status_t (*hsa_ven_amd_aqlprofile_iterate_data)( + const hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ven_amd_aqlprofile_data_callback_t callback, + void* data); + + hsa_status_t (*hsa_ven_amd_aqlprofile_iterate_event_ids)( + hsa_ven_amd_aqlprofile_eventname_callback_t + ); + + hsa_status_t (*hsa_ven_amd_aqlprofile_iterate_event_coord)( + hsa_agent_t agent, + hsa_ven_amd_aqlprofile_event_t event, + uint32_t sample_id, + hsa_ven_amd_aqlprofile_coordinate_callback_t callback, + void* userdata + ); + + hsa_status_t (*hsa_ven_amd_aqlprofile_att_marker)( + hsa_ven_amd_aqlprofile_profile_t* profile, + hsa_ext_amd_aql_pm4_packet_t* aql_packet, + uint32_t data, + hsa_ven_amd_aqlprofile_att_marker_channel_t channel + ); +} hsa_ven_amd_aqlprofile_1_00_pfn_t; + +typedef hsa_ven_amd_aqlprofile_1_00_pfn_t hsa_ven_amd_aqlprofile_pfn_t; + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // OPENSRC_HSA_RUNTIME_INC_HSA_VEN_AMD_AQLPROFILE_H_ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_loader.h b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_loader.h new file mode 100644 index 0000000000000000000000000000000000000000..47236c86e994706c726c0f062a8f5ba036f9ce7d --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/hsa/hsa_ven_amd_loader.h @@ -0,0 +1,667 @@ +//////////////////////////////////////////////////////////////////////////////// +// +// The University of Illinois/NCSA +// Open Source License (NCSA) +// +// Copyright (c) 2014-2020, Advanced Micro Devices, Inc. All rights reserved. +// +// Developed by: +// +// AMD Research and AMD HSA Software Development +// +// Advanced Micro Devices, Inc. +// +// www.amd.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal with the Software without restriction, including without limitation +// the rights to use, copy, modify, merge, publish, distribute, sublicense, +// and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// - Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimers. +// - Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimers in +// the documentation and/or other materials provided with the distribution. +// - Neither the names of Advanced Micro Devices, Inc, +// nor the names of its contributors may be used to endorse or promote +// products derived from this Software without specific prior written +// permission. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +// THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR +// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS WITH THE SOFTWARE. +// +//////////////////////////////////////////////////////////////////////////////// + +// HSA AMD extension for additional loader functionality. + +#ifndef HSA_VEN_AMD_LOADER_H +#define HSA_VEN_AMD_LOADER_H + +#include "hsa.h" + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +/** + * @brief Queries equivalent host address for given @p device_address, and + * records it in @p host_address. + * + * + * @details Contents of memory pointed to by @p host_address would be identical + * to contents of memory pointed to by @p device_address. Only difference + * between the two is host accessibility: @p host_address is always accessible + * from host, @p device_address might not be accessible from host. + * + * If @p device_address already points to host accessible memory, then the value + * of @p device_address is simply copied into @p host_address. + * + * The lifetime of @p host_address is the same as the lifetime of @p + * device_address, and both lifetimes are limited by the lifetime of the + * executable that is managing these addresses. + * + * + * @param[in] device_address Device address to query equivalent host address + * for. + * + * @param[out] host_address Pointer to application-allocated buffer to record + * queried equivalent host address in. + * + * + * @retval HSA_STATUS_SUCCESS Function is executed successfully. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED Runtime is not initialized. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p device_address is invalid or + * null, or @p host_address is null. + */ +hsa_status_t hsa_ven_amd_loader_query_host_address( + const void *device_address, + const void **host_address); + +/** + * @brief The storage type of the code object that is backing loaded memory + * segment. + */ +typedef enum { + /** + * Loaded memory segment is not backed by any code object (anonymous), as the + * case would be with BSS (uninitialized data). + */ + HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_NONE = 0, + /** + * Loaded memory segment is backed by the code object that is stored in the + * file. + */ + HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_FILE = 1, + /** + * Loaded memory segment is backed by the code object that is stored in the + * memory. + */ + HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_MEMORY = 2 +} hsa_ven_amd_loader_code_object_storage_type_t; + +/** + * @brief Loaded memory segment descriptor. + * + * + * @details Loaded memory segment descriptor describes underlying loaded memory + * segment. Loaded memory segment is created/allocated by the executable during + * the loading of the code object that is backing underlying memory segment. + * + * The lifetime of underlying memory segment is limited by the lifetime of the + * executable that is managing underlying memory segment. + */ +typedef struct hsa_ven_amd_loader_segment_descriptor_s { + /** + * Agent underlying memory segment is allocated on. If the code object that is + * backing underlying memory segment is program code object, then 0. + */ + hsa_agent_t agent; + /** + * Executable that is managing this underlying memory segment. + */ + hsa_executable_t executable; + /** + * Storage type of the code object that is backing underlying memory segment. + */ + hsa_ven_amd_loader_code_object_storage_type_t code_object_storage_type; + /** + * If the storage type of the code object that is backing underlying memory + * segment is: + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_NONE, then null; + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_FILE, then null-terminated + * filepath to the code object; + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_MEMORY, then host + * accessible pointer to the first byte of the code object. + */ + const void *code_object_storage_base; + /** + * If the storage type of the code object that is backing underlying memory + * segment is: + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_NONE, then 0; + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_FILE, then the length of + * the filepath to the code object (including null-terminating character); + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_MEMORY, then the size, in + * bytes, of the memory occupied by the code object. + */ + size_t code_object_storage_size; + /** + * If the storage type of the code object that is backing underlying memory + * segment is: + * - HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_NONE, then 0; + * - other, then offset, in bytes, from the beginning of the code object to + * the first byte in the code object data is copied from. + */ + size_t code_object_storage_offset; + /** + * Starting address of the underlying memory segment. + */ + const void *segment_base; + /** + * Size, in bytes, of the underlying memory segment. + */ + size_t segment_size; +} hsa_ven_amd_loader_segment_descriptor_t; + +/** + * @brief Either queries loaded memory segment descriptors, or total number of + * loaded memory segment descriptors. + * + * + * @details If @p segment_descriptors is not null and @p num_segment_descriptors + * points to number that exactly matches total number of loaded memory segment + * descriptors, then queries loaded memory segment descriptors, and records them + * in @p segment_descriptors. If @p segment_descriptors is null and @p + * num_segment_descriptors points to zero, then queries total number of loaded + * memory segment descriptors, and records it in @p num_segment_descriptors. In + * all other cases returns appropriate error code (see below). + * + * The caller of this function is responsible for the allocation/deallocation + * and the lifetime of @p segment_descriptors and @p num_segment_descriptors. + * + * The lifetime of loaded memory segments that are described by queried loaded + * memory segment descriptors is limited by the lifetime of the executable that + * is managing loaded memory segments. + * + * Queried loaded memory segment descriptors are always self-consistent: they + * describe a complete set of loaded memory segments that are being backed by + * fully loaded code objects that are present at the time (i.e. this function + * is blocked until all executable manipulations are fully complete). + * + * + * @param[out] segment_descriptors Pointer to application-allocated buffer to + * record queried loaded memory segment descriptors in. Can be null if @p + * num_segment_descriptors points to zero. + * + * @param[in,out] num_segment_descriptors Pointer to application-allocated + * buffer that contains either total number of loaded memory segment descriptors + * or zero. + * + * + * @retval HSA_STATUS_SUCCESS Function is executed successfully. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED Runtime is not initialized. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT @p segment_descriptors is null + * while @p num_segment_descriptors points to non-zero number, @p + * segment_descriptors is not null while @p num_segment_descriptors points to + * zero, or @p num_segment_descriptors is null. + * + * @retval HSA_STATUS_ERROR_INCOMPATIBLE_ARGUMENTS @p num_segment_descriptors + * does not point to number that exactly matches total number of loaded memory + * segment descriptors. + */ +hsa_status_t hsa_ven_amd_loader_query_segment_descriptors( + hsa_ven_amd_loader_segment_descriptor_t *segment_descriptors, + size_t *num_segment_descriptors); + +/** + * @brief Obtains the handle of executable to which the device address belongs. + * + * @details This method should not be used to obtain executable handle by using + * a host address. The executable returned is expected to be alive until its + * destroyed by the user. + * + * @retval HSA_STATUS_SUCCESS Function is executed successfully. + * + * @retval HSA_STATUS_ERROR_NOT_INITIALIZED Runtime is not initialized. + * + * @retval HSA_STATUS_ERROR_INVALID_ARGUMENT The input is invalid or there + * is no exectuable found for this kernel code object. + */ +hsa_status_t hsa_ven_amd_loader_query_executable( + const void *device_address, + hsa_executable_t *executable); + +//===----------------------------------------------------------------------===// + +/** + * @brief Iterate over the loaded code objects in an executable, and invoke + * an application-defined callback on every iteration. + * + * @param[in] executable Executable. + * + * @param[in] callback Callback to be invoked once per loaded code object. The + * HSA runtime passes three arguments to the callback: the executable, a + * loaded code object, and the application data. If @p callback returns a + * status other than ::HSA_STATUS_SUCCESS for a particular iteration, the + * traversal stops and + * ::hsa_ven_amd_loader_executable_iterate_loaded_code_objects returns that + * status value. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_EXECUTABLE The executable is invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. + */ +hsa_status_t hsa_ven_amd_loader_executable_iterate_loaded_code_objects( + hsa_executable_t executable, + hsa_status_t (*callback)( + hsa_executable_t executable, + hsa_loaded_code_object_t loaded_code_object, + void *data), + void *data); + +/** + * @brief Loaded code object kind. + */ +typedef enum { + /** + * Program code object. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_KIND_PROGRAM = 1, + /** + * Agent code object. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_KIND_AGENT = 2 +} hsa_ven_amd_loader_loaded_code_object_kind_t; + +/** + * @brief Loaded code object attributes. + */ +typedef enum hsa_ven_amd_loader_loaded_code_object_info_e { + /** + * The executable in which this loaded code object is loaded. The + * type of this attribute is ::hsa_executable_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_EXECUTABLE = 1, + /** + * The kind of this loaded code object. The type of this attribute is + * ::uint32_t interpreted as ::hsa_ven_amd_loader_loaded_code_object_kind_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_KIND = 2, + /** + * The agent on which this loaded code object is loaded. The + * value of this attribute is only defined if + * ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_KIND is + * ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_KIND_AGENT. The type of this + * attribute is ::hsa_agent_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_AGENT = 3, + /** + * The storage type of the code object reader used to load the loaded code object. + * The type of this attribute is ::uint32_t interpreted as a + * ::hsa_ven_amd_loader_code_object_storage_type_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_TYPE = 4, + /** + * The memory address of the first byte of the code object that was loaaded. + * The value of this attribute is only defined if + * ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_TYPE is + * ::HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_MEMORY. The type of this + * attribute is ::uint64_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_MEMORY_BASE = 5, + /** + * The memory size in bytes of the code object that was loaaded. + * The value of this attribute is only defined if + * ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_TYPE is + * ::HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_MEMORY. The type of this + * attribute is ::uint64_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_MEMORY_SIZE = 6, + /** + * The file descriptor of the code object that was loaaded. + * The value of this attribute is only defined if + * ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_TYPE is + * ::HSA_VEN_AMD_LOADER_CODE_OBJECT_STORAGE_TYPE_FILE. The type of this + * attribute is ::int. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_CODE_OBJECT_STORAGE_FILE = 7, + /** + * The signed byte address difference of the memory address at which the code + * object is loaded minus the virtual address specified in the code object + * that is loaded. The value of this attribute is only defined if the + * executable in which the code object is loaded is froozen. The type of this + * attribute is ::int64_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_LOAD_DELTA = 8, + /** + * The base memory address at which the code object is loaded. This is the + * base address of the allocation for the lowest addressed segment of the code + * object that is loaded. Note that any non-loaded segments before the first + * loaded segment are ignored. The value of this attribute is only defined if + * the executable in which the code object is loaded is froozen. The type of + * this attribute is ::uint64_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_LOAD_BASE = 9, + /** + * The byte size of the loaded code objects contiguous memory allocation. The + * value of this attribute is only defined if the executable in which the code + * object is loaded is froozen. The type of this attribute is ::uint64_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_LOAD_SIZE = 10, + /** + * The length of the URI in bytes, not including the NUL terminator. The type + * of this attribute is uint32_t. + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_URI_LENGTH = 11, + /** + * The URI name from which the code object was loaded. The type of this + * attribute is a NUL terminated \p char* with the length equal to the value + * of ::HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_URI_LENGTH attribute. + * The URI name syntax is defined by the following BNF syntax: + * + * code_object_uri ::== file_uri | memory_uri + * file_uri ::== "file://" file_path [ range_specifier ] + * memory_uri ::== "memory://" process_id range_specifier + * range_specifier ::== [ "#" | "?" ] "offset=" number "&" "size=" number + * file_path ::== URI_ENCODED_OS_FILE_PATH + * process_id ::== DECIMAL_NUMBER + * number ::== HEX_NUMBER | DECIMAL_NUMBER | OCTAL_NUMBER + * + * ``number`` is a C integral literal where hexadecimal values are prefixed by + * "0x" or "0X", and octal values by "0". + * + * ``file_path`` is the file's path specified as a URI encoded UTF-8 string. + * In URI encoding, every character that is not in the regular expression + * ``[a-zA-Z0-9/_.~-]`` is encoded as two uppercase hexidecimal digits + * proceeded by "%". Directories in the path are separated by "/". + * + * ``offset`` is a 0-based byte offset to the start of the code object. For a + * file URI, it is from the start of the file specified by the ``file_path``, + * and if omitted defaults to 0. For a memory URI, it is the memory address + * and is required. + * + * ``size`` is the number of bytes in the code object. For a file URI, if + * omitted it defaults to the size of the file. It is required for a memory + * URI. + * + * ``process_id`` is the identity of the process owning the memory. For Linux + * it is the C unsigned integral decimal literal for the process ID (PID). + * + * For example: + * + * file:///dir1/dir2/file1 + * file:///dir3/dir4/file2#offset=0x2000&size=3000 + * memory://1234#offset=0x20000&size=3000 + */ + HSA_VEN_AMD_LOADER_LOADED_CODE_OBJECT_INFO_URI = 12, +} hsa_ven_amd_loader_loaded_code_object_info_t; + +/** + * @brief Get the current value of an attribute for a given loaded code + * object. + * + * @param[in] loaded_code_object Loaded code object. + * + * @param[in] attribute Attribute to query. + * + * @param[out] value Pointer to an application-allocated buffer where to store + * the value of the attribute. If the buffer passed by the application is not + * large enough to hold the value of @p attribute, the behavior is undefined. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT The loaded code object is + * invalid. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p attribute is an invalid + * loaded code object attribute, or @p value is NULL. + */ +hsa_status_t hsa_ven_amd_loader_loaded_code_object_get_info( + hsa_loaded_code_object_t loaded_code_object, + hsa_ven_amd_loader_loaded_code_object_info_t attribute, + void *value); + +//===----------------------------------------------------------------------===// + +/** + * @brief Create a code object reader to operate on a file with size and offset. + * + * @param[in] file File descriptor. The file must have been opened by + * application with at least read permissions prior calling this function. The + * file must contain a vendor-specific code object. + * + * The file is owned and managed by the application; the lifetime of the file + * descriptor must exceed that of any associated code object reader. + * + * @param[in] size Size of the code object embedded in @p file. + * + * @param[in] offset 0-based offset relative to the beginning of the @p file + * that denotes the beginning of the code object embedded within the @p file. + * + * @param[out] code_object_reader Memory location to store the newly created + * code object reader handle. Must not be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_FILE @p file is not opened with at least + * read permissions. This condition may also be reported as + * ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT_READER by the + * ::hsa_executable_load_agent_code_object function. + * + * @retval ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT The bytes starting at offset + * do not form a valid code object. If file size is 0. Or offset > file size. + * This condition may also be reported as + * ::HSA_STATUS_ERROR_INVALID_CODE_OBJECT by the + * ::hsa_executable_load_agent_code_object function. + * + * @retval ::HSA_STATUS_ERROR_OUT_OF_RESOURCES The HSA runtime failed to + * allocate the required resources. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p code_object_reader is NULL. + */ +hsa_status_t +hsa_ven_amd_loader_code_object_reader_create_from_file_with_offset_size( + hsa_file_t file, + size_t offset, + size_t size, + hsa_code_object_reader_t *code_object_reader); + +//===----------------------------------------------------------------------===// + +/** + * @brief Iterate over the available executables, and invoke an + * application-defined callback on every iteration. While + * ::hsa_ven_amd_loader_iterate_executables is executing any calls to + * ::hsa_executable_create, ::hsa_executable_create_alt, or + * ::hsa_executable_destroy will be blocked. + * + * @param[in] callback Callback to be invoked once per executable. The HSA + * runtime passes two arguments to the callback: the executable and the + * application data. If @p callback returns a status other than + * ::HSA_STATUS_SUCCESS for a particular iteration, the traversal stops and + * ::hsa_ven_amd_loader_iterate_executables returns that status value. If + * @p callback invokes ::hsa_executable_create, ::hsa_executable_create_alt, or + * ::hsa_executable_destroy then the behavior is undefined. + * + * @param[in] data Application data that is passed to @p callback on every + * iteration. May be NULL. + * + * @retval ::HSA_STATUS_SUCCESS The function has been executed successfully. + * + * @retval ::HSA_STATUS_ERROR_NOT_INITIALIZED The HSA runtime has not been + * initialized. + * + * @retval ::HSA_STATUS_ERROR_INVALID_ARGUMENT @p callback is NULL. +*/ +hsa_status_t +hsa_ven_amd_loader_iterate_executables( + hsa_status_t (*callback)( + hsa_executable_t executable, + void *data), + void *data); + +//===----------------------------------------------------------------------===// + +/** + * @brief Extension version. + */ +#define hsa_ven_amd_loader 001003 + +/** + * @brief Extension function table version 1.00. + */ +typedef struct hsa_ven_amd_loader_1_00_pfn_s { + hsa_status_t (*hsa_ven_amd_loader_query_host_address)( + const void *device_address, + const void **host_address); + + hsa_status_t (*hsa_ven_amd_loader_query_segment_descriptors)( + hsa_ven_amd_loader_segment_descriptor_t *segment_descriptors, + size_t *num_segment_descriptors); + + hsa_status_t (*hsa_ven_amd_loader_query_executable)( + const void *device_address, + hsa_executable_t *executable); +} hsa_ven_amd_loader_1_00_pfn_t; + +/** + * @brief Extension function table version 1.01. + */ +typedef struct hsa_ven_amd_loader_1_01_pfn_s { + hsa_status_t (*hsa_ven_amd_loader_query_host_address)( + const void *device_address, + const void **host_address); + + hsa_status_t (*hsa_ven_amd_loader_query_segment_descriptors)( + hsa_ven_amd_loader_segment_descriptor_t *segment_descriptors, + size_t *num_segment_descriptors); + + hsa_status_t (*hsa_ven_amd_loader_query_executable)( + const void *device_address, + hsa_executable_t *executable); + + hsa_status_t (*hsa_ven_amd_loader_executable_iterate_loaded_code_objects)( + hsa_executable_t executable, + hsa_status_t (*callback)( + hsa_executable_t executable, + hsa_loaded_code_object_t loaded_code_object, + void *data), + void *data); + + hsa_status_t (*hsa_ven_amd_loader_loaded_code_object_get_info)( + hsa_loaded_code_object_t loaded_code_object, + hsa_ven_amd_loader_loaded_code_object_info_t attribute, + void *value); +} hsa_ven_amd_loader_1_01_pfn_t; + +/** + * @brief Extension function table version 1.02. + */ +typedef struct hsa_ven_amd_loader_1_02_pfn_s { + hsa_status_t (*hsa_ven_amd_loader_query_host_address)( + const void *device_address, + const void **host_address); + + hsa_status_t (*hsa_ven_amd_loader_query_segment_descriptors)( + hsa_ven_amd_loader_segment_descriptor_t *segment_descriptors, + size_t *num_segment_descriptors); + + hsa_status_t (*hsa_ven_amd_loader_query_executable)( + const void *device_address, + hsa_executable_t *executable); + + hsa_status_t (*hsa_ven_amd_loader_executable_iterate_loaded_code_objects)( + hsa_executable_t executable, + hsa_status_t (*callback)( + hsa_executable_t executable, + hsa_loaded_code_object_t loaded_code_object, + void *data), + void *data); + + hsa_status_t (*hsa_ven_amd_loader_loaded_code_object_get_info)( + hsa_loaded_code_object_t loaded_code_object, + hsa_ven_amd_loader_loaded_code_object_info_t attribute, + void *value); + + hsa_status_t + (*hsa_ven_amd_loader_code_object_reader_create_from_file_with_offset_size)( + hsa_file_t file, + size_t offset, + size_t size, + hsa_code_object_reader_t *code_object_reader); +} hsa_ven_amd_loader_1_02_pfn_t; + +/** + * @brief Extension function table version 1.03. + */ +typedef struct hsa_ven_amd_loader_1_03_pfn_s { + hsa_status_t (*hsa_ven_amd_loader_query_host_address)( + const void *device_address, + const void **host_address); + + hsa_status_t (*hsa_ven_amd_loader_query_segment_descriptors)( + hsa_ven_amd_loader_segment_descriptor_t *segment_descriptors, + size_t *num_segment_descriptors); + + hsa_status_t (*hsa_ven_amd_loader_query_executable)( + const void *device_address, + hsa_executable_t *executable); + + hsa_status_t (*hsa_ven_amd_loader_executable_iterate_loaded_code_objects)( + hsa_executable_t executable, + hsa_status_t (*callback)( + hsa_executable_t executable, + hsa_loaded_code_object_t loaded_code_object, + void *data), + void *data); + + hsa_status_t (*hsa_ven_amd_loader_loaded_code_object_get_info)( + hsa_loaded_code_object_t loaded_code_object, + hsa_ven_amd_loader_loaded_code_object_info_t attribute, + void *value); + + hsa_status_t + (*hsa_ven_amd_loader_code_object_reader_create_from_file_with_offset_size)( + hsa_file_t file, + size_t offset, + size_t size, + hsa_code_object_reader_t *code_object_reader); + + hsa_status_t + (*hsa_ven_amd_loader_iterate_executables)( + hsa_status_t (*callback)( + hsa_executable_t executable, + void *data), + void *data); +} hsa_ven_amd_loader_1_03_pfn_t; + +#ifdef __cplusplus +} +#endif /* __cplusplus */ + +#endif /* HSA_VEN_AMD_LOADER_H */ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/ext/prof_protocol.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/ext/prof_protocol.h new file mode 100644 index 0000000000000000000000000000000000000000..69a2b0b3471602c6b66cd2a9cf483b3d0ec0b91a --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/ext/prof_protocol.h @@ -0,0 +1,107 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +#ifndef EXT_PROF_PROTOCOL_H_ +#define EXT_PROF_PROTOCOL_H_ + +#include +#include + +/* Traced API domains */ +typedef enum { + ACTIVITY_DOMAIN_HSA_API = 0, /* HSA API domain */ + ACTIVITY_DOMAIN_HSA_OPS = 1, /* HSA async activity domain */ + ACTIVITY_DOMAIN_HIP_OPS = 2, /* HIP async activity domain */ + ACTIVITY_DOMAIN_HCC_OPS = + ACTIVITY_DOMAIN_HIP_OPS, /* HCC async activity domain */ + ACTIVITY_DOMAIN_HIP_VDI = + ACTIVITY_DOMAIN_HIP_OPS, /* HIP VDI async activity domain */ + ACTIVITY_DOMAIN_HIP_API = 3, /* HIP API domain */ + ACTIVITY_DOMAIN_KFD_API = 4, /* KFD API domain */ + ACTIVITY_DOMAIN_EXT_API = 5, /* External ID domain */ + ACTIVITY_DOMAIN_ROCTX = 6, /* ROCTX domain */ + ACTIVITY_DOMAIN_HSA_EVT = 7, /* HSA events */ + ACTIVITY_DOMAIN_NUMBER +} activity_domain_t; + +/* API callback type */ +typedef void (*activity_rtapi_callback_t)(uint32_t domain, uint32_t cid, + const void* data, void* arg); +typedef uint32_t activity_kind_t; +typedef uint32_t activity_op_t; + +/* API callback phase */ +typedef enum { + ACTIVITY_API_PHASE_ENTER = 0, + ACTIVITY_API_PHASE_EXIT = 1 +} activity_api_phase_t; + +/* Trace record types */ + +/* Correlation id */ +typedef uint64_t activity_correlation_id_t; + +/* Timestamp in nanoseconds */ +typedef uint64_t roctracer_timestamp_t; + +/* Activity record type */ +typedef struct activity_record_s { + uint32_t domain; /* activity domain id */ + activity_kind_t kind; /* activity kind */ + activity_op_t op; /* activity op */ + union { + struct { + activity_correlation_id_t correlation_id; /* activity ID */ + roctracer_timestamp_t begin_ns; /* host begin timestamp */ + roctracer_timestamp_t end_ns; /* host end timestamp */ + }; + struct { + uint32_t se; /* sampled SE */ + uint64_t cycle; /* sample cycle */ + uint64_t pc; /* sample PC */ + } pc_sample; + }; + union { + struct { + int device_id; /* device id */ + uint64_t queue_id; /* queue id */ + }; + struct { + uint32_t process_id; /* device id */ + uint32_t thread_id; /* thread id */ + }; + struct { + activity_correlation_id_t external_id; /* external correlation id */ + }; + }; + union { + size_t bytes; /* data size bytes */ + const char* kernel_name; /* kernel name */ + const char* mark_message; + }; +} activity_record_t; + +/* Activity sync callback type */ +typedef void (*activity_sync_callback_t)(uint32_t cid, activity_record_t* record, const void* data, + void* arg); +/* Activity async callback type */ +typedef void (*activity_async_callback_t)(uint32_t op, void* record, void* arg); + +#endif /* EXT_PROF_PROTOCOL_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hip_ostream_ops.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hip_ostream_ops.h new file mode 100644 index 0000000000000000000000000000000000000000..13ee9ac2d37948221eea1095ddeedbaa7d47c365 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hip_ostream_ops.h @@ -0,0 +1,4435 @@ +// automatically generated +/* +Copyright (c) 2018 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#ifndef INC_HIP_OSTREAM_OPS_H_ +#define INC_HIP_OSTREAM_OPS_H_ + +#include +#include +#include "roctracer.h" + +#ifdef __cplusplus +#include +#include +#include +#include + +namespace roctracer { +namespace hip_support { +static int HIP_depth_max = 1; +static int HIP_depth_max_cnt = 0; +static std::string HIP_structs_regex = ""; +// begin ostream ops for HIP +// basic ostream ops +namespace detail { + inline static void print_escaped_string(std::ostream& out, const char *v, size_t len) { + out << '"'; + for (size_t i = 0; i < len && v[i]; ++i) { + switch (v[i]) { + case '\"': out << "\\\""; break; + case '\\': out << "\\\\"; break; + case '\b': out << "\\\b"; break; + case '\f': out << "\\\f"; break; + case '\n': out << "\\\n"; break; + case '\r': out << "\\\r"; break; + case '\t': out << "\\\t"; break; + default: + if (std::isprint((unsigned char)v[i])) std::operator<<(out, v[i]); + else { + std::ios_base::fmtflags flags(out.flags()); + out << "\\x" << std::setfill('0') << std::setw(2) << std::hex << (unsigned int)(unsigned char)v[i]; + out.flags(flags); + } + break; + } + } + out << '"'; + } + + template + inline static std::ostream& operator<<(std::ostream& out, const T& v) { + using std::operator<<; + static bool recursion = false; + if (recursion == false) { recursion = true; out << v; recursion = false; } + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const unsigned char &v) { + out << (unsigned int)v; + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const char &v) { + out << (unsigned char)v; + return out; + } + + template + inline static std::ostream &operator<<(std::ostream &out, const char (&v)[N]) { + print_escaped_string(out, v, N); + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const char *v) { + print_escaped_string(out, v, strlen(v)); + return out; + } +// End of basic ostream ops + +inline static std::ostream& operator<<(std::ostream& out, const __locale_struct& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("__locale_struct::__names").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "__names="); + roctracer::hip_support::detail::operator<<(out, v.__names); + std::operator<<(out, ", "); + } + if (std::string("__locale_struct::__ctype_toupper").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "__ctype_toupper="); + roctracer::hip_support::detail::operator<<(out, v.__ctype_toupper); + std::operator<<(out, ", "); + } + if (std::string("__locale_struct::__ctype_tolower").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "__ctype_tolower="); + roctracer::hip_support::detail::operator<<(out, v.__ctype_tolower); + std::operator<<(out, ", "); + } + if (std::string("__locale_struct::__ctype_b").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "__ctype_b="); + roctracer::hip_support::detail::operator<<(out, v.__ctype_b); + std::operator<<(out, ", "); + } + if (std::string("__locale_struct::__locales").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "__locales="); + roctracer::hip_support::detail::operator<<(out, v.__locales); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceArch_t& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipDeviceArch_t::hasDynamicParallelism").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasDynamicParallelism="); + roctracer::hip_support::detail::operator<<(out, v.hasDynamicParallelism); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::has3dGrid").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "has3dGrid="); + roctracer::hip_support::detail::operator<<(out, v.has3dGrid); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasSurfaceFuncs").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasSurfaceFuncs="); + roctracer::hip_support::detail::operator<<(out, v.hasSurfaceFuncs); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasSyncThreadsExt").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasSyncThreadsExt="); + roctracer::hip_support::detail::operator<<(out, v.hasSyncThreadsExt); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasThreadFenceSystem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasThreadFenceSystem="); + roctracer::hip_support::detail::operator<<(out, v.hasThreadFenceSystem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasFunnelShift").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasFunnelShift="); + roctracer::hip_support::detail::operator<<(out, v.hasFunnelShift); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasWarpShuffle").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasWarpShuffle="); + roctracer::hip_support::detail::operator<<(out, v.hasWarpShuffle); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasWarpBallot").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasWarpBallot="); + roctracer::hip_support::detail::operator<<(out, v.hasWarpBallot); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasWarpVote").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasWarpVote="); + roctracer::hip_support::detail::operator<<(out, v.hasWarpVote); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasDoubles").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasDoubles="); + roctracer::hip_support::detail::operator<<(out, v.hasDoubles); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasSharedInt64Atomics").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasSharedInt64Atomics="); + roctracer::hip_support::detail::operator<<(out, v.hasSharedInt64Atomics); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasGlobalInt64Atomics").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasGlobalInt64Atomics="); + roctracer::hip_support::detail::operator<<(out, v.hasGlobalInt64Atomics); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasFloatAtomicAdd").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasFloatAtomicAdd="); + roctracer::hip_support::detail::operator<<(out, v.hasFloatAtomicAdd); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasSharedFloatAtomicExch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasSharedFloatAtomicExch="); + roctracer::hip_support::detail::operator<<(out, v.hasSharedFloatAtomicExch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasSharedInt32Atomics").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasSharedInt32Atomics="); + roctracer::hip_support::detail::operator<<(out, v.hasSharedInt32Atomics); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasGlobalFloatAtomicExch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasGlobalFloatAtomicExch="); + roctracer::hip_support::detail::operator<<(out, v.hasGlobalFloatAtomicExch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceArch_t::hasGlobalInt32Atomics").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hasGlobalInt32Atomics="); + roctracer::hip_support::detail::operator<<(out, v.hasGlobalInt32Atomics); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipUUID& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipUUID::bytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "bytes="); + roctracer::hip_support::detail::operator<<(out, v.bytes); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceProp_tR0600& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipDeviceProp_tR0600::asicRevision").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "asicRevision="); + roctracer::hip_support::detail::operator<<(out, v.asicRevision); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::isLargeBar").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "isLargeBar="); + roctracer::hip_support::detail::operator<<(out, v.isLargeBar); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeMultiDeviceUnmatchedSharedMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedSharedMem="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedSharedMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeMultiDeviceUnmatchedBlockDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedBlockDim="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedBlockDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeMultiDeviceUnmatchedGridDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedGridDim="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedGridDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeMultiDeviceUnmatchedFunc").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedFunc="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedFunc); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hdpRegFlushCntl").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hdpRegFlushCntl="); + roctracer::hip_support::detail::operator<<(out, v.hdpRegFlushCntl); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hdpMemFlushCntl").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hdpMemFlushCntl="); + roctracer::hip_support::detail::operator<<(out, v.hdpMemFlushCntl); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::arch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "arch="); + roctracer::hip_support::detail::operator<<(out, v.arch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::clockInstructionRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "clockInstructionRate="); + roctracer::hip_support::detail::operator<<(out, v.clockInstructionRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSharedMemoryPerMultiProcessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSharedMemoryPerMultiProcessor="); + roctracer::hip_support::detail::operator<<(out, v.maxSharedMemoryPerMultiProcessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::gcnArchName").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gcnArchName="); + roctracer::hip_support::detail::operator<<(out, v.gcnArchName); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hipReserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hipReserved="); + roctracer::hip_support::detail::operator<<(out, v.hipReserved); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::unifiedFunctionPointers").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "unifiedFunctionPointers="); + roctracer::hip_support::detail::operator<<(out, v.unifiedFunctionPointers); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::clusterLaunch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "clusterLaunch="); + roctracer::hip_support::detail::operator<<(out, v.clusterLaunch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::ipcEventSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "ipcEventSupported="); + roctracer::hip_support::detail::operator<<(out, v.ipcEventSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::deferredMappingHipArraySupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "deferredMappingHipArraySupported="); + roctracer::hip_support::detail::operator<<(out, v.deferredMappingHipArraySupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::memoryPoolSupportedHandleTypes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryPoolSupportedHandleTypes="); + roctracer::hip_support::detail::operator<<(out, v.memoryPoolSupportedHandleTypes); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::gpuDirectRDMAWritesOrdering").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gpuDirectRDMAWritesOrdering="); + roctracer::hip_support::detail::operator<<(out, v.gpuDirectRDMAWritesOrdering); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::gpuDirectRDMAFlushWritesOptions").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gpuDirectRDMAFlushWritesOptions="); + roctracer::hip_support::detail::operator<<(out, v.gpuDirectRDMAFlushWritesOptions); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::gpuDirectRDMASupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gpuDirectRDMASupported="); + roctracer::hip_support::detail::operator<<(out, v.gpuDirectRDMASupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::memoryPoolsSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryPoolsSupported="); + roctracer::hip_support::detail::operator<<(out, v.memoryPoolsSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::timelineSemaphoreInteropSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "timelineSemaphoreInteropSupported="); + roctracer::hip_support::detail::operator<<(out, v.timelineSemaphoreInteropSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hostRegisterReadOnlySupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hostRegisterReadOnlySupported="); + roctracer::hip_support::detail::operator<<(out, v.hostRegisterReadOnlySupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::sparseHipArraySupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sparseHipArraySupported="); + roctracer::hip_support::detail::operator<<(out, v.sparseHipArraySupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hostRegisterSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hostRegisterSupported="); + roctracer::hip_support::detail::operator<<(out, v.hostRegisterSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::reservedSharedMemPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reservedSharedMemPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.reservedSharedMemPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::accessPolicyMaxWindowSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "accessPolicyMaxWindowSize="); + roctracer::hip_support::detail::operator<<(out, v.accessPolicyMaxWindowSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxBlocksPerMultiProcessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxBlocksPerMultiProcessor="); + roctracer::hip_support::detail::operator<<(out, v.maxBlocksPerMultiProcessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::directManagedMemAccessFromHost").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "directManagedMemAccessFromHost="); + roctracer::hip_support::detail::operator<<(out, v.directManagedMemAccessFromHost); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::pageableMemoryAccessUsesHostPageTables").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pageableMemoryAccessUsesHostPageTables="); + roctracer::hip_support::detail::operator<<(out, v.pageableMemoryAccessUsesHostPageTables); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::sharedMemPerBlockOptin").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemPerBlockOptin="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemPerBlockOptin); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeMultiDeviceLaunch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceLaunch="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceLaunch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::cooperativeLaunch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeLaunch="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeLaunch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::canUseHostPointerForRegisteredMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "canUseHostPointerForRegisteredMem="); + roctracer::hip_support::detail::operator<<(out, v.canUseHostPointerForRegisteredMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::computePreemptionSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "computePreemptionSupported="); + roctracer::hip_support::detail::operator<<(out, v.computePreemptionSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::concurrentManagedAccess").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "concurrentManagedAccess="); + roctracer::hip_support::detail::operator<<(out, v.concurrentManagedAccess); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::pageableMemoryAccess").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pageableMemoryAccess="); + roctracer::hip_support::detail::operator<<(out, v.pageableMemoryAccess); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::singleToDoublePrecisionPerfRatio").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "singleToDoublePrecisionPerfRatio="); + roctracer::hip_support::detail::operator<<(out, v.singleToDoublePrecisionPerfRatio); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::hostNativeAtomicSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hostNativeAtomicSupported="); + roctracer::hip_support::detail::operator<<(out, v.hostNativeAtomicSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::multiGpuBoardGroupID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "multiGpuBoardGroupID="); + roctracer::hip_support::detail::operator<<(out, v.multiGpuBoardGroupID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::isMultiGpuBoard").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "isMultiGpuBoard="); + roctracer::hip_support::detail::operator<<(out, v.isMultiGpuBoard); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::managedMemory").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "managedMemory="); + roctracer::hip_support::detail::operator<<(out, v.managedMemory); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::regsPerMultiprocessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "regsPerMultiprocessor="); + roctracer::hip_support::detail::operator<<(out, v.regsPerMultiprocessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::sharedMemPerMultiprocessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemPerMultiprocessor="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemPerMultiprocessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::localL1CacheSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "localL1CacheSupported="); + roctracer::hip_support::detail::operator<<(out, v.localL1CacheSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::globalL1CacheSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "globalL1CacheSupported="); + roctracer::hip_support::detail::operator<<(out, v.globalL1CacheSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::streamPrioritiesSupported").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "streamPrioritiesSupported="); + roctracer::hip_support::detail::operator<<(out, v.streamPrioritiesSupported); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxThreadsPerMultiProcessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsPerMultiProcessor="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsPerMultiProcessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::persistingL2CacheMaxSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "persistingL2CacheMaxSize="); + roctracer::hip_support::detail::operator<<(out, v.persistingL2CacheMaxSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::l2CacheSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "l2CacheSize="); + roctracer::hip_support::detail::operator<<(out, v.l2CacheSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::memoryBusWidth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryBusWidth="); + roctracer::hip_support::detail::operator<<(out, v.memoryBusWidth); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::memoryClockRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryClockRate="); + roctracer::hip_support::detail::operator<<(out, v.memoryClockRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::unifiedAddressing").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "unifiedAddressing="); + roctracer::hip_support::detail::operator<<(out, v.unifiedAddressing); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::asyncEngineCount").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "asyncEngineCount="); + roctracer::hip_support::detail::operator<<(out, v.asyncEngineCount); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::tccDriver").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "tccDriver="); + roctracer::hip_support::detail::operator<<(out, v.tccDriver); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::pciDomainID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciDomainID="); + roctracer::hip_support::detail::operator<<(out, v.pciDomainID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::pciDeviceID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciDeviceID="); + roctracer::hip_support::detail::operator<<(out, v.pciDeviceID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::pciBusID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciBusID="); + roctracer::hip_support::detail::operator<<(out, v.pciBusID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::ECCEnabled").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "ECCEnabled="); + roctracer::hip_support::detail::operator<<(out, v.ECCEnabled); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::concurrentKernels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "concurrentKernels="); + roctracer::hip_support::detail::operator<<(out, v.concurrentKernels); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::surfaceAlignment").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "surfaceAlignment="); + roctracer::hip_support::detail::operator<<(out, v.surfaceAlignment); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurfaceCubemapLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurfaceCubemapLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxSurfaceCubemapLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurfaceCubemap").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurfaceCubemap="); + roctracer::hip_support::detail::operator<<(out, v.maxSurfaceCubemap); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurface2DLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurface2DLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxSurface2DLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurface1DLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurface1DLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxSurface1DLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurface3D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurface3D="); + roctracer::hip_support::detail::operator<<(out, v.maxSurface3D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurface2D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurface2D="); + roctracer::hip_support::detail::operator<<(out, v.maxSurface2D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxSurface1D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSurface1D="); + roctracer::hip_support::detail::operator<<(out, v.maxSurface1D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTextureCubemapLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTextureCubemapLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxTextureCubemapLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture2DLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2DLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2DLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture1DLayered").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1DLayered="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1DLayered); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTextureCubemap").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTextureCubemap="); + roctracer::hip_support::detail::operator<<(out, v.maxTextureCubemap); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture3DAlt").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture3DAlt="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture3DAlt); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture3D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture3D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture3D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture2DGather").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2DGather="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2DGather); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture2DLinear").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2DLinear="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2DLinear); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture2DMipmap").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2DMipmap="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2DMipmap); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture2D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture1DLinear").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1DLinear="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1DLinear); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture1DMipmap").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1DMipmap="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1DMipmap); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxTexture1D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::computeMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "computeMode="); + roctracer::hip_support::detail::operator<<(out, v.computeMode); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::canMapHostMemory").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "canMapHostMemory="); + roctracer::hip_support::detail::operator<<(out, v.canMapHostMemory); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::integrated").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "integrated="); + roctracer::hip_support::detail::operator<<(out, v.integrated); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::kernelExecTimeoutEnabled").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "kernelExecTimeoutEnabled="); + roctracer::hip_support::detail::operator<<(out, v.kernelExecTimeoutEnabled); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::multiProcessorCount").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "multiProcessorCount="); + roctracer::hip_support::detail::operator<<(out, v.multiProcessorCount); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::deviceOverlap").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "deviceOverlap="); + roctracer::hip_support::detail::operator<<(out, v.deviceOverlap); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::texturePitchAlignment").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "texturePitchAlignment="); + roctracer::hip_support::detail::operator<<(out, v.texturePitchAlignment); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::textureAlignment").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "textureAlignment="); + roctracer::hip_support::detail::operator<<(out, v.textureAlignment); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::minor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "minor="); + roctracer::hip_support::detail::operator<<(out, v.minor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::major").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "major="); + roctracer::hip_support::detail::operator<<(out, v.major); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::totalConstMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "totalConstMem="); + roctracer::hip_support::detail::operator<<(out, v.totalConstMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::clockRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "clockRate="); + roctracer::hip_support::detail::operator<<(out, v.clockRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxGridSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxGridSize="); + roctracer::hip_support::detail::operator<<(out, v.maxGridSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxThreadsDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsDim="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::maxThreadsPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::memPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memPitch="); + roctracer::hip_support::detail::operator<<(out, v.memPitch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::warpSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "warpSize="); + roctracer::hip_support::detail::operator<<(out, v.warpSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::regsPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "regsPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.regsPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::sharedMemPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::totalGlobalMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "totalGlobalMem="); + roctracer::hip_support::detail::operator<<(out, v.totalGlobalMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::luidDeviceNodeMask").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "luidDeviceNodeMask="); + roctracer::hip_support::detail::operator<<(out, v.luidDeviceNodeMask); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::luid").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "luid="); + roctracer::hip_support::detail::operator<<(out, v.luid); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::uuid").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "uuid="); + roctracer::hip_support::detail::operator<<(out, v.uuid); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0600::name").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "name="); + roctracer::hip_support::detail::operator<<(out, v.name); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipPointerAttribute_t& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipPointerAttribute_t::allocationFlags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "allocationFlags="); + roctracer::hip_support::detail::operator<<(out, v.allocationFlags); + std::operator<<(out, ", "); + } + if (std::string("hipPointerAttribute_t::isManaged").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "isManaged="); + roctracer::hip_support::detail::operator<<(out, v.isManaged); + std::operator<<(out, ", "); + } + if (std::string("hipPointerAttribute_t::device").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "device="); + roctracer::hip_support::detail::operator<<(out, v.device); + std::operator<<(out, ", "); + } + if (std::string("hipPointerAttribute_t::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipChannelFormatDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipChannelFormatDesc::f").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "f="); + roctracer::hip_support::detail::operator<<(out, v.f); + std::operator<<(out, ", "); + } + if (std::string("hipChannelFormatDesc::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("hipChannelFormatDesc::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("hipChannelFormatDesc::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("hipChannelFormatDesc::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_ARRAY_DESCRIPTOR& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_ARRAY_DESCRIPTOR::NumChannels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "NumChannels="); + roctracer::hip_support::detail::operator<<(out, v.NumChannels); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY_DESCRIPTOR::Format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Format="); + roctracer::hip_support::detail::operator<<(out, v.Format); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY_DESCRIPTOR::Height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Height="); + roctracer::hip_support::detail::operator<<(out, v.Height); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY_DESCRIPTOR::Width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Width="); + roctracer::hip_support::detail::operator<<(out, v.Width); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_ARRAY3D_DESCRIPTOR& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_ARRAY3D_DESCRIPTOR::Flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Flags="); + roctracer::hip_support::detail::operator<<(out, v.Flags); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY3D_DESCRIPTOR::NumChannels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "NumChannels="); + roctracer::hip_support::detail::operator<<(out, v.NumChannels); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY3D_DESCRIPTOR::Format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Format="); + roctracer::hip_support::detail::operator<<(out, v.Format); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY3D_DESCRIPTOR::Depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Depth="); + roctracer::hip_support::detail::operator<<(out, v.Depth); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY3D_DESCRIPTOR::Height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Height="); + roctracer::hip_support::detail::operator<<(out, v.Height); + std::operator<<(out, ", "); + } + if (std::string("HIP_ARRAY3D_DESCRIPTOR::Width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Width="); + roctracer::hip_support::detail::operator<<(out, v.Width); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hip_Memcpy2D& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hip_Memcpy2D::Height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Height="); + roctracer::hip_support::detail::operator<<(out, v.Height); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::WidthInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "WidthInBytes="); + roctracer::hip_support::detail::operator<<(out, v.WidthInBytes); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstPitch="); + roctracer::hip_support::detail::operator<<(out, v.dstPitch); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstArray="); + roctracer::hip_support::detail::operator<<(out, v.dstArray); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstDevice").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstDevice="); + roctracer::hip_support::detail::operator<<(out, v.dstDevice); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstMemoryType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstMemoryType="); + roctracer::hip_support::detail::operator<<(out, v.dstMemoryType); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstY="); + roctracer::hip_support::detail::operator<<(out, v.dstY); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::dstXInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstXInBytes="); + roctracer::hip_support::detail::operator<<(out, v.dstXInBytes); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcPitch="); + roctracer::hip_support::detail::operator<<(out, v.srcPitch); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcArray="); + roctracer::hip_support::detail::operator<<(out, v.srcArray); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcDevice").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcDevice="); + roctracer::hip_support::detail::operator<<(out, v.srcDevice); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcMemoryType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcMemoryType="); + roctracer::hip_support::detail::operator<<(out, v.srcMemoryType); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcY="); + roctracer::hip_support::detail::operator<<(out, v.srcY); + std::operator<<(out, ", "); + } + if (std::string("hip_Memcpy2D::srcXInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcXInBytes="); + roctracer::hip_support::detail::operator<<(out, v.srcXInBytes); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMipmappedArray& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMipmappedArray::num_channels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "num_channels="); + roctracer::hip_support::detail::operator<<(out, v.num_channels); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "format="); + roctracer::hip_support::detail::operator<<(out, v.format); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::max_mipmap_level").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "max_mipmap_level="); + roctracer::hip_support::detail::operator<<(out, v.max_mipmap_level); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::min_mipmap_level").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "min_mipmap_level="); + roctracer::hip_support::detail::operator<<(out, v.min_mipmap_level); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "depth="); + roctracer::hip_support::detail::operator<<(out, v.depth); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + std::operator<<(out, ", "); + } + if (std::string("hipMipmappedArray::desc").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "desc="); + roctracer::hip_support::detail::operator<<(out, v.desc); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_TEXTURE_DESC& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_TEXTURE_DESC::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::borderColor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "borderColor="); + roctracer::hip_support::detail::operator<<(out, v.borderColor); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::maxMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.maxMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::minMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "minMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.minMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::mipmapLevelBias").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapLevelBias="); + roctracer::hip_support::detail::operator<<(out, v.mipmapLevelBias); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::mipmapFilterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapFilterMode="); + roctracer::hip_support::detail::operator<<(out, v.mipmapFilterMode); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::maxAnisotropy").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxAnisotropy="); + roctracer::hip_support::detail::operator<<(out, v.maxAnisotropy); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::filterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "filterMode="); + roctracer::hip_support::detail::operator<<(out, v.filterMode); + std::operator<<(out, ", "); + } + if (std::string("HIP_TEXTURE_DESC::addressMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "addressMode="); + roctracer::hip_support::detail::operator<<(out, v.addressMode); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipResourceDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipResourceDesc::resType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "resType="); + roctracer::hip_support::detail::operator<<(out, v.resType); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_RESOURCE_DESC& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_RESOURCE_DESC::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_DESC::resType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "resType="); + roctracer::hip_support::detail::operator<<(out, v.resType); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipResourceViewDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipResourceViewDesc::lastLayer").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "lastLayer="); + roctracer::hip_support::detail::operator<<(out, v.lastLayer); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::firstLayer").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "firstLayer="); + roctracer::hip_support::detail::operator<<(out, v.firstLayer); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::lastMipmapLevel").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "lastMipmapLevel="); + roctracer::hip_support::detail::operator<<(out, v.lastMipmapLevel); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::firstMipmapLevel").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "firstMipmapLevel="); + roctracer::hip_support::detail::operator<<(out, v.firstMipmapLevel); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "depth="); + roctracer::hip_support::detail::operator<<(out, v.depth); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("hipResourceViewDesc::format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "format="); + roctracer::hip_support::detail::operator<<(out, v.format); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_RESOURCE_VIEW_DESC& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_RESOURCE_VIEW_DESC::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::lastLayer").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "lastLayer="); + roctracer::hip_support::detail::operator<<(out, v.lastLayer); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::firstLayer").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "firstLayer="); + roctracer::hip_support::detail::operator<<(out, v.firstLayer); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::lastMipmapLevel").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "lastMipmapLevel="); + roctracer::hip_support::detail::operator<<(out, v.lastMipmapLevel); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::firstMipmapLevel").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "firstMipmapLevel="); + roctracer::hip_support::detail::operator<<(out, v.firstMipmapLevel); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "depth="); + roctracer::hip_support::detail::operator<<(out, v.depth); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("HIP_RESOURCE_VIEW_DESC::format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "format="); + roctracer::hip_support::detail::operator<<(out, v.format); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipPitchedPtr& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipPitchedPtr::ysize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "ysize="); + roctracer::hip_support::detail::operator<<(out, v.ysize); + std::operator<<(out, ", "); + } + if (std::string("hipPitchedPtr::xsize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "xsize="); + roctracer::hip_support::detail::operator<<(out, v.xsize); + std::operator<<(out, ", "); + } + if (std::string("hipPitchedPtr::pitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pitch="); + roctracer::hip_support::detail::operator<<(out, v.pitch); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExtent& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExtent::depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "depth="); + roctracer::hip_support::detail::operator<<(out, v.depth); + std::operator<<(out, ", "); + } + if (std::string("hipExtent::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("hipExtent::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipPos& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipPos::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("hipPos::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("hipPos::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemcpy3DParms& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemcpy3DParms::kind").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "kind="); + roctracer::hip_support::detail::operator<<(out, v.kind); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::extent").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "extent="); + roctracer::hip_support::detail::operator<<(out, v.extent); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::dstPtr").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstPtr="); + roctracer::hip_support::detail::operator<<(out, v.dstPtr); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::dstPos").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstPos="); + roctracer::hip_support::detail::operator<<(out, v.dstPos); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::dstArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstArray="); + roctracer::hip_support::detail::operator<<(out, v.dstArray); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::srcPtr").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcPtr="); + roctracer::hip_support::detail::operator<<(out, v.srcPtr); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::srcPos").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcPos="); + roctracer::hip_support::detail::operator<<(out, v.srcPos); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpy3DParms::srcArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcArray="); + roctracer::hip_support::detail::operator<<(out, v.srcArray); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_MEMCPY3D& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_MEMCPY3D::Depth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Depth="); + roctracer::hip_support::detail::operator<<(out, v.Depth); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::Height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "Height="); + roctracer::hip_support::detail::operator<<(out, v.Height); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::WidthInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "WidthInBytes="); + roctracer::hip_support::detail::operator<<(out, v.WidthInBytes); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstHeight").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstHeight="); + roctracer::hip_support::detail::operator<<(out, v.dstHeight); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstPitch="); + roctracer::hip_support::detail::operator<<(out, v.dstPitch); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstArray="); + roctracer::hip_support::detail::operator<<(out, v.dstArray); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstDevice").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstDevice="); + roctracer::hip_support::detail::operator<<(out, v.dstDevice); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstMemoryType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstMemoryType="); + roctracer::hip_support::detail::operator<<(out, v.dstMemoryType); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstLOD").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstLOD="); + roctracer::hip_support::detail::operator<<(out, v.dstLOD); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstZ").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstZ="); + roctracer::hip_support::detail::operator<<(out, v.dstZ); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstY="); + roctracer::hip_support::detail::operator<<(out, v.dstY); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::dstXInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dstXInBytes="); + roctracer::hip_support::detail::operator<<(out, v.dstXInBytes); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcHeight").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcHeight="); + roctracer::hip_support::detail::operator<<(out, v.srcHeight); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcPitch="); + roctracer::hip_support::detail::operator<<(out, v.srcPitch); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcArray="); + roctracer::hip_support::detail::operator<<(out, v.srcArray); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcDevice").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcDevice="); + roctracer::hip_support::detail::operator<<(out, v.srcDevice); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcMemoryType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcMemoryType="); + roctracer::hip_support::detail::operator<<(out, v.srcMemoryType); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcLOD").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcLOD="); + roctracer::hip_support::detail::operator<<(out, v.srcLOD); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcZ").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcZ="); + roctracer::hip_support::detail::operator<<(out, v.srcZ); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcY="); + roctracer::hip_support::detail::operator<<(out, v.srcY); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMCPY3D::srcXInBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "srcXInBytes="); + roctracer::hip_support::detail::operator<<(out, v.srcXInBytes); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uchar1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uchar1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uchar2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uchar2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uchar2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uchar3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uchar3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("uchar3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uchar3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uchar4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uchar4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("uchar4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("uchar4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uchar4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const char1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("char1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const char2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("char2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("char2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const char3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("char3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("char3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("char3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const char4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("char4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("char4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("char4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("char4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ushort1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ushort1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ushort2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ushort2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ushort2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ushort3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ushort3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ushort3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ushort3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ushort4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ushort4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("ushort4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ushort4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ushort4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const short1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("short1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const short2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("short2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("short2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const short3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("short3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("short3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("short3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const short4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("short4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("short4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("short4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("short4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uint1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uint1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uint2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uint2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uint2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uint3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uint3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("uint3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uint3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const uint4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("uint4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("uint4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("uint4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("uint4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const int1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("int1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const int2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("int2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("int2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const int3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("int3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("int3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("int3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const int4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("int4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("int4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("int4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("int4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulong1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulong1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulong2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulong2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulong2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulong3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulong3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ulong3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulong3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulong4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulong4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("ulong4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ulong4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulong4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const long1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("long1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const long2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("long2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("long2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const long3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("long3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("long3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("long3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const long4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("long4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("long4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("long4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("long4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulonglong1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulonglong1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulonglong2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulonglong2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulonglong2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulonglong3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulonglong3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ulonglong3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulonglong3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const ulonglong4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("ulonglong4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("ulonglong4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("ulonglong4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("ulonglong4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const longlong1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("longlong1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const longlong2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("longlong2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("longlong2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const longlong3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("longlong3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("longlong3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("longlong3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const longlong4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("longlong4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("longlong4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("longlong4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("longlong4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const float1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("float1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const float2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("float2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("float2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const float3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("float3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("float3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("float3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const float4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("float4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("float4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("float4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("float4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const double1& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("double1::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const double2& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("double2::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("double2::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const double3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("double3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("double3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("double3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const double4& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("double4::w").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "w="); + roctracer::hip_support::detail::operator<<(out, v.w); + std::operator<<(out, ", "); + } + if (std::string("double4::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("double4::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("double4::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const textureReference& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("textureReference::format").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "format="); + roctracer::hip_support::detail::operator<<(out, v.format); + std::operator<<(out, ", "); + } + if (std::string("textureReference::numChannels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "numChannels="); + roctracer::hip_support::detail::operator<<(out, v.numChannels); + std::operator<<(out, ", "); + } + if (std::string("textureReference::textureObject").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "textureObject="); + roctracer::hip_support::detail::operator<<(out, v.textureObject); + std::operator<<(out, ", "); + } + if (std::string("textureReference::maxMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.maxMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("textureReference::minMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "minMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.minMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("textureReference::mipmapLevelBias").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapLevelBias="); + roctracer::hip_support::detail::operator<<(out, v.mipmapLevelBias); + std::operator<<(out, ", "); + } + if (std::string("textureReference::mipmapFilterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapFilterMode="); + roctracer::hip_support::detail::operator<<(out, v.mipmapFilterMode); + std::operator<<(out, ", "); + } + if (std::string("textureReference::maxAnisotropy").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxAnisotropy="); + roctracer::hip_support::detail::operator<<(out, v.maxAnisotropy); + std::operator<<(out, ", "); + } + if (std::string("textureReference::sRGB").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sRGB="); + roctracer::hip_support::detail::operator<<(out, v.sRGB); + std::operator<<(out, ", "); + } + if (std::string("textureReference::channelDesc").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "channelDesc="); + roctracer::hip_support::detail::operator<<(out, v.channelDesc); + std::operator<<(out, ", "); + } + if (std::string("textureReference::filterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "filterMode="); + roctracer::hip_support::detail::operator<<(out, v.filterMode); + std::operator<<(out, ", "); + } + if (std::string("textureReference::readMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "readMode="); + roctracer::hip_support::detail::operator<<(out, v.readMode); + std::operator<<(out, ", "); + } + if (std::string("textureReference::normalized").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "normalized="); + roctracer::hip_support::detail::operator<<(out, v.normalized); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipTextureDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipTextureDesc::maxMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.maxMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::minMipmapLevelClamp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "minMipmapLevelClamp="); + roctracer::hip_support::detail::operator<<(out, v.minMipmapLevelClamp); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::mipmapLevelBias").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapLevelBias="); + roctracer::hip_support::detail::operator<<(out, v.mipmapLevelBias); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::mipmapFilterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "mipmapFilterMode="); + roctracer::hip_support::detail::operator<<(out, v.mipmapFilterMode); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::maxAnisotropy").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxAnisotropy="); + roctracer::hip_support::detail::operator<<(out, v.maxAnisotropy); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::normalizedCoords").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "normalizedCoords="); + roctracer::hip_support::detail::operator<<(out, v.normalizedCoords); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::borderColor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "borderColor="); + roctracer::hip_support::detail::operator<<(out, v.borderColor); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::sRGB").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sRGB="); + roctracer::hip_support::detail::operator<<(out, v.sRGB); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::readMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "readMode="); + roctracer::hip_support::detail::operator<<(out, v.readMode); + std::operator<<(out, ", "); + } + if (std::string("hipTextureDesc::filterMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "filterMode="); + roctracer::hip_support::detail::operator<<(out, v.filterMode); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const surfaceReference& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("surfaceReference::surfaceObject").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "surfaceObject="); + roctracer::hip_support::detail::operator<<(out, v.surfaceObject); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipIpcMemHandle_t& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipIpcMemHandle_t::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipIpcEventHandle_t& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipIpcEventHandle_t::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipFuncAttributes& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipFuncAttributes::sharedSizeBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedSizeBytes="); + roctracer::hip_support::detail::operator<<(out, v.sharedSizeBytes); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::ptxVersion").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "ptxVersion="); + roctracer::hip_support::detail::operator<<(out, v.ptxVersion); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::preferredShmemCarveout").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "preferredShmemCarveout="); + roctracer::hip_support::detail::operator<<(out, v.preferredShmemCarveout); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::numRegs").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "numRegs="); + roctracer::hip_support::detail::operator<<(out, v.numRegs); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::maxThreadsPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::maxDynamicSharedSizeBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxDynamicSharedSizeBytes="); + roctracer::hip_support::detail::operator<<(out, v.maxDynamicSharedSizeBytes); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::localSizeBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "localSizeBytes="); + roctracer::hip_support::detail::operator<<(out, v.localSizeBytes); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::constSizeBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "constSizeBytes="); + roctracer::hip_support::detail::operator<<(out, v.constSizeBytes); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::cacheModeCA").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cacheModeCA="); + roctracer::hip_support::detail::operator<<(out, v.cacheModeCA); + std::operator<<(out, ", "); + } + if (std::string("hipFuncAttributes::binaryVersion").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "binaryVersion="); + roctracer::hip_support::detail::operator<<(out, v.binaryVersion); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemLocation& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemLocation::id").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "id="); + roctracer::hip_support::detail::operator<<(out, v.id); + std::operator<<(out, ", "); + } + if (std::string("hipMemLocation::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemAccessDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemAccessDesc::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipMemAccessDesc::location").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "location="); + roctracer::hip_support::detail::operator<<(out, v.location); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemPoolProps& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemPoolProps::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipMemPoolProps::location").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "location="); + roctracer::hip_support::detail::operator<<(out, v.location); + std::operator<<(out, ", "); + } + if (std::string("hipMemPoolProps::handleTypes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "handleTypes="); + roctracer::hip_support::detail::operator<<(out, v.handleTypes); + std::operator<<(out, ", "); + } + if (std::string("hipMemPoolProps::allocType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "allocType="); + roctracer::hip_support::detail::operator<<(out, v.allocType); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemPoolPtrExportData& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemPoolPtrExportData::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const dim3& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("dim3::z").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hip_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("dim3::y").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hip_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("dim3::x").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hip_support::detail::operator<<(out, v.x); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipLaunchParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipLaunchParams::stream").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "stream="); + roctracer::hip_support::detail::operator<<(out, v.stream); + std::operator<<(out, ", "); + } + if (std::string("hipLaunchParams::sharedMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMem="); + roctracer::hip_support::detail::operator<<(out, v.sharedMem); + std::operator<<(out, ", "); + } + if (std::string("hipLaunchParams::blockDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "blockDim="); + roctracer::hip_support::detail::operator<<(out, v.blockDim); + std::operator<<(out, ", "); + } + if (std::string("hipLaunchParams::gridDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gridDim="); + roctracer::hip_support::detail::operator<<(out, v.gridDim); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipFunctionLaunchParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipFunctionLaunchParams::hStream").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hStream="); + roctracer::hip_support::detail::operator<<(out, v.hStream); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::sharedMemBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemBytes="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemBytes); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::blockDimZ").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "blockDimZ="); + roctracer::hip_support::detail::operator<<(out, v.blockDimZ); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::blockDimY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "blockDimY="); + roctracer::hip_support::detail::operator<<(out, v.blockDimY); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::blockDimX").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "blockDimX="); + roctracer::hip_support::detail::operator<<(out, v.blockDimX); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::gridDimZ").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gridDimZ="); + roctracer::hip_support::detail::operator<<(out, v.gridDimZ); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::gridDimY").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gridDimY="); + roctracer::hip_support::detail::operator<<(out, v.gridDimY); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::gridDimX").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gridDimX="); + roctracer::hip_support::detail::operator<<(out, v.gridDimX); + std::operator<<(out, ", "); + } + if (std::string("hipFunctionLaunchParams::function").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "function="); + roctracer::hip_support::detail::operator<<(out, v.function); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryHandleDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalMemoryHandleDesc::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryHandleDesc::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryHandleDesc::size").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "size="); + roctracer::hip_support::detail::operator<<(out, v.size); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryHandleDesc_st::union ::handle.fd").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "handle.fd="); + roctracer::hip_support::detail::operator<<(out, v.handle.fd); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryHandleDesc::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryBufferDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalMemoryBufferDesc::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryBufferDesc::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryBufferDesc::size").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "size="); + roctracer::hip_support::detail::operator<<(out, v.size); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryBufferDesc::offset").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "offset="); + roctracer::hip_support::detail::operator<<(out, v.offset); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryMipmappedArrayDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalMemoryMipmappedArrayDesc::numLevels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "numLevels="); + roctracer::hip_support::detail::operator<<(out, v.numLevels); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryMipmappedArrayDesc::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryMipmappedArrayDesc::extent").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "extent="); + roctracer::hip_support::detail::operator<<(out, v.extent); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryMipmappedArrayDesc::formatDesc").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "formatDesc="); + roctracer::hip_support::detail::operator<<(out, v.formatDesc); + std::operator<<(out, ", "); + } + if (std::string("hipExternalMemoryMipmappedArrayDesc::offset").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "offset="); + roctracer::hip_support::detail::operator<<(out, v.offset); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreHandleDesc& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalSemaphoreHandleDesc::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreHandleDesc::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreHandleDesc_st::union ::handle.fd").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "handle.fd="); + roctracer::hip_support::detail::operator<<(out, v.handle.fd); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreHandleDesc::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreSignalParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalSemaphoreSignalParams::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreSignalParams::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreWaitParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalSemaphoreWaitParams::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreWaitParams::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipHostNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipHostNodeParams::fn").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "fn="); + roctracer::hip_support::detail::operator<<(out, v.fn); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipKernelNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipKernelNodeParams::sharedMemBytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemBytes="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemBytes); + std::operator<<(out, ", "); + } + if (std::string("hipKernelNodeParams::gridDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gridDim="); + roctracer::hip_support::detail::operator<<(out, v.gridDim); + std::operator<<(out, ", "); + } + if (std::string("hipKernelNodeParams::blockDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "blockDim="); + roctracer::hip_support::detail::operator<<(out, v.blockDim); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemsetParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemsetParams::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("hipMemsetParams::value").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "value="); + roctracer::hip_support::detail::operator<<(out, v.value); + std::operator<<(out, ", "); + } + if (std::string("hipMemsetParams::pitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pitch="); + roctracer::hip_support::detail::operator<<(out, v.pitch); + std::operator<<(out, ", "); + } + if (std::string("hipMemsetParams::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("hipMemsetParams::elementSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "elementSize="); + roctracer::hip_support::detail::operator<<(out, v.elementSize); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemAllocNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemAllocNodeParams::bytesize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "bytesize="); + roctracer::hip_support::detail::operator<<(out, v.bytesize); + std::operator<<(out, ", "); + } + if (std::string("hipMemAllocNodeParams::accessDescCount").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "accessDescCount="); + roctracer::hip_support::detail::operator<<(out, v.accessDescCount); + std::operator<<(out, ", "); + } + if (std::string("hipMemAllocNodeParams::accessDescs").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "accessDescs="); + roctracer::hip_support::detail::operator<<(out, v.accessDescs); + std::operator<<(out, ", "); + } + if (std::string("hipMemAllocNodeParams::poolProps").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "poolProps="); + roctracer::hip_support::detail::operator<<(out, v.poolProps); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipAccessPolicyWindow& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipAccessPolicyWindow::num_bytes").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "num_bytes="); + roctracer::hip_support::detail::operator<<(out, v.num_bytes); + std::operator<<(out, ", "); + } + if (std::string("hipAccessPolicyWindow::missProp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "missProp="); + roctracer::hip_support::detail::operator<<(out, v.missProp); + std::operator<<(out, ", "); + } + if (std::string("hipAccessPolicyWindow::hitRatio").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hitRatio="); + roctracer::hip_support::detail::operator<<(out, v.hitRatio); + std::operator<<(out, ", "); + } + if (std::string("hipAccessPolicyWindow::hitProp").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hitProp="); + roctracer::hip_support::detail::operator<<(out, v.hitProp); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipKernelNodeAttrValue& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipKernelNodeAttrValue::cooperative").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperative="); + roctracer::hip_support::detail::operator<<(out, v.cooperative); + std::operator<<(out, ", "); + } + if (std::string("hipKernelNodeAttrValue::accessPolicyWindow").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "accessPolicyWindow="); + roctracer::hip_support::detail::operator<<(out, v.accessPolicyWindow); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const HIP_MEMSET_NODE_PARAMS& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("HIP_MEMSET_NODE_PARAMS::height").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hip_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMSET_NODE_PARAMS::width").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hip_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMSET_NODE_PARAMS::elementSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "elementSize="); + roctracer::hip_support::detail::operator<<(out, v.elementSize); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMSET_NODE_PARAMS::value").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "value="); + roctracer::hip_support::detail::operator<<(out, v.value); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMSET_NODE_PARAMS::pitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pitch="); + roctracer::hip_support::detail::operator<<(out, v.pitch); + std::operator<<(out, ", "); + } + if (std::string("HIP_MEMSET_NODE_PARAMS::dst").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "dst="); + roctracer::hip_support::detail::operator<<(out, v.dst); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemAllocationProp& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemAllocationProp::location").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "location="); + roctracer::hip_support::detail::operator<<(out, v.location); + std::operator<<(out, ", "); + } + if (std::string("hipMemAllocationProp::requestedHandleType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "requestedHandleType="); + roctracer::hip_support::detail::operator<<(out, v.requestedHandleType); + std::operator<<(out, ", "); + } + if (std::string("hipMemAllocationProp::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreSignalNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalSemaphoreSignalNodeParams::numExtSems").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "numExtSems="); + roctracer::hip_support::detail::operator<<(out, v.numExtSems); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreSignalNodeParams::paramsArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "paramsArray="); + roctracer::hip_support::detail::operator<<(out, v.paramsArray); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreSignalNodeParams::extSemArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "extSemArray="); + roctracer::hip_support::detail::operator<<(out, v.extSemArray); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreWaitNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipExternalSemaphoreWaitNodeParams::numExtSems").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "numExtSems="); + roctracer::hip_support::detail::operator<<(out, v.numExtSems); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreWaitNodeParams::paramsArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "paramsArray="); + roctracer::hip_support::detail::operator<<(out, v.paramsArray); + std::operator<<(out, ", "); + } + if (std::string("hipExternalSemaphoreWaitNodeParams::extSemArray").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "extSemArray="); + roctracer::hip_support::detail::operator<<(out, v.extSemArray); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipArrayMapInfo& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipArrayMapInfo::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::deviceBitMask").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "deviceBitMask="); + roctracer::hip_support::detail::operator<<(out, v.deviceBitMask); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::offset").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "offset="); + roctracer::hip_support::detail::operator<<(out, v.offset); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::union ::memHandle.memHandle").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memHandle.memHandle="); + roctracer::hip_support::detail::operator<<(out, v.memHandle.memHandle); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::memHandleType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memHandleType="); + roctracer::hip_support::detail::operator<<(out, v.memHandleType); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::memOperationType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memOperationType="); + roctracer::hip_support::detail::operator<<(out, v.memOperationType); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::subresourceType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "subresourceType="); + roctracer::hip_support::detail::operator<<(out, v.subresourceType); + std::operator<<(out, ", "); + } + if (std::string("hipArrayMapInfo::resourceType").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "resourceType="); + roctracer::hip_support::detail::operator<<(out, v.resourceType); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemcpyNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipMemcpyNodeParams::copyParams").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "copyParams="); + roctracer::hip_support::detail::operator<<(out, v.copyParams); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpyNodeParams::reserved").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hip_support::detail::operator<<(out, 0); + std::operator<<(out, ", "); + } + if (std::string("hipMemcpyNodeParams::flags").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "flags="); + roctracer::hip_support::detail::operator<<(out, v.flags); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipChildGraphNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipChildGraphNodeParams::graph").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "graph="); + roctracer::hip_support::detail::operator<<(out, v.graph); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipEventWaitNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipEventWaitNodeParams::event").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "event="); + roctracer::hip_support::detail::operator<<(out, v.event); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipEventRecordNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipEventRecordNodeParams::event").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "event="); + roctracer::hip_support::detail::operator<<(out, v.event); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipMemFreeNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipGraphNodeParams& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipGraphNodeParams::reserved2").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hip_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hipGraphNodeParams::reserved0").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hip_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hipGraphNodeParams::type").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hip_support::detail::operator<<(out, v.type); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceProp_tR0000& v) +{ + std::operator<<(out, '{'); + HIP_depth_max_cnt++; + if (HIP_depth_max == -1 || HIP_depth_max_cnt <= HIP_depth_max) { + if (std::string("hipDeviceProp_tR0000::pageableMemoryAccessUsesHostPageTables").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pageableMemoryAccessUsesHostPageTables="); + roctracer::hip_support::detail::operator<<(out, v.pageableMemoryAccessUsesHostPageTables); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::pageableMemoryAccess").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pageableMemoryAccess="); + roctracer::hip_support::detail::operator<<(out, v.pageableMemoryAccess); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::concurrentManagedAccess").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "concurrentManagedAccess="); + roctracer::hip_support::detail::operator<<(out, v.concurrentManagedAccess); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::directManagedMemAccessFromHost").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "directManagedMemAccessFromHost="); + roctracer::hip_support::detail::operator<<(out, v.directManagedMemAccessFromHost); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::managedMemory").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "managedMemory="); + roctracer::hip_support::detail::operator<<(out, v.managedMemory); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::asicRevision").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "asicRevision="); + roctracer::hip_support::detail::operator<<(out, v.asicRevision); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::isLargeBar").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "isLargeBar="); + roctracer::hip_support::detail::operator<<(out, v.isLargeBar); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeMultiDeviceUnmatchedSharedMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedSharedMem="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedSharedMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeMultiDeviceUnmatchedBlockDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedBlockDim="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedBlockDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeMultiDeviceUnmatchedGridDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedGridDim="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedGridDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeMultiDeviceUnmatchedFunc").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceUnmatchedFunc="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceUnmatchedFunc); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::tccDriver").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "tccDriver="); + roctracer::hip_support::detail::operator<<(out, v.tccDriver); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::ECCEnabled").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "ECCEnabled="); + roctracer::hip_support::detail::operator<<(out, v.ECCEnabled); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::kernelExecTimeoutEnabled").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "kernelExecTimeoutEnabled="); + roctracer::hip_support::detail::operator<<(out, v.kernelExecTimeoutEnabled); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::texturePitchAlignment").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "texturePitchAlignment="); + roctracer::hip_support::detail::operator<<(out, v.texturePitchAlignment); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::textureAlignment").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "textureAlignment="); + roctracer::hip_support::detail::operator<<(out, v.textureAlignment); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::memPitch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memPitch="); + roctracer::hip_support::detail::operator<<(out, v.memPitch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::hdpRegFlushCntl").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hdpRegFlushCntl="); + roctracer::hip_support::detail::operator<<(out, v.hdpRegFlushCntl); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::hdpMemFlushCntl").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "hdpMemFlushCntl="); + roctracer::hip_support::detail::operator<<(out, v.hdpMemFlushCntl); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxTexture3D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture3D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture3D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxTexture2D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture2D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture2D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxTexture1D").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1D="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1D); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxTexture1DLinear").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxTexture1DLinear="); + roctracer::hip_support::detail::operator<<(out, v.maxTexture1DLinear); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeMultiDeviceLaunch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeMultiDeviceLaunch="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeMultiDeviceLaunch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::cooperativeLaunch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "cooperativeLaunch="); + roctracer::hip_support::detail::operator<<(out, v.cooperativeLaunch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::integrated").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "integrated="); + roctracer::hip_support::detail::operator<<(out, v.integrated); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::gcnArchName").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gcnArchName="); + roctracer::hip_support::detail::operator<<(out, v.gcnArchName); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::gcnArch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "gcnArch="); + roctracer::hip_support::detail::operator<<(out, v.gcnArch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::canMapHostMemory").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "canMapHostMemory="); + roctracer::hip_support::detail::operator<<(out, v.canMapHostMemory); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::isMultiGpuBoard").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "isMultiGpuBoard="); + roctracer::hip_support::detail::operator<<(out, v.isMultiGpuBoard); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxSharedMemoryPerMultiProcessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxSharedMemoryPerMultiProcessor="); + roctracer::hip_support::detail::operator<<(out, v.maxSharedMemoryPerMultiProcessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::pciDeviceID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciDeviceID="); + roctracer::hip_support::detail::operator<<(out, v.pciDeviceID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::pciBusID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciBusID="); + roctracer::hip_support::detail::operator<<(out, v.pciBusID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::pciDomainID").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "pciDomainID="); + roctracer::hip_support::detail::operator<<(out, v.pciDomainID); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::concurrentKernels").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "concurrentKernels="); + roctracer::hip_support::detail::operator<<(out, v.concurrentKernels); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::arch").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "arch="); + roctracer::hip_support::detail::operator<<(out, v.arch); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::clockInstructionRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "clockInstructionRate="); + roctracer::hip_support::detail::operator<<(out, v.clockInstructionRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::computeMode").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "computeMode="); + roctracer::hip_support::detail::operator<<(out, v.computeMode); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxThreadsPerMultiProcessor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsPerMultiProcessor="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsPerMultiProcessor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::l2CacheSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "l2CacheSize="); + roctracer::hip_support::detail::operator<<(out, v.l2CacheSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::multiProcessorCount").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "multiProcessorCount="); + roctracer::hip_support::detail::operator<<(out, v.multiProcessorCount); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::minor").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "minor="); + roctracer::hip_support::detail::operator<<(out, v.minor); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::major").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "major="); + roctracer::hip_support::detail::operator<<(out, v.major); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::totalConstMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "totalConstMem="); + roctracer::hip_support::detail::operator<<(out, v.totalConstMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::memoryBusWidth").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryBusWidth="); + roctracer::hip_support::detail::operator<<(out, v.memoryBusWidth); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::memoryClockRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "memoryClockRate="); + roctracer::hip_support::detail::operator<<(out, v.memoryClockRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::clockRate").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "clockRate="); + roctracer::hip_support::detail::operator<<(out, v.clockRate); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxGridSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxGridSize="); + roctracer::hip_support::detail::operator<<(out, v.maxGridSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxThreadsDim").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsDim="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsDim); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::maxThreadsPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "maxThreadsPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.maxThreadsPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::warpSize").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "warpSize="); + roctracer::hip_support::detail::operator<<(out, v.warpSize); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::regsPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "regsPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.regsPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::sharedMemPerBlock").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "sharedMemPerBlock="); + roctracer::hip_support::detail::operator<<(out, v.sharedMemPerBlock); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::totalGlobalMem").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "totalGlobalMem="); + roctracer::hip_support::detail::operator<<(out, v.totalGlobalMem); + std::operator<<(out, ", "); + } + if (std::string("hipDeviceProp_tR0000::name").find(HIP_structs_regex) != std::string::npos) { + std::operator<<(out, "name="); + roctracer::hip_support::detail::operator<<(out, v.name); + } + }; + HIP_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +// end ostream ops for HIP +};};}; + +inline static std::ostream& operator<<(std::ostream& out, const __locale_struct& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceArch_t& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipUUID& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceProp_tR0600& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipPointerAttribute_t& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipChannelFormatDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_ARRAY_DESCRIPTOR& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_ARRAY3D_DESCRIPTOR& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hip_Memcpy2D& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMipmappedArray& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_TEXTURE_DESC& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipResourceDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_RESOURCE_DESC& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipResourceViewDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_RESOURCE_VIEW_DESC& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipPitchedPtr& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExtent& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipPos& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemcpy3DParms& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_MEMCPY3D& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uchar1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uchar2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uchar3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uchar4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const char1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const char2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const char3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const char4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ushort1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ushort2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ushort3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ushort4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const short1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const short2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const short3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const short4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uint1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uint2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uint3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const uint4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const int1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const int2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const int3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const int4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulong1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulong2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulong3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulong4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const long1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const long2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const long3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const long4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulonglong1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulonglong2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulonglong3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const ulonglong4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const longlong1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const longlong2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const longlong3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const longlong4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const float1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const float2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const float3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const float4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const double1& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const double2& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const double3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const double4& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const textureReference& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipTextureDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const surfaceReference& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipIpcMemHandle_t& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipIpcEventHandle_t& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipFuncAttributes& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemLocation& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemAccessDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemPoolProps& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemPoolPtrExportData& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const dim3& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipLaunchParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipFunctionLaunchParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryHandleDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryBufferDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalMemoryMipmappedArrayDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreHandleDesc& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreSignalParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreWaitParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipHostNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipKernelNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemsetParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemAllocNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipAccessPolicyWindow& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipKernelNodeAttrValue& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const HIP_MEMSET_NODE_PARAMS& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemAllocationProp& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreSignalNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipExternalSemaphoreWaitNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipArrayMapInfo& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemcpyNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipChildGraphNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipEventWaitNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipEventRecordNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipMemFreeNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipGraphNodeParams& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hipDeviceProp_tR0000& v) +{ + roctracer::hip_support::detail::operator<<(out, v); + return out; +} + +#endif //__cplusplus +#endif // INC_HIP_OSTREAM_OPS_H_ + diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_ostream_ops.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_ostream_ops.h new file mode 100644 index 0000000000000000000000000000000000000000..353ddc6ba4ca8df157f5b5ad2a4c6ec7e01c8fe8 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_ostream_ops.h @@ -0,0 +1,1467 @@ +// automatically generated +/* +Copyright (c) 2018 Advanced Micro Devices, Inc. All rights reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*/ + +#ifndef INC_HSA_OSTREAM_OPS_H_ +#define INC_HSA_OSTREAM_OPS_H_ + +#include "roctracer.h" + +#ifdef __cplusplus +#include +#include +#include +#include + +namespace roctracer { +namespace hsa_support { +static int HSA_depth_max = 1; +static int HSA_depth_max_cnt = 0; +static std::string HSA_structs_regex = ""; +// begin ostream ops for HSA +// basic ostream ops +namespace detail { + inline static void print_escaped_string(std::ostream& out, const char *v, size_t len) { + out << '"'; + for (size_t i = 0; i < len && v[i]; ++i) { + switch (v[i]) { + case '\"': out << "\\\""; break; + case '\\': out << "\\\\"; break; + case '\b': out << "\\\b"; break; + case '\f': out << "\\\f"; break; + case '\n': out << "\\\n"; break; + case '\r': out << "\\\r"; break; + case '\t': out << "\\\t"; break; + default: + if (std::isprint((unsigned char)v[i])) std::operator<<(out, v[i]); + else { + std::ios_base::fmtflags flags(out.flags()); + out << "\\x" << std::setfill('0') << std::setw(2) << std::hex << (unsigned int)(unsigned char)v[i]; + out.flags(flags); + } + break; + } + } + out << '"'; + } + + template + inline static std::ostream& operator<<(std::ostream& out, const T& v) { + using std::operator<<; + static bool recursion = false; + if (recursion == false) { recursion = true; out << v; recursion = false; } + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const unsigned char &v) { + out << (unsigned int)v; + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const char &v) { + out << (unsigned char)v; + return out; + } + + template + inline static std::ostream &operator<<(std::ostream &out, const char (&v)[N]) { + print_escaped_string(out, v, N); + return out; + } + + inline static std::ostream &operator<<(std::ostream &out, const char *v) { + print_escaped_string(out, v, strlen(v)); + return out; + } +// End of basic ostream ops + +inline static std::ostream& operator<<(std::ostream& out, const hsa_dim3_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_dim3_t::z").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "z="); + roctracer::hsa_support::detail::operator<<(out, v.z); + std::operator<<(out, ", "); + } + if (std::string("hsa_dim3_t::y").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "y="); + roctracer::hsa_support::detail::operator<<(out, v.y); + std::operator<<(out, ", "); + } + if (std::string("hsa_dim3_t::x").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "x="); + roctracer::hsa_support::detail::operator<<(out, v.x); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_agent_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_agent_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_cache_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_cache_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_signal_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_signal_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_signal_group_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_signal_group_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_region_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_region_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_queue_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_queue_t::id").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "id="); + roctracer::hsa_support::detail::operator<<(out, v.id); + std::operator<<(out, ", "); + } + if (std::string("hsa_queue_t::reserved1").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved1="); + roctracer::hsa_support::detail::operator<<(out, v.reserved1); + std::operator<<(out, ", "); + } + if (std::string("hsa_queue_t::size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "size="); + roctracer::hsa_support::detail::operator<<(out, v.size); + std::operator<<(out, ", "); + } + if (std::string("hsa_queue_t::doorbell_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "doorbell_signal="); + roctracer::hsa_support::detail::operator<<(out, v.doorbell_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_queue_t::features").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "features="); + roctracer::hsa_support::detail::operator<<(out, v.features); + std::operator<<(out, ", "); + } + if (std::string("hsa_queue_t::type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hsa_support::detail::operator<<(out, v.type); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_kernel_dispatch_packet_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_kernel_dispatch_packet_t::completion_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "completion_signal="); + roctracer::hsa_support::detail::operator<<(out, v.completion_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::reserved2").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hsa_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::kernel_object").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "kernel_object="); + roctracer::hsa_support::detail::operator<<(out, v.kernel_object); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::group_segment_size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "group_segment_size="); + roctracer::hsa_support::detail::operator<<(out, v.group_segment_size); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::private_segment_size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "private_segment_size="); + roctracer::hsa_support::detail::operator<<(out, v.private_segment_size); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::grid_size_z").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "grid_size_z="); + roctracer::hsa_support::detail::operator<<(out, v.grid_size_z); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::grid_size_y").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "grid_size_y="); + roctracer::hsa_support::detail::operator<<(out, v.grid_size_y); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::grid_size_x").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "grid_size_x="); + roctracer::hsa_support::detail::operator<<(out, v.grid_size_x); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::reserved0").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hsa_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::workgroup_size_z").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "workgroup_size_z="); + roctracer::hsa_support::detail::operator<<(out, v.workgroup_size_z); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::workgroup_size_y").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "workgroup_size_y="); + roctracer::hsa_support::detail::operator<<(out, v.workgroup_size_y); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::workgroup_size_x").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "workgroup_size_x="); + roctracer::hsa_support::detail::operator<<(out, v.workgroup_size_x); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::setup").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "setup="); + roctracer::hsa_support::detail::operator<<(out, v.setup); + std::operator<<(out, ", "); + } + if (std::string("hsa_kernel_dispatch_packet_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_agent_dispatch_packet_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_agent_dispatch_packet_t::completion_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "completion_signal="); + roctracer::hsa_support::detail::operator<<(out, v.completion_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_agent_dispatch_packet_t::reserved2").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hsa_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hsa_agent_dispatch_packet_t::arg").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "arg="); + roctracer::hsa_support::detail::operator<<(out, v.arg); + std::operator<<(out, ", "); + } + if (std::string("hsa_agent_dispatch_packet_t::reserved0").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hsa_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hsa_agent_dispatch_packet_t::type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hsa_support::detail::operator<<(out, v.type); + std::operator<<(out, ", "); + } + if (std::string("hsa_agent_dispatch_packet_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_barrier_and_packet_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_barrier_and_packet_t::completion_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "completion_signal="); + roctracer::hsa_support::detail::operator<<(out, v.completion_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_and_packet_t::reserved2").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hsa_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_and_packet_t::dep_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "dep_signal="); + roctracer::hsa_support::detail::operator<<(out, v.dep_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_and_packet_t::reserved1").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved1="); + roctracer::hsa_support::detail::operator<<(out, v.reserved1); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_and_packet_t::reserved0").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hsa_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_and_packet_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_barrier_or_packet_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_barrier_or_packet_t::completion_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "completion_signal="); + roctracer::hsa_support::detail::operator<<(out, v.completion_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_or_packet_t::reserved2").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hsa_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_or_packet_t::dep_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "dep_signal="); + roctracer::hsa_support::detail::operator<<(out, v.dep_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_or_packet_t::reserved1").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved1="); + roctracer::hsa_support::detail::operator<<(out, v.reserved1); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_or_packet_t::reserved0").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hsa_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hsa_barrier_or_packet_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_isa_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_isa_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_wavefront_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_wavefront_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_object_reader_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_code_object_reader_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_executable_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_executable_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_loaded_code_object_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_loaded_code_object_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_executable_symbol_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_executable_symbol_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_object_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_code_object_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_callback_data_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_callback_data_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_symbol_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_code_symbol_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_image_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_format_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_image_format_t::channel_order").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "channel_order="); + roctracer::hsa_support::detail::operator<<(out, v.channel_order); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_format_t::channel_type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "channel_type="); + roctracer::hsa_support::detail::operator<<(out, v.channel_type); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_descriptor_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_image_descriptor_t::format").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "format="); + roctracer::hsa_support::detail::operator<<(out, v.format); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_descriptor_t::array_size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "array_size="); + roctracer::hsa_support::detail::operator<<(out, v.array_size); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_descriptor_t::depth").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "depth="); + roctracer::hsa_support::detail::operator<<(out, v.depth); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_descriptor_t::height").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "height="); + roctracer::hsa_support::detail::operator<<(out, v.height); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_descriptor_t::width").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "width="); + roctracer::hsa_support::detail::operator<<(out, v.width); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_descriptor_t::geometry").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "geometry="); + roctracer::hsa_support::detail::operator<<(out, v.geometry); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_data_info_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_image_data_info_t::alignment").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "alignment="); + roctracer::hsa_support::detail::operator<<(out, v.alignment); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_data_info_t::size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "size="); + roctracer::hsa_support::detail::operator<<(out, v.size); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_region_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_image_region_t::range").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "range="); + roctracer::hsa_support::detail::operator<<(out, v.range); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_image_region_t::offset").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "offset="); + roctracer::hsa_support::detail::operator<<(out, v.offset); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_sampler_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_sampler_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_sampler_descriptor_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_sampler_descriptor_t::address_mode").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "address_mode="); + roctracer::hsa_support::detail::operator<<(out, v.address_mode); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_sampler_descriptor_t::filter_mode").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "filter_mode="); + roctracer::hsa_support::detail::operator<<(out, v.filter_mode); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_sampler_descriptor_t::coordinate_mode").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "coordinate_mode="); + roctracer::hsa_support::detail::operator<<(out, v.coordinate_mode); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_images_1_00_pfn_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_sampler_destroy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_sampler_destroy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_sampler_destroy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_sampler_create").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_sampler_create="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_sampler_create); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_image_copy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_copy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_copy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_image_destroy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_destroy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_destroy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_image_data_get_info").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_data_get_info="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_data_get_info); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_00_pfn_t::hsa_ext_image_get_capability").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_get_capability="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_get_capability); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_images_1_pfn_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_data_get_info_with_layout").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_data_get_info_with_layout="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_data_get_info_with_layout); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_get_capability_with_layout").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_get_capability_with_layout="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_get_capability_with_layout); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_sampler_destroy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_sampler_destroy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_sampler_destroy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_sampler_create").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_sampler_create="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_sampler_create); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_copy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_copy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_copy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_destroy").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_destroy="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_destroy); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_data_get_info").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_data_get_info="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_data_get_info); + std::operator<<(out, ", "); + } + if (std::string("hsa_ext_images_1_pfn_t::hsa_ext_image_get_capability").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "hsa_ext_image_get_capability="); + roctracer::hsa_support::detail::operator<<(out, v.hsa_ext_image_get_capability); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_vendor_packet_header_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_vendor_packet_header_t::reserved").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved="); + roctracer::hsa_support::detail::operator<<(out, v.reserved); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_vendor_packet_header_t::AmdFormat").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "AmdFormat="); + roctracer::hsa_support::detail::operator<<(out, v.AmdFormat); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_vendor_packet_header_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_barrier_value_packet_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_barrier_value_packet_t::completion_signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "completion_signal="); + roctracer::hsa_support::detail::operator<<(out, v.completion_signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::reserved3").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved3="); + roctracer::hsa_support::detail::operator<<(out, v.reserved3); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::reserved2").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved2="); + roctracer::hsa_support::detail::operator<<(out, v.reserved2); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::reserved1").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved1="); + roctracer::hsa_support::detail::operator<<(out, v.reserved1); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::cond").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "cond="); + roctracer::hsa_support::detail::operator<<(out, v.cond); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::mask").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "mask="); + roctracer::hsa_support::detail::operator<<(out, v.mask); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::value").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "value="); + roctracer::hsa_support::detail::operator<<(out, v.value); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::signal").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "signal="); + roctracer::hsa_support::detail::operator<<(out, v.signal); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::reserved0").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reserved0="); + roctracer::hsa_support::detail::operator<<(out, v.reserved0); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_barrier_value_packet_t::header").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "header="); + roctracer::hsa_support::detail::operator<<(out, v.header); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_hdp_flush_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_hdp_flush_t::HDP_REG_FLUSH_CNTL").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "HDP_REG_FLUSH_CNTL="); + roctracer::hsa_support::detail::operator<<(out, v.HDP_REG_FLUSH_CNTL); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_hdp_flush_t::HDP_MEM_FLUSH_CNTL").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "HDP_MEM_FLUSH_CNTL="); + roctracer::hsa_support::detail::operator<<(out, v.HDP_MEM_FLUSH_CNTL); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_profiling_dispatch_time_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_profiling_dispatch_time_t::end").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "end="); + roctracer::hsa_support::detail::operator<<(out, v.end); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_profiling_dispatch_time_t::start").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "start="); + roctracer::hsa_support::detail::operator<<(out, v.start); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_profiling_async_copy_time_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_profiling_async_copy_time_t::end").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "end="); + roctracer::hsa_support::detail::operator<<(out, v.end); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_profiling_async_copy_time_t::start").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "start="); + roctracer::hsa_support::detail::operator<<(out, v.start); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_pool_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_memory_pool_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_pitched_ptr_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_pitched_ptr_t::slice").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "slice="); + roctracer::hsa_support::detail::operator<<(out, v.slice); + std::operator<<(out, ", "); + } + if (std::string("hsa_pitched_ptr_t::pitch").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "pitch="); + roctracer::hsa_support::detail::operator<<(out, v.pitch); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_pool_link_info_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_memory_pool_link_info_t::numa_distance").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "numa_distance="); + roctracer::hsa_support::detail::operator<<(out, v.numa_distance); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_pool_link_info_t::link_type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "link_type="); + roctracer::hsa_support::detail::operator<<(out, v.link_type); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_pool_link_info_t::max_bandwidth").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "max_bandwidth="); + roctracer::hsa_support::detail::operator<<(out, v.max_bandwidth); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_pool_link_info_t::min_bandwidth").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "min_bandwidth="); + roctracer::hsa_support::detail::operator<<(out, v.min_bandwidth); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_pool_link_info_t::max_latency").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "max_latency="); + roctracer::hsa_support::detail::operator<<(out, v.max_latency); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_pool_link_info_t::min_latency").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "min_latency="); + roctracer::hsa_support::detail::operator<<(out, v.min_latency); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_image_descriptor_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_image_descriptor_t::data").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "data="); + roctracer::hsa_support::detail::operator<<(out, v.data); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_image_descriptor_t::deviceID").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "deviceID="); + roctracer::hsa_support::detail::operator<<(out, v.deviceID); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_image_descriptor_t::version").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "version="); + roctracer::hsa_support::detail::operator<<(out, v.version); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_pointer_info_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_pointer_info_t::global_flags").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "global_flags="); + roctracer::hsa_support::detail::operator<<(out, v.global_flags); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_pointer_info_t::agentOwner").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "agentOwner="); + roctracer::hsa_support::detail::operator<<(out, v.agentOwner); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_pointer_info_t::sizeInBytes").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "sizeInBytes="); + roctracer::hsa_support::detail::operator<<(out, v.sizeInBytes); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_pointer_info_t::type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "type="); + roctracer::hsa_support::detail::operator<<(out, v.type); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_pointer_info_t::size").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "size="); + roctracer::hsa_support::detail::operator<<(out, v.size); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_ipc_memory_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_ipc_memory_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_gpu_memory_fault_info_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_gpu_memory_fault_info_t::fault_reason_mask").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "fault_reason_mask="); + roctracer::hsa_support::detail::operator<<(out, v.fault_reason_mask); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_gpu_memory_fault_info_t::virtual_address").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "virtual_address="); + roctracer::hsa_support::detail::operator<<(out, v.virtual_address); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_gpu_memory_fault_info_t::agent").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "agent="); + roctracer::hsa_support::detail::operator<<(out, v.agent); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_gpu_hw_exception_info_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_gpu_hw_exception_info_t::reset_cause").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reset_cause="); + roctracer::hsa_support::detail::operator<<(out, v.reset_cause); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_gpu_hw_exception_info_t::reset_type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "reset_type="); + roctracer::hsa_support::detail::operator<<(out, v.reset_type); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_gpu_hw_exception_info_t::agent").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "agent="); + roctracer::hsa_support::detail::operator<<(out, v.agent); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_event_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_event_t::event_type").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "event_type="); + roctracer::hsa_support::detail::operator<<(out, v.event_type); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_svm_attribute_pair_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_svm_attribute_pair_t::value").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "value="); + roctracer::hsa_support::detail::operator<<(out, v.value); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_svm_attribute_pair_t::attribute").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "attribute="); + roctracer::hsa_support::detail::operator<<(out, v.attribute); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_vmem_alloc_handle_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_vmem_alloc_handle_t::handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "handle="); + roctracer::hsa_support::detail::operator<<(out, v.handle); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_access_desc_t& v) +{ + std::operator<<(out, '{'); + HSA_depth_max_cnt++; + if (HSA_depth_max == -1 || HSA_depth_max_cnt <= HSA_depth_max) { + if (std::string("hsa_amd_memory_access_desc_t::agent_handle").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "agent_handle="); + roctracer::hsa_support::detail::operator<<(out, v.agent_handle); + std::operator<<(out, ", "); + } + if (std::string("hsa_amd_memory_access_desc_t::permissions").find(HSA_structs_regex) != std::string::npos) { + std::operator<<(out, "permissions="); + roctracer::hsa_support::detail::operator<<(out, v.permissions); + } + }; + HSA_depth_max_cnt--; + std::operator<<(out, '}'); + return out; +} +// end ostream ops for HSA +};};}; + +inline static std::ostream& operator<<(std::ostream& out, const hsa_dim3_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_agent_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_cache_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_signal_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_signal_group_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_region_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_queue_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_kernel_dispatch_packet_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_agent_dispatch_packet_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_barrier_and_packet_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_barrier_or_packet_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_isa_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_wavefront_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_object_reader_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_executable_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_loaded_code_object_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_executable_symbol_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_object_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_callback_data_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_code_symbol_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_format_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_descriptor_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_data_info_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_image_region_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_sampler_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_sampler_descriptor_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_images_1_00_pfn_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_ext_images_1_pfn_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_vendor_packet_header_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_barrier_value_packet_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_hdp_flush_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_profiling_dispatch_time_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_profiling_async_copy_time_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_pool_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_pitched_ptr_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_pool_link_info_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_image_descriptor_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_pointer_info_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_ipc_memory_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_gpu_memory_fault_info_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_gpu_hw_exception_info_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_event_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_svm_attribute_pair_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_vmem_alloc_handle_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +inline static std::ostream& operator<<(std::ostream& out, const hsa_amd_memory_access_desc_t& v) +{ + roctracer::hsa_support::detail::operator<<(out, v); + return out; +} + +#endif //__cplusplus +#endif // INC_HSA_OSTREAM_OPS_H_ + diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_prof_str.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_prof_str.h new file mode 100644 index 0000000000000000000000000000000000000000..28b2bf54d7c4a991f931b7bc921f5db43739eba3 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/hsa_prof_str.h @@ -0,0 +1,3027 @@ +/* Generated by hsaap.py */ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + + +/* HSA API tracing primitives + 'CoreApi', header 'hsa.h', 125 funcs + 'AmdExt', header 'hsa_ext_amd.h', 68 funcs + 'ImageExt', header 'hsa_ext_image.h', 13 funcs + 'AmdExt', header 'hsa_api_trace.h', 68 funcs + */ + +#ifndef HSA_PROF_STR_H_ +#define HSA_PROF_STR_H_ + +/* section: API ID enumeration */ + +enum hsa_api_id_t { + /* block: CoreApi API */ + HSA_API_ID_hsa_init = 0, + HSA_API_ID_hsa_shut_down = 1, + HSA_API_ID_hsa_system_get_info = 2, + HSA_API_ID_hsa_system_extension_supported = 3, + HSA_API_ID_hsa_system_get_extension_table = 4, + HSA_API_ID_hsa_iterate_agents = 5, + HSA_API_ID_hsa_agent_get_info = 6, + HSA_API_ID_hsa_queue_create = 7, + HSA_API_ID_hsa_soft_queue_create = 8, + HSA_API_ID_hsa_queue_destroy = 9, + HSA_API_ID_hsa_queue_inactivate = 10, + HSA_API_ID_hsa_queue_load_read_index_scacquire = 11, + HSA_API_ID_hsa_queue_load_read_index_relaxed = 12, + HSA_API_ID_hsa_queue_load_write_index_scacquire = 13, + HSA_API_ID_hsa_queue_load_write_index_relaxed = 14, + HSA_API_ID_hsa_queue_store_write_index_relaxed = 15, + HSA_API_ID_hsa_queue_store_write_index_screlease = 16, + HSA_API_ID_hsa_queue_cas_write_index_scacq_screl = 17, + HSA_API_ID_hsa_queue_cas_write_index_scacquire = 18, + HSA_API_ID_hsa_queue_cas_write_index_relaxed = 19, + HSA_API_ID_hsa_queue_cas_write_index_screlease = 20, + HSA_API_ID_hsa_queue_add_write_index_scacq_screl = 21, + HSA_API_ID_hsa_queue_add_write_index_scacquire = 22, + HSA_API_ID_hsa_queue_add_write_index_relaxed = 23, + HSA_API_ID_hsa_queue_add_write_index_screlease = 24, + HSA_API_ID_hsa_queue_store_read_index_relaxed = 25, + HSA_API_ID_hsa_queue_store_read_index_screlease = 26, + HSA_API_ID_hsa_agent_iterate_regions = 27, + HSA_API_ID_hsa_region_get_info = 28, + HSA_API_ID_hsa_agent_get_exception_policies = 29, + HSA_API_ID_hsa_agent_extension_supported = 30, + HSA_API_ID_hsa_memory_register = 31, + HSA_API_ID_hsa_memory_deregister = 32, + HSA_API_ID_hsa_memory_allocate = 33, + HSA_API_ID_hsa_memory_free = 34, + HSA_API_ID_hsa_memory_copy = 35, + HSA_API_ID_hsa_memory_assign_agent = 36, + HSA_API_ID_hsa_signal_create = 37, + HSA_API_ID_hsa_signal_destroy = 38, + HSA_API_ID_hsa_signal_load_relaxed = 39, + HSA_API_ID_hsa_signal_load_scacquire = 40, + HSA_API_ID_hsa_signal_store_relaxed = 41, + HSA_API_ID_hsa_signal_store_screlease = 42, + HSA_API_ID_hsa_signal_wait_relaxed = 43, + HSA_API_ID_hsa_signal_wait_scacquire = 44, + HSA_API_ID_hsa_signal_and_relaxed = 45, + HSA_API_ID_hsa_signal_and_scacquire = 46, + HSA_API_ID_hsa_signal_and_screlease = 47, + HSA_API_ID_hsa_signal_and_scacq_screl = 48, + HSA_API_ID_hsa_signal_or_relaxed = 49, + HSA_API_ID_hsa_signal_or_scacquire = 50, + HSA_API_ID_hsa_signal_or_screlease = 51, + HSA_API_ID_hsa_signal_or_scacq_screl = 52, + HSA_API_ID_hsa_signal_xor_relaxed = 53, + HSA_API_ID_hsa_signal_xor_scacquire = 54, + HSA_API_ID_hsa_signal_xor_screlease = 55, + HSA_API_ID_hsa_signal_xor_scacq_screl = 56, + HSA_API_ID_hsa_signal_exchange_relaxed = 57, + HSA_API_ID_hsa_signal_exchange_scacquire = 58, + HSA_API_ID_hsa_signal_exchange_screlease = 59, + HSA_API_ID_hsa_signal_exchange_scacq_screl = 60, + HSA_API_ID_hsa_signal_add_relaxed = 61, + HSA_API_ID_hsa_signal_add_scacquire = 62, + HSA_API_ID_hsa_signal_add_screlease = 63, + HSA_API_ID_hsa_signal_add_scacq_screl = 64, + HSA_API_ID_hsa_signal_subtract_relaxed = 65, + HSA_API_ID_hsa_signal_subtract_scacquire = 66, + HSA_API_ID_hsa_signal_subtract_screlease = 67, + HSA_API_ID_hsa_signal_subtract_scacq_screl = 68, + HSA_API_ID_hsa_signal_cas_relaxed = 69, + HSA_API_ID_hsa_signal_cas_scacquire = 70, + HSA_API_ID_hsa_signal_cas_screlease = 71, + HSA_API_ID_hsa_signal_cas_scacq_screl = 72, + HSA_API_ID_hsa_isa_from_name = 73, + HSA_API_ID_hsa_isa_get_info = 74, + HSA_API_ID_hsa_isa_compatible = 75, + HSA_API_ID_hsa_code_object_serialize = 76, + HSA_API_ID_hsa_code_object_deserialize = 77, + HSA_API_ID_hsa_code_object_destroy = 78, + HSA_API_ID_hsa_code_object_get_info = 79, + HSA_API_ID_hsa_code_object_get_symbol = 80, + HSA_API_ID_hsa_code_symbol_get_info = 81, + HSA_API_ID_hsa_code_object_iterate_symbols = 82, + HSA_API_ID_hsa_executable_create = 83, + HSA_API_ID_hsa_executable_destroy = 84, + HSA_API_ID_hsa_executable_load_code_object = 85, + HSA_API_ID_hsa_executable_freeze = 86, + HSA_API_ID_hsa_executable_get_info = 87, + HSA_API_ID_hsa_executable_global_variable_define = 88, + HSA_API_ID_hsa_executable_agent_global_variable_define = 89, + HSA_API_ID_hsa_executable_readonly_variable_define = 90, + HSA_API_ID_hsa_executable_validate = 91, + HSA_API_ID_hsa_executable_get_symbol = 92, + HSA_API_ID_hsa_executable_symbol_get_info = 93, + HSA_API_ID_hsa_executable_iterate_symbols = 94, + HSA_API_ID_hsa_status_string = 95, + HSA_API_ID_hsa_extension_get_name = 96, + HSA_API_ID_hsa_system_major_extension_supported = 97, + HSA_API_ID_hsa_system_get_major_extension_table = 98, + HSA_API_ID_hsa_agent_major_extension_supported = 99, + HSA_API_ID_hsa_cache_get_info = 100, + HSA_API_ID_hsa_agent_iterate_caches = 101, + HSA_API_ID_hsa_signal_silent_store_relaxed = 102, + HSA_API_ID_hsa_signal_silent_store_screlease = 103, + HSA_API_ID_hsa_signal_group_create = 104, + HSA_API_ID_hsa_signal_group_destroy = 105, + HSA_API_ID_hsa_signal_group_wait_any_scacquire = 106, + HSA_API_ID_hsa_signal_group_wait_any_relaxed = 107, + HSA_API_ID_hsa_agent_iterate_isas = 108, + HSA_API_ID_hsa_isa_get_info_alt = 109, + HSA_API_ID_hsa_isa_get_exception_policies = 110, + HSA_API_ID_hsa_isa_get_round_method = 111, + HSA_API_ID_hsa_wavefront_get_info = 112, + HSA_API_ID_hsa_isa_iterate_wavefronts = 113, + HSA_API_ID_hsa_code_object_get_symbol_from_name = 114, + HSA_API_ID_hsa_code_object_reader_create_from_file = 115, + HSA_API_ID_hsa_code_object_reader_create_from_memory = 116, + HSA_API_ID_hsa_code_object_reader_destroy = 117, + HSA_API_ID_hsa_executable_create_alt = 118, + HSA_API_ID_hsa_executable_load_program_code_object = 119, + HSA_API_ID_hsa_executable_load_agent_code_object = 120, + HSA_API_ID_hsa_executable_validate_alt = 121, + HSA_API_ID_hsa_executable_get_symbol_by_name = 122, + HSA_API_ID_hsa_executable_iterate_agent_symbols = 123, + HSA_API_ID_hsa_executable_iterate_program_symbols = 124, + + /* block: AmdExt API */ + HSA_API_ID_hsa_amd_coherency_get_type = 125, + HSA_API_ID_hsa_amd_coherency_set_type = 126, + HSA_API_ID_hsa_amd_profiling_set_profiler_enabled = 127, + HSA_API_ID_hsa_amd_profiling_async_copy_enable = 128, + HSA_API_ID_hsa_amd_profiling_get_dispatch_time = 129, + HSA_API_ID_hsa_amd_profiling_get_async_copy_time = 130, + HSA_API_ID_hsa_amd_profiling_convert_tick_to_system_domain = 131, + HSA_API_ID_hsa_amd_signal_async_handler = 132, + HSA_API_ID_hsa_amd_async_function = 133, + HSA_API_ID_hsa_amd_signal_wait_any = 134, + HSA_API_ID_hsa_amd_queue_cu_set_mask = 135, + HSA_API_ID_hsa_amd_memory_pool_get_info = 136, + HSA_API_ID_hsa_amd_agent_iterate_memory_pools = 137, + HSA_API_ID_hsa_amd_memory_pool_allocate = 138, + HSA_API_ID_hsa_amd_memory_pool_free = 139, + HSA_API_ID_hsa_amd_memory_async_copy = 140, + HSA_API_ID_hsa_amd_memory_async_copy_on_engine = 141, + HSA_API_ID_hsa_amd_memory_copy_engine_status = 142, + HSA_API_ID_hsa_amd_agent_memory_pool_get_info = 143, + HSA_API_ID_hsa_amd_agents_allow_access = 144, + HSA_API_ID_hsa_amd_memory_pool_can_migrate = 145, + HSA_API_ID_hsa_amd_memory_migrate = 146, + HSA_API_ID_hsa_amd_memory_lock = 147, + HSA_API_ID_hsa_amd_memory_unlock = 148, + HSA_API_ID_hsa_amd_memory_fill = 149, + HSA_API_ID_hsa_amd_interop_map_buffer = 150, + HSA_API_ID_hsa_amd_interop_unmap_buffer = 151, + HSA_API_ID_hsa_amd_image_create = 152, + HSA_API_ID_hsa_amd_pointer_info = 153, + HSA_API_ID_hsa_amd_pointer_info_set_userdata = 154, + HSA_API_ID_hsa_amd_ipc_memory_create = 155, + HSA_API_ID_hsa_amd_ipc_memory_attach = 156, + HSA_API_ID_hsa_amd_ipc_memory_detach = 157, + HSA_API_ID_hsa_amd_signal_create = 158, + HSA_API_ID_hsa_amd_ipc_signal_create = 159, + HSA_API_ID_hsa_amd_ipc_signal_attach = 160, + HSA_API_ID_hsa_amd_register_system_event_handler = 161, + HSA_API_ID_hsa_amd_queue_intercept_create = 162, + HSA_API_ID_hsa_amd_queue_intercept_register = 163, + HSA_API_ID_hsa_amd_queue_set_priority = 164, + HSA_API_ID_hsa_amd_memory_async_copy_rect = 165, + HSA_API_ID_hsa_amd_runtime_queue_create_register = 166, + HSA_API_ID_hsa_amd_memory_lock_to_pool = 167, + HSA_API_ID_hsa_amd_register_deallocation_callback = 168, + HSA_API_ID_hsa_amd_deregister_deallocation_callback = 169, + HSA_API_ID_hsa_amd_signal_value_pointer = 170, + HSA_API_ID_hsa_amd_svm_attributes_set = 171, + HSA_API_ID_hsa_amd_svm_attributes_get = 172, + HSA_API_ID_hsa_amd_svm_prefetch_async = 173, + HSA_API_ID_hsa_amd_spm_acquire = 174, + HSA_API_ID_hsa_amd_spm_release = 175, + HSA_API_ID_hsa_amd_spm_set_dest_buffer = 176, + HSA_API_ID_hsa_amd_queue_cu_get_mask = 177, + HSA_API_ID_hsa_amd_portable_export_dmabuf = 178, + HSA_API_ID_hsa_amd_portable_close_dmabuf = 179, + HSA_API_ID_hsa_amd_vmem_address_reserve = 180, + HSA_API_ID_hsa_amd_vmem_address_free = 181, + HSA_API_ID_hsa_amd_vmem_handle_create = 182, + HSA_API_ID_hsa_amd_vmem_handle_release = 183, + HSA_API_ID_hsa_amd_vmem_map = 184, + HSA_API_ID_hsa_amd_vmem_unmap = 185, + HSA_API_ID_hsa_amd_vmem_set_access = 186, + HSA_API_ID_hsa_amd_vmem_get_access = 187, + HSA_API_ID_hsa_amd_vmem_export_shareable_handle = 188, + HSA_API_ID_hsa_amd_vmem_import_shareable_handle = 189, + HSA_API_ID_hsa_amd_vmem_retain_alloc_handle = 190, + HSA_API_ID_hsa_amd_vmem_get_alloc_properties_from_handle = 191, + HSA_API_ID_hsa_amd_agent_set_async_scratch_limit = 192, + + /* block: ImageExt API */ + HSA_API_ID_hsa_ext_image_get_capability = 193, + HSA_API_ID_hsa_ext_image_data_get_info = 194, + HSA_API_ID_hsa_ext_image_create = 195, + HSA_API_ID_hsa_ext_image_import = 196, + HSA_API_ID_hsa_ext_image_export = 197, + HSA_API_ID_hsa_ext_image_copy = 198, + HSA_API_ID_hsa_ext_image_clear = 199, + HSA_API_ID_hsa_ext_image_destroy = 200, + HSA_API_ID_hsa_ext_sampler_create = 201, + HSA_API_ID_hsa_ext_sampler_destroy = 202, + HSA_API_ID_hsa_ext_image_get_capability_with_layout = 203, + HSA_API_ID_hsa_ext_image_data_get_info_with_layout = 204, + HSA_API_ID_hsa_ext_image_create_with_layout = 205, + + HSA_API_ID_DISPATCH = 206, + HSA_API_ID_NUMBER = 207, +}; +/* Declarations of APIs intended for use only by tools. */ +typedef void (*hsa_amd_queue_intercept_packet_writer)(const void*, uint64_t); +typedef void (*hsa_amd_queue_intercept_handler)(const void*, uint64_t, uint64_t, void*, + hsa_amd_queue_intercept_packet_writer); +typedef void (*hsa_amd_runtime_queue_notifier)(const hsa_queue_t*, hsa_agent_t, void*); + +/* section: API arg structure */ + +struct hsa_api_data_t { + uint64_t correlation_id; + uint32_t phase; + union { + uint64_t uint64_t_retval; + uint32_t uint32_t_retval; + hsa_signal_value_t hsa_signal_value_t_retval; + hsa_status_t hsa_status_t_retval; + }; + union { + /* block: CoreApi API */ + struct { + } hsa_init; + struct { + } hsa_shut_down; + struct { + hsa_system_info_t attribute; + void* value; + } hsa_system_get_info; + struct { + uint16_t extension; + uint16_t version_major; + uint16_t version_minor; + bool* result; + } hsa_system_extension_supported; + struct { + uint16_t extension; + uint16_t version_major; + uint16_t version_minor; + void* table; + } hsa_system_get_extension_table; + struct { + hsa_status_t (* callback)(hsa_agent_t agent,void* data); + void* data; + } hsa_iterate_agents; + struct { + hsa_agent_t agent; + hsa_agent_info_t attribute; + void* value; + } hsa_agent_get_info; + struct { + hsa_agent_t agent; + uint32_t size; + hsa_queue_type32_t type; + void (* callback)(hsa_status_t status,hsa_queue_t* source,void* data); + void* data; + uint32_t private_segment_size; + uint32_t group_segment_size; + hsa_queue_t** queue; + } hsa_queue_create; + struct { + hsa_region_t region; + uint32_t size; + hsa_queue_type32_t type; + uint32_t features; + hsa_signal_t doorbell_signal; + hsa_queue_t** queue; + } hsa_soft_queue_create; + struct { + hsa_queue_t* queue; + } hsa_queue_destroy; + struct { + hsa_queue_t* queue; + } hsa_queue_inactivate; + struct { + const hsa_queue_t* queue; + } hsa_queue_load_read_index_scacquire; + struct { + const hsa_queue_t* queue; + } hsa_queue_load_read_index_relaxed; + struct { + const hsa_queue_t* queue; + } hsa_queue_load_write_index_scacquire; + struct { + const hsa_queue_t* queue; + } hsa_queue_load_write_index_relaxed; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_store_write_index_relaxed; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_store_write_index_screlease; + struct { + const hsa_queue_t* queue; + uint64_t expected; + uint64_t value; + } hsa_queue_cas_write_index_scacq_screl; + struct { + const hsa_queue_t* queue; + uint64_t expected; + uint64_t value; + } hsa_queue_cas_write_index_scacquire; + struct { + const hsa_queue_t* queue; + uint64_t expected; + uint64_t value; + } hsa_queue_cas_write_index_relaxed; + struct { + const hsa_queue_t* queue; + uint64_t expected; + uint64_t value; + } hsa_queue_cas_write_index_screlease; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_add_write_index_scacq_screl; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_add_write_index_scacquire; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_add_write_index_relaxed; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_add_write_index_screlease; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_store_read_index_relaxed; + struct { + const hsa_queue_t* queue; + uint64_t value; + } hsa_queue_store_read_index_screlease; + struct { + hsa_agent_t agent; + hsa_status_t (* callback)(hsa_region_t region,void* data); + void* data; + } hsa_agent_iterate_regions; + struct { + hsa_region_t region; + hsa_region_info_t attribute; + void* value; + } hsa_region_get_info; + struct { + hsa_agent_t agent; + hsa_profile_t profile; + uint16_t* mask; + } hsa_agent_get_exception_policies; + struct { + uint16_t extension; + hsa_agent_t agent; + uint16_t version_major; + uint16_t version_minor; + bool* result; + } hsa_agent_extension_supported; + struct { + void* ptr; + size_t size; + } hsa_memory_register; + struct { + void* ptr; + size_t size; + } hsa_memory_deregister; + struct { + hsa_region_t region; + size_t size; + void** ptr; + } hsa_memory_allocate; + struct { + void* ptr; + } hsa_memory_free; + struct { + void* dst; + const void* src; + size_t size; + } hsa_memory_copy; + struct { + void* ptr; + hsa_agent_t agent; + hsa_access_permission_t access; + } hsa_memory_assign_agent; + struct { + hsa_signal_value_t initial_value; + uint32_t num_consumers; + const hsa_agent_t* consumers; + hsa_signal_t* signal; + } hsa_signal_create; + struct { + hsa_signal_t signal; + } hsa_signal_destroy; + struct { + hsa_signal_t signal; + } hsa_signal_load_relaxed; + struct { + hsa_signal_t signal; + } hsa_signal_load_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_store_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_store_screlease; + struct { + hsa_signal_t signal; + hsa_signal_condition_t condition; + hsa_signal_value_t compare_value; + uint64_t timeout_hint; + hsa_wait_state_t wait_state_hint; + } hsa_signal_wait_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_condition_t condition; + hsa_signal_value_t compare_value; + uint64_t timeout_hint; + hsa_wait_state_t wait_state_hint; + } hsa_signal_wait_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_and_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_and_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_and_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_and_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_or_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_or_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_or_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_or_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_xor_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_xor_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_xor_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_xor_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_exchange_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_exchange_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_exchange_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_exchange_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_add_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_add_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_add_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_add_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_subtract_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_subtract_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_subtract_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_subtract_scacq_screl; + struct { + hsa_signal_t signal; + hsa_signal_value_t expected; + hsa_signal_value_t value; + } hsa_signal_cas_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t expected; + hsa_signal_value_t value; + } hsa_signal_cas_scacquire; + struct { + hsa_signal_t signal; + hsa_signal_value_t expected; + hsa_signal_value_t value; + } hsa_signal_cas_screlease; + struct { + hsa_signal_t signal; + hsa_signal_value_t expected; + hsa_signal_value_t value; + } hsa_signal_cas_scacq_screl; + struct { + const char* name; + hsa_isa_t* isa; + } hsa_isa_from_name; + struct { + hsa_isa_t isa; + hsa_isa_info_t attribute; + uint32_t index; + void* value; + } hsa_isa_get_info; + struct { + hsa_isa_t code_object_isa; + hsa_isa_t agent_isa; + bool* result; + } hsa_isa_compatible; + struct { + hsa_code_object_t code_object; + hsa_status_t (* alloc_callback)(size_t size,hsa_callback_data_t data,void** address); + hsa_callback_data_t callback_data; + const char* options; + void** serialized_code_object; + size_t* serialized_code_object_size; + } hsa_code_object_serialize; + struct { + void* serialized_code_object; + size_t serialized_code_object_size; + const char* options; + hsa_code_object_t* code_object; + } hsa_code_object_deserialize; + struct { + hsa_code_object_t code_object; + } hsa_code_object_destroy; + struct { + hsa_code_object_t code_object; + hsa_code_object_info_t attribute; + void* value; + } hsa_code_object_get_info; + struct { + hsa_code_object_t code_object; + const char* symbol_name; + hsa_code_symbol_t* symbol; + } hsa_code_object_get_symbol; + struct { + hsa_code_symbol_t code_symbol; + hsa_code_symbol_info_t attribute; + void* value; + } hsa_code_symbol_get_info; + struct { + hsa_code_object_t code_object; + hsa_status_t (* callback)(hsa_code_object_t code_object,hsa_code_symbol_t symbol,void* data); + void* data; + } hsa_code_object_iterate_symbols; + struct { + hsa_profile_t profile; + hsa_executable_state_t executable_state; + const char* options; + hsa_executable_t* executable; + } hsa_executable_create; + struct { + hsa_executable_t executable; + } hsa_executable_destroy; + struct { + hsa_executable_t executable; + hsa_agent_t agent; + hsa_code_object_t code_object; + const char* options; + } hsa_executable_load_code_object; + struct { + hsa_executable_t executable; + const char* options; + } hsa_executable_freeze; + struct { + hsa_executable_t executable; + hsa_executable_info_t attribute; + void* value; + } hsa_executable_get_info; + struct { + hsa_executable_t executable; + const char* variable_name; + void* address; + } hsa_executable_global_variable_define; + struct { + hsa_executable_t executable; + hsa_agent_t agent; + const char* variable_name; + void* address; + } hsa_executable_agent_global_variable_define; + struct { + hsa_executable_t executable; + hsa_agent_t agent; + const char* variable_name; + void* address; + } hsa_executable_readonly_variable_define; + struct { + hsa_executable_t executable; + uint32_t* result; + } hsa_executable_validate; + struct { + hsa_executable_t executable; + const char* module_name; + const char* symbol_name; + hsa_agent_t agent; + int32_t call_convention; + hsa_executable_symbol_t* symbol; + } hsa_executable_get_symbol; + struct { + hsa_executable_symbol_t executable_symbol; + hsa_executable_symbol_info_t attribute; + void* value; + } hsa_executable_symbol_get_info; + struct { + hsa_executable_t executable; + hsa_status_t (* callback)(hsa_executable_t exec,hsa_executable_symbol_t symbol,void* data); + void* data; + } hsa_executable_iterate_symbols; + struct { + hsa_status_t status; + const char** status_string; + } hsa_status_string; + struct { + uint16_t extension; + const char** name; + } hsa_extension_get_name; + struct { + uint16_t extension; + uint16_t version_major; + uint16_t* version_minor; + bool* result; + } hsa_system_major_extension_supported; + struct { + uint16_t extension; + uint16_t version_major; + size_t table_length; + void* table; + } hsa_system_get_major_extension_table; + struct { + uint16_t extension; + hsa_agent_t agent; + uint16_t version_major; + uint16_t* version_minor; + bool* result; + } hsa_agent_major_extension_supported; + struct { + hsa_cache_t cache; + hsa_cache_info_t attribute; + void* value; + } hsa_cache_get_info; + struct { + hsa_agent_t agent; + hsa_status_t (* callback)(hsa_cache_t cache,void* data); + void* data; + } hsa_agent_iterate_caches; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_silent_store_relaxed; + struct { + hsa_signal_t signal; + hsa_signal_value_t value; + } hsa_signal_silent_store_screlease; + struct { + uint32_t num_signals; + const hsa_signal_t* signals; + uint32_t num_consumers; + const hsa_agent_t* consumers; + hsa_signal_group_t* signal_group; + } hsa_signal_group_create; + struct { + hsa_signal_group_t signal_group; + } hsa_signal_group_destroy; + struct { + hsa_signal_group_t signal_group; + const hsa_signal_condition_t* conditions; + const hsa_signal_value_t* compare_values; + hsa_wait_state_t wait_state_hint; + hsa_signal_t* signal; + hsa_signal_value_t* value; + } hsa_signal_group_wait_any_scacquire; + struct { + hsa_signal_group_t signal_group; + const hsa_signal_condition_t* conditions; + const hsa_signal_value_t* compare_values; + hsa_wait_state_t wait_state_hint; + hsa_signal_t* signal; + hsa_signal_value_t* value; + } hsa_signal_group_wait_any_relaxed; + struct { + hsa_agent_t agent; + hsa_status_t (* callback)(hsa_isa_t isa,void* data); + void* data; + } hsa_agent_iterate_isas; + struct { + hsa_isa_t isa; + hsa_isa_info_t attribute; + void* value; + } hsa_isa_get_info_alt; + struct { + hsa_isa_t isa; + hsa_profile_t profile; + uint16_t* mask; + } hsa_isa_get_exception_policies; + struct { + hsa_isa_t isa; + hsa_fp_type_t fp_type; + hsa_flush_mode_t flush_mode; + hsa_round_method_t* round_method; + } hsa_isa_get_round_method; + struct { + hsa_wavefront_t wavefront; + hsa_wavefront_info_t attribute; + void* value; + } hsa_wavefront_get_info; + struct { + hsa_isa_t isa; + hsa_status_t (* callback)(hsa_wavefront_t wavefront,void* data); + void* data; + } hsa_isa_iterate_wavefronts; + struct { + hsa_code_object_t code_object; + const char* module_name; + const char* symbol_name; + hsa_code_symbol_t* symbol; + } hsa_code_object_get_symbol_from_name; + struct { + hsa_file_t file; + hsa_code_object_reader_t* code_object_reader; + } hsa_code_object_reader_create_from_file; + struct { + const void* code_object; + size_t size; + hsa_code_object_reader_t* code_object_reader; + } hsa_code_object_reader_create_from_memory; + struct { + hsa_code_object_reader_t code_object_reader; + } hsa_code_object_reader_destroy; + struct { + hsa_profile_t profile; + hsa_default_float_rounding_mode_t default_float_rounding_mode; + const char* options; + hsa_executable_t* executable; + } hsa_executable_create_alt; + struct { + hsa_executable_t executable; + hsa_code_object_reader_t code_object_reader; + const char* options; + hsa_loaded_code_object_t* loaded_code_object; + } hsa_executable_load_program_code_object; + struct { + hsa_executable_t executable; + hsa_agent_t agent; + hsa_code_object_reader_t code_object_reader; + const char* options; + hsa_loaded_code_object_t* loaded_code_object; + } hsa_executable_load_agent_code_object; + struct { + hsa_executable_t executable; + const char* options; + uint32_t* result; + } hsa_executable_validate_alt; + struct { + hsa_executable_t executable; + const char* symbol_name; + const hsa_agent_t* agent; + hsa_executable_symbol_t* symbol; + } hsa_executable_get_symbol_by_name; + struct { + hsa_executable_t executable; + hsa_agent_t agent; + hsa_status_t (* callback)(hsa_executable_t exec,hsa_agent_t agent,hsa_executable_symbol_t symbol,void* data); + void* data; + } hsa_executable_iterate_agent_symbols; + struct { + hsa_executable_t executable; + hsa_status_t (* callback)(hsa_executable_t exec,hsa_executable_symbol_t symbol,void* data); + void* data; + } hsa_executable_iterate_program_symbols; + + /* block: AmdExt API */ + struct { + hsa_agent_t agent; + hsa_amd_coherency_type_t* type; + } hsa_amd_coherency_get_type; + struct { + hsa_agent_t agent; + hsa_amd_coherency_type_t type; + } hsa_amd_coherency_set_type; + struct { + hsa_queue_t* queue; + int enable; + } hsa_amd_profiling_set_profiler_enabled; + struct { + bool enable; + } hsa_amd_profiling_async_copy_enable; + struct { + hsa_agent_t agent; + hsa_signal_t signal; + hsa_amd_profiling_dispatch_time_t* time; + } hsa_amd_profiling_get_dispatch_time; + struct { + hsa_signal_t signal; + hsa_amd_profiling_async_copy_time_t* time; + } hsa_amd_profiling_get_async_copy_time; + struct { + hsa_agent_t agent; + uint64_t agent_tick; + uint64_t* system_tick; + } hsa_amd_profiling_convert_tick_to_system_domain; + struct { + hsa_signal_t signal; + hsa_signal_condition_t cond; + hsa_signal_value_t value; + hsa_amd_signal_handler handler; + void* arg; + } hsa_amd_signal_async_handler; + struct { + void (* callback)(void* arg); + void* arg; + } hsa_amd_async_function; + struct { + uint32_t signal_count; + hsa_signal_t* signals; + hsa_signal_condition_t* conds; + hsa_signal_value_t* values; + uint64_t timeout_hint; + hsa_wait_state_t wait_hint; + hsa_signal_value_t* satisfying_value; + } hsa_amd_signal_wait_any; + struct { + const hsa_queue_t* queue; + uint32_t num_cu_mask_count; + const uint32_t* cu_mask; + } hsa_amd_queue_cu_set_mask; + struct { + hsa_amd_memory_pool_t memory_pool; + hsa_amd_memory_pool_info_t attribute; + void* value; + } hsa_amd_memory_pool_get_info; + struct { + hsa_agent_t agent; + hsa_status_t (* callback)(hsa_amd_memory_pool_t memory_pool,void* data); + void* data; + } hsa_amd_agent_iterate_memory_pools; + struct { + hsa_amd_memory_pool_t memory_pool; + size_t size; + uint32_t flags; + void** ptr; + } hsa_amd_memory_pool_allocate; + struct { + void* ptr; + } hsa_amd_memory_pool_free; + struct { + void* dst; + hsa_agent_t dst_agent; + const void* src; + hsa_agent_t src_agent; + size_t size; + uint32_t num_dep_signals; + const hsa_signal_t* dep_signals; + hsa_signal_t completion_signal; + } hsa_amd_memory_async_copy; + struct { + void* dst; + hsa_agent_t dst_agent; + const void* src; + hsa_agent_t src_agent; + size_t size; + uint32_t num_dep_signals; + const hsa_signal_t* dep_signals; + hsa_signal_t completion_signal; + hsa_amd_sdma_engine_id_t engine_id; + bool force_copy_on_sdma; + } hsa_amd_memory_async_copy_on_engine; + struct { + hsa_agent_t dst_agent; + hsa_agent_t src_agent; + uint32_t* engine_ids_mask; + } hsa_amd_memory_copy_engine_status; + struct { + hsa_agent_t agent; + hsa_amd_memory_pool_t memory_pool; + hsa_amd_agent_memory_pool_info_t attribute; + void* value; + } hsa_amd_agent_memory_pool_get_info; + struct { + uint32_t num_agents; + const hsa_agent_t* agents; + const uint32_t* flags; + const void* ptr; + } hsa_amd_agents_allow_access; + struct { + hsa_amd_memory_pool_t src_memory_pool; + hsa_amd_memory_pool_t dst_memory_pool; + bool* result; + } hsa_amd_memory_pool_can_migrate; + struct { + const void* ptr; + hsa_amd_memory_pool_t memory_pool; + uint32_t flags; + } hsa_amd_memory_migrate; + struct { + void* host_ptr; + size_t size; + hsa_agent_t* agents; + int num_agent; + void** agent_ptr; + } hsa_amd_memory_lock; + struct { + void* host_ptr; + } hsa_amd_memory_unlock; + struct { + void* ptr; + uint32_t value; + size_t count; + } hsa_amd_memory_fill; + struct { + uint32_t num_agents; + hsa_agent_t* agents; + int interop_handle; + uint32_t flags; + size_t* size; + void** ptr; + size_t* metadata_size; + const void** metadata; + } hsa_amd_interop_map_buffer; + struct { + void* ptr; + } hsa_amd_interop_unmap_buffer; + struct { + hsa_agent_t agent; + const hsa_ext_image_descriptor_t* image_descriptor; + const hsa_amd_image_descriptor_t* image_layout; + const void* image_data; + hsa_access_permission_t access_permission; + hsa_ext_image_t* image; + } hsa_amd_image_create; + struct { + const void* ptr; + hsa_amd_pointer_info_t* info; + void* (* alloc)(size_t); + uint32_t* num_agents_accessible; + hsa_agent_t** accessible; + } hsa_amd_pointer_info; + struct { + const void* ptr; + void* userdata; + } hsa_amd_pointer_info_set_userdata; + struct { + void* ptr; + size_t len; + hsa_amd_ipc_memory_t* handle; + } hsa_amd_ipc_memory_create; + struct { + const hsa_amd_ipc_memory_t* handle; + size_t len; + uint32_t num_agents; + const hsa_agent_t* mapping_agents; + void** mapped_ptr; + } hsa_amd_ipc_memory_attach; + struct { + void* mapped_ptr; + } hsa_amd_ipc_memory_detach; + struct { + hsa_signal_value_t initial_value; + uint32_t num_consumers; + const hsa_agent_t* consumers; + uint64_t attributes; + hsa_signal_t* signal; + } hsa_amd_signal_create; + struct { + hsa_signal_t signal; + hsa_amd_ipc_signal_t* handle; + } hsa_amd_ipc_signal_create; + struct { + const hsa_amd_ipc_signal_t* handle; + hsa_signal_t* signal; + } hsa_amd_ipc_signal_attach; + struct { + hsa_amd_system_event_callback_t callback; + void* data; + } hsa_amd_register_system_event_handler; + struct { + hsa_agent_t agent_handle; + uint32_t size; + hsa_queue_type32_t type; + void (* callback)(hsa_status_t status,hsa_queue_t* source,void* data); + void* data; + uint32_t private_segment_size; + uint32_t group_segment_size; + hsa_queue_t** queue; + } hsa_amd_queue_intercept_create; + struct { + hsa_queue_t* queue; + hsa_amd_queue_intercept_handler callback; + void* user_data; + } hsa_amd_queue_intercept_register; + struct { + hsa_queue_t* queue; + hsa_amd_queue_priority_t priority; + } hsa_amd_queue_set_priority; + struct { + const hsa_pitched_ptr_t* dst; + const hsa_dim3_t* dst_offset; + const hsa_pitched_ptr_t* src; + const hsa_dim3_t* src_offset; + const hsa_dim3_t* range; + hsa_dim3_t range__val; + hsa_agent_t copy_agent; + hsa_amd_copy_direction_t dir; + uint32_t num_dep_signals; + const hsa_signal_t* dep_signals; + hsa_signal_t completion_signal; + } hsa_amd_memory_async_copy_rect; + struct { + hsa_amd_runtime_queue_notifier callback; + void* user_data; + } hsa_amd_runtime_queue_create_register; + struct { + void* host_ptr; + size_t size; + hsa_agent_t* agents; + int num_agent; + hsa_amd_memory_pool_t pool; + uint32_t flags; + void** agent_ptr; + } hsa_amd_memory_lock_to_pool; + struct { + void* ptr; + hsa_amd_deallocation_callback_t callback; + void* user_data; + } hsa_amd_register_deallocation_callback; + struct { + void* ptr; + hsa_amd_deallocation_callback_t callback; + } hsa_amd_deregister_deallocation_callback; + struct { + hsa_signal_t signal; + volatile hsa_signal_value_t** value_ptr; + } hsa_amd_signal_value_pointer; + struct { + void* ptr; + size_t size; + hsa_amd_svm_attribute_pair_t* attribute_list; + size_t attribute_count; + } hsa_amd_svm_attributes_set; + struct { + void* ptr; + size_t size; + hsa_amd_svm_attribute_pair_t* attribute_list; + size_t attribute_count; + } hsa_amd_svm_attributes_get; + struct { + void* ptr; + size_t size; + hsa_agent_t agent; + uint32_t num_dep_signals; + const hsa_signal_t* dep_signals; + hsa_signal_t completion_signal; + } hsa_amd_svm_prefetch_async; + struct { + hsa_agent_t preferred_agent; + } hsa_amd_spm_acquire; + struct { + hsa_agent_t preferred_agent; + } hsa_amd_spm_release; + struct { + hsa_agent_t preferred_agent; + size_t size_in_bytes; + uint32_t* timeout; + uint32_t* size_copied; + void* dest; + bool* is_data_loss; + } hsa_amd_spm_set_dest_buffer; + struct { + const hsa_queue_t* queue; + uint32_t num_cu_mask_count; + uint32_t* cu_mask; + } hsa_amd_queue_cu_get_mask; + struct { + const void* ptr; + size_t size; + int* dmabuf; + uint64_t* offset; + } hsa_amd_portable_export_dmabuf; + struct { + int dmabuf; + } hsa_amd_portable_close_dmabuf; + struct { + void** va; + size_t size; + uint64_t address; + uint64_t flags; + } hsa_amd_vmem_address_reserve; + struct { + void* va; + size_t size; + } hsa_amd_vmem_address_free; + struct { + hsa_amd_memory_pool_t pool; + size_t size; + hsa_amd_memory_type_t type; + uint64_t flags; + hsa_amd_vmem_alloc_handle_t* memory_handle; + } hsa_amd_vmem_handle_create; + struct { + hsa_amd_vmem_alloc_handle_t memory_handle; + } hsa_amd_vmem_handle_release; + struct { + void* va; + size_t size; + size_t in_offset; + hsa_amd_vmem_alloc_handle_t memory_handle; + uint64_t flags; + } hsa_amd_vmem_map; + struct { + void* va; + size_t size; + } hsa_amd_vmem_unmap; + struct { + void* va; + size_t size; + const hsa_amd_memory_access_desc_t* desc; + size_t desc_cnt; + } hsa_amd_vmem_set_access; + struct { + void* va; + hsa_access_permission_t* perms; + hsa_agent_t agent_handle; + } hsa_amd_vmem_get_access; + struct { + int* dmabuf_fd; + hsa_amd_vmem_alloc_handle_t handle; + uint64_t flags; + } hsa_amd_vmem_export_shareable_handle; + struct { + int dmabuf_fd; + hsa_amd_vmem_alloc_handle_t* handle; + } hsa_amd_vmem_import_shareable_handle; + struct { + hsa_amd_vmem_alloc_handle_t* memory_handle; + void* addr; + } hsa_amd_vmem_retain_alloc_handle; + struct { + hsa_amd_vmem_alloc_handle_t memory_handle; + hsa_amd_memory_pool_t* pool; + hsa_amd_memory_type_t* type; + } hsa_amd_vmem_get_alloc_properties_from_handle; + struct { + hsa_agent_t agent; + size_t threshold; + } hsa_amd_agent_set_async_scratch_limit; + + /* block: ImageExt API */ + struct { + hsa_agent_t agent; + hsa_ext_image_geometry_t geometry; + const hsa_ext_image_format_t* image_format; + uint32_t* capability_mask; + } hsa_ext_image_get_capability; + struct { + hsa_agent_t agent; + const hsa_ext_image_descriptor_t* image_descriptor; + hsa_access_permission_t access_permission; + hsa_ext_image_data_info_t* image_data_info; + } hsa_ext_image_data_get_info; + struct { + hsa_agent_t agent; + const hsa_ext_image_descriptor_t* image_descriptor; + const void* image_data; + hsa_access_permission_t access_permission; + hsa_ext_image_t* image; + } hsa_ext_image_create; + struct { + hsa_agent_t agent; + const void* src_memory; + size_t src_row_pitch; + size_t src_slice_pitch; + hsa_ext_image_t dst_image; + const hsa_ext_image_region_t* image_region; + } hsa_ext_image_import; + struct { + hsa_agent_t agent; + hsa_ext_image_t src_image; + void* dst_memory; + size_t dst_row_pitch; + size_t dst_slice_pitch; + const hsa_ext_image_region_t* image_region; + } hsa_ext_image_export; + struct { + hsa_agent_t agent; + hsa_ext_image_t src_image; + const hsa_dim3_t* src_offset; + hsa_ext_image_t dst_image; + const hsa_dim3_t* dst_offset; + const hsa_dim3_t* range; + } hsa_ext_image_copy; + struct { + hsa_agent_t agent; + hsa_ext_image_t image; + const void* data; + const hsa_ext_image_region_t* image_region; + } hsa_ext_image_clear; + struct { + hsa_agent_t agent; + hsa_ext_image_t image; + } hsa_ext_image_destroy; + struct { + hsa_agent_t agent; + const hsa_ext_sampler_descriptor_t* sampler_descriptor; + hsa_ext_sampler_t* sampler; + } hsa_ext_sampler_create; + struct { + hsa_agent_t agent; + hsa_ext_sampler_t sampler; + } hsa_ext_sampler_destroy; + struct { + hsa_agent_t agent; + hsa_ext_image_geometry_t geometry; + const hsa_ext_image_format_t* image_format; + hsa_ext_image_data_layout_t image_data_layout; + uint32_t* capability_mask; + } hsa_ext_image_get_capability_with_layout; + struct { + hsa_agent_t agent; + const hsa_ext_image_descriptor_t* image_descriptor; + hsa_access_permission_t access_permission; + hsa_ext_image_data_layout_t image_data_layout; + size_t image_data_row_pitch; + size_t image_data_slice_pitch; + hsa_ext_image_data_info_t* image_data_info; + } hsa_ext_image_data_get_info_with_layout; + struct { + hsa_agent_t agent; + const hsa_ext_image_descriptor_t* image_descriptor; + const void* image_data; + hsa_access_permission_t access_permission; + hsa_ext_image_data_layout_t image_data_layout; + size_t image_data_row_pitch; + size_t image_data_slice_pitch; + hsa_ext_image_t* image; + } hsa_ext_image_create_with_layout; + } args; + uint64_t *phase_data; +}; + +/* section: API output stream */ + +#ifdef __cplusplus +#include "hsa_ostream_ops.h" +typedef std::pair hsa_api_data_pair_t; +inline std::ostream& operator<< (std::ostream& out, const hsa_api_data_pair_t& data_pair) { + const uint32_t cid = data_pair.first; + const hsa_api_data_t& api_data = data_pair.second; + switch(cid) { + /* block: CoreApi API */ + case HSA_API_ID_hsa_init: { + out << "hsa_init("; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_shut_down: { + out << "hsa_shut_down("; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_system_get_info: { + out << "hsa_system_get_info("; + out << api_data.args.hsa_system_get_info.attribute << ", "; + out << api_data.args.hsa_system_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_system_extension_supported: { + out << "hsa_system_extension_supported("; + out << api_data.args.hsa_system_extension_supported.extension << ", "; + out << api_data.args.hsa_system_extension_supported.version_major << ", "; + out << api_data.args.hsa_system_extension_supported.version_minor << ", "; + out << api_data.args.hsa_system_extension_supported.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_system_get_extension_table: { + out << "hsa_system_get_extension_table("; + out << api_data.args.hsa_system_get_extension_table.extension << ", "; + out << api_data.args.hsa_system_get_extension_table.version_major << ", "; + out << api_data.args.hsa_system_get_extension_table.version_minor << ", "; + out << api_data.args.hsa_system_get_extension_table.table; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_iterate_agents: { + out << "hsa_iterate_agents("; + out << api_data.args.hsa_iterate_agents.callback << ", "; + out << api_data.args.hsa_iterate_agents.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_get_info: { + out << "hsa_agent_get_info("; + out << api_data.args.hsa_agent_get_info.agent << ", "; + out << api_data.args.hsa_agent_get_info.attribute << ", "; + out << api_data.args.hsa_agent_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_queue_create: { + out << "hsa_queue_create("; + out << api_data.args.hsa_queue_create.agent << ", "; + out << api_data.args.hsa_queue_create.size << ", "; + out << api_data.args.hsa_queue_create.type << ", "; + out << api_data.args.hsa_queue_create.callback << ", "; + out << api_data.args.hsa_queue_create.data << ", "; + out << api_data.args.hsa_queue_create.private_segment_size << ", "; + out << api_data.args.hsa_queue_create.group_segment_size << ", "; + out << api_data.args.hsa_queue_create.queue; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_soft_queue_create: { + out << "hsa_soft_queue_create("; + out << api_data.args.hsa_soft_queue_create.region << ", "; + out << api_data.args.hsa_soft_queue_create.size << ", "; + out << api_data.args.hsa_soft_queue_create.type << ", "; + out << api_data.args.hsa_soft_queue_create.features << ", "; + out << api_data.args.hsa_soft_queue_create.doorbell_signal << ", "; + out << api_data.args.hsa_soft_queue_create.queue; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_queue_destroy: { + out << "hsa_queue_destroy("; + out << api_data.args.hsa_queue_destroy.queue; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_queue_inactivate: { + out << "hsa_queue_inactivate("; + out << api_data.args.hsa_queue_inactivate.queue; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_queue_load_read_index_scacquire: { + out << "hsa_queue_load_read_index_scacquire("; + out << api_data.args.hsa_queue_load_read_index_scacquire.queue; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_load_read_index_relaxed: { + out << "hsa_queue_load_read_index_relaxed("; + out << api_data.args.hsa_queue_load_read_index_relaxed.queue; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_load_write_index_scacquire: { + out << "hsa_queue_load_write_index_scacquire("; + out << api_data.args.hsa_queue_load_write_index_scacquire.queue; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_load_write_index_relaxed: { + out << "hsa_queue_load_write_index_relaxed("; + out << api_data.args.hsa_queue_load_write_index_relaxed.queue; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_store_write_index_relaxed: { + out << "hsa_queue_store_write_index_relaxed("; + out << api_data.args.hsa_queue_store_write_index_relaxed.queue << ", "; + out << api_data.args.hsa_queue_store_write_index_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_queue_store_write_index_screlease: { + out << "hsa_queue_store_write_index_screlease("; + out << api_data.args.hsa_queue_store_write_index_screlease.queue << ", "; + out << api_data.args.hsa_queue_store_write_index_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_queue_cas_write_index_scacq_screl: { + out << "hsa_queue_cas_write_index_scacq_screl("; + out << api_data.args.hsa_queue_cas_write_index_scacq_screl.queue << ", "; + out << api_data.args.hsa_queue_cas_write_index_scacq_screl.expected << ", "; + out << api_data.args.hsa_queue_cas_write_index_scacq_screl.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_cas_write_index_scacquire: { + out << "hsa_queue_cas_write_index_scacquire("; + out << api_data.args.hsa_queue_cas_write_index_scacquire.queue << ", "; + out << api_data.args.hsa_queue_cas_write_index_scacquire.expected << ", "; + out << api_data.args.hsa_queue_cas_write_index_scacquire.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_cas_write_index_relaxed: { + out << "hsa_queue_cas_write_index_relaxed("; + out << api_data.args.hsa_queue_cas_write_index_relaxed.queue << ", "; + out << api_data.args.hsa_queue_cas_write_index_relaxed.expected << ", "; + out << api_data.args.hsa_queue_cas_write_index_relaxed.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_cas_write_index_screlease: { + out << "hsa_queue_cas_write_index_screlease("; + out << api_data.args.hsa_queue_cas_write_index_screlease.queue << ", "; + out << api_data.args.hsa_queue_cas_write_index_screlease.expected << ", "; + out << api_data.args.hsa_queue_cas_write_index_screlease.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_add_write_index_scacq_screl: { + out << "hsa_queue_add_write_index_scacq_screl("; + out << api_data.args.hsa_queue_add_write_index_scacq_screl.queue << ", "; + out << api_data.args.hsa_queue_add_write_index_scacq_screl.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_add_write_index_scacquire: { + out << "hsa_queue_add_write_index_scacquire("; + out << api_data.args.hsa_queue_add_write_index_scacquire.queue << ", "; + out << api_data.args.hsa_queue_add_write_index_scacquire.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_add_write_index_relaxed: { + out << "hsa_queue_add_write_index_relaxed("; + out << api_data.args.hsa_queue_add_write_index_relaxed.queue << ", "; + out << api_data.args.hsa_queue_add_write_index_relaxed.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_add_write_index_screlease: { + out << "hsa_queue_add_write_index_screlease("; + out << api_data.args.hsa_queue_add_write_index_screlease.queue << ", "; + out << api_data.args.hsa_queue_add_write_index_screlease.value; + out << ") = " << api_data.uint64_t_retval; + break; + } + case HSA_API_ID_hsa_queue_store_read_index_relaxed: { + out << "hsa_queue_store_read_index_relaxed("; + out << api_data.args.hsa_queue_store_read_index_relaxed.queue << ", "; + out << api_data.args.hsa_queue_store_read_index_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_queue_store_read_index_screlease: { + out << "hsa_queue_store_read_index_screlease("; + out << api_data.args.hsa_queue_store_read_index_screlease.queue << ", "; + out << api_data.args.hsa_queue_store_read_index_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_agent_iterate_regions: { + out << "hsa_agent_iterate_regions("; + out << api_data.args.hsa_agent_iterate_regions.agent << ", "; + out << api_data.args.hsa_agent_iterate_regions.callback << ", "; + out << api_data.args.hsa_agent_iterate_regions.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_region_get_info: { + out << "hsa_region_get_info("; + out << api_data.args.hsa_region_get_info.region << ", "; + out << api_data.args.hsa_region_get_info.attribute << ", "; + out << api_data.args.hsa_region_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_get_exception_policies: { + out << "hsa_agent_get_exception_policies("; + out << api_data.args.hsa_agent_get_exception_policies.agent << ", "; + out << api_data.args.hsa_agent_get_exception_policies.profile << ", "; + out << api_data.args.hsa_agent_get_exception_policies.mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_extension_supported: { + out << "hsa_agent_extension_supported("; + out << api_data.args.hsa_agent_extension_supported.extension << ", "; + out << api_data.args.hsa_agent_extension_supported.agent << ", "; + out << api_data.args.hsa_agent_extension_supported.version_major << ", "; + out << api_data.args.hsa_agent_extension_supported.version_minor << ", "; + out << api_data.args.hsa_agent_extension_supported.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_register: { + out << "hsa_memory_register("; + out << api_data.args.hsa_memory_register.ptr << ", "; + out << api_data.args.hsa_memory_register.size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_deregister: { + out << "hsa_memory_deregister("; + out << api_data.args.hsa_memory_deregister.ptr << ", "; + out << api_data.args.hsa_memory_deregister.size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_allocate: { + out << "hsa_memory_allocate("; + out << api_data.args.hsa_memory_allocate.region << ", "; + out << api_data.args.hsa_memory_allocate.size << ", "; + out << api_data.args.hsa_memory_allocate.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_free: { + out << "hsa_memory_free("; + out << api_data.args.hsa_memory_free.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_copy: { + out << "hsa_memory_copy("; + out << api_data.args.hsa_memory_copy.dst << ", "; + out << api_data.args.hsa_memory_copy.src << ", "; + out << api_data.args.hsa_memory_copy.size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_memory_assign_agent: { + out << "hsa_memory_assign_agent("; + out << api_data.args.hsa_memory_assign_agent.ptr << ", "; + out << api_data.args.hsa_memory_assign_agent.agent << ", "; + out << api_data.args.hsa_memory_assign_agent.access; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_create: { + out << "hsa_signal_create("; + out << api_data.args.hsa_signal_create.initial_value << ", "; + out << api_data.args.hsa_signal_create.num_consumers << ", "; + out << api_data.args.hsa_signal_create.consumers << ", "; + out << api_data.args.hsa_signal_create.signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_destroy: { + out << "hsa_signal_destroy("; + out << api_data.args.hsa_signal_destroy.signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_load_relaxed: { + out << "hsa_signal_load_relaxed("; + out << api_data.args.hsa_signal_load_relaxed.signal; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_load_scacquire: { + out << "hsa_signal_load_scacquire("; + out << api_data.args.hsa_signal_load_scacquire.signal; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_store_relaxed: { + out << "hsa_signal_store_relaxed("; + out << api_data.args.hsa_signal_store_relaxed.signal << ", "; + out << api_data.args.hsa_signal_store_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_store_screlease: { + out << "hsa_signal_store_screlease("; + out << api_data.args.hsa_signal_store_screlease.signal << ", "; + out << api_data.args.hsa_signal_store_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_wait_relaxed: { + out << "hsa_signal_wait_relaxed("; + out << api_data.args.hsa_signal_wait_relaxed.signal << ", "; + out << api_data.args.hsa_signal_wait_relaxed.condition << ", "; + out << api_data.args.hsa_signal_wait_relaxed.compare_value << ", "; + out << api_data.args.hsa_signal_wait_relaxed.timeout_hint << ", "; + out << api_data.args.hsa_signal_wait_relaxed.wait_state_hint; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_wait_scacquire: { + out << "hsa_signal_wait_scacquire("; + out << api_data.args.hsa_signal_wait_scacquire.signal << ", "; + out << api_data.args.hsa_signal_wait_scacquire.condition << ", "; + out << api_data.args.hsa_signal_wait_scacquire.compare_value << ", "; + out << api_data.args.hsa_signal_wait_scacquire.timeout_hint << ", "; + out << api_data.args.hsa_signal_wait_scacquire.wait_state_hint; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_and_relaxed: { + out << "hsa_signal_and_relaxed("; + out << api_data.args.hsa_signal_and_relaxed.signal << ", "; + out << api_data.args.hsa_signal_and_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_and_scacquire: { + out << "hsa_signal_and_scacquire("; + out << api_data.args.hsa_signal_and_scacquire.signal << ", "; + out << api_data.args.hsa_signal_and_scacquire.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_and_screlease: { + out << "hsa_signal_and_screlease("; + out << api_data.args.hsa_signal_and_screlease.signal << ", "; + out << api_data.args.hsa_signal_and_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_and_scacq_screl: { + out << "hsa_signal_and_scacq_screl("; + out << api_data.args.hsa_signal_and_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_and_scacq_screl.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_or_relaxed: { + out << "hsa_signal_or_relaxed("; + out << api_data.args.hsa_signal_or_relaxed.signal << ", "; + out << api_data.args.hsa_signal_or_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_or_scacquire: { + out << "hsa_signal_or_scacquire("; + out << api_data.args.hsa_signal_or_scacquire.signal << ", "; + out << api_data.args.hsa_signal_or_scacquire.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_or_screlease: { + out << "hsa_signal_or_screlease("; + out << api_data.args.hsa_signal_or_screlease.signal << ", "; + out << api_data.args.hsa_signal_or_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_or_scacq_screl: { + out << "hsa_signal_or_scacq_screl("; + out << api_data.args.hsa_signal_or_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_or_scacq_screl.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_xor_relaxed: { + out << "hsa_signal_xor_relaxed("; + out << api_data.args.hsa_signal_xor_relaxed.signal << ", "; + out << api_data.args.hsa_signal_xor_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_xor_scacquire: { + out << "hsa_signal_xor_scacquire("; + out << api_data.args.hsa_signal_xor_scacquire.signal << ", "; + out << api_data.args.hsa_signal_xor_scacquire.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_xor_screlease: { + out << "hsa_signal_xor_screlease("; + out << api_data.args.hsa_signal_xor_screlease.signal << ", "; + out << api_data.args.hsa_signal_xor_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_xor_scacq_screl: { + out << "hsa_signal_xor_scacq_screl("; + out << api_data.args.hsa_signal_xor_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_xor_scacq_screl.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_exchange_relaxed: { + out << "hsa_signal_exchange_relaxed("; + out << api_data.args.hsa_signal_exchange_relaxed.signal << ", "; + out << api_data.args.hsa_signal_exchange_relaxed.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_exchange_scacquire: { + out << "hsa_signal_exchange_scacquire("; + out << api_data.args.hsa_signal_exchange_scacquire.signal << ", "; + out << api_data.args.hsa_signal_exchange_scacquire.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_exchange_screlease: { + out << "hsa_signal_exchange_screlease("; + out << api_data.args.hsa_signal_exchange_screlease.signal << ", "; + out << api_data.args.hsa_signal_exchange_screlease.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_exchange_scacq_screl: { + out << "hsa_signal_exchange_scacq_screl("; + out << api_data.args.hsa_signal_exchange_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_exchange_scacq_screl.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_add_relaxed: { + out << "hsa_signal_add_relaxed("; + out << api_data.args.hsa_signal_add_relaxed.signal << ", "; + out << api_data.args.hsa_signal_add_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_add_scacquire: { + out << "hsa_signal_add_scacquire("; + out << api_data.args.hsa_signal_add_scacquire.signal << ", "; + out << api_data.args.hsa_signal_add_scacquire.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_add_screlease: { + out << "hsa_signal_add_screlease("; + out << api_data.args.hsa_signal_add_screlease.signal << ", "; + out << api_data.args.hsa_signal_add_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_add_scacq_screl: { + out << "hsa_signal_add_scacq_screl("; + out << api_data.args.hsa_signal_add_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_add_scacq_screl.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_subtract_relaxed: { + out << "hsa_signal_subtract_relaxed("; + out << api_data.args.hsa_signal_subtract_relaxed.signal << ", "; + out << api_data.args.hsa_signal_subtract_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_subtract_scacquire: { + out << "hsa_signal_subtract_scacquire("; + out << api_data.args.hsa_signal_subtract_scacquire.signal << ", "; + out << api_data.args.hsa_signal_subtract_scacquire.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_subtract_screlease: { + out << "hsa_signal_subtract_screlease("; + out << api_data.args.hsa_signal_subtract_screlease.signal << ", "; + out << api_data.args.hsa_signal_subtract_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_subtract_scacq_screl: { + out << "hsa_signal_subtract_scacq_screl("; + out << api_data.args.hsa_signal_subtract_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_subtract_scacq_screl.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_cas_relaxed: { + out << "hsa_signal_cas_relaxed("; + out << api_data.args.hsa_signal_cas_relaxed.signal << ", "; + out << api_data.args.hsa_signal_cas_relaxed.expected << ", "; + out << api_data.args.hsa_signal_cas_relaxed.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_cas_scacquire: { + out << "hsa_signal_cas_scacquire("; + out << api_data.args.hsa_signal_cas_scacquire.signal << ", "; + out << api_data.args.hsa_signal_cas_scacquire.expected << ", "; + out << api_data.args.hsa_signal_cas_scacquire.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_cas_screlease: { + out << "hsa_signal_cas_screlease("; + out << api_data.args.hsa_signal_cas_screlease.signal << ", "; + out << api_data.args.hsa_signal_cas_screlease.expected << ", "; + out << api_data.args.hsa_signal_cas_screlease.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_signal_cas_scacq_screl: { + out << "hsa_signal_cas_scacq_screl("; + out << api_data.args.hsa_signal_cas_scacq_screl.signal << ", "; + out << api_data.args.hsa_signal_cas_scacq_screl.expected << ", "; + out << api_data.args.hsa_signal_cas_scacq_screl.value; + out << ") = " << api_data.hsa_signal_value_t_retval; + break; + } + case HSA_API_ID_hsa_isa_from_name: { + out << "hsa_isa_from_name("; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_isa_from_name.name << ", "; + out << api_data.args.hsa_isa_from_name.isa; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_get_info: { + out << "hsa_isa_get_info("; + out << api_data.args.hsa_isa_get_info.isa << ", "; + out << api_data.args.hsa_isa_get_info.attribute << ", "; + out << api_data.args.hsa_isa_get_info.index << ", "; + out << api_data.args.hsa_isa_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_compatible: { + out << "hsa_isa_compatible("; + out << api_data.args.hsa_isa_compatible.code_object_isa << ", "; + out << api_data.args.hsa_isa_compatible.agent_isa << ", "; + out << api_data.args.hsa_isa_compatible.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_serialize: { + out << "hsa_code_object_serialize("; + out << api_data.args.hsa_code_object_serialize.code_object << ", "; + out << api_data.args.hsa_code_object_serialize.alloc_callback << ", "; + out << api_data.args.hsa_code_object_serialize.callback_data << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_code_object_serialize.options << ", "; + out << api_data.args.hsa_code_object_serialize.serialized_code_object << ", "; + out << api_data.args.hsa_code_object_serialize.serialized_code_object_size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_deserialize: { + out << "hsa_code_object_deserialize("; + out << api_data.args.hsa_code_object_deserialize.serialized_code_object << ", "; + out << api_data.args.hsa_code_object_deserialize.serialized_code_object_size << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_code_object_deserialize.options << ", "; + out << api_data.args.hsa_code_object_deserialize.code_object; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_destroy: { + out << "hsa_code_object_destroy("; + out << api_data.args.hsa_code_object_destroy.code_object; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_get_info: { + out << "hsa_code_object_get_info("; + out << api_data.args.hsa_code_object_get_info.code_object << ", "; + out << api_data.args.hsa_code_object_get_info.attribute << ", "; + out << api_data.args.hsa_code_object_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_get_symbol: { + out << "hsa_code_object_get_symbol("; + out << api_data.args.hsa_code_object_get_symbol.code_object << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_code_object_get_symbol.symbol_name << ", "; + out << api_data.args.hsa_code_object_get_symbol.symbol; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_symbol_get_info: { + out << "hsa_code_symbol_get_info("; + out << api_data.args.hsa_code_symbol_get_info.code_symbol << ", "; + out << api_data.args.hsa_code_symbol_get_info.attribute << ", "; + out << api_data.args.hsa_code_symbol_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_iterate_symbols: { + out << "hsa_code_object_iterate_symbols("; + out << api_data.args.hsa_code_object_iterate_symbols.code_object << ", "; + out << api_data.args.hsa_code_object_iterate_symbols.callback << ", "; + out << api_data.args.hsa_code_object_iterate_symbols.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_create: { + out << "hsa_executable_create("; + out << api_data.args.hsa_executable_create.profile << ", "; + out << api_data.args.hsa_executable_create.executable_state << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_create.options << ", "; + out << api_data.args.hsa_executable_create.executable; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_destroy: { + out << "hsa_executable_destroy("; + out << api_data.args.hsa_executable_destroy.executable; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_load_code_object: { + out << "hsa_executable_load_code_object("; + out << api_data.args.hsa_executable_load_code_object.executable << ", "; + out << api_data.args.hsa_executable_load_code_object.agent << ", "; + out << api_data.args.hsa_executable_load_code_object.code_object << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_load_code_object.options; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_freeze: { + out << "hsa_executable_freeze("; + out << api_data.args.hsa_executable_freeze.executable << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_freeze.options; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_get_info: { + out << "hsa_executable_get_info("; + out << api_data.args.hsa_executable_get_info.executable << ", "; + out << api_data.args.hsa_executable_get_info.attribute << ", "; + out << api_data.args.hsa_executable_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_global_variable_define: { + out << "hsa_executable_global_variable_define("; + out << api_data.args.hsa_executable_global_variable_define.executable << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_global_variable_define.variable_name << ", "; + out << api_data.args.hsa_executable_global_variable_define.address; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_agent_global_variable_define: { + out << "hsa_executable_agent_global_variable_define("; + out << api_data.args.hsa_executable_agent_global_variable_define.executable << ", "; + out << api_data.args.hsa_executable_agent_global_variable_define.agent << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_agent_global_variable_define.variable_name << ", "; + out << api_data.args.hsa_executable_agent_global_variable_define.address; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_readonly_variable_define: { + out << "hsa_executable_readonly_variable_define("; + out << api_data.args.hsa_executable_readonly_variable_define.executable << ", "; + out << api_data.args.hsa_executable_readonly_variable_define.agent << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_readonly_variable_define.variable_name << ", "; + out << api_data.args.hsa_executable_readonly_variable_define.address; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_validate: { + out << "hsa_executable_validate("; + out << api_data.args.hsa_executable_validate.executable << ", "; + out << api_data.args.hsa_executable_validate.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_get_symbol: { + out << "hsa_executable_get_symbol("; + out << api_data.args.hsa_executable_get_symbol.executable << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_get_symbol.module_name << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_get_symbol.symbol_name << ", "; + out << api_data.args.hsa_executable_get_symbol.agent << ", "; + out << api_data.args.hsa_executable_get_symbol.call_convention << ", "; + out << api_data.args.hsa_executable_get_symbol.symbol; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_symbol_get_info: { + out << "hsa_executable_symbol_get_info("; + out << api_data.args.hsa_executable_symbol_get_info.executable_symbol << ", "; + out << api_data.args.hsa_executable_symbol_get_info.attribute << ", "; + out << api_data.args.hsa_executable_symbol_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_iterate_symbols: { + out << "hsa_executable_iterate_symbols("; + out << api_data.args.hsa_executable_iterate_symbols.executable << ", "; + out << api_data.args.hsa_executable_iterate_symbols.callback << ", "; + out << api_data.args.hsa_executable_iterate_symbols.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_status_string: { + out << "hsa_status_string("; + out << api_data.args.hsa_status_string.status << ", "; + out << api_data.args.hsa_status_string.status_string; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_extension_get_name: { + out << "hsa_extension_get_name("; + out << api_data.args.hsa_extension_get_name.extension << ", "; + out << api_data.args.hsa_extension_get_name.name; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_system_major_extension_supported: { + out << "hsa_system_major_extension_supported("; + out << api_data.args.hsa_system_major_extension_supported.extension << ", "; + out << api_data.args.hsa_system_major_extension_supported.version_major << ", "; + out << api_data.args.hsa_system_major_extension_supported.version_minor << ", "; + out << api_data.args.hsa_system_major_extension_supported.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_system_get_major_extension_table: { + out << "hsa_system_get_major_extension_table("; + out << api_data.args.hsa_system_get_major_extension_table.extension << ", "; + out << api_data.args.hsa_system_get_major_extension_table.version_major << ", "; + out << api_data.args.hsa_system_get_major_extension_table.table_length << ", "; + out << api_data.args.hsa_system_get_major_extension_table.table; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_major_extension_supported: { + out << "hsa_agent_major_extension_supported("; + out << api_data.args.hsa_agent_major_extension_supported.extension << ", "; + out << api_data.args.hsa_agent_major_extension_supported.agent << ", "; + out << api_data.args.hsa_agent_major_extension_supported.version_major << ", "; + out << api_data.args.hsa_agent_major_extension_supported.version_minor << ", "; + out << api_data.args.hsa_agent_major_extension_supported.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_cache_get_info: { + out << "hsa_cache_get_info("; + out << api_data.args.hsa_cache_get_info.cache << ", "; + out << api_data.args.hsa_cache_get_info.attribute << ", "; + out << api_data.args.hsa_cache_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_iterate_caches: { + out << "hsa_agent_iterate_caches("; + out << api_data.args.hsa_agent_iterate_caches.agent << ", "; + out << api_data.args.hsa_agent_iterate_caches.callback << ", "; + out << api_data.args.hsa_agent_iterate_caches.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_silent_store_relaxed: { + out << "hsa_signal_silent_store_relaxed("; + out << api_data.args.hsa_signal_silent_store_relaxed.signal << ", "; + out << api_data.args.hsa_signal_silent_store_relaxed.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_silent_store_screlease: { + out << "hsa_signal_silent_store_screlease("; + out << api_data.args.hsa_signal_silent_store_screlease.signal << ", "; + out << api_data.args.hsa_signal_silent_store_screlease.value; + out << ") = void"; + break; + } + case HSA_API_ID_hsa_signal_group_create: { + out << "hsa_signal_group_create("; + out << api_data.args.hsa_signal_group_create.num_signals << ", "; + out << api_data.args.hsa_signal_group_create.signals << ", "; + out << api_data.args.hsa_signal_group_create.num_consumers << ", "; + out << api_data.args.hsa_signal_group_create.consumers << ", "; + out << api_data.args.hsa_signal_group_create.signal_group; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_group_destroy: { + out << "hsa_signal_group_destroy("; + out << api_data.args.hsa_signal_group_destroy.signal_group; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_group_wait_any_scacquire: { + out << "hsa_signal_group_wait_any_scacquire("; + out << api_data.args.hsa_signal_group_wait_any_scacquire.signal_group << ", "; + out << api_data.args.hsa_signal_group_wait_any_scacquire.conditions << ", "; + out << api_data.args.hsa_signal_group_wait_any_scacquire.compare_values << ", "; + out << api_data.args.hsa_signal_group_wait_any_scacquire.wait_state_hint << ", "; + out << api_data.args.hsa_signal_group_wait_any_scacquire.signal << ", "; + out << api_data.args.hsa_signal_group_wait_any_scacquire.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_signal_group_wait_any_relaxed: { + out << "hsa_signal_group_wait_any_relaxed("; + out << api_data.args.hsa_signal_group_wait_any_relaxed.signal_group << ", "; + out << api_data.args.hsa_signal_group_wait_any_relaxed.conditions << ", "; + out << api_data.args.hsa_signal_group_wait_any_relaxed.compare_values << ", "; + out << api_data.args.hsa_signal_group_wait_any_relaxed.wait_state_hint << ", "; + out << api_data.args.hsa_signal_group_wait_any_relaxed.signal << ", "; + out << api_data.args.hsa_signal_group_wait_any_relaxed.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_agent_iterate_isas: { + out << "hsa_agent_iterate_isas("; + out << api_data.args.hsa_agent_iterate_isas.agent << ", "; + out << api_data.args.hsa_agent_iterate_isas.callback << ", "; + out << api_data.args.hsa_agent_iterate_isas.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_get_info_alt: { + out << "hsa_isa_get_info_alt("; + out << api_data.args.hsa_isa_get_info_alt.isa << ", "; + out << api_data.args.hsa_isa_get_info_alt.attribute << ", "; + out << api_data.args.hsa_isa_get_info_alt.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_get_exception_policies: { + out << "hsa_isa_get_exception_policies("; + out << api_data.args.hsa_isa_get_exception_policies.isa << ", "; + out << api_data.args.hsa_isa_get_exception_policies.profile << ", "; + out << api_data.args.hsa_isa_get_exception_policies.mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_get_round_method: { + out << "hsa_isa_get_round_method("; + out << api_data.args.hsa_isa_get_round_method.isa << ", "; + out << api_data.args.hsa_isa_get_round_method.fp_type << ", "; + out << api_data.args.hsa_isa_get_round_method.flush_mode << ", "; + out << api_data.args.hsa_isa_get_round_method.round_method; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_wavefront_get_info: { + out << "hsa_wavefront_get_info("; + out << api_data.args.hsa_wavefront_get_info.wavefront << ", "; + out << api_data.args.hsa_wavefront_get_info.attribute << ", "; + out << api_data.args.hsa_wavefront_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_isa_iterate_wavefronts: { + out << "hsa_isa_iterate_wavefronts("; + out << api_data.args.hsa_isa_iterate_wavefronts.isa << ", "; + out << api_data.args.hsa_isa_iterate_wavefronts.callback << ", "; + out << api_data.args.hsa_isa_iterate_wavefronts.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_get_symbol_from_name: { + out << "hsa_code_object_get_symbol_from_name("; + out << api_data.args.hsa_code_object_get_symbol_from_name.code_object << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_code_object_get_symbol_from_name.module_name << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_code_object_get_symbol_from_name.symbol_name << ", "; + out << api_data.args.hsa_code_object_get_symbol_from_name.symbol; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_reader_create_from_file: { + out << "hsa_code_object_reader_create_from_file("; + out << api_data.args.hsa_code_object_reader_create_from_file.file << ", "; + out << api_data.args.hsa_code_object_reader_create_from_file.code_object_reader; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_reader_create_from_memory: { + out << "hsa_code_object_reader_create_from_memory("; + out << api_data.args.hsa_code_object_reader_create_from_memory.code_object << ", "; + out << api_data.args.hsa_code_object_reader_create_from_memory.size << ", "; + out << api_data.args.hsa_code_object_reader_create_from_memory.code_object_reader; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_code_object_reader_destroy: { + out << "hsa_code_object_reader_destroy("; + out << api_data.args.hsa_code_object_reader_destroy.code_object_reader; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_create_alt: { + out << "hsa_executable_create_alt("; + out << api_data.args.hsa_executable_create_alt.profile << ", "; + out << api_data.args.hsa_executable_create_alt.default_float_rounding_mode << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_create_alt.options << ", "; + out << api_data.args.hsa_executable_create_alt.executable; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_load_program_code_object: { + out << "hsa_executable_load_program_code_object("; + out << api_data.args.hsa_executable_load_program_code_object.executable << ", "; + out << api_data.args.hsa_executable_load_program_code_object.code_object_reader << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_load_program_code_object.options << ", "; + out << api_data.args.hsa_executable_load_program_code_object.loaded_code_object; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_load_agent_code_object: { + out << "hsa_executable_load_agent_code_object("; + out << api_data.args.hsa_executable_load_agent_code_object.executable << ", "; + out << api_data.args.hsa_executable_load_agent_code_object.agent << ", "; + out << api_data.args.hsa_executable_load_agent_code_object.code_object_reader << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_load_agent_code_object.options << ", "; + out << api_data.args.hsa_executable_load_agent_code_object.loaded_code_object; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_validate_alt: { + out << "hsa_executable_validate_alt("; + out << api_data.args.hsa_executable_validate_alt.executable << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_validate_alt.options << ", "; + out << api_data.args.hsa_executable_validate_alt.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_get_symbol_by_name: { + out << "hsa_executable_get_symbol_by_name("; + out << api_data.args.hsa_executable_get_symbol_by_name.executable << ", "; + out << "0x" << std::hex << (uint64_t)api_data.args.hsa_executable_get_symbol_by_name.symbol_name << ", "; + out << api_data.args.hsa_executable_get_symbol_by_name.agent << ", "; + out << api_data.args.hsa_executable_get_symbol_by_name.symbol; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_iterate_agent_symbols: { + out << "hsa_executable_iterate_agent_symbols("; + out << api_data.args.hsa_executable_iterate_agent_symbols.executable << ", "; + out << api_data.args.hsa_executable_iterate_agent_symbols.agent << ", "; + out << api_data.args.hsa_executable_iterate_agent_symbols.callback << ", "; + out << api_data.args.hsa_executable_iterate_agent_symbols.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_executable_iterate_program_symbols: { + out << "hsa_executable_iterate_program_symbols("; + out << api_data.args.hsa_executable_iterate_program_symbols.executable << ", "; + out << api_data.args.hsa_executable_iterate_program_symbols.callback << ", "; + out << api_data.args.hsa_executable_iterate_program_symbols.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + + /* block: AmdExt API */ + case HSA_API_ID_hsa_amd_coherency_get_type: { + out << "hsa_amd_coherency_get_type("; + out << api_data.args.hsa_amd_coherency_get_type.agent << ", "; + out << api_data.args.hsa_amd_coherency_get_type.type; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_coherency_set_type: { + out << "hsa_amd_coherency_set_type("; + out << api_data.args.hsa_amd_coherency_set_type.agent << ", "; + out << api_data.args.hsa_amd_coherency_set_type.type; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_profiling_set_profiler_enabled: { + out << "hsa_amd_profiling_set_profiler_enabled("; + out << api_data.args.hsa_amd_profiling_set_profiler_enabled.queue << ", "; + out << api_data.args.hsa_amd_profiling_set_profiler_enabled.enable; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_profiling_async_copy_enable: { + out << "hsa_amd_profiling_async_copy_enable("; + out << api_data.args.hsa_amd_profiling_async_copy_enable.enable; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_profiling_get_dispatch_time: { + out << "hsa_amd_profiling_get_dispatch_time("; + out << api_data.args.hsa_amd_profiling_get_dispatch_time.agent << ", "; + out << api_data.args.hsa_amd_profiling_get_dispatch_time.signal << ", "; + out << api_data.args.hsa_amd_profiling_get_dispatch_time.time; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_profiling_get_async_copy_time: { + out << "hsa_amd_profiling_get_async_copy_time("; + out << api_data.args.hsa_amd_profiling_get_async_copy_time.signal << ", "; + out << api_data.args.hsa_amd_profiling_get_async_copy_time.time; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_profiling_convert_tick_to_system_domain: { + out << "hsa_amd_profiling_convert_tick_to_system_domain("; + out << api_data.args.hsa_amd_profiling_convert_tick_to_system_domain.agent << ", "; + out << api_data.args.hsa_amd_profiling_convert_tick_to_system_domain.agent_tick << ", "; + out << api_data.args.hsa_amd_profiling_convert_tick_to_system_domain.system_tick; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_signal_async_handler: { + out << "hsa_amd_signal_async_handler("; + out << api_data.args.hsa_amd_signal_async_handler.signal << ", "; + out << api_data.args.hsa_amd_signal_async_handler.cond << ", "; + out << api_data.args.hsa_amd_signal_async_handler.value << ", "; + out << api_data.args.hsa_amd_signal_async_handler.handler << ", "; + out << api_data.args.hsa_amd_signal_async_handler.arg; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_async_function: { + out << "hsa_amd_async_function("; + out << api_data.args.hsa_amd_async_function.callback << ", "; + out << api_data.args.hsa_amd_async_function.arg; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_signal_wait_any: { + out << "hsa_amd_signal_wait_any("; + out << api_data.args.hsa_amd_signal_wait_any.signal_count << ", "; + out << api_data.args.hsa_amd_signal_wait_any.signals << ", "; + out << api_data.args.hsa_amd_signal_wait_any.conds << ", "; + out << api_data.args.hsa_amd_signal_wait_any.values << ", "; + out << api_data.args.hsa_amd_signal_wait_any.timeout_hint << ", "; + out << api_data.args.hsa_amd_signal_wait_any.wait_hint << ", "; + out << api_data.args.hsa_amd_signal_wait_any.satisfying_value; + out << ") = " << api_data.uint32_t_retval; + break; + } + case HSA_API_ID_hsa_amd_queue_cu_set_mask: { + out << "hsa_amd_queue_cu_set_mask("; + out << api_data.args.hsa_amd_queue_cu_set_mask.queue << ", "; + out << api_data.args.hsa_amd_queue_cu_set_mask.num_cu_mask_count << ", "; + out << api_data.args.hsa_amd_queue_cu_set_mask.cu_mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_pool_get_info: { + out << "hsa_amd_memory_pool_get_info("; + out << api_data.args.hsa_amd_memory_pool_get_info.memory_pool << ", "; + out << api_data.args.hsa_amd_memory_pool_get_info.attribute << ", "; + out << api_data.args.hsa_amd_memory_pool_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_agent_iterate_memory_pools: { + out << "hsa_amd_agent_iterate_memory_pools("; + out << api_data.args.hsa_amd_agent_iterate_memory_pools.agent << ", "; + out << api_data.args.hsa_amd_agent_iterate_memory_pools.callback << ", "; + out << api_data.args.hsa_amd_agent_iterate_memory_pools.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_pool_allocate: { + out << "hsa_amd_memory_pool_allocate("; + out << api_data.args.hsa_amd_memory_pool_allocate.memory_pool << ", "; + out << api_data.args.hsa_amd_memory_pool_allocate.size << ", "; + out << api_data.args.hsa_amd_memory_pool_allocate.flags << ", "; + out << api_data.args.hsa_amd_memory_pool_allocate.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_pool_free: { + out << "hsa_amd_memory_pool_free("; + out << api_data.args.hsa_amd_memory_pool_free.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_async_copy: { + out << "hsa_amd_memory_async_copy("; + out << api_data.args.hsa_amd_memory_async_copy.dst << ", "; + out << api_data.args.hsa_amd_memory_async_copy.dst_agent << ", "; + out << api_data.args.hsa_amd_memory_async_copy.src << ", "; + out << api_data.args.hsa_amd_memory_async_copy.src_agent << ", "; + out << api_data.args.hsa_amd_memory_async_copy.size << ", "; + out << api_data.args.hsa_amd_memory_async_copy.num_dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy.dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy.completion_signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_async_copy_on_engine: { + out << "hsa_amd_memory_async_copy_on_engine("; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.dst << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.dst_agent << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.src << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.src_agent << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.size << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.num_dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.completion_signal << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.engine_id << ", "; + out << api_data.args.hsa_amd_memory_async_copy_on_engine.force_copy_on_sdma; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_copy_engine_status: { + out << "hsa_amd_memory_copy_engine_status("; + out << api_data.args.hsa_amd_memory_copy_engine_status.dst_agent << ", "; + out << api_data.args.hsa_amd_memory_copy_engine_status.src_agent << ", "; + out << api_data.args.hsa_amd_memory_copy_engine_status.engine_ids_mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_agent_memory_pool_get_info: { + out << "hsa_amd_agent_memory_pool_get_info("; + out << api_data.args.hsa_amd_agent_memory_pool_get_info.agent << ", "; + out << api_data.args.hsa_amd_agent_memory_pool_get_info.memory_pool << ", "; + out << api_data.args.hsa_amd_agent_memory_pool_get_info.attribute << ", "; + out << api_data.args.hsa_amd_agent_memory_pool_get_info.value; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_agents_allow_access: { + out << "hsa_amd_agents_allow_access("; + out << api_data.args.hsa_amd_agents_allow_access.num_agents << ", "; + out << api_data.args.hsa_amd_agents_allow_access.agents << ", "; + out << api_data.args.hsa_amd_agents_allow_access.flags << ", "; + out << api_data.args.hsa_amd_agents_allow_access.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_pool_can_migrate: { + out << "hsa_amd_memory_pool_can_migrate("; + out << api_data.args.hsa_amd_memory_pool_can_migrate.src_memory_pool << ", "; + out << api_data.args.hsa_amd_memory_pool_can_migrate.dst_memory_pool << ", "; + out << api_data.args.hsa_amd_memory_pool_can_migrate.result; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_migrate: { + out << "hsa_amd_memory_migrate("; + out << api_data.args.hsa_amd_memory_migrate.ptr << ", "; + out << api_data.args.hsa_amd_memory_migrate.memory_pool << ", "; + out << api_data.args.hsa_amd_memory_migrate.flags; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_lock: { + out << "hsa_amd_memory_lock("; + out << api_data.args.hsa_amd_memory_lock.host_ptr << ", "; + out << api_data.args.hsa_amd_memory_lock.size << ", "; + out << api_data.args.hsa_amd_memory_lock.agents << ", "; + out << api_data.args.hsa_amd_memory_lock.num_agent << ", "; + out << api_data.args.hsa_amd_memory_lock.agent_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_unlock: { + out << "hsa_amd_memory_unlock("; + out << api_data.args.hsa_amd_memory_unlock.host_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_fill: { + out << "hsa_amd_memory_fill("; + out << api_data.args.hsa_amd_memory_fill.ptr << ", "; + out << api_data.args.hsa_amd_memory_fill.value << ", "; + out << api_data.args.hsa_amd_memory_fill.count; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_interop_map_buffer: { + out << "hsa_amd_interop_map_buffer("; + out << api_data.args.hsa_amd_interop_map_buffer.num_agents << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.agents << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.interop_handle << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.flags << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.size << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.ptr << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.metadata_size << ", "; + out << api_data.args.hsa_amd_interop_map_buffer.metadata; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_interop_unmap_buffer: { + out << "hsa_amd_interop_unmap_buffer("; + out << api_data.args.hsa_amd_interop_unmap_buffer.ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_image_create: { + out << "hsa_amd_image_create("; + out << api_data.args.hsa_amd_image_create.agent << ", "; + out << api_data.args.hsa_amd_image_create.image_descriptor << ", "; + out << api_data.args.hsa_amd_image_create.image_layout << ", "; + out << api_data.args.hsa_amd_image_create.image_data << ", "; + out << api_data.args.hsa_amd_image_create.access_permission << ", "; + out << api_data.args.hsa_amd_image_create.image; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_pointer_info: { + out << "hsa_amd_pointer_info("; + out << api_data.args.hsa_amd_pointer_info.ptr << ", "; + out << api_data.args.hsa_amd_pointer_info.info << ", "; + out << api_data.args.hsa_amd_pointer_info.alloc << ", "; + out << api_data.args.hsa_amd_pointer_info.num_agents_accessible << ", "; + out << api_data.args.hsa_amd_pointer_info.accessible; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_pointer_info_set_userdata: { + out << "hsa_amd_pointer_info_set_userdata("; + out << api_data.args.hsa_amd_pointer_info_set_userdata.ptr << ", "; + out << api_data.args.hsa_amd_pointer_info_set_userdata.userdata; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_ipc_memory_create: { + out << "hsa_amd_ipc_memory_create("; + out << api_data.args.hsa_amd_ipc_memory_create.ptr << ", "; + out << api_data.args.hsa_amd_ipc_memory_create.len << ", "; + out << api_data.args.hsa_amd_ipc_memory_create.handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_ipc_memory_attach: { + out << "hsa_amd_ipc_memory_attach("; + out << api_data.args.hsa_amd_ipc_memory_attach.handle << ", "; + out << api_data.args.hsa_amd_ipc_memory_attach.len << ", "; + out << api_data.args.hsa_amd_ipc_memory_attach.num_agents << ", "; + out << api_data.args.hsa_amd_ipc_memory_attach.mapping_agents << ", "; + out << api_data.args.hsa_amd_ipc_memory_attach.mapped_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_ipc_memory_detach: { + out << "hsa_amd_ipc_memory_detach("; + out << api_data.args.hsa_amd_ipc_memory_detach.mapped_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_signal_create: { + out << "hsa_amd_signal_create("; + out << api_data.args.hsa_amd_signal_create.initial_value << ", "; + out << api_data.args.hsa_amd_signal_create.num_consumers << ", "; + out << api_data.args.hsa_amd_signal_create.consumers << ", "; + out << api_data.args.hsa_amd_signal_create.attributes << ", "; + out << api_data.args.hsa_amd_signal_create.signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_ipc_signal_create: { + out << "hsa_amd_ipc_signal_create("; + out << api_data.args.hsa_amd_ipc_signal_create.signal << ", "; + out << api_data.args.hsa_amd_ipc_signal_create.handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_ipc_signal_attach: { + out << "hsa_amd_ipc_signal_attach("; + out << api_data.args.hsa_amd_ipc_signal_attach.handle << ", "; + out << api_data.args.hsa_amd_ipc_signal_attach.signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_register_system_event_handler: { + out << "hsa_amd_register_system_event_handler("; + out << api_data.args.hsa_amd_register_system_event_handler.callback << ", "; + out << api_data.args.hsa_amd_register_system_event_handler.data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_queue_intercept_create: { + out << "hsa_amd_queue_intercept_create("; + out << api_data.args.hsa_amd_queue_intercept_create.agent_handle << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.size << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.type << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.callback << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.data << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.private_segment_size << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.group_segment_size << ", "; + out << api_data.args.hsa_amd_queue_intercept_create.queue; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_queue_intercept_register: { + out << "hsa_amd_queue_intercept_register("; + out << api_data.args.hsa_amd_queue_intercept_register.queue << ", "; + out << api_data.args.hsa_amd_queue_intercept_register.callback << ", "; + out << api_data.args.hsa_amd_queue_intercept_register.user_data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_queue_set_priority: { + out << "hsa_amd_queue_set_priority("; + out << api_data.args.hsa_amd_queue_set_priority.queue << ", "; + out << api_data.args.hsa_amd_queue_set_priority.priority; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_async_copy_rect: { + out << "hsa_amd_memory_async_copy_rect("; + out << api_data.args.hsa_amd_memory_async_copy_rect.dst << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.dst_offset << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.src << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.src_offset << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.range << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.range__val << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.copy_agent << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.dir << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.num_dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.dep_signals << ", "; + out << api_data.args.hsa_amd_memory_async_copy_rect.completion_signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_runtime_queue_create_register: { + out << "hsa_amd_runtime_queue_create_register("; + out << api_data.args.hsa_amd_runtime_queue_create_register.callback << ", "; + out << api_data.args.hsa_amd_runtime_queue_create_register.user_data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_memory_lock_to_pool: { + out << "hsa_amd_memory_lock_to_pool("; + out << api_data.args.hsa_amd_memory_lock_to_pool.host_ptr << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.size << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.agents << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.num_agent << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.pool << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.flags << ", "; + out << api_data.args.hsa_amd_memory_lock_to_pool.agent_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_register_deallocation_callback: { + out << "hsa_amd_register_deallocation_callback("; + out << api_data.args.hsa_amd_register_deallocation_callback.ptr << ", "; + out << api_data.args.hsa_amd_register_deallocation_callback.callback << ", "; + out << api_data.args.hsa_amd_register_deallocation_callback.user_data; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_deregister_deallocation_callback: { + out << "hsa_amd_deregister_deallocation_callback("; + out << api_data.args.hsa_amd_deregister_deallocation_callback.ptr << ", "; + out << api_data.args.hsa_amd_deregister_deallocation_callback.callback; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_signal_value_pointer: { + out << "hsa_amd_signal_value_pointer("; + out << api_data.args.hsa_amd_signal_value_pointer.signal << ", "; + out << api_data.args.hsa_amd_signal_value_pointer.value_ptr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_svm_attributes_set: { + out << "hsa_amd_svm_attributes_set("; + out << api_data.args.hsa_amd_svm_attributes_set.ptr << ", "; + out << api_data.args.hsa_amd_svm_attributes_set.size << ", "; + out << api_data.args.hsa_amd_svm_attributes_set.attribute_list << ", "; + out << api_data.args.hsa_amd_svm_attributes_set.attribute_count; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_svm_attributes_get: { + out << "hsa_amd_svm_attributes_get("; + out << api_data.args.hsa_amd_svm_attributes_get.ptr << ", "; + out << api_data.args.hsa_amd_svm_attributes_get.size << ", "; + out << api_data.args.hsa_amd_svm_attributes_get.attribute_list << ", "; + out << api_data.args.hsa_amd_svm_attributes_get.attribute_count; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_svm_prefetch_async: { + out << "hsa_amd_svm_prefetch_async("; + out << api_data.args.hsa_amd_svm_prefetch_async.ptr << ", "; + out << api_data.args.hsa_amd_svm_prefetch_async.size << ", "; + out << api_data.args.hsa_amd_svm_prefetch_async.agent << ", "; + out << api_data.args.hsa_amd_svm_prefetch_async.num_dep_signals << ", "; + out << api_data.args.hsa_amd_svm_prefetch_async.dep_signals << ", "; + out << api_data.args.hsa_amd_svm_prefetch_async.completion_signal; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_spm_acquire: { + out << "hsa_amd_spm_acquire("; + out << api_data.args.hsa_amd_spm_acquire.preferred_agent; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_spm_release: { + out << "hsa_amd_spm_release("; + out << api_data.args.hsa_amd_spm_release.preferred_agent; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_spm_set_dest_buffer: { + out << "hsa_amd_spm_set_dest_buffer("; + out << api_data.args.hsa_amd_spm_set_dest_buffer.preferred_agent << ", "; + out << api_data.args.hsa_amd_spm_set_dest_buffer.size_in_bytes << ", "; + out << api_data.args.hsa_amd_spm_set_dest_buffer.timeout << ", "; + out << api_data.args.hsa_amd_spm_set_dest_buffer.size_copied << ", "; + out << api_data.args.hsa_amd_spm_set_dest_buffer.dest << ", "; + out << api_data.args.hsa_amd_spm_set_dest_buffer.is_data_loss; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_queue_cu_get_mask: { + out << "hsa_amd_queue_cu_get_mask("; + out << api_data.args.hsa_amd_queue_cu_get_mask.queue << ", "; + out << api_data.args.hsa_amd_queue_cu_get_mask.num_cu_mask_count << ", "; + out << api_data.args.hsa_amd_queue_cu_get_mask.cu_mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_portable_export_dmabuf: { + out << "hsa_amd_portable_export_dmabuf("; + out << api_data.args.hsa_amd_portable_export_dmabuf.ptr << ", "; + out << api_data.args.hsa_amd_portable_export_dmabuf.size << ", "; + out << api_data.args.hsa_amd_portable_export_dmabuf.dmabuf << ", "; + out << api_data.args.hsa_amd_portable_export_dmabuf.offset; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_portable_close_dmabuf: { + out << "hsa_amd_portable_close_dmabuf("; + out << api_data.args.hsa_amd_portable_close_dmabuf.dmabuf; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_address_reserve: { + out << "hsa_amd_vmem_address_reserve("; + out << api_data.args.hsa_amd_vmem_address_reserve.va << ", "; + out << api_data.args.hsa_amd_vmem_address_reserve.size << ", "; + out << api_data.args.hsa_amd_vmem_address_reserve.address << ", "; + out << api_data.args.hsa_amd_vmem_address_reserve.flags; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_address_free: { + out << "hsa_amd_vmem_address_free("; + out << api_data.args.hsa_amd_vmem_address_free.va << ", "; + out << api_data.args.hsa_amd_vmem_address_free.size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_handle_create: { + out << "hsa_amd_vmem_handle_create("; + out << api_data.args.hsa_amd_vmem_handle_create.pool << ", "; + out << api_data.args.hsa_amd_vmem_handle_create.size << ", "; + out << api_data.args.hsa_amd_vmem_handle_create.type << ", "; + out << api_data.args.hsa_amd_vmem_handle_create.flags << ", "; + out << api_data.args.hsa_amd_vmem_handle_create.memory_handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_handle_release: { + out << "hsa_amd_vmem_handle_release("; + out << api_data.args.hsa_amd_vmem_handle_release.memory_handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_map: { + out << "hsa_amd_vmem_map("; + out << api_data.args.hsa_amd_vmem_map.va << ", "; + out << api_data.args.hsa_amd_vmem_map.size << ", "; + out << api_data.args.hsa_amd_vmem_map.in_offset << ", "; + out << api_data.args.hsa_amd_vmem_map.memory_handle << ", "; + out << api_data.args.hsa_amd_vmem_map.flags; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_unmap: { + out << "hsa_amd_vmem_unmap("; + out << api_data.args.hsa_amd_vmem_unmap.va << ", "; + out << api_data.args.hsa_amd_vmem_unmap.size; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_set_access: { + out << "hsa_amd_vmem_set_access("; + out << api_data.args.hsa_amd_vmem_set_access.va << ", "; + out << api_data.args.hsa_amd_vmem_set_access.size << ", "; + out << api_data.args.hsa_amd_vmem_set_access.desc << ", "; + out << api_data.args.hsa_amd_vmem_set_access.desc_cnt; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_get_access: { + out << "hsa_amd_vmem_get_access("; + out << api_data.args.hsa_amd_vmem_get_access.va << ", "; + out << api_data.args.hsa_amd_vmem_get_access.perms << ", "; + out << api_data.args.hsa_amd_vmem_get_access.agent_handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_export_shareable_handle: { + out << "hsa_amd_vmem_export_shareable_handle("; + out << api_data.args.hsa_amd_vmem_export_shareable_handle.dmabuf_fd << ", "; + out << api_data.args.hsa_amd_vmem_export_shareable_handle.handle << ", "; + out << api_data.args.hsa_amd_vmem_export_shareable_handle.flags; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_import_shareable_handle: { + out << "hsa_amd_vmem_import_shareable_handle("; + out << api_data.args.hsa_amd_vmem_import_shareable_handle.dmabuf_fd << ", "; + out << api_data.args.hsa_amd_vmem_import_shareable_handle.handle; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_retain_alloc_handle: { + out << "hsa_amd_vmem_retain_alloc_handle("; + out << api_data.args.hsa_amd_vmem_retain_alloc_handle.memory_handle << ", "; + out << api_data.args.hsa_amd_vmem_retain_alloc_handle.addr; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_vmem_get_alloc_properties_from_handle: { + out << "hsa_amd_vmem_get_alloc_properties_from_handle("; + out << api_data.args.hsa_amd_vmem_get_alloc_properties_from_handle.memory_handle << ", "; + out << api_data.args.hsa_amd_vmem_get_alloc_properties_from_handle.pool << ", "; + out << api_data.args.hsa_amd_vmem_get_alloc_properties_from_handle.type; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_amd_agent_set_async_scratch_limit: { + out << "hsa_amd_agent_set_async_scratch_limit("; + out << api_data.args.hsa_amd_agent_set_async_scratch_limit.agent << ", "; + out << api_data.args.hsa_amd_agent_set_async_scratch_limit.threshold; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + + /* block: ImageExt API */ + case HSA_API_ID_hsa_ext_image_get_capability: { + out << "hsa_ext_image_get_capability("; + out << api_data.args.hsa_ext_image_get_capability.agent << ", "; + out << api_data.args.hsa_ext_image_get_capability.geometry << ", "; + out << api_data.args.hsa_ext_image_get_capability.image_format << ", "; + out << api_data.args.hsa_ext_image_get_capability.capability_mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_data_get_info: { + out << "hsa_ext_image_data_get_info("; + out << api_data.args.hsa_ext_image_data_get_info.agent << ", "; + out << api_data.args.hsa_ext_image_data_get_info.image_descriptor << ", "; + out << api_data.args.hsa_ext_image_data_get_info.access_permission << ", "; + out << api_data.args.hsa_ext_image_data_get_info.image_data_info; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_create: { + out << "hsa_ext_image_create("; + out << api_data.args.hsa_ext_image_create.agent << ", "; + out << api_data.args.hsa_ext_image_create.image_descriptor << ", "; + out << api_data.args.hsa_ext_image_create.image_data << ", "; + out << api_data.args.hsa_ext_image_create.access_permission << ", "; + out << api_data.args.hsa_ext_image_create.image; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_import: { + out << "hsa_ext_image_import("; + out << api_data.args.hsa_ext_image_import.agent << ", "; + out << api_data.args.hsa_ext_image_import.src_memory << ", "; + out << api_data.args.hsa_ext_image_import.src_row_pitch << ", "; + out << api_data.args.hsa_ext_image_import.src_slice_pitch << ", "; + out << api_data.args.hsa_ext_image_import.dst_image << ", "; + out << api_data.args.hsa_ext_image_import.image_region; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_export: { + out << "hsa_ext_image_export("; + out << api_data.args.hsa_ext_image_export.agent << ", "; + out << api_data.args.hsa_ext_image_export.src_image << ", "; + out << api_data.args.hsa_ext_image_export.dst_memory << ", "; + out << api_data.args.hsa_ext_image_export.dst_row_pitch << ", "; + out << api_data.args.hsa_ext_image_export.dst_slice_pitch << ", "; + out << api_data.args.hsa_ext_image_export.image_region; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_copy: { + out << "hsa_ext_image_copy("; + out << api_data.args.hsa_ext_image_copy.agent << ", "; + out << api_data.args.hsa_ext_image_copy.src_image << ", "; + out << api_data.args.hsa_ext_image_copy.src_offset << ", "; + out << api_data.args.hsa_ext_image_copy.dst_image << ", "; + out << api_data.args.hsa_ext_image_copy.dst_offset << ", "; + out << api_data.args.hsa_ext_image_copy.range; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_clear: { + out << "hsa_ext_image_clear("; + out << api_data.args.hsa_ext_image_clear.agent << ", "; + out << api_data.args.hsa_ext_image_clear.image << ", "; + out << api_data.args.hsa_ext_image_clear.data << ", "; + out << api_data.args.hsa_ext_image_clear.image_region; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_destroy: { + out << "hsa_ext_image_destroy("; + out << api_data.args.hsa_ext_image_destroy.agent << ", "; + out << api_data.args.hsa_ext_image_destroy.image; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_sampler_create: { + out << "hsa_ext_sampler_create("; + out << api_data.args.hsa_ext_sampler_create.agent << ", "; + out << api_data.args.hsa_ext_sampler_create.sampler_descriptor << ", "; + out << api_data.args.hsa_ext_sampler_create.sampler; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_sampler_destroy: { + out << "hsa_ext_sampler_destroy("; + out << api_data.args.hsa_ext_sampler_destroy.agent << ", "; + out << api_data.args.hsa_ext_sampler_destroy.sampler; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_get_capability_with_layout: { + out << "hsa_ext_image_get_capability_with_layout("; + out << api_data.args.hsa_ext_image_get_capability_with_layout.agent << ", "; + out << api_data.args.hsa_ext_image_get_capability_with_layout.geometry << ", "; + out << api_data.args.hsa_ext_image_get_capability_with_layout.image_format << ", "; + out << api_data.args.hsa_ext_image_get_capability_with_layout.image_data_layout << ", "; + out << api_data.args.hsa_ext_image_get_capability_with_layout.capability_mask; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_data_get_info_with_layout: { + out << "hsa_ext_image_data_get_info_with_layout("; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.agent << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.image_descriptor << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.access_permission << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.image_data_layout << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.image_data_row_pitch << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.image_data_slice_pitch << ", "; + out << api_data.args.hsa_ext_image_data_get_info_with_layout.image_data_info; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + case HSA_API_ID_hsa_ext_image_create_with_layout: { + out << "hsa_ext_image_create_with_layout("; + out << api_data.args.hsa_ext_image_create_with_layout.agent << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image_descriptor << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image_data << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.access_permission << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image_data_layout << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image_data_row_pitch << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image_data_slice_pitch << ", "; + out << api_data.args.hsa_ext_image_create_with_layout.image; + out << ") = " << api_data.hsa_status_t_retval; + break; + } + default: + out << "ERROR: unknown API"; + abort(); + } + return out; +} +#endif +#endif /* HSA_PROF_STR_H_ */ \ No newline at end of file diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer.h new file mode 100644 index 0000000000000000000000000000000000000000..cb9b13faccaf78fbb873e54163df930c7f0b4b3f --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer.h @@ -0,0 +1,779 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +/** \mainpage ROC Tracer API Specification + * + * \section introduction Introduction + * + * ROCtracer library, Runtimes Generic Callback/Activity APIs. + * + * The goal of the implementation is to provide a generic independent from + * specific runtime profiler to trace API and asynchronous activity. + * + * The API provides functionality for registering the runtimes API callbacks + * and asynchronous activity records pool support. + * + * \section known_limitations Known Limitations and Restrictions + * + * The ROCtracer API library implementation currently has the following + * restrictions. Future releases aim to address these restrictions. + * + * 1. The ACTIVITY_DOMAIN_HSA_OPS operations HSA_OP_ID_DISPATCH, + * HSA_OP_ID_BARRIER, and HSA_OP_ID_RESERVED1 are not currently implemented. + */ + +/** + * \file + * ROCtracer API interface. + */ + +#ifndef ROCTRACER_H_ +#define ROCTRACER_H_ + +/* Placeholder for calling convention and import/export macros */ +#if !defined(ROCTRACER_CALL) +#define ROCTRACER_CALL +#endif /* !defined (ROCTRACER_CALL) */ + +#if !defined(ROCTRACER_EXPORT_DECORATOR) +#if defined(__GNUC__) +#define ROCTRACER_EXPORT_DECORATOR __attribute__((visibility("default"))) +#elif defined(_MSC_VER) +#define ROCTRACER_EXPORT_DECORATOR __declspec(dllexport) +#endif /* defined (_MSC_VER) */ +#endif /* !defined (ROCTRACER_EXPORT_DECORATOR) */ + +#if !defined(ROCTRACER_IMPORT_DECORATOR) +#if defined(__GNUC__) +#define ROCTRACER_IMPORT_DECORATOR +#elif defined(_MSC_VER) +#define ROCTRACER_IMPORT_DECORATOR __declspec(dllimport) +#endif /* defined (_MSC_VER) */ +#endif /* !defined (ROCTRACER_IMPORT_DECORATOR) */ + +#define ROCTRACER_EXPORT ROCTRACER_EXPORT_DECORATOR ROCTRACER_CALL +#define ROCTRACER_IMPORT ROCTRACER_IMPORT_DECORATOR ROCTRACER_CALL + +#if !defined(ROCTRACER) +#if defined(ROCTRACER_EXPORTS) +#define ROCTRACER_API ROCTRACER_EXPORT +#else /* !defined (ROCTRACER_EXPORTS) */ +#define ROCTRACER_API ROCTRACER_IMPORT +#endif /* !defined (ROCTRACER_EXPORTS) */ +#endif /* !defined (ROCTRACER) */ + +#include +#include + +#include "ext/prof_protocol.h" + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +/** \defgroup symbol_versions_group Symbol Versions + * + * The names used for the shared library versioned symbols. + * + * Every function is annotated with one of the version macros defined in this + * section. Each macro specifies a corresponding symbol version string. After + * dynamically loading the shared library with \p dlopen, the address of each + * function can be obtained using \p dlvsym with the name of the function and + * its corresponding symbol version string. An error will be reported by \p + * dlvsym if the installed library does not support the version for the + * function specified in this version of the interface. + * + * @{ + */ + +/** + * The function was introduced in version 4.1 of the interface and has the + * symbol version string of ``"ROCTRACER_4.1"``. + */ +#define ROCTRACER_VERSION_4_1 + +/** @} */ + +/** \defgroup versioning_group Versioning + * + * Version information about the interface and the associated installed + * library. + * + * The semantic version of the interface following semver.org rules. A client + * that uses this interface is only compatible with the installed library if + * the major version numbers match and the interface minor version number is + * less than or equal to the installed library minor version number. + * + * @{ + */ + +/** + * The major version of the interface as a macro so it can be used by the + * preprocessor. + */ +#define ROCTRACER_VERSION_MAJOR 4 + +/** + * The minor version of the interface as a macro so it can be used by the + * preprocessor. + */ +#define ROCTRACER_VERSION_MINOR 1 + +/** + * Query the major version of the installed library. + * + * Return the major version of the installed library. This can be used to + * check if it is compatible with this interface version. This function can be + * used even when the library is not initialized. + */ +ROCTRACER_API uint32_t roctracer_version_major() ROCTRACER_VERSION_4_1; + +/** + * Query the minor version of the installed library. + * + * Return the minor version of the installed library. This can be used to + * check if it is compatible with this interface version. This function can be + * used even when the library is not initialized. + */ +ROCTRACER_API uint32_t roctracer_version_minor() ROCTRACER_VERSION_4_1; + +/** @} */ + +/** \defgroup status_codes_group Status Codes + * + * Most operations return a status code to indicate success or error. + * + * @{ + */ + +/** + * ROC Tracer API status codes. + */ +typedef enum { + /** + * The function has executed successfully. + */ + ROCTRACER_STATUS_SUCCESS = 0, + /** + * A generic error has occurred. + */ + ROCTRACER_STATUS_ERROR = -1, + /** + * The domain ID is invalid. + */ + ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID = -2, + /** + * An invalid argument was given to the function. + */ + ROCTRACER_STATUS_ERROR_INVALID_ARGUMENT = -3, + /** + * No default pool is defined. + */ + ROCTRACER_STATUS_ERROR_DEFAULT_POOL_UNDEFINED = -4, + /** + * The default pool is already defined. + */ + ROCTRACER_STATUS_ERROR_DEFAULT_POOL_ALREADY_DEFINED = -5, + /** + * Memory allocation error. + */ + ROCTRACER_STATUS_ERROR_MEMORY_ALLOCATION = -6, + /** + * External correlation ID pop mismatch. + */ + ROCTRACER_STATUS_ERROR_MISMATCHED_EXTERNAL_CORRELATION_ID = -7, + /** + * The operation is not currently implemented. This error may be reported by + * any function. Check the \ref known_limitations section to determine the + * status of the library implementation of the interface. + */ + ROCTRACER_STATUS_ERROR_NOT_IMPLEMENTED = -8, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_UNINIT = 2, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_BREAK = 3, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_BAD_DOMAIN = ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_BAD_PARAMETER = ROCTRACER_STATUS_ERROR_INVALID_ARGUMENT, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_HIP_API_ERR = 6, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_HIP_OPS_ERR = 7, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_HCC_OPS_ERR = ROCTRACER_STATUS_HIP_OPS_ERR, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_HSA_ERR = 7, + /** + * Deprecated error code. + */ + ROCTRACER_STATUS_ROCTX_ERR = 8, +} roctracer_status_t; + +/** + * Query the textual description of the last error for the current thread. + * + * Returns a NUL terminated string describing the error of the last ROC Tracer + * API call by the calling thread that did not return success. The empty + * string is returned if there is no previous error. The last error is not + * cleared. + * + * \return Return the error string. The caller owns the returned string and + * should use \p free() to deallocate it. + */ +ROCTRACER_API const char* roctracer_error_string() ROCTRACER_VERSION_4_1; + +/** @} */ + +/** \defgroup domain_group Traced Runtime Domains + * + * The ROC Tracer API can trace multiple runtime libraries. Each library can + * have API operations and asynchronous operations that can be traced. + * + * @{ + */ + +/** + * Enumeration of domains that can be traced. + */ +typedef activity_domain_t roctracer_domain_t; + +/** + * Query textual name of an operation of a domain. + * + * @param[in] domain Domain being queried. + * + * @param[in] op Operation within \p domain. + * + * @param[in] kind \todo Define kind. + * + * @return Returns the NUL terminated string for the operation name, or NULL if + * the domain or operation are invalid. The string is owned by the ROC Tracer + * library. + */ +ROCTRACER_API const char* roctracer_op_string( + uint32_t domain, uint32_t op, uint32_t kind) ROCTRACER_VERSION_4_1; + +/** + * Query the operation code given a domain and the name of an operation. + * + * @param[in] domain The domain being queried. + * + * @param[in] str The NUL terminated name of the operation name being queried. + * + * @param[out] op The operation code. + * + * @param[out] kind If not NULL then the operation kind code. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. \p op and \p kind have been updated. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_ARGUMENT The \p op is invalid for + * \p domain. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID The domain is invalid or + * not supported. + */ +ROCTRACER_API roctracer_status_t +roctracer_op_code(uint32_t domain, const char* str, uint32_t* op, + uint32_t* kind) ROCTRACER_VERSION_4_1; + +/** + * Set the properties of a domain. + * + * @param[in] domain The domain. + * + * @param[in] properties The properties. Each domain defines its own type for + * the properties. Some domains require the properties to be set before they + * can be enabled. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t roctracer_set_properties( + roctracer_domain_t domain, void* properties) ROCTRACER_VERSION_4_1; + +/** @} */ + +/** \defgroup callback_api_group Callback API + * + * ROC tracer provides support for runtime API callbacks and activity + * records logging. The API callbacks provide the API calls arguments and are + * called on different phases, on enter, on exit, on kernel completion. + * + * @{ + */ + +/** + * Runtime API callback type. + * + * The callback that will be invoked when an enabled runtime API is called. The + * callback is invoked on entry and on exit. + */ +typedef activity_rtapi_callback_t roctracer_rtapi_callback_t; + +/** + * Enable runtime API callback for a specific operation of a domain. + * + * @param domain The domain. + * + * @param op The operation ID in \p domain. + * + * @param callback The callback to invoke each time the operation is performed + * on entry and exit. + * + * @param arg Value to pass as last argument of \p callback. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID \p domain is invalid. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_ARGUMENT \p op is invalid for \p + * domain. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_op_callback( + activity_domain_t domain, uint32_t op, activity_rtapi_callback_t callback, + void* arg) ROCTRACER_VERSION_4_1; + +/** + * Enable runtime API callback for all operations of a domain. + * + * @param domain The domain + * + * @param callback The callback to invoke each time the operation is performed + * on entry and exit. + * + * @param arg Value to pass as last argument of \p callback. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID \p domain is invalid. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_domain_callback( + activity_domain_t domain, activity_rtapi_callback_t callback, + void* arg) ROCTRACER_VERSION_4_1; + +/** + * Disable runtime API callback for a specific operation of a domain. + * + * @param domain The domain + * + * @param op The operation in \p domain. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID \p domain is invalid. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_ARGUMENT \p op is invalid for \p + * domain. + */ +ROCTRACER_API roctracer_status_t roctracer_disable_op_callback( + activity_domain_t domain, uint32_t op) ROCTRACER_VERSION_4_1; + +/** + * Disable runtime API callback for all operations of a domain. + * + * @param domain The domain + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ::ROCTRACER_STATUS_ERROR_INVALID_DOMAIN_ID \p domain is invalid. + */ +ROCTRACER_API roctracer_status_t roctracer_disable_domain_callback( + activity_domain_t domain) ROCTRACER_VERSION_4_1; + +/** @} */ + +/** \defgroup activity_api_group Activity API + * + * The activity records are asynchronously logged to the pool and can be + * associated with the respective API callbacks using the correlation ID. + * Activity API can be used to enable collecting of the records with + * timestamping data for API calls and the kernel submits. + * + * @{ + */ + +/** + * Activity record. + * + * Asynchronous activity events generate activity records. + */ +typedef activity_record_t roctracer_record_t; + +/** + * Get a pointer to the next activity record. + * + * A memory pool generates buffers that contain multiple activity records. + * This function steps to the next activity record. + * + * @param[in] record Pointer to ac activity record in a memory pool buffer. + * + * @param[out] next Pointer to the following activity record in the memory pool + * buffer. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t +roctracer_next_record(const activity_record_t* record, + const activity_record_t** next) ROCTRACER_VERSION_4_1; + +/** + * Memory pool allocator callback. + * + * If \p *ptr is NULL, then allocate memory of \p size bytes and save address + * in \p *ptr. + * + * If \p *ptr is non-NULL and size is non-0, then reallocate the memory at \p + * *ptr with size \p size and save the address in \p *ptr. The memory will have + * been allocated by the same callback. + * + * If \p *ptr is non-NULL and size is 0, then deallocate the memory at \p *ptr. + * The memory will have been allocated by the same callback. + * + * \p size is the size of the memory allocation or reallocation, or 0 if + * deallocating. + * + * \p arg Argument provided in the ::roctracer_properties_t passed to the + * ::roctracer_open_pool function. + */ +typedef void (*roctracer_allocator_t)(char** ptr, size_t size, void* arg); + +/** + * Memory pool buffer callback. + * + * The callback that will be invoked when a memory pool buffer becomes full or + * is flushed. + * + * \p begin pointer to first entry entry in the buffer. + * + * \p end pointer to one past the end entry in the buffer. + * + * \p arg the argument specified when the callback was defined. + */ +typedef void (*roctracer_buffer_callback_t)(const char* begin, const char* end, + void* arg); + +/** + * Memory pool properties. + * + * Defines the properties when a tracer memory pool is created. + */ +typedef struct { + /** + * ROC Tracer mode. + */ + uint32_t mode; + + /** + * Size of buffer in bytes. + */ + size_t buffer_size; + + /** + * The allocator function to use to allocate and deallocate the buffer. If + * NULL then \p malloc, \p realloc, and \p free are used. + */ + roctracer_allocator_t alloc_fun; + + /** + * The argument to pass when invoking the \p alloc_fun allocator. + */ + void* alloc_arg; + + /** + * The function to call when a buffer becomes full or is flushed. + */ + roctracer_buffer_callback_t buffer_callback_fun; + + /** + * The argument to pass when invoking the \p buffer_callback_fun callback. + */ + void* buffer_callback_arg; +} roctracer_properties_t; + +/** + * Tracer memory pool type. + */ +typedef void roctracer_pool_t; + +/** + * Create tracer memory pool. + * + * If \p pool is not NULL, returns the created memory pool. Does not change the + * default memory pool. + * + * If \p pool is NULL, sets the default memory pool to the created pool if not + * already defined. Otherwise, return an error. + * + * @param[in] properties Tracer memory pool properties. + * + * @param[out] pool Tracer memory pool created if not NULL. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR_DEFAULT_POOL_ALREADY_DEFINED \p pool is NULL + * and the default pool is already defined. Unable to create the pool. + * + * @retval ROCTRACER_STATUS_ERROR_MEMORY_ALLOCATION Unable to allocate memory + * for the \p pool. Unable to create the pool. + */ +ROCTRACER_API roctracer_status_t +roctracer_open_pool_expl(const roctracer_properties_t* properties, + roctracer_pool_t** pool) ROCTRACER_VERSION_4_1; + +/** + * Create tracer memory pool. + * + * Sets the default memory pool to the created pool if not already defined. + * Otherwise, return an error. + * + * @param[in] properties Tracer memory pool properties. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR_DEFAULT_POOL_ALREADY_DEFINED The default pool + * is already defined. Unable to create the pool. + * + * @retval ROCTRACER_STATUS_ERROR_MEMORY_ALLOCATION Unable to allocate memory + * for the \p pool. Unable to create the pool. + */ +ROCTRACER_API roctracer_status_t roctracer_open_pool( + const roctracer_properties_t* properties) ROCTRACER_VERSION_4_1; + +/** + * Close tracer memory pool. + * + * All enabled activities that use the pool must have completed writing to the + * pool, before deleting the pool. Deleting a pool automatically disables any + * activities that specify the pool, and flushes it. + * + * @param[in] pool Memory pool to close. If NULL, the default memory pool is + * closed if defined. The default memory pool is set to undefined if closed. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully or pool was NULL and there is no default pool. + */ +ROCTRACER_API roctracer_status_t +roctracer_close_pool_expl(roctracer_pool_t* pool) ROCTRACER_VERSION_4_1; + +/** + * Close default tracer memory pool, if defined, and set to undefined. + * + * All enabled activities that use the pool must have completed writing to the + * pool, before deleting the pool. Deleting a pool automatically disables any + * activities that specify the pool, and flushes it. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully or there is no default pool. + */ +ROCTRACER_API roctracer_status_t roctracer_close_pool() ROCTRACER_VERSION_4_1; + +/** + * Query and set the default memory pool. + * + * @param[in] pool If not NULL, change the current default pool to \p pool. If + * NULL, the default pool is not changed. + * + * @return Return the current default memory pool before any change, or NULL if + * none is defined. + */ +ROCTRACER_API roctracer_pool_t* roctracer_default_pool_expl( + roctracer_pool_t* pool) ROCTRACER_VERSION_4_1; + +/** + * Query the current default memory pool. + * + * @return Return the current default memory pool, or NULL is none is defined. + */ +ROCTRACER_API roctracer_pool_t* roctracer_default_pool() ROCTRACER_VERSION_4_1; + +/** + * Enable activity record logging for a specified operation of a domain + * providing a memory pool. + * + * @param[in] domain The domain. + * + * @param[in] op The activity operation ID in \p domain. + * + * @param[in] pool The memory pool to write the activity record. If NULL, use + * the default memory pool. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR \p pool is NULL and no default pool is + * defined. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_op_activity_expl( + activity_domain_t domain, uint32_t op, + roctracer_pool_t* pool) ROCTRACER_VERSION_4_1; + +/** + * Enable activity record logging for a specified operation of a domain using + * the default memory pool. + * + * @param[in] domain The domain. + * + * @param[in] op The activity operation ID in \p domain. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR No default pool is defined. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_op_activity( + activity_domain_t domain, uint32_t op) ROCTRACER_VERSION_4_1; + +/** + * Enable activity record logging for all operations of a domain providing a + * memory pool. + * + * @param[in] domain The domain. + * + * @param[in] pool The memory pool to write the activity record. If NULL, use + * the default memory pool. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR \p pool is NULL and no default pool is + * defined. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_domain_activity_expl( + activity_domain_t domain, roctracer_pool_t* pool) ROCTRACER_VERSION_4_1; + +/** + * Enable activity record logging for all operations of a domain using the + * default memory pool. + * + * @param[in] domain The domain. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + * + * @retval ROCTRACER_STATUS_ERROR No default pool is defined. + */ +ROCTRACER_API roctracer_status_t roctracer_enable_domain_activity( + activity_domain_t domain) ROCTRACER_VERSION_4_1; + +/** + * Disable activity record logging for a specified operation of a domain. + * + * @param[in] domain The domain. + * + * @param[in] op The activity operation ID in \p domain. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t roctracer_disable_op_activity( + activity_domain_t domain, uint32_t op) ROCTRACER_VERSION_4_1; + +/** + * Disable activity record logging for all operations of a domain. + * + * @param[in] domain The domain. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t roctracer_disable_domain_activity( + activity_domain_t domain) ROCTRACER_VERSION_4_1; + +/** + * Flush available activity records for a memory pool. + * + * If flushing encounters an activity record still being written, flushing + * stops. Use a subsequent flush when the record has completed being written to + * resume the flush. + * + * @param[in] pool The memory pool to flush. If NULL, flushes the default + * memory pool. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t +roctracer_flush_activity_expl(roctracer_pool_t* pool) ROCTRACER_VERSION_4_1; + +/** + * Flush available activity records for the default memory pool. + * + * If flushing encounters an activity record still being written, flushing + * stops. Use a subsequent flush when the record has completed being written to + * resume the flush. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t roctracer_flush_activity() + ROCTRACER_VERSION_4_1; + +/** @} */ + +/** \defgroup timestamp_group Timestamp Operations + * + * + * + * @{ + */ + +/** + * Get the system clock timestamp. + * + * @param[out] timestamp The system clock timestamp in nano seconds. + * + * @retval ::ROCTRACER_STATUS_SUCCESS The function has been executed + * successfully. + */ +ROCTRACER_API roctracer_status_t roctracer_get_timestamp( + roctracer_timestamp_t* timestamp) ROCTRACER_VERSION_4_1; + +/** @} */ + +#ifdef __cplusplus +} /* extern "C" block */ +#endif /* __cplusplus */ + +#endif /* ROCTRACER_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_ext.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_ext.h new file mode 100644 index 0000000000000000000000000000000000000000..9fc4f6a67dc6e46053ac9a929b584cab00bc0368 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_ext.h @@ -0,0 +1,81 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +//////////////////////////////////////////////////////////////////////////////// +// +// ROC Tracer Extension API +// +// The API provides functionality for application annotation with event and +// external ranges correlation +// +//////////////////////////////////////////////////////////////////////////////// + +#ifndef ROCTRACER_EXT_H_ +#define ROCTRACER_EXT_H_ + +#include "roctracer.h" + +/* Extension API opcodes */ +typedef enum { + ACTIVITY_EXT_OP_MARK = 0, + ACTIVITY_EXT_OP_EXTERN_ID = 1 +} activity_ext_op_t; + +typedef void (*roctracer_start_cb_t)(); +typedef void (*roctracer_stop_cb_t)(); +typedef struct { + roctracer_start_cb_t start_cb; + roctracer_stop_cb_t stop_cb; +} roctracer_ext_properties_t; + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +//////////////////////////////////////////////////////////////////////////////// +// Application annotation API + +// Tracing start API +void ROCTRACER_API roctracer_start() ROCTRACER_VERSION_4_1; + +// Tracing stop API +void ROCTRACER_API roctracer_stop() ROCTRACER_VERSION_4_1; + +//////////////////////////////////////////////////////////////////////////////// +// External correlation id API + +// Notifies that the calling thread is entering an external API region. +// Push an external correlation id for the calling thread. +roctracer_status_t ROCTRACER_API +roctracer_activity_push_external_correlation_id(activity_correlation_id_t id) + ROCTRACER_VERSION_4_1; + +// Notifies that the calling thread is leaving an external API region. +// Pop an external correlation id for the calling thread. +// 'lastId' returns the last external correlation if not NULL +roctracer_status_t ROCTRACER_API +roctracer_activity_pop_external_correlation_id( + activity_correlation_id_t* last_id) ROCTRACER_VERSION_4_1; + +#ifdef __cplusplus +} // extern "C" block +#endif // __cplusplus + +#endif // ROCTRACER_EXT_H_ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hcc.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hcc.h new file mode 100644 index 0000000000000000000000000000000000000000..969282b7fccf50daab50069a24a82335e237ed9c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hcc.h @@ -0,0 +1,24 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +#pragma message( \ + "This file has been deprecated and marked for removal. Please use roctracer_hip.h instead.") + +#include "roctracer_hip.h" \ No newline at end of file diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hip.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hip.h new file mode 100644 index 0000000000000000000000000000000000000000..83ed7fc957e6bd1232887a4248c513668d0fcd61 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hip.h @@ -0,0 +1,37 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +#ifndef ROCTRACER_HIP_H_ +#define ROCTRACER_HIP_H_ + +#include "roctracer.h" + +#include +#include +#include + +typedef enum { + HIP_OP_ID_DISPATCH = 0, + HIP_OP_ID_COPY = 1, + HIP_OP_ID_BARRIER = 2, + HIP_OP_ID_NUMBER = 3 +} hip_op_id_t; + +#endif // ROCTRACER_HIP_H_ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hsa.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hsa.h new file mode 100644 index 0000000000000000000000000000000000000000..4af350016e931058f70fc64de9dbfd17e5c5d8ce --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_hsa.h @@ -0,0 +1,112 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +#ifndef ROCTRACER_HSA_H_ +#define ROCTRACER_HSA_H_ + +#include "roctracer.h" + +#include +#include +#include "hsa_ostream_ops.h" +#include "hsa_prof_str.h" + +// HSA OP ID enumeration +enum hsa_op_id_t { + HSA_OP_ID_DISPATCH = 0, + HSA_OP_ID_COPY = 1, + HSA_OP_ID_BARRIER = 2, + HSA_OP_ID_RESERVED1 = 3, + HSA_OP_ID_NUMBER +}; + +// HSA EVT ID enumeration +enum hsa_evt_id_t { + HSA_EVT_ID_ALLOCATE = 0, // Memory allocate callback + HSA_EVT_ID_DEVICE = 1, // Device assign callback + HSA_EVT_ID_MEMCOPY = 2, // Memcopy callback + HSA_EVT_ID_SUBMIT = 3, // Packet submission callback + HSA_EVT_ID_KSYMBOL = 4, // Loading/unloading of kernel symbol + HSA_EVT_ID_CODEOBJ = 5, // Loading/unloading of device code object + HSA_EVT_ID_NUMBER +}; + +struct hsa_ops_properties_t { + void* reserved1[4]; +}; + +// HSA EVT data type +typedef struct { + union { + struct { + const void* ptr; // allocated area ptr + size_t size; // allocated area size, zero size means 'free' callback + hsa_amd_segment_t segment; // allocated area's memory segment type + hsa_amd_memory_pool_global_flag_t + global_flag; // allocated area's memory global flag + int is_code; // equal to 1 if code is allocated + } allocate; + + struct { + hsa_device_type_t type; // type of assigned device + uint32_t id; // id of assigned device + hsa_agent_t agent; // device HSA agent handle + const void* ptr; // ptr the device is assigned to + } device; + + struct { + const void* dst; // memcopy dst ptr + const void* src; // memcopy src ptr + size_t size; // memcopy size bytes + } memcopy; + + struct { + const void* packet; // submitted to GPU packet + const char* + kernel_name; // kernel name, NULL if not a kernel dispatch packet + hsa_queue_t* queue; // HSA queue the packet was submitted to + uint32_t device_type; // type of device the packet is submitted to + uint32_t device_id; // id of device the packet is submitted to + } submit; + + struct { + uint64_t object; // kernel symbol object + const char* name; // kernel symbol name + uint32_t name_length; // kernel symbol name length + int unload; // symbol executable destroy + } ksymbol; + + struct { + uint32_t storage_type; // code object storage type + int storage_file; // origin file descriptor + uint64_t memory_base; // origin memory base + uint64_t memory_size; // origin memory size + uint64_t load_base; // code object load base + uint64_t load_size; // code object load size + uint64_t load_delta; // code object load size + uint32_t uri_length; // URI string length (not including the terminating + // NUL character) + const char* uri; // URI string + int unload; // unload flag + } codeobj; + }; +} hsa_evt_data_t; + +#endif // ROCTRACER_HSA_H_ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_plugin.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_plugin.h new file mode 100644 index 0000000000000000000000000000000000000000..da8a6d725e236faba3bc6191636cb7c256a62d8b --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_plugin.h @@ -0,0 +1,137 @@ +/* Copyright (c) 2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +/** \section roctracer_plugin_api ROCtracer Plugin API + * + * The ROCtracer Plugin API is used by the ROCtracer Tool to output all tracing + * information. Different implementations of the ROCtracer Plugin API can be + * developed that output the tracing data in different formats. + * The ROCtracer Tool can be configured to load a specific library that + * supports the user desired format. + * + * The API is not thread safe. It is the responsibility of the ROCtracer Tool + * to ensure the operations are synchronized and not called concurrently. There + * is no requirement for the ROCtracer Tool to report trace data in any + * specific order. If the format supported by plugin requires specific + * ordering, it is the responsibility of the plugin implementation to perform + * any necessary sorting. + */ + +/** + * \file + * ROCtracer Tool Plugin API interface. + */ + +#ifndef ROCTRACER_PLUGIN_H_ +#define ROCTRACER_PLUGIN_H_ + +#include "roctracer.h" + +#include + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +/** \defgroup initialization_group Initialization and Finalization + * + * The ROCtracer Plugin API must be initialized before using any of the + * operations to report trace data, and finalized after the last trace data has + * been reported. + * + * @{ + */ + +/** + * Initialize plugin. + * + * Must be called before any other operation. + * + * @param[in] roctracer_major_version The major version of the ROCtracer API + * being used by the ROCtracer Tool. An error is reported if this does not + * match the major version of the ROCtracer API used to build the plugin + * library. This ensures compatibility of the trace data format. + * + * @param[in] roctracer_minor_version The minor version of the ROCtracer API + * being used by the ROCtracer Tool. An error is reported if the + * \p roctracer_major_version matches and this is greater than the minor + * version of the ROCtracer API used to build the plugin library. This ensures + * compatibility of the trace data format. + * + * @return Returns 0 on success and -1 on error. + */ +ROCTRACER_EXPORT int roctracer_plugin_initialize( + uint32_t roctracer_major_version, uint32_t roctracer_minor_version); + +/** + * Finalize plugin. + * + * This must be called after ::roctracer_plugin_initialize and after all trace + * data has been reported by ::roctracer_plugin_write_callback_record and + * ::roctracer_plugin_write_activity_records. + */ +ROCTRACER_EXPORT void roctracer_plugin_finalize(); + +/** @} */ + +/** \defgroup trace_record_write_functions Trace data reporting + * + * Operations to output trace data. + * + * @{ + */ + +/** + * Report a single callback trace data. + * + * @param[in] record Primarily domain independent trace data. + * + * @param[in] callback_data Domain specific trace data. The type of this + * argument depends on the values of \p record.domain. + * + * @return Returns 0 on success and -1 on error. + */ +ROCTRACER_EXPORT int roctracer_plugin_write_callback_record( + const roctracer_record_t* record, const void* callback_data); + +/** + * Report a range of activity trace data. + * + * Reports a range of primarily domain independent trace data. The range is + * specified by a pointer to the first record and a pointer to one past the + * last record. ::roctracer_next_record is used to iterate the range in forward + * order. + * + * @param[in] begin Pointer to the first record. + * + * @param[in] end Pointer to one past the last record. + * + * @return Returns 0 on success and -1 on error. + */ +ROCTRACER_EXPORT int roctracer_plugin_write_activity_records( + const roctracer_record_t* begin, const roctracer_record_t* end); + +/** @} */ + +#ifdef __cplusplus +} /* extern "C" */ +#endif /* __cplusplus */ + +#endif /* ROCTRACER_PLUGIN_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_roctx.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_roctx.h new file mode 100644 index 0000000000000000000000000000000000000000..8ff3190f6336247c41b65c22680eff41c6b50d97 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctracer_roctx.h @@ -0,0 +1,67 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +#ifndef ROCTRACER_ROCTX_H_ +#define ROCTRACER_ROCTX_H_ + +#include "roctx.h" + +/** + * ROCTX API ID enumeration + */ +enum roctx_api_id_t { + ROCTX_API_ID_roctxMarkA = 0, + ROCTX_API_ID_roctxRangePushA = 1, + ROCTX_API_ID_roctxRangePop = 2, + ROCTX_API_ID_roctxRangeStartA = 3, + ROCTX_API_ID_roctxRangeStop = 4, + ROCTX_API_ID_NUMBER, +}; + +/** + * ROCTX callbacks data type + */ +typedef struct roctx_api_data_s { + union { + struct { + const char* message; + roctx_range_id_t id; + }; + struct { + const char* message; + } roctxMarkA; + struct { + const char* message; + } roctxRangePushA; + struct { + const char* message; + } roctxRangePop; + struct { + const char* message; + roctx_range_id_t id; + } roctxRangeStartA; + struct { + const char* message; + roctx_range_id_t id; + } roctxRangeStop; + } args; +} roctx_api_data_t; + +#endif /* ROCTRACER_ROCTX_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctx.h b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctx.h new file mode 100644 index 0000000000000000000000000000000000000000..ccec5a185badb7fc43d625c8987a65ecbe17a6e3 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/amd/include/roctracer/roctx.h @@ -0,0 +1,229 @@ +/* Copyright (c) 2018-2022 Advanced Micro Devices, Inc. + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. */ + +/** \mainpage ROCTX API Specification + * + * \section introduction Introduction + * ROCTX is a library that implements the AMD code annotation API. It provides + * the support necessary to annotate events and code ranges in applications. + */ + +/** + * \file + * ROCTX API interface. + */ + +#ifndef ROCTX_H_ +#define ROCTX_H_ 1 + +/* Placeholder for calling convention and import/export macros */ +#if !defined(ROCTX_CALL) +#define ROCTX_CALL +#endif /* !defined (ROCTX_CALL) */ + +#if !defined(ROCTX_EXPORT_DECORATOR) +#if defined(__GNUC__) +#define ROCTX_EXPORT_DECORATOR __attribute__((visibility("default"))) +#elif defined(_MSC_VER) +#define ROCTX_EXPORT_DECORATOR __declspec(dllexport) +#endif /* defined (_MSC_VER) */ +#endif /* !defined (ROCTX_EXPORT_DECORATOR) */ + +#if !defined(ROCTX_IMPORT_DECORATOR) +#if defined(__GNUC__) +#define ROCTX_IMPORT_DECORATOR +#elif defined(_MSC_VER) +#define ROCTX_IMPORT_DECORATOR __declspec(dllimport) +#endif /* defined (_MSC_VER) */ +#endif /* !defined (ROCTX_IMPORT_DECORATOR) */ + +#define ROCTX_EXPORT ROCTX_EXPORT_DECORATOR ROCTX_CALL +#define ROCTX_IMPORT ROCTX_IMPORT_DECORATOR ROCTX_CALL + +#if !defined(ROCTX) +#if defined(ROCTX_EXPORTS) +#define ROCTX_API ROCTX_EXPORT +#else /* !defined (ROCTX_EXPORTS) */ +#define ROCTX_API ROCTX_IMPORT +#endif /* !defined (ROCTX_EXPORTS) */ +#endif /* !defined (ROCTX) */ + +#include + +#if defined(__cplusplus) +extern "C" { +#endif /* defined(__cplusplus) */ + +/** \defgroup symbol_versions_group Symbol Versions + * + * The names used for the shared library versioned symbols. + * + * Every function is annotated with one of the version macros defined in this + * section. Each macro specifies a corresponding symbol version string. After + * dynamically loading the shared library with \p dlopen, the address of each + * function can be obtained using \p dlvsym with the name of the function and + * its corresponding symbol version string. An error will be reported by \p + * dlvsym if the installed library does not support the version for the + * function specified in this version of the interface. + * + * @{ + */ + +/** + * The function was introduced in version 4.1 of the interface and has the + * symbol version string of ``"ROCTX_4.1"``. + */ +#define ROCTX_VERSION_4_1 + +/** @} */ + +/** \defgroup versioning_group Versioning + * + * Version information about the interface and the associated installed + * library. + * + * @{ + */ + +/** + * The semantic version of the interface following + * [semver.org][semver] rules. + * + * A client that uses this interface is only compatible with the installed + * library if the major version numbers match and the interface minor version + * number is less than or equal to the installed library minor version number. + */ + +/** + * The major version of the interface as a macro so it can be used by the + * preprocessor. + */ +#define ROCTX_VERSION_MAJOR 4 + +/** + * The minor version of the interface as a macro so it can be used by the + * preprocessor. + */ +#define ROCTX_VERSION_MINOR 1 + +/** + * Query the major version of the installed library. + * + * Return the major version of the installed library. This can be used to check + * if it is compatible with this interface version. + * + * \return Returns the major version number. + */ +ROCTX_API uint32_t roctx_version_major() ROCTX_VERSION_4_1; + +/** + * Query the minor version of the installed library. + * + * Return the minor version of the installed library. This can be used to check + * if it is compatible with this interface version. + * + * \return Returns the minor version number. + */ +ROCTX_API uint32_t roctx_version_minor() ROCTX_VERSION_4_1; + +/** @} */ + +/** \defgroup marker_group ROCTX Markers + * + * Marker annotations are used to describe events in a ROCm application. + * + * @{ + */ + +/** + * Mark an event. + * + * \param[in] message The message associated with the event. + */ +ROCTX_API void roctxMarkA(const char* message) ROCTX_VERSION_4_1; +#define roctxMark(message) roctxMarkA(message) + +/** @} */ + +/** \defgroup range_group ROCTX Ranges + * + * Range annotations are used to describe events in a ROCm application. + * + * @{ + */ + +/** + * Start a new nested range. + * + * Nested ranges are stacked and local to the current CPU thread. + * + * \param[in] message The message associated with this range. + * + * \return Returns the level this nested range is started at. Nested range + * levels are 0 based. + */ +ROCTX_API int roctxRangePushA(const char* message) ROCTX_VERSION_4_1; +#define roctxRangePush(message) roctxRangePushA(message) + +/** + * Stop the current nested range. + * + * Stop the current nested range, and pop it from the stack. If a nested range + * was active before the last one was started, it becomes again the current + * nested range. + * + * \return Returns the level the stopped nested range was started at, or a + * negative value if there was no nested range active. + */ +ROCTX_API int roctxRangePop() ROCTX_VERSION_4_1; + +/** + * ROCTX range ID. + * + * This is the range ID used to identify start/end ranges. + */ +typedef uint64_t roctx_range_id_t; + +/** + * Starts a process range. + * + * Start/stop ranges can be started and stopped in different threads. Each + * timespan is assigned a unique range ID. + * + * \param[in] message The message associated with this range. + * + * \return Returns the ID of the new range. + */ +ROCTX_API roctx_range_id_t roctxRangeStartA(const char* message) + ROCTX_VERSION_4_1; +#define roctxRangeStart(message) roctxRangeStartA(message) + +/** + * Stop a process range. + */ +ROCTX_API void roctxRangeStop(roctx_range_id_t id) ROCTX_VERSION_4_1; + +/** @} */ + +#if defined(__cplusplus) +} /* extern "C" */ +#endif /* defined (__cplusplus) */ + +#endif /* ROCTX_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/__init__.py b/lib/python3.11/site-packages/triton/backends/nvidia/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/compiler.py b/lib/python3.11/site-packages/triton/backends/nvidia/compiler.py new file mode 100644 index 0000000000000000000000000000000000000000..ac53188931624bb0490a2db349e6619fb2457616 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/compiler.py @@ -0,0 +1,394 @@ +from triton.backends.compiler import BaseBackend, GPUTarget +from triton._C.libtriton import ir, passes, llvm, nvidia + +from dataclasses import dataclass +import functools +from typing import Any, Dict, Tuple, Optional +from types import ModuleType +import hashlib +import re +import tempfile +import signal +import os +import subprocess +from pathlib import Path + + +def min_dot_size(target: GPUTarget): + return lambda lhsType, rhsType: (16, 32, 16) if lhsType.is_int8() else (16, 16, 16) + + +@functools.lru_cache() +def _path_to_binary(binary: str): + paths = [ + os.environ.get(f"TRITON_{binary.upper()}_PATH", ""), + os.path.join(os.path.dirname(__file__), "bin", binary), + ] + + for bin in paths: + if os.path.exists(bin) and os.path.isfile(bin): + result = subprocess.check_output([bin, "--version"], stderr=subprocess.STDOUT) + if result is not None: + version = re.search(r".*release (\d+\.\d+).*", result.decode("utf-8"), flags=re.MULTILINE) + if version is not None: + return bin, version.group(1) + raise RuntimeError(f"Cannot find {binary}") + + +@functools.lru_cache() +def get_ptxas_version(): + version = subprocess.check_output([_path_to_binary("ptxas")[0], "--version"]).decode("utf-8") + return version + + +@functools.lru_cache() +def ptx_get_version(cuda_version) -> int: + ''' + Get the highest PTX version supported by the current CUDA driver. + ''' + assert isinstance(cuda_version, str) + major, minor = map(int, cuda_version.split('.')) + if major == 12: + if minor < 6: + return 80 + minor + elif minor == 6: + return 85 + if major == 11: + return 70 + minor + if major == 10: + return 63 + minor + raise RuntimeError("Triton only support CUDA 10.0 or higher, but got CUDA version: " + cuda_version) + + +def get_ptx_version_from_options(options): + ptx_version = options.ptx_version + if ptx_version is None: + _, cuda_version = _path_to_binary("ptxas") + ptx_version = ptx_get_version(cuda_version) + return ptx_version + + +@functools.lru_cache() +def get_features(options): + ptx_version = get_ptx_version_from_options(options) + + # PTX 8.3 is the max version supported by llvm 3a83162168. + # + # To check if a newer PTX version is supported, increase this value + # and run a test. If it's not supported, LLVM will print a warning + # like "+ptx8.4 is not a recognized feature for this target". + llvm_ptx_version = min(83, ptx_version) + features = f'+ptx{llvm_ptx_version}' + return features + + +@functools.lru_cache(None) +def file_hash(path): + with open(path, "rb") as f: + return hashlib.sha256(f.read()).hexdigest() + + +@dataclass(frozen=True) +class CUDAOptions: + num_warps: int = 4 + num_ctas: int = 1 + num_stages: int = 3 + num_buffers_warp_spec: int = 0 + num_consumer_groups: int = 0 + reg_dec_producer: int = 0 + reg_inc_consumer: int = 0 + # maxnreg corresponds to the ptx parameter .maxnreg, which controls the + # maximum number of 32-bit registers used by one thread. + maxnreg: Optional[int] = None + cluster_dims: tuple = (1, 1, 1) + ptx_version: int = None + enable_fp_fusion: bool = True + supported_fp8_dtypes: Tuple[str] = ("fp8e5", "fp8e4b15") + deprecated_fp8_dtypes: Tuple[str] = () + default_dot_input_precision: str = "tf32" + allowed_dot_input_precisions: Tuple[str] = ("tf32", "tf32x3", "ieee") + max_num_imprecise_acc_default: bool = None + extern_libs: dict = None + debug: bool = False + backend_name: str = 'cuda' + sanitize_overflow: bool = True + + def __post_init__(self): + default_libdir = Path(__file__).parent / 'lib' + extern_libs = {} if self.extern_libs is None else dict(self.extern_libs) + if not extern_libs.get('libdevice', None): + extern_libs['libdevice'] = os.getenv("TRITON_LIBDEVICE_PATH", str(default_libdir / 'libdevice.10.bc')) + object.__setattr__(self, 'extern_libs', tuple(extern_libs.items())) + assert self.num_warps > 0 and (self.num_warps & (self.num_warps - 1)) == 0, \ + "num_warps must be a power of 2" + + def hash(self): + hash_dict = dict(self.__dict__) + hash_dict["extern_libs"] = tuple((k, file_hash(v)) for k, v in sorted(hash_dict["extern_libs"])) + key = "_".join([f"{name}-{val}" for name, val in sorted(hash_dict.items())]) + return hashlib.sha256(key.encode("utf-8")).hexdigest() + + +class CUDABackend(BaseBackend): + + @staticmethod + def supports_target(target: GPUTarget): + return target.backend == 'cuda' + + def __init__(self, target: GPUTarget) -> None: + super().__init__(target) + self.capability = target.arch + assert isinstance(self.capability, int) + self.binary_ext = "cubin" + + def parse_options(self, opts) -> Any: + args = {k: opts[k] for k in CUDAOptions.__dataclass_fields__.keys() if k in opts} + if "supported_fp8_dtypes" not in args: + supported_fp8_dtypes = set(CUDAOptions.supported_fp8_dtypes) + if self.capability >= 89: + supported_fp8_dtypes.add("fp8e4nv") + args["supported_fp8_dtypes"] = tuple(sorted(supported_fp8_dtypes)) + + if "deprecated_fp8_dtypes" not in args: + if self.capability >= 90: + args["deprecated_fp8_dtypes"] = ("fp8e4b15", ) + + if "enable_fp_fusion" not in args: + args["enable_fp_fusion"] = os.getenv("TRITON_DEFAULT_FP_FUSION", "1") == "1" + args["max_num_imprecise_acc_default"] = 2**30 if self.capability == 90 else 0 + return CUDAOptions(**args) + + def pack_metadata(self, metadata): + return ( + metadata.num_warps, + metadata.num_ctas, + metadata.shared, + metadata.cluster_dims[0], + metadata.cluster_dims[1], + metadata.cluster_dims[2], + ) + + def get_codegen_implementation(self): + import triton.language.extra.cuda as cuda + codegen_fns = { + "convert_custom_types": + cuda.convert_custom_float8_sm80 if self.capability >= 80 else cuda.convert_custom_float8_sm70, + "min_dot_size": min_dot_size(self.target) + } + return codegen_fns + + def get_module_map(self) -> Dict[str, ModuleType]: + from triton.language.extra.cuda import libdevice + return {"triton.language.extra.libdevice": libdevice} + + def load_dialects(self, ctx): + nvidia.load_dialects(ctx) + + @staticmethod + def make_ttir(mod, metadata, opt): + pm = ir.pass_manager(mod.context) + pm.enable_debug() + passes.common.add_inliner(pm) + passes.ttir.add_rewrite_tensor_pointer(pm) + passes.ttir.add_combine(pm) + passes.common.add_canonicalizer(pm) + passes.ttir.add_reorder_broadcast(pm) + passes.common.add_cse(pm) + passes.common.add_licm(pm) + passes.common.add_symbol_dce(pm) + passes.ttir.add_loop_unroll(pm) + pm.run(mod) + return mod + + @staticmethod + def make_ttgir(mod, metadata, opt, capability): + cluster_info = nvidia.ClusterInfo() + if opt.cluster_dims is not None: + cluster_info.clusterDimX = opt.cluster_dims[0] + cluster_info.clusterDimY = opt.cluster_dims[1] + cluster_info.clusterDimZ = opt.cluster_dims[2] + # Set up Diagnostic + if os.environ.get("MLIR_ENABLE_REMARK", "0") == "1": + srcMgr = llvm.source_mgr() + diag = ir.source_mgr_diag(srcMgr, mod.context) + mod.context.printOpOnDiagnostic(True) + # TTIR -> TTGIR + pm = ir.pass_manager(mod.context) + pm.enable_debug() + passes.ttir.add_convert_to_ttgpuir(pm, f"cuda:{capability}", opt.num_warps, 32, opt.num_ctas) + # optimize TTGIR + passes.ttgpuir.add_coalesce(pm) + if capability // 10 >= 8: + passes.ttgpuir.add_f32_dot_tc(pm) + # TODO(Qingyi): Move PlanCTAPass to the front of CoalescePass + nvidia.passes.ttnvgpuir.add_plan_cta(pm, cluster_info) + passes.ttgpuir.add_remove_layout_conversions(pm) + passes.ttgpuir.add_optimize_thread_locality(pm) + passes.ttgpuir.add_accelerate_matmul(pm) + passes.ttgpuir.add_remove_layout_conversions(pm) + passes.ttgpuir.add_optimize_dot_operands(pm, capability >= 80) + passes.common.add_cse(pm) + if capability // 10 >= 8: + passes.ttgpuir.add_optimize_accumulator_init(pm) + passes.ttgpuir.add_combine_tensor_select_and_if(pm) + passes.ttgpuir.add_ws_task_partition(pm, opt.num_consumer_groups) + passes.ttgpuir.add_taskid_propagate(pm, opt.num_consumer_groups) + passes.ttgpuir.add_ws_data_partition(pm, opt.num_consumer_groups) + passes.ttgpuir.add_ws_code_partition(pm, opt.num_buffers_warp_spec, opt.num_consumer_groups, + opt.reg_dec_producer, opt.reg_inc_consumer) + passes.ttgpuir.add_pipeline(pm, opt.num_stages) + passes.ttgpuir.add_ws_lowering(pm, opt.num_consumer_groups) + passes.ttgpuir.add_prefetch(pm) + passes.ttgpuir.add_optimize_dot_operands(pm, capability >= 80) + passes.ttgpuir.add_remove_layout_conversions(pm) + passes.ttgpuir.add_reduce_data_duplication(pm) + passes.ttgpuir.add_reorder_instructions(pm) + passes.common.add_cse(pm) + passes.common.add_symbol_dce(pm) + if capability // 10 >= 9: + nvidia.passes.ttnvgpuir.add_fence_insertion(pm) + nvidia.passes.ttnvgpuir.add_tma_lowering(pm) + passes.common.add_canonicalizer(pm) + pm.run(mod) + metadata["cluster_dims"] = (cluster_info.clusterDimX, cluster_info.clusterDimY, cluster_info.clusterDimZ) + return mod + + @staticmethod + def make_llir(src, metadata, options, capability): + ptx_version = get_ptx_version_from_options(options) + + # warp-specialization mutates num_warps + num_warp_groups = src.get_int_attr("triton_gpu.num-warp-groups-per-cta") + if num_warp_groups is not None: + metadata["num_warps"] *= num_warp_groups + mod = src + # TritonGPU -> LLVM-IR (MLIR) + pm = ir.pass_manager(mod.context) + pm.enable_debug() + # Set up Diagnostic + if os.environ.get("MLIR_ENABLE_REMARK", "0") == "1": + srcMgr = llvm.source_mgr() + diag = ir.source_mgr_diag(srcMgr, mod.context) + mod.context.printOpOnDiagnostic(True) + nvidia.passes.ttgpuir.add_decompose_unsupported_conversions(pm) + passes.ttgpuir.add_combine_tensor_select_and_if(pm) + passes.convert.add_scf_to_cf(pm) + passes.convert.add_index_to_llvmir(pm) + passes.ttgpuir.add_allocate_shared_memory(pm) + nvidia.passes.ttgpuir.add_to_llvmir(pm, capability, ptx_version) + nvidia.passes.ttnvgpuir.add_nvgpu_to_llvm(pm) + passes.convert.add_arith_to_llvmir(pm) + passes.common.add_canonicalizer(pm) + passes.common.add_cse(pm) + passes.common.add_symbol_dce(pm) + if os.environ.get("TRITON_DISABLE_LINE_INFO", "0") == "0": + passes.llvmir.add_di_scope(pm) + pm.run(mod) + # LLVM-IR (MLIR) -> LLVM-IR (LLVM) + llvm.init_targets() + context = llvm.context() + + llvm_mod = llvm.to_module(mod, context) + proc = 'sm_90a' if capability == 90 else f'sm_{capability}' + features = get_features(options) + triple = 'nvptx64-nvidia-cuda' + llvm.attach_datalayout(llvm_mod, triple, proc, features) + nvidia.set_nvvm_reflect_ftz(llvm_mod) + + # Set maxnreg on all kernels, if it was provided. + if options.maxnreg is not None: + for k in llvm_mod.get_functions(): + if not k.is_declaration() and k.is_external_linkage(): + k.set_nvvm_maxnreg(options.maxnreg) + + if options.extern_libs: + paths = [path for (name, path) in options.extern_libs] + llvm.link_extern_libs(llvm_mod, paths) + + llvm.optimize_module(llvm_mod, llvm.OPTIMIZE_O3) + + # Get some metadata + metadata["shared"] = src.get_int_attr("triton_gpu.shared") + ret = str(llvm_mod) + del llvm_mod + del context + return ret + + @staticmethod + def make_ptx(src, metadata, opt, capability): + ptx_version = get_ptx_version_from_options(opt) + + triple = 'nvptx64-nvidia-cuda' + proc = 'sm_90a' if capability == 90 else f'sm_{capability}' + features = get_features(opt) + ret = llvm.translate_to_asm(src, triple, proc, features, ['nvptx-short-ptr'], opt.enable_fp_fusion, False) + # Find kernel names (there should only be one) + names = re.findall(r".visible .entry ([a-zA-Z_][a-zA-Z0-9_]*)", ret) + assert len(names) == 1 + metadata["name"] = names[0] + # post-process + ptx_version = f'{ptx_version//10}.{ptx_version%10}' + ret = re.sub(r'\.version \d+\.\d+', f'.version {ptx_version}', ret, flags=re.MULTILINE) + # Remove the debug flag that prevents ptxas from optimizing the code + ret = re.sub(r",\s*debug|debug,\s*", "", ret) + if os.environ.get("NVPTX_ENABLE_DUMP", "0") == "1": + print("// -----// NVPTX Dump //----- //") + print(ret) + return ret + + @staticmethod + def make_cubin(src, metadata, opt, capability): + ptxas, _ = _path_to_binary("ptxas") + with tempfile.NamedTemporaryFile(delete=False, mode='w', suffix='.ptx') as fsrc, \ + tempfile.NamedTemporaryFile(delete=False, mode='r', suffix='.log') as flog: + fsrc.write(src) + fsrc.flush() + fbin = fsrc.name + '.o' + + line_info = [] if os.environ.get('TRITON_DISABLE_LINE_INFO') else ['-lineinfo'] + fmad = [] if opt.enable_fp_fusion else ['--fmad=false'] + suffix = 'a' if capability == 90 else '' + opt_level = ['--opt-level', '0'] if os.environ.get("DISABLE_PTXAS_OPT", "0") == "1" else [] + ptxas_cmd = [ + ptxas, *line_info, *fmad, '-v', *opt_level, f'--gpu-name=sm_{capability}{suffix}', fsrc.name, '-o', fbin + ] + try: + subprocess.run(ptxas_cmd, check=True, close_fds=False, stderr=flog) + if os.path.exists(fsrc.name): + os.remove(fsrc.name) + if os.path.exists(flog.name): + os.remove(flog.name) + except subprocess.CalledProcessError as e: + with open(flog.name) as log_file: + log = log_file.read() + if os.path.exists(flog.name): + os.remove(flog.name) + + if e.returncode == 255: + error = 'Internal Triton PTX codegen error' + elif e.returncode == 128 + signal.SIGSEGV: + error = '`ptxas` raised SIGSEGV' + else: + error = f'`ptxas` failed with error code {e.returncode}' + + raise RuntimeError(f'{error}\n' + f'`ptxas` stderr:\n{log}\n' + f'Repro command: {" ".join(ptxas_cmd)}\n') + + with open(fbin, 'rb') as f: + cubin = f.read() + if os.path.exists(fbin): + os.remove(fbin) + return cubin + + def add_stages(self, stages, options): + stages["ttir"] = lambda src, metadata: self.make_ttir(src, metadata, options) + stages["ttgir"] = lambda src, metadata: self.make_ttgir(src, metadata, options, self.capability) + stages["llir"] = lambda src, metadata: self.make_llir(src, metadata, options, self.capability) + stages["ptx"] = lambda src, metadata: self.make_ptx(src, metadata, options, self.capability) + stages["cubin"] = lambda src, metadata: self.make_cubin(src, metadata, options, self.capability) + + @functools.lru_cache() + def hash(self): + version = get_ptxas_version() + return f'{version}-{self.capability}' diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/driver.c b/lib/python3.11/site-packages/triton/backends/nvidia/driver.c new file mode 100644 index 0000000000000000000000000000000000000000..bb0d868881205c52d12779a5a452562333e65135 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/driver.c @@ -0,0 +1,422 @@ +#include "cuda.h" +#include +#include +#define PY_SSIZE_T_CLEAN +#include +#include + +// Raises a Python exception and returns false if code is not CUDA_SUCCESS. +static bool gpuAssert(CUresult code, const char *file, int line) { + if (code == CUDA_SUCCESS) + return true; + + const char *prefix = "Triton Error [CUDA]: "; + const char *str; + cuGetErrorString(code, &str); + char err[1024] = {0}; + strcat(err, prefix); + strcat(err, str); + PyGILState_STATE gil_state; + gil_state = PyGILState_Ensure(); + PyErr_SetString(PyExc_RuntimeError, err); + PyGILState_Release(gil_state); + return false; +} + +// To be used only *outside* a Py_{BEGIN,END}_ALLOW_THREADS block. +#define CUDA_CHECK_AND_RETURN_NULL(ans) \ + do { \ + if (!gpuAssert((ans), __FILE__, __LINE__)) \ + return NULL; \ + } while (0) + +// To be used inside a Py_{BEGIN,END}_ALLOW_THREADS block. +#define CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(ans) \ + do { \ + if (!gpuAssert((ans), __FILE__, __LINE__)) { \ + PyEval_RestoreThread(_save); \ + return NULL; \ + } \ + } while (0) + +// Used to check if functions exist in old CUDA driver versions. +#define INITIALIZE_FUNCTION_POINTER_IF_NULL(funcPointer, initializerFunction) \ + do { \ + if ((funcPointer) == NULL) { \ + (funcPointer) = (initializerFunction)(); \ + if ((funcPointer) == NULL) { \ + return NULL; \ + } \ + } \ + } while (0) + +static PyObject *getDeviceProperties(PyObject *self, PyObject *args) { + int device_id; + if (!PyArg_ParseTuple(args, "i", &device_id)) + return NULL; + // Get device handle + CUdevice device; + cuDeviceGet(&device, device_id); + + // create a struct to hold device properties + int max_shared_mem; + int max_num_regs; + int multiprocessor_count; + int warp_size; + int sm_clock_rate; + int mem_clock_rate; + int mem_bus_width; + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &max_shared_mem, CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN, + device)); + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &max_num_regs, CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_BLOCK, device)); + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &multiprocessor_count, CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT, device)); + CUDA_CHECK_AND_RETURN_NULL( + cuDeviceGetAttribute(&warp_size, CU_DEVICE_ATTRIBUTE_WARP_SIZE, device)); + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &sm_clock_rate, CU_DEVICE_ATTRIBUTE_CLOCK_RATE, device)); + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &mem_clock_rate, CU_DEVICE_ATTRIBUTE_MEMORY_CLOCK_RATE, device)); + CUDA_CHECK_AND_RETURN_NULL(cuDeviceGetAttribute( + &mem_bus_width, CU_DEVICE_ATTRIBUTE_GLOBAL_MEMORY_BUS_WIDTH, device)); + + return Py_BuildValue("{s:i, s:i, s:i, s:i, s:i, s:i, s:i}", "max_shared_mem", + max_shared_mem, "max_num_regs", max_num_regs, + "multiprocessor_count", multiprocessor_count, "warpSize", + warp_size, "sm_clock_rate", sm_clock_rate, + "mem_clock_rate", mem_clock_rate, "mem_bus_width", + mem_bus_width); +} + +static PyObject *loadBinary(PyObject *self, PyObject *args) { + const char *name; + const char *data; + Py_ssize_t data_size; + int shared; + int device; + if (!PyArg_ParseTuple(args, "ss#ii", &name, &data, &data_size, &shared, + &device)) { + return NULL; + } + CUfunction fun; + CUmodule mod; + int32_t n_regs = 0; + int32_t n_spills = 0; + // create driver handles + CUcontext pctx = 0; + + Py_BEGIN_ALLOW_THREADS; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuCtxGetCurrent(&pctx)); + if (!pctx) { + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuDevicePrimaryCtxRetain(&pctx, device)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuCtxSetCurrent(pctx)); + } + + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuModuleLoadData(&mod, data)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuModuleGetFunction(&fun, mod, name)); + // get allocated registers and spilled registers from the function + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuFuncGetAttribute(&n_regs, CU_FUNC_ATTRIBUTE_NUM_REGS, fun)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuFuncGetAttribute(&n_spills, CU_FUNC_ATTRIBUTE_LOCAL_SIZE_BYTES, fun)); + n_spills /= 4; + // set dynamic shared memory if necessary + int shared_optin; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuDeviceGetAttribute( + &shared_optin, CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN, + device)); + if (shared > 49152 && shared_optin > 49152) { + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuFuncSetCacheConfig(fun, CU_FUNC_CACHE_PREFER_SHARED)); + int shared_total, shared_static; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuDeviceGetAttribute( + &shared_total, CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR, + device)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuFuncGetAttribute( + &shared_static, CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES, fun)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuFuncSetAttribute(fun, CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES, + shared_optin - shared_static)); + } + Py_END_ALLOW_THREADS; + + if (PyErr_Occurred()) { + return NULL; + } + return Py_BuildValue("(KKii)", (uint64_t)mod, (uint64_t)fun, n_regs, + n_spills); +} + +typedef CUresult (*cuOccupancyMaxActiveClusters_t)( + int *numClusters, CUfunction func, const CUlaunchConfig *config); + +typedef CUresult (*cuTensorMapEncodeTiled_t)( + CUtensorMap *tensorMap, CUtensorMapDataType tensorDataType, + cuuint32_t tensorRank, void *globalAddress, const cuuint64_t *globalDim, + const cuuint64_t *globalStrides, const cuuint32_t *boxDim, + const cuuint32_t *elementStrides, CUtensorMapInterleave interleave, + CUtensorMapSwizzle swizzle, CUtensorMapL2promotion l2Promotion, + CUtensorMapFloatOOBfill oobFill); + +#define defineGetFunctionHandle(name, symbolName) \ + static symbolName##_t name() { \ + /* Open the shared library */ \ + void *libHandle = dlopen("libcuda.so.1", RTLD_LAZY); \ + if (!libHandle) { \ + PyErr_SetString(PyExc_RuntimeError, "Failed to open libcuda.so.1"); \ + return NULL; \ + } \ + /* Clear any existing error */ \ + dlerror(); \ + symbolName##_t funcHandle = (symbolName##_t)dlsym(libHandle, #symbolName); \ + /* Check for errors */ \ + const char *err = dlerror(); \ + if (err) { \ + PyErr_SetString(PyExc_RuntimeError, \ + "Failed to retrieve " #symbolName " from libcuda.so.1"); \ + dlclose(libHandle); \ + return NULL; \ + } \ + return funcHandle; \ + } + +defineGetFunctionHandle(getCuOccupancyMaxActiveClustersHandle, + cuOccupancyMaxActiveClusters); + +defineGetFunctionHandle(getCuTensorMapEncodeTiledHandle, + cuTensorMapEncodeTiled); + +static PyObject *occupancyMaxActiveClusters(PyObject *self, PyObject *args) { + int clusterDimX = -1, clusterDimY = -1, clusterDimZ = -1, + maxActiveClusters = -1; + int shared = 0; + CUfunction func; + + if (!PyArg_ParseTuple(args, "Kiiii", &func, &shared, &clusterDimX, + &clusterDimY, &clusterDimZ)) { + return NULL; + } + + // Let each SM have one block + int maxActiveBlocks = 1; + Py_BEGIN_ALLOW_THREADS; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuFuncSetAttribute( + func, CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES, shared)); + Py_END_ALLOW_THREADS; + + CUlaunchAttribute launchAttr[1]; + launchAttr[0].id = CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION; + launchAttr[0].value.clusterDim.x = clusterDimX; + launchAttr[0].value.clusterDim.y = clusterDimY; + launchAttr[0].value.clusterDim.z = clusterDimZ; + CUlaunchConfig config; + config.gridDimX = clusterDimX; + config.gridDimY = maxActiveBlocks * clusterDimY; + config.gridDimZ = clusterDimZ; + config.blockDimX = 128; + config.blockDimY = 1; + config.blockDimZ = 1; + config.sharedMemBytes = shared; + config.hStream = 0; + config.numAttrs = 1; + config.attrs = launchAttr; + + static cuOccupancyMaxActiveClusters_t cuOccupancyMaxActiveClusters = NULL; + INITIALIZE_FUNCTION_POINTER_IF_NULL(cuOccupancyMaxActiveClusters, + getCuOccupancyMaxActiveClustersHandle); + + Py_BEGIN_ALLOW_THREADS; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuFuncSetAttribute( + func, CU_FUNC_ATTRIBUTE_NON_PORTABLE_CLUSTER_SIZE_ALLOWED, 1)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuOccupancyMaxActiveClusters(&maxActiveClusters, func, &config)); + Py_END_ALLOW_THREADS; + return PyLong_FromLong(maxActiveClusters); +} + +static PyObject *setPrintfFifoSize(PyObject *self, PyObject *args) { + long size; + if (!PyArg_ParseTuple(args, "l", &size)) { + return NULL; + } + if (size < 0) { + PyErr_SetString(PyExc_ValueError, "fifo size must be non-negative"); + return NULL; + } + + Py_BEGIN_ALLOW_THREADS; + + // Ensure we have an active context. + CUcontext ctx = NULL; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuCtxGetCurrent(&ctx)); + if (!ctx) { + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuDevicePrimaryCtxRetain(&ctx, /*device=*/0)); + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS(cuCtxSetCurrent(ctx)); + } + + // We can't set the fifo size after running a kernel that calls printf. This + // is true even if the set() call is a nop and the new size is the same as the + // old size. + // + // This is unfriendly, so check if the old size matches the new size, and skip + // the set() call if so. + size_t oldSize = 0; + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuCtxGetLimit(&oldSize, CU_LIMIT_PRINTF_FIFO_SIZE)); + if (oldSize != size) { + CUDA_CHECK_AND_RETURN_NULL_ALLOW_THREADS( + cuCtxSetLimit(CU_LIMIT_PRINTF_FIFO_SIZE, size)); + } + + Py_END_ALLOW_THREADS; + Py_INCREF(Py_None); + return Py_None; +} + +// Simple helper to experiment creating TMA descriptors on the host. +// This is a useful to test TMA operations independently. +static PyObject *fill1DTMADescriptor(PyObject *self, PyObject *args) { + unsigned long long global_address; + uint64_t dim; + uint32_t tensorDim; + int elementSize; + unsigned long long desc_address; + if (!PyArg_ParseTuple(args, "KKiiK", &global_address, &dim, &tensorDim, + &elementSize, &desc_address)) { + return NULL; + } + uint64_t dims[1] = {dim}; + uint64_t globalStrides[1] = {dim * elementSize}; + uint32_t boxDim[1] = {tensorDim}; + uint32_t elementStrides[1] = {1}; + CUtensorMapDataType type; + switch (elementSize) { + case 1: + type = CU_TENSOR_MAP_DATA_TYPE_UINT8; + break; + case 2: + type = CU_TENSOR_MAP_DATA_TYPE_UINT16; + break; + case 4: + type = CU_TENSOR_MAP_DATA_TYPE_UINT32; + break; + default: + PyErr_SetString(PyExc_ValueError, "elementSize must be 1, 2, or 4"); + return NULL; + } + assert((elementSize * tensorDim) >= 32 && "block size too small."); + int rank = 1; + static cuTensorMapEncodeTiled_t cuTensorMapEncodeTiled = NULL; + INITIALIZE_FUNCTION_POINTER_IF_NULL(cuTensorMapEncodeTiled, + getCuTensorMapEncodeTiledHandle); + CUDA_CHECK_AND_RETURN_NULL(cuTensorMapEncodeTiled( + (CUtensorMap *)desc_address, type, rank, (void *)global_address, dims, + globalStrides, boxDim, elementStrides, CU_TENSOR_MAP_INTERLEAVE_NONE, + CU_TENSOR_MAP_SWIZZLE_NONE, CU_TENSOR_MAP_L2_PROMOTION_NONE, + CU_TENSOR_MAP_FLOAT_OOB_FILL_NONE)); + Py_INCREF(Py_None); + return Py_None; +} + +// Simple helper to experiment creating TMA descriptors on the host. +// This is a useful to test TMA operations independently. +static PyObject *fill2DTMADescriptor(PyObject *self, PyObject *args) { + unsigned long long global_address; + uint64_t dims[2]; + uint32_t tensorDims[2]; + int elementSize; + unsigned long long desc_address; + if (!PyArg_ParseTuple(args, "KKKiiiK", &global_address, &dims[1], &dims[0], + &tensorDims[1], &tensorDims[0], &elementSize, + &desc_address)) { + return NULL; + } + uint64_t globalStrides[2] = {dims[0] * elementSize, + dims[0] * dims[1] * elementSize}; + uint32_t elementStrides[2] = {1, 1}; + CUtensorMapDataType type; + switch (elementSize) { + case 1: + type = CU_TENSOR_MAP_DATA_TYPE_UINT8; + break; + case 2: + type = CU_TENSOR_MAP_DATA_TYPE_UINT16; + break; + case 4: + type = CU_TENSOR_MAP_DATA_TYPE_UINT32; + break; + default: + PyErr_SetString(PyExc_ValueError, "elementSize must be 1, 2, or 4"); + } + int rank = 2; + // Swizzling should be picked in codegen but since we need to set it on the + // descriptor we rely on a convention between this function and codegen. + CUtensorMapSwizzle swizzle = CU_TENSOR_MAP_SWIZZLE_128B; + uint32_t contigDimSizeInByte = elementSize * tensorDims[0]; + if (contigDimSizeInByte >= 128) { + swizzle = CU_TENSOR_MAP_SWIZZLE_128B; + } else if (contigDimSizeInByte >= 64) { + swizzle = CU_TENSOR_MAP_SWIZZLE_64B; + } else if (contigDimSizeInByte >= 32) { + swizzle = CU_TENSOR_MAP_SWIZZLE_32B; + } else { + assert(false && "block size too small."); + } + // The bounding box inner dimension must be less than or equal to the swizzle + // size. + // https://docs.nvidia.com/cuda/cuda-driver-api/group__CUDA__TENSOR__MEMORY.html#group__CUDA__TENSOR__MEMORY_1ga7c7d2aaac9e49294304e755e6f341d7 + // We clamp the block size and the codegen will emit multiple copy operations. + if (contigDimSizeInByte > 128) { + tensorDims[0] = 128 / elementSize; + } + static cuTensorMapEncodeTiled_t cuTensorMapEncodeTiled = NULL; + INITIALIZE_FUNCTION_POINTER_IF_NULL(cuTensorMapEncodeTiled, + getCuTensorMapEncodeTiledHandle); + CUDA_CHECK_AND_RETURN_NULL(cuTensorMapEncodeTiled( + (CUtensorMap *)desc_address, type, rank, (void *)global_address, dims, + globalStrides, tensorDims, elementStrides, CU_TENSOR_MAP_INTERLEAVE_NONE, + swizzle, CU_TENSOR_MAP_L2_PROMOTION_L2_128B, + CU_TENSOR_MAP_FLOAT_OOB_FILL_NONE)); + Py_INCREF(Py_None); + return Py_None; +} + +static PyMethodDef ModuleMethods[] = { + {"load_binary", loadBinary, METH_VARARGS, + "Load provided cubin into CUDA driver"}, + {"get_device_properties", getDeviceProperties, METH_VARARGS, + "Get the properties for a given device"}, + {"cuOccupancyMaxActiveClusters", occupancyMaxActiveClusters, METH_VARARGS, + "Python interface for cuOccupancyMaxActiveClusters function"}, + {"set_printf_fifo_size", setPrintfFifoSize, METH_VARARGS, + "Python interface for cuCtxSetLimit(CU_LIMIT_PRINTF_FIFO_SIZE, x), which " + "controls how many bytes can be streamed from kernels before data starts " + "being dropped. This inherits all the limitations of this call; in " + "particular it's an error to change this value after launching any kernel " + "that calls printf()."}, + {"fill_1d_tma_descriptor", fill1DTMADescriptor, METH_VARARGS, "doc"}, + {"fill_2d_tma_descriptor", fill2DTMADescriptor, METH_VARARGS, "doc"}, + + {NULL, NULL, 0, NULL} // sentinel +}; + +static struct PyModuleDef ModuleDef = {PyModuleDef_HEAD_INIT, "cuda_utils", + NULL, // documentation + -1, // size + ModuleMethods}; + +PyMODINIT_FUNC PyInit_cuda_utils(void) { + PyObject *m = PyModule_Create(&ModuleDef); + if (m == NULL) { + return NULL; + } + + PyModule_AddFunctions(m, ModuleMethods); + + return m; +} diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/driver.py b/lib/python3.11/site-packages/triton/backends/nvidia/driver.py new file mode 100644 index 0000000000000000000000000000000000000000..0a62c378c4232322cfcf886389771f087a57eb52 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/driver.py @@ -0,0 +1,481 @@ +import functools +import os +import hashlib +import subprocess +import tempfile +from pathlib import Path +from triton.runtime.build import _build +from triton.runtime.cache import get_cache_manager +from triton.backends.compiler import GPUTarget +from triton.backends.driver import GPUDriver + +dirname = os.path.dirname(os.path.realpath(__file__)) +include_dir = [os.path.join(dirname, "include")] +libdevice_dir = os.path.join(dirname, "lib") +libraries = ['cuda'] + + +@functools.lru_cache() +def libcuda_dirs(): + env_libcuda_path = os.getenv("TRITON_LIBCUDA_PATH") + if env_libcuda_path: + return [env_libcuda_path] + + libs = subprocess.check_output(["/sbin/ldconfig", "-p"]).decode() + # each line looks like the following: + # libcuda.so.1 (libc6,x86-64) => /lib/x86_64-linux-gnu/libcuda.so.1 + locs = [line.split()[-1] for line in libs.splitlines() if "libcuda.so.1" in line] + dirs = [os.path.dirname(loc) for loc in locs] + env_ld_library_path = os.getenv("LD_LIBRARY_PATH") + if env_ld_library_path and not dirs: + dirs = [dir for dir in env_ld_library_path.split(":") if os.path.exists(os.path.join(dir, "libcuda.so.1"))] + msg = 'libcuda.so cannot found!\n' + if locs: + msg += 'Possible files are located at %s.' % str(locs) + msg += 'Please create a symlink of libcuda.so to any of the files.' + else: + msg += 'Please make sure GPU is set up and then run "/sbin/ldconfig"' + msg += ' (requires sudo) to refresh the linker cache.' + assert any(os.path.exists(os.path.join(path, 'libcuda.so.1')) for path in dirs), msg + return dirs + + +@functools.lru_cache() +def library_dirs(): + return [libdevice_dir, *libcuda_dirs()] + + +def compile_module_from_src(src, name): + key = hashlib.sha256(src.encode("utf-8")).hexdigest() + cache = get_cache_manager(key) + cache_path = cache.get_file(f"{name}.so") + if cache_path is None: + with tempfile.TemporaryDirectory() as tmpdir: + src_path = os.path.join(tmpdir, "main.c") + with open(src_path, "w") as f: + f.write(src) + so = _build(name, src_path, tmpdir, library_dirs(), include_dir, libraries) + with open(so, "rb") as f: + cache_path = cache.put(f.read(), f"{name}.so", binary=True) + import importlib.util + spec = importlib.util.spec_from_file_location(name, cache_path) + mod = importlib.util.module_from_spec(spec) + spec.loader.exec_module(mod) + return mod + + +# ------------------------ +# Utils +# ------------------------ + + +class CudaUtils(object): + + def __new__(cls): + if not hasattr(cls, "instance"): + cls.instance = super(CudaUtils, cls).__new__(cls) + return cls.instance + + def __init__(self): + mod = compile_module_from_src(Path(os.path.join(dirname, "driver.c")).read_text(), "cuda_utils") + self.load_binary = mod.load_binary + self.get_device_properties = mod.get_device_properties + self.cuOccupancyMaxActiveClusters = mod.cuOccupancyMaxActiveClusters + self.set_printf_fifo_size = mod.set_printf_fifo_size + self.fill_1d_tma_descriptor = mod.fill_1d_tma_descriptor + self.fill_2d_tma_descriptor = mod.fill_2d_tma_descriptor + + +# ------------------------ +# Launcher +# ------------------------ + + +def ty_to_cpp(ty): + if ty[0] == '*': + return "CUdeviceptr" + return { + "i1": "int32_t", + "i8": "int8_t", + "i16": "int16_t", + "i32": "int32_t", + "i64": "int64_t", + "u1": "uint32_t", + "u8": "uint8_t", + "u16": "uint16_t", + "u32": "uint32_t", + "u64": "uint64_t", + "fp16": "float", + "bf16": "float", + "fp32": "float", + "f32": "float", + "fp64": "double", + "nvTmaDesc": "CUtensorMap", + }[ty] + + +def make_launcher(constants, signature, ids): + # Record the end of regular arguments; + # subsequent arguments are architecture-specific descriptors, such as tensor descriptors for CUDA. + arg_decls = ', '.join(f"{ty_to_cpp(ty)} arg{i}" for i, ty in signature.items()) + + def _extracted_type(ty): + if ty[0] == '*': + return "PyObject*" + if ty == "nvTmaDesc": + return "PyObject*" + + return ty_to_cpp(ty) + + def format_of(ty): + return { + "PyObject*": "O", + "float": "f", + "double": "d", + "long": "l", + "int8_t": "b", + "int16_t": "h", + "int32_t": "i", + "int64_t": "l", + "uint8_t": "B", + "uint16_t": "H", + "uint32_t": "I", + "uint64_t": "K", + }[ty] + + args_format = ''.join([format_of(_extracted_type(ty)) for ty in signature.values()]) + format = "iiiKKOOOO" + args_format + args_list = ', ' + ', '.join(f"&_arg{i}" for i, ty in signature.items()) if len(signature) > 0 else '' + + internal_args_list = [] + for i, ty in signature.items(): + if ty[0] == "*": + internal_args_list.append(f"ptr_info{i}.dev_ptr") + elif ty == "nvTmaDesc": + # Note: we have to dereference the pointer + internal_args_list.append(f"*tma_ptr{i}") + else: + internal_args_list.append(f"_arg{i}") + + # generate glue code + params = [i for i in signature.keys() if i not in constants] + src = f""" +#include \"cuda.h\" +#include +#include +#include + +static inline void gpuAssert(CUresult code, const char *file, int line) +{{ + if (code != CUDA_SUCCESS) + {{ + const char* prefix = "Triton Error [CUDA]: "; + const char* str; + cuGetErrorString(code, &str); + char err[1024] = {{0}}; + strcat(err, prefix); + strcat(err, str); + PyGILState_STATE gil_state; + gil_state = PyGILState_Ensure(); + PyErr_SetString(PyExc_RuntimeError, err); + PyGILState_Release(gil_state); + }} +}} + +#define CUDA_CHECK(ans) {{ gpuAssert((ans), __FILE__, __LINE__); }} + +typedef CUresult (*cuLaunchKernelEx_t)(const CUlaunchConfig* config, CUfunction f, void** kernelParams, void** extra); + +static cuLaunchKernelEx_t getLaunchKernelExHandle() {{ + // Open the shared library + void* handle = dlopen("libcuda.so.1", RTLD_LAZY); + if (!handle) {{ + PyErr_SetString(PyExc_RuntimeError, "Failed to open libcuda.so.1"); + return NULL; + }} + // Clear any existing error + dlerror(); + cuLaunchKernelEx_t cuLaunchKernelExHandle = (cuLaunchKernelEx_t)dlsym(handle, "cuLaunchKernelEx"); + // Check for errors + const char *dlsym_error = dlerror(); + if (dlsym_error) {{ + PyErr_SetString(PyExc_RuntimeError, "Failed to retrieve cuLaunchKernelEx from libcuda.so.1"); + return NULL; + }} + return cuLaunchKernelExHandle; +}} + +static void _launch(int gridX, int gridY, int gridZ, int num_warps, int num_ctas, int clusterDimX, int clusterDimY, int clusterDimZ, int shared_memory, CUstream stream, CUfunction function{', ' + arg_decls if len(arg_decls) > 0 else ''}) {{ + void *params[] = {{ {', '.join(f"&arg{i}" for i in params)} }}; + if (gridX*gridY*gridZ > 0) {{ + if (num_ctas == 1) {{ + CUDA_CHECK(cuLaunchKernel(function, gridX, gridY, gridZ, 32*num_warps, 1, 1, shared_memory, stream, params, 0)); + }} else {{ + CUlaunchAttribute launchAttr[2]; + launchAttr[0].id = CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION; + launchAttr[0].value.clusterDim.x = clusterDimX; + launchAttr[0].value.clusterDim.y = clusterDimY; + launchAttr[0].value.clusterDim.z = clusterDimZ; + launchAttr[1].id = CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE; + launchAttr[1].value.clusterSchedulingPolicyPreference = CU_CLUSTER_SCHEDULING_POLICY_SPREAD; + CUlaunchConfig config; + config.gridDimX = gridX * clusterDimX; + config.gridDimY = gridY * clusterDimY; + config.gridDimZ = gridZ * clusterDimZ; + config.blockDimX = 32 * num_warps; + config.blockDimY = 1; + config.blockDimZ = 1; + config.sharedMemBytes = shared_memory; + config.hStream = stream; + config.attrs = launchAttr; + config.numAttrs = 2; + static cuLaunchKernelEx_t cuLaunchKernelExHandle = NULL; + if (cuLaunchKernelExHandle == NULL) {{ + cuLaunchKernelExHandle = getLaunchKernelExHandle(); + }} + CUDA_CHECK(cuLaunchKernelExHandle(&config, function, params, 0)); + }} + }} +}} + +typedef struct _DevicePtrInfo {{ + CUdeviceptr dev_ptr; + bool valid; +}} DevicePtrInfo; + +static inline DevicePtrInfo getPointer(PyObject *obj, int idx) {{ + DevicePtrInfo ptr_info; + ptr_info.dev_ptr = 0; + ptr_info.valid = true; + if (PyLong_Check(obj)) {{ + ptr_info.dev_ptr = PyLong_AsUnsignedLongLong(obj); + return ptr_info; + }} + if (obj == Py_None) {{ + // valid nullptr + return ptr_info; + }} + PyObject *ptr = PyObject_GetAttrString(obj, "data_ptr"); + if(ptr){{ + PyObject *empty_tuple = PyTuple_New(0); + PyObject *ret = PyObject_Call(ptr, empty_tuple, NULL); + Py_DECREF(empty_tuple); + Py_DECREF(ptr); + if (!PyLong_Check(ret)) {{ + PyErr_SetString(PyExc_TypeError, "data_ptr method of Pointer object must return 64-bit int"); + ptr_info.valid = false; + return ptr_info; + }} + ptr_info.dev_ptr = PyLong_AsUnsignedLongLong(ret); + if(!ptr_info.dev_ptr) + return ptr_info; + uint64_t dev_ptr; + int status = cuPointerGetAttribute(&dev_ptr, CU_POINTER_ATTRIBUTE_DEVICE_POINTER, ptr_info.dev_ptr); + if (status == CUDA_ERROR_INVALID_VALUE) {{ + PyErr_Format(PyExc_ValueError, + "Pointer argument (at %d) cannot be accessed from Triton (cpu tensor?)", idx); + ptr_info.valid = false; + }} else if (status != CUDA_SUCCESS) {{ + CUDA_CHECK(status); // Catch any other cuda API errors + ptr_info.valid = false; + }} + ptr_info.dev_ptr = dev_ptr; + Py_DECREF(ret); // Thanks ChatGPT! + return ptr_info; + }} + PyErr_SetString(PyExc_TypeError, "Pointer argument must be either uint64 or have data_ptr method"); + ptr_info.valid = false; + return ptr_info; +}} + +static inline CUtensorMap* getTmaDesc(PyObject *obj) {{ + if (sizeof(CUtensorMap*) != 8) {{ + PyErr_SetString(PyExc_SystemError, "getTmaDesc() requires 64-bit compilation"); + return NULL; + }} + + PyObject *method_handle = PyObject_GetAttrString(obj, "tma_desc_cpu_ptr"); + if (!method_handle) {{ + PyErr_SetString(PyExc_TypeError, "tma_desc_cpu_ptr() method does not exist"); + return NULL; + }} + + PyObject *empty_tuple = PyTuple_New(0); + if (!empty_tuple) {{ + Py_DECREF(method_handle); + PyErr_SetString(PyExc_SystemError, "Internal Python error!"); + return NULL; + }} + PyObject *method_ret = PyObject_Call(method_handle, empty_tuple, NULL); + Py_DECREF(empty_tuple); + Py_DECREF(method_handle); + if (!method_ret) {{ + PyErr_SetString(PyExc_SystemError, "Internal Python error!"); + return NULL; + }} + + if (!PyLong_Check(method_ret)) {{ + PyErr_SetString(PyExc_TypeError, "tma_desc_cpu_ptr() must return 64-bit int"); + Py_DECREF(method_ret); + return NULL; + }} + + uint64_t ptr_as_uint = PyLong_AsUnsignedLongLong(method_ret); + Py_DECREF(method_ret); + if (!ptr_as_uint) {{ + PyErr_SetString(PyExc_ValueError, "received NULL ptr from tma_desc_cpu_ptr()"); + return NULL; + }} + if (ptr_as_uint % 64 != 0) {{ + PyErr_SetString(PyExc_ValueError, "tma_desc_cpu_ptr() must be 64-byte aligned"); + return NULL; + }} + + return (CUtensorMap*)(ptr_as_uint); +}} + +static void ensureCudaContext() {{ + CUcontext pctx; + CUDA_CHECK(cuCtxGetCurrent(&pctx)); + if (!pctx) {{ + // Ensure device context. + CUdevice device; + CUDA_CHECK(cuDeviceGet(&device, 0)); + CUDA_CHECK(cuDevicePrimaryCtxRetain(&pctx, device)); + CUDA_CHECK(cuCtxSetCurrent(pctx)); + }} +}} + +static PyObject* launch(PyObject* self, PyObject* args) {{ + // ensure cuda context is valid before calling any CUDA APIs, e.g. before getPointer calls cuPointerGetAttributes + ensureCudaContext(); + + int gridX, gridY, gridZ; + uint64_t _stream; + uint64_t _function; + PyObject *launch_enter_hook = NULL; + PyObject *launch_exit_hook = NULL; + PyObject *kernel_metadata = NULL; + PyObject *launch_metadata = NULL; + {' '.join([f"{_extracted_type(ty)} _arg{i}; " for i, ty in signature.items()])} + if(!PyArg_ParseTuple(args, \"{format}\", &gridX, &gridY, &gridZ, &_stream, &_function, + &kernel_metadata, &launch_metadata, + &launch_enter_hook, &launch_exit_hook {args_list})) {{ + return NULL; + }} + + int num_warps, num_ctas, shared_memory, clusterDimX, clusterDimY, clusterDimZ; + if (!PyArg_ParseTuple(kernel_metadata, \"iiiiii\", &num_warps, &num_ctas, &shared_memory, &clusterDimX, &clusterDimY, &clusterDimZ)) {{ + PyErr_SetString(PyExc_TypeError, "kernel_metadata must be a tuple"); + return NULL; + }} + + // extract launch metadata + if (launch_enter_hook != Py_None){{ + PyObject* args = Py_BuildValue("(O)", launch_metadata); + PyObject* ret = PyObject_CallObject(launch_enter_hook, args); + Py_DECREF(args); + if (!ret) + return NULL; + }} + + // raise exception asap + {"".join([f"DevicePtrInfo ptr_info{i} = getPointer(_arg{i}, {i}); if (!ptr_info{i}.valid) return NULL;" if ty[0] == "*" else "" for i, ty in signature.items()])}; + {"".join([f"CUtensorMap* tma_ptr{i} = getTmaDesc(_arg{i}); if (!tma_ptr{i}) return NULL;" if ty == "nvTmaDesc" else "" for i, ty in signature.items()])}; + Py_BEGIN_ALLOW_THREADS; + _launch(gridX, gridY, gridZ, num_warps, num_ctas, clusterDimX, clusterDimY, clusterDimZ, shared_memory, (CUstream)_stream, (CUfunction)_function{', ' + ', '.join(internal_args_list) if len(internal_args_list) > 0 else ''}); + Py_END_ALLOW_THREADS; + if (PyErr_Occurred()) {{ + return NULL; + }} + + if(launch_exit_hook != Py_None){{ + PyObject* args = Py_BuildValue("(O)", launch_metadata); + PyObject* ret = PyObject_CallObject(launch_exit_hook, args); + Py_DECREF(args); + if (!ret) + return NULL; + + }} + + // return None + Py_INCREF(Py_None); + return Py_None; +}} + +static PyMethodDef ModuleMethods[] = {{ + {{"launch", launch, METH_VARARGS, "Entry point for all kernels with this signature"}}, + {{NULL, NULL, 0, NULL}} // sentinel +}}; + +static struct PyModuleDef ModuleDef = {{ + PyModuleDef_HEAD_INIT, + \"__triton_launcher\", + NULL, //documentation + -1, //size + ModuleMethods +}}; + +PyMODINIT_FUNC PyInit___triton_launcher(void) {{ + PyObject *m = PyModule_Create(&ModuleDef); + if(m == NULL) {{ + return NULL; + }} + PyModule_AddFunctions(m, ModuleMethods); + return m; +}} +""" + return src + + +class CudaLauncher(object): + + def __init__(self, src, metadata): + ids = {"ids_of_const_exprs": src.fn.constexprs if hasattr(src, "fn") else tuple()} + constants = src.constants if hasattr(src, "constants") else dict() + cst_key = lambda i: src.fn.arg_names.index(i) if isinstance(i, str) else i + constants = {cst_key(key): value for key, value in constants.items()} + signature = {cst_key(key): value for key, value in src.signature.items()} + src = make_launcher(constants, signature, ids) + mod = compile_module_from_src(src, "__triton_launcher") + self.launch = mod.launch + + def __call__(self, *args, **kwargs): + self.launch(*args, **kwargs) + + +class CudaDriver(GPUDriver): + + def __init__(self): + self.utils = CudaUtils() # TODO: make static + self.launcher_cls = CudaLauncher + super().__init__() + + def get_current_target(self): + device = self.get_current_device() + capability = self.get_device_capability(device) + capability = capability[0] * 10 + capability[1] + warp_size = 32 + return GPUTarget("cuda", capability, warp_size) + + def get_device_interface(self): + import torch + return torch.cuda + + @staticmethod + def is_active(): + import torch + return torch.cuda.is_available() and (torch.version.hip is None) + + def get_benchmarker(self): + from triton.testing import do_bench + return do_bench + + def get_empty_cache_for_benchmark(self): + import torch + + # We maintain a buffer of 256 MB that we clear + # before each kernel call to make sure that the L2 cache + # doesn't contain any input data before the run + cache_size = 256 * 1024 * 1024 + return torch.empty(int(cache_size // 4), dtype=torch.int, device='cuda') diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/builtin_types.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/builtin_types.h new file mode 100644 index 0000000000000000000000000000000000000000..5247c40807f0dd36a886513ab1bff5d2977364db --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/builtin_types.h @@ -0,0 +1,64 @@ +/* + * Copyright 1993-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#include "device_types.h" +#if !defined(__CUDACC_RTC__) +#define EXCLUDE_FROM_RTC +#include "driver_types.h" +#undef EXCLUDE_FROM_RTC +#endif /* !__CUDACC_RTC__ */ +#include "surface_types.h" +#include "texture_types.h" +#include "vector_types.h" diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/channel_descriptor.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/channel_descriptor.h new file mode 100644 index 0000000000000000000000000000000000000000..c6f039db8effce996015f901562009ebe976d832 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/channel_descriptor.h @@ -0,0 +1,588 @@ +/* + * Copyright 1993-2012 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CHANNEL_DESCRIPTOR_H__) +#define __CHANNEL_DESCRIPTOR_H__ + +#if defined(__cplusplus) + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#include "cuda_runtime_api.h" + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +/** + * \addtogroup CUDART_HIGHLEVEL + * + * @{ + */ + +/** + * \brief \hl Returns a channel descriptor using the specified format + * + * Returns a channel descriptor with format \p f and number of bits of each + * component \p x, \p y, \p z, and \p w. The ::cudaChannelFormatDesc is + * defined as: + * \code + struct cudaChannelFormatDesc { + int x, y, z, w; + enum cudaChannelFormatKind f; + }; + * \endcode + * + * where ::cudaChannelFormatKind is one of ::cudaChannelFormatKindSigned, + * ::cudaChannelFormatKindUnsigned, cudaChannelFormatKindFloat, + * ::cudaChannelFormatKindSignedNormalized8X1, ::cudaChannelFormatKindSignedNormalized8X2, + * ::cudaChannelFormatKindSignedNormalized8X4, + * ::cudaChannelFormatKindUnsignedNormalized8X1, ::cudaChannelFormatKindUnsignedNormalized8X2, + * ::cudaChannelFormatKindUnsignedNormalized8X4, + * ::cudaChannelFormatKindSignedNormalized16X1, ::cudaChannelFormatKindSignedNormalized16X2, + * ::cudaChannelFormatKindSignedNormalized16X4, + * ::cudaChannelFormatKindUnsignedNormalized16X1, ::cudaChannelFormatKindUnsignedNormalized16X2, + * ::cudaChannelFormatKindUnsignedNormalized16X4 + * or ::cudaChannelFormatKindNV12. + * + * The format is specified by the template specialization. + * + * The template function specializes for the following scalar types: + * char, signed char, unsigned char, short, unsigned short, int, unsigned int, long, unsigned long, and float. + * The template function specializes for the following vector types: + * char{1|2|4}, uchar{1|2|4}, short{1|2|4}, ushort{1|2|4}, int{1|2|4}, uint{1|2|4}, long{1|2|4}, ulong{1|2|4}, float{1|2|4}. + * The template function specializes for following cudaChannelFormatKind enum values: + * ::cudaChannelFormatKind{Uns|S}ignedNormalized{8|16}X{1|2|4}, and ::cudaChannelFormatKindNV12. + * + * Invoking the function on a type without a specialization defaults to creating a channel format of kind ::cudaChannelFormatKindNone + * + * \return + * Channel descriptor with format \p f + * + * \sa \ref ::cudaCreateChannelDesc(int,int,int,int,cudaChannelFormatKind) "cudaCreateChannelDesc (Low level)", + * ::cudaGetChannelDesc, + */ +template __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(0, 0, 0, 0, cudaChannelFormatKindNone); +} + +static __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDescHalf(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindFloat); +} + +static __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDescHalf1(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindFloat); +} + +static __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDescHalf2(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindFloat); +} + +static __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDescHalf4(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindFloat); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(char) * 8; + +#if defined(_CHAR_UNSIGNED) || defined(__CHAR_UNSIGNED__) + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +#else /* _CHAR_UNSIGNED || __CHAR_UNSIGNED__ */ + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +#endif /* _CHAR_UNSIGNED || __CHAR_UNSIGNED__ */ +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(signed char) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned char) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(signed char) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned char) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(signed char) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned char) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(signed char) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned char) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(short) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(short) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned short) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(int) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned int) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(int) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned int) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(int) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned int) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(int) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned int) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindUnsigned); +} + +#if !defined(__LP64__) + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(long) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned long) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(long) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned long) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(long) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned long) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindUnsigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(long) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindSigned); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(unsigned long) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindUnsigned); +} + +#endif /* !__LP64__ */ + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(float) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindFloat); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(float) * 8; + + return cudaCreateChannelDesc(e, 0, 0, 0, cudaChannelFormatKindFloat); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(float) * 8; + + return cudaCreateChannelDesc(e, e, 0, 0, cudaChannelFormatKindFloat); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + int e = (int)sizeof(float) * 8; + + return cudaCreateChannelDesc(e, e, e, e, cudaChannelFormatKindFloat); +} + +static __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDescNV12(void) +{ + int e = (int)sizeof(char) * 8; + + return cudaCreateChannelDesc(e, e, e, 0, cudaChannelFormatKindNV12); +} + +template __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(0, 0, 0, 0, cudaChannelFormatKindNone); +} + +/* Signed 8-bit normalized integer formats */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 0, 0, 0, cudaChannelFormatKindSignedNormalized8X1); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 0, 0, cudaChannelFormatKindSignedNormalized8X2); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindSignedNormalized8X4); +} + +/* Unsigned 8-bit normalized integer formats */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 0, 0, 0, cudaChannelFormatKindUnsignedNormalized8X1); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 0, 0, cudaChannelFormatKindUnsignedNormalized8X2); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedNormalized8X4); +} + +/* Signed 16-bit normalized integer formats */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 0, 0, 0, cudaChannelFormatKindSignedNormalized16X1); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 0, 0, cudaChannelFormatKindSignedNormalized16X2); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 16, 16, cudaChannelFormatKindSignedNormalized16X4); +} + +/* Unsigned 16-bit normalized integer formats */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 0, 0, 0, cudaChannelFormatKindUnsignedNormalized16X1); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 0, 0, cudaChannelFormatKindUnsignedNormalized16X2); +} + +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 16, 16, cudaChannelFormatKindUnsignedNormalized16X4); +} + +/* NV12 format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 0, cudaChannelFormatKindNV12); +} + +/* BC1 format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed1); +} + +/* BC1sRGB format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed1SRGB); +} + +/* BC2 format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed2); +} + +/* BC2sRGB format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed2SRGB); +} + +/* BC3 format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed3); +} + +/* BC3sRGB format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed3SRGB); +} + +/* BC4 unsigned format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 0, 0, 0, cudaChannelFormatKindUnsignedBlockCompressed4); +} + +/* BC4 signed format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 0, 0, 0, cudaChannelFormatKindSignedBlockCompressed4); +} + +/* BC5 unsigned format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 0, 0, cudaChannelFormatKindUnsignedBlockCompressed5); +} + +/* BC5 signed format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 0, 0, cudaChannelFormatKindSignedBlockCompressed5); +} + +/* BC6H unsigned format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 16, 0, cudaChannelFormatKindUnsignedBlockCompressed6H); +} + +/* BC6H signed format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(16, 16, 16, 0, cudaChannelFormatKindSignedBlockCompressed6H); +} + +/* BC7 format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed7); +} + +/* BC7sRGB format */ +template<> __inline__ __host__ cudaChannelFormatDesc cudaCreateChannelDesc(void) +{ + return cudaCreateChannelDesc(8, 8, 8, 8, cudaChannelFormatKindUnsignedBlockCompressed7SRGB); +} + +#endif /* __cplusplus */ + +/** @} */ +/** @} */ /* END CUDART_TEXTURE_HL */ + +#endif /* !__CHANNEL_DESCRIPTOR_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/common_functions.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/common_functions.h new file mode 100644 index 0000000000000000000000000000000000000000..5f8ea3d242640f2196b789c7da6c05d2ed1bed3e --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/common_functions.h @@ -0,0 +1,65 @@ +/* + * Copyright 1993-2018 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__) +#if defined(_MSC_VER) +#pragma message("common_functions.h is an internal header file and must not be used directly. This file will be removed in a future CUDA release. Please use cuda_runtime_api.h or cuda_runtime.h instead.") +#else +#warning "common_functions.h is an internal header file and must not be used directly. This file will be removed in a future CUDA release. Please use cuda_runtime_api.h or cuda_runtime.h instead." +#endif +#define __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#define __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_COMMON_FUNCTIONS_H_WRAPPER__ +#endif + +#include "crt/common_functions.h" + +#if defined(__UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_COMMON_FUNCTIONS_H_WRAPPER__) +#undef __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#undef __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_COMMON_FUNCTIONS_H_WRAPPER__ +#endif diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cooperative_groups.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cooperative_groups.h new file mode 100644 index 0000000000000000000000000000000000000000..e04314301c1cca9e2514f56367e1dbc45cfdad69 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cooperative_groups.h @@ -0,0 +1,1730 @@ +/* + * Copyright 1993-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _COOPERATIVE_GROUPS_H_ +#define _COOPERATIVE_GROUPS_H_ + +#if defined(__cplusplus) && defined(__CUDACC__) + +#include "cooperative_groups/details/info.h" +#include "cooperative_groups/details/driver_abi.h" +#include "cooperative_groups/details/helpers.h" +#include "cooperative_groups/details/memory.h" + +#if defined(_CG_HAS_STL_ATOMICS) +#include +#define _CG_THREAD_SCOPE(scope) _CG_STATIC_CONST_DECL cuda::thread_scope thread_scope = scope; +#else +#define _CG_THREAD_SCOPE(scope) +#endif + +_CG_BEGIN_NAMESPACE + +namespace details { + _CG_CONST_DECL unsigned int coalesced_group_id = 1; + _CG_CONST_DECL unsigned int multi_grid_group_id = 2; + _CG_CONST_DECL unsigned int grid_group_id = 3; + _CG_CONST_DECL unsigned int thread_block_id = 4; + _CG_CONST_DECL unsigned int multi_tile_group_id = 5; + _CG_CONST_DECL unsigned int cluster_group_id = 6; +} + +/** + * class thread_group; + * + * Generic thread group type, into which all groups are convertible. + * It acts as a container for all storage necessary for the derived groups, + * and will dispatch the API calls to the correct derived group. This means + * that all derived groups must implement the same interface as thread_group. + */ +class thread_group +{ +protected: + struct group_data { + unsigned int _unused : 1; + unsigned int type : 7, : 0; + }; + + struct gg_data { + details::grid_workspace *gridWs; + }; + +#if defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) + struct mg_data { + unsigned long long _unused : 1; + unsigned long long type : 7; + unsigned long long handle : 56; + const details::multi_grid::multi_grid_functions *functions; + }; +#endif + + struct tg_data { + unsigned int is_tiled : 1; + unsigned int type : 7; + unsigned int size : 24; + // packed to 4b + unsigned int metaGroupSize : 16; + unsigned int metaGroupRank : 16; + // packed to 8b + unsigned int mask; + // packed to 12b + unsigned int _res; + }; + + friend _CG_QUALIFIER thread_group tiled_partition(const thread_group& parent, unsigned int tilesz); + friend class thread_block; + + union __align__(8) { + group_data group; + tg_data coalesced; + gg_data grid; +#if defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) + mg_data multi_grid; +#endif + } _data; + + _CG_QUALIFIER thread_group operator=(const thread_group& src); + + _CG_QUALIFIER thread_group(unsigned int type) { + _data.group.type = type; + _data.group._unused = false; + } + +#ifdef _CG_CPP11_FEATURES + static_assert(sizeof(tg_data) <= 16, "Failed size check"); + static_assert(sizeof(gg_data) <= 16, "Failed size check"); +# ifdef _CG_ABI_EXPERIMENTAL + static_assert(sizeof(mg_data) <= 16, "Failed size check"); +# endif +#endif + +public: + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_device) + + _CG_QUALIFIER unsigned long long size() const; + _CG_QUALIFIER unsigned long long num_threads() const; + _CG_QUALIFIER unsigned long long thread_rank() const; + _CG_QUALIFIER void sync() const; + _CG_QUALIFIER unsigned int get_type() const { + return _data.group.type; + } + +}; + +template +struct thread_group_base : public thread_group { + _CG_QUALIFIER thread_group_base() : thread_group(TyId) {} + _CG_STATIC_CONST_DECL unsigned int id = TyId; +}; + +#if defined(_CG_HAS_MULTI_GRID_GROUP) + +/** + * class multi_grid_group; + * + * Threads within this this group are guaranteed to be co-resident on the + * same system, on multiple devices within the same launched kernels. + * To use this group, the kernel must have been launched with + * cuLaunchCooperativeKernelMultiDevice (or the CUDA Runtime equivalent), + * and the device must support it (queryable device attribute). + * + * Constructed via this_multi_grid(); + */ + + +# if defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) +class multi_grid_group; + +// Multi grid group requires these functions to be templated to prevent ptxas from trying to use CG syscalls +template +__device__ _CG_DEPRECATED multi_grid_group this_multi_grid(); + +class multi_grid_group : public thread_group_base +{ +private: + template + _CG_QUALIFIER multi_grid_group() { + _data.multi_grid.functions = details::multi_grid::load_grid_intrinsics(); + _data.multi_grid.handle = _data.multi_grid.functions->get_intrinsic_handle(); + } + + friend multi_grid_group this_multi_grid(); + +public: + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_system) + + _CG_QUALIFIER bool is_valid() const { + return (_data.multi_grid.handle != 0); + } + + _CG_QUALIFIER void sync() const { + if (!is_valid()) { + _CG_ABORT(); + } + _data.multi_grid.functions->sync(_data.multi_grid.handle); + } + + _CG_QUALIFIER unsigned long long num_threads() const { + _CG_ASSERT(is_valid()); + return _data.multi_grid.functions->size(_data.multi_grid.handle); + } + + _CG_QUALIFIER unsigned long long size() const { + return num_threads(); + } + + _CG_QUALIFIER unsigned long long thread_rank() const { + _CG_ASSERT(is_valid()); + return _data.multi_grid.functions->thread_rank(_data.multi_grid.handle); + } + + _CG_QUALIFIER unsigned int grid_rank() const { + _CG_ASSERT(is_valid()); + return (_data.multi_grid.functions->grid_rank(_data.multi_grid.handle)); + } + + _CG_QUALIFIER unsigned int num_grids() const { + _CG_ASSERT(is_valid()); + return (_data.multi_grid.functions->num_grids(_data.multi_grid.handle)); + } +}; +# else +class multi_grid_group +{ +private: + unsigned long long _handle; + unsigned int _size; + unsigned int _rank; + + friend _CG_QUALIFIER multi_grid_group this_multi_grid(); + + _CG_QUALIFIER multi_grid_group() { + _handle = details::multi_grid::get_intrinsic_handle(); + _size = details::multi_grid::size(_handle); + _rank = details::multi_grid::thread_rank(_handle); + } + +public: + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_system) + + _CG_QUALIFIER _CG_DEPRECATED bool is_valid() const { + return (_handle != 0); + } + + _CG_QUALIFIER _CG_DEPRECATED void sync() const { + if (!is_valid()) { + _CG_ABORT(); + } + details::multi_grid::sync(_handle); + } + + _CG_QUALIFIER _CG_DEPRECATED unsigned long long num_threads() const { + _CG_ASSERT(is_valid()); + return _size; + } + + _CG_QUALIFIER _CG_DEPRECATED unsigned long long size() const { + return num_threads(); + } + + _CG_QUALIFIER _CG_DEPRECATED unsigned long long thread_rank() const { + _CG_ASSERT(is_valid()); + return _rank; + } + + _CG_QUALIFIER _CG_DEPRECATED unsigned int grid_rank() const { + _CG_ASSERT(is_valid()); + return (details::multi_grid::grid_rank(_handle)); + } + + _CG_QUALIFIER _CG_DEPRECATED unsigned int num_grids() const { + _CG_ASSERT(is_valid()); + return (details::multi_grid::num_grids(_handle)); + } +}; +# endif + +/** + * multi_grid_group this_multi_grid() + * + * Constructs a multi_grid_group + */ +# if defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) +template +__device__ +#else +_CG_QUALIFIER +# endif +_CG_DEPRECATED +multi_grid_group this_multi_grid() +{ + return multi_grid_group(); +} +#endif + +/** + * class grid_group; + * + * Threads within this this group are guaranteed to be co-resident on the + * same device within the same launched kernel. To use this group, the kernel + * must have been launched with cuLaunchCooperativeKernel (or the CUDA Runtime equivalent), + * and the device must support it (queryable device attribute). + * + * Constructed via this_grid(); + */ +class grid_group : public thread_group_base +{ + _CG_STATIC_CONST_DECL unsigned int _group_id = details::grid_group_id; + friend _CG_QUALIFIER grid_group this_grid(); + +private: + _CG_QUALIFIER grid_group(details::grid_workspace *gridWs) { + _data.grid.gridWs = gridWs; + } + + public: + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_device) + + _CG_QUALIFIER bool is_valid() const { + return (_data.grid.gridWs != NULL); + } + + _CG_QUALIFIER void sync() const { + if (!is_valid()) { + _CG_ABORT(); + } + details::grid::sync(&_data.grid.gridWs->barrier); + } + +#if defined(_CG_CPP11_FEATURES) + using arrival_token = unsigned int; + + _CG_QUALIFIER arrival_token barrier_arrive() const { + if (!is_valid()) { + _CG_ABORT(); + } + return details::grid::barrier_arrive(&_data.grid.gridWs->barrier); + } + + _CG_QUALIFIER void barrier_wait(arrival_token&& token) const { + details::grid::barrier_wait(token, &_data.grid.gridWs->barrier); + } +#endif + + _CG_STATIC_QUALIFIER unsigned long long size() { + return details::grid::size(); + } + + _CG_STATIC_QUALIFIER dim3 group_dim() { + return details::grid::grid_dim(); + } + + _CG_STATIC_QUALIFIER dim3 dim_threads() { + return details::grid::dim_threads(); + } + + _CG_STATIC_QUALIFIER unsigned long long num_threads() { + return details::grid::num_threads(); + } + + _CG_STATIC_QUALIFIER dim3 thread_index() { + return details::grid::thread_index(); + } + + _CG_STATIC_QUALIFIER unsigned long long thread_rank() { + return details::grid::thread_rank(); + } + + _CG_STATIC_QUALIFIER dim3 dim_blocks() { + return details::grid::dim_blocks(); + } + + _CG_STATIC_QUALIFIER unsigned long long num_blocks() { + return details::grid::num_blocks(); + } + + _CG_STATIC_QUALIFIER dim3 block_index() { + return details::grid::block_index(); + } + + _CG_STATIC_QUALIFIER unsigned long long block_rank() { + return details::grid::block_rank(); + } + +# if defined(_CG_HAS_CLUSTER_GROUP) + _CG_STATIC_QUALIFIER dim3 dim_clusters() { + return details::grid::dim_clusters(); + } + + _CG_STATIC_QUALIFIER unsigned long long num_clusters() { + return details::grid::num_clusters(); + } + + _CG_STATIC_QUALIFIER dim3 cluster_index() { + return details::grid::cluster_index(); + } + + _CG_STATIC_QUALIFIER unsigned long long cluster_rank() { + return details::grid::cluster_rank(); + } +# endif +}; + +_CG_QUALIFIER grid_group this_grid() { + // Load a workspace from the driver + grid_group gg(details::get_grid_workspace()); +#ifdef _CG_DEBUG + // *all* threads must be available to synchronize + gg.sync(); +#endif // _CG_DEBUG + return gg; +} + +#if defined(_CG_HAS_CLUSTER_GROUP) +/** + * class cluster_group + * + * Every GPU kernel is executed by a grid of thread blocks. A grid can be evenly + * divided along all dimensions to form groups of blocks, each group of which is + * a block cluster. Clustered grids are subject to various restrictions and + * limitations. Primarily, a cluster consists of at most 8 blocks by default + * (although the user is allowed to opt-in to non-standard sizes,) and clustered + * grids are subject to additional occupancy limitations due to per-cluster + * hardware resource consumption. In exchange, a block cluster is guaranteed to + * be a cooperative group, with access to all cooperative group capabilities, as + * well as cluster specific capabilities and accelerations. A cluster_group + * represents a block cluster. + * + * Constructed via this_cluster_group(); + */ +class cluster_group : public thread_group_base +{ + // Friends + friend _CG_QUALIFIER cluster_group this_cluster(); + + // Disable constructor + _CG_QUALIFIER cluster_group() + { + } + + public: + //_CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_cluster) + + using arrival_token = struct {}; + + // Functionality exposed by the group + _CG_STATIC_QUALIFIER void sync() + { + return details::cluster::sync(); + } + + _CG_STATIC_QUALIFIER arrival_token barrier_arrive() + { + details::cluster::barrier_arrive(); + return arrival_token(); + } + + _CG_STATIC_QUALIFIER void barrier_wait() + { + return details::cluster::barrier_wait(); + } + + _CG_STATIC_QUALIFIER void barrier_wait(arrival_token&&) + { + return details::cluster::barrier_wait(); + } + + _CG_STATIC_QUALIFIER unsigned int query_shared_rank(const void *addr) + { + return details::cluster::query_shared_rank(addr); + } + + template + _CG_STATIC_QUALIFIER T* map_shared_rank(T *addr, int rank) + { + return details::cluster::map_shared_rank(addr, rank); + } + + _CG_STATIC_QUALIFIER dim3 block_index() + { + return details::cluster::block_index(); + } + + _CG_STATIC_QUALIFIER unsigned int block_rank() + { + return details::cluster::block_rank(); + } + + _CG_STATIC_QUALIFIER dim3 thread_index() + { + return details::cluster::thread_index(); + } + + _CG_STATIC_QUALIFIER unsigned int thread_rank() + { + return details::cluster::thread_rank(); + } + + _CG_STATIC_QUALIFIER dim3 dim_blocks() + { + return details::cluster::dim_blocks(); + } + + _CG_STATIC_QUALIFIER unsigned int num_blocks() + { + return details::cluster::num_blocks(); + } + + _CG_STATIC_QUALIFIER dim3 dim_threads() + { + return details::cluster::dim_threads(); + } + + _CG_STATIC_QUALIFIER unsigned int num_threads() + { + return details::cluster::num_threads(); + } + + // Legacy aliases + _CG_STATIC_QUALIFIER unsigned int size() + { + return num_threads(); + } +}; + +/* + * cluster_group this_cluster() + * + * Constructs a cluster_group + */ +_CG_QUALIFIER cluster_group this_cluster() +{ + cluster_group cg; +#ifdef _CG_DEBUG + cg.sync(); +#endif + return cg; +} +#endif + +#if defined(_CG_CPP11_FEATURES) +class thread_block; +template +_CG_QUALIFIER thread_block this_thread_block(block_tile_memory& scratch); +#endif + +/** + * class thread_block + * + * Every GPU kernel is executed by a grid of thread blocks, and threads within + * each block are guaranteed to reside on the same streaming multiprocessor. + * A thread_block represents a thread block whose dimensions are not known until runtime. + * + * Constructed via this_thread_block(); + */ +class thread_block : public thread_group_base +{ + // Friends + friend _CG_QUALIFIER thread_block this_thread_block(); + friend _CG_QUALIFIER thread_group tiled_partition(const thread_group& parent, unsigned int tilesz); + friend _CG_QUALIFIER thread_group tiled_partition(const thread_block& parent, unsigned int tilesz); + +#if defined(_CG_CPP11_FEATURES) + template + friend _CG_QUALIFIER thread_block this_thread_block(block_tile_memory& scratch); + template + friend class __static_size_multi_warp_tile_base; + + details::multi_warp_scratch* const tile_memory; + + template + _CG_QUALIFIER thread_block(block_tile_memory& scratch) : + tile_memory(details::get_scratch_ptr(&scratch)) { +#ifdef _CG_DEBUG + if (num_threads() > MaxBlockSize) { + details::abort(); + } +#endif +#if !defined(_CG_HAS_RESERVED_SHARED) + tile_memory->init_barriers(thread_rank()); + sync(); +#endif + } +#endif + + // Disable constructor + _CG_QUALIFIER thread_block() +#if defined(_CG_CPP11_FEATURES) + : tile_memory(details::get_scratch_ptr(NULL)) +#endif + { } + + // Internal Use + _CG_QUALIFIER thread_group _get_tiled_threads(unsigned int tilesz) const { + const bool pow2_tilesz = ((tilesz & (tilesz - 1)) == 0); + + // Invalid, immediately fail + if (tilesz == 0 || (tilesz > 32) || !pow2_tilesz) { + details::abort(); + return (thread_block()); + } + + unsigned int mask; + unsigned int base_offset = thread_rank() & (~(tilesz - 1)); + unsigned int masklength = min((unsigned int)size() - base_offset, tilesz); + + mask = (unsigned int)(-1) >> (32 - masklength); + mask <<= (details::laneid() & ~(tilesz - 1)); + thread_group tile = thread_group(details::coalesced_group_id); + tile._data.coalesced.mask = mask; + tile._data.coalesced.size = __popc(mask); + tile._data.coalesced.metaGroupSize = (details::cta::size() + tilesz - 1) / tilesz; + tile._data.coalesced.metaGroupRank = details::cta::thread_rank() / tilesz; + tile._data.coalesced.is_tiled = true; + return (tile); + } + + public: + _CG_STATIC_CONST_DECL unsigned int _group_id = details::thread_block_id; + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_block) + + _CG_STATIC_QUALIFIER void sync() { + details::cta::sync(); + } + +#if defined(_CG_CPP11_FEATURES) + struct arrival_token {}; + + _CG_QUALIFIER arrival_token barrier_arrive() const { + return arrival_token(); + } + + _CG_QUALIFIER void barrier_wait(arrival_token&&) const { + details::cta::sync(); + } +#endif + + _CG_STATIC_QUALIFIER unsigned int size() { + return details::cta::size(); + } + + _CG_STATIC_QUALIFIER unsigned int thread_rank() { + return details::cta::thread_rank(); + } + + // Additional functionality exposed by the group + _CG_STATIC_QUALIFIER dim3 group_index() { + return details::cta::group_index(); + } + + _CG_STATIC_QUALIFIER dim3 thread_index() { + return details::cta::thread_index(); + } + + _CG_STATIC_QUALIFIER dim3 group_dim() { + return details::cta::block_dim(); + } + + _CG_STATIC_QUALIFIER dim3 dim_threads() { + return details::cta::dim_threads(); + } + + _CG_STATIC_QUALIFIER unsigned int num_threads() { + return details::cta::num_threads(); + } + +}; + +/** + * thread_block this_thread_block() + * + * Constructs a thread_block group + */ +_CG_QUALIFIER thread_block this_thread_block() +{ + return (thread_block()); +} + +#if defined(_CG_CPP11_FEATURES) +template +_CG_QUALIFIER thread_block this_thread_block(block_tile_memory& scratch) { + return (thread_block(scratch)); +} +#endif + +/** + * class coalesced_group + * + * A group representing the current set of converged threads in a warp. + * The size of the group is not guaranteed and it may return a group of + * only one thread (itself). + * + * This group exposes warp-synchronous builtins. + * Constructed via coalesced_threads(); + */ +class coalesced_group : public thread_group_base +{ +private: + friend _CG_QUALIFIER coalesced_group coalesced_threads(); + friend _CG_QUALIFIER thread_group tiled_partition(const thread_group& parent, unsigned int tilesz); + friend _CG_QUALIFIER coalesced_group tiled_partition(const coalesced_group& parent, unsigned int tilesz); + friend class details::_coalesced_group_data_access; + + _CG_QUALIFIER unsigned int _packLanes(unsigned laneMask) const { + unsigned int member_pack = 0; + unsigned int member_rank = 0; + for (int bit_idx = 0; bit_idx < 32; bit_idx++) { + unsigned int lane_bit = _data.coalesced.mask & (1 << bit_idx); + if (lane_bit) { + if (laneMask & lane_bit) + member_pack |= 1 << member_rank; + member_rank++; + } + } + return (member_pack); + } + + // Internal Use + _CG_QUALIFIER coalesced_group _get_tiled_threads(unsigned int tilesz) const { + const bool pow2_tilesz = ((tilesz & (tilesz - 1)) == 0); + + // Invalid, immediately fail + if (tilesz == 0 || (tilesz > 32) || !pow2_tilesz) { + details::abort(); + return (coalesced_group(0)); + } + if (size() <= tilesz) { + return (*this); + } + + if ((_data.coalesced.is_tiled == true) && pow2_tilesz) { + unsigned int base_offset = (thread_rank() & (~(tilesz - 1))); + unsigned int masklength = min((unsigned int)size() - base_offset, tilesz); + unsigned int mask = (unsigned int)(-1) >> (32 - masklength); + + mask <<= (details::laneid() & ~(tilesz - 1)); + coalesced_group coalesced_tile = coalesced_group(mask); + coalesced_tile._data.coalesced.metaGroupSize = size() / tilesz; + coalesced_tile._data.coalesced.metaGroupRank = thread_rank() / tilesz; + coalesced_tile._data.coalesced.is_tiled = true; + return (coalesced_tile); + } + else if ((_data.coalesced.is_tiled == false) && pow2_tilesz) { + unsigned int mask = 0; + unsigned int member_rank = 0; + int seen_lanes = (thread_rank() / tilesz) * tilesz; + for (unsigned int bit_idx = 0; bit_idx < 32; bit_idx++) { + unsigned int lane_bit = _data.coalesced.mask & (1 << bit_idx); + if (lane_bit) { + if (seen_lanes <= 0 && member_rank < tilesz) { + mask |= lane_bit; + member_rank++; + } + seen_lanes--; + } + } + coalesced_group coalesced_tile = coalesced_group(mask); + // Override parent with the size of this group + coalesced_tile._data.coalesced.metaGroupSize = (size() + tilesz - 1) / tilesz; + coalesced_tile._data.coalesced.metaGroupRank = thread_rank() / tilesz; + return coalesced_tile; + } + else { + // None in _CG_VERSION 1000 + details::abort(); + } + + return (coalesced_group(0)); + } + + protected: + _CG_QUALIFIER coalesced_group(unsigned int mask) { + _data.coalesced.mask = mask; + _data.coalesced.size = __popc(mask); + _data.coalesced.metaGroupRank = 0; + _data.coalesced.metaGroupSize = 1; + _data.coalesced.is_tiled = false; + } + + _CG_QUALIFIER unsigned int get_mask() const { + return (_data.coalesced.mask); + } + + public: + _CG_STATIC_CONST_DECL unsigned int _group_id = details::coalesced_group_id; + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_block) + + _CG_QUALIFIER unsigned int num_threads() const { + return _data.coalesced.size; + } + + _CG_QUALIFIER unsigned int size() const { + return num_threads(); + } + + _CG_QUALIFIER unsigned int thread_rank() const { + return (__popc(_data.coalesced.mask & details::lanemask32_lt())); + } + + // Rank of this group in the upper level of the hierarchy + _CG_QUALIFIER unsigned int meta_group_rank() const { + return _data.coalesced.metaGroupRank; + } + + // Total num partitions created out of all CTAs when the group was created + _CG_QUALIFIER unsigned int meta_group_size() const { + return _data.coalesced.metaGroupSize; + } + + _CG_QUALIFIER void sync() const { + __syncwarp(_data.coalesced.mask); + } + +#ifdef _CG_CPP11_FEATURES + template > + _CG_QUALIFIER TyRet shfl(TyElem&& elem, int srcRank) const { + unsigned int lane = (srcRank == 0) ? __ffs(_data.coalesced.mask) - 1 : + (size() == 32) ? srcRank : __fns(_data.coalesced.mask, 0, (srcRank + 1)); + + return details::tile::shuffle_dispatch::shfl( + _CG_STL_NAMESPACE::forward(elem), _data.coalesced.mask, lane, 32); + } + + template > + _CG_QUALIFIER TyRet shfl_down(TyElem&& elem, unsigned int delta) const { + if (size() == 32) { + return details::tile::shuffle_dispatch::shfl_down( + _CG_STL_NAMESPACE::forward(elem), 0xFFFFFFFF, delta, 32); + } + + unsigned int lane = __fns(_data.coalesced.mask, details::laneid(), delta + 1); + + if (lane >= 32) + lane = details::laneid(); + + return details::tile::shuffle_dispatch::shfl( + _CG_STL_NAMESPACE::forward(elem), _data.coalesced.mask, lane, 32); + } + + template > + _CG_QUALIFIER TyRet shfl_up(TyElem&& elem, int delta) const { + if (size() == 32) { + return details::tile::shuffle_dispatch::shfl_up( + _CG_STL_NAMESPACE::forward(elem), 0xFFFFFFFF, delta, 32); + } + + unsigned lane = __fns(_data.coalesced.mask, details::laneid(), -(delta + 1)); + if (lane >= 32) + lane = details::laneid(); + + return details::tile::shuffle_dispatch::shfl( + _CG_STL_NAMESPACE::forward(elem), _data.coalesced.mask, lane, 32); + } +#else + template + _CG_QUALIFIER TyIntegral shfl(TyIntegral var, unsigned int src_rank) const { + details::assert_if_not_arithmetic(); + unsigned int lane = (src_rank == 0) ? __ffs(_data.coalesced.mask) - 1 : + (size() == 32) ? src_rank : __fns(_data.coalesced.mask, 0, (src_rank + 1)); + return (__shfl_sync(_data.coalesced.mask, var, lane, 32)); + } + + template + _CG_QUALIFIER TyIntegral shfl_up(TyIntegral var, int delta) const { + details::assert_if_not_arithmetic(); + if (size() == 32) { + return (__shfl_up_sync(0xFFFFFFFF, var, delta, 32)); + } + unsigned lane = __fns(_data.coalesced.mask, details::laneid(), -(delta + 1)); + if (lane >= 32) lane = details::laneid(); + return (__shfl_sync(_data.coalesced.mask, var, lane, 32)); + } + + template + _CG_QUALIFIER TyIntegral shfl_down(TyIntegral var, int delta) const { + details::assert_if_not_arithmetic(); + if (size() == 32) { + return (__shfl_down_sync(0xFFFFFFFF, var, delta, 32)); + } + unsigned int lane = __fns(_data.coalesced.mask, details::laneid(), delta + 1); + if (lane >= 32) lane = details::laneid(); + return (__shfl_sync(_data.coalesced.mask, var, lane, 32)); + } +#endif + + _CG_QUALIFIER int any(int predicate) const { + return (__ballot_sync(_data.coalesced.mask, predicate) != 0); + } + _CG_QUALIFIER int all(int predicate) const { + return (__ballot_sync(_data.coalesced.mask, predicate) == _data.coalesced.mask); + } + _CG_QUALIFIER unsigned int ballot(int predicate) const { + if (size() == 32) { + return (__ballot_sync(0xFFFFFFFF, predicate)); + } + unsigned int lane_ballot = __ballot_sync(_data.coalesced.mask, predicate); + return (_packLanes(lane_ballot)); + } + +#ifdef _CG_HAS_MATCH_COLLECTIVE + + template + _CG_QUALIFIER unsigned int match_any(TyIntegral val) const { + details::assert_if_not_arithmetic(); + if (size() == 32) { + return (__match_any_sync(0xFFFFFFFF, val)); + } + unsigned int lane_match = __match_any_sync(_data.coalesced.mask, val); + return (_packLanes(lane_match)); + } + + template + _CG_QUALIFIER unsigned int match_all(TyIntegral val, int &pred) const { + details::assert_if_not_arithmetic(); + if (size() == 32) { + return (__match_all_sync(0xFFFFFFFF, val, &pred)); + } + unsigned int lane_match = __match_all_sync(_data.coalesced.mask, val, &pred); + return (_packLanes(lane_match)); + } + +#endif /* !_CG_HAS_MATCH_COLLECTIVE */ + +}; + +_CG_QUALIFIER coalesced_group coalesced_threads() +{ + return (coalesced_group(__activemask())); +} + +namespace details { + template struct verify_thread_block_tile_size; + template <> struct verify_thread_block_tile_size<32> { typedef void OK; }; + template <> struct verify_thread_block_tile_size<16> { typedef void OK; }; + template <> struct verify_thread_block_tile_size<8> { typedef void OK; }; + template <> struct verify_thread_block_tile_size<4> { typedef void OK; }; + template <> struct verify_thread_block_tile_size<2> { typedef void OK; }; + template <> struct verify_thread_block_tile_size<1> { typedef void OK; }; + +#ifdef _CG_CPP11_FEATURES + template + using _is_power_of_2 = _CG_STL_NAMESPACE::integral_constant; + + template + using _is_single_warp = _CG_STL_NAMESPACE::integral_constant; + template + using _is_multi_warp = + _CG_STL_NAMESPACE::integral_constant 32) && (Size <= 1024)>; + + template + using _is_valid_single_warp_tile = + _CG_STL_NAMESPACE::integral_constant::value && _is_single_warp::value>; + template + using _is_valid_multi_warp_tile = + _CG_STL_NAMESPACE::integral_constant::value && _is_multi_warp::value>; +#else + template + struct _is_multi_warp { + static const bool value = false; + }; +#endif +} + +template +class __static_size_tile_base +{ +protected: + _CG_STATIC_CONST_DECL unsigned int numThreads = Size; + +public: + _CG_THREAD_SCOPE(cuda::thread_scope::thread_scope_block) + + // Rank of thread within tile + _CG_STATIC_QUALIFIER unsigned int thread_rank() { + return (details::cta::thread_rank() & (numThreads - 1)); + } + + // Number of threads within tile + _CG_STATIC_CONSTEXPR_QUALIFIER unsigned int num_threads() { + return numThreads; + } + + _CG_STATIC_CONSTEXPR_QUALIFIER unsigned int size() { + return num_threads(); + } +}; + +template +class __static_size_thread_block_tile_base : public __static_size_tile_base +{ + friend class details::_coalesced_group_data_access; + typedef details::tile::tile_helpers th; + +#ifdef _CG_CPP11_FEATURES + static_assert(details::_is_valid_single_warp_tile::value, "Size must be one of 1/2/4/8/16/32"); +#else + typedef typename details::verify_thread_block_tile_size::OK valid; +#endif + using __static_size_tile_base::numThreads; + _CG_STATIC_CONST_DECL unsigned int fullMask = 0xFFFFFFFF; + + protected: + _CG_STATIC_QUALIFIER unsigned int build_mask() { + unsigned int mask = fullMask; + if (numThreads != 32) { + // [0,31] representing the current active thread in the warp + unsigned int laneId = details::laneid(); + // shift mask according to the partition it belongs to + mask = th::tileMask << (laneId & ~(th::laneMask)); + } + return (mask); + } + +public: + _CG_STATIC_CONST_DECL unsigned int _group_id = details::coalesced_group_id; + + _CG_STATIC_QUALIFIER void sync() { + __syncwarp(build_mask()); + } + +#ifdef _CG_CPP11_FEATURES + // PTX supported collectives + template > + _CG_QUALIFIER TyRet shfl(TyElem&& elem, int srcRank) const { + return details::tile::shuffle_dispatch::shfl( + _CG_STL_NAMESPACE::forward(elem), build_mask(), srcRank, numThreads); + } + + template > + _CG_QUALIFIER TyRet shfl_down(TyElem&& elem, unsigned int delta) const { + return details::tile::shuffle_dispatch::shfl_down( + _CG_STL_NAMESPACE::forward(elem), build_mask(), delta, numThreads); + } + + template > + _CG_QUALIFIER TyRet shfl_up(TyElem&& elem, unsigned int delta) const { + return details::tile::shuffle_dispatch::shfl_up( + _CG_STL_NAMESPACE::forward(elem), build_mask(), delta, numThreads); + } + + template > + _CG_QUALIFIER TyRet shfl_xor(TyElem&& elem, unsigned int laneMask) const { + return details::tile::shuffle_dispatch::shfl_xor( + _CG_STL_NAMESPACE::forward(elem), build_mask(), laneMask, numThreads); + } +#else + template + _CG_QUALIFIER TyIntegral shfl(TyIntegral var, int srcRank) const { + details::assert_if_not_arithmetic(); + return (__shfl_sync(build_mask(), var, srcRank, numThreads)); + } + + template + _CG_QUALIFIER TyIntegral shfl_down(TyIntegral var, unsigned int delta) const { + details::assert_if_not_arithmetic(); + return (__shfl_down_sync(build_mask(), var, delta, numThreads)); + } + + template + _CG_QUALIFIER TyIntegral shfl_up(TyIntegral var, unsigned int delta) const { + details::assert_if_not_arithmetic(); + return (__shfl_up_sync(build_mask(), var, delta, numThreads)); + } + + template + _CG_QUALIFIER TyIntegral shfl_xor(TyIntegral var, unsigned int laneMask) const { + details::assert_if_not_arithmetic(); + return (__shfl_xor_sync(build_mask(), var, laneMask, numThreads)); + } +#endif //_CG_CPP11_FEATURES + + _CG_QUALIFIER int any(int predicate) const { + unsigned int lane_ballot = __ballot_sync(build_mask(), predicate); + return (lane_ballot != 0); + } + _CG_QUALIFIER int all(int predicate) const { + unsigned int lane_ballot = __ballot_sync(build_mask(), predicate); + return (lane_ballot == build_mask()); + } + _CG_QUALIFIER unsigned int ballot(int predicate) const { + unsigned int lane_ballot = __ballot_sync(build_mask(), predicate); + return (lane_ballot >> (details::laneid() & (~(th::laneMask)))); + } + +#ifdef _CG_HAS_MATCH_COLLECTIVE + template + _CG_QUALIFIER unsigned int match_any(TyIntegral val) const { + details::assert_if_not_arithmetic(); + unsigned int lane_match = __match_any_sync(build_mask(), val); + return (lane_match >> (details::laneid() & (~(th::laneMask)))); + } + + template + _CG_QUALIFIER unsigned int match_all(TyIntegral val, int &pred) const { + details::assert_if_not_arithmetic(); + unsigned int lane_match = __match_all_sync(build_mask(), val, &pred); + return (lane_match >> (details::laneid() & (~(th::laneMask)))); + } +#endif + +}; + +template +class __static_parent_thread_block_tile_base +{ +public: + // Rank of this group in the upper level of the hierarchy + _CG_STATIC_QUALIFIER unsigned int meta_group_rank() { + return ParentT::thread_rank() / Size; + } + + // Total num partitions created out of all CTAs when the group was created + _CG_STATIC_QUALIFIER unsigned int meta_group_size() { + return (ParentT::size() + Size - 1) / Size; + } +}; + +/** + * class thread_block_tile + * + * Statically-sized group type, representing one tile of a thread block. + * The only specializations currently supported are those with native + * hardware support (1/2/4/8/16/32) + * + * This group exposes warp-synchronous builtins. + * Can only be constructed via tiled_partition(ParentT&) + */ + +template +class __single_warp_thread_block_tile : + public __static_size_thread_block_tile_base, + public __static_parent_thread_block_tile_base +{ + typedef __static_parent_thread_block_tile_base staticParentBaseT; + friend class details::_coalesced_group_data_access; + +protected: + _CG_QUALIFIER __single_warp_thread_block_tile() { }; + _CG_QUALIFIER __single_warp_thread_block_tile(unsigned int, unsigned int) { }; + + _CG_STATIC_QUALIFIER unsigned int get_mask() { + return __static_size_thread_block_tile_base::build_mask(); + } +}; + +template +class __single_warp_thread_block_tile : + public __static_size_thread_block_tile_base, + public thread_group_base +{ + _CG_STATIC_CONST_DECL unsigned int numThreads = Size; + + template friend class __single_warp_thread_block_tile; + friend class details::_coalesced_group_data_access; + + typedef __static_size_thread_block_tile_base staticSizeBaseT; + +protected: + _CG_QUALIFIER __single_warp_thread_block_tile(unsigned int meta_group_rank = 0, unsigned int meta_group_size = 1) { + _data.coalesced.mask = staticSizeBaseT::build_mask(); + _data.coalesced.size = numThreads; + _data.coalesced.metaGroupRank = meta_group_rank; + _data.coalesced.metaGroupSize = meta_group_size; + _data.coalesced.is_tiled = true; + } + + _CG_QUALIFIER unsigned int get_mask() const { + return (_data.coalesced.mask); + } + +public: + using staticSizeBaseT::sync; + using staticSizeBaseT::size; + using staticSizeBaseT::num_threads; + using staticSizeBaseT::thread_rank; + + _CG_QUALIFIER unsigned int meta_group_rank() const { + return _data.coalesced.metaGroupRank; + } + + _CG_QUALIFIER unsigned int meta_group_size() const { + return _data.coalesced.metaGroupSize; + } +}; + +/** + * Outer level API calls + * void sync(GroupT) - see .sync() + * void thread_rank(GroupT) - see .thread_rank() + * void group_size(GroupT) - see .size() + */ +template +_CG_QUALIFIER void sync(GroupT const &g) +{ + g.sync(); +} + +// TODO: Use a static dispatch to determine appropriate return type +// C++03 is stuck with unsigned long long for now +#ifdef _CG_CPP11_FEATURES +template +_CG_QUALIFIER auto thread_rank(GroupT const& g) -> decltype(g.thread_rank()) { + return g.thread_rank(); +} + + +template +_CG_QUALIFIER auto group_size(GroupT const &g) -> decltype(g.num_threads()) { + return g.num_threads(); +} +#else +template +_CG_QUALIFIER unsigned long long thread_rank(GroupT const& g) { + return static_cast(g.thread_rank()); +} + + +template +_CG_QUALIFIER unsigned long long group_size(GroupT const &g) { + return static_cast(g.num_threads()); +} +#endif + + +/** + * tiled_partition + * + * The tiled_partition(parent, tilesz) method is a collective operation that + * partitions the parent group into a one-dimensional, row-major, tiling of subgroups. + * + * A total of ((size(parent)+tilesz-1)/tilesz) subgroups will + * be created where threads having identical k = (thread_rank(parent)/tilesz) + * will be members of the same subgroup. + * + * The implementation may cause the calling thread to wait until all the members + * of the parent group have invoked the operation before resuming execution. + * + * Functionality is limited to power-of-two sized subgorup instances of at most + * 32 threads. Only thread_block, thread_block_tile<>, and their subgroups can be + * tiled_partition() in _CG_VERSION 1000. + */ +_CG_QUALIFIER thread_group tiled_partition(const thread_group& parent, unsigned int tilesz) +{ + if (parent.get_type() == details::coalesced_group_id) { + const coalesced_group *_cg = static_cast(&parent); + return _cg->_get_tiled_threads(tilesz); + } + else { + const thread_block *_tb = static_cast(&parent); + return _tb->_get_tiled_threads(tilesz); + } +} + +// Thread block type overload: returns a basic thread_group for now (may be specialized later) +_CG_QUALIFIER thread_group tiled_partition(const thread_block& parent, unsigned int tilesz) +{ + return (parent._get_tiled_threads(tilesz)); +} + +// Coalesced group type overload: retains its ability to stay coalesced +_CG_QUALIFIER coalesced_group tiled_partition(const coalesced_group& parent, unsigned int tilesz) +{ + return (parent._get_tiled_threads(tilesz)); +} + +namespace details { + template + class internal_thread_block_tile : public __single_warp_thread_block_tile {}; + + template + _CG_QUALIFIER internal_thread_block_tile tiled_partition_internal() { + return internal_thread_block_tile(); + } + + template + _CG_QUALIFIER TyVal multi_warp_collectives_helper( + const GroupT& group, + WarpLambda warp_lambda, + InterWarpLambda inter_warp_lambda) { + return group.template collectives_scheme(warp_lambda, inter_warp_lambda); + } + + template + _CG_QUALIFIER T* multi_warp_scratch_location_getter(const GroupT& group, unsigned int warp_id) { + return group.template get_scratch_location(warp_id); + } + + template + _CG_QUALIFIER details::barrier_t* multi_warp_sync_location_getter(const GroupT& group) { + return group.get_sync_location(); + } + +} +/** + * tiled_partition + * + * The tiled_partition(parent) method is a collective operation that + * partitions the parent group into a one-dimensional, row-major, tiling of subgroups. + * + * A total of ((size(parent)/tilesz) subgroups will be created, + * therefore the parent group size must be evenly divisible by the tilesz. + * The allow parent groups are thread_block or thread_block_tile. + * + * The implementation may cause the calling thread to wait until all the members + * of the parent group have invoked the operation before resuming execution. + * + * Functionality is limited to native hardware sizes, 1/2/4/8/16/32. + * The size(parent) must be greater than the template Size parameter + * otherwise the results are undefined. + */ + +#if defined(_CG_CPP11_FEATURES) +template +class __static_size_multi_warp_tile_base : public __static_size_tile_base +{ + static_assert(details::_is_valid_multi_warp_tile::value, "Size must be one of 64/128/256/512"); + + template + friend __device__ TyVal details::multi_warp_collectives_helper( + const GroupT& group, + WarpLambda warp_lambda, + InterWarpLambda inter_warp_lambda); + template + friend __device__ T* details::multi_warp_scratch_location_getter(const GroupT& group, unsigned int warp_id); + template + friend __device__ details::barrier_t* details::multi_warp_sync_location_getter(const GroupT& group); + template + friend class __static_size_multi_warp_tile_base; + using WarpType = details::internal_thread_block_tile<32, __static_size_multi_warp_tile_base>; + using ThisType = __static_size_multi_warp_tile_base; + _CG_STATIC_CONST_DECL int numWarps = Size / 32; + +protected: + details::multi_warp_scratch* const tile_memory; + + template + _CG_QUALIFIER __static_size_multi_warp_tile_base(const GroupT& g) : tile_memory(g.tile_memory) { +#if defined(_CG_HAS_RESERVED_SHARED) + details::sync_warps_reset(get_sync_location(), details::cta::thread_rank()); + g.sync(); +#endif + } + + +private: + _CG_QUALIFIER details::barrier_t* get_sync_location() const { + // Different group sizes use different barriers, all groups of a given size share one barrier. + unsigned int sync_id = details::log2(Size / 64); + return &tile_memory->barriers[sync_id]; + } + + template + _CG_QUALIFIER T* get_scratch_location(unsigned int warp_id) const { + unsigned int scratch_id = (details::cta::thread_rank() - thread_rank()) / 32 + warp_id; + return reinterpret_cast(&tile_memory->communication_memory[scratch_id]); + } + + template + _CG_QUALIFIER T* get_scratch_location() const { + unsigned int scratch_id = details::cta::thread_rank() / 32; + return reinterpret_cast(&tile_memory->communication_memory[scratch_id]); + } + + template + _CG_QUALIFIER TyVal shfl_impl(TyVal val, unsigned int src) const { + unsigned int src_warp = src / 32; + auto warp = details::tiled_partition_internal<32, ThisType>(); + details::barrier_t* sync_location = get_sync_location(); + + // Get warp slot of the source threads warp. + TyVal* warp_scratch_location = get_scratch_location(src_warp); + + if (warp.meta_group_rank() == src_warp) { + warp.sync(); + // Put shuffled value into my warp slot and let my warp arrive at the barrier. + if (thread_rank() == src) { + *warp_scratch_location = val; + } + details::sync_warps_arrive(sync_location, details::cta::thread_rank(), numWarps); + TyVal result = *warp_scratch_location; + details::sync_warps_wait(sync_location, details::cta::thread_rank()); + return result; + } + else { + // Wait for the source warp to arrive on the barrier. + details::sync_warps_wait_for_specific_warp(sync_location, + (details::cta::thread_rank() / 32 - warp.meta_group_rank() + src_warp)); + TyVal result = *warp_scratch_location; + details::sync_warps(sync_location, details::cta::thread_rank(), numWarps); + return result; + } + } + + template + _CG_QUALIFIER TyVal collectives_scheme(const WarpLambda& warp_lambda, const InterWarpLambda& inter_warp_lambda) const { + static_assert(sizeof(TyVal) <= details::multi_warp_scratch::communication_size, + "Collectives with tiles larger than 32 threads are limited to types smaller then 8 bytes"); + auto warp = details::tiled_partition_internal<32, ThisType>(); + details::barrier_t* sync_location = get_sync_location(); + TyVal* warp_scratch_location = get_scratch_location(); + + warp_lambda(warp, warp_scratch_location); + + if (details::sync_warps_last_releases(sync_location, details::cta::thread_rank(), numWarps)) { + auto subwarp = details::tiled_partition_internal(); + if (subwarp.meta_group_rank() == 0) { + TyVal* thread_scratch_location = get_scratch_location(subwarp.thread_rank()); + inter_warp_lambda(subwarp, thread_scratch_location); + } + warp.sync(); + details::sync_warps_release(sync_location, warp.thread_rank() == 0, details::cta::thread_rank(), numWarps); + } + TyVal result = *warp_scratch_location; + return result; + } + +public: + _CG_STATIC_CONST_DECL unsigned int _group_id = details::multi_tile_group_id; + + using __static_size_tile_base::thread_rank; + + template + _CG_QUALIFIER TyVal shfl(TyVal val, unsigned int src) const { + static_assert(sizeof(TyVal) <= details::multi_warp_scratch::communication_size, + "Collectives with tiles larger than 32 threads are limited to types smaller then 8 bytes"); + return shfl_impl(val, src); + } + + _CG_QUALIFIER void sync() const { + details::sync_warps(get_sync_location(), details::cta::thread_rank(), numWarps); + } + + _CG_QUALIFIER int any(int predicate) const { + auto warp_lambda = [=] (WarpType& warp, int* warp_scratch_location) { + *warp_scratch_location = __any_sync(0xFFFFFFFF, predicate); + }; + auto inter_warp_lambda = + [] (details::internal_thread_block_tile& subwarp, int* thread_scratch_location) { + *thread_scratch_location = __any_sync(0xFFFFFFFFU >> (32 - numWarps), *thread_scratch_location); + }; + return collectives_scheme(warp_lambda, inter_warp_lambda); + } + + _CG_QUALIFIER int all(int predicate) const { + auto warp_lambda = [=] (WarpType& warp, int* warp_scratch_location) { + *warp_scratch_location = __all_sync(0xFFFFFFFF, predicate); + }; + auto inter_warp_lambda = + [] (details::internal_thread_block_tile& subwarp, int* thread_scratch_location) { + *thread_scratch_location = __all_sync(0xFFFFFFFFU >> (32 - numWarps), *thread_scratch_location); + }; + return collectives_scheme(warp_lambda, inter_warp_lambda); + } +}; + + +template +class __multi_warp_thread_block_tile : + public __static_size_multi_warp_tile_base, + public __static_parent_thread_block_tile_base +{ + typedef __static_parent_thread_block_tile_base staticParentBaseT; + typedef __static_size_multi_warp_tile_base staticTileBaseT; +protected: + _CG_QUALIFIER __multi_warp_thread_block_tile(const ParentT& g) : + __static_size_multi_warp_tile_base(g) {} +}; + +template +class __multi_warp_thread_block_tile : public __static_size_multi_warp_tile_base +{ + const unsigned int metaGroupRank; + const unsigned int metaGroupSize; + +protected: + template + _CG_QUALIFIER __multi_warp_thread_block_tile(const __multi_warp_thread_block_tile& g) : + __static_size_multi_warp_tile_base(g), metaGroupRank(g.meta_group_rank()), metaGroupSize(g.meta_group_size()) {} + +public: + _CG_QUALIFIER unsigned int meta_group_rank() const { + return metaGroupRank; + } + + _CG_QUALIFIER unsigned int meta_group_size() const { + return metaGroupSize; + } +}; +#endif + +template +class thread_block_tile; + +namespace details { + template + class thread_block_tile_impl; + + template + class thread_block_tile_impl: public __single_warp_thread_block_tile + { + protected: + template + _CG_QUALIFIER thread_block_tile_impl(const thread_block_tile_impl& g) : + __single_warp_thread_block_tile(g.meta_group_rank(), g.meta_group_size()) {} + + _CG_QUALIFIER thread_block_tile_impl(const thread_block& g) : + __single_warp_thread_block_tile() {} + }; + +#if defined(_CG_CPP11_FEATURES) + template + class thread_block_tile_impl : public __multi_warp_thread_block_tile + { + protected: + template + _CG_QUALIFIER thread_block_tile_impl(const GroupT& g) : + __multi_warp_thread_block_tile(g) {} + }; +#else + template + class thread_block_tile_impl + { + protected: + template + _CG_QUALIFIER thread_block_tile_impl(const GroupT& g) {} + }; +#endif +} + +template +class thread_block_tile : public details::thread_block_tile_impl::value> +{ + friend _CG_QUALIFIER thread_block_tile<1, void> this_thread(); + +protected: + _CG_QUALIFIER thread_block_tile(const ParentT& g) : + details::thread_block_tile_impl::value>(g) {} + +public: + _CG_QUALIFIER operator thread_block_tile() const { + return thread_block_tile(*this); + } +}; + +template +class thread_block_tile : public details::thread_block_tile_impl::value> +{ + template + friend class thread_block_tile; + +protected: + template + _CG_QUALIFIER thread_block_tile(const thread_block_tile& g) : + details::thread_block_tile_impl::value>(g) {} + +public: + template + _CG_QUALIFIER thread_block_tile(const thread_block_tile& g) : + details::thread_block_tile_impl::value>(g) {} +}; + +namespace details { + template + struct tiled_partition_impl; + + template + struct tiled_partition_impl : public thread_block_tile { + _CG_QUALIFIER tiled_partition_impl(const thread_block& g) : + thread_block_tile(g) {} + }; + + // ParentT = static thread_block_tile specialization + template + struct tiled_partition_impl > : + public thread_block_tile > { +#ifdef _CG_CPP11_FEATURES + static_assert(Size < ParentSize, "Tile size bigger or equal to the parent group size"); +#endif + _CG_QUALIFIER tiled_partition_impl(const thread_block_tile& g) : + thread_block_tile >(g) {} + }; + +} + +template +_CG_QUALIFIER thread_block_tile tiled_partition(const ParentT& g) +{ + return details::tiled_partition_impl(g); +} + +/** + * thread_group this_thread() + * + * Constructs a generic thread_group containing only the calling thread + */ +_CG_QUALIFIER thread_block_tile<1, void> this_thread() +{ + // Make thread_block_tile<1, thread_block> parent of the returned group, so it will have its + // meta group rank and size set to 0 and 1 respectively. + return thread_block_tile<1, thread_block_tile<1, thread_block> >(this_thread_block()); +} + +/** + * .sync() + * + * Executes a barrier across the group + * + * Implements both a compiler fence and an architectural fence to prevent, + * memory reordering around the barrier. + */ +_CG_QUALIFIER void thread_group::sync() const +{ + switch (_data.group.type) { + case details::coalesced_group_id: + cooperative_groups::sync(*static_cast(this)); + break; + case details::thread_block_id: + cooperative_groups::sync(*static_cast(this)); + break; + case details::grid_group_id: + cooperative_groups::sync(*static_cast(this)); + break; +#if defined(_CG_HAS_MULTI_GRID_GROUP) && defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) + case details::multi_grid_group_id: + cooperative_groups::sync(*static_cast(this)); + break; +#endif +#if defined(_CG_HAS_CLUSTER_GROUP) + case details::cluster_group_id: + cooperative_groups::sync(*static_cast(this)); + break; +#endif + default: + break; + } +} + +/** + * .size() + * + * Returns the total number of threads in the group. + */ +_CG_QUALIFIER unsigned long long thread_group::size() const +{ + unsigned long long size = 0; + switch (_data.group.type) { + case details::coalesced_group_id: + size = cooperative_groups::group_size(*static_cast(this)); + break; + case details::thread_block_id: + size = cooperative_groups::group_size(*static_cast(this)); + break; + case details::grid_group_id: + size = cooperative_groups::group_size(*static_cast(this)); + break; +#if defined(_CG_HAS_MULTI_GRID_GROUP) && defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) + case details::multi_grid_group_id: + size = cooperative_groups::group_size(*static_cast(this)); + break; +#endif +#if defined(_CG_HAS_CLUSTER_GROUP) + case details::cluster_group_id: + size = cooperative_groups::group_size(*static_cast(this)); + break; +#endif + default: + break; + } + return size; +} + +/** + * .thread_rank() + * + * Returns the linearized rank of the calling thread along the interval [0, size()). + */ +_CG_QUALIFIER unsigned long long thread_group::thread_rank() const +{ + unsigned long long rank = 0; + switch (_data.group.type) { + case details::coalesced_group_id: + rank = cooperative_groups::thread_rank(*static_cast(this)); + break; + case details::thread_block_id: + rank = cooperative_groups::thread_rank(*static_cast(this)); + break; + case details::grid_group_id: + rank = cooperative_groups::thread_rank(*static_cast(this)); + break; +#if defined(_CG_HAS_MULTI_GRID_GROUP) && defined(_CG_CPP11_FEATURES) && defined(_CG_ABI_EXPERIMENTAL) + case details::multi_grid_group_id: + rank = cooperative_groups::thread_rank(*static_cast(this)); + break; +#endif +#if defined(_CG_HAS_CLUSTER_GROUP) + case details::cluster_group_id: + rank = cooperative_groups::thread_rank(*static_cast(this)); + break; +#endif + default: + break; + } + return rank; +} + +_CG_END_NAMESPACE + +#include +#if (!defined(_MSC_VER) || defined(_WIN64)) +# include +#endif + +# endif /* ! (__cplusplus, __CUDACC__) */ + +#endif /* !_COOPERATIVE_GROUPS_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuComplex.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuComplex.h new file mode 100644 index 0000000000000000000000000000000000000000..7b167111b0b387a5279da6749d946560e1c42c1b --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuComplex.h @@ -0,0 +1,348 @@ +/* + * Copyright 1993-2012 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(CU_COMPLEX_H_) +#define CU_COMPLEX_H_ + +#if !defined(__CUDACC_RTC__) +#if defined(__GNUC__) +#if defined(__clang__) || (!defined(__PGIC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 2))) +#pragma GCC diagnostic ignored "-Wunused-function" +#endif +#endif +#endif + +/* When trying to include C header file in C++ Code extern "C" is required + * But the Standard QNX headers already have ifdef extern in them when compiling C++ Code + * extern "C" cannot be nested + * Hence keep the header out of extern "C" block + */ + +#if !defined(__CUDACC__) +#include /* import fabsf, sqrt */ +#endif /* !defined(__CUDACC__) */ + +#if defined(__cplusplus) +extern "C" { +#endif /* __cplusplus */ + +#include "vector_types.h" + +typedef float2 cuFloatComplex; + +__host__ __device__ static __inline__ float cuCrealf (cuFloatComplex x) +{ + return x.x; +} + +__host__ __device__ static __inline__ float cuCimagf (cuFloatComplex x) +{ + return x.y; +} + +__host__ __device__ static __inline__ cuFloatComplex make_cuFloatComplex + (float r, float i) +{ + cuFloatComplex res; + res.x = r; + res.y = i; + return res; +} + +__host__ __device__ static __inline__ cuFloatComplex cuConjf (cuFloatComplex x) +{ + return make_cuFloatComplex (cuCrealf(x), -cuCimagf(x)); +} +__host__ __device__ static __inline__ cuFloatComplex cuCaddf (cuFloatComplex x, + cuFloatComplex y) +{ + return make_cuFloatComplex (cuCrealf(x) + cuCrealf(y), + cuCimagf(x) + cuCimagf(y)); +} + +__host__ __device__ static __inline__ cuFloatComplex cuCsubf (cuFloatComplex x, + cuFloatComplex y) +{ + return make_cuFloatComplex (cuCrealf(x) - cuCrealf(y), + cuCimagf(x) - cuCimagf(y)); +} + +/* This implementation could suffer from intermediate overflow even though + * the final result would be in range. However, various implementations do + * not guard against this (presumably to avoid losing performance), so we + * don't do it either to stay competitive. + */ +__host__ __device__ static __inline__ cuFloatComplex cuCmulf (cuFloatComplex x, + cuFloatComplex y) +{ + cuFloatComplex prod; + prod = make_cuFloatComplex ((cuCrealf(x) * cuCrealf(y)) - + (cuCimagf(x) * cuCimagf(y)), + (cuCrealf(x) * cuCimagf(y)) + + (cuCimagf(x) * cuCrealf(y))); + return prod; +} + +/* This implementation guards against intermediate underflow and overflow + * by scaling. Such guarded implementations are usually the default for + * complex library implementations, with some also offering an unguarded, + * faster version. + */ +__host__ __device__ static __inline__ cuFloatComplex cuCdivf (cuFloatComplex x, + cuFloatComplex y) +{ + cuFloatComplex quot; + float s = fabsf(cuCrealf(y)) + fabsf(cuCimagf(y)); + float oos = 1.0f / s; + float ars = cuCrealf(x) * oos; + float ais = cuCimagf(x) * oos; + float brs = cuCrealf(y) * oos; + float bis = cuCimagf(y) * oos; + s = (brs * brs) + (bis * bis); + oos = 1.0f / s; + quot = make_cuFloatComplex (((ars * brs) + (ais * bis)) * oos, + ((ais * brs) - (ars * bis)) * oos); + return quot; +} + +/* + * We would like to call hypotf(), but it's not available on all platforms. + * This discrete implementation guards against intermediate underflow and + * overflow by scaling. Otherwise we would lose half the exponent range. + * There are various ways of doing guarded computation. For now chose the + * simplest and fastest solution, however this may suffer from inaccuracies + * if sqrt and division are not IEEE compliant. + */ +__host__ __device__ static __inline__ float cuCabsf (cuFloatComplex x) +{ + float a = cuCrealf(x); + float b = cuCimagf(x); + float v, w, t; + a = fabsf(a); + b = fabsf(b); + if (a > b) { + v = a; + w = b; + } else { + v = b; + w = a; + } + t = w / v; + t = 1.0f + t * t; + t = v * sqrtf(t); + if ((v == 0.0f) || (v > 3.402823466e38f) || (w > 3.402823466e38f)) { + t = v + w; + } + return t; +} + +/* Double precision */ +typedef double2 cuDoubleComplex; + +__host__ __device__ static __inline__ double cuCreal (cuDoubleComplex x) +{ + return x.x; +} + +__host__ __device__ static __inline__ double cuCimag (cuDoubleComplex x) +{ + return x.y; +} + +__host__ __device__ static __inline__ cuDoubleComplex make_cuDoubleComplex + (double r, double i) +{ + cuDoubleComplex res; + res.x = r; + res.y = i; + return res; +} + +__host__ __device__ static __inline__ cuDoubleComplex cuConj(cuDoubleComplex x) +{ + return make_cuDoubleComplex (cuCreal(x), -cuCimag(x)); +} + +__host__ __device__ static __inline__ cuDoubleComplex cuCadd(cuDoubleComplex x, + cuDoubleComplex y) +{ + return make_cuDoubleComplex (cuCreal(x) + cuCreal(y), + cuCimag(x) + cuCimag(y)); +} + +__host__ __device__ static __inline__ cuDoubleComplex cuCsub(cuDoubleComplex x, + cuDoubleComplex y) +{ + return make_cuDoubleComplex (cuCreal(x) - cuCreal(y), + cuCimag(x) - cuCimag(y)); +} + +/* This implementation could suffer from intermediate overflow even though + * the final result would be in range. However, various implementations do + * not guard against this (presumably to avoid losing performance), so we + * don't do it either to stay competitive. + */ +__host__ __device__ static __inline__ cuDoubleComplex cuCmul(cuDoubleComplex x, + cuDoubleComplex y) +{ + cuDoubleComplex prod; + prod = make_cuDoubleComplex ((cuCreal(x) * cuCreal(y)) - + (cuCimag(x) * cuCimag(y)), + (cuCreal(x) * cuCimag(y)) + + (cuCimag(x) * cuCreal(y))); + return prod; +} + +/* This implementation guards against intermediate underflow and overflow + * by scaling. Such guarded implementations are usually the default for + * complex library implementations, with some also offering an unguarded, + * faster version. + */ +__host__ __device__ static __inline__ cuDoubleComplex cuCdiv(cuDoubleComplex x, + cuDoubleComplex y) +{ + cuDoubleComplex quot; + double s = (fabs(cuCreal(y))) + (fabs(cuCimag(y))); + double oos = 1.0 / s; + double ars = cuCreal(x) * oos; + double ais = cuCimag(x) * oos; + double brs = cuCreal(y) * oos; + double bis = cuCimag(y) * oos; + s = (brs * brs) + (bis * bis); + oos = 1.0 / s; + quot = make_cuDoubleComplex (((ars * brs) + (ais * bis)) * oos, + ((ais * brs) - (ars * bis)) * oos); + return quot; +} + +/* This implementation guards against intermediate underflow and overflow + * by scaling. Otherwise we would lose half the exponent range. There are + * various ways of doing guarded computation. For now chose the simplest + * and fastest solution, however this may suffer from inaccuracies if sqrt + * and division are not IEEE compliant. + */ +__host__ __device__ static __inline__ double cuCabs (cuDoubleComplex x) +{ + double a = cuCreal(x); + double b = cuCimag(x); + double v, w, t; + a = fabs(a); + b = fabs(b); + if (a > b) { + v = a; + w = b; + } else { + v = b; + w = a; + } + t = w / v; + t = 1.0 + t * t; + t = v * sqrt(t); + if ((v == 0.0) || + (v > 1.79769313486231570e+308) || (w > 1.79769313486231570e+308)) { + t = v + w; + } + return t; +} + +#if defined(__cplusplus) +} +#endif /* __cplusplus */ + +/* aliases */ +typedef cuFloatComplex cuComplex; +__host__ __device__ static __inline__ cuComplex make_cuComplex (float x, + float y) +{ + return make_cuFloatComplex (x, y); +} + +/* float-to-double promotion */ +__host__ __device__ static __inline__ cuDoubleComplex cuComplexFloatToDouble + (cuFloatComplex c) +{ + return make_cuDoubleComplex ((double)cuCrealf(c), (double)cuCimagf(c)); +} + +__host__ __device__ static __inline__ cuFloatComplex cuComplexDoubleToFloat +(cuDoubleComplex c) +{ + return make_cuFloatComplex ((float)cuCreal(c), (float)cuCimag(c)); +} + + +__host__ __device__ static __inline__ cuComplex cuCfmaf( cuComplex x, cuComplex y, cuComplex d) +{ + float real_res; + float imag_res; + + real_res = (cuCrealf(x) * cuCrealf(y)) + cuCrealf(d); + imag_res = (cuCrealf(x) * cuCimagf(y)) + cuCimagf(d); + + real_res = -(cuCimagf(x) * cuCimagf(y)) + real_res; + imag_res = (cuCimagf(x) * cuCrealf(y)) + imag_res; + + return make_cuComplex(real_res, imag_res); +} + +__host__ __device__ static __inline__ cuDoubleComplex cuCfma( cuDoubleComplex x, cuDoubleComplex y, cuDoubleComplex d) +{ + double real_res; + double imag_res; + + real_res = (cuCreal(x) * cuCreal(y)) + cuCreal(d); + imag_res = (cuCreal(x) * cuCimag(y)) + cuCimag(d); + + real_res = -(cuCimag(x) * cuCimag(y)) + real_res; + imag_res = (cuCimag(x) * cuCreal(y)) + imag_res; + + return make_cuDoubleComplex(real_res, imag_res); +} + +#endif /* !defined(CU_COMPLEX_H_) */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda.h new file mode 100644 index 0000000000000000000000000000000000000000..806c957d0585ce0a7e935c02d5c17289e62a0054 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda.h @@ -0,0 +1,24359 @@ +/* + * Copyright 1993-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef __cuda_cuda_h__ +#define __cuda_cuda_h__ + + + + +#include +#ifdef _MSC_VER +typedef unsigned __int32 cuuint32_t; +typedef unsigned __int64 cuuint64_t; +#else +#include +typedef uint32_t cuuint32_t; +typedef uint64_t cuuint64_t; +#endif + +#if defined(__CUDA_API_VERSION_INTERNAL) || defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +#define __CUDA_DEPRECATED +#elif defined(_MSC_VER) +#define __CUDA_DEPRECATED __declspec(deprecated) +#elif defined(__GNUC__) +#define __CUDA_DEPRECATED __attribute__((deprecated)) +#else +#define __CUDA_DEPRECATED +#endif + +#if defined(CUDA_FORCE_API_VERSION) +#error "CUDA_FORCE_API_VERSION is no longer supported." +#endif + +#if defined(__CUDA_API_VERSION_INTERNAL) || defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) + #define __CUDA_API_PER_THREAD_DEFAULT_STREAM + #define __CUDA_API_PTDS(api) api ## _ptds + #define __CUDA_API_PTSZ(api) api ## _ptsz +#else + #define __CUDA_API_PTDS(api) api + #define __CUDA_API_PTSZ(api) api +#endif + +#define cuDeviceTotalMem cuDeviceTotalMem_v2 +#define cuCtxCreate cuCtxCreate_v2 +#define cuCtxCreate_v3 cuCtxCreate_v3 +#define cuModuleGetGlobal cuModuleGetGlobal_v2 +#define cuMemGetInfo cuMemGetInfo_v2 +#define cuMemAlloc cuMemAlloc_v2 +#define cuMemAllocPitch cuMemAllocPitch_v2 +#define cuMemFree cuMemFree_v2 +#define cuMemGetAddressRange cuMemGetAddressRange_v2 +#define cuMemAllocHost cuMemAllocHost_v2 +#define cuMemHostGetDevicePointer cuMemHostGetDevicePointer_v2 +#define cuMemcpyHtoD __CUDA_API_PTDS(cuMemcpyHtoD_v2) +#define cuMemcpyDtoH __CUDA_API_PTDS(cuMemcpyDtoH_v2) +#define cuMemcpyDtoD __CUDA_API_PTDS(cuMemcpyDtoD_v2) +#define cuMemcpyDtoA __CUDA_API_PTDS(cuMemcpyDtoA_v2) +#define cuMemcpyAtoD __CUDA_API_PTDS(cuMemcpyAtoD_v2) +#define cuMemcpyHtoA __CUDA_API_PTDS(cuMemcpyHtoA_v2) +#define cuMemcpyAtoH __CUDA_API_PTDS(cuMemcpyAtoH_v2) +#define cuMemcpyAtoA __CUDA_API_PTDS(cuMemcpyAtoA_v2) +#define cuMemcpyHtoAAsync __CUDA_API_PTSZ(cuMemcpyHtoAAsync_v2) +#define cuMemcpyAtoHAsync __CUDA_API_PTSZ(cuMemcpyAtoHAsync_v2) +#define cuMemcpy2D __CUDA_API_PTDS(cuMemcpy2D_v2) +#define cuMemcpy2DUnaligned __CUDA_API_PTDS(cuMemcpy2DUnaligned_v2) +#define cuMemcpy3D __CUDA_API_PTDS(cuMemcpy3D_v2) +#define cuMemcpyHtoDAsync __CUDA_API_PTSZ(cuMemcpyHtoDAsync_v2) +#define cuMemcpyDtoHAsync __CUDA_API_PTSZ(cuMemcpyDtoHAsync_v2) +#define cuMemcpyDtoDAsync __CUDA_API_PTSZ(cuMemcpyDtoDAsync_v2) +#define cuMemcpy2DAsync __CUDA_API_PTSZ(cuMemcpy2DAsync_v2) +#define cuMemcpy3DAsync __CUDA_API_PTSZ(cuMemcpy3DAsync_v2) +#define cuMemsetD8 __CUDA_API_PTDS(cuMemsetD8_v2) +#define cuMemsetD16 __CUDA_API_PTDS(cuMemsetD16_v2) +#define cuMemsetD32 __CUDA_API_PTDS(cuMemsetD32_v2) +#define cuMemsetD2D8 __CUDA_API_PTDS(cuMemsetD2D8_v2) +#define cuMemsetD2D16 __CUDA_API_PTDS(cuMemsetD2D16_v2) +#define cuMemsetD2D32 __CUDA_API_PTDS(cuMemsetD2D32_v2) +#define cuArrayCreate cuArrayCreate_v2 +#define cuArrayGetDescriptor cuArrayGetDescriptor_v2 +#define cuArray3DCreate cuArray3DCreate_v2 +#define cuArray3DGetDescriptor cuArray3DGetDescriptor_v2 +#define cuTexRefSetAddress cuTexRefSetAddress_v2 +#define cuTexRefGetAddress cuTexRefGetAddress_v2 +#define cuGraphicsResourceGetMappedPointer cuGraphicsResourceGetMappedPointer_v2 +#define cuCtxDestroy cuCtxDestroy_v2 +#define cuCtxPopCurrent cuCtxPopCurrent_v2 +#define cuCtxPushCurrent cuCtxPushCurrent_v2 +#define cuStreamDestroy cuStreamDestroy_v2 +#define cuEventDestroy cuEventDestroy_v2 +#define cuTexRefSetAddress2D cuTexRefSetAddress2D_v3 +#define cuLinkCreate cuLinkCreate_v2 +#define cuLinkAddData cuLinkAddData_v2 +#define cuLinkAddFile cuLinkAddFile_v2 +#define cuMemHostRegister cuMemHostRegister_v2 +#define cuGraphicsResourceSetMapFlags cuGraphicsResourceSetMapFlags_v2 +#define cuStreamBeginCapture __CUDA_API_PTSZ(cuStreamBeginCapture_v2) +#define cuDevicePrimaryCtxRelease cuDevicePrimaryCtxRelease_v2 +#define cuDevicePrimaryCtxReset cuDevicePrimaryCtxReset_v2 +#define cuDevicePrimaryCtxSetFlags cuDevicePrimaryCtxSetFlags_v2 +#define cuDeviceGetUuid_v2 cuDeviceGetUuid_v2 +#define cuIpcOpenMemHandle cuIpcOpenMemHandle_v2 + +#define cuGraphInstantiate cuGraphInstantiateWithFlags + +#define cuGraphExecUpdate cuGraphExecUpdate_v2 +#define cuGetProcAddress cuGetProcAddress_v2 +#define cuGraphAddKernelNode cuGraphAddKernelNode_v2 +#define cuGraphKernelNodeGetParams cuGraphKernelNodeGetParams_v2 +#define cuGraphKernelNodeSetParams cuGraphKernelNodeSetParams_v2 +#define cuGraphExecKernelNodeSetParams cuGraphExecKernelNodeSetParams_v2 + +#define cuStreamWriteValue32 __CUDA_API_PTSZ(cuStreamWriteValue32_v2) +#define cuStreamWaitValue32 __CUDA_API_PTSZ(cuStreamWaitValue32_v2) +#define cuStreamWriteValue64 __CUDA_API_PTSZ(cuStreamWriteValue64_v2) +#define cuStreamWaitValue64 __CUDA_API_PTSZ(cuStreamWaitValue64_v2) +#define cuStreamBatchMemOp __CUDA_API_PTSZ(cuStreamBatchMemOp_v2) +#define cuStreamGetCaptureInfo __CUDA_API_PTSZ(cuStreamGetCaptureInfo_v2) +#define cuStreamGetCaptureInfo_v2 __CUDA_API_PTSZ(cuStreamGetCaptureInfo_v2) + +#if defined(__CUDA_API_PER_THREAD_DEFAULT_STREAM) + #define cuMemcpy __CUDA_API_PTDS(cuMemcpy) + #define cuMemcpyAsync __CUDA_API_PTSZ(cuMemcpyAsync) + #define cuMemcpyPeer __CUDA_API_PTDS(cuMemcpyPeer) + #define cuMemcpyPeerAsync __CUDA_API_PTSZ(cuMemcpyPeerAsync) + #define cuMemcpy3DPeer __CUDA_API_PTDS(cuMemcpy3DPeer) + #define cuMemcpy3DPeerAsync __CUDA_API_PTSZ(cuMemcpy3DPeerAsync) + #define cuMemPrefetchAsync __CUDA_API_PTSZ(cuMemPrefetchAsync) + #define cuMemPrefetchAsync_v2 __CUDA_API_PTSZ(cuMemPrefetchAsync_v2) + + #define cuMemsetD8Async __CUDA_API_PTSZ(cuMemsetD8Async) + #define cuMemsetD16Async __CUDA_API_PTSZ(cuMemsetD16Async) + #define cuMemsetD32Async __CUDA_API_PTSZ(cuMemsetD32Async) + #define cuMemsetD2D8Async __CUDA_API_PTSZ(cuMemsetD2D8Async) + #define cuMemsetD2D16Async __CUDA_API_PTSZ(cuMemsetD2D16Async) + #define cuMemsetD2D32Async __CUDA_API_PTSZ(cuMemsetD2D32Async) + + #define cuStreamGetPriority __CUDA_API_PTSZ(cuStreamGetPriority) + #define cuStreamGetId __CUDA_API_PTSZ(cuStreamGetId) + #define cuStreamGetFlags __CUDA_API_PTSZ(cuStreamGetFlags) + #define cuStreamGetCtx __CUDA_API_PTSZ(cuStreamGetCtx) + #define cuStreamWaitEvent __CUDA_API_PTSZ(cuStreamWaitEvent) + #define cuStreamEndCapture __CUDA_API_PTSZ(cuStreamEndCapture) + #define cuStreamIsCapturing __CUDA_API_PTSZ(cuStreamIsCapturing) + #define cuStreamGetCaptureInfo_v3 __CUDA_API_PTSZ(cuStreamGetCaptureInfo_v3) + #define cuStreamUpdateCaptureDependencies __CUDA_API_PTSZ(cuStreamUpdateCaptureDependencies) + #define cuStreamUpdateCaptureDependencies_v2 __CUDA_API_PTSZ(cuStreamUpdateCaptureDependencies_v2) + #define cuStreamAddCallback __CUDA_API_PTSZ(cuStreamAddCallback) + #define cuStreamAttachMemAsync __CUDA_API_PTSZ(cuStreamAttachMemAsync) + #define cuStreamQuery __CUDA_API_PTSZ(cuStreamQuery) + #define cuStreamSynchronize __CUDA_API_PTSZ(cuStreamSynchronize) + #define cuEventRecord __CUDA_API_PTSZ(cuEventRecord) + #define cuEventRecordWithFlags __CUDA_API_PTSZ(cuEventRecordWithFlags) + #define cuLaunchKernel __CUDA_API_PTSZ(cuLaunchKernel) + #define cuLaunchKernelEx __CUDA_API_PTSZ(cuLaunchKernelEx) + #define cuLaunchHostFunc __CUDA_API_PTSZ(cuLaunchHostFunc) + #define cuGraphicsMapResources __CUDA_API_PTSZ(cuGraphicsMapResources) + #define cuGraphicsUnmapResources __CUDA_API_PTSZ(cuGraphicsUnmapResources) + + #define cuLaunchCooperativeKernel __CUDA_API_PTSZ(cuLaunchCooperativeKernel) + + #define cuSignalExternalSemaphoresAsync __CUDA_API_PTSZ(cuSignalExternalSemaphoresAsync) + #define cuWaitExternalSemaphoresAsync __CUDA_API_PTSZ(cuWaitExternalSemaphoresAsync) + + #define cuGraphInstantiateWithParams __CUDA_API_PTSZ(cuGraphInstantiateWithParams) + #define cuGraphUpload __CUDA_API_PTSZ(cuGraphUpload) + #define cuGraphLaunch __CUDA_API_PTSZ(cuGraphLaunch) + #define cuStreamCopyAttributes __CUDA_API_PTSZ(cuStreamCopyAttributes) + #define cuStreamGetAttribute __CUDA_API_PTSZ(cuStreamGetAttribute) + #define cuStreamSetAttribute __CUDA_API_PTSZ(cuStreamSetAttribute) + #define cuMemMapArrayAsync __CUDA_API_PTSZ(cuMemMapArrayAsync) + + #define cuMemFreeAsync __CUDA_API_PTSZ(cuMemFreeAsync) + #define cuMemAllocAsync __CUDA_API_PTSZ(cuMemAllocAsync) + #define cuMemAllocFromPoolAsync __CUDA_API_PTSZ(cuMemAllocFromPoolAsync) + + #define cuStreamBeginCaptureToGraph __CUDA_API_PTSZ(cuStreamBeginCaptureToGraph) + +#endif + +/** + * \file cuda.h + * \brief Header file for the CUDA Toolkit application programming interface. + * + * \file cudaGL.h + * \brief Header file for the OpenGL interoperability functions of the + * low-level CUDA driver application programming interface. + * + * \file cudaD3D9.h + * \brief Header file for the Direct3D 9 interoperability functions of the + * low-level CUDA driver application programming interface. + */ + +/** + * \defgroup CUDA_TYPES Data types used by CUDA driver + * @{ + */ + +/** + * CUDA API version number + */ +#define CUDA_VERSION 12040 + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * CUDA device pointer + * CUdeviceptr is defined as an unsigned integer type whose size matches the size of a pointer on the target platform. + */ +#if defined(_WIN64) || defined(__LP64__) +typedef unsigned long long CUdeviceptr_v2; +#else +typedef unsigned int CUdeviceptr_v2; +#endif +typedef CUdeviceptr_v2 CUdeviceptr; /**< CUDA device pointer */ + +typedef int CUdevice_v1; /**< CUDA device */ +typedef CUdevice_v1 CUdevice; /**< CUDA device */ +typedef struct CUctx_st *CUcontext; /**< CUDA context */ +typedef struct CUmod_st *CUmodule; /**< CUDA module */ +typedef struct CUfunc_st *CUfunction; /**< CUDA function */ +typedef struct CUlib_st *CUlibrary; /**< CUDA library */ +typedef struct CUkern_st *CUkernel; /**< CUDA kernel */ +typedef struct CUarray_st *CUarray; /**< CUDA array */ +typedef struct CUmipmappedArray_st *CUmipmappedArray; /**< CUDA mipmapped array */ +typedef struct CUtexref_st *CUtexref; /**< CUDA texture reference */ +typedef struct CUsurfref_st *CUsurfref; /**< CUDA surface reference */ +typedef struct CUevent_st *CUevent; /**< CUDA event */ +typedef struct CUstream_st *CUstream; /**< CUDA stream */ +typedef struct CUgraphicsResource_st *CUgraphicsResource; /**< CUDA graphics interop resource */ +typedef unsigned long long CUtexObject_v1; /**< An opaque value that represents a CUDA texture object */ +typedef CUtexObject_v1 CUtexObject; /**< An opaque value that represents a CUDA texture object */ +typedef unsigned long long CUsurfObject_v1; /**< An opaque value that represents a CUDA surface object */ +typedef CUsurfObject_v1 CUsurfObject; /**< An opaque value that represents a CUDA surface object */ +typedef struct CUextMemory_st *CUexternalMemory; /**< CUDA external memory */ +typedef struct CUextSemaphore_st *CUexternalSemaphore; /**< CUDA external semaphore */ +typedef struct CUgraph_st *CUgraph; /**< CUDA graph */ +typedef struct CUgraphNode_st *CUgraphNode; /**< CUDA graph node */ +typedef struct CUgraphExec_st *CUgraphExec; /**< CUDA executable graph */ +typedef struct CUmemPoolHandle_st *CUmemoryPool; /**< CUDA memory pool */ +typedef struct CUuserObject_st *CUuserObject; /**< CUDA user object for graphs */ +typedef cuuint64_t CUgraphConditionalHandle; /**< CUDA graph conditional handle */ +typedef struct CUgraphDeviceUpdatableNode_st *CUgraphDeviceNode; /**< CUDA graph device node handle */ +typedef struct CUasyncCallbackEntry_st *CUasyncCallbackHandle; /**< CUDA async notification callback handle */ + +#ifndef CU_UUID_HAS_BEEN_DEFINED +#define CU_UUID_HAS_BEEN_DEFINED +typedef struct CUuuid_st { /**< CUDA definition of UUID */ + char bytes[16]; +} CUuuid; +#endif + +/** + * CUDA IPC handle size + */ +#define CU_IPC_HANDLE_SIZE 64 + +/** + * Fabric handle - An opaque handle representing a memory allocation + * that can be exported to processes in same or different nodes. For IPC + * between processes on different nodes they must be connected via the + * NVSwitch fabric. + */ +typedef struct CUmemFabricHandle_st { + unsigned char data[CU_IPC_HANDLE_SIZE]; +} CUmemFabricHandle_v1; +typedef CUmemFabricHandle_v1 CUmemFabricHandle; + +/** + * CUDA IPC event handle + */ +typedef struct CUipcEventHandle_st { + char reserved[CU_IPC_HANDLE_SIZE]; +} CUipcEventHandle_v1; +typedef CUipcEventHandle_v1 CUipcEventHandle; + +/** + * CUDA IPC mem handle + */ +typedef struct CUipcMemHandle_st { + char reserved[CU_IPC_HANDLE_SIZE]; +} CUipcMemHandle_v1; +typedef CUipcMemHandle_v1 CUipcMemHandle; + +/** + * CUDA Ipc Mem Flags + */ +typedef enum CUipcMem_flags_enum { + CU_IPC_MEM_LAZY_ENABLE_PEER_ACCESS = 0x1 /**< Automatically enable peer access between remote devices as needed */ +} CUipcMem_flags; + + +/** + * CUDA Mem Attach Flags + */ +typedef enum CUmemAttach_flags_enum { + CU_MEM_ATTACH_GLOBAL = 0x1, /**< Memory can be accessed by any stream on any device */ + CU_MEM_ATTACH_HOST = 0x2, /**< Memory cannot be accessed by any stream on any device */ + CU_MEM_ATTACH_SINGLE = 0x4 /**< Memory can only be accessed by a single stream on the associated device */ +} CUmemAttach_flags; + +/** + * Context creation flags + */ +typedef enum CUctx_flags_enum { + CU_CTX_SCHED_AUTO = 0x00, /**< Automatic scheduling */ + CU_CTX_SCHED_SPIN = 0x01, /**< Set spin as default scheduling */ + CU_CTX_SCHED_YIELD = 0x02, /**< Set yield as default scheduling */ + CU_CTX_SCHED_BLOCKING_SYNC = 0x04, /**< Set blocking synchronization as default scheduling */ + CU_CTX_BLOCKING_SYNC = 0x04, /**< Set blocking synchronization as default scheduling + * \deprecated This flag was deprecated as of CUDA 4.0 + * and was replaced with ::CU_CTX_SCHED_BLOCKING_SYNC. */ + CU_CTX_SCHED_MASK = 0x07, + CU_CTX_MAP_HOST = 0x08, /**< \deprecated This flag was deprecated as of CUDA 11.0 + * and it no longer has any effect. All contexts + * as of CUDA 3.2 behave as though the flag is enabled. */ + CU_CTX_LMEM_RESIZE_TO_MAX = 0x10, /**< Keep local memory allocation after launch */ + CU_CTX_COREDUMP_ENABLE = 0x20, /**< Trigger coredumps from exceptions in this context */ + CU_CTX_USER_COREDUMP_ENABLE= 0x40, /**< Enable user pipe to trigger coredumps in this context */ + CU_CTX_SYNC_MEMOPS = 0x80, /**< Ensure synchronous memory operations on this context will synchronize */ + CU_CTX_FLAGS_MASK = 0xFF +} CUctx_flags; + +/** + * Event sched flags + */ +typedef enum CUevent_sched_flags_enum { + CU_EVENT_SCHED_AUTO = 0x00, /**< Automatic scheduling */ + CU_EVENT_SCHED_SPIN = 0x01, /**< Set spin as default scheduling */ + CU_EVENT_SCHED_YIELD = 0x02, /**< Set yield as default scheduling */ + CU_EVENT_SCHED_BLOCKING_SYNC = 0x04, /**< Set blocking synchronization as default scheduling */ +} CUevent_sched_flags; + +/** + * NVCL event scheduling flags + */ +typedef enum cl_event_flags_enum { + NVCL_EVENT_SCHED_AUTO = 0x00, /**< Automatic scheduling */ + NVCL_EVENT_SCHED_SPIN = 0x01, /**< Set spin as default scheduling */ + NVCL_EVENT_SCHED_YIELD = 0x02, /**< Set yield as default scheduling */ + NVCL_EVENT_SCHED_BLOCKING_SYNC = 0x04, /**< Set blocking synchronization as default scheduling */ +} cl_event_flags; + +/** + * NVCL context scheduling flags + */ +typedef enum cl_context_flags_enum { + NVCL_CTX_SCHED_AUTO = 0x00, /**< Automatic scheduling */ + NVCL_CTX_SCHED_SPIN = 0x01, /**< Set spin as default scheduling */ + NVCL_CTX_SCHED_YIELD = 0x02, /**< Set yield as default scheduling */ + NVCL_CTX_SCHED_BLOCKING_SYNC = 0x04, /**< Set blocking synchronization as default scheduling */ +} cl_context_flags; + + +/** + * Stream creation flags + */ +typedef enum CUstream_flags_enum { + CU_STREAM_DEFAULT = 0x0, /**< Default stream flag */ + CU_STREAM_NON_BLOCKING = 0x1 /**< Stream does not synchronize with stream 0 (the NULL stream) */ +} CUstream_flags; + +/** + * Legacy stream handle + * + * Stream handle that can be passed as a CUstream to use an implicit stream + * with legacy synchronization behavior. + * + * See details of the \link_sync_behavior + */ +#define CU_STREAM_LEGACY ((CUstream)0x1) + +/** + * Per-thread stream handle + * + * Stream handle that can be passed as a CUstream to use an implicit stream + * with per-thread synchronization behavior. + * + * See details of the \link_sync_behavior + */ +#define CU_STREAM_PER_THREAD ((CUstream)0x2) + +/** + * Event creation flags + */ +typedef enum CUevent_flags_enum { + CU_EVENT_DEFAULT = 0x0, /**< Default event flag */ + CU_EVENT_BLOCKING_SYNC = 0x1, /**< Event uses blocking synchronization */ + CU_EVENT_DISABLE_TIMING = 0x2, /**< Event will not record timing data */ + CU_EVENT_INTERPROCESS = 0x4 /**< Event is suitable for interprocess use. CU_EVENT_DISABLE_TIMING must be set */ +} CUevent_flags; + +/** + * Event record flags + */ +typedef enum CUevent_record_flags_enum { + CU_EVENT_RECORD_DEFAULT = 0x0, /**< Default event record flag */ + CU_EVENT_RECORD_EXTERNAL = 0x1 /**< When using stream capture, create an event record node + * instead of the default behavior. This flag is invalid + * when used outside of capture. */ +} CUevent_record_flags; + +/** + * Event wait flags + */ +typedef enum CUevent_wait_flags_enum { + CU_EVENT_WAIT_DEFAULT = 0x0, /**< Default event wait flag */ + CU_EVENT_WAIT_EXTERNAL = 0x1 /**< When using stream capture, create an event wait node + * instead of the default behavior. This flag is invalid + * when used outside of capture.*/ +} CUevent_wait_flags; + +/** + * Flags for ::cuStreamWaitValue32 and ::cuStreamWaitValue64 + */ +typedef enum CUstreamWaitValue_flags_enum { + CU_STREAM_WAIT_VALUE_GEQ = 0x0, /**< Wait until (int32_t)(*addr - value) >= 0 (or int64_t for 64 bit + values). Note this is a cyclic comparison which ignores wraparound. + (Default behavior.) */ + CU_STREAM_WAIT_VALUE_EQ = 0x1, /**< Wait until *addr == value. */ + CU_STREAM_WAIT_VALUE_AND = 0x2, /**< Wait until (*addr & value) != 0. */ + CU_STREAM_WAIT_VALUE_NOR = 0x3, /**< Wait until ~(*addr | value) != 0. Support for this operation can be + queried with ::cuDeviceGetAttribute() and + ::CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_WAIT_VALUE_NOR.*/ + CU_STREAM_WAIT_VALUE_FLUSH = 1<<30 /**< Follow the wait operation with a flush of outstanding remote writes. This + means that, if a remote write operation is guaranteed to have reached the + device before the wait can be satisfied, that write is guaranteed to be + visible to downstream device work. The device is permitted to reorder + remote writes internally. For example, this flag would be required if + two remote writes arrive in a defined order, the wait is satisfied by the + second write, and downstream work needs to observe the first write. + Support for this operation is restricted to selected platforms and can be + queried with ::CU_DEVICE_ATTRIBUTE_CAN_FLUSH_REMOTE_WRITES.*/ +} CUstreamWaitValue_flags; + +/** + * Flags for ::cuStreamWriteValue32 + */ +typedef enum CUstreamWriteValue_flags_enum { + CU_STREAM_WRITE_VALUE_DEFAULT = 0x0, /**< Default behavior */ + CU_STREAM_WRITE_VALUE_NO_MEMORY_BARRIER = 0x1 /**< Permits the write to be reordered with writes which were issued + before it, as a performance optimization. Normally, + ::cuStreamWriteValue32 will provide a memory fence before the + write, which has similar semantics to + __threadfence_system() but is scoped to the stream + rather than a CUDA thread. + This flag is not supported in the v2 API. */ +} CUstreamWriteValue_flags; + +/** + * Operations for ::cuStreamBatchMemOp + */ +typedef enum CUstreamBatchMemOpType_enum { + CU_STREAM_MEM_OP_WAIT_VALUE_32 = 1, /**< Represents a ::cuStreamWaitValue32 operation */ + CU_STREAM_MEM_OP_WRITE_VALUE_32 = 2, /**< Represents a ::cuStreamWriteValue32 operation */ + CU_STREAM_MEM_OP_WAIT_VALUE_64 = 4, /**< Represents a ::cuStreamWaitValue64 operation */ + CU_STREAM_MEM_OP_WRITE_VALUE_64 = 5, /**< Represents a ::cuStreamWriteValue64 operation */ + CU_STREAM_MEM_OP_BARRIER = 6, /**< Insert a memory barrier of the specified type */ + CU_STREAM_MEM_OP_FLUSH_REMOTE_WRITES = 3 /**< This has the same effect as ::CU_STREAM_WAIT_VALUE_FLUSH, but as a + standalone operation. */ +} CUstreamBatchMemOpType; + +/** + * Flags for ::cuStreamMemoryBarrier + */ +typedef enum CUstreamMemoryBarrier_flags_enum { + CU_STREAM_MEMORY_BARRIER_TYPE_SYS = 0x0, /**< System-wide memory barrier. */ + CU_STREAM_MEMORY_BARRIER_TYPE_GPU = 0x1 /**< Limit memory barrier scope to the GPU. */ +} CUstreamMemoryBarrier_flags; + +/** + * Per-operation parameters for ::cuStreamBatchMemOp + */ +typedef union CUstreamBatchMemOpParams_union { + CUstreamBatchMemOpType operation; + struct CUstreamMemOpWaitValueParams_st { + CUstreamBatchMemOpType operation; + CUdeviceptr address; + union { + cuuint32_t value; + cuuint64_t value64; + }; + unsigned int flags; + CUdeviceptr alias; /**< For driver internal use. Initial value is unimportant. */ + } waitValue; + struct CUstreamMemOpWriteValueParams_st { + CUstreamBatchMemOpType operation; + CUdeviceptr address; + union { + cuuint32_t value; + cuuint64_t value64; + }; + unsigned int flags; + CUdeviceptr alias; /**< For driver internal use. Initial value is unimportant. */ + } writeValue; + struct CUstreamMemOpFlushRemoteWritesParams_st { + CUstreamBatchMemOpType operation; + unsigned int flags; + } flushRemoteWrites; + struct CUstreamMemOpMemoryBarrierParams_st { /**< Only supported in the _v2 API */ + CUstreamBatchMemOpType operation; + unsigned int flags; + } memoryBarrier; + cuuint64_t pad[6]; +} CUstreamBatchMemOpParams_v1; +typedef CUstreamBatchMemOpParams_v1 CUstreamBatchMemOpParams; + +typedef struct CUDA_BATCH_MEM_OP_NODE_PARAMS_v1_st { + CUcontext ctx; + unsigned int count; + CUstreamBatchMemOpParams *paramArray; + unsigned int flags; +} CUDA_BATCH_MEM_OP_NODE_PARAMS_v1; +typedef CUDA_BATCH_MEM_OP_NODE_PARAMS_v1 CUDA_BATCH_MEM_OP_NODE_PARAMS; + +/** + * Batch memory operation node parameters + */ +typedef struct CUDA_BATCH_MEM_OP_NODE_PARAMS_v2_st { + CUcontext ctx; /**< Context to use for the operations. */ + unsigned int count; /**< Number of operations in paramArray. */ + CUstreamBatchMemOpParams *paramArray; /**< Array of batch memory operations. */ + unsigned int flags; /**< Flags to control the node. */ +} CUDA_BATCH_MEM_OP_NODE_PARAMS_v2; + +/** + * Occupancy calculator flag + */ +typedef enum CUoccupancy_flags_enum { + CU_OCCUPANCY_DEFAULT = 0x0, /**< Default behavior */ + CU_OCCUPANCY_DISABLE_CACHING_OVERRIDE = 0x1 /**< Assume global caching is enabled and cannot be automatically turned off */ +} CUoccupancy_flags; + +/** + * Flags for ::cuStreamUpdateCaptureDependencies + */ +typedef enum CUstreamUpdateCaptureDependencies_flags_enum { + CU_STREAM_ADD_CAPTURE_DEPENDENCIES = 0x0, /**< Add new nodes to the dependency set */ + CU_STREAM_SET_CAPTURE_DEPENDENCIES = 0x1 /**< Replace the dependency set with the new nodes */ +} CUstreamUpdateCaptureDependencies_flags; + +/** +* Types of async notification that can be sent +*/ +typedef enum CUasyncNotificationType_enum { + CU_ASYNC_NOTIFICATION_TYPE_OVER_BUDGET = 0x1 +} CUasyncNotificationType; + +/** +* Information passed to the user via the async notification callback +*/ +typedef struct CUasyncNotificationInfo_st { + CUasyncNotificationType type; + union { + struct { + unsigned long long bytesOverBudget; + } overBudget; + } info; +} CUasyncNotificationInfo; + +/** + * CUDA async notification callback + * \param info Information describing what actions to take as a result of this trim notification. + * \param userData Pointer to user defined data provided at registration. + * \param callback The callback handle associated with this specific callback. + */ +typedef void (*CUasyncCallback)(CUasyncNotificationInfo *info, void *userData, CUasyncCallbackHandle callback); + +/** + * Array formats + */ +typedef enum CUarray_format_enum { + CU_AD_FORMAT_UNSIGNED_INT8 = 0x01, /**< Unsigned 8-bit integers */ + CU_AD_FORMAT_UNSIGNED_INT16 = 0x02, /**< Unsigned 16-bit integers */ + CU_AD_FORMAT_UNSIGNED_INT32 = 0x03, /**< Unsigned 32-bit integers */ + CU_AD_FORMAT_SIGNED_INT8 = 0x08, /**< Signed 8-bit integers */ + CU_AD_FORMAT_SIGNED_INT16 = 0x09, /**< Signed 16-bit integers */ + CU_AD_FORMAT_SIGNED_INT32 = 0x0a, /**< Signed 32-bit integers */ + CU_AD_FORMAT_HALF = 0x10, /**< 16-bit floating point */ + CU_AD_FORMAT_FLOAT = 0x20, /**< 32-bit floating point */ + CU_AD_FORMAT_NV12 = 0xb0, /**< 8-bit YUV planar format, with 4:2:0 sampling */ + CU_AD_FORMAT_UNORM_INT8X1 = 0xc0, /**< 1 channel unsigned 8-bit normalized integer */ + CU_AD_FORMAT_UNORM_INT8X2 = 0xc1, /**< 2 channel unsigned 8-bit normalized integer */ + CU_AD_FORMAT_UNORM_INT8X4 = 0xc2, /**< 4 channel unsigned 8-bit normalized integer */ + CU_AD_FORMAT_UNORM_INT16X1 = 0xc3, /**< 1 channel unsigned 16-bit normalized integer */ + CU_AD_FORMAT_UNORM_INT16X2 = 0xc4, /**< 2 channel unsigned 16-bit normalized integer */ + CU_AD_FORMAT_UNORM_INT16X4 = 0xc5, /**< 4 channel unsigned 16-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT8X1 = 0xc6, /**< 1 channel signed 8-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT8X2 = 0xc7, /**< 2 channel signed 8-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT8X4 = 0xc8, /**< 4 channel signed 8-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT16X1 = 0xc9, /**< 1 channel signed 16-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT16X2 = 0xca, /**< 2 channel signed 16-bit normalized integer */ + CU_AD_FORMAT_SNORM_INT16X4 = 0xcb, /**< 4 channel signed 16-bit normalized integer */ + CU_AD_FORMAT_BC1_UNORM = 0x91, /**< 4 channel unsigned normalized block-compressed (BC1 compression) format */ + CU_AD_FORMAT_BC1_UNORM_SRGB = 0x92, /**< 4 channel unsigned normalized block-compressed (BC1 compression) format with sRGB encoding*/ + CU_AD_FORMAT_BC2_UNORM = 0x93, /**< 4 channel unsigned normalized block-compressed (BC2 compression) format */ + CU_AD_FORMAT_BC2_UNORM_SRGB = 0x94, /**< 4 channel unsigned normalized block-compressed (BC2 compression) format with sRGB encoding*/ + CU_AD_FORMAT_BC3_UNORM = 0x95, /**< 4 channel unsigned normalized block-compressed (BC3 compression) format */ + CU_AD_FORMAT_BC3_UNORM_SRGB = 0x96, /**< 4 channel unsigned normalized block-compressed (BC3 compression) format with sRGB encoding*/ + CU_AD_FORMAT_BC4_UNORM = 0x97, /**< 1 channel unsigned normalized block-compressed (BC4 compression) format */ + CU_AD_FORMAT_BC4_SNORM = 0x98, /**< 1 channel signed normalized block-compressed (BC4 compression) format */ + CU_AD_FORMAT_BC5_UNORM = 0x99, /**< 2 channel unsigned normalized block-compressed (BC5 compression) format */ + CU_AD_FORMAT_BC5_SNORM = 0x9a, /**< 2 channel signed normalized block-compressed (BC5 compression) format */ + CU_AD_FORMAT_BC6H_UF16 = 0x9b, /**< 3 channel unsigned half-float block-compressed (BC6H compression) format */ + CU_AD_FORMAT_BC6H_SF16 = 0x9c, /**< 3 channel signed half-float block-compressed (BC6H compression) format */ + CU_AD_FORMAT_BC7_UNORM = 0x9d, /**< 4 channel unsigned normalized block-compressed (BC7 compression) format */ + CU_AD_FORMAT_BC7_UNORM_SRGB = 0x9e /**< 4 channel unsigned normalized block-compressed (BC7 compression) format with sRGB encoding */ +} CUarray_format; + +/** + * Texture reference addressing modes + */ +typedef enum CUaddress_mode_enum { + CU_TR_ADDRESS_MODE_WRAP = 0, /**< Wrapping address mode */ + CU_TR_ADDRESS_MODE_CLAMP = 1, /**< Clamp to edge address mode */ + CU_TR_ADDRESS_MODE_MIRROR = 2, /**< Mirror address mode */ + CU_TR_ADDRESS_MODE_BORDER = 3 /**< Border address mode */ +} CUaddress_mode; + +/** + * Texture reference filtering modes + */ +typedef enum CUfilter_mode_enum { + CU_TR_FILTER_MODE_POINT = 0, /**< Point filter mode */ + CU_TR_FILTER_MODE_LINEAR = 1 /**< Linear filter mode */ +} CUfilter_mode; + +/** + * Device properties + */ +typedef enum CUdevice_attribute_enum { + CU_DEVICE_ATTRIBUTE_MAX_THREADS_PER_BLOCK = 1, /**< Maximum number of threads per block */ + CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_X = 2, /**< Maximum block dimension X */ + CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_Y = 3, /**< Maximum block dimension Y */ + CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_Z = 4, /**< Maximum block dimension Z */ + CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_X = 5, /**< Maximum grid dimension X */ + CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_Y = 6, /**< Maximum grid dimension Y */ + CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_Z = 7, /**< Maximum grid dimension Z */ + CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK = 8, /**< Maximum shared memory available per block in bytes */ + CU_DEVICE_ATTRIBUTE_SHARED_MEMORY_PER_BLOCK = 8, /**< Deprecated, use CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK */ + CU_DEVICE_ATTRIBUTE_TOTAL_CONSTANT_MEMORY = 9, /**< Memory available on device for __constant__ variables in a CUDA C kernel in bytes */ + CU_DEVICE_ATTRIBUTE_WARP_SIZE = 10, /**< Warp size in threads */ + CU_DEVICE_ATTRIBUTE_MAX_PITCH = 11, /**< Maximum pitch in bytes allowed by memory copies */ + CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_BLOCK = 12, /**< Maximum number of 32-bit registers available per block */ + CU_DEVICE_ATTRIBUTE_REGISTERS_PER_BLOCK = 12, /**< Deprecated, use CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_BLOCK */ + CU_DEVICE_ATTRIBUTE_CLOCK_RATE = 13, /**< Typical clock frequency in kilohertz */ + CU_DEVICE_ATTRIBUTE_TEXTURE_ALIGNMENT = 14, /**< Alignment requirement for textures */ + CU_DEVICE_ATTRIBUTE_GPU_OVERLAP = 15, /**< Device can possibly copy memory and execute a kernel concurrently. Deprecated. Use instead CU_DEVICE_ATTRIBUTE_ASYNC_ENGINE_COUNT. */ + CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT = 16, /**< Number of multiprocessors on device */ + CU_DEVICE_ATTRIBUTE_KERNEL_EXEC_TIMEOUT = 17, /**< Specifies whether there is a run time limit on kernels */ + CU_DEVICE_ATTRIBUTE_INTEGRATED = 18, /**< Device is integrated with host memory */ + CU_DEVICE_ATTRIBUTE_CAN_MAP_HOST_MEMORY = 19, /**< Device can map host memory into CUDA address space */ + CU_DEVICE_ATTRIBUTE_COMPUTE_MODE = 20, /**< Compute mode (See ::CUcomputemode for details) */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_WIDTH = 21, /**< Maximum 1D texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_WIDTH = 22, /**< Maximum 2D texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_HEIGHT = 23, /**< Maximum 2D texture height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_WIDTH = 24, /**< Maximum 3D texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_HEIGHT = 25, /**< Maximum 3D texture height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_DEPTH = 26, /**< Maximum 3D texture depth */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_WIDTH = 27, /**< Maximum 2D layered texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_HEIGHT = 28, /**< Maximum 2D layered texture height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_LAYERS = 29, /**< Maximum layers in a 2D layered texture */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_ARRAY_WIDTH = 27, /**< Deprecated, use CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_WIDTH */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_ARRAY_HEIGHT = 28, /**< Deprecated, use CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_HEIGHT */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_ARRAY_NUMSLICES = 29, /**< Deprecated, use CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_LAYERS */ + CU_DEVICE_ATTRIBUTE_SURFACE_ALIGNMENT = 30, /**< Alignment requirement for surfaces */ + CU_DEVICE_ATTRIBUTE_CONCURRENT_KERNELS = 31, /**< Device can possibly execute multiple kernels concurrently */ + CU_DEVICE_ATTRIBUTE_ECC_ENABLED = 32, /**< Device has ECC support enabled */ + CU_DEVICE_ATTRIBUTE_PCI_BUS_ID = 33, /**< PCI bus ID of the device */ + CU_DEVICE_ATTRIBUTE_PCI_DEVICE_ID = 34, /**< PCI device ID of the device */ + CU_DEVICE_ATTRIBUTE_TCC_DRIVER = 35, /**< Device is using TCC driver model */ + CU_DEVICE_ATTRIBUTE_MEMORY_CLOCK_RATE = 36, /**< Peak memory clock frequency in kilohertz */ + CU_DEVICE_ATTRIBUTE_GLOBAL_MEMORY_BUS_WIDTH = 37, /**< Global memory bus width in bits */ + CU_DEVICE_ATTRIBUTE_L2_CACHE_SIZE = 38, /**< Size of L2 cache in bytes */ + CU_DEVICE_ATTRIBUTE_MAX_THREADS_PER_MULTIPROCESSOR = 39, /**< Maximum resident threads per multiprocessor */ + CU_DEVICE_ATTRIBUTE_ASYNC_ENGINE_COUNT = 40, /**< Number of asynchronous engines */ + CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING = 41, /**< Device shares a unified address space with the host */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LAYERED_WIDTH = 42, /**< Maximum 1D layered texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LAYERED_LAYERS = 43, /**< Maximum layers in a 1D layered texture */ + CU_DEVICE_ATTRIBUTE_CAN_TEX2D_GATHER = 44, /**< Deprecated, do not use. */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_GATHER_WIDTH = 45, /**< Maximum 2D texture width if CUDA_ARRAY3D_TEXTURE_GATHER is set */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_GATHER_HEIGHT = 46, /**< Maximum 2D texture height if CUDA_ARRAY3D_TEXTURE_GATHER is set */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_WIDTH_ALTERNATE = 47, /**< Alternate maximum 3D texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_HEIGHT_ALTERNATE = 48, /**< Alternate maximum 3D texture height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_DEPTH_ALTERNATE = 49, /**< Alternate maximum 3D texture depth */ + CU_DEVICE_ATTRIBUTE_PCI_DOMAIN_ID = 50, /**< PCI domain ID of the device */ + CU_DEVICE_ATTRIBUTE_TEXTURE_PITCH_ALIGNMENT = 51, /**< Pitch alignment requirement for textures */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_WIDTH = 52, /**< Maximum cubemap texture width/height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_LAYERED_WIDTH = 53, /**< Maximum cubemap layered texture width/height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_LAYERED_LAYERS = 54, /**< Maximum layers in a cubemap layered texture */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_WIDTH = 55, /**< Maximum 1D surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_WIDTH = 56, /**< Maximum 2D surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_HEIGHT = 57, /**< Maximum 2D surface height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_WIDTH = 58, /**< Maximum 3D surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_HEIGHT = 59, /**< Maximum 3D surface height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_DEPTH = 60, /**< Maximum 3D surface depth */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_LAYERED_WIDTH = 61, /**< Maximum 1D layered surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_LAYERED_LAYERS = 62, /**< Maximum layers in a 1D layered surface */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_WIDTH = 63, /**< Maximum 2D layered surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_HEIGHT = 64, /**< Maximum 2D layered surface height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_LAYERS = 65, /**< Maximum layers in a 2D layered surface */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_WIDTH = 66, /**< Maximum cubemap surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_LAYERED_WIDTH = 67, /**< Maximum cubemap layered surface width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_LAYERED_LAYERS = 68, /**< Maximum layers in a cubemap layered surface */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LINEAR_WIDTH = 69, /**< Deprecated, do not use. Use cudaDeviceGetTexture1DLinearMaxWidth() or cuDeviceGetTexture1DLinearMaxWidth() instead. */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_WIDTH = 70, /**< Maximum 2D linear texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_HEIGHT = 71, /**< Maximum 2D linear texture height */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_PITCH = 72, /**< Maximum 2D linear texture pitch in bytes */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_MIPMAPPED_WIDTH = 73, /**< Maximum mipmapped 2D texture width */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_MIPMAPPED_HEIGHT = 74, /**< Maximum mipmapped 2D texture height */ + CU_DEVICE_ATTRIBUTE_COMPUTE_CAPABILITY_MAJOR = 75, /**< Major compute capability version number */ + CU_DEVICE_ATTRIBUTE_COMPUTE_CAPABILITY_MINOR = 76, /**< Minor compute capability version number */ + CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_MIPMAPPED_WIDTH = 77, /**< Maximum mipmapped 1D texture width */ + CU_DEVICE_ATTRIBUTE_STREAM_PRIORITIES_SUPPORTED = 78, /**< Device supports stream priorities */ + CU_DEVICE_ATTRIBUTE_GLOBAL_L1_CACHE_SUPPORTED = 79, /**< Device supports caching globals in L1 */ + CU_DEVICE_ATTRIBUTE_LOCAL_L1_CACHE_SUPPORTED = 80, /**< Device supports caching locals in L1 */ + CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR = 81, /**< Maximum shared memory available per multiprocessor in bytes */ + CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_MULTIPROCESSOR = 82, /**< Maximum number of 32-bit registers available per multiprocessor */ + CU_DEVICE_ATTRIBUTE_MANAGED_MEMORY = 83, /**< Device can allocate managed memory on this system */ + CU_DEVICE_ATTRIBUTE_MULTI_GPU_BOARD = 84, /**< Device is on a multi-GPU board */ + CU_DEVICE_ATTRIBUTE_MULTI_GPU_BOARD_GROUP_ID = 85, /**< Unique id for a group of devices on the same multi-GPU board */ + CU_DEVICE_ATTRIBUTE_HOST_NATIVE_ATOMIC_SUPPORTED = 86, /**< Link between the device and the host supports native atomic operations (this is a placeholder attribute, and is not supported on any current hardware)*/ + CU_DEVICE_ATTRIBUTE_SINGLE_TO_DOUBLE_PRECISION_PERF_RATIO = 87, /**< Ratio of single precision performance (in floating-point operations per second) to double precision performance */ + CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS = 88, /**< Device supports coherently accessing pageable memory without calling cudaHostRegister on it */ + CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS = 89, /**< Device can coherently access managed memory concurrently with the CPU */ + CU_DEVICE_ATTRIBUTE_COMPUTE_PREEMPTION_SUPPORTED = 90, /**< Device supports compute preemption. */ + CU_DEVICE_ATTRIBUTE_CAN_USE_HOST_POINTER_FOR_REGISTERED_MEM = 91, /**< Device can access host registered memory at the same virtual address as the CPU */ + CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_MEM_OPS_V1 = 92, /**< Deprecated, along with v1 MemOps API, ::cuStreamBatchMemOp and related APIs are supported. */ + CU_DEVICE_ATTRIBUTE_CAN_USE_64_BIT_STREAM_MEM_OPS_V1 = 93, /**< Deprecated, along with v1 MemOps API, 64-bit operations are supported in ::cuStreamBatchMemOp and related APIs. */ + CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_WAIT_VALUE_NOR_V1 = 94, /**< Deprecated, along with v1 MemOps API, ::CU_STREAM_WAIT_VALUE_NOR is supported. */ + CU_DEVICE_ATTRIBUTE_COOPERATIVE_LAUNCH = 95, /**< Device supports launching cooperative kernels via ::cuLaunchCooperativeKernel */ + CU_DEVICE_ATTRIBUTE_COOPERATIVE_MULTI_DEVICE_LAUNCH = 96, /**< Deprecated, ::cuLaunchCooperativeKernelMultiDevice is deprecated. */ + CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN = 97, /**< Maximum optin shared memory per block */ + CU_DEVICE_ATTRIBUTE_CAN_FLUSH_REMOTE_WRITES = 98, /**< The ::CU_STREAM_WAIT_VALUE_FLUSH flag and the ::CU_STREAM_MEM_OP_FLUSH_REMOTE_WRITES MemOp are supported on the device. See \ref CUDA_MEMOP for additional details. */ + CU_DEVICE_ATTRIBUTE_HOST_REGISTER_SUPPORTED = 99, /**< Device supports host memory registration via ::cudaHostRegister. */ + CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES = 100, /**< Device accesses pageable memory via the host's page tables. */ + CU_DEVICE_ATTRIBUTE_DIRECT_MANAGED_MEM_ACCESS_FROM_HOST = 101, /**< The host can directly access managed memory on the device without migration. */ + CU_DEVICE_ATTRIBUTE_VIRTUAL_ADDRESS_MANAGEMENT_SUPPORTED = 102, /**< Deprecated, Use CU_DEVICE_ATTRIBUTE_VIRTUAL_MEMORY_MANAGEMENT_SUPPORTED*/ + CU_DEVICE_ATTRIBUTE_VIRTUAL_MEMORY_MANAGEMENT_SUPPORTED = 102, /**< Device supports virtual memory management APIs like ::cuMemAddressReserve, ::cuMemCreate, ::cuMemMap and related APIs */ + CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_POSIX_FILE_DESCRIPTOR_SUPPORTED = 103, /**< Device supports exporting memory to a posix file descriptor with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate */ + CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_WIN32_HANDLE_SUPPORTED = 104, /**< Device supports exporting memory to a Win32 NT handle with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate */ + CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_WIN32_KMT_HANDLE_SUPPORTED = 105, /**< Device supports exporting memory to a Win32 KMT handle with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate */ + CU_DEVICE_ATTRIBUTE_MAX_BLOCKS_PER_MULTIPROCESSOR = 106, /**< Maximum number of blocks per multiprocessor */ + CU_DEVICE_ATTRIBUTE_GENERIC_COMPRESSION_SUPPORTED = 107, /**< Device supports compression of memory */ + CU_DEVICE_ATTRIBUTE_MAX_PERSISTING_L2_CACHE_SIZE = 108, /**< Maximum L2 persisting lines capacity setting in bytes. */ + CU_DEVICE_ATTRIBUTE_MAX_ACCESS_POLICY_WINDOW_SIZE = 109, /**< Maximum value of CUaccessPolicyWindow::num_bytes. */ + CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_WITH_CUDA_VMM_SUPPORTED = 110, /**< Device supports specifying the GPUDirect RDMA flag with ::cuMemCreate */ + CU_DEVICE_ATTRIBUTE_RESERVED_SHARED_MEMORY_PER_BLOCK = 111, /**< Shared memory reserved by CUDA driver per block in bytes */ + CU_DEVICE_ATTRIBUTE_SPARSE_CUDA_ARRAY_SUPPORTED = 112, /**< Device supports sparse CUDA arrays and sparse CUDA mipmapped arrays */ + CU_DEVICE_ATTRIBUTE_READ_ONLY_HOST_REGISTER_SUPPORTED = 113, /**< Device supports using the ::cuMemHostRegister flag ::CU_MEMHOSTERGISTER_READ_ONLY to register memory that must be mapped as read-only to the GPU */ + CU_DEVICE_ATTRIBUTE_TIMELINE_SEMAPHORE_INTEROP_SUPPORTED = 114, /**< External timeline semaphore interop is supported on the device */ + CU_DEVICE_ATTRIBUTE_MEMORY_POOLS_SUPPORTED = 115, /**< Device supports using the ::cuMemAllocAsync and ::cuMemPool family of APIs */ + CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_SUPPORTED = 116, /**< Device supports GPUDirect RDMA APIs, like nvidia_p2p_get_pages (see https://docs.nvidia.com/cuda/gpudirect-rdma for more information) */ + CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_FLUSH_WRITES_OPTIONS = 117, /**< The returned attribute shall be interpreted as a bitmask, where the individual bits are described by the ::CUflushGPUDirectRDMAWritesOptions enum */ + CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_WRITES_ORDERING = 118, /**< GPUDirect RDMA writes to the device do not need to be flushed for consumers within the scope indicated by the returned attribute. See ::CUGPUDirectRDMAWritesOrdering for the numerical values returned here. */ + CU_DEVICE_ATTRIBUTE_MEMPOOL_SUPPORTED_HANDLE_TYPES = 119, /**< Handle types supported with mempool based IPC */ + CU_DEVICE_ATTRIBUTE_CLUSTER_LAUNCH = 120, /**< Indicates device supports cluster launch */ + CU_DEVICE_ATTRIBUTE_DEFERRED_MAPPING_CUDA_ARRAY_SUPPORTED = 121, /**< Device supports deferred mapping CUDA arrays and CUDA mipmapped arrays */ + CU_DEVICE_ATTRIBUTE_CAN_USE_64_BIT_STREAM_MEM_OPS = 122, /**< 64-bit operations are supported in ::cuStreamBatchMemOp and related MemOp APIs. */ + CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_WAIT_VALUE_NOR = 123, /**< ::CU_STREAM_WAIT_VALUE_NOR is supported by MemOp APIs. */ + CU_DEVICE_ATTRIBUTE_DMA_BUF_SUPPORTED = 124, /**< Device supports buffer sharing with dma_buf mechanism. */ + CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED = 125, /**< Device supports IPC Events. */ + CU_DEVICE_ATTRIBUTE_MEM_SYNC_DOMAIN_COUNT = 126, /**< Number of memory domains the device supports. */ + CU_DEVICE_ATTRIBUTE_TENSOR_MAP_ACCESS_SUPPORTED = 127, /**< Device supports accessing memory using Tensor Map. */ + CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_FABRIC_SUPPORTED = 128, /**< Device supports exporting memory to a fabric handle with cuMemExportToShareableHandle() or requested with cuMemCreate() */ + CU_DEVICE_ATTRIBUTE_UNIFIED_FUNCTION_POINTERS = 129, /**< Device supports unified function pointers. */ + CU_DEVICE_ATTRIBUTE_NUMA_CONFIG = 130, + CU_DEVICE_ATTRIBUTE_NUMA_ID = 131, + CU_DEVICE_ATTRIBUTE_MULTICAST_SUPPORTED = 132, /**< Device supports switch multicast and reduction operations. */ + CU_DEVICE_ATTRIBUTE_MPS_ENABLED = 133, /**< Indicates if contexts created on this device will be shared via MPS */ + CU_DEVICE_ATTRIBUTE_HOST_NUMA_ID = 134, /**< NUMA ID of the host node closest to the device. Returns -1 when system does not support NUMA. */ + CU_DEVICE_ATTRIBUTE_MAX +} CUdevice_attribute; + +/** + * Legacy device properties + */ +typedef struct CUdevprop_st { + int maxThreadsPerBlock; /**< Maximum number of threads per block */ + int maxThreadsDim[3]; /**< Maximum size of each dimension of a block */ + int maxGridSize[3]; /**< Maximum size of each dimension of a grid */ + int sharedMemPerBlock; /**< Shared memory available per block in bytes */ + int totalConstantMemory; /**< Constant memory available on device in bytes */ + int SIMDWidth; /**< Warp size in threads */ + int memPitch; /**< Maximum pitch in bytes allowed by memory copies */ + int regsPerBlock; /**< 32-bit registers available per block */ + int clockRate; /**< Clock frequency in kilohertz */ + int textureAlign; /**< Alignment requirement for textures */ +} CUdevprop_v1; +typedef CUdevprop_v1 CUdevprop; + +/** + * Pointer information + */ +typedef enum CUpointer_attribute_enum { + CU_POINTER_ATTRIBUTE_CONTEXT = 1, /**< The ::CUcontext on which a pointer was allocated or registered */ + CU_POINTER_ATTRIBUTE_MEMORY_TYPE = 2, /**< The ::CUmemorytype describing the physical location of a pointer */ + CU_POINTER_ATTRIBUTE_DEVICE_POINTER = 3, /**< The address at which a pointer's memory may be accessed on the device */ + CU_POINTER_ATTRIBUTE_HOST_POINTER = 4, /**< The address at which a pointer's memory may be accessed on the host */ + CU_POINTER_ATTRIBUTE_P2P_TOKENS = 5, /**< A pair of tokens for use with the nv-p2p.h Linux kernel interface */ + CU_POINTER_ATTRIBUTE_SYNC_MEMOPS = 6, /**< Synchronize every synchronous memory operation initiated on this region */ + CU_POINTER_ATTRIBUTE_BUFFER_ID = 7, /**< A process-wide unique ID for an allocated memory region*/ + CU_POINTER_ATTRIBUTE_IS_MANAGED = 8, /**< Indicates if the pointer points to managed memory */ + CU_POINTER_ATTRIBUTE_DEVICE_ORDINAL = 9, /**< A device ordinal of a device on which a pointer was allocated or registered */ + CU_POINTER_ATTRIBUTE_IS_LEGACY_CUDA_IPC_CAPABLE = 10, /**< 1 if this pointer maps to an allocation that is suitable for ::cudaIpcGetMemHandle, 0 otherwise **/ + CU_POINTER_ATTRIBUTE_RANGE_START_ADDR = 11, /**< Starting address for this requested pointer */ + CU_POINTER_ATTRIBUTE_RANGE_SIZE = 12, /**< Size of the address range for this requested pointer */ + CU_POINTER_ATTRIBUTE_MAPPED = 13, /**< 1 if this pointer is in a valid address range that is mapped to a backing allocation, 0 otherwise **/ + CU_POINTER_ATTRIBUTE_ALLOWED_HANDLE_TYPES = 14, /**< Bitmask of allowed ::CUmemAllocationHandleType for this allocation **/ + CU_POINTER_ATTRIBUTE_IS_GPU_DIRECT_RDMA_CAPABLE = 15, /**< 1 if the memory this pointer is referencing can be used with the GPUDirect RDMA API **/ + CU_POINTER_ATTRIBUTE_ACCESS_FLAGS = 16, /**< Returns the access flags the device associated with the current context has on the corresponding memory referenced by the pointer given */ + CU_POINTER_ATTRIBUTE_MEMPOOL_HANDLE = 17, /**< Returns the mempool handle for the allocation if it was allocated from a mempool. Otherwise returns NULL. **/ + CU_POINTER_ATTRIBUTE_MAPPING_SIZE = 18, /**< Size of the actual underlying mapping that the pointer belongs to **/ + CU_POINTER_ATTRIBUTE_MAPPING_BASE_ADDR = 19, /**< The start address of the mapping that the pointer belongs to **/ + CU_POINTER_ATTRIBUTE_MEMORY_BLOCK_ID = 20 /**< A process-wide unique id corresponding to the physical allocation the pointer belongs to **/ +} CUpointer_attribute; + +/** + * Function properties + */ +typedef enum CUfunction_attribute_enum { + /** + * The maximum number of threads per block, beyond which a launch of the + * function would fail. This number depends on both the function and the + * device on which the function is currently loaded. + */ + CU_FUNC_ATTRIBUTE_MAX_THREADS_PER_BLOCK = 0, + + /** + * The size in bytes of statically-allocated shared memory required by + * this function. This does not include dynamically-allocated shared + * memory requested by the user at runtime. + */ + CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES = 1, + + /** + * The size in bytes of user-allocated constant memory required by this + * function. + */ + CU_FUNC_ATTRIBUTE_CONST_SIZE_BYTES = 2, + + /** + * The size in bytes of local memory used by each thread of this function. + */ + CU_FUNC_ATTRIBUTE_LOCAL_SIZE_BYTES = 3, + + /** + * The number of registers used by each thread of this function. + */ + CU_FUNC_ATTRIBUTE_NUM_REGS = 4, + + /** + * The PTX virtual architecture version for which the function was + * compiled. This value is the major PTX version * 10 + the minor PTX + * version, so a PTX version 1.3 function would return the value 13. + * Note that this may return the undefined value of 0 for cubins + * compiled prior to CUDA 3.0. + */ + CU_FUNC_ATTRIBUTE_PTX_VERSION = 5, + + /** + * The binary architecture version for which the function was compiled. + * This value is the major binary version * 10 + the minor binary version, + * so a binary version 1.3 function would return the value 13. Note that + * this will return a value of 10 for legacy cubins that do not have a + * properly-encoded binary architecture version. + */ + CU_FUNC_ATTRIBUTE_BINARY_VERSION = 6, + + /** + * The attribute to indicate whether the function has been compiled with + * user specified option "-Xptxas --dlcm=ca" set . + */ + CU_FUNC_ATTRIBUTE_CACHE_MODE_CA = 7, + + /** + * The maximum size in bytes of dynamically-allocated shared memory that can be used by + * this function. If the user-specified dynamic shared memory size is larger than this + * value, the launch will fail. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES = 8, + + /** + * On devices where the L1 cache and shared memory use the same hardware resources, + * this sets the shared memory carveout preference, in percent of the total shared memory. + * Refer to ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR. + * This is only a hint, and the driver can choose a different ratio if required to execute the function. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT = 9, + + /** + * If this attribute is set, the kernel must launch with a valid cluster + * size specified. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_CLUSTER_SIZE_MUST_BE_SET = 10, + + /** + * The required cluster width in blocks. The values must either all be 0 or + * all be positive. The validity of the cluster dimensions is otherwise + * checked at launch time. + * + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_WIDTH = 11, + + /** + * The required cluster height in blocks. The values must either all be 0 or + * all be positive. The validity of the cluster dimensions is otherwise + * checked at launch time. + * + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime should return CUDA_ERROR_NOT_PERMITTED. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_HEIGHT = 12, + + /** + * The required cluster depth in blocks. The values must either all be 0 or + * all be positive. The validity of the cluster dimensions is otherwise + * checked at launch time. + * + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime should return CUDA_ERROR_NOT_PERMITTED. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_DEPTH = 13, + + /** + * Whether the function can be launched with non-portable cluster size. 1 is + * allowed, 0 is disallowed. A non-portable cluster size may only function + * on the specific SKUs the program is tested on. The launch might fail if + * the program is run on a different hardware platform. + * + * CUDA API provides cudaOccupancyMaxActiveClusters to assist with checking + * whether the desired size can be launched on the current device. + * + * Portable Cluster Size + * + * A portable cluster size is guaranteed to be functional on all compute + * capabilities higher than the target compute capability. The portable + * cluster size for sm_90 is 8 blocks per cluster. This value may increase + * for future compute capabilities. + * + * The specific hardware unit may support higher cluster sizes that’s not + * guaranteed to be portable. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_NON_PORTABLE_CLUSTER_SIZE_ALLOWED = 14, + + /** + * The block scheduling policy of a function. The value type is + * CUclusterSchedulingPolicy / cudaClusterSchedulingPolicy. + * See ::cuFuncSetAttribute, ::cuKernelSetAttribute + */ + CU_FUNC_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE = 15, + + CU_FUNC_ATTRIBUTE_MAX +} CUfunction_attribute; + +/** + * Function cache configurations + */ +typedef enum CUfunc_cache_enum { + CU_FUNC_CACHE_PREFER_NONE = 0x00, /**< no preference for shared memory or L1 (default) */ + CU_FUNC_CACHE_PREFER_SHARED = 0x01, /**< prefer larger shared memory and smaller L1 cache */ + CU_FUNC_CACHE_PREFER_L1 = 0x02, /**< prefer larger L1 cache and smaller shared memory */ + CU_FUNC_CACHE_PREFER_EQUAL = 0x03 /**< prefer equal sized L1 cache and shared memory */ +} CUfunc_cache; + +/** + * \deprecated + * + * Shared memory configurations + */ +typedef enum CUsharedconfig_enum { + CU_SHARED_MEM_CONFIG_DEFAULT_BANK_SIZE = 0x00, /**< set default shared memory bank size */ + CU_SHARED_MEM_CONFIG_FOUR_BYTE_BANK_SIZE = 0x01, /**< set shared memory bank width to four bytes */ + CU_SHARED_MEM_CONFIG_EIGHT_BYTE_BANK_SIZE = 0x02 /**< set shared memory bank width to eight bytes */ +} CUsharedconfig; + +/** + * Shared memory carveout configurations. These may be passed to ::cuFuncSetAttribute or ::cuKernelSetAttribute + */ +typedef enum CUshared_carveout_enum { + CU_SHAREDMEM_CARVEOUT_DEFAULT = -1, /**< No preference for shared memory or L1 (default) */ + CU_SHAREDMEM_CARVEOUT_MAX_SHARED = 100, /**< Prefer maximum available shared memory, minimum L1 cache */ + CU_SHAREDMEM_CARVEOUT_MAX_L1 = 0 /**< Prefer maximum available L1 cache, minimum shared memory */ +} CUshared_carveout; + +/** + * Memory types + */ +typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, /**< Host memory */ + CU_MEMORYTYPE_DEVICE = 0x02, /**< Device memory */ + CU_MEMORYTYPE_ARRAY = 0x03, /**< Array memory */ + CU_MEMORYTYPE_UNIFIED = 0x04 /**< Unified device or host memory */ +} CUmemorytype; + +/** + * Compute Modes + */ +typedef enum CUcomputemode_enum { + CU_COMPUTEMODE_DEFAULT = 0, /**< Default compute mode (Multiple contexts allowed per device) */ + CU_COMPUTEMODE_PROHIBITED = 2, /**< Compute-prohibited mode (No contexts can be created on this device at this time) */ + CU_COMPUTEMODE_EXCLUSIVE_PROCESS = 3 /**< Compute-exclusive-process mode (Only one context used by a single process can be present on this device at a time) */ +} CUcomputemode; + +/** + * Memory advise values + */ +typedef enum CUmem_advise_enum { + CU_MEM_ADVISE_SET_READ_MOSTLY = 1, /**< Data will mostly be read and only occasionally be written to */ + CU_MEM_ADVISE_UNSET_READ_MOSTLY = 2, /**< Undo the effect of ::CU_MEM_ADVISE_SET_READ_MOSTLY */ + CU_MEM_ADVISE_SET_PREFERRED_LOCATION = 3, /**< Set the preferred location for the data as the specified device */ + CU_MEM_ADVISE_UNSET_PREFERRED_LOCATION = 4, /**< Clear the preferred location for the data */ + CU_MEM_ADVISE_SET_ACCESSED_BY = 5, /**< Data will be accessed by the specified device, so prevent page faults as much as possible */ + CU_MEM_ADVISE_UNSET_ACCESSED_BY = 6 /**< Let the Unified Memory subsystem decide on the page faulting policy for the specified device */ +} CUmem_advise; + +typedef enum CUmem_range_attribute_enum { + CU_MEM_RANGE_ATTRIBUTE_READ_MOSTLY = 1, /**< Whether the range will mostly be read and only occasionally be written to */ + CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION = 2, /**< The preferred location of the range */ + CU_MEM_RANGE_ATTRIBUTE_ACCESSED_BY = 3, /**< Memory range has ::CU_MEM_ADVISE_SET_ACCESSED_BY set for specified device */ + CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION = 4 /**< The last location to which the range was prefetched */ + , CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_TYPE = 5 /**< The preferred location type of the range */ + , CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_ID = 6 /**< The preferred location id of the range */ + , CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_TYPE = 7 /**< The last location type to which the range was prefetched */ + , CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_ID = 8 /**< The last location id to which the range was prefetched */ +} CUmem_range_attribute; + +/** + * Online compiler and linker options + */ +typedef enum CUjit_option_enum +{ + /** + * Max number of registers that a thread may use.\n + * Option type: unsigned int\n + * Applies to: compiler only + */ + CU_JIT_MAX_REGISTERS = 0, + + /** + * IN: Specifies minimum number of threads per block to target compilation + * for\n + * OUT: Returns the number of threads the compiler actually targeted. + * This restricts the resource utilization of the compiler (e.g. max + * registers) such that a block with the given number of threads should be + * able to launch based on register limitations. Note, this option does not + * currently take into account any other resource limitations, such as + * shared memory utilization.\n + * Cannot be combined with ::CU_JIT_TARGET.\n + * Option type: unsigned int\n + * Applies to: compiler only + */ + CU_JIT_THREADS_PER_BLOCK = 1, + + /** + * Overwrites the option value with the total wall clock time, in + * milliseconds, spent in the compiler and linker\n + * Option type: float\n + * Applies to: compiler and linker + */ + CU_JIT_WALL_TIME = 2, + + /** + * Pointer to a buffer in which to print any log messages + * that are informational in nature (the buffer size is specified via + * option ::CU_JIT_INFO_LOG_BUFFER_SIZE_BYTES)\n + * Option type: char *\n + * Applies to: compiler and linker + */ + CU_JIT_INFO_LOG_BUFFER = 3, + + /** + * IN: Log buffer size in bytes. Log messages will be capped at this size + * (including null terminator)\n + * OUT: Amount of log buffer filled with messages\n + * Option type: unsigned int\n + * Applies to: compiler and linker + */ + CU_JIT_INFO_LOG_BUFFER_SIZE_BYTES = 4, + + /** + * Pointer to a buffer in which to print any log messages that + * reflect errors (the buffer size is specified via option + * ::CU_JIT_ERROR_LOG_BUFFER_SIZE_BYTES)\n + * Option type: char *\n + * Applies to: compiler and linker + */ + CU_JIT_ERROR_LOG_BUFFER = 5, + + /** + * IN: Log buffer size in bytes. Log messages will be capped at this size + * (including null terminator)\n + * OUT: Amount of log buffer filled with messages\n + * Option type: unsigned int\n + * Applies to: compiler and linker + */ + CU_JIT_ERROR_LOG_BUFFER_SIZE_BYTES = 6, + + /** + * Level of optimizations to apply to generated code (0 - 4), with 4 + * being the default and highest level of optimizations.\n + * Option type: unsigned int\n + * Applies to: compiler only + */ + CU_JIT_OPTIMIZATION_LEVEL = 7, + + /** + * No option value required. Determines the target based on the current + * attached context (default)\n + * Option type: No option value needed\n + * Applies to: compiler and linker + */ + CU_JIT_TARGET_FROM_CUCONTEXT = 8, + + /** + * Target is chosen based on supplied ::CUjit_target. Cannot be + * combined with ::CU_JIT_THREADS_PER_BLOCK.\n + * Option type: unsigned int for enumerated type ::CUjit_target\n + * Applies to: compiler and linker + */ + CU_JIT_TARGET = 9, + + /** + * Specifies choice of fallback strategy if matching cubin is not found. + * Choice is based on supplied ::CUjit_fallback. This option cannot be + * used with cuLink* APIs as the linker requires exact matches.\n + * Option type: unsigned int for enumerated type ::CUjit_fallback\n + * Applies to: compiler only + */ + CU_JIT_FALLBACK_STRATEGY = 10, + + /** + * Specifies whether to create debug information in output (-g) + * (0: false, default)\n + * Option type: int\n + * Applies to: compiler and linker + */ + CU_JIT_GENERATE_DEBUG_INFO = 11, + + /** + * Generate verbose log messages (0: false, default)\n + * Option type: int\n + * Applies to: compiler and linker + */ + CU_JIT_LOG_VERBOSE = 12, + + /** + * Generate line number information (-lineinfo) (0: false, default)\n + * Option type: int\n + * Applies to: compiler only + */ + CU_JIT_GENERATE_LINE_INFO = 13, + + /** + * Specifies whether to enable caching explicitly (-dlcm) \n + * Choice is based on supplied ::CUjit_cacheMode_enum.\n + * Option type: unsigned int for enumerated type ::CUjit_cacheMode_enum\n + * Applies to: compiler only + */ + CU_JIT_CACHE_MODE = 14, + + /** + * \deprecated + * This jit option is deprecated and should not be used. + */ + CU_JIT_NEW_SM3X_OPT = 15, + + /** + * This jit option is used for internal purpose only. + */ + CU_JIT_FAST_COMPILE = 16, + + /** + * Array of device symbol names that will be relocated to the corresponding + * host addresses stored in ::CU_JIT_GLOBAL_SYMBOL_ADDRESSES.\n + * Must contain ::CU_JIT_GLOBAL_SYMBOL_COUNT entries.\n + * When loading a device module, driver will relocate all encountered + * unresolved symbols to the host addresses.\n + * It is only allowed to register symbols that correspond to unresolved + * global variables.\n + * It is illegal to register the same device symbol at multiple addresses.\n + * Option type: const char **\n + * Applies to: dynamic linker only + */ + CU_JIT_GLOBAL_SYMBOL_NAMES = 17, + + /** + * Array of host addresses that will be used to relocate corresponding + * device symbols stored in ::CU_JIT_GLOBAL_SYMBOL_NAMES.\n + * Must contain ::CU_JIT_GLOBAL_SYMBOL_COUNT entries.\n + * Option type: void **\n + * Applies to: dynamic linker only + */ + CU_JIT_GLOBAL_SYMBOL_ADDRESSES = 18, + + /** + * Number of entries in ::CU_JIT_GLOBAL_SYMBOL_NAMES and + * ::CU_JIT_GLOBAL_SYMBOL_ADDRESSES arrays.\n + * Option type: unsigned int\n + * Applies to: dynamic linker only + */ + CU_JIT_GLOBAL_SYMBOL_COUNT = 19, + + /** + * \deprecated + * Enable link-time optimization (-dlto) for device code (Disabled by default).\n + * This option is not supported on 32-bit platforms.\n + * Option type: int\n + * Applies to: compiler and linker + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_LTO = 20, + + /** + * \deprecated + * Control single-precision denormals (-ftz) support (0: false, default). + * 1 : flushes denormal values to zero + * 0 : preserves denormal values + * Option type: int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_FTZ = 21, + + /** + * \deprecated + * Control single-precision floating-point division and reciprocals + * (-prec-div) support (1: true, default). + * 1 : Enables the IEEE round-to-nearest mode + * 0 : Enables the fast approximation mode + * Option type: int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_PREC_DIV = 22, + + /** + * \deprecated + * Control single-precision floating-point square root + * (-prec-sqrt) support (1: true, default). + * 1 : Enables the IEEE round-to-nearest mode + * 0 : Enables the fast approximation mode + * Option type: int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_PREC_SQRT = 23, + + /** + * \deprecated + * Enable/Disable the contraction of floating-point multiplies + * and adds/subtracts into floating-point multiply-add (-fma) + * operations (1: Enable, default; 0: Disable). + * Option type: int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_FMA = 24, + + /** + * \deprecated + * Array of kernel names that should be preserved at link time while others + * can be removed.\n + * Must contain ::CU_JIT_REFERENCED_KERNEL_COUNT entries.\n + * Note that kernel names can be mangled by the compiler in which case the + * mangled name needs to be specified.\n + * Wildcard "*" can be used to represent zero or more characters instead of + * specifying the full or mangled name.\n + * It is important to note that the wildcard "*" is also added implicitly. + * For example, specifying "foo" will match "foobaz", "barfoo", "barfoobaz" and + * thus preserve all kernels with those names. This can be avoided by providing + * a more specific name like "barfoobaz".\n + * Option type: const char **\n + * Applies to: dynamic linker only + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_REFERENCED_KERNEL_NAMES = 25, + + /** + * \deprecated + * Number of entries in ::CU_JIT_REFERENCED_KERNEL_NAMES array.\n + * Option type: unsigned int\n + * Applies to: dynamic linker only + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_REFERENCED_KERNEL_COUNT = 26, + + /** + * \deprecated + * Array of variable names (__device__ and/or __constant__) that should be + * preserved at link time while others can be removed.\n + * Must contain ::CU_JIT_REFERENCED_VARIABLE_COUNT entries.\n + * Note that variable names can be mangled by the compiler in which case the + * mangled name needs to be specified.\n + * Wildcard "*" can be used to represent zero or more characters instead of + * specifying the full or mangled name.\n + * It is important to note that the wildcard "*" is also added implicitly. + * For example, specifying "foo" will match "foobaz", "barfoo", "barfoobaz" and + * thus preserve all variables with those names. This can be avoided by providing + * a more specific name like "barfoobaz".\n + * Option type: const char **\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_REFERENCED_VARIABLE_NAMES = 27, + + /** + * \deprecated + * Number of entries in ::CU_JIT_REFERENCED_VARIABLE_NAMES array.\n + * Option type: unsigned int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_REFERENCED_VARIABLE_COUNT = 28, + + /** + * \deprecated + * This option serves as a hint to enable the JIT compiler/linker + * to remove constant (__constant__) and device (__device__) variables + * unreferenced in device code (Disabled by default).\n + * Note that host references to constant and device variables using APIs like + * ::cuModuleGetGlobal() with this option specified may result in undefined behavior unless + * the variables are explicitly specified using ::CU_JIT_REFERENCED_VARIABLE_NAMES.\n + * Option type: int\n + * Applies to: link-time optimization specified with CU_JIT_LTO + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_OPTIMIZE_UNUSED_DEVICE_VARIABLES = 29, + + /** + * Generate position independent code (0: false)\n + * Option type: int\n + * Applies to: compiler only + */ + CU_JIT_POSITION_INDEPENDENT_CODE = 30, + + /** + * This option hints to the JIT compiler the minimum number of CTAs from the + * kernel’s grid to be mapped to a SM. This option is ignored when used together + * with ::CU_JIT_MAX_REGISTERS or ::CU_JIT_THREADS_PER_BLOCK. + * Optimizations based on this option need ::CU_JIT_MAX_THREADS_PER_BLOCK to + * be specified as well. For kernels already using PTX directive .minnctapersm, + * this option will be ignored by default. Use ::CU_JIT_OVERRIDE_DIRECTIVE_VALUES + * to let this option take precedence over the PTX directive. + * Option type: unsigned int\n + * Applies to: compiler only + */ + CU_JIT_MIN_CTA_PER_SM = 31, + + /** + * Maximum number threads in a thread block, computed as the product of + * the maximum extent specifed for each dimension of the block. This limit + * is guaranteed not to be exeeded in any invocation of the kernel. Exceeding + * the the maximum number of threads results in runtime error or kernel launch + * failure. For kernels already using PTX directive .maxntid, this option will + * be ignored by default. Use ::CU_JIT_OVERRIDE_DIRECTIVE_VALUES to let this + * option take precedence over the PTX directive. + * Option type: int\n + * Applies to: compiler only + */ + CU_JIT_MAX_THREADS_PER_BLOCK = 32, + + /** + * This option lets the values specified using ::CU_JIT_MAX_REGISTERS, + * ::CU_JIT_THREADS_PER_BLOCK, ::CU_JIT_MAX_THREADS_PER_BLOCK and + * ::CU_JIT_MIN_CTA_PER_SM take precedence over any PTX directives. + * (0: Disable, default; 1: Enable) + * Option type: int\n + * Applies to: compiler only + */ + CU_JIT_OVERRIDE_DIRECTIVE_VALUES = 33, + CU_JIT_NUM_OPTIONS + +} CUjit_option; + +/* + * Indicates that compute device class supports accelerated features. + */ +#define CU_COMPUTE_ACCELERATED_TARGET_BASE 0x10000 + +/** + * Online compilation targets + */ +typedef enum CUjit_target_enum +{ + CU_TARGET_COMPUTE_30 = 30, /**< Compute device class 3.0 */ + CU_TARGET_COMPUTE_32 = 32, /**< Compute device class 3.2 */ + CU_TARGET_COMPUTE_35 = 35, /**< Compute device class 3.5 */ + CU_TARGET_COMPUTE_37 = 37, /**< Compute device class 3.7 */ + CU_TARGET_COMPUTE_50 = 50, /**< Compute device class 5.0 */ + CU_TARGET_COMPUTE_52 = 52, /**< Compute device class 5.2 */ + CU_TARGET_COMPUTE_53 = 53, /**< Compute device class 5.3 */ + CU_TARGET_COMPUTE_60 = 60, /**< Compute device class 6.0.*/ + CU_TARGET_COMPUTE_61 = 61, /**< Compute device class 6.1.*/ + CU_TARGET_COMPUTE_62 = 62, /**< Compute device class 6.2.*/ + CU_TARGET_COMPUTE_70 = 70, /**< Compute device class 7.0.*/ + CU_TARGET_COMPUTE_72 = 72, /**< Compute device class 7.2.*/ + CU_TARGET_COMPUTE_75 = 75, /**< Compute device class 7.5.*/ + CU_TARGET_COMPUTE_80 = 80, /**< Compute device class 8.0.*/ + CU_TARGET_COMPUTE_86 = 86, /**< Compute device class 8.6.*/ + CU_TARGET_COMPUTE_87 = 87, /**< Compute device class 8.7.*/ + CU_TARGET_COMPUTE_89 = 89, /**< Compute device class 8.9.*/ + CU_TARGET_COMPUTE_90 = 90, /**< Compute device class 9.0.*/ + + /**< Compute device class 9.0. with accelerated features.*/ + CU_TARGET_COMPUTE_90A = CU_COMPUTE_ACCELERATED_TARGET_BASE + CU_TARGET_COMPUTE_90, +} CUjit_target; + +/** + * Cubin matching fallback strategies + */ +typedef enum CUjit_fallback_enum +{ + CU_PREFER_PTX = 0, /**< Prefer to compile ptx if exact binary match not found */ + + CU_PREFER_BINARY /**< Prefer to fall back to compatible binary code if exact match not found */ + +} CUjit_fallback; + +/** + * Caching modes for dlcm + */ +typedef enum CUjit_cacheMode_enum +{ + CU_JIT_CACHE_OPTION_NONE = 0, /**< Compile with no -dlcm flag specified */ + CU_JIT_CACHE_OPTION_CG, /**< Compile with L1 cache disabled */ + CU_JIT_CACHE_OPTION_CA /**< Compile with L1 cache enabled */ +} CUjit_cacheMode; + +/** + * Device code formats + */ +typedef enum CUjitInputType_enum +{ + /** + * Compiled device-class-specific device code\n + * Applicable options: none + */ + CU_JIT_INPUT_CUBIN = 0, + + /** + * PTX source code\n + * Applicable options: PTX compiler options + */ + CU_JIT_INPUT_PTX = 1, + + /** + * Bundle of multiple cubins and/or PTX of some device code\n + * Applicable options: PTX compiler options, ::CU_JIT_FALLBACK_STRATEGY + */ + CU_JIT_INPUT_FATBINARY = 2, + + /** + * Host object with embedded device code\n + * Applicable options: PTX compiler options, ::CU_JIT_FALLBACK_STRATEGY + */ + CU_JIT_INPUT_OBJECT = 3, + + /** + * Archive of host objects with embedded device code\n + * Applicable options: PTX compiler options, ::CU_JIT_FALLBACK_STRATEGY + */ + CU_JIT_INPUT_LIBRARY = 4, + + /** + * \deprecated + * High-level intermediate code for link-time optimization\n + * Applicable options: NVVM compiler options, PTX compiler options + * + * Only valid with LTO-IR compiled with toolkits prior to CUDA 12.0 + */ + CU_JIT_INPUT_NVVM = 5, + + CU_JIT_NUM_INPUT_TYPES = 6 +} CUjitInputType; + +typedef struct CUlinkState_st *CUlinkState; + +/** + * Flags to register a graphics resource + */ +typedef enum CUgraphicsRegisterFlags_enum { + CU_GRAPHICS_REGISTER_FLAGS_NONE = 0x00, + CU_GRAPHICS_REGISTER_FLAGS_READ_ONLY = 0x01, + CU_GRAPHICS_REGISTER_FLAGS_WRITE_DISCARD = 0x02, + CU_GRAPHICS_REGISTER_FLAGS_SURFACE_LDST = 0x04, + CU_GRAPHICS_REGISTER_FLAGS_TEXTURE_GATHER = 0x08 +} CUgraphicsRegisterFlags; + +/** + * Flags for mapping and unmapping interop resources + */ +typedef enum CUgraphicsMapResourceFlags_enum { + CU_GRAPHICS_MAP_RESOURCE_FLAGS_NONE = 0x00, + CU_GRAPHICS_MAP_RESOURCE_FLAGS_READ_ONLY = 0x01, + CU_GRAPHICS_MAP_RESOURCE_FLAGS_WRITE_DISCARD = 0x02 +} CUgraphicsMapResourceFlags; + +/** + * Array indices for cube faces + */ +typedef enum CUarray_cubemap_face_enum { + CU_CUBEMAP_FACE_POSITIVE_X = 0x00, /**< Positive X face of cubemap */ + CU_CUBEMAP_FACE_NEGATIVE_X = 0x01, /**< Negative X face of cubemap */ + CU_CUBEMAP_FACE_POSITIVE_Y = 0x02, /**< Positive Y face of cubemap */ + CU_CUBEMAP_FACE_NEGATIVE_Y = 0x03, /**< Negative Y face of cubemap */ + CU_CUBEMAP_FACE_POSITIVE_Z = 0x04, /**< Positive Z face of cubemap */ + CU_CUBEMAP_FACE_NEGATIVE_Z = 0x05 /**< Negative Z face of cubemap */ +} CUarray_cubemap_face; + +/** + * Limits + */ +typedef enum CUlimit_enum { + CU_LIMIT_STACK_SIZE = 0x00, /**< GPU thread stack size */ + CU_LIMIT_PRINTF_FIFO_SIZE = 0x01, /**< GPU printf FIFO size */ + CU_LIMIT_MALLOC_HEAP_SIZE = 0x02, /**< GPU malloc heap size */ + CU_LIMIT_DEV_RUNTIME_SYNC_DEPTH = 0x03, /**< GPU device runtime launch synchronize depth */ + CU_LIMIT_DEV_RUNTIME_PENDING_LAUNCH_COUNT = 0x04, /**< GPU device runtime pending launch count */ + CU_LIMIT_MAX_L2_FETCH_GRANULARITY = 0x05, /**< A value between 0 and 128 that indicates the maximum fetch granularity of L2 (in Bytes). This is a hint */ + CU_LIMIT_PERSISTING_L2_CACHE_SIZE = 0x06, /**< A size in bytes for L2 persisting lines cache size */ + CU_LIMIT_MAX +} CUlimit; + +/** + * Resource types + */ +typedef enum CUresourcetype_enum { + CU_RESOURCE_TYPE_ARRAY = 0x00, /**< Array resource */ + CU_RESOURCE_TYPE_MIPMAPPED_ARRAY = 0x01, /**< Mipmapped array resource */ + CU_RESOURCE_TYPE_LINEAR = 0x02, /**< Linear resource */ + CU_RESOURCE_TYPE_PITCH2D = 0x03 /**< Pitch 2D resource */ +} CUresourcetype; + +#ifdef _WIN32 +#define CUDA_CB __stdcall +#else +#define CUDA_CB +#endif + +/** + * CUDA host function + * \param userData Argument value passed to the function + */ +typedef void (CUDA_CB *CUhostFn)(void *userData); + +/** + * Specifies performance hint with ::CUaccessPolicyWindow for hitProp and missProp members. + */ +typedef enum CUaccessProperty_enum { + CU_ACCESS_PROPERTY_NORMAL = 0, /**< Normal cache persistence. */ + CU_ACCESS_PROPERTY_STREAMING = 1, /**< Streaming access is less likely to persit from cache. */ + CU_ACCESS_PROPERTY_PERSISTING = 2 /**< Persisting access is more likely to persist in cache.*/ +} CUaccessProperty; + +/** + * Specifies an access policy for a window, a contiguous extent of memory + * beginning at base_ptr and ending at base_ptr + num_bytes. + * num_bytes is limited by CU_DEVICE_ATTRIBUTE_MAX_ACCESS_POLICY_WINDOW_SIZE. + * Partition into many segments and assign segments such that: + * sum of "hit segments" / window == approx. ratio. + * sum of "miss segments" / window == approx 1-ratio. + * Segments and ratio specifications are fitted to the capabilities of + * the architecture. + * Accesses in a hit segment apply the hitProp access policy. + * Accesses in a miss segment apply the missProp access policy. + */ +typedef struct CUaccessPolicyWindow_st { + void *base_ptr; /**< Starting address of the access policy window. CUDA driver may align it. */ + size_t num_bytes; /**< Size in bytes of the window policy. CUDA driver may restrict the maximum size and alignment. */ + float hitRatio; /**< hitRatio specifies percentage of lines assigned hitProp, rest are assigned missProp. */ + CUaccessProperty hitProp; /**< ::CUaccessProperty set for hit. */ + CUaccessProperty missProp; /**< ::CUaccessProperty set for miss. Must be either NORMAL or STREAMING */ +} CUaccessPolicyWindow_v1; +/** + * Access policy window + */ +typedef CUaccessPolicyWindow_v1 CUaccessPolicyWindow; + +/** + * GPU kernel node parameters + */ +typedef struct CUDA_KERNEL_NODE_PARAMS_st { + CUfunction func; /**< Kernel to launch */ + unsigned int gridDimX; /**< Width of grid in blocks */ + unsigned int gridDimY; /**< Height of grid in blocks */ + unsigned int gridDimZ; /**< Depth of grid in blocks */ + unsigned int blockDimX; /**< X dimension of each thread block */ + unsigned int blockDimY; /**< Y dimension of each thread block */ + unsigned int blockDimZ; /**< Z dimension of each thread block */ + unsigned int sharedMemBytes; /**< Dynamic shared-memory size per thread block in bytes */ + void **kernelParams; /**< Array of pointers to kernel parameters */ + void **extra; /**< Extra options */ +} CUDA_KERNEL_NODE_PARAMS_v1; + +/** + * GPU kernel node parameters + */ +typedef struct CUDA_KERNEL_NODE_PARAMS_v2_st { + CUfunction func; /**< Kernel to launch */ + unsigned int gridDimX; /**< Width of grid in blocks */ + unsigned int gridDimY; /**< Height of grid in blocks */ + unsigned int gridDimZ; /**< Depth of grid in blocks */ + unsigned int blockDimX; /**< X dimension of each thread block */ + unsigned int blockDimY; /**< Y dimension of each thread block */ + unsigned int blockDimZ; /**< Z dimension of each thread block */ + unsigned int sharedMemBytes; /**< Dynamic shared-memory size per thread block in bytes */ + void **kernelParams; /**< Array of pointers to kernel parameters */ + void **extra; /**< Extra options */ + CUkernel kern; /**< Kernel to launch, will only be referenced if func is NULL */ + CUcontext ctx; /**< Context for the kernel task to run in. The value NULL will indicate the current context should be used by the api. This field is ignored if func is set. */ +} CUDA_KERNEL_NODE_PARAMS_v2; +typedef CUDA_KERNEL_NODE_PARAMS_v2 CUDA_KERNEL_NODE_PARAMS; + +/** + * GPU kernel node parameters + */ +typedef struct CUDA_KERNEL_NODE_PARAMS_v3_st { + CUfunction func; /**< Kernel to launch */ + unsigned int gridDimX; /**< Width of grid in blocks */ + unsigned int gridDimY; /**< Height of grid in blocks */ + unsigned int gridDimZ; /**< Depth of grid in blocks */ + unsigned int blockDimX; /**< X dimension of each thread block */ + unsigned int blockDimY; /**< Y dimension of each thread block */ + unsigned int blockDimZ; /**< Z dimension of each thread block */ + unsigned int sharedMemBytes; /**< Dynamic shared-memory size per thread block in bytes */ + void **kernelParams; /**< Array of pointers to kernel parameters */ + void **extra; /**< Extra options */ + CUkernel kern; /**< Kernel to launch, will only be referenced if func is NULL */ + CUcontext ctx; /**< Context for the kernel task to run in. The value NULL will indicate the current context should be used by the api. This field is ignored if func is set. */ +} CUDA_KERNEL_NODE_PARAMS_v3; + +/** + * Memset node parameters + */ +typedef struct CUDA_MEMSET_NODE_PARAMS_st { + CUdeviceptr dst; /**< Destination device pointer */ + size_t pitch; /**< Pitch of destination device pointer. Unused if height is 1 */ + unsigned int value; /**< Value to be set */ + unsigned int elementSize; /**< Size of each element in bytes. Must be 1, 2, or 4. */ + size_t width; /**< Width of the row in elements */ + size_t height; /**< Number of rows */ +} CUDA_MEMSET_NODE_PARAMS_v1; +typedef CUDA_MEMSET_NODE_PARAMS_v1 CUDA_MEMSET_NODE_PARAMS; + +/** + * Memset node parameters + */ +typedef struct CUDA_MEMSET_NODE_PARAMS_v2_st { + CUdeviceptr dst; /**< Destination device pointer */ + size_t pitch; /**< Pitch of destination device pointer. Unused if height is 1 */ + unsigned int value; /**< Value to be set */ + unsigned int elementSize; /**< Size of each element in bytes. Must be 1, 2, or 4. */ + size_t width; /**< Width of the row in elements */ + size_t height; /**< Number of rows */ + CUcontext ctx; /**< Context on which to run the node */ +} CUDA_MEMSET_NODE_PARAMS_v2; + +/** + * Host node parameters + */ +typedef struct CUDA_HOST_NODE_PARAMS_st { + CUhostFn fn; /**< The function to call when the node executes */ + void* userData; /**< Argument to pass to the function */ +} CUDA_HOST_NODE_PARAMS_v1; +typedef CUDA_HOST_NODE_PARAMS_v1 CUDA_HOST_NODE_PARAMS; + +/** + * Host node parameters + */ +typedef struct CUDA_HOST_NODE_PARAMS_v2_st { + CUhostFn fn; /**< The function to call when the node executes */ + void* userData; /**< Argument to pass to the function */ +} CUDA_HOST_NODE_PARAMS_v2; + +/** + * Conditional node handle flags + */ +#define CU_GRAPH_COND_ASSIGN_DEFAULT 0x1 /**< Default value is applied when graph is launched. */ + +/** + * Conditional node types + */ +typedef enum CUgraphConditionalNodeType_enum { + CU_GRAPH_COND_TYPE_IF = 0, /**< Conditional 'if' Node. Body executed once if condition value is non-zero. */ + CU_GRAPH_COND_TYPE_WHILE = 1, /**< Conditional 'while' Node. Body executed repeatedly while condition value is non-zero. */ +} CUgraphConditionalNodeType; + +/** + * Conditional node parameters + */ +typedef struct CUDA_CONDITIONAL_NODE_PARAMS { + CUgraphConditionalHandle handle; /**< Conditional node handle. + Handles must be created in advance of creating the node + using ::cuGraphConditionalHandleCreate. */ + CUgraphConditionalNodeType type; /**< Type of conditional node. */ + unsigned int size; /**< Size of graph output array. Must be 1. */ + CUgraph *phGraph_out; /**< CUDA-owned array populated with conditional node child graphs during creation of the node. + Valid for the lifetime of the conditional node. + The contents of the graph(s) are subject to the following constraints: + + - Allowed node types are kernel nodes, empty nodes, child graphs, memsets, + memcopies, and conditionals. This applies recursively to child graphs and conditional bodies. + - All kernels, including kernels in nested conditionals or child graphs at any level, + must belong to the same CUDA context. + + These graphs may be populated using graph node creation APIs or ::cuStreamBeginCaptureToGraph. */ + CUcontext ctx; /**< Context on which to run the node. Must match context used to create the handle and all body nodes. */ +} CUDA_CONDITIONAL_NODE_PARAMS; + +/** + * Graph node types + */ +typedef enum CUgraphNodeType_enum { + CU_GRAPH_NODE_TYPE_KERNEL = 0, /**< GPU kernel node */ + CU_GRAPH_NODE_TYPE_MEMCPY = 1, /**< Memcpy node */ + CU_GRAPH_NODE_TYPE_MEMSET = 2, /**< Memset node */ + CU_GRAPH_NODE_TYPE_HOST = 3, /**< Host (executable) node */ + CU_GRAPH_NODE_TYPE_GRAPH = 4, /**< Node which executes an embedded graph */ + CU_GRAPH_NODE_TYPE_EMPTY = 5, /**< Empty (no-op) node */ + CU_GRAPH_NODE_TYPE_WAIT_EVENT = 6, /**< External event wait node */ + CU_GRAPH_NODE_TYPE_EVENT_RECORD = 7, /**< External event record node */ + CU_GRAPH_NODE_TYPE_EXT_SEMAS_SIGNAL = 8, /**< External semaphore signal node */ + CU_GRAPH_NODE_TYPE_EXT_SEMAS_WAIT = 9, /**< External semaphore wait node */ + CU_GRAPH_NODE_TYPE_MEM_ALLOC = 10,/**< Memory Allocation Node */ + CU_GRAPH_NODE_TYPE_MEM_FREE = 11,/**< Memory Free Node */ + CU_GRAPH_NODE_TYPE_BATCH_MEM_OP = 12 /**< Batch MemOp Node */ + , + CU_GRAPH_NODE_TYPE_CONDITIONAL = 13 /**< Conditional Node + + May be used to implement a conditional execution path or loop + inside of a graph. The graph(s) contained within the body of the conditional node + can be selectively executed or iterated upon based on the value of a conditional + variable. + + Handles must be created in advance of creating the node + using ::cuGraphConditionalHandleCreate. + + The following restrictions apply to graphs which contain conditional nodes: + The graph cannot be used in a child node. + Only one instantiation of the graph may exist at any point in time. + The graph cannot be cloned. + + To set the control value, supply a default value when creating the handle and/or + call ::cudaGraphSetConditional from device code.*/ +} CUgraphNodeType; + +/** + * Type annotations that can be applied to graph edges as part of ::CUgraphEdgeData. + */ +typedef enum CUgraphDependencyType_enum { + CU_GRAPH_DEPENDENCY_TYPE_DEFAULT = 0, /**< This is an ordinary dependency. */ + CU_GRAPH_DEPENDENCY_TYPE_PROGRAMMATIC = 1 /**< This dependency type allows the downstream node to + use \c cudaGridDependencySynchronize(). It may only be used + between kernel nodes, and must be used with either the + ::CU_GRAPH_KERNEL_NODE_PORT_PROGRAMMATIC or + ::CU_GRAPH_KERNEL_NODE_PORT_LAUNCH_ORDER outgoing port. */ +} CUgraphDependencyType; + +/** + * This port activates when the kernel has finished executing. + */ +#define CU_GRAPH_KERNEL_NODE_PORT_DEFAULT 0 +/** + * This port activates when all blocks of the kernel have performed cudaTriggerProgrammaticLaunchCompletion() + * or have terminated. It must be used with edge type ::CU_GRAPH_DEPENDENCY_TYPE_PROGRAMMATIC. See also + * ::CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_EVENT. + */ +#define CU_GRAPH_KERNEL_NODE_PORT_PROGRAMMATIC 1 +/** + * This port activates when all blocks of the kernel have begun execution. See also + * ::CU_LAUNCH_ATTRIBUTE_LAUNCH_COMPLETION_EVENT. + */ +#define CU_GRAPH_KERNEL_NODE_PORT_LAUNCH_ORDER 2 + +/** + * Optional annotation for edges in a CUDA graph. Note, all edges implicitly have annotations and + * default to a zero-initialized value if not specified. A zero-initialized struct indicates a + * standard full serialization of two nodes with memory visibility. + */ +typedef struct CUgraphEdgeData_st { + unsigned char from_port; /**< This indicates when the dependency is triggered from the upstream + node on the edge. The meaning is specfic to the node type. A value + of 0 in all cases means full completion of the upstream node, with + memory visibility to the downstream node or portion thereof + (indicated by \c to_port). +
+ Only kernel nodes define non-zero ports. A kernel node + can use the following output port types: + ::CU_GRAPH_KERNEL_NODE_PORT_DEFAULT, ::CU_GRAPH_KERNEL_NODE_PORT_PROGRAMMATIC, + or ::CU_GRAPH_KERNEL_NODE_PORT_LAUNCH_ORDER. */ + unsigned char to_port; /**< This indicates what portion of the downstream node is dependent on + the upstream node or portion thereof (indicated by \c from_port). The + meaning is specific to the node type. A value of 0 in all cases means + the entirety of the downstream node is dependent on the upstream work. +
+ Currently no node types define non-zero ports. Accordingly, this field + must be set to zero. */ + unsigned char type; /**< This should be populated with a value from ::CUgraphDependencyType. (It + is typed as char due to compiler-specific layout of bitfields.) See + ::CUgraphDependencyType. */ + unsigned char reserved[5]; /**< These bytes are unused and must be zeroed. This ensures + compatibility if additional fields are added in the future. */ +} CUgraphEdgeData; + +/** + * Graph instantiation results +*/ +typedef enum CUgraphInstantiateResult_enum +{ + CUDA_GRAPH_INSTANTIATE_SUCCESS = 0, /**< Instantiation succeeded */ + CUDA_GRAPH_INSTANTIATE_ERROR = 1, /**< Instantiation failed for an unexpected reason which is described in the return value of the function */ + CUDA_GRAPH_INSTANTIATE_INVALID_STRUCTURE = 2, /**< Instantiation failed due to invalid structure, such as cycles */ + CUDA_GRAPH_INSTANTIATE_NODE_OPERATION_NOT_SUPPORTED = 3, /**< Instantiation for device launch failed because the graph contained an unsupported operation */ + CUDA_GRAPH_INSTANTIATE_MULTIPLE_CTXS_NOT_SUPPORTED = 4 /**< Instantiation for device launch failed due to the nodes belonging to different contexts */ +} CUgraphInstantiateResult; + +/** + * Graph instantiation parameters + */ +typedef struct CUDA_GRAPH_INSTANTIATE_PARAMS_st +{ + cuuint64_t flags; /**< Instantiation flags */ + CUstream hUploadStream; /**< Upload stream */ + CUgraphNode hErrNode_out; /**< The node which caused instantiation to fail, if any */ + CUgraphInstantiateResult result_out; /**< Whether instantiation was successful. If it failed, the reason why */ +} CUDA_GRAPH_INSTANTIATE_PARAMS; + +typedef enum CUsynchronizationPolicy_enum { + CU_SYNC_POLICY_AUTO = 1, + CU_SYNC_POLICY_SPIN = 2, + CU_SYNC_POLICY_YIELD = 3, + CU_SYNC_POLICY_BLOCKING_SYNC = 4 +} CUsynchronizationPolicy; + +/** + * Cluster scheduling policies. These may be passed to ::cuFuncSetAttribute or ::cuKernelSetAttribute + */ +typedef enum CUclusterSchedulingPolicy_enum { + CU_CLUSTER_SCHEDULING_POLICY_DEFAULT = 0, /**< the default policy */ + CU_CLUSTER_SCHEDULING_POLICY_SPREAD = 1, /**< spread the blocks within a cluster to the SMs */ + CU_CLUSTER_SCHEDULING_POLICY_LOAD_BALANCING = 2 /**< allow the hardware to load-balance the blocks in a cluster to the SMs */ +} CUclusterSchedulingPolicy; + +/** + * Memory Synchronization Domain + * + * A kernel can be launched in a specified memory synchronization domain that affects all memory operations issued by + * that kernel. A memory barrier issued in one domain will only order memory operations in that domain, thus eliminating + * latency increase from memory barriers ordering unrelated traffic. + * + * By default, kernels are launched in domain 0. Kernel launched with ::CU_LAUNCH_MEM_SYNC_DOMAIN_REMOTE will have a + * different domain ID. User may also alter the domain ID with ::CUlaunchMemSyncDomainMap for a specific stream / + * graph node / kernel launch. See ::CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN, ::cuStreamSetAttribute, ::cuLaunchKernelEx, + * ::cuGraphKernelNodeSetAttribute. + * + * Memory operations done in kernels launched in different domains are considered system-scope distanced. In other + * words, a GPU scoped memory synchronization is not sufficient for memory order to be observed by kernels in another + * memory synchronization domain even if they are on the same GPU. + */ +typedef enum CUlaunchMemSyncDomain_enum { + CU_LAUNCH_MEM_SYNC_DOMAIN_DEFAULT = 0, /**< Launch kernels in the default domain */ + CU_LAUNCH_MEM_SYNC_DOMAIN_REMOTE = 1 /**< Launch kernels in the remote domain */ +} CUlaunchMemSyncDomain; + +/** + * Memory Synchronization Domain map + * + * See ::cudaLaunchMemSyncDomain. + * + * By default, kernels are launched in domain 0. Kernel launched with ::CU_LAUNCH_MEM_SYNC_DOMAIN_REMOTE will have a + * different domain ID. User may also alter the domain ID with ::CUlaunchMemSyncDomainMap for a specific stream / + * graph node / kernel launch. See ::CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP. + * + * Domain ID range is available through ::CU_DEVICE_ATTRIBUTE_MEM_SYNC_DOMAIN_COUNT. + */ +typedef struct CUlaunchMemSyncDomainMap_st { + unsigned char default_; /**< The default domain ID to use for designated kernels */ + unsigned char remote; /**< The remote domain ID to use for designated kernels */ +} CUlaunchMemSyncDomainMap; + +/** + * Launch attributes enum; used as id field of ::CUlaunchAttribute + */ +typedef enum CUlaunchAttributeID_enum { + CU_LAUNCH_ATTRIBUTE_IGNORE = 0 /**< Ignored entry, for convenient composition */ + , CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW = 1 /**< Valid for streams, graph nodes, launches. See + ::CUlaunchAttributeValue::accessPolicyWindow. */ + , CU_LAUNCH_ATTRIBUTE_COOPERATIVE = 2 /**< Valid for graph nodes, launches. See + ::CUlaunchAttributeValue::cooperative. */ + , CU_LAUNCH_ATTRIBUTE_SYNCHRONIZATION_POLICY = 3 /**< Valid for streams. See + ::CUlaunchAttributeValue::syncPolicy. */ + , CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION = 4 /**< Valid for graph nodes, launches. See ::CUlaunchAttributeValue::clusterDim. */ + , CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE = 5 /**< Valid for graph nodes, launches. See ::CUlaunchAttributeValue::clusterSchedulingPolicyPreference. */ + , CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_STREAM_SERIALIZATION = 6 /**< Valid for launches. Setting + ::CUlaunchAttributeValue::programmaticStreamSerializationAllowed + to non-0 signals that the kernel will use programmatic + means to resolve its stream dependency, so that the + CUDA runtime should opportunistically allow the grid's + execution to overlap with the previous kernel in the + stream, if that kernel requests the overlap. The + dependent launches can choose to wait on the + dependency using the programmatic sync + (cudaGridDependencySynchronize() or equivalent PTX + instructions). */ + , CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_EVENT = 7 /**< Valid for launches. Set + ::CUlaunchAttributeValue::programmaticEvent to + record the event. Event recorded through this + launch attribute is guaranteed to only trigger + after all block in the associated kernel trigger + the event. A block can trigger the event through + PTX launchdep.release or CUDA builtin function + cudaTriggerProgrammaticLaunchCompletion(). A + trigger can also be inserted at the beginning of + each block's execution if triggerAtBlockStart is + set to non-0. The dependent launches can choose to + wait on the dependency using the programmatic sync + (cudaGridDependencySynchronize() or equivalent PTX + instructions). Note that dependents (including the + CPU thread calling cuEventSynchronize()) are not + guaranteed to observe the release precisely when + it is released. For example, cuEventSynchronize() + may only observe the event trigger long after the + associated kernel has completed. This recording + type is primarily meant for establishing + programmatic dependency between device tasks. Note + also this type of dependency allows, but does not + guarantee, concurrent execution of tasks. +
+ The event supplied must not be an interprocess or + interop event. The event must disable timing (i.e. + must be created with the ::CU_EVENT_DISABLE_TIMING + flag set). + */ + , CU_LAUNCH_ATTRIBUTE_PRIORITY = 8 /**< Valid for streams, graph nodes, launches. See + ::CUlaunchAttributeValue::priority. */ + , CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP = 9 /**< Valid for streams, graph nodes, launches. See + ::CUlaunchAttributeValue::memSyncDomainMap. */ + , CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN = 10 /**< Valid for streams, graph nodes, launches. See + ::CUlaunchAttributeValue::memSyncDomain. */ + , CU_LAUNCH_ATTRIBUTE_LAUNCH_COMPLETION_EVENT = 12 /**< Valid for launches. Set + ::CUlaunchAttributeValue::launchCompletionEvent to record the + event. +
+ Nominally, the event is triggered once all blocks of the kernel + have begun execution. Currently this is a best effort. If a kernel + B has a launch completion dependency on a kernel A, B may wait + until A is complete. Alternatively, blocks of B may begin before + all blocks of A have begun, for example if B can claim execution + resources unavailable to A (e.g. they run on different GPUs) or + if B is a higher priority than A. + Exercise caution if such an ordering inversion could lead + to deadlock. +
+ A launch completion event is nominally similar to a programmatic + event with \c triggerAtBlockStart set except that it is not + visible to \c cudaGridDependencySynchronize() and can be used with + compute capability less than 9.0. +
+ The event supplied must not be an interprocess or interop + event. The event must disable timing (i.e. must be created + with the ::CU_EVENT_DISABLE_TIMING flag set). */ + , CU_LAUNCH_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE = 13 /**< Valid for graph nodes, launches. This attribute is graphs-only, + and passing it to a launch in a non-capturing stream will result + in an error. +
+ ::CUlaunchAttributeValue::deviceUpdatableKernelNode::deviceUpdatable can + only be set to 0 or 1. Setting the field to 1 indicates that the + corresponding kernel node should be device-updatable. On success, a handle + will be returned via + ::CUlaunchAttributeValue::deviceUpdatableKernelNode::devNode which can be + passed to the various device-side update functions to update the node's + kernel parameters from within another kernel. For more information on the + types of device updates that can be made, as well as the relevant limitations + thereof, see ::cudaGraphKernelNodeUpdatesApply. +
+ Nodes which are device-updatable have additional restrictions compared to + regular kernel nodes. Firstly, device-updatable nodes cannot be removed + from their graph via ::cuGraphDestroyNode. Additionally, once opted-in + to this functionality, a node cannot opt out, and any attempt to set the + deviceUpdatable attribute to 0 will result in an error. Device-updatable + kernel nodes also cannot have their attributes copied to/from another kernel + node via ::cuGraphKernelNodeCopyAttributes. Graphs containing one or more + device-updatable nodes also do not allow multiple instantiation, and neither + the graph nor its instantiated version can be passed to ::cuGraphExecUpdate. +
+ If a graph contains device-updatable nodes and updates those nodes from the device + from within the graph, the graph must be uploaded with ::cuGraphUpload before it + is launched. For such a graph, if host-side executable graph updates are made to the + device-updatable nodes, the graph must be uploaded before it is launched again. */ +#ifdef __CUDA_API_VERSION_INTERNAL + , CU_LAUNCH_ATTRIBUTE_MAX +#endif +} CUlaunchAttributeID; + +/** + * Launch attributes union; used as value field of ::CUlaunchAttribute + */ +typedef union CUlaunchAttributeValue_union { + char pad[64]; /* Pad to 64 bytes */ + CUaccessPolicyWindow accessPolicyWindow; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW. */ + int cooperative; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_COOPERATIVE. Nonzero indicates a cooperative + kernel (see ::cuLaunchCooperativeKernel). */ + CUsynchronizationPolicy syncPolicy; /**< Value of launch attribute + ::CU_LAUNCH_ATTRIBUTE_SYNCHRONIZATION_POLICY. ::CUsynchronizationPolicy for + work queued up in this stream */ + + /** + * Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION that + * represents the desired cluster dimensions for the kernel. Opaque type + * with the following fields: + * - \p x - The X dimension of the cluster, in blocks. Must be a divisor + * of the grid X dimension. + * - \p y - The Y dimension of the cluster, in blocks. Must be a divisor + * of the grid Y dimension. + * - \p z - The Z dimension of the cluster, in blocks. Must be a divisor + * of the grid Z dimension. + */ + struct { + unsigned int x; + unsigned int y; + unsigned int z; + } clusterDim; + CUclusterSchedulingPolicy clusterSchedulingPolicyPreference; /**< Value of launch attribute + ::CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE. Cluster + scheduling policy preference for the kernel. */ + int programmaticStreamSerializationAllowed; /**< Value of launch attribute + ::CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_STREAM_SERIALIZATION. */ + struct { + CUevent event; /**< Event to fire when all blocks trigger it */ + int flags; /**< Event record flags, see ::cuEventRecordWithFlags. Does not accept + ::CU_EVENT_RECORD_EXTERNAL. */ + int triggerAtBlockStart; /**< If this is set to non-0, each block launch will automatically trigger the event */ + } programmaticEvent; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_EVENT. */ + struct { + CUevent event; /**< Event to fire when the last block launches */ + int flags; /**< Event record flags, see ::cuEventRecordWithFlags. Does not accept ::CU_EVENT_RECORD_EXTERNAL. */ + } launchCompletionEvent; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_LAUNCH_COMPLETION_EVENT. */ + int priority; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_PRIORITY. Execution priority of the kernel. */ + CUlaunchMemSyncDomainMap memSyncDomainMap; /**< Value of launch attribute + ::CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP. See + ::CUlaunchMemSyncDomainMap. */ + CUlaunchMemSyncDomain memSyncDomain; /**< Value of launch attribute + ::CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN. See::CUlaunchMemSyncDomain */ + + struct { + int deviceUpdatable; /**< Whether or not the resulting kernel node should be device-updatable. */ + CUgraphDeviceNode devNode; /**< Returns a handle to pass to the various device-side update functions. */ + } deviceUpdatableKernelNode; /**< Value of launch attribute ::CU_LAUNCH_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE. */ +} CUlaunchAttributeValue; + +/** + * Launch attribute + */ +typedef struct CUlaunchAttribute_st { + CUlaunchAttributeID id; /**< Attribute to set */ + char pad[8 - sizeof(CUlaunchAttributeID)]; + CUlaunchAttributeValue value; /**< Value of the attribute */ +} CUlaunchAttribute; + +/** + * CUDA extensible launch configuration + */ +typedef struct CUlaunchConfig_st { + unsigned int gridDimX; /**< Width of grid in blocks */ + unsigned int gridDimY; /**< Height of grid in blocks */ + unsigned int gridDimZ; /**< Depth of grid in blocks */ + unsigned int blockDimX; /**< X dimension of each thread block */ + unsigned int blockDimY; /**< Y dimension of each thread block */ + unsigned int blockDimZ; /**< Z dimension of each thread block */ + unsigned int sharedMemBytes; /**< Dynamic shared-memory size per thread block in bytes */ + CUstream hStream; /**< Stream identifier */ + CUlaunchAttribute *attrs; /**< List of attributes; nullable if ::CUlaunchConfig::numAttrs == 0 */ + unsigned int numAttrs; /**< Number of attributes populated in ::CUlaunchConfig::attrs */ +} CUlaunchConfig; + +typedef CUlaunchAttributeID CUkernelNodeAttrID; +#define CU_KERNEL_NODE_ATTRIBUTE_ACCESS_POLICY_WINDOW CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW +#define CU_KERNEL_NODE_ATTRIBUTE_COOPERATIVE CU_LAUNCH_ATTRIBUTE_COOPERATIVE +#define CU_KERNEL_NODE_ATTRIBUTE_CLUSTER_DIMENSION CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION +#define CU_KERNEL_NODE_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE +#define CU_KERNEL_NODE_ATTRIBUTE_PRIORITY CU_LAUNCH_ATTRIBUTE_PRIORITY +#define CU_KERNEL_NODE_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP +#define CU_KERNEL_NODE_ATTRIBUTE_MEM_SYNC_DOMAIN CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN +#define CU_KERNEL_NODE_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE CU_LAUNCH_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE + +typedef CUlaunchAttributeValue CUkernelNodeAttrValue_v1; +typedef CUkernelNodeAttrValue_v1 CUkernelNodeAttrValue; + +/** + * Possible stream capture statuses returned by ::cuStreamIsCapturing + */ +typedef enum CUstreamCaptureStatus_enum { + CU_STREAM_CAPTURE_STATUS_NONE = 0, /**< Stream is not capturing */ + CU_STREAM_CAPTURE_STATUS_ACTIVE = 1, /**< Stream is actively capturing */ + CU_STREAM_CAPTURE_STATUS_INVALIDATED = 2 /**< Stream is part of a capture sequence that + has been invalidated, but not terminated */ +} CUstreamCaptureStatus; + +/** + * Possible modes for stream capture thread interactions. For more details see + * ::cuStreamBeginCapture and ::cuThreadExchangeStreamCaptureMode + */ +typedef enum CUstreamCaptureMode_enum { + CU_STREAM_CAPTURE_MODE_GLOBAL = 0, + CU_STREAM_CAPTURE_MODE_THREAD_LOCAL = 1, + CU_STREAM_CAPTURE_MODE_RELAXED = 2 +} CUstreamCaptureMode; + +typedef CUlaunchAttributeID CUstreamAttrID; +#define CU_STREAM_ATTRIBUTE_ACCESS_POLICY_WINDOW CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW +#define CU_STREAM_ATTRIBUTE_SYNCHRONIZATION_POLICY CU_LAUNCH_ATTRIBUTE_SYNCHRONIZATION_POLICY +#define CU_STREAM_ATTRIBUTE_PRIORITY CU_LAUNCH_ATTRIBUTE_PRIORITY +#define CU_STREAM_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP +#define CU_STREAM_ATTRIBUTE_MEM_SYNC_DOMAIN CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN + +typedef CUlaunchAttributeValue CUstreamAttrValue_v1; +typedef CUstreamAttrValue_v1 CUstreamAttrValue; + +/** + * Flags to specify search options. For more details see ::cuGetProcAddress + */ +typedef enum CUdriverProcAddress_flags_enum { + CU_GET_PROC_ADDRESS_DEFAULT = 0, /**< Default search mode for driver symbols. */ + CU_GET_PROC_ADDRESS_LEGACY_STREAM = 1 << 0, /**< Search for legacy versions of driver symbols. */ + CU_GET_PROC_ADDRESS_PER_THREAD_DEFAULT_STREAM = 1 << 1 /**< Search for per-thread versions of driver symbols. */ +} CUdriverProcAddress_flags; + +/** + * Flags to indicate search status. For more details see ::cuGetProcAddress + */ +typedef enum CUdriverProcAddressQueryResult_enum { + CU_GET_PROC_ADDRESS_SUCCESS = 0, /**< Symbol was succesfully found */ + CU_GET_PROC_ADDRESS_SYMBOL_NOT_FOUND = 1, /**< Symbol was not found in search */ + CU_GET_PROC_ADDRESS_VERSION_NOT_SUFFICIENT = 2 /**< Symbol was found but version supplied was not sufficient */ +} CUdriverProcAddressQueryResult; + +/** + * Execution Affinity Types + */ +typedef enum CUexecAffinityType_enum { + CU_EXEC_AFFINITY_TYPE_SM_COUNT = 0, /**< Create a context with limited SMs. */ + CU_EXEC_AFFINITY_TYPE_MAX +} CUexecAffinityType; + +/** + * Value for ::CU_EXEC_AFFINITY_TYPE_SM_COUNT + */ +typedef struct CUexecAffinitySmCount_st { + unsigned int val; /**< The number of SMs the context is limited to use. */ +} CUexecAffinitySmCount_v1; +typedef CUexecAffinitySmCount_v1 CUexecAffinitySmCount; + +/** + * Execution Affinity Parameters + */ +typedef struct CUexecAffinityParam_st { + CUexecAffinityType type; + union { + CUexecAffinitySmCount smCount; /** Value for ::CU_EXEC_AFFINITY_TYPE_SM_COUNT */ + } param; +} CUexecAffinityParam_v1; +/** + * Execution Affinity Parameters + */ +typedef CUexecAffinityParam_v1 CUexecAffinityParam; + +/** + * Library options to be specified with ::cuLibraryLoadData() or ::cuLibraryLoadFromFile() + */ +typedef enum CUlibraryOption_enum +{ + CU_LIBRARY_HOST_UNIVERSAL_FUNCTION_AND_DATA_TABLE = 0, + + /** + * Specifes that the argument \p code passed to ::cuLibraryLoadData() will be preserved. + * Specifying this option will let the driver know that \p code can be accessed at any point + * until ::cuLibraryUnload(). The default behavior is for the driver to allocate and + * maintain its own copy of \p code. Note that this is only a memory usage optimization + * hint and the driver can choose to ignore it if required. + * Specifying this option with ::cuLibraryLoadFromFile() is invalid and + * will return ::CUDA_ERROR_INVALID_VALUE. + */ + CU_LIBRARY_BINARY_IS_PRESERVED = 1, + + CU_LIBRARY_NUM_OPTIONS +} CUlibraryOption; + +typedef struct CUlibraryHostUniversalFunctionAndDataTable_st +{ + void *functionTable; + size_t functionWindowSize; + void *dataTable; + size_t dataWindowSize; +} CUlibraryHostUniversalFunctionAndDataTable; + +/** + * Error codes + */ +typedef enum cudaError_enum { + /** + * The API call returned with no errors. In the case of query calls, this + * also means that the operation being queried is complete (see + * ::cuEventQuery() and ::cuStreamQuery()). + */ + CUDA_SUCCESS = 0, + + /** + * This indicates that one or more of the parameters passed to the API call + * is not within an acceptable range of values. + */ + CUDA_ERROR_INVALID_VALUE = 1, + + /** + * The API call failed because it was unable to allocate enough memory or + * other resources to perform the requested operation. + */ + CUDA_ERROR_OUT_OF_MEMORY = 2, + + /** + * This indicates that the CUDA driver has not been initialized with + * ::cuInit() or that initialization has failed. + */ + CUDA_ERROR_NOT_INITIALIZED = 3, + + /** + * This indicates that the CUDA driver is in the process of shutting down. + */ + CUDA_ERROR_DEINITIALIZED = 4, + + /** + * This indicates profiler is not initialized for this run. This can + * happen when the application is running with external profiling tools + * like visual profiler. + */ + CUDA_ERROR_PROFILER_DISABLED = 5, + + /** + * \deprecated + * This error return is deprecated as of CUDA 5.0. It is no longer an error + * to attempt to enable/disable the profiling via ::cuProfilerStart or + * ::cuProfilerStop without initialization. + */ + CUDA_ERROR_PROFILER_NOT_INITIALIZED = 6, + + /** + * \deprecated + * This error return is deprecated as of CUDA 5.0. It is no longer an error + * to call cuProfilerStart() when profiling is already enabled. + */ + CUDA_ERROR_PROFILER_ALREADY_STARTED = 7, + + /** + * \deprecated + * This error return is deprecated as of CUDA 5.0. It is no longer an error + * to call cuProfilerStop() when profiling is already disabled. + */ + CUDA_ERROR_PROFILER_ALREADY_STOPPED = 8, + + /** + * This indicates that the CUDA driver that the application has loaded is a + * stub library. Applications that run with the stub rather than a real + * driver loaded will result in CUDA API returning this error. + */ + CUDA_ERROR_STUB_LIBRARY = 34, + + /** + * This indicates that requested CUDA device is unavailable at the current + * time. Devices are often unavailable due to use of + * ::CU_COMPUTEMODE_EXCLUSIVE_PROCESS or ::CU_COMPUTEMODE_PROHIBITED. + */ + CUDA_ERROR_DEVICE_UNAVAILABLE = 46, + + /** + * This indicates that no CUDA-capable devices were detected by the installed + * CUDA driver. + */ + CUDA_ERROR_NO_DEVICE = 100, + + /** + * This indicates that the device ordinal supplied by the user does not + * correspond to a valid CUDA device or that the action requested is + * invalid for the specified device. + */ + CUDA_ERROR_INVALID_DEVICE = 101, + + /** + * This error indicates that the Grid license is not applied. + */ + CUDA_ERROR_DEVICE_NOT_LICENSED = 102, + + /** + * This indicates that the device kernel image is invalid. This can also + * indicate an invalid CUDA module. + */ + CUDA_ERROR_INVALID_IMAGE = 200, + + /** + * This most frequently indicates that there is no context bound to the + * current thread. This can also be returned if the context passed to an + * API call is not a valid handle (such as a context that has had + * ::cuCtxDestroy() invoked on it). This can also be returned if a user + * mixes different API versions (i.e. 3010 context with 3020 API calls). + * See ::cuCtxGetApiVersion() for more details. + * This can also be returned if the green context passed to an API call + * was not converted to a ::CUcontext using ::cuCtxFromGreenCtx API. + */ + CUDA_ERROR_INVALID_CONTEXT = 201, + + /** + * This indicated that the context being supplied as a parameter to the + * API call was already the active context. + * \deprecated + * This error return is deprecated as of CUDA 3.2. It is no longer an + * error to attempt to push the active context via ::cuCtxPushCurrent(). + */ + CUDA_ERROR_CONTEXT_ALREADY_CURRENT = 202, + + /** + * This indicates that a map or register operation has failed. + */ + CUDA_ERROR_MAP_FAILED = 205, + + /** + * This indicates that an unmap or unregister operation has failed. + */ + CUDA_ERROR_UNMAP_FAILED = 206, + + /** + * This indicates that the specified array is currently mapped and thus + * cannot be destroyed. + */ + CUDA_ERROR_ARRAY_IS_MAPPED = 207, + + /** + * This indicates that the resource is already mapped. + */ + CUDA_ERROR_ALREADY_MAPPED = 208, + + /** + * This indicates that there is no kernel image available that is suitable + * for the device. This can occur when a user specifies code generation + * options for a particular CUDA source file that do not include the + * corresponding device configuration. + */ + CUDA_ERROR_NO_BINARY_FOR_GPU = 209, + + /** + * This indicates that a resource has already been acquired. + */ + CUDA_ERROR_ALREADY_ACQUIRED = 210, + + /** + * This indicates that a resource is not mapped. + */ + CUDA_ERROR_NOT_MAPPED = 211, + + /** + * This indicates that a mapped resource is not available for access as an + * array. + */ + CUDA_ERROR_NOT_MAPPED_AS_ARRAY = 212, + + /** + * This indicates that a mapped resource is not available for access as a + * pointer. + */ + CUDA_ERROR_NOT_MAPPED_AS_POINTER = 213, + + /** + * This indicates that an uncorrectable ECC error was detected during + * execution. + */ + CUDA_ERROR_ECC_UNCORRECTABLE = 214, + + /** + * This indicates that the ::CUlimit passed to the API call is not + * supported by the active device. + */ + CUDA_ERROR_UNSUPPORTED_LIMIT = 215, + + /** + * This indicates that the ::CUcontext passed to the API call can + * only be bound to a single CPU thread at a time but is already + * bound to a CPU thread. + */ + CUDA_ERROR_CONTEXT_ALREADY_IN_USE = 216, + + /** + * This indicates that peer access is not supported across the given + * devices. + */ + CUDA_ERROR_PEER_ACCESS_UNSUPPORTED = 217, + + /** + * This indicates that a PTX JIT compilation failed. + */ + CUDA_ERROR_INVALID_PTX = 218, + + /** + * This indicates an error with OpenGL or DirectX context. + */ + CUDA_ERROR_INVALID_GRAPHICS_CONTEXT = 219, + + /** + * This indicates that an uncorrectable NVLink error was detected during the + * execution. + */ + CUDA_ERROR_NVLINK_UNCORRECTABLE = 220, + + /** + * This indicates that the PTX JIT compiler library was not found. + */ + CUDA_ERROR_JIT_COMPILER_NOT_FOUND = 221, + + /** + * This indicates that the provided PTX was compiled with an unsupported toolchain. + */ + + CUDA_ERROR_UNSUPPORTED_PTX_VERSION = 222, + + /** + * This indicates that the PTX JIT compilation was disabled. + */ + CUDA_ERROR_JIT_COMPILATION_DISABLED = 223, + + /** + * This indicates that the ::CUexecAffinityType passed to the API call is not + * supported by the active device. + */ + CUDA_ERROR_UNSUPPORTED_EXEC_AFFINITY = 224, + + /** + * This indicates that the code to be compiled by the PTX JIT contains + * unsupported call to cudaDeviceSynchronize. + */ + CUDA_ERROR_UNSUPPORTED_DEVSIDE_SYNC = 225, + + /** + * This indicates that the device kernel source is invalid. This includes + * compilation/linker errors encountered in device code or user error. + */ + CUDA_ERROR_INVALID_SOURCE = 300, + + /** + * This indicates that the file specified was not found. + */ + CUDA_ERROR_FILE_NOT_FOUND = 301, + + /** + * This indicates that a link to a shared object failed to resolve. + */ + CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND = 302, + + /** + * This indicates that initialization of a shared object failed. + */ + CUDA_ERROR_SHARED_OBJECT_INIT_FAILED = 303, + + /** + * This indicates that an OS call failed. + */ + CUDA_ERROR_OPERATING_SYSTEM = 304, + + /** + * This indicates that a resource handle passed to the API call was not + * valid. Resource handles are opaque types like ::CUstream and ::CUevent. + */ + CUDA_ERROR_INVALID_HANDLE = 400, + + /** + * This indicates that a resource required by the API call is not in a + * valid state to perform the requested operation. + */ + CUDA_ERROR_ILLEGAL_STATE = 401, + + /** + * This indicates an attempt was made to introspect an object in a way that + * would discard semantically important information. This is either due to + * the object using funtionality newer than the API version used to + * introspect it or omission of optional return arguments. + */ + CUDA_ERROR_LOSSY_QUERY = 402, + + /** + * This indicates that a named symbol was not found. Examples of symbols + * are global/constant variable names, driver function names, texture names, + * and surface names. + */ + CUDA_ERROR_NOT_FOUND = 500, + + /** + * This indicates that asynchronous operations issued previously have not + * completed yet. This result is not actually an error, but must be indicated + * differently than ::CUDA_SUCCESS (which indicates completion). Calls that + * may return this value include ::cuEventQuery() and ::cuStreamQuery(). + */ + CUDA_ERROR_NOT_READY = 600, + + /** + * While executing a kernel, the device encountered a + * load or store instruction on an invalid memory address. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_ILLEGAL_ADDRESS = 700, + + /** + * This indicates that a launch did not occur because it did not have + * appropriate resources. This error usually indicates that the user has + * attempted to pass too many arguments to the device kernel, or the + * kernel launch specifies too many threads for the kernel's register + * count. Passing arguments of the wrong size (i.e. a 64-bit pointer + * when a 32-bit int is expected) is equivalent to passing too many + * arguments and can also result in this error. + */ + CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES = 701, + + /** + * This indicates that the device kernel took too long to execute. This can + * only occur if timeouts are enabled - see the device attribute + * ::CU_DEVICE_ATTRIBUTE_KERNEL_EXEC_TIMEOUT for more information. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_LAUNCH_TIMEOUT = 702, + + /** + * This error indicates a kernel launch that uses an incompatible texturing + * mode. + */ + CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING = 703, + + /** + * This error indicates that a call to ::cuCtxEnablePeerAccess() is + * trying to re-enable peer access to a context which has already + * had peer access to it enabled. + */ + CUDA_ERROR_PEER_ACCESS_ALREADY_ENABLED = 704, + + /** + * This error indicates that ::cuCtxDisablePeerAccess() is + * trying to disable peer access which has not been enabled yet + * via ::cuCtxEnablePeerAccess(). + */ + CUDA_ERROR_PEER_ACCESS_NOT_ENABLED = 705, + + /** + * This error indicates that the primary context for the specified device + * has already been initialized. + */ + CUDA_ERROR_PRIMARY_CONTEXT_ACTIVE = 708, + + /** + * This error indicates that the context current to the calling thread + * has been destroyed using ::cuCtxDestroy, or is a primary context which + * has not yet been initialized. + */ + CUDA_ERROR_CONTEXT_IS_DESTROYED = 709, + + /** + * A device-side assert triggered during kernel execution. The context + * cannot be used anymore, and must be destroyed. All existing device + * memory allocations from this context are invalid and must be + * reconstructed if the program is to continue using CUDA. + */ + CUDA_ERROR_ASSERT = 710, + + /** + * This error indicates that the hardware resources required to enable + * peer access have been exhausted for one or more of the devices + * passed to ::cuCtxEnablePeerAccess(). + */ + CUDA_ERROR_TOO_MANY_PEERS = 711, + + /** + * This error indicates that the memory range passed to ::cuMemHostRegister() + * has already been registered. + */ + CUDA_ERROR_HOST_MEMORY_ALREADY_REGISTERED = 712, + + /** + * This error indicates that the pointer passed to ::cuMemHostUnregister() + * does not correspond to any currently registered memory region. + */ + CUDA_ERROR_HOST_MEMORY_NOT_REGISTERED = 713, + + /** + * While executing a kernel, the device encountered a stack error. + * This can be due to stack corruption or exceeding the stack size limit. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_HARDWARE_STACK_ERROR = 714, + + /** + * While executing a kernel, the device encountered an illegal instruction. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_ILLEGAL_INSTRUCTION = 715, + + /** + * While executing a kernel, the device encountered a load or store instruction + * on a memory address which is not aligned. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_MISALIGNED_ADDRESS = 716, + + /** + * While executing a kernel, the device encountered an instruction + * which can only operate on memory locations in certain address spaces + * (global, shared, or local), but was supplied a memory address not + * belonging to an allowed address space. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_INVALID_ADDRESS_SPACE = 717, + + /** + * While executing a kernel, the device program counter wrapped its address space. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_INVALID_PC = 718, + + /** + * An exception occurred on the device while executing a kernel. Common + * causes include dereferencing an invalid device pointer and accessing + * out of bounds shared memory. Less common cases can be system specific - more + * information about these cases can be found in the system specific user guide. + * This leaves the process in an inconsistent state and any further CUDA work + * will return the same error. To continue using CUDA, the process must be terminated + * and relaunched. + */ + CUDA_ERROR_LAUNCH_FAILED = 719, + + /** + * This error indicates that the number of blocks launched per grid for a kernel that was + * launched via either ::cuLaunchCooperativeKernel or ::cuLaunchCooperativeKernelMultiDevice + * exceeds the maximum number of blocks as allowed by ::cuOccupancyMaxActiveBlocksPerMultiprocessor + * or ::cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags times the number of multiprocessors + * as specified by the device attribute ::CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT. + */ + CUDA_ERROR_COOPERATIVE_LAUNCH_TOO_LARGE = 720, + + /** + * This error indicates that the attempted operation is not permitted. + */ + CUDA_ERROR_NOT_PERMITTED = 800, + + /** + * This error indicates that the attempted operation is not supported + * on the current system or device. + */ + CUDA_ERROR_NOT_SUPPORTED = 801, + + /** + * This error indicates that the system is not yet ready to start any CUDA + * work. To continue using CUDA, verify the system configuration is in a + * valid state and all required driver daemons are actively running. + * More information about this error can be found in the system specific + * user guide. + */ + CUDA_ERROR_SYSTEM_NOT_READY = 802, + + /** + * This error indicates that there is a mismatch between the versions of + * the display driver and the CUDA driver. Refer to the compatibility documentation + * for supported versions. + */ + CUDA_ERROR_SYSTEM_DRIVER_MISMATCH = 803, + + /** + * This error indicates that the system was upgraded to run with forward compatibility + * but the visible hardware detected by CUDA does not support this configuration. + * Refer to the compatibility documentation for the supported hardware matrix or ensure + * that only supported hardware is visible during initialization via the CUDA_VISIBLE_DEVICES + * environment variable. + */ + CUDA_ERROR_COMPAT_NOT_SUPPORTED_ON_DEVICE = 804, + + /** + * This error indicates that the MPS client failed to connect to the MPS control daemon or the MPS server. + */ + CUDA_ERROR_MPS_CONNECTION_FAILED = 805, + + /** + * This error indicates that the remote procedural call between the MPS server and the MPS client failed. + */ + CUDA_ERROR_MPS_RPC_FAILURE = 806, + + /** + * This error indicates that the MPS server is not ready to accept new MPS client requests. + * This error can be returned when the MPS server is in the process of recovering from a fatal failure. + */ + CUDA_ERROR_MPS_SERVER_NOT_READY = 807, + + /** + * This error indicates that the hardware resources required to create MPS client have been exhausted. + */ + CUDA_ERROR_MPS_MAX_CLIENTS_REACHED = 808, + + /** + * This error indicates the the hardware resources required to support device connections have been exhausted. + */ + CUDA_ERROR_MPS_MAX_CONNECTIONS_REACHED = 809, + + /** + * This error indicates that the MPS client has been terminated by the server. To continue using CUDA, the process must be terminated and relaunched. + */ + CUDA_ERROR_MPS_CLIENT_TERMINATED = 810, + + /** + * This error indicates that the module is using CUDA Dynamic Parallelism, but the current configuration, like MPS, does not support it. + */ + CUDA_ERROR_CDP_NOT_SUPPORTED = 811, + + /** + * This error indicates that a module contains an unsupported interaction between different versions of CUDA Dynamic Parallelism. + */ + CUDA_ERROR_CDP_VERSION_MISMATCH = 812, + + /** + * This error indicates that the operation is not permitted when + * the stream is capturing. + */ + CUDA_ERROR_STREAM_CAPTURE_UNSUPPORTED = 900, + + /** + * This error indicates that the current capture sequence on the stream + * has been invalidated due to a previous error. + */ + CUDA_ERROR_STREAM_CAPTURE_INVALIDATED = 901, + + /** + * This error indicates that the operation would have resulted in a merge + * of two independent capture sequences. + */ + CUDA_ERROR_STREAM_CAPTURE_MERGE = 902, + + /** + * This error indicates that the capture was not initiated in this stream. + */ + CUDA_ERROR_STREAM_CAPTURE_UNMATCHED = 903, + + /** + * This error indicates that the capture sequence contains a fork that was + * not joined to the primary stream. + */ + CUDA_ERROR_STREAM_CAPTURE_UNJOINED = 904, + + /** + * This error indicates that a dependency would have been created which + * crosses the capture sequence boundary. Only implicit in-stream ordering + * dependencies are allowed to cross the boundary. + */ + CUDA_ERROR_STREAM_CAPTURE_ISOLATION = 905, + + /** + * This error indicates a disallowed implicit dependency on a current capture + * sequence from cudaStreamLegacy. + */ + CUDA_ERROR_STREAM_CAPTURE_IMPLICIT = 906, + + /** + * This error indicates that the operation is not permitted on an event which + * was last recorded in a capturing stream. + */ + CUDA_ERROR_CAPTURED_EVENT = 907, + + /** + * A stream capture sequence not initiated with the ::CU_STREAM_CAPTURE_MODE_RELAXED + * argument to ::cuStreamBeginCapture was passed to ::cuStreamEndCapture in a + * different thread. + */ + CUDA_ERROR_STREAM_CAPTURE_WRONG_THREAD = 908, + + /** + * This error indicates that the timeout specified for the wait operation has lapsed. + */ + CUDA_ERROR_TIMEOUT = 909, + + /** + * This error indicates that the graph update was not performed because it included + * changes which violated constraints specific to instantiated graph update. + */ + CUDA_ERROR_GRAPH_EXEC_UPDATE_FAILURE = 910, + + /** + * This indicates that an async error has occurred in a device outside of CUDA. + * If CUDA was waiting for an external device's signal before consuming shared data, + * the external device signaled an error indicating that the data is not valid for + * consumption. This leaves the process in an inconsistent state and any further CUDA + * work will return the same error. To continue using CUDA, the process must be + * terminated and relaunched. + */ + CUDA_ERROR_EXTERNAL_DEVICE = 911, + + /** + * Indicates a kernel launch error due to cluster misconfiguration. + */ + CUDA_ERROR_INVALID_CLUSTER_SIZE = 912, + + /** + * Indiciates a function handle is not loaded when calling an API that requires + * a loaded function. + */ + CUDA_ERROR_FUNCTION_NOT_LOADED = 913, + + /** + * This error indicates one or more resources passed in are not valid resource + * types for the operation. + */ + CUDA_ERROR_INVALID_RESOURCE_TYPE = 914, + + /** + * This error indicates one or more resources are insufficient or non-applicable for + * the operation. + */ + CUDA_ERROR_INVALID_RESOURCE_CONFIGURATION = 915, + + /** + * This indicates that an unknown internal error has occurred. + */ + CUDA_ERROR_UNKNOWN = 999 +} CUresult; + +/** + * P2P Attributes + */ +typedef enum CUdevice_P2PAttribute_enum { + CU_DEVICE_P2P_ATTRIBUTE_PERFORMANCE_RANK = 0x01, /**< A relative value indicating the performance of the link between two devices */ + CU_DEVICE_P2P_ATTRIBUTE_ACCESS_SUPPORTED = 0x02, /**< P2P Access is enable */ + CU_DEVICE_P2P_ATTRIBUTE_NATIVE_ATOMIC_SUPPORTED = 0x03, /**< Atomic operation over the link supported */ + CU_DEVICE_P2P_ATTRIBUTE_ACCESS_ACCESS_SUPPORTED = 0x04, /**< \deprecated use CU_DEVICE_P2P_ATTRIBUTE_CUDA_ARRAY_ACCESS_SUPPORTED instead */ + CU_DEVICE_P2P_ATTRIBUTE_CUDA_ARRAY_ACCESS_SUPPORTED = 0x04 /**< Accessing CUDA arrays over the link supported */ +} CUdevice_P2PAttribute; + +/** + * CUDA stream callback + * \param hStream The stream the callback was added to, as passed to ::cuStreamAddCallback. May be NULL. + * \param status ::CUDA_SUCCESS or any persistent error on the stream. + * \param userData User parameter provided at registration. + */ +typedef void (CUDA_CB *CUstreamCallback)(CUstream hStream, CUresult status, void *userData); + +/** + * Block size to per-block dynamic shared memory mapping for a certain + * kernel \param blockSize Block size of the kernel. + * + * \return The dynamic shared memory needed by a block. + */ +typedef size_t (CUDA_CB *CUoccupancyB2DSize)(int blockSize); + +/** + * If set, host memory is portable between CUDA contexts. + * Flag for ::cuMemHostAlloc() + */ +#define CU_MEMHOSTALLOC_PORTABLE 0x01 + +/** + * If set, host memory is mapped into CUDA address space and + * ::cuMemHostGetDevicePointer() may be called on the host pointer. + * Flag for ::cuMemHostAlloc() + */ +#define CU_MEMHOSTALLOC_DEVICEMAP 0x02 + +/** + * If set, host memory is allocated as write-combined - fast to write, + * faster to DMA, slow to read except via SSE4 streaming load instruction + * (MOVNTDQA). + * Flag for ::cuMemHostAlloc() + */ +#define CU_MEMHOSTALLOC_WRITECOMBINED 0x04 + +/** + * If set, host memory is portable between CUDA contexts. + * Flag for ::cuMemHostRegister() + */ +#define CU_MEMHOSTREGISTER_PORTABLE 0x01 + +/** + * If set, host memory is mapped into CUDA address space and + * ::cuMemHostGetDevicePointer() may be called on the host pointer. + * Flag for ::cuMemHostRegister() + */ +#define CU_MEMHOSTREGISTER_DEVICEMAP 0x02 + +/** + * If set, the passed memory pointer is treated as pointing to some + * memory-mapped I/O space, e.g. belonging to a third-party PCIe device. + * On Windows the flag is a no-op. + * On Linux that memory is marked as non cache-coherent for the GPU and + * is expected to be physically contiguous. It may return + * ::CUDA_ERROR_NOT_PERMITTED if run as an unprivileged user, + * ::CUDA_ERROR_NOT_SUPPORTED on older Linux kernel versions. + * On all other platforms, it is not supported and ::CUDA_ERROR_NOT_SUPPORTED + * is returned. + * Flag for ::cuMemHostRegister() + */ +#define CU_MEMHOSTREGISTER_IOMEMORY 0x04 + +/** +* If set, the passed memory pointer is treated as pointing to memory that is +* considered read-only by the device. On platforms without +* ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, this flag is +* required in order to register memory mapped to the CPU as read-only. Support +* for the use of this flag can be queried from the device attribute +* ::CU_DEVICE_ATTRIBUTE_READ_ONLY_HOST_REGISTER_SUPPORTED. Using this flag with +* a current context associated with a device that does not have this attribute +* set will cause ::cuMemHostRegister to error with ::CUDA_ERROR_NOT_SUPPORTED. +*/ +#define CU_MEMHOSTREGISTER_READ_ONLY 0x08 + +/** + * 2D memory copy parameters + */ +typedef struct CUDA_MEMCPY2D_st { + size_t srcXInBytes; /**< Source X in bytes */ + size_t srcY; /**< Source Y */ + + CUmemorytype srcMemoryType; /**< Source memory type (host, device, array) */ + const void *srcHost; /**< Source host pointer */ + CUdeviceptr srcDevice; /**< Source device pointer */ + CUarray srcArray; /**< Source array reference */ + size_t srcPitch; /**< Source pitch (ignored when src is array) */ + + size_t dstXInBytes; /**< Destination X in bytes */ + size_t dstY; /**< Destination Y */ + + CUmemorytype dstMemoryType; /**< Destination memory type (host, device, array) */ + void *dstHost; /**< Destination host pointer */ + CUdeviceptr dstDevice; /**< Destination device pointer */ + CUarray dstArray; /**< Destination array reference */ + size_t dstPitch; /**< Destination pitch (ignored when dst is array) */ + + size_t WidthInBytes; /**< Width of 2D memory copy in bytes */ + size_t Height; /**< Height of 2D memory copy */ +} CUDA_MEMCPY2D_v2; +typedef CUDA_MEMCPY2D_v2 CUDA_MEMCPY2D; + +/** + * 3D memory copy parameters + */ +typedef struct CUDA_MEMCPY3D_st { + size_t srcXInBytes; /**< Source X in bytes */ + size_t srcY; /**< Source Y */ + size_t srcZ; /**< Source Z */ + size_t srcLOD; /**< Source LOD */ + CUmemorytype srcMemoryType; /**< Source memory type (host, device, array) */ + const void *srcHost; /**< Source host pointer */ + CUdeviceptr srcDevice; /**< Source device pointer */ + CUarray srcArray; /**< Source array reference */ + void *reserved0; /**< Must be NULL */ + size_t srcPitch; /**< Source pitch (ignored when src is array) */ + size_t srcHeight; /**< Source height (ignored when src is array; may be 0 if Depth==1) */ + + size_t dstXInBytes; /**< Destination X in bytes */ + size_t dstY; /**< Destination Y */ + size_t dstZ; /**< Destination Z */ + size_t dstLOD; /**< Destination LOD */ + CUmemorytype dstMemoryType; /**< Destination memory type (host, device, array) */ + void *dstHost; /**< Destination host pointer */ + CUdeviceptr dstDevice; /**< Destination device pointer */ + CUarray dstArray; /**< Destination array reference */ + void *reserved1; /**< Must be NULL */ + size_t dstPitch; /**< Destination pitch (ignored when dst is array) */ + size_t dstHeight; /**< Destination height (ignored when dst is array; may be 0 if Depth==1) */ + + size_t WidthInBytes; /**< Width of 3D memory copy in bytes */ + size_t Height; /**< Height of 3D memory copy */ + size_t Depth; /**< Depth of 3D memory copy */ +} CUDA_MEMCPY3D_v2; +typedef CUDA_MEMCPY3D_v2 CUDA_MEMCPY3D; + +/** + * 3D memory cross-context copy parameters + */ +typedef struct CUDA_MEMCPY3D_PEER_st { + size_t srcXInBytes; /**< Source X in bytes */ + size_t srcY; /**< Source Y */ + size_t srcZ; /**< Source Z */ + size_t srcLOD; /**< Source LOD */ + CUmemorytype srcMemoryType; /**< Source memory type (host, device, array) */ + const void *srcHost; /**< Source host pointer */ + CUdeviceptr srcDevice; /**< Source device pointer */ + CUarray srcArray; /**< Source array reference */ + CUcontext srcContext; /**< Source context (ignored with srcMemoryType is ::CU_MEMORYTYPE_ARRAY) */ + size_t srcPitch; /**< Source pitch (ignored when src is array) */ + size_t srcHeight; /**< Source height (ignored when src is array; may be 0 if Depth==1) */ + + size_t dstXInBytes; /**< Destination X in bytes */ + size_t dstY; /**< Destination Y */ + size_t dstZ; /**< Destination Z */ + size_t dstLOD; /**< Destination LOD */ + CUmemorytype dstMemoryType; /**< Destination memory type (host, device, array) */ + void *dstHost; /**< Destination host pointer */ + CUdeviceptr dstDevice; /**< Destination device pointer */ + CUarray dstArray; /**< Destination array reference */ + CUcontext dstContext; /**< Destination context (ignored with dstMemoryType is ::CU_MEMORYTYPE_ARRAY) */ + size_t dstPitch; /**< Destination pitch (ignored when dst is array) */ + size_t dstHeight; /**< Destination height (ignored when dst is array; may be 0 if Depth==1) */ + + size_t WidthInBytes; /**< Width of 3D memory copy in bytes */ + size_t Height; /**< Height of 3D memory copy */ + size_t Depth; /**< Depth of 3D memory copy */ +} CUDA_MEMCPY3D_PEER_v1; +typedef CUDA_MEMCPY3D_PEER_v1 CUDA_MEMCPY3D_PEER; + +/** + * Memcpy node parameters + */ +typedef struct CUDA_MEMCPY_NODE_PARAMS_st { + int flags; /**< Must be zero */ + int reserved; /**< Must be zero */ + CUcontext copyCtx; /**< Context on which to run the node */ + CUDA_MEMCPY3D copyParams; /**< Parameters for the memory copy */ +} CUDA_MEMCPY_NODE_PARAMS; + +/** + * Array descriptor + */ +typedef struct CUDA_ARRAY_DESCRIPTOR_st +{ + size_t Width; /**< Width of array */ + size_t Height; /**< Height of array */ + + CUarray_format Format; /**< Array format */ + unsigned int NumChannels; /**< Channels per array element */ +} CUDA_ARRAY_DESCRIPTOR_v2; +typedef CUDA_ARRAY_DESCRIPTOR_v2 CUDA_ARRAY_DESCRIPTOR; + +/** + * 3D array descriptor + */ +typedef struct CUDA_ARRAY3D_DESCRIPTOR_st +{ + size_t Width; /**< Width of 3D array */ + size_t Height; /**< Height of 3D array */ + size_t Depth; /**< Depth of 3D array */ + + CUarray_format Format; /**< Array format */ + unsigned int NumChannels; /**< Channels per array element */ + unsigned int Flags; /**< Flags */ +} CUDA_ARRAY3D_DESCRIPTOR_v2; +typedef CUDA_ARRAY3D_DESCRIPTOR_v2 CUDA_ARRAY3D_DESCRIPTOR; + +/** + * Indicates that the layered sparse CUDA array or CUDA mipmapped array has a single mip tail region for all layers + */ +#define CU_ARRAY_SPARSE_PROPERTIES_SINGLE_MIPTAIL 0x1 + +/** + * CUDA array sparse properties + */ +typedef struct CUDA_ARRAY_SPARSE_PROPERTIES_st { + struct { + unsigned int width; /**< Width of sparse tile in elements */ + unsigned int height; /**< Height of sparse tile in elements */ + unsigned int depth; /**< Depth of sparse tile in elements */ + } tileExtent; + + /** + * First mip level at which the mip tail begins. + */ + unsigned int miptailFirstLevel; + /** + * Total size of the mip tail. + */ + unsigned long long miptailSize; + /** + * Flags will either be zero or ::CU_ARRAY_SPARSE_PROPERTIES_SINGLE_MIPTAIL + */ + unsigned int flags; + unsigned int reserved[4]; +} CUDA_ARRAY_SPARSE_PROPERTIES_v1; +typedef CUDA_ARRAY_SPARSE_PROPERTIES_v1 CUDA_ARRAY_SPARSE_PROPERTIES; + +/** + * CUDA array memory requirements + */ +typedef struct CUDA_ARRAY_MEMORY_REQUIREMENTS_st { + size_t size; /**< Total required memory size */ + size_t alignment; /**< alignment requirement */ + unsigned int reserved[4]; +} CUDA_ARRAY_MEMORY_REQUIREMENTS_v1; +typedef CUDA_ARRAY_MEMORY_REQUIREMENTS_v1 CUDA_ARRAY_MEMORY_REQUIREMENTS; + +/** + * CUDA Resource descriptor + */ +typedef struct CUDA_RESOURCE_DESC_st +{ + CUresourcetype resType; /**< Resource type */ + + union { + struct { + CUarray hArray; /**< CUDA array */ + } array; + struct { + CUmipmappedArray hMipmappedArray; /**< CUDA mipmapped array */ + } mipmap; + struct { + CUdeviceptr devPtr; /**< Device pointer */ + CUarray_format format; /**< Array format */ + unsigned int numChannels; /**< Channels per array element */ + size_t sizeInBytes; /**< Size in bytes */ + } linear; + struct { + CUdeviceptr devPtr; /**< Device pointer */ + CUarray_format format; /**< Array format */ + unsigned int numChannels; /**< Channels per array element */ + size_t width; /**< Width of the array in elements */ + size_t height; /**< Height of the array in elements */ + size_t pitchInBytes; /**< Pitch between two rows in bytes */ + } pitch2D; + struct { + int reserved[32]; + } reserved; + } res; + + unsigned int flags; /**< Flags (must be zero) */ +} CUDA_RESOURCE_DESC_v1; +typedef CUDA_RESOURCE_DESC_v1 CUDA_RESOURCE_DESC; + +/** + * Texture descriptor + */ +typedef struct CUDA_TEXTURE_DESC_st { + CUaddress_mode addressMode[3]; /**< Address modes */ + CUfilter_mode filterMode; /**< Filter mode */ + unsigned int flags; /**< Flags */ + unsigned int maxAnisotropy; /**< Maximum anisotropy ratio */ + CUfilter_mode mipmapFilterMode; /**< Mipmap filter mode */ + float mipmapLevelBias; /**< Mipmap level bias */ + float minMipmapLevelClamp; /**< Mipmap minimum level clamp */ + float maxMipmapLevelClamp; /**< Mipmap maximum level clamp */ + float borderColor[4]; /**< Border Color */ + int reserved[12]; +} CUDA_TEXTURE_DESC_v1; +typedef CUDA_TEXTURE_DESC_v1 CUDA_TEXTURE_DESC; + +/** + * Resource view format + */ +typedef enum CUresourceViewFormat_enum +{ + CU_RES_VIEW_FORMAT_NONE = 0x00, /**< No resource view format (use underlying resource format) */ + CU_RES_VIEW_FORMAT_UINT_1X8 = 0x01, /**< 1 channel unsigned 8-bit integers */ + CU_RES_VIEW_FORMAT_UINT_2X8 = 0x02, /**< 2 channel unsigned 8-bit integers */ + CU_RES_VIEW_FORMAT_UINT_4X8 = 0x03, /**< 4 channel unsigned 8-bit integers */ + CU_RES_VIEW_FORMAT_SINT_1X8 = 0x04, /**< 1 channel signed 8-bit integers */ + CU_RES_VIEW_FORMAT_SINT_2X8 = 0x05, /**< 2 channel signed 8-bit integers */ + CU_RES_VIEW_FORMAT_SINT_4X8 = 0x06, /**< 4 channel signed 8-bit integers */ + CU_RES_VIEW_FORMAT_UINT_1X16 = 0x07, /**< 1 channel unsigned 16-bit integers */ + CU_RES_VIEW_FORMAT_UINT_2X16 = 0x08, /**< 2 channel unsigned 16-bit integers */ + CU_RES_VIEW_FORMAT_UINT_4X16 = 0x09, /**< 4 channel unsigned 16-bit integers */ + CU_RES_VIEW_FORMAT_SINT_1X16 = 0x0a, /**< 1 channel signed 16-bit integers */ + CU_RES_VIEW_FORMAT_SINT_2X16 = 0x0b, /**< 2 channel signed 16-bit integers */ + CU_RES_VIEW_FORMAT_SINT_4X16 = 0x0c, /**< 4 channel signed 16-bit integers */ + CU_RES_VIEW_FORMAT_UINT_1X32 = 0x0d, /**< 1 channel unsigned 32-bit integers */ + CU_RES_VIEW_FORMAT_UINT_2X32 = 0x0e, /**< 2 channel unsigned 32-bit integers */ + CU_RES_VIEW_FORMAT_UINT_4X32 = 0x0f, /**< 4 channel unsigned 32-bit integers */ + CU_RES_VIEW_FORMAT_SINT_1X32 = 0x10, /**< 1 channel signed 32-bit integers */ + CU_RES_VIEW_FORMAT_SINT_2X32 = 0x11, /**< 2 channel signed 32-bit integers */ + CU_RES_VIEW_FORMAT_SINT_4X32 = 0x12, /**< 4 channel signed 32-bit integers */ + CU_RES_VIEW_FORMAT_FLOAT_1X16 = 0x13, /**< 1 channel 16-bit floating point */ + CU_RES_VIEW_FORMAT_FLOAT_2X16 = 0x14, /**< 2 channel 16-bit floating point */ + CU_RES_VIEW_FORMAT_FLOAT_4X16 = 0x15, /**< 4 channel 16-bit floating point */ + CU_RES_VIEW_FORMAT_FLOAT_1X32 = 0x16, /**< 1 channel 32-bit floating point */ + CU_RES_VIEW_FORMAT_FLOAT_2X32 = 0x17, /**< 2 channel 32-bit floating point */ + CU_RES_VIEW_FORMAT_FLOAT_4X32 = 0x18, /**< 4 channel 32-bit floating point */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC1 = 0x19, /**< Block compressed 1 */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC2 = 0x1a, /**< Block compressed 2 */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC3 = 0x1b, /**< Block compressed 3 */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC4 = 0x1c, /**< Block compressed 4 unsigned */ + CU_RES_VIEW_FORMAT_SIGNED_BC4 = 0x1d, /**< Block compressed 4 signed */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC5 = 0x1e, /**< Block compressed 5 unsigned */ + CU_RES_VIEW_FORMAT_SIGNED_BC5 = 0x1f, /**< Block compressed 5 signed */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC6H = 0x20, /**< Block compressed 6 unsigned half-float */ + CU_RES_VIEW_FORMAT_SIGNED_BC6H = 0x21, /**< Block compressed 6 signed half-float */ + CU_RES_VIEW_FORMAT_UNSIGNED_BC7 = 0x22 /**< Block compressed 7 */ +} CUresourceViewFormat; + +/** + * Resource view descriptor + */ +typedef struct CUDA_RESOURCE_VIEW_DESC_st +{ + CUresourceViewFormat format; /**< Resource view format */ + size_t width; /**< Width of the resource view */ + size_t height; /**< Height of the resource view */ + size_t depth; /**< Depth of the resource view */ + unsigned int firstMipmapLevel; /**< First defined mipmap level */ + unsigned int lastMipmapLevel; /**< Last defined mipmap level */ + unsigned int firstLayer; /**< First layer index */ + unsigned int lastLayer; /**< Last layer index */ + unsigned int reserved[16]; +} CUDA_RESOURCE_VIEW_DESC_v1; +typedef CUDA_RESOURCE_VIEW_DESC_v1 CUDA_RESOURCE_VIEW_DESC; + +/** + * Size of tensor map descriptor + */ +#define CU_TENSOR_MAP_NUM_QWORDS 16 + +/** + * Tensor map descriptor. Requires compiler support for aligning to 64 bytes. + */ +typedef struct CUtensorMap_st { +#if defined(__cplusplus) && (__cplusplus >= 201103L) + alignas(64) +#elif __STDC_VERSION__ >= 201112L + _Alignas(64) +#endif + cuuint64_t opaque[CU_TENSOR_MAP_NUM_QWORDS]; +} CUtensorMap; + +/** + * Tensor map data type + */ +typedef enum CUtensorMapDataType_enum { + CU_TENSOR_MAP_DATA_TYPE_UINT8 = 0, + CU_TENSOR_MAP_DATA_TYPE_UINT16, + CU_TENSOR_MAP_DATA_TYPE_UINT32, + CU_TENSOR_MAP_DATA_TYPE_INT32, + CU_TENSOR_MAP_DATA_TYPE_UINT64, + CU_TENSOR_MAP_DATA_TYPE_INT64, + CU_TENSOR_MAP_DATA_TYPE_FLOAT16, + CU_TENSOR_MAP_DATA_TYPE_FLOAT32, + CU_TENSOR_MAP_DATA_TYPE_FLOAT64, + CU_TENSOR_MAP_DATA_TYPE_BFLOAT16, + CU_TENSOR_MAP_DATA_TYPE_FLOAT32_FTZ, + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32, + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32_FTZ +} CUtensorMapDataType; + +/** + * Tensor map interleave layout type + */ +typedef enum CUtensorMapInterleave_enum { + CU_TENSOR_MAP_INTERLEAVE_NONE = 0, + CU_TENSOR_MAP_INTERLEAVE_16B, + CU_TENSOR_MAP_INTERLEAVE_32B +} CUtensorMapInterleave; + +/** + * Tensor map swizzling mode of shared memory banks + */ +typedef enum CUtensorMapSwizzle_enum { + CU_TENSOR_MAP_SWIZZLE_NONE = 0, + CU_TENSOR_MAP_SWIZZLE_32B, + CU_TENSOR_MAP_SWIZZLE_64B, + CU_TENSOR_MAP_SWIZZLE_128B, +} CUtensorMapSwizzle; + +/** + * Tensor map L2 promotion type + */ +typedef enum CUtensorMapL2promotion_enum { + CU_TENSOR_MAP_L2_PROMOTION_NONE = 0, + CU_TENSOR_MAP_L2_PROMOTION_L2_64B, + CU_TENSOR_MAP_L2_PROMOTION_L2_128B, + CU_TENSOR_MAP_L2_PROMOTION_L2_256B +} CUtensorMapL2promotion; + +/** + * Tensor map out-of-bounds fill type + */ +typedef enum CUtensorMapFloatOOBfill_enum { + CU_TENSOR_MAP_FLOAT_OOB_FILL_NONE = 0, + CU_TENSOR_MAP_FLOAT_OOB_FILL_NAN_REQUEST_ZERO_FMA +} CUtensorMapFloatOOBfill; + +/** + * GPU Direct v3 tokens + */ +typedef struct CUDA_POINTER_ATTRIBUTE_P2P_TOKENS_st { + unsigned long long p2pToken; + unsigned int vaSpaceToken; +} CUDA_POINTER_ATTRIBUTE_P2P_TOKENS_v1; +typedef CUDA_POINTER_ATTRIBUTE_P2P_TOKENS_v1 CUDA_POINTER_ATTRIBUTE_P2P_TOKENS; + +/** +* Access flags that specify the level of access the current context's device has +* on the memory referenced. +*/ +typedef enum CUDA_POINTER_ATTRIBUTE_ACCESS_FLAGS_enum { + CU_POINTER_ATTRIBUTE_ACCESS_FLAG_NONE = 0x0, /**< No access, meaning the device cannot access this memory at all, thus must be staged through accessible memory in order to complete certain operations */ + CU_POINTER_ATTRIBUTE_ACCESS_FLAG_READ = 0x1, /**< Read-only access, meaning writes to this memory are considered invalid accesses and thus return error in that case. */ + CU_POINTER_ATTRIBUTE_ACCESS_FLAG_READWRITE = 0x3 /**< Read-write access, the device has full read-write access to the memory */ +} CUDA_POINTER_ATTRIBUTE_ACCESS_FLAGS; + +/** + * Kernel launch parameters + */ +typedef struct CUDA_LAUNCH_PARAMS_st { + CUfunction function; /**< Kernel to launch */ + unsigned int gridDimX; /**< Width of grid in blocks */ + unsigned int gridDimY; /**< Height of grid in blocks */ + unsigned int gridDimZ; /**< Depth of grid in blocks */ + unsigned int blockDimX; /**< X dimension of each thread block */ + unsigned int blockDimY; /**< Y dimension of each thread block */ + unsigned int blockDimZ; /**< Z dimension of each thread block */ + unsigned int sharedMemBytes; /**< Dynamic shared-memory size per thread block in bytes */ + CUstream hStream; /**< Stream identifier */ + void **kernelParams; /**< Array of pointers to kernel parameters */ +} CUDA_LAUNCH_PARAMS_v1; +typedef CUDA_LAUNCH_PARAMS_v1 CUDA_LAUNCH_PARAMS; + +/** + * External memory handle types + */ +typedef enum CUexternalMemoryHandleType_enum { + /** + * Handle is an opaque file descriptor + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_FD = 1, + /** + * Handle is an opaque shared NT handle + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32 = 2, + /** + * Handle is an opaque, globally shared handle + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32_KMT = 3, + /** + * Handle is a D3D12 heap object + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_HEAP = 4, + /** + * Handle is a D3D12 committed resource + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_RESOURCE = 5, + /** + * Handle is a shared NT handle to a D3D11 resource + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE = 6, + /** + * Handle is a globally shared handle to a D3D11 resource + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT = 7, + /** + * Handle is an NvSciBuf object + */ + CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF = 8 +} CUexternalMemoryHandleType; + +/** + * Indicates that the external memory object is a dedicated resource + */ +#define CUDA_EXTERNAL_MEMORY_DEDICATED 0x1 + +/** When the \p flags parameter of ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS + * contains this flag, it indicates that signaling an external semaphore object + * should skip performing appropriate memory synchronization operations over all + * the external memory objects that are imported as ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF, + * which otherwise are performed by default to ensure data coherency with other + * importers of the same NvSciBuf memory objects. + */ +#define CUDA_EXTERNAL_SEMAPHORE_SIGNAL_SKIP_NVSCIBUF_MEMSYNC 0x01 + +/** When the \p flags parameter of ::CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS + * contains this flag, it indicates that waiting on an external semaphore object + * should skip performing appropriate memory synchronization operations over all + * the external memory objects that are imported as ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF, + * which otherwise are performed by default to ensure data coherency with other + * importers of the same NvSciBuf memory objects. + */ +#define CUDA_EXTERNAL_SEMAPHORE_WAIT_SKIP_NVSCIBUF_MEMSYNC 0x02 + +/** + * When \p flags of ::cuDeviceGetNvSciSyncAttributes is set to this, + * it indicates that application needs signaler specific NvSciSyncAttr + * to be filled by ::cuDeviceGetNvSciSyncAttributes. + */ +#define CUDA_NVSCISYNC_ATTR_SIGNAL 0x1 + +/** + * When \p flags of ::cuDeviceGetNvSciSyncAttributes is set to this, + * it indicates that application needs waiter specific NvSciSyncAttr + * to be filled by ::cuDeviceGetNvSciSyncAttributes. + */ +#define CUDA_NVSCISYNC_ATTR_WAIT 0x2 +/** + * External memory handle descriptor + */ +typedef struct CUDA_EXTERNAL_MEMORY_HANDLE_DESC_st { + /** + * Type of the handle + */ + CUexternalMemoryHandleType type; + union { + /** + * File descriptor referencing the memory object. Valid + * when type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_FD + */ + int fd; + /** + * Win32 handle referencing the semaphore object. Valid when + * type is one of the following: + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32 + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32_KMT + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_HEAP + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_RESOURCE + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE + * - ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT + * Exactly one of 'handle' and 'name' must be non-NULL. If + * type is one of the following: + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32_KMT + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT + * then 'name' must be NULL. + */ + struct { + /** + * Valid NT handle. Must be NULL if 'name' is non-NULL + */ + void *handle; + /** + * Name of a valid memory object. + * Must be NULL if 'handle' is non-NULL. + */ + const void *name; + } win32; + /** + * A handle representing an NvSciBuf Object. Valid when type + * is ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF + */ + const void *nvSciBufObject; + } handle; + /** + * Size of the memory allocation + */ + unsigned long long size; + /** + * Flags must either be zero or ::CUDA_EXTERNAL_MEMORY_DEDICATED + */ + unsigned int flags; + unsigned int reserved[16]; +} CUDA_EXTERNAL_MEMORY_HANDLE_DESC_v1; +typedef CUDA_EXTERNAL_MEMORY_HANDLE_DESC_v1 CUDA_EXTERNAL_MEMORY_HANDLE_DESC; + +/** + * External memory buffer descriptor + */ +typedef struct CUDA_EXTERNAL_MEMORY_BUFFER_DESC_st { + /** + * Offset into the memory object where the buffer's base is + */ + unsigned long long offset; + /** + * Size of the buffer + */ + unsigned long long size; + /** + * Flags reserved for future use. Must be zero. + */ + unsigned int flags; + unsigned int reserved[16]; +} CUDA_EXTERNAL_MEMORY_BUFFER_DESC_v1; +typedef CUDA_EXTERNAL_MEMORY_BUFFER_DESC_v1 CUDA_EXTERNAL_MEMORY_BUFFER_DESC; + +/** + * External memory mipmap descriptor + */ +typedef struct CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC_st { + /** + * Offset into the memory object where the base level of the + * mipmap chain is. + */ + unsigned long long offset; + /** + * Format, dimension and type of base level of the mipmap chain + */ + CUDA_ARRAY3D_DESCRIPTOR arrayDesc; + /** + * Total number of levels in the mipmap chain + */ + unsigned int numLevels; + unsigned int reserved[16]; +} CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC_v1; +typedef CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC_v1 CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC; + +/** + * External semaphore handle types + */ +typedef enum CUexternalSemaphoreHandleType_enum { + /** + * Handle is an opaque file descriptor + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD = 1, + /** + * Handle is an opaque shared NT handle + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32 = 2, + /** + * Handle is an opaque, globally shared handle + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT = 3, + /** + * Handle is a shared NT handle referencing a D3D12 fence object + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE = 4, + /** + * Handle is a shared NT handle referencing a D3D11 fence object + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE = 5, + /** + * Opaque handle to NvSciSync Object + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC = 6, + /** + * Handle is a shared NT handle referencing a D3D11 keyed mutex object + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX = 7, + /** + * Handle is a globally shared handle referencing a D3D11 keyed mutex object + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT = 8, + /** + * Handle is an opaque file descriptor referencing a timeline semaphore + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD = 9, + /** + * Handle is an opaque shared NT handle referencing a timeline semaphore + */ + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32 = 10 +} CUexternalSemaphoreHandleType; + +/** + * External semaphore handle descriptor + */ +typedef struct CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC_st { + /** + * Type of the handle + */ + CUexternalSemaphoreHandleType type; + union { + /** + * File descriptor referencing the semaphore object. Valid + * when type is one of the following: + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD + */ + int fd; + /** + * Win32 handle referencing the semaphore object. Valid when + * type is one of the following: + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32 + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32 + * Exactly one of 'handle' and 'name' must be non-NULL. If + * type is one of the following: + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT + * - ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT + * then 'name' must be NULL. + */ + struct { + /** + * Valid NT handle. Must be NULL if 'name' is non-NULL + */ + void *handle; + /** + * Name of a valid synchronization primitive. + * Must be NULL if 'handle' is non-NULL. + */ + const void *name; + } win32; + /** + * Valid NvSciSyncObj. Must be non NULL + */ + const void* nvSciSyncObj; + } handle; + /** + * Flags reserved for the future. Must be zero. + */ + unsigned int flags; + unsigned int reserved[16]; +} CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC_v1; +typedef CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC_v1 CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC; + +/** + * External semaphore signal parameters + */ +typedef struct CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS_st { + struct { + /** + * Parameters for fence objects + */ + struct { + /** + * Value of fence to be signaled + */ + unsigned long long value; + } fence; + union { + /** + * Pointer to NvSciSyncFence. Valid if ::CUexternalSemaphoreHandleType + * is of type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC. + */ + void *fence; + unsigned long long reserved; + } nvSciSync; + /** + * Parameters for keyed mutex objects + */ + struct { + /** + * Value of key to release the mutex with + */ + unsigned long long key; + } keyedMutex; + unsigned int reserved[12]; + } params; + /** + * Only when ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS is used to + * signal a ::CUexternalSemaphore of type + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC, the valid flag is + * ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_SKIP_NVSCIBUF_MEMSYNC which indicates + * that while signaling the ::CUexternalSemaphore, no memory synchronization + * operations should be performed for any external memory object imported + * as ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF. + * For all other types of ::CUexternalSemaphore, flags must be zero. + */ + unsigned int flags; + unsigned int reserved[16]; +} CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS_v1; +typedef CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS_v1 CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS; + +/** + * External semaphore wait parameters + */ +typedef struct CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS_st { + struct { + /** + * Parameters for fence objects + */ + struct { + /** + * Value of fence to be waited on + */ + unsigned long long value; + } fence; + /** + * Pointer to NvSciSyncFence. Valid if CUexternalSemaphoreHandleType + * is of type CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC. + */ + union { + void *fence; + unsigned long long reserved; + } nvSciSync; + /** + * Parameters for keyed mutex objects + */ + struct { + /** + * Value of key to acquire the mutex with + */ + unsigned long long key; + /** + * Timeout in milliseconds to wait to acquire the mutex + */ + unsigned int timeoutMs; + } keyedMutex; + unsigned int reserved[10]; + } params; + /** + * Only when ::CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS is used to wait on + * a ::CUexternalSemaphore of type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC, + * the valid flag is ::CUDA_EXTERNAL_SEMAPHORE_WAIT_SKIP_NVSCIBUF_MEMSYNC + * which indicates that while waiting for the ::CUexternalSemaphore, no memory + * synchronization operations should be performed for any external memory + * object imported as ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF. + * For all other types of ::CUexternalSemaphore, flags must be zero. + */ + unsigned int flags; + unsigned int reserved[16]; +} CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS_v1; +typedef CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS_v1 CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS; + +/** + * Semaphore signal node parameters + */ +typedef struct CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_st { + CUexternalSemaphore* extSemArray; /**< Array of external semaphore handles. */ + const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS* paramsArray; /**< Array of external semaphore signal parameters. */ + unsigned int numExtSems; /**< Number of handles and parameters supplied in extSemArray and paramsArray. */ +} CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1; +typedef CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1 CUDA_EXT_SEM_SIGNAL_NODE_PARAMS; + +/** + * Semaphore signal node parameters + */ +typedef struct CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v2_st { + CUexternalSemaphore* extSemArray; /**< Array of external semaphore handles. */ + const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS* paramsArray; /**< Array of external semaphore signal parameters. */ + unsigned int numExtSems; /**< Number of handles and parameters supplied in extSemArray and paramsArray. */ +} CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v2; + +/** + * Semaphore wait node parameters + */ +typedef struct CUDA_EXT_SEM_WAIT_NODE_PARAMS_st { + CUexternalSemaphore* extSemArray; /**< Array of external semaphore handles. */ + const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS* paramsArray; /**< Array of external semaphore wait parameters. */ + unsigned int numExtSems; /**< Number of handles and parameters supplied in extSemArray and paramsArray. */ +} CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1; +typedef CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1 CUDA_EXT_SEM_WAIT_NODE_PARAMS; + +/** + * Semaphore wait node parameters + */ +typedef struct CUDA_EXT_SEM_WAIT_NODE_PARAMS_v2_st { + CUexternalSemaphore* extSemArray; /**< Array of external semaphore handles. */ + const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS* paramsArray; /**< Array of external semaphore wait parameters. */ + unsigned int numExtSems; /**< Number of handles and parameters supplied in extSemArray and paramsArray. */ +} CUDA_EXT_SEM_WAIT_NODE_PARAMS_v2; + +typedef unsigned long long CUmemGenericAllocationHandle_v1; +typedef CUmemGenericAllocationHandle_v1 CUmemGenericAllocationHandle; + +/** + * Flags for specifying particular handle types + */ +typedef enum CUmemAllocationHandleType_enum { + CU_MEM_HANDLE_TYPE_NONE = 0x0, /**< Does not allow any export mechanism. > */ + CU_MEM_HANDLE_TYPE_POSIX_FILE_DESCRIPTOR = 0x1, /**< Allows a file descriptor to be used for exporting. Permitted only on POSIX systems. (int) */ + CU_MEM_HANDLE_TYPE_WIN32 = 0x2, /**< Allows a Win32 NT handle to be used for exporting. (HANDLE) */ + CU_MEM_HANDLE_TYPE_WIN32_KMT = 0x4, /**< Allows a Win32 KMT handle to be used for exporting. (D3DKMT_HANDLE) */ + CU_MEM_HANDLE_TYPE_FABRIC = 0x8, /**< Allows a fabric handle to be used for exporting. (CUmemFabricHandle)*/ + CU_MEM_HANDLE_TYPE_MAX = 0x7FFFFFFF +} CUmemAllocationHandleType; + +/** + * Specifies the memory protection flags for mapping. + */ +typedef enum CUmemAccess_flags_enum { + CU_MEM_ACCESS_FLAGS_PROT_NONE = 0x0, /**< Default, make the address range not accessible */ + CU_MEM_ACCESS_FLAGS_PROT_READ = 0x1, /**< Make the address range read accessible */ + CU_MEM_ACCESS_FLAGS_PROT_READWRITE = 0x3, /**< Make the address range read-write accessible */ + CU_MEM_ACCESS_FLAGS_PROT_MAX = 0x7FFFFFFF +} CUmemAccess_flags; + +/** + * Specifies the type of location + */ +typedef enum CUmemLocationType_enum { + CU_MEM_LOCATION_TYPE_INVALID = 0x0, + CU_MEM_LOCATION_TYPE_DEVICE = 0x1, /**< Location is a device location, thus id is a device ordinal */ + CU_MEM_LOCATION_TYPE_HOST = 0x2, /**< Location is host, id is ignored */ + CU_MEM_LOCATION_TYPE_HOST_NUMA = 0x3, /**< Location is a host NUMA node, thus id is a host NUMA node id */ + CU_MEM_LOCATION_TYPE_HOST_NUMA_CURRENT = 0x4, /**< Location is a host NUMA node of the current thread, id is ignored */ + CU_MEM_LOCATION_TYPE_MAX = 0x7FFFFFFF +} CUmemLocationType; + +/** +* Defines the allocation types available +*/ +typedef enum CUmemAllocationType_enum { + CU_MEM_ALLOCATION_TYPE_INVALID = 0x0, + + /** This allocation type is 'pinned', i.e. cannot migrate from its current + * location while the application is actively using it + */ + CU_MEM_ALLOCATION_TYPE_PINNED = 0x1, + CU_MEM_ALLOCATION_TYPE_MAX = 0x7FFFFFFF +} CUmemAllocationType; + +/** +* Flag for requesting different optimal and required granularities for an allocation. +*/ +typedef enum CUmemAllocationGranularity_flags_enum { + CU_MEM_ALLOC_GRANULARITY_MINIMUM = 0x0, /**< Minimum required granularity for allocation */ + CU_MEM_ALLOC_GRANULARITY_RECOMMENDED = 0x1 /**< Recommended granularity for allocation for best performance */ +} CUmemAllocationGranularity_flags; + +/** +* Specifies the handle type for address range +*/ +typedef enum CUmemRangeHandleType_enum +{ + CU_MEM_RANGE_HANDLE_TYPE_DMA_BUF_FD = 0x1, + CU_MEM_RANGE_HANDLE_TYPE_MAX = 0x7FFFFFFF +} CUmemRangeHandleType; + +/** + * Sparse subresource types + */ +typedef enum CUarraySparseSubresourceType_enum { + CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_SPARSE_LEVEL = 0, + CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_MIPTAIL = 1 +} CUarraySparseSubresourceType; + +/** + * Memory operation types + */ +typedef enum CUmemOperationType_enum { + CU_MEM_OPERATION_TYPE_MAP = 1, + CU_MEM_OPERATION_TYPE_UNMAP = 2 +} CUmemOperationType; + +/** + * Memory handle types + */ +typedef enum CUmemHandleType_enum { + CU_MEM_HANDLE_TYPE_GENERIC = 0 +} CUmemHandleType; + +/** + * Specifies the CUDA array or CUDA mipmapped array memory mapping information + */ +typedef struct CUarrayMapInfo_st { + CUresourcetype resourceType; /**< Resource type */ + + union { + CUmipmappedArray mipmap; + CUarray array; + } resource; + + CUarraySparseSubresourceType subresourceType; /**< Sparse subresource type */ + + union { + struct { + unsigned int level; /**< For CUDA mipmapped arrays must a valid mipmap level. For CUDA arrays must be zero */ + unsigned int layer; /**< For CUDA layered arrays must be a valid layer index. Otherwise, must be zero */ + unsigned int offsetX; /**< Starting X offset in elements */ + unsigned int offsetY; /**< Starting Y offset in elements */ + unsigned int offsetZ; /**< Starting Z offset in elements */ + unsigned int extentWidth; /**< Width in elements */ + unsigned int extentHeight; /**< Height in elements */ + unsigned int extentDepth; /**< Depth in elements */ + } sparseLevel; + struct { + unsigned int layer; /**< For CUDA layered arrays must be a valid layer index. Otherwise, must be zero */ + unsigned long long offset; /**< Offset within mip tail */ + unsigned long long size; /**< Extent in bytes */ + } miptail; + } subresource; + + CUmemOperationType memOperationType; /**< Memory operation type */ + CUmemHandleType memHandleType; /**< Memory handle type */ + + union { + CUmemGenericAllocationHandle memHandle; + } memHandle; + + unsigned long long offset; /**< Offset within the memory */ + unsigned int deviceBitMask; /**< Device ordinal bit mask */ + unsigned int flags; /**< flags for future use, must be zero now. */ + unsigned int reserved[2]; /**< Reserved for future use, must be zero now. */ +} CUarrayMapInfo_v1; +typedef CUarrayMapInfo_v1 CUarrayMapInfo; + +/** + * Specifies a memory location. + */ +typedef struct CUmemLocation_st { + CUmemLocationType type; /**< Specifies the location type, which modifies the meaning of id. */ + int id; /**< identifier for a given this location's ::CUmemLocationType. */ +} CUmemLocation_v1; +typedef CUmemLocation_v1 CUmemLocation; + +/** + * Specifies compression attribute for an allocation. + */ +typedef enum CUmemAllocationCompType_enum { + CU_MEM_ALLOCATION_COMP_NONE = 0x0, /**< Allocating non-compressible memory */ + CU_MEM_ALLOCATION_COMP_GENERIC = 0x1 /**< Allocating compressible memory */ +} CUmemAllocationCompType; + +/** + * This flag if set indicates that the memory will be used as a tile pool. + */ +#define CU_MEM_CREATE_USAGE_TILE_POOL 0x1 + +/** +* Specifies the allocation properties for a allocation. +*/ +typedef struct CUmemAllocationProp_st { + /** Allocation type */ + CUmemAllocationType type; + /** requested ::CUmemAllocationHandleType */ + CUmemAllocationHandleType requestedHandleTypes; + /** Location of allocation */ + CUmemLocation location; + /** + * Windows-specific POBJECT_ATTRIBUTES required when + * ::CU_MEM_HANDLE_TYPE_WIN32 is specified. This object attributes structure + * includes security attributes that define + * the scope of which exported allocations may be transferred to other + * processes. In all other cases, this field is required to be zero. + */ + void *win32HandleMetaData; + struct { + /** + * Allocation hint for requesting compressible memory. + * On devices that support Compute Data Compression, compressible + * memory can be used to accelerate accesses to data with unstructured + * sparsity and other compressible data patterns. Applications are + * expected to query allocation property of the handle obtained with + * ::cuMemCreate using ::cuMemGetAllocationPropertiesFromHandle to + * validate if the obtained allocation is compressible or not. Note that + * compressed memory may not be mappable on all devices. + */ + unsigned char compressionType; + unsigned char gpuDirectRDMACapable; + /** Bitmask indicating intended usage for this allocation */ + unsigned short usage; + unsigned char reserved[4]; + } allocFlags; +} CUmemAllocationProp_v1; +typedef CUmemAllocationProp_v1 CUmemAllocationProp; + +/** +* Flags for querying different granularities for a multicast object +*/ +typedef enum CUmulticastGranularity_flags_enum { + CU_MULTICAST_GRANULARITY_MINIMUM = 0x0, /**< Minimum required granularity */ + CU_MULTICAST_GRANULARITY_RECOMMENDED = 0x1 /**< Recommended granularity for best performance */ +} CUmulticastGranularity_flags; + +/** +* Specifies the properties for a multicast object. +*/ +typedef struct CUmulticastObjectProp_st { + /** + * The number of devices in the multicast team that will bind memory to this + * object + */ + unsigned int numDevices; + /** + * The maximum amount of memory that can be bound to this multicast object + * per device + */ + size_t size; + /** + * Bitmask of exportable handle types (see ::CUmemAllocationHandleType) for + * this object + */ + unsigned long long handleTypes; + /** + * Flags for future use, must be zero now + */ + unsigned long long flags; +} CUmulticastObjectProp_v1; +typedef CUmulticastObjectProp_v1 CUmulticastObjectProp; + +/** + * Memory access descriptor + */ +typedef struct CUmemAccessDesc_st { + CUmemLocation location; /**< Location on which the request is to change it's accessibility */ + CUmemAccess_flags flags; /**< ::CUmemProt accessibility flags to set on the request */ +} CUmemAccessDesc_v1; +typedef CUmemAccessDesc_v1 CUmemAccessDesc; + +/** + * CUDA Graph Update error types + */ +typedef enum CUgraphExecUpdateResult_enum { + CU_GRAPH_EXEC_UPDATE_SUCCESS = 0x0, /**< The update succeeded */ + CU_GRAPH_EXEC_UPDATE_ERROR = 0x1, /**< The update failed for an unexpected reason which is described in the return value of the function */ + CU_GRAPH_EXEC_UPDATE_ERROR_TOPOLOGY_CHANGED = 0x2, /**< The update failed because the topology changed */ + CU_GRAPH_EXEC_UPDATE_ERROR_NODE_TYPE_CHANGED = 0x3, /**< The update failed because a node type changed */ + CU_GRAPH_EXEC_UPDATE_ERROR_FUNCTION_CHANGED = 0x4, /**< The update failed because the function of a kernel node changed (CUDA driver < 11.2) */ + CU_GRAPH_EXEC_UPDATE_ERROR_PARAMETERS_CHANGED = 0x5, /**< The update failed because the parameters changed in a way that is not supported */ + CU_GRAPH_EXEC_UPDATE_ERROR_NOT_SUPPORTED = 0x6, /**< The update failed because something about the node is not supported */ + CU_GRAPH_EXEC_UPDATE_ERROR_UNSUPPORTED_FUNCTION_CHANGE = 0x7, /**< The update failed because the function of a kernel node changed in an unsupported way */ + CU_GRAPH_EXEC_UPDATE_ERROR_ATTRIBUTES_CHANGED = 0x8 /**< The update failed because the node attributes changed in a way that is not supported */ +} CUgraphExecUpdateResult; + +/** + * Result information returned by cuGraphExecUpdate + */ +typedef struct CUgraphExecUpdateResultInfo_st { + /** + * Gives more specific detail when a cuda graph update fails. + */ + CUgraphExecUpdateResult result; + + /** + * The "to node" of the error edge when the topologies do not match. + * The error node when the error is associated with a specific node. + * NULL when the error is generic. + */ + CUgraphNode errorNode; + + /** + * The from node of error edge when the topologies do not match. Otherwise NULL. + */ + CUgraphNode errorFromNode; +} CUgraphExecUpdateResultInfo_v1; +typedef CUgraphExecUpdateResultInfo_v1 CUgraphExecUpdateResultInfo; + +/** + * CUDA memory pool attributes + */ +typedef enum CUmemPool_attribute_enum { + /** + * (value type = int) + * Allow cuMemAllocAsync to use memory asynchronously freed + * in another streams as long as a stream ordering dependency + * of the allocating stream on the free action exists. + * Cuda events and null stream interactions can create the required + * stream ordered dependencies. (default enabled) + */ + CU_MEMPOOL_ATTR_REUSE_FOLLOW_EVENT_DEPENDENCIES = 1, + + /** + * (value type = int) + * Allow reuse of already completed frees when there is no dependency + * between the free and allocation. (default enabled) + */ + CU_MEMPOOL_ATTR_REUSE_ALLOW_OPPORTUNISTIC, + + /** + * (value type = int) + * Allow cuMemAllocAsync to insert new stream dependencies + * in order to establish the stream ordering required to reuse + * a piece of memory released by cuFreeAsync (default enabled). + */ + CU_MEMPOOL_ATTR_REUSE_ALLOW_INTERNAL_DEPENDENCIES, + + /** + * (value type = cuuint64_t) + * Amount of reserved memory in bytes to hold onto before trying + * to release memory back to the OS. When more than the release + * threshold bytes of memory are held by the memory pool, the + * allocator will try to release memory back to the OS on the + * next call to stream, event or context synchronize. (default 0) + */ + CU_MEMPOOL_ATTR_RELEASE_THRESHOLD, + + /** + * (value type = cuuint64_t) + * Amount of backing memory currently allocated for the mempool. + */ + CU_MEMPOOL_ATTR_RESERVED_MEM_CURRENT, + + /** + * (value type = cuuint64_t) + * High watermark of backing memory allocated for the mempool since the + * last time it was reset. High watermark can only be reset to zero. + */ + CU_MEMPOOL_ATTR_RESERVED_MEM_HIGH, + + /** + * (value type = cuuint64_t) + * Amount of memory from the pool that is currently in use by the application. + */ + CU_MEMPOOL_ATTR_USED_MEM_CURRENT, + + /** + * (value type = cuuint64_t) + * High watermark of the amount of memory from the pool that was in use by the application since + * the last time it was reset. High watermark can only be reset to zero. + */ + CU_MEMPOOL_ATTR_USED_MEM_HIGH +} CUmemPool_attribute; + +/** + * Specifies the properties of allocations made from the pool. + */ +typedef struct CUmemPoolProps_st { + CUmemAllocationType allocType; /**< Allocation type. Currently must be specified as CU_MEM_ALLOCATION_TYPE_PINNED */ + CUmemAllocationHandleType handleTypes; /**< Handle types that will be supported by allocations from the pool. */ + CUmemLocation location; /**< Location where allocations should reside. */ + /** + * Windows-specific LPSECURITYATTRIBUTES required when + * ::CU_MEM_HANDLE_TYPE_WIN32 is specified. This security attribute defines + * the scope of which exported allocations may be transferred to other + * processes. In all other cases, this field is required to be zero. + */ + void *win32SecurityAttributes; + size_t maxSize; /**< Maximum pool size. When set to 0, defaults to a system dependent value. */ + unsigned char reserved[56]; /**< reserved for future use, must be 0 */ +} CUmemPoolProps_v1; +typedef CUmemPoolProps_v1 CUmemPoolProps; + +/** + * Opaque data for exporting a pool allocation + */ +typedef struct CUmemPoolPtrExportData_st { + unsigned char reserved[64]; +} CUmemPoolPtrExportData_v1; +typedef CUmemPoolPtrExportData_v1 CUmemPoolPtrExportData; + +/** + * Memory allocation node parameters + */ +typedef struct CUDA_MEM_ALLOC_NODE_PARAMS_v1_st { + /** + * in: location where the allocation should reside (specified in ::location). + * ::handleTypes must be ::CU_MEM_HANDLE_TYPE_NONE. IPC is not supported. + */ + CUmemPoolProps poolProps; + const CUmemAccessDesc *accessDescs; /**< in: array of memory access descriptors. Used to describe peer GPU access */ + size_t accessDescCount; /**< in: number of memory access descriptors. Must not exceed the number of GPUs. */ + size_t bytesize; /**< in: size in bytes of the requested allocation */ + CUdeviceptr dptr; /**< out: address of the allocation returned by CUDA */ +} CUDA_MEM_ALLOC_NODE_PARAMS_v1; +typedef CUDA_MEM_ALLOC_NODE_PARAMS_v1 CUDA_MEM_ALLOC_NODE_PARAMS; + +/** + * Memory allocation node parameters + */ +typedef struct CUDA_MEM_ALLOC_NODE_PARAMS_v2_st { + /** + * in: location where the allocation should reside (specified in ::location). + * ::handleTypes must be ::CU_MEM_HANDLE_TYPE_NONE. IPC is not supported. + */ + CUmemPoolProps poolProps; + const CUmemAccessDesc *accessDescs; /**< in: array of memory access descriptors. Used to describe peer GPU access */ + size_t accessDescCount; /**< in: number of memory access descriptors. Must not exceed the number of GPUs. */ + size_t bytesize; /**< in: size in bytes of the requested allocation */ + CUdeviceptr dptr; /**< out: address of the allocation returned by CUDA */ +} CUDA_MEM_ALLOC_NODE_PARAMS_v2; + +/** + * Memory free node parameters + */ +typedef struct CUDA_MEM_FREE_NODE_PARAMS_st { + CUdeviceptr dptr; /**< in: the pointer to free */ +} CUDA_MEM_FREE_NODE_PARAMS; + +typedef enum CUgraphMem_attribute_enum { + /** + * (value type = cuuint64_t) + * Amount of memory, in bytes, currently associated with graphs + */ + CU_GRAPH_MEM_ATTR_USED_MEM_CURRENT, + + /** + * (value type = cuuint64_t) + * High watermark of memory, in bytes, associated with graphs since the + * last time it was reset. High watermark can only be reset to zero. + */ + CU_GRAPH_MEM_ATTR_USED_MEM_HIGH, + + /** + * (value type = cuuint64_t) + * Amount of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + */ + CU_GRAPH_MEM_ATTR_RESERVED_MEM_CURRENT, + + /** + * (value type = cuuint64_t) + * High watermark of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + */ + CU_GRAPH_MEM_ATTR_RESERVED_MEM_HIGH +} CUgraphMem_attribute; + +/** + * Child graph node parameters + */ +typedef struct CUDA_CHILD_GRAPH_NODE_PARAMS_st { + CUgraph graph; /**< The child graph to clone into the node for node creation, or + a handle to the graph owned by the node for node query */ +} CUDA_CHILD_GRAPH_NODE_PARAMS; + +/** + * Event record node parameters + */ +typedef struct CUDA_EVENT_RECORD_NODE_PARAMS_st { + CUevent event; /**< The event to record when the node executes */ +} CUDA_EVENT_RECORD_NODE_PARAMS; + +/** + * Event wait node parameters + */ +typedef struct CUDA_EVENT_WAIT_NODE_PARAMS_st { + CUevent event; /**< The event to wait on from the node */ +} CUDA_EVENT_WAIT_NODE_PARAMS; + +/** + * Graph node parameters. See ::cuGraphAddNode. + */ +typedef struct CUgraphNodeParams_st { + CUgraphNodeType type; /**< Type of the node */ + int reserved0[3]; /**< Reserved. Must be zero. */ + + union { + long long reserved1[29]; /**< Padding. Unused bytes must be zero. */ + CUDA_KERNEL_NODE_PARAMS_v3 kernel; /**< Kernel node parameters. */ + CUDA_MEMCPY_NODE_PARAMS memcpy; /**< Memcpy node parameters. */ + CUDA_MEMSET_NODE_PARAMS_v2 memset; /**< Memset node parameters. */ + CUDA_HOST_NODE_PARAMS_v2 host; /**< Host node parameters. */ + CUDA_CHILD_GRAPH_NODE_PARAMS graph; /**< Child graph node parameters. */ + CUDA_EVENT_WAIT_NODE_PARAMS eventWait; /**< Event wait node parameters. */ + CUDA_EVENT_RECORD_NODE_PARAMS eventRecord; /**< Event record node parameters. */ + CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v2 extSemSignal; /**< External semaphore signal node parameters. */ + CUDA_EXT_SEM_WAIT_NODE_PARAMS_v2 extSemWait; /**< External semaphore wait node parameters. */ + CUDA_MEM_ALLOC_NODE_PARAMS_v2 alloc; /**< Memory allocation node parameters. */ + CUDA_MEM_FREE_NODE_PARAMS free; /**< Memory free node parameters. */ + CUDA_BATCH_MEM_OP_NODE_PARAMS_v2 memOp; /**< MemOp node parameters. */ + CUDA_CONDITIONAL_NODE_PARAMS conditional; /**< Conditional node parameters. */ + }; + + long long reserved2; /**< Reserved bytes. Must be zero. */ +} CUgraphNodeParams; + +/** + * If set, each kernel launched as part of ::cuLaunchCooperativeKernelMultiDevice only + * waits for prior work in the stream corresponding to that GPU to complete before the + * kernel begins execution. + */ +#define CUDA_COOPERATIVE_LAUNCH_MULTI_DEVICE_NO_PRE_LAUNCH_SYNC 0x01 + +/** + * If set, any subsequent work pushed in a stream that participated in a call to + * ::cuLaunchCooperativeKernelMultiDevice will only wait for the kernel launched on + * the GPU corresponding to that stream to complete before it begins execution. + */ +#define CUDA_COOPERATIVE_LAUNCH_MULTI_DEVICE_NO_POST_LAUNCH_SYNC 0x02 + +/** + * If set, the CUDA array is a collection of layers, where each layer is either a 1D + * or a 2D array and the Depth member of CUDA_ARRAY3D_DESCRIPTOR specifies the number + * of layers, not the depth of a 3D array. + */ +#define CUDA_ARRAY3D_LAYERED 0x01 + +/** + * Deprecated, use CUDA_ARRAY3D_LAYERED + */ +#define CUDA_ARRAY3D_2DARRAY 0x01 + +/** + * This flag must be set in order to bind a surface reference + * to the CUDA array + */ +#define CUDA_ARRAY3D_SURFACE_LDST 0x02 + +/** + * If set, the CUDA array is a collection of six 2D arrays, representing faces of a cube. The + * width of such a CUDA array must be equal to its height, and Depth must be six. + * If ::CUDA_ARRAY3D_LAYERED flag is also set, then the CUDA array is a collection of cubemaps + * and Depth must be a multiple of six. + */ +#define CUDA_ARRAY3D_CUBEMAP 0x04 + +/** + * This flag must be set in order to perform texture gather operations + * on a CUDA array. + */ +#define CUDA_ARRAY3D_TEXTURE_GATHER 0x08 + +/** + * This flag if set indicates that the CUDA + * array is a DEPTH_TEXTURE. + */ +#define CUDA_ARRAY3D_DEPTH_TEXTURE 0x10 + +/** + * This flag indicates that the CUDA array may be bound as a color target + * in an external graphics API + */ +#define CUDA_ARRAY3D_COLOR_ATTACHMENT 0x20 + +/** + * This flag if set indicates that the CUDA array or CUDA mipmapped array + * is a sparse CUDA array or CUDA mipmapped array respectively + */ +#define CUDA_ARRAY3D_SPARSE 0x40 + +/** + * This flag if set indicates that the CUDA array or CUDA mipmapped array + * will allow deferred memory mapping + */ +#define CUDA_ARRAY3D_DEFERRED_MAPPING 0x80 + +/** + * Override the texref format with a format inferred from the array. + * Flag for ::cuTexRefSetArray() + */ +#define CU_TRSA_OVERRIDE_FORMAT 0x01 + +/** + * Read the texture as integers rather than promoting the values to floats + * in the range [0,1]. + * Flag for ::cuTexRefSetFlags() and ::cuTexObjectCreate() + */ +#define CU_TRSF_READ_AS_INTEGER 0x01 + +/** + * Use normalized texture coordinates in the range [0,1) instead of [0,dim). + * Flag for ::cuTexRefSetFlags() and ::cuTexObjectCreate() + */ +#define CU_TRSF_NORMALIZED_COORDINATES 0x02 + +/** + * Perform sRGB->linear conversion during texture read. + * Flag for ::cuTexRefSetFlags() and ::cuTexObjectCreate() + */ +#define CU_TRSF_SRGB 0x10 + + /** + * Disable any trilinear filtering optimizations. + * Flag for ::cuTexRefSetFlags() and ::cuTexObjectCreate() + */ +#define CU_TRSF_DISABLE_TRILINEAR_OPTIMIZATION 0x20 + +/** + * Enable seamless cube map filtering. + * Flag for ::cuTexObjectCreate() + */ +#define CU_TRSF_SEAMLESS_CUBEMAP 0x40 + +/** + * C++ compile time constant for CU_LAUNCH_PARAM_END + */ +#define CU_LAUNCH_PARAM_END_AS_INT 0x00 + +/** + * End of array terminator for the \p extra parameter to + * ::cuLaunchKernel + */ +#define CU_LAUNCH_PARAM_END ((void*)CU_LAUNCH_PARAM_END_AS_INT) + +/** + * C++ compile time constant for CU_LAUNCH_PARAM_BUFFER_POINTER + */ +#define CU_LAUNCH_PARAM_BUFFER_POINTER_AS_INT 0x01 + +/** + * Indicator that the next value in the \p extra parameter to + * ::cuLaunchKernel will be a pointer to a buffer containing all kernel + * parameters used for launching kernel \p f. This buffer needs to + * honor all alignment/padding requirements of the individual parameters. + * If ::CU_LAUNCH_PARAM_BUFFER_SIZE is not also specified in the + * \p extra array, then ::CU_LAUNCH_PARAM_BUFFER_POINTER will have no + * effect. + */ +#define CU_LAUNCH_PARAM_BUFFER_POINTER ((void*)CU_LAUNCH_PARAM_BUFFER_POINTER_AS_INT) + +/** + * C++ compile time constant for CU_LAUNCH_PARAM_BUFFER_SIZE + */ +#define CU_LAUNCH_PARAM_BUFFER_SIZE_AS_INT 0x02 + +/** + * Indicator that the next value in the \p extra parameter to + * ::cuLaunchKernel will be a pointer to a size_t which contains the + * size of the buffer specified with ::CU_LAUNCH_PARAM_BUFFER_POINTER. + * It is required that ::CU_LAUNCH_PARAM_BUFFER_POINTER also be specified + * in the \p extra array if the value associated with + * ::CU_LAUNCH_PARAM_BUFFER_SIZE is not zero. + */ +#define CU_LAUNCH_PARAM_BUFFER_SIZE ((void*)CU_LAUNCH_PARAM_BUFFER_SIZE_AS_INT) + +/** + * For texture references loaded into the module, use default texunit from + * texture reference. + */ +#define CU_PARAM_TR_DEFAULT -1 + +/** + * Device that represents the CPU + */ +#define CU_DEVICE_CPU ((CUdevice)-1) + +/** + * Device that represents an invalid device + */ +#define CU_DEVICE_INVALID ((CUdevice)-2) + +/** + * Bitmasks for ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_FLUSH_WRITES_OPTIONS + */ +typedef enum CUflushGPUDirectRDMAWritesOptions_enum { + CU_FLUSH_GPU_DIRECT_RDMA_WRITES_OPTION_HOST = 1<<0, /**< ::cuFlushGPUDirectRDMAWrites() and its CUDA Runtime API counterpart are supported on the device. */ + CU_FLUSH_GPU_DIRECT_RDMA_WRITES_OPTION_MEMOPS = 1<<1 /**< The ::CU_STREAM_WAIT_VALUE_FLUSH flag and the ::CU_STREAM_MEM_OP_FLUSH_REMOTE_WRITES MemOp are supported on the device. */ +} CUflushGPUDirectRDMAWritesOptions; + +/** + * Platform native ordering for GPUDirect RDMA writes + */ +typedef enum CUGPUDirectRDMAWritesOrdering_enum { + CU_GPU_DIRECT_RDMA_WRITES_ORDERING_NONE = 0, /**< The device does not natively support ordering of remote writes. ::cuFlushGPUDirectRDMAWrites() can be leveraged if supported. */ + CU_GPU_DIRECT_RDMA_WRITES_ORDERING_OWNER = 100, /**< Natively, the device can consistently consume remote writes, although other CUDA devices may not. */ + CU_GPU_DIRECT_RDMA_WRITES_ORDERING_ALL_DEVICES = 200 /**< Any CUDA device in the system can consistently consume remote writes to this device. */ +} CUGPUDirectRDMAWritesOrdering; + +/** + * The scopes for ::cuFlushGPUDirectRDMAWrites + */ +typedef enum CUflushGPUDirectRDMAWritesScope_enum { + CU_FLUSH_GPU_DIRECT_RDMA_WRITES_TO_OWNER = 100, /**< Blocks until remote writes are visible to the CUDA device context owning the data. */ + CU_FLUSH_GPU_DIRECT_RDMA_WRITES_TO_ALL_DEVICES = 200 /**< Blocks until remote writes are visible to all CUDA device contexts. */ +} CUflushGPUDirectRDMAWritesScope; + +/** + * The targets for ::cuFlushGPUDirectRDMAWrites + */ +typedef enum CUflushGPUDirectRDMAWritesTarget_enum { + CU_FLUSH_GPU_DIRECT_RDMA_WRITES_TARGET_CURRENT_CTX = 0 /**< Sets the target for ::cuFlushGPUDirectRDMAWrites() to the currently active CUDA device context. */ +} CUflushGPUDirectRDMAWritesTarget; + +/** + * The additional write options for ::cuGraphDebugDotPrint + */ +typedef enum CUgraphDebugDot_flags_enum { + CU_GRAPH_DEBUG_DOT_FLAGS_VERBOSE = 1<<0, /**< Output all debug data as if every debug flag is enabled */ + CU_GRAPH_DEBUG_DOT_FLAGS_RUNTIME_TYPES = 1<<1, /**< Use CUDA Runtime structures for output */ + CU_GRAPH_DEBUG_DOT_FLAGS_KERNEL_NODE_PARAMS = 1<<2, /**< Adds CUDA_KERNEL_NODE_PARAMS values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_MEMCPY_NODE_PARAMS = 1<<3, /**< Adds CUDA_MEMCPY3D values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_MEMSET_NODE_PARAMS = 1<<4, /**< Adds CUDA_MEMSET_NODE_PARAMS values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_HOST_NODE_PARAMS = 1<<5, /**< Adds CUDA_HOST_NODE_PARAMS values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_EVENT_NODE_PARAMS = 1<<6, /**< Adds CUevent handle from record and wait nodes to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_EXT_SEMAS_SIGNAL_NODE_PARAMS = 1<<7, /**< Adds CUDA_EXT_SEM_SIGNAL_NODE_PARAMS values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_EXT_SEMAS_WAIT_NODE_PARAMS = 1<<8, /**< Adds CUDA_EXT_SEM_WAIT_NODE_PARAMS values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_KERNEL_NODE_ATTRIBUTES = 1<<9, /**< Adds CUkernelNodeAttrValue values to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_HANDLES = 1<<10, /**< Adds node handles and every kernel function handle to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_MEM_ALLOC_NODE_PARAMS = 1<<11, /**< Adds memory alloc node parameters to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_MEM_FREE_NODE_PARAMS = 1<<12, /**< Adds memory free node parameters to output */ + CU_GRAPH_DEBUG_DOT_FLAGS_BATCH_MEM_OP_NODE_PARAMS = 1<<13 /**< Adds batch mem op node parameters to output */ + , CU_GRAPH_DEBUG_DOT_FLAGS_EXTRA_TOPO_INFO = 1<<14 /**< Adds edge numbering information */ + , CU_GRAPH_DEBUG_DOT_FLAGS_CONDITIONAL_NODE_PARAMS = 1<<15 /**< Adds conditional node parameters to output */ +} CUgraphDebugDot_flags; + +/** + * Flags for user objects for graphs + */ +typedef enum CUuserObject_flags_enum { + CU_USER_OBJECT_NO_DESTRUCTOR_SYNC = 1 /**< Indicates the destructor execution is not synchronized by any CUDA handle. */ +} CUuserObject_flags; + +/** + * Flags for retaining user object references for graphs + */ +typedef enum CUuserObjectRetain_flags_enum { + CU_GRAPH_USER_OBJECT_MOVE = 1 /**< Transfer references from the caller rather than creating new references. */ +} CUuserObjectRetain_flags; + +/** + * Flags for instantiating a graph + */ +typedef enum CUgraphInstantiate_flags_enum { + CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH = 1 /**< Automatically free memory allocated in a graph before relaunching. */ + , CUDA_GRAPH_INSTANTIATE_FLAG_UPLOAD = 2 /**< Automatically upload the graph after instantiation. Only supported by + ::cuGraphInstantiateWithParams. The upload will be performed using the + stream provided in \p instantiateParams. */ + , CUDA_GRAPH_INSTANTIATE_FLAG_DEVICE_LAUNCH = 4 /**< Instantiate the graph to be launchable from the device. This flag can only + be used on platforms which support unified addressing. This flag cannot be + used in conjunction with CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH. */ + , CUDA_GRAPH_INSTANTIATE_FLAG_USE_NODE_PRIORITY = 8 /**< Run the graph using the per-node priority attributes rather than the + priority of the stream it is launched into. */ +} CUgraphInstantiate_flags; + +typedef enum CUdeviceNumaConfig_enum { + CU_DEVICE_NUMA_CONFIG_NONE = 0, /**< The GPU is not a NUMA node */ + CU_DEVICE_NUMA_CONFIG_NUMA_NODE, /**< The GPU is a NUMA node, CU_DEVICE_ATTRIBUTE_NUMA_ID contains its NUMA ID */ +} CUdeviceNumaConfig; + +/** @} */ /* END CUDA_TYPES */ + +#if defined(__GNUC__) + #if defined(__CUDA_API_PUSH_VISIBILITY_DEFAULT) + #pragma GCC visibility push(default) + #endif +#endif + +#ifdef _WIN32 +#define CUDAAPI __stdcall +#else +#define CUDAAPI +#endif + +/** + * \defgroup CUDA_ERROR Error Handling + * + * ___MANBRIEF___ error handling functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the error handling functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Gets the string description of an error code + * + * Sets \p *pStr to the address of a NULL-terminated string description + * of the error code \p error. + * If the error code is not recognized, ::CUDA_ERROR_INVALID_VALUE + * will be returned and \p *pStr will be set to the NULL address. + * + * \param error - Error code to convert to string + * \param pStr - Address of the string pointer. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::CUresult, + * ::cudaGetErrorString + */ +CUresult CUDAAPI cuGetErrorString(CUresult error, const char **pStr); + +/** + * \brief Gets the string representation of an error code enum name + * + * Sets \p *pStr to the address of a NULL-terminated string representation + * of the name of the enum error code \p error. + * If the error code is not recognized, ::CUDA_ERROR_INVALID_VALUE + * will be returned and \p *pStr will be set to the NULL address. + * + * \param error - Error code to convert to string + * \param pStr - Address of the string pointer. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::CUresult, + * ::cudaGetErrorName + */ +CUresult CUDAAPI cuGetErrorName(CUresult error, const char **pStr); + +/** @} */ /* END CUDA_ERROR */ + +/** + * \defgroup CUDA_INITIALIZE Initialization + * + * ___MANBRIEF___ initialization functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the initialization functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Initialize the CUDA driver API + * Initializes the driver API and must be called before any other function from + * the driver API in the current process. Currently, the \p Flags parameter must be 0. If ::cuInit() + * has not been called, any function from the driver API will return + * ::CUDA_ERROR_NOT_INITIALIZED. + * + * \param Flags - Initialization flag for CUDA. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_SYSTEM_DRIVER_MISMATCH, + * ::CUDA_ERROR_COMPAT_NOT_SUPPORTED_ON_DEVICE + * \notefnerr + */ +CUresult CUDAAPI cuInit(unsigned int Flags); + +/** @} */ /* END CUDA_INITIALIZE */ + +/** + * \defgroup CUDA_VERSION Version Management + * + * ___MANBRIEF___ version management functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the version management functions of the low-level + * CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns the latest CUDA version supported by driver + * + * Returns in \p *driverVersion the version of CUDA supported by + * the driver. The version is returned as + * (1000 × major + 10 × minor). For example, CUDA 9.2 + * would be represented by 9020. + * + * This function automatically returns ::CUDA_ERROR_INVALID_VALUE if + * \p driverVersion is NULL. + * + * \param driverVersion - Returns the CUDA driver version + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cudaDriverGetVersion, + * ::cudaRuntimeGetVersion + */ +CUresult CUDAAPI cuDriverGetVersion(int *driverVersion); + +/** @} */ /* END CUDA_VERSION */ + +/** + * \defgroup CUDA_DEVICE Device Management + * + * ___MANBRIEF___ device management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the device management functions of the low-level + * CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns a handle to a compute device + * + * Returns in \p *device a device handle given an ordinal in the range [0, + * ::cuDeviceGetCount()-1]. + * + * \param device - Returned device handle + * \param ordinal - Device number to get handle for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGetLuid, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport + */ +CUresult CUDAAPI cuDeviceGet(CUdevice *device, int ordinal); + +/** + * \brief Returns the number of compute-capable devices + * + * Returns in \p *count the number of devices with compute capability greater + * than or equal to 2.0 that are available for execution. If there is no such + * device, ::cuDeviceGetCount() returns 0. + * + * \param count - Returned number of compute-capable devices + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGetLuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaGetDeviceCount + */ +CUresult CUDAAPI cuDeviceGetCount(int *count); + +/** + * \brief Returns an identifier string for the device + * + * Returns an ASCII string identifying the device \p dev in the NULL-terminated + * string pointed to by \p name. \p len specifies the maximum length of the + * string that may be returned. + * + * \param name - Returned identifier string for the device + * \param len - Maximum length of string to store in \p name + * \param dev - Device to get identifier string for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetUuid, + * ::cuDeviceGetLuid, + * ::cuDeviceGetCount, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaGetDeviceProperties + */ +CUresult CUDAAPI cuDeviceGetName(char *name, int len, CUdevice dev); + +/** + * \brief Return an UUID for the device + * + * Note there is a later version of this API, ::cuDeviceGetUuid_v2. It will + * supplant this version in 12.0, which is retained for minor version compatibility. + * + * Returns 16-octets identifying the device \p dev in the structure + * pointed by the \p uuid. + * + * \param uuid - Returned UUID + * \param dev - Device to get identifier string for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetUuid_v2 + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetLuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaGetDeviceProperties + */ +CUresult CUDAAPI cuDeviceGetUuid(CUuuid *uuid, CUdevice dev); + +/** + * \brief Return an UUID for the device (11.4+) + * + * Returns 16-octets identifying the device \p dev in the structure + * pointed by the \p uuid. If the device is in MIG mode, returns its + * MIG UUID which uniquely identifies the subscribed MIG compute instance. + * + * \param uuid - Returned UUID + * \param dev - Device to get identifier string for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetLuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cudaGetDeviceProperties + */ +CUresult CUDAAPI cuDeviceGetUuid_v2(CUuuid *uuid, CUdevice dev); + +/** + * \brief Return an LUID and device node mask for the device + * + * Return identifying information (\p luid and \p deviceNodeMask) to allow + * matching device with graphics APIs. + * + * \param luid - Returned LUID + * \param deviceNodeMask - Returned device node mask + * \param dev - Device to get identifier string for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaGetDeviceProperties + */ +CUresult CUDAAPI cuDeviceGetLuid(char *luid, unsigned int *deviceNodeMask, CUdevice dev); + +/** + * \brief Returns the total amount of memory on the device + * + * Returns in \p *bytes the total amount of memory available on the device + * \p dev in bytes. + * + * \param bytes - Returned memory available on device in bytes + * \param dev - Device handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaMemGetInfo + */ +CUresult CUDAAPI cuDeviceTotalMem(size_t *bytes, CUdevice dev); + +/** + * \brief Returns the maximum number of elements allocatable in a 1D linear texture for a given texture element size. + * + * Returns in \p maxWidthInElements the maximum number of texture elements allocatable in a 1D linear texture + * for given \p format and \p numChannels. + * + * \param maxWidthInElements - Returned maximum number of texture elements allocatable for given \p format and \p numChannels. + * \param format - Texture format. + * \param numChannels - Number of channels per texture element. + * \param dev - Device handle. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cudaMemGetInfo, + * ::cuDeviceTotalMem + */ +CUresult CUDAAPI cuDeviceGetTexture1DLinearMaxWidth(size_t *maxWidthInElements, CUarray_format format, unsigned numChannels, CUdevice dev); + +/** + * \brief Returns information about the device + * + * Returns in \p *pi the integer value of the attribute \p attrib on device + * \p dev. The supported attributes are: + * - ::CU_DEVICE_ATTRIBUTE_MAX_THREADS_PER_BLOCK: Maximum number of threads per + * block; + * - ::CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_X: Maximum x-dimension of a block + * - ::CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_Y: Maximum y-dimension of a block + * - ::CU_DEVICE_ATTRIBUTE_MAX_BLOCK_DIM_Z: Maximum z-dimension of a block + * - ::CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_X: Maximum x-dimension of a grid + * - ::CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_Y: Maximum y-dimension of a grid + * - ::CU_DEVICE_ATTRIBUTE_MAX_GRID_DIM_Z: Maximum z-dimension of a grid + * - ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK: Maximum amount of + * shared memory available to a thread block in bytes + * - ::CU_DEVICE_ATTRIBUTE_TOTAL_CONSTANT_MEMORY: Memory available on device for + * __constant__ variables in a CUDA C kernel in bytes + * - ::CU_DEVICE_ATTRIBUTE_WARP_SIZE: Warp size in threads + * - ::CU_DEVICE_ATTRIBUTE_MAX_PITCH: Maximum pitch in bytes allowed by the + * memory copy functions that involve memory regions allocated through + * ::cuMemAllocPitch() + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_WIDTH: Maximum 1D + * texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LINEAR_WIDTH: Maximum width + * for a 1D texture bound to linear memory + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_MIPMAPPED_WIDTH: Maximum + * mipmapped 1D texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_WIDTH: Maximum 2D + * texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_HEIGHT: Maximum 2D + * texture height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_WIDTH: Maximum width + * for a 2D texture bound to linear memory + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_HEIGHT: Maximum height + * for a 2D texture bound to linear memory + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_PITCH: Maximum pitch + * in bytes for a 2D texture bound to linear memory + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_MIPMAPPED_WIDTH: Maximum + * mipmapped 2D texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_MIPMAPPED_HEIGHT: Maximum + * mipmapped 2D texture height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_WIDTH: Maximum 3D + * texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_HEIGHT: Maximum 3D + * texture height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_DEPTH: Maximum 3D + * texture depth + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_WIDTH_ALTERNATE: + * Alternate maximum 3D texture width, 0 if no alternate + * maximum 3D texture size is supported + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_HEIGHT_ALTERNATE: + * Alternate maximum 3D texture height, 0 if no alternate + * maximum 3D texture size is supported + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE3D_DEPTH_ALTERNATE: + * Alternate maximum 3D texture depth, 0 if no alternate + * maximum 3D texture size is supported + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_WIDTH: + * Maximum cubemap texture width or height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LAYERED_WIDTH: + * Maximum 1D layered texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LAYERED_LAYERS: + * Maximum layers in a 1D layered texture + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_WIDTH: + * Maximum 2D layered texture width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_HEIGHT: + * Maximum 2D layered texture height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LAYERED_LAYERS: + * Maximum layers in a 2D layered texture + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_LAYERED_WIDTH: + * Maximum cubemap layered texture width or height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURECUBEMAP_LAYERED_LAYERS: + * Maximum layers in a cubemap layered texture + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_WIDTH: + * Maximum 1D surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_WIDTH: + * Maximum 2D surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_HEIGHT: + * Maximum 2D surface height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_WIDTH: + * Maximum 3D surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_HEIGHT: + * Maximum 3D surface height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE3D_DEPTH: + * Maximum 3D surface depth + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_LAYERED_WIDTH: + * Maximum 1D layered surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE1D_LAYERED_LAYERS: + * Maximum layers in a 1D layered surface + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_WIDTH: + * Maximum 2D layered surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_HEIGHT: + * Maximum 2D layered surface height + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACE2D_LAYERED_LAYERS: + * Maximum layers in a 2D layered surface + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_WIDTH: + * Maximum cubemap surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_LAYERED_WIDTH: + * Maximum cubemap layered surface width + * - ::CU_DEVICE_ATTRIBUTE_MAXIMUM_SURFACECUBEMAP_LAYERED_LAYERS: + * Maximum layers in a cubemap layered surface + * - ::CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_BLOCK: Maximum number of 32-bit + * registers available to a thread block + * - ::CU_DEVICE_ATTRIBUTE_CLOCK_RATE: The typical clock frequency in kilohertz + * - ::CU_DEVICE_ATTRIBUTE_TEXTURE_ALIGNMENT: Alignment requirement; texture + * base addresses aligned to ::textureAlign bytes do not need an offset + * applied to texture fetches + * - ::CU_DEVICE_ATTRIBUTE_TEXTURE_PITCH_ALIGNMENT: Pitch alignment requirement + * for 2D texture references bound to pitched memory + * - ::CU_DEVICE_ATTRIBUTE_GPU_OVERLAP: 1 if the device can concurrently copy + * memory between host and device while executing a kernel, or 0 if not + * - ::CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT: Number of multiprocessors on + * the device + * - ::CU_DEVICE_ATTRIBUTE_KERNEL_EXEC_TIMEOUT: 1 if there is a run time limit + * for kernels executed on the device, or 0 if not + * - ::CU_DEVICE_ATTRIBUTE_INTEGRATED: 1 if the device is integrated with the + * memory subsystem, or 0 if not + * - ::CU_DEVICE_ATTRIBUTE_CAN_MAP_HOST_MEMORY: 1 if the device can map host + * memory into the CUDA address space, or 0 if not + * - ::CU_DEVICE_ATTRIBUTE_COMPUTE_MODE: Compute mode that device is currently + * in. Available modes are as follows: + * - ::CU_COMPUTEMODE_DEFAULT: Default mode - Device is not restricted and + * can have multiple CUDA contexts present at a single time. + * - ::CU_COMPUTEMODE_PROHIBITED: Compute-prohibited mode - Device is + * prohibited from creating new CUDA contexts. + * - ::CU_COMPUTEMODE_EXCLUSIVE_PROCESS: Compute-exclusive-process mode - Device + * can have only one context used by a single process at a time. + * - ::CU_DEVICE_ATTRIBUTE_CONCURRENT_KERNELS: 1 if the device supports + * executing multiple kernels within the same context simultaneously, or 0 if + * not. It is not guaranteed that multiple kernels will be resident + * on the device concurrently so this feature should not be relied upon for + * correctness. + * - ::CU_DEVICE_ATTRIBUTE_ECC_ENABLED: 1 if error correction is enabled on the + * device, 0 if error correction is disabled or not supported by the device + * - ::CU_DEVICE_ATTRIBUTE_PCI_BUS_ID: PCI bus identifier of the device + * - ::CU_DEVICE_ATTRIBUTE_PCI_DEVICE_ID: PCI device (also known as slot) identifier + * of the device + * - ::CU_DEVICE_ATTRIBUTE_PCI_DOMAIN_ID: PCI domain identifier of the device + * - ::CU_DEVICE_ATTRIBUTE_TCC_DRIVER: 1 if the device is using a TCC driver. TCC + * is only available on Tesla hardware running Windows Vista or later + * - ::CU_DEVICE_ATTRIBUTE_MEMORY_CLOCK_RATE: Peak memory clock frequency in kilohertz + * - ::CU_DEVICE_ATTRIBUTE_GLOBAL_MEMORY_BUS_WIDTH: Global memory bus width in bits + * - ::CU_DEVICE_ATTRIBUTE_L2_CACHE_SIZE: Size of L2 cache in bytes. 0 if the device doesn't have L2 cache + * - ::CU_DEVICE_ATTRIBUTE_MAX_THREADS_PER_MULTIPROCESSOR: Maximum resident threads per multiprocessor + * - ::CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING: 1 if the device shares a unified address space with + * the host, or 0 if not + * - ::CU_DEVICE_ATTRIBUTE_COMPUTE_CAPABILITY_MAJOR: Major compute capability version number + * - ::CU_DEVICE_ATTRIBUTE_COMPUTE_CAPABILITY_MINOR: Minor compute capability version number + * - ::CU_DEVICE_ATTRIBUTE_GLOBAL_L1_CACHE_SUPPORTED: 1 if device supports caching globals + * in L1 cache, 0 if caching globals in L1 cache is not supported by the device + * - ::CU_DEVICE_ATTRIBUTE_LOCAL_L1_CACHE_SUPPORTED: 1 if device supports caching locals + * in L1 cache, 0 if caching locals in L1 cache is not supported by the device + * - ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR: Maximum amount of + * shared memory available to a multiprocessor in bytes; this amount is shared + * by all thread blocks simultaneously resident on a multiprocessor + * - ::CU_DEVICE_ATTRIBUTE_MAX_REGISTERS_PER_MULTIPROCESSOR: Maximum number of 32-bit + * registers available to a multiprocessor; this number is shared by all thread + * blocks simultaneously resident on a multiprocessor + * - ::CU_DEVICE_ATTRIBUTE_MANAGED_MEMORY: 1 if device supports allocating managed memory + * on this system, 0 if allocating managed memory is not supported by the device on this system. + * - ::CU_DEVICE_ATTRIBUTE_MULTI_GPU_BOARD: 1 if device is on a multi-GPU board, 0 if not. + * - ::CU_DEVICE_ATTRIBUTE_MULTI_GPU_BOARD_GROUP_ID: Unique identifier for a group of devices + * associated with the same board. Devices on the same multi-GPU board will share the same identifier. + * - ::CU_DEVICE_ATTRIBUTE_HOST_NATIVE_ATOMIC_SUPPORTED: 1 if Link between the device and the host + * supports native atomic operations. + * - ::CU_DEVICE_ATTRIBUTE_SINGLE_TO_DOUBLE_PRECISION_PERF_RATIO: Ratio of single precision performance + * (in floating-point operations per second) to double precision performance. + * - ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS: Device supports coherently accessing + * pageable memory without calling cudaHostRegister on it. + * - ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS: Device can coherently access managed memory + * concurrently with the CPU. + * - ::CU_DEVICE_ATTRIBUTE_COMPUTE_PREEMPTION_SUPPORTED: Device supports Compute Preemption. + * - ::CU_DEVICE_ATTRIBUTE_CAN_USE_HOST_POINTER_FOR_REGISTERED_MEM: Device can access host registered + * memory at the same virtual address as the CPU. + * - ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN: The maximum per block shared memory size + * supported on this device. This is the maximum value that can be opted into when using the cuFuncSetAttribute() or cuKernelSetAttribute() call. + * For more details see ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES + * - ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES: Device accesses pageable memory via the host's + * page tables. + * - ::CU_DEVICE_ATTRIBUTE_DIRECT_MANAGED_MEM_ACCESS_FROM_HOST: The host can directly access managed memory on the device without migration. + * - ::CU_DEVICE_ATTRIBUTE_VIRTUAL_MEMORY_MANAGEMENT_SUPPORTED: Device supports virtual memory management APIs like ::cuMemAddressReserve, ::cuMemCreate, ::cuMemMap and related APIs + * - ::CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_POSIX_FILE_DESCRIPTOR_SUPPORTED: Device supports exporting memory to a posix file descriptor with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate + * - ::CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_WIN32_HANDLE_SUPPORTED: Device supports exporting memory to a Win32 NT handle with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate + * - ::CU_DEVICE_ATTRIBUTE_HANDLE_TYPE_WIN32_KMT_HANDLE_SUPPORTED: Device supports exporting memory to a Win32 KMT handle with ::cuMemExportToShareableHandle, if requested via ::cuMemCreate + * - ::CU_DEVICE_ATTRIBUTE_MAX_BLOCKS_PER_MULTIPROCESSOR: Maximum number of thread blocks that can reside on a multiprocessor + * - ::CU_DEVICE_ATTRIBUTE_GENERIC_COMPRESSION_SUPPORTED: Device supports compressible memory allocation via ::cuMemCreate + * - ::CU_DEVICE_ATTRIBUTE_MAX_PERSISTING_L2_CACHE_SIZE: Maximum L2 persisting lines capacity setting in bytes + * - ::CU_DEVICE_ATTRIBUTE_MAX_ACCESS_POLICY_WINDOW_SIZE: Maximum value of CUaccessPolicyWindow::num_bytes + * - ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_WITH_CUDA_VMM_SUPPORTED: Device supports specifying the GPUDirect RDMA flag with ::cuMemCreate. + * - ::CU_DEVICE_ATTRIBUTE_RESERVED_SHARED_MEMORY_PER_BLOCK: Amount of shared memory per block reserved by CUDA driver in bytes + * - ::CU_DEVICE_ATTRIBUTE_SPARSE_CUDA_ARRAY_SUPPORTED: Device supports sparse CUDA arrays and sparse CUDA mipmapped arrays. + * - ::CU_DEVICE_ATTRIBUTE_READ_ONLY_HOST_REGISTER_SUPPORTED: Device supports using the ::cuMemHostRegister flag ::CU_MEMHOSTERGISTER_READ_ONLY to register memory that must be mapped as read-only to the GPU + * - ::CU_DEVICE_ATTRIBUTE_MEMORY_POOLS_SUPPORTED: Device supports using the ::cuMemAllocAsync and ::cuMemPool family of APIs + * - ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_SUPPORTED: Device supports GPUDirect RDMA APIs, like nvidia_p2p_get_pages (see https://docs.nvidia.com/cuda/gpudirect-rdma for more information) + * - ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_FLUSH_WRITES_OPTIONS: The returned attribute shall be interpreted as a bitmask, where the individual bits are described by the ::CUflushGPUDirectRDMAWritesOptions enum + * - ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_WRITES_ORDERING: GPUDirect RDMA writes to the device do not need to be flushed for consumers within the scope indicated by the returned attribute. See ::CUGPUDirectRDMAWritesOrdering for the numerical values returned here. + * - ::CU_DEVICE_ATTRIBUTE_MEMPOOL_SUPPORTED_HANDLE_TYPES: Bitmask of handle types supported with mempool based IPC + * - ::CU_DEVICE_ATTRIBUTE_DEFERRED_MAPPING_CUDA_ARRAY_SUPPORTED: Device supports deferred mapping CUDA arrays and CUDA mipmapped arrays. + * + * \param pi - Returned device attribute value + * \param attrib - Device attribute to query + * \param dev - Device handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem, + * ::cuDeviceGetExecAffinitySupport, + * ::cudaDeviceGetAttribute, + * ::cudaGetDeviceProperties + */ +CUresult CUDAAPI cuDeviceGetAttribute(int *pi, CUdevice_attribute attrib, CUdevice dev); + +/** + * \brief Return NvSciSync attributes that this device can support. + * + * Returns in \p nvSciSyncAttrList, the properties of NvSciSync that + * this CUDA device, \p dev can support. The returned \p nvSciSyncAttrList + * can be used to create an NvSciSync object that matches this device's capabilities. + * + * If NvSciSyncAttrKey_RequiredPerm field in \p nvSciSyncAttrList is + * already set this API will return ::CUDA_ERROR_INVALID_VALUE. + * + * The applications should set \p nvSciSyncAttrList to a valid + * NvSciSyncAttrList failing which this API will return + * ::CUDA_ERROR_INVALID_HANDLE. + * + * The \p flags controls how applications intends to use + * the NvSciSync created from the \p nvSciSyncAttrList. The valid flags are: + * - ::CUDA_NVSCISYNC_ATTR_SIGNAL, specifies that the applications intends to + * signal an NvSciSync on this CUDA device. + * - ::CUDA_NVSCISYNC_ATTR_WAIT, specifies that the applications intends to + * wait on an NvSciSync on this CUDA device. + * + * At least one of these flags must be set, failing which the API + * returns ::CUDA_ERROR_INVALID_VALUE. Both the flags are orthogonal + * to one another: a developer may set both these flags that allows to + * set both wait and signal specific attributes in the same \p nvSciSyncAttrList. + * + * Note that this API updates the input \p nvSciSyncAttrList with values equivalent + * to the following public attribute key-values: + * NvSciSyncAttrKey_RequiredPerm is set to + * - NvSciSyncAccessPerm_SignalOnly if ::CUDA_NVSCISYNC_ATTR_SIGNAL is set in \p flags. + * - NvSciSyncAccessPerm_WaitOnly if ::CUDA_NVSCISYNC_ATTR_WAIT is set in \p flags. + * - NvSciSyncAccessPerm_WaitSignal if both ::CUDA_NVSCISYNC_ATTR_WAIT and + * ::CUDA_NVSCISYNC_ATTR_SIGNAL are set in \p flags. + * NvSciSyncAttrKey_PrimitiveInfo is set to + * - NvSciSyncAttrValPrimitiveType_SysmemSemaphore on any valid \p device. + * - NvSciSyncAttrValPrimitiveType_Syncpoint if \p device is a Tegra device. + * - NvSciSyncAttrValPrimitiveType_SysmemSemaphorePayload64b if \p device is GA10X+. + * NvSciSyncAttrKey_GpuId is set to the same UUID that is returned for this + * \p device from ::cuDeviceGetUuid. + * + * \param nvSciSyncAttrList - Return NvSciSync attributes supported. + * \param dev - Valid Cuda Device to get NvSciSync attributes for. + * \param flags - flags describing NvSciSync usage. + * + * \return + * + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa + * ::cuImportExternalSemaphore, + * ::cuDestroyExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuDeviceGetNvSciSyncAttributes(void *nvSciSyncAttrList, CUdevice dev, int flags); + +/** + * \brief Sets the current memory pool of a device + * + * The memory pool must be local to the specified device. + * ::cuMemAllocAsync allocates from the current mempool of the provided stream's device. + * By default, a device's current memory pool is its default memory pool. + * + * \note Use ::cuMemAllocFromPoolAsync to specify asynchronous allocations from a device different + * than the one the stream runs on. + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuDeviceGetDefaultMemPool, ::cuDeviceGetMemPool, ::cuMemPoolCreate, ::cuMemPoolDestroy, ::cuMemAllocFromPoolAsync + */ +CUresult CUDAAPI cuDeviceSetMemPool(CUdevice dev, CUmemoryPool pool); + +/** + * \brief Gets the current mempool for a device + * + * Returns the last pool provided to ::cuDeviceSetMemPool for this device + * or the device's default memory pool if ::cuDeviceSetMemPool has never been called. + * By default the current mempool is the default mempool for a device. + * Otherwise the returned pool must have been set with ::cuDeviceSetMemPool. + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuDeviceGetDefaultMemPool, ::cuMemPoolCreate, ::cuDeviceSetMemPool + */ +CUresult CUDAAPI cuDeviceGetMemPool(CUmemoryPool *pool, CUdevice dev); + +/** + * \brief Returns the default mempool of a device + * + * The default mempool of a device contains device memory from that device. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuMemAllocAsync, ::cuMemPoolTrimTo, ::cuMemPoolGetAttribute, ::cuMemPoolSetAttribute, cuMemPoolSetAccess, ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuDeviceGetDefaultMemPool(CUmemoryPool *pool_out, CUdevice dev); + +/** + * \brief Returns information about the execution affinity support of the device. + * + * Returns in \p *pi whether execution affinity type \p type is supported by device \p dev. + * The supported types are: + * - ::CU_EXEC_AFFINITY_TYPE_SM_COUNT: 1 if context with limited SMs is supported by the device, + * or 0 if not; + * + * \param pi - 1 if the execution affinity type \p type is supported by the device, or 0 if not + * \param type - Execution affinity type to query + * \param dev - Device handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem + */ +CUresult CUDAAPI cuDeviceGetExecAffinitySupport(int *pi, CUexecAffinityType type, CUdevice dev); + +/** + * \brief Blocks until remote writes are visible to the specified scope + * + * Blocks until GPUDirect RDMA writes to the target context via mappings + * created through APIs like nvidia_p2p_get_pages (see + * https://docs.nvidia.com/cuda/gpudirect-rdma for more information), are + * visible to the specified scope. + * + * If the scope equals or lies within the scope indicated by + * ::CU_DEVICE_ATTRIBUTE_GPU_DIRECT_RDMA_WRITES_ORDERING, the call + * will be a no-op and can be safely omitted for performance. This can be + * determined by comparing the numerical values between the two enums, with + * smaller scopes having smaller values. + * + * Users may query support for this API via + * ::CU_DEVICE_ATTRIBUTE_FLUSH_FLUSH_GPU_DIRECT_RDMA_OPTIONS. + * + * \param target - The target of the operation, see ::CUflushGPUDirectRDMAWritesTarget + * \param scope - The scope of the operation, see ::CUflushGPUDirectRDMAWritesScope + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + */ +CUresult CUDAAPI cuFlushGPUDirectRDMAWrites(CUflushGPUDirectRDMAWritesTarget target, CUflushGPUDirectRDMAWritesScope scope); + +/** @} */ /* END CUDA_DEVICE */ + +/** + * \defgroup CUDA_DEVICE_DEPRECATED Device Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated device management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the device management functions of the low-level + * CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns properties for a selected device + * + * \deprecated + * + * This function was deprecated as of CUDA 5.0 and replaced by ::cuDeviceGetAttribute(). + * + * Returns in \p *prop the properties of device \p dev. The ::CUdevprop + * structure is defined as: + * + * \code + typedef struct CUdevprop_st { + int maxThreadsPerBlock; + int maxThreadsDim[3]; + int maxGridSize[3]; + int sharedMemPerBlock; + int totalConstantMemory; + int SIMDWidth; + int memPitch; + int regsPerBlock; + int clockRate; + int textureAlign + } CUdevprop; + * \endcode + * where: + * + * - ::maxThreadsPerBlock is the maximum number of threads per block; + * - ::maxThreadsDim[3] is the maximum sizes of each dimension of a block; + * - ::maxGridSize[3] is the maximum sizes of each dimension of a grid; + * - ::sharedMemPerBlock is the total amount of shared memory available per + * block in bytes; + * - ::totalConstantMemory is the total amount of constant memory available on + * the device in bytes; + * - ::SIMDWidth is the warp size; + * - ::memPitch is the maximum pitch allowed by the memory copy functions that + * involve memory regions allocated through ::cuMemAllocPitch(); + * - ::regsPerBlock is the total number of registers available per block; + * - ::clockRate is the clock frequency in kilohertz; + * - ::textureAlign is the alignment requirement; texture base addresses that + * are aligned to ::textureAlign bytes do not need an offset applied to + * texture fetches. + * + * \param prop - Returned properties of device + * \param dev - Device to get properties for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuDeviceGetProperties(CUdevprop *prop, CUdevice dev); + +/** + * \brief Returns the compute capability of the device + * + * \deprecated + * + * This function was deprecated as of CUDA 5.0 and its functionality superseded + * by ::cuDeviceGetAttribute(). + * + * Returns in \p *major and \p *minor the major and minor revision numbers that + * define the compute capability of the device \p dev. + * + * \param major - Major revision number + * \param minor - Minor revision number + * \param dev - Device handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGetAttribute, + * ::cuDeviceGetCount, + * ::cuDeviceGetName, + * ::cuDeviceGetUuid, + * ::cuDeviceGet, + * ::cuDeviceTotalMem + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuDeviceComputeCapability(int *major, int *minor, CUdevice dev); + +/** @} */ /* END CUDA_DEVICE_DEPRECATED */ + +/** + * \defgroup CUDA_PRIMARY_CTX Primary Context Management + * + * ___MANBRIEF___ primary context management functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the primary context management functions of the low-level + * CUDA driver application programming interface. + * + * The primary context is unique per device and shared with the CUDA runtime API. + * These functions allow integration with other libraries using CUDA. + * + * @{ + */ + +/** + * \brief Retain the primary context on the GPU + * + * Retains the primary context on the device. + * Once the user successfully retains the primary context, the primary context + * will be active and available to the user until the user releases it + * with ::cuDevicePrimaryCtxRelease() or resets it with ::cuDevicePrimaryCtxReset(). + * Unlike ::cuCtxCreate() the newly retained context is not pushed onto the stack. + * + * Retaining the primary context for the first time will fail with ::CUDA_ERROR_UNKNOWN + * if the compute mode of the device is ::CU_COMPUTEMODE_PROHIBITED. The function + * ::cuDeviceGetAttribute() can be used with ::CU_DEVICE_ATTRIBUTE_COMPUTE_MODE to + * determine the compute mode of the device. + * The nvidia-smi tool can be used to set the compute mode for + * devices. Documentation for nvidia-smi can be obtained by passing a + * -h option to it. + * + * Please note that the primary context always supports pinned allocations. Other + * flags can be specified by ::cuDevicePrimaryCtxSetFlags(). + * + * \param pctx - Returned context handle of the new context + * \param dev - Device for which primary context is requested + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuDevicePrimaryCtxRelease, + * ::cuDevicePrimaryCtxSetFlags, + * ::cuCtxCreate, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuDevicePrimaryCtxRetain(CUcontext *pctx, CUdevice dev); + +/** + * \brief Release the primary context on the GPU + * + * Releases the primary context interop on the device. + * A retained context should always be released once the user is done using + * it. The context is automatically reset once the last reference to it is + * released. This behavior is different when the primary context was retained + * by the CUDA runtime from CUDA 4.0 and earlier. In this case, the primary + * context remains always active. + * + * Releasing a primary context that has not been previously retained will + * fail with ::CUDA_ERROR_INVALID_CONTEXT. + * + * Please note that unlike ::cuCtxDestroy() this method does not pop the context + * from stack in any circumstances. + * + * \param dev - Device which primary context is released + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuDevicePrimaryCtxRetain, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuDevicePrimaryCtxRelease(CUdevice dev); + +/** + * \brief Set flags for the primary context + * + * Sets the flags for the primary context on the device overwriting perviously + * set ones. + * + * The three LSBs of the \p flags parameter can be used to control how the OS + * thread, which owns the CUDA context at the time of an API call, interacts + * with the OS scheduler when waiting for results from the GPU. Only one of + * the scheduling flags can be set when creating a context. + * + * - ::CU_CTX_SCHED_SPIN: Instruct CUDA to actively spin when waiting for + * results from the GPU. This can decrease latency when waiting for the GPU, + * but may lower the performance of CPU threads if they are performing work in + * parallel with the CUDA thread. + * + * - ::CU_CTX_SCHED_YIELD: Instruct CUDA to yield its thread when waiting for + * results from the GPU. This can increase latency when waiting for the GPU, + * but can increase the performance of CPU threads performing work in parallel + * with the GPU. + * + * - ::CU_CTX_SCHED_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work. + * + * - ::CU_CTX_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work.
+ * Deprecated: This flag was deprecated as of CUDA 4.0 and was + * replaced with ::CU_CTX_SCHED_BLOCKING_SYNC. + * + * - ::CU_CTX_SCHED_AUTO: The default value if the \p flags parameter is zero, + * uses a heuristic based on the number of active CUDA contexts in the + * process \e C and the number of logical processors in the system \e P. If + * \e C > \e P, then CUDA will yield to other OS threads when waiting for + * the GPU (::CU_CTX_SCHED_YIELD), otherwise CUDA will not yield while + * waiting for results and actively spin on the processor (::CU_CTX_SCHED_SPIN). + * Additionally, on Tegra devices, ::CU_CTX_SCHED_AUTO uses a heuristic based on + * the power profile of the platform and may choose ::CU_CTX_SCHED_BLOCKING_SYNC + * for low-powered devices. + * + * - ::CU_CTX_LMEM_RESIZE_TO_MAX: Instruct CUDA to not reduce local memory + * after resizing local memory for a kernel. This can prevent thrashing by + * local memory allocations when launching many kernels with high local + * memory usage at the cost of potentially increased memory usage.
+ * Deprecated: This flag is deprecated and the behavior enabled + * by this flag is now the default and cannot be disabled. + * + * - ::CU_CTX_COREDUMP_ENABLE: If GPU coredumps have not been enabled globally + * with ::cuCoredumpSetAttributeGlobal or environment variables, this flag can + * be set during context creation to instruct CUDA to create a coredump if + * this context raises an exception during execution. These environment variables + * are described in the CUDA-GDB user guide under the "GPU core dump support" + * section. + * The initial settings will be taken from the global settings at the time of + * context creation. The other settings that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * + * - ::CU_CTX_USER_COREDUMP_ENABLE: If user-triggered GPU coredumps have not + * been enabled globally with ::cuCoredumpSetAttributeGlobal or environment + * variables, this flag can be set during context creation to instruct CUDA to + * create a coredump if data is written to a certain pipe that is present in the + * OS space. These environment variables are described in the CUDA-GDB user + * guide under the "GPU core dump support" section. + * It is important to note that the pipe name *must* be set with + * ::cuCoredumpSetAttributeGlobal before creating the context if this flag is + * used. Setting this flag implies that ::CU_CTX_COREDUMP_ENABLE is set. + * The initial settings will be taken from the global settings at the time of + * context creation. The other settings that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * + * - ::CU_CTX_SYNC_MEMOPS: Ensures that synchronous memory operations initiated + * on this context will always synchronize. See further documentation in the + * section titled "API Synchronization behavior" to learn more about cases when + * synchronous memory operations can exhibit asynchronous behavior. + * + * \param dev - Device for which the primary context flags are set + * \param flags - New flags for the device + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa ::cuDevicePrimaryCtxRetain, + * ::cuDevicePrimaryCtxGetState, + * ::cuCtxCreate, + * ::cuCtxGetFlags, + * ::cuCtxSetFlags, + * ::cudaSetDeviceFlags + */ +CUresult CUDAAPI cuDevicePrimaryCtxSetFlags(CUdevice dev, unsigned int flags); + +/** + * \brief Get the state of the primary context + * + * Returns in \p *flags the flags for the primary context of \p dev, and in + * \p *active whether it is active. See ::cuDevicePrimaryCtxSetFlags for flag + * values. + * + * \param dev - Device to get primary context flags for + * \param flags - Pointer to store flags + * \param active - Pointer to store context state; 0 = inactive, 1 = active + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa + * ::cuDevicePrimaryCtxSetFlags, + * ::cuCtxGetFlags, + * ::cuCtxSetFlags, + * ::cudaGetDeviceFlags + */ +CUresult CUDAAPI cuDevicePrimaryCtxGetState(CUdevice dev, unsigned int *flags, int *active); + +/** + * \brief Destroy all allocations and reset all state on the primary context + * + * Explicitly destroys and cleans up all resources associated with the current + * device in the current process. + * + * Note that it is responsibility of the calling function to ensure that no + * other module in the process is using the device any more. For that reason + * it is recommended to use ::cuDevicePrimaryCtxRelease() in most cases. + * However it is safe for other modules to call ::cuDevicePrimaryCtxRelease() + * even after resetting the device. + * Resetting the primary context does not release it, an application that has + * retained the primary context should explicitly release its usage. + * + * \param dev - Device for which primary context is destroyed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_PRIMARY_CONTEXT_ACTIVE + * \notefnerr + * + * \sa ::cuDevicePrimaryCtxRetain, + * ::cuDevicePrimaryCtxRelease, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cudaDeviceReset + */ +CUresult CUDAAPI cuDevicePrimaryCtxReset(CUdevice dev); + +/** @} */ /* END CUDA_PRIMARY_CTX */ + +/** + * \defgroup CUDA_CTX Context Management + * + * ___MANBRIEF___ context management functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the context management functions of the low-level + * CUDA driver application programming interface. + * + * Please note that some functions are described in + * \ref CUDA_PRIMARY_CTX "Primary Context Management" section. + * + * @{ + */ + +/** + * \brief Create a CUDA context + * + * \note In most cases it is recommended to use ::cuDevicePrimaryCtxRetain. + * + * Creates a new CUDA context and associates it with the calling thread. The + * \p flags parameter is described below. The context is created with a usage + * count of 1 and the caller of ::cuCtxCreate() must call ::cuCtxDestroy() + * when done using the context. If a context is already current to the thread, + * it is supplanted by the newly created context and may be restored by a subsequent + * call to ::cuCtxPopCurrent(). + * + * The three LSBs of the \p flags parameter can be used to control how the OS + * thread, which owns the CUDA context at the time of an API call, interacts + * with the OS scheduler when waiting for results from the GPU. Only one of + * the scheduling flags can be set when creating a context. + * + * - ::CU_CTX_SCHED_SPIN: Instruct CUDA to actively spin when waiting for + * results from the GPU. This can decrease latency when waiting for the GPU, + * but may lower the performance of CPU threads if they are performing work in + * parallel with the CUDA thread. + * + * - ::CU_CTX_SCHED_YIELD: Instruct CUDA to yield its thread when waiting for + * results from the GPU. This can increase latency when waiting for the GPU, + * but can increase the performance of CPU threads performing work in parallel + * with the GPU. + * + * - ::CU_CTX_SCHED_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work. + * + * - ::CU_CTX_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work.
+ * Deprecated: This flag was deprecated as of CUDA 4.0 and was + * replaced with ::CU_CTX_SCHED_BLOCKING_SYNC. + * + * - ::CU_CTX_SCHED_AUTO: The default value if the \p flags parameter is zero, + * uses a heuristic based on the number of active CUDA contexts in the + * process \e C and the number of logical processors in the system \e P. If + * \e C > \e P, then CUDA will yield to other OS threads when waiting for + * the GPU (::CU_CTX_SCHED_YIELD), otherwise CUDA will not yield while + * waiting for results and actively spin on the processor (::CU_CTX_SCHED_SPIN). + * Additionally, on Tegra devices, ::CU_CTX_SCHED_AUTO uses a heuristic based on + * the power profile of the platform and may choose ::CU_CTX_SCHED_BLOCKING_SYNC + * for low-powered devices. + * + * - ::CU_CTX_MAP_HOST: Instruct CUDA to support mapped pinned allocations. + * This flag must be set in order to allocate pinned host memory that is + * accessible to the GPU. + * + * - ::CU_CTX_LMEM_RESIZE_TO_MAX: Instruct CUDA to not reduce local memory + * after resizing local memory for a kernel. This can prevent thrashing by + * local memory allocations when launching many kernels with high local + * memory usage at the cost of potentially increased memory usage.
+ * Deprecated: This flag is deprecated and the behavior enabled + * by this flag is now the default and cannot be disabled. + * Instead, the per-thread stack size can be controlled with ::cuCtxSetLimit(). + * + * - ::CU_CTX_COREDUMP_ENABLE: If GPU coredumps have not been enabled globally + * with ::cuCoredumpSetAttributeGlobal or environment variables, this flag can + * be set during context creation to instruct CUDA to create a coredump if + * this context raises an exception during execution. These environment variables + * are described in the CUDA-GDB user guide under the "GPU core dump support" + * section. + * The initial attributes will be taken from the global attributes at the time of + * context creation. The other attributes that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * + * - ::CU_CTX_USER_COREDUMP_ENABLE: If user-triggered GPU coredumps have not + * been enabled globally with ::cuCoredumpSetAttributeGlobal or environment + * variables, this flag can be set during context creation to instruct CUDA to + * create a coredump if data is written to a certain pipe that is present in the + * OS space. These environment variables are described in the CUDA-GDB user + * guide under the "GPU core dump support" section. + * It is important to note that the pipe name *must* be set with + * ::cuCoredumpSetAttributeGlobal before creating the context if this flag is + * used. Setting this flag implies that ::CU_CTX_COREDUMP_ENABLE is set. + * The initial attributes will be taken from the global attributes at the time of + * context creation. The other attributes that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * Setting this flag on any context creation is equivalent to setting the + * ::CU_COREDUMP_ENABLE_USER_TRIGGER attribute to \p true globally. + * + * - ::CU_CTX_SYNC_MEMOPS: Ensures that synchronous memory operations initiated + * on this context will always synchronize. See further documentation in the + * section titled "API Synchronization behavior" to learn more about cases when + * synchronous memory operations can exhibit asynchronous behavior. + * + * Context creation will fail with ::CUDA_ERROR_UNKNOWN if the compute mode of + * the device is ::CU_COMPUTEMODE_PROHIBITED. The function ::cuDeviceGetAttribute() + * can be used with ::CU_DEVICE_ATTRIBUTE_COMPUTE_MODE to determine the + * compute mode of the device. The nvidia-smi tool can be used to set + * the compute mode for * devices. + * Documentation for nvidia-smi can be obtained by passing a + * -h option to it. + * + * \param pctx - Returned context handle of the new context + * \param flags - Context creation flags + * \param dev - Device to create context on + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCoredumpSetAttributeGlobal, + * ::cuCoredumpSetAttribute, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuCtxCreate(CUcontext *pctx, unsigned int flags, CUdevice dev); + +/** + * \brief Create a CUDA context with execution affinity + * + * Creates a new CUDA context with execution affinity and associates it with + * the calling thread. The \p paramsArray and \p flags parameter are described below. + * The context is created with a usage count of 1 and the caller of ::cuCtxCreate() must + * call ::cuCtxDestroy() when done using the context. If a context is already + * current to the thread, it is supplanted by the newly created context and may + * be restored by a subsequent call to ::cuCtxPopCurrent(). + * + * The type and the amount of execution resource the context can use is limited by \p paramsArray + * and \p numParams. The \p paramsArray is an array of \p CUexecAffinityParam and the \p numParams + * describes the size of the array. If two \p CUexecAffinityParam in the array have the same type, + * the latter execution affinity parameter overrides the former execution affinity parameter. + * The supported execution affinity types are: + * - ::CU_EXEC_AFFINITY_TYPE_SM_COUNT limits the portion of SMs that the context can use. The portion + * of SMs is specified as the number of SMs via \p CUexecAffinitySmCount. This limit will be internally + * rounded up to the next hardware-supported amount. Hence, it is imperative to query the actual execution + * affinity of the context via \p cuCtxGetExecAffinity after context creation. Currently, this attribute + * is only supported under Volta+ MPS. + * + * The three LSBs of the \p flags parameter can be used to control how the OS + * thread, which owns the CUDA context at the time of an API call, interacts + * with the OS scheduler when waiting for results from the GPU. Only one of + * the scheduling flags can be set when creating a context. + * + * - ::CU_CTX_SCHED_SPIN: Instruct CUDA to actively spin when waiting for + * results from the GPU. This can decrease latency when waiting for the GPU, + * but may lower the performance of CPU threads if they are performing work in + * parallel with the CUDA thread. + * + * - ::CU_CTX_SCHED_YIELD: Instruct CUDA to yield its thread when waiting for + * results from the GPU. This can increase latency when waiting for the GPU, + * but can increase the performance of CPU threads performing work in parallel + * with the GPU. + * + * - ::CU_CTX_SCHED_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work. + * + * - ::CU_CTX_BLOCKING_SYNC: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the GPU to finish work.
+ * Deprecated: This flag was deprecated as of CUDA 4.0 and was + * replaced with ::CU_CTX_SCHED_BLOCKING_SYNC. + * + * - ::CU_CTX_SCHED_AUTO: The default value if the \p flags parameter is zero, + * uses a heuristic based on the number of active CUDA contexts in the + * process \e C and the number of logical processors in the system \e P. If + * \e C > \e P, then CUDA will yield to other OS threads when waiting for + * the GPU (::CU_CTX_SCHED_YIELD), otherwise CUDA will not yield while + * waiting for results and actively spin on the processor (::CU_CTX_SCHED_SPIN). + * Additionally, on Tegra devices, ::CU_CTX_SCHED_AUTO uses a heuristic based on + * the power profile of the platform and may choose ::CU_CTX_SCHED_BLOCKING_SYNC + * for low-powered devices. + * + * - ::CU_CTX_MAP_HOST: Instruct CUDA to support mapped pinned allocations. + * This flag must be set in order to allocate pinned host memory that is + * accessible to the GPU. + * + * - ::CU_CTX_LMEM_RESIZE_TO_MAX: Instruct CUDA to not reduce local memory + * after resizing local memory for a kernel. This can prevent thrashing by + * local memory allocations when launching many kernels with high local + * memory usage at the cost of potentially increased memory usage.
+ * Deprecated: This flag is deprecated and the behavior enabled + * by this flag is now the default and cannot be disabled. + * Instead, the per-thread stack size can be controlled with ::cuCtxSetLimit(). + * + * - ::CU_CTX_COREDUMP_ENABLE: If GPU coredumps have not been enabled globally + * with ::cuCoredumpSetAttributeGlobal or environment variables, this flag can + * be set during context creation to instruct CUDA to create a coredump if + * this context raises an exception during execution. These environment variables + * are described in the CUDA-GDB user guide under the "GPU core dump support" + * section. + * The initial attributes will be taken from the global attributes at the time of + * context creation. The other attributes that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * + * - ::CU_CTX_USER_COREDUMP_ENABLE: If user-triggered GPU coredumps have not + * been enabled globally with ::cuCoredumpSetAttributeGlobal or environment + * variables, this flag can be set during context creation to instruct CUDA to + * create a coredump if data is written to a certain pipe that is present in the + * OS space. These environment variables are described in the CUDA-GDB user + * guide under the "GPU core dump support" section. + * It is important to note that the pipe name *must* be set with + * ::cuCoredumpSetAttributeGlobal before creating the context if this flag is + * used. Setting this flag implies that ::CU_CTX_COREDUMP_ENABLE is set. + * The initial attributes will be taken from the global attributes at the time of + * context creation. The other attributes that control coredump output can be + * modified by calling ::cuCoredumpSetAttribute from the created context after + * it becomes current. + * Setting this flag on any context creation is equivalent to setting the + * ::CU_COREDUMP_ENABLE_USER_TRIGGER attribute to \p true globally. + * + * Context creation will fail with ::CUDA_ERROR_UNKNOWN if the compute mode of + * the device is ::CU_COMPUTEMODE_PROHIBITED. The function ::cuDeviceGetAttribute() + * can be used with ::CU_DEVICE_ATTRIBUTE_COMPUTE_MODE to determine the + * compute mode of the device. The nvidia-smi tool can be used to set + * the compute mode for * devices. + * Documentation for nvidia-smi can be obtained by passing a + * -h option to it. + * + * \param pctx - Returned context handle of the new context + * \param paramsArray - Execution affinity parameters + * \param numParams - Number of execution affinity parameters + * \param flags - Context creation flags + * \param dev - Device to create context on + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNSUPPORTED_EXEC_AFFINITY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cuCoredumpSetAttributeGlobal, + * ::cuCoredumpSetAttribute, + * ::CUexecAffinityParam + */ +CUresult CUDAAPI cuCtxCreate_v3(CUcontext *pctx, CUexecAffinityParam *paramsArray, int numParams, unsigned int flags, CUdevice dev); + +/** + * \brief Destroy a CUDA context + * + * Destroys the CUDA context specified by \p ctx. The context \p ctx will be + * destroyed regardless of how many threads it is current to. + * It is the responsibility of the calling function to ensure that no API + * call issues using \p ctx while ::cuCtxDestroy() is executing. + * + * Destroys and cleans up all resources associated with the context. + * It is the caller's responsibility to ensure that the context or its resources + * are not accessed or passed in subsequent API calls and doing so will result in undefined behavior. + * These resources include CUDA types such as ::CUmodule, ::CUfunction, ::CUstream, ::CUevent, + * ::CUarray, ::CUmipmappedArray, ::CUtexObject, ::CUsurfObject, ::CUtexref, ::CUsurfref, + * ::CUgraphicsResource, ::CUlinkState, ::CUexternalMemory and ::CUexternalSemaphore. + * + * If \p ctx is current to the calling thread then \p ctx will also be + * popped from the current thread's context stack (as though ::cuCtxPopCurrent() + * were called). If \p ctx is current to other threads, then \p ctx will + * remain current to those threads, and attempting to access \p ctx from + * those threads will result in the error ::CUDA_ERROR_CONTEXT_IS_DESTROYED. + * + * \param ctx - Context to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuCtxDestroy(CUcontext ctx); + +/** + * \brief Pushes a context on the current CPU thread + * + * Pushes the given context \p ctx onto the CPU thread's stack of current + * contexts. The specified context becomes the CPU thread's current context, so + * all CUDA functions that operate on the current context are affected. + * + * The previous current context may be made current again by calling + * ::cuCtxDestroy() or ::cuCtxPopCurrent(). + * + * \param ctx - Context to push + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuCtxPushCurrent(CUcontext ctx); + +/** + * \brief Pops the current CUDA context from the current CPU thread. + * + * Pops the current CUDA context from the CPU thread and passes back the + * old context handle in \p *pctx. That context may then be made current + * to a different CPU thread by calling ::cuCtxPushCurrent(). + * + * If a context was current to the CPU thread before ::cuCtxCreate() or + * ::cuCtxPushCurrent() was called, this function makes that context current to + * the CPU thread again. + * + * \param pctx - Returned popped context handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuCtxPopCurrent(CUcontext *pctx); + +/** + * \brief Binds the specified CUDA context to the calling CPU thread + * + * Binds the specified CUDA context to the calling CPU thread. + * If \p ctx is NULL then the CUDA context previously bound to the + * calling CPU thread is unbound and ::CUDA_SUCCESS is returned. + * + * If there exists a CUDA context stack on the calling CPU thread, this + * will replace the top of that stack with \p ctx. + * If \p ctx is NULL then this will be equivalent to popping the top + * of the calling CPU thread's CUDA context stack (or a no-op if the + * calling CPU thread's CUDA context stack is empty). + * + * \param ctx - Context to bind to the calling CPU thread + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa + * ::cuCtxGetCurrent, + * ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cudaSetDevice + */ +CUresult CUDAAPI cuCtxSetCurrent(CUcontext ctx); + +/** + * \brief Returns the CUDA context bound to the calling CPU thread. + * + * Returns in \p *pctx the CUDA context bound to the calling CPU thread. + * If no context is bound to the calling CPU thread then \p *pctx is + * set to NULL and ::CUDA_SUCCESS is returned. + * + * \param pctx - Returned context handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * \notefnerr + * + * \sa + * ::cuCtxSetCurrent, + * ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cudaGetDevice + */ +CUresult CUDAAPI cuCtxGetCurrent(CUcontext *pctx); + +/** + * \brief Returns the device ID for the current context + * + * Returns in \p *device the ordinal of the current context's device. + * + * \param device - Returned device ID for the current context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cudaGetDevice + */ +CUresult CUDAAPI cuCtxGetDevice(CUdevice *device); + +/** + * \brief Returns the flags for the current context + * + * Returns in \p *flags the flags of the current context. See ::cuCtxCreate + * for flag values. + * + * \param flags - Pointer to store flags of current context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetCurrent, + * ::cuCtxGetDevice, + * ::cuCtxGetLimit, + * ::cuCtxGetSharedMemConfig, + * ::cuCtxGetStreamPriorityRange, + * ::cuCtxSetFlags, + * ::cudaGetDeviceFlags + */ +CUresult CUDAAPI cuCtxGetFlags(unsigned int *flags); + +/** + * \brief Sets the flags for the current context + * + * Sets the flags for the current context overwriting previously set ones. See + * ::cuDevicePrimaryCtxSetFlags for flag values. + * + * \param flags - Flags to set on the current context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetCurrent, + * ::cuCtxGetDevice, + * ::cuCtxGetLimit, + * ::cuCtxGetSharedMemConfig, + * ::cuCtxGetStreamPriorityRange, + * ::cuCtxGetFlags, + * ::cudaGetDeviceFlags, + * ::cuDevicePrimaryCtxSetFlags, + */ +CUresult CUDAAPI cuCtxSetFlags(unsigned int flags); + +/** + * \brief Returns the unique Id associated with the context supplied + * + * Returns in \p ctxId the unique Id which is associated with a given context. + * The Id is unique for the life of the program for this instance of CUDA. + * If context is supplied as NULL and there is one current, the Id of the + * current context is returned. + * + * \param ctx - Context for which to obtain the Id + * \param ctxId - Pointer to store the Id of the context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPushCurrent + */ +CUresult CUDAAPI cuCtxGetId(CUcontext ctx, unsigned long long *ctxId); + +/** + * \brief Block for a context's tasks to complete + * + * Blocks until the device has completed all preceding requested tasks. + * ::cuCtxSynchronize() returns an error if one of the preceding tasks failed. + * If the context was created with the ::CU_CTX_SCHED_BLOCKING_SYNC flag, the + * CPU thread will block until the GPU context has finished its work. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cudaDeviceSynchronize + */ +CUresult CUDAAPI cuCtxSynchronize(void); + +/** + * \brief Set resource limits + * + * Setting \p limit to \p value is a request by the application to update + * the current limit maintained by the context. The driver is free to + * modify the requested value to meet h/w requirements (this could be + * clamping to minimum or maximum values, rounding up to nearest element + * size, etc). The application can use ::cuCtxGetLimit() to find out exactly + * what the limit has been set to. + * + * Setting each ::CUlimit has its own specific restrictions, so each is + * discussed here. + * + * - ::CU_LIMIT_STACK_SIZE controls the stack size in bytes of each GPU thread. + * The driver automatically increases the per-thread stack size + * for each kernel launch as needed. This size isn't reset back to the + * original value after each launch. Setting this value will take effect + * immediately, and if necessary, the device will block until all preceding + * requested tasks are complete. + * + * - ::CU_LIMIT_PRINTF_FIFO_SIZE controls the size in bytes of the FIFO used + * by the ::printf() device system call. Setting ::CU_LIMIT_PRINTF_FIFO_SIZE + * must be performed before launching any kernel that uses the ::printf() + * device system call, otherwise ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * - ::CU_LIMIT_MALLOC_HEAP_SIZE controls the size in bytes of the heap used + * by the ::malloc() and ::free() device system calls. Setting + * ::CU_LIMIT_MALLOC_HEAP_SIZE must be performed before launching any kernel + * that uses the ::malloc() or ::free() device system calls, otherwise + * ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * - ::CU_LIMIT_DEV_RUNTIME_SYNC_DEPTH controls the maximum nesting depth of + * a grid at which a thread can safely call ::cudaDeviceSynchronize(). Setting + * this limit must be performed before any launch of a kernel that uses the + * device runtime and calls ::cudaDeviceSynchronize() above the default sync + * depth, two levels of grids. Calls to ::cudaDeviceSynchronize() will fail + * with error code ::cudaErrorSyncDepthExceeded if the limitation is + * violated. This limit can be set smaller than the default or up the maximum + * launch depth of 24. When setting this limit, keep in mind that additional + * levels of sync depth require the driver to reserve large amounts of device + * memory which can no longer be used for user allocations. If these + * reservations of device memory fail, ::cuCtxSetLimit() will return + * ::CUDA_ERROR_OUT_OF_MEMORY, and the limit can be reset to a lower value. + * This limit is only applicable to devices of compute capability < 9.0. + * Attempting to set this limit on devices of other compute capability + * versions will result in the error ::CUDA_ERROR_UNSUPPORTED_LIMIT being + * returned. + * + * - ::CU_LIMIT_DEV_RUNTIME_PENDING_LAUNCH_COUNT controls the maximum number of + * outstanding device runtime launches that can be made from the current + * context. A grid is outstanding from the point of launch up until the grid + * is known to have been completed. Device runtime launches which violate + * this limitation fail and return ::cudaErrorLaunchPendingCountExceeded when + * ::cudaGetLastError() is called after launch. If more pending launches than + * the default (2048 launches) are needed for a module using the device + * runtime, this limit can be increased. Keep in mind that being able to + * sustain additional pending launches will require the driver to reserve + * larger amounts of device memory upfront which can no longer be used for + * allocations. If these reservations fail, ::cuCtxSetLimit() will return + * ::CUDA_ERROR_OUT_OF_MEMORY, and the limit can be reset to a lower value. + * This limit is only applicable to devices of compute capability 3.5 and + * higher. Attempting to set this limit on devices of compute capability less + * than 3.5 will result in the error ::CUDA_ERROR_UNSUPPORTED_LIMIT being + * returned. + * + * - ::CU_LIMIT_MAX_L2_FETCH_GRANULARITY controls the L2 cache fetch granularity. + * Values can range from 0B to 128B. This is purely a performance hint and + * it can be ignored or clamped depending on the platform. + * + * - ::CU_LIMIT_PERSISTING_L2_CACHE_SIZE controls size in bytes available for + * persisting L2 cache. This is purely a performance hint and it can be + * ignored or clamped depending on the platform. + * + * \param limit - Limit to set + * \param value - Size of limit + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNSUPPORTED_LIMIT, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSynchronize, + * ::cudaDeviceSetLimit + */ +CUresult CUDAAPI cuCtxSetLimit(CUlimit limit, size_t value); + +/** + * \brief Returns resource limits + * + * Returns in \p *pvalue the current size of \p limit. The supported + * ::CUlimit values are: + * - ::CU_LIMIT_STACK_SIZE: stack size in bytes of each GPU thread. + * - ::CU_LIMIT_PRINTF_FIFO_SIZE: size in bytes of the FIFO used by the + * ::printf() device system call. + * - ::CU_LIMIT_MALLOC_HEAP_SIZE: size in bytes of the heap used by the + * ::malloc() and ::free() device system calls. + * - ::CU_LIMIT_DEV_RUNTIME_SYNC_DEPTH: maximum grid depth at which a thread + * can issue the device runtime call ::cudaDeviceSynchronize() to wait on + * child grid launches to complete. + * - ::CU_LIMIT_DEV_RUNTIME_PENDING_LAUNCH_COUNT: maximum number of outstanding + * device runtime launches that can be made from this context. + * - ::CU_LIMIT_MAX_L2_FETCH_GRANULARITY: L2 cache fetch granularity. + * - ::CU_LIMIT_PERSISTING_L2_CACHE_SIZE: Persisting L2 cache size in bytes + * + * \param limit - Limit to query + * \param pvalue - Returned size of limit + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNSUPPORTED_LIMIT + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cudaDeviceGetLimit + */ +CUresult CUDAAPI cuCtxGetLimit(size_t *pvalue, CUlimit limit); + +/** + * \brief Returns the preferred cache configuration for the current context. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this function returns through \p pconfig the preferred cache configuration + * for the current context. This is only a preference. The driver will use + * the requested configuration if possible, but it is free to choose a different + * configuration if required to execute functions. + * + * This will return a \p pconfig of ::CU_FUNC_CACHE_PREFER_NONE on devices + * where the size of the L1 cache and shared memory are fixed. + * + * The supported cache configurations are: + * - ::CU_FUNC_CACHE_PREFER_NONE: no preference for shared memory or L1 (default) + * - ::CU_FUNC_CACHE_PREFER_SHARED: prefer larger shared memory and smaller L1 cache + * - ::CU_FUNC_CACHE_PREFER_L1: prefer larger L1 cache and smaller shared memory + * - ::CU_FUNC_CACHE_PREFER_EQUAL: prefer equal sized L1 cache and shared memory + * + * \param pconfig - Returned cache configuration + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cuFuncSetCacheConfig, + * ::cudaDeviceGetCacheConfig + */ +CUresult CUDAAPI cuCtxGetCacheConfig(CUfunc_cache *pconfig); + +/** + * \brief Sets the preferred cache configuration for the current context. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p config the preferred cache configuration for + * the current context. This is only a preference. The driver will use + * the requested configuration if possible, but it is free to choose a different + * configuration if required to execute the function. Any function preference + * set via ::cuFuncSetCacheConfig() or ::cuKernelSetCacheConfig() will be preferred over this context-wide + * setting. Setting the context-wide cache configuration to + * ::CU_FUNC_CACHE_PREFER_NONE will cause subsequent kernel launches to prefer + * to not change the cache configuration unless required to launch the kernel. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * The supported cache configurations are: + * - ::CU_FUNC_CACHE_PREFER_NONE: no preference for shared memory or L1 (default) + * - ::CU_FUNC_CACHE_PREFER_SHARED: prefer larger shared memory and smaller L1 cache + * - ::CU_FUNC_CACHE_PREFER_L1: prefer larger L1 cache and smaller shared memory + * - ::CU_FUNC_CACHE_PREFER_EQUAL: prefer equal sized L1 cache and shared memory + * + * \param config - Requested cache configuration + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cuFuncSetCacheConfig, + * ::cudaDeviceSetCacheConfig, + * ::cuKernelSetCacheConfig + */ +CUresult CUDAAPI cuCtxSetCacheConfig(CUfunc_cache config); + +/** + * \brief Gets the context's API version. + * + * Returns a version number in \p version corresponding to the capabilities of + * the context (e.g. 3010 or 3020), which library developers can use to direct + * callers to a specific API version. If \p ctx is NULL, returns the API version + * used to create the currently bound context. + * + * Note that new API versions are only introduced when context capabilities are + * changed that break binary compatibility, so the API version and driver version + * may be different. For example, it is valid for the API version to be 3020 while + * the driver version is 4020. + * + * \param ctx - Context to check + * \param version - Pointer to version + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +CUresult CUDAAPI cuCtxGetApiVersion(CUcontext ctx, unsigned int *version); + +/** + * \brief Returns numerical values that correspond to the least and + * greatest stream priorities. + * + * Returns in \p *leastPriority and \p *greatestPriority the numerical values that correspond + * to the least and greatest stream priorities respectively. Stream priorities + * follow a convention where lower numbers imply greater priorities. The range of + * meaningful stream priorities is given by [\p *greatestPriority, \p *leastPriority]. + * If the user attempts to create a stream with a priority value that is + * outside the meaningful range as specified by this API, the priority is + * automatically clamped down or up to either \p *leastPriority or \p *greatestPriority + * respectively. See ::cuStreamCreateWithPriority for details on creating a + * priority stream. + * A NULL may be passed in for \p *leastPriority or \p *greatestPriority if the value + * is not desired. + * + * This function will return '0' in both \p *leastPriority and \p *greatestPriority if + * the current context's device does not support stream priorities + * (see ::cuDeviceGetAttribute). + * + * \param leastPriority - Pointer to an int in which the numerical value for least + * stream priority is returned + * \param greatestPriority - Pointer to an int in which the numerical value for greatest + * stream priority is returned + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa ::cuStreamCreateWithPriority, + * ::cuStreamGetPriority, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cudaDeviceGetStreamPriorityRange + */ +CUresult CUDAAPI cuCtxGetStreamPriorityRange(int *leastPriority, int *greatestPriority); + +/** + * \brief Resets all persisting lines in cache to normal status. + * + * ::cuCtxResetPersistingL2Cache Resets all persisting lines in cache to normal + * status. Takes effect on function return. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuCtxResetPersistingL2Cache(void); + +/** + * \brief Returns the execution affinity setting for the current context. + * + * Returns in \p *pExecAffinity the current value of \p type. The supported + * ::CUexecAffinityType values are: + * - ::CU_EXEC_AFFINITY_TYPE_SM_COUNT: number of SMs the context is limited to use. + * + * \param type - Execution affinity type to query + * \param pExecAffinity - Returned execution affinity + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNSUPPORTED_EXEC_AFFINITY + * \notefnerr + * + * \sa + * ::CUexecAffinityParam + */ +CUresult CUDAAPI cuCtxGetExecAffinity(CUexecAffinityParam *pExecAffinity, CUexecAffinityType type); + + +/** @} */ /* END CUDA_CTX */ + +/** + * \defgroup CUDA_CTX_DEPRECATED Context Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated context management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated context management functions of the low-level + * CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Increment a context's usage-count + * + * \deprecated + * + * Note that this function is deprecated and should not be used. + * + * Increments the usage count of the context and passes back a context handle + * in \p *pctx that must be passed to ::cuCtxDetach() when the application is + * done with the context. ::cuCtxAttach() fails if there is no context current + * to the thread. + * + * Currently, the \p flags parameter must be 0. + * + * \param pctx - Returned context handle of the current context + * \param flags - Context attach flags (must be 0) + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxDetach, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuCtxAttach(CUcontext *pctx, unsigned int flags); + +/** + * \brief Decrement a context's usage-count + * + * \deprecated + * + * Note that this function is deprecated and should not be used. + * + * Decrements the usage count of the context \p ctx, and destroys the context + * if the usage count goes to 0. The context must be a handle that was passed + * back by ::cuCtxCreate() or ::cuCtxAttach(), and must be current to the + * calling thread. + * + * \param ctx - Context to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetCacheConfig, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuCtxDetach(CUcontext ctx); + + +/** + * \brief Returns the current shared memory configuration for the current context. + * + * \deprecated + * + * This function will return in \p pConfig the current size of shared memory banks + * in the current context. On devices with configurable shared memory banks, + * ::cuCtxSetSharedMemConfig can be used to change this setting, so that all + * subsequent kernel launches will by default use the new bank size. When + * ::cuCtxGetSharedMemConfig is called on devices without configurable shared + * memory, it will return the fixed bank size of the hardware. + * + * The returned bank configurations can be either: + * - ::CU_SHARED_MEM_CONFIG_FOUR_BYTE_BANK_SIZE: shared memory bank width is + * four bytes. + * - ::CU_SHARED_MEM_CONFIG_EIGHT_BYTE_BANK_SIZE: shared memory bank width will + * eight bytes. + * + * \param pConfig - returned shared memory configuration + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cuCtxGetSharedMemConfig, + * ::cuFuncSetCacheConfig, + * ::cudaDeviceGetSharedMemConfig + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuCtxGetSharedMemConfig(CUsharedconfig *pConfig); + +/** + * \brief Sets the shared memory configuration for the current context. + * + * \deprecated + * + * On devices with configurable shared memory banks, this function will set + * the context's shared memory bank size which is used for subsequent kernel + * launches. + * + * Changed the shared memory configuration between launches may insert a device + * side synchronization point between those launches. + * + * Changing the shared memory bank size will not increase shared memory usage + * or affect occupancy of kernels, but may have major effects on performance. + * Larger bank sizes will allow for greater potential bandwidth to shared memory, + * but will change what kinds of accesses to shared memory will result in bank + * conflicts. + * + * This function will do nothing on devices with fixed shared memory bank size. + * + * The supported bank configurations are: + * - ::CU_SHARED_MEM_CONFIG_DEFAULT_BANK_SIZE: set bank width to the default initial + * setting (currently, four bytes). + * - ::CU_SHARED_MEM_CONFIG_FOUR_BYTE_BANK_SIZE: set shared memory bank width to + * be natively four bytes. + * - ::CU_SHARED_MEM_CONFIG_EIGHT_BYTE_BANK_SIZE: set shared memory bank width to + * be natively eight bytes. + * + * \param config - requested shared memory configuration + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, + * ::cuCtxDestroy, + * ::cuCtxGetApiVersion, + * ::cuCtxGetCacheConfig, + * ::cuCtxGetDevice, + * ::cuCtxGetFlags, + * ::cuCtxGetLimit, + * ::cuCtxPopCurrent, + * ::cuCtxPushCurrent, + * ::cuCtxSetLimit, + * ::cuCtxSynchronize, + * ::cuCtxGetSharedMemConfig, + * ::cuFuncSetCacheConfig, + * ::cudaDeviceSetSharedMemConfig + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuCtxSetSharedMemConfig(CUsharedconfig config); + +/** @} */ /* END CUDA_CTX_DEPRECATED */ + + +/** + * \defgroup CUDA_MODULE Module Management + * + * ___MANBRIEF___ module management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the module management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Loads a compute module + * + * Takes a filename \p fname and loads the corresponding module \p module into + * the current context. The CUDA driver API does not attempt to lazily + * allocate the resources needed by a module; if the memory for functions and + * data (constant and global) needed by the module cannot be allocated, + * ::cuModuleLoad() fails. The file should be a \e cubin file as output by + * \b nvcc, or a \e PTX file either as output by \b nvcc or handwritten, or + * a \e fatbin file as output by \b nvcc from toolchain 4.0 or later. + * + * \param module - Returned module + * \param fname - Filename of module to load + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_FILE_NOT_FOUND, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuModuleLoad(CUmodule *module, const char *fname); + +/** + * \brief Load a module's data + * + * Takes a pointer \p image and loads the corresponding module \p module into + * the current context. The \p image may be a \e cubin or \e fatbin + * as output by \b nvcc, or a NULL-terminated \e PTX, either as output by \b nvcc + * or hand-written. + * + * \param module - Returned module + * \param image - Module data to load + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuModuleLoadData(CUmodule *module, const void *image); + +/** + * \brief Load a module's data with options + * + * Takes a pointer \p image and loads the corresponding module \p module into + * the current context. The \p image may be a \e cubin or \e fatbin + * as output by \b nvcc, or a NULL-terminated \e PTX, either as output by \b nvcc + * or hand-written. + * + * \param module - Returned module + * \param image - Module data to load + * \param numOptions - Number of options + * \param options - Options for JIT + * \param optionValues - Option values for JIT + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuModuleLoadDataEx(CUmodule *module, const void *image, unsigned int numOptions, CUjit_option *options, void **optionValues); + +/** + * \brief Load a module's data + * + * Takes a pointer \p fatCubin and loads the corresponding module \p module + * into the current context. The pointer represents a fat binary object, + * which is a collection of different \e cubin and/or \e PTX files, all + * representing the same device code, but compiled and optimized for different + * architectures. + * + * Prior to CUDA 4.0, there was no documented API for constructing and using + * fat binary objects by programmers. Starting with CUDA 4.0, fat binary + * objects can be constructed by providing the -fatbin option to \b nvcc. + * More information can be found in the \b nvcc document. + * + * \param module - Returned module + * \param fatCubin - Fat binary to load + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuModuleLoadFatBinary(CUmodule *module, const void *fatCubin); + +/** + * \brief Unloads a module + * + * Unloads a module \p hmod from the current context. Attempting to unload + * a module which was obtained from the Library Management API such as + * ::cuLibraryGetModule will return ::CUDA_ERROR_NOT_PERMITTED. + * + * \param hmod - Module to unload + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_PERMITTED + * \notefnerr + * \note_destroy_ub + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary + */ +CUresult CUDAAPI cuModuleUnload(CUmodule hmod); + +/** + * CUDA Lazy Loading status + */ +typedef enum CUmoduleLoadingMode_enum { + CU_MODULE_EAGER_LOADING = 0x1, /**< Lazy Kernel Loading is not enabled */ + CU_MODULE_LAZY_LOADING = 0x2, /**< Lazy Kernel Loading is enabled */ +} CUmoduleLoadingMode; + +/** + * \brief Query lazy loading mode + * + * Returns lazy loading mode + * Module loading mode is controlled by CUDA_MODULE_LOADING env variable + * + * \param mode - Returns the lazy loading mode + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + * \sa + * ::cuModuleLoad, + */ +CUresult CUDAAPI cuModuleGetLoadingMode(CUmoduleLoadingMode *mode); + +/** + * \brief Returns a function handle + * + * Returns in \p *hfunc the handle of the function of name \p name located in + * module \p hmod. If no function of that name exists, ::cuModuleGetFunction() + * returns ::CUDA_ERROR_NOT_FOUND. + * + * \param hfunc - Returned function handle + * \param hmod - Module to retrieve function from + * \param name - Name of function to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuModuleGetFunction(CUfunction *hfunc, CUmodule hmod, const char *name); + +/** + * \brief Returns the number of functions within a module + * + * Returns in \p count the number of functions in \p mod. + * + * \param count - Number of functions found within the module + * \param mod - Module to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + */ +CUresult CUDAAPI cuModuleGetFunctionCount(unsigned int *count, CUmodule mod); + +/** + * \brief Returns the function handles within a module. + * + * Returns in \p functions a maximum number of \p numFunctions function handles within \p mod. When + * function loading mode is set to LAZY the function retrieved may be partially loaded. The loading + * state of a function can be queried using ::cuFunctionIsLoaded. CUDA APIs may load the function + * automatically when called with partially loaded function handle which may incur additional + * latency. Alternatively, ::cuFunctionLoad can be used to explicitly load a function. The returned + * function handles become invalid when the module is unloaded. + * + * \param functions - Buffer where the function handles are returned to + * \param numFunctions - Maximum number of function handles may be returned to the buffer + * \param mod - Module to query from + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetFunctionCount, + * ::cuFuncIsLoaded, + * ::cuFuncLoad + */ +CUresult CUDAAPI cuModuleEnumerateFunctions(CUfunction *functions, unsigned int numFunctions, CUmodule mod); + +/** + * \brief Returns a global pointer from a module + * + * Returns in \p *dptr and \p *bytes the base pointer and size of the + * global of name \p name located in module \p hmod. If no variable of that name + * exists, ::cuModuleGetGlobal() returns ::CUDA_ERROR_NOT_FOUND. + * One of the parameters \p dptr or \p bytes (not both) can be NULL in which + * case it is ignored. + * + * \param dptr - Returned global device pointer + * \param bytes - Returned global size in bytes + * \param hmod - Module to retrieve global from + * \param name - Name of global to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_FOUND + * \notefnerr + * + * \sa ::cuModuleGetFunction, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload, + * ::cudaGetSymbolAddress, + * ::cudaGetSymbolSize + */ +CUresult CUDAAPI cuModuleGetGlobal(CUdeviceptr *dptr, size_t *bytes, CUmodule hmod, const char *name); + +/** + * \brief Creates a pending JIT linker invocation. + * + * If the call is successful, the caller owns the returned CUlinkState, which + * should eventually be destroyed with ::cuLinkDestroy. The + * device code machine size (32 or 64 bit) will match the calling application. + * + * Both linker and compiler options may be specified. Compiler options will + * be applied to inputs to this linker action which must be compiled from PTX. + * The options ::CU_JIT_WALL_TIME, + * ::CU_JIT_INFO_LOG_BUFFER_SIZE_BYTES, and ::CU_JIT_ERROR_LOG_BUFFER_SIZE_BYTES + * will accumulate data until the CUlinkState is destroyed. + * + * \p optionValues must remain valid for the life of the CUlinkState if output + * options are used. No other references to inputs are maintained after this + * call returns. + * + * \note For LTO-IR input, only LTO-IR compiled with toolkits prior to CUDA 12.0 will be accepted + * + * \param numOptions Size of options arrays + * \param options Array of linker and compiler options + * \param optionValues Array of option values, each cast to void * + * \param stateOut On success, this will contain a CUlinkState to specify + * and complete this action + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * \notefnerr + * + * \sa ::cuLinkAddData, + * ::cuLinkAddFile, + * ::cuLinkComplete, + * ::cuLinkDestroy + */ +CUresult CUDAAPI +cuLinkCreate(unsigned int numOptions, CUjit_option *options, void **optionValues, CUlinkState *stateOut); + +/** + * \brief Add an input to a pending linker invocation + * + * Ownership of \p data is retained by the caller. No reference is retained to any + * inputs after this call returns. + * + * This method accepts only compiler options, which are used if the data must + * be compiled from PTX, and does not accept any of + * ::CU_JIT_WALL_TIME, ::CU_JIT_INFO_LOG_BUFFER, ::CU_JIT_ERROR_LOG_BUFFER, + * ::CU_JIT_TARGET_FROM_CUCONTEXT, or ::CU_JIT_TARGET. + * + * \note For LTO-IR input, only LTO-IR compiled with toolkits prior to CUDA 12.0 will be accepted + * + * \param state A pending linker action. + * \param type The type of the input data. + * \param data The input data. PTX must be NULL-terminated. + * \param size The length of the input data. + * \param name An optional name for this input in log messages. + * \param numOptions Size of options. + * \param options Options to be applied only for this input (overrides options from ::cuLinkCreate). + * \param optionValues Array of option values, each cast to void *. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU + * + * \sa ::cuLinkCreate, + * ::cuLinkAddFile, + * ::cuLinkComplete, + * ::cuLinkDestroy + */ +CUresult CUDAAPI +cuLinkAddData(CUlinkState state, CUjitInputType type, void *data, size_t size, const char *name, + unsigned int numOptions, CUjit_option *options, void **optionValues); + +/** + * \brief Add a file input to a pending linker invocation + * + * No reference is retained to any inputs after this call returns. + * + * This method accepts only compiler options, which are used if the input + * must be compiled from PTX, and does not accept any of + * ::CU_JIT_WALL_TIME, ::CU_JIT_INFO_LOG_BUFFER, ::CU_JIT_ERROR_LOG_BUFFER, + * ::CU_JIT_TARGET_FROM_CUCONTEXT, or ::CU_JIT_TARGET. + * + * This method is equivalent to invoking ::cuLinkAddData on the contents + * of the file. + * + * \note For LTO-IR input, only LTO-IR compiled with toolkits prior to CUDA 12.0 will be accepted + * + * \param state A pending linker action + * \param type The type of the input data + * \param path Path to the input file + * \param numOptions Size of options + * \param options Options to be applied only for this input (overrides options from ::cuLinkCreate) + * \param optionValues Array of option values, each cast to void * + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_FILE_NOT_FOUND + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU + * + * \sa ::cuLinkCreate, + * ::cuLinkAddData, + * ::cuLinkComplete, + * ::cuLinkDestroy + */ +CUresult CUDAAPI +cuLinkAddFile(CUlinkState state, CUjitInputType type, const char *path, + unsigned int numOptions, CUjit_option *options, void **optionValues); + +/** + * \brief Complete a pending linker invocation + * + * Completes the pending linker action and returns the cubin image for the linked + * device code, which can be used with ::cuModuleLoadData. The cubin is owned by + * \p state, so it should be loaded before \p state is destroyed via ::cuLinkDestroy. + * This call does not destroy \p state. + * + * \param state A pending linker invocation + * \param cubinOut On success, this will point to the output image + * \param sizeOut Optional parameter to receive the size of the generated image + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuLinkCreate, + * ::cuLinkAddData, + * ::cuLinkAddFile, + * ::cuLinkDestroy, + * ::cuModuleLoadData + */ +CUresult CUDAAPI +cuLinkComplete(CUlinkState state, void **cubinOut, size_t *sizeOut); + +/** + * \brief Destroys state for a JIT linker invocation. + * + * \param state State object for the linker invocation + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE + * + * \sa ::cuLinkCreate + */ +CUresult CUDAAPI +cuLinkDestroy(CUlinkState state); + +/** @} */ /* END CUDA_MODULE */ + +/** + * \defgroup CUDA_MODULE_DEPRECATED Module Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated module management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated module management functions of the low-level + * CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns a handle to a texture reference + * + * \deprecated + * + * Returns in \p *pTexRef the handle of the texture reference of name \p name + * in the module \p hmod. If no texture reference of that name exists, + * ::cuModuleGetTexRef() returns ::CUDA_ERROR_NOT_FOUND. This texture reference + * handle should not be destroyed, since it will be destroyed when the module + * is unloaded. + * + * \param pTexRef - Returned texture reference + * \param hmod - Module to retrieve texture reference from + * \param name - Name of texture reference to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_FOUND + * \notefnerr + * + * \sa + * ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetSurfRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuModuleGetTexRef(CUtexref *pTexRef, CUmodule hmod, const char *name); + +/** + * \brief Returns a handle to a surface reference + * + * \deprecated + * + * Returns in \p *pSurfRef the handle of the surface reference of name \p name + * in the module \p hmod. If no surface reference of that name exists, + * ::cuModuleGetSurfRef() returns ::CUDA_ERROR_NOT_FOUND. + * + * \param pSurfRef - Returned surface reference + * \param hmod - Module to retrieve surface reference from + * \param name - Name of surface reference to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_FOUND + * \notefnerr + * + * \sa + * ::cuModuleGetFunction, + * ::cuModuleGetGlobal, + * ::cuModuleGetTexRef, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx, + * ::cuModuleLoadFatBinary, + * ::cuModuleUnload + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuModuleGetSurfRef(CUsurfref *pSurfRef, CUmodule hmod, const char *name); + +/** @} */ /* END CUDA_MODULE_DEPRECATED */ + +/** + * \defgroup CUDA_LIBRARY Library Management + * + * ___MANBRIEF___ library management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the library management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Load a library with specified code and options + * + * Takes a pointer \p code and loads the corresponding library \p library based on + * the application defined library loading mode: + * - If module loading is set to EAGER, via the environment variables described in "Module loading", + * \p library is loaded eagerly into all contexts at the time of the call and future contexts + * at the time of creation until the library is unloaded with ::cuLibraryUnload(). + * - If the environment variables are set to LAZY, \p library + * is not immediately loaded onto all existent contexts and will only be + * loaded when a function is needed for that context, such as a kernel launch. + * + * These environment variables are described in the CUDA programming guide under the + * "CUDA environment variables" section. + * + * The \p code may be a \e cubin or \e fatbin as output by \b nvcc, + * or a NULL-terminated \e PTX, either as output by \b nvcc or hand-written. + * + * Options are passed as an array via \p jitOptions and any corresponding parameters are passed in + * \p jitOptionsValues. The number of total JIT options is supplied via \p numJitOptions. + * Any outputs will be returned via \p jitOptionsValues. + * + * Library load options are passed as an array via \p libraryOptions and any corresponding parameters are passed in + * \p libraryOptionValues. The number of total library load options is supplied via \p numLibraryOptions. + * + * \param library - Returned library + * \param code - Code to load + * \param jitOptions - Options for JIT + * \param jitOptionsValues - Option values for JIT + * \param numJitOptions - Number of options + * \param libraryOptions - Options for loading + * \param libraryOptionValues - Option values for loading + * \param numLibraryOptions - Number of options for loading + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * + * \sa ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx + */ +CUresult CUDAAPI cuLibraryLoadData(CUlibrary *library, const void *code, + CUjit_option *jitOptions, void **jitOptionsValues, unsigned int numJitOptions, + CUlibraryOption *libraryOptions, void** libraryOptionValues, unsigned int numLibraryOptions); + +/** + * \brief Load a library with specified file and options + * + * Takes a pointer \p code and loads the corresponding library \p library based on + * the application defined library loading mode: + * - If module loading is set to EAGER, via the environment variables described in "Module loading", + * \p library is loaded eagerly into all contexts at the time of the call and future contexts + * at the time of creation until the library is unloaded with ::cuLibraryUnload(). + * - If the environment variables are set to LAZY, \p library + * is not immediately loaded onto all existent contexts and will only be + * loaded when a function is needed for that context, such as a kernel launch. + * + * These environment variables are described in the CUDA programming guide under the + * "CUDA environment variables" section. + * + * The file should be a \e cubin file as output by \b nvcc, or a \e PTX file either + * as output by \b nvcc or handwritten, or a \e fatbin file as output by \b nvcc. + * + * Options are passed as an array via \p jitOptions and any corresponding parameters are + * passed in \p jitOptionsValues. The number of total options is supplied via \p numJitOptions. + * Any outputs will be returned via \p jitOptionsValues. + * + * Library load options are passed as an array via \p libraryOptions and any corresponding parameters are passed in + * \p libraryOptionValues. The number of total library load options is supplied via \p numLibraryOptions. + * + * \param library - Returned library + * \param fileName - File to load from + * \param jitOptions - Options for JIT + * \param jitOptionsValues - Option values for JIT + * \param numJitOptions - Number of options + * \param libraryOptions - Options for loading + * \param libraryOptionValues - Option values for loading + * \param numLibraryOptions - Number of options for loading + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_PTX, + * ::CUDA_ERROR_UNSUPPORTED_PTX_VERSION, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NO_BINARY_FOR_GPU, + * ::CUDA_ERROR_SHARED_OBJECT_SYMBOL_NOT_FOUND, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_JIT_COMPILER_NOT_FOUND + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryUnload, + * ::cuModuleLoad, + * ::cuModuleLoadData, + * ::cuModuleLoadDataEx + */ +CUresult CUDAAPI cuLibraryLoadFromFile(CUlibrary *library, const char *fileName, + CUjit_option *jitOptions, void **jitOptionsValues, unsigned int numJitOptions, + CUlibraryOption *libraryOptions, void **libraryOptionValues, unsigned int numLibraryOptions); + +/** + * \brief Unloads a library + * + * Unloads the library specified with \p library + * + * \param library - Library to unload + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuModuleUnload + */ +CUresult CUDAAPI cuLibraryUnload(CUlibrary library); + +/** + * \brief Returns a kernel handle + * + * Returns in \p pKernel the handle of the kernel with name \p name located in library \p library. + * If kernel handle is not found, the call returns ::CUDA_ERROR_NOT_FOUND. + * + * \param pKernel - Returned kernel handle + * \param library - Library to retrieve kernel from + * \param name - Name of kernel to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuKernelGetFunction, + * ::cuLibraryGetModule, + * ::cuModuleGetFunction + */ +CUresult CUDAAPI cuLibraryGetKernel(CUkernel *pKernel, CUlibrary library, const char *name); + +/** + * \brief Returns the number of kernels within a library + * + * Returns in \p count the number of kernels in \p lib. + * + * \param count - Number of kernels found within the library + * \param lib - Library to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + */ +CUresult CUDAAPI cuLibraryGetKernelCount(unsigned int *count, CUlibrary lib); + +/** + * \brief Retrieve the kernel handles within a library. + * + * Returns in \p kernels a maximum number of \p numKernels kernel handles within \p lib. + * The returned kernel handle becomes invalid when the library is unloaded. + * + * \param kernels - Buffer where the kernel handles are returned to + * \param numKernels - Maximum number of kernel handles may be returned to the buffer + * \param lib - Library to query from + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuLibraryGetKernelCount + */ +CUresult CUDAAPI cuLibraryEnumerateKernels(CUkernel *kernels, unsigned int numKernels, CUlibrary lib); + +/** + * \brief Returns a module handle + * + * Returns in \p pMod the module handle associated with the current context located in + * library \p library. If module handle is not found, the call returns ::CUDA_ERROR_NOT_FOUND. + * + * \param pMod - Returned module handle + * \param library - Library to retrieve module from + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuModuleGetFunction + */ +CUresult CUDAAPI cuLibraryGetModule(CUmodule *pMod, CUlibrary library); + +/** + * \brief Returns a function handle + * + * Returns in \p pFunc the handle of the function for the requested kernel \p kernel and + * the current context. If function handle is not found, the call returns ::CUDA_ERROR_NOT_FOUND. + * + * \param pFunc - Returned function handle + * \param kernel - Kernel to retrieve function for the requested context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuLibraryGetKernel, + * ::cuLibraryGetModule, + * ::cuModuleGetFunction + */ +CUresult CUDAAPI cuKernelGetFunction(CUfunction *pFunc, CUkernel kernel); + +/** + * \brief Returns a global device pointer + * + * Returns in \p *dptr and \p *bytes the base pointer and size of the global with + * name \p name for the requested library \p library and the current context. + * If no global for the requested name \p name exists, the call returns ::CUDA_ERROR_NOT_FOUND. + * One of the parameters \p dptr or \p bytes (not both) can be NULL in which + * case it is ignored. + * + * \param dptr - Returned global device pointer for the requested context + * \param bytes - Returned global size in bytes + * \param library - Library to retrieve global from + * \param name - Name of global to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuLibraryGetModule, + * cuModuleGetGlobal + */ +CUresult CUDAAPI cuLibraryGetGlobal(CUdeviceptr *dptr, size_t *bytes, CUlibrary library, const char *name); + +/** + * \brief Returns a pointer to managed memory + * + * Returns in \p *dptr and \p *bytes the base pointer and size of the managed memory with + * name \p name for the requested library \p library. If no managed memory with the + * requested name \p name exists, the call returns ::CUDA_ERROR_NOT_FOUND. One of the parameters + * \p dptr or \p bytes (not both) can be NULL in which case it is ignored. + * Note that managed memory for library \p library is shared across devices and is registered + * when the library is loaded into atleast one context. + * + * \note The API requires a CUDA context to be present and initialized on at least one device. + * If no context is present, the call returns ::CUDA_ERROR_NOT_FOUND. + * + * \param dptr - Returned pointer to the managed memory + * \param bytes - Returned memory size in bytes + * \param library - Library to retrieve managed memory from + * \param name - Name of managed memory to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload + */ +CUresult CUDAAPI cuLibraryGetManaged(CUdeviceptr *dptr, size_t *bytes, CUlibrary library, const char *name); + +/** + * \brief Returns a pointer to a unified function + * + * Returns in \p *fptr the function pointer to a unified function denoted by \p symbol. + * If no unified function with name \p symbol exists, the call returns ::CUDA_ERROR_NOT_FOUND. + * If there is no device with attribute ::CU_DEVICE_ATTRIBUTE_UNIFIED_FUNCTION_POINTERS present in the system, + * the call may return ::CUDA_ERROR_NOT_FOUND. + * + * \param fptr - Returned pointer to a unified function + * \param library - Library to retrieve function pointer memory from + * \param symbol - Name of function pointer to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_FOUND + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload + */ +CUresult CUDAAPI cuLibraryGetUnifiedFunction(void **fptr, CUlibrary library, const char *symbol); + +/** + * \brief Returns information about a kernel + * + * Returns in \p *pi the integer value of the attribute \p attrib for the kernel + * \p kernel for the requested device \p dev. The supported attributes are: + * - ::CU_FUNC_ATTRIBUTE_MAX_THREADS_PER_BLOCK: The maximum number of threads + * per block, beyond which a launch of the kernel would fail. This number + * depends on both the kernel and the requested device. + * - ::CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES: The size in bytes of + * statically-allocated shared memory per block required by this kernel. + * This does not include dynamically-allocated shared memory requested by + * the user at runtime. + * - ::CU_FUNC_ATTRIBUTE_CONST_SIZE_BYTES: The size in bytes of user-allocated + * constant memory required by this kernel. + * - ::CU_FUNC_ATTRIBUTE_LOCAL_SIZE_BYTES: The size in bytes of local memory + * used by each thread of this kernel. + * - ::CU_FUNC_ATTRIBUTE_NUM_REGS: The number of registers used by each thread + * of this kernel. + * - ::CU_FUNC_ATTRIBUTE_PTX_VERSION: The PTX virtual architecture version for + * which the kernel was compiled. This value is the major PTX version * 10 + * + the minor PTX version, so a PTX version 1.3 function would return the + * value 13. Note that this may return the undefined value of 0 for cubins + * compiled prior to CUDA 3.0. + * - ::CU_FUNC_ATTRIBUTE_BINARY_VERSION: The binary architecture version for + * which the kernel was compiled. This value is the major binary + * version * 10 + the minor binary version, so a binary version 1.3 function + * would return the value 13. Note that this will return a value of 10 for + * legacy cubins that do not have a properly-encoded binary architecture + * version. + * - ::CU_FUNC_CACHE_MODE_CA: The attribute to indicate whether the kernel has + * been compiled with user specified option "-Xptxas --dlcm=ca" set. + * - ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES: The maximum size in bytes of + * dynamically-allocated shared memory. + * - ::CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT: Preferred shared memory-L1 + * cache split ratio in percent of total shared memory. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SIZE_MUST_BE_SET: If this attribute is set, the + * kernel must launch with a valid cluster size specified. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_WIDTH: The required cluster width in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_HEIGHT: The required cluster height in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_DEPTH: The required cluster depth in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_NON_PORTABLE_CLUSTER_SIZE_ALLOWED: Indicates whether + * the function can be launched with non-portable cluster size. 1 is allowed, + * 0 is disallowed. A non-portable cluster size may only function on the + * specific SKUs the program is tested on. The launch might fail if the + * program is run on a different hardware platform. CUDA API provides + * cudaOccupancyMaxActiveClusters to assist with checking whether the desired + * size can be launched on the current device. A portable cluster size is + * guaranteed to be functional on all compute capabilities higher than the + * target compute capability. The portable cluster size for sm_90 is 8 blocks + * per cluster. This value may increase for future compute capabilities. The + * specific hardware unit may support higher cluster sizes that’s not + * guaranteed to be portable. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE: The block + * scheduling policy of a function. The value type is CUclusterSchedulingPolicy. + * + * \note If another thread is trying to set the same attribute on the same device using + * ::cuKernelSetAttribute() simultaneously, the attribute query will give the old or new + * value depending on the interleavings chosen by the OS scheduler and memory consistency. + * + * \param pi - Returned attribute value + * \param attrib - Attribute requested + * \param kernel - Kernel to query attribute of + * \param dev - Device to query attribute of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuKernelSetAttribute, + * ::cuLibraryGetKernel, + * ::cuLaunchKernel, + * ::cuKernelGetFunction, + * ::cuLibraryGetModule, + * ::cuModuleGetFunction, + * ::cuFuncGetAttribute + */ +CUresult CUDAAPI cuKernelGetAttribute(int *pi, CUfunction_attribute attrib, CUkernel kernel, CUdevice dev); + +/** + * \brief Sets information about a kernel + * + * This call sets the value of a specified attribute \p attrib on the kernel \p kernel + * for the requested device \p dev to an integer value specified by \p val. + * This function returns CUDA_SUCCESS if the new value of the attribute could be + * successfully set. If the set fails, this call will return an error. + * Not all attributes can have values set. Attempting to set a value on a read-only + * attribute will result in an error (CUDA_ERROR_INVALID_VALUE) + * + * Note that attributes set using ::cuFuncSetAttribute() will override the attribute + * set by this API irrespective of whether the call to ::cuFuncSetAttribute() is made + * before or after this API call. However, ::cuKernelGetAttribute() will always + * return the attribute value set by this API. + * + * Supported attributes are: + * - ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES: This is the maximum size in bytes of + * dynamically-allocated shared memory. The value should contain the requested + * maximum size of dynamically-allocated shared memory. The sum of this value and + * the function attribute ::CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES cannot exceed the + * device attribute ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN. + * The maximal size of requestable dynamic shared memory may differ by GPU + * architecture. + * - ::CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT: On devices where the L1 + * cache and shared memory use the same hardware resources, this sets the shared memory + * carveout preference, in percent of the total shared memory. + * See ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR + * This is only a hint, and the driver can choose a different ratio if required to execute the function. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_WIDTH: The required cluster width in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_HEIGHT: The required cluster height in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_DEPTH: The required cluster depth in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE: The block + * scheduling policy of a function. The value type is CUclusterSchedulingPolicy. + * + * \note The API has stricter locking requirements in comparison to its legacy counterpart + * ::cuFuncSetAttribute() due to device-wide semantics. If multiple threads are trying to + * set the same attribute on the same device simultaneously, the attribute setting will depend + * on the interleavings chosen by the OS scheduler and memory consistency. + * + * \param attrib - Attribute requested + * \param val - Value to set + * \param kernel - Kernel to set attribute of + * \param dev - Device to set attribute of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuKernelGetAttribute, + * ::cuLibraryGetKernel, + * ::cuLaunchKernel, + * ::cuKernelGetFunction, + * ::cuLibraryGetModule, + * ::cuModuleGetFunction, + * ::cuFuncSetAttribute + */ +CUresult CUDAAPI cuKernelSetAttribute(CUfunction_attribute attrib, int val, CUkernel kernel, CUdevice dev); + +/** + * \brief Sets the preferred cache configuration for a device kernel. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p config the preferred cache configuration for + * the device kernel \p kernel on the requested device \p dev. This is only a preference. + * The driver will use the requested configuration if possible, but it is free to choose a different + * configuration if required to execute \p kernel. Any context-wide preference + * set via ::cuCtxSetCacheConfig() will be overridden by this per-kernel + * setting. + * + * Note that attributes set using ::cuFuncSetCacheConfig() will override the attribute + * set by this API irrespective of whether the call to ::cuFuncSetCacheConfig() is made + * before or after this API call. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * + * The supported cache configurations are: + * - ::CU_FUNC_CACHE_PREFER_NONE: no preference for shared memory or L1 (default) + * - ::CU_FUNC_CACHE_PREFER_SHARED: prefer larger shared memory and smaller L1 cache + * - ::CU_FUNC_CACHE_PREFER_L1: prefer larger L1 cache and smaller shared memory + * - ::CU_FUNC_CACHE_PREFER_EQUAL: prefer equal sized L1 cache and shared memory + * + * \note The API has stricter locking requirements in comparison to its legacy counterpart + * ::cuFuncSetCacheConfig() due to device-wide semantics. If multiple threads are trying to + * set a config on the same device simultaneously, the cache config setting will depend + * on the interleavings chosen by the OS scheduler and memory consistency. + * + * \param kernel - Kernel to configure cache for + * \param config - Requested cache configuration + * \param dev - Device to set attribute of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuLibraryLoadData, + * ::cuLibraryLoadFromFile, + * ::cuLibraryUnload, + * ::cuLibraryGetKernel, + * ::cuKernelGetFunction, + * ::cuLibraryGetModule, + * ::cuModuleGetFunction, + * ::cuFuncSetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuLaunchKernel + */ +CUresult CUDAAPI cuKernelSetCacheConfig(CUkernel kernel, CUfunc_cache config, CUdevice dev); + +/** + * \brief Returns the function name for a ::CUkernel handle + * + * Returns in \p **name the function name associated with the kernel handle \p hfunc . + * The function name is returned as a null-terminated string. The returned name is only + * valid when the kernel handle is valid. If the library is unloaded or reloaded, one + * must call the API again to get the updated name. This API may return a mangled name if + * the function is not declared as having C linkage. If either \p **name or \p hfunc + * is NULL, ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \param name - The returned name of the function + * \param hfunc - The function handle to retrieve the name for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + */ +CUresult CUDAAPI cuKernelGetName(const char **name, CUkernel hfunc); + +/** + * \brief Returns the offset and size of a kernel parameter in the device-side parameter layout + * + * Queries the kernel parameter at \p paramIndex into \p kernel's list of parameters, and returns + * in \p paramOffset and \p paramSize the offset and size, respectively, where the parameter + * will reside in the device-side parameter layout. This information can be used to update kernel + * node parameters from the device via ::cudaGraphKernelNodeSetParam() and + * ::cudaGraphKernelNodeUpdatesApply(). \p paramIndex must be less than the number of parameters + * that \p kernel takes. \p paramSize can be set to NULL if only the parameter offset is desired. + * + * \param kernel - The kernel to query + * \param paramIndex - The parameter index to query + * \param paramOffset - Returns the offset into the device-side parameter layout at which the parameter resides + * \param paramSize - Optionally returns the size of the parameter in the device-side parameter layout + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * +* \sa ::cuFuncGetParamInfo + */ +CUresult CUDAAPI cuKernelGetParamInfo(CUkernel kernel, size_t paramIndex, size_t *paramOffset, size_t *paramSize); +/** @} */ /* END CUDA_LIBRARY */ + +/** + * \defgroup CUDA_MEM Memory Management + * + * ___MANBRIEF___ memory management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the memory management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Gets free and total memory + * + * Returns in \p *total the total amount of memory available to the the current context. + * Returns in \p *free the amount of memory on the device that is free according to the OS. + * CUDA is not guaranteed to be able to allocate all of the memory that the OS reports as free. + * In a multi-tenet situation, free estimate returned is prone to race condition where + * a new allocation/free done by a different process or a different thread in the same + * process between the time when free memory was estimated and reported, will result in + * deviation in free value reported and actual free memory. + * + * The integrated GPU on Tegra shares memory with CPU and other component + * of the SoC. The free and total values returned by the API excludes + * the SWAP memory space maintained by the OS on some platforms. + * The OS may move some of the memory pages into swap area as the GPU or + * CPU allocate or access memory. See Tegra app note on how to calculate + * total and free memory on Tegra. + * + * \param free - Returned free memory in bytes + * \param total - Returned total memory in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemGetInfo + */ +CUresult CUDAAPI cuMemGetInfo(size_t *free, size_t *total); + +/** + * \brief Allocates device memory + * + * Allocates \p bytesize bytes of linear memory on the device and returns in + * \p *dptr a pointer to the allocated memory. The allocated memory is suitably + * aligned for any kind of variable. The memory is not cleared. If \p bytesize + * is 0, ::cuMemAlloc() returns ::CUDA_ERROR_INVALID_VALUE. + * + * \param dptr - Returned device pointer + * \param bytesize - Requested allocation size in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMalloc + */ +CUresult CUDAAPI cuMemAlloc(CUdeviceptr *dptr, size_t bytesize); + +/** + * \brief Allocates pitched device memory + * + * Allocates at least \p WidthInBytes * \p Height bytes of linear memory on + * the device and returns in \p *dptr a pointer to the allocated memory. The + * function may pad the allocation to ensure that corresponding pointers in + * any given row will continue to meet the alignment requirements for + * coalescing as the address is updated from row to row. \p ElementSizeBytes + * specifies the size of the largest reads and writes that will be performed + * on the memory range. \p ElementSizeBytes may be 4, 8 or 16 (since coalesced + * memory transactions are not possible on other data sizes). If + * \p ElementSizeBytes is smaller than the actual read/write size of a kernel, + * the kernel will run correctly, but possibly at reduced speed. The pitch + * returned in \p *pPitch by ::cuMemAllocPitch() is the width in bytes of the + * allocation. The intended usage of pitch is as a separate parameter of the + * allocation, used to compute addresses within the 2D array. Given the row + * and column of an array element of type \b T, the address is computed as: + * \code + T* pElement = (T*)((char*)BaseAddress + Row * Pitch) + Column; + * \endcode + * + * The pitch returned by ::cuMemAllocPitch() is guaranteed to work with + * ::cuMemcpy2D() under all circumstances. For allocations of 2D arrays, it is + * recommended that programmers consider performing pitch allocations using + * ::cuMemAllocPitch(). Due to alignment restrictions in the hardware, this is + * especially true if the application will be performing 2D memory copies + * between different regions of device memory (whether linear memory or CUDA + * arrays). + * + * The byte alignment of the pitch returned by ::cuMemAllocPitch() is guaranteed + * to match or exceed the alignment requirement for texture binding with + * ::cuTexRefSetAddress2D(). + * + * \param dptr - Returned device pointer + * \param pPitch - Returned pitch of allocation in bytes + * \param WidthInBytes - Requested allocation width in bytes + * \param Height - Requested allocation height in rows + * \param ElementSizeBytes - Size of largest reads/writes for range + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMallocPitch + */ +CUresult CUDAAPI cuMemAllocPitch(CUdeviceptr *dptr, size_t *pPitch, size_t WidthInBytes, size_t Height, unsigned int ElementSizeBytes); + +/** + * \brief Frees device memory + * + * Frees the memory space pointed to by \p dptr, which must have been returned + * by a previous call to one of the following memory allocation APIs - ::cuMemAlloc(), + * ::cuMemAllocPitch(), ::cuMemAllocManaged(), ::cuMemAllocAsync(), ::cuMemAllocFromPoolAsync() + * + * Note - This API will not perform any implict synchronization when the pointer was allocated with + * ::cuMemAllocAsync or ::cuMemAllocFromPoolAsync. Callers must ensure that all accesses to the + * pointer have completed before invoking ::cuMemFree. For best performance and memory reuse, users + * should use ::cuMemFreeAsync to free memory allocated via the stream ordered memory allocator. + * + * \param dptr - Pointer to memory to free + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemAllocManaged, ::cuMemAllocAsync, ::cuMemAllocFromPoolAsync, + * ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, ::cuMemcpy3D, ::cuMemcpy3DAsync, + * ::cuMemcpyAtoA, ::cuMemcpyAtoD, ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, + * ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, + * ::cuMemcpyHtoAAsync, ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, ::cuMemFreeAsync, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaFree + */ +CUresult CUDAAPI cuMemFree(CUdeviceptr dptr); + +/** + * \brief Get information on memory allocations + * + * Returns the base address in \p *pbase and size in \p *psize of the + * allocation by ::cuMemAlloc() or ::cuMemAllocPitch() that contains the input + * pointer \p dptr. Both parameters \p pbase and \p psize are optional. If one + * of them is NULL, it is ignored. + * + * \param pbase - Returned base address + * \param psize - Returned size of device memory allocation + * \param dptr - Device pointer to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_NOT_FOUND, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32 + */ +CUresult CUDAAPI cuMemGetAddressRange(CUdeviceptr *pbase, size_t *psize, CUdeviceptr dptr); + +/** + * \brief Allocates page-locked host memory + * + * Allocates \p bytesize bytes of host memory that is page-locked and + * accessible to the device. The driver tracks the virtual memory ranges + * allocated with this function and automatically accelerates calls to + * functions such as ::cuMemcpy(). Since the memory can be accessed directly by + * the device, it can be read or written with much higher bandwidth than + * pageable memory obtained with functions such as ::malloc(). + * + * On systems where ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES + * is true, ::cuMemAllocHost may not page-lock the allocated memory. + * + * Page-locking excessive amounts of memory with ::cuMemAllocHost() may degrade system + * performance, since it reduces the amount of memory available to the system + * for paging. As a result, this function is best used sparingly to allocate + * staging areas for data exchange between host and device. + * + * Note all host memory allocated using ::cuMemAllocHost() will automatically + * be immediately accessible to all contexts on all devices which support unified + * addressing (as may be queried using ::CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING). + * The device pointer that may be used to access this host memory from those + * contexts is always equal to the returned host pointer \p *pp. + * See \ref CUDA_UNIFIED for additional details. + * + * \param pp - Returned pointer to host memory + * \param bytesize - Requested allocation size in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMallocHost + */ +CUresult CUDAAPI cuMemAllocHost(void **pp, size_t bytesize); + +/** + * \brief Frees page-locked host memory + * + * Frees the memory space pointed to by \p p, which must have been returned by + * a previous call to ::cuMemAllocHost(). + * + * \param p - Pointer to memory to free + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaFreeHost + */ +CUresult CUDAAPI cuMemFreeHost(void *p); + +/** + * \brief Allocates page-locked host memory + * + * Allocates \p bytesize bytes of host memory that is page-locked and accessible + * to the device. The driver tracks the virtual memory ranges allocated with + * this function and automatically accelerates calls to functions such as + * ::cuMemcpyHtoD(). Since the memory can be accessed directly by the device, + * it can be read or written with much higher bandwidth than pageable memory + * obtained with functions such as ::malloc(). + * + * On systems where ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES + * is true, ::cuMemHostAlloc may not page-lock the allocated memory. + * + * Page-locking excessive amounts of memory may degrade system performance, + * since it reduces the amount of memory available to the system for paging. + * As a result, this function is best used sparingly to allocate staging areas + * for data exchange between host and device. + * + * The \p Flags parameter enables different options to be specified that + * affect the allocation, as follows. + * + * - ::CU_MEMHOSTALLOC_PORTABLE: The memory returned by this call will be + * considered as pinned memory by all CUDA contexts, not just the one that + * performed the allocation. + * + * - ::CU_MEMHOSTALLOC_DEVICEMAP: Maps the allocation into the CUDA address + * space. The device pointer to the memory may be obtained by calling + * ::cuMemHostGetDevicePointer(). + * + * - ::CU_MEMHOSTALLOC_WRITECOMBINED: Allocates the memory as write-combined + * (WC). WC memory can be transferred across the PCI Express bus more + * quickly on some system configurations, but cannot be read efficiently by + * most CPUs. WC memory is a good option for buffers that will be written by + * the CPU and read by the GPU via mapped pinned memory or host->device + * transfers. + * + * All of these flags are orthogonal to one another: a developer may allocate + * memory that is portable, mapped and/or write-combined with no restrictions. + * + * The ::CU_MEMHOSTALLOC_DEVICEMAP flag may be specified on CUDA contexts for + * devices that do not support mapped pinned memory. The failure is deferred + * to ::cuMemHostGetDevicePointer() because the memory may be mapped into + * other CUDA contexts via the ::CU_MEMHOSTALLOC_PORTABLE flag. + * + * The memory allocated by this function must be freed with ::cuMemFreeHost(). + * + * Note all host memory allocated using ::cuMemHostAlloc() will automatically + * be immediately accessible to all contexts on all devices which support unified + * addressing (as may be queried using ::CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING). + * Unless the flag ::CU_MEMHOSTALLOC_WRITECOMBINED is specified, the device pointer + * that may be used to access this host memory from those contexts is always equal + * to the returned host pointer \p *pp. If the flag ::CU_MEMHOSTALLOC_WRITECOMBINED + * is specified, then the function ::cuMemHostGetDevicePointer() must be used + * to query the device pointer, even if the context supports unified addressing. + * See \ref CUDA_UNIFIED for additional details. + * + * \param pp - Returned pointer to host memory + * \param bytesize - Requested allocation size in bytes + * \param Flags - Flags for allocation request + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaHostAlloc + */ +CUresult CUDAAPI cuMemHostAlloc(void **pp, size_t bytesize, unsigned int Flags); + +/** + * \brief Passes back device pointer of mapped pinned memory + * + * Passes back the device pointer \p pdptr corresponding to the mapped, pinned + * host buffer \p p allocated by ::cuMemHostAlloc. + * + * ::cuMemHostGetDevicePointer() will fail if the ::CU_MEMHOSTALLOC_DEVICEMAP + * flag was not specified at the time the memory was allocated, or if the + * function is called on a GPU that does not support mapped pinned memory. + * + * For devices that have a non-zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_HOST_POINTER_FOR_REGISTERED_MEM, the memory + * can also be accessed from the device using the host pointer \p p. + * The device pointer returned by ::cuMemHostGetDevicePointer() may or may not + * match the original host pointer \p p and depends on the devices visible to the + * application. If all devices visible to the application have a non-zero value for the + * device attribute, the device pointer returned by ::cuMemHostGetDevicePointer() + * will match the original pointer \p p. If any device visible to the application + * has a zero value for the device attribute, the device pointer returned by + * ::cuMemHostGetDevicePointer() will not match the original host pointer \p p, + * but it will be suitable for use on all devices provided Unified Virtual Addressing + * is enabled. In such systems, it is valid to access the memory using either pointer + * on devices that have a non-zero value for the device attribute. Note however that + * such devices should access the memory using only one of the two pointers and not both. + * + * \p Flags provides for future releases. For now, it must be set to 0. + * + * \param pdptr - Returned device pointer + * \param p - Host pointer + * \param Flags - Options (must be 0) + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaHostGetDevicePointer + */ +CUresult CUDAAPI cuMemHostGetDevicePointer(CUdeviceptr *pdptr, void *p, unsigned int Flags); + +/** + * \brief Passes back flags that were used for a pinned allocation + * + * Passes back the flags \p pFlags that were specified when allocating + * the pinned host buffer \p p allocated by ::cuMemHostAlloc. + * + * ::cuMemHostGetFlags() will fail if the pointer does not reside in + * an allocation performed by ::cuMemAllocHost() or ::cuMemHostAlloc(). + * + * \param pFlags - Returned flags word + * \param p - Host pointer + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuMemAllocHost, + * ::cuMemHostAlloc, + * ::cudaHostGetFlags + */ +CUresult CUDAAPI cuMemHostGetFlags(unsigned int *pFlags, void *p); + +/** + * \brief Allocates memory that will be automatically managed by the Unified Memory system + * + * Allocates \p bytesize bytes of managed memory on the device and returns in + * \p *dptr a pointer to the allocated memory. If the device doesn't support + * allocating managed memory, ::CUDA_ERROR_NOT_SUPPORTED is returned. Support + * for managed memory can be queried using the device attribute + * ::CU_DEVICE_ATTRIBUTE_MANAGED_MEMORY. The allocated memory is suitably + * aligned for any kind of variable. The memory is not cleared. If \p bytesize + * is 0, ::cuMemAllocManaged returns ::CUDA_ERROR_INVALID_VALUE. The pointer + * is valid on the CPU and on all GPUs in the system that support managed memory. + * All accesses to this pointer must obey the Unified Memory programming model. + * + * \p flags specifies the default stream association for this allocation. + * \p flags must be one of ::CU_MEM_ATTACH_GLOBAL or ::CU_MEM_ATTACH_HOST. If + * ::CU_MEM_ATTACH_GLOBAL is specified, then this memory is accessible from + * any stream on any device. If ::CU_MEM_ATTACH_HOST is specified, then the + * allocation should not be accessed from devices that have a zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS; an explicit call to + * ::cuStreamAttachMemAsync will be required to enable access on such devices. + * + * If the association is later changed via ::cuStreamAttachMemAsync to + * a single stream, the default association as specified during ::cuMemAllocManaged + * is restored when that stream is destroyed. For __managed__ variables, the + * default association is always ::CU_MEM_ATTACH_GLOBAL. Note that destroying a + * stream is an asynchronous operation, and as a result, the change to default + * association won't happen until all work in the stream has completed. + * + * Memory allocated with ::cuMemAllocManaged should be released with ::cuMemFree. + * + * Device memory oversubscription is possible for GPUs that have a non-zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. Managed memory on + * such GPUs may be evicted from device memory to host memory at any time by the Unified + * Memory driver in order to make room for other allocations. + * + * In a system where all GPUs have a non-zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS, managed memory may not be populated when this + * API returns and instead may be populated on access. In such systems, managed memory can + * migrate to any processor's memory at any time. The Unified Memory driver will employ heuristics to + * maintain data locality and prevent excessive page faults to the extent possible. The application + * can also guide the driver about memory usage patterns via ::cuMemAdvise. The application + * can also explicitly migrate memory to a desired processor's memory via + * ::cuMemPrefetchAsync. + * + * In a multi-GPU system where all of the GPUs have a zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS and all the GPUs have peer-to-peer support + * with each other, the physical storage for managed memory is created on the GPU which is active + * at the time ::cuMemAllocManaged is called. All other GPUs will reference the data at reduced + * bandwidth via peer mappings over the PCIe bus. The Unified Memory driver does not migrate + * memory among such GPUs. + * + * In a multi-GPU system where not all GPUs have peer-to-peer support with each other and + * where the value of the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS + * is zero for at least one of those GPUs, the location chosen for physical storage of managed + * memory is system-dependent. + * - On Linux, the location chosen will be device memory as long as the current set of active + * contexts are on devices that either have peer-to-peer support with each other or have a + * non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * If there is an active context on a GPU that does not have a non-zero value for that device + * attribute and it does not have peer-to-peer support with the other devices that have active + * contexts on them, then the location for physical storage will be 'zero-copy' or host memory. + * Note that this means that managed memory that is located in device memory is migrated to + * host memory if a new context is created on a GPU that doesn't have a non-zero value for + * the device attribute and does not support peer-to-peer with at least one of the other devices + * that has an active context. This in turn implies that context creation may fail if there is + * insufficient host memory to migrate all managed allocations. + * - On Windows, the physical storage is always created in 'zero-copy' or host memory. + * All GPUs will reference the data at reduced bandwidth over the PCIe bus. In these + * circumstances, use of the environment variable CUDA_VISIBLE_DEVICES is recommended to + * restrict CUDA to only use those GPUs that have peer-to-peer support. + * Alternatively, users can also set CUDA_MANAGED_FORCE_DEVICE_ALLOC to a + * non-zero value to force the driver to always use device memory for physical storage. + * When this environment variable is set to a non-zero value, all contexts created in + * that process on devices that support managed memory have to be peer-to-peer compatible + * with each other. Context creation will fail if a context is created on a device that + * supports managed memory and is not peer-to-peer compatible with any of the other + * managed memory supporting devices on which contexts were previously created, even if + * those contexts have been destroyed. These environment variables are described + * in the CUDA programming guide under the "CUDA environment variables" section. + * - On ARM, managed memory is not available on discrete gpu with Drive PX-2. + * + * \param dptr - Returned device pointer + * \param bytesize - Requested allocation size in bytes + * \param flags - Must be one of ::CU_MEM_ATTACH_GLOBAL or ::CU_MEM_ATTACH_HOST + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cuDeviceGetAttribute, ::cuStreamAttachMemAsync, + * ::cudaMallocManaged + */ +CUresult CUDAAPI cuMemAllocManaged(CUdeviceptr *dptr, size_t bytesize, unsigned int flags); + +/** +* \brief Registers a callback function to receive async notifications +* +* Registers \p callbackFunc to receive async notifications. +* +* The \p userData parameter is passed to the callback function at async notification time. +* Likewise, \p callback is also passed to the callback function to distinguish between +* multiple registered callbacks. +* +* The callback function being registered should be designed to return quickly (~10ms). +* Any long running tasks should be queued for execution on an application thread. +* +* Callbacks may not call cuDeviceRegisterAsyncNotification or cuDeviceUnregisterAsyncNotification. +* Doing so will result in ::CUDA_ERROR_NOT_PERMITTED. Async notification callbacks execute +* in an undefined order and may be serialized. +* +* Returns in \p *callback a handle representing the registered callback instance. +* +* \param device - The device on which to register the callback +* \param callbackFunc - The function to register as a callback +* \param userData - A generic pointer to user data. This is passed into the callback function. +* \param callback - A handle representing the registered callback instance +* +* \return +* ::CUDA_SUCCESS +* ::CUDA_ERROR_NOT_SUPPORTED +* ::CUDA_ERROR_INVALID_DEVICE +* ::CUDA_ERROR_INVALID_VALUE +* ::CUDA_ERROR_NOT_PERMITTED +* ::CUDA_ERROR_UNKNOWN +* \notefnerr +* +* \sa +* ::cuDeviceUnregisterAsyncNotification +*/ +CUresult CUDAAPI cuDeviceRegisterAsyncNotification(CUdevice device, CUasyncCallback callbackFunc, void *userData, CUasyncCallbackHandle *callback); + +/** +* \brief Unregisters an async notification callback +* +* Unregisters \p callback so that the corresponding callback function will stop receiving +* async notifications. +* +* \param device - The device from which to remove \p callback. +* \param callback - The callback instance to unregister from receiving async notifications. +* +* \return +* ::CUDA_SUCCESS +* ::CUDA_ERROR_NOT_SUPPORTED +* ::CUDA_ERROR_INVALID_DEVICE +* ::CUDA_ERROR_INVALID_VALUE +* ::CUDA_ERROR_NOT_PERMITTED +* ::CUDA_ERROR_UNKNOWN +* \notefnerr +* +* \sa +* ::cuDeviceRegisterAsyncNotification +*/ +CUresult CUDAAPI cuDeviceUnregisterAsyncNotification(CUdevice device, CUasyncCallbackHandle callback); + +/** + * \brief Returns a handle to a compute device + * + * Returns in \p *device a device handle given a PCI bus ID string. + * + * \param dev - Returned device handle + * + * \param pciBusId - String in one of the following forms: + * [domain]:[bus]:[device].[function] + * [domain]:[bus]:[device] + * [bus]:[device].[function] + * where \p domain, \p bus, \p device, and \p function are all hexadecimal values + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGet, + * ::cuDeviceGetAttribute, + * ::cuDeviceGetPCIBusId, + * ::cudaDeviceGetByPCIBusId + */ +CUresult CUDAAPI cuDeviceGetByPCIBusId(CUdevice *dev, const char *pciBusId); + +/** + * \brief Returns a PCI Bus Id string for the device + * + * Returns an ASCII string identifying the device \p dev in the NULL-terminated + * string pointed to by \p pciBusId. \p len specifies the maximum length of the + * string that may be returned. + * + * \param pciBusId - Returned identifier string for the device in the following format + * [domain]:[bus]:[device].[function] + * where \p domain, \p bus, \p device, and \p function are all hexadecimal values. + * pciBusId should be large enough to store 13 characters including the NULL-terminator. + * + * \param len - Maximum length of string to store in \p name + * + * \param dev - Device to get identifier string for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuDeviceGet, + * ::cuDeviceGetAttribute, + * ::cuDeviceGetByPCIBusId, + * ::cudaDeviceGetPCIBusId + */ +CUresult CUDAAPI cuDeviceGetPCIBusId(char *pciBusId, int len, CUdevice dev); + +/** + * \brief Gets an interprocess handle for a previously allocated event + * + * Takes as input a previously allocated event. This event must have been + * created with the ::CU_EVENT_INTERPROCESS and ::CU_EVENT_DISABLE_TIMING + * flags set. This opaque handle may be copied into other processes and + * opened with ::cuIpcOpenEventHandle to allow efficient hardware + * synchronization between GPU work in different processes. + * + * After the event has been opened in the importing process, + * ::cuEventRecord, ::cuEventSynchronize, ::cuStreamWaitEvent and + * ::cuEventQuery may be used in either process. Performing operations + * on the imported event after the exported event has been freed + * with ::cuEventDestroy will result in undefined behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode + * Users can test their device for IPC functionality by calling + * ::cuapiDeviceGetAttribute with ::CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED + * + * \param pHandle - Pointer to a user allocated CUipcEventHandle + * in which to return the opaque event handle + * \param event - Event allocated with ::CU_EVENT_INTERPROCESS and + * ::CU_EVENT_DISABLE_TIMING flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_MAP_FAILED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuEventCreate, + * ::cuEventDestroy, + * ::cuEventSynchronize, + * ::cuEventQuery, + * ::cuStreamWaitEvent, + * ::cuIpcOpenEventHandle, + * ::cuIpcGetMemHandle, + * ::cuIpcOpenMemHandle, + * ::cuIpcCloseMemHandle, + * ::cudaIpcGetEventHandle + */ +CUresult CUDAAPI cuIpcGetEventHandle(CUipcEventHandle *pHandle, CUevent event); + +/** + * \brief Opens an interprocess event handle for use in the current process + * + * Opens an interprocess event handle exported from another process with + * ::cuIpcGetEventHandle. This function returns a ::CUevent that behaves like + * a locally created event with the ::CU_EVENT_DISABLE_TIMING flag specified. + * This event must be freed with ::cuEventDestroy. + * + * Performing operations on the imported event after the exported event has + * been freed with ::cuEventDestroy will result in undefined behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode + * Users can test their device for IPC functionality by calling + * ::cuapiDeviceGetAttribute with ::CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED + * + * \param phEvent - Returns the imported event + * \param handle - Interprocess handle to open + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_MAP_FAILED, + * ::CUDA_ERROR_PEER_ACCESS_UNSUPPORTED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuEventCreate, + * ::cuEventDestroy, + * ::cuEventSynchronize, + * ::cuEventQuery, + * ::cuStreamWaitEvent, + * ::cuIpcGetEventHandle, + * ::cuIpcGetMemHandle, + * ::cuIpcOpenMemHandle, + * ::cuIpcCloseMemHandle, + * ::cudaIpcOpenEventHandle + */ +CUresult CUDAAPI cuIpcOpenEventHandle(CUevent *phEvent, CUipcEventHandle handle); + +/** + * \brief Gets an interprocess memory handle for an existing device memory + * allocation + * + * Takes a pointer to the base of an existing device memory allocation created + * with ::cuMemAlloc and exports it for use in another process. This is a + * lightweight operation and may be called multiple times on an allocation + * without adverse effects. + * + * If a region of memory is freed with ::cuMemFree and a subsequent call + * to ::cuMemAlloc returns memory with the same device address, + * ::cuIpcGetMemHandle will return a unique handle for the + * new memory. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode + * Users can test their device for IPC functionality by calling + * ::cuapiDeviceGetAttribute with ::CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED + * + * \param pHandle - Pointer to user allocated ::CUipcMemHandle to return + * the handle in. + * \param dptr - Base pointer to previously allocated device memory + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_MAP_FAILED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuMemAlloc, + * ::cuMemFree, + * ::cuIpcGetEventHandle, + * ::cuIpcOpenEventHandle, + * ::cuIpcOpenMemHandle, + * ::cuIpcCloseMemHandle, + * ::cudaIpcGetMemHandle + */ +CUresult CUDAAPI cuIpcGetMemHandle(CUipcMemHandle *pHandle, CUdeviceptr dptr); + +/** + * \brief Opens an interprocess memory handle exported from another process + * and returns a device pointer usable in the local process. + * + * Maps memory exported from another process with ::cuIpcGetMemHandle into + * the current device address space. For contexts on different devices + * ::cuIpcOpenMemHandle can attempt to enable peer access between the + * devices as if the user called ::cuCtxEnablePeerAccess. This behavior is + * controlled by the ::CU_IPC_MEM_LAZY_ENABLE_PEER_ACCESS flag. + * ::cuDeviceCanAccessPeer can determine if a mapping is possible. + * + * Contexts that may open ::CUipcMemHandles are restricted in the following way. + * ::CUipcMemHandles from each ::CUdevice in a given process may only be opened + * by one ::CUcontext per ::CUdevice per other process. + * + * If the memory handle has already been opened by the current context, the + * reference count on the handle is incremented by 1 and the existing device pointer + * is returned. + * + * Memory returned from ::cuIpcOpenMemHandle must be freed with + * ::cuIpcCloseMemHandle. + * + * Calling ::cuMemFree on an exported memory region before calling + * ::cuIpcCloseMemHandle in the importing context will result in undefined + * behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode + * Users can test their device for IPC functionality by calling + * ::cuapiDeviceGetAttribute with ::CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED + * + * \param pdptr - Returned device pointer + * \param handle - ::CUipcMemHandle to open + * \param Flags - Flags for this operation. Must be specified as ::CU_IPC_MEM_LAZY_ENABLE_PEER_ACCESS + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_MAP_FAILED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_TOO_MANY_PEERS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \note No guarantees are made about the address returned in \p *pdptr. + * In particular, multiple processes may not receive the same address for the same \p handle. + * + * \sa + * ::cuMemAlloc, + * ::cuMemFree, + * ::cuIpcGetEventHandle, + * ::cuIpcOpenEventHandle, + * ::cuIpcGetMemHandle, + * ::cuIpcCloseMemHandle, + * ::cuCtxEnablePeerAccess, + * ::cuDeviceCanAccessPeer, + * ::cudaIpcOpenMemHandle + */ +CUresult CUDAAPI cuIpcOpenMemHandle(CUdeviceptr *pdptr, CUipcMemHandle handle, unsigned int Flags); + +/** + * \brief Attempts to close memory mapped with ::cuIpcOpenMemHandle + * + * Decrements the reference count of the memory returned by ::cuIpcOpenMemHandle by 1. + * When the reference count reaches 0, this API unmaps the memory. The original allocation + * in the exporting process as well as imported mappings in other processes + * will be unaffected. + * + * Any resources used to enable peer access will be freed if this is the + * last mapping using them. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode + * Users can test their device for IPC functionality by calling + * ::cuapiDeviceGetAttribute with ::CU_DEVICE_ATTRIBUTE_IPC_EVENT_SUPPORTED + * + * \param dptr - Device pointer returned by ::cuIpcOpenMemHandle + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_MAP_FAILED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \sa + * ::cuMemAlloc, + * ::cuMemFree, + * ::cuIpcGetEventHandle, + * ::cuIpcOpenEventHandle, + * ::cuIpcGetMemHandle, + * ::cuIpcOpenMemHandle, + * ::cudaIpcCloseMemHandle + */ +CUresult CUDAAPI cuIpcCloseMemHandle(CUdeviceptr dptr); + +/** + * \brief Registers an existing host memory range for use by CUDA + * + * Page-locks the memory range specified by \p p and \p bytesize and maps it + * for the device(s) as specified by \p Flags. This memory range also is added + * to the same tracking mechanism as ::cuMemHostAlloc to automatically accelerate + * calls to functions such as ::cuMemcpyHtoD(). Since the memory can be accessed + * directly by the device, it can be read or written with much higher bandwidth + * than pageable memory that has not been registered. Page-locking excessive + * amounts of memory may degrade system performance, since it reduces the amount + * of memory available to the system for paging. As a result, this function is + * best used sparingly to register staging areas for data exchange between + * host and device. + * + * On systems where ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES + * is true, ::cuMemHostRegister will not page-lock the memory range specified + * by \p ptr but only populate unpopulated pages. + * + * The \p Flags parameter enables different options to be specified that + * affect the allocation, as follows. + * + * - ::CU_MEMHOSTREGISTER_PORTABLE: The memory returned by this call will be + * considered as pinned memory by all CUDA contexts, not just the one that + * performed the allocation. + * + * - ::CU_MEMHOSTREGISTER_DEVICEMAP: Maps the allocation into the CUDA address + * space. The device pointer to the memory may be obtained by calling + * ::cuMemHostGetDevicePointer(). + * + * - ::CU_MEMHOSTREGISTER_IOMEMORY: The pointer is treated as pointing to some + * I/O memory space, e.g. the PCI Express resource of a 3rd party device. + * + * - ::CU_MEMHOSTREGISTER_READ_ONLY: The pointer is treated as pointing to memory + * that is considered read-only by the device. On platforms without + * ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, this flag is + * required in order to register memory mapped to the CPU as read-only. Support + * for the use of this flag can be queried from the device attribute + * ::CU_DEVICE_ATTRIBUTE_READ_ONLY_HOST_REGISTER_SUPPORTED. Using this flag with + * a current context associated with a device that does not have this attribute + * set will cause ::cuMemHostRegister to error with CUDA_ERROR_NOT_SUPPORTED. + * + * All of these flags are orthogonal to one another: a developer may page-lock + * memory that is portable or mapped with no restrictions. + * + * The ::CU_MEMHOSTREGISTER_DEVICEMAP flag may be specified on CUDA contexts for + * devices that do not support mapped pinned memory. The failure is deferred + * to ::cuMemHostGetDevicePointer() because the memory may be mapped into + * other CUDA contexts via the ::CU_MEMHOSTREGISTER_PORTABLE flag. + * + * For devices that have a non-zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_HOST_POINTER_FOR_REGISTERED_MEM, the memory + * can also be accessed from the device using the host pointer \p p. + * The device pointer returned by ::cuMemHostGetDevicePointer() may or may not + * match the original host pointer \p ptr and depends on the devices visible to the + * application. If all devices visible to the application have a non-zero value for the + * device attribute, the device pointer returned by ::cuMemHostGetDevicePointer() + * will match the original pointer \p ptr. If any device visible to the application + * has a zero value for the device attribute, the device pointer returned by + * ::cuMemHostGetDevicePointer() will not match the original host pointer \p ptr, + * but it will be suitable for use on all devices provided Unified Virtual Addressing + * is enabled. In such systems, it is valid to access the memory using either pointer + * on devices that have a non-zero value for the device attribute. Note however that + * such devices should access the memory using only of the two pointers and not both. + * + * The memory page-locked by this function must be unregistered with + * ::cuMemHostUnregister(). + * + * \param p - Host pointer to memory to page-lock + * \param bytesize - Size in bytes of the address range to page-lock + * \param Flags - Flags for allocation request + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_HOST_MEMORY_ALREADY_REGISTERED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa + * ::cuMemHostUnregister, + * ::cuMemHostGetFlags, + * ::cuMemHostGetDevicePointer, + * ::cudaHostRegister + */ +CUresult CUDAAPI cuMemHostRegister(void *p, size_t bytesize, unsigned int Flags); + +/** + * \brief Unregisters a memory range that was registered with cuMemHostRegister. + * + * Unmaps the memory range whose base address is specified by \p p, and makes + * it pageable again. + * + * The base address must be the same one specified to ::cuMemHostRegister(). + * + * \param p - Host pointer to memory to unregister + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_HOST_MEMORY_NOT_REGISTERED, + * \notefnerr + * + * \sa + * ::cuMemHostRegister, + * ::cudaHostUnregister + */ +CUresult CUDAAPI cuMemHostUnregister(void *p); + +/** + * \brief Copies memory + * + * Copies data between two pointers. + * \p dst and \p src are base pointers of the destination and source, respectively. + * \p ByteCount specifies the number of bytes to copy. + * Note that this function infers the type of the transfer (host to host, host to + * device, device to device, or device to host) from the pointer values. This + * function is only allowed in contexts which support unified addressing. + * + * \param dst - Destination unified virtual address space pointer + * \param src - Source unified virtual address space pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy, + * ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol + */ +CUresult CUDAAPI cuMemcpy(CUdeviceptr dst, CUdeviceptr src, size_t ByteCount); + +/** + * \brief Copies device memory between two contexts + * + * Copies from device memory in one context to device memory in another + * context. \p dstDevice is the base device pointer of the destination memory + * and \p dstContext is the destination context. \p srcDevice is the base + * device pointer of the source memory and \p srcContext is the source pointer. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param dstContext - Destination context + * \param srcDevice - Source device pointer + * \param srcContext - Source context + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuMemcpyDtoD, ::cuMemcpy3DPeer, ::cuMemcpyDtoDAsync, ::cuMemcpyPeerAsync, + * ::cuMemcpy3DPeerAsync, + * ::cudaMemcpyPeer + */ +CUresult CUDAAPI cuMemcpyPeer(CUdeviceptr dstDevice, CUcontext dstContext, CUdeviceptr srcDevice, CUcontext srcContext, size_t ByteCount); + +/** + * \brief Copies memory from Host to Device + * + * Copies from host memory to device memory. \p dstDevice and \p srcHost are + * the base addresses of the destination and source, respectively. \p ByteCount + * specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param srcHost - Source host pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy, + * ::cudaMemcpyToSymbol + */ +CUresult CUDAAPI cuMemcpyHtoD(CUdeviceptr dstDevice, const void *srcHost, size_t ByteCount); + +/** + * \brief Copies memory from Device to Host + * + * Copies from device to host memory. \p dstHost and \p srcDevice specify the + * base pointers of the destination and source, respectively. \p ByteCount + * specifies the number of bytes to copy. + * + * \param dstHost - Destination host pointer + * \param srcDevice - Source device pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy, + * ::cudaMemcpyFromSymbol + */ +CUresult CUDAAPI cuMemcpyDtoH(void *dstHost, CUdeviceptr srcDevice, size_t ByteCount); + +/** + * \brief Copies memory from Device to Device + * + * Copies from device memory to device memory. \p dstDevice and \p srcDevice + * are the base pointers of the destination and source, respectively. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param srcDevice - Source device pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy, + * ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol + */ +CUresult CUDAAPI cuMemcpyDtoD(CUdeviceptr dstDevice, CUdeviceptr srcDevice, size_t ByteCount); + +/** + * \brief Copies memory from Device to Array + * + * Copies from device memory to a 1D CUDA array. \p dstArray and \p dstOffset + * specify the CUDA array handle and starting index of the destination data. + * \p srcDevice specifies the base pointer of the source. \p ByteCount + * specifies the number of bytes to copy. + * + * \param dstArray - Destination array + * \param dstOffset - Offset in bytes of destination array + * \param srcDevice - Source device pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpyToArray + */ +CUresult CUDAAPI cuMemcpyDtoA(CUarray dstArray, size_t dstOffset, CUdeviceptr srcDevice, size_t ByteCount); + +/** + * \brief Copies memory from Array to Device + * + * Copies from one 1D CUDA array to device memory. \p dstDevice specifies the + * base pointer of the destination and must be naturally aligned with the CUDA + * array elements. \p srcArray and \p srcOffset specify the CUDA array handle + * and the offset in bytes into the array where the copy is to begin. + * \p ByteCount specifies the number of bytes to copy and must be evenly + * divisible by the array element size. + * + * \param dstDevice - Destination device pointer + * \param srcArray - Source array + * \param srcOffset - Offset in bytes of source array + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpyFromArray + */ +CUresult CUDAAPI cuMemcpyAtoD(CUdeviceptr dstDevice, CUarray srcArray, size_t srcOffset, size_t ByteCount); + +/** + * \brief Copies memory from Host to Array + * + * Copies from host memory to a 1D CUDA array. \p dstArray and \p dstOffset + * specify the CUDA array handle and starting offset in bytes of the destination + * data. \p pSrc specifies the base address of the source. \p ByteCount specifies + * the number of bytes to copy. + * + * \param dstArray - Destination array + * \param dstOffset - Offset in bytes of destination array + * \param srcHost - Source host pointer + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpyToArray + */ +CUresult CUDAAPI cuMemcpyHtoA(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount); + +/** + * \brief Copies memory from Array to Host + * + * Copies from one 1D CUDA array to host memory. \p dstHost specifies the base + * pointer of the destination. \p srcArray and \p srcOffset specify the CUDA + * array handle and starting offset in bytes of the source data. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstHost - Destination device pointer + * \param srcArray - Source array + * \param srcOffset - Offset in bytes of source array + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpyFromArray + */ +CUresult CUDAAPI cuMemcpyAtoH(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount); + +/** + * \brief Copies memory from Array to Array + * + * Copies from one 1D CUDA array to another. \p dstArray and \p srcArray + * specify the handles of the destination and source CUDA arrays for the copy, + * respectively. \p dstOffset and \p srcOffset specify the destination and + * source offsets in bytes into the CUDA arrays. \p ByteCount is the number of + * bytes to be copied. The size of the elements in the CUDA arrays need not be + * the same format, but the elements must be the same size; and count must be + * evenly divisible by that size. + * + * \param dstArray - Destination array + * \param dstOffset - Offset in bytes of destination array + * \param srcArray - Source array + * \param srcOffset - Offset in bytes of source array + * \param ByteCount - Size of memory copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpyArrayToArray + */ +CUresult CUDAAPI cuMemcpyAtoA(CUarray dstArray, size_t dstOffset, CUarray srcArray, size_t srcOffset, size_t ByteCount); + +/** + * \brief Copies memory for 2D arrays + * + * Perform a 2D memory copy according to the parameters specified in \p pCopy. + * The ::CUDA_MEMCPY2D structure is defined as: + * + * \code + typedef struct CUDA_MEMCPY2D_st { + unsigned int srcXInBytes, srcY; + CUmemorytype srcMemoryType; + const void *srcHost; + CUdeviceptr srcDevice; + CUarray srcArray; + unsigned int srcPitch; + + unsigned int dstXInBytes, dstY; + CUmemorytype dstMemoryType; + void *dstHost; + CUdeviceptr dstDevice; + CUarray dstArray; + unsigned int dstPitch; + + unsigned int WidthInBytes; + unsigned int Height; + } CUDA_MEMCPY2D; + * \endcode + * where: + * - ::srcMemoryType and ::dstMemoryType specify the type of memory of the + * source and destination, respectively; ::CUmemorytype_enum is defined as: + * + * \code + typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, + CU_MEMORYTYPE_DEVICE = 0x02, + CU_MEMORYTYPE_ARRAY = 0x03, + CU_MEMORYTYPE_UNIFIED = 0x04 + } CUmemorytype; + * \endcode + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::srcDevice and ::srcPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::srcArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_HOST, ::srcHost and ::srcPitch + * specify the (host) base address of the source data and the bytes per row to + * apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_DEVICE, ::srcDevice and ::srcPitch + * specify the (device) base address of the source data and the bytes per row + * to apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_ARRAY, ::srcArray specifies the + * handle of the source data. ::srcHost, ::srcDevice and ::srcPitch are + * ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_HOST, ::dstHost and ::dstPitch + * specify the (host) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::dstDevice and ::dstPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::dstArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_DEVICE, ::dstDevice and ::dstPitch + * specify the (device) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_ARRAY, ::dstArray specifies the + * handle of the destination data. ::dstHost, ::dstDevice and ::dstPitch are + * ignored. + * + * - ::srcXInBytes and ::srcY specify the base address of the source data for + * the copy. + * + * \par + * For host pointers, the starting address is + * \code + void* Start = (void*)((char*)srcHost+srcY*srcPitch + srcXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr Start = srcDevice+srcY*srcPitch+srcXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::srcXInBytes must be evenly divisible by the array + * element size. + * + * - ::dstXInBytes and ::dstY specify the base address of the destination data + * for the copy. + * + * \par + * For host pointers, the base address is + * \code + void* dstStart = (void*)((char*)dstHost+dstY*dstPitch + dstXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr dstStart = dstDevice+dstY*dstPitch+dstXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::dstXInBytes must be evenly divisible by the array + * element size. + * + * - ::WidthInBytes and ::Height specify the width (in bytes) and height of + * the 2D copy being performed. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * + * \par + * ::cuMemcpy2D() returns an error if any pitch is greater than the maximum + * allowed (::CU_DEVICE_ATTRIBUTE_MAX_PITCH). ::cuMemAllocPitch() passes back + * pitches that always work with ::cuMemcpy2D(). On intra-device memory copies + * (device to device, CUDA array to device, CUDA array to CUDA array), + * ::cuMemcpy2D() may fail for pitches not computed by ::cuMemAllocPitch(). + * ::cuMemcpy2DUnaligned() does not have this restriction, but may run + * significantly slower in the cases where ::cuMemcpy2D() would have returned + * an error code. + * + * \param pCopy - Parameters for the memory copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, + * ::cudaMemcpy2DFromArray + */ +CUresult CUDAAPI cuMemcpy2D(const CUDA_MEMCPY2D *pCopy); + +/** + * \brief Copies memory for 2D arrays + * + * Perform a 2D memory copy according to the parameters specified in \p pCopy. + * The ::CUDA_MEMCPY2D structure is defined as: + * + * \code + typedef struct CUDA_MEMCPY2D_st { + unsigned int srcXInBytes, srcY; + CUmemorytype srcMemoryType; + const void *srcHost; + CUdeviceptr srcDevice; + CUarray srcArray; + unsigned int srcPitch; + unsigned int dstXInBytes, dstY; + CUmemorytype dstMemoryType; + void *dstHost; + CUdeviceptr dstDevice; + CUarray dstArray; + unsigned int dstPitch; + unsigned int WidthInBytes; + unsigned int Height; + } CUDA_MEMCPY2D; + * \endcode + * where: + * - ::srcMemoryType and ::dstMemoryType specify the type of memory of the + * source and destination, respectively; ::CUmemorytype_enum is defined as: + * + * \code + typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, + CU_MEMORYTYPE_DEVICE = 0x02, + CU_MEMORYTYPE_ARRAY = 0x03, + CU_MEMORYTYPE_UNIFIED = 0x04 + } CUmemorytype; + * \endcode + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::srcDevice and ::srcPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::srcArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_HOST, ::srcHost and ::srcPitch + * specify the (host) base address of the source data and the bytes per row to + * apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_DEVICE, ::srcDevice and ::srcPitch + * specify the (device) base address of the source data and the bytes per row + * to apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_ARRAY, ::srcArray specifies the + * handle of the source data. ::srcHost, ::srcDevice and ::srcPitch are + * ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::dstDevice and ::dstPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::dstArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_HOST, ::dstHost and ::dstPitch + * specify the (host) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_DEVICE, ::dstDevice and ::dstPitch + * specify the (device) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_ARRAY, ::dstArray specifies the + * handle of the destination data. ::dstHost, ::dstDevice and ::dstPitch are + * ignored. + * + * - ::srcXInBytes and ::srcY specify the base address of the source data for + * the copy. + * + * \par + * For host pointers, the starting address is + * \code + void* Start = (void*)((char*)srcHost+srcY*srcPitch + srcXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr Start = srcDevice+srcY*srcPitch+srcXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::srcXInBytes must be evenly divisible by the array + * element size. + * + * - ::dstXInBytes and ::dstY specify the base address of the destination data + * for the copy. + * + * \par + * For host pointers, the base address is + * \code + void* dstStart = (void*)((char*)dstHost+dstY*dstPitch + dstXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr dstStart = dstDevice+dstY*dstPitch+dstXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::dstXInBytes must be evenly divisible by the array + * element size. + * + * - ::WidthInBytes and ::Height specify the width (in bytes) and height of + * the 2D copy being performed. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * + * \par + * ::cuMemcpy2D() returns an error if any pitch is greater than the maximum + * allowed (::CU_DEVICE_ATTRIBUTE_MAX_PITCH). ::cuMemAllocPitch() passes back + * pitches that always work with ::cuMemcpy2D(). On intra-device memory copies + * (device to device, CUDA array to device, CUDA array to CUDA array), + * ::cuMemcpy2D() may fail for pitches not computed by ::cuMemAllocPitch(). + * ::cuMemcpy2DUnaligned() does not have this restriction, but may run + * significantly slower in the cases where ::cuMemcpy2D() would have returned + * an error code. + * + * \param pCopy - Parameters for the memory copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, + * ::cudaMemcpy2DFromArray + */ +CUresult CUDAAPI cuMemcpy2DUnaligned(const CUDA_MEMCPY2D *pCopy); + +/** + * \brief Copies memory for 3D arrays + * + * Perform a 3D memory copy according to the parameters specified in + * \p pCopy. The ::CUDA_MEMCPY3D structure is defined as: + * + * \code + typedef struct CUDA_MEMCPY3D_st { + + unsigned int srcXInBytes, srcY, srcZ; + unsigned int srcLOD; + CUmemorytype srcMemoryType; + const void *srcHost; + CUdeviceptr srcDevice; + CUarray srcArray; + unsigned int srcPitch; // ignored when src is array + unsigned int srcHeight; // ignored when src is array; may be 0 if Depth==1 + + unsigned int dstXInBytes, dstY, dstZ; + unsigned int dstLOD; + CUmemorytype dstMemoryType; + void *dstHost; + CUdeviceptr dstDevice; + CUarray dstArray; + unsigned int dstPitch; // ignored when dst is array + unsigned int dstHeight; // ignored when dst is array; may be 0 if Depth==1 + + unsigned int WidthInBytes; + unsigned int Height; + unsigned int Depth; + } CUDA_MEMCPY3D; + * \endcode + * where: + * - ::srcMemoryType and ::dstMemoryType specify the type of memory of the + * source and destination, respectively; ::CUmemorytype_enum is defined as: + * + * \code + typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, + CU_MEMORYTYPE_DEVICE = 0x02, + CU_MEMORYTYPE_ARRAY = 0x03, + CU_MEMORYTYPE_UNIFIED = 0x04 + } CUmemorytype; + * \endcode + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::srcDevice and ::srcPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::srcArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_HOST, ::srcHost, ::srcPitch and + * ::srcHeight specify the (host) base address of the source data, the bytes + * per row, and the height of each 2D slice of the 3D array. ::srcArray is + * ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_DEVICE, ::srcDevice, ::srcPitch and + * ::srcHeight specify the (device) base address of the source data, the bytes + * per row, and the height of each 2D slice of the 3D array. ::srcArray is + * ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_ARRAY, ::srcArray specifies the + * handle of the source data. ::srcHost, ::srcDevice, ::srcPitch and + * ::srcHeight are ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::dstDevice and ::dstPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::dstArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_HOST, ::dstHost and ::dstPitch + * specify the (host) base address of the destination data, the bytes per row, + * and the height of each 2D slice of the 3D array. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_DEVICE, ::dstDevice and ::dstPitch + * specify the (device) base address of the destination data, the bytes per + * row, and the height of each 2D slice of the 3D array. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_ARRAY, ::dstArray specifies the + * handle of the destination data. ::dstHost, ::dstDevice, ::dstPitch and + * ::dstHeight are ignored. + * + * - ::srcXInBytes, ::srcY and ::srcZ specify the base address of the source + * data for the copy. + * + * \par + * For host pointers, the starting address is + * \code + void* Start = (void*)((char*)srcHost+(srcZ*srcHeight+srcY)*srcPitch + srcXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr Start = srcDevice+(srcZ*srcHeight+srcY)*srcPitch+srcXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::srcXInBytes must be evenly divisible by the array + * element size. + * + * - dstXInBytes, ::dstY and ::dstZ specify the base address of the + * destination data for the copy. + * + * \par + * For host pointers, the base address is + * \code + void* dstStart = (void*)((char*)dstHost+(dstZ*dstHeight+dstY)*dstPitch + dstXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr dstStart = dstDevice+(dstZ*dstHeight+dstY)*dstPitch+dstXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::dstXInBytes must be evenly divisible by the array + * element size. + * + * - ::WidthInBytes, ::Height and ::Depth specify the width (in bytes), height + * and depth of the 3D copy being performed. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * - If specified, ::srcHeight must be greater than or equal to ::Height + + * ::srcY, and ::dstHeight must be greater than or equal to ::Height + ::dstY. + * + * \par + * ::cuMemcpy3D() returns an error if any pitch is greater than the maximum + * allowed (::CU_DEVICE_ATTRIBUTE_MAX_PITCH). + * + * The ::srcLOD and ::dstLOD members of the ::CUDA_MEMCPY3D structure must be + * set to 0. + * + * \param pCopy - Parameters for the memory copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMemcpy3D + */ +CUresult CUDAAPI cuMemcpy3D(const CUDA_MEMCPY3D *pCopy); + +/** + * \brief Copies memory between contexts + * + * Perform a 3D memory copy according to the parameters specified in + * \p pCopy. See the definition of the ::CUDA_MEMCPY3D_PEER structure + * for documentation of its parameters. + * + * \param pCopy - Parameters for the memory copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_sync + * + * \sa ::cuMemcpyDtoD, ::cuMemcpyPeer, ::cuMemcpyDtoDAsync, ::cuMemcpyPeerAsync, + * ::cuMemcpy3DPeerAsync, + * ::cudaMemcpy3DPeer + */ +CUresult CUDAAPI cuMemcpy3DPeer(const CUDA_MEMCPY3D_PEER *pCopy); + +/** + * \brief Copies memory asynchronously + * + * Copies data between two pointers. + * \p dst and \p src are base pointers of the destination and source, respectively. + * \p ByteCount specifies the number of bytes to copy. + * Note that this function infers the type of the transfer (host to host, host to + * device, device to device, or device to host) from the pointer values. This + * function is only allowed in contexts which support unified addressing. + * + * \param dst - Destination unified virtual address space pointer + * \param src - Source unified virtual address space pointer + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyAsync, + * ::cudaMemcpyToSymbolAsync, + * ::cudaMemcpyFromSymbolAsync + */ +CUresult CUDAAPI cuMemcpyAsync(CUdeviceptr dst, CUdeviceptr src, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies device memory between two contexts asynchronously. + * + * Copies from device memory in one context to device memory in another + * context. \p dstDevice is the base device pointer of the destination memory + * and \p dstContext is the destination context. \p srcDevice is the base + * device pointer of the source memory and \p srcContext is the source pointer. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param dstContext - Destination context + * \param srcDevice - Source device pointer + * \param srcContext - Source context + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpyDtoD, ::cuMemcpyPeer, ::cuMemcpy3DPeer, ::cuMemcpyDtoDAsync, + * ::cuMemcpy3DPeerAsync, + * ::cudaMemcpyPeerAsync + */ +CUresult CUDAAPI cuMemcpyPeerAsync(CUdeviceptr dstDevice, CUcontext dstContext, CUdeviceptr srcDevice, CUcontext srcContext, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory from Host to Device + * + * Copies from host memory to device memory. \p dstDevice and \p srcHost are + * the base addresses of the destination and source, respectively. \p ByteCount + * specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param srcHost - Source host pointer + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyAsync, + * ::cudaMemcpyToSymbolAsync + */ +CUresult CUDAAPI cuMemcpyHtoDAsync(CUdeviceptr dstDevice, const void *srcHost, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory from Device to Host + * + * Copies from device to host memory. \p dstHost and \p srcDevice specify the + * base pointers of the destination and source, respectively. \p ByteCount + * specifies the number of bytes to copy. + * + * \param dstHost - Destination host pointer + * \param srcDevice - Source device pointer + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyAsync, + * ::cudaMemcpyFromSymbolAsync + */ +CUresult CUDAAPI cuMemcpyDtoHAsync(void *dstHost, CUdeviceptr srcDevice, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory from Device to Device + * + * Copies from device memory to device memory. \p dstDevice and \p srcDevice + * are the base pointers of the destination and source, respectively. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstDevice - Destination device pointer + * \param srcDevice - Source device pointer + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyAsync, + * ::cudaMemcpyToSymbolAsync, + * ::cudaMemcpyFromSymbolAsync + */ +CUresult CUDAAPI cuMemcpyDtoDAsync(CUdeviceptr dstDevice, CUdeviceptr srcDevice, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory from Host to Array + * + * Copies from host memory to a 1D CUDA array. \p dstArray and \p dstOffset + * specify the CUDA array handle and starting offset in bytes of the + * destination data. \p srcHost specifies the base address of the source. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstArray - Destination array + * \param dstOffset - Offset in bytes of destination array + * \param srcHost - Source host pointer + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyToArrayAsync + */ +CUresult CUDAAPI cuMemcpyHtoAAsync(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory from Array to Host + * + * Copies from one 1D CUDA array to host memory. \p dstHost specifies the base + * pointer of the destination. \p srcArray and \p srcOffset specify the CUDA + * array handle and starting offset in bytes of the source data. + * \p ByteCount specifies the number of bytes to copy. + * + * \param dstHost - Destination pointer + * \param srcArray - Source array + * \param srcOffset - Offset in bytes of source array + * \param ByteCount - Size of memory copy in bytes + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * \note_memcpy + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpyFromArrayAsync + */ +CUresult CUDAAPI cuMemcpyAtoHAsync(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount, CUstream hStream); + +/** + * \brief Copies memory for 2D arrays + * + * Perform a 2D memory copy according to the parameters specified in \p pCopy. + * The ::CUDA_MEMCPY2D structure is defined as: + * + * \code + typedef struct CUDA_MEMCPY2D_st { + unsigned int srcXInBytes, srcY; + CUmemorytype srcMemoryType; + const void *srcHost; + CUdeviceptr srcDevice; + CUarray srcArray; + unsigned int srcPitch; + unsigned int dstXInBytes, dstY; + CUmemorytype dstMemoryType; + void *dstHost; + CUdeviceptr dstDevice; + CUarray dstArray; + unsigned int dstPitch; + unsigned int WidthInBytes; + unsigned int Height; + } CUDA_MEMCPY2D; + * \endcode + * where: + * - ::srcMemoryType and ::dstMemoryType specify the type of memory of the + * source and destination, respectively; ::CUmemorytype_enum is defined as: + * + * \code + typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, + CU_MEMORYTYPE_DEVICE = 0x02, + CU_MEMORYTYPE_ARRAY = 0x03, + CU_MEMORYTYPE_UNIFIED = 0x04 + } CUmemorytype; + * \endcode + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_HOST, ::srcHost and ::srcPitch + * specify the (host) base address of the source data and the bytes per row to + * apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::srcDevice and ::srcPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::srcArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_DEVICE, ::srcDevice and ::srcPitch + * specify the (device) base address of the source data and the bytes per row + * to apply. ::srcArray is ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_ARRAY, ::srcArray specifies the + * handle of the source data. ::srcHost, ::srcDevice and ::srcPitch are + * ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::dstDevice and ::dstPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::dstArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_HOST, ::dstHost and ::dstPitch + * specify the (host) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_DEVICE, ::dstDevice and ::dstPitch + * specify the (device) base address of the destination data and the bytes per + * row to apply. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_ARRAY, ::dstArray specifies the + * handle of the destination data. ::dstHost, ::dstDevice and ::dstPitch are + * ignored. + * + * - ::srcXInBytes and ::srcY specify the base address of the source data for + * the copy. + * + * \par + * For host pointers, the starting address is + * \code + void* Start = (void*)((char*)srcHost+srcY*srcPitch + srcXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr Start = srcDevice+srcY*srcPitch+srcXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::srcXInBytes must be evenly divisible by the array + * element size. + * + * - ::dstXInBytes and ::dstY specify the base address of the destination data + * for the copy. + * + * \par + * For host pointers, the base address is + * \code + void* dstStart = (void*)((char*)dstHost+dstY*dstPitch + dstXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr dstStart = dstDevice+dstY*dstPitch+dstXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::dstXInBytes must be evenly divisible by the array + * element size. + * + * - ::WidthInBytes and ::Height specify the width (in bytes) and height of + * the 2D copy being performed. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * - If specified, ::srcHeight must be greater than or equal to ::Height + + * ::srcY, and ::dstHeight must be greater than or equal to ::Height + ::dstY. + * + * \par + * ::cuMemcpy2DAsync() returns an error if any pitch is greater than the maximum + * allowed (::CU_DEVICE_ATTRIBUTE_MAX_PITCH). ::cuMemAllocPitch() passes back + * pitches that always work with ::cuMemcpy2D(). On intra-device memory copies + * (device to device, CUDA array to device, CUDA array to CUDA array), + * ::cuMemcpy2DAsync() may fail for pitches not computed by ::cuMemAllocPitch(). + * + * \param pCopy - Parameters for the memory copy + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync + */ +CUresult CUDAAPI cuMemcpy2DAsync(const CUDA_MEMCPY2D *pCopy, CUstream hStream); + +/** + * \brief Copies memory for 3D arrays + * + * Perform a 3D memory copy according to the parameters specified in + * \p pCopy. The ::CUDA_MEMCPY3D structure is defined as: + * + * \code + typedef struct CUDA_MEMCPY3D_st { + + unsigned int srcXInBytes, srcY, srcZ; + unsigned int srcLOD; + CUmemorytype srcMemoryType; + const void *srcHost; + CUdeviceptr srcDevice; + CUarray srcArray; + unsigned int srcPitch; // ignored when src is array + unsigned int srcHeight; // ignored when src is array; may be 0 if Depth==1 + + unsigned int dstXInBytes, dstY, dstZ; + unsigned int dstLOD; + CUmemorytype dstMemoryType; + void *dstHost; + CUdeviceptr dstDevice; + CUarray dstArray; + unsigned int dstPitch; // ignored when dst is array + unsigned int dstHeight; // ignored when dst is array; may be 0 if Depth==1 + + unsigned int WidthInBytes; + unsigned int Height; + unsigned int Depth; + } CUDA_MEMCPY3D; + * \endcode + * where: + * - ::srcMemoryType and ::dstMemoryType specify the type of memory of the + * source and destination, respectively; ::CUmemorytype_enum is defined as: + * + * \code + typedef enum CUmemorytype_enum { + CU_MEMORYTYPE_HOST = 0x01, + CU_MEMORYTYPE_DEVICE = 0x02, + CU_MEMORYTYPE_ARRAY = 0x03, + CU_MEMORYTYPE_UNIFIED = 0x04 + } CUmemorytype; + * \endcode + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::srcDevice and ::srcPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::srcArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_HOST, ::srcHost, ::srcPitch and + * ::srcHeight specify the (host) base address of the source data, the bytes + * per row, and the height of each 2D slice of the 3D array. ::srcArray is + * ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_DEVICE, ::srcDevice, ::srcPitch and + * ::srcHeight specify the (device) base address of the source data, the bytes + * per row, and the height of each 2D slice of the 3D array. ::srcArray is + * ignored. + * + * \par + * If ::srcMemoryType is ::CU_MEMORYTYPE_ARRAY, ::srcArray specifies the + * handle of the source data. ::srcHost, ::srcDevice, ::srcPitch and + * ::srcHeight are ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_UNIFIED, ::dstDevice and ::dstPitch + * specify the (unified virtual address space) base address of the source data + * and the bytes per row to apply. ::dstArray is ignored. + * This value may be used only if unified addressing is supported in the calling + * context. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_HOST, ::dstHost and ::dstPitch + * specify the (host) base address of the destination data, the bytes per row, + * and the height of each 2D slice of the 3D array. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_DEVICE, ::dstDevice and ::dstPitch + * specify the (device) base address of the destination data, the bytes per + * row, and the height of each 2D slice of the 3D array. ::dstArray is ignored. + * + * \par + * If ::dstMemoryType is ::CU_MEMORYTYPE_ARRAY, ::dstArray specifies the + * handle of the destination data. ::dstHost, ::dstDevice, ::dstPitch and + * ::dstHeight are ignored. + * + * - ::srcXInBytes, ::srcY and ::srcZ specify the base address of the source + * data for the copy. + * + * \par + * For host pointers, the starting address is + * \code + void* Start = (void*)((char*)srcHost+(srcZ*srcHeight+srcY)*srcPitch + srcXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr Start = srcDevice+(srcZ*srcHeight+srcY)*srcPitch+srcXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::srcXInBytes must be evenly divisible by the array + * element size. + * + * - dstXInBytes, ::dstY and ::dstZ specify the base address of the + * destination data for the copy. + * + * \par + * For host pointers, the base address is + * \code + void* dstStart = (void*)((char*)dstHost+(dstZ*dstHeight+dstY)*dstPitch + dstXInBytes); + * \endcode + * + * \par + * For device pointers, the starting address is + * \code + CUdeviceptr dstStart = dstDevice+(dstZ*dstHeight+dstY)*dstPitch+dstXInBytes; + * \endcode + * + * \par + * For CUDA arrays, ::dstXInBytes must be evenly divisible by the array + * element size. + * + * - ::WidthInBytes, ::Height and ::Depth specify the width (in bytes), height + * and depth of the 3D copy being performed. + * - If specified, ::srcPitch must be greater than or equal to ::WidthInBytes + + * ::srcXInBytes, and ::dstPitch must be greater than or equal to + * ::WidthInBytes + dstXInBytes. + * - If specified, ::srcHeight must be greater than or equal to ::Height + + * ::srcY, and ::dstHeight must be greater than or equal to ::Height + ::dstY. + * + * \par + * ::cuMemcpy3DAsync() returns an error if any pitch is greater than the maximum + * allowed (::CU_DEVICE_ATTRIBUTE_MAX_PITCH). + * + * The ::srcLOD and ::dstLOD members of the ::CUDA_MEMCPY3D structure must be + * set to 0. + * + * \param pCopy - Parameters for the memory copy + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemcpy3DAsync + */ +CUresult CUDAAPI cuMemcpy3DAsync(const CUDA_MEMCPY3D *pCopy, CUstream hStream); + +/** + * \brief Copies memory between contexts asynchronously. + * + * Perform a 3D memory copy according to the parameters specified in + * \p pCopy. See the definition of the ::CUDA_MEMCPY3D_PEER structure + * for documentation of its parameters. + * + * \param pCopy - Parameters for the memory copy + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpyDtoD, ::cuMemcpyPeer, ::cuMemcpyDtoDAsync, ::cuMemcpyPeerAsync, + * ::cuMemcpy3DPeerAsync, + * ::cudaMemcpy3DPeerAsync + */ +CUresult CUDAAPI cuMemcpy3DPeerAsync(const CUDA_MEMCPY3D_PEER *pCopy, CUstream hStream); + +/** + * \brief Initializes device memory + * + * Sets the memory range of \p N 8-bit values to the specified value + * \p uc. + * + * \param dstDevice - Destination device pointer + * \param uc - Value to set + * \param N - Number of elements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset + */ +CUresult CUDAAPI cuMemsetD8(CUdeviceptr dstDevice, unsigned char uc, size_t N); + +/** + * \brief Initializes device memory + * + * Sets the memory range of \p N 16-bit values to the specified value + * \p us. The \p dstDevice pointer must be two byte aligned. + * + * \param dstDevice - Destination device pointer + * \param us - Value to set + * \param N - Number of elements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset + */ +CUresult CUDAAPI cuMemsetD16(CUdeviceptr dstDevice, unsigned short us, size_t N); + +/** + * \brief Initializes device memory + * + * Sets the memory range of \p N 32-bit values to the specified value + * \p ui. The \p dstDevice pointer must be four byte aligned. + * + * \param dstDevice - Destination device pointer + * \param ui - Value to set + * \param N - Number of elements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32Async, + * ::cudaMemset + */ +CUresult CUDAAPI cuMemsetD32(CUdeviceptr dstDevice, unsigned int ui, size_t N); + +/** + * \brief Initializes device memory + * + * Sets the 2D memory range of \p Width 8-bit values to the specified value + * \p uc. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param uc - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2D + */ +CUresult CUDAAPI cuMemsetD2D8(CUdeviceptr dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height); + +/** + * \brief Initializes device memory + * + * Sets the 2D memory range of \p Width 16-bit values to the specified value + * \p us. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. The \p dstDevice pointer + * and \p dstPitch offset must be two byte aligned. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param us - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2D + */ +CUresult CUDAAPI cuMemsetD2D16(CUdeviceptr dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height); + +/** + * \brief Initializes device memory + * + * Sets the 2D memory range of \p Width 32-bit values to the specified value + * \p ui. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. The \p dstDevice pointer + * and \p dstPitch offset must be four byte aligned. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param ui - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2D + */ +CUresult CUDAAPI cuMemsetD2D32(CUdeviceptr dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height); + +/** + * \brief Sets device memory + * + * Sets the memory range of \p N 8-bit values to the specified value + * \p uc. + * + * \param dstDevice - Destination device pointer + * \param uc - Value to set + * \param N - Number of elements + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemsetAsync + */ +CUresult CUDAAPI cuMemsetD8Async(CUdeviceptr dstDevice, unsigned char uc, size_t N, CUstream hStream); + +/** + * \brief Sets device memory + * + * Sets the memory range of \p N 16-bit values to the specified value + * \p us. The \p dstDevice pointer must be two byte aligned. + * + * \param dstDevice - Destination device pointer + * \param us - Value to set + * \param N - Number of elements + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemsetAsync + */ +CUresult CUDAAPI cuMemsetD16Async(CUdeviceptr dstDevice, unsigned short us, size_t N, CUstream hStream); + +/** + * \brief Sets device memory + * + * Sets the memory range of \p N 32-bit values to the specified value + * \p ui. The \p dstDevice pointer must be four byte aligned. + * + * \param dstDevice - Destination device pointer + * \param ui - Value to set + * \param N - Number of elements + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, ::cuMemsetD32, + * ::cudaMemsetAsync + */ +CUresult CUDAAPI cuMemsetD32Async(CUdeviceptr dstDevice, unsigned int ui, size_t N, CUstream hStream); + +/** + * \brief Sets device memory + * + * Sets the 2D memory range of \p Width 8-bit values to the specified value + * \p uc. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param uc - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2DAsync + */ +CUresult CUDAAPI cuMemsetD2D8Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height, CUstream hStream); + +/** + * \brief Sets device memory + * + * Sets the 2D memory range of \p Width 16-bit values to the specified value + * \p us. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. The \p dstDevice pointer + * and \p dstPitch offset must be two byte aligned. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param us - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D32, ::cuMemsetD2D32Async, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2DAsync + */ +CUresult CUDAAPI cuMemsetD2D16Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height, CUstream hStream); + +/** + * \brief Sets device memory + * + * Sets the 2D memory range of \p Width 32-bit values to the specified value + * \p ui. \p Height specifies the number of rows to set, and \p dstPitch + * specifies the number of bytes between each row. The \p dstDevice pointer + * and \p dstPitch offset must be four byte aligned. This function performs + * fastest when the pitch is one that has been passed back by + * ::cuMemAllocPitch(). + * + * \param dstDevice - Destination device pointer + * \param dstPitch - Pitch of destination device pointer(Unused if \p Height is 1) + * \param ui - Value to set + * \param Width - Width of row + * \param Height - Number of rows + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * \note_memset + * \note_null_stream + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D8Async, + * ::cuMemsetD2D16, ::cuMemsetD2D16Async, ::cuMemsetD2D32, + * ::cuMemsetD8, ::cuMemsetD8Async, ::cuMemsetD16, ::cuMemsetD16Async, + * ::cuMemsetD32, ::cuMemsetD32Async, + * ::cudaMemset2DAsync + */ +CUresult CUDAAPI cuMemsetD2D32Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height, CUstream hStream); + +/** + * \brief Creates a 1D or 2D CUDA array + * + * Creates a CUDA array according to the ::CUDA_ARRAY_DESCRIPTOR structure + * \p pAllocateArray and returns a handle to the new CUDA array in \p *pHandle. + * The ::CUDA_ARRAY_DESCRIPTOR is defined as: + * + * \code + typedef struct { + unsigned int Width; + unsigned int Height; + CUarray_format Format; + unsigned int NumChannels; + } CUDA_ARRAY_DESCRIPTOR; + * \endcode + * where: + * + * - \p Width, and \p Height are the width, and height of the CUDA array (in + * elements); the CUDA array is one-dimensional if height is 0, two-dimensional + * otherwise; + * - ::Format specifies the format of the elements; ::CUarray_format is + * defined as: + * \code + typedef enum CUarray_format_enum { + CU_AD_FORMAT_UNSIGNED_INT8 = 0x01, + CU_AD_FORMAT_UNSIGNED_INT16 = 0x02, + CU_AD_FORMAT_UNSIGNED_INT32 = 0x03, + CU_AD_FORMAT_SIGNED_INT8 = 0x08, + CU_AD_FORMAT_SIGNED_INT16 = 0x09, + CU_AD_FORMAT_SIGNED_INT32 = 0x0a, + CU_AD_FORMAT_HALF = 0x10, + CU_AD_FORMAT_FLOAT = 0x20 + } CUarray_format; + * \endcode + * - \p NumChannels specifies the number of packed components per CUDA array + * element; it may be 1, 2, or 4; + * + * Here are examples of CUDA array descriptions: + * + * Description for a CUDA array of 2048 floats: + * \code + CUDA_ARRAY_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_FLOAT; + desc.NumChannels = 1; + desc.Width = 2048; + desc.Height = 1; + * \endcode + * + * Description for a 64 x 64 CUDA array of floats: + * \code + CUDA_ARRAY_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_FLOAT; + desc.NumChannels = 1; + desc.Width = 64; + desc.Height = 64; + * \endcode + * + * Description for a \p width x \p height CUDA array of 64-bit, 4x16-bit + * float16's: + * \code + CUDA_ARRAY_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_HALF; + desc.NumChannels = 4; + desc.Width = width; + desc.Height = height; + * \endcode + * + * Description for a \p width x \p height CUDA array of 16-bit elements, each + * of which is two 8-bit unsigned chars: + * \code + CUDA_ARRAY_DESCRIPTOR arrayDesc; + desc.Format = CU_AD_FORMAT_UNSIGNED_INT8; + desc.NumChannels = 2; + desc.Width = width; + desc.Height = height; + * \endcode + * + * \param pHandle - Returned array + * \param pAllocateArray - Array descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMallocArray + */ +CUresult CUDAAPI cuArrayCreate(CUarray *pHandle, const CUDA_ARRAY_DESCRIPTOR *pAllocateArray); + +/** + * \brief Get a 1D or 2D CUDA array descriptor + * + * Returns in \p *pArrayDescriptor a descriptor containing information on the + * format and dimensions of the CUDA array \p hArray. It is useful for + * subroutines that have been passed a CUDA array, but need to know the CUDA + * array parameters for validation or other purposes. + * + * \param pArrayDescriptor - Returned array descriptor + * \param hArray - Array to get descriptor of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaArrayGetInfo + */ +CUresult CUDAAPI cuArrayGetDescriptor(CUDA_ARRAY_DESCRIPTOR *pArrayDescriptor, CUarray hArray); + +/** + * \brief Returns the layout properties of a sparse CUDA array + * + * Returns the layout properties of a sparse CUDA array in \p sparseProperties + * If the CUDA array is not allocated with flag ::CUDA_ARRAY3D_SPARSE + * ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * If the returned value in ::CUDA_ARRAY_SPARSE_PROPERTIES::flags contains ::CU_ARRAY_SPARSE_PROPERTIES_SINGLE_MIPTAIL, + * then ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailSize represents the total size of the array. Otherwise, it will be zero. + * Also, the returned value in ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailFirstLevel is always zero. + * Note that the \p array must have been allocated using ::cuArrayCreate or ::cuArray3DCreate. For CUDA arrays obtained + * using ::cuMipmappedArrayGetLevel, ::CUDA_ERROR_INVALID_VALUE will be returned. Instead, ::cuMipmappedArrayGetSparseProperties + * must be used to obtain the sparse properties of the entire CUDA mipmapped array to which \p array belongs to. + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_INVALID_VALUE + * + * \param[out] sparseProperties - Pointer to ::CUDA_ARRAY_SPARSE_PROPERTIES + * \param[in] array - CUDA array to get the sparse properties of + * \sa ::cuMipmappedArrayGetSparseProperties, ::cuMemMapArrayAsync + */ +CUresult CUDAAPI cuArrayGetSparseProperties(CUDA_ARRAY_SPARSE_PROPERTIES *sparseProperties, CUarray array); + +/** + * \brief Returns the layout properties of a sparse CUDA mipmapped array + * + * Returns the sparse array layout properties in \p sparseProperties + * If the CUDA mipmapped array is not allocated with flag ::CUDA_ARRAY3D_SPARSE + * ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * For non-layered CUDA mipmapped arrays, ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailSize returns the + * size of the mip tail region. The mip tail region includes all mip levels whose width, height or depth + * is less than that of the tile. + * For layered CUDA mipmapped arrays, if ::CUDA_ARRAY_SPARSE_PROPERTIES::flags contains ::CU_ARRAY_SPARSE_PROPERTIES_SINGLE_MIPTAIL, + * then ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailSize specifies the size of the mip tail of all layers combined. + * Otherwise, ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailSize specifies mip tail size per layer. + * The returned value of ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailFirstLevel is valid only if ::CUDA_ARRAY_SPARSE_PROPERTIES::miptailSize is non-zero. + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_INVALID_VALUE + * + * \param[out] sparseProperties - Pointer to ::CUDA_ARRAY_SPARSE_PROPERTIES + * \param[in] mipmap - CUDA mipmapped array to get the sparse properties of + * \sa ::cuArrayGetSparseProperties, ::cuMemMapArrayAsync + */ +CUresult CUDAAPI cuMipmappedArrayGetSparseProperties(CUDA_ARRAY_SPARSE_PROPERTIES *sparseProperties, CUmipmappedArray mipmap); + +/** + * \brief Returns the memory requirements of a CUDA array + * + * Returns the memory requirements of a CUDA array in \p memoryRequirements + * If the CUDA array is not allocated with flag ::CUDA_ARRAY3D_DEFERRED_MAPPING + * ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * The returned value in ::CUDA_ARRAY_MEMORY_REQUIREMENTS::size + * represents the total size of the CUDA array. + * The returned value in ::CUDA_ARRAY_MEMORY_REQUIREMENTS::alignment + * represents the alignment necessary for mapping the CUDA array. + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_INVALID_VALUE + * + * \param[out] memoryRequirements - Pointer to ::CUDA_ARRAY_MEMORY_REQUIREMENTS + * \param[in] array - CUDA array to get the memory requirements of + * \param[in] device - Device to get the memory requirements for + * \sa ::cuMipmappedArrayGetMemoryRequirements, ::cuMemMapArrayAsync + */ +CUresult CUDAAPI cuArrayGetMemoryRequirements(CUDA_ARRAY_MEMORY_REQUIREMENTS *memoryRequirements, CUarray array, CUdevice device); + +/** + * \brief Returns the memory requirements of a CUDA mipmapped array + * + * Returns the memory requirements of a CUDA mipmapped array in \p memoryRequirements + * If the CUDA mipmapped array is not allocated with flag ::CUDA_ARRAY3D_DEFERRED_MAPPING + * ::CUDA_ERROR_INVALID_VALUE will be returned. + * + * The returned value in ::CUDA_ARRAY_MEMORY_REQUIREMENTS::size + * represents the total size of the CUDA mipmapped array. + * The returned value in ::CUDA_ARRAY_MEMORY_REQUIREMENTS::alignment + * represents the alignment necessary for mapping the CUDA mipmapped + * array. + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_INVALID_VALUE + * + * \param[out] memoryRequirements - Pointer to ::CUDA_ARRAY_MEMORY_REQUIREMENTS + * \param[in] mipmap - CUDA mipmapped array to get the memory requirements of + * \param[in] device - Device to get the memory requirements for + * \sa ::cuArrayGetMemoryRequirements, ::cuMemMapArrayAsync + */ +CUresult CUDAAPI cuMipmappedArrayGetMemoryRequirements(CUDA_ARRAY_MEMORY_REQUIREMENTS *memoryRequirements, CUmipmappedArray mipmap, CUdevice device); + +/** + * \brief Gets a CUDA array plane from a CUDA array + * + * Returns in \p pPlaneArray a CUDA array that represents a single format plane + * of the CUDA array \p hArray. + * + * If \p planeIdx is greater than the maximum number of planes in this array or if the array does + * not have a multi-planar format e.g: ::CU_AD_FORMAT_NV12, then ::CUDA_ERROR_INVALID_VALUE is returned. + * + * Note that if the \p hArray has format ::CU_AD_FORMAT_NV12, then passing in 0 for \p planeIdx returns + * a CUDA array of the same size as \p hArray but with one channel and ::CU_AD_FORMAT_UNSIGNED_INT8 as its format. + * If 1 is passed for \p planeIdx, then the returned CUDA array has half the height and width + * of \p hArray with two channels and ::CU_AD_FORMAT_UNSIGNED_INT8 as its format. + * + * \param pPlaneArray - Returned CUDA array referenced by the \p planeIdx + * \param hArray - Multiplanar CUDA array + * \param planeIdx - Plane index + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::cuArrayCreate, + * ::cudaArrayGetPlane + */ +CUresult CUDAAPI cuArrayGetPlane(CUarray *pPlaneArray, CUarray hArray, unsigned int planeIdx); + +/** + * \brief Destroys a CUDA array + * + * Destroys the CUDA array \p hArray. + * + * \param hArray - Array to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ARRAY_IS_MAPPED, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaFreeArray + */ +CUresult CUDAAPI cuArrayDestroy(CUarray hArray); + +/** + * \brief Creates a 3D CUDA array + * + * Creates a CUDA array according to the ::CUDA_ARRAY3D_DESCRIPTOR structure + * \p pAllocateArray and returns a handle to the new CUDA array in \p *pHandle. + * The ::CUDA_ARRAY3D_DESCRIPTOR is defined as: + * + * \code + typedef struct { + unsigned int Width; + unsigned int Height; + unsigned int Depth; + CUarray_format Format; + unsigned int NumChannels; + unsigned int Flags; + } CUDA_ARRAY3D_DESCRIPTOR; + * \endcode + * where: + * + * - \p Width, \p Height, and \p Depth are the width, height, and depth of the + * CUDA array (in elements); the following types of CUDA arrays can be allocated: + * - A 1D array is allocated if \p Height and \p Depth extents are both zero. + * - A 2D array is allocated if only \p Depth extent is zero. + * - A 3D array is allocated if all three extents are non-zero. + * - A 1D layered CUDA array is allocated if only \p Height is zero and the + * ::CUDA_ARRAY3D_LAYERED flag is set. Each layer is a 1D array. The number + * of layers is determined by the depth extent. + * - A 2D layered CUDA array is allocated if all three extents are non-zero and + * the ::CUDA_ARRAY3D_LAYERED flag is set. Each layer is a 2D array. The number + * of layers is determined by the depth extent. + * - A cubemap CUDA array is allocated if all three extents are non-zero and the + * ::CUDA_ARRAY3D_CUBEMAP flag is set. \p Width must be equal to \p Height, and + * \p Depth must be six. A cubemap is a special type of 2D layered CUDA array, + * where the six layers represent the six faces of a cube. The order of the six + * layers in memory is the same as that listed in ::CUarray_cubemap_face. + * - A cubemap layered CUDA array is allocated if all three extents are non-zero, + * and both, ::CUDA_ARRAY3D_CUBEMAP and ::CUDA_ARRAY3D_LAYERED flags are set. + * \p Width must be equal to \p Height, and \p Depth must be a multiple of six. + * A cubemap layered CUDA array is a special type of 2D layered CUDA array that + * consists of a collection of cubemaps. The first six layers represent the first + * cubemap, the next six layers form the second cubemap, and so on. + * + * - ::Format specifies the format of the elements; ::CUarray_format is + * defined as: + * \code + typedef enum CUarray_format_enum { + CU_AD_FORMAT_UNSIGNED_INT8 = 0x01, + CU_AD_FORMAT_UNSIGNED_INT16 = 0x02, + CU_AD_FORMAT_UNSIGNED_INT32 = 0x03, + CU_AD_FORMAT_SIGNED_INT8 = 0x08, + CU_AD_FORMAT_SIGNED_INT16 = 0x09, + CU_AD_FORMAT_SIGNED_INT32 = 0x0a, + CU_AD_FORMAT_HALF = 0x10, + CU_AD_FORMAT_FLOAT = 0x20 + } CUarray_format; + * \endcode + * + * - \p NumChannels specifies the number of packed components per CUDA array + * element; it may be 1, 2, or 4; + * + * - ::Flags may be set to + * - ::CUDA_ARRAY3D_LAYERED to enable creation of layered CUDA arrays. If this flag is set, + * \p Depth specifies the number of layers, not the depth of a 3D array. + * - ::CUDA_ARRAY3D_SURFACE_LDST to enable surface references to be bound to the CUDA array. + * If this flag is not set, ::cuSurfRefSetArray will fail when attempting to bind the CUDA array + * to a surface reference. + * - ::CUDA_ARRAY3D_CUBEMAP to enable creation of cubemaps. If this flag is set, \p Width must be + * equal to \p Height, and \p Depth must be six. If the ::CUDA_ARRAY3D_LAYERED flag is also set, + * then \p Depth must be a multiple of six. + * - ::CUDA_ARRAY3D_TEXTURE_GATHER to indicate that the CUDA array will be used for texture gather. + * Texture gather can only be performed on 2D CUDA arrays. + * + * \p Width, \p Height and \p Depth must meet certain size requirements as listed in the following table. + * All values are specified in elements. Note that for brevity's sake, the full name of the device attribute + * is not specified. For ex., TEXTURE1D_WIDTH refers to the device attribute + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_WIDTH. + * + * Note that 2D CUDA arrays have different size requirements if the ::CUDA_ARRAY3D_TEXTURE_GATHER flag + * is set. \p Width and \p Height must not be greater than ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_GATHER_WIDTH + * and ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_GATHER_HEIGHT respectively, in that case. + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + *
CUDA array typeValid extents that must always be met
{(width range in elements), (height range), + * (depth range)}		Valid extents with CUDA_ARRAY3D_SURFACE_LDST set
+ * {(width range in elements), (height range), (depth range)}
1D{ (1,TEXTURE1D_WIDTH), 0, 0 }{ (1,SURFACE1D_WIDTH), 0, 0 }
2D{ (1,TEXTURE2D_WIDTH), (1,TEXTURE2D_HEIGHT), 0 }{ (1,SURFACE2D_WIDTH), (1,SURFACE2D_HEIGHT), 0 }
3D{ (1,TEXTURE3D_WIDTH), (1,TEXTURE3D_HEIGHT), (1,TEXTURE3D_DEPTH) } + *
OR
{ (1,TEXTURE3D_WIDTH_ALTERNATE), (1,TEXTURE3D_HEIGHT_ALTERNATE), + * (1,TEXTURE3D_DEPTH_ALTERNATE) }		{ (1,SURFACE3D_WIDTH), (1,SURFACE3D_HEIGHT), + * (1,SURFACE3D_DEPTH) }
1D Layered{ (1,TEXTURE1D_LAYERED_WIDTH), 0, + * (1,TEXTURE1D_LAYERED_LAYERS) }{ (1,SURFACE1D_LAYERED_WIDTH), 0, + * (1,SURFACE1D_LAYERED_LAYERS) }
2D Layered{ (1,TEXTURE2D_LAYERED_WIDTH), (1,TEXTURE2D_LAYERED_HEIGHT), + * (1,TEXTURE2D_LAYERED_LAYERS) }{ (1,SURFACE2D_LAYERED_WIDTH), (1,SURFACE2D_LAYERED_HEIGHT), + * (1,SURFACE2D_LAYERED_LAYERS) }
Cubemap{ (1,TEXTURECUBEMAP_WIDTH), (1,TEXTURECUBEMAP_WIDTH), 6 }{ (1,SURFACECUBEMAP_WIDTH), + * (1,SURFACECUBEMAP_WIDTH), 6 }
Cubemap Layered{ (1,TEXTURECUBEMAP_LAYERED_WIDTH), (1,TEXTURECUBEMAP_LAYERED_WIDTH), + * (1,TEXTURECUBEMAP_LAYERED_LAYERS) }{ (1,SURFACECUBEMAP_LAYERED_WIDTH), (1,SURFACECUBEMAP_LAYERED_WIDTH), + * (1,SURFACECUBEMAP_LAYERED_LAYERS) }
+ * + * Here are examples of CUDA array descriptions: + * + * Description for a CUDA array of 2048 floats: + * \code + CUDA_ARRAY3D_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_FLOAT; + desc.NumChannels = 1; + desc.Width = 2048; + desc.Height = 0; + desc.Depth = 0; + * \endcode + * + * Description for a 64 x 64 CUDA array of floats: + * \code + CUDA_ARRAY3D_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_FLOAT; + desc.NumChannels = 1; + desc.Width = 64; + desc.Height = 64; + desc.Depth = 0; + * \endcode + * + * Description for a \p width x \p height x \p depth CUDA array of 64-bit, + * 4x16-bit float16's: + * \code + CUDA_ARRAY3D_DESCRIPTOR desc; + desc.Format = CU_AD_FORMAT_HALF; + desc.NumChannels = 4; + desc.Width = width; + desc.Height = height; + desc.Depth = depth; + * \endcode + * + * \param pHandle - Returned array + * \param pAllocateArray - 3D array descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuArray3DGetDescriptor, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaMalloc3DArray + */ +CUresult CUDAAPI cuArray3DCreate(CUarray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR *pAllocateArray); + +/** + * \brief Get a 3D CUDA array descriptor + * + * Returns in \p *pArrayDescriptor a descriptor containing information on the + * format and dimensions of the CUDA array \p hArray. It is useful for + * subroutines that have been passed a CUDA array, but need to know the CUDA + * array parameters for validation or other purposes. + * + * This function may be called on 1D and 2D arrays, in which case the \p Height + * and/or \p Depth members of the descriptor struct will be set to 0. + * + * \param pArrayDescriptor - Returned 3D array descriptor + * \param hArray - 3D array to get descriptor of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * \notefnerr + * + * \sa ::cuArray3DCreate, ::cuArrayCreate, + * ::cuArrayDestroy, ::cuArrayGetDescriptor, ::cuMemAlloc, ::cuMemAllocHost, + * ::cuMemAllocPitch, ::cuMemcpy2D, ::cuMemcpy2DAsync, ::cuMemcpy2DUnaligned, + * ::cuMemcpy3D, ::cuMemcpy3DAsync, ::cuMemcpyAtoA, ::cuMemcpyAtoD, + * ::cuMemcpyAtoH, ::cuMemcpyAtoHAsync, ::cuMemcpyDtoA, ::cuMemcpyDtoD, ::cuMemcpyDtoDAsync, + * ::cuMemcpyDtoH, ::cuMemcpyDtoHAsync, ::cuMemcpyHtoA, ::cuMemcpyHtoAAsync, + * ::cuMemcpyHtoD, ::cuMemcpyHtoDAsync, ::cuMemFree, ::cuMemFreeHost, + * ::cuMemGetAddressRange, ::cuMemGetInfo, ::cuMemHostAlloc, + * ::cuMemHostGetDevicePointer, ::cuMemsetD2D8, ::cuMemsetD2D16, + * ::cuMemsetD2D32, ::cuMemsetD8, ::cuMemsetD16, ::cuMemsetD32, + * ::cudaArrayGetInfo + */ +CUresult CUDAAPI cuArray3DGetDescriptor(CUDA_ARRAY3D_DESCRIPTOR *pArrayDescriptor, CUarray hArray); + +/** + * \brief Creates a CUDA mipmapped array + * + * Creates a CUDA mipmapped array according to the ::CUDA_ARRAY3D_DESCRIPTOR structure + * \p pMipmappedArrayDesc and returns a handle to the new CUDA mipmapped array in \p *pHandle. + * \p numMipmapLevels specifies the number of mipmap levels to be allocated. This value is + * clamped to the range [1, 1 + floor(log2(max(width, height, depth)))]. + * + * The ::CUDA_ARRAY3D_DESCRIPTOR is defined as: + * + * \code + typedef struct { + unsigned int Width; + unsigned int Height; + unsigned int Depth; + CUarray_format Format; + unsigned int NumChannels; + unsigned int Flags; + } CUDA_ARRAY3D_DESCRIPTOR; + * \endcode + * where: + * + * - \p Width, \p Height, and \p Depth are the width, height, and depth of the + * CUDA array (in elements); the following types of CUDA arrays can be allocated: + * - A 1D mipmapped array is allocated if \p Height and \p Depth extents are both zero. + * - A 2D mipmapped array is allocated if only \p Depth extent is zero. + * - A 3D mipmapped array is allocated if all three extents are non-zero. + * - A 1D layered CUDA mipmapped array is allocated if only \p Height is zero and the + * ::CUDA_ARRAY3D_LAYERED flag is set. Each layer is a 1D array. The number + * of layers is determined by the depth extent. + * - A 2D layered CUDA mipmapped array is allocated if all three extents are non-zero and + * the ::CUDA_ARRAY3D_LAYERED flag is set. Each layer is a 2D array. The number + * of layers is determined by the depth extent. + * - A cubemap CUDA mipmapped array is allocated if all three extents are non-zero and the + * ::CUDA_ARRAY3D_CUBEMAP flag is set. \p Width must be equal to \p Height, and + * \p Depth must be six. A cubemap is a special type of 2D layered CUDA array, + * where the six layers represent the six faces of a cube. The order of the six + * layers in memory is the same as that listed in ::CUarray_cubemap_face. + * - A cubemap layered CUDA mipmapped array is allocated if all three extents are non-zero, + * and both, ::CUDA_ARRAY3D_CUBEMAP and ::CUDA_ARRAY3D_LAYERED flags are set. + * \p Width must be equal to \p Height, and \p Depth must be a multiple of six. + * A cubemap layered CUDA array is a special type of 2D layered CUDA array that + * consists of a collection of cubemaps. The first six layers represent the first + * cubemap, the next six layers form the second cubemap, and so on. + * + * - ::Format specifies the format of the elements; ::CUarray_format is + * defined as: + * \code + typedef enum CUarray_format_enum { + CU_AD_FORMAT_UNSIGNED_INT8 = 0x01, + CU_AD_FORMAT_UNSIGNED_INT16 = 0x02, + CU_AD_FORMAT_UNSIGNED_INT32 = 0x03, + CU_AD_FORMAT_SIGNED_INT8 = 0x08, + CU_AD_FORMAT_SIGNED_INT16 = 0x09, + CU_AD_FORMAT_SIGNED_INT32 = 0x0a, + CU_AD_FORMAT_HALF = 0x10, + CU_AD_FORMAT_FLOAT = 0x20 + } CUarray_format; + * \endcode + * + * - \p NumChannels specifies the number of packed components per CUDA array + * element; it may be 1, 2, or 4; + * + * - ::Flags may be set to + * - ::CUDA_ARRAY3D_LAYERED to enable creation of layered CUDA mipmapped arrays. If this flag is set, + * \p Depth specifies the number of layers, not the depth of a 3D array. + * - ::CUDA_ARRAY3D_SURFACE_LDST to enable surface references to be bound to individual mipmap levels of + * the CUDA mipmapped array. If this flag is not set, ::cuSurfRefSetArray will fail when attempting to + * bind a mipmap level of the CUDA mipmapped array to a surface reference. + * - ::CUDA_ARRAY3D_CUBEMAP to enable creation of mipmapped cubemaps. If this flag is set, \p Width must be + * equal to \p Height, and \p Depth must be six. If the ::CUDA_ARRAY3D_LAYERED flag is also set, + * then \p Depth must be a multiple of six. + * - ::CUDA_ARRAY3D_TEXTURE_GATHER to indicate that the CUDA mipmapped array will be used for texture gather. + * Texture gather can only be performed on 2D CUDA mipmapped arrays. + * + * \p Width, \p Height and \p Depth must meet certain size requirements as listed in the following table. + * All values are specified in elements. Note that for brevity's sake, the full name of the device attribute + * is not specified. For ex., TEXTURE1D_MIPMAPPED_WIDTH refers to the device attribute + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_MIPMAPPED_WIDTH. + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + * + *
CUDA array typeValid extents that must always be met
{(width range in elements), (height range), + * (depth range)}		Valid extents with CUDA_ARRAY3D_SURFACE_LDST set
+ * {(width range in elements), (height range), (depth range)}
1D{ (1,TEXTURE1D_MIPMAPPED_WIDTH), 0, 0 }{ (1,SURFACE1D_WIDTH), 0, 0 }
2D{ (1,TEXTURE2D_MIPMAPPED_WIDTH), (1,TEXTURE2D_MIPMAPPED_HEIGHT), 0 }{ (1,SURFACE2D_WIDTH), (1,SURFACE2D_HEIGHT), 0 }
3D{ (1,TEXTURE3D_WIDTH), (1,TEXTURE3D_HEIGHT), (1,TEXTURE3D_DEPTH) } + *
OR
{ (1,TEXTURE3D_WIDTH_ALTERNATE), (1,TEXTURE3D_HEIGHT_ALTERNATE), + * (1,TEXTURE3D_DEPTH_ALTERNATE) }		{ (1,SURFACE3D_WIDTH), (1,SURFACE3D_HEIGHT), + * (1,SURFACE3D_DEPTH) }
1D Layered{ (1,TEXTURE1D_LAYERED_WIDTH), 0, + * (1,TEXTURE1D_LAYERED_LAYERS) }{ (1,SURFACE1D_LAYERED_WIDTH), 0, + * (1,SURFACE1D_LAYERED_LAYERS) }
2D Layered{ (1,TEXTURE2D_LAYERED_WIDTH), (1,TEXTURE2D_LAYERED_HEIGHT), + * (1,TEXTURE2D_LAYERED_LAYERS) }{ (1,SURFACE2D_LAYERED_WIDTH), (1,SURFACE2D_LAYERED_HEIGHT), + * (1,SURFACE2D_LAYERED_LAYERS) }
Cubemap{ (1,TEXTURECUBEMAP_WIDTH), (1,TEXTURECUBEMAP_WIDTH), 6 }{ (1,SURFACECUBEMAP_WIDTH), + * (1,SURFACECUBEMAP_WIDTH), 6 }
Cubemap Layered{ (1,TEXTURECUBEMAP_LAYERED_WIDTH), (1,TEXTURECUBEMAP_LAYERED_WIDTH), + * (1,TEXTURECUBEMAP_LAYERED_LAYERS) }{ (1,SURFACECUBEMAP_LAYERED_WIDTH), (1,SURFACECUBEMAP_LAYERED_WIDTH), + * (1,SURFACECUBEMAP_LAYERED_LAYERS) }
+ * + * + * \param pHandle - Returned mipmapped array + * \param pMipmappedArrayDesc - mipmapped array descriptor + * \param numMipmapLevels - Number of mipmap levels + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cuMipmappedArrayDestroy, + * ::cuMipmappedArrayGetLevel, + * ::cuArrayCreate, + * ::cudaMallocMipmappedArray + */ +CUresult CUDAAPI cuMipmappedArrayCreate(CUmipmappedArray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR *pMipmappedArrayDesc, unsigned int numMipmapLevels); + +/** + * \brief Gets a mipmap level of a CUDA mipmapped array + * + * Returns in \p *pLevelArray a CUDA array that represents a single mipmap level + * of the CUDA mipmapped array \p hMipmappedArray. + * + * If \p level is greater than the maximum number of levels in this mipmapped array, + * ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \param pLevelArray - Returned mipmap level CUDA array + * \param hMipmappedArray - CUDA mipmapped array + * \param level - Mipmap level + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::cuMipmappedArrayCreate, + * ::cuMipmappedArrayDestroy, + * ::cuArrayCreate, + * ::cudaGetMipmappedArrayLevel + */ +CUresult CUDAAPI cuMipmappedArrayGetLevel(CUarray *pLevelArray, CUmipmappedArray hMipmappedArray, unsigned int level); + +/** + * \brief Destroys a CUDA mipmapped array + * + * Destroys the CUDA mipmapped array \p hMipmappedArray. + * + * \param hMipmappedArray - Mipmapped array to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ARRAY_IS_MAPPED, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * \notefnerr + * + * \sa + * ::cuMipmappedArrayCreate, + * ::cuMipmappedArrayGetLevel, + * ::cuArrayCreate, + * ::cudaFreeMipmappedArray + */ +CUresult CUDAAPI cuMipmappedArrayDestroy(CUmipmappedArray hMipmappedArray); + +/** +* \brief Retrieve handle for an address range +* +* Get a handle of the specified type to an address range. The address range +* must have been obtained by a prior call to either ::cuMemAlloc or ::cuMemAddressReserve. +* If the address range was obtained via ::cuMemAddressReserve, it must also be fully mapped via ::cuMemMap. +* The address range must have been obtained by a prior call to either ::cuMemAllocHost or +* ::cuMemHostAlloc on Tegra. +* +* Users must ensure the \p dptr and \p size are aligned to the host page size. +* +* When requesting CUmemRangeHandleType::CU_MEM_RANGE_HANDLE_TYPE_DMA_BUF_FD, +* users are expected to query for dma_buf support for the platform +* by using ::CU_DEVICE_ATTRIBUTE_DMA_BUF_SUPPORTED device attribute before calling +* this API. The \p handle will be interpreted as a pointer to an integer to store the dma_buf file descriptor. +* Users must ensure the entire address range is backed and mapped when +* the address range is allocated by ::cuMemAddressReserve. All the physical +* allocations backing the address range must be resident on the same device and +* have identical allocation properties. Users are also expected to retrieve a +* new handle every time the underlying physical allocation(s) corresponding +* to a previously queried VA range are changed. +* +* \param[out] handle - Pointer to the location where the returned handle will be stored. +* \param[in] dptr - Pointer to a valid CUDA device allocation. Must be aligned to host page size. +* \param[in] size - Length of the address range. Must be aligned to host page size. +* \param[in] handleType - Type of handle requested (defines type and size of the \p handle output parameter) +* \param[in] flags - Reserved, must be zero +* +* \return +* CUDA_SUCCESS +* CUDA_ERROR_INVALID_VALUE +* CUDA_ERROR_NOT_SUPPORTED +*/ +CUresult CUDAAPI cuMemGetHandleForAddressRange(void *handle, CUdeviceptr dptr, size_t size, CUmemRangeHandleType handleType, unsigned long long flags); + +/** @} */ /* END CUDA_MEM */ + +/** + * \defgroup CUDA_VA Virtual Memory Management + * + * ___MANBRIEF___ virtual memory management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the virtual memory management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** +* \brief Allocate an address range reservation. +* +* Reserves a virtual address range based on the given parameters, giving +* the starting address of the range in \p ptr. This API requires a system that +* supports UVA. The size and address parameters must be a multiple of the +* host page size and the alignment must be a power of two or zero for default +* alignment. +* +* \param[out] ptr - Resulting pointer to start of virtual address range allocated +* \param[in] size - Size of the reserved virtual address range requested +* \param[in] alignment - Alignment of the reserved virtual address range requested +* \param[in] addr - Fixed starting address range requested +* \param[in] flags - Currently unused, must be zero +* \return +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_OUT_OF_MEMORY, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemAddressFree +*/ +CUresult CUDAAPI cuMemAddressReserve(CUdeviceptr *ptr, size_t size, size_t alignment, CUdeviceptr addr, unsigned long long flags); + +/** +* \brief Free an address range reservation. +* +* Frees a virtual address range reserved by cuMemAddressReserve. The size +* must match what was given to memAddressReserve and the ptr given must +* match what was returned from memAddressReserve. +* +* \param[in] ptr - Starting address of the virtual address range to free +* \param[in] size - Size of the virtual address region to free +* \return +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemAddressReserve +*/ +CUresult CUDAAPI cuMemAddressFree(CUdeviceptr ptr, size_t size); + +/** +* \brief Create a CUDA memory handle representing a memory allocation of a given size described by the given properties +* +* This creates a memory allocation on the target device specified through the +* \p prop structure. The created allocation will not have any device or host +* mappings. The generic memory \p handle for the allocation can be +* mapped to the address space of calling process via ::cuMemMap. This handle +* cannot be transmitted directly to other processes (see +* ::cuMemExportToShareableHandle). On Windows, the caller must also pass +* an LPSECURITYATTRIBUTE in \p prop to be associated with this handle which +* limits or allows access to this handle for a recipient process (see +* ::CUmemAllocationProp::win32HandleMetaData for more). The \p size of this +* allocation must be a multiple of the the value given via +* ::cuMemGetAllocationGranularity with the ::CU_MEM_ALLOC_GRANULARITY_MINIMUM +* flag. +* To create a CPU allocation targeting a specific host NUMA node, applications must +* set ::CUmemAllocationProp::CUmemLocation::type to ::CU_MEM_LOCATION_TYPE_HOST_NUMA and +* ::CUmemAllocationProp::CUmemLocation::id must specify the NUMA ID of the CPU. +* On systems where NUMA is not available ::CUmemAllocationProp::CUmemLocation::id must be set to 0. +* +* Applications can set ::CUmemAllocationProp::requestedHandleTypes to +* ::CU_MEM_HANDLE_TYPE_FABRIC in order to create allocations suitable for sharing +* within an IMEX domain. An IMEX domain is either an OS instance or a group of securely +* connected OS instances using the NVIDIA IMEX daemon. An IMEX channel is a global resource +* within the IMEX domain that represents a logical entity that aims to provide fine grained +* accessibility control for the participating processes. When exporter and importer CUDA processes +* have been granted access to the same IMEX channel, they can securely share memory. +* If the allocating process does not have access setup for an IMEX channel, attempting to create +* a ::CUmemGenericAllocationHandle with ::CU_MEM_HANDLE_TYPE_FABRIC will result in ::CUDA_ERROR_NOT_PERMITTED. +* The nvidia-modprobe CLI provides more information regarding setting up of IMEX channels. +* +* If ::CUmemAllocationProp::allocFlags::usage contains ::CU_MEM_CREATE_USAGE_TILE_POOL flag then +* the memory allocation is intended only to be used as backing tile pool for sparse CUDA arrays +* and sparse CUDA mipmapped arrays. +* (see ::cuMemMapArrayAsync). +* +* \param[out] handle - Value of handle returned. All operations on this allocation are to be performed using this handle. +* \param[in] size - Size of the allocation requested +* \param[in] prop - Properties of the allocation to create. +* \param[in] flags - flags for future use, must be zero now. +* \return +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_OUT_OF_MEMORY, +* ::CUDA_ERROR_INVALID_DEVICE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* \notefnerr +* +* \sa ::cuMemRelease, ::cuMemExportToShareableHandle, ::cuMemImportFromShareableHandle +*/ +CUresult CUDAAPI cuMemCreate(CUmemGenericAllocationHandle *handle, size_t size, const CUmemAllocationProp *prop, unsigned long long flags); + +/** +* \brief Release a memory handle representing a memory allocation which was previously allocated through cuMemCreate. +* +* Frees the memory that was allocated on a device through cuMemCreate. +* +* The memory allocation will be freed when all outstanding mappings to the memory +* are unmapped and when all outstanding references to the handle (including it's +* shareable counterparts) are also released. The generic memory handle can be +* freed when there are still outstanding mappings made with this handle. Each +* time a recipient process imports a shareable handle, it needs to pair it with +* ::cuMemRelease for the handle to be freed. If \p handle is not a valid handle +* the behavior is undefined. +* +* \param[in] handle Value of handle which was returned previously by cuMemCreate. +* \return +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* \notefnerr +* +* \sa ::cuMemCreate +*/ +CUresult CUDAAPI cuMemRelease(CUmemGenericAllocationHandle handle); + +/** +* \brief Maps an allocation handle to a reserved virtual address range. +* +* Maps bytes of memory represented by \p handle starting from byte \p offset to +* \p size to address range [\p addr, \p addr + \p size]. This range must be an +* address reservation previously reserved with ::cuMemAddressReserve, and +* \p offset + \p size must be less than the size of the memory allocation. +* Both \p ptr, \p size, and \p offset must be a multiple of the value given via +* ::cuMemGetAllocationGranularity with the ::CU_MEM_ALLOC_GRANULARITY_MINIMUM flag. +* If \p handle represents a multicast object, \p ptr, \p size and \p offset must +* be aligned to the value returned by ::cuMulticastGetGranularity with the flag +* ::CU_MULTICAST_MINIMUM_GRANULARITY. For best performance however, it is +* recommended that \p ptr, \p size and \p offset be aligned to the value +* returned by ::cuMulticastGetGranularity with the flag +* ::CU_MULTICAST_RECOMMENDED_GRANULARITY. +* +* Please note calling ::cuMemMap does not make the address accessible, +* the caller needs to update accessibility of a contiguous mapped VA +* range by calling ::cuMemSetAccess. +* +* Once a recipient process obtains a shareable memory handle +* from ::cuMemImportFromShareableHandle, the process must +* use ::cuMemMap to map the memory into its address ranges before +* setting accessibility with ::cuMemSetAccess. +* +* ::cuMemMap can only create mappings on VA range reservations +* that are not currently mapped. +* +* \param[in] ptr - Address where memory will be mapped. +* \param[in] size - Size of the memory mapping. +* \param[in] offset - Offset into the memory represented by +* - \p handle from which to start mapping +* - Note: currently must be zero. +* \param[in] handle - Handle to a shareable memory +* \param[in] flags - flags for future use, must be zero now. +* \return +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_INVALID_DEVICE, +* ::CUDA_ERROR_OUT_OF_MEMORY, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* \notefnerr +* +* \sa ::cuMemUnmap, ::cuMemSetAccess, ::cuMemCreate, ::cuMemAddressReserve, ::cuMemImportFromShareableHandle +*/ +CUresult CUDAAPI cuMemMap(CUdeviceptr ptr, size_t size, size_t offset, CUmemGenericAllocationHandle handle, unsigned long long flags); + +/** + * \brief Maps or unmaps subregions of sparse CUDA arrays and sparse CUDA mipmapped arrays + * + * Performs map or unmap operations on subregions of sparse CUDA arrays and sparse CUDA mipmapped arrays. + * Each operation is specified by a ::CUarrayMapInfo entry in the \p mapInfoList array of size \p count. + * The structure ::CUarrayMapInfo is defined as follow: + \code + typedef struct CUarrayMapInfo_st { + CUresourcetype resourceType; + union { + CUmipmappedArray mipmap; + CUarray array; + } resource; + + CUarraySparseSubresourceType subresourceType; + union { + struct { + unsigned int level; + unsigned int layer; + unsigned int offsetX; + unsigned int offsetY; + unsigned int offsetZ; + unsigned int extentWidth; + unsigned int extentHeight; + unsigned int extentDepth; + } sparseLevel; + struct { + unsigned int layer; + unsigned long long offset; + unsigned long long size; + } miptail; + } subresource; + + CUmemOperationType memOperationType; + + CUmemHandleType memHandleType; + union { + CUmemGenericAllocationHandle memHandle; + } memHandle; + + unsigned long long offset; + unsigned int deviceBitMask; + unsigned int flags; + unsigned int reserved[2]; + } CUarrayMapInfo; + \endcode + * + * where ::CUarrayMapInfo::resourceType specifies the type of resource to be operated on. + * If ::CUarrayMapInfo::resourceType is set to ::CUresourcetype::CU_RESOURCE_TYPE_ARRAY then + * ::CUarrayMapInfo::resource::array must be set to a valid sparse CUDA array handle. + * The CUDA array must be either a 2D, 2D layered or 3D CUDA array and must have been allocated using + * ::cuArrayCreate or ::cuArray3DCreate with the flag ::CUDA_ARRAY3D_SPARSE + * or ::CUDA_ARRAY3D_DEFERRED_MAPPING. + * For CUDA arrays obtained using ::cuMipmappedArrayGetLevel, ::CUDA_ERROR_INVALID_VALUE will be returned. + * If ::CUarrayMapInfo::resourceType is set to ::CUresourcetype::CU_RESOURCE_TYPE_MIPMAPPED_ARRAY + * then ::CUarrayMapInfo::resource::mipmap must be set to a valid sparse CUDA mipmapped array handle. + * The CUDA mipmapped array must be either a 2D, 2D layered or 3D CUDA mipmapped array and must have been + * allocated using ::cuMipmappedArrayCreate with the flag ::CUDA_ARRAY3D_SPARSE + * or ::CUDA_ARRAY3D_DEFERRED_MAPPING. + * + * ::CUarrayMapInfo::subresourceType specifies the type of subresource within the resource. + * ::CUarraySparseSubresourceType_enum is defined as: + \code + typedef enum CUarraySparseSubresourceType_enum { + CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_SPARSE_LEVEL = 0, + CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_MIPTAIL = 1 + } CUarraySparseSubresourceType; + \endcode + * + * where ::CUarraySparseSubresourceType::CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_SPARSE_LEVEL indicates a + * sparse-miplevel which spans at least one tile in every dimension. The remaining miplevels which + * are too small to span at least one tile in any dimension constitute the mip tail region as indicated by + * ::CUarraySparseSubresourceType::CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_MIPTAIL subresource type. + * + * If ::CUarrayMapInfo::subresourceType is set to ::CUarraySparseSubresourceType::CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_SPARSE_LEVEL + * then ::CUarrayMapInfo::subresource::sparseLevel struct must contain valid array subregion offsets and extents. + * The ::CUarrayMapInfo::subresource::sparseLevel::offsetX, ::CUarrayMapInfo::subresource::sparseLevel::offsetY + * and ::CUarrayMapInfo::subresource::sparseLevel::offsetZ must specify valid X, Y and Z offsets respectively. + * The ::CUarrayMapInfo::subresource::sparseLevel::extentWidth, ::CUarrayMapInfo::subresource::sparseLevel::extentHeight + * and ::CUarrayMapInfo::subresource::sparseLevel::extentDepth must specify valid width, height and depth extents respectively. + * These offsets and extents must be aligned to the corresponding tile dimension. + * For CUDA mipmapped arrays ::CUarrayMapInfo::subresource::sparseLevel::level must specify a valid mip level index. Otherwise, + * must be zero. + * For layered CUDA arrays and layered CUDA mipmapped arrays ::CUarrayMapInfo::subresource::sparseLevel::layer must specify a valid layer index. Otherwise, + * must be zero. + * ::CUarrayMapInfo::subresource::sparseLevel::offsetZ must be zero and ::CUarrayMapInfo::subresource::sparseLevel::extentDepth + * must be set to 1 for 2D and 2D layered CUDA arrays and CUDA mipmapped arrays. + * Tile extents can be obtained by calling ::cuArrayGetSparseProperties and ::cuMipmappedArrayGetSparseProperties + * + * If ::CUarrayMapInfo::subresourceType is set to ::CUarraySparseSubresourceType::CU_ARRAY_SPARSE_SUBRESOURCE_TYPE_MIPTAIL + * then ::CUarrayMapInfo::subresource::miptail struct must contain valid mip tail offset in + * ::CUarrayMapInfo::subresource::miptail::offset and size in ::CUarrayMapInfo::subresource::miptail::size. + * Both, mip tail offset and mip tail size must be aligned to the tile size. + * For layered CUDA mipmapped arrays which don't have the flag ::CU_ARRAY_SPARSE_PROPERTIES_SINGLE_MIPTAIL set in ::CUDA_ARRAY_SPARSE_PROPERTIES::flags + * as returned by ::cuMipmappedArrayGetSparseProperties, ::CUarrayMapInfo::subresource::miptail::layer must specify a valid layer index. + * Otherwise, must be zero. + * + * If ::CUarrayMapInfo::resource::array or ::CUarrayMapInfo::resource::mipmap was created with ::CUDA_ARRAY3D_DEFERRED_MAPPING + * flag set the ::CUarrayMapInfo::subresourceType and the contents of ::CUarrayMapInfo::subresource will be ignored. + * + * ::CUarrayMapInfo::memOperationType specifies the type of operation. ::CUmemOperationType is defined as: + \code + typedef enum CUmemOperationType_enum { + CU_MEM_OPERATION_TYPE_MAP = 1, + CU_MEM_OPERATION_TYPE_UNMAP = 2 + } CUmemOperationType; + \endcode + * If ::CUarrayMapInfo::memOperationType is set to ::CUmemOperationType::CU_MEM_OPERATION_TYPE_MAP then the subresource + * will be mapped onto the tile pool memory specified by ::CUarrayMapInfo::memHandle at offset ::CUarrayMapInfo::offset. + * The tile pool allocation has to be created by specifying the ::CU_MEM_CREATE_USAGE_TILE_POOL flag when calling ::cuMemCreate. Also, + * ::CUarrayMapInfo::memHandleType must be set to ::CUmemHandleType::CU_MEM_HANDLE_TYPE_GENERIC. + * + * If ::CUarrayMapInfo::memOperationType is set to ::CUmemOperationType::CU_MEM_OPERATION_TYPE_UNMAP then an unmapping operation + * is performed. ::CUarrayMapInfo::memHandle must be NULL. + * + * ::CUarrayMapInfo::deviceBitMask specifies the list of devices that must map or unmap physical memory. + * Currently, this mask must have exactly one bit set, and the corresponding device must match the device associated with the stream. + * If ::CUarrayMapInfo::memOperationType is set to ::CUmemOperationType::CU_MEM_OPERATION_TYPE_MAP, the device must also match + * the device associated with the tile pool memory allocation as specified by ::CUarrayMapInfo::memHandle. + * + * ::CUarrayMapInfo::flags and ::CUarrayMapInfo::reserved[] are unused and must be set to zero. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * + * \param[in] mapInfoList - List of ::CUarrayMapInfo + * \param[in] count - Count of ::CUarrayMapInfo in \p mapInfoList + * \param[in] hStream - Stream identifier for the stream to use for map or unmap operations + * + * \sa ::cuMipmappedArrayCreate, ::cuArrayCreate, ::cuArray3DCreate, ::cuMemCreate, ::cuArrayGetSparseProperties, ::cuMipmappedArrayGetSparseProperties + */ +CUresult CUDAAPI cuMemMapArrayAsync(CUarrayMapInfo *mapInfoList, unsigned int count, CUstream hStream); + +/** +* \brief Unmap the backing memory of a given address range. +* +* The range must be the entire contiguous address range that was mapped to. In +* other words, ::cuMemUnmap cannot unmap a sub-range of an address range mapped +* by ::cuMemCreate / ::cuMemMap. Any backing memory allocations will be freed +* if there are no existing mappings and there are no unreleased memory handles. +* +* When ::cuMemUnmap returns successfully the address range is converted to an +* address reservation and can be used for a future calls to ::cuMemMap. Any new +* mapping to this virtual address will need to have access granted through +* ::cuMemSetAccess, as all mappings start with no accessibility setup. +* +* \param[in] ptr - Starting address for the virtual address range to unmap +* \param[in] size - Size of the virtual address range to unmap +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* \notefnerr +* \note_sync +* +* \sa ::cuMemCreate, ::cuMemAddressReserve +*/ +CUresult CUDAAPI cuMemUnmap(CUdeviceptr ptr, size_t size); + +/** +* \brief Set the access flags for each location specified in \p desc for the given virtual address range +* +* Given the virtual address range via \p ptr and \p size, and the locations +* in the array given by \p desc and \p count, set the access flags for the +* target locations. The range must be a fully mapped address range +* containing all allocations created by ::cuMemMap / ::cuMemCreate. +* Users cannot specify ::CU_MEM_LOCATION_TYPE_HOST_NUMA accessibility for allocations created on with other location types. +* Note: When ::CUmemAccessDesc::CUmemLocation::type is ::CU_MEM_LOCATION_TYPE_HOST_NUMA, ::CUmemAccessDesc::CUmemLocation::id +* is ignored. +* When setting the access flags for a virtual address range mapping a multicast +* object, \p ptr and \p size must be aligned to the value returned by +* ::cuMulticastGetGranularity with the flag ::CU_MULTICAST_MINIMUM_GRANULARITY. +* For best performance however, it is recommended that \p ptr and \p size be +* aligned to the value returned by ::cuMulticastGetGranularity with the flag +* ::CU_MULTICAST_RECOMMENDED_GRANULARITY. +* +* \param[in] ptr - Starting address for the virtual address range +* \param[in] size - Length of the virtual address range +* \param[in] desc - Array of ::CUmemAccessDesc that describe how to change the +* - mapping for each location specified +* \param[in] count - Number of ::CUmemAccessDesc in \p desc +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_INVALID_DEVICE, +* ::CUDA_ERROR_NOT_SUPPORTED +* \notefnerr +* \note_sync +* +* \sa ::cuMemSetAccess, ::cuMemCreate, :cuMemMap +*/ +CUresult CUDAAPI cuMemSetAccess(CUdeviceptr ptr, size_t size, const CUmemAccessDesc *desc, size_t count); + +/** +* \brief Get the access \p flags set for the given \p location and \p ptr +* +* \param[out] flags - Flags set for this location +* \param[in] location - Location in which to check the flags for +* \param[in] ptr - Address in which to check the access flags for +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_INVALID_DEVICE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemSetAccess +*/ +CUresult CUDAAPI cuMemGetAccess(unsigned long long *flags, const CUmemLocation *location, CUdeviceptr ptr); + +/** +* \brief Exports an allocation to a requested shareable handle type +* +* Given a CUDA memory handle, create a shareable memory +* allocation handle that can be used to share the memory with other +* processes. The recipient process can convert the shareable handle back into a +* CUDA memory handle using ::cuMemImportFromShareableHandle and map +* it with ::cuMemMap. The implementation of what this handle is and how it +* can be transferred is defined by the requested handle type in \p handleType +* +* Once all shareable handles are closed and the allocation is released, the allocated +* memory referenced will be released back to the OS and uses of the CUDA handle afterward +* will lead to undefined behavior. +* +* This API can also be used in conjunction with other APIs (e.g. Vulkan, OpenGL) +* that support importing memory from the shareable type +* +* \param[out] shareableHandle - Pointer to the location in which to store the requested handle type +* \param[in] handle - CUDA handle for the memory allocation +* \param[in] handleType - Type of shareable handle requested (defines type and size of the \p shareableHandle output parameter) +* \param[in] flags - Reserved, must be zero +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemImportFromShareableHandle +*/ +CUresult CUDAAPI cuMemExportToShareableHandle(void *shareableHandle, CUmemGenericAllocationHandle handle, CUmemAllocationHandleType handleType, unsigned long long flags); + +/** +* \brief Imports an allocation from a requested shareable handle type. +* +* If the current process cannot support the memory described by this shareable +* handle, this API will error as ::CUDA_ERROR_NOT_SUPPORTED. +* +* If \p shHandleType is ::CU_MEM_HANDLE_TYPE_FABRIC and the importer process has not been +* granted access to the same IMEX channel as the exporter process, this API will error +* as ::CUDA_ERROR_NOT_PERMITTED. +* +* \note Importing shareable handles exported from some graphics APIs(VUlkan, OpenGL, etc) +* created on devices under an SLI group may not be supported, and thus this API will +* return CUDA_ERROR_NOT_SUPPORTED. +* There is no guarantee that the contents of \p handle will be the same CUDA memory handle +* for the same given OS shareable handle, or the same underlying allocation. +* +* \param[out] handle - CUDA Memory handle for the memory allocation. +* \param[in] osHandle - Shareable Handle representing the memory allocation that is to be imported. +* \param[in] shHandleType - handle type of the exported handle ::CUmemAllocationHandleType. +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemExportToShareableHandle, ::cuMemMap, ::cuMemRelease +*/ +CUresult CUDAAPI cuMemImportFromShareableHandle(CUmemGenericAllocationHandle *handle, void *osHandle, CUmemAllocationHandleType shHandleType); + +/** +* \brief Calculates either the minimal or recommended granularity +* +* Calculates either the minimal or recommended granularity +* for a given allocation specification and returns it in granularity. This +* granularity can be used as a multiple for alignment, size, or address mapping. +* +* \param[out] granularity Returned granularity. +* \param[in] prop Property for which to determine the granularity for +* \param[in] option Determines which granularity to return +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemCreate, ::cuMemMap +*/ +CUresult CUDAAPI cuMemGetAllocationGranularity(size_t *granularity, const CUmemAllocationProp *prop, CUmemAllocationGranularity_flags option); + +/** +* \brief Retrieve the contents of the property structure defining properties for this handle +* +* \param[out] prop - Pointer to a properties structure which will hold the information about this handle +* \param[in] handle - Handle which to perform the query on +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemCreate, ::cuMemImportFromShareableHandle +*/ +CUresult CUDAAPI cuMemGetAllocationPropertiesFromHandle(CUmemAllocationProp *prop, CUmemGenericAllocationHandle handle); + +/** +* \brief Given an address \p addr, returns the allocation handle of the backing memory allocation. +* +* The handle is guaranteed to be the same handle value used to map the memory. If the address +* requested is not mapped, the function will fail. The returned handle must be released with +* corresponding number of calls to ::cuMemRelease. +* +* \note The address \p addr, can be any address in a range previously mapped +* by ::cuMemMap, and not necessarily the start address. +* +* \param[out] handle CUDA Memory handle for the backing memory allocation. +* \param[in] addr Memory address to query, that has been mapped previously. +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMemCreate, ::cuMemRelease, ::cuMemMap +*/ +CUresult CUDAAPI cuMemRetainAllocationHandle(CUmemGenericAllocationHandle *handle, void *addr); + +/** @} */ /* END CUDA_VA */ + +/** + * \defgroup CUDA_MALLOC_ASYNC Stream Ordered Memory Allocator + * + * ___MANBRIEF___ Functions for performing allocation and free operations in stream order. + * Functions for controlling the behavior of the underlying allocator. + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the stream ordered memory allocator exposed by the + * low-level CUDA driver application programming interface. + * + * @{ + * + * \section CUDA_MALLOC_ASYNC_overview overview + * + * The asynchronous allocator allows the user to allocate and free in stream order. + * All asynchronous accesses of the allocation must happen between + * the stream executions of the allocation and the free. If the memory is accessed + * outside of the promised stream order, a use before allocation / use after free error + * will cause undefined behavior. + * + * The allocator is free to reallocate the memory as long as it can guarantee + * that compliant memory accesses will not overlap temporally. + * The allocator may refer to internal stream ordering as well as inter-stream dependencies + * (such as CUDA events and null stream dependencies) when establishing the temporal guarantee. + * The allocator may also insert inter-stream dependencies to establish the temporal guarantee. + * + * \section CUDA_MALLOC_ASYNC_support Supported Platforms + * + * Whether or not a device supports the integrated stream ordered memory allocator + * may be queried by calling ::cuDeviceGetAttribute() with the device attribute + * ::CU_DEVICE_ATTRIBUTE_MEMORY_POOLS_SUPPORTED + */ + +/** + * \brief Frees memory with stream ordered semantics + * + * Inserts a free operation into \p hStream. + * The allocation must not be accessed after stream execution reaches the free. + * After this API returns, accessing the memory from any subsequent work launched on the GPU + * or querying its pointer attributes results in undefined behavior. + * + * \note During stream capture, this function results in the creation of a free node and + * must therefore be passed the address of a graph allocation. + * + * \param dptr - memory to free + * \param hStream - The stream establishing the stream ordering contract. + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT (default stream specified with no current context), + * ::CUDA_ERROR_NOT_SUPPORTED + */ +CUresult CUDAAPI cuMemFreeAsync(CUdeviceptr dptr, CUstream hStream); + +/** + * \brief Allocates memory with stream ordered semantics + * + * Inserts an allocation operation into \p hStream. + * A pointer to the allocated memory is returned immediately in *dptr. + * The allocation must not be accessed until the the allocation operation completes. + * The allocation comes from the memory pool current to the stream's device. + * + * \note The default memory pool of a device contains device memory from that device. + * \note Basic stream ordering allows future work submitted into the same stream to use the allocation. + * Stream query, stream synchronize, and CUDA events can be used to guarantee that the allocation + * operation completes before work submitted in a separate stream runs. + * \note During stream capture, this function results in the creation of an allocation node. In this case, + * the allocation is owned by the graph instead of the memory pool. The memory pool's properties + * are used to set the node's creation parameters. + * + * \param[out] dptr - Returned device pointer + * \param[in] bytesize - Number of bytes to allocate + * \param[in] hStream - The stream establishing the stream ordering contract and the memory pool to allocate from + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT (default stream specified with no current context), + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemAllocFromPoolAsync, ::cuMemFreeAsync, ::cuDeviceSetMemPool, + * ::cuDeviceGetDefaultMemPool, ::cuDeviceGetMemPool, ::cuMemPoolCreate, + * ::cuMemPoolSetAccess, ::cuMemPoolSetAttribute + */ +CUresult CUDAAPI cuMemAllocAsync(CUdeviceptr *dptr, size_t bytesize, CUstream hStream); + +/** + * \brief Tries to release memory back to the OS + * + * Releases memory back to the OS until the pool contains fewer than minBytesToKeep + * reserved bytes, or there is no more memory that the allocator can safely release. + * The allocator cannot release OS allocations that back outstanding asynchronous allocations. + * The OS allocations may happen at different granularity from the user allocations. + * + * \note: Allocations that have not been freed count as outstanding. + * \note: Allocations that have been asynchronously freed but whose completion has + * not been observed on the host (eg. by a synchronize) can count as outstanding. + * + * \param[in] pool - The memory pool to trim + * \param[in] minBytesToKeep - If the pool has less than minBytesToKeep reserved, + * the TrimTo operation is a no-op. Otherwise the pool will be guaranteed to have + * at least minBytesToKeep bytes reserved after the operation. + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolTrimTo(CUmemoryPool pool, size_t minBytesToKeep); + +/** + * \brief Sets attributes of a memory pool + * + * Supported attributes are: + * - ::CU_MEMPOOL_ATTR_RELEASE_THRESHOLD: (value type = cuuint64_t) + * Amount of reserved memory in bytes to hold onto before trying + * to release memory back to the OS. When more than the release + * threshold bytes of memory are held by the memory pool, the + * allocator will try to release memory back to the OS on the + * next call to stream, event or context synchronize. (default 0) + * - ::CU_MEMPOOL_ATTR_REUSE_FOLLOW_EVENT_DEPENDENCIES: (value type = int) + * Allow ::cuMemAllocAsync to use memory asynchronously freed + * in another stream as long as a stream ordering dependency + * of the allocating stream on the free action exists. + * Cuda events and null stream interactions can create the required + * stream ordered dependencies. (default enabled) + * - ::CU_MEMPOOL_ATTR_REUSE_ALLOW_OPPORTUNISTIC: (value type = int) + * Allow reuse of already completed frees when there is no dependency + * between the free and allocation. (default enabled) + * - ::CU_MEMPOOL_ATTR_REUSE_ALLOW_INTERNAL_DEPENDENCIES: (value type = int) + * Allow ::cuMemAllocAsync to insert new stream dependencies + * in order to establish the stream ordering required to reuse + * a piece of memory released by ::cuMemFreeAsync (default enabled). + * - ::CU_MEMPOOL_ATTR_RESERVED_MEM_HIGH: (value type = cuuint64_t) + * Reset the high watermark that tracks the amount of backing memory that was + * allocated for the memory pool. It is illegal to set this attribute to a non-zero value. + * - ::CU_MEMPOOL_ATTR_USED_MEM_HIGH: (value type = cuuint64_t) + * Reset the high watermark that tracks the amount of used memory that was + * allocated for the memory pool. + * + * \param[in] pool - The memory pool to modify + * \param[in] attr - The attribute to modify + * \param[in] value - Pointer to the value to assign + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolSetAttribute(CUmemoryPool pool, CUmemPool_attribute attr, void *value); + +/** + * \brief Gets attributes of a memory pool + * + * Supported attributes are: + * - ::CU_MEMPOOL_ATTR_RELEASE_THRESHOLD: (value type = cuuint64_t) + * Amount of reserved memory in bytes to hold onto before trying + * to release memory back to the OS. When more than the release + * threshold bytes of memory are held by the memory pool, the + * allocator will try to release memory back to the OS on the + * next call to stream, event or context synchronize. (default 0) + * - ::CU_MEMPOOL_ATTR_REUSE_FOLLOW_EVENT_DEPENDENCIES: (value type = int) + * Allow ::cuMemAllocAsync to use memory asynchronously freed + * in another stream as long as a stream ordering dependency + * of the allocating stream on the free action exists. + * Cuda events and null stream interactions can create the required + * stream ordered dependencies. (default enabled) + * - ::CU_MEMPOOL_ATTR_REUSE_ALLOW_OPPORTUNISTIC: (value type = int) + * Allow reuse of already completed frees when there is no dependency + * between the free and allocation. (default enabled) + * - ::CU_MEMPOOL_ATTR_REUSE_ALLOW_INTERNAL_DEPENDENCIES: (value type = int) + * Allow ::cuMemAllocAsync to insert new stream dependencies + * in order to establish the stream ordering required to reuse + * a piece of memory released by ::cuMemFreeAsync (default enabled). + * - ::CU_MEMPOOL_ATTR_RESERVED_MEM_CURRENT: (value type = cuuint64_t) + * Amount of backing memory currently allocated for the mempool + * - ::CU_MEMPOOL_ATTR_RESERVED_MEM_HIGH: (value type = cuuint64_t) + * High watermark of backing memory allocated for the mempool since the + * last time it was reset. + * - ::CU_MEMPOOL_ATTR_USED_MEM_CURRENT: (value type = cuuint64_t) + * Amount of memory from the pool that is currently in use by the application. + * - ::CU_MEMPOOL_ATTR_USED_MEM_HIGH: (value type = cuuint64_t) + * High watermark of the amount of memory from the pool that was in use by the application. + * + * \param[in] pool - The memory pool to get attributes of + * \param[in] attr - The attribute to get + * \param[out] value - Retrieved value + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolGetAttribute(CUmemoryPool pool, CUmemPool_attribute attr, void *value); + +/** + * \brief Controls visibility of pools between devices + * + * \param[in] pool - The pool being modified + * \param[in] map - Array of access descriptors. Each descriptor instructs the access to enable for a single gpu. + * \param[in] count - Number of descriptors in the map array. + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolSetAccess(CUmemoryPool pool, const CUmemAccessDesc *map, size_t count); + +/** + * \brief Returns the accessibility of a pool from a device + * + * Returns the accessibility of the pool's memory from the specified location. + * + * \param[out] flags - the accessibility of the pool from the specified location + * \param[in] memPool - the pool being queried + * \param[in] location - the location accessing the pool + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolGetAccess(CUmemAccess_flags *flags, CUmemoryPool memPool, CUmemLocation *location); + +/** + * \brief Creates a memory pool + * + * Creates a CUDA memory pool and returns the handle in \p pool. The \p poolProps determines + * the properties of the pool such as the backing device and IPC capabilities. + * +* To create a memory pool targeting a specific host NUMA node, applications must +* set ::CUmemPoolProps::CUmemLocation::type to ::CU_MEM_LOCATION_TYPE_HOST_NUMA and +* ::CUmemPoolProps::CUmemLocation::id must specify the NUMA ID of the host memory node. +* By default, the pool's memory will be accessible from the device it is allocated on. + * In the case of pools created with ::CU_MEM_LOCATION_TYPE_HOST_NUMA, their default accessibility + * will be from the host CPU. + * Applications can control the maximum size of the pool by specifying a non-zero value for ::CUmemPoolProps::maxSize. + * If set to 0, the maximum size of the pool will default to a system dependent value. + * + * Applications can set ::CUmemPoolProps::handleTypes to ::CU_MEM_HANDLE_TYPE_FABRIC + * in order to create ::CUmemoryPool suitable for sharing within an IMEX domain. + * An IMEX domain is either an OS instance or a group of securely connected OS instances + * using the NVIDIA IMEX daemon. An IMEX channel is a global resource within the IMEX domain + * that represents a logical entity that aims to provide fine grained accessibility control + * for the participating processes. When exporter and importer CUDA processes have been + * granted access to the same IMEX channel, they can securely share memory. + * If the allocating process does not have access setup for an IMEX channel, attempting to export + * a ::CUmemoryPool with ::CU_MEM_HANDLE_TYPE_FABRIC will result in ::CUDA_ERROR_NOT_PERMITTED. + * The nvidia-modprobe CLI provides more information regarding setting up of IMEX channels. + * + * \note Specifying CU_MEM_HANDLE_TYPE_NONE creates a memory pool that will not support IPC. + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_NOT_PERMITTED + * ::CUDA_ERROR_NOT_SUPPORTED + * + * \sa ::cuDeviceSetMemPool, ::cuDeviceGetMemPool, ::cuDeviceGetDefaultMemPool, + * ::cuMemAllocFromPoolAsync, ::cuMemPoolExportToShareableHandle + */ +CUresult CUDAAPI cuMemPoolCreate(CUmemoryPool *pool, const CUmemPoolProps *poolProps); + +/** + * \brief Destroys the specified memory pool + * + * If any pointers obtained from this pool haven't been freed or + * the pool has free operations that haven't completed + * when ::cuMemPoolDestroy is invoked, the function will return immediately and the + * resources associated with the pool will be released automatically + * once there are no more outstanding allocations. + * + * Destroying the current mempool of a device sets the default mempool of + * that device as the current mempool for that device. + * + * \note A device's default memory pool cannot be destroyed. + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuMemFreeAsync, ::cuDeviceSetMemPool, ::cuDeviceGetMemPool, + * ::cuDeviceGetDefaultMemPool, ::cuMemPoolCreate + */ +CUresult CUDAAPI cuMemPoolDestroy(CUmemoryPool pool); + +/** + * \brief Allocates memory from a specified pool with stream ordered semantics. + * + * Inserts an allocation operation into \p hStream. + * A pointer to the allocated memory is returned immediately in *dptr. + * The allocation must not be accessed until the the allocation operation completes. + * The allocation comes from the specified memory pool. + * + * \note + * - The specified memory pool may be from a device different than that of the specified \p hStream. + * + * - Basic stream ordering allows future work submitted into the same stream to use the allocation. + * Stream query, stream synchronize, and CUDA events can be used to guarantee that the allocation + * operation completes before work submitted in a separate stream runs. + * + * \note During stream capture, this function results in the creation of an allocation node. In this case, + * the allocation is owned by the graph instead of the memory pool. The memory pool's properties + * are used to set the node's creation parameters. + * + * \param[out] dptr - Returned device pointer + * \param[in] bytesize - Number of bytes to allocate + * \param[in] pool - The pool to allocate from + * \param[in] hStream - The stream establishing the stream ordering semantic + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT (default stream specified with no current context), + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemAllocAsync, ::cuMemFreeAsync, ::cuDeviceGetDefaultMemPool, + * ::cuDeviceGetMemPool, ::cuMemPoolCreate, ::cuMemPoolSetAccess, + * ::cuMemPoolSetAttribute + */ +CUresult CUDAAPI cuMemAllocFromPoolAsync(CUdeviceptr *dptr, size_t bytesize, CUmemoryPool pool, CUstream hStream); + +/** + * \brief Exports a memory pool to the requested handle type. + * + * Given an IPC capable mempool, create an OS handle to share the pool with another process. + * A recipient process can convert the shareable handle into a mempool with ::cuMemPoolImportFromShareableHandle. + * Individual pointers can then be shared with the ::cuMemPoolExportPointer and ::cuMemPoolImportPointer APIs. + * The implementation of what the shareable handle is and how it can be transferred is defined by the requested + * handle type. + * + * \note: To create an IPC capable mempool, create a mempool with a CUmemAllocationHandleType other than CU_MEM_HANDLE_TYPE_NONE. + * + * \param[out] handle_out - Returned OS handle + * \param[in] pool - pool to export + * \param[in] handleType - the type of handle to create + * \param[in] flags - must be 0 + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemPoolImportFromShareableHandle, ::cuMemPoolExportPointer, + * ::cuMemPoolImportPointer, ::cuMemAllocAsync, ::cuMemFreeAsync, + * ::cuDeviceGetDefaultMemPool, ::cuDeviceGetMemPool, ::cuMemPoolCreate, + * ::cuMemPoolSetAccess, ::cuMemPoolSetAttribute + */ +CUresult CUDAAPI cuMemPoolExportToShareableHandle(void *handle_out, CUmemoryPool pool, CUmemAllocationHandleType handleType, unsigned long long flags); + +/** + * \brief imports a memory pool from a shared handle. + * + * Specific allocations can be imported from the imported pool with cuMemPoolImportPointer. + * + * If \p handleType is ::CU_MEM_HANDLE_TYPE_FABRIC and the importer process has not been + * granted access to the same IMEX channel as the exporter process, this API will error + * as ::CUDA_ERROR_NOT_PERMITTED. + * + * + * \note Imported memory pools do not support creating new allocations. + * As such imported memory pools may not be used in cuDeviceSetMemPool + * or ::cuMemAllocFromPoolAsync calls. + * + * \param[out] pool_out - Returned memory pool + * \param[in] handle - OS handle of the pool to open + * \param[in] handleType - The type of handle being imported + * \param[in] flags - must be 0 + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemPoolExportToShareableHandle, ::cuMemPoolExportPointer, ::cuMemPoolImportPointer + */ +CUresult CUDAAPI cuMemPoolImportFromShareableHandle( + CUmemoryPool *pool_out, + void *handle, + CUmemAllocationHandleType handleType, + unsigned long long flags); + +/** + * \brief Export data to share a memory pool allocation between processes. + * + * Constructs \p shareData_out for sharing a specific allocation from an already shared memory pool. + * The recipient process can import the allocation with the ::cuMemPoolImportPointer api. + * The data is not a handle and may be shared through any IPC mechanism. + * + * \param[out] shareData_out - Returned export data + * \param[in] ptr - pointer to memory being exported + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemPoolExportToShareableHandle, ::cuMemPoolImportFromShareableHandle, ::cuMemPoolImportPointer + */ +CUresult CUDAAPI cuMemPoolExportPointer(CUmemPoolPtrExportData *shareData_out, CUdeviceptr ptr); + +/** + * \brief Import a memory pool allocation from another process. + * + * Returns in \p ptr_out a pointer to the imported memory. + * The imported memory must not be accessed before the allocation operation completes + * in the exporting process. The imported memory must be freed from all importing processes before + * being freed in the exporting process. The pointer may be freed with cuMemFree + * or cuMemFreeAsync. If cuMemFreeAsync is used, the free must be completed + * on the importing process before the free operation on the exporting process. + * + * \note The cuMemFreeAsync api may be used in the exporting process before + * the cuMemFreeAsync operation completes in its stream as long as the + * cuMemFreeAsync in the exporting process specifies a stream with + * a stream dependency on the importing process's cuMemFreeAsync. + * + * \param[out] ptr_out - pointer to imported memory + * \param[in] pool - pool from which to import + * \param[in] shareData - data specifying the memory to import + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemPoolExportToShareableHandle, ::cuMemPoolImportFromShareableHandle, ::cuMemPoolExportPointer + */ +CUresult CUDAAPI cuMemPoolImportPointer(CUdeviceptr *ptr_out, CUmemoryPool pool, CUmemPoolPtrExportData *shareData); + +/** @} */ /* END CUDA_MALLOC_ASYNC */ + +/** + * \defgroup CUDA_MULTICAST Multicast Object Management + * + * ___MANBRIEF___ Functions for creating multicast objects, adding devices to them and binding/unbinding memory + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the CUDA multicast object operations exposed by the + * low-level CUDA driver application programming interface. + * + * @{ + * + * \section CUDA_MULTICAST_overview overview + * + * A multicast object created via ::cuMulticastCreate enables certain memory + * operations to be broadcast to a team of devices. Devices can be added to a + * multicast object via ::cuMulticastAddDevice. Memory can be bound on each + * participating device via either ::cuMulticastBindMem or ::cuMulticastBindAddr. + * Multicast objects can be mapped into a device's virtual address space using + * the virtual memmory management APIs (see ::cuMemMap and ::cuMemSetAccess). + * + * \section CUDA_MULTICAST_support Supported Platforms + * + * Support for multicast on a specific device can be queried using the device + * attribute ::CU_DEVICE_ATTRIBUTE_MULTICAST_SUPPORTED + */ + +/** + * \brief Create a generic allocation handle representing a multicast object described by the given properties. + * + * This creates a multicast object as described by \p prop. The number of + * participating devices is specified by ::CUmulticastObjectProp::numDevices. + * Devices can be added to the multicast object via ::cuMulticastAddDevice. + * All participating devices must be added to the multicast object before memory + * can be bound to it. Memory is bound to the multicast object via either + * ::cuMulticastBindMem or ::cuMulticastBindAddr, and can be unbound via + * ::cuMulticastUnbind. The total amount of memory that can be bound per device + * is specified by :CUmulticastObjectProp::size. This size must be a multiple of + * the value returned by ::cuMulticastGetGranularity with the flag + * ::CU_MULTICAST_GRANULARITY_MINIMUM. For best performance however, the size + * should be aligned to the value returned by ::cuMulticastGetGranularity with + * the flag ::CU_MULTICAST_GRANULARITY_RECOMMENDED. + * + * After all participating devices have been added, multicast objects can also + * be mapped to a device's virtual address space using the virtual memory + * management APIs (see ::cuMemMap and ::cuMemSetAccess). Multicast objects can + * also be shared with other processes by requesting a shareable handle via + * ::cuMemExportToShareableHandle. Note that the desired types of shareable + * handles must be specified in the bitmask ::CUmulticastObjectProp::handleTypes. + * Multicast objects can be released using the virtual memory management API + * ::cuMemRelease. + * + * \param[out] mcHandle Value of handle returned. + * \param[in] prop Properties of the multicast object to create. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED + * + * \sa ::cuMulticastAddDevice, ::cuMulticastBindMem, ::cuMulticastBindAddr, ::cuMulticastUnbind + * \sa ::cuMemCreate, ::cuMemRelease, ::cuMemExportToShareableHandle, ::cuMemImportFromShareableHandle + */ +CUresult CUDAAPI cuMulticastCreate(CUmemGenericAllocationHandle *mcHandle, const CUmulticastObjectProp *prop); + +/** + * \brief Associate a device to a multicast object. + * + * Associates a device to a multicast object. The added device will be a part of + * the multicast team of size specified by CUmulticastObjectProp::numDevices + * during ::cuMulticastCreate. + * The association of the device to the multicast object is permanent during + * the life time of the multicast object. + * All devices must be added to the multicast team before any memory can be + * bound to any device in the team. Any calls to ::cuMulticastBindMem or + * ::cuMulticastBindAddr will block until all devices have been added. + * Similarly all devices must be added to the multicast team before a virtual + * address range can be mapped to the multicast object. A call to ::cuMemMap + * will block until all devices have been added. + * + * \param[in] mcHandle Handle representing a multicast object. + * \param[in] dev Device that will be associated to the multicast + * object. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED + * + * \sa ::cuMulticastCreate, ::cuMulticastBindMem, ::cuMulticastBindAddr + */ +CUresult CUDAAPI cuMulticastAddDevice(CUmemGenericAllocationHandle mcHandle, CUdevice dev); + +/** + * \brief Bind a memory allocation represented by a handle to a multicast object. + * + * Binds a memory allocation specified by \p memHandle and created via + * ::cuMemCreate to a multicast object represented by \p mcHandle and created + * via ::cuMulticastCreate. The intended \p size of the bind, the offset in the + * multicast range \p mcOffset as well as the offset in the memory \p memOffset + * must be a multiple of the value returned by ::cuMulticastGetGranularity with + * the flag ::CU_MULTICAST_GRANULARITY_MINIMUM. For best performance however, + * \p size, \p mcOffset and \p memOffset should be aligned to the granularity of + * the memory allocation(see ::cuMemGetAllocationGranularity) or to the value + * returned by ::cuMulticastGetGranularity with the flag + * ::CU_MULTICAST_GRANULARITY_RECOMMENDED. + * + * The \p size + \p memOffset must be smaller than the size of the allocated + * memory. Similarly the \p size + \p mcOffset must be smaller than the size + * of the multicast object. + * The memory allocation must have beeen created on one of the devices + * that was added to the multicast team via ::cuMulticastAddDevice. + * Externally shareable as well as imported multicast objects can be bound only + * to externally shareable memory. + * Note that this call will return CUDA_ERROR_OUT_OF_MEMORY if there are + * insufficient resources required to perform the bind. This call may also + * return CUDA_ERROR_SYSTEM_NOT_READY if the necessary system software is not + * initialized or running. + * + * \param[in] mcHandle Handle representing a multicast object. + * \param[in] mcOffset Offset into the multicast object for attachment. + * \param[in] memHandle Handle representing a memory allocation. + * \param[in] memOffset Offset into the memory for attachment. + * \param[in] size Size of the memory that will be bound to the + * multicast object. + * \param[in] flags Flags for future use, must be zero for now. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_SYSTEM_NOT_READY + * + * \sa ::cuMulticastCreate, ::cuMulticastAddDevice, ::cuMemCreate + */ +CUresult CUDAAPI cuMulticastBindMem(CUmemGenericAllocationHandle mcHandle, size_t mcOffset, CUmemGenericAllocationHandle memHandle, size_t memOffset, size_t size, unsigned long long flags); + +/** + * \brief Bind a memory allocation represented by a virtual address to a multicast object. + * + * Binds a memory allocation specified by its mapped address \p memptr to a + * multicast object represented by \p mcHandle. + * The memory must have been allocated via ::cuMemCreate or ::cudaMallocAsync. + * The intended \p size of the bind, the offset in the multicast range + * \p mcOffset and \p memptr must be a multiple of the value returned by + * ::cuMulticastGetGranularity with the flag ::CU_MULTICAST_GRANULARITY_MINIMUM. + * For best performance however, \p size, \p mcOffset and \p memptr should be + * aligned to the value returned by ::cuMulticastGetGranularity with the flag + * ::CU_MULTICAST_GRANULARITY_RECOMMENDED. + * + * The \p size must be smaller than the size of the allocated memory. + * Similarly the \p size + \p mcOffset must be smaller than the total size + * of the multicast object. + * The memory allocation must have beeen created on one of the devices + * that was added to the multicast team via ::cuMulticastAddDevice. + * Externally shareable as well as imported multicast objects can be bound only + * to externally shareable memory. + * Note that this call will return CUDA_ERROR_OUT_OF_MEMORY if there are + * insufficient resources required to perform the bind. This call may also + * return CUDA_ERROR_SYSTEM_NOT_READY if the necessary system software is not + * initialized or running. + * + * \param[in] mcHandle Handle representing a multicast object. + * \param[in] mcOffset Offset into multicast va range for attachment. + * \param[in] memptr Virtual address of the memory allocation. + * \param[in] size Size of memory that will be bound to the + * multicast object. + * \param[in] flags Flags for future use, must be zero now. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY, + * ::CUDA_ERROR_SYSTEM_NOT_READY + * + * \sa ::cuMulticastCreate, ::cuMulticastAddDevice, ::cuMemCreate + */ +CUresult CUDAAPI cuMulticastBindAddr(CUmemGenericAllocationHandle mcHandle, size_t mcOffset, CUdeviceptr memptr, size_t size, unsigned long long flags); + +/** + * \brief Unbind any memory allocations bound to a multicast object at a given offset and upto a given size. + * + * Unbinds any memory allocations hosted on \p dev and bound to a multicast + * object at \p mcOffset and upto a given \p size. + * The intended \p size of the unbind and the offset in the multicast range + * ( \p mcOffset ) must be a multiple of the value returned by + * ::cuMulticastGetGranularity flag ::CU_MULTICAST_GRANULARITY_MINIMUM. + * The \p size + \p mcOffset must be smaller than the total size of the + * multicast object. + * + * \note + * Warning: + * The \p mcOffset and the \p size must match the corresponding values specified + * during the bind call. Any other values may result in undefined behavior. + * + * \param[in] mcHandle Handle representing a multicast object. + * \param[in] dev Device that hosts the memory allocation. + * \param[in] mcOffset Offset into the multicast object. + * \param[in] size Desired size to unbind. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_NOT_SUPPORTED + * + * \sa ::cuMulticastBindMem, ::cuMulticastBindAddr + */ +CUresult CUDAAPI cuMulticastUnbind(CUmemGenericAllocationHandle mcHandle, CUdevice dev, size_t mcOffset, size_t size); + +/** +* \brief Calculates either the minimal or recommended granularity for multicast object +* +* Calculates either the minimal or recommended granularity for a given set of +* multicast object properties and returns it in granularity. This granularity +* can be used as a multiple for size, bind offsets and address mappings of the +* multicast object. +* +* \param[out] granularity Returned granularity. +* \param[in] prop Properties of the multicast object. +* \param[in] option Determines which granularity to return. +* +* \returns +* ::CUDA_SUCCESS, +* ::CUDA_ERROR_INVALID_VALUE, +* ::CUDA_ERROR_NOT_INITIALIZED, +* ::CUDA_ERROR_DEINITIALIZED, +* ::CUDA_ERROR_NOT_PERMITTED, +* ::CUDA_ERROR_NOT_SUPPORTED +* +* \sa ::cuMulticastCreate, ::cuMulticastBindMem, ::cuMulticastBindAddr, ::cuMulticastUnbind +*/ +CUresult CUDAAPI cuMulticastGetGranularity(size_t *granularity, const CUmulticastObjectProp *prop, CUmulticastGranularity_flags option); + +/** @} */ /* END CUDA_MULTICAST */ + +/** + * \defgroup CUDA_UNIFIED Unified Addressing + * + * ___MANBRIEF___ unified addressing functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the unified addressing functions of the + * low-level CUDA driver application programming interface. + * + * @{ + * + * \section CUDA_UNIFIED_overview Overview + * + * CUDA devices can share a unified address space with the host. + * For these devices there is no distinction between a device + * pointer and a host pointer -- the same pointer value may be + * used to access memory from the host program and from a kernel + * running on the device (with exceptions enumerated below). + * + * \section CUDA_UNIFIED_support Supported Platforms + * + * Whether or not a device supports unified addressing may be + * queried by calling ::cuDeviceGetAttribute() with the device + * attribute ::CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING. + * + * Unified addressing is automatically enabled in 64-bit processes + * + * \section CUDA_UNIFIED_lookup Looking Up Information from Pointer Values + * + * It is possible to look up information about the memory which backs a + * pointer value. For instance, one may want to know if a pointer points + * to host or device memory. As another example, in the case of device + * memory, one may want to know on which CUDA device the memory + * resides. These properties may be queried using the function + * ::cuPointerGetAttribute() + * + * Since pointers are unique, it is not necessary to specify information + * about the pointers specified to the various copy functions in the + * CUDA API. The function ::cuMemcpy() may be used to perform a copy + * between two pointers, ignoring whether they point to host or device + * memory (making ::cuMemcpyHtoD(), ::cuMemcpyDtoD(), and ::cuMemcpyDtoH() + * unnecessary for devices supporting unified addressing). For + * multidimensional copies, the memory type ::CU_MEMORYTYPE_UNIFIED may be + * used to specify that the CUDA driver should infer the location of the + * pointer from its value. + * + * \section CUDA_UNIFIED_automaphost Automatic Mapping of Host Allocated Host Memory + * + * All host memory allocated in all contexts using ::cuMemAllocHost() and + * ::cuMemHostAlloc() is always directly accessible from all contexts on + * all devices that support unified addressing. This is the case regardless + * of whether or not the flags ::CU_MEMHOSTALLOC_PORTABLE and + * ::CU_MEMHOSTALLOC_DEVICEMAP are specified. + * + * The pointer value through which allocated host memory may be accessed + * in kernels on all devices that support unified addressing is the same + * as the pointer value through which that memory is accessed on the host, + * so it is not necessary to call ::cuMemHostGetDevicePointer() to get the device + * pointer for these allocations. + * + * Note that this is not the case for memory allocated using the flag + * ::CU_MEMHOSTALLOC_WRITECOMBINED, as discussed below. + * + * \section CUDA_UNIFIED_autopeerregister Automatic Registration of Peer Memory + * + * Upon enabling direct access from a context that supports unified addressing + * to another peer context that supports unified addressing using + * ::cuCtxEnablePeerAccess() all memory allocated in the peer context using + * ::cuMemAlloc() and ::cuMemAllocPitch() will immediately be accessible + * by the current context. The device pointer value through + * which any peer memory may be accessed in the current context + * is the same pointer value through which that memory may be + * accessed in the peer context. + * + * \section CUDA_UNIFIED_exceptions Exceptions, Disjoint Addressing + * + * Not all memory may be accessed on devices through the same pointer + * value through which they are accessed on the host. These exceptions + * are host memory registered using ::cuMemHostRegister() and host memory + * allocated using the flag ::CU_MEMHOSTALLOC_WRITECOMBINED. For these + * exceptions, there exists a distinct host and device address for the + * memory. The device address is guaranteed to not overlap any valid host + * pointer range and is guaranteed to have the same value across all + * contexts that support unified addressing. + * + * This device address may be queried using ::cuMemHostGetDevicePointer() + * when a context using unified addressing is current. Either the host + * or the unified device pointer value may be used to refer to this memory + * through ::cuMemcpy() and similar functions using the + * ::CU_MEMORYTYPE_UNIFIED memory type. + * + */ + +/** + * \brief Returns information about a pointer + * + * The supported attributes are: + * + * - ::CU_POINTER_ATTRIBUTE_CONTEXT: + * + * Returns in \p *data the ::CUcontext in which \p ptr was allocated or + * registered. + * The type of \p data must be ::CUcontext *. + * + * If \p ptr was not allocated by, mapped by, or registered with + * a ::CUcontext which uses unified virtual addressing then + * ::CUDA_ERROR_INVALID_VALUE is returned. + * + * - ::CU_POINTER_ATTRIBUTE_MEMORY_TYPE: + * + * Returns in \p *data the physical memory type of the memory that + * \p ptr addresses as a ::CUmemorytype enumerated value. + * The type of \p data must be unsigned int. + * + * If \p ptr addresses device memory then \p *data is set to + * ::CU_MEMORYTYPE_DEVICE. The particular ::CUdevice on which the + * memory resides is the ::CUdevice of the ::CUcontext returned by the + * ::CU_POINTER_ATTRIBUTE_CONTEXT attribute of \p ptr. + * + * If \p ptr addresses host memory then \p *data is set to + * ::CU_MEMORYTYPE_HOST. + * + * If \p ptr was not allocated by, mapped by, or registered with + * a ::CUcontext which uses unified virtual addressing then + * ::CUDA_ERROR_INVALID_VALUE is returned. + * + * If the current ::CUcontext does not support unified virtual + * addressing then ::CUDA_ERROR_INVALID_CONTEXT is returned. + * + * - ::CU_POINTER_ATTRIBUTE_DEVICE_POINTER: + * + * Returns in \p *data the device pointer value through which + * \p ptr may be accessed by kernels running in the current + * ::CUcontext. + * The type of \p data must be CUdeviceptr *. + * + * If there exists no device pointer value through which + * kernels running in the current ::CUcontext may access + * \p ptr then ::CUDA_ERROR_INVALID_VALUE is returned. + * + * If there is no current ::CUcontext then + * ::CUDA_ERROR_INVALID_CONTEXT is returned. + * + * Except in the exceptional disjoint addressing cases discussed + * below, the value returned in \p *data will equal the input + * value \p ptr. + * + * - ::CU_POINTER_ATTRIBUTE_HOST_POINTER: + * + * Returns in \p *data the host pointer value through which + * \p ptr may be accessed by by the host program. + * The type of \p data must be void **. + * If there exists no host pointer value through which + * the host program may directly access \p ptr then + * ::CUDA_ERROR_INVALID_VALUE is returned. + * + * Except in the exceptional disjoint addressing cases discussed + * below, the value returned in \p *data will equal the input + * value \p ptr. + * + * - ::CU_POINTER_ATTRIBUTE_P2P_TOKENS: + * + * Returns in \p *data two tokens for use with the nv-p2p.h Linux + * kernel interface. \p data must be a struct of type + * CUDA_POINTER_ATTRIBUTE_P2P_TOKENS. + * + * \p ptr must be a pointer to memory obtained from :cuMemAlloc(). + * Note that p2pToken and vaSpaceToken are only valid for the + * lifetime of the source allocation. A subsequent allocation at + * the same address may return completely different tokens. + * Querying this attribute has a side effect of setting the attribute + * ::CU_POINTER_ATTRIBUTE_SYNC_MEMOPS for the region of memory that + * \p ptr points to. + * + * - ::CU_POINTER_ATTRIBUTE_SYNC_MEMOPS: + * + * A boolean attribute which when set, ensures that synchronous memory operations + * initiated on the region of memory that \p ptr points to will always synchronize. + * See further documentation in the section titled "API synchronization behavior" + * to learn more about cases when synchronous memory operations can + * exhibit asynchronous behavior. + * + * - ::CU_POINTER_ATTRIBUTE_BUFFER_ID: + * + * Returns in \p *data a buffer ID which is guaranteed to be unique within the process. + * \p data must point to an unsigned long long. + * + * \p ptr must be a pointer to memory obtained from a CUDA memory allocation API. + * Every memory allocation from any of the CUDA memory allocation APIs will + * have a unique ID over a process lifetime. Subsequent allocations do not reuse IDs + * from previous freed allocations. IDs are only unique within a single process. + * + * + * - ::CU_POINTER_ATTRIBUTE_IS_MANAGED: + * + * Returns in \p *data a boolean that indicates whether the pointer points to + * managed memory or not. + * + * If \p ptr is not a valid CUDA pointer then ::CUDA_ERROR_INVALID_VALUE is returned. + * + * - ::CU_POINTER_ATTRIBUTE_DEVICE_ORDINAL: + * + * Returns in \p *data an integer representing a device ordinal of a device against + * which the memory was allocated or registered. + * + * - ::CU_POINTER_ATTRIBUTE_IS_LEGACY_CUDA_IPC_CAPABLE: + * + * Returns in \p *data a boolean that indicates if this pointer maps to + * an allocation that is suitable for ::cudaIpcGetMemHandle. + * + * - ::CU_POINTER_ATTRIBUTE_RANGE_START_ADDR: + * + * Returns in \p *data the starting address for the allocation referenced + * by the device pointer \p ptr. Note that this is not necessarily the + * address of the mapped region, but the address of the mappable address + * range \p ptr references (e.g. from ::cuMemAddressReserve). + * + * - ::CU_POINTER_ATTRIBUTE_RANGE_SIZE: + * + * Returns in \p *data the size for the allocation referenced by the device + * pointer \p ptr. Note that this is not necessarily the size of the mapped + * region, but the size of the mappable address range \p ptr references + * (e.g. from ::cuMemAddressReserve). To retrieve the size of the mapped + * region, see ::cuMemGetAddressRange + * + * - ::CU_POINTER_ATTRIBUTE_MAPPED: + * + * Returns in \p *data a boolean that indicates if this pointer is in a + * valid address range that is mapped to a backing allocation. + * + * - ::CU_POINTER_ATTRIBUTE_ALLOWED_HANDLE_TYPES: + * + * Returns a bitmask of the allowed handle types for an allocation that may + * be passed to ::cuMemExportToShareableHandle. + * + * - ::CU_POINTER_ATTRIBUTE_MEMPOOL_HANDLE: + * + * Returns in \p *data the handle to the mempool that the allocation was obtained from. + * + * \par + * + * Note that for most allocations in the unified virtual address space + * the host and device pointer for accessing the allocation will be the + * same. The exceptions to this are + * - user memory registered using ::cuMemHostRegister + * - host memory allocated using ::cuMemHostAlloc with the + * ::CU_MEMHOSTALLOC_WRITECOMBINED flag + * For these types of allocation there will exist separate, disjoint host + * and device addresses for accessing the allocation. In particular + * - The host address will correspond to an invalid unmapped device address + * (which will result in an exception if accessed from the device) + * - The device address will correspond to an invalid unmapped host address + * (which will result in an exception if accessed from the host). + * For these types of allocations, querying ::CU_POINTER_ATTRIBUTE_HOST_POINTER + * and ::CU_POINTER_ATTRIBUTE_DEVICE_POINTER may be used to retrieve the host + * and device addresses from either address. + * + * \param data - Returned pointer attribute value + * \param attribute - Pointer attribute to query + * \param ptr - Pointer + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuPointerSetAttribute, + * ::cuMemAlloc, + * ::cuMemFree, + * ::cuMemAllocHost, + * ::cuMemFreeHost, + * ::cuMemHostAlloc, + * ::cuMemHostRegister, + * ::cuMemHostUnregister, + * ::cudaPointerGetAttributes + */ +CUresult CUDAAPI cuPointerGetAttribute(void *data, CUpointer_attribute attribute, CUdeviceptr ptr); + +/** + * \brief Prefetches memory to the specified destination device + * + * Note there is a later version of this API, ::cuMemPrefetchAsync_v2. It will + * supplant this version in 13.0, which is retained for minor version compatibility. + * + * Prefetches memory to the specified destination device. \p devPtr is the + * base device pointer of the memory to be prefetched and \p dstDevice is the + * destination device. \p count specifies the number of bytes to copy. \p hStream + * is the stream in which the operation is enqueued. The memory range must refer + * to managed memory allocated via ::cuMemAllocManaged or declared via __managed__ variables. + * + * Passing in CU_DEVICE_CPU for \p dstDevice will prefetch the data to host memory. If + * \p dstDevice is a GPU, then the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS + * must be non-zero. Additionally, \p hStream must be associated with a device that has a + * non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * + * The start address and end address of the memory range will be rounded down and rounded up + * respectively to be aligned to CPU page size before the prefetch operation is enqueued + * in the stream. + * + * If no physical memory has been allocated for this region, then this memory region + * will be populated and mapped on the destination device. If there's insufficient + * memory to prefetch the desired region, the Unified Memory driver may evict pages from other + * ::cuMemAllocManaged allocations to host memory in order to make room. Device memory + * allocated using ::cuMemAlloc or ::cuArrayCreate will not be evicted. + * + * By default, any mappings to the previous location of the migrated pages are removed and + * mappings for the new location are only setup on \p dstDevice. The exact behavior however + * also depends on the settings applied to this memory range via ::cuMemAdvise as described + * below: + * + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY was set on any subset of this memory range, + * then that subset will create a read-only copy of the pages on \p dstDevice. + * + * If ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION was called on any subset of this memory + * range, then the pages will be migrated to \p dstDevice even if \p dstDevice is not the + * preferred location of any pages in the memory range. + * + * If ::CU_MEM_ADVISE_SET_ACCESSED_BY was called on any subset of this memory range, + * then mappings to those pages from all the appropriate processors are updated to + * refer to the new location if establishing such a mapping is possible. Otherwise, + * those mappings are cleared. + * + * Note that this API is not required for functionality and only serves to improve performance + * by allowing the application to migrate data to a suitable location before it is accessed. + * Memory accesses to this range are always coherent and are allowed even when the data is + * actively being migrated. + * + * Note that this function is asynchronous with respect to the host and all work + * on other devices. + * + * \param devPtr - Pointer to be prefetched + * \param count - Size in bytes + * \param dstDevice - Destination device to prefetch to + * \param hStream - Stream to enqueue prefetch operation + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpy, ::cuMemcpyPeer, ::cuMemcpyAsync, + * ::cuMemcpy3DPeerAsync, ::cuMemAdvise, ::cuMemPrefetchAsync + * ::cudaMemPrefetchAsync_v2 + */ +CUresult CUDAAPI cuMemPrefetchAsync(CUdeviceptr devPtr, size_t count, CUdevice dstDevice, CUstream hStream); + +/** + * \brief Prefetches memory to the specified destination location + * + * Prefetches memory to the specified destination location. \p devPtr is the + * base device pointer of the memory to be prefetched and \p location specifies the + * destination location. \p count specifies the number of bytes to copy. \p hStream + * is the stream in which the operation is enqueued. The memory range must refer + * to managed memory allocated via ::cuMemAllocManaged or declared via __managed__ variables. + * + * Specifying ::CU_MEM_LOCATION_TYPE_DEVICE for ::CUmemLocation::type will prefetch memory to GPU + * specified by device ordinal ::CUmemLocation::id which must have non-zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. Additionally, \p hStream must be associated with a device + * that has a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * Specifying ::CU_MEM_LOCATION_TYPE_HOST as ::CUmemLocation::type will prefetch data to host memory. + * Applications can request prefetching memory to a specific host NUMA node by specifying + * ::CU_MEM_LOCATION_TYPE_HOST_NUMA for ::CUmemLocation::type and a valid host NUMA node id in ::CUmemLocation::id + * Users can also request prefetching memory to the host NUMA node closest to the current thread's CPU by specifying + * ::CU_MEM_LOCATION_TYPE_HOST_NUMA_CURRENT for ::CUmemLocation::type. Note when ::CUmemLocation::type is etiher + * ::CU_MEM_LOCATION_TYPE_HOST OR ::CU_MEM_LOCATION_TYPE_HOST_NUMA_CURRENT, ::CUmemLocation::id will be ignored. + * + * The start address and end address of the memory range will be rounded down and rounded up + * respectively to be aligned to CPU page size before the prefetch operation is enqueued + * in the stream. + * + * If no physical memory has been allocated for this region, then this memory region + * will be populated and mapped on the destination device. If there's insufficient + * memory to prefetch the desired region, the Unified Memory driver may evict pages from other + * ::cuMemAllocManaged allocations to host memory in order to make room. Device memory + * allocated using ::cuMemAlloc or ::cuArrayCreate will not be evicted. + * + * By default, any mappings to the previous location of the migrated pages are removed and + * mappings for the new location are only setup on the destination location. The exact behavior however + * also depends on the settings applied to this memory range via ::cuMemAdvise as described + * below: + * + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY was set on any subset of this memory range, + * then that subset will create a read-only copy of the pages on destination location. + * If however the destination location is a host NUMA node, then any pages of that subset + * that are already in another host NUMA node will be transferred to the destination. + * + * If ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION was called on any subset of this memory + * range, then the pages will be migrated to \p location even if \p location is not the + * preferred location of any pages in the memory range. + * + * If ::CU_MEM_ADVISE_SET_ACCESSED_BY was called on any subset of this memory range, + * then mappings to those pages from all the appropriate processors are updated to + * refer to the new location if establishing such a mapping is possible. Otherwise, + * those mappings are cleared. + * + * Note that this API is not required for functionality and only serves to improve performance + * by allowing the application to migrate data to a suitable location before it is accessed. + * Memory accesses to this range are always coherent and are allowed even when the data is + * actively being migrated. + * + * Note that this function is asynchronous with respect to the host and all work + * on other devices. + * + * \param devPtr - Pointer to be prefetched + * \param count - Size in bytes + * \param dstDevice - Destination device to prefetch to + * \param flags - flags for future use, must be zero now. + * \param hStream - Stream to enqueue prefetch operation + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpy, ::cuMemcpyPeer, ::cuMemcpyAsync, + * ::cuMemcpy3DPeerAsync, ::cuMemAdvise, ::cuMemPrefetchAsync + * ::cudaMemPrefetchAsync_v2 + */ +CUresult CUDAAPI cuMemPrefetchAsync_v2(CUdeviceptr devPtr, size_t count, CUmemLocation location, unsigned int flags, CUstream hStream); + +/** + * \brief Advise about the usage of a given memory range + * + * Note there is a later version of this API, ::cuMemAdvise_v2. It will + * supplant this version in 13.0, which is retained for minor version compatibility. + * + * Advise the Unified Memory subsystem about the usage pattern for the memory range + * starting at \p devPtr with a size of \p count bytes. The start address and end address of the memory + * range will be rounded down and rounded up respectively to be aligned to CPU page size before the + * advice is applied. The memory range must refer to managed memory allocated via ::cuMemAllocManaged + * or declared via __managed__ variables. The memory range could also refer to system-allocated pageable + * memory provided it represents a valid, host-accessible region of memory and all additional constraints + * imposed by \p advice as outlined below are also satisfied. Specifying an invalid system-allocated pageable + * memory range results in an error being returned. + * + * The \p advice parameter can take the following values: + * - ::CU_MEM_ADVISE_SET_READ_MOSTLY: This implies that the data is mostly going to be read + * from and only occasionally written to. Any read accesses from any processor to this region will create a + * read-only copy of at least the accessed pages in that processor's memory. Additionally, if ::cuMemPrefetchAsync + * is called on this region, it will create a read-only copy of the data on the destination processor. + * If any processor writes to this region, all copies of the corresponding page will be invalidated + * except for the one where the write occurred. The \p device argument is ignored for this advice. + * Note that for a page to be read-duplicated, the accessing processor must either be the CPU or a GPU + * that has a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * Also, if a context is created on a device that does not have the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS set, then read-duplication will not occur until + * all such contexts are destroyed. + * If the memory region refers to valid system-allocated pageable memory, then the accessing device must + * have a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS for a read-only + * copy to be created on that device. Note however that if the accessing device also has a non-zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, then setting this advice + * will not create a read-only copy when that device accesses this memory region. + * + * - ::CU_MEM_ADVISE_UNSET_READ_MOSTLY: Undoes the effect of ::CU_MEM_ADVISE_SET_READ_MOSTLY and also prevents the + * Unified Memory driver from attempting heuristic read-duplication on the memory range. Any read-duplicated + * copies of the data will be collapsed into a single copy. The location for the collapsed + * copy will be the preferred location if the page has a preferred location and one of the read-duplicated + * copies was resident at that location. Otherwise, the location chosen is arbitrary. + * + * - ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION: This advice sets the preferred location for the + * data to be the memory belonging to \p device. Passing in CU_DEVICE_CPU for \p device sets the + * preferred location as host memory. If \p device is a GPU, then it must have a non-zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. Setting the preferred location + * does not cause data to migrate to that location immediately. Instead, it guides the migration policy + * when a fault occurs on that memory region. If the data is already in its preferred location and the + * faulting processor can establish a mapping without requiring the data to be migrated, then + * data migration will be avoided. On the other hand, if the data is not in its preferred location + * or if a direct mapping cannot be established, then it will be migrated to the processor accessing + * it. It is important to note that setting the preferred location does not prevent data prefetching + * done using ::cuMemPrefetchAsync. + * Having a preferred location can override the page thrash detection and resolution logic in the Unified + * Memory driver. Normally, if a page is detected to be constantly thrashing between for example host and device + * memory, the page may eventually be pinned to host memory by the Unified Memory driver. But + * if the preferred location is set as device memory, then the page will continue to thrash indefinitely. + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice, unless read accesses from + * \p device will not result in a read-only copy being created on that device as outlined in description for + * the advice ::CU_MEM_ADVISE_SET_READ_MOSTLY. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. + * + * - ::CU_MEM_ADVISE_UNSET_PREFERRED_LOCATION: Undoes the effect of ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION + * and changes the preferred location to none. + * + * - ::CU_MEM_ADVISE_SET_ACCESSED_BY: This advice implies that the data will be accessed by \p device. + * Passing in ::CU_DEVICE_CPU for \p device will set the advice for the CPU. If \p device is a GPU, then + * the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS must be non-zero. + * This advice does not cause data migration and has no impact on the location of the data per se. Instead, + * it causes the data to always be mapped in the specified processor's page tables, as long as the + * location of the data permits a mapping to be established. If the data gets migrated for any reason, + * the mappings are updated accordingly. + * This advice is recommended in scenarios where data locality is not important, but avoiding faults is. + * Consider for example a system containing multiple GPUs with peer-to-peer access enabled, where the + * data located on one GPU is occasionally accessed by peer GPUs. In such scenarios, migrating data + * over to the other GPUs is not as important because the accesses are infrequent and the overhead of + * migration may be too high. But preventing faults can still help improve performance, and so having + * a mapping set up in advance is useful. Note that on CPU access of this data, the data may be migrated + * to host memory because the CPU typically cannot access device memory directly. Any GPU that had the + * ::CU_MEM_ADVISE_SET_ACCESSED_BY flag set for this data will now have its mapping updated to point to the + * page in host memory. + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice. Additionally, if the + * preferred location of this memory region or any subset of it is also \p device, then the policies + * associated with ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION will override the policies of this advice. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. Additionally, if \p device has + * a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, + * then this call has no effect. + * + * - ::CU_MEM_ADVISE_UNSET_ACCESSED_BY: Undoes the effect of ::CU_MEM_ADVISE_SET_ACCESSED_BY. Any mappings to + * the data from \p device may be removed at any time causing accesses to result in non-fatal page faults. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. Additionally, if \p device has + * a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, + * then this call has no effect. + * + * \param devPtr - Pointer to memory to set the advice for + * \param count - Size in bytes of the memory range + * \param advice - Advice to be applied for the specified memory range + * \param device - Device to apply the advice for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpy, ::cuMemcpyPeer, ::cuMemcpyAsync, + * ::cuMemcpy3DPeerAsync, ::cuMemPrefetchAsync, ::cuMemAdvise_v2 + * ::cudaMemAdvise + */ +CUresult CUDAAPI cuMemAdvise(CUdeviceptr devPtr, size_t count, CUmem_advise advice, CUdevice device); + +/** + * \brief Advise about the usage of a given memory range + * + * Advise the Unified Memory subsystem about the usage pattern for the memory range + * starting at \p devPtr with a size of \p count bytes. The start address and end address of the memory + * range will be rounded down and rounded up respectively to be aligned to CPU page size before the + * advice is applied. The memory range must refer to managed memory allocated via ::cuMemAllocManaged + * or declared via __managed__ variables. The memory range could also refer to system-allocated pageable + * memory provided it represents a valid, host-accessible region of memory and all additional constraints + * imposed by \p advice as outlined below are also satisfied. Specifying an invalid system-allocated pageable + * memory range results in an error being returned. + * + * The \p advice parameter can take the following values: + * - ::CU_MEM_ADVISE_SET_READ_MOSTLY: This implies that the data is mostly going to be read + * from and only occasionally written to. Any read accesses from any processor to this region will create a + * read-only copy of at least the accessed pages in that processor's memory. Additionally, if ::cuMemPrefetchAsync + * or ::cuMemPrefetchAsync_v2 is called on this region, it will create a read-only copy of the data on the destination processor. + * If the target location for ::cuMemPrefetchAsync_v2 is a host NUMA node and a read-only copy already exists on + * another host NUMA node, that copy will be migrated to the targeted host NUMA node. + * If any processor writes to this region, all copies of the corresponding page will be invalidated + * except for the one where the write occurred. If the writing processor is the CPU and the preferred location of + * the page is a host NUMA node, then the page will also be migrated to that host NUMA node. The \p location argument is ignored for this advice. + * Note that for a page to be read-duplicated, the accessing processor must either be the CPU or a GPU + * that has a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * Also, if a context is created on a device that does not have the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS set, then read-duplication will not occur until + * all such contexts are destroyed. + * If the memory region refers to valid system-allocated pageable memory, then the accessing device must + * have a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS for a read-only + * copy to be created on that device. Note however that if the accessing device also has a non-zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, then setting this advice + * will not create a read-only copy when that device accesses this memory region. + * + * - ::CU_MEM_ADVISE_UNSET_READ_MOSTLY: Undoes the effect of ::CU_MEM_ADVISE_SET_READ_MOSTLY and also prevents the + * Unified Memory driver from attempting heuristic read-duplication on the memory range. Any read-duplicated + * copies of the data will be collapsed into a single copy. The location for the collapsed + * copy will be the preferred location if the page has a preferred location and one of the read-duplicated + * copies was resident at that location. Otherwise, the location chosen is arbitrary. + * Note: The \p location argument is ignored for this advice. + * + * - ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION: This advice sets the preferred location for the + * data to be the memory belonging to \p location. When ::CUmemLocation::type is ::CU_MEM_LOCATION_TYPE_HOST, + * ::CUmemLocation::id is ignored and the preferred location is set to be host memory. To set the preferred location + * to a specific host NUMA node, applications must set ::CUmemLocation::type to ::CU_MEM_LOCATION_TYPE_HOST_NUMA and + * ::CUmemLocation::id must specify the NUMA ID of the host NUMA node. If ::CUmemLocation::type is set to ::CU_MEM_LOCATION_TYPE_HOST_NUMA_CURRENT, + * ::CUmemLocation::id will be ignored and the the host NUMA node closest to the calling thread's CPU will be used as the preferred location. + * If ::CUmemLocation::type is a ::CU_MEM_LOCATION_TYPE_DEVICE, then ::CUmemLocation::id must be a valid device ordinal + * and the device must have a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * Setting the preferred location does not cause data to migrate to that location immediately. Instead, it guides the migration policy + * when a fault occurs on that memory region. If the data is already in its preferred location and the + * faulting processor can establish a mapping without requiring the data to be migrated, then + * data migration will be avoided. On the other hand, if the data is not in its preferred location + * or if a direct mapping cannot be established, then it will be migrated to the processor accessing + * it. It is important to note that setting the preferred location does not prevent data prefetching + * done using ::cuMemPrefetchAsync. + * Having a preferred location can override the page thrash detection and resolution logic in the Unified + * Memory driver. Normally, if a page is detected to be constantly thrashing between for example host and device + * memory, the page may eventually be pinned to host memory by the Unified Memory driver. But + * if the preferred location is set as device memory, then the page will continue to thrash indefinitely. + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice, unless read accesses from + * \p location will not result in a read-only copy being created on that procesor as outlined in description for + * the advice ::CU_MEM_ADVISE_SET_READ_MOSTLY. + * If the memory region refers to valid system-allocated pageable memory, and ::CUmemLocation::type is CU_MEM_LOCATION_TYPE_DEVICE + * then ::CUmemLocation::id must be a valid device that has a non-zero alue for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. + * + * - ::CU_MEM_ADVISE_UNSET_PREFERRED_LOCATION: Undoes the effect of ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION + * and changes the preferred location to none. The \p location argument is ignored for this advice. + * + * - ::CU_MEM_ADVISE_SET_ACCESSED_BY: This advice implies that the data will be accessed by processor \p location. + * The ::CUmemLocation::type must be either ::CU_MEM_LOCATION_TYPE_DEVICE with ::CUmemLocation::id representing a valid device + * ordinal or ::CU_MEM_LOCATION_TYPE_HOST and ::CUmemLocation::id will be ignored. All other location types are invalid. + * If ::CUmemLocation::id is a GPU, then the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS must be non-zero. + * This advice does not cause data migration and has no impact on the location of the data per se. Instead, + * it causes the data to always be mapped in the specified processor's page tables, as long as the + * location of the data permits a mapping to be established. If the data gets migrated for any reason, + * the mappings are updated accordingly. + * This advice is recommended in scenarios where data locality is not important, but avoiding faults is. + * Consider for example a system containing multiple GPUs with peer-to-peer access enabled, where the + * data located on one GPU is occasionally accessed by peer GPUs. In such scenarios, migrating data + * over to the other GPUs is not as important because the accesses are infrequent and the overhead of + * migration may be too high. But preventing faults can still help improve performance, and so having + * a mapping set up in advance is useful. Note that on CPU access of this data, the data may be migrated + * to host memory because the CPU typically cannot access device memory directly. Any GPU that had the + * ::CU_MEM_ADVISE_SET_ACCESSED_BY flag set for this data will now have its mapping updated to point to the + * page in host memory. + * If ::CU_MEM_ADVISE_SET_READ_MOSTLY is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice. Additionally, if the + * preferred location of this memory region or any subset of it is also \p location, then the policies + * associated with ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION will override the policies of this advice. + * If the memory region refers to valid system-allocated pageable memory, and ::CUmemLocation::type is ::CU_MEM_LOCATION_TYPE_DEVICE + * then device in ::CUmemLocation::id must have a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. + * Additionally, if ::CUmemLocation::id has a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, + * then this call has no effect. + * + * - ::CU_MEM_ADVISE_UNSET_ACCESSED_BY: Undoes the effect of ::CU_MEM_ADVISE_SET_ACCESSED_BY. Any mappings to + * the data from \p location may be removed at any time causing accesses to result in non-fatal page faults. + * If the memory region refers to valid system-allocated pageable memory, and ::CUmemLocation::type is ::CU_MEM_LOCATION_TYPE_DEVICE + * then device in ::CUmemLocation::id must have a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. + * Additionally, if ::CUmemLocation::id has a non-zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS_USES_HOST_PAGE_TABLES, + * then this call has no effect. + * + * \param devPtr - Pointer to memory to set the advice for + * \param count - Size in bytes of the memory range + * \param advice - Advice to be applied for the specified memory range + * \param location - location to apply the advice for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemcpy, ::cuMemcpyPeer, ::cuMemcpyAsync, + * ::cuMemcpy3DPeerAsync, ::cuMemPrefetchAsync, ::cuMemAdvise + * ::cudaMemAdvise + */ +CUresult CUDAAPI cuMemAdvise_v2(CUdeviceptr devPtr, size_t count, CUmem_advise advice, CUmemLocation location); + +/** + * \brief Query an attribute of a given memory range + * + * Query an attribute about the memory range starting at \p devPtr with a size of \p count bytes. The + * memory range must refer to managed memory allocated via ::cuMemAllocManaged or declared via + * __managed__ variables. + * + * The \p attribute parameter can take the following values: + * - ::CU_MEM_RANGE_ATTRIBUTE_READ_MOSTLY: If this attribute is specified, \p data will be interpreted + * as a 32-bit integer, and \p dataSize must be 4. The result returned will be 1 if all pages in the given + * memory range have read-duplication enabled, or 0 otherwise. + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. The result returned will be a GPU device + * id if all pages in the memory range have that GPU as their preferred location, or it will be CU_DEVICE_CPU + * if all pages in the memory range have the CPU as their preferred location, or it will be CU_DEVICE_INVALID + * if either all the pages don't have the same preferred location or some of the pages don't have a + * preferred location at all. Note that the actual location of the pages in the memory range at the time of + * the query may be different from the preferred location. + * - ::CU_MEM_RANGE_ATTRIBUTE_ACCESSED_BY: If this attribute is specified, \p data will be interpreted + * as an array of 32-bit integers, and \p dataSize must be a non-zero multiple of 4. The result returned + * will be a list of device ids that had ::CU_MEM_ADVISE_SET_ACCESSED_BY set for that entire memory range. + * If any device does not have that advice set for the entire memory range, that device will not be included. + * If \p data is larger than the number of devices that have that advice set for that memory range, + * CU_DEVICE_INVALID will be returned in all the extra space provided. For ex., if \p dataSize is 12 + * (i.e. \p data has 3 elements) and only device 0 has the advice set, then the result returned will be + * { 0, CU_DEVICE_INVALID, CU_DEVICE_INVALID }. If \p data is smaller than the number of devices that have + * that advice set, then only as many devices will be returned as can fit in the array. There is no + * guarantee on which specific devices will be returned, however. + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. The result returned will be the last location + * to which all pages in the memory range were prefetched explicitly via ::cuMemPrefetchAsync. This will either be + * a GPU id or CU_DEVICE_CPU depending on whether the last location for prefetch was a GPU or the CPU + * respectively. If any page in the memory range was never explicitly prefetched or if all pages were not + * prefetched to the same location, CU_DEVICE_INVALID will be returned. Note that this simply returns the + * last location that the application requested to prefetch the memory range to. It gives no indication as to + * whether the prefetch operation to that location has completed or even begun. + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_TYPE: If this attribute is specified, \p data will be + * interpreted as a ::CUmemLocationType, and \p dataSize must be sizeof(CUmemLocationType). The ::CUmemLocationType returned will be + * ::CU_MEM_LOCATION_TYPE_DEVICE if all pages in the memory range have the same GPU as their preferred location, or ::CUmemLocationType + * will be ::CU_MEM_LOCATION_TYPE_HOST if all pages in the memory range have the CPU as their preferred location, or it will be ::CU_MEM_LOCATION_TYPE_HOST_NUMA + * if all the pages in the memory range have the same host NUMA node ID as their preferred location or it will be ::CU_MEM_LOCATION_TYPE_INVALID + * if either all the pages don't have the same preferred location or some of the pages don't have a preferred location at all. + * Note that the actual location type of the pages in the memory range at the time of the query may be different from the preferred location type. + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_ID: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. If the ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_TYPE query for the same address range + * returns ::CU_MEM_LOCATION_TYPE_DEVICE, it will be a valid device ordinal or if it returns ::CU_MEM_LOCATION_TYPE_HOST_NUMA, it will be a valid host NUMA node ID + * or if it returns any other location type, the id should be ignored. + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_TYPE: If this attribute is specified, \p data will be + * interpreted as a ::CUmemLocationType, and \p dataSize must be sizeof(CUmemLocationType). The result returned will be the last location + * to which all pages in the memory range were prefetched explicitly via ::cuMemPrefetchAsync. The ::CUmemLocationType returned + * will be ::CU_MEM_LOCATION_TYPE_DEVICE if the last prefetch location was a GPU or ::CU_MEM_LOCATION_TYPE_HOST if it was the CPU or ::CU_MEM_LOCATION_TYPE_HOST_NUMA if + * the last prefetch location was a specific host NUMA node. If any page in the memory range was never explicitly prefetched or if all pages were not + * prefetched to the same location, ::CUmemLocationType will be ::CU_MEM_LOCATION_TYPE_INVALID. + * Note that this simply returns the last location type that the application requested to prefetch the memory range to. It gives no indication as to + * whether the prefetch operation to that location has completed or even begun. + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_ID: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. If the ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_TYPE query for the same address range + * returns ::CU_MEM_LOCATION_TYPE_DEVICE, it will be a valid device ordinal or if it returns ::CU_MEM_LOCATION_TYPE_HOST_NUMA, it will be a valid host NUMA node ID + * or if it returns any other location type, the id should be ignored. + * + * \param data - A pointers to a memory location where the result + * of each attribute query will be written to. + * \param dataSize - Array containing the size of data + * \param attribute - The attribute to query + * \param devPtr - Start of the range to query + * \param count - Size of the range to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * \note_async + * \note_null_stream + * + * \sa ::cuMemRangeGetAttributes, ::cuMemPrefetchAsync, + * ::cuMemAdvise, + * ::cudaMemRangeGetAttribute + */ +CUresult CUDAAPI cuMemRangeGetAttribute(void *data, size_t dataSize, CUmem_range_attribute attribute, CUdeviceptr devPtr, size_t count); + +/** + * \brief Query attributes of a given memory range. + * + * Query attributes of the memory range starting at \p devPtr with a size of \p count bytes. The + * memory range must refer to managed memory allocated via ::cuMemAllocManaged or declared via + * __managed__ variables. The \p attributes array will be interpreted to have \p numAttributes + * entries. The \p dataSizes array will also be interpreted to have \p numAttributes entries. + * The results of the query will be stored in \p data. + * + * The list of supported attributes are given below. Please refer to ::cuMemRangeGetAttribute for + * attribute descriptions and restrictions. + * + * - ::CU_MEM_RANGE_ATTRIBUTE_READ_MOSTLY + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION + * - ::CU_MEM_RANGE_ATTRIBUTE_ACCESSED_BY + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_TYPE + * - ::CU_MEM_RANGE_ATTRIBUTE_PREFERRED_LOCATION_ID + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_TYPE + * - ::CU_MEM_RANGE_ATTRIBUTE_LAST_PREFETCH_LOCATION_ID + * + * \param data - A two-dimensional array containing pointers to memory + * locations where the result of each attribute query will be written to. + * \param dataSizes - Array containing the sizes of each result + * \param attributes - An array of attributes to query + * (numAttributes and the number of attributes in this array should match) + * \param numAttributes - Number of attributes to query + * \param devPtr - Start of the range to query + * \param count - Size of the range to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa ::cuMemRangeGetAttribute, ::cuMemAdvise, + * ::cuMemPrefetchAsync, + * ::cudaMemRangeGetAttributes + */ +CUresult CUDAAPI cuMemRangeGetAttributes(void **data, size_t *dataSizes, CUmem_range_attribute *attributes, size_t numAttributes, CUdeviceptr devPtr, size_t count); + +/** + * \brief Set attributes on a previously allocated memory region + * + * The supported attributes are: + * + * - ::CU_POINTER_ATTRIBUTE_SYNC_MEMOPS: + * + * A boolean attribute that can either be set (1) or unset (0). When set, + * the region of memory that \p ptr points to is guaranteed to always synchronize + * memory operations that are synchronous. If there are some previously initiated + * synchronous memory operations that are pending when this attribute is set, the + * function does not return until those memory operations are complete. + * See further documentation in the section titled "API synchronization behavior" + * to learn more about cases when synchronous memory operations can + * exhibit asynchronous behavior. + * \p value will be considered as a pointer to an unsigned integer to which this attribute is to be set. + * + * \param value - Pointer to memory containing the value to be set + * \param attribute - Pointer attribute to set + * \param ptr - Pointer to a memory region allocated using CUDA memory allocation APIs + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa ::cuPointerGetAttribute, + * ::cuPointerGetAttributes, + * ::cuMemAlloc, + * ::cuMemFree, + * ::cuMemAllocHost, + * ::cuMemFreeHost, + * ::cuMemHostAlloc, + * ::cuMemHostRegister, + * ::cuMemHostUnregister + */ +CUresult CUDAAPI cuPointerSetAttribute(const void *value, CUpointer_attribute attribute, CUdeviceptr ptr); + +/** + * \brief Returns information about a pointer. + * + * The supported attributes are (refer to ::cuPointerGetAttribute for attribute descriptions and restrictions): + * + * - ::CU_POINTER_ATTRIBUTE_CONTEXT + * - ::CU_POINTER_ATTRIBUTE_MEMORY_TYPE + * - ::CU_POINTER_ATTRIBUTE_DEVICE_POINTER + * - ::CU_POINTER_ATTRIBUTE_HOST_POINTER + * - ::CU_POINTER_ATTRIBUTE_SYNC_MEMOPS + * - ::CU_POINTER_ATTRIBUTE_BUFFER_ID + * - ::CU_POINTER_ATTRIBUTE_IS_MANAGED + * - ::CU_POINTER_ATTRIBUTE_DEVICE_ORDINAL + * - ::CU_POINTER_ATTRIBUTE_RANGE_START_ADDR + * - ::CU_POINTER_ATTRIBUTE_RANGE_SIZE + * - ::CU_POINTER_ATTRIBUTE_MAPPED + * - ::CU_POINTER_ATTRIBUTE_IS_LEGACY_CUDA_IPC_CAPABLE + * - ::CU_POINTER_ATTRIBUTE_ALLOWED_HANDLE_TYPES + * - ::CU_POINTER_ATTRIBUTE_MEMPOOL_HANDLE + * + * \param numAttributes - Number of attributes to query + * \param attributes - An array of attributes to query + * (numAttributes and the number of attributes in this array should match) + * \param data - A two-dimensional array containing pointers to memory + * locations where the result of each attribute query will be written to. + * \param ptr - Pointer to query + * + * Unlike ::cuPointerGetAttribute, this function will not return an error when the \p ptr + * encountered is not a valid CUDA pointer. Instead, the attributes are assigned default NULL values + * and CUDA_SUCCESS is returned. + * + * If \p ptr was not allocated by, mapped by, or registered with a ::CUcontext which uses UVA + * (Unified Virtual Addressing), ::CUDA_ERROR_INVALID_CONTEXT is returned. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuPointerGetAttribute, + * ::cuPointerSetAttribute, + * ::cudaPointerGetAttributes + */ +CUresult CUDAAPI cuPointerGetAttributes(unsigned int numAttributes, CUpointer_attribute *attributes, void **data, CUdeviceptr ptr); + +/** @} */ /* END CUDA_UNIFIED */ + +/** + * \defgroup CUDA_STREAM Stream Management + * + * ___MANBRIEF___ stream management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the stream management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Create a stream + * + * Creates a stream and returns a handle in \p phStream. The \p Flags argument + * determines behaviors of the stream. + * + * Valid values for \p Flags are: + * - ::CU_STREAM_DEFAULT: Default stream creation flag. + * - ::CU_STREAM_NON_BLOCKING: Specifies that work running in the created + * stream may run concurrently with work in stream 0 (the NULL stream), and that + * the created stream should perform no implicit synchronization with stream 0. + * + * \param phStream - Returned newly created stream + * \param Flags - Parameters for stream creation + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreateWithPriority, + * ::cuStreamGetPriority, + * ::cuStreamGetFlags, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags + */ +CUresult CUDAAPI cuStreamCreate(CUstream *phStream, unsigned int Flags); + +/** + * \brief Create a stream with the given priority + * + * Creates a stream with the specified priority and returns a handle in \p phStream. + * This affects the scheduling priority of work in the stream. Priorities provide a + * hint to preferentially run work with higher priority when possible, but do + * not preempt already-running work or provide any other functional guarantee on + * execution order. + * + * \p priority follows a convention where lower numbers represent higher priorities. + * '0' represents default priority. The range of meaningful numerical priorities can + * be queried using ::cuCtxGetStreamPriorityRange. If the specified priority is + * outside the numerical range returned by ::cuCtxGetStreamPriorityRange, + * it will automatically be clamped to the lowest or the highest number in the range. + * + * \param phStream - Returned newly created stream + * \param flags - Flags for stream creation. See ::cuStreamCreate for a list of + * valid flags + * \param priority - Stream priority. Lower numbers represent higher priorities. + * See ::cuCtxGetStreamPriorityRange for more information about + * meaningful stream priorities that can be passed. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \note Stream priorities are supported only on GPUs + * with compute capability 3.5 or higher. + * + * \note In the current implementation, only compute kernels launched in + * priority streams are affected by the stream's priority. Stream priorities have + * no effect on host-to-device and device-to-host memory operations. + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreate, + * ::cuStreamGetPriority, + * ::cuCtxGetStreamPriorityRange, + * ::cuStreamGetFlags, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamCreateWithPriority + */ +CUresult CUDAAPI cuStreamCreateWithPriority(CUstream *phStream, unsigned int flags, int priority); + + +/** + * \brief Query the priority of a given stream + * + * Query the priority of a stream created using ::cuStreamCreate or ::cuStreamCreateWithPriority + * and return the priority in \p priority. Note that if the stream was created with a + * priority outside the numerical range returned by ::cuCtxGetStreamPriorityRange, + * this function returns the clamped priority. + * See ::cuStreamCreateWithPriority for details about priority clamping. + * + * \param hStream - Handle to the stream to be queried + * \param priority - Pointer to a signed integer in which the stream's priority is returned + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreate, + * ::cuStreamCreateWithPriority, + * ::cuCtxGetStreamPriorityRange, + * ::cuStreamGetFlags, + * ::cudaStreamGetPriority + */ +CUresult CUDAAPI cuStreamGetPriority(CUstream hStream, int *priority); + +/** + * \brief Query the flags of a given stream + * + * Query the flags of a stream created using ::cuStreamCreate or ::cuStreamCreateWithPriority + * and return the flags in \p flags. + * + * \param hStream - Handle to the stream to be queried + * \param flags - Pointer to an unsigned integer in which the stream's flags are returned + * The value returned in \p flags is a logical 'OR' of all flags that + * were used while creating this stream. See ::cuStreamCreate for the list + * of valid flags + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreate, + * ::cuStreamGetPriority, + * ::cudaStreamGetFlags + */ +CUresult CUDAAPI cuStreamGetFlags(CUstream hStream, unsigned int *flags); + +/** + * \brief Returns the unique Id associated with the stream handle supplied + * + * Returns in \p streamId the unique Id which is associated with the given stream handle. + * The Id is unique for the life of the program. + * + * The stream handle \p hStream can refer to any of the following: + *
    + *
  • a stream created via any of the CUDA driver APIs such as ::cuStreamCreate + * and ::cuStreamCreateWithPriority, or their runtime API equivalents such as + * ::cudaStreamCreate, ::cudaStreamCreateWithFlags and ::cudaStreamCreateWithPriority. + * Passing an invalid handle will result in undefined behavior.
    • + *
  • any of the special streams such as the NULL stream, ::CU_STREAM_LEGACY and + * ::CU_STREAM_PER_THREAD. The runtime API equivalents of these are also accepted, + * which are NULL, ::cudaStreamLegacy and ::cudaStreamPerThread respectively.
    • + *
+ * + * \param hStream - Handle to the stream to be queried + * \param streamId - Pointer to store the Id of the stream + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreate, + * ::cuStreamGetPriority, + * ::cudaStreamGetId + */ +CUresult CUDAAPI cuStreamGetId(CUstream hStream, unsigned long long *streamId); + +/** + * \brief Query the context associated with a stream + * + * Returns the CUDA context that the stream is associated with. + * + * The stream handle \p hStream can refer to any of the following: + *
    + *
  • a stream created via any of the CUDA driver APIs such as ::cuStreamCreate + * and ::cuStreamCreateWithPriority, or their runtime API equivalents such as + * ::cudaStreamCreate, ::cudaStreamCreateWithFlags and ::cudaStreamCreateWithPriority. + * The returned context is the context that was active in the calling thread when the + * stream was created. Passing an invalid handle will result in undefined behavior.
    • + *
  • any of the special streams such as the NULL stream, ::CU_STREAM_LEGACY and + * ::CU_STREAM_PER_THREAD. The runtime API equivalents of these are also accepted, + * which are NULL, ::cudaStreamLegacy and ::cudaStreamPerThread respectively. + * Specifying any of the special handles will return the context current to the + * calling thread. If no context is current to the calling thread, + * ::CUDA_ERROR_INVALID_CONTEXT is returned.
    • + *
+ * + * \param hStream - Handle to the stream to be queried + * \param pctx - Returned context associated with the stream + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreateWithPriority, + * ::cuStreamGetPriority, + * ::cuStreamGetFlags, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags + */ +CUresult CUDAAPI cuStreamGetCtx(CUstream hStream, CUcontext *pctx); + +/** + * \brief Make a compute stream wait on an event + * + * Makes all future work submitted to \p hStream wait for all work captured in + * \p hEvent. See ::cuEventRecord() for details on what is captured by an event. + * The synchronization will be performed efficiently on the device when applicable. + * \p hEvent may be from a different context or device than \p hStream. + * + * flags include: + * - ::CU_EVENT_WAIT_DEFAULT: Default event creation flag. + * - ::CU_EVENT_WAIT_EXTERNAL: Event is captured in the graph as an external + * event node when performing stream capture. This flag is invalid outside + * of stream capture. + * + * \param hStream - Stream to wait + * \param hEvent - Event to wait on (may not be NULL) + * \param Flags - See ::CUevent_capture_flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuEventRecord, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cuStreamDestroy, + * ::cudaStreamWaitEvent + */ +CUresult CUDAAPI cuStreamWaitEvent(CUstream hStream, CUevent hEvent, unsigned int Flags); + +/** + * \brief Add a callback to a compute stream + * + * \note This function is slated for eventual deprecation and removal. If + * you do not require the callback to execute in case of a device error, + * consider using ::cuLaunchHostFunc. Additionally, this function is not + * supported with ::cuStreamBeginCapture and ::cuStreamEndCapture, unlike + * ::cuLaunchHostFunc. + * + * Adds a callback to be called on the host after all currently enqueued + * items in the stream have completed. For each + * cuStreamAddCallback call, the callback will be executed exactly once. + * The callback will block later work in the stream until it is finished. + * + * The callback may be passed ::CUDA_SUCCESS or an error code. In the event + * of a device error, all subsequently executed callbacks will receive an + * appropriate ::CUresult. + * + * Callbacks must not make any CUDA API calls. Attempting to use a CUDA API + * will result in ::CUDA_ERROR_NOT_PERMITTED. Callbacks must not perform any + * synchronization that may depend on outstanding device work or other callbacks + * that are not mandated to run earlier. Callbacks without a mandated order + * (in independent streams) execute in undefined order and may be serialized. + * + * For the purposes of Unified Memory, callback execution makes a number of + * guarantees: + *
    + *
  • The callback stream is considered idle for the duration of the + * callback. Thus, for example, a callback may always use memory attached + * to the callback stream.
    • + *
  • The start of execution of a callback has the same effect as + * synchronizing an event recorded in the same stream immediately prior to + * the callback. It thus synchronizes streams which have been "joined" + * prior to the callback.
    • + *
  • Adding device work to any stream does not have the effect of making + * the stream active until all preceding host functions and stream callbacks + * have executed. Thus, for + * example, a callback might use global attached memory even if work has + * been added to another stream, if the work has been ordered behind the + * callback with an event.
    • + *
  • Completion of a callback does not cause a stream to become + * active except as described above. The callback stream will remain idle + * if no device work follows the callback, and will remain idle across + * consecutive callbacks without device work in between. Thus, for example, + * stream synchronization can be done by signaling from a callback at the + * end of the stream.
    • + *
+ * + * \param hStream - Stream to add callback to + * \param callback - The function to call once preceding stream operations are complete + * \param userData - User specified data to be passed to the callback function + * \param flags - Reserved for future use, must be 0 + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamWaitEvent, + * ::cuStreamDestroy, + * ::cuMemAllocManaged, + * ::cuStreamAttachMemAsync, + * ::cuLaunchHostFunc, + * ::cudaStreamAddCallback + */ +CUresult CUDAAPI cuStreamAddCallback(CUstream hStream, CUstreamCallback callback, void *userData, unsigned int flags); + +/** + * \brief Begins graph capture on a stream + * + * Begin graph capture on \p hStream. When a stream is in capture mode, all operations + * pushed into the stream will not be executed, but will instead be captured into + * a graph, which will be returned via ::cuStreamEndCapture. Capture may not be initiated + * if \p stream is CU_STREAM_LEGACY. Capture must be ended on the same stream in which + * it was initiated, and it may only be initiated if the stream is not already in capture + * mode. The capture mode may be queried via ::cuStreamIsCapturing. A unique id + * representing the capture sequence may be queried via ::cuStreamGetCaptureInfo. + * + * If \p mode is not ::CU_STREAM_CAPTURE_MODE_RELAXED, ::cuStreamEndCapture must be + * called on this stream from the same thread. + * + * \param hStream - Stream in which to initiate capture + * \param mode - Controls the interaction of this capture sequence with other API + * calls that are potentially unsafe. For more details see + * ::cuThreadExchangeStreamCaptureMode. + * + * \note Kernels captured using this API must not use texture and surface references. + * Reading or writing through any texture or surface reference is undefined + * behavior. This restriction does not apply to texture and surface objects. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuStreamCreate, + * ::cuStreamIsCapturing, + * ::cuStreamEndCapture, + * ::cuThreadExchangeStreamCaptureMode + */ +CUresult CUDAAPI cuStreamBeginCapture(CUstream hStream, CUstreamCaptureMode mode); + +/** + * \brief Begins graph capture on a stream to an existing graph + * + * Begin graph capture on \p hStream, placing new nodes into an existing graph. When a stream is + * in capture mode, all operations pushed into the stream will not be executed, but will instead + * be captured into \p hGraph. The graph will not be instantiable until the user calls + * ::cuStreamEndCapture. + * + * Capture may not be initiated if \p stream is CU_STREAM_LEGACY. Capture must be ended on the + * same stream in which it was initiated, and it may only be initiated if the stream is not + * already in capture mode. The capture mode may be queried via ::cuStreamIsCapturing. A unique id + * representing the capture sequence may be queried via ::cuStreamGetCaptureInfo. + * + * If \p mode is not ::CU_STREAM_CAPTURE_MODE_RELAXED, ::cuStreamEndCapture must be + * called on this stream from the same thread. + * + * \param hStream - Stream in which to initiate capture. + * \param hGraph - Graph to capture into. + * \param dependencies - Dependencies of the first node captured in the stream. Can be NULL if numDependencies is 0. + * \param dependencyData - Optional array of data associated with each dependency. + * \param numDependencies - Number of dependencies. + * \param mode - Controls the interaction of this capture sequence with other API + * calls that are potentially unsafe. For more details see + * ::cuThreadExchangeStreamCaptureMode. + * + * \note Kernels captured using this API must not use texture and surface references. + * Reading or writing through any texture or surface reference is undefined + * behavior. This restriction does not apply to texture and surface objects. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuStreamBeginCapture, + * ::cuStreamCreate, + * ::cuStreamIsCapturing, + * ::cuStreamEndCapture, + * ::cuThreadExchangeStreamCaptureMode, + * ::cuGraphAddNode, + */ +CUresult CUDAAPI cuStreamBeginCaptureToGraph(CUstream hStream, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUstreamCaptureMode mode); + +/** + * \brief Swaps the stream capture interaction mode for a thread + * + * Sets the calling thread's stream capture interaction mode to the value contained + * in \p *mode, and overwrites \p *mode with the previous mode for the thread. To + * facilitate deterministic behavior across function or module boundaries, callers + * are encouraged to use this API in a push-pop fashion: \code + CUstreamCaptureMode mode = desiredMode; + cuThreadExchangeStreamCaptureMode(&mode); + ... + cuThreadExchangeStreamCaptureMode(&mode); // restore previous mode + * \endcode + * + * During stream capture (see ::cuStreamBeginCapture), some actions, such as a call + * to ::cudaMalloc, may be unsafe. In the case of ::cudaMalloc, the operation is + * not enqueued asynchronously to a stream, and is not observed by stream capture. + * Therefore, if the sequence of operations captured via ::cuStreamBeginCapture + * depended on the allocation being replayed whenever the graph is launched, the + * captured graph would be invalid. + * + * Therefore, stream capture places restrictions on API calls that can be made within + * or concurrently to a ::cuStreamBeginCapture-::cuStreamEndCapture sequence. This + * behavior can be controlled via this API and flags to ::cuStreamBeginCapture. + * + * A thread's mode is one of the following: + * - \p CU_STREAM_CAPTURE_MODE_GLOBAL: This is the default mode. If the local thread has + * an ongoing capture sequence that was not initiated with + * \p CU_STREAM_CAPTURE_MODE_RELAXED at \p cuStreamBeginCapture, or if any other thread + * has a concurrent capture sequence initiated with \p CU_STREAM_CAPTURE_MODE_GLOBAL, + * this thread is prohibited from potentially unsafe API calls. + * - \p CU_STREAM_CAPTURE_MODE_THREAD_LOCAL: If the local thread has an ongoing capture + * sequence not initiated with \p CU_STREAM_CAPTURE_MODE_RELAXED, it is prohibited + * from potentially unsafe API calls. Concurrent capture sequences in other threads + * are ignored. + * - \p CU_STREAM_CAPTURE_MODE_RELAXED: The local thread is not prohibited from potentially + * unsafe API calls. Note that the thread is still prohibited from API calls which + * necessarily conflict with stream capture, for example, attempting ::cuEventQuery + * on an event that was last recorded inside a capture sequence. + * + * \param mode - Pointer to mode value to swap with the current mode + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuStreamBeginCapture + */ +CUresult CUDAAPI cuThreadExchangeStreamCaptureMode(CUstreamCaptureMode *mode); + +/** + * \brief Ends capture on a stream, returning the captured graph + * + * End capture on \p hStream, returning the captured graph via \p phGraph. + * Capture must have been initiated on \p hStream via a call to ::cuStreamBeginCapture. + * If capture was invalidated, due to a violation of the rules of stream capture, then + * a NULL graph will be returned. + * + * If the \p mode argument to ::cuStreamBeginCapture was not + * ::CU_STREAM_CAPTURE_MODE_RELAXED, this call must be from the same thread as + * ::cuStreamBeginCapture. + * + * \param hStream - Stream to query + * \param phGraph - The captured graph + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_STREAM_CAPTURE_WRONG_THREAD + * \notefnerr + * + * \sa + * ::cuStreamCreate, + * ::cuStreamBeginCapture, + * ::cuStreamIsCapturing, + * ::cuGraphDestroy + */ +CUresult CUDAAPI cuStreamEndCapture(CUstream hStream, CUgraph *phGraph); + +/** + * \brief Returns a stream's capture status + * + * Return the capture status of \p hStream via \p captureStatus. After a successful + * call, \p *captureStatus will contain one of the following: + * - ::CU_STREAM_CAPTURE_STATUS_NONE: The stream is not capturing. + * - ::CU_STREAM_CAPTURE_STATUS_ACTIVE: The stream is capturing. + * - ::CU_STREAM_CAPTURE_STATUS_INVALIDATED: The stream was capturing but an error + * has invalidated the capture sequence. The capture sequence must be terminated + * with ::cuStreamEndCapture on the stream where it was initiated in order to + * continue using \p hStream. + * + * Note that, if this is called on ::CU_STREAM_LEGACY (the "null stream") while + * a blocking stream in the same context is capturing, it will return + * ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT and \p *captureStatus is unspecified + * after the call. The blocking stream capture is not invalidated. + * + * When a blocking stream is capturing, the legacy stream is in an + * unusable state until the blocking stream capture is terminated. The legacy + * stream is not supported for stream capture, but attempted use would have an + * implicit dependency on the capturing stream(s). + * + * \param hStream - Stream to query + * \param captureStatus - Returns the stream's capture status + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT + * \notefnerr + * + * \sa + * ::cuStreamCreate, + * ::cuStreamBeginCapture, + * ::cuStreamEndCapture + */ +CUresult CUDAAPI cuStreamIsCapturing(CUstream hStream, CUstreamCaptureStatus *captureStatus); + +/** + * \brief Query a stream's capture state + * + * Query stream state related to stream capture. + * + * If called on ::CU_STREAM_LEGACY (the "null stream") while a stream not created + * with ::CU_STREAM_NON_BLOCKING is capturing, returns ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT. + * + * Valid data (other than capture status) is returned only if both of the following are true: + * - the call returns CUDA_SUCCESS + * - the returned capture status is ::CU_STREAM_CAPTURE_STATUS_ACTIVE + * + * \param hStream - The stream to query + * \param captureStatus_out - Location to return the capture status of the stream; required + * \param id_out - Optional location to return an id for the capture sequence, which is + * unique over the lifetime of the process + * \param graph_out - Optional location to return the graph being captured into. All + * operations other than destroy and node removal are permitted on the graph + * while the capture sequence is in progress. This API does not transfer + * ownership of the graph, which is transferred or destroyed at + * ::cuStreamEndCapture. Note that the graph handle may be invalidated before + * end of capture for certain errors. Nodes that are or become + * unreachable from the original stream at ::cuStreamEndCapture due to direct + * actions on the graph do not trigger ::CUDA_ERROR_STREAM_CAPTURE_UNJOINED. + * \param dependencies_out - Optional location to store a pointer to an array of nodes. + * The next node to be captured in the stream will depend on this set of nodes, + * absent operations such as event wait which modify this set. The array pointer + * is valid until the next API call which operates on the stream or until the + * capture is terminated. The node handles may be copied out and are valid until + * they or the graph is destroyed. The driver-owned array may also be passed + * directly to APIs that operate on the graph (not the stream) without copying. + * \param numDependencies_out - Optional location to store the size of the array + * returned in dependencies_out. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuStreamGetCaptureInfo_v3 + * ::cuStreamBeginCapture, + * ::cuStreamIsCapturing, + * ::cuStreamUpdateCaptureDependencies + */ +CUresult CUDAAPI cuStreamGetCaptureInfo(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, + cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, size_t *numDependencies_out); + +/** + * \brief Query a stream's capture state (12.3+) + * + * Query stream state related to stream capture. + * + * If called on ::CU_STREAM_LEGACY (the "null stream") while a stream not created + * with ::CU_STREAM_NON_BLOCKING is capturing, returns ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT. + * + * Valid data (other than capture status) is returned only if both of the following are true: + * - the call returns CUDA_SUCCESS + * - the returned capture status is ::CU_STREAM_CAPTURE_STATUS_ACTIVE + * + * If \p edgeData_out is non-NULL then \p dependencies_out must be as well. If + * \p dependencies_out is non-NULL and \p edgeData_out is NULL, but there is non-zero edge + * data for one or more of the current stream dependencies, the call will return + * ::CUDA_ERROR_LOSSY_QUERY. + * + * \param hStream - The stream to query + * \param captureStatus_out - Location to return the capture status of the stream; required + * \param id_out - Optional location to return an id for the capture sequence, which is + * unique over the lifetime of the process + * \param graph_out - Optional location to return the graph being captured into. All + * operations other than destroy and node removal are permitted on the graph + * while the capture sequence is in progress. This API does not transfer + * ownership of the graph, which is transferred or destroyed at + * ::cuStreamEndCapture. Note that the graph handle may be invalidated before + * end of capture for certain errors. Nodes that are or become + * unreachable from the original stream at ::cuStreamEndCapture due to direct + * actions on the graph do not trigger ::CUDA_ERROR_STREAM_CAPTURE_UNJOINED. + * \param dependencies_out - Optional location to store a pointer to an array of nodes. + * The next node to be captured in the stream will depend on this set of nodes, + * absent operations such as event wait which modify this set. The array pointer + * is valid until the next API call which operates on the stream or until the + * capture is terminated. The node handles may be copied out and are valid until + * they or the graph is destroyed. The driver-owned array may also be passed + * directly to APIs that operate on the graph (not the stream) without copying. + * \param edgeData_out - Optional location to store a pointer to an array of graph edge + * data. This array parallels \c dependencies_out; the next node to be added + * has an edge to \c dependencies_out[i] with annotation \c edgeData_out[i] for + * each \c i. The array pointer is valid until the next API call which operates + * on the stream or until the capture is terminated. + * \param numDependencies_out - Optional location to store the size of the array + * returned in dependencies_out. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_STREAM_CAPTURE_IMPLICIT, + * ::CUDA_ERROR_LOSSY_QUERY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuStreamGetCaptureInfo + * ::cuStreamBeginCapture, + * ::cuStreamIsCapturing, + * ::cuStreamUpdateCaptureDependencies + */ +CUresult CUDAAPI cuStreamGetCaptureInfo_v3(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, + cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, + const CUgraphEdgeData **edgeData_out, size_t *numDependencies_out); + +/** + * \brief Update the set of dependencies in a capturing stream (11.3+) + * + * Modifies the dependency set of a capturing stream. The dependency set is the set + * of nodes that the next captured node in the stream will depend on. + * + * Valid flags are ::CU_STREAM_ADD_CAPTURE_DEPENDENCIES and + * ::CU_STREAM_SET_CAPTURE_DEPENDENCIES. These control whether the set passed to + * the API is added to the existing set or replaces it. A flags value of 0 defaults + * to ::CU_STREAM_ADD_CAPTURE_DEPENDENCIES. + * + * Nodes that are removed from the dependency set via this API do not result in + * ::CUDA_ERROR_STREAM_CAPTURE_UNJOINED if they are unreachable from the stream at + * ::cuStreamEndCapture. + * + * Returns ::CUDA_ERROR_ILLEGAL_STATE if the stream is not capturing. + * + * This API is new in CUDA 11.3. Developers requiring compatibility across minor + * versions to CUDA 11.0 should not use this API or provide a fallback. + * + * \param hStream - The stream to update + * \param dependencies - The set of dependencies to add + * \param numDependencies - The size of the dependencies array + * \param flags - See above + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_ILLEGAL_STATE + * + * \sa + * ::cuStreamBeginCapture, + * ::cuStreamGetCaptureInfo, + */ +CUresult CUDAAPI cuStreamUpdateCaptureDependencies(CUstream hStream, CUgraphNode *dependencies, size_t numDependencies, unsigned int flags); + +/** + * \brief Update the set of dependencies in a capturing stream (12.3+) + * + * Modifies the dependency set of a capturing stream. The dependency set is the set + * of nodes that the next captured node in the stream will depend on along with the + * edge data for those dependencies. + * + * Valid flags are ::CU_STREAM_ADD_CAPTURE_DEPENDENCIES and + * ::CU_STREAM_SET_CAPTURE_DEPENDENCIES. These control whether the set passed to + * the API is added to the existing set or replaces it. A flags value of 0 defaults + * to ::CU_STREAM_ADD_CAPTURE_DEPENDENCIES. + * + * Nodes that are removed from the dependency set via this API do not result in + * ::CUDA_ERROR_STREAM_CAPTURE_UNJOINED if they are unreachable from the stream at + * ::cuStreamEndCapture. + * + * Returns ::CUDA_ERROR_ILLEGAL_STATE if the stream is not capturing. + * + * \param hStream - The stream to update + * \param dependencies - The set of dependencies to add + * \param dependencyData - Optional array of data associated with each dependency. + * \param numDependencies - The size of the dependencies array + * \param flags - See above + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_ILLEGAL_STATE + * + * \sa + * ::cuStreamBeginCapture, + * ::cuStreamGetCaptureInfo, + */ +CUresult CUDAAPI cuStreamUpdateCaptureDependencies_v2(CUstream hStream, CUgraphNode *dependencies, + const CUgraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags); + +/** + * \brief Attach memory to a stream asynchronously + * + * Enqueues an operation in \p hStream to specify stream association of + * \p length bytes of memory starting from \p dptr. This function is a + * stream-ordered operation, meaning that it is dependent on, and will + * only take effect when, previous work in stream has completed. Any + * previous association is automatically replaced. + * + * \p dptr must point to one of the following types of memories: + * - managed memory declared using the __managed__ keyword or allocated with + * ::cuMemAllocManaged. + * - a valid host-accessible region of system-allocated pageable memory. This + * type of memory may only be specified if the device associated with the + * stream reports a non-zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_PAGEABLE_MEMORY_ACCESS. + * + * For managed allocations, \p length must be either zero or the entire + * allocation's size. Both indicate that the entire allocation's stream + * association is being changed. Currently, it is not possible to change stream + * association for a portion of a managed allocation. + * + * For pageable host allocations, \p length must be non-zero. + * + * The stream association is specified using \p flags which must be + * one of ::CUmemAttach_flags. + * If the ::CU_MEM_ATTACH_GLOBAL flag is specified, the memory can be accessed + * by any stream on any device. + * If the ::CU_MEM_ATTACH_HOST flag is specified, the program makes a guarantee + * that it won't access the memory on the device from any stream on a device that + * has a zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. + * If the ::CU_MEM_ATTACH_SINGLE flag is specified and \p hStream is associated with + * a device that has a zero value for the device attribute ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS, + * the program makes a guarantee that it will only access the memory on the device + * from \p hStream. It is illegal to attach singly to the NULL stream, because the + * NULL stream is a virtual global stream and not a specific stream. An error will + * be returned in this case. + * + * When memory is associated with a single stream, the Unified Memory system will + * allow CPU access to this memory region so long as all operations in \p hStream + * have completed, regardless of whether other streams are active. In effect, + * this constrains exclusive ownership of the managed memory region by + * an active GPU to per-stream activity instead of whole-GPU activity. + * + * Accessing memory on the device from streams that are not associated with + * it will produce undefined results. No error checking is performed by the + * Unified Memory system to ensure that kernels launched into other streams + * do not access this region. + * + * It is a program's responsibility to order calls to ::cuStreamAttachMemAsync + * via events, synchronization or other means to ensure legal access to memory + * at all times. Data visibility and coherency will be changed appropriately + * for all kernels which follow a stream-association change. + * + * If \p hStream is destroyed while data is associated with it, the association is + * removed and the association reverts to the default visibility of the allocation + * as specified at ::cuMemAllocManaged. For __managed__ variables, the default + * association is always ::CU_MEM_ATTACH_GLOBAL. Note that destroying a stream is an + * asynchronous operation, and as a result, the change to default association won't + * happen until all work in the stream has completed. + * + * \param hStream - Stream in which to enqueue the attach operation + * \param dptr - Pointer to memory (must be a pointer to managed memory or + * to a valid host-accessible region of system-allocated + * pageable memory) + * \param length - Length of memory + * \param flags - Must be one of ::CUmemAttach_flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamWaitEvent, + * ::cuStreamDestroy, + * ::cuMemAllocManaged, + * ::cudaStreamAttachMemAsync + */ +CUresult CUDAAPI cuStreamAttachMemAsync(CUstream hStream, CUdeviceptr dptr, size_t length, unsigned int flags); + +/** + * \brief Determine status of a compute stream + * + * Returns ::CUDA_SUCCESS if all operations in the stream specified by + * \p hStream have completed, or ::CUDA_ERROR_NOT_READY if not. + * + * For the purposes of Unified Memory, a return value of ::CUDA_SUCCESS + * is equivalent to having called ::cuStreamSynchronize(). + * + * \param hStream - Stream to query status of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_READY + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamWaitEvent, + * ::cuStreamDestroy, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamQuery + */ +CUresult CUDAAPI cuStreamQuery(CUstream hStream); + +/** + * \brief Wait until a stream's tasks are completed + * + * Waits until the device has completed all operations in the stream specified + * by \p hStream. If the context was created with the + * ::CU_CTX_SCHED_BLOCKING_SYNC flag, the CPU thread will block until the + * stream is finished with all of its tasks. + * + * \param hStream - Stream to wait for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE + + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamDestroy, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamAddCallback, + * ::cudaStreamSynchronize + */ +CUresult CUDAAPI cuStreamSynchronize(CUstream hStream); + +/** + * \brief Destroys a stream + * + * Destroys the stream specified by \p hStream. + * + * In case the device is still doing work in the stream \p hStream + * when ::cuStreamDestroy() is called, the function will return immediately + * and the resources associated with \p hStream will be released automatically + * once the device has completed all work in \p hStream. + * + * \param hStream - Stream to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamDestroy + */ +CUresult CUDAAPI cuStreamDestroy(CUstream hStream); + +/** + * \brief Copies attributes from source stream to destination stream. + * + * Copies attributes from source stream \p src to destination stream \p dst. + * Both streams must have the same context. + * + * \param[out] dst Destination stream + * \param[in] src Source stream + * For list of attributes see ::CUstreamAttrID + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuStreamCopyAttributes(CUstream dst, CUstream src); + +/** + * \brief Queries stream attribute. + * + * Queries attribute \p attr from \p hStream and stores it in corresponding + * member of \p value_out. + * + * \param[in] hStream + * \param[in] attr + * \param[out] value_out + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuStreamGetAttribute(CUstream hStream, CUstreamAttrID attr, + CUstreamAttrValue *value_out); + +/** + * \brief Sets stream attribute. + * + * Sets attribute \p attr on \p hStream from corresponding attribute of + * \p value. The updated attribute will be applied to subsequent work + * submitted to the stream. It will not affect previously submitted work. + * + * \param[out] hStream + * \param[in] attr + * \param[in] value + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuStreamSetAttribute(CUstream hStream, CUstreamAttrID attr, + const CUstreamAttrValue *value); + +/** @} */ /* END CUDA_STREAM */ + + +/** + * \defgroup CUDA_EVENT Event Management + * + * ___MANBRIEF___ event management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the event management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Creates an event + * + * Creates an event *phEvent for the current context with the flags specified via + * \p Flags. Valid flags include: + * - ::CU_EVENT_DEFAULT: Default event creation flag. + * - ::CU_EVENT_BLOCKING_SYNC: Specifies that the created event should use blocking + * synchronization. A CPU thread that uses ::cuEventSynchronize() to wait on + * an event created with this flag will block until the event has actually + * been recorded. + * - ::CU_EVENT_DISABLE_TIMING: Specifies that the created event does not need + * to record timing data. Events created with this flag specified and + * the ::CU_EVENT_BLOCKING_SYNC flag not specified will provide the best + * performance when used with ::cuStreamWaitEvent() and ::cuEventQuery(). + * - ::CU_EVENT_INTERPROCESS: Specifies that the created event may be used as an + * interprocess event by ::cuIpcGetEventHandle(). ::CU_EVENT_INTERPROCESS must + * be specified along with ::CU_EVENT_DISABLE_TIMING. + * + * \param phEvent - Returns newly created event + * \param Flags - Event creation flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa + * ::cuEventRecord, + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuEventDestroy, + * ::cuEventElapsedTime, + * ::cudaEventCreate, + * ::cudaEventCreateWithFlags + */ +CUresult CUDAAPI cuEventCreate(CUevent *phEvent, unsigned int Flags); + +/** + * \brief Records an event + * + * Captures in \p hEvent the contents of \p hStream at the time of this call. + * \p hEvent and \p hStream must be from the same context. + * Calls such as ::cuEventQuery() or ::cuStreamWaitEvent() will then + * examine or wait for completion of the work that was captured. Uses of + * \p hStream after this call do not modify \p hEvent. See note on default + * stream behavior for what is captured in the default case. + * + * ::cuEventRecord() can be called multiple times on the same event and + * will overwrite the previously captured state. Other APIs such as + * ::cuStreamWaitEvent() use the most recently captured state at the time + * of the API call, and are not affected by later calls to + * ::cuEventRecord(). Before the first call to ::cuEventRecord(), an + * event represents an empty set of work, so for example ::cuEventQuery() + * would return ::CUDA_SUCCESS. + * + * \param hEvent - Event to record + * \param hStream - Stream to record event for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \note_null_stream + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuStreamWaitEvent, + * ::cuEventDestroy, + * ::cuEventElapsedTime, + * ::cudaEventRecord, + * ::cuEventRecordWithFlags + */ +CUresult CUDAAPI cuEventRecord(CUevent hEvent, CUstream hStream); + +/** + * \brief Records an event + * + * Captures in \p hEvent the contents of \p hStream at the time of this call. + * \p hEvent and \p hStream must be from the same context. + * Calls such as ::cuEventQuery() or ::cuStreamWaitEvent() will then + * examine or wait for completion of the work that was captured. Uses of + * \p hStream after this call do not modify \p hEvent. See note on default + * stream behavior for what is captured in the default case. + * + * ::cuEventRecordWithFlags() can be called multiple times on the same event and + * will overwrite the previously captured state. Other APIs such as + * ::cuStreamWaitEvent() use the most recently captured state at the time + * of the API call, and are not affected by later calls to + * ::cuEventRecordWithFlags(). Before the first call to ::cuEventRecordWithFlags(), an + * event represents an empty set of work, so for example ::cuEventQuery() + * would return ::CUDA_SUCCESS. + * + * flags include: + * - ::CU_EVENT_RECORD_DEFAULT: Default event creation flag. + * - ::CU_EVENT_RECORD_EXTERNAL: Event is captured in the graph as an external + * event node when performing stream capture. This flag is invalid outside + * of stream capture. + * + * \param hEvent - Event to record + * \param hStream - Stream to record event for + * \param flags - See ::CUevent_capture_flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \note_null_stream + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuStreamWaitEvent, + * ::cuEventDestroy, + * ::cuEventElapsedTime, + * ::cuEventRecord, + * ::cudaEventRecord + */ +CUresult CUDAAPI cuEventRecordWithFlags(CUevent hEvent, CUstream hStream, unsigned int flags); + +/** + * \brief Queries an event's status + * + * Queries the status of all work currently captured by \p hEvent. See + * ::cuEventRecord() for details on what is captured by an event. + * + * Returns ::CUDA_SUCCESS if all captured work has been completed, or + * ::CUDA_ERROR_NOT_READY if any captured work is incomplete. + * + * For the purposes of Unified Memory, a return value of ::CUDA_SUCCESS + * is equivalent to having called ::cuEventSynchronize(). + * + * \param hEvent - Event to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_READY + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventRecord, + * ::cuEventSynchronize, + * ::cuEventDestroy, + * ::cuEventElapsedTime, + * ::cudaEventQuery + */ +CUresult CUDAAPI cuEventQuery(CUevent hEvent); + +/** + * \brief Waits for an event to complete + * + * Waits until the completion of all work currently captured in \p hEvent. + * See ::cuEventRecord() for details on what is captured by an event. + * + * Waiting for an event that was created with the ::CU_EVENT_BLOCKING_SYNC + * flag will cause the calling CPU thread to block until the event has + * been completed by the device. If the ::CU_EVENT_BLOCKING_SYNC flag has + * not been set, then the CPU thread will busy-wait until the event has + * been completed by the device. + * + * \param hEvent - Event to wait for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventRecord, + * ::cuEventQuery, + * ::cuEventDestroy, + * ::cuEventElapsedTime, + * ::cudaEventSynchronize + */ +CUresult CUDAAPI cuEventSynchronize(CUevent hEvent); + +/** + * \brief Destroys an event + * + * Destroys the event specified by \p hEvent. + * + * An event may be destroyed before it is complete (i.e., while + * ::cuEventQuery() would return ::CUDA_ERROR_NOT_READY). In this case, the + * call does not block on completion of the event, and any associated + * resources will automatically be released asynchronously at completion. + * + * \param hEvent - Event to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventRecord, + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuEventElapsedTime, + * ::cudaEventDestroy + */ +CUresult CUDAAPI cuEventDestroy(CUevent hEvent); + +/** + * \brief Computes the elapsed time between two events + * + * Computes the elapsed time between two events (in milliseconds with a + * resolution of around 0.5 microseconds). + * + * If either event was last recorded in a non-NULL stream, the resulting time + * may be greater than expected (even if both used the same stream handle). This + * happens because the ::cuEventRecord() operation takes place asynchronously + * and there is no guarantee that the measured latency is actually just between + * the two events. Any number of other different stream operations could execute + * in between the two measured events, thus altering the timing in a significant + * way. + * + * If ::cuEventRecord() has not been called on either event then + * ::CUDA_ERROR_INVALID_HANDLE is returned. If ::cuEventRecord() has been called + * on both events but one or both of them has not yet been completed (that is, + * ::cuEventQuery() would return ::CUDA_ERROR_NOT_READY on at least one of the + * events), ::CUDA_ERROR_NOT_READY is returned. If either event was created with + * the ::CU_EVENT_DISABLE_TIMING flag, then this function will return + * ::CUDA_ERROR_INVALID_HANDLE. + * + * \param pMilliseconds - Time between \p hStart and \p hEnd in ms + * \param hStart - Starting event + * \param hEnd - Ending event + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_READY, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuEventCreate, + * ::cuEventRecord, + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuEventDestroy, + * ::cudaEventElapsedTime + */ +CUresult CUDAAPI cuEventElapsedTime(float *pMilliseconds, CUevent hStart, CUevent hEnd); + +/** @} */ /* END CUDA_EVENT */ + +/** + * \defgroup CUDA_EXTRES_INTEROP External Resource Interoperability + * + * ___MANBRIEF___ External resource interoperability functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the external resource interoperability functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + + /** + * \brief Imports an external memory object + * + * Imports an externally allocated memory object and returns + * a handle to that in \p extMem_out. + * + * The properties of the handle being imported must be described in + * \p memHandleDesc. The ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC structure + * is defined as follows: + * + * \code + typedef struct CUDA_EXTERNAL_MEMORY_HANDLE_DESC_st { + CUexternalMemoryHandleType type; + union { + int fd; + struct { + void *handle; + const void *name; + } win32; + const void *nvSciBufObject; + } handle; + unsigned long long size; + unsigned int flags; + } CUDA_EXTERNAL_MEMORY_HANDLE_DESC; + * \endcode + * + * where ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type specifies the type + * of handle being imported. ::CUexternalMemoryHandleType is + * defined as: + * + * \code + typedef enum CUexternalMemoryHandleType_enum { + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_FD = 1, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32 = 2, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32_KMT = 3, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_HEAP = 4, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_RESOURCE = 5, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE = 6, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT = 7, + CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF = 8 + } CUexternalMemoryHandleType; + * \endcode + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_FD, then + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::fd must be a valid + * file descriptor referencing a memory object. Ownership of + * the file descriptor is transferred to the CUDA driver when the + * handle is imported successfully. Performing any operations on the + * file descriptor after it is imported results in undefined behavior. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32, then exactly one + * of ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name must not be + * NULL. If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a memory object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a memory object. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_OPAQUE_WIN32_KMT, then + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle must + * be non-NULL and + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * must be NULL. The handle specified must be a globally shared KMT + * handle. This handle does not hold a reference to the underlying + * object, and thus will be invalid when all references to the + * memory object are destroyed. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_HEAP, then exactly one + * of ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name must not be + * NULL. If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Heap object. This handle holds a reference to the underlying + * object. If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D12Heap object. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_RESOURCE, then exactly one + * of ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name must not be + * NULL. If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Resource object. This handle holds a reference to the + * underlying object. If + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D12Resource object. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE, then + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle must + * represent a valid shared NT handle that is returned by + * IDXGIResource1::CreateSharedHandle when referring to a + * ID3D11Resource object. If + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D11Resource object. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT, then + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::handle must + * represent a valid shared KMT handle that is returned by + * IDXGIResource::GetSharedHandle when referring to a + * ID3D11Resource object and + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::win32::name + * must be NULL. + * + * If ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type is + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF, then + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::handle::nvSciBufObject must be non-NULL + * and reference a valid NvSciBuf object. + * If the NvSciBuf object imported into CUDA is also mapped by other drivers, then the + * application must use ::cuWaitExternalSemaphoresAsync or ::cuSignalExternalSemaphoresAsync + * as appropriate barriers to maintain coherence between CUDA and the other drivers. + * See ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_SKIP_NVSCIBUF_MEMSYNC and ::CUDA_EXTERNAL_SEMAPHORE_WAIT_SKIP_NVSCIBUF_MEMSYNC + * for memory synchronization. + * + * + * The size of the memory object must be specified in + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::size. + * + * Specifying the flag ::CUDA_EXTERNAL_MEMORY_DEDICATED in + * ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::flags indicates that the + * resource is a dedicated resource. The definition of what a + * dedicated resource is outside the scope of this extension. + * This flag must be set if ::CUDA_EXTERNAL_MEMORY_HANDLE_DESC::type + * is one of the following: + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D12_RESOURCE + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_D3D11_RESOURCE_KMT + * + * \param extMem_out - Returned handle to an external memory object + * \param memHandleDesc - Memory import handle descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OPERATING_SYSTEM + * \notefnerr + * + * \note If the Vulkan memory imported into CUDA is mapped on the CPU then the + * application must use vkInvalidateMappedMemoryRanges/vkFlushMappedMemoryRanges + * as well as appropriate Vulkan pipeline barriers to maintain coherence between + * CPU and GPU. For more information on these APIs, please refer to "Synchronization + * and Cache Control" chapter from Vulkan specification. + * + * \sa ::cuDestroyExternalMemory, + * ::cuExternalMemoryGetMappedBuffer, + * ::cuExternalMemoryGetMappedMipmappedArray + */ +CUresult CUDAAPI cuImportExternalMemory(CUexternalMemory *extMem_out, const CUDA_EXTERNAL_MEMORY_HANDLE_DESC *memHandleDesc); + +/** + * \brief Maps a buffer onto an imported memory object + * + * Maps a buffer onto an imported memory object and returns a device + * pointer in \p devPtr. + * + * The properties of the buffer being mapped must be described in + * \p bufferDesc. The ::CUDA_EXTERNAL_MEMORY_BUFFER_DESC structure is + * defined as follows: + * + * \code + typedef struct CUDA_EXTERNAL_MEMORY_BUFFER_DESC_st { + unsigned long long offset; + unsigned long long size; + unsigned int flags; + } CUDA_EXTERNAL_MEMORY_BUFFER_DESC; + * \endcode + * + * where ::CUDA_EXTERNAL_MEMORY_BUFFER_DESC::offset is the offset in + * the memory object where the buffer's base address is. + * ::CUDA_EXTERNAL_MEMORY_BUFFER_DESC::size is the size of the buffer. + * ::CUDA_EXTERNAL_MEMORY_BUFFER_DESC::flags must be zero. + * + * The offset and size have to be suitably aligned to match the + * requirements of the external API. Mapping two buffers whose ranges + * overlap may or may not result in the same virtual address being + * returned for the overlapped portion. In such cases, the application + * must ensure that all accesses to that region from the GPU are + * volatile. Otherwise writes made via one address are not guaranteed + * to be visible via the other address, even if they're issued by the + * same thread. It is recommended that applications map the combined + * range instead of mapping separate buffers and then apply the + * appropriate offsets to the returned pointer to derive the + * individual buffers. + * + * The returned pointer \p devPtr must be freed using ::cuMemFree. + * + * \param devPtr - Returned device pointer to buffer + * \param extMem - Handle to external memory object + * \param bufferDesc - Buffer descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuImportExternalMemory, + * ::cuDestroyExternalMemory, + * ::cuExternalMemoryGetMappedMipmappedArray + */ +CUresult CUDAAPI cuExternalMemoryGetMappedBuffer(CUdeviceptr *devPtr, CUexternalMemory extMem, const CUDA_EXTERNAL_MEMORY_BUFFER_DESC *bufferDesc); + +/** + * \brief Maps a CUDA mipmapped array onto an external memory object + * + * Maps a CUDA mipmapped array onto an external object and returns a + * handle to it in \p mipmap. + * + * The properties of the CUDA mipmapped array being mapped must be + * described in \p mipmapDesc. The structure + * ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC is defined as follows: + * + * \code + typedef struct CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC_st { + unsigned long long offset; + CUDA_ARRAY3D_DESCRIPTOR arrayDesc; + unsigned int numLevels; + } CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC; + * \endcode + * + * where ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC::offset is the + * offset in the memory object where the base level of the mipmap + * chain is. + * ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC::arrayDesc describes + * the format, dimensions and type of the base level of the mipmap + * chain. For further details on these parameters, please refer to the + * documentation for ::cuMipmappedArrayCreate. Note that if the mipmapped + * array is bound as a color target in the graphics API, then the flag + * ::CUDA_ARRAY3D_COLOR_ATTACHMENT must be specified in + * ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC::arrayDesc::Flags. + * ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC::numLevels specifies + * the total number of levels in the mipmap chain. + * + * If \p extMem was imported from a handle of type ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF, then + * ::CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC::numLevels must be equal to 1. + * + * The returned CUDA mipmapped array must be freed using ::cuMipmappedArrayDestroy. + * + * \param mipmap - Returned CUDA mipmapped array + * \param extMem - Handle to external memory object + * \param mipmapDesc - CUDA array descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuImportExternalMemory, + * ::cuDestroyExternalMemory, + * ::cuExternalMemoryGetMappedBuffer + */ +CUresult CUDAAPI cuExternalMemoryGetMappedMipmappedArray(CUmipmappedArray *mipmap, CUexternalMemory extMem, const CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC *mipmapDesc); + +/** + * \brief Destroys an external memory object. + * + * Destroys the specified external memory object. Any existing buffers + * and CUDA mipmapped arrays mapped onto this object must no longer be + * used and must be explicitly freed using ::cuMemFree and + * ::cuMipmappedArrayDestroy respectively. + * + * \param extMem - External memory object to be destroyed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuImportExternalMemory, + * ::cuExternalMemoryGetMappedBuffer, + * ::cuExternalMemoryGetMappedMipmappedArray + */ +CUresult CUDAAPI cuDestroyExternalMemory(CUexternalMemory extMem); + +/** + * \brief Imports an external semaphore + * + * Imports an externally allocated synchronization object and returns + * a handle to that in \p extSem_out. + * + * The properties of the handle being imported must be described in + * \p semHandleDesc. The ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC is + * defined as follows: + * + * \code + typedef struct CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC_st { + CUexternalSemaphoreHandleType type; + union { + int fd; + struct { + void *handle; + const void *name; + } win32; + const void* NvSciSyncObj; + } handle; + unsigned int flags; + } CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC; + * \endcode + * + * where ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type specifies the type of + * handle being imported. ::CUexternalSemaphoreHandleType is defined + * as: + * + * \code + typedef enum CUexternalSemaphoreHandleType_enum { + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD = 1, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32 = 2, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT = 3, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE = 4, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE = 5, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC = 6, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX = 7, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT = 8, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD = 9, + CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32 = 10 + } CUexternalSemaphoreHandleType; + * \endcode + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::fd must be a valid + * file descriptor referencing a synchronization object. Ownership of + * the file descriptor is transferred to the CUDA driver when the + * handle is imported successfully. Performing any operations on the + * file descriptor after it is imported results in undefined behavior. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32, then exactly one + * of ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name must not be + * NULL. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a synchronization object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * is not NULL, then it must name a valid synchronization object. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle must + * be non-NULL and + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * must be NULL. The handle specified must be a globally shared KMT + * handle. This handle does not hold a reference to the underlying + * object, and thus will be invalid when all references to the + * synchronization object are destroyed. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE, then exactly one + * of ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name must not be + * NULL. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Fence object. This handle holds a reference to the underlying + * object. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * is not NULL, then it must name a valid synchronization object that + * refers to a valid ID3D12Fence object. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * represents a valid shared NT handle that is returned by + * ID3D11Fence::CreateSharedHandle. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * is not NULL, then it must name a valid synchronization object that + * refers to a valid ID3D11Fence object. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::nvSciSyncObj + * represents a valid NvSciSyncObj. + * + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * represents a valid shared NT handle that + * is returned by IDXGIResource1::CreateSharedHandle when referring to + * a IDXGIKeyedMutex object. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * is not NULL, then it must name a valid synchronization object that + * refers to a valid IDXGIKeyedMutex object. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * represents a valid shared KMT handle that + * is returned by IDXGIResource::GetSharedHandle when referring to + * a IDXGIKeyedMutex object and + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name must be NULL. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD, then + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::fd must be a valid + * file descriptor referencing a synchronization object. Ownership of + * the file descriptor is transferred to the CUDA driver when the + * handle is imported successfully. Performing any operations on the + * file descriptor after it is imported results in undefined behavior. + * + * If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::type is + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32, then exactly one + * of ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle and + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name must not be + * NULL. If + * ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a synchronization object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC::handle::win32::name + * is not NULL, then it must name a valid synchronization object. + * + * \param extSem_out - Returned handle to an external semaphore + * \param semHandleDesc - Semaphore import handle descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OPERATING_SYSTEM + * \notefnerr + * + * \sa ::cuDestroyExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuImportExternalSemaphore(CUexternalSemaphore *extSem_out, const CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC *semHandleDesc); + +/** + * \brief Signals a set of external semaphore objects + * + * Enqueues a signal operation on a set of externally allocated + * semaphore object in the specified stream. The operations will be + * executed when all prior operations in the stream complete. + * + * The exact semantics of signaling a semaphore depends on the type of + * the object. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT + * then signaling the semaphore will set it to the signaled state. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32 + * then the semaphore will be set to the value specified in + * ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS::params::fence::value. + * + * If the semaphore object is of the type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC + * this API sets ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS::params::nvSciSync::fence + * to a value that can be used by subsequent waiters of the same NvSciSync object + * to order operations with those currently submitted in \p stream. Such an update + * will overwrite previous contents of + * ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS::params::nvSciSync::fence. By default, + * signaling such an external semaphore object causes appropriate memory synchronization + * operations to be performed over all external memory objects that are imported as + * ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF. This ensures that any subsequent accesses + * made by other importers of the same set of NvSciBuf memory object(s) are coherent. + * These operations can be skipped by specifying the flag + * ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_SKIP_NVSCIBUF_MEMSYNC, which can be used as a + * performance optimization when data coherency is not required. But specifying this + * flag in scenarios where data coherency is required results in undefined behavior. + * Also, for semaphore object of the type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC, + * if the NvSciSyncAttrList used to create the NvSciSyncObj had not set the flags in + * ::cuDeviceGetNvSciSyncAttributes to CUDA_NVSCISYNC_ATTR_SIGNAL, this API will return + * CUDA_ERROR_NOT_SUPPORTED. + * NvSciSyncFence associated with semaphore object of the type + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC can be deterministic. For this the + * NvSciSyncAttrList used to create the semaphore object must have value of + * NvSciSyncAttrKey_RequireDeterministicFences key set to true. Deterministic fences + * allow users to enqueue a wait over the semaphore object even before corresponding + * signal is enqueued. For such a semaphore object, CUDA guarantees that each signal + * operation will increment the fence value by '1'. Users are expected to track count + * of signals enqueued on the semaphore object and insert waits accordingly. When such + * a semaphore object is signaled from multiple streams, due to concurrent stream + * execution, it is possible that the order in which the semaphore gets signaled is + * indeterministic. This could lead to waiters of the semaphore getting unblocked + * incorrectly. Users are expected to handle such situations, either by not using the + * same semaphore object with deterministic fence support enabled in different streams + * or by adding explicit dependency amongst such streams so that the semaphore is + * signaled in order. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT + * then the keyed mutex will be released with the key specified in + * ::CUDA_EXTERNAL_SEMAPHORE_PARAMS::params::keyedmutex::key. + * + * \param extSemArray - Set of external semaphores to be signaled + * \param paramsArray - Array of semaphore parameters + * \param numExtSems - Number of semaphores to signal + * \param stream - Stream to enqueue the signal operations in + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuImportExternalSemaphore, + * ::cuDestroyExternalSemaphore, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuSignalExternalSemaphoresAsync(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS *paramsArray, unsigned int numExtSems, CUstream stream); + +/** + * \brief Waits on a set of external semaphore objects + * + * Enqueues a wait operation on a set of externally allocated + * semaphore object in the specified stream. The operations will be + * executed when all prior operations in the stream complete. + * + * The exact semantics of waiting on a semaphore depends on the type + * of the object. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_FD, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_OPAQUE_WIN32_KMT + * then waiting on the semaphore will wait until the semaphore reaches + * the signaled state. The semaphore will then be reset to the + * unsignaled state. Therefore for every signal operation, there can + * only be one wait operation. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D12_FENCE, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_FENCE, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_FD, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_TIMELINE_SEMAPHORE_WIN32 + * then waiting on the semaphore will wait until the value of the + * semaphore is greater than or equal to + * ::CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS::params::fence::value. + * + * If the semaphore object is of the type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC + * then, waiting on the semaphore will wait until the + * ::CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS::params::nvSciSync::fence is signaled by the + * signaler of the NvSciSyncObj that was associated with this semaphore object. + * By default, waiting on such an external semaphore object causes appropriate + * memory synchronization operations to be performed over all external memory objects + * that are imported as ::CU_EXTERNAL_MEMORY_HANDLE_TYPE_NVSCIBUF. This ensures that + * any subsequent accesses made by other importers of the same set of NvSciBuf memory + * object(s) are coherent. These operations can be skipped by specifying the flag + * ::CUDA_EXTERNAL_SEMAPHORE_WAIT_SKIP_NVSCIBUF_MEMSYNC, which can be used as a + * performance optimization when data coherency is not required. But specifying this + * flag in scenarios where data coherency is required results in undefined behavior. + * Also, for semaphore object of the type ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_NVSCISYNC, + * if the NvSciSyncAttrList used to create the NvSciSyncObj had not set the flags in + * ::cuDeviceGetNvSciSyncAttributes to CUDA_NVSCISYNC_ATTR_WAIT, this API will return + * CUDA_ERROR_NOT_SUPPORTED. + * + * If the semaphore object is any one of the following types: + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX, + * ::CU_EXTERNAL_SEMAPHORE_HANDLE_TYPE_D3D11_KEYED_MUTEX_KMT + * then the keyed mutex will be acquired when it is released with the key + * specified in ::CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS::params::keyedmutex::key + * or until the timeout specified by + * ::CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS::params::keyedmutex::timeoutMs + * has lapsed. The timeout interval can either be a finite value + * specified in milliseconds or an infinite value. In case an infinite + * value is specified the timeout never elapses. The windows INFINITE + * macro must be used to specify infinite timeout. + * + * \param extSemArray - External semaphores to be waited on + * \param paramsArray - Array of semaphore parameters + * \param numExtSems - Number of semaphores to wait on + * \param stream - Stream to enqueue the wait operations in + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_TIMEOUT + * \notefnerr + * + * \sa ::cuImportExternalSemaphore, + * ::cuDestroyExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync + */ +CUresult CUDAAPI cuWaitExternalSemaphoresAsync(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS *paramsArray, unsigned int numExtSems, CUstream stream); + +/** + * \brief Destroys an external semaphore + * + * Destroys an external semaphore object and releases any references + * to the underlying resource. Any outstanding signals or waits must + * have completed before the semaphore is destroyed. + * + * \param extSem - External semaphore to be destroyed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa ::cuImportExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuDestroyExternalSemaphore(CUexternalSemaphore extSem); + +/** @} */ /* END CUDA_EXTRES_INTEROP */ + +/** + * \defgroup CUDA_MEMOP Stream Memory Operations + * + * ___MANBRIEF___ Stream memory operations of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the stream memory operations of the low-level CUDA + * driver application programming interface. + * + * Support for the ::CU_STREAM_WAIT_VALUE_NOR flag can be queried with + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_WAIT_VALUE_NOR_V2. + * + * Support for the ::cuStreamWriteValue64() and ::cuStreamWaitValue64() + * functions, as well as for the ::CU_STREAM_MEM_OP_WAIT_VALUE_64 and + * ::CU_STREAM_MEM_OP_WRITE_VALUE_64 flags, can be queried with + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_64_BIT_STREAM_MEM_OPS. + * + * Support for both ::CU_STREAM_WAIT_VALUE_FLUSH and + * ::CU_STREAM_MEM_OP_FLUSH_REMOTE_WRITES requires dedicated platform + * hardware features and can be queried with ::cuDeviceGetAttribute() and + * ::CU_DEVICE_ATTRIBUTE_CAN_FLUSH_REMOTE_WRITES. + * + * Note that all memory pointers passed as parameters to these operations + * are device pointers. Where necessary a device pointer should be + * obtained, for example with ::cuMemHostGetDevicePointer(). + * + * None of the operations accepts pointers to managed memory buffers + * (::cuMemAllocManaged). + * + * \note + * Warning: + * Improper use of these APIs may deadlock the application. Synchronization + * ordering established through these APIs is not visible to CUDA. CUDA tasks + * that are (even indirectly) ordered by these APIs should also have that order + * expressed with CUDA-visible dependencies such as events. This ensures that + * the scheduler does not serialize them in an improper order. + * + * @{ + */ + +/** + * \brief Wait on a memory location + * + * Enqueues a synchronization of the stream on the given memory location. Work + * ordered after the operation will block until the given condition on the + * memory is satisfied. By default, the condition is to wait for + * (int32_t)(*addr - value) >= 0, a cyclic greater-or-equal. + * Other condition types can be specified via \p flags. + * + * If the memory was registered via ::cuMemHostRegister(), the device pointer + * should be obtained with ::cuMemHostGetDevicePointer(). This function cannot + * be used with managed memory (::cuMemAllocManaged). + * + * Support for CU_STREAM_WAIT_VALUE_NOR can be queried with ::cuDeviceGetAttribute() and + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_STREAM_WAIT_VALUE_NOR_V2. + * + * \note + * Warning: + * Improper use of this API may deadlock the application. Synchronization + * ordering established through this API is not visible to CUDA. CUDA tasks + * that are (even indirectly) ordered by this API should also have that order + * expressed with CUDA-visible dependencies such as events. This ensures that + * the scheduler does not serialize them in an improper order. + * + * \param stream The stream to synchronize on the memory location. + * \param addr The memory location to wait on. + * \param value The value to compare with the memory location. + * \param flags See ::CUstreamWaitValue_flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuStreamWaitValue64, + * ::cuStreamWriteValue32, + * ::cuStreamWriteValue64, + * ::cuStreamBatchMemOp, + * ::cuMemHostRegister, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuStreamWaitValue32(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + +/** + * \brief Wait on a memory location + * + * Enqueues a synchronization of the stream on the given memory location. Work + * ordered after the operation will block until the given condition on the + * memory is satisfied. By default, the condition is to wait for + * (int64_t)(*addr - value) >= 0, a cyclic greater-or-equal. + * Other condition types can be specified via \p flags. + * + * If the memory was registered via ::cuMemHostRegister(), the device pointer + * should be obtained with ::cuMemHostGetDevicePointer(). + * + * Support for this can be queried with ::cuDeviceGetAttribute() and + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_64_BIT_STREAM_MEM_OPS. + * + * \note + * Warning: + * Improper use of this API may deadlock the application. Synchronization + * ordering established through this API is not visible to CUDA. CUDA tasks + * that are (even indirectly) ordered by this API should also have that order + * expressed with CUDA-visible dependencies such as events. This ensures that + * the scheduler does not serialize them in an improper order. + * + * \param stream The stream to synchronize on the memory location. + * \param addr The memory location to wait on. + * \param value The value to compare with the memory location. + * \param flags See ::CUstreamWaitValue_flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuStreamWaitValue32, + * ::cuStreamWriteValue32, + * ::cuStreamWriteValue64, + * ::cuStreamBatchMemOp, + * ::cuMemHostRegister, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuStreamWaitValue64(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + +/** + * \brief Write a value to memory + * + * Write a value to memory. + * + * If the memory was registered via ::cuMemHostRegister(), the device pointer + * should be obtained with ::cuMemHostGetDevicePointer(). This function cannot + * be used with managed memory (::cuMemAllocManaged). + * + * \param stream The stream to do the write in. + * \param addr The device address to write to. + * \param value The value to write. + * \param flags See ::CUstreamWriteValue_flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuStreamWriteValue64, + * ::cuStreamWaitValue32, + * ::cuStreamWaitValue64, + * ::cuStreamBatchMemOp, + * ::cuMemHostRegister, + * ::cuEventRecord + */ +CUresult CUDAAPI cuStreamWriteValue32(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + +/** + * \brief Write a value to memory + * + * Write a value to memory. + * + * If the memory was registered via ::cuMemHostRegister(), the device pointer + * should be obtained with ::cuMemHostGetDevicePointer(). + * + * Support for this can be queried with ::cuDeviceGetAttribute() and + * ::CU_DEVICE_ATTRIBUTE_CAN_USE_64_BIT_STREAM_MEM_OPS. + * + * \param stream The stream to do the write in. + * \param addr The device address to write to. + * \param value The value to write. + * \param flags See ::CUstreamWriteValue_flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuStreamWriteValue32, + * ::cuStreamWaitValue32, + * ::cuStreamWaitValue64, + * ::cuStreamBatchMemOp, + * ::cuMemHostRegister, + * ::cuEventRecord + */ +CUresult CUDAAPI cuStreamWriteValue64(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + +/** + * \brief Batch operations to synchronize the stream via memory operations + * + * This is a batch version of ::cuStreamWaitValue32() and ::cuStreamWriteValue32(). + * Batching operations may avoid some performance overhead in both the API call + * and the device execution versus adding them to the stream in separate API + * calls. The operations are enqueued in the order they appear in the array. + * + * See ::CUstreamBatchMemOpType for the full set of supported operations, and + * ::cuStreamWaitValue32(), ::cuStreamWaitValue64(), ::cuStreamWriteValue32(), + * and ::cuStreamWriteValue64() for details of specific operations. + * + * See related APIs for details on querying support for specific operations. + * + * \note + * Warning: + * Improper use of this API may deadlock the application. Synchronization + * ordering established through this API is not visible to CUDA. CUDA tasks + * that are (even indirectly) ordered by this API should also have that order + * expressed with CUDA-visible dependencies such as events. This ensures that + * the scheduler does not serialize them in an improper order. For more + * information, see the Stream Memory Operations section in the programming + * guide(https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html). + * + * \param stream The stream to enqueue the operations in. + * \param count The number of operations in the array. Must be less than 256. + * \param paramArray The types and parameters of the individual operations. + * \param flags Reserved for future expansion; must be 0. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \notefnerr + * + * \sa ::cuStreamWaitValue32, + * ::cuStreamWaitValue64, + * ::cuStreamWriteValue32, + * ::cuStreamWriteValue64, + * ::cuMemHostRegister + */ +CUresult CUDAAPI cuStreamBatchMemOp(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); + +/** @} */ /* END CUDA_MEMOP */ + +/** + * \defgroup CUDA_EXEC Execution Control + * + * ___MANBRIEF___ execution control functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the execution control functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns information about a function + * + * Returns in \p *pi the integer value of the attribute \p attrib on the kernel + * given by \p hfunc. The supported attributes are: + * - ::CU_FUNC_ATTRIBUTE_MAX_THREADS_PER_BLOCK: The maximum number of threads + * per block, beyond which a launch of the function would fail. This number + * depends on both the function and the device on which the function is + * currently loaded. + * - ::CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES: The size in bytes of + * statically-allocated shared memory per block required by this function. + * This does not include dynamically-allocated shared memory requested by + * the user at runtime. + * - ::CU_FUNC_ATTRIBUTE_CONST_SIZE_BYTES: The size in bytes of user-allocated + * constant memory required by this function. + * - ::CU_FUNC_ATTRIBUTE_LOCAL_SIZE_BYTES: The size in bytes of local memory + * used by each thread of this function. + * - ::CU_FUNC_ATTRIBUTE_NUM_REGS: The number of registers used by each thread + * of this function. + * - ::CU_FUNC_ATTRIBUTE_PTX_VERSION: The PTX virtual architecture version for + * which the function was compiled. This value is the major PTX version * 10 + * + the minor PTX version, so a PTX version 1.3 function would return the + * value 13. Note that this may return the undefined value of 0 for cubins + * compiled prior to CUDA 3.0. + * - ::CU_FUNC_ATTRIBUTE_BINARY_VERSION: The binary architecture version for + * which the function was compiled. This value is the major binary + * version * 10 + the minor binary version, so a binary version 1.3 function + * would return the value 13. Note that this will return a value of 10 for + * legacy cubins that do not have a properly-encoded binary architecture + * version. + * - ::CU_FUNC_CACHE_MODE_CA: The attribute to indicate whether the function has + * been compiled with user specified option "-Xptxas --dlcm=ca" set . + * - ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES: The maximum size in bytes of + * dynamically-allocated shared memory. + * - ::CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT: Preferred shared memory-L1 + * cache split ratio in percent of total shared memory. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SIZE_MUST_BE_SET: If this attribute is set, the + * kernel must launch with a valid cluster size specified. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_WIDTH: The required cluster width in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_HEIGHT: The required cluster height in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_DEPTH: The required cluster depth in + * blocks. + * - ::CU_FUNC_ATTRIBUTE_NON_PORTABLE_CLUSTER_SIZE_ALLOWED: Indicates whether + * the function can be launched with non-portable cluster size. 1 is allowed, + * 0 is disallowed. A non-portable cluster size may only function on the + * specific SKUs the program is tested on. The launch might fail if the + * program is run on a different hardware platform. CUDA API provides + * cudaOccupancyMaxActiveClusters to assist with checking whether the desired + * size can be launched on the current device. A portable cluster size is + * guaranteed to be functional on all compute capabilities higher than the + * target compute capability. The portable cluster size for sm_90 is 8 blocks + * per cluster. This value may increase for future compute capabilities. The + * specific hardware unit may support higher cluster sizes that’s not + * guaranteed to be portable. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE: The block + * scheduling policy of a function. The value type is CUclusterSchedulingPolicy. + * + * With a few execeptions, function attributes may also be queried on unloaded + * function handles returned from ::cuModuleEnumerateFunctions. + * ::CUDA_ERROR_FUNCTION_NOT_LOADED is returned if the attribute requires a fully + * loaded function but the function is not loaded. The loading state of a function + * may be queried using ::cuFuncIsloaded. ::cuFuncLoad may be called to explicitly + * load a function before querying the following attributes that require the function + * to be loaded: + * - ::CU_FUNC_ATTRIBUTE_MAX_THREADS_PER_BLOCK + * - ::CU_FUNC_ATTRIBUTE_CONST_SIZE_BYTES + * - ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES + * + * \param pi - Returned attribute value + * \param attrib - Attribute requested + * \param hfunc - Function to query attribute of + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_FUNCTION_NOT_LOADED + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuLaunchKernel, + * ::cudaFuncGetAttributes, + * ::cudaFuncSetAttribute, + * ::cuFuncIsLoaded, + * ::cuFuncLoad, + * ::cuKernelGetAttribute + */ +CUresult CUDAAPI cuFuncGetAttribute(int *pi, CUfunction_attribute attrib, CUfunction hfunc); + +/** + * \brief Sets information about a function + * + * This call sets the value of a specified attribute \p attrib on the kernel given + * by \p hfunc to an integer value specified by \p val + * This function returns CUDA_SUCCESS if the new value of the attribute could be + * successfully set. If the set fails, this call will return an error. + * Not all attributes can have values set. Attempting to set a value on a read-only + * attribute will result in an error (CUDA_ERROR_INVALID_VALUE) + * + * Supported attributes for the cuFuncSetAttribute call are: + * - ::CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES: This maximum size in bytes of + * dynamically-allocated shared memory. The value should contain the requested + * maximum size of dynamically-allocated shared memory. The sum of this value and + * the function attribute ::CU_FUNC_ATTRIBUTE_SHARED_SIZE_BYTES cannot exceed the + * device attribute ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN. + * The maximal size of requestable dynamic shared memory may differ by GPU + * architecture. + * - ::CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT: On devices where the L1 + * cache and shared memory use the same hardware resources, this sets the shared memory + * carveout preference, in percent of the total shared memory. + * See ::CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_MULTIPROCESSOR + * This is only a hint, and the driver can choose a different ratio if required to execute the function. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_WIDTH: The required cluster width in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_HEIGHT: The required cluster height in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_REQUIRED_CLUSTER_DEPTH: The required cluster depth in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return CUDA_ERROR_NOT_PERMITTED. + * - ::CU_FUNC_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE: The block + * scheduling policy of a function. The value type is CUclusterSchedulingPolicy. + * + * \param hfunc - Function to query attribute of + * \param attrib - Attribute requested + * \param value - The value to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuLaunchKernel, + * ::cudaFuncGetAttributes, + * ::cudaFuncSetAttribute, + * ::cuKernelSetAttribute + */ +CUresult CUDAAPI cuFuncSetAttribute(CUfunction hfunc, CUfunction_attribute attrib, int value); + +/** + * \brief Sets the preferred cache configuration for a device function + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p config the preferred cache configuration for + * the device function \p hfunc. This is only a preference. The driver will use + * the requested configuration if possible, but it is free to choose a different + * configuration if required to execute \p hfunc. Any context-wide preference + * set via ::cuCtxSetCacheConfig() will be overridden by this per-function + * setting unless the per-function setting is ::CU_FUNC_CACHE_PREFER_NONE. In + * that case, the current context-wide setting will be used. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * + * The supported cache configurations are: + * - ::CU_FUNC_CACHE_PREFER_NONE: no preference for shared memory or L1 (default) + * - ::CU_FUNC_CACHE_PREFER_SHARED: prefer larger shared memory and smaller L1 cache + * - ::CU_FUNC_CACHE_PREFER_L1: prefer larger L1 cache and smaller shared memory + * - ::CU_FUNC_CACHE_PREFER_EQUAL: prefer equal sized L1 cache and shared memory + * + * \param hfunc - Kernel to configure cache for + * \param config - Requested cache configuration + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cuLaunchKernel, + * ::cudaFuncSetCacheConfig, + * ::cuKernelSetCacheConfig + */ +CUresult CUDAAPI cuFuncSetCacheConfig(CUfunction hfunc, CUfunc_cache config); + + +/** + * \brief Returns a module handle + * + * Returns in \p *hmod the handle of the module that function \p hfunc + * is located in. The lifetime of the module corresponds to the lifetime of + * the context it was loaded in or until the module is explicitly unloaded. + * + * The CUDA runtime manages its own modules loaded into the primary context. + * If the handle returned by this API refers to a module loaded by the CUDA runtime, + * calling ::cuModuleUnload() on that module will result in undefined behavior. + * + * \param hmod - Returned module handle + * \param hfunc - Function to retrieve module for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_FOUND + * \notefnerr + * + */ +CUresult CUDAAPI cuFuncGetModule(CUmodule *hmod, CUfunction hfunc); + +/** + * \brief Returns the function name for a ::CUfunction handle + * + * Returns in \p **name the function name associated with the function handle \p hfunc . + * The function name is returned as a null-terminated string. The returned name is only + * valid when the function handle is valid. If the module is unloaded or reloaded, one + * must call the API again to get the updated name. This API may return a mangled name if + * the function is not declared as having C linkage. If either \p **name or \p hfunc + * is NULL, ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \param name - The returned name of the function + * \param hfunc - The function handle to retrieve the name for + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * + */ +CUresult CUDAAPI cuFuncGetName(const char **name, CUfunction hfunc); + +/** + * \brief Returns the offset and size of a kernel parameter in the device-side parameter layout + * + * Queries the kernel parameter at \p paramIndex into \p func's list of parameters, and returns + * in \p paramOffset and \p paramSize the offset and size, respectively, where the parameter + * will reside in the device-side parameter layout. This information can be used to update kernel + * node parameters from the device via ::cudaGraphKernelNodeSetParam() and + * ::cudaGraphKernelNodeUpdatesApply(). \p paramIndex must be less than the number of parameters + * that \p func takes. \p paramSize can be set to NULL if only the parameter offset is desired. + * + * \param func - The function to query + * \param paramIndex - The parameter index to query + * \param paramOffset - Returns the offset into the device-side parameter layout at which the parameter resides + * \param paramSize - Optionally returns the size of the parameter in the device-side parameter layout + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + * +* \sa ::cuKernelGetParamInfo + */ +CUresult CUDAAPI cuFuncGetParamInfo(CUfunction func, size_t paramIndex, size_t *paramOffset, size_t *paramSize); + +typedef enum CUfunctionLoadingState_enum { + CU_FUNCTION_LOADING_STATE_UNLOADED = 0, + CU_FUNCTION_LOADING_STATE_LOADED = 1, + CU_FUNCTION_LOADING_STATE_MAX +} CUfunctionLoadingState; + +/** + * \brief Returns if the function is loaded + * + * Returns in \p state the loading state of \p function. + * + * \param state - returned loading state + * \param function - the function to check + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuFuncLoad, + * ::cuModuleEnumerateFunctions + */ +CUresult CUDAAPI cuFuncIsLoaded(CUfunctionLoadingState *state, CUfunction function); + +/** + * \brief Loads a function + * + * Finalizes function loading for \p function. Calling this API with a + * fully loaded function has no effect. + * + * \param function - the function to load + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuModuleEnumerateFunctions, + * ::cuFuncIsLoaded + */ +CUresult CUDAAPI cuFuncLoad(CUfunction function); + +/** + * \brief Launches a CUDA function ::CUfunction or a CUDA kernel ::CUkernel + * + * Invokes the function ::CUfunction or the kernel ::CUkernel \p f + * on a \p gridDimX x \p gridDimY x \p gridDimZ grid of blocks. + * Each block contains \p blockDimX x \p blockDimY x + * \p blockDimZ threads. + * + * \p sharedMemBytes sets the amount of dynamic shared memory that will be + * available to each thread block. + * + * Kernel parameters to \p f can be specified in one of two ways: + * + * 1) Kernel parameters can be specified via \p kernelParams. If \p f + * has N parameters, then \p kernelParams needs to be an array of N + * pointers. Each of \p kernelParams[0] through \p kernelParams[N-1] + * must point to a region of memory from which the actual kernel + * parameter will be copied. The number of kernel parameters and their + * offsets and sizes do not need to be specified as that information is + * retrieved directly from the kernel's image. + * + * 2) Kernel parameters can also be packaged by the application into + * a single buffer that is passed in via the \p extra parameter. + * This places the burden on the application of knowing each kernel + * parameter's size and alignment/padding within the buffer. Here is + * an example of using the \p extra parameter in this manner: + * \code + size_t argBufferSize; + char argBuffer[256]; + + // populate argBuffer and argBufferSize + + void *config[] = { + CU_LAUNCH_PARAM_BUFFER_POINTER, argBuffer, + CU_LAUNCH_PARAM_BUFFER_SIZE, &argBufferSize, + CU_LAUNCH_PARAM_END + }; + status = cuLaunchKernel(f, gx, gy, gz, bx, by, bz, sh, s, NULL, config); + * \endcode + * + * The \p extra parameter exists to allow ::cuLaunchKernel to take + * additional less commonly used arguments. \p extra specifies a list of + * names of extra settings and their corresponding values. Each extra + * setting name is immediately followed by the corresponding value. The + * list must be terminated with either NULL or ::CU_LAUNCH_PARAM_END. + * + * - ::CU_LAUNCH_PARAM_END, which indicates the end of the \p extra + * array; + * - ::CU_LAUNCH_PARAM_BUFFER_POINTER, which specifies that the next + * value in \p extra will be a pointer to a buffer containing all + * the kernel parameters for launching kernel \p f; + * - ::CU_LAUNCH_PARAM_BUFFER_SIZE, which specifies that the next + * value in \p extra will be a pointer to a size_t containing the + * size of the buffer specified with ::CU_LAUNCH_PARAM_BUFFER_POINTER; + * + * The error ::CUDA_ERROR_INVALID_VALUE will be returned if kernel + * parameters are specified with both \p kernelParams and \p extra + * (i.e. both \p kernelParams and \p extra are non-NULL). + * + * Calling ::cuLaunchKernel() invalidates the persistent function state + * set through the following deprecated APIs: + * ::cuFuncSetBlockShape(), + * ::cuFuncSetSharedSize(), + * ::cuParamSetSize(), + * ::cuParamSeti(), + * ::cuParamSetf(), + * ::cuParamSetv(). + * + * Note that to use ::cuLaunchKernel(), the kernel \p f must either have + * been compiled with toolchain version 3.2 or later so that it will + * contain kernel parameter information, or have no kernel parameters. + * If either of these conditions is not met, then ::cuLaunchKernel() will + * return ::CUDA_ERROR_INVALID_IMAGE. + * + * Note that the API can also be used to launch context-less kernel ::CUkernel + * by querying the handle using ::cuLibraryGetKernel() and then passing it + * to the API by casting to ::CUfunction. Here, the context to launch + * the kernel on will either be taken from the specified stream \p hStream + * or the current context in case of NULL stream. + * + * \param f - Function ::CUfunction or Kernel ::CUkernel to launch + * \param gridDimX - Width of grid in blocks + * \param gridDimY - Height of grid in blocks + * \param gridDimZ - Depth of grid in blocks + * \param blockDimX - X dimension of each thread block + * \param blockDimY - Y dimension of each thread block + * \param blockDimZ - Z dimension of each thread block + * \param sharedMemBytes - Dynamic shared-memory size per thread block in bytes + * \param hStream - Stream identifier + * \param kernelParams - Array of pointers to kernel parameters + * \param extra - Extra options + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_NOT_FOUND + * \note_null_stream + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cudaLaunchKernel, + * ::cuLibraryGetKernel, + * ::cuKernelSetCacheConfig, + * ::cuKernelGetAttribute, + * ::cuKernelSetAttribute + */ +CUresult CUDAAPI cuLaunchKernel(CUfunction f, + unsigned int gridDimX, + unsigned int gridDimY, + unsigned int gridDimZ, + unsigned int blockDimX, + unsigned int blockDimY, + unsigned int blockDimZ, + unsigned int sharedMemBytes, + CUstream hStream, + void **kernelParams, + void **extra); + +/** + * \brief Launches a CUDA function ::CUfunction or a CUDA kernel ::CUkernel with launch-time configuration + * + * Invokes the function ::CUfunction or the kernel ::CUkernel \p f with the specified launch-time configuration + * \p config. + * + * The ::CUlaunchConfig structure is defined as: + * + * \code + * typedef struct CUlaunchConfig_st { + * unsigned int gridDimX; + * unsigned int gridDimY; + * unsigned int gridDimZ; + * unsigned int blockDimX; + * unsigned int blockDimY; + * unsigned int blockDimZ; + * unsigned int sharedMemBytes; + * CUstream hStream; + * CUlaunchAttribute *attrs; + * unsigned int numAttrs; + * } CUlaunchConfig; + * \endcode + * + * where: + * - ::CUlaunchConfig::gridDimX is the width of the grid in blocks. + * - ::CUlaunchConfig::gridDimY is the height of the grid in blocks. + * - ::CUlaunchConfig::gridDimZ is the depth of the grid in blocks. + * - ::CUlaunchConfig::blockDimX is the X dimension of each thread block. + * - ::CUlaunchConfig::blockDimX is the Y dimension of each thread block. + * - ::CUlaunchConfig::blockDimZ is the Z dimension of each thread block. + * - ::CUlaunchConfig::sharedMemBytes is the dynamic shared-memory size per + * thread block in bytes. + * - ::CUlaunchConfig::hStream is the handle to the stream to perform the launch + * in. The CUDA context associated with this stream must match that associated + * with function f. + * - ::CUlaunchConfig::attrs is an array of ::CUlaunchConfig::numAttrs + * continguous ::CUlaunchAttribute elements. The value of this pointer is not + * considered if ::CUlaunchConfig::numAttrs is zero. However, in that case, it + * is recommended to set the pointer to NULL. + * - ::CUlaunchConfig::numAttrs is the number of attributes populating the + * first ::CUlaunchConfig::numAttrs positions of the ::CUlaunchConfig::attrs + * array. + * + * Launch-time configuration is specified by adding entries to + * ::CUlaunchConfig::attrs. Each entry is an attribute ID and a corresponding + * attribute value. + * + * The ::CUlaunchAttribute structure is defined as: + * \code + * typedef struct CUlaunchAttribute_st { + * CUlaunchAttributeID id; + * CUlaunchAttributeValue value; + * } CUlaunchAttribute; + * \endcode + * where: + * - ::CUlaunchAttribute::id is a unique enum identifying the attribute. + * - ::CUlaunchAttribute::value is a union that hold the attribute value. + * + * An example of using the \p config parameter: + * \code + * CUlaunchAttribute coopAttr = {.id = CU_LAUNCH_ATTRIBUTE_COOPERATIVE, + * .value = 1}; + * CUlaunchConfig config = {... // set block and grid dimensions + * .attrs = &coopAttr, + * .numAttrs = 1}; + * + * cuLaunchKernelEx(&config, kernel, NULL, NULL); + * \endcode + * + * The ::CUlaunchAttributeID enum is defined as: + * \code + * typedef enum CUlaunchAttributeID_enum { + * CU_LAUNCH_ATTRIBUTE_IGNORE = 0, + * CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW = 1, + * CU_LAUNCH_ATTRIBUTE_COOPERATIVE = 2, + * CU_LAUNCH_ATTRIBUTE_SYNCHRONIZATION_POLICY = 3, + * CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION = 4, + * CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE = 5, + * CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_STREAM_SERIALIZATION = 6, + * CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_EVENT = 7, + * CU_LAUNCH_ATTRIBUTE_PRIORITY = 8, + * CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN_MAP = 9, + * CU_LAUNCH_ATTRIBUTE_MEM_SYNC_DOMAIN = 10, + * CU_LAUNCH_ATTRIBUTE_LAUNCH_COMPLETION_EVENT = 12, + * CU_LAUNCH_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE = 13, + * } CUlaunchAttributeID; + * \endcode + * + * and the corresponding ::CUlaunchAttributeValue union as : + * \code + * typedef union CUlaunchAttributeValue_union { + * CUaccessPolicyWindow accessPolicyWindow; + * int cooperative; + * CUsynchronizationPolicy syncPolicy; + * struct { + * unsigned int x; + * unsigned int y; + * unsigned int z; + * } clusterDim; + * CUclusterSchedulingPolicy clusterSchedulingPolicyPreference; + * int programmaticStreamSerializationAllowed; + * struct { + * CUevent event; + * int flags; + * int triggerAtBlockStart; + * } programmaticEvent; + * int priority; + * CUlaunchMemSyncDomainMap memSyncDomainMap; + * CUlaunchMemSyncDomain memSyncDomain; + * struct { + * CUevent event; + * int flags; + * } launchCompletionEvent; + * struct { + * int deviceUpdatable; + * CUgraphDeviceNode devNode; + * } deviceUpdatableKernelNode; + * } CUlaunchAttributeValue; + * \endcode + * + * Setting ::CU_LAUNCH_ATTRIBUTE_COOPERATIVE to a non-zero value causes the + * kernel launch to be a cooperative launch, with exactly the same usage and + * semantics of ::cuLaunchCooperativeKernel. + * + * Setting ::CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_STREAM_SERIALIZATION to a non-zero + * values causes the kernel to use programmatic means to resolve its stream + * dependency -- enabling the CUDA runtime to opportunistically allow the grid's + * execution to overlap with the previous kernel in the stream, if that kernel + * requests the overlap. + * + * ::CU_LAUNCH_ATTRIBUTE_PROGRAMMATIC_EVENT records an event along with the + * kernel launch. Event recorded through this launch attribute is guaranteed to + * only trigger after all block in the associated kernel trigger the event. A + * block can trigger the event through PTX launchdep.release or CUDA builtin + * function cudaTriggerProgrammaticLaunchCompletion(). A trigger can also be + * inserted at the beginning of each block's execution if triggerAtBlockStart is + * set to non-0. Note that dependents (including the CPU thread calling + * cuEventSynchronize()) are not guaranteed to observe the release precisely + * when it is released. For example, cuEventSynchronize() may only observe the + * event trigger long after the associated kernel has completed. This recording + * type is primarily meant for establishing programmatic dependency between + * device tasks. The event supplied must not be an interprocess or interop + * event. The event must disable timing (i.e. created with + * ::CU_EVENT_DISABLE_TIMING flag set). + * + * ::CU_LAUNCH_ATTRIBUTE_LAUNCH_COMPLETION_EVENT records an event along with + * the kernel launch. Nominally, the event is triggered once all blocks of the + * kernel have begun execution. Currently this is a best effort. If a kernel B + * has a launch completion dependency on a kernel A, B may wait until A is + * complete. Alternatively, blocks of B may begin before all blocks of A have + * begun, for example: + * + * - If B can claim execution resources unavaiable to A, for example if they + * run on different GPUs. + * - If B is a higher priority than A. + * + * Exercise caution if such an ordering inversion could lead to deadlock. The + * event supplied must not be an interprocess or interop event. The event must + * disable timing (i.e. must be created with the ::CU_EVENT_DISABLE_TIMING flag + * set). + * + * Setting ::CU_LAUNCH_ATTRIBUTE_DEVICE_UPDATABLE_KERNEL_NODE to 1 + * on a captured launch causes the resulting kernel node to be device-updatable. + * This attribute is specific to graphs, and passing it to a launch in a + * non-capturing stream results in an error. Passing a value other than 0 or 1 is + * not allowed. + * + * On success, a handle will be returned via + * ::CUlaunchAttributeValue::deviceUpdatableKernelNode::devNode which can be passed + * to the various device-side update functions to update the node's kernel parameters + * from within another kernel. For more information on the types of device updates + * that can be made, as well as the relevant limitations thereof, see + * ::cudaGraphKernelNodeUpdatesApply. + * + * Kernel nodes which are device-updatable have additional restrictions compared to regular + * kernel nodes. Firstly, device-updatable nodes cannot be removed from their graph via + * ::cuGraphDestroyNode. Additionally, once opted-in to this functionality, a node cannot + * opt out, and any attempt to set the attribute to 0 will result in an error. Graphs + * containing one or more device-updatable node also do not allow multiple instantiation. + * + * + * The effect of other attributes is consistent with their effect when set via + * persistent APIs. + * + * See ::cuStreamSetAttribute for + * - ::CU_LAUNCH_ATTRIBUTE_ACCESS_POLICY_WINDOW + * - ::CU_LAUNCH_ATTRIBUTE_SYNCHRONIZATION_POLICY + * + * See ::cuFuncSetAttribute for + * - ::CU_LAUNCH_ATTRIBUTE_CLUSTER_DIMENSION + * - ::CU_LAUNCH_ATTRIBUTE_CLUSTER_SCHEDULING_POLICY_PREFERENCE + * + * Kernel parameters to \p f can be specified in the same ways that they can be + * using ::cuLaunchKernel. + * + * Note that the API can also be used to launch context-less kernel ::CUkernel + * by querying the handle using ::cuLibraryGetKernel() and then passing it + * to the API by casting to ::CUfunction. Here, the context to launch + * the kernel on will either be taken from the specified stream ::CUlaunchConfig::hStream + * or the current context in case of NULL stream. + * + * \param config - Config to launch + * \param f - Function ::CUfunction or Kernel ::CUkernel to launch + * \param kernelParams - Array of pointers to kernel parameters + * \param extra - Extra options + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_COOPERATIVE_LAUNCH_TOO_LARGE, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_NOT_FOUND + * \note_null_stream + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cudaLaunchKernel, + * ::cudaLaunchKernelEx, + * ::cuLibraryGetKernel, + * ::cuKernelSetCacheConfig, + * ::cuKernelGetAttribute, + * ::cuKernelSetAttribute + */ +CUresult CUDAAPI cuLaunchKernelEx(const CUlaunchConfig *config, + CUfunction f, + void **kernelParams, + void **extra); + +/** + * \brief Launches a CUDA function ::CUfunction or a CUDA kernel ::CUkernel where thread blocks + * can cooperate and synchronize as they execute + * + * Invokes the function ::CUfunction or the kernel ::CUkernel \p f on a \p gridDimX x \p gridDimY x \p gridDimZ + * grid of blocks. Each block contains \p blockDimX x \p blockDimY x + * \p blockDimZ threads. + * + * Note that the API can also be used to launch context-less kernel ::CUkernel + * by querying the handle using ::cuLibraryGetKernel() and then passing it + * to the API by casting to ::CUfunction. Here, the context to launch + * the kernel on will either be taken from the specified stream \p hStream + * or the current context in case of NULL stream. + * + * \p sharedMemBytes sets the amount of dynamic shared memory that will be + * available to each thread block. + * + * The device on which this kernel is invoked must have a non-zero value for + * the device attribute ::CU_DEVICE_ATTRIBUTE_COOPERATIVE_LAUNCH. + * + * The total number of blocks launched cannot exceed the maximum number of blocks per + * multiprocessor as returned by ::cuOccupancyMaxActiveBlocksPerMultiprocessor (or + * ::cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags) times the number of multiprocessors + * as specified by the device attribute ::CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT. + * + * The kernel cannot make use of CUDA dynamic parallelism. + * + * Kernel parameters must be specified via \p kernelParams. If \p f + * has N parameters, then \p kernelParams needs to be an array of N + * pointers. Each of \p kernelParams[0] through \p kernelParams[N-1] + * must point to a region of memory from which the actual kernel + * parameter will be copied. The number of kernel parameters and their + * offsets and sizes do not need to be specified as that information is + * retrieved directly from the kernel's image. + * + * Calling ::cuLaunchCooperativeKernel() sets persistent function state that is + * the same as function state set through ::cuLaunchKernel API + * + * When the kernel \p f is launched via ::cuLaunchCooperativeKernel(), the previous + * block shape, shared size and parameter info associated with \p f + * is overwritten. + * + * Note that to use ::cuLaunchCooperativeKernel(), the kernel \p f must either have + * been compiled with toolchain version 3.2 or later so that it will + * contain kernel parameter information, or have no kernel parameters. + * If either of these conditions is not met, then ::cuLaunchCooperativeKernel() will + * return ::CUDA_ERROR_INVALID_IMAGE. + * + * Note that the API can also be used to launch context-less kernel ::CUkernel + * by querying the handle using ::cuLibraryGetKernel() and then passing it + * to the API by casting to ::CUfunction. Here, the context to launch + * the kernel on will either be taken from the specified stream \p hStream + * or the current context in case of NULL stream. + * + * \param f - Function ::CUfunction or Kernel ::CUkernel to launch + * \param gridDimX - Width of grid in blocks + * \param gridDimY - Height of grid in blocks + * \param gridDimZ - Depth of grid in blocks + * \param blockDimX - X dimension of each thread block + * \param blockDimY - Y dimension of each thread block + * \param blockDimZ - Z dimension of each thread block + * \param sharedMemBytes - Dynamic shared-memory size per thread block in bytes + * \param hStream - Stream identifier + * \param kernelParams - Array of pointers to kernel parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_COOPERATIVE_LAUNCH_TOO_LARGE, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED, + * ::CUDA_ERROR_NOT_FOUND + * \note_null_stream + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cuLaunchCooperativeKernelMultiDevice, + * ::cudaLaunchCooperativeKernel, + * ::cuLibraryGetKernel, + * ::cuKernelSetCacheConfig, + * ::cuKernelGetAttribute, + * ::cuKernelSetAttribute + */ +CUresult CUDAAPI cuLaunchCooperativeKernel(CUfunction f, + unsigned int gridDimX, + unsigned int gridDimY, + unsigned int gridDimZ, + unsigned int blockDimX, + unsigned int blockDimY, + unsigned int blockDimZ, + unsigned int sharedMemBytes, + CUstream hStream, + void **kernelParams); + +/** + * \brief Launches CUDA functions on multiple devices where thread blocks can cooperate and synchronize as they execute + * + * \deprecated This function is deprecated as of CUDA 11.3. + * + * Invokes kernels as specified in the \p launchParamsList array where each element + * of the array specifies all the parameters required to perform a single kernel launch. + * These kernels can cooperate and synchronize as they execute. The size of the array is + * specified by \p numDevices. + * + * No two kernels can be launched on the same device. All the devices targeted by this + * multi-device launch must be identical. All devices must have a non-zero value for the + * device attribute ::CU_DEVICE_ATTRIBUTE_COOPERATIVE_MULTI_DEVICE_LAUNCH. + * + * All kernels launched must be identical with respect to the compiled code. Note that + * any __device__, __constant__ or __managed__ variables present in the module that owns + * the kernel launched on each device, are independently instantiated on every device. + * It is the application's responsibility to ensure these variables are initialized and + * used appropriately. + * + * The size of the grids as specified in blocks, the size of the blocks themselves + * and the amount of shared memory used by each thread block must also match across + * all launched kernels. + * + * The streams used to launch these kernels must have been created via either ::cuStreamCreate + * or ::cuStreamCreateWithPriority. The NULL stream or ::CU_STREAM_LEGACY or ::CU_STREAM_PER_THREAD + * cannot be used. + * + * The total number of blocks launched per kernel cannot exceed the maximum number of blocks + * per multiprocessor as returned by ::cuOccupancyMaxActiveBlocksPerMultiprocessor (or + * ::cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags) times the number of multiprocessors + * as specified by the device attribute ::CU_DEVICE_ATTRIBUTE_MULTIPROCESSOR_COUNT. Since the + * total number of blocks launched per device has to match across all devices, the maximum + * number of blocks that can be launched per device will be limited by the device with the + * least number of multiprocessors. + * + * The kernels cannot make use of CUDA dynamic parallelism. + * + * The ::CUDA_LAUNCH_PARAMS structure is defined as: + * \code + typedef struct CUDA_LAUNCH_PARAMS_st + { + CUfunction function; + unsigned int gridDimX; + unsigned int gridDimY; + unsigned int gridDimZ; + unsigned int blockDimX; + unsigned int blockDimY; + unsigned int blockDimZ; + unsigned int sharedMemBytes; + CUstream hStream; + void **kernelParams; + } CUDA_LAUNCH_PARAMS; + * \endcode + * where: + * - ::CUDA_LAUNCH_PARAMS::function specifies the kernel to be launched. All functions must + * be identical with respect to the compiled code. + * Note that you can also specify context-less kernel ::CUkernel by querying the handle + * using ::cuLibraryGetKernel() and then casting to ::CUfunction. In this case, the context to + * launch the kernel on be taken from the specified stream ::CUDA_LAUNCH_PARAMS::hStream. + * - ::CUDA_LAUNCH_PARAMS::gridDimX is the width of the grid in blocks. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::gridDimY is the height of the grid in blocks. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::gridDimZ is the depth of the grid in blocks. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::blockDimX is the X dimension of each thread block. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::blockDimX is the Y dimension of each thread block. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::blockDimZ is the Z dimension of each thread block. This must match across + * all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::sharedMemBytes is the dynamic shared-memory size per thread block in bytes. + * This must match across all kernels launched. + * - ::CUDA_LAUNCH_PARAMS::hStream is the handle to the stream to perform the launch in. This cannot + * be the NULL stream or ::CU_STREAM_LEGACY or ::CU_STREAM_PER_THREAD. The CUDA context associated + * with this stream must match that associated with ::CUDA_LAUNCH_PARAMS::function. + * - ::CUDA_LAUNCH_PARAMS::kernelParams is an array of pointers to kernel parameters. If + * ::CUDA_LAUNCH_PARAMS::function has N parameters, then ::CUDA_LAUNCH_PARAMS::kernelParams + * needs to be an array of N pointers. Each of ::CUDA_LAUNCH_PARAMS::kernelParams[0] through + * ::CUDA_LAUNCH_PARAMS::kernelParams[N-1] must point to a region of memory from which the actual + * kernel parameter will be copied. The number of kernel parameters and their offsets and sizes + * do not need to be specified as that information is retrieved directly from the kernel's image. + * + * By default, the kernel won't begin execution on any GPU until all prior work in all the specified + * streams has completed. This behavior can be overridden by specifying the flag + * ::CUDA_COOPERATIVE_LAUNCH_MULTI_DEVICE_NO_PRE_LAUNCH_SYNC. When this flag is specified, each kernel + * will only wait for prior work in the stream corresponding to that GPU to complete before it begins + * execution. + * + * Similarly, by default, any subsequent work pushed in any of the specified streams will not begin + * execution until the kernels on all GPUs have completed. This behavior can be overridden by specifying + * the flag ::CUDA_COOPERATIVE_LAUNCH_MULTI_DEVICE_NO_POST_LAUNCH_SYNC. When this flag is specified, + * any subsequent work pushed in any of the specified streams will only wait for the kernel launched + * on the GPU corresponding to that stream to complete before it begins execution. + * + * Calling ::cuLaunchCooperativeKernelMultiDevice() sets persistent function state that is + * the same as function state set through ::cuLaunchKernel API when called individually for each + * element in \p launchParamsList. + * + * When kernels are launched via ::cuLaunchCooperativeKernelMultiDevice(), the previous + * block shape, shared size and parameter info associated with each ::CUDA_LAUNCH_PARAMS::function + * in \p launchParamsList is overwritten. + * + * Note that to use ::cuLaunchCooperativeKernelMultiDevice(), the kernels must either have + * been compiled with toolchain version 3.2 or later so that it will + * contain kernel parameter information, or have no kernel parameters. + * If either of these conditions is not met, then ::cuLaunchCooperativeKernelMultiDevice() will + * return ::CUDA_ERROR_INVALID_IMAGE. + * + * \param launchParamsList - List of launch parameters, one per device + * \param numDevices - Size of the \p launchParamsList array + * \param flags - Flags to control launch behavior + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_IMAGE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_COOPERATIVE_LAUNCH_TOO_LARGE, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED + * \note_null_stream + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cuLaunchCooperativeKernel, + * ::cudaLaunchCooperativeKernelMultiDevice + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuLaunchCooperativeKernelMultiDevice(CUDA_LAUNCH_PARAMS *launchParamsList, unsigned int numDevices, unsigned int flags); + +/** + * \brief Enqueues a host function call in a stream + * + * Enqueues a host function to run in a stream. The function will be called + * after currently enqueued work and will block work added after it. + * + * The host function must not make any CUDA API calls. Attempting to use a + * CUDA API may result in ::CUDA_ERROR_NOT_PERMITTED, but this is not required. + * The host function must not perform any synchronization that may depend on + * outstanding CUDA work not mandated to run earlier. Host functions without a + * mandated order (such as in independent streams) execute in undefined order + * and may be serialized. + * + * For the purposes of Unified Memory, execution makes a number of guarantees: + *
    + *
  • The stream is considered idle for the duration of the function's + * execution. Thus, for example, the function may always use memory attached + * to the stream it was enqueued in.
    • + *
  • The start of execution of the function has the same effect as + * synchronizing an event recorded in the same stream immediately prior to + * the function. It thus synchronizes streams which have been "joined" + * prior to the function.
    • + *
  • Adding device work to any stream does not have the effect of making + * the stream active until all preceding host functions and stream callbacks + * have executed. Thus, for + * example, a function might use global attached memory even if work has + * been added to another stream, if the work has been ordered behind the + * function call with an event.
    • + *
  • Completion of the function does not cause a stream to become + * active except as described above. The stream will remain idle + * if no device work follows the function, and will remain idle across + * consecutive host functions or stream callbacks without device work in + * between. Thus, for example, + * stream synchronization can be done by signaling from a host function at the + * end of the stream.
    • + *
+ * + * Note that, in contrast to ::cuStreamAddCallback, the function will not be + * called in the event of an error in the CUDA context. + * + * \param hStream - Stream to enqueue function call in + * \param fn - The function to call once preceding stream operations are complete + * \param userData - User-specified data to be passed to the function + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_null_stream + * \notefnerr + * + * \sa ::cuStreamCreate, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamWaitEvent, + * ::cuStreamDestroy, + * ::cuMemAllocManaged, + * ::cuStreamAttachMemAsync, + * ::cuStreamAddCallback + */ +CUresult CUDAAPI cuLaunchHostFunc(CUstream hStream, CUhostFn fn, void *userData); + +/** @} */ /* END CUDA_EXEC */ + +/** + * \defgroup CUDA_EXEC_DEPRECATED Execution Control [DEPRECATED] + * + * ___MANBRIEF___ deprecated execution control functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated execution control functions of the + * low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Sets the block-dimensions for the function + * + * \deprecated + * + * Specifies the \p x, \p y, and \p z dimensions of the thread blocks that are + * created when the kernel given by \p hfunc is launched. + * + * \param hfunc - Kernel to specify dimensions of + * \param x - X dimension + * \param y - Y dimension + * \param z - Z dimension + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetSharedSize, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSeti, + * ::cuParamSetf, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuFuncSetBlockShape(CUfunction hfunc, int x, int y, int z); + +/** + * \brief Sets the dynamic shared-memory size for the function + * + * \deprecated + * + * Sets through \p bytes the amount of dynamic shared memory that will be + * available to each thread block when the kernel given by \p hfunc is launched. + * + * \param hfunc - Kernel to specify dynamic shared-memory size for + * \param bytes - Dynamic shared-memory size per thread in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetCacheConfig, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSeti, + * ::cuParamSetf, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuFuncSetSharedSize(CUfunction hfunc, unsigned int bytes); + +/** + * \brief Sets the parameter size for the function + * + * \deprecated + * + * Sets through \p numbytes the total size in bytes needed by the function + * parameters of the kernel corresponding to \p hfunc. + * + * \param hfunc - Kernel to set parameter size for + * \param numbytes - Size of parameter list in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetf, + * ::cuParamSeti, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuParamSetSize(CUfunction hfunc, unsigned int numbytes); + +/** + * \brief Adds an integer parameter to the function's argument list + * + * \deprecated + * + * Sets an integer parameter that will be specified the next time the + * kernel corresponding to \p hfunc will be invoked. \p offset is a byte offset. + * + * \param hfunc - Kernel to add parameter to + * \param offset - Offset to add parameter to argument list + * \param value - Value of parameter + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSetf, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuParamSeti(CUfunction hfunc, int offset, unsigned int value); + +/** + * \brief Adds a floating-point parameter to the function's argument list + * + * \deprecated + * + * Sets a floating-point parameter that will be specified the next time the + * kernel corresponding to \p hfunc will be invoked. \p offset is a byte offset. + * + * \param hfunc - Kernel to add parameter to + * \param offset - Offset to add parameter to argument list + * \param value - Value of parameter + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSeti, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuParamSetf(CUfunction hfunc, int offset, float value); + +/** + * \brief Adds arbitrary data to the function's argument list + * + * \deprecated + * + * Copies an arbitrary amount of data (specified in \p numbytes) from \p ptr + * into the parameter space of the kernel corresponding to \p hfunc. \p offset + * is a byte offset. + * + * \param hfunc - Kernel to add data to + * \param offset - Offset to add data to argument list + * \param ptr - Pointer to arbitrary data + * \param numbytes - Size of data to copy in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSetf, + * ::cuParamSeti, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuParamSetv(CUfunction hfunc, int offset, void *ptr, unsigned int numbytes); + +/** + * \brief Launches a CUDA function + * + * \deprecated + * + * Invokes the kernel \p f on a 1 x 1 x 1 grid of blocks. The block + * contains the number of threads specified by a previous call to + * ::cuFuncSetBlockShape(). + * + * The block shape, dynamic shared memory size, and parameter information + * must be set using + * ::cuFuncSetBlockShape(), + * ::cuFuncSetSharedSize(), + * ::cuParamSetSize(), + * ::cuParamSeti(), + * ::cuParamSetf(), and + * ::cuParamSetv() + * prior to calling this function. + * + * Launching a function via ::cuLaunchKernel() invalidates the function's + * block shape, dynamic shared memory size, and parameter information. After + * launching via cuLaunchKernel, this state must be re-initialized prior to + * calling this function. Failure to do so results in undefined behavior. + * + * \param f - Kernel to launch + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSetf, + * ::cuParamSeti, + * ::cuParamSetv, + * ::cuLaunchGrid, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuLaunch(CUfunction f); + +/** + * \brief Launches a CUDA function + * + * \deprecated + * + * Invokes the kernel \p f on a \p grid_width x \p grid_height grid of + * blocks. Each block contains the number of threads specified by a previous + * call to ::cuFuncSetBlockShape(). + * + * The block shape, dynamic shared memory size, and parameter information + * must be set using + * ::cuFuncSetBlockShape(), + * ::cuFuncSetSharedSize(), + * ::cuParamSetSize(), + * ::cuParamSeti(), + * ::cuParamSetf(), and + * ::cuParamSetv() + * prior to calling this function. + * + * Launching a function via ::cuLaunchKernel() invalidates the function's + * block shape, dynamic shared memory size, and parameter information. After + * launching via cuLaunchKernel, this state must be re-initialized prior to + * calling this function. Failure to do so results in undefined behavior. + * + * \param f - Kernel to launch + * \param grid_width - Width of grid in blocks + * \param grid_height - Height of grid in blocks + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSetf, + * ::cuParamSeti, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGridAsync, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuLaunchGrid(CUfunction f, int grid_width, int grid_height); + +/** + * \brief Launches a CUDA function + * + * \deprecated + * + * Invokes the kernel \p f on a \p grid_width x \p grid_height grid of + * blocks. Each block contains the number of threads specified by a previous + * call to ::cuFuncSetBlockShape(). + * + * The block shape, dynamic shared memory size, and parameter information + * must be set using + * ::cuFuncSetBlockShape(), + * ::cuFuncSetSharedSize(), + * ::cuParamSetSize(), + * ::cuParamSeti(), + * ::cuParamSetf(), and + * ::cuParamSetv() + * prior to calling this function. + * + * Launching a function via ::cuLaunchKernel() invalidates the function's + * block shape, dynamic shared memory size, and parameter information. After + * launching via cuLaunchKernel, this state must be re-initialized prior to + * calling this function. Failure to do so results in undefined behavior. + * + * \param f - Kernel to launch + * \param grid_width - Width of grid in blocks + * \param grid_height - Height of grid in blocks + * \param hStream - Stream identifier + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_LAUNCH_FAILED, + * ::CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * ::CUDA_ERROR_LAUNCH_INCOMPATIBLE_TEXTURING, + * ::CUDA_ERROR_SHARED_OBJECT_INIT_FAILED + * + * \note In certain cases where cubins are created with no ABI (i.e., using \p ptxas \p --abi-compile \p no), + * this function may serialize kernel launches. The CUDA driver retains asynchronous behavior by + * growing the per-thread stack as needed per launch and not shrinking it afterwards. + * + * \note_null_stream + * \notefnerr + * + * \sa ::cuFuncSetBlockShape, + * ::cuFuncSetSharedSize, + * ::cuFuncGetAttribute, + * ::cuParamSetSize, + * ::cuParamSetf, + * ::cuParamSeti, + * ::cuParamSetv, + * ::cuLaunch, + * ::cuLaunchGrid, + * ::cuLaunchKernel + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuLaunchGridAsync(CUfunction f, int grid_width, int grid_height, CUstream hStream); + + +/** + * \brief Adds a texture-reference to the function's argument list + * + * \deprecated + * + * Makes the CUDA array or linear memory bound to the texture reference + * \p hTexRef available to a device program as a texture. In this version of + * CUDA, the texture-reference must be obtained via ::cuModuleGetTexRef() and + * the \p texunit parameter must be set to ::CU_PARAM_TR_DEFAULT. + * + * \param hfunc - Kernel to add texture-reference to + * \param texunit - Texture unit (must be ::CU_PARAM_TR_DEFAULT) + * \param hTexRef - Texture-reference to add to argument list + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuParamSetTexRef(CUfunction hfunc, int texunit, CUtexref hTexRef); + +/** + * \brief Sets the shared memory configuration for a device function. + * + * \deprecated + * + * On devices with configurable shared memory banks, this function will + * force all subsequent launches of the specified device function to have + * the given shared memory bank size configuration. On any given launch of the + * function, the shared memory configuration of the device will be temporarily + * changed if needed to suit the function's preferred configuration. Changes in + * shared memory configuration between subsequent launches of functions, + * may introduce a device side synchronization point. + * + * Any per-function setting of shared memory bank size set via + * ::cuFuncSetSharedMemConfig will override the context wide setting set with + * ::cuCtxSetSharedMemConfig. + * + * Changing the shared memory bank size will not increase shared memory usage + * or affect occupancy of kernels, but may have major effects on performance. + * Larger bank sizes will allow for greater potential bandwidth to shared memory, + * but will change what kinds of accesses to shared memory will result in bank + * conflicts. + * + * This function will do nothing on devices with fixed shared memory bank size. + * + * The supported bank configurations are: + * - ::CU_SHARED_MEM_CONFIG_DEFAULT_BANK_SIZE: use the context's shared memory + * configuration when launching this function. + * - ::CU_SHARED_MEM_CONFIG_FOUR_BYTE_BANK_SIZE: set shared memory bank width to + * be natively four bytes when launching this function. + * - ::CU_SHARED_MEM_CONFIG_EIGHT_BYTE_BANK_SIZE: set shared memory bank width to + * be natively eight bytes when launching this function. + * + * \param hfunc - kernel to be given a shared memory config + * \param config - requested shared memory configuration + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT + * \notefnerr + * + * \sa ::cuCtxGetCacheConfig, + * ::cuCtxSetCacheConfig, + * ::cuCtxGetSharedMemConfig, + * ::cuCtxSetSharedMemConfig, + * ::cuFuncGetAttribute, + * ::cuLaunchKernel, + * ::cudaFuncSetSharedMemConfig + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuFuncSetSharedMemConfig(CUfunction hfunc, CUsharedconfig config); + +/** @} */ /* END CUDA_EXEC_DEPRECATED */ + +/** + * \defgroup CUDA_GRAPH Graph Management + * + * ___MANBRIEF___ graph management functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the graph management functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Creates a graph + * + * Creates an empty graph, which is returned via \p phGraph. + * + * \param phGraph - Returns newly created graph + * \param flags - Graph creation flags, must be 0 + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode, + * ::cuGraphInstantiate, + * ::cuGraphDestroy, + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphClone + */ +CUresult CUDAAPI cuGraphCreate(CUgraph *phGraph, unsigned int flags); + +/** + * \brief Creates a kernel execution node and adds it to a graph + * + * Creates a new kernel execution node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * The CUDA_KERNEL_NODE_PARAMS structure is defined as: + * + * \code + * typedef struct CUDA_KERNEL_NODE_PARAMS_st { + * CUfunction func; + * unsigned int gridDimX; + * unsigned int gridDimY; + * unsigned int gridDimZ; + * unsigned int blockDimX; + * unsigned int blockDimY; + * unsigned int blockDimZ; + * unsigned int sharedMemBytes; + * void **kernelParams; + * void **extra; + * CUkernel kern; + * CUcontext ctx; + * } CUDA_KERNEL_NODE_PARAMS; + * \endcode + * + * When the graph is launched, the node will invoke kernel \p func on a (\p gridDimX x + * \p gridDimY x \p gridDimZ) grid of blocks. Each block contains + * (\p blockDimX x \p blockDimY x \p blockDimZ) threads. + * + * \p sharedMemBytes sets the amount of dynamic shared memory that will be + * available to each thread block. + * + * Kernel parameters to \p func can be specified in one of two ways: + * + * 1) Kernel parameters can be specified via \p kernelParams. If the kernel has N + * parameters, then \p kernelParams needs to be an array of N pointers. Each pointer, + * from \p kernelParams[0] to \p kernelParams[N-1], points to the region of memory from which the actual + * parameter will be copied. The number of kernel parameters and their offsets and sizes do not need + * to be specified as that information is retrieved directly from the kernel's image. + * + * 2) Kernel parameters for non-cooperative kernels can also be packaged by the application into a single + * buffer that is passed in via \p extra. This places the burden on the application of knowing each + * kernel parameter's size and alignment/padding within the buffer. The \p extra parameter exists + * to allow this function to take additional less commonly used arguments. \p extra specifies + * a list of names of extra settings and their corresponding values. Each extra setting name is + * immediately followed by the corresponding value. The list must be terminated with either NULL or + * CU_LAUNCH_PARAM_END. + * + * - ::CU_LAUNCH_PARAM_END, which indicates the end of the \p extra + * array; + * - ::CU_LAUNCH_PARAM_BUFFER_POINTER, which specifies that the next + * value in \p extra will be a pointer to a buffer + * containing all the kernel parameters for launching kernel + * \p func; + * - ::CU_LAUNCH_PARAM_BUFFER_SIZE, which specifies that the next + * value in \p extra will be a pointer to a size_t + * containing the size of the buffer specified with + * ::CU_LAUNCH_PARAM_BUFFER_POINTER; + * + * The error ::CUDA_ERROR_INVALID_VALUE will be returned if kernel parameters are specified with both + * \p kernelParams and \p extra (i.e. both \p kernelParams and \p extra are non-NULL). + * ::CUDA_ERROR_INVALID_VALUE will be returned if \p extra is used for a cooperative kernel. + * + * The \p kernelParams or \p extra array, as well as the argument values it points to, + * are copied during this call. + * + * \note Kernels launched using graphs must not use texture and surface references. Reading or + * writing through any texture or surface reference is undefined behavior. + * This restriction does not apply to texture and surface objects. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the GPU execution node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuLaunchKernel, + * ::cuLaunchCooperativeKernel, + * ::cuGraphKernelNodeGetParams, + * ::cuGraphKernelNodeSetParams, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddKernelNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_KERNEL_NODE_PARAMS *nodeParams); + +/** + * \brief Returns a kernel node's parameters + * + * Returns the parameters of kernel node \p hNode in \p nodeParams. + * The \p kernelParams or \p extra array returned in \p nodeParams, + * as well as the argument values it points to, are owned by the node. + * This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cuGraphKernelNodeSetParams to update the + * parameters of this node. + * + * The params will contain either \p kernelParams or \p extra, + * according to which of these was most recently set on the node. + * + * \param hNode - Node to get the parameters for + * \param nodeParams - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuLaunchKernel, + * ::cuGraphAddKernelNode, + * ::cuGraphKernelNodeSetParams + */ +CUresult CUDAAPI cuGraphKernelNodeGetParams(CUgraphNode hNode, CUDA_KERNEL_NODE_PARAMS *nodeParams); + +/** + * \brief Sets a kernel node's parameters + * + * Sets the parameters of kernel node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuLaunchKernel, + * ::cuGraphAddKernelNode, + * ::cuGraphKernelNodeGetParams + */ +CUresult CUDAAPI cuGraphKernelNodeSetParams(CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS *nodeParams); + +/** + * \brief Creates a memcpy node and adds it to a graph + * + * Creates a new memcpy node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * When the graph is launched, the node will perform the memcpy described by \p copyParams. + * See ::cuMemcpy3D() for a description of the structure and its restrictions. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::CU_DEVICE_ATTRIBUTE_CONCURRENT_MANAGED_ACCESS. If one or more of the operands refer + * to managed memory, then using the memory type ::CU_MEMORYTYPE_UNIFIED is disallowed + * for those operand(s). The managed memory will be treated as residing on either the + * host or the device, depending on which memory type is specified. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param copyParams - Parameters for the memory copy + * \param ctx - Context on which to run the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuMemcpy3D, + * ::cuGraphMemcpyNodeGetParams, + * ::cuGraphMemcpyNodeSetParams, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddMemcpyNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_MEMCPY3D *copyParams, CUcontext ctx); + +/** + * \brief Returns a memcpy node's parameters + * + * Returns the parameters of memcpy node \p hNode in \p nodeParams. + * + * \param hNode - Node to get the parameters for + * \param nodeParams - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuMemcpy3D, + * ::cuGraphAddMemcpyNode, + * ::cuGraphMemcpyNodeSetParams + */ +CUresult CUDAAPI cuGraphMemcpyNodeGetParams(CUgraphNode hNode, CUDA_MEMCPY3D *nodeParams); + +/** + * \brief Sets a memcpy node's parameters + * + * Sets the parameters of memcpy node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuMemcpy3D, + * ::cuGraphAddMemcpyNode, + * ::cuGraphMemcpyNodeGetParams + */ +CUresult CUDAAPI cuGraphMemcpyNodeSetParams(CUgraphNode hNode, const CUDA_MEMCPY3D *nodeParams); + +/** + * \brief Creates a memset node and adds it to a graph + * + * Creates a new memset node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * The element size must be 1, 2, or 4 bytes. + * When the graph is launched, the node will perform the memset described by \p memsetParams. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param memsetParams - Parameters for the memory set + * \param ctx - Context on which to run the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CONTEXT + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuMemsetD2D32, + * ::cuGraphMemsetNodeGetParams, + * ::cuGraphMemsetNodeSetParams, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode + */ +CUresult CUDAAPI cuGraphAddMemsetNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_MEMSET_NODE_PARAMS *memsetParams, CUcontext ctx); + +/** + * \brief Returns a memset node's parameters + * + * Returns the parameters of memset node \p hNode in \p nodeParams. + * + * \param hNode - Node to get the parameters for + * \param nodeParams - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuMemsetD2D32, + * ::cuGraphAddMemsetNode, + * ::cuGraphMemsetNodeSetParams + */ +CUresult CUDAAPI cuGraphMemsetNodeGetParams(CUgraphNode hNode, CUDA_MEMSET_NODE_PARAMS *nodeParams); + +/** + * \brief Sets a memset node's parameters + * + * Sets the parameters of memset node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuMemsetD2D32, + * ::cuGraphAddMemsetNode, + * ::cuGraphMemsetNodeGetParams + */ +CUresult CUDAAPI cuGraphMemsetNodeSetParams(CUgraphNode hNode, const CUDA_MEMSET_NODE_PARAMS *nodeParams); + +/** + * \brief Creates a host execution node and adds it to a graph + * + * Creates a new CPU execution node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * When the graph is launched, the node will invoke the specified CPU function. + * Host nodes are not supported under MPS with pre-Volta GPUs. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the host node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuLaunchHostFunc, + * ::cuGraphHostNodeGetParams, + * ::cuGraphHostNodeSetParams, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddHostNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_HOST_NODE_PARAMS *nodeParams); + +/** + * \brief Returns a host node's parameters + * + * Returns the parameters of host node \p hNode in \p nodeParams. + * + * \param hNode - Node to get the parameters for + * \param nodeParams - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuLaunchHostFunc, + * ::cuGraphAddHostNode, + * ::cuGraphHostNodeSetParams + */ +CUresult CUDAAPI cuGraphHostNodeGetParams(CUgraphNode hNode, CUDA_HOST_NODE_PARAMS *nodeParams); + +/** + * \brief Sets a host node's parameters + * + * Sets the parameters of host node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuLaunchHostFunc, + * ::cuGraphAddHostNode, + * ::cuGraphHostNodeGetParams + */ +CUresult CUDAAPI cuGraphHostNodeSetParams(CUgraphNode hNode, const CUDA_HOST_NODE_PARAMS *nodeParams); + +/** + * \brief Creates a child graph node and adds it to a graph + * + * Creates a new node which executes an embedded graph, and adds it to \p hGraph with + * \p numDependencies dependencies specified via \p dependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * If \p hGraph contains allocation or free nodes, this call will return an error. + * + * The node executes an embedded child graph. The child graph is cloned in this call. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param childGraph - The graph to clone into this node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphChildGraphNodeGetGraph, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode, + * ::cuGraphClone + */ +CUresult CUDAAPI cuGraphAddChildGraphNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUgraph childGraph); + +/** + * \brief Gets a handle to the embedded graph of a child graph node + * + * Gets a handle to the embedded graph in a child graph node. This call + * does not clone the graph. Changes to the graph will be reflected in + * the node, and the node retains ownership of the graph. + * + * Allocation and free nodes cannot be added to the returned graph. + * Attempting to do so will return an error. + * + * \param hNode - Node to get the embedded graph for + * \param phGraph - Location to store a handle to the graph + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddChildGraphNode, + * ::cuGraphNodeFindInClone + */ +CUresult CUDAAPI cuGraphChildGraphNodeGetGraph(CUgraphNode hNode, CUgraph *phGraph); + +/** + * \brief Creates an empty node and adds it to a graph + * + * Creates a new node which performs no operation, and adds it to \p hGraph with + * \p numDependencies dependencies specified via \p dependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * An empty node performs no operation during execution, but can be used for + * transitive ordering. For example, a phased execution graph with 2 groups of n + * nodes with a barrier between them can be represented using an empty node and + * 2*n dependency edges, rather than no empty node and n^2 dependency edges. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddEmptyNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies); + +/** + * \brief Creates an event record node and adds it to a graph + * + * Creates a new event record node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and event specified in \p event. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * Each launch of the graph will record \p event to capture execution of the + * node's dependencies. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param event - Event for the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphAddEventWaitNode, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddEventRecordNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUevent event); + +/** + * \brief Returns the event associated with an event record node + * + * Returns the event of event record node \p hNode in \p event_out. + * + * \param hNode - Node to get the event for + * \param event_out - Pointer to return the event + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddEventRecordNode, + * ::cuGraphEventRecordNodeSetEvent, + * ::cuGraphEventWaitNodeGetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuGraphEventRecordNodeGetEvent(CUgraphNode hNode, CUevent *event_out); + +/** + * \brief Sets an event record node's event + * + * Sets the event of event record node \p hNode to \p event. + * + * \param hNode - Node to set the event for + * \param event - Event to use + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuGraphAddEventRecordNode, + * ::cuGraphEventRecordNodeGetEvent, + * ::cuGraphEventWaitNodeSetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuGraphEventRecordNodeSetEvent(CUgraphNode hNode, CUevent event); + +/** + * \brief Creates an event wait node and adds it to a graph + * + * Creates a new event wait node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and event specified in \p event. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * The graph node will wait for all work captured in \p event. See ::cuEventRecord() + * for details on what is captured by an event. \p event may be from a different context + * or device than the launch stream. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param event - Event for the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphAddEventRecordNode, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddEventWaitNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUevent event); + +/** + * \brief Returns the event associated with an event wait node + * + * Returns the event of event wait node \p hNode in \p event_out. + * + * \param hNode - Node to get the event for + * \param event_out - Pointer to return the event + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddEventWaitNode, + * ::cuGraphEventWaitNodeSetEvent, + * ::cuGraphEventRecordNodeGetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuGraphEventWaitNodeGetEvent(CUgraphNode hNode, CUevent *event_out); + +/** + * \brief Sets an event wait node's event + * + * Sets the event of event wait node \p hNode to \p event. + * + * \param hNode - Node to set the event for + * \param event - Event to use + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuGraphAddEventWaitNode, + * ::cuGraphEventWaitNodeGetEvent, + * ::cuGraphEventRecordNodeSetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuGraphEventWaitNodeSetEvent(CUgraphNode hNode, CUevent event); + +/** + * \brief Creates an external semaphore signal node and adds it to a graph + * + * Creates a new external semaphore signal node and adds it to \p hGraph with \p + * numDependencies dependencies specified via \p dependencies and arguments specified + * in \p nodeParams. It is possible for \p numDependencies to be 0, in which case the + * node will be placed at the root of the graph. \p dependencies may not have any + * duplicate entries. A handle to the new node will be returned in \p phGraphNode. + * + * Performs a signal operation on a set of externally allocated semaphore objects + * when the node is launched. The operation(s) will occur after all of the node's + * dependencies have completed. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphExternalSemaphoresSignalNodeGetParams, + * ::cuGraphExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuImportExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddEventRecordNode, + * ::cuGraphAddEventWaitNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddExternalSemaphoresSignalNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS *nodeParams); + +/** + * \brief Returns an external semaphore signal node's parameters + * + * Returns the parameters of an external semaphore signal node \p hNode in \p params_out. + * The \p extSemArray and \p paramsArray returned in \p params_out, + * are owned by the node. This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cuGraphExternalSemaphoresSignalNodeSetParams to update the + * parameters of this node. + * + * \param hNode - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuLaunchKernel, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuGraphExternalSemaphoresSignalNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuGraphExternalSemaphoresSignalNodeGetParams(CUgraphNode hNode, CUDA_EXT_SEM_SIGNAL_NODE_PARAMS *params_out); + +/** + * \brief Sets an external semaphore signal node's parameters + * + * Sets the parameters of an external semaphore signal node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuGraphExternalSemaphoresSignalNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuGraphExternalSemaphoresSignalNodeSetParams(CUgraphNode hNode, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS *nodeParams); + +/** + * \brief Creates an external semaphore wait node and adds it to a graph + * + * Creates a new external semaphore wait node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p phGraphNode. + * + * Performs a wait operation on a set of externally allocated semaphore objects + * when the node is launched. The node's dependencies will not be launched until + * the wait operation has completed. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphExternalSemaphoresWaitNodeGetParams, + * ::cuGraphExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuImportExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddEventRecordNode, + * ::cuGraphAddEventWaitNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddExternalSemaphoresWaitNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_EXT_SEM_WAIT_NODE_PARAMS *nodeParams); + +/** + * \brief Returns an external semaphore wait node's parameters + * + * Returns the parameters of an external semaphore wait node \p hNode in \p params_out. + * The \p extSemArray and \p paramsArray returned in \p params_out, + * are owned by the node. This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cuGraphExternalSemaphoresSignalNodeSetParams to update the + * parameters of this node. + * + * \param hNode - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuLaunchKernel, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuGraphExternalSemaphoresWaitNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuGraphExternalSemaphoresWaitNodeGetParams(CUgraphNode hNode, CUDA_EXT_SEM_WAIT_NODE_PARAMS *params_out); + +/** + * \brief Sets an external semaphore wait node's parameters + * + * Sets the parameters of an external semaphore wait node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuGraphExternalSemaphoresWaitNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync + */ +CUresult CUDAAPI cuGraphExternalSemaphoresWaitNodeSetParams(CUgraphNode hNode, const CUDA_EXT_SEM_WAIT_NODE_PARAMS *nodeParams); + +/** + * \brief Creates a batch memory operation node and adds it to a graph + * + * Creates a new batch memory operation node and adds it to \p hGraph with \p + * numDependencies dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * When the node is added, the paramArray inside \p nodeParams is copied and therefore it can be + * freed after the call returns. + * + * \note + * Warning: + * Improper use of this API may deadlock the application. Synchronization + * ordering established through this API is not visible to CUDA. CUDA tasks + * that are (even indirectly) ordered by this API should also have that order + * expressed with CUDA-visible dependencies such as events. This ensures that + * the scheduler does not serialize them in an improper order. For more + * information, see the Stream Memory Operations section in the programming + * guide(https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html). + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuStreamBatchMemOp, + * ::cuStreamWaitValue32, + * ::cuStreamWriteValue32, + * ::cuStreamWaitValue64, + * ::cuStreamWriteValue64, + * ::cuGraphBatchMemOpNodeGetParams, + * ::cuGraphBatchMemOpNodeSetParams, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddBatchMemOpNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); + +/** + * \brief Returns a batch mem op node's parameters + * + * Returns the parameters of batch mem op node \p hNode in \p nodeParams_out. + * The \p paramArray returned in \p nodeParams_out is owned by the node. + * This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cuGraphBatchMemOpNodeSetParams to update the + * parameters of this node. + * + * \param hNode - Node to get the parameters for + * \param nodeParams_out - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuStreamBatchMemOp, + * ::cuGraphAddBatchMemOpNode, + * ::cuGraphBatchMemOpNodeSetParams + */ +CUresult CUDAAPI cuGraphBatchMemOpNodeGetParams(CUgraphNode hNode, CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams_out); + +/** + * \brief Sets a batch mem op node's parameters + * + * Sets the parameters of batch mem op node \p hNode to \p nodeParams. + * + * The paramArray inside \p nodeParams is copied and therefore it can be + * freed after the call returns. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetParams, + * ::cuStreamBatchMemOp, + * ::cuGraphAddBatchMemOpNode, + * ::cuGraphBatchMemOpNodeGetParams + */ +CUresult CUDAAPI cuGraphBatchMemOpNodeSetParams(CUgraphNode hNode, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); + +/** + * \brief Sets the parameters for a batch mem op node in the given graphExec + * + * Sets the parameters of a batch mem op node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * The following fields on operations may be modified on an executable graph: + * + * op.waitValue.address + * op.waitValue.value[64] + * op.waitValue.flags bits corresponding to wait type (i.e. CU_STREAM_WAIT_VALUE_FLUSH bit cannot be modified) + * op.writeValue.address + * op.writeValue.value[64] + * + * Other fields, such as the context, count or type of operations, and other types of operations such as membars, + * may not be modified. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * The paramArray inside \p nodeParams is copied and therefore it can be + * freed after the call returns. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Batch mem op node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuStreamBatchMemOp, + * ::cuGraphAddBatchMemOpNode, + * ::cuGraphBatchMemOpNodeGetParams, + * ::cuGraphBatchMemOpNodeSetParams, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecBatchMemOpNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); + +/** + * \brief Creates an allocation node and adds it to a graph + * + * Creates a new allocation node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p phGraphNode. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * When ::cuGraphAddMemAllocNode creates an allocation node, it returns the address of the allocation in + * \p nodeParams.dptr. The allocation's address remains fixed across instantiations and launches. + * + * If the allocation is freed in the same graph, by creating a free node using ::cuGraphAddMemFreeNode, + * the allocation can be accessed by nodes ordered after the allocation node but before the free node. + * These allocations cannot be freed outside the owning graph, and they can only be freed once in the + * owning graph. + * + * If the allocation is not freed in the same graph, then it can be accessed not only by nodes in the + * graph which are ordered after the allocation node, but also by stream operations ordered after the + * graph's execution but before the allocation is freed. + * + * Allocations which are not freed in the same graph can be freed by: + * - passing the allocation to ::cuMemFreeAsync or ::cuMemFree; + * - launching a graph with a free node for that allocation; or + * - specifying ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH during instantiation, which makes + * each launch behave as though it called ::cuMemFreeAsync for every unfreed allocation. + * + * It is not possible to free an allocation in both the owning graph and another graph. If the allocation + * is freed in the same graph, a free node cannot be added to another graph. If the allocation is freed + * in another graph, a free node can no longer be added to the owning graph. + * + * The following restrictions apply to graphs which contain allocation and/or memory free nodes: + * - Nodes and edges of the graph cannot be deleted. + * - The graph cannot be used in a child node. + * - Only one instantiation of the graph may exist at any point in time. + * - The graph cannot be cloned. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphAddMemFreeNode, + * ::cuGraphMemAllocNodeGetParams, + * ::cuDeviceGraphMemTrim, + * ::cuDeviceGetGraphMemAttribute, + * ::cuDeviceSetGraphMemAttribute, + * ::cuMemAllocAsync, + * ::cuMemFreeAsync, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddEventRecordNode, + * ::cuGraphAddEventWaitNode, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddMemAllocNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUDA_MEM_ALLOC_NODE_PARAMS *nodeParams); + +/** + * \brief Returns a memory alloc node's parameters + * + * Returns the parameters of a memory alloc node \p hNode in \p params_out. + * The \p poolProps and \p accessDescs returned in \p params_out, are owned by the + * node. This memory remains valid until the node is destroyed. The returned + * parameters must not be modified. + * + * \param hNode - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddMemAllocNode, + * ::cuGraphMemFreeNodeGetParams + */ +CUresult CUDAAPI cuGraphMemAllocNodeGetParams(CUgraphNode hNode, CUDA_MEM_ALLOC_NODE_PARAMS *params_out); + +/** + * \brief Creates a memory free node and adds it to a graph + * + * Creates a new memory free node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p phGraphNode. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param dptr - Address of memory to free + * + * ::cuGraphAddMemFreeNode will return ::CUDA_ERROR_INVALID_VALUE if the user attempts to free: + * - an allocation twice in the same graph. + * - an address that was not returned by an allocation node. + * - an invalid address. + * + * The following restrictions apply to graphs which contain allocation and/or memory free nodes: + * - Nodes and edges of the graph cannot be deleted. + * - The graph cannot be used in a child node. + * - Only one instantiation of the graph may exist at any point in time. + * - The graph cannot be cloned. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphAddMemAllocNode, + * ::cuGraphMemFreeNodeGetParams, + * ::cuDeviceGraphMemTrim, + * ::cuDeviceGetGraphMemAttribute, + * ::cuDeviceSetGraphMemAttribute, + * ::cuMemAllocAsync, + * ::cuMemFreeAsync, + * ::cuGraphCreate, + * ::cuGraphDestroyNode, + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddEventRecordNode, + * ::cuGraphAddEventWaitNode, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphAddMemFreeNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUdeviceptr dptr); + +/** + * \brief Returns a memory free node's parameters + * + * Returns the address of a memory free node \p hNode in \p dptr_out. + * + * \param hNode - Node to get the parameters for + * \param dptr_out - Pointer to return the device address + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddMemFreeNode, + * ::cuGraphMemAllocNodeGetParams + */ +CUresult CUDAAPI cuGraphMemFreeNodeGetParams(CUgraphNode hNode, CUdeviceptr *dptr_out); + +/** + * \brief Free unused memory that was cached on the specified device for use with graphs back to the OS. + * + * Blocks which are not in use by a graph that is either currently executing or scheduled to execute are + * freed back to the operating system. + * + * \param device - The device for which cached memory should be freed. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_DEVICE + * + * \sa + * ::cuGraphAddMemAllocNode, + * ::cuGraphAddMemFreeNode, + * ::cuDeviceSetGraphMemAttribute, + * ::cuDeviceGetGraphMemAttribute + */ +CUresult CUDAAPI cuDeviceGraphMemTrim(CUdevice device); + +/** + * \brief Query asynchronous allocation attributes related to graphs + * + * Valid attributes are: + * + * - ::CU_GRAPH_MEM_ATTR_USED_MEM_CURRENT: Amount of memory, in bytes, currently associated with graphs + * - ::CU_GRAPH_MEM_ATTR_USED_MEM_HIGH: High watermark of memory, in bytes, associated with graphs since the + * last time it was reset. High watermark can only be reset to zero. + * - ::CU_GRAPH_MEM_ATTR_RESERVED_MEM_CURRENT: Amount of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * - ::CU_GRAPH_MEM_ATTR_RESERVED_MEM_HIGH: High watermark of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * + * \param device - Specifies the scope of the query + * \param attr - attribute to get + * \param value - retrieved value + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_DEVICE + * + * \sa + * ::cuDeviceSetGraphMemAttribute, + * ::cuGraphAddMemAllocNode, + * ::cuGraphAddMemFreeNode + */ +CUresult CUDAAPI cuDeviceGetGraphMemAttribute(CUdevice device, CUgraphMem_attribute attr, void* value); + +/** + * \brief Set asynchronous allocation attributes related to graphs + * + * Valid attributes are: + * + * - ::CU_GRAPH_MEM_ATTR_USED_MEM_HIGH: High watermark of memory, in bytes, associated with graphs since the + * last time it was reset. High watermark can only be reset to zero. + * - ::CU_GRAPH_MEM_ATTR_RESERVED_MEM_HIGH: High watermark of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * + * \param device - Specifies the scope of the query + * \param attr - attribute to get + * \param value - pointer to value to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_DEVICE + * + * \sa + * ::cuDeviceGetGraphMemAttribute, + * ::cuGraphAddMemAllocNode, + * ::cuGraphAddMemFreeNode + */ +CUresult CUDAAPI cuDeviceSetGraphMemAttribute(CUdevice device, CUgraphMem_attribute attr, void* value); + +/** + * \brief Clones a graph + * + * This function creates a copy of \p originalGraph and returns it in \p phGraphClone. + * All parameters are copied into the cloned graph. The original graph may be modified + * after this call without affecting the clone. + * + * Child graph nodes in the original graph are recursively copied into the clone. + * + * \param phGraphClone - Returns newly created cloned graph + * \param originalGraph - Graph to clone + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphNodeFindInClone + */ +CUresult CUDAAPI cuGraphClone(CUgraph *phGraphClone, CUgraph originalGraph); + +/** + * \brief Finds a cloned version of a node + * + * This function returns the node in \p hClonedGraph corresponding to \p hOriginalNode + * in the original graph. + * + * \p hClonedGraph must have been cloned from \p hOriginalGraph via ::cuGraphClone. + * \p hOriginalNode must have been in \p hOriginalGraph at the time of the call to + * ::cuGraphClone, and the corresponding cloned node in \p hClonedGraph must not have + * been removed. The cloned node is then returned via \p phClonedNode. + * + * \param phNode - Returns handle to the cloned node + * \param hOriginalNode - Handle to the original node + * \param hClonedGraph - Cloned graph to query + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphClone + */ +CUresult CUDAAPI cuGraphNodeFindInClone(CUgraphNode *phNode, CUgraphNode hOriginalNode, CUgraph hClonedGraph); + +/** + * \brief Returns a node's type + * + * Returns the node type of \p hNode in \p type. + * + * \param hNode - Node to query + * \param type - Pointer to return the node type + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphChildGraphNodeGetGraph, + * ::cuGraphKernelNodeGetParams, + * ::cuGraphKernelNodeSetParams, + * ::cuGraphHostNodeGetParams, + * ::cuGraphHostNodeSetParams, + * ::cuGraphMemcpyNodeGetParams, + * ::cuGraphMemcpyNodeSetParams, + * ::cuGraphMemsetNodeGetParams, + * ::cuGraphMemsetNodeSetParams + */ +CUresult CUDAAPI cuGraphNodeGetType(CUgraphNode hNode, CUgraphNodeType *type); + +/** + * \brief Returns a graph's nodes + * + * Returns a list of \p hGraph's nodes. \p nodes may be NULL, in which case this + * function will return the number of nodes in \p numNodes. Otherwise, + * \p numNodes entries will be filled in. If \p numNodes is higher than the actual + * number of nodes, the remaining entries in \p nodes will be set to NULL, and the + * number of nodes actually obtained will be returned in \p numNodes. + * + * \param hGraph - Graph to query + * \param nodes - Pointer to return the nodes + * \param numNodes - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetType, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphGetNodes(CUgraph hGraph, CUgraphNode *nodes, size_t *numNodes); + +/** + * \brief Returns a graph's root nodes + * + * Returns a list of \p hGraph's root nodes. \p rootNodes may be NULL, in which case this + * function will return the number of root nodes in \p numRootNodes. Otherwise, + * \p numRootNodes entries will be filled in. If \p numRootNodes is higher than the actual + * number of root nodes, the remaining entries in \p rootNodes will be set to NULL, and the + * number of nodes actually obtained will be returned in \p numRootNodes. + * + * \param hGraph - Graph to query + * \param rootNodes - Pointer to return the root nodes + * \param numRootNodes - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphGetNodes, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetType, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphGetRootNodes(CUgraph hGraph, CUgraphNode *rootNodes, size_t *numRootNodes); + +/** + * \brief Returns a graph's dependency edges + * + * Returns a list of \p hGraph's dependency edges. Edges are returned via corresponding + * indices in \p from and \p to; that is, the node in \p to[i] has a dependency on the + * node in \p from[i]. \p from and \p to may both be NULL, in which + * case this function only returns the number of edges in \p numEdges. Otherwise, + * \p numEdges entries will be filled in. If \p numEdges is higher than the actual + * number of edges, the remaining entries in \p from and \p to will be set to NULL, and + * the number of edges actually returned will be written to \p numEdges. + * + * \param hGraph - Graph to get the edges from + * \param from - Location to return edge endpoints + * \param to - Location to return edge endpoints + * \param numEdges - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphGetEdges(CUgraph hGraph, CUgraphNode *from, CUgraphNode *to, size_t *numEdges); + +/** + * \brief Returns a graph's dependency edges (12.3+) + * + * Returns a list of \p hGraph's dependency edges. Edges are returned via corresponding + * indices in \p from, \p to and \p edgeData; that is, the node in \p to[i] has a + * dependency on the node in \p from[i] with data \p edgeData[i]. \p from and \p to may + * both be NULL, in which case this function only returns the number of edges in + * \p numEdges. Otherwise, \p numEdges entries will be filled in. If \p numEdges is higher + * than the actual number of edges, the remaining entries in \p from and \p to will be + * set to NULL, and the number of edges actually returned will be written to \p numEdges. + * \p edgeData may alone be NULL, in which case the edges must all have default (zeroed) + * edge data. Attempting a lossy query via NULL \p edgeData will result in + * ::CUDA_ERROR_LOSSY_QUERY. If \p edgeData is non-NULL then \p from and \p to must be + * as well. + * + * \param hGraph - Graph to get the edges from + * \param from - Location to return edge endpoints + * \param to - Location to return edge endpoints + * \param edgeData - Optional location to return edge data + * \param numEdges - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_LOSSY_QUERY, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphGetEdges_v2(CUgraph hGraph, CUgraphNode *from, CUgraphNode *to, CUgraphEdgeData *edgeData, size_t *numEdges); + +/** + * \brief Returns a node's dependencies + * + * Returns a list of \p node's dependencies. \p dependencies may be NULL, in which case this + * function will return the number of dependencies in \p numDependencies. Otherwise, + * \p numDependencies entries will be filled in. If \p numDependencies is higher than the actual + * number of dependencies, the remaining entries in \p dependencies will be set to NULL, and the + * number of nodes actually obtained will be returned in \p numDependencies. + * + * \param hNode - Node to query + * \param dependencies - Pointer to return the dependencies + * \param numDependencies - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeGetDependentNodes, + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies + */ +CUresult CUDAAPI cuGraphNodeGetDependencies(CUgraphNode hNode, CUgraphNode *dependencies, size_t *numDependencies); + +/** + * \brief Returns a node's dependencies (12.3+) + * + * Returns a list of \p node's dependencies. \p dependencies may be NULL, in which case this + * function will return the number of dependencies in \p numDependencies. Otherwise, + * \p numDependencies entries will be filled in. If \p numDependencies is higher than the actual + * number of dependencies, the remaining entries in \p dependencies will be set to NULL, and the + * number of nodes actually obtained will be returned in \p numDependencies. + * + * Note that if an edge has non-zero (non-default) edge data and \p edgeData is NULL, + * this API will return ::CUDA_ERROR_LOSSY_QUERY. If \p edgeData is non-NULL, then + * \p dependencies must be as well. + * + * \param hNode - Node to query + * \param dependencies - Pointer to return the dependencies + * \param edgeData - Optional array to return edge data for each dependency + * \param numDependencies - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_LOSSY_QUERY, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeGetDependentNodes, + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies + */ +CUresult CUDAAPI cuGraphNodeGetDependencies_v2(CUgraphNode hNode, CUgraphNode *dependencies, CUgraphEdgeData *edgeData, size_t *numDependencies); + +/** + * \brief Returns a node's dependent nodes + * + * Returns a list of \p node's dependent nodes. \p dependentNodes may be NULL, in which + * case this function will return the number of dependent nodes in \p numDependentNodes. + * Otherwise, \p numDependentNodes entries will be filled in. If \p numDependentNodes is + * higher than the actual number of dependent nodes, the remaining entries in + * \p dependentNodes will be set to NULL, and the number of nodes actually obtained will + * be returned in \p numDependentNodes. + * + * \param hNode - Node to query + * \param dependentNodes - Pointer to return the dependent nodes + * \param numDependentNodes - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeGetDependencies, + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies + */ +CUresult CUDAAPI cuGraphNodeGetDependentNodes(CUgraphNode hNode, CUgraphNode *dependentNodes, size_t *numDependentNodes); + +/** + * \brief Returns a node's dependent nodes (12.3+) + * + * Returns a list of \p node's dependent nodes. \p dependentNodes may be NULL, in which + * case this function will return the number of dependent nodes in \p numDependentNodes. + * Otherwise, \p numDependentNodes entries will be filled in. If \p numDependentNodes is + * higher than the actual number of dependent nodes, the remaining entries in + * \p dependentNodes will be set to NULL, and the number of nodes actually obtained will + * be returned in \p numDependentNodes. + * + * Note that if an edge has non-zero (non-default) edge data and \p edgeData is NULL, + * this API will return ::CUDA_ERROR_LOSSY_QUERY. If \p edgeData is non-NULL, then + * \p dependentNodes must be as well. + * + * \param hNode - Node to query + * \param dependentNodes - Pointer to return the dependent nodes + * \param edgeData - Optional pointer to return edge data for dependent nodes + * \param numDependentNodes - See description + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_LOSSY_QUERY, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeGetDependencies, + * ::cuGraphGetNodes, + * ::cuGraphGetRootNodes, + * ::cuGraphGetEdges, + * ::cuGraphAddDependencies, + * ::cuGraphRemoveDependencies + */ +CUresult CUDAAPI cuGraphNodeGetDependentNodes_v2(CUgraphNode hNode, CUgraphNode *dependentNodes, CUgraphEdgeData *edgeData, size_t *numDependentNodes); + +/** + * \brief Adds dependency edges to a graph + * + * The number of dependencies to be added is defined by \p numDependencies + * Elements in \p from and \p to at corresponding indices define a dependency. + * Each node in \p from and \p to must belong to \p hGraph. + * + * If \p numDependencies is 0, elements in \p from and \p to will be ignored. + * Specifying an existing dependency will return an error. + * + * \param hGraph - Graph to which dependencies are added + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param numDependencies - Number of dependencies to be added + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphRemoveDependencies, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphAddDependencies(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, size_t numDependencies); + +/** + * \brief Adds dependency edges to a graph (12.3+) + * + * The number of dependencies to be added is defined by \p numDependencies + * Elements in \p from and \p to at corresponding indices define a dependency. + * Each node in \p from and \p to must belong to \p hGraph. + * + * If \p numDependencies is 0, elements in \p from and \p to will be ignored. + * Specifying an existing dependency will return an error. + * + * \param hGraph - Graph to which dependencies are added + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param edgeData - Optional array of edge data. If NULL, default (zeroed) edge data is assumed. + * \param numDependencies - Number of dependencies to be added + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphRemoveDependencies, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphAddDependencies_v2(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, const CUgraphEdgeData *edgeData, size_t numDependencies); + +/** + * \brief Removes dependency edges from a graph + * + * The number of \p dependencies to be removed is defined by \p numDependencies. + * Elements in \p from and \p to at corresponding indices define a dependency. + * Each node in \p from and \p to must belong to \p hGraph. + * + * If \p numDependencies is 0, elements in \p from and \p to will be ignored. + * Specifying a non-existing dependency will return an error. + * + * Dependencies cannot be removed from graphs which contain allocation or free nodes. + * Any attempt to do so will return an error. + * + * \param hGraph - Graph from which to remove dependencies + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param numDependencies - Number of dependencies to be removed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddDependencies, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphRemoveDependencies(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, size_t numDependencies); + +/** + * \brief Removes dependency edges from a graph (12.3+) + * + * The number of \p dependencies to be removed is defined by \p numDependencies. + * Elements in \p from and \p to at corresponding indices define a dependency. + * Each node in \p from and \p to must belong to \p hGraph. + * + * If \p numDependencies is 0, elements in \p from and \p to will be ignored. + * Specifying an edge that does not exist in the graph, with data matching + * \p edgeData, results in an error. \p edgeData is nullable, which is equivalent + * to passing default (zeroed) data for each edge. + * + * Dependencies cannot be removed from graphs which contain allocation or free nodes. + * Any attempt to do so will return an error. + * + * \param hGraph - Graph from which to remove dependencies + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param edgeData - Optional array of edge data. If NULL, edge data is assumed to + * be default (zeroed). + * \param numDependencies - Number of dependencies to be removed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddDependencies, + * ::cuGraphGetEdges, + * ::cuGraphNodeGetDependencies, + * ::cuGraphNodeGetDependentNodes + */ +CUresult CUDAAPI cuGraphRemoveDependencies_v2(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, const CUgraphEdgeData *edgeData, size_t numDependencies); + +/** + * \brief Remove a node from the graph + * + * Removes \p hNode from its graph. This operation also severs any dependencies of other nodes + * on \p hNode and vice versa. + * + * Nodes which belong to a graph which contains allocation or free nodes cannot be destroyed. + * Any attempt to do so will return an error. + * + * \param hNode - Node to remove + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddChildGraphNode, + * ::cuGraphAddEmptyNode, + * ::cuGraphAddKernelNode, + * ::cuGraphAddHostNode, + * ::cuGraphAddMemcpyNode, + * ::cuGraphAddMemsetNode + */ +CUresult CUDAAPI cuGraphDestroyNode(CUgraphNode hNode); + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p hGraph as an executable graph. The graph is validated for any + * structural constraints or intra-node constraints which were not previously + * validated. If instantiation is successful, a handle to the instantiated graph + * is returned in \p phGraphExec. + * + * The \p flags parameter controls the behavior of instantiation and subsequent + * graph launches. Valid flags are: + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH, which configures a + * graph containing memory allocation nodes to automatically free any + * unfreed memory allocations before the graph is relaunched. + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_DEVICE_LAUNCH, which configures the graph for launch + * from the device. If this flag is passed, the executable graph handle returned can be + * used to launch the graph from both the host and device. This flag can only be used + * on platforms which support unified addressing. This flag cannot be used in + * conjunction with ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH. + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_USE_NODE_PRIORITY, which causes the graph + * to use the priorities from the per-node attributes rather than the priority + * of the launch stream during execution. Note that priorities are only available + * on kernel nodes, and are copied from stream priority during stream capture. + * + * If \p hGraph contains any allocation or free nodes, there can be at most one + * executable graph in existence for that graph at a time. An attempt to instantiate + * a second executable graph before destroying the first with ::cuGraphExecDestroy + * will result in an error. + * The same also applies if \p hGraph contains any device-updatable kernel nodes. + * + * If \p hGraph contains kernels which call device-side cudaGraphLaunch() from multiple + * contexts, this will result in an error. + * + * Graphs instantiated for launch on the device have additional restrictions which do not + * apply to host graphs: + * + * - The graph's nodes must reside on a single context. + * - The graph can only contain kernel nodes, memcpy nodes, memset nodes, and child graph nodes. + * - The graph cannot be empty and must contain at least one kernel, memcpy, or memset node. + * Operation-specific restrictions are outlined below. + * - Kernel nodes: + * - Use of CUDA Dynamic Parallelism is not permitted. + * - Cooperative launches are permitted as long as MPS is not in use. + * - Memcpy nodes: + * - Only copies involving device memory and/or pinned device-mapped host memory are permitted. + * - Copies involving CUDA arrays are not permitted. + * - Both operands must be accessible from the current context, and the current context must + * match the context of other nodes in the graph. + * + * \param phGraphExec - Returns instantiated graph + * \param hGraph - Graph to instantiate + * \param flags - Flags to control instantiation. See ::CUgraphInstantiate_flags. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate, + * ::cuGraphCreate, + * ::cuGraphUpload, + * ::cuGraphLaunch, + * ::cuGraphExecDestroy + */ +CUresult CUDAAPI cuGraphInstantiate(CUgraphExec *phGraphExec, CUgraph hGraph, unsigned long long flags); + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p hGraph as an executable graph according to the \p instantiateParams structure. + * The graph is validated for any structural constraints or intra-node constraints + * which were not previously validated. If instantiation is successful, a handle to + * the instantiated graph is returned in \p phGraphExec. + * + * \p instantiateParams controls the behavior of instantiation and subsequent + * graph launches, as well as returning more detailed information in the event of an error. + * ::CUDA_GRAPH_INSTANTIATE_PARAMS is defined as: + * + * \code + typedef struct { + cuuint64_t flags; + CUstream hUploadStream; + CUgraphNode hErrNode_out; + CUgraphInstantiateResult result_out; + } CUDA_GRAPH_INSTANTIATE_PARAMS; + * \endcode + * + * The \p flags field controls the behavior of instantiation and subsequent + * graph launches. Valid flags are: + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH, which configures a + * graph containing memory allocation nodes to automatically free any + * unfreed memory allocations before the graph is relaunched. + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_UPLOAD, which will perform an upload of the graph + * into \p hUploadStream once the graph has been instantiated. + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_DEVICE_LAUNCH, which configures the graph for launch + * from the device. If this flag is passed, the executable graph handle returned can be + * used to launch the graph from both the host and device. This flag can only be used + * on platforms which support unified addressing. This flag cannot be used in + * conjunction with ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH. + * + * - ::CUDA_GRAPH_INSTANTIATE_FLAG_USE_NODE_PRIORITY, which causes the graph + * to use the priorities from the per-node attributes rather than the priority + * of the launch stream during execution. Note that priorities are only available + * on kernel nodes, and are copied from stream priority during stream capture. + * + * If \p hGraph contains any allocation or free nodes, there can be at most one + * executable graph in existence for that graph at a time. An attempt to instantiate a + * second executable graph before destroying the first with ::cuGraphExecDestroy will + * result in an error. + * The same also applies if \p hGraph contains any device-updatable kernel nodes. + * + * If \p hGraph contains kernels which call device-side cudaGraphLaunch() from multiple + * contexts, this will result in an error. + * + * Graphs instantiated for launch on the device have additional restrictions which do not + * apply to host graphs: + * + * - The graph's nodes must reside on a single context. + * - The graph can only contain kernel nodes, memcpy nodes, memset nodes, and child graph nodes. + * - The graph cannot be empty and must contain at least one kernel, memcpy, or memset node. + * Operation-specific restrictions are outlined below. + * - Kernel nodes: + * - Use of CUDA Dynamic Parallelism is not permitted. + * - Cooperative launches are permitted as long as MPS is not in use. + * - Memcpy nodes: + * - Only copies involving device memory and/or pinned device-mapped host memory are permitted. + * - Copies involving CUDA arrays are not permitted. + * - Both operands must be accessible from the current context, and the current context must + * match the context of other nodes in the graph. + * + * In the event of an error, the \p result_out and \p hErrNode_out fields will contain more + * information about the nature of the error. Possible error reporting includes: + * + * - ::CUDA_GRAPH_INSTANTIATE_ERROR, if passed an invalid value or if an unexpected error occurred + * which is described by the return value of the function. \p hErrNode_out will be set to NULL. + * - ::CUDA_GRAPH_INSTANTIATE_INVALID_STRUCTURE, if the graph structure is invalid. \p hErrNode_out + * will be set to one of the offending nodes. + * - ::CUDA_GRAPH_INSTANTIATE_NODE_OPERATION_NOT_SUPPORTED, if the graph is instantiated for device + * launch but contains a node of an unsupported node type, or a node which performs unsupported + * operations, such as use of CUDA dynamic parallelism within a kernel node. \p hErrNode_out will + * be set to this node. + * - ::CUDA_GRAPH_INSTANTIATE_MULTIPLE_CTXS_NOT_SUPPORTED, if the graph is instantiated for device + * launch but a node’s context differs from that of another node. This error can also be returned + * if a graph is not instantiated for device launch and it contains kernels which call device-side + * cudaGraphLaunch() from multiple contexts. \p hErrNode_out will be set to this node. + * + * If instantiation is successful, \p result_out will be set to ::CUDA_GRAPH_INSTANTIATE_SUCCESS, + * and \p hErrNode_out will be set to NULL. + * + * \param phGraphExec - Returns instantiated graph + * \param hGraph - Graph to instantiate + * \param instantiateParams - Instantiation parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphInstantiate, + * ::cuGraphExecDestroy + */ +CUresult CUDAAPI cuGraphInstantiateWithParams(CUgraphExec *phGraphExec, CUgraph hGraph, CUDA_GRAPH_INSTANTIATE_PARAMS *instantiateParams); + +/** + * \brief Query the instantiation flags of an executable graph + * + * Returns the flags that were passed to instantiation for the given executable graph. + * ::CUDA_GRAPH_INSTANTIATE_FLAG_UPLOAD will not be returned by this API as it does + * not affect the resulting executable graph. + * + * \param hGraphExec - The executable graph to query + * \param flags - Returns the instantiation flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate, + * ::cuGraphInstantiateWithParams + */ +CUresult CUDAAPI cuGraphExecGetFlags(CUgraphExec hGraphExec, cuuint64_t *flags); + +/** + * \brief Sets the parameters for a kernel node in the given graphExec + * + * Sets the parameters of a kernel node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. All \p nodeParams + * fields may change, but the following restrictions apply to \p func updates: + * + * - The owning context of the function cannot change. + * - A node whose function originally did not use CUDA dynamic parallelism cannot be updated + * to a function which uses CDP + * - A node whose function originally did not make device-side update calls cannot be updated + * to a function which makes device-side update calls. + * - If \p hGraphExec was not instantiated for device launch, a node whose function originally + * did not use device-side cudaGraphLaunch() cannot be updated to a function which uses + * device-side cudaGraphLaunch() unless the node resides on the same context as nodes which + * contained such calls at instantiate-time. If no such calls were present at instantiation, + * these updates cannot be performed at all. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * If \p hNode is a device-updatable kernel node, the next upload/launch of \p hGraphExec + * will overwrite any previous device-side updates. Additionally, applying host updates to a + * device-updatable kernel node while it is being updated from the device will result in + * undefined behavior. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - kernel node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddKernelNode, + * ::cuGraphKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecKernelNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS *nodeParams); + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec. + * + * Updates the work represented by \p hNode in \p hGraphExec as though \p hNode had + * contained \p copyParams at instantiation. hNode must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from hNode are ignored. + * + * The source and destination memory in \p copyParams must be allocated from the same + * contexts as the original source and destination memory. Both the instantiation-time + * memory operands and the memory operands in \p copyParams must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. hNode is also + * not modified by this call. + * + * Returns CUDA_ERROR_INVALID_VALUE if the memory operands' mappings changed or + * either the original or new memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Memcpy node from the graph which was used to instantiate graphExec + * \param copyParams - The updated parameters to set + * \param ctx - Context on which to run the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddMemcpyNode, + * ::cuGraphMemcpyNodeSetParams, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecMemcpyNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_MEMCPY3D *copyParams, CUcontext ctx); + +/** + * \brief Sets the parameters for a memset node in the given graphExec. + * + * Updates the work represented by \p hNode in \p hGraphExec as though \p hNode had + * contained \p memsetParams at instantiation. hNode must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from hNode are ignored. + * + * The destination memory in \p memsetParams must be allocated from the same + * contexts as the original destination memory. Both the instantiation-time + * memory operand and the memory operand in \p memsetParams must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. hNode is also + * not modified by this call. + * + * Returns CUDA_ERROR_INVALID_VALUE if the memory operand's mappings changed or + * either the original or new memory operand are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Memset node from the graph which was used to instantiate graphExec + * \param memsetParams - The updated parameters to set + * \param ctx - Context on which to run the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddMemsetNode, + * ::cuGraphMemsetNodeSetParams, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecMemsetNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_MEMSET_NODE_PARAMS *memsetParams, CUcontext ctx); + +/** + * \brief Sets the parameters for a host node in the given graphExec. + * + * Updates the work represented by \p hNode in \p hGraphExec as though \p hNode had + * contained \p nodeParams at instantiation. hNode must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from hNode are ignored. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. hNode is also + * not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Host node from the graph which was used to instantiate graphExec + * \param nodeParams - The updated parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddHostNode, + * ::cuGraphHostNodeSetParams, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecHostNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_HOST_NODE_PARAMS *nodeParams); + +/** + * \brief Updates node parameters in the child graph node in the given graphExec. + * + * Updates the work represented by \p hNode in \p hGraphExec as though the nodes contained + * in \p hNode's graph had the parameters contained in \p childGraph's nodes at instantiation. + * \p hNode must remain in the graph which was used to instantiate \p hGraphExec. + * Changed edges to and from \p hNode are ignored. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p hNode is also + * not modified by this call. + * + * The topology of \p childGraph, as well as the node insertion order, must match that + * of the graph contained in \p hNode. See ::cuGraphExecUpdate() for a list of restrictions + * on what can be updated in an instantiated graph. The update is recursive, so child graph + * nodes contained within the top level child graph will also be updated. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Host node from the graph which was used to instantiate graphExec + * \param childGraph - The graph supplying the updated parameters + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddChildGraphNode, + * ::cuGraphChildGraphNodeGetGraph, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecChildGraphNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, CUgraph childGraph); + +/** + * \brief Sets the event for an event record node in the given graphExec + * + * Sets the event of an event record node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - event record node from the graph from which graphExec was instantiated + * \param event - Updated event to use + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddEventRecordNode, + * ::cuGraphEventRecordNodeGetEvent, + * ::cuGraphEventWaitNodeSetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecEventRecordNodeSetEvent(CUgraphExec hGraphExec, CUgraphNode hNode, CUevent event); + +/** + * \brief Sets the event for an event wait node in the given graphExec + * + * Sets the event of an event wait node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - event wait node from the graph from which graphExec was instantiated + * \param event - Updated event to use + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddEventWaitNode, + * ::cuGraphEventWaitNodeGetEvent, + * ::cuGraphEventRecordNodeSetEvent, + * ::cuEventRecordWithFlags, + * ::cuStreamWaitEvent, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecEventWaitNodeSetEvent(CUgraphExec hGraphExec, CUgraphNode hNode, CUevent event); + +/** + * \brief Sets the parameters for an external semaphore signal node in the given graphExec + * + * Sets the parameters of an external semaphore signal node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * Changing \p nodeParams->numExtSems is not supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - semaphore signal node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddExternalSemaphoresSignalNode, + * ::cuImportExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecExternalSemaphoresSignalNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS *nodeParams); + +/** + * \brief Sets the parameters for an external semaphore wait node in the given graphExec + * + * Sets the parameters of an external semaphore wait node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * Changing \p nodeParams->numExtSems is not supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - semaphore wait node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphExecNodeSetParams, + * ::cuGraphAddExternalSemaphoresWaitNode, + * ::cuImportExternalSemaphore, + * ::cuSignalExternalSemaphoresAsync, + * ::cuWaitExternalSemaphoresAsync, + * ::cuGraphExecKernelNodeSetParams, + * ::cuGraphExecMemcpyNodeSetParams, + * ::cuGraphExecMemsetNodeSetParams, + * ::cuGraphExecHostNodeSetParams, + * ::cuGraphExecChildGraphNodeSetParams, + * ::cuGraphExecEventRecordNodeSetEvent, + * ::cuGraphExecEventWaitNodeSetEvent, + * ::cuGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecExternalSemaphoresWaitNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_EXT_SEM_WAIT_NODE_PARAMS *nodeParams); + +/** + * \brief Enables or disables the specified node in the given graphExec + * + * Sets \p hNode to be either enabled or disabled. Disabled nodes are functionally equivalent + * to empty nodes until they are reenabled. Existing node parameters are not affected by + * disabling/enabling the node. + * + * The node is identified by the corresponding node \p hNode in the non-executable + * graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * If \p hNode is a device-updatable kernel node, the next upload/launch of \p hGraphExec + * will overwrite any previous device-side updates. Additionally, applying host updates to a + * device-updatable kernel node while it is being updated from the device will result in + * undefined behavior. + * + * \note Currently only kernel, memset and memcpy nodes are supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Node from the graph from which graphExec was instantiated + * \param isEnabled - Node is enabled if != 0, otherwise the node is disabled + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeGetEnabled, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + * ::cuGraphLaunch + */ +CUresult CUDAAPI cuGraphNodeSetEnabled(CUgraphExec hGraphExec, CUgraphNode hNode, unsigned int isEnabled); + +/** + * \brief Query whether a node in the given graphExec is enabled + * + * Sets isEnabled to 1 if \p hNode is enabled, or 0 if \p hNode is disabled. + * + * The node is identified by the corresponding node \p hNode in the non-executable + * graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * \note Currently only kernel, memset and memcpy nodes are supported. + * \note This function will not reflect device-side updates for device-updatable kernel nodes. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Node from the graph from which graphExec was instantiated + * \param isEnabled - Location to return the enabled status of the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphNodeSetEnabled, + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + * ::cuGraphLaunch + */ +CUresult CUDAAPI cuGraphNodeGetEnabled(CUgraphExec hGraphExec, CUgraphNode hNode, unsigned int *isEnabled); + +/** + * \brief Uploads an executable graph in a stream + * + * Uploads \p hGraphExec to the device in \p hStream without executing it. Uploads of + * the same \p hGraphExec will be serialized. Each upload is ordered behind both any + * previous work in \p hStream and any previous launches of \p hGraphExec. + * Uses memory cached by \p stream to back the allocations owned by \p hGraphExec. + * + * \param hGraphExec - Executable graph to upload + * \param hStream - Stream in which to upload the graph + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate, + * ::cuGraphLaunch, + * ::cuGraphExecDestroy + */ +CUresult CUDAAPI cuGraphUpload(CUgraphExec hGraphExec, CUstream hStream); + +/** + * \brief Launches an executable graph in a stream + * + * Executes \p hGraphExec in \p hStream. Only one instance of \p hGraphExec may be executing + * at a time. Each launch is ordered behind both any previous work in \p hStream + * and any previous launches of \p hGraphExec. To execute a graph concurrently, it must be + * instantiated multiple times into multiple executable graphs. + * + * If any allocations created by \p hGraphExec remain unfreed (from a previous launch) and + * \p hGraphExec was not instantiated with ::CUDA_GRAPH_INSTANTIATE_FLAG_AUTO_FREE_ON_LAUNCH, + * the launch will fail with ::CUDA_ERROR_INVALID_VALUE. + * + * \param hGraphExec - Executable graph to launch + * \param hStream - Stream in which to launch the graph + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate, + * ::cuGraphUpload, + * ::cuGraphExecDestroy + */ +CUresult CUDAAPI cuGraphLaunch(CUgraphExec hGraphExec, CUstream hStream); + +/** + * \brief Destroys an executable graph + * + * Destroys the executable graph specified by \p hGraphExec, as well + * as all of its executable nodes. If the executable graph is + * in-flight, it will not be terminated, but rather freed + * asynchronously on completion. + * + * \param hGraphExec - Executable graph to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate, + * ::cuGraphUpload, + * ::cuGraphLaunch + */ +CUresult CUDAAPI cuGraphExecDestroy(CUgraphExec hGraphExec); + +/** + * \brief Destroys a graph + * + * Destroys the graph specified by \p hGraph, as well as all of its nodes. + * + * \param hGraph - Graph to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate + */ +CUresult CUDAAPI cuGraphDestroy(CUgraph hGraph); + +/** + * \brief Check whether an executable graph can be updated with a graph and perform the update if possible + * + * Updates the node parameters in the instantiated graph specified by \p hGraphExec with the + * node parameters in a topologically identical graph specified by \p hGraph. + * + * Limitations: + * + * - Kernel nodes: + * - The owning context of the function cannot change. + * - A node whose function originally did not use CUDA dynamic parallelism cannot be updated + * to a function which uses CDP. + * - A node whose function originally did not make device-side update calls cannot be updated + * to a function which makes device-side update calls. + * - A cooperative node cannot be updated to a non-cooperative node, and vice-versa. + * - If the graph was instantiated with CUDA_GRAPH_INSTANTIATE_FLAG_USE_NODE_PRIORITY, the + * priority attribute cannot change. Equality is checked on the originally requested + * priority values, before they are clamped to the device's supported range. + * - If \p hGraphExec was not instantiated for device launch, a node whose function originally + * did not use device-side cudaGraphLaunch() cannot be updated to a function which uses + * device-side cudaGraphLaunch() unless the node resides on the same context as nodes which + * contained such calls at instantiate-time. If no such calls were present at instantiation, + * these updates cannot be performed at all. + * - Neither \p hGraph nor \p hGraphExec may contain device-updatable kernel nodes. + * - Memset and memcpy nodes: + * - The CUDA device(s) to which the operand(s) was allocated/mapped cannot change. + * - The source/destination memory must be allocated from the same contexts as the original + * source/destination memory. + * - Only 1D memsets can be changed. + * - Additional memcpy node restrictions: + * - Changing either the source or destination memory type(i.e. CU_MEMORYTYPE_DEVICE, + * CU_MEMORYTYPE_ARRAY, etc.) is not supported. + * - External semaphore wait nodes and record nodes: + * - Changing the number of semaphores is not supported. + * - Conditional nodes: + * - Changing node parameters is not supported. + * - Changeing parameters of nodes within the conditional body graph is subject to the rules above. + * - Conditional handle flags and default values are updated as part of the graph update. + * + * Note: The API may add further restrictions in future releases. The return code should always be checked. + * + * cuGraphExecUpdate sets the result member of \p resultInfo to CU_GRAPH_EXEC_UPDATE_ERROR_TOPOLOGY_CHANGED + * under the following conditions: + * - The count of nodes directly in \p hGraphExec and \p hGraph differ, in which case resultInfo->errorNode + * is set to NULL. + * - \p hGraph has more exit nodes than \p hGraph, in which case resultInfo->errorNode is set to one of + * the exit nodes in hGraph. + * - A node in \p hGraph has a different number of dependencies than the node from \p hGraphExec it is paired with, + * in which case resultInfo->errorNode is set to the node from \p hGraph. + * - A node in \p hGraph has a dependency that does not match with the corresponding dependency of the paired node + * from \p hGraphExec. resultInfo->errorNode will be set to the node from \p hGraph. resultInfo->errorFromNode + * will be set to the mismatched dependency. The dependencies are paired based on edge order and a dependency + * does not match when the nodes are already paired based on other edges examined in the graph. + * + * cuGraphExecUpdate sets the result member of \p resultInfo to: + * - CU_GRAPH_EXEC_UPDATE_ERROR if passed an invalid value. + * - CU_GRAPH_EXEC_UPDATE_ERROR_TOPOLOGY_CHANGED if the graph topology changed + * - CU_GRAPH_EXEC_UPDATE_ERROR_NODE_TYPE_CHANGED if the type of a node changed, in which case + * \p hErrorNode_out is set to the node from \p hGraph. + * - CU_GRAPH_EXEC_UPDATE_ERROR_UNSUPPORTED_FUNCTION_CHANGE if the function changed in an unsupported + * way(see note above), in which case \p hErrorNode_out is set to the node from \p hGraph + * - CU_GRAPH_EXEC_UPDATE_ERROR_PARAMETERS_CHANGED if any parameters to a node changed in a way + * that is not supported, in which case \p hErrorNode_out is set to the node from \p hGraph. + * - CU_GRAPH_EXEC_UPDATE_ERROR_ATTRIBUTES_CHANGED if any attributes of a node changed in a way + * that is not supported, in which case \p hErrorNode_out is set to the node from \p hGraph. + * - CU_GRAPH_EXEC_UPDATE_ERROR_NOT_SUPPORTED if something about a node is unsupported, like + * the node's type or configuration, in which case \p hErrorNode_out is set to the node from \p hGraph + * + * If the update fails for a reason not listed above, the result member of \p resultInfo will be set + * to CU_GRAPH_EXEC_UPDATE_ERROR. If the update succeeds, the result member will be set to CU_GRAPH_EXEC_UPDATE_SUCCESS. + * + * cuGraphExecUpdate returns CUDA_SUCCESS when the updated was performed successfully. It returns + * CUDA_ERROR_GRAPH_EXEC_UPDATE_FAILURE if the graph update was not performed because it included + * changes which violated constraints specific to instantiated graph update. + * + * \param hGraphExec The instantiated graph to be updated + * \param hGraph The graph containing the updated parameters + * \param resultInfo the error info structure + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_GRAPH_EXEC_UPDATE_FAILURE, + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecUpdate(CUgraphExec hGraphExec, CUgraph hGraph, CUgraphExecUpdateResultInfo *resultInfo); + +/** + * \brief Copies attributes from source node to destination node. + * + * Copies attributes from source node \p src to destination node \p dst. + * Both node must have the same context. + * + * \param[out] dst Destination node + * \param[in] src Source node + * For list of attributes see ::CUkernelNodeAttrID + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuGraphKernelNodeCopyAttributes(CUgraphNode dst, CUgraphNode src); + +/** + * \brief Queries node attribute. + * + * Queries attribute \p attr from node \p hNode and stores it in corresponding + * member of \p value_out. + * + * \param[in] hNode + * \param[in] attr + * \param[out] value_out + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuGraphKernelNodeGetAttribute(CUgraphNode hNode, CUkernelNodeAttrID attr, + CUkernelNodeAttrValue *value_out); + +/** + * \brief Sets node attribute. + * + * Sets attribute \p attr on node \p hNode from corresponding attribute of + * \p value. + * + * \param[out] hNode + * \param[in] attr + * \param[out] value + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE + * \notefnerr + * + * \sa + * ::CUaccessPolicyWindow + */ +CUresult CUDAAPI cuGraphKernelNodeSetAttribute(CUgraphNode hNode, CUkernelNodeAttrID attr, + const CUkernelNodeAttrValue *value); + +/** + * \brief Write a DOT file describing graph structure + * + * Using the provided \p hGraph, write to \p path a DOT formatted description of the graph. + * By default this includes the graph topology, node types, node id, kernel names and memcpy direction. + * \p flags can be specified to write more detailed information about each node type such as + * parameter values, kernel attributes, node and function handles. + * + * \param hGraph - The graph to create a DOT file from + * \param path - The path to write the DOT file to + * \param flags - Flags from CUgraphDebugDot_flags for specifying which additional node information to write + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OPERATING_SYSTEM + */ +CUresult CUDAAPI cuGraphDebugDotPrint(CUgraph hGraph, const char *path, unsigned int flags); + +/** + * \brief Create a user object + * + * Create a user object with the specified destructor callback and initial reference count. The + * initial references are owned by the caller. + * + * Destructor callbacks cannot make CUDA API calls and should avoid blocking behavior, as they + * are executed by a shared internal thread. Another thread may be signaled to perform such + * actions, if it does not block forward progress of tasks scheduled through CUDA. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object_out - Location to return the user object handle + * \param ptr - The pointer to pass to the destroy function + * \param destroy - Callback to free the user object when it is no longer in use + * \param initialRefcount - The initial refcount to create the object with, typically 1. The + * initial references are owned by the calling thread. + * \param flags - Currently it is required to pass ::CU_USER_OBJECT_NO_DESTRUCTOR_SYNC, + * which is the only defined flag. This indicates that the destroy + * callback cannot be waited on by any CUDA API. Users requiring + * synchronization of the callback should signal its completion + * manually. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuUserObjectRetain, + * ::cuUserObjectRelease, + * ::cuGraphRetainUserObject, + * ::cuGraphReleaseUserObject, + * ::cuGraphCreate + */ +CUresult CUDAAPI cuUserObjectCreate(CUuserObject *object_out, void *ptr, CUhostFn destroy, + unsigned int initialRefcount, unsigned int flags); + +/** + * \brief Retain a reference to a user object + * + * Retains new references to a user object. The new references are owned by the caller. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object - The object to retain + * \param count - The number of references to retain, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuUserObjectCreate, + * ::cuUserObjectRelease, + * ::cuGraphRetainUserObject, + * ::cuGraphReleaseUserObject, + * ::cuGraphCreate + */ +CUresult CUDAAPI cuUserObjectRetain(CUuserObject object, unsigned int count); + +/** + * \brief Release a reference to a user object + * + * Releases user object references owned by the caller. The object's destructor is invoked if + * the reference count reaches zero. + * + * It is undefined behavior to release references not owned by the caller, or to use a user + * object handle after all references are released. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object - The object to release + * \param count - The number of references to release, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuUserObjectCreate, + * ::cuUserObjectRetain, + * ::cuGraphRetainUserObject, + * ::cuGraphReleaseUserObject, + * ::cuGraphCreate + */ +CUresult CUDAAPI cuUserObjectRelease(CUuserObject object, unsigned int count); + +/** + * \brief Retain a reference to a user object from a graph + * + * Creates or moves user object references that will be owned by a CUDA graph. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param graph - The graph to associate the reference with + * \param object - The user object to retain a reference for + * \param count - The number of references to add to the graph, typically 1. Must be + * nonzero and not larger than INT_MAX. + * \param flags - The optional flag ::CU_GRAPH_USER_OBJECT_MOVE transfers references + * from the calling thread, rather than create new references. Pass 0 + * to create new references. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuUserObjectCreate, + * ::cuUserObjectRetain, + * ::cuUserObjectRelease, + * ::cuGraphReleaseUserObject, + * ::cuGraphCreate + */ +CUresult CUDAAPI cuGraphRetainUserObject(CUgraph graph, CUuserObject object, unsigned int count, unsigned int flags); + +/** + * \brief Release a user object reference from a graph + * + * Releases user object references owned by a graph. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param graph - The graph that will release the reference + * \param object - The user object to release a reference for + * \param count - The number of references to release, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuUserObjectCreate, + * ::cuUserObjectRetain, + * ::cuUserObjectRelease, + * ::cuGraphRetainUserObject, + * ::cuGraphCreate + */ +CUresult CUDAAPI cuGraphReleaseUserObject(CUgraph graph, CUuserObject object, unsigned int count); + +/** + * \brief Adds a node of arbitrary type to a graph + * + * Creates a new node in \p hGraph described by \p nodeParams with \p numDependencies + * dependencies specified via \p dependencies. \p numDependencies may be 0. + * \p dependencies may be null if \p numDependencies is 0. \p dependencies may not have + * any duplicate entries. + * + * \p nodeParams is a tagged union. The node type should be specified in the \p type field, + * and type-specific parameters in the corresponding union member. All unused bytes - that + * is, \p reserved0 and all bytes past the utilized union member - must be set to zero. + * It is recommended to use brace initialization or memset to ensure all bytes are + * initialized. + * + * Note that for some node types, \p nodeParams may contain "out parameters" which are + * modified during the call, such as \p nodeParams->alloc.dptr. + * + * A handle to the new node will be returned in \p phGraphNode. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Specification of the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphNodeSetParams, + * ::cuGraphExecNodeSetParams + */ +CUresult CUDAAPI cuGraphAddNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUgraphNodeParams *nodeParams); + +/** + * \brief Adds a node of arbitrary type to a graph (12.3+) + * + * Creates a new node in \p hGraph described by \p nodeParams with \p numDependencies + * dependencies specified via \p dependencies. \p numDependencies may be 0. + * \p dependencies may be null if \p numDependencies is 0. \p dependencies may not have + * any duplicate entries. + * + * \p nodeParams is a tagged union. The node type should be specified in the \p type field, + * and type-specific parameters in the corresponding union member. All unused bytes - that + * is, \p reserved0 and all bytes past the utilized union member - must be set to zero. + * It is recommended to use brace initialization or memset to ensure all bytes are + * initialized. + * + * Note that for some node types, \p nodeParams may contain "out parameters" which are + * modified during the call, such as \p nodeParams->alloc.dptr. + * + * A handle to the new node will be returned in \p phGraphNode. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param dependencyData - Optional edge data for the dependencies. If NULL, the data is + * assumed to be default (zeroed) for all dependencies. + * \param numDependencies - Number of dependencies + * \param nodeParams - Specification of the node + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphCreate, + * ::cuGraphNodeSetParams, + * ::cuGraphExecNodeSetParams + */ +CUresult CUDAAPI cuGraphAddNode_v2(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUgraphNodeParams *nodeParams); + +/** + * \brief Update's a graph node's parameters + * + * Sets the parameters of graph node \p hNode to \p nodeParams. The node type specified by + * \p nodeParams->type must match the type of \p hNode. \p nodeParams must be fully + * initialized and all unused bytes (reserved, padding) zeroed. + * + * Modifying parameters is not supported for node types CU_GRAPH_NODE_TYPE_MEM_ALLOC and + * CU_GRAPH_NODE_TYPE_MEM_FREE. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphExecNodeSetParams + */ +CUresult CUDAAPI cuGraphNodeSetParams(CUgraphNode hNode, CUgraphNodeParams *nodeParams); + +/** + * \brief Update's a graph node's parameters in an instantiated graph + * + * Sets the parameters of a node in an executable graph \p hGraphExec. The node is identified + * by the corresponding node \p hNode in the non-executable graph from which the executable + * graph was instantiated. \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * Allowed changes to parameters on executable graphs are as follows: + * + *
Node typeAllowed changes + *
kernelSee ::cuGraphExecKernelNodeSetParams + *
memcpyAddresses for 1-dimensional copies if allocated in same context; see ::cuGraphExecMemcpyNodeSetParams + *
memsetAddresses for 1-dimensional memsets if allocated in same context; see ::cuGraphExecMemsetNodeSetParams + *
hostUnrestricted + *
child graphTopology must match and restrictions apply recursively; see ::cuGraphExecUpdate + *
event waitUnrestricted + *
event recordUnrestricted + *
external semaphore signalNumber of semaphore operations cannot change + *
external semaphore waitNumber of semaphore operations cannot change + *
memory allocationAPI unsupported + *
memory freeAPI unsupported + *
batch memopsAddresses, values, and operation type for wait operations; see ::cuGraphExecBatchMemOpNodeSetParams + *
+ * + * \param hGraphExec - The executable graph in which to update the specified node + * \param hNode - Corresponding node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + * ::cuGraphNodeSetParams + * ::cuGraphExecUpdate, + * ::cuGraphInstantiate + */ +CUresult CUDAAPI cuGraphExecNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, CUgraphNodeParams *nodeParams); + +/** + * \brief Create a conditional handle + * + * Creates a conditional handle associated with \p hGraph. + * + * The conditional handle must be associated with a conditional node in this graph or one of its children. + * + * Handles not associated with a conditional node may cause graph instantiation to fail. + * + * Handles can only be set from the context with which they are associated. + * + * \param pHandle_out - Pointer used to return the handle to the caller. + * \param hGraph - Graph which will contain the conditional node using this handle. + * \param ctx - Context for the handle and associated conditional node. + * \param defaultLaunchValue - Optional initial value for the conditional variable. + * \param flags - Currently must be CU_GRAPH_COND_ASSIGN_DEFAULT or 0. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode + */ +CUresult CUDAAPI cuGraphConditionalHandleCreate(CUgraphConditionalHandle *pHandle_out, CUgraph hGraph, CUcontext ctx, unsigned int defaultLaunchValue, unsigned int flags); + +/** @} */ /* END CUDA_GRAPH */ + +/** + * \defgroup CUDA_OCCUPANCY Occupancy + * + * ___MANBRIEF___ occupancy calculation functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the occupancy calculation functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns occupancy of a function + * + * Returns in \p *numBlocks the number of the maximum active blocks per + * streaming multiprocessor. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel for which occupancy is calculated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + */ +CUresult CUDAAPI cuOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, CUfunction func, int blockSize, size_t dynamicSMemSize); + +/** + * \brief Returns occupancy of a function + * + * Returns in \p *numBlocks the number of the maximum active blocks per + * streaming multiprocessor. + * + * The \p Flags parameter controls how special cases are handled. The + * valid flags are: + * + * - ::CU_OCCUPANCY_DEFAULT, which maintains the default behavior as + * ::cuOccupancyMaxActiveBlocksPerMultiprocessor; + * + * - ::CU_OCCUPANCY_DISABLE_CACHING_OVERRIDE, which suppresses the + * default behavior on platform where global caching affects + * occupancy. On such platforms, if caching is enabled, but + * per-block SM resource usage would result in zero occupancy, the + * occupancy calculator will calculate the occupancy as if caching + * is disabled. Setting ::CU_OCCUPANCY_DISABLE_CACHING_OVERRIDE makes + * the occupancy calculator to return 0 in such cases. More information + * can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel for which occupancy is calculated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * \param flags - Requested behavior for the occupancy calculator + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + */ +CUresult CUDAAPI cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, CUfunction func, int blockSize, size_t dynamicSMemSize, unsigned int flags); + +/** + * \brief Suggest a launch configuration with reasonable occupancy + * + * Returns in \p *blockSize a reasonable block size that can achieve + * the maximum occupancy (or, the maximum number of active warps with + * the fewest blocks per multiprocessor), and in \p *minGridSize the + * minimum grid size to achieve the maximum occupancy. + * + * If \p blockSizeLimit is 0, the configurator will use the maximum + * block size permitted by the device / function instead. + * + * If per-block dynamic shared memory allocation is not needed, the + * user should leave both \p blockSizeToDynamicSMemSize and \p + * dynamicSMemSize as 0. + * + * If per-block dynamic shared memory allocation is needed, then if + * the dynamic shared memory size is constant regardless of block + * size, the size should be passed through \p dynamicSMemSize, and \p + * blockSizeToDynamicSMemSize should be NULL. + * + * Otherwise, if the per-block dynamic shared memory size varies with + * different block sizes, the user needs to provide a unary function + * through \p blockSizeToDynamicSMemSize that computes the dynamic + * shared memory needed by \p func for any given block size. \p + * dynamicSMemSize is ignored. An example signature is: + * + * \code + * // Take block size, returns dynamic shared memory needed + * size_t blockToSmem(int blockSize); + * \endcode + * + * \param minGridSize - Returned minimum grid size needed to achieve the maximum occupancy + * \param blockSize - Returned maximum block size that can achieve the maximum occupancy + * \param func - Kernel for which launch configuration is calculated + * \param blockSizeToDynamicSMemSize - A function that calculates how much per-block dynamic shared memory \p func uses based on the block size + * \param dynamicSMemSize - Dynamic shared memory usage intended, in bytes + * \param blockSizeLimit - The maximum block size \p func is designed to handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaOccupancyMaxPotentialBlockSize + */ +CUresult CUDAAPI cuOccupancyMaxPotentialBlockSize(int *minGridSize, int *blockSize, CUfunction func, CUoccupancyB2DSize blockSizeToDynamicSMemSize, size_t dynamicSMemSize, int blockSizeLimit); + +/** + * \brief Suggest a launch configuration with reasonable occupancy + * + * An extended version of ::cuOccupancyMaxPotentialBlockSize. In + * addition to arguments passed to ::cuOccupancyMaxPotentialBlockSize, + * ::cuOccupancyMaxPotentialBlockSizeWithFlags also takes a \p Flags + * parameter. + * + * The \p Flags parameter controls how special cases are handled. The + * valid flags are: + * + * - ::CU_OCCUPANCY_DEFAULT, which maintains the default behavior as + * ::cuOccupancyMaxPotentialBlockSize; + * + * - ::CU_OCCUPANCY_DISABLE_CACHING_OVERRIDE, which suppresses the + * default behavior on platform where global caching affects + * occupancy. On such platforms, the launch configurations that + * produces maximal occupancy might not support global + * caching. Setting ::CU_OCCUPANCY_DISABLE_CACHING_OVERRIDE + * guarantees that the the produced launch configuration is global + * caching compatible at a potential cost of occupancy. More information + * can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * \param minGridSize - Returned minimum grid size needed to achieve the maximum occupancy + * \param blockSize - Returned maximum block size that can achieve the maximum occupancy + * \param func - Kernel for which launch configuration is calculated + * \param blockSizeToDynamicSMemSize - A function that calculates how much per-block dynamic shared memory \p func uses based on the block size + * \param dynamicSMemSize - Dynamic shared memory usage intended, in bytes + * \param blockSizeLimit - The maximum block size \p func is designed to handle + * \param flags - Options + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaOccupancyMaxPotentialBlockSizeWithFlags + */ +CUresult CUDAAPI cuOccupancyMaxPotentialBlockSizeWithFlags(int *minGridSize, int *blockSize, CUfunction func, CUoccupancyB2DSize blockSizeToDynamicSMemSize, size_t dynamicSMemSize, int blockSizeLimit, unsigned int flags); + +/** + * \brief Returns dynamic shared memory available per block when launching \p numBlocks blocks on SM + * + * Returns in \p *dynamicSmemSize the maximum size of dynamic shared memory to allow \p numBlocks blocks per SM. + * + * \param dynamicSmemSize - Returned maximum dynamic shared memory + * \param func - Kernel function for which occupancy is calculated + * \param numBlocks - Number of blocks to fit on SM + * \param blockSize - Size of the blocks + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + */ +CUresult CUDAAPI cuOccupancyAvailableDynamicSMemPerBlock(size_t *dynamicSmemSize, CUfunction func, int numBlocks, int blockSize); + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum cluster size in \p *clusterSize. + * + * The cluster dimensions in \p config are ignored. If func has a required + * cluster size set (see ::cudaFuncGetAttributes / ::cuFuncGetAttribute),\p + * *clusterSize will reflect the required cluster size. + * + * By default this function will always return a value that's portable on + * future hardware. A higher value may be returned if the kernel function + * allows non-portable cluster sizes. + * + * This function will respect the compile time launch bounds. + * + * \param clusterSize - Returned maximum cluster size that can be launched + * for the given kernel function and launch configuration + * \param func - Kernel function for which maximum cluster + * size is calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaFuncGetAttributes, + * ::cuFuncGetAttribute + */ +CUresult CUDAAPI cuOccupancyMaxPotentialClusterSize(int *clusterSize, CUfunction func, const CUlaunchConfig *config); + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum number of clusters that could co-exist + * on the target device in \p *numClusters. + * + * If the function has required cluster size already set (see + * ::cudaFuncGetAttributes / ::cuFuncGetAttribute), the cluster size + * from config must either be unspecified or match the required size. + * Without required sizes, the cluster size must be specified in config, + * else the function will return an error. + * + * Note that various attributes of the kernel function may affect occupancy + * calculation. Runtime environment may affect how the hardware schedules + * the clusters, so the calculated occupancy is not guaranteed to be achievable. + * + * \param numClusters - Returned maximum number of clusters that + * could co-exist on the target device + * \param func - Kernel function for which maximum number + * of clusters are calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CLUSTER_SIZE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cudaFuncGetAttributes, + * ::cuFuncGetAttribute + */ +CUresult CUDAAPI cuOccupancyMaxActiveClusters(int *numClusters, CUfunction func, const CUlaunchConfig *config); +/** @} */ /* END CUDA_OCCUPANCY */ + +/** + * \defgroup CUDA_TEXREF_DEPRECATED Texture Reference Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated texture reference management functions of the + * low-level CUDA driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated texture reference management + * functions of the low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Binds an array as a texture reference + * + * \deprecated + * + * Binds the CUDA array \p hArray to the texture reference \p hTexRef. Any + * previous address or CUDA array state associated with the texture reference + * is superseded by this function. \p Flags must be set to + * ::CU_TRSA_OVERRIDE_FORMAT. Any CUDA array previously bound to \p hTexRef is + * unbound. + * + * \param hTexRef - Texture reference to bind + * \param hArray - Array to bind + * \param Flags - Options (must be ::CU_TRSA_OVERRIDE_FORMAT) + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetArray(CUtexref hTexRef, CUarray hArray, unsigned int Flags); + +/** + * \brief Binds a mipmapped array to a texture reference + * + * \deprecated + * + * Binds the CUDA mipmapped array \p hMipmappedArray to the texture reference \p hTexRef. + * Any previous address or CUDA array state associated with the texture reference + * is superseded by this function. \p Flags must be set to ::CU_TRSA_OVERRIDE_FORMAT. + * Any CUDA array previously bound to \p hTexRef is unbound. + * + * \param hTexRef - Texture reference to bind + * \param hMipmappedArray - Mipmapped array to bind + * \param Flags - Options (must be ::CU_TRSA_OVERRIDE_FORMAT) + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetMipmappedArray(CUtexref hTexRef, CUmipmappedArray hMipmappedArray, unsigned int Flags); + +/** + * \brief Binds an address as a texture reference + * + * \deprecated + * + * Binds a linear address range to the texture reference \p hTexRef. Any + * previous address or CUDA array state associated with the texture reference + * is superseded by this function. Any memory previously bound to \p hTexRef + * is unbound. + * + * Since the hardware enforces an alignment requirement on texture base + * addresses, ::cuTexRefSetAddress() passes back a byte offset in + * \p *ByteOffset that must be applied to texture fetches in order to read from + * the desired memory. This offset must be divided by the texel size and + * passed to kernels that read from the texture so they can be applied to the + * ::tex1Dfetch() function. + * + * If the device memory pointer was returned from ::cuMemAlloc(), the offset + * is guaranteed to be 0 and NULL may be passed as the \p ByteOffset parameter. + * + * The total number of elements (or texels) in the linear address range + * cannot exceed ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LINEAR_WIDTH. + * The number of elements is computed as (\p bytes / bytesPerElement), + * where bytesPerElement is determined from the data format and number of + * components set using ::cuTexRefSetFormat(). + * + * \param ByteOffset - Returned byte offset + * \param hTexRef - Texture reference to bind + * \param dptr - Device pointer to bind + * \param bytes - Size of memory to bind in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetAddress(size_t *ByteOffset, CUtexref hTexRef, CUdeviceptr dptr, size_t bytes); + +/** + * \brief Binds an address as a 2D texture reference + * + * \deprecated + * + * Binds a linear address range to the texture reference \p hTexRef. Any + * previous address or CUDA array state associated with the texture reference + * is superseded by this function. Any memory previously bound to \p hTexRef + * is unbound. + * + * Using a ::tex2D() function inside a kernel requires a call to either + * ::cuTexRefSetArray() to bind the corresponding texture reference to an + * array, or ::cuTexRefSetAddress2D() to bind the texture reference to linear + * memory. + * + * Function calls to ::cuTexRefSetFormat() cannot follow calls to + * ::cuTexRefSetAddress2D() for the same texture reference. + * + * It is required that \p dptr be aligned to the appropriate hardware-specific + * texture alignment. You can query this value using the device attribute + * ::CU_DEVICE_ATTRIBUTE_TEXTURE_ALIGNMENT. If an unaligned \p dptr is + * supplied, ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \p Pitch has to be aligned to the hardware-specific texture pitch alignment. + * This value can be queried using the device attribute + * ::CU_DEVICE_ATTRIBUTE_TEXTURE_PITCH_ALIGNMENT. If an unaligned \p Pitch is + * supplied, ::CUDA_ERROR_INVALID_VALUE is returned. + * + * Width and Height, which are specified in elements (or texels), cannot exceed + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_WIDTH and + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_HEIGHT respectively. + * \p Pitch, which is specified in bytes, cannot exceed + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_PITCH. + * + * \param hTexRef - Texture reference to bind + * \param desc - Descriptor of CUDA array + * \param dptr - Device pointer to bind + * \param Pitch - Line pitch in bytes + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetAddress2D(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR *desc, CUdeviceptr dptr, size_t Pitch); + +/** + * \brief Sets the format for a texture reference + * + * \deprecated + * + * Specifies the format of the data to be read by the texture reference + * \p hTexRef. \p fmt and \p NumPackedComponents are exactly analogous to the + * ::Format and ::NumChannels members of the ::CUDA_ARRAY_DESCRIPTOR structure: + * They specify the format of each component and the number of components per + * array element. + * + * \param hTexRef - Texture reference + * \param fmt - Format to set + * \param NumPackedComponents - Number of components per array element + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat, + * ::cudaCreateChannelDesc + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetFormat(CUtexref hTexRef, CUarray_format fmt, int NumPackedComponents); + +/** + * \brief Sets the addressing mode for a texture reference + * + * \deprecated + * + * Specifies the addressing mode \p am for the given dimension \p dim of the + * texture reference \p hTexRef. If \p dim is zero, the addressing mode is + * applied to the first parameter of the functions used to fetch from the + * texture; if \p dim is 1, the second, and so on. ::CUaddress_mode is defined + * as: + * \code + typedef enum CUaddress_mode_enum { + CU_TR_ADDRESS_MODE_WRAP = 0, + CU_TR_ADDRESS_MODE_CLAMP = 1, + CU_TR_ADDRESS_MODE_MIRROR = 2, + CU_TR_ADDRESS_MODE_BORDER = 3 + } CUaddress_mode; + * \endcode + * + * Note that this call has no effect if \p hTexRef is bound to linear memory. + * Also, if the flag, ::CU_TRSF_NORMALIZED_COORDINATES, is not set, the only + * supported address mode is ::CU_TR_ADDRESS_MODE_CLAMP. + * + * \param hTexRef - Texture reference + * \param dim - Dimension + * \param am - Addressing mode to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetAddressMode(CUtexref hTexRef, int dim, CUaddress_mode am); + +/** + * \brief Sets the filtering mode for a texture reference + * + * \deprecated + * + * Specifies the filtering mode \p fm to be used when reading memory through + * the texture reference \p hTexRef. ::CUfilter_mode_enum is defined as: + * + * \code + typedef enum CUfilter_mode_enum { + CU_TR_FILTER_MODE_POINT = 0, + CU_TR_FILTER_MODE_LINEAR = 1 + } CUfilter_mode; + * \endcode + * + * Note that this call has no effect if \p hTexRef is bound to linear memory. + * + * \param hTexRef - Texture reference + * \param fm - Filtering mode to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetFilterMode(CUtexref hTexRef, CUfilter_mode fm); + +/** + * \brief Sets the mipmap filtering mode for a texture reference + * + * \deprecated + * + * Specifies the mipmap filtering mode \p fm to be used when reading memory through + * the texture reference \p hTexRef. ::CUfilter_mode_enum is defined as: + * + * \code + typedef enum CUfilter_mode_enum { + CU_TR_FILTER_MODE_POINT = 0, + CU_TR_FILTER_MODE_LINEAR = 1 + } CUfilter_mode; + * \endcode + * + * Note that this call has no effect if \p hTexRef is not bound to a mipmapped array. + * + * \param hTexRef - Texture reference + * \param fm - Filtering mode to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetMipmapFilterMode(CUtexref hTexRef, CUfilter_mode fm); + +/** + * \brief Sets the mipmap level bias for a texture reference + * + * \deprecated + * + * Specifies the mipmap level bias \p bias to be added to the specified mipmap level when + * reading memory through the texture reference \p hTexRef. + * + * Note that this call has no effect if \p hTexRef is not bound to a mipmapped array. + * + * \param hTexRef - Texture reference + * \param bias - Mipmap level bias + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetMipmapLevelBias(CUtexref hTexRef, float bias); + +/** + * \brief Sets the mipmap min/max mipmap level clamps for a texture reference + * + * \deprecated + * + * Specifies the min/max mipmap level clamps, \p minMipmapLevelClamp and \p maxMipmapLevelClamp + * respectively, to be used when reading memory through the texture reference + * \p hTexRef. + * + * Note that this call has no effect if \p hTexRef is not bound to a mipmapped array. + * + * \param hTexRef - Texture reference + * \param minMipmapLevelClamp - Mipmap min level clamp + * \param maxMipmapLevelClamp - Mipmap max level clamp + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetMipmapLevelClamp(CUtexref hTexRef, float minMipmapLevelClamp, float maxMipmapLevelClamp); + +/** + * \brief Sets the maximum anisotropy for a texture reference + * + * \deprecated + * + * Specifies the maximum anisotropy \p maxAniso to be used when reading memory through + * the texture reference \p hTexRef. + * + * Note that this call has no effect if \p hTexRef is bound to linear memory. + * + * \param hTexRef - Texture reference + * \param maxAniso - Maximum anisotropy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetMaxAnisotropy(CUtexref hTexRef, unsigned int maxAniso); + +/** + * \brief Sets the border color for a texture reference + * + * \deprecated + * + * Specifies the value of the RGBA color via the \p pBorderColor to the texture reference + * \p hTexRef. The color value supports only float type and holds color components in + * the following sequence: + * pBorderColor[0] holds 'R' component + * pBorderColor[1] holds 'G' component + * pBorderColor[2] holds 'B' component + * pBorderColor[3] holds 'A' component + * + * Note that the color values can be set only when the Address mode is set to + * CU_TR_ADDRESS_MODE_BORDER using ::cuTexRefSetAddressMode. + * Applications using integer border color values have to "reinterpret_cast" their values to float. + * + * \param hTexRef - Texture reference + * \param pBorderColor - RGBA color + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddressMode, + * ::cuTexRefGetAddressMode, ::cuTexRefGetBorderColor + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetBorderColor(CUtexref hTexRef, float *pBorderColor); + +/** + * \brief Sets the flags for a texture reference + * + * \deprecated + * + * Specifies optional flags via \p Flags to specify the behavior of data + * returned through the texture reference \p hTexRef. The valid flags are: + * + * - ::CU_TRSF_READ_AS_INTEGER, which suppresses the default behavior of + * having the texture promote integer data to floating point data in the + * range [0, 1]. Note that texture with 32-bit integer format + * would not be promoted, regardless of whether or not this + * flag is specified; + * - ::CU_TRSF_NORMALIZED_COORDINATES, which suppresses the + * default behavior of having the texture coordinates range + * from [0, Dim) where Dim is the width or height of the CUDA + * array. Instead, the texture coordinates [0, 1.0) reference + * the entire breadth of the array dimension; + * - ::CU_TRSF_DISABLE_TRILINEAR_OPTIMIZATION, which disables any trilinear + * filtering optimizations. Trilinear optimizations improve texture filtering + * performance by allowing bilinear filtering on textures in scenarios where + * it can closely approximate the expected results. + * + * \param hTexRef - Texture reference + * \param Flags - Optional flags to set + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefSetFlags(CUtexref hTexRef, unsigned int Flags); + +/** + * \brief Gets the address associated with a texture reference + * + * \deprecated + * + * Returns in \p *pdptr the base address bound to the texture reference + * \p hTexRef, or returns ::CUDA_ERROR_INVALID_VALUE if the texture reference + * is not bound to any device memory range. + * + * \param pdptr - Returned device address + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetAddress(CUdeviceptr *pdptr, CUtexref hTexRef); + +/** + * \brief Gets the array bound to a texture reference + * + * \deprecated + * + * Returns in \p *phArray the CUDA array bound to the texture reference + * \p hTexRef, or returns ::CUDA_ERROR_INVALID_VALUE if the texture reference + * is not bound to any CUDA array. + * + * \param phArray - Returned array + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetArray(CUarray *phArray, CUtexref hTexRef); + +/** + * \brief Gets the mipmapped array bound to a texture reference + * + * \deprecated + * + * Returns in \p *phMipmappedArray the CUDA mipmapped array bound to the texture + * reference \p hTexRef, or returns ::CUDA_ERROR_INVALID_VALUE if the texture reference + * is not bound to any CUDA mipmapped array. + * + * \param phMipmappedArray - Returned mipmapped array + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetMipmappedArray(CUmipmappedArray *phMipmappedArray, CUtexref hTexRef); + +/** + * \brief Gets the addressing mode used by a texture reference + * + * \deprecated + * + * Returns in \p *pam the addressing mode corresponding to the + * dimension \p dim of the texture reference \p hTexRef. Currently, the only + * valid value for \p dim are 0 and 1. + * + * \param pam - Returned addressing mode + * \param hTexRef - Texture reference + * \param dim - Dimension + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetAddressMode(CUaddress_mode *pam, CUtexref hTexRef, int dim); + +/** + * \brief Gets the filter-mode used by a texture reference + * + * \deprecated + * + * Returns in \p *pfm the filtering mode of the texture reference + * \p hTexRef. + * + * \param pfm - Returned filtering mode + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetFilterMode(CUfilter_mode *pfm, CUtexref hTexRef); + +/** + * \brief Gets the format used by a texture reference + * + * \deprecated + * + * Returns in \p *pFormat and \p *pNumChannels the format and number + * of components of the CUDA array bound to the texture reference \p hTexRef. + * If \p pFormat or \p pNumChannels is NULL, it will be ignored. + * + * \param pFormat - Returned format + * \param pNumChannels - Returned number of components + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetFormat(CUarray_format *pFormat, int *pNumChannels, CUtexref hTexRef); + +/** + * \brief Gets the mipmap filtering mode for a texture reference + * + * \deprecated + * + * Returns the mipmap filtering mode in \p pfm that's used when reading memory through + * the texture reference \p hTexRef. + * + * \param pfm - Returned mipmap filtering mode + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetMipmapFilterMode(CUfilter_mode *pfm, CUtexref hTexRef); + +/** + * \brief Gets the mipmap level bias for a texture reference + * + * \deprecated + * + * Returns the mipmap level bias in \p pBias that's added to the specified mipmap + * level when reading memory through the texture reference \p hTexRef. + * + * \param pbias - Returned mipmap level bias + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetMipmapLevelBias(float *pbias, CUtexref hTexRef); + +/** + * \brief Gets the min/max mipmap level clamps for a texture reference + * + * \deprecated + * + * Returns the min/max mipmap level clamps in \p pminMipmapLevelClamp and \p pmaxMipmapLevelClamp + * that's used when reading memory through the texture reference \p hTexRef. + * + * \param pminMipmapLevelClamp - Returned mipmap min level clamp + * \param pmaxMipmapLevelClamp - Returned mipmap max level clamp + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetMipmapLevelClamp(float *pminMipmapLevelClamp, float *pmaxMipmapLevelClamp, CUtexref hTexRef); + +/** + * \brief Gets the maximum anisotropy for a texture reference + * + * \deprecated + * + * Returns the maximum anisotropy in \p pmaxAniso that's used when reading memory through + * the texture reference \p hTexRef. + * + * \param pmaxAniso - Returned maximum anisotropy + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFlags, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetMaxAnisotropy(int *pmaxAniso, CUtexref hTexRef); + +/** + * \brief Gets the border color used by a texture reference + * + * \deprecated + * + * Returns in \p pBorderColor, values of the RGBA color used by + * the texture reference \p hTexRef. + * The color value is of type float and holds color components in + * the following sequence: + * pBorderColor[0] holds 'R' component + * pBorderColor[1] holds 'G' component + * pBorderColor[2] holds 'B' component + * pBorderColor[3] holds 'A' component + * + * \param hTexRef - Texture reference + * \param pBorderColor - Returned Type and Value of RGBA color + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddressMode, + * ::cuTexRefSetAddressMode, ::cuTexRefSetBorderColor + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetBorderColor(float *pBorderColor, CUtexref hTexRef); + +/** + * \brief Gets the flags used by a texture reference + * + * \deprecated + * + * Returns in \p *pFlags the flags of the texture reference \p hTexRef. + * + * \param pFlags - Returned flags + * \param hTexRef - Texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefSetAddress, + * ::cuTexRefSetAddress2D, ::cuTexRefSetAddressMode, ::cuTexRefSetArray, + * ::cuTexRefSetFilterMode, ::cuTexRefSetFlags, ::cuTexRefSetFormat, + * ::cuTexRefGetAddress, ::cuTexRefGetAddressMode, ::cuTexRefGetArray, + * ::cuTexRefGetFilterMode, ::cuTexRefGetFormat + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefGetFlags(unsigned int *pFlags, CUtexref hTexRef); + +/** + * \brief Creates a texture reference + * + * \deprecated + * + * Creates a texture reference and returns its handle in \p *pTexRef. Once + * created, the application must call ::cuTexRefSetArray() or + * ::cuTexRefSetAddress() to associate the reference with allocated memory. + * Other texture reference functions are used to specify the format and + * interpretation (addressing, filtering, etc.) to be used when the memory is + * read through this texture reference. + * + * \param pTexRef - Returned texture reference + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefDestroy + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefCreate(CUtexref *pTexRef); + +/** + * \brief Destroys a texture reference + * + * \deprecated + * + * Destroys the texture reference specified by \p hTexRef. + * + * \param hTexRef - Texture reference to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuTexRefCreate + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuTexRefDestroy(CUtexref hTexRef); + +/** @} */ /* END CUDA_TEXREF_DEPRECATED */ + + +/** + * \defgroup CUDA_SURFREF_DEPRECATED Surface Reference Management [DEPRECATED] + * + * ___MANBRIEF___ surface reference management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the surface reference management functions of the + * low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Sets the CUDA array for a surface reference. + * + * \deprecated + * + * Sets the CUDA array \p hArray to be read and written by the surface reference + * \p hSurfRef. Any previous CUDA array state associated with the surface + * reference is superseded by this function. \p Flags must be set to 0. + * The ::CUDA_ARRAY3D_SURFACE_LDST flag must have been set for the CUDA array. + * Any CUDA array previously bound to \p hSurfRef is unbound. + + * \param hSurfRef - Surface reference handle + * \param hArray - CUDA array handle + * \param Flags - set to 0 + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuModuleGetSurfRef, + * ::cuSurfRefGetArray + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuSurfRefSetArray(CUsurfref hSurfRef, CUarray hArray, unsigned int Flags); + +/** + * \brief Passes back the CUDA array bound to a surface reference. + * + * \deprecated + * + * Returns in \p *phArray the CUDA array bound to the surface reference + * \p hSurfRef, or returns ::CUDA_ERROR_INVALID_VALUE if the surface reference + * is not bound to any CUDA array. + + * \param phArray - Surface reference handle + * \param hSurfRef - Surface reference handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa ::cuModuleGetSurfRef, ::cuSurfRefSetArray + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuSurfRefGetArray(CUarray *phArray, CUsurfref hSurfRef); + +/** @} */ /* END CUDA_SURFREF_DEPRECATED */ + +/** + * \defgroup CUDA_TEXOBJECT Texture Object Management + * + * ___MANBRIEF___ texture object management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the texture object management functions of the + * low-level CUDA driver application programming interface. The texture + * object API is only supported on devices of compute capability 3.0 or higher. + * + * @{ + */ + +/** + * \brief Creates a texture object + * + * Creates a texture object and returns it in \p pTexObject. \p pResDesc describes + * the data to texture from. \p pTexDesc describes how the data should be sampled. + * \p pResViewDesc is an optional argument that specifies an alternate format for + * the data described by \p pResDesc, and also describes the subresource region + * to restrict access to when texturing. \p pResViewDesc can only be specified if + * the type of resource is a CUDA array or a CUDA mipmapped array. + * + * Texture objects are only supported on devices of compute capability 3.0 or higher. + * Additionally, a texture object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * The ::CUDA_RESOURCE_DESC structure is defined as: + * \code + typedef struct CUDA_RESOURCE_DESC_st + { + CUresourcetype resType; + + union { + struct { + CUarray hArray; + } array; + struct { + CUmipmappedArray hMipmappedArray; + } mipmap; + struct { + CUdeviceptr devPtr; + CUarray_format format; + unsigned int numChannels; + size_t sizeInBytes; + } linear; + struct { + CUdeviceptr devPtr; + CUarray_format format; + unsigned int numChannels; + size_t width; + size_t height; + size_t pitchInBytes; + } pitch2D; + } res; + + unsigned int flags; + } CUDA_RESOURCE_DESC; + + * \endcode + * where: + * - ::CUDA_RESOURCE_DESC::resType specifies the type of resource to texture from. + * CUresourceType is defined as: + * \code + typedef enum CUresourcetype_enum { + CU_RESOURCE_TYPE_ARRAY = 0x00, + CU_RESOURCE_TYPE_MIPMAPPED_ARRAY = 0x01, + CU_RESOURCE_TYPE_LINEAR = 0x02, + CU_RESOURCE_TYPE_PITCH2D = 0x03 + } CUresourcetype; + * \endcode + * + * \par + * If ::CUDA_RESOURCE_DESC::resType is set to ::CU_RESOURCE_TYPE_ARRAY, ::CUDA_RESOURCE_DESC::res::array::hArray + * must be set to a valid CUDA array handle. + * + * \par + * If ::CUDA_RESOURCE_DESC::resType is set to ::CU_RESOURCE_TYPE_MIPMAPPED_ARRAY, ::CUDA_RESOURCE_DESC::res::mipmap::hMipmappedArray + * must be set to a valid CUDA mipmapped array handle. + * + * \par + * If ::CUDA_RESOURCE_DESC::resType is set to ::CU_RESOURCE_TYPE_LINEAR, ::CUDA_RESOURCE_DESC::res::linear::devPtr + * must be set to a valid device pointer, that is aligned to ::CU_DEVICE_ATTRIBUTE_TEXTURE_ALIGNMENT. + * ::CUDA_RESOURCE_DESC::res::linear::format and ::CUDA_RESOURCE_DESC::res::linear::numChannels + * describe the format of each component and the number of components per array element. ::CUDA_RESOURCE_DESC::res::linear::sizeInBytes + * specifies the size of the array in bytes. The total number of elements in the linear address range cannot exceed + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE1D_LINEAR_WIDTH. The number of elements is computed as (sizeInBytes / (sizeof(format) * numChannels)). + * + * \par + * If ::CUDA_RESOURCE_DESC::resType is set to ::CU_RESOURCE_TYPE_PITCH2D, ::CUDA_RESOURCE_DESC::res::pitch2D::devPtr + * must be set to a valid device pointer, that is aligned to ::CU_DEVICE_ATTRIBUTE_TEXTURE_ALIGNMENT. + * ::CUDA_RESOURCE_DESC::res::pitch2D::format and ::CUDA_RESOURCE_DESC::res::pitch2D::numChannels + * describe the format of each component and the number of components per array element. ::CUDA_RESOURCE_DESC::res::pitch2D::width + * and ::CUDA_RESOURCE_DESC::res::pitch2D::height specify the width and height of the array in elements, and cannot exceed + * ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_WIDTH and ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_HEIGHT respectively. + * ::CUDA_RESOURCE_DESC::res::pitch2D::pitchInBytes specifies the pitch between two rows in bytes and has to be aligned to + * ::CU_DEVICE_ATTRIBUTE_TEXTURE_PITCH_ALIGNMENT. Pitch cannot exceed ::CU_DEVICE_ATTRIBUTE_MAXIMUM_TEXTURE2D_LINEAR_PITCH. + * + * - ::flags must be set to zero. + * + * + * The ::CUDA_TEXTURE_DESC struct is defined as + * \code + typedef struct CUDA_TEXTURE_DESC_st { + CUaddress_mode addressMode[3]; + CUfilter_mode filterMode; + unsigned int flags; + unsigned int maxAnisotropy; + CUfilter_mode mipmapFilterMode; + float mipmapLevelBias; + float minMipmapLevelClamp; + float maxMipmapLevelClamp; + } CUDA_TEXTURE_DESC; + * \endcode + * where + * - ::CUDA_TEXTURE_DESC::addressMode specifies the addressing mode for each dimension of the texture data. ::CUaddress_mode is defined as: + * \code + typedef enum CUaddress_mode_enum { + CU_TR_ADDRESS_MODE_WRAP = 0, + CU_TR_ADDRESS_MODE_CLAMP = 1, + CU_TR_ADDRESS_MODE_MIRROR = 2, + CU_TR_ADDRESS_MODE_BORDER = 3 + } CUaddress_mode; + * \endcode + * This is ignored if ::CUDA_RESOURCE_DESC::resType is ::CU_RESOURCE_TYPE_LINEAR. Also, if the flag, ::CU_TRSF_NORMALIZED_COORDINATES + * is not set, the only supported address mode is ::CU_TR_ADDRESS_MODE_CLAMP. + * + * - ::CUDA_TEXTURE_DESC::filterMode specifies the filtering mode to be used when fetching from the texture. CUfilter_mode is defined as: + * \code + typedef enum CUfilter_mode_enum { + CU_TR_FILTER_MODE_POINT = 0, + CU_TR_FILTER_MODE_LINEAR = 1 + } CUfilter_mode; + * \endcode + * This is ignored if ::CUDA_RESOURCE_DESC::resType is ::CU_RESOURCE_TYPE_LINEAR. + * + * - ::CUDA_TEXTURE_DESC::flags can be any combination of the following: + * - ::CU_TRSF_READ_AS_INTEGER, which suppresses the default behavior of + * having the texture promote integer data to floating point data in the + * range [0, 1]. Note that texture with 32-bit integer format would not be + * promoted, regardless of whether or not this flag is specified. + * - ::CU_TRSF_NORMALIZED_COORDINATES, which suppresses the default behavior + * of having the texture coordinates range from [0, Dim) where Dim is the + * width or height of the CUDA array. Instead, the texture coordinates + * [0, 1.0) reference the entire breadth of the array dimension; Note that + * for CUDA mipmapped arrays, this flag has to be set. + * - ::CU_TRSF_DISABLE_TRILINEAR_OPTIMIZATION, which disables any trilinear + * filtering optimizations. Trilinear optimizations improve texture filtering + * performance by allowing bilinear filtering on textures in scenarios where + * it can closely approximate the expected results. + * - ::CU_TRSF_SEAMLESS_CUBEMAP, which enables seamless cube map filtering. + * This flag can only be specified if the underlying resource is a CUDA array + * or a CUDA mipmapped array that was created with the flag ::CUDA_ARRAY3D_CUBEMAP. + * When seamless cube map filtering is enabled, texture address modes specified + * by ::CUDA_TEXTURE_DESC::addressMode are ignored. Instead, if the ::CUDA_TEXTURE_DESC::filterMode + * is set to ::CU_TR_FILTER_MODE_POINT the address mode ::CU_TR_ADDRESS_MODE_CLAMP + * will be applied for all dimensions. If the ::CUDA_TEXTURE_DESC::filterMode is + * set to ::CU_TR_FILTER_MODE_LINEAR seamless cube map filtering will be performed + * when sampling along the cube face borders. + * + * - ::CUDA_TEXTURE_DESC::maxAnisotropy specifies the maximum anisotropy ratio to be used when doing anisotropic filtering. This value will be + * clamped to the range [1,16]. + * + * - ::CUDA_TEXTURE_DESC::mipmapFilterMode specifies the filter mode when the calculated mipmap level lies between two defined mipmap levels. + * + * - ::CUDA_TEXTURE_DESC::mipmapLevelBias specifies the offset to be applied to the calculated mipmap level. + * + * - ::CUDA_TEXTURE_DESC::minMipmapLevelClamp specifies the lower end of the mipmap level range to clamp access to. + * + * - ::CUDA_TEXTURE_DESC::maxMipmapLevelClamp specifies the upper end of the mipmap level range to clamp access to. + * + * + * The ::CUDA_RESOURCE_VIEW_DESC struct is defined as + * \code + typedef struct CUDA_RESOURCE_VIEW_DESC_st + { + CUresourceViewFormat format; + size_t width; + size_t height; + size_t depth; + unsigned int firstMipmapLevel; + unsigned int lastMipmapLevel; + unsigned int firstLayer; + unsigned int lastLayer; + } CUDA_RESOURCE_VIEW_DESC; + * \endcode + * where: + * - ::CUDA_RESOURCE_VIEW_DESC::format specifies how the data contained in the CUDA array or CUDA mipmapped array should + * be interpreted. Note that this can incur a change in size of the texture data. If the resource view format is a block + * compressed format, then the underlying CUDA array or CUDA mipmapped array has to have a base of format ::CU_AD_FORMAT_UNSIGNED_INT32. + * with 2 or 4 channels, depending on the block compressed format. For ex., BC1 and BC4 require the underlying CUDA array to have + * a format of ::CU_AD_FORMAT_UNSIGNED_INT32 with 2 channels. The other BC formats require the underlying resource to have the same base + * format but with 4 channels. + * + * - ::CUDA_RESOURCE_VIEW_DESC::width specifies the new width of the texture data. If the resource view format is a block + * compressed format, this value has to be 4 times the original width of the resource. For non block compressed formats, + * this value has to be equal to that of the original resource. + * + * - ::CUDA_RESOURCE_VIEW_DESC::height specifies the new height of the texture data. If the resource view format is a block + * compressed format, this value has to be 4 times the original height of the resource. For non block compressed formats, + * this value has to be equal to that of the original resource. + * + * - ::CUDA_RESOURCE_VIEW_DESC::depth specifies the new depth of the texture data. This value has to be equal to that of the + * original resource. + * + * - ::CUDA_RESOURCE_VIEW_DESC::firstMipmapLevel specifies the most detailed mipmap level. This will be the new mipmap level zero. + * For non-mipmapped resources, this value has to be zero.::CUDA_TEXTURE_DESC::minMipmapLevelClamp and ::CUDA_TEXTURE_DESC::maxMipmapLevelClamp + * will be relative to this value. For ex., if the firstMipmapLevel is set to 2, and a minMipmapLevelClamp of 1.2 is specified, + * then the actual minimum mipmap level clamp will be 3.2. + * + * - ::CUDA_RESOURCE_VIEW_DESC::lastMipmapLevel specifies the least detailed mipmap level. For non-mipmapped resources, this value + * has to be zero. + * + * - ::CUDA_RESOURCE_VIEW_DESC::firstLayer specifies the first layer index for layered textures. This will be the new layer zero. + * For non-layered resources, this value has to be zero. + * + * - ::CUDA_RESOURCE_VIEW_DESC::lastLayer specifies the last layer index for layered textures. For non-layered resources, + * this value has to be zero. + * + * + * \param pTexObject - Texture object to create + * \param pResDesc - Resource descriptor + * \param pTexDesc - Texture descriptor + * \param pResViewDesc - Resource view descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexObjectDestroy, + * ::cudaCreateTextureObject + */ +CUresult CUDAAPI cuTexObjectCreate(CUtexObject *pTexObject, const CUDA_RESOURCE_DESC *pResDesc, const CUDA_TEXTURE_DESC *pTexDesc, const CUDA_RESOURCE_VIEW_DESC *pResViewDesc); + +/** + * \brief Destroys a texture object + * + * Destroys the texture object specified by \p texObject. + * + * \param texObject - Texture object to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexObjectCreate, + * ::cudaDestroyTextureObject + */ +CUresult CUDAAPI cuTexObjectDestroy(CUtexObject texObject); + +/** + * \brief Returns a texture object's resource descriptor + * + * Returns the resource descriptor for the texture object specified by \p texObject. + * + * \param pResDesc - Resource descriptor + * \param texObject - Texture object + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexObjectCreate, + * ::cudaGetTextureObjectResourceDesc, + */ +CUresult CUDAAPI cuTexObjectGetResourceDesc(CUDA_RESOURCE_DESC *pResDesc, CUtexObject texObject); + +/** + * \brief Returns a texture object's texture descriptor + * + * Returns the texture descriptor for the texture object specified by \p texObject. + * + * \param pTexDesc - Texture descriptor + * \param texObject - Texture object + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexObjectCreate, + * ::cudaGetTextureObjectTextureDesc + */ +CUresult CUDAAPI cuTexObjectGetTextureDesc(CUDA_TEXTURE_DESC *pTexDesc, CUtexObject texObject); + +/** + * \brief Returns a texture object's resource view descriptor + * + * Returns the resource view descriptor for the texture object specified by \p texObject. + * If no resource view was set for \p texObject, the ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \param pResViewDesc - Resource view descriptor + * \param texObject - Texture object + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTexObjectCreate, + * ::cudaGetTextureObjectResourceViewDesc + */ +CUresult CUDAAPI cuTexObjectGetResourceViewDesc(CUDA_RESOURCE_VIEW_DESC *pResViewDesc, CUtexObject texObject); + +/** @} */ /* END CUDA_TEXOBJECT */ + +/** + * \defgroup CUDA_SURFOBJECT Surface Object Management + * + * ___MANBRIEF___ surface object management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the surface object management functions of the + * low-level CUDA driver application programming interface. The surface + * object API is only supported on devices of compute capability 3.0 or higher. + * + * @{ + */ + +/** + * \brief Creates a surface object + * + * Creates a surface object and returns it in \p pSurfObject. \p pResDesc describes + * the data to perform surface load/stores on. ::CUDA_RESOURCE_DESC::resType must be + * ::CU_RESOURCE_TYPE_ARRAY and ::CUDA_RESOURCE_DESC::res::array::hArray + * must be set to a valid CUDA array handle. ::CUDA_RESOURCE_DESC::flags must be set to zero. + * + * Surface objects are only supported on devices of compute capability 3.0 or higher. + * Additionally, a surface object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * \param pSurfObject - Surface object to create + * \param pResDesc - Resource descriptor + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuSurfObjectDestroy, + * ::cudaCreateSurfaceObject + */ +CUresult CUDAAPI cuSurfObjectCreate(CUsurfObject *pSurfObject, const CUDA_RESOURCE_DESC *pResDesc); + +/** + * \brief Destroys a surface object + * + * Destroys the surface object specified by \p surfObject. + * + * \param surfObject - Surface object to destroy + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuSurfObjectCreate, + * ::cudaDestroySurfaceObject + */ +CUresult CUDAAPI cuSurfObjectDestroy(CUsurfObject surfObject); + +/** + * \brief Returns a surface object's resource descriptor + * + * Returns the resource descriptor for the surface object specified by \p surfObject. + * + * \param pResDesc - Resource descriptor + * \param surfObject - Surface object + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuSurfObjectCreate, + * ::cudaGetSurfaceObjectResourceDesc + */ +CUresult CUDAAPI cuSurfObjectGetResourceDesc(CUDA_RESOURCE_DESC *pResDesc, CUsurfObject surfObject); + +/** @} */ /* END CUDA_SURFOBJECT */ + +/** + * \defgroup CUDA_TENSOR_MEMORY Tensor Map Object Managment + * + * ___MANBRIEF___ tensor map object management functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the tensor map object management functions of the + * low-level CUDA driver application programming interface. The tensor + * core API is only supported on devices of compute capability 9.0 or higher. + * + * @{ + */ + +/** + * \brief Create a tensor map descriptor object representing tiled memory region + * + * Creates a descriptor for Tensor Memory Access (TMA) object specified + * by the parameters describing a tiled region and returns it in \p tensorMap. + * + * Tensor map objects are only supported on devices of compute capability 9.0 or higher. + * Additionally, a tensor map object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * The parameters passed are bound to the following requirements: + * + * - \p tensorMap address must be aligned to 64 bytes. + * + * - \p tensorDataType has to be an enum from ::CUtensorMapDataType which is defined as: + * \code + typedef enum CUtensorMapDataType_enum { + CU_TENSOR_MAP_DATA_TYPE_UINT8 = 0, // 1 byte + CU_TENSOR_MAP_DATA_TYPE_UINT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_UINT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_INT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_UINT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_INT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_BFLOAT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT32_FTZ, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32_FTZ // 4 bytes + } CUtensorMapDataType; + * \endcode + * + * - \p tensorRank must be non-zero and less than or equal to the maximum supported dimensionality of 5. If \p interleave is not + * ::CU_TENSOR_MAP_INTERLEAVE_NONE, then \p tensorRank must additionally be greater than or equal to 3. + * + * - \p globalAddress, which specifies the starting address of the memory region described, must be 32 byte aligned when \p interleave is + * ::CU_TENSOR_MAP_INTERLEAVE_32B and 16 byte aligned otherwise. + * + * - \p globalDim array, which specifies tensor size of each of the \p tensorRank dimensions, must be non-zero and less than or + * equal to 2^32. + * + * - \p globalStrides array, which specifies tensor stride of each of the lower \p tensorRank - 1 dimensions in bytes, must be a + * multiple of 16 and less than 2^40. Additionally, the stride must be a multiple of 32 when \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_32B. + * Each following dimension specified includes previous dimension stride: + * \code + globalStrides[0] = globalDim[0] * elementSizeInBytes(tensorDataType) + padding[0]; + for (i = 1; i < tensorRank - 1; i++) + globalStrides[i] = globalStrides[i – 1] * (globalDim[i] + padding[i]); + assert(globalStrides[i] >= globalDim[i]); + * \endcode + * + * - \p boxDim array, which specifies number of elements to be traversed along each of the \p tensorRank dimensions, must be non-zero + * and less than or equal to 256. + * When \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_NONE, { \p boxDim[0] * elementSizeInBytes( \p tensorDataType ) } must be a multiple + * of 16 bytes. + * + * - \p elementStrides array, which specifies the iteration step along each of the \p tensorRank dimensions, must be non-zero and less + * than or equal to 8. Note that when \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_NONE, the first element of this array is ignored since + * TMA doesn’t support the stride for dimension zero. + * When all elements of \p elementStrides array is one, \p boxDim specifies the number of elements to load. However, if the \p elementStrides[i] + * is not equal to one, then TMA loads ceil( \p boxDim[i] / \p elementStrides[i]) number of elements along i-th dimension. To load N elements along + * i-th dimension, \p boxDim[i] must be set to N * \p elementStrides[i]. + * + * - \p interleave specifies the interleaved layout of type ::CUtensorMapInterleave, which is defined as: + * \code + typedef enum CUtensorMapInterleave_enum { + CU_TENSOR_MAP_INTERLEAVE_NONE = 0, + CU_TENSOR_MAP_INTERLEAVE_16B, + CU_TENSOR_MAP_INTERLEAVE_32B + } CUtensorMapInterleave; + * \endcode + * TMA supports interleaved layouts like NC/8HWC8 where C8 utilizes 16 bytes in memory assuming 2 byte per channel or NC/16HWC16 where C16 + * uses 32 bytes. + * When \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_NONE and \p swizzle is not ::CU_TENSOR_MAP_SWIZZLE_NONE, the bounding box inner dimension + * (computed as \p boxDim[0] multiplied by element size derived from \p tensorDataType) must be less than or equal to the swizzle size. + * - CU_TENSOR_MAP_SWIZZLE_32B implies the bounding box inner dimension will be <= 32. + * - CU_TENSOR_MAP_SWIZZLE_64B implies the bounding box inner dimension will be <= 64. + * - CU_TENSOR_MAP_SWIZZLE_128B implies the bounding box inner dimension will be <= 128. + * + * - \p swizzle, which specifies the shared memory bank swizzling pattern, has to be of type ::CUtensorMapSwizzle which is defined as: + * \code + typedef enum CUtensorMapSwizzle_enum { + CU_TENSOR_MAP_SWIZZLE_NONE = 0, + CU_TENSOR_MAP_SWIZZLE_32B, + CU_TENSOR_MAP_SWIZZLE_64B, + CU_TENSOR_MAP_SWIZZLE_128B + } CUtensorMapSwizzle; + * \endcode + * Data are organized in a specific order in global memory; however, this may not match the order in which the application accesses data + * in shared memory. This difference in data organization may cause bank conflicts when shared memory is accessed. In order to avoid this + * problem, data can be loaded to shared memory with shuffling across shared memory banks. + * When \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_32B, \p swizzle must be ::CU_TENSOR_MAP_SWIZZLE_32B. + * Other interleave modes can have any swizzling pattern. + * + * - \p l2Promotion specifies L2 fetch size which indicates the byte granurality at which L2 requests is filled from DRAM. It must be of + * type ::CUtensorMapL2promotion, which is defined as: + * \code + typedef enum CUtensorMapL2promotion_enum { + CU_TENSOR_MAP_L2_PROMOTION_NONE = 0, + CU_TENSOR_MAP_L2_PROMOTION_L2_64B, + CU_TENSOR_MAP_L2_PROMOTION_L2_128B, + CU_TENSOR_MAP_L2_PROMOTION_L2_256B + } CUtensorMapL2promotion; + * \endcode + * + * - \p oobFill, which indicates whether zero or a special NaN constant should be used to fill out-of-bound elements, must be of type + * ::CUtensorMapFloatOOBfill which is defined as: + * \code + typedef enum CUtensorMapFloatOOBfill_enum { + CU_TENSOR_MAP_FLOAT_OOB_FILL_NONE = 0, + CU_TENSOR_MAP_FLOAT_OOB_FILL_NAN_REQUEST_ZERO_FMA + } CUtensorMapFloatOOBfill; + * \endcode + * Note that ::CU_TENSOR_MAP_FLOAT_OOB_FILL_NAN_REQUEST_ZERO_FMA can only be used when \p tensorDataType represents a floating-point data type. + * + * \param tensorMap - Tensor map object to create + * \param tensorDataType - Tensor data type + * \param tensorRank - Dimensionality of tensor + * \param globalAddress - Starting address of memory region described by tensor + * \param globalDim - Array containing tensor size (number of elements) along each of the \p tensorRank dimensions + * \param globalStrides - Array containing stride size (in bytes) along each of the \p tensorRank - 1 dimensions + * \param boxDim - Array containing traversal box size (number of elments) along each of the \p tensorRank dimensions. Specifies how many elements to be traversed along each tensor dimension. + * \param elementStrides - Array containing traversal stride in each of the \p tensorRank dimensions + * \param interleave - Type of interleaved layout the tensor addresses + * \param swizzle - Bank swizzling pattern inside shared memory + * \param l2Promotion - L2 promotion size + * \param oobFill - Indicate whether zero or special NaN constant must be used to fill out-of-bound elements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTensorMapEncodeIm2col, + * ::cuTensorMapReplaceAddress + */ +CUresult CUDAAPI cuTensorMapEncodeTiled(CUtensorMap *tensorMap, CUtensorMapDataType tensorDataType, cuuint32_t tensorRank, void *globalAddress, const cuuint64_t *globalDim, const cuuint64_t *globalStrides, const cuuint32_t *boxDim, const cuuint32_t *elementStrides, CUtensorMapInterleave interleave, CUtensorMapSwizzle swizzle, CUtensorMapL2promotion l2Promotion, CUtensorMapFloatOOBfill oobFill); + + +/** + * \brief Create a tensor map descriptor object representing im2col memory region + * + * Creates a descriptor for Tensor Memory Access (TMA) object specified + * by the parameters describing a im2col memory layout and returns it in \p tensorMap. + * + * Tensor map objects are only supported on devices of compute capability 9.0 or higher. + * Additionally, a tensor map object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * The parameters passed are bound to the following requirements: + * + * - \p tensorMap address must be aligned to 64 bytes. + * + * - \p tensorDataType has to be an enum from ::CUtensorMapDataType which is defined as: + * \code + typedef enum CUtensorMapDataType_enum { + CU_TENSOR_MAP_DATA_TYPE_UINT8 = 0, // 1 byte + CU_TENSOR_MAP_DATA_TYPE_UINT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_UINT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_INT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_UINT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_INT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT64, // 8 bytes + CU_TENSOR_MAP_DATA_TYPE_BFLOAT16, // 2 bytes + CU_TENSOR_MAP_DATA_TYPE_FLOAT32_FTZ, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32, // 4 bytes + CU_TENSOR_MAP_DATA_TYPE_TFLOAT32_FTZ // 4 bytes + } CUtensorMapDataType; + * \endcode + * + * - \p tensorRank, which specifies the number of tensor dimensions, must be 3, 4, or 5. + * + * - \p globalAddress, which specifies the starting address of the memory region described, must be 32 byte aligned when \p interleave is + * ::CU_TENSOR_MAP_INTERLEAVE_32B and 16 byte aligned otherwise. + * + * - \p globalDim array, which specifies tensor size of each of the \p tensorRank dimensions, must be non-zero and less than or + * equal to 2^32. + * + * - \p globalStrides array, which specifies tensor stride of each of the lower \p tensorRank - 1 dimensions in bytes, must be a + * multiple of 16 and less than 2^40. Additionally, the stride must be a multiple of 32 when \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_32B. + * Each following dimension specified includes previous dimension stride: + * \code + globalStrides[0] = globalDim[0] * elementSizeInBytes(tensorDataType) + padding[0]; + for (i = 1; i < tensorRank - 1; i++) + globalStrides[i] = globalStrides[i – 1] * (globalDim[i] + padding[i]); + assert(globalStrides[i] >= globalDim[i]); + * \endcode + * + * - \p pixelBoxLowerCorner array specifies the coordinate offsets {D, H, W} of the bounding box from top/left/front corner. The number of + * offsets and their precision depend on the tensor dimensionality: + * - When \p tensorRank is 3, one signed offset within range [-32768, 32767] is supported. + * - When \p tensorRank is 4, two signed offsets each within range [-128, 127] are supported. + * - When \p tensorRank is 5, three offsets each within range [-16, 15] are supported. + * + * - \p pixelBoxUpperCorner array specifies the coordinate offsets {D, H, W} of the bounding box from bottom/right/back corner. The number of + * offsets and their precision depend on the tensor dimensionality: + * - When \p tensorRank is 3, one signed offset within range [-32768, 32767] is supported. + * - When \p tensorRank is 4, two signed offsets each within range [-128, 127] are supported. + * - When \p tensorRank is 5, three offsets each within range [-16, 15] are supported. + * The bounding box specified by \p pixelBoxLowerCorner and \p pixelBoxUpperCorner must have non-zero area. + * + * - \p channelsPerPixel, which specifies the number of elements which must be accessed along C dimension, must be less than or equal to 256. + * + * - \p pixelsPerColumn, which specifies the number of elements that must be accessed along the {N, D, H, W} dimensions, must be less than or + * equal to 1024. + * + * - \p elementStrides array, which specifies the iteration step along each of the \p tensorRank dimensions, must be non-zero and less + * than or equal to 8. Note that when \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_NONE, the first element of this array is ignored since + * TMA doesn’t support the stride for dimension zero. + * When all elements of the \p elementStrides array are one, \p boxDim specifies the number of elements to load. However, if \p elementStrides[i] + * is not equal to one for some \p i, then TMA loads ceil( \p boxDim[i] / \p elementStrides[i]) number of elements along i-th dimension. + * To load N elements along i-th dimension, \p boxDim[i] must be set to N * \p elementStrides[i]. + * + * - \p interleave specifies the interleaved layout of type ::CUtensorMapInterleave, which is defined as: + * \code + typedef enum CUtensorMapInterleave_enum { + CU_TENSOR_MAP_INTERLEAVE_NONE = 0, + CU_TENSOR_MAP_INTERLEAVE_16B, + CU_TENSOR_MAP_INTERLEAVE_32B + } CUtensorMapInterleave; + * \endcode + * TMA supports interleaved layouts like NC/8HWC8 where C8 utilizes 16 bytes in memory assuming 2 byte per channel or NC/16HWC16 where C16 + * uses 32 bytes. + * When \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_NONE and \p swizzle is not ::CU_TENSOR_MAP_SWIZZLE_NONE, the bounding box inner dimension + * (computed as \p boxDim[0] multiplied by element size derived from \p tensorDataType) must be less than or equal to the swizzle size. + * - CU_TENSOR_MAP_SWIZZLE_32B implies the bounding box inner dimension will be <= 32. + * - CU_TENSOR_MAP_SWIZZLE_64B implies the bounding box inner dimension will be <= 64. + * - CU_TENSOR_MAP_SWIZZLE_128B implies the bounding box inner dimension will be <= 128. + * + * - \p swizzle, which specifies the shared memory bank swizzling pattern, has to be of type ::CUtensorMapSwizzle which is defined as: + * \code + typedef enum CUtensorMapSwizzle_enum { + CU_TENSOR_MAP_SWIZZLE_NONE = 0, + CU_TENSOR_MAP_SWIZZLE_32B, + CU_TENSOR_MAP_SWIZZLE_64B, + CU_TENSOR_MAP_SWIZZLE_128B + } CUtensorMapSwizzle; + * \endcode + * Data are organized in a specific order in global memory; however, this may not match the order in which the application accesses data + * in shared memory. This difference in data organization may cause bank conflicts when shared memory is accessed. In order to avoid this + * problem, data can be loaded to shared memory with shuffling across shared memory banks. + * When \p interleave is ::CU_TENSOR_MAP_INTERLEAVE_32B, \p swizzle must be ::CU_TENSOR_MAP_SWIZZLE_32B. + * Other interleave modes can have any swizzling pattern. + * + * - \p l2Promotion specifies L2 fetch size which indicates the byte granularity at which L2 requests are filled from DRAM. It must be of + * type ::CUtensorMapL2promotion, which is defined as: + * \code + typedef enum CUtensorMapL2promotion_enum { + CU_TENSOR_MAP_L2_PROMOTION_NONE = 0, + CU_TENSOR_MAP_L2_PROMOTION_L2_64B, + CU_TENSOR_MAP_L2_PROMOTION_L2_128B, + CU_TENSOR_MAP_L2_PROMOTION_L2_256B + } CUtensorMapL2promotion; + * \endcode + * + * - \p oobFill, which indicates whether zero or a special NaN constant should be used to fill out-of-bound elements, must be of type + * ::CUtensorMapFloatOOBfill which is defined as: + * \code + typedef enum CUtensorMapFloatOOBfill_enum { + CU_TENSOR_MAP_FLOAT_OOB_FILL_NONE = 0, + CU_TENSOR_MAP_FLOAT_OOB_FILL_NAN_REQUEST_ZERO_FMA + } CUtensorMapFloatOOBfill; + * \endcode + * Note that ::CU_TENSOR_MAP_FLOAT_OOB_FILL_NAN_REQUEST_ZERO_FMA can only be used when \p tensorDataType represents a floating-point data type. + * + * \param tensorMap - Tensor map object to create + * \param tensorDataType - Tensor data type + * \param tensorRank - Dimensionality of tensor; must be at least 3 + * \param globalAddress - Starting address of memory region described by tensor + * \param globalDim - Array containing tensor size (number of elements) along each of the \p tensorRank dimensions + * \param globalStrides - Array containing stride size (in bytes) along each of the \p tensorRank - 1 dimensions + * \param pixelBoxLowerCorner - Array containing DHW dimensions of lower box corner + * \param pixelBoxUpperCorner - Array containing DHW dimensions of upper box corner + * \param channelsPerPixel - Number of channels per pixel + * \param pixelsPerColumn - Number of pixels per column + * \param elementStrides - Array containing traversal stride in each of the \p tensorRank dimensions + * \param interleave - Type of interleaved layout the tensor addresses + * \param swizzle - Bank swizzling pattern inside shared memory + * \param l2Promotion - L2 promotion size + * \param oobFill - Indicate whether zero or special NaN constant will be used to fill out-of-bound elements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTensorMapEncodeTiled, + * ::cuTensorMapReplaceAddress + */ +CUresult CUDAAPI cuTensorMapEncodeIm2col(CUtensorMap *tensorMap, CUtensorMapDataType tensorDataType, cuuint32_t tensorRank, void *globalAddress, const cuuint64_t *globalDim, const cuuint64_t *globalStrides, const int *pixelBoxLowerCorner, const int *pixelBoxUpperCorner, cuuint32_t channelsPerPixel, cuuint32_t pixelsPerColumn, const cuuint32_t *elementStrides, CUtensorMapInterleave interleave, CUtensorMapSwizzle swizzle, CUtensorMapL2promotion l2Promotion, CUtensorMapFloatOOBfill oobFill); + +/** + * \brief Modify an existing tensor map descriptor with an updated global address + * + * Modifies the descriptor for Tensor Memory Access (TMA) object passed in \p tensorMap with + * an updated \p globalAddress. + * + * Tensor map objects are only supported on devices of compute capability 9.0 or higher. + * Additionally, a tensor map object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * \param tensorMap - Tensor map object to modify + * \param globalAddress - Starting address of memory region described by tensor, must follow previous alignment requirements + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuTensorMapEncodeTiled, + * ::cuTensorMapEncodeIm2col + */ +CUresult CUDAAPI cuTensorMapReplaceAddress(CUtensorMap *tensorMap, void *globalAddress); + +/** @} */ +/* END CUDA_TENSOR_MEMORY */ + +/** + * \defgroup CUDA_PEER_ACCESS Peer Context Memory Access + * + * ___MANBRIEF___ direct peer context memory access functions of the low-level + * CUDA driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the direct peer context memory access functions + * of the low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Queries if a device may directly access a peer device's memory. + * + * Returns in \p *canAccessPeer a value of 1 if contexts on \p dev are capable of + * directly accessing memory from contexts on \p peerDev and 0 otherwise. + * If direct access of \p peerDev from \p dev is possible, then access may be + * enabled on two specific contexts by calling ::cuCtxEnablePeerAccess(). + * + * \param canAccessPeer - Returned access capability + * \param dev - Device from which allocations on \p peerDev are to + * be directly accessed. + * \param peerDev - Device on which the allocations to be directly accessed + * by \p dev reside. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE + * \notefnerr + * + * \sa + * ::cuCtxEnablePeerAccess, + * ::cuCtxDisablePeerAccess, + * ::cudaDeviceCanAccessPeer + */ +CUresult CUDAAPI cuDeviceCanAccessPeer(int *canAccessPeer, CUdevice dev, CUdevice peerDev); + +/** + * \brief Enables direct access to memory allocations in a peer context. + * + * If both the current context and \p peerContext are on devices which support unified + * addressing (as may be queried using ::CU_DEVICE_ATTRIBUTE_UNIFIED_ADDRESSING) and same + * major compute capability, then on success all allocations from \p peerContext will + * immediately be accessible by the current context. See \ref CUDA_UNIFIED for additional + * details. + * + * Note that access granted by this call is unidirectional and that in order to access + * memory from the current context in \p peerContext, a separate symmetric call + * to ::cuCtxEnablePeerAccess() is required. + * + * Note that there are both device-wide and system-wide limitations per system + * configuration, as noted in the CUDA Programming Guide under the section + * "Peer-to-Peer Memory Access". + * + * Returns ::CUDA_ERROR_PEER_ACCESS_UNSUPPORTED if ::cuDeviceCanAccessPeer() indicates + * that the ::CUdevice of the current context cannot directly access memory + * from the ::CUdevice of \p peerContext. + * + * Returns ::CUDA_ERROR_PEER_ACCESS_ALREADY_ENABLED if direct access of + * \p peerContext from the current context has already been enabled. + * + * Returns ::CUDA_ERROR_TOO_MANY_PEERS if direct peer access is not possible + * because hardware resources required for peer access have been exhausted. + * + * Returns ::CUDA_ERROR_INVALID_CONTEXT if there is no current context, \p peerContext + * is not a valid context, or if the current context is \p peerContext. + * + * Returns ::CUDA_ERROR_INVALID_VALUE if \p Flags is not 0. + * + * \param peerContext - Peer context to enable direct access to from the current context + * \param Flags - Reserved for future use and must be set to 0 + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_PEER_ACCESS_ALREADY_ENABLED, + * ::CUDA_ERROR_TOO_MANY_PEERS, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_PEER_ACCESS_UNSUPPORTED, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuDeviceCanAccessPeer, + * ::cuCtxDisablePeerAccess, + * ::cudaDeviceEnablePeerAccess + */ +CUresult CUDAAPI cuCtxEnablePeerAccess(CUcontext peerContext, unsigned int Flags); + +/** + * \brief Disables direct access to memory allocations in a peer context and + * unregisters any registered allocations. + * + Returns ::CUDA_ERROR_PEER_ACCESS_NOT_ENABLED if direct peer access has + * not yet been enabled from \p peerContext to the current context. + * + * Returns ::CUDA_ERROR_INVALID_CONTEXT if there is no current context, or if + * \p peerContext is not a valid context. + * + * \param peerContext - Peer context to disable direct access to + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_PEER_ACCESS_NOT_ENABLED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * \notefnerr + * + * \sa + * ::cuDeviceCanAccessPeer, + * ::cuCtxEnablePeerAccess, + * ::cudaDeviceDisablePeerAccess + */ +CUresult CUDAAPI cuCtxDisablePeerAccess(CUcontext peerContext); + +/** + * \brief Queries attributes of the link between two devices. + * + * Returns in \p *value the value of the requested attribute \p attrib of the + * link between \p srcDevice and \p dstDevice. The supported attributes are: + * - ::CU_DEVICE_P2P_ATTRIBUTE_PERFORMANCE_RANK: A relative value indicating the + * performance of the link between two devices. + * - ::CU_DEVICE_P2P_ATTRIBUTE_ACCESS_SUPPORTED P2P: 1 if P2P Access is enable. + * - ::CU_DEVICE_P2P_ATTRIBUTE_NATIVE_ATOMIC_SUPPORTED: 1 if Atomic operations over + * the link are supported. + * - ::CU_DEVICE_P2P_ATTRIBUTE_CUDA_ARRAY_ACCESS_SUPPORTED: 1 if cudaArray can + * be accessed over the link. + * + * Returns ::CUDA_ERROR_INVALID_DEVICE if \p srcDevice or \p dstDevice are not valid + * or if they represent the same device. + * + * Returns ::CUDA_ERROR_INVALID_VALUE if \p attrib is not valid or if \p value is + * a null pointer. + * + * \param value - Returned value of the requested attribute + * \param attrib - The requested attribute of the link between \p srcDevice and \p dstDevice. + * \param srcDevice - The source device of the target link. + * \param dstDevice - The destination device of the target link. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa + * ::cuCtxEnablePeerAccess, + * ::cuCtxDisablePeerAccess, + * ::cuDeviceCanAccessPeer, + * ::cudaDeviceGetP2PAttribute + */ +CUresult CUDAAPI cuDeviceGetP2PAttribute(int* value, CUdevice_P2PAttribute attrib, CUdevice srcDevice, CUdevice dstDevice); + +/** @} */ /* END CUDA_PEER_ACCESS */ + +/** + * \defgroup CUDA_GRAPHICS Graphics Interoperability + * + * ___MANBRIEF___ graphics interoperability functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the graphics interoperability functions of the + * low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Unregisters a graphics resource for access by CUDA + * + * Unregisters the graphics resource \p resource so it is not accessible by + * CUDA unless registered again. + * + * If \p resource is invalid then ::CUDA_ERROR_INVALID_HANDLE is + * returned. + * + * \param resource - Resource to unregister + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa + * ::cuGraphicsD3D9RegisterResource, + * ::cuGraphicsD3D10RegisterResource, + * ::cuGraphicsD3D11RegisterResource, + * ::cuGraphicsGLRegisterBuffer, + * ::cuGraphicsGLRegisterImage, + * ::cudaGraphicsUnregisterResource + */ +CUresult CUDAAPI cuGraphicsUnregisterResource(CUgraphicsResource resource); + +/** + * \brief Get an array through which to access a subresource of a mapped graphics resource. + * + * Returns in \p *pArray an array through which the subresource of the mapped + * graphics resource \p resource which corresponds to array index \p arrayIndex + * and mipmap level \p mipLevel may be accessed. The value set in \p *pArray may + * change every time that \p resource is mapped. + * + * If \p resource is not a texture then it cannot be accessed via an array and + * ::CUDA_ERROR_NOT_MAPPED_AS_ARRAY is returned. + * If \p arrayIndex is not a valid array index for \p resource then + * ::CUDA_ERROR_INVALID_VALUE is returned. + * If \p mipLevel is not a valid mipmap level for \p resource then + * ::CUDA_ERROR_INVALID_VALUE is returned. + * If \p resource is not mapped then ::CUDA_ERROR_NOT_MAPPED is returned. + * + * \param pArray - Returned array through which a subresource of \p resource may be accessed + * \param resource - Mapped resource to access + * \param arrayIndex - Array index for array textures or cubemap face + * index as defined by ::CUarray_cubemap_face for + * cubemap textures for the subresource to access + * \param mipLevel - Mipmap level for the subresource to access + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_MAPPED, + * ::CUDA_ERROR_NOT_MAPPED_AS_ARRAY + * \notefnerr + * + * \sa + * ::cuGraphicsResourceGetMappedPointer, + * ::cudaGraphicsSubResourceGetMappedArray + */ +CUresult CUDAAPI cuGraphicsSubResourceGetMappedArray(CUarray *pArray, CUgraphicsResource resource, unsigned int arrayIndex, unsigned int mipLevel); + +/** + * \brief Get a mipmapped array through which to access a mapped graphics resource. + * + * Returns in \p *pMipmappedArray a mipmapped array through which the mapped graphics + * resource \p resource. The value set in \p *pMipmappedArray may change every time + * that \p resource is mapped. + * + * If \p resource is not a texture then it cannot be accessed via a mipmapped array and + * ::CUDA_ERROR_NOT_MAPPED_AS_ARRAY is returned. + * If \p resource is not mapped then ::CUDA_ERROR_NOT_MAPPED is returned. + * + * \param pMipmappedArray - Returned mipmapped array through which \p resource may be accessed + * \param resource - Mapped resource to access + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_MAPPED, + * ::CUDA_ERROR_NOT_MAPPED_AS_ARRAY + * \notefnerr + * + * \sa + * ::cuGraphicsResourceGetMappedPointer, + * ::cudaGraphicsResourceGetMappedMipmappedArray + */ +CUresult CUDAAPI cuGraphicsResourceGetMappedMipmappedArray(CUmipmappedArray *pMipmappedArray, CUgraphicsResource resource); + +/** + * \brief Get a device pointer through which to access a mapped graphics resource. + * + * Returns in \p *pDevPtr a pointer through which the mapped graphics resource + * \p resource may be accessed. + * Returns in \p pSize the size of the memory in bytes which may be accessed from that pointer. + * The value set in \p pPointer may change every time that \p resource is mapped. + * + * If \p resource is not a buffer then it cannot be accessed via a pointer and + * ::CUDA_ERROR_NOT_MAPPED_AS_POINTER is returned. + * If \p resource is not mapped then ::CUDA_ERROR_NOT_MAPPED is returned. + * * + * \param pDevPtr - Returned pointer through which \p resource may be accessed + * \param pSize - Returned size of the buffer accessible starting at \p *pPointer + * \param resource - Mapped resource to access + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_MAPPED, + * ::CUDA_ERROR_NOT_MAPPED_AS_POINTER + * \notefnerr + * + * \sa + * ::cuGraphicsMapResources, + * ::cuGraphicsSubResourceGetMappedArray, + * ::cudaGraphicsResourceGetMappedPointer + */ +CUresult CUDAAPI cuGraphicsResourceGetMappedPointer(CUdeviceptr *pDevPtr, size_t *pSize, CUgraphicsResource resource); + +/** + * \brief Set usage flags for mapping a graphics resource + * + * Set \p flags for mapping the graphics resource \p resource. + * + * Changes to \p flags will take effect the next time \p resource is mapped. + * The \p flags argument may be any of the following: + + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA kernels. This is the default value. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_READONLY: Specifies that CUDA kernels which + * access this resource will not write to this resource. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_WRITEDISCARD: Specifies that CUDA kernels + * which access this resource will not read from this resource and will + * write over the entire contents of the resource, so none of the data + * previously stored in the resource will be preserved. + * + * If \p resource is presently mapped for access by CUDA then + * ::CUDA_ERROR_ALREADY_MAPPED is returned. + * If \p flags is not one of the above values then ::CUDA_ERROR_INVALID_VALUE is returned. + * + * \param resource - Registered resource to set flags for + * \param flags - Parameters for resource mapping + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED + * \notefnerr + * + * \sa + * ::cuGraphicsMapResources, + * ::cudaGraphicsResourceSetMapFlags + */ +CUresult CUDAAPI cuGraphicsResourceSetMapFlags(CUgraphicsResource resource, unsigned int flags); + +/** + * \brief Map graphics resources for access by CUDA + * + * Maps the \p count graphics resources in \p resources for access by CUDA. + * + * The resources in \p resources may be accessed by CUDA until they + * are unmapped. The graphics API from which \p resources were registered + * should not access any resources while they are mapped by CUDA. If an + * application does so, the results are undefined. + * + * This function provides the synchronization guarantee that any graphics calls + * issued before ::cuGraphicsMapResources() will complete before any subsequent CUDA + * work issued in \p stream begins. + * + * If \p resources includes any duplicate entries then ::CUDA_ERROR_INVALID_HANDLE is returned. + * If any of \p resources are presently mapped for access by CUDA then ::CUDA_ERROR_ALREADY_MAPPED is returned. + * + * \param count - Number of resources to map + * \param resources - Resources to map for CUDA usage + * \param hStream - Stream with which to synchronize + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_UNKNOWN + * \note_null_stream + * \notefnerr + * + * \sa + * ::cuGraphicsResourceGetMappedPointer, + * ::cuGraphicsSubResourceGetMappedArray, + * ::cuGraphicsUnmapResources, + * ::cudaGraphicsMapResources + */ +CUresult CUDAAPI cuGraphicsMapResources(unsigned int count, CUgraphicsResource *resources, CUstream hStream); + +/** + * \brief Unmap graphics resources. + * + * Unmaps the \p count graphics resources in \p resources. + * + * Once unmapped, the resources in \p resources may not be accessed by CUDA + * until they are mapped again. + * + * This function provides the synchronization guarantee that any CUDA work issued + * in \p stream before ::cuGraphicsUnmapResources() will complete before any + * subsequently issued graphics work begins. + * + * + * If \p resources includes any duplicate entries then ::CUDA_ERROR_INVALID_HANDLE is returned. + * If any of \p resources are not presently mapped for access by CUDA then ::CUDA_ERROR_NOT_MAPPED is returned. + * + * \param count - Number of resources to unmap + * \param resources - Resources to unmap + * \param hStream - Stream with which to synchronize + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_MAPPED, + * ::CUDA_ERROR_UNKNOWN + * \note_null_stream + * \notefnerr + * + * \sa + * ::cuGraphicsMapResources, + * ::cudaGraphicsUnmapResources + */ +CUresult CUDAAPI cuGraphicsUnmapResources(unsigned int count, CUgraphicsResource *resources, CUstream hStream); + +/** @} */ /* END CUDA_GRAPHICS */ + +/** + * \defgroup CUDA_DRIVER_ENTRY_POINT Driver Entry Point Access + * + * ___MANBRIEF___ driver entry point access functions of the low-level CUDA driver API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the driver entry point access functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * \brief Returns the requested driver API function pointer + * + * Returns in \p **pfn the address of the CUDA driver function for the requested + * CUDA version and flags. + * + * The CUDA version is specified as (1000 * major + 10 * minor), so CUDA 11.2 + * should be specified as 11020. For a requested driver symbol, if the specified + * CUDA version is greater than or equal to the CUDA version in which the driver symbol + * was introduced, this API will return the function pointer to the corresponding + * versioned function. + * + * The pointer returned by the API should be cast to a function pointer matching the + * requested driver function's definition in the API header file. The function pointer + * typedef can be picked up from the corresponding typedefs header file. For example, + * cudaTypedefs.h consists of function pointer typedefs for driver APIs defined in cuda.h. + * + * The API will return ::CUDA_SUCCESS and set the returned \p pfn to NULL if the + * requested driver function is not supported on the platform, no ABI + * compatible driver function exists for the specified \p cudaVersion or if the + * driver symbol is invalid. + * + * It will also set the optional \p symbolStatus to one of the values in + * ::CUdriverProcAddressQueryResult with the following meanings: + * - ::CU_GET_PROC_ADDRESS_SUCCESS - The requested symbol was succesfully found based + * on input arguments and \p pfn is valid + * - ::CU_GET_PROC_ADDRESS_SYMBOL_NOT_FOUND - The requested symbol was not found + * - ::CU_GET_PROC_ADDRESS_VERSION_NOT_SUFFICIENT - The requested symbol was found but is + * not supported by cudaVersion specified + * + * The requested flags can be: + * - ::CU_GET_PROC_ADDRESS_DEFAULT: This is the default mode. This is equivalent to + * ::CU_GET_PROC_ADDRESS_PER_THREAD_DEFAULT_STREAM if the code is compiled with + * --default-stream per-thread compilation flag or the macro CUDA_API_PER_THREAD_DEFAULT_STREAM + * is defined; ::CU_GET_PROC_ADDRESS_LEGACY_STREAM otherwise. + * - ::CU_GET_PROC_ADDRESS_LEGACY_STREAM: This will enable the search for all driver symbols + * that match the requested driver symbol name except the corresponding per-thread versions. + * - ::CU_GET_PROC_ADDRESS_PER_THREAD_DEFAULT_STREAM: This will enable the search for all + * driver symbols that match the requested driver symbol name including the per-thread + * versions. If a per-thread version is not found, the API will return the legacy version + * of the driver function. + * + * \param symbol - The base name of the driver API function to look for. As an example, + * for the driver API ::cuMemAlloc_v2, \p symbol would be cuMemAlloc and + * \p cudaVersion would be the ABI compatible CUDA version for the _v2 variant. + * \param pfn - Location to return the function pointer to the requested driver function + * \param cudaVersion - The CUDA version to look for the requested driver symbol + * \param flags - Flags to specify search options. + * \param symbolStatus - Optional location to store the status of the search for + * \p symbol based on \p cudaVersion. See ::CUdriverProcAddressQueryResult + * for possible values. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_version_mixing + * + * \sa + * ::cudaGetDriverEntryPoint + */ +CUresult CUDAAPI cuGetProcAddress(const char *symbol, void **pfn, int cudaVersion, cuuint64_t flags, CUdriverProcAddressQueryResult *symbolStatus); + +/** @} */ /* END CUDA_DRIVER_ENTRY_POINT */ + +/** + * \defgroup CUDA_COREDUMP Coredump Attributes Control API + * + * ___MANBRIEF___ coredump attribute control functions for the low-level CUDA API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the coredump attribute control functions of the low-level CUDA + * driver application programming interface. + * + * @{ + */ + +/** + * Flags for choosing a coredump attribute to get/set + */ +typedef enum CUcoredumpSettings_enum { + CU_COREDUMP_ENABLE_ON_EXCEPTION = 1, + CU_COREDUMP_TRIGGER_HOST, + CU_COREDUMP_LIGHTWEIGHT, + CU_COREDUMP_ENABLE_USER_TRIGGER, + CU_COREDUMP_FILE, + CU_COREDUMP_PIPE, + CU_COREDUMP_MAX +} CUcoredumpSettings; + +/** + * \brief Allows caller to fetch a coredump attribute value for the current context + * + * Returns in \p *value the requested value specified by \p attrib. It is up to the caller + * to ensure that the data type and size of \p *value matches the request. + * + * If the caller calls this function with \p *value equal to NULL, the size of the memory + * region (in bytes) expected for \p attrib will be placed in \p size. + * + * The supported attributes are: + * - ::CU_COREDUMP_ENABLE_ON_EXCEPTION: Bool where ::true means that GPU exceptions from + * this context will create a coredump at the location specified by ::CU_COREDUMP_FILE. + * The default value is ::false unless set to ::true globally or locally, or the + * CU_CTX_USER_COREDUMP_ENABLE flag was set during context creation. + * - ::CU_COREDUMP_TRIGGER_HOST: Bool where ::true means that the host CPU will + * also create a coredump. The default value is ::true unless set to ::false globally or + * or locally. + * - ::CU_COREDUMP_LIGHTWEIGHT: Bool where ::true means that any resulting coredumps + * will not have a dump of GPU memory or non-reloc ELF images. The default value is + * ::false unless set to ::true globally or locally. + * - ::CU_COREDUMP_ENABLE_USER_TRIGGER: Bool where ::true means that a coredump can be + * created by writing to the system pipe specified by ::CU_COREDUMP_PIPE. The default + * value is ::false unless set to ::true globally or locally. + * - ::CU_COREDUMP_FILE: String of up to 1023 characters that defines the location where + * any coredumps generated by this context will be written. The default value is + * ::core.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA applications and ::PID is the process ID of the CUDA application. + * - ::CU_COREDUMP_PIPE: String of up to 1023 characters that defines the name of the pipe + * that will be monitored if user-triggered coredumps are enabled. The default value is + * ::corepipe.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA application and ::PID is the process ID of the CUDA application. + * + * \param attrib - The enum defining which value to fetch. + * \param value - void* containing the requested data. + * \param size - The size of the memory region \p value points to. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * + * \sa + * ::cuCoredumpGetAttributeGlobal, + * ::cuCoredumpSetAttribute, + * ::cuCoredumpSetAttributeGlobal + */ +CUresult CUDAAPI cuCoredumpGetAttribute(CUcoredumpSettings attrib, void* value, size_t *size); + +/** + * \brief Allows caller to fetch a coredump attribute value for the entire application + * + * Returns in \p *value the requested value specified by \p attrib. It is up to the caller + * to ensure that the data type and size of \p *value matches the request. + * + * If the caller calls this function with \p *value equal to NULL, the size of the memory + * region (in bytes) expected for \p attrib will be placed in \p size. + * + * The supported attributes are: + * - ::CU_COREDUMP_ENABLE_ON_EXCEPTION: Bool where ::true means that GPU exceptions from + * this context will create a coredump at the location specified by ::CU_COREDUMP_FILE. + * The default value is ::false. + * - ::CU_COREDUMP_TRIGGER_HOST: Bool where ::true means that the host CPU will + * also create a coredump. The default value is ::true. + * - ::CU_COREDUMP_LIGHTWEIGHT: Bool where ::true means that any resulting coredumps + * will not have a dump of GPU memory or non-reloc ELF images. The default value is + * ::false. + * - ::CU_COREDUMP_ENABLE_USER_TRIGGER: Bool where ::true means that a coredump can be + * created by writing to the system pipe specified by ::CU_COREDUMP_PIPE. The default + * value is ::false. + * - ::CU_COREDUMP_FILE: String of up to 1023 characters that defines the location where + * any coredumps generated by this context will be written. The default value is + * ::core.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA applications and ::PID is the process ID of the CUDA application. + * - ::CU_COREDUMP_PIPE: String of up to 1023 characters that defines the name of the pipe + * that will be monitored if user-triggered coredumps are enabled. The default value is + * ::corepipe.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA application and ::PID is the process ID of the CUDA application. + * + * \param attrib - The enum defining which value to fetch. + * \param value - void* containing the requested data. + * \param size - The size of the memory region \p value points to. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuCoredumpGetAttribute, + * ::cuCoredumpSetAttribute, + * ::cuCoredumpSetAttributeGlobal + */ +CUresult CUDAAPI cuCoredumpGetAttributeGlobal(CUcoredumpSettings attrib, void *value, size_t *size); + +/** + * \brief Allows caller to set a coredump attribute value for the current context + * + * This function should be considered an alternate interface to the CUDA-GDB environment + * variables defined in this document: https://docs.nvidia.com/cuda/cuda-gdb/index.html#gpu-coredump + * + * An important design decision to note is that any coredump environment variable values + * set before CUDA initializes will take permanent precedence over any values set with this + * this function. This decision was made to ensure no change in behavior for any users that + * may be currently using these variables to get coredumps. + * + * \p *value shall contain the requested value specified by \p set. It is up to the caller + * to ensure that the data type and size of \p *value matches the request. + * + * If the caller calls this function with \p *value equal to NULL, the size of the memory + * region (in bytes) expected for \p set will be placed in \p size. + * + * /note This function will return ::CUDA_ERROR_NOT_SUPPORTED if the caller attempts to set + * ::CU_COREDUMP_ENABLE_ON_EXCEPTION on a GPU of with Compute Capability < 6.0. ::cuCoredumpSetAttributeGlobal + * works on those platforms as an alternative. + * + * /note ::CU_COREDUMP_ENABLE_USER_TRIGGER and ::CU_COREDUMP_PIPE cannot be set on a per-context basis. + * + * The supported attributes are: + * - ::CU_COREDUMP_ENABLE_ON_EXCEPTION: Bool where ::true means that GPU exceptions from + * this context will create a coredump at the location specified by ::CU_COREDUMP_FILE. + * The default value is ::false. + * - ::CU_COREDUMP_TRIGGER_HOST: Bool where ::true means that the host CPU will + * also create a coredump. The default value is ::true. + * - ::CU_COREDUMP_LIGHTWEIGHT: Bool where ::true means that any resulting coredumps + * will not have a dump of GPU memory or non-reloc ELF images. The default value is + * ::false. + * - ::CU_COREDUMP_FILE: String of up to 1023 characters that defines the location where + * any coredumps generated by this context will be written. The default value is + * ::core.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA applications and ::PID is the process ID of the CUDA application. + * + * \param attrib - The enum defining which value to set. + * \param value - void* containing the requested data. + * \param size - The size of the memory region \p value points to. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_PERMITTED, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED, + * ::CUDA_ERROR_NOT_SUPPORTED + * + * \sa + * ::cuCoredumpGetAttributeGlobal, + * ::cuCoredumpGetAttribute, + * ::cuCoredumpSetAttributeGlobal + */ +CUresult CUDAAPI cuCoredumpSetAttribute(CUcoredumpSettings attrib, void* value, size_t *size); + +/** + * \brief Allows caller to set a coredump attribute value globally + * + * This function should be considered an alternate interface to the CUDA-GDB environment + * variables defined in this document: https://docs.nvidia.com/cuda/cuda-gdb/index.html#gpu-coredump + * + * An important design decision to note is that any coredump environment variable values + * set before CUDA initializes will take permanent precedence over any values set with this + * this function. This decision was made to ensure no change in behavior for any users that + * may be currently using these variables to get coredumps. + * + * \p *value shall contain the requested value specified by \p set. It is up to the caller + * to ensure that the data type and size of \p *value matches the request. + * + * If the caller calls this function with \p *value equal to NULL, the size of the memory + * region (in bytes) expected for \p set will be placed in \p size. + * + * The supported attributes are: + * - ::CU_COREDUMP_ENABLE_ON_EXCEPTION: Bool where ::true means that GPU exceptions from + * this context will create a coredump at the location specified by ::CU_COREDUMP_FILE. + * The default value is ::false. + * - ::CU_COREDUMP_TRIGGER_HOST: Bool where ::true means that the host CPU will + * also create a coredump. The default value is ::true. + * - ::CU_COREDUMP_LIGHTWEIGHT: Bool where ::true means that any resulting coredumps + * will not have a dump of GPU memory or non-reloc ELF images. The default value is + * ::false. + * - ::CU_COREDUMP_ENABLE_USER_TRIGGER: Bool where ::true means that a coredump can be + * created by writing to the system pipe specified by ::CU_COREDUMP_PIPE. The default + * value is ::false. + * - ::CU_COREDUMP_FILE: String of up to 1023 characters that defines the location where + * any coredumps generated by this context will be written. The default value is + * ::core.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine running + * the CUDA applications and ::PID is the process ID of the CUDA application. + * - ::CU_COREDUMP_PIPE: String of up to 1023 characters that defines the name of the pipe + * that will be monitored if user-triggered coredumps are enabled. This value may not be + * changed after ::CU_COREDUMP_ENABLE_USER_TRIGGER is set to ::true. The default + * value is ::corepipe.cuda.HOSTNAME.PID where ::HOSTNAME is the host name of the machine + * running the CUDA application and ::PID is the process ID of the CUDA application. + * + * \param attrib - The enum defining which value to set. + * \param value - void* containing the requested data. + * \param size - The size of the memory region \p value points to. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_PERMITTED + * + * \sa + * ::cuCoredumpGetAttribute, + * ::cuCoredumpGetAttributeGlobal, + * ::cuCoredumpSetAttribute + */ +CUresult CUDAAPI cuCoredumpSetAttributeGlobal(CUcoredumpSettings attrib, void *value, size_t *size); + +/** @} */ /* END CUDA_COREDUMP */ + +CUresult CUDAAPI cuGetExportTable(const void **ppExportTable, const CUuuid *pExportTableId); + +/* +** ******************* GREEN CONTEXTS ********************** +*/ + +/** + * \defgroup CUDA_GREEN_CONTEXTS Green Contexts + * + * ___MANBRIEF___ Driver level API for creation and manipulation of green contexts + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the APIs for creation and manipulation of green contexts in the CUDA + * driver. Green contexts are a lightweight alternative to traditional contexts, with the ability + * to pass in a set of resources that they should be initialized with. This allows the developer to + * represent distinct spatial partitions of the GPU, provision resources for them, and target them + * via the same programming model that CUDA exposes (streams, kernel launches, etc.). + * + * There are 4 main steps to using these new set of APIs. + * - (1) Start with an initial set of resources, for example via ::cuDeviceGetDevResource. Only SM type is supported today. + * - (2) Partition this set of resources by providing them as input to a partition API, for example: ::cuDevSmResourceSplitByCount. + * - (3) Finalize the specification of resources by creating a descriptor via ::cuDevResourceGenerateDesc. + * - (4) Provision the resources and create a green context via ::cuGreenCtxCreate. + * + * For \p CU_DEV_RESOURCE_TYPE_SM, the partitions created have minimum SM count requirements, often rounding up and aligning the + * minCount provided to ::cuDevSmResourceSplitByCount. The following is a guideline for each architecture + * and may be subject to change: + * - On Compute Architecture 6.X: The minimum count is 1 SM. + * - On Compute Architecture 7.X: The minimum count is 2 SMs and must be a multiple of 2. + * - On Compute Architecture 8.X: The minimum count is 4 SMs and must be a multiple of 2. + * - On Compute Architecture 9.0+: The minimum count is 8 SMs and must be a multiple of 8. + * + * In the future, flags can be provided to tradeoff functional and performance characteristics versus finer grained SM partitions. + * + * Even if the green contexts have disjoint SM partitions, it is not guaranteed that the kernels launched + * in them will run concurrently or have forward progress guarantees. This is due to other resources (like HW connections, + * see ::CUDA_DEVICE_MAX_CONNECTIONS) that could cause a dependency. Additionally, in certain scenarios, + * it is possible for the workload to run on more SMs than was provisioned (but never less). + * The following are two scenarios which can exhibit this behavior: + * - On Volta+ MPS: When \p CUDA_MPS_ACTIVE_THREAD_PERCENTAGE is used, + * the set of SMs that are used for running kernels can be scaled up to the value of SMs used for the MPS client. + * - On Compute Architecture 9.x: When a module with dynamic parallelism (CDP) is loaded, all future + * kernels running under green contexts may use and share an additional set of 2 SMs. + * + * @{ + */ + +/*! + * \typedef typedef struct CUgreenCtx_st* CUgreenCtx + * A green context handle. This handle can be used safely from only one CPU thread at a time. + * Created via ::cuGreenCtxCreate + */ +typedef struct CUgreenCtx_st *CUgreenCtx; + +/*! + * \typedef struct CUdevResourceDesc_st* CUdevResourceDesc; + * An opaque descriptor handle. The descriptor encapsulates multiple created and configured resources. + * Created via ::cuDevResourceGenerateDesc + */ +typedef struct CUdevResourceDesc_st *CUdevResourceDesc; + +typedef enum { + CU_GREEN_CTX_DEFAULT_STREAM = 0x1, /**< Required. Creates a default stream to use inside the green context */ +} CUgreenCtxCreate_flags; + +#define RESOURCE_ABI_VERSION 1 +#define RESOURCE_ABI_EXTERNAL_BYTES 48 + +#define _CONCAT_INNER(x, y) x ## y +#define _CONCAT_OUTER(x, y) _CONCAT_INNER(x, y) + +/*! + * \typedef enum CUdevResourceType + * Type of resource + */ +typedef enum { + CU_DEV_RESOURCE_TYPE_INVALID = 0, + CU_DEV_RESOURCE_TYPE_SM = 1, /**< Streaming multiprocessors related information */ +#ifdef __CUDA_API_VERSION_INTERNAL + CU_DEV_RESOURCE_TYPE_MAX, +#endif +} CUdevResourceType; + +/*! + * \struct CUdevSmResource + * Data for SM-related resources + */ +typedef struct CUdevSmResource_st { + unsigned int smCount; /**< The amount of streaming multiprocessors available in this resource. This is an output parameter only, do not write to this field. */ +} CUdevSmResource; + +/*! + * \struct CUdevResource + * A tagged union describing different resources identified by the type field. This structure should not be directly modified outside of the API that created it. + * \code + * struct { + * CUdevResourceType type; + * union { + * CUdevSmResource sm; + * }; + * }; + * \endcode + * - If \p type is \p CU_DEV_RESOURCE_TYPE_INVALID, this resoure is not valid and cannot be further accessed. + * - If \p type is \p CU_DEV_RESOURCE_TYPE_SM, the ::CUdevSmResource structure \p sm is filled in. For example, + * \p sm.smCount will reflect the amount of streaming multiprocessors available in this resource. + */ +typedef struct CUdevResource_st { + CUdevResourceType type; /**< Type of resource, dictates which union field was last set */ + unsigned char _internal_padding[92]; + union { + CUdevSmResource sm; /**< Resource corresponding to CU_DEV_RESOURCE_TYPE_SM \p. type. */ + unsigned char _oversize[RESOURCE_ABI_EXTERNAL_BYTES]; + }; +} _CONCAT_OUTER(CUdevResource_v, RESOURCE_ABI_VERSION); +typedef _CONCAT_OUTER(CUdevResource_v, RESOURCE_ABI_VERSION) CUdevResource; + +#undef _CONCAT_INNER +#undef _CONCAT_OUTER + +#undef ABI_PER_RESOURCE_EXTERNAL_BYTES +#undef ABI_RESOURCE_VERSION + +/** + * \brief Creates a green context with a specified set of resources. + * + * This API creates a green context with the resources specified in the descriptor \p desc and + * returns it in the handle represented by \p phCtx. This API will retain the primary context on device \p dev, + * which will is released when the green context is destroyed. It is advised to have the primary context active + * before calling this API to avoid the heavy cost of triggering primary context initialization and + * deinitialization multiple times. + * + * The API does not set the green context current. In order to set it current, you need to explicitly set it current + * by first converting the green context to a CUcontext using ::cuCtxFromGreenCtx and subsequently calling + * ::cuCtxSetCurrent / ::cuCtxPushCurrent. It should be noted that a green context can be current to only one + * thread at a time. There is no internal synchronization to make API calls accessing the same green context + * from multiple threads work. + * + * Note: The API is not supported on 32-bit platforms. + * + * \param phCtx - Pointer for the output handle to the green context + * \param desc - Descriptor generated via ::cuDevResourceGenerateDesc which contains the set of resources to be used + * \param dev - Device on which to create the green context. + * \param flags - One of the supported green context creation flags. \p CU_GREEN_CTX_DEFAULT_STREAM is required. + * + * The supported flags are: + * - \p CU_GREEN_CTX_DEFAULT_STREAM : Creates a default stream to use inside the green context. Required. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa + * ::cuGreenCtxDestroy, + * ::cuCtxFromGreenCtx, + * ::cuCtxSetCurrent, + * ::cuCtxPushCurrent, + * ::cuDevResourceGenerateDesc, + * ::cuDevicePrimaryCtxRetain, + * ::cuCtxCreate, + * ::cuCtxCreate_v3 + */ +CUresult CUDAAPI cuGreenCtxCreate(CUgreenCtx* phCtx, CUdevResourceDesc desc, CUdevice dev, unsigned int flags); + +/** + * \brief Destroys a green context + * + * Destroys the green context, releasing the primary context of the device that this green context was created for. + * Any resources provisioned for this green context (that were initially available via the resource descriptor) + * are released as well. + * \param hCtx - Green context to be destroyed + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_CONTEXT_IS_DESTROYED + * + * \sa + * ::cuGreenCtxCreate, + * ::cuCtxDestroy + */ +CUresult CUDAAPI cuGreenCtxDestroy(CUgreenCtx hCtx); + +/** + * \brief Converts a green context into the primary context + * + * The API converts a green context into the primary context returned in \p pContext. It is important + * to note that the converted context \p pContext is a normal primary context but with + * the resources of the specified green context \p hCtx. Once converted, it can then + * be used to set the context current with ::cuCtxSetCurrent or with any of the CUDA APIs + * that accept a CUcontext parameter. + * + * Users are expected to call this API before calling any CUDA APIs that accept a + * CUcontext. Failing to do so will result in the APIs returning ::CUDA_ERROR_INVALID_CONTEXT. + * + * \param pContext Returned primary context with green context resources + * \param hCtx Green context to convert + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuGreenCtxCreate + */ +CUresult CUDAAPI cuCtxFromGreenCtx(CUcontext *pContext, CUgreenCtx hCtx); + +/** + * \brief Get device resources + * + * Get the \p type resources available to the \p device. + * This may often be the starting point for further partitioning or configuring of resources. + * + * Note: The API is not supported on 32-bit platforms. + * + * \param device - Device to get resource for + * \param resource - Output pointer to a CUdevResource structure + * \param type - Type of resource to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_RESOURCE_TYPE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_DEVICE + * + * \sa + * ::cuDevResourceGenerateDesc + */ +CUresult CUDAAPI cuDeviceGetDevResource(CUdevice device, CUdevResource* resource, CUdevResourceType type); + +/** + * \brief Get context resources + * + * Get the \p type resources available to the context represented by \p hCtx + * \param hCtx - Context to get resource for + * + * Note: The API is not supported on 32-bit platforms. + * + * \param resource - Output pointer to a CUdevResource structure + * \param type - Type of resource to retrieve + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_RESOURCE_TYPE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CONTEXT + * + * \sa + * ::cuDevResourceGenerateDesc + */ +CUresult CUDAAPI cuCtxGetDevResource(CUcontext hCtx, CUdevResource* resource, CUdevResourceType type); + +/** + * \brief Get green context resources + * + * Get the \p type resources available to the green context represented by \p hCtx + * \param hCtx - Green context to get resource for + * \param resource - Output pointer to a CUdevResource structure + * \param type - Type of resource to retrieve + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_RESOURCE_TYPE, + * ::CUDA_ERROR_INVALID_VALUE + * + * \sa + * ::cuDevResourceGenerateDesc + */ +CUresult CUDAAPI cuGreenCtxGetDevResource(CUgreenCtx hCtx, CUdevResource* resource, CUdevResourceType type); + +/** + * \brief Splits \p CU_DEV_RESOURCE_TYPE_SM resources. + * + * Splits \p CU_DEV_RESOURCE_TYPE_SM resources into \p nbGroups, adhering to the minimum SM count specified in \p minCount + * and the usage flags in \p useFlags. If \p result is NULL, the API simulates a split and provides the amount of groups that + * would be created in \p nbGroups. Otherwise, \p nbGroups must point to the amount of elements in \p result and on return, + * the API will overwrite \p nbGroups with the amount actually created. The groups are written to the array in \p result. + * \p nbGroups can be less than the total amount if a smaller number of groups is needed. + * + * This API is used to spatially partition the input resource. The input resource needs to come from one of + * ::cuDeviceGetDevResource, ::cuCtxGetDevResource, or ::cuGreenCtxGetDevResource. + * A limitation of the API is that the output results cannot be split again without + * first creating a descriptor and a green context with that descriptor. + * + * When creating the groups, the API will take into account the performance and functional characteristics of the + * input resource, and guarantee a split that will create a disjoint set of symmetrical partitions. This may lead to less groups created + * than purely dividing the total SM count by the \p minCount due to cluster requirements or + * alignment and granularity requirements for the minCount. + * + * The \p remainder set, might not have the same functional or performance guarantees as the groups in \p result. + * Its use should be carefully planned and future partitions of the \p remainder set are discouraged. + * + * A successful API call must either have: + * - A valid array of \p result pointers of size passed in \p nbGroups, with \p Input of type \p CU_DEV_RESOURCE_TYPE_SM. + * Value of \p minCount must be between 0 and the SM count specified in \p input. \p remaining and \p useFlags are optional. + * - NULL passed in for \p result, with a valid integer pointer in \p nbGroups and \p Input of type \p CU_DEV_RESOURCE_TYPE_SM. + * Value of \p minCount must be between 0 and the SM count specified in \p input. + * This queries the number of groups that would be created by the API. + * + * Note: The API is not supported on 32-bit platforms. + * + * \param result - Output array of \p CUdevResource resources. Can be NULL to query the number of groups. + * \param nbGroups - This is a pointer, specifying the number of groups that would be or should be created as described below. + * \param input - Input SM resource to be split. Must be a valid \p CU_DEV_RESOURCE_TYPE_SM resource. + * \param remaining - If the input resource cannot be cleanly split among \p nbGroups, the remaining is placed in here. + * Can be ommitted (NULL) if the user does not need the remaining set. + * \param useFlags - Flags specifying how these partitions are used or which constraints to abide by when splitting the input. + * \param minCount - Minimum number of SMs required + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_RESOURCE_TYPE, + * ::CUDA_ERROR_INVALID_RESOURCE_CONFIGURATION + * + * \sa + * ::cuGreenCtxGetDevResource, + * ::cuCtxGetDevResource, + * ::cuDeviceGetDevResource + */ +CUresult CUDAAPI cuDevSmResourceSplitByCount( + CUdevResource* result, unsigned int* nbGroups, const CUdevResource* input, CUdevResource* remaining, unsigned int useFlags, unsigned int minCount); + +/** + * \brief Generate a resource descriptor + * + * Generates a resource descriptor with the set of resources specified in \p resources. + * The generated resource descriptor is necessary for the creation of green contexts via the ::cuGreenCtxCreate API. + * The API expects \p nbResources == 1, as there is only one type of resource and merging the same + * types of resource is currently not supported. + * + * Note: The API is not supported on 32-bit platforms. + * + * \param phDesc - Output descriptor + * \param resources - Array of resources to be included in the descriptor + * \param nbResources - Number of resources passed in \p resources + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_RESOURCE_TYPE, + * ::CUDA_ERROR_INVALID_RESOURCE_CONFIGURATION + * + * \sa + * ::cuDevSmResourceSplitByCount + */ +CUresult CUDAAPI cuDevResourceGenerateDesc(CUdevResourceDesc *phDesc, CUdevResource *resources, unsigned int nbResources); + +/** + * \brief Records an event. + * + * Captures in \phEvent all the activities of the green context of \phCtx + * at the time of this call. \phEvent and \phCtx must be from the same + * CUDA context. Calls such as ::cuEventQuery() or ::cuGreenCtxWaitEvent() will + * then examine or wait for completion of the work that was captured. Uses of + * \p hCtx after this call do not modify \p hEvent. + * + * \note The API will return an error if the specified green context \p hCtx + * has a stream in the capture mode. In such a case, the call will invalidate + * all the conflicting captures. + * + * \param hCtx - Green context to record event for + * \param hEvent - Event to record + * + * \return + * ::CUDA_SUCCESS + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE + * + * \sa + * ::cuGreenCtxWaitEvent, + * ::cuEventRecord + */ +CUresult CUDAAPI cuGreenCtxRecordEvent(CUgreenCtx hCtx, CUevent hEvent); + +/** + * \brief Make a green context wait on an event + * + * Makes all future work submitted to green context \phCtx wait for all work + * captured in \phEvent. The synchronization will be performed on the device + * and will not block the calling CPU thread. See ::cuGreenCtxRecordEvent() + * for details on what is captured by an event. + * + * \note The API will return an error and invalidate the capture if the specified + * event \p hEvent is part of an ongoing capture sequence. + * + * \param hCtx - Green context to wait + * \param hEvent - Event to wait on (may not be NULL) + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE + * + * \sa + * ::cuGreenCtxRecordEvent, + * ::cuStreamWaitEvent + */ +CUresult CUDAAPI cuGreenCtxWaitEvent(CUgreenCtx hCtx, CUevent hEvent); + +/** + * \brief Query the green context associated with a stream + * + * Returns the CUDA green context that the stream is associated with, or NULL if the stream + * is not associated with any green context. + * + * The stream handle \p hStream can refer to any of the following: + *
    + *
  • + * a stream created via any of the CUDA driver APIs such as ::cuStreamCreate. + * If during stream creation the context that was active in the calling thread was obtained + * with cuCtxFromGreenCtx, that green context is returned in \p phCtx. + * Otherwise, \p *phCtx is set to NULL instead. + *
    • + *
  • + * special stream such as the NULL stream or ::CU_STREAM_LEGACY. + * In that case if context that is active in the calling thread was obtained + * with cuCtxFromGreenCtx, that green context is returned. + * Otherwise, \p *phCtx is set to NULL instead. + *
    • + *
+ * Passing an invalid handle will result in undefined behavior. + * + * \param hStream - Handle to the stream to be queried + * \param phCtx - Returned green context associated with the stream + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_HANDLE, + * \notefnerr + * + * \sa ::cuStreamDestroy, + * ::cuStreamCreateWithPriority, + * ::cuStreamGetPriority, + * ::cuStreamGetFlags, + * ::cuStreamWaitEvent, + * ::cuStreamQuery, + * ::cuStreamSynchronize, + * ::cuStreamAddCallback, + * ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags + */ +CUresult CUDAAPI cuStreamGetGreenCtx(CUstream hStream, CUgreenCtx *phCtx); + +/** @} */ + +/* +** *************** END CUDA_GREEN_CONTEXTS ***************** +*/ + +/** + * CUDA API versioning support + */ +#if defined(__CUDA_API_VERSION_INTERNAL) + #undef cuMemHostRegister + #undef cuGraphicsResourceSetMapFlags + #undef cuLinkCreate + #undef cuLinkAddData + #undef cuLinkAddFile + #undef cuDeviceTotalMem + #undef cuCtxCreate + #undef cuModuleGetGlobal + #undef cuMemGetInfo + #undef cuMemAlloc + #undef cuMemAllocPitch + #undef cuMemFree + #undef cuMemGetAddressRange + #undef cuMemAllocHost + #undef cuMemHostGetDevicePointer + #undef cuMemcpyHtoD + #undef cuMemcpyDtoH + #undef cuMemcpyDtoD + #undef cuMemcpyDtoA + #undef cuMemcpyAtoD + #undef cuMemcpyHtoA + #undef cuMemcpyAtoH + #undef cuMemcpyAtoA + #undef cuMemcpyHtoAAsync + #undef cuMemcpyAtoHAsync + #undef cuMemcpy2D + #undef cuMemcpy2DUnaligned + #undef cuMemcpy3D + #undef cuMemcpyHtoDAsync + #undef cuMemcpyDtoHAsync + #undef cuMemcpyDtoDAsync + #undef cuMemcpy2DAsync + #undef cuMemcpy3DAsync + #undef cuMemsetD8 + #undef cuMemsetD16 + #undef cuMemsetD32 + #undef cuMemsetD2D8 + #undef cuMemsetD2D16 + #undef cuMemsetD2D32 + #undef cuArrayCreate + #undef cuArrayGetDescriptor + #undef cuArray3DCreate + #undef cuArray3DGetDescriptor + #undef cuTexRefSetAddress + #undef cuTexRefSetAddress2D + #undef cuTexRefGetAddress + #undef cuGraphicsResourceGetMappedPointer + #undef cuCtxDestroy + #undef cuCtxPopCurrent + #undef cuCtxPushCurrent + #undef cuStreamDestroy + #undef cuEventDestroy + #undef cuMemcpy + #undef cuMemcpyAsync + #undef cuMemcpyPeer + #undef cuMemcpyPeerAsync + #undef cuMemcpy3DPeer + #undef cuMemcpy3DPeerAsync + #undef cuMemsetD8Async + #undef cuMemsetD16Async + #undef cuMemsetD32Async + #undef cuMemsetD2D8Async + #undef cuMemsetD2D16Async + #undef cuMemsetD2D32Async + #undef cuStreamGetPriority + #undef cuStreamGetId + #undef cuStreamGetFlags + #undef cuStreamGetCtx + #undef cuStreamWaitEvent + #undef cuStreamAddCallback + #undef cuStreamAttachMemAsync + #undef cuStreamQuery + #undef cuStreamSynchronize + #undef cuEventRecord + #undef cuEventRecordWithFlags + #undef cuLaunchKernel + #undef cuLaunchKernelEx + #undef cuLaunchHostFunc + #undef cuGraphicsMapResources + #undef cuGraphicsUnmapResources + #undef cuStreamWriteValue32 + #undef cuStreamWaitValue32 + #undef cuStreamWriteValue64 + #undef cuStreamWaitValue64 + #undef cuStreamBatchMemOp + #undef cuStreamWriteValue32_v2 + #undef cuStreamWaitValue32_v2 + #undef cuStreamWriteValue64_v2 + #undef cuStreamWaitValue64_v2 + #undef cuStreamBatchMemOp_v2 + #undef cuMemPrefetchAsync + #undef cuMemPrefetchAsync_v2 + #undef cuLaunchCooperativeKernel + #undef cuSignalExternalSemaphoresAsync + #undef cuWaitExternalSemaphoresAsync + #undef cuStreamBeginCapture + #undef cuStreamBeginCaptureToGraph + #undef cuStreamEndCapture + #undef cuStreamIsCapturing + #undef cuStreamGetCaptureInfo + #undef cuStreamGetCaptureInfo_v2 + #undef cuStreamGetCaptureInfo_v3 + #undef cuGraphInstantiateWithParams + #undef cuGraphExecUpdate + #undef cuGraphUpload + #undef cuGraphLaunch + #undef cuDevicePrimaryCtxRelease + #undef cuDevicePrimaryCtxReset + #undef cuDevicePrimaryCtxSetFlags + #undef cuIpcOpenMemHandle + #undef cuStreamCopyAttributes + #undef cuStreamSetAttribute + #undef cuStreamGetAttribute + #undef cuGraphInstantiate + #undef cuGraphAddKernelNode + #undef cuGraphKernelNodeGetParams + #undef cuGraphKernelNodeSetParams + #undef cuGraphExecKernelNodeSetParams + #undef cuMemMapArrayAsync + #undef cuMemFreeAsync + #undef cuMemAllocAsync + #undef cuMemAllocFromPoolAsync + #undef cuStreamUpdateCaptureDependencies + #undef cuStreamUpdateCaptureDependencies_v2 + #undef cuGetProcAddress + + CUresult CUDAAPI cuMemHostRegister(void *p, size_t bytesize, unsigned int Flags); + CUresult CUDAAPI cuGraphicsResourceSetMapFlags(CUgraphicsResource resource, unsigned int flags); + CUresult CUDAAPI cuLinkCreate(unsigned int numOptions, CUjit_option *options, void **optionValues, CUlinkState *stateOut); + CUresult CUDAAPI cuLinkAddData(CUlinkState state, CUjitInputType type, void *data, size_t size, const char *name, + unsigned int numOptions, CUjit_option *options, void **optionValues); + CUresult CUDAAPI cuLinkAddFile(CUlinkState state, CUjitInputType type, const char *path, + unsigned int numOptions, CUjit_option *options, void **optionValues); + CUresult CUDAAPI cuTexRefSetAddress2D_v2(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR *desc, CUdeviceptr dptr, size_t Pitch); + + typedef unsigned int CUdeviceptr_v1; + + typedef struct CUDA_MEMCPY2D_v1_st + { + unsigned int srcXInBytes; /**< Source X in bytes */ + unsigned int srcY; /**< Source Y */ + CUmemorytype srcMemoryType; /**< Source memory type (host, device, array) */ + const void *srcHost; /**< Source host pointer */ + CUdeviceptr_v1 srcDevice; /**< Source device pointer */ + CUarray srcArray; /**< Source array reference */ + unsigned int srcPitch; /**< Source pitch (ignored when src is array) */ + + unsigned int dstXInBytes; /**< Destination X in bytes */ + unsigned int dstY; /**< Destination Y */ + CUmemorytype dstMemoryType; /**< Destination memory type (host, device, array) */ + void *dstHost; /**< Destination host pointer */ + CUdeviceptr_v1 dstDevice; /**< Destination device pointer */ + CUarray dstArray; /**< Destination array reference */ + unsigned int dstPitch; /**< Destination pitch (ignored when dst is array) */ + + unsigned int WidthInBytes; /**< Width of 2D memory copy in bytes */ + unsigned int Height; /**< Height of 2D memory copy */ + } CUDA_MEMCPY2D_v1; + + typedef struct CUDA_MEMCPY3D_v1_st + { + unsigned int srcXInBytes; /**< Source X in bytes */ + unsigned int srcY; /**< Source Y */ + unsigned int srcZ; /**< Source Z */ + unsigned int srcLOD; /**< Source LOD */ + CUmemorytype srcMemoryType; /**< Source memory type (host, device, array) */ + const void *srcHost; /**< Source host pointer */ + CUdeviceptr_v1 srcDevice; /**< Source device pointer */ + CUarray srcArray; /**< Source array reference */ + void *reserved0; /**< Must be NULL */ + unsigned int srcPitch; /**< Source pitch (ignored when src is array) */ + unsigned int srcHeight; /**< Source height (ignored when src is array; may be 0 if Depth==1) */ + + unsigned int dstXInBytes; /**< Destination X in bytes */ + unsigned int dstY; /**< Destination Y */ + unsigned int dstZ; /**< Destination Z */ + unsigned int dstLOD; /**< Destination LOD */ + CUmemorytype dstMemoryType; /**< Destination memory type (host, device, array) */ + void *dstHost; /**< Destination host pointer */ + CUdeviceptr_v1 dstDevice; /**< Destination device pointer */ + CUarray dstArray; /**< Destination array reference */ + void *reserved1; /**< Must be NULL */ + unsigned int dstPitch; /**< Destination pitch (ignored when dst is array) */ + unsigned int dstHeight; /**< Destination height (ignored when dst is array; may be 0 if Depth==1) */ + + unsigned int WidthInBytes; /**< Width of 3D memory copy in bytes */ + unsigned int Height; /**< Height of 3D memory copy */ + unsigned int Depth; /**< Depth of 3D memory copy */ + } CUDA_MEMCPY3D_v1; + + typedef struct CUDA_ARRAY_DESCRIPTOR_v1_st + { + unsigned int Width; /**< Width of array */ + unsigned int Height; /**< Height of array */ + + CUarray_format Format; /**< Array format */ + unsigned int NumChannels; /**< Channels per array element */ + } CUDA_ARRAY_DESCRIPTOR_v1; + + typedef struct CUDA_ARRAY3D_DESCRIPTOR_v1_st + { + unsigned int Width; /**< Width of 3D array */ + unsigned int Height; /**< Height of 3D array */ + unsigned int Depth; /**< Depth of 3D array */ + + CUarray_format Format; /**< Array format */ + unsigned int NumChannels; /**< Channels per array element */ + unsigned int Flags; /**< Flags */ + } CUDA_ARRAY3D_DESCRIPTOR_v1; + + CUresult CUDAAPI cuDeviceTotalMem(unsigned int *bytes, CUdevice dev); + CUresult CUDAAPI cuCtxCreate(CUcontext *pctx, unsigned int flags, CUdevice dev); + CUresult CUDAAPI cuModuleGetGlobal(CUdeviceptr_v1 *dptr, unsigned int *bytes, CUmodule hmod, const char *name); + CUresult CUDAAPI cuMemGetInfo(unsigned int *free, unsigned int *total); + CUresult CUDAAPI cuMemAlloc(CUdeviceptr_v1 *dptr, unsigned int bytesize); + CUresult CUDAAPI cuMemAllocPitch(CUdeviceptr_v1 *dptr, unsigned int *pPitch, unsigned int WidthInBytes, unsigned int Height, unsigned int ElementSizeBytes); + CUresult CUDAAPI cuMemFree(CUdeviceptr_v1 dptr); + CUresult CUDAAPI cuMemGetAddressRange(CUdeviceptr_v1 *pbase, unsigned int *psize, CUdeviceptr_v1 dptr); + CUresult CUDAAPI cuMemAllocHost(void **pp, unsigned int bytesize); + CUresult CUDAAPI cuMemHostGetDevicePointer(CUdeviceptr_v1 *pdptr, void *p, unsigned int Flags); + CUresult CUDAAPI cuMemcpyHtoD(CUdeviceptr_v1 dstDevice, const void *srcHost, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyDtoH(void *dstHost, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyDtoD(CUdeviceptr_v1 dstDevice, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyDtoA(CUarray dstArray, unsigned int dstOffset, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyAtoD(CUdeviceptr_v1 dstDevice, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyHtoA(CUarray dstArray, unsigned int dstOffset, const void *srcHost, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyAtoH(void *dstHost, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyAtoA(CUarray dstArray, unsigned int dstOffset, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + CUresult CUDAAPI cuMemcpyHtoAAsync(CUarray dstArray, unsigned int dstOffset, const void *srcHost, unsigned int ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyAtoHAsync(void *dstHost, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpy2D(const CUDA_MEMCPY2D_v1 *pCopy); + CUresult CUDAAPI cuMemcpy2DUnaligned(const CUDA_MEMCPY2D_v1 *pCopy); + CUresult CUDAAPI cuMemcpy3D(const CUDA_MEMCPY3D_v1 *pCopy); + CUresult CUDAAPI cuMemcpyHtoDAsync(CUdeviceptr_v1 dstDevice, const void *srcHost, unsigned int ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyDtoHAsync(void *dstHost, CUdeviceptr_v1 srcDevice, unsigned int ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyDtoDAsync(CUdeviceptr_v1 dstDevice, CUdeviceptr_v1 srcDevice, unsigned int ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpy2DAsync(const CUDA_MEMCPY2D_v1 *pCopy, CUstream hStream); + CUresult CUDAAPI cuMemcpy3DAsync(const CUDA_MEMCPY3D_v1 *pCopy, CUstream hStream); + CUresult CUDAAPI cuMemsetD8(CUdeviceptr_v1 dstDevice, unsigned char uc, unsigned int N); + CUresult CUDAAPI cuMemsetD16(CUdeviceptr_v1 dstDevice, unsigned short us, unsigned int N); + CUresult CUDAAPI cuMemsetD32(CUdeviceptr_v1 dstDevice, unsigned int ui, unsigned int N); + CUresult CUDAAPI cuMemsetD2D8(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned char uc, unsigned int Width, unsigned int Height); + CUresult CUDAAPI cuMemsetD2D16(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned short us, unsigned int Width, unsigned int Height); + CUresult CUDAAPI cuMemsetD2D32(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned int ui, unsigned int Width, unsigned int Height); + CUresult CUDAAPI cuArrayCreate(CUarray *pHandle, const CUDA_ARRAY_DESCRIPTOR_v1 *pAllocateArray); + CUresult CUDAAPI cuArrayGetDescriptor(CUDA_ARRAY_DESCRIPTOR_v1 *pArrayDescriptor, CUarray hArray); + CUresult CUDAAPI cuArray3DCreate(CUarray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR_v1 *pAllocateArray); + CUresult CUDAAPI cuArray3DGetDescriptor(CUDA_ARRAY3D_DESCRIPTOR_v1 *pArrayDescriptor, CUarray hArray); + CUresult CUDAAPI cuTexRefSetAddress(unsigned int *ByteOffset, CUtexref hTexRef, CUdeviceptr_v1 dptr, unsigned int bytes); + CUresult CUDAAPI cuTexRefSetAddress2D(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR_v1 *desc, CUdeviceptr_v1 dptr, unsigned int Pitch); + CUresult CUDAAPI cuTexRefGetAddress(CUdeviceptr_v1 *pdptr, CUtexref hTexRef); + CUresult CUDAAPI cuGraphicsResourceGetMappedPointer(CUdeviceptr_v1 *pDevPtr, unsigned int *pSize, CUgraphicsResource resource); + + CUresult CUDAAPI cuCtxDestroy(CUcontext ctx); + CUresult CUDAAPI cuCtxPopCurrent(CUcontext *pctx); + CUresult CUDAAPI cuCtxPushCurrent(CUcontext ctx); + CUresult CUDAAPI cuStreamDestroy(CUstream hStream); + CUresult CUDAAPI cuEventDestroy(CUevent hEvent); + CUresult CUDAAPI cuDevicePrimaryCtxRelease(CUdevice dev); + CUresult CUDAAPI cuDevicePrimaryCtxReset(CUdevice dev); + CUresult CUDAAPI cuDevicePrimaryCtxSetFlags(CUdevice dev, unsigned int flags); + + CUresult CUDAAPI cuMemcpyHtoD_v2(CUdeviceptr dstDevice, const void *srcHost, size_t ByteCount); + CUresult CUDAAPI cuMemcpyDtoH_v2(void *dstHost, CUdeviceptr srcDevice, size_t ByteCount); + CUresult CUDAAPI cuMemcpyDtoD_v2(CUdeviceptr dstDevice, CUdeviceptr srcDevice, size_t ByteCount); + CUresult CUDAAPI cuMemcpyDtoA_v2(CUarray dstArray, size_t dstOffset, CUdeviceptr srcDevice, size_t ByteCount); + CUresult CUDAAPI cuMemcpyAtoD_v2(CUdeviceptr dstDevice, CUarray srcArray, size_t srcOffset, size_t ByteCount); + CUresult CUDAAPI cuMemcpyHtoA_v2(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount); + CUresult CUDAAPI cuMemcpyAtoH_v2(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount); + CUresult CUDAAPI cuMemcpyAtoA_v2(CUarray dstArray, size_t dstOffset, CUarray srcArray, size_t srcOffset, size_t ByteCount); + CUresult CUDAAPI cuMemcpyHtoAAsync_v2(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyAtoHAsync_v2(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpy2D_v2(const CUDA_MEMCPY2D *pCopy); + CUresult CUDAAPI cuMemcpy2DUnaligned_v2(const CUDA_MEMCPY2D *pCopy); + CUresult CUDAAPI cuMemcpy3D_v2(const CUDA_MEMCPY3D *pCopy); + CUresult CUDAAPI cuMemcpyHtoDAsync_v2(CUdeviceptr dstDevice, const void *srcHost, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyDtoHAsync_v2(void *dstHost, CUdeviceptr srcDevice, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyDtoDAsync_v2(CUdeviceptr dstDevice, CUdeviceptr srcDevice, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpy2DAsync_v2(const CUDA_MEMCPY2D *pCopy, CUstream hStream); + CUresult CUDAAPI cuMemcpy3DAsync_v2(const CUDA_MEMCPY3D *pCopy, CUstream hStream); + CUresult CUDAAPI cuMemsetD8_v2(CUdeviceptr dstDevice, unsigned char uc, size_t N); + CUresult CUDAAPI cuMemsetD16_v2(CUdeviceptr dstDevice, unsigned short us, size_t N); + CUresult CUDAAPI cuMemsetD32_v2(CUdeviceptr dstDevice, unsigned int ui, size_t N); + CUresult CUDAAPI cuMemsetD2D8_v2(CUdeviceptr dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height); + CUresult CUDAAPI cuMemsetD2D16_v2(CUdeviceptr dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height); + CUresult CUDAAPI cuMemsetD2D32_v2(CUdeviceptr dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height); + CUresult CUDAAPI cuMemcpy(CUdeviceptr dst, CUdeviceptr src, size_t ByteCount); + CUresult CUDAAPI cuMemcpyAsync(CUdeviceptr dst, CUdeviceptr src, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpyPeer(CUdeviceptr dstDevice, CUcontext dstContext, CUdeviceptr srcDevice, CUcontext srcContext, size_t ByteCount); + CUresult CUDAAPI cuMemcpyPeerAsync(CUdeviceptr dstDevice, CUcontext dstContext, CUdeviceptr srcDevice, CUcontext srcContext, size_t ByteCount, CUstream hStream); + CUresult CUDAAPI cuMemcpy3DPeer(const CUDA_MEMCPY3D_PEER *pCopy); + CUresult CUDAAPI cuMemcpy3DPeerAsync(const CUDA_MEMCPY3D_PEER *pCopy, CUstream hStream); + + CUresult CUDAAPI cuMemsetD8Async(CUdeviceptr dstDevice, unsigned char uc, size_t N, CUstream hStream); + CUresult CUDAAPI cuMemsetD16Async(CUdeviceptr dstDevice, unsigned short us, size_t N, CUstream hStream); + CUresult CUDAAPI cuMemsetD32Async(CUdeviceptr dstDevice, unsigned int ui, size_t N, CUstream hStream); + CUresult CUDAAPI cuMemsetD2D8Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height, CUstream hStream); + CUresult CUDAAPI cuMemsetD2D16Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height, CUstream hStream); + CUresult CUDAAPI cuMemsetD2D32Async(CUdeviceptr dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height, CUstream hStream); + + CUresult CUDAAPI cuStreamGetPriority(CUstream hStream, int *priority); + CUresult CUDAAPI cuStreamGetId(CUstream hStream, unsigned long long *streamId); + CUresult CUDAAPI cuStreamGetFlags(CUstream hStream, unsigned int *flags); + CUresult CUDAAPI cuStreamGetCtx(CUstream hStream, CUcontext *pctx); + CUresult CUDAAPI cuStreamWaitEvent(CUstream hStream, CUevent hEvent, unsigned int Flags); + CUresult CUDAAPI cuStreamAddCallback(CUstream hStream, CUstreamCallback callback, void *userData, unsigned int flags); + CUresult CUDAAPI cuStreamAttachMemAsync(CUstream hStream, CUdeviceptr dptr, size_t length, unsigned int flags); + CUresult CUDAAPI cuStreamQuery(CUstream hStream); + CUresult CUDAAPI cuStreamSynchronize(CUstream hStream); + CUresult CUDAAPI cuEventRecord(CUevent hEvent, CUstream hStream); + CUresult CUDAAPI cuEventRecordWithFlags(CUevent hEvent, CUstream hStream, unsigned int flags); + CUresult CUDAAPI cuLaunchKernel(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams, void **extra); + CUresult CUDAAPI cuLaunchKernelEx(const CUlaunchConfig *config, CUfunction f, void **kernelParams, void **extra); + CUresult CUDAAPI cuLaunchHostFunc(CUstream hStream, CUhostFn fn, void *userData); + CUresult CUDAAPI cuGraphicsMapResources(unsigned int count, CUgraphicsResource *resources, CUstream hStream); + CUresult CUDAAPI cuGraphicsUnmapResources(unsigned int count, CUgraphicsResource *resources, CUstream hStream); + CUresult CUDAAPI cuStreamWriteValue32(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue32(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWriteValue64(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue64(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamBatchMemOp(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); + + CUresult CUDAAPI cuStreamWriteValue32_ptsz(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue32_ptsz(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWriteValue64_ptsz(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue64_ptsz(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamBatchMemOp_ptsz(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); + + CUresult CUDAAPI cuStreamWriteValue32_v2(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue32_v2(CUstream stream, CUdeviceptr addr, cuuint32_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWriteValue64_v2(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamWaitValue64_v2(CUstream stream, CUdeviceptr addr, cuuint64_t value, unsigned int flags); + CUresult CUDAAPI cuStreamBatchMemOp_v2(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); + CUresult CUDAAPI cuMemPrefetchAsync(CUdeviceptr devPtr, size_t count, CUdevice dstDevice, CUstream hStream); + CUresult CUDAAPI cuMemPrefetchAsync_v2(CUdeviceptr devPtr, size_t count, CUmemLocation location, unsigned int flags, CUstream hStream); + CUresult CUDAAPI cuLaunchCooperativeKernel(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams); + CUresult CUDAAPI cuSignalExternalSemaphoresAsync(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS *paramsArray, unsigned int numExtSems, CUstream stream); + CUresult CUDAAPI cuWaitExternalSemaphoresAsync(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS *paramsArray, unsigned int numExtSems, CUstream stream); + CUresult CUDAAPI cuStreamBeginCapture(CUstream hStream); + CUresult CUDAAPI cuStreamBeginCapture_ptsz(CUstream hStream); + CUresult CUDAAPI cuStreamBeginCapture_v2(CUstream hStream, CUstreamCaptureMode mode); + CUresult CUDAAPI cuStreamBeginCaptureToGraph(CUstream hStream, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUstreamCaptureMode mode); + CUresult CUDAAPI cuStreamEndCapture(CUstream hStream, CUgraph *phGraph); + CUresult CUDAAPI cuStreamIsCapturing(CUstream hStream, CUstreamCaptureStatus *captureStatus); + CUresult CUDAAPI cuStreamGetCaptureInfo(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out); + CUresult CUDAAPI cuStreamGetCaptureInfo_ptsz(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out); + CUresult CUDAAPI cuStreamGetCaptureInfo_v2(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, size_t *numDependencies_out); + CUresult CUDAAPI cuStreamGetCaptureInfo_v3(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, const CUgraphEdgeData **edgeData_out, size_t *numDependencies_out); + CUresult CUDAAPI cuGraphAddKernelNode(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); + CUresult CUDAAPI cuGraphKernelNodeGetParams(CUgraphNode hNode, CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); + CUresult CUDAAPI cuGraphKernelNodeSetParams(CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); + CUresult CUDAAPI cuGraphExecKernelNodeSetParams(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); + CUresult CUDAAPI cuGraphInstantiateWithParams(CUgraphExec *phGraphExec, CUgraph hGraph, CUDA_GRAPH_INSTANTIATE_PARAMS *instantiateParams); + CUresult CUDAAPI cuGraphExecUpdate(CUgraphExec hGraphExec, CUgraph hGraph, CUgraphNode *hErrorNode_out, CUgraphExecUpdateResult *updateResult_out); + CUresult CUDAAPI cuGraphUpload(CUgraphExec hGraph, CUstream hStream); + CUresult CUDAAPI cuGraphLaunch(CUgraphExec hGraph, CUstream hStream); + CUresult CUDAAPI cuStreamCopyAttributes(CUstream dstStream, CUstream srcStream); + CUresult CUDAAPI cuStreamGetAttribute(CUstream hStream, CUstreamAttrID attr, CUstreamAttrValue *value); + CUresult CUDAAPI cuStreamSetAttribute(CUstream hStream, CUstreamAttrID attr, const CUstreamAttrValue *param); + + CUresult CUDAAPI cuIpcOpenMemHandle(CUdeviceptr *pdptr, CUipcMemHandle handle, unsigned int Flags); + CUresult CUDAAPI cuGraphInstantiate(CUgraphExec *phGraphExec, CUgraph hGraph, CUgraphNode *phErrorNode, char *logBuffer, size_t bufferSize); + CUresult CUDAAPI cuGraphInstantiate_v2(CUgraphExec *phGraphExec, CUgraph hGraph, CUgraphNode *phErrorNode, char *logBuffer, size_t bufferSize); + + CUresult CUDAAPI cuMemMapArrayAsync(CUarrayMapInfo *mapInfoList, unsigned int count, CUstream hStream); + + CUresult CUDAAPI cuMemFreeAsync(CUdeviceptr dptr, CUstream hStream); + CUresult CUDAAPI cuMemAllocAsync(CUdeviceptr *dptr, size_t bytesize, CUstream hStream); + CUresult CUDAAPI cuMemAllocFromPoolAsync(CUdeviceptr *dptr, size_t bytesize, CUmemoryPool pool, CUstream hStream); + + CUresult CUDAAPI cuStreamUpdateCaptureDependencies(CUstream hStream, CUgraphNode *dependencies, size_t numDependencies, unsigned int flags); + CUresult CUDAAPI cuStreamUpdateCaptureDependencies_v2(CUstream hStream, CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags); + CUresult CUDAAPI cuGetProcAddress(const char *symbol, void **pfn, int cudaVersion, cuuint64_t flags); + +#elif defined(__CUDA_API_PER_THREAD_DEFAULT_STREAM) +static inline CUresult cuGetProcAddress_v2_ptsz(const char *symbol, void **funcPtr, int driverVersion, cuuint64_t flags, CUdriverProcAddressQueryResult *symbolStatus) { + const int procAddressMask = (CU_GET_PROC_ADDRESS_LEGACY_STREAM| + CU_GET_PROC_ADDRESS_PER_THREAD_DEFAULT_STREAM); + if ((flags & procAddressMask) == 0) { + flags |= CU_GET_PROC_ADDRESS_PER_THREAD_DEFAULT_STREAM; + } + return cuGetProcAddress_v2(symbol, funcPtr, driverVersion, flags, symbolStatus); +} +#define cuGetProcAddress_v2 cuGetProcAddress_v2_ptsz +#endif + +#ifdef __cplusplus +} +#endif + +#if defined(__GNUC__) + #if defined(__CUDA_API_PUSH_VISIBILITY_DEFAULT) + #pragma GCC visibility pop + #endif +#endif + +#undef __CUDA_DEPRECATED + +#endif /* __cuda_cuda_h__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGL.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGL.h new file mode 100644 index 0000000000000000000000000000000000000000..e304ae904c42dc2f05fa403b15ec02c0bb6e376c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGL.h @@ -0,0 +1,659 @@ +/* + * Copyright 2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAEGL_H +#define CUDAEGL_H + +#include "cuda.h" +#include "EGL/egl.h" +#include "EGL/eglext.h" + + +#ifdef CUDA_FORCE_API_VERSION +#error "CUDA_FORCE_API_VERSION is no longer supported." +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * \addtogroup CUDA_TYPES + * @{ + */ + +/** + * Maximum number of planes per frame + */ +#define MAX_PLANES 3 + +/** + * CUDA EglFrame type - array or pointer + */ +typedef enum CUeglFrameType_enum { + CU_EGL_FRAME_TYPE_ARRAY = 0, /**< Frame type CUDA array */ + CU_EGL_FRAME_TYPE_PITCH = 1, /**< Frame type pointer */ +} CUeglFrameType; + +/** + * Indicates that timeout for ::cuEGLStreamConsumerAcquireFrame is infinite. + */ +#define CUDA_EGL_INFINITE_TIMEOUT 0xFFFFFFFF + +/** + * Resource location flags- sysmem or vidmem + * + * For CUDA context on iGPU, since video and system memory are equivalent - + * these flags will not have an effect on the execution. + * + * For CUDA context on dGPU, applications can use the flag ::CUeglResourceLocationFlags + * to give a hint about the desired location. + * + * ::CU_EGL_RESOURCE_LOCATION_SYSMEM - the frame data is made resident on the system memory + * to be accessed by CUDA. + * + * ::CU_EGL_RESOURCE_LOCATION_VIDMEM - the frame data is made resident on the dedicated + * video memory to be accessed by CUDA. + * + * There may be an additional latency due to new allocation and data migration, + * if the frame is produced on a different memory. + + */ +typedef enum CUeglResourceLocationFlags_enum { + CU_EGL_RESOURCE_LOCATION_SYSMEM = 0x00, /**< Resource location sysmem */ + CU_EGL_RESOURCE_LOCATION_VIDMEM = 0x01 /**< Resource location vidmem */ +} CUeglResourceLocationFlags; + +/** + * CUDA EGL Color Format - The different planar and multiplanar formats currently supported for CUDA_EGL interops. + * Three channel formats are currently not supported for ::CU_EGL_FRAME_TYPE_ARRAY + */ +typedef enum CUeglColorFormat_enum { + CU_EGL_COLOR_FORMAT_YUV420_PLANAR = 0x00, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_SEMIPLANAR = 0x01, /**< Y, UV in two surfaces (UV as one surface) with VU byte ordering, width, height ratio same as YUV420Planar. */ + CU_EGL_COLOR_FORMAT_YUV422_PLANAR = 0x02, /**< Y, U, V each in a separate surface, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV422_SEMIPLANAR = 0x03, /**< Y, UV in two surfaces with VU byte ordering, width, height ratio same as YUV422Planar. */ + CU_EGL_COLOR_FORMAT_RGB = 0x04, /**< R/G/B three channels in one surface with BGR byte ordering. Only pitch linear format supported. */ + CU_EGL_COLOR_FORMAT_BGR = 0x05, /**< R/G/B three channels in one surface with RGB byte ordering. Only pitch linear format supported. */ + CU_EGL_COLOR_FORMAT_ARGB = 0x06, /**< R/G/B/A four channels in one surface with BGRA byte ordering. */ + CU_EGL_COLOR_FORMAT_RGBA = 0x07, /**< R/G/B/A four channels in one surface with ABGR byte ordering. */ + CU_EGL_COLOR_FORMAT_L = 0x08, /**< single luminance channel in one surface. */ + CU_EGL_COLOR_FORMAT_R = 0x09, /**< single color channel in one surface. */ + CU_EGL_COLOR_FORMAT_YUV444_PLANAR = 0x0A, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV444_SEMIPLANAR = 0x0B, /**< Y, UV in two surfaces (UV as one surface) with VU byte ordering, width, height ratio same as YUV444Planar. */ + CU_EGL_COLOR_FORMAT_YUYV_422 = 0x0C, /**< Y, U, V in one surface, interleaved as UYVY in one channel. */ + CU_EGL_COLOR_FORMAT_UYVY_422 = 0x0D, /**< Y, U, V in one surface, interleaved as YUYV in one channel. */ + CU_EGL_COLOR_FORMAT_ABGR = 0x0E, /**< R/G/B/A four channels in one surface with RGBA byte ordering. */ + CU_EGL_COLOR_FORMAT_BGRA = 0x0F, /**< R/G/B/A four channels in one surface with ARGB byte ordering. */ + CU_EGL_COLOR_FORMAT_A = 0x10, /**< Alpha color format - one channel in one surface. */ + CU_EGL_COLOR_FORMAT_RG = 0x11, /**< R/G color format - two channels in one surface with GR byte ordering */ + CU_EGL_COLOR_FORMAT_AYUV = 0x12, /**< Y, U, V, A four channels in one surface, interleaved as VUYA. */ + CU_EGL_COLOR_FORMAT_YVU444_SEMIPLANAR = 0x13, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU422_SEMIPLANAR = 0x14, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_SEMIPLANAR = 0x15, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_444_SEMIPLANAR = 0x16, /**< Y10, V10U10 in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_420_SEMIPLANAR = 0x17, /**< Y10, V10U10 in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_444_SEMIPLANAR = 0x18, /**< Y12, V12U12 in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_420_SEMIPLANAR = 0x19, /**< Y12, V12U12 in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_VYUY_ER = 0x1A, /**< Extended Range Y, U, V in one surface, interleaved as YVYU in one channel. */ + CU_EGL_COLOR_FORMAT_UYVY_ER = 0x1B, /**< Extended Range Y, U, V in one surface, interleaved as YUYV in one channel. */ + CU_EGL_COLOR_FORMAT_YUYV_ER = 0x1C, /**< Extended Range Y, U, V in one surface, interleaved as UYVY in one channel. */ + CU_EGL_COLOR_FORMAT_YVYU_ER = 0x1D, /**< Extended Range Y, U, V in one surface, interleaved as VYUY in one channel. */ + CU_EGL_COLOR_FORMAT_YUV_ER = 0x1E, /**< Extended Range Y, U, V three channels in one surface, interleaved as VUY. Only pitch linear format supported. */ + CU_EGL_COLOR_FORMAT_YUVA_ER = 0x1F, /**< Extended Range Y, U, V, A four channels in one surface, interleaved as AVUY. */ + CU_EGL_COLOR_FORMAT_AYUV_ER = 0x20, /**< Extended Range Y, U, V, A four channels in one surface, interleaved as VUYA. */ + CU_EGL_COLOR_FORMAT_YUV444_PLANAR_ER = 0x21, /**< Extended Range Y, U, V in three surfaces, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV422_PLANAR_ER = 0x22, /**< Extended Range Y, U, V in three surfaces, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_PLANAR_ER = 0x23, /**< Extended Range Y, U, V in three surfaces, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YUV444_SEMIPLANAR_ER = 0x24, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV422_SEMIPLANAR_ER = 0x25, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_SEMIPLANAR_ER = 0x26, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU444_PLANAR_ER = 0x27, /**< Extended Range Y, V, U in three surfaces, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU422_PLANAR_ER = 0x28, /**< Extended Range Y, V, U in three surfaces, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_PLANAR_ER = 0x29, /**< Extended Range Y, V, U in three surfaces, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU444_SEMIPLANAR_ER = 0x2A, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU422_SEMIPLANAR_ER = 0x2B, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_SEMIPLANAR_ER = 0x2C, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_BAYER_RGGB = 0x2D, /**< Bayer format - one channel in one surface with interleaved RGGB ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_BGGR = 0x2E, /**< Bayer format - one channel in one surface with interleaved BGGR ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_GRBG = 0x2F, /**< Bayer format - one channel in one surface with interleaved GRBG ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_GBRG = 0x30, /**< Bayer format - one channel in one surface with interleaved GBRG ordering. */ + CU_EGL_COLOR_FORMAT_BAYER10_RGGB = 0x31, /**< Bayer10 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER10_BGGR = 0x32, /**< Bayer10 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER10_GRBG = 0x33, /**< Bayer10 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER10_GBRG = 0x34, /**< Bayer10 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_RGGB = 0x35, /**< Bayer12 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_BGGR = 0x36, /**< Bayer12 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_GRBG = 0x37, /**< Bayer12 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_GBRG = 0x38, /**< Bayer12 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER14_RGGB = 0x39, /**< Bayer14 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER14_BGGR = 0x3A, /**< Bayer14 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER14_GRBG = 0x3B, /**< Bayer14 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER14_GBRG = 0x3C, /**< Bayer14 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER20_RGGB = 0x3D, /**< Bayer20 format - one channel in one surface with interleaved RGGB ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER20_BGGR = 0x3E, /**< Bayer20 format - one channel in one surface with interleaved BGGR ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER20_GRBG = 0x3F, /**< Bayer20 format - one channel in one surface with interleaved GRBG ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER20_GBRG = 0x40, /**< Bayer20 format - one channel in one surface with interleaved GBRG ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + CU_EGL_COLOR_FORMAT_YVU444_PLANAR = 0x41, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU422_PLANAR = 0x42, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_PLANAR = 0x43, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_BAYER_ISP_RGGB = 0x44, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved RGGB ordering and mapped to opaque integer datatype. */ + CU_EGL_COLOR_FORMAT_BAYER_ISP_BGGR = 0x45, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved BGGR ordering and mapped to opaque integer datatype. */ + CU_EGL_COLOR_FORMAT_BAYER_ISP_GRBG = 0x46, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved GRBG ordering and mapped to opaque integer datatype. */ + CU_EGL_COLOR_FORMAT_BAYER_ISP_GBRG = 0x47, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved GBRG ordering and mapped to opaque integer datatype. */ + CU_EGL_COLOR_FORMAT_BAYER_BCCR = 0x48, /**< Bayer format - one channel in one surface with interleaved BCCR ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_RCCB = 0x49, /**< Bayer format - one channel in one surface with interleaved RCCB ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_CRBC = 0x4A, /**< Bayer format - one channel in one surface with interleaved CRBC ordering. */ + CU_EGL_COLOR_FORMAT_BAYER_CBRC = 0x4B, /**< Bayer format - one channel in one surface with interleaved CBRC ordering. */ + CU_EGL_COLOR_FORMAT_BAYER10_CCCC = 0x4C, /**< Bayer10 format - one channel in one surface with interleaved CCCC ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_BCCR = 0x4D, /**< Bayer12 format - one channel in one surface with interleaved BCCR ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_RCCB = 0x4E, /**< Bayer12 format - one channel in one surface with interleaved RCCB ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_CRBC = 0x4F, /**< Bayer12 format - one channel in one surface with interleaved CRBC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_CBRC = 0x50, /**< Bayer12 format - one channel in one surface with interleaved CBRC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_BAYER12_CCCC = 0x51, /**< Bayer12 format - one channel in one surface with interleaved CCCC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + CU_EGL_COLOR_FORMAT_Y = 0x52, /**< Color format for single Y plane. */ + CU_EGL_COLOR_FORMAT_YUV420_SEMIPLANAR_2020 = 0x53, /**< Y, UV in two surfaces (UV as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_SEMIPLANAR_2020 = 0x54, /**< Y, VU in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_PLANAR_2020 = 0x55, /**< Y, U, V each in a separate surface, U/V width = 1/2 Y width, U/V height= 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_PLANAR_2020 = 0x56, /**< Y, V, U each in a separate surface, U/V width = 1/2 Y width, U/V height += 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_SEMIPLANAR_709 = 0x57, /**< Y, UV in two surfaces (UV as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_SEMIPLANAR_709 = 0x58, /**< Y, VU in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YUV420_PLANAR_709 = 0x59, /**< Y, U, V each in a separate surface, U/V width = 1/2 Y width, U/V height += 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_YVU420_PLANAR_709 = 0x5A, /**< Y, V, U each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_420_SEMIPLANAR_709 = 0x5B, /**< Y10, V10U10 in two surfaces (VU as one surface), U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_420_SEMIPLANAR_2020 = 0x5C, /**< Y10, V10U10 in two surfaces (VU as one surface), U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_422_SEMIPLANAR_2020 = 0x5D, /**< Y10, V10U10 in two surfaces(VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_422_SEMIPLANAR = 0x5E, /**< Y10, V10U10 in two surfaces(VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_422_SEMIPLANAR_709 = 0x5F, /**< Y10, V10U10 in two surfaces(VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y_ER = 0x60, /**< Extended Range Color format for single Y plane. */ + CU_EGL_COLOR_FORMAT_Y_709_ER = 0x61, /**< Extended Range Color format for single Y plane. */ + CU_EGL_COLOR_FORMAT_Y10_ER = 0x62, /**< Extended Range Color format for single Y10 plane. */ + CU_EGL_COLOR_FORMAT_Y10_709_ER = 0x63, /**< Extended Range Color format for single Y10 plane. */ + CU_EGL_COLOR_FORMAT_Y12_ER = 0x64, /**< Extended Range Color format for single Y12 plane. */ + CU_EGL_COLOR_FORMAT_Y12_709_ER = 0x65, /**< Extended Range Color format for single Y12 plane. */ + CU_EGL_COLOR_FORMAT_YUVA = 0x66, /**< Y, U, V, A four channels in one surface, interleaved as AVUY. */ + CU_EGL_COLOR_FORMAT_YUV = 0x67, /**< Y, U, V three channels in one surface, interleaved as VUY. Only pitch linear format supported. */ + CU_EGL_COLOR_FORMAT_YVYU = 0x68, /**< Y, U, V in one surface, interleaved as YVYU in one channel. */ + CU_EGL_COLOR_FORMAT_VYUY = 0x69, /**< Y, U, V in one surface, interleaved as VYUY in one channel. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_420_SEMIPLANAR_ER = 0x6A, /**< Extended Range Y10, V10U10 in two surfaces(VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_420_SEMIPLANAR_709_ER = 0x6B, /**< Extended Range Y10, V10U10 in two surfaces(VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_444_SEMIPLANAR_ER = 0x6C, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y10V10U10_444_SEMIPLANAR_709_ER = 0x6D, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_420_SEMIPLANAR_ER = 0x6E, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_420_SEMIPLANAR_709_ER = 0x6F, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_444_SEMIPLANAR_ER = 0x70, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_Y12V12U12_444_SEMIPLANAR_709_ER = 0x71, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + CU_EGL_COLOR_FORMAT_MAX +} CUeglColorFormat; + +/** + * CUDA EGLFrame structure Descriptor - structure defining one frame of EGL. + * + * Each frame may contain one or more planes depending on whether the surface * is Multiplanar or not. + */ +typedef struct CUeglFrame_st { + union { + CUarray pArray[MAX_PLANES]; /**< Array of CUarray corresponding to each plane*/ + void* pPitch[MAX_PLANES]; /**< Array of Pointers corresponding to each plane*/ + } frame; + unsigned int width; /**< Width of first plane */ + unsigned int height; /**< Height of first plane */ + unsigned int depth; /**< Depth of first plane */ + unsigned int pitch; /**< Pitch of first plane */ + unsigned int planeCount; /**< Number of planes */ + unsigned int numChannels; /**< Number of channels for the plane */ + CUeglFrameType frameType; /**< Array or Pitch */ + CUeglColorFormat eglColorFormat; /**< CUDA EGL Color Format*/ + CUarray_format cuFormat; /**< CUDA Array Format*/ +} CUeglFrame_v1; +typedef CUeglFrame_v1 CUeglFrame; + +/** + * CUDA EGLSream Connection + */ +typedef struct CUeglStreamConnection_st* CUeglStreamConnection; + +/** @} */ /* END CUDA_TYPES */ + +/** + * \file cudaEGL.h + * \brief Header file for the EGL interoperability functions of the + * low-level CUDA driver application programming interface. + */ + +/** + * \defgroup CUDA_EGL EGL Interoperability + * \ingroup CUDA_DRIVER + * + * ___MANBRIEF___ EGL interoperability functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the EGL interoperability functions of the + * low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Registers an EGL image + * + * Registers the EGLImageKHR specified by \p image for access by + * CUDA. A handle to the registered object is returned as \p pCudaResource. + * Additional Mapping/Unmapping is not required for the registered resource and + * ::cuGraphicsResourceGetMappedEglFrame can be directly called on the \p pCudaResource. + * + * The application will be responsible for synchronizing access to shared objects. + * The application must ensure that any pending operation which access the objects have completed + * before passing control to CUDA. This may be accomplished by issuing and waiting for + * glFinish command on all GLcontexts (for OpenGL and likewise for other APIs). + * The application will be also responsible for ensuring that any pending operation on the + * registered CUDA resource has completed prior to executing subsequent commands in other APIs + * accesing the same memory objects. + * This can be accomplished by calling cuCtxSynchronize or cuEventSynchronize (preferably). + * + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_READ_ONLY: Specifies that CUDA + * will not write to this resource. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_WRITE_DISCARD: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * The EGLImageKHR is an object which can be used to create EGLImage target resource. It is defined as a void pointer. + * typedef void* EGLImageKHR + * + * \param pCudaResource - Pointer to the returned object handle + * \param image - An EGLImageKHR image which can be used to create target resource. + * \param flags - Map flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuGraphicsEGLRegisterImage, ::cuGraphicsUnregisterResource, + * ::cuGraphicsResourceSetMapFlags, ::cuGraphicsMapResources, + * ::cuGraphicsUnmapResources, + * ::cudaGraphicsEGLRegisterImage + */ +CUresult CUDAAPI cuGraphicsEGLRegisterImage(CUgraphicsResource *pCudaResource, EGLImageKHR image, unsigned int flags); + +/** + * \brief Connect CUDA to EGLStream as a consumer. + * + * Connect CUDA as a consumer to EGLStreamKHR specified by \p stream. + * + * The EGLStreamKHR is an EGL object that transfers a sequence of image frames from one + * API to another. + * + * \param conn - Pointer to the returned connection handle + * \param stream - EGLStreamKHR handle + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuEGLStreamConsumerConnect, ::cuEGLStreamConsumerDisconnect, + * ::cuEGLStreamConsumerAcquireFrame, ::cuEGLStreamConsumerReleaseFrame, + * ::cudaEGLStreamConsumerConnect + */ +CUresult CUDAAPI cuEGLStreamConsumerConnect(CUeglStreamConnection *conn, EGLStreamKHR stream); + +/** + * \brief Connect CUDA to EGLStream as a consumer with given flags. + * + * Connect CUDA as a consumer to EGLStreamKHR specified by \p stream with specified \p flags defined by CUeglResourceLocationFlags. + * + * The flags specify whether the consumer wants to access frames from system memory or video memory. + * Default is ::CU_EGL_RESOURCE_LOCATION_VIDMEM. + * + * \param conn - Pointer to the returned connection handle + * \param stream - EGLStreamKHR handle + * \param flags - Flags denote intended location - system or video. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuEGLStreamConsumerConnect, ::cuEGLStreamConsumerDisconnect, + * ::cuEGLStreamConsumerAcquireFrame, ::cuEGLStreamConsumerReleaseFrame, + * ::cudaEGLStreamConsumerConnectWithFlags + */ + +CUresult CUDAAPI cuEGLStreamConsumerConnectWithFlags(CUeglStreamConnection *conn, EGLStreamKHR stream, unsigned int flags); + +/** + * \brief Disconnect CUDA as a consumer to EGLStream . + * + * Disconnect CUDA as a consumer to EGLStreamKHR. + * + * \param conn - Conection to disconnect. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuEGLStreamConsumerConnect, ::cuEGLStreamConsumerDisconnect, + * ::cuEGLStreamConsumerAcquireFrame, ::cuEGLStreamConsumerReleaseFrame, + * ::cudaEGLStreamConsumerDisconnect + */ +CUresult CUDAAPI cuEGLStreamConsumerDisconnect(CUeglStreamConnection *conn); + +/** + * \brief Acquire an image frame from the EGLStream with CUDA as a consumer. + * + * Acquire an image frame from EGLStreamKHR. This API can also acquire an old frame presented + * by the producer unless explicitly disabled by setting EGL_SUPPORT_REUSE_NV flag to EGL_FALSE + * during stream initialization. By default, EGLStream is created with this flag set to EGL_TRUE. + * ::cuGraphicsResourceGetMappedEglFrame can be called on \p pCudaResource to get + * ::CUeglFrame. + * + * \param conn - Connection on which to acquire + * \param pCudaResource - CUDA resource on which the stream frame will be mapped for use. + * \param pStream - CUDA stream for synchronization and any data migrations + * implied by ::CUeglResourceLocationFlags. + * \param timeout - Desired timeout in usec for a new frame to be acquired. + * If set as ::CUDA_EGL_INFINITE_TIMEOUT, acquire waits infinitely. + * After timeout occurs CUDA consumer tries to acquire an old frame + * if available and EGL_SUPPORT_REUSE_NV flag is set. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_LAUNCH_TIMEOUT, + * + * \sa ::cuEGLStreamConsumerConnect, ::cuEGLStreamConsumerDisconnect, + * ::cuEGLStreamConsumerAcquireFrame, ::cuEGLStreamConsumerReleaseFrame, + * ::cudaEGLStreamConsumerAcquireFrame + */ +CUresult CUDAAPI cuEGLStreamConsumerAcquireFrame(CUeglStreamConnection *conn, + CUgraphicsResource *pCudaResource, CUstream *pStream, unsigned int timeout); +/** + * \brief Releases the last frame acquired from the EGLStream. + * + * Release the acquired image frame specified by \p pCudaResource to EGLStreamKHR. + * If EGL_SUPPORT_REUSE_NV flag is set to EGL_TRUE, at the time of EGL creation + * this API doesn't release the last frame acquired on the EGLStream. + * By default, EGLStream is created with this flag set to EGL_TRUE. + * + * \param conn - Connection on which to release + * \param pCudaResource - CUDA resource whose corresponding frame is to be released + * \param pStream - CUDA stream on which release will be done. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * + * \sa ::cuEGLStreamConsumerConnect, ::cuEGLStreamConsumerDisconnect, + * ::cuEGLStreamConsumerAcquireFrame, ::cuEGLStreamConsumerReleaseFrame, + * ::cudaEGLStreamConsumerReleaseFrame + */ +CUresult CUDAAPI cuEGLStreamConsumerReleaseFrame(CUeglStreamConnection *conn, + CUgraphicsResource pCudaResource, CUstream *pStream); + +/** + * \brief Connect CUDA to EGLStream as a producer. + * + * Connect CUDA as a producer to EGLStreamKHR specified by \p stream. + * + * The EGLStreamKHR is an EGL object that transfers a sequence of image frames from one + * API to another. + * + * \param conn - Pointer to the returned connection handle + * \param stream - EGLStreamKHR handle + * \param width - width of the image to be submitted to the stream + * \param height - height of the image to be submitted to the stream + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuEGLStreamProducerConnect, ::cuEGLStreamProducerDisconnect, + * ::cuEGLStreamProducerPresentFrame, + * ::cudaEGLStreamProducerConnect + */ +CUresult CUDAAPI cuEGLStreamProducerConnect(CUeglStreamConnection *conn, EGLStreamKHR stream, + EGLint width, EGLint height); + +/** + * \brief Disconnect CUDA as a producer to EGLStream . + * + * Disconnect CUDA as a producer to EGLStreamKHR. + * + * \param conn - Conection to disconnect. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * + * \sa ::cuEGLStreamProducerConnect, ::cuEGLStreamProducerDisconnect, + * ::cuEGLStreamProducerPresentFrame, + * ::cudaEGLStreamProducerDisconnect + */ +CUresult CUDAAPI cuEGLStreamProducerDisconnect(CUeglStreamConnection *conn); + +/** + * \brief Present a CUDA eglFrame to the EGLStream with CUDA as a producer. + * + * When a frame is presented by the producer, it gets associated with the EGLStream + * and thus it is illegal to free the frame before the producer is disconnected. + * If a frame is freed and reused it may lead to undefined behavior. + * + * If producer and consumer are on different GPUs (iGPU and dGPU) then frametype + * ::CU_EGL_FRAME_TYPE_ARRAY is not supported. ::CU_EGL_FRAME_TYPE_PITCH can be used for + * such cross-device applications. + * + * The ::CUeglFrame is defined as: + * \code + * typedef struct CUeglFrame_st { + * union { + * CUarray pArray[MAX_PLANES]; + * void* pPitch[MAX_PLANES]; + * } frame; + * unsigned int width; + * unsigned int height; + * unsigned int depth; + * unsigned int pitch; + * unsigned int planeCount; + * unsigned int numChannels; + * CUeglFrameType frameType; + * CUeglColorFormat eglColorFormat; + * CUarray_format cuFormat; + * } CUeglFrame; + * \endcode + * + * For ::CUeglFrame of type ::CU_EGL_FRAME_TYPE_PITCH, the application may present sub-region of a memory + * allocation. In that case, the pitched pointer will specify the start address of the sub-region in + * the allocation and corresponding ::CUeglFrame fields will specify the dimensions of the sub-region. + * + * \param conn - Connection on which to present the CUDA array + * \param eglframe - CUDA Eglstream Proucer Frame handle to be sent to the consumer over EglStream. + * \param pStream - CUDA stream on which to present the frame. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * + * \sa ::cuEGLStreamProducerConnect, ::cuEGLStreamProducerDisconnect, + * ::cuEGLStreamProducerReturnFrame, + * ::cudaEGLStreamProducerPresentFrame + */ +CUresult CUDAAPI cuEGLStreamProducerPresentFrame(CUeglStreamConnection *conn, + CUeglFrame eglframe, CUstream *pStream); + +/** + * \brief Return the CUDA eglFrame to the EGLStream released by the consumer. + * + * This API can potentially return CUDA_ERROR_LAUNCH_TIMEOUT if the consumer has not + * returned a frame to EGL stream. If timeout is returned the application can retry. + * + * \param conn - Connection on which to return + * \param eglframe - CUDA Eglstream Proucer Frame handle returned from the consumer over EglStream. + * \param pStream - CUDA stream on which to return the frame. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_LAUNCH_TIMEOUT + * + * \sa ::cuEGLStreamProducerConnect, ::cuEGLStreamProducerDisconnect, + * ::cuEGLStreamProducerPresentFrame, + * ::cudaEGLStreamProducerReturnFrame + */ +CUresult CUDAAPI cuEGLStreamProducerReturnFrame(CUeglStreamConnection *conn, + CUeglFrame *eglframe, CUstream *pStream); + +/** + * \brief Get an eglFrame through which to access a registered EGL graphics resource. + * + * Returns in \p *eglFrame an eglFrame pointer through which the registered graphics resource + * \p resource may be accessed. + * This API can only be called for registered EGL graphics resources. + * + * The ::CUeglFrame is defined as: + * \code + * typedef struct CUeglFrame_st { + * union { + * CUarray pArray[MAX_PLANES]; + * void* pPitch[MAX_PLANES]; + * } frame; + * unsigned int width; + * unsigned int height; + * unsigned int depth; + * unsigned int pitch; + * unsigned int planeCount; + * unsigned int numChannels; + * CUeglFrameType frameType; + * CUeglColorFormat eglColorFormat; + * CUarray_format cuFormat; + * } CUeglFrame; + * \endcode + * + * If \p resource is not registered then ::CUDA_ERROR_NOT_MAPPED is returned. + * * + * \param eglFrame - Returned eglFrame. + * \param resource - Registered resource to access. + * \param index - Index for cubemap surfaces. + * \param mipLevel - Mipmap level for the subresource to access. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_NOT_MAPPED + * + * \sa + * ::cuGraphicsMapResources, + * ::cuGraphicsSubResourceGetMappedArray, + * ::cuGraphicsResourceGetMappedPointer, + * ::cudaGraphicsResourceGetMappedEglFrame + */ +CUresult CUDAAPI cuGraphicsResourceGetMappedEglFrame(CUeglFrame* eglFrame, CUgraphicsResource resource, unsigned int index, unsigned int mipLevel); + +/** + * \brief Creates an event from EGLSync object + * + * Creates an event *phEvent from an EGLSyncKHR eglSync with the flags specified + * via \p flags. Valid flags include: + * - ::CU_EVENT_DEFAULT: Default event creation flag. + * - ::CU_EVENT_BLOCKING_SYNC: Specifies that the created event should use blocking + * synchronization. A CPU thread that uses ::cuEventSynchronize() to wait on + * an event created with this flag will block until the event has actually + * been completed. + * + * Once the \p eglSync gets destroyed, ::cuEventDestroy is the only API + * that can be invoked on the event. + * + * ::cuEventRecord and TimingData are not supported for events created from EGLSync. + * + * The EGLSyncKHR is an opaque handle to an EGL sync object. + * typedef void* EGLSyncKHR + * + * \param phEvent - Returns newly created event + * \param eglSync - Opaque handle to EGLSync object + * \param flags - Event creation flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa + * ::cuEventQuery, + * ::cuEventSynchronize, + * ::cuEventDestroy + */ +CUresult CUDAAPI cuEventCreateFromEGLSync(CUevent *phEvent, EGLSyncKHR eglSync, unsigned int flags); + +/** @} */ /* END CUDA_EGL */ + +#ifdef __cplusplus +}; +#endif + +#endif + diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGLTypedefs.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGLTypedefs.h new file mode 100644 index 0000000000000000000000000000000000000000..61b82337dc4bb280869934b11c2105db62ae20c3 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaEGLTypedefs.h @@ -0,0 +1,96 @@ +/* + * Copyright 2020-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAEGLTYPEDEFS_H +#define CUDAEGLTYPEDEFS_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +/* + * Macros for the latest version for each driver function in cudaEGL.h + */ +#define PFN_cuGraphicsEGLRegisterImage PFN_cuGraphicsEGLRegisterImage_v7000 +#define PFN_cuEGLStreamConsumerConnect PFN_cuEGLStreamConsumerConnect_v7000 +#define PFN_cuEGLStreamConsumerConnectWithFlags PFN_cuEGLStreamConsumerConnectWithFlags_v8000 +#define PFN_cuEGLStreamConsumerDisconnect PFN_cuEGLStreamConsumerDisconnect_v7000 +#define PFN_cuEGLStreamConsumerAcquireFrame PFN_cuEGLStreamConsumerAcquireFrame_v7000 +#define PFN_cuEGLStreamConsumerReleaseFrame PFN_cuEGLStreamConsumerReleaseFrame_v7000 +#define PFN_cuEGLStreamProducerConnect PFN_cuEGLStreamProducerConnect_v7000 +#define PFN_cuEGLStreamProducerDisconnect PFN_cuEGLStreamProducerDisconnect_v7000 +#define PFN_cuEGLStreamProducerPresentFrame PFN_cuEGLStreamProducerPresentFrame_v7000 +#define PFN_cuEGLStreamProducerReturnFrame PFN_cuEGLStreamProducerReturnFrame_v7000 +#define PFN_cuGraphicsResourceGetMappedEglFrame PFN_cuGraphicsResourceGetMappedEglFrame_v7000 +#define PFN_cuEventCreateFromEGLSync PFN_cuEventCreateFromEGLSync_v9000 + + +/** + * Type definitions for functions defined in cudaEGL.h + */ +typedef CUresult (CUDAAPI *PFN_cuGraphicsEGLRegisterImage_v7000)(CUgraphicsResource CUDAAPI *pCudaResource, EGLImageKHR image, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamConsumerConnect_v7000)(CUeglStreamConnection CUDAAPI *conn, EGLStreamKHR stream); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamConsumerConnectWithFlags_v8000)(CUeglStreamConnection CUDAAPI *conn, EGLStreamKHR stream, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamConsumerDisconnect_v7000)(CUeglStreamConnection CUDAAPI *conn); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamConsumerAcquireFrame_v7000)(CUeglStreamConnection CUDAAPI *conn, CUgraphicsResource CUDAAPI *pCudaResource, CUstream CUDAAPI *pStream, unsigned int timeout); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamConsumerReleaseFrame_v7000)(CUeglStreamConnection CUDAAPI *conn, CUgraphicsResource pCudaResource, CUstream CUDAAPI *pStream); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamProducerConnect_v7000)(CUeglStreamConnection CUDAAPI *conn, EGLStreamKHR stream, EGLint width, EGLint height); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamProducerDisconnect_v7000)(CUeglStreamConnection CUDAAPI *conn); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamProducerPresentFrame_v7000)(CUeglStreamConnection CUDAAPI *conn, CUeglFrame_v1 eglframe, CUstream CUDAAPI *pStream); +typedef CUresult (CUDAAPI *PFN_cuEGLStreamProducerReturnFrame_v7000)(CUeglStreamConnection CUDAAPI *conn, CUeglFrame_v1 CUDAAPI *eglframe, CUstream CUDAAPI *pStream); +typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceGetMappedEglFrame_v7000)(CUeglFrame_v1 CUDAAPI *eglFrame, CUgraphicsResource resource, unsigned int index, unsigned int mipLevel); +typedef CUresult (CUDAAPI *PFN_cuEventCreateFromEGLSync_v9000)(CUevent CUDAAPI *phEvent, EGLSyncKHR eglSync, unsigned int flags); + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGL.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGL.h new file mode 100644 index 0000000000000000000000000000000000000000..1a9c70e881774c8f3cf8b6430e7aa53a98d74669 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGL.h @@ -0,0 +1,608 @@ +/* + * Copyright 1993-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAGL_H +#define CUDAGL_H + +#include +#include + +#if defined(__CUDA_API_VERSION_INTERNAL) || defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +#define __CUDA_DEPRECATED +#elif defined(_MSC_VER) +#define __CUDA_DEPRECATED __declspec(deprecated) +#elif defined(__GNUC__) +#define __CUDA_DEPRECATED __attribute__((deprecated)) +#else +#define __CUDA_DEPRECATED +#endif + +#ifdef CUDA_FORCE_API_VERSION +#error "CUDA_FORCE_API_VERSION is no longer supported." +#endif + +#if defined(__CUDA_API_VERSION_INTERNAL) || defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) + #define __CUDA_API_PER_THREAD_DEFAULT_STREAM + #define __CUDA_API_PTDS(api) api ## _ptds + #define __CUDA_API_PTSZ(api) api ## _ptsz +#else + #define __CUDA_API_PTDS(api) api + #define __CUDA_API_PTSZ(api) api +#endif + +#define cuGLCtxCreate cuGLCtxCreate_v2 +#define cuGLMapBufferObject __CUDA_API_PTDS(cuGLMapBufferObject_v2) +#define cuGLMapBufferObjectAsync __CUDA_API_PTSZ(cuGLMapBufferObjectAsync_v2) +#define cuGLGetDevices cuGLGetDevices_v2 + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * \file cudaGL.h + * \brief Header file for the OpenGL interoperability functions of the + * low-level CUDA driver application programming interface. + */ + +/** + * \defgroup CUDA_GL OpenGL Interoperability + * \ingroup CUDA_DRIVER + * + * ___MANBRIEF___ OpenGL interoperability functions of the low-level CUDA + * driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the OpenGL interoperability functions of the + * low-level CUDA driver application programming interface. Note that mapping + * of OpenGL resources is performed with the graphics API agnostic, resource + * mapping interface described in \ref CUDA_GRAPHICS "Graphics Interoperability". + * + * @{ + */ + +#if defined(_WIN32) +#if !defined(WGL_NV_gpu_affinity) +typedef void* HGPUNV; +#endif +#endif /* _WIN32 */ + +/** + * \brief Registers an OpenGL buffer object + * + * Registers the buffer object specified by \p buffer for access by + * CUDA. A handle to the registered object is returned as \p + * pCudaResource. The register flags \p Flags specify the intended usage, + * as follows: + * + * - ::CU_GRAPHICS_REGISTER_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::CU_GRAPHICS_REGISTER_FLAGS_READ_ONLY: Specifies that CUDA + * will not write to this resource. + * - ::CU_GRAPHICS_REGISTER_FLAGS_WRITE_DISCARD: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * \param pCudaResource - Pointer to the returned object handle + * \param buffer - name of buffer object to be registered + * \param Flags - Register flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_OPERATING_SYSTEM + * \notefnerr + * + * \sa + * ::cuGraphicsUnregisterResource, + * ::cuGraphicsMapResources, + * ::cuGraphicsResourceGetMappedPointer, + * ::cudaGraphicsGLRegisterBuffer + */ +CUresult CUDAAPI cuGraphicsGLRegisterBuffer(CUgraphicsResource *pCudaResource, GLuint buffer, unsigned int Flags); + +/** + * \brief Register an OpenGL texture or renderbuffer object + * + * Registers the texture or renderbuffer object specified by \p image for access by CUDA. + * A handle to the registered object is returned as \p pCudaResource. + * + * \p target must match the type of the object, and must be one of ::GL_TEXTURE_2D, + * ::GL_TEXTURE_RECTANGLE, ::GL_TEXTURE_CUBE_MAP, ::GL_TEXTURE_3D, ::GL_TEXTURE_2D_ARRAY, + * or ::GL_RENDERBUFFER. + * + * The register flags \p Flags specify the intended usage, as follows: + * + * - ::CU_GRAPHICS_REGISTER_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::CU_GRAPHICS_REGISTER_FLAGS_READ_ONLY: Specifies that CUDA + * will not write to this resource. + * - ::CU_GRAPHICS_REGISTER_FLAGS_WRITE_DISCARD: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * - ::CU_GRAPHICS_REGISTER_FLAGS_SURFACE_LDST: Specifies that CUDA will + * bind this resource to a surface reference. + * - ::CU_GRAPHICS_REGISTER_FLAGS_TEXTURE_GATHER: Specifies that CUDA will perform + * texture gather operations on this resource. + * + * The following image formats are supported. For brevity's sake, the list is abbreviated. + * For ex., {GL_R, GL_RG} X {8, 16} would expand to the following 4 formats + * {GL_R8, GL_R16, GL_RG8, GL_RG16} : + * - GL_RED, GL_RG, GL_RGBA, GL_LUMINANCE, GL_ALPHA, GL_LUMINANCE_ALPHA, GL_INTENSITY + * - {GL_R, GL_RG, GL_RGBA} X {8, 16, 16F, 32F, 8UI, 16UI, 32UI, 8I, 16I, 32I} + * - {GL_LUMINANCE, GL_ALPHA, GL_LUMINANCE_ALPHA, GL_INTENSITY} X + * {8, 16, 16F_ARB, 32F_ARB, 8UI_EXT, 16UI_EXT, 32UI_EXT, 8I_EXT, 16I_EXT, 32I_EXT} + * + * The following image classes are currently disallowed: + * - Textures with borders + * - Multisampled renderbuffers + * + * \param pCudaResource - Pointer to the returned object handle + * \param image - name of texture or renderbuffer object to be registered + * \param target - Identifies the type of object specified by \p image + * \param Flags - Register flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_OPERATING_SYSTEM + * \notefnerr + * + * \sa + * ::cuGraphicsUnregisterResource, + * ::cuGraphicsMapResources, + * ::cuGraphicsSubResourceGetMappedArray, + * ::cudaGraphicsGLRegisterImage + */ +CUresult CUDAAPI cuGraphicsGLRegisterImage(CUgraphicsResource *pCudaResource, GLuint image, GLenum target, unsigned int Flags); + +#ifdef _WIN32 +/** + * \brief Gets the CUDA device associated with hGpu + * + * Returns in \p *pDevice the CUDA device associated with a \p hGpu, if + * applicable. + * + * \param pDevice - Device associated with hGpu + * \param hGpu - Handle to a GPU, as queried via ::WGL_NV_gpu_affinity() + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuGLMapBufferObject, + * ::cuGLRegisterBufferObject, ::cuGLUnmapBufferObject, + * ::cuGLUnregisterBufferObject, ::cuGLUnmapBufferObjectAsync, + * ::cuGLSetBufferObjectMapFlags, + * ::cudaWGLGetDevice + */ +CUresult CUDAAPI cuWGLGetDevice(CUdevice *pDevice, HGPUNV hGpu); +#endif /* _WIN32 */ + +/** + * CUDA devices corresponding to an OpenGL device + */ +typedef enum CUGLDeviceList_enum { + CU_GL_DEVICE_LIST_ALL = 0x01, /**< The CUDA devices for all GPUs used by the current OpenGL context */ + CU_GL_DEVICE_LIST_CURRENT_FRAME = 0x02, /**< The CUDA devices for the GPUs used by the current OpenGL context in its currently rendering frame */ + CU_GL_DEVICE_LIST_NEXT_FRAME = 0x03, /**< The CUDA devices for the GPUs to be used by the current OpenGL context in the next frame */ +} CUGLDeviceList; + +/** + * \brief Gets the CUDA devices associated with the current OpenGL context + * + * Returns in \p *pCudaDeviceCount the number of CUDA-compatible devices + * corresponding to the current OpenGL context. Also returns in \p *pCudaDevices + * at most cudaDeviceCount of the CUDA-compatible devices corresponding to + * the current OpenGL context. If any of the GPUs being used by the current OpenGL + * context are not CUDA capable then the call will return CUDA_ERROR_NO_DEVICE. + * + * The \p deviceList argument may be any of the following: + * - ::CU_GL_DEVICE_LIST_ALL: Query all devices used by the current OpenGL context. + * - ::CU_GL_DEVICE_LIST_CURRENT_FRAME: Query the devices used by the current OpenGL context to + * render the current frame (in SLI). + * - ::CU_GL_DEVICE_LIST_NEXT_FRAME: Query the devices used by the current OpenGL context to + * render the next frame (in SLI). Note that this is a prediction, it can't be guaranteed that + * this is correct in all cases. + * + * \param pCudaDeviceCount - Returned number of CUDA devices. + * \param pCudaDevices - Returned CUDA devices. + * \param cudaDeviceCount - The size of the output device array pCudaDevices. + * \param deviceList - The set of devices to return. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NO_DEVICE, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_GRAPHICS_CONTEXT, + * ::CUDA_ERROR_OPERATING_SYSTEM + * + * \notefnerr + * + * \sa + * ::cuWGLGetDevice, + * ::cudaGLGetDevices + */ +CUresult CUDAAPI cuGLGetDevices(unsigned int *pCudaDeviceCount, CUdevice *pCudaDevices, unsigned int cudaDeviceCount, CUGLDeviceList deviceList); + +/** + * \defgroup CUDA_GL_DEPRECATED OpenGL Interoperability [DEPRECATED] + * + * ___MANBRIEF___ deprecated OpenGL interoperability functions of the low-level + * CUDA driver API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes deprecated OpenGL interoperability functionality. + * + * @{ + */ + +/** Flags to map or unmap a resource */ +typedef enum CUGLmap_flags_enum { + CU_GL_MAP_RESOURCE_FLAGS_NONE = 0x00, + CU_GL_MAP_RESOURCE_FLAGS_READ_ONLY = 0x01, + CU_GL_MAP_RESOURCE_FLAGS_WRITE_DISCARD = 0x02, +} CUGLmap_flags; + +/** + * \brief Create a CUDA context for interoperability with OpenGL + * + * \deprecated This function is deprecated as of Cuda 5.0. + * + * This function is deprecated and should no longer be used. It is + * no longer necessary to associate a CUDA context with an OpenGL + * context in order to achieve maximum interoperability performance. + * + * \param pCtx - Returned CUDA context + * \param Flags - Options for CUDA context creation + * \param device - Device on which to create the context + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuCtxCreate, ::cuGLInit, ::cuGLMapBufferObject, + * ::cuGLRegisterBufferObject, ::cuGLUnmapBufferObject, + * ::cuGLUnregisterBufferObject, ::cuGLMapBufferObjectAsync, + * ::cuGLUnmapBufferObjectAsync, ::cuGLSetBufferObjectMapFlags, + * ::cuWGLGetDevice + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLCtxCreate(CUcontext *pCtx, unsigned int Flags, CUdevice device ); + +/** + * \brief Initializes OpenGL interoperability + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Initializes OpenGL interoperability. This function is deprecated + * and calling it is no longer required. It may fail if the needed + * OpenGL driver facilities are not available. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_UNKNOWN + * \notefnerr + * + * \sa ::cuGLMapBufferObject, + * ::cuGLRegisterBufferObject, ::cuGLUnmapBufferObject, + * ::cuGLUnregisterBufferObject, ::cuGLMapBufferObjectAsync, + * ::cuGLUnmapBufferObjectAsync, ::cuGLSetBufferObjectMapFlags, + * ::cuWGLGetDevice + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLInit(void); + +/** + * \brief Registers an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Registers the buffer object specified by \p buffer for access by + * CUDA. This function must be called before CUDA can map the buffer + * object. There must be a valid OpenGL context bound to the current + * thread when this function is called, and the buffer name is + * resolved by that context. + * + * \param buffer - The name of the buffer object to register. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_ALREADY_MAPPED + * \notefnerr + * + * \sa ::cuGraphicsGLRegisterBuffer + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLRegisterBufferObject(GLuint buffer); + +/** + * \brief Maps an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Maps the buffer object specified by \p buffer into the address space of the + * current CUDA context and returns in \p *dptr and \p *size the base pointer + * and size of the resulting mapping. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * All streams in the current CUDA context are synchronized with the + * current GL context. + * + * \param dptr - Returned mapped base pointer + * \param size - Returned size of mapping + * \param buffer - The name of the buffer object to map + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_MAP_FAILED + * \notefnerr + * + * \sa ::cuGraphicsMapResources + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLMapBufferObject(CUdeviceptr *dptr, size_t *size, GLuint buffer); + +/** + * \brief Unmaps an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Unmaps the buffer object specified by \p buffer for access by CUDA. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * All streams in the current CUDA context are synchronized with the + * current GL context. + * + * \param buffer - Buffer object to unmap + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuGraphicsUnmapResources + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLUnmapBufferObject(GLuint buffer); + +/** + * \brief Unregister an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Unregisters the buffer object specified by \p buffer. This + * releases any resources associated with the registered buffer. + * After this call, the buffer may no longer be mapped for access by + * CUDA. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * \param buffer - Name of the buffer object to unregister + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuGraphicsUnregisterResource + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLUnregisterBufferObject(GLuint buffer); + +/** + * \brief Set the map flags for an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Sets the map flags for the buffer object specified by \p buffer. + * + * Changes to \p Flags will take effect the next time \p buffer is mapped. + * The \p Flags argument may be any of the following: + * - ::CU_GL_MAP_RESOURCE_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA kernels. This is the default value. + * - ::CU_GL_MAP_RESOURCE_FLAGS_READ_ONLY: Specifies that CUDA kernels which + * access this resource will not write to this resource. + * - ::CU_GL_MAP_RESOURCE_FLAGS_WRITE_DISCARD: Specifies that CUDA kernels + * which access this resource will not read from this resource and will + * write over the entire contents of the resource, so none of the data + * previously stored in the resource will be preserved. + * + * If \p buffer has not been registered for use with CUDA, then + * ::CUDA_ERROR_INVALID_HANDLE is returned. If \p buffer is presently + * mapped for access by CUDA, then ::CUDA_ERROR_ALREADY_MAPPED is returned. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * \param buffer - Buffer object to unmap + * \param Flags - Map flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * \notefnerr + * + * \sa ::cuGraphicsResourceSetMapFlags + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLSetBufferObjectMapFlags(GLuint buffer, unsigned int Flags); + +/** + * \brief Maps an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Maps the buffer object specified by \p buffer into the address space of the + * current CUDA context and returns in \p *dptr and \p *size the base pointer + * and size of the resulting mapping. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * Stream \p hStream in the current CUDA context is synchronized with + * the current GL context. + * + * \param dptr - Returned mapped base pointer + * \param size - Returned size of mapping + * \param buffer - The name of the buffer object to map + * \param hStream - Stream to synchronize + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_MAP_FAILED + * \notefnerr + * + * \sa ::cuGraphicsMapResources + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLMapBufferObjectAsync(CUdeviceptr *dptr, size_t *size, GLuint buffer, CUstream hStream); + +/** + * \brief Unmaps an OpenGL buffer object + * + * \deprecated This function is deprecated as of Cuda 3.0. + * + * Unmaps the buffer object specified by \p buffer for access by CUDA. + * + * There must be a valid OpenGL context bound to the current thread + * when this function is called. This must be the same context, or a + * member of the same shareGroup, as the context that was bound when + * the buffer was registered. + * + * Stream \p hStream in the current CUDA context is synchronized with + * the current GL context. + * + * \param buffer - Name of the buffer object to unmap + * \param hStream - Stream to synchronize + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuGraphicsUnmapResources + */ +__CUDA_DEPRECATED CUresult CUDAAPI cuGLUnmapBufferObjectAsync(GLuint buffer, CUstream hStream); + +/** @} */ /* END CUDA_GL_DEPRECATED */ +/** @} */ /* END CUDA_GL */ + + +#if defined(__CUDA_API_VERSION_INTERNAL) + #undef cuGLCtxCreate + #undef cuGLMapBufferObject + #undef cuGLMapBufferObjectAsync + #undef cuGLGetDevices + + CUresult CUDAAPI cuGLGetDevices(unsigned int *pCudaDeviceCount, CUdevice *pCudaDevices, unsigned int cudaDeviceCount, CUGLDeviceList deviceList); + CUresult CUDAAPI cuGLMapBufferObject_v2(CUdeviceptr *dptr, size_t *size, GLuint buffer); + CUresult CUDAAPI cuGLMapBufferObjectAsync_v2(CUdeviceptr *dptr, size_t *size, GLuint buffer, CUstream hStream); + CUresult CUDAAPI cuGLCtxCreate(CUcontext *pCtx, unsigned int Flags, CUdevice device ); + CUresult CUDAAPI cuGLMapBufferObject(CUdeviceptr_v1 *dptr, unsigned int *size, GLuint buffer); + CUresult CUDAAPI cuGLMapBufferObjectAsync(CUdeviceptr_v1 *dptr, unsigned int *size, GLuint buffer, CUstream hStream); +#endif /* __CUDA_API_VERSION_INTERNAL */ + +#ifdef __cplusplus +}; +#endif + +#undef __CUDA_DEPRECATED + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGLTypedefs.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGLTypedefs.h new file mode 100644 index 0000000000000000000000000000000000000000..81f0d5349e435159647af9af379d1e8e8441221c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaGLTypedefs.h @@ -0,0 +1,123 @@ +/* + * Copyright 2020-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAGLTYPEDEFS_H +#define CUDAGLTYPEDEFS_H + +// Dependent includes for cudagl.h +#include + +#include + +#if defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) + #define __API_TYPEDEF_PTDS(api, default_version, ptds_version) api ## _v ## ptds_version ## _ptds + #define __API_TYPEDEF_PTSZ(api, default_version, ptds_version) api ## _v ## ptds_version ## _ptsz +#else + #define __API_TYPEDEF_PTDS(api, default_version, ptds_version) api ## _v ## default_version + #define __API_TYPEDEF_PTSZ(api, default_version, ptds_version) api ## _v ## default_version +#endif + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +/* + * Macros for the latest version for each driver function in cudaGL.h + */ +#define PFN_cuGraphicsGLRegisterBuffer PFN_cuGraphicsGLRegisterBuffer_v3000 +#define PFN_cuGraphicsGLRegisterImage PFN_cuGraphicsGLRegisterImage_v3000 +#define PFN_cuWGLGetDevice PFN_cuWGLGetDevice_v2020 +#define PFN_cuGLGetDevices PFN_cuGLGetDevices_v6050 +#define PFN_cuGLCtxCreate PFN_cuGLCtxCreate_v3020 +#define PFN_cuGLInit PFN_cuGLInit_v2000 +#define PFN_cuGLRegisterBufferObject PFN_cuGLRegisterBufferObject_v2000 +#define PFN_cuGLMapBufferObject __API_TYPEDEF_PTDS(PFN_cuGLMapBufferObject, 3020, 7000) +#define PFN_cuGLUnmapBufferObject PFN_cuGLUnmapBufferObject_v2000 +#define PFN_cuGLUnregisterBufferObject PFN_cuGLUnregisterBufferObject_v2000 +#define PFN_cuGLSetBufferObjectMapFlags PFN_cuGLSetBufferObjectMapFlags_v2030 +#define PFN_cuGLMapBufferObjectAsync __API_TYPEDEF_PTSZ(PFN_cuGLMapBufferObjectAsync, 3020, 7000) +#define PFN_cuGLUnmapBufferObjectAsync PFN_cuGLUnmapBufferObjectAsync_v2030 + + +/** + * Type definitions for functions defined in cudaGL.h + */ +typedef CUresult (CUDAAPI *PFN_cuGraphicsGLRegisterBuffer_v3000)(CUgraphicsResource *pCudaResource, GLuint buffer, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuGraphicsGLRegisterImage_v3000)(CUgraphicsResource *pCudaResource, GLuint image, GLenum target, unsigned int Flags); +#ifdef _WIN32 +typedef CUresult (CUDAAPI *PFN_cuWGLGetDevice_v2020)(CUdevice_v1 *pDevice, HGPUNV hGpu); +#endif +typedef CUresult (CUDAAPI *PFN_cuGLGetDevices_v6050)(unsigned int *pCudaDeviceCount, CUdevice_v1 *pCudaDevices, unsigned int cudaDeviceCount, CUGLDeviceList deviceList); +typedef CUresult (CUDAAPI *PFN_cuGLCtxCreate_v3020)(CUcontext *pCtx, unsigned int Flags, CUdevice_v1 device); +typedef CUresult (CUDAAPI *PFN_cuGLInit_v2000)(void); +typedef CUresult (CUDAAPI *PFN_cuGLRegisterBufferObject_v2000)(GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObject_v7000_ptds)(CUdeviceptr_v2 *dptr, size_t *size, GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLUnmapBufferObject_v2000)(GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLUnregisterBufferObject_v2000)(GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLSetBufferObjectMapFlags_v2030)(GLuint buffer, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObjectAsync_v7000_ptsz)(CUdeviceptr_v2 *dptr, size_t *size, GLuint buffer, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGLUnmapBufferObjectAsync_v2030)(GLuint buffer, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObject_v3020)(CUdeviceptr_v2 *dptr, size_t *size, GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObjectAsync_v3020)(CUdeviceptr_v2 *dptr, size_t *size, GLuint buffer, CUstream hStream); + +/* + * Type definitions for older versioned functions in cuda.h + */ +#if defined(__CUDA_API_VERSION_INTERNAL) +typedef CUresult (CUDAAPI *PFN_cuGLGetDevices_v4010)(unsigned int *pCudaDeviceCount, CUdevice_v1 *pCudaDevices, unsigned int cudaDeviceCount, CUGLDeviceList deviceList); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObject_v2000)(CUdeviceptr_v1 *dptr, unsigned int *size, GLuint buffer); +typedef CUresult (CUDAAPI *PFN_cuGLMapBufferObjectAsync_v2030)(CUdeviceptr_v1 *dptr, unsigned int *size, GLuint buffer, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGLCtxCreate_v2000)(CUcontext *pCtx, unsigned int Flags, CUdevice_v1 device); +#endif + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaProfilerTypedefs.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaProfilerTypedefs.h new file mode 100644 index 0000000000000000000000000000000000000000..bea7df4573aff2fa5b0d0029ce9d40a7ebe2de46 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaProfilerTypedefs.h @@ -0,0 +1,78 @@ +/* + * Copyright 2020-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAPROFILERTYPEDEFS_H +#define CUDAPROFILERTYPEDEFS_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +/* + * Macros for the latest version for each driver function in cudaProfiler.h + */ +#define PFN_cuProfilerInitialize PFN_cuProfilerInitialize_v4000 +#define PFN_cuProfilerStart PFN_cuProfilerStart_v4000 +#define PFN_cuProfilerStop PFN_cuProfilerStop_v4000 + + +/** + * Type definitions for functions defined in cudaProfiler.h + */ +typedef CUresult (CUDAAPI *PFN_cuProfilerInitialize_v4000)(const char *configFile, const char *outputFile, CUoutput_mode outputMode); +typedef CUresult (CUDAAPI *PFN_cuProfilerStart_v4000)(void); +typedef CUresult (CUDAAPI *PFN_cuProfilerStop_v4000)(void); + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaTypedefs.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaTypedefs.h new file mode 100644 index 0000000000000000000000000000000000000000..18fd7a559a81e59e4533ed175b1815209897e9ea --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaTypedefs.h @@ -0,0 +1,1102 @@ +/* + * Copyright 2020-2022 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDATYPEDEFS_H +#define CUDATYPEDEFS_H + +#include + +#if defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) + #define __API_TYPEDEF_PTDS(api, default_version, ptds_version) api ## _v ## ptds_version ## _ptds + #define __API_TYPEDEF_PTSZ(api, default_version, ptds_version) api ## _v ## ptds_version ## _ptsz +#else + #define __API_TYPEDEF_PTDS(api, default_version, ptds_version) api ## _v ## default_version + #define __API_TYPEDEF_PTSZ(api, default_version, ptds_version) api ## _v ## default_version +#endif + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +/* + * Macros for the latest version for each driver function in cuda.h + */ +#define PFN_cuGetErrorString PFN_cuGetErrorString_v6000 +#define PFN_cuGetErrorName PFN_cuGetErrorName_v6000 +#define PFN_cuInit PFN_cuInit_v2000 +#define PFN_cuDriverGetVersion PFN_cuDriverGetVersion_v2020 +#define PFN_cuDeviceGet PFN_cuDeviceGet_v2000 +#define PFN_cuDeviceGetCount PFN_cuDeviceGetCount_v2000 +#define PFN_cuDeviceGetName PFN_cuDeviceGetName_v2000 +#define PFN_cuDeviceGetUuid PFN_cuDeviceGetUuid_v11040 +#define PFN_cuDeviceGetLuid PFN_cuDeviceGetLuid_v10000 +#define PFN_cuDeviceTotalMem PFN_cuDeviceTotalMem_v3020 +#define PFN_cuDeviceGetTexture1DLinearMaxWidth PFN_cuDeviceGetTexture1DLinearMaxWidth_v11010 +#define PFN_cuDeviceGetAttribute PFN_cuDeviceGetAttribute_v2000 +#define PFN_cuDeviceGetNvSciSyncAttributes PFN_cuDeviceGetNvSciSyncAttributes_v10020 +#define PFN_cuDeviceSetMemPool PFN_cuDeviceSetMemPool_v11020 +#define PFN_cuDeviceGetMemPool PFN_cuDeviceGetMemPool_v11020 +#define PFN_cuDeviceGetDefaultMemPool PFN_cuDeviceGetDefaultMemPool_v11020 +#define PFN_cuDeviceGetProperties PFN_cuDeviceGetProperties_v2000 +#define PFN_cuDeviceComputeCapability PFN_cuDeviceComputeCapability_v2000 +#define PFN_cuDevicePrimaryCtxRetain PFN_cuDevicePrimaryCtxRetain_v7000 +#define PFN_cuDevicePrimaryCtxRelease PFN_cuDevicePrimaryCtxRelease_v11000 +#define PFN_cuDevicePrimaryCtxSetFlags PFN_cuDevicePrimaryCtxSetFlags_v11000 +#define PFN_cuDevicePrimaryCtxGetState PFN_cuDevicePrimaryCtxGetState_v7000 +#define PFN_cuDevicePrimaryCtxReset PFN_cuDevicePrimaryCtxReset_v11000 +#define PFN_cuDeviceGetExecAffinitySupport PFN_cuDeviceGetExecAffinitySupport_v11040 +#define PFN_cuCtxCreate PFN_cuCtxCreate_v11040 +#define PFN_cuCtxGetId PFN_cuCtxGetId_v12000 +#define PFN_cuCtxDestroy PFN_cuCtxDestroy_v4000 +#define PFN_cuCtxPushCurrent PFN_cuCtxPushCurrent_v4000 +#define PFN_cuCtxPopCurrent PFN_cuCtxPopCurrent_v4000 +#define PFN_cuCtxSetCurrent PFN_cuCtxSetCurrent_v4000 +#define PFN_cuCtxGetCurrent PFN_cuCtxGetCurrent_v4000 +#define PFN_cuCtxGetDevice PFN_cuCtxGetDevice_v2000 +#define PFN_cuCtxGetFlags PFN_cuCtxGetFlags_v7000 +#define PFN_cuCtxSetFlags PFN_cuCtxSetFlags_v12010 +#define PFN_cuCtxSynchronize PFN_cuCtxSynchronize_v2000 +#define PFN_cuCtxSetLimit PFN_cuCtxSetLimit_v3010 +#define PFN_cuCtxGetLimit PFN_cuCtxGetLimit_v3010 +#define PFN_cuCtxGetCacheConfig PFN_cuCtxGetCacheConfig_v3020 +#define PFN_cuCtxSetCacheConfig PFN_cuCtxSetCacheConfig_v3020 +#define PFN_cuCtxGetSharedMemConfig PFN_cuCtxGetSharedMemConfig_v4020 +#define PFN_cuCtxSetSharedMemConfig PFN_cuCtxSetSharedMemConfig_v4020 +#define PFN_cuCtxGetApiVersion PFN_cuCtxGetApiVersion_v3020 +#define PFN_cuCtxGetStreamPriorityRange PFN_cuCtxGetStreamPriorityRange_v5050 +#define PFN_cuCtxResetPersistingL2Cache PFN_cuCtxResetPersistingL2Cache_v11000 +#define PFN_cuCtxAttach PFN_cuCtxAttach_v2000 +#define PFN_cuCtxDetach PFN_cuCtxDetach_v2000 +#define PFN_cuCtxGetExecAffinity PFN_cuCtxGetExecAffinity_v11040 +#define PFN_cuModuleLoad PFN_cuModuleLoad_v2000 +#define PFN_cuModuleLoadData PFN_cuModuleLoadData_v2000 +#define PFN_cuModuleLoadDataEx PFN_cuModuleLoadDataEx_v2010 +#define PFN_cuModuleLoadFatBinary PFN_cuModuleLoadFatBinary_v2000 +#define PFN_cuModuleUnload PFN_cuModuleUnload_v2000 +#define PFN_cuModuleGetFunction PFN_cuModuleGetFunction_v2000 +#define PFN_cuModuleGetGlobal PFN_cuModuleGetGlobal_v3020 +#define PFN_cuModuleGetTexRef PFN_cuModuleGetTexRef_v2000 +#define PFN_cuModuleGetSurfRef PFN_cuModuleGetSurfRef_v3000 +#define PFN_cuModuleGetFunctionCount PFN_cuModuleGetFunctionCount_v12040 +#define PFN_cuModuleEnumerateFunctions PFN_cuModuleEnumerateFunctions_v12040 +#define PFN_cuLinkCreate PFN_cuLinkCreate_v6050 +#define PFN_cuLinkAddData PFN_cuLinkAddData_v6050 +#define PFN_cuLinkAddFile PFN_cuLinkAddFile_v6050 +#define PFN_cuLinkComplete PFN_cuLinkComplete_v5050 +#define PFN_cuLinkDestroy PFN_cuLinkDestroy_v5050 +#define PFN_cuMemGetInfo PFN_cuMemGetInfo_v3020 +#define PFN_cuMemAlloc PFN_cuMemAlloc_v3020 +#define PFN_cuMemAllocPitch PFN_cuMemAllocPitch_v3020 +#define PFN_cuMemFree PFN_cuMemFree_v3020 +#define PFN_cuMemGetAddressRange PFN_cuMemGetAddressRange_v3020 +#define PFN_cuMemAllocHost PFN_cuMemAllocHost_v3020 +#define PFN_cuMemFreeHost PFN_cuMemFreeHost_v2000 +#define PFN_cuMemHostAlloc PFN_cuMemHostAlloc_v2020 +#define PFN_cuMemHostGetDevicePointer PFN_cuMemHostGetDevicePointer_v3020 +#define PFN_cuMemHostGetFlags PFN_cuMemHostGetFlags_v2030 +#define PFN_cuMemAllocManaged PFN_cuMemAllocManaged_v6000 +#define PFN_cuDeviceGetByPCIBusId PFN_cuDeviceGetByPCIBusId_v4010 +#define PFN_cuDeviceGetPCIBusId PFN_cuDeviceGetPCIBusId_v4010 +#define PFN_cuIpcGetEventHandle PFN_cuIpcGetEventHandle_v4010 +#define PFN_cuIpcOpenEventHandle PFN_cuIpcOpenEventHandle_v4010 +#define PFN_cuIpcGetMemHandle PFN_cuIpcGetMemHandle_v4010 +#define PFN_cuIpcOpenMemHandle PFN_cuIpcOpenMemHandle_v11000 +#define PFN_cuIpcCloseMemHandle PFN_cuIpcCloseMemHandle_v4010 +#define PFN_cuMemHostRegister PFN_cuMemHostRegister_v6050 +#define PFN_cuMemHostUnregister PFN_cuMemHostUnregister_v4000 +#define PFN_cuMemcpy __API_TYPEDEF_PTDS(PFN_cuMemcpy, 4000, 7000) +#define PFN_cuMemcpyPeer __API_TYPEDEF_PTDS(PFN_cuMemcpyPeer, 4000, 7000) +#define PFN_cuMemcpyHtoD __API_TYPEDEF_PTDS(PFN_cuMemcpyHtoD, 3020, 7000) +#define PFN_cuMemcpyDtoH __API_TYPEDEF_PTDS(PFN_cuMemcpyDtoH, 3020, 7000) +#define PFN_cuMemcpyDtoD __API_TYPEDEF_PTDS(PFN_cuMemcpyDtoD, 3020, 7000) +#define PFN_cuMemcpyDtoA __API_TYPEDEF_PTDS(PFN_cuMemcpyDtoA, 3020, 7000) +#define PFN_cuMemcpyAtoD __API_TYPEDEF_PTDS(PFN_cuMemcpyAtoD, 3020, 7000) +#define PFN_cuMemcpyHtoA __API_TYPEDEF_PTDS(PFN_cuMemcpyHtoA, 3020, 7000) +#define PFN_cuMemcpyAtoH __API_TYPEDEF_PTDS(PFN_cuMemcpyAtoH, 3020, 7000) +#define PFN_cuMemcpyAtoA __API_TYPEDEF_PTDS(PFN_cuMemcpyAtoA, 3020, 7000) +#define PFN_cuMemcpy2D __API_TYPEDEF_PTDS(PFN_cuMemcpy2D, 3020, 7000) +#define PFN_cuMemcpy2DUnaligned __API_TYPEDEF_PTDS(PFN_cuMemcpy2DUnaligned, 3020, 7000) +#define PFN_cuMemcpy3D __API_TYPEDEF_PTDS(PFN_cuMemcpy3D, 3020, 7000) +#define PFN_cuMemcpy3DPeer __API_TYPEDEF_PTDS(PFN_cuMemcpy3DPeer, 4000, 7000) +#define PFN_cuMemcpyAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyAsync, 4000, 7000) +#define PFN_cuMemcpyPeerAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyPeerAsync, 4000, 7000) +#define PFN_cuMemcpyHtoDAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyHtoDAsync, 3020, 7000) +#define PFN_cuMemcpyDtoHAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyDtoHAsync, 3020, 7000) +#define PFN_cuMemcpyDtoDAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyDtoDAsync, 3020, 7000) +#define PFN_cuMemcpyHtoAAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyHtoAAsync, 3020, 7000) +#define PFN_cuMemcpyAtoHAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpyAtoHAsync, 3020, 7000) +#define PFN_cuMemcpy2DAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpy2DAsync, 3020, 7000) +#define PFN_cuMemcpy3DAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpy3DAsync, 3020, 7000) +#define PFN_cuMemcpy3DPeerAsync __API_TYPEDEF_PTSZ(PFN_cuMemcpy3DPeerAsync, 4000, 7000) +#define PFN_cuMemsetD8 __API_TYPEDEF_PTDS(PFN_cuMemsetD8, 3020, 7000) +#define PFN_cuMemsetD16 __API_TYPEDEF_PTDS(PFN_cuMemsetD16, 3020, 7000) +#define PFN_cuMemsetD32 __API_TYPEDEF_PTDS(PFN_cuMemsetD32, 3020, 7000) +#define PFN_cuMemsetD2D8 __API_TYPEDEF_PTDS(PFN_cuMemsetD2D8, 3020, 7000) +#define PFN_cuMemsetD2D16 __API_TYPEDEF_PTDS(PFN_cuMemsetD2D16, 3020, 7000) +#define PFN_cuMemsetD2D32 __API_TYPEDEF_PTDS(PFN_cuMemsetD2D32, 3020, 7000) +#define PFN_cuMemsetD8Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD8Async, 3020, 7000) +#define PFN_cuMemsetD16Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD16Async, 3020, 7000) +#define PFN_cuMemsetD32Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD32Async, 3020, 7000) +#define PFN_cuMemsetD2D8Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD2D8Async, 3020, 7000) +#define PFN_cuMemsetD2D16Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD2D16Async, 3020, 7000) +#define PFN_cuMemsetD2D32Async __API_TYPEDEF_PTSZ(PFN_cuMemsetD2D32Async, 3020, 7000) +#define PFN_cuArrayCreate PFN_cuArrayCreate_v3020 +#define PFN_cuArrayGetDescriptor PFN_cuArrayGetDescriptor_v3020 +#define PFN_cuArrayGetSparseProperties PFN_cuArrayGetSparseProperties_v11010 +#define PFN_cuMipmappedArrayGetSparseProperties PFN_cuMipmappedArrayGetSparseProperties_v11010 +#define PFN_cuArrayGetMemoryRequirements PFN_cuArrayGetMemoryRequirements_v11060 +#define PFN_cuMipmappedArrayGetMemoryRequirements PFN_cuMipmappedArrayGetMemoryRequirements_v11060 +#define PFN_cuArrayGetPlane PFN_cuArrayGetPlane_v11020 +#define PFN_cuArrayDestroy PFN_cuArrayDestroy_v2000 +#define PFN_cuArray3DCreate PFN_cuArray3DCreate_v3020 +#define PFN_cuArray3DGetDescriptor PFN_cuArray3DGetDescriptor_v3020 +#define PFN_cuMipmappedArrayCreate PFN_cuMipmappedArrayCreate_v5000 +#define PFN_cuMipmappedArrayGetLevel PFN_cuMipmappedArrayGetLevel_v5000 +#define PFN_cuMipmappedArrayDestroy PFN_cuMipmappedArrayDestroy_v5000 +#define PFN_cuMemAddressReserve PFN_cuMemAddressReserve_v10020 +#define PFN_cuMemAddressFree PFN_cuMemAddressFree_v10020 +#define PFN_cuMemCreate PFN_cuMemCreate_v10020 +#define PFN_cuMemRelease PFN_cuMemRelease_v10020 +#define PFN_cuMemMap PFN_cuMemMap_v10020 +#define PFN_cuMemMapArrayAsync __API_TYPEDEF_PTSZ(PFN_cuMemMapArrayAsync, 11010, 11010) +#define PFN_cuMemUnmap PFN_cuMemUnmap_v10020 +#define PFN_cuMemSetAccess PFN_cuMemSetAccess_v10020 +#define PFN_cuMemGetAccess PFN_cuMemGetAccess_v10020 +#define PFN_cuMemExportToShareableHandle PFN_cuMemExportToShareableHandle_v10020 +#define PFN_cuMemImportFromShareableHandle PFN_cuMemImportFromShareableHandle_v10020 +#define PFN_cuMemGetAllocationGranularity PFN_cuMemGetAllocationGranularity_v10020 +#define PFN_cuMemGetAllocationPropertiesFromHandle PFN_cuMemGetAllocationPropertiesFromHandle_v10020 +#define PFN_cuMemRetainAllocationHandle PFN_cuMemRetainAllocationHandle_v11000 +#define PFN_cuMemFreeAsync __API_TYPEDEF_PTSZ(PFN_cuMemFreeAsync, 11020, 11020) +#define PFN_cuMemAllocAsync __API_TYPEDEF_PTSZ(PFN_cuMemAllocAsync, 11020, 11020) +#define PFN_cuMemPoolTrimTo PFN_cuMemPoolTrimTo_v11020 +#define PFN_cuMemPoolSetAttribute PFN_cuMemPoolSetAttribute_v11020 +#define PFN_cuMemPoolGetAttribute PFN_cuMemPoolGetAttribute_v11020 +#define PFN_cuMemPoolSetAccess PFN_cuMemPoolSetAccess_v11020 +#define PFN_cuMemPoolGetAccess PFN_cuMemPoolGetAccess_v11020 +#define PFN_cuMemPoolCreate PFN_cuMemPoolCreate_v11020 +#define PFN_cuMemPoolDestroy PFN_cuMemPoolDestroy_v11020 +#define PFN_cuMemAllocFromPoolAsync __API_TYPEDEF_PTSZ(PFN_cuMemAllocFromPoolAsync, 11020, 11020) +#define PFN_cuMemPoolExportToShareableHandle PFN_cuMemPoolExportToShareableHandle_v11020 +#define PFN_cuMemPoolImportFromShareableHandle PFN_cuMemPoolImportFromShareableHandle_v11020 +#define PFN_cuMemPoolExportPointer PFN_cuMemPoolExportPointer_v11020 +#define PFN_cuMemPoolImportPointer PFN_cuMemPoolImportPointer_v11020 +#define PFN_cuPointerGetAttribute PFN_cuPointerGetAttribute_v4000 +#define PFN_cuMemPrefetchAsync __API_TYPEDEF_PTSZ(PFN_cuMemPrefetchAsync, 8000, 8000) +#define PFN_cuMemAdvise PFN_cuMemAdvise_v8000 +#define PFN_cuMemAdvise_v2 PFN_cuMemAdvise_v12020 +#define PFN_cuMemPrefetchAsync_v2 __API_TYPEDEF_PTSZ(PFN_cuMemPrefetchAsync, 12020, 12020) +#define PFN_cuMemRangeGetAttribute PFN_cuMemRangeGetAttribute_v8000 +#define PFN_cuMemRangeGetAttributes PFN_cuMemRangeGetAttributes_v8000 +#define PFN_cuMulticastCreate PFN_cuMulticastCreate_v12010 +#define PFN_cuMulticastAddDevice PFN_cuMulticastAddDevice_v12010 +#define PFN_cuMulticastBindMem PFN_cuMulticastBindMem_v12010 +#define PFN_cuMulticastBindAddr PFN_cuMulticastBindAddr_v12010 +#define PFN_cuMulticastUnbind PFN_cuMulticastUnbind_v12010 +#define PFN_cuMulticastGetGranularity PFN_cuMulticastGetGranularity_v12010 +#define PFN_cuPointerSetAttribute PFN_cuPointerSetAttribute_v6000 +#define PFN_cuPointerGetAttributes PFN_cuPointerGetAttributes_v7000 +#define PFN_cuStreamCreate PFN_cuStreamCreate_v2000 +#define PFN_cuStreamCreateWithPriority PFN_cuStreamCreateWithPriority_v5050 +#define PFN_cuStreamGetId __API_TYPEDEF_PTSZ(PFN_cuStreamGetId_v12000, 12000, 12000) +#define PFN_cuStreamGetPriority __API_TYPEDEF_PTSZ(PFN_cuStreamGetPriority, 5050, 7000) +#define PFN_cuStreamGetFlags __API_TYPEDEF_PTSZ(PFN_cuStreamGetFlags, 5050, 7000) +#define PFN_cuStreamGetCtx __API_TYPEDEF_PTSZ(PFN_cuStreamGetCtx, 9020, 9020) +#define PFN_cuStreamWaitEvent __API_TYPEDEF_PTSZ(PFN_cuStreamWaitEvent, 3020, 7000) +#define PFN_cuStreamAddCallback __API_TYPEDEF_PTSZ(PFN_cuStreamAddCallback, 5000, 7000) +#define PFN_cuStreamBeginCapture __API_TYPEDEF_PTSZ(PFN_cuStreamBeginCapture, 10010, 10010) +#define PFN_cuStreamBeginCaptureToGraph __API_TYPEDEF_PTSZ(PFN_cuStreamBeginCaptureToGraph, 12030, 12030) +#define PFN_cuThreadExchangeStreamCaptureMode PFN_cuThreadExchangeStreamCaptureMode_v10010 +#define PFN_cuStreamEndCapture __API_TYPEDEF_PTSZ(PFN_cuStreamEndCapture, 10000, 10000) +#define PFN_cuStreamIsCapturing __API_TYPEDEF_PTSZ(PFN_cuStreamIsCapturing, 10000, 10000) +#define PFN_cuStreamGetCaptureInfo __API_TYPEDEF_PTSZ(PFN_cuStreamGetCaptureInfo, 10010, 10010) +#define PFN_cuStreamGetCaptureInfo_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamGetCaptureInfo, 11030, 11030) +#define PFN_cuStreamGetCaptureInfo_v3 __API_TYPEDEF_PTSZ(PFN_cuStreamGetCaptureInfo, 12030, 12030) +#define PFN_cuStreamUpdateCaptureDependencies __API_TYPEDEF_PTSZ(PFN_cuStreamUpdateCaptureDependencies, 11030, 11030) +#define PFN_cuStreamUpdateCaptureDependencies_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamUpdateCaptureDependencies, 12030, 12030) +#define PFN_cuStreamAttachMemAsync __API_TYPEDEF_PTSZ(PFN_cuStreamAttachMemAsync, 6000, 7000) +#define PFN_cuStreamQuery __API_TYPEDEF_PTSZ(PFN_cuStreamQuery, 2000, 7000) +#define PFN_cuStreamSynchronize __API_TYPEDEF_PTSZ(PFN_cuStreamSynchronize, 2000, 7000) +#define PFN_cuStreamDestroy PFN_cuStreamDestroy_v4000 +#define PFN_cuStreamCopyAttributes __API_TYPEDEF_PTSZ(PFN_cuStreamCopyAttributes, 11000, 11000) +#define PFN_cuStreamGetAttribute __API_TYPEDEF_PTSZ(PFN_cuStreamGetAttribute, 11000, 11000) +#define PFN_cuStreamSetAttribute __API_TYPEDEF_PTSZ(PFN_cuStreamSetAttribute, 11000, 11000) +#define PFN_cuEventCreate PFN_cuEventCreate_v2000 +#define PFN_cuEventRecord __API_TYPEDEF_PTSZ(PFN_cuEventRecord, 2000, 7000) +#define PFN_cuEventRecordWithFlags __API_TYPEDEF_PTSZ(PFN_cuEventRecordWithFlags, 11010, 11010) +#define PFN_cuEventQuery PFN_cuEventQuery_v2000 +#define PFN_cuEventSynchronize PFN_cuEventSynchronize_v2000 +#define PFN_cuEventDestroy PFN_cuEventDestroy_v4000 +#define PFN_cuEventElapsedTime PFN_cuEventElapsedTime_v2000 +#define PFN_cuImportExternalMemory PFN_cuImportExternalMemory_v10000 +#define PFN_cuExternalMemoryGetMappedBuffer PFN_cuExternalMemoryGetMappedBuffer_v10000 +#define PFN_cuExternalMemoryGetMappedMipmappedArray PFN_cuExternalMemoryGetMappedMipmappedArray_v10000 +#define PFN_cuDestroyExternalMemory PFN_cuDestroyExternalMemory_v10000 +#define PFN_cuImportExternalSemaphore PFN_cuImportExternalSemaphore_v10000 +#define PFN_cuSignalExternalSemaphoresAsync __API_TYPEDEF_PTSZ(PFN_cuSignalExternalSemaphoresAsync, 10000, 10000) +#define PFN_cuWaitExternalSemaphoresAsync __API_TYPEDEF_PTSZ(PFN_cuWaitExternalSemaphoresAsync, 10000, 10000) +#define PFN_cuDestroyExternalSemaphore PFN_cuDestroyExternalSemaphore_v10000 +#define PFN_cuStreamWaitValue32 __API_TYPEDEF_PTSZ(PFN_cuStreamWaitValue32, 8000, 8000) +#define PFN_cuStreamWaitValue64 __API_TYPEDEF_PTSZ(PFN_cuStreamWaitValue64, 9000, 9000) +#define PFN_cuStreamWriteValue32 __API_TYPEDEF_PTSZ(PFN_cuStreamWriteValue32, 8000, 8000) +#define PFN_cuStreamWriteValue64 __API_TYPEDEF_PTSZ(PFN_cuStreamWriteValue64, 9000, 9000) +#define PFN_cuStreamBatchMemOp __API_TYPEDEF_PTSZ(PFN_cuStreamBatchMemOp, 8000, 8000) +#define PFN_cuStreamWaitValue32_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamWaitValue32, 11070, 11070) +#define PFN_cuStreamWaitValue64_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamWaitValue64, 11070, 11070) +#define PFN_cuStreamWriteValue32_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamWriteValue32, 11070, 11070) +#define PFN_cuStreamWriteValue64_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamWriteValue64, 11070, 11070) +#define PFN_cuStreamBatchMemOp_v2 __API_TYPEDEF_PTSZ(PFN_cuStreamBatchMemOp, 11070, 11070) +#define PFN_cuFuncGetAttribute PFN_cuFuncGetAttribute_v2020 +#define PFN_cuFuncSetAttribute PFN_cuFuncSetAttribute_v9000 +#define PFN_cuFuncSetCacheConfig PFN_cuFuncSetCacheConfig_v3000 +#define PFN_cuFuncSetSharedMemConfig PFN_cuFuncSetSharedMemConfig_v4020 +#define PFN_cuFuncGetName PFN_cuFuncGetName_v12030 +#define PFN_cuFuncGetParamInfo PFN_cuFuncGetParamInfo_v12040 +#define PFN_cuFuncIsLoaded PFN_cuFuncIsLoaded_v12040 +#define PFN_cuFuncLoad PFN_cuFuncLoad_v12040 +#define PFN_cuLaunchKernel __API_TYPEDEF_PTSZ(PFN_cuLaunchKernel, 4000, 7000) +#define PFN_cuLaunchKernelEx __API_TYPEDEF_PTSZ(PFN_cuLaunchKernelEx, 11060, 11060) +#define PFN_cuLaunchCooperativeKernel __API_TYPEDEF_PTSZ(PFN_cuLaunchCooperativeKernel, 9000, 9000) +#define PFN_cuLaunchCooperativeKernelMultiDevice PFN_cuLaunchCooperativeKernelMultiDevice_v9000 +#define PFN_cuLaunchHostFunc __API_TYPEDEF_PTSZ(PFN_cuLaunchHostFunc, 10000, 10000) +#define PFN_cuFuncSetBlockShape PFN_cuFuncSetBlockShape_v2000 +#define PFN_cuFuncSetSharedSize PFN_cuFuncSetSharedSize_v2000 +#define PFN_cuParamSetSize PFN_cuParamSetSize_v2000 +#define PFN_cuParamSeti PFN_cuParamSeti_v2000 +#define PFN_cuParamSetf PFN_cuParamSetf_v2000 +#define PFN_cuParamSetv PFN_cuParamSetv_v2000 +#define PFN_cuLaunch PFN_cuLaunch_v2000 +#define PFN_cuLaunchGrid PFN_cuLaunchGrid_v2000 +#define PFN_cuLaunchGridAsync PFN_cuLaunchGridAsync_v2000 +#define PFN_cuParamSetTexRef PFN_cuParamSetTexRef_v2000 +#define PFN_cuGraphCreate PFN_cuGraphCreate_v10000 +#define PFN_cuGraphAddKernelNode PFN_cuGraphAddKernelNode_v12000 +#define PFN_cuGraphKernelNodeGetParams PFN_cuGraphKernelNodeGetParams_v12000 +#define PFN_cuGraphKernelNodeSetParams PFN_cuGraphKernelNodeSetParams_v12000 +#define PFN_cuGraphAddMemcpyNode PFN_cuGraphAddMemcpyNode_v10000 +#define PFN_cuGraphMemcpyNodeGetParams PFN_cuGraphMemcpyNodeGetParams_v10000 +#define PFN_cuGraphMemcpyNodeSetParams PFN_cuGraphMemcpyNodeSetParams_v10000 +#define PFN_cuGraphAddMemsetNode PFN_cuGraphAddMemsetNode_v10000 +#define PFN_cuGraphMemsetNodeGetParams PFN_cuGraphMemsetNodeGetParams_v10000 +#define PFN_cuGraphMemsetNodeSetParams PFN_cuGraphMemsetNodeSetParams_v10000 +#define PFN_cuGraphAddHostNode PFN_cuGraphAddHostNode_v10000 +#define PFN_cuGraphHostNodeGetParams PFN_cuGraphHostNodeGetParams_v10000 +#define PFN_cuGraphHostNodeSetParams PFN_cuGraphHostNodeSetParams_v10000 +#define PFN_cuGraphAddChildGraphNode PFN_cuGraphAddChildGraphNode_v10000 +#define PFN_cuGraphChildGraphNodeGetGraph PFN_cuGraphChildGraphNodeGetGraph_v10000 +#define PFN_cuGraphAddEmptyNode PFN_cuGraphAddEmptyNode_v10000 +#define PFN_cuGraphAddEventRecordNode PFN_cuGraphAddEventRecordNode_v11010 +#define PFN_cuGraphEventRecordNodeGetEvent PFN_cuGraphEventRecordNodeGetEvent_v11010 +#define PFN_cuGraphEventRecordNodeSetEvent PFN_cuGraphEventRecordNodeSetEvent_v11010 +#define PFN_cuGraphAddEventWaitNode PFN_cuGraphAddEventWaitNode_v11010 +#define PFN_cuGraphEventWaitNodeGetEvent PFN_cuGraphEventWaitNodeGetEvent_v11010 +#define PFN_cuGraphEventWaitNodeSetEvent PFN_cuGraphEventWaitNodeSetEvent_v11010 +#define PFN_cuGraphAddExternalSemaphoresSignalNode PFN_cuGraphAddExternalSemaphoresSignalNode_v11020 +#define PFN_cuGraphExternalSemaphoresSignalNodeGetParams PFN_cuGraphExternalSemaphoresSignalNodeGetParams_v11020 +#define PFN_cuGraphExternalSemaphoresSignalNodeSetParams PFN_cuGraphExternalSemaphoresSignalNodeSetParams_v11020 +#define PFN_cuGraphAddExternalSemaphoresWaitNode PFN_cuGraphAddExternalSemaphoresWaitNode_v11020 +#define PFN_cuGraphExternalSemaphoresWaitNodeGetParams PFN_cuGraphExternalSemaphoresWaitNodeGetParams_v11020 +#define PFN_cuGraphExternalSemaphoresWaitNodeSetParams PFN_cuGraphExternalSemaphoresWaitNodeSetParams_v11020 +#define PFN_cuGraphAddBatchMemOpNode PFN_cuGraphAddBatchMemOpNode_v11070 +#define PFN_cuGraphBatchMemOpNodeGetParams PFN_cuGraphBatchMemOpNodeGetParams_v11070 +#define PFN_cuGraphBatchMemOpNodeSetParams PFN_cuGraphBatchMemOpNodeSetParams _v11070 +#define PFN_cuGraphExecBatchMemOpNodeSetParams PFN_cuGraphExecBatchMemOpNodeSetParams_v11070 +#define PFN_cuGraphClone PFN_cuGraphClone_v10000 +#define PFN_cuGraphNodeFindInClone PFN_cuGraphNodeFindInClone_v10000 +#define PFN_cuGraphNodeGetType PFN_cuGraphNodeGetType_v10000 +#define PFN_cuGraphGetNodes PFN_cuGraphGetNodes_v10000 +#define PFN_cuGraphGetRootNodes PFN_cuGraphGetRootNodes_v10000 +#define PFN_cuGraphGetEdges PFN_cuGraphGetEdges_v12030 +#define PFN_cuGraphNodeGetDependencies PFN_cuGraphNodeGetDependencies_v12030 +#define PFN_cuGraphNodeGetDependentNodes PFN_cuGraphNodeGetDependentNodes_v12030 +#define PFN_cuGraphAddDependencies PFN_cuGraphAddDependencies_v12030 +#define PFN_cuGraphRemoveDependencies PFN_cuGraphRemoveDependencies_v12030 +#define PFN_cuGraphDestroyNode PFN_cuGraphDestroyNode_v10000 + +#define PFN_cuGraphInstantiate PFN_cuGraphInstantiateWithFlags_v11040 + +#define PFN_cuGraphInstantiateWithFlags PFN_cuGraphInstantiateWithFlags_v11040 +#define PFN_cuGraphInstantiateWithParams __API_TYPEDEF_PTSZ(PFN_cuGraphInstantiateWithParams, 12000, 12000) +#define PFN_cuGraphExecGetFlags PFN_cuGraphExecGetFlags_v12000 +#define PFN_cuGraphExecKernelNodeSetParams PFN_cuGraphExecKernelNodeSetParams_v12000 +#define PFN_cuGraphExecMemcpyNodeSetParams PFN_cuGraphExecMemcpyNodeSetParams_v10020 +#define PFN_cuGraphExecMemsetNodeSetParams PFN_cuGraphExecMemsetNodeSetParams_v10020 +#define PFN_cuGraphExecHostNodeSetParams PFN_cuGraphExecHostNodeSetParams_v10020 +#define PFN_cuGraphExecChildGraphNodeSetParams PFN_cuGraphExecChildGraphNodeSetParams_v11010 +#define PFN_cuGraphExecEventRecordNodeSetEvent PFN_cuGraphExecEventRecordNodeSetEvent_v11010 +#define PFN_cuGraphExecEventWaitNodeSetEvent PFN_cuGraphExecEventWaitNodeSetEvent_v11010 +#define PFN_cuGraphExecExternalSemaphoresSignalNodeSetParams PFN_cuGraphExecExternalSemaphoresSignalNodeSetParams_v11020 +#define PFN_cuGraphExecExternalSemaphoresWaitNodeSetParams PFN_cuGraphExecExternalSemaphoresWaitNodeSetParams_v11020 +#define PFN_cuGraphUpload __API_TYPEDEF_PTSZ(PFN_cuGraphUpload, 11010, 11010) +#define PFN_cuGraphLaunch __API_TYPEDEF_PTSZ(PFN_cuGraphLaunch, 10000, 10000) +#define PFN_cuGraphExecDestroy PFN_cuGraphExecDestroy_v10000 +#define PFN_cuGraphDestroy PFN_cuGraphDestroy_v10000 +#define PFN_cuGraphExecUpdate PFN_cuGraphExecUpdate_v12000 +#define PFN_cuGraphKernelNodeCopyAttributes PFN_cuGraphKernelNodeCopyAttributes_v11000 +#define PFN_cuGraphKernelNodeGetAttribute PFN_cuGraphKernelNodeGetAttribute_v11000 +#define PFN_cuGraphKernelNodeSetAttribute PFN_cuGraphKernelNodeSetAttribute_v11000 +#define PFN_cuGraphDebugDotPrint PFN_cuGraphDebugDotPrint_v11030 +#define PFN_cuGraphAddMemAllocNode PFN_cuGraphAddMemAllocNode_v11040 +#define PFN_cuGraphMemAllocNodeGetParams PFN_cuGraphMemAllocNodeGetParams_v11040 +#define PFN_cuGraphAddMemFreeNode PFN_cuGraphAddMemFreeNode_v11040 +#define PFN_cuGraphMemFreeNodeGetParams PFN_cuGraphMemFreeNodeGetParams_v11040 +#define PFN_cuGraphNodeSetEnabled PFN_cuGraphNodeSetEnabled_v11060 +#define PFN_cuGraphNodeGetEnabled PFN_cuGraphNodeGetEnabled_v11060 +#define PFN_cuGraphAddNode PFN_cuGraphAddNode_v12030 +#define PFN_cuGraphNodeSetParams PFN_cuGraphNodeSetParams_v12020 +#define PFN_cuGraphExecNodeSetParams PFN_cuGraphExecNodeSetParams_v12020 +#define PFN_GraphConditionalHandleCreate PFN_cuGraphConditionalHandleCreate_v12030 +#define PFN_cuDeviceGraphMemTrim PFN_cuDeviceGraphMemTrim_v11040 +#define PFN_cuDeviceGetGraphMemAttribute PFN_cuDeviceGetGraphMemAttribute_v11040 +#define PFN_cuDeviceSetGraphMemAttribute PFN_cuDeviceSetGraphMemAttribute_v11040 +#define PFN_cuOccupancyMaxActiveBlocksPerMultiprocessor PFN_cuOccupancyMaxActiveBlocksPerMultiprocessor_v6050 +#define PFN_cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags PFN_cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_v7000 +#define PFN_cuOccupancyMaxPotentialBlockSize PFN_cuOccupancyMaxPotentialBlockSize_v6050 +#define PFN_cuOccupancyMaxPotentialBlockSizeWithFlags PFN_cuOccupancyMaxPotentialBlockSizeWithFlags_v7000 +#define PFN_cuOccupancyAvailableDynamicSMemPerBlock PFN_cuOccupancyAvailableDynamicSMemPerBlock_v10020 +#define PFN_cuOccupancyMaxPotentialClusterSize PFN_cuOccupancyMaxPotentialClusterSize_v11070 +#define PFN_cuOccupancyMaxActiveClusters PFN_cuOccupancyMaxActiveClusters_v11070 +#define PFN_cuTexRefSetArray PFN_cuTexRefSetArray_v2000 +#define PFN_cuTexRefSetMipmappedArray PFN_cuTexRefSetMipmappedArray_v5000 +#define PFN_cuTexRefSetAddress PFN_cuTexRefSetAddress_v3020 +#define PFN_cuTexRefSetAddress2D PFN_cuTexRefSetAddress2D_v4010 +#define PFN_cuTexRefSetFormat PFN_cuTexRefSetFormat_v2000 +#define PFN_cuTexRefSetAddressMode PFN_cuTexRefSetAddressMode_v2000 +#define PFN_cuTexRefSetFilterMode PFN_cuTexRefSetFilterMode_v2000 +#define PFN_cuTexRefSetMipmapFilterMode PFN_cuTexRefSetMipmapFilterMode_v5000 +#define PFN_cuTexRefSetMipmapLevelBias PFN_cuTexRefSetMipmapLevelBias_v5000 +#define PFN_cuTexRefSetMipmapLevelClamp PFN_cuTexRefSetMipmapLevelClamp_v5000 +#define PFN_cuTexRefSetMaxAnisotropy PFN_cuTexRefSetMaxAnisotropy_v5000 +#define PFN_cuTexRefSetBorderColor PFN_cuTexRefSetBorderColor_v8000 +#define PFN_cuTexRefSetFlags PFN_cuTexRefSetFlags_v2000 +#define PFN_cuTexRefGetAddress PFN_cuTexRefGetAddress_v3020 +#define PFN_cuTexRefGetArray PFN_cuTexRefGetArray_v2000 +#define PFN_cuTexRefGetMipmappedArray PFN_cuTexRefGetMipmappedArray_v5000 +#define PFN_cuTexRefGetAddressMode PFN_cuTexRefGetAddressMode_v2000 +#define PFN_cuTexRefGetFilterMode PFN_cuTexRefGetFilterMode_v2000 +#define PFN_cuTexRefGetFormat PFN_cuTexRefGetFormat_v2000 +#define PFN_cuTexRefGetMipmapFilterMode PFN_cuTexRefGetMipmapFilterMode_v5000 +#define PFN_cuTexRefGetMipmapLevelBias PFN_cuTexRefGetMipmapLevelBias_v5000 +#define PFN_cuTexRefGetMipmapLevelClamp PFN_cuTexRefGetMipmapLevelClamp_v5000 +#define PFN_cuTexRefGetMaxAnisotropy PFN_cuTexRefGetMaxAnisotropy_v5000 +#define PFN_cuTexRefGetBorderColor PFN_cuTexRefGetBorderColor_v8000 +#define PFN_cuTexRefGetFlags PFN_cuTexRefGetFlags_v2000 +#define PFN_cuTexRefCreate PFN_cuTexRefCreate_v2000 +#define PFN_cuTexRefDestroy PFN_cuTexRefDestroy_v2000 +#define PFN_cuSurfRefSetArray PFN_cuSurfRefSetArray_v3000 +#define PFN_cuSurfRefGetArray PFN_cuSurfRefGetArray_v3000 +#define PFN_cuTexObjectCreate PFN_cuTexObjectCreate_v5000 +#define PFN_cuTexObjectDestroy PFN_cuTexObjectDestroy_v5000 +#define PFN_cuTexObjectGetResourceDesc PFN_cuTexObjectGetResourceDesc_v5000 +#define PFN_cuTexObjectGetTextureDesc PFN_cuTexObjectGetTextureDesc_v5000 +#define PFN_cuTexObjectGetResourceViewDesc PFN_cuTexObjectGetResourceViewDesc_v5000 +#define PFN_cuSurfObjectCreate PFN_cuSurfObjectCreate_v5000 +#define PFN_cuSurfObjectDestroy PFN_cuSurfObjectDestroy_v5000 +#define PFN_cuSurfObjectGetResourceDesc PFN_cuSurfObjectGetResourceDesc_v5000 +#define PFN_cuTensorMapEncodeTiled PFN_cuTensorMapEncodeTiled_v12000 +#define PFN_cuTensorMapEncodeIm2col PFN_cuTensorMapEncodeIm2col_v12000 +#define PFN_cuTensorMapReplaceAddress PFN_cuTensorMapReplaceAddress_v12000 +#define PFN_cuDeviceCanAccessPeer PFN_cuDeviceCanAccessPeer_v4000 +#define PFN_cuCtxEnablePeerAccess PFN_cuCtxEnablePeerAccess_v4000 +#define PFN_cuCtxDisablePeerAccess PFN_cuCtxDisablePeerAccess_v4000 +#define PFN_cuDeviceGetP2PAttribute PFN_cuDeviceGetP2PAttribute_v8000 +#define PFN_cuGraphicsUnregisterResource PFN_cuGraphicsUnregisterResource_v3000 +#define PFN_cuGraphicsSubResourceGetMappedArray PFN_cuGraphicsSubResourceGetMappedArray_v3000 +#define PFN_cuGraphicsResourceGetMappedMipmappedArray PFN_cuGraphicsResourceGetMappedMipmappedArray_v5000 +#define PFN_cuGraphicsResourceGetMappedPointer PFN_cuGraphicsResourceGetMappedPointer_v3020 +#define PFN_cuGraphicsResourceSetMapFlags PFN_cuGraphicsResourceSetMapFlags_v6050 +#define PFN_cuGraphicsMapResources __API_TYPEDEF_PTSZ(PFN_cuGraphicsMapResources, 3000, 7000) +#define PFN_cuGraphicsUnmapResources __API_TYPEDEF_PTSZ(PFN_cuGraphicsUnmapResources, 3000, 7000) +#define PFN_cuGetExportTable PFN_cuGetExportTable_v3000 +#define PFN_cuFuncGetModule PFN_cuFuncGetModule_v11000 +#define PFN_cuFlushGPUDirectRDMAWrites PFN_cuFlushGPUDirectRDMAWrites_v11030 +#define PFN_cuGetProcAddress PFN_cuGetProcAddress_v12000 +#define PFN_cuUserObjectCreate PFN_cuUserObjectCreate_v11030 +#define PFN_cuUserObjectRetain PFN_cuUserObjectRetain_v11030 +#define PFN_cuUserObjectRelease PFN_cuUserObjectRelease_v11030 +#define PFN_cuGraphRetainUserObject PFN_cuGraphRetainUserObject_v11030 +#define PFN_cuGraphReleaseUserObject PFN_cuGraphReleaseUserObject_v11030 +#define PFN_cuModuleGetLoadingMode PFN_cuModuleGetLoadingMode_v11070 +#define PFN_cuMemGetHandleForAddressRange PFN_cuMemGetHandleForAddressRange_v11070 +#define PFN_cuLibraryLoadData PFN_cuLibraryLoadData_v12000 +#define PFN_cuLibraryLoadFromFile PFN_cuLibraryLoadFromFile_v12000 +#define PFN_cuLibraryUnload PFN_cuLibraryUnload_v12000 +#define PFN_cuLibraryGetKernel PFN_cuLibraryGetKernel_v12000 +#define PFN_cuLibraryGetModule PFN_cuLibraryGetModule_v12000 +#define PFN_cuKernelGetFunction PFN_cuKernelGetFunction_v12000 +#define PFN_cuLibraryGetGlobal PFN_cuLibraryGetGlobal_v12000 +#define PFN_cuLibraryGetManaged PFN_cuLibraryGetManaged_v12000 +#define PFN_cuLibraryGetKernelCount PFN_cuLibraryGetKernelCount_v12040 +#define PFN_cuLibraryEnumerateKernels PFN_cuLibraryEnumerateKernels_v12040 +#define PFN_cuKernelGetAttribute PFN_cuKernelGetAttribute_v12000 +#define PFN_cuKernelSetAttribute PFN_cuKernelSetAttribute_v12000 +#define PFN_cuKernelSetCacheConfig PFN_cuKernelSetCacheConfig_v12000 +#define PFN_cuKernelGetName PFN_cuKernelGetName_v12030 +#define PFN_cuKernelGetParamInfo PFN_cuKernelGetParamInfo_v12040 +#define PFN_cuLibraryGetUnifiedFunction PFN_cuLibraryGetUnifiedFunction_v12000 +#define PFN_cuCoredumpGetAttribute PFN_cuCoredumpGetAttribute_v12010 +#define PFN_cuCoredumpGetAttributeGlobal PFN_cuCoredumpGetAttributeGlobal_v12010 +#define PFN_cuCoredumpSetAttribute PFN_cuCoredumpSetAttribute_v12010 +#define PFN_cuCoredumpSetAttributeGlobal PFN_cuCoredumpSetAttributeGlobal_v12010 +#define PFN_cuDeviceRegisterAsyncNotification PFN_cuDeviceRegisterAsyncNotification_v12040 +#define PFN_cuDeviceUnregisterAsyncNotification PFN_cuDeviceUnregisterAsyncNotification_v12040 +#define PFN_cuGreenCtxCreate PFN_cuGreenCtxCreate_v12040 +#define PFN_cuGreenCtxDestroy PFN_cuGreenCtxDestroy_v12040 +#define PFN_cuDeviceGetDevResource PFN_cuDeviceGetDevResource_v12040 +#define PFN_cuCtxGetDevResource PFN_cuCtxGetDevResource_v12040 +#define PFN_cuGreenCtxGetDevResource PFN_cuGreenCtxGetDevResource_v12040 +#define PFN_cuGreenCtxRecordEvent PFN_cuGreenCtxRecordEvent_v12040 +#define PFN_cuGreenCtxWaitEvent PFN_cuGreenCtxWaitEvent_v12040 +#define PFN_cuDevResourceGenerateDesc PFN_cuDevResourceGenerateDesc_v12040 +#define PFN_cuDevSmResourceSplitByCount PFN_cuDevSmResourceSplitByCount_v12040 +#define PFN_cuStreamGetGreenCtx PFN_cuStreamGetGreenCtx_v12040 +#define PFN_cuCtxFromGreenCtx PFN_cuCtxFromGreenCtx_v12040 + +/* + * Type definitions for functions defined in cuda.h + */ +typedef CUresult (CUDAAPI *PFN_cuGetErrorString_v6000)(CUresult error, const char **pStr); +typedef CUresult (CUDAAPI *PFN_cuGetErrorName_v6000)(CUresult error, const char **pStr); +typedef CUresult (CUDAAPI *PFN_cuInit_v2000)(unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuDriverGetVersion_v2020)(int *driverVersion); +typedef CUresult (CUDAAPI *PFN_cuDeviceGet_v2000)(CUdevice_v1 *device, int ordinal); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetCount_v2000)(int *count); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetName_v2000)(char *name, int len, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetUuid_v9020)(CUuuid *uuid, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetUuid_v11040)(CUuuid *uuid, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetLuid_v10000)(char *luid, unsigned int *deviceNodeMask, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceTotalMem_v3020)(size_t *bytes, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetTexture1DLinearMaxWidth_v11010)(size_t *maxWidthInElements, CUarray_format format, unsigned numChannels, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetAttribute_v2000)(int *pi, CUdevice_attribute attrib, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetNvSciSyncAttributes_v10020)(void *nvSciSyncAttrList, CUdevice_v1 dev, int flags); +typedef CUresult (CUDAAPI *PFN_cuDeviceSetMemPool_v11020)(CUdevice_v1 dev, CUmemoryPool pool); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetMemPool_v11020)(CUmemoryPool *pool, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetDefaultMemPool_v11020)(CUmemoryPool *pool_out, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetProperties_v2000)(CUdevprop_v1 *prop, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceComputeCapability_v2000)(int *major, int *minor, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxRetain_v7000)(CUcontext *pctx, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxRelease_v11000)(CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxSetFlags_v11000)(CUdevice_v1 dev, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxGetState_v7000)(CUdevice_v1 dev, unsigned int *flags, int *active); +typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxReset_v11000)(CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetExecAffinitySupport_v11040)(int *pi, CUexecAffinityType type, CUdevice dev); +typedef CUresult (CUDAAPI *PFN_cuCtxCreate_v3020)(CUcontext *pctx, unsigned int flags, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuCtxCreate_v11040)(CUcontext *pctx, CUexecAffinityParam *paramsArray, int numParams, unsigned int flags, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuCtxGetId_v12000)(CUcontext ctx, unsigned long long *ctxId); +typedef CUresult (CUDAAPI *PFN_cuCtxDestroy_v4000)(CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuCtxPushCurrent_v4000)(CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuCtxPopCurrent_v4000)(CUcontext *pctx); +typedef CUresult (CUDAAPI *PFN_cuCtxSetCurrent_v4000)(CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuCtxGetCurrent_v4000)(CUcontext *pctx); +typedef CUresult (CUDAAPI *PFN_cuCtxGetDevice_v2000)(CUdevice_v1 *device); +typedef CUresult (CUDAAPI *PFN_cuCtxGetFlags_v7000)(unsigned int *flags); +typedef CUresult (CUDAAPI *PFN_cuCtxSetFlags_v12010)(unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuCtxSynchronize_v2000)(void); +typedef CUresult (CUDAAPI *PFN_cuCtxSetLimit_v3010)(CUlimit limit, size_t value); +typedef CUresult (CUDAAPI *PFN_cuCtxGetLimit_v3010)(size_t *pvalue, CUlimit limit); +typedef CUresult (CUDAAPI *PFN_cuCtxGetCacheConfig_v3020)(CUfunc_cache *pconfig); +typedef CUresult (CUDAAPI *PFN_cuCtxSetCacheConfig_v3020)(CUfunc_cache config); +typedef CUresult (CUDAAPI *PFN_cuCtxGetSharedMemConfig_v4020)(CUsharedconfig *pConfig); +typedef CUresult (CUDAAPI *PFN_cuCtxSetSharedMemConfig_v4020)(CUsharedconfig config); +typedef CUresult (CUDAAPI *PFN_cuCtxGetApiVersion_v3020)(CUcontext ctx, unsigned int *version); +typedef CUresult (CUDAAPI *PFN_cuCtxGetStreamPriorityRange_v5050)(int *leastPriority, int *greatestPriority); +typedef CUresult (CUDAAPI *PFN_cuCtxResetPersistingL2Cache_v11000)(void); +typedef CUresult (CUDAAPI *PFN_cuCtxAttach_v2000)(CUcontext *pctx, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuCtxDetach_v2000)(CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuCtxGetExecAffinity_v11040)(CUexecAffinityParam *pExecAffinity, CUexecAffinityType type); +typedef CUresult (CUDAAPI *PFN_cuModuleLoad_v2000)(CUmodule *module, const char *fname); +typedef CUresult (CUDAAPI *PFN_cuModuleLoadData_v2000)(CUmodule *module, const void *image); +typedef CUresult (CUDAAPI *PFN_cuModuleLoadDataEx_v2010)(CUmodule *module, const void *image, unsigned int numOptions, CUjit_option *options, void **optionValues); +typedef CUresult (CUDAAPI *PFN_cuModuleLoadFatBinary_v2000)(CUmodule *module, const void *fatCubin); +typedef CUresult (CUDAAPI *PFN_cuModuleUnload_v2000)(CUmodule hmod); +typedef CUresult (CUDAAPI *PFN_cuModuleGetFunction_v2000)(CUfunction *hfunc, CUmodule hmod, const char *name); +typedef CUresult (CUDAAPI *PFN_cuModuleGetGlobal_v3020)(CUdeviceptr_v2 *dptr, size_t *bytes, CUmodule hmod, const char *name); +typedef CUresult (CUDAAPI *PFN_cuModuleGetTexRef_v2000)(CUtexref *pTexRef, CUmodule hmod, const char *name); +typedef CUresult (CUDAAPI *PFN_cuModuleGetSurfRef_v3000)(CUsurfref *pSurfRef, CUmodule hmod, const char *name); +typedef CUresult (CUDAAPI *PFN_cuModuleGetFunctionCount)(unsigned int *count, CUmodule hmod); +typedef CUresult (CUDAAPI *PFN_cuModuleEnumerateFunctions)(CUfunction *functions, unsigned int numFunctions, CUmodule mod); +typedef CUresult (CUDAAPI *PFN_cuLinkCreate_v6050)(unsigned int numOptions, CUjit_option *options, void **optionValues, CUlinkState *stateOut); +typedef CUresult (CUDAAPI *PFN_cuLinkAddData_v6050)(CUlinkState state, CUjitInputType type, void *data, size_t size, const char *name, unsigned int numOptions, CUjit_option *options, void **optionValues); +typedef CUresult (CUDAAPI *PFN_cuLinkAddFile_v6050)(CUlinkState state, CUjitInputType type, const char *path, unsigned int numOptions, CUjit_option *options, void **optionValues); +typedef CUresult (CUDAAPI *PFN_cuLinkComplete_v5050)(CUlinkState state, void **cubinOut, size_t *sizeOut); +typedef CUresult (CUDAAPI *PFN_cuLinkDestroy_v5050)(CUlinkState state); +typedef CUresult (CUDAAPI *PFN_cuMemGetInfo_v3020)(size_t *free, size_t *total); +typedef CUresult (CUDAAPI *PFN_cuMemAlloc_v3020)(CUdeviceptr_v2 *dptr, size_t bytesize); +typedef CUresult (CUDAAPI *PFN_cuMemAllocPitch_v3020)(CUdeviceptr_v2 *dptr, size_t *pPitch, size_t WidthInBytes, size_t Height, unsigned int ElementSizeBytes); +typedef CUresult (CUDAAPI *PFN_cuMemFree_v3020)(CUdeviceptr_v2 dptr); +typedef CUresult (CUDAAPI *PFN_cuMemGetAddressRange_v3020)(CUdeviceptr_v2 *pbase, size_t *psize, CUdeviceptr_v2 dptr); +typedef CUresult (CUDAAPI *PFN_cuMemAllocHost_v3020)(void **pp, size_t bytesize); +typedef CUresult (CUDAAPI *PFN_cuMemFreeHost_v2000)(void *p); +typedef CUresult (CUDAAPI *PFN_cuMemHostAlloc_v2020)(void **pp, size_t bytesize, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuMemHostGetDevicePointer_v3020)(CUdeviceptr_v2 *pdptr, void *p, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuMemHostGetFlags_v2030)(unsigned int *pFlags, void *p); +typedef CUresult (CUDAAPI *PFN_cuMemAllocManaged_v6000)(CUdeviceptr_v2 *dptr, size_t bytesize, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetByPCIBusId_v4010)(CUdevice_v1 *dev, const char *pciBusId); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetPCIBusId_v4010)(char *pciBusId, int len, CUdevice_v1 dev); +typedef CUresult (CUDAAPI *PFN_cuIpcGetEventHandle_v4010)(CUipcEventHandle_v1 *pHandle, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuIpcOpenEventHandle_v4010)(CUevent *phEvent, CUipcEventHandle_v1 handle); +typedef CUresult (CUDAAPI *PFN_cuIpcGetMemHandle_v4010)(CUipcMemHandle_v1 *pHandle, CUdeviceptr_v2 dptr); +typedef CUresult (CUDAAPI *PFN_cuIpcOpenMemHandle_v11000)(CUdeviceptr_v2 *pdptr, CUipcMemHandle_v1 handle, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuIpcCloseMemHandle_v4010)(CUdeviceptr_v2 dptr); +typedef CUresult (CUDAAPI *PFN_cuMemHostRegister_v6050)(void *p, size_t bytesize, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuMemHostUnregister_v4000)(void *p); +typedef CUresult (CUDAAPI *PFN_cuMemcpy_v7000_ptds)(CUdeviceptr_v2 dst, CUdeviceptr_v2 src, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyPeer_v7000_ptds)(CUdeviceptr_v2 dstDevice, CUcontext dstContext, CUdeviceptr_v2 srcDevice, CUcontext srcContext, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoD_v7000_ptds)(CUdeviceptr_v2 dstDevice, const void *srcHost, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoH_v7000_ptds)(void *dstHost, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoD_v7000_ptds)(CUdeviceptr_v2 dstDevice, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoA_v7000_ptds)(CUarray dstArray, size_t dstOffset, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoD_v7000_ptds)(CUdeviceptr_v2 dstDevice, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoA_v7000_ptds)(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoH_v7000_ptds)(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoA_v7000_ptds)(CUarray dstArray, size_t dstOffset, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2D_v7000_ptds)(const CUDA_MEMCPY2D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2DUnaligned_v7000_ptds)(const CUDA_MEMCPY2D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3D_v7000_ptds)(const CUDA_MEMCPY3D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DPeer_v7000_ptds)(const CUDA_MEMCPY3D_PEER_v1 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAsync_v7000_ptsz)(CUdeviceptr_v2 dst, CUdeviceptr_v2 src, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyPeerAsync_v7000_ptsz)(CUdeviceptr_v2 dstDevice, CUcontext dstContext, CUdeviceptr_v2 srcDevice, CUcontext srcContext, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoDAsync_v7000_ptsz)(CUdeviceptr_v2 dstDevice, const void *srcHost, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoHAsync_v7000_ptsz)(void *dstHost, CUdeviceptr_v2 srcDevice, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoDAsync_v7000_ptsz)(CUdeviceptr_v2 dstDevice, CUdeviceptr_v2 srcDevice, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoAAsync_v7000_ptsz)(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoHAsync_v7000_ptsz)(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2DAsync_v7000_ptsz)(const CUDA_MEMCPY2D_v2 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DAsync_v7000_ptsz)(const CUDA_MEMCPY3D_v2 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DPeerAsync_v7000_ptsz)(const CUDA_MEMCPY3D_PEER_v1 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD8_v7000_ptds)(CUdeviceptr_v2 dstDevice, unsigned char uc, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD16_v7000_ptds)(CUdeviceptr_v2 dstDevice, unsigned short us, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD32_v7000_ptds)(CUdeviceptr_v2 dstDevice, unsigned int ui, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D8_v7000_ptds)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D16_v7000_ptds)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D32_v7000_ptds)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemsetD8Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, unsigned char uc, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD16Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, unsigned short us, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD32Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, unsigned int ui, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D8Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D16Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D32Async_v7000_ptsz)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuArrayCreate_v3020)(CUarray *pHandle, const CUDA_ARRAY_DESCRIPTOR_v2 *pAllocateArray); +typedef CUresult (CUDAAPI *PFN_cuArrayGetDescriptor_v3020)(CUDA_ARRAY_DESCRIPTOR_v2 *pArrayDescriptor, CUarray hArray); +typedef CUresult (CUDAAPI *PFN_cuArrayGetSparseProperties_v11010)(CUDA_ARRAY_SPARSE_PROPERTIES_v1 *sparseProperties, CUarray array); +typedef CUresult (CUDAAPI *PFN_cuMipmappedArrayGetSparseProperties_v11010)(CUDA_ARRAY_SPARSE_PROPERTIES_v1 *sparseProperties, CUmipmappedArray mipmap); +typedef CUresult (CUDAAPI *PFN_cuArrayGetMemoryRequirements_v11060)(CUDA_ARRAY_MEMORY_REQUIREMENTS_v1 *memoryRequirements, CUarray array, CUdevice device); +typedef CUresult (CUDAAPI *PFN_cuMipmappedArrayGetMemoryRequirements_v11060)(CUDA_ARRAY_MEMORY_REQUIREMENTS_v1 *memoryRequirements, CUmipmappedArray mipmap, CUdevice device); +typedef CUresult (CUDAAPI *PFN_cuArrayGetPlane_v11020)(CUarray *pPlaneArray, CUarray hArray, unsigned int planeIdx); +typedef CUresult (CUDAAPI *PFN_cuArrayDestroy_v2000)(CUarray hArray); +typedef CUresult (CUDAAPI *PFN_cuArray3DCreate_v3020)(CUarray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR_v2 *pAllocateArray); +typedef CUresult (CUDAAPI *PFN_cuArray3DGetDescriptor_v3020)(CUDA_ARRAY3D_DESCRIPTOR_v2 *pArrayDescriptor, CUarray hArray); +typedef CUresult (CUDAAPI *PFN_cuMipmappedArrayCreate_v5000)(CUmipmappedArray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR_v2 *pMipmappedArrayDesc, unsigned int numMipmapLevels); +typedef CUresult (CUDAAPI *PFN_cuMipmappedArrayGetLevel_v5000)(CUarray *pLevelArray, CUmipmappedArray hMipmappedArray, unsigned int level); +typedef CUresult (CUDAAPI *PFN_cuMipmappedArrayDestroy_v5000)(CUmipmappedArray hMipmappedArray); +typedef CUresult (CUDAAPI *PFN_cuMemAddressReserve_v10020)(CUdeviceptr_v2 *ptr, size_t size, size_t alignment, CUdeviceptr_v2 addr, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemAddressFree_v10020)(CUdeviceptr_v2 ptr, size_t size); +typedef CUresult (CUDAAPI *PFN_cuMemCreate_v10020)(CUmemGenericAllocationHandle_v1 *handle, size_t size, const CUmemAllocationProp_v1 *prop, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemRelease_v10020)(CUmemGenericAllocationHandle_v1 handle); +typedef CUresult (CUDAAPI *PFN_cuMemMap_v10020)(CUdeviceptr_v2 ptr, size_t size, size_t offset, CUmemGenericAllocationHandle_v1 handle, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemMapArrayAsync_v11010_ptsz)(CUarrayMapInfo_v1 *mapInfoList, unsigned int count, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemUnmap_v10020)(CUdeviceptr_v2 ptr, size_t size); +typedef CUresult (CUDAAPI *PFN_cuMemSetAccess_v10020)(CUdeviceptr_v2 ptr, size_t size, const CUmemAccessDesc_v1 *desc, size_t count); +typedef CUresult (CUDAAPI *PFN_cuMemGetAccess_v10020)(unsigned long long *flags, const CUmemLocation_v1 *location, CUdeviceptr_v2 ptr); +typedef CUresult (CUDAAPI *PFN_cuMemExportToShareableHandle_v10020)(void *shareableHandle, CUmemGenericAllocationHandle_v1 handle, CUmemAllocationHandleType handleType, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemImportFromShareableHandle_v10020)(CUmemGenericAllocationHandle_v1 *handle, void *osHandle, CUmemAllocationHandleType shHandleType); +typedef CUresult (CUDAAPI *PFN_cuMemGetAllocationGranularity_v10020)(size_t *granularity, const CUmemAllocationProp_v1 *prop, CUmemAllocationGranularity_flags option); +typedef CUresult (CUDAAPI *PFN_cuMemGetAllocationPropertiesFromHandle_v10020)(CUmemAllocationProp_v1 *prop, CUmemGenericAllocationHandle_v1 handle); +typedef CUresult (CUDAAPI *PFN_cuMemRetainAllocationHandle_v11000)(CUmemGenericAllocationHandle_v1 *handle, void *addr); +typedef CUresult (CUDAAPI *PFN_cuMemFreeAsync_v11020_ptsz)(CUdeviceptr_v2 dptr, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemAllocAsync_v11020_ptsz)(CUdeviceptr_v2 *dptr, size_t bytesize, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemPoolTrimTo_v11020)(CUmemoryPool pool, size_t minBytesToKeep); +typedef CUresult (CUDAAPI *PFN_cuMemPoolSetAttribute_v11020)(CUmemoryPool pool, CUmemPool_attribute attr, void *value); +typedef CUresult (CUDAAPI *PFN_cuMemPoolGetAttribute_v11020)(CUmemoryPool pool, CUmemPool_attribute attr, void *value); +typedef CUresult (CUDAAPI *PFN_cuMemPoolSetAccess_v11020)(CUmemoryPool pool, const CUmemAccessDesc_v1 *map, size_t count); +typedef CUresult (CUDAAPI *PFN_cuMemPoolGetAccess_v11020)(CUmemAccess_flags *flags, CUmemoryPool memPool, CUmemLocation_v1 *location); +typedef CUresult (CUDAAPI *PFN_cuMemPoolCreate_v11020)(CUmemoryPool *pool, const CUmemPoolProps_v1 *poolProps); +typedef CUresult (CUDAAPI *PFN_cuMemPoolDestroy_v11020)(CUmemoryPool pool); +typedef CUresult (CUDAAPI *PFN_cuMemAllocFromPoolAsync_v11020_ptsz)(CUdeviceptr_v2 *dptr, size_t bytesize, CUmemoryPool pool, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemPoolExportToShareableHandle_v11020)(void *handle_out, CUmemoryPool pool, CUmemAllocationHandleType handleType, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemPoolImportFromShareableHandle_v11020)(CUmemoryPool *pool_out, void *handle, CUmemAllocationHandleType handleType, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMemPoolExportPointer_v11020)(CUmemPoolPtrExportData_v1 *shareData_out, CUdeviceptr_v2 ptr); +typedef CUresult (CUDAAPI *PFN_cuMemPoolImportPointer_v11020)(CUdeviceptr_v2 *ptr_out, CUmemoryPool pool, CUmemPoolPtrExportData_v1 *shareData); +typedef CUresult (CUDAAPI *PFN_cuPointerGetAttribute_v4000)(void *data, CUpointer_attribute attribute, CUdeviceptr_v2 ptr); +typedef CUresult (CUDAAPI *PFN_cuMemPrefetchAsync_v8000_ptsz)(CUdeviceptr_v2 devPtr, size_t count, CUdevice_v1 dstDevice, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemAdvise_v8000)(CUdeviceptr_v2 devPtr, size_t count, CUmem_advise advice, CUdevice_v1 device); +typedef CUresult (CUDAAPI *PFN_cuMemAdvise_v12020)(CUdeviceptr_v2 devPtr, size_t count, CUmem_advise advice, CUmemLocation_v1 location); +typedef CUresult (CUDAAPI *PFN_cuMemPrefetchAsync_v12020_ptsz)(CUdeviceptr_v2 devPtr, size_t count, CUmemLocation_v1 location, unsigned int flags, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemRangeGetAttribute_v8000)(void *data, size_t dataSize, CUmem_range_attribute attribute, CUdeviceptr_v2 devPtr, size_t count); +typedef CUresult (CUDAAPI *PFN_cuMemRangeGetAttributes_v8000)(void **data, size_t *dataSizes, CUmem_range_attribute *attributes, size_t numAttributes, CUdeviceptr_v2 devPtr, size_t count); +typedef CUresult (CUDAAPI *PFN_cuMulticastCreate_v12010)(CUmemGenericAllocationHandle *mcHandle, const CUmulticastObjectProp *prop); +typedef CUresult (CUDAAPI *PFN_cuMulticastAddDevice_v12010)(CUmemGenericAllocationHandle mcHandle, CUdevice dev); +typedef CUresult (CUDAAPI *PFN_cuMulticastBindMem_v12010)(CUmemGenericAllocationHandle mcHandle, size_t mcOffset, CUmemGenericAllocationHandle memHandle, size_t memOffset, size_t size, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMulticastBindAddr_v12010)(CUmemGenericAllocationHandle mcHandle, size_t mcOffset, CUdeviceptr memptr, size_t size, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuMulticastUnbind_v12010)(CUmemGenericAllocationHandle mcHandle, CUdevice dev, size_t mcOffset, size_t size); +typedef CUresult (CUDAAPI *PFN_cuMulticastGetGranularity_v12010)(size_t *granularity, const CUmulticastObjectProp *prop, CUmulticastGranularity_flags option); +typedef CUresult (CUDAAPI *PFN_cuPointerSetAttribute_v6000)(const void *value, CUpointer_attribute attribute, CUdeviceptr_v2 ptr); +typedef CUresult (CUDAAPI *PFN_cuPointerGetAttributes_v7000)(unsigned int numAttributes, CUpointer_attribute *attributes, void **data, CUdeviceptr_v2 ptr); +typedef CUresult (CUDAAPI *PFN_cuStreamCreate_v2000)(CUstream *phStream, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuStreamCreateWithPriority_v5050)(CUstream *phStream, unsigned int flags, int priority); +typedef CUresult (CUDAAPI *PFN_cuStreamGetId_v12000)(CUstream hStream, unsigned long long *streamId); +typedef CUresult (CUDAAPI *PFN_cuStreamGetId_v12000_ptsz)(CUstream hStream, unsigned long long *streamId); +typedef CUresult (CUDAAPI *PFN_cuStreamGetPriority_v7000_ptsz)(CUstream hStream, int *priority); +typedef CUresult (CUDAAPI *PFN_cuStreamGetFlags_v7000_ptsz)(CUstream hStream, unsigned int *flags); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCtx_v9020_ptsz)(CUstream hStream, CUcontext *pctx); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitEvent_v7000_ptsz)(CUstream hStream, CUevent hEvent, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuStreamAddCallback_v7000_ptsz)(CUstream hStream, CUstreamCallback callback, void *userData, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamBeginCapture_v10010_ptsz)(CUstream hStream, CUstreamCaptureMode mode); +typedef CUresult (CUDAAPI *PFN_cuStreamBeginCaptureToGraph_v12030_ptsz)(CUstream hStream, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUstreamCaptureMode mode); +typedef CUresult (CUDAAPI *PFN_cuThreadExchangeStreamCaptureMode_v10010)(CUstreamCaptureMode *mode); +typedef CUresult (CUDAAPI *PFN_cuStreamEndCapture_v10000_ptsz)(CUstream hStream, CUgraph *phGraph); +typedef CUresult (CUDAAPI *PFN_cuStreamIsCapturing_v10000_ptsz)(CUstream hStream, CUstreamCaptureStatus *captureStatus); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v10010_ptsz)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v11030_ptsz)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, size_t *numDependencies_out); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v12030_ptsz)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, const CUgraphEdgeData **edgeData_out, size_t *numDependencies_out); +typedef CUresult (CUDAAPI *PFN_cuStreamUpdateCaptureDependencies_v11030_ptsz)(CUstream hStream, CUgraphNode *dependencies, size_t numDependencies, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamUpdateCaptureDependencies_v12030_ptsz)(CUstream hStream, CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamAttachMemAsync_v7000_ptsz)(CUstream hStream, CUdeviceptr_v2 dptr, size_t length, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamQuery_v7000_ptsz)(CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamSynchronize_v7000_ptsz)(CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamDestroy_v4000)(CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamCopyAttributes_v11000_ptsz)(CUstream dst, CUstream src); +typedef CUresult (CUDAAPI *PFN_cuStreamGetAttribute_v11000_ptsz)(CUstream hStream, CUstreamAttrID attr, CUstreamAttrValue_v1 *value_out); +typedef CUresult (CUDAAPI *PFN_cuStreamSetAttribute_v11000_ptsz)(CUstream hStream, CUstreamAttrID attr, const CUstreamAttrValue_v1 *value); +typedef CUresult (CUDAAPI *PFN_cuEventCreate_v2000)(CUevent *phEvent, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuEventRecord_v7000_ptsz)(CUevent hEvent, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuEventRecordWithFlags_v11010_ptsz)(CUevent hEvent, CUstream hStream, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuEventQuery_v2000)(CUevent hEvent); +typedef CUresult (CUDAAPI *PFN_cuEventSynchronize_v2000)(CUevent hEvent); +typedef CUresult (CUDAAPI *PFN_cuEventDestroy_v4000)(CUevent hEvent); +typedef CUresult (CUDAAPI *PFN_cuEventElapsedTime_v2000)(float *pMilliseconds, CUevent hStart, CUevent hEnd); +typedef CUresult (CUDAAPI *PFN_cuImportExternalMemory_v10000)(CUexternalMemory *extMem_out, const CUDA_EXTERNAL_MEMORY_HANDLE_DESC_v1 *memHandleDesc); +typedef CUresult (CUDAAPI *PFN_cuExternalMemoryGetMappedBuffer_v10000)(CUdeviceptr_v2 *devPtr, CUexternalMemory extMem, const CUDA_EXTERNAL_MEMORY_BUFFER_DESC_v1 *bufferDesc); +typedef CUresult (CUDAAPI *PFN_cuExternalMemoryGetMappedMipmappedArray_v10000)(CUmipmappedArray *mipmap, CUexternalMemory extMem, const CUDA_EXTERNAL_MEMORY_MIPMAPPED_ARRAY_DESC_v1 *mipmapDesc); +typedef CUresult (CUDAAPI *PFN_cuDestroyExternalMemory_v10000)(CUexternalMemory extMem); +typedef CUresult (CUDAAPI *PFN_cuImportExternalSemaphore_v10000)(CUexternalSemaphore *extSem_out, const CUDA_EXTERNAL_SEMAPHORE_HANDLE_DESC_v1 *semHandleDesc); +typedef CUresult (CUDAAPI *PFN_cuSignalExternalSemaphoresAsync_v10000_ptsz)(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS_v1 *paramsArray, unsigned int numExtSems, CUstream stream); +typedef CUresult (CUDAAPI *PFN_cuWaitExternalSemaphoresAsync_v10000_ptsz)(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS_v1 *paramsArray, unsigned int numExtSems, CUstream stream); +typedef CUresult (CUDAAPI *PFN_cuDestroyExternalSemaphore_v10000)(CUexternalSemaphore extSem); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue32_v8000_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue64_v9000_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue32_v8000_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue64_v9000_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamBatchMemOp_v8000_ptsz)(CUstream stream, unsigned int count, CUstreamBatchMemOpParams_v1 *paramArray, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue32_v11070_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue64_v11070_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue32_v11070_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue64_v11070_ptsz)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamBatchMemOp_v11070_ptsz)(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuFuncGetAttribute_v2020)(int *pi, CUfunction_attribute attrib, CUfunction hfunc); +typedef CUresult (CUDAAPI *PFN_cuFuncSetAttribute_v9000)(CUfunction hfunc, CUfunction_attribute attrib, int value); +typedef CUresult (CUDAAPI *PFN_cuFuncSetCacheConfig_v3000)(CUfunction hfunc, CUfunc_cache config); +typedef CUresult (CUDAAPI *PFN_cuFuncSetSharedMemConfig_v4020)(CUfunction hfunc, CUsharedconfig config); +typedef CUresult (CUDAAPI *PFN_cuFuncGetName_v12030)(const char **name, CUfunction hfunc); +typedef CUresult (CUDAAPI *PFN_cuFuncGetParamInfo_v12040)(CUfunction func, size_t paramIndex, size_t *paramOffset, size_t *paramSize); +typedef CUresult (CUDAAPI *PFN_cuFuncIsLoaded_v12040)(CUfunctionLoadingState *state, CUfunction hfunc); +typedef CUresult (CUDAAPI *PFN_cuFuncLoad_v12040)(CUfunction hfunc); +typedef CUresult (CUDAAPI *PFN_cuLaunchKernel_v7000_ptsz)(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams, void **extra); +typedef CUresult (CUDAAPI *PFN_cuLaunchKernelEx_v11060_ptsz)(const CUlaunchConfig *config, CUfunction f, void **kernelParams, void **extra); +typedef CUresult (CUDAAPI *PFN_cuLaunchCooperativeKernel_v9000_ptsz)(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams); +typedef CUresult (CUDAAPI *PFN_cuLaunchCooperativeKernelMultiDevice_v9000)(CUDA_LAUNCH_PARAMS_v1 *launchParamsList, unsigned int numDevices, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuLaunchHostFunc_v10000_ptsz)(CUstream hStream, CUhostFn fn, void *userData); +typedef CUresult (CUDAAPI *PFN_cuFuncSetBlockShape_v2000)(CUfunction hfunc, int x, int y, int z); +typedef CUresult (CUDAAPI *PFN_cuFuncSetSharedSize_v2000)(CUfunction hfunc, unsigned int bytes); +typedef CUresult (CUDAAPI *PFN_cuParamSetSize_v2000)(CUfunction hfunc, unsigned int numbytes); +typedef CUresult (CUDAAPI *PFN_cuParamSeti_v2000)(CUfunction hfunc, int offset, unsigned int value); +typedef CUresult (CUDAAPI *PFN_cuParamSetf_v2000)(CUfunction hfunc, int offset, float value); +typedef CUresult (CUDAAPI *PFN_cuParamSetv_v2000)(CUfunction hfunc, int offset, void *ptr, unsigned int numbytes); +typedef CUresult (CUDAAPI *PFN_cuLaunch_v2000)(CUfunction f); +typedef CUresult (CUDAAPI *PFN_cuLaunchGrid_v2000)(CUfunction f, int grid_width, int grid_height); +typedef CUresult (CUDAAPI *PFN_cuLaunchGridAsync_v2000)(CUfunction f, int grid_width, int grid_height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuParamSetTexRef_v2000)(CUfunction hfunc, int texunit, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuGraphCreate_v10000)(CUgraph *phGraph, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphAddKernelNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeGetParams_v10000)(CUgraphNode hNode, CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeSetParams_v10000)(CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddKernelNode_v12000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_KERNEL_NODE_PARAMS_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeGetParams_v12000)(CUgraphNode hNode, CUDA_KERNEL_NODE_PARAMS_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeSetParams_v12000)(CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddMemcpyNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_MEMCPY3D_v2 *copyParams, CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuGraphMemcpyNodeGetParams_v10000)(CUgraphNode hNode, CUDA_MEMCPY3D_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphMemcpyNodeSetParams_v10000)(CUgraphNode hNode, const CUDA_MEMCPY3D_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddMemsetNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_MEMSET_NODE_PARAMS_v1 *memsetParams, CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuGraphMemsetNodeGetParams_v10000)(CUgraphNode hNode, CUDA_MEMSET_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphMemsetNodeSetParams_v10000)(CUgraphNode hNode, const CUDA_MEMSET_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddHostNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_HOST_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphHostNodeGetParams_v10000)(CUgraphNode hNode, CUDA_HOST_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphHostNodeSetParams_v10000)(CUgraphNode hNode, const CUDA_HOST_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddChildGraphNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUgraph childGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphChildGraphNodeGetGraph_v10000)(CUgraphNode hNode, CUgraph *phGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphAddEmptyNode_v10000)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphAddEventRecordNode_v11010)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphEventRecordNodeGetEvent_v11010)(CUgraphNode hNode, CUevent *event_out); +typedef CUresult (CUDAAPI *PFN_cuGraphEventRecordNodeSetEvent_v11010)(CUgraphNode hNode, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphAddEventWaitNode_v11010)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphEventWaitNodeGetEvent_v11010)(CUgraphNode hNode, CUevent *event_out); +typedef CUresult (CUDAAPI *PFN_cuGraphEventWaitNodeSetEvent_v11010)(CUgraphNode hNode, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphAddExternalSemaphoresSignalNode_v11020)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExternalSemaphoresSignalNodeGetParams_v11020)(CUgraphNode hNode, CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1 *params_out); +typedef CUresult (CUDAAPI *PFN_cuGraphExternalSemaphoresSignalNodeSetParams_v11020)(CUgraphNode hNode, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddExternalSemaphoresWaitNode_v11020)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExternalSemaphoresWaitNodeGetParams_v11020)(CUgraphNode hNode, CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1 *params_out); +typedef CUresult (CUDAAPI *PFN_cuGraphExternalSemaphoresWaitNodeSetParams_v11020)(CUgraphNode hNode, const CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddBatchMemOpNode_v11070)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphBatchMemOpNodeGetParams_v11070)(CUgraphNode hNode, CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams_out); +typedef CUresult (CUDAAPI *PFN_cuGraphBatchMemOpNodeSetParams_v11070)(CUgraphNode hNode, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecBatchMemOpNodeSetParams_v11070)(CUgraphExec graphExec, CUgraphNode node, const CUDA_BATCH_MEM_OP_NODE_PARAMS *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphClone_v10000)(CUgraph *phGraphClone, CUgraph originalGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeFindInClone_v10000)(CUgraphNode *phNode, CUgraphNode hOriginalNode, CUgraph hClonedGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetType_v10000)(CUgraphNode hNode, CUgraphNodeType *type); +typedef CUresult (CUDAAPI *PFN_cuGraphGetNodes_v10000)(CUgraph hGraph, CUgraphNode *nodes, size_t *numNodes); +typedef CUresult (CUDAAPI *PFN_cuGraphGetRootNodes_v10000)(CUgraph hGraph, CUgraphNode *rootNodes, size_t *numRootNodes); +typedef CUresult (CUDAAPI *PFN_cuGraphGetEdges_v10000)(CUgraph hGraph, CUgraphNode *from, CUgraphNode *to, size_t *numEdges); +typedef CUresult (CUDAAPI *PFN_cuGraphGetEdges_v12030)(CUgraph hGraph, CUgraphNode *from, CUgraphNode *to, CUgraphEdgeData *edgeData, size_t *numEdges); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetDependencies_v10000)(CUgraphNode hNode, CUgraphNode *dependencies, size_t *numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetDependencies_v12030)(CUgraphNode hNode, CUgraphNode *dependencies, CUgraphEdgeData *edgeData, size_t *numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetDependentNodes_v10000)(CUgraphNode hNode, CUgraphNode *dependentNodes, size_t *numDependentNodes); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetDependentNodes_v12030)(CUgraphNode hNode, CUgraphNode *dependentNodes, CUgraphEdgeData *edgeData, size_t *numDependentNodes); +typedef CUresult (CUDAAPI *PFN_cuGraphAddDependencies_v10000)(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, size_t numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphAddDependencies_v12030)(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, const CUgraphEdgeData *edgeData, size_t numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphRemoveDependencies_v10000)(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, size_t numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphRemoveDependencies_v12030)(CUgraph hGraph, const CUgraphNode *from, const CUgraphNode *to, const CUgraphEdgeData *edgeData, size_t numDependencies); +typedef CUresult (CUDAAPI *PFN_cuGraphDestroyNode_v10000)(CUgraphNode hNode); +typedef CUresult (CUDAAPI *PFN_cuGraphInstantiateWithFlags_v11040)(CUgraphExec *phGraphExec, CUgraph hGraph, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuGraphInstantiateWithParams_v12000_ptsz)(CUgraphExec *phGraphExec, CUgraph hGraph, CUDA_GRAPH_INSTANTIATE_PARAMS *instantiateParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecGetFlags_v12000)(CUgraphExec hGraphExec, cuuint64_t *flags); +typedef CUresult (CUDAAPI *PFN_cuGraphExecKernelNodeSetParams_v10010)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecKernelNodeSetParams_v12000)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_KERNEL_NODE_PARAMS_v2 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecMemcpyNodeSetParams_v10020)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_MEMCPY3D_v2 *copyParams, CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuGraphExecMemsetNodeSetParams_v10020)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_MEMSET_NODE_PARAMS_v1 *memsetParams, CUcontext ctx); +typedef CUresult (CUDAAPI *PFN_cuGraphExecHostNodeSetParams_v10020)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_HOST_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecChildGraphNodeSetParams_v11010)(CUgraphExec hGraphExec, CUgraphNode hNode, CUgraph childGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphExecEventRecordNodeSetEvent_v11010)(CUgraphExec hGraphExec, CUgraphNode hNode, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphExecEventWaitNodeSetEvent_v11010)(CUgraphExec hGraphExec, CUgraphNode hNode, CUevent event); +typedef CUresult (CUDAAPI *PFN_cuGraphExecExternalSemaphoresSignalNodeSetParams_v11020)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_EXT_SEM_SIGNAL_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecExternalSemaphoresWaitNodeSetParams_v11020)(CUgraphExec hGraphExec, CUgraphNode hNode, const CUDA_EXT_SEM_WAIT_NODE_PARAMS_v1 *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphUpload_v11010_ptsz)(CUgraphExec hGraphExec, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGraphLaunch_v10000_ptsz)(CUgraphExec hGraphExec, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGraphExecDestroy_v10000)(CUgraphExec hGraphExec); +typedef CUresult (CUDAAPI *PFN_cuGraphDestroy_v10000)(CUgraph hGraph); +typedef CUresult (CUDAAPI *PFN_cuGraphExecUpdate_v10020)(CUgraphExec hGraphExec, CUgraph hGraph, CUgraphNode *hErrorNode_out, CUgraphExecUpdateResult *updateResult_out); +typedef CUresult (CUDAAPI *PFN_cuGraphExecUpdate_v12000)(CUgraphExec hGraphExec, CUgraph hGraph, CUgraphExecUpdateResultInfo *resultInfo); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeCopyAttributes_v11000)(CUgraphNode dst, CUgraphNode src); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeGetAttribute_v11000)(CUgraphNode hNode, CUkernelNodeAttrID attr, CUkernelNodeAttrValue_v1 *value_out); +typedef CUresult (CUDAAPI *PFN_cuGraphKernelNodeSetAttribute_v11000)(CUgraphNode hNode, CUkernelNodeAttrID attr, const CUkernelNodeAttrValue_v1 *value); +typedef CUresult (CUDAAPI *PFN_cuGraphDebugDotPrint_v11030)(CUgraph hGraph, const char *path, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphAddMemAllocNode_v11040)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUDA_MEM_ALLOC_NODE_PARAMS *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphMemAllocNodeGetParams_v11040)(CUgraphNode hNode, CUDA_MEM_ALLOC_NODE_PARAMS *params_out); +typedef CUresult (CUDAAPI *PFN_cuGraphAddMemFreeNode_v11040)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUdeviceptr dptr); +typedef CUresult (CUDAAPI *PFN_cuGraphMemFreeNodeGetParams_v11040)(CUgraphNode hNode, CUdeviceptr *dptr_out); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeSetEnabled_v11060)(CUgraphExec hGraphExec, CUgraphNode hNode, unsigned int isEnabled); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeGetEnabled_v11060)(CUgraphExec hGraphExec, CUgraphNode hNode, unsigned int *isEnabled); +typedef CUresult (CUDAAPI *PFN_cuGraphAddNode_v12020)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, size_t numDependencies, CUgraphNodeParams *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphAddNode_v12030)(CUgraphNode *phGraphNode, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUgraphNodeParams *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphNodeSetParams_v12020)(CUgraphNode hNode, CUgraphNodeParams *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphExecNodeSetParams_v12020)(CUgraphExec hGraphExec, CUgraphNode hNode, CUgraphNodeParams *nodeParams); +typedef CUresult (CUDAAPI *PFN_cuGraphConditionalHandleCreate_v12030)(CUgraphConditionalHandle *pHandle_out, CUgraph hGraph, CUcontext ctx, unsigned int defaultLaunchValue, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuDeviceGraphMemTrim_v11040)(CUdevice device); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetGraphMemAttribute_v11040)(CUdevice device, CUgraphMem_attribute attr, void* value); +typedef CUresult (CUDAAPI *PFN_cuDeviceSetGraphMemAttribute_v11040)(CUdevice device, CUgraphMem_attribute attr, void* value); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxActiveBlocksPerMultiprocessor_v6050)(int *numBlocks, CUfunction func, int blockSize, size_t dynamicSMemSize); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags_v7000)(int *numBlocks, CUfunction func, int blockSize, size_t dynamicSMemSize, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxPotentialBlockSize_v6050)(int *minGridSize, int *blockSize, CUfunction func, CUoccupancyB2DSize blockSizeToDynamicSMemSize, size_t dynamicSMemSize, int blockSizeLimit); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxPotentialBlockSizeWithFlags_v7000)(int *minGridSize, int *blockSize, CUfunction func, CUoccupancyB2DSize blockSizeToDynamicSMemSize, size_t dynamicSMemSize, int blockSizeLimit, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuOccupancyAvailableDynamicSMemPerBlock_v10020)(size_t *dynamicSmemSize, CUfunction func, int numBlocks, int blockSize); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxPotentialClusterSize_v11070)(int *clusterSize, CUfunction func, const CUlaunchConfig *config); +typedef CUresult (CUDAAPI *PFN_cuOccupancyMaxActiveClusters_v11070)(int *numClusters, CUfunction func, const CUlaunchConfig *config); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetArray_v2000)(CUtexref hTexRef, CUarray hArray, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetMipmappedArray_v5000)(CUtexref hTexRef, CUmipmappedArray hMipmappedArray, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddress_v3020)(size_t *ByteOffset, CUtexref hTexRef, CUdeviceptr_v2 dptr, size_t bytes); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddress2D_v4010)(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR_v2 *desc, CUdeviceptr_v2 dptr, size_t Pitch); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetFormat_v2000)(CUtexref hTexRef, CUarray_format fmt, int NumPackedComponents); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddressMode_v2000)(CUtexref hTexRef, int dim, CUaddress_mode am); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetFilterMode_v2000)(CUtexref hTexRef, CUfilter_mode fm); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetMipmapFilterMode_v5000)(CUtexref hTexRef, CUfilter_mode fm); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetMipmapLevelBias_v5000)(CUtexref hTexRef, float bias); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetMipmapLevelClamp_v5000)(CUtexref hTexRef, float minMipmapLevelClamp, float maxMipmapLevelClamp); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetMaxAnisotropy_v5000)(CUtexref hTexRef, unsigned int maxAniso); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetBorderColor_v8000)(CUtexref hTexRef, float *pBorderColor); +typedef CUresult (CUDAAPI *PFN_cuTexRefSetFlags_v2000)(CUtexref hTexRef, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetAddress_v3020)(CUdeviceptr_v2 *pdptr, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetArray_v2000)(CUarray *phArray, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetMipmappedArray_v5000)(CUmipmappedArray *phMipmappedArray, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetAddressMode_v2000)(CUaddress_mode *pam, CUtexref hTexRef, int dim); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetFilterMode_v2000)(CUfilter_mode *pfm, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetFormat_v2000)(CUarray_format *pFormat, int *pNumChannels, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetMipmapFilterMode_v5000)(CUfilter_mode *pfm, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetMipmapLevelBias_v5000)(float *pbias, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetMipmapLevelClamp_v5000)(float *pminMipmapLevelClamp, float *pmaxMipmapLevelClamp, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetMaxAnisotropy_v5000)(int *pmaxAniso, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetBorderColor_v8000)(float *pBorderColor, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefGetFlags_v2000)(unsigned int *pFlags, CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefCreate_v2000)(CUtexref *pTexRef); +typedef CUresult (CUDAAPI *PFN_cuTexRefDestroy_v2000)(CUtexref hTexRef); +typedef CUresult (CUDAAPI *PFN_cuSurfRefSetArray_v3000)(CUsurfref hSurfRef, CUarray hArray, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuSurfRefGetArray_v3000)(CUarray *phArray, CUsurfref hSurfRef); +typedef CUresult (CUDAAPI *PFN_cuTexObjectCreate_v5000)(CUtexObject_v1 *pTexObject, const CUDA_RESOURCE_DESC_v1 *pResDesc, const CUDA_TEXTURE_DESC_v1 *pTexDesc, const CUDA_RESOURCE_VIEW_DESC_v1 *pResViewDesc); +typedef CUresult (CUDAAPI *PFN_cuTexObjectDestroy_v5000)(CUtexObject_v1 texObject); +typedef CUresult (CUDAAPI *PFN_cuTexObjectGetResourceDesc_v5000)(CUDA_RESOURCE_DESC_v1 *pResDesc, CUtexObject_v1 texObject); +typedef CUresult (CUDAAPI *PFN_cuTexObjectGetTextureDesc_v5000)(CUDA_TEXTURE_DESC_v1 *pTexDesc, CUtexObject_v1 texObject); +typedef CUresult (CUDAAPI *PFN_cuTexObjectGetResourceViewDesc_v5000)(CUDA_RESOURCE_VIEW_DESC_v1 *pResViewDesc, CUtexObject_v1 texObject); +typedef CUresult (CUDAAPI *PFN_cuSurfObjectCreate_v5000)(CUsurfObject_v1 *pSurfObject, const CUDA_RESOURCE_DESC_v1 *pResDesc); +typedef CUresult (CUDAAPI *PFN_cuSurfObjectDestroy_v5000)(CUsurfObject_v1 surfObject); +typedef CUresult (CUDAAPI *PFN_cuSurfObjectGetResourceDesc_v5000)(CUDA_RESOURCE_DESC_v1 *pResDesc, CUsurfObject_v1 surfObject); +typedef CUresult (CUDAAPI *PFN_cuTensorMapEncodeTiled_v12000)(CUtensorMap *tensorMap, CUtensorMapDataType tensorDataType, cuuint32_t tensorRank, void *globalAddress, const cuuint64_t *globalDim, const cuuint64_t *globalStrides, const cuuint32_t *boxDim, const cuuint32_t *elementStrides, CUtensorMapInterleave interleave, CUtensorMapSwizzle swizzle, CUtensorMapL2promotion l2Promotion, CUtensorMapFloatOOBfill oobFill); +typedef CUresult (CUDAAPI *PFN_cuTensorMapEncodeIm2col_v12000)(CUtensorMap *tensorMap, CUtensorMapDataType tensorDataType, cuuint32_t tensorRank, void *globalAddress, const cuuint64_t *globalDim, const cuuint64_t *globalStrides, const int *pixelBoxLowerCorner, const int *pixelBoxUpperCorner, cuuint32_t channelsPerPixel, cuuint32_t pixelsPerColumn, const cuuint32_t *elementStrides, CUtensorMapInterleave interleave, CUtensorMapSwizzle swizzle, CUtensorMapL2promotion l2Promotion, CUtensorMapFloatOOBfill oobFill); +typedef CUresult (CUDAAPI *PFN_cuTensorMapReplaceAddress_v12000)(CUtensorMap *tensorMap, void *globalAddress); +typedef CUresult (CUDAAPI *PFN_cuDeviceCanAccessPeer_v4000)(int *canAccessPeer, CUdevice_v1 dev, CUdevice_v1 peerDev); +typedef CUresult (CUDAAPI *PFN_cuCtxEnablePeerAccess_v4000)(CUcontext peerContext, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuCtxDisablePeerAccess_v4000)(CUcontext peerContext); +typedef CUresult (CUDAAPI *PFN_cuDeviceGetP2PAttribute_v8000)(int *value, CUdevice_P2PAttribute attrib, CUdevice_v1 srcDevice, CUdevice_v1 dstDevice); +typedef CUresult (CUDAAPI *PFN_cuGraphicsUnregisterResource_v3000)(CUgraphicsResource resource); +typedef CUresult (CUDAAPI *PFN_cuGraphicsSubResourceGetMappedArray_v3000)(CUarray *pArray, CUgraphicsResource resource, unsigned int arrayIndex, unsigned int mipLevel); +typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceGetMappedMipmappedArray_v5000)(CUmipmappedArray *pMipmappedArray, CUgraphicsResource resource); +typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceGetMappedPointer_v3020)(CUdeviceptr_v2 *pDevPtr, size_t *pSize, CUgraphicsResource resource); +typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceSetMapFlags_v6050)(CUgraphicsResource resource, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphicsMapResources_v7000_ptsz)(unsigned int count, CUgraphicsResource *resources, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGraphicsUnmapResources_v7000_ptsz)(unsigned int count, CUgraphicsResource *resources, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGetExportTable_v3000)(const void **ppExportTable, const CUuuid *pExportTableId); +typedef CUresult (CUDAAPI *PFN_cuFuncGetModule_v11000)(CUmodule *hmod, CUfunction hfunc); +typedef CUresult (CUDAAPI *PFN_cuGetProcAddress_v11030)(const char *symbol, void **pfn, int driverVersion, cuuint64_t flags); +typedef CUresult (CUDAAPI *PFN_cuGetProcAddress_v12000)(const char *symbol, void **pfn, int driverVersion, cuuint64_t flags, CUdriverProcAddressQueryResult *symbolFound); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoD_v3020)(CUdeviceptr_v2 dstDevice, const void *srcHost, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoH_v3020)(void *dstHost, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoD_v3020)(CUdeviceptr_v2 dstDevice, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoA_v3020)(CUarray dstArray, size_t dstOffset, CUdeviceptr_v2 srcDevice, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoD_v3020)(CUdeviceptr_v2 dstDevice, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoA_v3020)(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoH_v3020)(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoA_v3020)(CUarray dstArray, size_t dstOffset, CUarray srcArray, size_t srcOffset, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoAAsync_v3020)(CUarray dstArray, size_t dstOffset, const void *srcHost, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoHAsync_v3020)(void *dstHost, CUarray srcArray, size_t srcOffset, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2D_v3020)(const CUDA_MEMCPY2D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2DUnaligned_v3020)(const CUDA_MEMCPY2D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3D_v3020)(const CUDA_MEMCPY3D_v2 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoDAsync_v3020)(CUdeviceptr_v2 dstDevice, const void *srcHost, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoHAsync_v3020)(void *dstHost, CUdeviceptr_v2 srcDevice, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoDAsync_v3020)(CUdeviceptr_v2 dstDevice, CUdeviceptr_v2 srcDevice, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy2DAsync_v3020)(const CUDA_MEMCPY2D_v2 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DAsync_v3020)(const CUDA_MEMCPY3D_v2 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD8_v3020)(CUdeviceptr_v2 dstDevice, unsigned char uc, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD16_v3020)(CUdeviceptr_v2 dstDevice, unsigned short us, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD32_v3020)(CUdeviceptr_v2 dstDevice, unsigned int ui, size_t N); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D8_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D16_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D32_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height); +typedef CUresult (CUDAAPI *PFN_cuMemcpy_v4000)(CUdeviceptr_v2 dst, CUdeviceptr_v2 src, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyAsync_v4000)(CUdeviceptr_v2 dst, CUdeviceptr_v2 src, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpyPeer_v4000)(CUdeviceptr_v2 dstDevice, CUcontext dstContext, CUdeviceptr_v2 srcDevice, CUcontext srcContext, size_t ByteCount); +typedef CUresult (CUDAAPI *PFN_cuMemcpyPeerAsync_v4000)(CUdeviceptr_v2 dstDevice, CUcontext dstContext, CUdeviceptr_v2 srcDevice, CUcontext srcContext, size_t ByteCount, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DPeer_v4000)(const CUDA_MEMCPY3D_PEER_v1 *pCopy); +typedef CUresult (CUDAAPI *PFN_cuMemcpy3DPeerAsync_v4000)(const CUDA_MEMCPY3D_PEER_v1 *pCopy, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD8Async_v3020)(CUdeviceptr_v2 dstDevice, unsigned char uc, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD16Async_v3020)(CUdeviceptr_v2 dstDevice, unsigned short us, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD32Async_v3020)(CUdeviceptr_v2 dstDevice, unsigned int ui, size_t N, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D8Async_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned char uc, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D16Async_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned short us, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemsetD2D32Async_v3020)(CUdeviceptr_v2 dstDevice, size_t dstPitch, unsigned int ui, size_t Width, size_t Height, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamGetPriority_v5050)(CUstream hStream, int *priority); +typedef CUresult (CUDAAPI *PFN_cuStreamGetFlags_v5050)(CUstream hStream, unsigned int *flags); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCtx_v9020)(CUstream hStream, CUcontext *pctx); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitEvent_v3020)(CUstream hStream, CUevent hEvent, unsigned int Flags); +typedef CUresult (CUDAAPI *PFN_cuStreamAddCallback_v5000)(CUstream hStream, CUstreamCallback callback, void *userData, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamAttachMemAsync_v6000)(CUstream hStream, CUdeviceptr_v2 dptr, size_t length, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamQuery_v2000)(CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamSynchronize_v2000)(CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuEventRecord_v2000)(CUevent hEvent, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuEventRecordWithFlags_v11010)(CUevent hEvent, CUstream hStream, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuLaunchKernel_v4000)(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams, void **extra); +typedef CUresult (CUDAAPI *PFN_cuLaunchKernelEx_v11060)(const CUlaunchConfig *config, CUfunction f, void **kernelParams, void **extra); +typedef CUresult (CUDAAPI *PFN_cuLaunchHostFunc_v10000)(CUstream hStream, CUhostFn fn, void *userData); +typedef CUresult (CUDAAPI *PFN_cuGraphicsMapResources_v3000)(unsigned int count, CUgraphicsResource *resources, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGraphicsUnmapResources_v3000)(unsigned int count, CUgraphicsResource *resources, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue32_v8000)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue32_v8000)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue64_v9000)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue64_v9000)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamBatchMemOp_v8000)(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue32_v11070)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue32_v11070)(CUstream stream, CUdeviceptr_v2 addr, cuuint32_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWriteValue64_v11070)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamWaitValue64_v11070)(CUstream stream, CUdeviceptr_v2 addr, cuuint64_t value, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamBatchMemOp_v11070)(CUstream stream, unsigned int count, CUstreamBatchMemOpParams *paramArray, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuMemPrefetchAsync_v8000)(CUdeviceptr_v2 devPtr, size_t count, CUdevice_v1 dstDevice, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemPrefetchAsync_v12020)(CUdeviceptr_v2 devPtr, size_t count, CUmemLocation_v1 location, unsigned int flags, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuLaunchCooperativeKernel_v9000)(CUfunction f, unsigned int gridDimX, unsigned int gridDimY, unsigned int gridDimZ, unsigned int blockDimX, unsigned int blockDimY, unsigned int blockDimZ, unsigned int sharedMemBytes, CUstream hStream, void **kernelParams); +typedef CUresult (CUDAAPI *PFN_cuSignalExternalSemaphoresAsync_v10000)(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_SIGNAL_PARAMS_v1 *paramsArray, unsigned int numExtSems, CUstream stream); +typedef CUresult (CUDAAPI *PFN_cuWaitExternalSemaphoresAsync_v10000)(const CUexternalSemaphore *extSemArray, const CUDA_EXTERNAL_SEMAPHORE_WAIT_PARAMS_v1 *paramsArray, unsigned int numExtSems, CUstream stream); +typedef CUresult (CUDAAPI *PFN_cuStreamBeginCapture_v10010)(CUstream hStream, CUstreamCaptureMode mode); +typedef CUresult (CUDAAPI *PFN_cuStreamBeginCaptureToGraph_v12030)(CUstream hStream, CUgraph hGraph, const CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, CUstreamCaptureMode mode); +typedef CUresult (CUDAAPI *PFN_cuStreamEndCapture_v10000)(CUstream hStream, CUgraph *phGraph); +typedef CUresult (CUDAAPI *PFN_cuStreamIsCapturing_v10000)(CUstream hStream, CUstreamCaptureStatus *captureStatus); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v10010)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v11030)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, size_t *numDependencies_out); +typedef CUresult (CUDAAPI *PFN_cuStreamGetCaptureInfo_v12030)(CUstream hStream, CUstreamCaptureStatus *captureStatus_out, cuuint64_t *id_out, CUgraph *graph_out, const CUgraphNode **dependencies_out, const CUgraphEdgeData **edgeData_out, size_t *numDependencies_out); +typedef CUresult (CUDAAPI *PFN_cuStreamUpdateCaptureDependencies_v11030)(CUstream hStream, CUgraphNode *dependencies, size_t numDependencies, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuStreamUpdateCaptureDependencies_v12030)(CUstream hStream, CUgraphNode *dependencies, const CUgraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphInstantiateWithParams_v12000)(CUgraphExec *phGraphExec, CUgraph hGraph, CUDA_GRAPH_INSTANTIATE_PARAMS *instantiateParams); +typedef CUresult (CUDAAPI *PFN_cuGraphUpload_v11010)(CUgraphExec hGraph, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuGraphLaunch_v10000)(CUgraphExec hGraph, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuStreamCopyAttributes_v11000)(CUstream dstStream, CUstream srcStream); +typedef CUresult (CUDAAPI *PFN_cuStreamGetAttribute_v11000)(CUstream hStream, CUstreamAttrID attr, CUstreamAttrValue_v1 *value); +typedef CUresult (CUDAAPI *PFN_cuStreamSetAttribute_v11000)(CUstream hStream, CUstreamAttrID attr, const CUstreamAttrValue_v1 *param); +typedef CUresult (CUDAAPI *PFN_cuMemMapArrayAsync_v11010)(CUarrayMapInfo_v1 *mapInfoList, unsigned int count, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemFreeAsync_v11020)(CUdeviceptr_v2 dptr, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemAllocAsync_v11020)(CUdeviceptr_v2 *dptr, size_t bytesize, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuMemAllocFromPoolAsync_v11020)(CUdeviceptr_v2 *dptr, size_t bytesize, CUmemoryPool pool, CUstream hStream); +typedef CUresult (CUDAAPI *PFN_cuFlushGPUDirectRDMAWrites_v11030)(CUflushGPUDirectRDMAWritesTarget target, CUflushGPUDirectRDMAWritesScope scope); +typedef CUresult (CUDAAPI *PFN_cuUserObjectCreate_v11030)(CUuserObject *object_out, void *ptr, CUhostFn destroy, unsigned int initialRefcount, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuUserObjectRetain_v11030)(CUuserObject object, unsigned int count); +typedef CUresult (CUDAAPI *PFN_cuUserObjectRelease_v11030)(CUuserObject object, unsigned int count); +typedef CUresult (CUDAAPI *PFN_cuGraphRetainUserObject_v11030)(CUgraph graph, CUuserObject object, unsigned int count, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphReleaseUserObject_v11030)(CUgraph graph, CUuserObject object, unsigned int count); +typedef CUresult (CUDAAPI *PFN_cuModuleGetLoadingMode_v11070)(CUmoduleLoadingMode *mode); +typedef CUresult (CUDAAPI *PFN_cuMemGetHandleForAddressRange_v11070)(void *handle, CUdeviceptr dptr, size_t size, CUmemRangeHandleType handleType, unsigned long long flags); +typedef CUresult (CUDAAPI *PFN_cuLibraryLoadData_v12000)(CUlibrary *library, const void *code, CUjit_option *jitOptions, void **jitOptionsValues, unsigned int numJitOptions, CUlibraryOption *libraryOptions, void** libraryOptionValues, unsigned int numLibraryOptions); +typedef CUresult (CUDAAPI *PFN_cuLibraryLoadFromFile_v12000)(CUlibrary *library, const char *fileName, CUjit_option *jitOptions, void **jitOptionsValues, unsigned int numJitOptions, CUlibraryOption *libraryOptions, void **libraryOptionValues, unsigned int numLibraryOptions); +typedef CUresult (CUDAAPI *PFN_cuLibraryUnload_v12000)(CUlibrary library); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetKernel_v12000)(CUkernel *pKernel, CUlibrary library, const char *name); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetModule_v12000)(CUmodule *pMod, CUlibrary library); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetKernelCount)(unsigned int *count, CUlibrary lib); +typedef CUresult (CUDAAPI *PFN_cuLibraryEnumerateKernels)(CUkernel *kernels, unsigned int numKernels, CUlibrary lib); +typedef CUresult (CUDAAPI *PFN_cuKernelGetFunction_v12000)(CUfunction *pFunc, CUkernel kernel); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetGlobal_v12000)(CUdeviceptr *dptr, size_t *bytes, CUlibrary library, const char *name); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetManaged_v12000)(CUdeviceptr *dptr, size_t *bytes, CUlibrary library, const char *name); +typedef CUresult (CUDAAPI *PFN_cuKernelGetAttribute_v12000)(int *pi, CUfunction_attribute attrib, CUkernel kernel, CUdevice dev); +typedef CUresult (CUDAAPI *PFN_cuKernelSetAttribute_v12000)(CUfunction_attribute attrib, int val, CUkernel kernel, CUdevice dev); +typedef CUresult (CUDAAPI *PFN_cuKernelSetCacheConfig_v12000)(CUkernel kernel, CUfunc_cache config, CUdevice dev); +typedef CUresult (CUDAAPI *PFN_cuKernelGetName_v12030)(const char **name, CUkernel hfunc); +typedef CUresult (CUDAAPI *PFN_cuKernelGetParamInfo_v12040)(CUkernel kernel, size_t paramIndex, size_t *paramOffset, size_t *paramSize); +typedef CUresult (CUDAAPI *PFN_cuLibraryGetUnifiedFunction_v12000)(void **fptr, CUlibrary library, const char *symbol); +typedef CUresult(CUDAAPI *PFN_cuCoredumpGetAttribute_v12010)(CUcoredumpSettings get, void *value, size_t *size); +typedef CUresult(CUDAAPI *PFN_cuCoredumpGetAttributeGlobal_v12010)(CUcoredumpSettings get, void *value, size_t *size); +typedef CUresult(CUDAAPI *PFN_cuCoredumpSetAttribute_v12010)(CUcoredumpSettings set, void *value, size_t *size); +typedef CUresult(CUDAAPI *PFN_cuCoredumpSetAttributeGlobal_v12010)(CUcoredumpSettings set, void *value, size_t *size); +typedef CUresult(CUDAAPI *PFN_cuDeviceRegisterAsyncNotification_v12040)(CUdevice device, CUasyncCallback callbackFunc, void *userData, CUasyncCallbackHandle *callback); +typedef CUresult(CUDAAPI *PFN_cuDeviceUnregisterAsyncNotification_v12040)(CUdevice device, CUasyncCallbackHandle callback); +typedef CUresult(CUDAAPI *PFN_cuGreenCtxCreate_v12040)(CUgreenCtx* phCtx, CUdevResourceDesc desc, CUdevice dev, unsigned int flags); +typedef CUresult(CUDAAPI *PFN_cuGreenCtxDestroy_v12040)(CUgreenCtx hCtx); +typedef CUresult(CUDAAPI *PFN_cuDeviceGetDevResource_v12040)(CUdevice dev, CUdevResource* result, CUdevResourceType type); +typedef CUresult(CUDAAPI *PFN_cuCtxGetDevResource_v12040)(CUcontext hCtx, CUdevResource* result, CUdevResourceType type); +typedef CUresult(CUDAAPI *PFN_cuGreenCtxGetDevResource_v12040)(CUgreenCtx hCtx, CUdevResource* result, CUdevResourceType type); +typedef CUresult(CUDAAPI *PFN_cuGreenCtxRecordEvent_v12040)(CUgreenCtx hCtx, CUevent hEvent); +typedef CUresult(CUDAAPI *PFN_cuGreenCtxWaitEvent_v12040)(CUgreenCtx hCtx, CUevent hEvent); +typedef CUresult(CUDAAPI *PFN_cuDevResourceGenerateDesc_v12040)(CUdevResourceDesc* phDesc, CUdevResource* resources, unsigned int nbResources); +typedef CUresult(CUDAAPI *PFN_cuDevSmResourceSplitByCount_v12040)(CUdevResource* result, unsigned int* nbGroups, const CUdevResource* input, CUdevResource* remaining, unsigned int useFlags, unsigned int minCount); +typedef CUresult(CUDAAPI *PFN_cuStreamGetGreenCtx_v12040)(CUstream hStream, CUgreenCtx *phCtx); +typedef CUresult(CUDAAPI *PFN_cuCtxFromGreenCtx_v12040)(CUcontext *pContext, CUgreenCtx hCtx); +/* + * Type definitions for older versioned functions in cuda.h + */ +#if defined(__CUDA_API_VERSION_INTERNAL) + typedef CUresult (CUDAAPI *PFN_cuMemHostRegister_v4000)(void *p, size_t bytesize, unsigned int Flags); + typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceSetMapFlags_v3000)(CUgraphicsResource resource, unsigned int flags); + typedef CUresult (CUDAAPI *PFN_cuLinkCreate_v5050)(unsigned int numOptions, CUjit_option *options, void **optionValues, CUlinkState *stateOut); + typedef CUresult (CUDAAPI *PFN_cuLinkAddData_v5050)(CUlinkState state, CUjitInputType type, void *data, size_t size, const char *name, unsigned int numOptions, CUjit_option *options, void **optionValues); + typedef CUresult (CUDAAPI *PFN_cuLinkAddFile_v5050)(CUlinkState state, CUjitInputType type, const char *path, unsigned int numOptions, CUjit_option *options, void **optionValues); + typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddress2D_v3020)(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR_v2 *desc, CUdeviceptr_v2 dptr, size_t Pitch); + typedef CUresult (CUDAAPI *PFN_cuDeviceTotalMem_v2000)(unsigned int *bytes, CUdevice_v1 dev); + typedef CUresult (CUDAAPI *PFN_cuCtxCreate_v2000)(CUcontext *pctx, unsigned int flags, CUdevice_v1 dev); + typedef CUresult (CUDAAPI *PFN_cuModuleGetGlobal_v2000)(CUdeviceptr_v1 *dptr, unsigned int *bytes, CUmodule hmod, const char *name); + typedef CUresult (CUDAAPI *PFN_cuMemGetInfo_v2000)(unsigned int *free, unsigned int *total); + typedef CUresult (CUDAAPI *PFN_cuMemAlloc_v2000)(CUdeviceptr_v1 *dptr, unsigned int bytesize); + typedef CUresult (CUDAAPI *PFN_cuMemAllocPitch_v2000)(CUdeviceptr_v1 *dptr, unsigned int *pPitch, unsigned int WidthInBytes, unsigned int Height, unsigned int ElementSizeBytes); + typedef CUresult (CUDAAPI *PFN_cuMemFree_v2000)(CUdeviceptr_v1 dptr); + typedef CUresult (CUDAAPI *PFN_cuMemGetAddressRange_v2000)(CUdeviceptr_v1 *pbase, unsigned int *psize, CUdeviceptr_v1 dptr); + typedef CUresult (CUDAAPI *PFN_cuMemAllocHost_v2000)(void **pp, unsigned int bytesize); + typedef CUresult (CUDAAPI *PFN_cuMemHostGetDevicePointer_v2020)(CUdeviceptr_v1 *pdptr, void *p, unsigned int Flags); + typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoD_v2000)(CUdeviceptr_v1 dstDevice, const void *srcHost, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoH_v2000)(void *dstHost, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoD_v2000)(CUdeviceptr_v1 dstDevice, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoA_v2000)(CUarray dstArray, unsigned int dstOffset, CUdeviceptr_v1 srcDevice, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoD_v2000)(CUdeviceptr_v1 dstDevice, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoA_v2000)(CUarray dstArray, unsigned int dstOffset, const void *srcHost, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoH_v2000)(void *dstHost, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoA_v2000)(CUarray dstArray, unsigned int dstOffset, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount); + typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoAAsync_v2000)(CUarray dstArray, unsigned int dstOffset, const void *srcHost, unsigned int ByteCount, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpyAtoHAsync_v2000)(void *dstHost, CUarray srcArray, unsigned int srcOffset, unsigned int ByteCount, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpy2D_v2000)(const CUDA_MEMCPY2D_v1 *pCopy); + typedef CUresult (CUDAAPI *PFN_cuMemcpy2DUnaligned_v2000)(const CUDA_MEMCPY2D_v1 *pCopy); + typedef CUresult (CUDAAPI *PFN_cuMemcpy3D_v2000)(const CUDA_MEMCPY3D_v1 *pCopy); + typedef CUresult (CUDAAPI *PFN_cuMemcpyHtoDAsync_v2000)(CUdeviceptr_v1 dstDevice, const void *srcHost, unsigned int ByteCount, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoHAsync_v2000)(void *dstHost, CUdeviceptr_v1 srcDevice, unsigned int ByteCount, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpyDtoDAsync_v3000)(CUdeviceptr_v1 dstDevice, CUdeviceptr_v1 srcDevice, unsigned int ByteCount, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpy2DAsync_v2000)(const CUDA_MEMCPY2D_v1 *pCopy, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemcpy3DAsync_v2000)(const CUDA_MEMCPY3D_v1 *pCopy, CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuMemsetD8_v2000)(CUdeviceptr_v1 dstDevice, unsigned char uc, unsigned int N); + typedef CUresult (CUDAAPI *PFN_cuMemsetD16_v2000)(CUdeviceptr_v1 dstDevice, unsigned short us, unsigned int N); + typedef CUresult (CUDAAPI *PFN_cuMemsetD32_v2000)(CUdeviceptr_v1 dstDevice, unsigned int ui, unsigned int N); + typedef CUresult (CUDAAPI *PFN_cuMemsetD2D8_v2000)(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned char uc, unsigned int Width, unsigned int Height); + typedef CUresult (CUDAAPI *PFN_cuMemsetD2D16_v2000)(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned short us, unsigned int Width, unsigned int Height); + typedef CUresult (CUDAAPI *PFN_cuMemsetD2D32_v2000)(CUdeviceptr_v1 dstDevice, unsigned int dstPitch, unsigned int ui, unsigned int Width, unsigned int Height); + typedef CUresult (CUDAAPI *PFN_cuArrayCreate_v2000)(CUarray *pHandle, const CUDA_ARRAY_DESCRIPTOR_v1 *pAllocateArray); + typedef CUresult (CUDAAPI *PFN_cuArrayGetDescriptor_v2000)(CUDA_ARRAY_DESCRIPTOR_v1 *pArrayDescriptor, CUarray hArray); + typedef CUresult (CUDAAPI *PFN_cuArray3DCreate_v2000)(CUarray *pHandle, const CUDA_ARRAY3D_DESCRIPTOR_v1 *pAllocateArray); + typedef CUresult (CUDAAPI *PFN_cuArray3DGetDescriptor_v2000)(CUDA_ARRAY3D_DESCRIPTOR_v1 *pArrayDescriptor, CUarray hArray); + typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddress_v2000)(unsigned int *ByteOffset, CUtexref hTexRef, CUdeviceptr_v1 dptr, unsigned int bytes); + typedef CUresult (CUDAAPI *PFN_cuTexRefSetAddress2D_v2020)(CUtexref hTexRef, const CUDA_ARRAY_DESCRIPTOR_v1 *desc, CUdeviceptr_v1 dptr, unsigned int Pitch); + typedef CUresult (CUDAAPI *PFN_cuTexRefGetAddress_v2000)(CUdeviceptr_v1 *pdptr, CUtexref hTexRef); + typedef CUresult (CUDAAPI *PFN_cuGraphicsResourceGetMappedPointer_v3000)(CUdeviceptr_v1 *pDevPtr, unsigned int *pSize, CUgraphicsResource resource); + typedef CUresult (CUDAAPI *PFN_cuCtxDestroy_v2000)(CUcontext ctx); + typedef CUresult (CUDAAPI *PFN_cuCtxPopCurrent_v2000)(CUcontext *pctx); + typedef CUresult (CUDAAPI *PFN_cuCtxPushCurrent_v2000)(CUcontext ctx); + typedef CUresult (CUDAAPI *PFN_cuStreamDestroy_v2000)(CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuEventDestroy_v2000)(CUevent hEvent); + typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxRelease_v7000)(CUdevice_v1 dev); + typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxReset_v7000)(CUdevice_v1 dev); + typedef CUresult (CUDAAPI *PFN_cuDevicePrimaryCtxSetFlags_v7000)(CUdevice_v1 dev, unsigned int flags); + typedef CUresult (CUDAAPI *PFN_cuStreamBeginCapture_v10000)(CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuStreamBeginCapture_v10000_ptsz)(CUstream hStream); + typedef CUresult (CUDAAPI *PFN_cuIpcOpenMemHandle_v4010)(CUdeviceptr_v2 *pdptr, CUipcMemHandle_v1 handle, unsigned int Flags); + typedef CUresult (CUDAAPI *PFN_cuGraphInstantiate_v10000)(CUgraphExec *phGraphExec, CUgraph hGraph, CUgraphNode *phErrorNode, char *logBuffer, size_t bufferSize); + typedef CUresult (CUDAAPI *PFN_cuGraphInstantiate_v11000)(CUgraphExec *phGraphExec, CUgraph hGraph, CUgraphNode *phErrorNode, char *logBuffer, size_t bufferSize); +#endif + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAU.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAU.h new file mode 100644 index 0000000000000000000000000000000000000000..97de57ae494d62ae176fc02ad3c0c3f4d43e1526 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAU.h @@ -0,0 +1,282 @@ +/* + * Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAVDPAU_H +#define CUDAVDPAU_H + +#ifdef CUDA_FORCE_API_VERSION +#error "CUDA_FORCE_API_VERSION is no longer supported." +#endif + +#define cuVDPAUCtxCreate cuVDPAUCtxCreate_v2 + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * \defgroup CUDA_VDPAU VDPAU Interoperability + * \ingroup CUDA_DRIVER + * + * ___MANBRIEF___ VDPAU interoperability functions of the low-level CUDA driver + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the VDPAU interoperability functions of the + * low-level CUDA driver application programming interface. + * + * @{ + */ + +/** + * \brief Gets the CUDA device associated with a VDPAU device + * + * Returns in \p *pDevice the CUDA device associated with a \p vdpDevice, if + * applicable. + * + * \param pDevice - Device associated with vdpDevice + * \param vdpDevice - A VdpDevice handle + * \param vdpGetProcAddress - VDPAU's VdpGetProcAddress function pointer + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE + * \notefnerr + * + * \sa ::cuCtxCreate, ::cuVDPAUCtxCreate, ::cuGraphicsVDPAURegisterVideoSurface, + * ::cuGraphicsVDPAURegisterOutputSurface, ::cuGraphicsUnregisterResource, + * ::cuGraphicsResourceSetMapFlags, ::cuGraphicsMapResources, + * ::cuGraphicsUnmapResources, ::cuGraphicsSubResourceGetMappedArray, + * ::cudaVDPAUGetDevice + */ +CUresult CUDAAPI cuVDPAUGetDevice(CUdevice *pDevice, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); + +/** + * \brief Create a CUDA context for interoperability with VDPAU + * + * Creates a new CUDA context, initializes VDPAU interoperability, and + * associates the CUDA context with the calling thread. It must be called + * before performing any other VDPAU interoperability operations. It may fail + * if the needed VDPAU driver facilities are not available. For usage of the + * \p flags parameter, see ::cuCtxCreate(). + * + * \param pCtx - Returned CUDA context + * \param flags - Options for CUDA context creation + * \param device - Device on which to create the context + * \param vdpDevice - The VdpDevice to interop with + * \param vdpGetProcAddress - VDPAU's VdpGetProcAddress function pointer + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_DEINITIALIZED, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_OUT_OF_MEMORY + * \notefnerr + * + * \sa ::cuCtxCreate, ::cuGraphicsVDPAURegisterVideoSurface, + * ::cuGraphicsVDPAURegisterOutputSurface, ::cuGraphicsUnregisterResource, + * ::cuGraphicsResourceSetMapFlags, ::cuGraphicsMapResources, + * ::cuGraphicsUnmapResources, ::cuGraphicsSubResourceGetMappedArray, + * ::cuVDPAUGetDevice + */ +CUresult CUDAAPI cuVDPAUCtxCreate(CUcontext *pCtx, unsigned int flags, CUdevice device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); + +/** + * \brief Registers a VDPAU VdpVideoSurface object + * + * Registers the VdpVideoSurface specified by \p vdpSurface for access by + * CUDA. A handle to the registered object is returned as \p pCudaResource. + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_READ_ONLY: Specifies that CUDA + * will not write to this resource. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_WRITE_DISCARD: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * The VdpVideoSurface is presented as an array of subresources that may be + * accessed using pointers returned by ::cuGraphicsSubResourceGetMappedArray. + * The exact number of valid \p arrayIndex values depends on the VDPAU surface + * format. The mapping is shown in the table below. \p mipLevel must be 0. + * + * \htmlonly + * + * + * + * + * + * + * + * + * + * + *
VdpChromaType arrayIndexSize FormatContent
VDP_CHROMA_TYPE_4200 w x h/2R8 Top-field luma
1 w x h/2R8 Bottom-field luma
2 w/2 x h/4R8G8 Top-field chroma
3 w/2 x h/4R8G8 Bottom-field chroma
VDP_CHROMA_TYPE_4220 w x h/2R8 Top-field luma
1 w x h/2R8 Bottom-field luma
2 w/2 x h/2R8G8 Top-field chroma
3 w/2 x h/2R8G8 Bottom-field chroma
+ * \endhtmlonly + * + * \latexonly + * \begin{tabular}{|l|l|l|l|l|} + * \hline + * VdpChromaType & arrayIndex & Size & Format & Content \\ + * \hline + * VDP\_CHROMA\_TYPE\_420 & 0 & w x h/2 & R8 & Top-field luma \\ + * & 1 & w x h/2 & R8 & Bottom-field luma \\ + * & 2 & w/2 x h/4 & R8G8 & Top-field chroma \\ + * & 3 & w/2 x h/4 & R8G8 & Bottom-field chroma \\ + * \hline + * VDP\_CHROMA\_TYPE\_422 & 0 & w x h/2 & R8 & Top-field luma \\ + * & 1 & w x h/2 & R8 & Bottom-field luma \\ + * & 2 & w/2 x h/2 & R8G8 & Top-field chroma \\ + * & 3 & w/2 x h/2 & R8G8 & Bottom-field chroma \\ + * \hline + * \end{tabular} + * \endlatexonly + * + * \param pCudaResource - Pointer to the returned object handle + * \param vdpSurface - The VdpVideoSurface to be registered + * \param flags - Map flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * \notefnerr + * + * \sa ::cuCtxCreate, ::cuVDPAUCtxCreate, + * ::cuGraphicsVDPAURegisterOutputSurface, ::cuGraphicsUnregisterResource, + * ::cuGraphicsResourceSetMapFlags, ::cuGraphicsMapResources, + * ::cuGraphicsUnmapResources, ::cuGraphicsSubResourceGetMappedArray, + * ::cuVDPAUGetDevice, + * ::cudaGraphicsVDPAURegisterVideoSurface + */ +CUresult CUDAAPI cuGraphicsVDPAURegisterVideoSurface(CUgraphicsResource *pCudaResource, VdpVideoSurface vdpSurface, unsigned int flags); + +/** + * \brief Registers a VDPAU VdpOutputSurface object + * + * Registers the VdpOutputSurface specified by \p vdpSurface for access by + * CUDA. A handle to the registered object is returned as \p pCudaResource. + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_NONE: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_READ_ONLY: Specifies that CUDA + * will not write to this resource. + * - ::CU_GRAPHICS_MAP_RESOURCE_FLAGS_WRITE_DISCARD: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * The VdpOutputSurface is presented as an array of subresources that may be + * accessed using pointers returned by ::cuGraphicsSubResourceGetMappedArray. + * The exact number of valid \p arrayIndex values depends on the VDPAU surface + * format. The mapping is shown in the table below. \p mipLevel must be 0. + * + * \htmlonly + * + * + * + * + *
VdpRGBAFormat arrayIndexSize Format Content
VDP_RGBA_FORMAT_B8G8R8A8 0 w x hARGB8 Entire surface
VDP_RGBA_FORMAT_R10G10B10A20 w x hA2BGR10Entire surface
+ * \endhtmlonly + * + * \latexonly + * \begin{tabular}{|l|l|l|l|l|} + * \hline + * VdpRGBAFormat & arrayIndex & Size & Format & Content \\ + * \hline + * VDP\_RGBA\_FORMAT\_B8G8R8A8 & 0 & w x h & ARGB8 & Entire surface \\ + * VDP\_RGBA\_FORMAT\_R10G10B10A2 & 0 & w x h & A2BGR10 & Entire surface \\ + * \hline + * \end{tabular} + * \endlatexonly + * + * \param pCudaResource - Pointer to the returned object handle + * \param vdpSurface - The VdpOutputSurface to be registered + * \param flags - Map flags + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_HANDLE, + * ::CUDA_ERROR_ALREADY_MAPPED, + * ::CUDA_ERROR_INVALID_CONTEXT, + * \notefnerr + * + * \sa ::cuCtxCreate, ::cuVDPAUCtxCreate, + * ::cuGraphicsVDPAURegisterVideoSurface, ::cuGraphicsUnregisterResource, + * ::cuGraphicsResourceSetMapFlags, ::cuGraphicsMapResources, + * ::cuGraphicsUnmapResources, ::cuGraphicsSubResourceGetMappedArray, + * ::cuVDPAUGetDevice, + * ::cudaGraphicsVDPAURegisterOutputSurface + */ +CUresult CUDAAPI cuGraphicsVDPAURegisterOutputSurface(CUgraphicsResource *pCudaResource, VdpOutputSurface vdpSurface, unsigned int flags); + +/** @} */ /* END CUDA_VDPAU */ + + +#if defined(__CUDA_API_VERSION_INTERNAL) + #undef cuVDPAUCtxCreate + + CUresult CUDAAPI cuVDPAUCtxCreate(CUcontext *pCtx, unsigned int flags, CUdevice device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); +#endif /* __CUDA_API_VERSION_INTERNAL */ + +#ifdef __cplusplus +}; +#endif + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAUTypedefs.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAUTypedefs.h new file mode 100644 index 0000000000000000000000000000000000000000..2bfd148632827d222548be49b3a2ffb7caa1c4dc --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudaVDPAUTypedefs.h @@ -0,0 +1,90 @@ +/* + * Copyright 2020-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef CUDAVDPAUTYPEDEFS_H +#define CUDAVDPAUTYPEDEFS_H + +// Dependent includes for cudavdpau.h +#include + +#include + +#ifdef __cplusplus +extern "C" { +#endif // __cplusplus + +/* + * Macros for the latest version for each driver function in cudaVDPAU.h + */ +#define PFN_cuVDPAUGetDevice PFN_cuVDPAUGetDevice_v3010 +#define PFN_cuVDPAUCtxCreate PFN_cuVDPAUCtxCreate_v3020 +#define PFN_cuGraphicsVDPAURegisterVideoSurface PFN_cuGraphicsVDPAURegisterVideoSurface_v3010 +#define PFN_cuGraphicsVDPAURegisterOutputSurface PFN_cuGraphicsVDPAURegisterOutputSurface_v3010 + + +/** + * Type definitions for functions defined in cudaVDPAU.h + */ +typedef CUresult (CUDAAPI *PFN_cuVDPAUGetDevice_v3010)(CUdevice_v1 *pDevice, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); +typedef CUresult (CUDAAPI *PFN_cuVDPAUCtxCreate_v3020)(CUcontext *pCtx, unsigned int flags, CUdevice_v1 device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); +typedef CUresult (CUDAAPI *PFN_cuGraphicsVDPAURegisterVideoSurface_v3010)(CUgraphicsResource *pCudaResource, VdpVideoSurface vdpSurface, unsigned int flags); +typedef CUresult (CUDAAPI *PFN_cuGraphicsVDPAURegisterOutputSurface_v3010)(CUgraphicsResource *pCudaResource, VdpOutputSurface vdpSurface, unsigned int flags); + +/* + * Type definitions for older versioned functions in cudaVDPAU.h + */ +#if defined(__CUDA_API_VERSION_INTERNAL) +typedef CUresult (CUDAAPI *PFN_cuVDPAUCtxCreate_v3010)(CUcontext *pCtx, unsigned int flags, CUdevice_v1 device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); +#endif + +#ifdef __cplusplus +} +#endif // __cplusplus + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier.h new file mode 100644 index 0000000000000000000000000000000000000000..12fd878dd10d9f18ad944a0d62ae1caba123fd06 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier.h @@ -0,0 +1,280 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_AWBARRIER_H_ +# define _CUDA_AWBARRIER_H_ + +# include "cuda_awbarrier_primitives.h" + +# if !defined(_CUDA_AWBARRIER_SM_TARGET) +# error This file requires compute capability 7.0 or greater. +# endif + +# if !defined(_CUDA_AWBARRIER_CPLUSPLUS_11_OR_LATER) +# error This file requires compiler support for the ISO C++ 2011 standard. This support must be enabled with the \ + -std=c++11 compiler option. +# endif + +_CUDA_AWBARRIER_BEGIN_NAMESPACE + +class awbarrier { +public: + class arrival_token { + public: + arrival_token() = default; + ~arrival_token() = default; + _CUDA_AWBARRIER_QUALIFIER uint32_t pending_count() const; + private: + _CUDA_AWBARRIER_QUALIFIER arrival_token(uint64_t token); + uint64_t token; + friend awbarrier; + }; + awbarrier() = default; + awbarrier(const awbarrier&) = delete; + awbarrier& operator=(const awbarrier&) = delete; + ~awbarrier() = default; + + _CUDA_AWBARRIER_QUALIFIER arrival_token arrive(); + _CUDA_AWBARRIER_QUALIFIER arrival_token arrive_and_drop(); + _CUDA_AWBARRIER_QUALIFIER bool timed_wait(arrival_token token, uint32_t hint_cycles); + _CUDA_AWBARRIER_QUALIFIER bool timed_wait_parity(bool phase, uint32_t hint_cycles); + _CUDA_AWBARRIER_QUALIFIER void wait(arrival_token token); + _CUDA_AWBARRIER_QUALIFIER void arrive_and_wait(); + _CUDA_AWBARRIER_QUALIFIER bool try_wait(arrival_token token, uint32_t maxSleepNanosec); + _CUDA_AWBARRIER_QUALIFIER bool try_wait_parity(bool phase, uint32_t maxSleepNanosec); + _CUDA_AWBARRIER_STATIC_QUALIFIER __host__ constexpr uint32_t max(); + +private: + uint64_t barrier; + friend _CUDA_AWBARRIER_QUALIFIER void init(awbarrier* barrier, uint32_t expected_count); + friend _CUDA_AWBARRIER_QUALIFIER void inval(awbarrier* barrier); + friend class pipeline; +}; + +_CUDA_AWBARRIER_QUALIFIER +uint32_t awbarrier::arrival_token::pending_count() const +{ + const uint32_t pending_count = _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_token_pending_count(this->token); +#if (__CUDA_ARCH__ >= 900) + return pending_count; +#else + return (pending_count >> 15); +#endif +} + +_CUDA_AWBARRIER_QUALIFIER +awbarrier::arrival_token::arrival_token(uint64_t token) + : token(token) +{ +} + +_CUDA_AWBARRIER_QUALIFIER +void init(awbarrier* barrier, uint32_t expected_count) +{ + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + _CUDA_AWBARRIER_ASSERT(expected_count > 0 && expected_count <= _CUDA_AWBARRIER_MAX_COUNT); + +#if (__CUDA_ARCH__ >= 900) + const uint32_t init_count = expected_count; +#else + const uint32_t init_count = (expected_count << 15) + expected_count; +#endif + + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_init(&barrier->barrier, init_count); +} + +_CUDA_AWBARRIER_QUALIFIER +void inval(awbarrier* barrier) +{ + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_inval(&barrier->barrier); +} + +_CUDA_AWBARRIER_QUALIFIER +awbarrier::arrival_token awbarrier::arrive() +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + #if (__CUDA_ARCH__ < 900) + const uint32_t arrive_count = 1 << 15; + const uint64_t token = _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop_no_complete(&this->barrier, arrive_count); + (void) +#else + const uint64_t token = + #endif + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop(&this->barrier); + + return arrival_token(token); +} + +_CUDA_AWBARRIER_QUALIFIER +awbarrier::arrival_token awbarrier::arrive_and_drop() +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + #if (__CUDA_ARCH__ < 900) + const uint32_t arrive_count = 1 << 15; + const uint64_t token = _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop_no_complete(&this->barrier, arrive_count); + (void) +#else + const uint64_t token = + #endif + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop(&this->barrier); + + return arrival_token(token); +} + +_CUDA_AWBARRIER_QUALIFIER +bool awbarrier::timed_wait(arrival_token token, uint32_t hint_cycles) +{ + constexpr uint64_t max_busy_wait_cycles = 1024; + constexpr uint32_t max_sleep_ns = 1 << 20; + + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + if (_CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait(&this->barrier, token.token)) { + return true; + } + + uint64_t start_cycles = clock64(); + uint64_t elapsed_cycles = 0; + uint32_t sleep_ns = 32; + while (elapsed_cycles < hint_cycles) { + if (_CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait(&this->barrier, token.token)) { + return true; + } + + if (elapsed_cycles > max_busy_wait_cycles) { + __nanosleep(sleep_ns); + if (sleep_ns < max_sleep_ns) { + sleep_ns *= 2; + } + } + + elapsed_cycles = clock64() - start_cycles; + } + + return false; +} + +_CUDA_AWBARRIER_QUALIFIER +bool awbarrier::timed_wait_parity(bool phase, uint32_t hint_cycles) +{ + constexpr uint64_t max_busy_wait_cycles = 1024; + constexpr uint32_t max_sleep_ns = 1 << 20; + + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + if (_CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait_parity(&this->barrier, phase)) { + return true; + } + + uint64_t start_cycles = clock64(); + uint64_t elapsed_cycles = 0; + uint32_t sleep_ns = 32; + while (elapsed_cycles < hint_cycles) { + if (_CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait_parity(&this->barrier, phase)) { + return true; + } + + if (elapsed_cycles > max_busy_wait_cycles) { + __nanosleep(sleep_ns); + if (sleep_ns < max_sleep_ns) { + sleep_ns *= 2; + } + } + + elapsed_cycles = clock64() - start_cycles; + } + + return false; +} + +_CUDA_AWBARRIER_QUALIFIER +bool awbarrier::try_wait(arrival_token token, uint32_t maxSleepNanosec) +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_try_wait(&this->barrier, token.token, maxSleepNanosec); +} + +_CUDA_AWBARRIER_QUALIFIER +bool awbarrier::try_wait_parity(bool phase, uint32_t maxSleepNanosec) +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_try_wait_parity(&this->barrier, phase, maxSleepNanosec); +} + +_CUDA_AWBARRIER_QUALIFIER +void awbarrier::wait(arrival_token token) +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + while (!timed_wait(token, ~0u)); +} + +_CUDA_AWBARRIER_QUALIFIER +void awbarrier::arrive_and_wait() +{ + _CUDA_AWBARRIER_ASSERT(__isShared(&this->barrier)); + + this->wait(this->arrive()); +} + +_CUDA_AWBARRIER_QUALIFIER __host__ +constexpr uint32_t awbarrier::max() +{ + return _CUDA_AWBARRIER_MAX_COUNT; +} + +_CUDA_AWBARRIER_END_NAMESPACE + +#endif /* !_CUDA_AWBARRIER_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_helpers.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_helpers.h new file mode 100644 index 0000000000000000000000000000000000000000..7c58346fe78c59329aca138ebc92add9015c005c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_helpers.h @@ -0,0 +1,365 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_AWBARRIER_HELPERS_H_ +#define _CUDA_AWBARRIER_HELPERS_H_ + +#define _CUDA_AWBARRIER_NAMESPACE nvcuda::experimental +#define _CUDA_AWBARRIER_BEGIN_NAMESPACE namespace nvcuda { namespace experimental { +#define _CUDA_AWBARRIER_END_NAMESPACE } } + +#define _CUDA_AWBARRIER_INTERNAL_NAMESPACE _CUDA_AWBARRIER_NAMESPACE::__awbarrier_internal +#define _CUDA_AWBARRIER_BEGIN_INTERNAL_NAMESPACE _CUDA_AWBARRIER_BEGIN_NAMESPACE namespace __awbarrier_internal { +#define _CUDA_AWBARRIER_END_INTERNAL_NAMESPACE } _CUDA_AWBARRIER_END_NAMESPACE + +# if !defined(_CUDA_AWBARRIER_QUALIFIER) +# define _CUDA_AWBARRIER_QUALIFIER inline __device__ +# endif +# if !defined(_CUDA_AWBARRIER_STATIC_QUALIFIER) +# define _CUDA_AWBARRIER_STATIC_QUALIFIER static inline __device__ +#endif + +#if defined(__CUDA_ARCH__) +#if (__CUDA_ARCH__ >= 900) +# define _CUDA_AWBARRIER_SM_TARGET _CUDA_AWBARRIER_SM_90 +#elif (__CUDA_ARCH__ >= 800) +# define _CUDA_AWBARRIER_SM_TARGET _CUDA_AWBARRIER_SM_80 +#elif (__CUDA_ARCH__ >= 700) +# define _CUDA_AWBARRIER_SM_TARGET _CUDA_AWBARRIER_SM_70 +#endif +#else +# define _CUDA_AWBARRIER_SM_TARGET _CUDA_AWBARRIER_SM_70 +#endif + +#define _CUDA_AWBARRIER_MAX_COUNT ((1 << 14) - 1) + +#if defined(__cplusplus) && ((__cplusplus >= 201103L) || (defined(_MSC_VER) && (_MSC_VER >= 1900))) +# define _CUDA_AWBARRIER_CPLUSPLUS_11_OR_LATER +#endif + +#if !defined(_CUDA_AWBARRIER_DEBUG) +# if defined(__CUDACC_DEBUG__) +# define _CUDA_AWBARRIER_DEBUG 1 +# else +# define _CUDA_AWBARRIER_DEBUG 0 +# endif +#endif + +#if defined(_CUDA_AWBARRIER_DEBUG) && (_CUDA_AWBARRIER_DEBUG == 1) && !defined(NDEBUG) +# if !defined(__CUDACC_RTC__) +# include +# endif +# define _CUDA_AWBARRIER_ASSERT(x) assert((x)); +# define _CUDA_AWBARRIER_ABORT() assert(0); +#else +# define _CUDA_AWBARRIER_ASSERT(x) +# define _CUDA_AWBARRIER_ABORT() __trap(); +#endif + +#if defined(__CUDACC_RTC__) +typedef unsigned short uint16_t; +typedef unsigned int uint32_t; +typedef unsigned long long uint64_t; +typedef uint64_t uintptr_t; +#else +# include +#endif + +// implicitly provided by NVRTC +#ifndef __CUDACC_RTC__ +#include +#endif /* !defined(__CUDACC_RTC__) */ + +typedef uint64_t __mbarrier_t; +typedef uint64_t __mbarrier_token_t; + +_CUDA_AWBARRIER_BEGIN_INTERNAL_NAMESPACE + +extern "C" __device__ uint32_t __nvvm_get_smem_pointer(void *); + +union AWBarrier { + struct { + uint32_t expected; + uint32_t pending; + } split; + uint64_t raw; +}; + +_CUDA_AWBARRIER_STATIC_QUALIFIER +void awbarrier_init(uint64_t* barrier, uint32_t expected_count) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + _CUDA_AWBARRIER_ASSERT(expected_count > 0 && expected_count < (1 << 29)); + + NV_IF_TARGET(NV_PROVIDES_SM_80, + asm volatile ("mbarrier.init.shared.b64 [%0], %1;" + : + : "r"(__nvvm_get_smem_pointer(barrier)), "r"(expected_count) + : "memory"); + return; + ) + NV_IF_TARGET(NV_PROVIDES_SM_70, + AWBarrier* awbarrier = reinterpret_cast(barrier); + + awbarrier->split.expected = 0x40000000 - expected_count; + awbarrier->split.pending = 0x80000000 - expected_count; + return; + ) +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +void awbarrier_inval(uint64_t* barrier) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_80, + asm volatile ("mbarrier.inval.shared.b64 [%0];" + : + : "r"(__nvvm_get_smem_pointer(barrier)) + : "memory"); + return; + ) + return; +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +uint32_t awbarrier_token_pending_count(uint64_t token) { + NV_IF_TARGET(NV_PROVIDES_SM_80, + uint32_t __pending_count; + + asm ("mbarrier.pending_count.b64 %0, %1;" + : "=r"(__pending_count) + : "l"(token)); + return __pending_count; + ) + NV_IF_TARGET(NV_PROVIDES_SM_70, + const uint32_t pending = token >> 32; + return 0x80000000 - (pending & 0x7fffffff); + ) +} + +template +_CUDA_AWBARRIER_STATIC_QUALIFIER +uint64_t awbarrier_arrive_drop(uint64_t* barrier) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_80, + uint64_t token; + + if (_Drop) { + asm volatile ("mbarrier.arrive_drop.shared.b64 %0, [%1];" + : "=l"(token) + : "r"(__nvvm_get_smem_pointer(barrier)) + : "memory"); + } else { + asm volatile ("mbarrier.arrive.shared.b64 %0, [%1];" + : "=l"(token) + : "r"(__nvvm_get_smem_pointer(barrier)) + : "memory"); + } + + return token; + ) + NV_IF_TARGET(NV_PROVIDES_SM_70, + AWBarrier* awbarrier = reinterpret_cast(barrier); + + while ((*reinterpret_cast(&awbarrier->split.pending) & 0x7fffffff) == 0); + + if (_Drop) { + (void)atomicAdd_block(&awbarrier->split.expected, 1); + } + + __threadfence_block(); + + const uint32_t old_pending = atomicAdd_block(&awbarrier->split.pending, 1); + const uint32_t new_pending = old_pending + 1; + const bool reset = (old_pending ^ new_pending) & 0x80000000; + + if (reset) { + __threadfence_block(); + + uint32_t new_expected = *reinterpret_cast(&awbarrier->split.expected); + new_expected &= ~0x40000000; + if (new_expected & 0x20000000) { + new_expected |= 0x40000000; + } + atomicAdd_block(&awbarrier->split.pending, new_expected); + } + + return static_cast(old_pending) << 32; + ) +} + +template +_CUDA_AWBARRIER_STATIC_QUALIFIER +uint64_t awbarrier_arrive_drop_no_complete(uint64_t* barrier, uint32_t count) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + _CUDA_AWBARRIER_ASSERT(count > 0 && count < (1 << 29)); + + NV_IF_TARGET(NV_PROVIDES_SM_80, + uint64_t token; + + if (_Drop) { + asm volatile ("mbarrier.arrive_drop.noComplete.shared.b64 %0, [%1], %2;" + : "=l"(token) + : "r"(__nvvm_get_smem_pointer(barrier)), "r"(count) + : "memory"); + } else { + asm volatile ("mbarrier.arrive.noComplete.shared.b64 %0, [%1], %2;" + : "=l"(token) + : "r"(__nvvm_get_smem_pointer(barrier)), "r"(count) + : "memory"); + } + + return token; + ) + NV_IF_TARGET(NV_PROVIDES_SM_70, + AWBarrier* awbarrier = reinterpret_cast(barrier); + + while ((*reinterpret_cast(&awbarrier->split.pending) & 0x7fffffff) == 0); + + if (_Drop) { + (void)atomicAdd_block(&awbarrier->split.expected, count); + } + + return static_cast(atomicAdd_block(&awbarrier->split.pending, count)) << 32; + ) +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool awbarrier_test_wait(uint64_t* barrier, uint64_t token) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_80, + uint32_t __wait_complete; + + asm volatile ("{" + " .reg .pred %%p;" + " mbarrier.test_wait.shared.b64 %%p, [%1], %2;" + " selp.b32 %0, 1, 0, %%p;" + "}" + : "=r"(__wait_complete) + : "r"(__nvvm_get_smem_pointer(barrier)), "l"(token) + : "memory"); + return bool(__wait_complete); + ) + NV_IF_TARGET(NV_PROVIDES_SM_70, + volatile AWBarrier* awbarrier = reinterpret_cast(barrier); + + return ((token >> 32) ^ awbarrier->split.pending) & 0x80000000; + ) +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool awbarrier_test_wait_parity(uint64_t* barrier, bool phase_parity) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_90, + uint32_t __wait_complete = 0; + + asm volatile ("{" + ".reg .pred %%p;" + "mbarrier.test_wait.parity.shared.b64 %%p, [%1], %2;" + "selp.b32 %0, 1, 0, %%p;" + "}" + : "=r"(__wait_complete) + : "r"(__nvvm_get_smem_pointer(barrier)), "r"(static_cast(phase_parity)) + : "memory"); + + return __wait_complete; + ) + _CUDA_AWBARRIER_ABORT() + return false; +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool awbarrier_try_wait(uint64_t* barrier, uint64_t token, uint32_t max_sleep_nanosec) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_90, + uint32_t __wait_complete = 0; + + asm volatile ("{\n\t" + ".reg .pred p;\n\t" + "mbarrier.try_wait.shared.b64 p, [%1], %2, %3;\n\t" + "selp.b32 %0, 1, 0, p;\n\t" + "}" + : "=r"(__wait_complete) + : "r"(__nvvm_get_smem_pointer(barrier)), "l"(token), "r"(max_sleep_nanosec) + : "memory"); + + return __wait_complete; + ) + _CUDA_AWBARRIER_ABORT() + return false; +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool awbarrier_try_wait_parity(uint64_t* barrier, bool phase_parity, uint32_t max_sleep_nanosec) { + _CUDA_AWBARRIER_ASSERT(__isShared(barrier)); + + NV_IF_TARGET(NV_PROVIDES_SM_90, + uint32_t __wait_complete = 0; + + asm volatile ("{\n\t" + ".reg .pred p;\n\t" + "mbarrier.try_wait.parity.shared.b64 p, [%1], %2, %3;\n\t" + "selp.b32 %0, 1, 0, p;\n\t" + "}" + : "=r"(__wait_complete) + : "r"(__nvvm_get_smem_pointer(barrier)), "r"(static_cast(phase_parity)), "r"(max_sleep_nanosec) + : "memory"); + + return __wait_complete; + ) + _CUDA_AWBARRIER_ABORT() + return false; +} + +_CUDA_AWBARRIER_END_INTERNAL_NAMESPACE + +#endif /* !_CUDA_AWBARRIER_HELPERS_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_primitives.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_primitives.h new file mode 100644 index 0000000000000000000000000000000000000000..5562ef3f6afeb7fce4bad4cb8067b3cb1b9a690f --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_awbarrier_primitives.h @@ -0,0 +1,109 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_AWBARRIER_PRIMITIVES_H_ +#define _CUDA_AWBARRIER_PRIMITIVES_H_ + +#include "cuda_awbarrier_helpers.h" + +#if !defined(_CUDA_AWBARRIER_SM_TARGET) +# error This file requires compute capability 7.0 or greater. +#endif + +_CUDA_AWBARRIER_STATIC_QUALIFIER __host__ +uint32_t __mbarrier_maximum_count() { + return _CUDA_AWBARRIER_MAX_COUNT; +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +void __mbarrier_init(__mbarrier_t* barrier, uint32_t expected_count) { + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_init(barrier, expected_count); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +void __mbarrier_inval(__mbarrier_t* barrier) { + _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_inval(barrier); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +__mbarrier_token_t __mbarrier_arrive(__mbarrier_t* barrier) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop(barrier); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +__mbarrier_token_t __mbarrier_arrive_and_drop(__mbarrier_t* barrier) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_arrive_drop(barrier); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool __mbarrier_test_wait(__mbarrier_t* barrier, __mbarrier_token_t token) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait(barrier, token); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +uint32_t __mbarrier_token_pending_count(__mbarrier_token_t token) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_token_pending_count(token); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool __mbarrier_test_wait_parity(__mbarrier_t* barrier, bool phase_parity) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_test_wait_parity(barrier, phase_parity); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool __mbarrier_try_wait(__mbarrier_t* barrier, __mbarrier_token_t token, uint32_t max_sleep_nanosec) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_try_wait(barrier, token, max_sleep_nanosec); +} + +_CUDA_AWBARRIER_STATIC_QUALIFIER +bool __mbarrier_try_wait_parity(__mbarrier_t* barrier, bool phase_parity, uint32_t max_sleep_nanosec) { + return _CUDA_AWBARRIER_INTERNAL_NAMESPACE::awbarrier_try_wait_parity(barrier, phase_parity, max_sleep_nanosec); +} + +#endif /* !_CUDA_AWBARRIER_PRIMITIVES_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.h new file mode 100644 index 0000000000000000000000000000000000000000..765f2c9d9708c881d90392e6a01cbd8b06a1cd5c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.h @@ -0,0 +1,4795 @@ +/* +* Copyright 1993-2023 NVIDIA Corporation. All rights reserved. +* +* NOTICE TO LICENSEE: +* +* This source code and/or documentation ("Licensed Deliverables") are +* subject to NVIDIA intellectual property rights under U.S. and +* international Copyright laws. +* +* These Licensed Deliverables contained herein is PROPRIETARY and +* CONFIDENTIAL to NVIDIA and is being provided under the terms and +* conditions of a form of NVIDIA software license agreement by and +* between NVIDIA and Licensee ("License Agreement") or electronically +* accepted by Licensee. Notwithstanding any terms or conditions to +* the contrary in the License Agreement, reproduction or disclosure +* of the Licensed Deliverables to any third party without the express +* written consent of NVIDIA is prohibited. +* +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE +* SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS +* PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. +* NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED +* DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, +* NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY +* SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY +* DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, +* WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS +* ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE +* OF THESE LICENSED DELIVERABLES. +* +* U.S. Government End Users. These Licensed Deliverables are a +* "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT +* 1995), consisting of "commercial computer software" and "commercial +* computer software documentation" as such terms are used in 48 +* C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government +* only as a commercial end item. Consistent with 48 C.F.R.12.212 and +* 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all +* U.S. Government End Users acquire the Licensed Deliverables with +* only those rights set forth herein. +* +* Any use of the Licensed Deliverables in individual and commercial +* software must include, in the user documentation and internal +* comments to the code, the above Disclaimer and U.S. Government End +* Users Notice. +*/ + +/** +* \defgroup CUDA_MATH_INTRINSIC_BFLOAT16 Bfloat16 Precision Intrinsics +* This section describes nv_bfloat16 precision intrinsic functions. +* To use these functions, include the header file \p cuda_bf16.h in your program. +* All of the functions defined here are available in device code. +* Some of the functions are also available to host compilers, please +* refer to respective functions' documentation for details. +* +* NOTE: Aggressive floating-point optimizations performed by host or device +* compilers may affect numeric behavior of the functions implemented in this +* header. Specific examples are: +* - hsin(__nv_bfloat16); +* - hcos(__nv_bfloat16); +* - h2sin(__nv_bfloat162); +* - h2cos(__nv_bfloat162); +* +* The following macros are available to help users selectively enable/disable +* various definitions present in the header file: +* - \p CUDA_NO_BFLOAT16 - If defined, this macro will prevent the definition of +* additional type aliases in the global namespace, helping to avoid potential +* conflicts with symbols defined in the user program. +* - \p __CUDA_NO_BFLOAT16_CONVERSIONS__ - If defined, this macro will prevent +* the use of the C++ type conversions (converting constructors and conversion +* operators) that are common for built-in floating-point types, but may be +* undesirable for \p __nv_bfloat16 which is essentially a user-defined type. +* - \p __CUDA_NO_BFLOAT16_OPERATORS__ and \p __CUDA_NO_BFLOAT162_OPERATORS__ - +* If defined, these macros will prevent the inadvertent use of usual arithmetic +* and comparison operators. This enforces the storage-only type semantics and +* prevents C++ style computations on \p __nv_bfloat16 and \p __nv_bfloat162 types. +*/ + +/** +* \defgroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS Bfloat16 Arithmetic Constants +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these constants, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT16_ARITHMETIC Bfloat16 Arithmetic Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT162_ARITHMETIC Bfloat162 Arithmetic Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT16_COMPARISON Bfloat16 Comparison Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT162_COMPARISON Bfloat162 Comparison Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT16_MISC Bfloat16 Precision Conversion and Data Movement +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT16_FUNCTIONS Bfloat16 Math Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__BFLOAT162_FUNCTIONS Bfloat162 Math Functions +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 +* To use these functions, include the header file \p cuda_bf16.h in your program. +*/ + +#ifndef __CUDA_BF16_H__ +#define __CUDA_BF16_H__ + +/* bring in __half data type and operations, for use in converting constructors */ +#include "cuda_fp16.h" +/* bring in float2, double4, etc vector types */ +#include "vector_types.h" +/* bring in operations on vector types like: make_float2 */ +#include "vector_functions.h" + +#define ___CUDA_BF16_STRINGIFY_INNERMOST(x) #x +#define __CUDA_BF16_STRINGIFY(x) ___CUDA_BF16_STRINGIFY_INNERMOST(x) + +#if defined(__cplusplus) + +/* Set up function decorations */ +#if (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) +#define __CUDA_BF16_DECL__ __device__ +#define __CUDA_HOSTDEVICE_BF16_DECL__ __device__ +#define __CUDA_HOSTDEVICE__ __device__ +#elif defined(__CUDACC__) || defined(_NVHPC_CUDA) +#define __CUDA_BF16_DECL__ static __device__ __inline__ +#define __CUDA_HOSTDEVICE_BF16_DECL__ static __host__ __device__ __inline__ +#define __CUDA_HOSTDEVICE__ __host__ __device__ +#else /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +#if defined(__GNUC__) +#define __CUDA_HOSTDEVICE_BF16_DECL__ static __attribute__ ((unused)) +#else +#define __CUDA_HOSTDEVICE_BF16_DECL__ static +#endif /* defined(__GNUC__) */ +#define __CUDA_HOSTDEVICE__ +#endif /* (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3))))) */ + +#define __CUDA_BF16_TYPES_EXIST__ + +/* Forward-declaration of structures defined in "cuda_bf16.hpp" */ +struct __nv_bfloat16; +struct __nv_bfloat162; + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts double number to nv_bfloat16 precision in round-to-nearest-even mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts double number \p a to nv_bfloat16 precision in round-to-nearest-even mode. +* \param[in] a - double. Is only being read. +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __double2bfloat16(const double a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts float number to nv_bfloat16 precision in round-to-nearest-even mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts float number \p a to nv_bfloat16 precision in round-to-nearest-even mode. +* \param[in] a - float. Is only being read. +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts float number to nv_bfloat16 precision in round-to-nearest-even mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts float number \p a to nv_bfloat16 precision in round-to-nearest-even mode. +* \param[in] a - float. Is only being read. +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rn(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts float number to nv_bfloat16 precision in round-towards-zero mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts float number \p a to nv_bfloat16 precision in round-towards-zero mode. +* \param[in] a - float. Is only being read. +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rz(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts float number to nv_bfloat16 precision in round-down mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts float number \p a to nv_bfloat16 precision in round-down mode. +* \param[in] a - float. Is only being read. +* +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rd(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts float number to nv_bfloat16 precision in round-up mode +* and returns \p nv_bfloat16 with converted value. +* +* \details Converts float number \p a to nv_bfloat16 precision in round-up mode. +* \param[in] a - float. Is only being read. +* +* \returns nv_bfloat16 +* - \p a converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_ru(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts \p nv_bfloat16 number to float. +* +* \details Converts nv_bfloat16 number \p a to float. +* \param[in] a - float. Is only being read. +* +* \returns float +* - \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ float __bfloat162float(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts input to nv_bfloat16 precision in round-to-nearest-even mode and +* populates both halves of \p nv_bfloat162 with converted value. +* +* \details Converts input \p a to nv_bfloat16 precision in round-to-nearest-even mode and +* populates both halves of \p nv_bfloat162 with converted value. +* \param[in] a - float. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 value with both halves equal to the converted nv_bfloat16 +* precision number. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __float2bfloat162_rn(const float a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts both input floats to nv_bfloat16 precision in round-to-nearest-even +* mode and returns \p nv_bfloat162 with converted values. +* +* \details Converts both input floats to nv_bfloat16 precision in round-to-nearest-even mode +* and combines the results into one \p nv_bfloat162 number. Low 16 bits of the return +* value correspond to the input \p a, high 16 bits correspond to the input \p +* b. +* \param[in] a - float. Is only being read. +* \param[in] b - float. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 value with corresponding halves equal to the +* converted input floats. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __floats2bfloat162_rn(const float a, const float b); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts low 16 bits of \p nv_bfloat162 to float and returns the result +* +* \details Converts low 16 bits of \p nv_bfloat162 input \p a to 32-bit floating-point number +* and returns the result. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns float +* - The low 16 bits of \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ float __low2float(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts high 16 bits of \p nv_bfloat162 to float and returns the result +* +* \details Converts high 16 bits of \p nv_bfloat162 input \p a to 32-bit floating-point number +* and returns the result. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns float +* - The high 16 bits of \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ float __high2float(const __nv_bfloat162 a); + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts both components of float2 number to nv_bfloat16 precision in +* round-to-nearest-even mode and returns \p nv_bfloat162 with converted values. +* +* \details Converts both components of float2 to nv_bfloat16 precision in round-to-nearest-even +* mode and combines the results into one \p nv_bfloat162 number. Low 16 bits of the +* return value correspond to \p a.x and high 16 bits of the return value +* correspond to \p a.y. +* \param[in] a - float2. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 which has corresponding halves equal to the +* converted float2 components. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __float22bfloat162_rn(const float2 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Converts both halves of \p nv_bfloat162 to float2 and returns the result. +* +* \details Converts both halves of \p nv_bfloat162 input \p a to float2 and returns the +* result. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns float2 +* - \p a converted to float2. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ float2 __bfloat1622float2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed char in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed +* char in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns signed char +* - \p h converted to a signed char. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ signed char __bfloat162char_rz(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned char in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned +* char in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned char +* - \p h converted to an unsigned char. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned char __bfloat162uchar_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed integer in round-to-nearest-even mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed integer in +* round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ int __bfloat162int_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed integer in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed integer in +* round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ int __bfloat162int_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed integer in +* round-down mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ int __bfloat162int_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed integer in +* round-up mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ int __bfloat162int_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed integer to a nv_bfloat16 in round-to-nearest-even mode. +* +* \details Convert the signed integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rn(const int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed integer to a nv_bfloat16 in round-towards-zero mode. +* +* \details Convert the signed integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rz(const int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the signed integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rd(const int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the signed integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_ru(const int i); + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed short integer in round-to-nearest-even +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed short +* integer in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ short int __bfloat162short_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed short integer in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed short +* integer in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ short int __bfloat162short_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed short integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed short +* integer in round-down mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ short int __bfloat162short_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed short integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed short +* integer in round-up mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ short int __bfloat162short_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed short integer to a nv_bfloat16 in round-to-nearest-even +* mode. +* +* \details Convert the signed short integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rn(const short int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed short integer to a nv_bfloat16 in round-towards-zero mode. +* +* \details Convert the signed short integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rz(const short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed short integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the signed short integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rd(const short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed short integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the signed short integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_ru(const short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned integer in round-to-nearest-even mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned integer +* in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned integer in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned integer +* in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned int __bfloat162uint_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned integer +* in round-down mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned integer +* in round-up mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned integer to a nv_bfloat16 in round-to-nearest-even mode. +* +* \details Convert the unsigned integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rn(const unsigned int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned integer to a nv_bfloat16 in round-towards-zero mode. +* +* \details Convert the unsigned integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rz(const unsigned int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the unsigned integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rd(const unsigned int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the unsigned integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_ru(const unsigned int i); + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned short integer in round-to-nearest-even +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned short +* integer in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned short integer in round-towards-zero +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned short +* integer in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned short int __bfloat162ushort_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned short integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned short +* integer in round-down mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +*/ +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned short integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned short +* integer in round-up mode. NaN inputs are converted to 0. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +*/ +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned short integer to a nv_bfloat16 in round-to-nearest-even +* mode. +* +* \details Convert the unsigned short integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rn(const unsigned short int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned short integer to a nv_bfloat16 in round-towards-zero +* mode. +* +* \details Convert the unsigned short integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rz(const unsigned short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned short integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the unsigned short integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rd(const unsigned short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned short integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the unsigned short integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_ru(const unsigned short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned 64-bit integer in round-to-nearest-even +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned 64-bit +* integer in round-to-nearest-even mode. NaN inputs return 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned 64-bit integer in round-towards-zero +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned 64-bit +* integer in round-towards-zero mode. NaN inputs return 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned long long int __bfloat162ull_rz(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Vector function, combines two \p nv_bfloat16 numbers into one \p nv_bfloat162 number. +* +* \details Combines two input \p nv_bfloat16 number \p x and \p y into one \p nv_bfloat162 number. +* Input \p x is stored in low 16 bits of the return value, input \p y is stored +* in high 16 bits of the return value. +* \param[in] x - nv_bfloat16. Is only being read. +* \param[in] y - nv_bfloat16. Is only being read. +* +* \returns __nv_bfloat162 +* - The \p __nv_bfloat162 vector with one half equal to \p x and the other to \p y. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 make_bfloat162(const __nv_bfloat16 x, const __nv_bfloat16 y); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned 64-bit integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned 64-bit +* integer in round-down mode. NaN inputs return 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to an unsigned 64-bit integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to an unsigned 64-bit +* integer in round-up mode. NaN inputs return 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned 64-bit integer to a nv_bfloat16 in round-to-nearest-even +* mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rn(const unsigned long long int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned 64-bit integer to a nv_bfloat16 in round-towards-zero +* mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rz(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned 64-bit integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rd(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert an unsigned 64-bit integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_ru(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed 64-bit integer in round-to-nearest-even +* mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed 64-bit +* integer in round-to-nearest-even mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ long long int __bfloat162ll_rn(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed 64-bit integer in round-towards-zero mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed 64-bit +* integer in round-towards-zero mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ long long int __bfloat162ll_rz(const __nv_bfloat16 h); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed 64-bit integer in round-down mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed 64-bit +* integer in round-down mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ long long int __bfloat162ll_rd(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a nv_bfloat16 to a signed 64-bit integer in round-up mode. +* +* \details Convert the nv_bfloat16 floating-point value \p h to a signed 64-bit +* integer in round-up mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ long long int __bfloat162ll_ru(const __nv_bfloat16 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed 64-bit integer to a nv_bfloat16 in round-to-nearest-even +* mode. +* +* \details Convert the signed 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-to-nearest-even mode. +* \param[in] i - long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rn(const long long int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed 64-bit integer to a nv_bfloat16 in round-towards-zero mode. +* +* \details Convert the signed 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-towards-zero mode. +* \param[in] i - long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rz(const long long int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed 64-bit integer to a nv_bfloat16 in round-down mode. +* +* \details Convert the signed 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-down mode. +* \param[in] i - long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rd(const long long int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Convert a signed 64-bit integer to a nv_bfloat16 in round-up mode. +* +* \details Convert the signed 64-bit integer value \p i to a nv_bfloat16 floating-point +* value in round-up mode. +* \param[in] i - long long int. Is only being read. +* +* \returns nv_bfloat16 +* - \p i converted to nv_bfloat16. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_ru(const long long int i); + +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Truncate input argument to the integral part. +* +* \details Round \p h to the nearest integer value that does not exceed \p h in +* magnitude. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The truncated integer value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 htrunc(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculate ceiling of the input argument. +* +* \details Compute the smallest integer value not less than \p h. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The smallest integer value not less than \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hceil(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculate the largest integer less than or equal to \p h. +* +* \details Calculate the largest integer value which is less than or equal to \p h. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The largest integer value which is less than or equal to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hfloor(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Round input to nearest integer value in nv_bfloat16 floating-point +* number. +* +* \details Round \p h to the nearest integer value in nv_bfloat16 floating-point +* format, with bfloat16way cases rounded to the nearest even integer value. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The nearest integer to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hrint(const __nv_bfloat16 h); + +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Truncate \p nv_bfloat162 vector input argument to the integral part. +* +* \details Round each component of vector \p h to the nearest integer value that does +* not exceed \p h in magnitude. +* \param[in] h - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The truncated \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2trunc(const __nv_bfloat162 h); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculate \p nv_bfloat162 vector ceiling of the input argument. +* +* \details For each component of vector \p h compute the smallest integer value not less +* than \p h. +* \param[in] h - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector of smallest integers not less than \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2ceil(const __nv_bfloat162 h); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculate the largest integer less than or equal to \p h. +* +* \details For each component of vector \p h calculate the largest integer value which +* is less than or equal to \p h. +* \param[in] h - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector of largest integers which is less than or equal to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2floor(const __nv_bfloat162 h); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Round input to nearest integer value in nv_bfloat16 floating-point +* number. +* +* \details Round each component of \p nv_bfloat162 vector \p h to the nearest integer value in +* nv_bfloat16 floating-point format, with bfloat16way cases rounded to the +* nearest even integer value. +* \param[in] h - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector of rounded integer values. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2rint(const __nv_bfloat162 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Returns \p nv_bfloat162 with both halves equal to the input value. +* +* \details Returns \p nv_bfloat162 number with both halves equal to the input \p a \p nv_bfloat16 +* number. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat162 +* - The vector which has both its halves equal to the input \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __bfloat162bfloat162(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Swaps both halves of the \p nv_bfloat162 input. +* +* \details Swaps both halves of the \p nv_bfloat162 input and returns a new \p nv_bfloat162 number +* with swapped halves. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - \p a with its halves being swapped. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __lowhigh2highlow(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Extracts low 16 bits from each of the two \p nv_bfloat162 inputs and combines +* into one \p nv_bfloat162 number. +* +* \details Extracts low 16 bits from each of the two \p nv_bfloat162 inputs and combines into +* one \p nv_bfloat162 number. Low 16 bits from input \p a is stored in low 16 bits of +* the return value, low 16 bits from input \p b is stored in high 16 bits of +* the return value. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The low 16 bits of \p a and of \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __lows2bfloat162(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Extracts high 16 bits from each of the two \p nv_bfloat162 inputs and +* combines into one \p nv_bfloat162 number. +* +* \details Extracts high 16 bits from each of the two \p nv_bfloat162 inputs and combines into +* one \p nv_bfloat162 number. High 16 bits from input \p a is stored in low 16 bits of +* the return value, high 16 bits from input \p b is stored in high 16 bits of +* the return value. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The high 16 bits of \p a and of \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __highs2bfloat162(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Returns high 16 bits of \p nv_bfloat162 input. +* +* \details Returns high 16 bits of \p nv_bfloat162 input \p a. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat16 +* - The high 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __high2bfloat16(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Returns low 16 bits of \p nv_bfloat162 input. +* +* \details Returns low 16 bits of \p nv_bfloat162 input \p a. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat16 +* - Returns \p nv_bfloat16 which contains low 16 bits of the input \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __low2bfloat16(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Checks if the input \p nv_bfloat16 number is infinite. +* +* \details Checks if the input \p nv_bfloat16 number \p a is infinite. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns int +* - -1 iff \p a is equal to negative infinity, +* - 1 iff \p a is equal to positive infinity, +* - 0 otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ int __hisinf(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Combines two \p nv_bfloat16 numbers into one \p nv_bfloat162 number. +* +* \details Combines two input \p nv_bfloat16 number \p a and \p b into one \p nv_bfloat162 number. +* Input \p a is stored in low 16 bits of the return value, input \p b is stored +* in high 16 bits of the return value. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat162 +* - The nv_bfloat162 with one nv_bfloat16 equal to \p a and the other to \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __halves2bfloat162(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Extracts low 16 bits from \p nv_bfloat162 input. +* +* \details Extracts low 16 bits from \p nv_bfloat162 input \p a and returns a new \p nv_bfloat162 +* number which has both halves equal to the extracted bits. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The nv_bfloat162 with both halves equal to the low 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __low2bfloat162(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Extracts high 16 bits from \p nv_bfloat162 input. +* +* \details Extracts high 16 bits from \p nv_bfloat162 input \p a and returns a new \p nv_bfloat162 +* number which has both halves equal to the extracted bits. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The nv_bfloat162 with both halves equal to the high 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __high2bfloat162(const __nv_bfloat162 a); + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Reinterprets bits in a \p nv_bfloat16 as a signed short integer. +* +* \details Reinterprets the bits in the nv_bfloat16 floating-point number \p h +* as a signed short integer. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns short int +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ short int __bfloat16_as_short(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Reinterprets bits in a \p nv_bfloat16 as an unsigned short integer. +* +* \details Reinterprets the bits in the nv_bfloat16 floating-point \p h +* as an unsigned short number. +* \param[in] h - nv_bfloat16. Is only being read. +* +* \returns unsigned short int +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned short int __bfloat16_as_ushort(const __nv_bfloat16 h); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Reinterprets bits in a signed short integer as a \p nv_bfloat16. +* +* \details Reinterprets the bits in the signed short integer \p i as a +* nv_bfloat16 floating-point number. +* \param[in] i - short int. Is only being read. +* +* \returns nv_bfloat16 +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __short_as_bfloat16(const short int i); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Reinterprets bits in an unsigned short integer as a \p nv_bfloat16. +* +* \details Reinterprets the bits in the unsigned short integer \p i as a +* nv_bfloat16 floating-point number. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns nv_bfloat16 +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ushort_as_bfloat16(const unsigned short int i); + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300))) || defined(_NVHPC_CUDA) + +#if !defined warpSize && !defined __local_warpSize +#define warpSize 32 +#define __local_warpSize +#endif + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Direct copy from indexed thread. +* +* \details Returns the value of var held by the thread whose ID is given by delta. +* If width is less than warpSize then each subsection of the warp behaves as a separate +* entity with a starting logical thread ID of 0. If delta is outside the range [0:width-1], +* the value returned corresponds to the value of var held by the delta modulo width (i.e. +* within the same subsection). width must have a value which is a power of 2; +* results are undefined if width is not a power of 2, or is a number greater than +* warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat162. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as nv_bfloat162. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_sync(const unsigned mask, const __nv_bfloat162 var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with lower ID relative to the caller. +* +* \details Calculates a source thread ID by subtracting delta from the caller's lane ID. +* The value of var held by the resulting lane ID is returned: in effect, var is shifted up +* the warp by delta threads. If width is less than warpSize then each subsection of the warp +* behaves as a separate entity with a starting logical thread ID of 0. The source thread index +* will not wrap around the value of width, so effectively the lower delta threads will be unchanged. +* width must have a value which is a power of 2; results are undefined if width is not a power of 2, +* or is a number greater than warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat162. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as nv_bfloat162. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_up_sync(const unsigned mask, const __nv_bfloat162 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with higher ID relative to the caller. +* +* \details Calculates a source thread ID by adding delta to the caller's thread ID. +* The value of var held by the resulting thread ID is returned: this has the effect +* of shifting var down the warp by delta threads. If width is less than warpSize then +* each subsection of the warp behaves as a separate entity with a starting logical +* thread ID of 0. As for __shfl_up_sync(), the ID number of the source thread +* will not wrap around the value of width and so the upper delta threads +* will remain unchanged. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat162. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as nv_bfloat162. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_down_sync(const unsigned mask, const __nv_bfloat162 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread based on bitwise XOR of own thread ID. +* +* \details Calculates a source thread ID by performing a bitwise XOR of the caller's thread ID with mask: +* the value of var held by the resulting thread ID is returned. If width is less than warpSize then each +* group of width consecutive threads are able to access elements from earlier groups of threads, +* however if they attempt to access elements from later groups of threads their own value of var +* will be returned. This mode implements a butterfly addressing pattern such as is used in tree +* reduction and broadcast. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat162. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as nv_bfloat162. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_xor_sync(const unsigned mask, const __nv_bfloat162 var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Direct copy from indexed thread. +* +* \details Returns the value of var held by the thread whose ID is given by delta. +* If width is less than warpSize then each subsection of the warp behaves as a separate +* entity with a starting logical thread ID of 0. If delta is outside the range [0:width-1], +* the value returned corresponds to the value of var held by the delta modulo width (i.e. +* within the same subsection). width must have a value which is a power of 2; +* results are undefined if width is not a power of 2, or is a number greater than +* warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat16. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as nv_bfloat16. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_sync(const unsigned mask, const __nv_bfloat16 var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with lower ID relative to the caller. +* \details Calculates a source thread ID by subtracting delta from the caller's lane ID. +* The value of var held by the resulting lane ID is returned: in effect, var is shifted up +* the warp by delta threads. If width is less than warpSize then each subsection of the warp +* behaves as a separate entity with a starting logical thread ID of 0. The source thread index +* will not wrap around the value of width, so effectively the lower delta threads will be unchanged. +* width must have a value which is a power of 2; results are undefined if width is not a power of 2, +* or is a number greater than warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat16. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as nv_bfloat16. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_up_sync(const unsigned mask, const __nv_bfloat16 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with higher ID relative to the caller. +* +* \details Calculates a source thread ID by adding delta to the caller's thread ID. +* The value of var held by the resulting thread ID is returned: this has the effect +* of shifting var down the warp by delta threads. If width is less than warpSize then +* each subsection of the warp behaves as a separate entity with a starting logical +* thread ID of 0. As for __shfl_up_sync(), the ID number of the source thread +* will not wrap around the value of width and so the upper delta threads +* will remain unchanged. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat16. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as nv_bfloat16. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_down_sync(const unsigned mask, const __nv_bfloat16 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread based on bitwise XOR of own thread ID. +* +* \details Calculates a source thread ID by performing a bitwise XOR of the caller's thread ID with mask: +* the value of var held by the resulting thread ID is returned. If width is less than warpSize then each +* group of width consecutive threads are able to access elements from earlier groups of threads, +* however if they attempt to access elements from later groups of threads their own value of var +* will be returned. This mode implements a butterfly addressing pattern such as is used in tree +* reduction and broadcast. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - nv_bfloat16. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as nv_bfloat16. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_xor_sync(const unsigned mask, const __nv_bfloat16 var, const int delta, const int width = warpSize); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300))) || defined(_NVHPC_CUDA) */ + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320))) || defined(_NVHPC_CUDA) +#if defined(__local_warpSize) +#undef warpSize +#undef __local_warpSize +#endif + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.nc` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldg(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.nc` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldg(const __nv_bfloat16 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cg` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcg(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cg` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcg(const __nv_bfloat16 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.ca` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldca(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.ca` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldca(const __nv_bfloat16 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cs` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcs(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cs` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcs(const __nv_bfloat16 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.lu` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldlu(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.lu` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldlu(const __nv_bfloat16 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cv` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcv(const __nv_bfloat162 *const ptr); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `ld.global.cv` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcv(const __nv_bfloat16 *const ptr); + +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.wb` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stwb(__nv_bfloat162 *const ptr, const __nv_bfloat162 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.wb` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stwb(__nv_bfloat16 *const ptr, const __nv_bfloat16 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.cg` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stcg(__nv_bfloat162 *const ptr, const __nv_bfloat162 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.cg` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stcg(__nv_bfloat16 *const ptr, const __nv_bfloat16 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.cs` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stcs(__nv_bfloat162 *const ptr, const __nv_bfloat162 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.cs` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stcs(__nv_bfloat16 *const ptr, const __nv_bfloat16 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.wt` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stwt(__nv_bfloat162 *const ptr, const __nv_bfloat162 value); +/** +* \ingroup CUDA_MATH__BFLOAT16_MISC +* \brief Generates a `st.global.wt` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_BF16_DECL__ void __stwt(__nv_bfloat16 *const ptr, const __nv_bfloat16 value); + +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320))) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs nv_bfloat162 vector if-equal comparison. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __heq2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector not-equal comparison. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hne2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-equal comparison. +* +* \details Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 result of less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hle2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-equal comparison. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hge2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-than comparison. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The nv_bfloat162 vector result of less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hlt2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-than comparison. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgt2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered if-equal comparison. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of unordered if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hequ2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered not-equal comparison. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of unordered not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hneu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-equal comparison. +* +* Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of unordered less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hleu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-equal comparison. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 vector result of unordered greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgeu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-than comparison. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The vector result of unordered less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hltu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-than comparison. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p nv_bfloat16 results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The \p nv_bfloat162 vector result of unordered greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgtu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs nv_bfloat162 vector if-equal comparison. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __heq2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector not-equal comparison. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hne2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-equal comparison. +* +* \details Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hle2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-equal comparison. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hge2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-than comparison. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hlt2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-than comparison. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgt2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered if-equal comparison. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hequ2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered not-equal comparison. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hneu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-equal comparison. +* +* Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hleu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-equal comparison. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgeu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-than comparison. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hltu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-than comparison. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgtu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Determine whether \p nv_bfloat162 argument is a NaN. +* +* \details Determine whether each nv_bfloat16 of input \p nv_bfloat162 number \p a is a NaN. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The nv_bfloat162 with the corresponding \p nv_bfloat16 results set to +* 1.0 for NaN, 0.0 otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hisnan2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector addition in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat162 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-95 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The sum of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p nv_bfloat162 input vector \p b from input vector \p a in +* round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-104 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The subtraction of vector \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector multiplication in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat162 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-102 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise multiplying the vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector addition in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat162 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-95 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The sum of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p nv_bfloat162 input vector \p b from input vector \p a in +* round-to-nearest-even mode. Prevents floating-point contractions of mul+sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-104 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The subtraction of vector \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector multiplication in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat162 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode. Prevents floating-point contractions of mul+add +* or sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-102 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise multiplying the vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector division in round-to-nearest-even mode. +* +* \details Divides \p nv_bfloat162 input vector \p a by input vector \p b in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-103 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise division of \p a with \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __h2div(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Calculates the absolute value of both halves of the input \p nv_bfloat162 number and +* returns the result. +* +* \details Calculates the absolute value of both halves of the input \p nv_bfloat162 number and +* returns the result. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns bfloat2 +* - Returns \p a with the absolute value of both halves. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __habs2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector addition in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat162 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode, and clamps the results to range [0.0, 1.0]. NaN results are flushed to +* +0.0. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The sum of \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector subtraction in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Subtracts \p nv_bfloat162 input vector \p b from input vector \p a in +* round-to-nearest-even mode, and clamps the results to range [0.0, 1.0]. NaN +* results are flushed to +0.0. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The subtraction of vector \p b from \p a, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector multiplication in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat162 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode, and clamps the results to range [0.0, 1.0]. NaN +* results are flushed to +0.0. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise multiplication of vectors \p a and \p b, +* with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b); +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector fused multiply-add in round-to-nearest-even +* mode. +* +* \details Performs \p nv_bfloat162 vector multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat162 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-105 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* \param[in] c - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector fused multiply-add in round-to-nearest-even +* mode, with saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat162 vector multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat162 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode, and clamps the +* results to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* \param[in] c - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c, +* with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Negates both halves of the input \p nv_bfloat162 number and returns the +* result. +* +* \details Negates both halves of the input \p nv_bfloat162 number \p a and returns the result. +* \internal +* \req DEEPLEARN-SRM_REQ-101 +* \endinternal +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - Returns \p a with both halves negated. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hneg2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Calculates the absolute value of input \p nv_bfloat16 number and returns the result. +* +* \details Calculates the absolute value of input \p nv_bfloat16 number and returns the result. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The absolute value of a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __habs(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 addition in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat16 addition of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-94 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The sum of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p nv_bfloat16 input \p b from input \p a in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-97 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of subtracting \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 multiplication in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat16 multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-99 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of multiplying \p a and \p b. +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 addition in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat16 addition of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-94 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The sum of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd_rn(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p nv_bfloat16 input \p b from input \p a in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-97 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of subtracting \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub_rn(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 multiplication in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat16 multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add or sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-99 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of multiplying \p a and \p b. +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul_rn(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 division in round-to-nearest-even mode. +* +* \details Divides \p nv_bfloat16 input \p a by input \p b in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-98 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of dividing \p a by \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hdiv(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 addition in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat16 add of inputs \p a and \p b, in round-to-nearest-even mode, +* and clamps the result to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The sum of \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd_sat(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 subtraction in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Subtracts \p nv_bfloat16 input \p b from input \p a in round-to-nearest-even +* mode, +* and clamps the result to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of subtraction of \p b from \p a, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub_sat(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 multiplication in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat16 multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode, and clamps the result to range [0.0, 1.0]. NaN results are flushed to +* +0.0. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of multiplying \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul_sat(const __nv_bfloat16 a, const __nv_bfloat16 b); +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 fused multiply-add in round-to-nearest-even mode. +* +* \details Performs \p nv_bfloat16 multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat16 add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-96 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* \param[in] c - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c); +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 fused multiply-add in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Performs \p nv_bfloat16 multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat16 add of the result with \p c, +* rounding the result once in round-to-nearest-even mode, and clamps the result +* to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* \param[in] c - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma_sat(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Negates input \p nv_bfloat16 number and returns the result. +* +* \details Negates input \p nv_bfloat16 number and returns the result. +* \internal +* \req DEEPLEARN-SRM_REQ-100 +* \endinternal +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - minus a +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hneg(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector if-equal comparison and returns boolean true +* iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 if-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of if-equal comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbeq2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector not-equal comparison and returns boolean +* true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 not-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of not-equal comparison +* of vectors \p a and \p b are true, +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbne2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-equal comparison and returns boolean +* true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 less-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of less-equal comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hble2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-equal comparison and returns boolean +* true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 greater-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of greater-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbge2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector less-than comparison and returns boolean +* true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 less-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of less-than comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hblt2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector greater-than comparison and returns boolean +* true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 greater-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of greater-than +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgt2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered if-equal comparison and returns +* boolean true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector if-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 if-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered if-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbequ2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered not-equal comparison and returns +* boolean true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector not-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 not-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered not-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbneu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-equal comparison and returns +* boolean true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector less-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 less-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered less-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbleu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-equal comparison and +* returns boolean true iff both \p nv_bfloat16 results are true, boolean false +* otherwise. +* +* \details Performs \p nv_bfloat162 vector greater-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 greater-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered +* greater-equal comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgeu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered less-than comparison and returns +* boolean true iff both \p nv_bfloat16 results are true, boolean false otherwise. +* +* \details Performs \p nv_bfloat162 vector less-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 less-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered less-than comparison of +* vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbltu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Performs \p nv_bfloat162 vector unordered greater-than comparison and +* returns boolean true iff both \p nv_bfloat16 results are true, boolean false +* otherwise. +* +* \details Performs \p nv_bfloat162 vector greater-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p nv_bfloat16 greater-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns bool +* - true if both \p nv_bfloat16 results of unordered +* greater-than comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgtu2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 if-equal comparison. +* +* \details Performs \p nv_bfloat16 if-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of if-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __heq(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 not-equal comparison. +* +* \details Performs \p nv_bfloat16 not-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of not-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hne(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 less-equal comparison. +* +* \details Performs \p nv_bfloat16 less-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of less-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hle(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 greater-equal comparison. +* +* \details Performs \p nv_bfloat16 greater-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of greater-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hge(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 less-than comparison. +* +* \details Performs \p nv_bfloat16 less-than comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of less-than comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hlt(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 greater-than comparison. +* +* \details Performs \p nv_bfloat16 greater-than comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of greater-than comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgt(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered if-equal comparison. +* +* \details Performs \p nv_bfloat16 if-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered if-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hequ(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered not-equal comparison. +* +* \details Performs \p nv_bfloat16 not-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered not-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hneu(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered less-equal comparison. +* +* \details Performs \p nv_bfloat16 less-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered less-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hleu(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered greater-equal comparison. +* +* \details Performs \p nv_bfloat16 greater-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered greater-equal comparison of \p a +* and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgeu(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered less-than comparison. +* +* \details Performs \p nv_bfloat16 less-than comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered less-than comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hltu(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Performs \p nv_bfloat16 unordered greater-than comparison. +* +* \details Performs \p nv_bfloat16 greater-than comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns bool +* - The boolean result of unordered greater-than comparison of \p a +* and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgtu(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Determine whether \p nv_bfloat16 argument is a NaN. +* +* \details Determine whether \p nv_bfloat16 value \p a is a NaN. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns bool +* - true iff argument is NaN. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hisnan(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Calculates \p nv_bfloat16 maximum of two input values. +* +* \details Calculates \p nv_bfloat16 max(\p a, \p b) +* defined as (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmax(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Calculates \p nv_bfloat16 minimum of two input values. +* +* \details Calculates \p nv_bfloat16 min(\p a, \p b) +* defined as (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmin(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Calculates \p nv_bfloat16 maximum of two input values, NaNs pass through. +* +* \details Calculates \p nv_bfloat16 max(\p a, \p b) +* defined as (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmax_nan(const __nv_bfloat16 a, const __nv_bfloat16 b); +/** +* \ingroup CUDA_MATH__BFLOAT16_COMPARISON +* \brief Calculates \p nv_bfloat16 minimum of two input values, NaNs pass through. +* +* \details Calculates \p nv_bfloat16 min(\p a, \p b) +* defined as (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmin_nan(const __nv_bfloat16 a, const __nv_bfloat16 b); +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Performs \p nv_bfloat16 fused multiply-add in round-to-nearest-even mode with relu saturation. +* +* \details Performs \p nv_bfloat16 multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat16 add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* Then negative result is clamped to 0. +* NaN result is converted to canonical NaN. +* \param[in] a - nv_bfloat16. Is only being read. +* \param[in] b - nv_bfloat16. Is only being read. +* \param[in] c - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c with relu saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma_relu(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Calculates \p nv_bfloat162 vector maximum of two inputs. +* +* \details Calculates \p nv_bfloat162 vector max(\p a, \p b). +* Elementwise \p nv_bfloat16 operation is defined as +* (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise maximum of vectors \p a and \p b +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmax2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Calculates \p nv_bfloat162 vector minimum of two inputs. +* +* \details Calculates \p nv_bfloat162 vector min(\p a, \p b). +* Elementwise \p nv_bfloat16 operation is defined as +* (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise minimum of vectors \p a and \p b +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmin2(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Calculates \p nv_bfloat162 vector maximum of two inputs, NaNs pass through. +* +* \details Calculates \p nv_bfloat162 vector max(\p a, \p b). +* Elementwise \p nv_bfloat16 operation is defined as +* (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise maximum of vectors \p a and \p b, with NaNs pass through +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmax2_nan(const __nv_bfloat162 a, const __nv_bfloat162 b); +/** +* \ingroup CUDA_MATH__BFLOAT162_COMPARISON +* \brief Calculates \p nv_bfloat162 vector minimum of two inputs, NaNs pass through. +* +* \details Calculates \p nv_bfloat162 vector min(\p a, \p b). +* Elementwise \p nv_bfloat16 operation is defined as +* (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise minimum of vectors \p a and \p b, with NaNs pass through +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmin2_nan(const __nv_bfloat162 a, const __nv_bfloat162 b); +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs \p nv_bfloat162 vector fused multiply-add in round-to-nearest-even +* mode with relu saturation. +* +* \details Performs \p nv_bfloat162 vector multiply on inputs \p a and \p b, +* then performs a \p nv_bfloat162 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* Then negative result is clamped to 0. +* NaN result is converted to canonical NaN. +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* \param[in] c - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c with relu saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2_relu(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c); +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Performs fast complex multiply-accumulate +* +* \details Interprets vector \p nv_bfloat162 input pairs \p a, \p b, and \p c as +* complex numbers in \p nv_bfloat16 precision and performs +* complex multiply-accumulate operation: a*b + c +* \param[in] a - nv_bfloat162. Is only being read. +* \param[in] b - nv_bfloat162. Is only being read. +* \param[in] c - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The result of complex multiply-accumulate operation on complex numbers \p a, \p b, and \p c +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __hcmadd(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 square root in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 square root of input \p a in round-to-nearest-even mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The square root of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hsqrt(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 reciprocal square root in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat16 reciprocal square root of input \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The reciprocal square root of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hrsqrt(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 reciprocal in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 reciprocal of input \p a in round-to-nearest-even mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The reciprocal of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hrcp(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 natural logarithm in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 natural logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The natural logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hlog(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 binary logarithm in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 binary logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The binary logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hlog2(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 decimal logarithm in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 decimal logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The decimal logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hlog10(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 natural exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat16 natural exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The natural exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hexp(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 binary exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat16 binary exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The binary exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hexp2(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 decimal exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat16 decimal exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The decimal exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hexp10(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 cosine in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 cosine of input \p a in round-to-nearest-even mode. +* +* NOTE: this function's implementation calls cosf(float) function and is exposed +* to compiler optimizations. Specifically, \p --use_fast_math flag changes cosf(float) +* into an intrinsic __cosf(float), which has less accurate numeric behavior. +* +* \param[in] a - nv_bfloat16. Is only being read. +* \returns nv_bfloat16 +* - The cosine of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hcos(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT16_FUNCTIONS +* \brief Calculates \p nv_bfloat16 sine in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat16 sine of input \p a in round-to-nearest-even mode. +* +* NOTE: this function's implementation calls sinf(float) function and is exposed +* to compiler optimizations. Specifically, \p --use_fast_math flag changes sinf(float) +* into an intrinsic __sinf(float), which has less accurate numeric behavior. +* +* \param[in] a - nv_bfloat16. Is only being read. +* +* \returns nv_bfloat16 +* - The sine of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 hsin(const __nv_bfloat16 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector square root in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 square root of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise square root on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2sqrt(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector reciprocal square root in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat162 reciprocal square root of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise reciprocal square root on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2rsqrt(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector reciprocal in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 reciprocal of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise reciprocal on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2rcp(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector natural logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat162 natural logarithm of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise natural logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2log(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector binary logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat162 binary logarithm of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise binary logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2log2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector decimal logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat162 decimal logarithm of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise decimal logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2log10(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p nv_bfloat162 exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector binary exponential function in +* round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 binary exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise binary exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp2(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector decimal exponential function in +* round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 decimal exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - nv_bfloat162. Is only being read. +* +* \returns nv_bfloat162 +* - The elementwise decimal exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp10(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector cosine in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 cosine of input vector \p a in round-to-nearest-even +* mode. +* +* NOTE: this function's implementation calls cosf(float) function and is exposed +* to compiler optimizations. Specifically, \p --use_fast_math flag changes cosf(float) +* into an intrinsic __cosf(float), which has less accurate numeric behavior. +* +* \param[in] a - nv_bfloat162. Is only being read. +* \returns nv_bfloat162 +* - The elementwise cosine on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2cos(const __nv_bfloat162 a); +/** +* \ingroup CUDA_MATH__BFLOAT162_FUNCTIONS +* \brief Calculates \p nv_bfloat162 vector sine in round-to-nearest-even mode. +* +* \details Calculates \p nv_bfloat162 sine of input vector \p a in round-to-nearest-even mode. +* +* NOTE: this function's implementation calls sinf(float) function and is exposed +* to compiler optimizations. Specifically, \p --use_fast_math flag changes sinf(float) +* into an intrinsic __sinf(float), which has less accurate numeric behavior. +* +* \param[in] a - nv_bfloat162. Is only being read. +* \returns nv_bfloat162 +* - The elementwise sine on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 h2sin(const __nv_bfloat162 a); + +/** +* \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC +* \brief Vector add \p val to the value stored at \p address in global or shared memory, and writes this +* value back to \p address. The atomicity of the add operation is guaranteed separately for each of the +* two nv_bfloat16 elements; the entire __nv_bfloat162 is not guaranteed to be atomic as a single 32-bit access. +* +* \details The location of \p address must be in global or shared memory. This operation has undefined +* behavior otherwise. This operation is natively supported by devices of compute capability 9.x and higher, +* older devices use emulation path. +* +* \param[in] address - __nv_bfloat162*. An address in global or shared memory. +* \param[in] val - __nv_bfloat162. The value to be added. +* +* \returns __nv_bfloat162 +* - The old value read from \p address. +* +* \note_ref_guide_atomic +*/ +__CUDA_BF16_DECL__ __nv_bfloat162 atomicAdd(__nv_bfloat162 *const address, const __nv_bfloat162 val); + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC +* \brief Adds \p val to the value stored at \p address in global or shared memory, and writes this value +* back to \p address. This operation is performed in one atomic operation. +* +* \details The location of \p address must be in global or shared memory. This operation has undefined +* behavior otherwise. This operation is natively supported by devices of compute capability 9.x and higher, +* older devices of compute capability 7.x and 8.x use emulation path. +* +* \param[in] address - __nv_bfloat16*. An address in global or shared memory. +* \param[in] val - __nv_bfloat16. The value to be added. +* +* \returns __nv_bfloat16 +* - The old value read from \p address. +* +* \note_ref_guide_atomic +*/ +__CUDA_BF16_DECL__ __nv_bfloat16 atomicAdd(__nv_bfloat16 *const address, const __nv_bfloat16 val); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) */ + +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +#endif /* defined(__cplusplus) */ + +#if !defined(_MSC_VER) && __cplusplus >= 201103L +# define __CPP_VERSION_AT_LEAST_11_BF16 +#elif _MSC_FULL_VER >= 190024210 && _MSVC_LANG >= 201103L +# define __CPP_VERSION_AT_LEAST_11_BF16 +#endif + +/* C++11 header for std::move. + * In RTC mode, std::move is provided implicitly; don't include the header + */ +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) && !defined(__CUDACC_RTC__) +#include +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) && !defined(__CUDACC_RTC__) */ + +/* C++ header for std::memcpy (used for type punning in host-side implementations). + * When compiling as a CUDA source file memcpy is provided implicitly. + * !defined(__CUDACC__) implies !defined(__CUDACC_RTC__). + */ +#if defined(__cplusplus) && !defined(__CUDACC__) +#include +#endif /* defined(__cplusplus) && !defined(__CUDACC__) */ + +// implicitly provided by NVRTC +#if !defined(__CUDACC_RTC__) +#include +#endif /* !defined(__CUDACC_RTC__) */ + +#if (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) +#define __CUDA_BF16_INLINE__ +#define __CUDA_BF16_FORCEINLINE__ +#else +#define __CUDA_BF16_INLINE__ inline +#define __CUDA_BF16_FORCEINLINE__ __forceinline__ +#endif /* #if (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) */ + +/* Set up structure-alignment attribute */ +#if defined(__CUDACC__) +#define __CUDA_ALIGN__(align) __align__(align) +#else +/* Define alignment macro based on compiler type (cannot assume C11 "_Alignas" is available) */ +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) +#define __CUDA_ALIGN__(n) alignas(n) /* C++11 kindly gives us a keyword for this */ +#else /* defined(__CPP_VERSION_AT_LEAST_11_BF16)*/ +#if defined(__GNUC__) +#define __CUDA_ALIGN__(n) __attribute__ ((aligned(n))) +#elif defined(_MSC_VER) +#define __CUDA_ALIGN__(n) __declspec(align(n)) +#else +#define __CUDA_ALIGN__(n) +#endif /* defined(__GNUC__) */ +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ +#endif /* defined(__CUDACC__) */ + +// define __CUDA_BF16_CONSTEXPR__ in order to +// use constexpr where possible, with supporting C++ dialects +// undef after use +#if (defined __CPP_VERSION_AT_LEAST_11_BF16) +#define __CUDA_BF16_CONSTEXPR__ constexpr +#else +#define __CUDA_BF16_CONSTEXPR__ +#endif + +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief __nv_bfloat16_raw data type + * \details Type allows static initialization of \p nv_bfloat16 until it becomes + * a builtin type. + * + * - Note: this initialization is as a bit-field representation of \p nv_bfloat16, + * and not a conversion from \p short to \p nv_bfloat16. + * Such representation will be deprecated in a future version of CUDA. + * + * - Note: this is visible to non-nvcc compilers, including C-only compilations + */ +typedef struct __CUDA_ALIGN__(2) { + unsigned short x; +} __nv_bfloat16_raw; + +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief __nv_bfloat162_raw data type + * \details Type allows static initialization of \p nv_bfloat162 until it becomes + * a builtin type. + * + * - Note: this initialization is as a bit-field representation of \p nv_bfloat162, + * and not a conversion from \p short2 to \p nv_bfloat162. + * Such representation will be deprecated in a future version of CUDA. + * + * - Note: this is visible to non-nvcc compilers, including C-only compilations + */ +typedef struct __CUDA_ALIGN__(4) { + unsigned short x; + unsigned short y; +} __nv_bfloat162_raw; + +/* All other definitions in this file are only visible to C++ compilers */ +#if defined(__cplusplus) + +/* Hide GCC member initialization list warnings because of host/device in-function init requirement */ +#if defined(__GNUC__) +#if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Weffc++" +#endif /* __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) */ +#endif /* defined(__GNUC__) */ + +/* class' : multiple assignment operators specified + The class has multiple assignment operators of a single type. This warning is informational */ +#if defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning( push ) +#pragma warning( disable:4522 ) +#endif /* defined(__GNUC__) */ + +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief nv_bfloat16 datatype + * + * \details This structure implements the datatype for storing + * nv_bfloat16 floating-point numbers. The structure implements + * assignment operators and type conversions. 16 bits are being + * used in total: 1 sign bit, 8 bits for the exponent, and + * the significand is being stored in 7 bits. The total + * precision is 8 bits. + * + */ +struct __CUDA_ALIGN__(2) __nv_bfloat16 { +protected: + /** + * Protected storage variable contains the bits of floating-point data. + */ + unsigned short __x; + +public: + + /** + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) + __nv_bfloat16() = default; +#else + __CUDA_HOSTDEVICE__ __nv_bfloat16(); +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + + /* Convert to/from __nv_bfloat16_raw */ + /** + * Constructor from \p __nv_bfloat16_raw. + */ + __CUDA_HOSTDEVICE__ __CUDA_BF16_CONSTEXPR__ __nv_bfloat16(const __nv_bfloat16_raw &hr) : __x(hr.x) { } + /** + * Assignment operator from \p __nv_bfloat16_raw. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(const __nv_bfloat16_raw &hr); + /** + * Assignment operator from \p __nv_bfloat16_raw to \p volatile \p __nv_bfloat16. + */ + __CUDA_HOSTDEVICE__ volatile __nv_bfloat16 &operator=(const __nv_bfloat16_raw &hr) volatile; + /** + * Assignment operator from \p volatile \p __nv_bfloat16_raw to \p volatile \p __nv_bfloat16. + */ + __CUDA_HOSTDEVICE__ volatile __nv_bfloat16 &operator=(const volatile __nv_bfloat16_raw &hr) volatile; + /** + * Type cast to \p __nv_bfloat16_raw operator. + */ + __CUDA_HOSTDEVICE__ operator __nv_bfloat16_raw() const; + /** + * Type cast to \p __nv_bfloat16_raw operator with \p volatile input. + */ + __CUDA_HOSTDEVICE__ operator __nv_bfloat16_raw() const volatile; + +#if !defined(__CUDA_NO_BFLOAT16_CONVERSIONS__) +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) + /** + * Construct \p __nv_bfloat16 from \p __half input using default round-to-nearest-even rounding mode. + */ + explicit __CUDA_HOSTDEVICE__ __nv_bfloat16(const __half f); +#endif /* #if defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + + /* Construct from float/double */ + /** + * Construct \p __nv_bfloat16 from \p float input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(const float f); + /** + * Construct \p __nv_bfloat16 from \p double input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(const double f); + /** + * Type cast to \p float operator. + */ + __CUDA_HOSTDEVICE__ operator float() const; + /** + * Type cast to \p __nv_bfloat16 assignment operator from \p float input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(const float f); + + /* We omit "cast to double" operator, so as to not be ambiguous about up-cast */ + /** + * Type cast to \p __nv_bfloat16 assignment operator from \p double input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(const double f); + +/* + * Implicit type conversions to/from integer types were only available to nvcc compilation. + * Introducing them for all compilers is a potentially breaking change that may affect + * overloads resolution and will require users to update their code. + * Define __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__ to opt-out. + */ +#if !(defined __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) + /* Allow automatic construction from types supported natively in hardware */ + /* Note we do avoid constructor init-list because of special host/device compilation rules */ + + /** + * Construct \p __nv_bfloat16 from \p short integer input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(short val); + /** + * Construct \p __nv_bfloat16 from \p unsigned \p short integer input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(unsigned short val); + /** + * Construct \p __nv_bfloat16 from \p int input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(int val); + /** + * Construct \p __nv_bfloat16 from \p unsigned \p int input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(unsigned int val); + /** + * Construct \p __nv_bfloat16 from \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(const long val); + + /** + * Construct \p __nv_bfloat16 from \p unsigned \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(const unsigned long val); + /** + * Construct \p __nv_bfloat16 from \p long \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(long long val); + /** + * Construct \p __nv_bfloat16 from \p unsigned \p long \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16(unsigned long long val); + + /* Allow automatic casts to supported builtin types, matching all that are permitted with float */ + + /** + * Conversion operator to \p signed \p char data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162char_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator signed char() const; + /** + * Conversion operator to \p unsigned \p char data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162uchar_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned char() const; + /** + * Conversion operator to an implementation defined \p char data type. + * Using round-toward-zero rounding mode. + * + * Detects signedness of the \p char type and proceeds accordingly, see + * further details in signed and unsigned char operators. + */ + __CUDA_HOSTDEVICE__ operator char() const; + /** + * Conversion operator to \p short data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162short_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator short() const; + /** + * Conversion operator to \p unsigned \p short data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162ushort_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned short() const; + /** + * Conversion operator to \p int data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162int_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator int() const; + /** + * Conversion operator to \p unsigned \p int data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162uint_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned int() const; + /** + * Conversion operator to \p long data type. + * Using round-toward-zero rounding mode. + */ + __CUDA_HOSTDEVICE__ operator long() const; + /** + * Conversion operator to \p unsigned \p long data type. + * Using round-toward-zero rounding mode. + */ + __CUDA_HOSTDEVICE__ operator unsigned long() const; + /** + * Conversion operator to \p long \p long data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162ll_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator long long() const; + /** + * Conversion operator to \p unsigned \p long \p long data type. + * Using round-toward-zero rounding mode. + * + * See __bfloat162ull_rz(__nv_bfloat16) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned long long() const; + /** + * Type cast from \p short assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(short val); + /** + * Type cast from \p unsigned \p short assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(unsigned short val); + /** + * Type cast from \p int assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(int val); + /** + * Type cast from \p unsigned \p int assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(unsigned int val); + /** + * Type cast from \p long \p long assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(long long val); + /** + * Type cast from \p unsigned \p long \p long assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __nv_bfloat16 &operator=(unsigned long long val); + /** + * Conversion operator to \p bool data type. + * +0 and -0 inputs convert to \p false. + * Non-zero inputs convert to \p true. + */ + __CUDA_HOSTDEVICE__ __CUDA_BF16_CONSTEXPR__ operator bool() const { return (__x & 0x7FFFU) != 0U; } +#endif /* !(defined __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) */ +#endif /* !defined(__CUDA_NO_BFLOAT16_CONVERSIONS__) */ +}; + +#if !defined(__CUDA_NO_BFLOAT16_OPERATORS__) +/* Some basic arithmetic operations expected of a builtin */ +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 addition operation. + * See also __hadd(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator+(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 subtraction operation. + * See also __hsub(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator-(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 multiplication operation. + * See also __hmul(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator*(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 division operation. + * See also __hdiv(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator/(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); + +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 compound assignment with addition operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator+=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 compound assignment with subtraction operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator-=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 compound assignment with multiplication operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator*=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 compound assignment with division operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator/=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh); + +/* Note for increment and decrement we use the raw value 0x3F80U equating to nv_bfloat16(1.0F), to avoid the extra conversion */ +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 prefix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator++(__nv_bfloat16 &h); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 prefix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator--(__nv_bfloat16 &h); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 postfix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator++(__nv_bfloat16 &h, const int ignored); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Performs \p nv_bfloat16 postfix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator--(__nv_bfloat16 &h, const int ignored); +/* Unary plus and inverse operators */ +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Implements \p nv_bfloat16 unary plus operator, returns input value. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator+(const __nv_bfloat16 &h); +/** + * \ingroup CUDA_MATH__BFLOAT16_ARITHMETIC + * Implements \p nv_bfloat16 unary minus operator. + * See also __hneg(__nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator-(const __nv_bfloat16 &h); + +/* Some basic comparison operations to make it look like a builtin */ +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 ordered compare equal operation. + * See also __heq(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator==(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 unordered compare not-equal operation. + * See also __hneu(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator!=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 ordered greater-than compare operation. + * See also __hgt(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator> (const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 ordered less-than compare operation. + * See also __hlt(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator< (const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 ordered greater-or-equal compare operation. + * See also __hge(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT16_COMPARISON + * Performs \p nv_bfloat16 ordered less-or-equal compare operation. + * See also __hle(__nv_bfloat16, __nv_bfloat16) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh); +#endif /* !defined(__CUDA_NO_BFLOAT16_OPERATORS__) */ + +/** +* \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief nv_bfloat162 datatype + * \details This structure implements the datatype for storing two + * nv_bfloat16 floating-point numbers. + * The structure implements assignment, arithmetic and comparison + * operators, and type conversions. + * + * - NOTE: __nv_bfloat162 is visible to non-nvcc host compilers + */ +struct __CUDA_ALIGN__(4) __nv_bfloat162 { + /** + * Storage field holding lower \p __nv_bfloat16 part. + */ + __nv_bfloat16 x; + /** + * Storage field holding upper \p __nv_bfloat16 part. + */ + __nv_bfloat16 y; + + // All construct/copy/assign/move +public: + /** + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) + __nv_bfloat162() = default; + /** + * Move constructor, available for \p C++11 and later dialects + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162(__nv_bfloat162 &&src); + /** + * Move assignment operator, available for \p C++11 and later dialects + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162 &operator=(__nv_bfloat162 &&src); +#else + __CUDA_HOSTDEVICE__ __nv_bfloat162(); +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + + /** + * Constructor from two \p __nv_bfloat16 variables + */ + __CUDA_HOSTDEVICE__ __CUDA_BF16_CONSTEXPR__ __nv_bfloat162(const __nv_bfloat16 &a, const __nv_bfloat16 &b) : x(a), y(b) { } + /** + * Copy constructor + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162(const __nv_bfloat162 &src); + /** + * Copy assignment operator + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162 &operator=(const __nv_bfloat162 &src); + + /* Convert to/from __nv_bfloat162_raw */ + /** + * Constructor from \p __nv_bfloat162_raw + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162(const __nv_bfloat162_raw &h2r ); + /** + * Assignment operator from \p __nv_bfloat162_raw + */ + __CUDA_HOSTDEVICE__ __nv_bfloat162 &operator=(const __nv_bfloat162_raw &h2r); + /** + * Conversion operator to \p __nv_bfloat162_raw + */ + __CUDA_HOSTDEVICE__ operator __nv_bfloat162_raw() const; +}; + +#if !defined(__CUDA_NO_BFLOAT162_OPERATORS__) +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 addition operation. + * See also __hadd2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator+(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 subtraction operation. + * See also __hsub2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator-(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 multiplication operation. + * See also __hmul2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator*(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 division operation. + * See also __h2div(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator/(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 compound assignment with addition operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator+=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 compound assignment with subtraction operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator-=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 compound assignment with multiplication operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator*=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 compound assignment with division operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator/=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 prefix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 &operator++(__nv_bfloat162 &h); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 prefix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 &operator--(__nv_bfloat162 &h); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 postfix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator++(__nv_bfloat162 &h, const int ignored); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Performs packed \p nv_bfloat16 postfix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator--(__nv_bfloat162 &h, const int ignored); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Implements packed \p nv_bfloat16 unary plus operator, returns input value. + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator+(const __nv_bfloat162 &h); +/** + * \ingroup CUDA_MATH__BFLOAT162_ARITHMETIC + * Implements packed \p nv_bfloat16 unary minus operator. + * See also __hneg2(__nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator-(const __nv_bfloat162 &h); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 ordered compare equal operation. + * See also __hbeq2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator==(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 unordered compare not-equal operation. + * See also __hbneu2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator!=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 ordered greater-than compare operation. + * See also __hbgt2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 ordered less-than compare operation. + * See also __hblt2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 ordered greater-or-equal compare operation. + * See also __hbge2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); +/** + * \ingroup CUDA_MATH__BFLOAT162_COMPARISON + * Performs packed \p nv_bfloat16 ordered less-or-equal compare operation. + * See also __hble2(__nv_bfloat162, __nv_bfloat162) + */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh); + +#endif /* !defined(__CUDA_NO_BFLOAT162_OPERATORS__) */ + +#endif /* defined(__cplusplus) */ + +#if (defined(__FORCE_INCLUDE_CUDA_BF16_HPP_FROM_BF16_H__) || \ + !(defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3))))) +/* Note the .hpp file is included to capture the "nv_bfloat16" & "nv_bfloat162" builtin function definitions. For NVRTC, the builtin + function definitions are compiled at NVRTC library build-time and are available through the NVRTC builtins library at + link time. +*/ +#include "cuda_bf16.hpp" +#endif /* (defined(__FORCE_INCLUDE_CUDA_BF16_HPP_FROM_BF16_H__) || \ + !(defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3))))) */ + +/* Define first-class types "nv_bfloat16" and "nv_bfloat162", unless user specifies otherwise via "#define CUDA_NO_BFLOAT16" */ +/* C cannot ever have these types defined here, because __nv_bfloat16 and __nv_bfloat162 are C++ classes */ +#if defined(__cplusplus) && !defined(CUDA_NO_BFLOAT16) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief This datatype is meant to be the first-class or fundamental + * implementation of the bfloat16 numbers format. + * + * \details Should be implemented in the compiler in the future. + * Current implementation is a simple typedef to a respective + * user-level type with underscores. + */ +typedef __nv_bfloat16 nv_bfloat16; + +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16 + * \brief This datatype is meant to be the first-class or fundamental + * implementation of type for pairs of bfloat16 numbers. + * + * \details Should be implemented in the compiler in the future. + * Current implementation is a simple typedef to a respective + * user-level type with underscores. + */ +typedef __nv_bfloat162 nv_bfloat162; + +#endif /* defined(__cplusplus) && !defined(CUDA_NO_BFLOAT16) */ + +#undef __CUDA_BF16_DECL__ +#undef __CUDA_HOSTDEVICE_BF16_DECL__ +#undef __CUDA_HOSTDEVICE__ +#undef __CUDA_BF16_INLINE__ +#undef __CUDA_BF16_FORCEINLINE__ + +#undef ___CUDA_BF16_STRINGIFY_INNERMOST +#undef __CUDA_BF16_STRINGIFY + +#endif /* end of include guard: __CUDA_BF16_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.hpp b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.hpp new file mode 100644 index 0000000000000000000000000000000000000000..9ee6683d82fda666fd9e585e8e992d0fdbf4ea9c --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_bf16.hpp @@ -0,0 +1,3868 @@ +/* +* Copyright 1993-2023 NVIDIA Corporation. All rights reserved. +* +* NOTICE TO LICENSEE: +* +* This source code and/or documentation ("Licensed Deliverables") are +* subject to NVIDIA intellectual property rights under U.S. and +* international Copyright laws. +* +* These Licensed Deliverables contained herein is PROPRIETARY and +* CONFIDENTIAL to NVIDIA and is being provided under the terms and +* conditions of a form of NVIDIA software license agreement by and +* between NVIDIA and Licensee ("License Agreement") or electronically +* accepted by Licensee. Notwithstanding any terms or conditions to +* the contrary in the License Agreement, reproduction or disclosure +* of the Licensed Deliverables to any third party without the express +* written consent of NVIDIA is prohibited. +* +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE +* SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS +* PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. +* NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED +* DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, +* NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY +* SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY +* DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, +* WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS +* ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE +* OF THESE LICENSED DELIVERABLES. +* +* U.S. Government End Users. These Licensed Deliverables are a +* "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT +* 1995), consisting of "commercial computer software" and "commercial +* computer software documentation" as such terms are used in 48 +* C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government +* only as a commercial end item. Consistent with 48 C.F.R.12.212 and +* 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all +* U.S. Government End Users acquire the Licensed Deliverables with +* only those rights set forth herein. +* +* Any use of the Licensed Deliverables in individual and commercial +* software must include, in the user documentation and internal +* comments to the code, the above Disclaimer and U.S. Government End +* Users Notice. +*/ + +#if !defined(__CUDA_BF16_HPP__) +#define __CUDA_BF16_HPP__ + +#if !defined(__CUDA_BF16_H__) +#error "Do not include this file directly. Instead, include cuda_bf16.h." +#endif + +#if !defined(IF_DEVICE_OR_CUDACC) +#if defined(__CUDACC__) + #define IF_DEVICE_OR_CUDACC(d, c, f) NV_IF_ELSE_TARGET(NV_IS_DEVICE, d, c) +#else + #define IF_DEVICE_OR_CUDACC(d, c, f) NV_IF_ELSE_TARGET(NV_IS_DEVICE, d, f) +#endif +#endif + +/* Macros to allow nv_bfloat16 & nv_bfloat162 to be used by inline assembly */ +#define __BFLOAT16_TO_US(var) *(reinterpret_cast(&(var))) +#define __BFLOAT16_TO_CUS(var) *(reinterpret_cast(&(var))) +#define __BFLOAT162_TO_UI(var) *(reinterpret_cast(&(var))) +#define __BFLOAT162_TO_CUI(var) *(reinterpret_cast(&(var))) + +/* All other definitions in this file are only visible to C++ compilers */ +#if defined(__cplusplus) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines floating-point positive infinity value for the \p nv_bfloat16 data type + */ +#define CUDART_INF_BF16 __ushort_as_bfloat16((unsigned short)0x7F80U) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines canonical NaN value for the \p nv_bfloat16 data type + */ +#define CUDART_NAN_BF16 __ushort_as_bfloat16((unsigned short)0x7FFFU) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines a minimum representable (denormalized) value for the \p nv_bfloat16 data type + */ +#define CUDART_MIN_DENORM_BF16 __ushort_as_bfloat16((unsigned short)0x0001U) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines a maximum representable value for the \p nv_bfloat16 data type + */ +#define CUDART_MAX_NORMAL_BF16 __ushort_as_bfloat16((unsigned short)0x7F7FU) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines a negative zero value for the \p nv_bfloat16 data type + */ +#define CUDART_NEG_ZERO_BF16 __ushort_as_bfloat16((unsigned short)0x8000U) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines a positive zero value for the \p nv_bfloat16 data type + */ +#define CUDART_ZERO_BF16 __ushort_as_bfloat16((unsigned short)0x0000U) +/** + * \ingroup CUDA_MATH_INTRINSIC_BFLOAT16_CONSTANTS + * \brief Defines a value of 1.0 for the \p nv_bfloat16 data type + */ +#define CUDART_ONE_BF16 __ushort_as_bfloat16((unsigned short)0x3F80U) + +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) +#else + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16() { } +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(const __nv_bfloat16_raw &hr) { __x = hr.x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ volatile __nv_bfloat16 &__nv_bfloat16::operator=(const __nv_bfloat16_raw &hr) volatile { __x = hr.x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ volatile __nv_bfloat16 &__nv_bfloat16::operator=(const volatile __nv_bfloat16_raw &hr) volatile { __x = hr.x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator __nv_bfloat16_raw() const { __nv_bfloat16_raw ret; ret.x = __x; return ret; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator __nv_bfloat16_raw() const volatile { __nv_bfloat16_raw ret; ret.x = __x; return ret; } + +#if !defined(__CUDA_NO_BFLOAT16_CONVERSIONS__) + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(const float f) { __x = __float2bfloat16(f).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(const double f) { __x = __double2bfloat16(f).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator float() const { return __bfloat162float(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(const float f) { __x = __float2bfloat16(f).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(const double f) { __x = __double2bfloat16(f).__x; return *this; } + +/* + * Implicit type conversions to/from integer types were only available to nvcc compilation. + * Introducing them for all compilers is a potentially breaking change that may affect + * overloads resolution and will require users to update their code. + * Define __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__ to opt-out. + */ +#if !(defined __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(short val) { __x = __short2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(unsigned short val) { __x = __ushort2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(int val) { __x = __int2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(unsigned int val) { __x = __uint2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(const long val) { + + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + + { + __x = __ll2bfloat16_rn(static_cast(val)).__x; + } else { + __x = __int2bfloat16_rn(static_cast(val)).__x; + } + } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(const unsigned long val) { + + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + + { + __x = __ull2bfloat16_rn(static_cast(val)).__x; + } else { + __x = __uint2bfloat16_rn(static_cast(val)).__x; + } + } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(long long val) { __x = __ll2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::__nv_bfloat16(unsigned long long val) { __x = __ull2bfloat16_rn(val).__x; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator signed char() const { return __bfloat162char_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator unsigned char() const { return __bfloat162uchar_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator char() const { + char value; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (((char)-1) < (char)0) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + value = static_cast(__bfloat162char_rz(*this)); + } + else + { + value = static_cast(__bfloat162uchar_rz(*this)); + } + return value; + } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator short() const { return __bfloat162short_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator unsigned short() const { return __bfloat162ushort_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator int() const { return __bfloat162int_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator unsigned int() const { return __bfloat162uint_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator long() const { + long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__bfloat162ll_rz(*this)); + } + else + { + retval = static_cast(__bfloat162int_rz(*this)); + } + return retval; + } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator unsigned long() const { + unsigned long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__bfloat162ull_rz(*this)); + } + else + { + retval = static_cast(__bfloat162uint_rz(*this)); + } + return retval; + } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator long long() const { return __bfloat162ll_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16::operator unsigned long long() const { return __bfloat162ull_rz(*this); } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(short val) { __x = __short2bfloat16_rn(val).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(unsigned short val) { __x = __ushort2bfloat16_rn(val).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(int val) { __x = __int2bfloat16_rn(val).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(unsigned int val) { __x = __uint2bfloat16_rn(val).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(long long val) { __x = __ll2bfloat16_rn(val).__x; return *this; } + __CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat16 &__nv_bfloat16::operator=(unsigned long long val) { __x = __ull2bfloat16_rn(val).__x; return *this; } +#endif /* !(defined __CUDA_BF16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) */ +#endif /* !defined(__CUDA_NO_BFLOAT16_CONVERSIONS__) */ + +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) +#if !defined(__CUDA_NO_BFLOAT16_CONVERSIONS__) +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16::__nv_bfloat16(const __half f) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.rn.bf16.f16 %0, %1;}\n" : "=h"(__x) : "h"(__BFLOAT16_TO_CUS(f))); +, + __x = __float2bfloat16(__half2float(f)).__x; +) +} +#endif + +#if !defined(__CUDA_NO_HALF_CONVERSIONS__) +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __half::__half(const __nv_bfloat16 f) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.rn.f16.bf16 %0, %1;}\n" : "=h"(__x) : "h"(__BFLOAT16_TO_CUS(f))); +, + __x = __float2half_rn(__bfloat162float(f)).__x; +) +} +#endif +#endif /* #if defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + +#if !defined(__CUDA_NO_BFLOAT16_OPERATORS__) +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator+(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hadd(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator-(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hsub(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator*(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hmul(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator/(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hdiv(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator+=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh) { lh = __hadd(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator-=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh) { lh = __hsub(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator*=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh) { lh = __hmul(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator/=(__nv_bfloat16 &lh, const __nv_bfloat16 &rh) { lh = __hdiv(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator++(__nv_bfloat16 &h) { __nv_bfloat16_raw one; one.x = 0x3F80U; h += one; return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 &operator--(__nv_bfloat16 &h) { __nv_bfloat16_raw one; one.x = 0x3F80U; h -= one; return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator++(__nv_bfloat16 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __nv_bfloat16 ret = h; + __nv_bfloat16_raw one; + one.x = 0x3F80U; + h += one; + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator--(__nv_bfloat16 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __nv_bfloat16 ret = h; + __nv_bfloat16_raw one; + one.x = 0x3F80U; + h -= one; + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator+(const __nv_bfloat16 &h) { return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat16 operator-(const __nv_bfloat16 &h) { return __hneg(h); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator==(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __heq(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator!=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hneu(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator> (const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hgt(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator< (const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hlt(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hge(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<=(const __nv_bfloat16 &lh, const __nv_bfloat16 &rh) { return __hle(lh, rh); } +#endif /* !defined(__CUDA_NO_BFLOAT16_OPERATORS__) */ + +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162::__nv_bfloat162(__nv_bfloat162 &&src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = std::move(__BFLOAT162_TO_CUI(src)); +, + this->x = src.x; + this->y = src.y; +) +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162 &__nv_bfloat162::operator=(__nv_bfloat162 &&src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = std::move(__BFLOAT162_TO_CUI(src)); +, + this->x = src.x; + this->y = src.y; +) + return *this; +} +#else +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162::__nv_bfloat162() { } +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162::__nv_bfloat162(const __nv_bfloat162 &src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = __BFLOAT162_TO_CUI(src); +, + this->x = src.x; + this->y = src.y; +) +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162 &__nv_bfloat162::operator=(const __nv_bfloat162 &src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = __BFLOAT162_TO_CUI(src); +, + this->x = src.x; + this->y = src.y; +) + return *this; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162::__nv_bfloat162(const __nv_bfloat162_raw &h2r ) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = __BFLOAT162_TO_CUI(h2r); +, + __nv_bfloat16_raw tr; + tr.x = h2r.x; + this->x = static_cast<__nv_bfloat16>(tr); + tr.x = h2r.y; + this->y = static_cast<__nv_bfloat16>(tr); +) +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162 &__nv_bfloat162::operator=(const __nv_bfloat162_raw &h2r) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __BFLOAT162_TO_UI(*this) = __BFLOAT162_TO_CUI(h2r); +, + __nv_bfloat16_raw tr; + tr.x = h2r.x; + this->x = static_cast<__nv_bfloat16>(tr); + tr.x = h2r.y; + this->y = static_cast<__nv_bfloat16>(tr); +) + return *this; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_INLINE__ __nv_bfloat162::operator __nv_bfloat162_raw() const { + __nv_bfloat162_raw ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + ret.x = 0U; + ret.y = 0U; + __BFLOAT162_TO_UI(ret) = __BFLOAT162_TO_CUI(*this); +, + ret.x = static_cast<__nv_bfloat16_raw>(this->x).x; + ret.y = static_cast<__nv_bfloat16_raw>(this->y).x; +) + return ret; +} + +#if !defined(__CUDA_NO_BFLOAT162_OPERATORS__) +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator+(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hadd2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator-(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hsub2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator*(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hmul2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator/(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __h2div(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator+=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh) { lh = __hadd2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator-=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh) { lh = __hsub2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator*=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh) { lh = __hmul2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162& operator/=(__nv_bfloat162 &lh, const __nv_bfloat162 &rh) { lh = __h2div(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 &operator++(__nv_bfloat162 &h) { __nv_bfloat162_raw one; one.x = 0x3F80U; one.y = 0x3F80U; h = __hadd2(h, one); return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 &operator--(__nv_bfloat162 &h) { __nv_bfloat162_raw one; one.x = 0x3F80U; one.y = 0x3F80U; h = __hsub2(h, one); return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator++(__nv_bfloat162 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __nv_bfloat162 ret = h; + __nv_bfloat162_raw one; + one.x = 0x3F80U; + one.y = 0x3F80U; + h = __hadd2(h, one); + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator--(__nv_bfloat162 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __nv_bfloat162 ret = h; + __nv_bfloat162_raw one; + one.x = 0x3F80U; + one.y = 0x3F80U; + h = __hsub2(h, one); + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator+(const __nv_bfloat162 &h) { return h; } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ __nv_bfloat162 operator-(const __nv_bfloat162 &h) { return __hneg2(h); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator==(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hbeq2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator!=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hbneu2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hbgt2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hblt2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator>=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hbge2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_BF16_FORCEINLINE__ bool operator<=(const __nv_bfloat162 &lh, const __nv_bfloat162 &rh) { return __hble2(lh, rh); } +#endif /* !defined(__CUDA_NO_BFLOAT162_OPERATORS__) */ + +/* Restore warning for multiple assignment operators */ +#if defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning( pop ) +#endif /* defined(_MSC_VER) && _MSC_VER >= 1500 */ + +/* Restore -Weffc++ warnings from here on */ +#if defined(__GNUC__) +#if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) +#pragma GCC diagnostic pop +#endif /* __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) */ +#endif /* defined(__GNUC__) */ + +#undef __CUDA_HOSTDEVICE__ +#undef __CUDA_ALIGN__ + +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned int __internal_float_as_uint(const float f) +{ + unsigned int u; +IF_DEVICE_OR_CUDACC( + u = __float_as_uint(f); +, + memcpy(&u, &f, sizeof(f)); +, + std::memcpy(&u, &f, sizeof(f)); +) + return u; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ float __internal_uint_as_float(const unsigned int u) +{ + float f; +IF_DEVICE_OR_CUDACC( + f = __uint_as_float(u); +, + memcpy(&f, &u, sizeof(u)); +, + std::memcpy(&f, &u, sizeof(u)); +) + return f; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned short __internal_float2bfloat16(const float f, unsigned int &sign, unsigned int &remainder) +{ + unsigned int x; + + x = __internal_float_as_uint(f); + + if ((x & 0x7fffffffU) > 0x7f800000U) { + sign = 0U; + remainder = 0U; + return static_cast(0x7fffU); + } + sign = x >> 31U; + remainder = x << 16U; + return static_cast(x >> 16U); +} + +__CUDA_HOSTDEVICE_BF16_DECL__ float __internal_double2float_rn(const double x) +{ + float r; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f32.f64 %0, %1;" : "=f"(r) : "d"(x)); +, + r = static_cast(x); +) + return r; +} +__CUDA_HOSTDEVICE_BF16_DECL__ double __internal_float2double(const float x) +{ + double r; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.f64.f32 %0, %1;" : "=d"(r) : "f"(x)); +, + r = static_cast(x); +) + return r; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __double2bfloat16(const double x) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("{ cvt.rn.bf16.f64 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "d"(x)); + return val; +, + float f = __internal_double2float_rn(x); + const double d = __internal_float2double(f); + unsigned int u = __internal_float_as_uint(f); + + bool x_is_not_nan = ((u << (unsigned)1U) <= (unsigned)0xFF000000U); + + + if ((x > 0.0) && (d > x)) { + u--; + } + if ((x < 0.0) && (d < x)) { + u--; + } + if ((d != x) && x_is_not_nan) { + u |= 1U; + } + + f = __internal_uint_as_float(u); + + return __float2bfloat16(f); +) +} + +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16(const float a) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{ cvt.rn.bf16.f32 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "f"(a)); +, + __nv_bfloat16_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2bfloat16(a, sign, remainder); + if ((remainder > 0x80000000U) || ((remainder == 0x80000000U) && ((r.x & 0x1U) != 0U))) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rn(const float a) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{ cvt.rn.bf16.f32 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "f"(a)); +, + __nv_bfloat16_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2bfloat16(a, sign, remainder); + if ((remainder > 0x80000000U) || ((remainder == 0x80000000U) && ((r.x & 0x1U) != 0U))) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rz(const float a) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{ cvt.rz.bf16.f32 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "f"(a)); +, + __nv_bfloat16_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2bfloat16(a, sign, remainder); + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_rd(const float a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("{ cvt.rm.bf16.f32 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "f"(a)); + return val; +, + __nv_bfloat16 val; + __nv_bfloat16_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2bfloat16(a, sign, remainder); + if ((remainder != 0U) && (sign != 0U)) { + r.x++; + } + val = r; + return val; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __float2bfloat16_ru(const float a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("{ cvt.rp.bf16.f32 %0, %1;}\n" : "=h"(__BFLOAT16_TO_US(val)) : "f"(a)); + return val; +, + __nv_bfloat16 val; + __nv_bfloat16_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2bfloat16(a, sign, remainder); + if ((remainder != 0U) && (sign == 0U)) { + r.x++; + } + val = r; + return val; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __float2bfloat162_rn(const float a) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{.reg .b16 low;\n" + " cvt.rn.bf16.f32 low, %1;\n" + " mov.b32 %0, {low,low};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "f"(a)); +, + val = __nv_bfloat162(__float2bfloat16_rn(a), __float2bfloat16_rn(a)); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __floats2bfloat162_rn(const float a, const float b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{ cvt.rn.bf16x2.f32 %0, %2, %1;}\n" + : "=r"(__BFLOAT162_TO_UI(val)) : "f"(a), "f"(b)); +, + val = __nv_bfloat162(__float2bfloat16_rn(a), __float2bfloat16_rn(b)); +) + return val; +} + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ float __internal_device_bfloat162float(const unsigned short h) +{ + float f; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.f32.bf16 %0, %1;}\n" : "=f"(f) : "h"(h)); +, + asm("{ mov.b32 %0, {0,%1};}\n" : "=f"(f) : "h"(h)); +) + return f; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_BF16_DECL__ float __internal_bfloat162float(const unsigned short h) +{ + float f; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + f = __internal_device_bfloat162float(h); +, + unsigned int u = static_cast(h) << 16; + f = __internal_uint_as_float(u); +) + return f; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ float __bfloat162float(const __nv_bfloat16 a) +{ + return __internal_bfloat162float(static_cast<__nv_bfloat16_raw>(a).x); +} +__CUDA_HOSTDEVICE_BF16_DECL__ float __low2float(const __nv_bfloat162 a) +{ + return __internal_bfloat162float(static_cast<__nv_bfloat162_raw>(a).x); +} + +__CUDA_HOSTDEVICE_BF16_DECL__ float __high2float(const __nv_bfloat162 a) +{ + return __internal_bfloat162float(static_cast<__nv_bfloat162_raw>(a).y); +} + +/* CUDA vector-types compatible vector creation function (note returns __nv_bfloat162, not nv_bfloat162) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 make_bfloat162(const __nv_bfloat16 x, const __nv_bfloat16 y) +{ + __nv_bfloat162 t; t.x = x; t.y = y; return t; +} + +/* Definitions of intrinsics */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __float22bfloat162_rn(const float2 a) +{ + __nv_bfloat162 val = __floats2bfloat162_rn(a.x, a.y); + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ float2 __bfloat1622float2(const __nv_bfloat162 a) +{ + float hi_float; + float lo_float; + lo_float = __internal_bfloat162float(((__nv_bfloat162_raw)a).x); + hi_float = __internal_bfloat162float(((__nv_bfloat162_raw)a).y); + return make_float2(lo_float, hi_float); +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ int __bfloat162int_rn(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + int val; + asm("{ cvt.rni.s32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); + return val; +, + return __float2int_rn(__bfloat162float(h)); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_BF16_DECL__ int __internal_bfloat162int_rz(const __nv_bfloat16 h) +{ + const float f = __bfloat162float(h); + int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + i = __float2int_rz(f); +, + const int max_val = (int)0x7fffffffU; + const int min_val = (int)0x80000000U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = 0; + } else if (f >= static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + i = static_cast(f); + } +) + return i; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ int __bfloat162int_rz(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + int val; + asm("{ cvt.rzi.s32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); + return val; +, + return __internal_bfloat162int_rz(h); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ int __bfloat162int_rd(const __nv_bfloat16 h) +{ + int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.rmi.s32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rmi.s32.f32 %0, %1;" : "=r"(val) : "f"(f)); +) + return val; +} +__CUDA_BF16_DECL__ int __bfloat162int_ru(const __nv_bfloat16 h) +{ + int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.rpi.s32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rpi.s32.f32 %0, %1;" : "=r"(val) : "f"(f)); +) + return val; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_int2bfloat16_rn(const int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rn.bf16.s32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + const float ru = __int2float_ru(i); + const float rd = __int2float_rd(i); + float rz = __int2float_rz(i); + if (ru != rd) { + rz = __uint_as_float(__float_as_uint(rz) | 1U); + } + return __float2bfloat16_rn(rz); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rn(const int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_int2bfloat16_rn(i); +, + const double d = static_cast(i); + return __double2bfloat16(d); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ signed char __bfloat162char_rz(const __nv_bfloat16 h) +{ + signed char i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned short tmp = 0; + asm("{ .reg.b8 myreg;\n" + " cvt.rzi.s8.bf16 myreg, %1;\n" + " mov.b16 %0, {myreg, 0};\n}" + :"=h"(tmp) : "h"(__BFLOAT16_TO_CUS(h))); + const unsigned char u = static_cast(tmp); + i = static_cast(u); +, + const float f = __bfloat162float(h); + const signed char max_val = (signed char)0x7fU; + const signed char min_val = (signed char)0x80U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned char __bfloat162uchar_rz(const __nv_bfloat16 h) +{ + unsigned char i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned short tmp = 0; + asm("{ .reg.b8 myreg;\n" + " cvt.rzi.u8.bf16 myreg, %1;\n" + " mov.b16 %0, {myreg, 0};\n}" + :"=h"(tmp) : "h"(__BFLOAT16_TO_CUS(h))); + i = static_cast(tmp); +, + const float f = __bfloat162float(h); + const unsigned char max_val = 0xffU; + const unsigned char min_val = 0U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = 0U; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rz(const int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rz.bf16.s32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_rz(__int2float_rz(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_rd(const int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rm.bf16.s32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_rd(__int2float_rd(i)); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat16 __int2bfloat16_ru(const int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rp.bf16.s32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_ru(__int2float_ru(i)); +) +} + +__CUDA_BF16_DECL__ short int __bfloat162short_rn(const __nv_bfloat16 h) +{ + short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rni.s16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rni.s16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} + +__CUDA_BF16_DECL__ short int __internal_device_bfloat162short_rz(const __nv_bfloat16 h) +{ + short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rzi.s16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rzi.s16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ short int __bfloat162short_rz(const __nv_bfloat16 h) +{ + short int val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + val = __internal_device_bfloat162short_rz(h); +, + const float f = __bfloat162float(h); + const short int max_val = (short int)0x7fffU; + const short int min_val = (short int)0x8000U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + val = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + val = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + val = min_val; + } else { + val = static_cast(f); + } +) + return val; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ short int __bfloat162short_rd(const __nv_bfloat16 h) +{ + short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rmi.s16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rmi.s16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +__CUDA_BF16_DECL__ short int __bfloat162short_ru(const __nv_bfloat16 h) +{ + short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rpi.s16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rpi.s16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rn(const short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rn.bf16.s16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + const float f = static_cast(i); + return __float2bfloat16_rn(f); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rz(const short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rz.bf16.s16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_rz(__int2float_rz(static_cast(i))); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_rd(const short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rm.bf16.s16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_rd(__int2float_rd(static_cast(i))); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __short2bfloat16_ru(const short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rp.bf16.s16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_ru(__int2float_ru(static_cast(i))); +) +} + +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_rn(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned int val; + asm("{ cvt.rni.u32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); + return val; +, + return __float2uint_rn(__bfloat162float(h)); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned int __internal_bfloat162uint_rz(const __nv_bfloat16 h) +{ + const float f = __bfloat162float(h); + unsigned int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + i = __float2uint_rz(f); +, + const unsigned int max_val = 0xffffffffU; + const unsigned int min_val = 0U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = 0U; + } else if (f >= static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + i = static_cast(f); + } +) + return i; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned int __bfloat162uint_rz(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned int val; + asm("{ cvt.rzi.u32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); + return val; +, + return __internal_bfloat162uint_rz(h); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_rd(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned int val; + asm("{ cvt.rmi.u32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); + return val; +, + return __float2uint_rd(__bfloat162float(h)); +) +} +__CUDA_BF16_DECL__ unsigned int __bfloat162uint_ru(const __nv_bfloat16 h) +{ + unsigned int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{ cvt.rpi.u32.bf16 %0, %1;}\n" : "=r"(val) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rpi.u32.f32 %0, %1;" : "=r"(val) : "f"(f)); +) + return val; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_uint2bfloat16_rn(const unsigned int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rn.bf16.u32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + const float ru = __uint2float_ru(i); + const float rd = __uint2float_rd(i); + float rz = __uint2float_rz(i); + if (ru != rd) { + rz = __uint_as_float(__float_as_uint(rz) | 1U); + } + return __float2bfloat16_rn(rz); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rn(const unsigned int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_uint2bfloat16_rn(i); +, + const double d = static_cast(i); + return __double2bfloat16(d); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rz(const unsigned int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rz.bf16.u32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_rz(__uint2float_rz(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_rd(const unsigned int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rm.bf16.u32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_rd(__uint2float_rd(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __uint2bfloat16_ru(const unsigned int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rp.bf16.u32 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "r"(i)); + return val; +, + return __float2bfloat16_ru(__uint2float_ru(i)); +) +} + +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_rn(const __nv_bfloat16 h) +{ + unsigned short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rni.u16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rni.u16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} + +__CUDA_BF16_DECL__ unsigned short int __internal_device_bfloat162ushort_rz(const __nv_bfloat16 h) +{ + unsigned short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rzi.u16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rzi.u16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned short int __bfloat162ushort_rz(const __nv_bfloat16 h) +{ + unsigned short int val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + val = __internal_device_bfloat162ushort_rz(h); +, + const float f = __bfloat162float(h); + const unsigned short int max_val = 0xffffU; + const unsigned short int min_val = 0U; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + val = 0U; + } else if (f > static_cast(max_val)) { + // saturate maximum + val = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + val = min_val; + } else { + val = static_cast(f); + } +) + return val; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_rd(const __nv_bfloat16 h) +{ + unsigned short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rmi.u16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rmi.u16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +__CUDA_BF16_DECL__ unsigned short int __bfloat162ushort_ru(const __nv_bfloat16 h) +{ + unsigned short int val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rpi.u16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +, + asm("{ .reg.f32 f;\n" + " mov.b32 f, {0,%1};\n" + " cvt.rpi.u16.f32 %0,f;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(h))); +) + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rn(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rn.bf16.u16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + const float f = static_cast(i); + return __float2bfloat16_rn(f); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rz(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rz.bf16.u16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_rz(__uint2float_rz(static_cast(i))); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_rd(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rm.bf16.u16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_rd(__uint2float_rd(static_cast(i))); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ushort2bfloat16_ru(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 val; + asm("cvt.rp.bf16.u16 %0, %1;" : "=h"(__BFLOAT16_TO_US(val)) : "h"(i)); + return val; +, + return __float2bfloat16_ru(__uint2float_ru(static_cast(i))); +) +} + +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_rn(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned long long int i; + asm("cvt.rni.u64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); + return i; +, + return __float2ull_rn(__bfloat162float(h)); +) +} + +__CUDA_BF16_DECL__ unsigned long long int __internal_device_bfloat162ull_rz(const __nv_bfloat16 h) +{ + unsigned long long int i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rzi.u64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + i = __float2ull_rz(f); +) + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned long long int __bfloat162ull_rz(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_bfloat162ull_rz(h); +, + const float f = __bfloat162float(h); + unsigned long long int i; + const unsigned long long int max_val = 0xffffffffffffffffULL; + const unsigned long long int min_val = 0ULL; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = 0x8000000000000000ULL; + } else if (f >= static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + i = static_cast(f); + } + return i; +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_rd(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned long long int i; + asm("cvt.rmi.u64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); + return i; +, + return __float2ull_rd(__bfloat162float(h)); +) +} +__CUDA_BF16_DECL__ unsigned long long int __bfloat162ull_ru(const __nv_bfloat16 h) +{ + unsigned long long int i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rpi.u64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rpi.u64.f32 %0, %1;" : "=l"(i) : "f"(f)); +) + return i; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_ull2bfloat16_rn(const unsigned long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rn.bf16.u64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + const float ru = __ull2float_ru(i); + const float rd = __ull2float_rd(i); + float rz = __ull2float_rz(i); + if (ru != rd) { + rz = __uint_as_float(__float_as_uint(rz) | 1U); + } + return __float2bfloat16_rn(rz); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rn(const unsigned long long int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_ull2bfloat16_rn(i); +, + float f = static_cast(i); + const unsigned long long int uf = static_cast(f); + unsigned int u = __internal_float_as_uint(f); + // round up happened here + // note: no need to handle round up to f == 0x1.p64 specially + if (uf > i) { + u--; + } + if (uf != i) { + u |= 1U; + } + f = __internal_uint_as_float(u); + return __float2bfloat16_rn(f); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rz(const unsigned long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rz.bf16.u64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_rz(__ull2float_rz(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_rd(const unsigned long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rm.bf16.u64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_rd(__ull2float_rd(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ull2bfloat16_ru(const unsigned long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rp.bf16.u64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_ru(__ull2float_ru(i)); +) +} +__CUDA_BF16_DECL__ long long int __bfloat162ll_rn(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + long long int i; + asm("cvt.rni.s64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); + return i; +, + return __float2ll_rn(__bfloat162float(h)); +) +} + +__CUDA_BF16_DECL__ long long int __internal_device_bfloat162ll_rz(const __nv_bfloat16 h) +{ + long long int i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rzi.s64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + i = __float2ll_rz(f); +) + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ long long int __bfloat162ll_rz(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_bfloat162ll_rz(h); +, + long long int i; + const float f = __bfloat162float(h); + const long long int max_val = (long long int)0x7fffffffffffffffULL; + const long long int min_val = (long long int)0x8000000000000000ULL; + const unsigned short bits = static_cast(static_cast<__nv_bfloat16_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xFF00U) { + // NaN + i = min_val; + } else if (f >= static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + i = static_cast(f); + } + return i; +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ long long int __bfloat162ll_rd(const __nv_bfloat16 h) +{ + long long int i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rmi.s64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rmi.s64.f32 %0, %1;" : "=l"(i) : "f"(f)); +) + return i; +} +__CUDA_BF16_DECL__ long long int __bfloat162ll_ru(const __nv_bfloat16 h) +{ + long long int i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("cvt.rpi.s64.bf16 %0, %1;" : "=l"(i) : "h"(__BFLOAT16_TO_CUS(h))); +, + const float f = __bfloat162float(h); + asm("cvt.rpi.s64.f32 %0, %1;" : "=l"(i) : "f"(f)); +) + return i; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_ll2bfloat16_rn(const long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rn.bf16.s64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + const float ru = __ll2float_ru(i); + const float rd = __ll2float_rd(i); + float rz = __ll2float_rz(i); + if (ru != rd) { + rz = __uint_as_float(__float_as_uint(rz) | 1U); + } + return __float2bfloat16_rn(rz); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rn(const long long int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_ll2bfloat16_rn(i); +, + float f = static_cast(i); + const long long int lf = static_cast(f); + unsigned int u = __internal_float_as_uint(f); + + if ((f > 0.0f) && (lf > i)) { + u--; + } + if ((f < 0.0f) && (lf < i)) { + u--; + } + if (lf != i) { + u |= 1U; + } + + f = __internal_uint_as_float(u); + return __float2bfloat16_rn(f); +) +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rz(const long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rz.bf16.s64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_rz(__ll2float_rz(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_rd(const long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rm.bf16.s64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_rd(__ll2float_rd(i)); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ll2bfloat16_ru(const long long int i) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 h; + asm("cvt.rp.bf16.s64 %0, %1;" : "=h"(__BFLOAT16_TO_US(h)) : "l"(i)); + return h; +, + return __float2bfloat16_ru(__ll2float_ru(i)); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat16 htrunc(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm("cvt.rzi.bf16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(h))); + return r; +, + return __float2bfloat16_rz(truncf(__bfloat162float(h))); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hceil(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm("cvt.rpi.bf16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(h))); + return r; +, + float fh = __bfloat162float(h); + asm( "{ cvt.rpi.f32.f32 %0, %0; }\n" + :"+f"(fh)); + return __float2bfloat16_rz(fh); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hfloor(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm("cvt.rmi.bf16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(h))); + return r; +, + float fh = __bfloat162float(h); + asm( "{ cvt.rmi.f32.f32 %0, %0; }\n" + :"+f"(fh)); + return __float2bfloat16_rz(fh); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hrint(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm("cvt.rni.bf16.bf16 %0, %1;" : "=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(h))); + return r; +, + return __float2bfloat16_rz(rintf(__bfloat162float(h))); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat162 h2trunc(const __nv_bfloat162 h) +{ + const __nv_bfloat16 low = htrunc(h.x); + const __nv_bfloat16 high = htrunc(h.y); + return __nv_bfloat162(low, high); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2ceil(const __nv_bfloat162 h) +{ + const __nv_bfloat16 low = hceil(h.x); + const __nv_bfloat16 high = hceil(h.y); + return __nv_bfloat162(low, high); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2floor(const __nv_bfloat162 h) +{ + const __nv_bfloat16 low = hfloor(h.x); + const __nv_bfloat16 high = hfloor(h.y); + return __nv_bfloat162(low, high); +} + +__CUDA_BF16_DECL__ __nv_bfloat162 h2rint(const __nv_bfloat162 h) +{ + return __halves2bfloat162(hrint(__low2bfloat16(h)), hrint(__high2bfloat16(h))); +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __lows2bfloat162(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 alow,ahigh,blow,bhigh;\n" + " mov.b32 {alow,ahigh}, %1;\n" + " mov.b32 {blow,bhigh}, %2;\n" + " mov.b32 %0, {alow,blow};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)), "r"(__BFLOAT162_TO_CUI(b))); +, + val.x = a.x; + val.y = b.x; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __highs2bfloat162(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 alow,ahigh,blow,bhigh;\n" + " mov.b32 {alow,ahigh}, %1;\n" + " mov.b32 {blow,bhigh}, %2;\n" + " mov.b32 %0, {ahigh,bhigh};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)), "r"(__BFLOAT162_TO_CUI(b))); +, + val.x = a.y; + val.y = b.y; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __low2bfloat16(const __nv_bfloat162 a) +{ + __nv_bfloat16 ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b16 %0, low;}" : "=h"(__BFLOAT16_TO_US(ret)) : "r"(__BFLOAT162_TO_CUI(a))); +, + ret = a.x; +) + return ret; +} +__CUDA_HOSTDEVICE_BF16_DECL__ int __hisinf(const __nv_bfloat16 a) +{ + int retval; + const __nv_bfloat16_raw araw = __nv_bfloat16_raw(a); + if (araw.x == 0xFF80U) { + retval = -1; + } else if (araw.x == 0x7F80U) { + retval = 1; + } else { + retval = 0; + } + return retval; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __low2bfloat162(const __nv_bfloat162 a) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {low,low};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); +, + val.x = a.x; + val.y = a.x; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __high2bfloat162(const __nv_bfloat162 a) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {high,high};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); +, + val.x = a.y; + val.y = a.y; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __high2bfloat16(const __nv_bfloat162 a) +{ + __nv_bfloat16 ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b16 %0, high;}" : "=h"(__BFLOAT16_TO_US(ret)) : "r"(__BFLOAT162_TO_CUI(a))); +, + ret = a.y; +) + return ret; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __halves2bfloat162(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ mov.b32 %0, {%1,%2};}\n" + : "=r"(__BFLOAT162_TO_UI(val)) : "h"(__BFLOAT16_TO_CUS(a)), "h"(__BFLOAT16_TO_CUS(b))); +, + val.x = a; + val.y = b; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __bfloat162bfloat162(const __nv_bfloat16 a) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ mov.b32 %0, {%1,%1};}\n" + : "=r"(__BFLOAT162_TO_UI(val)) : "h"(__BFLOAT16_TO_CUS(a))); +, + val.x = a; + val.y = a; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __lowhigh2highlow(const __nv_bfloat162 a) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .b16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {high,low};}\n" : "=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); +, + val.x = a.y; + val.y = a.x; +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ short int __bfloat16_as_short(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return static_cast(__BFLOAT16_TO_CUS(h)); +, + return static_cast(__nv_bfloat16_raw(h).x); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned short int __bfloat16_as_ushort(const __nv_bfloat16 h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __BFLOAT16_TO_CUS(h); +, + return __nv_bfloat16_raw(h).x; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __short_as_bfloat16(const short int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __nv_bfloat16 h; + __BFLOAT16_TO_US(h) = static_cast(i); + return h; +, + __nv_bfloat16_raw hr; + hr.x = static_cast(i); + return __nv_bfloat16(hr); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __ushort_as_bfloat16(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __nv_bfloat16 h; + __BFLOAT16_TO_US(h) = i; + return h; +, + __nv_bfloat16_raw hr; + hr.x = i; + return __nv_bfloat16(hr); +) +} + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300))) || defined(_NVHPC_CUDA) +/****************************************************************************** +* __nv_bfloat16, __nv_bfloat162 warp shuffle * +******************************************************************************/ +#define __SHUFFLE_SYNC_BFLOAT162_MACRO(name) /* do */ {\ + __nv_bfloat162 r; \ + asm volatile ("{" __CUDA_BF16_STRINGIFY(name) " %0,%1,%2,%3,%4;\n}" \ + :"=r"(__BFLOAT162_TO_UI(r)): "r"(__BFLOAT162_TO_CUI(var)), "r"(delta), "r"(c), "r"(mask)); \ + return r; \ +} /* while(0) */ + +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_sync(const unsigned mask, const __nv_bfloat162 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_BFLOAT162_MACRO(shfl.sync.idx.b32) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_up_sync(const unsigned mask, const __nv_bfloat162 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = (warp_size - static_cast(width)) << 8U; + __SHUFFLE_SYNC_BFLOAT162_MACRO(shfl.sync.up.b32) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_down_sync(const unsigned mask, const __nv_bfloat162 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_BFLOAT162_MACRO(shfl.sync.down.b32) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __shfl_xor_sync(const unsigned mask, const __nv_bfloat162 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_BFLOAT162_MACRO(shfl.sync.bfly.b32) +} + +#undef __SHUFFLE_SYNC_BFLOAT162_MACRO + +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_sync(const unsigned mask, const __nv_bfloat16 var, const int delta, const int width) +{ + const __nv_bfloat162 temp1 = __halves2bfloat162(var, var); + const __nv_bfloat162 temp2 = __shfl_sync(mask, temp1, delta, width); + return __low2bfloat16(temp2); +} +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_up_sync(const unsigned mask, const __nv_bfloat16 var, const unsigned int delta, const int width) +{ + const __nv_bfloat162 temp1 = __halves2bfloat162(var, var); + const __nv_bfloat162 temp2 = __shfl_up_sync(mask, temp1, delta, width); + return __low2bfloat16(temp2); +} +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_down_sync(const unsigned mask, const __nv_bfloat16 var, const unsigned int delta, const int width) +{ + const __nv_bfloat162 temp1 = __halves2bfloat162(var, var); + const __nv_bfloat162 temp2 = __shfl_down_sync(mask, temp1, delta, width); + return __low2bfloat16(temp2); +} +__CUDA_BF16_DECL__ __nv_bfloat16 __shfl_xor_sync(const unsigned mask, const __nv_bfloat16 var, const int delta, const int width) +{ + const __nv_bfloat162 temp1 = __halves2bfloat162(var, var); + const __nv_bfloat162 temp2 = __shfl_xor_sync(mask, temp1, delta, width); + return __low2bfloat16(temp2); +} + +/****************************************************************************** +* __nv_bfloat16 and __nv_bfloat162 __ldg,__ldcg,__ldca,__ldcs * +******************************************************************************/ + +#if (defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__) +#define __LDG_PTR "l" +#else +#define __LDG_PTR "r" +#endif /*(defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__)*/ +__CUDA_BF16_DECL__ __nv_bfloat162 __ldg(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.nc.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldg(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.nc.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcg(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.cg.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcg(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.cg.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __ldca(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.ca.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldca(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.ca.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcs(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.cs.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcs(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.cs.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __ldlu(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.lu.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldlu(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.lu.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __ldcv(const __nv_bfloat162 *const ptr) +{ + __nv_bfloat162 ret; + asm ("ld.global.cv.b32 %0, [%1];" : "=r"(__BFLOAT162_TO_UI(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __ldcv(const __nv_bfloat16 *const ptr) +{ + __nv_bfloat16 ret; + asm ("ld.global.cv.b16 %0, [%1];" : "=h"(__BFLOAT16_TO_US(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} + +__CUDA_BF16_DECL__ void __stwb(__nv_bfloat162 *const ptr, const __nv_bfloat162 value) +{ + asm ("st.global.wb.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__BFLOAT162_TO_CUI(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stwb(__nv_bfloat16 *const ptr, const __nv_bfloat16 value) +{ + asm ("st.global.wb.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__BFLOAT16_TO_CUS(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stcg(__nv_bfloat162 *const ptr, const __nv_bfloat162 value) +{ + asm ("st.global.cg.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__BFLOAT162_TO_CUI(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stcg(__nv_bfloat16 *const ptr, const __nv_bfloat16 value) +{ + asm ("st.global.cg.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__BFLOAT16_TO_CUS(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stcs(__nv_bfloat162 *const ptr, const __nv_bfloat162 value) +{ + asm ("st.global.cs.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__BFLOAT162_TO_CUI(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stcs(__nv_bfloat16 *const ptr, const __nv_bfloat16 value) +{ + asm ("st.global.cs.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__BFLOAT16_TO_CUS(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stwt(__nv_bfloat162 *const ptr, const __nv_bfloat162 value) +{ + asm ("st.global.wt.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__BFLOAT162_TO_CUI(value)) : "memory"); +} +__CUDA_BF16_DECL__ void __stwt(__nv_bfloat16 *const ptr, const __nv_bfloat16 value) +{ + asm ("st.global.wt.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__BFLOAT16_TO_CUS(value)) : "memory"); +} + +#undef __LDG_PTR +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300))) || defined(_NVHPC_CUDA) */ +/****************************************************************************** +* __nv_bfloat162 comparison * +******************************************************************************/ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +#define __COMPARISON_OP_BFLOAT162_MACRO(name) {\ + __nv_bfloat162 val; \ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90,\ + asm( "{ " __CUDA_BF16_STRINGIFY(name) ".bf16x2.bf16x2 %0,%1,%2;\n}" \ + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); \ +,\ + asm( "{.reg .b32 low_a,low_b,high_a,high_b,high_res,low_res;\n"\ + " and.b32 high_a, %1, 0xffff0000U;\n"\ + " and.b32 high_b, %2, 0xffff0000U;\n"\ + " shl.b32 low_a, %1, 16;\n"\ + " shl.b32 low_b, %2, 16;\n"\ + " " __CUDA_BF16_STRINGIFY(name) ".f32.f32 low_res, low_a, low_b;\n"\ + " " __CUDA_BF16_STRINGIFY(name) ".f32.f32 high_res, high_a, high_b;\n"\ + " shr.u32 low_res, low_res, 16;\n"\ + " or.b32 %0, high_res, low_res;}\n"\ + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); \ +)\ + return val; \ +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_heq2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.eq) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hne2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.ne) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hle2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.le) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hge2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.ge) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hlt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.lt) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hgt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.gt) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hequ2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.equ) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hneu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.neu) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hleu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.leu) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hgeu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.geu) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hltu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.ltu) +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hgtu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __COMPARISON_OP_BFLOAT162_MACRO(set.gtu) +} +#undef __COMPARISON_OP_BFLOAT162_MACRO +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __heq2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_heq2(a, b); +, + __nv_bfloat162_raw val; + val.x = __heq(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __heq(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hne2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hne2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hne(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hne(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hle2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hle2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hle(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hle(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hge2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hge2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hge(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hge(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hlt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hlt2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hlt(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hlt(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hgt2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hgt(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hgt(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hequ2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hequ2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hequ(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hequ(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hneu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hneu2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hneu(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hneu(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hleu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hleu2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hleu(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hleu(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgeu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hgeu2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hgeu(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hgeu(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hltu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hltu2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hltu(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hltu(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hgtu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hgtu2(a, b); +, + __nv_bfloat162_raw val; + val.x = __hgtu(a.x, b.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hgtu(a.y, b.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + return __nv_bfloat162(val); +) +} + +/****************************************************************************** +* __nv_bfloat162 comparison with mask output * +******************************************************************************/ +#define __COMPARISON_OP_BFLOAT162_MACRO_MASK(name) {\ + unsigned val; \ + asm( "{ " __CUDA_BF16_STRINGIFY(name) ".u32.bf16x2 %0,%1,%2;\n}" \ + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); \ + return val; \ +} + +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __heq2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.eq) +, + const unsigned short px = __heq(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __heq(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hne2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.ne) +, + const unsigned short px = __hne(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hne(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hle2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.le) +, + const unsigned short px = __hle(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hle(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hge2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.ge) +, + const unsigned short px = __hge(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hge(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hlt2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.lt) +, + const unsigned short px = __hlt(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hlt(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgt2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.gt) +, + const unsigned short px = __hgt(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgt(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hequ2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.equ) +, + const unsigned short px = __hequ(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hequ(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hneu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.neu) +, + const unsigned short px = __hneu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hneu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hleu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.leu) +, + const unsigned short px = __hleu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hleu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgeu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.geu) +, + const unsigned short px = __hgeu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgeu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hltu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.ltu) +, + const unsigned short px = __hltu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hltu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ unsigned __hgtu2_mask(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __COMPARISON_OP_BFLOAT162_MACRO_MASK(set.gtu) +, + const unsigned short px = __hgtu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgtu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +#undef __COMPARISON_OP_BFLOAT162_MACRO_MASK + +#define __BOOL_COMPARISON_OP_BFLOAT162_MACRO(name) {\ + unsigned int val; \ + bool retval; \ + asm( "{ " __CUDA_BF16_STRINGIFY(name) ".bf16x2.bf16x2 %0,%1,%2;\n}" \ + :"=r"(val) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); \ + if (val == 0x3F803F80U) {\ + retval = true; \ + } else { \ + retval = false; \ + }\ + return retval;\ +} + +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbeq2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.eq) +, + return (__heq(a.x, b.x) && __heq(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbne2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.ne) +, + return (__hne(a.x, b.x) && __hne(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hble2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.le) +, + return (__hle(a.x, b.x) && __hle(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbge2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.ge) +, + return (__hge(a.x, b.x) && __hge(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hblt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.lt) +, + return (__hlt(a.x, b.x) && __hlt(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgt2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.gt) +, + return (__hgt(a.x, b.x) && __hgt(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbequ2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.equ) +, + return (__hequ(a.x, b.x) && __hequ(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbneu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.neu) +, + return (__hneu(a.x, b.x) && __hneu(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbleu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.leu) +, + return (__hleu(a.x, b.x) && __hleu(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgeu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.geu) +, + return (__hgeu(a.x, b.x) && __hgeu(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbltu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.ltu) +, + return (__hltu(a.x, b.x) && __hltu(a.y, b.y)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hbgtu2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __BOOL_COMPARISON_OP_BFLOAT162_MACRO(set.gtu) +, + return (__hgtu(a.x, b.x) && __hgtu(a.y, b.y)); +) +} +#undef __BOOL_COMPARISON_OP_BFLOAT162_MACRO +/****************************************************************************** +* __nv_bfloat16 comparison * +******************************************************************************/ +#define __COMPARISON_OP_BFLOAT16_MACRO(name) {\ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90,\ + unsigned short val; \ + asm( "{ .reg .pred __$temp3;\n" \ + " setp." __CUDA_BF16_STRINGIFY(name) ".bf16 __$temp3, %1, %2;\n" \ + " selp.u16 %0, 1, 0, __$temp3;}" \ + : "=h"(val) : "h"(__BFLOAT16_TO_CUS(a)), "h"(__BFLOAT16_TO_CUS(b))); \ + return (val != 0U) ? true : false; \ +,\ + unsigned int val; \ + asm( "{.reg .b32 a,b;\n"\ + " mov.b32 a, {0, %1};\n"\ + " mov.b32 b, {0, %2};\n"\ + " set." __CUDA_BF16_STRINGIFY(name) ".f32.f32 %0, a, b;}\n"\ + :"=r"(val) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); \ + return (val != 0U) ? true : false; \ +)\ +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __heq(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(eq) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa == fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hne(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(ne) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa != fb) && (!__hisnan(a)) && (!__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hle(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(le) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa <= fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hge(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(ge) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa >= fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hlt(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(lt) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa < fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgt(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(gt) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa > fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hequ(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(equ) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa == fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hneu(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(neu) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa != fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hleu(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(leu) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa <= fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgeu(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(geu) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa >= fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hltu(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(ltu) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa < fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hgtu(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __COMPARISON_OP_BFLOAT16_MACRO(gtu) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return (fa > fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +#undef __COMPARISON_OP_BFLOAT16_MACRO +/****************************************************************************** +* __nv_bfloat162 arithmetic * +******************************************************************************/ +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hadd2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ add.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0x3f803f80U;\n" + " fma.rn.bf16x2 %0,%1,c,%2;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} + +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hsub2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ sub.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0xbf80bf80U;\n" + " fma.rn.bf16x2 %0,%2,c,%1;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hmul2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ mul.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0x80008000U;\n" + " fma.rn.bf16x2 %0,%1,%2,c;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hadd2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ add.rn.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0x3f803f80U;\n" + " fma.rn.bf16x2 %0,%1,c,%2;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hsub2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ sub.rn.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0xbf80bf80U;\n" + " fma.rn.bf16x2 %0,%2,c,%1;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __internal_device_hmul2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ mul.rn.bf16x2 %0,%1,%2; }\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + asm( "{.reg .b32 c;\n" + " mov.b32 c, 0x80008000U;\n" + " fma.rn.bf16x2 %0,%1,%2,c;}\n" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +) + return val; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hadd2(a, b); +, + val.x = __hadd(a.x, b.x); + val.y = __hadd(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hsub2(a, b); +, + val.x = __hsub(a.x, b.x); + val.y = __hsub(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hmul2(a, b); +, + val.x = __hmul(a.x, b.x); + val.y = __hmul(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hadd2_rn(a, b); +, + val.x = __hadd_rn(a.x, b.x); + val.y = __hadd_rn(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hsub2_rn(a, b); +, + val.x = __hsub_rn(a.x, b.x); + val.y = __hsub_rn(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2_rn(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_device_hmul2_rn(a, b); +, + val.x = __hmul_rn(a.x, b.x); + val.y = __hmul_rn(a.y, b.y); +) + return val; +} + +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hadd2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{.reg .b32 f, one, zero;\n" + " mov.b32 one, 0x3f803f80U;\n" + " mov.b32 zero, 0;\n" + " fma.rn.bf16x2 f,%1,one,%2;\n" + " max.bf16x2 f, f, zero;\n" + " min.bf16x2 %0, f, one;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + val.x = __hadd_sat(a.x, b.x); + val.y = __hadd_sat(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hsub2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{.reg .b32 f, one, zero, mone;\n" + " mov.b32 one, 0x3f803f80U;\n" + " mov.b32 zero, 0;\n" + " mov.b32 mone, 0xbf80bf80U;\n" + " fma.rn.bf16x2 f,%2,mone,%1;\n" + " max.bf16x2 f, f, zero;\n" + " min.bf16x2 %0, f, one;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + val.x = __hsub_sat(a.x, b.x); + val.y = __hsub_sat(a.y, b.y); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmul2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ + __nv_bfloat162 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{.reg .b32 f, one, zero, mzero;\n" + " mov.b32 one, 0x3f803f80U;\n" + " mov.b32 zero, 0;\n" + " mov.b32 mzero, 0x80008000U;\n" + " fma.rn.bf16x2 f,%1,%2,mzero;\n" + " max.bf16x2 f, f, zero;\n" + " min.bf16x2 %0, f, one;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); +, + val.x = __hmul_sat(a.x, b.x); + val.y = __hmul_sat(a.y, b.y); +) + return val; +} +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c) +{ + __nv_bfloat162 val; + asm( "{fma.rn.bf16x2 %0,%1,%2,%3;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b)),"r"(__BFLOAT162_TO_CUI(c))); + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2_sat(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c) +{ + __nv_bfloat162 val; + asm( "{ .reg .b32 f, one, zero;\n" + " mov.b32 one, 0x3f803f80U;\n" + " mov.b32 zero, 0;\n" + " fma.rn.bf16x2 f, %1, %2, %3;\n" + " max.bf16x2 f, f, zero;\n" + " min.bf16x2 %0, f, one;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b)),"r"(__BFLOAT162_TO_CUI(c))); + return val; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __h2div(const __nv_bfloat162 a, const __nv_bfloat162 b) { + __nv_bfloat16 ha, hb; + + ha = __low2bfloat16(a); + hb = __low2bfloat16(b); + + const __nv_bfloat16 v1 = __hdiv(ha, hb); + + ha = __high2bfloat16(a); + hb = __high2bfloat16(b); + + const __nv_bfloat16 v2 = __hdiv(ha, hb); + + return __halves2bfloat162(v1, v2); +} +/****************************************************************************** +* __nv_bfloat16 arithmetic * +******************************************************************************/ +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hadd(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ add.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0x3f80U;\n" + " fma.rn.bf16 %0,%1,c,%2;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hsub(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ sub.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0xbf80U;\n" + " fma.rn.bf16 %0,%2,c,%1;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hmul(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ mul.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0x8000U;\n" + " fma.rn.bf16 %0,%1,%2,c;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hadd_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ add.rn.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0x3f80U;\n" + " fma.rn.bf16 %0,%1,c,%2;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hsub_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ sub.rn.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0xbf80U;\n" + " fma.rn.bf16 %0,%2,c,%1;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_sm80_device_hmul_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm( "{ mul.rn.bf16 %0,%1,%2; }\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + asm( "{.reg .b16 c;\n" + " mov.b16 c, 0x8000U;\n" + " fma.rn.bf16 %0,%1,%2,c;}\n" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +) + return val; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_hadd(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_sm80_device_hadd(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + // avoid ftz in device code + val = __float2bfloat16(__fmaf_ieee_rn(fa, 1.0f, fb)); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_hsub(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_sm80_device_hsub(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + // avoid ftz in device code + val = __float2bfloat16(__fmaf_ieee_rn(fb, -1.0f, fa)); +) + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_hmul(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + val = __internal_sm80_device_hmul(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + // avoid ftz in device code + val = __float2bfloat16(__fmaf_ieee_rn(fa, fb, -0.0f)); +) + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hadd(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return __float2bfloat16(fa + fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hsub(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return __float2bfloat16(fa - fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hmul(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return __float2bfloat16(fa * fb); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + return __internal_sm80_device_hadd_rn(a, b); +, + return __hadd(a, b); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + return __internal_sm80_device_hsub_rn(a, b); +, + return __hsub(a, b); + +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul_rn(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + return __internal_sm80_device_hmul_rn(a, b); +, + return __hmul(a, b); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hadd_sat(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{ .reg .b16 f, one, zero;\n" + " mov.b16 one, 0x3f80U;\n" + " mov.b16 zero, 0;\n" + " fma.rn.bf16 f, %1, one, %2;\n" + " max.bf16 f, f, zero;\n" + " min.bf16 %0, f, one;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + val = __hmin(__hmax(__hadd(a, b), CUDART_ZERO_BF16), CUDART_ONE_BF16); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hsub_sat(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{ .reg .b16 f, one, zero, mone;\n" + " mov.b16 one, 0x3f80U;\n" + " mov.b16 zero, 0;\n" + " mov.b16 mone, 0xbf80U;\n" + " fma.rn.bf16 f, %2, mone, %1;\n" + " max.bf16 f, f, zero;\n" + " min.bf16 %0, f, one;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + val = __hmin(__hmax(__hsub(a, b), CUDART_ZERO_BF16), CUDART_ONE_BF16); +) + return val; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmul_sat(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ + __nv_bfloat16 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm( "{ .reg .b16 f, one, zero, mzero;\n" + " mov.b16 one, 0x3f80U;\n" + " mov.b16 zero, 0;\n" + " mov.b16 mzero, 0x8000U;\n" + " fma.rn.bf16 f, %1, %2, mzero;\n" + " max.bf16 f, f, zero;\n" + " min.bf16 %0, f, one;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); +, + val = __hmin(__hmax(__hmul(a, b), CUDART_ZERO_BF16), CUDART_ONE_BF16); +) + return val; +} +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c) +{ + __nv_bfloat16 val; + asm( "{fma.rn.bf16 %0,%1,%2,%3;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b)),"h"(__BFLOAT16_TO_CUS(c))); + return val; +} +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma_sat(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c) +{ + __nv_bfloat16 val; + asm( "{ .reg .b16 f, one, zero;\n" + " mov.b16 one, 0x3f80U;\n" + " mov.b16 zero, 0;\n" + " fma.rn.bf16 f, %1, %2, %3;\n" + " max.bf16 f, f, zero;\n" + " min.bf16 %0, f, one;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b)),"h"(__BFLOAT16_TO_CUS(c))); + return val; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +#define __BINARY_OP_BFLOAT16_MACRO(name) /* do */ {\ + __nv_bfloat16 val; \ + asm( "{.reg .b32 a,b,res;\n"\ + " mov.b32 a, {0,%1};\n"\ + " mov.b32 b, {0,%2};\n"\ + " " __CUDA_BF16_STRINGIFY(name) ".f32 res, a, b;\n"\ + " cvt.rn.bf16.f32 %0, res;}\n"\ + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); \ + return val; \ +} /* while(0) */ +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_hdiv(const __nv_bfloat16 a, const __nv_bfloat16 b) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_BFLOAT16_MACRO(div.rn) +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + float fr; + asm( "{ div.rn.f32 %0, %1, %2; }\n" + :"=f"(fr) : "f"(fa),"f"(fb)); + return __float2bfloat16(fr); +) +} +#undef __BINARY_OP_BFLOAT16_MACRO +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hdiv(const __nv_bfloat16 a, const __nv_bfloat16 b) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hdiv(a, b); +, + const float fa = __bfloat162float(a); + const float fb = __bfloat162float(b); + return __float2bfloat16(fa / fb); +) +} + +/****************************************************************************** +* __nv_bfloat162 functions * +******************************************************************************/ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __hsin_internal(const __nv_bfloat16 a) { + float f = __bfloat162float(a); + float r = sinf(f); + // Detect compile-time FTZ setting: + // if subnormal constant is not flushed to zero at compile-time, then + // ftz=off, and it is safe to return result of sinf() + // Otherwise, ftz=on, then sinf() result is valid for non-flushed + // values, and subnormal input is returned unchanged via else + // branch. + if ((__uint_as_float(0x00000001U) > 0.0f) || (f != 0.0f)) + { + f = r; + } + return __float2bfloat16_rn(f); +} +__CUDA_BF16_DECL__ __nv_bfloat16 hsin(const __nv_bfloat16 a) { + return __hsin_internal(a); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2sin(const __nv_bfloat162 a) { + const __nv_bfloat16 l = __low2bfloat16(a); + const __nv_bfloat16 h = __high2bfloat16(a); + return __halves2bfloat162(__hsin_internal(l), __hsin_internal(h)); +} +__CUDA_BF16_DECL__ __nv_bfloat16 __hcos_internal(const __nv_bfloat16 a) { + float f = __bfloat162float(a); + f = cosf(f); + return __float2bfloat16_rn(f); +} +__CUDA_BF16_DECL__ __nv_bfloat16 hcos(const __nv_bfloat16 a) { + return __hcos_internal(a); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2cos(const __nv_bfloat162 a) { + const __nv_bfloat16 l = __low2bfloat16(a); + const __nv_bfloat16 h = __high2bfloat16(a); + return __halves2bfloat162(__hcos_internal(l), __hcos_internal(h)); +} + +__CUDA_BF16_DECL__ float __internal_device_fast_bf16exp(const float x) +{ + const float log2e_up = __uint_as_float(0x3FB8AA3CU); + float fa = x * log2e_up; + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fa)); + return fa; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 hexp(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + fa = __internal_device_fast_bf16exp(fa); + return __float2bfloat16_rn(fa); +} + +#define __APPROX_FCAST2(fun) /* do */ {\ + __nv_bfloat162 val;\ + asm("{.reg.b16 hl, hu; \n"\ + " .reg.b32 fl, fu; \n"\ + " mov.b32 {hl, hu}, %1; \n"\ + " mov.b32 fl, {0,hl}; \n"\ + " mov.b32 fu, {0,hu}; \n"\ + " " __CUDA_BF16_STRINGIFY(fun) ".approx.f32 fl, fl; \n"\ + " " __CUDA_BF16_STRINGIFY(fun) ".approx.f32 fu, fu; \n"\ + " cvt.rn.bf16.f32 hl, fl; \n"\ + " cvt.rn.bf16.f32 hu, fu; \n"\ + " mov.b32 %0, {hl, hu}; \n"\ + "}":"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); \ + return val;\ +} /* while(0) */ +#define __BF16_SPEC_CASE2(i,r, spc, ulp) \ + "{.reg.b32 spc, ulp, p;\n"\ + " mov.b32 spc," __CUDA_BF16_STRINGIFY(spc) ";\n"\ + " mov.b32 ulp," __CUDA_BF16_STRINGIFY(ulp) ";\n"\ + " set.eq.f16x2.f16x2 p," __CUDA_BF16_STRINGIFY(i) ", spc;\n"\ + " fma.rn.bf16x2 " __CUDA_BF16_STRINGIFY(r) ",p,ulp," __CUDA_BF16_STRINGIFY(r) ";\n}\n" + +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 h,r,fl,fu, C; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " mov.b32 fl, {0,hl}; \n" + " mov.b32 fu, {0,hu}; \n" + " mov.b32 C, 0x3FB8AA3CU; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " ex2.approx.f32 fl, fl; \n" + " ex2.approx.f32 fu, fu; \n" + " cvt.rn.bf16.f32 hl, fl; \n" + " cvt.rn.bf16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + " mov.b32 %0, r; \n" + "}":"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); + return val; +, + return __floats2bfloat162_rn( __internal_device_fast_bf16exp(__low2float(a)), __internal_device_fast_bf16exp(__high2float(a)) ); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hexp2(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fa)); + return __float2bfloat16_rn(fa); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp2(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __APPROX_FCAST2(ex2) +, + float fl = __low2float(a); + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fl)); + float fh = __high2float(a); + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fh)); + return __floats2bfloat162_rn( fl, fh ); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat16 hexp10(const __nv_bfloat16 a) { + const float log10_2 = __uint_as_float(0x40549A78U); + float fa = __bfloat162float(a) * log10_2; + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fa)); + __nv_bfloat16 r = __float2bfloat16_rn(fa); + __nv_bfloat16_raw araw = static_cast<__nv_bfloat16_raw>(a); + if (araw.x == (unsigned short)0xBC95U) + { + araw.x = 0x3f75U; + r = static_cast<__nv_bfloat16>(araw); + } + return r; +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2exp10(const __nv_bfloat162 a) { + __nv_bfloat162 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 h,r,fl,fu, C; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 fl, {0,hl}; \n" + " mov.b32 fu, {0,hu}; \n" + " mov.b32 C, 0x40549A78U; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " ex2.approx.f32 fl, fl; \n" + " ex2.approx.f32 fu, fu; \n" + " cvt.rn.bf16.f32 hl, fl; \n" + " cvt.rn.bf16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __BF16_SPEC_CASE2(%1, r, 0xBC95BC95U,0xBF00BF00U) + " mov.b32 %0, r; \n" + "}":"=r"(__BFLOAT162_TO_UI(r)) : "r"(__BFLOAT162_TO_CUI(a))); +, + const float log10_2 = __uint_as_float(0x40549A78U); + float fl = __low2float(a) * log10_2; + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fl)); + + float fh = __high2float(a) * log10_2; + asm("{ ex2.approx.f32 %0, %0; }" : "+f"(fh)); + + r = __floats2bfloat162_rn( fl, fh ); + + const __nv_bfloat162_raw araw = static_cast<__nv_bfloat162_raw>(a); + if (araw.x == (unsigned short)0xBC95U) + { + __nv_bfloat16_raw raw_fix; + raw_fix.x = (unsigned short)0x3f75U; + r.x = static_cast<__nv_bfloat16>(raw_fix); + } + if (araw.y == (unsigned short)0xBC95U) + { + __nv_bfloat16_raw raw_fix; + raw_fix.x = (unsigned short)0x3f75U; + r.y = static_cast<__nv_bfloat16>(raw_fix); + } +) + return r; +} + +__CUDA_BF16_DECL__ float __internal_device_fast_bf16log2(float x) +{ + asm("{ lg2.approx.f32 %0, %0; }" : "+f"(x)); + return x; +} + +__CUDA_BF16_DECL__ __nv_bfloat16 hlog2(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + fa = __internal_device_fast_bf16log2(fa); + return __float2bfloat16_rn(fa); +} + +__CUDA_BF16_DECL__ __nv_bfloat162 h2log2(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __APPROX_FCAST2(lg2) +, + float fl = __low2float(a); + fl = __internal_device_fast_bf16log2(fl); + float fh = __high2float(a); + fh = __internal_device_fast_bf16log2(fh); + return __floats2bfloat162_rn( fl, fh ); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat16 hlog(const __nv_bfloat16 a) { + const float flt_ln2 = __uint_as_float(0x3f317218U); + float fa = __bfloat162float(a); + fa = __internal_device_fast_bf16log2(fa); + fa = fa * flt_ln2; + return __float2bfloat16_rn(fa); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2log(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 r, fl, fu, C, h; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " mov.b32 fl, {0,hl}; \n" + " mov.b32 fu, {0,hu}; \n" + " lg2.approx.f32 fl, fl; \n" + " lg2.approx.f32 fu, fu; \n" + " mov.b32 C, 0x3f317218U; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " cvt.rn.bf16.f32 hl, fl; \n" + " cvt.rn.bf16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + " mov.b32 %0, r; \n" + "}":"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); + return val; +, + const float flt_ln2 = __uint_as_float(0x3f317218U); + + float fl = __low2float(a); + fl = __internal_device_fast_bf16log2(fl); + fl = fl * flt_ln2; + + float fh = __high2float(a); + fh = __internal_device_fast_bf16log2(fh); + fh = fh * flt_ln2; + + return __floats2bfloat162_rn( fl, fh ); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat16 hlog10(const __nv_bfloat16 a) { + const float flt_log10_2 = __uint_as_float(0x3E9A209BU); + float fa = __bfloat162float(a); + fa = __internal_device_fast_bf16log2(fa); + fa = fa * flt_log10_2; + return __float2bfloat16_rn(fa); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2log10(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 r, fl, fu, C, h; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " mov.b32 fl, {0,hl}; \n" + " mov.b32 fu, {0,hu}; \n" + " lg2.approx.f32 fl, fl; \n" + " lg2.approx.f32 fu, fu; \n" + " mov.b32 C, 0x3E9A209BU; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " cvt.rn.bf16.f32 hl, fl; \n" + " cvt.rn.bf16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + " mov.b32 %0, r; \n" + "}":"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a))); + return val; +, + const float flt_log10_2 = __uint_as_float(0x3E9A209BU); + + float fl = __low2float(a); + fl = __internal_device_fast_bf16log2(fl); + fl = fl * flt_log10_2; + + float fh = __high2float(a); + fh = __internal_device_fast_bf16log2(fh); + fh = fh * flt_log10_2; + + return __floats2bfloat162_rn( fl, fh ); +) +} + +__CUDA_BF16_DECL__ __nv_bfloat162 h2rcp(const __nv_bfloat162 a) { + float fl = __low2float(a); + asm("{ rcp.approx.f32 %0, %0; }" : "+f"(fl)); + float fh = __high2float(a); + asm("{ rcp.approx.f32 %0, %0; }" : "+f"(fh)); + return __floats2bfloat162_rn( fl, fh ); +} +__CUDA_BF16_DECL__ __nv_bfloat16 hrcp(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + asm("{ rcp.approx.f32 %0, %0; }" : "+f"(fa)); + return __float2bfloat16_rn(fa); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2rsqrt(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __APPROX_FCAST2(rsqrt) +, + float fl = __low2float(a); + asm("{ rsqrt.approx.f32 %0, %0; }" : "+f"(fl)); + float fh = __high2float(a); + asm("{ rsqrt.approx.f32 %0, %0; }" : "+f"(fh)); + return __floats2bfloat162_rn( fl, fh ); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hrsqrt(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + asm("{ rsqrt.approx.f32 %0, %0; }" : "+f"(fa)); + return __float2bfloat16_rn(fa); +} +__CUDA_BF16_DECL__ __nv_bfloat162 h2sqrt(const __nv_bfloat162 a) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __APPROX_FCAST2(sqrt) +, + float fl = __low2float(a); + asm("{ sqrt.approx.f32 %0, %0; }" : "+f"(fl)); + float fh = __high2float(a); + asm("{ sqrt.approx.f32 %0, %0; }" : "+f"(fh)); + return __floats2bfloat162_rn( fl, fh ); +) +} +__CUDA_BF16_DECL__ __nv_bfloat16 hsqrt(const __nv_bfloat16 a) { + float fa = __bfloat162float(a); + asm("{ sqrt.approx.f32 %0, %0; }" : "+f"(fa)); + return __float2bfloat16_rn(fa); +} +#undef __APPROX_FCAST2 +#undef __BF16_SPEC_CASE2 + +__CUDA_BF16_DECL__ bool __internal_device_hisnan(const __nv_bfloat16 a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm("{set.nan.bf16.bf16 %0,%1,%1;\n}" + :"=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(a))); + return __BFLOAT16_TO_CUS(r) != 0U; +, + unsigned int r; + asm( "{.reg .b32 a;\n" + " mov.b32 a, {0,%1};\n" + " set.nan.f32.f32 %0, a, a;}\n" + :"=r"(r) : "h"(__BFLOAT16_TO_CUS(a))); + return r != 0U; +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hisnan2(const __nv_bfloat162 a) +{ + __nv_bfloat162 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + asm("{set.nan.bf16x2.bf16x2 %0,%1,%1;\n}" + :"=r"(__BFLOAT162_TO_UI(r)) : "r"(__BFLOAT162_TO_CUI(a))); +, + __nv_bfloat162_raw val; + val.x = __hisnan(a.x) ? (unsigned short)0x3F80U : (unsigned short)0U; + val.y = __hisnan(a.y) ? (unsigned short)0x3F80U : (unsigned short)0U; + r = __nv_bfloat162(val); +) + return r; +} +__CUDA_HOSTDEVICE_BF16_DECL__ bool __hisnan(const __nv_bfloat16 a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hisnan(a); +, + const __nv_bfloat16_raw hr = static_cast<__nv_bfloat16_raw>(a); + return ((hr.x & 0x7FFFU) > 0x7F80U); +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hneg2(const __nv_bfloat162 a) +{ + __nv_bfloat162 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{neg.bf16x2 %0,%1;\n}" + :"=r"(__BFLOAT162_TO_UI(r)) : "r"(__BFLOAT162_TO_CUI(a))); +, + r.x = __hneg(a.x); + r.y = __hneg(a.y); +) + return r; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __internal_device_hneg(const __nv_bfloat16 a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 r; + asm("{neg.bf16 %0,%1;\n}" + :"=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(a))); + return r; +, + const float fa = __bfloat162float(a); + return __float2bfloat16(__fmaf_ieee_rn(fa, -1.0f, -0.0f)); +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hneg(const __nv_bfloat16 a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hneg(a); +, + const float fa = __bfloat162float(a); + return __float2bfloat16(-fa); +) +} + +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __habs2(const __nv_bfloat162 a) +{ + __nv_bfloat162 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{abs.bf16x2 %0,%1;\n}" + :"=r"(__BFLOAT162_TO_UI(r)) : "r"(__BFLOAT162_TO_CUI(a))); +, + r.x = __habs(a.x); + r.y = __habs(a.y); +) + return r; +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __habs(const __nv_bfloat16 a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 r; + asm("{abs.bf16 %0,%1;\n}" + :"=h"(__BFLOAT16_TO_US(r)) : "h"(__BFLOAT16_TO_CUS(a))); + return r; +, + __nv_bfloat16_raw abs_a_raw = static_cast<__nv_bfloat16_raw>(a); + abs_a_raw.x &= (unsigned short)0x7FFFU; + if (abs_a_raw.x > (unsigned short)0x7F80U) + { + // return canonical NaN + abs_a_raw.x = (unsigned short)0x7FFFU; + } + return static_cast<__nv_bfloat16>(abs_a_raw); +) +} + +/****************************************************************************** +* __nv_bfloat16 arithmetic * +******************************************************************************/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmax(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 val; + asm( "{ max.bf16 %0,%1,%2;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); + return val; +, + __nv_bfloat16 maxval; + + maxval = (__hge(a, b) || __hisnan(b)) ? a : b; + + if (__hisnan(maxval)) + { + // if both inputs are NaN, return canonical NaN + maxval = CUDART_NAN_BF16; + } + else if (__heq(a, b)) + { + // hmax(+0.0, -0.0) = +0.0 + // unsigned compare 0x8000U > 0x0000U + __nv_bfloat16_raw ra = __nv_bfloat16_raw(a); + __nv_bfloat16_raw rb = __nv_bfloat16_raw(b); + maxval = (ra.x > rb.x) ? b : a; + } + + return maxval; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmin(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 val; + asm( "{ min.bf16 %0,%1,%2;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); + return val; +, + __nv_bfloat16 minval; + + minval = (__hle(a, b) || __hisnan(b)) ? a : b; + + if (__hisnan(minval)) + { + // if both inputs are NaN, return canonical NaN + minval = CUDART_NAN_BF16; + } + else if (__heq(a, b)) + { + // hmin(+0.0, -0.0) = -0.0 + // unsigned compare 0x8000U > 0x0000U + __nv_bfloat16_raw ra = __nv_bfloat16_raw(a); + __nv_bfloat16_raw rb = __nv_bfloat16_raw(b); + minval = (ra.x > rb.x) ? a : b; + } + + return minval; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmax_nan(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 val; + asm( "{ max.NaN.bf16 %0,%1,%2;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); + return val; +, + __nv_bfloat16 maxval; + + if (__hisnan(a) || __hisnan(b)) + { + // if either input is NaN, return canonical NaN + maxval = CUDART_NAN_BF16; + } + else + { + maxval = __hge(a, b) ? a : b; + } + + return maxval; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat16 __hmin_nan(const __nv_bfloat16 a, const __nv_bfloat16 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat16 val; + asm( "{ min.NaN.bf16 %0,%1,%2;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b))); + return val; +, + __nv_bfloat16 minval; + + if (__hisnan(a) || __hisnan(b)) + { + // if either input is NaN, return canonical NaN + minval = CUDART_NAN_BF16; + } + else + { + minval = __hle(a, b) ? a : b; + } + + return minval; +) +} +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 __hfma_relu(const __nv_bfloat16 a, const __nv_bfloat16 b, const __nv_bfloat16 c) +{ + __nv_bfloat16 val; + asm( "{ fma.rn.relu.bf16 %0,%1,%2,%3;\n}" + :"=h"(__BFLOAT16_TO_US(val)) : "h"(__BFLOAT16_TO_CUS(a)),"h"(__BFLOAT16_TO_CUS(b)),"h"(__BFLOAT16_TO_CUS(c))); + return val; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ +/****************************************************************************** +* __nv_bfloat162 arithmetic * +******************************************************************************/ +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmax2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm( "{ max.bf16x2 %0,%1,%2;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); + return val; +, + __nv_bfloat162 val; + val.x = __hmax(a.x, b.x); + val.y = __hmax(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmin2(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm( "{ min.bf16x2 %0,%1,%2;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); + return val; +, + __nv_bfloat162 val; + val.x = __hmin(a.x, b.x); + val.y = __hmin(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmax2_nan(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm( "{ max.NaN.bf16x2 %0,%1,%2;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); + return val; +, + __nv_bfloat162 val; + val.x = __hmax_nan(a.x, b.x); + val.y = __hmax_nan(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_BF16_DECL__ __nv_bfloat162 __hmin2_nan(const __nv_bfloat162 a, const __nv_bfloat162 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __nv_bfloat162 val; + asm( "{ min.NaN.bf16x2 %0,%1,%2;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b))); + return val; +, + __nv_bfloat162 val; + val.x = __hmin_nan(a.x, b.x); + val.y = __hmin_nan(a.y, b.y); + return val; +) +} +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat162 __hfma2_relu(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c) +{ + __nv_bfloat162 val; + asm( "{ fma.rn.relu.bf16x2 %0,%1,%2,%3;\n}" + :"=r"(__BFLOAT162_TO_UI(val)) : "r"(__BFLOAT162_TO_CUI(a)),"r"(__BFLOAT162_TO_CUI(b)),"r"(__BFLOAT162_TO_CUI(c))); + return val; +} + +__CUDA_BF16_DECL__ __nv_bfloat162 __hcmadd(const __nv_bfloat162 a, const __nv_bfloat162 b, const __nv_bfloat162 c) +{ + // fast version of complex multiply-accumulate + // (a.re, a.im) * (b.re, b.im) + (c.re, c.im) + // acc.re = (c.re + a.re*b.re) - a.im*b.im + // acc.im = (c.im + a.re*b.im) + a.im*b.re + __nv_bfloat16 real_tmp = __hfma(a.x, b.x, c.x); + __nv_bfloat16 img_tmp = __hfma(a.x, b.y, c.y); + real_tmp = __hfma(__hneg(a.y), b.y, real_tmp); + img_tmp = __hfma(a.y, b.x, img_tmp); + return make_bfloat162(real_tmp, img_tmp); +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 800))) || defined(_NVHPC_CUDA) */ + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/* Define __PTR for atomicAdd prototypes below, undef after done */ +#if (defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__) +#define __PTR "l" +#else +#define __PTR "r" +#endif /*(defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__)*/ + +__CUDA_BF16_DECL__ __nv_bfloat162 atomicAdd(__nv_bfloat162 *const address, const __nv_bfloat162 val) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat162 r; + asm volatile ("{ atom.add.noftz.bf16x2 %0,[%1],%2; }\n" + : "=r"(__BFLOAT162_TO_UI(r)) : __PTR(address), "r"(__BFLOAT162_TO_CUI(val)) + : "memory"); + return r; +, + unsigned int* address_as_uint = (unsigned int*)address; + unsigned int old = *address_as_uint; + unsigned int assumed; + do { + assumed = old; + __nv_bfloat162 new_val = __hadd2(val, *(__nv_bfloat162*)&assumed); + old = atomicCAS(address_as_uint, assumed, *(unsigned int*)&new_val); + } while (assumed != old); + return *(__nv_bfloat162*)&old; +) +} + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) +__CUDA_BF16_DECL__ __nv_bfloat16 atomicAdd(__nv_bfloat16 *const address, const __nv_bfloat16 val) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + __nv_bfloat16 r; + asm volatile ("{ atom.add.noftz.bf16 %0,[%1],%2; }\n" + : "=h"(__BFLOAT16_TO_US(r)) + : __PTR(address), "h"(__BFLOAT16_TO_CUS(val)) + : "memory"); + return r; +, + unsigned short int* address_as_us = (unsigned short int*)address; + unsigned short int old = *address_as_us; + unsigned short int assumed; + do { + assumed = old; + old = atomicCAS(address_as_us, assumed, + __bfloat16_as_ushort(__hadd(val, __ushort_as_bfloat16(assumed)))); + } while (assumed != old); + return __ushort_as_bfloat16(old); +) +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) */ + +#undef __PTR +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +#endif /* defined(__cplusplus) */ + +#undef __CUDA_HOSTDEVICE_BF16_DECL__ +#undef __CUDA_BF16_DECL__ +#undef __CUDA_BF16_CONSTEXPR__ + +#if defined(__CPP_VERSION_AT_LEAST_11_BF16) +#undef __CPP_VERSION_AT_LEAST_11_BF16 +#endif /* defined(__CPP_VERSION_AT_LEAST_11_BF16) */ + +#endif /* end of include guard: __CUDA_BF16_HPP__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_device_runtime_api.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_device_runtime_api.h new file mode 100644 index 0000000000000000000000000000000000000000..0ff2892ca6c92a5cc0f637133006383cd81700a0 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_device_runtime_api.h @@ -0,0 +1,889 @@ +/* + * Copyright 1993-2021 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_DEVICE_RUNTIME_API_H__) +#define __CUDA_DEVICE_RUNTIME_API_H__ + +#if defined(__CUDACC__) && !defined(__CUDACC_RTC__) +#include +#endif + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#if !defined(CUDA_FORCE_CDP1_IF_SUPPORTED) && !defined(__CUDADEVRT_INTERNAL__) && !defined(_NVHPC_CUDA) && !(defined(_WIN32) && !defined(_WIN64)) +#define __CUDA_INTERNAL_USE_CDP2 +#endif + +#if !defined(__CUDACC_RTC__) + +#if !defined(__CUDACC_INTERNAL_NO_STUBS__) && !defined(__CUDACC_RDC__) && !defined(__CUDACC_EWP__) && defined(__CUDA_ARCH__) && (__CUDA_ARCH__ >= 350) && !defined(__CUDADEVRT_INTERNAL__) + +#if defined(__cplusplus) +extern "C" { +#endif + +struct cudaFuncAttributes; + + +#ifndef __CUDA_INTERNAL_USE_CDP2 +inline __device__ cudaError_t CUDARTAPI cudaMalloc(void **p, size_t s) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI cudaFuncGetAttributes(struct cudaFuncAttributes *p, const void *c) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI cudaDeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI cudaGetDevice(int *device) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize, unsigned int flags) +{ + return cudaErrorUnknown; +} +#else // __CUDA_INTERNAL_USE_CDP2 +inline __device__ cudaError_t CUDARTAPI __cudaCDP2Malloc(void **p, size_t s) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI __cudaCDP2FuncGetAttributes(struct cudaFuncAttributes *p, const void *c) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI __cudaCDP2DeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI __cudaCDP2GetDevice(int *device) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize) +{ + return cudaErrorUnknown; +} + +inline __device__ cudaError_t CUDARTAPI __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize, unsigned int flags) +{ + return cudaErrorUnknown; +} +#endif // __CUDA_INTERNAL_USE_CDP2 + + +#if defined(__cplusplus) +} +#endif + +#endif /* !defined(__CUDACC_INTERNAL_NO_STUBS__) && !defined(__CUDACC_RDC__) && !defined(__CUDACC_EWP__) && defined(__CUDA_ARCH__) && (__CUDA_ARCH__ >= 350) && !defined(__CUDADEVRT_INTERNAL__) */ + +#endif /* !defined(__CUDACC_RTC__) */ + +#if defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +# define __DEPRECATED__(msg) +#elif defined(_WIN32) +# define __DEPRECATED__(msg) __declspec(deprecated(msg)) +#elif (defined(__GNUC__) && (__GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 5 && !defined(__clang__)))) +# define __DEPRECATED__(msg) __attribute__((deprecated)) +#else +# define __DEPRECATED__(msg) __attribute__((deprecated(msg))) +#endif + +#if defined(__CUDA_ARCH__) && !defined(__CDPRT_SUPPRESS_SYNC_DEPRECATION_WARNING) +# define __CDPRT_DEPRECATED(func_name) __DEPRECATED__("Use of "#func_name" from device code is deprecated. Moreover, such use will cause this module to fail to load on sm_90+ devices. If calls to "#func_name" from device code cannot be removed for older devices at this time, you may guard them with __CUDA_ARCH__ macros to remove them only for sm_90+ devices, making sure to generate code for compute_90 for the macros to take effect. Note that this mitigation will no longer work when support for "#func_name" from device code is eventually dropped for all devices. Disable this warning with -D__CDPRT_SUPPRESS_SYNC_DEPRECATION_WARNING.") +#else +# define __CDPRT_DEPRECATED(func_name) +#endif + +#if defined(__cplusplus) && defined(__CUDACC__) /* Visible to nvcc front-end only */ +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 350) // Visible to SM>=3.5 and "__host__ __device__" only + +#include "driver_types.h" +#include "crt/host_defines.h" + +#define cudaStreamGraphTailLaunch (cudaStream_t)0x0100000000000000 +#define cudaStreamGraphFireAndForget (cudaStream_t)0x0200000000000000 +#define cudaStreamGraphFireAndForgetAsSibling (cudaStream_t)0x0300000000000000 + +#ifdef __CUDA_INTERNAL_USE_CDP2 +#define cudaStreamTailLaunch ((cudaStream_t)0x3) /**< Per-grid stream with a tail launch semantics. Only applicable when used with CUDA Dynamic Parallelism. */ +#define cudaStreamFireAndForget ((cudaStream_t)0x4) /**< Per-grid stream with a fire-and-forget synchronization behavior. Only applicable when used with CUDA Dynamic Parallelism. */ +#endif + +extern "C" +{ + +// Symbols beginning with __cudaCDP* should not be used outside +// this header file. Instead, compile with -DCUDA_FORCE_CDP1_IF_SUPPORTED if +// CDP1 support is required. + +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaDeviceSynchronizeDeprecationAvoidance(void); + +#ifndef __CUDA_INTERNAL_USE_CDP2 +//// CDP1 endpoints +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetLimit(size_t *pValue, enum cudaLimit limit); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetCacheConfig(enum cudaFuncCache *pCacheConfig); +extern __DEPRECATED__("cudaDeviceGetSharedMemConfig deprecated") __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetSharedMemConfig(enum cudaSharedMemConfig *pConfig); +#if (__CUDA_ARCH__ < 900) && (defined(CUDA_FORCE_CDP1_IF_SUPPORTED) || (defined(_WIN32) && !defined(_WIN64))) +// cudaDeviceSynchronize is removed on sm_90+ +extern __device__ __cudart_builtin__ __CDPRT_DEPRECATED(cudaDeviceSynchronize) cudaError_t CUDARTAPI cudaDeviceSynchronize(void); +#endif +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetLastError(void); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaPeekAtLastError(void); +extern __device__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorString(cudaError_t error); +extern __device__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorName(cudaError_t error); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDeviceCount(int *count); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDevice(int *device); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamCreateWithFlags(cudaStream_t *pStream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamDestroy(cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent(cudaStream_t stream, cudaEvent_t event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent_ptsz(cudaStream_t stream, cudaEvent_t event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventCreateWithFlags(cudaEvent_t *event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord(cudaEvent_t event, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord_ptsz(cudaEvent_t event, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags(cudaEvent_t event, cudaStream_t stream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags_ptsz(cudaEvent_t event, cudaStream_t stream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventDestroy(cudaEvent_t event); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncGetAttributes(struct cudaFuncAttributes *attr, const void *func); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFree(void *devPtr); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMalloc(void **devPtr, size_t size); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync_ptsz(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync_ptsz(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync(const struct cudaMemcpy3DParms *p, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync_ptsz(const struct cudaMemcpy3DParms *p, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync(void *devPtr, int value, size_t count, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync_ptsz(void *devPtr, int value, size_t count, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync_ptsz(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync_ptsz(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaRuntimeGetVersion(int *runtimeVersion); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize, unsigned int flags); +#endif // __CUDA_INTERNAL_USE_CDP2 + +//// CDP2 endpoints +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2DeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2DeviceGetLimit(size_t *pValue, enum cudaLimit limit); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2DeviceGetCacheConfig(enum cudaFuncCache *pCacheConfig); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2DeviceGetSharedMemConfig(enum cudaSharedMemConfig *pConfig); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2GetLastError(void); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2PeekAtLastError(void); +extern __device__ __cudart_builtin__ const char* CUDARTAPI __cudaCDP2GetErrorString(cudaError_t error); +extern __device__ __cudart_builtin__ const char* CUDARTAPI __cudaCDP2GetErrorName(cudaError_t error); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2GetDeviceCount(int *count); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2GetDevice(int *device); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2StreamCreateWithFlags(cudaStream_t *pStream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2StreamDestroy(cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2StreamWaitEvent(cudaStream_t stream, cudaEvent_t event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2StreamWaitEvent_ptsz(cudaStream_t stream, cudaEvent_t event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventCreateWithFlags(cudaEvent_t *event, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventRecord(cudaEvent_t event, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventRecord_ptsz(cudaEvent_t event, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventRecordWithFlags(cudaEvent_t event, cudaStream_t stream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventRecordWithFlags_ptsz(cudaEvent_t event, cudaStream_t stream, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2EventDestroy(cudaEvent_t event); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2FuncGetAttributes(struct cudaFuncAttributes *attr, const void *func); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Free(void *devPtr); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Malloc(void **devPtr, size_t size); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2MemcpyAsync(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2MemcpyAsync_ptsz(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memcpy2DAsync(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memcpy2DAsync_ptsz(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memcpy3DAsync(const struct cudaMemcpy3DParms *p, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memcpy3DAsync_ptsz(const struct cudaMemcpy3DParms *p, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2MemsetAsync(void *devPtr, int value, size_t count, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2MemsetAsync_ptsz(void *devPtr, int value, size_t count, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memset2DAsync(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memset2DAsync_ptsz(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memset3DAsync(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2Memset3DAsync_ptsz(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2RuntimeGetVersion(int *runtimeVersion); +extern __device__ __cudart_builtin__ void * CUDARTAPI __cudaCDP2GetParameterBuffer(size_t alignment, size_t size); +extern __device__ __cudart_builtin__ void * CUDARTAPI __cudaCDP2GetParameterBufferV2(void *func, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2LaunchDevice_ptsz(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2LaunchDeviceV2_ptsz(void *parameterBuffer, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2LaunchDevice(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2LaunchDeviceV2(void *parameterBuffer, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize, unsigned int flags); + + +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphLaunch(cudaGraphExec_t graphExec, cudaStream_t stream); +#if defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) +static inline __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphLaunch_ptsz(cudaGraphExec_t graphExec, cudaStream_t stream) +{ + if (stream == 0) { + stream = cudaStreamPerThread; + } + return cudaGraphLaunch(graphExec, stream); +} +#endif + +/** + * \ingroup CUDART_GRAPH + * \brief Get the currently running device graph id. + * + * Get the currently running device graph id. + * \return Returns the current device graph id, 0 if the call is outside of a device graph. + * \sa cudaGraphLaunch + */ +static inline __device__ __cudart_builtin__ cudaGraphExec_t CUDARTAPI cudaGetCurrentGraphExec(void) +{ + unsigned long long current_graph_exec; + asm ("mov.u64 %0, %%current_graph_exec;" : "=l"(current_graph_exec)); + return (cudaGraphExec_t)current_graph_exec; +} + +/** + * \ingroup CUDART_GRAPH + * \brief Updates the kernel parameters of the given kernel node + * + * Updates \p size bytes in the kernel parameters of \p node at \p offset to + * the contents of \p value. \p node must be device-updatable, and must reside upon the same + * device as the calling kernel. + * + * If this function is called for the node's immediate dependent and that dependent is configured + * for programmatic dependent launch, then a memory fence must be invoked via __threadfence() before + * kickoff of the dependent is triggered via ::cudaTriggerProgrammaticLaunchCompletion() to ensure + * that the update is visible to that dependent node before it is launched. + * + * \param node - The node to update + * \param offset - The offset into the params at which to make the update + * \param value - Buffer containing the params to write + * \param size - Size in bytes to update + * + * \return + * cudaSucces, + * cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaGraphKernelNodeSetEnabled, + * ::cudaGraphKernelNodeSetGridDim, + * ::cudaGraphKernelNodeUpdatesApply + */ +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetParam(cudaGraphDeviceNode_t node, size_t offset, const void *value , size_t size); + +/** + * \ingroup CUDART_GRAPH + * \brief Enables or disables the given kernel node + * + * Enables or disables \p node based upon \p enable. If \p enable is true, the node will be enabled; + * if it is false, the node will be disabled. Disabled nodes will act as a NOP during execution. + * \p node must be device-updatable, and must reside upon the same device as the calling kernel. + * + * If this function is called for the node's immediate dependent and that dependent is configured + * for programmatic dependent launch, then a memory fence must be invoked via __threadfence() before + * kickoff of the dependent is triggered via ::cudaTriggerProgrammaticLaunchCompletion() to ensure + * that the update is visible to that dependent node before it is launched. + * + * \param node - The node to update + * \param enable - Whether to enable or disable the node + * + * \return + * cudaSucces, + * cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaGraphKernelNodeSetParam, + * ::cudaGraphKernelNodeSetGridDim, + * ::cudaGraphKernelNodeUpdatesApply + */ +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetEnabled(cudaGraphDeviceNode_t node, bool enable); + +/** + * \ingroup CUDART_GRAPH + * \brief Updates the grid dimensions of the given kernel node + * + * Sets the grid dimensions of \p node to \p gridDim. \p node must be device-updatable, + * and must reside upon the same device as thecalling kernel. + * + * If this function is called for the node's immediate dependent and that dependent is configured + * for programmatic dependent launch, then a memory fence must be invoked via __threadfence() before + * kickoff of the dependent is triggered via ::cudaTriggerProgrammaticLaunchCompletion() to ensure + * that the update is visible to that dependent node before it is launched. + * + * \param node - The node to update + * \param gridDim - The grid dimensions to set + * + * \return + * cudaSucces, + * cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaGraphKernelNodeSetParam, + * ::cudaGraphKernelNodeSetEnabled, + * ::cudaGraphKernelNodeUpdatesApply + */ +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetGridDim(cudaGraphDeviceNode_t node, dim3 gridDim); + +/** + * \ingroup CUDART_GRAPH + * \brief Batch applies multiple kernel node updates + * + * Batch applies one or more kernel node updates based on the information provided in \p updates. + * \p updateCount specifies the number of updates to apply. Each entry in \p updates must specify + * a node to update, the type of update to apply, and the parameters for that type of update. See + * the documentation for ::cudaGraphKernelNodeUpdate for more detail. + * + * If this function is called for the node's immediate dependent and that dependent is configured + * for programmatic dependent launch, then a memory fence must be invoked via __threadfence() before + * kickoff of the dependent is triggered via ::cudaTriggerProgrammaticLaunchCompletion() to ensure + * that the update is visible to that dependent node before it is launched. + * + * \param updates - The updates to apply + * \param updateCount - The number of updates to apply + * + * \return + * cudaSucces, + * cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaGraphKernelNodeSetParam, + * ::cudaGraphKernelNodeSetEnabled, + * ::cudaGraphKernelNodeSetGridDim + */ +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphKernelNodeUpdatesApply(const cudaGraphKernelNodeUpdate *updates, size_t updateCount); + +/** + * \ingroup CUDART_EXECUTION + * \brief Programmatic dependency trigger + * + * This device function ensures the programmatic launch completion edges / + * events are fulfilled. See + * ::cudaLaunchAttributeID::cudaLaunchAttributeProgrammaticStreamSerialization + * and ::cudaLaunchAttributeID::cudaLaunchAttributeProgrammaticEvent for more + * information. The event / edge kick off only happens when every CTAs + * in the grid has either exited or called this function at least once, + * otherwise the kick off happens automatically after all warps finishes + * execution but before the grid completes. The kick off only enables + * scheduling of the secondary kernel. It provides no memory visibility + * guarantee itself. The user could enforce memory visibility by inserting a + * memory fence of the correct scope. + */ +static inline __device__ __cudart_builtin__ void CUDARTAPI cudaTriggerProgrammaticLaunchCompletion(void) +{ + asm volatile("griddepcontrol.launch_dependents;":::); +} + +/** + * \ingroup CUDART_EXECUTION + * \brief Programmatic grid dependency synchronization + * + * This device function will block the thread until all direct grid + * dependencies have completed. This API is intended to use in conjuncture with + * programmatic / launch event / dependency. See + * ::cudaLaunchAttributeID::cudaLaunchAttributeProgrammaticStreamSerialization + * and ::cudaLaunchAttributeID::cudaLaunchAttributeProgrammaticEvent for more + * information. + */ +static inline __device__ __cudart_builtin__ void CUDARTAPI cudaGridDependencySynchronize(void) +{ + asm volatile("griddepcontrol.wait;":::"memory"); +} + +/** + * \ingroup CUDART_GRAPH + * \brief Sets the condition value associated with a conditional node. + * + * Sets the condition value associated with a conditional node. + * \sa cudaGraphConditionalHandleCreate + */ +extern __device__ __cudart_builtin__ void CUDARTAPI cudaGraphSetConditional(cudaGraphConditionalHandle handle, unsigned int value); + +//// CG API +extern __device__ __cudart_builtin__ unsigned long long CUDARTAPI cudaCGGetIntrinsicHandle(enum cudaCGScope scope); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaCGSynchronize(unsigned long long handle, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaCGSynchronizeGrid(unsigned long long handle, unsigned int flags); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaCGGetSize(unsigned int *numThreads, unsigned int *numGrids, unsigned long long handle); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaCGGetRank(unsigned int *threadRank, unsigned int *gridRank, unsigned long long handle); + + +//// CDP API + +#ifdef __CUDA_ARCH__ + +#ifdef __CUDA_INTERNAL_USE_CDP2 +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device) +{ + return __cudaCDP2DeviceGetAttribute(value, attr, device); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetLimit(size_t *pValue, enum cudaLimit limit) +{ + return __cudaCDP2DeviceGetLimit(pValue, limit); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetCacheConfig(enum cudaFuncCache *pCacheConfig) +{ + return __cudaCDP2DeviceGetCacheConfig(pCacheConfig); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetSharedMemConfig(enum cudaSharedMemConfig *pConfig) +{ + return __cudaCDP2DeviceGetSharedMemConfig(pConfig); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetLastError(void) +{ + return __cudaCDP2GetLastError(); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaPeekAtLastError(void) +{ + return __cudaCDP2PeekAtLastError(); +} + +static __inline__ __device__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorString(cudaError_t error) +{ + return __cudaCDP2GetErrorString(error); +} + +static __inline__ __device__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorName(cudaError_t error) +{ + return __cudaCDP2GetErrorName(error); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDeviceCount(int *count) +{ + return __cudaCDP2GetDeviceCount(count); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDevice(int *device) +{ + return __cudaCDP2GetDevice(device); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamCreateWithFlags(cudaStream_t *pStream, unsigned int flags) +{ + return __cudaCDP2StreamCreateWithFlags(pStream, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamDestroy(cudaStream_t stream) +{ + return __cudaCDP2StreamDestroy(stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent(cudaStream_t stream, cudaEvent_t event, unsigned int flags) +{ + return __cudaCDP2StreamWaitEvent(stream, event, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent_ptsz(cudaStream_t stream, cudaEvent_t event, unsigned int flags) +{ + return __cudaCDP2StreamWaitEvent_ptsz(stream, event, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventCreateWithFlags(cudaEvent_t *event, unsigned int flags) +{ + return __cudaCDP2EventCreateWithFlags(event, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord(cudaEvent_t event, cudaStream_t stream) +{ + return __cudaCDP2EventRecord(event, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord_ptsz(cudaEvent_t event, cudaStream_t stream) +{ + return __cudaCDP2EventRecord_ptsz(event, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags(cudaEvent_t event, cudaStream_t stream, unsigned int flags) +{ + return __cudaCDP2EventRecordWithFlags(event, stream, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags_ptsz(cudaEvent_t event, cudaStream_t stream, unsigned int flags) +{ + return __cudaCDP2EventRecordWithFlags_ptsz(event, stream, flags); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventDestroy(cudaEvent_t event) +{ + return __cudaCDP2EventDestroy(event); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncGetAttributes(struct cudaFuncAttributes *attr, const void *func) +{ + return __cudaCDP2FuncGetAttributes(attr, func); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFree(void *devPtr) +{ + return __cudaCDP2Free(devPtr); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMalloc(void **devPtr, size_t size) +{ + return __cudaCDP2Malloc(devPtr, size); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream) +{ + return __cudaCDP2MemcpyAsync(dst, src, count, kind, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync_ptsz(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream) +{ + return __cudaCDP2MemcpyAsync_ptsz(dst, src, count, kind, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream) +{ + return __cudaCDP2Memcpy2DAsync(dst, dpitch, src, spitch, width, height, kind, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync_ptsz(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream) +{ + return __cudaCDP2Memcpy2DAsync_ptsz(dst, dpitch, src, spitch, width, height, kind, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync(const struct cudaMemcpy3DParms *p, cudaStream_t stream) +{ + return __cudaCDP2Memcpy3DAsync(p, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync_ptsz(const struct cudaMemcpy3DParms *p, cudaStream_t stream) +{ + return __cudaCDP2Memcpy3DAsync_ptsz(p, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync(void *devPtr, int value, size_t count, cudaStream_t stream) +{ + return __cudaCDP2MemsetAsync(devPtr, value, count, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync_ptsz(void *devPtr, int value, size_t count, cudaStream_t stream) +{ + return __cudaCDP2MemsetAsync_ptsz(devPtr, value, count, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream) +{ + return __cudaCDP2Memset2DAsync(devPtr, pitch, value, width, height, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync_ptsz(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream) +{ + return __cudaCDP2Memset2DAsync_ptsz(devPtr, pitch, value, width, height, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream) +{ + return __cudaCDP2Memset3DAsync(pitchedDevPtr, value, extent, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync_ptsz(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream) +{ + return __cudaCDP2Memset3DAsync_ptsz(pitchedDevPtr, value, extent, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaRuntimeGetVersion(int *runtimeVersion) +{ + return __cudaCDP2RuntimeGetVersion(runtimeVersion); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize) +{ + return __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessor(numBlocks, func, blockSize, dynamicSmemSize); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSmemSize, unsigned int flags) +{ + return __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessorWithFlags(numBlocks, func, blockSize, dynamicSmemSize, flags); +} +#endif // __CUDA_INTERNAL_USE_CDP2 + +#endif // __CUDA_ARCH__ + + +/** + * \ingroup CUDART_EXECUTION + * \brief Obtains a parameter buffer + * + * Obtains a parameter buffer which can be filled with parameters for a kernel launch. + * Parameters passed to ::cudaLaunchDevice must be allocated via this function. + * + * This is a low level API and can only be accessed from Parallel Thread Execution (PTX). + * CUDA user code should use <<< >>> to launch kernels. + * + * \param alignment - Specifies alignment requirement of the parameter buffer + * \param size - Specifies size requirement in bytes + * + * \return + * Returns pointer to the allocated parameterBuffer + * \notefnerr + * + * \sa cudaLaunchDevice + */ +#ifdef __CUDA_INTERNAL_USE_CDP2 +static __inline__ __device__ __cudart_builtin__ void * CUDARTAPI cudaGetParameterBuffer(size_t alignment, size_t size) +{ + return __cudaCDP2GetParameterBuffer(alignment, size); +} +#else +extern __device__ __cudart_builtin__ void * CUDARTAPI cudaGetParameterBuffer(size_t alignment, size_t size); +#endif + + +#ifdef __CUDA_INTERNAL_USE_CDP2 +static __inline__ __device__ __cudart_builtin__ void * CUDARTAPI cudaGetParameterBufferV2(void *func, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize) +{ + return __cudaCDP2GetParameterBufferV2(func, gridDimension, blockDimension, sharedMemSize); +} +#else +extern __device__ __cudart_builtin__ void * CUDARTAPI cudaGetParameterBufferV2(void *func, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize); +#endif + + +#ifdef __CUDA_INTERNAL_USE_CDP2 +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDevice_ptsz(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream) +{ + return __cudaCDP2LaunchDevice_ptsz(func, parameterBuffer, gridDimension, blockDimension, sharedMemSize, stream); +} + +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDeviceV2_ptsz(void *parameterBuffer, cudaStream_t stream) +{ + return __cudaCDP2LaunchDeviceV2_ptsz(parameterBuffer, stream); +} +#else +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDevice_ptsz(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDeviceV2_ptsz(void *parameterBuffer, cudaStream_t stream); +#endif + + +/** + * \ingroup CUDART_EXECUTION + * \brief Launches a specified kernel + * + * Launches a specified kernel with the specified parameter buffer. A parameter buffer can be obtained + * by calling ::cudaGetParameterBuffer(). + * + * This is a low level API and can only be accessed from Parallel Thread Execution (PTX). + * CUDA user code should use <<< >>> to launch the kernels. + * + * \param func - Pointer to the kernel to be launched + * \param parameterBuffer - Holds the parameters to the launched kernel. parameterBuffer can be NULL. (Optional) + * \param gridDimension - Specifies grid dimensions + * \param blockDimension - Specifies block dimensions + * \param sharedMemSize - Specifies size of shared memory + * \param stream - Specifies the stream to be used + * + * \return + * ::cudaSuccess, ::cudaErrorInvalidDevice, ::cudaErrorLaunchMaxDepthExceeded, ::cudaErrorInvalidConfiguration, + * ::cudaErrorStartupFailure, ::cudaErrorLaunchPendingCountExceeded, ::cudaErrorLaunchOutOfResources + * \notefnerr + * \n Please refer to Execution Configuration and Parameter Buffer Layout from the CUDA Programming + * Guide for the detailed descriptions of launch configuration and parameter layout respectively. + * + * \sa cudaGetParameterBuffer + */ +#if defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) && defined(__CUDA_ARCH__) + // When compiling for the device and per thread default stream is enabled, add + // a static inline redirect to the per thread stream entry points. + + static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI + cudaLaunchDevice(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream) + { +#ifdef __CUDA_INTERNAL_USE_CDP2 + return __cudaCDP2LaunchDevice_ptsz(func, parameterBuffer, gridDimension, blockDimension, sharedMemSize, stream); +#else + return cudaLaunchDevice_ptsz(func, parameterBuffer, gridDimension, blockDimension, sharedMemSize, stream); +#endif + } + + static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI + cudaLaunchDeviceV2(void *parameterBuffer, cudaStream_t stream) + { +#ifdef __CUDA_INTERNAL_USE_CDP2 + return __cudaCDP2LaunchDeviceV2_ptsz(parameterBuffer, stream); +#else + return cudaLaunchDeviceV2_ptsz(parameterBuffer, stream); +#endif + } +#else // defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) && defined(__CUDA_ARCH__) +#ifdef __CUDA_INTERNAL_USE_CDP2 + static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDevice(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream) + { + return __cudaCDP2LaunchDevice(func, parameterBuffer, gridDimension, blockDimension, sharedMemSize, stream); + } + + static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDeviceV2(void *parameterBuffer, cudaStream_t stream) + { + return __cudaCDP2LaunchDeviceV2(parameterBuffer, stream); + } +#else // __CUDA_INTERNAL_USE_CDP2 +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDevice(void *func, void *parameterBuffer, dim3 gridDimension, dim3 blockDimension, unsigned int sharedMemSize, cudaStream_t stream); +extern __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaLaunchDeviceV2(void *parameterBuffer, cudaStream_t stream); +#endif // __CUDA_INTERNAL_USE_CDP2 +#endif // defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) && defined(__CUDA_ARCH__) + + +// These symbols should not be used outside of this header file. +#define __cudaCDP2DeviceGetAttribute +#define __cudaCDP2DeviceGetLimit +#define __cudaCDP2DeviceGetCacheConfig +#define __cudaCDP2DeviceGetSharedMemConfig +#define __cudaCDP2GetLastError +#define __cudaCDP2PeekAtLastError +#define __cudaCDP2GetErrorString +#define __cudaCDP2GetErrorName +#define __cudaCDP2GetDeviceCount +#define __cudaCDP2GetDevice +#define __cudaCDP2StreamCreateWithFlags +#define __cudaCDP2StreamDestroy +#define __cudaCDP2StreamWaitEvent +#define __cudaCDP2StreamWaitEvent_ptsz +#define __cudaCDP2EventCreateWithFlags +#define __cudaCDP2EventRecord +#define __cudaCDP2EventRecord_ptsz +#define __cudaCDP2EventRecordWithFlags +#define __cudaCDP2EventRecordWithFlags_ptsz +#define __cudaCDP2EventDestroy +#define __cudaCDP2FuncGetAttributes +#define __cudaCDP2Free +#define __cudaCDP2Malloc +#define __cudaCDP2MemcpyAsync +#define __cudaCDP2MemcpyAsync_ptsz +#define __cudaCDP2Memcpy2DAsync +#define __cudaCDP2Memcpy2DAsync_ptsz +#define __cudaCDP2Memcpy3DAsync +#define __cudaCDP2Memcpy3DAsync_ptsz +#define __cudaCDP2MemsetAsync +#define __cudaCDP2MemsetAsync_ptsz +#define __cudaCDP2Memset2DAsync +#define __cudaCDP2Memset2DAsync_ptsz +#define __cudaCDP2Memset3DAsync +#define __cudaCDP2Memset3DAsync_ptsz +#define __cudaCDP2RuntimeGetVersion +#define __cudaCDP2GetParameterBuffer +#define __cudaCDP2GetParameterBufferV2 +#define __cudaCDP2LaunchDevice_ptsz +#define __cudaCDP2LaunchDeviceV2_ptsz +#define __cudaCDP2LaunchDevice +#define __cudaCDP2LaunchDeviceV2 +#define __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessor +#define __cudaCDP2OccupancyMaxActiveBlocksPerMultiprocessorWithFlags + +} + +template static __inline__ __device__ __cudart_builtin__ cudaError_t cudaMalloc(T **devPtr, size_t size); +template static __inline__ __device__ __cudart_builtin__ cudaError_t cudaFuncGetAttributes(struct cudaFuncAttributes *attr, T *entry); +template static __inline__ __device__ __cudart_builtin__ cudaError_t cudaOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, T func, int blockSize, size_t dynamicSmemSize); +template static __inline__ __device__ __cudart_builtin__ cudaError_t cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, T func, int blockSize, size_t dynamicSmemSize, unsigned int flags); + +/** + * \ingroup CUDART_GRAPH + * \brief Updates the kernel parameters of the given kernel node + * + * Updates the kernel parameters of \p node at \p offset to \p value. \p node must be + * device-updatable, and must reside upon the same device as the calling kernel. + * + * If this function is called for the node's immediate dependent and that dependent is configured + * for programmatic dependent launch, then a memory fence must be invoked via __threadfence() before + * kickoff of the dependent is triggered via ::cudaTriggerProgrammaticLaunchCompletion() to ensure + * that the update is visible to that dependent node before it is launched. + * + * \param node - The node to update + * \param offset - The offset into the params at which to make the update + * \param value - Parameter value to write + * + * \return + * cudaSucces, + * cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::etblGraphKernelNodeSetEnabled, + * ::etblGraphKernelNodeSetGridDim, + * ::etblGraphKernelNodeUpdatesApply + */ +template +static __inline__ __device__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetParam(cudaGraphDeviceNode_t node, size_t offset, const T &value) +{ + return cudaGraphKernelNodeSetParam(node, offset, &value, sizeof(T)); +} + +#endif // !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 350) +#endif /* defined(__cplusplus) && defined(__CUDACC__) */ + +#undef __DEPRECATED__ +#undef __CDPRT_DEPRECATED +#undef __CUDA_INTERNAL_USE_CDP2 + +#endif /* !__CUDA_DEVICE_RUNTIME_API_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_egl_interop.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_egl_interop.h new file mode 100644 index 0000000000000000000000000000000000000000..40ab01b33e0e9bec536192676c2a804809276fc4 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_egl_interop.h @@ -0,0 +1,642 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_EGL_INTEROP_H__) +#define __CUDA_EGL_INTEROP_H__ + +#include "cuda_runtime_api.h" +#include "cuda_runtime.h" +#include "cudart_platform.h" +#include "EGL/egl.h" +#include "EGL/eglext.h" + +#if defined(__cplusplus) +extern "C" { +#endif /* __cplusplus */ + +/** + * \addtogroup CUDART_TYPES + * @{ + */ + + /** + * Maximum number of planes per frame + */ +#define CUDA_EGL_MAX_PLANES 3 + +/** + * CUDA EglFrame type - array or pointer + */ +typedef enum cudaEglFrameType_enum +{ + cudaEglFrameTypeArray = 0, /**< Frame type CUDA array */ + cudaEglFrameTypePitch = 1, /**< Frame type CUDA pointer */ +} cudaEglFrameType; + +/** + * Resource location flags- sysmem or vidmem + * + * For CUDA context on iGPU, since video and system memory are equivalent - + * these flags will not have an effect on the execution. + * + * For CUDA context on dGPU, applications can use the flag ::cudaEglResourceLocationFlags + * to give a hint about the desired location. + * + * ::cudaEglResourceLocationSysmem - the frame data is made resident on the system memory + * to be accessed by CUDA. + * + * ::cudaEglResourceLocationVidmem - the frame data is made resident on the dedicated + * video memory to be accessed by CUDA. + * + * There may be an additional latency due to new allocation and data migration, + * if the frame is produced on a different memory. + */ +typedef enum cudaEglResourceLocationFlags_enum { + cudaEglResourceLocationSysmem = 0x00, /**< Resource location sysmem */ + cudaEglResourceLocationVidmem = 0x01, /**< Resource location vidmem */ +} cudaEglResourceLocationFlags; + +/** + * CUDA EGL Color Format - The different planar and multiplanar formats currently supported for CUDA_EGL interops. + */ +typedef enum cudaEglColorFormat_enum { + cudaEglColorFormatYUV420Planar = 0, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYUV420SemiPlanar = 1, /**< Y, UV in two surfaces (UV as one surface) with VU byte ordering, width, height ratio same as YUV420Planar. */ + cudaEglColorFormatYUV422Planar = 2, /**< Y, U, V each in a separate surface, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYUV422SemiPlanar = 3, /**< Y, UV in two surfaces with VU byte ordering, width, height ratio same as YUV422Planar. */ + cudaEglColorFormatARGB = 6, /**< R/G/B/A four channels in one surface with BGRA byte ordering. */ + cudaEglColorFormatRGBA = 7, /**< R/G/B/A four channels in one surface with ABGR byte ordering. */ + cudaEglColorFormatL = 8, /**< single luminance channel in one surface. */ + cudaEglColorFormatR = 9, /**< single color channel in one surface. */ + cudaEglColorFormatYUV444Planar = 10, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYUV444SemiPlanar = 11, /**< Y, UV in two surfaces (UV as one surface) with VU byte ordering, width, height ratio same as YUV444Planar. */ + cudaEglColorFormatYUYV422 = 12, /**< Y, U, V in one surface, interleaved as UYVY in one channel. */ + cudaEglColorFormatUYVY422 = 13, /**< Y, U, V in one surface, interleaved as YUYV in one channel. */ + cudaEglColorFormatABGR = 14, /**< R/G/B/A four channels in one surface with RGBA byte ordering. */ + cudaEglColorFormatBGRA = 15, /**< R/G/B/A four channels in one surface with ARGB byte ordering. */ + cudaEglColorFormatA = 16, /**< Alpha color format - one channel in one surface. */ + cudaEglColorFormatRG = 17, /**< R/G color format - two channels in one surface with GR byte ordering */ + cudaEglColorFormatAYUV = 18, /**< Y, U, V, A four channels in one surface, interleaved as VUYA. */ + cudaEglColorFormatYVU444SemiPlanar = 19, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYVU422SemiPlanar = 20, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYVU420SemiPlanar = 21, /**< Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_444SemiPlanar = 22, /**< Y10, V10U10 in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatY10V10U10_420SemiPlanar = 23, /**< Y10, V10U10 in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY12V12U12_444SemiPlanar = 24, /**< Y12, V12U12 in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatY12V12U12_420SemiPlanar = 25, /**< Y12, V12U12 in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatVYUY_ER = 26, /**< Extended Range Y, U, V in one surface, interleaved as YVYU in one channel. */ + cudaEglColorFormatUYVY_ER = 27, /**< Extended Range Y, U, V in one surface, interleaved as YUYV in one channel. */ + cudaEglColorFormatYUYV_ER = 28, /**< Extended Range Y, U, V in one surface, interleaved as UYVY in one channel. */ + cudaEglColorFormatYVYU_ER = 29, /**< Extended Range Y, U, V in one surface, interleaved as VYUY in one channel. */ + cudaEglColorFormatYUVA_ER = 31, /**< Extended Range Y, U, V, A four channels in one surface, interleaved as AVUY. */ + cudaEglColorFormatAYUV_ER = 32, /**< Extended Range Y, U, V, A four channels in one surface, interleaved as VUYA. */ + cudaEglColorFormatYUV444Planar_ER = 33, /**< Extended Range Y, U, V in three surfaces, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYUV422Planar_ER = 34, /**< Extended Range Y, U, V in three surfaces, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYUV420Planar_ER = 35, /**< Extended Range Y, U, V in three surfaces, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYUV444SemiPlanar_ER = 36, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYUV422SemiPlanar_ER = 37, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYUV420SemiPlanar_ER = 38, /**< Extended Range Y, UV in two surfaces (UV as one surface) with VU byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU444Planar_ER = 39, /**< Extended Range Y, V, U in three surfaces, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYVU422Planar_ER = 40, /**< Extended Range Y, V, U in three surfaces, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYVU420Planar_ER = 41, /**< Extended Range Y, V, U in three surfaces, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU444SemiPlanar_ER = 42, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYVU422SemiPlanar_ER = 43, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYVU420SemiPlanar_ER = 44, /**< Extended Range Y, VU in two surfaces (VU as one surface) with UV byte ordering, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatBayerRGGB = 45, /**< Bayer format - one channel in one surface with interleaved RGGB ordering. */ + cudaEglColorFormatBayerBGGR = 46, /**< Bayer format - one channel in one surface with interleaved BGGR ordering. */ + cudaEglColorFormatBayerGRBG = 47, /**< Bayer format - one channel in one surface with interleaved GRBG ordering. */ + cudaEglColorFormatBayerGBRG = 48, /**< Bayer format - one channel in one surface with interleaved GBRG ordering. */ + cudaEglColorFormatBayer10RGGB = 49, /**< Bayer10 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + cudaEglColorFormatBayer10BGGR = 50, /**< Bayer10 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + cudaEglColorFormatBayer10GRBG = 51, /**< Bayer10 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + cudaEglColorFormatBayer10GBRG = 52, /**< Bayer10 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + cudaEglColorFormatBayer12RGGB = 53, /**< Bayer12 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12BGGR = 54, /**< Bayer12 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12GRBG = 55, /**< Bayer12 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12GBRG = 56, /**< Bayer12 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer14RGGB = 57, /**< Bayer14 format - one channel in one surface with interleaved RGGB ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + cudaEglColorFormatBayer14BGGR = 58, /**< Bayer14 format - one channel in one surface with interleaved BGGR ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + cudaEglColorFormatBayer14GRBG = 59, /**< Bayer14 format - one channel in one surface with interleaved GRBG ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + cudaEglColorFormatBayer14GBRG = 60, /**< Bayer14 format - one channel in one surface with interleaved GBRG ordering. Out of 16 bits, 14 bits used 2 bits No-op. */ + cudaEglColorFormatBayer20RGGB = 61, /**< Bayer20 format - one channel in one surface with interleaved RGGB ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + cudaEglColorFormatBayer20BGGR = 62, /**< Bayer20 format - one channel in one surface with interleaved BGGR ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + cudaEglColorFormatBayer20GRBG = 63, /**< Bayer20 format - one channel in one surface with interleaved GRBG ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + cudaEglColorFormatBayer20GBRG = 64, /**< Bayer20 format - one channel in one surface with interleaved GBRG ordering. Out of 32 bits, 20 bits used 12 bits No-op. */ + cudaEglColorFormatYVU444Planar = 65, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatYVU422Planar = 66, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatYVU420Planar = 67, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatBayerIspRGGB = 68, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved RGGB ordering and mapped to opaque integer datatype. */ + cudaEglColorFormatBayerIspBGGR = 69, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved BGGR ordering and mapped to opaque integer datatype. */ + cudaEglColorFormatBayerIspGRBG = 70, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved GRBG ordering and mapped to opaque integer datatype. */ + cudaEglColorFormatBayerIspGBRG = 71, /**< Nvidia proprietary Bayer ISP format - one channel in one surface with interleaved GBRG ordering and mapped to opaque integer datatype. */ + cudaEglColorFormatBayerBCCR = 72, /**< Bayer format - one channel in one surface with interleaved BCCR ordering. */ + cudaEglColorFormatBayerRCCB = 73, /**< Bayer format - one channel in one surface with interleaved RCCB ordering. */ + cudaEglColorFormatBayerCRBC = 74, /**< Bayer format - one channel in one surface with interleaved CRBC ordering. */ + cudaEglColorFormatBayerCBRC = 75, /**< Bayer format - one channel in one surface with interleaved CBRC ordering. */ + cudaEglColorFormatBayer10CCCC = 76, /**< Bayer10 format - one channel in one surface with interleaved CCCC ordering. Out of 16 bits, 10 bits used 6 bits No-op. */ + cudaEglColorFormatBayer12BCCR = 77, /**< Bayer12 format - one channel in one surface with interleaved BCCR ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12RCCB = 78, /**< Bayer12 format - one channel in one surface with interleaved RCCB ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12CRBC = 79, /**< Bayer12 format - one channel in one surface with interleaved CRBC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12CBRC = 80, /**< Bayer12 format - one channel in one surface with interleaved CBRC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatBayer12CCCC = 81, /**< Bayer12 format - one channel in one surface with interleaved CCCC ordering. Out of 16 bits, 12 bits used 4 bits No-op. */ + cudaEglColorFormatY = 82, /**< Color format for single Y plane. */ + cudaEglColorFormatYUV420SemiPlanar_2020 = 83, /**< Y, UV in two surfaces (UV as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU420SemiPlanar_2020 = 84, /**< Y, VU in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYUV420Planar_2020 = 85, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU420Planar_2020 = 86, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYUV420SemiPlanar_709 = 87, /**< Y, UV in two surfaces (UV as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU420SemiPlanar_709 = 88, /**< Y, VU in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYUV420Planar_709 = 89, /**< Y, U, V in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatYVU420Planar_709 = 90, /**< Y, V, U in three surfaces, each in a separate surface, U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_420SemiPlanar_709 = 91, /**< Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_420SemiPlanar_2020 = 92, /**< Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_422SemiPlanar_2020 = 93, /**< Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatY10V10U10_422SemiPlanar = 94, /**< Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatY10V10U10_422SemiPlanar_709 = 95, /**< Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = Y height. */ + cudaEglColorFormatY_ER = 96, /**< Extended Range Color format for single Y plane. */ + cudaEglColorFormatY_709_ER = 97, /**< Extended Range Color format for single Y plane. */ + cudaEglColorFormatY10_ER = 98, /**< Extended Range Color format for single Y10 plane. */ + cudaEglColorFormatY10_709_ER = 99, /**< Extended Range Color format for single Y10 plane. */ + cudaEglColorFormatY12_ER = 100, /**< Extended Range Color format for single Y12 plane. */ + cudaEglColorFormatY12_709_ER = 101, /**< Extended Range Color format for single Y12 plane. */ + cudaEglColorFormatYUVA = 102, /**< Y, U, V, A four channels in one surface, interleaved as AVUY. */ + cudaEglColorFormatYVYU = 104, /**< Y, U, V in one surface, interleaved as YVYU in one channel. */ + cudaEglColorFormatVYUY = 105, /**< Y, U, V in one surface, interleaved as VYUY in one channel. */ + cudaEglColorFormatY10V10U10_420SemiPlanar_ER = 106, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_420SemiPlanar_709_ER = 107, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY10V10U10_444SemiPlanar_ER = 108, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatY10V10U10_444SemiPlanar_709_ER = 109, /**< Extended Range Y10, V10U10 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatY12V12U12_420SemiPlanar_ER = 110, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY12V12U12_420SemiPlanar_709_ER = 111, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = 1/2 Y width, U/V height = 1/2 Y height. */ + cudaEglColorFormatY12V12U12_444SemiPlanar_ER = 112, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ + cudaEglColorFormatY12V12U12_444SemiPlanar_709_ER = 113, /**< Extended Range Y12, V12U12 in two surfaces (VU as one surface) U/V width = Y width, U/V height = Y height. */ +} cudaEglColorFormat; + +/** + * CUDA EGL Plane Descriptor - structure defining each plane of a CUDA EGLFrame + */ +typedef struct cudaEglPlaneDesc_st { + unsigned int width; /**< Width of plane */ + unsigned int height; /**< Height of plane */ + unsigned int depth; /**< Depth of plane */ + unsigned int pitch; /**< Pitch of plane */ + unsigned int numChannels; /**< Number of channels for the plane */ + struct cudaChannelFormatDesc channelDesc; /**< Channel Format Descriptor */ + unsigned int reserved[4]; /**< Reserved for future use */ +} cudaEglPlaneDesc; + +/** + * CUDA EGLFrame Descriptor - structure defining one frame of EGL. + * + * Each frame may contain one or more planes depending on whether the surface is Multiplanar or not. + * Each plane of EGLFrame is represented by ::cudaEglPlaneDesc which is defined as: + * \code + * typedef struct cudaEglPlaneDesc_st { + * unsigned int width; + * unsigned int height; + * unsigned int depth; + * unsigned int pitch; + * unsigned int numChannels; + * struct cudaChannelFormatDesc channelDesc; + * unsigned int reserved[4]; + * } cudaEglPlaneDesc; + * \endcode + +*/ +typedef struct cudaEglFrame_st { + union { + cudaArray_t pArray[CUDA_EGL_MAX_PLANES]; /**< Array of CUDA arrays corresponding to each plane*/ + struct cudaPitchedPtr pPitch[CUDA_EGL_MAX_PLANES]; /**< Array of Pointers corresponding to each plane*/ + } frame; + cudaEglPlaneDesc planeDesc[CUDA_EGL_MAX_PLANES]; /**< CUDA EGL Plane Descriptor ::cudaEglPlaneDesc*/ + unsigned int planeCount; /**< Number of planes */ + cudaEglFrameType frameType; /**< Array or Pitch */ + cudaEglColorFormat eglColorFormat; /**< CUDA EGL Color Format*/ +} cudaEglFrame; + +/** + * CUDA EGLSream Connection + */ +typedef struct CUeglStreamConnection_st *cudaEglStreamConnection; + +/** @} */ /* END CUDART_TYPES */ + +/** + * \addtogroup CUDART_EGL EGL Interoperability + * This section describes the EGL interoperability functions of the CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Registers an EGL image + * + * Registers the EGLImageKHR specified by \p image for access by + * CUDA. A handle to the registered object is returned as \p pCudaResource. + * Additional Mapping/Unmapping is not required for the registered resource and + * ::cudaGraphicsResourceGetMappedEglFrame can be directly called on the \p pCudaResource. + * + * The application will be responsible for synchronizing access to shared objects. + * The application must ensure that any pending operation which access the objects have completed + * before passing control to CUDA. This may be accomplished by issuing and waiting for + * glFinish command on all GLcontexts (for OpenGL and likewise for other APIs). + * The application will be also responsible for ensuring that any pending operation on the + * registered CUDA resource has completed prior to executing subsequent commands in other APIs + * accesing the same memory objects. + * This can be accomplished by calling cuCtxSynchronize or cuEventSynchronize (preferably). + * + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::cudaGraphicsRegisterFlagsNone: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::cudaGraphicsRegisterFlagsReadOnly: Specifies that CUDA + * will not write to this resource. + * - ::cudaGraphicsRegisterFlagsWriteDiscard: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * The EGLImageKHR is an object which can be used to create EGLImage target resource. It is defined as a void pointer. + * typedef void* EGLImageKHR + * + * \param pCudaResource - Pointer to the returned object handle + * \param image - An EGLImageKHR image which can be used to create target resource. + * \param flags - Map flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsResourceGetMappedEglFrame, + * ::cuGraphicsEGLRegisterImage + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsEGLRegisterImage(struct cudaGraphicsResource **pCudaResource, EGLImageKHR image, unsigned int flags); + +/** + * \brief Connect CUDA to EGLStream as a consumer. + * + * Connect CUDA as a consumer to EGLStreamKHR specified by \p eglStream. + * + * The EGLStreamKHR is an EGL object that transfers a sequence of image frames from one + * API to another. + * + * \param conn - Pointer to the returned connection handle + * \param eglStream - EGLStreamKHR handle + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamConsumerDisconnect, + * ::cudaEGLStreamConsumerAcquireFrame, + * ::cudaEGLStreamConsumerReleaseFrame, + * ::cuEGLStreamConsumerConnect + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamConsumerConnect(cudaEglStreamConnection *conn, EGLStreamKHR eglStream); + +/** + * \brief Connect CUDA to EGLStream as a consumer with given flags. + * + * Connect CUDA as a consumer to EGLStreamKHR specified by \p stream with specified \p flags defined by + * ::cudaEglResourceLocationFlags. + * + * The flags specify whether the consumer wants to access frames from system memory or video memory. + * Default is ::cudaEglResourceLocationVidmem. + * + * \param conn - Pointer to the returned connection handle + * \param eglStream - EGLStreamKHR handle + * \param flags - Flags denote intended location - system or video. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamConsumerDisconnect, + * ::cudaEGLStreamConsumerAcquireFrame, + * ::cudaEGLStreamConsumerReleaseFrame, + * ::cuEGLStreamConsumerConnectWithFlags + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamConsumerConnectWithFlags(cudaEglStreamConnection *conn, EGLStreamKHR eglStream, unsigned int flags); + +/** + * \brief Disconnect CUDA as a consumer to EGLStream . + * + * Disconnect CUDA as a consumer to EGLStreamKHR. + * + * \param conn - Conection to disconnect. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamConsumerConnect, + * ::cudaEGLStreamConsumerAcquireFrame, + * ::cudaEGLStreamConsumerReleaseFrame, + * ::cuEGLStreamConsumerDisconnect + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamConsumerDisconnect(cudaEglStreamConnection *conn); + +/** + * \brief Acquire an image frame from the EGLStream with CUDA as a consumer. + * + * Acquire an image frame from EGLStreamKHR. + * ::cudaGraphicsResourceGetMappedEglFrame can be called on \p pCudaResource to get + * ::cudaEglFrame. + * + * \param conn - Connection on which to acquire + * \param pCudaResource - CUDA resource on which the EGLStream frame will be mapped for use. + * \param pStream - CUDA stream for synchronization and any data migrations + * implied by ::cudaEglResourceLocationFlags. + * \param timeout - Desired timeout in usec. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * ::cudaErrorLaunchTimeout + * + * \sa + * ::cudaEGLStreamConsumerConnect, + * ::cudaEGLStreamConsumerDisconnect, + * ::cudaEGLStreamConsumerReleaseFrame, + * ::cuEGLStreamConsumerAcquireFrame + */ + +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamConsumerAcquireFrame(cudaEglStreamConnection *conn, + cudaGraphicsResource_t *pCudaResource, cudaStream_t *pStream, unsigned int timeout); +/** + * \brief Releases the last frame acquired from the EGLStream. + * + * Release the acquired image frame specified by \p pCudaResource to EGLStreamKHR. + * + * \param conn - Connection on which to release + * \param pCudaResource - CUDA resource whose corresponding frame is to be released + * \param pStream - CUDA stream on which release will be done. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamConsumerConnect, + * ::cudaEGLStreamConsumerDisconnect, + * ::cudaEGLStreamConsumerAcquireFrame, + * ::cuEGLStreamConsumerReleaseFrame + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamConsumerReleaseFrame(cudaEglStreamConnection *conn, + cudaGraphicsResource_t pCudaResource, cudaStream_t *pStream); + +/** + * \brief Connect CUDA to EGLStream as a producer. + * + * Connect CUDA as a producer to EGLStreamKHR specified by \p stream. + * + * The EGLStreamKHR is an EGL object that transfers a sequence of image frames from one + * API to another. + * + * \param conn - Pointer to the returned connection handle + * \param eglStream - EGLStreamKHR handle + * \param width - width of the image to be submitted to the stream + * \param height - height of the image to be submitted to the stream + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamProducerDisconnect, + * ::cudaEGLStreamProducerPresentFrame, + * ::cudaEGLStreamProducerReturnFrame, + * ::cuEGLStreamProducerConnect + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamProducerConnect(cudaEglStreamConnection *conn, + EGLStreamKHR eglStream, EGLint width, EGLint height); + +/** + * \brief Disconnect CUDA as a producer to EGLStream . + * + * Disconnect CUDA as a producer to EGLStreamKHR. + * + * \param conn - Conection to disconnect. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamProducerConnect, + * ::cudaEGLStreamProducerPresentFrame, + * ::cudaEGLStreamProducerReturnFrame, + * ::cuEGLStreamProducerDisconnect + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamProducerDisconnect(cudaEglStreamConnection *conn); + +/** + * \brief Present a CUDA eglFrame to the EGLStream with CUDA as a producer. + * + * The ::cudaEglFrame is defined as: + * \code + * typedef struct cudaEglFrame_st { + * union { + * cudaArray_t pArray[CUDA_EGL_MAX_PLANES]; + * struct cudaPitchedPtr pPitch[CUDA_EGL_MAX_PLANES]; + * } frame; + * cudaEglPlaneDesc planeDesc[CUDA_EGL_MAX_PLANES]; + * unsigned int planeCount; + * cudaEglFrameType frameType; + * cudaEglColorFormat eglColorFormat; + * } cudaEglFrame; + * \endcode + * + * For ::cudaEglFrame of type ::cudaEglFrameTypePitch, the application may present sub-region of a memory + * allocation. In that case, ::cudaPitchedPtr::ptr will specify the start address of the sub-region in + * the allocation and ::cudaEglPlaneDesc will specify the dimensions of the sub-region. + * + * \param conn - Connection on which to present the CUDA array + * \param eglframe - CUDA Eglstream Proucer Frame handle to be sent to the consumer over EglStream. + * \param pStream - CUDA stream on which to present the frame. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamProducerConnect, + * ::cudaEGLStreamProducerDisconnect, + * ::cudaEGLStreamProducerReturnFrame, + * ::cuEGLStreamProducerPresentFrame + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamProducerPresentFrame(cudaEglStreamConnection *conn, + cudaEglFrame eglframe, cudaStream_t *pStream); + +/** + * \brief Return the CUDA eglFrame to the EGLStream last released by the consumer. + * + * This API can potentially return cudaErrorLaunchTimeout if the consumer has not + * returned a frame to EGL stream. If timeout is returned the application can retry. + * + * \param conn - Connection on which to present the CUDA array + * \param eglframe - CUDA Eglstream Proucer Frame handle returned from the consumer over EglStream. + * \param pStream - CUDA stream on which to return the frame. + * + * \return + * ::cudaSuccess, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \sa + * ::cudaEGLStreamProducerConnect, + * ::cudaEGLStreamProducerDisconnect, + * ::cudaEGLStreamProducerPresentFrame, + * ::cuEGLStreamProducerReturnFrame + */ +extern __host__ cudaError_t CUDARTAPI cudaEGLStreamProducerReturnFrame(cudaEglStreamConnection *conn, + cudaEglFrame *eglframe, cudaStream_t *pStream); + +/** + * \brief Get an eglFrame through which to access a registered EGL graphics resource. + * + * Returns in \p *eglFrame an eglFrame pointer through which the registered graphics resource + * \p resource may be accessed. + * This API can only be called for EGL graphics resources. + * + * The ::cudaEglFrame is defined as + * \code + * typedef struct cudaEglFrame_st { + * union { + * cudaArray_t pArray[CUDA_EGL_MAX_PLANES]; + * struct cudaPitchedPtr pPitch[CUDA_EGL_MAX_PLANES]; + * } frame; + * cudaEglPlaneDesc planeDesc[CUDA_EGL_MAX_PLANES]; + * unsigned int planeCount; + * cudaEglFrameType frameType; + * cudaEglColorFormat eglColorFormat; + * } cudaEglFrame; + * \endcode + * + * + * \param eglFrame - Returned eglFrame. + * \param resource - Registered resource to access. + * \param index - Index for cubemap surfaces. + * \param mipLevel - Mipmap level for the subresource to access. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown + * + * \note Note that in case of multiplanar \p *eglFrame, pitch of only first plane (unsigned int cudaEglPlaneDesc::pitch) is to be considered by the application. + * + * \sa + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cudaGraphicsResourceGetMappedPointer, + * ::cuGraphicsResourceGetMappedEglFrame + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsResourceGetMappedEglFrame(cudaEglFrame* eglFrame, + cudaGraphicsResource_t resource, unsigned int index, unsigned int mipLevel); + +/** + * \brief Creates an event from EGLSync object + * + * Creates an event *phEvent from an EGLSyncKHR eglSync with the flages specified + * via \p flags. Valid flags include: + * - ::cudaEventDefault: Default event creation flag. + * - ::cudaEventBlockingSync: Specifies that the created event should use blocking + * synchronization. A CPU thread that uses ::cudaEventSynchronize() to wait on + * an event created with this flag will block until the event has actually + * been completed. + * + * ::cudaEventRecord and TimingData are not supported for events created from EGLSync. + * + * The EGLSyncKHR is an opaque handle to an EGL sync object. + * typedef void* EGLSyncKHR + * + * \param phEvent - Returns newly created event + * \param eglSync - Opaque handle to EGLSync object + * \param flags - Event creation flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInitializationError, + * ::cudaErrorInvalidValue, + * ::cudaErrorLaunchFailure, + * ::cudaErrorMemoryAllocation + * + * \sa + * ::cudaEventQuery, + * ::cudaEventSynchronize, + * ::cudaEventDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaEventCreateFromEGLSync(cudaEvent_t *phEvent, EGLSyncKHR eglSync, unsigned int flags); + +/** @} */ /* END CUDART_EGL */ + +#if defined(__cplusplus) +} +#endif /* __cplusplus */ + +#endif /* __CUDA_EGL_INTEROP_H__ */ + diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.h new file mode 100644 index 0000000000000000000000000000000000000000..dfadd9619cec8ef04dee6b201468a2b849596d91 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.h @@ -0,0 +1,4826 @@ +/* +* Copyright 1993-2023 NVIDIA Corporation. All rights reserved. +* +* NOTICE TO LICENSEE: +* +* This source code and/or documentation ("Licensed Deliverables") are +* subject to NVIDIA intellectual property rights under U.S. and +* international Copyright laws. +* +* These Licensed Deliverables contained herein is PROPRIETARY and +* CONFIDENTIAL to NVIDIA and is being provided under the terms and +* conditions of a form of NVIDIA software license agreement by and +* between NVIDIA and Licensee ("License Agreement") or electronically +* accepted by Licensee. Notwithstanding any terms or conditions to +* the contrary in the License Agreement, reproduction or disclosure +* of the Licensed Deliverables to any third party without the express +* written consent of NVIDIA is prohibited. +* +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE +* SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS +* PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. +* NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED +* DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, +* NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY +* SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY +* DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, +* WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS +* ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE +* OF THESE LICENSED DELIVERABLES. +* +* U.S. Government End Users. These Licensed Deliverables are a +* "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT +* 1995), consisting of "commercial computer software" and "commercial +* computer software documentation" as such terms are used in 48 +* C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government +* only as a commercial end item. Consistent with 48 C.F.R.12.212 and +* 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all +* U.S. Government End Users acquire the Licensed Deliverables with +* only those rights set forth herein. +* +* Any use of the Licensed Deliverables in individual and commercial +* software must include, in the user documentation and internal +* comments to the code, the above Disclaimer and U.S. Government End +* Users Notice. +*/ + +/** +* \defgroup CUDA_MATH_INTRINSIC_HALF Half Precision Intrinsics +* This section describes half precision intrinsic functions. +* To use these functions, include the header file \p cuda_fp16.h in your program. +* All of the functions defined here are available in device code. +* Some of the functions are also available to host compilers, please +* refer to respective functions' documentation for details. +* +* NOTE: Aggressive floating-point optimizations performed by host or device +* compilers may affect numeric behavior of the functions implemented in this +* header. +* +* The following macros are available to help users selectively enable/disable +* various definitions present in the header file: +* - \p CUDA_NO_HALF - If defined, this macro will prevent the definition of +* additional type aliases in the global namespace, helping to avoid potential +* conflicts with symbols defined in the user program. +* - \p __CUDA_NO_HALF_CONVERSIONS__ - If defined, this macro will prevent the +* use of the C++ type conversions (converting constructors and conversion +* operators) that are common for built-in floating-point types, but may be +* undesirable for \p half which is essentially a user-defined type. +* - \p __CUDA_NO_HALF_OPERATORS__ and \p __CUDA_NO_HALF2_OPERATORS__ - If +* defined, these macros will prevent the inadvertent use of usual arithmetic +* and comparison operators. This enforces the storage-only type semantics and +* prevents C++ style computations on \p half and \p half2 types. +*/ + +/** +* \defgroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS Half Arithmetic Constants +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these constants, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF_ARITHMETIC Half Arithmetic Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF2_ARITHMETIC Half2 Arithmetic Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF_COMPARISON Half Comparison Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF2_COMPARISON Half2 Comparison Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF_MISC Half Precision Conversion and Data Movement +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF_FUNCTIONS Half Math Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +/** +* \defgroup CUDA_MATH__HALF2_FUNCTIONS Half2 Math Functions +* \ingroup CUDA_MATH_INTRINSIC_HALF +* To use these functions, include the header file \p cuda_fp16.h in your program. +*/ + +#ifndef __CUDA_FP16_H__ +#define __CUDA_FP16_H__ + +/* bring in float2, double4, etc vector types */ +#include "vector_types.h" +/* bring in operations on vector types like: make_float2 */ +#include "vector_functions.h" + +#define ___CUDA_FP16_STRINGIFY_INNERMOST(x) #x +#define __CUDA_FP16_STRINGIFY(x) ___CUDA_FP16_STRINGIFY_INNERMOST(x) + +#if defined(__cplusplus) + +/* Set up function decorations */ +#if (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) +#define __CUDA_FP16_DECL__ __device__ +#define __CUDA_HOSTDEVICE_FP16_DECL__ __device__ +#define __CUDA_HOSTDEVICE__ __device__ +#elif defined(__CUDACC__) || defined(_NVHPC_CUDA) +#define __CUDA_FP16_DECL__ static __device__ __inline__ +#define __CUDA_HOSTDEVICE_FP16_DECL__ static __host__ __device__ __inline__ +#define __CUDA_HOSTDEVICE__ __host__ __device__ +#else /* !defined(__CUDACC__) */ +#if defined(__GNUC__) +#define __CUDA_HOSTDEVICE_FP16_DECL__ static __attribute__ ((unused)) +#else +#define __CUDA_HOSTDEVICE_FP16_DECL__ static +#endif /* defined(__GNUC__) */ +#define __CUDA_HOSTDEVICE__ +#endif /* (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) */ + +#define __CUDA_FP16_TYPES_EXIST__ + +/* Forward-declaration of structures defined in "cuda_fp16.hpp" */ +struct __half; +struct __half2; + +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts double number to half precision in round-to-nearest-even mode +* and returns \p half with converted value. +* +* \details Converts double number \p a to half precision in round-to-nearest-even mode. +* \param[in] a - double. Is only being read. +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __double2half(const double a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts float number to half precision in round-to-nearest-even mode +* and returns \p half with converted value. +* +* \details Converts float number \p a to half precision in round-to-nearest-even mode. +* \param[in] a - float. Is only being read. +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts float number to half precision in round-to-nearest-even mode +* and returns \p half with converted value. +* +* \details Converts float number \p a to half precision in round-to-nearest-even mode. +* \param[in] a - float. Is only being read. +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rn(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts float number to half precision in round-towards-zero mode +* and returns \p half with converted value. +* +* \details Converts float number \p a to half precision in round-towards-zero mode. +* \param[in] a - float. Is only being read. +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rz(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts float number to half precision in round-down mode +* and returns \p half with converted value. +* +* \details Converts float number \p a to half precision in round-down mode. +* \param[in] a - float. Is only being read. +* +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rd(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts float number to half precision in round-up mode +* and returns \p half with converted value. +* +* \details Converts float number \p a to half precision in round-up mode. +* \param[in] a - float. Is only being read. +* +* \returns half +* - \p a converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_ru(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts \p half number to float. +* +* \details Converts half number \p a to float. +* \param[in] a - float. Is only being read. +* +* \returns float +* - \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ float __half2float(const __half a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts input to half precision in round-to-nearest-even mode and +* populates both halves of \p half2 with converted value. +* +* \details Converts input \p a to half precision in round-to-nearest-even mode and +* populates both halves of \p half2 with converted value. +* \param[in] a - float. Is only being read. +* +* \returns half2 +* - The \p half2 value with both halves equal to the converted half +* precision number. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __float2half2_rn(const float a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts both input floats to half precision in round-to-nearest-even +* mode and returns \p half2 with converted values. +* +* \details Converts both input floats to half precision in round-to-nearest-even mode +* and combines the results into one \p half2 number. Low 16 bits of the return +* value correspond to the input \p a, high 16 bits correspond to the input \p +* b. +* \param[in] a - float. Is only being read. +* \param[in] b - float. Is only being read. +* +* \returns half2 +* - The \p half2 value with corresponding halves equal to the +* converted input floats. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __floats2half2_rn(const float a, const float b); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts low 16 bits of \p half2 to float and returns the result +* +* \details Converts low 16 bits of \p half2 input \p a to 32-bit floating-point number +* and returns the result. +* \param[in] a - half2. Is only being read. +* +* \returns float +* - The low 16 bits of \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ float __low2float(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts high 16 bits of \p half2 to float and returns the result +* +* \details Converts high 16 bits of \p half2 input \p a to 32-bit floating-point number +* and returns the result. +* \param[in] a - half2. Is only being read. +* +* \returns float +* - The high 16 bits of \p a converted to float. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ float __high2float(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed char in round-towards-zero mode. +* +* \details Convert the half-precision floating-point value \p h to a signed char +* integer in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns signed char +* - \p h converted to a signed char. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ signed char __half2char_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned char in round-towards-zero +* mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned +* char in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned char +* - \p h converted to an unsigned char. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned char __half2uchar_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed short integer in round-towards-zero mode. +* +* \details Convert the half-precision floating-point value \p h to a signed short +* integer in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ short int __half2short_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned short integer in round-towards-zero +* mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned short +* integer in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned short int __half2ushort_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed integer in round-towards-zero mode. +* +* \details Convert the half-precision floating-point value \p h to a signed integer in +* round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ int __half2int_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned integer in round-towards-zero mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned integer +* in round-towards-zero mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned int __half2uint_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed 64-bit integer in round-towards-zero mode. +* +* \details Convert the half-precision floating-point value \p h to a signed 64-bit +* integer in round-towards-zero mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ long long int __half2ll_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned 64-bit integer in round-towards-zero +* mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned 64-bit +* integer in round-towards-zero mode. NaN inputs return 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned long long int __half2ull_rz(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Vector function, combines two \p __half numbers into one \p __half2 number. +* +* \details Combines two input \p __half number \p x and \p y into one \p __half2 number. +* Input \p x is stored in low 16 bits of the return value, input \p y is stored +* in high 16 bits of the return value. +* \param[in] x - half. Is only being read. +* \param[in] y - half. Is only being read. +* +* \returns __half2 +* - The \p __half2 vector with one half equal to \p x and the other to \p y. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 make_half2(const __half x, const __half y); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts both components of float2 number to half precision in +* round-to-nearest-even mode and returns \p half2 with converted values. +* +* \details Converts both components of float2 to half precision in round-to-nearest-even +* mode and combines the results into one \p half2 number. Low 16 bits of the +* return value correspond to \p a.x and high 16 bits of the return value +* correspond to \p a.y. +* \param[in] a - float2. Is only being read. +* +* \returns half2 +* - The \p half2 which has corresponding halves equal to the +* converted float2 components. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __float22half2_rn(const float2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Converts both halves of \p half2 to float2 and returns the result. +* +* \details Converts both halves of \p half2 input \p a to float2 and returns the +* result. +* \param[in] a - half2. Is only being read. +* +* \returns float2 +* - \p a converted to float2. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ float2 __half22float2(const __half2 a); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed integer in round-to-nearest-even mode. +* +* \details Convert the half-precision floating-point value \p h to a signed integer in +* round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ int __half2int_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to a signed integer in +* round-down mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ int __half2int_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to a signed integer in +* round-up mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns int +* - \p h converted to a signed integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ int __half2int_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed integer to a half in round-to-nearest-even mode. +* +* \details Convert the signed integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rn(const int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed integer to a half in round-towards-zero mode. +* +* \details Convert the signed integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rz(const int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed integer to a half in round-down mode. +* +* \details Convert the signed integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rd(const int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed integer to a half in round-up mode. +* +* \details Convert the signed integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_ru(const int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed short integer in round-to-nearest-even +* mode. +* +* \details Convert the half-precision floating-point value \p h to a signed short +* integer in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ short int __half2short_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed short integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to a signed short +* integer in round-down mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ short int __half2short_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed short integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to a signed short +* integer in round-up mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns short int +* - \p h converted to a signed short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ short int __half2short_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed short integer to a half in round-to-nearest-even +* mode. +* +* \details Convert the signed short integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rn(const short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed short integer to a half in round-towards-zero mode. +* +* \details Convert the signed short integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rz(const short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed short integer to a half in round-down mode. +* +* \details Convert the signed short integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rd(const short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed short integer to a half in round-up mode. +* +* \details Convert the signed short integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_ru(const short int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned integer in round-to-nearest-even mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned integer +* in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned int __half2uint_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned integer +* in round-down mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned int __half2uint_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned integer +* in round-up mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned int +* - \p h converted to an unsigned integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned int __half2uint_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned integer to a half in round-to-nearest-even mode. +* +* \details Convert the unsigned integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rn(const unsigned int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned integer to a half in round-towards-zero mode. +* +* \details Convert the unsigned integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rz(const unsigned int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned integer to a half in round-down mode. +* +* \details Convert the unsigned integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rd(const unsigned int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned integer to a half in round-up mode. +* +* \details Convert the unsigned integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - unsigned int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_ru(const unsigned int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned short integer in round-to-nearest-even +* mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned short +* integer in round-to-nearest-even mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned short int __half2ushort_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned short integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned short +* integer in round-down mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +*/ +__CUDA_FP16_DECL__ unsigned short int __half2ushort_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned short integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned short +* integer in round-up mode. NaN inputs are converted to 0. +* \param[in] h - half. Is only being read. +* +* \returns unsigned short int +* - \p h converted to an unsigned short integer. +*/ +__CUDA_FP16_DECL__ unsigned short int __half2ushort_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned short integer to a half in round-to-nearest-even +* mode. +* +* \details Convert the unsigned short integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rn(const unsigned short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned short integer to a half in round-towards-zero +* mode. +* +* \details Convert the unsigned short integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rz(const unsigned short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned short integer to a half in round-down mode. +* +* \details Convert the unsigned short integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rd(const unsigned short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned short integer to a half in round-up mode. +* +* \details Convert the unsigned short integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_ru(const unsigned short int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned 64-bit integer in round-to-nearest-even +* mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned 64-bit +* integer in round-to-nearest-even mode. NaN inputs return 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned long long int __half2ull_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned 64-bit integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned 64-bit +* integer in round-down mode. NaN inputs return 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned long long int __half2ull_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to an unsigned 64-bit integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to an unsigned 64-bit +* integer in round-up mode. NaN inputs return 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns unsigned long long int +* - \p h converted to an unsigned 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ unsigned long long int __half2ull_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned 64-bit integer to a half in round-to-nearest-even +* mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rn(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned 64-bit integer to a half in round-towards-zero +* mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rz(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned 64-bit integer to a half in round-down mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rd(const unsigned long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert an unsigned 64-bit integer to a half in round-up mode. +* +* \details Convert the unsigned 64-bit integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - unsigned long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_ru(const unsigned long long int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed 64-bit integer in round-to-nearest-even +* mode. +* +* \details Convert the half-precision floating-point value \p h to a signed 64-bit +* integer in round-to-nearest-even mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ long long int __half2ll_rn(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed 64-bit integer in round-down mode. +* +* \details Convert the half-precision floating-point value \p h to a signed 64-bit +* integer in round-down mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ long long int __half2ll_rd(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a half to a signed 64-bit integer in round-up mode. +* +* \details Convert the half-precision floating-point value \p h to a signed 64-bit +* integer in round-up mode. NaN inputs return a long long int with hex value of 0x8000000000000000. +* \param[in] h - half. Is only being read. +* +* \returns long long int +* - \p h converted to a signed 64-bit integer. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ long long int __half2ll_ru(const __half h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed 64-bit integer to a half in round-to-nearest-even +* mode. +* +* \details Convert the signed 64-bit integer value \p i to a half-precision floating-point +* value in round-to-nearest-even mode. +* \param[in] i - long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rn(const long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed 64-bit integer to a half in round-towards-zero mode. +* +* \details Convert the signed 64-bit integer value \p i to a half-precision floating-point +* value in round-towards-zero mode. +* \param[in] i - long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rz(const long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed 64-bit integer to a half in round-down mode. +* +* \details Convert the signed 64-bit integer value \p i to a half-precision floating-point +* value in round-down mode. +* \param[in] i - long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rd(const long long int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Convert a signed 64-bit integer to a half in round-up mode. +* +* \details Convert the signed 64-bit integer value \p i to a half-precision floating-point +* value in round-up mode. +* \param[in] i - long long int. Is only being read. +* +* \returns half +* - \p i converted to half. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_ru(const long long int i); +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Truncate input argument to the integral part. +* +* \details Round \p h to the nearest integer value that does not exceed \p h in +* magnitude. +* \param[in] h - half. Is only being read. +* +* \returns half +* - The truncated integer value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half htrunc(const __half h); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculate ceiling of the input argument. +* +* \details Compute the smallest integer value not less than \p h. +* \param[in] h - half. Is only being read. +* +* \returns half +* - The smallest integer value not less than \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hceil(const __half h); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculate the largest integer less than or equal to \p h. +* +* \details Calculate the largest integer value which is less than or equal to \p h. +* \param[in] h - half. Is only being read. +* +* \returns half +* - The largest integer value which is less than or equal to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hfloor(const __half h); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Round input to nearest integer value in half-precision floating-point +* number. +* +* \details Round \p h to the nearest integer value in half-precision floating-point +* format, with halfway cases rounded to the nearest even integer value. +* \param[in] h - half. Is only being read. +* +* \returns half +* - The nearest integer to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hrint(const __half h); + +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Truncate \p half2 vector input argument to the integral part. +* +* \details Round each component of vector \p h to the nearest integer value that does +* not exceed \p h in magnitude. +* \param[in] h - half2. Is only being read. +* +* \returns half2 +* - The truncated \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2trunc(const __half2 h); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculate \p half2 vector ceiling of the input argument. +* +* \details For each component of vector \p h compute the smallest integer value not less +* than \p h. +* \param[in] h - half2. Is only being read. +* +* \returns half2 +* - The vector of smallest integers not less than \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2ceil(const __half2 h); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculate the largest integer less than or equal to \p h. +* +* \details For each component of vector \p h calculate the largest integer value which +* is less than or equal to \p h. +* \param[in] h - half2. Is only being read. +* +* \returns half2 +* - The vector of largest integers which is less than or equal to \p h. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2floor(const __half2 h); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Round input to nearest integer value in half-precision floating-point +* number. +* +* \details Round each component of \p half2 vector \p h to the nearest integer value in +* half-precision floating-point format, with halfway cases rounded to the +* nearest even integer value. +* \param[in] h - half2. Is only being read. +* +* \returns half2 +* - The vector of rounded integer values. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2rint(const __half2 h); +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Returns \p half2 with both halves equal to the input value. +* +* \details Returns \p half2 number with both halves equal to the input \p a \p half +* number. +* \param[in] a - half. Is only being read. +* +* \returns half2 +* - The vector which has both its halves equal to the input \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __half2half2(const __half a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Swaps both halves of the \p half2 input. +* +* \details Swaps both halves of the \p half2 input and returns a new \p half2 number +* with swapped halves. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - \p a with its halves being swapped. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __lowhigh2highlow(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Extracts low 16 bits from each of the two \p half2 inputs and combines +* into one \p half2 number. +* +* \details Extracts low 16 bits from each of the two \p half2 inputs and combines into +* one \p half2 number. Low 16 bits from input \p a is stored in low 16 bits of +* the return value, low 16 bits from input \p b is stored in high 16 bits of +* the return value. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The low 16 bits of \p a and of \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __lows2half2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Extracts high 16 bits from each of the two \p half2 inputs and +* combines into one \p half2 number. +* +* \details Extracts high 16 bits from each of the two \p half2 inputs and combines into +* one \p half2 number. High 16 bits from input \p a is stored in low 16 bits of +* the return value, high 16 bits from input \p b is stored in high 16 bits of +* the return value. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The high 16 bits of \p a and of \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __highs2half2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Returns high 16 bits of \p half2 input. +* +* \details Returns high 16 bits of \p half2 input \p a. +* \param[in] a - half2. Is only being read. +* +* \returns half +* - The high 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __high2half(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Returns low 16 bits of \p half2 input. +* +* \details Returns low 16 bits of \p half2 input \p a. +* \param[in] a - half2. Is only being read. +* +* \returns half +* - Returns \p half which contains low 16 bits of the input \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __low2half(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Checks if the input \p half number is infinite. +* +* \details Checks if the input \p half number \p a is infinite. +* \param[in] a - half. Is only being read. +* +* \returns int +* - -1 iff \p a is equal to negative infinity, +* - 1 iff \p a is equal to positive infinity, +* - 0 otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ int __hisinf(const __half a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Combines two \p half numbers into one \p half2 number. +* +* \details Combines two input \p half number \p a and \p b into one \p half2 number. +* Input \p a is stored in low 16 bits of the return value, input \p b is stored +* in high 16 bits of the return value. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half2 +* - The half2 with one half equal to \p a and the other to \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __halves2half2(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Extracts low 16 bits from \p half2 input. +* +* \details Extracts low 16 bits from \p half2 input \p a and returns a new \p half2 +* number which has both halves equal to the extracted bits. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The half2 with both halves equal to the low 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __low2half2(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Extracts high 16 bits from \p half2 input. +* +* \details Extracts high 16 bits from \p half2 input \p a and returns a new \p half2 +* number which has both halves equal to the extracted bits. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The half2 with both halves equal to the high 16 bits of the input. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __high2half2(const __half2 a); + +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Reinterprets bits in a \p half as a signed short integer. +* +* \details Reinterprets the bits in the half-precision floating-point number \p h +* as a signed short integer. +* \param[in] h - half. Is only being read. +* +* \returns short int +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ short int __half_as_short(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Reinterprets bits in a \p half as an unsigned short integer. +* +* \details Reinterprets the bits in the half-precision floating-point \p h +* as an unsigned short number. +* \param[in] h - half. Is only being read. +* +* \returns unsigned short int +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned short int __half_as_ushort(const __half h); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Reinterprets bits in a signed short integer as a \p half. +* +* \details Reinterprets the bits in the signed short integer \p i as a +* half-precision floating-point number. +* \param[in] i - short int. Is only being read. +* +* \returns half +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short_as_half(const short int i); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Reinterprets bits in an unsigned short integer as a \p half. +* +* \details Reinterprets the bits in the unsigned short integer \p i as a +* half-precision floating-point number. +* \param[in] i - unsigned short int. Is only being read. +* +* \returns half +* - The reinterpreted value. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort_as_half(const unsigned short int i); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Calculates \p half maximum of two input values. +* +* \details Calculates \p half max(\p a, \p b) +* defined as (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmax(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Calculates \p half minimum of two input values. +* +* \details Calculates \p half min(\p a, \p b) +* defined as (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmin(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Calculates \p half2 vector maximum of two inputs. +* +* \details Calculates \p half2 vector max(\p a, \p b). +* Elementwise \p half operation is defined as +* (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise maximum of vectors \p a and \p b +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmax2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Calculates \p half2 vector minimum of two inputs. +* +* \details Calculates \p half2 vector min(\p a, \p b). +* Elementwise \p half operation is defined as +* (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, the other input is returned. +* - If both inputs are NaNs, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise minimum of vectors \p a and \p b +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmin2(const __half2 a, const __half2 b); + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300) +#if !defined warpSize && !defined __local_warpSize +#define warpSize 32 +#define __local_warpSize +#endif + +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ < 700) + +#if defined(_WIN32) +# define __CUDA_FP16_DEPRECATED__(msg) __declspec(deprecated(msg)) +#elif (defined(__GNUC__) && (__GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 5 && !defined(__clang__)))) +# define __CUDA_FP16_DEPRECATED__(msg) __attribute__((deprecated)) +#else +# define __CUDA_FP16_DEPRECATED__(msg) __attribute__((deprecated(msg))) +#endif + +#if defined(_NVHPC_CUDA) +#define __CUDA_FP16_WSB_DEPRECATION_MESSAGE(x) __CUDA_FP16_STRINGIFY(x) "() is deprecated in favor of " __CUDA_FP16_STRINGIFY(x) "_sync() and may be removed in a future release." +#else +#define __CUDA_FP16_WSB_DEPRECATION_MESSAGE(x) __CUDA_FP16_STRINGIFY(x) "() is deprecated in favor of " __CUDA_FP16_STRINGIFY(x) "_sync() and may be removed in a future release (Use -Wno-deprecated-declarations to suppress this warning)." +#endif + +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl)) __half2 __shfl(const __half2 var, const int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_up)) __half2 __shfl_up(const __half2 var, const unsigned int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_down))__half2 __shfl_down(const __half2 var, const unsigned int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_xor)) __half2 __shfl_xor(const __half2 var, const int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl)) __half __shfl(const __half var, const int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_up)) __half __shfl_up(const __half var, const unsigned int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_down)) __half __shfl_down(const __half var, const unsigned int delta, const int width = warpSize); +__CUDA_FP16_DECL__ __CUDA_FP16_DEPRECATED__(__CUDA_FP16_WSB_DEPRECATION_MESSAGE(__shfl_xor)) __half __shfl_xor(const __half var, const int delta, const int width = warpSize); + +#undef __CUDA_FP16_WSB_DEPRECATION_MESSAGE +#undef __CUDA_FP16_DEPRECATED__ +#endif /* !defined(__CUDA_ARCH__) || __CUDA_ARCH__ < 700 */ + +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Direct copy from indexed thread. +* +* \details Returns the value of var held by the thread whose ID is given by delta. +* If width is less than warpSize then each subsection of the warp behaves as a separate +* entity with a starting logical thread ID of 0. If delta is outside the range [0:width-1], +* the value returned corresponds to the value of var held by the delta modulo width (i.e. +* within the same subsection). width must have a value which is a power of 2; +* results are undefined if width is not a power of 2, or is a number greater than +* warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half2. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as half2. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __shfl_sync(const unsigned mask, const __half2 var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with lower ID relative to the caller. +* +* \details Calculates a source thread ID by subtracting delta from the caller's lane ID. +* The value of var held by the resulting lane ID is returned: in effect, var is shifted up +* the warp by delta threads. If width is less than warpSize then each subsection of the warp +* behaves as a separate entity with a starting logical thread ID of 0. The source thread index +* will not wrap around the value of width, so effectively the lower delta threads will be unchanged. +* width must have a value which is a power of 2; results are undefined if width is not a power of 2, +* or is a number greater than warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half2. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as half2. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __shfl_up_sync(const unsigned mask, const __half2 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with higher ID relative to the caller. +* +* \details Calculates a source thread ID by adding delta to the caller's thread ID. +* The value of var held by the resulting thread ID is returned: this has the effect +* of shifting var down the warp by delta threads. If width is less than warpSize then +* each subsection of the warp behaves as a separate entity with a starting logical +* thread ID of 0. As for __shfl_up_sync(), the ID number of the source thread +* will not wrap around the value of width and so the upper delta threads +* will remain unchanged. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half2. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as half2. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __shfl_down_sync(const unsigned mask, const __half2 var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread based on bitwise XOR of own thread ID. +* +* \details Calculates a source thread ID by performing a bitwise XOR of the caller's thread ID with mask: +* the value of var held by the resulting thread ID is returned. If width is less than warpSize then each +* group of width consecutive threads are able to access elements from earlier groups of threads, +* however if they attempt to access elements from later groups of threads their own value of var +* will be returned. This mode implements a butterfly addressing pattern such as is used in tree +* reduction and broadcast. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half2. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 4-byte word referenced by var from the source thread ID as half2. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __shfl_xor_sync(const unsigned mask, const __half2 var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Direct copy from indexed thread. +* +* \details Returns the value of var held by the thread whose ID is given by delta. +* If width is less than warpSize then each subsection of the warp behaves as a separate +* entity with a starting logical thread ID of 0. If delta is outside the range [0:width-1], +* the value returned corresponds to the value of var held by the delta modulo width (i.e. +* within the same subsection). width must have a value which is a power of 2; +* results are undefined if width is not a power of 2, or is a number greater than +* warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as half. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __shfl_sync(const unsigned mask, const __half var, const int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with lower ID relative to the caller. +* \details Calculates a source thread ID by subtracting delta from the caller's lane ID. +* The value of var held by the resulting lane ID is returned: in effect, var is shifted up +* the warp by delta threads. If width is less than warpSize then each subsection of the warp +* behaves as a separate entity with a starting logical thread ID of 0. The source thread index +* will not wrap around the value of width, so effectively the lower delta threads will be unchanged. +* width must have a value which is a power of 2; results are undefined if width is not a power of 2, +* or is a number greater than warpSize. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as half. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __shfl_up_sync(const unsigned mask, const __half var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread with higher ID relative to the caller. +* +* \details Calculates a source thread ID by adding delta to the caller's thread ID. +* The value of var held by the resulting thread ID is returned: this has the effect +* of shifting var down the warp by delta threads. If width is less than warpSize then +* each subsection of the warp behaves as a separate entity with a starting logical +* thread ID of 0. As for __shfl_up_sync(), the ID number of the source thread +* will not wrap around the value of width and so the upper delta threads +* will remain unchanged. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as half. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __shfl_down_sync(const unsigned mask, const __half var, const unsigned int delta, const int width = warpSize); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Exchange a variable between threads within a warp. Copy from a thread based on bitwise XOR of own thread ID. +* +* \details Calculates a source thread ID by performing a bitwise XOR of the caller's thread ID with mask: +* the value of var held by the resulting thread ID is returned. If width is less than warpSize then each +* group of width consecutive threads are able to access elements from earlier groups of threads, +* however if they attempt to access elements from later groups of threads their own value of var +* will be returned. This mode implements a butterfly addressing pattern such as is used in tree +* reduction and broadcast. +* \param[in] mask - unsigned int. Is only being read. +* \param[in] var - half. Is only being read. +* \param[in] delta - int. Is only being read. +* \param[in] width - int. Is only being read. +* +* \returns Returns the 2-byte word referenced by var from the source thread ID as half. +* If the source thread ID is out of range or the source thread has exited, the calling thread's own var is returned. +* \note_ref_guide_warp_shuffle +* \internal +* \exception-guarantee no-throw guarantee +* \behavior not reentrant, not thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __shfl_xor_sync(const unsigned mask, const __half var, const int delta, const int width = warpSize); + +#if defined(__local_warpSize) +#undef warpSize +#undef __local_warpSize +#endif +#endif /*!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300) */ + +#if defined(__cplusplus) && ( !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320) ) +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.nc` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldg(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.nc` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldg(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cg` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldcg(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cg` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldcg(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.ca` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldca(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.ca` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldca(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cs` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldcs(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cs` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldcs(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.lu` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldlu(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.lu` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldlu(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cv` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half2 __ldcv(const __half2 *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `ld.global.cv` load instruction. +* \param[in] ptr - memory location +* \returns The value pointed by `ptr` +*/ +__CUDA_FP16_DECL__ __half __ldcv(const __half *const ptr); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.wb` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stwb(__half2 *const ptr, const __half2 value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.wb` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stwb(__half *const ptr, const __half value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.cg` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stcg(__half2 *const ptr, const __half2 value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.cg` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stcg(__half *const ptr, const __half value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.cs` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stcs(__half2 *const ptr, const __half2 value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.cs` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stcs(__half *const ptr, const __half value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.wt` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stwt(__half2 *const ptr, const __half2 value); +/** +* \ingroup CUDA_MATH__HALF_MISC +* \brief Generates a `st.global.wt` store instruction. +* \param[out] ptr - memory location +* \param[in] value - the value to be stored +*/ +__CUDA_FP16_DECL__ void __stwt(__half *const ptr, const __half value); +#endif /*defined(__cplusplus) && ( !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320) )*/ +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs half2 vector if-equal comparison. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __heq2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector not-equal comparison. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hne2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-equal comparison. +* +* \details Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The \p half2 result of less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hle2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-equal comparison. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hge2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-than comparison. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The half2 vector result of less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hlt2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-than comparison. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgt2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered if-equal comparison. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of unordered if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hequ2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered not-equal comparison. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of unordered not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hneu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-equal comparison. +* +* Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of unordered less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hleu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-equal comparison. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The \p half2 vector result of unordered greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgeu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-than comparison. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The vector result of unordered less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hltu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-than comparison. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p half results are set to 1.0 for true, or 0.0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The \p half2 vector result of unordered greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgtu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs half2 vector if-equal comparison. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __heq2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector not-equal comparison. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hne2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-equal comparison. +* +* \details Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hle2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-equal comparison. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hge2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-than comparison. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hlt2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-than comparison. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgt2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered if-equal comparison. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered if-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hequ2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered not-equal comparison. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered not-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hneu2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-equal comparison. +* +* Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered less-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hleu2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-equal comparison. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered greater-equal comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgeu2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-than comparison. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered less-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hltu2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-than comparison. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The corresponding \p unsigned bits are set to 0xFFFF for true, or 0x0 for false. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns unsigned int +* - The vector mask result of unordered greater-than comparison of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgtu2_mask(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Determine whether \p half2 argument is a NaN. +* +* \details Determine whether each half of input \p half2 number \p a is a NaN. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The half2 with the corresponding \p half results set to +* 1.0 for NaN, 0.0 otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hisnan2(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector addition in round-to-nearest-even mode. +* +* \details Performs \p half2 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-95 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The sum of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p half2 input vector \p b from input vector \p a in +* round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-104 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The subtraction of vector \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector multiplication in round-to-nearest-even mode. +* +* \details Performs \p half2 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-102 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise multiplying the vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector addition in round-to-nearest-even mode. +* +* \details Performs \p half2 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-95 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The sum of vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2_rn(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p half2 input vector \p b from input vector \p a in +* round-to-nearest-even mode. Prevents floating-point contractions of mul+sub +* into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-104 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The subtraction of vector \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2_rn(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector multiplication in round-to-nearest-even mode. +* +* \details Performs \p half2 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode. Prevents floating-point contractions of +* mul+add or sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-102 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise multiplying the vectors \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2_rn(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector division in round-to-nearest-even mode. +* +* \details Divides \p half2 input vector \p a by input vector \p b in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-103 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The elementwise division of \p a with \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __h2div(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Calculates the absolute value of both halves of the input \p half2 number and +* returns the result. +* +* \details Calculates the absolute value of both halves of the input \p half2 number and +* returns the result. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - Returns \p a with the absolute value of both halves. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __habs2(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector addition in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p half2 vector add of inputs \p a and \p b, in round-to-nearest-even +* mode, and clamps the results to range [0.0, 1.0]. NaN results are flushed to +* +0.0. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The sum of \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2_sat(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector subtraction in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Subtracts \p half2 input vector \p b from input vector \p a in +* round-to-nearest-even mode, and clamps the results to range [0.0, 1.0]. NaN +* results are flushed to +0.0. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The subtraction of vector \p b from \p a, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2_sat(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector multiplication in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Performs \p half2 vector multiplication of inputs \p a and \p b, in +* round-to-nearest-even mode, and clamps the results to range [0.0, 1.0]. NaN +* results are flushed to +0.0. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise multiplication of vectors \p a and \p b, +* with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2_sat(const __half2 a, const __half2 b); + +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector fused multiply-add in round-to-nearest-even +* mode. +* +* \details Performs \p half2 vector multiply on inputs \p a and \p b, +* then performs a \p half2 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-105 +* \endinternal +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* \param[in] c - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __hfma2(const __half2 a, const __half2 b, const __half2 c); +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector fused multiply-add in round-to-nearest-even +* mode, with saturation to [0.0, 1.0]. +* +* \details Performs \p half2 vector multiply on inputs \p a and \p b, +* then performs a \p half2 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode, and clamps the +* results to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* \param[in] c - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c, +* with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __hfma2_sat(const __half2 a, const __half2 b, const __half2 c); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Negates both halves of the input \p half2 number and returns the +* result. +* +* \details Negates both halves of the input \p half2 number \p a and returns the result. +* \internal +* \req DEEPLEARN-SRM_REQ-101 +* \endinternal +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - Returns \p a with both halves negated. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hneg2(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Calculates the absolute value of input \p half number and returns the result. +* +* \details Calculates the absolute value of input \p half number and returns the result. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The absolute value of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __habs(const __half a); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half addition in round-to-nearest-even mode. +* +* \details Performs \p half addition of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-94 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The sum of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p half input \p b from input \p a in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-97 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of subtracting \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half multiplication in round-to-nearest-even mode. +* +* \details Performs \p half multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-99 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of multiplying \p a and \p b. +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half addition in round-to-nearest-even mode. +* +* \details Performs \p half addition of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-94 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The sum of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd_rn(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half subtraction in round-to-nearest-even mode. +* +* \details Subtracts \p half input \p b from input \p a in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-97 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of subtracting \p b from \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub_rn(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half multiplication in round-to-nearest-even mode. +* +* \details Performs \p half multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode. Prevents floating-point contractions of mul+add or sub into fma. +* \internal +* \req DEEPLEARN-SRM_REQ-99 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of multiplying \p a and \p b. +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul_rn(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half division in round-to-nearest-even mode. +* +* \details Divides \p half input \p a by input \p b in round-to-nearest-even +* mode. +* \internal +* \req DEEPLEARN-SRM_REQ-98 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of dividing \p a by \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hdiv(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half addition in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p half add of inputs \p a and \p b, in round-to-nearest-even mode, +* and clamps the result to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The sum of \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd_sat(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half subtraction in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Subtracts \p half input \p b from input \p a in round-to-nearest-even +* mode, +* and clamps the result to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of subtraction of \p b from \p a, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub_sat(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half multiplication in round-to-nearest-even mode, with +* saturation to [0.0, 1.0]. +* +* \details Performs \p half multiplication of inputs \p a and \p b, in round-to-nearest-even +* mode, and clamps the result to range [0.0, 1.0]. NaN results are flushed to +* +0.0. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* - The result of multiplying \p a and \p b, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul_sat(const __half a, const __half b); + +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half fused multiply-add in round-to-nearest-even mode. +* +* \details Performs \p half multiply on inputs \p a and \p b, +* then performs a \p half add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* \internal +* \req DEEPLEARN-SRM_REQ-96 +* \endinternal +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* \param[in] c - half. Is only being read. +* +* \returns half +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __hfma(const __half a, const __half b, const __half c); +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half fused multiply-add in round-to-nearest-even mode, +* with saturation to [0.0, 1.0]. +* +* \details Performs \p half multiply on inputs \p a and \p b, +* then performs a \p half add of the result with \p c, +* rounding the result once in round-to-nearest-even mode, and clamps the result +* to range [0.0, 1.0]. NaN results are flushed to +0.0. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* \param[in] c - half. Is only being read. +* +* \returns half +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c, with respect to saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __hfma_sat(const __half a, const __half b, const __half c); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Negates input \p half number and returns the result. +* +* \details Negates input \p half number and returns the result. +* \internal +* \req DEEPLEARN-SRM_REQ-100 +* \endinternal +* \param[in] a - half. Is only being read. +* +* \returns half +* - minus a +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hneg(const __half a); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector if-equal comparison and returns boolean true +* iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half if-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of if-equal comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbeq2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector not-equal comparison and returns boolean +* true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half not-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of not-equal comparison +* of vectors \p a and \p b are true, +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbne2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-equal comparison and returns boolean +* true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half less-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of less-equal comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hble2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-equal comparison and returns boolean +* true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half greater-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of greater-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbge2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector less-than comparison and returns boolean +* true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half less-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of less-than comparison +* of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hblt2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector greater-than comparison and returns boolean +* true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half greater-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate false results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of greater-than +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgt2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered if-equal comparison and returns +* boolean true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector if-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half if-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered if-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbequ2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered not-equal comparison and returns +* boolean true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector not-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half not-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered not-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbneu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-equal comparison and returns +* boolean true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector less-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half less-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered less-equal +* comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbleu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-equal comparison and +* returns boolean true iff both \p half results are true, boolean false +* otherwise. +* +* \details Performs \p half2 vector greater-equal comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half greater-equal comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered +* greater-equal comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgeu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered less-than comparison and returns +* boolean true iff both \p half results are true, boolean false otherwise. +* +* \details Performs \p half2 vector less-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half less-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered less-than comparison of +* vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbltu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Performs \p half2 vector unordered greater-than comparison and +* returns boolean true iff both \p half results are true, boolean false +* otherwise. +* +* \details Performs \p half2 vector greater-than comparison of inputs \p a and \p b. +* The bool result is set to true only if both \p half greater-than comparisons +* evaluate to true, or false otherwise. +* NaN inputs generate true results. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns bool +* - true if both \p half results of unordered +* greater-than comparison of vectors \p a and \p b are true; +* - false otherwise. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgtu2(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half if-equal comparison. +* +* \details Performs \p half if-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of if-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __heq(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half not-equal comparison. +* +* \details Performs \p half not-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of not-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hne(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half less-equal comparison. +* +* \details Performs \p half less-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of less-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hle(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half greater-equal comparison. +* +* \details Performs \p half greater-equal comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of greater-equal comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hge(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half less-than comparison. +* +* \details Performs \p half less-than comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of less-than comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hlt(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half greater-than comparison. +* +* \details Performs \p half greater-than comparison of inputs \p a and \p b. +* NaN inputs generate false results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of greater-than comparison of \p a and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgt(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered if-equal comparison. +* +* \details Performs \p half if-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered if-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hequ(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered not-equal comparison. +* +* \details Performs \p half not-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered not-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hneu(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered less-equal comparison. +* +* \details Performs \p half less-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered less-equal comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hleu(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered greater-equal comparison. +* +* \details Performs \p half greater-equal comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered greater-equal comparison of \p a +* and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgeu(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered less-than comparison. +* +* \details Performs \p half less-than comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered less-than comparison of \p a and +* \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hltu(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Performs \p half unordered greater-than comparison. +* +* \details Performs \p half greater-than comparison of inputs \p a and \p b. +* NaN inputs generate true results. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns bool +* - The boolean result of unordered greater-than comparison of \p a +* and \p b. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgtu(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Determine whether \p half argument is a NaN. +* +* \details Determine whether \p half value \p a is a NaN. +* \param[in] a - half. Is only being read. +* +* \returns bool +* - true iff argument is NaN. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hisnan(const __half a); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Calculates \p half maximum of two input values, NaNs pass through. +* +* \details Calculates \p half max(\p a, \p b) +* defined as (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmax_nan(const __half a, const __half b); +/** +* \ingroup CUDA_MATH__HALF_COMPARISON +* \brief Calculates \p half minimum of two input values, NaNs pass through. +* +* \details Calculates \p half min(\p a, \p b) +* defined as (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* +* \returns half +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmin_nan(const __half a, const __half b); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Performs \p half fused multiply-add in round-to-nearest-even mode with relu saturation. +* +* \details Performs \p half multiply on inputs \p a and \p b, +* then performs a \p half add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* Then negative result is clamped to 0. +* NaN result is converted to canonical NaN. +* \param[in] a - half. Is only being read. +* \param[in] b - half. Is only being read. +* \param[in] c - half. Is only being read. +* +* \returns half +* - The result of fused multiply-add operation on \p +* a, \p b, and \p c with relu saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half __hfma_relu(const __half a, const __half b, const __half c); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Calculates \p half2 vector maximum of two inputs, NaNs pass through. +* +* \details Calculates \p half2 vector max(\p a, \p b). +* Elementwise \p half operation is defined as +* (\p a > \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise maximum of vectors \p a and \p b, with NaNs pass through +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmax2_nan(const __half2 a, const __half2 b); +/** +* \ingroup CUDA_MATH__HALF2_COMPARISON +* \brief Calculates \p half2 vector minimum of two inputs, NaNs pass through. +* +* \details Calculates \p half2 vector min(\p a, \p b). +* Elementwise \p half operation is defined as +* (\p a < \p b) ? \p a : \p b. +* - If either of inputs is NaN, then canonical NaN is returned. +* - If values of both inputs are 0.0, then +0.0 > -0.0 +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise minimum of vectors \p a and \p b, with NaNs pass through +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmin2_nan(const __half2 a, const __half2 b); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs \p half2 vector fused multiply-add in round-to-nearest-even +* mode with relu saturation. +* +* \details Performs \p half2 vector multiply on inputs \p a and \p b, +* then performs a \p half2 vector add of the result with \p c, +* rounding the result once in round-to-nearest-even mode. +* Then negative result is clamped to 0. +* NaN result is converted to canonical NaN. +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* \param[in] c - half2. Is only being read. +* +* \returns half2 +* - The result of elementwise fused multiply-add operation on vectors \p a, \p b, and \p c with relu saturation. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __hfma2_relu(const __half2 a, const __half2 b, const __half2 c); + +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Performs fast complex multiply-accumulate +* +* \details Interprets vector \p half2 input pairs \p a, \p b, and \p c as +* complex numbers in \p half precision and performs +* complex multiply-accumulate operation: a*b + c +* \param[in] a - half2. Is only being read. +* \param[in] b - half2. Is only being read. +* \param[in] c - half2. Is only being read. +* +* \returns half2 +* - The result of complex multiply-accumulate operation on complex numbers \p a, \p b, and \p c +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 __hcmadd(const __half2 a, const __half2 b, const __half2 c); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half square root in round-to-nearest-even mode. +* +* \details Calculates \p half square root of input \p a in round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The square root of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hsqrt(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half reciprocal square root in round-to-nearest-even +* mode. +* +* \details Calculates \p half reciprocal square root of input \p a in round-to-nearest-even +* mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The reciprocal square root of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hrsqrt(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half reciprocal in round-to-nearest-even mode. +* +* \details Calculates \p half reciprocal of input \p a in round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The reciprocal of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hrcp(const __half a); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half natural logarithm in round-to-nearest-even mode. +* +* \details Calculates \p half natural logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The natural logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hlog(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half binary logarithm in round-to-nearest-even mode. +* +* \details Calculates \p half binary logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The binary logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hlog2(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half decimal logarithm in round-to-nearest-even mode. +* +* \details Calculates \p half decimal logarithm of input \p a in round-to-nearest-even +* mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The decimal logarithm of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hlog10(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half natural exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p half natural exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The natural exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hexp(const __half a); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half binary exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p half binary exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The binary exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hexp2(const __half a); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half decimal exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p half decimal exponential function of input \p a in +* round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The decimal exponential function on \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hexp10(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half cosine in round-to-nearest-even mode. +* +* \details Calculates \p half cosine of input \p a in round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The cosine of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hcos(const __half a); +/** +* \ingroup CUDA_MATH__HALF_FUNCTIONS +* \brief Calculates \p half sine in round-to-nearest-even mode. +* +* \details Calculates \p half sine of input \p a in round-to-nearest-even mode. +* \param[in] a - half. Is only being read. +* +* \returns half +* - The sine of \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half hsin(const __half a); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector square root in round-to-nearest-even mode. +* +* \details Calculates \p half2 square root of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise square root on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2sqrt(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector reciprocal square root in round-to-nearest-even +* mode. +* +* \details Calculates \p half2 reciprocal square root of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise reciprocal square root on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2rsqrt(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector reciprocal in round-to-nearest-even mode. +* +* \details Calculates \p half2 reciprocal of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise reciprocal on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2rcp(const __half2 a); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector natural logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p half2 natural logarithm of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise natural logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2log(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector binary logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p half2 binary logarithm of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise binary logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2log2(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector decimal logarithm in round-to-nearest-even +* mode. +* +* \details Calculates \p half2 decimal logarithm of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise decimal logarithm on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2log10(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector exponential function in round-to-nearest-even +* mode. +* +* \details Calculates \p half2 exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2exp(const __half2 a); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector binary exponential function in +* round-to-nearest-even mode. +* +* \details Calculates \p half2 binary exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise binary exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2exp2(const __half2 a); +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector decimal exponential function in +* round-to-nearest-even mode. +* +* \details Calculates \p half2 decimal exponential function of input vector \p a in +* round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise decimal exponential function on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2exp10(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector cosine in round-to-nearest-even mode. +* +* \details Calculates \p half2 cosine of input vector \p a in round-to-nearest-even +* mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise cosine on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2cos(const __half2 a); +/** +* \ingroup CUDA_MATH__HALF2_FUNCTIONS +* \brief Calculates \p half2 vector sine in round-to-nearest-even mode. +* +* \details Calculates \p half2 sine of input vector \p a in round-to-nearest-even mode. +* \param[in] a - half2. Is only being read. +* +* \returns half2 +* - The elementwise sine on vector \p a. +* \internal +* \exception-guarantee no-throw guarantee +* \behavior reentrant, thread safe +* \endinternal +*/ +__CUDA_FP16_DECL__ __half2 h2sin(const __half2 a); +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ + +/** +* \ingroup CUDA_MATH__HALF2_ARITHMETIC +* \brief Vector add \p val to the value stored at \p address in global or shared memory, and writes this +* value back to \p address. The atomicity of the add operation is guaranteed separately for each of the +* two __half elements; the entire __half2 is not guaranteed to be atomic as a single 32-bit access. +* +* \details The location of \p address must be in global or shared memory. This operation has undefined +* behavior otherwise. This operation is natively supported by devices of compute capability 6.x and higher, +* older devices use emulation path. +* +* \param[in] address - half2*. An address in global or shared memory. +* \param[in] val - half2. The value to be added. +* +* \returns half2 +* - The old value read from \p address. +* +* \note_ref_guide_atomic +*/ +__CUDA_FP16_DECL__ __half2 atomicAdd(__half2 *const address, const __half2 val); + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) +/** +* \ingroup CUDA_MATH__HALF_ARITHMETIC +* \brief Adds \p val to the value stored at \p address in global or shared memory, and writes this value +* back to \p address. This operation is performed in one atomic operation. +* +* \details The location of \p address must be in global or shared memory. This operation has undefined +* behavior otherwise. This operation is only supported by devices of compute capability 7.x and higher. +* +* \param[in] address - half*. An address in global or shared memory. +* \param[in] val - half. The value to be added. +* +* \returns half +* - The old value read from \p address. +* +* \note_ref_guide_atomic +*/ +__CUDA_FP16_DECL__ __half atomicAdd(__half *const address, const __half val); +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) */ + +#endif /*defined(__CUDACC__) || defined(_NVHPC_CUDA)*/ + +#endif /* defined(__cplusplus) */ + +#if !defined(_MSC_VER) && __cplusplus >= 201103L +# define __CPP_VERSION_AT_LEAST_11_FP16 +#elif _MSC_FULL_VER >= 190024210 && _MSVC_LANG >= 201103L +# define __CPP_VERSION_AT_LEAST_11_FP16 +#endif + +// implicitly provided by NVRTC +#if !defined(__CUDACC_RTC__) +#include +#endif /* !defined(__CUDACC_RTC__) */ + +/* C++11 header for std::move. + * In RTC mode, std::move is provided implicitly; don't include the header + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) && !defined(__CUDACC_RTC__) +#include +#endif /* __cplusplus >= 201103L && !defined(__CUDACC_RTC__) */ + +/* C++ header for std::memcpy (used for type punning in host-side implementations). + * When compiling as a CUDA source file memcpy is provided implicitly. + * !defined(__CUDACC__) implies !defined(__CUDACC_RTC__). + */ +#if defined(__cplusplus) && !defined(__CUDACC__) +#include +#endif /* defined(__cplusplus) && !defined(__CUDACC__) */ + +#if (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) +#define __CUDA_FP16_INLINE__ +#define __CUDA_FP16_FORCEINLINE__ +#else +#define __CUDA_FP16_INLINE__ inline +#define __CUDA_FP16_FORCEINLINE__ __forceinline__ +#endif /* (defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3)))) */ + +/* Set up structure-alignment attribute */ +#if defined(__CUDACC__) +#define __CUDA_ALIGN__(align) __align__(align) +#else +/* Define alignment macro based on compiler type (cannot assume C11 "_Alignas" is available) */ +#if __cplusplus >= 201103L +#define __CUDA_ALIGN__(n) alignas(n) /* C++11 kindly gives us a keyword for this */ +#else /* !defined(__CPP_VERSION_AT_LEAST_11_FP16)*/ +#if defined(__GNUC__) +#define __CUDA_ALIGN__(n) __attribute__ ((aligned(n))) +#elif defined(_MSC_VER) +#define __CUDA_ALIGN__(n) __declspec(align(n)) +#else +#define __CUDA_ALIGN__(n) +#endif /* defined(__GNUC__) */ +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ +#endif /* defined(__CUDACC__) */ + +// define __CUDA_FP16_CONSTEXPR__ in order to +// use constexpr where possible, with supporting C++ dialects +// undef after use +#if (defined __CPP_VERSION_AT_LEAST_11_FP16) +#define __CUDA_FP16_CONSTEXPR__ constexpr +#else +#define __CUDA_FP16_CONSTEXPR__ +#endif + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief __half_raw data type + * \details Type allows static initialization of \p half until it becomes + * a builtin type. + * + * - Note: this initialization is as a bit-field representation of \p half, + * and not a conversion from \p short to \p half. + * Such representation will be deprecated in a future version of CUDA. + * + * - Note: this is visible to non-nvcc compilers, including C-only compilations + */ +typedef struct __CUDA_ALIGN__(2) { + unsigned short x; +} __half_raw; + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief __half2_raw data type + * \details Type allows static initialization of \p half2 until it becomes + * a builtin type. + * + * - Note: this initialization is as a bit-field representation of \p half2, + * and not a conversion from \p short2 to \p half2. + * Such representation will be deprecated in a future version of CUDA. + * + * - Note: this is visible to non-nvcc compilers, including C-only compilations + */ +typedef struct __CUDA_ALIGN__(4) { + unsigned short x; + unsigned short y; +} __half2_raw; + +/* All other definitions in this file are only visible to C++ compilers */ +#if defined(__cplusplus) + +/* Hide GCC member initialization list warnings because of host/device in-function init requirement */ +#if defined(__GNUC__) +#if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Weffc++" +#endif /* __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) */ +#endif /* defined(__GNUC__) */ + +/* class' : multiple assignment operators specified + The class has multiple assignment operators of a single type. This warning is informational */ +#if defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning( push ) +#pragma warning( disable:4522 ) +#endif /* defined(_MSC_VER) && _MSC_VER >= 1500 */ + +// forward-declaration of bfloat type to be used in converting constructor +struct __nv_bfloat16; + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief __half data type + * \details This structure implements the datatype for storing + * half-precision floating-point numbers. The structure implements + * assignment, arithmetic and comparison operators, and type conversions. + * 16 bits are being used in total: 1 sign bit, 5 bits for the exponent, + * and the significand is being stored in 10 bits. + * The total precision is 11 bits. There are 15361 representable + * numbers within the interval [0.0, 1.0], endpoints included. + * On average we have log10(2**11) ~ 3.311 decimal digits. + * + * The objective here is to provide IEEE754-compliant implementation + * of \p binary16 type and arithmetic with limitations due to + * device HW not supporting floating-point exceptions. + */ +struct __CUDA_ALIGN__(2) __half { +protected: + /** + * Protected storage variable contains the bits of floating-point data. + */ + unsigned short __x; + +public: + /** + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) + __half() = default; +#else + __CUDA_HOSTDEVICE__ __half(); +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ + + /* Convert to/from __half_raw */ + /** + * Constructor from \p __half_raw. + */ + __CUDA_HOSTDEVICE__ __CUDA_FP16_CONSTEXPR__ __half(const __half_raw &hr) : __x(hr.x) { } + /** + * Assignment operator from \p __half_raw. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const __half_raw &hr); + /** + * Assignment operator from \p __half_raw to \p volatile \p __half. + */ + __CUDA_HOSTDEVICE__ volatile __half &operator=(const __half_raw &hr) volatile; + /** + * Assignment operator from \p volatile \p __half_raw to \p volatile \p __half. + */ + __CUDA_HOSTDEVICE__ volatile __half &operator=(const volatile __half_raw &hr) volatile; + /** + * Type cast to \p __half_raw operator. + */ + __CUDA_HOSTDEVICE__ operator __half_raw() const; + /** + * Type cast to \p __half_raw operator with \p volatile input. + */ + __CUDA_HOSTDEVICE__ operator __half_raw() const volatile; +#if !defined(__CUDA_NO_HALF_CONVERSIONS__) +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) + /** + * Construct \p __half from \p __nv_bfloat16 input using default round-to-nearest-even rounding mode. + * Need to include the header file \p cuda_bf16.h + */ + explicit __CUDA_HOSTDEVICE__ __half(const __nv_bfloat16 f); //forward declaration only, implemented in cuda_bf16.hpp +#endif /* #if defined(__CPP_VERSION_AT_LEAST_11_FP16) */ + /* Construct from float/double */ + /** + * Construct \p __half from \p float input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const float f); + /** + * Construct \p __half from \p double input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const double f); + /** + * Type cast to \p float operator. + */ + __CUDA_HOSTDEVICE__ operator float() const; + /** + * Type cast to \p __half assignment operator from \p float input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const float f); + + /* We omit "cast to double" operator, so as to not be ambiguous about up-cast */ + /** + * Type cast to \p __half assignment operator from \p double input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const double f); + + /* Allow automatic construction from types supported natively in hardware */ + /* Note we do avoid constructor init-list because of special host/device compilation rules */ + +/* + * Implicit type conversions to/from integer types were only available to nvcc compilation. + * Introducing them for all compilers is a potentially breaking change that may affect + * overloads resolution and will require users to update their code. + * Define __CUDA_FP16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__ to opt-out. + */ +#if !(defined __CUDA_FP16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) + /** + * Construct \p __half from \p short integer input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const short val); + /** + * Construct \p __half from \p unsigned \p short integer input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const unsigned short val); + /** + * Construct \p __half from \p int input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const int val); + /** + * Construct \p __half from \p unsigned \p int input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const unsigned int val); + /** + * Construct \p __half from \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const long val); + /** + * Construct \p __half from \p unsigned \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const unsigned long val); + + /** + * Construct \p __half from \p long \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const long long val); + /** + * Construct \p __half from \p unsigned \p long \p long input using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half(const unsigned long long val); + + /* Allow automatic casts to supported builtin types, matching all that are permitted with float */ + + /** + * Conversion operator to \p signed \p char data type. + * Using round-toward-zero rounding mode. + * + * See __half2char_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator signed char() const; + /** + * Conversion operator to \p unsigned \p char data type. + * Using round-toward-zero rounding mode. + * + * See __half2uchar_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned char() const; + /** + * Conversion operator to an implementation defined \p char data type. + * Using round-toward-zero rounding mode. + * + * Detects signedness of the \p char type and proceeds accordingly, see + * further details in signed and unsigned char operators. + */ + __CUDA_HOSTDEVICE__ operator char() const; + /** + * Conversion operator to \p short data type. + * Using round-toward-zero rounding mode. + * + * See __half2short_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator short() const; + /** + * Conversion operator to \p unsigned \p short data type. + * Using round-toward-zero rounding mode. + * + * See __half2ushort_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned short() const; + /** + * Conversion operator to \p int data type. + * Using round-toward-zero rounding mode. + * + * See __half2int_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator int() const; + /** + * Conversion operator to \p unsigned \p int data type. + * Using round-toward-zero rounding mode. + * + * See __half2uint_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned int() const; + /** + * Conversion operator to \p long data type. + * Using round-toward-zero rounding mode. + */ + __CUDA_HOSTDEVICE__ operator long() const; + /** + * Conversion operator to \p unsigned \p long data type. + * Using round-toward-zero rounding mode. + */ + __CUDA_HOSTDEVICE__ operator unsigned long() const; + /** + * Conversion operator to \p long \p long data type. + * Using round-toward-zero rounding mode. + * + * See __half2ll_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator long long() const; + /** + * Conversion operator to \p unsigned \p long \p long data type. + * Using round-toward-zero rounding mode. + * + * See __half2ull_rz(__half) for further details + */ + __CUDA_HOSTDEVICE__ operator unsigned long long() const; + /** + * Type cast from \p short assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const short val); + /** + * Type cast from \p unsigned \p short assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const unsigned short val); + /** + * Type cast from \p int assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const int val); + /** + * Type cast from \p unsigned \p int assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const unsigned int val); + /** + * Type cast from \p long \p long assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const long long val); + /** + * Type cast from \p unsigned \p long \p long assignment operator, using default round-to-nearest-even rounding mode. + */ + __CUDA_HOSTDEVICE__ __half &operator=(const unsigned long long val); + /** + * Conversion operator to \p bool data type. + * +0 and -0 inputs convert to \p false. + * Non-zero inputs convert to \p true. + */ + __CUDA_HOSTDEVICE__ __CUDA_FP16_CONSTEXPR__ operator bool() const { return (__x & 0x7FFFU) != 0U; } +#endif /* #if !(defined __CUDA_FP16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) */ +#endif /* !defined(__CUDA_NO_HALF_CONVERSIONS__) */ +}; + +#if !defined(__CUDA_NO_HALF_OPERATORS__) +/* Some basic arithmetic operations expected of a builtin */ + +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half addition operation. + * See also __hadd(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator+(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half subtraction operation. + * See also __hsub(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator-(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half multiplication operation. + * See also __hmul(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator*(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half division operation. + * See also __hdiv(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator/(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half compound assignment with addition operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator+=(__half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half compound assignment with subtraction operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator-=(__half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half compound assignment with multiplication operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator*=(__half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half compound assignment with division operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator/=(__half &lh, const __half &rh); +/* Note for increment and decrement we use the raw value 0x3C00U equating to half(1.0F), to avoid the extra conversion */ +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half prefix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator++(__half &h); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half prefix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator--(__half &h); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half postfix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator++(__half &h, const int ignored); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Performs \p half postfix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator--(__half &h, const int ignored); + +/* Unary plus and inverse operators */ +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Implements \p half unary plus operator, returns input value. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator+(const __half &h); +/** + * \ingroup CUDA_MATH__HALF_ARITHMETIC + * Implements \p half unary minus operator. + * See also __hneg(__half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator-(const __half &h); +/* Some basic comparison operations to make it look like a builtin */ +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half ordered compare equal operation. + * See also __heq(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator==(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half unordered compare not-equal operation. + * See also __hneu(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator!=(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half ordered greater-than compare operation. + * See also __hgt(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator> (const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half ordered less-than compare operation. + * See also __hlt(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator< (const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half ordered greater-or-equal compare operation. + * See also __hge(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>=(const __half &lh, const __half &rh); +/** + * \ingroup CUDA_MATH__HALF_COMPARISON + * Performs \p half ordered less-or-equal compare operation. + * See also __hle(__half, __half) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<=(const __half &lh, const __half &rh); +#endif /* !defined(__CUDA_NO_HALF_OPERATORS__) */ + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief __half2 data type + * \details This structure implements the datatype for storing two + * half-precision floating-point numbers. + * The structure implements assignment, arithmetic and comparison + * operators, and type conversions. + * + * - NOTE: __half2 is visible to non-nvcc host compilers + */ +struct __CUDA_ALIGN__(4) __half2 { + /** + * Storage field holding lower \p __half part. + */ + __half x; + /** + * Storage field holding upper \p __half part. + */ + __half y; + + // All construct/copy/assign/move +public: + /** + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) + __half2() = default; + /** + * Move constructor, available for \p C++11 and later dialects + */ + __CUDA_HOSTDEVICE__ __half2(const __half2 &&src); + /** + * Move assignment operator, available for \p C++11 and later dialects + */ + __CUDA_HOSTDEVICE__ __half2 &operator=(const __half2 &&src); +#else + __CUDA_HOSTDEVICE__ __half2(); +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ + + /** + * Constructor from two \p __half variables + */ + __CUDA_HOSTDEVICE__ __CUDA_FP16_CONSTEXPR__ __half2(const __half &a, const __half &b) : x(a), y(b) { } + /** + * Copy constructor + */ + __CUDA_HOSTDEVICE__ __half2(const __half2 &src); + /** + * Copy assignment operator + */ + __CUDA_HOSTDEVICE__ __half2 &operator=(const __half2 &src); + + /* Convert to/from __half2_raw */ + /** + * Constructor from \p __half2_raw + */ + __CUDA_HOSTDEVICE__ __half2(const __half2_raw &h2r ); + /** + * Assignment operator from \p __half2_raw + */ + __CUDA_HOSTDEVICE__ __half2 &operator=(const __half2_raw &h2r); + /** + * Conversion operator to \p __half2_raw + */ + __CUDA_HOSTDEVICE__ operator __half2_raw() const; +}; + +#if !defined(__CUDA_NO_HALF2_OPERATORS__) +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half addition operation. + * See also __hadd2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator+(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half subtraction operation. + * See also __hsub2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator-(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half multiplication operation. + * See also __hmul2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator*(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half division operation. + * See also __h2div(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator/(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half compound assignment with addition operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator+=(__half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half compound assignment with subtraction operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator-=(__half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half compound assignment with multiplication operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator*=(__half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half compound assignment with division operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator/=(__half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half prefix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 &operator++(__half2 &h); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half prefix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 &operator--(__half2 &h); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half postfix increment operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator++(__half2 &h, const int ignored); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Performs packed \p half postfix decrement operation. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator--(__half2 &h, const int ignored); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Implements packed \p half unary plus operator, returns input value. + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator+(const __half2 &h); +/** + * \ingroup CUDA_MATH__HALF2_ARITHMETIC + * Implements packed \p half unary minus operator. + * See also __hneg2(__half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator-(const __half2 &h); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half ordered compare equal operation. + * See also __hbeq2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator==(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half unordered compare not-equal operation. + * See also __hbneu2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator!=(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half ordered greater-than compare operation. + * See also __hbgt2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half ordered less-than compare operation. + * See also __hblt2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half ordered greater-or-equal compare operation. + * See also __hbge2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>=(const __half2 &lh, const __half2 &rh); +/** + * \ingroup CUDA_MATH__HALF2_COMPARISON + * Performs packed \p half ordered less-or-equal compare operation. + * See also __hble2(__half2, __half2) + */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<=(const __half2 &lh, const __half2 &rh); + +#endif /* !defined(__CUDA_NO_HALF2_OPERATORS__) */ + +#endif /* defined(__cplusplus) */ + +#if (defined(__FORCE_INCLUDE_CUDA_FP16_HPP_FROM_FP16_H__) || \ + !(defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3))))) +/* Note the .hpp file is included to capture the "half" & "half2" builtin function definitions. For NVRTC, the builtin + function definitions are compiled at NVRTC library build-time and are available through the NVRTC builtins library at + link time. +*/ +#include "cuda_fp16.hpp" +#endif /* (defined(__FORCE_INCLUDE_CUDA_FP16_HPP_FROM_FP16_H__) || \ + !(defined(__CUDACC_RTC__) && ((__CUDACC_VER_MAJOR__ > 12) || ((__CUDACC_VER_MAJOR__ == 12) && (__CUDACC_VER_MINOR__ >= 3))))) */ + +/* Define first-class types "half" and "half2", unless user specifies otherwise via "#define CUDA_NO_HALF" */ +/* C cannot ever have these types defined here, because __half and __half2 are C++ classes */ +#if defined(__cplusplus) && !defined(CUDA_NO_HALF) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is meant to be the first-class or fundamental + * implementation of the half-precision numbers format. + * + * \details Should be implemented in the compiler in the future. + * Current implementation is a simple typedef to a respective + * user-level type with underscores. + */ +typedef __half half; + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is meant to be the first-class or fundamental + * implementation of type for pairs of half-precision numbers. + * + * \details Should be implemented in the compiler in the future. + * Current implementation is a simple typedef to a respective + * user-level type with underscores. + */ +typedef __half2 half2; +// for consistency with __nv_bfloat16 + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p __nv_ prefixed alias + */ +typedef __half __nv_half; +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p __nv_ prefixed alias + */ +typedef __half2 __nv_half2; +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p __nv_ prefixed alias + */ +typedef __half_raw __nv_half_raw; +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p __nv_ prefixed alias + */ +typedef __half2_raw __nv_half2_raw; +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p nv_ prefixed alias + */ +typedef __half nv_half; +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF + * \brief This datatype is an \p nv_ prefixed alias + */ +typedef __half2 nv_half2; +#endif /* defined(__cplusplus) && !defined(CUDA_NO_HALF) */ + +#undef __CUDA_FP16_DECL__ +#undef __CUDA_HOSTDEVICE_FP16_DECL__ +#undef __CUDA_HOSTDEVICE__ +#undef __CUDA_FP16_INLINE__ +#undef __CUDA_FP16_FORCEINLINE__ + +#undef ___CUDA_FP16_STRINGIFY_INNERMOST +#undef __CUDA_FP16_STRINGIFY + +#endif /* end of include guard: __CUDA_FP16_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.hpp b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.hpp new file mode 100644 index 0000000000000000000000000000000000000000..31688456148773afbe3900cf5c59197dbeb83ab4 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp16.hpp @@ -0,0 +1,3523 @@ +/* +* Copyright 1993-2023 NVIDIA Corporation. All rights reserved. +* +* NOTICE TO LICENSEE: +* +* This source code and/or documentation ("Licensed Deliverables") are +* subject to NVIDIA intellectual property rights under U.S. and +* international Copyright laws. +* +* These Licensed Deliverables contained herein is PROPRIETARY and +* CONFIDENTIAL to NVIDIA and is being provided under the terms and +* conditions of a form of NVIDIA software license agreement by and +* between NVIDIA and Licensee ("License Agreement") or electronically +* accepted by Licensee. Notwithstanding any terms or conditions to +* the contrary in the License Agreement, reproduction or disclosure +* of the Licensed Deliverables to any third party without the express +* written consent of NVIDIA is prohibited. +* +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE +* SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS +* PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. +* NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED +* DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, +* NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. +* NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE +* LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY +* SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY +* DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, +* WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS +* ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE +* OF THESE LICENSED DELIVERABLES. +* +* U.S. Government End Users. These Licensed Deliverables are a +* "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT +* 1995), consisting of "commercial computer software" and "commercial +* computer software documentation" as such terms are used in 48 +* C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government +* only as a commercial end item. Consistent with 48 C.F.R.12.212 and +* 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all +* U.S. Government End Users acquire the Licensed Deliverables with +* only those rights set forth herein. +* +* Any use of the Licensed Deliverables in individual and commercial +* software must include, in the user documentation and internal +* comments to the code, the above Disclaimer and U.S. Government End +* Users Notice. +*/ + +#if !defined(__CUDA_FP16_HPP__) +#define __CUDA_FP16_HPP__ + +#if !defined(__CUDA_FP16_H__) +#error "Do not include this file directly. Instead, include cuda_fp16.h." +#endif + +#if !defined(IF_DEVICE_OR_CUDACC) +#if defined(__CUDACC__) + #define IF_DEVICE_OR_CUDACC(d, c, f) NV_IF_ELSE_TARGET(NV_IS_DEVICE, d, c) +#else + #define IF_DEVICE_OR_CUDACC(d, c, f) NV_IF_ELSE_TARGET(NV_IS_DEVICE, d, f) +#endif +#endif + +/* Macros to allow half & half2 to be used by inline assembly */ +#define __HALF_TO_US(var) *(reinterpret_cast(&(var))) +#define __HALF_TO_CUS(var) *(reinterpret_cast(&(var))) +#define __HALF2_TO_UI(var) *(reinterpret_cast(&(var))) +#define __HALF2_TO_CUI(var) *(reinterpret_cast(&(var))) + +/* Macros for half & half2 binary arithmetic */ +#define __BINARY_OP_HALF_MACRO(name) /* do */ {\ + __half val; \ + asm( "{" __CUDA_FP16_STRINGIFY(name) ".f16 %0,%1,%2;\n}" \ + :"=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a)),"h"(__HALF_TO_CUS(b))); \ + return val; \ +} /* while(0) */ +#define __BINARY_OP_HALF2_MACRO(name) /* do */ {\ + __half2 val; \ + asm( "{" __CUDA_FP16_STRINGIFY(name) ".f16x2 %0,%1,%2;\n}" \ + :"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)),"r"(__HALF2_TO_CUI(b))); \ + return val; \ +} /* while(0) */ +#define __TERNARY_OP_HALF_MACRO(name) /* do */ {\ + __half val; \ + asm( "{" __CUDA_FP16_STRINGIFY(name) ".f16 %0,%1,%2,%3;\n}" \ + :"=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a)),"h"(__HALF_TO_CUS(b)),"h"(__HALF_TO_CUS(c))); \ + return val; \ +} /* while(0) */ +#define __TERNARY_OP_HALF2_MACRO(name) /* do */ {\ + __half2 val; \ + asm( "{" __CUDA_FP16_STRINGIFY(name) ".f16x2 %0,%1,%2,%3;\n}" \ + :"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)),"r"(__HALF2_TO_CUI(b)),"r"(__HALF2_TO_CUI(c))); \ + return val; \ +} /* while(0) */ + +/* All other definitions in this file are only visible to C++ compilers */ +#if defined(__cplusplus) + +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines floating-point positive infinity value for the \p half data type + */ +#define CUDART_INF_FP16 __ushort_as_half((unsigned short)0x7C00U) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines canonical NaN value for the \p half data type + */ +#define CUDART_NAN_FP16 __ushort_as_half((unsigned short)0x7FFFU) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines a minimum representable (denormalized) value for the \p half data type + */ +#define CUDART_MIN_DENORM_FP16 __ushort_as_half((unsigned short)0x0001U) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines a maximum representable value for the \p half data type + */ +#define CUDART_MAX_NORMAL_FP16 __ushort_as_half((unsigned short)0x7BFFU) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines a negative zero value for the \p half data type + */ +#define CUDART_NEG_ZERO_FP16 __ushort_as_half((unsigned short)0x8000U) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines a positive zero value for the \p half data type + */ +#define CUDART_ZERO_FP16 __ushort_as_half((unsigned short)0x0000U) +/** + * \ingroup CUDA_MATH_INTRINSIC_HALF_CONSTANTS + * \brief Defines a value of 1.0 for the \p half data type + */ +#define CUDART_ONE_FP16 __ushort_as_half((unsigned short)0x3C00U) + +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) +#else + __CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half() { } +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const __half_raw &hr) { __x = hr.x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ volatile __half &__half::operator=(const __half_raw &hr) volatile { __x = hr.x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ volatile __half &__half::operator=(const volatile __half_raw &hr) volatile { __x = hr.x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator __half_raw() const { __half_raw ret; ret.x = __x; return ret; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator __half_raw() const volatile { __half_raw ret; ret.x = __x; return ret; } +#if !defined(__CUDA_NO_HALF_CONVERSIONS__) +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const float f) { __x = __float2half(f).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const double f) { __x = __double2half(f).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator float() const { return __half2float(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const float f) { __x = __float2half(f).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const double f) { __x = __double2half(f).__x; return *this; } +#if !(defined __CUDA_FP16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const short val) { __x = __short2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const unsigned short val) { __x = __ushort2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const int val) { __x = __int2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const unsigned int val) { __x = __uint2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const long val) { + + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + + { + __x = __ll2half_rn(static_cast(val)).__x; + } else { + __x = __int2half_rn(static_cast(val)).__x; + } +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const unsigned long val) { + + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + + { + __x = __ull2half_rn(static_cast(val)).__x; + } else { + __x = __uint2half_rn(static_cast(val)).__x; + } +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const long long val) { __x = __ll2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::__half(const unsigned long long val) { __x = __ull2half_rn(val).__x; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator signed char() const { return __half2char_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator unsigned char() const { return __half2uchar_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator char() const { + char value; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (((char)-1) < (char)0) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + value = static_cast(__half2char_rz(*this)); + } + else + { + value = static_cast(__half2uchar_rz(*this)); + } + return value; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator short() const { return __half2short_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator unsigned short() const { return __half2ushort_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator int() const { return __half2int_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator unsigned int() const { return __half2uint_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator long() const { + long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ll_rz(*this)); + } + else + { + retval = static_cast(__half2int_rz(*this)); + } + return retval; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator unsigned long() const { + unsigned long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ull_rz(*this)); + } + else + { + retval = static_cast(__half2uint_rz(*this)); + } + return retval; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator long long() const { return __half2ll_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half::operator unsigned long long() const { return __half2ull_rz(*this); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const short val) { __x = __short2half_rn(val).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const unsigned short val) { __x = __ushort2half_rn(val).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const int val) { __x = __int2half_rn(val).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const unsigned int val) { __x = __uint2half_rn(val).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const long long val) { __x = __ll2half_rn(val).__x; return *this; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half &__half::operator=(const unsigned long long val) { __x = __ull2half_rn(val).__x; return *this; } +#endif /* #if !(defined __CUDA_FP16_DISABLE_IMPLICIT_INTEGER_CONVERTS_FOR_HOST_COMPILERS__) || (defined __CUDACC__) */ +#endif /* !defined(__CUDA_NO_HALF_CONVERSIONS__) */ +#if !defined(__CUDA_NO_HALF_OPERATORS__) +/* Some basic arithmetic operations expected of a builtin */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator+(const __half &lh, const __half &rh) { return __hadd(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator-(const __half &lh, const __half &rh) { return __hsub(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator*(const __half &lh, const __half &rh) { return __hmul(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator/(const __half &lh, const __half &rh) { return __hdiv(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator+=(__half &lh, const __half &rh) { lh = __hadd(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator-=(__half &lh, const __half &rh) { lh = __hsub(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator*=(__half &lh, const __half &rh) { lh = __hmul(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator/=(__half &lh, const __half &rh) { lh = __hdiv(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator++(__half &h) { __half_raw one; one.x = 0x3C00U; h += one; return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half &operator--(__half &h) { __half_raw one; one.x = 0x3C00U; h -= one; return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator++(__half &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __half ret = h; + __half_raw one; + one.x = 0x3C00U; + h += one; + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator--(__half &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __half ret = h; + __half_raw one; + one.x = 0x3C00U; + h -= one; + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator+(const __half &h) { return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half operator-(const __half &h) { return __hneg(h); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator==(const __half &lh, const __half &rh) { return __heq(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator!=(const __half &lh, const __half &rh) { return __hneu(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator> (const __half &lh, const __half &rh) { return __hgt(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator< (const __half &lh, const __half &rh) { return __hlt(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>=(const __half &lh, const __half &rh) { return __hge(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<=(const __half &lh, const __half &rh) { return __hle(lh, rh); } +#endif /* !defined(__CUDA_NO_HALF_OPERATORS__) */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2::__half2(const __half2 &&src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = std::move(__HALF2_TO_CUI(src)); +, + this->x = src.x; + this->y = src.y; +) +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2 &__half2::operator=(const __half2 &&src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = std::move(__HALF2_TO_CUI(src)); +, + this->x = src.x; + this->y = src.y; +) + return *this; +} +#else +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2::__half2() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2::__half2(const __half2 &src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = __HALF2_TO_CUI(src); +, + this->x = src.x; + this->y = src.y; +) +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2 &__half2::operator=(const __half2 &src) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = __HALF2_TO_CUI(src); +, + this->x = src.x; + this->y = src.y; +) + return *this; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2::__half2(const __half2_raw &h2r ) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = __HALF2_TO_CUI(h2r); +, + __half_raw tr; + tr.x = h2r.x; + this->x = static_cast<__half>(tr); + tr.x = h2r.y; + this->y = static_cast<__half>(tr); +) +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2 &__half2::operator=(const __half2_raw &h2r) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __HALF2_TO_UI(*this) = __HALF2_TO_CUI(h2r); +, + __half_raw tr; + tr.x = h2r.x; + this->x = static_cast<__half>(tr); + tr.x = h2r.y; + this->y = static_cast<__half>(tr); +) + return *this; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_INLINE__ __half2::operator __half2_raw() const { + __half2_raw ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + ret.x = 0U; + ret.y = 0U; + __HALF2_TO_UI(ret) = __HALF2_TO_CUI(*this); +, + ret.x = static_cast<__half_raw>(this->x).x; + ret.y = static_cast<__half_raw>(this->y).x; +) + return ret; +} +#if !defined(__CUDA_NO_HALF2_OPERATORS__) +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator+(const __half2 &lh, const __half2 &rh) { return __hadd2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator-(const __half2 &lh, const __half2 &rh) { return __hsub2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator*(const __half2 &lh, const __half2 &rh) { return __hmul2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator/(const __half2 &lh, const __half2 &rh) { return __h2div(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator+=(__half2 &lh, const __half2 &rh) { lh = __hadd2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator-=(__half2 &lh, const __half2 &rh) { lh = __hsub2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator*=(__half2 &lh, const __half2 &rh) { lh = __hmul2(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2& operator/=(__half2 &lh, const __half2 &rh) { lh = __h2div(lh, rh); return lh; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 &operator++(__half2 &h) { __half2_raw one; one.x = 0x3C00U; one.y = 0x3C00U; h = __hadd2(h, one); return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 &operator--(__half2 &h) { __half2_raw one; one.x = 0x3C00U; one.y = 0x3C00U; h = __hsub2(h, one); return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator++(__half2 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __half2 ret = h; + __half2_raw one; + one.x = 0x3C00U; + one.y = 0x3C00U; + h = __hadd2(h, one); + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator--(__half2 &h, const int ignored) +{ + // ignored on purpose. Parameter only needed to distinguish the function declaration from other types of operators. + static_cast(ignored); + + const __half2 ret = h; + __half2_raw one; + one.x = 0x3C00U; + one.y = 0x3C00U; + h = __hsub2(h, one); + return ret; +} +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator+(const __half2 &h) { return h; } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ __half2 operator-(const __half2 &h) { return __hneg2(h); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator==(const __half2 &lh, const __half2 &rh) { return __hbeq2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator!=(const __half2 &lh, const __half2 &rh) { return __hbneu2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>(const __half2 &lh, const __half2 &rh) { return __hbgt2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<(const __half2 &lh, const __half2 &rh) { return __hblt2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator>=(const __half2 &lh, const __half2 &rh) { return __hbge2(lh, rh); } +__CUDA_HOSTDEVICE__ __CUDA_FP16_FORCEINLINE__ bool operator<=(const __half2 &lh, const __half2 &rh) { return __hble2(lh, rh); } +#endif /* !defined(__CUDA_NO_HALF2_OPERATORS__) */ + +/* Restore warning for multiple assignment operators */ +#if defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning( pop ) +#endif /* defined(_MSC_VER) && _MSC_VER >= 1500 */ + +/* Restore -Weffc++ warnings from here on */ +#if defined(__GNUC__) +#if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) +#pragma GCC diagnostic pop +#endif /* __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) */ +#endif /* defined(__GNUC__) */ + +#undef __CUDA_HOSTDEVICE__ +#undef __CUDA_ALIGN__ + +#ifndef __CUDACC_RTC__ /* no host functions in NVRTC mode */ +static inline unsigned short __internal_float2half(const float f, unsigned int &sign, unsigned int &remainder) +{ + unsigned int x; + unsigned int u; + unsigned int result; +#if defined(__CUDACC__) + (void)memcpy(&x, &f, sizeof(f)); +#else + (void)std::memcpy(&x, &f, sizeof(f)); +#endif + u = (x & 0x7fffffffU); + sign = ((x >> 16U) & 0x8000U); + // NaN/+Inf/-Inf + if (u >= 0x7f800000U) { + remainder = 0U; + result = ((u == 0x7f800000U) ? (sign | 0x7c00U) : 0x7fffU); + } else if (u > 0x477fefffU) { // Overflows + remainder = 0x80000000U; + result = (sign | 0x7bffU); + } else if (u >= 0x38800000U) { // Normal numbers + remainder = u << 19U; + u -= 0x38000000U; + result = (sign | (u >> 13U)); + } else if (u < 0x33000001U) { // +0/-0 + remainder = u; + result = sign; + } else { // Denormal numbers + const unsigned int exponent = u >> 23U; + const unsigned int shift = 0x7eU - exponent; + unsigned int mantissa = (u & 0x7fffffU); + mantissa |= 0x800000U; + remainder = mantissa << (32U - shift); + result = (sign | (mantissa >> shift)); + result &= 0x0000FFFFU; + } + return static_cast(result); +} +#endif /* #if !defined(__CUDACC_RTC__) */ + +__CUDA_HOSTDEVICE_FP16_DECL__ __half __double2half(const double a) +{ +IF_DEVICE_OR_CUDACC( + __half val; + asm("{ cvt.rn.f16.f64 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "d"(a)); + return val; +, + __half result; + // Perform rounding to 11 bits of precision, convert value + // to float and call existing float to half conversion. + // By pre-rounding to 11 bits we avoid additional rounding + // in float to half conversion. + unsigned long long int absa; + unsigned long long int ua; + (void)memcpy(&ua, &a, sizeof(a)); + absa = (ua & 0x7fffffffffffffffULL); + if ((absa >= 0x40f0000000000000ULL) || (absa <= 0x3e60000000000000ULL)) + { + // |a| >= 2^16 or NaN or |a| <= 2^(-25) + // double-rounding is not a problem + result = __float2half(static_cast(a)); + } + else + { + // here 2^(-25) < |a| < 2^16 + // prepare shifter value such that a + shifter + // done in double precision performs round-to-nearest-even + // and (a + shifter) - shifter results in a rounded to + // 11 bits of precision. Shifter needs to have exponent of + // a plus 53 - 11 = 42 and a leading bit in mantissa to guard + // against negative values. + // So need to have |a| capped to avoid overflow in exponent. + // For inputs that are smaller than half precision minnorm + // we prepare fixed shifter exponent. + unsigned long long shifterBits; + if (absa >= 0x3f10000000000000ULL) + { // Here if |a| >= 2^(-14) + // add 42 to exponent bits + shifterBits = (ua & 0x7ff0000000000000ULL) + 0x02A0000000000000ULL; + } + else + { // 2^(-25) < |a| < 2^(-14), potentially results in denormal + // set exponent bits to 42 - 14 + bias + shifterBits = 0x41B0000000000000ULL; + } + // set leading mantissa bit to protect against negative inputs + shifterBits |= 0x0008000000000000ULL; + double shifter; + (void)memcpy(&shifter, &shifterBits, sizeof(shifterBits)); + double aShiftRound = a + shifter; + + // Prevent the compiler from optimizing away a + shifter - shifter + // by doing intermediate memcopy and harmless bitwize operation + unsigned long long int aShiftRoundBits; + (void)memcpy(&aShiftRoundBits, &aShiftRound, sizeof(aShiftRound)); + + // the value is positive, so this operation doesn't change anything + aShiftRoundBits &= 0x7fffffffffffffffULL; + + (void)memcpy(&aShiftRound, &aShiftRoundBits, sizeof(aShiftRound)); + + result = __float2half(static_cast(aShiftRound - shifter)); + } + + return result; +, + __half result; + /* + // Perform rounding to 11 bits of precision, convert value + // to float and call existing float to half conversion. + // By pre-rounding to 11 bits we avoid additional rounding + // in float to half conversion. + */ + unsigned long long int absa; + unsigned long long int ua; + (void)std::memcpy(&ua, &a, sizeof(a)); + absa = (ua & 0x7fffffffffffffffULL); + if ((absa >= 0x40f0000000000000ULL) || (absa <= 0x3e60000000000000ULL)) + { + /* + // |a| >= 2^16 or NaN or |a| <= 2^(-25) + // double-rounding is not a problem + */ + result = __float2half(static_cast(a)); + } + else + { + /* + // here 2^(-25) < |a| < 2^16 + // prepare shifter value such that a + shifter + // done in double precision performs round-to-nearest-even + // and (a + shifter) - shifter results in a rounded to + // 11 bits of precision. Shifter needs to have exponent of + // a plus 53 - 11 = 42 and a leading bit in mantissa to guard + // against negative values. + // So need to have |a| capped to avoid overflow in exponent. + // For inputs that are smaller than half precision minnorm + // we prepare fixed shifter exponent. + */ + unsigned long long shifterBits; + if (absa >= 0x3f10000000000000ULL) + { + /* + // Here if |a| >= 2^(-14) + // add 42 to exponent bits + */ + shifterBits = (ua & 0x7ff0000000000000ULL) + 0x02A0000000000000ULL; + } + else + { + /* + // 2^(-25) < |a| < 2^(-14), potentially results in denormal + // set exponent bits to 42 - 14 + bias + */ + shifterBits = 0x41B0000000000000ULL; + } + // set leading mantissa bit to protect against negative inputs + shifterBits |= 0x0008000000000000ULL; + double shifter; + (void)std::memcpy(&shifter, &shifterBits, sizeof(shifterBits)); + double aShiftRound = a + shifter; + + /* + // Prevent the compiler from optimizing away a + shifter - shifter + // by doing intermediate memcopy and harmless bitwize operation + */ + unsigned long long int aShiftRoundBits; + (void)std::memcpy(&aShiftRoundBits, &aShiftRound, sizeof(aShiftRound)); + + // the value is positive, so this operation doesn't change anything + aShiftRoundBits &= 0x7fffffffffffffffULL; + + (void)std::memcpy(&aShiftRound, &aShiftRoundBits, sizeof(aShiftRound)); + + result = __float2half(static_cast(aShiftRound - shifter)); + } + + return result; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half(const float a) +{ + __half val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.rn.f16.f32 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "f"(a)); +, + __half_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2half(a, sign, remainder); + if ((remainder > 0x80000000U) || ((remainder == 0x80000000U) && ((r.x & 0x1U) != 0U))) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rn(const float a) +{ + __half val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.rn.f16.f32 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "f"(a)); +, + __half_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2half(a, sign, remainder); + if ((remainder > 0x80000000U) || ((remainder == 0x80000000U) && ((r.x & 0x1U) != 0U))) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rz(const float a) +{ + __half val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.rz.f16.f32 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "f"(a)); +, + __half_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2half(a, sign, remainder); + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_rd(const float a) +{ + __half val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.rm.f16.f32 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "f"(a)); +, + __half_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2half(a, sign, remainder); + if ((remainder != 0U) && (sign != 0U)) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __float2half_ru(const float a) +{ + __half val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.rp.f16.f32 %0, %1;}\n" : "=h"(__HALF_TO_US(val)) : "f"(a)); +, + __half_raw r; + unsigned int sign = 0U; + unsigned int remainder = 0U; + r.x = __internal_float2half(a, sign, remainder); + if ((remainder != 0U) && (sign == 0U)) { + r.x++; + } + val = r; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __float2half2_rn(const float a) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low;\n" + " cvt.rn.f16.f32 low, %1;\n" + " mov.b32 %0, {low,low};}\n" : "=r"(__HALF2_TO_UI(val)) : "f"(a)); +, + val = __half2(__float2half_rn(a), __float2half_rn(a)); +) + return val; +} + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half2 __internal_device_float2_to_half2_rn(const float a, const float b) { + __half2 val; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + asm("{ cvt.rn.f16x2.f32 %0, %2, %1; }\n" + : "=r"(__HALF2_TO_UI(val)) : "f"(a), "f"(b)); +, + asm("{.reg .f16 low,high;\n" + " cvt.rn.f16.f32 low, %1;\n" + " cvt.rn.f16.f32 high, %2;\n" + " mov.b32 %0, {low,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "f"(a), "f"(b)); +) + return val; +} + +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __floats2half2_rn(const float a, const float b) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + val = __internal_device_float2_to_half2_rn(a,b); +, + val = __half2(__float2half_rn(a), __float2half_rn(b)); +) + return val; +} + +#ifndef __CUDACC_RTC__ /* no host functions in NVRTC mode */ +static inline float __internal_half2float(const unsigned short h) +{ + unsigned int sign = ((static_cast(h) >> 15U) & 1U); + unsigned int exponent = ((static_cast(h) >> 10U) & 0x1fU); + unsigned int mantissa = ((static_cast(h) & 0x3ffU) << 13U); + float f; + if (exponent == 0x1fU) { /* NaN or Inf */ + /* discard sign of a NaN */ + sign = ((mantissa != 0U) ? (sign >> 1U) : sign); + mantissa = ((mantissa != 0U) ? 0x7fffffU : 0U); + exponent = 0xffU; + } else if (exponent == 0U) { /* Denorm or Zero */ + if (mantissa != 0U) { + unsigned int msb; + exponent = 0x71U; + do { + msb = (mantissa & 0x400000U); + mantissa <<= 1U; /* normalize */ + --exponent; + } while (msb == 0U); + mantissa &= 0x7fffffU; /* 1.mantissa is implicit */ + } + } else { + exponent += 0x70U; + } + const unsigned int u = ((sign << 31U) | (exponent << 23U) | mantissa); +#if defined(__CUDACC__) + (void)memcpy(&f, &u, sizeof(u)); +#else + (void)std::memcpy(&f, &u, sizeof(u)); +#endif + return f; +} +#endif /* !defined(__CUDACC_RTC__) */ + +__CUDA_HOSTDEVICE_FP16_DECL__ float __half2float(const __half a) +{ + float val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ cvt.f32.f16 %0, %1;}\n" : "=f"(val) : "h"(__HALF_TO_CUS(a))); +, + val = __internal_half2float(static_cast<__half_raw>(a).x); +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ float __low2float(const __half2 a) +{ + float val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high},%1;\n" + " cvt.f32.f16 %0, low;}\n" : "=f"(val) : "r"(__HALF2_TO_CUI(a))); +, + val = __internal_half2float(static_cast<__half2_raw>(a).x); +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ float __high2float(const __half2 a) +{ + float val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high},%1;\n" + " cvt.f32.f16 %0, high;}\n" : "=f"(val) : "r"(__HALF2_TO_CUI(a))); +, + val = __internal_half2float(static_cast<__half2_raw>(a).y); +) + return val; +} + +__CUDA_HOSTDEVICE_FP16_DECL__ signed char __half2char_rz(const __half h) +{ + signed char i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned int tmp; + asm("cvt.rzi.s8.f16 %0, %1;" : "=r"(tmp) : "h"(__HALF_TO_CUS(h))); + const unsigned char u = static_cast(tmp); + i = static_cast(u); +, + const float f = __half2float(h); + const signed char max_val = (signed char)0x7fU; + const signed char min_val = (signed char)0x80U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} + +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned char __half2uchar_rz(const __half h) +{ + unsigned char i; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_90, + unsigned int tmp; + asm("cvt.rzi.u8.f16 %0, %1;" : "=r"(tmp) : "h"(__HALF_TO_CUS(h))); + i = static_cast(tmp); +, + const float f = __half2float(h); + const unsigned char max_val = 0xffU; + const unsigned char min_val = 0U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0U; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} + +__CUDA_HOSTDEVICE_FP16_DECL__ short int __half2short_rz(const __half h) +{ + short int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.s16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const short int max_val = (short int)0x7fffU; + const short int min_val = (short int)0x8000U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned short int __half2ushort_rz(const __half h) +{ + unsigned short int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.u16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const unsigned short int max_val = 0xffffU; + const unsigned short int min_val = 0U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0U; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +__CUDA_HOSTDEVICE_FP16_DECL__ int __half2int_rz(const __half h) +{ + int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.s32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const int max_val = (int)0x7fffffffU; + const int min_val = (int)0x80000000U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned int __half2uint_rz(const __half h) +{ + unsigned int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.u32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const unsigned int max_val = 0xffffffffU; + const unsigned int min_val = 0U; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0U; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +__CUDA_HOSTDEVICE_FP16_DECL__ long long int __half2ll_rz(const __half h) +{ + long long int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.s64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const long long int max_val = (long long int)0x7fffffffffffffffULL; + const long long int min_val = (long long int)0x8000000000000000ULL; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = min_val; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned long long int __half2ull_rz(const __half h) +{ + unsigned long long int i; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rzi.u64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); +, + const float f = __half2float(h); + const unsigned long long int max_val = 0xffffffffffffffffULL; + const unsigned long long int min_val = 0ULL; + const unsigned short bits = static_cast(static_cast<__half_raw>(h).x << 1U); + // saturation fixup + if (bits > (unsigned short)0xF800U) { + // NaN + i = 0x8000000000000000ULL; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value, conversion is well-defined + i = static_cast(f); + } +) + return i; +} +/* CUDA vector-types compatible vector creation function (note returns __half2, not half2) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 make_half2(const __half x, const __half y) +{ + __half2 t; t.x = x; t.y = y; return t; +} + + +/* Definitions of intrinsics */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __float22half2_rn(const float2 a) +{ + const __half2 val = __floats2half2_rn(a.x, a.y); + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ float2 __half22float2(const __half2 a) +{ + float hi_float; + float lo_float; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high},%1;\n" + " cvt.f32.f16 %0, low;}\n" : "=f"(lo_float) : "r"(__HALF2_TO_CUI(a))); + + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high},%1;\n" + " cvt.f32.f16 %0, high;}\n" : "=f"(hi_float) : "r"(__HALF2_TO_CUI(a))); +, + lo_float = __internal_half2float(((__half2_raw)a).x); + hi_float = __internal_half2float(((__half2_raw)a).y); +) + return make_float2(lo_float, hi_float); +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ int __half2int_rn(const __half h) +{ + int i; + asm("cvt.rni.s32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ int __half2int_rd(const __half h) +{ + int i; + asm("cvt.rmi.s32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ int __half2int_ru(const __half h) +{ + int i; + asm("cvt.rpi.s32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rn(const int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.s32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + // double-rounding is not a problem here: if integer + // has more than 24 bits, it is already too large to + // be represented in half precision, and result will + // be infinity. + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rz(const int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.s32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_rd(const int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.s32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __int2half_ru(const int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.s32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ short int __half2short_rn(const __half h) +{ + short int i; + asm("cvt.rni.s16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ short int __half2short_rd(const __half h) +{ + short int i; + asm("cvt.rmi.s16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ short int __half2short_ru(const __half h) +{ + short int i; + asm("cvt.rpi.s16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rn(const short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.s16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rz(const short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.s16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_rd(const short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.s16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short2half_ru(const short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.s16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ unsigned int __half2uint_rn(const __half h) +{ + unsigned int i; + asm("cvt.rni.u32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned int __half2uint_rd(const __half h) +{ + unsigned int i; + asm("cvt.rmi.u32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned int __half2uint_ru(const __half h) +{ + unsigned int i; + asm("cvt.rpi.u32.f16 %0, %1;" : "=r"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rn(const unsigned int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.u32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + // double-rounding is not a problem here: if integer + // has more than 24 bits, it is already too large to + // be represented in half precision, and result will + // be infinity. + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rz(const unsigned int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.u32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_rd(const unsigned int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.u32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __uint2half_ru(const unsigned int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.u32 %0, %1;" : "=h"(__HALF_TO_US(h)) : "r"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ unsigned short int __half2ushort_rn(const __half h) +{ + unsigned short int i; + asm("cvt.rni.u16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned short int __half2ushort_rd(const __half h) +{ + unsigned short int i; + asm("cvt.rmi.u16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned short int __half2ushort_ru(const __half h) +{ + unsigned short int i; + asm("cvt.rpi.u16.f16 %0, %1;" : "=h"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rn(const unsigned short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.u16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rz(const unsigned short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.u16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_rd(const unsigned short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.u16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort2half_ru(const unsigned short int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.u16 %0, %1;" : "=h"(__HALF_TO_US(h)) : "h"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ unsigned long long int __half2ull_rn(const __half h) +{ + unsigned long long int i; + asm("cvt.rni.u64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned long long int __half2ull_rd(const __half h) +{ + unsigned long long int i; + asm("cvt.rmi.u64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ unsigned long long int __half2ull_ru(const __half h) +{ + unsigned long long int i; + asm("cvt.rpi.u64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rn(const unsigned long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.u64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + // double-rounding is not a problem here: if integer + // has more than 24 bits, it is already too large to + // be represented in half precision, and result will + // be infinity. + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rz(const unsigned long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.u64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_rd(const unsigned long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.u64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ull2half_ru(const unsigned long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.u64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ long long int __half2ll_rn(const __half h) +{ + long long int i; + asm("cvt.rni.s64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ long long int __half2ll_rd(const __half h) +{ + long long int i; + asm("cvt.rmi.s64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +__CUDA_FP16_DECL__ long long int __half2ll_ru(const __half h) +{ + long long int i; + asm("cvt.rpi.s64.f16 %0, %1;" : "=l"(i) : "h"(__HALF_TO_CUS(h))); + return i; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rn(const long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rn.f16.s64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + // double-rounding is not a problem here: if integer + // has more than 24 bits, it is already too large to + // be represented in half precision, and result will + // be infinity. + const float f = static_cast(i); + h = __float2half_rn(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rz(const long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rz.f16.s64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_rz(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_rd(const long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rm.f16.s64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_rd(f); +) + return h; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ll2half_ru(const long long int i) +{ + __half h; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("cvt.rp.f16.s64 %0, %1;" : "=h"(__HALF_TO_US(h)) : "l"(i)); +, + const float f = static_cast(i); + h = __float2half_ru(f); +) + return h; +} +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half htrunc(const __half h) +{ + __half r; + asm("cvt.rzi.f16.f16 %0, %1;" : "=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(h))); + return r; +} +__CUDA_FP16_DECL__ __half hceil(const __half h) +{ + __half r; + asm("cvt.rpi.f16.f16 %0, %1;" : "=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(h))); + return r; +} +__CUDA_FP16_DECL__ __half hfloor(const __half h) +{ + __half r; + asm("cvt.rmi.f16.f16 %0, %1;" : "=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(h))); + return r; +} +__CUDA_FP16_DECL__ __half hrint(const __half h) +{ + __half r; + asm("cvt.rni.f16.f16 %0, %1;" : "=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(h))); + return r; +} + +__CUDA_FP16_DECL__ __half2 h2trunc(const __half2 h) +{ + __half2 val; + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " cvt.rzi.f16.f16 low, low;\n" + " cvt.rzi.f16.f16 high, high;\n" + " mov.b32 %0, {low,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(h))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2ceil(const __half2 h) +{ + __half2 val; + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " cvt.rpi.f16.f16 low, low;\n" + " cvt.rpi.f16.f16 high, high;\n" + " mov.b32 %0, {low,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(h))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2floor(const __half2 h) +{ + __half2 val; + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " cvt.rmi.f16.f16 low, low;\n" + " cvt.rmi.f16.f16 high, high;\n" + " mov.b32 %0, {low,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(h))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2rint(const __half2 h) +{ + __half2 val; + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " cvt.rni.f16.f16 low, low;\n" + " cvt.rni.f16.f16 high, high;\n" + " mov.b32 %0, {low,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(h))); + return val; +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __lows2half2(const __half2 a, const __half2 b) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 alow,ahigh,blow,bhigh;\n" + " mov.b32 {alow,ahigh}, %1;\n" + " mov.b32 {blow,bhigh}, %2;\n" + " mov.b32 %0, {alow,blow};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)), "r"(__HALF2_TO_CUI(b))); +, + val.x = a.x; + val.y = b.x; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __highs2half2(const __half2 a, const __half2 b) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 alow,ahigh,blow,bhigh;\n" + " mov.b32 {alow,ahigh}, %1;\n" + " mov.b32 {blow,bhigh}, %2;\n" + " mov.b32 %0, {ahigh,bhigh};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)), "r"(__HALF2_TO_CUI(b))); +, + val.x = a.y; + val.y = b.y; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __low2half(const __half2 a) +{ + __half ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b16 %0, low;}" : "=h"(__HALF_TO_US(ret)) : "r"(__HALF2_TO_CUI(a))); +, + ret = a.x; +) + return ret; +} +__CUDA_HOSTDEVICE_FP16_DECL__ int __hisinf(const __half a) +{ + int retval; + const __half_raw araw = __half_raw(a); + if (araw.x == 0xFC00U) { + retval = -1; + } else if (araw.x == 0x7C00U) { + retval = 1; + } else { + retval = 0; + } + return retval; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __low2half2(const __half2 a) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {low,low};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); +, + val.x = a.x; + val.y = a.x; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __high2half2(const __half2 a) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {high,high};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); +, + val.x = a.y; + val.y = a.y; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __high2half(const __half2 a) +{ + __half ret; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b16 %0, high;}" : "=h"(__HALF_TO_US(ret)) : "r"(__HALF2_TO_CUI(a))); +, + ret = a.y; +) + return ret; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __halves2half2(const __half a, const __half b) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ mov.b32 %0, {%1,%2};}\n" + : "=r"(__HALF2_TO_UI(val)) : "h"(__HALF_TO_CUS(a)), "h"(__HALF_TO_CUS(b))); +, + val.x = a; + val.y = b; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __half2half2(const __half a) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{ mov.b32 %0, {%1,%1};}\n" + : "=r"(__HALF2_TO_UI(val)) : "h"(__HALF_TO_CUS(a))); +, + val.x = a; + val.y = a; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __lowhigh2highlow(const __half2 a) +{ + __half2 val; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm("{.reg .f16 low,high;\n" + " mov.b32 {low,high}, %1;\n" + " mov.b32 %0, {high,low};}\n" : "=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); +, + val.x = a.y; + val.y = a.x; +) + return val; +} +__CUDA_HOSTDEVICE_FP16_DECL__ short int __half_as_short(const __half h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return static_cast(__HALF_TO_CUS(h)); +, + return static_cast(__half_raw(h).x); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned short int __half_as_ushort(const __half h) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __HALF_TO_CUS(h); +, + return __half_raw(h).x; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __short_as_half(const short int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __half h; + __HALF_TO_US(h) = static_cast(i); + return h; +, + __half_raw hr; + hr.x = static_cast(i); + return __half(hr); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __ushort_as_half(const unsigned short int i) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __half h; + __HALF_TO_US(h) = i; + return h; +, + __half_raw hr; + hr.x = i; + return __half(hr);) +} + +/****************************************************************************** +* __half arithmetic * +******************************************************************************/ +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half __internal_device_hmax(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF_MACRO(max) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + float fr; + asm("{max.f32 %0,%1,%2;\n}" + :"=f"(fr) : "f"(fa), "f"(fb)); + const __half hr = __float2half(fr); + return hr; +) +} +__CUDA_FP16_DECL__ __half __internal_device_hmin(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF_MACRO(min) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + float fr; + asm("{min.f32 %0,%1,%2;\n}" + :"=f"(fr) : "f"(fa), "f"(fb)); + const __half hr = __float2half(fr); + return hr; +) +} +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmax(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hmax(a, b); +, + __half maxval; + + maxval = (__hge(a, b) || __hisnan(b)) ? a : b; + + if (__hisnan(maxval)) + { + // if both inputs are NaN, return canonical NaN + maxval = CUDART_NAN_FP16; + } + else if (__heq(a, b)) + { + // hmax(+0.0, -0.0) = +0.0 + // unsigned compare 0x8000U > 0x0000U + __half_raw ra = __half_raw(a); + __half_raw rb = __half_raw(b); + maxval = (ra.x > rb.x) ? b : a; + } + return maxval; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmin(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __internal_device_hmin(a, b); +, + __half minval; + + minval = (__hle(a, b) || __hisnan(b)) ? a : b; + + if (__hisnan(minval)) + { + // if both inputs are NaN, return canonical NaN + minval = CUDART_NAN_FP16; + } + else if (__heq(a, b)) + { + // hmin(+0.0, -0.0) = -0.0 + // unsigned compare 0x8000U > 0x0000U + __half_raw ra = __half_raw(a); + __half_raw rb = __half_raw(b); + minval = (ra.x > rb.x) ? a : b; + } + + return minval; +) +} + + +/****************************************************************************** +* __half2 arithmetic * +******************************************************************************/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmax2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF2_MACRO(max) +, + __half2 val; + val.x = __hmax(a.x, b.x); + val.y = __hmax(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmin2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF2_MACRO(min) +, + __half2 val; + val.x = __hmin(a.x, b.x); + val.y = __hmin(a.y, b.y); + return val; +) +} + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300) || defined(_NVHPC_CUDA) +/****************************************************************************** +* __half, __half2 warp shuffle * +******************************************************************************/ +#define __SHUFFLE_HALF2_MACRO(name) /* do */ {\ + __half2 r; \ + asm volatile ("{" __CUDA_FP16_STRINGIFY(name) " %0,%1,%2,%3;\n}" \ + :"=r"(__HALF2_TO_UI(r)): "r"(__HALF2_TO_CUI(var)), "r"(delta), "r"(c)); \ + return r; \ +} /* while(0) */ + +#define __SHUFFLE_SYNC_HALF2_MACRO(name) /* do */ {\ + __half2 r; \ + asm volatile ("{" __CUDA_FP16_STRINGIFY(name) " %0,%1,%2,%3,%4;\n}" \ + :"=r"(__HALF2_TO_UI(r)): "r"(__HALF2_TO_CUI(var)), "r"(delta), "r"(c), "r"(mask)); \ + return r; \ +} /* while(0) */ + +#if defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ < 700) + +__CUDA_FP16_DECL__ __half2 __shfl(const __half2 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_HALF2_MACRO(shfl.idx.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_up(const __half2 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = (warp_size - static_cast(width)) << 8U; + __SHUFFLE_HALF2_MACRO(shfl.up.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_down(const __half2 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_HALF2_MACRO(shfl.down.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_xor(const __half2 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_HALF2_MACRO(shfl.bfly.b32) +} + +#endif /* defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ < 700) */ + +__CUDA_FP16_DECL__ __half2 __shfl_sync(const unsigned mask, const __half2 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_HALF2_MACRO(shfl.sync.idx.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_up_sync(const unsigned mask, const __half2 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = (warp_size - static_cast(width)) << 8U; + __SHUFFLE_SYNC_HALF2_MACRO(shfl.sync.up.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_down_sync(const unsigned mask, const __half2 var, const unsigned int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_HALF2_MACRO(shfl.sync.down.b32) +} +__CUDA_FP16_DECL__ __half2 __shfl_xor_sync(const unsigned mask, const __half2 var, const int delta, const int width) +{ + unsigned int warp_size; + asm("{mov.u32 %0, WARP_SZ;\n}" : "=r"(warp_size)); + const unsigned int c = ((warp_size - static_cast(width)) << 8U) | 0x1fU; + __SHUFFLE_SYNC_HALF2_MACRO(shfl.sync.bfly.b32) +} + +#undef __SHUFFLE_HALF2_MACRO +#undef __SHUFFLE_SYNC_HALF2_MACRO + +#if defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ < 700) + +__CUDA_FP16_DECL__ __half __shfl(const __half var, const int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl(temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_up(const __half var, const unsigned int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_up(temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_down(const __half var, const unsigned int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_down(temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_xor(const __half var, const int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_xor(temp1, delta, width); + return __low2half(temp2); +} + +#endif /* defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ < 700) */ + +__CUDA_FP16_DECL__ __half __shfl_sync(const unsigned mask, const __half var, const int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_sync(mask, temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_up_sync(const unsigned mask, const __half var, const unsigned int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_up_sync(mask, temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_down_sync(const unsigned mask, const __half var, const unsigned int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_down_sync(mask, temp1, delta, width); + return __low2half(temp2); +} +__CUDA_FP16_DECL__ __half __shfl_xor_sync(const unsigned mask, const __half var, const int delta, const int width) +{ + const __half2 temp1 = __halves2half2(var, var); + const __half2 temp2 = __shfl_xor_sync(mask, temp1, delta, width); + return __low2half(temp2); +} + +#endif /* !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 300) || defined(_NVHPC_CUDA) */ +/****************************************************************************** +* __half and __half2 __ldg,__ldcg,__ldca,__ldcs * +******************************************************************************/ + +#if defined(__cplusplus) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320) || defined(_NVHPC_CUDA)) +#if (defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__) +#define __LDG_PTR "l" +#else +#define __LDG_PTR "r" +#endif /*(defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__)*/ +__CUDA_FP16_DECL__ __half2 __ldg(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.nc.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half __ldg(const __half *const ptr) +{ + __half ret; + asm ("ld.global.nc.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half2 __ldcg(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.cg.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half __ldcg(const __half *const ptr) +{ + __half ret; + asm ("ld.global.cg.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half2 __ldca(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.ca.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half __ldca(const __half *const ptr) +{ + __half ret; + asm ("ld.global.ca.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half2 __ldcs(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.cs.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half __ldcs(const __half *const ptr) +{ + __half ret; + asm ("ld.global.cs.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr)); + return ret; +} +__CUDA_FP16_DECL__ __half2 __ldlu(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.lu.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_FP16_DECL__ __half __ldlu(const __half *const ptr) +{ + __half ret; + asm ("ld.global.lu.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_FP16_DECL__ __half2 __ldcv(const __half2 *const ptr) +{ + __half2 ret; + asm ("ld.global.cv.b32 %0, [%1];" : "=r"(__HALF2_TO_UI(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_FP16_DECL__ __half __ldcv(const __half *const ptr) +{ + __half ret; + asm ("ld.global.cv.b16 %0, [%1];" : "=h"(__HALF_TO_US(ret)) : __LDG_PTR(ptr) : "memory"); + return ret; +} +__CUDA_FP16_DECL__ void __stwb(__half2 *const ptr, const __half2 value) +{ + asm ("st.global.wb.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__HALF2_TO_CUI(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stwb(__half *const ptr, const __half value) +{ + asm ("st.global.wb.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__HALF_TO_CUS(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stcg(__half2 *const ptr, const __half2 value) +{ + asm ("st.global.cg.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__HALF2_TO_CUI(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stcg(__half *const ptr, const __half value) +{ + asm ("st.global.cg.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__HALF_TO_CUS(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stcs(__half2 *const ptr, const __half2 value) +{ + asm ("st.global.cs.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__HALF2_TO_CUI(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stcs(__half *const ptr, const __half value) +{ + asm ("st.global.cs.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__HALF_TO_CUS(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stwt(__half2 *const ptr, const __half2 value) +{ + asm ("st.global.wt.b32 [%0], %1;" :: __LDG_PTR(ptr), "r"(__HALF2_TO_CUI(value)) : "memory"); +} +__CUDA_FP16_DECL__ void __stwt(__half *const ptr, const __half value) +{ + asm ("st.global.wt.b16 [%0], %1;" :: __LDG_PTR(ptr), "h"(__HALF_TO_CUS(value)) : "memory"); +} +#undef __LDG_PTR +#endif /* defined(__cplusplus) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 320) || defined(_NVHPC_CUDA)) */ +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ + +/****************************************************************************** +* __half2 comparison * +******************************************************************************/ +#define __COMPARISON_OP_HALF2_MACRO(name) /* do */ {\ + __half2 val; \ + asm( "{ " __CUDA_FP16_STRINGIFY(name) ".f16x2.f16x2 %0,%1,%2;\n}" \ + :"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)),"r"(__HALF2_TO_CUI(b))); \ + return val; \ +} /* while(0) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __heq2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.eq) +, + __half2_raw val; + val.x = __heq(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __heq(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hne2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.ne) +, + __half2_raw val; + val.x = __hne(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hne(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hle2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.le) +, + __half2_raw val; + val.x = __hle(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hle(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hge2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.ge) +, + __half2_raw val; + val.x = __hge(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hge(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hlt2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.lt) +, + __half2_raw val; + val.x = __hlt(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hlt(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgt2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.gt) +, + __half2_raw val; + val.x = __hgt(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hgt(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hequ2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.equ) +, + __half2_raw val; + val.x = __hequ(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hequ(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hneu2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.neu) +, + __half2_raw val; + val.x = __hneu(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hneu(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hleu2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.leu) +, + __half2_raw val; + val.x = __hleu(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hleu(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgeu2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.geu) +, + __half2_raw val; + val.x = __hgeu(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hgeu(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hltu2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.ltu) +, + __half2_raw val; + val.x = __hltu(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hltu(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hgtu2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO(set.gtu) +, + __half2_raw val; + val.x = __hgtu(a.x, b.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hgtu(a.y, b.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + return __half2(val); +) +} +#undef __COMPARISON_OP_HALF2_MACRO +/****************************************************************************** +* __half2 comparison with mask output * +******************************************************************************/ +#define __COMPARISON_OP_HALF2_MACRO_MASK(name) /* do */ {\ + unsigned val; \ + asm( "{ " __CUDA_FP16_STRINGIFY(name) ".u32.f16x2 %0,%1,%2;\n}" \ + :"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a)),"r"(__HALF2_TO_CUI(b))); \ + return val; \ +} /* while(0) */ +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __heq2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.eq) +, + const unsigned short px = __heq(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __heq(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hne2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.ne) +, + const unsigned short px = __hne(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hne(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hle2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.le) +, + const unsigned short px = __hle(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hle(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hge2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.ge) +, + const unsigned short px = __hge(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hge(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hlt2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.lt) +, + const unsigned short px = __hlt(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hlt(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgt2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.gt) +, + const unsigned short px = __hgt(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgt(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hequ2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.equ) +, + const unsigned short px = __hequ(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hequ(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hneu2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.neu) +, + const unsigned short px = __hneu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hneu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hleu2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.leu) +, + const unsigned short px = __hleu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hleu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgeu2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.geu) +, + const unsigned short px = __hgeu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgeu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hltu2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.ltu) +, + const unsigned short px = __hltu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hltu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ unsigned __hgtu2_mask(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF2_MACRO_MASK(set.gtu) +, + const unsigned short px = __hgtu(a.x, b.x) ? (unsigned short)0xFFFFU : (unsigned short)0U; + const unsigned short py = __hgtu(a.y, b.y) ? (unsigned short)0xFFFFU : (unsigned short)0U; + unsigned ur = (unsigned)py; + ur <<= (unsigned)16U; + ur |= (unsigned)px; + return ur; +) +} +#undef __COMPARISON_OP_HALF2_MACRO_MASK + +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbeq2(const __half2 a, const __half2 b) +{ + const unsigned mask = __heq2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbne2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hne2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hble2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hle2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbge2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hge2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hblt2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hlt2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgt2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hgt2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbequ2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hequ2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbneu2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hneu2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbleu2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hleu2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgeu2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hgeu2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbltu2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hltu2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hbgtu2(const __half2 a, const __half2 b) +{ + const unsigned mask = __hgtu2_mask(a, b); + return (mask == 0xFFFFFFFFU); +} +/****************************************************************************** +* __half comparison * +******************************************************************************/ +#define __COMPARISON_OP_HALF_MACRO(name) /* do */ {\ + unsigned short val; \ + asm( "{ .reg .pred __$temp3;\n" \ + " setp." __CUDA_FP16_STRINGIFY(name) ".f16 __$temp3, %1, %2;\n" \ + " selp.u16 %0, 1, 0, __$temp3;}" \ + : "=h"(val) : "h"(__HALF_TO_CUS(a)), "h"(__HALF_TO_CUS(b))); \ + return (val != 0U) ? true : false; \ +} /* while(0) */ +__CUDA_HOSTDEVICE_FP16_DECL__ bool __heq(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(eq) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa == fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hne(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(ne) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa != fb) && (!__hisnan(a)) && (!__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hle(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(le) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa <= fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hge(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(ge) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa >= fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hlt(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(lt) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa < fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgt(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(gt) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa > fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hequ(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(equ) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa == fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hneu(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(neu) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa != fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hleu(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(leu) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa <= fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgeu(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(geu) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa >= fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hltu(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(ltu) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa < fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hgtu(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __COMPARISON_OP_HALF_MACRO(gtu) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return (fa > fb) || (__hisnan(a)) || (__hisnan(b)); +) +} +#undef __COMPARISON_OP_HALF_MACRO +/****************************************************************************** +* __half2 arithmetic * +******************************************************************************/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(add) +, + __half2 val; + val.x = __hadd(a.x, b.x); + val.y = __hadd(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(sub) +, + __half2 val; + val.x = __hsub(a.x, b.x); + val.y = __hsub(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(mul) +, + __half2 val; + val.x = __hmul(a.x, b.x); + val.y = __hmul(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2_sat(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(add.sat) +, + __half2 val; + val.x = __hadd_sat(a.x, b.x); + val.y = __hadd_sat(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2_sat(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(sub.sat) +, + __half2 val; + val.x = __hsub_sat(a.x, b.x); + val.y = __hsub_sat(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2_sat(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(mul.sat) +, + __half2 val; + val.x = __hmul_sat(a.x, b.x); + val.y = __hmul_sat(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hadd2_rn(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(add.rn) +, + __half2 val; + val.x = __hadd_rn(a.x, b.x); + val.y = __hadd_rn(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hsub2_rn(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(sub.rn) +, + __half2 val; + val.x = __hsub_rn(a.x, b.x); + val.y = __hsub_rn(a.y, b.y); + return val; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmul2_rn(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF2_MACRO(mul.rn) +, + __half2 val; + val.x = __hmul_rn(a.x, b.x); + val.y = __hmul_rn(a.y, b.y); + return val; +) +} +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half2 __hfma2(const __half2 a, const __half2 b, const __half2 c) +{ + __TERNARY_OP_HALF2_MACRO(fma.rn) +} +__CUDA_FP16_DECL__ __half2 __hfma2_sat(const __half2 a, const __half2 b, const __half2 c) +{ + __TERNARY_OP_HALF2_MACRO(fma.rn.sat) +} +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __h2div(const __half2 a, const __half2 b) { + __half ha = __low2half(a); + __half hb = __low2half(b); + + const __half v1 = __hdiv(ha, hb); + + ha = __high2half(a); + hb = __high2half(b); + + const __half v2 = __hdiv(ha, hb); + + return __halves2half2(v1, v2); +} + +/****************************************************************************** +* __half arithmetic * +******************************************************************************/ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(add) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa + fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(sub) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa - fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(mul) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa * fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd_sat(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(add.sat) +, + return __hmin(__hmax(__hadd(a, b), CUDART_ZERO_FP16), CUDART_ONE_FP16); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub_sat(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(sub.sat) +, + return __hmin(__hmax(__hsub(a, b), CUDART_ZERO_FP16), CUDART_ONE_FP16); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul_sat(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(mul.sat) +, + return __hmin(__hmax(__hmul(a, b), CUDART_ZERO_FP16), CUDART_ONE_FP16); +) +} + +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hadd_rn(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(add.rn) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa + fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hsub_rn(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(sub.rn) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa - fb); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmul_rn(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __BINARY_OP_HALF_MACRO(mul.rn) +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa * fb); +) +} +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half __hfma(const __half a, const __half b, const __half c) +{ + __TERNARY_OP_HALF_MACRO(fma.rn) +} +__CUDA_FP16_DECL__ __half __hfma_sat(const __half a, const __half b, const __half c) +{ + __TERNARY_OP_HALF_MACRO(fma.rn.sat) +} +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hdiv(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __half v; + __half abs; + __half den; + __HALF_TO_US(den) = 0x008FU; + + float rcp; + const float fa = __half2float(a); + const float fb = __half2float(b); + + asm("{rcp.approx.ftz.f32 %0, %1;\n}" :"=f"(rcp) : "f"(fb)); + + float fv = rcp * fa; + + v = __float2half(fv); + abs = __habs(v); + if (__hlt(abs, den) && __hlt(__float2half(0.0f), abs)) { + const float err = __fmaf_rn(-fb, fv, fa); + fv = __fmaf_rn(rcp, err, fv); + v = __float2half(fv); + } + return v; +, + const float fa = __half2float(a); + const float fb = __half2float(b); + return __float2half(fa / fb); +) +} + +/****************************************************************************** +* __half2 functions * +******************************************************************************/ +#if defined(_NVHPC_CUDA) || defined(__CUDACC__) +#define __APPROX_FCAST(fun) /* do */ {\ + __half val;\ + asm("{.reg.b32 f; \n"\ + " .reg.b16 r; \n"\ + " mov.b16 r,%1; \n"\ + " cvt.f32.f16 f,r; \n"\ + " " __CUDA_FP16_STRINGIFY(fun) ".approx.ftz.f32 f,f; \n"\ + " cvt.rn.f16.f32 r,f; \n"\ + " mov.b16 %0,r; \n"\ + "}": "=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a)));\ + return val;\ +} /* while(0) */ +#define __APPROX_FCAST2(fun) /* do */ {\ + __half2 val;\ + asm("{.reg.b16 hl, hu; \n"\ + " .reg.b32 fl, fu; \n"\ + " mov.b32 {hl, hu}, %1; \n"\ + " cvt.f32.f16 fl, hl; \n"\ + " cvt.f32.f16 fu, hu; \n"\ + " " __CUDA_FP16_STRINGIFY(fun) ".approx.ftz.f32 fl, fl; \n"\ + " " __CUDA_FP16_STRINGIFY(fun) ".approx.ftz.f32 fu, fu; \n"\ + " cvt.rn.f16.f32 hl, fl; \n"\ + " cvt.rn.f16.f32 hu, fu; \n"\ + " mov.b32 %0, {hl, hu}; \n"\ + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); \ + return val;\ +} /* while(0) */ +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530) || defined(_NVHPC_CUDA) +#define __SPEC_CASE2(i,r, spc, ulp) \ + "{.reg.b32 spc, ulp, p;\n"\ + " mov.b32 spc," __CUDA_FP16_STRINGIFY(spc) ";\n"\ + " mov.b32 ulp," __CUDA_FP16_STRINGIFY(ulp) ";\n"\ + " set.eq.f16x2.f16x2 p," __CUDA_FP16_STRINGIFY(i) ", spc;\n"\ + " fma.rn.f16x2 " __CUDA_FP16_STRINGIFY(r) ",p,ulp," __CUDA_FP16_STRINGIFY(r) ";\n}\n" +#define __SPEC_CASE(i,r, spc, ulp) \ + "{.reg.b16 spc, ulp, p;\n"\ + " mov.b16 spc," __CUDA_FP16_STRINGIFY(spc) ";\n"\ + " mov.b16 ulp," __CUDA_FP16_STRINGIFY(ulp) ";\n"\ + " set.eq.f16.f16 p," __CUDA_FP16_STRINGIFY(i) ", spc;\n"\ + " fma.rn.f16 " __CUDA_FP16_STRINGIFY(r) ",p,ulp," __CUDA_FP16_STRINGIFY(r) ";\n}\n" +static __device__ __forceinline__ float __float_simpl_sinf(float a); +static __device__ __forceinline__ float __float_simpl_cosf(float a); +__CUDA_FP16_DECL__ __half hsin(const __half a) { + const float sl = __float_simpl_sinf(__half2float(a)); + __half r = __float2half_rn(sl); + asm("{\n\t" + " .reg.b16 i,r,t; \n\t" + " mov.b16 r, %0; \n\t" + " mov.b16 i, %1; \n\t" + " and.b16 t, r, 0x8000U; \n\t" + " abs.f16 r, r; \n\t" + " abs.f16 i, i; \n\t" + __SPEC_CASE(i, r, 0X32B3U, 0x0800U) + __SPEC_CASE(i, r, 0X5CB0U, 0x9000U) + " or.b16 r,r,t; \n\t" + " mov.b16 %0, r; \n" + "}\n" : "+h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(a))); + return r; +} +__CUDA_FP16_DECL__ __half2 h2sin(const __half2 a) { + const float sl = __float_simpl_sinf(__half2float(a.x)); + const float sh = __float_simpl_sinf(__half2float(a.y)); + __half2 r = __floats2half2_rn(sl, sh); + asm("{\n\t" + " .reg.b32 i,r,t; \n\t" + " mov.b32 r, %0; \n\t" + " mov.b32 i, %1; \n\t" + " and.b32 t, r, 0x80008000U; \n\t" + " abs.f16x2 r, r; \n\t" + " abs.f16x2 i, i; \n\t" + __SPEC_CASE2(i, r, 0X32B332B3U, 0x08000800U) + __SPEC_CASE2(i, r, 0X5CB05CB0U, 0x90009000U) + " or.b32 r, r, t; \n\t" + " mov.b32 %0, r; \n" + "}\n" : "+r"(__HALF2_TO_UI(r)) : "r"(__HALF2_TO_CUI(a))); + return r; +} +__CUDA_FP16_DECL__ __half hcos(const __half a) { + const float cl = __float_simpl_cosf(__half2float(a)); + __half r = __float2half_rn(cl); + asm("{\n\t" + " .reg.b16 i,r; \n\t" + " mov.b16 r, %0; \n\t" + " mov.b16 i, %1; \n\t" + " abs.f16 i, i; \n\t" + __SPEC_CASE(i, r, 0X2B7CU, 0x1000U) + " mov.b16 %0, r; \n" + "}\n" : "+h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(a))); + return r; +} +__CUDA_FP16_DECL__ __half2 h2cos(const __half2 a) { + const float cl = __float_simpl_cosf(__half2float(a.x)); + const float ch = __float_simpl_cosf(__half2float(a.y)); + __half2 r = __floats2half2_rn(cl, ch); + asm("{\n\t" + " .reg.b32 i,r; \n\t" + " mov.b32 r, %0; \n\t" + " mov.b32 i, %1; \n\t" + " abs.f16x2 i, i; \n\t" + __SPEC_CASE2(i, r, 0X2B7C2B7CU, 0x10001000U) + " mov.b32 %0, r; \n" + "}\n" : "+r"(__HALF2_TO_UI(r)) : "r"(__HALF2_TO_CUI(a))); + return r; +} +static __device__ __forceinline__ float __internal_trig_reduction_kernel(const float a, unsigned int *const quadrant) +{ + const float ar = __fmaf_rn(a, 0.636619772F, 12582912.0F); + const unsigned q = __float_as_uint(ar); + const float j = __fsub_rn(ar, 12582912.0F); + float t = __fmaf_rn(j, -1.5707962512969971e+000F, a); + t = __fmaf_rn(j, -7.5497894158615964e-008F, t); + *quadrant = q; + return t; +} +static __device__ __forceinline__ float __internal_sin_cos_kernel(const float x, const unsigned int i) +{ + float z; + const float x2 = x*x; + float a8; + float a6; + float a4; + float a2; + float a1; + float a0; + + if ((i & 1U) != 0U) { + // cos + a8 = 2.44331571e-5F; + a6 = -1.38873163e-3F; + a4 = 4.16666457e-2F; + a2 = -5.00000000e-1F; + a1 = x2; + a0 = 1.0F; + } + else { + // sin + a8 = -1.95152959e-4F; + a6 = 8.33216087e-3F; + a4 = -1.66666546e-1F; + a2 = 0.0F; + a1 = x; + a0 = x; + } + + z = __fmaf_rn(a8, x2, a6); + z = __fmaf_rn(z, x2, a4); + z = __fmaf_rn(z, x2, a2); + z = __fmaf_rn(z, a1, a0); + + if ((i & 2U) != 0U) { + z = -z; + } + return z; +} +static __device__ __forceinline__ float __float_simpl_sinf(float a) +{ + float z; + unsigned i; + a = __internal_trig_reduction_kernel(a, &i); + z = __internal_sin_cos_kernel(a, i); + return z; +} +static __device__ __forceinline__ float __float_simpl_cosf(float a) +{ + float z; + unsigned i; + a = __internal_trig_reduction_kernel(a, &i); + z = __internal_sin_cos_kernel(a, (i & 0x3U) + 1U); + return z; +} + +__CUDA_FP16_DECL__ __half hexp(const __half a) { + __half val; + asm("{.reg.b32 f, C, nZ; \n" + " .reg.b16 h,r; \n" + " mov.b16 h,%1; \n" + " cvt.f32.f16 f,h; \n" + " mov.b32 C, 0x3fb8aa3bU; \n" + " mov.b32 nZ, 0x80000000U;\n" + " fma.rn.f32 f,f,C,nZ; \n" + " ex2.approx.ftz.f32 f,f; \n" + " cvt.rn.f16.f32 r,f; \n" + __SPEC_CASE(h, r, 0X1F79U, 0x9400U) + __SPEC_CASE(h, r, 0X25CFU, 0x9400U) + __SPEC_CASE(h, r, 0XC13BU, 0x0400U) + __SPEC_CASE(h, r, 0XC1EFU, 0x0200U) + " mov.b16 %0,r; \n" + "}": "=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2exp(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 h,r,fl,fu,C,nZ; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " mov.b32 C, 0x3fb8aa3bU; \n" + " mov.b32 nZ, 0x80000000U;\n" + " fma.rn.f32 fl,fl,C,nZ; \n" + " fma.rn.f32 fu,fu,C,nZ; \n" + " ex2.approx.ftz.f32 fl, fl; \n" + " ex2.approx.ftz.f32 fu, fu; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __SPEC_CASE2(h, r, 0X1F791F79U, 0x94009400U) + __SPEC_CASE2(h, r, 0X25CF25CFU, 0x94009400U) + __SPEC_CASE2(h, r, 0XC13BC13BU, 0x04000400U) + __SPEC_CASE2(h, r, 0XC1EFC1EFU, 0x02000200U) + " mov.b32 %0, r; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +#endif /* !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530) || defined(_NVHPC_CUDA) */ +__CUDA_FP16_DECL__ __half hexp2(const __half a) { + __half val; + asm("{.reg.b32 f, ULP; \n" + " .reg.b16 r; \n" + " mov.b16 r,%1; \n" + " cvt.f32.f16 f,r; \n" + " ex2.approx.ftz.f32 f,f; \n" + " mov.b32 ULP, 0x33800000U;\n" + " fma.rn.f32 f,f,ULP,f; \n" + " cvt.rn.f16.f32 r,f; \n" + " mov.b16 %0,r; \n" + "}": "=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2exp2(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 fl, fu, ULP; \n" + " mov.b32 {hl, hu}, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " ex2.approx.ftz.f32 fl, fl; \n" + " ex2.approx.ftz.f32 fu, fu; \n" + " mov.b32 ULP, 0x33800000U;\n" + " fma.rn.f32 fl,fl,ULP,fl; \n" + " fma.rn.f32 fu,fu,ULP,fu; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 %0, {hl, hu}; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +#if !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half hexp10(const __half a) { + __half val; + asm("{.reg.b16 h,r; \n" + " .reg.b32 f, C, nZ; \n" + " mov.b16 h, %1; \n" + " cvt.f32.f16 f, h; \n" + " mov.b32 C, 0x40549A78U; \n" + " mov.b32 nZ, 0x80000000U;\n" + " fma.rn.f32 f,f,C,nZ; \n" + " ex2.approx.ftz.f32 f, f; \n" + " cvt.rn.f16.f32 r, f; \n" + __SPEC_CASE(h, r, 0x34DEU, 0x9800U) + __SPEC_CASE(h, r, 0x9766U, 0x9000U) + __SPEC_CASE(h, r, 0x9972U, 0x1000U) + __SPEC_CASE(h, r, 0xA5C4U, 0x1000U) + __SPEC_CASE(h, r, 0xBF0AU, 0x8100U) + " mov.b16 %0, r; \n" + "}":"=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2exp10(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 h,r,fl,fu,C,nZ; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " mov.b32 C, 0x40549A78U; \n" + " mov.b32 nZ, 0x80000000U;\n" + " fma.rn.f32 fl,fl,C,nZ; \n" + " fma.rn.f32 fu,fu,C,nZ; \n" + " ex2.approx.ftz.f32 fl, fl; \n" + " ex2.approx.ftz.f32 fu, fu; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __SPEC_CASE2(h, r, 0x34DE34DEU, 0x98009800U) + __SPEC_CASE2(h, r, 0x97669766U, 0x90009000U) + __SPEC_CASE2(h, r, 0x99729972U, 0x10001000U) + __SPEC_CASE2(h, r, 0xA5C4A5C4U, 0x10001000U) + __SPEC_CASE2(h, r, 0xBF0ABF0AU, 0x81008100U) + " mov.b32 %0, r; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +__CUDA_FP16_DECL__ __half hlog2(const __half a) { + __half val; + asm("{.reg.b16 h, r; \n" + " .reg.b32 f; \n" + " mov.b16 h, %1; \n" + " cvt.f32.f16 f, h; \n" + " lg2.approx.ftz.f32 f, f; \n" + " cvt.rn.f16.f32 r, f; \n" + __SPEC_CASE(r, r, 0xA2E2U, 0x8080U) + __SPEC_CASE(r, r, 0xBF46U, 0x9400U) + " mov.b16 %0, r; \n" + "}":"=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2log2(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 fl, fu, r, p; \n" + " mov.b32 {hl, hu}, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " lg2.approx.ftz.f32 fl, fl; \n" + " lg2.approx.ftz.f32 fu, fu; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __SPEC_CASE2(r, r, 0xA2E2A2E2U, 0x80808080U) + __SPEC_CASE2(r, r, 0xBF46BF46U, 0x94009400U) + " mov.b32 %0, r; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +__CUDA_FP16_DECL__ __half hlog(const __half a) { + __half val; + asm("{.reg.b32 f, C; \n" + " .reg.b16 r,h; \n" + " mov.b16 h,%1; \n" + " cvt.f32.f16 f,h; \n" + " lg2.approx.ftz.f32 f,f; \n" + " mov.b32 C, 0x3f317218U; \n" + " mul.f32 f,f,C; \n" + " cvt.rn.f16.f32 r,f; \n" + __SPEC_CASE(h, r, 0X160DU, 0x9C00U) + __SPEC_CASE(h, r, 0X3BFEU, 0x8010U) + __SPEC_CASE(h, r, 0X3C0BU, 0x8080U) + __SPEC_CASE(h, r, 0X6051U, 0x1C00U) + " mov.b16 %0,r; \n" + "}": "=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2log(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 r, fl, fu, C, h; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " lg2.approx.ftz.f32 fl, fl; \n" + " lg2.approx.ftz.f32 fu, fu; \n" + " mov.b32 C, 0x3f317218U; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __SPEC_CASE2(h, r, 0X160D160DU, 0x9C009C00U) + __SPEC_CASE2(h, r, 0X3BFE3BFEU, 0x80108010U) + __SPEC_CASE2(h, r, 0X3C0B3C0BU, 0x80808080U) + __SPEC_CASE2(h, r, 0X60516051U, 0x1C001C00U) + " mov.b32 %0, r; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +__CUDA_FP16_DECL__ __half hlog10(const __half a) { + __half val; + asm("{.reg.b16 h, r; \n" + " .reg.b32 f, C; \n" + " mov.b16 h, %1; \n" + " cvt.f32.f16 f, h; \n" + " lg2.approx.ftz.f32 f, f; \n" + " mov.b32 C, 0x3E9A209BU; \n" + " mul.f32 f,f,C; \n" + " cvt.rn.f16.f32 r, f; \n" + __SPEC_CASE(h, r, 0x338FU, 0x1000U) + __SPEC_CASE(h, r, 0x33F8U, 0x9000U) + __SPEC_CASE(h, r, 0x57E1U, 0x9800U) + __SPEC_CASE(h, r, 0x719DU, 0x9C00U) + " mov.b16 %0, r; \n" + "}":"=h"(__HALF_TO_US(val)) : "h"(__HALF_TO_CUS(a))); + return val; +} +__CUDA_FP16_DECL__ __half2 h2log10(const __half2 a) { + __half2 val; + asm("{.reg.b16 hl, hu; \n" + " .reg.b32 r, fl, fu, C, h; \n" + " mov.b32 {hl, hu}, %1; \n" + " mov.b32 h, %1; \n" + " cvt.f32.f16 fl, hl; \n" + " cvt.f32.f16 fu, hu; \n" + " lg2.approx.ftz.f32 fl, fl; \n" + " lg2.approx.ftz.f32 fu, fu; \n" + " mov.b32 C, 0x3E9A209BU; \n" + " mul.f32 fl,fl,C; \n" + " mul.f32 fu,fu,C; \n" + " cvt.rn.f16.f32 hl, fl; \n" + " cvt.rn.f16.f32 hu, fu; \n" + " mov.b32 r, {hl, hu}; \n" + __SPEC_CASE2(h, r, 0x338F338FU, 0x10001000U) + __SPEC_CASE2(h, r, 0x33F833F8U, 0x90009000U) + __SPEC_CASE2(h, r, 0x57E157E1U, 0x98009800U) + __SPEC_CASE2(h, r, 0x719D719DU, 0x9C009C00U) + " mov.b32 %0, r; \n" + "}":"=r"(__HALF2_TO_UI(val)) : "r"(__HALF2_TO_CUI(a))); + return val; +} +#undef __SPEC_CASE2 +#undef __SPEC_CASE +#endif /* !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530) || defined(_NVHPC_CUDA) */ +__CUDA_FP16_DECL__ __half2 h2rcp(const __half2 a) { + __APPROX_FCAST2(rcp) +} +__CUDA_FP16_DECL__ __half hrcp(const __half a) { + __APPROX_FCAST(rcp) +} +__CUDA_FP16_DECL__ __half2 h2rsqrt(const __half2 a) { + __APPROX_FCAST2(rsqrt) +} +__CUDA_FP16_DECL__ __half hrsqrt(const __half a) { + __APPROX_FCAST(rsqrt) +} +__CUDA_FP16_DECL__ __half2 h2sqrt(const __half2 a) { + __APPROX_FCAST2(sqrt) +} +__CUDA_FP16_DECL__ __half hsqrt(const __half a) { + __APPROX_FCAST(sqrt) +} +#undef __APPROX_FCAST +#undef __APPROX_FCAST2 +#endif /* defined(_NVHPC_CUDA) || defined(__CUDACC__) */ +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hisnan2(const __half2 a) +{ + __half2 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + asm("{set.nan.f16x2.f16x2 %0,%1,%2;\n}" + :"=r"(__HALF2_TO_UI(r)) : "r"(__HALF2_TO_CUI(a)), "r"(__HALF2_TO_CUI(a))); +, + __half2_raw val; + val.x = __hisnan(a.x) ? (unsigned short)0x3C00U : (unsigned short)0U; + val.y = __hisnan(a.y) ? (unsigned short)0x3C00U : (unsigned short)0U; + r = __half2(val); +) + return r; +} +__CUDA_HOSTDEVICE_FP16_DECL__ bool __hisnan(const __half a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __half r; + asm("{set.nan.f16.f16 %0,%1,%2;\n}" + :"=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(a)), "h"(__HALF_TO_CUS(a))); + return __HALF_TO_CUS(r) != 0U; +, + const __half_raw hr = static_cast<__half_raw>(a); + return ((hr.x & (unsigned short)0x7FFFU) > (unsigned short)0x7C00U); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hneg2(const __half2 a) +{ + __half2 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + asm("{neg.f16x2 %0,%1;\n}" + :"=r"(__HALF2_TO_UI(r)) : "r"(__HALF2_TO_CUI(a))); +, + r.x = __hneg(a.x); + r.y = __hneg(a.y); +) + return r; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hneg(const __half a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __half r; + asm("{neg.f16 %0,%1;\n}" + :"=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(a))); + return r; +, + const float fa = __half2float(a); + return __float2half(-fa); +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __habs2(const __half2 a) +{ + __half2 r; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + asm("{abs.f16x2 %0,%1;\n}" + :"=r"(__HALF2_TO_UI(r)) : "r"(__HALF2_TO_CUI(a))); +, + r.x = __habs(a.x); + r.y = __habs(a.y); +) + return r; +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __habs(const __half a) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_53, + __half r; + asm("{abs.f16 %0,%1;\n}" + :"=h"(__HALF_TO_US(r)) : "h"(__HALF_TO_CUS(a))); + return r; +, + __half_raw abs_a_raw = static_cast<__half_raw>(a); + abs_a_raw.x &= (unsigned short)0x7FFFU; + if (abs_a_raw.x > (unsigned short)0x7C00U) + { + // return canonical NaN + abs_a_raw.x = (unsigned short)0x7FFFU; + } + return static_cast<__half>(abs_a_raw); +) +} +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half2 __hcmadd(const __half2 a, const __half2 b, const __half2 c) +{ + // fast version of complex multiply-accumulate + // (a.re, a.im) * (b.re, b.im) + (c.re, c.im) + // acc.re = (c.re + a.re*b.re) - a.im*b.im + // acc.im = (c.im + a.re*b.im) + a.im*b.re + __half real_tmp = __hfma(a.x, b.x, c.x); + __half img_tmp = __hfma(a.x, b.y, c.y); + real_tmp = __hfma(__hneg(a.y), b.y, real_tmp); + img_tmp = __hfma(a.y, b.x, img_tmp); + return make_half2(real_tmp, img_tmp); +} +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmax_nan(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF_MACRO(max.NaN) +, + __half maxval; + if (__hisnan(a) || __hisnan(b)) + { + maxval = CUDART_NAN_FP16; + } + else + { + maxval = __hmax(a, b); + } + return maxval; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half __hmin_nan(const __half a, const __half b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF_MACRO(min.NaN) +, + __half minval; + if (__hisnan(a) || __hisnan(b)) + { + minval = CUDART_NAN_FP16; + } + else + { + minval = __hmin(a, b); + } + return minval; +) +} + +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half __hfma_relu(const __half a, const __half b, const __half c) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __TERNARY_OP_HALF_MACRO(fma.rn.relu) +, + return __hmax_nan(__hfma(a, b, c), CUDART_ZERO_FP16); +) +} +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ + +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmax2_nan(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF2_MACRO(max.NaN) +, + __half2 result = __hmax2(a, b); + if (__hisnan(a.x) || __hisnan(b.x)) + { + result.x = CUDART_NAN_FP16; + } + if (__hisnan(a.y) || __hisnan(b.y)) + { + result.y = CUDART_NAN_FP16; + } + return result; +) +} +__CUDA_HOSTDEVICE_FP16_DECL__ __half2 __hmin2_nan(const __half2 a, const __half2 b) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __BINARY_OP_HALF2_MACRO(min.NaN) +, + __half2 result = __hmin2(a, b); + if (__hisnan(a.x) || __hisnan(b.x)) + { + result.x = CUDART_NAN_FP16; + } + if (__hisnan(a.y) || __hisnan(b.y)) + { + result.y = CUDART_NAN_FP16; + } + return result; +) +} +#if defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half2 __hfma2_relu(const __half2 a, const __half2 b, const __half2 c) +{ +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_80, + __TERNARY_OP_HALF2_MACRO(fma.rn.relu) +, + __half2_raw hzero; + hzero.x = (unsigned short)0U; + hzero.y = (unsigned short)0U; + return __hmax2_nan(__hfma2(a, b, c), __half2(hzero)); +) +} +#endif /* defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 530)) || defined(_NVHPC_CUDA) */ + +#if defined(__CUDACC__) || defined(_NVHPC_CUDA) +/* Define __PTR for atomicAdd prototypes below, undef after done */ +#if (defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__) +#define __PTR "l" +#else +#define __PTR "r" +#endif /*(defined(_MSC_VER) && defined(_WIN64)) || defined(__LP64__) || defined(__CUDACC_RTC__)*/ + +__CUDA_FP16_DECL__ __half2 atomicAdd(__half2 *const address, const __half2 val) { +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_60, + __half2 r; + asm volatile ("{ atom.add.noftz.f16x2 %0,[%1],%2; }\n" + : "=r"(__HALF2_TO_UI(r)) : __PTR(address), "r"(__HALF2_TO_CUI(val)) + : "memory"); + return r; +, + unsigned int* address_as_uint = (unsigned int*)address; + unsigned int old = *address_as_uint; + unsigned int assumed; + do { + assumed = old; + __half2 new_val = __hadd2(val, *(__half2*)&assumed); + old = atomicCAS(address_as_uint, assumed, *(unsigned int*)&new_val); + } while (assumed != old); + return *(__half2*)&old; +) +} + +#if (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) +__CUDA_FP16_DECL__ __half atomicAdd(__half *const address, const __half val) { + __half r; + asm volatile ("{ atom.add.noftz.f16 %0,[%1],%2; }\n" + : "=h"(__HALF_TO_US(r)) + : __PTR(address), "h"(__HALF_TO_CUS(val)) + : "memory"); + return r; +} +#endif /* (defined(__CUDACC__) && (!defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700))) || defined(_NVHPC_CUDA) */ + +#undef __PTR +#endif /* defined(__CUDACC__) || defined(_NVHPC_CUDA) */ +#endif /* defined(__cplusplus) */ + +#undef __TERNARY_OP_HALF2_MACRO +#undef __TERNARY_OP_HALF_MACRO +#undef __BINARY_OP_HALF2_MACRO +#undef __BINARY_OP_HALF_MACRO + +#undef __CUDA_HOSTDEVICE_FP16_DECL__ +#undef __CUDA_FP16_DECL__ + +#undef __HALF_TO_US +#undef __HALF_TO_CUS +#undef __HALF2_TO_UI +#undef __HALF2_TO_CUI +#undef __CUDA_FP16_CONSTEXPR__ + +#if defined(__CPP_VERSION_AT_LEAST_11_FP16) +#undef __CPP_VERSION_AT_LEAST_11_FP16 +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP16) */ + +#endif /* end of include guard: __CUDA_FP16_HPP__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.h new file mode 100644 index 0000000000000000000000000000000000000000..d47c9a9100b13192e1e6376001a4989e9c077340 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.h @@ -0,0 +1,367 @@ +/* + * Copyright 2022 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef __CUDA_FP8_H__ +#define __CUDA_FP8_H__ + +/* Set up function decorations */ +#if defined(__CUDACC__) +#define __CUDA_FP8_DECL__ static __device__ __inline__ +#define __CUDA_HOSTDEVICE_FP8__ __host__ __device__ +#define __CUDA_HOSTDEVICE_FP8_DECL__ static __host__ __device__ __inline__ +#else /* !defined(__CUDACC__) */ +#if defined(__GNUC__) +#define __CUDA_HOSTDEVICE_FP8_DECL__ static __attribute__((unused)) +#else +#define __CUDA_HOSTDEVICE_FP8_DECL__ static +#endif /* defined(__GNUC__) */ +#define __CUDA_HOSTDEVICE_FP8__ +#endif /* defined(__CUDACC_) */ + +#if !defined(_MSC_VER) && __cplusplus >= 201103L +#define __CPP_VERSION_AT_LEAST_11_FP8 +#elif _MSC_FULL_VER >= 190024210 && _MSVC_LANG >= 201103L +#define __CPP_VERSION_AT_LEAST_11_FP8 +#endif + +/* bring in __half_raw data type */ +#include "cuda_fp16.h" +/* bring in __nv_bfloat16_raw data type */ +#include "cuda_bf16.h" +/* bring in float2, double4, etc vector types */ +#include "vector_types.h" + +/** + * \defgroup CUDA_MATH_INTRINSIC_FP8 FP8 Intrinsics + * This section describes fp8 intrinsic functions. + * To use these functions, include the header file \p cuda_fp8.h in your + * program. + * The following macros are available to help users selectively enable/disable + * various definitions present in the header file: + * - \p __CUDA_NO_FP8_CONVERSIONS__ - If defined, this macro will prevent any + * use of the C++ type conversions (converting constructors and conversion + * operators) defined in the header. + * - \p __CUDA_NO_FP8_CONVERSION_OPERATORS__ - If defined, this macro will + * prevent any use of the C++ conversion operators from \p fp8 to other types. + */ + +/** + * \defgroup CUDA_MATH_FP8_MISC FP8 Conversion and Data Movement + * \ingroup CUDA_MATH_INTRINSIC_FP8 + * To use these functions, include the header file \p cuda_fp8.h in your + * program. + */ + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief 8-bit \p unsigned \p integer + * type abstraction used to for \p fp8 floating-point + * numbers storage. + */ +typedef unsigned char __nv_fp8_storage_t; + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief 16-bit \p unsigned \p integer + * type abstraction used to for storage of pairs of + * \p fp8 floating-point numbers. + */ +typedef unsigned short int __nv_fp8x2_storage_t; + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief 32-bit \p unsigned \p integer + * type abstraction used to for storage of tetrads of + * \p fp8 floating-point numbers. + */ +typedef unsigned int __nv_fp8x4_storage_t; + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Enumerates the modes applicable when + * performing a narrowing conversion to \p fp8 destination types. + */ +typedef enum __nv_saturation_t { + /** + * Means no saturation to finite is performed when conversion + * results in rounding values outside the range of destination + * type. + * NOTE: for fp8 type of e4m3 kind, the results that are larger + * than the maximum representable finite number of the target + * format become NaN. + */ + __NV_NOSAT, + /** + * Means input larger than the maximum representable + * finite number MAXNORM of the target format round to the + * MAXNORM of the same sign as input. + */ + __NV_SATFINITE, +} __nv_saturation_t; + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Enumerates the possible + * interpretations of the 8-bit values when referring to them as + * \p fp8 types. + */ +typedef enum __nv_fp8_interpretation_t { + __NV_E4M3, /**< Stands for \p fp8 numbers of \p e4m3 kind. */ + __NV_E5M2, /**< Stands for \p fp8 numbers of \p e5m2 kind. */ +} __nv_fp8_interpretation_t; + +/* Forward-declaration of C-style APIs */ + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input \p double precision \p x to \p fp8 type of the + * requested kind using round-to-nearest-even rounding and requested saturation + * mode. + * + * \details Converts input \p x to \p fp8 type of the kind specified by + * \p fp8_interpretation parameter, + * using round-to-nearest-even rounding and + * saturation mode specified by \p saturate parameter. + * + * \returns + * - The \p __nv_fp8_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_double_to_fp8(const double x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input vector of two \p double precision numbers packed + * in \p double2 \p x into a vector of two values of \p fp8 type of + * the requested kind using round-to-nearest-even rounding and requested + * saturation mode. + * + * \details Converts input vector \p x to a vector of two \p fp8 values of the + * kind specified by \p fp8_interpretation parameter, using + * round-to-nearest-even rounding and saturation mode specified by \p saturate + * parameter. + * + * \returns + * - The \p __nv_fp8x2_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_double2_to_fp8x2(const double2 x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input \p single precision \p x to \p fp8 type of the + * requested kind using round-to-nearest-even rounding and requested saturation + * mode. + * + * \details Converts input \p x to \p fp8 type of the kind specified by + * \p fp8_interpretation parameter, + * using round-to-nearest-even rounding and + * saturation mode specified by \p saturate parameter. + * + * \returns + * - The \p __nv_fp8_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_float_to_fp8(const float x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input vector of two \p single precision numbers packed + * in \p float2 \p x into a vector of two values of \p fp8 type of + * the requested kind using round-to-nearest-even rounding and requested + * saturation mode. + * + * \details Converts input vector \p x to a vector of two \p fp8 values of the + * kind specified by \p fp8_interpretation parameter, using + * round-to-nearest-even rounding and saturation mode specified by \p saturate + * parameter. + * + * \returns + * - The \p __nv_fp8x2_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_float2_to_fp8x2(const float2 x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input \p half precision \p x to \p fp8 type of the requested + * kind using round-to-nearest-even rounding and requested saturation mode. + * + * \details Converts input \p x to \p fp8 type of the kind specified by + * \p fp8_interpretation parameter, + * using round-to-nearest-even rounding and + * saturation mode specified by \p saturate parameter. + * + * \returns + * - The \p __nv_fp8_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_halfraw_to_fp8(const __half_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input vector of two \p half precision numbers packed + * in \p __half2_raw \p x into a vector of two values of \p fp8 type of + * the requested kind using round-to-nearest-even rounding and requested + * saturation mode. + * + * \details Converts input vector \p x to a vector of two \p fp8 values of the + * kind specified by \p fp8_interpretation parameter, using + * round-to-nearest-even rounding and saturation mode specified by \p saturate + * parameter. + * + * \returns + * - The \p __nv_fp8x2_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t __nv_cvt_halfraw2_to_fp8x2( + const __half2_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input \p nv_bfloat16 precision \p x to \p fp8 type of the + * requested kind using round-to-nearest-even rounding and requested saturation + * mode. + * + * \details Converts input \p x to \p fp8 type of the kind specified by + * \p fp8_interpretation parameter, + * using round-to-nearest-even rounding and + * saturation mode specified by \p saturate parameter. + * + * \returns + * - The \p __nv_fp8_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t __nv_cvt_bfloat16raw_to_fp8( + const __nv_bfloat16_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input vector of two \p nv_bfloat16 precision numbers packed + * in \p __nv_bfloat162_raw \p x into a vector of two values of \p fp8 type of + * the requested kind using round-to-nearest-even rounding and requested + * saturation mode. + * + * \details Converts input vector \p x to a vector of two \p fp8 values of the + * kind specified by \p fp8_interpretation parameter, using + * round-to-nearest-even rounding and saturation mode specified by \p saturate + * parameter. + * + * \returns + * - The \p __nv_fp8x2_storage_t value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_bfloat16raw2_to_fp8x2( + const __nv_bfloat162_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation); + +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input \p fp8 \p x of the specified kind + * to \p half precision. + * + * \details Converts input \p x of \p fp8 type of the kind specified by + * \p fp8_interpretation parameter + * to \p half precision. + * + * \returns + * - The \p __half_raw value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __half_raw +__nv_cvt_fp8_to_halfraw(const __nv_fp8_storage_t x, + const __nv_fp8_interpretation_t fp8_interpretation); +/** + * \ingroup CUDA_MATH_FP8_MISC + * \brief Converts input vector of two \p fp8 values of the specified kind + * to a vector of two \p half precision values packed in \p __half2_raw + * structure. + * + * \details Converts input vector \p x of \p fp8 type of the kind specified by + * \p fp8_interpretation parameter + * to a vector of two \p half precision values and returns as \p __half2_raw + * structure. + * + * \returns + * - The \p __half2_raw value holds the result of conversion. + */ +__CUDA_HOSTDEVICE_FP8_DECL__ __half2_raw +__nv_cvt_fp8x2_to_halfraw2(const __nv_fp8x2_storage_t x, + const __nv_fp8_interpretation_t fp8_interpretation); + +#if defined(__cplusplus) + +#define __CUDA_FP8_TYPES_EXIST__ + +/* Forward-declaration of structures defined in "cuda_fp8.hpp" */ +struct __nv_fp8_e5m2; +struct __nv_fp8x2_e5m2; +struct __nv_fp8x4_e5m2; + +struct __nv_fp8_e4m3; +struct __nv_fp8x2_e4m3; +struct __nv_fp8x4_e4m3; + +#endif /* defined(__cplusplus) */ + +#include "cuda_fp8.hpp" + +#undef __CUDA_FP8_DECL__ +#undef __CUDA_HOSTDEVICE_FP8__ +#undef __CUDA_HOSTDEVICE_FP8_DECL__ + +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) +#undef __CPP_VERSION_AT_LEAST_11_FP8 +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#endif /* end of include guard: __CUDA_FP8_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.hpp b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.hpp new file mode 100644 index 0000000000000000000000000000000000000000..d1331494525242720d9f93e2b2306c4a83e35f5d --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_fp8.hpp @@ -0,0 +1,1750 @@ +/* + * Copyright 2022-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_FP8_HPP__) +#define __CUDA_FP8_HPP__ + +#if !defined(__CUDA_FP8_H__) +#error "Do not include this file directly. Instead, include cuda_fp8.h." +#endif + +/* C++ header for std::memcpy (used for type punning in host-side + * implementations). When compiling as a CUDA source file memcpy is provided + * implicitly. !defined(__CUDACC__) implies !defined(__CUDACC_RTC__). + */ +#if defined(__cplusplus) && !defined(__CUDACC__) +#include +#elif !defined(__cplusplus) && !defined(__CUDACC__) +#include +#endif /* defined(__cplusplus) && !defined(__CUDACC__) */ + +/* Set up structure-alignment attribute */ +#if !(defined __CUDA_ALIGN__) +#if defined(__CUDACC__) +#define __CUDA_ALIGN__(align) __align__(align) +#else +/* Define alignment macro based on compiler type (cannot assume C11 "_Alignas" + * is available) */ +#if __cplusplus >= 201103L +#define __CUDA_ALIGN__(n) \ + alignas(n) /* C++11 kindly gives us a keyword for this */ +#else /* !defined(__CPP_VERSION_AT_LEAST_11_FP8)*/ +#if defined(__GNUC__) +#define __CUDA_ALIGN__(n) __attribute__((aligned(n))) +#elif defined(_MSC_VER) +#define __CUDA_ALIGN__(n) __declspec(align(n)) +#else +#define __CUDA_ALIGN__(n) +#endif /* defined(__GNUC__) */ +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ +#endif /* defined(__CUDACC__) */ +#endif /* !(defined __CUDA_ALIGN__) */ + +#if !(defined __CPP_VERSION_AT_LEAST_11_FP8) +/* need c++11 for explicit operators */ +#define __CUDA_NO_FP8_CONVERSION_OPERATORS__ +#endif + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_double_to_fp8(const double x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + unsigned char res; + unsigned long long int xbits; + +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&xbits, &x, sizeof(x)); +#else + (void)std::memcpy(&xbits, &x, sizeof(x)); +#endif + unsigned char FP8_MAXNORM; + unsigned char FP8_MANTISSA_MASK; + unsigned short int FP8_EXP_BIAS; + unsigned long long int FP8_SIGNIFICAND_BITS; + const unsigned long long int DP_INF_BITS = 0x7FF0000000000000ULL; + unsigned long long int FP8_MINDENORM_O2; + unsigned long long int FP8_OVERFLOW_THRESHOLD; + unsigned long long int FP8_MINNORM; + + if (fp8_interpretation == __NV_E4M3) { + FP8_EXP_BIAS = 7U; + FP8_SIGNIFICAND_BITS = 4ULL; + FP8_MANTISSA_MASK = 0x7U; + FP8_MINDENORM_O2 = 0x3F50000000000000ULL; // mindenorm/2 = 2^-10 + FP8_OVERFLOW_THRESHOLD = + 0x407D000000000000ULL; // maxnorm + 1/2ulp = 0x1.Cp+8 + 0x1p+4 + FP8_MAXNORM = 0x7EU; + FP8_MINNORM = 0x3F90000000000000ULL; // minnorm = 2^-6 + } else { //__NV_E5M2 + FP8_EXP_BIAS = 15U; + FP8_SIGNIFICAND_BITS = 3ULL; + FP8_MANTISSA_MASK = 0x3U; + FP8_MINDENORM_O2 = 0x3EE0000000000000ULL; // mindenorm/2 = 2^-17 + FP8_OVERFLOW_THRESHOLD = + 0x40EE000000000000ULL - + 1ULL; // maxnorm + 1/2ulp = 0x1.Ep+15, and -1 to have common code + FP8_MAXNORM = 0x7BU; + FP8_MINNORM = 0x3F10000000000000ULL; // minnorm = 2^-14 + } + + // 1/2 LSB of the target format, positioned in double precision mantissa + // helpful in midpoints detection during round-to-nearest-even step + const unsigned long long int FP8_DP_HALF_ULP = + (unsigned long long int)1ULL << (53ULL - FP8_SIGNIFICAND_BITS - 1ULL); + // prepare sign bit in target format + unsigned char sign = (unsigned char)((xbits >> 63ULL) << 7U); + // prepare exponent field in target format + unsigned char exp = + (unsigned char)((((unsigned short int)(xbits >> 52ULL)) & 0x7FFU) - + 1023U + FP8_EXP_BIAS); + // round mantissa to target format width, rounding towards zero + unsigned char mantissa = + (unsigned char)(xbits >> (53ULL - FP8_SIGNIFICAND_BITS)) & + FP8_MANTISSA_MASK; + unsigned long long int absx = xbits & 0x7FFFFFFFFFFFFFFFULL; + + if (absx <= FP8_MINDENORM_O2) { + // zero or underflow + res = 0U; + } else if (absx > DP_INF_BITS) { + // NaN + if (fp8_interpretation == __NV_E4M3) { + res = 0x7FU; + } else { + // NaN --> QNaN + res = 0x7EU | mantissa; + } + } else if (absx > FP8_OVERFLOW_THRESHOLD) { + if (saturate == __NV_SATFINITE) { + res = FP8_MAXNORM; + } else { + // __NV_NOSAT + if (fp8_interpretation == __NV_E4M3) { + // no Inf in E4M3 + res = 0x7FU; // NaN + } else { + res = 0x7CU; // Inf in E5M2 + } + } + } else if (absx >= FP8_MINNORM) { + res = (unsigned char)((exp << (FP8_SIGNIFICAND_BITS - 1U)) | mantissa); + // rounded-off bits + unsigned long long int round = + xbits & ((FP8_DP_HALF_ULP << 1ULL) - 1ULL); + // round-to-nearest-even adjustment + if ((round > FP8_DP_HALF_ULP) || + ((round == FP8_DP_HALF_ULP) && (mantissa & 1U))) { + res = (unsigned char)(res + 1U); + } + } else // Denormal range + { + unsigned char shift = (unsigned char)(1U - exp); + // add implicit leading bit + mantissa |= (unsigned char)(1U << (FP8_SIGNIFICAND_BITS - 1U)); + // additional round-off due to denormalization + res = (unsigned char)(mantissa >> shift); + + // rounded-off bits, including implicit leading bit + unsigned long long int round = + (xbits | ((unsigned long long int)1ULL << (53ULL - 1ULL))) & + ((FP8_DP_HALF_ULP << (shift + 1ULL)) - 1ULL); + // round-to-nearest-even adjustment + if ((round > (FP8_DP_HALF_ULP << shift)) || + ((round == (FP8_DP_HALF_ULP << shift)) && (res & 1U))) { + res = (unsigned char)(res + 1U); + } + } + + res |= sign; + + return (__nv_fp8_storage_t)res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_double2_to_fp8x2(const double2 x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_fp8x2_storage_t storage = (__nv_fp8x2_storage_t)__nv_cvt_double_to_fp8( + x.y, saturate, fp8_interpretation); + storage = (__nv_fp8x2_storage_t)(storage << 8U); + storage = (__nv_fp8x2_storage_t)(storage | + __nv_cvt_double_to_fp8( + x.x, saturate, fp8_interpretation)); + return storage; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_float_to_fp8(const float x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_fp8_storage_t res = 0U; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + if (saturate == __NV_SATFINITE) { + __nv_fp8x2_storage_t storage; + if (fp8_interpretation == __NV_E5M2) { + asm("{cvt.rn.satfinite.e5m2x2.f32 %0, %2, %1;}\n" + : "=h"(storage) + : "f"(x), "f"(0.0f)); + } else { + asm("{cvt.rn.satfinite.e4m3x2.f32 %0, %2, %1;}\n" + : "=h"(storage) + : "f"(x), "f"(0.0f)); + } + res = (__nv_fp8_storage_t)storage; + } else +#endif + { + unsigned int xbits; +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&xbits, &x, sizeof(x)); +#else + (void)std::memcpy(&xbits, &x, sizeof(x)); +#endif + + // isnan + if ((xbits & 0x7FFFFFFFU) > 0x7F800000U) { + // Canonical NaN + xbits = 0x7FFFFFFFU; + } + + float fx; +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&fx, &xbits, sizeof(xbits)); +#else + (void)std::memcpy(&fx, &xbits, sizeof(xbits)); +#endif + + const double dx = (double)fx; + res = __nv_cvt_double_to_fp8(dx, saturate, fp8_interpretation); + } + return res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_float2_to_fp8x2(const float2 x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_fp8x2_storage_t storage; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + if (saturate == __NV_SATFINITE) { + if (fp8_interpretation == __NV_E5M2) { + asm("{cvt.rn.satfinite.e5m2x2.f32 %0, %2, %1;}\n" + : "=h"(storage) + : "f"(x.x), "f"(x.y)); + } else { + asm("{cvt.rn.satfinite.e4m3x2.f32 %0, %2, %1;}\n" + : "=h"(storage) + : "f"(x.x), "f"(x.y)); + } + } else +#endif + { + storage = (__nv_fp8x2_storage_t)__nv_cvt_float_to_fp8( + x.y, saturate, fp8_interpretation); + storage = (__nv_fp8x2_storage_t)(storage << 8U); + storage = (__nv_fp8x2_storage_t)(storage | __nv_cvt_float_to_fp8( + x.x, saturate, + fp8_interpretation)); + } + return storage; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ float +__internal_halfraw_to_float(const __half_raw x) { + float f; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 530) + asm("{cvt.f32.f16 %0, %1;}\n" : "=f"(f) : "h"(x.x)); +#else + const unsigned int ux = (unsigned int)x.x; + unsigned int sign = (ux >> 15U) & 1U; + unsigned int exponent = (ux >> 10U) & 0x1fU; + unsigned int mantissa = (ux & 0x3ffU) << 13U; + if (exponent == 0x1fU) { /* NaN or Inf */ + /* discard sign of a NaN */ + sign = ((mantissa != 0U) ? (sign >> 1U) : sign); + mantissa = ((mantissa != 0U) ? 0x7fffffU : 0U); + exponent = 0xffU; + } else if (exponent == 0U) { /* Denorm or Zero */ + if (mantissa != 0U) { + unsigned int msb; + exponent = 0x71U; + do { + msb = (mantissa & 0x400000U); + mantissa <<= 1U; /* normalize */ + --exponent; + } while (msb == 0U); + mantissa &= 0x7fffffU; /* 1.mantissa is implicit */ + } + } else { + exponent += 0x70U; + } + const unsigned int u = ((sign << 31U) | (exponent << 23U) | mantissa); +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&f, &u, sizeof(u)); +#else + (void)std::memcpy(&f, &u, sizeof(u)); +#endif +#endif /* (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 530) */ + return f; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ float2 +__internal_halfraw2_to_float2(const __half2_raw x) { + __half_raw raw; + float2 res; + raw.x = x.x; + res.x = __internal_halfraw_to_float(raw); + raw.x = x.y; + res.y = __internal_halfraw_to_float(raw); + return res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t +__nv_cvt_halfraw_to_fp8(const __half_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_fp8_storage_t res = 0U; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + if (saturate == __NV_SATFINITE) { + unsigned int half2_storage = (unsigned int)(x.x); + __nv_fp8x2_storage_t tmp; + if (fp8_interpretation == __NV_E5M2) { + asm("{cvt.rn.satfinite.e5m2x2.f16x2 %0, %1;}\n" + : "=h"(tmp) + : "r"(half2_storage)); + } else { + asm("{cvt.rn.satfinite.e4m3x2.f16x2 %0, %1;}\n" + : "=h"(tmp) + : "r"(half2_storage)); + } + res = (__nv_fp8_storage_t)tmp; + } else +#endif + { + float fx = __internal_halfraw_to_float(x); + res = __nv_cvt_float_to_fp8(fx, saturate, fp8_interpretation); + } + return res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t __nv_cvt_halfraw2_to_fp8x2( + const __half2_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_fp8x2_storage_t tmp; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + if (saturate == __NV_SATFINITE) { + unsigned int half2_storage; + (void)memcpy(&half2_storage, &x, sizeof(x)); + + if (fp8_interpretation == __NV_E5M2) { + asm("{cvt.rn.satfinite.e5m2x2.f16x2 %0, %1;}\n" + : "=h"(tmp) + : "r"(half2_storage)); + } else { + asm("{cvt.rn.satfinite.e4m3x2.f16x2 %0, %1;}\n" + : "=h"(tmp) + : "r"(half2_storage)); + } + } else +#endif + { + __half_raw raw; + raw.x = x.x; + __nv_fp8_storage_t lo = + __nv_cvt_halfraw_to_fp8(raw, saturate, fp8_interpretation); + raw.x = x.y; + __nv_fp8_storage_t hi = + __nv_cvt_halfraw_to_fp8(raw, saturate, fp8_interpretation); + tmp = hi; + tmp = (__nv_fp8x2_storage_t)(tmp << 8U); + tmp = (__nv_fp8x2_storage_t)(tmp | lo); + } + return tmp; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ float +__internal_bf16raw_to_float(const __nv_bfloat16_raw x) { + const unsigned int ux = ((unsigned int)x.x) << 16U; + float fx; +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&fx, &ux, sizeof(ux)); +#else + (void)std::memcpy(&fx, &ux, sizeof(ux)); +#endif + return fx; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_bfloat16_raw +__internal_float_to_bf16raw_rz(const float x) { + unsigned int ux; + __nv_bfloat16_raw r; +#if defined(__CUDACC__) || (!defined __cplusplus) + (void)memcpy(&ux, &x, sizeof(x)); +#else + (void)std::memcpy(&ux, &x, sizeof(x)); +#endif + r.x = (unsigned short int)(ux >> 16U); + return r; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8_storage_t __nv_cvt_bfloat16raw_to_fp8( + const __nv_bfloat16_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + const float fx = __internal_bf16raw_to_float(x); + const __nv_fp8_storage_t res = + __nv_cvt_float_to_fp8(fx, saturate, fp8_interpretation); + return res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __nv_fp8x2_storage_t +__nv_cvt_bfloat16raw2_to_fp8x2( + const __nv_bfloat162_raw x, const __nv_saturation_t saturate, + const __nv_fp8_interpretation_t fp8_interpretation) { + __nv_bfloat16_raw raw; + raw.x = x.y; + __nv_fp8x2_storage_t storage = + (__nv_fp8x2_storage_t)__nv_cvt_bfloat16raw_to_fp8(raw, saturate, + fp8_interpretation); + storage = (__nv_fp8x2_storage_t)(storage << 8U); + raw.x = x.x; + storage = (__nv_fp8x2_storage_t)(storage | + __nv_cvt_bfloat16raw_to_fp8( + raw, saturate, fp8_interpretation)); + return storage; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __half2_raw +__nv_cvt_fp8x2_to_halfraw2(const __nv_fp8x2_storage_t x, + const __nv_fp8_interpretation_t fp8_interpretation); +__CUDA_HOSTDEVICE_FP8_DECL__ __half_raw +__nv_cvt_fp8_to_halfraw(const __nv_fp8_storage_t x, + const __nv_fp8_interpretation_t fp8_interpretation) { + __half_raw res; + res.x = 0U; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + res.x = + __nv_cvt_fp8x2_to_halfraw2((__nv_fp8x2_storage_t)x, fp8_interpretation) + .x; +#else + unsigned short int ur = (unsigned short int)x; + ur = (unsigned short int)(ur << 8U); + + if (fp8_interpretation == __NV_E5M2) { + if ((ur & 0x7FFFU) > 0x7C00U) { + /* If NaN, return canonical NaN */ + ur = 0x7FFFU; + } + } else { // __NV_E4M3 + unsigned short int sign = ur & 0x8000U; + unsigned short int exponent = + (unsigned short int)(((ur & 0x7800U) >> 1U) + 0x2000U); + unsigned short int mantissa = (ur & 0x0700U) >> 1U; + unsigned char absx = 0x7FU & (unsigned char)x; + + if (absx == 0x7FU) // NaN + { + ur = 0x7FFFU; // fp16 canonical NaN, discard sign + } else if (exponent == 0x2000U) { + // zero or denormal + if (mantissa != 0U) { + // normalize + mantissa = (unsigned short int)(mantissa << 1U); + while ((mantissa & 0x0400U) == 0U) { + mantissa = (unsigned short int)(mantissa << 1U); + exponent = (unsigned short int)(exponent - 0x0400U); + } + // discard implicit leading bit + mantissa &= 0x03FFU; + } else { // Zero + exponent = 0U; + } + + ur = (sign | exponent) | mantissa; + } else { + ur = (sign | exponent) | mantissa; + } + } + res.x = ur; +#endif + return res; +} + +__CUDA_HOSTDEVICE_FP8_DECL__ __half2_raw +__nv_cvt_fp8x2_to_halfraw2(const __nv_fp8x2_storage_t x, + const __nv_fp8_interpretation_t fp8_interpretation) { + __half2_raw res; +#if (defined __CUDA_ARCH__) && (__CUDA_ARCH__ >= 890) + unsigned int half2_storage; + if (fp8_interpretation == __NV_E5M2) { + asm("{cvt.rn.f16x2.e5m2x2 %0, %1;}\n" : "=r"(half2_storage) : "h"(x)); + } else { + asm("{cvt.rn.f16x2.e4m3x2 %0, %1;}\n" : "=r"(half2_storage) : "h"(x)); + } + (void)memcpy(&res, &half2_storage, sizeof(half2_storage)); +#else + res.x = + __nv_cvt_fp8_to_halfraw((__nv_fp8_storage_t)x, fp8_interpretation).x; + res.y = __nv_cvt_fp8_to_halfraw((__nv_fp8_storage_t)(x >> 8U), + fp8_interpretation) + .x; +#endif + return res; +} + +/* All other definitions in this file are only visible to C++ compilers */ +#if defined(__cplusplus) + +/** + * \defgroup CUDA_MATH_FP8_E5M2_STRUCT C++ struct for handling fp8 data type of e5m2 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * \brief __nv_fp8_e5m2 datatype + * + * \details This structure implements the datatype for handling + * \p fp8 floating-point numbers of \p e5m2 kind: + * with 1 sign, 5 exponent, 1 implicit and 2 explicit mantissa bits. + * + * The structure implements converting constructors and operators. + */ +struct __CUDA_ALIGN__(1) __nv_fp8_e5m2 { + public: + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Storage variable contains the \p fp8 floating-point data. + */ + __nv_fp8_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8_e5m2() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider FP types */ + /* Note we do avoid constructor init-list because of special host/device + * compilation rules */ + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p __half data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const __half f) { + __x = __nv_cvt_halfraw_to_fp8(static_cast<__half_raw>(f), + __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p __nv_bfloat16 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const __nv_bfloat16 f) { + __x = __nv_cvt_bfloat16raw_to_fp8(static_cast<__nv_bfloat16_raw>(f), + __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p float data type, relies on \p __NV_SATFINITE behavior + * for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const float f) { + __x = __nv_cvt_float_to_fp8(f, __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p double data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const double f) { + __x = __nv_cvt_double_to_fp8(f, __NV_SATFINITE, __NV_E5M2); + } + + /* Converts from integral */ + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p unsigned \p short \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ + __nv_fp8_e5m2(const unsigned short int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p unsigned \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const unsigned int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p unsigned \p long \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const unsigned long int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p unsigned \p long \p long \p int data type, relies on + * \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ + __nv_fp8_e5m2(const unsigned long long int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p short \p int data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const short int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p int data type, relies on \p __NV_SATFINITE behavior + * for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p long \p int data type, relies on \p __NV_SATFINITE behavior + * for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const long int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Constructor from \p long \p long \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e5m2(const long long int val) { + __x = static_cast<__nv_fp8_e5m2>(static_cast(val)).__x; + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening FP converts */ + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p __half data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __half() const { + return static_cast<__half>(__nv_cvt_fp8_to_halfraw(__x, __NV_E5M2)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p float data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float() const { + return __internal_halfraw_to_float( + __nv_cvt_fp8_to_halfraw(__x, __NV_E5M2)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p __nv_bfloat16 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __nv_bfloat16() const { + return static_cast<__nv_bfloat16>( + __internal_float_to_bf16raw_rz(float(*this))); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p double data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator double() const { + return static_cast(float(*this)); + } + + /* Convert to integral */ + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p unsigned \p char data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned char() const { + unsigned char i; + const float f = float(*this); + const unsigned char max_val = 0xFFU; + const unsigned char min_val = 0U; + const unsigned char bits = (*this).__x; + // saturation fixup + if ((bits & 0x7FU) > 0x7CU) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value + i = static_cast(f); + } + return i; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p unsigned \p short \p int data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned short int() const { + return __half2ushort_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p unsigned \p int data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned int() const { + return __half2uint_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p unsigned \p long \p int data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero if output type is 32-bit. + * \p NaN inputs convert to \p 0x8000000000000000ULL if output type is 64-bit. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned long int() const { + unsigned long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ull_rz(__half(*this))); + } + else + { + retval = static_cast(__half2uint_rz(__half(*this))); + } + return retval; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p unsigned \p long \p long \p int data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p 0x8000000000000000ULL. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned long long int() const { + return __half2ull_rz(__half(*this)); + } + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p signed \p char data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator signed char() const { + signed char i; + const float f = float(*this); + const signed char max_val = (signed char)0x7FU; + const signed char min_val = (signed char)0x80U; + const unsigned char bits = (*this).__x; + // saturation fixup + if ((bits & 0x7FU) > 0x7CU) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value + i = static_cast(f); + } + return i; + } + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to an implementation defined \p char data type. + * + * Detects signedness of the \p char type and proceeds accordingly, see + * further details in signed and unsigned char operators. + + * Clamps inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator char() const { + char value; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (((char)-1) < (char)0) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + value = static_cast(static_cast(*this)); + } + else + { + value = static_cast(static_cast(*this)); + } + return value; + } + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p short \p int data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator short int() const { + return __half2short_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p int data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator int() const { + return __half2int_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p long \p int data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero if output type is 32-bit. + * \p NaN inputs convert to \p 0x8000000000000000ULL if output type is 64-bit. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator long int() const { + long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ll_rz(__half(*this))); + } + else + { + retval = static_cast(__half2int_rz(__half(*this))); + } + return retval; + } + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p long \p long \p int data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p 0x8000000000000000LL. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator long long int() const { + return __half2ll_rz(__half(*this)); + } + + /** + * \ingroup CUDA_MATH_FP8_E5M2_STRUCT + * Conversion operator to \p bool data type. + * +0 and -0 inputs convert to \p false. + * Non-zero inputs convert to \p true. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator bool() const { + return (__x & 0x7FU) != 0U; + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +/** + * \defgroup CUDA_MATH_FP8X2_E5M2_STRUCT C++ struct for handling vector type of two fp8 values of e5m2 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * \brief __nv_fp8x2_e5m2 datatype + * + * \details This structure implements the datatype for handling two + * \p fp8 floating-point numbers of \p e5m2 kind each: + * with 1 sign, 5 exponent, 1 implicit and 2 explicit mantissa bits. + * + * The structure implements converting constructors and operators. + */ +struct __CUDA_ALIGN__(2) __nv_fp8x2_e5m2 { + public: + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Storage variable contains the vector of two \p fp8 floating-point data + * values. + */ + __nv_fp8x2_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8x2_e5m2() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e5m2() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider types */ + + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Constructor from \p __half2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e5m2(const __half2 f) { + __x = __nv_cvt_halfraw2_to_fp8x2(static_cast<__half2_raw>(f), + __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Constructor from \p __nv_bfloat162 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e5m2(const __nv_bfloat162 f) { + __x = __nv_cvt_bfloat16raw2_to_fp8x2(static_cast<__nv_bfloat162_raw>(f), + __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Constructor from \p float2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e5m2(const float2 f) { + __x = __nv_cvt_float2_to_fp8x2(f, __NV_SATFINITE, __NV_E5M2); + } + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Constructor from \p double2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e5m2(const double2 f) { + __x = __nv_cvt_double2_to_fp8x2(f, __NV_SATFINITE, __NV_E5M2); + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening converts */ + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Conversion operator to \p __half2 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __half2() const { + return static_cast<__half2>(__nv_cvt_fp8x2_to_halfraw2(__x, __NV_E5M2)); + } + /** + * \ingroup CUDA_MATH_FP8X2_E5M2_STRUCT + * Conversion operator to \p float2 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float2() const { + return __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(__x, __NV_E5M2)); + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +__CUDA_HOSTDEVICE_FP8_DECL__ unsigned int +__internal_pack_u16x2_to_u32(const unsigned short int src_lo, + const unsigned short int src_hi) { + unsigned int dst; +#if (defined __CUDACC__) && (defined __CUDA_ARCH__) + asm("{ mov.b32 %0, {%1,%2};}\n" : "=r"(dst) : "h"(src_lo), "h"(src_hi)); +#else + dst = (static_cast(src_hi) << 16U) | + static_cast(src_lo); +#endif + return dst; +} + +/** + * \defgroup CUDA_MATH_FP8X4_E5M2_STRUCT C++ struct for handling vector type of four fp8 values of e5m2 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * \brief __nv_fp8x4_e5m2 datatype + * + * \details This structure implements the datatype for handling four + * \p fp8 floating-point numbers of \p e5m2 kind each: + * with 1 sign, 5 exponent, 1 implicit and 2 explicit mantissa bits. + * + * The structure implements converting constructors and operators. + */ +struct __CUDA_ALIGN__(4) __nv_fp8x4_e5m2 { + public: + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Storage variable contains the vector of four \p fp8 floating-point data + * values. + */ + __nv_fp8x4_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8x4_e5m2() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e5m2() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider types */ + + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Constructor from a pair of \p __half2 data type values, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e5m2(const __half2 flo, + const __half2 fhi) { + const __nv_fp8x2_storage_t rlo = __nv_cvt_halfraw2_to_fp8x2( + static_cast<__half2_raw>(flo), __NV_SATFINITE, __NV_E5M2); + const __nv_fp8x2_storage_t rhi = __nv_cvt_halfraw2_to_fp8x2( + static_cast<__half2_raw>(fhi), __NV_SATFINITE, __NV_E5M2); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Constructor from a pair of \p __nv_bfloat162 data type values, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e5m2(const __nv_bfloat162 flo, + const __nv_bfloat162 fhi) { + const __nv_fp8x2_storage_t rlo = __nv_cvt_bfloat16raw2_to_fp8x2( + static_cast<__nv_bfloat162_raw>(flo), __NV_SATFINITE, __NV_E5M2); + const __nv_fp8x2_storage_t rhi = __nv_cvt_bfloat16raw2_to_fp8x2( + static_cast<__nv_bfloat162_raw>(fhi), __NV_SATFINITE, __NV_E5M2); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Constructor from \p float4 vector data type, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e5m2(const float4 f) { + const float2 flo = {f.x, f.y}; + const float2 fhi = {f.z, f.w}; + const __nv_fp8x2_storage_t rlo = + __nv_cvt_float2_to_fp8x2(flo, __NV_SATFINITE, __NV_E5M2); + const __nv_fp8x2_storage_t rhi = + __nv_cvt_float2_to_fp8x2(fhi, __NV_SATFINITE, __NV_E5M2); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Constructor from \p double4 vector data type, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e5m2(const double4 f) { + const double2 flo = {f.x, f.y}; + const double2 fhi = {f.z, f.w}; + const __nv_fp8x2_storage_t rlo = + __nv_cvt_double2_to_fp8x2(flo, __NV_SATFINITE, __NV_E5M2); + const __nv_fp8x2_storage_t rhi = + __nv_cvt_double2_to_fp8x2(fhi, __NV_SATFINITE, __NV_E5M2); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening converts */ + + /** + * \ingroup CUDA_MATH_FP8X4_E5M2_STRUCT + * Conversion operator to \p float4 vector data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float4() const { + const __nv_fp8x2_storage_t slo = static_cast<__nv_fp8x2_storage_t>(__x); + const __nv_fp8x2_storage_t shi = + static_cast<__nv_fp8x2_storage_t>(__x >> 16U); + float2 rlo = __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(slo, __NV_E5M2)); + float2 rhi = __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(shi, __NV_E5M2)); + float4 res = {rlo.x, rlo.y, rhi.x, rhi.y}; + return res; + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +/** + * \defgroup CUDA_MATH_FP8_E4M3_STRUCT C++ struct for handling fp8 data type of e4m3 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * \brief __nv_fp8_e4m3 datatype + * + * \details This structure implements the datatype for storing + * \p fp8 floating-point numbers of \p e4m3 kind: + * with 1 sign, 4 exponent, 1 implicit and 3 explicit mantissa bits. + * The encoding doesn't support Infinity. + * NaNs are limited to 0x7F and 0xFF values. + * + * The structure implements converting constructors and operators. + */ +struct __CUDA_ALIGN__(1) __nv_fp8_e4m3 { + public: + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Storage variable contains the \p fp8 floating-point data. + */ + __nv_fp8_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8_e4m3() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider FP types */ + /* Note we do avoid constructor init-list because of special host/device + * compilation rules */ + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p __half data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const __half f) { + __x = __nv_cvt_halfraw_to_fp8(static_cast<__half_raw>(f), + __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p __nv_bfloat16 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const __nv_bfloat16 f) { + __x = __nv_cvt_bfloat16raw_to_fp8(static_cast<__nv_bfloat16_raw>(f), + __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p float data type, relies on \p __NV_SATFINITE behavior + * for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const float f) { + __x = __nv_cvt_float_to_fp8(f, __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p double data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const double f) { + __x = __nv_cvt_double_to_fp8(f, __NV_SATFINITE, __NV_E4M3); + } + + /* Converts from integral */ + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p unsigned \p short \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ + __nv_fp8_e4m3(const unsigned short int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p unsigned \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const unsigned int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p unsigned \p long \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const unsigned long int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p unsigned \p long \p long \p int data type, relies on + * \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ + __nv_fp8_e4m3(const unsigned long long int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p short \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const short int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p int data type, relies on \p __NV_SATFINITE behavior + * for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p long \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const long int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Constructor from \p long \p long \p int data type, relies on \p + * __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8_e4m3(const long long int val) { + __x = static_cast<__nv_fp8_e4m3>(static_cast(val)).__x; + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening FP converts */ + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p __half data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __half() const { + return static_cast<__half>(__nv_cvt_fp8_to_halfraw(__x, __NV_E4M3)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p float data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float() const { + return __internal_halfraw_to_float( + __nv_cvt_fp8_to_halfraw(__x, __NV_E4M3)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p __nv_bfloat16 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __nv_bfloat16() const { + return static_cast<__nv_bfloat16>( + __internal_float_to_bf16raw_rz(float(*this))); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p double data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator double() const { + return static_cast(float(*this)); + } + + /* Convert to integral */ + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p unsigned \p char data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned char() const { + unsigned char i; + const float f = float(*this); + const unsigned char max_val = 0xFFU; + const unsigned char min_val = 0U; + const unsigned char bits = (*this).__x; + // saturation fixup + if ((bits & 0x7FU) == 0x7FU) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value + i = static_cast(f); + } + return i; + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p unsigned \p short \p int data type. + * Clamps negative inputs to zero. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned short int() const { + return __half2ushort_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p unsigned \p int data type. + * Clamps negative inputs to zero. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned int() const { + return __half2uint_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p unsigned \p long \p int data type. + * Clamps negative and too large inputs to the output range. + * \p NaN inputs convert to \p zero if output type is 32-bit. + * \p NaN inputs convert to \p 0x8000000000000000ULL if output type is 64-bit. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned long int() const { + unsigned long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(unsigned long) == sizeof(unsigned long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ull_rz(__half(*this))); + } + else + { + retval = static_cast(__half2uint_rz(__half(*this))); + } + return retval; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p unsigned \p long \p long \p int data type. + * Clamps negative inputs to zero. + * \p NaN inputs convert to \p 0x8000000000000000ULL. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator unsigned long long int() const { + return __half2ull_rz(__half(*this)); + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p signed \p char data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator signed char() const { + signed char i; + const float f = float(*this); + const signed char max_val = (signed char)0x7FU; + const signed char min_val = (signed char)0x80U; + const unsigned char bits = (*this).__x; + // saturation fixup + if ((bits & 0x7FU) == 0x7FU) { + // NaN + i = 0; + } else if (f > static_cast(max_val)) { + // saturate maximum + i = max_val; + } else if (f < static_cast(min_val)) { + // saturate minimum + i = min_val; + } else { + // normal value + i = static_cast(f); + } + return i; + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to an implementation defined \p char data type. + * + * Detects signedness of the \p char type and proceeds accordingly, see + * further details in signed and unsigned char operators. + + * Clamps inputs to the output range. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator char() const { + char value; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (((char)-1) < (char)0) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + value = static_cast(static_cast(*this)); + } + else + { + value = static_cast(static_cast(*this)); + } + return value; + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p short \p int data type. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator short int() const { + return __half2short_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p int data type. + * \p NaN inputs convert to \p zero. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator int() const { + return __half2int_rz(__half(*this)); + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p long \p int data type. + * Clamps too large inputs to the output range. + * \p NaN inputs convert to \p zero if output type is 32-bit. + * \p NaN inputs convert to \p 0x8000000000000000ULL if output type is 64-bit. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator long int() const { + long retval; + /* Suppress VS warning: warning C4127: conditional expression is constant */ +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (push) +#pragma warning (disable: 4127) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + if (sizeof(long) == sizeof(long long)) +#if defined(_MSC_VER) && !defined(__CUDA_ARCH__) +#pragma warning (pop) +#endif /* _MSC_VER && !defined(__CUDA_ARCH__) */ + { + retval = static_cast(__half2ll_rz(__half(*this))); + } + else + { + retval = static_cast(__half2int_rz(__half(*this))); + } + return retval; + } + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p long \p long \p int data type. + * \p NaN inputs convert to \p 0x8000000000000000LL. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator long long int() const { + return __half2ll_rz(__half(*this)); + } + + /** + * \ingroup CUDA_MATH_FP8_E4M3_STRUCT + * Conversion operator to \p bool data type. + * +0 and -0 inputs convert to \p false. + * Non-zero inputs convert to \p true. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator bool() const { + return (__x & 0x7FU) != 0U; + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +/** + * \defgroup CUDA_MATH_FP8X2_E4M3_STRUCT C++ struct for handling vector type of two fp8 values of e4m3 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * \brief __nv_fp8x2_e4m3 datatype + * + * \details This structure implements the datatype for storage + * and operations on the vector of two \p fp8 values of \p e4m3 kind each: + * with 1 sign, 4 exponent, 1 implicit and 3 explicit mantissa bits. + * The encoding doesn't support Infinity. + * NaNs are limited to 0x7F and 0xFF values. + */ +struct __CUDA_ALIGN__(2) __nv_fp8x2_e4m3 { + public: + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Storage variable contains the vector of two \p fp8 floating-point data + * values. + */ + __nv_fp8x2_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8x2_e4m3() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e4m3() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider types */ + + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Constructor from \p __half2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e4m3(const __half2 f) { + __x = __nv_cvt_halfraw2_to_fp8x2(static_cast<__half2_raw>(f), + __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Constructor from \p __nv_bfloat162 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e4m3(const __nv_bfloat162 f) { + __x = __nv_cvt_bfloat16raw2_to_fp8x2(static_cast<__nv_bfloat162_raw>(f), + __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Constructor from \p float2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e4m3(const float2 f) { + __x = __nv_cvt_float2_to_fp8x2(f, __NV_SATFINITE, __NV_E4M3); + } + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Constructor from \p double2 data type, relies on \p __NV_SATFINITE + * behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x2_e4m3(const double2 f) { + __x = __nv_cvt_double2_to_fp8x2(f, __NV_SATFINITE, __NV_E4M3); + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening converts */ + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Conversion operator to \p __half2 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator __half2() const { + return static_cast<__half2>(__nv_cvt_fp8x2_to_halfraw2(__x, __NV_E4M3)); + } + /** + * \ingroup CUDA_MATH_FP8X2_E4M3_STRUCT + * Conversion operator to \p float2 data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float2() const { + return __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(__x, __NV_E4M3)); + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +/** + * \defgroup CUDA_MATH_FP8X4_E4M3_STRUCT C++ struct for handling vector type of four fp8 values of e4m3 kind. + * \ingroup CUDA_MATH_INTRINSIC_FP8 + */ + +/** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * \brief __nv_fp8x4_e4m3 datatype + * + * \details This structure implements the datatype for storage + * and operations on the vector of four \p fp8 values of \p e4m3 kind each: + * with 1 sign, 4 exponent, 1 implicit and 3 explicit mantissa bits. + * The encoding doesn't support Infinity. + * NaNs are limited to 0x7F and 0xFF values. + */ +struct __CUDA_ALIGN__(4) __nv_fp8x4_e4m3 { + public: + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Storage variable contains the vector of four \p fp8 floating-point data + * values. + */ + __nv_fp8x4_storage_t __x; + + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Constructor by default. + */ +#if defined(__CPP_VERSION_AT_LEAST_11_FP8) + __nv_fp8x4_e4m3() = default; +#else + __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e4m3() {} +#endif /* defined(__CPP_VERSION_AT_LEAST_11_FP8) */ + +#if !defined(__CUDA_NO_FP8_CONVERSIONS__) + + /* Construct from wider types */ + + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Constructor from a pair of \p __half2 data type values, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e4m3(const __half2 flo, + const __half2 fhi) { + const __nv_fp8x2_storage_t rlo = __nv_cvt_halfraw2_to_fp8x2( + static_cast<__half2_raw>(flo), __NV_SATFINITE, __NV_E4M3); + const __nv_fp8x2_storage_t rhi = __nv_cvt_halfraw2_to_fp8x2( + static_cast<__half2_raw>(fhi), __NV_SATFINITE, __NV_E4M3); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Constructor from a pair of \p __nv_bfloat162 data type values, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e4m3(const __nv_bfloat162 flo, + const __nv_bfloat162 fhi) { + const __nv_fp8x2_storage_t rlo = __nv_cvt_bfloat16raw2_to_fp8x2( + static_cast<__nv_bfloat162_raw>(flo), __NV_SATFINITE, __NV_E4M3); + const __nv_fp8x2_storage_t rhi = __nv_cvt_bfloat16raw2_to_fp8x2( + static_cast<__nv_bfloat162_raw>(fhi), __NV_SATFINITE, __NV_E4M3); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Constructor from \p float4 vector data type, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e4m3(const float4 f) { + const float2 flo = {f.x, f.y}; + const float2 fhi = {f.z, f.w}; + const __nv_fp8x2_storage_t rlo = + __nv_cvt_float2_to_fp8x2(flo, __NV_SATFINITE, __NV_E4M3); + const __nv_fp8x2_storage_t rhi = + __nv_cvt_float2_to_fp8x2(fhi, __NV_SATFINITE, __NV_E4M3); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Constructor from \p double4 vector data type, + * relies on \p __NV_SATFINITE behavior for out-of-range values. + */ + explicit __CUDA_HOSTDEVICE_FP8__ __nv_fp8x4_e4m3(const double4 f) { + const double2 flo = {f.x, f.y}; + const double2 fhi = {f.z, f.w}; + const __nv_fp8x2_storage_t rlo = + __nv_cvt_double2_to_fp8x2(flo, __NV_SATFINITE, __NV_E4M3); + const __nv_fp8x2_storage_t rhi = + __nv_cvt_double2_to_fp8x2(fhi, __NV_SATFINITE, __NV_E4M3); + __x = __internal_pack_u16x2_to_u32(rlo, rhi); + } + +#if !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) + /* Widening converts */ + + /** + * \ingroup CUDA_MATH_FP8X4_E4M3_STRUCT + * Conversion operator to \p float4 vector data type. + */ + explicit __CUDA_HOSTDEVICE_FP8__ operator float4() const { + const __nv_fp8x2_storage_t slo = static_cast<__nv_fp8x2_storage_t>(__x); + const __nv_fp8x2_storage_t shi = + static_cast<__nv_fp8x2_storage_t>(__x >> 16U); + float2 rlo = __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(slo, __NV_E4M3)); + float2 rhi = __internal_halfraw2_to_float2( + __nv_cvt_fp8x2_to_halfraw2(shi, __NV_E4M3)); + float4 res = {rlo.x, rlo.y, rhi.x, rhi.y}; + return res; + } +#endif /* !defined(__CUDA_NO_FP8_CONVERSION_OPERATORS__) */ +#endif /* !defined(__CUDA_NO_FP8_CONVERSIONS__) */ +}; + +#endif /* defined(__cplusplus) */ + +#endif /* end of include guard: __CUDA_FP8_HPP__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_gl_interop.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_gl_interop.h new file mode 100644 index 0000000000000000000000000000000000000000..df64a8afa14f695bb05810266ac40b227c078cc5 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_gl_interop.h @@ -0,0 +1,514 @@ +/* + * Copyright 1993-2012 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_GL_INTEROP_H__) +#define __CUDA_GL_INTEROP_H__ + +#include "cuda_runtime_api.h" + +#if defined(__APPLE__) + +#include + +#else /* __APPLE__ */ + +#if defined(__arm__) || defined(__aarch64__) +#ifndef GL_VERSION +#error Please include the appropriate gl headers before including cuda_gl_interop.h +#endif +#else +#include +#endif + +#endif /* __APPLE__ */ + +/** \cond impl_private */ +#if defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +#define __CUDA_DEPRECATED +#elif defined(_MSC_VER) +#define __CUDA_DEPRECATED __declspec(deprecated) +#elif defined(__GNUC__) +#define __CUDA_DEPRECATED __attribute__((deprecated)) +#else +#define __CUDA_DEPRECATED +#endif +/** \endcond impl_private */ + +#if defined(__cplusplus) +extern "C" { +#endif /* __cplusplus */ + +/** + * \addtogroup CUDART_OPENGL OpenGL Interoperability + * This section describes the OpenGL interoperability functions of the CUDA + * runtime application programming interface. Note that mapping of OpenGL + * resources is performed with the graphics API agnostic, resource mapping + * interface described in \ref CUDART_INTEROP "Graphics Interopability". + * + * @{ + */ + +/** + * CUDA devices corresponding to the current OpenGL context + */ +enum cudaGLDeviceList +{ + cudaGLDeviceListAll = 1, /**< The CUDA devices for all GPUs used by the current OpenGL context */ + cudaGLDeviceListCurrentFrame = 2, /**< The CUDA devices for the GPUs used by the current OpenGL context in its currently rendering frame */ + cudaGLDeviceListNextFrame = 3 /**< The CUDA devices for the GPUs to be used by the current OpenGL context in the next frame */ +}; + +/** + * \brief Gets the CUDA devices associated with the current OpenGL context + * + * Returns in \p *pCudaDeviceCount the number of CUDA-compatible devices + * corresponding to the current OpenGL context. Also returns in \p *pCudaDevices + * at most \p cudaDeviceCount of the CUDA-compatible devices corresponding to + * the current OpenGL context. If any of the GPUs being used by the current OpenGL + * context are not CUDA capable then the call will return ::cudaErrorNoDevice. + * + * \param pCudaDeviceCount - Returned number of CUDA devices corresponding to the + * current OpenGL context + * \param pCudaDevices - Returned CUDA devices corresponding to the current + * OpenGL context + * \param cudaDeviceCount - The size of the output device array \p pCudaDevices + * \param deviceList - The set of devices to return. This set may be + * ::cudaGLDeviceListAll for all devices, + * ::cudaGLDeviceListCurrentFrame for the devices used to + * render the current frame (in SLI), or + * ::cudaGLDeviceListNextFrame for the devices used to + * render the next frame (in SLI). + * + * \return + * ::cudaSuccess, + * ::cudaErrorNoDevice, + * ::cudaErrorInvalidGraphicsContext, + * ::cudaErrorOperatingSystem, + * ::cudaErrorUnknown + * + * \note This function is not supported on Mac OS X. + * \notefnerr + * + * \sa + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsMapResources, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cudaGraphicsResourceGetMappedPointer, + * ::cuGLGetDevices + */ +extern __host__ cudaError_t CUDARTAPI cudaGLGetDevices(unsigned int *pCudaDeviceCount, int *pCudaDevices, unsigned int cudaDeviceCount, enum cudaGLDeviceList deviceList); + +/** + * \brief Register an OpenGL texture or renderbuffer object + * + * Registers the texture or renderbuffer object specified by \p image for access by CUDA. + * A handle to the registered object is returned as \p resource. + * + * \p target must match the type of the object, and must be one of ::GL_TEXTURE_2D, + * ::GL_TEXTURE_RECTANGLE, ::GL_TEXTURE_CUBE_MAP, ::GL_TEXTURE_3D, ::GL_TEXTURE_2D_ARRAY, + * or ::GL_RENDERBUFFER. + * + * The register flags \p flags specify the intended usage, as follows: + * - ::cudaGraphicsRegisterFlagsNone: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::cudaGraphicsRegisterFlagsReadOnly: Specifies that CUDA + * will not write to this resource. + * - ::cudaGraphicsRegisterFlagsWriteDiscard: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * - ::cudaGraphicsRegisterFlagsSurfaceLoadStore: Specifies that CUDA will + * bind this resource to a surface reference. + * - ::cudaGraphicsRegisterFlagsTextureGather: Specifies that CUDA will perform + * texture gather operations on this resource. + * + * The following image formats are supported. For brevity's sake, the list is abbreviated. + * For ex., {GL_R, GL_RG} X {8, 16} would expand to the following 4 formats + * {GL_R8, GL_R16, GL_RG8, GL_RG16} : + * - GL_RED, GL_RG, GL_RGBA, GL_LUMINANCE, GL_ALPHA, GL_LUMINANCE_ALPHA, GL_INTENSITY + * - {GL_R, GL_RG, GL_RGBA} X {8, 16, 16F, 32F, 8UI, 16UI, 32UI, 8I, 16I, 32I} + * - {GL_LUMINANCE, GL_ALPHA, GL_LUMINANCE_ALPHA, GL_INTENSITY} X + * {8, 16, 16F_ARB, 32F_ARB, 8UI_EXT, 16UI_EXT, 32UI_EXT, 8I_EXT, 16I_EXT, 32I_EXT} + * + * The following image classes are currently disallowed: + * - Textures with borders + * - Multisampled renderbuffers + * + * \param resource - Pointer to the returned object handle + * \param image - name of texture or renderbuffer object to be registered + * \param target - Identifies the type of object specified by \p image + * \param flags - Register flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorOperatingSystem, + * ::cudaErrorUnknown + * \notefnerr + * + * \sa + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsMapResources, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cuGraphicsGLRegisterImage + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsGLRegisterImage(struct cudaGraphicsResource **resource, GLuint image, GLenum target, unsigned int flags); + +/** + * \brief Registers an OpenGL buffer object + * + * Registers the buffer object specified by \p buffer for access by + * CUDA. A handle to the registered object is returned as \p + * resource. The register flags \p flags specify the intended usage, + * as follows: + * + * - ::cudaGraphicsRegisterFlagsNone: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::cudaGraphicsRegisterFlagsReadOnly: Specifies that CUDA + * will not write to this resource. + * - ::cudaGraphicsRegisterFlagsWriteDiscard: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * \param resource - Pointer to the returned object handle + * \param buffer - name of buffer object to be registered + * \param flags - Register flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorOperatingSystem, + * ::cudaErrorUnknown + * \notefnerr + * + * \sa + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsMapResources, + * ::cudaGraphicsResourceGetMappedPointer, + * ::cuGraphicsGLRegisterBuffer + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsGLRegisterBuffer(struct cudaGraphicsResource **resource, GLuint buffer, unsigned int flags); + +#ifdef _WIN32 +#ifndef WGL_NV_gpu_affinity +typedef void* HGPUNV; +#endif + +/** + * \brief Gets the CUDA device associated with hGpu + * + * Returns the CUDA device associated with a hGpu, if applicable. + * + * \param device - Returns the device associated with hGpu, or -1 if hGpu is + * not a compute device. + * \param hGpu - Handle to a GPU, as queried via WGL_NV_gpu_affinity + * + * \return + * ::cudaSuccess + * \notefnerr + * + * \sa + * ::WGL_NV_gpu_affinity, + * ::cuWGLGetDevice + */ +extern __host__ cudaError_t CUDARTAPI cudaWGLGetDevice(int *device, HGPUNV hGpu); +#endif + +/** @} */ /* END CUDART_OPENGL */ + +/** + * \addtogroup CUDART_OPENGL_DEPRECATED OpenGL Interoperability [DEPRECATED] + * This section describes deprecated OpenGL interoperability functionality. + * + * @{ + */ + +/** + * CUDA GL Map Flags + */ +enum cudaGLMapFlags +{ + cudaGLMapFlagsNone = 0, /**< Default; Assume resource can be read/written */ + cudaGLMapFlagsReadOnly = 1, /**< CUDA kernels will not write to this resource */ + cudaGLMapFlagsWriteDiscard = 2 /**< CUDA kernels will only write to and will not read from this resource */ +}; + +/** + * \brief Sets a CUDA device to use OpenGL interoperability + * + * \deprecated This function is deprecated as of CUDA 5.0. + * + * This function is deprecated and should no longer be used. It is + * no longer necessary to associate a CUDA device with an OpenGL + * context in order to achieve maximum interoperability performance. + * + * This function will immediately initialize the primary context on + * \p device if needed. + * + * \param device - Device to use for OpenGL interoperability + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorSetOnActiveProcess + * \notefnerr + * + * \sa ::cudaGraphicsGLRegisterBuffer, ::cudaGraphicsGLRegisterImage + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLSetGLDevice(int device); + +/** + * \brief Registers a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Registers the buffer object of ID \p bufObj for access by + * CUDA. This function must be called before CUDA can map the buffer + * object. The OpenGL context used to create the buffer, or another + * context from the same share group, must be bound to the current + * thread when this is called. + * + * \param bufObj - Buffer object ID to register + * + * \return + * ::cudaSuccess, + * ::cudaErrorInitializationError + * \notefnerr + * + * \sa ::cudaGraphicsGLRegisterBuffer + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLRegisterBufferObject(GLuint bufObj); + +/** + * \brief Maps a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Maps the buffer object of ID \p bufObj into the address space of + * CUDA and returns in \p *devPtr the base pointer of the resulting + * mapping. The buffer must have previously been registered by + * calling ::cudaGLRegisterBufferObject(). While a buffer is mapped + * by CUDA, any OpenGL operation which references the buffer will + * result in undefined behavior. The OpenGL context used to create + * the buffer, or another context from the same share group, must be + * bound to the current thread when this is called. + * + * All streams in the current thread are synchronized with the current + * GL context. + * + * \param devPtr - Returned device pointer to CUDA object + * \param bufObj - Buffer object ID to map + * + * \return + * ::cudaSuccess, + * ::cudaErrorMapBufferObjectFailed + * \notefnerr + * + * \sa ::cudaGraphicsMapResources + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLMapBufferObject(void **devPtr, GLuint bufObj); + +/** + * \brief Unmaps a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Unmaps the buffer object of ID \p bufObj for access by CUDA. When + * a buffer is unmapped, the base address returned by + * ::cudaGLMapBufferObject() is invalid and subsequent references to + * the address result in undefined behavior. The OpenGL context used + * to create the buffer, or another context from the same share group, + * must be bound to the current thread when this is called. + * + * All streams in the current thread are synchronized with the current + * GL context. + * + * \param bufObj - Buffer object to unmap + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnmapBufferObjectFailed + * \notefnerr + * + * \sa ::cudaGraphicsUnmapResources + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLUnmapBufferObject(GLuint bufObj); + +/** + * \brief Unregisters a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Unregisters the buffer object of ID \p bufObj for access by CUDA + * and releases any CUDA resources associated with the buffer. Once a + * buffer is unregistered, it may no longer be mapped by CUDA. The GL + * context used to create the buffer, or another context from the + * same share group, must be bound to the current thread when this is + * called. + * + * \param bufObj - Buffer object to unregister + * + * \return + * ::cudaSuccess + * \notefnerr + * + * \sa ::cudaGraphicsUnregisterResource + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLUnregisterBufferObject(GLuint bufObj); + +/** + * \brief Set usage flags for mapping an OpenGL buffer + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Set flags for mapping the OpenGL buffer \p bufObj + * + * Changes to flags will take effect the next time \p bufObj is mapped. + * The \p flags argument may be any of the following: + * + * - ::cudaGLMapFlagsNone: Specifies no hints about how this buffer will + * be used. It is therefore assumed that this buffer will be read from and + * written to by CUDA kernels. This is the default value. + * - ::cudaGLMapFlagsReadOnly: Specifies that CUDA kernels which access this + * buffer will not write to the buffer. + * - ::cudaGLMapFlagsWriteDiscard: Specifies that CUDA kernels which access + * this buffer will not read from the buffer and will write over the + * entire contents of the buffer, so none of the data previously stored in + * the buffer will be preserved. + * + * If \p bufObj has not been registered for use with CUDA, then + * ::cudaErrorInvalidResourceHandle is returned. If \p bufObj is presently + * mapped for access by CUDA, then ::cudaErrorUnknown is returned. + * + * \param bufObj - Registered buffer object to set flags for + * \param flags - Parameters for buffer mapping + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * + * \sa ::cudaGraphicsResourceSetMapFlags + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLSetBufferObjectMapFlags(GLuint bufObj, unsigned int flags); + +/** + * \brief Maps a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Maps the buffer object of ID \p bufObj into the address space of + * CUDA and returns in \p *devPtr the base pointer of the resulting + * mapping. The buffer must have previously been registered by + * calling ::cudaGLRegisterBufferObject(). While a buffer is mapped + * by CUDA, any OpenGL operation which references the buffer will + * result in undefined behavior. The OpenGL context used to create + * the buffer, or another context from the same share group, must be + * bound to the current thread when this is called. + * + * Stream /p stream is synchronized with the current GL context. + * + * \param devPtr - Returned device pointer to CUDA object + * \param bufObj - Buffer object ID to map + * \param stream - Stream to synchronize + * + * \return + * ::cudaSuccess, + * ::cudaErrorMapBufferObjectFailed + * \notefnerr + * + * \sa ::cudaGraphicsMapResources + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLMapBufferObjectAsync(void **devPtr, GLuint bufObj, cudaStream_t stream); + +/** + * \brief Unmaps a buffer object for access by CUDA + * + * \deprecated This function is deprecated as of CUDA 3.0. + * + * Unmaps the buffer object of ID \p bufObj for access by CUDA. When + * a buffer is unmapped, the base address returned by + * ::cudaGLMapBufferObject() is invalid and subsequent references to + * the address result in undefined behavior. The OpenGL context used + * to create the buffer, or another context from the same share group, + * must be bound to the current thread when this is called. + * + * Stream /p stream is synchronized with the current GL context. + * + * \param bufObj - Buffer object to unmap + * \param stream - Stream to synchronize + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnmapBufferObjectFailed + * \notefnerr + * + * \sa ::cudaGraphicsUnmapResources + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaGLUnmapBufferObjectAsync(GLuint bufObj, cudaStream_t stream); + +/** @} */ /* END CUDART_OPENGL_DEPRECATED */ + +#if defined(__cplusplus) +} +#endif /* __cplusplus */ + +#undef __CUDA_DEPRECATED + +#endif /* __CUDA_GL_INTEROP_H__ */ + diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_occupancy.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_occupancy.h new file mode 100644 index 0000000000000000000000000000000000000000..ffe55709f8ccdebf7341180f043006b68c08e104 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_occupancy.h @@ -0,0 +1,1958 @@ +/* + * Copyright 1993-2017 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +/** + * CUDA Occupancy Calculator + * + * NAME + * + * cudaOccMaxActiveBlocksPerMultiprocessor, + * cudaOccMaxPotentialOccupancyBlockSize, + * cudaOccMaxPotentialOccupancyBlockSizeVariableSMem + * cudaOccAvailableDynamicSMemPerBlock + * + * DESCRIPTION + * + * The CUDA occupancy calculator provides a standalone, programmatical + * interface to compute the occupancy of a function on a device. It can also + * provide occupancy-oriented launch configuration suggestions. + * + * The function and device are defined by the user through + * cudaOccFuncAttributes, cudaOccDeviceProp, and cudaOccDeviceState + * structures. All APIs require all 3 of them. + * + * See the structure definition for more details about the device / function + * descriptors. + * + * See each API's prototype for API usage. + * + * COMPATIBILITY + * + * The occupancy calculator will be updated on each major CUDA toolkit + * release. It does not provide forward compatibility, i.e. new hardwares + * released after this implementation's release will not be supported. + * + * NOTE + * + * If there is access to CUDA runtime, and the sole intent is to calculate + * occupancy related values on one of the accessible CUDA devices, using CUDA + * runtime's occupancy calculation APIs is recommended. + * + */ + +#ifndef __cuda_occupancy_h__ +#define __cuda_occupancy_h__ + +#include +#include +#include + + +// __OCC_INLINE will be undefined at the end of this header +// +#ifdef __CUDACC__ +#define __OCC_INLINE inline __host__ __device__ +#elif defined _MSC_VER +#define __OCC_INLINE __inline +#else // GNUCC assumed +#define __OCC_INLINE inline +#endif + +enum cudaOccError_enum { + CUDA_OCC_SUCCESS = 0, // no error encountered + CUDA_OCC_ERROR_INVALID_INPUT = 1, // input parameter is invalid + CUDA_OCC_ERROR_UNKNOWN_DEVICE = 2, // requested device is not supported in + // current implementation or device is + // invalid +}; +typedef enum cudaOccError_enum cudaOccError; + +typedef struct cudaOccResult cudaOccResult; +typedef struct cudaOccDeviceProp cudaOccDeviceProp; +typedef struct cudaOccFuncAttributes cudaOccFuncAttributes; +typedef struct cudaOccDeviceState cudaOccDeviceState; + +/** + * The CUDA occupancy calculator computes the occupancy of the function + * described by attributes with the given block size (blockSize), static device + * properties (properties), dynamic device states (states) and per-block dynamic + * shared memory allocation (dynamicSMemSize) in bytes, and output it through + * result along with other useful information. The occupancy is computed in + * terms of the maximum number of active blocks per multiprocessor. The user can + * then convert it to other metrics, such as number of active warps. + * + * RETURN VALUE + * + * The occupancy and related information is returned through result. + * + * If result->activeBlocksPerMultiprocessor is 0, then the given parameter + * combination cannot run on the device. + * + * ERRORS + * + * CUDA_OCC_ERROR_INVALID_INPUT input parameter is invalid. + * CUDA_OCC_ERROR_UNKNOWN_DEVICE requested device is not supported in + * current implementation or device is invalid + */ +static __OCC_INLINE +cudaOccError cudaOccMaxActiveBlocksPerMultiprocessor( + cudaOccResult *result, // out + const cudaOccDeviceProp *properties, // in + const cudaOccFuncAttributes *attributes, // in + const cudaOccDeviceState *state, // in + int blockSize, // in + size_t dynamicSmemSize); // in + +/** + * The CUDA launch configurator C API suggests a grid / block size pair (in + * minGridSize and blockSize) that achieves the best potential occupancy + * (i.e. maximum number of active warps with the smallest number of blocks) for + * the given function described by attributes, on a device described by + * properties with settings in state. + * + * If per-block dynamic shared memory allocation is not needed, the user should + * leave both blockSizeToDynamicSMemSize and dynamicSMemSize as 0. + * + * If per-block dynamic shared memory allocation is needed, then if the dynamic + * shared memory size is constant regardless of block size, the size should be + * passed through dynamicSMemSize, and blockSizeToDynamicSMemSize should be + * NULL. + * + * Otherwise, if the per-block dynamic shared memory size varies with different + * block sizes, the user needs to provide a pointer to an unary function through + * blockSizeToDynamicSMemSize that computes the dynamic shared memory needed by + * a block of the function for any given block size. dynamicSMemSize is + * ignored. An example signature is: + * + * // Take block size, returns dynamic shared memory needed + * size_t blockToSmem(int blockSize); + * + * RETURN VALUE + * + * The suggested block size and the minimum number of blocks needed to achieve + * the maximum occupancy are returned through blockSize and minGridSize. + * + * If *blockSize is 0, then the given combination cannot run on the device. + * + * ERRORS + * + * CUDA_OCC_ERROR_INVALID_INPUT input parameter is invalid. + * CUDA_OCC_ERROR_UNKNOWN_DEVICE requested device is not supported in + * current implementation or device is invalid + * + */ +static __OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSize( + int *minGridSize, // out + int *blockSize, // out + const cudaOccDeviceProp *properties, // in + const cudaOccFuncAttributes *attributes, // in + const cudaOccDeviceState *state, // in + size_t (*blockSizeToDynamicSMemSize)(int), // in + size_t dynamicSMemSize); // in + +/** + * The CUDA launch configurator C++ API suggests a grid / block size pair (in + * minGridSize and blockSize) that achieves the best potential occupancy + * (i.e. the maximum number of active warps with the smallest number of blocks) + * for the given function described by attributes, on a device described by + * properties with settings in state. + * + * If per-block dynamic shared memory allocation is 0 or constant regardless of + * block size, the user can use cudaOccMaxPotentialOccupancyBlockSize to + * configure the launch. A constant dynamic shared memory allocation size in + * bytes can be passed through dynamicSMemSize. + * + * Otherwise, if the per-block dynamic shared memory size varies with different + * block sizes, the user needs to use + * cudaOccMaxPotentialOccupancyBlockSizeVariableSmem instead, and provide a + * functor / pointer to an unary function (blockSizeToDynamicSMemSize) that + * computes the dynamic shared memory needed by func for any given block + * size. An example signature is: + * + * // Take block size, returns per-block dynamic shared memory needed + * size_t blockToSmem(int blockSize); + * + * RETURN VALUE + * + * The suggested block size and the minimum number of blocks needed to achieve + * the maximum occupancy are returned through blockSize and minGridSize. + * + * If *blockSize is 0, then the given combination cannot run on the device. + * + * ERRORS + * + * CUDA_OCC_ERROR_INVALID_INPUT input parameter is invalid. + * CUDA_OCC_ERROR_UNKNOWN_DEVICE requested device is not supported in + * current implementation or device is invalid + * + */ + +#if defined(__cplusplus) +namespace { + +__OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSize( + int *minGridSize, // out + int *blockSize, // out + const cudaOccDeviceProp *properties, // in + const cudaOccFuncAttributes *attributes, // in + const cudaOccDeviceState *state, // in + size_t dynamicSMemSize = 0); // in + +template +__OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSizeVariableSMem( + int *minGridSize, // out + int *blockSize, // out + const cudaOccDeviceProp *properties, // in + const cudaOccFuncAttributes *attributes, // in + const cudaOccDeviceState *state, // in + UnaryFunction blockSizeToDynamicSMemSize); // in + +} // namespace anonymous +#endif // defined(__cplusplus) + +/** + * + * The CUDA dynamic shared memory calculator computes the maximum size of + * per-block dynamic shared memory if we want to place numBlocks blocks + * on an SM. + * + * RETURN VALUE + * + * Returns in *dynamicSmemSize the maximum size of dynamic shared memory to allow + * numBlocks blocks per SM. + * + * ERRORS + * + * CUDA_OCC_ERROR_INVALID_INPUT input parameter is invalid. + * CUDA_OCC_ERROR_UNKNOWN_DEVICE requested device is not supported in + * current implementation or device is invalid + * + */ +static __OCC_INLINE +cudaOccError cudaOccAvailableDynamicSMemPerBlock( + size_t *dynamicSmemSize, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + int numBlocks, + int blockSize); + +/** + * Data structures + * + * These structures are subject to change for future architecture and CUDA + * releases. C users should initialize the structure as {0}. + * + */ + +/** + * Device descriptor + * + * This structure describes a device. + */ +struct cudaOccDeviceProp { + int computeMajor; // Compute capability major version + int computeMinor; // Compute capability minor + // version. None supported minor version + // may cause error + int maxThreadsPerBlock; // Maximum number of threads per block + int maxThreadsPerMultiprocessor; // Maximum number of threads per SM + // i.e. (Max. number of warps) x (warp + // size) + int regsPerBlock; // Maximum number of registers per block + int regsPerMultiprocessor; // Maximum number of registers per SM + int warpSize; // Warp size + size_t sharedMemPerBlock; // Maximum shared memory size per block + size_t sharedMemPerMultiprocessor; // Maximum shared memory size per SM + int numSms; // Number of SMs available + size_t sharedMemPerBlockOptin; // Maximum optin shared memory size per block + size_t reservedSharedMemPerBlock; // Shared memory per block reserved by driver + +#ifdef __cplusplus + // This structure can be converted from a cudaDeviceProp structure for users + // that use this header in their CUDA applications. + // + // If the application have access to the CUDA Runtime API, the application + // can obtain the device properties of a CUDA device through + // cudaGetDeviceProperties, and initialize a cudaOccDeviceProp with the + // cudaDeviceProp structure. + // + // Example: + /* + { + cudaDeviceProp prop; + + cudaGetDeviceProperties(&prop, ...); + + cudaOccDeviceProp occProp = prop; + + ... + + cudaOccMaxPotentialOccupancyBlockSize(..., &occProp, ...); + } + */ + // + template + __OCC_INLINE + cudaOccDeviceProp(const DeviceProp &props) + : computeMajor (props.major), + computeMinor (props.minor), + maxThreadsPerBlock (props.maxThreadsPerBlock), + maxThreadsPerMultiprocessor (props.maxThreadsPerMultiProcessor), + regsPerBlock (props.regsPerBlock), + regsPerMultiprocessor (props.regsPerMultiprocessor), + warpSize (props.warpSize), + sharedMemPerBlock (props.sharedMemPerBlock), + sharedMemPerMultiprocessor (props.sharedMemPerMultiprocessor), + numSms (props.multiProcessorCount), + sharedMemPerBlockOptin (props.sharedMemPerBlockOptin), + reservedSharedMemPerBlock (props.reservedSharedMemPerBlock) + {} + + __OCC_INLINE + cudaOccDeviceProp() + : computeMajor (0), + computeMinor (0), + maxThreadsPerBlock (0), + maxThreadsPerMultiprocessor (0), + regsPerBlock (0), + regsPerMultiprocessor (0), + warpSize (0), + sharedMemPerBlock (0), + sharedMemPerMultiprocessor (0), + numSms (0), + sharedMemPerBlockOptin (0), + reservedSharedMemPerBlock (0) + {} +#endif // __cplusplus +}; + +/** + * Partitioned global caching option + */ +typedef enum cudaOccPartitionedGCConfig_enum { + PARTITIONED_GC_OFF, // Disable partitioned global caching + PARTITIONED_GC_ON, // Prefer partitioned global caching + PARTITIONED_GC_ON_STRICT // Force partitioned global caching +} cudaOccPartitionedGCConfig; + +/** + * Per function opt in maximum dynamic shared memory limit + */ +typedef enum cudaOccFuncShmemConfig_enum { + FUNC_SHMEM_LIMIT_DEFAULT, // Default shmem limit + FUNC_SHMEM_LIMIT_OPTIN, // Use the optin shmem limit +} cudaOccFuncShmemConfig; + +/** + * Function descriptor + * + * This structure describes a CUDA function. + */ +struct cudaOccFuncAttributes { + int maxThreadsPerBlock; // Maximum block size the function can work with. If + // unlimited, use INT_MAX or any value greater than + // or equal to maxThreadsPerBlock of the device + int numRegs; // Number of registers used. When the function is + // launched on device, the register count may change + // due to internal tools requirements. + size_t sharedSizeBytes; // Number of static shared memory used + + cudaOccPartitionedGCConfig partitionedGCConfig; + // Partitioned global caching is required to enable + // caching on certain chips, such as sm_52 + // devices. Partitioned global caching can be + // automatically disabled if the occupancy + // requirement of the launch cannot support caching. + // + // To override this behavior with caching on and + // calculate occupancy strictly according to the + // preference, set partitionedGCConfig to + // PARTITIONED_GC_ON_STRICT. This is especially + // useful for experimenting and finding launch + // configurations (MaxPotentialOccupancyBlockSize) + // that allow global caching to take effect. + // + // This flag only affects the occupancy calculation. + + cudaOccFuncShmemConfig shmemLimitConfig; + // Certain chips like sm_70 allow a user to opt into + // a higher per block limit of dynamic shared memory + // This optin is performed on a per function basis + // using the cuFuncSetAttribute function + + size_t maxDynamicSharedSizeBytes; + // User set limit on maximum dynamic shared memory + // usable by the kernel + // This limit is set using the cuFuncSetAttribute + // function. + + int numBlockBarriers; // Number of block barriers used (default to 1) +#ifdef __cplusplus + // This structure can be converted from a cudaFuncAttributes structure for + // users that use this header in their CUDA applications. + // + // If the application have access to the CUDA Runtime API, the application + // can obtain the function attributes of a CUDA kernel function through + // cudaFuncGetAttributes, and initialize a cudaOccFuncAttributes with the + // cudaFuncAttributes structure. + // + // Example: + /* + __global__ void foo() {...} + + ... + + { + cudaFuncAttributes attr; + + cudaFuncGetAttributes(&attr, foo); + + cudaOccFuncAttributes occAttr = attr; + + ... + + cudaOccMaxPotentialOccupancyBlockSize(..., &occAttr, ...); + } + */ + // + template + __OCC_INLINE + cudaOccFuncAttributes(const FuncAttributes &attr) + : maxThreadsPerBlock (attr.maxThreadsPerBlock), + numRegs (attr.numRegs), + sharedSizeBytes (attr.sharedSizeBytes), + partitionedGCConfig (PARTITIONED_GC_OFF), + shmemLimitConfig (FUNC_SHMEM_LIMIT_OPTIN), + maxDynamicSharedSizeBytes (attr.maxDynamicSharedSizeBytes), + numBlockBarriers (1) + {} + + __OCC_INLINE + cudaOccFuncAttributes() + : maxThreadsPerBlock (0), + numRegs (0), + sharedSizeBytes (0), + partitionedGCConfig (PARTITIONED_GC_OFF), + shmemLimitConfig (FUNC_SHMEM_LIMIT_DEFAULT), + maxDynamicSharedSizeBytes (0), + numBlockBarriers (0) + {} +#endif +}; + +typedef enum cudaOccCacheConfig_enum { + CACHE_PREFER_NONE = 0x00, // no preference for shared memory or L1 (default) + CACHE_PREFER_SHARED = 0x01, // prefer larger shared memory and smaller L1 cache + CACHE_PREFER_L1 = 0x02, // prefer larger L1 cache and smaller shared memory + CACHE_PREFER_EQUAL = 0x03 // prefer equal sized L1 cache and shared memory +} cudaOccCacheConfig; + +typedef enum cudaOccCarveoutConfig_enum { + SHAREDMEM_CARVEOUT_DEFAULT = -1, // no preference for shared memory or L1 (default) + SHAREDMEM_CARVEOUT_MAX_SHARED = 100, // prefer maximum available shared memory, minimum L1 cache + SHAREDMEM_CARVEOUT_MAX_L1 = 0, // prefer maximum available L1 cache, minimum shared memory + SHAREDMEM_CARVEOUT_HALF = 50 // prefer half of maximum available shared memory, with the rest as L1 cache +} cudaOccCarveoutConfig; + +/** + * Device state descriptor + * + * This structure describes device settings that affect occupancy calculation. + */ +struct cudaOccDeviceState +{ + // Cache / shared memory split preference. Deprecated on Volta + cudaOccCacheConfig cacheConfig; + // Shared memory / L1 split preference. Supported on only Volta + int carveoutConfig; + +#ifdef __cplusplus + __OCC_INLINE + cudaOccDeviceState() + : cacheConfig (CACHE_PREFER_NONE), + carveoutConfig (SHAREDMEM_CARVEOUT_DEFAULT) + {} +#endif +}; + +typedef enum cudaOccLimitingFactor_enum { + // Occupancy limited due to: + OCC_LIMIT_WARPS = 0x01, // - warps available + OCC_LIMIT_REGISTERS = 0x02, // - registers available + OCC_LIMIT_SHARED_MEMORY = 0x04, // - shared memory available + OCC_LIMIT_BLOCKS = 0x08, // - blocks available + OCC_LIMIT_BARRIERS = 0x10 // - barrier available +} cudaOccLimitingFactor; + +/** + * Occupancy output + * + * This structure contains occupancy calculator's output. + */ +struct cudaOccResult { + int activeBlocksPerMultiprocessor; // Occupancy + unsigned int limitingFactors; // Factors that limited occupancy. A bit + // field that counts the limiting + // factors, see cudaOccLimitingFactor + int blockLimitRegs; // Occupancy due to register + // usage, INT_MAX if the kernel does not + // use any register. + int blockLimitSharedMem; // Occupancy due to shared memory + // usage, INT_MAX if the kernel does not + // use shared memory. + int blockLimitWarps; // Occupancy due to block size limit + int blockLimitBlocks; // Occupancy due to maximum number of blocks + // managable per SM + int blockLimitBarriers; // Occupancy due to block barrier usage + int allocatedRegistersPerBlock; // Actual number of registers allocated per + // block + size_t allocatedSharedMemPerBlock; // Actual size of shared memory allocated + // per block + cudaOccPartitionedGCConfig partitionedGCConfig; + // Report if partitioned global caching + // is actually enabled. +}; + +/** + * Partitioned global caching support + * + * See cudaOccPartitionedGlobalCachingModeSupport + */ +typedef enum cudaOccPartitionedGCSupport_enum { + PARTITIONED_GC_NOT_SUPPORTED, // Partitioned global caching is not supported + PARTITIONED_GC_SUPPORTED, // Partitioned global caching is supported +} cudaOccPartitionedGCSupport; + +/** + * Implementation + */ + +/** + * Max compute capability supported + */ +#define __CUDA_OCC_MAJOR__ 9 +#define __CUDA_OCC_MINOR__ 0 + +////////////////////////////////////////// +// Mathematical Helper Functions // +////////////////////////////////////////// + +static __OCC_INLINE int __occMin(int lhs, int rhs) +{ + return rhs < lhs ? rhs : lhs; +} + +static __OCC_INLINE int __occDivideRoundUp(int x, int y) +{ + return (x + (y - 1)) / y; +} + +static __OCC_INLINE int __occRoundUp(int x, int y) +{ + return y * __occDivideRoundUp(x, y); +} + +////////////////////////////////////////// +// Architectural Properties // +////////////////////////////////////////// + +/** + * Granularity of shared memory allocation + */ +static __OCC_INLINE cudaOccError cudaOccSMemAllocationGranularity(int *limit, const cudaOccDeviceProp *properties) +{ + int value; + + switch(properties->computeMajor) { + case 3: + case 5: + case 6: + case 7: + value = 256; + break; + case 8: + case 9: + value = 128; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = value; + + return CUDA_OCC_SUCCESS; +} + +/** + * Maximum number of registers per thread + */ +static __OCC_INLINE cudaOccError cudaOccRegAllocationMaxPerThread(int *limit, const cudaOccDeviceProp *properties) +{ + int value; + + switch(properties->computeMajor) { + case 3: + case 5: + case 6: + value = 255; + break; + case 7: + case 8: + case 9: + value = 256; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = value; + + return CUDA_OCC_SUCCESS; +} + +/** + * Granularity of register allocation + */ +static __OCC_INLINE cudaOccError cudaOccRegAllocationGranularity(int *limit, const cudaOccDeviceProp *properties) +{ + int value; + + switch(properties->computeMajor) { + case 3: + case 5: + case 6: + case 7: + case 8: + case 9: + value = 256; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = value; + + return CUDA_OCC_SUCCESS; +} + +/** + * Number of sub-partitions + */ +static __OCC_INLINE cudaOccError cudaOccSubPartitionsPerMultiprocessor(int *limit, const cudaOccDeviceProp *properties) +{ + int value; + + switch(properties->computeMajor) { + case 3: + case 5: + case 7: + case 8: + case 9: + value = 4; + break; + case 6: + value = properties->computeMinor ? 4 : 2; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = value; + + return CUDA_OCC_SUCCESS; +} + + +/** + * Maximum number of blocks that can run simultaneously on a multiprocessor + */ +static __OCC_INLINE cudaOccError cudaOccMaxBlocksPerMultiprocessor(int* limit, const cudaOccDeviceProp *properties) +{ + int value; + + switch(properties->computeMajor) { + case 3: + value = 16; + break; + case 5: + case 6: + value = 32; + break; + case 7: { + int isTuring = properties->computeMinor == 5; + value = (isTuring) ? 16 : 32; + break; + } + case 8: + if (properties->computeMinor == 0) { + value = 32; + } + else if (properties->computeMinor == 9) { + value = 24; + } + else { + value = 16; + } + break; + case 9: + value = 32; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = value; + + return CUDA_OCC_SUCCESS; +} + +/** + * Align up shared memory based on compute major configurations + */ +static __OCC_INLINE cudaOccError cudaOccAlignUpShmemSizeVoltaPlus(size_t *shMemSize, const cudaOccDeviceProp *properties) +{ + // Volta and Turing have shared L1 cache / shared memory, and support cache + // configuration to trade one for the other. These values are needed to + // map carveout config ratio to the next available architecture size + size_t size = *shMemSize; + + switch (properties->computeMajor) { + case 7: { + // Turing supports 32KB and 64KB shared mem. + int isTuring = properties->computeMinor == 5; + if (isTuring) { + if (size <= 32 * 1024) { + *shMemSize = 32 * 1024; + } + else if (size <= 64 * 1024) { + *shMemSize = 64 * 1024; + } + else { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + } + // Volta supports 0KB, 8KB, 16KB, 32KB, 64KB, and 96KB shared mem. + else { + if (size == 0) { + *shMemSize = 0; + } + else if (size <= 8 * 1024) { + *shMemSize = 8 * 1024; + } + else if (size <= 16 * 1024) { + *shMemSize = 16 * 1024; + } + else if (size <= 32 * 1024) { + *shMemSize = 32 * 1024; + } + else if (size <= 64 * 1024) { + *shMemSize = 64 * 1024; + } + else if (size <= 96 * 1024) { + *shMemSize = 96 * 1024; + } + else { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + } + break; + } + case 8: + if (properties->computeMinor == 0 || properties->computeMinor == 7) { + if (size == 0) { + *shMemSize = 0; + } + else if (size <= 8 * 1024) { + *shMemSize = 8 * 1024; + } + else if (size <= 16 * 1024) { + *shMemSize = 16 * 1024; + } + else if (size <= 32 * 1024) { + *shMemSize = 32 * 1024; + } + else if (size <= 64 * 1024) { + *shMemSize = 64 * 1024; + } + else if (size <= 100 * 1024) { + *shMemSize = 100 * 1024; + } + else if (size <= 132 * 1024) { + *shMemSize = 132 * 1024; + } + else if (size <= 164 * 1024) { + *shMemSize = 164 * 1024; + } + else { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + } + else { + if (size == 0) { + *shMemSize = 0; + } + else if (size <= 8 * 1024) { + *shMemSize = 8 * 1024; + } + else if (size <= 16 * 1024) { + *shMemSize = 16 * 1024; + } + else if (size <= 32 * 1024) { + *shMemSize = 32 * 1024; + } + else if (size <= 64 * 1024) { + *shMemSize = 64 * 1024; + } + else if (size <= 100 * 1024) { + *shMemSize = 100 * 1024; + } + else { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + } + break; + case 9: { + if (size == 0) { + *shMemSize = 0; + } + else if (size <= 8 * 1024) { + *shMemSize = 8 * 1024; + } + else if (size <= 16 * 1024) { + *shMemSize = 16 * 1024; + } + else if (size <= 32 * 1024) { + *shMemSize = 32 * 1024; + } + else if (size <= 64 * 1024) { + *shMemSize = 64 * 1024; + } + else if (size <= 100 * 1024) { + *shMemSize = 100 * 1024; + } + else if (size <= 132 * 1024) { + *shMemSize = 132 * 1024; + } + else if (size <= 164 * 1024) { + *shMemSize = 164 * 1024; + } + else if (size <= 196 * 1024) { + *shMemSize = 196 * 1024; + } + else if (size <= 228 * 1024) { + *shMemSize = 228 * 1024; + } + else { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + break; + } + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + return CUDA_OCC_SUCCESS; +} + +/** + * Shared memory based on the new carveoutConfig API introduced with Volta + */ +static __OCC_INLINE cudaOccError cudaOccSMemPreferenceVoltaPlus(size_t *limit, const cudaOccDeviceProp *properties, const cudaOccDeviceState *state) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + size_t preferenceShmemSize; + + // CUDA 9.0 introduces a new API to set shared memory - L1 configuration on supported + // devices. This preference will take precedence over the older cacheConfig setting. + // Map cacheConfig to its effective preference value. + int effectivePreference = state->carveoutConfig; + if ((effectivePreference < SHAREDMEM_CARVEOUT_DEFAULT) || (effectivePreference > SHAREDMEM_CARVEOUT_MAX_SHARED)) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + if (effectivePreference == SHAREDMEM_CARVEOUT_DEFAULT) { + switch (state->cacheConfig) + { + case CACHE_PREFER_L1: + effectivePreference = SHAREDMEM_CARVEOUT_MAX_L1; + break; + case CACHE_PREFER_SHARED: + effectivePreference = SHAREDMEM_CARVEOUT_MAX_SHARED; + break; + case CACHE_PREFER_EQUAL: + effectivePreference = SHAREDMEM_CARVEOUT_HALF; + break; + default: + effectivePreference = SHAREDMEM_CARVEOUT_DEFAULT; + break; + } + } + + if (effectivePreference == SHAREDMEM_CARVEOUT_DEFAULT) { + preferenceShmemSize = properties->sharedMemPerMultiprocessor; + } + else { + preferenceShmemSize = (size_t) (effectivePreference * properties->sharedMemPerMultiprocessor) / 100; + } + + status = cudaOccAlignUpShmemSizeVoltaPlus(&preferenceShmemSize, properties); + *limit = preferenceShmemSize; + return status; +} + +/** + * Shared memory based on the cacheConfig + */ +static __OCC_INLINE cudaOccError cudaOccSMemPreference(size_t *limit, const cudaOccDeviceProp *properties, const cudaOccDeviceState *state) +{ + size_t bytes = 0; + size_t sharedMemPerMultiprocessorHigh = properties->sharedMemPerMultiprocessor; + cudaOccCacheConfig cacheConfig = state->cacheConfig; + + // Kepler has shared L1 cache / shared memory, and support cache + // configuration to trade one for the other. These values are needed to + // calculate the correct shared memory size for user requested cache + // configuration. + // + size_t minCacheSize = 16384; + size_t maxCacheSize = 49152; + size_t cacheAndSharedTotal = sharedMemPerMultiprocessorHigh + minCacheSize; + size_t sharedMemPerMultiprocessorLow = cacheAndSharedTotal - maxCacheSize; + + switch (properties->computeMajor) { + case 3: + // Kepler supports 16KB, 32KB, or 48KB partitions for L1. The rest + // is shared memory. + // + switch (cacheConfig) { + default : + case CACHE_PREFER_NONE: + case CACHE_PREFER_SHARED: + bytes = sharedMemPerMultiprocessorHigh; + break; + case CACHE_PREFER_L1: + bytes = sharedMemPerMultiprocessorLow; + break; + case CACHE_PREFER_EQUAL: + // Equal is the mid-point between high and low. It should be + // equivalent to low + 16KB. + // + bytes = (sharedMemPerMultiprocessorHigh + sharedMemPerMultiprocessorLow) / 2; + break; + } + break; + case 5: + case 6: + // Maxwell and Pascal have dedicated shared memory. + // + bytes = sharedMemPerMultiprocessorHigh; + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + *limit = bytes; + + return CUDA_OCC_SUCCESS; +} + +/** + * Shared memory based on config requested by User + */ +static __OCC_INLINE cudaOccError cudaOccSMemPerMultiprocessor(size_t *limit, const cudaOccDeviceProp *properties, const cudaOccDeviceState *state) +{ + // Volta introduces a new API that allows for shared memory carveout preference. Because it is a shared memory preference, + // it is handled separately from the cache config preference. + if (properties->computeMajor >= 7) { + return cudaOccSMemPreferenceVoltaPlus(limit, properties, state); + } + return cudaOccSMemPreference(limit, properties, state); +} + +/** + * Return the per block shared memory limit based on function config + */ +static __OCC_INLINE cudaOccError cudaOccSMemPerBlock(size_t *limit, const cudaOccDeviceProp *properties, cudaOccFuncShmemConfig shmemLimitConfig, size_t smemPerCta) +{ + switch (properties->computeMajor) { + case 2: + case 3: + case 4: + case 5: + case 6: + *limit = properties->sharedMemPerBlock; + break; + case 7: + case 8: + case 9: + switch (shmemLimitConfig) { + default: + case FUNC_SHMEM_LIMIT_DEFAULT: + *limit = properties->sharedMemPerBlock; + break; + case FUNC_SHMEM_LIMIT_OPTIN: + if (smemPerCta > properties->sharedMemPerBlock) { + *limit = properties->sharedMemPerBlockOptin; + } + else { + *limit = properties->sharedMemPerBlock; + } + break; + } + break; + default: + return CUDA_OCC_ERROR_UNKNOWN_DEVICE; + } + + // Starting Ampere, CUDA driver reserves additional shared memory per block + if (properties->computeMajor >= 8) { + *limit += properties->reservedSharedMemPerBlock; + } + + return CUDA_OCC_SUCCESS; +} + +/** + * Partitioned global caching mode support + */ +static __OCC_INLINE cudaOccError cudaOccPartitionedGlobalCachingModeSupport(cudaOccPartitionedGCSupport *limit, const cudaOccDeviceProp *properties) +{ + *limit = PARTITIONED_GC_NOT_SUPPORTED; + + if ((properties->computeMajor == 5 && (properties->computeMinor == 2 || properties->computeMinor == 3)) || + properties->computeMajor == 6) { + *limit = PARTITIONED_GC_SUPPORTED; + } + + if (properties->computeMajor == 6 && properties->computeMinor == 0) { + *limit = PARTITIONED_GC_NOT_SUPPORTED; + } + + return CUDA_OCC_SUCCESS; +} + +/////////////////////////////////////////////// +// User Input Sanity // +/////////////////////////////////////////////// + +static __OCC_INLINE cudaOccError cudaOccDevicePropCheck(const cudaOccDeviceProp *properties) +{ + // Verify device properties + // + // Each of these limits must be a positive number. + // + // Compute capacity is checked during the occupancy calculation + // + if (properties->maxThreadsPerBlock <= 0 || + properties->maxThreadsPerMultiprocessor <= 0 || + properties->regsPerBlock <= 0 || + properties->regsPerMultiprocessor <= 0 || + properties->warpSize <= 0 || + properties->sharedMemPerBlock <= 0 || + properties->sharedMemPerMultiprocessor <= 0 || + properties->numSms <= 0) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + return CUDA_OCC_SUCCESS; +} + +static __OCC_INLINE cudaOccError cudaOccFuncAttributesCheck(const cudaOccFuncAttributes *attributes) +{ + // Verify function attributes + // + if (attributes->maxThreadsPerBlock <= 0 || + attributes->numRegs < 0) { // Compiler may choose not to use + // any register (empty kernels, + // etc.) + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + return CUDA_OCC_SUCCESS; +} + +static __OCC_INLINE cudaOccError cudaOccDeviceStateCheck(const cudaOccDeviceState *state) +{ + (void)state; // silence unused-variable warning + // Placeholder + // + + return CUDA_OCC_SUCCESS; +} + +static __OCC_INLINE cudaOccError cudaOccInputCheck( + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + + status = cudaOccDevicePropCheck(properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + status = cudaOccFuncAttributesCheck(attributes); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + status = cudaOccDeviceStateCheck(state); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + return status; +} + +/////////////////////////////////////////////// +// Occupancy calculation Functions // +/////////////////////////////////////////////// + +static __OCC_INLINE cudaOccPartitionedGCConfig cudaOccPartitionedGCExpected( + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes) +{ + cudaOccPartitionedGCSupport gcSupport; + cudaOccPartitionedGCConfig gcConfig; + + cudaOccPartitionedGlobalCachingModeSupport(&gcSupport, properties); + + gcConfig = attributes->partitionedGCConfig; + + if (gcSupport == PARTITIONED_GC_NOT_SUPPORTED) { + gcConfig = PARTITIONED_GC_OFF; + } + + return gcConfig; +} + +// Warp limit +// +static __OCC_INLINE cudaOccError cudaOccMaxBlocksPerSMWarpsLimit( + int *limit, + cudaOccPartitionedGCConfig gcConfig, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + int blockSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + int maxWarpsPerSm; + int warpsAllocatedPerCTA; + int maxBlocks; + (void)attributes; // silence unused-variable warning + + if (blockSize > properties->maxThreadsPerBlock) { + maxBlocks = 0; + } + else { + maxWarpsPerSm = properties->maxThreadsPerMultiprocessor / properties->warpSize; + warpsAllocatedPerCTA = __occDivideRoundUp(blockSize, properties->warpSize); + maxBlocks = 0; + + if (gcConfig != PARTITIONED_GC_OFF) { + int maxBlocksPerSmPartition; + int maxWarpsPerSmPartition; + + // If partitioned global caching is on, then a CTA can only use a SM + // partition (a half SM), and thus a half of the warp slots + // available per SM + // + maxWarpsPerSmPartition = maxWarpsPerSm / 2; + maxBlocksPerSmPartition = maxWarpsPerSmPartition / warpsAllocatedPerCTA; + maxBlocks = maxBlocksPerSmPartition * 2; + } + // On hardware that supports partitioned global caching, each half SM is + // guaranteed to support at least 32 warps (maximum number of warps of a + // CTA), so caching will not cause 0 occupancy due to insufficient warp + // allocation slots. + // + else { + maxBlocks = maxWarpsPerSm / warpsAllocatedPerCTA; + } + } + + *limit = maxBlocks; + + return status; +} + +// Shared memory limit +// +static __OCC_INLINE cudaOccError cudaOccMaxBlocksPerSMSmemLimit( + int *limit, + cudaOccResult *result, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + int blockSize, + size_t dynamicSmemSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + int allocationGranularity; + size_t userSmemPreference = 0; + size_t totalSmemUsagePerCTA; + size_t maxSmemUsagePerCTA; + size_t smemAllocatedPerCTA; + size_t staticSmemSize; + size_t sharedMemPerMultiprocessor; + size_t smemLimitPerCTA; + int maxBlocks; + int dynamicSmemSizeExceeded = 0; + int totalSmemSizeExceeded = 0; + (void)blockSize; // silence unused-variable warning + + status = cudaOccSMemAllocationGranularity(&allocationGranularity, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // Obtain the user preferred shared memory size. This setting is ignored if + // user requests more shared memory than preferred. + // + status = cudaOccSMemPerMultiprocessor(&userSmemPreference, properties, state); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + staticSmemSize = attributes->sharedSizeBytes + properties->reservedSharedMemPerBlock; + totalSmemUsagePerCTA = staticSmemSize + dynamicSmemSize; + smemAllocatedPerCTA = __occRoundUp((int)totalSmemUsagePerCTA, (int)allocationGranularity); + + maxSmemUsagePerCTA = staticSmemSize + attributes->maxDynamicSharedSizeBytes; + + dynamicSmemSizeExceeded = 0; + totalSmemSizeExceeded = 0; + + // Obtain the user set maximum dynamic size if it exists + // If so, the current launch dynamic shared memory must not + // exceed the set limit + if (attributes->shmemLimitConfig != FUNC_SHMEM_LIMIT_DEFAULT && + dynamicSmemSize > attributes->maxDynamicSharedSizeBytes) { + dynamicSmemSizeExceeded = 1; + } + + status = cudaOccSMemPerBlock(&smemLimitPerCTA, properties, attributes->shmemLimitConfig, maxSmemUsagePerCTA); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + if (smemAllocatedPerCTA > smemLimitPerCTA) { + totalSmemSizeExceeded = 1; + } + + if (dynamicSmemSizeExceeded || totalSmemSizeExceeded) { + maxBlocks = 0; + } + else { + // User requested shared memory limit is used as long as it is greater + // than the total shared memory used per CTA, i.e. as long as at least + // one CTA can be launched. + if (userSmemPreference >= smemAllocatedPerCTA) { + sharedMemPerMultiprocessor = userSmemPreference; + } + else { + // On Volta+, user requested shared memory will limit occupancy + // if it's less than shared memory per CTA. Otherwise, the + // maximum shared memory limit is used. + if (properties->computeMajor >= 7) { + sharedMemPerMultiprocessor = smemAllocatedPerCTA; + status = cudaOccAlignUpShmemSizeVoltaPlus(&sharedMemPerMultiprocessor, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + } + else { + sharedMemPerMultiprocessor = properties->sharedMemPerMultiprocessor; + } + } + + if (smemAllocatedPerCTA > 0) { + maxBlocks = (int)(sharedMemPerMultiprocessor / smemAllocatedPerCTA); + } + else { + maxBlocks = INT_MAX; + } + } + + result->allocatedSharedMemPerBlock = smemAllocatedPerCTA; + + *limit = maxBlocks; + + return status; +} + +static __OCC_INLINE +cudaOccError cudaOccMaxBlocksPerSMRegsLimit( + int *limit, + cudaOccPartitionedGCConfig *gcConfig, + cudaOccResult *result, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + int blockSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + int allocationGranularity; + int warpsAllocatedPerCTA; + int regsAllocatedPerCTA; + int regsAssumedPerCTA; + int regsPerWarp; + int regsAllocatedPerWarp; + int numSubPartitions; + int numRegsPerSubPartition; + int numWarpsPerSubPartition; + int numWarpsPerSM; + int maxBlocks; + int maxRegsPerThread; + + status = cudaOccRegAllocationGranularity( + &allocationGranularity, + properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + status = cudaOccRegAllocationMaxPerThread( + &maxRegsPerThread, + properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + status = cudaOccSubPartitionsPerMultiprocessor(&numSubPartitions, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + warpsAllocatedPerCTA = __occDivideRoundUp(blockSize, properties->warpSize); + + // GPUs of compute capability 2.x and higher allocate registers to warps + // + // Number of regs per warp is regs per thread x warp size, rounded up to + // register allocation granularity + // + regsPerWarp = attributes->numRegs * properties->warpSize; + regsAllocatedPerWarp = __occRoundUp(regsPerWarp, allocationGranularity); + regsAllocatedPerCTA = regsAllocatedPerWarp * warpsAllocatedPerCTA; + + // Hardware verifies if a launch fits the per-CTA register limit. For + // historical reasons, the verification logic assumes register + // allocations are made to all partitions simultaneously. Therefore, to + // simulate the hardware check, the warp allocation needs to be rounded + // up to the number of partitions. + // + regsAssumedPerCTA = regsAllocatedPerWarp * __occRoundUp(warpsAllocatedPerCTA, numSubPartitions); + + if (properties->regsPerBlock < regsAssumedPerCTA || // Hardware check + properties->regsPerBlock < regsAllocatedPerCTA || // Software check + attributes->numRegs > maxRegsPerThread) { // Per thread limit check + maxBlocks = 0; + } + else { + if (regsAllocatedPerWarp > 0) { + // Registers are allocated in each sub-partition. The max number + // of warps that can fit on an SM is equal to the max number of + // warps per sub-partition x number of sub-partitions. + // + numRegsPerSubPartition = properties->regsPerMultiprocessor / numSubPartitions; + numWarpsPerSubPartition = numRegsPerSubPartition / regsAllocatedPerWarp; + + maxBlocks = 0; + + if (*gcConfig != PARTITIONED_GC_OFF) { + int numSubPartitionsPerSmPartition; + int numWarpsPerSmPartition; + int maxBlocksPerSmPartition; + + // If partitioned global caching is on, then a CTA can only + // use a half SM, and thus a half of the registers available + // per SM + // + numSubPartitionsPerSmPartition = numSubPartitions / 2; + numWarpsPerSmPartition = numWarpsPerSubPartition * numSubPartitionsPerSmPartition; + maxBlocksPerSmPartition = numWarpsPerSmPartition / warpsAllocatedPerCTA; + maxBlocks = maxBlocksPerSmPartition * 2; + } + + // Try again if partitioned global caching is not enabled, or if + // the CTA cannot fit on the SM with caching on (maxBlocks == 0). In the latter + // case, the device will automatically turn off caching, except + // if the user forces enablement via PARTITIONED_GC_ON_STRICT to calculate + // occupancy and launch configuration. + // + if (maxBlocks == 0 && *gcConfig != PARTITIONED_GC_ON_STRICT) { + // In case *gcConfig was PARTITIONED_GC_ON flip it OFF since + // this is what it will be if we spread CTA across partitions. + // + *gcConfig = PARTITIONED_GC_OFF; + numWarpsPerSM = numWarpsPerSubPartition * numSubPartitions; + maxBlocks = numWarpsPerSM / warpsAllocatedPerCTA; + } + } + else { + maxBlocks = INT_MAX; + } + } + + + result->allocatedRegistersPerBlock = regsAllocatedPerCTA; + + *limit = maxBlocks; + + return status; +} + +// Barrier limit +// +static __OCC_INLINE cudaOccError cudaOccMaxBlocksPerSMBlockBarrierLimit( + int *limit, + int ctaLimitBlocks, + const cudaOccFuncAttributes *attributes) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + int numBarriersAvailable = ctaLimitBlocks * 2; + int numBarriersUsed = attributes->numBlockBarriers; + int maxBlocks = INT_MAX; + + if (numBarriersUsed) { + maxBlocks = numBarriersAvailable / numBarriersUsed; + } + + *limit = maxBlocks; + + return status; +} + +/////////////////////////////////// +// API Implementations // +/////////////////////////////////// + +static __OCC_INLINE +cudaOccError cudaOccMaxActiveBlocksPerMultiprocessor( + cudaOccResult *result, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + int blockSize, + size_t dynamicSmemSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + int ctaLimitWarps = 0; + int ctaLimitBlocks = 0; + int ctaLimitSMem = 0; + int ctaLimitRegs = 0; + int ctaLimitBars = 0; + int ctaLimit = 0; + unsigned int limitingFactors = 0; + + cudaOccPartitionedGCConfig gcConfig = PARTITIONED_GC_OFF; + + if (!result || !properties || !attributes || !state || blockSize <= 0) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + /////////////////////////// + // Check user input + /////////////////////////// + + status = cudaOccInputCheck(properties, attributes, state); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + /////////////////////////// + // Initialization + /////////////////////////// + + gcConfig = cudaOccPartitionedGCExpected(properties, attributes); + + /////////////////////////// + // Compute occupancy + /////////////////////////// + + // Limits due to registers/SM + // Also compute if partitioned global caching has to be turned off + // + status = cudaOccMaxBlocksPerSMRegsLimit(&ctaLimitRegs, &gcConfig, result, properties, attributes, blockSize); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // SMs on GP100 (6.0) have 2 subpartitions, while those on GP10x have 4. + // As a result, an SM on GP100 may be able to run more CTAs than the one on GP10x. + // For forward compatibility within Pascal family, if a function cannot run on GP10x (maxBlock == 0), + // we do not let it run on any Pascal processor, even though it may be able to run on GP100. + // Therefore, we check the occupancy on GP10x when it can run on GP100 + // + if (properties->computeMajor == 6 && properties->computeMinor == 0 && ctaLimitRegs) { + cudaOccDeviceProp propertiesGP10x; + cudaOccPartitionedGCConfig gcConfigGP10x = gcConfig; + int ctaLimitRegsGP10x = 0; + + // Set up properties for GP10x + memcpy(&propertiesGP10x, properties, sizeof(propertiesGP10x)); + propertiesGP10x.computeMinor = 1; + + status = cudaOccMaxBlocksPerSMRegsLimit(&ctaLimitRegsGP10x, &gcConfigGP10x, result, &propertiesGP10x, attributes, blockSize); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + if (ctaLimitRegsGP10x == 0) { + ctaLimitRegs = 0; + } + } + + // Limits due to warps/SM + // + status = cudaOccMaxBlocksPerSMWarpsLimit(&ctaLimitWarps, gcConfig, properties, attributes, blockSize); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // Limits due to blocks/SM + // + status = cudaOccMaxBlocksPerMultiprocessor(&ctaLimitBlocks, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // Limits due to shared memory/SM + // + status = cudaOccMaxBlocksPerSMSmemLimit(&ctaLimitSMem, result, properties, attributes, state, blockSize, dynamicSmemSize); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + /////////////////////////// + // Overall occupancy + /////////////////////////// + + // Overall limit is min() of limits due to above reasons + // + ctaLimit = __occMin(ctaLimitRegs, __occMin(ctaLimitSMem, __occMin(ctaLimitWarps, ctaLimitBlocks))); + + // Determine occupancy limiting factors + // + if (ctaLimit == ctaLimitWarps) { + limitingFactors |= OCC_LIMIT_WARPS; + } + if (ctaLimit == ctaLimitRegs) { + limitingFactors |= OCC_LIMIT_REGISTERS; + } + if (ctaLimit == ctaLimitSMem) { + limitingFactors |= OCC_LIMIT_SHARED_MEMORY; + } + if (ctaLimit == ctaLimitBlocks) { + limitingFactors |= OCC_LIMIT_BLOCKS; + } + + // For Hopper onwards compute the limits to occupancy based on block barrier count + // + if (properties->computeMajor >= 9 && attributes->numBlockBarriers > 0) { + // Limits due to barrier/SM + // + status = cudaOccMaxBlocksPerSMBlockBarrierLimit(&ctaLimitBars, ctaLimitBlocks, attributes); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // Recompute overall limit based on barrier/SM + // + ctaLimit = __occMin(ctaLimitBars, ctaLimit); + + // Determine if this is occupancy limiting factor + // + if (ctaLimit == ctaLimitBars) { + limitingFactors |= OCC_LIMIT_BARRIERS; + } + } + else { + ctaLimitBars = INT_MAX; + } + + // Fill in the return values + // + result->limitingFactors = limitingFactors; + + result->blockLimitRegs = ctaLimitRegs; + result->blockLimitSharedMem = ctaLimitSMem; + result->blockLimitWarps = ctaLimitWarps; + result->blockLimitBlocks = ctaLimitBlocks; + result->blockLimitBarriers = ctaLimitBars; + result->partitionedGCConfig = gcConfig; + + // Final occupancy + result->activeBlocksPerMultiprocessor = ctaLimit; + + return CUDA_OCC_SUCCESS; +} + +static __OCC_INLINE +cudaOccError cudaOccAvailableDynamicSMemPerBlock( + size_t *bytesAvailable, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + int numBlocks, + int blockSize) +{ + int allocationGranularity; + size_t smemLimitPerBlock; + size_t smemAvailableForDynamic; + size_t userSmemPreference = 0; + size_t sharedMemPerMultiprocessor; + cudaOccResult result; + cudaOccError status = CUDA_OCC_SUCCESS; + + if (numBlocks <= 0) + return CUDA_OCC_ERROR_INVALID_INPUT; + + // First compute occupancy of potential kernel launch. + // + status = cudaOccMaxActiveBlocksPerMultiprocessor(&result, properties, attributes, state, blockSize, 0); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + // Check if occupancy is achievable given user requested number of blocks. + // + if (result.activeBlocksPerMultiprocessor < numBlocks) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + status = cudaOccSMemAllocationGranularity(&allocationGranularity, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // Return the per block shared memory limit based on function config. + // + status = cudaOccSMemPerBlock(&smemLimitPerBlock, properties, attributes->shmemLimitConfig, properties->sharedMemPerMultiprocessor); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + // If there is only a single block needed per SM, then the user preference can be ignored and the fully SW + // limit is allowed to be used as shared memory otherwise if more than one block is needed, then the user + // preference sets the total limit of available shared memory. + // + cudaOccSMemPerMultiprocessor(&userSmemPreference, properties, state); + if (numBlocks == 1) { + sharedMemPerMultiprocessor = smemLimitPerBlock; + } + else { + if (!userSmemPreference) { + userSmemPreference = 1 ; + status = cudaOccAlignUpShmemSizeVoltaPlus(&userSmemPreference, properties); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + } + sharedMemPerMultiprocessor = userSmemPreference; + } + + // Compute total shared memory available per SM + // + smemAvailableForDynamic = sharedMemPerMultiprocessor / numBlocks; + smemAvailableForDynamic = (smemAvailableForDynamic / allocationGranularity) * allocationGranularity; + + // Cap shared memory + // + if (smemAvailableForDynamic > smemLimitPerBlock) { + smemAvailableForDynamic = smemLimitPerBlock; + } + + // Now compute dynamic shared memory size + smemAvailableForDynamic = smemAvailableForDynamic - attributes->sharedSizeBytes; + + // Cap computed dynamic SM by user requested limit specified via cuFuncSetAttribute() + // + if (smemAvailableForDynamic > attributes->maxDynamicSharedSizeBytes) + smemAvailableForDynamic = attributes->maxDynamicSharedSizeBytes; + + *bytesAvailable = smemAvailableForDynamic; + return CUDA_OCC_SUCCESS; +} + +static __OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSize( + int *minGridSize, + int *blockSize, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + size_t (*blockSizeToDynamicSMemSize)(int), + size_t dynamicSMemSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + cudaOccResult result; + + // Limits + int occupancyLimit; + int granularity; + int blockSizeLimit; + + // Recorded maximum + int maxBlockSize = 0; + int numBlocks = 0; + int maxOccupancy = 0; + + // Temporary + int blockSizeToTryAligned; + int blockSizeToTry; + int blockSizeLimitAligned; + int occupancyInBlocks; + int occupancyInThreads; + + /////////////////////////// + // Check user input + /////////////////////////// + + if (!minGridSize || !blockSize || !properties || !attributes || !state) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + status = cudaOccInputCheck(properties, attributes, state); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + ///////////////////////////////////////////////////////////////////////////////// + // Try each block size, and pick the block size with maximum occupancy + ///////////////////////////////////////////////////////////////////////////////// + + occupancyLimit = properties->maxThreadsPerMultiprocessor; + granularity = properties->warpSize; + + blockSizeLimit = __occMin(properties->maxThreadsPerBlock, attributes->maxThreadsPerBlock); + blockSizeLimitAligned = __occRoundUp(blockSizeLimit, granularity); + + for (blockSizeToTryAligned = blockSizeLimitAligned; blockSizeToTryAligned > 0; blockSizeToTryAligned -= granularity) { + blockSizeToTry = __occMin(blockSizeLimit, blockSizeToTryAligned); + + // Ignore dynamicSMemSize if the user provides a mapping + // + if (blockSizeToDynamicSMemSize) { + dynamicSMemSize = (*blockSizeToDynamicSMemSize)(blockSizeToTry); + } + + status = cudaOccMaxActiveBlocksPerMultiprocessor( + &result, + properties, + attributes, + state, + blockSizeToTry, + dynamicSMemSize); + + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + occupancyInBlocks = result.activeBlocksPerMultiprocessor; + occupancyInThreads = blockSizeToTry * occupancyInBlocks; + + if (occupancyInThreads > maxOccupancy) { + maxBlockSize = blockSizeToTry; + numBlocks = occupancyInBlocks; + maxOccupancy = occupancyInThreads; + } + + // Early out if we have reached the maximum + // + if (occupancyLimit == maxOccupancy) { + break; + } + } + + /////////////////////////// + // Return best available + /////////////////////////// + + // Suggested min grid size to achieve a full machine launch + // + *minGridSize = numBlocks * properties->numSms; + *blockSize = maxBlockSize; + + return status; +} + + +#if defined(__cplusplus) + +namespace { + +__OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSize( + int *minGridSize, + int *blockSize, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + size_t dynamicSMemSize) +{ + return cudaOccMaxPotentialOccupancyBlockSize( + minGridSize, + blockSize, + properties, + attributes, + state, + NULL, + dynamicSMemSize); +} + +template +__OCC_INLINE +cudaOccError cudaOccMaxPotentialOccupancyBlockSizeVariableSMem( + int *minGridSize, + int *blockSize, + const cudaOccDeviceProp *properties, + const cudaOccFuncAttributes *attributes, + const cudaOccDeviceState *state, + UnaryFunction blockSizeToDynamicSMemSize) +{ + cudaOccError status = CUDA_OCC_SUCCESS; + cudaOccResult result; + + // Limits + int occupancyLimit; + int granularity; + int blockSizeLimit; + + // Recorded maximum + int maxBlockSize = 0; + int numBlocks = 0; + int maxOccupancy = 0; + + // Temporary + int blockSizeToTryAligned; + int blockSizeToTry; + int blockSizeLimitAligned; + int occupancyInBlocks; + int occupancyInThreads; + size_t dynamicSMemSize; + + /////////////////////////// + // Check user input + /////////////////////////// + + if (!minGridSize || !blockSize || !properties || !attributes || !state) { + return CUDA_OCC_ERROR_INVALID_INPUT; + } + + status = cudaOccInputCheck(properties, attributes, state); + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + ///////////////////////////////////////////////////////////////////////////////// + // Try each block size, and pick the block size with maximum occupancy + ///////////////////////////////////////////////////////////////////////////////// + + occupancyLimit = properties->maxThreadsPerMultiprocessor; + granularity = properties->warpSize; + blockSizeLimit = __occMin(properties->maxThreadsPerBlock, attributes->maxThreadsPerBlock); + blockSizeLimitAligned = __occRoundUp(blockSizeLimit, granularity); + + for (blockSizeToTryAligned = blockSizeLimitAligned; blockSizeToTryAligned > 0; blockSizeToTryAligned -= granularity) { + blockSizeToTry = __occMin(blockSizeLimit, blockSizeToTryAligned); + + dynamicSMemSize = blockSizeToDynamicSMemSize(blockSizeToTry); + + status = cudaOccMaxActiveBlocksPerMultiprocessor( + &result, + properties, + attributes, + state, + blockSizeToTry, + dynamicSMemSize); + + if (status != CUDA_OCC_SUCCESS) { + return status; + } + + occupancyInBlocks = result.activeBlocksPerMultiprocessor; + + occupancyInThreads = blockSizeToTry * occupancyInBlocks; + + if (occupancyInThreads > maxOccupancy) { + maxBlockSize = blockSizeToTry; + numBlocks = occupancyInBlocks; + maxOccupancy = occupancyInThreads; + } + + // Early out if we have reached the maximum + // + if (occupancyLimit == maxOccupancy) { + break; + } + } + + /////////////////////////// + // Return best available + /////////////////////////// + + // Suggested min grid size to achieve a full machine launch + // + *minGridSize = numBlocks * properties->numSms; + *blockSize = maxBlockSize; + + return status; +} + +} // namespace anonymous + +#endif /*__cplusplus */ + +#undef __OCC_INLINE + +#endif /*__cuda_occupancy_h__*/ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline.h new file mode 100644 index 0000000000000000000000000000000000000000..46bc89e4499576f1ae58848cd8684ba3e32420cf --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline.h @@ -0,0 +1,224 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_PIPELINE_H_ +# define _CUDA_PIPELINE_H_ + +# include "cuda_pipeline_primitives.h" + +# if !defined(_CUDA_PIPELINE_CPLUSPLUS_11_OR_LATER) +# error This file requires compiler support for the ISO C++ 2011 standard. This support must be enabled with the \ + -std=c++11 compiler option. +# endif + +# if defined(_CUDA_PIPELINE_ARCH_700_OR_LATER) +# include "cuda_awbarrier.h" +# endif + +// Integration with libcu++'s cuda::barrier. + +# if defined(_CUDA_PIPELINE_ARCH_700_OR_LATER) +# if defined(_LIBCUDACXX_CUDA_ABI_VERSION) +# define _LIBCUDACXX_PIPELINE_ASSUMED_ABI_VERSION _LIBCUDACXX_CUDA_ABI_VERSION +# else +# define _LIBCUDACXX_PIPELINE_ASSUMED_ABI_VERSION 4 +# endif + +# define _LIBCUDACXX_PIPELINE_CONCAT(X, Y) X ## Y +# define _LIBCUDACXX_PIPELINE_CONCAT2(X, Y) _LIBCUDACXX_PIPELINE_CONCAT(X, Y) +# define _LIBCUDACXX_PIPELINE_INLINE_NAMESPACE _LIBCUDACXX_PIPELINE_CONCAT2(__, _LIBCUDACXX_PIPELINE_ASSUMED_ABI_VERSION) + +namespace cuda { inline namespace _LIBCUDACXX_PIPELINE_INLINE_NAMESPACE { + struct __block_scope_barrier_base; +}} + +# endif + +_CUDA_PIPELINE_BEGIN_NAMESPACE + +template +_CUDA_PIPELINE_QUALIFIER +auto segment(T* ptr) -> T(*)[N]; + +class pipeline { +public: + pipeline(const pipeline&) = delete; + pipeline(pipeline&&) = delete; + pipeline& operator=(const pipeline&) = delete; + pipeline& operator=(pipeline&&) = delete; + + _CUDA_PIPELINE_QUALIFIER pipeline(); + _CUDA_PIPELINE_QUALIFIER size_t commit(); + _CUDA_PIPELINE_QUALIFIER void commit_and_wait(); + _CUDA_PIPELINE_QUALIFIER void wait(size_t batch); + template + _CUDA_PIPELINE_QUALIFIER void wait_prior(); + +# if defined(_CUDA_PIPELINE_ARCH_700_OR_LATER) + _CUDA_PIPELINE_QUALIFIER void arrive_on(awbarrier& barrier); + _CUDA_PIPELINE_QUALIFIER void arrive_on(cuda::__block_scope_barrier_base& barrier); +# endif + +private: + size_t current_batch; +}; + +template +_CUDA_PIPELINE_QUALIFIER +void memcpy_async(T& dst, const T& src, pipeline& pipe); + +template +_CUDA_PIPELINE_QUALIFIER +void memcpy_async(T(*dst)[DstN], const T(*src)[SrcN], pipeline& pipe); + +template +_CUDA_PIPELINE_QUALIFIER +auto segment(T* ptr) -> T(*)[N] +{ + return (T(*)[N])ptr; +} + +_CUDA_PIPELINE_QUALIFIER +pipeline::pipeline() + : current_batch(0) +{ +} + +_CUDA_PIPELINE_QUALIFIER +size_t pipeline::commit() +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_commit(); + return this->current_batch++; +} + +_CUDA_PIPELINE_QUALIFIER +void pipeline::commit_and_wait() +{ + (void)pipeline::commit(); + pipeline::wait_prior<0>(); +} + +_CUDA_PIPELINE_QUALIFIER +void pipeline::wait(size_t batch) +{ + const size_t prior = this->current_batch > batch ? this->current_batch - batch : 0; + + switch (prior) { + case 0 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<0>(); break; + case 1 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<1>(); break; + case 2 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<2>(); break; + case 3 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<3>(); break; + case 4 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<4>(); break; + case 5 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<5>(); break; + case 6 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<6>(); break; + case 7 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<7>(); break; + default : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<8>(); break; + } +} + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline::wait_prior() +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior(); +} + +# if defined(_CUDA_PIPELINE_ARCH_700_OR_LATER) +_CUDA_PIPELINE_QUALIFIER +void pipeline::arrive_on(awbarrier& barrier) +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_arrive_on(&barrier.barrier); +} + +_CUDA_PIPELINE_QUALIFIER +void pipeline::arrive_on(cuda::__block_scope_barrier_base & barrier) +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_arrive_on(reinterpret_cast(&barrier)); +} +# endif + +template +_CUDA_PIPELINE_QUALIFIER +void memcpy_async(T& dst, const T& src, pipeline& pipe) +{ + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(&src) & (alignof(T) - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(&dst) & (alignof(T) - 1))); + + if (__is_trivially_copyable(T)) { + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_copy_relaxed( + reinterpret_cast(&dst), reinterpret_cast(&src)); + } else { + dst = src; + } +} + +template +_CUDA_PIPELINE_QUALIFIER +void memcpy_async(T(*dst)[DstN], const T(*src)[SrcN], pipeline& pipe) +{ + constexpr size_t dst_size = sizeof(*dst); + constexpr size_t src_size = sizeof(*src); + static_assert(dst_size == 4 || dst_size == 8 || dst_size == 16, "Unsupported copy size."); + static_assert(src_size <= dst_size, "Source size must be less than or equal to destination size."); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (dst_size - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (dst_size - 1))); + + if (__is_trivially_copyable(T)) { + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_copy_strict( + reinterpret_cast(*dst), reinterpret_cast(*src)); + } else { + for (size_t i = 0; i < DstN; ++i) { + (*dst)[i] = (i < SrcN) ? (*src)[i] : T(); + } + } +} + +_CUDA_PIPELINE_END_NAMESPACE + +#endif /* !_CUDA_PIPELINE_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_helpers.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_helpers.h new file mode 100644 index 0000000000000000000000000000000000000000..01882b6b976347b9bfdf276c3d0adcec1d8a55fa --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_helpers.h @@ -0,0 +1,373 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_PIPELINE_HELPERS_H_ +# define _CUDA_PIPELINE_HELPERS_H_ + +# define _CUDA_PIPELINE_NAMESPACE nvcuda::experimental +# define _CUDA_PIPELINE_BEGIN_NAMESPACE namespace nvcuda { namespace experimental { +# define _CUDA_PIPELINE_END_NAMESPACE } } + +# define _CUDA_PIPELINE_INTERNAL_NAMESPACE _CUDA_PIPELINE_NAMESPACE::__pipeline_internal +# define _CUDA_PIPELINE_BEGIN_INTERNAL_NAMESPACE _CUDA_PIPELINE_BEGIN_NAMESPACE namespace __pipeline_internal { +# define _CUDA_PIPELINE_END_INTERNAL_NAMESPACE } _CUDA_PIPELINE_END_NAMESPACE + +# if !defined(_CUDA_PIPELINE_QUALIFIER) +# define _CUDA_PIPELINE_QUALIFIER inline __device__ +# endif +# if !defined(_CUDA_PIPELINE_STATIC_QUALIFIER) +# define _CUDA_PIPELINE_STATIC_QUALIFIER static inline __device__ +# endif + +# if defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 700) +# define _CUDA_PIPELINE_ARCH_700_OR_LATER +# endif + +# if (__CUDA_ARCH__ >= 800) +# define _CUDA_PIPELINE_HAS_ASYNC_COPY 1 +# else +# define _CUDA_PIPELINE_HAS_ASYNC_COPY 0 +# endif + +# if !defined(_CUDA_PIPELINE_MAX_STAGES) +# define _CUDA_PIPELINE_MAX_STAGES 8 +# endif + +# if defined(__cplusplus) && ((__cplusplus >= 201103L) || (defined(_MSC_VER) && (_MSC_VER >= 1900))) +# define _CUDA_PIPELINE_CPLUSPLUS_11_OR_LATER +# endif + +# if !defined(_CUDA_PIPELINE_DEBUG) +# if defined(__CUDACC_DEBUG__) +# define _CUDA_PIPELINE_DEBUG 1 +# else +# define _CUDA_PIPELINE_DEBUG 0 +# endif +# endif + +# if defined(_CUDA_PIPELINE_DEBUG) && (_CUDA_PIPELINE_DEBUG == 1) && !defined(NDEBUG) +# if !defined(__CUDACC_RTC__) +# include +# endif +# define _CUDA_PIPELINE_ASSERT(x) assert((x)); +# define _CUDA_PIPELINE_ABORT() assert(0); +# else +# define _CUDA_PIPELINE_ASSERT(x) +# define _CUDA_PIPELINE_ABORT() __trap(); +# endif + +# if defined(_CUDA_PIPELINE_CPLUSPLUS_11_OR_LATER) +# define _CUDA_PIPELINE_STATIC_ASSERT(c, m) static_assert(c, m) +# else +# define _CUDA_PIPELINE_STATIC_ASSERT(c, m) +# endif + +# if (defined(_MSC_VER) && !defined(_WIN64)) || defined(__arm__) +# define _CUDA_PIPELINE_ASM_PTR_CONSTRAINT "r" +# else +# define _CUDA_PIPELINE_ASM_PTR_CONSTRAINT "l" +# endif + +# if defined(__CUDACC_RTC__) +typedef unsigned int uint32_t; +typedef unsigned long long uint64_t; +typedef uint64_t uintptr_t; +# else +# include +# endif + +_CUDA_PIPELINE_BEGIN_INTERNAL_NAMESPACE + +_CUDA_PIPELINE_STATIC_ASSERT(sizeof(short) == 2, "Size mismatch for type 'short'"); +_CUDA_PIPELINE_STATIC_ASSERT(sizeof(int) == 4, "Size mismatch for type 'int'"); +_CUDA_PIPELINE_STATIC_ASSERT(sizeof(int2) == 8, "Size mismatch for type 'int2'"); +_CUDA_PIPELINE_STATIC_ASSERT(sizeof(int4) == 16, "Size mismatch for type 'int4'"); + +extern "C" __device__ uint32_t __nvvm_get_smem_pointer(void *); + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline_memcpy_sync(void* __restrict__ dst, const void* __restrict__ src) +{ + _CUDA_PIPELINE_STATIC_ASSERT(CopySize == 4 || CopySize == 8 || CopySize == 16, "Unsupported copy size."); + _CUDA_PIPELINE_STATIC_ASSERT(SourceSize <= CopySize, "Source size must be less than or equal to copy size"); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (CopySize - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (CopySize - 1))); + + char* const d = reinterpret_cast(dst); + const char* const s = reinterpret_cast(src); + + size_t copy_step_size; + if (SourceSize == 0) { + copy_step_size = CopySize; + } else if (SourceSize == 2 || SourceSize == 4 || SourceSize == 8 || SourceSize == 16) { + copy_step_size = SourceSize; + } else { + copy_step_size = 1; + } + + for (size_t i = 0; i < CopySize; i += copy_step_size) { + const bool copy_source = SourceSize && (i < SourceSize); + + switch (copy_step_size) { + case 1: + d[i] = copy_source ? s[i] : char(); + break; + case 2: + *reinterpret_cast(d + i) = copy_source ? *reinterpret_cast(s + i) : short(); + break; + case 4: + *reinterpret_cast(d + i) = copy_source ? *reinterpret_cast(s + i) : int(); + break; + case 8: + *reinterpret_cast(d + i) = copy_source ? *reinterpret_cast(s + i) : int2(); + break; + case 16: + *reinterpret_cast(d + i) = copy_source ? *reinterpret_cast(s + i) : int4(); + break; + } + } +} + +template +struct ImplementationChooser; + +template<> +struct ImplementationChooser { + template + struct CpAsyncChooser { + _CUDA_PIPELINE_STATIC_QUALIFIER + void cp_async(void* __restrict__ dst, const void* __restrict__ src) + { + asm volatile ("cp.async.ca.shared.global [%0], [%1], %2, %3;" + : + : "r"(__nvvm_get_smem_pointer(dst)), _CUDA_PIPELINE_ASM_PTR_CONSTRAINT(src), "n"(CopySize), + "n"(SourceSize) + : "memory"); + } + }; + + template + struct CpAsyncChooser<16, SourceSize> { + _CUDA_PIPELINE_STATIC_QUALIFIER + void cp_async(void* __restrict__ dst, const void* __restrict__ src) + { + asm volatile ("cp.async.cg.shared.global [%0], [%1], %2, %3;" + : + : "r"(__nvvm_get_smem_pointer(dst)), _CUDA_PIPELINE_ASM_PTR_CONSTRAINT(src), "n"(16), "n"(SourceSize) + : "memory"); + } + }; + + template + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_memcpy_async(void* __restrict__ dst, const void* __restrict__ src) + { + _CUDA_PIPELINE_STATIC_ASSERT(CopySize == 4 || CopySize == 8 || CopySize == 16, "Unsupported copy size."); + _CUDA_PIPELINE_STATIC_ASSERT(SourceSize <= CopySize, "Source size must be less than or equal to copy size"); + _CUDA_PIPELINE_ASSERT(__isShared(dst)); + _CUDA_PIPELINE_ASSERT(__isGlobal(src)); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (CopySize - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (CopySize - 1))); + + CpAsyncChooser::cp_async(dst, src); + } + + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_commit() + { + asm volatile ("cp.async.commit_group;"); + } + + template + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_wait_prior() + { + asm volatile ("cp.async.wait_group %0;" + : + : "n"(N < _CUDA_PIPELINE_MAX_STAGES ? N : _CUDA_PIPELINE_MAX_STAGES)); + } + + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_arrive_on(uint64_t* barrier) + { + _CUDA_PIPELINE_ASSERT(__isShared(barrier)); + + asm volatile ("cp.async.mbarrier.arrive.shared.b64 [%0];" + : + : "r"(__nvvm_get_smem_pointer(barrier))); + } +}; + +template<> +struct ImplementationChooser { + template + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_memcpy_async(void* __restrict__ dst, const void* __restrict__ src) + { + _CUDA_PIPELINE_STATIC_ASSERT(CopySize == 4 || CopySize == 8 || CopySize == 16, "Unsupported copy size."); + _CUDA_PIPELINE_STATIC_ASSERT(SourceSize <= CopySize, "Source size must be less than or equal to copy size"); + _CUDA_PIPELINE_ASSERT(__isShared(dst)); + _CUDA_PIPELINE_ASSERT(__isGlobal(src)); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (CopySize - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (CopySize - 1))); + + pipeline_memcpy_sync(dst, src); + } + + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_commit() + { + } + + template + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_wait_prior() + { + } + + _CUDA_PIPELINE_STATIC_QUALIFIER + void pipeline_arrive_on(uint64_t* barrier) + { + } +}; + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline_memcpy_async(void* __restrict__ dst, const void* __restrict__ src) +{ + _CUDA_PIPELINE_STATIC_ASSERT(CopySize == 4 || CopySize == 8 || CopySize == 16, "Unsupported copy size."); + _CUDA_PIPELINE_STATIC_ASSERT(SourceSize <= CopySize, "Source size must be less than or equal to copy size"); + _CUDA_PIPELINE_ASSERT(__isShared(dst)); + _CUDA_PIPELINE_ASSERT(__isGlobal(src)); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (CopySize - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (CopySize - 1))); + + ImplementationChooser<_CUDA_PIPELINE_HAS_ASYNC_COPY>::pipeline_memcpy_async(dst, src); +} + +_CUDA_PIPELINE_QUALIFIER +void pipeline_commit() +{ + ImplementationChooser<_CUDA_PIPELINE_HAS_ASYNC_COPY>::pipeline_commit(); +} + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline_wait_prior() +{ + ImplementationChooser<_CUDA_PIPELINE_HAS_ASYNC_COPY>::pipeline_wait_prior(); +} + +_CUDA_PIPELINE_QUALIFIER +void pipeline_arrive_on(uint64_t* barrier) +{ + ImplementationChooser<_CUDA_PIPELINE_HAS_ASYNC_COPY>::pipeline_arrive_on(barrier); +} + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline_copy_strict(void* __restrict__ dst, const void* __restrict__ src) +{ + _CUDA_PIPELINE_STATIC_ASSERT(CopySize == 4 || CopySize == 8 || CopySize == 16, "Unsupported copy size."); + _CUDA_PIPELINE_STATIC_ASSERT(SourceSize <= CopySize, "Source size must be less than or equal to copy size."); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (CopySize - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (CopySize - 1))); + + if (__isGlobal(src) && __isShared(dst)) { + pipeline_memcpy_async(dst, src); + } else { + pipeline_memcpy_sync(dst, src); + } +} + +template +_CUDA_PIPELINE_QUALIFIER +void pipeline_copy_relaxed(void* __restrict__ dst, const void* __restrict__ src) +{ + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src) & (Align - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst) & (Align - 1))); + + const char* s = reinterpret_cast(src); + char* d = reinterpret_cast(dst); + size_t remaining = CopySize; + + while (remaining) { + if ((Align >= 16) && (remaining >= 16)) { + pipeline_copy_strict<16, 16>(dst, src); + d += 16; + s += 16; + remaining -= 16; + } else if ((Align >= 8) && (remaining >= 8)) { + pipeline_copy_strict<8, 8>(dst, src); + d += 8; + s += 8; + remaining -= 8; + } else if ((Align >= 4) && (remaining >= 4)) { + pipeline_copy_strict<4, 4>(dst, src); + d += 4; + s += 4; + remaining -= 4; + } else if ((Align >= 2) && (remaining >= 2)) { + *reinterpret_cast(d) = *reinterpret_cast(s); + d += 2; + s += 2; + remaining -= 2; + } else { + *d = *s; + d += 1; + s += 1; + remaining -= 1; + } + } +} + +_CUDA_PIPELINE_END_INTERNAL_NAMESPACE + +#endif /* !_CUDA_PIPELINE_HELPERS_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_primitives.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_primitives.h new file mode 100644 index 0000000000000000000000000000000000000000..eaba0cfb5ac9184bec5e837d2ec2f9db11d873ae --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_pipeline_primitives.h @@ -0,0 +1,148 @@ +/* + * Copyright 1993-2019 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef _CUDA_PIPELINE_PRIMITIVES_H_ +# define _CUDA_PIPELINE_PRIMITIVES_H_ + +# include "cuda_pipeline_helpers.h" + +_CUDA_PIPELINE_STATIC_QUALIFIER +void __pipeline_memcpy_async(void* __restrict__ dst_shared, const void* __restrict__ src_global, size_t size_and_align, + size_t zfill = 0) +{ + _CUDA_PIPELINE_ASSERT(size_and_align == 4 || size_and_align == 8 || size_and_align == 16); + _CUDA_PIPELINE_ASSERT(zfill <= size_and_align); + _CUDA_PIPELINE_ASSERT(__isShared(dst_shared)); + _CUDA_PIPELINE_ASSERT(__isGlobal(src_global)); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(dst_shared) & (size_and_align - 1))); + _CUDA_PIPELINE_ASSERT(!(reinterpret_cast(src_global) & (size_and_align - 1))); + + switch (size_and_align) { + case 16: + switch (zfill) { + case 0: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 16>(dst_shared, src_global); return; + case 1: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 15>(dst_shared, src_global); return; + case 2: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 14>(dst_shared, src_global); return; + case 3: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 13>(dst_shared, src_global); return; + case 4: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 12>(dst_shared, src_global); return; + case 5: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 11>(dst_shared, src_global); return; + case 6: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 10>(dst_shared, src_global); return; + case 7: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 9>(dst_shared, src_global); return; + case 8: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 8>(dst_shared, src_global); return; + case 9: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 7>(dst_shared, src_global); return; + case 10: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 6>(dst_shared, src_global); return; + case 11: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 5>(dst_shared, src_global); return; + case 12: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 4>(dst_shared, src_global); return; + case 13: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 3>(dst_shared, src_global); return; + case 14: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 2>(dst_shared, src_global); return; + case 15: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 1>(dst_shared, src_global); return; + case 16: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async<16, 0>(dst_shared, src_global); return; + default: _CUDA_PIPELINE_ABORT(); return; + } + case 8: + switch (zfill) { + case 0: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 8>(dst_shared, src_global); return; + case 1: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 7>(dst_shared, src_global); return; + case 2: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 6>(dst_shared, src_global); return; + case 3: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 5>(dst_shared, src_global); return; + case 4: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 4>(dst_shared, src_global); return; + case 5: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 3>(dst_shared, src_global); return; + case 6: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 2>(dst_shared, src_global); return; + case 7: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 1>(dst_shared, src_global); return; + case 8: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 8, 0>(dst_shared, src_global); return; + default: _CUDA_PIPELINE_ABORT(); return; + } + case 4: + switch (zfill) { + case 0: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 4, 4>(dst_shared, src_global); return; + case 1: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 4, 3>(dst_shared, src_global); return; + case 2: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 4, 2>(dst_shared, src_global); return; + case 3: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 4, 1>(dst_shared, src_global); return; + case 4: _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_memcpy_async< 4, 0>(dst_shared, src_global); return; + default: _CUDA_PIPELINE_ABORT(); return; + } + default: + _CUDA_PIPELINE_ABORT(); + return; + } +} + +_CUDA_PIPELINE_STATIC_QUALIFIER +void __pipeline_commit() +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_commit(); +} + +_CUDA_PIPELINE_STATIC_QUALIFIER +void __pipeline_wait_prior(size_t prior) +{ + switch (prior) { + case 0 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<0>(); return; + case 1 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<1>(); return; + case 2 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<2>(); return; + case 3 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<3>(); return; + case 4 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<4>(); return; + case 5 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<5>(); return; + case 6 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<6>(); return; + case 7 : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<7>(); return; + default : _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_wait_prior<8>(); return; + } +} + +# if defined(_CUDA_PIPELINE_ARCH_700_OR_LATER) +# include "cuda_awbarrier_primitives.h" + +_CUDA_PIPELINE_STATIC_QUALIFIER +void __pipeline_arrive_on(__mbarrier_t* barrier) +{ + _CUDA_PIPELINE_INTERNAL_NAMESPACE::pipeline_arrive_on(barrier); +} +# endif + +#endif /* !_CUDA_PIPELINE_PRIMITIVES_H_ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime.h new file mode 100644 index 0000000000000000000000000000000000000000..f75b2cb50b65d111c2e0f3c01fccd26bb1b47aea --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime.h @@ -0,0 +1,2374 @@ +/* + * Copyright 1993-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_RUNTIME_H__) +#define __CUDA_RUNTIME_H__ + +#if !defined(__CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__) +#define __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#define __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_H__ +#endif + +#define EXCLUDE_FROM_RTC +#if defined(__GNUC__) +#if defined(__clang__) || (!defined(__PGIC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))) +#pragma GCC diagnostic push +#endif +#if defined(__clang__) || (!defined(__PGIC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 2))) +#pragma GCC diagnostic ignored "-Wunused-function" +#endif +#elif defined(_MSC_VER) +#pragma warning(push) +#pragma warning(disable: 4820) +#endif +#ifdef __QNX__ +#if (__GNUC__ == 4 && __GNUC_MINOR__ >= 7) +typedef unsigned size_t; +#endif +#endif +#undef EXCLUDE_FROM_RTC +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#include "crt/host_config.h" + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#include "builtin_types.h" +#include "library_types.h" +#if !defined(__CUDACC_RTC__) +#define EXCLUDE_FROM_RTC +#include "channel_descriptor.h" +#include "cuda_runtime_api.h" +#include "driver_functions.h" +#undef EXCLUDE_FROM_RTC +#endif /* !__CUDACC_RTC__ */ +#include "crt/host_defines.h" +#ifdef __CUDACC_RTC__ +#include "target" +#endif /* defined(__CUDACC_RTC__) */ + + +#include "vector_functions.h" + +#if defined(__CUDACC__) + +#if defined(__CUDACC_RTC__) +#include "nvrtc_device_runtime.h" +#include "crt/device_functions.h" +#include "crt/common_functions.h" +#include "device_launch_parameters.h" + +#else /* !__CUDACC_RTC__ */ +#define EXCLUDE_FROM_RTC +#include "crt/common_functions.h" +#include "crt/device_functions.h" +#include "device_launch_parameters.h" + +#if defined(__CUDACC_EXTENDED_LAMBDA__) +#include +#include +struct __device_builtin__ __nv_lambda_preheader_injection { }; +#endif /* defined(__CUDACC_EXTENDED_LAMBDA__) */ + +#undef EXCLUDE_FROM_RTC +#endif /* __CUDACC_RTC__ */ + +#endif /* __CUDACC__ */ + +/** \cond impl_private */ +#if defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +#define __CUDA_DEPRECATED +#elif defined(_MSC_VER) +#define __CUDA_DEPRECATED __declspec(deprecated) +#elif defined(__GNUC__) +#define __CUDA_DEPRECATED __attribute__((deprecated)) +#else +#define __CUDA_DEPRECATED +#endif +/** \endcond impl_private */ + +#define EXCLUDE_FROM_RTC +#if defined(__cplusplus) && !defined(__CUDACC_RTC__) + +#if __cplusplus >= 201103L || (defined(_MSC_VER) && (_MSC_VER >= 1900)) +#include +#endif + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +/** + * \addtogroup CUDART_HIGHLEVEL + * @{ + */ + +/** + *\brief Launches a device function + * + * The function invokes kernel \p func on \p gridDim (\p gridDim.x × \p gridDim.y + * × \p gridDim.z) grid of blocks. Each block contains \p blockDim (\p blockDim.x × + * \p blockDim.y × \p blockDim.z) threads. + * + * If the kernel has N parameters the \p args should point to array of N pointers. + * Each pointer, from args[0] to args[N - 1], point to the region + * of memory from which the actual parameter will be copied. + * + * \p sharedMem sets the amount of dynamic shared memory that will be available to + * each thread block. + * + * \p stream specifies a stream the invocation is associated to. + * + * \param func - Device function symbol + * \param gridDim - Grid dimentions + * \param blockDim - Block dimentions + * \param args - Arguments + * \param sharedMem - Shared memory (defaults to 0) + * \param stream - Stream identifier (defaults to NULL) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorSharedObjectInitFailed, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C API)" + */ +template +static __inline__ __host__ cudaError_t cudaLaunchKernel( + const T *func, + dim3 gridDim, + dim3 blockDim, + void **args, + size_t sharedMem = 0, + cudaStream_t stream = 0 +) +{ + return ::cudaLaunchKernel((const void *)func, gridDim, blockDim, args, sharedMem, stream); +} + + +#if __cplusplus >= 201103L || (defined(_MSC_VER) && (_MSC_VER >= 1900)) || defined(__DOXYGEN_ONLY__) +/** + * \brief Launches a CUDA function with launch-time configuration + * + * Invokes the kernel \p func on \p config->gridDim (\p config->gridDim.x + * × \p config->gridDim.y × \p config->gridDim.z) grid of blocks. + * Each block contains \p config->blockDim (\p config->blockDim.x × + * \p config->blockDim.y × \p config->blockDim.z) threads. + * + * \p config->dynamicSmemBytes sets the amount of dynamic shared memory that + * will be available to each thread block. + * + * \p config->stream specifies a stream the invocation is associated to. + * + * Configuration beyond grid and block dimensions, dynamic shared memory size, + * and stream can be provided with the following two fields of \p config: + * + * \p config->attrs is an array of \p config->numAttrs contiguous + * ::cudaLaunchAttribute elements. The value of this pointer is not considered + * if \p config->numAttrs is zero. However, in that case, it is recommended to + * set the pointer to NULL. + * \p config->numAttrs is the number of attributes populating the first + * \p config->numAttrs positions of the \p config->attrs array. + * + * The kernel arguments should be passed as arguments to this function via the + * \p args parameter pack. + * + * The C API version of this function, \p cudaLaunchKernelExC, is also available + * for pre-C++11 compilers and for use cases where the ability to pass kernel + * parameters via void* array is preferable. + * + * \param config - Launch configuration + * \param func - Kernel to launch + * \param args - Parameter pack of kernel parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorSharedObjectInitFailed, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaLaunchKernelExC(const cudaLaunchConfig_t *config, const void *func, void **args) "cudaLaunchKernelEx (C API)", + * ::cuLaunchKernelEx + */ +template +static __inline__ __host__ cudaError_t cudaLaunchKernelEx( + const cudaLaunchConfig_t *config, + void (*kernel)(ExpTypes...), + ActTypes &&... args +) +{ + return [&](ExpTypes... coercedArgs){ + void *pArgs[] = { &coercedArgs... }; + return ::cudaLaunchKernelExC(config, (const void *)kernel, pArgs); + }(std::forward(args)...); +} +#endif + +/** + *\brief Launches a device function + * + * The function invokes kernel \p func on \p gridDim (\p gridDim.x × \p gridDim.y + * × \p gridDim.z) grid of blocks. Each block contains \p blockDim (\p blockDim.x × + * \p blockDim.y × \p blockDim.z) threads. + * + * The device on which this kernel is invoked must have a non-zero value for + * the device attribute ::cudaDevAttrCooperativeLaunch. + * + * The total number of blocks launched cannot exceed the maximum number of blocks per + * multiprocessor as returned by ::cudaOccupancyMaxActiveBlocksPerMultiprocessor (or + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags) times the number of multiprocessors + * as specified by the device attribute ::cudaDevAttrMultiProcessorCount. + * + * The kernel cannot make use of CUDA dynamic parallelism. + * + * If the kernel has N parameters the \p args should point to array of N pointers. + * Each pointer, from args[0] to args[N - 1], point to the region + * of memory from which the actual parameter will be copied. + * + * \p sharedMem sets the amount of dynamic shared memory that will be available to + * each thread block. + * + * \p stream specifies a stream the invocation is associated to. + * + * \param func - Device function symbol + * \param gridDim - Grid dimentions + * \param blockDim - Block dimentions + * \param args - Arguments + * \param sharedMem - Shared memory (defaults to 0) + * \param stream - Stream identifier (defaults to NULL) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorSharedObjectInitFailed + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchCooperativeKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchCooperativeKernel (C API)" + */ +template +static __inline__ __host__ cudaError_t cudaLaunchCooperativeKernel( + const T *func, + dim3 gridDim, + dim3 blockDim, + void **args, + size_t sharedMem = 0, + cudaStream_t stream = 0 +) +{ + return ::cudaLaunchCooperativeKernel((const void *)func, gridDim, blockDim, args, sharedMem, stream); +} + +/** + * \brief \hl Creates an event object with the specified flags + * + * Creates an event object with the specified flags. Valid flags include: + * - ::cudaEventDefault: Default event creation flag. + * - ::cudaEventBlockingSync: Specifies that event should use blocking + * synchronization. A host thread that uses ::cudaEventSynchronize() to wait + * on an event created with this flag will block until the event actually + * completes. + * - ::cudaEventDisableTiming: Specifies that the created event does not need + * to record timing data. Events created with this flag specified and + * the ::cudaEventBlockingSync flag not specified will provide the best + * performance when used with ::cudaStreamWaitEvent() and ::cudaEventQuery(). + * + * \param event - Newly created event + * \param flags - Flags for new event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorLaunchFailure, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventRecord, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cudaStreamWaitEvent + */ +static __inline__ __host__ cudaError_t cudaEventCreate( + cudaEvent_t *event, + unsigned int flags +) +{ + return ::cudaEventCreateWithFlags(event, flags); +} + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p graph as an executable graph. The graph is validated for any + * structural constraints or intra-node constraints which were not previously + * validated. If instantiation is successful, a handle to the instantiated graph + * is returned in \p pGraphExec. + * + * If there are any errors, diagnostic information may be returned in \p pErrorNode and + * \p pLogBuffer. This is the primary way to inspect instantiation errors. The output + * will be null terminated unless the diagnostics overflow + * the buffer. In this case, they will be truncated, and the last byte can be + * inspected to determine if truncation occurred. + * + * \param pGraphExec - Returns instantiated graph + * \param graph - Graph to instantiate + * \param pErrorNode - In case of an instantiation error, this may be modified to + * indicate a node contributing to the error + * \param pLogBuffer - A character buffer to store diagnostic messages + * \param bufferSize - Size of the log buffer in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiateWithFlags, + * ::cudaGraphCreate, + * ::cudaGraphUpload, + * ::cudaGraphLaunch, + * ::cudaGraphExecDestroy + */ +static __inline__ __host__ cudaError_t cudaGraphInstantiate( + cudaGraphExec_t *pGraphExec, + cudaGraph_t graph, + cudaGraphNode_t *pErrorNode, + char *pLogBuffer, + size_t bufferSize +) +{ + (void)pErrorNode; + (void)pLogBuffer; + (void)bufferSize; + return ::cudaGraphInstantiate(pGraphExec, graph, 0); +} + +/** + * \brief \hl Allocates page-locked memory on the host + * + * Allocates \p size bytes of host memory that is page-locked and accessible + * to the device. The driver tracks the virtual memory ranges allocated with + * this function and automatically accelerates calls to functions such as + * ::cudaMemcpy(). Since the memory can be accessed directly by the device, it + * can be read or written with much higher bandwidth than pageable memory + * obtained with functions such as ::malloc(). Allocating excessive amounts of + * pinned memory may degrade system performance, since it reduces the amount + * of memory available to the system for paging. As a result, this function is + * best used sparingly to allocate staging areas for data exchange between host + * and device. + * + * The \p flags parameter enables different options to be specified that affect + * the allocation, as follows. + * - ::cudaHostAllocDefault: This flag's value is defined to be 0. + * - ::cudaHostAllocPortable: The memory returned by this call will be + * considered as pinned memory by all CUDA contexts, not just the one that + * performed the allocation. + * - ::cudaHostAllocMapped: Maps the allocation into the CUDA address space. + * The device pointer to the memory may be obtained by calling + * ::cudaHostGetDevicePointer(). + * - ::cudaHostAllocWriteCombined: Allocates the memory as write-combined (WC). + * WC memory can be transferred across the PCI Express bus more quickly on some + * system configurations, but cannot be read efficiently by most CPUs. WC + * memory is a good option for buffers that will be written by the CPU and read + * by the device via mapped pinned memory or host->device transfers. + * + * All of these flags are orthogonal to one another: a developer may allocate + * memory that is portable, mapped and/or write-combined with no restrictions. + * + * ::cudaSetDeviceFlags() must have been called with the ::cudaDeviceMapHost + * flag in order for the ::cudaHostAllocMapped flag to have any effect. + * + * The ::cudaHostAllocMapped flag may be specified on CUDA contexts for devices + * that do not support mapped pinned memory. The failure is deferred to + * ::cudaHostGetDevicePointer() because the memory may be mapped into other + * CUDA contexts via the ::cudaHostAllocPortable flag. + * + * Memory allocated by this function must be freed with ::cudaFreeHost(). + * + * \param ptr - Device pointer to allocated memory + * \param size - Requested allocation size in bytes + * \param flags - Requested properties of allocated memory + * + * \return + * ::cudaSuccess, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaSetDeviceFlags, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc + */ +static __inline__ __host__ cudaError_t cudaMallocHost( + void **ptr, + size_t size, + unsigned int flags +) +{ + return ::cudaHostAlloc(ptr, size, flags); +} + +template +static __inline__ __host__ cudaError_t cudaHostAlloc( + T **ptr, + size_t size, + unsigned int flags +) +{ + return ::cudaHostAlloc((void**)(void*)ptr, size, flags); +} + +template +static __inline__ __host__ cudaError_t cudaHostGetDevicePointer( + T **pDevice, + void *pHost, + unsigned int flags +) +{ + return ::cudaHostGetDevicePointer((void**)(void*)pDevice, pHost, flags); +} + +/** + * \brief Allocates memory that will be automatically managed by the Unified Memory system + * + * Allocates \p size bytes of managed memory on the device and returns in + * \p *devPtr a pointer to the allocated memory. If the device doesn't support + * allocating managed memory, ::cudaErrorNotSupported is returned. Support + * for managed memory can be queried using the device attribute + * ::cudaDevAttrManagedMemory. The allocated memory is suitably + * aligned for any kind of variable. The memory is not cleared. If \p size + * is 0, ::cudaMallocManaged returns ::cudaErrorInvalidValue. The pointer + * is valid on the CPU and on all GPUs in the system that support managed memory. + * All accesses to this pointer must obey the Unified Memory programming model. + * + * \p flags specifies the default stream association for this allocation. + * \p flags must be one of ::cudaMemAttachGlobal or ::cudaMemAttachHost. The + * default value for \p flags is ::cudaMemAttachGlobal. + * If ::cudaMemAttachGlobal is specified, then this memory is accessible from + * any stream on any device. If ::cudaMemAttachHost is specified, then the + * allocation should not be accessed from devices that have a zero value for the + * device attribute ::cudaDevAttrConcurrentManagedAccess; an explicit call to + * ::cudaStreamAttachMemAsync will be required to enable access on such devices. + * + * If the association is later changed via ::cudaStreamAttachMemAsync to + * a single stream, the default association, as specifed during ::cudaMallocManaged, + * is restored when that stream is destroyed. For __managed__ variables, the + * default association is always ::cudaMemAttachGlobal. Note that destroying a + * stream is an asynchronous operation, and as a result, the change to default + * association won't happen until all work in the stream has completed. + * + * Memory allocated with ::cudaMallocManaged should be released with ::cudaFree. + * + * Device memory oversubscription is possible for GPUs that have a non-zero value for the + * device attribute ::cudaDevAttrConcurrentManagedAccess. Managed memory on + * such GPUs may be evicted from device memory to host memory at any time by the Unified + * Memory driver in order to make room for other allocations. + * + * In a multi-GPU system where all GPUs have a non-zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess, managed memory may not be populated when this + * API returns and instead may be populated on access. In such systems, managed memory can + * migrate to any processor's memory at any time. The Unified Memory driver will employ heuristics to + * maintain data locality and prevent excessive page faults to the extent possible. The application + * can also guide the driver about memory usage patterns via ::cudaMemAdvise. The application + * can also explicitly migrate memory to a desired processor's memory via + * ::cudaMemPrefetchAsync. + * + * In a multi-GPU system where all of the GPUs have a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess and all the GPUs have peer-to-peer support + * with each other, the physical storage for managed memory is created on the GPU which is active + * at the time ::cudaMallocManaged is called. All other GPUs will reference the data at reduced + * bandwidth via peer mappings over the PCIe bus. The Unified Memory driver does not migrate + * memory among such GPUs. + * + * In a multi-GPU system where not all GPUs have peer-to-peer support with each other and + * where the value of the device attribute ::cudaDevAttrConcurrentManagedAccess + * is zero for at least one of those GPUs, the location chosen for physical storage of managed + * memory is system-dependent. + * - On Linux, the location chosen will be device memory as long as the current set of active + * contexts are on devices that either have peer-to-peer support with each other or have a + * non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * If there is an active context on a GPU that does not have a non-zero value for that device + * attribute and it does not have peer-to-peer support with the other devices that have active + * contexts on them, then the location for physical storage will be 'zero-copy' or host memory. + * Note that this means that managed memory that is located in device memory is migrated to + * host memory if a new context is created on a GPU that doesn't have a non-zero value for + * the device attribute and does not support peer-to-peer with at least one of the other devices + * that has an active context. This in turn implies that context creation may fail if there is + * insufficient host memory to migrate all managed allocations. + * - On Windows, the physical storage is always created in 'zero-copy' or host memory. + * All GPUs will reference the data at reduced bandwidth over the PCIe bus. In these + * circumstances, use of the environment variable CUDA_VISIBLE_DEVICES is recommended to + * restrict CUDA to only use those GPUs that have peer-to-peer support. + * Alternatively, users can also set CUDA_MANAGED_FORCE_DEVICE_ALLOC to a non-zero + * value to force the driver to always use device memory for physical storage. + * When this environment variable is set to a non-zero value, all devices used in + * that process that support managed memory have to be peer-to-peer compatible + * with each other. The error ::cudaErrorInvalidDevice will be returned if a device + * that supports managed memory is used and it is not peer-to-peer compatible with + * any of the other managed memory supporting devices that were previously used in + * that process, even if ::cudaDeviceReset has been called on those devices. These + * environment variables are described in the CUDA programming guide under the + * "CUDA environment variables" section. + * - On ARM, managed memory is not available on discrete gpu with Drive PX-2. + * + * \param devPtr - Pointer to allocated device memory + * \param size - Requested allocation size in bytes + * \param flags - Must be either ::cudaMemAttachGlobal or ::cudaMemAttachHost (defaults to ::cudaMemAttachGlobal) + * + * \return + * ::cudaSuccess, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, ::cudaFreeArray, + * ::cudaMalloc3D, ::cudaMalloc3DArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, ::cudaDeviceGetAttribute, ::cudaStreamAttachMemAsync + */ +template +static __inline__ __host__ cudaError_t cudaMallocManaged( + T **devPtr, + size_t size, + unsigned int flags = cudaMemAttachGlobal +) +{ + return ::cudaMallocManaged((void**)(void*)devPtr, size, flags); +} + +/** + * \brief Advise about the usage of a given memory range. + * + * This is an alternate spelling for cudaMemAdvise made available through operator overloading. + * + * \sa ::cudaMemAdvise, + * \ref ::cudaMemAdvise(const void* devPtr, size_t count, enum cudaMemoryAdvise advice, struct cudaMemLocation location) "cudaMemAdvise (C API)" + */ +template +cudaError_t cudaMemAdvise( + T *devPtr, + size_t count, + enum cudaMemoryAdvise advice, + struct cudaMemLocation location +) +{ + return ::cudaMemAdvise_v2((const void *)devPtr, count, advice, location); +} + +template +static __inline__ __host__ cudaError_t cudaMemPrefetchAsync( + T *devPtr, + size_t count, + struct cudaMemLocation location, + unsigned int flags, + cudaStream_t stream = 0 +) +{ + return ::cudaMemPrefetchAsync_v2((const void *)devPtr, count, location, flags, stream); +} + +/** + * \brief Attach memory to a stream asynchronously + * + * Enqueues an operation in \p stream to specify stream association of + * \p length bytes of memory starting from \p devPtr. This function is a + * stream-ordered operation, meaning that it is dependent on, and will + * only take effect when, previous work in stream has completed. Any + * previous association is automatically replaced. + * + * \p devPtr must point to an one of the following types of memories: + * - managed memory declared using the __managed__ keyword or allocated with + * ::cudaMallocManaged. + * - a valid host-accessible region of system-allocated pageable memory. This + * type of memory may only be specified if the device associated with the + * stream reports a non-zero value for the device attribute + * ::cudaDevAttrPageableMemoryAccess. + * + * For managed allocations, \p length must be either zero or the entire + * allocation's size. Both indicate that the entire allocation's stream + * association is being changed. Currently, it is not possible to change stream + * association for a portion of a managed allocation. + * + * For pageable allocations, \p length must be non-zero. + * + * The stream association is specified using \p flags which must be + * one of ::cudaMemAttachGlobal, ::cudaMemAttachHost or ::cudaMemAttachSingle. + * The default value for \p flags is ::cudaMemAttachSingle + * If the ::cudaMemAttachGlobal flag is specified, the memory can be accessed + * by any stream on any device. + * If the ::cudaMemAttachHost flag is specified, the program makes a guarantee + * that it won't access the memory on the device from any stream on a device that + * has a zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * If the ::cudaMemAttachSingle flag is specified and \p stream is associated with + * a device that has a zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess, + * the program makes a guarantee that it will only access the memory on the device + * from \p stream. It is illegal to attach singly to the NULL stream, because the + * NULL stream is a virtual global stream and not a specific stream. An error will + * be returned in this case. + * + * When memory is associated with a single stream, the Unified Memory system will + * allow CPU access to this memory region so long as all operations in \p stream + * have completed, regardless of whether other streams are active. In effect, + * this constrains exclusive ownership of the managed memory region by + * an active GPU to per-stream activity instead of whole-GPU activity. + * + * Accessing memory on the device from streams that are not associated with + * it will produce undefined results. No error checking is performed by the + * Unified Memory system to ensure that kernels launched into other streams + * do not access this region. + * + * It is a program's responsibility to order calls to ::cudaStreamAttachMemAsync + * via events, synchronization or other means to ensure legal access to memory + * at all times. Data visibility and coherency will be changed appropriately + * for all kernels which follow a stream-association change. + * + * If \p stream is destroyed while data is associated with it, the association is + * removed and the association reverts to the default visibility of the allocation + * as specified at ::cudaMallocManaged. For __managed__ variables, the default + * association is always ::cudaMemAttachGlobal. Note that destroying a stream is an + * asynchronous operation, and as a result, the change to default association won't + * happen until all work in the stream has completed. + * + * \param stream - Stream in which to enqueue the attach operation + * \param devPtr - Pointer to memory (must be a pointer to managed memory or + * to a valid host-accessible region of system-allocated + * memory) + * \param length - Length of memory (defaults to zero) + * \param flags - Must be one of ::cudaMemAttachGlobal, ::cudaMemAttachHost or ::cudaMemAttachSingle (defaults to ::cudaMemAttachSingle) + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotReady, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamWaitEvent, ::cudaStreamSynchronize, ::cudaStreamAddCallback, ::cudaStreamDestroy, ::cudaMallocManaged + */ +template +static __inline__ __host__ cudaError_t cudaStreamAttachMemAsync( + cudaStream_t stream, + T *devPtr, + size_t length = 0, + unsigned int flags = cudaMemAttachSingle +) +{ + return ::cudaStreamAttachMemAsync(stream, (void*)devPtr, length, flags); +} + +template +static __inline__ __host__ cudaError_t cudaMalloc( + T **devPtr, + size_t size +) +{ + return ::cudaMalloc((void**)(void*)devPtr, size); +} + +template +static __inline__ __host__ cudaError_t cudaMallocHost( + T **ptr, + size_t size, + unsigned int flags = 0 +) +{ + return cudaMallocHost((void**)(void*)ptr, size, flags); +} + +template +static __inline__ __host__ cudaError_t cudaMallocPitch( + T **devPtr, + size_t *pitch, + size_t width, + size_t height +) +{ + return ::cudaMallocPitch((void**)(void*)devPtr, pitch, width, height); +} + +/** + * \brief Allocate from a pool + * + * This is an alternate spelling for cudaMallocFromPoolAsync + * made available through operator overloading. + * + * \sa ::cudaMallocFromPoolAsync, + * \ref ::cudaMallocAsync(void** ptr, size_t size, cudaStream_t hStream) "cudaMallocAsync (C API)" + */ +static __inline__ __host__ cudaError_t cudaMallocAsync( + void **ptr, + size_t size, + cudaMemPool_t memPool, + cudaStream_t stream +) +{ + return ::cudaMallocFromPoolAsync(ptr, size, memPool, stream); +} + +template +static __inline__ __host__ cudaError_t cudaMallocAsync( + T **ptr, + size_t size, + cudaMemPool_t memPool, + cudaStream_t stream +) +{ + return ::cudaMallocFromPoolAsync((void**)(void*)ptr, size, memPool, stream); +} + +template +static __inline__ __host__ cudaError_t cudaMallocAsync( + T **ptr, + size_t size, + cudaStream_t stream +) +{ + return ::cudaMallocAsync((void**)(void*)ptr, size, stream); +} + +template +static __inline__ __host__ cudaError_t cudaMallocFromPoolAsync( + T **ptr, + size_t size, + cudaMemPool_t memPool, + cudaStream_t stream +) +{ + return ::cudaMallocFromPoolAsync((void**)(void*)ptr, size, memPool, stream); +} + +#if defined(__CUDACC__) + +/** + * \brief \hl Copies data to the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p src + * to the memory area \p offset bytes from the start of symbol + * \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToDevice. + * + * \param symbol - Device symbol reference + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_sync + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync + */ +template +static __inline__ __host__ cudaError_t cudaMemcpyToSymbol( + const T &symbol, + const void *src, + size_t count, + size_t offset = 0, + enum cudaMemcpyKind kind = cudaMemcpyHostToDevice +) +{ + return ::cudaMemcpyToSymbol((const void*)&symbol, src, count, offset, kind); +} + +/** + * \brief \hl Copies data to the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p src + * to the memory area \p offset bytes from the start of symbol + * \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToDevice. + * + * ::cudaMemcpyToSymbolAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If + * \p kind is ::cudaMemcpyHostToDevice and \p stream is non-zero, the copy + * may overlap with operations in other streams. + * + * \param symbol - Device symbol reference + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_async + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyFromSymbolAsync + */ +template +static __inline__ __host__ cudaError_t cudaMemcpyToSymbolAsync( + const T &symbol, + const void *src, + size_t count, + size_t offset = 0, + enum cudaMemcpyKind kind = cudaMemcpyHostToDevice, + cudaStream_t stream = 0 +) +{ + return ::cudaMemcpyToSymbolAsync((const void*)&symbol, src, count, offset, kind, stream); +} + +/** + * \brief \hl Copies data from the given symbol on the device + * + * Copies \p count bytes from the memory area \p offset bytes + * from the start of symbol \p symbol to the memory area pointed to by \p dst. + * The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost or ::cudaMemcpyDeviceToDevice. + * + * \param dst - Destination memory address + * \param symbol - Device symbol reference + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_sync + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync + */ +template +static __inline__ __host__ cudaError_t cudaMemcpyFromSymbol( + void *dst, + const T &symbol, + size_t count, + size_t offset = 0, + enum cudaMemcpyKind kind = cudaMemcpyDeviceToHost +) +{ + return ::cudaMemcpyFromSymbol(dst, (const void*)&symbol, count, offset, kind); +} + +/** + * \brief \hl Copies data from the given symbol on the device + * + * Copies \p count bytes from the memory area \p offset bytes + * from the start of symbol \p symbol to the memory area pointed to by \p dst. + * The memory areas may not overlap. \p symbol is a variable that resides in + * global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost or ::cudaMemcpyDeviceToDevice. + * + * ::cudaMemcpyFromSymbolAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally be + * associated to a stream by passing a non-zero \p stream argument. If \p kind + * is ::cudaMemcpyDeviceToHost and \p stream is non-zero, the copy may overlap + * with operations in other streams. + * + * \param dst - Destination memory address + * \param symbol - Device symbol reference + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_async + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync + */ +template +static __inline__ __host__ cudaError_t cudaMemcpyFromSymbolAsync( + void *dst, + const T &symbol, + size_t count, + size_t offset = 0, + enum cudaMemcpyKind kind = cudaMemcpyDeviceToHost, + cudaStream_t stream = 0 +) +{ + return ::cudaMemcpyFromSymbolAsync(dst, (const void*)&symbol, count, offset, kind, stream); +} + +/** + * \brief Creates a memcpy node to copy to a symbol on the device and adds it to a graph + * + * Creates a new memcpy node to copy to \p symbol and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p src to the memory area pointed to by \p offset bytes from the start + * of symbol \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyToSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeFromSymbol, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +template +static __inline__ __host__ cudaError_t cudaGraphAddMemcpyNodeToSymbol( + cudaGraphNode_t *pGraphNode, + cudaGraph_t graph, + const cudaGraphNode_t *pDependencies, + size_t numDependencies, + const T &symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphAddMemcpyNodeToSymbol(pGraphNode, graph, pDependencies, numDependencies, (const void*)&symbol, src, count, offset, kind); +} + +/** + * \brief Creates a memcpy node to copy from a symbol on the device and adds it to a graph + * + * Creates a new memcpy node to copy from \p symbol and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p offset bytes from the start of symbol \p symbol to the memory area + * pointed to by \p dst. The memory areas may not overlap. \p symbol is a variable + * that resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyFromSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeToSymbol, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +template +static __inline__ __host__ cudaError_t cudaGraphAddMemcpyNodeFromSymbol( + cudaGraphNode_t* pGraphNode, + cudaGraph_t graph, + const cudaGraphNode_t* pDependencies, + size_t numDependencies, + void* dst, + const T &symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphAddMemcpyNodeFromSymbol(pGraphNode, graph, pDependencies, numDependencies, dst, (const void*)&symbol, count, offset, kind); +} + +/** + * \brief Sets a memcpy node's parameters to copy to a symbol on the device + * + * Sets the parameters of memcpy node \p node to the copy described by the provided parameters. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p src to the memory area pointed to by \p offset bytes from the start + * of symbol \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * \param node - Node to set the parameters for + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyToSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +template +static __inline__ __host__ cudaError_t cudaGraphMemcpyNodeSetParamsToSymbol( + cudaGraphNode_t node, + const T &symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphMemcpyNodeSetParamsToSymbol(node, (const void*)&symbol, src, count, offset, kind); +} + +/** + * \brief Sets a memcpy node's parameters to copy from a symbol on the device + * + * Sets the parameters of memcpy node \p node to the copy described by the provided parameters. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p offset bytes from the start of symbol \p symbol to the memory area + * pointed to by \p dst. The memory areas may not overlap. \p symbol is a variable + * that resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * \param node - Node to set the parameters for + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyFromSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +template +static __inline__ __host__ cudaError_t cudaGraphMemcpyNodeSetParamsFromSymbol( + cudaGraphNode_t node, + void* dst, + const T &symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphMemcpyNodeSetParamsFromSymbol(node, dst, (const void*)&symbol, count, offset, kind); +} + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec to copy to a symbol on the device + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained the given params at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * \p src and \p symbol must be allocated from the same contexts as the original source and + * destination memory. The instantiation-time memory operands must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * the original memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeToSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphInstantiate, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams + */ +template +static __inline__ __host__ cudaError_t cudaGraphExecMemcpyNodeSetParamsToSymbol( + cudaGraphExec_t hGraphExec, + cudaGraphNode_t node, + const T &symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphExecMemcpyNodeSetParamsToSymbol(hGraphExec, node, (const void*)&symbol, src, count, offset, kind); +} + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec to copy from a symbol on the device + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained the given params at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * \p symbol and \p dst must be allocated from the same contexts as the original source and + * destination memory. The instantiation-time memory operands must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * the original memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeFromSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphInstantiate, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParamsToSymbol, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams + */ +template +static __inline__ __host__ cudaError_t cudaGraphExecMemcpyNodeSetParamsFromSymbol( + cudaGraphExec_t hGraphExec, + cudaGraphNode_t node, + void* dst, + const T &symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind) +{ + return ::cudaGraphExecMemcpyNodeSetParamsFromSymbol(hGraphExec, node, dst, (const void*)&symbol, count, offset, kind); +} + +// convenience function to avoid source breakage in c++ code +static __inline__ __host__ cudaError_t CUDARTAPI cudaGraphExecUpdate(cudaGraphExec_t hGraphExec, cudaGraph_t hGraph, cudaGraphNode_t *hErrorNode_out, enum cudaGraphExecUpdateResult *updateResult_out) +{ + cudaGraphExecUpdateResultInfo resultInfo; + cudaError_t status = cudaGraphExecUpdate(hGraphExec, hGraph, &resultInfo); + if (hErrorNode_out) { + *hErrorNode_out = resultInfo.errorNode; + } + if (updateResult_out) { + *updateResult_out = resultInfo.result; + } + return status; +} + +#if __cplusplus >= 201103L || (defined(_MSC_VER) && (_MSC_VER >= 1900)) + +/** + * \brief Creates a user object by wrapping a C++ object + * + * TODO detail + * + * \param object_out - Location to return the user object handle + * \param objectToWrap - This becomes the \ptr argument to ::cudaUserObjectCreate. A + * lambda will be passed for the \p destroy argument, which calls + * delete on this object pointer. + * \param initialRefcount - The initial refcount to create the object with, typically 1. The + * initial references are owned by the calling thread. + * \param flags - Currently it is required to pass cudaUserObjectNoDestructorSync, + * which is the only defined flag. This indicates that the destroy + * callback cannot be waited on by any CUDA API. Users requiring + * synchronization of the callback should signal its completion + * manually. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectCreate + */ +template +static __inline__ __host__ cudaError_t cudaUserObjectCreate( + cudaUserObject_t *object_out, + T *objectToWrap, + unsigned int initialRefcount, + unsigned int flags) +{ + return ::cudaUserObjectCreate( + object_out, + objectToWrap, + [](void *vpObj) { delete reinterpret_cast(vpObj); }, + initialRefcount, + flags); +} + +template +static __inline__ __host__ cudaError_t cudaUserObjectCreate( + cudaUserObject_t *object_out, + T *objectToWrap, + unsigned int initialRefcount, + cudaUserObjectFlags flags) +{ + return cudaUserObjectCreate(object_out, objectToWrap, initialRefcount, (unsigned int)flags); +} + +#endif + +/** + * \brief \hl Finds the address associated with a CUDA symbol + * + * Returns in \p *devPtr the address of symbol \p symbol on the device. + * \p symbol can either be a variable that resides in global or constant memory space. + * If \p symbol cannot be found, or if \p symbol is not declared + * in the global or constant memory space, \p *devPtr is unchanged and the error + * ::cudaErrorInvalidSymbol is returned. + * + * \param devPtr - Return device pointer associated with symbol + * \param symbol - Device symbol reference + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaGetSymbolAddress(void**, const void*) "cudaGetSymbolAddress (C API)", + * \ref ::cudaGetSymbolSize(size_t*, const T&) "cudaGetSymbolSize (C++ API)" + */ +template +static __inline__ __host__ cudaError_t cudaGetSymbolAddress( + void **devPtr, + const T &symbol +) +{ + return ::cudaGetSymbolAddress(devPtr, (const void*)&symbol); +} + +/** + * \brief \hl Finds the size of the object associated with a CUDA symbol + * + * Returns in \p *size the size of symbol \p symbol. \p symbol must be a + * variable that resides in global or constant memory space. + * If \p symbol cannot be found, or if \p symbol is not declared + * in global or constant memory space, \p *size is unchanged and the error + * ::cudaErrorInvalidSymbol is returned. + * + * \param size - Size of object associated with symbol + * \param symbol - Device symbol reference + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaGetSymbolAddress(void**, const T&) "cudaGetSymbolAddress (C++ API)", + * \ref ::cudaGetSymbolSize(size_t*, const void*) "cudaGetSymbolSize (C API)" + */ +template +static __inline__ __host__ cudaError_t cudaGetSymbolSize( + size_t *size, + const T &symbol +) +{ + return ::cudaGetSymbolSize(size, (const void*)&symbol); +} + +/** + * \brief \hl Sets the preferred cache configuration for a device function + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p cacheConfig the preferred cache configuration + * for the function specified via \p func. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute \p func. + * + * \p func must be a pointer to a function that executes on the device. + * The parameter specified by \p func must be declared as a \p __global__ + * function. If the specified function does not exist, + * then ::cudaErrorInvalidDeviceFunction is returned. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * + * \param func - device function pointer + * \param cacheConfig - Requested cache configuration + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C++ API)", + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, T*) "cudaFuncGetAttributes (C++ API)", + * ::cudaSetDoubleForDevice, + * ::cudaSetDoubleForHost, + * ::cudaThreadGetCacheConfig, + * ::cudaThreadSetCacheConfig + */ +template +static __inline__ __host__ cudaError_t cudaFuncSetCacheConfig( + T *func, + enum cudaFuncCache cacheConfig +) +{ + return ::cudaFuncSetCacheConfig((const void*)func, cacheConfig); +} + +template +static __inline__ +__CUDA_DEPRECATED +__host__ cudaError_t cudaFuncSetSharedMemConfig( + T *func, + enum cudaSharedMemConfig config +) +{ +#if defined(__GNUC__) +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wdeprecated-declarations" +#elif defined(_MSC_VER) +#pragma warning(suppress: 4996) +#endif + return ::cudaFuncSetSharedMemConfig((const void*)func, config); +#if defined(__GNUC__) +#pragma GCC diagnostic pop +#endif +} + +#endif // __CUDACC__ + +/** + * \brief Returns occupancy for a device function + * + * Returns in \p *numBlocks the maximum number of active blocks per + * streaming multiprocessor for the device function. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel function for which occupancy is calulated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ +template +static __inline__ __host__ cudaError_t cudaOccupancyMaxActiveBlocksPerMultiprocessor( + int *numBlocks, + T func, + int blockSize, + size_t dynamicSMemSize) +{ + return ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(numBlocks, (const void*)func, blockSize, dynamicSMemSize, cudaOccupancyDefault); +} + +/** + * \brief Returns occupancy for a device function with the specified flags + * + * Returns in \p *numBlocks the maximum number of active blocks per + * streaming multiprocessor for the device function. + * + * The \p flags parameter controls how special cases are handled. Valid flags include: + * + * - ::cudaOccupancyDefault: keeps the default behavior as + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * + * - ::cudaOccupancyDisableCachingOverride: suppresses the default behavior + * on platform where global caching affects occupancy. On such platforms, if caching + * is enabled, but per-block SM resource usage would result in zero occupancy, the + * occupancy calculator will calculate the occupancy as if caching is disabled. + * Setting this flag makes the occupancy calculator to return 0 in such cases. + * More information can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel function for which occupancy is calulated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * \param flags - Requested behavior for the occupancy calculator + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ +template +static __inline__ __host__ cudaError_t cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags( + int *numBlocks, + T func, + int blockSize, + size_t dynamicSMemSize, + unsigned int flags) +{ + return ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(numBlocks, (const void*)func, blockSize, dynamicSMemSize, flags); +} + +/** + * Helper functor for cudaOccupancyMaxPotentialBlockSize + */ +class __cudaOccupancyB2DHelper { + size_t n; +public: + inline __host__ CUDART_DEVICE __cudaOccupancyB2DHelper(size_t n_) : n(n_) {} + inline __host__ CUDART_DEVICE size_t operator()(int) + { + return n; + } +}; + +/** + * \brief Returns grid and block size that achieves maximum potential occupancy for a device function + * + * Returns in \p *minGridSize and \p *blocksize a suggested grid / + * block size pair that achieves the best potential occupancy + * (i.e. the maximum number of active warps with the smallest number + * of blocks). + * + * The \p flags parameter controls how special cases are handled. Valid flags include: + * + * - ::cudaOccupancyDefault: keeps the default behavior as + * ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * + * - ::cudaOccupancyDisableCachingOverride: This flag suppresses the default behavior + * on platform where global caching affects occupancy. On such platforms, if caching + * is enabled, but per-block SM resource usage would result in zero occupancy, the + * occupancy calculator will calculate the occupancy as if caching is disabled. + * Setting this flag makes the occupancy calculator to return 0 in such cases. + * More information can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * \param minGridSize - Returned minimum grid size needed to achieve the best potential occupancy + * \param blockSize - Returned block size + * \param func - Device function symbol + * \param blockSizeToDynamicSMemSize - A unary function / functor that takes block size, and returns the size, in bytes, of dynamic shared memory needed for a block + * \param blockSizeLimit - The maximum block size \p func is designed to work with. 0 means no limit. + * \param flags - Requested behavior for the occupancy calculator + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ + +template +static __inline__ __host__ CUDART_DEVICE cudaError_t cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags( + int *minGridSize, + int *blockSize, + T func, + UnaryFunction blockSizeToDynamicSMemSize, + int blockSizeLimit = 0, + unsigned int flags = 0) +{ + cudaError_t status; + + // Device and function properties + int device; + struct cudaFuncAttributes attr; + + // Limits + int maxThreadsPerMultiProcessor; + int warpSize; + int devMaxThreadsPerBlock; + int multiProcessorCount; + int funcMaxThreadsPerBlock; + int occupancyLimit; + int granularity; + + // Recorded maximum + int maxBlockSize = 0; + int numBlocks = 0; + int maxOccupancy = 0; + + // Temporary + int blockSizeToTryAligned; + int blockSizeToTry; + int blockSizeLimitAligned; + int occupancyInBlocks; + int occupancyInThreads; + size_t dynamicSMemSize; + + /////////////////////////// + // Check user input + /////////////////////////// + + if (!minGridSize || !blockSize || !func) { + return cudaErrorInvalidValue; + } + + ////////////////////////////////////////////// + // Obtain device and function properties + ////////////////////////////////////////////// + + status = ::cudaGetDevice(&device); + if (status != cudaSuccess) { + return status; + } + + status = cudaDeviceGetAttribute( + &maxThreadsPerMultiProcessor, + cudaDevAttrMaxThreadsPerMultiProcessor, + device); + if (status != cudaSuccess) { + return status; + } + + status = cudaDeviceGetAttribute( + &warpSize, + cudaDevAttrWarpSize, + device); + if (status != cudaSuccess) { + return status; + } + + status = cudaDeviceGetAttribute( + &devMaxThreadsPerBlock, + cudaDevAttrMaxThreadsPerBlock, + device); + if (status != cudaSuccess) { + return status; + } + + status = cudaDeviceGetAttribute( + &multiProcessorCount, + cudaDevAttrMultiProcessorCount, + device); + if (status != cudaSuccess) { + return status; + } + + status = cudaFuncGetAttributes(&attr, func); + if (status != cudaSuccess) { + return status; + } + + funcMaxThreadsPerBlock = attr.maxThreadsPerBlock; + + ///////////////////////////////////////////////////////////////////////////////// + // Try each block size, and pick the block size with maximum occupancy + ///////////////////////////////////////////////////////////////////////////////// + + occupancyLimit = maxThreadsPerMultiProcessor; + granularity = warpSize; + + if (blockSizeLimit == 0) { + blockSizeLimit = devMaxThreadsPerBlock; + } + + if (devMaxThreadsPerBlock < blockSizeLimit) { + blockSizeLimit = devMaxThreadsPerBlock; + } + + if (funcMaxThreadsPerBlock < blockSizeLimit) { + blockSizeLimit = funcMaxThreadsPerBlock; + } + + blockSizeLimitAligned = ((blockSizeLimit + (granularity - 1)) / granularity) * granularity; + + for (blockSizeToTryAligned = blockSizeLimitAligned; blockSizeToTryAligned > 0; blockSizeToTryAligned -= granularity) { + // This is needed for the first iteration, because + // blockSizeLimitAligned could be greater than blockSizeLimit + // + if (blockSizeLimit < blockSizeToTryAligned) { + blockSizeToTry = blockSizeLimit; + } else { + blockSizeToTry = blockSizeToTryAligned; + } + + dynamicSMemSize = blockSizeToDynamicSMemSize(blockSizeToTry); + + status = cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags( + &occupancyInBlocks, + func, + blockSizeToTry, + dynamicSMemSize, + flags); + + if (status != cudaSuccess) { + return status; + } + + occupancyInThreads = blockSizeToTry * occupancyInBlocks; + + if (occupancyInThreads > maxOccupancy) { + maxBlockSize = blockSizeToTry; + numBlocks = occupancyInBlocks; + maxOccupancy = occupancyInThreads; + } + + // Early out if we have reached the maximum + // + if (occupancyLimit == maxOccupancy) { + break; + } + } + + /////////////////////////// + // Return best available + /////////////////////////// + + // Suggested min grid size to achieve a full machine launch + // + *minGridSize = numBlocks * multiProcessorCount; + *blockSize = maxBlockSize; + + return status; +} + +/** + * \brief Returns grid and block size that achieves maximum potential occupancy for a device function + * + * Returns in \p *minGridSize and \p *blocksize a suggested grid / + * block size pair that achieves the best potential occupancy + * (i.e. the maximum number of active warps with the smallest number + * of blocks). + * + * \param minGridSize - Returned minimum grid size needed to achieve the best potential occupancy + * \param blockSize - Returned block size + * \param func - Device function symbol + * \param blockSizeToDynamicSMemSize - A unary function / functor that takes block size, and returns the size, in bytes, of dynamic shared memory needed for a block + * \param blockSizeLimit - The maximum block size \p func is designed to work with. 0 means no limit. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ + +template +static __inline__ __host__ CUDART_DEVICE cudaError_t cudaOccupancyMaxPotentialBlockSizeVariableSMem( + int *minGridSize, + int *blockSize, + T func, + UnaryFunction blockSizeToDynamicSMemSize, + int blockSizeLimit = 0) +{ + return cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(minGridSize, blockSize, func, blockSizeToDynamicSMemSize, blockSizeLimit, cudaOccupancyDefault); +} + +/** + * \brief Returns grid and block size that achieves maximum potential occupancy for a device function + * + * Returns in \p *minGridSize and \p *blocksize a suggested grid / + * block size pair that achieves the best potential occupancy + * (i.e. the maximum number of active warps with the smallest number + * of blocks). + * + * Use \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem if the + * amount of per-block dynamic shared memory changes with different + * block sizes. + * + * \param minGridSize - Returned minimum grid size needed to achieve the best potential occupancy + * \param blockSize - Returned block size + * \param func - Device function symbol + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * \param blockSizeLimit - The maximum block size \p func is designed to work with. 0 means no limit. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ +template +static __inline__ __host__ CUDART_DEVICE cudaError_t cudaOccupancyMaxPotentialBlockSize( + int *minGridSize, + int *blockSize, + T func, + size_t dynamicSMemSize = 0, + int blockSizeLimit = 0) +{ + return cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(minGridSize, blockSize, func, __cudaOccupancyB2DHelper(dynamicSMemSize), blockSizeLimit, cudaOccupancyDefault); +} + +/** + * \brief Returns dynamic shared memory available per block when launching \p numBlocks blocks on SM. + * + * Returns in \p *dynamicSmemSize the maximum size of dynamic shared memory to allow \p numBlocks blocks per SM. + * + * \param dynamicSmemSize - Returned maximum dynamic shared memory + * \param func - Kernel function for which occupancy is calculated + * \param numBlocks - Number of blocks to fit on SM + * \param blockSize - Size of the block + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxPotentialBlockSizeWithFlags + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + */ +template +static __inline__ __host__ cudaError_t cudaOccupancyAvailableDynamicSMemPerBlock( + size_t *dynamicSmemSize, + T func, + int numBlocks, + int blockSize) +{ + return ::cudaOccupancyAvailableDynamicSMemPerBlock(dynamicSmemSize, (const void*)func, numBlocks, blockSize); +} + +/** + * \brief Returns grid and block size that achived maximum potential occupancy for a device function with the specified flags + * + * Returns in \p *minGridSize and \p *blocksize a suggested grid / + * block size pair that achieves the best potential occupancy + * (i.e. the maximum number of active warps with the smallest number + * of blocks). + * + * The \p flags parameter controls how special cases are handle. Valid flags include: + * + * - ::cudaOccupancyDefault: keeps the default behavior as + * ::cudaOccupancyMaxPotentialBlockSize + * + * - ::cudaOccupancyDisableCachingOverride: This flag suppresses the default behavior + * on platform where global caching affects occupancy. On such platforms, if caching + * is enabled, but per-block SM resource usage would result in zero occupancy, the + * occupancy calculator will calculate the occupancy as if caching is disabled. + * Setting this flag makes the occupancy calculator to return 0 in such cases. + * More information can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * Use \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem if the + * amount of per-block dynamic shared memory changes with different + * block sizes. + * + * \param minGridSize - Returned minimum grid size needed to achieve the best potential occupancy + * \param blockSize - Returned block size + * \param func - Device function symbol + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * \param blockSizeLimit - The maximum block size \p func is designed to work with. 0 means no limit. + * \param flags - Requested behavior for the occupancy calculator + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxPotentialBlockSize + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMem + * \sa ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags + * \sa ::cudaOccupancyAvailableDynamicSMemPerBlock + */ +template +static __inline__ __host__ CUDART_DEVICE cudaError_t cudaOccupancyMaxPotentialBlockSizeWithFlags( + int *minGridSize, + int *blockSize, + T func, + size_t dynamicSMemSize = 0, + int blockSizeLimit = 0, + unsigned int flags = 0) +{ + return cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(minGridSize, blockSize, func, __cudaOccupancyB2DHelper(dynamicSMemSize), blockSizeLimit, flags); +} + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum cluster size in \p *clusterSize. + * + * The cluster dimensions in \p config are ignored. If func has a required + * cluster size set (see ::cudaFuncGetAttributes),\p *clusterSize will reflect + * the required cluster size. + * + * By default this function will always return a value that's portable on + * future hardware. A higher value may be returned if the kernel function + * allows non-portable cluster sizes. + * + * This function will respect the compile time launch bounds. + * + * \param clusterSize - Returned maximum cluster size that can be launched + * for the given kernel function and launch configuration + * \param func - Kernel function for which maximum cluster + * size is calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaFuncGetAttributes + */ +template +static __inline__ __host__ cudaError_t cudaOccupancyMaxPotentialClusterSize( + int *clusterSize, + T *func, + const cudaLaunchConfig_t *config) +{ + return ::cudaOccupancyMaxPotentialClusterSize(clusterSize, (const void*)func, config); +} + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum number of clusters that could co-exist + * on the target device in \p *numClusters. + * + * If the function has required cluster size already set (see + * ::cudaFuncGetAttributes), the cluster size from config must either be + * unspecified or match the required size. + * Without required sizes, the cluster size must be specified in config, + * else the function will return an error. + * + * Note that various attributes of the kernel function may affect occupancy + * calculation. Runtime environment may affect how the hardware schedules + * the clusters, so the calculated occupancy is not guaranteed to be achievable. + * + * \param numClusters - Returned maximum number of clusters that + * could co-exist on the target device + * \param func - Kernel function for which maximum number + * of clusters are calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidClusterSize, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaFuncGetAttributes + */ +template +static __inline__ __host__ cudaError_t cudaOccupancyMaxActiveClusters( + int *numClusters, + T *func, + const cudaLaunchConfig_t *config) +{ + return ::cudaOccupancyMaxActiveClusters(numClusters, (const void*)func, config); +} + +#if defined __CUDACC__ + +/** + * \brief \hl Find out attributes for a given function + * + * This function obtains the attributes of a function specified via \p entry. + * The parameter \p entry must be a pointer to a function that executes + * on the device. The parameter specified by \p entry must be declared as a \p __global__ + * function. The fetched attributes are placed in \p attr. If the specified + * function does not exist, then ::cudaErrorInvalidDeviceFunction is returned. + * + * Note that some function attributes such as + * \ref ::cudaFuncAttributes::maxThreadsPerBlock "maxThreadsPerBlock" + * may vary based on the device that is currently being used. + * + * \param attr - Return pointer to function's attributes + * \param entry - Function to get attributes of + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C++ API)", + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + * ::cudaSetDoubleForDevice, + * ::cudaSetDoubleForHost + */ +template +static __inline__ __host__ cudaError_t cudaFuncGetAttributes( + struct cudaFuncAttributes *attr, + T *entry +) +{ + return ::cudaFuncGetAttributes(attr, (const void*)entry); +} + +/** + * \brief \hl Set attributes for a given function + * + * This function sets the attributes of a function specified via \p entry. + * The parameter \p entry must be a pointer to a function that executes + * on the device. The parameter specified by \p entry must be declared as a \p __global__ + * function. The enumeration defined by \p attr is set to the value defined by \p value. + * If the specified function does not exist, then ::cudaErrorInvalidDeviceFunction is returned. + * If the specified attribute cannot be written, or if the value is incorrect, + * then ::cudaErrorInvalidValue is returned. + * + * Valid values for \p attr are: + * - ::cudaFuncAttributeMaxDynamicSharedMemorySize - The requested maximum size in bytes of dynamically-allocated shared memory. The sum of this value and the function attribute ::sharedSizeBytes + * cannot exceed the device attribute ::cudaDevAttrMaxSharedMemoryPerBlockOptin. The maximal size of requestable dynamic shared memory may differ by GPU architecture. + * - ::cudaFuncAttributePreferredSharedMemoryCarveout - On devices where the L1 cache and shared memory use the same hardware resources, + * this sets the shared memory carveout preference, in percent of the total shared memory. See ::cudaDevAttrMaxSharedMemoryPerMultiprocessor. + * This is only a hint, and the driver can choose a different ratio if required to execute the function. + * - ::cudaFuncAttributeRequiredClusterWidth: The required cluster width in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return cudaErrorNotPermitted. + * - ::cudaFuncAttributeRequiredClusterHeight: The required cluster height in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return cudaErrorNotPermitted. + * - ::cudaFuncAttributeRequiredClusterDepth: The required cluster depth in + * blocks. The width, height, and depth values must either all be 0 or all be + * positive. The validity of the cluster dimensions is checked at launch time. + * If the value is set during compile time, it cannot be set at runtime. + * Setting it at runtime will return cudaErrorNotPermitted. + * - ::cudaFuncAttributeClusterSchedulingPolicyPreference: The block + * scheduling policy of a function. The value type is cudaClusterSchedulingPolicy. + * + * \param entry - Function to get attributes of + * \param attr - Attribute to set + * \param value - Value to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C++ API)", + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + * ::cudaSetDoubleForDevice, + * ::cudaSetDoubleForHost + */ +template +static __inline__ __host__ cudaError_t cudaFuncSetAttribute( + T *entry, + enum cudaFuncAttribute attr, + int value +) +{ + return ::cudaFuncSetAttribute((const void*)entry, attr, value); +} + +/** + * \brief Returns the function name for a device entry function pointer. + * + * Returns in \p **name the function name associated with the symbol \p func . + * The function name is returned as a null-terminated string. This API may + * return a mangled name if the function is not declared as having C linkage. + * If \p **name is NULL, ::cudaErrorInvalidValue is returned. If \p func is + * not a device entry function, ::cudaErrorInvalidDeviceFunction is returned. + * + * \param name - The returned name of the function + * \param func - The function pointer to retrieve name for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaFuncGetName(const char **name, const void *func) "cudaFuncGetName (C API)" + */ +template +static __inline__ __host__ cudaError_t CUDARTAPI cudaFuncGetName( + const char **name, + const T *func +) +{ + return ::cudaFuncGetName(name, (const void *)func); +} + +/** + * \brief Get pointer to device kernel that matches entry function \p entryFuncAddr + * + * Returns in \p kernelPtr the device kernel corresponding to the entry function \p entryFuncAddr. + * + * \param kernelPtr - Returns the device kernel + * \param entryFuncAddr - Address of device entry function to search kernel for + * + * \return + * ::cudaSuccess + * + * \sa + * \ref ::cudaGetKernel(cudaKernel_t *kernelPtr, const void *entryFuncAddr) "cudaGetKernel (C API)" + */ +template +static __inline__ __host__ cudaError_t cudaGetKernel( + cudaKernel_t *kernelPtr, + const T *entryFuncAddr +) +{ + return ::cudaGetKernel(kernelPtr, (const void *)entryFuncAddr); +} + +#endif /* __CUDACC__ */ + +/** @} */ /* END CUDART_HIGHLEVEL */ + +#endif /* __cplusplus && !__CUDACC_RTC__ */ + +#if !defined(__CUDACC_RTC__) +#if defined(__GNUC__) +#if defined(__clang__) || (!defined(__PGIC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))) +#pragma GCC diagnostic pop +#endif +#elif defined(_MSC_VER) +#pragma warning(pop) +#endif +#endif + +#undef EXCLUDE_FROM_RTC +#undef __CUDA_DEPRECATED + +#if defined(__UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_H__) +#undef __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#undef __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_H__ +#endif + +#endif /* !__CUDA_RUNTIME_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime_api.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime_api.h new file mode 100644 index 0000000000000000000000000000000000000000..64c92003b6f30d4050eb7f888db3b74e99492f24 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_runtime_api.h @@ -0,0 +1,14059 @@ +/* + * Copyright 1993-2018 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + + +#if !defined(__CUDA_RUNTIME_API_H__) +#define __CUDA_RUNTIME_API_H__ + +#if !defined(__CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__) +#define __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#define __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_API_H__ +#endif + +/** + * \latexonly + * \page sync_async API synchronization behavior + * + * \section memcpy_sync_async_behavior Memcpy + * The API provides memcpy/memset functions in both synchronous and asynchronous forms, + * the latter having an \e "Async" suffix. This is a misnomer as each function + * may exhibit synchronous or asynchronous behavior depending on the arguments + * passed to the function. In the reference documentation, each memcpy function is + * categorized as \e synchronous or \e asynchronous, corresponding to the definitions + * below. + * + * \subsection MemcpySynchronousBehavior Synchronous + * + *
    + *
  1. For transfers from pageable host memory to device memory, a stream sync is performed + * before the copy is initiated. The function will return once the pageable + * buffer has been copied to the staging memory for DMA transfer to device memory, + * but the DMA to final destination may not have completed. + * + *
  2. For transfers from pinned host memory to device memory, the function is synchronous + * with respect to the host. + * + *
  3. For transfers from device to either pageable or pinned host memory, the function returns + * only once the copy has completed. + * + *
  4. For transfers from device memory to device memory, no host-side synchronization is + * performed. + * + *
  5. For transfers from any host memory to any host memory, the function is fully + * synchronous with respect to the host. + *
+ * + * \subsection MemcpyAsynchronousBehavior Asynchronous + * + *
    + *
  1. For transfers between device memory and pageable host memory, the function might + * be synchronous with respect to host. + * + *
  2. For transfers from any host memory to any host memory, the function is fully + * synchronous with respect to the host. + * + *
  3. If pageable memory must first be staged to pinned memory, the driver may + * synchronize with the stream and stage the copy into pinned memory. + * + *
  4. For all other transfers, the function should be fully asynchronous. + *
+ * + * \section memset_sync_async_behavior Memset + * The cudaMemset functions are asynchronous with respect to the host + * except when the target memory is pinned host memory. The \e Async + * versions are always asynchronous with respect to the host. + * + * \section kernel_launch_details Kernel Launches + * Kernel launches are asynchronous with respect to the host. Details of + * concurrent kernel execution and data transfers can be found in the CUDA + * Programmers Guide. + * + * \endlatexonly + */ + +/** + * There are two levels for the runtime API. + * + * The C API (cuda_runtime_api.h) is + * a C-style interface that does not require compiling with \p nvcc. + * + * The \ref CUDART_HIGHLEVEL "C++ API" (cuda_runtime.h) is a + * C++-style interface built on top of the C API. It wraps some of the + * C API routines, using overloading, references and default arguments. + * These wrappers can be used from C++ code and can be compiled with any C++ + * compiler. The C++ API also has some CUDA-specific wrappers that wrap + * C API routines that deal with symbols, textures, and device functions. + * These wrappers require the use of \p nvcc because they depend on code being + * generated by the compiler. For example, the execution configuration syntax + * to invoke kernels is only available in source code compiled with \p nvcc. + */ + +/** CUDA Runtime API Version */ +#define CUDART_VERSION 12040 + +#if defined(__CUDA_API_VER_MAJOR__) && defined(__CUDA_API_VER_MINOR__) +# define __CUDART_API_VERSION ((__CUDA_API_VER_MAJOR__ * 1000) + (__CUDA_API_VER_MINOR__ * 10)) +#else +# define __CUDART_API_VERSION CUDART_VERSION +#endif + +#ifndef __DOXYGEN_ONLY__ +#include "crt/host_defines.h" +#endif +#include "builtin_types.h" + +#if !defined(__CUDACC_RTC_MINIMAL__) && ((defined(__CUDACC_RDC__) || defined(__CUDACC_EWP__) || !defined(__CUDACC_RTC__))) +#include "cuda_device_runtime_api.h" +#endif /* !defined(__CUDACC_RTC_MINIMAL__) && (defined(__CUDACC_RDC__) || defined(__CUDACC_EWP__) || !defined(__CUDACC_RTC__)) */ + + +#ifndef __CUDACC_RTC_MINIMAL__ +#if defined(CUDA_API_PER_THREAD_DEFAULT_STREAM) || defined(__CUDA_API_VERSION_INTERNAL) + #define __CUDART_API_PER_THREAD_DEFAULT_STREAM + #define __CUDART_API_PTDS(api) api ## _ptds + #define __CUDART_API_PTSZ(api) api ## _ptsz +#else + #define __CUDART_API_PTDS(api) api + #define __CUDART_API_PTSZ(api) api +#endif + +#define cudaSignalExternalSemaphoresAsync __CUDART_API_PTSZ(cudaSignalExternalSemaphoresAsync_v2) +#define cudaWaitExternalSemaphoresAsync __CUDART_API_PTSZ(cudaWaitExternalSemaphoresAsync_v2) + + #define cudaStreamGetCaptureInfo __CUDART_API_PTSZ(cudaStreamGetCaptureInfo_v2) + +#define cudaGetDeviceProperties cudaGetDeviceProperties_v2 + +#if defined(__CUDART_API_PER_THREAD_DEFAULT_STREAM) + #define cudaMemcpy __CUDART_API_PTDS(cudaMemcpy) + #define cudaMemcpyToSymbol __CUDART_API_PTDS(cudaMemcpyToSymbol) + #define cudaMemcpyFromSymbol __CUDART_API_PTDS(cudaMemcpyFromSymbol) + #define cudaMemcpy2D __CUDART_API_PTDS(cudaMemcpy2D) + #define cudaMemcpyToArray __CUDART_API_PTDS(cudaMemcpyToArray) + #define cudaMemcpy2DToArray __CUDART_API_PTDS(cudaMemcpy2DToArray) + #define cudaMemcpyFromArray __CUDART_API_PTDS(cudaMemcpyFromArray) + #define cudaMemcpy2DFromArray __CUDART_API_PTDS(cudaMemcpy2DFromArray) + #define cudaMemcpyArrayToArray __CUDART_API_PTDS(cudaMemcpyArrayToArray) + #define cudaMemcpy2DArrayToArray __CUDART_API_PTDS(cudaMemcpy2DArrayToArray) + #define cudaMemcpy3D __CUDART_API_PTDS(cudaMemcpy3D) + #define cudaMemcpy3DPeer __CUDART_API_PTDS(cudaMemcpy3DPeer) + #define cudaMemset __CUDART_API_PTDS(cudaMemset) + #define cudaMemset2D __CUDART_API_PTDS(cudaMemset2D) + #define cudaMemset3D __CUDART_API_PTDS(cudaMemset3D) + #define cudaGraphInstantiateWithParams __CUDART_API_PTSZ(cudaGraphInstantiateWithParams) + #define cudaGraphUpload __CUDART_API_PTSZ(cudaGraphUpload) + #define cudaGraphLaunch __CUDART_API_PTSZ(cudaGraphLaunch) + #define cudaStreamBeginCapture __CUDART_API_PTSZ(cudaStreamBeginCapture) + #define cudaStreamBeginCaptureToGraph __CUDART_API_PTSZ(cudaStreamBeginCaptureToGraph) + #define cudaStreamEndCapture __CUDART_API_PTSZ(cudaStreamEndCapture) + #define cudaStreamGetCaptureInfo_v3 __CUDART_API_PTSZ(cudaStreamGetCaptureInfo_v3) + #define cudaStreamUpdateCaptureDependencies __CUDART_API_PTSZ(cudaStreamUpdateCaptureDependencies) + #define cudaStreamUpdateCaptureDependencies_v2 __CUDART_API_PTSZ(cudaStreamUpdateCaptureDependencies_v2) + #define cudaStreamIsCapturing __CUDART_API_PTSZ(cudaStreamIsCapturing) + #define cudaMemcpyAsync __CUDART_API_PTSZ(cudaMemcpyAsync) + #define cudaMemcpyToSymbolAsync __CUDART_API_PTSZ(cudaMemcpyToSymbolAsync) + #define cudaMemcpyFromSymbolAsync __CUDART_API_PTSZ(cudaMemcpyFromSymbolAsync) + #define cudaMemcpy2DAsync __CUDART_API_PTSZ(cudaMemcpy2DAsync) + #define cudaMemcpyToArrayAsync __CUDART_API_PTSZ(cudaMemcpyToArrayAsync) + #define cudaMemcpy2DToArrayAsync __CUDART_API_PTSZ(cudaMemcpy2DToArrayAsync) + #define cudaMemcpyFromArrayAsync __CUDART_API_PTSZ(cudaMemcpyFromArrayAsync) + #define cudaMemcpy2DFromArrayAsync __CUDART_API_PTSZ(cudaMemcpy2DFromArrayAsync) + #define cudaMemcpy3DAsync __CUDART_API_PTSZ(cudaMemcpy3DAsync) + #define cudaMemcpy3DPeerAsync __CUDART_API_PTSZ(cudaMemcpy3DPeerAsync) + #define cudaMemsetAsync __CUDART_API_PTSZ(cudaMemsetAsync) + #define cudaMemset2DAsync __CUDART_API_PTSZ(cudaMemset2DAsync) + #define cudaMemset3DAsync __CUDART_API_PTSZ(cudaMemset3DAsync) + #define cudaStreamQuery __CUDART_API_PTSZ(cudaStreamQuery) + #define cudaStreamGetFlags __CUDART_API_PTSZ(cudaStreamGetFlags) + #define cudaStreamGetId __CUDART_API_PTSZ(cudaStreamGetId) + #define cudaStreamGetPriority __CUDART_API_PTSZ(cudaStreamGetPriority) + #define cudaEventRecord __CUDART_API_PTSZ(cudaEventRecord) + #define cudaEventRecordWithFlags __CUDART_API_PTSZ(cudaEventRecordWithFlags) + #define cudaStreamWaitEvent __CUDART_API_PTSZ(cudaStreamWaitEvent) + #define cudaStreamAddCallback __CUDART_API_PTSZ(cudaStreamAddCallback) + #define cudaStreamAttachMemAsync __CUDART_API_PTSZ(cudaStreamAttachMemAsync) + #define cudaStreamSynchronize __CUDART_API_PTSZ(cudaStreamSynchronize) + #define cudaLaunchKernel __CUDART_API_PTSZ(cudaLaunchKernel) + #define cudaLaunchKernelExC __CUDART_API_PTSZ(cudaLaunchKernelExC) + #define cudaLaunchHostFunc __CUDART_API_PTSZ(cudaLaunchHostFunc) + #define cudaMemPrefetchAsync __CUDART_API_PTSZ(cudaMemPrefetchAsync) + #define cudaMemPrefetchAsync_v2 __CUDART_API_PTSZ(cudaMemPrefetchAsync_v2) + #define cudaLaunchCooperativeKernel __CUDART_API_PTSZ(cudaLaunchCooperativeKernel) + #define cudaStreamCopyAttributes __CUDART_API_PTSZ(cudaStreamCopyAttributes) + #define cudaStreamGetAttribute __CUDART_API_PTSZ(cudaStreamGetAttribute) + #define cudaStreamSetAttribute __CUDART_API_PTSZ(cudaStreamSetAttribute) + #define cudaMallocAsync __CUDART_API_PTSZ(cudaMallocAsync) + #define cudaFreeAsync __CUDART_API_PTSZ(cudaFreeAsync) + #define cudaMallocFromPoolAsync __CUDART_API_PTSZ(cudaMallocFromPoolAsync) + #define cudaGetDriverEntryPoint __CUDART_API_PTSZ(cudaGetDriverEntryPoint) +#endif + +#endif /* __CUDACC_RTC_MINIMAL__ */ + +/** \cond impl_private */ +#if !defined(__dv) + +#if defined(__cplusplus) + +#define __dv(v) \ + = v + +#else /* __cplusplus */ + +#define __dv(v) + +#endif /* __cplusplus */ + +#endif /* !__dv */ +/** \endcond impl_private */ + +#if (defined(_NVHPC_CUDA) || !defined(__CUDA_ARCH__) || (__CUDA_ARCH__ >= 350)) /** Visible to SM>=3.5 and "__host__ __device__" only **/ + +#define CUDART_DEVICE __device__ + +#else + +#define CUDART_DEVICE + +#endif /** CUDART_DEVICE */ + +#if !defined(__CUDACC_RTC__) +#define EXCLUDE_FROM_RTC + +/** \cond impl_private */ +#if defined(__DOXYGEN_ONLY__) || defined(CUDA_ENABLE_DEPRECATED) +#define __CUDA_DEPRECATED +#elif defined(_MSC_VER) +#define __CUDA_DEPRECATED __declspec(deprecated) +#elif defined(__GNUC__) +#define __CUDA_DEPRECATED __attribute__((deprecated)) +#else +#define __CUDA_DEPRECATED +#endif +/** \endcond impl_private */ + +#if defined(__cplusplus) +extern "C" { +#endif /* __cplusplus */ + +/** + * \defgroup CUDART_DEVICE Device Management + * + * ___MANBRIEF___ device management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the device management functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Destroy all allocations and reset all state on the current device + * in the current process. + * + * Explicitly destroys and cleans up all resources associated with the current + * device in the current process. It is the caller's responsibility to ensure + * that the resources are not accessed or passed in subsequent API calls and + * doing so will result in undefined behavior. These resources include CUDA types + * such as ::cudaStream_t, ::cudaEvent_t, ::cudaArray_t, ::cudaMipmappedArray_t, + * ::cudaTextureObject_t, ::cudaSurfaceObject_t, ::textureReference, ::surfaceReference, + * ::cudaExternalMemory_t, ::cudaExternalSemaphore_t and ::cudaGraphicsResource_t. + * Any subsequent API call to this device will reinitialize the device. + * + * Note that this function will reset the device immediately. It is the caller's + * responsibility to ensure that the device is not being accessed by any + * other host threads from the process when this function is called. + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSynchronize + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceReset(void); + +/** + * \brief Wait for compute device to finish + * + * Blocks until the device has completed all preceding requested tasks. + * ::cudaDeviceSynchronize() returns an error if one of the preceding tasks + * has failed. If the ::cudaDeviceScheduleBlockingSync flag was set for + * this device, the host thread will block until the device has finished + * its work. + * + * \return + * ::cudaSuccess + * \note_device_sync_deprecated + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceReset, + * ::cuCtxSynchronize + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceSynchronize(void); + +/** + * \brief Set resource limits + * + * Setting \p limit to \p value is a request by the application to update + * the current limit maintained by the device. The driver is free to + * modify the requested value to meet h/w requirements (this could be + * clamping to minimum or maximum values, rounding up to nearest element + * size, etc). The application can use ::cudaDeviceGetLimit() to find out + * exactly what the limit has been set to. + * + * Setting each ::cudaLimit has its own specific restrictions, so each is + * discussed here. + * + * - ::cudaLimitStackSize controls the stack size in bytes of each GPU thread. + * + * - ::cudaLimitPrintfFifoSize controls the size in bytes of the shared FIFO + * used by the ::printf() device system call. Setting + * ::cudaLimitPrintfFifoSize must not be performed after launching any kernel + * that uses the ::printf() device system call - in such case + * ::cudaErrorInvalidValue will be returned. + * + * - ::cudaLimitMallocHeapSize controls the size in bytes of the heap used by + * the ::malloc() and ::free() device system calls. Setting + * ::cudaLimitMallocHeapSize must not be performed after launching any kernel + * that uses the ::malloc() or ::free() device system calls - in such case + * ::cudaErrorInvalidValue will be returned. + * + * - ::cudaLimitDevRuntimeSyncDepth controls the maximum nesting depth of a + * grid at which a thread can safely call ::cudaDeviceSynchronize(). Setting + * this limit must be performed before any launch of a kernel that uses the + * device runtime and calls ::cudaDeviceSynchronize() above the default sync + * depth, two levels of grids. Calls to ::cudaDeviceSynchronize() will fail + * with error code ::cudaErrorSyncDepthExceeded if the limitation is + * violated. This limit can be set smaller than the default or up the maximum + * launch depth of 24. When setting this limit, keep in mind that additional + * levels of sync depth require the runtime to reserve large amounts of + * device memory which can no longer be used for user allocations. If these + * reservations of device memory fail, ::cudaDeviceSetLimit will return + * ::cudaErrorMemoryAllocation, and the limit can be reset to a lower value. + * This limit is only applicable to devices of compute capability < 9.0. + * Attempting to set this limit on devices of other compute capability will + * results in error ::cudaErrorUnsupportedLimit being returned. + * + * - ::cudaLimitDevRuntimePendingLaunchCount controls the maximum number of + * outstanding device runtime launches that can be made from the current + * device. A grid is outstanding from the point of launch up until the grid + * is known to have been completed. Device runtime launches which violate + * this limitation fail and return ::cudaErrorLaunchPendingCountExceeded when + * ::cudaGetLastError() is called after launch. If more pending launches than + * the default (2048 launches) are needed for a module using the device + * runtime, this limit can be increased. Keep in mind that being able to + * sustain additional pending launches will require the runtime to reserve + * larger amounts of device memory upfront which can no longer be used for + * allocations. If these reservations fail, ::cudaDeviceSetLimit will return + * ::cudaErrorMemoryAllocation, and the limit can be reset to a lower value. + * This limit is only applicable to devices of compute capability 3.5 and + * higher. Attempting to set this limit on devices of compute capability less + * than 3.5 will result in the error ::cudaErrorUnsupportedLimit being + * returned. + * + * - ::cudaLimitMaxL2FetchGranularity controls the L2 cache fetch granularity. + * Values can range from 0B to 128B. This is purely a performance hint and + * it can be ignored or clamped depending on the platform. + * + * - ::cudaLimitPersistingL2CacheSize controls size in bytes available + * for persisting L2 cache. This is purely a performance hint and it + * can be ignored or clamped depending on the platform. + * + * \param limit - Limit to set + * \param value - Size of limit + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnsupportedLimit, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceGetLimit, + * ::cuCtxSetLimit + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceSetLimit(enum cudaLimit limit, size_t value); + +/** + * \brief Return resource limits + * + * Returns in \p *pValue the current size of \p limit. The following ::cudaLimit values are supported. + * - ::cudaLimitStackSize is the stack size in bytes of each GPU thread. + * - ::cudaLimitPrintfFifoSize is the size in bytes of the shared FIFO used by the + * ::printf() device system call. + * - ::cudaLimitMallocHeapSize is the size in bytes of the heap used by the + * ::malloc() and ::free() device system calls. + * - ::cudaLimitDevRuntimeSyncDepth is the maximum grid depth at which a + * thread can isssue the device runtime call ::cudaDeviceSynchronize() + * to wait on child grid launches to complete. This functionality is removed + * for devices of compute capability >= 9.0, and hence will return error + * ::cudaErrorUnsupportedLimit on such devices. + * - ::cudaLimitDevRuntimePendingLaunchCount is the maximum number of outstanding + * device runtime launches. + * - ::cudaLimitMaxL2FetchGranularity is the L2 cache fetch granularity. + * - ::cudaLimitPersistingL2CacheSize is the persisting L2 cache size in bytes. + * + * \param limit - Limit to query + * \param pValue - Returned size of the limit + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnsupportedLimit, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceSetLimit, + * ::cuCtxGetLimit + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetLimit(size_t *pValue, enum cudaLimit limit); + +/** + * \brief Returns the maximum number of elements allocatable in a 1D linear texture for a given element size. + * + * Returns in \p maxWidthInElements the maximum number of elements allocatable in a 1D linear texture + * for given format descriptor \p fmtDesc. + * + * \param maxWidthInElements - Returns maximum number of texture elements allocatable for given \p fmtDesc. + * \param fmtDesc - Texture format description. + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnsupportedLimit, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cuDeviceGetTexture1DLinearMaxWidth + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetTexture1DLinearMaxWidth(size_t *maxWidthInElements, const struct cudaChannelFormatDesc *fmtDesc, int device); +#endif + +/** + * \brief Returns the preferred cache configuration for the current device. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this returns through \p pCacheConfig the preferred cache + * configuration for the current device. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute functions. + * + * This will return a \p pCacheConfig of ::cudaFuncCachePreferNone on devices + * where the size of the L1 cache and shared memory are fixed. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * - ::cudaFuncCachePreferEqual: prefer equal size L1 cache and shared memory + * + * \param pCacheConfig - Returned cache configuration + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetCacheConfig, + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * ::cuCtxGetCacheConfig + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetCacheConfig(enum cudaFuncCache *pCacheConfig); + +/** + * \brief Returns numerical values that correspond to the least and + * greatest stream priorities. + * + * Returns in \p *leastPriority and \p *greatestPriority the numerical values that correspond + * to the least and greatest stream priorities respectively. Stream priorities + * follow a convention where lower numbers imply greater priorities. The range of + * meaningful stream priorities is given by [\p *greatestPriority, \p *leastPriority]. + * If the user attempts to create a stream with a priority value that is + * outside the the meaningful range as specified by this API, the priority is + * automatically clamped down or up to either \p *leastPriority or \p *greatestPriority + * respectively. See ::cudaStreamCreateWithPriority for details on creating a + * priority stream. + * A NULL may be passed in for \p *leastPriority or \p *greatestPriority if the value + * is not desired. + * + * This function will return '0' in both \p *leastPriority and \p *greatestPriority if + * the current context's device does not support stream priorities + * (see ::cudaDeviceGetAttribute). + * + * \param leastPriority - Pointer to an int in which the numerical value for least + * stream priority is returned + * \param greatestPriority - Pointer to an int in which the numerical value for greatest + * stream priority is returned + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreateWithPriority, + * ::cudaStreamGetPriority, + * ::cuCtxGetStreamPriorityRange + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetStreamPriorityRange(int *leastPriority, int *greatestPriority); + +/** + * \brief Sets the preferred cache configuration for the current device. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p cacheConfig the preferred cache + * configuration for the current device. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute the function. Any + * function preference set via + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)" + * or + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)" + * will be preferred over this device-wide setting. Setting the device-wide + * cache configuration to ::cudaFuncCachePreferNone will cause subsequent + * kernel launches to prefer to not change the cache configuration unless + * required to launch the kernel. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * - ::cudaFuncCachePreferEqual: prefer equal size L1 cache and shared memory + * + * \param cacheConfig - Requested cache configuration + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceGetCacheConfig, + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * ::cuCtxSetCacheConfig + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceSetCacheConfig(enum cudaFuncCache cacheConfig); + +/** + * \brief Returns a handle to a compute device + * + * Returns in \p *device a device ordinal given a PCI bus ID string. + * + * \param device - Returned device ordinal + * + * \param pciBusId - String in one of the following forms: + * [domain]:[bus]:[device].[function] + * [domain]:[bus]:[device] + * [bus]:[device].[function] + * where \p domain, \p bus, \p device, and \p function are all hexadecimal values + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceGetPCIBusId, + * ::cuDeviceGetByPCIBusId + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetByPCIBusId(int *device, const char *pciBusId); + +/** + * \brief Returns a PCI Bus Id string for the device + * + * Returns an ASCII string identifying the device \p dev in the NULL-terminated + * string pointed to by \p pciBusId. \p len specifies the maximum length of the + * string that may be returned. + * + * \param pciBusId - Returned identifier string for the device in the following format + * [domain]:[bus]:[device].[function] + * where \p domain, \p bus, \p device, and \p function are all hexadecimal values. + * pciBusId should be large enough to store 13 characters including the NULL-terminator. + * + * \param len - Maximum length of string to store in \p name + * + * \param device - Device to get identifier string for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceGetByPCIBusId, + * ::cuDeviceGetPCIBusId + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetPCIBusId(char *pciBusId, int len, int device); + +/** + * \brief Gets an interprocess handle for a previously allocated event + * + * Takes as input a previously allocated event. This event must have been + * created with the ::cudaEventInterprocess and ::cudaEventDisableTiming + * flags set. This opaque handle may be copied into other processes and + * opened with ::cudaIpcOpenEventHandle to allow efficient hardware + * synchronization between GPU work in different processes. + * + * After the event has been been opened in the importing process, + * ::cudaEventRecord, ::cudaEventSynchronize, ::cudaStreamWaitEvent and + * ::cudaEventQuery may be used in either process. Performing operations + * on the imported event after the exported event has been freed + * with ::cudaEventDestroy will result in undefined behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode. + * Users can test their device for IPC functionality by calling + * ::cudaDeviceGetAttribute with ::cudaDevAttrIpcEventSupport + * + * \param handle - Pointer to a user allocated cudaIpcEventHandle + * in which to return the opaque event handle + * \param event - Event allocated with ::cudaEventInterprocess and + * ::cudaEventDisableTiming flags. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorMapBufferObjectFailed, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaEventCreate, + * ::cudaEventDestroy, + * ::cudaEventSynchronize, + * ::cudaEventQuery, + * ::cudaStreamWaitEvent, + * ::cudaIpcOpenEventHandle, + * ::cudaIpcGetMemHandle, + * ::cudaIpcOpenMemHandle, + * ::cudaIpcCloseMemHandle, + * ::cuIpcGetEventHandle + */ +extern __host__ cudaError_t CUDARTAPI cudaIpcGetEventHandle(cudaIpcEventHandle_t *handle, cudaEvent_t event); + +/** + * \brief Opens an interprocess event handle for use in the current process + * + * Opens an interprocess event handle exported from another process with + * ::cudaIpcGetEventHandle. This function returns a ::cudaEvent_t that behaves like + * a locally created event with the ::cudaEventDisableTiming flag specified. + * This event must be freed with ::cudaEventDestroy. + * + * Performing operations on the imported event after the exported event has + * been freed with ::cudaEventDestroy will result in undefined behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode. + * Users can test their device for IPC functionality by calling + * ::cudaDeviceGetAttribute with ::cudaDevAttrIpcEventSupport + * + * \param event - Returns the imported event + * \param handle - Interprocess handle to open + * + * \returns + * ::cudaSuccess, + * ::cudaErrorMapBufferObjectFailed, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue, + * ::cudaErrorDeviceUninitialized + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaEventCreate, + * ::cudaEventDestroy, + * ::cudaEventSynchronize, + * ::cudaEventQuery, + * ::cudaStreamWaitEvent, + * ::cudaIpcGetEventHandle, + * ::cudaIpcGetMemHandle, + * ::cudaIpcOpenMemHandle, + * ::cudaIpcCloseMemHandle, + * ::cuIpcOpenEventHandle + */ +extern __host__ cudaError_t CUDARTAPI cudaIpcOpenEventHandle(cudaEvent_t *event, cudaIpcEventHandle_t handle); + +/** + * \brief Gets an interprocess memory handle for an existing device memory + * allocation + * + * Takes a pointer to the base of an existing device memory allocation created + * with ::cudaMalloc and exports it for use in another process. This is a + * lightweight operation and may be called multiple times on an allocation + * without adverse effects. + * + * If a region of memory is freed with ::cudaFree and a subsequent call + * to ::cudaMalloc returns memory with the same device address, + * ::cudaIpcGetMemHandle will return a unique handle for the + * new memory. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode. + * Users can test their device for IPC functionality by calling + * ::cudaDeviceGetAttribute with ::cudaDevAttrIpcEventSupport + * + * \param handle - Pointer to user allocated ::cudaIpcMemHandle to return + * the handle in. + * \param devPtr - Base pointer to previously allocated device memory + * + * \returns + * ::cudaSuccess, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorMapBufferObjectFailed, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMalloc, + * ::cudaFree, + * ::cudaIpcGetEventHandle, + * ::cudaIpcOpenEventHandle, + * ::cudaIpcOpenMemHandle, + * ::cudaIpcCloseMemHandle, + * ::cuIpcGetMemHandle + */ +extern __host__ cudaError_t CUDARTAPI cudaIpcGetMemHandle(cudaIpcMemHandle_t *handle, void *devPtr); + +/** + * \brief Opens an interprocess memory handle exported from another process + * and returns a device pointer usable in the local process. + * + * Maps memory exported from another process with ::cudaIpcGetMemHandle into + * the current device address space. For contexts on different devices + * ::cudaIpcOpenMemHandle can attempt to enable peer access between the + * devices as if the user called ::cudaDeviceEnablePeerAccess. This behavior is + * controlled by the ::cudaIpcMemLazyEnablePeerAccess flag. + * ::cudaDeviceCanAccessPeer can determine if a mapping is possible. + * + * ::cudaIpcOpenMemHandle can open handles to devices that may not be visible + * in the process calling the API. + * + * Contexts that may open ::cudaIpcMemHandles are restricted in the following way. + * ::cudaIpcMemHandles from each device in a given process may only be opened + * by one context per device per other process. + * + * If the memory handle has already been opened by the current context, the + * reference count on the handle is incremented by 1 and the existing device pointer + * is returned. + * + * Memory returned from ::cudaIpcOpenMemHandle must be freed with + * ::cudaIpcCloseMemHandle. + * + * Calling ::cudaFree on an exported memory region before calling + * ::cudaIpcCloseMemHandle in the importing context will result in undefined + * behavior. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode. + * Users can test their device for IPC functionality by calling + * ::cudaDeviceGetAttribute with ::cudaDevAttrIpcEventSupport + * + * \param devPtr - Returned device pointer + * \param handle - ::cudaIpcMemHandle to open + * \param flags - Flags for this operation. Must be specified as ::cudaIpcMemLazyEnablePeerAccess + * + * \returns + * ::cudaSuccess, + * ::cudaErrorMapBufferObjectFailed, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorDeviceUninitialized, + * ::cudaErrorTooManyPeers, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \note No guarantees are made about the address returned in \p *devPtr. + * In particular, multiple processes may not receive the same address for the same \p handle. + * + * \sa + * ::cudaMalloc, + * ::cudaFree, + * ::cudaIpcGetEventHandle, + * ::cudaIpcOpenEventHandle, + * ::cudaIpcGetMemHandle, + * ::cudaIpcCloseMemHandle, + * ::cudaDeviceEnablePeerAccess, + * ::cudaDeviceCanAccessPeer, + * ::cuIpcOpenMemHandle + */ +extern __host__ cudaError_t CUDARTAPI cudaIpcOpenMemHandle(void **devPtr, cudaIpcMemHandle_t handle, unsigned int flags); + +/** + * \brief Attempts to close memory mapped with cudaIpcOpenMemHandle + * + * Decrements the reference count of the memory returnd by ::cudaIpcOpenMemHandle by 1. + * When the reference count reaches 0, this API unmaps the memory. The original allocation + * in the exporting process as well as imported mappings in other processes + * will be unaffected. + * + * Any resources used to enable peer access will be freed if this is the + * last mapping using them. + * + * IPC functionality is restricted to devices with support for unified + * addressing on Linux and Windows operating systems. + * IPC functionality on Windows is restricted to GPUs in TCC mode. + * Users can test their device for IPC functionality by calling + * ::cudaDeviceGetAttribute with ::cudaDevAttrIpcEventSupport + * + * \param devPtr - Device pointer returned by ::cudaIpcOpenMemHandle + * + * \returns + * ::cudaSuccess, + * ::cudaErrorMapBufferObjectFailed, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMalloc, + * ::cudaFree, + * ::cudaIpcGetEventHandle, + * ::cudaIpcOpenEventHandle, + * ::cudaIpcGetMemHandle, + * ::cudaIpcOpenMemHandle, + * ::cuIpcCloseMemHandle + */ +extern __host__ cudaError_t CUDARTAPI cudaIpcCloseMemHandle(void *devPtr); + +/** + * \brief Blocks until remote writes are visible to the specified scope + * + * Blocks until remote writes to the target context via mappings created + * through GPUDirect RDMA APIs, like nvidia_p2p_get_pages (see + * https://docs.nvidia.com/cuda/gpudirect-rdma for more information), are + * visible to the specified scope. + * + * If the scope equals or lies within the scope indicated by + * ::cudaDevAttrGPUDirectRDMAWritesOrdering, the call will be a no-op and + * can be safely omitted for performance. This can be determined by + * comparing the numerical values between the two enums, with smaller + * scopes having smaller values. + * + * Users may query support for this API via ::cudaDevAttrGPUDirectRDMAFlushWritesOptions. + * + * \param target - The target of the operation, see cudaFlushGPUDirectRDMAWritesTarget + * \param scope - The scope of the operation, see cudaFlushGPUDirectRDMAWritesScope + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotSupported, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cuFlushGPUDirectRDMAWrites + */ +#if __CUDART_API_VERSION >= 11030 +extern __host__ cudaError_t CUDARTAPI cudaDeviceFlushGPUDirectRDMAWrites(enum cudaFlushGPUDirectRDMAWritesTarget target, enum cudaFlushGPUDirectRDMAWritesScope scope); +#endif + +/** +* \brief Registers a callback function to receive async notifications +* +* Registers \p callbackFunc to receive async notifications. +* +* The \p userData parameter is passed to the callback function at async notification time. +* Likewise, \p callback is also passed to the callback function to distinguish between +* multiple registered callbacks. +* +* The callback function being registered should be designed to return quickly (~10ms). +* Any long running tasks should be queued for execution on an application thread. +* +* Callbacks may not call cudaDeviceRegisterAsyncNotification or cudaDeviceUnregisterAsyncNotification. +* Doing so will result in ::cudaErrorNotPermitted. Async notification callbacks execute +* in an undefined order and may be serialized. +* +* Returns in \p *callback a handle representing the registered callback instance. +* +* \param device - The device on which to register the callback +* \param callbackFunc - The function to register as a callback +* \param userData - A generic pointer to user data. This is passed into the callback function. +* \param callback - A handle representing the registered callback instance +* +* \return +* ::cudaSuccess +* ::cudaErrorNotSupported +* ::cudaErrorInvalidDevice +* ::cudaErrorInvalidValue +* ::cudaErrorNotPermitted +* ::cudaErrorUnknown +* \notefnerr +* +* \sa +* ::cudaDeviceUnregisterAsyncNotification +*/ +extern __host__ cudaError_t CUDARTAPI cudaDeviceRegisterAsyncNotification(int device, cudaAsyncCallback callbackFunc, void* userData, cudaAsyncCallbackHandle_t* callback); + +/** +* \brief Unregisters an async notification callback +* +* Unregisters \p callback so that the corresponding callback function will stop receiving +* async notifications. +* +* \param device - The device from which to remove \p callback. +* \param callback - The callback instance to unregister from receiving async notifications. +* +* \return +* ::cudaSuccess +* ::cudaErrorNotSupported +* ::cudaErrorInvalidDevice +* ::cudaErrorInvalidValue +* ::cudaErrorNotPermitted +* ::cudaErrorUnknown +* \notefnerr +* +* \sa +* ::cudaDeviceRegisterAsyncNotification +*/ +extern __host__ cudaError_t CUDARTAPI cudaDeviceUnregisterAsyncNotification(int device, cudaAsyncCallbackHandle_t callback); + +/** @} */ /* END CUDART_DEVICE */ + +/** + * \defgroup CUDART_DEVICE_DEPRECATED Device Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated device management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated device management functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Returns the shared memory configuration for the current device. + * + * \deprecated + * + * This function will return in \p pConfig the current size of shared memory banks + * on the current device. On devices with configurable shared memory banks, + * ::cudaDeviceSetSharedMemConfig can be used to change this setting, so that all + * subsequent kernel launches will by default use the new bank size. When + * ::cudaDeviceGetSharedMemConfig is called on devices without configurable shared + * memory, it will return the fixed bank size of the hardware. + * + * The returned bank configurations can be either: + * - ::cudaSharedMemBankSizeFourByte - shared memory bank width is four bytes. + * - ::cudaSharedMemBankSizeEightByte - shared memory bank width is eight bytes. + * + * \param pConfig - Returned cache configuration + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetCacheConfig, + * ::cudaDeviceGetCacheConfig, + * ::cudaDeviceSetSharedMemConfig, + * ::cudaFuncSetCacheConfig, + * ::cuCtxGetSharedMemConfig + */ +extern __CUDA_DEPRECATED __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetSharedMemConfig(enum cudaSharedMemConfig *pConfig); + +/** + * \brief Sets the shared memory configuration for the current device. + * + * \deprecated + * + * On devices with configurable shared memory banks, this function will set + * the shared memory bank size which is used for all subsequent kernel launches. + * Any per-function setting of shared memory set via ::cudaFuncSetSharedMemConfig + * will override the device wide setting. + * + * Changing the shared memory configuration between launches may introduce + * a device side synchronization point. + * + * Changing the shared memory bank size will not increase shared memory usage + * or affect occupancy of kernels, but may have major effects on performance. + * Larger bank sizes will allow for greater potential bandwidth to shared memory, + * but will change what kinds of accesses to shared memory will result in bank + * conflicts. + * + * This function will do nothing on devices with fixed shared memory bank size. + * + * The supported bank configurations are: + * - ::cudaSharedMemBankSizeDefault: set bank width the device default (currently, + * four bytes) + * - ::cudaSharedMemBankSizeFourByte: set shared memory bank width to be four bytes + * natively. + * - ::cudaSharedMemBankSizeEightByte: set shared memory bank width to be eight + * bytes natively. + * + * \param config - Requested cache configuration + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetCacheConfig, + * ::cudaDeviceGetCacheConfig, + * ::cudaDeviceGetSharedMemConfig, + * ::cudaFuncSetCacheConfig, + * ::cuCtxSetSharedMemConfig + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaDeviceSetSharedMemConfig(enum cudaSharedMemConfig config); +/** @} */ /* END CUDART_DEVICE_DEPRECATED */ + +/** + * \defgroup CUDART_THREAD_DEPRECATED Thread Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated thread management functions of the CUDA runtime + * API (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes deprecated thread management functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Exit and clean up from CUDA launches + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is identical to the + * non-deprecated function ::cudaDeviceReset(), which should be used + * instead. + * + * Explicitly destroys all cleans up all resources associated with the current + * device in the current process. Any subsequent API call to this device will + * reinitialize the device. + * + * Note that this function will reset the device immediately. It is the caller's + * responsibility to ensure that the device is not being accessed by any + * other host threads from the process when this function is called. + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceReset + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadExit(void); + +/** + * \brief Wait for compute device to finish + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is similar to the + * non-deprecated function ::cudaDeviceSynchronize(), which should be used + * instead. + * + * Blocks until the device has completed all preceding requested tasks. + * ::cudaThreadSynchronize() returns an error if one of the preceding tasks + * has failed. If the ::cudaDeviceScheduleBlockingSync flag was set for + * this device, the host thread will block until the device has finished + * its work. + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSynchronize + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadSynchronize(void); + +/** + * \brief Set resource limits + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is identical to the + * non-deprecated function ::cudaDeviceSetLimit(), which should be used + * instead. + * + * Setting \p limit to \p value is a request by the application to update + * the current limit maintained by the device. The driver is free to + * modify the requested value to meet h/w requirements (this could be + * clamping to minimum or maximum values, rounding up to nearest element + * size, etc). The application can use ::cudaThreadGetLimit() to find out + * exactly what the limit has been set to. + * + * Setting each ::cudaLimit has its own specific restrictions, so each is + * discussed here. + * + * - ::cudaLimitStackSize controls the stack size of each GPU thread. + * + * - ::cudaLimitPrintfFifoSize controls the size of the shared FIFO + * used by the ::printf() device system call. + * Setting ::cudaLimitPrintfFifoSize must be performed before + * launching any kernel that uses the ::printf() device + * system call, otherwise ::cudaErrorInvalidValue will be returned. + * + * - ::cudaLimitMallocHeapSize controls the size of the heap used + * by the ::malloc() and ::free() device system calls. Setting + * ::cudaLimitMallocHeapSize must be performed before launching + * any kernel that uses the ::malloc() or ::free() device system calls, + * otherwise ::cudaErrorInvalidValue will be returned. + * + * \param limit - Limit to set + * \param value - Size in bytes of limit + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnsupportedLimit, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetLimit + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadSetLimit(enum cudaLimit limit, size_t value); + +/** + * \brief Returns resource limits + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is identical to the + * non-deprecated function ::cudaDeviceGetLimit(), which should be used + * instead. + * + * Returns in \p *pValue the current size of \p limit. The supported + * ::cudaLimit values are: + * - ::cudaLimitStackSize: stack size of each GPU thread; + * - ::cudaLimitPrintfFifoSize: size of the shared FIFO used by the + * ::printf() device system call. + * - ::cudaLimitMallocHeapSize: size of the heap used by the + * ::malloc() and ::free() device system calls; + * + * \param limit - Limit to query + * \param pValue - Returned size in bytes of limit + * + * \return + * ::cudaSuccess, + * ::cudaErrorUnsupportedLimit, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceGetLimit + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadGetLimit(size_t *pValue, enum cudaLimit limit); + +/** + * \brief Returns the preferred cache configuration for the current device. + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is identical to the + * non-deprecated function ::cudaDeviceGetCacheConfig(), which should be + * used instead. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this returns through \p pCacheConfig the preferred cache + * configuration for the current device. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute functions. + * + * This will return a \p pCacheConfig of ::cudaFuncCachePreferNone on devices + * where the size of the L1 cache and shared memory are fixed. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * + * \param pCacheConfig - Returned cache configuration + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceGetCacheConfig + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadGetCacheConfig(enum cudaFuncCache *pCacheConfig); + +/** + * \brief Sets the preferred cache configuration for the current device. + * + * \deprecated + * + * Note that this function is deprecated because its name does not + * reflect its behavior. Its functionality is identical to the + * non-deprecated function ::cudaDeviceSetCacheConfig(), which should be + * used instead. + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p cacheConfig the preferred cache + * configuration for the current device. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute the function. Any + * function preference set via + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)" + * or + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)" + * will be preferred over this device-wide setting. Setting the device-wide + * cache configuration to ::cudaFuncCachePreferNone will cause subsequent + * kernel launches to prefer to not change the cache configuration unless + * required to launch the kernel. + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * + * \param cacheConfig - Requested cache configuration + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetCacheConfig + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaThreadSetCacheConfig(enum cudaFuncCache cacheConfig); + +/** @} */ /* END CUDART_THREAD_DEPRECATED */ + +/** + * \defgroup CUDART_ERROR Error Handling + * + * ___MANBRIEF___ error handling functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the error handling functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Returns the last error from a runtime call + * + * Returns the last error that has been produced by any of the runtime calls + * in the same instance of the CUDA Runtime library in the host thread and + * resets it to ::cudaSuccess. + * + * Note: Multiple instances of the CUDA Runtime library can be present in an + * application when using a library that statically links the CUDA Runtime. + * + * \return + * ::cudaSuccess, + * ::cudaErrorMissingConfiguration, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorInitializationError, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorUnmapBufferObjectFailed, + * ::cudaErrorInvalidDevicePointer, + * ::cudaErrorInvalidTexture, + * ::cudaErrorInvalidTextureBinding, + * ::cudaErrorInvalidChannelDescriptor, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorInvalidFilterSetting, + * ::cudaErrorInvalidNormSetting, + * ::cudaErrorUnknown, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorInsufficientDriver, + * ::cudaErrorNoDevice, + * ::cudaErrorSetOnActiveProcess, + * ::cudaErrorStartupFailure, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaPeekAtLastError, ::cudaGetErrorName, ::cudaGetErrorString, ::cudaError + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetLastError(void); + +/** + * \brief Returns the last error from a runtime call + * + * Returns the last error that has been produced by any of the runtime calls + * in the same instance of the CUDA Runtime library in the host thread. This + * call does not reset the error to ::cudaSuccess like ::cudaGetLastError(). + * + * Note: Multiple instances of the CUDA Runtime library can be present in an + * application when using a library that statically links the CUDA Runtime. + * + * \return + * ::cudaSuccess, + * ::cudaErrorMissingConfiguration, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorInitializationError, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorUnmapBufferObjectFailed, + * ::cudaErrorInvalidDevicePointer, + * ::cudaErrorInvalidTexture, + * ::cudaErrorInvalidTextureBinding, + * ::cudaErrorInvalidChannelDescriptor, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorInvalidFilterSetting, + * ::cudaErrorInvalidNormSetting, + * ::cudaErrorUnknown, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorInsufficientDriver, + * ::cudaErrorNoDevice, + * ::cudaErrorSetOnActiveProcess, + * ::cudaErrorStartupFailure, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetLastError, ::cudaGetErrorName, ::cudaGetErrorString, ::cudaError + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaPeekAtLastError(void); + +/** + * \brief Returns the string representation of an error code enum name + * + * Returns a string containing the name of an error code in the enum. If the error + * code is not recognized, "unrecognized error code" is returned. + * + * \param error - Error code to convert to string + * + * \return + * \p char* pointer to a NULL-terminated string + * + * \sa ::cudaGetErrorString, ::cudaGetLastError, ::cudaPeekAtLastError, ::cudaError, + * ::cuGetErrorName + */ +extern __host__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorName(cudaError_t error); + +/** + * \brief Returns the description string for an error code + * + * Returns the description string for an error code. If the error + * code is not recognized, "unrecognized error code" is returned. + * + * \param error - Error code to convert to string + * + * \return + * \p char* pointer to a NULL-terminated string + * + * \sa ::cudaGetErrorName, ::cudaGetLastError, ::cudaPeekAtLastError, ::cudaError, + * ::cuGetErrorString + */ +extern __host__ __cudart_builtin__ const char* CUDARTAPI cudaGetErrorString(cudaError_t error); +/** @} */ /* END CUDART_ERROR */ + +/** + * \addtogroup CUDART_DEVICE + * + * @{ + */ + +/** + * \brief Returns the number of compute-capable devices + * + * Returns in \p *count the number of devices with compute capability greater + * or equal to 2.0 that are available for execution. + * + * \param count - Returns the number of devices with compute capability + * greater or equal to 2.0 + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDevice, ::cudaSetDevice, ::cudaGetDeviceProperties, + * ::cudaChooseDevice, + * ::cudaInitDevice, + * ::cuDeviceGetCount + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDeviceCount(int *count); + +/** + * \brief Returns information about the compute-device + * + * Returns in \p *prop the properties of device \p dev. The ::cudaDeviceProp + * structure is defined as: + * \code + struct cudaDeviceProp { + char name[256]; + cudaUUID_t uuid; + size_t totalGlobalMem; + size_t sharedMemPerBlock; + int regsPerBlock; + int warpSize; + size_t memPitch; + int maxThreadsPerBlock; + int maxThreadsDim[3]; + int maxGridSize[3]; + int clockRate; + size_t totalConstMem; + int major; + int minor; + size_t textureAlignment; + size_t texturePitchAlignment; + int deviceOverlap; + int multiProcessorCount; + int kernelExecTimeoutEnabled; + int integrated; + int canMapHostMemory; + int computeMode; + int maxTexture1D; + int maxTexture1DMipmap; + int maxTexture1DLinear; + int maxTexture2D[2]; + int maxTexture2DMipmap[2]; + int maxTexture2DLinear[3]; + int maxTexture2DGather[2]; + int maxTexture3D[3]; + int maxTexture3DAlt[3]; + int maxTextureCubemap; + int maxTexture1DLayered[2]; + int maxTexture2DLayered[3]; + int maxTextureCubemapLayered[2]; + int maxSurface1D; + int maxSurface2D[2]; + int maxSurface3D[3]; + int maxSurface1DLayered[2]; + int maxSurface2DLayered[3]; + int maxSurfaceCubemap; + int maxSurfaceCubemapLayered[2]; + size_t surfaceAlignment; + int concurrentKernels; + int ECCEnabled; + int pciBusID; + int pciDeviceID; + int pciDomainID; + int tccDriver; + int asyncEngineCount; + int unifiedAddressing; + int memoryClockRate; + int memoryBusWidth; + int l2CacheSize; + int persistingL2CacheMaxSize; + int maxThreadsPerMultiProcessor; + int streamPrioritiesSupported; + int globalL1CacheSupported; + int localL1CacheSupported; + size_t sharedMemPerMultiprocessor; + int regsPerMultiprocessor; + int managedMemory; + int isMultiGpuBoard; + int multiGpuBoardGroupID; + int singleToDoublePrecisionPerfRatio; + int pageableMemoryAccess; + int concurrentManagedAccess; + int computePreemptionSupported; + int canUseHostPointerForRegisteredMem; + int cooperativeLaunch; + int cooperativeMultiDeviceLaunch; + int pageableMemoryAccessUsesHostPageTables; + int directManagedMemAccessFromHost; + int accessPolicyMaxWindowSize; + } + \endcode + * where: + * - \ref ::cudaDeviceProp::name "name[256]" is an ASCII string identifying + * the device. + * - \ref ::cudaDeviceProp::uuid "uuid" is a 16-byte unique identifier. + * - \ref ::cudaDeviceProp::totalGlobalMem "totalGlobalMem" is the total + * amount of global memory available on the device in bytes. + * - \ref ::cudaDeviceProp::sharedMemPerBlock "sharedMemPerBlock" is the + * maximum amount of shared memory available to a thread block in bytes. + * - \ref ::cudaDeviceProp::regsPerBlock "regsPerBlock" is the maximum number + * of 32-bit registers available to a thread block. + * - \ref ::cudaDeviceProp::warpSize "warpSize" is the warp size in threads. + * - \ref ::cudaDeviceProp::memPitch "memPitch" is the maximum pitch in + * bytes allowed by the memory copy functions that involve memory regions + * allocated through ::cudaMallocPitch(). + * - \ref ::cudaDeviceProp::maxThreadsPerBlock "maxThreadsPerBlock" is the + * maximum number of threads per block. + * - \ref ::cudaDeviceProp::maxThreadsDim "maxThreadsDim[3]" contains the + * maximum size of each dimension of a block. + * - \ref ::cudaDeviceProp::maxGridSize "maxGridSize[3]" contains the + * maximum size of each dimension of a grid. + * - \ref ::cudaDeviceProp::clockRate "clockRate" is the clock frequency in + * kilohertz. + * - \ref ::cudaDeviceProp::totalConstMem "totalConstMem" is the total amount + * of constant memory available on the device in bytes. + * - \ref ::cudaDeviceProp::major "major", + * \ref ::cudaDeviceProp::minor "minor" are the major and minor revision + * numbers defining the device's compute capability. + * - \ref ::cudaDeviceProp::textureAlignment "textureAlignment" is the + * alignment requirement; texture base addresses that are aligned to + * \ref ::cudaDeviceProp::textureAlignment "textureAlignment" bytes do not + * need an offset applied to texture fetches. + * - \ref ::cudaDeviceProp::texturePitchAlignment "texturePitchAlignment" is the + * pitch alignment requirement for 2D texture references that are bound to + * pitched memory. + * - \ref ::cudaDeviceProp::deviceOverlap "deviceOverlap" is 1 if the device + * can concurrently copy memory between host and device while executing a + * kernel, or 0 if not. Deprecated, use instead asyncEngineCount. + * - \ref ::cudaDeviceProp::multiProcessorCount "multiProcessorCount" is the + * number of multiprocessors on the device. + * - \ref ::cudaDeviceProp::kernelExecTimeoutEnabled "kernelExecTimeoutEnabled" + * is 1 if there is a run time limit for kernels executed on the device, or + * 0 if not. + * - \ref ::cudaDeviceProp::integrated "integrated" is 1 if the device is an + * integrated (motherboard) GPU and 0 if it is a discrete (card) component. + * - \ref ::cudaDeviceProp::canMapHostMemory "canMapHostMemory" is 1 if the + * device can map host memory into the CUDA address space for use with + * ::cudaHostAlloc()/::cudaHostGetDevicePointer(), or 0 if not. + * - \ref ::cudaDeviceProp::computeMode "computeMode" is the compute mode + * that the device is currently in. Available modes are as follows: + * - cudaComputeModeDefault: Default mode - Device is not restricted and + * multiple threads can use ::cudaSetDevice() with this device. + * - cudaComputeModeProhibited: Compute-prohibited mode - No threads can use + * ::cudaSetDevice() with this device. + * - cudaComputeModeExclusiveProcess: Compute-exclusive-process mode - Many + * threads in one process will be able to use ::cudaSetDevice() with this device. + *
When an occupied exclusive mode device is chosen with ::cudaSetDevice, + * all subsequent non-device management runtime functions will return + * ::cudaErrorDevicesUnavailable. + * - \ref ::cudaDeviceProp::maxTexture1D "maxTexture1D" is the maximum 1D + * texture size. + * - \ref ::cudaDeviceProp::maxTexture1DMipmap "maxTexture1DMipmap" is the maximum + * 1D mipmapped texture texture size. + * - \ref ::cudaDeviceProp::maxTexture1DLinear "maxTexture1DLinear" is the maximum + * 1D texture size for textures bound to linear memory. + * - \ref ::cudaDeviceProp::maxTexture2D "maxTexture2D[2]" contains the maximum + * 2D texture dimensions. + * - \ref ::cudaDeviceProp::maxTexture2DMipmap "maxTexture2DMipmap[2]" contains the + * maximum 2D mipmapped texture dimensions. + * - \ref ::cudaDeviceProp::maxTexture2DLinear "maxTexture2DLinear[3]" contains the + * maximum 2D texture dimensions for 2D textures bound to pitch linear memory. + * - \ref ::cudaDeviceProp::maxTexture2DGather "maxTexture2DGather[2]" contains the + * maximum 2D texture dimensions if texture gather operations have to be performed. + * - \ref ::cudaDeviceProp::maxTexture3D "maxTexture3D[3]" contains the maximum + * 3D texture dimensions. + * - \ref ::cudaDeviceProp::maxTexture3DAlt "maxTexture3DAlt[3]" + * contains the maximum alternate 3D texture dimensions. + * - \ref ::cudaDeviceProp::maxTextureCubemap "maxTextureCubemap" is the + * maximum cubemap texture width or height. + * - \ref ::cudaDeviceProp::maxTexture1DLayered "maxTexture1DLayered[2]" contains + * the maximum 1D layered texture dimensions. + * - \ref ::cudaDeviceProp::maxTexture2DLayered "maxTexture2DLayered[3]" contains + * the maximum 2D layered texture dimensions. + * - \ref ::cudaDeviceProp::maxTextureCubemapLayered "maxTextureCubemapLayered[2]" + * contains the maximum cubemap layered texture dimensions. + * - \ref ::cudaDeviceProp::maxSurface1D "maxSurface1D" is the maximum 1D + * surface size. + * - \ref ::cudaDeviceProp::maxSurface2D "maxSurface2D[2]" contains the maximum + * 2D surface dimensions. + * - \ref ::cudaDeviceProp::maxSurface3D "maxSurface3D[3]" contains the maximum + * 3D surface dimensions. + * - \ref ::cudaDeviceProp::maxSurface1DLayered "maxSurface1DLayered[2]" contains + * the maximum 1D layered surface dimensions. + * - \ref ::cudaDeviceProp::maxSurface2DLayered "maxSurface2DLayered[3]" contains + * the maximum 2D layered surface dimensions. + * - \ref ::cudaDeviceProp::maxSurfaceCubemap "maxSurfaceCubemap" is the maximum + * cubemap surface width or height. + * - \ref ::cudaDeviceProp::maxSurfaceCubemapLayered "maxSurfaceCubemapLayered[2]" + * contains the maximum cubemap layered surface dimensions. + * - \ref ::cudaDeviceProp::surfaceAlignment "surfaceAlignment" specifies the + * alignment requirements for surfaces. + * - \ref ::cudaDeviceProp::concurrentKernels "concurrentKernels" is 1 if the + * device supports executing multiple kernels within the same context + * simultaneously, or 0 if not. It is not guaranteed that multiple kernels + * will be resident on the device concurrently so this feature should not be + * relied upon for correctness. + * - \ref ::cudaDeviceProp::ECCEnabled "ECCEnabled" is 1 if the device has ECC + * support turned on, or 0 if not. + * - \ref ::cudaDeviceProp::pciBusID "pciBusID" is the PCI bus identifier of + * the device. + * - \ref ::cudaDeviceProp::pciDeviceID "pciDeviceID" is the PCI device + * (sometimes called slot) identifier of the device. + * - \ref ::cudaDeviceProp::pciDomainID "pciDomainID" is the PCI domain identifier + * of the device. + * - \ref ::cudaDeviceProp::tccDriver "tccDriver" is 1 if the device is using a + * TCC driver or 0 if not. + * - \ref ::cudaDeviceProp::asyncEngineCount "asyncEngineCount" is 1 when the + * device can concurrently copy memory between host and device while executing + * a kernel. It is 2 when the device can concurrently copy memory between host + * and device in both directions and execute a kernel at the same time. It is + * 0 if neither of these is supported. + * - \ref ::cudaDeviceProp::unifiedAddressing "unifiedAddressing" is 1 if the device + * shares a unified address space with the host and 0 otherwise. + * - \ref ::cudaDeviceProp::memoryClockRate "memoryClockRate" is the peak memory + * clock frequency in kilohertz. + * - \ref ::cudaDeviceProp::memoryBusWidth "memoryBusWidth" is the memory bus width + * in bits. + * - \ref ::cudaDeviceProp::l2CacheSize "l2CacheSize" is L2 cache size in bytes. + * - \ref ::cudaDeviceProp::persistingL2CacheMaxSize "persistingL2CacheMaxSize" is L2 cache's maximum persisting lines size in bytes. + * - \ref ::cudaDeviceProp::maxThreadsPerMultiProcessor "maxThreadsPerMultiProcessor" + * is the number of maximum resident threads per multiprocessor. + * - \ref ::cudaDeviceProp::streamPrioritiesSupported "streamPrioritiesSupported" + * is 1 if the device supports stream priorities, or 0 if it is not supported. + * - \ref ::cudaDeviceProp::globalL1CacheSupported "globalL1CacheSupported" + * is 1 if the device supports caching of globals in L1 cache, or 0 if it is not supported. + * - \ref ::cudaDeviceProp::localL1CacheSupported "localL1CacheSupported" + * is 1 if the device supports caching of locals in L1 cache, or 0 if it is not supported. + * - \ref ::cudaDeviceProp::sharedMemPerMultiprocessor "sharedMemPerMultiprocessor" is the + * maximum amount of shared memory available to a multiprocessor in bytes; this amount is + * shared by all thread blocks simultaneously resident on a multiprocessor. + * - \ref ::cudaDeviceProp::regsPerMultiprocessor "regsPerMultiprocessor" is the maximum number + * of 32-bit registers available to a multiprocessor; this number is shared + * by all thread blocks simultaneously resident on a multiprocessor. + * - \ref ::cudaDeviceProp::managedMemory "managedMemory" + * is 1 if the device supports allocating managed memory on this system, or 0 if it is not supported. + * - \ref ::cudaDeviceProp::isMultiGpuBoard "isMultiGpuBoard" + * is 1 if the device is on a multi-GPU board (e.g. Gemini cards), and 0 if not; + * - \ref ::cudaDeviceProp::multiGpuBoardGroupID "multiGpuBoardGroupID" is a unique identifier + * for a group of devices associated with the same board. + * Devices on the same multi-GPU board will share the same identifier. + * - \ref ::cudaDeviceProp::hostNativeAtomicSupported "hostNativeAtomicSupported" + * is 1 if the link between the device and the host supports native atomic operations, or 0 if it is not supported. + * - \ref ::cudaDeviceProp::singleToDoublePrecisionPerfRatio "singleToDoublePrecisionPerfRatio" + * is the ratio of single precision performance (in floating-point operations per second) + * to double precision performance. + * - \ref ::cudaDeviceProp::pageableMemoryAccess "pageableMemoryAccess" is 1 if the device supports + * coherently accessing pageable memory without calling cudaHostRegister on it, and 0 otherwise. + * - \ref ::cudaDeviceProp::concurrentManagedAccess "concurrentManagedAccess" is 1 if the device can + * coherently access managed memory concurrently with the CPU, and 0 otherwise. + * - \ref ::cudaDeviceProp::computePreemptionSupported "computePreemptionSupported" is 1 if the device + * supports Compute Preemption, and 0 otherwise. + * - \ref ::cudaDeviceProp::canUseHostPointerForRegisteredMem "canUseHostPointerForRegisteredMem" is 1 if + * the device can access host registered memory at the same virtual address as the CPU, and 0 otherwise. + * - \ref ::cudaDeviceProp::cooperativeLaunch "cooperativeLaunch" is 1 if the device supports launching + * cooperative kernels via ::cudaLaunchCooperativeKernel, and 0 otherwise. + * - \ref ::cudaDeviceProp::cooperativeMultiDeviceLaunch "cooperativeMultiDeviceLaunch" is 1 if the device + * supports launching cooperative kernels via ::cudaLaunchCooperativeKernelMultiDevice, and 0 otherwise. + * - \ref ::cudaDeviceProp::sharedMemPerBlockOptin "sharedMemPerBlockOptin" + * is the per device maximum shared memory per block usable by special opt in + * - \ref ::cudaDeviceProp::pageableMemoryAccessUsesHostPageTables "pageableMemoryAccessUsesHostPageTables" is 1 if the device accesses + * pageable memory via the host's page tables, and 0 otherwise. + * - \ref ::cudaDeviceProp::directManagedMemAccessFromHost "directManagedMemAccessFromHost" is 1 if the host can directly access managed + * memory on the device without migration, and 0 otherwise. + * - \ref ::cudaDeviceProp::maxBlocksPerMultiProcessor "maxBlocksPerMultiProcessor" is the maximum number of thread blocks + * that can reside on a multiprocessor. + * - \ref ::cudaDeviceProp::accessPolicyMaxWindowSize "accessPolicyMaxWindowSize" is + * the maximum value of ::cudaAccessPolicyWindow::num_bytes. + * - \ref ::cudaDeviceProp::reservedSharedMemPerBlock "reservedSharedMemPerBlock" + * is the shared memory reserved by CUDA driver per block in bytes + * - \ref ::cudaDeviceProp::hostRegisterSupported "hostRegisterSupported" + * is 1 if the device supports host memory registration via ::cudaHostRegister, and 0 otherwise. + * - \ref ::cudaDeviceProp::sparseCudaArraySupported "sparseCudaArraySupported" + * is 1 if the device supports sparse CUDA arrays and sparse CUDA mipmapped arrays, 0 otherwise + * - \ref ::cudaDeviceProp::hostRegisterReadOnlySupported "hostRegisterReadOnlySupported" + * is 1 if the device supports using the ::cudaHostRegister flag cudaHostRegisterReadOnly to register memory that must be mapped as + * read-only to the GPU + * - \ref ::cudaDeviceProp::timelineSemaphoreInteropSupported "timelineSemaphoreInteropSupported" + * is 1 if external timeline semaphore interop is supported on the device, 0 otherwise + * - \ref ::cudaDeviceProp::memoryPoolsSupported "memoryPoolsSupported" + * is 1 if the device supports using the cudaMallocAsync and cudaMemPool family of APIs, 0 otherwise + * - \ref ::cudaDeviceProp::gpuDirectRDMASupported "gpuDirectRDMASupported" + * is 1 if the device supports GPUDirect RDMA APIs, 0 otherwise + * - \ref ::cudaDeviceProp::gpuDirectRDMAFlushWritesOptions "gpuDirectRDMAFlushWritesOptions" + * is a bitmask to be interpreted according to the ::cudaFlushGPUDirectRDMAWritesOptions enum + * - \ref ::cudaDeviceProp::gpuDirectRDMAWritesOrdering "gpuDirectRDMAWritesOrdering" + * See the ::cudaGPUDirectRDMAWritesOrdering enum for numerical values + * - \ref ::cudaDeviceProp::memoryPoolSupportedHandleTypes "memoryPoolSupportedHandleTypes" + * is a bitmask of handle types supported with mempool-based IPC + * - \ref ::cudaDeviceProp::deferredMappingCudaArraySupported "deferredMappingCudaArraySupported" + * is 1 if the device supports deferred mapping CUDA arrays and CUDA mipmapped arrays + * - \ref ::cudaDeviceProp::ipcEventSupported "ipcEventSupported" + * is 1 if the device supports IPC Events, and 0 otherwise + * - \ref ::cudaDeviceProp::unifiedFunctionPointers "unifiedFunctionPointers" + * is 1 if the device support unified pointers, and 0 otherwise + * + * \param prop - Properties for the specified device + * \param device - Device number to get properties for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaSetDevice, ::cudaChooseDevice, + * ::cudaDeviceGetAttribute, + * ::cudaInitDevice, + * ::cuDeviceGetAttribute, + * ::cuDeviceGetName + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDeviceProperties(struct cudaDeviceProp *prop, int device); + +/** + * \brief Returns information about the device + * + * Returns in \p *value the integer value of the attribute \p attr on device + * \p device. The supported attributes are: + * - ::cudaDevAttrMaxThreadsPerBlock: Maximum number of threads per block + * - ::cudaDevAttrMaxBlockDimX: Maximum x-dimension of a block + * - ::cudaDevAttrMaxBlockDimY: Maximum y-dimension of a block + * - ::cudaDevAttrMaxBlockDimZ: Maximum z-dimension of a block + * - ::cudaDevAttrMaxGridDimX: Maximum x-dimension of a grid + * - ::cudaDevAttrMaxGridDimY: Maximum y-dimension of a grid + * - ::cudaDevAttrMaxGridDimZ: Maximum z-dimension of a grid + * - ::cudaDevAttrMaxSharedMemoryPerBlock: Maximum amount of shared memory + * available to a thread block in bytes + * - ::cudaDevAttrTotalConstantMemory: Memory available on device for + * __constant__ variables in a CUDA C kernel in bytes + * - ::cudaDevAttrWarpSize: Warp size in threads + * - ::cudaDevAttrMaxPitch: Maximum pitch in bytes allowed by the memory copy + * functions that involve memory regions allocated through ::cudaMallocPitch() + * - ::cudaDevAttrMaxTexture1DWidth: Maximum 1D texture width + * - ::cudaDevAttrMaxTexture1DLinearWidth: Maximum width for a 1D texture bound + * to linear memory + * - ::cudaDevAttrMaxTexture1DMipmappedWidth: Maximum mipmapped 1D texture width + * - ::cudaDevAttrMaxTexture2DWidth: Maximum 2D texture width + * - ::cudaDevAttrMaxTexture2DHeight: Maximum 2D texture height + * - ::cudaDevAttrMaxTexture2DLinearWidth: Maximum width for a 2D texture + * bound to linear memory + * - ::cudaDevAttrMaxTexture2DLinearHeight: Maximum height for a 2D texture + * bound to linear memory + * - ::cudaDevAttrMaxTexture2DLinearPitch: Maximum pitch in bytes for a 2D + * texture bound to linear memory + * - ::cudaDevAttrMaxTexture2DMipmappedWidth: Maximum mipmapped 2D texture + * width + * - ::cudaDevAttrMaxTexture2DMipmappedHeight: Maximum mipmapped 2D texture + * height + * - ::cudaDevAttrMaxTexture3DWidth: Maximum 3D texture width + * - ::cudaDevAttrMaxTexture3DHeight: Maximum 3D texture height + * - ::cudaDevAttrMaxTexture3DDepth: Maximum 3D texture depth + * - ::cudaDevAttrMaxTexture3DWidthAlt: Alternate maximum 3D texture width, + * 0 if no alternate maximum 3D texture size is supported + * - ::cudaDevAttrMaxTexture3DHeightAlt: Alternate maximum 3D texture height, + * 0 if no alternate maximum 3D texture size is supported + * - ::cudaDevAttrMaxTexture3DDepthAlt: Alternate maximum 3D texture depth, + * 0 if no alternate maximum 3D texture size is supported + * - ::cudaDevAttrMaxTextureCubemapWidth: Maximum cubemap texture width or + * height + * - ::cudaDevAttrMaxTexture1DLayeredWidth: Maximum 1D layered texture width + * - ::cudaDevAttrMaxTexture1DLayeredLayers: Maximum layers in a 1D layered + * texture + * - ::cudaDevAttrMaxTexture2DLayeredWidth: Maximum 2D layered texture width + * - ::cudaDevAttrMaxTexture2DLayeredHeight: Maximum 2D layered texture height + * - ::cudaDevAttrMaxTexture2DLayeredLayers: Maximum layers in a 2D layered + * texture + * - ::cudaDevAttrMaxTextureCubemapLayeredWidth: Maximum cubemap layered + * texture width or height + * - ::cudaDevAttrMaxTextureCubemapLayeredLayers: Maximum layers in a cubemap + * layered texture + * - ::cudaDevAttrMaxSurface1DWidth: Maximum 1D surface width + * - ::cudaDevAttrMaxSurface2DWidth: Maximum 2D surface width + * - ::cudaDevAttrMaxSurface2DHeight: Maximum 2D surface height + * - ::cudaDevAttrMaxSurface3DWidth: Maximum 3D surface width + * - ::cudaDevAttrMaxSurface3DHeight: Maximum 3D surface height + * - ::cudaDevAttrMaxSurface3DDepth: Maximum 3D surface depth + * - ::cudaDevAttrMaxSurface1DLayeredWidth: Maximum 1D layered surface width + * - ::cudaDevAttrMaxSurface1DLayeredLayers: Maximum layers in a 1D layered + * surface + * - ::cudaDevAttrMaxSurface2DLayeredWidth: Maximum 2D layered surface width + * - ::cudaDevAttrMaxSurface2DLayeredHeight: Maximum 2D layered surface height + * - ::cudaDevAttrMaxSurface2DLayeredLayers: Maximum layers in a 2D layered + * surface + * - ::cudaDevAttrMaxSurfaceCubemapWidth: Maximum cubemap surface width + * - ::cudaDevAttrMaxSurfaceCubemapLayeredWidth: Maximum cubemap layered + * surface width + * - ::cudaDevAttrMaxSurfaceCubemapLayeredLayers: Maximum layers in a cubemap + * layered surface + * - ::cudaDevAttrMaxRegistersPerBlock: Maximum number of 32-bit registers + * available to a thread block + * - ::cudaDevAttrClockRate: Peak clock frequency in kilohertz + * - ::cudaDevAttrTextureAlignment: Alignment requirement; texture base + * addresses aligned to ::textureAlign bytes do not need an offset applied + * to texture fetches + * - ::cudaDevAttrTexturePitchAlignment: Pitch alignment requirement for 2D + * texture references bound to pitched memory + * - ::cudaDevAttrGpuOverlap: 1 if the device can concurrently copy memory + * between host and device while executing a kernel, or 0 if not + * - ::cudaDevAttrMultiProcessorCount: Number of multiprocessors on the device + * - ::cudaDevAttrKernelExecTimeout: 1 if there is a run time limit for kernels + * executed on the device, or 0 if not + * - ::cudaDevAttrIntegrated: 1 if the device is integrated with the memory + * subsystem, or 0 if not + * - ::cudaDevAttrCanMapHostMemory: 1 if the device can map host memory into + * the CUDA address space, or 0 if not + * - ::cudaDevAttrComputeMode: Compute mode is the compute mode that the device + * is currently in. Available modes are as follows: + * - ::cudaComputeModeDefault: Default mode - Device is not restricted and + * multiple threads can use ::cudaSetDevice() with this device. + * - ::cudaComputeModeProhibited: Compute-prohibited mode - No threads can use + * ::cudaSetDevice() with this device. + * - ::cudaComputeModeExclusiveProcess: Compute-exclusive-process mode - Many + * threads in one process will be able to use ::cudaSetDevice() with this + * device. + * - ::cudaDevAttrConcurrentKernels: 1 if the device supports executing + * multiple kernels within the same context simultaneously, or 0 if + * not. It is not guaranteed that multiple kernels will be resident on the + * device concurrently so this feature should not be relied upon for + * correctness. + * - ::cudaDevAttrEccEnabled: 1 if error correction is enabled on the device, + * 0 if error correction is disabled or not supported by the device + * - ::cudaDevAttrPciBusId: PCI bus identifier of the device + * - ::cudaDevAttrPciDeviceId: PCI device (also known as slot) identifier of + * the device + * - ::cudaDevAttrTccDriver: 1 if the device is using a TCC driver. TCC is only + * available on Tesla hardware running Windows Vista or later. + * - ::cudaDevAttrMemoryClockRate: Peak memory clock frequency in kilohertz + * - ::cudaDevAttrGlobalMemoryBusWidth: Global memory bus width in bits + * - ::cudaDevAttrL2CacheSize: Size of L2 cache in bytes. 0 if the device + * doesn't have L2 cache. + * - ::cudaDevAttrMaxThreadsPerMultiProcessor: Maximum resident threads per + * multiprocessor + * - ::cudaDevAttrUnifiedAddressing: 1 if the device shares a unified address + * space with the host, or 0 if not + * - ::cudaDevAttrComputeCapabilityMajor: Major compute capability version + * number + * - ::cudaDevAttrComputeCapabilityMinor: Minor compute capability version + * number + * - ::cudaDevAttrStreamPrioritiesSupported: 1 if the device supports stream + * priorities, or 0 if not + * - ::cudaDevAttrGlobalL1CacheSupported: 1 if device supports caching globals + * in L1 cache, 0 if not + * - ::cudaDevAttrLocalL1CacheSupported: 1 if device supports caching locals + * in L1 cache, 0 if not + * - ::cudaDevAttrMaxSharedMemoryPerMultiprocessor: Maximum amount of shared memory + * available to a multiprocessor in bytes; this amount is shared by all + * thread blocks simultaneously resident on a multiprocessor + * - ::cudaDevAttrMaxRegistersPerMultiprocessor: Maximum number of 32-bit registers + * available to a multiprocessor; this number is shared by all thread blocks + * simultaneously resident on a multiprocessor + * - ::cudaDevAttrManagedMemory: 1 if device supports allocating + * managed memory, 0 if not + * - ::cudaDevAttrIsMultiGpuBoard: 1 if device is on a multi-GPU board, 0 if not + * - ::cudaDevAttrMultiGpuBoardGroupID: Unique identifier for a group of devices on the + * same multi-GPU board + * - ::cudaDevAttrHostNativeAtomicSupported: 1 if the link between the device and the + * host supports native atomic operations + * - ::cudaDevAttrSingleToDoublePrecisionPerfRatio: Ratio of single precision performance + * (in floating-point operations per second) to double precision performance + * - ::cudaDevAttrPageableMemoryAccess: 1 if the device supports coherently accessing + * pageable memory without calling cudaHostRegister on it, and 0 otherwise + * - ::cudaDevAttrConcurrentManagedAccess: 1 if the device can coherently access managed + * memory concurrently with the CPU, and 0 otherwise + * - ::cudaDevAttrComputePreemptionSupported: 1 if the device supports + * Compute Preemption, 0 if not + * - ::cudaDevAttrCanUseHostPointerForRegisteredMem: 1 if the device can access host + * registered memory at the same virtual address as the CPU, and 0 otherwise + * - ::cudaDevAttrCooperativeLaunch: 1 if the device supports launching cooperative kernels + * via ::cudaLaunchCooperativeKernel, and 0 otherwise + * - ::cudaDevAttrCooperativeMultiDeviceLaunch: 1 if the device supports launching cooperative + * kernels via ::cudaLaunchCooperativeKernelMultiDevice, and 0 otherwise + * - ::cudaDevAttrCanFlushRemoteWrites: 1 if the device supports flushing of outstanding + * remote writes, and 0 otherwise + * - ::cudaDevAttrHostRegisterSupported: 1 if the device supports host memory registration + * via ::cudaHostRegister, and 0 otherwise + * - ::cudaDevAttrPageableMemoryAccessUsesHostPageTables: 1 if the device accesses pageable memory via the + * host's page tables, and 0 otherwise + * - ::cudaDevAttrDirectManagedMemAccessFromHost: 1 if the host can directly access managed memory on the device + * without migration, and 0 otherwise + * - ::cudaDevAttrMaxSharedMemoryPerBlockOptin: Maximum per block shared memory size on the device. This value can + * be opted into when using ::cudaFuncSetAttribute + * - ::cudaDevAttrMaxBlocksPerMultiprocessor: Maximum number of thread blocks that can reside on a multiprocessor + * - ::cudaDevAttrMaxPersistingL2CacheSize: Maximum L2 persisting lines capacity setting in bytes + * - ::cudaDevAttrMaxAccessPolicyWindowSize: Maximum value of cudaAccessPolicyWindow::num_bytes + * - ::cudaDevAttrReservedSharedMemoryPerBlock: Shared memory reserved by CUDA driver per block in bytes + * - ::cudaDevAttrSparseCudaArraySupported: 1 if the device supports sparse CUDA arrays and sparse CUDA mipmapped arrays. + * - ::cudaDevAttrHostRegisterReadOnlySupported: Device supports using the ::cudaHostRegister flag cudaHostRegisterReadOnly + * to register memory that must be mapped as read-only to the GPU + * - ::cudaDevAttrMemoryPoolsSupported: 1 if the device supports using the cudaMallocAsync and cudaMemPool family of APIs, and 0 otherwise + * - ::cudaDevAttrGPUDirectRDMASupported: 1 if the device supports GPUDirect RDMA APIs, and 0 otherwise + * - ::cudaDevAttrGPUDirectRDMAFlushWritesOptions: bitmask to be interpreted according to the ::cudaFlushGPUDirectRDMAWritesOptions enum + * - ::cudaDevAttrGPUDirectRDMAWritesOrdering: see the ::cudaGPUDirectRDMAWritesOrdering enum for numerical values + * - ::cudaDevAttrMemoryPoolSupportedHandleTypes: Bitmask of handle types supported with mempool based IPC + * - ::cudaDevAttrDeferredMappingCudaArraySupported : 1 if the device supports deferred mapping CUDA arrays and CUDA mipmapped arrays. + * - ::cudaDevAttrIpcEventSupport: 1 if the device supports IPC Events. + * + * \param value - Returned device attribute value + * \param attr - Device attribute to query + * \param device - Device number to query + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaSetDevice, ::cudaChooseDevice, + * ::cudaGetDeviceProperties, + * ::cudaInitDevice, + * ::cuDeviceGetAttribute + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetAttribute(int *value, enum cudaDeviceAttr attr, int device); + +/** + * \brief Returns the default mempool of a device + * + * The default mempool of a device contains device memory from that device. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue + * ::cudaErrorNotSupported + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cuDeviceGetDefaultMemPool, ::cudaMallocAsync, ::cudaMemPoolTrimTo, ::cudaMemPoolGetAttribute, ::cudaDeviceSetMemPool, ::cudaMemPoolSetAttribute, ::cudaMemPoolSetAccess + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetDefaultMemPool(cudaMemPool_t *memPool, int device); + + +/** + * \brief Sets the current memory pool of a device + * + * The memory pool must be local to the specified device. + * Unless a mempool is specified in the ::cudaMallocAsync call, + * ::cudaMallocAsync allocates from the current mempool of the provided stream's device. + * By default, a device's current memory pool is its default memory pool. + * + * \note Use ::cudaMallocFromPoolAsync to specify asynchronous allocations from a device different + * than the one the stream runs on. + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * ::cudaErrorInvalidDevice + * ::cudaErrorNotSupported + * \notefnerr + * \note_callback + * + * \sa ::cuDeviceSetMemPool, ::cudaDeviceGetMemPool, ::cudaDeviceGetDefaultMemPool, ::cudaMemPoolCreate, ::cudaMemPoolDestroy, ::cudaMallocFromPoolAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceSetMemPool(int device, cudaMemPool_t memPool); + +/** + * \brief Gets the current mempool for a device + * + * Returns the last pool provided to ::cudaDeviceSetMemPool for this device + * or the device's default memory pool if ::cudaDeviceSetMemPool has never been called. + * By default the current mempool is the default mempool for a device, + * otherwise the returned pool must have been set with ::cuDeviceSetMemPool or ::cudaDeviceSetMemPool. + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * ::cudaErrorNotSupported + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cuDeviceGetMemPool, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceSetMemPool + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetMemPool(cudaMemPool_t *memPool, int device); + +/** + * \brief Return NvSciSync attributes that this device can support. + * + * Returns in \p nvSciSyncAttrList, the properties of NvSciSync that + * this CUDA device, \p dev can support. The returned \p nvSciSyncAttrList + * can be used to create an NvSciSync that matches this device's capabilities. + * + * If NvSciSyncAttrKey_RequiredPerm field in \p nvSciSyncAttrList is + * already set this API will return ::cudaErrorInvalidValue. + * + * The applications should set \p nvSciSyncAttrList to a valid + * NvSciSyncAttrList failing which this API will return + * ::cudaErrorInvalidHandle. + * + * The \p flags controls how applications intends to use + * the NvSciSync created from the \p nvSciSyncAttrList. The valid flags are: + * - ::cudaNvSciSyncAttrSignal, specifies that the applications intends to + * signal an NvSciSync on this CUDA device. + * - ::cudaNvSciSyncAttrWait, specifies that the applications intends to + * wait on an NvSciSync on this CUDA device. + * + * At least one of these flags must be set, failing which the API + * returns ::cudaErrorInvalidValue. Both the flags are orthogonal + * to one another: a developer may set both these flags that allows to + * set both wait and signal specific attributes in the same \p nvSciSyncAttrList. + * + * Note that this API updates the input \p nvSciSyncAttrList with values equivalent + * to the following public attribute key-values: + * NvSciSyncAttrKey_RequiredPerm is set to + * - NvSciSyncAccessPerm_SignalOnly if ::cudaNvSciSyncAttrSignal is set in \p flags. + * - NvSciSyncAccessPerm_WaitOnly if ::cudaNvSciSyncAttrWait is set in \p flags. + * - NvSciSyncAccessPerm_WaitSignal if both ::cudaNvSciSyncAttrWait and + * ::cudaNvSciSyncAttrSignal are set in \p flags. + * NvSciSyncAttrKey_PrimitiveInfo is set to + * - NvSciSyncAttrValPrimitiveType_SysmemSemaphore on any valid \p device. + * - NvSciSyncAttrValPrimitiveType_Syncpoint if \p device is a Tegra device. + * - NvSciSyncAttrValPrimitiveType_SysmemSemaphorePayload64b if \p device is GA10X+. + * NvSciSyncAttrKey_GpuId is set to the same UUID that is returned in + * \p cudaDeviceProp.uuid from ::cudaDeviceGetProperties for this \p device. + * + * \param nvSciSyncAttrList - Return NvSciSync attributes supported. + * \param device - Valid Cuda Device to get NvSciSync attributes for. + * \param flags - flags describing NvSciSync usage. + * + * \return + * + * ::cudaSuccess, + * ::cudaErrorDeviceUninitialized, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidHandle, + * ::cudaErrorInvalidDevice, + * ::cudaErrorNotSupported, + * ::cudaErrorMemoryAllocation + * + * \sa + * ::cudaImportExternalSemaphore, + * ::cudaDestroyExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetNvSciSyncAttributes(void *nvSciSyncAttrList, int device, int flags); + +/** + * \brief Queries attributes of the link between two devices. + * + * Returns in \p *value the value of the requested attribute \p attrib of the + * link between \p srcDevice and \p dstDevice. The supported attributes are: + * - ::cudaDevP2PAttrPerformanceRank: A relative value indicating the + * performance of the link between two devices. Lower value means better + * performance (0 being the value used for most performant link). + * - ::cudaDevP2PAttrAccessSupported: 1 if peer access is enabled. + * - ::cudaDevP2PAttrNativeAtomicSupported: 1 if native atomic operations over + * the link are supported. + * - ::cudaDevP2PAttrCudaArrayAccessSupported: 1 if accessing CUDA arrays over + * the link is supported. + * + * Returns ::cudaErrorInvalidDevice if \p srcDevice or \p dstDevice are not valid + * or if they represent the same device. + * + * Returns ::cudaErrorInvalidValue if \p attrib is not valid or if \p value is + * a null pointer. + * + * \param value - Returned value of the requested attribute + * \param attrib - The requested attribute of the link between \p srcDevice and \p dstDevice. + * \param srcDevice - The source device of the target link. + * \param dstDevice - The destination device of the target link. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceEnablePeerAccess, + * ::cudaDeviceDisablePeerAccess, + * ::cudaDeviceCanAccessPeer, + * ::cuDeviceGetP2PAttribute + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaDeviceGetP2PAttribute(int *value, enum cudaDeviceP2PAttr attr, int srcDevice, int dstDevice); + +/** + * \brief Select compute-device which best matches criteria + * + * Returns in \p *device the device which has properties that best match + * \p *prop. + * + * \param device - Device with best match + * \param prop - Desired device properties + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaSetDevice, + * ::cudaGetDeviceProperties, + * ::cudaInitDevice + */ +extern __host__ cudaError_t CUDARTAPI cudaChooseDevice(int *device, const struct cudaDeviceProp *prop); +/** + * \brief Initialize device to be used for GPU executions + * + * This function will initialize the CUDA Runtime structures and primary context on \p device when called, + * but the context will not be made current to \p device. + * + * When ::cudaInitDeviceFlagsAreValid is set in \p flags, deviceFlags are applied to the requested device. + * The values of deviceFlags match those of the flags parameters in ::cudaSetDeviceFlags. + * The effect may be verified by ::cudaGetDeviceFlags. + * + * This function will return an error if the device is in ::cudaComputeModeExclusiveProcess + * and is occupied by another process or if the device is in ::cudaComputeModeProhibited. + * + * \param device - Device on which the runtime will initialize itself. + * \param deviceFlags - Parameters for device operation. + * \param flags - Flags for controlling the device initialization. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaGetDeviceProperties, + * ::cudaChooseDevice, ::cudaSetDevice + * ::cuCtxSetCurrent + */ +extern __host__ cudaError_t CUDARTAPI cudaInitDevice(int device, unsigned int deviceFlags, unsigned int flags); +/** + * \brief Set device to be used for GPU executions + * + * Sets \p device as the current device for the calling host thread. + * Valid device id's are 0 to (::cudaGetDeviceCount() - 1). + * + * Any device memory subsequently allocated from this host thread + * using ::cudaMalloc(), ::cudaMallocPitch() or ::cudaMallocArray() + * will be physically resident on \p device. Any host memory allocated + * from this host thread using ::cudaMallocHost() or ::cudaHostAlloc() + * or ::cudaHostRegister() will have its lifetime associated with + * \p device. Any streams or events created from this host thread will + * be associated with \p device. Any kernels launched from this host + * thread using the <<<>>> operator or ::cudaLaunchKernel() will be executed + * on \p device. + * + * This call may be made from any host thread, to any device, and at + * any time. This function will do no synchronization with the previous + * or new device, + * and should only take significant time when it initializes the runtime's context state. + * This call will bind the primary context of the specified device to the calling thread and all the + * subsequent memory allocations, stream and event creations, and kernel launches + * will be associated with the primary context. + * This function will also immediately initialize the runtime state on the primary context, + * and the context will be current on \p device immediately. This function will return an + * error if the device is in ::cudaComputeModeExclusiveProcess and is occupied by another + * process or if the device is in ::cudaComputeModeProhibited. + * + * It is not required to call ::cudaInitDevice before using this function. + * \param device - Device on which the active host thread should execute the + * device code. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorDeviceUnavailable, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaGetDeviceProperties, + * ::cudaChooseDevice, + * ::cudaInitDevice, + * ::cuCtxSetCurrent + */ +extern __host__ cudaError_t CUDARTAPI cudaSetDevice(int device); + +/** + * \brief Returns which device is currently being used + * + * Returns in \p *device the current device for the calling host thread. + * + * \param device - Returns the device on which the active host thread + * executes the device code. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorDeviceUnavailable, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaSetDevice, ::cudaGetDeviceProperties, + * ::cudaChooseDevice, + * ::cuCtxGetCurrent + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDevice(int *device); + +/** + * \brief Set a list of devices that can be used for CUDA + * + * Sets a list of devices for CUDA execution in priority order using + * \p device_arr. The parameter \p len specifies the number of elements in the + * list. CUDA will try devices from the list sequentially until it finds one + * that works. If this function is not called, or if it is called with a \p len + * of 0, then CUDA will go back to its default behavior of trying devices + * sequentially from a default list containing all of the available CUDA + * devices in the system. If a specified device ID in the list does not exist, + * this function will return ::cudaErrorInvalidDevice. If \p len is not 0 and + * \p device_arr is NULL or if \p len exceeds the number of devices in + * the system, then ::cudaErrorInvalidValue is returned. + * + * \param device_arr - List of devices to try + * \param len - Number of devices in specified list + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaSetDevice, ::cudaGetDeviceProperties, + * ::cudaSetDeviceFlags, + * ::cudaChooseDevice + */ +extern __host__ cudaError_t CUDARTAPI cudaSetValidDevices(int *device_arr, int len); + +/** + * \brief Sets flags to be used for device executions + * + * Records \p flags as the flags for the current device. If the current device + * has been set and that device has already been initialized, the previous flags + * are overwritten. If the current device has not been initialized, it is + * initialized with the provided flags. If no device has been made current to + * the calling thread, a default device is selected and initialized with the + * provided flags. + * + * The two LSBs of the \p flags parameter can be used to control how the CPU + * thread interacts with the OS scheduler when waiting for results from the + * device. + * + * - ::cudaDeviceScheduleAuto: The default value if the \p flags parameter is + * zero, uses a heuristic based on the number of active CUDA contexts in the + * process \p C and the number of logical processors in the system \p P. If + * \p C \> \p P, then CUDA will yield to other OS threads when waiting for the + * device, otherwise CUDA will not yield while waiting for results and + * actively spin on the processor. Additionally, on Tegra devices, + * ::cudaDeviceScheduleAuto uses a heuristic based on the power profile of + * the platform and may choose ::cudaDeviceScheduleBlockingSync for low-powered + * devices. + * - ::cudaDeviceScheduleSpin: Instruct CUDA to actively spin when waiting for + * results from the device. This can decrease latency when waiting for the + * device, but may lower the performance of CPU threads if they are performing + * work in parallel with the CUDA thread. + * - ::cudaDeviceScheduleYield: Instruct CUDA to yield its thread when waiting + * for results from the device. This can increase latency when waiting for the + * device, but can increase the performance of CPU threads performing work in + * parallel with the device. + * - ::cudaDeviceScheduleBlockingSync: Instruct CUDA to block the CPU thread + * on a synchronization primitive when waiting for the device to finish work. + * - ::cudaDeviceBlockingSync: Instruct CUDA to block the CPU thread on a + * synchronization primitive when waiting for the device to finish work.
+ * \ref deprecated "Deprecated:" This flag was deprecated as of CUDA 4.0 and + * replaced with ::cudaDeviceScheduleBlockingSync. + * - ::cudaDeviceMapHost: This flag enables allocating pinned + * host memory that is accessible to the device. It is implicit for the + * runtime but may be absent if a context is created using the driver API. + * If this flag is not set, ::cudaHostGetDevicePointer() will always return + * a failure code. + * - ::cudaDeviceLmemResizeToMax: Instruct CUDA to not reduce local memory + * after resizing local memory for a kernel. This can prevent thrashing by + * local memory allocations when launching many kernels with high local + * memory usage at the cost of potentially increased memory usage.
+ * \ref deprecated "Deprecated:" This flag is deprecated and the behavior enabled + * by this flag is now the default and cannot be disabled. + * - ::cudaDeviceSyncMemops: Ensures that synchronous memory operations initiated + * on this context will always synchronize. See further documentation in the + * section titled "API Synchronization behavior" to learn more about cases when + * synchronous memory operations can exhibit asynchronous behavior. + * + * \param flags - Parameters for device operation + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceFlags, ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaGetDeviceProperties, + * ::cudaSetDevice, ::cudaSetValidDevices, + * ::cudaInitDevice, + * ::cudaChooseDevice, + * ::cuDevicePrimaryCtxSetFlags + */ +extern __host__ cudaError_t CUDARTAPI cudaSetDeviceFlags( unsigned int flags ); + +/** + * \brief Gets the flags for the current device + * + * + * Returns in \p flags the flags for the current device. If there is a current + * device for the calling thread, the flags for the device are returned. If + * there is no current device, the flags for the first device are returned, + * which may be the default flags. Compare to the behavior of + * ::cudaSetDeviceFlags. + * + * Typically, the flags returned should match the behavior that will be seen + * if the calling thread uses a device after this call, without any change to + * the flags or current device inbetween by this or another thread. Note that + * if the device is not initialized, it is possible for another thread to + * change the flags for the current device before it is initialized. + * Additionally, when using exclusive mode, if this thread has not requested a + * specific device, it may use a device other than the first device, contrary + * to the assumption made by this function. + * + * If a context has been created via the driver API and is current to the + * calling thread, the flags for that context are always returned. + * + * Flags returned by this function may specifically include ::cudaDeviceMapHost + * even though it is not accepted by ::cudaSetDeviceFlags because it is + * implicit in runtime API flags. The reason for this is that the current + * context may have been created via the driver API in which case the flag is + * not implicit and may be unset. + * + * \param flags - Pointer to store the device flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDevice, ::cudaGetDeviceProperties, + * ::cudaSetDevice, ::cudaSetDeviceFlags, + * ::cudaInitDevice, + * ::cuCtxGetFlags, + * ::cuDevicePrimaryCtxGetState + */ +extern __host__ cudaError_t CUDARTAPI cudaGetDeviceFlags( unsigned int *flags ); +/** @} */ /* END CUDART_DEVICE */ + +/** + * \defgroup CUDART_STREAM Stream Management + * + * ___MANBRIEF___ stream management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the stream management functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Create an asynchronous stream + * + * Creates a new asynchronous stream. + * + * \param pStream - Pointer to new stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreateWithPriority, + * ::cudaStreamCreateWithFlags, + * ::cudaStreamGetPriority, + * ::cudaStreamGetFlags, + * ::cudaStreamQuery, + * ::cudaStreamSynchronize, + * ::cudaStreamWaitEvent, + * ::cudaStreamAddCallback, + * ::cudaStreamDestroy, + * ::cuStreamCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamCreate(cudaStream_t *pStream); + +/** + * \brief Create an asynchronous stream + * + * Creates a new asynchronous stream. The \p flags argument determines the + * behaviors of the stream. Valid values for \p flags are + * - ::cudaStreamDefault: Default stream creation flag. + * - ::cudaStreamNonBlocking: Specifies that work running in the created + * stream may run concurrently with work in stream 0 (the NULL stream), and that + * the created stream should perform no implicit synchronization with stream 0. + * + * \param pStream - Pointer to new stream identifier + * \param flags - Parameters for stream creation + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, + * ::cudaStreamCreateWithPriority, + * ::cudaStreamGetFlags, + * ::cudaStreamQuery, + * ::cudaStreamSynchronize, + * ::cudaStreamWaitEvent, + * ::cudaStreamAddCallback, + * ::cudaStreamDestroy, + * ::cuStreamCreate + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamCreateWithFlags(cudaStream_t *pStream, unsigned int flags); + +/** + * \brief Create an asynchronous stream with the specified priority + * + * Creates a stream with the specified priority and returns a handle in \p pStream. + * This affects the scheduling priority of work in the stream. Priorities provide a + * hint to preferentially run work with higher priority when possible, but do + * not preempt already-running work or provide any other functional guarantee on + * execution order. + * + * \p priority follows a convention where lower numbers represent higher priorities. + * '0' represents default priority. The range of meaningful numerical priorities can + * be queried using ::cudaDeviceGetStreamPriorityRange. If the specified priority is + * outside the numerical range returned by ::cudaDeviceGetStreamPriorityRange, + * it will automatically be clamped to the lowest or the highest number in the range. + * + * \param pStream - Pointer to new stream identifier + * \param flags - Flags for stream creation. See ::cudaStreamCreateWithFlags for a list of valid flags that can be passed + * \param priority - Priority of the stream. Lower numbers represent higher priorities. + * See ::cudaDeviceGetStreamPriorityRange for more information about + * the meaningful stream priorities that can be passed. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \note Stream priorities are supported only on GPUs + * with compute capability 3.5 or higher. + * + * \note In the current implementation, only compute kernels launched in + * priority streams are affected by the stream's priority. Stream priorities have + * no effect on host-to-device and device-to-host memory operations. + * + * \sa ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags, + * ::cudaDeviceGetStreamPriorityRange, + * ::cudaStreamGetPriority, + * ::cudaStreamQuery, + * ::cudaStreamWaitEvent, + * ::cudaStreamAddCallback, + * ::cudaStreamSynchronize, + * ::cudaStreamDestroy, + * ::cuStreamCreateWithPriority + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamCreateWithPriority(cudaStream_t *pStream, unsigned int flags, int priority); + +/** + * \brief Query the priority of a stream + * + * Query the priority of a stream. The priority is returned in in \p priority. + * Note that if the stream was created with a priority outside the meaningful + * numerical range returned by ::cudaDeviceGetStreamPriorityRange, + * this function returns the clamped priority. + * See ::cudaStreamCreateWithPriority for details about priority clamping. + * + * \param hStream - Handle to the stream to be queried + * \param priority - Pointer to a signed integer in which the stream's priority is returned + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreateWithPriority, + * ::cudaDeviceGetStreamPriorityRange, + * ::cudaStreamGetFlags, + * ::cuStreamGetPriority + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetPriority(cudaStream_t hStream, int *priority); + +/** + * \brief Query the flags of a stream + * + * Query the flags of a stream. The flags are returned in \p flags. + * See ::cudaStreamCreateWithFlags for a list of valid flags. + * + * \param hStream - Handle to the stream to be queried + * \param flags - Pointer to an unsigned integer in which the stream's flags are returned + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreateWithPriority, + * ::cudaStreamCreateWithFlags, + * ::cudaStreamGetPriority, + * ::cuStreamGetFlags + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetFlags(cudaStream_t hStream, unsigned int *flags); + +/** + * \brief Query the Id of a stream + * + * Query the Id of a stream. The Id is returned in \p streamId. + * The Id is unique for the life of the program. + * + * The stream handle \p hStream can refer to any of the following: + *
    + *
  • a stream created via any of the CUDA runtime APIs such as ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags and ::cudaStreamCreateWithPriority, or their driver + * API equivalents such as ::cuStreamCreate or ::cuStreamCreateWithPriority. + * Passing an invalid handle will result in undefined behavior.
    • + *
  • any of the special streams such as the NULL stream, ::cudaStreamLegacy + * and ::cudaStreamPerThread respectively. The driver API equivalents of these + * are also accepted which are NULL, ::CU_STREAM_LEGACY and ::CU_STREAM_PER_THREAD.
    • + *
+ * + * \param hStream - Handle to the stream to be queried + * \param streamId - Pointer to an unsigned long long in which the stream Id is returned + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreateWithPriority, + * ::cudaStreamCreateWithFlags, + * ::cudaStreamGetPriority, + * ::cudaStreamGetFlags, + * ::cuStreamGetId + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetId(cudaStream_t hStream, unsigned long long *streamId); + +/** + * \brief Resets all persisting lines in cache to normal status. + * + * Resets all persisting lines in cache to normal status. + * Takes effect on function return. + * + * \return + * ::cudaSuccess, + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ cudaError_t CUDARTAPI cudaCtxResetPersistingL2Cache(void); + +/** + * \brief Copies attributes from source stream to destination stream. + * + * Copies attributes from source stream \p src to destination stream \p dst. + * Both streams must have the same context. + * + * \param[out] dst Destination stream + * \param[in] src Source stream + * For attributes see ::cudaStreamAttrID + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotSupported + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamCopyAttributes(cudaStream_t dst, cudaStream_t src); + + /** + * \brief Queries stream attribute. + * + * Queries attribute \p attr from \p hStream and stores it in corresponding + * member of \p value_out. + * + * \param[in] hStream + * \param[in] attr + * \param[out] value_out + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetAttribute( + cudaStream_t hStream, cudaStreamAttrID attr, + cudaStreamAttrValue *value_out); + + /** + * \brief Sets stream attribute. + * + * Sets attribute \p attr on \p hStream from corresponding attribute of + * \p value. The updated attribute will be applied to subsequent work + * submitted to the stream. It will not affect previously submitted work. + * + * \param[out] hStream + * \param[in] attr + * \param[in] value + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamSetAttribute( + cudaStream_t hStream, cudaStreamAttrID attr, + const cudaStreamAttrValue *value); + + /** + * \brief Destroys and cleans up an asynchronous stream + * + * Destroys and cleans up the asynchronous stream specified by \p stream. + * + * In case the device is still doing work in the stream \p stream + * when ::cudaStreamDestroy() is called, the function will return immediately + * and the resources associated with \p stream will be released automatically + * once the device has completed all work in \p stream. + * + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa ::cudaStreamCreate, + * ::cudaStreamCreateWithFlags, + * ::cudaStreamQuery, + * ::cudaStreamWaitEvent, + * ::cudaStreamSynchronize, + * ::cudaStreamAddCallback, + * ::cuStreamDestroy + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamDestroy(cudaStream_t stream); + +/** + * \brief Make a compute stream wait on an event + * + * Makes all future work submitted to \p stream wait for all work captured in + * \p event. See ::cudaEventRecord() for details on what is captured by an event. + * The synchronization will be performed efficiently on the device when applicable. + * \p event may be from a different device than \p stream. + * + * flags include: + * - ::cudaEventWaitDefault: Default event creation flag. + * - ::cudaEventWaitExternal: Event is captured in the graph as an external + * event node when performing stream capture. + * + * \param stream - Stream to wait + * \param event - Event to wait on + * \param flags - Parameters for the operation(See above) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamQuery, ::cudaStreamSynchronize, ::cudaStreamAddCallback, ::cudaStreamDestroy, + * ::cuStreamWaitEvent + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent(cudaStream_t stream, cudaEvent_t event, unsigned int flags __dv(0)); + +/** + * Type of stream callback functions. + * \param stream The stream as passed to ::cudaStreamAddCallback, may be NULL. + * \param status ::cudaSuccess or any persistent error on the stream. + * \param userData User parameter provided at registration. + */ +typedef void (CUDART_CB *cudaStreamCallback_t)(cudaStream_t stream, cudaError_t status, void *userData); + +/** + * \brief Add a callback to a compute stream + * + * \note This function is slated for eventual deprecation and removal. If + * you do not require the callback to execute in case of a device error, + * consider using ::cudaLaunchHostFunc. Additionally, this function is not + * supported with ::cudaStreamBeginCapture and ::cudaStreamEndCapture, unlike + * ::cudaLaunchHostFunc. + * + * Adds a callback to be called on the host after all currently enqueued + * items in the stream have completed. For each + * cudaStreamAddCallback call, a callback will be executed exactly once. + * The callback will block later work in the stream until it is finished. + * + * The callback may be passed ::cudaSuccess or an error code. In the event + * of a device error, all subsequently executed callbacks will receive an + * appropriate ::cudaError_t. + * + * Callbacks must not make any CUDA API calls. Attempting to use CUDA APIs + * may result in ::cudaErrorNotPermitted. Callbacks must not perform any + * synchronization that may depend on outstanding device work or other callbacks + * that are not mandated to run earlier. Callbacks without a mandated order + * (in independent streams) execute in undefined order and may be serialized. + * + * For the purposes of Unified Memory, callback execution makes a number of + * guarantees: + *
    + *
  • The callback stream is considered idle for the duration of the + * callback. Thus, for example, a callback may always use memory attached + * to the callback stream.
    • + *
  • The start of execution of a callback has the same effect as + * synchronizing an event recorded in the same stream immediately prior to + * the callback. It thus synchronizes streams which have been "joined" + * prior to the callback.
    • + *
  • Adding device work to any stream does not have the effect of making + * the stream active until all preceding callbacks have executed. Thus, for + * example, a callback might use global attached memory even if work has + * been added to another stream, if it has been properly ordered with an + * event.
    • + *
  • Completion of a callback does not cause a stream to become + * active except as described above. The callback stream will remain idle + * if no device work follows the callback, and will remain idle across + * consecutive callbacks without device work in between. Thus, for example, + * stream synchronization can be done by signaling from a callback at the + * end of the stream.
    • + *
+ * + * \param stream - Stream to add callback to + * \param callback - The function to call once preceding stream operations are complete + * \param userData - User specified data to be passed to the callback function + * \param flags - Reserved for future use, must be 0 + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamQuery, ::cudaStreamSynchronize, ::cudaStreamWaitEvent, ::cudaStreamDestroy, ::cudaMallocManaged, ::cudaStreamAttachMemAsync, + * ::cudaLaunchHostFunc, ::cuStreamAddCallback + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamAddCallback(cudaStream_t stream, + cudaStreamCallback_t callback, void *userData, unsigned int flags); + +/** + * \brief Waits for stream tasks to complete + * + * Blocks until \p stream has completed all operations. If the + * ::cudaDeviceScheduleBlockingSync flag was set for this device, + * the host thread will block until the stream is finished with + * all of its tasks. + * + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamQuery, ::cudaStreamWaitEvent, ::cudaStreamAddCallback, ::cudaStreamDestroy, + * ::cuStreamSynchronize + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamSynchronize(cudaStream_t stream); + +/** + * \brief Queries an asynchronous stream for completion status + * + * Returns ::cudaSuccess if all operations in \p stream have + * completed, or ::cudaErrorNotReady if not. + * + * For the purposes of Unified Memory, a return value of ::cudaSuccess + * is equivalent to having called ::cudaStreamSynchronize(). + * + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotReady, + * ::cudaErrorInvalidResourceHandle + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamWaitEvent, ::cudaStreamSynchronize, ::cudaStreamAddCallback, ::cudaStreamDestroy, + * ::cuStreamQuery + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamQuery(cudaStream_t stream); + +/** + * \brief Attach memory to a stream asynchronously + * + * Enqueues an operation in \p stream to specify stream association of + * \p length bytes of memory starting from \p devPtr. This function is a + * stream-ordered operation, meaning that it is dependent on, and will + * only take effect when, previous work in stream has completed. Any + * previous association is automatically replaced. + * + * \p devPtr must point to an one of the following types of memories: + * - managed memory declared using the __managed__ keyword or allocated with + * ::cudaMallocManaged. + * - a valid host-accessible region of system-allocated pageable memory. This + * type of memory may only be specified if the device associated with the + * stream reports a non-zero value for the device attribute + * ::cudaDevAttrPageableMemoryAccess. + * + * For managed allocations, \p length must be either zero or the entire + * allocation's size. Both indicate that the entire allocation's stream + * association is being changed. Currently, it is not possible to change stream + * association for a portion of a managed allocation. + * + * For pageable allocations, \p length must be non-zero. + * + * The stream association is specified using \p flags which must be + * one of ::cudaMemAttachGlobal, ::cudaMemAttachHost or ::cudaMemAttachSingle. + * The default value for \p flags is ::cudaMemAttachSingle + * If the ::cudaMemAttachGlobal flag is specified, the memory can be accessed + * by any stream on any device. + * If the ::cudaMemAttachHost flag is specified, the program makes a guarantee + * that it won't access the memory on the device from any stream on a device that + * has a zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * If the ::cudaMemAttachSingle flag is specified and \p stream is associated with + * a device that has a zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess, + * the program makes a guarantee that it will only access the memory on the device + * from \p stream. It is illegal to attach singly to the NULL stream, because the + * NULL stream is a virtual global stream and not a specific stream. An error will + * be returned in this case. + * + * When memory is associated with a single stream, the Unified Memory system will + * allow CPU access to this memory region so long as all operations in \p stream + * have completed, regardless of whether other streams are active. In effect, + * this constrains exclusive ownership of the managed memory region by + * an active GPU to per-stream activity instead of whole-GPU activity. + * + * Accessing memory on the device from streams that are not associated with + * it will produce undefined results. No error checking is performed by the + * Unified Memory system to ensure that kernels launched into other streams + * do not access this region. + * + * It is a program's responsibility to order calls to ::cudaStreamAttachMemAsync + * via events, synchronization or other means to ensure legal access to memory + * at all times. Data visibility and coherency will be changed appropriately + * for all kernels which follow a stream-association change. + * + * If \p stream is destroyed while data is associated with it, the association is + * removed and the association reverts to the default visibility of the allocation + * as specified at ::cudaMallocManaged. For __managed__ variables, the default + * association is always ::cudaMemAttachGlobal. Note that destroying a stream is an + * asynchronous operation, and as a result, the change to default association won't + * happen until all work in the stream has completed. + * + * \param stream - Stream in which to enqueue the attach operation + * \param devPtr - Pointer to memory (must be a pointer to managed memory or + * to a valid host-accessible region of system-allocated + * memory) + * \param length - Length of memory (defaults to zero) + * \param flags - Must be one of ::cudaMemAttachGlobal, ::cudaMemAttachHost or ::cudaMemAttachSingle (defaults to ::cudaMemAttachSingle) + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotReady, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, ::cudaStreamCreateWithFlags, ::cudaStreamWaitEvent, ::cudaStreamSynchronize, ::cudaStreamAddCallback, ::cudaStreamDestroy, ::cudaMallocManaged, + * ::cuStreamAttachMemAsync + */ +#if defined(__cplusplus) +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamAttachMemAsync(cudaStream_t stream, void *devPtr, size_t length __dv(0), unsigned int flags = cudaMemAttachSingle); +#else +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamAttachMemAsync(cudaStream_t stream, void *devPtr, size_t length __dv(0), unsigned int flags); +#endif + +/** + * \brief Begins graph capture on a stream + * + * Begin graph capture on \p stream. When a stream is in capture mode, all operations + * pushed into the stream will not be executed, but will instead be captured into + * a graph, which will be returned via ::cudaStreamEndCapture. Capture may not be initiated + * if \p stream is ::cudaStreamLegacy. Capture must be ended on the same stream in which + * it was initiated, and it may only be initiated if the stream is not already in capture + * mode. The capture mode may be queried via ::cudaStreamIsCapturing. A unique id + * representing the capture sequence may be queried via ::cudaStreamGetCaptureInfo. + * + * If \p mode is not ::cudaStreamCaptureModeRelaxed, ::cudaStreamEndCapture must be + * called on this stream from the same thread. + * + * \note Kernels captured using this API must not use texture and surface references. + * Reading or writing through any texture or surface reference is undefined + * behavior. This restriction does not apply to texture and surface objects. + * + * \param stream - Stream in which to initiate capture + * \param mode - Controls the interaction of this capture sequence with other API + * calls that are potentially unsafe. For more details see + * ::cudaThreadExchangeStreamCaptureMode. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaStreamCreate, + * ::cudaStreamIsCapturing, + * ::cudaStreamEndCapture, + * ::cudaThreadExchangeStreamCaptureMode + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamBeginCapture(cudaStream_t stream, enum cudaStreamCaptureMode mode); + +/** + * \brief Begins graph capture on a stream to an existing graph + * + * Begin graph capture on \p stream. When a stream is in capture mode, all operations + * pushed into the stream will not be executed, but will instead be captured into + * \p graph, which will be returned via ::cudaStreamEndCapture. + * + * Capture may not be initiated if \p stream is ::cudaStreamLegacy. Capture must be ended on the + * same stream in which it was initiated, and it may only be initiated if the stream is not + * already in capture mode. The capture mode may be queried via ::cudaStreamIsCapturing. A unique id + * representing the capture sequence may be queried via ::cudaStreamGetCaptureInfo. + * + * If \p mode is not ::cudaStreamCaptureModeRelaxed, ::cudaStreamEndCapture must be + * called on this stream from the same thread. + * + * \note Kernels captured using this API must not use texture and surface references. + * Reading or writing through any texture or surface reference is undefined + * behavior. This restriction does not apply to texture and surface objects. + * + * \param stream - Stream in which to initiate capture. + * \param graph - Graph to capture into. + * \param dependencies - Dependencies of the first node captured in the stream. Can be NULL if numDependencies is 0. + * \param dependencyData - Optional array of data associated with each dependency. + * \param numDependencies - Number of dependencies. + * \param mode - Controls the interaction of this capture sequence with other API + * calls that are potentially unsafe. For more details see + * ::cudaThreadExchangeStreamCaptureMode. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaStreamCreate, + * ::cudaStreamIsCapturing, + * ::cudaStreamEndCapture, + * ::cudaThreadExchangeStreamCaptureMode + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamBeginCaptureToGraph(cudaStream_t stream, cudaGraph_t graph, const cudaGraphNode_t *dependencies, const cudaGraphEdgeData *dependencyData, size_t numDependencies, enum cudaStreamCaptureMode mode); + +/** + * \brief Swaps the stream capture interaction mode for a thread + * + * Sets the calling thread's stream capture interaction mode to the value contained + * in \p *mode, and overwrites \p *mode with the previous mode for the thread. To + * facilitate deterministic behavior across function or module boundaries, callers + * are encouraged to use this API in a push-pop fashion: \code + cudaStreamCaptureMode mode = desiredMode; + cudaThreadExchangeStreamCaptureMode(&mode); + ... + cudaThreadExchangeStreamCaptureMode(&mode); // restore previous mode + * \endcode + * + * During stream capture (see ::cudaStreamBeginCapture), some actions, such as a call + * to ::cudaMalloc, may be unsafe. In the case of ::cudaMalloc, the operation is + * not enqueued asynchronously to a stream, and is not observed by stream capture. + * Therefore, if the sequence of operations captured via ::cudaStreamBeginCapture + * depended on the allocation being replayed whenever the graph is launched, the + * captured graph would be invalid. + * + * Therefore, stream capture places restrictions on API calls that can be made within + * or concurrently to a ::cudaStreamBeginCapture-::cudaStreamEndCapture sequence. This + * behavior can be controlled via this API and flags to ::cudaStreamBeginCapture. + * + * A thread's mode is one of the following: + * - \p cudaStreamCaptureModeGlobal: This is the default mode. If the local thread has + * an ongoing capture sequence that was not initiated with + * \p cudaStreamCaptureModeRelaxed at \p cuStreamBeginCapture, or if any other thread + * has a concurrent capture sequence initiated with \p cudaStreamCaptureModeGlobal, + * this thread is prohibited from potentially unsafe API calls. + * - \p cudaStreamCaptureModeThreadLocal: If the local thread has an ongoing capture + * sequence not initiated with \p cudaStreamCaptureModeRelaxed, it is prohibited + * from potentially unsafe API calls. Concurrent capture sequences in other threads + * are ignored. + * - \p cudaStreamCaptureModeRelaxed: The local thread is not prohibited from potentially + * unsafe API calls. Note that the thread is still prohibited from API calls which + * necessarily conflict with stream capture, for example, attempting ::cudaEventQuery + * on an event that was last recorded inside a capture sequence. + * + * \param mode - Pointer to mode value to swap with the current mode + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * + * \sa + * ::cudaStreamBeginCapture + */ +extern __host__ cudaError_t CUDARTAPI cudaThreadExchangeStreamCaptureMode(enum cudaStreamCaptureMode *mode); + +/** + * \brief Ends capture on a stream, returning the captured graph + * + * End capture on \p stream, returning the captured graph via \p pGraph. + * Capture must have been initiated on \p stream via a call to ::cudaStreamBeginCapture. + * If capture was invalidated, due to a violation of the rules of stream capture, then + * a NULL graph will be returned. + * + * If the \p mode argument to ::cudaStreamBeginCapture was not + * ::cudaStreamCaptureModeRelaxed, this call must be from the same thread as + * ::cudaStreamBeginCapture. + * + * \param stream - Stream to query + * \param pGraph - The captured graph + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorStreamCaptureWrongThread + * \notefnerr + * + * \sa + * ::cudaStreamCreate, + * ::cudaStreamBeginCapture, + * ::cudaStreamIsCapturing, + * ::cudaGraphDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamEndCapture(cudaStream_t stream, cudaGraph_t *pGraph); + +/** + * \brief Returns a stream's capture status + * + * Return the capture status of \p stream via \p pCaptureStatus. After a successful + * call, \p *pCaptureStatus will contain one of the following: + * - ::cudaStreamCaptureStatusNone: The stream is not capturing. + * - ::cudaStreamCaptureStatusActive: The stream is capturing. + * - ::cudaStreamCaptureStatusInvalidated: The stream was capturing but an error + * has invalidated the capture sequence. The capture sequence must be terminated + * with ::cudaStreamEndCapture on the stream where it was initiated in order to + * continue using \p stream. + * + * Note that, if this is called on ::cudaStreamLegacy (the "null stream") while + * a blocking stream on the same device is capturing, it will return + * ::cudaErrorStreamCaptureImplicit and \p *pCaptureStatus is unspecified + * after the call. The blocking stream capture is not invalidated. + * + * When a blocking stream is capturing, the legacy stream is in an + * unusable state until the blocking stream capture is terminated. The legacy + * stream is not supported for stream capture, but attempted use would have an + * implicit dependency on the capturing stream(s). + * + * \param stream - Stream to query + * \param pCaptureStatus - Returns the stream's capture status + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorStreamCaptureImplicit + * \notefnerr + * + * \sa + * ::cudaStreamCreate, + * ::cudaStreamBeginCapture, + * ::cudaStreamEndCapture + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamIsCapturing(cudaStream_t stream, enum cudaStreamCaptureStatus *pCaptureStatus); + +/** + * \brief Query a stream's capture state + * + * Query stream state related to stream capture. + * + * If called on ::cudaStreamLegacy (the "null stream") while a stream not created + * with ::cudaStreamNonBlocking is capturing, returns ::cudaErrorStreamCaptureImplicit. + * + * Valid data (other than capture status) is returned only if both of the following are true: + * - the call returns cudaSuccess + * - the returned capture status is ::cudaStreamCaptureStatusActive + * + * \param stream - The stream to query + * \param captureStatus_out - Location to return the capture status of the stream; required + * \param id_out - Optional location to return an id for the capture sequence, which is + * unique over the lifetime of the process + * \param graph_out - Optional location to return the graph being captured into. All + * operations other than destroy and node removal are permitted on the graph + * while the capture sequence is in progress. This API does not transfer + * ownership of the graph, which is transferred or destroyed at + * ::cudaStreamEndCapture. Note that the graph handle may be invalidated before + * end of capture for certain errors. Nodes that are or become + * unreachable from the original stream at ::cudaStreamEndCapture due to direct + * actions on the graph do not trigger ::cudaErrorStreamCaptureUnjoined. + * \param dependencies_out - Optional location to store a pointer to an array of nodes. + * The next node to be captured in the stream will depend on this set of nodes, + * absent operations such as event wait which modify this set. The array pointer + * is valid until the next API call which operates on the stream or until the + * capture is terminated. The node handles may be copied out and are valid until + * they or the graph is destroyed. The driver-owned array may also be passed + * directly to APIs that operate on the graph (not the stream) without copying. + * \param numDependencies_out - Optional location to store the size of the array + * returned in dependencies_out. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorStreamCaptureImplicit + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cudaStreamGetCaptureInfo_v3, + * ::cudaStreamBeginCapture, + * ::cudaStreamIsCapturing, + * ::cudaStreamUpdateCaptureDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo(cudaStream_t stream, enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out __dv(0), cudaGraph_t *graph_out __dv(0), const cudaGraphNode_t **dependencies_out __dv(0), size_t *numDependencies_out __dv(0)); + +/** + * \brief Query a stream's capture state (12.3+) + * + * Query stream state related to stream capture. + * + * If called on ::cudaStreamLegacy (the "null stream") while a stream not created + * with ::cudaStreamNonBlocking is capturing, returns ::cudaErrorStreamCaptureImplicit. + * + * Valid data (other than capture status) is returned only if both of the following are true: + * - the call returns cudaSuccess + * - the returned capture status is ::cudaStreamCaptureStatusActive + * + * If \p edgeData_out is non-NULL then \p dependencies_out must be as well. If + * \p dependencies_out is non-NULL and \p edgeData_out is NULL, but there is non-zero edge + * data for one or more of the current stream dependencies, the call will return + * ::cudaErrorLossyQuery. + * + * \param stream - The stream to query + * \param captureStatus_out - Location to return the capture status of the stream; required + * \param id_out - Optional location to return an id for the capture sequence, which is + * unique over the lifetime of the process + * \param graph_out - Optional location to return the graph being captured into. All + * operations other than destroy and node removal are permitted on the graph + * while the capture sequence is in progress. This API does not transfer + * ownership of the graph, which is transferred or destroyed at + * ::cudaStreamEndCapture. Note that the graph handle may be invalidated before + * end of capture for certain errors. Nodes that are or become + * unreachable from the original stream at ::cudaStreamEndCapture due to direct + * actions on the graph do not trigger ::cudaErrorStreamCaptureUnjoined. + * \param dependencies_out - Optional location to store a pointer to an array of nodes. + * The next node to be captured in the stream will depend on this set of nodes, + * absent operations such as event wait which modify this set. The array pointer + * is valid until the next API call which operates on the stream or until the + * capture is terminated. The node handles may be copied out and are valid until + * they or the graph is destroyed. The driver-owned array may also be passed + * directly to APIs that operate on the graph (not the stream) without copying. + * \param edgeData_out - Optional location to store a pointer to an array of graph edge + * data. This array parallels \c dependencies_out; the next node to be added + * has an edge to \c dependencies_out[i] with annotation \c edgeData_out[i] for + * each \c i. The array pointer is valid until the next API call which operates + * on the stream or until the capture is terminated. + * \param numDependencies_out - Optional location to store the size of the array + * returned in dependencies_out. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorStreamCaptureImplicit, + * ::cudaErrorLossyQuery + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cudaStreamBeginCapture, + * ::cudaStreamIsCapturing, + * ::cudaStreamUpdateCaptureDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo_v3(cudaStream_t stream, + enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out __dv(0), + cudaGraph_t *graph_out __dv(0), const cudaGraphNode_t **dependencies_out __dv(0), + const cudaGraphEdgeData **edgeData_out __dv(0), size_t *numDependencies_out __dv(0)); + +/** + * \brief Update the set of dependencies in a capturing stream (11.3+) + * + * Modifies the dependency set of a capturing stream. The dependency set is the set + * of nodes that the next captured node in the stream will depend on. + * + * Valid flags are ::cudaStreamAddCaptureDependencies and + * ::cudaStreamSetCaptureDependencies. These control whether the set passed to + * the API is added to the existing set or replaces it. A flags value of 0 defaults + * to ::cudaStreamAddCaptureDependencies. + * + * Nodes that are removed from the dependency set via this API do not result in + * ::cudaErrorStreamCaptureUnjoined if they are unreachable from the stream at + * ::cudaStreamEndCapture. + * + * Returns ::cudaErrorIllegalState if the stream is not capturing. + * + * This API is new in CUDA 11.3. Developers requiring compatibility across minor + * versions of the CUDA driver to 11.0 should not use this API or provide a fallback. + * + * \param stream - The stream to update + * \param dependencies - The set of dependencies to add + * \param numDependencies - The size of the dependencies array + * \param flags - See above + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorIllegalState + * \notefnerr + * + * \sa + * ::cudaStreamBeginCapture, + * ::cudaStreamGetCaptureInfo, + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamUpdateCaptureDependencies(cudaStream_t stream, cudaGraphNode_t *dependencies, size_t numDependencies, unsigned int flags __dv(0)); + +/** + * \brief Update the set of dependencies in a capturing stream (12.3+) + * + * Modifies the dependency set of a capturing stream. The dependency set is the set + * of nodes that the next captured node in the stream will depend on. + * + * Valid flags are ::cudaStreamAddCaptureDependencies and + * ::cudaStreamSetCaptureDependencies. These control whether the set passed to + * the API is added to the existing set or replaces it. A flags value of 0 defaults + * to ::cudaStreamAddCaptureDependencies. + * + * Nodes that are removed from the dependency set via this API do not result in + * ::cudaErrorStreamCaptureUnjoined if they are unreachable from the stream at + * ::cudaStreamEndCapture. + * + * Returns ::cudaErrorIllegalState if the stream is not capturing. + * + * \param stream - The stream to update + * \param dependencies - The set of dependencies to add + * \param dependencyData - Optional array of data associated with each dependency. + * \param numDependencies - The size of the dependencies array + * \param flags - See above + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorIllegalState + * \notefnerr + * + * \sa + * ::cudaStreamBeginCapture, + * ::cudaStreamGetCaptureInfo, + */ +extern __host__ cudaError_t CUDARTAPI cudaStreamUpdateCaptureDependencies_v2(cudaStream_t stream, cudaGraphNode_t *dependencies, const cudaGraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags __dv(0)); +/** @} */ /* END CUDART_STREAM */ + +/** + * \defgroup CUDART_EVENT Event Management + * + * ___MANBRIEF___ event management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the event management functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Creates an event object + * + * Creates an event object for the current device using ::cudaEventDefault. + * + * \param event - Newly created event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorLaunchFailure, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*, unsigned int) "cudaEventCreate (C++ API)", + * ::cudaEventCreateWithFlags, ::cudaEventRecord, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cudaStreamWaitEvent, + * ::cuEventCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaEventCreate(cudaEvent_t *event); + +/** + * \brief Creates an event object with the specified flags + * + * Creates an event object for the current device with the specified flags. Valid + * flags include: + * - ::cudaEventDefault: Default event creation flag. + * - ::cudaEventBlockingSync: Specifies that event should use blocking + * synchronization. A host thread that uses ::cudaEventSynchronize() to wait + * on an event created with this flag will block until the event actually + * completes. + * - ::cudaEventDisableTiming: Specifies that the created event does not need + * to record timing data. Events created with this flag specified and + * the ::cudaEventBlockingSync flag not specified will provide the best + * performance when used with ::cudaStreamWaitEvent() and ::cudaEventQuery(). + * - ::cudaEventInterprocess: Specifies that the created event may be used as an + * interprocess event by ::cudaIpcGetEventHandle(). ::cudaEventInterprocess must + * be specified along with ::cudaEventDisableTiming. + * + * \param event - Newly created event + * \param flags - Flags for new event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorLaunchFailure, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cudaStreamWaitEvent, + * ::cuEventCreate + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventCreateWithFlags(cudaEvent_t *event, unsigned int flags); + +/** + * \brief Records an event + * + * Captures in \p event the contents of \p stream at the time of this call. + * \p event and \p stream must be on the same CUDA context. + * Calls such as ::cudaEventQuery() or ::cudaStreamWaitEvent() will then + * examine or wait for completion of the work that was captured. Uses of + * \p stream after this call do not modify \p event. See note on default + * stream behavior for what is captured in the default case. + * + * ::cudaEventRecord() can be called multiple times on the same event and + * will overwrite the previously captured state. Other APIs such as + * ::cudaStreamWaitEvent() use the most recently captured state at the time + * of the API call, and are not affected by later calls to + * ::cudaEventRecord(). Before the first call to ::cudaEventRecord(), an + * event represents an empty set of work, so for example ::cudaEventQuery() + * would return ::cudaSuccess. + * + * \param event - Event to record + * \param stream - Stream in which to record event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cudaStreamWaitEvent, + * ::cudaEventRecordWithFlags, + * ::cuEventRecord + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord(cudaEvent_t event, cudaStream_t stream __dv(0)); + +/** + * \brief Records an event + * + * Captures in \p event the contents of \p stream at the time of this call. + * \p event and \p stream must be on the same CUDA context. + * Calls such as ::cudaEventQuery() or ::cudaStreamWaitEvent() will then + * examine or wait for completion of the work that was captured. Uses of + * \p stream after this call do not modify \p event. See note on default + * stream behavior for what is captured in the default case. + * + * ::cudaEventRecordWithFlags() can be called multiple times on the same event and + * will overwrite the previously captured state. Other APIs such as + * ::cudaStreamWaitEvent() use the most recently captured state at the time + * of the API call, and are not affected by later calls to + * ::cudaEventRecordWithFlags(). Before the first call to ::cudaEventRecordWithFlags(), an + * event represents an empty set of work, so for example ::cudaEventQuery() + * would return ::cudaSuccess. + * + * flags include: + * - ::cudaEventRecordDefault: Default event creation flag. + * - ::cudaEventRecordExternal: Event is captured in the graph as an external + * event node when performing stream capture. + * + * \param event - Event to record + * \param stream - Stream in which to record event + * \param flags - Parameters for the operation(See above) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cudaStreamWaitEvent, + * ::cudaEventRecord, + * ::cuEventRecord, + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags(cudaEvent_t event, cudaStream_t stream __dv(0), unsigned int flags __dv(0)); +#endif + +/** + * \brief Queries an event's status + * + * Queries the status of all work currently captured by \p event. See + * ::cudaEventRecord() for details on what is captured by an event. + * + * Returns ::cudaSuccess if all captured work has been completed, or + * ::cudaErrorNotReady if any captured work is incomplete. + * + * For the purposes of Unified Memory, a return value of ::cudaSuccess + * is equivalent to having called ::cudaEventSynchronize(). + * + * \param event - Event to query + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotReady, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure + * \notefnerr + * \note_init_rt + * \note_callback + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventRecord, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cuEventQuery + */ +extern __host__ cudaError_t CUDARTAPI cudaEventQuery(cudaEvent_t event); + +/** + * \brief Waits for an event to complete + * + * Waits until the completion of all work currently captured in \p event. + * See ::cudaEventRecord() for details on what is captured by an event. + * + * Waiting for an event that was created with the ::cudaEventBlockingSync + * flag will cause the calling CPU thread to block until the event has + * been completed by the device. If the ::cudaEventBlockingSync flag has + * not been set, then the CPU thread will busy-wait until the event has + * been completed by the device. + * + * \param event - Event to wait for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure + * \notefnerr + * \note_init_rt + * \note_callback + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventRecord, + * ::cudaEventQuery, ::cudaEventDestroy, ::cudaEventElapsedTime, + * ::cuEventSynchronize + */ +extern __host__ cudaError_t CUDARTAPI cudaEventSynchronize(cudaEvent_t event); + +/** + * \brief Destroys an event object + * + * Destroys the event specified by \p event. + * + * An event may be destroyed before it is complete (i.e., while + * ::cudaEventQuery() would return ::cudaErrorNotReady). In this case, the + * call does not block on completion of the event, and any associated + * resources will automatically be released asynchronously at completion. + * + * \param event - Event to destroy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventRecord, ::cudaEventElapsedTime, + * ::cuEventDestroy + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventDestroy(cudaEvent_t event); + +/** + * \brief Computes the elapsed time between events + * + * Computes the elapsed time between two events (in milliseconds with a + * resolution of around 0.5 microseconds). + * + * If either event was last recorded in a non-NULL stream, the resulting time + * may be greater than expected (even if both used the same stream handle). This + * happens because the ::cudaEventRecord() operation takes place asynchronously + * and there is no guarantee that the measured latency is actually just between + * the two events. Any number of other different stream operations could execute + * in between the two measured events, thus altering the timing in a significant + * way. + * + * If ::cudaEventRecord() has not been called on either event, then + * ::cudaErrorInvalidResourceHandle is returned. If ::cudaEventRecord() has been + * called on both events but one or both of them has not yet been completed + * (that is, ::cudaEventQuery() would return ::cudaErrorNotReady on at least one + * of the events), ::cudaErrorNotReady is returned. If either event was created + * with the ::cudaEventDisableTiming flag, then this function will return + * ::cudaErrorInvalidResourceHandle. + * + * \param ms - Time between \p start and \p end in ms + * \param start - Starting event + * \param end - Ending event + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotReady, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorLaunchFailure, + * ::cudaErrorUnknown + * \notefnerr + * \note_init_rt + * \note_callback + * \note_null_event + * + * \sa \ref ::cudaEventCreate(cudaEvent_t*) "cudaEventCreate (C API)", + * ::cudaEventCreateWithFlags, ::cudaEventQuery, + * ::cudaEventSynchronize, ::cudaEventDestroy, ::cudaEventRecord, + * ::cuEventElapsedTime + */ +extern __host__ cudaError_t CUDARTAPI cudaEventElapsedTime(float *ms, cudaEvent_t start, cudaEvent_t end); + +/** @} */ /* END CUDART_EVENT */ + +/** + * \defgroup CUDART_EXTRES_INTEROP External Resource Interoperability + * + * ___MANBRIEF___ External resource interoperability functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the external resource interoperability functions of the CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Imports an external memory object + * + * Imports an externally allocated memory object and returns + * a handle to that in \p extMem_out. + * + * The properties of the handle being imported must be described in + * \p memHandleDesc. The ::cudaExternalMemoryHandleDesc structure + * is defined as follows: + * + * \code + typedef struct cudaExternalMemoryHandleDesc_st { + cudaExternalMemoryHandleType type; + union { + int fd; + struct { + void *handle; + const void *name; + } win32; + const void *nvSciBufObject; + } handle; + unsigned long long size; + unsigned int flags; + } cudaExternalMemoryHandleDesc; + * \endcode + * + * where ::cudaExternalMemoryHandleDesc::type specifies the type + * of handle being imported. ::cudaExternalMemoryHandleType is + * defined as: + * + * \code + typedef enum cudaExternalMemoryHandleType_enum { + cudaExternalMemoryHandleTypeOpaqueFd = 1, + cudaExternalMemoryHandleTypeOpaqueWin32 = 2, + cudaExternalMemoryHandleTypeOpaqueWin32Kmt = 3, + cudaExternalMemoryHandleTypeD3D12Heap = 4, + cudaExternalMemoryHandleTypeD3D12Resource = 5, + cudaExternalMemoryHandleTypeD3D11Resource = 6, + cudaExternalMemoryHandleTypeD3D11ResourceKmt = 7, + cudaExternalMemoryHandleTypeNvSciBuf = 8 + } cudaExternalMemoryHandleType; + * \endcode + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeOpaqueFd, then + * ::cudaExternalMemoryHandleDesc::handle::fd must be a valid + * file descriptor referencing a memory object. Ownership of + * the file descriptor is transferred to the CUDA driver when the + * handle is imported successfully. Performing any operations on the + * file descriptor after it is imported results in undefined behavior. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeOpaqueWin32, then exactly one + * of ::cudaExternalMemoryHandleDesc::handle::win32::handle and + * ::cudaExternalMemoryHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalMemoryHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a memory object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::cudaExternalMemoryHandleDesc::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a memory object. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeOpaqueWin32Kmt, then + * ::cudaExternalMemoryHandleDesc::handle::win32::handle must + * be non-NULL and + * ::cudaExternalMemoryHandleDesc::handle::win32::name + * must be NULL. The handle specified must be a globally shared KMT + * handle. This handle does not hold a reference to the underlying + * object, and thus will be invalid when all references to the + * memory object are destroyed. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeD3D12Heap, then exactly one + * of ::cudaExternalMemoryHandleDesc::handle::win32::handle and + * ::cudaExternalMemoryHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalMemoryHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Heap object. This handle holds a reference to the underlying + * object. If ::cudaExternalMemoryHandleDesc::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D12Heap object. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeD3D12Resource, then exactly one + * of ::cudaExternalMemoryHandleDesc::handle::win32::handle and + * ::cudaExternalMemoryHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalMemoryHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Resource object. This handle holds a reference to the + * underlying object. If + * ::cudaExternalMemoryHandleDesc::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D12Resource object. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeD3D11Resource,then exactly one + * of ::cudaExternalMemoryHandleDesc::handle::win32::handle and + * ::cudaExternalMemoryHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalMemoryHandleDesc::handle::win32::handle is + * not NULL, then it must represent a valid shared NT handle that is + * returned by IDXGIResource1::CreateSharedHandle when referring to a + * ID3D11Resource object. If + * ::cudaExternalMemoryHandleDesc::handle::win32::name + * is not NULL, then it must point to a NULL-terminated array of + * UTF-16 characters that refers to a ID3D11Resource object. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeD3D11ResourceKmt, then + * ::cudaExternalMemoryHandleDesc::handle::win32::handle must + * be non-NULL and ::cudaExternalMemoryHandleDesc::handle::win32::name + * must be NULL. The handle specified must be a valid shared KMT + * handle that is returned by IDXGIResource::GetSharedHandle when + * referring to a ID3D11Resource object. + * + * If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeNvSciBuf, then + * ::cudaExternalMemoryHandleDesc::handle::nvSciBufObject must be NON-NULL + * and reference a valid NvSciBuf object. + * If the NvSciBuf object imported into CUDA is also mapped by other drivers, then the + * application must use ::cudaWaitExternalSemaphoresAsync or ::cudaSignalExternalSemaphoresAsync + * as approprriate barriers to maintain coherence between CUDA and the other drivers. + * See ::cudaExternalSemaphoreWaitSkipNvSciBufMemSync and ::cudaExternalSemaphoreSignalSkipNvSciBufMemSync + * for memory synchronization. + * + * The size of the memory object must be specified in + * ::cudaExternalMemoryHandleDesc::size. + * + * Specifying the flag ::cudaExternalMemoryDedicated in + * ::cudaExternalMemoryHandleDesc::flags indicates that the + * resource is a dedicated resource. The definition of what a + * dedicated resource is outside the scope of this extension. + * This flag must be set if ::cudaExternalMemoryHandleDesc::type + * is one of the following: + * ::cudaExternalMemoryHandleTypeD3D12Resource + * ::cudaExternalMemoryHandleTypeD3D11Resource + * ::cudaExternalMemoryHandleTypeD3D11ResourceKmt + * + * \param extMem_out - Returned handle to an external memory object + * \param memHandleDesc - Memory import handle descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorOperatingSystem + * \notefnerr + * \note_init_rt + * \note_callback + * + * \note If the Vulkan memory imported into CUDA is mapped on the CPU then the + * application must use vkInvalidateMappedMemoryRanges/vkFlushMappedMemoryRanges + * as well as appropriate Vulkan pipeline barriers to maintain coherence between + * CPU and GPU. For more information on these APIs, please refer to "Synchronization + * and Cache Control" chapter from Vulkan specification. + * + * + * \sa ::cudaDestroyExternalMemory, + * ::cudaExternalMemoryGetMappedBuffer, + * ::cudaExternalMemoryGetMappedMipmappedArray + */ +extern __host__ cudaError_t CUDARTAPI cudaImportExternalMemory(cudaExternalMemory_t *extMem_out, const struct cudaExternalMemoryHandleDesc *memHandleDesc); + +/** + * \brief Maps a buffer onto an imported memory object + * + * Maps a buffer onto an imported memory object and returns a device + * pointer in \p devPtr. + * + * The properties of the buffer being mapped must be described in + * \p bufferDesc. The ::cudaExternalMemoryBufferDesc structure is + * defined as follows: + * + * \code + typedef struct cudaExternalMemoryBufferDesc_st { + unsigned long long offset; + unsigned long long size; + unsigned int flags; + } cudaExternalMemoryBufferDesc; + * \endcode + * + * where ::cudaExternalMemoryBufferDesc::offset is the offset in + * the memory object where the buffer's base address is. + * ::cudaExternalMemoryBufferDesc::size is the size of the buffer. + * ::cudaExternalMemoryBufferDesc::flags must be zero. + * + * The offset and size have to be suitably aligned to match the + * requirements of the external API. Mapping two buffers whose ranges + * overlap may or may not result in the same virtual address being + * returned for the overlapped portion. In such cases, the application + * must ensure that all accesses to that region from the GPU are + * volatile. Otherwise writes made via one address are not guaranteed + * to be visible via the other address, even if they're issued by the + * same thread. It is recommended that applications map the combined + * range instead of mapping separate buffers and then apply the + * appropriate offsets to the returned pointer to derive the + * individual buffers. + * + * The returned pointer \p devPtr must be freed using ::cudaFree. + * + * \param devPtr - Returned device pointer to buffer + * \param extMem - Handle to external memory object + * \param bufferDesc - Buffer descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaImportExternalMemory, + * ::cudaDestroyExternalMemory, + * ::cudaExternalMemoryGetMappedMipmappedArray + */ +extern __host__ cudaError_t CUDARTAPI cudaExternalMemoryGetMappedBuffer(void **devPtr, cudaExternalMemory_t extMem, const struct cudaExternalMemoryBufferDesc *bufferDesc); + +/** + * \brief Maps a CUDA mipmapped array onto an external memory object + * + * Maps a CUDA mipmapped array onto an external object and returns a + * handle to it in \p mipmap. + * + * The properties of the CUDA mipmapped array being mapped must be + * described in \p mipmapDesc. The structure + * ::cudaExternalMemoryMipmappedArrayDesc is defined as follows: + * + * \code + typedef struct cudaExternalMemoryMipmappedArrayDesc_st { + unsigned long long offset; + cudaChannelFormatDesc formatDesc; + cudaExtent extent; + unsigned int flags; + unsigned int numLevels; + } cudaExternalMemoryMipmappedArrayDesc; + * \endcode + * + * where ::cudaExternalMemoryMipmappedArrayDesc::offset is the + * offset in the memory object where the base level of the mipmap + * chain is. + * ::cudaExternalMemoryMipmappedArrayDesc::formatDesc describes the + * format of the data. + * ::cudaExternalMemoryMipmappedArrayDesc::extent specifies the + * dimensions of the base level of the mipmap chain. + * ::cudaExternalMemoryMipmappedArrayDesc::flags are flags associated + * with CUDA mipmapped arrays. For further details, please refer to + * the documentation for ::cudaMalloc3DArray. Note that if the mipmapped + * array is bound as a color target in the graphics API, then the flag + * ::cudaArrayColorAttachment must be specified in + * ::cudaExternalMemoryMipmappedArrayDesc::flags. + * ::cudaExternalMemoryMipmappedArrayDesc::numLevels specifies + * the total number of levels in the mipmap chain. + * + * The returned CUDA mipmapped array must be freed using ::cudaFreeMipmappedArray. + * + * \param mipmap - Returned CUDA mipmapped array + * \param extMem - Handle to external memory object + * \param mipmapDesc - CUDA array descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaImportExternalMemory, + * ::cudaDestroyExternalMemory, + * ::cudaExternalMemoryGetMappedBuffer + * + * \note If ::cudaExternalMemoryHandleDesc::type is + * ::cudaExternalMemoryHandleTypeNvSciBuf, then + * ::cudaExternalMemoryMipmappedArrayDesc::numLevels must not be greater than 1. + */ +extern __host__ cudaError_t CUDARTAPI cudaExternalMemoryGetMappedMipmappedArray(cudaMipmappedArray_t *mipmap, cudaExternalMemory_t extMem, const struct cudaExternalMemoryMipmappedArrayDesc *mipmapDesc); + +/** + * \brief Destroys an external memory object. + * + * Destroys the specified external memory object. Any existing buffers + * and CUDA mipmapped arrays mapped onto this object must no longer be + * used and must be explicitly freed using ::cudaFree and + * ::cudaFreeMipmappedArray respectively. + * + * \param extMem - External memory object to be destroyed + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa ::cudaImportExternalMemory, + * ::cudaExternalMemoryGetMappedBuffer, + * ::cudaExternalMemoryGetMappedMipmappedArray + */ +extern __host__ cudaError_t CUDARTAPI cudaDestroyExternalMemory(cudaExternalMemory_t extMem); + +/** + * \brief Imports an external semaphore + * + * Imports an externally allocated synchronization object and returns + * a handle to that in \p extSem_out. + * + * The properties of the handle being imported must be described in + * \p semHandleDesc. The ::cudaExternalSemaphoreHandleDesc is defined + * as follows: + * + * \code + typedef struct cudaExternalSemaphoreHandleDesc_st { + cudaExternalSemaphoreHandleType type; + union { + int fd; + struct { + void *handle; + const void *name; + } win32; + const void* NvSciSyncObj; + } handle; + unsigned int flags; + } cudaExternalSemaphoreHandleDesc; + * \endcode + * + * where ::cudaExternalSemaphoreHandleDesc::type specifies the type of + * handle being imported. ::cudaExternalSemaphoreHandleType is defined + * as: + * + * \code + typedef enum cudaExternalSemaphoreHandleType_enum { + cudaExternalSemaphoreHandleTypeOpaqueFd = 1, + cudaExternalSemaphoreHandleTypeOpaqueWin32 = 2, + cudaExternalSemaphoreHandleTypeOpaqueWin32Kmt = 3, + cudaExternalSemaphoreHandleTypeD3D12Fence = 4, + cudaExternalSemaphoreHandleTypeD3D11Fence = 5, + cudaExternalSemaphoreHandleTypeNvSciSync = 6, + cudaExternalSemaphoreHandleTypeKeyedMutex = 7, + cudaExternalSemaphoreHandleTypeKeyedMutexKmt = 8, + cudaExternalSemaphoreHandleTypeTimelineSemaphoreFd = 9, + cudaExternalSemaphoreHandleTypeTimelineSemaphoreWin32 = 10 + } cudaExternalSemaphoreHandleType; + * \endcode + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeOpaqueFd, then + * ::cudaExternalSemaphoreHandleDesc::handle::fd must be a valid file + * descriptor referencing a synchronization object. Ownership of the + * file descriptor is transferred to the CUDA driver when the handle + * is imported successfully. Performing any operations on the file + * descriptor after it is imported results in undefined behavior. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32, then exactly one of + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle and + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalSemaphoreHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a synchronization object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::cudaExternalSemaphoreHandleDesc::handle::win32::name is + * not NULL, then it must name a valid synchronization object. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32Kmt, then + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle must be + * non-NULL and ::cudaExternalSemaphoreHandleDesc::handle::win32::name + * must be NULL. The handle specified must be a globally shared KMT + * handle. This handle does not hold a reference to the underlying + * object, and thus will be invalid when all references to the + * synchronization object are destroyed. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeD3D12Fence, then exactly one of + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle and + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalSemaphoreHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D12Device::CreateSharedHandle when referring to a + * ID3D12Fence object. This handle holds a reference to the underlying + * object. If ::cudaExternalSemaphoreHandleDesc::handle::win32::name + * is not NULL, then it must name a valid synchronization object that + * refers to a valid ID3D12Fence object. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeD3D11Fence, then exactly one of + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle and + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalSemaphoreHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * is returned by ID3D11Fence::CreateSharedHandle. If + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name + * is not NULL, then it must name a valid synchronization object that + * refers to a valid ID3D11Fence object. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeNvSciSync, then + * ::cudaExternalSemaphoreHandleDesc::handle::nvSciSyncObj + * represents a valid NvSciSyncObj. + * + * ::cudaExternalSemaphoreHandleTypeKeyedMutex, then exactly one of + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle and + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalSemaphoreHandleDesc::handle::win32::handle + * is not NULL, then it represent a valid shared NT handle that + * is returned by IDXGIResource1::CreateSharedHandle when referring to + * a IDXGIKeyedMutex object. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeKeyedMutexKmt, then + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle must be + * non-NULL and ::cudaExternalSemaphoreHandleDesc::handle::win32::name + * must be NULL. The handle specified must represent a valid KMT + * handle that is returned by IDXGIResource::GetSharedHandle when + * referring to a IDXGIKeyedMutex object. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreFd, then + * ::cudaExternalSemaphoreHandleDesc::handle::fd must be a valid file + * descriptor referencing a synchronization object. Ownership of the + * file descriptor is transferred to the CUDA driver when the handle + * is imported successfully. Performing any operations on the file + * descriptor after it is imported results in undefined behavior. + * + * If ::cudaExternalSemaphoreHandleDesc::type is + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreWin32, then exactly one of + * ::cudaExternalSemaphoreHandleDesc::handle::win32::handle and + * ::cudaExternalSemaphoreHandleDesc::handle::win32::name must not be + * NULL. If ::cudaExternalSemaphoreHandleDesc::handle::win32::handle + * is not NULL, then it must represent a valid shared NT handle that + * references a synchronization object. Ownership of this handle is + * not transferred to CUDA after the import operation, so the + * application must release the handle using the appropriate system + * call. If ::cudaExternalSemaphoreHandleDesc::handle::win32::name is + * not NULL, then it must name a valid synchronization object. + * + * \param extSem_out - Returned handle to an external semaphore + * \param semHandleDesc - Semaphore import handle descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorOperatingSystem + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDestroyExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaImportExternalSemaphore(cudaExternalSemaphore_t *extSem_out, const struct cudaExternalSemaphoreHandleDesc *semHandleDesc); + +/** + * \brief Signals a set of external semaphore objects + * + * Enqueues a signal operation on a set of externally allocated + * semaphore object in the specified stream. The operations will be + * executed when all prior operations in the stream complete. + * + * The exact semantics of signaling a semaphore depends on the type of + * the object. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeOpaqueFd, + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32, + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32Kmt + * then signaling the semaphore will set it to the signaled state. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeD3D12Fence, + * ::cudaExternalSemaphoreHandleTypeD3D11Fence, + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreFd, + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreWin32 + * then the semaphore will be set to the value specified in + * ::cudaExternalSemaphoreSignalParams::params::fence::value. + * + * If the semaphore object is of the type ::cudaExternalSemaphoreHandleTypeNvSciSync + * this API sets ::cudaExternalSemaphoreSignalParams::params::nvSciSync::fence to a + * value that can be used by subsequent waiters of the same NvSciSync object to + * order operations with those currently submitted in \p stream. Such an update + * will overwrite previous contents of + * ::cudaExternalSemaphoreSignalParams::params::nvSciSync::fence. By default, + * signaling such an external semaphore object causes appropriate memory synchronization + * operations to be performed over all the external memory objects that are imported as + * ::cudaExternalMemoryHandleTypeNvSciBuf. This ensures that any subsequent accesses + * made by other importers of the same set of NvSciBuf memory object(s) are coherent. + * These operations can be skipped by specifying the flag + * ::cudaExternalSemaphoreSignalSkipNvSciBufMemSync, which can be used as a + * performance optimization when data coherency is not required. But specifying this + * flag in scenarios where data coherency is required results in undefined behavior. + * Also, for semaphore object of the type ::cudaExternalSemaphoreHandleTypeNvSciSync, + * if the NvSciSyncAttrList used to create the NvSciSyncObj had not set the flags in + * ::cudaDeviceGetNvSciSyncAttributes to cudaNvSciSyncAttrSignal, this API will return + * cudaErrorNotSupported. + * + * ::cudaExternalSemaphoreSignalParams::params::nvSciSync::fence associated with + * semaphore object of the type ::cudaExternalSemaphoreHandleTypeNvSciSync can be + * deterministic. For this the NvSciSyncAttrList used to create the semaphore object + * must have value of NvSciSyncAttrKey_RequireDeterministicFences key set to true. + * Deterministic fences allow users to enqueue a wait over the semaphore object even + * before corresponding signal is enqueued. For such a semaphore object, CUDA guarantees + * that each signal operation will increment the fence value by '1'. Users are expected + * to track count of signals enqueued on the semaphore object and insert waits accordingly. + * When such a semaphore object is signaled from multiple streams, due to concurrent + * stream execution, it is possible that the order in which the semaphore gets signaled + * is indeterministic. This could lead to waiters of the semaphore getting unblocked + * incorrectly. Users are expected to handle such situations, either by not using the + * same semaphore object with deterministic fence support enabled in different streams + * or by adding explicit dependency amongst such streams so that the semaphore is + * signaled in order. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeKeyedMutex, + * ::cudaExternalSemaphoreHandleTypeKeyedMutexKmt, + * then the keyed mutex will be released with the key specified in + * ::cudaExternalSemaphoreSignalParams::params::keyedmutex::key. + * + * \param extSemArray - Set of external semaphores to be signaled + * \param paramsArray - Array of semaphore parameters + * \param numExtSems - Number of semaphores to signal + * \param stream - Stream to enqueue the signal operations in + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaImportExternalSemaphore, + * ::cudaDestroyExternalSemaphore, + * ::cudaWaitExternalSemaphoresAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaSignalExternalSemaphoresAsync(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreSignalParams *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + +/** + * \brief Waits on a set of external semaphore objects + * + * Enqueues a wait operation on a set of externally allocated + * semaphore object in the specified stream. The operations will be + * executed when all prior operations in the stream complete. + * + * The exact semantics of waiting on a semaphore depends on the type + * of the object. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeOpaqueFd, + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32, + * ::cudaExternalSemaphoreHandleTypeOpaqueWin32Kmt + * then waiting on the semaphore will wait until the semaphore reaches + * the signaled state. The semaphore will then be reset to the + * unsignaled state. Therefore for every signal operation, there can + * only be one wait operation. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeD3D12Fence, + * ::cudaExternalSemaphoreHandleTypeD3D11Fence, + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreFd, + * ::cudaExternalSemaphoreHandleTypeTimelineSemaphoreWin32 + * then waiting on the semaphore will wait until the value of the + * semaphore is greater than or equal to + * ::cudaExternalSemaphoreWaitParams::params::fence::value. + * + * If the semaphore object is of the type ::cudaExternalSemaphoreHandleTypeNvSciSync + * then, waiting on the semaphore will wait until the + * ::cudaExternalSemaphoreSignalParams::params::nvSciSync::fence is signaled by the + * signaler of the NvSciSyncObj that was associated with this semaphore object. + * By default, waiting on such an external semaphore object causes appropriate + * memory synchronization operations to be performed over all external memory objects + * that are imported as ::cudaExternalMemoryHandleTypeNvSciBuf. This ensures that + * any subsequent accesses made by other importers of the same set of NvSciBuf memory + * object(s) are coherent. These operations can be skipped by specifying the flag + * ::cudaExternalSemaphoreWaitSkipNvSciBufMemSync, which can be used as a + * performance optimization when data coherency is not required. But specifying this + * flag in scenarios where data coherency is required results in undefined behavior. + * Also, for semaphore object of the type ::cudaExternalSemaphoreHandleTypeNvSciSync, + * if the NvSciSyncAttrList used to create the NvSciSyncObj had not set the flags in + * ::cudaDeviceGetNvSciSyncAttributes to cudaNvSciSyncAttrWait, this API will return + * cudaErrorNotSupported. + * + * If the semaphore object is any one of the following types: + * ::cudaExternalSemaphoreHandleTypeKeyedMutex, + * ::cudaExternalSemaphoreHandleTypeKeyedMutexKmt, + * then the keyed mutex will be acquired when it is released with the key specified + * in ::cudaExternalSemaphoreSignalParams::params::keyedmutex::key or + * until the timeout specified by + * ::cudaExternalSemaphoreSignalParams::params::keyedmutex::timeoutMs + * has lapsed. The timeout interval can either be a finite value + * specified in milliseconds or an infinite value. In case an infinite + * value is specified the timeout never elapses. The windows INFINITE + * macro must be used to specify infinite timeout + * + * \param extSemArray - External semaphores to be waited on + * \param paramsArray - Array of semaphore parameters + * \param numExtSems - Number of semaphores to wait on + * \param stream - Stream to enqueue the wait operations in + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle + * ::cudaErrorTimeout + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaImportExternalSemaphore, + * ::cudaDestroyExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaWaitExternalSemaphoresAsync(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreWaitParams *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + +/** + * \brief Destroys an external semaphore + * + * Destroys an external semaphore object and releases any references + * to the underlying resource. Any outstanding signals or waits must + * have completed before the semaphore is destroyed. + * + * \param extSem - External semaphore to be destroyed + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa ::cudaImportExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaDestroyExternalSemaphore(cudaExternalSemaphore_t extSem); + +/** @} */ /* END CUDART_EXTRES_INTEROP */ + +/** + * \defgroup CUDART_EXECUTION Execution Control + * + * ___MANBRIEF___ execution control functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the execution control functions of the CUDA runtime + * application programming interface. + * + * Some functions have overloaded C++ API template versions documented separately in the + * \ref CUDART_HIGHLEVEL "C++ API Routines" module. + * + * @{ + */ + +/** + * \brief Launches a device function + * + * The function invokes kernel \p func on \p gridDim (\p gridDim.x × \p gridDim.y + * × \p gridDim.z) grid of blocks. Each block contains \p blockDim (\p blockDim.x × + * \p blockDim.y × \p blockDim.z) threads. + * + * If the kernel has N parameters the \p args should point to array of N pointers. + * Each pointer, from args[0] to args[N - 1], point to the region + * of memory from which the actual parameter will be copied. + * + * For templated functions, pass the function symbol as follows: + * func_name + * + * \p sharedMem sets the amount of dynamic shared memory that will be available to + * each thread block. + * + * \p stream specifies a stream the invocation is associated to. + * + * \param func - Device function symbol + * \param gridDim - Grid dimentions + * \param blockDim - Block dimentions + * \param args - Arguments + * \param sharedMem - Shared memory + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorSharedObjectInitFailed, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaLaunchKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C++ API)", + * ::cuLaunchKernel + */ +extern __host__ cudaError_t CUDARTAPI cudaLaunchKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream); + +/** + * \brief Launches a CUDA function with launch-time configuration + * + * Note that the functionally equivalent variadic template ::cudaLaunchKernelEx + * is available for C++11 and newer. + * + * Invokes the kernel \p func on \p config->gridDim (\p config->gridDim.x + * × \p config->gridDim.y × \p config->gridDim.z) grid of blocks. + * Each block contains \p config->blockDim (\p config->blockDim.x × + * \p config->blockDim.y × \p config->blockDim.z) threads. + * + * \p config->dynamicSmemBytes sets the amount of dynamic shared memory that + * will be available to each thread block. + * + * \p config->stream specifies a stream the invocation is associated to. + * + * Configuration beyond grid and block dimensions, dynamic shared memory size, + * and stream can be provided with the following two fields of \p config: + * + * \p config->attrs is an array of \p config->numAttrs contiguous + * ::cudaLaunchAttribute elements. The value of this pointer is not considered + * if \p config->numAttrs is zero. However, in that case, it is recommended to + * set the pointer to NULL. + * \p config->numAttrs is the number of attributes populating the first + * \p config->numAttrs positions of the \p config->attrs array. + * + * If the kernel has N parameters the \p args should point to array of N + * pointers. Each pointer, from args[0] to args[N - 1], point + * to the region of memory from which the actual parameter will be copied. + * + * N.B. This function is so named to avoid unintentionally invoking the + * templated version, \p cudaLaunchKernelEx, for kernels taking a single + * void** or void* parameter. + * + * \param config - Launch configuration + * \param func - Kernel to launch + * \param args - Array of pointers to kernel parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorSharedObjectInitFailed, + * ::cudaErrorInvalidPtx, + * ::cudaErrorUnsupportedPtxVersion, + * ::cudaErrorNoKernelImageForDevice, + * ::cudaErrorJitCompilerNotFound, + * ::cudaErrorJitCompilationDisabled + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaLaunchKernelEx(const cudaLaunchConfig_t *config, void (*kernel)(ExpTypes...), ActTypes &&... args) "cudaLaunchKernelEx (C++ API)", + * ::cuLaunchKernelEx + */ +extern __host__ cudaError_t CUDARTAPI cudaLaunchKernelExC(const cudaLaunchConfig_t *config, const void *func, void **args); + +/** + * \brief Launches a device function where thread blocks can cooperate and synchronize as they execute + * + * The function invokes kernel \p func on \p gridDim (\p gridDim.x × \p gridDim.y + * × \p gridDim.z) grid of blocks. Each block contains \p blockDim (\p blockDim.x × + * \p blockDim.y × \p blockDim.z) threads. + * + * The device on which this kernel is invoked must have a non-zero value for + * the device attribute ::cudaDevAttrCooperativeLaunch. + * + * The total number of blocks launched cannot exceed the maximum number of blocks per + * multiprocessor as returned by ::cudaOccupancyMaxActiveBlocksPerMultiprocessor (or + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags) times the number of multiprocessors + * as specified by the device attribute ::cudaDevAttrMultiProcessorCount. + * + * The kernel cannot make use of CUDA dynamic parallelism. + * + * If the kernel has N parameters the \p args should point to array of N pointers. + * Each pointer, from args[0] to args[N - 1], point to the region + * of memory from which the actual parameter will be copied. + * + * For templated functions, pass the function symbol as follows: + * func_name + * + * \p sharedMem sets the amount of dynamic shared memory that will be available to + * each thread block. + * + * \p stream specifies a stream the invocation is associated to. + * + * \param func - Device function symbol + * \param gridDim - Grid dimentions + * \param blockDim - Block dimentions + * \param args - Arguments + * \param sharedMem - Shared memory + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorCooperativeLaunchTooLarge, + * ::cudaErrorSharedObjectInitFailed + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaLaunchCooperativeKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchCooperativeKernel (C++ API)", + * ::cudaLaunchCooperativeKernelMultiDevice, + * ::cuLaunchCooperativeKernel + */ +extern __host__ cudaError_t CUDARTAPI cudaLaunchCooperativeKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream); + +/** + * \brief Launches device functions on multiple devices where thread blocks can cooperate and synchronize as they execute + * + * \deprecated This function is deprecated as of CUDA 11.3. + * + * Invokes kernels as specified in the \p launchParamsList array where each element + * of the array specifies all the parameters required to perform a single kernel launch. + * These kernels can cooperate and synchronize as they execute. The size of the array is + * specified by \p numDevices. + * + * No two kernels can be launched on the same device. All the devices targeted by this + * multi-device launch must be identical. All devices must have a non-zero value for the + * device attribute ::cudaDevAttrCooperativeMultiDeviceLaunch. + * + * The same kernel must be launched on all devices. Note that any __device__ or __constant__ + * variables are independently instantiated on every device. It is the application's + * responsiblity to ensure these variables are initialized and used appropriately. + * + * The size of the grids as specified in blocks, the size of the blocks themselves and the + * amount of shared memory used by each thread block must also match across all launched kernels. + * + * The streams used to launch these kernels must have been created via either ::cudaStreamCreate + * or ::cudaStreamCreateWithPriority or ::cudaStreamCreateWithPriority. The NULL stream or + * ::cudaStreamLegacy or ::cudaStreamPerThread cannot be used. + * + * The total number of blocks launched per kernel cannot exceed the maximum number of blocks + * per multiprocessor as returned by ::cudaOccupancyMaxActiveBlocksPerMultiprocessor (or + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags) times the number of multiprocessors + * as specified by the device attribute ::cudaDevAttrMultiProcessorCount. Since the + * total number of blocks launched per device has to match across all devices, the maximum + * number of blocks that can be launched per device will be limited by the device with the + * least number of multiprocessors. + * + * The kernel cannot make use of CUDA dynamic parallelism. + * + * The ::cudaLaunchParams structure is defined as: + * \code + struct cudaLaunchParams + { + void *func; + dim3 gridDim; + dim3 blockDim; + void **args; + size_t sharedMem; + cudaStream_t stream; + }; + * \endcode + * where: + * - ::cudaLaunchParams::func specifies the kernel to be launched. This same functions must + * be launched on all devices. For templated functions, pass the function symbol as follows: + * func_name + * - ::cudaLaunchParams::gridDim specifies the width, height and depth of the grid in blocks. + * This must match across all kernels launched. + * - ::cudaLaunchParams::blockDim is the width, height and depth of each thread block. This + * must match across all kernels launched. + * - ::cudaLaunchParams::args specifies the arguments to the kernel. If the kernel has + * N parameters then ::cudaLaunchParams::args should point to array of N pointers. Each + * pointer, from ::cudaLaunchParams::args[0] to ::cudaLaunchParams::args[N - 1], + * point to the region of memory from which the actual parameter will be copied. + * - ::cudaLaunchParams::sharedMem is the dynamic shared-memory size per thread block in bytes. + * This must match across all kernels launched. + * - ::cudaLaunchParams::stream is the handle to the stream to perform the launch in. This cannot + * be the NULL stream or ::cudaStreamLegacy or ::cudaStreamPerThread. + * + * By default, the kernel won't begin execution on any GPU until all prior work in all the specified + * streams has completed. This behavior can be overridden by specifying the flag + * ::cudaCooperativeLaunchMultiDeviceNoPreSync. When this flag is specified, each kernel + * will only wait for prior work in the stream corresponding to that GPU to complete before it begins + * execution. + * + * Similarly, by default, any subsequent work pushed in any of the specified streams will not begin + * execution until the kernels on all GPUs have completed. This behavior can be overridden by specifying + * the flag ::cudaCooperativeLaunchMultiDeviceNoPostSync. When this flag is specified, + * any subsequent work pushed in any of the specified streams will only wait for the kernel launched + * on the GPU corresponding to that stream to complete before it begins execution. + * + * \param launchParamsList - List of launch parameters, one per device + * \param numDevices - Size of the \p launchParamsList array + * \param flags - Flags to control launch behavior + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidConfiguration, + * ::cudaErrorLaunchFailure, + * ::cudaErrorLaunchTimeout, + * ::cudaErrorLaunchOutOfResources, + * ::cudaErrorCooperativeLaunchTooLarge, + * ::cudaErrorSharedObjectInitFailed + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaLaunchCooperativeKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchCooperativeKernel (C++ API)", + * ::cudaLaunchCooperativeKernel, + * ::cuLaunchCooperativeKernelMultiDevice + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaLaunchCooperativeKernelMultiDevice(struct cudaLaunchParams *launchParamsList, unsigned int numDevices, unsigned int flags __dv(0)); + +/** + * \brief Sets the preferred cache configuration for a device function + * + * On devices where the L1 cache and shared memory use the same hardware + * resources, this sets through \p cacheConfig the preferred cache configuration + * for the function specified via \p func. This is only a preference. The + * runtime will use the requested configuration if possible, but it is free to + * choose a different configuration if required to execute \p func. + * + * \p func is a device function symbol and must be declared as a + * \c __global__ function. If the specified function does not exist, + * then ::cudaErrorInvalidDeviceFunction is returned. For templated functions, + * pass the function symbol as follows: func_name + * + * This setting does nothing on devices where the size of the L1 cache and + * shared memory are fixed. + * + * Launching a kernel with a different preference than the most recent + * preference setting may insert a device-side synchronization point. + * + * The supported cache configurations are: + * - ::cudaFuncCachePreferNone: no preference for shared memory or L1 (default) + * - ::cudaFuncCachePreferShared: prefer larger shared memory and smaller L1 cache + * - ::cudaFuncCachePreferL1: prefer larger L1 cache and smaller shared memory + * - ::cudaFuncCachePreferEqual: prefer equal size L1 cache and shared memory + * + * \param func - Device function symbol + * \param cacheConfig - Requested cache configuration + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_string_api_deprecation2 + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + * \ref ::cudaLaunchKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C API)", + * ::cuFuncSetCacheConfig + */ +extern __host__ cudaError_t CUDARTAPI cudaFuncSetCacheConfig(const void *func, enum cudaFuncCache cacheConfig); + +/** + * \brief Find out attributes for a given function + * + * This function obtains the attributes of a function specified via \p func. + * \p func is a device function symbol and must be declared as a + * \c __global__ function. The fetched attributes are placed in \p attr. + * If the specified function does not exist, then + * ::cudaErrorInvalidDeviceFunction is returned. For templated functions, pass + * the function symbol as follows: func_name + * + * Note that some function attributes such as + * \ref ::cudaFuncAttributes::maxThreadsPerBlock "maxThreadsPerBlock" + * may vary based on the device that is currently being used. + * + * \param attr - Return pointer to function's attributes + * \param func - Device function symbol + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_string_api_deprecation2 + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, T*) "cudaFuncGetAttributes (C++ API)", + * \ref ::cudaLaunchKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C API)", + * ::cuFuncGetAttribute + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncGetAttributes(struct cudaFuncAttributes *attr, const void *func); + + +/** + * \brief Set attributes for a given function + * + * This function sets the attributes of a function specified via \p func. + * The parameter \p func must be a pointer to a function that executes + * on the device. The parameter specified by \p func must be declared as a \p __global__ + * function. The enumeration defined by \p attr is set to the value defined by \p value. + * If the specified function does not exist, then ::cudaErrorInvalidDeviceFunction is returned. + * If the specified attribute cannot be written, or if the value is incorrect, + * then ::cudaErrorInvalidValue is returned. + * + * Valid values for \p attr are: + * - ::cudaFuncAttributeMaxDynamicSharedMemorySize - The requested maximum size in bytes of dynamically-allocated shared memory. The sum of this value and the function attribute ::sharedSizeBytes + * cannot exceed the device attribute ::cudaDevAttrMaxSharedMemoryPerBlockOptin. The maximal size of requestable dynamic shared memory may differ by GPU architecture. + * - ::cudaFuncAttributePreferredSharedMemoryCarveout - On devices where the L1 cache and shared memory use the same hardware resources, + * this sets the shared memory carveout preference, in percent of the total shared memory. See ::cudaDevAttrMaxSharedMemoryPerMultiprocessor. + * This is only a hint, and the driver can choose a different ratio if required to execute the function. + * + * \param func - Function to get attributes of + * \param attr - Attribute to set + * \param value - Value to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaLaunchKernel(const T *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream) "cudaLaunchKernel (C++ API)", + * \ref ::cudaFuncSetCacheConfig(T*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C++ API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncSetAttribute(const void *func, enum cudaFuncAttribute attr, int value); + +/** + * \brief Returns the function name for a device entry function pointer. + * + * Returns in \p **name the function name associated with the symbol \p func . + * The function name is returned as a null-terminated string. This API may + * return a mangled name if the function is not declared as having C linkage. + * If \p **name is NULL, ::cudaErrorInvalidValue is returned. If \p func is + * not a device entry function, ::cudaErrorInvalidDeviceFunction is returned. + * + * \param name - The returned name of the function + * \param func - The function pointer to retrieve name for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction + * \notefnerr + * \note_init_rt + * \note_callback + * + * \ref ::cudaFuncGetName(const char **name, const T *func) "cudaFuncGetName (C++ API)" + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncGetName(const char **name, const void *func); + +/** + * \brief Returns the offset and size of a kernel parameter in the device-side parameter layout. + * + * Queries the kernel parameter at \p paramIndex in \p func's list of parameters and returns + * parameter information via \p paramOffset and \p paramSize. \p paramOffset returns the + * offset of the parameter in the device-side parameter layout. \p paramSize returns the size + * in bytes of the parameter. This information can be used to update kernel node parameters + * from the device via ::cudaGraphKernelNodeSetParam() and ::cudaGraphKernelNodeUpdatesApply(). + * \p paramIndex must be less than the number of parameters that \p func takes. + * + * \param func - The function to query + * \param paramIndex - The parameter index to query + * \param paramOffset - The offset into the device-side parameter layout at which the parameter resides + * \param paramSize - The size of the parameter in the device-side parameter layout + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * \notefnerr + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFuncGetParamInfo(const void *func, size_t paramIndex, size_t *paramOffset, size_t *paramSize); + +/** + * \brief Converts a double argument to be executed on a device + * + * \param d - Double to convert + * + * \deprecated This function is deprecated as of CUDA 7.5 + * + * Converts the double value of \p d to an internal float representation if + * the device does not support double arithmetic. If the device does natively + * support doubles, then this function does nothing. + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + * ::cudaSetDoubleForHost + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaSetDoubleForDevice(double *d); + +/** + * \brief Converts a double argument after execution on a device + * + * \deprecated This function is deprecated as of CUDA 7.5 + * + * Converts the double value of \p d from a potentially internal float + * representation if the device does not support double arithmetic. If the + * device does natively support doubles, then this function does nothing. + * + * \param d - Double to convert + * + * \return + * ::cudaSuccess + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaFuncSetCacheConfig(const void*, enum cudaFuncCache) "cudaFuncSetCacheConfig (C API)", + * \ref ::cudaFuncGetAttributes(struct cudaFuncAttributes*, const void*) "cudaFuncGetAttributes (C API)", + * ::cudaSetDoubleForDevice + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaSetDoubleForHost(double *d); + +/** + * \brief Enqueues a host function call in a stream + * + * Enqueues a host function to run in a stream. The function will be called + * after currently enqueued work and will block work added after it. + * + * The host function must not make any CUDA API calls. Attempting to use a + * CUDA API may result in ::cudaErrorNotPermitted, but this is not required. + * The host function must not perform any synchronization that may depend on + * outstanding CUDA work not mandated to run earlier. Host functions without a + * mandated order (such as in independent streams) execute in undefined order + * and may be serialized. + * + * For the purposes of Unified Memory, execution makes a number of guarantees: + *
    + *
  • The stream is considered idle for the duration of the function's + * execution. Thus, for example, the function may always use memory attached + * to the stream it was enqueued in.
    • + *
  • The start of execution of the function has the same effect as + * synchronizing an event recorded in the same stream immediately prior to + * the function. It thus synchronizes streams which have been "joined" + * prior to the function.
    • + *
  • Adding device work to any stream does not have the effect of making + * the stream active until all preceding host functions and stream callbacks + * have executed. Thus, for + * example, a function might use global attached memory even if work has + * been added to another stream, if the work has been ordered behind the + * function call with an event.
    • + *
  • Completion of the function does not cause a stream to become + * active except as described above. The stream will remain idle + * if no device work follows the function, and will remain idle across + * consecutive host functions or stream callbacks without device work in + * between. Thus, for example, + * stream synchronization can be done by signaling from a host function at the + * end of the stream.
    • + *
+ * + * Note that, in constrast to ::cuStreamAddCallback, the function will not be + * called in the event of an error in the CUDA context. + * + * \param hStream - Stream to enqueue function call in + * \param fn - The function to call once preceding stream operations are complete + * \param userData - User-specified data to be passed to the function + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaStreamCreate, + * ::cudaStreamQuery, + * ::cudaStreamSynchronize, + * ::cudaStreamWaitEvent, + * ::cudaStreamDestroy, + * ::cudaMallocManaged, + * ::cudaStreamAttachMemAsync, + * ::cudaStreamAddCallback, + * ::cuLaunchHostFunc + */ +extern __host__ cudaError_t CUDARTAPI cudaLaunchHostFunc(cudaStream_t stream, cudaHostFn_t fn, void *userData); + +/** @} */ /* END CUDART_EXECUTION */ + +/** + * \defgroup CUDART_EXECUTION_DEPRECATED Execution Control [DEPRECATED] + * + * ___MANBRIEF___ deprecated execution control functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the deprecated execution control functions of the CUDA runtime + * application programming interface. + * + * Some functions have overloaded C++ API template versions documented separately in the + * \ref CUDART_HIGHLEVEL "C++ API Routines" module. + * + * @{ + */ + +/** + * \brief Sets the shared memory configuration for a device function + * + * \deprecated + * + * On devices with configurable shared memory banks, this function will + * force all subsequent launches of the specified device function to have + * the given shared memory bank size configuration. On any given launch of the + * function, the shared memory configuration of the device will be temporarily + * changed if needed to suit the function's preferred configuration. Changes in + * shared memory configuration between subsequent launches of functions, + * may introduce a device side synchronization point. + * + * Any per-function setting of shared memory bank size set via + * ::cudaFuncSetSharedMemConfig will override the device wide setting set by + * ::cudaDeviceSetSharedMemConfig. + * + * Changing the shared memory bank size will not increase shared memory usage + * or affect occupancy of kernels, but may have major effects on performance. + * Larger bank sizes will allow for greater potential bandwidth to shared memory, + * but will change what kinds of accesses to shared memory will result in bank + * conflicts. + * + * This function will do nothing on devices with fixed shared memory bank size. + * + * For templated functions, pass the function symbol as follows: + * func_name + * + * The supported bank configurations are: + * - ::cudaSharedMemBankSizeDefault: use the device's shared memory configuration + * when launching this function. + * - ::cudaSharedMemBankSizeFourByte: set shared memory bank width to be + * four bytes natively when launching this function. + * - ::cudaSharedMemBankSizeEightByte: set shared memory bank width to be eight + * bytes natively when launching this function. + * + * \param func - Device function symbol + * \param config - Requested shared memory configuration + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_string_api_deprecation2 + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceSetSharedMemConfig, + * ::cudaDeviceGetSharedMemConfig, + * ::cudaDeviceSetCacheConfig, + * ::cudaDeviceGetCacheConfig, + * ::cudaFuncSetCacheConfig, + * ::cuFuncSetSharedMemConfig + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaFuncSetSharedMemConfig(const void *func, enum cudaSharedMemConfig config); +/** @} */ /* END CUDART_EXECUTION_DEPRECATED */ + +/** + * \defgroup CUDART_OCCUPANCY Occupancy + * + * ___MANBRIEF___ occupancy calculation functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the occupancy calculation functions of the CUDA runtime + * application programming interface. + * + * Besides the occupancy calculator functions + * (\ref ::cudaOccupancyMaxActiveBlocksPerMultiprocessor and \ref ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags), + * there are also C++ only occupancy-based launch configuration functions documented in + * \ref CUDART_HIGHLEVEL "C++ API Routines" module. + * + * See + * \ref ::cudaOccupancyMaxPotentialBlockSize(int*, int*, T, size_t, int) "cudaOccupancyMaxPotentialBlockSize (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeWithFlags(int*, int*, T, size_t, int, unsigned int) "cudaOccupancyMaxPotentialBlockSize (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMem(int*, int*, T, UnaryFunction, int) "cudaOccupancyMaxPotentialBlockSizeVariableSMem (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(int*, int*, T, UnaryFunction, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeVariableSMem (C++ API)" + * \ref ::cudaOccupancyAvailableDynamicSMemPerBlock(size_t*, T, int, int) "cudaOccupancyAvailableDynamicSMemPerBlock (C++ API)", + * + * @{ + */ + +/** + * \brief Returns occupancy for a device function + * + * Returns in \p *numBlocks the maximum number of active blocks per + * streaming multiprocessor for the device function. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel function for which occupancy is calculated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags, + * \ref ::cudaOccupancyMaxPotentialBlockSize(int*, int*, T, size_t, int) "cudaOccupancyMaxPotentialBlockSize (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeWithFlags(int*, int*, T, size_t, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeWithFlags (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMem(int*, int*, T, UnaryFunction, int) "cudaOccupancyMaxPotentialBlockSizeVariableSMem (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(int*, int*, T, UnaryFunction, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags (C++ API)", + * \ref ::cudaOccupancyAvailableDynamicSMemPerBlock(size_t*, T, int, int) "cudaOccupancyAvailableDynamicSMemPerBlock (C++ API)", + * ::cuOccupancyMaxActiveBlocksPerMultiprocessor + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessor(int *numBlocks, const void *func, int blockSize, size_t dynamicSMemSize); + +/** + * \brief Returns dynamic shared memory available per block when launching \p numBlocks blocks on SM. + * + * Returns in \p *dynamicSmemSize the maximum size of dynamic shared memory to allow \p numBlocks blocks per SM. + * + * \param dynamicSmemSize - Returned maximum dynamic shared memory + * \param func - Kernel function for which occupancy is calculated + * \param numBlocks - Number of blocks to fit on SM + * \param blockSize - Size of the block + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags, + * \ref ::cudaOccupancyMaxPotentialBlockSize(int*, int*, T, size_t, int) "cudaOccupancyMaxPotentialBlockSize (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeWithFlags(int*, int*, T, size_t, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeWithFlags (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMem(int*, int*, T, UnaryFunction, int) "cudaOccupancyMaxPotentialBlockSizeVariableSMem (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(int*, int*, T, UnaryFunction, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags (C++ API)", + * ::cudaOccupancyAvailableDynamicSMemPerBlock + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyAvailableDynamicSMemPerBlock(size_t *dynamicSmemSize, const void *func, int numBlocks, int blockSize); + +/** + * \brief Returns occupancy for a device function with the specified flags + * + * Returns in \p *numBlocks the maximum number of active blocks per + * streaming multiprocessor for the device function. + * + * The \p flags parameter controls how special cases are handled. Valid flags include: + * + * - ::cudaOccupancyDefault: keeps the default behavior as + * ::cudaOccupancyMaxActiveBlocksPerMultiprocessor + * + * - ::cudaOccupancyDisableCachingOverride: This flag suppresses the default behavior + * on platform where global caching affects occupancy. On such platforms, if caching + * is enabled, but per-block SM resource usage would result in zero occupancy, the + * occupancy calculator will calculate the occupancy as if caching is disabled. + * Setting this flag makes the occupancy calculator to return 0 in such cases. + * More information can be found about this feature in the "Unified L1/Texture Cache" + * section of the Maxwell tuning guide. + * + * \param numBlocks - Returned occupancy + * \param func - Kernel function for which occupancy is calculated + * \param blockSize - Block size the kernel is intended to be launched with + * \param dynamicSMemSize - Per-block dynamic shared memory usage intended, in bytes + * \param flags - Requested behavior for the occupancy calculator + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaOccupancyMaxActiveBlocksPerMultiprocessor, + * \ref ::cudaOccupancyMaxPotentialBlockSize(int*, int*, T, size_t, int) "cudaOccupancyMaxPotentialBlockSize (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeWithFlags(int*, int*, T, size_t, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeWithFlags (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMem(int*, int*, T, UnaryFunction, int) "cudaOccupancyMaxPotentialBlockSizeVariableSMem (C++ API)", + * \ref ::cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags(int*, int*, T, UnaryFunction, int, unsigned int) "cudaOccupancyMaxPotentialBlockSizeVariableSMemWithFlags (C++ API)", + * \ref ::cudaOccupancyAvailableDynamicSMemPerBlock(size_t*, T, int, int) "cudaOccupancyAvailableDynamicSMemPerBlock (C++ API)", + * ::cuOccupancyMaxActiveBlocksPerMultiprocessorWithFlags + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveBlocksPerMultiprocessorWithFlags(int *numBlocks, const void *func, int blockSize, size_t dynamicSMemSize, unsigned int flags); + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum cluster size in \p *clusterSize. + * + * The cluster dimensions in \p config are ignored. If func has a required + * cluster size set (see ::cudaFuncGetAttributes),\p *clusterSize will reflect + * the required cluster size. + * + * By default this function will always return a value that's portable on + * future hardware. A higher value may be returned if the kernel function + * allows non-portable cluster sizes. + * + * This function will respect the compile time launch bounds. + * + * \param clusterSize - Returned maximum cluster size that can be launched + * for the given kernel function and launch configuration + * \param func - Kernel function for which maximum cluster + * size is calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaFuncGetAttributes + * \ref ::cudaOccupancyMaxPotentialClusterSize(int*, T, const cudaLaunchConfig_t*) "cudaOccupancyMaxPotentialClusterSize (C++ API)", + * ::cuOccupancyMaxPotentialClusterSize + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxPotentialClusterSize(int *clusterSize, const void *func, const cudaLaunchConfig_t *launchConfig); + + +/** + * \brief Given the kernel function (\p func) and launch configuration + * (\p config), return the maximum number of clusters that could co-exist + * on the target device in \p *numClusters. + * + * If the function has required cluster size already set (see + * ::cudaFuncGetAttributes), the cluster size from config must either be + * unspecified or match the required size. + * Without required sizes, the cluster size must be specified in config, + * else the function will return an error. + * + * Note that various attributes of the kernel function may affect occupancy + * calculation. Runtime environment may affect how the hardware schedules + * the clusters, so the calculated occupancy is not guaranteed to be achievable. + * + * \param numClusters - Returned maximum number of clusters that + * could co-exist on the target device + * \param func - Kernel function for which maximum number + * of clusters are calculated + * \param config - Launch configuration for the given kernel function + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidClusterSize, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaFuncGetAttributes + * \ref ::cudaOccupancyMaxActiveClusters(int*, T, const cudaLaunchConfig_t*) "cudaOccupancyMaxActiveClusters (C++ API)", + * ::cuOccupancyMaxActiveClusters + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaOccupancyMaxActiveClusters(int *numClusters, const void *func, const cudaLaunchConfig_t *launchConfig); +/** @} */ /* END CUDA_OCCUPANCY */ + +/** + * \defgroup CUDART_MEMORY Memory Management + * + * ___MANBRIEF___ memory management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the memory management functions of the CUDA runtime + * application programming interface. + * + * Some functions have overloaded C++ API template versions documented separately in the + * \ref CUDART_HIGHLEVEL "C++ API Routines" module. + * + * @{ + */ + +/** + * \brief Allocates memory that will be automatically managed by the Unified Memory system + * + * Allocates \p size bytes of managed memory on the device and returns in + * \p *devPtr a pointer to the allocated memory. If the device doesn't support + * allocating managed memory, ::cudaErrorNotSupported is returned. Support + * for managed memory can be queried using the device attribute + * ::cudaDevAttrManagedMemory. The allocated memory is suitably + * aligned for any kind of variable. The memory is not cleared. If \p size + * is 0, ::cudaMallocManaged returns ::cudaErrorInvalidValue. The pointer + * is valid on the CPU and on all GPUs in the system that support managed memory. + * All accesses to this pointer must obey the Unified Memory programming model. + * + * \p flags specifies the default stream association for this allocation. + * \p flags must be one of ::cudaMemAttachGlobal or ::cudaMemAttachHost. The + * default value for \p flags is ::cudaMemAttachGlobal. + * If ::cudaMemAttachGlobal is specified, then this memory is accessible from + * any stream on any device. If ::cudaMemAttachHost is specified, then the + * allocation should not be accessed from devices that have a zero value for the + * device attribute ::cudaDevAttrConcurrentManagedAccess; an explicit call to + * ::cudaStreamAttachMemAsync will be required to enable access on such devices. + * + * If the association is later changed via ::cudaStreamAttachMemAsync to + * a single stream, the default association, as specifed during ::cudaMallocManaged, + * is restored when that stream is destroyed. For __managed__ variables, the + * default association is always ::cudaMemAttachGlobal. Note that destroying a + * stream is an asynchronous operation, and as a result, the change to default + * association won't happen until all work in the stream has completed. + * + * Memory allocated with ::cudaMallocManaged should be released with ::cudaFree. + * + * Device memory oversubscription is possible for GPUs that have a non-zero value for the + * device attribute ::cudaDevAttrConcurrentManagedAccess. Managed memory on + * such GPUs may be evicted from device memory to host memory at any time by the Unified + * Memory driver in order to make room for other allocations. + * + * In a system where all GPUs have a non-zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess, managed memory may not be populated when this + * API returns and instead may be populated on access. In such systems, managed memory can + * migrate to any processor's memory at any time. The Unified Memory driver will employ heuristics to + * maintain data locality and prevent excessive page faults to the extent possible. The application + * can also guide the driver about memory usage patterns via ::cudaMemAdvise. The application + * can also explicitly migrate memory to a desired processor's memory via + * ::cudaMemPrefetchAsync. + * + * In a multi-GPU system where all of the GPUs have a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess and all the GPUs have peer-to-peer support + * with each other, the physical storage for managed memory is created on the GPU which is active + * at the time ::cudaMallocManaged is called. All other GPUs will reference the data at reduced + * bandwidth via peer mappings over the PCIe bus. The Unified Memory driver does not migrate + * memory among such GPUs. + * + * In a multi-GPU system where not all GPUs have peer-to-peer support with each other and + * where the value of the device attribute ::cudaDevAttrConcurrentManagedAccess + * is zero for at least one of those GPUs, the location chosen for physical storage of managed + * memory is system-dependent. + * - On Linux, the location chosen will be device memory as long as the current set of active + * contexts are on devices that either have peer-to-peer support with each other or have a + * non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * If there is an active context on a GPU that does not have a non-zero value for that device + * attribute and it does not have peer-to-peer support with the other devices that have active + * contexts on them, then the location for physical storage will be 'zero-copy' or host memory. + * Note that this means that managed memory that is located in device memory is migrated to + * host memory if a new context is created on a GPU that doesn't have a non-zero value for + * the device attribute and does not support peer-to-peer with at least one of the other devices + * that has an active context. This in turn implies that context creation may fail if there is + * insufficient host memory to migrate all managed allocations. + * - On Windows, the physical storage is always created in 'zero-copy' or host memory. + * All GPUs will reference the data at reduced bandwidth over the PCIe bus. In these + * circumstances, use of the environment variable CUDA_VISIBLE_DEVICES is recommended to + * restrict CUDA to only use those GPUs that have peer-to-peer support. + * Alternatively, users can also set CUDA_MANAGED_FORCE_DEVICE_ALLOC to a non-zero + * value to force the driver to always use device memory for physical storage. + * When this environment variable is set to a non-zero value, all devices used in + * that process that support managed memory have to be peer-to-peer compatible + * with each other. The error ::cudaErrorInvalidDevice will be returned if a device + * that supports managed memory is used and it is not peer-to-peer compatible with + * any of the other managed memory supporting devices that were previously used in + * that process, even if ::cudaDeviceReset has been called on those devices. These + * environment variables are described in the CUDA programming guide under the + * "CUDA environment variables" section. + * + * \param devPtr - Pointer to allocated device memory + * \param size - Requested allocation size in bytes + * \param flags - Must be either ::cudaMemAttachGlobal or ::cudaMemAttachHost (defaults to ::cudaMemAttachGlobal) + * + * \return + * ::cudaSuccess, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, ::cudaFreeArray, + * ::cudaMalloc3D, ::cudaMalloc3DArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, ::cudaDeviceGetAttribute, ::cudaStreamAttachMemAsync, + * ::cuMemAllocManaged + */ +#if defined(__cplusplus) +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMallocManaged(void **devPtr, size_t size, unsigned int flags = cudaMemAttachGlobal); +#else +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMallocManaged(void **devPtr, size_t size, unsigned int flags); +#endif + +/** + * \brief Allocate memory on the device + * + * Allocates \p size bytes of linear memory on the device and returns in + * \p *devPtr a pointer to the allocated memory. The allocated memory is + * suitably aligned for any kind of variable. The memory is not cleared. + * ::cudaMalloc() returns ::cudaErrorMemoryAllocation in case of failure. + * + * The device version of ::cudaFree cannot be used with a \p *devPtr + * allocated using the host API, and vice versa. + * + * \param devPtr - Pointer to allocated device memory + * \param size - Requested allocation size in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, ::cudaFreeArray, + * ::cudaMalloc3D, ::cudaMalloc3DArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::cuMemAlloc + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMalloc(void **devPtr, size_t size); + +/** + * \brief Allocates page-locked memory on the host + * + * Allocates \p size bytes of host memory that is page-locked and accessible + * to the device. The driver tracks the virtual memory ranges allocated with + * this function and automatically accelerates calls to functions such as + * ::cudaMemcpy*(). Since the memory can be accessed directly by the device, + * it can be read or written with much higher bandwidth than pageable memory + * obtained with functions such as ::malloc(). + + * On systems where ::pageableMemoryAccessUsesHostPageTables + * is true, ::cudaMallocHost may not page-lock the allocated memory. + + * Page-locking excessive amounts of memory with ::cudaMallocHost() may degrade + * system performance, since it reduces the amount of memory available to the + * system for paging. As a result, this function is best used sparingly to allocate + * staging areas for data exchange between host and device. + * + * \param ptr - Pointer to allocated host memory + * \param size - Requested allocation size in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaMallocArray, ::cudaMalloc3D, + * ::cudaMalloc3DArray, ::cudaHostAlloc, ::cudaFree, ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t, unsigned int) "cudaMallocHost (C++ API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::cuMemAllocHost + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocHost(void **ptr, size_t size); + +/** + * \brief Allocates pitched memory on the device + * + * Allocates at least \p width (in bytes) * \p height bytes of linear memory + * on the device and returns in \p *devPtr a pointer to the allocated memory. + * The function may pad the allocation to ensure that corresponding pointers + * in any given row will continue to meet the alignment requirements for + * coalescing as the address is updated from row to row. The pitch returned in + * \p *pitch by ::cudaMallocPitch() is the width in bytes of the allocation. + * The intended usage of \p pitch is as a separate parameter of the allocation, + * used to compute addresses within the 2D array. Given the row and column of + * an array element of type \p T, the address is computed as: + * \code + T* pElement = (T*)((char*)BaseAddress + Row * pitch) + Column; + \endcode + * + * For allocations of 2D arrays, it is recommended that programmers consider + * performing pitch allocations using ::cudaMallocPitch(). Due to pitch + * alignment restrictions in the hardware, this is especially true if the + * application will be performing 2D memory copies between different regions + * of device memory (whether linear memory or CUDA arrays). + * + * \param devPtr - Pointer to allocated pitched device memory + * \param pitch - Pitch for allocation + * \param width - Requested pitched allocation width (in bytes) + * \param height - Requested pitched allocation height + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaFree, ::cudaMallocArray, ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaMalloc3D, ::cudaMalloc3DArray, + * ::cudaHostAlloc, + * ::cuMemAllocPitch + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocPitch(void **devPtr, size_t *pitch, size_t width, size_t height); + +/** + * \brief Allocate an array on the device + * + * Allocates a CUDA array according to the ::cudaChannelFormatDesc structure + * \p desc and returns a handle to the new CUDA array in \p *array. + * + * The ::cudaChannelFormatDesc is defined as: + * \code + struct cudaChannelFormatDesc { + int x, y, z, w; + enum cudaChannelFormatKind f; + }; + \endcode + * where ::cudaChannelFormatKind is one of ::cudaChannelFormatKindSigned, + * ::cudaChannelFormatKindUnsigned, or ::cudaChannelFormatKindFloat. + * + * The \p flags parameter enables different options to be specified that affect + * the allocation, as follows. + * - ::cudaArrayDefault: This flag's value is defined to be 0 and provides default array allocation + * - ::cudaArraySurfaceLoadStore: Allocates an array that can be read from or written to using a surface reference + * - ::cudaArrayTextureGather: This flag indicates that texture gather operations will be performed on the array. + * - ::cudaArraySparse: Allocates a CUDA array without physical backing memory. The subregions within this sparse array + * can later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. + * The physical backing memory must be allocated via ::cuMemCreate. + * - ::cudaArrayDeferredMapping: Allocates a CUDA array without physical backing memory. The entire array can + * later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. + * The physical backing memory must be allocated via ::cuMemCreate. + * + * \p width and \p height must meet certain size requirements. See ::cudaMalloc3DArray() for more details. + * + * \param array - Pointer to allocated array in device memory + * \param desc - Requested channel format + * \param width - Requested array allocation width + * \param height - Requested array allocation height + * \param flags - Requested properties of allocated array + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaMalloc3D, ::cudaMalloc3DArray, + * ::cudaHostAlloc, + * ::cuArrayCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocArray(cudaArray_t *array, const struct cudaChannelFormatDesc *desc, size_t width, size_t height __dv(0), unsigned int flags __dv(0)); + +/** + * \brief Frees memory on the device + * + * Frees the memory space pointed to by \p devPtr, which must have been + * returned by a previous call to one of the following memory allocation APIs - + * ::cudaMalloc(), ::cudaMallocPitch(), ::cudaMallocManaged(), ::cudaMallocAsync(), + * ::cudaMallocFromPoolAsync(). + * + * Note - This API will not perform any implicit synchronization when the pointer was + * allocated with ::cudaMallocAsync or ::cudaMallocFromPoolAsync. Callers must ensure + * that all accesses to the pointer have completed before invoking ::cudaFree. For + * best performance and memory reuse, users should use ::cudaFreeAsync to free memory + * allocated via the stream ordered memory allocator. + * + * If ::cudaFree(\p devPtr) has already been called before, + * an error is returned. If \p devPtr is 0, no operation is performed. + * ::cudaFree() returns ::cudaErrorValue in case of failure. + * + * The device version of ::cudaFree cannot be used with a \p *devPtr + * allocated using the host API, and vice versa. + * + * \param devPtr - Device pointer to memory to free + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaMallocManaged, ::cudaMallocArray, ::cudaFreeArray, ::cudaMallocAsync, ::cudaMallocFromPoolAsync + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaMalloc3D, ::cudaMalloc3DArray, ::cudaFreeAsync + * ::cudaHostAlloc, + * ::cuMemFree + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaFree(void *devPtr); + +/** + * \brief Frees page-locked memory + * + * Frees the memory space pointed to by \p hostPtr, which must have been + * returned by a previous call to ::cudaMallocHost() or ::cudaHostAlloc(). + * + * \param ptr - Pointer to memory to free + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, + * ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaMalloc3D, ::cudaMalloc3DArray, ::cudaHostAlloc, + * ::cuMemFreeHost + */ +extern __host__ cudaError_t CUDARTAPI cudaFreeHost(void *ptr); + +/** + * \brief Frees an array on the device + * + * Frees the CUDA array \p array, which must have been returned by a + * previous call to ::cudaMallocArray(). If \p devPtr is 0, + * no operation is performed. + * + * \param array - Pointer to array to free + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::cuArrayDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaFreeArray(cudaArray_t array); + +/** + * \brief Frees a mipmapped array on the device + * + * Frees the CUDA mipmapped array \p mipmappedArray, which must have been + * returned by a previous call to ::cudaMallocMipmappedArray(). If \p devPtr + * is 0, no operation is performed. + * + * \param mipmappedArray - Pointer to mipmapped array to free + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, ::cudaMallocArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::cuMipmappedArrayDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaFreeMipmappedArray(cudaMipmappedArray_t mipmappedArray); + + +/** + * \brief Allocates page-locked memory on the host + * + * Allocates \p size bytes of host memory that is page-locked and accessible + * to the device. The driver tracks the virtual memory ranges allocated with + * this function and automatically accelerates calls to functions such as + * ::cudaMemcpy(). Since the memory can be accessed directly by the device, it + * can be read or written with much higher bandwidth than pageable memory + * obtained with functions such as ::malloc(). Allocating excessive amounts of + * pinned memory may degrade system performance, since it reduces the amount + * of memory available to the system for paging. As a result, this function is + * best used sparingly to allocate staging areas for data exchange between host + * and device. + * + * The \p flags parameter enables different options to be specified that affect + * the allocation, as follows. + * - ::cudaHostAllocDefault: This flag's value is defined to be 0 and causes + * ::cudaHostAlloc() to emulate ::cudaMallocHost(). + * - ::cudaHostAllocPortable: The memory returned by this call will be + * considered as pinned memory by all CUDA contexts, not just the one that + * performed the allocation. + * - ::cudaHostAllocMapped: Maps the allocation into the CUDA address space. + * The device pointer to the memory may be obtained by calling + * ::cudaHostGetDevicePointer(). + * - ::cudaHostAllocWriteCombined: Allocates the memory as write-combined (WC). + * WC memory can be transferred across the PCI Express bus more quickly on some + * system configurations, but cannot be read efficiently by most CPUs. WC + * memory is a good option for buffers that will be written by the CPU and read + * by the device via mapped pinned memory or host->device transfers. + * + * All of these flags are orthogonal to one another: a developer may allocate + * memory that is portable, mapped and/or write-combined with no restrictions. + * + * In order for the ::cudaHostAllocMapped flag to have any effect, the CUDA context + * must support the ::cudaDeviceMapHost flag, which can be checked via + * ::cudaGetDeviceFlags(). The ::cudaDeviceMapHost flag is implicitly set for + * contexts created via the runtime API. + * + * The ::cudaHostAllocMapped flag may be specified on CUDA contexts for devices + * that do not support mapped pinned memory. The failure is deferred to + * ::cudaHostGetDevicePointer() because the memory may be mapped into other + * CUDA contexts via the ::cudaHostAllocPortable flag. + * + * Memory allocated by this function must be freed with ::cudaFreeHost(). + * + * \param pHost - Device pointer to allocated memory + * \param size - Requested allocation size in bytes + * \param flags - Requested properties of allocated memory + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaSetDeviceFlags, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, + * ::cudaGetDeviceFlags, + * ::cuMemHostAlloc + */ +extern __host__ cudaError_t CUDARTAPI cudaHostAlloc(void **pHost, size_t size, unsigned int flags); + +/** + * \brief Registers an existing host memory range for use by CUDA + * + * Page-locks the memory range specified by \p ptr and \p size and maps it + * for the device(s) as specified by \p flags. This memory range also is added + * to the same tracking mechanism as ::cudaHostAlloc() to automatically accelerate + * calls to functions such as ::cudaMemcpy(). Since the memory can be accessed + * directly by the device, it can be read or written with much higher bandwidth + * than pageable memory that has not been registered. Page-locking excessive + * amounts of memory may degrade system performance, since it reduces the amount + * of memory available to the system for paging. As a result, this function is + * best used sparingly to register staging areas for data exchange between + * host and device. + * + * On systems where ::pageableMemoryAccessUsesHostPageTables is true, ::cudaHostRegister + * will not page-lock the memory range specified by \p ptr but only populate + * unpopulated pages. + * + * ::cudaHostRegister is supported only on I/O coherent devices that have a non-zero + * value for the device attribute ::cudaDevAttrHostRegisterSupported. + * + * The \p flags parameter enables different options to be specified that + * affect the allocation, as follows. + * + * - ::cudaHostRegisterDefault: On a system with unified virtual addressing, + * the memory will be both mapped and portable. On a system with no unified + * virtual addressing, the memory will be neither mapped nor portable. + * + * - ::cudaHostRegisterPortable: The memory returned by this call will be + * considered as pinned memory by all CUDA contexts, not just the one that + * performed the allocation. + * + * - ::cudaHostRegisterMapped: Maps the allocation into the CUDA address + * space. The device pointer to the memory may be obtained by calling + * ::cudaHostGetDevicePointer(). + * + * - ::cudaHostRegisterIoMemory: The passed memory pointer is treated as + * pointing to some memory-mapped I/O space, e.g. belonging to a + * third-party PCIe device, and it will marked as non cache-coherent and + * contiguous. + * + * - ::cudaHostRegisterReadOnly: The passed memory pointer is treated as + * pointing to memory that is considered read-only by the device. On + * platforms without ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, this + * flag is required in order to register memory mapped to the CPU as + * read-only. Support for the use of this flag can be queried from the device + * attribute cudaDeviceAttrReadOnlyHostRegisterSupported. Using this flag with + * a current context associated with a device that does not have this attribute + * set will cause ::cudaHostRegister to error with cudaErrorNotSupported. + * + * All of these flags are orthogonal to one another: a developer may page-lock + * memory that is portable or mapped with no restrictions. + * + * The CUDA context must have been created with the ::cudaMapHost flag in + * order for the ::cudaHostRegisterMapped flag to have any effect. + * + * The ::cudaHostRegisterMapped flag may be specified on CUDA contexts for + * devices that do not support mapped pinned memory. The failure is deferred + * to ::cudaHostGetDevicePointer() because the memory may be mapped into + * other CUDA contexts via the ::cudaHostRegisterPortable flag. + * + * For devices that have a non-zero value for the device attribute + * ::cudaDevAttrCanUseHostPointerForRegisteredMem, the memory + * can also be accessed from the device using the host pointer \p ptr. + * The device pointer returned by ::cudaHostGetDevicePointer() may or may not + * match the original host pointer \p ptr and depends on the devices visible to the + * application. If all devices visible to the application have a non-zero value for the + * device attribute, the device pointer returned by ::cudaHostGetDevicePointer() + * will match the original pointer \p ptr. If any device visible to the application + * has a zero value for the device attribute, the device pointer returned by + * ::cudaHostGetDevicePointer() will not match the original host pointer \p ptr, + * but it will be suitable for use on all devices provided Unified Virtual Addressing + * is enabled. In such systems, it is valid to access the memory using either pointer + * on devices that have a non-zero value for the device attribute. Note however that + * such devices should access the memory using only of the two pointers and not both. + * + * The memory page-locked by this function must be unregistered with ::cudaHostUnregister(). + * + * \param ptr - Host pointer to memory to page-lock + * \param size - Size in bytes of the address range to page-lock in bytes + * \param flags - Flags for allocation request + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation, + * ::cudaErrorHostMemoryAlreadyRegistered, + * ::cudaErrorNotSupported + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaHostUnregister, ::cudaHostGetFlags, ::cudaHostGetDevicePointer, + * ::cuMemHostRegister + */ +extern __host__ cudaError_t CUDARTAPI cudaHostRegister(void *ptr, size_t size, unsigned int flags); + +/** + * \brief Unregisters a memory range that was registered with cudaHostRegister + * + * Unmaps the memory range whose base address is specified by \p ptr, and makes + * it pageable again. + * + * The base address must be the same one specified to ::cudaHostRegister(). + * + * \param ptr - Host pointer to memory to unregister + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorHostMemoryNotRegistered + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaHostUnregister, + * ::cuMemHostUnregister + */ +extern __host__ cudaError_t CUDARTAPI cudaHostUnregister(void *ptr); + +/** + * \brief Passes back device pointer of mapped host memory allocated by + * cudaHostAlloc or registered by cudaHostRegister + * + * Passes back the device pointer corresponding to the mapped, pinned host + * buffer allocated by ::cudaHostAlloc() or registered by ::cudaHostRegister(). + * + * ::cudaHostGetDevicePointer() will fail if the ::cudaDeviceMapHost flag was + * not specified before deferred context creation occurred, or if called on a + * device that does not support mapped, pinned memory. + * + * For devices that have a non-zero value for the device attribute + * ::cudaDevAttrCanUseHostPointerForRegisteredMem, the memory + * can also be accessed from the device using the host pointer \p pHost. + * The device pointer returned by ::cudaHostGetDevicePointer() may or may not + * match the original host pointer \p pHost and depends on the devices visible to the + * application. If all devices visible to the application have a non-zero value for the + * device attribute, the device pointer returned by ::cudaHostGetDevicePointer() + * will match the original pointer \p pHost. If any device visible to the application + * has a zero value for the device attribute, the device pointer returned by + * ::cudaHostGetDevicePointer() will not match the original host pointer \p pHost, + * but it will be suitable for use on all devices provided Unified Virtual Addressing + * is enabled. In such systems, it is valid to access the memory using either pointer + * on devices that have a non-zero value for the device attribute. Note however that + * such devices should access the memory using only of the two pointers and not both. + * + * \p flags provides for future releases. For now, it must be set to 0. + * + * \param pDevice - Returned device pointer for mapped memory + * \param pHost - Requested host pointer mapping + * \param flags - Flags for extensions (must be 0 for now) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaSetDeviceFlags, ::cudaHostAlloc, + * ::cuMemHostGetDevicePointer + */ +extern __host__ cudaError_t CUDARTAPI cudaHostGetDevicePointer(void **pDevice, void *pHost, unsigned int flags); + +/** + * \brief Passes back flags used to allocate pinned host memory allocated by + * cudaHostAlloc + * + * ::cudaHostGetFlags() will fail if the input pointer does not + * reside in an address range allocated by ::cudaHostAlloc(). + * + * \param pFlags - Returned flags word + * \param pHost - Host pointer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaHostAlloc, + * ::cuMemHostGetFlags + */ +extern __host__ cudaError_t CUDARTAPI cudaHostGetFlags(unsigned int *pFlags, void *pHost); + +/** + * \brief Allocates logical 1D, 2D, or 3D memory objects on the device + * + * Allocates at least \p width * \p height * \p depth bytes of linear memory + * on the device and returns a ::cudaPitchedPtr in which \p ptr is a pointer + * to the allocated memory. The function may pad the allocation to ensure + * hardware alignment requirements are met. The pitch returned in the \p pitch + * field of \p pitchedDevPtr is the width in bytes of the allocation. + * + * The returned ::cudaPitchedPtr contains additional fields \p xsize and + * \p ysize, the logical width and height of the allocation, which are + * equivalent to the \p width and \p height \p extent parameters provided by + * the programmer during allocation. + * + * For allocations of 2D and 3D objects, it is highly recommended that + * programmers perform allocations using ::cudaMalloc3D() or + * ::cudaMallocPitch(). Due to alignment restrictions in the hardware, this is + * especially true if the application will be performing memory copies + * involving 2D or 3D objects (whether linear memory or CUDA arrays). + * + * \param pitchedDevPtr - Pointer to allocated pitched device memory + * \param extent - Requested allocation size (\p width field in bytes) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMallocPitch, ::cudaFree, ::cudaMemcpy3D, ::cudaMemset3D, + * ::cudaMalloc3DArray, ::cudaMallocArray, ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, ::make_cudaPitchedPtr, ::make_cudaExtent, + * ::cuMemAllocPitch + */ +extern __host__ cudaError_t CUDARTAPI cudaMalloc3D(struct cudaPitchedPtr* pitchedDevPtr, struct cudaExtent extent); + +/** + * \brief Allocate an array on the device + * + * Allocates a CUDA array according to the ::cudaChannelFormatDesc structure + * \p desc and returns a handle to the new CUDA array in \p *array. + * + * The ::cudaChannelFormatDesc is defined as: + * \code + struct cudaChannelFormatDesc { + int x, y, z, w; + enum cudaChannelFormatKind f; + }; + \endcode + * where ::cudaChannelFormatKind is one of ::cudaChannelFormatKindSigned, + * ::cudaChannelFormatKindUnsigned, or ::cudaChannelFormatKindFloat. + * + * ::cudaMalloc3DArray() can allocate the following: + * + * - A 1D array is allocated if the height and depth extents are both zero. + * - A 2D array is allocated if only the depth extent is zero. + * - A 3D array is allocated if all three extents are non-zero. + * - A 1D layered CUDA array is allocated if only the height extent is zero and + * the cudaArrayLayered flag is set. Each layer is a 1D array. The number of layers is + * determined by the depth extent. + * - A 2D layered CUDA array is allocated if all three extents are non-zero and + * the cudaArrayLayered flag is set. Each layer is a 2D array. The number of layers is + * determined by the depth extent. + * - A cubemap CUDA array is allocated if all three extents are non-zero and the + * cudaArrayCubemap flag is set. Width must be equal to height, and depth must be six. A cubemap is + * a special type of 2D layered CUDA array, where the six layers represent the six faces of a cube. + * The order of the six layers in memory is the same as that listed in ::cudaGraphicsCubeFace. + * - A cubemap layered CUDA array is allocated if all three extents are non-zero, and both, + * cudaArrayCubemap and cudaArrayLayered flags are set. Width must be equal to height, and depth must be + * a multiple of six. A cubemap layered CUDA array is a special type of 2D layered CUDA array that consists + * of a collection of cubemaps. The first six layers represent the first cubemap, the next six layers form + * the second cubemap, and so on. + * + * + * The \p flags parameter enables different options to be specified that affect + * the allocation, as follows. + * - ::cudaArrayDefault: This flag's value is defined to be 0 and provides default array allocation + * - ::cudaArrayLayered: Allocates a layered CUDA array, with the depth extent indicating the number of layers + * - ::cudaArrayCubemap: Allocates a cubemap CUDA array. Width must be equal to height, and depth must be six. + * If the cudaArrayLayered flag is also set, depth must be a multiple of six. + * - ::cudaArraySurfaceLoadStore: Allocates a CUDA array that could be read from or written to using a surface + * reference. + * - ::cudaArrayTextureGather: This flag indicates that texture gather operations will be performed on the CUDA + * array. Texture gather can only be performed on 2D CUDA arrays. + * - ::cudaArraySparse: Allocates a CUDA array without physical backing memory. The subregions within this sparse array + * can later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. This flag can only be used for + * creating 2D, 3D or 2D layered sparse CUDA arrays. The physical backing memory must be allocated via ::cuMemCreate. + * - ::cudaArrayDeferredMapping: Allocates a CUDA array without physical backing memory. The entire array can + * later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. The physical backing memory must be allocated + * via ::cuMemCreate. + * + * The width, height and depth extents must meet certain size requirements as listed in the following table. + * All values are specified in elements. + * + * Note that 2D CUDA arrays have different size requirements if the ::cudaArrayTextureGather flag is set. In that + * case, the valid range for (width, height, depth) is ((1,maxTexture2DGather[0]), (1,maxTexture2DGather[1]), 0). + * + * \xmlonly + * + * + * + * + * + * + * + * CUDA array type + * Valid extents that must always be met {(width range in elements), + * (height range), (depth range)} + * Valid extents with cudaArraySurfaceLoadStore set {(width range in + * elements), (height range), (depth range)} + * + * + * + * + * 1D + * { (1,maxTexture1D), 0, 0 } + * { (1,maxSurface1D), 0, 0 } + * + * + * 2D + * { (1,maxTexture2D[0]), (1,maxTexture2D[1]), 0 } + * { (1,maxSurface2D[0]), (1,maxSurface2D[1]), 0 } + * + * + * 3D + * { (1,maxTexture3D[0]), (1,maxTexture3D[1]), (1,maxTexture3D[2]) } + * OR { (1,maxTexture3DAlt[0]), (1,maxTexture3DAlt[1]), + * (1,maxTexture3DAlt[2]) } + * { (1,maxSurface3D[0]), (1,maxSurface3D[1]), (1,maxSurface3D[2]) } + * + * + * 1D Layered + * { (1,maxTexture1DLayered[0]), 0, (1,maxTexture1DLayered[1]) } + * { (1,maxSurface1DLayered[0]), 0, (1,maxSurface1DLayered[1]) } + * + * + * 2D Layered + * { (1,maxTexture2DLayered[0]), (1,maxTexture2DLayered[1]), + * (1,maxTexture2DLayered[2]) } + * { (1,maxSurface2DLayered[0]), (1,maxSurface2DLayered[1]), + * (1,maxSurface2DLayered[2]) } + * + * + * Cubemap + * { (1,maxTextureCubemap), (1,maxTextureCubemap), 6 } + * { (1,maxSurfaceCubemap), (1,maxSurfaceCubemap), 6 } + * + * + * Cubemap Layered + * { (1,maxTextureCubemapLayered[0]), (1,maxTextureCubemapLayered[0]), + * (1,maxTextureCubemapLayered[1]) } + * { (1,maxSurfaceCubemapLayered[0]), (1,maxSurfaceCubemapLayered[0]), + * (1,maxSurfaceCubemapLayered[1]) } + * + * + * + *
+ * \endxmlonly + * + * \param array - Pointer to allocated array in device memory + * \param desc - Requested channel format + * \param extent - Requested allocation size (\p width field in elements) + * \param flags - Flags for extensions + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc3D, ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, + * ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::make_cudaExtent, + * ::cuArray3DCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaMalloc3DArray(cudaArray_t *array, const struct cudaChannelFormatDesc* desc, struct cudaExtent extent, unsigned int flags __dv(0)); + +/** + * \brief Allocate a mipmapped array on the device + * + * Allocates a CUDA mipmapped array according to the ::cudaChannelFormatDesc structure + * \p desc and returns a handle to the new CUDA mipmapped array in \p *mipmappedArray. + * \p numLevels specifies the number of mipmap levels to be allocated. This value is + * clamped to the range [1, 1 + floor(log2(max(width, height, depth)))]. + * + * The ::cudaChannelFormatDesc is defined as: + * \code + struct cudaChannelFormatDesc { + int x, y, z, w; + enum cudaChannelFormatKind f; + }; + \endcode + * where ::cudaChannelFormatKind is one of ::cudaChannelFormatKindSigned, + * ::cudaChannelFormatKindUnsigned, or ::cudaChannelFormatKindFloat. + * + * ::cudaMallocMipmappedArray() can allocate the following: + * + * - A 1D mipmapped array is allocated if the height and depth extents are both zero. + * - A 2D mipmapped array is allocated if only the depth extent is zero. + * - A 3D mipmapped array is allocated if all three extents are non-zero. + * - A 1D layered CUDA mipmapped array is allocated if only the height extent is zero and + * the cudaArrayLayered flag is set. Each layer is a 1D mipmapped array. The number of layers is + * determined by the depth extent. + * - A 2D layered CUDA mipmapped array is allocated if all three extents are non-zero and + * the cudaArrayLayered flag is set. Each layer is a 2D mipmapped array. The number of layers is + * determined by the depth extent. + * - A cubemap CUDA mipmapped array is allocated if all three extents are non-zero and the + * cudaArrayCubemap flag is set. Width must be equal to height, and depth must be six. + * The order of the six layers in memory is the same as that listed in ::cudaGraphicsCubeFace. + * - A cubemap layered CUDA mipmapped array is allocated if all three extents are non-zero, and both, + * cudaArrayCubemap and cudaArrayLayered flags are set. Width must be equal to height, and depth must be + * a multiple of six. A cubemap layered CUDA mipmapped array is a special type of 2D layered CUDA mipmapped + * array that consists of a collection of cubemap mipmapped arrays. The first six layers represent the + * first cubemap mipmapped array, the next six layers form the second cubemap mipmapped array, and so on. + * + * + * The \p flags parameter enables different options to be specified that affect + * the allocation, as follows. + * - ::cudaArrayDefault: This flag's value is defined to be 0 and provides default mipmapped array allocation + * - ::cudaArrayLayered: Allocates a layered CUDA mipmapped array, with the depth extent indicating the number of layers + * - ::cudaArrayCubemap: Allocates a cubemap CUDA mipmapped array. Width must be equal to height, and depth must be six. + * If the cudaArrayLayered flag is also set, depth must be a multiple of six. + * - ::cudaArraySurfaceLoadStore: This flag indicates that individual mipmap levels of the CUDA mipmapped array + * will be read from or written to using a surface reference. + * - ::cudaArrayTextureGather: This flag indicates that texture gather operations will be performed on the CUDA + * array. Texture gather can only be performed on 2D CUDA mipmapped arrays, and the gather operations are + * performed only on the most detailed mipmap level. + * - ::cudaArraySparse: Allocates a CUDA mipmapped array without physical backing memory. The subregions within this sparse array + * can later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. This flag can only be used for creating + * 2D, 3D or 2D layered sparse CUDA mipmapped arrays. The physical backing memory must be allocated via ::cuMemCreate. + * - ::cudaArrayDeferredMapping: Allocates a CUDA mipmapped array without physical backing memory. The entire array can + * later be mapped onto a physical memory allocation by calling ::cuMemMapArrayAsync. The physical backing memory must be allocated + * via ::cuMemCreate. + * + * The width, height and depth extents must meet certain size requirements as listed in the following table. + * All values are specified in elements. + * + * \xmlonly + * + * + * + * + * + * + * + * CUDA array type + * Valid extents that must always be met {(width range in elements), + * (height range), (depth range)} + * Valid extents with cudaArraySurfaceLoadStore set {(width range in + * elements), (height range), (depth range)} + * + * + * + * + * 1D + * { (1,maxTexture1DMipmap), 0, 0 } + * { (1,maxSurface1D), 0, 0 } + * + * + * 2D + * { (1,maxTexture2DMipmap[0]), (1,maxTexture2DMipmap[1]), 0 } + * { (1,maxSurface2D[0]), (1,maxSurface2D[1]), 0 } + * + * + * 3D + * { (1,maxTexture3D[0]), (1,maxTexture3D[1]), (1,maxTexture3D[2]) } + * OR { (1,maxTexture3DAlt[0]), (1,maxTexture3DAlt[1]), + * (1,maxTexture3DAlt[2]) } + * { (1,maxSurface3D[0]), (1,maxSurface3D[1]), (1,maxSurface3D[2]) } + * + * + * 1D Layered + * { (1,maxTexture1DLayered[0]), 0, (1,maxTexture1DLayered[1]) } + * { (1,maxSurface1DLayered[0]), 0, (1,maxSurface1DLayered[1]) } + * + * + * 2D Layered + * { (1,maxTexture2DLayered[0]), (1,maxTexture2DLayered[1]), + * (1,maxTexture2DLayered[2]) } + * { (1,maxSurface2DLayered[0]), (1,maxSurface2DLayered[1]), + * (1,maxSurface2DLayered[2]) } + * + * + * Cubemap + * { (1,maxTextureCubemap), (1,maxTextureCubemap), 6 } + * { (1,maxSurfaceCubemap), (1,maxSurfaceCubemap), 6 } + * + * + * Cubemap Layered + * { (1,maxTextureCubemapLayered[0]), (1,maxTextureCubemapLayered[0]), + * (1,maxTextureCubemapLayered[1]) } + * { (1,maxSurfaceCubemapLayered[0]), (1,maxSurfaceCubemapLayered[0]), + * (1,maxSurfaceCubemapLayered[1]) } + * + * + * + *
+ * \endxmlonly + * + * \param mipmappedArray - Pointer to allocated mipmapped array in device memory + * \param desc - Requested channel format + * \param extent - Requested allocation size (\p width field in elements) + * \param numLevels - Number of mipmap levels to allocate + * \param flags - Flags for extensions + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc3D, ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, + * ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::make_cudaExtent, + * ::cuMipmappedArrayCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocMipmappedArray(cudaMipmappedArray_t *mipmappedArray, const struct cudaChannelFormatDesc* desc, struct cudaExtent extent, unsigned int numLevels, unsigned int flags __dv(0)); + +/** + * \brief Gets a mipmap level of a CUDA mipmapped array + * + * Returns in \p *levelArray a CUDA array that represents a single mipmap level + * of the CUDA mipmapped array \p mipmappedArray. + * + * If \p level is greater than the maximum number of levels in this mipmapped array, + * ::cudaErrorInvalidValue is returned. + * + * If \p mipmappedArray is NULL, + * ::cudaErrorInvalidResourceHandle is returned. + * + * \param levelArray - Returned mipmap level CUDA array + * \param mipmappedArray - CUDA mipmapped array + * \param level - Mipmap level + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc3D, ::cudaMalloc, ::cudaMallocPitch, ::cudaFree, + * ::cudaFreeArray, + * \ref ::cudaMallocHost(void**, size_t) "cudaMallocHost (C API)", + * ::cudaFreeHost, ::cudaHostAlloc, + * ::make_cudaExtent, + * ::cuMipmappedArrayGetLevel + */ +extern __host__ cudaError_t CUDARTAPI cudaGetMipmappedArrayLevel(cudaArray_t *levelArray, cudaMipmappedArray_const_t mipmappedArray, unsigned int level); + +/** + * \brief Copies data between 3D objects + * +\code +struct cudaExtent { + size_t width; + size_t height; + size_t depth; +}; +struct cudaExtent make_cudaExtent(size_t w, size_t h, size_t d); + +struct cudaPos { + size_t x; + size_t y; + size_t z; +}; +struct cudaPos make_cudaPos(size_t x, size_t y, size_t z); + +struct cudaMemcpy3DParms { + cudaArray_t srcArray; + struct cudaPos srcPos; + struct cudaPitchedPtr srcPtr; + cudaArray_t dstArray; + struct cudaPos dstPos; + struct cudaPitchedPtr dstPtr; + struct cudaExtent extent; + enum cudaMemcpyKind kind; +}; +\endcode + * + * ::cudaMemcpy3D() copies data betwen two 3D objects. The source and + * destination objects may be in either host memory, device memory, or a CUDA + * array. The source, destination, extent, and kind of copy performed is + * specified by the ::cudaMemcpy3DParms struct which should be initialized to + * zero before use: +\code +cudaMemcpy3DParms myParms = {0}; +\endcode + * + * The struct passed to ::cudaMemcpy3D() must specify one of \p srcArray or + * \p srcPtr and one of \p dstArray or \p dstPtr. Passing more than one + * non-zero source or destination will cause ::cudaMemcpy3D() to return an + * error. + * + * The \p srcPos and \p dstPos fields are optional offsets into the source and + * destination objects and are defined in units of each object's elements. The + * element for a host or device pointer is assumed to be unsigned char. + * + * The \p extent field defines the dimensions of the transferred area in + * elements. If a CUDA array is participating in the copy, the extent is + * defined in terms of that array's elements. If no CUDA array is + * participating in the copy then the extents are defined in elements of + * unsigned char. + * + * The \p kind field defines the direction of the copy. It must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * For ::cudaMemcpyHostToHost or ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost + * passed as kind and cudaArray type passed as source or destination, if the kind + * implies cudaArray type to be present on the host, ::cudaMemcpy3D() will + * disregard that implication and silently correct the kind based on the fact that + * cudaArray type can only be present on the device. + * + * If the source and destination are both arrays, ::cudaMemcpy3D() will return + * an error if they do not have the same element size. + * + * The source and destination object may not overlap. If overlapping source + * and destination objects are specified, undefined behavior will result. + * + * The source object must entirely contain the region defined by \p srcPos + * and \p extent. The destination object must entirely contain the region + * defined by \p dstPos and \p extent. + * + * ::cudaMemcpy3D() returns an error if the pitch of \p srcPtr or \p dstPtr + * exceeds the maximum allowed. The pitch of a ::cudaPitchedPtr allocated + * with ::cudaMalloc3D() will always be valid. + * + * \param p - 3D memory copy parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc3D, ::cudaMalloc3DArray, ::cudaMemset3D, ::cudaMemcpy3DAsync, + * ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::make_cudaExtent, ::make_cudaPos, + * ::cuMemcpy3D + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy3D(const struct cudaMemcpy3DParms *p); + +/** + * \brief Copies memory between devices + * + * Perform a 3D memory copy according to the parameters specified in + * \p p. See the definition of the ::cudaMemcpy3DPeerParms structure + * for documentation of its parameters. + * + * Note that this function is synchronous with respect to the host only if + * the source or destination of the transfer is host memory. Note also + * that this copy is serialized with respect to all pending and future + * asynchronous work in to the current device, the copy's source device, + * and the copy's destination device (use ::cudaMemcpy3DPeerAsync to avoid + * this synchronization). + * + * \param p - Parameters for the memory copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidPitchValue + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, ::cudaMemcpyPeerAsync, + * ::cudaMemcpy3DPeerAsync, + * ::cuMemcpy3DPeer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy3DPeer(const struct cudaMemcpy3DPeerParms *p); + +/** + * \brief Copies data between 3D objects + * +\code +struct cudaExtent { + size_t width; + size_t height; + size_t depth; +}; +struct cudaExtent make_cudaExtent(size_t w, size_t h, size_t d); + +struct cudaPos { + size_t x; + size_t y; + size_t z; +}; +struct cudaPos make_cudaPos(size_t x, size_t y, size_t z); + +struct cudaMemcpy3DParms { + cudaArray_t srcArray; + struct cudaPos srcPos; + struct cudaPitchedPtr srcPtr; + cudaArray_t dstArray; + struct cudaPos dstPos; + struct cudaPitchedPtr dstPtr; + struct cudaExtent extent; + enum cudaMemcpyKind kind; +}; +\endcode + * + * ::cudaMemcpy3DAsync() copies data betwen two 3D objects. The source and + * destination objects may be in either host memory, device memory, or a CUDA + * array. The source, destination, extent, and kind of copy performed is + * specified by the ::cudaMemcpy3DParms struct which should be initialized to + * zero before use: +\code +cudaMemcpy3DParms myParms = {0}; +\endcode + * + * The struct passed to ::cudaMemcpy3DAsync() must specify one of \p srcArray + * or \p srcPtr and one of \p dstArray or \p dstPtr. Passing more than one + * non-zero source or destination will cause ::cudaMemcpy3DAsync() to return an + * error. + * + * The \p srcPos and \p dstPos fields are optional offsets into the source and + * destination objects and are defined in units of each object's elements. The + * element for a host or device pointer is assumed to be unsigned char. + * For CUDA arrays, positions must be in the range [0, 2048) for any + * dimension. + * + * The \p extent field defines the dimensions of the transferred area in + * elements. If a CUDA array is participating in the copy, the extent is + * defined in terms of that array's elements. If no CUDA array is + * participating in the copy then the extents are defined in elements of + * unsigned char. + * + * The \p kind field defines the direction of the copy. It must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * For ::cudaMemcpyHostToHost or ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost + * passed as kind and cudaArray type passed as source or destination, if the kind + * implies cudaArray type to be present on the host, ::cudaMemcpy3DAsync() will + * disregard that implication and silently correct the kind based on the fact that + * cudaArray type can only be present on the device. + * + * If the source and destination are both arrays, ::cudaMemcpy3DAsync() will + * return an error if they do not have the same element size. + * + * The source and destination object may not overlap. If overlapping source + * and destination objects are specified, undefined behavior will result. + * + * The source object must lie entirely within the region defined by \p srcPos + * and \p extent. The destination object must lie entirely within the region + * defined by \p dstPos and \p extent. + * + * ::cudaMemcpy3DAsync() returns an error if the pitch of \p srcPtr or + * \p dstPtr exceeds the maximum allowed. The pitch of a + * ::cudaPitchedPtr allocated with ::cudaMalloc3D() will always be valid. + * + * ::cudaMemcpy3DAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If + * \p kind is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and \p stream + * is non-zero, the copy may overlap with operations in other streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param p - 3D memory copy parameters + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMalloc3D, ::cudaMalloc3DArray, ::cudaMemset3D, ::cudaMemcpy3D, + * ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, :::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::make_cudaExtent, ::make_cudaPos, + * ::cuMemcpy3DAsync + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync(const struct cudaMemcpy3DParms *p, cudaStream_t stream __dv(0)); + +/** + * \brief Copies memory between devices asynchronously. + * + * Perform a 3D memory copy according to the parameters specified in + * \p p. See the definition of the ::cudaMemcpy3DPeerParms structure + * for documentation of its parameters. + * + * \param p - Parameters for the memory copy + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidPitchValue + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, ::cudaMemcpyPeerAsync, + * ::cudaMemcpy3DPeerAsync, + * ::cuMemcpy3DPeerAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy3DPeerAsync(const struct cudaMemcpy3DPeerParms *p, cudaStream_t stream __dv(0)); + +/** + * \brief Gets free and total device memory + * + * Returns in \p *total the total amount of memory available to the the current context. + * Returns in \p *free the amount of memory on the device that is free according to the OS. + * CUDA is not guaranteed to be able to allocate all of the memory that the OS reports as free. + * In a multi-tenet situation, free estimate returned is prone to race condition where + * a new allocation/free done by a different process or a different thread in the same + * process between the time when free memory was estimated and reported, will result in + * deviation in free value reported and actual free memory. + * + * The integrated GPU on Tegra shares memory with CPU and other component + * of the SoC. The free and total values returned by the API excludes + * the SWAP memory space maintained by the OS on some platforms. + * The OS may move some of the memory pages into swap area as the GPU or + * CPU allocate or access memory. See Tegra app note on how to calculate + * total and free memory on Tegra. + * + * \param free - Returned free memory in bytes + * \param total - Returned total memory in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorLaunchFailure + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cuMemGetInfo + */ +extern __host__ cudaError_t CUDARTAPI cudaMemGetInfo(size_t *free, size_t *total); + +/** + * \brief Gets info about the specified cudaArray + * + * Returns in \p *desc, \p *extent and \p *flags respectively, the type, shape + * and flags of \p array. + * + * Any of \p *desc, \p *extent and \p *flags may be specified as NULL. + * + * \param desc - Returned array type + * \param extent - Returned array shape. 2D arrays will have depth of zero + * \param flags - Returned array flags + * \param array - The ::cudaArray to get info for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cuArrayGetDescriptor, + * ::cuArray3DGetDescriptor + */ +extern __host__ cudaError_t CUDARTAPI cudaArrayGetInfo(struct cudaChannelFormatDesc *desc, struct cudaExtent *extent, unsigned int *flags, cudaArray_t array); + +/** + * \brief Gets a CUDA array plane from a CUDA array + * + * Returns in \p pPlaneArray a CUDA array that represents a single format plane + * of the CUDA array \p hArray. + * + * If \p planeIdx is greater than the maximum number of planes in this array or if the array does + * not have a multi-planar format e.g: ::cudaChannelFormatKindNV12, then ::cudaErrorInvalidValue is returned. + * + * Note that if the \p hArray has format ::cudaChannelFormatKindNV12, then passing in 0 for \p planeIdx returns + * a CUDA array of the same size as \p hArray but with one 8-bit channel and ::cudaChannelFormatKindUnsigned as its format kind. + * If 1 is passed for \p planeIdx, then the returned CUDA array has half the height and width + * of \p hArray with two 8-bit channels and ::cudaChannelFormatKindUnsigned as its format kind. + * + * \param pPlaneArray - Returned CUDA array referenced by the \p planeIdx + * \param hArray - CUDA array + * \param planeIdx - Plane index + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * + * \sa + * ::cuArrayGetPlane + */ +extern __host__ cudaError_t CUDARTAPI cudaArrayGetPlane(cudaArray_t *pPlaneArray, cudaArray_t hArray, unsigned int planeIdx); + +/** + * \brief Returns the memory requirements of a CUDA array + * + * Returns the memory requirements of a CUDA array in \p memoryRequirements + * If the CUDA array is not allocated with flag ::cudaArrayDeferredMapping + * ::cudaErrorInvalidValue will be returned. + * + * The returned value in ::cudaArrayMemoryRequirements::size + * represents the total size of the CUDA array. + * The returned value in ::cudaArrayMemoryRequirements::alignment + * represents the alignment necessary for mapping the CUDA array. + * + * \return + * ::cudaSuccess + * ::cudaErrorInvalidValue + * + * \param[out] memoryRequirements - Pointer to ::cudaArrayMemoryRequirements + * \param[in] array - CUDA array to get the memory requirements of + * \param[in] device - Device to get the memory requirements for + * \sa ::cudaMipmappedArrayGetMemoryRequirements + */ +extern __host__ cudaError_t CUDARTAPI cudaArrayGetMemoryRequirements(struct cudaArrayMemoryRequirements *memoryRequirements, cudaArray_t array, int device); + +/** + * \brief Returns the memory requirements of a CUDA mipmapped array + * + * Returns the memory requirements of a CUDA mipmapped array in \p memoryRequirements + * If the CUDA mipmapped array is not allocated with flag ::cudaArrayDeferredMapping + * ::cudaErrorInvalidValue will be returned. + * + * The returned value in ::cudaArrayMemoryRequirements::size + * represents the total size of the CUDA mipmapped array. + * The returned value in ::cudaArrayMemoryRequirements::alignment + * represents the alignment necessary for mapping the CUDA mipmapped + * array. + * + * \return + * ::cudaSuccess + * ::cudaErrorInvalidValue + * + * \param[out] memoryRequirements - Pointer to ::cudaArrayMemoryRequirements + * \param[in] mipmap - CUDA mipmapped array to get the memory requirements of + * \param[in] device - Device to get the memory requirements for + * \sa ::cudaArrayGetMemoryRequirements + */ +extern __host__ cudaError_t CUDARTAPI cudaMipmappedArrayGetMemoryRequirements(struct cudaArrayMemoryRequirements *memoryRequirements, cudaMipmappedArray_t mipmap, int device); + +/** + * \brief Returns the layout properties of a sparse CUDA array + * + * Returns the layout properties of a sparse CUDA array in \p sparseProperties. + * If the CUDA array is not allocated with flag ::cudaArraySparse + * ::cudaErrorInvalidValue will be returned. + * + * If the returned value in ::cudaArraySparseProperties::flags contains ::cudaArraySparsePropertiesSingleMipTail, + * then ::cudaArraySparseProperties::miptailSize represents the total size of the array. Otherwise, it will be zero. + * Also, the returned value in ::cudaArraySparseProperties::miptailFirstLevel is always zero. + * Note that the \p array must have been allocated using ::cudaMallocArray or ::cudaMalloc3DArray. For CUDA arrays obtained + * using ::cudaMipmappedArrayGetLevel, ::cudaErrorInvalidValue will be returned. Instead, ::cudaMipmappedArrayGetSparseProperties + * must be used to obtain the sparse properties of the entire CUDA mipmapped array to which \p array belongs to. + * + * \return + * ::cudaSuccess + * ::cudaErrorInvalidValue + * + * \param[out] sparseProperties - Pointer to return the ::cudaArraySparseProperties + * \param[in] array - The CUDA array to get the sparse properties of + * + * \sa + * ::cudaMipmappedArrayGetSparseProperties, + * ::cuMemMapArrayAsync + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaArrayGetSparseProperties(struct cudaArraySparseProperties *sparseProperties, cudaArray_t array); +#endif + +/** + * \brief Returns the layout properties of a sparse CUDA mipmapped array + * + * Returns the sparse array layout properties in \p sparseProperties. + * If the CUDA mipmapped array is not allocated with flag ::cudaArraySparse + * ::cudaErrorInvalidValue will be returned. + * + * For non-layered CUDA mipmapped arrays, ::cudaArraySparseProperties::miptailSize returns the + * size of the mip tail region. The mip tail region includes all mip levels whose width, height or depth + * is less than that of the tile. + * For layered CUDA mipmapped arrays, if ::cudaArraySparseProperties::flags contains ::cudaArraySparsePropertiesSingleMipTail, + * then ::cudaArraySparseProperties::miptailSize specifies the size of the mip tail of all layers combined. + * Otherwise, ::cudaArraySparseProperties::miptailSize specifies mip tail size per layer. + * The returned value of ::cudaArraySparseProperties::miptailFirstLevel is valid only if ::cudaArraySparseProperties::miptailSize is non-zero. + * + * \return + * ::cudaSuccess + * ::cudaErrorInvalidValue + * + * \param[out] sparseProperties - Pointer to return ::cudaArraySparseProperties + * \param[in] mipmap - The CUDA mipmapped array to get the sparse properties of + * + * \sa + * ::cudaArrayGetSparseProperties, + * ::cuMemMapArrayAsync + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaMipmappedArrayGetSparseProperties(struct cudaArraySparseProperties *sparseProperties, cudaMipmappedArray_t mipmap); +#endif + +/** + * \brief Copies data between host and device + * + * Copies \p count bytes from the memory area pointed to by \p src to the + * memory area pointed to by \p dst, where \p kind specifies the direction + * of the copy, and must be one of ::cudaMemcpyHostToHost, + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. Calling + * ::cudaMemcpy() with dst and src pointers that do not match the direction of + * the copy results in an undefined behavior. + * + * \param dst - Destination memory address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_init_rt + * \note_callback + * + * \note_sync + * \note_memcpy + * + * \sa ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyDtoH, + * ::cuMemcpyHtoD, + * ::cuMemcpyDtoD, + * ::cuMemcpy + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind); + +/** + * \brief Copies memory between two devices + * + * Copies memory from one device to memory on another device. \p dst is the + * base device pointer of the destination memory and \p dstDevice is the + * destination device. \p src is the base device pointer of the source memory + * and \p srcDevice is the source device. \p count specifies the number of bytes + * to copy. + * + * Note that this function is asynchronous with respect to the host, but + * serialized with respect all pending and future asynchronous work in to the + * current device, \p srcDevice, and \p dstDevice (use ::cudaMemcpyPeerAsync + * to avoid this synchronization). + * + * \param dst - Destination device pointer + * \param dstDevice - Destination device + * \param src - Source device pointer + * \param srcDevice - Source device + * \param count - Size of memory copy in bytes + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyAsync, ::cudaMemcpyPeerAsync, + * ::cudaMemcpy3DPeerAsync, + * ::cuMemcpyPeer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyPeer(void *dst, int dstDevice, const void *src, int srcDevice, size_t count); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the memory + * area pointed to by \p src to the memory area pointed to by \p dst, where + * \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. \p dpitch and + * \p spitch are the widths in memory in bytes of the 2D arrays pointed to by + * \p dst and \p src, including any padding added to the end of each row. The + * memory areas may not overlap. \p width must not exceed either \p dpitch or + * \p spitch. Calling ::cudaMemcpy2D() with \p dst and \p src pointers that do + * not match the direction of the copy results in an undefined behavior. + * ::cudaMemcpy2D() returns an error if \p dpitch or \p spitch exceeds + * the maximum allowed. + * + * \param dst - Destination memory address + * \param dpitch - Pitch of destination memory + * \param src - Source memory address + * \param spitch - Pitch of source memory + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2D, + * ::cuMemcpy2DUnaligned + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2D(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the memory + * area pointed to by \p src to the CUDA array \p dst starting at + * \p hOffset rows and \p wOffset bytes from the upper left corner, + * where \p kind specifies the direction of the copy, and must be one + * of ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * \p spitch is the width in memory in bytes of the 2D array pointed to by + * \p src, including any padding added to the end of each row. \p wOffset + + * \p width must not exceed the width of the CUDA array \p dst. \p width must + * not exceed \p spitch. ::cudaMemcpy2DToArray() returns an error if \p spitch + * exceeds the maximum allowed. + * + * \param dst - Destination memory address + * \param wOffset - Destination starting X offset (columns in bytes) + * \param hOffset - Destination starting Y offset (rows) + * \param src - Source memory address + * \param spitch - Pitch of source memory + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2D, + * ::cuMemcpy2DUnaligned + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DToArray(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the CUDA + * array \p src starting at \p hOffset rows and \p wOffset bytes from the + * upper left corner to the memory area pointed to by \p dst, where + * \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. \p dpitch is the + * width in memory in bytes of the 2D array pointed to by \p dst, including any + * padding added to the end of each row. \p wOffset + \p width must not exceed + * the width of the CUDA array \p src. \p width must not exceed \p dpitch. + * ::cudaMemcpy2DFromArray() returns an error if \p dpitch exceeds the maximum + * allowed. + * + * \param dst - Destination memory address + * \param dpitch - Pitch of destination memory + * \param src - Source memory address + * \param wOffset - Source starting X offset (columns in bytes) + * \param hOffset - Source starting Y offset (rows) + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2D, + * ::cuMemcpy2DUnaligned + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DFromArray(void *dst, size_t dpitch, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t width, size_t height, enum cudaMemcpyKind kind); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the CUDA + * array \p src starting at \p hOffsetSrc rows and \p wOffsetSrc bytes from the + * upper left corner to the CUDA array \p dst starting at \p hOffsetDst rows + * and \p wOffsetDst bytes from the upper left corner, where \p kind + * specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * \p wOffsetDst + \p width must not exceed the width of the CUDA array \p dst. + * \p wOffsetSrc + \p width must not exceed the width of the CUDA array \p src. + * + * \param dst - Destination memory address + * \param wOffsetDst - Destination starting X offset (columns in bytes) + * \param hOffsetDst - Destination starting Y offset (rows) + * \param src - Source memory address + * \param wOffsetSrc - Source starting X offset (columns in bytes) + * \param hOffsetSrc - Source starting Y offset (rows) + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2D, + * ::cuMemcpy2DUnaligned + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DArrayToArray(cudaArray_t dst, size_t wOffsetDst, size_t hOffsetDst, cudaArray_const_t src, size_t wOffsetSrc, size_t hOffsetSrc, size_t width, size_t height, enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToDevice)); + +/** + * \brief Copies data to the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p src + * to the memory area pointed to by \p offset bytes from the start of symbol + * \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_sync + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy, + * ::cuMemcpyHtoD, + * ::cuMemcpyDtoD + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyToSymbol(const void *symbol, const void *src, size_t count, size_t offset __dv(0), enum cudaMemcpyKind kind __dv(cudaMemcpyHostToDevice)); + + +/** + * \brief Copies data from the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p offset bytes + * from the start of symbol \p symbol to the memory area pointed to by \p dst. + * The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_sync + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy, + * ::cuMemcpyDtoH, + * ::cuMemcpyDtoD + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromSymbol(void *dst, const void *symbol, size_t count, size_t offset __dv(0), enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToHost)); + + +/** + * \brief Copies data between host and device + * + * Copies \p count bytes from the memory area pointed to by \p src to the + * memory area pointed to by \p dst, where \p kind specifies the + * direction of the copy, and must be one of ::cudaMemcpyHostToHost, + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * The memory areas may not overlap. Calling ::cudaMemcpyAsync() with \p dst and + * \p src pointers that do not match the direction of the copy results in an + * undefined behavior. + * + * ::cudaMemcpyAsync() is asynchronous with respect to the host, so the call + * may return before the copy is complete. The copy can optionally be + * associated to a stream by passing a non-zero \p stream argument. If \p kind + * is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and the \p stream is + * non-zero, the copy may overlap with operations in other streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param dst - Destination memory address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyAsync, + * ::cuMemcpyDtoHAsync, + * ::cuMemcpyHtoDAsync, + * ::cuMemcpyDtoDAsync + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies memory between two devices asynchronously. + * + * Copies memory from one device to memory on another device. \p dst is the + * base device pointer of the destination memory and \p dstDevice is the + * destination device. \p src is the base device pointer of the source memory + * and \p srcDevice is the source device. \p count specifies the number of bytes + * to copy. + * + * Note that this function is asynchronous with respect to the host and all work + * on other devices. + * + * \param dst - Destination device pointer + * \param dstDevice - Destination device + * \param src - Source device pointer + * \param srcDevice - Source device + * \param count - Size of memory copy in bytes + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, + * ::cudaMemcpy3DPeerAsync, + * ::cuMemcpyPeerAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyPeerAsync(void *dst, int dstDevice, const void *src, int srcDevice, size_t count, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the memory + * area pointed to by \p src to the memory area pointed to by \p dst, where + * \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * \p dpitch and \p spitch are the widths in memory in bytes of the 2D arrays + * pointed to by \p dst and \p src, including any padding added to the end of + * each row. The memory areas may not overlap. \p width must not exceed either + * \p dpitch or \p spitch. + * + * Calling ::cudaMemcpy2DAsync() with \p dst and \p src pointers that do not + * match the direction of the copy results in an undefined behavior. + * ::cudaMemcpy2DAsync() returns an error if \p dpitch or \p spitch is greater + * than the maximum allowed. + * + * ::cudaMemcpy2DAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If + * \p kind is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and + * \p stream is non-zero, the copy may overlap with operations in other + * streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param dst - Destination memory address + * \param dpitch - Pitch of destination memory + * \param src - Source memory address + * \param spitch - Pitch of source memory + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2DAsync + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the memory + * area pointed to by \p src to the CUDA array \p dst starting at \p hOffset + * rows and \p wOffset bytes from the upper left corner, where \p kind specifies + * the direction of the copy, and must be one of ::cudaMemcpyHostToHost, + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * \p spitch is the width in memory in bytes of the 2D array pointed to by + * \p src, including any padding added to the end of each row. \p wOffset + + * \p width must not exceed the width of the CUDA array \p dst. \p width must + * not exceed \p spitch. ::cudaMemcpy2DToArrayAsync() returns an error if + * \p spitch exceeds the maximum allowed. + * + * ::cudaMemcpy2DToArrayAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If + * \p kind is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and + * \p stream is non-zero, the copy may overlap with operations in other + * streams. + * + * \param dst - Destination memory address + * \param wOffset - Destination starting X offset (columns in bytes) + * \param hOffset - Destination starting Y offset (rows) + * \param src - Source memory address + * \param spitch - Pitch of source memory + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2DAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DToArrayAsync(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data between host and device + * + * Copies a matrix (\p height rows of \p width bytes each) from the CUDA + * array \p src starting at \p hOffset rows and \p wOffset bytes from the + * upper left corner to the memory area pointed to by \p dst, + * where \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * \p dpitch is the width in memory in bytes of the 2D + * array pointed to by \p dst, including any padding added to the end of each + * row. \p wOffset + \p width must not exceed the width of the CUDA array + * \p src. \p width must not exceed \p dpitch. ::cudaMemcpy2DFromArrayAsync() + * returns an error if \p dpitch exceeds the maximum allowed. + * + * ::cudaMemcpy2DFromArrayAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally be + * associated to a stream by passing a non-zero \p stream argument. If \p kind + * is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and \p stream is + * non-zero, the copy may overlap with operations in other streams. + * + * \param dst - Destination memory address + * \param dpitch - Pitch of destination memory + * \param src - Source memory address + * \param wOffset - Source starting X offset (columns in bytes) + * \param hOffset - Source starting Y offset (rows) + * \param width - Width of matrix transfer (columns in bytes) + * \param height - Height of matrix transfer (rows) + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidPitchValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * \note_memcpy + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpy2DAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DFromArrayAsync(void *dst, size_t dpitch, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data to the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p src + * to the memory area pointed to by \p offset bytes from the start of symbol + * \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * ::cudaMemcpyToSymbolAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If + * \p kind is ::cudaMemcpyHostToDevice and \p stream is non-zero, the copy + * may overlap with operations in other streams. + * + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyAsync, + * ::cuMemcpyHtoDAsync, + * ::cuMemcpyDtoDAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyToSymbolAsync(const void *symbol, const void *src, size_t count, size_t offset, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data from the given symbol on the device + * + * Copies \p count bytes from the memory area pointed to by \p offset bytes + * from the start of symbol \p symbol to the memory area pointed to by \p dst. + * The memory areas may not overlap. \p symbol is a variable that resides in + * global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * ::cudaMemcpyFromSymbolAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally be + * associated to a stream by passing a non-zero \p stream argument. If \p kind + * is ::cudaMemcpyDeviceToHost and \p stream is non-zero, the copy may overlap + * with operations in other streams. + * + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorInvalidMemcpyDirection, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, + * ::cuMemcpyAsync, + * ::cuMemcpyDtoHAsync, + * ::cuMemcpyDtoDAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromSymbolAsync(void *dst, const void *symbol, size_t count, size_t offset, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + + +/** + * \brief Initializes or sets device memory to a value + * + * Fills the first \p count bytes of the memory area pointed to by \p devPtr + * with the constant byte value \p value. + * + * Note that this function is asynchronous with respect to the host unless + * \p devPtr refers to pinned host memory. + * + * \param devPtr - Pointer to device memory + * \param value - Value to set for each byte of specified memory + * \param count - Size in bytes to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_init_rt + * \note_callback + * + * \sa + * ::cuMemsetD8, + * ::cuMemsetD16, + * ::cuMemsetD32 + */ +extern __host__ cudaError_t CUDARTAPI cudaMemset(void *devPtr, int value, size_t count); + +/** + * \brief Initializes or sets device memory to a value + * + * Sets to the specified value \p value a matrix (\p height rows of \p width + * bytes each) pointed to by \p dstPtr. \p pitch is the width in bytes of the + * 2D array pointed to by \p dstPtr, including any padding added to the end + * of each row. This function performs fastest when the pitch is one that has + * been passed back by ::cudaMallocPitch(). + * + * Note that this function is asynchronous with respect to the host unless + * \p devPtr refers to pinned host memory. + * + * \param devPtr - Pointer to 2D device memory + * \param pitch - Pitch in bytes of 2D device memory(Unused if \p height is 1) + * \param value - Value to set for each byte of specified memory + * \param width - Width of matrix set (columns in bytes) + * \param height - Height of matrix set (rows) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemset, ::cudaMemset3D, ::cudaMemsetAsync, + * ::cudaMemset2DAsync, ::cudaMemset3DAsync, + * ::cuMemsetD2D8, + * ::cuMemsetD2D16, + * ::cuMemsetD2D32 + */ +extern __host__ cudaError_t CUDARTAPI cudaMemset2D(void *devPtr, size_t pitch, int value, size_t width, size_t height); + +/** + * \brief Initializes or sets device memory to a value + * + * Initializes each element of a 3D array to the specified value \p value. + * The object to initialize is defined by \p pitchedDevPtr. The \p pitch field + * of \p pitchedDevPtr is the width in memory in bytes of the 3D array pointed + * to by \p pitchedDevPtr, including any padding added to the end of each row. + * The \p xsize field specifies the logical width of each row in bytes, while + * the \p ysize field specifies the height of each 2D slice in rows. + * The \p pitch field of \p pitchedDevPtr is ignored when \p height and \p depth + * are both equal to 1. + * + * The extents of the initialized region are specified as a \p width in bytes, + * a \p height in rows, and a \p depth in slices. + * + * Extents with \p width greater than or equal to the \p xsize of + * \p pitchedDevPtr may perform significantly faster than extents narrower + * than the \p xsize. Secondarily, extents with \p height equal to the + * \p ysize of \p pitchedDevPtr will perform faster than when the \p height is + * shorter than the \p ysize. + * + * This function performs fastest when the \p pitchedDevPtr has been allocated + * by ::cudaMalloc3D(). + * + * Note that this function is asynchronous with respect to the host unless + * \p pitchedDevPtr refers to pinned host memory. + * + * \param pitchedDevPtr - Pointer to pitched device memory + * \param value - Value to set for each byte of specified memory + * \param extent - Size parameters for where to set device memory (\p width field in bytes) + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemset, ::cudaMemset2D, + * ::cudaMemsetAsync, ::cudaMemset2DAsync, ::cudaMemset3DAsync, + * ::cudaMalloc3D, ::make_cudaPitchedPtr, + * ::make_cudaExtent + */ +extern __host__ cudaError_t CUDARTAPI cudaMemset3D(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent); + +/** + * \brief Initializes or sets device memory to a value + * + * Fills the first \p count bytes of the memory area pointed to by \p devPtr + * with the constant byte value \p value. + * + * ::cudaMemsetAsync() is asynchronous with respect to the host, so + * the call may return before the memset is complete. The operation can optionally + * be associated to a stream by passing a non-zero \p stream argument. + * If \p stream is non-zero, the operation may overlap with operations in other streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param devPtr - Pointer to device memory + * \param value - Value to set for each byte of specified memory + * \param count - Size in bytes to set + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemset, ::cudaMemset2D, ::cudaMemset3D, + * ::cudaMemset2DAsync, ::cudaMemset3DAsync, + * ::cuMemsetD8Async, + * ::cuMemsetD16Async, + * ::cuMemsetD32Async + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync(void *devPtr, int value, size_t count, cudaStream_t stream __dv(0)); + +/** + * \brief Initializes or sets device memory to a value + * + * Sets to the specified value \p value a matrix (\p height rows of \p width + * bytes each) pointed to by \p dstPtr. \p pitch is the width in bytes of the + * 2D array pointed to by \p dstPtr, including any padding added to the end + * of each row. This function performs fastest when the pitch is one that has + * been passed back by ::cudaMallocPitch(). + * + * ::cudaMemset2DAsync() is asynchronous with respect to the host, so + * the call may return before the memset is complete. The operation can optionally + * be associated to a stream by passing a non-zero \p stream argument. + * If \p stream is non-zero, the operation may overlap with operations in other streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param devPtr - Pointer to 2D device memory + * \param pitch - Pitch in bytes of 2D device memory(Unused if \p height is 1) + * \param value - Value to set for each byte of specified memory + * \param width - Width of matrix set (columns in bytes) + * \param height - Height of matrix set (rows) + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemset, ::cudaMemset2D, ::cudaMemset3D, + * ::cudaMemsetAsync, ::cudaMemset3DAsync, + * ::cuMemsetD2D8Async, + * ::cuMemsetD2D16Async, + * ::cuMemsetD2D32Async + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream __dv(0)); + +/** + * \brief Initializes or sets device memory to a value + * + * Initializes each element of a 3D array to the specified value \p value. + * The object to initialize is defined by \p pitchedDevPtr. The \p pitch field + * of \p pitchedDevPtr is the width in memory in bytes of the 3D array pointed + * to by \p pitchedDevPtr, including any padding added to the end of each row. + * The \p xsize field specifies the logical width of each row in bytes, while + * the \p ysize field specifies the height of each 2D slice in rows. + * The \p pitch field of \p pitchedDevPtr is ignored when \p height and \p depth + * are both equal to 1. + * + * The extents of the initialized region are specified as a \p width in bytes, + * a \p height in rows, and a \p depth in slices. + * + * Extents with \p width greater than or equal to the \p xsize of + * \p pitchedDevPtr may perform significantly faster than extents narrower + * than the \p xsize. Secondarily, extents with \p height equal to the + * \p ysize of \p pitchedDevPtr will perform faster than when the \p height is + * shorter than the \p ysize. + * + * This function performs fastest when the \p pitchedDevPtr has been allocated + * by ::cudaMalloc3D(). + * + * ::cudaMemset3DAsync() is asynchronous with respect to the host, so + * the call may return before the memset is complete. The operation can optionally + * be associated to a stream by passing a non-zero \p stream argument. + * If \p stream is non-zero, the operation may overlap with operations in other streams. + * + * The device version of this function only handles device to device copies and + * cannot be given local or shared pointers. + * + * \param pitchedDevPtr - Pointer to pitched device memory + * \param value - Value to set for each byte of specified memory + * \param extent - Size parameters for where to set device memory (\p width field in bytes) + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_memset + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemset, ::cudaMemset2D, ::cudaMemset3D, + * ::cudaMemsetAsync, ::cudaMemset2DAsync, + * ::cudaMalloc3D, ::make_cudaPitchedPtr, + * ::make_cudaExtent + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream __dv(0)); + +/** + * \brief Finds the address associated with a CUDA symbol + * + * Returns in \p *devPtr the address of symbol \p symbol on the device. + * \p symbol is a variable that resides in global or constant memory space. + * If \p symbol cannot be found, or if \p symbol is not declared in the + * global or constant memory space, \p *devPtr is unchanged and the error + * ::cudaErrorInvalidSymbol is returned. + * + * \param devPtr - Return device pointer associated with symbol + * \param symbol - Device symbol address + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaGetSymbolAddress(void**, const T&) "cudaGetSymbolAddress (C++ API)", + * \ref ::cudaGetSymbolSize(size_t*, const void*) "cudaGetSymbolSize (C API)", + * ::cuModuleGetGlobal + */ +extern __host__ cudaError_t CUDARTAPI cudaGetSymbolAddress(void **devPtr, const void *symbol); + +/** + * \brief Finds the size of the object associated with a CUDA symbol + * + * Returns in \p *size the size of symbol \p symbol. \p symbol is a variable that + * resides in global or constant memory space. If \p symbol cannot be found, or + * if \p symbol is not declared in global or constant memory space, \p *size is + * unchanged and the error ::cudaErrorInvalidSymbol is returned. + * + * \param size - Size of object associated with symbol + * \param symbol - Device symbol address + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidSymbol, + * ::cudaErrorNoKernelImageForDevice + * \notefnerr + * \note_string_api_deprecation + * \note_init_rt + * \note_callback + * + * \sa + * \ref ::cudaGetSymbolAddress(void**, const void*) "cudaGetSymbolAddress (C API)", + * \ref ::cudaGetSymbolSize(size_t*, const T&) "cudaGetSymbolSize (C++ API)", + * ::cuModuleGetGlobal + */ +extern __host__ cudaError_t CUDARTAPI cudaGetSymbolSize(size_t *size, const void *symbol); + +/** + * \brief Prefetches memory to the specified destination device + * + * Prefetches memory to the specified destination device. \p devPtr is the + * base device pointer of the memory to be prefetched and \p dstDevice is the + * destination device. \p count specifies the number of bytes to copy. \p stream + * is the stream in which the operation is enqueued. The memory range must refer + * to managed memory allocated via ::cudaMallocManaged or declared via __managed__ variables. + * + * Passing in cudaCpuDeviceId for \p dstDevice will prefetch the data to host memory. If + * \p dstDevice is a GPU, then the device attribute ::cudaDevAttrConcurrentManagedAccess + * must be non-zero. Additionally, \p stream must be associated with a device that has a + * non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * + * The start address and end address of the memory range will be rounded down and rounded up + * respectively to be aligned to CPU page size before the prefetch operation is enqueued + * in the stream. + * + * If no physical memory has been allocated for this region, then this memory region + * will be populated and mapped on the destination device. If there's insufficient + * memory to prefetch the desired region, the Unified Memory driver may evict pages from other + * ::cudaMallocManaged allocations to host memory in order to make room. Device memory + * allocated using ::cudaMalloc or ::cudaMallocArray will not be evicted. + * + * By default, any mappings to the previous location of the migrated pages are removed and + * mappings for the new location are only setup on \p dstDevice. The exact behavior however + * also depends on the settings applied to this memory range via ::cudaMemAdvise as described + * below: + * + * If ::cudaMemAdviseSetReadMostly was set on any subset of this memory range, + * then that subset will create a read-only copy of the pages on \p dstDevice. + * + * If ::cudaMemAdviseSetPreferredLocation was called on any subset of this memory + * range, then the pages will be migrated to \p dstDevice even if \p dstDevice is not the + * preferred location of any pages in the memory range. + * + * If ::cudaMemAdviseSetAccessedBy was called on any subset of this memory range, + * then mappings to those pages from all the appropriate processors are updated to + * refer to the new location if establishing such a mapping is possible. Otherwise, + * those mappings are cleared. + * + * Note that this API is not required for functionality and only serves to improve performance + * by allowing the application to migrate data to a suitable location before it is accessed. + * Memory accesses to this range are always coherent and are allowed even when the data is + * actively being migrated. + * + * Note that this function is asynchronous with respect to the host and all work + * on other devices. + * + * \param devPtr - Pointer to be prefetched + * \param count - Size in bytes + * \param dstDevice - Destination device to prefetch to + * \param stream - Stream to enqueue prefetch operation + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, + * ::cudaMemcpy3DPeerAsync, ::cudaMemAdvise, ::cudaMemAdvise_v2 + * ::cuMemPrefetchAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPrefetchAsync(const void *devPtr, size_t count, int dstDevice, cudaStream_t stream __dv(0)); + +extern __host__ cudaError_t CUDARTAPI cudaMemPrefetchAsync_v2(const void *devPtr, size_t count, struct cudaMemLocation location, unsigned int flags, cudaStream_t stream __dv(0)); + +/** + * \brief Advise about the usage of a given memory range + * + * Advise the Unified Memory subsystem about the usage pattern for the memory range + * starting at \p devPtr with a size of \p count bytes. The start address and end address of the memory + * range will be rounded down and rounded up respectively to be aligned to CPU page size before the + * advice is applied. The memory range must refer to managed memory allocated via ::cudaMallocManaged + * or declared via __managed__ variables. The memory range could also refer to system-allocated pageable + * memory provided it represents a valid, host-accessible region of memory and all additional constraints + * imposed by \p advice as outlined below are also satisfied. Specifying an invalid system-allocated pageable + * memory range results in an error being returned. + * + * The \p advice parameter can take the following values: + * - ::cudaMemAdviseSetReadMostly: This implies that the data is mostly going to be read + * from and only occasionally written to. Any read accesses from any processor to this region will create a + * read-only copy of at least the accessed pages in that processor's memory. Additionally, if ::cudaMemPrefetchAsync + * is called on this region, it will create a read-only copy of the data on the destination processor. + * If any processor writes to this region, all copies of the corresponding page will be invalidated + * except for the one where the write occurred. The \p device argument is ignored for this advice. + * Note that for a page to be read-duplicated, the accessing processor must either be the CPU or a GPU + * that has a non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * Also, if a context is created on a device that does not have the device attribute + * ::cudaDevAttrConcurrentManagedAccess set, then read-duplication will not occur until + * all such contexts are destroyed. + * If the memory region refers to valid system-allocated pageable memory, then the accessing device must + * have a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccess for a read-only + * copy to be created on that device. Note however that if the accessing device also has a non-zero value for the + * device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, then setting this advice + * will not create a read-only copy when that device accesses this memory region. + * + * - ::cudaMemAdviceUnsetReadMostly: Undoes the effect of ::cudaMemAdviceReadMostly and also prevents the + * Unified Memory driver from attempting heuristic read-duplication on the memory range. Any read-duplicated + * copies of the data will be collapsed into a single copy. The location for the collapsed + * copy will be the preferred location if the page has a preferred location and one of the read-duplicated + * copies was resident at that location. Otherwise, the location chosen is arbitrary. + * + * - ::cudaMemAdviseSetPreferredLocation: This advice sets the preferred location for the + * data to be the memory belonging to \p device. Passing in cudaCpuDeviceId for \p device sets the + * preferred location as host memory. If \p device is a GPU, then it must have a non-zero value for the + * device attribute ::cudaDevAttrConcurrentManagedAccess. Setting the preferred location + * does not cause data to migrate to that location immediately. Instead, it guides the migration policy + * when a fault occurs on that memory region. If the data is already in its preferred location and the + * faulting processor can establish a mapping without requiring the data to be migrated, then + * data migration will be avoided. On the other hand, if the data is not in its preferred location + * or if a direct mapping cannot be established, then it will be migrated to the processor accessing + * it. It is important to note that setting the preferred location does not prevent data prefetching + * done using ::cudaMemPrefetchAsync. + * Having a preferred location can override the page thrash detection and resolution logic in the Unified + * Memory driver. Normally, if a page is detected to be constantly thrashing between for example host and device + * memory, the page may eventually be pinned to host memory by the Unified Memory driver. But + * if the preferred location is set as device memory, then the page will continue to thrash indefinitely. + * If ::cudaMemAdviseSetReadMostly is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice, unless read accesses from + * \p device will not result in a read-only copy being created on that device as outlined in description for + * the advice ::cudaMemAdviseSetReadMostly. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::cudaDevAttrPageableMemoryAccess. + * + * - ::cudaMemAdviseUnsetPreferredLocation: Undoes the effect of ::cudaMemAdviseSetPreferredLocation + * and changes the preferred location to none. + * + * - ::cudaMemAdviseSetAccessedBy: This advice implies that the data will be accessed by \p device. + * Passing in ::cudaCpuDeviceId for \p device will set the advice for the CPU. If \p device is a GPU, then + * the device attribute ::cudaDevAttrConcurrentManagedAccess must be non-zero. + * This advice does not cause data migration and has no impact on the location of the data per se. Instead, + * it causes the data to always be mapped in the specified processor's page tables, as long as the + * location of the data permits a mapping to be established. If the data gets migrated for any reason, + * the mappings are updated accordingly. + * This advice is recommended in scenarios where data locality is not important, but avoiding faults is. + * Consider for example a system containing multiple GPUs with peer-to-peer access enabled, where the + * data located on one GPU is occasionally accessed by peer GPUs. In such scenarios, migrating data + * over to the other GPUs is not as important because the accesses are infrequent and the overhead of + * migration may be too high. But preventing faults can still help improve performance, and so having + * a mapping set up in advance is useful. Note that on CPU access of this data, the data may be migrated + * to host memory because the CPU typically cannot access device memory directly. Any GPU that had the + * ::cudaMemAdviceSetAccessedBy flag set for this data will now have its mapping updated to point to the + * page in host memory. + * If ::cudaMemAdviseSetReadMostly is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice. Additionally, if the + * preferred location of this memory region or any subset of it is also \p device, then the policies + * associated with ::cudaMemAdviseSetPreferredLocation will override the policies of this advice. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::cudaDevAttrPageableMemoryAccess. Additionally, if \p device has + * a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, + * then this call has no effect. + * + * - ::cudaMemAdviseUnsetAccessedBy: Undoes the effect of ::cudaMemAdviseSetAccessedBy. Any mappings to + * the data from \p device may be removed at any time causing accesses to result in non-fatal page faults. + * If the memory region refers to valid system-allocated pageable memory, then \p device must have a non-zero + * value for the device attribute ::cudaDevAttrPageableMemoryAccess. Additionally, if \p device has + * a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, + * then this call has no effect. + * + * \param devPtr - Pointer to memory to set the advice for + * \param count - Size in bytes of the memory range + * \param advice - Advice to be applied for the specified memory range + * \param device - Device to apply the advice for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, + * ::cudaMemcpy3DPeerAsync, ::cudaMemPrefetchAsync, + * ::cuMemAdvise + */ +extern __host__ cudaError_t CUDARTAPI cudaMemAdvise(const void *devPtr, size_t count, enum cudaMemoryAdvise advice, int device); + +/** + * \brief Advise about the usage of a given memory range + * + * Advise the Unified Memory subsystem about the usage pattern for the memory range + * starting at \p devPtr with a size of \p count bytes. The start address and end address of the memory + * range will be rounded down and rounded up respectively to be aligned to CPU page size before the + * advice is applied. The memory range must refer to managed memory allocated via ::cudaMemAllocManaged + * or declared via __managed__ variables. The memory range could also refer to system-allocated pageable + * memory provided it represents a valid, host-accessible region of memory and all additional constraints + * imposed by \p advice as outlined below are also satisfied. Specifying an invalid system-allocated pageable + * memory range results in an error being returned. + * + * The \p advice parameter can take the following values: + * - ::cudaMemAdviseSetReadMostly: This implies that the data is mostly going to be read + * from and only occasionally written to. Any read accesses from any processor to this region will create a + * read-only copy of at least the accessed pages in that processor's memory. Additionally, if ::cudaMemPrefetchAsync + * or ::cudaMemPrefetchAsync_v2 is called on this region, it will create a read-only copy of the data on the destination processor. + * If the target location for ::cudaMemPrefetchAsync_v2 is a host NUMA node and a read-only copy already exists on + * another host NUMA node, that copy will be migrated to the targeted host NUMA node. + * If any processor writes to this region, all copies of the corresponding page will be invalidated + * except for the one where the write occurred. If the writing processor is the CPU and the preferred location of + * the page is a host NUMA node, then the page will also be migrated to that host NUMA node. The \p location argument is ignored for this advice. + * Note that for a page to be read-duplicated, the accessing processor must either be the CPU or a GPU + * that has a non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * Also, if a context is created on a device that does not have the device attribute + * ::cudaDevAttrConcurrentManagedAccess set, then read-duplication will not occur until + * all such contexts are destroyed. + * If the memory region refers to valid system-allocated pageable memory, then the accessing device must + * have a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccess for a read-only + * copy to be created on that device. Note however that if the accessing device also has a non-zero value for the + * device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, then setting this advice + * will not create a read-only copy when that device accesses this memory region. + * + * - ::cudaMemAdviceUnsetReadMostly: Undoes the effect of ::cudaMemAdviseSetReadMostly and also prevents the + * Unified Memory driver from attempting heuristic read-duplication on the memory range. Any read-duplicated + * copies of the data will be collapsed into a single copy. The location for the collapsed + * copy will be the preferred location if the page has a preferred location and one of the read-duplicated + * copies was resident at that location. Otherwise, the location chosen is arbitrary. + * Note: The \p location argument is ignored for this advice. + * + * - ::cudaMemAdviseSetPreferredLocation: This advice sets the preferred location for the + * data to be the memory belonging to \p location. When ::cudaMemLocation::type is ::cudaMemLocationTypeHost, + * ::cudaMemLocation::id is ignored and the preferred location is set to be host memory. To set the preferred location + * to a specific host NUMA node, applications must set ::cudaMemLocation::type to ::cudaMemLocationTypeHostNuma and + * ::cudaMemLocation::id must specify the NUMA ID of the host NUMA node. If ::cudaMemLocation::type is set to ::cudaMemLocationTypeHostNumaCurrent, + * ::cudaMemLocation::id will be ignored and the host NUMA node closest to the calling thread's CPU will be used as the preferred location. + * If ::cudaMemLocation::type is a ::cudaMemLocationTypeDevice, then ::cudaMemLocation::id must be a valid device ordinal + * and the device must have a non-zero value for the device attribute ::cudaDevAttrConcurrentManagedAccess. + * Setting the preferred location does not cause data to migrate to that location immediately. Instead, it guides the migration policy + * when a fault occurs on that memory region. If the data is already in its preferred location and the + * faulting processor can establish a mapping without requiring the data to be migrated, then + * data migration will be avoided. On the other hand, if the data is not in its preferred location + * or if a direct mapping cannot be established, then it will be migrated to the processor accessing + * it. It is important to note that setting the preferred location does not prevent data prefetching + * done using ::cudaMemPrefetchAsync. + * Having a preferred location can override the page thrash detection and resolution logic in the Unified + * Memory driver. Normally, if a page is detected to be constantly thrashing between for example host and device + * memory, the page may eventually be pinned to host memory by the Unified Memory driver. But + * if the preferred location is set as device memory, then the page will continue to thrash indefinitely. + * If ::cudaMemAdviseSetReadMostly is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice, unless read accesses from + * \p location will not result in a read-only copy being created on that procesor as outlined in description for + * the advice ::cudaMemAdviseSetReadMostly. + * If the memory region refers to valid system-allocated pageable memory, and ::cudaMemLocation::type is ::cudaMemLocationTypeDevice + * then ::cudaMemLocation::id must be a valid device that has a non-zero alue for the device attribute ::cudaDevAttrPageableMemoryAccess. + * + * - ::cudaMemAdviseUnsetPreferredLocation: Undoes the effect of ::cudaMemAdviseSetPreferredLocation + * and changes the preferred location to none. The \p location argument is ignored for this advice. + * + * - ::cudaMemAdviseSetAccessedBy: This advice implies that the data will be accessed by processor \p location. + * The ::cudaMemLocation::type must be either ::cudaMemLocationTypeDevice with ::cudaMemLocation::id representing a valid device + * ordinal or ::cudaMemLocationTypeHost and ::cudaMemLocation::id will be ignored. All other location types are invalid. + * If ::cudaMemLocation::id is a GPU, then the device attribute ::cudaDevAttrConcurrentManagedAccess must be non-zero. + * This advice does not cause data migration and has no impact on the location of the data per se. Instead, + * it causes the data to always be mapped in the specified processor's page tables, as long as the + * location of the data permits a mapping to be established. If the data gets migrated for any reason, + * the mappings are updated accordingly. + * This advice is recommended in scenarios where data locality is not important, but avoiding faults is. + * Consider for example a system containing multiple GPUs with peer-to-peer access enabled, where the + * data located on one GPU is occasionally accessed by peer GPUs. In such scenarios, migrating data + * over to the other GPUs is not as important because the accesses are infrequent and the overhead of + * migration may be too high. But preventing faults can still help improve performance, and so having + * a mapping set up in advance is useful. Note that on CPU access of this data, the data may be migrated + * to host memory because the CPU typically cannot access device memory directly. Any GPU that had the + * ::cudaMemAdviseSetAccessedBy flag set for this data will now have its mapping updated to point to the + * page in host memory. + * If ::cudaMemAdviseSetReadMostly is also set on this memory region or any subset of it, then the + * policies associated with that advice will override the policies of this advice. Additionally, if the + * preferred location of this memory region or any subset of it is also \p location, then the policies + * associated with ::CU_MEM_ADVISE_SET_PREFERRED_LOCATION will override the policies of this advice. + * If the memory region refers to valid system-allocated pageable memory, and ::cudaMemLocation::type is ::cudaMemLocationTypeDevice + * then device in ::cudaMemLocation::id must have a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccess. + * Additionally, if ::cudaMemLocation::id has a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, + * then this call has no effect. + * + * - ::CU_MEM_ADVISE_UNSET_ACCESSED_BY: Undoes the effect of ::cudaMemAdviseSetAccessedBy. Any mappings to + * the data from \p location may be removed at any time causing accesses to result in non-fatal page faults. + * If the memory region refers to valid system-allocated pageable memory, and ::cudaMemLocation::type is ::cudaMemLocationTypeDevice + * then device in ::cudaMemLocation::id must have a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccess. + * Additionally, if ::cudaMemLocation::id has a non-zero value for the device attribute ::cudaDevAttrPageableMemoryAccessUsesHostPageTables, + * then this call has no effect. + * + * \param devPtr - Pointer to memory to set the advice for + * \param count - Size in bytes of the memory range + * \param advice - Advice to be applied for the specified memory range + * \param location - location to apply the advice for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpyPeer, ::cudaMemcpyAsync, + * ::cudaMemcpy3DPeerAsync, ::cudaMemPrefetchAsync, + * ::cuMemAdvise, ::cuMemAdvise_v2 + */ +extern __host__ cudaError_t CUDARTAPI cudaMemAdvise_v2(const void *devPtr, size_t count, enum cudaMemoryAdvise advice, struct cudaMemLocation location); + +/** +* \brief Query an attribute of a given memory range +* +* Query an attribute about the memory range starting at \p devPtr with a size of \p count bytes. The +* memory range must refer to managed memory allocated via ::cudaMallocManaged or declared via +* __managed__ variables. +* +* The \p attribute parameter can take the following values: +* - ::cudaMemRangeAttributeReadMostly: If this attribute is specified, \p data will be interpreted +* as a 32-bit integer, and \p dataSize must be 4. The result returned will be 1 if all pages in the given +* memory range have read-duplication enabled, or 0 otherwise. +* - ::cudaMemRangeAttributePreferredLocation: If this attribute is specified, \p data will be +* interpreted as a 32-bit integer, and \p dataSize must be 4. The result returned will be a GPU device +* id if all pages in the memory range have that GPU as their preferred location, or it will be cudaCpuDeviceId +* if all pages in the memory range have the CPU as their preferred location, or it will be cudaInvalidDeviceId +* if either all the pages don't have the same preferred location or some of the pages don't have a +* preferred location at all. Note that the actual location of the pages in the memory range at the time of +* the query may be different from the preferred location. +* - ::cudaMemRangeAttributeAccessedBy: If this attribute is specified, \p data will be interpreted +* as an array of 32-bit integers, and \p dataSize must be a non-zero multiple of 4. The result returned +* will be a list of device ids that had ::cudaMemAdviceSetAccessedBy set for that entire memory range. +* If any device does not have that advice set for the entire memory range, that device will not be included. +* If \p data is larger than the number of devices that have that advice set for that memory range, +* cudaInvalidDeviceId will be returned in all the extra space provided. For ex., if \p dataSize is 12 +* (i.e. \p data has 3 elements) and only device 0 has the advice set, then the result returned will be +* { 0, cudaInvalidDeviceId, cudaInvalidDeviceId }. If \p data is smaller than the number of devices that have +* that advice set, then only as many devices will be returned as can fit in the array. There is no +* guarantee on which specific devices will be returned, however. +* - ::cudaMemRangeAttributeLastPrefetchLocation: If this attribute is specified, \p data will be +* interpreted as a 32-bit integer, and \p dataSize must be 4. The result returned will be the last location +* to which all pages in the memory range were prefetched explicitly via ::cudaMemPrefetchAsync. This will either be +* a GPU id or cudaCpuDeviceId depending on whether the last location for prefetch was a GPU or the CPU +* respectively. If any page in the memory range was never explicitly prefetched or if all pages were not +* prefetched to the same location, cudaInvalidDeviceId will be returned. Note that this simply returns the +* last location that the applicaton requested to prefetch the memory range to. It gives no indication as to +* whether the prefetch operation to that location has completed or even begun. + * - ::cudaMemRangeAttributePreferredLocationType: If this attribute is specified, \p data will be + * interpreted as a ::cudaMemLocationType, and \p dataSize must be sizeof(cudaMemLocationType). The ::cudaMemLocationType returned will be + * ::cudaMemLocationTypeDevice if all pages in the memory range have the same GPU as their preferred location, or ::cudaMemLocationType + * will be ::cudaMemLocationTypeHost if all pages in the memory range have the CPU as their preferred location, or or it will be ::cudaMemLocationTypeHostNuma + * if all the pages in the memory range have the same host NUMA node ID as their preferred location or it will be ::cudaMemLocationTypeInvalid + * if either all the pages don't have the same preferred location or some of the pages don't have a preferred location at all. + * Note that the actual location type of the pages in the memory range at the time of the query may be different from the preferred location type. + * - ::cudaMemRangeAttributePreferredLocationId: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. If the ::cudaMemRangeAttributePreferredLocationType query for the same address range + * returns ::cudaMemLocationTypeDevice, it will be a valid device ordinal or if it returns ::cudaMemLocationTypeHostNuma, it will be a valid host NUMA node ID + * or if it returns any other location type, the id should be ignored. + * - ::cudaMemRangeAttributeLastPrefetchLocationType: If this attribute is specified, \p data will be + * interpreted as a ::cudaMemLocationType, and \p dataSize must be sizeof(cudaMemLocationType). The result returned will be the last location type + * to which all pages in the memory range were prefetched explicitly via ::cuMemPrefetchAsync. The ::cudaMemLocationType returned + * will be ::cudaMemLocationTypeDevice if the last prefetch location was the GPU or ::cudaMemLocationTypeHost if it was the CPU or ::cudaMemLocationTypeHostNuma if + * the last prefetch location was a specific host NUMA node. If any page in the memory range was never explicitly prefetched or if all pages were not + * prefetched to the same location, ::CUmemLocationType will be ::cudaMemLocationTypeInvalid. + * Note that this simply returns the last location type that the application requested to prefetch the memory range to. It gives no indication as to + * whether the prefetch operation to that location has completed or even begun. + * - ::cudaMemRangeAttributeLastPrefetchLocationId: If this attribute is specified, \p data will be + * interpreted as a 32-bit integer, and \p dataSize must be 4. If the ::cudaMemRangeAttributeLastPrefetchLocationType query for the same address range + * returns ::cudaMemLocationTypeDevice, it will be a valid device ordinal or if it returns ::cudaMemLocationTypeHostNuma, it will be a valid host NUMA node ID + * or if it returns any other location type, the id should be ignored. +* +* \param data - A pointers to a memory location where the result +* of each attribute query will be written to. +* \param dataSize - Array containing the size of data +* \param attribute - The attribute to query +* \param devPtr - Start of the range to query +* \param count - Size of the range to query + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemRangeGetAttributes, ::cudaMemPrefetchAsync, + * ::cudaMemAdvise, + * ::cuMemRangeGetAttribute + */ +extern __host__ cudaError_t CUDARTAPI cudaMemRangeGetAttribute(void *data, size_t dataSize, enum cudaMemRangeAttribute attribute, const void *devPtr, size_t count); + +/** + * \brief Query attributes of a given memory range. + * + * Query attributes of the memory range starting at \p devPtr with a size of \p count bytes. The + * memory range must refer to managed memory allocated via ::cudaMallocManaged or declared via + * __managed__ variables. The \p attributes array will be interpreted to have \p numAttributes + * entries. The \p dataSizes array will also be interpreted to have \p numAttributes entries. + * The results of the query will be stored in \p data. + * + * The list of supported attributes are given below. Please refer to ::cudaMemRangeGetAttribute for + * attribute descriptions and restrictions. + * + * - ::cudaMemRangeAttributeReadMostly + * - ::cudaMemRangeAttributePreferredLocation + * - ::cudaMemRangeAttributeAccessedBy + * - ::cudaMemRangeAttributeLastPrefetchLocation + * - :: cudaMemRangeAttributePreferredLocationType + * - :: cudaMemRangeAttributePreferredLocationId + * - :: cudaMemRangeAttributeLastPrefetchLocationType + * - :: cudaMemRangeAttributeLastPrefetchLocationId + * + * \param data - A two-dimensional array containing pointers to memory + * locations where the result of each attribute query will be written to. + * \param dataSizes - Array containing the sizes of each result + * \param attributes - An array of attributes to query + * (numAttributes and the number of attributes in this array should match) + * \param numAttributes - Number of attributes to query + * \param devPtr - Start of the range to query + * \param count - Size of the range to query + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemRangeGetAttribute, ::cudaMemAdvise, + * ::cudaMemPrefetchAsync, + * ::cuMemRangeGetAttributes + */ +extern __host__ cudaError_t CUDARTAPI cudaMemRangeGetAttributes(void **data, size_t *dataSizes, enum cudaMemRangeAttribute *attributes, size_t numAttributes, const void *devPtr, size_t count); + +/** @} */ /* END CUDART_MEMORY */ + +/** + * \defgroup CUDART_MEMORY_DEPRECATED Memory Management [DEPRECATED] + * + * ___MANBRIEF___ deprecated memory management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes deprecated memory management functions of the CUDA runtime + * application programming interface. + * + * Some functions have overloaded C++ API template versions documented separately in the + * \ref CUDART_HIGHLEVEL "C++ API Routines" module. + * + * @{ + */ + +/** + * \brief Copies data between host and device + * + * \deprecated + * + * Copies \p count bytes from the memory area pointed to by \p src to the + * CUDA array \p dst starting at \p hOffset rows and \p wOffset bytes from + * the upper left corner, where \p kind specifies the direction + * of the copy, and must be one of ::cudaMemcpyHostToHost, + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * \param dst - Destination memory address + * \param wOffset - Destination starting X offset (columns in bytes) + * \param hOffset - Destination starting Y offset (rows) + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, + * ::cudaMemcpy2DToArray, ::cudaMemcpyFromArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpyArrayToArray, ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpyToArrayAsync, ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpyFromArrayAsync, ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyHtoA, + * ::cuMemcpyDtoA + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaMemcpyToArray(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t count, enum cudaMemcpyKind kind); + +/** + * \brief Copies data between host and device + * + * \deprecated + * + * Copies \p count bytes from the CUDA array \p src starting at \p hOffset rows + * and \p wOffset bytes from the upper left corner to the memory area pointed to + * by \p dst, where \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * \param dst - Destination memory address + * \param src - Source memory address + * \param wOffset - Source starting X offset (columns in bytes) + * \param hOffset - Source starting Y offset (rows) + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_sync + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, ::cudaMemcpyToArray, + * ::cudaMemcpy2DToArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpyArrayToArray, ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpyToArrayAsync, ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpyFromArrayAsync, ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyAtoH, + * ::cuMemcpyAtoD + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaMemcpyFromArray(void *dst, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t count, enum cudaMemcpyKind kind); + +/** + * \brief Copies data between host and device + * + * \deprecated + * + * Copies \p count bytes from the CUDA array \p src starting at \p hOffsetSrc + * rows and \p wOffsetSrc bytes from the upper left corner to the CUDA array + * \p dst starting at \p hOffsetDst rows and \p wOffsetDst bytes from the upper + * left corner, where \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * \param dst - Destination memory address + * \param wOffsetDst - Destination starting X offset (columns in bytes) + * \param hOffsetDst - Destination starting Y offset (rows) + * \param src - Source memory address + * \param wOffsetSrc - Source starting X offset (columns in bytes) + * \param hOffsetSrc - Source starting Y offset (rows) + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, ::cudaMemcpyToArray, + * ::cudaMemcpy2DToArray, ::cudaMemcpyFromArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpyToArrayAsync, ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpyFromArrayAsync, ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyAtoA + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaMemcpyArrayToArray(cudaArray_t dst, size_t wOffsetDst, size_t hOffsetDst, cudaArray_const_t src, size_t wOffsetSrc, size_t hOffsetSrc, size_t count, enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToDevice)); + +/** + * \brief Copies data between host and device + * + * \deprecated + * + * Copies \p count bytes from the memory area pointed to by \p src to the + * CUDA array \p dst starting at \p hOffset rows and \p wOffset bytes from + * the upper left corner, where \p kind specifies the + * direction of the copy, and must be one of ::cudaMemcpyHostToHost, + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * ::cudaMemcpyToArrayAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If \p + * kind is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and \p stream + * is non-zero, the copy may overlap with operations in other streams. + * + * \param dst - Destination memory address + * \param wOffset - Destination starting X offset (columns in bytes) + * \param hOffset - Destination starting Y offset (rows) + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, ::cudaMemcpyToArray, + * ::cudaMemcpy2DToArray, ::cudaMemcpyFromArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpyArrayToArray, ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpyFromArrayAsync, ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyHtoAAsync, + * ::cuMemcpy2DAsync + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaMemcpyToArrayAsync(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** + * \brief Copies data between host and device + * + * \deprecated + * + * Copies \p count bytes from the CUDA array \p src starting at \p hOffset rows + * and \p wOffset bytes from the upper left corner to the memory area pointed to + * by \p dst, where \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * ::cudaMemcpyFromArrayAsync() is asynchronous with respect to the host, so + * the call may return before the copy is complete. The copy can optionally + * be associated to a stream by passing a non-zero \p stream argument. If \p + * kind is ::cudaMemcpyHostToDevice or ::cudaMemcpyDeviceToHost and \p stream + * is non-zero, the copy may overlap with operations in other streams. + * + * \param dst - Destination memory address + * \param src - Source memory address + * \param wOffset - Source starting X offset (columns in bytes) + * \param hOffset - Source starting Y offset (rows) + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * \param stream - Stream identifier + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidMemcpyDirection + * \notefnerr + * \note_async + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cudaMemcpy, ::cudaMemcpy2D, ::cudaMemcpyToArray, + * ::cudaMemcpy2DToArray, ::cudaMemcpyFromArray, ::cudaMemcpy2DFromArray, + * ::cudaMemcpyArrayToArray, ::cudaMemcpy2DArrayToArray, ::cudaMemcpyToSymbol, + * ::cudaMemcpyFromSymbol, ::cudaMemcpyAsync, ::cudaMemcpy2DAsync, + * ::cudaMemcpyToArrayAsync, ::cudaMemcpy2DToArrayAsync, + * ::cudaMemcpy2DFromArrayAsync, + * ::cudaMemcpyToSymbolAsync, ::cudaMemcpyFromSymbolAsync, + * ::cuMemcpyAtoHAsync, + * ::cuMemcpy2DAsync + */ +extern __CUDA_DEPRECATED __host__ cudaError_t CUDARTAPI cudaMemcpyFromArrayAsync(void *dst, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + +/** @} */ /* END CUDART_MEMORY_DEPRECATED */ + +/** + * \defgroup CUDART_MEMORY_POOLS Stream Ordered Memory Allocator + * + * ___MANBRIEF___ Functions for performing allocation and free operations in stream order. + * Functions for controlling the behavior of the underlying allocator. + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * + * @{ + * + * \section CUDART_MEMORY_POOLS_overview overview + * + * The asynchronous allocator allows the user to allocate and free in stream order. + * All asynchronous accesses of the allocation must happen between + * the stream executions of the allocation and the free. If the memory is accessed + * outside of the promised stream order, a use before allocation / use after free error + * will cause undefined behavior. + * + * The allocator is free to reallocate the memory as long as it can guarantee + * that compliant memory accesses will not overlap temporally. + * The allocator may refer to internal stream ordering as well as inter-stream dependencies + * (such as CUDA events and null stream dependencies) when establishing the temporal guarantee. + * The allocator may also insert inter-stream dependencies to establish the temporal guarantee. + * + * \section CUDART_MEMORY_POOLS_support Supported Platforms + * + * Whether or not a device supports the integrated stream ordered memory allocator + * may be queried by calling ::cudaDeviceGetAttribute() with the device attribute + * ::cudaDevAttrMemoryPoolsSupported. + */ + +/** + * \brief Allocates memory with stream ordered semantics + * + * Inserts an allocation operation into \p hStream. + * A pointer to the allocated memory is returned immediately in *dptr. + * The allocation must not be accessed until the the allocation operation completes. + * The allocation comes from the memory pool associated with the stream's device. + * + * \note The default memory pool of a device contains device memory from that device. + * \note Basic stream ordering allows future work submitted into the same stream to use the allocation. + * Stream query, stream synchronize, and CUDA events can be used to guarantee that the allocation + * operation completes before work submitted in a separate stream runs. + * \note During stream capture, this function results in the creation of an allocation node. In this case, + * the allocation is owned by the graph instead of the memory pool. The memory pool's properties + * are used to set the node's creation parameters. + * + * \param[out] devPtr - Returned device pointer + * \param[in] size - Number of bytes to allocate + * \param[in] hStream - The stream establishing the stream ordering contract and the memory pool to allocate from + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported, + * ::cudaErrorOutOfMemory, + * \notefnerr + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cuMemAllocAsync, + * \ref ::cudaMallocAsync(void** ptr, size_t size, cudaMemPool_t memPool, cudaStream_t stream) "cudaMallocAsync (C++ API)", + * ::cudaMallocFromPoolAsync, ::cudaFreeAsync, ::cudaDeviceSetMemPool, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool, ::cudaMemPoolSetAccess, ::cudaMemPoolSetAttribute, ::cudaMemPoolGetAttribute + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocAsync(void **devPtr, size_t size, cudaStream_t hStream); + +/** + * \brief Frees memory with stream ordered semantics + * + * Inserts a free operation into \p hStream. + * The allocation must not be accessed after stream execution reaches the free. + * After this API returns, accessing the memory from any subsequent work launched on the GPU + * or querying its pointer attributes results in undefined behavior. + * + * \note During stream capture, this function results in the creation of a free node and + * must therefore be passed the address of a graph allocation. + * + * \param dptr - memory to free + * \param hStream - The stream establishing the stream ordering promise + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported + * \notefnerr + * \note_null_stream + * \note_init_rt + * \note_callback + * + * \sa ::cuMemFreeAsync, ::cudaMallocAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaFreeAsync(void *devPtr, cudaStream_t hStream); + +/** + * \brief Tries to release memory back to the OS + * + * Releases memory back to the OS until the pool contains fewer than minBytesToKeep + * reserved bytes, or there is no more memory that the allocator can safely release. + * The allocator cannot release OS allocations that back outstanding asynchronous allocations. + * The OS allocations may happen at different granularity from the user allocations. + * + * \note: Allocations that have not been freed count as outstanding. + * \note: Allocations that have been asynchronously freed but whose completion has + * not been observed on the host (eg. by a synchronize) can count as outstanding. + * + * \param[in] pool - The memory pool to trim + * \param[in] minBytesToKeep - If the pool has less than minBytesToKeep reserved, + * the TrimTo operation is a no-op. Otherwise the pool will be guaranteed to have + * at least minBytesToKeep bytes reserved after the operation. + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_callback + * + * \sa ::cuMemPoolTrimTo, ::cudaMallocAsync, ::cudaFreeAsync, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool, ::cudaMemPoolCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolTrimTo(cudaMemPool_t memPool, size_t minBytesToKeep); + +/** + * \brief Sets attributes of a memory pool + * + * Supported attributes are: + * - ::cudaMemPoolAttrReleaseThreshold: (value type = cuuint64_t) + * Amount of reserved memory in bytes to hold onto before trying + * to release memory back to the OS. When more than the release + * threshold bytes of memory are held by the memory pool, the + * allocator will try to release memory back to the OS on the + * next call to stream, event or context synchronize. (default 0) + * - ::cudaMemPoolReuseFollowEventDependencies: (value type = int) + * Allow ::cudaMallocAsync to use memory asynchronously freed + * in another stream as long as a stream ordering dependency + * of the allocating stream on the free action exists. + * Cuda events and null stream interactions can create the required + * stream ordered dependencies. (default enabled) + * - ::cudaMemPoolReuseAllowOpportunistic: (value type = int) + * Allow reuse of already completed frees when there is no dependency + * between the free and allocation. (default enabled) + * - ::cudaMemPoolReuseAllowInternalDependencies: (value type = int) + * Allow ::cudaMallocAsync to insert new stream dependencies + * in order to establish the stream ordering required to reuse + * a piece of memory released by ::cudaFreeAsync (default enabled). + * - ::cudaMemPoolAttrReservedMemHigh: (value type = cuuint64_t) + * Reset the high watermark that tracks the amount of backing memory that was + * allocated for the memory pool. It is illegal to set this attribute to a non-zero value. + * - ::cudaMemPoolAttrUsedMemHigh: (value type = cuuint64_t) + * Reset the high watermark that tracks the amount of used memory that was + * allocated for the memory pool. It is illegal to set this attribute to a non-zero value. + * + * \param[in] pool - The memory pool to modify + * \param[in] attr - The attribute to modify + * \param[in] value - Pointer to the value to assign + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_callback + * + * \sa ::cuMemPoolSetAttribute, ::cudaMallocAsync, ::cudaFreeAsync, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool, ::cudaMemPoolCreate + + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolSetAttribute(cudaMemPool_t memPool, enum cudaMemPoolAttr attr, void *value ); + +/** + * \brief Gets attributes of a memory pool + * + * Supported attributes are: + * - ::cudaMemPoolAttrReleaseThreshold: (value type = cuuint64_t) + * Amount of reserved memory in bytes to hold onto before trying + * to release memory back to the OS. When more than the release + * threshold bytes of memory are held by the memory pool, the + * allocator will try to release memory back to the OS on the + * next call to stream, event or context synchronize. (default 0) + * - ::cudaMemPoolReuseFollowEventDependencies: (value type = int) + * Allow ::cudaMallocAsync to use memory asynchronously freed + * in another stream as long as a stream ordering dependency + * of the allocating stream on the free action exists. + * Cuda events and null stream interactions can create the required + * stream ordered dependencies. (default enabled) + * - ::cudaMemPoolReuseAllowOpportunistic: (value type = int) + * Allow reuse of already completed frees when there is no dependency + * between the free and allocation. (default enabled) + * - ::cudaMemPoolReuseAllowInternalDependencies: (value type = int) + * Allow ::cudaMallocAsync to insert new stream dependencies + * in order to establish the stream ordering required to reuse + * a piece of memory released by ::cudaFreeAsync (default enabled). + * - ::cudaMemPoolAttrReservedMemCurrent: (value type = cuuint64_t) + * Amount of backing memory currently allocated for the mempool. + * - ::cudaMemPoolAttrReservedMemHigh: (value type = cuuint64_t) + * High watermark of backing memory allocated for the mempool since + * the last time it was reset. + * - ::cudaMemPoolAttrUsedMemCurrent: (value type = cuuint64_t) + * Amount of memory from the pool that is currently in use by the application. + * - ::cudaMemPoolAttrUsedMemHigh: (value type = cuuint64_t) + * High watermark of the amount of memory from the pool that was in use by the + * application since the last time it was reset. + * + * \param[in] pool - The memory pool to get attributes of + * \param[in] attr - The attribute to get + * \param[in] value - Retrieved value + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_callback + * + * \sa ::cuMemPoolGetAttribute, ::cudaMallocAsync, ::cudaFreeAsync, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool, ::cudaMemPoolCreate + + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolGetAttribute(cudaMemPool_t memPool, enum cudaMemPoolAttr attr, void *value ); + +/** + * \brief Controls visibility of pools between devices + * + * \param[in] pool - The pool being modified + * \param[in] map - Array of access descriptors. Each descriptor instructs the access to enable for a single gpu + * \param[in] count - Number of descriptors in the map array. + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa ::cuMemPoolSetAccess, ::cudaMemPoolGetAccess, ::cudaMallocAsync, cudaFreeAsync + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolSetAccess(cudaMemPool_t memPool, const struct cudaMemAccessDesc *descList, size_t count); + +/** + * \brief Returns the accessibility of a pool from a device + * + * Returns the accessibility of the pool's memory from the specified location. + * + * \param[out] flags - the accessibility of the pool from the specified location + * \param[in] memPool - the pool being queried + * \param[in] location - the location accessing the pool + * + * \sa ::cuMemPoolGetAccess, ::cudaMemPoolSetAccess + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolGetAccess(enum cudaMemAccessFlags *flags, cudaMemPool_t memPool, struct cudaMemLocation *location); + +/** + * \brief Creates a memory pool + * + * Creates a CUDA memory pool and returns the handle in \p pool. The \p poolProps determines + * the properties of the pool such as the backing device and IPC capabilities. + * +* To create a memory pool targeting a specific host NUMA node, applications must +* set ::cudaMemPoolProps::cudaMemLocation::type to ::cudaMemLocationTypeHostNuma and +* ::cudaMemPoolProps::cudaMemLocation::id must specify the NUMA ID of the host memory node. +* By default, the pool's memory will be accessible from the device it is allocated on. + * In the case of pools created with ::cudaMemLocationTypeHostNuma, their default accessibility + * will be from the host CPU. + * Applications can control the maximum size of the pool by specifying a non-zero value for ::cudaMemPoolProps::maxSize. + * If set to 0, the maximum size of the pool will default to a system dependent value. + * + * Applications can set ::cudaMemPoolProps::handleTypes to ::cudaMemHandleTypeFabric + * in order to create ::cudaMemPool_t suitable for sharing within an IMEX domain. + * An IMEX domain is either an OS instance or a group of securely connected OS instances + * using the NVIDIA IMEX daemon. An IMEX channel is a global resource within the IMEX domain + * that represents a logical entity that aims to provide fine grained accessibility control + * for the participating processes. When exporter and importer CUDA processes have been + * granted access to the same IMEX channel, they can securely share memory. + * If the allocating process does not have access setup for an IMEX channel, attempting to export + * a ::CUmemoryPool with ::cudaMemHandleTypeFabric will result in ::cudaErrorNotPermitted. + * The nvidia-modprobe CLI provides more information regarding setting up of IMEX channels. + * + * \note Specifying cudaMemHandleTypeNone creates a memory pool that will not support IPC. + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported + * + * \sa ::cuMemPoolCreate, ::cudaDeviceSetMemPool, ::cudaMallocFromPoolAsync, ::cudaMemPoolExportToShareableHandle, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool + + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolCreate(cudaMemPool_t *memPool, const struct cudaMemPoolProps *poolProps); + +/** + * \brief Destroys the specified memory pool + * + * If any pointers obtained from this pool haven't been freed or + * the pool has free operations that haven't completed + * when ::cudaMemPoolDestroy is invoked, the function will return immediately and the + * resources associated with the pool will be released automatically + * once there are no more outstanding allocations. + * + * Destroying the current mempool of a device sets the default mempool of + * that device as the current mempool for that device. + * + * \note A device's default memory pool cannot be destroyed. + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa cuMemPoolDestroy, ::cudaFreeAsync, ::cudaDeviceSetMemPool, ::cudaDeviceGetDefaultMemPool, ::cudaDeviceGetMemPool, ::cudaMemPoolCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolDestroy(cudaMemPool_t memPool); + +/** + * \brief Allocates memory from a specified pool with stream ordered semantics. + * + * Inserts an allocation operation into \p hStream. + * A pointer to the allocated memory is returned immediately in *dptr. + * The allocation must not be accessed until the the allocation operation completes. + * The allocation comes from the specified memory pool. + * + * \note + * - The specified memory pool may be from a device different than that of the specified \p hStream. + * + * - Basic stream ordering allows future work submitted into the same stream to use the allocation. + * Stream query, stream synchronize, and CUDA events can be used to guarantee that the allocation + * operation completes before work submitted in a separate stream runs. + * + * \note During stream capture, this function results in the creation of an allocation node. In this case, + * the allocation is owned by the graph instead of the memory pool. The memory pool's properties + * are used to set the node's creation parameters. + * + * \param[out] ptr - Returned device pointer + * \param[in] bytesize - Number of bytes to allocate + * \param[in] memPool - The pool to allocate from + * \param[in] stream - The stream establishing the stream ordering semantic + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported, + * ::cudaErrorOutOfMemory + * + * \sa ::cuMemAllocFromPoolAsync, + * \ref ::cudaMallocAsync(void** ptr, size_t size, cudaMemPool_t memPool, cudaStream_t stream) "cudaMallocAsync (C++ API)", + * ::cudaMallocAsync, ::cudaFreeAsync, ::cudaDeviceGetDefaultMemPool, ::cudaMemPoolCreate, ::cudaMemPoolSetAccess, ::cudaMemPoolSetAttribute + */ +extern __host__ cudaError_t CUDARTAPI cudaMallocFromPoolAsync(void **ptr, size_t size, cudaMemPool_t memPool, cudaStream_t stream); + +/** + * \brief Exports a memory pool to the requested handle type. + * + * Given an IPC capable mempool, create an OS handle to share the pool with another process. + * A recipient process can convert the shareable handle into a mempool with ::cudaMemPoolImportFromShareableHandle. + * Individual pointers can then be shared with the ::cudaMemPoolExportPointer and ::cudaMemPoolImportPointer APIs. + * The implementation of what the shareable handle is and how it can be transferred is defined by the requested + * handle type. + * + * \note: To create an IPC capable mempool, create a mempool with a CUmemAllocationHandleType other than cudaMemHandleTypeNone. + * + * \param[out] handle_out - pointer to the location in which to store the requested handle + * \param[in] pool - pool to export + * \param[in] handleType - the type of handle to create + * \param[in] flags - must be 0 + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorOutOfMemory + * + * \sa ::cuMemPoolExportToShareableHandle, ::cudaMemPoolImportFromShareableHandle, ::cudaMemPoolExportPointer, ::cudaMemPoolImportPointer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolExportToShareableHandle( + void *shareableHandle, + cudaMemPool_t memPool, + enum cudaMemAllocationHandleType handleType, + unsigned int flags); + +/** + * \brief imports a memory pool from a shared handle. + * + * Specific allocations can be imported from the imported pool with ::cudaMemPoolImportPointer. + * + * \note Imported memory pools do not support creating new allocations. + * As such imported memory pools may not be used in ::cudaDeviceSetMemPool + * or ::cudaMallocFromPoolAsync calls. + * + * \param[out] pool_out - Returned memory pool + * \param[in] handle - OS handle of the pool to open + * \param[in] handleType - The type of handle being imported + * \param[in] flags - must be 0 + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorOutOfMemory + * + * \sa ::cuMemPoolImportFromShareableHandle, ::cudaMemPoolExportToShareableHandle, ::cudaMemPoolExportPointer, ::cudaMemPoolImportPointer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolImportFromShareableHandle( + cudaMemPool_t *memPool, + void *shareableHandle, + enum cudaMemAllocationHandleType handleType, + unsigned int flags); + +/** + * \brief Export data to share a memory pool allocation between processes. + * + * Constructs \p shareData_out for sharing a specific allocation from an already shared memory pool. + * The recipient process can import the allocation with the ::cudaMemPoolImportPointer api. + * The data is not a handle and may be shared through any IPC mechanism. + * + * \param[out] shareData_out - Returned export data + * \param[in] ptr - pointer to memory being exported + * + * \returns + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorOutOfMemory + * + * \sa ::cuMemPoolExportPointer, ::cudaMemPoolExportToShareableHandle, ::cudaMemPoolImportFromShareableHandle, ::cudaMemPoolImportPointer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolExportPointer(struct cudaMemPoolPtrExportData *exportData, void *ptr); + +/** + * \brief Import a memory pool allocation from another process. + * + * Returns in \p ptr_out a pointer to the imported memory. + * The imported memory must not be accessed before the allocation operation completes + * in the exporting process. The imported memory must be freed from all importing processes before + * being freed in the exporting process. The pointer may be freed with cudaFree + * or cudaFreeAsync. If ::cudaFreeAsync is used, the free must be completed + * on the importing process before the free operation on the exporting process. + * + * \note The ::cudaFreeAsync api may be used in the exporting process before + * the ::cudaFreeAsync operation completes in its stream as long as the + * ::cudaFreeAsync in the exporting process specifies a stream with + * a stream dependency on the importing process's ::cudaFreeAsync. + * + * \param[out] ptr_out - pointer to imported memory + * \param[in] pool - pool from which to import + * \param[in] shareData - data specifying the memory to import + * + * \returns + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_INITIALIZED, + * ::CUDA_ERROR_OUT_OF_MEMORY + * + * \sa ::cuMemPoolImportPointer, ::cudaMemPoolExportToShareableHandle, ::cudaMemPoolImportFromShareableHandle, ::cudaMemPoolExportPointer + */ +extern __host__ cudaError_t CUDARTAPI cudaMemPoolImportPointer(void **ptr, cudaMemPool_t memPool, struct cudaMemPoolPtrExportData *exportData); + +/** @} */ /* END CUDART_MEMORY_POOLS */ + +/** + * \defgroup CUDART_UNIFIED Unified Addressing + * + * ___MANBRIEF___ unified addressing functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the unified addressing functions of the CUDA + * runtime application programming interface. + * + * @{ + * + * \section CUDART_UNIFIED_overview Overview + * + * CUDA devices can share a unified address space with the host. + * For these devices there is no distinction between a device + * pointer and a host pointer -- the same pointer value may be + * used to access memory from the host program and from a kernel + * running on the device (with exceptions enumerated below). + * + * \section CUDART_UNIFIED_support Supported Platforms + * + * Whether or not a device supports unified addressing may be + * queried by calling ::cudaGetDeviceProperties() with the device + * property ::cudaDeviceProp::unifiedAddressing. + * + * Unified addressing is automatically enabled in 64-bit processes . + * + * \section CUDART_UNIFIED_lookup Looking Up Information from Pointer Values + * + * It is possible to look up information about the memory which backs a + * pointer value. For instance, one may want to know if a pointer points + * to host or device memory. As another example, in the case of device + * memory, one may want to know on which CUDA device the memory + * resides. These properties may be queried using the function + * ::cudaPointerGetAttributes() + * + * Since pointers are unique, it is not necessary to specify information + * about the pointers specified to ::cudaMemcpy() and other copy functions. + * The copy direction ::cudaMemcpyDefault may be used to specify that the + * CUDA runtime should infer the location of the pointer from its value. + * + * \section CUDART_UNIFIED_automaphost Automatic Mapping of Host Allocated Host Memory + * + * All host memory allocated through all devices using ::cudaMallocHost() and + * ::cudaHostAlloc() is always directly accessible from all devices that + * support unified addressing. This is the case regardless of whether or + * not the flags ::cudaHostAllocPortable and ::cudaHostAllocMapped are + * specified. + * + * The pointer value through which allocated host memory may be accessed + * in kernels on all devices that support unified addressing is the same + * as the pointer value through which that memory is accessed on the host. + * It is not necessary to call ::cudaHostGetDevicePointer() to get the device + * pointer for these allocations. + * + * Note that this is not the case for memory allocated using the flag + * ::cudaHostAllocWriteCombined, as discussed below. + * + * \section CUDART_UNIFIED_autopeerregister Direct Access of Peer Memory + + * Upon enabling direct access from a device that supports unified addressing + * to another peer device that supports unified addressing using + * ::cudaDeviceEnablePeerAccess() all memory allocated in the peer device using + * ::cudaMalloc() and ::cudaMallocPitch() will immediately be accessible + * by the current device. The device pointer value through + * which any peer's memory may be accessed in the current device + * is the same pointer value through which that memory may be + * accessed from the peer device. + * + * \section CUDART_UNIFIED_exceptions Exceptions, Disjoint Addressing + * + * Not all memory may be accessed on devices through the same pointer + * value through which they are accessed on the host. These exceptions + * are host memory registered using ::cudaHostRegister() and host memory + * allocated using the flag ::cudaHostAllocWriteCombined. For these + * exceptions, there exists a distinct host and device address for the + * memory. The device address is guaranteed to not overlap any valid host + * pointer range and is guaranteed to have the same value across all devices + * that support unified addressing. + * + * This device address may be queried using ::cudaHostGetDevicePointer() + * when a device using unified addressing is current. Either the host + * or the unified device pointer value may be used to refer to this memory + * in ::cudaMemcpy() and similar functions using the ::cudaMemcpyDefault + * memory direction. + * + */ + +/** + * \brief Returns attributes about a specified pointer + * + * Returns in \p *attributes the attributes of the pointer \p ptr. + * If pointer was not allocated in, mapped by or registered with context + * supporting unified addressing ::cudaErrorInvalidValue is returned. + * + * \note In CUDA 11.0 forward passing host pointer will return ::cudaMemoryTypeUnregistered + * in ::cudaPointerAttributes::type and call will return ::cudaSuccess. + * + * The ::cudaPointerAttributes structure is defined as: + * \code + struct cudaPointerAttributes { + enum cudaMemoryType type; + int device; + void *devicePointer; + void *hostPointer; + } + \endcode + * In this structure, the individual fields mean + * + * - \ref ::cudaPointerAttributes::type identifies type of memory. It can be + * ::cudaMemoryTypeUnregistered for unregistered host memory, + * ::cudaMemoryTypeHost for registered host memory, ::cudaMemoryTypeDevice for device + * memory or ::cudaMemoryTypeManaged for managed memory. + * + * - \ref ::cudaPointerAttributes::device "device" is the device against which + * \p ptr was allocated. If \p ptr has memory type ::cudaMemoryTypeDevice + * then this identifies the device on which the memory referred to by \p ptr + * physically resides. If \p ptr has memory type ::cudaMemoryTypeHost then this + * identifies the device which was current when the allocation was made + * (and if that device is deinitialized then this allocation will vanish + * with that device's state). + * + * - \ref ::cudaPointerAttributes::devicePointer "devicePointer" is + * the device pointer alias through which the memory referred to by \p ptr + * may be accessed on the current device. + * If the memory referred to by \p ptr cannot be accessed directly by the + * current device then this is NULL. + * + * - \ref ::cudaPointerAttributes::hostPointer "hostPointer" is + * the host pointer alias through which the memory referred to by \p ptr + * may be accessed on the host. + * If the memory referred to by \p ptr cannot be accessed directly by the + * host then this is NULL. + * + * \param attributes - Attributes for the specified pointer + * \param ptr - Pointer to get attributes for + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa ::cudaGetDeviceCount, ::cudaGetDevice, ::cudaSetDevice, + * ::cudaChooseDevice, + * ::cudaInitDevice, + * ::cuPointerGetAttributes + */ +extern __host__ cudaError_t CUDARTAPI cudaPointerGetAttributes(struct cudaPointerAttributes *attributes, const void *ptr); + +/** @} */ /* END CUDART_UNIFIED */ + +/** + * \defgroup CUDART_PEER Peer Device Memory Access + * + * ___MANBRIEF___ peer device memory access functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the peer device memory access functions of the CUDA runtime + * application programming interface. + * + * @{ + */ + +/** + * \brief Queries if a device may directly access a peer device's memory. + * + * Returns in \p *canAccessPeer a value of 1 if device \p device is capable of + * directly accessing memory from \p peerDevice and 0 otherwise. If direct + * access of \p peerDevice from \p device is possible, then access may be + * enabled by calling ::cudaDeviceEnablePeerAccess(). + * + * \param canAccessPeer - Returned access capability + * \param device - Device from which allocations on \p peerDevice are to + * be directly accessed. + * \param peerDevice - Device on which the allocations to be directly accessed + * by \p device reside. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceEnablePeerAccess, + * ::cudaDeviceDisablePeerAccess, + * ::cuDeviceCanAccessPeer + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceCanAccessPeer(int *canAccessPeer, int device, int peerDevice); + +/** + * \brief Enables direct access to memory allocations on a peer device. + * + * On success, all allocations from \p peerDevice will immediately be accessible by + * the current device. They will remain accessible until access is explicitly + * disabled using ::cudaDeviceDisablePeerAccess() or either device is reset using + * ::cudaDeviceReset(). + * + * Note that access granted by this call is unidirectional and that in order to access + * memory on the current device from \p peerDevice, a separate symmetric call + * to ::cudaDeviceEnablePeerAccess() is required. + * + * Note that there are both device-wide and system-wide limitations per system + * configuration, as noted in the CUDA Programming Guide under the section + * "Peer-to-Peer Memory Access". + * + * Returns ::cudaErrorInvalidDevice if ::cudaDeviceCanAccessPeer() indicates + * that the current device cannot directly access memory from \p peerDevice. + * + * Returns ::cudaErrorPeerAccessAlreadyEnabled if direct access of + * \p peerDevice from the current device has already been enabled. + * + * Returns ::cudaErrorInvalidValue if \p flags is not 0. + * + * \param peerDevice - Peer device to enable direct access to from the current device + * \param flags - Reserved for future use and must be set to 0 + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorPeerAccessAlreadyEnabled, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceCanAccessPeer, + * ::cudaDeviceDisablePeerAccess, + * ::cuCtxEnablePeerAccess + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceEnablePeerAccess(int peerDevice, unsigned int flags); + +/** + * \brief Disables direct access to memory allocations on a peer device. + * + * Returns ::cudaErrorPeerAccessNotEnabled if direct access to memory on + * \p peerDevice has not yet been enabled from the current device. + * + * \param peerDevice - Peer device to disable direct access to + * + * \return + * ::cudaSuccess, + * ::cudaErrorPeerAccessNotEnabled, + * ::cudaErrorInvalidDevice + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa ::cudaDeviceCanAccessPeer, + * ::cudaDeviceEnablePeerAccess, + * ::cuCtxDisablePeerAccess + */ +extern __host__ cudaError_t CUDARTAPI cudaDeviceDisablePeerAccess(int peerDevice); + +/** @} */ /* END CUDART_PEER */ + +/** \defgroup CUDART_OPENGL OpenGL Interoperability */ + +/** \defgroup CUDART_OPENGL_DEPRECATED OpenGL Interoperability [DEPRECATED] */ + +/** \defgroup CUDART_D3D9 Direct3D 9 Interoperability */ + +/** \defgroup CUDART_D3D9_DEPRECATED Direct3D 9 Interoperability [DEPRECATED] */ + +/** \defgroup CUDART_D3D10 Direct3D 10 Interoperability */ + +/** \defgroup CUDART_D3D10_DEPRECATED Direct3D 10 Interoperability [DEPRECATED] */ + +/** \defgroup CUDART_D3D11 Direct3D 11 Interoperability */ + +/** \defgroup CUDART_D3D11_DEPRECATED Direct3D 11 Interoperability [DEPRECATED] */ + +/** \defgroup CUDART_VDPAU VDPAU Interoperability */ + +/** \defgroup CUDART_EGL EGL Interoperability */ + +/** + * \defgroup CUDART_INTEROP Graphics Interoperability + * + * ___MANBRIEF___ graphics interoperability functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the graphics interoperability functions of the CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Unregisters a graphics resource for access by CUDA + * + * Unregisters the graphics resource \p resource so it is not accessible by + * CUDA unless registered again. + * + * If \p resource is invalid then ::cudaErrorInvalidResourceHandle is + * returned. + * + * \param resource - Resource to unregister + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaGraphicsD3D9RegisterResource, + * ::cudaGraphicsD3D10RegisterResource, + * ::cudaGraphicsD3D11RegisterResource, + * ::cudaGraphicsGLRegisterBuffer, + * ::cudaGraphicsGLRegisterImage, + * ::cuGraphicsUnregisterResource + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsUnregisterResource(cudaGraphicsResource_t resource); + +/** + * \brief Set usage flags for mapping a graphics resource + * + * Set \p flags for mapping the graphics resource \p resource. + * + * Changes to \p flags will take effect the next time \p resource is mapped. + * The \p flags argument may be any of the following: + * - ::cudaGraphicsMapFlagsNone: Specifies no hints about how \p resource will + * be used. It is therefore assumed that CUDA may read from or write to \p resource. + * - ::cudaGraphicsMapFlagsReadOnly: Specifies that CUDA will not write to \p resource. + * - ::cudaGraphicsMapFlagsWriteDiscard: Specifies CUDA will not read from \p resource and will + * write over the entire contents of \p resource, so none of the data + * previously stored in \p resource will be preserved. + * + * If \p resource is presently mapped for access by CUDA then ::cudaErrorUnknown is returned. + * If \p flags is not one of the above values then ::cudaErrorInvalidValue is returned. + * + * \param resource - Registered resource to set flags for + * \param flags - Parameters for resource mapping + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown, + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsMapResources, + * ::cuGraphicsResourceSetMapFlags + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsResourceSetMapFlags(cudaGraphicsResource_t resource, unsigned int flags); + +/** + * \brief Map graphics resources for access by CUDA + * + * Maps the \p count graphics resources in \p resources for access by CUDA. + * + * The resources in \p resources may be accessed by CUDA until they + * are unmapped. The graphics API from which \p resources were registered + * should not access any resources while they are mapped by CUDA. If an + * application does so, the results are undefined. + * + * This function provides the synchronization guarantee that any graphics calls + * issued before ::cudaGraphicsMapResources() will complete before any subsequent CUDA + * work issued in \p stream begins. + * + * If \p resources contains any duplicate entries then ::cudaErrorInvalidResourceHandle + * is returned. If any of \p resources are presently mapped for access by + * CUDA then ::cudaErrorUnknown is returned. + * + * \param count - Number of resources to map + * \param resources - Resources to map for CUDA + * \param stream - Stream for synchronization + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsResourceGetMappedPointer, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cudaGraphicsUnmapResources, + * ::cuGraphicsMapResources + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsMapResources(int count, cudaGraphicsResource_t *resources, cudaStream_t stream __dv(0)); + +/** + * \brief Unmap graphics resources. + * + * Unmaps the \p count graphics resources in \p resources. + * + * Once unmapped, the resources in \p resources may not be accessed by CUDA + * until they are mapped again. + * + * This function provides the synchronization guarantee that any CUDA work issued + * in \p stream before ::cudaGraphicsUnmapResources() will complete before any + * subsequently issued graphics work begins. + * + * If \p resources contains any duplicate entries then ::cudaErrorInvalidResourceHandle + * is returned. If any of \p resources are not presently mapped for access by + * CUDA then ::cudaErrorUnknown is returned. + * + * \param count - Number of resources to unmap + * \param resources - Resources to unmap + * \param stream - Stream for synchronization + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \note_null_stream + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsMapResources, + * ::cuGraphicsUnmapResources + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsUnmapResources(int count, cudaGraphicsResource_t *resources, cudaStream_t stream __dv(0)); + +/** + * \brief Get an device pointer through which to access a mapped graphics resource. + * + * Returns in \p *devPtr a pointer through which the mapped graphics resource + * \p resource may be accessed. + * Returns in \p *size the size of the memory in bytes which may be accessed from that pointer. + * The value set in \p devPtr may change every time that \p resource is mapped. + * + * If \p resource is not a buffer then it cannot be accessed via a pointer and + * ::cudaErrorUnknown is returned. + * If \p resource is not mapped then ::cudaErrorUnknown is returned. + * * + * \param devPtr - Returned pointer through which \p resource may be accessed + * \param size - Returned size of the buffer accessible starting at \p *devPtr + * \param resource - Mapped resource to access + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsMapResources, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cuGraphicsResourceGetMappedPointer + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsResourceGetMappedPointer(void **devPtr, size_t *size, cudaGraphicsResource_t resource); + +/** + * \brief Get an array through which to access a subresource of a mapped graphics resource. + * + * Returns in \p *array an array through which the subresource of the mapped + * graphics resource \p resource which corresponds to array index \p arrayIndex + * and mipmap level \p mipLevel may be accessed. The value set in \p array may + * change every time that \p resource is mapped. + * + * If \p resource is not a texture then it cannot be accessed via an array and + * ::cudaErrorUnknown is returned. + * If \p arrayIndex is not a valid array index for \p resource then + * ::cudaErrorInvalidValue is returned. + * If \p mipLevel is not a valid mipmap level for \p resource then + * ::cudaErrorInvalidValue is returned. + * If \p resource is not mapped then ::cudaErrorUnknown is returned. + * + * \param array - Returned array through which a subresource of \p resource may be accessed + * \param resource - Mapped resource to access + * \param arrayIndex - Array index for array textures or cubemap face + * index as defined by ::cudaGraphicsCubeFace for + * cubemap textures for the subresource to access + * \param mipLevel - Mipmap level for the subresource to access + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsResourceGetMappedPointer, + * ::cuGraphicsSubResourceGetMappedArray + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsSubResourceGetMappedArray(cudaArray_t *array, cudaGraphicsResource_t resource, unsigned int arrayIndex, unsigned int mipLevel); + +/** + * \brief Get a mipmapped array through which to access a mapped graphics resource. + * + * Returns in \p *mipmappedArray a mipmapped array through which the mapped + * graphics resource \p resource may be accessed. The value set in \p mipmappedArray may + * change every time that \p resource is mapped. + * + * If \p resource is not a texture then it cannot be accessed via an array and + * ::cudaErrorUnknown is returned. + * If \p resource is not mapped then ::cudaErrorUnknown is returned. + * + * \param mipmappedArray - Returned mipmapped array through which \p resource may be accessed + * \param resource - Mapped resource to access + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphicsResourceGetMappedPointer, + * ::cuGraphicsResourceGetMappedMipmappedArray + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsResourceGetMappedMipmappedArray(cudaMipmappedArray_t *mipmappedArray, cudaGraphicsResource_t resource); + +/** @} */ /* END CUDART_INTEROP */ + +/** + * \defgroup CUDART_TEXTURE_OBJECT Texture Object Management + * + * ___MANBRIEF___ texture object management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the low level texture object management functions + * of the CUDA runtime application programming interface. The texture + * object API is only supported on devices of compute capability 3.0 or higher. + * + * @{ + */ + +/** + * \brief Get the channel descriptor of an array + * + * Returns in \p *desc the channel descriptor of the CUDA array \p array. + * + * \param desc - Channel format + * \param array - Memory array on device + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa \ref ::cudaCreateChannelDesc(int, int, int, int, cudaChannelFormatKind) "cudaCreateChannelDesc (C API)", + * ::cudaCreateTextureObject, ::cudaCreateSurfaceObject + */ +extern __host__ cudaError_t CUDARTAPI cudaGetChannelDesc(struct cudaChannelFormatDesc *desc, cudaArray_const_t array); + +/** + * \brief Returns a channel descriptor using the specified format + * + * Returns a channel descriptor with format \p f and number of bits of each + * component \p x, \p y, \p z, and \p w. The ::cudaChannelFormatDesc is + * defined as: + * \code + struct cudaChannelFormatDesc { + int x, y, z, w; + enum cudaChannelFormatKind f; + }; + * \endcode + * + * where ::cudaChannelFormatKind is one of ::cudaChannelFormatKindSigned, + * ::cudaChannelFormatKindUnsigned, or ::cudaChannelFormatKindFloat. + * + * \param x - X component + * \param y - Y component + * \param z - Z component + * \param w - W component + * \param f - Channel format + * + * \return + * Channel descriptor with format \p f + * + * \sa \ref ::cudaCreateChannelDesc(void) "cudaCreateChannelDesc (C++ API)", + * ::cudaGetChannelDesc, ::cudaCreateTextureObject, ::cudaCreateSurfaceObject + */ +extern __host__ struct cudaChannelFormatDesc CUDARTAPI cudaCreateChannelDesc(int x, int y, int z, int w, enum cudaChannelFormatKind f); + +/** + * \brief Creates a texture object + * + * Creates a texture object and returns it in \p pTexObject. \p pResDesc describes + * the data to texture from. \p pTexDesc describes how the data should be sampled. + * \p pResViewDesc is an optional argument that specifies an alternate format for + * the data described by \p pResDesc, and also describes the subresource region + * to restrict access to when texturing. \p pResViewDesc can only be specified if + * the type of resource is a CUDA array or a CUDA mipmapped array. + * + * Texture objects are only supported on devices of compute capability 3.0 or higher. + * Additionally, a texture object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * The ::cudaResourceDesc structure is defined as: + * \code + struct cudaResourceDesc { + enum cudaResourceType resType; + + union { + struct { + cudaArray_t array; + } array; + struct { + cudaMipmappedArray_t mipmap; + } mipmap; + struct { + void *devPtr; + struct cudaChannelFormatDesc desc; + size_t sizeInBytes; + } linear; + struct { + void *devPtr; + struct cudaChannelFormatDesc desc; + size_t width; + size_t height; + size_t pitchInBytes; + } pitch2D; + } res; + }; + * \endcode + * where: + * - ::cudaResourceDesc::resType specifies the type of resource to texture from. + * CUresourceType is defined as: + * \code + enum cudaResourceType { + cudaResourceTypeArray = 0x00, + cudaResourceTypeMipmappedArray = 0x01, + cudaResourceTypeLinear = 0x02, + cudaResourceTypePitch2D = 0x03 + }; + * \endcode + * + * \par + * If ::cudaResourceDesc::resType is set to ::cudaResourceTypeArray, ::cudaResourceDesc::res::array::array + * must be set to a valid CUDA array handle. + * + * \par + * If ::cudaResourceDesc::resType is set to ::cudaResourceTypeMipmappedArray, ::cudaResourceDesc::res::mipmap::mipmap + * must be set to a valid CUDA mipmapped array handle and ::cudaTextureDesc::normalizedCoords must be set to true. + * + * \par + * If ::cudaResourceDesc::resType is set to ::cudaResourceTypeLinear, ::cudaResourceDesc::res::linear::devPtr + * must be set to a valid device pointer, that is aligned to ::cudaDeviceProp::textureAlignment. + * ::cudaResourceDesc::res::linear::desc describes the format and the number of components per array element. ::cudaResourceDesc::res::linear::sizeInBytes + * specifies the size of the array in bytes. The total number of elements in the linear address range cannot exceed + * ::cudaDeviceProp::maxTexture1DLinear. The number of elements is computed as (sizeInBytes / sizeof(desc)). + * + * \par + * If ::cudaResourceDesc::resType is set to ::cudaResourceTypePitch2D, ::cudaResourceDesc::res::pitch2D::devPtr + * must be set to a valid device pointer, that is aligned to ::cudaDeviceProp::textureAlignment. + * ::cudaResourceDesc::res::pitch2D::desc describes the format and the number of components per array element. ::cudaResourceDesc::res::pitch2D::width + * and ::cudaResourceDesc::res::pitch2D::height specify the width and height of the array in elements, and cannot exceed + * ::cudaDeviceProp::maxTexture2DLinear[0] and ::cudaDeviceProp::maxTexture2DLinear[1] respectively. + * ::cudaResourceDesc::res::pitch2D::pitchInBytes specifies the pitch between two rows in bytes and has to be aligned to + * ::cudaDeviceProp::texturePitchAlignment. Pitch cannot exceed ::cudaDeviceProp::maxTexture2DLinear[2]. + * + * + * The ::cudaTextureDesc struct is defined as + * \code + struct cudaTextureDesc { + enum cudaTextureAddressMode addressMode[3]; + enum cudaTextureFilterMode filterMode; + enum cudaTextureReadMode readMode; + int sRGB; + float borderColor[4]; + int normalizedCoords; + unsigned int maxAnisotropy; + enum cudaTextureFilterMode mipmapFilterMode; + float mipmapLevelBias; + float minMipmapLevelClamp; + float maxMipmapLevelClamp; + int disableTrilinearOptimization; + int seamlessCubemap; + }; + * \endcode + * where + * - ::cudaTextureDesc::addressMode specifies the addressing mode for each dimension of the texture data. ::cudaTextureAddressMode is defined as: + * \code + enum cudaTextureAddressMode { + cudaAddressModeWrap = 0, + cudaAddressModeClamp = 1, + cudaAddressModeMirror = 2, + cudaAddressModeBorder = 3 + }; + * \endcode + * This is ignored if ::cudaResourceDesc::resType is ::cudaResourceTypeLinear. Also, if ::cudaTextureDesc::normalizedCoords + * is set to zero, ::cudaAddressModeWrap and ::cudaAddressModeMirror won't be supported and will be switched to ::cudaAddressModeClamp. + * + * - ::cudaTextureDesc::filterMode specifies the filtering mode to be used when fetching from the texture. ::cudaTextureFilterMode is defined as: + * \code + enum cudaTextureFilterMode { + cudaFilterModePoint = 0, + cudaFilterModeLinear = 1 + }; + * \endcode + * This is ignored if ::cudaResourceDesc::resType is ::cudaResourceTypeLinear. + * + * - ::cudaTextureDesc::readMode specifies whether integer data should be converted to floating point or not. ::cudaTextureReadMode is defined as: + * \code + enum cudaTextureReadMode { + cudaReadModeElementType = 0, + cudaReadModeNormalizedFloat = 1 + }; + * \endcode + * Note that this applies only to 8-bit and 16-bit integer formats. 32-bit integer format would not be promoted, regardless of + * whether or not this ::cudaTextureDesc::readMode is set ::cudaReadModeNormalizedFloat is specified. + * + * - ::cudaTextureDesc::sRGB specifies whether sRGB to linear conversion should be performed during texture fetch. + * + * - ::cudaTextureDesc::borderColor specifies the float values of color. where: + * ::cudaTextureDesc::borderColor[0] contains value of 'R', + * ::cudaTextureDesc::borderColor[1] contains value of 'G', + * ::cudaTextureDesc::borderColor[2] contains value of 'B', + * ::cudaTextureDesc::borderColor[3] contains value of 'A' + * Note that application using integer border color values will need to these values to float. + * The values are set only when the addressing mode specified by ::cudaTextureDesc::addressMode is cudaAddressModeBorder. + * + * - ::cudaTextureDesc::normalizedCoords specifies whether the texture coordinates will be normalized or not. + * + * - ::cudaTextureDesc::maxAnisotropy specifies the maximum anistropy ratio to be used when doing anisotropic filtering. This value will be + * clamped to the range [1,16]. + * + * - ::cudaTextureDesc::mipmapFilterMode specifies the filter mode when the calculated mipmap level lies between two defined mipmap levels. + * + * - ::cudaTextureDesc::mipmapLevelBias specifies the offset to be applied to the calculated mipmap level. + * + * - ::cudaTextureDesc::minMipmapLevelClamp specifies the lower end of the mipmap level range to clamp access to. + * + * - ::cudaTextureDesc::maxMipmapLevelClamp specifies the upper end of the mipmap level range to clamp access to. + * + * - ::cudaTextureDesc::disableTrilinearOptimization specifies whether the trilinear filtering optimizations will be disabled. + * + * - ::cudaTextureDesc::seamlessCubemap specifies whether seamless cube map filtering is enabled. This flag can only be specified if the + * underlying resource is a CUDA array or a CUDA mipmapped array that was created with the flag ::cudaArrayCubemap. + * When seamless cube map filtering is enabled, texture address modes specified by ::cudaTextureDesc::addressMode are ignored. + * Instead, if the ::cudaTextureDesc::filterMode is set to ::cudaFilterModePoint the address mode ::cudaAddressModeClamp will be applied for all dimensions. + * If the ::cudaTextureDesc::filterMode is set to ::cudaFilterModeLinear seamless cube map filtering will be performed when sampling along the cube face borders. + * + * The ::cudaResourceViewDesc struct is defined as + * \code + struct cudaResourceViewDesc { + enum cudaResourceViewFormat format; + size_t width; + size_t height; + size_t depth; + unsigned int firstMipmapLevel; + unsigned int lastMipmapLevel; + unsigned int firstLayer; + unsigned int lastLayer; + }; + * \endcode + * where: + * - ::cudaResourceViewDesc::format specifies how the data contained in the CUDA array or CUDA mipmapped array should + * be interpreted. Note that this can incur a change in size of the texture data. If the resource view format is a block + * compressed format, then the underlying CUDA array or CUDA mipmapped array has to have a 32-bit unsigned integer format + * with 2 or 4 channels, depending on the block compressed format. For ex., BC1 and BC4 require the underlying CUDA array to have + * a 32-bit unsigned int with 2 channels. The other BC formats require the underlying resource to have the same 32-bit unsigned int + * format but with 4 channels. + * + * - ::cudaResourceViewDesc::width specifies the new width of the texture data. If the resource view format is a block + * compressed format, this value has to be 4 times the original width of the resource. For non block compressed formats, + * this value has to be equal to that of the original resource. + * + * - ::cudaResourceViewDesc::height specifies the new height of the texture data. If the resource view format is a block + * compressed format, this value has to be 4 times the original height of the resource. For non block compressed formats, + * this value has to be equal to that of the original resource. + * + * - ::cudaResourceViewDesc::depth specifies the new depth of the texture data. This value has to be equal to that of the + * original resource. + * + * - ::cudaResourceViewDesc::firstMipmapLevel specifies the most detailed mipmap level. This will be the new mipmap level zero. + * For non-mipmapped resources, this value has to be zero.::cudaTextureDesc::minMipmapLevelClamp and ::cudaTextureDesc::maxMipmapLevelClamp + * will be relative to this value. For ex., if the firstMipmapLevel is set to 2, and a minMipmapLevelClamp of 1.2 is specified, + * then the actual minimum mipmap level clamp will be 3.2. + * + * - ::cudaResourceViewDesc::lastMipmapLevel specifies the least detailed mipmap level. For non-mipmapped resources, this value + * has to be zero. + * + * - ::cudaResourceViewDesc::firstLayer specifies the first layer index for layered textures. This will be the new layer zero. + * For non-layered resources, this value has to be zero. + * + * - ::cudaResourceViewDesc::lastLayer specifies the last layer index for layered textures. For non-layered resources, + * this value has to be zero. + * + * + * \param pTexObject - Texture object to create + * \param pResDesc - Resource descriptor + * \param pTexDesc - Texture descriptor + * \param pResViewDesc - Resource view descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDestroyTextureObject, + * ::cuTexObjectCreate + */ + +extern __host__ cudaError_t CUDARTAPI cudaCreateTextureObject(cudaTextureObject_t *pTexObject, const struct cudaResourceDesc *pResDesc, const struct cudaTextureDesc *pTexDesc, const struct cudaResourceViewDesc *pResViewDesc); + +/** + * \brief Destroys a texture object + * + * Destroys the texture object specified by \p texObject. + * + * \param texObject - Texture object to destroy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaCreateTextureObject, + * ::cuTexObjectDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaDestroyTextureObject(cudaTextureObject_t texObject); + +/** + * \brief Returns a texture object's resource descriptor + * + * Returns the resource descriptor for the texture object specified by \p texObject. + * + * \param pResDesc - Resource descriptor + * \param texObject - Texture object + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaCreateTextureObject, + * ::cuTexObjectGetResourceDesc + */ +extern __host__ cudaError_t CUDARTAPI cudaGetTextureObjectResourceDesc(struct cudaResourceDesc *pResDesc, cudaTextureObject_t texObject); + +/** + * \brief Returns a texture object's texture descriptor + * + * Returns the texture descriptor for the texture object specified by \p texObject. + * + * \param pTexDesc - Texture descriptor + * \param texObject - Texture object + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaCreateTextureObject, + * ::cuTexObjectGetTextureDesc + */ +extern __host__ cudaError_t CUDARTAPI cudaGetTextureObjectTextureDesc(struct cudaTextureDesc *pTexDesc, cudaTextureObject_t texObject); + +/** + * \brief Returns a texture object's resource view descriptor + * + * Returns the resource view descriptor for the texture object specified by \p texObject. + * If no resource view was specified, ::cudaErrorInvalidValue is returned. + * + * \param pResViewDesc - Resource view descriptor + * \param texObject - Texture object + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaCreateTextureObject, + * ::cuTexObjectGetResourceViewDesc + */ +extern __host__ cudaError_t CUDARTAPI cudaGetTextureObjectResourceViewDesc(struct cudaResourceViewDesc *pResViewDesc, cudaTextureObject_t texObject); + +/** @} */ /* END CUDART_TEXTURE_OBJECT */ + +/** + * \defgroup CUDART_SURFACE_OBJECT Surface Object Management + * + * ___MANBRIEF___ surface object management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the low level texture object management functions + * of the CUDA runtime application programming interface. The surface object + * API is only supported on devices of compute capability 3.0 or higher. + * + * @{ + */ + +/** + * \brief Creates a surface object + * + * Creates a surface object and returns it in \p pSurfObject. \p pResDesc describes + * the data to perform surface load/stores on. ::cudaResourceDesc::resType must be + * ::cudaResourceTypeArray and ::cudaResourceDesc::res::array::array + * must be set to a valid CUDA array handle. + * + * Surface objects are only supported on devices of compute capability 3.0 or higher. + * Additionally, a surface object is an opaque value, and, as such, should only be + * accessed through CUDA API calls. + * + * \param pSurfObject - Surface object to create + * \param pResDesc - Resource descriptor + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidChannelDescriptor, + * ::cudaErrorInvalidResourceHandle + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDestroySurfaceObject, + * ::cuSurfObjectCreate + */ + +extern __host__ cudaError_t CUDARTAPI cudaCreateSurfaceObject(cudaSurfaceObject_t *pSurfObject, const struct cudaResourceDesc *pResDesc); + +/** + * \brief Destroys a surface object + * + * Destroys the surface object specified by \p surfObject. + * + * \param surfObject - Surface object to destroy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaCreateSurfaceObject, + * ::cuSurfObjectDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaDestroySurfaceObject(cudaSurfaceObject_t surfObject); + +/** + * \brief Returns a surface object's resource descriptor + * Returns the resource descriptor for the surface object specified by \p surfObject. + * + * \param pResDesc - Resource descriptor + * \param surfObject - Surface object + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaCreateSurfaceObject, + * ::cuSurfObjectGetResourceDesc + */ +extern __host__ cudaError_t CUDARTAPI cudaGetSurfaceObjectResourceDesc(struct cudaResourceDesc *pResDesc, cudaSurfaceObject_t surfObject); + +/** @} */ /* END CUDART_SURFACE_OBJECT */ + +/** + * \defgroup CUDART__VERSION Version Management + * + * @{ + */ + +/** + * \brief Returns the latest version of CUDA supported by the driver + * + * Returns in \p *driverVersion the latest version of CUDA supported by + * the driver. The version is returned as (1000 × major + 10 × minor). + * For example, CUDA 9.2 would be represented by 9020. If no driver is installed, + * then 0 is returned as the driver version. + * + * This function automatically returns ::cudaErrorInvalidValue + * if \p driverVersion is NULL. + * + * \param driverVersion - Returns the CUDA driver version. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaRuntimeGetVersion, + * ::cuDriverGetVersion + */ +extern __host__ cudaError_t CUDARTAPI cudaDriverGetVersion(int *driverVersion); + +/** + * \brief Returns the CUDA Runtime version + * + * Returns in \p *runtimeVersion the version number of the current CUDA + * Runtime instance. The version is returned as + * (1000 × major + 10 × minor). For example, + * CUDA 9.2 would be represented by 9020. + * + * As of CUDA 12.0, this function no longer initializes CUDA. The purpose + * of this API is solely to return a compile-time constant stating the + * CUDA Toolkit version in the above format. + * + * This function automatically returns ::cudaErrorInvalidValue if + * the \p runtimeVersion argument is NULL. + * + * \param runtimeVersion - Returns the CUDA Runtime version. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDriverGetVersion, + * ::cuDriverGetVersion + */ +extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaRuntimeGetVersion(int *runtimeVersion); + +/** @} */ /* END CUDART__VERSION */ + +/** + * \defgroup CUDART_GRAPH Graph Management + * + * ___MANBRIEF___ graph management functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the graph management functions of CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Creates a graph + * + * Creates an empty graph, which is returned via \p pGraph. + * + * \param pGraph - Returns newly created graph + * \param flags - Graph creation flags, must be 0 + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode, + * ::cudaGraphInstantiate, + * ::cudaGraphDestroy, + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphClone + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphCreate(cudaGraph_t *pGraph, unsigned int flags); + +/** + * \brief Creates a kernel execution node and adds it to a graph + * + * Creates a new kernel execution node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies and arguments specified in \p pNodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * The cudaKernelNodeParams structure is defined as: + * + * \code + * struct cudaKernelNodeParams + * { + * void* func; + * dim3 gridDim; + * dim3 blockDim; + * unsigned int sharedMemBytes; + * void **kernelParams; + * void **extra; + * }; + * \endcode + * + * When the graph is launched, the node will invoke kernel \p func on a (\p gridDim.x x + * \p gridDim.y x \p gridDim.z) grid of blocks. Each block contains + * (\p blockDim.x x \p blockDim.y x \p blockDim.z) threads. + * + * \p sharedMem sets the amount of dynamic shared memory that will be + * available to each thread block. + * + * Kernel parameters to \p func can be specified in one of two ways: + * + * 1) Kernel parameters can be specified via \p kernelParams. If the kernel has N + * parameters, then \p kernelParams needs to be an array of N pointers. Each pointer, + * from \p kernelParams[0] to \p kernelParams[N-1], points to the region of memory from which the actual + * parameter will be copied. The number of kernel parameters and their offsets and sizes do not need + * to be specified as that information is retrieved directly from the kernel's image. + * + * 2) Kernel parameters can also be packaged by the application into a single buffer that is passed in + * via \p extra. This places the burden on the application of knowing each kernel + * parameter's size and alignment/padding within the buffer. The \p extra parameter exists + * to allow this function to take additional less commonly used arguments. \p extra specifies + * a list of names of extra settings and their corresponding values. Each extra setting name is + * immediately followed by the corresponding value. The list must be terminated with either NULL or + * CU_LAUNCH_PARAM_END. + * + * - ::CU_LAUNCH_PARAM_END, which indicates the end of the \p extra + * array; + * - ::CU_LAUNCH_PARAM_BUFFER_POINTER, which specifies that the next + * value in \p extra will be a pointer to a buffer + * containing all the kernel parameters for launching kernel + * \p func; + * - ::CU_LAUNCH_PARAM_BUFFER_SIZE, which specifies that the next + * value in \p extra will be a pointer to a size_t + * containing the size of the buffer specified with + * ::CU_LAUNCH_PARAM_BUFFER_POINTER; + * + * The error ::cudaErrorInvalidValue will be returned if kernel parameters are specified with both + * \p kernelParams and \p extra (i.e. both \p kernelParams and + * \p extra are non-NULL). + * + * The \p kernelParams or \p extra array, as well as the argument values it points to, + * are copied during this call. + * + * \note Kernels launched using graphs must not use texture and surface references. Reading or + * writing through any texture or surface reference is undefined behavior. + * This restriction does not apply to texture and surface objects. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param pNodeParams - Parameters for the GPU execution node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaLaunchKernel, + * ::cudaGraphKernelNodeGetParams, + * ::cudaGraphKernelNodeSetParams, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddKernelNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaKernelNodeParams *pNodeParams); + +/** + * \brief Returns a kernel node's parameters + * + * Returns the parameters of kernel node \p node in \p pNodeParams. + * The \p kernelParams or \p extra array returned in \p pNodeParams, + * as well as the argument values it points to, are owned by the node. + * This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cudaGraphKernelNodeSetParams to update the + * parameters of this node. + * + * The params will contain either \p kernelParams or \p extra, + * according to which of these was most recently set on the node. + * + * \param node - Node to get the parameters for + * \param pNodeParams - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaLaunchKernel, + * ::cudaGraphAddKernelNode, + * ::cudaGraphKernelNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphKernelNodeGetParams(cudaGraphNode_t node, struct cudaKernelNodeParams *pNodeParams); + +/** + * \brief Sets a kernel node's parameters + * + * Sets the parameters of kernel node \p node to \p pNodeParams. + * + * \param node - Node to set the parameters for + * \param pNodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorMemoryAllocation + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaLaunchKernel, + * ::cudaGraphAddKernelNode, + * ::cudaGraphKernelNodeGetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetParams(cudaGraphNode_t node, const struct cudaKernelNodeParams *pNodeParams); + +/** + * \brief Copies attributes from source node to destination node. + * + * Copies attributes from source node \p src to destination node \p dst. + * Both node must have the same context. + * + * \param[out] dst Destination node + * \param[in] src Source node + * For list of attributes see ::cudaKernelNodeAttrID + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidContext + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphKernelNodeCopyAttributes( + cudaGraphNode_t hSrc, + cudaGraphNode_t hDst); + +/** + * \brief Queries node attribute. + * + * Queries attribute \p attr from node \p hNode and stores it in corresponding + * member of \p value_out. + * + * \param[in] hNode + * \param[in] attr + * \param[out] value_out + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphKernelNodeGetAttribute( + cudaGraphNode_t hNode, + cudaKernelNodeAttrID attr, + cudaKernelNodeAttrValue *value_out); + +/** + * \brief Sets node attribute. + * + * Sets attribute \p attr on node \p hNode from corresponding attribute of + * \p value. + * + * \param[out] hNode + * \param[in] attr + * \param[out] value + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle + * \notefnerr + * + * \sa + * ::cudaAccessPolicyWindow + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphKernelNodeSetAttribute( + cudaGraphNode_t hNode, + cudaKernelNodeAttrID attr, + const cudaKernelNodeAttrValue *value); + +/** + * \brief Creates a memcpy node and adds it to a graph + * + * Creates a new memcpy node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will perform the memcpy described by \p pCopyParams. + * See ::cudaMemcpy3D() for a description of the structure and its restrictions. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param pCopyParams - Parameters for the memory copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaMemcpy3D, + * ::cudaGraphAddMemcpyNodeToSymbol, + * ::cudaGraphAddMemcpyNodeFromSymbol, + * ::cudaGraphAddMemcpyNode1D, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemcpyNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaMemcpy3DParms *pCopyParams); + +/** + * \brief Creates a memcpy node to copy to a symbol on the device and adds it to a graph + * + * Creates a new memcpy node to copy to \p symbol and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p src to the memory area pointed to by \p offset bytes from the start + * of symbol \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyToSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeFromSymbol, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemcpyNodeToSymbol( + cudaGraphNode_t *pGraphNode, + cudaGraph_t graph, + const cudaGraphNode_t *pDependencies, + size_t numDependencies, + const void* symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Creates a memcpy node to copy from a symbol on the device and adds it to a graph + * + * Creates a new memcpy node to copy from \p symbol and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p offset bytes from the start of symbol \p symbol to the memory area + * pointed to by \p dst. The memory areas may not overlap. \p symbol is a variable + * that resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyFromSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeToSymbol, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemcpyNodeFromSymbol( + cudaGraphNode_t* pGraphNode, + cudaGraph_t graph, + const cudaGraphNode_t* pDependencies, + size_t numDependencies, + void* dst, + const void* symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Creates a 1D memcpy node and adds it to a graph + * + * Creates a new 1D memcpy node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will copy \p count bytes from the memory + * area pointed to by \p src to the memory area pointed to by \p dst, where + * \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. Launching a + * memcpy node with dst and src pointers that do not match the direction of + * the copy results in an undefined behavior. + * + * Memcpy nodes have some additional restrictions with regards to managed memory, if the + * system contains at least one device which has a zero value for the device attribute + * ::cudaDevAttrConcurrentManagedAccess. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param dst - Destination memory address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpy, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParams1D, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemcpyNode1D( + cudaGraphNode_t *pGraphNode, + cudaGraph_t graph, + const cudaGraphNode_t *pDependencies, + size_t numDependencies, + void* dst, + const void* src, + size_t count, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Returns a memcpy node's parameters + * + * Returns the parameters of memcpy node \p node in \p pNodeParams. + * + * \param node - Node to get the parameters for + * \param pNodeParams - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpy3D, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphMemcpyNodeGetParams(cudaGraphNode_t node, struct cudaMemcpy3DParms *pNodeParams); + +/** + * \brief Sets a memcpy node's parameters + * + * Sets the parameters of memcpy node \p node to \p pNodeParams. + * + * \param node - Node to set the parameters for + * \param pNodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaMemcpy3D, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphMemcpyNodeSetParams1D, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphMemcpyNodeSetParams(cudaGraphNode_t node, const struct cudaMemcpy3DParms *pNodeParams); + +/** + * \brief Sets a memcpy node's parameters to copy to a symbol on the device + * + * Sets the parameters of memcpy node \p node to the copy described by the provided parameters. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p src to the memory area pointed to by \p offset bytes from the start + * of symbol \p symbol. The memory areas may not overlap. \p symbol is a variable that + * resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of + * transfer is inferred from the pointer values. However, ::cudaMemcpyDefault + * is only allowed on systems that support unified virtual addressing. + * + * \param node - Node to set the parameters for + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyToSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphMemcpyNodeSetParamsToSymbol( + cudaGraphNode_t node, + const void* symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Sets a memcpy node's parameters to copy from a symbol on the device + * + * Sets the parameters of memcpy node \p node to the copy described by the provided parameters. + * + * When the graph is launched, the node will copy \p count bytes from the memory area + * pointed to by \p offset bytes from the start of symbol \p symbol to the memory area + * pointed to by \p dst. The memory areas may not overlap. \p symbol is a variable + * that resides in global or constant memory space. \p kind can be either + * ::cudaMemcpyDeviceToHost, ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. + * Passing ::cudaMemcpyDefault is recommended, in which case the type of transfer + * is inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. + * + * \param node - Node to set the parameters for + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpyFromSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphMemcpyNodeSetParamsFromSymbol( + cudaGraphNode_t node, + void* dst, + const void* symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Sets a memcpy node's parameters to perform a 1-dimensional copy + * + * Sets the parameters of memcpy node \p node to the copy described by the provided parameters. + * + * When the graph is launched, the node will copy \p count bytes from the memory + * area pointed to by \p src to the memory area pointed to by \p dst, where + * \p kind specifies the direction of the copy, and must be one of + * ::cudaMemcpyHostToHost, ::cudaMemcpyHostToDevice, ::cudaMemcpyDeviceToHost, + * ::cudaMemcpyDeviceToDevice, or ::cudaMemcpyDefault. Passing + * ::cudaMemcpyDefault is recommended, in which case the type of transfer is + * inferred from the pointer values. However, ::cudaMemcpyDefault is only + * allowed on systems that support unified virtual addressing. Launching a + * memcpy node with dst and src pointers that do not match the direction of + * the copy results in an undefined behavior. + * + * \param node - Node to set the parameters for + * \param dst - Destination memory address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemcpy, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeGetParams + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphMemcpyNodeSetParams1D( + cudaGraphNode_t node, + void* dst, + const void* src, + size_t count, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Creates a memset node and adds it to a graph + * + * Creates a new memset node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * The element size must be 1, 2, or 4 bytes. + * When the graph is launched, the node will perform the memset described by \p pMemsetParams. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param pMemsetParams - Parameters for the memory set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDevice + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaMemset2D, + * ::cudaGraphMemsetNodeGetParams, + * ::cudaGraphMemsetNodeSetParams, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemsetNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaMemsetParams *pMemsetParams); + +/** + * \brief Returns a memset node's parameters + * + * Returns the parameters of memset node \p node in \p pNodeParams. + * + * \param node - Node to get the parameters for + * \param pNodeParams - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaMemset2D, + * ::cudaGraphAddMemsetNode, + * ::cudaGraphMemsetNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphMemsetNodeGetParams(cudaGraphNode_t node, struct cudaMemsetParams *pNodeParams); + +/** + * \brief Sets a memset node's parameters + * + * Sets the parameters of memset node \p node to \p pNodeParams. + * + * \param node - Node to set the parameters for + * \param pNodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaMemset2D, + * ::cudaGraphAddMemsetNode, + * ::cudaGraphMemsetNodeGetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphMemsetNodeSetParams(cudaGraphNode_t node, const struct cudaMemsetParams *pNodeParams); + +/** + * \brief Creates a host execution node and adds it to a graph + * + * Creates a new CPU execution node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies and arguments specified in \p pNodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * When the graph is launched, the node will invoke the specified CPU function. + * Host nodes are not supported under MPS with pre-Volta GPUs. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param pNodeParams - Parameters for the host node + * + * \return + * ::cudaSuccess, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaLaunchHostFunc, + * ::cudaGraphHostNodeGetParams, + * ::cudaGraphHostNodeSetParams, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddHostNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaHostNodeParams *pNodeParams); + +/** + * \brief Returns a host node's parameters + * + * Returns the parameters of host node \p node in \p pNodeParams. + * + * \param node - Node to get the parameters for + * \param pNodeParams - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaLaunchHostFunc, + * ::cudaGraphAddHostNode, + * ::cudaGraphHostNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphHostNodeGetParams(cudaGraphNode_t node, struct cudaHostNodeParams *pNodeParams); + +/** + * \brief Sets a host node's parameters + * + * Sets the parameters of host node \p node to \p nodeParams. + * + * \param node - Node to set the parameters for + * \param pNodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaLaunchHostFunc, + * ::cudaGraphAddHostNode, + * ::cudaGraphHostNodeGetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphHostNodeSetParams(cudaGraphNode_t node, const struct cudaHostNodeParams *pNodeParams); + +/** + * \brief Creates a child graph node and adds it to a graph + * + * Creates a new node which executes an embedded graph, and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * If \p hGraph contains allocation or free nodes, this call will return an error. + * + * The node executes an embedded child graph. The child graph is cloned in this call. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param childGraph - The graph to clone into this node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphChildGraphNodeGetGraph, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode, + * ::cudaGraphClone + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddChildGraphNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, cudaGraph_t childGraph); + +/** + * \brief Gets a handle to the embedded graph of a child graph node + * + * Gets a handle to the embedded graph in a child graph node. This call + * does not clone the graph. Changes to the graph will be reflected in + * the node, and the node retains ownership of the graph. + * + * Allocation and free nodes cannot be added to the returned graph. + * Attempting to do so will return an error. + * + * \param node - Node to get the embedded graph for + * \param pGraph - Location to store a handle to the graph + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphNodeFindInClone + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphChildGraphNodeGetGraph(cudaGraphNode_t node, cudaGraph_t *pGraph); + +/** + * \brief Creates an empty node and adds it to a graph + * + * Creates a new node which performs no operation, and adds it to \p graph with + * \p numDependencies dependencies specified via \p pDependencies. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p pGraphNode. + * + * An empty node performs no operation during execution, but can be used for + * transitive ordering. For example, a phased execution graph with 2 groups of n + * nodes with a barrier between them can be represented using an empty node and + * 2*n dependency edges, rather than no empty node and n^2 dependency edges. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddEmptyNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies); + +/** + * \brief Creates an event record node and adds it to a graph + * + * Creates a new event record node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and event specified in \p event. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * Each launch of the graph will record \p event to capture execution of the + * node's dependencies. + * + * These nodes may not be used in loops or conditionals. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param event - Event for the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphAddEventWaitNode, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphAddEventRecordNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, cudaEvent_t event); +#endif + +/** + * \brief Returns the event associated with an event record node + * + * Returns the event of event record node \p hNode in \p event_out. + * + * \param hNode - Node to get the event for + * \param event_out - Pointer to return the event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphEventRecordNodeSetEvent, + * ::cudaGraphEventWaitNodeGetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphEventRecordNodeGetEvent(cudaGraphNode_t node, cudaEvent_t *event_out); +#endif + +/** + * \brief Sets an event record node's event + * + * Sets the event of event record node \p hNode to \p event. + * + * \param hNode - Node to set the event for + * \param event - Event to use + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphEventRecordNodeGetEvent, + * ::cudaGraphEventWaitNodeSetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphEventRecordNodeSetEvent(cudaGraphNode_t node, cudaEvent_t event); +#endif + +/** + * \brief Creates an event wait node and adds it to a graph + * + * Creates a new event wait node and adds it to \p hGraph with \p numDependencies + * dependencies specified via \p dependencies and event specified in \p event. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. + * A handle to the new node will be returned in \p phGraphNode. + * + * The graph node will wait for all work captured in \p event. See ::cuEventRecord() + * for details on what is captured by an event. The synchronization will be performed + * efficiently on the device when applicable. \p event may be from a different context + * or device than the launch stream. + * + * These nodes may not be used in loops or conditionals. + * + * \param phGraphNode - Returns newly created node + * \param hGraph - Graph to which to add the node + * \param dependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param event - Event for the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphAddEventRecordNode, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphAddEventWaitNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, cudaEvent_t event); +#endif + +/** + * \brief Returns the event associated with an event wait node + * + * Returns the event of event wait node \p hNode in \p event_out. + * + * \param hNode - Node to get the event for + * \param event_out - Pointer to return the event + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphEventWaitNodeSetEvent, + * ::cudaGraphEventRecordNodeGetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphEventWaitNodeGetEvent(cudaGraphNode_t node, cudaEvent_t *event_out); +#endif + +/** + * \brief Sets an event wait node's event + * + * Sets the event of event wait node \p hNode to \p event. + * + * \param hNode - Node to set the event for + * \param event - Event to use + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphEventWaitNodeGetEvent, + * ::cudaGraphEventRecordNodeSetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphEventWaitNodeSetEvent(cudaGraphNode_t node, cudaEvent_t event); +#endif + +/** + * \brief Creates an external semaphore signal node and adds it to a graph + * + * Creates a new external semaphore signal node and adds it to \p graph with \p + * numDependencies dependencies specified via \p dependencies and arguments specified + * in \p nodeParams. It is possible for \p numDependencies to be 0, in which case the + * node will be placed at the root of the graph. \p dependencies may not have any + * duplicate entries. A handle to the new node will be returned in \p pGraphNode. + * + * Performs a signal operation on a set of externally allocated semaphore objects + * when the node is launched. The operation(s) will occur after all of the node's + * dependencies have completed. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphExternalSemaphoresSignalNodeGetParams, + * ::cudaGraphExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaImportExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphAddExternalSemaphoresSignalNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaExternalSemaphoreSignalNodeParams *nodeParams); +#endif + +/** + * \brief Returns an external semaphore signal node's parameters + * + * Returns the parameters of an external semaphore signal node \p hNode in \p params_out. + * The \p extSemArray and \p paramsArray returned in \p params_out, + * are owned by the node. This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cudaGraphExternalSemaphoresSignalNodeSetParams to update the + * parameters of this node. + * + * \param hNode - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaLaunchKernel, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaGraphExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExternalSemaphoresSignalNodeGetParams(cudaGraphNode_t hNode, struct cudaExternalSemaphoreSignalNodeParams *params_out); +#endif + +/** + * \brief Sets an external semaphore signal node's parameters + * + * Sets the parameters of an external semaphore signal node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaGraphExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExternalSemaphoresSignalNodeSetParams(cudaGraphNode_t hNode, const struct cudaExternalSemaphoreSignalNodeParams *nodeParams); +#endif + +/** + * \brief Creates an external semaphore wait node and adds it to a graph + * + * Creates a new external semaphore wait node and adds it to \p graph with \p numDependencies + * dependencies specified via \p dependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p dependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p pGraphNode. + * + * Performs a wait operation on a set of externally allocated semaphore objects + * when the node is launched. The node's dependencies will not be launched until + * the wait operation has completed. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphExternalSemaphoresWaitNodeGetParams, + * ::cudaGraphExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaImportExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphAddExternalSemaphoresWaitNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, const struct cudaExternalSemaphoreWaitNodeParams *nodeParams); +#endif + +/** + * \brief Returns an external semaphore wait node's parameters + * + * Returns the parameters of an external semaphore wait node \p hNode in \p params_out. + * The \p extSemArray and \p paramsArray returned in \p params_out, + * are owned by the node. This memory remains valid until the node is destroyed or its + * parameters are modified, and should not be modified + * directly. Use ::cudaGraphExternalSemaphoresSignalNodeSetParams to update the + * parameters of this node. + * + * \param hNode - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaLaunchKernel, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaGraphExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExternalSemaphoresWaitNodeGetParams(cudaGraphNode_t hNode, struct cudaExternalSemaphoreWaitNodeParams *params_out); +#endif + +/** + * \brief Sets an external semaphore wait node's parameters + * + * Sets the parameters of an external semaphore wait node \p hNode to \p nodeParams. + * + * \param hNode - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaGraphExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExternalSemaphoresWaitNodeSetParams(cudaGraphNode_t hNode, const struct cudaExternalSemaphoreWaitNodeParams *nodeParams); +#endif + +/** + * \brief Creates an allocation node and adds it to a graph + * + * Creates a new allocation node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies and arguments specified in \p nodeParams. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p pGraphNode. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Parameters for the node + * + * When ::cudaGraphAddMemAllocNode creates an allocation node, it returns the address of the allocation in + * \p nodeParams.dptr. The allocation's address remains fixed across instantiations and launches. + * + * If the allocation is freed in the same graph, by creating a free node using ::cudaGraphAddMemFreeNode, + * the allocation can be accessed by nodes ordered after the allocation node but before the free node. + * These allocations cannot be freed outside the owning graph, and they can only be freed once in the + * owning graph. + * + * If the allocation is not freed in the same graph, then it can be accessed not only by nodes in the + * graph which are ordered after the allocation node, but also by stream operations ordered after the + * graph's execution but before the allocation is freed. + * + * Allocations which are not freed in the same graph can be freed by: + * - passing the allocation to ::cudaMemFreeAsync or ::cudaMemFree; + * - launching a graph with a free node for that allocation; or + * - specifying ::cudaGraphInstantiateFlagAutoFreeOnLaunch during instantiation, which makes + * each launch behave as though it called ::cudaMemFreeAsync for every unfreed allocation. + * + * It is not possible to free an allocation in both the owning graph and another graph. If the allocation + * is freed in the same graph, a free node cannot be added to another graph. If the allocation is freed + * in another graph, a free node can no longer be added to the owning graph. + * + * The following restrictions apply to graphs which contain allocation and/or memory free nodes: + * - Nodes and edges of the graph cannot be deleted. + * - The graph cannot be used in a child node. + * - Only one instantiation of the graph may exist at any point in time. + * - The graph cannot be cloned. + * + * \return + * ::cudaSuccess, + * ::cudaErrorCudartUnloading, + * ::cudaErrorInitializationError, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue, + * ::cudaErrorOutOfMemory + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphAddMemFreeNode, + * ::cudaGraphMemAllocNodeGetParams, + * ::cudaDeviceGraphMemTrim, + * ::cudaDeviceGetGraphMemAttribute, + * ::cudaDeviceSetGraphMemAttribute, + * ::cudaMallocAsync, + * ::cudaFreeAsync, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemAllocNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, struct cudaMemAllocNodeParams *nodeParams); +#endif + +/** + * \brief Returns a memory alloc node's parameters + * + * Returns the parameters of a memory alloc node \p hNode in \p params_out. + * The \p poolProps and \p accessDescs returned in \p params_out, are owned by the + * node. This memory remains valid until the node is destroyed. The returned + * parameters must not be modified. + * + * \param node - Node to get the parameters for + * \param params_out - Pointer to return the parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemAllocNode, + * ::cudaGraphMemFreeNodeGetParams + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaGraphMemAllocNodeGetParams(cudaGraphNode_t node, struct cudaMemAllocNodeParams *params_out); +#endif + +/** + * \brief Creates a memory free node and adds it to a graph + * + * Creates a new memory free node and adds it to \p graph with \p numDependencies + * dependencies specified via \p pDependencies and address specified in \p dptr. + * It is possible for \p numDependencies to be 0, in which case the node will be placed + * at the root of the graph. \p pDependencies may not have any duplicate entries. A handle + * to the new node will be returned in \p pGraphNode. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param dptr - Address of memory to free + * + * ::cudaGraphAddMemFreeNode will return ::cudaErrorInvalidValue if the user attempts to free: + * - an allocation twice in the same graph. + * - an address that was not returned by an allocation node. + * - an invalid address. + * + * The following restrictions apply to graphs which contain allocation and/or memory free nodes: + * - Nodes and edges of the graph cannot be deleted. + * - The graph cannot be used in a child node. + * - Only one instantiation of the graph may exist at any point in time. + * - The graph cannot be cloned. + * + * \return + * ::cudaSuccess, + * ::cudaErrorCudartUnloading, + * ::cudaErrorInitializationError, + * ::cudaErrorNotSupported, + * ::cudaErrorInvalidValue, + * ::cudaErrorOutOfMemory + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphAddMemAllocNode, + * ::cudaGraphMemFreeNodeGetParams, + * ::cudaDeviceGraphMemTrim, + * ::cudaDeviceGetGraphMemAttribute, + * ::cudaDeviceSetGraphMemAttribute, + * ::cudaMallocAsync, + * ::cudaFreeAsync, + * ::cudaGraphCreate, + * ::cudaGraphDestroyNode, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaGraphAddMemFreeNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, void *dptr); +#endif + +/** + * \brief Returns a memory free node's parameters + * + * Returns the address of a memory free node \p hNode in \p dptr_out. + * + * \param node - Node to get the parameters for + * \param dptr_out - Pointer to return the device address + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemFreeNode, + * ::cudaGraphMemFreeNodeGetParams + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaGraphMemFreeNodeGetParams(cudaGraphNode_t node, void *dptr_out); +#endif + +/** + * \brief Free unused memory that was cached on the specified device for use with graphs back to the OS. + * + * Blocks which are not in use by a graph that is either currently executing or scheduled to execute are + * freed back to the operating system. + * + * \param device - The device for which cached memory should be freed. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemAllocNode, + * ::cudaGraphAddMemFreeNode, + * ::cudaDeviceGetGraphMemAttribute, + * ::cudaDeviceSetGraphMemAttribute, + * ::cudaMallocAsync, + * ::cudaFreeAsync + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaDeviceGraphMemTrim(int device); +#endif + +/** + * \brief Query asynchronous allocation attributes related to graphs + * + * Valid attributes are: + * + * - ::cudaGraphMemAttrUsedMemCurrent: Amount of memory, in bytes, currently associated with graphs + * - ::cudaGraphMemAttrUsedMemHigh: High watermark of memory, in bytes, associated with graphs since the + * last time it was reset. High watermark can only be reset to zero. + * - ::cudaGraphMemAttrReservedMemCurrent: Amount of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * - ::cudaGraphMemAttrReservedMemHigh: High watermark of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * + * \param device - Specifies the scope of the query + * \param attr - attribute to get + * \param value - retrieved value + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceSetGraphMemAttribute, + * ::cudaGraphAddMemAllocNode, + * ::cudaGraphAddMemFreeNode, + * ::cudaDeviceGraphMemTrim, + * ::cudaMallocAsync, + * ::cudaFreeAsync + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaDeviceGetGraphMemAttribute(int device, enum cudaGraphMemAttributeType attr, void* value); +#endif + +/** + * \brief Set asynchronous allocation attributes related to graphs + * + * Valid attributes are: + * + * - ::cudaGraphMemAttrUsedMemHigh: High watermark of memory, in bytes, associated with graphs since the + * last time it was reset. High watermark can only be reset to zero. + * - ::cudaGraphMemAttrReservedMemHigh: High watermark of memory, in bytes, currently allocated for use by + * the CUDA graphs asynchronous allocator. + * + * \param device - Specifies the scope of the query + * \param attr - attribute to get + * \param value - pointer to value to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaDeviceGetGraphMemAttribute, + * ::cudaGraphAddMemAllocNode, + * ::cudaGraphAddMemFreeNode, + * ::cudaDeviceGraphMemTrim, + * ::cudaMallocAsync, + * ::cudaFreeAsync + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaDeviceSetGraphMemAttribute(int device, enum cudaGraphMemAttributeType attr, void* value); +#endif + +/** + * \brief Clones a graph + * + * This function creates a copy of \p originalGraph and returns it in \p pGraphClone. + * All parameters are copied into the cloned graph. The original graph may be modified + * after this call without affecting the clone. + * + * Child graph nodes in the original graph are recursively copied into the clone. + * + * \param pGraphClone - Returns newly created cloned graph + * \param originalGraph - Graph to clone + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorMemoryAllocation + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphNodeFindInClone + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphClone(cudaGraph_t *pGraphClone, cudaGraph_t originalGraph); + +/** + * \brief Finds a cloned version of a node + * + * This function returns the node in \p clonedGraph corresponding to \p originalNode + * in the original graph. + * + * \p clonedGraph must have been cloned from \p originalGraph via ::cudaGraphClone. + * \p originalNode must have been in \p originalGraph at the time of the call to + * ::cudaGraphClone, and the corresponding cloned node in \p clonedGraph must not have + * been removed. The cloned node is then returned via \p pClonedNode. + * + * \param pNode - Returns handle to the cloned node + * \param originalNode - Handle to the original node + * \param clonedGraph - Cloned graph to query + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphClone + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeFindInClone(cudaGraphNode_t *pNode, cudaGraphNode_t originalNode, cudaGraph_t clonedGraph); + +/** + * \brief Returns a node's type + * + * Returns the node type of \p node in \p pType. + * + * \param node - Node to query + * \param pType - Pointer to return the node type + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphChildGraphNodeGetGraph, + * ::cudaGraphKernelNodeGetParams, + * ::cudaGraphKernelNodeSetParams, + * ::cudaGraphHostNodeGetParams, + * ::cudaGraphHostNodeSetParams, + * ::cudaGraphMemcpyNodeGetParams, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemsetNodeGetParams, + * ::cudaGraphMemsetNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetType(cudaGraphNode_t node, enum cudaGraphNodeType *pType); + +/** + * \brief Returns a graph's nodes + * + * Returns a list of \p graph's nodes. \p nodes may be NULL, in which case this + * function will return the number of nodes in \p numNodes. Otherwise, + * \p numNodes entries will be filled in. If \p numNodes is higher than the actual + * number of nodes, the remaining entries in \p nodes will be set to NULL, and the + * number of nodes actually obtained will be returned in \p numNodes. + * + * \param graph - Graph to query + * \param nodes - Pointer to return the nodes + * \param numNodes - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetType, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphGetNodes(cudaGraph_t graph, cudaGraphNode_t *nodes, size_t *numNodes); + +/** + * \brief Returns a graph's root nodes + * + * Returns a list of \p graph's root nodes. \p pRootNodes may be NULL, in which case this + * function will return the number of root nodes in \p pNumRootNodes. Otherwise, + * \p pNumRootNodes entries will be filled in. If \p pNumRootNodes is higher than the actual + * number of root nodes, the remaining entries in \p pRootNodes will be set to NULL, and the + * number of nodes actually obtained will be returned in \p pNumRootNodes. + * + * \param graph - Graph to query + * \param pRootNodes - Pointer to return the root nodes + * \param pNumRootNodes - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphGetNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetType, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphGetRootNodes(cudaGraph_t graph, cudaGraphNode_t *pRootNodes, size_t *pNumRootNodes); + +/** + * \brief Returns a graph's dependency edges + * + * Returns a list of \p graph's dependency edges. Edges are returned via corresponding + * indices in \p from and \p to; that is, the node in \p to[i] has a dependency on the + * node in \p from[i]. \p from and \p to may both be NULL, in which + * case this function only returns the number of edges in \p numEdges. Otherwise, + * \p numEdges entries will be filled in. If \p numEdges is higher than the actual + * number of edges, the remaining entries in \p from and \p to will be set to NULL, and + * the number of edges actually returned will be written to \p numEdges. + * + * \param graph - Graph to get the edges from + * \param from - Location to return edge endpoints + * \param to - Location to return edge endpoints + * \param numEdges - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphGetEdges(cudaGraph_t graph, cudaGraphNode_t *from, cudaGraphNode_t *to, size_t *numEdges); + +/** + * \brief Returns a graph's dependency edges (12.3+) + * + * Returns a list of \p graph's dependency edges. Edges are returned via corresponding + * indices in \p from, \p to and \p edgeData; that is, the node in \p to[i] has a + * dependency on the node in \p from[i] with data \p edgeData[i]. \p from and \p to may + * both be NULL, in which case this function only returns the number of edges in + * \p numEdges. Otherwise, \p numEdges entries will be filled in. If \p numEdges is higher + * than the actual number of edges, the remaining entries in \p from and \p to will be + * set to NULL, and the number of edges actually returned will be written to \p numEdges. + * \p edgeData may alone be NULL, in which case the edges must all have default (zeroed) + * edge data. Attempting a losst query via NULL \p edgeData will result in + * ::cudaErrorLossyQuery. If \p edgeData is non-NULL then \p from and \p to must be as + * well. + * + * \param graph - Graph to get the edges from + * \param from - Location to return edge endpoints + * \param to - Location to return edge endpoints + * \param edgeData - Optional location to return edge data + * \param numEdges - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorLossyQuery, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphGetEdges_v2(cudaGraph_t graph, cudaGraphNode_t *from, cudaGraphNode_t *to, cudaGraphEdgeData *edgeData, size_t *numEdges); + +/** + * \brief Returns a node's dependencies + * + * Returns a list of \p node's dependencies. \p pDependencies may be NULL, in which case this + * function will return the number of dependencies in \p pNumDependencies. Otherwise, + * \p pNumDependencies entries will be filled in. If \p pNumDependencies is higher than the actual + * number of dependencies, the remaining entries in \p pDependencies will be set to NULL, and the + * number of nodes actually obtained will be returned in \p pNumDependencies. + * + * \param node - Node to query + * \param pDependencies - Pointer to return the dependencies + * \param pNumDependencies - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeGetDependentNodes, + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetDependencies(cudaGraphNode_t node, cudaGraphNode_t *pDependencies, size_t *pNumDependencies); + +/** + * \brief Returns a node's dependencies (12.3+) + * + * Returns a list of \p node's dependencies. \p pDependencies may be NULL, in which case this + * function will return the number of dependencies in \p pNumDependencies. Otherwise, + * \p pNumDependencies entries will be filled in. If \p pNumDependencies is higher than the actual + * number of dependencies, the remaining entries in \p pDependencies will be set to NULL, and the + * number of nodes actually obtained will be returned in \p pNumDependencies. + * + * Note that if an edge has non-zero (non-default) edge data and \p edgeData is NULL, + * this API will return ::cudaErrorLossyQuery. If \p edgeData is non-NULL, then + * \p pDependencies must be as well. + * + * \param node - Node to query + * \param pDependencies - Pointer to return the dependencies + * \param edgeData - Optional array to return edge data for each dependency + * \param pNumDependencies - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorLossyQuery, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeGetDependentNodes, + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetDependencies_v2(cudaGraphNode_t node, cudaGraphNode_t *pDependencies, cudaGraphEdgeData *edgeData, size_t *pNumDependencies); + +/** + * \brief Returns a node's dependent nodes + * + * Returns a list of \p node's dependent nodes. \p pDependentNodes may be NULL, in which + * case this function will return the number of dependent nodes in \p pNumDependentNodes. + * Otherwise, \p pNumDependentNodes entries will be filled in. If \p pNumDependentNodes is + * higher than the actual number of dependent nodes, the remaining entries in + * \p pDependentNodes will be set to NULL, and the number of nodes actually obtained will + * be returned in \p pNumDependentNodes. + * + * \param node - Node to query + * \param pDependentNodes - Pointer to return the dependent nodes + * \param pNumDependentNodes - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetDependentNodes(cudaGraphNode_t node, cudaGraphNode_t *pDependentNodes, size_t *pNumDependentNodes); + +/** + * \brief Returns a node's dependent nodes (12.3+) + * + * Returns a list of \p node's dependent nodes. \p pDependentNodes may be NULL, in which + * case this function will return the number of dependent nodes in \p pNumDependentNodes. + * Otherwise, \p pNumDependentNodes entries will be filled in. If \p pNumDependentNodes is + * higher than the actual number of dependent nodes, the remaining entries in + * \p pDependentNodes will be set to NULL, and the number of nodes actually obtained will + * be returned in \p pNumDependentNodes. + * + * Note that if an edge has non-zero (non-default) edge data and \p edgeData is NULL, + * this API will return ::cudaErrorLossyQuery. If \p edgeData is non-NULL, then + * \p pDependentNodes must be as well. + * + * \param node - Node to query + * \param pDependentNodes - Pointer to return the dependent nodes + * \param edgeData - Optional pointer to return edge data for dependent nodes + * \param pNumDependentNodes - See description + * + * \return + * ::cudaSuccess, + * ::cudaErrorLossyQuery, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphGetNodes, + * ::cudaGraphGetRootNodes, + * ::cudaGraphGetEdges, + * ::cudaGraphAddDependencies, + * ::cudaGraphRemoveDependencies + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetDependentNodes_v2(cudaGraphNode_t node, cudaGraphNode_t *pDependentNodes, cudaGraphEdgeData *edgeData, size_t *pNumDependentNodes); + +/** + * \brief Adds dependency edges to a graph. + * + * The number of dependencies to be added is defined by \p numDependencies + * Elements in \p pFrom and \p pTo at corresponding indices define a dependency. + * Each node in \p pFrom and \p pTo must belong to \p graph. + * + * If \p numDependencies is 0, elements in \p pFrom and \p pTo will be ignored. + * Specifying an existing dependency will return an error. + * + * \param graph - Graph to which dependencies are added + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param numDependencies - Number of dependencies to be added + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphRemoveDependencies, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddDependencies(cudaGraph_t graph, const cudaGraphNode_t *from, const cudaGraphNode_t *to, size_t numDependencies); + +/** + * \brief Adds dependency edges to a graph. (12.3+) + * + * The number of dependencies to be added is defined by \p numDependencies + * Elements in \p pFrom and \p pTo at corresponding indices define a dependency. + * Each node in \p pFrom and \p pTo must belong to \p graph. + * + * If \p numDependencies is 0, elements in \p pFrom and \p pTo will be ignored. + * Specifying an existing dependency will return an error. + * + * \param graph - Graph to which dependencies are added + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param edgeData - Optional array of edge data. If NULL, default (zeroed) edge data is assumed. + * \param numDependencies - Number of dependencies to be added + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphRemoveDependencies, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddDependencies_v2(cudaGraph_t graph, const cudaGraphNode_t *from, const cudaGraphNode_t *to, const cudaGraphEdgeData *edgeData, size_t numDependencies); + +/** + * \brief Removes dependency edges from a graph. + * + * The number of \p pDependencies to be removed is defined by \p numDependencies. + * Elements in \p pFrom and \p pTo at corresponding indices define a dependency. + * Each node in \p pFrom and \p pTo must belong to \p graph. + * + * If \p numDependencies is 0, elements in \p pFrom and \p pTo will be ignored. + * Specifying a non-existing dependency will return an error. + * + * \param graph - Graph from which to remove dependencies + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param numDependencies - Number of dependencies to be removed + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddDependencies, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphRemoveDependencies(cudaGraph_t graph, const cudaGraphNode_t *from, const cudaGraphNode_t *to, size_t numDependencies); + +/** + * \brief Removes dependency edges from a graph. (12.3+) + * + * The number of \p pDependencies to be removed is defined by \p numDependencies. + * Elements in \p pFrom and \p pTo at corresponding indices define a dependency. + * Each node in \p pFrom and \p pTo must belong to \p graph. + * + * If \p numDependencies is 0, elements in \p pFrom and \p pTo will be ignored. + * Specifying an edge that does not exist in the graph, with data matching + * \p edgeData, results in an error. \p edgeData is nullable, which is equivalent + * to passing default (zeroed) data for each edge. + * + * \param graph - Graph from which to remove dependencies + * \param from - Array of nodes that provide the dependencies + * \param to - Array of dependent nodes + * \param edgeData - Optional array of edge data. If NULL, edge data is assumed to + * be default (zeroed). + * \param numDependencies - Number of dependencies to be removed + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddDependencies, + * ::cudaGraphGetEdges, + * ::cudaGraphNodeGetDependencies, + * ::cudaGraphNodeGetDependentNodes + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphRemoveDependencies_v2(cudaGraph_t graph, const cudaGraphNode_t *from, const cudaGraphNode_t *to, const cudaGraphEdgeData *edgeData, size_t numDependencies); + +/** + * \brief Remove a node from the graph + * + * Removes \p node from its graph. This operation also severs any dependencies of other nodes + * on \p node and vice versa. + * + * Dependencies cannot be removed from graphs which contain allocation or free nodes. + * Any attempt to do so will return an error. + * + * \param node - Node to remove + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphAddEmptyNode, + * ::cudaGraphAddKernelNode, + * ::cudaGraphAddHostNode, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemsetNode + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphDestroyNode(cudaGraphNode_t node); + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p graph as an executable graph. The graph is validated for any + * structural constraints or intra-node constraints which were not previously + * validated. If instantiation is successful, a handle to the instantiated graph + * is returned in \p pGraphExec. + * + * The \p flags parameter controls the behavior of instantiation and subsequent + * graph launches. Valid flags are: + * + * - ::cudaGraphInstantiateFlagAutoFreeOnLaunch, which configures a + * graph containing memory allocation nodes to automatically free any + * unfreed memory allocations before the graph is relaunched. + * + * - ::cudaGraphInstantiateFlagDeviceLaunch, which configures the graph for launch + * from the device. If this flag is passed, the executable graph handle returned can be + * used to launch the graph from both the host and device. This flag cannot be used in + * conjunction with ::cudaGraphInstantiateFlagAutoFreeOnLaunch. + * + * - ::cudaGraphInstantiateFlagUseNodePriority, which causes the graph + * to use the priorities from the per-node attributes rather than the priority + * of the launch stream during execution. Note that priorities are only available + * on kernel nodes, and are copied from stream priority during stream capture. + * + * If \p graph contains any allocation or free nodes, there can be at most one + * executable graph in existence for that graph at a time. An attempt to + * instantiate a second executable graph before destroying the first with + * ::cudaGraphExecDestroy will result in an error. + * The same also applies if \p graph contains any device-updatable kernel nodes. + * + * Graphs instantiated for launch on the device have additional restrictions which do not + * apply to host graphs: + * + * - The graph's nodes must reside on a single device. + * - The graph can only contain kernel nodes, memcpy nodes, memset nodes, and child graph nodes. + * - The graph cannot be empty and must contain at least one kernel, memcpy, or memset node. + * Operation-specific restrictions are outlined below. + * - Kernel nodes: + * - Use of CUDA Dynamic Parallelism is not permitted. + * - Cooperative launches are permitted as long as MPS is not in use. + * - Memcpy nodes: + * - Only copies involving device memory and/or pinned device-mapped host memory are permitted. + * - Copies involving CUDA arrays are not permitted. + * - Both operands must be accessible from the current device, and the current device must + * match the device of other nodes in the graph. + * + * If \p graph is not instantiated for launch on the device but contains kernels which + * call device-side cudaGraphLaunch() from multiple devices, this will result in an error. + * + * \param pGraphExec - Returns instantiated graph + * \param graph - Graph to instantiate + * \param flags - Flags to control instantiation. See ::CUgraphInstantiate_flags. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiateWithFlags, + * ::cudaGraphCreate, + * ::cudaGraphUpload, + * ::cudaGraphLaunch, + * ::cudaGraphExecDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphInstantiate(cudaGraphExec_t *pGraphExec, cudaGraph_t graph, unsigned long long flags __dv(0)); + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p graph as an executable graph. The graph is validated for any + * structural constraints or intra-node constraints which were not previously + * validated. If instantiation is successful, a handle to the instantiated graph + * is returned in \p pGraphExec. + * + * The \p flags parameter controls the behavior of instantiation and subsequent + * graph launches. Valid flags are: + * + * - ::cudaGraphInstantiateFlagAutoFreeOnLaunch, which configures a + * graph containing memory allocation nodes to automatically free any + * unfreed memory allocations before the graph is relaunched. + * + * - ::cudaGraphInstantiateFlagDeviceLaunch, which configures the graph for launch + * from the device. If this flag is passed, the executable graph handle returned can be + * used to launch the graph from both the host and device. This flag can only be used + * on platforms which support unified addressing. This flag cannot be used in + * conjunction with ::cudaGraphInstantiateFlagAutoFreeOnLaunch. + * + * - ::cudaGraphInstantiateFlagUseNodePriority, which causes the graph + * to use the priorities from the per-node attributes rather than the priority + * of the launch stream during execution. Note that priorities are only available + * on kernel nodes, and are copied from stream priority during stream capture. + * + * If \p graph contains any allocation or free nodes, there can be at most one + * executable graph in existence for that graph at a time. An attempt to + * instantiate a second executable graph before destroying the first with + * ::cudaGraphExecDestroy will result in an error. + * The same also applies if \p graph contains any device-updatable kernel nodes. + * + * If \p graph contains kernels which call device-side cudaGraphLaunch() from multiple + * devices, this will result in an error. + * + * Graphs instantiated for launch on the device have additional restrictions which do not + * apply to host graphs: + * + * - The graph's nodes must reside on a single device. + * - The graph can only contain kernel nodes, memcpy nodes, memset nodes, and child graph nodes. + * - The graph cannot be empty and must contain at least one kernel, memcpy, or memset node. + * Operation-specific restrictions are outlined below. + * - Kernel nodes: + * - Use of CUDA Dynamic Parallelism is not permitted. + * - Cooperative launches are permitted as long as MPS is not in use. + * - Memcpy nodes: + * - Only copies involving device memory and/or pinned device-mapped host memory are permitted. + * - Copies involving CUDA arrays are not permitted. + * - Both operands must be accessible from the current device, and the current device must + * match the device of other nodes in the graph. + * + * \param pGraphExec - Returns instantiated graph + * \param graph - Graph to instantiate + * \param flags - Flags to control instantiation. See ::CUgraphInstantiate_flags. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiate, + * ::cudaGraphCreate, + * ::cudaGraphUpload, + * ::cudaGraphLaunch, + * ::cudaGraphExecDestroy + */ +#if __CUDART_API_VERSION >= 11040 +extern __host__ cudaError_t CUDARTAPI cudaGraphInstantiateWithFlags(cudaGraphExec_t *pGraphExec, cudaGraph_t graph, unsigned long long flags __dv(0)); +#endif + +/** + * \brief Creates an executable graph from a graph + * + * Instantiates \p graph as an executable graph according to the \p instantiateParams structure. + * The graph is validated for any structural constraints or intra-node constraints + * which were not previously validated. If instantiation is successful, a handle to + * the instantiated graph is returned in \p pGraphExec. + * + * \p instantiateParams controls the behavior of instantiation and subsequent + * graph launches, as well as returning more detailed information in the event of an error. + * ::cudaGraphInstantiateParams is defined as: + * + * \code + typedef struct { + unsigned long long flags; + cudaStream_t uploadStream; + cudaGraphNode_t errNode_out; + cudaGraphInstantiateResult result_out; + } cudaGraphInstantiateParams; + * \endcode + * + * The \p flags field controls the behavior of instantiation and subsequent + * graph launches. Valid flags are: + * + * - ::cudaGraphInstantiateFlagAutoFreeOnLaunch, which configures a + * graph containing memory allocation nodes to automatically free any + * unfreed memory allocations before the graph is relaunched. + * + * - ::cudaGraphInstantiateFlagUpload, which will perform an upload of the graph + * into \p uploadStream once the graph has been instantiated. + * + * - ::cudaGraphInstantiateFlagDeviceLaunch, which configures the graph for launch + * from the device. If this flag is passed, the executable graph handle returned can be + * used to launch the graph from both the host and device. This flag can only be used + * on platforms which support unified addressing. This flag cannot be used in + * conjunction with ::cudaGraphInstantiateFlagAutoFreeOnLaunch. + * + * - ::cudaGraphInstantiateFlagUseNodePriority, which causes the graph + * to use the priorities from the per-node attributes rather than the priority + * of the launch stream during execution. Note that priorities are only available + * on kernel nodes, and are copied from stream priority during stream capture. + * + * If \p graph contains any allocation or free nodes, there can be at most one + * executable graph in existence for that graph at a time. An attempt to instantiate a + * second executable graph before destroying the first with ::cudaGraphExecDestroy will + * result in an error. + * The same also applies if \p graph contains any device-updatable kernel nodes. + * + * If \p graph contains kernels which call device-side cudaGraphLaunch() from multiple + * devices, this will result in an error. + * + * Graphs instantiated for launch on the device have additional restrictions which do not + * apply to host graphs: + * + * - The graph's nodes must reside on a single device. + * - The graph can only contain kernel nodes, memcpy nodes, memset nodes, and child graph nodes. + * - The graph cannot be empty and must contain at least one kernel, memcpy, or memset node. + * Operation-specific restrictions are outlined below. + * - Kernel nodes: + * - Use of CUDA Dynamic Parallelism is not permitted. + * - Cooperative launches are permitted as long as MPS is not in use. + * - Memcpy nodes: + * - Only copies involving device memory and/or pinned device-mapped host memory are permitted. + * - Copies involving CUDA arrays are not permitted. + * - Both operands must be accessible from the current device, and the current device must + * match the device of other nodes in the graph. + * + * In the event of an error, the \p result_out and \p errNode_out fields will contain more + * information about the nature of the error. Possible error reporting includes: + * + * - ::cudaGraphInstantiateError, if passed an invalid value or if an unexpected error occurred + * which is described by the return value of the function. \p errNode_out will be set to NULL. + * - ::cudaGraphInstantiateInvalidStructure, if the graph structure is invalid. \p errNode_out + * will be set to one of the offending nodes. + * - ::cudaGraphInstantiateNodeOperationNotSupported, if the graph is instantiated for device + * launch but contains a node of an unsupported node type, or a node which performs unsupported + * operations, such as use of CUDA dynamic parallelism within a kernel node. \p errNode_out will + * be set to this node. + * - ::cudaGraphInstantiateMultipleDevicesNotSupported, if the graph is instantiated for device + * launch but a node’s device differs from that of another node. This error can also be returned + * if a graph is not instantiated for device launch and it contains kernels which call device-side + * cudaGraphLaunch() from multiple devices. \p errNode_out will be set to this node. + * + * If instantiation is successful, \p result_out will be set to ::cudaGraphInstantiateSuccess, + * and \p hErrNode_out will be set to NULL. + * + * \param pGraphExec - Returns instantiated graph + * \param graph - Graph to instantiate + * \param instantiateParams - Instantiation parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphInstantiate, + * ::cudaGraphInstantiateWithFlags, + * ::cudaGraphExecDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphInstantiateWithParams(cudaGraphExec_t *pGraphExec, cudaGraph_t graph, cudaGraphInstantiateParams *instantiateParams); + +/** + * \brief Query the instantiation flags of an executable graph + * + * Returns the flags that were passed to instantiation for the given executable graph. + * ::cudaGraphInstantiateFlagUpload will not be returned by this API as it does + * not affect the resulting executable graph. + * + * \param graphExec - The executable graph to query + * \param flags - Returns the instantiation flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiate, + * ::cudaGraphInstantiateWithFlags, + * ::cudaGraphInstantiateWithParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecGetFlags(cudaGraphExec_t graphExec, unsigned long long *flags); + +/** + * \brief Sets the parameters for a kernel node in the given graphExec + * + * Sets the parameters of a kernel node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p node in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p node must not have been removed from the original graph. All \p nodeParams + * fields may change, but the following restrictions apply to \p func updates: + * + * - The owning device of the function cannot change. + * - A node whose function originally did not use CUDA dynamic parallelism cannot be updated + * to a function which uses CDP + * - A node whose function originally did not make device-side update calls cannot be updated + * to a function which makes device-side update calls. + * - If \p hGraphExec was not instantiated for device launch, a node whose function originally + * did not use device-side cudaGraphLaunch() cannot be updated to a function which uses + * device-side cudaGraphLaunch() unless the node resides on the same device as nodes which + * contained such calls at instantiate-time. If no such calls were present at instantiation, + * these updates cannot be performed at all. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p node is also not modified by this call. + * + * If \p node is a device-updatable kernel node, the next upload/launch of \p hGraphExec + * will overwrite any previous device-side updates. Additionally, applying host updates to a + * device-updatable kernel node while it is being updated from the device will result in + * undefined behavior. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - kernel node from the graph from which graphExec was instantiated + * \param pNodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddKernelNode, + * ::cudaGraphKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecKernelNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t node, const struct cudaKernelNodeParams *pNodeParams); + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec. + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained \p pNodeParams at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * The source and destination memory in \p pNodeParams must be allocated from the same + * contexts as the original source and destination memory. Both the instantiation-time + * memory operands and the memory operands in \p pNodeParams must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * either the original or new memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param pNodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParamsToSymbol, + * ::cudaGraphExecMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphExecMemcpyNodeSetParams1D, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecMemcpyNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t node, const struct cudaMemcpy3DParms *pNodeParams); + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec to copy to a symbol on the device + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained the given params at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * \p src and \p symbol must be allocated from the same contexts as the original source and + * destination memory. The instantiation-time memory operands must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * the original memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param symbol - Device symbol address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeToSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsToSymbol, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecMemcpyNodeSetParamsToSymbol( + cudaGraphExec_t hGraphExec, + cudaGraphNode_t node, + const void* symbol, + const void* src, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec to copy from a symbol on the device + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained the given params at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * \p symbol and \p dst must be allocated from the same contexts as the original source and + * destination memory. The instantiation-time memory operands must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * the original memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param dst - Destination memory address + * \param symbol - Device symbol address + * \param count - Size in bytes to copy + * \param offset - Offset from start of symbol in bytes + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNodeFromSymbol, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParamsFromSymbol, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParamsToSymbol, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecMemcpyNodeSetParamsFromSymbol( + cudaGraphExec_t hGraphExec, + cudaGraphNode_t node, + void* dst, + const void* symbol, + size_t count, + size_t offset, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Sets the parameters for a memcpy node in the given graphExec to perform a 1-dimensional copy + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained the given params at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * \p src and \p dst must be allocated from the same contexts as the original source + * and destination memory. The instantiation-time memory operands must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns ::cudaErrorInvalidValue if the memory operands' mappings changed or + * the original memory operands are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memcpy node from the graph which was used to instantiate graphExec + * \param dst - Destination memory address + * \param src - Source memory address + * \param count - Size in bytes to copy + * \param kind - Type of transfer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddMemcpyNode, + * ::cudaGraphAddMemcpyNode1D, + * ::cudaGraphMemcpyNodeSetParams, + * ::cudaGraphMemcpyNodeSetParams1D, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecMemcpyNodeSetParams1D( + cudaGraphExec_t hGraphExec, + cudaGraphNode_t node, + void* dst, + const void* src, + size_t count, + enum cudaMemcpyKind kind); +#endif + +/** + * \brief Sets the parameters for a memset node in the given graphExec. + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained \p pNodeParams at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * The destination memory in \p pNodeParams must be allocated from the same + * context as the original destination memory. Both the instantiation-time + * memory operand and the memory operand in \p pNodeParams must be 1-dimensional. + * Zero-length operations are not supported. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * Returns cudaErrorInvalidValue if the memory operand's mappings changed or + * either the original or new memory operand are multidimensional. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Memset node from the graph which was used to instantiate graphExec + * \param pNodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddMemsetNode, + * ::cudaGraphMemsetNodeSetParams, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecMemsetNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t node, const struct cudaMemsetParams *pNodeParams); + +/** + * \brief Sets the parameters for a host node in the given graphExec. + * + * Updates the work represented by \p node in \p hGraphExec as though \p node had + * contained \p pNodeParams at instantiation. \p node must remain in the graph which was + * used to instantiate \p hGraphExec. Changed edges to and from \p node are ignored. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Host node from the graph which was used to instantiate graphExec + * \param pNodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddHostNode, + * ::cudaGraphHostNodeSetParams, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecHostNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t node, const struct cudaHostNodeParams *pNodeParams); + +/** + * \brief Updates node parameters in the child graph node in the given graphExec. + * + * Updates the work represented by \p node in \p hGraphExec as though the nodes contained + * in \p node's graph had the parameters contained in \p childGraph's nodes at instantiation. + * \p node must remain in the graph which was used to instantiate \p hGraphExec. + * Changed edges to and from \p node are ignored. + * + * The modifications only affect future launches of \p hGraphExec. Already enqueued + * or running launches of \p hGraphExec are not affected by this call. \p node is also + * not modified by this call. + * + * The topology of \p childGraph, as well as the node insertion order, must match that + * of the graph contained in \p node. See ::cudaGraphExecUpdate() for a list of restrictions + * on what can be updated in an instantiated graph. The update is recursive, so child graph + * nodes contained within the top level child graph will also be updated. + + * \param hGraphExec - The executable graph in which to set the specified node + * \param node - Host node from the graph which was used to instantiate graphExec + * \param childGraph - The graph supplying the updated parameters + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddChildGraphNode, + * ::cudaGraphChildGraphNodeGetGraph, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecChildGraphNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t node, cudaGraph_t childGraph); +#endif + +/** + * \brief Sets the event for an event record node in the given graphExec + * + * Sets the event of an event record node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Event record node from the graph from which graphExec was instantiated + * \param event - Updated event to use + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddEventRecordNode, + * ::cudaGraphEventRecordNodeGetEvent, + * ::cudaGraphEventWaitNodeSetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecEventRecordNodeSetEvent(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, cudaEvent_t event); +#endif + +/** + * \brief Sets the event for an event wait node in the given graphExec + * + * Sets the event of an event wait node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Event wait node from the graph from which graphExec was instantiated + * \param event - Updated event to use + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddEventWaitNode, + * ::cudaGraphEventWaitNodeGetEvent, + * ::cudaGraphEventRecordNodeSetEvent, + * ::cudaEventRecordWithFlags, + * ::cudaStreamWaitEvent, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphExecEventWaitNodeSetEvent(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, cudaEvent_t event); +#endif + +/** + * \brief Sets the parameters for an external semaphore signal node in the given graphExec + * + * Sets the parameters of an external semaphore signal node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * Changing \p nodeParams->numExtSems is not supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - semaphore signal node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddExternalSemaphoresSignalNode, + * ::cudaImportExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresWaitNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExecExternalSemaphoresSignalNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, const struct cudaExternalSemaphoreSignalNodeParams *nodeParams); +#endif + +/** + * \brief Sets the parameters for an external semaphore wait node in the given graphExec + * + * Sets the parameters of an external semaphore wait node in an executable graph \p hGraphExec. + * The node is identified by the corresponding node \p hNode in the + * non-executable graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * Changing \p nodeParams->numExtSems is not supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - semaphore wait node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphExecNodeSetParams, + * ::cudaGraphAddExternalSemaphoresWaitNode, + * ::cudaImportExternalSemaphore, + * ::cudaSignalExternalSemaphoresAsync, + * ::cudaWaitExternalSemaphoresAsync, + * ::cudaGraphExecKernelNodeSetParams, + * ::cudaGraphExecMemcpyNodeSetParams, + * ::cudaGraphExecMemsetNodeSetParams, + * ::cudaGraphExecHostNodeSetParams, + * ::cudaGraphExecChildGraphNodeSetParams, + * ::cudaGraphExecEventRecordNodeSetEvent, + * ::cudaGraphExecEventWaitNodeSetEvent, + * ::cudaGraphExecExternalSemaphoresSignalNodeSetParams, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +#if __CUDART_API_VERSION >= 11020 +extern __host__ cudaError_t CUDARTAPI cudaGraphExecExternalSemaphoresWaitNodeSetParams(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, const struct cudaExternalSemaphoreWaitNodeParams *nodeParams); +#endif + +/** + * \brief Enables or disables the specified node in the given graphExec + * + * Sets \p hNode to be either enabled or disabled. Disabled nodes are functionally equivalent + * to empty nodes until they are reenabled. Existing node parameters are not affected by + * disabling/enabling the node. + * + * The node is identified by the corresponding node \p hNode in the non-executable + * graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * The modifications only affect future launches of \p hGraphExec. Already + * enqueued or running launches of \p hGraphExec are not affected by this call. + * \p hNode is also not modified by this call. + * + * \note Currently only kernel, memset and memcpy nodes are supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Node from the graph from which graphExec was instantiated + * \param isEnabled - Node is enabled if != 0, otherwise the node is disabled + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeGetEnabled, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + * ::cudaGraphLaunch + */ +#if __CUDART_API_VERSION >= 11060 +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeSetEnabled(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, unsigned int isEnabled); +#endif + +/** + * \brief Query whether a node in the given graphExec is enabled + * + * Sets isEnabled to 1 if \p hNode is enabled, or 0 if \p hNode is disabled. + * + * The node is identified by the corresponding node \p hNode in the non-executable + * graph, from which the executable graph was instantiated. + * + * \p hNode must not have been removed from the original graph. + * + * \note Currently only kernel, memset and memcpy nodes are supported. + * + * \param hGraphExec - The executable graph in which to set the specified node + * \param hNode - Node from the graph from which graphExec was instantiated + * \param isEnabled - Location to return the enabled status of the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphNodeSetEnabled, + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + * ::cudaGraphLaunch + */ +#if __CUDART_API_VERSION >= 11060 +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeGetEnabled(cudaGraphExec_t hGraphExec, cudaGraphNode_t hNode, unsigned int *isEnabled); +#endif + +/** + * \brief Check whether an executable graph can be updated with a graph and perform the update if possible + * + * Updates the node parameters in the instantiated graph specified by \p hGraphExec with the + * node parameters in a topologically identical graph specified by \p hGraph. + * + * Limitations: + * + * - Kernel nodes: + * - The owning context of the function cannot change. + * - A node whose function originally did not use CUDA dynamic parallelism cannot be updated + * to a function which uses CDP. + * - A node whose function originally did not make device-side update calls cannot be updated + * to a function which makes device-side update calls. + * - A cooperative node cannot be updated to a non-cooperative node, and vice-versa. + * - If the graph was instantiated with cudaGraphInstantiateFlagUseNodePriority, the + * priority attribute cannot change. Equality is checked on the originally requested + * priority values, before they are clamped to the device's supported range. + * - If \p hGraphExec was not instantiated for device launch, a node whose function originally + * did not use device-side cudaGraphLaunch() cannot be updated to a function which uses + * device-side cudaGraphLaunch() unless the node resides on the same device as nodes which + * contained such calls at instantiate-time. If no such calls were present at instantiation, + * these updates cannot be performed at all. + * - Neither \p hGraph nor \p hGraphExec may contain device-updatable kernel nodes. + * - Memset and memcpy nodes: + * - The CUDA device(s) to which the operand(s) was allocated/mapped cannot change. + * - The source/destination memory must be allocated from the same contexts as the original + * source/destination memory. + * - Only 1D memsets can be changed. + * - Additional memcpy node restrictions: + * - Changing either the source or destination memory type(i.e. CU_MEMORYTYPE_DEVICE, + * CU_MEMORYTYPE_ARRAY, etc.) is not supported. + * - Conditional nodes: + * - Changing node parameters is not supported. + * - Changeing parameters of nodes within the conditional body graph is subject to the rules above. + * - Conditional handle flags and default values are updated as part of the graph update. + * + * Note: The API may add further restrictions in future releases. The return code should always be checked. + * + * cudaGraphExecUpdate sets the result member of \p resultInfo to cudaGraphExecUpdateErrorTopologyChanged + * under the following conditions: + * - The count of nodes directly in \p hGraphExec and \p hGraph differ, in which case resultInfo->errorNode + * is set to NULL. + * - \p hGraph has more exit nodes than \p hGraph, in which case resultInfo->errorNode is set to one of + * the exit nodes in hGraph. + * - A node in \p hGraph has a different number of dependencies than the node from \p hGraphExec it is paired with, + * in which case resultInfo->errorNode is set to the node from \p hGraph. + * - A node in \p hGraph has a dependency that does not match with the corresponding dependency of the paired node + * from \p hGraphExec. resultInfo->errorNode will be set to the node from \p hGraph. resultInfo->errorFromNode + * will be set to the mismatched dependency. The dependencies are paired based on edge order and a dependency + * does not match when the nodes are already paired based on other edges examined in the graph. + * + * cudaGraphExecUpdate sets \p the result member of \p resultInfo to: + * - cudaGraphExecUpdateError if passed an invalid value. + * - cudaGraphExecUpdateErrorTopologyChanged if the graph topology changed + * - cudaGraphExecUpdateErrorNodeTypeChanged if the type of a node changed, in which case + * \p hErrorNode_out is set to the node from \p hGraph. + * - cudaGraphExecUpdateErrorFunctionChanged if the function of a kernel node changed (CUDA driver < 11.2) + * - cudaGraphExecUpdateErrorUnsupportedFunctionChange if the func field of a kernel changed in an + * unsupported way(see note above), in which case \p hErrorNode_out is set to the node from \p hGraph + * - cudaGraphExecUpdateErrorParametersChanged if any parameters to a node changed in a way + * that is not supported, in which case \p hErrorNode_out is set to the node from \p hGraph + * - cudaGraphExecUpdateErrorAttributesChanged if any attributes of a node changed in a way + * that is not supported, in which case \p hErrorNode_out is set to the node from \p hGraph + * - cudaGraphExecUpdateErrorNotSupported if something about a node is unsupported, like + * the node's type or configuration, in which case \p hErrorNode_out is set to the node from \p hGraph + * + * If the update fails for a reason not listed above, the result member of \p resultInfo will be set + * to cudaGraphExecUpdateError. If the update succeeds, the result member will be set to cudaGraphExecUpdateSuccess. + * + * cudaGraphExecUpdate returns cudaSuccess when the updated was performed successfully. It returns + * cudaErrorGraphExecUpdateFailure if the graph update was not performed because it included + * changes which violated constraints specific to instantiated graph update. + * + * \param hGraphExec The instantiated graph to be updated + * \param hGraph The graph containing the updated parameters + \param resultInfo the error info structure + * + * \return + * ::cudaSuccess, + * ::cudaErrorGraphExecUpdateFailure, + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecUpdate(cudaGraphExec_t hGraphExec, cudaGraph_t hGraph, cudaGraphExecUpdateResultInfo *resultInfo); + +/** + * \brief Uploads an executable graph in a stream + * + * Uploads \p hGraphExec to the device in \p hStream without executing it. Uploads of + * the same \p hGraphExec will be serialized. Each upload is ordered behind both any + * previous work in \p hStream and any previous launches of \p hGraphExec. + * Uses memory cached by \p stream to back the allocations owned by \p graphExec. + * + * \param hGraphExec - Executable graph to upload + * \param hStream - Stream in which to upload the graph + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * \notefnerr + * \note_init_rt + * + * \sa + * ::cudaGraphInstantiate, + * ::cudaGraphLaunch, + * ::cudaGraphExecDestroy + */ +#if __CUDART_API_VERSION >= 11010 + extern __host__ cudaError_t CUDARTAPI cudaGraphUpload(cudaGraphExec_t graphExec, cudaStream_t stream); +#endif + +/** + * \brief Launches an executable graph in a stream + * + * Executes \p graphExec in \p stream. Only one instance of \p graphExec may be executing + * at a time. Each launch is ordered behind both any previous work in \p stream + * and any previous launches of \p graphExec. To execute a graph concurrently, it must be + * instantiated multiple times into multiple executable graphs. + * + * If any allocations created by \p graphExec remain unfreed (from a previous launch) and + * \p graphExec was not instantiated with ::cudaGraphInstantiateFlagAutoFreeOnLaunch, + * the launch will fail with ::cudaErrorInvalidValue. + * + * \param graphExec - Executable graph to launch + * \param stream - Stream in which to launch the graph + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphInstantiate, + * ::cudaGraphUpload, + * ::cudaGraphExecDestroy + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphLaunch(cudaGraphExec_t graphExec, cudaStream_t stream); + +/** + * \brief Destroys an executable graph + * + * Destroys the executable graph specified by \p graphExec. + * + * \param graphExec - Executable graph to destroy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaGraphInstantiate, + * ::cudaGraphUpload, + * ::cudaGraphLaunch + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecDestroy(cudaGraphExec_t graphExec); + +/** + * \brief Destroys a graph + * + * Destroys the graph specified by \p graph, as well as all of its nodes. + * + * \param graph - Graph to destroy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * \note_destroy_ub + * + * \sa + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphDestroy(cudaGraph_t graph); + +/** + * \brief Write a DOT file describing graph structure + * + * Using the provided \p graph, write to \p path a DOT formatted description of the graph. + * By default this includes the graph topology, node types, node id, kernel names and memcpy direction. + * \p flags can be specified to write more detailed information about each node type such as + * parameter values, kernel attributes, node and function handles. + * + * \param graph - The graph to create a DOT file from + * \param path - The path to write the DOT file to + * \param flags - Flags from cudaGraphDebugDotFlags for specifying which additional node information to write + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorOperatingSystem + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphDebugDotPrint(cudaGraph_t graph, const char *path, unsigned int flags); + +/** + * \brief Create a user object + * + * Create a user object with the specified destructor callback and initial reference count. The + * initial references are owned by the caller. + * + * Destructor callbacks cannot make CUDA API calls and should avoid blocking behavior, as they + * are executed by a shared internal thread. Another thread may be signaled to perform such + * actions, if it does not block forward progress of tasks scheduled through CUDA. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object_out - Location to return the user object handle + * \param ptr - The pointer to pass to the destroy function + * \param destroy - Callback to free the user object when it is no longer in use + * \param initialRefcount - The initial refcount to create the object with, typically 1. The + * initial references are owned by the calling thread. + * \param flags - Currently it is required to pass ::cudaUserObjectNoDestructorSync, + * which is the only defined flag. This indicates that the destroy + * callback cannot be waited on by any CUDA API. Users requiring + * synchronization of the callback should signal its completion + * manually. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectRetain, + * ::cudaUserObjectRelease, + * ::cudaGraphRetainUserObject, + * ::cudaGraphReleaseUserObject, + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaUserObjectCreate(cudaUserObject_t *object_out, void *ptr, cudaHostFn_t destroy, unsigned int initialRefcount, unsigned int flags); + +/** + * \brief Retain a reference to a user object + * + * Retains new references to a user object. The new references are owned by the caller. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object - The object to retain + * \param count - The number of references to retain, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectCreate, + * ::cudaUserObjectRelease, + * ::cudaGraphRetainUserObject, + * ::cudaGraphReleaseUserObject, + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaUserObjectRetain(cudaUserObject_t object, unsigned int count __dv(1)); + +/** + * \brief Release a reference to a user object + * + * Releases user object references owned by the caller. The object's destructor is invoked if + * the reference count reaches zero. + * + * It is undefined behavior to release references not owned by the caller, or to use a user + * object handle after all references are released. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param object - The object to release + * \param count - The number of references to release, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectCreate, + * ::cudaUserObjectRetain, + * ::cudaGraphRetainUserObject, + * ::cudaGraphReleaseUserObject, + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaUserObjectRelease(cudaUserObject_t object, unsigned int count __dv(1)); + +/** + * \brief Retain a reference to a user object from a graph + * + * Creates or moves user object references that will be owned by a CUDA graph. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param graph - The graph to associate the reference with + * \param object - The user object to retain a reference for + * \param count - The number of references to add to the graph, typically 1. Must be + * nonzero and not larger than INT_MAX. + * \param flags - The optional flag ::cudaGraphUserObjectMove transfers references + * from the calling thread, rather than create new references. Pass 0 + * to create new references. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectCreate + * ::cudaUserObjectRetain, + * ::cudaUserObjectRelease, + * ::cudaGraphReleaseUserObject, + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphRetainUserObject(cudaGraph_t graph, cudaUserObject_t object, unsigned int count __dv(1), unsigned int flags __dv(0)); + +/** + * \brief Release a user object reference from a graph + * + * Releases user object references owned by a graph. + * + * See CUDA User Objects in the CUDA C++ Programming Guide for more information on user objects. + * + * \param graph - The graph that will release the reference + * \param object - The user object to release a reference for + * \param count - The number of references to release, typically 1. Must be nonzero + * and not larger than INT_MAX. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue + * + * \sa + * ::cudaUserObjectCreate + * ::cudaUserObjectRetain, + * ::cudaUserObjectRelease, + * ::cudaGraphRetainUserObject, + * ::cudaGraphCreate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphReleaseUserObject(cudaGraph_t graph, cudaUserObject_t object, unsigned int count __dv(1)); + +/** + * \brief Adds a node of arbitrary type to a graph + * + * Creates a new node in \p graph described by \p nodeParams with \p numDependencies + * dependencies specified via \p pDependencies. \p numDependencies may be 0. + * \p pDependencies may be null if \p numDependencies is 0. \p pDependencies may not have + * any duplicate entries. + * + * \p nodeParams is a tagged union. The node type should be specified in the \p type field, + * and type-specific parameters in the corresponding union member. All unused bytes - that + * is, \p reserved0 and all bytes past the utilized union member - must be set to zero. + * It is recommended to use brace initialization or memset to ensure all bytes are + * initialized. + * + * Note that for some node types, \p nodeParams may contain "out parameters" which are + * modified during the call, such as \p nodeParams->alloc.dptr. + * + * A handle to the new node will be returned in \p phGraphNode. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param numDependencies - Number of dependencies + * \param nodeParams - Specification of the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorNotSupported + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphNodeSetParams, + * ::cudaGraphExecNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddNode(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, size_t numDependencies, struct cudaGraphNodeParams *nodeParams); + +/** + * \brief Adds a node of arbitrary type to a graph (12.3+) + * + * Creates a new node in \p graph described by \p nodeParams with \p numDependencies + * dependencies specified via \p pDependencies. \p numDependencies may be 0. + * \p pDependencies may be null if \p numDependencies is 0. \p pDependencies may not have + * any duplicate entries. + * + * \p nodeParams is a tagged union. The node type should be specified in the \p type field, + * and type-specific parameters in the corresponding union member. All unused bytes - that + * is, \p reserved0 and all bytes past the utilized union member - must be set to zero. + * It is recommended to use brace initialization or memset to ensure all bytes are + * initialized. + * + * Note that for some node types, \p nodeParams may contain "out parameters" which are + * modified during the call, such as \p nodeParams->alloc.dptr. + * + * A handle to the new node will be returned in \p phGraphNode. + * + * \param pGraphNode - Returns newly created node + * \param graph - Graph to which to add the node + * \param pDependencies - Dependencies of the node + * \param dependencyData - Optional edge data for the dependencies. If NULL, the data is + * assumed to be default (zeroed) for all dependencies. + * \param numDependencies - Number of dependencies + * \param nodeParams - Specification of the node + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorNotSupported + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphCreate, + * ::cudaGraphNodeSetParams, + * ::cudaGraphExecNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphAddNode_v2(cudaGraphNode_t *pGraphNode, cudaGraph_t graph, const cudaGraphNode_t *pDependencies, const cudaGraphEdgeData *dependencyData, size_t numDependencies, struct cudaGraphNodeParams *nodeParams); + +/** + * \brief Update's a graph node's parameters + * + * Sets the parameters of graph node \p node to \p nodeParams. The node type specified by + * \p nodeParams->type must match the type of \p node. \p nodeParams must be fully + * initialized and all unused bytes (reserved, padding) zeroed. + * + * Modifying parameters is not supported for node types cudaGraphNodeTypeMemAlloc and + * cudaGraphNodeTypeMemFree. + * + * \param node - Node to set the parameters for + * \param nodeParams - Parameters to copy + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorNotSupported + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphExecNodeSetParams + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphNodeSetParams(cudaGraphNode_t node, struct cudaGraphNodeParams *nodeParams); + +/** + * \brief Update's a graph node's parameters in an instantiated graph + * + * Sets the parameters of a node in an executable graph \p graphExec. The node is identified + * by the corresponding node \p node in the non-executable graph from which the executable + * graph was instantiated. \p node must not have been removed from the original graph. + * + * The modifications only affect future launches of \p graphExec. Already + * enqueued or running launches of \p graphExec are not affected by this call. + * \p node is also not modified by this call. + * + * Allowed changes to parameters on executable graphs are as follows: + * + *
Node typeAllowed changes + *
kernelSee ::cudaGraphExecKernelNodeSetParams + *
memcpyAddresses for 1-dimensional copies if allocated in same context; see ::cudaGraphExecMemcpyNodeSetParams + *
memsetAddresses for 1-dimensional memsets if allocated in same context; see ::cudaGraphExecMemsetNodeSetParams + *
hostUnrestricted + *
child graphTopology must match and restrictions apply recursively; see ::cudaGraphExecUpdate + *
event waitUnrestricted + *
event recordUnrestricted + *
external semaphore signalNumber of semaphore operations cannot change + *
external semaphore waitNumber of semaphore operations cannot change + *
memory allocationAPI unsupported + *
memory freeAPI unsupported + *
+ * + * \param graphExec - The executable graph in which to update the specified node + * \param node - Corresponding node from the graph from which graphExec was instantiated + * \param nodeParams - Updated Parameters to set + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidDeviceFunction, + * ::cudaErrorNotSupported + * \note_graph_thread_safety + * \notefnerr + * \note_init_rt + * \note_callback + * + * \sa + * ::cudaGraphAddNode, + * ::cudaGraphNodeSetParams + * ::cudaGraphExecUpdate, + * ::cudaGraphInstantiate + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphExecNodeSetParams(cudaGraphExec_t graphExec, cudaGraphNode_t node, struct cudaGraphNodeParams *nodeParams); + +/** + * \brief Create a conditional handle + * + * Creates a conditional handle associated with \p hGraph. + * + * The conditional handle must be associated with a conditional node in this graph or one of its children. + * + * Handles not associated with a conditional node may cause graph instantiation to fail. + * + * \param pHandle_out - Pointer used to return the handle to the caller. + * \param hGraph - Graph which will contain the conditional node using this handle. + * \param defaultLaunchValue - Optional initial value for the conditional variable. + * \param flags - Currently must be cudaGraphCondAssignDefault or 0. + * + * \return + * ::CUDA_SUCCESS, + * ::CUDA_ERROR_INVALID_VALUE, + * ::CUDA_ERROR_NOT_SUPPORTED + * \note_graph_thread_safety + * \notefnerr + * + * \sa + * ::cuGraphAddNode, + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphConditionalHandleCreate(cudaGraphConditionalHandle *pHandle_out, cudaGraph_t graph, unsigned int defaultLaunchValue __dv(0), unsigned int flags __dv(0)); + +/** @} */ /* END CUDART_GRAPH */ + +/** + * \defgroup CUDART_DRIVER_ENTRY_POINT Driver Entry Point Access + * + * ___MANBRIEF___ driver entry point access functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the driver entry point access functions of CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Returns the requested driver API function pointer + * + * Returns in \p **funcPtr the address of the CUDA driver function for the requested flags. + * + * For a requested driver symbol, if the CUDA version in which the driver symbol was + * introduced is less than or equal to the CUDA runtime version, the API will return + * the function pointer to the corresponding versioned driver function. + * + * The pointer returned by the API should be cast to a function pointer matching the + * requested driver function's definition in the API header file. The function pointer + * typedef can be picked up from the corresponding typedefs header file. For example, + * cudaTypedefs.h consists of function pointer typedefs for driver APIs defined in cuda.h. + * + * The API will return ::cudaSuccess and set the returned \p funcPtr to NULL if the + * requested driver function is not supported on the platform, no ABI + * compatible driver function exists for the CUDA runtime version or if the + * driver symbol is invalid. + * + * It will also set the optional \p driverStatus to one of the values in + * ::cudaDriverEntryPointQueryResult with the following meanings: + * - ::cudaDriverEntryPointSuccess - The requested symbol was succesfully found based + * on input arguments and \p pfn is valid + * - ::cudaDriverEntryPointSymbolNotFound - The requested symbol was not found + * - ::cudaDriverEntryPointVersionNotSufficent - The requested symbol was found but is + * not supported by the current runtime version (CUDART_VERSION) + * + * The requested flags can be: + * - ::cudaEnableDefault: This is the default mode. This is equivalent to + * ::cudaEnablePerThreadDefaultStream if the code is compiled with + * --default-stream per-thread compilation flag or the macro CUDA_API_PER_THREAD_DEFAULT_STREAM + * is defined; ::cudaEnableLegacyStream otherwise. + * - ::cudaEnableLegacyStream: This will enable the search for all driver symbols + * that match the requested driver symbol name except the corresponding per-thread versions. + * - ::cudaEnablePerThreadDefaultStream: This will enable the search for all + * driver symbols that match the requested driver symbol name including the per-thread + * versions. If a per-thread version is not found, the API will return the legacy version + * of the driver function. + * + * \param symbol - The base name of the driver API function to look for. As an example, + * for the driver API ::cuMemAlloc_v2, \p symbol would be cuMemAlloc. + * Note that the API will use the CUDA runtime version to return the + * address to the most recent ABI compatible driver symbol, ::cuMemAlloc + * or ::cuMemAlloc_v2. + * \param funcPtr - Location to return the function pointer to the requested driver function + * \param flags - Flags to specify search options. + * \param driverStatus - Optional location to store the status of finding the symbol from + * the driver. See ::cudaDriverEntryPointQueryResult for + * possible values. + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidValue, + * ::cudaErrorNotSupported + * \note_version_mixing + * \note_init_rt + * \note_callback + * + * \sa + * ::cuGetProcAddress + */ +#if defined(__cplusplus) +extern __host__ cudaError_t CUDARTAPI cudaGetDriverEntryPoint(const char *symbol, void **funcPtr, unsigned long long flags, enum cudaDriverEntryPointQueryResult *driverStatus = NULL); +#else +extern __host__ cudaError_t CUDARTAPI cudaGetDriverEntryPoint(const char *symbol, void **funcPtr, unsigned long long flags, enum cudaDriverEntryPointQueryResult *driverStatus); +#endif + +/** @} */ /* END CUDART_DRIVER_ENTRY_POINT */ + +/** \cond impl_private */ +extern __host__ cudaError_t CUDARTAPI cudaGetExportTable(const void **ppExportTable, const cudaUUID_t *pExportTableId); +/** \endcond impl_private */ + +/** + * \defgroup CUDART_HIGHLEVEL C++ API Routines + * + * ___MANBRIEF___ C++ high level API functions of the CUDA runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the C++ high level API functions of the CUDA runtime + * application programming interface. To use these functions, your + * application needs to be compiled with the \p nvcc compiler. + * + * \brief C++-style interface built on top of CUDA runtime API + */ + +/** + * \defgroup CUDART_DRIVER Interactions with the CUDA Driver API + * + * ___MANBRIEF___ interactions between CUDA Driver API and CUDA Runtime API + * (___CURRENT_FILE___) ___ENDMANBRIEF___ + * + * This section describes the interactions between the CUDA Driver API and the CUDA Runtime API + * + * @{ + * + * \section CUDART_CUDA_primary Primary Contexts + * + * There exists a one to one relationship between CUDA devices in the CUDA Runtime + * API and ::CUcontext s in the CUDA Driver API within a process. The specific + * context which the CUDA Runtime API uses for a device is called the device's + * primary context. From the perspective of the CUDA Runtime API, a device and + * its primary context are synonymous. + * + * \section CUDART_CUDA_init Initialization and Tear-Down + * + * CUDA Runtime API calls operate on the CUDA Driver API ::CUcontext which is current to + * to the calling host thread. + * + * The function ::cudaInitDevice() ensures that the primary context is initialized + * for the requested device but does not make it current to the calling thread. + * + * The function ::cudaSetDevice() initializes the primary context for the + * specified device and makes it current to the calling thread by calling ::cuCtxSetCurrent(). + * + * The CUDA Runtime API will automatically initialize the primary context for + * a device at the first CUDA Runtime API call which requires an active context. + * If no ::CUcontext is current to the calling thread when a CUDA Runtime API call + * which requires an active context is made, then the primary context for a device + * will be selected, made current to the calling thread, and initialized. + * + * The context which the CUDA Runtime API initializes will be initialized using + * the parameters specified by the CUDA Runtime API functions + * ::cudaSetDeviceFlags(), + * ::cudaD3D9SetDirect3DDevice(), + * ::cudaD3D10SetDirect3DDevice(), + * ::cudaD3D11SetDirect3DDevice(), + * ::cudaGLSetGLDevice(), and + * ::cudaVDPAUSetVDPAUDevice(). + * Note that these functions will fail with ::cudaErrorSetOnActiveProcess if they are + * called when the primary context for the specified device has already been initialized. + * (or if the current device has already been initialized, in the case of + * ::cudaSetDeviceFlags()). + * + * Primary contexts will remain active until they are explicitly deinitialized + * using ::cudaDeviceReset(). The function ::cudaDeviceReset() will deinitialize the + * primary context for the calling thread's current device immediately. The context + * will remain current to all of the threads that it was current to. The next CUDA + * Runtime API call on any thread which requires an active context will trigger the + * reinitialization of that device's primary context. + * + * Note that primary contexts are shared resources. It is recommended that + * the primary context not be reset except just before exit or to recover from an + * unspecified launch failure. + * + * \section CUDART_CUDA_context Context Interoperability + * + * Note that the use of multiple ::CUcontext s per device within a single process + * will substantially degrade performance and is strongly discouraged. Instead, + * it is highly recommended that the implicit one-to-one device-to-context mapping + * for the process provided by the CUDA Runtime API be used. + * + * If a non-primary ::CUcontext created by the CUDA Driver API is current to a + * thread then the CUDA Runtime API calls to that thread will operate on that + * ::CUcontext, with some exceptions listed below. Interoperability between data + * types is discussed in the following sections. + * + * The function ::cudaPointerGetAttributes() will return the error + * ::cudaErrorIncompatibleDriverContext if the pointer being queried was allocated by a + * non-primary context. The function ::cudaDeviceEnablePeerAccess() and the rest of + * the peer access API may not be called when a non-primary ::CUcontext is current. + * To use the pointer query and peer access APIs with a context created using the + * CUDA Driver API, it is necessary that the CUDA Driver API be used to access + * these features. + * + * All CUDA Runtime API state (e.g, global variables' addresses and values) travels + * with its underlying ::CUcontext. In particular, if a ::CUcontext is moved from one + * thread to another then all CUDA Runtime API state will move to that thread as well. + * + * Please note that attaching to legacy contexts (those with a version of 3010 as returned + * by ::cuCtxGetApiVersion()) is not possible. The CUDA Runtime will return + * ::cudaErrorIncompatibleDriverContext in such cases. + * + * \section CUDART_CUDA_stream Interactions between CUstream and cudaStream_t + * + * The types ::CUstream and ::cudaStream_t are identical and may be used interchangeably. + * + * \section CUDART_CUDA_event Interactions between CUevent and cudaEvent_t + * + * The types ::CUevent and ::cudaEvent_t are identical and may be used interchangeably. + * + * \section CUDART_CUDA_array Interactions between CUarray and cudaArray_t + * + * The types ::CUarray and struct ::cudaArray * represent the same data type and may be used + * interchangeably by casting the two types between each other. + * + * In order to use a ::CUarray in a CUDA Runtime API function which takes a struct ::cudaArray *, + * it is necessary to explicitly cast the ::CUarray to a struct ::cudaArray *. + * + * In order to use a struct ::cudaArray * in a CUDA Driver API function which takes a ::CUarray, + * it is necessary to explicitly cast the struct ::cudaArray * to a ::CUarray . + * + * \section CUDART_CUDA_graphicsResource Interactions between CUgraphicsResource and cudaGraphicsResource_t + * + * The types ::CUgraphicsResource and ::cudaGraphicsResource_t represent the same data type and may be used + * interchangeably by casting the two types between each other. + * + * In order to use a ::CUgraphicsResource in a CUDA Runtime API function which takes a + * ::cudaGraphicsResource_t, it is necessary to explicitly cast the ::CUgraphicsResource + * to a ::cudaGraphicsResource_t. + * + * In order to use a ::cudaGraphicsResource_t in a CUDA Driver API function which takes a + * ::CUgraphicsResource, it is necessary to explicitly cast the ::cudaGraphicsResource_t + * to a ::CUgraphicsResource. + * + * \section CUDART_CUDA_texture_objects Interactions between CUtexObject and cudaTextureObject_t + * + * The types ::CUtexObject and ::cudaTextureObject_t represent the same data type and may be used + * interchangeably by casting the two types between each other. + * + * In order to use a ::CUtexObject in a CUDA Runtime API function which takes a ::cudaTextureObject_t, + * it is necessary to explicitly cast the ::CUtexObject to a ::cudaTextureObject_t. + * + * In order to use a ::cudaTextureObject_t in a CUDA Driver API function which takes a ::CUtexObject, + * it is necessary to explicitly cast the ::cudaTextureObject_t to a ::CUtexObject. + * + * \section CUDART_CUDA_surface_objects Interactions between CUsurfObject and cudaSurfaceObject_t + * + * The types ::CUsurfObject and ::cudaSurfaceObject_t represent the same data type and may be used + * interchangeably by casting the two types between each other. + * + * In order to use a ::CUsurfObject in a CUDA Runtime API function which takes a ::cudaSurfaceObject_t, + * it is necessary to explicitly cast the ::CUsurfObject to a ::cudaSurfaceObject_t. + * + * In order to use a ::cudaSurfaceObject_t in a CUDA Driver API function which takes a ::CUsurfObject, + * it is necessary to explicitly cast the ::cudaSurfaceObject_t to a ::CUsurfObject. + * + * \section CUDART_CUDA_module Interactions between CUfunction and cudaFunction_t + * + * The types ::CUfunction and ::cudaFunction_t represent the same data type and may be used + * interchangeably by casting the two types between each other. + * + * In order to use a ::cudaFunction_t in a CUDA Driver API function which takes a ::CUfunction, + * it is necessary to explicitly cast the ::cudaFunction_t to a ::CUfunction. + * + */ + + /** + * \brief Get pointer to device entry function that matches entry function \p symbolPtr + * + * Returns in \p functionPtr the device entry function corresponding to the symbol \p symbolPtr. + * + * \param functionPtr - Returns the device entry function + * \param symbolPtr - Pointer to device entry function to search for + * + * \return + * ::cudaSuccess + * + */ +extern __host__ cudaError_t cudaGetFuncBySymbol(cudaFunction_t* functionPtr, const void* symbolPtr); + +/** + * \brief Get pointer to device kernel that matches entry function \p entryFuncAddr + * + * Returns in \p kernelPtr the device kernel corresponding to the entry function \p entryFuncAddr. + * + * \param kernelPtr - Returns the device kernel + * \param entryFuncAddr - Address of device entry function to search kernel for + * + * \return + * ::cudaSuccess + * + * \sa + * \ref ::cudaGetKernel(cudaKernel_t *kernelPtr, const T *entryFuncAddr) "cudaGetKernel (C++ API)" + */ +extern __host__ cudaError_t CUDARTAPI cudaGetKernel(cudaKernel_t *kernelPtr, const void *entryFuncAddr); + +/** @} */ /* END CUDART_DRIVER */ + +#if defined(__CUDA_API_VERSION_INTERNAL) + #undef cudaMemcpy + #undef cudaMemcpyToSymbol + #undef cudaMemcpyFromSymbol + #undef cudaMemcpy2D + #undef cudaMemcpyToArray + #undef cudaMemcpy2DToArray + #undef cudaMemcpyFromArray + #undef cudaMemcpy2DFromArray + #undef cudaMemcpyArrayToArray + #undef cudaMemcpy2DArrayToArray + #undef cudaMemcpy3D + #undef cudaMemcpy3DPeer + #undef cudaMemset + #undef cudaMemset2D + #undef cudaMemset3D + #undef cudaMemcpyAsync + #undef cudaMemcpyToSymbolAsync + #undef cudaMemcpyFromSymbolAsync + #undef cudaMemcpy2DAsync + #undef cudaMemcpyToArrayAsync + #undef cudaMemcpy2DToArrayAsync + #undef cudaMemcpyFromArrayAsync + #undef cudaMemcpy2DFromArrayAsync + #undef cudaMemcpy3DAsync + #undef cudaMemcpy3DPeerAsync + #undef cudaMemsetAsync + #undef cudaMemset2DAsync + #undef cudaMemset3DAsync + #undef cudaStreamQuery + #undef cudaStreamGetFlags + #undef cudaStreamGetId + #undef cudaStreamGetPriority + #undef cudaEventRecord + #undef cudaEventRecordWithFlags + #undef cudaStreamWaitEvent + #undef cudaStreamAddCallback + #undef cudaStreamAttachMemAsync + #undef cudaStreamSynchronize + #undef cudaLaunchKernel + #undef cudaLaunchKernelExC + #undef cudaLaunchHostFunc + #undef cudaMemPrefetchAsync + #undef cudaMemPrefetchAsync_v2 + #undef cudaLaunchCooperativeKernel + #undef cudaSignalExternalSemaphoresAsync + #undef cudaWaitExternalSemaphoresAsync + #undef cudaGraphInstantiateWithParams + #undef cudaGraphUpload + #undef cudaGraphLaunch + #undef cudaStreamBeginCapture + #undef cudaStreamBeginCaptureToGraph + #undef cudaStreamEndCapture + #undef cudaStreamIsCapturing + #undef cudaStreamGetCaptureInfo + #undef cudaStreamGetCaptureInfo_v2 + #undef cudaStreamGetCaptureInfo_v3 + #undef cudaStreamUpdateCaptureDependencies + #undef cudaStreamUpdateCaptureDependencies_v2 + #undef cudaStreamCopyAttributes + #undef cudaStreamGetAttribute + #undef cudaStreamSetAttribute + #undef cudaMallocAsync + #undef cudaFreeAsync + #undef cudaMallocFromPoolAsync + #undef cudaGetDriverEntryPoint + + #undef cudaGetDeviceProperties + + extern __host__ cudaError_t CUDARTAPI cudaMemcpy(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyToSymbol(const void *symbol, const void *src, size_t count, size_t offset __dv(0), enum cudaMemcpyKind kind __dv(cudaMemcpyHostToDevice)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromSymbol(void *dst, const void *symbol, size_t count, size_t offset __dv(0), enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToHost)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2D(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyToArray(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t count, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DToArray(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromArray(void *dst, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t count, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DFromArray(void *dst, size_t dpitch, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t width, size_t height, enum cudaMemcpyKind kind); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyArrayToArray(cudaArray_t dst, size_t wOffsetDst, size_t hOffsetDst, cudaArray_const_t src, size_t wOffsetSrc, size_t hOffsetSrc, size_t count, enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToDevice)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DArrayToArray(cudaArray_t dst, size_t wOffsetDst, size_t hOffsetDst, cudaArray_const_t src, size_t wOffsetSrc, size_t hOffsetSrc, size_t width, size_t height, enum cudaMemcpyKind kind __dv(cudaMemcpyDeviceToDevice)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy3D(const struct cudaMemcpy3DParms *p); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy3DPeer(const struct cudaMemcpy3DPeerParms *p); + extern __host__ cudaError_t CUDARTAPI cudaMemset(void *devPtr, int value, size_t count); + extern __host__ cudaError_t CUDARTAPI cudaMemset2D(void *devPtr, size_t pitch, int value, size_t width, size_t height); + extern __host__ cudaError_t CUDARTAPI cudaMemset3D(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpyAsync(void *dst, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyToSymbolAsync(const void *symbol, const void *src, size_t count, size_t offset, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromSymbolAsync(void *dst, const void *symbol, size_t count, size_t offset, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy2DAsync(void *dst, size_t dpitch, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyToArrayAsync(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DToArrayAsync(cudaArray_t dst, size_t wOffset, size_t hOffset, const void *src, size_t spitch, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpyFromArrayAsync(void *dst, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t count, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy2DFromArrayAsync(void *dst, size_t dpitch, cudaArray_const_t src, size_t wOffset, size_t hOffset, size_t width, size_t height, enum cudaMemcpyKind kind, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemcpy3DAsync(const struct cudaMemcpy3DParms *p, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaMemcpy3DPeerAsync(const struct cudaMemcpy3DPeerParms *p, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemsetAsync(void *devPtr, int value, size_t count, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset2DAsync(void *devPtr, size_t pitch, int value, size_t width, size_t height, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaMemset3DAsync(struct cudaPitchedPtr pitchedDevPtr, int value, struct cudaExtent extent, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaStreamQuery(cudaStream_t stream); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetFlags(cudaStream_t hStream, unsigned int *flags); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetId(cudaStream_t hStream, unsigned long long *streamId); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamGetPriority(cudaStream_t hStream, int *priority); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecord(cudaEvent_t event, cudaStream_t stream __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaEventRecordWithFlags(cudaEvent_t event, cudaStream_t stream __dv(0), unsigned int flags __dv(0)); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamWaitEvent(cudaStream_t stream, cudaEvent_t event, unsigned int flags); + extern __host__ cudaError_t CUDARTAPI cudaStreamAddCallback(cudaStream_t stream, cudaStreamCallback_t callback, void *userData, unsigned int flags); + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaStreamAttachMemAsync(cudaStream_t stream, void *devPtr, size_t length, unsigned int flags); + extern __host__ cudaError_t CUDARTAPI cudaStreamSynchronize(cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaLaunchKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaLaunchKernelExC(const cudaLaunchConfig_t *config, const void *func, void **args); + extern __host__ cudaError_t CUDARTAPI cudaLaunchCooperativeKernel(const void *func, dim3 gridDim, dim3 blockDim, void **args, size_t sharedMem, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaLaunchHostFunc(cudaStream_t stream, cudaHostFn_t fn, void *userData); + extern __host__ cudaError_t CUDARTAPI cudaMemPrefetchAsync(const void *devPtr, size_t count, int dstDevice, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaMemPrefetchAsync_v2(const void *devPtr, size_t count, struct cudaMemLocation location, unsigned int flags, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaSignalExternalSemaphoresAsync(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreSignalParams_v1 *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaSignalExternalSemaphoresAsync_ptsz(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreSignalParams_v1 *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaSignalExternalSemaphoresAsync_v2(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreSignalParams *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaWaitExternalSemaphoresAsync(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreWaitParams_v1 *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaWaitExternalSemaphoresAsync_ptsz(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreWaitParams_v1 *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaWaitExternalSemaphoresAsync_v2(const cudaExternalSemaphore_t *extSemArray, const struct cudaExternalSemaphoreWaitParams *paramsArray, unsigned int numExtSems, cudaStream_t stream __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaGraphInstantiateWithParams(cudaGraphExec_t *pGraphExec, cudaGraph_t graph, cudaGraphInstantiateParams *instantiateParams); + extern __host__ cudaError_t CUDARTAPI cudaGraphUpload(cudaGraphExec_t graphExec, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaGraphLaunch(cudaGraphExec_t graphExec, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaStreamBeginCapture(cudaStream_t stream, enum cudaStreamCaptureMode mode); + extern __host__ cudaError_t CUDARTAPI cudaStreamBeginCaptureToGraph(cudaStream_t stream, cudaGraph_t graph, const cudaGraphNode_t *dependencies, const cudaGraphEdgeData *dependencyData, size_t numDependencies, enum cudaStreamCaptureMode mode); + extern __host__ cudaError_t CUDARTAPI cudaStreamEndCapture(cudaStream_t stream, cudaGraph_t *pGraph); + extern __host__ cudaError_t CUDARTAPI cudaStreamIsCapturing(cudaStream_t stream, enum cudaStreamCaptureStatus *pCaptureStatus); + extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo(cudaStream_t stream, enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out); + extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo_ptsz(cudaStream_t stream, enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out); + extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo_v2(cudaStream_t stream, enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out __dv(0), cudaGraph_t *graph_out __dv(0), const cudaGraphNode_t **dependencies_out __dv(0), size_t *numDependencies_out __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaStreamGetCaptureInfo_v3(cudaStream_t stream, enum cudaStreamCaptureStatus *captureStatus_out, unsigned long long *id_out __dv(0), cudaGraph_t *graph_out __dv(0), const cudaGraphNode_t **dependencies_out __dv(0), const cudaGraphEdgeData **edgeData_out __dv(0), size_t *numDependencies_out __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaStreamUpdateCaptureDependencies(cudaStream_t stream, cudaGraphNode_t *dependencies, size_t numDependencies, unsigned int flags __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaStreamUpdateCaptureDependencies_v2(cudaStream_t stream, cudaGraphNode_t *dependencies, const cudaGraphEdgeData *dependencyData, size_t numDependencies, unsigned int flags __dv(0)); + extern __host__ cudaError_t CUDARTAPI cudaStreamCopyAttributes(cudaStream_t dstStream, cudaStream_t srcStream); + extern __host__ cudaError_t CUDARTAPI cudaStreamGetAttribute(cudaStream_t stream, cudaStreamAttrID attr, cudaStreamAttrValue *value); + extern __host__ cudaError_t CUDARTAPI cudaStreamSetAttribute(cudaStream_t stream, cudaStreamAttrID attr, const cudaStreamAttrValue *param); + + extern __host__ cudaError_t CUDARTAPI cudaMallocAsync(void **devPtr, size_t size, cudaStream_t hStream); + extern __host__ cudaError_t CUDARTAPI cudaFreeAsync(void *devPtr, cudaStream_t hStream); + extern __host__ cudaError_t CUDARTAPI cudaMallocFromPoolAsync(void **ptr, size_t size, cudaMemPool_t memPool, cudaStream_t stream); + extern __host__ cudaError_t CUDARTAPI cudaGetDriverEntryPoint(const char *symbol, void **funcPtr, unsigned long long flags, enum cudaDriverEntryPointQueryResult *driverStatus); + + extern __host__ __cudart_builtin__ cudaError_t CUDARTAPI cudaGetDeviceProperties(struct cudaDeviceProp *prop, int device); + +#elif defined(__CUDART_API_PER_THREAD_DEFAULT_STREAM) + // nvcc stubs reference the 'cudaLaunch'/'cudaLaunchKernel' identifier even if it was defined + // to 'cudaLaunch_ptsz'/'cudaLaunchKernel_ptsz'. Redirect through a static inline function. + #undef cudaLaunchKernel + static __inline__ __host__ cudaError_t cudaLaunchKernel(const void *func, + dim3 gridDim, dim3 blockDim, + void **args, size_t sharedMem, + cudaStream_t stream) + { + return cudaLaunchKernel_ptsz(func, gridDim, blockDim, args, sharedMem, stream); + } + #define cudaLaunchKernel __CUDART_API_PTSZ(cudaLaunchKernel) + #undef cudaLaunchKernelExC + static __inline__ __host__ cudaError_t cudaLaunchKernelExC(const cudaLaunchConfig_t *config, + const void *func, + void **args) + { + return cudaLaunchKernelExC_ptsz(config, func, args); + } + #define cudaLaunchKernelExC __CUDART_API_PTSZ(cudaLaunchKernelExC) +#endif + +#if defined(__cplusplus) +} + +#endif /* __cplusplus */ + +#undef EXCLUDE_FROM_RTC +#endif /* !__CUDACC_RTC__ */ + +#undef __dv +#undef __CUDA_DEPRECATED + +#if defined(__UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_API_H__) +#undef __CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS__ +#undef __UNDEF_CUDA_INCLUDE_COMPILER_INTERNAL_HEADERS_CUDA_RUNTIME_API_H__ +#endif + +#endif /* !__CUDA_RUNTIME_API_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_stdint.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_stdint.h new file mode 100644 index 0000000000000000000000000000000000000000..8a9814410e4b6fb4f07ad9edc8394e956b77dbcd --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_stdint.h @@ -0,0 +1,112 @@ +/* + * Copyright 2009-2017 NVIDIA Corporation. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * * Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * * Neither the name of NVIDIA CORPORATION nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY + * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY + * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#ifndef __cuda_stdint_h__ +#define __cuda_stdint_h__ + +// Compiler-specific treatment for C99's stdint.h +// +// By default, this header will use the standard headers (so it +// is your responsibility to make sure they are available), except +// on MSVC before Visual Studio 2010, when they were not provided. +// To support old MSVC, a few of the commonly-used definitions are +// provided here. If more definitions are needed, add them here, +// or replace these definitions with a complete implementation, +// such as the ones available from Google, Boost, or MSVC10. You +// can prevent the definition of any of these types (in order to +// use your own) by #defining CU_STDINT_TYPES_ALREADY_DEFINED. + +#if !defined(CU_STDINT_TYPES_ALREADY_DEFINED) + +// In VS including stdint.h forces the C++ runtime dep - provide an opt-out +// (CU_STDINT_VS_FORCE_NO_STDINT_H) for users that care (notably static +// cudart). +#if defined(_MSC_VER) && ((_MSC_VER < 1600) || defined(CU_STDINT_VS_FORCE_NO_STDINT_H)) + +// These definitions can be used with MSVC 8 and 9, +// which don't ship with stdint.h: + +typedef unsigned char uint8_t; + +typedef short int16_t; +typedef unsigned short uint16_t; + +// To keep it consistent with all MSVC build. define those types +// in the exact same way they are defined with the MSVC headers +#if defined(_MSC_VER) +typedef signed char int8_t; + +typedef int int32_t; +typedef unsigned int uint32_t; + +typedef long long int64_t; +typedef unsigned long long uint64_t; +#else +typedef char int8_t; + +typedef long int32_t; +typedef unsigned long uint32_t; + +typedef __int64 int64_t; +typedef unsigned __int64 uint64_t; +#endif + +#elif defined(__DJGPP__) + +// These definitions can be used when compiling +// C code with DJGPP, which only provides stdint.h +// when compiling C++ code with TR1 enabled. + +typedef char int8_t; +typedef unsigned char uint8_t; + +typedef short int16_t; +typedef unsigned short uint16_t; + +typedef long int32_t; +typedef unsigned long uint32_t; + +typedef long long int64_t; +typedef unsigned long long uint64_t; + +#else + +// Use standard headers, as specified by C99 and C++ TR1. +// Known to be provided by: +// - gcc/glibc, supported by all versions of glibc +// - djgpp, supported since 2001 +// - MSVC, supported by Visual Studio 2010 and later + +#include + +#endif + +#endif // !defined(CU_STDINT_TYPES_ALREADY_DEFINED) + + +#endif // file guard diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_surface_types.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_surface_types.h new file mode 100644 index 0000000000000000000000000000000000000000..4a35c215668e98006c3eaa286deb70461eb1fa62 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_surface_types.h @@ -0,0 +1,76 @@ +/* + * Copyright 1993-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_SURFACE_TYPES_H__) +#define __CUDA_SURFACE_TYPES_H__ + +#if defined(__cplusplus) && defined(__CUDACC__) + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#if !defined(__CUDACC_RTC__) +#define EXCLUDE_FROM_RTC +#include "channel_descriptor.h" +#undef EXCLUDE_FROM_RTC +#endif /* !__CUDACC_RTC__ */ +#include "cuda_runtime_api.h" + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#endif /* __cplusplus && __CUDACC__ */ + +#endif /* !__CUDA_SURFACE_TYPES_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_texture_types.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_texture_types.h new file mode 100644 index 0000000000000000000000000000000000000000..4f723db5c682a7b4b05491219df8993f0f6ebd59 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_texture_types.h @@ -0,0 +1,76 @@ +/* + * Copyright 1993-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_TEXTURE_TYPES_H__) +#define __CUDA_TEXTURE_TYPES_H__ + +#if defined(__cplusplus) && defined(__CUDACC__) + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#if !defined(__CUDACC_RTC__) +#define EXCLUDE_FROM_RTC +#include "channel_descriptor.h" +#undef EXCLUDE_FROM_RTC +#endif /* !__CUDACC_RTC__ */ +#include "cuda_runtime_api.h" + +/******************************************************************************* +* * +* * +* * +*******************************************************************************/ + +#endif /* __cplusplus && __CUDACC__ */ + +#endif /* !__CUDA_TEXTURE_TYPES_H__ */ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_vdpau_interop.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_vdpau_interop.h new file mode 100644 index 0000000000000000000000000000000000000000..2cf1ba357eb02ed82afc2f1812627a8a2d88c6f7 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cuda_vdpau_interop.h @@ -0,0 +1,201 @@ +/* + * Copyright 1993-2012 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUDA_VDPAU_INTEROP_H__) +#define __CUDA_VDPAU_INTEROP_H__ + +#include "cuda_runtime_api.h" + +#include + +#if defined(__cplusplus) +extern "C" { +#endif /* __cplusplus */ + +/** + * \addtogroup CUDART_VDPAU VDPAU Interoperability + * This section describes the VDPAU interoperability functions of the CUDA + * runtime application programming interface. + * + * @{ + */ + +/** + * \brief Gets the CUDA device associated with a VdpDevice. + * + * Returns the CUDA device associated with a VdpDevice, if applicable. + * + * \param device - Returns the device associated with vdpDevice, or -1 if + * the device associated with vdpDevice is not a compute device. + * \param vdpDevice - A VdpDevice handle + * \param vdpGetProcAddress - VDPAU's VdpGetProcAddress function pointer + * + * \return + * ::cudaSuccess + * \notefnerr + * + * \sa + * ::cudaVDPAUSetVDPAUDevice, + * ::cuVDPAUGetDevice + */ +extern __host__ cudaError_t CUDARTAPI cudaVDPAUGetDevice(int *device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); + +/** + * \brief Sets a CUDA device to use VDPAU interoperability + * + * Records \p vdpDevice as the VdpDevice for VDPAU interoperability + * with the CUDA device \p device and sets \p device as the current + * device for the calling host thread. + * + * This function will immediately initialize the primary context on + * \p device if needed. + * + * If \p device has already been initialized then this call will fail + * with the error ::cudaErrorSetOnActiveProcess. In this case it is + * necessary to reset \p device using ::cudaDeviceReset() before + * VDPAU interoperability on \p device may be enabled. + * + * \param device - Device to use for VDPAU interoperability + * \param vdpDevice - The VdpDevice to interoperate with + * \param vdpGetProcAddress - VDPAU's VdpGetProcAddress function pointer + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorSetOnActiveProcess + * \notefnerr + * + * \sa ::cudaGraphicsVDPAURegisterVideoSurface, + * ::cudaGraphicsVDPAURegisterOutputSurface, + * ::cudaDeviceReset + */ +extern __host__ cudaError_t CUDARTAPI cudaVDPAUSetVDPAUDevice(int device, VdpDevice vdpDevice, VdpGetProcAddress *vdpGetProcAddress); + +/** + * \brief Register a VdpVideoSurface object + * + * Registers the VdpVideoSurface specified by \p vdpSurface for access by CUDA. + * A handle to the registered object is returned as \p resource. + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::cudaGraphicsMapFlagsNone: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::cudaGraphicsMapFlagsReadOnly: Specifies that CUDA + * will not write to this resource. + * - ::cudaGraphicsMapFlagsWriteDiscard: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * \param resource - Pointer to the returned object handle + * \param vdpSurface - VDPAU object to be registered + * \param flags - Map flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * + * \sa + * ::cudaVDPAUSetVDPAUDevice, + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cuGraphicsVDPAURegisterVideoSurface + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsVDPAURegisterVideoSurface(struct cudaGraphicsResource **resource, VdpVideoSurface vdpSurface, unsigned int flags); + +/** + * \brief Register a VdpOutputSurface object + * + * Registers the VdpOutputSurface specified by \p vdpSurface for access by CUDA. + * A handle to the registered object is returned as \p resource. + * The surface's intended usage is specified using \p flags, as follows: + * + * - ::cudaGraphicsMapFlagsNone: Specifies no hints about how this + * resource will be used. It is therefore assumed that this resource will be + * read from and written to by CUDA. This is the default value. + * - ::cudaGraphicsMapFlagsReadOnly: Specifies that CUDA + * will not write to this resource. + * - ::cudaGraphicsMapFlagsWriteDiscard: Specifies that + * CUDA will not read from this resource and will write over the + * entire contents of the resource, so none of the data previously + * stored in the resource will be preserved. + * + * \param resource - Pointer to the returned object handle + * \param vdpSurface - VDPAU object to be registered + * \param flags - Map flags + * + * \return + * ::cudaSuccess, + * ::cudaErrorInvalidDevice, + * ::cudaErrorInvalidValue, + * ::cudaErrorInvalidResourceHandle, + * ::cudaErrorUnknown + * \notefnerr + * + * \sa + * ::cudaVDPAUSetVDPAUDevice, + * ::cudaGraphicsUnregisterResource, + * ::cudaGraphicsSubResourceGetMappedArray, + * ::cuGraphicsVDPAURegisterOutputSurface + */ +extern __host__ cudaError_t CUDARTAPI cudaGraphicsVDPAURegisterOutputSurface(struct cudaGraphicsResource **resource, VdpOutputSurface vdpSurface, unsigned int flags); + +/** @} */ /* END CUDART_VDPAU */ + +#if defined(__cplusplus) +} +#endif /* __cplusplus */ + +#endif /* __CUDA_VDPAU_INTEROP_H__ */ + diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cudart_platform.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudart_platform.h new file mode 100644 index 0000000000000000000000000000000000000000..0f022bbe349eba2219a6b74f1ea315c1ce8551b7 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cudart_platform.h @@ -0,0 +1,57 @@ +/* + * Copyright 2016 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#ifndef __CUDART_PLATFORM_H__ +#define __CUDART_PLATFORM_H__ + +#if ((defined(__linux__) || defined(__QNX__)) && (defined(__arm__) || defined(__aarch64__) || defined(__x86_64__))) +#define isEglSupported 1 +#endif + +#endif diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti.h new file mode 100644 index 0000000000000000000000000000000000000000..be316531dcfd846bcea8feadf3604437ce2447a1 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti.h @@ -0,0 +1,123 @@ +/* + * Copyright 2010-2017 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(_CUPTI_H_) +#define _CUPTI_H_ + +#ifdef _WIN32 +#ifndef WIN32_LEAN_AND_MEAN +#define WIN32_LEAN_AND_MEAN +#endif +#ifdef NOMINMAX +#include +#else +#define NOMINMAX +#include +#undef NOMINMAX +#endif +#endif + +#include +#include +#include + +/* Activity, callback, event and metric APIs */ +#include +#include +#include +#include + +/* Runtime, driver, and nvtx function identifiers */ +#include +#include +#include + +/* To support function parameter structures for obsoleted API. See + cuda.h for the actual definition of these structures. */ +typedef unsigned int CUdeviceptr_v1; +typedef struct CUDA_MEMCPY2D_v1_st { int dummy; } CUDA_MEMCPY2D_v1; +typedef struct CUDA_MEMCPY3D_v1_st { int dummy; } CUDA_MEMCPY3D_v1; +typedef struct CUDA_ARRAY_DESCRIPTOR_v1_st { int dummy; } CUDA_ARRAY_DESCRIPTOR_v1; +typedef struct CUDA_ARRAY3D_DESCRIPTOR_v1_st { int dummy; } CUDA_ARRAY3D_DESCRIPTOR_v1; + +/* Function parameter structures */ +#include +#include + +/* The following parameter structures cannot be included unless a + header that defines GL_VERSION is included before including them. + If these are needed then make sure such a header is included + already. */ +#ifdef GL_VERSION +#include +#include +#endif + +//#include + +/* The following parameter structures cannot be included by default as + they are not guaranteed to be available on all systems. Uncomment + the includes that are available, or use the include explicitly. */ +#if defined(__linux__) +//#include +//#include +#endif + +#ifdef _WIN32 +//#include +//#include +//#include +//#include +//#include +//#include +#endif + +#endif /*_CUPTI_H_*/ + + diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity.h new file mode 100644 index 0000000000000000000000000000000000000000..48a6c146a62b68f7970bfeb1129802ffeeb2c5ba --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity.h @@ -0,0 +1,7541 @@ +/* + * Copyright 2011-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(_CUPTI_ACTIVITY_H_) +#define _CUPTI_ACTIVITY_H_ + +/** + * Deprecated APIs and structures have been moved to the + * header :doc: `cupti_activity_deprecated.h`, which is included at + * the bottom of this file. Header cupti_activity.h contains + * only the latest version of APIs and structures. + */ + +#include +#include +#include +#include +#include + +#if defined(CUPTI_DIRECTIVE_SUPPORT) +#include +#include +#endif + +#include + +#define CUPTI_UNIFIED_MEMORY_CPU_DEVICE_ID ((uint32_t) 0xFFFFFFFFU) +#define CUPTI_INVALID_CONTEXT_ID ((uint32_t) 0xFFFFFFFFU) +#define CUPTI_INVALID_STREAM_ID ((uint32_t) 0xFFFFFFFFU) +#define CUPTI_INVALID_CHANNEL_ID ((uint32_t) 0xFFFFFFFFU) + +#if defined(__cplusplus) +extern "C" { +#endif + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility push(default) +#endif + +#define invalidNumaId ((uint32_t) 0xFFFFFFFF) + +/** + * \defgroup CUPTI_ACTIVITY_API CUPTI Activity API + * Functions, types, and enums that implement the CUPTI Activity API. + * @{ + */ + +/** + * \brief The kinds of activity records. + * + * Each activity record kind represents information about a GPU or an + * activity occurring on a CPU or GPU. Each kind is associated with a + * activity record structure that holds the information associated + * with the kind. + * \see CUpti_Activity + * \see CUpti_ActivityAPI + * \see CUpti_ActivityContext + * \see CUpti_ActivityContext2 + * \see CUpti_ActivityDevice + * \see CUpti_ActivityDevice2 + * \see CUpti_ActivityDevice3 + * \see CUpti_ActivityDevice4 + * \see CUpti_ActivityDeviceAttribute + * \see CUpti_ActivityEvent + * \see CUpti_ActivityEventInstance + * \see CUpti_ActivityKernel + * \see CUpti_ActivityKernel2 + * \see CUpti_ActivityKernel3 + * \see CUpti_ActivityKernel4 + * \see CUpti_ActivityKernel5 + * \see CUpti_ActivityKernel6 + * \see CUpti_ActivityKernel7 + * \see CUpti_ActivityKernel8 + * \see CUpti_ActivityKernel9 + * \see CUpti_ActivityCdpKernel + * \see CUpti_ActivityPreemption + * \see CUpti_ActivityMemcpy + * \see CUpti_ActivityMemcpy3 + * \see CUpti_ActivityMemcpy4 + * \see CUpti_ActivityMemcpy5 + * \see CUpti_ActivityMemcpyPtoP + * \see CUpti_ActivityMemcpyPtoP2 + * \see CUpti_ActivityMemcpyPtoP3 + * \see CUpti_ActivityMemcpyPtoP4 + * \see CUpti_ActivityMemset + * \see CUpti_ActivityMemset2 + * \see CUpti_ActivityMemset3 + * \see CUpti_ActivityMemset4 + * \see CUpti_ActivityMemory + * \see CUpti_ActivityMemory2 + * \see CUpti_ActivityMemory3 + * \see CUpti_ActivityMemoryPool + * \see CUpti_ActivityMemoryPool2 + * \see CUpti_ActivityMetric + * \see CUpti_ActivityMetricInstance + * \see CUpti_ActivityName + * \see CUpti_ActivityMarker + * \see CUpti_ActivityMarker2 + * \see CUpti_ActivityMarkerData + * \see CUpti_ActivitySourceLocator + * \see CUpti_ActivityGlobalAccess + * \see CUpti_ActivityGlobalAccess2 + * \see CUpti_ActivityGlobalAccess3 + * \see CUpti_ActivityBranch + * \see CUpti_ActivityBranch2 + * \see CUpti_ActivityOverhead3 + * \see CUpti_ActivityEnvironment + * \see CUpti_ActivityInstructionExecution + * \see CUpti_ActivityUnifiedMemoryCounter + * \see CUpti_ActivityFunction + * \see CUpti_ActivityModule + * \see CUpti_ActivitySharedAccess + * \see CUpti_ActivityPCSampling + * \see CUpti_ActivityPCSampling2 + * \see CUpti_ActivityPCSampling3 + * \see CUpti_ActivityPCSamplingRecordInfo + * \see CUpti_ActivityCudaEvent + * \see CUpti_ActivityStream + * \see CUpti_ActivitySynchronization + * \see CUpti_ActivityInstructionCorrelation + * \see CUpti_ActivityExternalCorrelation + * \see CUpti_ActivityUnifiedMemoryCounter2 + * \see CUpti_ActivityOpenAccData + * \see CUpti_ActivityOpenAccLaunch + * \see CUpti_ActivityOpenAccOther + * \see CUpti_ActivityOpenMp + * \see CUpti_ActivityNvLink + * \see CUpti_ActivityNvLink2 + * \see CUpti_ActivityNvLink3 + * \see CUpti_ActivityNvLink4 + * \see CUpti_ActivityPcie + */ + +typedef enum { + /** + * The activity record is invalid. + */ + CUPTI_ACTIVITY_KIND_INVALID = 0, + + /** + * A host<->host, host<->device, or device<->device memory copy. The + * corresponding activity record structure is \ref + * CUpti_ActivityMemcpy5. + */ + CUPTI_ACTIVITY_KIND_MEMCPY = 1, + + /** + * A memory set executing on the GPU. The corresponding activity + * record structure is \ref CUpti_ActivityMemset4. + */ + CUPTI_ACTIVITY_KIND_MEMSET = 2, + + /** + * A kernel executing on the GPU. This activity kind may significantly change + * the overall performance characteristics of the application because all + * kernel executions are serialized on the GPU. Other activity kind for kernel + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL doesn't break kernel concurrency. + * The corresponding activity record structure is \ref CUpti_ActivityKernel9. + */ + CUPTI_ACTIVITY_KIND_KERNEL = 3, + + /** + * A CUDA driver API function execution. The corresponding activity + * record structure is \ref CUpti_ActivityAPI. + */ + CUPTI_ACTIVITY_KIND_DRIVER = 4, + + /** + * A CUDA runtime API function execution. The corresponding activity + * record structure is \ref CUpti_ActivityAPI. + */ + CUPTI_ACTIVITY_KIND_RUNTIME = 5, + + /** + * An event value. The corresponding activity record structure is + * \ref CUpti_ActivityEvent. + */ + CUPTI_ACTIVITY_KIND_EVENT = 6, + + /** + * A metric value. The corresponding activity record structure is + * \ref CUpti_ActivityMetric. + */ + CUPTI_ACTIVITY_KIND_METRIC = 7, + + /** + * Information about a device. The corresponding activity record + * structure is \ref CUpti_ActivityDevice5. + */ + CUPTI_ACTIVITY_KIND_DEVICE = 8, + + /** + * Information about a context. The corresponding activity record + * structure is \ref CUpti_ActivityContext2. + */ + CUPTI_ACTIVITY_KIND_CONTEXT = 9, + + /** + * A kernel executing on the GPU. This activity kind doesn't break + * kernel concurrency. The corresponding activity record structure + * is \ref CUpti_ActivityKernel9. + */ + CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL = 10, + + /** + * Resource naming done via NVTX APIs for thread, device, context, etc. + * The corresponding activity record structure is \ref CUpti_ActivityName. + */ + CUPTI_ACTIVITY_KIND_NAME = 11, + + /** + * Instantaneous, start, or end NVTX marker. The corresponding activity + * record structure is \ref CUpti_ActivityMarker2. + */ + CUPTI_ACTIVITY_KIND_MARKER = 12, + + /** + * Extended, optional, data about a marker. The corresponding + * activity record structure is \ref CUpti_ActivityMarkerData. + */ + CUPTI_ACTIVITY_KIND_MARKER_DATA = 13, + + /** + * Source information about source level result. The corresponding + * activity record structure is \ref CUpti_ActivitySourceLocator. + */ + CUPTI_ACTIVITY_KIND_SOURCE_LOCATOR = 14, + + /** + * Results for source-level global access. The + * corresponding activity record structure is \ref + * CUpti_ActivityGlobalAccess3. + */ + CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS = 15, + + /** + * Results for source-level branch. The corresponding + * activity record structure is \ref CUpti_ActivityBranch2. + */ + CUPTI_ACTIVITY_KIND_BRANCH = 16, + + /** + * Overhead activity records. The + * corresponding activity record structure is + * \ref CUpti_ActivityOverhead3. + */ + CUPTI_ACTIVITY_KIND_OVERHEAD = 17, + + /** + * A CDP (CUDA Dynamic Parallel) kernel executing on the GPU. The + * corresponding activity record structure is \ref + * CUpti_ActivityCdpKernel. This activity can not be directly + * enabled or disabled. It is enabled and disabled through + * concurrent kernel activity i.e. _CONCURRENT_KERNEL. + */ + CUPTI_ACTIVITY_KIND_CDP_KERNEL = 18, + /** + * Preemption activity record indicating a preemption of a CDP (CUDA + * Dynamic Parallel) kernel executing on the GPU. The corresponding + * activity record structure is \ref CUpti_ActivityPreemption. + */ + CUPTI_ACTIVITY_KIND_PREEMPTION = 19, + + /** + * Environment activity records indicating power, clock, thermal, + * etc. levels of the GPU. The corresponding activity record + * structure is \ref CUpti_ActivityEnvironment. + */ + CUPTI_ACTIVITY_KIND_ENVIRONMENT = 20, + + /** + * An event value associated with a specific event domain + * instance. The corresponding activity record structure is \ref + * CUpti_ActivityEventInstance. + */ + CUPTI_ACTIVITY_KIND_EVENT_INSTANCE = 21, + + /** + * A peer to peer memory copy. The corresponding activity record + * structure is \ref CUpti_ActivityMemcpyPtoP4. + */ + CUPTI_ACTIVITY_KIND_MEMCPY2 = 22, + + /** + * A metric value associated with a specific metric domain + * instance. The corresponding activity record structure is \ref + * CUpti_ActivityMetricInstance. + */ + CUPTI_ACTIVITY_KIND_METRIC_INSTANCE = 23, + + /** + * Results for source-level instruction execution. + * The corresponding activity record structure is \ref + * CUpti_ActivityInstructionExecution. + */ + CUPTI_ACTIVITY_KIND_INSTRUCTION_EXECUTION = 24, + + /** + * Unified Memory counter record. The corresponding activity + * record structure is \ref CUpti_ActivityUnifiedMemoryCounter2. + */ + CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER = 25, + + /** + * Device global/function record. The corresponding activity + * record structure is \ref CUpti_ActivityFunction. + */ + CUPTI_ACTIVITY_KIND_FUNCTION = 26, + + /** + * CUDA Module record. The corresponding activity + * record structure is \ref CUpti_ActivityModule. + */ + CUPTI_ACTIVITY_KIND_MODULE = 27, + + /** + * A device attribute value. The corresponding activity record + * structure is \ref CUpti_ActivityDeviceAttribute. + */ + CUPTI_ACTIVITY_KIND_DEVICE_ATTRIBUTE = 28, + + /** + * Results for source-level shared access. The + * corresponding activity record structure is \ref + * CUpti_ActivitySharedAccess. + */ + CUPTI_ACTIVITY_KIND_SHARED_ACCESS = 29, + + /** + * Enable PC sampling for kernels. This will serialize + * kernels. The corresponding activity record structure + * is \ref CUpti_ActivityPCSampling3. + */ + CUPTI_ACTIVITY_KIND_PC_SAMPLING = 30, + + /** + * Summary information about PC sampling records. The + * corresponding activity record structure is \ref + * CUpti_ActivityPCSamplingRecordInfo. + */ + CUPTI_ACTIVITY_KIND_PC_SAMPLING_RECORD_INFO = 31, + + /** + * SASS/Source line-by-line correlation record. + * This will generate sass/source correlation for functions that have source + * level analysis or pc sampling results. The records will be generated only + * when either of source level analysis or pc sampling activity is enabled. + * The corresponding activity record structure is \ref + * CUpti_ActivityInstructionCorrelation. + */ + CUPTI_ACTIVITY_KIND_INSTRUCTION_CORRELATION = 32, + + /** + * OpenACC data events. + * The corresponding activity record structure is \ref + * CUpti_ActivityOpenAccData. + */ + CUPTI_ACTIVITY_KIND_OPENACC_DATA = 33, + + /** + * OpenACC launch events. + * The corresponding activity record structure is \ref + * CUpti_ActivityOpenAccLaunch. + */ + CUPTI_ACTIVITY_KIND_OPENACC_LAUNCH = 34, + + /** + * OpenACC other events. + * The corresponding activity record structure is \ref + * CUpti_ActivityOpenAccOther. + */ + CUPTI_ACTIVITY_KIND_OPENACC_OTHER = 35, + + /** + * Information about a CUDA event. The + * corresponding activity record structure is \ref + * CUpti_ActivityCudaEvent. + */ + CUPTI_ACTIVITY_KIND_CUDA_EVENT = 36, + + /** + * Information about a CUDA stream. The + * corresponding activity record structure is \ref + * CUpti_ActivityStream. + */ + CUPTI_ACTIVITY_KIND_STREAM = 37, + + /** + * Records for synchronization management. The + * corresponding activity record structure is \ref + * CUpti_ActivitySynchronization. + */ + CUPTI_ACTIVITY_KIND_SYNCHRONIZATION = 38, + + /** + * Records for correlation of different programming APIs. The + * corresponding activity record structure is \ref + * CUpti_ActivityExternalCorrelation. + */ + CUPTI_ACTIVITY_KIND_EXTERNAL_CORRELATION = 39, + + /** + * NVLink information. + * The corresponding activity record structure is \ref + * CUpti_ActivityNvLink4. + */ + CUPTI_ACTIVITY_KIND_NVLINK = 40, + + /** + * Instantaneous Event information. + * The corresponding activity record structure is \ref + * CUpti_ActivityInstantaneousEvent. + */ + CUPTI_ACTIVITY_KIND_INSTANTANEOUS_EVENT = 41, + + /** + * Instantaneous Event information for a specific event + * domain instance. + * The corresponding activity record structure is \ref + * CUpti_ActivityInstantaneousEventInstance + */ + CUPTI_ACTIVITY_KIND_INSTANTANEOUS_EVENT_INSTANCE = 42, + + /** + * Instantaneous Metric information + * The corresponding activity record structure is \ref + * CUpti_ActivityInstantaneousMetric. + */ + CUPTI_ACTIVITY_KIND_INSTANTANEOUS_METRIC = 43, + + /** + * Instantaneous Metric information for a specific metric + * domain instance. + * The corresponding activity record structure is \ref + * CUpti_ActivityInstantaneousMetricInstance. + */ + CUPTI_ACTIVITY_KIND_INSTANTANEOUS_METRIC_INSTANCE = 44, + + /** + * Memory activity tracking allocation and freeing of the memory + * The corresponding activity record structure is \ref + * CUpti_ActivityMemory. + */ + CUPTI_ACTIVITY_KIND_MEMORY = 45, + + /** + * PCI devices information used for PCI topology. + * The corresponding activity record structure is \ref + * CUpti_ActivityPcie. + */ + CUPTI_ACTIVITY_KIND_PCIE = 46, + + /** + * OpenMP parallel events. + * The corresponding activity record structure is \ref + * CUpti_ActivityOpenMp. + */ + CUPTI_ACTIVITY_KIND_OPENMP = 47, + + /** + * A CUDA driver kernel launch occurring outside of any + * public API function execution. Tools can handle these + * like records for driver API launch functions, although + * the cbid field is not used here. + * The corresponding activity record structure is \ref + * CUpti_ActivityAPI. + */ + CUPTI_ACTIVITY_KIND_INTERNAL_LAUNCH_API = 48, + + /** + * Memory activity tracking allocation and freeing of the memory + * The corresponding activity record structure is \ref + * CUpti_ActivityMemory3. + */ + CUPTI_ACTIVITY_KIND_MEMORY2 = 49, + + /** + * Memory pool activity tracking creation, destruction and + * trimming of the memory pool. + * The corresponding activity record structure is \ref + * CUpti_ActivityMemoryPool2. + */ + CUPTI_ACTIVITY_KIND_MEMORY_POOL = 50, + + /** + * The corresponding activity record structure is + * \ref CUpti_ActivityGraphTrace2. + */ + CUPTI_ACTIVITY_KIND_GRAPH_TRACE = 51, + + /** + * JIT operation tracking + * The corresponding activity record structure is \ref + * CUpti_ActivityJit. + */ + CUPTI_ACTIVITY_KIND_JIT = 52, + + CUPTI_ACTIVITY_KIND_COUNT, + + CUPTI_ACTIVITY_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityKind; + +/** + * \brief The kinds of activity objects. + * \see CUpti_ActivityObjectKindId + */ +typedef enum { + /** + * The object kind is not known. + */ + CUPTI_ACTIVITY_OBJECT_UNKNOWN = 0, + + /** + * A process. + */ + CUPTI_ACTIVITY_OBJECT_PROCESS = 1, + + /** + * A thread. + */ + CUPTI_ACTIVITY_OBJECT_THREAD = 2, + + /** + * A device. + */ + CUPTI_ACTIVITY_OBJECT_DEVICE = 3, + + /** + * A context. + */ + CUPTI_ACTIVITY_OBJECT_CONTEXT = 4, + + /** + * A stream. + */ + CUPTI_ACTIVITY_OBJECT_STREAM = 5, + + CUPTI_ACTIVITY_OBJECT_FORCE_INT = 0x7fffffff +} CUpti_ActivityObjectKind; + +/** + * \brief Identifiers for object kinds as specified by + * CUpti_ActivityObjectKind. + * \see CUpti_ActivityObjectKind + */ +typedef union { + /** + * A process object requires that we identify the process ID. A + * thread object requires that we identify both the process and + * thread ID. + */ + struct { + uint32_t processId; + uint32_t threadId; + } pt; + + /** + * A device object requires that we identify the device ID. A + * context object requires that we identify both the device and + * context ID. A stream object requires that we identify device, + * context, and stream ID. + */ + struct { + uint32_t deviceId; + uint32_t contextId; + uint32_t streamId; + } dcs; +} CUpti_ActivityObjectKindId; + +/** + * \brief The structure to provide additional data for CUPTI_ACTIVITY_OVERHEAD_COMMAND_BUFFER_FULL. + */ +typedef struct { + /** + * The length of the command buffer. + * + */ + uint32_t commandBufferLength; + /** + * The channel ID of the command buffer. + * + */ + uint32_t channelID; + /** + * The channel type of the command buffer. + * + */ + uint32_t channelType; +} CUpti_ActivityOverheadCommandBufferFullData; + +/** + * \brief The kinds of activity overhead. + */ +typedef enum { + /** + * The overhead kind is not known. + */ + CUPTI_ACTIVITY_OVERHEAD_UNKNOWN = 0, + + /** + * Compiler overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_DRIVER_COMPILER = 1, + + /** + * Activity buffer flush overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_CUPTI_BUFFER_FLUSH = 1<<16, + + /** + * CUPTI instrumentation overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_CUPTI_INSTRUMENTATION = 2<<16, + + /** + * CUPTI resource creation and destruction overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_CUPTI_RESOURCE = 3<<16, + + /** + * CUDA Runtime triggered module loading overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_RUNTIME_TRIGGERED_MODULE_LOADING = 4<<16, + + /** + * Lazy function loading overhead. + */ + CUPTI_ACTIVITY_OVERHEAD_LAZY_FUNCTION_LOADING = 5<<16, + + /** + * Overhead due to lack of command buffer space. + * Refer CUpti_ActivityOverheadCommandBufferFullData for more details. + */ + CUPTI_ACTIVITY_OVERHEAD_COMMAND_BUFFER_FULL = 6<<16, + + CUPTI_ACTIVITY_OVERHEAD_FORCE_INT = 0x7fffffff +} CUpti_ActivityOverheadKind; + +/** + * \brief The kind of a compute API. + */ +typedef enum { + /** + * The compute API is not known. + */ + CUPTI_ACTIVITY_COMPUTE_API_UNKNOWN = 0, + + /** + * The compute APIs are for CUDA. + */ + CUPTI_ACTIVITY_COMPUTE_API_CUDA = 1, + + /** + * The compute APIs are for CUDA running + * in MPS (Multi-Process Service) environment. + */ + CUPTI_ACTIVITY_COMPUTE_API_CUDA_MPS = 2, + + CUPTI_ACTIVITY_COMPUTE_API_FORCE_INT = 0x7fffffff +} CUpti_ActivityComputeApiKind; + +/** + * \brief Flags associated with activity records. + * + * Activity record flags. Flags can be combined by bitwise OR to + * associated multiple flags with an activity record. Each flag is + * specific to a certain activity kind, as noted below. + */ +typedef enum { + /** + * Indicates the activity record has no flags. + */ + CUPTI_ACTIVITY_FLAG_NONE = 0, + + /** + * Indicates the activity represents a device that supports + * concurrent kernel execution. Valid for + * CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUPTI_ACTIVITY_FLAG_DEVICE_CONCURRENT_KERNELS = 1 << 0, + + /** + * Indicates if the activity represents a CUdevice_attribute value + * or a CUpti_DeviceAttribute value. Valid for + * CUPTI_ACTIVITY_KIND_DEVICE_ATTRIBUTE. + */ + CUPTI_ACTIVITY_FLAG_DEVICE_ATTRIBUTE_CUDEVICE = 1 << 0, + + /** + * Indicates the activity represents an asynchronous memcpy + * operation. Valid for CUPTI_ACTIVITY_KIND_MEMCPY. + */ + CUPTI_ACTIVITY_FLAG_MEMCPY_ASYNC = 1 << 0, + + /** + * Indicates the activity represents an instantaneous marker. Valid + * for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_INSTANTANEOUS = 1 << 0, + + /** + * Indicates the activity represents a region start marker. Valid + * for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_START = 1 << 1, + + /** + * Indicates the activity represents a region end marker. Valid for + * CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_END = 1 << 2, + + /** + * Indicates the activity represents an attempt to acquire a user + * defined synchronization object. + * Valid for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_SYNC_ACQUIRE = 1 << 3, + + /** + * Indicates the activity represents success in acquiring the + * user defined synchronization object. + * Valid for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_SYNC_ACQUIRE_SUCCESS = 1 << 4, + + /** + * Indicates the activity represents failure in acquiring the + * user defined synchronization object. + * Valid for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_SYNC_ACQUIRE_FAILED = 1 << 5, + + /** + * Indicates the activity represents releasing a reservation on + * user defined synchronization object. + * Valid for CUPTI_ACTIVITY_KIND_MARKER. + */ + CUPTI_ACTIVITY_FLAG_MARKER_SYNC_RELEASE = 1 << 6, + + /** + * Indicates the activity represents a marker that does not specify + * a color. Valid for CUPTI_ACTIVITY_KIND_MARKER_DATA. + */ + CUPTI_ACTIVITY_FLAG_MARKER_COLOR_NONE = 1 << 0, + + /** + * Indicates the activity represents a marker that specifies a color + * in alpha-red-green-blue format. Valid for + * CUPTI_ACTIVITY_KIND_MARKER_DATA. + */ + CUPTI_ACTIVITY_FLAG_MARKER_COLOR_ARGB = 1 << 1, + + /** + * The number of bytes requested by each thread + * Valid for CUpti_ActivityGlobalAccess3. + */ + CUPTI_ACTIVITY_FLAG_GLOBAL_ACCESS_KIND_SIZE_MASK = 0xFF << 0, + + /** + * If bit in this flag is set, the access was load, else it is a + * store access. Valid for CUpti_ActivityGlobalAccess3. + */ + CUPTI_ACTIVITY_FLAG_GLOBAL_ACCESS_KIND_LOAD = 1 << 8, + + /** + * If this bit in flag is set, the load access was cached else it is + * uncached. Valid for CUpti_ActivityGlobalAccess3. + */ + CUPTI_ACTIVITY_FLAG_GLOBAL_ACCESS_KIND_CACHED = 1 << 9, + + /** + * If this bit in flag is set, the metric value overflowed. Valid + * for CUpti_ActivityMetric and CUpti_ActivityMetricInstance. + */ + CUPTI_ACTIVITY_FLAG_METRIC_OVERFLOWED = 1 << 0, + + /** + * If this bit in flag is set, the metric value couldn't be + * calculated. This occurs when a value(s) required to calculate the + * metric is missing. Valid for CUpti_ActivityMetric and + * CUpti_ActivityMetricInstance. + */ + CUPTI_ACTIVITY_FLAG_METRIC_VALUE_INVALID = 1 << 1, + + /** + * If this bit in flag is set, the source level metric value couldn't be + * calculated. This occurs when a value(s) required to calculate the + * source level metric cannot be evaluated. + * Valid for CUpti_ActivityInstructionExecution. + */ + CUPTI_ACTIVITY_FLAG_INSTRUCTION_VALUE_INVALID = 1 << 0, + + /** + * The mask for the instruction class, \ref CUpti_ActivityInstructionClass + * Valid for CUpti_ActivityInstructionExecution and + * CUpti_ActivityInstructionCorrelation + */ + CUPTI_ACTIVITY_FLAG_INSTRUCTION_CLASS_MASK = 0xFF << 1, + + /** + * When calling cuptiActivityFlushAll, this flag + * can be set to force CUPTI to flush all records in the buffer, whether + * finished or not + */ + CUPTI_ACTIVITY_FLAG_FLUSH_FORCED = 1 << 0, + + /** + * The number of bytes requested by each thread + * Valid for CUpti_ActivitySharedAccess. + */ + CUPTI_ACTIVITY_FLAG_SHARED_ACCESS_KIND_SIZE_MASK = 0xFF << 0, + + /** + * If bit in this flag is set, the access was load, else it is a + * store access. Valid for CUpti_ActivitySharedAccess. + */ + CUPTI_ACTIVITY_FLAG_SHARED_ACCESS_KIND_LOAD = 1 << 8, + + /** + * Indicates the activity represents an asynchronous memset + * operation. Valid for CUPTI_ACTIVITY_KIND_MEMSET. + */ + CUPTI_ACTIVITY_FLAG_MEMSET_ASYNC = 1 << 0, + + /** + * Indicates the activity represents thrashing in CPU. + * Valid for counter of kind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING in + * CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER + */ + CUPTI_ACTIVITY_FLAG_THRASHING_IN_CPU = 1 << 0, + + /** + * Indicates the activity represents page throttling in CPU. + * Valid for counter of kind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING in + * CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER + */ + CUPTI_ACTIVITY_FLAG_THROTTLING_IN_CPU = 1 << 0, + + CUPTI_ACTIVITY_FLAG_FORCE_INT = 0x7fffffff +} CUpti_ActivityFlag; + +/** + * \brief The stall reason for PC sampling activity. + */ +typedef enum { + /** + * Invalid reason + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_INVALID = 0, + + /** + * No stall, instruction is selected for issue + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_NONE = 1, + + /** + * Warp is blocked because next instruction is not yet available, + * because of instruction cache miss, or because of branching effects + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_INST_FETCH = 2, + + /** + * Instruction is waiting on an arithmetic dependency + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_EXEC_DEPENDENCY = 3, + + /** + * Warp is blocked because it is waiting for a memory access to complete. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_MEMORY_DEPENDENCY = 4, + + /** + * Texture sub-system is fully utilized or has too many outstanding requests. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_TEXTURE = 5, + + /** + * Warp is blocked as it is waiting at __syncthreads() or at memory barrier. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_SYNC = 6, + + /** + * Warp is blocked waiting for __constant__ memory and immediate memory access to complete. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_CONSTANT_MEMORY_DEPENDENCY = 7, + + /** + * Compute operation cannot be performed due to the required resources not + * being available. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_PIPE_BUSY = 8, + + /** + * Warp is blocked because there are too many pending memory operations. + * In Kepler architecture it often indicates high number of memory replays. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_MEMORY_THROTTLE = 9, + + /** + * Warp was ready to issue, but some other warp issued instead. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_NOT_SELECTED = 10, + + /** + * Miscellaneous reasons + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_OTHER = 11, + + /** + * Sleeping. + */ + CUPTI_ACTIVITY_PC_SAMPLING_STALL_SLEEPING = 12, + + CUPTI_ACTIVITY_PC_SAMPLING_STALL_FORCE_INT = 0x7fffffff +} CUpti_ActivityPCSamplingStallReason; + +/** + * \brief Sampling period for PC sampling method + * + * Sampling period can be set using \ref cuptiActivityConfigurePCSampling + */ +typedef enum { + /** + * The PC sampling period is not set. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_INVALID = 0, + + /** + * Minimum sampling period available on the device. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_MIN = 1, + + /** + * Sampling period in lower range. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_LOW = 2, + + /** + * Medium sampling period. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_MID = 3, + + /** + * Sampling period in higher range. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_HIGH = 4, + + /** + * Maximum sampling period available on the device. + */ + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_MAX = 5, + + CUPTI_ACTIVITY_PC_SAMPLING_PERIOD_FORCE_INT = 0x7fffffff +} CUpti_ActivityPCSamplingPeriod; + +/** + * \brief The kind of a memory copy, indicating the source and + * destination targets of the copy. + * + * Each kind represents the source and destination targets of a memory + * copy. Targets are host, device, and array. + */ +typedef enum { + /** + * The memory copy kind is not known. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_UNKNOWN = 0, + + /** + * A host to device memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_HTOD = 1, + + /** + * A device to host memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_DTOH = 2, + + /** + * A host to device array memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_HTOA = 3, + + /** + * A device array to host memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_ATOH = 4, + + /** + * A device array to device array memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_ATOA = 5, + + /** + * A device array to device memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_ATOD = 6, + + /** + * A device to device array memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_DTOA = 7, + + /** + * A device to device memory copy on the same device. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_DTOD = 8, + + /** + * A host to host memory copy. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_HTOH = 9, + + /** + * A peer to peer memory copy across different devices. + */ + CUPTI_ACTIVITY_MEMCPY_KIND_PTOP = 10, + + CUPTI_ACTIVITY_MEMCPY_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityMemcpyKind; + +/** + * \brief The kinds of memory accessed by a memory operation/copy. + * + * Each kind represents the type of the memory + * accessed by a memory operation/copy. + */ +typedef enum { + /** + * The memory kind is unknown. + */ + CUPTI_ACTIVITY_MEMORY_KIND_UNKNOWN = 0, + + /** + * The memory is pageable. + */ + CUPTI_ACTIVITY_MEMORY_KIND_PAGEABLE = 1, + + /** + * The memory is pinned. + */ + CUPTI_ACTIVITY_MEMORY_KIND_PINNED = 2, + + /** + * The memory is on the device. + */ + CUPTI_ACTIVITY_MEMORY_KIND_DEVICE = 3, + + /** + * The memory is an array. + */ + CUPTI_ACTIVITY_MEMORY_KIND_ARRAY = 4, + + /** + * The memory is managed + */ + CUPTI_ACTIVITY_MEMORY_KIND_MANAGED = 5, + + /** + * The memory is device static + */ + CUPTI_ACTIVITY_MEMORY_KIND_DEVICE_STATIC = 6, + + /** + * The memory is managed static + */ + CUPTI_ACTIVITY_MEMORY_KIND_MANAGED_STATIC = 7, + + CUPTI_ACTIVITY_MEMORY_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityMemoryKind; + +/** + * \brief The kind of a preemption activity. + */ +typedef enum { + /** + * The preemption kind is not known. + */ + CUPTI_ACTIVITY_PREEMPTION_KIND_UNKNOWN = 0, + + /** + * Preemption to save CDP block. + */ + CUPTI_ACTIVITY_PREEMPTION_KIND_SAVE = 1, + + /** + * Preemption to restore CDP block. + */ + CUPTI_ACTIVITY_PREEMPTION_KIND_RESTORE = 2, + + CUPTI_ACTIVITY_PREEMPTION_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityPreemptionKind; + +/** + * \brief The kind of environment data. Used to indicate what type of + * data is being reported by an environment activity record. + */ +typedef enum { + /** + * Unknown data. + */ + CUPTI_ACTIVITY_ENVIRONMENT_UNKNOWN = 0, + + /** + * The environment data is related to speed. + */ + CUPTI_ACTIVITY_ENVIRONMENT_SPEED = 1, + + /** + * The environment data is related to temperature. + */ + CUPTI_ACTIVITY_ENVIRONMENT_TEMPERATURE = 2, + + /** + * The environment data is related to power. + */ + CUPTI_ACTIVITY_ENVIRONMENT_POWER = 3, + + /** + * The environment data is related to cooling. + */ + CUPTI_ACTIVITY_ENVIRONMENT_COOLING = 4, + + CUPTI_ACTIVITY_ENVIRONMENT_COUNT, + + CUPTI_ACTIVITY_ENVIRONMENT_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityEnvironmentKind; + +/** + * \brief Reasons for clock throttling. + * + * The possible reasons that a clock can be throttled. There can be + * more than one reason that a clock is being throttled so these types + * can be combined by bitwise OR. These are used in the + * clocksThrottleReason field in the Environment Activity Record. + */ +typedef enum { + /** + * Nothing is running on the GPU and the clocks are dropping to idle + * state. + */ + CUPTI_CLOCKS_THROTTLE_REASON_GPU_IDLE = 0x00000001, + + /** + * The GPU clocks are limited by a user specified limit. + */ + CUPTI_CLOCKS_THROTTLE_REASON_USER_DEFINED_CLOCKS = 0x00000002, + + /** + * A software power scaling algorithm is reducing the clocks below + * requested clocks. + */ + CUPTI_CLOCKS_THROTTLE_REASON_SW_POWER_CAP = 0x00000004, + + /** + * Hardware slowdown to reduce the clock by a factor of two or more + * is engaged. This is an indicator of one of the following: 1) + * Temperature is too high, 2) External power brake assertion is + * being triggered (e.g. by the system power supply), 3) Change in + * power state. + */ + CUPTI_CLOCKS_THROTTLE_REASON_HW_SLOWDOWN = 0x00000008, + + /** + * Some unspecified factor is reducing the clocks. + */ + CUPTI_CLOCKS_THROTTLE_REASON_UNKNOWN = 0x80000000, + + /** + * Throttle reason is not supported for this GPU. + */ + CUPTI_CLOCKS_THROTTLE_REASON_UNSUPPORTED = 0x40000000, + + /** + * No clock throttling. + */ + CUPTI_CLOCKS_THROTTLE_REASON_NONE = 0x00000000, + + CUPTI_CLOCKS_THROTTLE_REASON_FORCE_INT = 0x7fffffff +} CUpti_EnvironmentClocksThrottleReason; + +/** + * \brief Scope of the unified memory counter (deprecated in CUDA 7.0) + */ +typedef enum { + /** + * The unified memory counter scope is not known. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_SCOPE_UNKNOWN = 0, + + /** + * Collect unified memory counter for single process on one device + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_SCOPE_PROCESS_SINGLE_DEVICE = 1, + + /** + * Collect unified memory counter for single process across all devices + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_SCOPE_PROCESS_ALL_DEVICES = 2, + + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_SCOPE_COUNT, + + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_SCOPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityUnifiedMemoryCounterScope; + +/** + * \brief Kind of the Unified Memory counter + * + * Many activities are associated with Unified Memory mechanism; among them + * are transfers from host to device, device to host, page fault at + * host side. + */ +typedef enum { + /** + * The unified memory counter kind is not known. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_UNKNOWN = 0, + + /** + * Number of bytes transferred from host to device + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD = 1, + + /** + * Number of bytes transferred from device to host + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOH = 2, + + /** + * Number of CPU page faults, this is only supported on 64 bit + * Linux and Mac platforms + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT = 3, + + /** + * Number of GPU page faults, this is only supported on devices with + * compute capability 6.0 and higher and 64 bit Linux platforms + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT = 4, + + /** + * Thrashing occurs when data is frequently accessed by + * multiple processors and has to be constantly migrated around + * to achieve data locality. In this case the overhead of migration + * may exceed the benefits of locality. + * This is only supported on 64 bit Linux platforms. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING = 5, + + /** + * Throttling is a prevention technique used by the driver to avoid + * further thrashing. Here, the driver doesn't service the fault for + * one of the contending processors for a specific period of time, + * so that the other processor can run at full-speed. + * This is only supported on 64 bit Linux platforms. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING = 6, + + /** + * In case throttling does not help, the driver tries to pin the memory + * to a processor for a specific period of time. One of the contending + * processors will have slow access to the memory, while the other will + * have fast access. + * This is only supported on 64 bit Linux platforms. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP = 7, + + /** + * Number of bytes transferred from one device to another device. + * This is only supported on 64 bit Linux platforms. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOD = 8, + + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_COUNT, + + CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityUnifiedMemoryCounterKind; + +/** + * \brief Memory access type for unified memory page faults + * + * This is valid for \ref CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT + * and \ref CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT + */ +typedef enum { + /** + * The unified memory access type is not known + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_ACCESS_TYPE_UNKNOWN = 0, + + /** + * The page fault was triggered by read memory instruction + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_ACCESS_TYPE_READ = 1, + + /** + * The page fault was triggered by write memory instruction + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_ACCESS_TYPE_WRITE = 2, + + /** + * The page fault was triggered by atomic memory instruction + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_ACCESS_TYPE_ATOMIC = 3, + + /** + * The page fault was triggered by memory prefetch operation + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_ACCESS_TYPE_PREFETCH = 4 +} CUpti_ActivityUnifiedMemoryAccessType; + +/** + * \brief Migration cause of the Unified Memory counter + * + * This is valid for \ref CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD and + * \ref CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOH + */ +typedef enum { + /** + * The unified memory migration cause is not known + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_UNKNOWN = 0, + + /** + * The unified memory migrated due to an explicit call from + * the user e.g. cudaMemPrefetchAsync + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_USER = 1, + + /** + * The unified memory migrated to guarantee data coherence + * e.g. CPU/GPU faults on Pascal+ and kernel launch on pre-Pascal GPUs + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_COHERENCE = 2, + + /** + * The unified memory was speculatively migrated by the UVM driver + * before being accessed by the destination processor to improve + * performance + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_PREFETCH = 3, + + /** + * The unified memory migrated to the CPU because it was evicted to make + * room for another block of memory on the GPU + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_EVICTION = 4, + + /** + * The unified memory migrated to another processor because of access counter + * notifications. Only frequently accessed pages are migrated between CPU and GPU, or + * between peer GPUs. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_MIGRATION_CAUSE_ACCESS_COUNTERS = 5, +} CUpti_ActivityUnifiedMemoryMigrationCause; + +/** + * \brief Remote memory map cause of the Unified Memory counter + * + * This is valid for \ref CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP + */ +typedef enum { + /** + * The cause of mapping to remote memory was unknown + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_UNKNOWN = 0, + + /** + * Mapping to remote memory was added to maintain data coherence. + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_COHERENCE = 1, + + /** + * Mapping to remote memory was added to prevent further thrashing + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_THRASHING = 2, + + /** + * Mapping to remote memory was added to enforce the hints + * specified by the programmer or by performance heuristics of the + * UVM driver + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_POLICY = 3, + + /** + * Mapping to remote memory was added because there is no more + * memory available on the processor and eviction was not + * possible + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_OUT_OF_MEMORY = 4, + + /** + * Mapping to remote memory was added after the memory was + * evicted to make room for another block of memory on the GPU + */ + CUPTI_ACTIVITY_UNIFIED_MEMORY_REMOTE_MAP_CAUSE_EVICTION = 5, +} CUpti_ActivityUnifiedMemoryRemoteMapCause; + +/** + * \brief SASS instruction classification. + * + * The sass instruction are broadly divided into different class. Each enum represents a classification. + */ +typedef enum { + /** + * The instruction class is not known. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_UNKNOWN = 0, + + /** + * Represents a 32 bit floating point operation. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_FP_32 = 1, + + /** + * Represents a 64 bit floating point operation. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_FP_64 = 2, + + /** + * Represents an integer operation. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_INTEGER = 3, + + /** + * Represents a bit conversion operation. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_BIT_CONVERSION = 4, + + /** + * Represents a control flow instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_CONTROL_FLOW = 5, + + /** + * Represents a global load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_GLOBAL = 6, + + /** + * Represents a shared load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_SHARED = 7, + + /** + * Represents a local load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_LOCAL = 8, + + /** + * Represents a generic load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_GENERIC = 9, + + /** + * Represents a surface load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_SURFACE = 10, + + /** + * Represents a constant load instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_CONSTANT = 11, + + /** + * Represents a texture load-store instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_TEXTURE = 12, + + /** + * Represents a global atomic instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_GLOBAL_ATOMIC = 13, + + /** + * Represents a shared atomic instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_SHARED_ATOMIC = 14, + + /** + * Represents a surface atomic instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_SURFACE_ATOMIC = 15, + + /** + * Represents a inter-thread communication instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_INTER_THREAD_COMMUNICATION = 16, + + /** + * Represents a barrier instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_BARRIER = 17, + + /** + * Represents some miscellaneous instructions which do not fit in the above classification. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_MISCELLANEOUS = 18, + + /** + * Represents a 16 bit floating point operation. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_FP_16 = 19, + + /** + * Represents uniform instruction. + */ + CUPTI_ACTIVITY_INSTRUCTION_CLASS_UNIFORM = 20, + + CUPTI_ACTIVITY_INSTRUCTION_CLASS_KIND_FORCE_INT = 0x7fffffff +} CUpti_ActivityInstructionClass; + +/** + * \brief Partitioned global caching option + */ +typedef enum { + /** + * Partitioned global cache config unknown. + */ + CUPTI_ACTIVITY_PARTITIONED_GLOBAL_CACHE_CONFIG_UNKNOWN = 0, + + /** + * Partitioned global cache not supported. + */ + CUPTI_ACTIVITY_PARTITIONED_GLOBAL_CACHE_CONFIG_NOT_SUPPORTED = 1, + + /** + * Partitioned global cache config off. + */ + CUPTI_ACTIVITY_PARTITIONED_GLOBAL_CACHE_CONFIG_OFF = 2, + + /** + * Partitioned global cache config on. + */ + CUPTI_ACTIVITY_PARTITIONED_GLOBAL_CACHE_CONFIG_ON = 3, + + CUPTI_ACTIVITY_PARTITIONED_GLOBAL_CACHE_CONFIG_FORCE_INT = 0x7fffffff +} CUpti_ActivityPartitionedGlobalCacheConfig; + +/** + * \brief Synchronization type. + * + * The types of synchronization to be used with CUpti_ActivitySynchronization. + */ + +typedef enum { + /** + * Unknown data. + */ + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_UNKNOWN = 0, + + /** + * Event synchronize API. + */ + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_EVENT_SYNCHRONIZE = 1, + + /** + * Stream wait event API. + */ + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_STREAM_WAIT_EVENT = 2, + + /** + * Stream synchronize API. + */ + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_STREAM_SYNCHRONIZE = 3, + + /** + * Context synchronize API. + */ + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_CONTEXT_SYNCHRONIZE = 4, + + CUPTI_ACTIVITY_SYNCHRONIZATION_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivitySynchronizationType; + +/** + * \brief stream type. + * + * The types of stream to be used with CUpti_ActivityStream. + */ + +typedef enum { + /** + * Unknown data. + */ + CUPTI_ACTIVITY_STREAM_CREATE_FLAG_UNKNOWN = 0, + + /** + * Default stream. + */ + CUPTI_ACTIVITY_STREAM_CREATE_FLAG_DEFAULT = 1, + + /** + * Non-blocking stream. + */ + CUPTI_ACTIVITY_STREAM_CREATE_FLAG_NON_BLOCKING = 2, + + /** + * Null stream. + */ + CUPTI_ACTIVITY_STREAM_CREATE_FLAG_NULL = 3, + + /** + * Stream create Mask + */ + CUPTI_ACTIVITY_STREAM_CREATE_MASK = 0xFFFF, + + CUPTI_ACTIVITY_STREAM_CREATE_FLAG_FORCE_INT = 0x7fffffff +} CUpti_ActivityStreamFlag; + +/** +* \brief Link flags. +* +* Describes link properties, to be used with CUpti_ActivityNvLink. +*/ + +typedef enum { + /** + * The flag is invalid. + */ + CUPTI_LINK_FLAG_INVALID = 0, + + /** + * Is peer to peer access supported by this link. + */ + CUPTI_LINK_FLAG_PEER_ACCESS = (1 << 1), + + /** + * Is system memory access supported by this link. + */ + CUPTI_LINK_FLAG_SYSMEM_ACCESS = (1 << 2), + + /** + * Is peer atomic access supported by this link. + */ + CUPTI_LINK_FLAG_PEER_ATOMICS = (1 << 3), + + /** + * Is system memory atomic access supported by this link. + */ + CUPTI_LINK_FLAG_SYSMEM_ATOMICS = (1 << 4), + + CUPTI_LINK_FLAG_FORCE_INT = 0x7fffffff +} CUpti_LinkFlag; + +/** +* \brief Memory operation types. +* +* Describes the type of memory operation, to be used with CUpti_ActivityMemory3. +*/ + +typedef enum { + /** + * The operation is invalid. + */ + CUPTI_ACTIVITY_MEMORY_OPERATION_TYPE_INVALID = 0, + + /** + * Memory is allocated. + */ + CUPTI_ACTIVITY_MEMORY_OPERATION_TYPE_ALLOCATION = 1, + + /** + * Memory is released. + */ + CUPTI_ACTIVITY_MEMORY_OPERATION_TYPE_RELEASE = 2, + + CUPTI_ACTIVITY_MEMORY_OPERATION_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityMemoryOperationType; + +/** +* \brief Memory pool types. +* +* Describes the type of memory pool, to be used with CUpti_ActivityMemory3. +*/ + +typedef enum { + /** + * The operation is invalid. + */ + CUPTI_ACTIVITY_MEMORY_POOL_TYPE_INVALID = 0, + + /** + * Memory pool is local to the process. + */ + CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL = 1, + + /** + * Memory pool is imported by the process. + */ + CUPTI_ACTIVITY_MEMORY_POOL_TYPE_IMPORTED = 2, + + CUPTI_ACTIVITY_MEMORY_POOL_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityMemoryPoolType; + +/** +* \brief Memory pool operation types. +* +* Describes the type of memory pool operation, to be used with CUpti_ActivityMemoryPool2. +*/ + +typedef enum { + /** + * The operation is invalid. + */ + CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_INVALID = 0, + + /** + * Memory pool is created. + */ + CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_CREATED = 1, + + /** + * Memory pool is destroyed. + */ + CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_DESTROYED = 2, + + /** + * Memory pool is trimmed. + */ + CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_TRIMMED = 3, + + CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityMemoryPoolOperationType; + +typedef enum { + CUPTI_CHANNEL_TYPE_INVALID = 0, + + CUPTI_CHANNEL_TYPE_COMPUTE = 1, + + CUPTI_CHANNEL_TYPE_ASYNC_MEMCPY = 2 +} CUpti_ChannelType; + +/** + * The source-locator ID that indicates an unknown source + * location. There is not an actual CUpti_ActivitySourceLocator object + * corresponding to this value. + */ +#define CUPTI_SOURCE_LOCATOR_ID_UNKNOWN 0 + +/** + * An invalid function index ID. + */ +#define CUPTI_FUNCTION_INDEX_ID_INVALID 0 + +/** + * An invalid/unknown correlation ID. A correlation ID of this value + * indicates that there is no correlation for the activity record. + */ +#define CUPTI_CORRELATION_ID_UNKNOWN 0 + +/** + * An invalid/unknown grid ID. + */ +#define CUPTI_GRID_ID_UNKNOWN 0LL + +/** + * An invalid/unknown timestamp for a start, end, queued, submitted, + * or completed time. + */ +#define CUPTI_TIMESTAMP_UNKNOWN 0LL + +/** + * An invalid/unknown value. + */ +#define CUPTI_SYNCHRONIZATION_INVALID_VALUE -1 + +/** + * An invalid/unknown process id. + */ +#define CUPTI_AUTO_BOOST_INVALID_CLIENT_PID 0 + +/** + * Invalid/unknown NVLink port number. +*/ +#define CUPTI_NVLINK_INVALID_PORT -1 + +/** + * Maximum NVLink port numbers. +*/ +#define CUPTI_MAX_NVLINK_PORTS 32 + +START_PACKED_ALIGNMENT +/** + * \brief Unified Memory counters configuration structure + * + * This structure controls the enable/disable of the various + * Unified Memory counters consisting of scope, kind and other parameters. + * See function \ref cuptiActivityConfigureUnifiedMemoryCounter + */ +typedef struct PACKED_ALIGNMENT { + /** + * Unified Memory counter Counter scope. (deprecated in CUDA 7.0) + */ + CUpti_ActivityUnifiedMemoryCounterScope scope; + + /** + * Unified Memory counter Counter kind + */ + CUpti_ActivityUnifiedMemoryCounterKind kind; + + /** + * Device id of the target device. This is relevant only + * for single device scopes. (deprecated in CUDA 7.0) + */ + uint32_t deviceId; + + /** + * Control to enable/disable the counter. To enable the counter + * set it to non-zero value while disable is indicated by zero. + */ + uint32_t enable; +} CUpti_ActivityUnifiedMemoryCounterConfig; + +/** + * \brief Device auto boost state structure + * + * This structure defines auto boost state for a device. + * See function \ref cuptiGetAutoBoostState + */ +typedef struct PACKED_ALIGNMENT { + /** + * Returned auto boost state. 1 is returned in case auto boost is enabled, 0 + * otherwise + */ + uint32_t enabled; + + /** + * Id of process that has set the current boost state. The value will be + * CUPTI_AUTO_BOOST_INVALID_CLIENT_PID if the user does not have the + * permission to query process ids or there is an error in querying the + * process id. + */ + uint32_t pid; + +} CUpti_ActivityAutoBoostState; + +/** + * \brief PC sampling configuration structure + * + * This structure defines the pc sampling configuration. + * + * See function \ref cuptiActivityConfigurePCSampling + */ +typedef struct PACKED_ALIGNMENT { + /** + * Size of configuration structure. + * CUPTI client should set the size of the structure. It will be used in CUPTI to check what fields are + * available in the structure. Used to preserve backward compatibility. + */ + uint32_t size; + + /** + * There are 5 level provided for sampling period. The level + * internally maps to a period in terms of cycles. Same level can + * map to different number of cycles on different gpus. No of + * cycles will be chosen to minimize information loss. The period + * chosen will be given by samplingPeriodInCycles in + * \ref CUpti_ActivityPCSamplingRecordInfo for each kernel instance. + */ + CUpti_ActivityPCSamplingPeriod samplingPeriod; + + /** + * This will override the period set by samplingPeriod. Value 0 in samplingPeriod2 will be + * considered as samplingPeriod2 should not be used and samplingPeriod should be used. + * Valid values for samplingPeriod2 are between 5 to 31 both inclusive. + * This will set the sampling period to (2^samplingPeriod2) cycles. + */ + uint32_t samplingPeriod2; +} CUpti_ActivityPCSamplingConfig; + +/** + * \brief The base activity record. + * + * The activity API uses a CUpti_Activity as a generic representation + * for any activity. The 'kind' field is used to determine the + * specific activity kind, and from that the CUpti_Activity object can + * be cast to the specific activity record type appropriate for that kind. + * + * Note that all activity record types are padded and aligned to + * ensure that each member of the record is naturally aligned. + * + * \see CUpti_ActivityKind + */ +typedef struct PACKED_ALIGNMENT { + /** + * The kind of this activity. + */ + CUpti_ActivityKind kind; +} CUpti_Activity; + +/** + * \brief The activity record for memory copies. + * + * This activity record represents a memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the memory copy. + */ + uint32_t correlationId; + + /** + * The runtime correlation ID of the memory copy. Each memory copy + * is assigned a unique runtime correlation ID that is identical to + * the correlation ID in the runtime API activity record that + * launched the memory copy. + */ + uint32_t runtimeCorrelationId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint32_t graphId; + + /** + * The ID of the HW channel on which the memory copy is occurring. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; + + /** + * Reserved for internal use. + */ + uint32_t pad2; +} CUpti_ActivityMemcpy5; + +/** + * \brief The activity record for peer-to-peer memory copies. + * + * This activity record represents a peer-to-peer memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY2). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY2. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see + * CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The ID of the device where memory is being copied from. + */ + uint32_t srcDeviceId; + + /** + * The ID of the context owning the memory being copied from. + */ + uint32_t srcContextId; + + /** + * The ID of the device where memory is being copied to. + */ + uint32_t dstDeviceId; + + /** + * The ID of the context owning the memory being copied to. + */ + uint32_t dstContextId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory copy. + */ + uint32_t correlationId; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed the memcpy through graph launch. + * This field will be 0 if memcpy is not done using graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint32_t graphId; + + /** + * The ID of the HW channel on which the memory copy is occurring. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; +} CUpti_ActivityMemcpyPtoP4; + +/** + * \brief The activity record for memset. + * + * This activity record represents a memory set operation + * (CUPTI_ACTIVITY_KIND_MEMSET). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMSET. + */ + CUpti_ActivityKind kind; + + /** + * The value being assigned to memory by the memory set. + */ + uint32_t value; + + /** + * The number of bytes being set by the memory set. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t start; + + /** + * The end timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t end; + + /** + * The ID of the device where the memory set is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory set is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory set is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory set. Each memory set is assigned + * a unique correlation ID that is identical to the correlation ID + * in the driver API activity record that launched the memory set. + */ + uint32_t correlationId; + + /** + * The flags associated with the memset. \see CUpti_ActivityFlag + */ + uint16_t flags; + + /** + * The memory kind of the memory set \see CUpti_ActivityMemoryKind + */ + uint16_t memoryKind; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memset through graph launch. + * This field will be 0 if the memset is not executed through graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memset through graph launch. + * This field will be 0 if the memset is not executed through graph launch. + */ + uint32_t graphId; + + /** + * The ID of the HW channel on which the memory set is occurring. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; + + /** + * Undefined. Reserved for internal use + */ + uint32_t pad2; +} CUpti_ActivityMemset4; + +/** + * \brief The activity record for memory. + * + * This activity record represents a memory allocation and free operation + * (CUPTI_ACTIVITY_KIND_MEMORY). + * This activity record provides a single record for the memory + * allocation and memory release operations. + * + * Note: It is recommended to move to the new activity record \ref CUpti_ActivityMemory3 + * enabled using the kind \ref CUPTI_ACTIVITY_KIND_MEMORY2. + * \ref CUpti_ActivityMemory3 provides separate records for memory + * allocation and memory release operations. This allows to correlate the + * corresponding driver and runtime API activity record with the memory operation. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMORY + */ + CUpti_ActivityKind kind; + + /** + * The memory kind requested by the user + */ + CUpti_ActivityMemoryKind memoryKind; + + /** + * The virtual address of the allocation + */ + uint64_t address; + + /** + * The number of bytes of memory allocated. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory operation, i.e. + * the time when memory was allocated, in ns. + */ + uint64_t start; + + /** + * The end timestamp for the memory operation, i.e. + * the time when memory was freed, in ns. + * This will be 0 if memory is not freed in the application + */ + uint64_t end; + + /** + * The program counter of the allocation of memory + */ + uint64_t allocPC; + + /** + * The program counter of the freeing of memory. This will + * be 0 if memory is not freed in the application + */ + uint64_t freePC; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The ID of the device where the memory allocation is taking place. + */ + uint32_t deviceId; + + /** + * The ID of the context. If context is NULL, \p contextId is set to CUPTI_INVALID_CONTEXT_ID. + */ + uint32_t contextId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Variable name. This name is shared across all activity + * records representing the same symbol, and so should not be + * modified. + */ + const char* name; +} CUpti_ActivityMemory; + +/** + * \brief The activity record for memory. + * + * This activity record represents a memory allocation and free operation + * (CUPTI_ACTIVITY_KIND_MEMORY2). + * This activity record provides separate records for memory allocation and + * memory release operations. + * This allows to correlate the corresponding driver and runtime API + * activity record with the memory operation. + * + * Note: This activity record is an upgrade over \ref CUpti_ActivityMemory + * enabled using the kind \ref CUPTI_ACTIVITY_KIND_MEMORY. + * \ref CUpti_ActivityMemory provides a single record for the memory + * allocation and memory release operations. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMORY2 + */ + CUpti_ActivityKind kind; + + /** + * The memory operation requested by the user, \ref CUpti_ActivityMemoryOperationType. + */ + CUpti_ActivityMemoryOperationType memoryOperationType; + + /** + * The memory kind requested by the user, \ref CUpti_ActivityMemoryKind. + */ + CUpti_ActivityMemoryKind memoryKind; + + /** + * The correlation ID of the memory operation. Each memory operation is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory operation. + */ + uint32_t correlationId; + + /** + * The virtual address of the allocation. + */ + uint64_t address; + + /** + * The number of bytes of memory allocated. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory operation, in ns. + */ + uint64_t timestamp; + + /** + * The program counter of the memory operation. + */ + uint64_t PC; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The ID of the device where the memory operation is taking place. + */ + uint32_t deviceId; + + /** + * The ID of the context. If context is NULL, \p contextId is set to CUPTI_INVALID_CONTEXT_ID. + */ + uint32_t contextId; + + /** + * The ID of the stream. If memory operation is not async, \p streamId is set to CUPTI_INVALID_STREAM_ID. + */ + uint32_t streamId; + + /** + * Variable name. This name is shared across all activity + * records representing the same symbol, and so should not be + * modified. + */ + const char* name; + + /** + * \p isAsync is set if memory operation happens through async memory APIs. + */ + uint32_t isAsync; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad1; +#endif + + /** + * The memory pool configuration used for the memory operations. + */ + struct PACKED_ALIGNMENT { + /** + * The type of the memory pool, \ref CUpti_ActivityMemoryPoolType + */ + CUpti_ActivityMemoryPoolType memoryPoolType; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad2; +#endif + + /** + * The base address of the memory pool. + */ + uint64_t address; + + /** + * The release threshold of the memory pool in bytes. \p releaseThreshold is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t releaseThreshold; + + /** + * The size of memory pool in bytes and the processId of the memory pools + * \p size is valid if \p memoryPoolType is + * CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + * \p processId is valid if \p memoryPoolType is + * CUPTI_ACTIVITY_MEMORY_POOL_TYPE_IMPORTED, \ref CUpti_ActivityMemoryPoolType + */ + union { + uint64_t size; + uint64_t processId; + } pool; + + /** + * The utilized size of the memory pool. \p utilizedSize is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t utilizedSize; + } memoryPoolConfig; + +} CUpti_ActivityMemory3; + +/** + * \brief The activity record for memory pool. + * + * This activity record represents a memory pool creation, destruction and + * trimming (CUPTI_ACTIVITY_KIND_MEMORY_POOL). + * This activity record provides separate records for memory pool creation, + * destruction and trimming operations. + * This allows to correlate the corresponding driver and runtime API + * activity record with the memory pool operation. + * + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMORY_POOL + */ + CUpti_ActivityKind kind; + + /** + * The memory operation requested by the user, \ref CUpti_ActivityMemoryPoolOperationType. + */ + CUpti_ActivityMemoryPoolOperationType memoryPoolOperationType; + + /** + * The type of the memory pool, \ref CUpti_ActivityMemoryPoolType + */ + CUpti_ActivityMemoryPoolType memoryPoolType; + + /** + * The correlation ID of the memory pool operation. Each memory pool + * operation is assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory operation. + */ + uint32_t correlationId; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The ID of the device where the memory pool is created. + */ + uint32_t deviceId; + + /** + * The minimum bytes to keep of the memory pool. \p minBytesToKeep is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_TRIMMED, + * \ref CUpti_ActivityMemoryPoolOperationType + */ + size_t minBytesToKeep; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The virtual address of the allocation. + */ + uint64_t address; + + /** + * The size of the memory pool operation in bytes. \p size is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t size; + + /** + * The release threshold of the memory pool. \p releaseThreshold is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t releaseThreshold; + + /** + * The start timestamp for the memory operation, in ns. + */ + uint64_t timestamp; + + /** + * The utilized size of the memory pool. \p utilizedSize is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t utilizedSize; +} CUpti_ActivityMemoryPool2; + +/** + * \brief The type of the CUDA kernel launch. + */ +typedef enum { + /** + * The kernel was launched via a regular kernel call + */ + CUPTI_ACTIVITY_LAUNCH_TYPE_REGULAR = 0, + + /** + * The kernel was launched via API \ref cudaLaunchCooperativeKernel() or + * \ref cuLaunchCooperativeKernel() + */ + CUPTI_ACTIVITY_LAUNCH_TYPE_COOPERATIVE_SINGLE_DEVICE = 1, + + /** + * The kernel was launched via API \ref cudaLaunchCooperativeKernelMultiDevice() or + * \ref cuLaunchCooperativeKernelMultiDevice() + */ + CUPTI_ACTIVITY_LAUNCH_TYPE_COOPERATIVE_MULTI_DEVICE = 2, + + /** + * The kernel was launched as a CBL commandlist + */ + CUPTI_ACTIVITY_LAUNCH_TYPE_CBL_COMMANDLIST = 3, +} CUpti_ActivityLaunchType; + +/** + * \brief The shared memory limit per block config for a kernel + * This should be used to set 'cudaOccFuncShmemConfig' field in occupancy calculator API + */ +typedef enum { + /** The shared memory limit config is default + */ + CUPTI_FUNC_SHMEM_LIMIT_DEFAULT = 0x00, + + /** User has opted for a higher dynamic shared memory limit using function attribute + * 'cudaFuncAttributeMaxDynamicSharedMemorySize' for runtime API or + * CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES for driver API + */ + CUPTI_FUNC_SHMEM_LIMIT_OPTIN = 0x01, + + CUPTI_FUNC_SHMEM_LIMIT_FORCE_INT = 0x7fffffff +} CUpti_FuncShmemLimitConfig; + +/** + * \brief The activity record for kernel. + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes (deprecated in CUDA 11.8). + * Refer field localMemoryTotal_v2 + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; + + /** + * The unique ID of the graph node that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint64_t graphNodeId; + + /** + * The shared memory limit config for the kernel. This field shows whether user has opted for a + * higher per block limit of dynamic shared memory. + */ + CUpti_FuncShmemLimitConfig shmemLimitConfig; + + /** + * The unique ID of the graph that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint32_t graphId; + + /** + * The pointer to the access policy window. The structure CUaccessPolicyWindow is + * defined in cuda.h. + */ + CUaccessPolicyWindow *pAccessPolicyWindow; + + /** + * The ID of the HW channel on which the kernel is launched. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; + + /** + * The X-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterX; + + /** + * The Y-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterY; + + /** + * The Z-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterZ; + + /** + * The cluster scheduling policy for the kernel. Refer CUclusterSchedulingPolicy + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterSchedulingPolicy; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint64_t localMemoryTotal_v2; + + /** + * The maximum cluster size for the kernel + */ + uint32_t maxPotentialClusterSize; + + /** + * The maximum clusters that could co-exist on the target device for the kernel + */ + uint32_t maxActiveClusters; +} CUpti_ActivityKernel9; + +/** + * \brief The activity record for CDP (CUDA Dynamic Parallelism) + * kernel. + * + * This activity record represents a CDP kernel execution. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_CDP_KERNEL + */ + CUpti_ActivityKind kind; + + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel execution + * is assigned a unique grid ID. + */ + int64_t gridId; + + /** + * The grid ID of the parent kernel. + */ + int64_t parentGridId; + + /** + * The timestamp when kernel is queued up, in ns. A value of + * CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time is + * unknown. + */ + uint64_t queued; + + /** + * The timestamp when kernel is submitted to the gpu, in ns. A value + * of CUPTI_TIMESTAMP_UNKNOWN indicates that the submission time is + * unknown. + */ + uint64_t submitted; + + /** + * The timestamp when kernel is marked as completed, in ns. A value + * of CUPTI_TIMESTAMP_UNKNOWN indicates that the completion time is + * unknown. + */ + uint64_t completed; + + /** + * The X-dimension of the parent block. + */ + uint32_t parentBlockX; + + /** + * The Y-dimension of the parent block. + */ + uint32_t parentBlockY; + + /** + * The Z-dimension of the parent block. + */ + uint32_t parentBlockZ; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; +} CUpti_ActivityCdpKernel; + +/** + * \brief The activity record for a preemption of a CDP kernel. + * + * This activity record represents a preemption of a CDP kernel. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PREEMPTION + */ + CUpti_ActivityKind kind; + + /** + * kind of the preemption + */ + CUpti_ActivityPreemptionKind preemptionKind; + + /** + * The timestamp of the preemption, in ns. A value of 0 indicates + * that timestamp information could not be collected for the + * preemption. + */ + uint64_t timestamp; + + /** + * The grid-id of the block that is preempted + */ + int64_t gridId; + + /** + * The X-dimension of the block that is preempted + */ + uint32_t blockX; + + /** + * The Y-dimension of the block that is preempted + */ + uint32_t blockY; + + /** + * The Z-dimension of the block that is preempted + */ + uint32_t blockZ; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityPreemption; + +/** + * \brief The activity record for a driver or runtime API invocation. + * + * This activity record represents an invocation of a driver or + * runtime API (CUPTI_ACTIVITY_KIND_DRIVER and + * CUPTI_ACTIVITY_KIND_RUNTIME). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DRIVER, + * CUPTI_ACTIVITY_KIND_RUNTIME, or CUPTI_ACTIVITY_KIND_INTERNAL_LAUNCH_API. + */ + CUpti_ActivityKind kind; + + /** + * The ID of the driver or runtime function. + */ + CUpti_CallbackId cbid; + + /** + * The start timestamp for the function, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the function. + */ + uint64_t start; + + /** + * The end timestamp for the function, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the function. + */ + uint64_t end; + + /** + * The ID of the process where the driver or runtime CUDA function + * is executing. + */ + uint32_t processId; + + /** + * The ID of the thread where the driver or runtime CUDA function is + * executing. + */ + uint32_t threadId; + + /** + * The correlation ID of the driver or runtime CUDA function. Each + * function invocation is assigned a unique correlation ID that is + * identical to the correlation ID in the memcpy, memset, or kernel + * activity record that is associated with this function. + */ + uint32_t correlationId; + + /** + * The return value for the function. For a CUDA driver function + * with will be a CUresult value, and for a CUDA runtime function + * this will be a cudaError_t value. + */ + uint32_t returnValue; +} CUpti_ActivityAPI; + +/** + * \brief The activity record for a CUPTI event. + * + * This activity record represents a CUPTI event value + * (CUPTI_ACTIVITY_KIND_EVENT). This activity record kind is not + * produced by the activity API but is included for completeness and + * ease-of-use. Profile frameworks built on top of CUPTI that collect + * event data may choose to use this type to store the collected event + * data. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_EVENT. + */ + CUpti_ActivityKind kind; + + /** + * The event ID. + */ + CUpti_EventID id; + + /** + * The event value. + */ + uint64_t value; + + /** + * The event domain ID. + */ + CUpti_EventDomainID domain; + + /** + * The correlation ID of the event. Use of this ID is user-defined, + * but typically this ID value will equal the correlation ID of the + * kernel for which the event was gathered. + */ + uint32_t correlationId; +} CUpti_ActivityEvent; + +/** + * \brief The activity record for a CUPTI event with instance + * information. + * + * This activity record represents the a CUPTI event value for a + * specific event domain instance + * (CUPTI_ACTIVITY_KIND_EVENT_INSTANCE). This activity record kind is + * not produced by the activity API but is included for completeness + * and ease-of-use. Profile frameworks built on top of CUPTI that + * collect event data may choose to use this type to store the + * collected event data. This activity record should be used when + * event domain instance information needs to be associated with the + * event. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be + * CUPTI_ACTIVITY_KIND_EVENT_INSTANCE. + */ + CUpti_ActivityKind kind; + + /** + * The event ID. + */ + CUpti_EventID id; + + /** + * The event domain ID. + */ + CUpti_EventDomainID domain; + + /** + * The event domain instance. + */ + uint32_t instance; + + /** + * The event value. + */ + uint64_t value; + + /** + * The correlation ID of the event. Use of this ID is user-defined, + * but typically this ID value will equal the correlation ID of the + * kernel for which the event was gathered. + */ + uint32_t correlationId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityEventInstance; + +/** + * \brief The activity record for a CUPTI metric. + * + * This activity record represents the collection of a CUPTI metric + * value (CUPTI_ACTIVITY_KIND_METRIC). This activity record kind is not + * produced by the activity API but is included for completeness and + * ease-of-use. Profile frameworks built on top of CUPTI that collect + * metric data may choose to use this type to store the collected metric + * data. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_METRIC. + */ + CUpti_ActivityKind kind; + + /** + * The metric ID. + */ + CUpti_MetricID id; + + /** + * The metric value. + */ + CUpti_MetricValue value; + + /** + * The correlation ID of the metric. Use of this ID is user-defined, + * but typically this ID value will equal the correlation ID of the + * kernel for which the metric was gathered. + */ + uint32_t correlationId; + + /** + * The properties of this metric. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t pad[3]; +} CUpti_ActivityMetric; + +/** + * \brief The activity record for a CUPTI metric with instance + * information. + * + * This activity record represents a CUPTI metric value + * for a specific metric domain instance + * (CUPTI_ACTIVITY_KIND_METRIC_INSTANCE). This activity record kind + * is not produced by the activity API but is included for + * completeness and ease-of-use. Profile frameworks built on top of + * CUPTI that collect metric data may choose to use this type to store + * the collected metric data. This activity record should be used when + * metric domain instance information needs to be associated with the + * metric. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be + * CUPTI_ACTIVITY_KIND_METRIC_INSTANCE. + */ + CUpti_ActivityKind kind; + + /** + * The metric ID. + */ + CUpti_MetricID id; + + /** + * The metric value. + */ + CUpti_MetricValue value; + + /** + * The metric domain instance. + */ + uint32_t instance; + + /** + * The correlation ID of the metric. Use of this ID is user-defined, + * but typically this ID value will equal the correlation ID of the + * kernel for which the metric was gathered. + */ + uint32_t correlationId; + + /** + * The properties of this metric. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t pad[7]; +} CUpti_ActivityMetricInstance; + +/** + * \brief The activity record for source locator. + * + * This activity record represents a source locator + * (CUPTI_ACTIVITY_KIND_SOURCE_LOCATOR). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_SOURCE_LOCATOR. + */ + CUpti_ActivityKind kind; + + /** + * The ID for the source path, will be used in all the source level + * results. + */ + uint32_t id; + + /** + * The line number in the source . + */ + uint32_t lineNumber; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The path for the file. + */ + const char *fileName; +} CUpti_ActivitySourceLocator; + +/** + * \brief The activity record for source-level global + * access. + * + * This activity records the locations of the global + * accesses in the source (CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this global access. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * when at least one of thread among warp is active with predicate and condition code + * evaluating to true. + */ + uint32_t executed; + + /** + * The pc offset for the access. + */ + uint64_t pcOffset; + + /** + * This increments each time when this instruction is executed by number of + * threads that executed this instruction with predicate and condition code + * evaluating to true. + */ + uint64_t threadsExecuted; + + /** + * The total number of 32 bytes transactions to L2 cache generated by this + access + */ + uint64_t l2_transactions; + + /** + * The minimum number of L2 transactions possible based on the access pattern. + */ + uint64_t theoreticalL2Transactions; +} CUpti_ActivityGlobalAccess3; + +/** + * \brief The activity record for source level result + * branch. + * + * This activity record the locations of the branches in the + * source (CUPTI_ACTIVITY_KIND_BRANCH). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_BRANCH. + */ + CUpti_ActivityKind kind; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the branch. + */ + uint32_t pcOffset; + + /** + * Number of times this branch diverged + */ + uint32_t diverged; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction + */ + uint64_t threadsExecuted; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * regardless of predicate or condition code. + */ + uint32_t executed; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityBranch2; + +/** + * \brief The activity record for a device. (CUDA 11.6 onwards) + * + * This activity record represents information about a GPU device + * (CUPTI_ACTIVITY_KIND_DEVICE). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The global memory bandwidth available on the device, in + * kBytes/sec. + */ + uint64_t globalMemoryBandwidth; + + /** + * The amount of global memory on the device, in bytes. + */ + uint64_t globalMemorySize; + + /** + * The amount of constant memory on the device, in bytes. + */ + uint32_t constantMemorySize; + + /** + * The size of the L2 cache on the device, in bytes. + */ + uint32_t l2CacheSize; + + /** + * The number of threads per warp on the device. + */ + uint32_t numThreadsPerWarp; + + /** + * The core clock rate of the device, in kHz. + */ + uint32_t coreClockRate; + + /** + * Number of memory copy engines on the device. + */ + uint32_t numMemcpyEngines; + + /** + * Number of multiprocessors on the device. + */ + uint32_t numMultiprocessors; + + /** + * The maximum "instructions per cycle" possible on each device + * multiprocessor. + */ + uint32_t maxIPC; + + /** + * Maximum number of warps that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxWarpsPerMultiprocessor; + + /** + * Maximum number of blocks that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxBlocksPerMultiprocessor; + + /** + * Maximum amount of shared memory available per multiprocessor, in bytes. + */ + uint32_t maxSharedMemoryPerMultiprocessor; + + /** + * Maximum number of 32-bit registers available per multiprocessor. + */ + uint32_t maxRegistersPerMultiprocessor; + + /** + * Maximum number of registers that can be allocated to a block. + */ + uint32_t maxRegistersPerBlock; + + /** + * Maximum amount of shared memory that can be assigned to a block, + * in bytes. + */ + uint32_t maxSharedMemoryPerBlock; + + /** + * Maximum number of threads allowed in a block. + */ + uint32_t maxThreadsPerBlock; + + /** + * Maximum allowed X dimension for a block. + */ + uint32_t maxBlockDimX; + + /** + * Maximum allowed Y dimension for a block. + */ + uint32_t maxBlockDimY; + + /** + * Maximum allowed Z dimension for a block. + */ + uint32_t maxBlockDimZ; + + /** + * Maximum allowed X dimension for a grid. + */ + uint32_t maxGridDimX; + + /** + * Maximum allowed Y dimension for a grid. + */ + uint32_t maxGridDimY; + + /** + * Maximum allowed Z dimension for a grid. + */ + uint32_t maxGridDimZ; + + /** + * Compute capability for the device, major number. + */ + uint32_t computeCapabilityMajor; + + /** + * Compute capability for the device, minor number. + */ + uint32_t computeCapabilityMinor; + + /** + * The device ID. + */ + uint32_t id; + + /** + * ECC enabled flag for device + */ + uint32_t eccEnabled; + + /** + * The device UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid uuid; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The device name. This name is shared across all activity records + * representing instances of the device, and so should not be + * modified. + */ + const char *name; + + /** + * Flag to indicate whether the device is visible to CUDA. Users can + * set the device visibility using CUDA_VISIBLE_DEVICES environment + */ + uint8_t isCudaVisible; + + /** + * MIG enabled flag for device + */ + uint8_t isMigEnabled; + + uint8_t reserved[6]; + + /** + * GPU Instance id for MIG enabled devices. + * If mig mode is disabled value is set to UINT32_MAX + */ + uint32_t gpuInstanceId; + + /** + * Compute Instance id for MIG enabled devices. + * If mig mode is disabled value is set to UINT32_MAX + */ + uint32_t computeInstanceId; + + /** + * The MIG UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid migUuid; + + /** + * Numa (Non-uniform memory access) information for device + * GPU is a NUMA node or not + */ + uint32_t isNumaNode; + + /** + * Numa (Non-uniform memory access) information for device + * NUMA node ID of the GPU memory + * if GPU is not a NUMA node, it returns invalidNumaId + */ + uint32_t numaId; +} CUpti_ActivityDevice5; + +/** + * \brief The activity record for a device attribute. + * + * This activity record represents information about a GPU device: + * either a CUpti_DeviceAttribute or CUdevice_attribute value + * (CUPTI_ACTIVITY_KIND_DEVICE_ATTRIBUTE). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be + * CUPTI_ACTIVITY_KIND_DEVICE_ATTRIBUTE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The ID of the device that this attribute applies to. + */ + uint32_t deviceId; + + /** + * The attribute, either a CUpti_DeviceAttribute or + * CUdevice_attribute. Flag + * CUPTI_ACTIVITY_FLAG_DEVICE_ATTRIBUTE_CUDEVICE is used to indicate + * what kind of attribute this is. If + * CUPTI_ACTIVITY_FLAG_DEVICE_ATTRIBUTE_CUDEVICE is 1 then + * CUdevice_attribute field is value, otherwise + * CUpti_DeviceAttribute field is valid. + */ + union { + CUdevice_attribute cu; + CUpti_DeviceAttribute cupti; + } attribute; + + /** + * The value for the attribute. See CUpti_DeviceAttribute and + * CUdevice_attribute for the type of the value for a given + * attribute. + */ + union { + double vDouble; + uint32_t vUint32; + uint64_t vUint64; + int32_t vInt32; + int64_t vInt64; + } value; +} CUpti_ActivityDeviceAttribute; + +/** + * \brief The activity record for a context. + * + * This activity record represents information about a context + * (CUPTI_ACTIVITY_KIND_CONTEXT). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_CONTEXT. + */ + CUpti_ActivityKind kind; + + /** + * The context ID. + */ + uint32_t contextId; + + /** + * The device ID. + */ + uint32_t deviceId; + + /** + * The compute API kind. \see CUpti_ActivityComputeApiKind + */ + uint16_t computeApiKind; + + /** + * The ID for the NULL stream in this context + */ + uint16_t nullStreamId; + + /** + * The ID of the parent context. It would be 0 if + * context does not have parent + */ + uint32_t parentContextId; + + /** + * This field indicates whether the context is a green context + */ + uint8_t isGreenContext; + + uint8_t padding[3]; +} CUpti_ActivityContext2; + +/** + * \brief The activity record providing a name. + * + * This activity record provides a name for a device, context, thread, + * etc. and other resource naming done via NVTX APIs + * (CUPTI_ACTIVITY_KIND_NAME). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_NAME. + */ + CUpti_ActivityKind kind; + + /** + * The kind of activity object being named. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object. 'objectKind' indicates + * which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The name. + */ + const char *name; + +} CUpti_ActivityName; + +/** + * \brief The activity record providing a marker which is an + * instantaneous point in time. + * + * The marker is specified with a descriptive name and unique id + * (CUPTI_ACTIVITY_KIND_MARKER). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MARKER. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the marker. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The timestamp for the marker, in ns. A value of 0 indicates that + * timestamp information could not be collected for the marker. + */ + uint64_t timestamp; + + /** + * The marker ID. + */ + uint32_t id; + + /** + * The kind of activity object associated with this marker. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object associated with this + * marker. 'objectKind' indicates which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; + + + /** + * The marker name for an instantaneous or start marker. This will + * be NULL for an end marker. + */ + const char *name; + + /** + * The name of the domain to which this marker belongs to. + * This will be NULL for default domain. + */ + const char *domain; + +} CUpti_ActivityMarker2; + +/** + * \brief The activity record providing detailed information for a marker. + * + * The marker data contains color, payload, and category. + * (CUPTI_ACTIVITY_KIND_MARKER_DATA). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be + * CUPTI_ACTIVITY_KIND_MARKER_DATA. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the marker. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The marker ID. + */ + uint32_t id; + + /** + * Defines the payload format for the value associated with the marker. + */ + CUpti_MetricValueKind payloadKind; + + /** + * The payload value. + */ + CUpti_MetricValue payload; + + /** + * The color for the marker. + */ + uint32_t color; + + /** + * The category for the marker. + */ + uint32_t category; + +} CUpti_ActivityMarkerData; + +/** + * \brief The activity record for CUPTI and driver overheads. + * + * This activity record provides CUPTI and driver overhead information + * (CUPTI_ACTIVITY_OVERHEAD). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_OVERHEAD. + */ + CUpti_ActivityKind kind; + + /** + * The kind of overhead, CUPTI, DRIVER, COMPILER etc. + */ + CUpti_ActivityOverheadKind overheadKind; + + /** + * The kind of activity object that the overhead is associated with. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object. 'objectKind' indicates + * which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + + /** + * The start timestamp for the overhead, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the overhead. + */ + uint64_t start; + + /** + * The end timestamp for the overhead, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the overhead. + */ + uint64_t end; + + /** + * The correlation ID of the overhead operation to which + * records belong to. This ID is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the overhead operation. + * In some cases, it can be zero, such as for CUPTI_ACTIVITY_OVERHEAD_CUPTI_BUFFER_FLUSH records. + */ + uint32_t correlationId; + + /** + * Reserved for internal use. + */ + uint32_t reserved0; + + /** + * Pointer to the struct with additional details about the overhead. + * Refer CUpti_ActivityOverheadKind enum and the corresponding structure to typecast and access additional overhead data. + * Client is responsible for freeing this memory using the free function when done. + */ + void *overheadData; + +} CUpti_ActivityOverhead3; + +/** + * \brief The activity record for CUPTI environmental data. + * + * This activity record provides CUPTI environmental data, include + * power, clocks, and thermals. This information is sampled at + * various rates and returned in this activity record. The consumer + * of the record needs to check the environmentKind field to figure + * out what kind of environmental record this is. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_ENVIRONMENT. + */ + CUpti_ActivityKind kind; + + /** + * The ID of the device + */ + uint32_t deviceId; + + /** + * The timestamp when this sample was retrieved, in ns. A value of 0 + * indicates that timestamp information could not be collected for + * the marker. + */ + uint64_t timestamp; + + /** + * The kind of data reported in this record. + */ + CUpti_ActivityEnvironmentKind environmentKind; + + union { + /** + * Data returned for CUPTI_ACTIVITY_ENVIRONMENT_SPEED environment + * kind. + */ + struct { + /** + * The SM frequency in MHz + */ + uint32_t smClock; + + /** + * The memory frequency in MHz + */ + uint32_t memoryClock; + + /** + * The PCIe link generation. + */ + uint32_t pcieLinkGen; + + /** + * The PCIe link width. + */ + uint32_t pcieLinkWidth; + + /** + * The clocks throttle reasons. + */ + CUpti_EnvironmentClocksThrottleReason clocksThrottleReasons; + } speed; + + /** + * Data returned for CUPTI_ACTIVITY_ENVIRONMENT_TEMPERATURE + * environment kind. + */ + struct { + /** + * The GPU temperature in degrees C. + */ + uint32_t gpuTemperature; + } temperature; + + /** + * Data returned for CUPTI_ACTIVITY_ENVIRONMENT_POWER environment kind. + * The power in milliwatts consumed by GPU and associated circuitry. + * The power in milliwatts that will trigger power management algorithm. + */ + struct { + + uint32_t power; + uint32_t powerLimit; + } power; + + /** + * Data returned for CUPTI_ACTIVITY_ENVIRONMENT_COOLING + * environment kind. + */ + struct { + /** + * The fan speed as percentage of maximum. + */ + uint32_t fanSpeed; + } cooling; + } data; +} CUpti_ActivityEnvironment; + +/** + * \brief The activity record for source-level instruction execution. + * + * This activity records result for source level instruction execution. + * (CUPTI_ACTIVITY_KIND_INSTRUCTION_EXECUTION). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTRUCTION_EXECUTION. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this instruction execution. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the instruction. + */ + uint32_t pcOffset; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction, regardless of predicate or condition code. + */ + uint64_t threadsExecuted; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction with predicate and condition code evaluating to true. + */ + uint64_t notPredOffThreadsExecuted; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * regardless of predicate or condition code. + */ + uint32_t executed; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityInstructionExecution; + +/** + * \brief The activity record for PC sampling. + * + * This activity records information obtained by sampling PC + * (CUPTI_ACTIVITY_KIND_PC_SAMPLING). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PC_SAMPLING. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this instruction. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * Number of times the PC was sampled with the stallReason in the record. + * These samples indicate that no instruction was issued in that cycle from + * the warp scheduler from where the warp was sampled. + * Field is valid for devices with compute capability 6.0 and higher + */ + uint32_t latencySamples; + + /** + * Number of times the PC was sampled with the stallReason in the record. + * The same PC can be sampled with different stall reasons. The count includes + * latencySamples. + */ + uint32_t samples; + + /** + * Current stall reason. Includes one of the reasons from + * \ref CUpti_ActivityPCSamplingStallReason + */ + CUpti_ActivityPCSamplingStallReason stallReason; + + /** + * The pc offset for the instruction. + */ + uint64_t pcOffset; +} CUpti_ActivityPCSampling3; + +/** + * \brief The activity record for record status for PC sampling. + * + * This activity records information obtained by sampling PC + * (CUPTI_ACTIVITY_KIND_PC_SAMPLING_RECORD_INFO). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PC_SAMPLING_RECORD_INFO. + */ + CUpti_ActivityKind kind; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Number of times the PC was sampled for this kernel instance including all + * dropped samples. + */ + uint64_t totalSamples; + + /** + * Number of samples that were dropped by hardware due to backpressure/overflow. + */ + uint64_t droppedSamples; + /** + * Sampling period in terms of number of cycles . + */ + uint64_t samplingPeriodInCycles; +} CUpti_ActivityPCSamplingRecordInfo; + +/** + * \brief The activity record for Unified Memory counters (CUDA 7.0 and beyond) + * + * This activity record represents a Unified Memory counter + * (CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER + */ + CUpti_ActivityKind kind; + + /** + * The Unified Memory counter kind + */ + CUpti_ActivityUnifiedMemoryCounterKind counterKind; + + /** + * Value of the counter + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD, + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOH, + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THREASHING and + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP, it is the size of the + * memory region in bytes. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT, it + * is the number of page fault groups for the same page. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT, + * it is the program counter for the instruction that caused fault. + */ + uint64_t value; + + /** + * The start timestamp of the counter, in ns. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD and + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOH, timestamp is + * captured when activity starts on GPU. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT and + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT, timestamp is + * captured when CUDA driver started processing the fault. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING, timestamp + * is captured when CUDA driver detected thrashing of memory region. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING, + * timestamp is captured when throttling operation was started by CUDA driver. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP, + * timestamp is captured when CUDA driver has pushed all required operations + * to the processor specified by dstId. + */ + uint64_t start; + + /** + * The end timestamp of the counter, in ns. + * Ignore this field if counterKind is + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD and + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_DTOH, timestamp is + * captured when activity finishes on GPU. + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT, timestamp is + * captured when CUDA driver queues the replay of faulting memory accesses on the GPU + * For counterKind CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING, timestamp + * is captured when throttling operation was finished by CUDA driver + */ + uint64_t end; + + /** + * This is the virtual base address of the page/s being transferred. For cpu and + * gpu faults, the virtual address for the page that faulted. + */ + uint64_t address; + + /** + * The ID of the source CPU/device involved in the memory transfer, page fault, thrashing, + * throttling or remote map operation. For counterKind + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING, it is a bitwise ORing of the + * device IDs fighting for the memory region. Ignore this field if counterKind is + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT + */ + uint32_t srcId; + + /** + * The ID of the destination CPU/device involved in the memory transfer or remote map + * operation. Ignore this field if counterKind is + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_CPU_PAGE_FAULT_COUNT or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING + */ + uint32_t dstId; + + /** + * The ID of the stream causing the transfer. + * This value of this field is invalid. + */ + uint32_t streamId; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The flags associated with this record. See enums \ref CUpti_ActivityUnifiedMemoryAccessType + * if counterKind is CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_GPU_PAGE_FAULT + * and \ref CUpti_ActivityUnifiedMemoryMigrationCause if counterKind is + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_BYTES_TRANSFER_HTOD + * and \ref CUpti_ActivityUnifiedMemoryRemoteMapCause if counterKind is + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_REMOTE_MAP and \ref CUpti_ActivityFlag + * if counterKind is CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THRASHING or + * CUPTI_ACTIVITY_UNIFIED_MEMORY_COUNTER_KIND_THROTTLING + */ + uint32_t flags; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityUnifiedMemoryCounter2; + +/** + * \brief The activity record for global/device functions. + * + * This activity records function name and corresponding module + * information. + * (CUPTI_ACTIVITY_KIND_FUNCTION). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_FUNCTION. + */ + CUpti_ActivityKind kind; + + /** + * ID to uniquely identify the record + */ + uint32_t id; + + /** + * The ID of the context where the function is launched. + */ + uint32_t contextId; + + /** + * The module ID in which this global/device function is present. + */ + uint32_t moduleId; + + /** + * The function's unique symbol index in the module. + */ + uint32_t functionIndex; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The name of the function. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; +} CUpti_ActivityFunction; + +/** + * \brief The activity record for a CUDA module. + * + * This activity record represents a CUDA module + * (CUPTI_ACTIVITY_KIND_MODULE). This activity record kind is not + * produced by the activity API but is included for completeness and + * ease-of-use. Profile frameworks built on top of CUPTI that collect + * module data from the module callback may choose to use this type to + * store the collected module data. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MODULE. + */ + CUpti_ActivityKind kind; + + /** + * The ID of the context where the module is loaded. + */ + uint32_t contextId; + + /** + * The module ID. + */ + uint32_t id; + + /** + * The cubin size. + */ + uint32_t cubinSize; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The pointer to cubin. + */ + const void *cubin; +} CUpti_ActivityModule; + +/** + * \brief The activity record for source-level shared + * access. + * + * This activity records the locations of the shared + * accesses in the source + * (CUPTI_ACTIVITY_KIND_SHARED_ACCESS). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_SHARED_ACCESS. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this shared access. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the access. + */ + uint32_t pcOffset; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction with predicate and condition code evaluating to true. + */ + uint64_t threadsExecuted; + + /** + * The total number of shared memory transactions generated by this access + */ + uint64_t sharedTransactions; + + /** + * The minimum number of shared memory transactions possible based on the access pattern. + */ + uint64_t theoreticalSharedTransactions; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * when at least one of thread among warp is active with predicate and condition code + * evaluating to true. + */ + uint32_t executed; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivitySharedAccess; + +/** + * \brief The activity record for CUDA event. + * + * This activity is used to track recorded events. + * (CUPTI_ACTIVITY_KIND_CUDA_EVENT). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_CUDA_EVENT. + */ + CUpti_ActivityKind kind; + + /** + * The correlation ID of the API to which this result is associated. + */ + uint32_t correlationId; + + /** + * The ID of the context where the event was recorded. + */ + uint32_t contextId; + + /** + * The compute stream where the event was recorded. + */ + uint32_t streamId; + + /** + * A unique event ID to identify the event record. + */ + uint32_t eventId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityCudaEvent; + +/** + * \brief The activity record for CUDA stream. + * + * This activity is used to track created streams. + * (CUPTI_ACTIVITY_KIND_STREAM). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_STREAM. + */ + CUpti_ActivityKind kind; + /** + * The ID of the context where the stream was created. + */ + uint32_t contextId; + + /** + * A unique stream ID to identify the stream. + */ + uint32_t streamId; + + /** + * The clamped priority for the stream. + */ + uint32_t priority; + + /** + * Flags associated with the stream. + */ + CUpti_ActivityStreamFlag flag; + + /** + * The correlation ID of the API to which this result is associated. + */ + uint32_t correlationId; +} CUpti_ActivityStream; + +/** + * \brief The activity record for synchronization management. + * + * This activity is used to track various CUDA synchronization APIs. + * (CUPTI_ACTIVITY_KIND_SYNCHRONIZATION). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_SYNCHRONIZATION. + */ + CUpti_ActivityKind kind; + + /** + * The type of record. + */ + CUpti_ActivitySynchronizationType type; + + /** + * The start timestamp for the function, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the function. + */ + uint64_t start; + + /** + * The end timestamp for the function, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the function. + */ + uint64_t end; + + /** + * The correlation ID of the API to which this result is associated. + */ + uint32_t correlationId; + + /** + * The ID of the context for which the synchronization API is called. + * In case of context synchronization API it is the context id for which the API is called. + * In case of stream/event synchronization it is the ID of the context where the stream/event was created. + */ + uint32_t contextId; + + /** + * The compute stream for which the synchronization API is called. + * A CUPTI_SYNCHRONIZATION_INVALID_VALUE value indicate the field is not applicable for this record. + * Not valid for cuCtxSynchronize, cuEventSynchronize. + */ + uint32_t streamId; + + /** + * The event ID for which the synchronization API is called. + * A CUPTI_SYNCHRONIZATION_INVALID_VALUE value indicate the field is not applicable for this record. + * Not valid for cuCtxSynchronize, cuStreamSynchronize. + */ + uint32_t cudaEventId; +} CUpti_ActivitySynchronization; + +/** + * \brief The activity record for source-level sass/source + * line-by-line correlation. + * + * This activity records source level sass/source correlation + * information. + * (CUPTI_ACTIVITY_KIND_INSTRUCTION_CORRELATION). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTRUCTION_CORRELATION. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this instruction. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the instruction. + */ + uint32_t pcOffset; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityInstructionCorrelation; + +/** + * \brief The OpenAcc event kind for OpenAcc activity records. + * + * \see CUpti_ActivityKindOpenAcc + */ +typedef enum { + CUPTI_OPENACC_EVENT_KIND_INVALID = 0, + CUPTI_OPENACC_EVENT_KIND_DEVICE_INIT = 1, + CUPTI_OPENACC_EVENT_KIND_DEVICE_SHUTDOWN = 2, + CUPTI_OPENACC_EVENT_KIND_RUNTIME_SHUTDOWN = 3, + CUPTI_OPENACC_EVENT_KIND_ENQUEUE_LAUNCH = 4, + CUPTI_OPENACC_EVENT_KIND_ENQUEUE_UPLOAD = 5, + CUPTI_OPENACC_EVENT_KIND_ENQUEUE_DOWNLOAD = 6, + CUPTI_OPENACC_EVENT_KIND_WAIT = 7, + CUPTI_OPENACC_EVENT_KIND_IMPLICIT_WAIT = 8, + CUPTI_OPENACC_EVENT_KIND_COMPUTE_CONSTRUCT = 9, + CUPTI_OPENACC_EVENT_KIND_UPDATE = 10, + CUPTI_OPENACC_EVENT_KIND_ENTER_DATA = 11, + CUPTI_OPENACC_EVENT_KIND_EXIT_DATA = 12, + CUPTI_OPENACC_EVENT_KIND_CREATE = 13, + CUPTI_OPENACC_EVENT_KIND_DELETE = 14, + CUPTI_OPENACC_EVENT_KIND_ALLOC = 15, + CUPTI_OPENACC_EVENT_KIND_FREE = 16, + CUPTI_OPENACC_EVENT_KIND_FORCE_INT = 0x7fffffff +} CUpti_OpenAccEventKind; + +/** + * \brief The OpenAcc parent construct kind for OpenAcc activity records. + */ +typedef enum { + CUPTI_OPENACC_CONSTRUCT_KIND_UNKNOWN = 0, + CUPTI_OPENACC_CONSTRUCT_KIND_PARALLEL = 1, + CUPTI_OPENACC_CONSTRUCT_KIND_KERNELS = 2, + CUPTI_OPENACC_CONSTRUCT_KIND_LOOP = 3, + CUPTI_OPENACC_CONSTRUCT_KIND_DATA = 4, + CUPTI_OPENACC_CONSTRUCT_KIND_ENTER_DATA = 5, + CUPTI_OPENACC_CONSTRUCT_KIND_EXIT_DATA = 6, + CUPTI_OPENACC_CONSTRUCT_KIND_HOST_DATA = 7, + CUPTI_OPENACC_CONSTRUCT_KIND_ATOMIC = 8, + CUPTI_OPENACC_CONSTRUCT_KIND_DECLARE = 9, + CUPTI_OPENACC_CONSTRUCT_KIND_INIT = 10, + CUPTI_OPENACC_CONSTRUCT_KIND_SHUTDOWN = 11, + CUPTI_OPENACC_CONSTRUCT_KIND_SET = 12, + CUPTI_OPENACC_CONSTRUCT_KIND_UPDATE = 13, + CUPTI_OPENACC_CONSTRUCT_KIND_ROUTINE = 14, + CUPTI_OPENACC_CONSTRUCT_KIND_WAIT = 15, + CUPTI_OPENACC_CONSTRUCT_KIND_RUNTIME_API = 16, + CUPTI_OPENACC_CONSTRUCT_KIND_FORCE_INT = 0x7fffffff + +} CUpti_OpenAccConstructKind; + +typedef enum { + CUPTI_OPENMP_EVENT_KIND_INVALID = 0, + CUPTI_OPENMP_EVENT_KIND_PARALLEL = 1, + CUPTI_OPENMP_EVENT_KIND_TASK = 2, + CUPTI_OPENMP_EVENT_KIND_THREAD = 3, + CUPTI_OPENMP_EVENT_KIND_IDLE = 4, + CUPTI_OPENMP_EVENT_KIND_WAIT_BARRIER = 5, + CUPTI_OPENMP_EVENT_KIND_WAIT_TASKWAIT = 6, + CUPTI_OPENMP_EVENT_KIND_FORCE_INT = 0x7fffffff +} CUpti_OpenMpEventKind; + +/** + * \brief The base activity record for OpenAcc records. + * + * The OpenACC activity API part uses a CUpti_ActivityOpenAcc as a generic + * representation for any OpenACC activity. The 'kind' field is used to determine the + * specific activity kind, and from that the CUpti_ActivityOpenAcc object can + * be cast to the specific OpenACC activity record type appropriate for that kind. + * + * Note that all OpenACC activity record types are padded and aligned to + * ensure that each member of the record is naturally aligned. + * + * \see CUpti_ActivityKind + */ +typedef struct PACKED_ALIGNMENT { + /** + * The kind of this activity. + */ + CUpti_ActivityKind kind; + + /** + * CUPTI OpenACC event kind (\see CUpti_OpenAccEventKind) + */ + CUpti_OpenAccEventKind eventKind; + + /** + * CUPTI OpenACC parent construct kind (\see CUpti_OpenAccConstructKind) + * + * Note that for applications using PGI OpenACC runtime < 16.1, this + * will always be CUPTI_OPENACC_CONSTRUCT_KIND_UNKNOWN. + */ + CUpti_OpenAccConstructKind parentConstruct; + + /** + * Version number + */ + uint32_t version; + + /** + * 1 for any implicit event, such as an implicit wait at a synchronous data construct + * 0 otherwise + */ + uint32_t implicit; + + /** + * Device type + */ + uint32_t deviceType; + + /** + * Device number + */ + uint32_t deviceNumber; + + /** + * ThreadId + */ + uint32_t threadId; + + /** + * Value of async() clause of the corresponding directive + */ + uint64_t async; + + /** + * Internal asynchronous queue number used + */ + uint64_t asyncMap; + + /** + * The line number of the directive or program construct or the starting line + * number of the OpenACC construct corresponding to the event. + * A zero value means the line number is not known. + */ + uint32_t lineNo; + + /** + * For an OpenACC construct, this contains the line number of the end + * of the construct. A zero value means the line number is not known. + */ + uint32_t endLineNo; + + /** + * The line number of the first line of the function named in funcName. + * A zero value means the line number is not known. + */ + uint32_t funcLineNo; + + /** + * The last line number of the function named in funcName. + * A zero value means the line number is not known. + */ + uint32_t funcEndLineNo; + + /** + * CUPTI start timestamp + */ + uint64_t start; + + /** + * CUPTI end timestamp + */ + uint64_t end; + + /** + * CUDA device id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuDeviceId; + + /** + * CUDA context id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuContextId; + + /** + * CUDA stream id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuStreamId; + + /** + * The ID of the process where the OpenACC activity is executing. + */ + uint32_t cuProcessId; + + /** + * The ID of the thread where the OpenACC activity is executing. + */ + uint32_t cuThreadId; + + /** + * The OpenACC correlation ID. + * Valid only if deviceType is acc_device_nvidia. + * If not 0, it uniquely identifies this record. It is identical to the + * externalId in the preceding external correlation record of type + * CUPTI_EXTERNAL_CORRELATION_KIND_OPENACC. + */ + uint32_t externalId; + + /* + * A pointer to null-terminated string containing the name of or path to + * the source file, if known, or a null pointer if not. + */ + const char *srcFile; + + /* + * A pointer to a null-terminated string containing the name of the + * function in which the event occurred. + */ + const char *funcName; +} CUpti_ActivityOpenAcc; + +/** + * \brief The activity record for OpenACC data. + * + * (CUPTI_ACTIVITY_KIND_OPENACC_DATA). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_OPENACC_DATA. + */ + CUpti_ActivityKind kind; + + /** + * CUPTI OpenACC event kind (\see CUpti_OpenAccEventKind) + */ + CUpti_OpenAccEventKind eventKind; + + /* + * CUPTI OpenACC parent construct kind (\see CUpti_OpenAccConstructKind) + * + * Note that for applications using PGI OpenACC runtime < 16.1, this + * will always be CUPTI_OPENACC_CONSTRUCT_KIND_UNKNOWN. + */ + CUpti_OpenAccConstructKind parentConstruct; + + /* + * Version number + */ + uint32_t version; + + /* + * 1 for any implicit event, such as an implicit wait at a synchronous data construct + * 0 otherwise + */ + uint32_t implicit; + + /* + * Device type + */ + uint32_t deviceType; + + /* + * Device number + */ + uint32_t deviceNumber; + + /** + * ThreadId + */ + uint32_t threadId; + + /* + * Value of async() clause of the corresponding directive + */ + uint64_t async; + + /* + * Internal asynchronous queue number used + */ + uint64_t asyncMap; + + /* + * The line number of the directive or program construct or the starting line + * number of the OpenACC construct corresponding to the event. + * A negative or zero value means the line number is not known. + */ + uint32_t lineNo; + + /* + * For an OpenACC construct, this contains the line number of the end + * of the construct. A negative or zero value means the line number is not known. + */ + uint32_t endLineNo; + + /* + * The line number of the first line of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcLineNo; + + /* + * The last line number of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcEndLineNo; + + /** + * CUPTI start timestamp + */ + uint64_t start; + + /** + * CUPTI end timestamp + */ + uint64_t end; + + /** + * CUDA device id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuDeviceId; + + /** + * CUDA context id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuContextId; + + /** + * CUDA stream id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuStreamId; + + /** + * The ID of the process where the OpenACC activity is executing. + */ + uint32_t cuProcessId; + + /** + * The ID of the thread where the OpenACC activity is executing. + */ + uint32_t cuThreadId; + + /** + * The OpenACC correlation ID. + * Valid only if deviceType is acc_device_nvidia. + * If not 0, it uniquely identifies this record. It is identical to the + * externalId in the preceding external correlation record of type + * CUPTI_EXTERNAL_CORRELATION_KIND_OPENACC. + */ + uint32_t externalId; + + /* + * A pointer to null-terminated string containing the name of or path to + * the source file, if known, or a null pointer if not. + */ + const char *srcFile; + + /* + * A pointer to a null-terminated string containing the name of the + * function in which the event occurred. + */ + const char *funcName; + + /* --- end of common CUpti_ActivityOpenAcc part --- */ + + /** + * Number of bytes + */ + uint64_t bytes; + + /** + * Host pointer if available + */ + uint64_t hostPtr; + + /** + * Device pointer if available + */ + uint64_t devicePtr; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad1; +#endif + + /* + * A pointer to null-terminated string containing the name of the variable + * for which this event is triggered, if known, or a null pointer if not. + */ + const char *varName; + +} CUpti_ActivityOpenAccData; + +/** + * \brief The activity record for OpenACC launch. + * + * (CUPTI_ACTIVITY_KIND_OPENACC_LAUNCH). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_OPENACC_LAUNCH. + */ + CUpti_ActivityKind kind; + + /** + * CUPTI OpenACC event kind (\see CUpti_OpenAccEventKind) + */ + CUpti_OpenAccEventKind eventKind; + + /** + * CUPTI OpenACC parent construct kind (\see CUpti_OpenAccConstructKind) + * + * Note that for applications using PGI OpenACC runtime < 16.1, this + * will always be CUPTI_OPENACC_CONSTRUCT_KIND_UNKNOWN. + */ + CUpti_OpenAccConstructKind parentConstruct; + + /** + * Version number + */ + uint32_t version; + + /** + * 1 for any implicit event, such as an implicit wait at a synchronous data construct + * 0 otherwise + */ + uint32_t implicit; + + /** + * Device type + */ + uint32_t deviceType; + + /** + * Device number + */ + uint32_t deviceNumber; + + /** + * ThreadId + */ + uint32_t threadId; + + /** + * Value of async() clause of the corresponding directive + */ + uint64_t async; + + /** + * Internal asynchronous queue number used + */ + uint64_t asyncMap; + + /** + * The line number of the directive or program construct or the starting line + * number of the OpenACC construct corresponding to the event. + * A negative or zero value means the line number is not known. + */ + uint32_t lineNo; + + /** + * For an OpenACC construct, this contains the line number of the end + * of the construct. A negative or zero value means the line number is not known. + */ + uint32_t endLineNo; + + /** + * The line number of the first line of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcLineNo; + + /** + * The last line number of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcEndLineNo; + + /** + * CUPTI start timestamp + */ + uint64_t start; + + /** + * CUPTI end timestamp + */ + uint64_t end; + + /** + * CUDA device id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuDeviceId; + + /** + * CUDA context id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuContextId; + + /** + * CUDA stream id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuStreamId; + + /** + * The ID of the process where the OpenACC activity is executing. + */ + uint32_t cuProcessId; + + /** + * The ID of the thread where the OpenACC activity is executing. + */ + uint32_t cuThreadId; + + /** + * The OpenACC correlation ID. + * Valid only if deviceType is acc_device_nvidia. + * If not 0, it uniquely identifies this record. It is identical to the + * externalId in the preceding external correlation record of type + * CUPTI_EXTERNAL_CORRELATION_KIND_OPENACC. + */ + uint32_t externalId; + + /** + * A pointer to null-terminated string containing the name of or path to + * the source file, if known, or a null pointer if not. + */ + const char *srcFile; + + /** + * A pointer to a null-terminated string containing the name of the + * function in which the event occurred. + */ + const char *funcName; + + /* --- end of common CUpti_ActivityOpenAcc part --- */ + + /** + * The number of gangs created for this kernel launch + */ + uint64_t numGangs; + + /** + * The number of workers created for this kernel launch + */ + uint64_t numWorkers; + + /** + * The number of vector lanes created for this kernel launch + */ + uint64_t vectorLength; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad1; +#endif + + /** + * A pointer to null-terminated string containing the name of the + * kernel being launched, if known, or a null pointer if not. + */ + const char *kernelName; + +} CUpti_ActivityOpenAccLaunch; + +/** + * \brief The activity record for OpenACC other. + * + * (CUPTI_ACTIVITY_KIND_OPENACC_OTHER). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_OPENACC_OTHER. + */ + CUpti_ActivityKind kind; + + /** + * CUPTI OpenACC event kind (\see CUpti_OpenAccEventKind) + */ + CUpti_OpenAccEventKind eventKind; + + /** + * CUPTI OpenACC parent construct kind (\see CUpti_OpenAccConstructKind) + * + * Note that for applications using PGI OpenACC runtime < 16.1, this + * will always be CUPTI_OPENACC_CONSTRUCT_KIND_UNKNOWN. + */ + CUpti_OpenAccConstructKind parentConstruct; + + /** + * Version number + */ + uint32_t version; + + /** + * 1 for any implicit event, such as an implicit wait at a synchronous data construct + * 0 otherwise + */ + uint32_t implicit; + + /** + * Device type + */ + uint32_t deviceType; + + /** + * Device number + */ + uint32_t deviceNumber; + + /** + * ThreadId + */ + uint32_t threadId; + + /** + * Value of async() clause of the corresponding directive + */ + uint64_t async; + + /** + * Internal asynchronous queue number used + */ + uint64_t asyncMap; + + /** + * The line number of the directive or program construct or the starting line + * number of the OpenACC construct corresponding to the event. + * A negative or zero value means the line number is not known. + */ + uint32_t lineNo; + + /** + * For an OpenACC construct, this contains the line number of the end + * of the construct. A negative or zero value means the line number is not known. + */ + uint32_t endLineNo; + + /** + * The line number of the first line of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcLineNo; + + /** + * The last line number of the function named in func_name. + * A negative or zero value means the line number is not known. + */ + uint32_t funcEndLineNo; + + /** + * CUPTI start timestamp + */ + uint64_t start; + + /** + * CUPTI end timestamp + */ + uint64_t end; + + /** + * CUDA device id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuDeviceId; + + /** + * CUDA context id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuContextId; + + /** + * CUDA stream id + * Valid only if deviceType is acc_device_nvidia. + */ + uint32_t cuStreamId; + + /** + * The ID of the process where the OpenACC activity is executing. + */ + uint32_t cuProcessId; + + /** + * The ID of the thread where the OpenACC activity is executing. + */ + uint32_t cuThreadId; + + /** + * The OpenACC correlation ID. + * Valid only if deviceType is acc_device_nvidia. + * If not 0, it uniquely identifies this record. It is identical to the + * externalId in the preceding external correlation record of type + * CUPTI_EXTERNAL_CORRELATION_KIND_OPENACC. + */ + uint32_t externalId; + + /** + * A pointer to null-terminated string containing the name of or path to + * the source file, if known, or a null pointer if not. + */ + const char *srcFile; + + /** + * A pointer to a null-terminated string containing the name of the + * function in which the event occurred. + */ + const char *funcName; + + /* --- end of common CUpti_ActivityOpenAcc part --- */ +} CUpti_ActivityOpenAccOther; + +/** + * \brief The base activity record for OpenMp records. + * + * \see CUpti_ActivityKind + */ +typedef struct PACKED_ALIGNMENT { + + /** + * The kind of this activity. + */ + CUpti_ActivityKind kind; + + /** + * CUPTI OpenMP event kind (\see CUpti_OpenMpEventKind) + */ + CUpti_OpenMpEventKind eventKind; + + /** + * Version number + */ + uint32_t version; + + /** + * ThreadId + */ + uint32_t threadId; + + /** + * CUPTI start timestamp + */ + uint64_t start; + + /** + * CUPTI end timestamp + */ + uint64_t end; + + /** + * The ID of the process where the OpenMP activity is executing. + */ + uint32_t cuProcessId; + + /** + * The ID of the thread where the OpenMP activity is executing. + */ + uint32_t cuThreadId; +} CUpti_ActivityOpenMp; + +/** + * \brief The kind of external APIs supported for correlation. + * + * Custom correlation kinds are reserved for usage in external tools. + * + * \see CUpti_ActivityExternalCorrelation + */ +typedef enum { + CUPTI_EXTERNAL_CORRELATION_KIND_INVALID = 0, + + /** + * The external API is unknown to CUPTI + */ + CUPTI_EXTERNAL_CORRELATION_KIND_UNKNOWN = 1, + + /** + * The external API is OpenACC + */ + CUPTI_EXTERNAL_CORRELATION_KIND_OPENACC = 2, + + /** + * The external API is custom0 + */ + CUPTI_EXTERNAL_CORRELATION_KIND_CUSTOM0 = 3, + + /** + * The external API is custom1 + */ + CUPTI_EXTERNAL_CORRELATION_KIND_CUSTOM1 = 4, + + /** + * The external API is custom2 + */ + CUPTI_EXTERNAL_CORRELATION_KIND_CUSTOM2 = 5, + + /** + * Add new kinds before this line + */ + CUPTI_EXTERNAL_CORRELATION_KIND_SIZE, + + CUPTI_EXTERNAL_CORRELATION_KIND_FORCE_INT = 0x7fffffff +} CUpti_ExternalCorrelationKind; + +/** + * \brief The activity record for correlation with external records + * + * This activity record correlates native CUDA records (e.g. CUDA Driver API, + * kernels, memcpys, ...) with records from external APIs such as OpenACC. + * (CUPTI_ACTIVITY_KIND_EXTERNAL_CORRELATION). + * + * \see CUpti_ActivityKind + */ +typedef struct PACKED_ALIGNMENT { + /** + * The kind of this activity. + */ + CUpti_ActivityKind kind; + + /** + * The kind of external API this record correlated to. + */ + CUpti_ExternalCorrelationKind externalKind; + + /** + * The correlation ID of the associated non-CUDA API record. + * The exact field in the associated external record depends + * on that record's activity kind (\see externalKind). + */ + uint64_t externalId; + + /** + * The correlation ID of the associated CUDA driver or runtime API record. + */ + uint32_t correlationId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t reserved; +} CUpti_ActivityExternalCorrelation; + +/** +* \brief The device type for device connected to NVLink. +*/ +typedef enum { + CUPTI_DEV_TYPE_INVALID = 0, + + /** + * The device type is GPU. + */ + CUPTI_DEV_TYPE_GPU = 1, + + /** + * The device type is NVLink processing unit in CPU. + */ + CUPTI_DEV_TYPE_NPU = 2, + + CUPTI_DEV_TYPE_FORCE_INT = 0x7fffffff +} CUpti_DevType; + +/** +* \brief NVLink information. +* +* This structure gives capabilities of each logical NVLink connection between two devices, +* gpu<->gpu or gpu<->CPU which can be used to understand the topology. +*/ + +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_NVLINK. + */ + CUpti_ActivityKind kind; + + /** + * NvLink version. + */ + uint32_t nvlinkVersion; + + /** + * Type of device 0 \ref CUpti_DevType + */ + CUpti_DevType typeDev0; + + /** + * Type of device 1 \ref CUpti_DevType + */ + CUpti_DevType typeDev1; + + /** + * If typeDev0 is CUPTI_DEV_TYPE_GPU, UUID for device 0. \ref CUpti_ActivityDevice5. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev0; + + /** + * If typeDev1 is CUPTI_DEV_TYPE_GPU, UUID for device 1. \ref CUpti_ActivityDevice5. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev1; + + /** + * Flag gives capabilities of the link \see CUpti_LinkFlag + */ + uint32_t flag; + + /** + * Number of physical NVLinks present between two devices. + */ + uint32_t physicalNvLinkCount; + + /** + * Port numbers for maximum 32 NVLinks connected to device 0. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev0[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Port numbers for maximum 32 NVLinks connected to device 1. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev1[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Bandwidth of NVLink in kbytes/sec + */ + uint64_t bandwidth; + + /** + * NVSwitch is connected as an intermediate node. + */ + uint8_t nvswitchConnected; + + /** + * Undefined. reserved for internal use + */ + uint8_t pad[7]; +} CUpti_ActivityNvLink4; + +#define CUPTI_MAX_GPUS 32 +/** + * Field to differentiate whether PCIE Activity record + * is of a GPU or a PCI Bridge + */ +typedef enum { + /** + * PCIE GPU record + */ + CUPTI_PCIE_DEVICE_TYPE_GPU = 0, + + /** + * PCIE Bridge record + */ + CUPTI_PCIE_DEVICE_TYPE_BRIDGE = 1, + + CUPTI_PCIE_DEVICE_TYPE_FORCE_INT = 0x7fffffff +} CUpti_PcieDeviceType; + +/** + * \brief PCI devices information required to construct topology + * + * This structure gives capabilities of GPU and PCI bridge connected to the PCIE bus + * which can be used to understand the topology. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PCIE. + */ + CUpti_ActivityKind kind; + + /** + * Type of device in topology, \ref CUpti_PcieDeviceType. If type is + * CUPTI_PCIE_DEVICE_TYPE_GPU use devId for id and gpuAttr and if type is + * CUPTI_PCIE_DEVICE_TYPE_BRIDGE use bridgeId for id and bridgeAttr. + */ + CUpti_PcieDeviceType type; + + /** + * A unique identifier for GPU or Bridge in Topology + */ + union { + /** + * GPU device ID + */ + CUdevice devId; + + /** + * A unique identifier for Bridge in the Topology + */ + uint32_t bridgeId; + } id; + + /** + * Domain for the GPU or Bridge, required to identify which PCIE bus it belongs to in + * multiple NUMA systems. + */ + uint32_t domain; + + /** + * PCIE Generation of GPU or Bridge. + */ + uint16_t pcieGeneration; + + /** + * Link rate of the GPU or bridge in gigatransfers per second (GT/s) + */ + uint16_t linkRate; + + /** + * Link width of the GPU or bridge + */ + uint16_t linkWidth; + + /** + * Upstream bus ID for the GPU or PCI bridge. Required to identify which bus it is + * connected to in the topology. + */ + uint16_t upstreamBus; + + /** + * Attributes for more information about GPU (gpuAttr) or PCI Bridge (bridgeAttr) + */ + union { + struct { + /** + * UUID for the device. \ref CUpti_ActivityDevice5. + */ + CUuuid uuidDev; + + /** + * CUdevice with which this device has P2P capability. + * This can also be obtained by querying cuDeviceCanAccessPeer or + * cudaDeviceCanAccessPeer APIs + */ + CUdevice peerDev[CUPTI_MAX_GPUS]; + } gpuAttr; + + struct { + /** + * The downstream bus number, used to search downstream devices/bridges connected + * to this bridge. + */ + uint16_t secondaryBus; + + /** + * Device ID of the bridge + */ + uint16_t deviceId; + + /** + * Vendor ID of the bridge + */ + uint16_t vendorId; + + /** + * Padding for alignment + */ + uint16_t pad0; + } bridgeAttr; + } attr; +} CUpti_ActivityPcie; + +/** + * \brief PCIE Generation. + * + * Enumeration of PCIE Generation for + * pcie activity attribute pcieGeneration + */ +typedef enum { + /** + * PCIE Generation 1 + */ + CUPTI_PCIE_GEN_GEN1 = 1, + + /** + * PCIE Generation 2 + */ + CUPTI_PCIE_GEN_GEN2 = 2, + + /** + * PCIE Generation 3 + */ + CUPTI_PCIE_GEN_GEN3 = 3, + + /** + * PCIE Generation 4 + */ + CUPTI_PCIE_GEN_GEN4 = 4, + + /** + * PCIE Generation 5 + */ + CUPTI_PCIE_GEN_GEN5 = 5, + + CUPTI_PCIE_GEN_FORCE_INT = 0x7fffffff +} CUpti_PcieGen; + +/** + * \brief The activity record for an instantaneous CUPTI event. + * + * This activity record represents a CUPTI event value + * (CUPTI_ACTIVITY_KIND_EVENT) sampled at a particular instant. + * This activity record kind is not produced by the activity API but is + * included for completeness and ease-of-use. Profiler frameworks built on + * top of CUPTI that collect event data at a particular time may choose to + * use this type to store the collected event data. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTANTANEOUS_EVENT. + */ + CUpti_ActivityKind kind; + + /** + * The event ID. + */ + CUpti_EventID id; + + /** + * The event value. + */ + uint64_t value; + + /** + * The timestamp at which event is sampled + */ + uint64_t timestamp; + + /** + * The device id + */ + uint32_t deviceId; + + /** + * Undefined. reserved for internal use + */ + uint32_t reserved; +} CUpti_ActivityInstantaneousEvent; + +/** + * \brief The activity record for an instantaneous CUPTI event + * with event domain instance information. + * + * This activity record represents the a CUPTI event value for a + * specific event domain instance + * (CUPTI_ACTIVITY_KIND_EVENT_INSTANCE) sampled at a particular instant. + * This activity record kind is not produced by the activity API but is + * included for completeness and ease-of-use. Profiler frameworks built on + * top of CUPTI that collect event data may choose to use this type to store the + * collected event data. This activity record should be used when + * event domain instance information needs to be associated with the + * event. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTANTANEOUS_EVENT_INSTANCE. + */ + CUpti_ActivityKind kind; + + /** + * The event ID. + */ + CUpti_EventID id; + + /** + * The event value. + */ + uint64_t value; + + /** + * The timestamp at which event is sampled + */ + uint64_t timestamp; + + /** + * The device id + */ + uint32_t deviceId; + + /** + * The event domain instance + */ + uint8_t instance; + + /** + * Undefined. reserved for internal use + */ + uint8_t pad[3]; +} CUpti_ActivityInstantaneousEventInstance; + +/** + * \brief The activity record for an instantaneous CUPTI metric. + * + * This activity record represents the collection of a CUPTI metric + * value (CUPTI_ACTIVITY_KIND_METRIC) at a particular instance. + * This activity record kind is not produced by the activity API but + * is included for completeness and ease-of-use. Profiler frameworks built + * on top of CUPTI that collect metric data may choose to use this type to + * store the collected metric data. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTANTANEOUS_METRIC. + */ + CUpti_ActivityKind kind; + + /** + * The metric ID. + */ + CUpti_MetricID id; + + /** + * The metric value. + */ + CUpti_MetricValue value; + + /** + * The timestamp at which metric is sampled + */ + uint64_t timestamp; + + /** + * The device id + */ + uint32_t deviceId; + + /** + * The properties of this metric. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * Undefined. reserved for internal use + */ + uint8_t pad[3]; +} CUpti_ActivityInstantaneousMetric; + +/** + * \brief The instantaneous activity record for a CUPTI metric with instance + * information. + + * This activity record represents a CUPTI metric value + * for a specific metric domain instance + * (CUPTI_ACTIVITY_KIND_METRIC_INSTANCE) sampled at a particular time. This + * activity record kind is not produced by the activity API but is included for + * completeness and ease-of-use. Profiler frameworks built on top of + * CUPTI that collect metric data may choose to use this type to store + * the collected metric data. This activity record should be used when + * metric domain instance information needs to be associated with the + * metric. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_INSTANTANEOUS_METRIC_INSTANCE. + */ + CUpti_ActivityKind kind; + + /** + * The metric ID. + */ + CUpti_MetricID id; + + /** + * The metric value. + */ + CUpti_MetricValue value; + + /** + * The timestamp at which metric is sampled + */ + uint64_t timestamp; + + /** + * The device id + */ + uint32_t deviceId; + + /** + * The properties of this metric. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The metric domain instance + */ + uint8_t instance; + + /** + * Undefined. reserved for internal use + */ + uint8_t pad[2]; +} CUpti_ActivityInstantaneousMetricInstance; + +/** + * \brief The types of JIT entry. + * + * To be used in CUpti_ActivityJit. + */ +typedef enum { + CUPTI_ACTIVITY_JIT_ENTRY_INVALID= 0, + + /** + * PTX to CUBIN. + */ + CUPTI_ACTIVITY_JIT_ENTRY_PTX_TO_CUBIN = 1, + + /** + * NVVM-IR to PTX + */ + CUPTI_ACTIVITY_JIT_ENTRY_NVVM_IR_TO_PTX = 2, + + CUPTI_ACTIVITY_JIT_ENTRY_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityJitEntryType; + +/** + * \brief The types of JIT compilation operations. + * + * To be used in CUpti_ActivityJit. + */ + +typedef enum { + CUPTI_ACTIVITY_JIT_OPERATION_INVALID = 0, + /** + * Loaded from the compute cache. + */ + CUPTI_ACTIVITY_JIT_OPERATION_CACHE_LOAD = 1, + + /** + * Stored in the compute cache. + */ + CUPTI_ACTIVITY_JIT_OPERATION_CACHE_STORE = 2, + + /** + * JIT compilation. + */ + CUPTI_ACTIVITY_JIT_OPERATION_COMPILE = 3, + + CUPTI_ACTIVITY_JIT_OPERATION_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityJitOperationType; + +/** + * \brief The activity record for JIT operations. + * This activity represents the JIT operations (compile, load, store) of a CUmodule + * from the Compute Cache. + * Gives the exact hashed path of where the cached module is loaded from, + * or where the module will be stored after Just-In-Time (JIT) compilation. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind must be CUPTI_ACTIVITY_KIND_JIT. + */ + CUpti_ActivityKind kind; + + /** + * The JIT entry type. + */ + CUpti_ActivityJitEntryType jitEntryType; + + /** + * The JIT operation type. + */ + CUpti_ActivityJitOperationType jitOperationType; + + /** + * The device ID. + */ + uint32_t deviceId; + + /** + * The start timestamp for the JIT operation, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the JIT operation. + */ + uint64_t start; + + /** + * The end timestamp for the JIT operation, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the JIT operation. + */ + uint64_t end; + + /** + * The correlation ID of the JIT operation to which + * records belong to. Each JIT operation is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the JIT operation. + */ + uint32_t correlationId; + + /** + * Internal use. + */ + uint32_t padding; + + /** + * The correlation ID to correlate JIT compilation, load and store operations. + * Each JIT compilation unit is assigned a unique correlation ID + * at the time of the JIT compilation. This correlation id can be used + * to find the matching JIT cache load/store records. + */ + uint64_t jitOperationCorrelationId; + + /** + * The size of compute cache. + */ + uint64_t cacheSize; + + /** + * The path where the fat binary is cached. + */ + const char* cachePath; + + /** + * The ID of the process where the JIT operation is executing. + */ + uint32_t processId; + + /** + * The ID of the thread where the JIT operation is executing. + */ + uint32_t threadId; +} CUpti_ActivityJit2; + + +/** + * \brief The activity record for trace of graph execution. + * + * This activity record represents execution for a graph without giving visibility + * about the execution of its nodes. This is intended to reduce overheads in tracing + * each node. The activity kind is CUPTI_ACTIVITY_KIND_GRAPH_TRACE + */ +typedef struct { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_GRAPH_TRACE + */ + CUpti_ActivityKind kind; + + /** + * The correlation ID of the graph launch. Each graph launch is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the graph. + */ + uint32_t correlationId; + + /** + * The start timestamp for the graph execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the graph. + */ + uint64_t start; + + /** + * The end timestamp for the graph execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the graph. + */ + uint64_t end; + + /** + * The ID of the device where the first node of the graph is executed. + */ + uint32_t deviceId; + + /** + * The unique ID of the graph that is launched. + */ + uint32_t graphId; + + /** + * The ID of the context where the first node of the graph is executed. + */ + uint32_t contextId; + + /** + * The ID of the stream where the graph is being launched. + */ + uint32_t streamId; + + /** + * This field is reserved for internal use + */ + void *reserved; + + /** + * The ID of the device where last node of the graph is executed + */ + uint32_t endDeviceId; + + /** + * The ID of the context where the last node of the graph is executed. + */ + uint32_t endContextId; +} CUpti_ActivityGraphTrace2; + +END_PACKED_ALIGNMENT + +/** + * \brief Activity attributes. + * + * These attributes are used to control the behavior of the activity + * API. + */ +typedef enum { + /** + * The device memory size (in bytes) reserved for storing profiling data for concurrent + * kernels (activity kind \ref CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL), memcopies and memsets + * for each buffer on a context. The value is a size_t. + * + * There is a limit on how many device buffers can be allocated per context. User + * can query and set this limit using the attribute + * \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_POOL_LIMIT. + * CUPTI doesn't pre-allocate all the buffers, it pre-allocates only those many + * buffers as set by the attribute \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_PRE_ALLOCATE_VALUE. + * When all of the data in a buffer is consumed, it is added in the reuse pool, and + * CUPTI picks a buffer from this pool when a new buffer is needed. Thus memory + * footprint does not scale with the kernel count. Applications with the high density + * of kernels, memcopies and memsets might result in having CUPTI to allocate more device buffers. + * CUPTI allocates another buffer only when it runs out of the buffers in the + * reuse pool. + * + * Since buffer allocation happens in the main application thread, this might result + * in stalls in the critical path. CUPTI pre-allocates 3 buffers of the same size to + * mitigate this issue. User can query and set the pre-allocation limit using the + * attribute \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_PRE_ALLOCATE_VALUE. + * + * Having larger buffer size leaves less device memory for the application. + * Having smaller buffer size increases the risk of dropping timestamps for + * records if too many kernels or memcopies or memsets are launched at one time. + * + * This value only applies to new buffer allocations. Set this value before initializing + * CUDA or before creating a context to ensure it is considered for the following allocations. + * + * The default value is 3200000 (~3MB) which can accommodate profiling data + * up to 100,000 kernels, memcopies and memsets combined. + * + * Note: Starting with the CUDA 12.0 Update 1 release, CUPTI allocates profiling buffer in the + * device memory by default as this might help in improving the performance of the + * tracing run. Refer to the description of the attribute + * \ref CUPTI_ACTIVITY_ATTR_MEM_ALLOCATION_TYPE_HOST_PINNED for more details. + * Size of the memory and maximum number of pools are still controlled by the attributes + * \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE and \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_POOL_LIMIT. + * + * Note: The actual amount of device memory per buffer reserved by CUPTI might be larger. + */ + CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE = 0, + + /** + * The device memory size (in bytes) reserved for storing profiling + * data for CDP operations for each buffer on a context. The + * value is a size_t. + * + * Having larger buffer size means less flush operations but + * consumes more device memory. This value only applies to new + * allocations. + * + * Set this value before initializing CUDA or before creating a + * context to ensure it is considered for the following allocations. + * + * The default value is 8388608 (8MB). + * + * Note: The actual amount of device memory per context reserved by + * CUPTI might be larger. + */ + CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE_CDP = 1, + + /** + * The maximum number of device memory buffers per context. The value is a size_t. + * + * For an application with high rate of kernel launches, memcopies and memsets having a bigger pool + * limit helps in timestamp collection for all these activities at the expense of a larger memory footprint. + * Refer to the description of the attribute \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE + * for more details. + * + * Setting this value will not modify the number of memory buffers + * currently stored. + * + * Set this value before initializing CUDA to ensure the limit is + * not exceeded. + * + * The default value is 250. + */ + CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_POOL_LIMIT = 2, + + /** + * This attribute is not supported starting with CUDA 12.3 + * CUPTI no longer uses profiling semaphore pool to store profiling data. + * + * There is a limit on how many semaphore pools can be allocated per context. User + * can query and set this limit using the attribute + * \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_LIMIT. + * CUPTI doesn't pre-allocate all the semaphore pools, it pre-allocates only those many + * semaphore pools as set by the attribute \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_PRE_ALLOCATE_VALUE. + * When all of the data in a semaphore pool is consumed, it is added in the reuse pool, and + * CUPTI picks a semaphore pool from the reuse pool when a new semaphore pool is needed. Thus memory + * footprint does not scale with the kernel count. Applications with the high density + * of kernels might result in having CUPTI to allocate more semaphore pools. + * CUPTI allocates another semaphore pool only when it runs out of the semaphore pools in the + * reuse pool. + * + * Since semaphore pool allocation happens in the main application thread, this might result + * in stalls in the critical path. CUPTI pre-allocates 3 semaphore pools of the same size to + * mitigate this issue. User can query and set the pre-allocation limit using the + * attribute \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_PRE_ALLOCATE_VALUE. + * + * Having larger semaphore pool size leaves less device memory for the application. + * Having smaller semaphore pool size increases the risk of dropping timestamps for + * kernel records if too many kernels are issued/launched at one time. + * + * This value only applies to new semaphore pool allocations. Set this value before initializing + * CUDA or before creating a context to ensure it is considered for the following allocations. + * + * The default value is 25000 which can accommodate profiling data for upto 25,000 kernels. + * + */ + CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_SIZE = 3, + + /** + * This attribute is not supported starting with CUDA 12.3 + * CUPTI no longer uses profiling semaphore pool to store profiling data. + * + * The maximum number of profiling semaphore pools per context. The value is a size_t. + * + * Refer to the description of the attribute \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_SIZE + * for more details. + * + * Set this value before initializing CUDA to ensure the limit is not exceeded. + * + * The default value is 250. + */ + CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_LIMIT = 4, + + /** + * The flag to indicate whether user should provide activity buffer of zero value. + * The value is a uint8_t. + * + * If the value of this attribute is non-zero, user should provide + * a zero value buffer in the \ref CUpti_BuffersCallbackRequestFunc. + * If the user does not provide a zero value buffer after setting this to non-zero, + * the activity buffer may contain some uninitialized values when CUPTI returns it in + * \ref CUpti_BuffersCallbackCompleteFunc + * + * If the value of this attribute is zero, CUPTI will initialize the user buffer + * received in the \ref CUpti_BuffersCallbackRequestFunc to zero before filling it. + * If the user sets this to zero, a few stalls may appear in critical path because CUPTI + * will zero out the buffer in the main thread. + * Set this value before returning from \ref CUpti_BuffersCallbackRequestFunc to + * ensure it is considered for all the subsequent user buffers. + * + * The default value is 0. + */ + CUPTI_ACTIVITY_ATTR_ZEROED_OUT_ACTIVITY_BUFFER = 5, + + /** + * Number of device buffers to pre-allocate for a context during the initialization phase. + * The value is a size_t. + * + * Refer to the description of the attribute \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE + * for details. + * + * This value must be less than the maximum number of device buffers set using + * the attribute \ref CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_POOL_LIMIT + * + * Set this value before initializing CUDA or before creating a context to ensure it + * is considered by the CUPTI. + * + * The default value is set to 3 to ping pong between these buffers (if possible). + */ + CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_PRE_ALLOCATE_VALUE = 6, + + /** + * This attribute is not supported starting with CUDA 12.3 + * CUPTI no longer uses profiling semaphore pool to store profiling data. + * + * Number of profiling semaphore pools to pre-allocate for a context during the + * initialization phase. The value is a size_t. + * + * Refer to the description of the attribute \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_SIZE + * for details. + * + * This value must be less than the maximum number of profiling semaphore pools set + * using the attribute \ref CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_POOL_LIMIT + * + * Set this value before initializing CUDA or before creating a context to ensure it + * is considered by the CUPTI. + * + * The default value is set to 3 to ping pong between these pools (if possible). + */ + CUPTI_ACTIVITY_ATTR_PROFILING_SEMAPHORE_PRE_ALLOCATE_VALUE = 7, + + /** + * Allocate page-locked (pinned) host memory for storing profiling data for concurrent + * kernels, memcopies and memsets for each buffer on a context. The value is a uint8_t. + * + * Starting with the CUDA 11.2 release, CUPTI allocates profiling buffer in the pinned host + * memory by default as this might help in improving the performance of the tracing run. + * Allocating excessive amounts of pinned memory may degrade system performance, since it + * reduces the amount of memory available to the system for paging. For this reason user + * might want to change the location from pinned host memory to device memory by setting + * value of this attribute to 0. + * + * Using page-locked (pinned) host memory buffers is not supported on confidential computing + * devices. On setting this attribute to 1, CUPTI will return CUPTI_ERROR_NOT_SUPPORTED. + * + * The default value is 1. + */ + CUPTI_ACTIVITY_ATTR_MEM_ALLOCATION_TYPE_HOST_PINNED = 8, + + /** + * Request activity buffers per-thread to store CUPTI activity records + * in the activity buffer on per-thread basis. The value is a uint8_t. + * + * The attribute should be set before registering the buffer callbacks using + * cuptiActivityRegisterCallbacks API and before any of the CUPTI activity kinds are enabled. + * This makes sure that all the records are stored in activity buffers allocated per-thread. + * Changing this attribute in the middle of the profiling session will result in undefined behavior. + * + * The default value is 0. + */ + CUPTI_ACTIVITY_ATTR_PER_THREAD_ACTIVITY_BUFFER, + + + + CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_FORCE_INT = 0x7fffffff +} CUpti_ActivityAttribute; + +/** + * \brief Thread-Id types. + * + * CUPTI uses different methods to obtain the thread-id depending on the + * support and the underlying platform. This enum documents these methods + * for each type. APIs \ref cuptiSetThreadIdType and \ref cuptiGetThreadIdType + * can be used to set and get the thread-id type. + */ +typedef enum { + /** + * Default type + * Windows uses API GetCurrentThreadId() + * Linux/Mac/Android/QNX use POSIX pthread API pthread_self() + */ + CUPTI_ACTIVITY_THREAD_ID_TYPE_DEFAULT = 0, + + /** + * This type is based on the system API available on the underlying platform + * and thread-id obtained is supposed to be unique for the process lifetime. + * Windows uses API GetCurrentThreadId() + * Linux uses syscall SYS_gettid + * Mac uses syscall SYS_thread_selfid + * Android/QNX use gettid() + */ + CUPTI_ACTIVITY_THREAD_ID_TYPE_SYSTEM = 1, + + /** + * Add new enums before this field. + */ + CUPTI_ACTIVITY_THREAD_ID_TYPE_SIZE = 2, + + CUPTI_ACTIVITY_THREAD_ID_TYPE_FORCE_INT = 0x7fffffff +} CUpti_ActivityThreadIdType; + +/** + * \brief Get the CUPTI timestamp. + * + * Returns a timestamp normalized to correspond with the start and end + * timestamps reported in the CUPTI activity records. The timestamp is + * reported in nanoseconds. + * + * \param timestamp Returns the CUPTI timestamp + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p timestamp is NULL + */ +CUptiResult CUPTIAPI cuptiGetTimestamp(uint64_t *timestamp); + +/** + * \brief Get the ID of a context. + * + * Get the ID of a context. + * + * \param context The context + * \param contextId Returns a process-unique ID for the context + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_CONTEXT The context is NULL or not valid. + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p contextId is NULL + */ +CUptiResult CUPTIAPI cuptiGetContextId(CUcontext context, uint32_t *contextId); + +/** + * \brief Get the ID of a stream. + * + * Get the ID of a stream. The stream ID is unique within a context + * (i.e. all streams within a context will have unique stream + * IDs). + * + * \param context If non-NULL then the stream is checked to ensure + * that it belongs to this context. Typically this parameter should be + * null. + * \param stream The stream + * \param streamId Returns a context-unique ID for the stream + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_STREAM if unable to get stream ID, or + * if \p context is non-NULL and \p stream does not belong to the + * context + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p streamId is NULL + * + * **DEPRECATED** This method is deprecated as of CUDA 8.0. + * Use method cuptiGetStreamIdEx instead. + */ +CUptiResult CUPTIAPI cuptiGetStreamId(CUcontext context, CUstream stream, uint32_t *streamId); + +/** +* \brief Get the ID of a stream. +* +* Get the ID of a stream. The stream ID is unique within a context +* (i.e. all streams within a context will have unique stream +* IDs). +* +* \param context If non-NULL then the stream is checked to ensure +* that it belongs to this context. Typically this parameter should be +* null. +* \param stream The stream +* \param perThreadStream Flag to indicate if program is compiled for per-thread streams +* \param streamId Returns a context-unique ID for the stream +* +* \retval CUPTI_SUCCESS +* \retval CUPTI_ERROR_NOT_INITIALIZED +* \retval CUPTI_ERROR_INVALID_STREAM if unable to get stream ID, or +* if \p context is non-NULL and \p stream does not belong to the +* context +* \retval CUPTI_ERROR_INVALID_PARAMETER if \p streamId is NULL +*/ +CUptiResult CUPTIAPI cuptiGetStreamIdEx(CUcontext context, CUstream stream, uint8_t perThreadStream, uint32_t *streamId); + +/** + * \brief Get the ID of a device + * + * If \p context is NULL, returns the ID of the device that contains + * the currently active context. If \p context is non-NULL, returns + * the ID of the device which contains that context. Operates in a + * similar manner to cudaGetDevice() or cuCtxGetDevice() but may be + * called from within callback functions. + * + * \param context The context, or NULL to indicate the current context. + * \param deviceId Returns the ID of the device that is current for + * the calling thread. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_DEVICE if unable to get device ID + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p deviceId is NULL + */ +CUptiResult CUPTIAPI cuptiGetDeviceId(CUcontext context, uint32_t *deviceId); + +/** + * \brief Get the unique ID of a graph node + * + * Returns the unique ID of the CUDA graph node. + * + * \param node The graph node. + * \param nodeId Returns the unique ID of the node + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p node is NULL + */ +CUptiResult CUPTIAPI cuptiGetGraphNodeId(CUgraphNode node, uint64_t *nodeId); + +/** + * \brief Get the unique ID of graph + * + * Returns the unique ID of CUDA graph. + * + * \param graph The graph. + * \param pId Returns the unique ID of the graph + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p graph is NULL + */ +CUptiResult CUPTIAPI cuptiGetGraphId(CUgraph graph, uint32_t *pId); + +/** + * \brief Get the unique ID of executable graph + * + * Returns the unique ID of executable CUDA graph. + * + * \param graphExec The executable graph. + * \param pId Returns the unique ID of the executable graph + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p graph is NULL + */ +CUptiResult CUPTIAPI cuptiGetGraphExecId(CUgraphExec graphExec, uint32_t *pId); + +/** + * \brief Enable collection of a specific kind of activity record. + * + * Enable collection of a specific kind of activity record. Multiple + * kinds can be enabled by calling this function multiple times. By + * default all activity kinds are disabled for collection. + * + * \param kind The kind of activity record to collect + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_NOT_COMPATIBLE if the activity kind cannot be enabled + * \retval CUPTI_ERROR_INVALID_KIND if the activity kind is not supported + */ +CUptiResult CUPTIAPI cuptiActivityEnable(CUpti_ActivityKind kind); + +/** + * \brief Enable collection of a specific kind of activity record. For certain activity kinds + * it dumps existing records. + * + * In general, the behavior of this API is similar to the API \ref cuptiActivityEnable i.e. it + * enables the collection of a specific kind of activity record. + * Additionally, this API can help in dumping the records for activities which happened in + * the past before enabling the corresponding activity kind. + * The API allows to get records for the current resource allocations done in CUDA + * For CUPTI_ACTIVITY_KIND_DEVICE, existing device records are dumped + * For CUPTI_ACTIVITY_KIND_CONTEXT, existing context records are dumped + * For CUPTI_ACTIVITY_KIND_STREAM, existing stream records are dumped + * For CUPTI_ACTIVITY_KIND_ NVLINK, existing NVLINK records are dumped + * For CUPTI_ACTIVITY_KIND_PCIE, existing PCIE records are dumped + * For other activities, the behavior is similar to the API \ref cuptiActivityEnable + * + * Device records are emitted in CUPTI on CUDA driver initialization. Those records + * can only be retrieved by the user if CUPTI is attached before CUDA initialization. + * Context and stream records are emitted on context and stream creation. + * The use case of the API is to provide the records for CUDA resources + * (contexts/streams/devices) that are currently active if user late attaches CUPTI. + * + * Before calling this function, the user must register buffer callbacks + * to get the activity records by calling \ref cuptiActivityRegisterCallbacks. + * If the user does not register the buffers and calls API \ref cuptiActivityEnableAndDump, + * then CUPTI will enable the activity kind but not provide any records for that + * activity kind. + * + * \param kind The kind of activity record to collect + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_UNKNOWN if buffer is not initialized. + * \retval CUPTI_ERROR_NOT_COMPATIBLE if the activity kind cannot be enabled + * \retval CUPTI_ERROR_INVALID_KIND if the activity kind is not supported + */ +CUptiResult CUPTIAPI cuptiActivityEnableAndDump(CUpti_ActivityKind kind); + +/** + * \brief Disable collection of a specific kind of activity record. + * + * Disable collection of a specific kind of activity record. Multiple + * kinds can be disabled by calling this function multiple times. By + * default all activity kinds are disabled for collection. + * + * \param kind The kind of activity record to stop collecting + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_KIND if the activity kind is not supported + */ +CUptiResult CUPTIAPI cuptiActivityDisable(CUpti_ActivityKind kind); + +/** + * \brief Enable collection of a specific kind of activity record for + * a context. + * + * Enable collection of a specific kind of activity record for a + * context. This setting done by this API will supersede the global + * settings for activity records enabled by \ref cuptiActivityEnable. + * Multiple kinds can be enabled by calling this function multiple + * times. + * + * \param context The context for which activity is to be enabled + * \param kind The kind of activity record to collect + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_NOT_COMPATIBLE if the activity kind cannot be enabled + * \retval CUPTI_ERROR_INVALID_KIND if the activity kind is not supported + */ +CUptiResult CUPTIAPI cuptiActivityEnableContext(CUcontext context, CUpti_ActivityKind kind); + +/** + * \brief Disable collection of a specific kind of activity record for + * a context. + * + * Disable collection of a specific kind of activity record for a context. + * This setting done by this API will supersede the global settings + * for activity records. + * Multiple kinds can be enabled by calling this function multiple times. + * + * \param context The context for which activity is to be disabled + * \param kind The kind of activity record to stop collecting + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_KIND if the activity kind is not supported + */ +CUptiResult CUPTIAPI cuptiActivityDisableContext(CUcontext context, CUpti_ActivityKind kind); + +/** + * \brief Get the number of activity records that were dropped of + * insufficient buffer space. + * + * Get the number of records that were dropped because of insufficient + * buffer space. The dropped count includes records that could not be + * recorded because CUPTI did not have activity buffer space available + * for the record (because the CUpti_BuffersCallbackRequestFunc + * callback did not return an empty buffer of sufficient size) and + * also CDP records that could not be record because the device-size + * buffer was full (size is controlled by the + * CUPTI_ACTIVITY_ATTR_DEVICE_BUFFER_SIZE_CDP attribute). The dropped + * count maintained for the queue is reset to zero when this function + * is called. + * + * \param context The context, or NULL to get dropped count from global queue + * \param streamId The stream ID + * \param dropped The number of records that were dropped since the last call + * to this function. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p dropped is NULL + */ +CUptiResult CUPTIAPI cuptiActivityGetNumDroppedRecords(CUcontext context, uint32_t streamId, + size_t *dropped); + +/** + * \brief Iterate over the activity records in a buffer. + * + * This is a helper function to iterate over the activity records in a + * buffer. A buffer of activity records is typically obtained by + * receiving a CUpti_BuffersCallbackCompleteFunc callback. + * + * An example of typical usage: + * \code + * CUpti_Activity *record = NULL; + * CUptiResult status = CUPTI_SUCCESS; + * do { + * status = cuptiActivityGetNextRecord(buffer, validSize, &record); + * if(status == CUPTI_SUCCESS) { + * // Use record here... + * } + * else if (status == CUPTI_ERROR_MAX_LIMIT_REACHED) + * break; + * else { + * goto Error; + * } + * } while (1); + * \endcode + * + * \param buffer The buffer containing activity records + * \param record Inputs the previous record returned by + * cuptiActivityGetNextRecord and returns the next activity record + * from the buffer. If input value is NULL, returns the first activity + * record in the buffer. Records of kind CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL + * may contain invalid (0) timestamps, indicating that no timing information could + * be collected for lack of device memory. + * \param validBufferSizeBytes The number of valid bytes in the buffer. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_MAX_LIMIT_REACHED if no more records in the buffer + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p buffer is NULL. + */ +CUptiResult CUPTIAPI cuptiActivityGetNextRecord(uint8_t* buffer, size_t validBufferSizeBytes, + CUpti_Activity **record); + +/** + * \brief Function type for callback used by CUPTI to request an empty + * buffer for storing activity records. + * + * This callback function signals the CUPTI client that an activity + * buffer is needed by CUPTI. The activity buffer is used by CUPTI to + * store activity records. The callback function can decline the + * request by setting \p *buffer to NULL. In this case CUPTI may drop + * activity records. + * + * \param buffer Returns the new buffer. If set to NULL then no buffer + * is returned. + * \param size Returns the size of the returned buffer. + * \param maxNumRecords Returns the maximum number of records that + * should be placed in the buffer. If 0 then the buffer is filled with + * as many records as possible. If > 0 the buffer is filled with at + * most that many records before it is returned. + */ +typedef void (CUPTIAPI *CUpti_BuffersCallbackRequestFunc)( + uint8_t **buffer, + size_t *size, + size_t *maxNumRecords); + +/** + * \brief Function type for callback used by CUPTI to return a buffer + * of activity records. + * + * This callback function returns to the CUPTI client a buffer + * containing activity records. The buffer contains \p validSize + * bytes of activity records which should be read using + * cuptiActivityGetNextRecord. The number of dropped records can be + * read using cuptiActivityGetNumDroppedRecords. After this call CUPTI + * relinquished ownership of the buffer and will not use it + * anymore. The client may return the buffer to CUPTI using the + * CUpti_BuffersCallbackRequestFunc callback. + * Note: CUDA 6.0 onwards, all buffers returned by this callback are + * global buffers i.e. there is no context/stream specific buffer. + * User needs to parse the global buffer to extract the context/stream + * specific activity records. + * + * \param context The context this buffer is associated with. If NULL, the + * buffer is associated with the global activities. This field is deprecated + * as of CUDA 6.0 and will always be NULL. + * \param streamId The stream id this buffer is associated with. + * This field is deprecated as of CUDA 6.0 and will always be NULL. + * \param buffer The activity record buffer. + * \param size The total size of the buffer in bytes as set in + * CUpti_BuffersCallbackRequestFunc. + * \param validSize The number of valid bytes in the buffer. + */ +typedef void (CUPTIAPI *CUpti_BuffersCallbackCompleteFunc)( + CUcontext context, + uint32_t streamId, + uint8_t *buffer, + size_t size, + size_t validSize); + +/** + * \brief Registers callback functions with CUPTI for activity buffer + * handling. + * + * This function registers two callback functions to be used in asynchronous + * buffer handling. If registered, activity record buffers are handled using + * asynchronous requested/completed callbacks from CUPTI. + * + * Registering these callbacks prevents the client from using CUPTI's + * blocking enqueue/dequeue functions. + * + * \param funcBufferRequested callback which is invoked when an empty + * buffer is requested by CUPTI + * \param funcBufferCompleted callback which is invoked when a buffer + * containing activity records is available from CUPTI + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER if either \p + * funcBufferRequested or \p funcBufferCompleted is NULL + */ +CUptiResult CUPTIAPI cuptiActivityRegisterCallbacks(CUpti_BuffersCallbackRequestFunc funcBufferRequested, + CUpti_BuffersCallbackCompleteFunc funcBufferCompleted); + +/** + * \brief Wait for all activity records to be delivered via the + * completion callback. + * + * This function does not return until all activity records associated + * with the specified context/stream are returned to the CUPTI client + * using the callback registered in cuptiActivityRegisterCallbacks. To + * ensure that all activity records are complete, the requested + * stream(s), if any, are synchronized. + * + * If \p context is NULL, the global activity records (i.e. those not + * associated with a particular stream) are flushed (in this case no + * streams are synchronized). If \p context is a valid CUcontext and + * \p streamId is 0, the buffers of all streams of this context are + * flushed. Otherwise, the buffers of the specified stream in this + * context is flushed. + * + * Before calling this function, the buffer handling callback api + * must be activated by calling cuptiActivityRegisterCallbacks. + * + * \param context A valid CUcontext or NULL. + * \param streamId The stream ID. + * \param flag The flag can be set to indicate a forced flush. See CUpti_ActivityFlag + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_CUPTI_ERROR_INVALID_OPERATION if not preceded + * by a successful call to cuptiActivityRegisterCallbacks + * \retval CUPTI_ERROR_UNKNOWN an internal error occurred + * + * **DEPRECATED** This method is deprecated + * CONTEXT and STREAMID will be ignored. Use cuptiActivityFlushAll + * to flush all data. + */ +CUptiResult CUPTIAPI cuptiActivityFlush(CUcontext context, uint32_t streamId, uint32_t flag); + +/** + * \brief Request to deliver activity records via the buffer completion callback. + * + * This function returns the activity records associated with all contexts/streams + * (and the global buffers not associated with any stream) to the CUPTI client + * using the callback registered in cuptiActivityRegisterCallbacks. + * + * This is a blocking call but it doesn't issue any CUDA synchronization calls + * implicitly thus it's not guaranteed that all activities are completed on the + * underlying devices. Activity record is considered as completed if it has all + * the information filled up including the timestamps if any. It is the client's + * responsibility to issue necessary CUDA synchronization calls before calling + * this function if all activity records with complete information are expected + * to be delivered. + * + * Behavior of the function based on the input flag: + * (-) ::For default flush i.e. when flag is set as 0, it returns all the + * activity buffers which have all the activity records completed, buffers need not + * to be full though. It doesn't return buffers which have one or more incomplete + * records. Default flush can be done at a regular interval in a separate thread. + * (-) ::For forced flush i.e. when flag CUPTI_ACTIVITY_FLAG_FLUSH_FORCED is passed + * to the function, it returns all the activity buffers including the ones which have + * one or more incomplete activity records. It's suggested for clients to do the + * force flush before the termination of the profiling session to allow remaining + * buffers to be delivered. In general, it can be done in the at-exit handler. + * + * Before calling this function, the buffer handling callback api must be activated + * by calling cuptiActivityRegisterCallbacks. + * + * \param flag The flag can be set to indicate a forced flush. See CUpti_ActivityFlag + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_OPERATION if not preceded by a + * successful call to cuptiActivityRegisterCallbacks + * \retval CUPTI_ERROR_UNKNOWN an internal error occurred + * + * \see cuptiActivityFlushPeriod + */ +CUptiResult CUPTIAPI cuptiActivityFlushAll(uint32_t flag); + +/** + * \brief Read an activity API attribute. + * + * Read an activity API attribute and return it in \p *value. + * + * \param attr The attribute to read + * \param valueSize Size of buffer pointed by the value, and + * returns the number of bytes written to \p value + * \param value Returns the value of the attribute + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p valueSize or \p value is NULL, or + * if \p attr is not an activity attribute + * \retval CUPTI_ERROR_PARAMETER_SIZE_NOT_SUFFICIENT Indicates that + * the \p value buffer is too small to hold the attribute value. + */ +CUptiResult CUPTIAPI cuptiActivityGetAttribute(CUpti_ActivityAttribute attr, + size_t *valueSize, void* value); + +/** + * \brief Write an activity API attribute. + * + * Write an activity API attribute. + * + * \param attr The attribute to write + * \param valueSize The size, in bytes, of the value + * \param value The attribute value to write + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p valueSize or \p value is NULL, or + * if \p attr is not an activity attribute + * \retval CUPTI_ERROR_PARAMETER_SIZE_NOT_SUFFICIENT Indicates that + * the \p value buffer is too small to hold the attribute value. + */ +CUptiResult CUPTIAPI cuptiActivitySetAttribute(CUpti_ActivityAttribute attr, + size_t *valueSize, void* value); + + +/** + * \brief Set Unified Memory Counter configuration. + * + * \param config A pointer to \ref CUpti_ActivityUnifiedMemoryCounterConfig structures + * containing Unified Memory counter configuration. + * \param count Number of Unified Memory counter configuration structures + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p config is NULL or + * any parameter in the \p config structures is not a valid value + * \retval CUPTI_ERROR_UM_PROFILING_NOT_SUPPORTED One potential reason is that + * platform (OS/arch) does not support the unified memory counters + * \retval CUPTI_ERROR_UM_PROFILING_NOT_SUPPORTED_ON_DEVICE Indicates that the device + * does not support the unified memory counters + * \retval CUPTI_ERROR_UM_PROFILING_NOT_SUPPORTED_ON_NON_P2P_DEVICES Indicates that + * multi-GPU configuration without P2P support between any pair of devices + * does not support the unified memory counters + */ +CUptiResult CUPTIAPI cuptiActivityConfigureUnifiedMemoryCounter(CUpti_ActivityUnifiedMemoryCounterConfig *config, uint32_t count); + +/** + * \brief Get auto boost state + * + * The profiling results can be inconsistent in case auto boost is enabled. + * CUPTI tries to disable auto boost while profiling. It can fail to disable in + * cases where user does not have the permissions or CUDA_AUTO_BOOST env + * variable is set. The function can be used to query whether auto boost is + * enabled. + * + * \param context A valid CUcontext. + * \param state A pointer to \ref CUpti_ActivityAutoBoostState structure which + * contains the current state and the id of the process that has requested the + * current state + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p CUcontext or \p state is NULL + * \retval CUPTI_ERROR_NOT_SUPPORTED Indicates that the device does not support auto boost + * \retval CUPTI_ERROR_UNKNOWN an internal error occurred + */ +CUptiResult CUPTIAPI cuptiGetAutoBoostState(CUcontext context, CUpti_ActivityAutoBoostState *state); + +/** + * \brief Set PC sampling configuration. + * + * For Pascal and older GPU architectures this API must be called before enabling + * activity kind CUPTI_ACTIVITY_KIND_PC_SAMPLING. There is no such requirement + * for Volta and newer GPU architectures. + * + * For Volta and newer GPU architectures if this API is called in the middle of + * execution, PC sampling configuration will be updated for subsequent kernel launches. + * + * \param ctx The context + * \param config A pointer to \ref CUpti_ActivityPCSamplingConfig structure + * containing PC sampling configuration. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_OPERATION if this api is called while + * some valid event collection method is set. + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p config is NULL or + * any parameter in the \p config structures is not a valid value + * \retval CUPTI_ERROR_NOT_SUPPORTED Indicates that the system/device + * does not support the unified memory counters + */ +CUptiResult CUPTIAPI cuptiActivityConfigurePCSampling(CUcontext ctx, CUpti_ActivityPCSamplingConfig *config); + +/** + * \brief Returns the last error from a cupti call or callback + * + * Returns the last error that has been produced by any of the cupti api calls + * or the callback in the same host thread and resets it to CUPTI_SUCCESS. + */ +CUptiResult CUPTIAPI cuptiGetLastError(void); + +/** + * \brief Set the thread-id type + * + * CUPTI uses the method corresponding to set type to generate the thread-id. + * See enum \ref CUpti_ActivityThreadIdType for the list of methods. + * Activity records having thread-id field contain the same value. + * Thread id type must not be changed during the profiling session to + * avoid thread-id value mismatch across activity records. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_SUPPORTED if \p type is not supported on the platform + */ +CUptiResult CUPTIAPI cuptiSetThreadIdType(CUpti_ActivityThreadIdType type); + +/** + * \brief Get the thread-id type + * + * Returns the thread-id type used in CUPTI + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p type is NULL + */ +CUptiResult CUPTIAPI cuptiGetThreadIdType(CUpti_ActivityThreadIdType *type); + +/** +* \brief Check support for a compute capability +* +* This function is used to check the support for a device based on +* it's compute capability. It sets the \p support when the compute +* capability is supported by the current version of CUPTI, and clears +* it otherwise. This version of CUPTI might not support all GPUs sharing +* the same compute capability. It is suggested to use API \ref +* cuptiDeviceSupported which provides correct information. +* +* \param major The major revision number of the compute capability +* \param minor The minor revision number of the compute capability +* \param support Pointer to an integer to return the support status +* +* \retval CUPTI_SUCCESS +* \retval CUPTI_ERROR_INVALID_PARAMETER if \p support is NULL +* +* \sa ::cuptiDeviceSupported +*/ +CUptiResult CUPTIAPI cuptiComputeCapabilitySupported(int major, int minor, int *support); + +/** +* \brief Check support for a compute device +* +* This function is used to check the support for a compute device. +* It sets the \p support when the device is supported by the current +* version of CUPTI, and clears it otherwise. +* +* \param dev The device handle returned by CUDA Driver API cuDeviceGet +* \param support Pointer to an integer to return the support status +* +* \retval CUPTI_SUCCESS +* \retval CUPTI_ERROR_INVALID_PARAMETER if \p support is NULL +* \retval CUPTI_ERROR_INVALID_DEVICE if \p dev is not a valid device +* +* \sa ::cuptiComputeCapabilitySupported +*/ +CUptiResult CUPTIAPI cuptiDeviceSupported(CUdevice dev, int *support); + +/** + * This indicates the virtualization mode in which CUDA device is running + */ +typedef enum { + /** + * No virtualization mode is associated with the device + * i.e. it's a baremetal GPU + */ + CUPTI_DEVICE_VIRTUALIZATION_MODE_NONE = 0, + /** + * The device is associated with the pass-through GPU. + * In this mode, an entire physical GPU is directly assigned + * to one virtual machine (VM). + */ + CUPTI_DEVICE_VIRTUALIZATION_MODE_PASS_THROUGH = 1, + /** + * The device is associated with the virtual GPU (vGPU). + * In this mode multiple virtual machines (VMs) have simultaneous, + * direct access to a single physical GPU. + */ + CUPTI_DEVICE_VIRTUALIZATION_MODE_VIRTUAL_GPU = 2, + + CUPTI_DEVICE_VIRTUALIZATION_MODE_FORCE_INT = 0x7fffffff +} CUpti_DeviceVirtualizationMode; + +/** + * \brief Query the virtualization mode of the device + * + * This function is used to query the virtualization mode of the CUDA device. + * + * \param dev The device handle returned by CUDA Driver API cuDeviceGet + * \param mode Pointer to an CUpti_DeviceVirtualizationMode to return the virtualization mode + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_DEVICE if \p dev is not a valid device + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p mode is NULL + * + */ +CUptiResult CUPTIAPI cuptiDeviceVirtualizationMode(CUdevice dev, CUpti_DeviceVirtualizationMode *mode); + +/** + * \brief Detach CUPTI from the running process + * + * This API detaches the CUPTI from the running process. It destroys and cleans up all the + * resources associated with CUPTI in the current process. After CUPTI detaches from the process, + * the process will keep on running with no CUPTI attached to it. + * For safe operation of the API, it is recommended this API is invoked from the exit callsite + * of any of the CUDA Driver or Runtime API. Otherwise CUPTI client needs to make sure that + * required CUDA synchronization and CUPTI activity buffer flush is done before calling the API. + * Sample code showing the usage of the API in the cupti callback handler code: + * \code + void CUPTIAPI + cuptiCallbackHandler(void *userdata, CUpti_CallbackDomain domain, + CUpti_CallbackId cbid, void *cbdata) + { + const CUpti_CallbackData *cbInfo = (CUpti_CallbackData *)cbdata; + + // Take this code path when CUPTI detach is requested + if (detachCupti) { + switch(domain) + { + case CUPTI_CB_DOMAIN_RUNTIME_API: + case CUPTI_CB_DOMAIN_DRIVER_API: + if (cbInfo->callbackSite == CUPTI_API_EXIT) { + // call the CUPTI detach API + cuptiFinalize(); + } + break; + default: + break; + } + } + } + \endcode + */ +CUptiResult CUPTIAPI cuptiFinalize(void); + +/** + * \brief Push an external correlation id for the calling thread + * + * This function notifies CUPTI that the calling thread is entering an external API region. + * When a CUPTI activity API record is created while within an external API region and + * CUPTI_ACTIVITY_KIND_EXTERNAL_CORRELATION is enabled, the activity API record will + * be preceded by a CUpti_ActivityExternalCorrelation record for each \ref CUpti_ExternalCorrelationKind. + * + * \param kind The kind of external API activities should be correlated with. + * \param id External correlation id. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER The external API kind is invalid + */ +CUptiResult CUPTIAPI cuptiActivityPushExternalCorrelationId(CUpti_ExternalCorrelationKind kind, uint64_t id); + +/** + * \brief Pop an external correlation id for the calling thread + * + * This function notifies CUPTI that the calling thread is leaving an external API region. + * + * \param kind The kind of external API activities should be correlated with. + * \param lastId If the function returns successful, contains the last external correlation id for this \p kind, can be NULL. + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER The external API kind is invalid. + * \retval CUPTI_ERROR_QUEUE_EMPTY No external id is currently associated with \p kind. + */ +CUptiResult CUPTIAPI cuptiActivityPopExternalCorrelationId(CUpti_ExternalCorrelationKind kind, uint64_t *lastId); + +/** + * \brief Controls the collection of queued and submitted timestamps for kernels. + * + * This API is used to control the collection of queued and submitted timestamps + * for kernels whose records are provided through the struct \ref CUpti_ActivityKernel9. + * Default value is 0, i.e. these timestamps are not collected. This API needs + * to be called before initialization of CUDA and this setting should not be + * changed during the profiling session. + * + * \param enable is a boolean, denoting whether these timestamps should be + * collected + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + */ +CUptiResult CUPTIAPI cuptiActivityEnableLatencyTimestamps(uint8_t enable); + +/** + * \brief Sets the flush period for the worker thread + * + * CUPTI creates a worker thread to minimize the perturbance for the application created + * threads. CUPTI offloads certain operations from the application threads to the worker + * thread, this includes synchronization of profiling resources between host and device, + * delivery of the activity buffers to the client using the callback registered in + * cuptiActivityRegisterCallbacks. For performance reasons, CUPTI wakes up the worker + * thread based on certain heuristics. + * + * This API is used to control the flush period of the worker thread. This setting will + * override the CUPTI heuristics. Setting time to zero disables the periodic flush and + * restores the default behavior. + * + * Periodic flush can return only those activity buffers which are full and have all the + * activity records completed. + * + * It's allowed to use the API \ref cuptiActivityFlushAll to flush the data on-demand, even + * when client sets the periodic flush. + * + * \param time flush period in milliseconds (ms) + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + * + * \see cuptiActivityFlushAll + */ +CUptiResult CUPTIAPI cuptiActivityFlushPeriod(uint32_t time); + +/** + * \brief Controls the collection of launch attributes for kernels. + * + * This API is used to control the collection of launch attributes for kernels whose + * records are provided through the struct \ref CUpti_ActivityKernel9. + * Default value is 0, i.e. these attributes are not collected. + * + * \param enable is a boolean denoting whether these launch attributes should be collected + */ +CUptiResult CUPTIAPI cuptiActivityEnableLaunchAttributes(uint8_t enable); + +/** + * \brief Function type for callback used by CUPTI to request a timestamp + * to be used in activity records. + * + * This callback function signals the CUPTI client that a timestamp needs + * to be returned. This timestamp would be treated as normalized timestamp + * to be used for various purposes in CUPTI. For example to store start and + * end timestamps reported in the CUPTI activity records. + * The returned timestamp must be in nanoseconds. + * + * \sa ::cuptiActivityRegisterTimestampCallback + */ +typedef uint64_t (CUPTIAPI *CUpti_TimestampCallbackFunc)(void); + +/** + * \brief Registers callback function with CUPTI for providing timestamp. + * + * This function registers a callback function to obtain timestamp of user's + * choice instead of using CUPTI provided timestamp. + * By default CUPTI uses different methods, based on the underlying platform, + * to retrieve the timestamp + * Linux and Android use clock_gettime(CLOCK_REALTIME, ..) + * Windows uses QueryPerformanceCounter() + * Mac uses mach_absolute_time() + * QNX uses ClockCycles() + * Timestamps retrieved using these methods are converted to nanosecond if needed + * before usage. + * + * The registration of timestamp callback should be done before any of the CUPTI + * activity kinds are enabled to make sure that all the records report the timestamp using + * the callback function registered through cuptiActivityRegisterTimestampCallback API. + * + * Changing the timestamp callback function in CUPTI through + * cuptiActivityRegisterTimestampCallback API in the middle of the profiling + * session can cause records generated prior to the change to report + * timestamps through previous timestamp method. + * + * \param funcTimestamp callback which is invoked when a timestamp is + * needed by CUPTI + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p funcTimestamp is NULL + * \retval CUPTI_ERROR_NOT_INITIALIZED + */ +CUptiResult CUPTIAPI cuptiActivityRegisterTimestampCallback(CUpti_TimestampCallbackFunc funcTimestamp); + +/** + * \brief Controls the collection of records for device launched graphs. + * + * This API is used to control the collection of records for device launched graphs. + * Default value is 0, i.e. these records are not collected. This API needs + * to be called before initialization of CUDA and this setting should not be + * changed during the profiling session. + * + * \param enable is a boolean, denoting whether these records should be + * collected + * + * \retval CUPTI_SUCCESS + * \retval CUPTI_ERROR_NOT_INITIALIZED + */ +CUptiResult CUPTIAPI cuptiActivityEnableDeviceGraph(uint8_t enable); + +/** @} */ /* END CUPTI_ACTIVITY_API */ + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility pop +#endif + +#if defined(__cplusplus) +} +#endif + +// Including deprecated structures of CUPTI_ACTIVITY_API +#include "cupti_activity_deprecated.h" + +#endif /*_CUPTI_ACTIVITY_H_*/ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity_deprecated.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity_deprecated.h new file mode 100644 index 0000000000000000000000000000000000000000..084ea84ed7be17af6d1634d772fd270fb5a0351f --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_activity_deprecated.h @@ -0,0 +1,4784 @@ +/* + * Copyright 2011-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(_CUPTI_ACTIVITY_DEPRECATED_H_) +#define _CUPTI_ACTIVITY_DEPRECATED_H_ + +#if defined(__cplusplus) +extern "C" { +#endif + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility push(default) +#endif + +/** + * \brief The kinds of activity records. + * + * Each activity record kind represents information about a GPU or an + * activity occurring on a CPU or GPU. Each kind is associated with a + * activity record structure that holds the information associated + * with the kind. + * \see CUpti_ActivityOverhead + * \see CUpti_ActivityOverhead2 + * \see CUpti_ActivityDevice + * \see CUpti_ActivityDevice2 + * \see CUpti_ActivityDevice3 + * \see CUpti_ActivityDevice4 + * \see CUpti_ActivityKernel + * \see CUpti_ActivityKernel2 + * \see CUpti_ActivityKernel3 + * \see CUpti_ActivityKernel4 + * \see CUpti_ActivityKernel5 + * \see CUpti_ActivityKernel6 + * \see CUpti_ActivityKernel7 + * \see CUpti_ActivityKernel8 + * \see CUpti_ActivityMemcpy + * \see CUpti_ActivityMemcpy3 + * \see CUpti_ActivityMemcpy4 + * \see CUpti_ActivityMemcpyPtoP + * \see CUpti_ActivityMemcpyPtoP2 + * \see CUpti_ActivityMemcpyPtoP3 + * \see CUpti_ActivityMemset + * \see CUpti_ActivityMemset2 + * \see CUpti_ActivityMemset3 + * \see CUpti_ActivityMemory2 + * \see CUpti_ActivityMemoryPool + * \see CUpti_ActivityMarker + * \see CUpti_ActivityGlobalAccess + * \see CUpti_ActivityGlobalAccess2 + * \see CUpti_ActivityBranch + * \see CUpti_ActivityPCSampling + * \see CUpti_ActivityPCSampling2 + * \see CUpti_ActivityUnifiedMemoryCounter + * \see CUpti_ActivityNvLink + * \see CUpti_ActivityNvLink2 + * \see CUpti_ActivityNvLink3 + */ + +/** + * \brief The activity record for CUPTI and driver overheads. + * (Deprecated in CUDA 12.2) + * + * This activity record provides CUPTI and driver overhead information + * (CUPTI_ACTIVITY_OVERHEAD). These records are now reported using + * CUpti_ActivityOverhead3 + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_OVERHEAD. + */ + CUpti_ActivityKind kind; + + /** + * The kind of overhead, CUPTI, DRIVER, COMPILER etc. + */ + CUpti_ActivityOverheadKind overheadKind; + + /** + * The kind of activity object that the overhead is associated with. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object. 'objectKind' indicates + * which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + + /** + * The start timestamp for the overhead, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the overhead. + */ + uint64_t start; + + /** + * The end timestamp for the overhead, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the overhead. + */ + uint64_t end; +} CUpti_ActivityOverhead; + +/** + * \brief The activity record for CUPTI and driver overheads. + * + * This activity record provides CUPTI and driver overhead information + * (CUPTI_ACTIVITY_OVERHEAD). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_OVERHEAD. + */ + CUpti_ActivityKind kind; + + /** + * The kind of overhead, CUPTI, DRIVER, COMPILER etc. + */ + CUpti_ActivityOverheadKind overheadKind; + + /** + * The kind of activity object that the overhead is associated with. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object. 'objectKind' indicates + * which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + + /** + * The start timestamp for the overhead, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the overhead. + */ + uint64_t start; + + /** + * The end timestamp for the overhead, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the overhead. + */ + uint64_t end; + + /** + * The correlation ID of the overhead operation to which + * records belong to. This ID is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the overhead operation. + * In some cases, it can be zero, such as for CUPTI_ACTIVITY_OVERHEAD_CUPTI_BUFFER_FLUSH records. + */ + uint32_t correlationId; + + /** + * Reserved for internal use. + */ + uint32_t reserved0; +} CUpti_ActivityOverhead2; + +/** + * \brief The activity record for a device. (deprecated) + * + * This activity record represents information about a GPU device + * (CUPTI_ACTIVITY_KIND_DEVICE). + * Device activity is now reported using the + * CUpti_ActivityDevice5 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The global memory bandwidth available on the device, in + * kBytes/sec. + */ + uint64_t globalMemoryBandwidth; + + /** + * The amount of global memory on the device, in bytes. + */ + uint64_t globalMemorySize; + + /** + * The amount of constant memory on the device, in bytes. + */ + uint32_t constantMemorySize; + + /** + * The size of the L2 cache on the device, in bytes. + */ + uint32_t l2CacheSize; + + /** + * The number of threads per warp on the device. + */ + uint32_t numThreadsPerWarp; + + /** + * The core clock rate of the device, in kHz. + */ + uint32_t coreClockRate; + + /** + * Number of memory copy engines on the device. + */ + uint32_t numMemcpyEngines; + + /** + * Number of multiprocessors on the device. + */ + uint32_t numMultiprocessors; + + /** + * The maximum "instructions per cycle" possible on each device + * multiprocessor. + */ + uint32_t maxIPC; + + /** + * Maximum number of warps that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxWarpsPerMultiprocessor; + + /** + * Maximum number of blocks that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxBlocksPerMultiprocessor; + + /** + * Maximum number of registers that can be allocated to a block. + */ + uint32_t maxRegistersPerBlock; + + /** + * Maximum amount of shared memory that can be assigned to a block, + * in bytes. + */ + uint32_t maxSharedMemoryPerBlock; + + /** + * Maximum number of threads allowed in a block. + */ + uint32_t maxThreadsPerBlock; + + /** + * Maximum allowed X dimension for a block. + */ + uint32_t maxBlockDimX; + + /** + * Maximum allowed Y dimension for a block. + */ + uint32_t maxBlockDimY; + + /** + * Maximum allowed Z dimension for a block. + */ + uint32_t maxBlockDimZ; + + /** + * Maximum allowed X dimension for a grid. + */ + uint32_t maxGridDimX; + + /** + * Maximum allowed Y dimension for a grid. + */ + uint32_t maxGridDimY; + + /** + * Maximum allowed Z dimension for a grid. + */ + uint32_t maxGridDimZ; + + /** + * Compute capability for the device, major number. + */ + uint32_t computeCapabilityMajor; + + /** + * Compute capability for the device, minor number. + */ + uint32_t computeCapabilityMinor; + + /** + * The device ID. + */ + uint32_t id; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The device name. This name is shared across all activity records + * representing instances of the device, and so should not be + * modified. + */ + const char *name; +} CUpti_ActivityDevice; + +/** + * \brief The activity record for a device. (deprecated) + * + * This activity record represents information about a GPU device + * (CUPTI_ACTIVITY_KIND_DEVICE). + * Device activity is now reported using the + * CUpti_ActivityDevice5 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The global memory bandwidth available on the device, in + * kBytes/sec. + */ + uint64_t globalMemoryBandwidth; + + /** + * The amount of global memory on the device, in bytes. + */ + uint64_t globalMemorySize; + + /** + * The amount of constant memory on the device, in bytes. + */ + uint32_t constantMemorySize; + + /** + * The size of the L2 cache on the device, in bytes. + */ + uint32_t l2CacheSize; + + /** + * The number of threads per warp on the device. + */ + uint32_t numThreadsPerWarp; + + /** + * The core clock rate of the device, in kHz. + */ + uint32_t coreClockRate; + + /** + * Number of memory copy engines on the device. + */ + uint32_t numMemcpyEngines; + + /** + * Number of multiprocessors on the device. + */ + uint32_t numMultiprocessors; + + /** + * The maximum "instructions per cycle" possible on each device + * multiprocessor. + */ + uint32_t maxIPC; + + /** + * Maximum number of warps that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxWarpsPerMultiprocessor; + + /** + * Maximum number of blocks that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxBlocksPerMultiprocessor; + + /** + * Maximum amount of shared memory available per multiprocessor, in bytes. + */ + uint32_t maxSharedMemoryPerMultiprocessor; + + /** + * Maximum number of 32-bit registers available per multiprocessor. + */ + uint32_t maxRegistersPerMultiprocessor; + + /** + * Maximum number of registers that can be allocated to a block. + */ + uint32_t maxRegistersPerBlock; + + /** + * Maximum amount of shared memory that can be assigned to a block, + * in bytes. + */ + uint32_t maxSharedMemoryPerBlock; + + /** + * Maximum number of threads allowed in a block. + */ + uint32_t maxThreadsPerBlock; + + /** + * Maximum allowed X dimension for a block. + */ + uint32_t maxBlockDimX; + + /** + * Maximum allowed Y dimension for a block. + */ + uint32_t maxBlockDimY; + + /** + * Maximum allowed Z dimension for a block. + */ + uint32_t maxBlockDimZ; + + /** + * Maximum allowed X dimension for a grid. + */ + uint32_t maxGridDimX; + + /** + * Maximum allowed Y dimension for a grid. + */ + uint32_t maxGridDimY; + + /** + * Maximum allowed Z dimension for a grid. + */ + uint32_t maxGridDimZ; + + /** + * Compute capability for the device, major number. + */ + uint32_t computeCapabilityMajor; + + /** + * Compute capability for the device, minor number. + */ + uint32_t computeCapabilityMinor; + + /** + * The device ID. + */ + uint32_t id; + + /** + * ECC enabled flag for device + */ + uint32_t eccEnabled; + + /** + * The device UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid uuid; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The device name. This name is shared across all activity records + * representing instances of the device, and so should not be + * modified. + */ + const char *name; +} CUpti_ActivityDevice2; + +/** + * \brief The activity record for a device. (CUDA 7.0 onwards) + * + * This activity record represents information about a GPU device + * (CUPTI_ACTIVITY_KIND_DEVICE). + * Device activity is now reported using the + * CUpti_ActivityDevice5 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The global memory bandwidth available on the device, in + * kBytes/sec. + */ + uint64_t globalMemoryBandwidth; + + /** + * The amount of global memory on the device, in bytes. + */ + uint64_t globalMemorySize; + + /** + * The amount of constant memory on the device, in bytes. + */ + uint32_t constantMemorySize; + + /** + * The size of the L2 cache on the device, in bytes. + */ + uint32_t l2CacheSize; + + /** + * The number of threads per warp on the device. + */ + uint32_t numThreadsPerWarp; + + /** + * The core clock rate of the device, in kHz. + */ + uint32_t coreClockRate; + + /** + * Number of memory copy engines on the device. + */ + uint32_t numMemcpyEngines; + + /** + * Number of multiprocessors on the device. + */ + uint32_t numMultiprocessors; + + /** + * The maximum "instructions per cycle" possible on each device + * multiprocessor. + */ + uint32_t maxIPC; + + /** + * Maximum number of warps that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxWarpsPerMultiprocessor; + + /** + * Maximum number of blocks that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxBlocksPerMultiprocessor; + + /** + * Maximum amount of shared memory available per multiprocessor, in bytes. + */ + uint32_t maxSharedMemoryPerMultiprocessor; + + /** + * Maximum number of 32-bit registers available per multiprocessor. + */ + uint32_t maxRegistersPerMultiprocessor; + + /** + * Maximum number of registers that can be allocated to a block. + */ + uint32_t maxRegistersPerBlock; + + /** + * Maximum amount of shared memory that can be assigned to a block, + * in bytes. + */ + uint32_t maxSharedMemoryPerBlock; + + /** + * Maximum number of threads allowed in a block. + */ + uint32_t maxThreadsPerBlock; + + /** + * Maximum allowed X dimension for a block. + */ + uint32_t maxBlockDimX; + + /** + * Maximum allowed Y dimension for a block. + */ + uint32_t maxBlockDimY; + + /** + * Maximum allowed Z dimension for a block. + */ + uint32_t maxBlockDimZ; + + /** + * Maximum allowed X dimension for a grid. + */ + uint32_t maxGridDimX; + + /** + * Maximum allowed Y dimension for a grid. + */ + uint32_t maxGridDimY; + + /** + * Maximum allowed Z dimension for a grid. + */ + uint32_t maxGridDimZ; + + /** + * Compute capability for the device, major number. + */ + uint32_t computeCapabilityMajor; + + /** + * Compute capability for the device, minor number. + */ + uint32_t computeCapabilityMinor; + + /** + * The device ID. + */ + uint32_t id; + + /** + * ECC enabled flag for device + */ + uint32_t eccEnabled; + + /** + * The device UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid uuid; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The device name. This name is shared across all activity records + * representing instances of the device, and so should not be + * modified. + */ + const char *name; + + /** + * Flag to indicate whether the device is visible to CUDA. Users can + * set the device visibility using CUDA_VISIBLE_DEVICES environment + */ + uint8_t isCudaVisible; + + uint8_t reserved[7]; +} CUpti_ActivityDevice3; + +/** + * \brief The activity record for a device. (CUDA 11.6 onwards) + * + * This activity record represents information about a GPU device + * (CUPTI_ACTIVITY_KIND_DEVICE). + * Device activity is now reported using the + * CUpti_ActivityDevice5 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_DEVICE. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the device. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The global memory bandwidth available on the device, in + * kBytes/sec. + */ + uint64_t globalMemoryBandwidth; + + /** + * The amount of global memory on the device, in bytes. + */ + uint64_t globalMemorySize; + + /** + * The amount of constant memory on the device, in bytes. + */ + uint32_t constantMemorySize; + + /** + * The size of the L2 cache on the device, in bytes. + */ + uint32_t l2CacheSize; + + /** + * The number of threads per warp on the device. + */ + uint32_t numThreadsPerWarp; + + /** + * The core clock rate of the device, in kHz. + */ + uint32_t coreClockRate; + + /** + * Number of memory copy engines on the device. + */ + uint32_t numMemcpyEngines; + + /** + * Number of multiprocessors on the device. + */ + uint32_t numMultiprocessors; + + /** + * The maximum "instructions per cycle" possible on each device + * multiprocessor. + */ + uint32_t maxIPC; + + /** + * Maximum number of warps that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxWarpsPerMultiprocessor; + + /** + * Maximum number of blocks that can be present on a multiprocessor + * at any given time. + */ + uint32_t maxBlocksPerMultiprocessor; + + /** + * Maximum amount of shared memory available per multiprocessor, in bytes. + */ + uint32_t maxSharedMemoryPerMultiprocessor; + + /** + * Maximum number of 32-bit registers available per multiprocessor. + */ + uint32_t maxRegistersPerMultiprocessor; + + /** + * Maximum number of registers that can be allocated to a block. + */ + uint32_t maxRegistersPerBlock; + + /** + * Maximum amount of shared memory that can be assigned to a block, + * in bytes. + */ + uint32_t maxSharedMemoryPerBlock; + + /** + * Maximum number of threads allowed in a block. + */ + uint32_t maxThreadsPerBlock; + + /** + * Maximum allowed X dimension for a block. + */ + uint32_t maxBlockDimX; + + /** + * Maximum allowed Y dimension for a block. + */ + uint32_t maxBlockDimY; + + /** + * Maximum allowed Z dimension for a block. + */ + uint32_t maxBlockDimZ; + + /** + * Maximum allowed X dimension for a grid. + */ + uint32_t maxGridDimX; + + /** + * Maximum allowed Y dimension for a grid. + */ + uint32_t maxGridDimY; + + /** + * Maximum allowed Z dimension for a grid. + */ + uint32_t maxGridDimZ; + + /** + * Compute capability for the device, major number. + */ + uint32_t computeCapabilityMajor; + + /** + * Compute capability for the device, minor number. + */ + uint32_t computeCapabilityMinor; + + /** + * The device ID. + */ + uint32_t id; + + /** + * ECC enabled flag for device + */ + uint32_t eccEnabled; + + /** + * The device UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid uuid; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The device name. This name is shared across all activity records + * representing instances of the device, and so should not be + * modified. + */ + const char *name; + + /** + * Flag to indicate whether the device is visible to CUDA. Users can + * set the device visibility using CUDA_VISIBLE_DEVICES environment + */ + uint8_t isCudaVisible; + + /** + * MIG enabled flag for device + */ + uint8_t isMigEnabled; + + uint8_t reserved[6]; + + /** + * GPU Instance id for MIG enabled devices. + * If mig mode is disabled value is set to UINT32_MAX + */ + uint32_t gpuInstanceId; + + /** + * Compute Instance id for MIG enabled devices. + * If mig mode is disabled value is set to UINT32_MAX + */ + uint32_t computeInstanceId; + + /** + * The MIG UUID. This value is the globally unique immutable + * alphanumeric identifier of the device. + */ + CUuuid migUuid; + +} CUpti_ActivityDevice4; + +/** + * \brief The activity record for kernel. (deprecated) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) but is no longer generated + * by CUPTI. Kernel activities are now reported using the + * CUpti_ActivityKernel9 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL + * or CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t cacheConfigRequested; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t cacheConfigExecuted; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the kernel. + */ + uint32_t correlationId; + + /** + * The runtime correlation ID of the kernel. Each kernel execution + * is assigned a unique runtime correlation ID that is identical to + * the correlation ID in the runtime API activity record that + * launched the kernel. + */ + uint32_t runtimeCorrelationId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityKernel; + +/** + * \brief The activity record for kernel. (deprecated) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) but is no longer generated + * by CUPTI. Kernel activities are now reported using the + * CUpti_ActivityKernel9 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityKernel2; + +/** + * \brief The activity record for a kernel (CUDA 6.5(with sm_52 support) onwards). + * (deprecated in CUDA 9.0) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL). + * Kernel activities are now reported using the CUpti_ActivityKernel9 activity + * record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityKernel3; + +/** + * \brief The activity record for a kernel (CUDA 9.0(with sm_70 support) onwards). + * (deprecated in CUDA 11.0) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL). + * Kernel activities are now reported using the CUpti_ActivityKernel9 activity + * record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; +} CUpti_ActivityKernel4; + +/** + * \brief The activity record for a kernel (CUDA 11.0(with sm_80 support) onwards). + * (deprecated in CUDA 11.2) + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) but is no longer generated + * by CUPTI. Kernel activities are now reported using the + * CUpti_ActivityKernel9 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; + + /** + * The unique ID of the graph node that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint64_t graphNodeId; + + /** + * The shared memory limit config for the kernel. This field shows whether user has opted for a + * higher per block limit of dynamic shared memory. + */ + CUpti_FuncShmemLimitConfig shmemLimitConfig; + + /** + * The unique ID of the graph that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint32_t graphId; +} CUpti_ActivityKernel5; + +/** + * \brief The activity record for kernel. (deprecated in CUDA 11.6) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) but is no longer generated + * by CUPTI. Kernel activities are now reported using the + * CUpti_ActivityKernel9 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; + + /** + * The unique ID of the graph node that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint64_t graphNodeId; + + /** + * The shared memory limit config for the kernel. This field shows whether user has opted for a + * higher per block limit of dynamic shared memory. + */ + CUpti_FuncShmemLimitConfig shmemLimitConfig; + + /** + * The unique ID of the graph that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint32_t graphId; + + /** + * The pointer to the access policy window. The structure CUaccessPolicyWindow is + * defined in cuda.h. + */ + CUaccessPolicyWindow *pAccessPolicyWindow; +} CUpti_ActivityKernel6; + +/** + * \brief The activity record for kernel. (deprecated in CUDA 11.8) + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) but is no longer generated + * by CUPTI. Kernel activities are now reported using the + * CUpti_ActivityKernel9 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; + + /** + * The unique ID of the graph node that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint64_t graphNodeId; + + /** + * The shared memory limit config for the kernel. This field shows whether user has opted for a + * higher per block limit of dynamic shared memory. + */ + CUpti_FuncShmemLimitConfig shmemLimitConfig; + + /** + * The unique ID of the graph that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint32_t graphId; + + /** + * The pointer to the access policy window. The structure CUaccessPolicyWindow is + * defined in cuda.h. + */ + CUaccessPolicyWindow *pAccessPolicyWindow; + + /** + * The ID of the HW channel on which the kernel is launched. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; +} CUpti_ActivityKernel7; + +/** + * \brief The activity record for kernel. + * + * This activity record represents a kernel execution + * (CUPTI_ACTIVITY_KIND_KERNEL and + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL) + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_KERNEL or + * CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL. + */ + CUpti_ActivityKind kind; + + /** + * For devices with compute capability 7.0+ cacheConfig values are not updated + * in case field isSharedMemoryCarveoutRequested is set + */ + union { + uint8_t both; + struct { + /** + * The cache configuration requested by the kernel. The value is one + * of the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t requested:4; + + /** + * The cache configuration used for the kernel. The value is one of + * the CUfunc_cache enumeration values from cuda.h. + */ + uint8_t executed:4; + } config; + } cacheConfig; + + /** + * The shared memory configuration used for the kernel. The value is one of + * the CUsharedconfig enumeration values from cuda.h. + */ + uint8_t sharedMemoryConfig; + + /** + * The number of registers required for each thread executing the + * kernel. + */ + uint16_t registersPerThread; + + /** + * The partitioned global caching requested for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheRequested; + + /** + * The partitioned global caching executed for the kernel. Partitioned + * global caching is required to enable caching on certain chips, such as + * devices with compute capability 5.2. Partitioned global caching can be + * automatically disabled if the occupancy requirement of the launch cannot + * support caching. + */ + CUpti_ActivityPartitionedGlobalCacheConfig partitionedGlobalCacheExecuted; + + /** + * The start timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t start; + + /** + * The end timestamp for the kernel execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the kernel. + */ + uint64_t end; + + /** + * The completed timestamp for the kernel execution, in ns. It + * represents the completion of all it's child kernels and the + * kernel itself. A value of CUPTI_TIMESTAMP_UNKNOWN indicates that + * the completion time is unknown. + */ + uint64_t completed; + + /** + * The ID of the device where the kernel is executing. + */ + uint32_t deviceId; + + /** + * The ID of the context where the kernel is executing. + */ + uint32_t contextId; + + /** + * The ID of the stream where the kernel is executing. + */ + uint32_t streamId; + + /** + * The X-dimension grid size for the kernel. + */ + int32_t gridX; + + /** + * The Y-dimension grid size for the kernel. + */ + int32_t gridY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t gridZ; + + /** + * The X-dimension block size for the kernel. + */ + int32_t blockX; + + /** + * The Y-dimension block size for the kernel. + */ + int32_t blockY; + + /** + * The Z-dimension grid size for the kernel. + */ + int32_t blockZ; + + /** + * The static shared memory allocated for the kernel, in bytes. + */ + int32_t staticSharedMemory; + + /** + * The dynamic shared memory reserved for the kernel, in bytes. + */ + int32_t dynamicSharedMemory; + + /** + * The amount of local memory reserved for each thread, in bytes. + */ + uint32_t localMemoryPerThread; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes (deprecated in CUDA 11.8). + * Refer field localMemoryTotal_v2 + */ + uint32_t localMemoryTotal; + + /** + * The correlation ID of the kernel. Each kernel execution is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the kernel. + */ + uint32_t correlationId; + + /** + * The grid ID of the kernel. Each kernel is assigned a unique + * grid ID at runtime. + */ + int64_t gridId; + + /** + * The name of the kernel. This name is shared across all activity + * records representing the same kernel, and so should not be + * modified. + */ + const char *name; + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The timestamp when the kernel is queued up in the command buffer, in ns. + * A value of CUPTI_TIMESTAMP_UNKNOWN indicates that the queued time + * could not be collected for the kernel. This timestamp is not collected + * by default. Use API \ref cuptiActivityEnableLatencyTimestamps() to + * enable collection. + * + * Command buffer is a buffer written by CUDA driver to send commands + * like kernel launch, memory copy etc to the GPU. All launches of CUDA + * kernels are asynchronous with respect to the host, the host requests + * the launch by writing commands into the command buffer, then returns + * without checking the GPU's progress. + */ + uint64_t queued; + + /** + * The timestamp when the command buffer containing the kernel launch + * is submitted to the GPU, in ns. A value of CUPTI_TIMESTAMP_UNKNOWN + * indicates that the submitted time could not be collected for the kernel. + * This timestamp is not collected by default. Use API \ref + * cuptiActivityEnableLatencyTimestamps() to enable collection. + */ + uint64_t submitted; + + /** + * The indicates if the kernel was executed via a regular launch or via a + * single/multi device cooperative launch. \see CUpti_ActivityLaunchType + */ + uint8_t launchType; + + /** + * This indicates if CU_FUNC_ATTRIBUTE_PREFERRED_SHARED_MEMORY_CARVEOUT was + * updated for the kernel launch + */ + uint8_t isSharedMemoryCarveoutRequested; + + /** + * Shared memory carveout value requested for the function in percentage of + * the total resource. The value will be updated only if field + * isSharedMemoryCarveoutRequested is set. + */ + uint8_t sharedMemoryCarveoutRequested; + + /** + * Undefined. Reserved for internal use. + */ + uint8_t padding; + + /** + * Shared memory size set by the driver. + */ + uint32_t sharedMemoryExecuted; + + /** + * The unique ID of the graph node that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint64_t graphNodeId; + + /** + * The shared memory limit config for the kernel. This field shows whether user has opted for a + * higher per block limit of dynamic shared memory. + */ + CUpti_FuncShmemLimitConfig shmemLimitConfig; + + /** + * The unique ID of the graph that launched this kernel through graph launch APIs. + * This field will be 0 if the kernel is not launched through graph launch APIs. + */ + uint32_t graphId; + + /** + * The pointer to the access policy window. The structure CUaccessPolicyWindow is + * defined in cuda.h. + */ + CUaccessPolicyWindow *pAccessPolicyWindow; + + /** + * The ID of the HW channel on which the kernel is launched. + */ + uint32_t channelID; + + /** + * The type of the channel + */ + CUpti_ChannelType channelType; + + /** + * The X-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterX; + + /** + * The Y-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterY; + + /** + * The Z-dimension cluster size for the kernel. + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterZ; + + /** + * The cluster scheduling policy for the kernel. Refer CUclusterSchedulingPolicy + * Field is valid for devices with compute capability 9.0 and higher + */ + uint32_t clusterSchedulingPolicy; + + /** + * The total amount of local memory reserved for the kernel, in + * bytes. + */ + uint64_t localMemoryTotal_v2; +} CUpti_ActivityKernel8; + +/** + * \brief The activity record for memory copies. (deprecated) + * + * This activity record represents a memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the memory copy. + */ + uint32_t correlationId; + + /** + * The runtime correlation ID of the memory copy. Each memory copy + * is assigned a unique runtime correlation ID that is identical to + * the correlation ID in the runtime API activity record that + * launched the memory copy. + */ + uint32_t runtimeCorrelationId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityMemcpy; + +/** + * \brief The activity record for memory copies. (deprecated in CUDA 11.1) + * + * This activity record represents a memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the memory copy. + */ + uint32_t correlationId; + + /** + * The runtime correlation ID of the memory copy. Each memory copy + * is assigned a unique runtime correlation ID that is identical to + * the correlation ID in the runtime API activity record that + * launched the memory copy. + */ + uint32_t runtimeCorrelationId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint64_t graphNodeId; +} CUpti_ActivityMemcpy3; + +/** + * \brief The activity record for memory copies. (deprecated in CUDA 11.6) + * + * This activity record represents a memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the memory copy. + */ + uint32_t correlationId; + + /** + * The runtime correlation ID of the memory copy. Each memory copy + * is assigned a unique runtime correlation ID that is identical to + * the correlation ID in the runtime API activity record that + * launched the memory copy. + */ + uint32_t runtimeCorrelationId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint32_t graphId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t padding; +} CUpti_ActivityMemcpy4; + +/** + * \brief The activity record for peer-to-peer memory copies. + * + * This activity record represents a peer-to-peer memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY2) but is no longer generated + * by CUPTI. Peer-to-peer memory copy activities are now reported using the + * CUpti_ActivityMemcpyPtoP2 activity record.. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY2. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see + * CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The ID of the device where memory is being copied from. + */ + uint32_t srcDeviceId; + + /** + * The ID of the context owning the memory being copied from. + */ + uint32_t srcContextId; + + /** + * The ID of the device where memory is being copied to. + */ + uint32_t dstDeviceId; + + /** + * The ID of the context owning the memory being copied to. + */ + uint32_t dstContextId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory copy. + */ + uint32_t correlationId; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityMemcpyPtoP; + +typedef CUpti_ActivityMemcpyPtoP CUpti_ActivityMemcpy2; + +/** + * \brief The activity record for peer-to-peer memory copies. + * (deprecated in CUDA 11.1) + * + * This activity record represents a peer-to-peer memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY2). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY2. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see + * CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The ID of the device where memory is being copied from. + */ + uint32_t srcDeviceId; + + /** + * The ID of the context owning the memory being copied from. + */ + uint32_t srcContextId; + + /** + * The ID of the device where memory is being copied to. + */ + uint32_t dstDeviceId; + + /** + * The ID of the context owning the memory being copied to. + */ + uint32_t dstContextId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory copy. + */ + uint32_t correlationId; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed the memcpy through graph launch. + * This field will be 0 if memcpy is not done using graph launch. + */ + uint64_t graphNodeId; +} CUpti_ActivityMemcpyPtoP2; + +/** + * \brief The activity record for peer-to-peer memory copies. + * (deprecated in CUDA 11.6) + * + * This activity record represents a peer-to-peer memory copy + * (CUPTI_ACTIVITY_KIND_MEMCPY2). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMCPY2. + */ + CUpti_ActivityKind kind; + + /** + * The kind of the memory copy, stored as a byte to reduce record + * size. \see CUpti_ActivityMemcpyKind + */ + uint8_t copyKind; + + /** + * The source memory kind read by the memory copy, stored as a byte + * to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t srcKind; + + /** + * The destination memory kind read by the memory copy, stored as a + * byte to reduce record size. \see CUpti_ActivityMemoryKind + */ + uint8_t dstKind; + + /** + * The flags associated with the memory copy. \see + * CUpti_ActivityFlag + */ + uint8_t flags; + + /** + * The number of bytes transferred by the memory copy. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t start; + + /** + * The end timestamp for the memory copy, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory copy. + */ + uint64_t end; + + /** + * The ID of the device where the memory copy is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory copy is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory copy is occurring. + */ + uint32_t streamId; + + /** + * The ID of the device where memory is being copied from. + */ + uint32_t srcDeviceId; + + /** + * The ID of the context owning the memory being copied from. + */ + uint32_t srcContextId; + + /** + * The ID of the device where memory is being copied to. + */ + uint32_t dstDeviceId; + + /** + * The ID of the context owning the memory being copied to. + */ + uint32_t dstContextId; + + /** + * The correlation ID of the memory copy. Each memory copy is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory copy. + */ + uint32_t correlationId; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed the memcpy through graph launch. + * This field will be 0 if memcpy is not done using graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memcpy through graph launch. + * This field will be 0 if the memcpy is not done through graph launch. + */ + uint32_t graphId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t padding; +} CUpti_ActivityMemcpyPtoP3; + +/** + * \brief The activity record for memset. (deprecated) + * + * This activity record represents a memory set operation + * (CUPTI_ACTIVITY_KIND_MEMSET). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMSET. + */ + CUpti_ActivityKind kind; + + /** + * The value being assigned to memory by the memory set. + */ + uint32_t value; + + /** + * The number of bytes being set by the memory set. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t start; + + /** + * The end timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t end; + + /** + * The ID of the device where the memory set is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory set is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory set is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory set. Each memory set is assigned + * a unique correlation ID that is identical to the correlation ID + * in the driver API activity record that launched the memory set. + */ + uint32_t correlationId; + + /** + * The flags associated with the memset. \see CUpti_ActivityFlag + */ + uint16_t flags; + + /** + * The memory kind of the memory set \see CUpti_ActivityMemoryKind + */ + uint16_t memoryKind; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; +} CUpti_ActivityMemset; + +/** + * \brief The activity record for memset. (deprecated in CUDA 11.1) + * + * This activity record represents a memory set operation + * (CUPTI_ACTIVITY_KIND_MEMSET). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMSET. + */ + CUpti_ActivityKind kind; + + /** + * The value being assigned to memory by the memory set. + */ + uint32_t value; + + /** + * The number of bytes being set by the memory set. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t start; + + /** + * The end timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t end; + + /** + * The ID of the device where the memory set is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory set is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory set is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory set. Each memory set is assigned + * a unique correlation ID that is identical to the correlation ID + * in the driver API activity record that launched the memory set. + */ + uint32_t correlationId; + + /** + * The flags associated with the memset. \see CUpti_ActivityFlag + */ + uint16_t flags; + + /** + * The memory kind of the memory set \see CUpti_ActivityMemoryKind + */ + uint16_t memoryKind; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memset through graph launch. + * This field will be 0 if the memset is not executed through graph launch. + */ + uint64_t graphNodeId; +} CUpti_ActivityMemset2; + +/** + * \brief The activity record for memset. (deprecated in CUDA 11.6) + * + * This activity record represents a memory set operation + * (CUPTI_ACTIVITY_KIND_MEMSET). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMSET. + */ + CUpti_ActivityKind kind; + + /** + * The value being assigned to memory by the memory set. + */ + uint32_t value; + + /** + * The number of bytes being set by the memory set. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t start; + + /** + * The end timestamp for the memory set, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the memory set. + */ + uint64_t end; + + /** + * The ID of the device where the memory set is occurring. + */ + uint32_t deviceId; + + /** + * The ID of the context where the memory set is occurring. + */ + uint32_t contextId; + + /** + * The ID of the stream where the memory set is occurring. + */ + uint32_t streamId; + + /** + * The correlation ID of the memory set. Each memory set is assigned + * a unique correlation ID that is identical to the correlation ID + * in the driver API activity record that launched the memory set. + */ + uint32_t correlationId; + + /** + * The flags associated with the memset. \see CUpti_ActivityFlag + */ + uint16_t flags; + + /** + * The memory kind of the memory set \see CUpti_ActivityMemoryKind + */ + uint16_t memoryKind; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * Undefined. Reserved for internal use. + */ + void *reserved0; + + /** + * The unique ID of the graph node that executed this memset through graph launch. + * This field will be 0 if the memset is not executed through graph launch. + */ + uint64_t graphNodeId; + + /** + * The unique ID of the graph that executed this memset through graph launch. + * This field will be 0 if the memset is not executed through graph launch. + */ + uint32_t graphId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t padding; +} CUpti_ActivityMemset3; + +/** + * \brief The activity record for memory. + * + * This activity record represents a memory allocation and free operation + * (CUPTI_ACTIVITY_KIND_MEMORY2). + * This activity record provides separate records for memory allocation and + * memory release operations. + * This allows to correlate the corresponding driver and runtime API + * activity record with the memory operation. + * + * Note: This activity record is an upgrade over \ref CUpti_ActivityMemory + * enabled using the kind \ref CUPTI_ACTIVITY_KIND_MEMORY. + * \ref CUpti_ActivityMemory provides a single record for the memory + * allocation and memory release operations. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMORY2 + */ + CUpti_ActivityKind kind; + + /** + * The memory operation requested by the user, \ref CUpti_ActivityMemoryOperationType. + */ + CUpti_ActivityMemoryOperationType memoryOperationType; + + /** + * The memory kind requested by the user, \ref CUpti_ActivityMemoryKind. + */ + CUpti_ActivityMemoryKind memoryKind; + + /** + * The correlation ID of the memory operation. Each memory operation is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory operation. + */ + uint32_t correlationId; + + /** + * The virtual address of the allocation. + */ + uint64_t address; + + /** + * The number of bytes of memory allocated. + */ + uint64_t bytes; + + /** + * The start timestamp for the memory operation, in ns. + */ + uint64_t timestamp; + + /** + * The program counter of the memory operation. + */ + uint64_t PC; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The ID of the device where the memory operation is taking place. + */ + uint32_t deviceId; + + /** + * The ID of the context. If context is NULL, \p contextId is set to CUPTI_INVALID_CONTEXT_ID. + */ + uint32_t contextId; + + /** + * The ID of the stream. If memory operation is not async, \p streamId is set to CUPTI_INVALID_STREAM_ID. + */ + uint32_t streamId; + + /** + * Variable name. This name is shared across all activity + * records representing the same symbol, and so should not be + * modified. + */ + const char* name; + + /** + * \p isAsync is set if memory operation happens through async memory APIs. + */ + uint32_t isAsync; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad1; +#endif + + /** + * The memory pool configuration used for the memory operations. + */ + struct { + /** + * The type of the memory pool, \ref CUpti_ActivityMemoryPoolType + */ + CUpti_ActivityMemoryPoolType memoryPoolType; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad2; +#endif + + /** + * The base address of the memory pool. + */ + uint64_t address; + + /** + * The release threshold of the memory pool in bytes. \p releaseThreshold is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t releaseThreshold; + + /** + * The size of the memory pool in bytes and the processID of the memory pool. + * \p size is valid if \p memoryPoolType is + * CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + * \p processId is valid if \p memoryPoolType is + * CUPTI_ACTIVITY_MEMORY_POOL_TYPE_IMPORTED, \ref CUpti_ActivityMemoryPoolType. + */ + union { + uint64_t size; + uint64_t processId; + } pool; + } memoryPoolConfig; + +} CUpti_ActivityMemory2; + +/** + * \brief The activity record for memory pool. + * + * This activity record represents a memory pool creation, destruction and + * trimming (CUPTI_ACTIVITY_KIND_MEMORY_POOL). + * This activity record provides separate records for memory pool creation, + * destruction and trimming operations. + * This allows to correlate the corresponding driver and runtime API + * activity record with the memory pool operation. + * + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MEMORY_POOL + */ + CUpti_ActivityKind kind; + + /** + * The memory operation requested by the user, \ref CUpti_ActivityMemoryPoolOperationType. + */ + CUpti_ActivityMemoryPoolOperationType memoryPoolOperationType; + + /** + * The type of the memory pool, \ref CUpti_ActivityMemoryPoolType + */ + CUpti_ActivityMemoryPoolType memoryPoolType; + + /** + * The correlation ID of the memory pool operation. Each memory pool + * operation is assigned a unique correlation ID that is identical to the + * correlation ID in the driver and runtime API activity record that + * launched the memory operation. + */ + uint32_t correlationId; + + /** + * The ID of the process to which this record belongs to. + */ + uint32_t processId; + + /** + * The ID of the device where the memory pool is created. + */ + uint32_t deviceId; + + /** + * The minimum bytes to keep of the memory pool. \p minBytesToKeep is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_OPERATION_TYPE_TRIMMED, + * \ref CUpti_ActivityMemoryPoolOperationType + */ + size_t minBytesToKeep; + +#ifndef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The virtual address of the allocation. + */ + uint64_t address; + + /** + * The size of the memory pool operation in bytes. \p size is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t size; + + /** + * The release threshold of the memory pool. \p releaseThreshold is + * valid for CUPTI_ACTIVITY_MEMORY_POOL_TYPE_LOCAL, \ref CUpti_ActivityMemoryPoolType. + */ + uint64_t releaseThreshold; + + /** + * The start timestamp for the memory operation, in ns. + */ + uint64_t timestamp; +} CUpti_ActivityMemoryPool; + +/** + * \brief The activity record providing a marker which is an + * instantaneous point in time. (deprecated in CUDA 8.0) + * + * The marker is specified with a descriptive name and unique id + * (CUPTI_ACTIVITY_KIND_MARKER). + * Marker activity is now reported using the + * CUpti_ActivityMarker2 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_MARKER. + */ + CUpti_ActivityKind kind; + + /** + * The flags associated with the marker. \see CUpti_ActivityFlag + */ + CUpti_ActivityFlag flags; + + /** + * The timestamp for the marker, in ns. A value of 0 indicates that + * timestamp information could not be collected for the marker. + */ + uint64_t timestamp; + + /** + * The marker ID. + */ + uint32_t id; + + /** + * The kind of activity object associated with this marker. + */ + CUpti_ActivityObjectKind objectKind; + + /** + * The identifier for the activity object associated with this + * marker. 'objectKind' indicates which ID is valid for this record. + */ + CUpti_ActivityObjectKindId objectId; + +#ifdef CUPTILP64 + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +#endif + + /** + * The marker name for an instantaneous or start marker. This will + * be NULL for an end marker. + */ + const char *name; + +} CUpti_ActivityMarker; + +/** + * \brief The activity record for source-level global + * access. (deprecated) + * + * This activity records the locations of the global + * accesses in the source (CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS). + * Global access activities are now reported using the + * CUpti_ActivityGlobalAccess3 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this global access. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * The pc offset for the access. + */ + uint32_t pcOffset; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * when at least one of thread among warp is active with predicate and condition code + * evaluating to true. + */ + uint32_t executed; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction with predicate and condition code evaluating to true. + */ + uint64_t threadsExecuted; + + /** + * The total number of 32 bytes transactions to L2 cache generated by this access + */ + uint64_t l2_transactions; +} CUpti_ActivityGlobalAccess; + +/** + * \brief The activity record for source-level global + * access. (deprecated in CUDA 9.0) + * + * This activity records the locations of the global + * accesses in the source (CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS). + * Global access activities are now reported using the + * CUpti_ActivityGlobalAccess3 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_GLOBAL_ACCESS. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this global access. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the access. + */ + uint32_t pcOffset; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction with predicate and condition code evaluating to true. + */ + uint64_t threadsExecuted; + + /** + * The total number of 32 bytes transactions to L2 cache generated by this access + */ + uint64_t l2_transactions; + + /** + * The minimum number of L2 transactions possible based on the access pattern. + */ + uint64_t theoreticalL2Transactions; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * when at least one of thread among warp is active with predicate and condition code + * evaluating to true. + */ + uint32_t executed; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityGlobalAccess2; + +/** + * \brief The activity record for source level result + * branch. (deprecated) + * + * This activity record the locations of the branches in the + * source (CUPTI_ACTIVITY_KIND_BRANCH). + * Branch activities are now reported using the + * CUpti_ActivityBranch2 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_BRANCH. + */ + CUpti_ActivityKind kind; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * The pc offset for the branch. + */ + uint32_t pcOffset; + + /** + * The number of times this instruction was executed per warp. It will be incremented + * regardless of predicate or condition code. + */ + uint32_t executed; + + /** + * Number of times this branch diverged + */ + uint32_t diverged; + + /** + * This increments each time when this instruction is executed by number + * of threads that executed this instruction + */ + uint64_t threadsExecuted; +} CUpti_ActivityBranch; + +/** + * \brief The activity record for PC sampling. (deprecated in CUDA 8.0) + * + * This activity records information obtained by sampling PC + * (CUPTI_ACTIVITY_KIND_PC_SAMPLING). + * PC sampling activities are now reported using the + * CUpti_ActivityPCSampling2 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PC_SAMPLING. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this instruction. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the instruction. + */ + uint32_t pcOffset; + + /** + * Number of times the PC was sampled with the stallReason in the record. + * The same PC can be sampled with different stall reasons. + */ + uint32_t samples; + + /** + * Current stall reason. Includes one of the reasons from + * \ref CUpti_ActivityPCSamplingStallReason + */ + CUpti_ActivityPCSamplingStallReason stallReason; +} CUpti_ActivityPCSampling; + +/** + * \brief The activity record for PC sampling. (deprecated in CUDA 9.0) + * + * This activity records information obtained by sampling PC + * (CUPTI_ACTIVITY_KIND_PC_SAMPLING). + * PC sampling activities are now reported using the + * CUpti_ActivityPCSampling3 activity record. + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_PC_SAMPLING. + */ + CUpti_ActivityKind kind; + + /** + * The properties of this instruction. + */ + CUpti_ActivityFlag flags; + + /** + * The ID for source locator. + */ + uint32_t sourceLocatorId; + + /** + * The correlation ID of the kernel to which this result is associated. + */ + uint32_t correlationId; + + /** + * Correlation ID with global/device function name + */ + uint32_t functionId; + + /** + * The pc offset for the instruction. + */ + uint32_t pcOffset; + + /** + * Number of times the PC was sampled with the stallReason in the record. + * These samples indicate that no instruction was issued in that cycle from + * the warp scheduler from where the warp was sampled. + * Field is valid for devices with compute capability 6.0 and higher + */ + uint32_t latencySamples; + + /** + * Number of times the PC was sampled with the stallReason in the record. + * The same PC can be sampled with different stall reasons. The count includes + * latencySamples. + */ + uint32_t samples; + + /** + * Current stall reason. Includes one of the reasons from + * \ref CUpti_ActivityPCSamplingStallReason + */ + CUpti_ActivityPCSamplingStallReason stallReason; + + uint32_t pad; +} CUpti_ActivityPCSampling2; + +/** + * \brief The activity record for Unified Memory counters (deprecated in CUDA 7.0) + * + * This activity record represents a Unified Memory counter + * (CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER). + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_UNIFIED_MEMORY_COUNTER + */ + CUpti_ActivityKind kind; + + /** + * The Unified Memory counter kind. See \ref CUpti_ActivityUnifiedMemoryCounterKind + */ + CUpti_ActivityUnifiedMemoryCounterKind counterKind; + + /** + * Scope of the Unified Memory counter. See \ref CUpti_ActivityUnifiedMemoryCounterScope + */ + CUpti_ActivityUnifiedMemoryCounterScope scope; + + /** + * The ID of the device involved in the memory transfer operation. + * It is not relevant if the scope of the counter is global (all devices). + */ + uint32_t deviceId; + + /** + * Value of the counter + * + */ + uint64_t value; + + /** + * The timestamp when this sample was retrieved, in ns. A value of 0 + * indicates that timestamp information could not be collected + */ + uint64_t timestamp; + + /** + * The ID of the process to which this record belongs to. In case of + * global scope, processId is undefined. + */ + uint32_t processId; + + /** + * Undefined. Reserved for internal use. + */ + uint32_t pad; +} CUpti_ActivityUnifiedMemoryCounter; + +/** +* \brief NVLink information. (deprecated in CUDA 9.0) +* +* This structure gives capabilities of each logical NVLink connection between two devices, +* gpu<->gpu or gpu<->CPU which can be used to understand the topology. +* NVLink information are now reported using the +* CUpti_ActivityNvLink2 activity record. +*/ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_NVLINK. + */ + CUpti_ActivityKind kind; + + /** + * NVLink version. + */ + uint32_t nvlinkVersion; + + /** + * Type of device 0 \ref CUpti_DevType + */ + CUpti_DevType typeDev0; + + /** + * Type of device 1 \ref CUpti_DevType + */ + CUpti_DevType typeDev1; + + /** + * If typeDev0 is CUPTI_DEV_TYPE_GPU, UUID for device 0. \ref CUpti_ActivityDevice5. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev0; + + /** + * If typeDev1 is CUPTI_DEV_TYPE_GPU, UUID for device 1. \ref CUpti_ActivityDevice5. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev1; + + /** + * Flag gives capabilities of the link \see CUpti_LinkFlag + */ + uint32_t flag; + + /** + * Number of physical NVLinks present between two devices. + */ + uint32_t physicalNvLinkCount; + + /** + * Port numbers for maximum 4 NVLinks connected to device 0. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev0[4]; + + /** + * Port numbers for maximum 4 NVLinks connected to device 1. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev1[4]; + + /** + * Bandwidth of NVLink in kbytes/sec + */ + uint64_t bandwidth; +} CUpti_ActivityNvLink; + +/** +* \brief NVLink information. (deprecated in CUDA 10.0) +* +* This structure gives capabilities of each logical NVLink connection between two devices, +* gpu<->gpu or gpu<->CPU which can be used to understand the topology. +* NvLink information are now reported using the +* CUpti_ActivityNvLink4 activity record. +*/ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_NVLINK. + */ + CUpti_ActivityKind kind; + + /** + * NvLink version. + */ + uint32_t nvlinkVersion; + + /** + * Type of device 0 \ref CUpti_DevType + */ + CUpti_DevType typeDev0; + + /** + * Type of device 1 \ref CUpti_DevType + */ + CUpti_DevType typeDev1; + + /** + * If typeDev0 is CUPTI_DEV_TYPE_GPU, UUID for device 0. \ref CUpti_ActivityDevice5. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev0; + + /** + * If typeDev1 is CUPTI_DEV_TYPE_GPU, UUID for device 1. \ref CUpti_ActivityDevice5. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev1; + + /** + * Flag gives capabilities of the link \see CUpti_LinkFlag + */ + uint32_t flag; + + /** + * Number of physical NVLinks present between two devices. + */ + uint32_t physicalNvLinkCount; + + /** + * Port numbers for maximum 16 NVLinks connected to device 0. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev0[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Port numbers for maximum 16 NVLinks connected to device 1. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev1[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Bandwidth of NVLink in kbytes/sec + */ + uint64_t bandwidth; +} CUpti_ActivityNvLink2; + +/** +* \brief NVLink information. +* +* This structure gives capabilities of each logical NVLink connection between two devices, +* gpu<->gpu or gpu<->CPU which can be used to understand the topology. +* NvLink information are now reported using the +* CUpti_ActivityNvLink4 activity record. +*/ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_NVLINK. + */ + CUpti_ActivityKind kind; + /** + * NvLink version. + */ + uint32_t nvlinkVersion; + + /** + * Type of device 0 \ref CUpti_DevType + */ + CUpti_DevType typeDev0; + + /** + * Type of device 1 \ref CUpti_DevType + */ + CUpti_DevType typeDev1; + + /** + * If typeDev0 is CUPTI_DEV_TYPE_GPU, UUID for device 0. \ref CUpti_ActivityDevice5. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev0; + + /** + * If typeDev1 is CUPTI_DEV_TYPE_GPU, UUID for device 1. \ref CUpti_ActivityDevice5. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, struct npu for NPU. + */ + union { + CUuuid uuidDev; + struct { + /** + * Index of the NPU. First index will always be zero. + */ + uint32_t index; + + /** + * Domain ID of NPU. On Linux, this can be queried using lspci. + */ + uint32_t domainId; + } npu; + } idDev1; + + /** + * Flag gives capabilities of the link \see CUpti_LinkFlag + */ + uint32_t flag; + + /** + * Number of physical NVLinks present between two devices. + */ + uint32_t physicalNvLinkCount; + + /** + * Port numbers for maximum 16 NVLinks connected to device 0. + * If typeDev0 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev0[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Port numbers for maximum 16 NVLinks connected to device 1. + * If typeDev1 is CUPTI_DEV_TYPE_NPU, ignore this field. + * In case of invalid/unknown port number, this field will be set + * to value CUPTI_NVLINK_INVALID_PORT. + * This will be used to correlate the metric values to individual + * physical link and attribute traffic to the logical NVLink in + * the topology. + */ + int8_t portDev1[CUPTI_MAX_NVLINK_PORTS]; + + /** + * Bandwidth of NVLink in kbytes/sec + */ + uint64_t bandwidth; + + /** + * NVSwitch is connected as an intermediate node. + */ + uint8_t nvswitchConnected; + + /** + * Undefined. reserved for internal use + */ + uint8_t pad[7]; +} CUpti_ActivityNvLink3; + +/** + * \brief The activity record for trace of graph execution. + * + * This activity record represents execution for a graph without giving visibility + * about the execution of its nodes. This is intended to reduce overheads in tracing + * each node. The activity kind is CUPTI_ACTIVITY_KIND_GRAPH_TRACE + * Graph trace activity is now reported using CUpti_ActivityGraphTrace2 record. + */ +typedef struct { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_GRAPH_TRACE + */ + CUpti_ActivityKind kind; + + /** + * The correlation ID of the graph launch. Each graph launch is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver API activity record that launched + * the graph. + */ + uint32_t correlationId; + + /** + * The start timestamp for the graph execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the graph. + */ + uint64_t start; + + /** + * The end timestamp for the graph execution, in ns. A value of 0 + * for both the start and end timestamps indicates that timestamp + * information could not be collected for the graph. + */ + uint64_t end; + + /** + * The ID of the device where the graph execution is occurring. + */ + uint32_t deviceId; + + /** + * The unique ID of the graph that is launched. + */ + uint32_t graphId; + + /** + * The ID of the context where the graph is being launched. + */ + uint32_t contextId; + + /** + * The ID of the stream where the graph is being launched. + */ + uint32_t streamId; + + /** + * This field is reserved for internal use + */ + void *reserved; +} CUpti_ActivityGraphTrace; + +/** + * \brief The activity record for a context. + * + * This activity record represents information about a context + * (CUPTI_ACTIVITY_KIND_CONTEXT). + * Context activity is now reported using CUpti_ActivityContext2 record + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind, must be CUPTI_ACTIVITY_KIND_CONTEXT. + */ + CUpti_ActivityKind kind; + + /** + * The context ID. + */ + uint32_t contextId; + + /** + * The device ID. + */ + uint32_t deviceId; + + /** + * The compute API kind. \see CUpti_ActivityComputeApiKind + */ + uint16_t computeApiKind; + + /** + * The ID for the NULL stream in this context + */ + uint16_t nullStreamId; +} CUpti_ActivityContext; + +/** + * \brief The activity record for JIT operations. + * This activity represents the JIT operations (compile, load, store) of a CUmodule + * from the Compute Cache. + * Gives the exact hashed path of where the cached module is loaded from, + * or where the module will be stored after Just-In-Time (JIT) compilation. + * + * JIT activity is now reported using CUpti_ActivityJit2 record + */ +typedef struct PACKED_ALIGNMENT { + /** + * The activity record kind must be CUPTI_ACTIVITY_KIND_JIT. + */ + CUpti_ActivityKind kind; + + /** + * The JIT entry type. + */ + CUpti_ActivityJitEntryType jitEntryType; + + /** + * The JIT operation type. + */ + CUpti_ActivityJitOperationType jitOperationType; + + /** + * The device ID. + */ + uint32_t deviceId; + + /** + * The start timestamp for the JIT operation, in ns. A value of 0 for + * both the start and end timestamps indicates that timestamp + * information could not be collected for the JIT operation. + */ + uint64_t start; + + /** + * The end timestamp for the JIT operation, in ns. A value of 0 for both + * the start and end timestamps indicates that timestamp information + * could not be collected for the JIT operation. + */ + uint64_t end; + + /** + * The correlation ID of the JIT operation to which + * records belong to. Each JIT operation is + * assigned a unique correlation ID that is identical to the + * correlation ID in the driver or runtime API activity record that + * launched the JIT operation. + */ + uint32_t correlationId; + + /** + * Internal use. + */ + uint32_t padding; + + /** + * The correlation ID to correlate JIT compilation, load and store operations. + * Each JIT compilation unit is assigned a unique correlation ID + * at the time of the JIT compilation. This correlation id can be used + * to find the matching JIT cache load/store records. + */ + uint64_t jitOperationCorrelationId; + + /** + * The size of compute cache. + */ + uint64_t cacheSize; + + /** + * The path where the fat binary is cached. + */ + const char* cachePath; +} CUpti_ActivityJit; + + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility pop +#endif + +#if defined(__cplusplus) +} +#endif + +#endif /*_CUPTI_ACTIVITY_DEPRECATED_H_*/ diff --git a/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_callbacks.h b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_callbacks.h new file mode 100644 index 0000000000000000000000000000000000000000..afc6939244ef7a06c598c1d5750f638305a31501 --- /dev/null +++ b/lib/python3.11/site-packages/triton/backends/nvidia/include/cupti_callbacks.h @@ -0,0 +1,860 @@ +/* + * Copyright 2010-2023 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +#if !defined(__CUPTI_CALLBACKS_H__) +#define __CUPTI_CALLBACKS_H__ + +#include +#include +#include +#include +#include + +#ifndef CUPTIAPI +#ifdef _WIN32 +#define CUPTIAPI __stdcall +#else +#define CUPTIAPI +#endif +#endif + +#if defined(__cplusplus) +extern "C" { +#endif + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility push(default) +#endif + +/** + * \defgroup CUPTI_CALLBACK_API CUPTI Callback API + * Functions, types, and enums that implement the CUPTI Callback API. + * @{ + */ + +/** + * \brief Specifies the point in an API call that a callback is issued. + * + * Specifies the point in an API call that a callback is issued. This + * value is communicated to the callback function via \ref + * CUpti_CallbackData::callbackSite. + */ +typedef enum { + /** + * The callback is at the entry of the API call. + */ + CUPTI_API_ENTER = 0, + /** + * The callback is at the exit of the API call. + */ + CUPTI_API_EXIT = 1, + CUPTI_API_CBSITE_FORCE_INT = 0x7fffffff +} CUpti_ApiCallbackSite; + +/** + * \brief Callback domains. + * + * Callback domains. Each domain represents callback points for a + * group of related API functions or CUDA driver activity. + */ +typedef enum { + /** + * Invalid domain. + */ + CUPTI_CB_DOMAIN_INVALID = 0, + /** + * Domain containing callback points for all driver API functions. + */ + CUPTI_CB_DOMAIN_DRIVER_API = 1, + /** + * Domain containing callback points for all runtime API + * functions. + */ + CUPTI_CB_DOMAIN_RUNTIME_API = 2, + /** + * Domain containing callback points for CUDA resource tracking. + */ + CUPTI_CB_DOMAIN_RESOURCE = 3, + /** + * Domain containing callback points for CUDA synchronization. + */ + CUPTI_CB_DOMAIN_SYNCHRONIZE = 4, + /** + * Domain containing callback points for NVTX API functions. + */ + CUPTI_CB_DOMAIN_NVTX = 5, + /** + * Domain containing callback points for various states. + */ + CUPTI_CB_DOMAIN_STATE, + CUPTI_CB_DOMAIN_SIZE, + + CUPTI_CB_DOMAIN_FORCE_INT = 0x7fffffff +} CUpti_CallbackDomain; + +/** + * \brief Callback IDs for resource domain. + * + * Callback IDs for resource domain, CUPTI_CB_DOMAIN_RESOURCE. This + * value is communicated to the callback function via the \p cbid + * parameter. + */ +typedef enum { + /** + * Invalid resource callback ID. + */ + CUPTI_CBID_RESOURCE_INVALID = 0, + /** + * A new context has been created. + */ + CUPTI_CBID_RESOURCE_CONTEXT_CREATED = 1, + /** + * A context is about to be destroyed. + */ + CUPTI_CBID_RESOURCE_CONTEXT_DESTROY_STARTING = 2, + /** + * A new stream has been created. + */ + CUPTI_CBID_RESOURCE_STREAM_CREATED = 3, + /** + * A stream is about to be destroyed. + */ + CUPTI_CBID_RESOURCE_STREAM_DESTROY_STARTING = 4, + /** + * The driver has finished initializing. + */ + CUPTI_CBID_RESOURCE_CU_INIT_FINISHED = 5, + /** + * A module has been loaded. + */ + CUPTI_CBID_RESOURCE_MODULE_LOADED = 6, + /** + * A module is about to be unloaded. + */ + CUPTI_CBID_RESOURCE_MODULE_UNLOAD_STARTING = 7, + /** + * The current module which is being profiled. + */ + CUPTI_CBID_RESOURCE_MODULE_PROFILED = 8, + /** + * CUDA graph has been created. + */ + CUPTI_CBID_RESOURCE_GRAPH_CREATED = 9, + /** + * CUDA graph is about to be destroyed. + */ + CUPTI_CBID_RESOURCE_GRAPH_DESTROY_STARTING = 10, + /** + * CUDA graph is cloned. + */ + CUPTI_CBID_RESOURCE_GRAPH_CLONED = 11, + /** + * CUDA graph node is about to be created + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_CREATE_STARTING = 12, + /** + * CUDA graph node is created. + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_CREATED = 13, + /** + * CUDA graph node is about to be destroyed. + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_DESTROY_STARTING = 14, + /** + * Dependency on a CUDA graph node is created. + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_DEPENDENCY_CREATED = 15, + /** + * Dependency on a CUDA graph node is destroyed. + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_DEPENDENCY_DESTROY_STARTING = 16, + /** + * An executable CUDA graph is about to be created. + */ + CUPTI_CBID_RESOURCE_GRAPHEXEC_CREATE_STARTING = 17, + /** + * An executable CUDA graph is created. + */ + CUPTI_CBID_RESOURCE_GRAPHEXEC_CREATED = 18, + /** + * An executable CUDA graph is about to be destroyed. + */ + CUPTI_CBID_RESOURCE_GRAPHEXEC_DESTROY_STARTING = 19, + /** + * CUDA graph node is cloned. + */ + CUPTI_CBID_RESOURCE_GRAPHNODE_CLONED = 20, + /** + * CUDA stream attribute is changed. + */ + CUPTI_CBID_RESOURCE_STREAM_ATTRIBUTE_CHANGED = 21, + + CUPTI_CBID_RESOURCE_SIZE, + CUPTI_CBID_RESOURCE_FORCE_INT = 0x7fffffff +} CUpti_CallbackIdResource; + +/** + * \brief Callback IDs for synchronization domain. + * + * Callback IDs for synchronization domain, + * CUPTI_CB_DOMAIN_SYNCHRONIZE. This value is communicated to the + * callback function via the \p cbid parameter. + */ +typedef enum { + /** + * Invalid synchronize callback ID. + */ + CUPTI_CBID_SYNCHRONIZE_INVALID = 0, + /** + * Stream synchronization has completed for the stream. + */ + CUPTI_CBID_SYNCHRONIZE_STREAM_SYNCHRONIZED = 1, + /** + * Context synchronization has completed for the context. + */ + CUPTI_CBID_SYNCHRONIZE_CONTEXT_SYNCHRONIZED = 2, + CUPTI_CBID_SYNCHRONIZE_SIZE, + CUPTI_CBID_SYNCHRONIZE_FORCE_INT = 0x7fffffff +} CUpti_CallbackIdSync; + +/** + * \brief Callback IDs for state domain. + * + * Callback IDs for state domain, + * CUPTI_CB_DOMAIN_STATE. This value is communicated to the + * callback function via the \p cbid parameter. + */ +typedef enum { + /** + * Invalid state callback ID. + */ + CUPTI_CBID_STATE_INVALID = 0, + /** + * Notification of fatal errors - high impact, non-recoverable + * When encountered, CUPTI automatically invokes cuptiFinalize() + * User can control behavior of the application in future from + * receiving this callback - such as continuing without profiling, or + * terminating the whole application. + */ + CUPTI_CBID_STATE_FATAL_ERROR = 1, + /** + * Notification of non fatal errors - high impact, but recoverable + * This notification is not issued in the current release. + */ + CUPTI_CBID_STATE_ERROR = 2, + /** + * Notification of warnings - low impact, recoverable + * This notification is not issued in the current release. + */ + CUPTI_CBID_STATE_WARNING = 3, + + CUPTI_CBID_STATE_SIZE, + CUPTI_CBID_STATE_FORCE_INT = 0x7fffffff +} CUpti_CallbackIdState; + +/** + * \brief Data passed into a runtime or driver API callback function. + * + * Data passed into a runtime or driver API callback function as the + * \p cbdata argument to \ref CUpti_CallbackFunc. The \p cbdata will + * be this type for \p domain equal to CUPTI_CB_DOMAIN_DRIVER_API or + * CUPTI_CB_DOMAIN_RUNTIME_API. The callback data is valid only within + * the invocation of the callback function that is passed the data. If + * you need to retain some data for use outside of the callback, you + * must make a copy of that data. For example, if you make a shallow + * copy of CUpti_CallbackData within a callback, you cannot + * dereference \p functionParams outside of that callback to access + * the function parameters. \p functionName is an exception: the + * string pointed to by \p functionName is a global constant and so + * may be accessed outside of the callback. + */ +typedef struct { + /** + * Point in the runtime or driver function from where the callback + * was issued. + */ + CUpti_ApiCallbackSite callbackSite; + + /** + * Name of the runtime or driver API function which issued the + * callback. This string is a global constant and so may be + * accessed outside of the callback. + */ + const char *functionName; + + /** + * Pointer to the arguments passed to the runtime or driver API + * call. See generated_cuda_runtime_api_meta.h and + * generated_cuda_meta.h for structure definitions for the + * parameters for each runtime and driver API function. + */ + const void *functionParams; + + /** + * Pointer to the return value of the runtime or driver API + * call. This field is only valid within the exit::CUPTI_API_EXIT + * callback. For a runtime API \p functionReturnValue points to a + * \p cudaError_t. For a driver API \p functionReturnValue points + * to a \p CUresult. + */ + void *functionReturnValue; + + /** + * Name of the symbol operated on by the runtime or driver API + * function which issued the callback. This entry is valid only for + * driver and runtime launch callbacks, where it returns the name of + * the kernel. + */ + const char *symbolName; + + /** + * Driver context current to the thread, or null if no context is + * current. This value can change from the entry to exit callback + * of a runtime API function if the runtime initializes a context. + */ + CUcontext context; + + /** + * Unique ID for the CUDA context associated with the thread. The + * UIDs are assigned sequentially as contexts are created and are + * unique within a process. + */ + uint32_t contextUid; + + /** + * Pointer to data shared between the entry and exit callbacks of + * a given runtime or drive API function invocation. This field + * can be used to pass 64-bit values from the entry callback to + * the corresponding exit callback. + */ + uint64_t *correlationData; + + /** + * The activity record correlation ID for this callback. For a + * driver domain callback (i.e. \p domain + * CUPTI_CB_DOMAIN_DRIVER_API) this ID will equal the correlation ID + * in the CUpti_ActivityAPI record corresponding to the CUDA driver + * function call. For a runtime domain callback (i.e. \p domain + * CUPTI_CB_DOMAIN_RUNTIME_API) this ID will equal the correlation + * ID in the CUpti_ActivityAPI record corresponding to the CUDA + * runtime function call. Within the callback, this ID can be + * recorded to correlate user data with the activity record. This + * field is new in 4.1. + */ + uint32_t correlationId; + +} CUpti_CallbackData; + +/** + * \brief Data passed into a resource callback function. + * + * Data passed into a resource callback function as the \p cbdata + * argument to \ref CUpti_CallbackFunc. The \p cbdata will be this + * type for \p domain equal to CUPTI_CB_DOMAIN_RESOURCE. The callback + * data is valid only within the invocation of the callback function + * that is passed the data. If you need to retain some data for use + * outside of the callback, you must make a copy of that data. + */ +typedef struct { + /** + * For CUPTI_CBID_RESOURCE_CONTEXT_CREATED and + * CUPTI_CBID_RESOURCE_CONTEXT_DESTROY_STARTING, the context being + * created or destroyed. For CUPTI_CBID_RESOURCE_STREAM_CREATED and + * CUPTI_CBID_RESOURCE_STREAM_DESTROY_STARTING, the context + * containing the stream being created or destroyed. + */ + CUcontext context; + + union { + /** + * For CUPTI_CBID_RESOURCE_STREAM_CREATED and + * CUPTI_CBID_RESOURCE_STREAM_DESTROY_STARTING, the stream being + * created or destroyed. + */ + CUstream stream; + } resourceHandle; + + /** + * Reserved for future use. + */ + void *resourceDescriptor; +} CUpti_ResourceData; + + +/** + * \brief Module data passed into a resource callback function. + * + * CUDA module data passed into a resource callback function as the \p cbdata + * argument to \ref CUpti_CallbackFunc. The \p cbdata will be this + * type for \p domain equal to CUPTI_CB_DOMAIN_RESOURCE. The module + * data is valid only within the invocation of the callback function + * that is passed the data. If you need to retain some data for use + * outside of the callback, you must make a copy of that data. + */ + +typedef struct { + /** + * Identifier to associate with the CUDA module. + */ + uint32_t moduleId; + + /** + * The size of the cubin. + */ + size_t cubinSize; + + /** + * Pointer to the associated cubin. + */ + const char *pCubin; +} CUpti_ModuleResourceData; + +/** + * \brief CUDA graphs data passed into a resource callback function. + * + * CUDA graphs data passed into a resource callback function as the \p cbdata + * argument to \ref CUpti_CallbackFunc. The \p cbdata will be this + * type for \p domain equal to CUPTI_CB_DOMAIN_RESOURCE. The graph + * data is valid only within the invocation of the callback function + * that is passed the data. If you need to retain some data for use + * outside of the callback, you must make a copy of that data. + */ + +typedef struct { + /** + * CUDA graph + */ + CUgraph graph; + /** + * The original CUDA graph from which \param graph is cloned + */ + CUgraph originalGraph; + /** + * CUDA graph node + */ + CUgraphNode node; + /** + * The original CUDA graph node from which \param node is cloned + */ + CUgraphNode originalNode; + /** + * Type of the \param node + */ + CUgraphNodeType nodeType; + /** + * The dependent graph node + * The size of the array is \param numDependencies. + */ + CUgraphNode dependency; + /** + * CUDA executable graph + */ + CUgraphExec graphExec; +} CUpti_GraphData; + +/** + * \brief Data passed into a synchronize callback function. + * + * Data passed into a synchronize callback function as the \p cbdata + * argument to \ref CUpti_CallbackFunc. The \p cbdata will be this + * type for \p domain equal to CUPTI_CB_DOMAIN_SYNCHRONIZE. The + * callback data is valid only within the invocation of the callback + * function that is passed the data. If you need to retain some data + * for use outside of the callback, you must make a copy of that data. + */ +typedef struct { + /** + * The context of the stream being synchronized. + */ + CUcontext context; + /** + * The stream being synchronized. + */ + CUstream stream; +} CUpti_SynchronizeData; + +/** + * \brief Data passed into a NVTX callback function. + * + * Data passed into a NVTX callback function as the \p cbdata argument + * to \ref CUpti_CallbackFunc. The \p cbdata will be this type for \p + * domain equal to CUPTI_CB_DOMAIN_NVTX. Unless otherwise notes, the + * callback data is valid only within the invocation of the callback + * function that is passed the data. If you need to retain some data + * for use outside of the callback, you must make a copy of that data. + */ +typedef struct { + /** + * Name of the NVTX API function which issued the callback. This + * string is a global constant and so may be accessed outside of the + * callback. + */ + const char *functionName; + + /** + * Pointer to the arguments passed to the NVTX API call. See + * generated_nvtx_meta.h for structure definitions for the + * parameters for each NVTX API function. + */ + const void *functionParams; + + /** + * Pointer to the return value of the NVTX API call. See + * nvToolsExt.h for each NVTX API function's return value. + */ + const void *functionReturnValue; +} CUpti_NvtxData; + +/** + * \brief Stream attribute data passed into a resource callback function + * for CUPTI_CBID_RESOURCE_STREAM_ATTRIBUTE_CHANGED callback + + * Data passed into a resource callback function as the \p cbdata + * argument to \ref CUpti_CallbackFunc. The \p cbdata will be this + * type for \p domain equal to CUPTI_CB_DOMAIN_RESOURCE. The + * stream attribute data is valid only within the invocation of the callback + * function that is passed the data. If you need to retain some data + * for use outside of the callback, you must make a copy of that data. + */ +typedef struct { + /** + * The CUDA stream handle for the attribute + */ + CUstream stream; + + /** + * The type of the CUDA stream attribute + */ + CUstreamAttrID attr; + + /** + * The value of the CUDA stream attribute + */ + const CUstreamAttrValue *value; +} CUpti_StreamAttrData; + +/** + * \brief Data passed into a State callback function. + * + * Data passed into a State callback function as the \p cbdata argument + * to \ref CUpti_CallbackFunc. The \p cbdata will be this type for \p + * domain equal to CUPTI_CB_DOMAIN_STATE and callback Ids belonging to CUpti_CallbackIdState. + * Unless otherwise noted, the callback data is valid only within the invocation of the callback + * function that is passed the data. If you need to retain some data + * for use outside of the callback, you must make a copy of that data. + */ +typedef struct { + union { + /** + * Data passed along with the callback Ids + * Enum CUpti_CallbackIdState used to denote callback ids + */ + struct { + /** + * Error code + */ + CUptiResult result; + /** + * String containing more details. It can be NULL. + */ + const char *message; + } notification; + }; +} CUpti_StateData; +/** + * \brief An ID for a driver API, runtime API, resource or + * synchronization callback. + * + * An ID for a driver API, runtime API, resource or synchronization + * callback. Within a driver API callback this should be interpreted + * as a CUpti_driver_api_trace_cbid value (these values are defined in + * cupti_driver_cbid.h). Within a runtime API callback this should be + * interpreted as a CUpti_runtime_api_trace_cbid value (these values + * are defined in cupti_runtime_cbid.h). Within a resource API + * callback this should be interpreted as a \ref + * CUpti_CallbackIdResource value. Within a synchronize API callback + * this should be interpreted as a \ref CUpti_CallbackIdSync value. + */ +typedef uint32_t CUpti_CallbackId; + +/** + * \brief Function type for a callback. + * + * Function type for a callback. The type of the data passed to the + * callback in \p cbdata depends on the \p domain. If \p domain is + * CUPTI_CB_DOMAIN_DRIVER_API or CUPTI_CB_DOMAIN_RUNTIME_API the type + * of \p cbdata will be CUpti_CallbackData. If \p domain is + * CUPTI_CB_DOMAIN_RESOURCE the type of \p cbdata will be + * CUpti_ResourceData. If \p domain is CUPTI_CB_DOMAIN_SYNCHRONIZE the + * type of \p cbdata will be CUpti_SynchronizeData. If \p domain is + * CUPTI_CB_DOMAIN_NVTX the type of \p cbdata will be CUpti_NvtxData. + * + * \param userdata User data supplied at subscription of the callback + * \param domain The domain of the callback + * \param cbid The ID of the callback + * \param cbdata Data passed to the callback. + */ +typedef void (CUPTIAPI *CUpti_CallbackFunc)( + void *userdata, + CUpti_CallbackDomain domain, + CUpti_CallbackId cbid, + const void *cbdata); + +/** + * \brief A callback subscriber. + */ +typedef struct CUpti_Subscriber_st *CUpti_SubscriberHandle; + +/** + * \brief Pointer to an array of callback domains. + */ +typedef CUpti_CallbackDomain *CUpti_DomainTable; + +/** + * \brief Get the available callback domains. + * + * Returns in \p *domainTable an array of size \p *domainCount of all + * the available callback domains. + * \note \b Thread-safety: this function is thread safe. + * + * \param domainCount Returns number of callback domains + * \param domainTable Returns pointer to array of available callback domains + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialize CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p domainCount or \p domainTable are NULL + */ +CUptiResult CUPTIAPI cuptiSupportedDomains(size_t *domainCount, + CUpti_DomainTable *domainTable); + +/** + * \brief Initialize a callback subscriber with a callback function + * and user data. + * + * Initializes a callback subscriber with a callback function and + * (optionally) a pointer to user data. The returned subscriber handle + * can be used to enable and disable the callback for specific domains + * and callback IDs. + * \note Only a single subscriber can be registered at a time. To ensure + * that no other CUPTI client interrupts the profiling session, it's the + * responsibility of all the CUPTI clients to call this function before + * starting the profling session. In case profiling session is already + * started by another CUPTI client, this function returns the error code + * CUPTI_ERROR_MULTIPLE_SUBSCRIBERS_NOT_SUPPORTED. + * Note that this function returns the same error when application is + * launched using NVIDIA tools like nvprof, Visual Profiler, Nsight Systems, + * Nsight Compute, cuda-gdb and cuda-memcheck. + * \note This function does not enable any callbacks. + * \note \b Thread-safety: this function is thread safe. + * + * \param subscriber Returns handle to initialize subscriber + * \param callback The callback function + * \param userdata A pointer to user data. This data will be passed to + * the callback function via the \p userdata parameter. + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialize CUPTI + * \retval CUPTI_ERROR_MULTIPLE_SUBSCRIBERS_NOT_SUPPORTED if there is already a CUPTI subscriber + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p subscriber is NULL + */ +CUptiResult CUPTIAPI cuptiSubscribe(CUpti_SubscriberHandle *subscriber, + CUpti_CallbackFunc callback, + void *userdata); + +/** + * \brief Unregister a callback subscriber. + * + * Removes a callback subscriber so that no future callbacks will be + * issued to that subscriber. + * \note \b Thread-safety: this function is thread safe. + * + * \param subscriber Handle to the initialize subscriber + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialized CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p subscriber is NULL or not initialized + */ +CUptiResult CUPTIAPI cuptiUnsubscribe(CUpti_SubscriberHandle subscriber); + +/** + * \brief Get the current enabled/disabled state of a callback for a specific + * domain and function ID. + * + * Returns non-zero in \p *enable if the callback for a domain and + * callback ID is enabled, and zero if not enabled. + * + * \note \b Thread-safety: a subscriber must serialize access to + * cuptiGetCallbackState, cuptiEnableCallback, cuptiEnableDomain, and + * cuptiEnableAllDomains. For example, if cuptiGetCallbackState(sub, + * d, c) and cuptiEnableCallback(sub, d, c) are called concurrently, + * the results are undefined. + * + * \param enable Returns non-zero if callback enabled, zero if not enabled + * \param subscriber Handle to the initialize subscriber + * \param domain The domain of the callback + * \param cbid The ID of the callback + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialized CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p enabled is NULL, or if \p + * subscriber, \p domain or \p cbid is invalid. + */ +CUptiResult CUPTIAPI cuptiGetCallbackState(uint32_t *enable, + CUpti_SubscriberHandle subscriber, + CUpti_CallbackDomain domain, + CUpti_CallbackId cbid); + +/** + * \brief Enable or disabled callbacks for a specific domain and + * callback ID. + * + * Enable or disabled callbacks for a subscriber for a specific domain + * and callback ID. + * + * \note \b Thread-safety: a subscriber must serialize access to + * cuptiGetCallbackState, cuptiEnableCallback, cuptiEnableDomain, and + * cuptiEnableAllDomains. For example, if cuptiGetCallbackState(sub, + * d, c) and cuptiEnableCallback(sub, d, c) are called concurrently, + * the results are undefined. + * + * \param enable New enable state for the callback. Zero disables the + * callback, non-zero enables the callback. + * \param subscriber - Handle to callback subscription + * \param domain The domain of the callback + * \param cbid The ID of the callback + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialized CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p subscriber, \p domain or \p + * cbid is invalid. + */ +CUptiResult CUPTIAPI cuptiEnableCallback(uint32_t enable, + CUpti_SubscriberHandle subscriber, + CUpti_CallbackDomain domain, + CUpti_CallbackId cbid); + +/** + * \brief Enable or disabled all callbacks for a specific domain. + * + * Enable or disabled all callbacks for a specific domain. + * + * \note \b Thread-safety: a subscriber must serialize access to + * cuptiGetCallbackState, cuptiEnableCallback, cuptiEnableDomain, and + * cuptiEnableAllDomains. For example, if cuptiGetCallbackEnabled(sub, + * d, *) and cuptiEnableDomain(sub, d) are called concurrently, the + * results are undefined. + * + * \param enable New enable state for all callbacks in the + * domain. Zero disables all callbacks, non-zero enables all + * callbacks. + * \param subscriber - Handle to callback subscription + * \param domain The domain of the callback + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialized CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p subscriber or \p domain is invalid + */ +CUptiResult CUPTIAPI cuptiEnableDomain(uint32_t enable, + CUpti_SubscriberHandle subscriber, + CUpti_CallbackDomain domain); + +/** + * \brief Enable or disable all callbacks in all domains. + * + * Enable or disable all callbacks in all domains. + * + * \note \b Thread-safety: a subscriber must serialize access to + * cuptiGetCallbackState, cuptiEnableCallback, cuptiEnableDomain, and + * cuptiEnableAllDomains. For example, if cuptiGetCallbackState(sub, + * d, *) and cuptiEnableAllDomains(sub) are called concurrently, the + * results are undefined. + * + * \param enable New enable state for all callbacks in all + * domain. Zero disables all callbacks, non-zero enables all + * callbacks. + * \param subscriber - Handle to callback subscription + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_NOT_INITIALIZED if unable to initialized CUPTI + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p subscriber is invalid + */ +CUptiResult CUPTIAPI cuptiEnableAllDomains(uint32_t enable, + CUpti_SubscriberHandle subscriber); + +/** + * \brief Get the name of a callback for a specific domain and callback ID. + * + * Returns a pointer to the name c_string in \p **name. + * + * \note \b Names are available only for the DRIVER and RUNTIME domains. + * + * \param domain The domain of the callback + * \param cbid The ID of the callback + * \param name Returns pointer to the name string on success, NULL otherwise + * + * \retval CUPTI_SUCCESS on success + * \retval CUPTI_ERROR_INVALID_PARAMETER if \p name is NULL, or if + * \p domain or \p cbid is invalid. + */ +CUptiResult CUPTIAPI cuptiGetCallbackName(CUpti_CallbackDomain domain, + uint32_t cbid, + const char **name); + +/** @} */ /* END CUPTI_CALLBACK_API */ + +#if defined(__GNUC__) && defined(CUPTI_LIB) + #pragma GCC visibility pop +#endif + +#if defined(__cplusplus) +} +#endif + +#endif // file guard + diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..00c097e3ee7655fbcc2adfa5092c465b6f4894cc Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/autotuner.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/autotuner.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..fe25bc408ca7f144649ca53e05c988fe660d6dc4 Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/autotuner.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/build.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/build.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..5ff0c82f4f36136e4e6e38141dffdd057da2b766 Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/build.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/cache.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/cache.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..74e0bfbb720b082e35c2385d33cd94261dc34def Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/cache.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/driver.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/driver.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1325bb7b4489aad69e0ee204855b61a613c9a606 Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/driver.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/errors.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/errors.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ed54b47d9947980e60e83dbd89ae67c6d868eacc Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/errors.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/interpreter.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/interpreter.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..18244fc39e9ae94e689578774b0621fb81989aa2 Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/interpreter.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/__pycache__/jit.cpython-311.pyc b/lib/python3.11/site-packages/triton/runtime/__pycache__/jit.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f58d2905844cc42ee24e715376ba1fd4b4f57a45 Binary files /dev/null and b/lib/python3.11/site-packages/triton/runtime/__pycache__/jit.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/runtime/errors.py b/lib/python3.11/site-packages/triton/runtime/errors.py new file mode 100644 index 0000000000000000000000000000000000000000..4dce9176709a91675921af217b55f530ff57ddc9 --- /dev/null +++ b/lib/python3.11/site-packages/triton/runtime/errors.py @@ -0,0 +1,26 @@ +from ..errors import TritonError +from typing import Optional + + +class InterpreterError(TritonError): + + def __init__(self, error_message: Optional[str] = None): + self.error_message = error_message + + def __str__(self) -> str: + return self.error_message or "" + + +class OutOfResources(TritonError): + + def __init__(self, required, limit, name): + self.required = required + self.limit = limit + self.name = name + + def __str__(self) -> str: + return f"out of resource: {self.name}, Required: {self.required}, Hardware limit: {self.limit}. Reducing block sizes or `num_stages` may help." + + def __reduce__(self): + # this is necessary to make CompilationError picklable + return (type(self), (self.required, self.limit, self.name)) diff --git a/lib/python3.11/site-packages/triton/runtime/jit.py b/lib/python3.11/site-packages/triton/runtime/jit.py new file mode 100644 index 0000000000000000000000000000000000000000..45178a40bb29069f9f7c7f33a23df54ce891433d --- /dev/null +++ b/lib/python3.11/site-packages/triton/runtime/jit.py @@ -0,0 +1,951 @@ +from __future__ import annotations, division +import ast +import hashlib +import inspect +import itertools +import os +import re +import textwrap +from collections import defaultdict +from functools import cached_property +from typing import Callable, Generic, Iterable, Optional, TypeVar, Union, overload, Dict, Any, Tuple +from ..runtime.driver import driver +from types import ModuleType + +TRITON_MODULE = __name__[:-len(".runtime.jit")] + +T = TypeVar("T") + +# ----------------------------------------------------------------------------- +# Dependencies Finder +# ----------------------------------------------------------------------------- + + +class DependenciesFinder(ast.NodeVisitor): + """ + This AST visitor is used to find dependencies of a JITFunction. This can + be used to invalidate a JITFunction's hash when its source code -- or + that of its dependencies -- changes. + + This visitor also keeps track of the global variables touched by the + JITFunction. When we launch the kernel, we check that these have the same + values as they did when we ran this visitor. If not, we raise an error (or + otherwise we could recompile). + """ + + def __init__(self, name, globals, src) -> None: + super().__init__() + self.name = name + self.hasher = hashlib.sha256(src.encode("utf-8")) + + # This function's __globals__ dict. + self.globals = globals + + # Python builtins that can be accessed from Triton kernels. + self.supported_python_builtins = { + 'float', + 'getattr', + 'int', + 'isinstance', + 'len', + 'list', + 'max', + 'min', + 'print', + 'range', + } + + # used_global_vals tells us which global variables are used by this + # function and all those it transitively calls, plus the values of those + # variables when each function was initially run. (That is, if A calls + # C, and B calls C, then the values for C in used_global_vals will be + # from the first time C was run, either by A or B.) + # + # Each function may have a different __globals__ dict, so the global + # variable `foo` may actually have a different value in the different + # functions. Thus this map is actually + # (var_name, id(__globals__)) -> (var_value, __globals__). + self.used_global_vals: Dict[Tuple[str, int], Tuple[Any, Dict[str, Any]]] = {} + + self.visiting_arg_default_value = False + + @property + def ret(self): + return self.hasher.hexdigest() + + def _is_triton_builtin(self, node, func): + if inspect.isbuiltin(node.func): + return True + module = getattr(func, "__module__", "") + return module.startswith(TRITON_MODULE) + + def _update_hash(self, func): + if isinstance(func, JITFunction): + # Merge our used_global_vals with those of the called function, + # after checking that all overlapping values are consistent. + for k in self.used_global_vals.keys() & func.used_global_vals.keys(): + var_name, _ = k + v1, _ = self.used_global_vals[k] + v2, _ = func.used_global_vals[k] + if v1 != v2: + raise RuntimeError( + f"Global variable {var_name} has value {v1} when compiling {self.name}, but inner kernel {func.__name__} has conflicting value {v2} from when it was first compiled. This is not allowed." + ) + self.used_global_vals.update(func.used_global_vals) + # update hash + func_key = func.cache_key + func_key += str(getattr(func, "noinline", False)) + self.hasher.update(func_key.encode("utf-8")) + + def visit_Name(self, node): + if type(node.ctx) is ast.Store: + return node.id + + if node.id in self.local_names: + # The global name is hidden by the local name. + return None + + val = self.globals.get(node.id, None) + + # Only keep track of "interesting" global variables, that non-evil users + # might change. Don't consider functions, modules, builtins, etc. This + # helps keep the list of vars we have to check small. + if (val is not None # + # Python default arguments are resolved only once, when the + # function is defined. So if you do `foo(a=A)` and the value of + # A changes, foo will still use the old value of A. + and not self.visiting_arg_default_value + # It would be pretty evil if someone did `import x` and then + # `x = blah`. + and type(val) is not ModuleType + # It would be pretty evil if we used function `foo` inside of + # `bar` and then someone did `foo = baz`. + and not isinstance(val, JITFunction) and not getattr(val, "__triton_builtin__", False) # + and node.id not in self.supported_python_builtins): + self.used_global_vals[(node.id, id(self.globals))] = (val, self.globals) + + self._update_hash(val) + return val + + def visit_Tuple(self, node): + # We need to explicitly return the tuple values so that visit_Assign can + # access them in the case of `a, b = ...`. + return [self.visit(elt) for elt in node.elts] + + def visit_Attribute(self, node): + lhs = self.visit(node.value) + while isinstance(lhs, ast.Attribute): + lhs = self.visit(lhs.value) + if lhs is None or (getattr(lhs, "__name__", "") == TRITON_MODULE): + return None + ret = getattr(lhs, node.attr) + self._update_hash(ret) + return ret + + def visit_FunctionDef(self, node): + # Save the local name, which may hide the global name. + self.local_names = {arg.arg for arg in node.args.args} + self.generic_visit(node) + + def visit_arguments(self, node): + # The purpose of this function is to visit everything in `arguments` + # just like `generic_visit`, except when we're visiting default values + # (i.e. the `foo` part of `def fn(x = foo)`), we set + # self.visiting_arg_default_value = True. This allows visit_Name to be + # aware that we're inside function default values, which have special + # semantics. + + # According to the AST docs, the arguments node has the following structure. + # + # arguments = (arg* posonlyargs, arg* args, arg? vararg, arg* kwonlyargs, + # expr* kw_defaults, arg? kwarg, expr* defaults) + def visit_defaults(defaults): + try: + assert not self.visiting_arg_default_value + self.visiting_arg_default_value = True + for expr in defaults: + if expr is not None: + self.visit(expr) + finally: + self.visiting_arg_default_value = False + + for arg in itertools.chain(node.posonlyargs, node.args, [node.vararg] if node.vararg else [], node.kwonlyargs): + self.visit(arg) + + visit_defaults(node.kw_defaults) + + if node.kwarg is not None: + self.visit(node.kwarg) + + visit_defaults(node.defaults) + + def visitAssnTarget(self, node): + # Target is either a single string, or a list of strings (if the assn + # target is a tuple). + target = self.visit(node) + if isinstance(target, list): + self.local_names |= set(target) + else: + self.local_names.add(target) + + def visit_Assign(self, node): + if len(node.targets) != 1: + # TODO(jlebar): I don't actually know how to hit this. You don't + # get it from `a, b = ...` -- in that case, node.targets is a single + # Tuple, and in fact we *do* need to handle that case if we want + # existing code to work. + raise TypeError("Simultaneous multiple assignment is not supported.") + + self.visitAssnTarget(node.targets[0]) + + # This will re-visit the target, but that's OK. + self.generic_visit(node) + + def visit_AnnAssign(self, node): + self.visitAssnTarget(node.target) + + # This will re-visit the target, but that's OK. + self.generic_visit(node) + + def visit_For(self, node): + self.visitAssnTarget(node.target) + + # This will re-visit the target, but that's fine. + self.generic_visit(node) + + +# ----------------------------------------------------------------------------- +# JITFunction +# ----------------------------------------------------------------------------- + + +def _normalize_ty(ty) -> str: + if isinstance(ty, type): + return ty.__name__ + elif isinstance(ty, str): + return ty + return repr(ty) + + +class KernelParam: + """Represents a parameter (name plus metadata) to a @jit'ed function.""" + + def __init__(self, num: int, param: inspect.Parameter, do_not_specialize: bool, + do_not_specialize_on_alignment: bool): + self.num = num + self._param = param + self.do_not_specialize = do_not_specialize + self.do_not_specialize_on_alignment = do_not_specialize_on_alignment + + @cached_property + def name(self): + return self._param.name + + @cached_property + def annotation(self): + if not self._param.annotation or self._param.annotation == inspect.Parameter.empty: + return "" + return _normalize_ty(self._param.annotation) + + @cached_property + def annotation_type(self): + annotation = self.annotation + for ty1, ty2 in [("uint", 'u'), ("int", 'i')]: + width = annotation[annotation.find(ty1) + len(ty1):] + if width and ty1 in annotation: + return f"{ty2}{width}" + if annotation == "bool": + return "u1" + return "" + + @cached_property + def is_constexpr(self): + return "constexpr" in self.annotation + + @cached_property + def is_const(self): + return "const" in self.annotation and not self.is_constexpr + + @property + def default(self): + return self._param.default + + @property + def has_default(self): + return self._param.default != inspect.Parameter.empty + + +def compute_spec_key(v, align): + + if align and hasattr(v, "data_ptr") and (v.data_ptr() % 16 == 0): + return "D" + elif isinstance(v, int): + # bool is a subclass of int, so we don't check explicitly above. + if align and (v % 16 == 0): + return "D" + elif v == 1: + return "1" + return "N" + + +dtype2str = {} + + +def mangle_type(arg, is_const=False): + + if arg is None: + return "none" + elif isinstance(arg, bool): + return "i1" + elif isinstance(arg, int): + if -(2**31) <= arg and arg <= 2**31 - 1: + return "i32" + elif 2**63 <= arg and arg <= 2**64 - 1: + return "u64" + else: + return "i64" + elif isinstance(arg, float): + return "fp32" + elif hasattr(arg, "tma_desc_cpu_ptr"): + return "nvTmaDesc" + else: + # dtypes are hashable so we can memoize this mapping: + dsk = (arg.dtype, is_const) + res = dtype2str.get(dsk, None) + if res is None: + res = ("*k" if dsk[1] else "*") + type_canonicalisation_dict[str(dsk[0]).split('.')[-1]] + dtype2str[dsk] = res + return res + + +class KernelInterface(Generic[T]): + run: T + + def __getitem__(self, grid) -> T: + """ + A JIT function is launched with: fn[grid](*args, **kwargs). + Hence JITFunction.__getitem__ returns a callable proxy that + memorizes the grid. + """ + return lambda *args, **kwargs: self.run(grid=grid, warmup=False, *args, **kwargs) + # return cast(T, functools.partial(cast(Callable, self.run), grid=grid)) + + +def serialize_specialization_data(name, signature, constants, attrs, options, key): + constants = {key: str(value) if value.__class__.__name__ == "dtype" else value for key, value in constants.items()} + import json + obj = { + 'name': name, 'signature': signature, 'constants': constants, 'attrs': attrs.to_dict(), 'options': + options.__dict__, 'key': key + } + serialized_obj = json.dumps(obj) + return serialized_obj + + +def create_function_from_signature(sig, kparams, backend): + """ + Equivalent to sig.bind followed by apply_defaults. This generates a + native Python function (using exec) which can be memoized on a per-kernel + basis to avoid having to run these expensive functions -- which constitute + much of the kernel launch overhead -- every time we run the kernel. + """ + + assert len(sig.parameters) == len(kparams) + + # Create the function argument list and the dict entries for the return statement + func_args = [] + dict_entries = [] + constexpr_vals = [] + non_constexpr_vals = [] + signature_types = [] + specialisations = [] + + for ((name, sp), kp) in zip(sig.parameters.items(), kparams): + if sp.default is inspect.Parameter.empty: + func_args.append(name) + dict_entries.append(f"'{name}': {name}") + else: + func_args.append(f"{name}=default_{name}") + dict_entries.append(f"'{name}': {name}") + if kp.is_constexpr: + constexpr_vals.append(name) + else: + non_constexpr_vals.append(name) + if not kp.do_not_specialize: + if not kp.do_not_specialize_on_alignment: + specialisations.append('compute_spec_key(%s, align=True)' % name) + else: + specialisations.append('compute_spec_key(%s, align=False)' % name) + if kp.annotation_type: + signature_types.append('"%s"' % kp.annotation_type) + else: + signature_types.append('mangle_type(%s, %s)' % (name, 'True' if kp.is_const else 'False')) + + cache_key = ''.join([x + ', ' for x in signature_types + specialisations]) + constexpr_vals = ''.join([x + ', ' for x in constexpr_vals]) + non_constexpr_vals = ''.join([x + ', ' for x in non_constexpr_vals]) + + func_args.append('**excess_kwargs') + + # Join all arguments into a function definition string + args_str = ', '.join(func_args) + dict_str = ', '.join(dict_entries) + func_body = "def dynamic_func(%s):\n return {%s}, (%s), (%s), (%s), excess_kwargs" % ( + args_str, dict_str, cache_key, constexpr_vals, non_constexpr_vals) + + # Prepare defaults to be inserted into function namespace + func_namespace = { + f"default_{name}": param.default + for name, param in sig.parameters.items() + if param.default is not inspect.Parameter.empty + } + + func_namespace['mangle_type'] = mangle_type + func_namespace['compute_spec_key'] = backend.compute_spec_key + + # Execute the function string in func_namespace to create the function + exec(func_body, func_namespace) + + # Extract the newly created function from the namespace + return func_namespace['dynamic_func'] + + +type_canonicalisation_dict = { + "bool": "i1", + "float8e4nv": "fp8e4nv", + "float8e5": "fp8e5", + "float8e4b15": "fp8e4b15", + "float8_e4m3fn": "fp8e4nv", + "float8e4b8": "fp8e4b8", + "float8_e4m3fnuz": "fp8e4b8", + "float8_e5m2": "fp8e5", + "float8e5b16": "fp8e5b16", + "float8_e5m2fnuz": "fp8e5b16", + "float16": "fp16", + "bfloat16": "bf16", + "float32": "fp32", + "float64": "fp64", + "int8": "i8", + "int16": "i16", + "int32": "i32", + "int64": "i64", + "uint8": "u8", + "uint16": "u16", + "uint32": "u32", + "uint64": "u64", +} + +for v in list(type_canonicalisation_dict.values()): + type_canonicalisation_dict[v] = v + + +class JITFunction(KernelInterface[T]): + # Hook for inspecting compiled functions and modules + cache_hook = None + # Hook to signal that a kernel is done compiling and inspect compiled function. + # cache_hook will always be called before compilation and compiled_hook after. + compiled_hook = None + + @staticmethod + def _key_of(arg): + if hasattr(arg, "dtype"): + return arg.dtype + elif isinstance(arg, bool): + return "i1" + elif isinstance(arg, int): + if -(2**31) <= arg and arg <= 2**31 - 1: + return "i32" + elif 2**63 <= arg and arg <= 2**64 - 1: + return "u64" + else: + return "i64" + elif isinstance(arg, float): + return "fp32" + elif arg is None: + return None + else: + raise TypeError(f"Unsupported type {type(arg)} for {arg}") + + @staticmethod + def _type_of(key, is_const=False): + # `None` is nullptr. Implicitly convert to *i8. + if key is None: + return "*i8" + elif isinstance(key, str): + return key + + dtype_str = str(key).split(".")[-1] + dtype_str = type_canonicalisation_dict[dtype_str] + const_str = "*k" if is_const else "*" + return const_str + dtype_str + + def _make_constants(self, constexpr_key): + constants = dict(zip(self.constexprs, constexpr_key)) + return constants + + def _call_hook( + self, + key, + signature, + device, + constants, + options, + configs, + is_warmup, + before, + ): + hook = JITFunction.cache_hook if before else JITFunction.compiled_hook + if hook is None: + return False + + name = self.fn.__name__ + module = self.fn.__module__ + arg_reprs = ", ".join([f"{param.name}: {ty}" for param, ty in zip(self.params, key[1])]) + repr = f"{name}[num_warps={options.num_warps}, num_ctas={options.num_ctas}, num_stages={options.num_stages}, enable_fp_fusion={options.enable_fp_fusion}]({arg_reprs})" + + class JitFunctionInfo: + + def __init__(self, module, name, jit_function): + self.module = module + self.name = name + self.jit_function = jit_function + pass + + specialization_data = serialize_specialization_data(name, signature, constants, configs[0], options, key) + + kwargs = { + 'signature': signature, + 'device': device, + 'constants': constants, + 'num_warps': options.num_warps, + 'num_ctas': options.num_ctas, + 'num_stages': options.num_stages, + 'enable_fp_fusion': options.enable_fp_fusion, + 'extern_libs': options.extern_libs, + 'configs': configs, + 'specialization_data': specialization_data, + 'is_warmup': is_warmup, + } + + return hook( + key=key, + repr=repr, + fn=JitFunctionInfo(module, name, self), + compile={"key": key, **kwargs}, + is_manual_warmup=is_warmup, + already_compiled=False, + ) + + def add_pre_run_hook(self, hook): + ''' + Add a hook that will be executed prior to the execution of run + function with args and kwargs passed into the kernel + ''' + assert callable(hook) + self.pre_run_hooks.append(hook) + + def create_binder(self, backend): + """ + Precompute as much as possible. + """ + from ..compiler import CompiledKernel, compile, ASTSource, make_backend + self.CompiledKernel = CompiledKernel + self.compile = compile + self.ASTSource = ASTSource + self.make_backend = make_backend + self.binder = create_function_from_signature(self.signature, self.params, backend) + self.constexpr_indices = [i for (i, p) in enumerate(self.params) if p.is_constexpr] + self.non_constexpr_indices = [i for (i, p) in enumerate(self.params) if not p.is_constexpr] + self.specialised_indices = [ + i for (i, p) in enumerate(self.params) if (not p.do_not_specialize) and (not p.is_constexpr) + ] + + def run(self, *args, grid, warmup, **kwargs): + kwargs["debug"] = kwargs.get("debug", False) or os.environ.get("TRITON_DEBUG", "0") == "1" + + # parse options + from ..compiler import make_backend + device = driver.active.get_current_device() + stream = driver.active.get_current_stream(device) + target = driver.active.get_current_target() + backend = make_backend(target) + + # Execute pre run hooks with args and kwargs + for hook in self.pre_run_hooks: + hook(*args, **kwargs) + + if self.binder is None: + self.create_binder(backend) + + bound_args, sig_and_spec, constexpr_vals, non_constexpr_vals, excess_kwargs = self.binder(*args, **kwargs) + + # compute cache key + key = ''.join(sig_and_spec) + str((constexpr_vals, excess_kwargs)) + kernel = self.cache[device].get(key, None) + + if kernel is None: + # Kernel is not cached; we have to compile. + options = backend.parse_options(kwargs) + + # deprecated arguments + assert "device_type" not in kwargs, "device_type option is deprecated; current target will be used" + assert "device" not in kwargs, "device option is deprecated; current device will be used" + assert "stream" not in kwargs, "stream option is deprecated; current stream will be used" + for k in excess_kwargs: + if k not in options.__dict__: + raise KeyError("Keyword argument %s was specified but unrecognised" % k) + + bound_vals = tuple(bound_args.values()) + + # `None` is nullptr. Implicitly convert to *i8. This needs to be + # done here rather than when we build the signature as otherwise + # the kernel cache key could not distinguish between byte pointers + # and None arguments, resulting in a downstream mismatch: + sigkeys = [self.params[i].name for i in self.non_constexpr_indices] + sigvals = sig_and_spec[:len(sigkeys)] + signature = {k: ('*i8' if (v == 'none') else v) for (k, v) in zip(sigkeys, sigvals)} + + configs = (backend.get_attrs_descriptor(self.params, bound_vals), ) + constant_params = configs[0].get_constants() + constants = { + p.name: v + for (v, p) in zip(bound_vals, self.params) + if p.is_constexpr or (p.num in constant_params) or v is None + } + for i, arg in constants.items(): + if callable(arg): + raise TypeError(f"Callable constexpr at index {i} is not supported") + + if self._call_hook(key, signature, device, constants, options, configs, warmup, before=True): + return None + # compile the kernel + src = self.ASTSource(self, signature, constants, configs[0]) + kernel = self.compile( + src, + target=target, + options=options.__dict__, + ) + self.cache[device][key] = kernel + self._call_hook(key, signature, device, constants, options, configs, warmup, before=False) + + # Check that used global values have not changed. + not_present = object() + for (name, _), (val, globals_dict) in self.used_global_vals.items(): + if (newVal := globals_dict.get(name, not_present)) != val: + raise RuntimeError( + f"Global variable {name} has changed since we compiled this kernel, from {val} to {newVal}") + + if not warmup: + # canonicalize grid + assert grid is not None + if callable(grid): + # Arguments are passed as a dict to `grid`, by contract. + # TODO(jlebar): In the new launch API, pass the compiler flags as a + # second parameter to `grid`. + grid = grid(bound_args) + grid_size = len(grid) + grid_0 = grid[0] + grid_1 = grid[1] if grid_size > 1 else 1 + grid_2 = grid[2] if grid_size > 2 else 1 + + # launch kernel + launch_metadata = kernel.launch_metadata(grid, stream, *non_constexpr_vals) + kernel.run(grid_0, grid_1, grid_2, stream, kernel.function, kernel.packed_metadata, launch_metadata, + self.CompiledKernel.launch_enter_hook, self.CompiledKernel.launch_exit_hook, *non_constexpr_vals) + return kernel + + def __init__(self, fn, version=None, do_not_specialize=None, do_not_specialize_on_alignment=None, debug=None, + noinline=None, repr=None, launch_metadata=None): + do_not_specialize = do_not_specialize if do_not_specialize else [] + do_not_specialize_on_alignment = do_not_specialize_on_alignment if do_not_specialize_on_alignment else [] + + self.fn = fn + self.module = fn.__module__ + self.version = version + self.signature = inspect.signature(fn) + self.do_not_specialize = do_not_specialize + self.do_not_specialize_on_alignment = do_not_specialize_on_alignment + self.starting_line_number = inspect.getsourcelines(fn)[1] + self.repr = lambda _: fn.__name__ if repr is None else repr(_) + self.launch_metadata = launch_metadata + + self.binder = None + + self.params = [] + for i, param in enumerate(self.signature.parameters.values()): + dns = i in do_not_specialize or param.name in do_not_specialize + dns_oa = i in do_not_specialize_on_alignment or param.name in do_not_specialize_on_alignment + self.params.append(KernelParam(i, param, dns, dns_oa)) + + # function source code (without decorators) + self.src = textwrap.dedent(inspect.getsource(fn)) + self.src = self.src[re.search(r"^def\s+\w+\s*\(", self.src, re.MULTILINE).start():] + # cache of just-in-time compiled kernels + self.cache = defaultdict(dict) + self.hash = None + + # Map of global variables used by the function and any functions it + # transitively calls, plus their values. The values are collected when + # the function is first compiled. Then every time we run the function, + # we check that the values of the globals match what's expected, + # otherwise we raise an error. + # + # Different functions can have different __globals__ maps, so the map + # key is actually (var name, id(__globals__)), and the map value is + # (value, __globals__). + self.used_global_vals: Dict[Tuple[str, int], Tuple[Any, Dict[str, Any]]] = {} + + # JITFunction can be instantiated as kernel + # when called with a grid using __getitem__ + self.kernel = None + self.noinline = noinline + + # TODO(jlebar): Remove uses of these fields outside this file, then + # remove the fields here. + self.arg_names = [p.name for p in self.params] + self.constexprs = [p.num for p in self.params if p.is_constexpr] + + # Hooks that will be called prior to executing "run" + self.pre_run_hooks = [] + + # reuse docs of wrapped function + self.__doc__ = fn.__doc__ + self.__name__ = fn.__name__ + self.__globals__ = fn.__globals__ + self.__module__ = fn.__module__ + + @property + def cache_key(self): + # TODO : hash should be attribute of `self` + if self.hash is None: + dependencies_finder = DependenciesFinder(name=self.__name__, globals=self.__globals__, src=self.src) + dependencies_finder.visit(self.parse()) + self.hash = dependencies_finder.ret + str(self.starting_line_number) + self.used_global_vals = dict(sorted(dependencies_finder.used_global_vals.items())) + return self.hash + + def warmup(self, *args, grid, **kwargs): + return self.run(grid=grid, warmup=True, *map(MockTensor.wrap_dtype, args), **kwargs) + + def preload(self, specialization_data): + from ..compiler import compile, ASTSource + from triton.backends.compiler import AttrsDescriptor + import json + import triton.language as tl + device = driver.active.get_current_device() + deserialized_obj = json.loads(specialization_data) + if deserialized_obj['name'] != self.fn.__name__: + raise RuntimeError( + f"Specialization data is for {deserialized_obj['name']} but trying to preload for {self.fn.__name__}") + constants = { + key: tl.dtype(value) if tl.dtype.is_dtype(value) else value + for key, value in deserialized_obj['constants'].items() + } + signature = dict(deserialized_obj['signature'].items()) + src = ASTSource(self, signature, constants, AttrsDescriptor.from_dict(deserialized_obj['attrs'])) + options = { + key: tuple(value) if isinstance(value, list) else value + for key, value in deserialized_obj['options'].items() + } + key = deserialized_obj['key'] + kernel = compile(src, None, options) + self.cache[device][key] = kernel + return kernel + + # we do not parse `src` in the constructor because + # the user might want to monkey-patch self.src dynamically. + # Our unit tests do this, for example. + def parse(self): + tree = ast.parse(self.src) + assert isinstance(tree, ast.Module) + assert len(tree.body) == 1 + assert isinstance(tree.body[0], ast.FunctionDef) + return tree + + def __call__(self, *args, **kwargs): + raise RuntimeError("Cannot call @triton.jit'd outside of the scope of a kernel") + + def __setattr__(self, name, value): + super(JITFunction, self).__setattr__(name, value) + # - when `.src` attribute is set, cache path needs + # to be reinitialized + if name == "src": + self.hash = None + + def __repr__(self): + return f"JITFunction({self.module}:{self.fn.__name__})" + + +# ----------------------------------------------------------------------------- +# `jit` decorator +# ----------------------------------------------------------------------------- + + +@overload +def jit(fn: T) -> JITFunction[T]: + ... + + +@overload +def jit( + *, + version=None, + repr: Optional[Callable] = None, + launch_metadata: Optional[Callable] = None, + do_not_specialize: Optional[Iterable[int]] = None, + do_not_specialize_on_alignment: Optional[Iterable[int]] = None, + debug: Optional[bool] = None, + noinline: Optional[bool] = None, +) -> Callable[[T], JITFunction[T]]: + ... + + +def jit( + fn: Optional[T] = None, + *, + version=None, + repr: Optional[Callable] = None, + launch_metadata: Optional[Callable] = None, + do_not_specialize: Optional[Iterable[int]] = None, + do_not_specialize_on_alignment: Optional[Iterable[int]] = None, + debug: Optional[bool] = None, + noinline: Optional[bool] = None, +) -> Union[JITFunction[T], Callable[[T], JITFunction[T]]]: + """ + Decorator for JIT-compiling a function using the Triton compiler. + + :note: When a jit'd function is called, arguments are + implicitly converted to pointers if they have a :code:`.data_ptr()` method + and a `.dtype` attribute. + + :note: This function will be compiled and run on the GPU. It will only have access to: + + * python primitives, + * builtins within the triton package, + * arguments to this function, + * other jit'd functions + + :param fn: the function to be jit-compiled + :type fn: Callable + """ + + def decorator(fn: T) -> JITFunction[T]: + assert callable(fn) + if os.getenv("TRITON_INTERPRET", "0") == "1": + from .interpreter import InterpretedFunction + return InterpretedFunction(fn, version=version, do_not_specialize=do_not_specialize, + do_not_specialize_on_alignment=do_not_specialize_on_alignment, debug=debug, + noinline=noinline, repr=repr, launch_metadata=launch_metadata) + else: + return JITFunction( + fn, + version=version, + do_not_specialize=do_not_specialize, + do_not_specialize_on_alignment=do_not_specialize_on_alignment, + debug=debug, + noinline=noinline, + repr=repr, + launch_metadata=launch_metadata, + ) + + if fn is not None: + return decorator(fn) + + else: + return decorator + + +# ----------------------------------------------------------------------------- +# Utilities for mocking tensors +# ----------------------------------------------------------------------------- + + +class MockTensor: + """ + Can be used in place of real tensors when calling: + kernel.warmup(MockTensor(torch.float32), ...) + """ + + @staticmethod + def wrap_dtype(arg): + if arg.__class__.__name__ == "dtype" and arg.__module__ == "torch": + return MockTensor(arg) + return arg + + def __init__(self, dtype): + self.dtype = dtype + + @staticmethod + def data_ptr(): + return 0 # optimistically assumes multiple of 16 + + @staticmethod + def ptr_range(): + return 0 # optimistically assumes 32 bit pointer range + + +class TensorWrapper: + + def __init__(self, base, dtype): + self.dtype = dtype + self.base = base + self.data = base.data + self.device = base.device + self.shape = self.base.shape + + def data_ptr(self): + return self.base.data_ptr() + + def stride(self, i): + return self.base.stride(i) + + def __str__(self) -> str: + return f"TensorWrapper[{self.dtype}]({self.base})" + + def element_size(self): + return self.base.element_size() + + def cpu(self): + return TensorWrapper(self.base.cpu(), self.dtype) + + def copy_(self, other): + self.base.copy_(other.base) + + def clone(self): + return TensorWrapper(self.base.clone(), self.dtype) + + def to(self, device): + return TensorWrapper(self.base.to(device), self.dtype) + + +def reinterpret(tensor, dtype): + if isinstance(tensor, TensorWrapper): + if dtype == tensor.base.dtype: + # Reinterpreting to the original interpretation; return the base. + return tensor.base + else: + # Reinterpreting a wrapped tensor to a different type. + return TensorWrapper(tensor.base, dtype) + elif hasattr(tensor, "data_ptr"): + # A new wrapper is needed around an unwrapped tensor. + return TensorWrapper(tensor, dtype) + else: + raise TypeError(f"Cannot reinterpret a {type(tensor)}.") + + +def get_jit_fn_file_line(fn): + base_fn = fn + while not isinstance(base_fn, JITFunction): + base_fn = base_fn.fn + file_name = base_fn.fn.__code__.co_filename + lines, begin_line = inspect.getsourcelines(base_fn.fn) + # Match the following pattern: + # @triton.autotune(...) <- foo.__code__.co_firstlineno + # @triton.heuristics(...) + # @triton.jit + # def foo(...): <- this line is the first line + for idx, line in enumerate(lines): + if line.strip().startswith("def "): + begin_line += idx + break + return file_name, begin_line diff --git a/lib/python3.11/site-packages/triton/tools/__init__.py b/lib/python3.11/site-packages/triton/tools/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/triton/tools/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/triton/tools/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 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b/lib/python3.11/site-packages/triton/tools/__pycache__/link.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..959c0665717f65b2a0d4b1f71cb069cc975c1bb5 Binary files /dev/null and b/lib/python3.11/site-packages/triton/tools/__pycache__/link.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/triton/tools/build_extern.py b/lib/python3.11/site-packages/triton/tools/build_extern.py new file mode 100644 index 0000000000000000000000000000000000000000..8f0168d59d7af045bde68a508a000654f4893bb1 --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/build_extern.py @@ -0,0 +1,365 @@ +import argparse +import subprocess +from abc import ABC, abstractmethod +from typing import Dict, List, Optional + + +class Symbol: + _name: str + _op_name: str + _ret_type: str + _arg_names: List[str] + _arg_types: List[str] + + def __init__( + self, + name: str, + op_name: str, + ret_type: str, + arg_names: List[str], + arg_types: List[str], + ) -> None: + ''' + A symbol is a function declaration. + :param name: name of the symbol + :param op_name: name of the operation + :param ret_type: return type of the operation + :param arg_names: names of the arguments + :param arg_types: types of the arguments + ''' + self._name = name + self._op_name = op_name + self._ret_type = ret_type + self._arg_names = list(arg_names) + self._arg_types = list(arg_types) + + @property + def name(self) -> str: + return self._name + + @property + def op_name(self) -> str: + return self._op_name + + @property + def ret_type(self) -> str: + return self._ret_type + + @property + def arg_names(self) -> List[str]: + return self._arg_names + + @property + def arg_types(self) -> List[str]: + return self._arg_types + + +def convert_type(type_str) -> Optional[str]: + if type_str == "i32": + return "int32" + elif type_str == "u32": + return "uint32" + elif type_str == "i64": + return "int64" + elif type_str == "u64": + return "uint64" + elif type_str == "float": + return "fp32" + elif type_str == "double": + return "fp64" + else: + # ignore other types, such as pointer types + return None + + +def to_unsigned(type_str) -> str: + if type_str == "int32": + return "uint32" + elif type_str == "int64": + return "uint64" + else: + return type_str + + +class ExternLibrary(ABC): + _name: str + _path: str + _symbols: Dict[str, Symbol] + _format: bool + _grouping: bool + + def __init__( + self, + name: str, + path: str, + format: bool = True, + grouping: bool = True, + ) -> None: + ''' + Abstract class for extern library. + :param name: name of the library + :param path: path of the library + :param format: whether to format the generated stub file + ''' + self._name = name + self._path = path + self._symbols = {} + self._format = format + self._grouping = grouping + + @property + def name(self) -> str: + return self._name + + @property + def path(self) -> str: + return self._path + + @property + def symbols(self) -> Dict[str, Symbol]: + return self._symbols + + @property + def grouping(self) -> bool: + return self._grouping + + @abstractmethod + def parse_symbols(self, input_file) -> None: + pass + + @abstractmethod + def _output_stubs(self) -> str: + pass + + def generate_stub_file(self, output_dir) -> None: + file_str = self._output_stubs() + if file_str is None or len(file_str) == 0: + raise Exception("file_str is empty") + + output_file = f"{output_dir}/{self._name}.py" + with open(output_file, "w") as f: + f.write(file_str) + f.close() + if self._format: + subprocess.Popen(["autopep8", "-a", "-r", "-i", output_file], stdout=subprocess.PIPE).communicate() + subprocess.Popen(["isort", output_file], stdout=subprocess.PIPE).communicate() + + +class Libdevice(ExternLibrary): + _symbol_groups: Dict[str, List[Symbol]] + + def __init__(self, path) -> None: + ''' + Constructor for Libdevice. + :param path: path of the libdevice library + ''' + super().__init__("libdevice", path) + self._symbol_groups = {} + self.is_pure = True + + @staticmethod + def _extract_symbol(line) -> Optional[Symbol]: + # Extract symbols from line in the following format: + # "define [internal] @(,)" + entries = line.split("@") + ret_str = entries[0] + func_str = entries[1] + # Get ret_type, skip internal symbols + ret_strs = ret_str.split() + if ret_strs[1] == "internal": + return None + ret_type = convert_type(ret_strs[1]) + if ret_type is None: + return None + # Get function name + func_strs = func_str.split("(") + func_name = func_strs[0].replace("@", "") + op_name = func_name.replace("__nv_", "") + if 'ieee' in op_name: + return None + # Get arg_types + arg_strs = func_strs[1].split(",") + arg_types = [] + arg_names = [] + for i, arg_str in enumerate(arg_strs): + arg_type = convert_type(arg_str.split()[0]) + if arg_type is None: + return None + arg_name = 'arg' + str(i) + arg_types.append(arg_type) + arg_names.append(arg_name) + if op_name == "sad": + # Special case for sad, where the last argument is an unsigned int + arg_types[-1] = to_unsigned(arg_types[-1]) + elif op_name.startswith("u"): + # LLVM does not differentiate between signed and unsigned integer type. + # We have to convert the types to unsigned + ret_type = to_unsigned(ret_type) + for i, arg_type in enumerate(arg_types): + arg_types[i] = to_unsigned(arg_type) + return Symbol(func_name, op_name, ret_type, arg_names, arg_types) + + def _group_symbols(self) -> None: + symbol_set = {} + for symbol in self._symbols.values(): + op_name = symbol.op_name + symbol_set[op_name] = symbol + + # Group functions together by renaming. + renaming = { + 'llabs': 'abs', 'acosf': 'acos', 'acoshf': 'acosh', 'dadd_rd': 'add_rd', 'fadd_rd': 'add_rd', 'dadd_rn': + 'add_rn', 'fadd_rn': 'add_rn', 'dadd_ru': 'add_ru', 'fadd_ru': 'add_ru', 'dadd_rz': 'add_rz', 'fadd_rz': + 'add_rz', 'asinf': 'asin', 'asinhf': 'asinh', 'atanf': 'atan', 'atan2f': 'atan2', 'atanhf': 'atanh', + 'brevll': 'brev', 'cbrtf': 'cbrt', 'ceilf': 'ceil', 'clzll': 'clz', 'copysignf': 'copysign', 'cosf': 'cos', + 'coshf': 'cosh', 'cospif': 'cospi', 'cyl_bessel_i0f': 'cyl_bessel_i0', 'cyl_bessel_i1f': 'cyl_bessel_i1', + 'fdiv_rd': 'div_rd', 'ddiv_rd': 'div_rd', 'fdiv_rn': 'div_rn', 'ddiv_rn': 'div_rn', 'fdiv_ru': 'div_ru', + 'ddiv_ru': 'div_ru', 'fdiv_rz': 'div_rz', 'ddiv_rz': 'div_rz', 'erff': 'erf', 'erfcf': 'erfc', 'erfcinvf': + 'erfcinv', 'erfcxf': 'erfcx', 'erfinvf': 'erfinv', 'expf': 'exp', 'exp10f': 'exp10', 'exp2f': 'exp2', + 'expm1f': 'expm1', 'fabsf': 'abs', 'fabs': 'abs', 'fast_fdividef': 'fast_dividef', 'fdimf': 'fdim', 'ffsll': + 'ffs', 'floorf': 'floor', 'fmaf': 'fma', 'fmaf_rd': 'fma_rd', 'fmaf_rn': 'fma_rn', 'fmaf_ru': 'fma_ru', + 'fmaf_rz': 'fma_rz', 'fmodf': 'fmod', 'uhadd': 'hadd', 'hypotf': 'hypot', 'ilogbf': 'ilogb', 'isinff': + 'isinf', 'isinfd': 'isinf', 'isnanf': 'isnan', 'isnand': 'isnan', 'j0f': 'j0', 'j1f': 'j1', 'jnf': 'jn', + 'ldexpf': 'ldexp', 'lgammaf': 'lgamma', 'llrintf': 'llrint', 'llroundf': 'llround', 'logf': 'log', 'log10f': + 'log10', 'log1pf': 'log1p', 'log2f': 'log2', 'logbf': 'logb', 'umax': 'max', 'llmax': 'max', 'ullmax': + 'max', 'fmaxf': 'max', 'fmax': 'max', 'umin': 'min', 'llmin': 'min', 'ullmin': 'min', 'fminf': 'min', + 'fmin': 'min', 'dmul_rd': 'mul_rd', 'fmul_rd': 'mul_rd', 'dmul_rn': 'mul_rn', 'fmul_rn': 'mul_rn', + 'dmul_ru': 'mul_ru', 'fmul_ru': 'mul_ru', 'dmul_rz': 'mul_rz', 'fmul_rz': 'mul_rz', 'umul24': 'mul24', + 'umulhi': 'mulhi', 'mul64hi': 'mulhi', 'umul64hi': 'mulhi', 'nearbyintf': 'nearbyint', 'nextafterf': + 'nextafter', 'norm3df': 'norm3d', 'norm4df': 'norm4d', 'normcdff': 'normcdf', 'normcdfinvf': 'normcdfinv', + 'popcll': 'popc', 'powif': 'pow', 'powi': 'pow', 'powf': 'pow', 'rcbrtf': 'rcbrt', 'frcp_rd': 'rcp_rd', + 'drcp_rd': 'rcp_rd', 'frcp_rn': 'rcp_rn', 'drcp_rn': 'rcp_rn', 'frcp_ru': 'rcp_ru', 'drcp_ru': 'rcp_ru', + 'frcp_rz': 'rcp_rz', 'drcp_rz': 'rcp_rz', 'remainderf': 'remainder', 'urhadd': 'rhadd', 'rhypotf': 'rhypot', + 'rintf': 'rint', 'rnorm3df': 'rnorm3d', 'rnorm4df': 'rnorm4d', 'roundf': 'round', 'rsqrtf': 'rsqrt', + 'frsqrt_rn': 'rsqrt_rn', 'usad': 'sad', 'scalbnf': 'scalbn', 'signbitf': 'signbit', 'signbitd': 'signbit', + 'sinf': 'sin', 'sinhf': 'sinh', 'sinpif': 'sinpi', 'sqrtf': 'sqrt', 'fsqrt_rd': 'sqrt_rd', 'dsqrt_rd': + 'sqrt_rd', 'fsqrt_rn': 'sqrt_rn', 'dsqrt_rn': 'sqrt_rn', 'fsqrt_ru': 'sqrt_ru', 'dsqrt_ru': 'sqrt_ru', + 'fsqrt_rz': 'sqrt_rz', 'dsqrt_rz': 'sqrt_rz', 'fsub_rd': 'sub_rd', 'dsub_rd': 'sub_rd', 'fsub_rn': 'sub_rn', + 'dsub_rn': 'sub_rn', 'fsub_ru': 'sub_ru', 'dsub_ru': 'sub_ru', 'fsub_rz': 'sub_rz', 'dsub_rz': 'sub_rz', + 'tanf': 'tan', 'tanhf': 'tanh', 'tgammaf': 'tgamma', 'truncf': 'trunc', 'y0f': 'y0', 'y1f': 'y1', 'ynf': + 'yn' + } + + for symbol in self._symbols.values(): + op_name = symbol.op_name + if op_name in renaming: + op_name = renaming[op_name] + symbol._op_name = op_name + if op_name in self._symbol_groups: + self._symbol_groups[op_name].append(symbol) + else: + self._symbol_groups[op_name] = [symbol] + + def parse_symbols(self, input_file) -> None: + if len(self.symbols) > 0: + return + output = subprocess.check_output(["grep", "define", input_file]).decode().splitlines() + for line in output: + symbol = self._extract_symbol(line) + if symbol is None: + continue + self._symbols[symbol.name] = symbol + + self._group_symbols() + + def _output_stubs(self) -> str: + # Generate python functions in the following format: + # @extern.extern + # def (, _builder=None): + # arg_type_symbol_dict = {[arg_type]: {(symbol, ret_type)}} + # return core.extern_elementwise("libdevice", , , , _builder) + import_str = "from . import core\n" + + header_str = "" + func_str = "" + for symbols in self._symbol_groups.values(): + func_str += "@core.extern\n" + func_name_str = f"def {symbols[0].op_name}(" + for arg_name in symbols[0].arg_names: + func_name_str += f"{arg_name}, " + func_name_str += "_builder=None):\n" + + return_str = f"\treturn core.extern_elementwise(\"{self._name}\", libdevice_path(), [" + for arg_name in symbols[0].arg_names: + return_str += f"{arg_name}, " + return_str += "], \n" + + arg_type_symbol_dict_str = "{" + for symbol in symbols: + arg_type_symbol_dict_str += "(" + for arg_type in symbol.arg_types: + arg_type_symbol_dict_str += f'core.dtype("{arg_type}"),' + ret_type = f'core.dtype("{symbol.ret_type}")' + arg_type_symbol_dict_str += "): (\"" + symbol.name + "\", " + ret_type + "),\n" + arg_type_symbol_dict_str += "}" + + return_str += arg_type_symbol_dict_str + return_str += f", is_pure={self.is_pure}" + return_str += ", _builder=_builder)\n" + + func_str += func_name_str + return_str + "\n" + file_str = import_str + header_str + func_str + + return file_str + + +class LLVMDisassembler: + _path: str + _ll_file: str + + def __init__(self, path) -> None: + ''' + Invoke llvm-dis to disassemble the given file. + :param path: path to llvm-dis + ''' + self._path = path + self._ll_file = "/tmp/extern_lib.ll" + + def disasm(self, lib_path: str) -> None: + subprocess.Popen([self._path, lib_path, "-o", self.ll_file], stdout=subprocess.PIPE).communicate() + + @property + def ll_file(self) -> str: + return self._ll_file + + @property + def path(self) -> str: + return self._path + + +extern_libs = ["libdevice"] + + +def build( + llvm_dis_path: str, + lib_path: str, + lib_name: str, + output_dir: str, +) -> None: + ''' + Interface function to build the library file. + :param llvm_dis_path: path to the llvm-dis binary + :param lib_path: path to the external library file + :param lib_name: name of the library + :param output_dir: path to the output directory + ''' + if lib_name == "libdevice": + extern_lib = Libdevice(lib_path) + else: + raise Exception(f"Unknown extern library: {lib_name}") + + llvm_disassembler = LLVMDisassembler(llvm_dis_path) + llvm_disassembler.disasm(lib_path) + + extern_lib.parse_symbols(llvm_disassembler.ll_file) + extern_lib.generate_stub_file(output_dir) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser() + parser.add_argument("--llvm-dis", dest="llvm_dis_path", help="Path to llvm-dis", default="llvm-dis") + parser.add_argument("--lib-path", dest="lib_path", help="Path to the extern library") + parser.add_argument("--lib-name", dest="lib_name", help="Name of the extern library") + parser.add_argument("--output", dest="output_dir", help="Output file path", default="/tmp/") + args = parser.parse_args() + + build(args.llvm_dis_path, args.lib_path, args.lib_name, args.output_dir) diff --git a/lib/python3.11/site-packages/triton/tools/compile.c b/lib/python3.11/site-packages/triton/tools/compile.c new file mode 100644 index 0000000000000000000000000000000000000000..971bf61912a752465c83a0b17ae131bee6f5cc74 --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/compile.c @@ -0,0 +1,67 @@ +/* clang-format off */ +#include +#include +#include +#include +#include + + +// helpers to check for cuda errors +#define CUDA_CHECK(ans) {{\ + gpuAssert((ans), __FILE__, __LINE__);\ + }}\ + +static inline void gpuAssert(CUresult code, const char *file, int line) {{ + if (code != CUDA_SUCCESS) {{ + const char *prefix = "Triton Error [CUDA]: "; + const char *str; + cuGetErrorString(code, &str); + char err[1024] = {{0}}; + strcat(err, prefix); + strcat(err, str); + printf("%s\\n", err); + exit(code); + }} +}} + +// globals +#define CUBIN_NAME {kernel_name}_cubin +CUmodule {kernel_name}_mod = NULL; +CUfunction {kernel_name}_func = NULL; +unsigned char CUBIN_NAME[{bin_size}] = {{ {bin_data} }}; + + +void unload_{kernel_name}(void) {{ + CUDA_CHECK(cuModuleUnload({kernel_name}_mod)); +}} + +// TODO: some code duplication with `runtime/backend/cuda.c` +void load_{kernel_name}() {{ + int dev = 0; + void *bin = (void *)&CUBIN_NAME; + int shared = {shared}; + CUDA_CHECK(cuModuleLoadData(&{kernel_name}_mod, bin)); + CUDA_CHECK(cuModuleGetFunction(&{kernel_name}_func, {kernel_name}_mod, "{triton_kernel_name}")); + // set dynamic shared memory if necessary + int shared_optin; + CUDA_CHECK(cuDeviceGetAttribute(&shared_optin, CU_DEVICE_ATTRIBUTE_MAX_SHARED_MEMORY_PER_BLOCK_OPTIN, dev)); + if (shared > 49152 && shared_optin > 49152) {{ + CUDA_CHECK(cuFuncSetCacheConfig({kernel_name}_func, CU_FUNC_CACHE_PREFER_SHARED)); + CUDA_CHECK(cuFuncSetAttribute({kernel_name}_func, CU_FUNC_ATTRIBUTE_MAX_DYNAMIC_SHARED_SIZE_BYTES, shared_optin)) + }} +}} + +/* +{kernel_docstring} +*/ +CUresult {kernel_name}(CUstream stream, {signature}) {{ + if ({kernel_name}_func == NULL) + load_{kernel_name}(); + unsigned int gX = {gridX}; + unsigned int gY = {gridY}; + unsigned int gZ = {gridZ}; + void *args[{num_args}] = {{ {arg_pointers} }}; + // TODO: shared memory + if(gX * gY * gZ > 0) + return cuLaunchKernel({kernel_name}_func, gX, gY, gZ, {num_warps} * 32, 1, 1, {shared}, stream, args, NULL); +}} diff --git a/lib/python3.11/site-packages/triton/tools/compile.h b/lib/python3.11/site-packages/triton/tools/compile.h new file mode 100644 index 0000000000000000000000000000000000000000..d98b7063b6ae6292b65b61abf5a30c58b7d28e95 --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/compile.h @@ -0,0 +1,14 @@ +#ifndef TT_KERNEL_INCLUDES +#define TT_KERNEL_INCLUDES + +#include +#include +#include +#include + +#endif + +void unload_{kernel_name}(void); +void load_{kernel_name}(void); +// tt-linker: {kernel_name}:{full_signature}:{algo_info} +CUresult{_placeholder} {kernel_name}(CUstream stream, {signature}); diff --git a/lib/python3.11/site-packages/triton/tools/compile.py b/lib/python3.11/site-packages/triton/tools/compile.py new file mode 100644 index 0000000000000000000000000000000000000000..443341fa0d474610d758855053cf5fc25a6ea68d --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/compile.py @@ -0,0 +1,155 @@ +import binascii +import hashlib +import importlib.util +import sys +from argparse import ArgumentParser +from pathlib import Path +from typing import List + +import triton +import triton.backends +from triton.compiler.code_generator import kernel_suffix +from triton.backends.nvidia.driver import ty_to_cpp + +desc = """ +Triton ahead-of-time compiler: + +This program compiles the kernel with name `kernel-name` in the file at the +provided `path` into self-contained C source-code that embeds the `cubin` +data along with utilities to load, unload and launch the kernel. + +signature is provided as a list of (optionally divisibility-hinted) types +or constexpr values, e.g. + +`compile.py --kernel-name kernel --signature "*fp32:16, i32:16, 1024, i32" --out-name kernel /path/to/kernel.py` + +will compile triton.JITFunction of name `kernel` inside the file `/path/to/kernel.py`. +Said kernel will be specialized such that argument 0, 1 are assumed to be multiple of 16, +and argument 2 is assumed to be a compile-time constant of value 1024, i.e. it won't be part of the generated prototype. + +The resulting entry point will have signature + +CUresult kernel_{specialization_suffix}(CUstream stream, unsigned gX, unsigned gY, unsigned gZ, float* arg0, int32_t arg1, int32_t arg2) + +Different such specialized entry points can be combined using the `linker.py` script. + +NOTE: when resolving the scope of /path/to/kernel.py, the file will be executed from within its parent directory with the python interpreter +used to run this `compile.py` script +""" + +if __name__ == "__main__": + + # command-line arguments + parser = ArgumentParser(description=desc) + parser.add_argument("path", + help="Path to Python source containing desired kernel in its scope. File will be executed.") + parser.add_argument("--kernel-name", "-n", type=str, default="", help="Name of the kernel to compile", + required=True) + parser.add_argument("--num-warps", "-w", type=int, default=1, help="Number of warps to launch the kernel") + parser.add_argument("--num-stages", "-ns", type=int, default=3, + help="Number of stages (meta-parameter of the kernel)") + parser.add_argument("--out-name", "-on", type=str, default=None, help="Out name for the compiled kernel") + parser.add_argument("--out-path", "-o", type=Path, default=None, help="Out filename") + parser.add_argument("--signature", "-s", type=str, help="Signature of the kernel", required=True) + parser.add_argument("--grid", "-g", type=str, help="Launch grid of the kernel", required=True) + args = parser.parse_args() + + out_name = args.out_name if args.out_name else args.kernel_name + out_path = args.out_path if args.out_path else Path(out_name) + + # execute python sources and extract functions wrapped in JITFunction + arg_path = Path(args.path) + sys.path.insert(0, str(arg_path.parent)) + spec = importlib.util.spec_from_file_location(arg_path.stem, arg_path) + mod = importlib.util.module_from_spec(spec) + spec.loader.exec_module(mod) + kernel = getattr(mod, args.kernel_name) + grid = args.grid.split(",") + assert len(grid) == 3 + + # validate and parse signature + signature = list(map(lambda s: s.strip(" "), args.signature.split(","))) + + def hash_signature(signature: List[str]): + m = hashlib.sha256() + m.update(" ".join(signature).encode()) + return m.hexdigest()[:8] + + meta_sig = f"warps{args.num_warps}xstages{args.num_stages}" + sig_hash = hash_signature(signature + [meta_sig]) + + def constexpr(s): + try: + ret = int(s) + return ret + except ValueError: + pass + try: + ret = float(s) + return ret + except ValueError: + pass + return None + + hints = {i: constexpr(s.split(":")[1]) for i, s in enumerate(signature) if ":" in s} + hints = {k: v for k, v in hints.items() if v is not None} + constants = {kernel.arg_names[i]: constexpr(s) for i, s in enumerate(signature)} + constants = {k: v for k, v in constants.items() if v is not None} + signature = { + kernel.arg_names[i]: s.split(":")[0] + for i, s in enumerate(signature) + if kernel.arg_names[i] not in constants + } + const_sig = 'x'.join([str(v) for v in constants.values()]) + doc_string = [f"{k}={v}" for k, v in constants.items()] + doc_string += [f"num_warps={args.num_warps}", f"num_stages={args.num_stages}"] + + # compile ast into cubin + for h in hints.values(): + assert h in [1, 16], f"Only 1 and 16 are valid hints, got {h}" + attrs = triton.backends.compiler.AttrsDescriptor.from_hints(hints) + for p, v in attrs.get_constants().items(): + constants.update({kernel.arg_names[p]: v}) + src = triton.compiler.ASTSource(fn=kernel, constants=constants, signature=signature, attrs=attrs) + opts = {"num_warps": args.num_warps, "num_stages": args.num_stages} + ccinfo = triton.compile(src, options=opts) + arg_names = [] + arg_types = [] + arg_names_not_1 = [] + arg_types_not_1 = [] + for i, arg_name in enumerate(kernel.arg_names): + if arg_name not in constants: + arg_names.append(arg_name) + arg_types.append(signature[arg_name]) + arg_names_not_1.append(arg_name) + arg_types_not_1.append(signature[arg_name]) + elif i in attrs.equal_to_1: + arg_names.append(arg_name) + arg_types.append(signature[arg_name]) + + # dump C stub code + suffix = kernel_suffix(signature.values(), attrs) + func_name = '_'.join([out_name, sig_hash, suffix]) + hex_ = str(binascii.hexlify(ccinfo.asm["cubin"]))[2:-1] + params = { + "kernel_name": func_name, + "triton_kernel_name": args.kernel_name, + "bin_size": len(hex_), + "bin_data": ", ".join([f"0x{x}{y}" for x, y in zip(hex_[::2], hex_[1::2])]), + "signature": ", ".join([f"{ty_to_cpp(ty)} {name}" for name, ty in zip(arg_names_not_1, arg_types_not_1)]), + "full_signature": ", ".join([f"{ty_to_cpp(ty)} {name}" for name, ty in zip(arg_names, arg_types)]), + "arg_pointers": ", ".join([f"&{arg}" for arg in arg_names_not_1]), + "num_args": len(arg_names_not_1), + "kernel_docstring": doc_string, + "shared": ccinfo.metadata.shared, + "num_warps": args.num_warps, + "algo_info": '_'.join([const_sig, meta_sig]), + "gridX": grid[0], + "gridY": grid[1], + "gridZ": grid[2], + "_placeholder": "", + } + for ext in ['h', 'c']: + template_path = Path(__file__).parent / f"compile.{ext}" + with out_path.with_suffix(f".{sig_hash}_{suffix}.{ext}").open("w") as fp: + fp.write(Path(template_path).read_text().format(**params)) diff --git a/lib/python3.11/site-packages/triton/tools/disasm.py b/lib/python3.11/site-packages/triton/tools/disasm.py new file mode 100644 index 0000000000000000000000000000000000000000..002c4e9b5b59c59c5d6804bc2a19c5a28be9cdfc --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/disasm.py @@ -0,0 +1,144 @@ +# MIT License + +# Copyright (c) 2020 Da Yan @ HKUST + +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: + +# The above copyright notice and this permission notice shall be included in all +# copies or substantial portions of the Software. + +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. + +import functools +import os +import re +import subprocess +import tempfile + +FLINE_RE = re.compile(r'\s*/\*\w{4}\*/\s*([^;]*;)\s*/\* 0x(\w{16}) \*/\s*') +SLINE_RE = re.compile(r'\s*/\* 0x(\w{16}) \*/\s*') +FNAME_RE = re.compile(r'\s*Function : (\w+)\s*') +BRA_RE = re.compile(r'(.*BRA(?:\.U)? )(0x\w+);') + + +def parseCtrl(sline): + enc = int(SLINE_RE.match(sline).group(1), 16) + stall = (enc >> 41) & 0xf + yld = (enc >> 45) & 0x1 + wrtdb = (enc >> 46) & 0x7 + readb = (enc >> 49) & 0x7 + watdb = (enc >> 52) & 0x3f + + yld_str = 'Y' if yld == 0 else '-' + wrtdb_str = '-' if wrtdb == 7 else str(wrtdb) + readb_str = '-' if readb == 7 else str(readb) + watdb_str = '--' if watdb == 0 else f'{watdb:02d}' + return f'{watdb_str}:{readb_str}:{wrtdb_str}:{yld_str}:{stall:x}' + + +def processSassLines(fline, sline, labels): + asm = FLINE_RE.match(fline).group(1) + # Remove tailing space + if asm.endswith(" ;"): + asm = asm[:-2] + ";" + ctrl = parseCtrl(sline) + # BRA target address + if BRA_RE.match(asm) is not None: + target = int(BRA_RE.match(asm).group(2), 16) + if target in labels: + pass + else: + labels[target] = len(labels) + return (f'{ctrl}', f'{asm}') + + +@functools.lru_cache() +def get_sass(cubin_asm, fun=None): + fd, path = tempfile.mkstemp() + try: + with open(fd, 'wb') as cubin: + cubin.write(cubin_asm) + sass = extract(path, fun) + finally: + os.remove(path) + return sass + + +@functools.lru_cache() +def path_to_cuobjdump(): + from triton.backends.nvidia.compiler import _path_to_binary + return _path_to_binary("cuobjdump") + + +def extract(file_path, fun): + cuobjdump, _ = path_to_cuobjdump() + if fun is None: + sass_str = subprocess.check_output([cuobjdump, "-sass", file_path]) + else: + sass_str = subprocess.check_output([cuobjdump, "-fun", fun, "-sass", file_path]) + sass_lines = sass_str.splitlines() + line_idx = 0 + while line_idx < len(sass_lines): + line = sass_lines[line_idx].decode() + # format: + # function : + # .headerflags: ... + # /*0000*/ asmstr /*0x...*/ + # /*0x...*/ + + # Looking for new function header (function: ) + while FNAME_RE.match(line) is None: + line_idx += 1 + if line_idx < len(sass_lines): + line = sass_lines[line_idx].decode() + else: + return + + fname = FNAME_RE.match(line).group(1) + ret = '' + ret += f'Function:{fname}\n' + line_idx += 2 # bypass .headerflags + line = sass_lines[line_idx].decode() + # Remapping address to label + labels = {} # address -> label_idx + # store sass asm in buffer and them print them (for labels) + # (ctrl, asm) + asm_buffer = [] + while FLINE_RE.match(line) is not None: + # First line (Offset ASM Encoding) + fline = sass_lines[line_idx].decode() + line_idx += 1 + # Second line (Encoding) + sline = sass_lines[line_idx].decode() + line_idx += 1 + asm_buffer.append(processSassLines(fline, sline, labels)) + # peek the next line + line = sass_lines[line_idx].decode() + # Print sass + # label naming convention: LBB#i + for idx, (ctrl, asm) in enumerate(asm_buffer): + # Print label if this is BRA target + offset = idx * 16 + if offset in labels: + label_name = f'LBB{labels[offset]}' + ret += f'{label_name}:\n' + ret += ctrl + '\t' + # if this is BRA, remap offset to label + if BRA_RE.match(asm): + target = int(BRA_RE.match(asm).group(2), 16) + target_name = f'LBB{labels[target]}' + asm = BRA_RE.sub(rf'\1{target_name};', asm) + ret += asm + '\n' + ret += '\n' + return ret diff --git a/lib/python3.11/site-packages/triton/tools/experimental_descriptor.py b/lib/python3.11/site-packages/triton/tools/experimental_descriptor.py new file mode 100644 index 0000000000000000000000000000000000000000..6077cab6f5fcd1973434911c1be730ed47b1a17f --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/experimental_descriptor.py @@ -0,0 +1,32 @@ +import torch + +import triton + + +class TmaDescKernelParam: + TMA_DESC_SIZE = 128 + + def __init__(self, ptr, dims, block_dims, element_size): + self.desc = torch.empty(self.TMA_DESC_SIZE, dtype=torch.uint8, device="cpu") + assert len(dims) == len(block_dims) + assert 1 <= len(dims) <= 2 + assert self.desc.data_ptr() % 64 == 0 + + if len(dims) == 1: + triton.runtime.driver.active.utils.fill_1d_tma_descriptor(ptr, dims[0], block_dims[0], element_size, + self.desc.data_ptr()) + else: + triton.runtime.driver.active.utils.fill_2d_tma_descriptor(ptr, dims[0], dims[1], block_dims[0], + block_dims[1], element_size, self.desc.data_ptr()) + + # Return a CUtensorMap* pointer in host memory + def tma_desc_cpu_ptr(self): + return self.desc.data_ptr() + + +def create_1d_tma_descriptor(ptr, dim, block_dim, element_size): + return TmaDescKernelParam(ptr, [dim], [block_dim], element_size) + + +def create_2d_tma_descriptor(ptr, dim1, dim0, block_dim1, block_dim0, element_size): + return TmaDescKernelParam(ptr, [dim1, dim0], [block_dim1, block_dim0], element_size) diff --git a/lib/python3.11/site-packages/triton/tools/link.py b/lib/python3.11/site-packages/triton/tools/link.py new file mode 100644 index 0000000000000000000000000000000000000000..75a1157a52f92bbd5d2eae640af97ea360da2ef3 --- /dev/null +++ b/lib/python3.11/site-packages/triton/tools/link.py @@ -0,0 +1,322 @@ +from collections import defaultdict +from pathlib import Path +from typing import Sequence, Union + +from dataclasses import dataclass + + +def _exists(x): + return x is not None + + +class LinkerError(Exception): + pass + + +@dataclass +class KernelLinkerMeta: + orig_kernel_name: str + arg_names: Sequence[str] + arg_ctypes: Sequence[str] + sizes: Sequence[Union[int, None]] + sig_hash: str + triton_suffix: str + suffix: str + num_specs: int + """ number of specialized arguments """ + + +class HeaderParser: + + def __init__(self) -> None: + import re + + # [kernel_name, c signature] + self.linker_directives = re.compile("//[\\s]*tt-linker:[\\s]*([\\w]+):(.+):(.+)") + # [name, hash, suffix] + self.kernel_name = re.compile("^([\\w]+)_([\\w]+)_([\\w]+)$") + # [(type, name)] + self.c_sig = re.compile("[\\s]*(\\w+)\\s(\\w+)[,]?") + # [d|c] + self.arg_suffix = re.compile("[c,d]") + + self.kernels = defaultdict(list) + + def extract_linker_meta(self, header: str): + for ln in header.splitlines(): + if ln.startswith("//"): + m = self.linker_directives.match(ln) + if _exists(m): + ker_name, c_sig, algo_info = m.group(1), m.group(2), m.group(3) + name, sig_hash, suffix = self._match_name(ker_name) + c_types, arg_names = self._match_c_sig(c_sig) + num_specs, sizes = self._match_suffix(suffix, c_sig) + self._add_kernel( + "_".join([name, algo_info]), + KernelLinkerMeta( + orig_kernel_name=name, + arg_names=arg_names, + arg_ctypes=c_types, + sizes=sizes, + sig_hash=sig_hash, + triton_suffix=suffix, + suffix=suffix, + num_specs=num_specs, + ), + ) + + def _match_name(self, ker_name: str): + m = self.kernel_name.match(ker_name) + if _exists(m): + name, sig_hash, suffix = m.group(1), m.group(2), m.group(3) + return name, sig_hash, suffix + raise LinkerError(f"{ker_name} is not a valid kernel name") + + def _match_c_sig(self, c_sig: str): + m = self.c_sig.findall(c_sig) + if len(m): + tys, args = [], [] + for ty, arg_name in m: + tys.append(ty) + args.append(arg_name) + return tys, args + + raise LinkerError(f"{c_sig} is not a valid argument signature") + + def _match_suffix(self, suffix: str, c_sig: str): + args = c_sig.split(",") + s2i = {"c": 1, "d": 16} + num_specs = 0 + sizes = [] + # scan through suffix, first find the index, + # then see if it is followed by d or c + for i in range(len(args)): + pos = suffix.find(str(i)) + if pos == -1: + raise LinkerError(f"{suffix} is not a valid kernel suffix") + pos += len(str(i)) + if self.arg_suffix.match(suffix, pos): + num_specs += 1 + sizes.extend([None] * (i - len(sizes))) + sizes.append(s2i[suffix[pos]]) + pos += 1 + if i < len(args) - 1: + suffix = suffix[pos:] + else: + sizes.extend([None] * (len(args) - len(sizes))) + return num_specs, sizes + + def _add_kernel(self, name: str, ker: KernelLinkerMeta): + if name in self.kernels: + last: KernelLinkerMeta = self.kernels[name][-1] + + for cur, new_ in zip(last.arg_ctypes, ker.arg_ctypes): + if cur != new_: + raise LinkerError( + f"Mismatched signature for kernel {name}: \n\texisting sig is: {','.join(last.arg_ctypes)}\n\tcurrent is: {','.join(ker.arg_ctypes)}" + ) + + self.kernels[name].append(ker) + + +def gen_signature_with_full_args(m): + return ", ".join([f"{ty} {arg}" for ty, arg in zip(m.arg_ctypes, m.arg_names)]) + + +def gen_signature(m): + arg_types = [ty for ty, hint in zip(m.arg_ctypes, m.sizes) if hint != 1] + arg_names = [arg for arg, hint in zip(m.arg_names, m.sizes) if hint != 1] + sig = ", ".join([f"{ty} {arg}" for ty, arg in zip(arg_types, arg_names)]) + return sig + + +# generate declarations of kernels with meta-parameter and constant values +def make_algo_decls(name: str, metas: Sequence[KernelLinkerMeta]) -> str: + return f""" +CUresult {name}(CUstream stream, {gen_signature_with_full_args(metas[-1])}); +void load_{name}(); +void unload_{name}(); + """ + + +# generate declarations of kernels with meta-parameter and constant values +def make_global_decl(meta: KernelLinkerMeta) -> str: + return f""" +CUresult {meta.orig_kernel_name}_default(CUstream stream, {gen_signature_with_full_args(meta)}); +CUresult {meta.orig_kernel_name}(CUstream stream, {gen_signature_with_full_args(meta)}, int algo_id); +void load_{meta.orig_kernel_name}(); +void unload_{meta.orig_kernel_name}(); + """ + + +# generate dispatcher function for kernels with different meta-parameter and constant values +def make_default_algo_kernel(meta: KernelLinkerMeta) -> str: + src = f"CUresult {meta.orig_kernel_name}_default(CUstream stream, {gen_signature_with_full_args(meta)}){{\n" + src += (f" return {meta.orig_kernel_name}(stream, {', '.join(meta.arg_names)}, 0);\n") + src += "}\n" + return src + + +# generate dispatcher function for kernels with different integer value hints +def make_kernel_hints_dispatcher(name: str, metas: Sequence[KernelLinkerMeta]) -> str: + src = f"// launcher for: {name}\n" + for meta in sorted(metas, key=lambda m: -m.num_specs): + src += f"CUresult {meta.orig_kernel_name}_{meta.sig_hash}_{meta.suffix}(CUstream stream, {gen_signature(meta)});\n" + src += "\n" + + src += (f"CUresult {name}(CUstream stream, {gen_signature_with_full_args(metas[-1])}){{") + src += "\n" + for meta in sorted(metas, key=lambda m: -m.num_specs): + cond_fn = ( # + lambda val, hint: f"({val} % {hint} == 0)" # + if hint == 16 # + else f"({val} == {hint})" # + if hint == 1 # + else None) + conds = " && ".join([ # + cond_fn(val, hint) # + for val, hint in zip(meta.arg_names, meta.sizes) # + if hint is not None + ]) + src += (f" if ({conds})\n" if any(meta.sizes) else "if (1)\n" + ) # Edge case where no specializations hence no dispatching required + arg_names = [arg for arg, hint in zip(meta.arg_names, meta.sizes) if hint != 1] + src += f" return {meta.orig_kernel_name}_{meta.sig_hash}_{meta.suffix}(stream, {', '.join(arg_names)});\n" + src += "\n" + src += " return CUDA_ERROR_INVALID_VALUE;\n" + src += "}\n" + + for mode in ["load", "unload"]: + src += f"\n// {mode} for: {name}\n" + for meta in sorted(metas, key=lambda m: -m.num_specs): + src += f"void {mode}_{meta.orig_kernel_name}_{meta.sig_hash}_{meta.suffix}();\n" + src += f"void {mode}_{name}() {{" + src += "\n" + for meta in sorted(metas, key=lambda m: -m.num_specs): + src += (f" {mode}_{meta.orig_kernel_name}_{meta.sig_hash}_{meta.suffix}();\n") + src += "}\n" + return src + + +# generate dispatcher function for kernels with different meta-parameter and constant values +def make_kernel_meta_const_dispatcher(meta: KernelLinkerMeta) -> str: + src = f"CUresult {meta.orig_kernel_name}(CUstream stream, {gen_signature_with_full_args(meta)}, int algo_id){{\n" + src += f" assert (algo_id < (int)sizeof({meta.orig_kernel_name}_kernels));\n" + src += f" return {meta.orig_kernel_name}_kernels[algo_id](stream, {', '.join(meta.arg_names)});\n" + src += "}\n" + return src + + +# generate definition of function pointers of kernel dispatchers based on meta-parameter and constant values +def make_func_pointers(names: str, meta: KernelLinkerMeta) -> str: + # the table of hint dispatchers + src = f"typedef CUresult (*kernel_func_t)(CUstream stream, {gen_signature_with_full_args(meta)});\n" + src += f"kernel_func_t {meta.orig_kernel_name}_kernels[] = {{\n" + for name in names: + src += f" {name},\n" + src += "};\n" + return src + + +# generate definition for load/unload functions for kernels with different meta-parameter and constant values +def make_kernel_load_def(names: str, meta: KernelLinkerMeta) -> str: + src = "" + for mode in ["load", "unload"]: + src += f"void {mode}_{meta.orig_kernel_name}(void){{\n" + for name in names: + src += f" {mode}_{name}();\n" + src += "}\n\n" + return src + + +def make_get_num_algos_decl(meta: KernelLinkerMeta) -> str: + src = f"int {meta.orig_kernel_name}_get_num_algos(void);" + return src + + +def make_get_num_algos_def(meta: KernelLinkerMeta) -> str: + src = f"int {meta.orig_kernel_name}_get_num_algos(void){{\n" + src += f" return (int)(sizeof({meta.orig_kernel_name}_kernels) / sizeof({meta.orig_kernel_name}_kernels[0]));\n" + src += "}\n" + return src + + +desc = """ +Triton ahead-of-time linker: + +This program takes in header files generated by compile.py, and generates a +single entry-point responsible for dispatching the user's input to the right +kernel given the specializations that were compiled. + +Example usage: +python link.py /path/to/headers/*.h -o kernel_name +""" + +if __name__ == "__main__": + from argparse import ArgumentParser + + parser = ArgumentParser(description=desc) + parser.add_argument( + "headers", + nargs="+", + help="Paths to header files to link. Must include linker directive annotations (autogenerated by ttc)", + ) + parser.add_argument("--out", "-o", type=Path, help="Out filename") + parser.add_argument( + "--prefix", + type=str, + default="", + help="String to prefix kernel dispatcher names", + ) + args = parser.parse_args() + + # metadata + parser = HeaderParser() + includes = [] + for header in args.headers: + h_path = Path(header) + h_str = h_path.read_text() + includes.append(h_path.name) + parser.extract_linker_meta(h_str) + + # generate headers + algo_decls = [make_algo_decls(name, meta) for name, meta in parser.kernels.items()] + meta_lists = [meta for name, meta in parser.kernels.items()] + meta = meta_lists[0][0] + get_num_algos_decl = make_get_num_algos_decl(meta) + global_decl = make_global_decl(meta) + with args.out.with_suffix(".h").open("w") as fp: + out = "#include \n" + out += "\n".join(algo_decls) + out += "\n" + out += get_num_algos_decl + out += "\n" + out += global_decl + fp.write(out) + + # generate source + defs = [make_kernel_hints_dispatcher(name, meta) for name, meta in parser.kernels.items()] + names = [name for name in parser.kernels.keys()] + func_pointers_def = make_func_pointers(names, meta) + meta_const_def = make_kernel_meta_const_dispatcher(meta) + load_unload_def = make_kernel_load_def(names, meta) + get_num_algos_def = make_get_num_algos_def(meta) + default_algo_kernel = make_default_algo_kernel(meta) + with args.out.with_suffix(".c").open("w") as fp: + out = "" + out += "#include \n" + out += "#include \n" + out += "#include \n" + out += "\n" + out += "\n".join(defs) + out += "\n" + out += func_pointers_def + out += "\n" + out += get_num_algos_def + out += "\n" + out += meta_const_def + out += "\n" + out += load_unload_def + out += "\n" + out += default_algo_kernel + fp.write(out) diff --git a/lib/python3.11/site-packages/typing_inspection/__init__.py b/lib/python3.11/site-packages/typing_inspection/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/typing_inspection/__pycache__/__init__.cpython-311.pyc b/lib/python3.11/site-packages/typing_inspection/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ef4a4fde85cc9dfce6f1acf3475d3cfb5114bc8e Binary files /dev/null and b/lib/python3.11/site-packages/typing_inspection/__pycache__/__init__.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/typing_inspection/__pycache__/introspection.cpython-311.pyc b/lib/python3.11/site-packages/typing_inspection/__pycache__/introspection.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..e7d6819af385ed5d9bf3a697b7f339f4ae16423c Binary files /dev/null and b/lib/python3.11/site-packages/typing_inspection/__pycache__/introspection.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/typing_inspection/__pycache__/typing_objects.cpython-311.pyc b/lib/python3.11/site-packages/typing_inspection/__pycache__/typing_objects.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..79820d7d91c62d3ecfb79f0d844c492664d74218 Binary files /dev/null and b/lib/python3.11/site-packages/typing_inspection/__pycache__/typing_objects.cpython-311.pyc differ diff --git a/lib/python3.11/site-packages/typing_inspection/introspection.py b/lib/python3.11/site-packages/typing_inspection/introspection.py new file mode 100644 index 0000000000000000000000000000000000000000..d6c083e5456c8ad5da7559a3c0a901e0812a5014 --- /dev/null +++ b/lib/python3.11/site-packages/typing_inspection/introspection.py @@ -0,0 +1,587 @@ +"""High-level introspection utilities, used to inspect type annotations.""" + +from __future__ import annotations + +import sys +import types +from collections.abc import Generator +from dataclasses import InitVar +from enum import Enum, IntEnum, auto +from typing import Any, Literal, NamedTuple, cast + +from typing_extensions import TypeAlias, assert_never, get_args, get_origin + +from . import typing_objects + +__all__ = ( + 'AnnotationSource', + 'ForbiddenQualifier', + 'InspectedAnnotation', + 'Qualifier', + 'get_literal_values', + 'inspect_annotation', + 'is_union_origin', +) + +if sys.version_info >= (3, 14) or sys.version_info < (3, 10): + + def is_union_origin(obj: Any, /) -> bool: + """Return whether the provided origin is the union form. + + ```pycon + >>> is_union_origin(typing.Union) + True + >>> is_union_origin(get_origin(int | str)) + True + >>> is_union_origin(types.UnionType) + True + ``` + + !!! note + Since Python 3.14, both `Union[, , ...]` and ` | | ...` forms create instances + of the same [`typing.Union`][] class. As such, it is recommended to not use this function + anymore (provided that you only support Python 3.14 or greater), and instead use the + [`typing_objects.is_union()`][typing_inspection.typing_objects.is_union] function directly: + + ```python + from typing import Union, get_origin + + from typing_inspection import typing_objects + + typ = int | str # Or Union[int, str] + origin = get_origin(typ) + if typing_objects.is_union(origin): + ... + ``` + """ + return typing_objects.is_union(obj) + + +else: + + def is_union_origin(obj: Any, /) -> bool: + """Return whether the provided origin is the union form. + + ```pycon + >>> is_union_origin(typing.Union) + True + >>> is_union_origin(get_origin(int | str)) + True + >>> is_union_origin(types.UnionType) + True + ``` + + !!! note + Since Python 3.14, both `Union[, , ...]` and ` | | ...` forms create instances + of the same [`typing.Union`][] class. As such, it is recommended to not use this function + anymore (provided that you only support Python 3.14 or greater), and instead use the + [`typing_objects.is_union()`][typing_inspection.typing_objects.is_union] function directly: + + ```python + from typing import Union, get_origin + + from typing_inspection import typing_objects + + typ = int | str # Or Union[int, str] + origin = get_origin(typ) + if typing_objects.is_union(origin): + ... + ``` + """ + return typing_objects.is_union(obj) or obj is types.UnionType + + +def _literal_type_check(value: Any, /) -> None: + """Type check the provided literal value against the legal parameters.""" + if ( + not isinstance(value, (int, bytes, str, bool, Enum, typing_objects.NoneType)) + and value is not typing_objects.NoneType + ): + raise TypeError(f'{value} is not a valid literal value, must be one of: int, bytes, str, Enum, None.') + + +def get_literal_values( + annotation: Any, + /, + *, + type_check: bool = False, + unpack_type_aliases: Literal['skip', 'lenient', 'eager'] = 'eager', +) -> Generator[Any]: + """Yield the values contained in the provided [`Literal`][typing.Literal] [special form][]. + + Args: + annotation: The [`Literal`][typing.Literal] [special form][] to unpack. + type_check: Whether to check if the literal values are [legal parameters][literal-legal-parameters]. + Raises a [`TypeError`][] otherwise. + unpack_type_aliases: What to do when encountering [PEP 695](https://peps.python.org/pep-0695/) + [type aliases][type-aliases]. Can be one of: + + - `'skip'`: Do not try to parse type aliases. Note that this can lead to incorrect results: + ```pycon + >>> type MyAlias = Literal[1, 2] + >>> list(get_literal_values(Literal[MyAlias, 3], unpack_type_aliases="skip")) + [MyAlias, 3] + ``` + + - `'lenient'`: Try to parse type aliases, and fallback to `'skip'` if the type alias can't be inspected + (because of an undefined forward reference). + + - `'eager'`: Parse type aliases and raise any encountered [`NameError`][] exceptions (the default): + ```pycon + >>> type MyAlias = Literal[1, 2] + >>> list(get_literal_values(Literal[MyAlias, 3], unpack_type_aliases="eager")) + [1, 2, 3] + ``` + + Note: + While `None` is [equivalent to][none] `type(None)`, the runtime implementation of [`Literal`][typing.Literal] + does not de-duplicate them. This function makes sure this de-duplication is applied: + + ```pycon + >>> list(get_literal_values(Literal[NoneType, None])) + [None] + ``` + + Example: + ```pycon + >>> type Ints = Literal[1, 2] + >>> list(get_literal_values(Literal[1, Ints], unpack_type_alias="skip")) + ["a", Ints] + >>> list(get_literal_values(Literal[1, Ints])) + [1, 2] + >>> list(get_literal_values(Literal[1.0], type_check=True)) + Traceback (most recent call last): + ... + TypeError: 1.0 is not a valid literal value, must be one of: int, bytes, str, Enum, None. + ``` + """ + # `literal` is guaranteed to be a `Literal[...]` special form, so use + # `__args__` directly instead of calling `get_args()`. + + if unpack_type_aliases == 'skip': + _has_none = False + # `Literal` parameters are already deduplicated, no need to do it ourselves. + # (we only check for `None` and `NoneType`, which should be considered as duplicates). + for arg in annotation.__args__: + if type_check: + _literal_type_check(arg) + if arg is None or arg is typing_objects.NoneType: + if not _has_none: + yield None + _has_none = True + else: + yield arg + else: + # We'll need to manually deduplicate parameters, see the `Literal` implementation in `typing`. + values_and_type: list[tuple[Any, type[Any]]] = [] + + for arg in annotation.__args__: + # Note: we could also check for generic aliases with a type alias as an origin. + # However, it is very unlikely that this happens as type variables can't appear in + # `Literal` forms, so the only valid (but unnecessary) use case would be something like: + # `type Test[T] = Literal['a']` (and then use `Test[SomeType]`). + if typing_objects.is_typealiastype(arg): + try: + alias_value = arg.__value__ + except NameError: + if unpack_type_aliases == 'eager': + raise + # unpack_type_aliases == "lenient": + if type_check: + _literal_type_check(arg) + values_and_type.append((arg, type(arg))) + else: + sub_args = get_literal_values( + alias_value, type_check=type_check, unpack_type_aliases=unpack_type_aliases + ) + values_and_type.extend((a, type(a)) for a in sub_args) # pyright: ignore[reportUnknownArgumentType] + else: + if type_check: + _literal_type_check(arg) + if arg is typing_objects.NoneType: + values_and_type.append((None, typing_objects.NoneType)) + else: + values_and_type.append((arg, type(arg))) # pyright: ignore[reportUnknownArgumentType] + + try: + dct = dict.fromkeys(values_and_type) + except TypeError: + # Unhashable parameters, the Python implementation allows them + yield from (p for p, _ in values_and_type) + else: + yield from (p for p, _ in dct) + + +Qualifier: TypeAlias = Literal['required', 'not_required', 'read_only', 'class_var', 'init_var', 'final'] +"""A [type qualifier][].""" + +_all_qualifiers: set[Qualifier] = set(get_args(Qualifier)) + + +# TODO at some point, we could switch to an enum flag, so that multiple sources +# can be combined. However, is there a need for this? +class AnnotationSource(IntEnum): + # TODO if/when https://peps.python.org/pep-0767/ is accepted, add 'read_only' + # to CLASS and NAMED_TUPLE (even though for named tuples it is redundant). + + """The source of an annotation, e.g. a class or a function. + + Depending on the source, different [type qualifiers][type qualifier] may be (dis)allowed. + """ + + ASSIGNMENT_OR_VARIABLE = auto() + """An annotation used in an assignment or variable annotation: + + ```python + x: Final[int] = 1 + y: Final[str] + ``` + + **Allowed type qualifiers:** [`Final`][typing.Final]. + """ + + CLASS = auto() + """An annotation used in the body of a class: + + ```python + class Test: + x: Final[int] = 1 + y: ClassVar[str] + ``` + + **Allowed type qualifiers:** [`ClassVar`][typing.ClassVar], [`Final`][typing.Final]. + """ + + DATACLASS = auto() + """An annotation used in the body of a dataclass: + + ```python + @dataclass + class Test: + x: Final[int] = 1 + y: InitVar[str] = 'test' + ``` + + **Allowed type qualifiers:** [`ClassVar`][typing.ClassVar], [`Final`][typing.Final], [`InitVar`][dataclasses.InitVar]. + """ # noqa: E501 + + TYPED_DICT = auto() + """An annotation used in the body of a [`TypedDict`][typing.TypedDict]: + + ```python + class TD(TypedDict): + x: Required[ReadOnly[int]] + y: ReadOnly[NotRequired[str]] + ``` + + **Allowed type qualifiers:** [`ReadOnly`][typing.ReadOnly], [`Required`][typing.Required], + [`NotRequired`][typing.NotRequired]. + """ + + NAMED_TUPLE = auto() + """An annotation used in the body of a [`NamedTuple`][typing.NamedTuple]. + + ```python + class NT(NamedTuple): + x: int + y: str + ``` + + **Allowed type qualifiers:** none. + """ + + FUNCTION = auto() + """An annotation used in a function, either for a parameter or the return value. + + ```python + def func(a: int) -> str: + ... + ``` + + **Allowed type qualifiers:** none. + """ + + ANY = auto() + """An annotation that might come from any source. + + **Allowed type qualifiers:** all. + """ + + BARE = auto() + """An annotation that is inspected as is. + + **Allowed type qualifiers:** none. + """ + + @property + def allowed_qualifiers(self) -> set[Qualifier]: + """The allowed [type qualifiers][type qualifier] for this annotation source.""" + # TODO use a match statement when Python 3.9 support is dropped. + if self is AnnotationSource.ASSIGNMENT_OR_VARIABLE: + return {'final'} + elif self is AnnotationSource.CLASS: + return {'final', 'class_var'} + elif self is AnnotationSource.DATACLASS: + return {'final', 'class_var', 'init_var'} + elif self is AnnotationSource.TYPED_DICT: + return {'required', 'not_required', 'read_only'} + elif self in (AnnotationSource.NAMED_TUPLE, AnnotationSource.FUNCTION, AnnotationSource.BARE): + return set() + elif self is AnnotationSource.ANY: + return _all_qualifiers + else: # pragma: no cover + assert_never(self) + + +class ForbiddenQualifier(Exception): + """The provided [type qualifier][] is forbidden.""" + + qualifier: Qualifier + """The forbidden qualifier.""" + + def __init__(self, qualifier: Qualifier, /) -> None: + self.qualifier = qualifier + + +class _UnknownTypeEnum(Enum): + UNKNOWN = auto() + + def __str__(self) -> str: + return 'UNKNOWN' + + def __repr__(self) -> str: + return '' + + +UNKNOWN = _UnknownTypeEnum.UNKNOWN +"""A sentinel value used when no [type expression][] is present.""" + +_UnkownType: TypeAlias = Literal[_UnknownTypeEnum.UNKNOWN] +"""The type of the [`UNKNOWN`][typing_inspection.introspection.UNKNOWN] sentinel value.""" + + +class InspectedAnnotation(NamedTuple): + """The result of the inspected annotation.""" + + type: Any | _UnkownType + """The final [type expression][], with [type qualifiers][type qualifier] and annotated metadata stripped. + + If no type expression is available, the [`UNKNOWN`][typing_inspection.introspection.UNKNOWN] sentinel + value is used instead. This is the case when a [type qualifier][] is used with no type annotation: + + ```python + ID: Final = 1 + + class C: + x: ClassVar = 'test' + ``` + """ + + qualifiers: set[Qualifier] + """The [type qualifiers][type qualifier] present on the annotation.""" + + metadata: list[Any] + """The annotated metadata.""" + + +def inspect_annotation( # noqa: PLR0915 + annotation: Any, + /, + *, + annotation_source: AnnotationSource, + unpack_type_aliases: Literal['skip', 'lenient', 'eager'] = 'skip', +) -> InspectedAnnotation: + """Inspect an [annotation expression][], extracting any [type qualifier][] and metadata. + + An [annotation expression][] is a [type expression][] optionally surrounded by one or more + [type qualifiers][type qualifier] or by [`Annotated`][typing.Annotated]. This function will: + + - Unwrap the type expression, keeping track of the type qualifiers. + - Unwrap [`Annotated`][typing.Annotated] forms, keeping track of the annotated metadata. + + Args: + annotation: The annotation expression to be inspected. + annotation_source: The source of the annotation. Depending on the source (e.g. a class), different type + qualifiers may be (dis)allowed. To allow any type qualifier, use + [`AnnotationSource.ANY`][typing_inspection.introspection.AnnotationSource.ANY]. + unpack_type_aliases: What to do when encountering [PEP 695](https://peps.python.org/pep-0695/) + [type aliases][type-aliases]. Can be one of: + + - `'skip'`: Do not try to parse type aliases (the default): + ```pycon + >>> type MyInt = Annotated[int, 'meta'] + >>> inspect_annotation(MyInt, annotation_source=AnnotationSource.BARE, unpack_type_aliases='skip') + InspectedAnnotation(type=MyInt, qualifiers={}, metadata=[]) + ``` + + - `'lenient'`: Try to parse type aliases, and fallback to `'skip'` if the type alias + can't be inspected (because of an undefined forward reference): + ```pycon + >>> type MyInt = Annotated[Undefined, 'meta'] + >>> inspect_annotation(MyInt, annotation_source=AnnotationSource.BARE, unpack_type_aliases='lenient') + InspectedAnnotation(type=MyInt, qualifiers={}, metadata=[]) + >>> Undefined = int + >>> inspect_annotation(MyInt, annotation_source=AnnotationSource.BARE, unpack_type_aliases='lenient') + InspectedAnnotation(type=int, qualifiers={}, metadata=['meta']) + ``` + + - `'eager'`: Parse type aliases and raise any encountered [`NameError`][] exceptions. + + Returns: + The result of the inspected annotation, where the type expression, used qualifiers and metadata is stored. + + Example: + ```pycon + >>> inspect_annotation( + ... Final[Annotated[ClassVar[Annotated[int, 'meta_1']], 'meta_2']], + ... annotation_source=AnnotationSource.CLASS, + ... ) + ... + InspectedAnnotation(type=int, qualifiers={'class_var', 'final'}, metadata=['meta_1', 'meta_2']) + ``` + """ + allowed_qualifiers = annotation_source.allowed_qualifiers + qualifiers: set[Qualifier] = set() + metadata: list[Any] = [] + + while True: + annotation, _meta = _unpack_annotated(annotation, unpack_type_aliases=unpack_type_aliases) + if _meta: + metadata = _meta + metadata + continue + + origin = get_origin(annotation) + if origin is not None: + if typing_objects.is_classvar(origin): + if 'class_var' not in allowed_qualifiers: + raise ForbiddenQualifier('class_var') + qualifiers.add('class_var') + annotation = annotation.__args__[0] + elif typing_objects.is_final(origin): + if 'final' not in allowed_qualifiers: + raise ForbiddenQualifier('final') + qualifiers.add('final') + annotation = annotation.__args__[0] + elif typing_objects.is_required(origin): + if 'required' not in allowed_qualifiers: + raise ForbiddenQualifier('required') + qualifiers.add('required') + annotation = annotation.__args__[0] + elif typing_objects.is_notrequired(origin): + if 'not_required' not in allowed_qualifiers: + raise ForbiddenQualifier('not_required') + qualifiers.add('not_required') + annotation = annotation.__args__[0] + elif typing_objects.is_readonly(origin): + if 'read_only' not in allowed_qualifiers: + raise ForbiddenQualifier('not_required') + qualifiers.add('read_only') + annotation = annotation.__args__[0] + else: + # origin is not None but not a type qualifier nor `Annotated` (e.g. `list[int]`): + break + elif isinstance(annotation, InitVar): + if 'init_var' not in allowed_qualifiers: + raise ForbiddenQualifier('init_var') + qualifiers.add('init_var') + annotation = cast(Any, annotation.type) + else: + break + + # `Final`, `ClassVar` and `InitVar` are type qualifiers allowed to be used as a bare annotation: + if typing_objects.is_final(annotation): + if 'final' not in allowed_qualifiers: + raise ForbiddenQualifier('final') + qualifiers.add('final') + annotation = UNKNOWN + elif typing_objects.is_classvar(annotation): + if 'class_var' not in allowed_qualifiers: + raise ForbiddenQualifier('class_var') + qualifiers.add('class_var') + annotation = UNKNOWN + elif annotation is InitVar: + if 'init_var' not in allowed_qualifiers: + raise ForbiddenQualifier('init_var') + qualifiers.add('init_var') + annotation = UNKNOWN + + return InspectedAnnotation(annotation, qualifiers, metadata) + + +def _unpack_annotated_inner( + annotation: Any, unpack_type_aliases: Literal['lenient', 'eager'], check_annotated: bool +) -> tuple[Any, list[Any]]: + origin = get_origin(annotation) + if check_annotated and typing_objects.is_annotated(origin): + annotated_type = annotation.__origin__ + metadata = list(annotation.__metadata__) + + # The annotated type might be a PEP 695 type alias, so we need to recursively + # unpack it. Because Python already flattens `Annotated[Annotated[, ...], ...]` forms, + # we can skip the `is_annotated()` check in the next call: + annotated_type, sub_meta = _unpack_annotated_inner( + annotated_type, unpack_type_aliases=unpack_type_aliases, check_annotated=False + ) + metadata = sub_meta + metadata + return annotated_type, metadata + elif typing_objects.is_typealiastype(annotation): + try: + value = annotation.__value__ + except NameError: + if unpack_type_aliases == 'eager': + raise + else: + typ, metadata = _unpack_annotated_inner( + value, unpack_type_aliases=unpack_type_aliases, check_annotated=True + ) + if metadata: + # Having metadata means the type alias' `__value__` was an `Annotated` form + # (or, recursively, a type alias to an `Annotated` form). It is important to check + # for this, as we don't want to unpack other type aliases (e.g. `type MyInt = int`). + return typ, metadata + return annotation, [] + elif typing_objects.is_typealiastype(origin): + # When parameterized, PEP 695 type aliases become generic aliases + # (e.g. with `type MyList[T] = Annotated[list[T], ...]`, `MyList[int]` + # is a generic alias). + try: + value = origin.__value__ + except NameError: + if unpack_type_aliases == 'eager': + raise + else: + # While Python already handles type variable replacement for simple `Annotated` forms, + # we need to manually apply the same logic for PEP 695 type aliases: + # - With `MyList = Annotated[list[T], ...]`, `MyList[int] == Annotated[list[int], ...]` + # - With `type MyList[T] = Annotated[list[T], ...]`, `MyList[int].__value__ == Annotated[list[T], ...]`. + + try: + # To do so, we emulate the parameterization of the value with the arguments: + # with `type MyList[T] = Annotated[list[T], ...]`, to emulate `MyList[int]`, + # we do `Annotated[list[T], ...][int]` (which gives `Annotated[list[T], ...]`): + value = value[annotation.__args__] + except TypeError: + # Might happen if the type alias is parameterized, but its value doesn't have any + # type variables, e.g. `type MyInt[T] = int`. + pass + typ, metadata = _unpack_annotated_inner( + value, unpack_type_aliases=unpack_type_aliases, check_annotated=True + ) + if metadata: + return typ, metadata + return annotation, [] + + return annotation, [] + + +# This could eventually be made public: +def _unpack_annotated( + annotation: Any, /, *, unpack_type_aliases: Literal['skip', 'lenient', 'eager'] = 'eager' +) -> tuple[Any, list[Any]]: + if unpack_type_aliases == 'skip': + if typing_objects.is_annotated(get_origin(annotation)): + return annotation.__origin__, list(annotation.__metadata__) + else: + return annotation, [] + + return _unpack_annotated_inner(annotation, unpack_type_aliases=unpack_type_aliases, check_annotated=True) diff --git a/lib/python3.11/site-packages/typing_inspection/py.typed b/lib/python3.11/site-packages/typing_inspection/py.typed new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/lib/python3.11/site-packages/typing_inspection/typing_objects.py b/lib/python3.11/site-packages/typing_inspection/typing_objects.py new file mode 100644 index 0000000000000000000000000000000000000000..dc44ba98cd8ccdba374982819083d89bbf808c2e --- /dev/null +++ b/lib/python3.11/site-packages/typing_inspection/typing_objects.py @@ -0,0 +1,607 @@ +"""Low-level introspection utilities for [`typing`][] members. + +The provided functions in this module check against both the [`typing`][] and [`typing_extensions`][] +variants, if they exists and are different. +""" +# ruff: noqa: UP006 + +import collections.abc +import contextlib +import re +import sys +import typing +import warnings +from textwrap import dedent +from types import FunctionType, GenericAlias +from typing import Any, Final + +import typing_extensions +from typing_extensions import LiteralString, TypeAliasType, TypeIs, deprecated + +__all__ = ( + 'DEPRECATED_ALIASES', + 'NoneType', + 'is_annotated', + 'is_any', + 'is_classvar', + 'is_concatenate', + 'is_deprecated', + 'is_final', + 'is_forwardref', + 'is_generic', + 'is_literal', + 'is_literalstring', + 'is_namedtuple', + 'is_never', + 'is_newtype', + 'is_nodefault', + 'is_noextraitems', + 'is_noreturn', + 'is_notrequired', + 'is_paramspec', + 'is_paramspecargs', + 'is_paramspeckwargs', + 'is_readonly', + 'is_required', + 'is_self', + 'is_typealias', + 'is_typealiastype', + 'is_typeguard', + 'is_typeis', + 'is_typevar', + 'is_typevartuple', + 'is_union', + 'is_unpack', +) + +_IS_PY310 = sys.version_info[:2] == (3, 10) + + +def _compile_identity_check_function(member: LiteralString, function_name: LiteralString) -> FunctionType: + """Create a function checking that the function argument is the (unparameterized) typing `member`. + + The function will make sure to check against both the `typing` and `typing_extensions` + variants as depending on the Python version, the `typing_extensions` variant might be different. + For instance, on Python 3.9: + + ```pycon + >>> from typing import Literal as t_Literal + >>> from typing_extensions import Literal as te_Literal, get_origin + + >>> t_Literal is te_Literal + False + >>> get_origin(t_Literal[1]) + typing.Literal + >>> get_origin(te_Literal[1]) + typing_extensions.Literal + ``` + """ + in_typing = hasattr(typing, member) + in_typing_extensions = hasattr(typing_extensions, member) + + if in_typing and in_typing_extensions: + if getattr(typing, member) is getattr(typing_extensions, member): + check_code = f'obj is typing.{member}' + else: + check_code = f'obj is typing.{member} or obj is typing_extensions.{member}' + elif in_typing and not in_typing_extensions: + check_code = f'obj is typing.{member}' + elif not in_typing and in_typing_extensions: + check_code = f'obj is typing_extensions.{member}' + else: + check_code = 'False' + + func_code = dedent(f""" + def {function_name}(obj: Any, /) -> bool: + return {check_code} + """) + + locals_: dict[str, Any] = {} + globals_: dict[str, Any] = {'Any': Any, 'typing': typing, 'typing_extensions': typing_extensions} + exec(func_code, globals_, locals_) + return locals_[function_name] + + +def _compile_isinstance_check_function(member: LiteralString, function_name: LiteralString) -> FunctionType: + """Create a function checking that the function is an instance of the typing `member`. + + The function will make sure to check against both the `typing` and `typing_extensions` + variants as depending on the Python version, the `typing_extensions` variant might be different. + """ + in_typing = hasattr(typing, member) + in_typing_extensions = hasattr(typing_extensions, member) + + if in_typing and in_typing_extensions: + if getattr(typing, member) is getattr(typing_extensions, member): + check_code = f'isinstance(obj, typing.{member})' + else: + check_code = f'isinstance(obj, (typing.{member}, typing_extensions.{member}))' + elif in_typing and not in_typing_extensions: + check_code = f'isinstance(obj, typing.{member})' + elif not in_typing and in_typing_extensions: + check_code = f'isinstance(obj, typing_extensions.{member})' + else: + check_code = 'False' + + func_code = dedent(f""" + def {function_name}(obj: Any, /) -> 'TypeIs[{member}]': + return {check_code} + """) + + locals_: dict[str, Any] = {} + globals_: dict[str, Any] = {'Any': Any, 'typing': typing, 'typing_extensions': typing_extensions} + exec(func_code, globals_, locals_) + return locals_[function_name] + + +if sys.version_info >= (3, 10): + from types import NoneType +else: + NoneType = type(None) + +# Keep this ordered, as per `typing.__all__`: + +is_annotated = _compile_identity_check_function('Annotated', 'is_annotated') +is_annotated.__doc__ = """ +Return whether the argument is the [`Annotated`][typing.Annotated] [special form][]. + +```pycon +>>> is_annotated(Annotated) +True +>>> is_annotated(Annotated[int, ...]) +False +``` +""" + +is_any = _compile_identity_check_function('Any', 'is_any') +is_any.__doc__ = """ +Return whether the argument is the [`Any`][typing.Any] [special form][]. + +```pycon +>>> is_any(Any) +True +``` +""" + +is_classvar = _compile_identity_check_function('ClassVar', 'is_classvar') +is_classvar.__doc__ = """ +Return whether the argument is the [`ClassVar`][typing.ClassVar] [type qualifier][]. + +```pycon +>>> is_classvar(ClassVar) +True +>>> is_classvar(ClassVar[int]) +>>> False +``` +""" + +is_concatenate = _compile_identity_check_function('Concatenate', 'is_concatenate') +is_concatenate.__doc__ = """ +Return whether the argument is the [`Concatenate`][typing.Concatenate] [special form][]. + +```pycon +>>> is_concatenate(Concatenate) +True +>>> is_concatenate(Concatenate[int, P]) +False +``` +""" + +is_final = _compile_identity_check_function('Final', 'is_final') +is_final.__doc__ = """ +Return whether the argument is the [`Final`][typing.Final] [type qualifier][]. + +```pycon +>>> is_final(Final) +True +>>> is_final(Final[int]) +False +``` +""" + + +# Unlikely to have a different version in `typing-extensions`, but keep it consistent. +# Also note that starting in 3.14, this is an alias to `annotationlib.ForwardRef`, but +# accessing it from `typing` doesn't seem to be deprecated. +is_forwardref = _compile_isinstance_check_function('ForwardRef', 'is_forwardref') +is_forwardref.__doc__ = """ +Return whether the argument is an instance of [`ForwardRef`][typing.ForwardRef]. + +```pycon +>>> is_forwardref(ForwardRef('T')) +True +``` +""" + + +is_generic = _compile_identity_check_function('Generic', 'is_generic') +is_generic.__doc__ = """ +Return whether the argument is the [`Generic`][typing.Generic] [special form][]. + +```pycon +>>> is_generic(Generic) +True +>>> is_generic(Generic[T]) +False +``` +""" + +is_literal = _compile_identity_check_function('Literal', 'is_literal') +is_literal.__doc__ = """ +Return whether the argument is the [`Literal`][typing.Literal] [special form][]. + +```pycon +>>> is_literal(Literal) +True +>>> is_literal(Literal["a"]) +False +``` +""" + + +# `get_origin(Optional[int]) is Union`, so `is_optional()` isn't implemented. + +is_paramspec = _compile_isinstance_check_function('ParamSpec', 'is_paramspec') +is_paramspec.__doc__ = """ +Return whether the argument is an instance of [`ParamSpec`][typing.ParamSpec]. + +```pycon +>>> P = ParamSpec('P') +>>> is_paramspec(P) +True +``` +""" + +# Protocol? + +is_typevar = _compile_isinstance_check_function('TypeVar', 'is_typevar') +is_typevar.__doc__ = """ +Return whether the argument is an instance of [`TypeVar`][typing.TypeVar]. + +```pycon +>>> T = TypeVar('T') +>>> is_typevar(T) +True +``` +""" + +is_typevartuple = _compile_isinstance_check_function('TypeVarTuple', 'is_typevartuple') +is_typevartuple.__doc__ = """ +Return whether the argument is an instance of [`TypeVarTuple`][typing.TypeVarTuple]. + +```pycon +>>> Ts = TypeVarTuple('Ts') +>>> is_typevartuple(Ts) +True +``` +""" + +is_union = _compile_identity_check_function('Union', 'is_union') +is_union.__doc__ = """ +Return whether the argument is the [`Union`][typing.Union] [special form][]. + +This function can also be used to check for the [`Optional`][typing.Optional] [special form][], +as at runtime, `Optional[int]` is equivalent to `Union[int, None]`. + +```pycon +>>> is_union(Union) +True +>>> is_union(Union[int, str]) +False +``` + +!!! warning + This does not check for unions using the [new syntax][types-union] (e.g. `int | str`). +""" + + +def is_namedtuple(obj: Any, /) -> bool: + """Return whether the argument is a named tuple type. + + This includes [`NamedTuple`][typing.NamedTuple] subclasses and classes created from the + [`collections.namedtuple`][] factory function. + + ```pycon + >>> class User(NamedTuple): + ... name: str + ... + >>> is_namedtuple(User) + True + >>> City = collections.namedtuple('City', []) + >>> is_namedtuple(City) + True + >>> is_namedtuple(NamedTuple) + False + ``` + """ + return isinstance(obj, type) and issubclass(obj, tuple) and hasattr(obj, '_fields') # pyright: ignore[reportUnknownArgumentType] + + +# TypedDict? + +# BinaryIO? IO? TextIO? + +is_literalstring = _compile_identity_check_function('LiteralString', 'is_literalstring') +is_literalstring.__doc__ = """ +Return whether the argument is the [`LiteralString`][typing.LiteralString] [special form][]. + +```pycon +>>> is_literalstring(LiteralString) +True +``` +""" + +is_never = _compile_identity_check_function('Never', 'is_never') +is_never.__doc__ = """ +Return whether the argument is the [`Never`][typing.Never] [special form][]. + +```pycon +>>> is_never(Never) +True +``` +""" + +if sys.version_info >= (3, 10): + is_newtype = _compile_isinstance_check_function('NewType', 'is_newtype') +else: # On Python 3.10, `NewType` is a function. + + def is_newtype(obj: Any, /) -> bool: + return hasattr(obj, '__supertype__') + + +is_newtype.__doc__ = """ +Return whether the argument is a [`NewType`][typing.NewType]. + +```pycon +>>> UserId = NewType("UserId", int) +>>> is_newtype(UserId) +True +``` +""" + +is_nodefault = _compile_identity_check_function('NoDefault', 'is_nodefault') +is_nodefault.__doc__ = """ +Return whether the argument is the [`NoDefault`][typing.NoDefault] sentinel object. + +```pycon +>>> is_nodefault(NoDefault) +True +``` +""" + +is_noextraitems = _compile_identity_check_function('NoExtraItems', 'is_noextraitems') +is_noextraitems.__doc__ = """ +Return whether the argument is the `NoExtraItems` sentinel object. + +```pycon +>>> is_noextraitems(NoExtraItems) +True +``` +""" + +is_noreturn = _compile_identity_check_function('NoReturn', 'is_noreturn') +is_noreturn.__doc__ = """ +Return whether the argument is the [`NoReturn`][typing.NoReturn] [special form][]. + +```pycon +>>> is_noreturn(NoReturn) +True +>>> is_noreturn(Never) +False +``` +""" + +is_notrequired = _compile_identity_check_function('NotRequired', 'is_notrequired') +is_notrequired.__doc__ = """ +Return whether the argument is the [`NotRequired`][typing.NotRequired] [special form][]. + +```pycon +>>> is_notrequired(NotRequired) +True +``` +""" + +is_paramspecargs = _compile_isinstance_check_function('ParamSpecArgs', 'is_paramspecargs') +is_paramspecargs.__doc__ = """ +Return whether the argument is an instance of [`ParamSpecArgs`][typing.ParamSpecArgs]. + +```pycon +>>> P = ParamSpec('P') +>>> is_paramspecargs(P.args) +True +``` +""" + +is_paramspeckwargs = _compile_isinstance_check_function('ParamSpecKwargs', 'is_paramspeckwargs') +is_paramspeckwargs.__doc__ = """ +Return whether the argument is an instance of [`ParamSpecKwargs`][typing.ParamSpecKwargs]. + +```pycon +>>> P = ParamSpec('P') +>>> is_paramspeckwargs(P.kwargs) +True +``` +""" + +is_readonly = _compile_identity_check_function('ReadOnly', 'is_readonly') +is_readonly.__doc__ = """ +Return whether the argument is the [`ReadOnly`][typing.ReadOnly] [special form][]. + +```pycon +>>> is_readonly(ReadOnly) +True +``` +""" + +is_required = _compile_identity_check_function('Required', 'is_required') +is_required.__doc__ = """ +Return whether the argument is the [`Required`][typing.Required] [special form][]. + +```pycon +>>> is_required(Required) +True +``` +""" + +is_self = _compile_identity_check_function('Self', 'is_self') +is_self.__doc__ = """ +Return whether the argument is the [`Self`][typing.Self] [special form][]. + +```pycon +>>> is_self(Self) +True +``` +""" + +# TYPE_CHECKING? + +is_typealias = _compile_identity_check_function('TypeAlias', 'is_typealias') +is_typealias.__doc__ = """ +Return whether the argument is the [`TypeAlias`][typing.TypeAlias] [special form][]. + +```pycon +>>> is_typealias(TypeAlias) +True +``` +""" + +is_typeguard = _compile_identity_check_function('TypeGuard', 'is_typeguard') +is_typeguard.__doc__ = """ +Return whether the argument is the [`TypeGuard`][typing.TypeGuard] [special form][]. + +```pycon +>>> is_typeguard(TypeGuard) +True +``` +""" + +is_typeis = _compile_identity_check_function('TypeIs', 'is_typeis') +is_typeis.__doc__ = """ +Return whether the argument is the [`TypeIs`][typing.TypeIs] [special form][]. + +```pycon +>>> is_typeis(TypeIs) +True +``` +""" + +_is_typealiastype_inner = _compile_isinstance_check_function('TypeAliasType', '_is_typealiastype_inner') + + +if _IS_PY310: + # Parameterized PEP 695 type aliases are instances of `types.GenericAlias` in typing_extensions>=4.13.0. + # On Python 3.10, with `Alias[int]` being such an instance of `GenericAlias`, + # `isinstance(Alias[int], TypeAliasType)` returns `True`. + # See https://github.com/python/cpython/issues/89828. + def is_typealiastype(obj: Any, /) -> 'TypeIs[TypeAliasType]': + return type(obj) is not GenericAlias and _is_typealiastype_inner(obj) +else: + is_typealiastype = _compile_isinstance_check_function('TypeAliasType', 'is_typealiastype') + +is_typealiastype.__doc__ = """ +Return whether the argument is a [`TypeAliasType`][typing.TypeAliasType] instance. + +```pycon +>>> type MyInt = int +>>> is_typealiastype(MyInt) +True +>>> MyStr = TypeAliasType("MyStr", str) +>>> is_typealiastype(MyStr): +True +>>> type MyList[T] = list[T] +>>> is_typealiastype(MyList[int]) +False +``` +""" + +is_unpack = _compile_identity_check_function('Unpack', 'is_unpack') +is_unpack.__doc__ = """ +Return whether the argument is the [`Unpack`][typing.Unpack] [special form][]. + +```pycon +>>> is_unpack(Unpack) +True +>>> is_unpack(Unpack[Ts]) +False +``` +""" + + +if sys.version_info >= (3, 13): + + def is_deprecated(obj: Any, /) -> 'TypeIs[deprecated]': + return isinstance(obj, (warnings.deprecated, typing_extensions.deprecated)) + +else: + + def is_deprecated(obj: Any, /) -> 'TypeIs[deprecated]': + return isinstance(obj, typing_extensions.deprecated) + + +is_deprecated.__doc__ = """ +Return whether the argument is a [`deprecated`][warnings.deprecated] instance. + +This also includes the [`typing_extensions` backport][typing_extensions.deprecated]. + +```pycon +>>> is_deprecated(warnings.deprecated('message')) +True +>>> is_deprecated(typing_extensions.deprecated('message')) +True +``` +""" + + +# Aliases defined in the `typing` module using `typing._SpecialGenericAlias` (itself aliased as `alias()`): +DEPRECATED_ALIASES: Final[dict[Any, type[Any]]] = { + typing.Hashable: collections.abc.Hashable, + typing.Awaitable: collections.abc.Awaitable, + typing.Coroutine: collections.abc.Coroutine, + typing.AsyncIterable: collections.abc.AsyncIterable, + typing.AsyncIterator: collections.abc.AsyncIterator, + typing.Iterable: collections.abc.Iterable, + typing.Iterator: collections.abc.Iterator, + typing.Reversible: collections.abc.Reversible, + typing.Sized: collections.abc.Sized, + typing.Container: collections.abc.Container, + typing.Collection: collections.abc.Collection, + # type ignore reason: https://github.com/python/typeshed/issues/6257: + typing.Callable: collections.abc.Callable, # pyright: ignore[reportAssignmentType, reportUnknownMemberType] + typing.AbstractSet: collections.abc.Set, + typing.MutableSet: collections.abc.MutableSet, + typing.Mapping: collections.abc.Mapping, + typing.MutableMapping: collections.abc.MutableMapping, + typing.Sequence: collections.abc.Sequence, + typing.MutableSequence: collections.abc.MutableSequence, + typing.Tuple: tuple, + typing.List: list, + typing.Deque: collections.deque, + typing.Set: set, + typing.FrozenSet: frozenset, + typing.MappingView: collections.abc.MappingView, + typing.KeysView: collections.abc.KeysView, + typing.ItemsView: collections.abc.ItemsView, + typing.ValuesView: collections.abc.ValuesView, + typing.Dict: dict, + typing.DefaultDict: collections.defaultdict, + typing.OrderedDict: collections.OrderedDict, + typing.Counter: collections.Counter, + typing.ChainMap: collections.ChainMap, + typing.Generator: collections.abc.Generator, + typing.AsyncGenerator: collections.abc.AsyncGenerator, + typing.Type: type, + # Defined in `typing.__getattr__`: + typing.Pattern: re.Pattern, + typing.Match: re.Match, + typing.ContextManager: contextlib.AbstractContextManager, + typing.AsyncContextManager: contextlib.AbstractAsyncContextManager, + # Skipped: `ByteString` (deprecated, removed in 3.14) +} +"""A mapping between the deprecated typing aliases to their replacement, as per [PEP 585](https://peps.python.org/pep-0585/).""" + + +# Add the `typing_extensions` aliases: +for alias, target in list(DEPRECATED_ALIASES.items()): + # Use `alias.__name__` when we drop support for Python 3.9 + if (te_alias := getattr(typing_extensions, alias._name, None)) is not None: + DEPRECATED_ALIASES[te_alias] = target diff --git a/lib/python3.11/site-packages/typing_inspection/typing_objects.pyi b/lib/python3.11/site-packages/typing_inspection/typing_objects.pyi new file mode 100644 index 0000000000000000000000000000000000000000..5071598005a21063ff3b2a2a1dedced885267de6 --- /dev/null +++ b/lib/python3.11/site-packages/typing_inspection/typing_objects.pyi @@ -0,0 +1,417 @@ +# Stub file generated using: +# `stubgen --inspect-mode --include-docstrings -m typing_inspection.typing_objects` +# (manual edits need to be applied). +"""Low-level introspection utilities for [`typing`][] members. + +The provided functions in this module check against both the [`typing`][] and [`typing_extensions`][] +variants, if they exists and are different. +""" + +import sys +from typing import Any, Final, ForwardRef, NewType, TypeVar + +from typing_extensions import ParamSpec, ParamSpecArgs, ParamSpecKwargs, TypeAliasType, TypeIs, TypeVarTuple, deprecated + +__all__ = [ + 'DEPRECATED_ALIASES', + 'NoneType', + 'is_annotated', + 'is_any', + 'is_classvar', + 'is_concatenate', + 'is_deprecated', + 'is_final', + 'is_generic', + 'is_literal', + 'is_literalstring', + 'is_namedtuple', + 'is_never', + 'is_newtype', + 'is_nodefault', + 'is_noextraitems', + 'is_noreturn', + 'is_notrequired', + 'is_paramspec', + 'is_paramspecargs', + 'is_paramspeckwargs', + 'is_readonly', + 'is_required', + 'is_self', + 'is_typealias', + 'is_typealiastype', + 'is_typeguard', + 'is_typeis', + 'is_typevar', + 'is_typevartuple', + 'is_union', + 'is_unpack', +] + +if sys.version_info >= (3, 10): + from types import NoneType +else: + NoneType = type(None) + +def is_annotated(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Annotated`][typing.Annotated] [special form][]. + + ```pycon + >>> is_annotated(Annotated) + True + >>> is_annotated(Annotated[int, ...]) + False + ``` + """ + +def is_any(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Any`][typing.Any] [special form][]. + + ```pycon + >>> is_any(Any) + True + ``` + """ + +def is_classvar(obj: Any, /) -> bool: + """ + Return whether the argument is the [`ClassVar`][typing.ClassVar] [type qualifier][]. + + ```pycon + >>> is_classvar(ClassVar) + True + >>> is_classvar(ClassVar[int]) + >>> False + ``` + """ + +def is_concatenate(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Concatenate`][typing.Concatenate] [special form][]. + + ```pycon + >>> is_concatenate(Concatenate) + True + >>> is_concatenate(Concatenate[int, P]) + False + ``` + """ + +def is_final(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Final`][typing.Final] [type qualifier][]. + + ```pycon + >>> is_final(Final) + True + >>> is_final(Final[int]) + False + ``` + """ + +def is_forwardref(obj: Any, /) -> TypeIs[ForwardRef]: + """ + Return whether the argument is an instance of [`ForwardRef`][typing.ForwardRef]. + + ```pycon + >>> is_forwardref(ForwardRef('T')) + True + ``` + """ + +def is_generic(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Generic`][typing.Generic] [special form][]. + + ```pycon + >>> is_generic(Generic) + True + >>> is_generic(Generic[T]) + False + ``` + """ + +def is_literal(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Literal`][typing.Literal] [special form][]. + + ```pycon + >>> is_literal(Literal) + True + >>> is_literal(Literal["a"]) + False + ``` + """ + +def is_paramspec(obj: Any, /) -> TypeIs[ParamSpec]: + """ + Return whether the argument is an instance of [`ParamSpec`][typing.ParamSpec]. + + ```pycon + >>> P = ParamSpec('P') + >>> is_paramspec(P) + True + ``` + """ + +def is_typevar(obj: Any, /) -> TypeIs[TypeVar]: + """ + Return whether the argument is an instance of [`TypeVar`][typing.TypeVar]. + + ```pycon + >>> T = TypeVar('T') + >>> is_typevar(T) + True + ``` + """ + +def is_typevartuple(obj: Any, /) -> TypeIs[TypeVarTuple]: + """ + Return whether the argument is an instance of [`TypeVarTuple`][typing.TypeVarTuple]. + + ```pycon + >>> Ts = TypeVarTuple('Ts') + >>> is_typevartuple(Ts) + True + ``` + """ + +def is_union(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Union`][typing.Union] [special form][]. + + This function can also be used to check for the [`Optional`][typing.Optional] [special form][], + as at runtime, `Optional[int]` is equivalent to `Union[int, None]`. + + ```pycon + >>> is_union(Union) + True + >>> is_union(Union[int, str]) + False + ``` + + !!! warning + This does not check for unions using the [new syntax][types-union] (e.g. `int | str`). + """ + +def is_namedtuple(obj: Any, /) -> bool: + """Return whether the argument is a named tuple type. + + This includes [`NamedTuple`][typing.NamedTuple] subclasses and classes created from the + [`collections.namedtuple`][] factory function. + + ```pycon + >>> class User(NamedTuple): + ... name: str + ... + >>> is_namedtuple(User) + True + >>> City = collections.namedtuple('City', []) + >>> is_namedtuple(City) + True + >>> is_namedtuple(NamedTuple) + False + ``` + """ + +def is_literalstring(obj: Any, /) -> bool: + """ + Return whether the argument is the [`LiteralString`][typing.LiteralString] [special form][]. + + ```pycon + >>> is_literalstring(LiteralString) + True + ``` + """ + +def is_never(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Never`][typing.Never] [special form][]. + + ```pycon + >>> is_never(Never) + True + ``` + """ + +def is_newtype(obj: Any, /) -> TypeIs[NewType]: + """ + Return whether the argument is a [`NewType`][typing.NewType]. + + ```pycon + >>> UserId = NewType("UserId", int) + >>> is_newtype(UserId) + True + ``` + """ + +def is_nodefault(obj: Any, /) -> bool: + """ + Return whether the argument is the [`NoDefault`][typing.NoDefault] sentinel object. + + ```pycon + >>> is_nodefault(NoDefault) + True + ``` + """ + +def is_noextraitems(obj: Any, /) -> bool: + """ + Return whether the argument is the `NoExtraItems` sentinel object. + + ```pycon + >>> is_noextraitems(NoExtraItems) + True + ``` + """ + +def is_noreturn(obj: Any, /) -> bool: + """ + Return whether the argument is the [`NoReturn`][typing.NoReturn] [special form][]. + + ```pycon + >>> is_noreturn(NoReturn) + True + >>> is_noreturn(Never) + False + ``` + """ + +def is_notrequired(obj: Any, /) -> bool: + """ + Return whether the argument is the [`NotRequired`][typing.NotRequired] [special form][]. + + ```pycon + >>> is_notrequired(NotRequired) + True + ``` + """ + +def is_paramspecargs(obj: Any, /) -> TypeIs[ParamSpecArgs]: + """ + Return whether the argument is an instance of [`ParamSpecArgs`][typing.ParamSpecArgs]. + + ```pycon + >>> P = ParamSpec('P') + >>> is_paramspecargs(P.args) + True + ``` + """ + +def is_paramspeckwargs(obj: Any, /) -> TypeIs[ParamSpecKwargs]: + """ + Return whether the argument is an instance of [`ParamSpecKwargs`][typing.ParamSpecKwargs]. + + ```pycon + >>> P = ParamSpec('P') + >>> is_paramspeckwargs(P.kwargs) + True + ``` + """ + +def is_readonly(obj: Any, /) -> bool: + """ + Return whether the argument is the [`ReadOnly`][typing.ReadOnly] [special form][]. + + ```pycon + >>> is_readonly(ReadOnly) + True + ``` + """ + +def is_required(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Required`][typing.Required] [special form][]. + + ```pycon + >>> is_required(Required) + True + ``` + """ + +def is_self(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Self`][typing.Self] [special form][]. + + ```pycon + >>> is_self(Self) + True + ``` + """ + +def is_typealias(obj: Any, /) -> bool: + """ + Return whether the argument is the [`TypeAlias`][typing.TypeAlias] [special form][]. + + ```pycon + >>> is_typealias(TypeAlias) + True + ``` + """ + +def is_typeguard(obj: Any, /) -> bool: + """ + Return whether the argument is the [`TypeGuard`][typing.TypeGuard] [special form][]. + + ```pycon + >>> is_typeguard(TypeGuard) + True + ``` + """ + +def is_typeis(obj: Any, /) -> bool: + """ + Return whether the argument is the [`TypeIs`][typing.TypeIs] [special form][]. + + ```pycon + >>> is_typeis(TypeIs) + True + ``` + """ + +def is_typealiastype(obj: Any, /) -> TypeIs[TypeAliasType]: + """ + Return whether the argument is a [`TypeAliasType`][typing.TypeAliasType] instance. + + ```pycon + >>> type MyInt = int + >>> is_typealiastype(MyInt) + True + >>> MyStr = TypeAliasType("MyStr", str) + >>> is_typealiastype(MyStr): + True + >>> type MyList[T] = list[T] + >>> is_typealiastype(MyList[int]) + False + ``` + """ + +def is_unpack(obj: Any, /) -> bool: + """ + Return whether the argument is the [`Unpack`][typing.Unpack] [special form][]. + + ```pycon + >>> is_unpack(Unpack) + True + >>> is_unpack(Unpack[Ts]) + False + ``` + """ + +def is_deprecated(obj: Any, /) -> TypeIs[deprecated]: + """ + Return whether the argument is a [`deprecated`][warnings.deprecated] instance. + + This also includes the [`typing_extensions` backport][typing_extensions.deprecated]. + + ```pycon + >>> is_deprecated(warnings.deprecated('message')) + True + >>> is_deprecated(typing_extensions.deprecated('deprecated')) + True + ``` + """ + +DEPRECATED_ALIASES: Final[dict[Any, type[Any]]] +"""A mapping between the deprecated typing aliases to their replacement, as per [PEP 585](https://peps.python.org/pep-0585/)."""